Properties

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

Related objects

Downloads

Learn more

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 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +(1.50000 + 2.59808i) q^{11} -1.00000 q^{13} +(2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(0.500000 - 0.866025i) q^{19} -1.00000 q^{20} -3.00000 q^{22} +(4.50000 - 7.79423i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(0.500000 - 0.866025i) q^{26} +(-0.500000 + 2.59808i) q^{28} -6.00000 q^{29} +(-4.00000 - 6.92820i) q^{31} +(-0.500000 - 0.866025i) q^{32} +6.00000 q^{34} +(-2.50000 + 0.866025i) q^{35} +(3.50000 - 6.06218i) q^{37} +(0.500000 + 0.866025i) q^{38} +(0.500000 - 0.866025i) q^{40} -3.00000 q^{41} +2.00000 q^{43} +(1.50000 - 2.59808i) q^{44} +(4.50000 + 7.79423i) q^{46} +(4.50000 - 7.79423i) q^{47} +(1.00000 + 6.92820i) q^{49} +1.00000 q^{50} +(0.500000 + 0.866025i) q^{52} +(4.50000 + 7.79423i) q^{53} +3.00000 q^{55} +(-2.00000 - 1.73205i) q^{56} +(3.00000 - 5.19615i) q^{58} +(-4.00000 + 6.92820i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(-4.00000 - 6.92820i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(0.500000 - 2.59808i) q^{70} +(2.00000 + 3.46410i) q^{73} +(3.50000 + 6.06218i) q^{74} -1.00000 q^{76} +(1.50000 - 7.79423i) q^{77} +(5.00000 - 8.66025i) q^{79} +(0.500000 + 0.866025i) q^{80} +(1.50000 - 2.59808i) q^{82} -6.00000 q^{85} +(-1.00000 + 1.73205i) q^{86} +(1.50000 + 2.59808i) q^{88} +(3.00000 - 5.19615i) q^{89} +(2.00000 + 1.73205i) q^{91} -9.00000 q^{92} +(4.50000 + 7.79423i) q^{94} +(-0.500000 - 0.866025i) q^{95} -10.0000 q^{97} +(-6.50000 - 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{4} + q^{5} - 4q^{7} + 2q^{8} + O(q^{10}) \) \( 2q - q^{2} - q^{4} + q^{5} - 4q^{7} + 2q^{8} + q^{10} + 3q^{11} - 2q^{13} + 5q^{14} - q^{16} - 6q^{17} + q^{19} - 2q^{20} - 6q^{22} + 9q^{23} - q^{25} + q^{26} - q^{28} - 12q^{29} - 8q^{31} - q^{32} + 12q^{34} - 5q^{35} + 7q^{37} + q^{38} + q^{40} - 6q^{41} + 4q^{43} + 3q^{44} + 9q^{46} + 9q^{47} + 2q^{49} + 2q^{50} + q^{52} + 9q^{53} + 6q^{55} - 4q^{56} + 6q^{58} - 8q^{61} + 16q^{62} + 2q^{64} - q^{65} - 8q^{67} - 6q^{68} + q^{70} + 4q^{73} + 7q^{74} - 2q^{76} + 3q^{77} + 10q^{79} + q^{80} + 3q^{82} - 12q^{85} - 2q^{86} + 3q^{88} + 6q^{89} + 4q^{91} - 18q^{92} + 9q^{94} - q^{95} - 20q^{97} - 13q^{98} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) −2.00000 1.73205i −0.755929 0.654654i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 2.50000 0.866025i 0.668153 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.00000 5.19615i −0.727607 1.26025i −0.957892 0.287129i \(-0.907299\pi\)
0.230285 0.973123i \(-0.426034\pi\)
\(18\) 0 0
\(19\) 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i \(-0.796740\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) −3.00000 −0.639602
\(23\) 4.50000 7.79423i 0.938315 1.62521i 0.169701 0.985496i \(-0.445720\pi\)
0.768613 0.639713i \(-0.220947\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0.500000 0.866025i 0.0980581 0.169842i
\(27\) 0 0
\(28\) −0.500000 + 2.59808i −0.0944911 + 0.490990i
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) −4.00000 6.92820i −0.718421 1.24434i −0.961625 0.274367i \(-0.911532\pi\)
0.243204 0.969975i \(-0.421802\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) −2.50000 + 0.866025i −0.422577 + 0.146385i
\(36\) 0 0
\(37\) 3.50000 6.06218i 0.575396 0.996616i −0.420602 0.907245i \(-0.638181\pi\)
0.995998 0.0893706i \(-0.0284856\pi\)
\(38\) 0.500000 + 0.866025i 0.0811107 + 0.140488i
\(39\) 0 0
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) −3.00000 −0.468521 −0.234261 0.972174i \(-0.575267\pi\)
−0.234261 + 0.972174i \(0.575267\pi\)
\(42\) 0 0
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 1.50000 2.59808i 0.226134 0.391675i
\(45\) 0 0
\(46\) 4.50000 + 7.79423i 0.663489 + 1.14920i
\(47\) 4.50000 7.79423i 0.656392 1.13691i −0.325150 0.945662i \(-0.605415\pi\)
0.981543 0.191243i \(-0.0612518\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 1.00000 0.141421
\(51\) 0 0
\(52\) 0.500000 + 0.866025i 0.0693375 + 0.120096i
\(53\) 4.50000 + 7.79423i 0.618123 + 1.07062i 0.989828 + 0.142269i \(0.0454398\pi\)
−0.371706 + 0.928351i \(0.621227\pi\)
\(54\) 0 0
\(55\) 3.00000 0.404520
