Properties

Label 675.2.k.a.424.2
Level $675$
Weight $2$
Character 675.424
Analytic conductor $5.390$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 424.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 675.424
Dual form 675.2.k.a.199.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.59808 + 1.50000i) q^{7} -3.00000i q^{8} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.59808 + 1.50000i) q^{7} -3.00000i q^{8} +(-1.00000 + 1.73205i) q^{11} +(1.73205 - 1.00000i) q^{13} +(1.50000 + 2.59808i) q^{14} +(0.500000 - 0.866025i) q^{16} -4.00000i q^{17} +8.00000 q^{19} +(-1.73205 + 1.00000i) q^{22} +(2.59808 - 1.50000i) q^{23} +2.00000 q^{26} -3.00000i q^{28} +(0.500000 - 0.866025i) q^{29} +(-4.33013 + 2.50000i) q^{32} +(2.00000 - 3.46410i) q^{34} -4.00000i q^{37} +(6.92820 + 4.00000i) q^{38} +(2.50000 + 4.33013i) q^{41} +(-6.92820 - 4.00000i) q^{43} +2.00000 q^{44} +3.00000 q^{46} +(6.06218 + 3.50000i) q^{47} +(1.00000 + 1.73205i) q^{49} +(-1.73205 - 1.00000i) q^{52} -2.00000i q^{53} +(4.50000 - 7.79423i) q^{56} +(0.866025 - 0.500000i) q^{58} +(7.00000 + 12.1244i) q^{59} +(-3.50000 + 6.06218i) q^{61} -7.00000 q^{64} +(-2.59808 + 1.50000i) q^{67} +(-3.46410 + 2.00000i) q^{68} -2.00000 q^{71} -4.00000i q^{73} +(2.00000 - 3.46410i) q^{74} +(-4.00000 - 6.92820i) q^{76} +(-5.19615 + 3.00000i) q^{77} +(-3.00000 + 5.19615i) q^{79} +5.00000i q^{82} +(-7.79423 - 4.50000i) q^{83} +(-4.00000 - 6.92820i) q^{86} +(5.19615 + 3.00000i) q^{88} -15.0000 q^{89} +6.00000 q^{91} +(-2.59808 - 1.50000i) q^{92} +(3.50000 + 6.06218i) q^{94} +(-1.73205 - 1.00000i) q^{97} +2.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{4} - 4 q^{11} + 6 q^{14} + 2 q^{16} + 32 q^{19} + 8 q^{26} + 2 q^{29} + 8 q^{34} + 10 q^{41} + 8 q^{44} + 12 q^{46} + 4 q^{49} + 18 q^{56} + 28 q^{59} - 14 q^{61} - 28 q^{64} - 8 q^{71} + 8 q^{74} - 16 q^{76} - 12 q^{79} - 16 q^{86} - 60 q^{89} + 24 q^{91} + 14 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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 0.773893 0.633316i \(-0.218307\pi\)
−0.161521 + 0.986869i \(0.551640\pi\)
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) 2.59808 + 1.50000i 0.981981 + 0.566947i 0.902867 0.429919i \(-0.141458\pi\)
0.0791130 + 0.996866i \(0.474791\pi\)
\(8\) 3.00000i 1.06066i
\(9\) 0 0
\(10\) 0 0
\(11\) −1.00000 + 1.73205i −0.301511 + 0.522233i −0.976478 0.215615i \(-0.930824\pi\)
0.674967 + 0.737848i \(0.264158\pi\)
\(12\) 0 0
\(13\) 1.73205 1.00000i 0.480384 0.277350i −0.240192 0.970725i \(-0.577210\pi\)
0.720577 + 0.693375i \(0.243877\pi\)
\(14\) 1.50000 + 2.59808i 0.400892 + 0.694365i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 4.00000i 0.970143i −0.874475 0.485071i \(-0.838794\pi\)
0.874475 0.485071i \(-0.161206\pi\)
\(18\) 0 0
\(19\) 8.00000 1.83