\(56\) −2.00000 1.73205i −0.267261 0.231455i
\(57\) 0 0
\(58\) 3.00000 5.19615i 0.393919 0.682288i
\(59\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 0 0
\(61\) −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i \(0.337817\pi\)
−0.999901 + 0.0140840i \(0.995517\pi\)
\(62\) 8.00000 1.01600
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −0.500000 + 0.866025i −0.0620174 + 0.107417i
\(66\) 0 0
\(67\) −4.00000 6.92820i −0.488678 0.846415i 0.511237 0.859440i \(-0.329187\pi\)
−0.999915 + 0.0130248i \(0.995854\pi\)
\(68\) −3.00000 + 5.19615i −0.363803 + 0.630126i
\(69\) 0 0
\(70\) 0.500000 2.59808i 0.0597614 0.310530i
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 2.00000 + 3.46410i 0.234082 + 0.405442i 0.959006 0.283387i \(-0.0914581\pi\)
−0.724923 + 0.688830i \(0.758125\pi\)
\(74\) 3.50000 + 6.06218i 0.406867 + 0.704714i
\(75\) 0 0
\(76\) −1.00000 −0.114708
\(77\) 1.50000 7.79423i 0.170941 0.888235i
\(78\) 0 0
\(79\) 5.00000 8.66025i 0.562544 0.974355i −0.434730 0.900561i \(-0.643156\pi\)
0.997274 0.0737937i \(-0.0235106\pi\)
\(80\) 0.500000 + 0.866025i 0.0559017 + 0.0968246i
\(81\) 0 0
\(82\) 1.50000 2.59808i 0.165647 0.286910i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) −6.00000 −0.650791
\(86\) −1.00000 + 1.73205i −0.107833 + 0.186772i
\(87\) 0 0
\(88\) 1.50000 + 2.59808i 0.159901 + 0.276956i
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 0 0
\(91\) 2.00000 + 1.73205i 0.209657 + 0.181568i
\(92\) −9.00000 −0.938315
\(93\) 0 0
\(94\) 4.50000 + 7.79423i 0.464140 + 0.803913i
\(95\) −0.500000 0.866025i −0.0512989 0.0888523i
\(96\) 0 0
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) −6.50000 2.59808i −0.656599 0.262445i
\(99\) 0 0
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 6.00000 + 10.3923i 0.597022 + 1.03407i 0.993258 + 0.115924i \(0.0369830\pi\)
−0.396236 + 0.918149i \(0.629684\pi\)
\(102\) 0 0
\(103\) 2.00000 3.46410i 0.197066 0.341328i −0.750510 0.660859i \(-0.770192\pi\)
0.947576 + 0.319531i \(0.103525\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) −9.00000 −0.874157
\(107\) −6.00000 + 10.3923i −0.580042 + 1.00466i 0.415432 + 0.909624i \(0.363630\pi\)
−0.995474 + 0.0950377i \(0.969703\pi\)
\(108\) 0 0
\(109\) 8.00000 + 13.8564i 0.766261 + 1.32720i 0.939577 + 0.342337i \(0.111218\pi\)
−0.173316 + 0.984866i \(0.555448\pi\)
\(110\) −1.50000 + 2.59808i −0.143019 + 0.247717i
\(111\) 0 0
\(112\) 2.50000 0.866025i 0.236228 0.0818317i
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) −4.50000 7.79423i −0.419627 0.726816i
\(116\) 3.00000 + 5.19615i 0.278543 + 0.482451i
\(117\) 0 0
\(118\) 0 0
\(119\) −3.00000 + 15.5885i −0.275010 + 1.42899i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) −4.00000 6.92820i −0.362143 0.627250i
\(123\) 0 0
\(124\) −4.00000 + 6.92820i −0.359211 + 0.622171i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −1.00000 −0.0887357 −0.0443678 0.999015i \(-0.514127\pi\)
−0.0443678 + 0.999015i \(0.514127\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −0.500000 0.866025i −0.0438529 0.0759555i
\(131\) 1.50000 2.59808i 0.131056 0.226995i −0.793028 0.609185i \(-0.791497\pi\)
0.924084 + 0.382190i \(0.124830\pi\)
\(132\) 0 0
\(133\) −2.50000 + 0.866025i −0.216777 + 0.0750939i
\(134\) 8.00000 0.691095
\(135\) 0 0
\(136\) −3.00000 5.19615i −0.257248 0.445566i
\(137\) 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i \(0.00465636\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(138\) 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
\(142\) 0 0
\(143\) −1.50000 2.59808i −0.125436 0.217262i
\(144\) 0 0
\(145\) −3.00000 + 5.19615i −0.249136 + 0.431517i
\(146\) −4.00000 −0.331042
\(147\) 0 0
\(148\) −7.00000 −0.575396
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) 0 0
\(151\) 5.00000 + 8.66025i 0.406894 + 0.704761i 0.994540 0.104357i \(-0.0332784\pi\)
−0.587646 + 0.809118i \(0.699945\pi\)
\(152\) 0.500000 0.866025i 0.0405554 0.0702439i
\(153\) 0 0
\(154\) 6.00000 + 5.19615i 0.483494 + 0.418718i
\(155\) −8.00000 −0.642575
\(156\) 0 0
\(157\) −11.5000 19.9186i −0.917800 1.58968i −0.802749 0.596316i \(-0.796630\pi\)
−0.115050 0.993360i \(-0.536703\pi\)
\(158\) 5.00000 + 8.66025i 0.397779 + 0.688973i
\(159\) 0 0
\(160\) −1.00000 −0.0790569
\(161\) −22.5000 + 7.79423i −1.77325 + 0.614271i
\(162\) 0 0
\(163\) −10.0000 + 17.3205i −0.783260 + 1.35665i 0.146772 + 0.989170i \(0.453112\pi\)
−0.930033 + 0.367477i \(0.880222\pi\)
\(164\) 1.50000 + 2.59808i 0.117130 + 0.202876i
\(165\) 0 0
\(166\) 0 0
\(167\) −3.00000 −0.232147 −0.116073 0.993241i \(-0.537031\pi\)
−0.116073 + 0.993241i \(0.537031\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 3.00000 5.19615i 0.230089 0.398527i
\(171\) 0 0
\(172\) −1.00000 1.73205i −0.0762493 0.132068i
\(173\) 4.50000 7.79423i 0.342129 0.592584i −0.642699 0.766119i \(-0.722185\pi\)
0.984828 + 0.173534i \(0.0555188\pi\)
\(174\) 0 0
\(175\) −0.500000 + 2.59808i −0.0377964 + 0.196396i
\(176\) −3.00000 −0.226134
\(177\) 0 0
\(178\) 3.00000 + 5.19615i 0.224860 + 0.389468i
\(179\) −1.50000 2.59808i −0.112115 0.194189i 0.804508 0.593942i \(-0.202429\pi\)
−0.916623 + 0.399753i \(0.869096\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) −2.50000 + 0.866025i −0.185312 + 0.0641941i
\(183\) 0 0
\(184\) 4.50000 7.79423i 0.331744 0.574598i
\(185\) −3.50000 6.06218i −0.257325 0.445700i
\(186\) 0 0
\(187\) 9.00000 15.5885i 0.658145 1.13994i
\(188\) −9.00000 −0.656392
\(189\) 0 0
\(190\) 1.00000 0.0725476
\(191\) 6.00000 10.3923i 0.434145 0.751961i −0.563081 0.826402i \(-0.690384\pi\)
0.997225 + 0.0744412i \(0.0237173\pi\)
\(192\) 0 0
\(193\) 8.00000 + 13.8564i 0.575853 + 0.997406i 0.995948 + 0.0899262i \(0.0286631\pi\)
−0.420096 + 0.907480i \(0.638004\pi\)
\(194\) 5.00000 8.66025i 0.358979 0.621770i
\(195\) 0 0
\(196\) 5.50000 4.33013i 0.392857 0.309295i
\(197\) −15.0000 −1.06871 −0.534353 0.845262i \(-0.679445\pi\)
−0.534353 + 0.845262i \(0.679445\pi\)
\(198\) 0 0
\(199\) 8.00000 + 13.8564i 0.567105 + 0.982255i 0.996850 + 0.0793045i \(0.0252700\pi\)
−0.429745 + 0.902950i \(0.641397\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) 0 0
\(202\) −12.0000 −0.844317
\(203\) 12.0000 + 10.3923i 0.842235 + 0.729397i
\(204\) 0 0
\(205\) −1.50000 + 2.59808i −0.104765 + 0.181458i
\(206\) 2.00000 + 3.46410i 0.139347 + 0.241355i
\(207\) 0 0
\(208\) 0.500000 0.866025i 0.0346688 0.0600481i
\(209\) 3.00000 0.207514
\(210\) 0 0
\(211\) 23.0000 1.58339 0.791693 0.610920i \(-0.209200\pi\)
0.791693 + 0.610920i \(0.209200\pi\)
\(212\) 4.50000 7.79423i 0.309061 0.535310i
\(213\) 0 0
\(214\) −6.00000 10.3923i −0.410152 0.710403i
\(215\) 1.00000 1.73205i 0.0681994 0.118125i
\(216\) 0 0
\(217\) −4.00000 + 20.7846i −0.271538 + 1.41095i
\(218\) −16.0000 −1.08366
\(219\) 0 0
\(220\) −1.50000 2.59808i −0.101130 0.175162i
\(221\) 3.00000 + 5.19615i 0.201802 + 0.349531i
\(222\) 0 0
\(223\) 8.00000 0.535720 0.267860 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) −0.500000 + 2.59808i −0.0334077 + 0.173591i
\(225\) 0 0
\(226\) 0 0
\(227\) −6.00000 10.3923i −0.398234 0.689761i 0.595274 0.803523i \(-0.297043\pi\)
−0.993508 + 0.113761i \(0.963710\pi\)
\(228\) 0 0
\(229\) 2.00000 3.46410i 0.132164 0.228914i −0.792347 0.610071i \(-0.791141\pi\)
0.924510 + 0.381157i \(0.124474\pi\)
\(230\) 9.00000 0.593442
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) −3.00000 + 5.19615i −0.196537 + 0.340411i −0.947403 0.320043i \(-0.896303\pi\)
0.750867 + 0.660454i \(0.229636\pi\)
\(234\) 0 0
\(235\) −4.50000 7.79423i −0.293548 0.508439i
\(236\) 0 0
\(237\) 0 0
\(238\) −12.0000 10.3923i −0.777844 0.673633i
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 0 0
\(241\) 0.500000 + 0.866025i 0.0322078 + 0.0557856i 0.881680 0.471848i \(-0.156413\pi\)
−0.849472 + 0.527633i \(0.823079\pi\)
\(242\) 1.00000 + 1.73205i 0.0642824 + 0.111340i
\(243\) 0 0
\(244\) 8.00000 0.512148
\(245\) 6.50000 + 2.59808i 0.415270 + 0.165985i
\(246\) 0 0
\(247\) −0.500000 + 0.866025i −0.0318142 + 0.0551039i
\(248\) −4.00000 6.92820i −0.254000 0.439941i
\(249\) 0 0
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) 15.0000 0.946792 0.473396 0.880850i \(-0.343028\pi\)
0.473396 + 0.880850i \(0.343028\pi\)
\(252\) 0 0
\(253\) 27.0000 1.69748
\(254\) 0.500000 0.866025i 0.0313728 0.0543393i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(258\) 0 0
\(259\) −17.5000 + 6.06218i −1.08740 + 0.376685i
\(260\) 1.00000 0.0620174
\(261\) 0 0
\(262\) 1.50000 + 2.59808i 0.0926703 + 0.160510i
\(263\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) 0 0
\(265\) 9.00000 0.552866
\(266\) 0.500000 2.59808i 0.0306570 0.159298i
\(267\) 0 0
\(268\) −4.00000 + 6.92820i −0.244339 + 0.423207i
\(269\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(270\) 0 0
\(271\) 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i \(-0.671801\pi\)
0.999870 + 0.0161307i \(0.00513477\pi\)
\(272\) 6.00000 0.363803
\(273\) 0 0
\(274\) −12.0000 −0.724947
\(275\) 1.50000 2.59808i 0.0904534 0.156670i
\(276\) 0 0
\(277\) 5.00000 + 8.66025i 0.300421 + 0.520344i 0.976231 0.216731i \(-0.0695395\pi\)
−0.675810 + 0.737075i \(0.736206\pi\)
\(278\) 2.00000 3.46410i 0.119952 0.207763i
\(279\) 0 0
\(280\) −2.50000 + 0.866025i −0.149404 + 0.0517549i
\(281\) 27.0000 1.61068 0.805342 0.592810i \(-0.201981\pi\)
0.805342 + 0.592810i \(0.201981\pi\)
\(282\) 0 0
\(283\) −7.00000 12.1244i −0.416107 0.720718i 0.579437 0.815017i \(-0.303272\pi\)
−0.995544 + 0.0942988i \(0.969939\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 3.00000 0.177394
\(287\) 6.00000 + 5.19615i 0.354169 + 0.306719i
\(288\) 0 0
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) −3.00000 5.19615i −0.176166 0.305129i
\(291\) 0 0
\(292\) 2.00000 3.46410i 0.117041 0.202721i
\(293\) 9.00000 0.525786 0.262893 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 3.50000 6.06218i 0.203433 0.352357i
\(297\) 0 0
\(298\) −3.00000 5.19615i −0.173785 0.301005i
\(299\) −4.50000 + 7.79423i −0.260242 + 0.450752i
\(300\) 0 0
\(301\) −4.00000 3.46410i −0.230556 0.199667i
\(302\) −10.0000 −0.575435
\(303\) 0 0
\(304\) 0.500000 + 0.866025i 0.0286770 + 0.0496700i
\(305\) 4.00000 + 6.92820i 0.229039 + 0.396708i
\(306\) 0 0
\(307\) 14.0000 0.799022 0.399511 0.916728i \(-0.369180\pi\)
0.399511 + 0.916728i \(0.369180\pi\)
\(308\) −7.50000 + 2.59808i −0.427352 + 0.148039i
\(309\) 0 0
\(310\) 4.00000 6.92820i 0.227185 0.393496i
\(311\) −12.0000 20.7846i −0.680458 1.17859i −0.974841 0.222900i \(-0.928448\pi\)
0.294384 0.955687i \(-0.404886\pi\)
\(312\) 0 0
\(313\) 14.0000 24.2487i 0.791327 1.37062i −0.133819 0.991006i \(-0.542724\pi\)
0.925146 0.379612i \(-0.123943\pi\)
\(314\) 23.0000 1.29797
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) 3.00000 5.19615i 0.168497 0.291845i −0.769395 0.638774i \(-0.779442\pi\)
0.937892 + 0.346929i \(0.112775\pi\)
\(318\) 0 0
\(319\) −9.00000 15.5885i −0.503903 0.872786i
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) 0 0
\(322\) 4.50000 23.3827i 0.250775 1.30307i
\(323\) −6.00000 −0.333849
\(324\) 0 0
\(325\) 0.500000 + 0.866025i 0.0277350 + 0.0480384i
\(326\) −10.0000 17.3205i −0.553849 0.959294i
\(327\) 0 0
\(328\) −3.00000 −0.165647
\(329\) −22.5000 + 7.79423i −1.24047 + 0.429710i
\(330\) 0 0
\(331\) 3.50000 6.06218i 0.192377 0.333207i −0.753660 0.657264i \(-0.771714\pi\)
0.946038 + 0.324057i \(0.105047\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 1.50000 2.59808i 0.0820763 0.142160i
\(335\) −8.00000 −0.437087
\(336\) 0 0
\(337\) −22.0000 −1.19842 −0.599208 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) 6.00000 10.3923i 0.326357 0.565267i
\(339\) 0 0
\(340\) 3.00000 + 5.19615i 0.162698 + 0.281801i
\(341\) 12.0000 20.7846i 0.649836 1.12555i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 2.00000 0.107833
\(345\) 0 0
\(346\) 4.50000 + 7.79423i 0.241921 + 0.419020i
\(347\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(348\) 0 0
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) −2.00000 1.73205i −0.106904 0.0925820i
\(351\) 0 0
\(352\) 1.50000 2.59808i 0.0799503 0.138478i
\(353\) 6.00000 + 10.3923i 0.319348 + 0.553127i 0.980352 0.197256i \(-0.0632029\pi\)
−0.661004 + 0.750382i \(0.729870\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) 3.00000 0.158555
\(359\) 9.00000 15.5885i 0.475002 0.822727i −0.524588 0.851356i \(-0.675781\pi\)
0.999590 + 0.0286287i \(0.00911406\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) −1.00000 + 1.73205i −0.0525588 + 0.0910346i
\(363\) 0 0
\(364\) 0.500000 2.59808i 0.0262071 0.136176i
\(365\) 4.00000 0.209370
\(366\) 0 0
\(367\) 9.50000 + 16.4545i 0.495896 + 0.858917i 0.999989 0.00473247i \(-0.00150640\pi\)
−0.504093 + 0.863649i \(0.668173\pi\)
\(368\) 4.50000 + 7.79423i 0.234579 + 0.406302i
\(369\) 0 0
\(370\) 7.00000 0.363913
\(371\) 4.50000 23.3827i 0.233628 1.21397i
\(372\) 0 0
\(373\) −1.00000 + 1.73205i −0.0517780 + 0.0896822i −0.890753 0.454488i \(-0.849822\pi\)
0.838975 + 0.544170i \(0.183156\pi\)
\(374\) 9.00000 + 15.5885i 0.465379 + 0.806060i
\(375\) 0 0
\(376\) 4.50000 7.79423i 0.232070 0.401957i
\(377\) 6.00000 0.309016
\(378\) 0 0
\(379\) 23.0000 1.18143 0.590715 0.806880i \(-0.298846\pi\)
0.590715 + 0.806880i \(0.298846\pi\)
\(380\) −0.500000 + 0.866025i −0.0256495 + 0.0444262i
\(381\) 0 0
\(382\) 6.00000 + 10.3923i 0.306987 + 0.531717i
\(383\) 10.5000 18.1865i 0.536525 0.929288i −0.462563 0.886586i \(-0.653070\pi\)
0.999088 0.0427020i \(-0.0135966\pi\)
\(384\) 0 0
\(385\) −6.00000 5.19615i −0.305788 0.264820i
\(386\) −16.0000 −0.814379
\(387\) 0 0
\(388\) 5.00000 + 8.66025i 0.253837 + 0.439658i
\(389\) −6.00000 10.3923i −0.304212 0.526911i 0.672874 0.739758i \(-0.265060\pi\)
−0.977086 + 0.212847i \(0.931726\pi\)
\(390\) 0 0
\(391\) −54.0000 −2.73090
\(392\) 1.00000 + 6.92820i 0.0505076 + 0.349927i
\(393\) 0 0
\(394\) 7.50000 12.9904i 0.377845 0.654446i
\(395\) −5.00000 8.66025i −0.251577 0.435745i
\(396\) 0 0
\(397\) −7.00000 + 12.1244i −0.351320 + 0.608504i −0.986481 0.163876i \(-0.947600\pi\)
0.635161 + 0.772380i \(0.280934\pi\)
\(398\) −16.0000 −0.802008
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −13.5000 + 23.3827i −0.674158 + 1.16768i 0.302556 + 0.953131i \(0.402160\pi\)
−0.976714 + 0.214544i \(0.931173\pi\)
\(402\) 0 0
\(403\) 4.00000 + 6.92820i 0.199254 + 0.345118i
\(404\) 6.00000 10.3923i 0.298511 0.517036i
\(405\) 0 0
\(406\) −15.0000 + 5.19615i −0.744438 + 0.257881i
\(407\) 21.0000 1.04093
\(408\) 0 0
\(409\) −13.0000 22.5167i −0.642809 1.11338i −0.984803 0.173675i \(-0.944436\pi\)
0.341994 0.939702i \(-0.388898\pi\)
\(410\) −1.50000 2.59808i −0.0740797 0.128310i
\(411\) 0 0
\(412\) −4.00000 −0.197066
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0.500000 + 0.866025i 0.0245145 + 0.0424604i
\(417\) 0 0
\(418\) −1.50000 + 2.59808i −0.0733674 + 0.127076i
\(419\) 9.00000 0.439679 0.219839 0.975536i \(-0.429447\pi\)
0.219839 + 0.975536i \(0.429447\pi\)
\(420\) 0 0
\(421\) 2.00000 0.0974740 0.0487370 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) −11.5000 + 19.9186i −0.559811 + 0.969622i
\(423\) 0 0
\(424\) 4.50000 + 7.79423i 0.218539 + 0.378521i
\(425\) −3.00000 + 5.19615i −0.145521 + 0.252050i
\(426\) 0 0
\(427\) 20.0000 6.92820i 0.967868 0.335279i
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) 1.00000 + 1.73205i 0.0482243 + 0.0835269i
\(431\) 6.00000 + 10.3923i 0.289010 + 0.500580i 0.973574 0.228373i \(-0.0733406\pi\)
−0.684564 + 0.728953i \(0.740007\pi\)
\(432\) 0 0
\(433\) −40.0000 −1.92228 −0.961139 0.276066i \(-0.910969\pi\)
−0.961139 + 0.276066i \(0.910969\pi\)
\(434\) −16.0000 13.8564i −0.768025 0.665129i
\(435\) 0 0
\(436\) 8.00000 13.8564i 0.383131 0.663602i
\(437\) −4.50000 7.79423i −0.215264 0.372849i
\(438\) 0 0
\(439\) −13.0000 + 22.5167i −0.620456 + 1.07466i 0.368945 + 0.929451i \(0.379719\pi\)
−0.989401 + 0.145210i \(0.953614\pi\)
\(440\) 3.00000 0.143019
\(441\) 0 0
\(442\) −6.00000 −0.285391
\(443\) 6.00000 10.3923i 0.285069 0.493753i −0.687557 0.726130i \(-0.741317\pi\)
0.972626 + 0.232377i \(0.0746503\pi\)
\(444\) 0 0
\(445\) −3.00000 5.19615i −0.142214 0.246321i
\(446\) −4.00000 + 6.92820i −0.189405 + 0.328060i
\(447\) 0 0
\(448\) −2.00000 1.73205i −0.0944911 0.0818317i
\(449\) −21.0000 −0.991051 −0.495526 0.868593i \(-0.665025\pi\)
−0.495526 + 0.868593i \(0.665025\pi\)
\(450\) 0 0
\(451\) −4.50000 7.79423i −0.211897 0.367016i
\(452\) 0 0
\(453\) 0 0
\(454\) 12.0000 0.563188
\(455\) 2.50000 0.866025i 0.117202 0.0405999i
\(456\) 0 0
\(457\) −7.00000 + 12.1244i −0.327446 + 0.567153i −0.982004 0.188858i \(-0.939521\pi\)
0.654558 + 0.756012i \(0.272855\pi\)
\(458\) 2.00000 + 3.46410i 0.0934539 + 0.161867i
\(459\) 0 0
\(460\) −4.50000 + 7.79423i −0.209814 + 0.363408i
\(461\) 30.0000 1.39724 0.698620 0.715493i \(-0.253798\pi\)
0.698620 + 0.715493i \(0.253798\pi\)
\(462\) 0 0
\(463\) −1.00000 −0.0464739 −0.0232370 0.999730i \(-0.507397\pi\)
−0.0232370 + 0.999730i \(0.507397\pi\)
\(464\) 3.00000 5.19615i 0.139272 0.241225i
\(465\) 0 0
\(466\) −3.00000 5.19615i −0.138972 0.240707i
\(467\) −3.00000 + 5.19615i −0.138823 + 0.240449i −0.927052 0.374934i \(-0.877665\pi\)
0.788228 + 0.615383i \(0.210999\pi\)
\(468\) 0 0
\(469\) −4.00000 + 20.7846i −0.184703 + 0.959744i
\(470\) 9.00000 0.415139
\(471\) 0 0
\(472\) 0 0
\(473\) 3.00000 + 5.19615i 0.137940 + 0.238919i
\(474\) 0 0
\(475\) −1.00000 −0.0458831
\(476\) 15.0000 5.19615i 0.687524 0.238165i
\(477\) 0 0
\(478\) −3.00000 + 5.19615i −0.137217 + 0.237666i
\(479\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) 0 0
\(481\) −3.50000 + 6.06218i −0.159586 + 0.276412i
\(482\) −1.00000 −0.0455488
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) −5.00000 + 8.66025i −0.227038 + 0.393242i
\(486\) 0 0
\(487\) 8.00000 + 13.8564i 0.362515 + 0.627894i 0.988374 0.152042i \(-0.0485850\pi\)
−0.625859 + 0.779936i \(0.715252\pi\)
\(488\) −4.00000 + 6.92820i −0.181071 + 0.313625i
\(489\) 0 0
\(490\) −5.50000 + 4.33013i −0.248465 + 0.195615i
\(491\) −36.0000 −1.62466 −0.812329 0.583200i \(-0.801800\pi\)
−0.812329 + 0.583200i \(0.801800\pi\)
\(492\) 0 0
\(493\) 18.0000 + 31.1769i 0.810679 + 1.40414i
\(494\) −0.500000 0.866025i −0.0224961 0.0389643i
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) 0 0
\(498\) 0 0
\(499\) 2.00000 3.46410i 0.0895323 0.155074i −0.817781 0.575529i \(-0.804796\pi\)
0.907314 + 0.420455i \(0.138129\pi\)
\(500\) 0.500000 + 0.866025i 0.0223607 + 0.0387298i
\(501\) 0 0
\(502\) −7.50000 + 12.9904i −0.334741 + 0.579789i
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 0 0
\(505\) 12.0000 0.533993
\(506\) −13.5000 + 23.3827i −0.600148 + 1.03949i
\(507\) 0 0
\(508\) 0.500000 + 0.866025i 0.0221839 + 0.0384237i
\(509\) −21.0000 + 36.3731i −0.930809 + 1.61221i −0.148866 + 0.988857i \(0.547562\pi\)
−0.781943 + 0.623350i \(0.785771\pi\)
\(510\) 0 0
\(511\) 2.00000 10.3923i 0.0884748 0.459728i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 0 0
\(515\) −2.00000 3.46410i −0.0881305 0.152647i
\(516\) 0 0
\(517\) 27.0000 1.18746
\(518\) 3.50000 18.1865i 0.153781 0.799070i
\(519\) 0 0
\(520\) −0.500000 + 0.866025i −0.0219265 + 0.0379777i
\(521\) −7.50000 12.9904i −0.328581 0.569119i 0.653650 0.756797i \(-0.273237\pi\)
−0.982231 + 0.187678i \(0.939904\pi\)
\(522\) 0 0
\(523\) 14.0000 24.2487i 0.612177 1.06032i −0.378695 0.925521i \(-0.623627\pi\)
0.990873 0.134801i \(-0.0430394\pi\)
\(524\) −3.00000 −0.131056
\(525\) 0 0
\(526\) 0 0
\(527\) −24.0000 + 41.5692i −1.04546 + 1.81078i
\(528\) 0 0
\(529\) −29.0000 50.2295i −1.26087 2.18389i
\(530\) −4.50000 + 7.79423i −0.195468 + 0.338560i
\(531\) 0 0
\(532\) 2.00000 + 1.73205i 0.0867110 + 0.0750939i
\(533\) 3.00000 0.129944
\(534\) 0 0
\(535\) 6.00000 + 10.3923i 0.259403 + 0.449299i
\(536\) −4.00000 6.92820i −0.172774 0.299253i
\(537\) 0 0
\(538\) 0 0
\(539\) −16.5000 + 12.9904i −0.710705 + 0.559535i
\(540\) 0 0
\(541\) −4.00000 + 6.92820i −0.171973 + 0.297867i −0.939110 0.343617i \(-0.888348\pi\)
0.767136 + 0.641484i \(0.221681\pi\)
\(542\) 8.00000 + 13.8564i 0.343629 + 0.595184i
\(543\) 0 0
\(544\) −3.00000 + 5.19615i −0.128624 + 0.222783i
\(545\) 16.0000 0.685365
\(546\) 0 0
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) 6.00000 10.3923i 0.256307 0.443937i
\(549\) 0 0
\(550\) 1.50000 + 2.59808i 0.0639602 + 0.110782i
\(551\) −3.00000 + 5.19615i −0.127804 + 0.221364i
\(552\) 0 0
\(553\) −25.0000 + 8.66025i −1.06311 + 0.368271i
\(554\) −10.0000 −0.424859
\(555\) 0 0
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) −4.50000 7.79423i −0.190671 0.330252i 0.754802 0.655953i \(-0.227733\pi\)
−0.945473 + 0.325701i \(0.894400\pi\)
\(558\) 0 0
\(559\) −2.00000 −0.0845910
\(560\) 0.500000 2.59808i 0.0211289 0.109789i
\(561\) 0 0
\(562\) −13.5000 + 23.3827i −0.569463 + 0.986339i
\(563\) 21.0000 + 36.3731i 0.885044 + 1.53294i 0.845663 + 0.533718i \(0.179206\pi\)
0.0393818 + 0.999224i \(0.487461\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 14.0000 0.588464
\(567\) 0 0
\(568\) 0 0
\(569\) 10.5000 18.1865i 0.440183 0.762419i −0.557520 0.830164i \(-0.688247\pi\)
0.997703 + 0.0677445i \(0.0215803\pi\)
\(570\) 0 0
\(571\) −10.0000 17.3205i −0.418487 0.724841i 0.577301 0.816532i \(-0.304106\pi\)
−0.995788 + 0.0916910i \(0.970773\pi\)
\(572\) −1.50000 + 2.59808i −0.0627182 + 0.108631i
\(573\) 0 0
\(574\) −7.50000 + 2.59808i −0.313044 + 0.108442i
\(575\) −9.00000 −0.375326
\(576\) 0 0
\(577\) −22.0000 38.1051i −0.915872 1.58634i −0.805620 0.592433i \(-0.798167\pi\)
−0.110252 0.993904i \(-0.535166\pi\)
\(578\) −9.50000 16.4545i −0.395148 0.684416i
\(579\) 0 0
\(580\) 6.00000 0.249136
\(581\) 0 0
\(582\) 0 0
\(583\) −13.5000 + 23.3827i −0.559113 + 0.968412i
\(584\) 2.00000 + 3.46410i 0.0827606 + 0.143346i
\(585\) 0 0
\(586\) −4.50000 + 7.79423i −0.185893 + 0.321977i
\(587\) 24.0000 0.990586 0.495293 0.868726i \(-0.335061\pi\)
0.495293 + 0.868726i \(0.335061\pi\)
\(588\) 0 0
\(589\) −8.00000 −0.329634
\(590\) 0 0
\(591\) 0 0
\(592\) 3.50000 + 6.06218i 0.143849 + 0.249154i
\(593\) 12.0000 20.7846i 0.492781 0.853522i −0.507184 0.861838i \(-0.669314\pi\)
0.999965 + 0.00831589i \(0.00264706\pi\)
\(594\) 0 0
\(595\) 12.0000 + 10.3923i 0.491952 + 0.426043i
\(596\) 6.00000 0.245770
\(597\) 0 0
\(598\) −4.50000 7.79423i −0.184019 0.318730i
\(599\) −21.0000 36.3731i −0.858037 1.48616i −0.873799 0.486287i \(-0.838351\pi\)
0.0157622 0.999876i \(-0.494983\pi\)
\(600\) 0 0
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) 5.00000 1.73205i 0.203785 0.0705931i
\(603\) 0 0
\(604\) 5.00000 8.66025i 0.203447 0.352381i
\(605\) −1.00000 1.73205i −0.0406558 0.0704179i
\(606\) 0 0
\(607\) 0.500000 0.866025i 0.0202944 0.0351509i −0.855700 0.517472i \(-0.826873\pi\)
0.875994 + 0.482322i \(0.160206\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 0 0
\(610\) −8.00000 −0.323911
\(611\) −4.50000 + 7.79423i −0.182051 + 0.315321i
\(612\) 0 0
\(613\) −14.5000 25.1147i −0.585649 1.01437i −0.994794 0.101905i \(-0.967506\pi\)
0.409145 0.912470i \(-0.365827\pi\)
\(614\) −7.00000 + 12.1244i −0.282497 + 0.489299i
\(615\) 0 0
\(616\) 1.50000 7.79423i 0.0604367 0.314038i
\(617\) 18.0000 0.724653 0.362326 0.932051i \(-0.381983\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(618\) 0 0
\(619\) −11.5000 19.9186i −0.462224 0.800595i 0.536847 0.843679i \(-0.319615\pi\)
−0.999071 + 0.0430838i \(0.986282\pi\)
\(620\) 4.00000 + 6.92820i 0.160644 + 0.278243i
\(621\) 0 0
\(622\) 24.0000 0.962312
\(623\) −15.0000 + 5.19615i −0.600962 + 0.208179i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 14.0000 + 24.2487i 0.559553 + 0.969173i
\(627\) 0 0
\(628\) −11.5000 + 19.9186i −0.458900 + 0.794838i
\(629\) −42.0000 −1.67465
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) 5.00000 8.66025i 0.198889 0.344486i
\(633\) 0 0
\(634\) 3.00000 + 5.19615i 0.119145 + 0.206366i
\(635\) −0.500000 + 0.866025i −0.0198419 + 0.0343672i
\(636\) 0 0
\(637\) −1.00000 6.92820i −0.0396214 0.274505i
\(638\) 18.0000 0.712627
\(639\) 0 0
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) 13.5000 + 23.3827i 0.533218 + 0.923561i 0.999247 + 0.0387913i \(0.0123508\pi\)
−0.466029 + 0.884769i \(0.654316\pi\)
\(642\) 0 0
\(643\) 2.00000 0.0788723 0.0394362 0.999222i \(-0.487444\pi\)
0.0394362 + 0.999222i \(0.487444\pi\)
\(644\) 18.0000 + 15.5885i 0.709299 + 0.614271i
\(645\) 0 0
\(646\) 3.00000 5.19615i 0.118033 0.204440i
\(647\) 16.5000 + 28.5788i 0.648682 + 1.12355i 0.983438 + 0.181245i \(0.0580128\pi\)
−0.334756 + 0.942305i \(0.608654\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −1.00000 −0.0392232
\(651\) 0 0
\(652\) 20.0000 0.783260
\(653\) −4.50000 + 7.79423i −0.176099 + 0.305012i −0.940541 0.339680i \(-0.889681\pi\)
0.764442 + 0.644692i \(0.223014\pi\)
\(654\) 0 0
\(655\) −1.50000 2.59808i −0.0586098 0.101515i
\(656\) 1.50000 2.59808i 0.0585652 0.101438i
\(657\) 0 0
\(658\) 4.50000 23.3827i 0.175428 0.911552i
\(659\) 24.0000 0.934907 0.467454 0.884018i \(-0.345171\pi\)
0.467454 + 0.884018i \(0.345171\pi\)
\(660\) 0 0
\(661\) 14.0000 + 24.2487i 0.544537 + 0.943166i 0.998636 + 0.0522143i \(0.0166279\pi\)
−0.454099 + 0.890951i \(0.650039\pi\)
\(662\) 3.50000 + 6.06218i 0.136031 + 0.235613i
\(663\) 0 0
\(664\) 0 0
\(665\) −0.500000 + 2.59808i −0.0193892 + 0.100749i
\(666\) 0 0
\(667\) −27.0000 + 46.7654i −1.04544 + 1.81076i
\(668\) 1.50000 + 2.59808i 0.0580367 + 0.100523i
\(669\) 0 0
\(670\) 4.00000 6.92820i 0.154533 0.267660i
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) −34.0000 −1.31060 −0.655302 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) 11.0000 19.0526i 0.423704 0.733877i
\(675\) 0 0
\(676\) 6.00000 + 10.3923i 0.230769 + 0.399704i
\(677\) −4.50000 + 7.79423i −0.172949 + 0.299557i −0.939450 0.342687i \(-0.888663\pi\)
0.766501 + 0.642244i \(0.221996\pi\)
\(678\) 0 0
\(679\) 20.0000 + 17.3205i 0.767530 + 0.664700i
\(680\) −6.00000 −0.230089
\(681\) 0 0
\(682\) 12.0000 + 20.7846i 0.459504 + 0.795884i
\(683\) 6.00000 + 10.3923i 0.229584 + 0.397650i 0.957685 0.287819i \(-0.0929302\pi\)
−0.728101 + 0.685470i \(0.759597\pi\)
\(684\) 0 0
\(685\) 12.0000 0.458496
\(686\) 8.50000 + 16.4545i 0.324532 + 0.628235i
\(687\) 0 0
\(688\) −1.00000 + 1.73205i −0.0381246 + 0.0660338i
\(689\) −4.50000 7.79423i −0.171436 0.296936i
\(690\) 0 0
\(691\) −16.0000 + 27.7128i −0.608669 + 1.05425i 0.382791 + 0.923835i \(0.374963\pi\)
−0.991460 + 0.130410i \(0.958371\pi\)
\(692\) −9.00000 −0.342129
\(693\) 0 0
\(694\) 0 0
\(695\) −2.00000 + 3.46410i −0.0758643 + 0.131401i
\(696\) 0 0
\(697\) 9.00000 + 15.5885i 0.340899 + 0.590455i
\(698\) −13.0000 + 22.5167i −0.492057 + 0.852268i
\(699\) 0 0
\(700\) 2.50000 0.866025i 0.0944911 0.0327327i
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0 0
\(703\) −3.50000 6.06218i −0.132005 0.228639i
\(704\) 1.50000 + 2.59808i 0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) −12.0000 −0.451626
\(707\) 6.00000 31.1769i 0.225653 1.17253i
\(708\) 0 0
\(709\) 23.0000 39.8372i 0.863783 1.49612i −0.00446726 0.999990i \(-0.501422\pi\)
0.868250 0.496126i \(-0.165245\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 3.00000 5.19615i 0.112430 0.194734i
\(713\) −72.0000 −2.69642
\(714\) 0 0
\(715\) −3.00000 −0.112194
\(716\) −1.50000 + 2.59808i −0.0560576 + 0.0970947i
\(717\) 0 0
\(718\) 9.00000 + 15.5885i 0.335877 + 0.581756i
\(719\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(720\) 0 0
\(721\) −10.0000 + 3.46410i −0.372419 + 0.129010i
\(722\) −18.0000 −0.669891
\(723\) 0 0
\(724\) −1.00000 1.73205i −0.0371647 0.0643712i
\(725\) 3.00000 + 5.19615i 0.111417 + 0.192980i
\(726\) 0 0
\(727\) −1.00000 −0.0370879 −0.0185440 0.999828i \(-0.505903\pi\)
−0.0185440 + 0.999828i \(0.505903\pi\)
\(728\) 2.00000 + 1.73205i 0.0741249 + 0.0641941i
\(729\) 0 0
\(730\) −2.00000 + 3.46410i −0.0740233 + 0.128212i
\(731\) −6.00000 10.3923i −0.221918 0.384373i
\(732\) 0 0
\(733\) 21.5000 37.2391i 0.794121 1.37546i −0.129275 0.991609i \(-0.541265\pi\)
0.923396 0.383849i \(-0.125402\pi\)
\(734\) −19.0000 −0.701303
\(735\) 0 0
\(736\) −9.00000 −0.331744
\(737\) 12.0000 20.7846i 0.442026 0.765611i
\(738\) 0 0
\(739\) −17.5000 30.3109i −0.643748 1.11500i −0.984589 0.174883i \(-0.944045\pi\)
0.340841 0.940121i \(-0.389288\pi\)
\(740\) −3.50000 + 6.06218i −0.128663 + 0.222850i
\(741\) 0 0
\(742\) 18.0000 + 15.5885i 0.660801 + 0.572270i
\(743\) 45.0000 1.65089 0.825445 0.564483i \(-0.190924\pi\)
0.825445 + 0.564483i \(0.190924\pi\)
\(744\) 0 0
\(745\) 3.00000 + 5.19615i 0.109911 + 0.190372i
\(746\) −1.00000 1.73205i −0.0366126 0.0634149i
\(747\) 0 0
\(748\) −18.0000 −0.658145
\(749\) 30.0000 10.3923i 1.09618 0.379727i
\(750\) 0 0
\(751\) 5.00000 8.66025i 0.182453 0.316017i −0.760263 0.649616i \(-0.774930\pi\)
0.942715 + 0.333599i \(0.108263\pi\)
\(752\) 4.50000 + 7.79423i 0.164098 + 0.284226i
\(753\) 0 0
\(754\) −3.00000 + 5.19615i −0.109254 + 0.189233i
\(755\) 10.0000 0.363937
\(756\) 0 0
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) −11.5000 + 19.9186i −0.417699 + 0.723476i
\(759\) 0 0
\(760\) −0.500000 0.866025i −0.0181369 0.0314140i
\(761\) −13.5000 + 23.3827i −0.489375 + 0.847622i −0.999925 0.0122260i \(-0.996108\pi\)
0.510551 + 0.859848i \(0.329442\pi\)
\(762\) 0 0
\(763\) 8.00000 41.5692i 0.289619 1.50491i
\(764\) −12.0000 −0.434145
\(765\) 0 0
\(766\) 10.5000 + 18.1865i 0.379380 + 0.657106i
\(767\) 0 0
\(768\) 0 0
\(769\) 23.0000 0.829401 0.414701 0.909958i \(-0.363886\pi\)
0.414701 + 0.909958i \(0.363886\pi\)
\(770\) 7.50000 2.59808i 0.270281 0.0936282i
\(771\) 0 0
\(772\) 8.00000 13.8564i 0.287926 0.498703i
\(773\) −25.5000 44.1673i −0.917171 1.58859i −0.803691 0.595047i \(-0.797133\pi\)
−0.113480 0.993540i \(-0.536200\pi\)
\(774\) 0 0
\(775\) −4.00000 + 6.92820i −0.143684 + 0.248868i
\(776\) −10.0000 −0.358979
\(777\) 0 0
\(778\) 12.0000 0.430221
\(779\) −1.50000 + 2.59808i −0.0537431 + 0.0930857i
\(780\) 0 0
\(781\) 0 0
\(782\) 27.0000 46.7654i 0.965518 1.67233i
\(783\) 0 0
\(784\) −6.50000 2.59808i −0.232143 0.0927884i
\(785\) −23.0000 −0.820905
\(786\) 0 0
\(787\) 11.0000 + 19.0526i 0.392108 + 0.679150i 0.992727 0.120384i \(-0.0384127\pi\)
−0.600620 + 0.799535i \(0.705079\pi\)
\(788\) 7.50000 + 12.9904i 0.267176 + 0.462763i
\(789\) 0 0
\(790\) 10.0000 0.355784
\(791\) 0 0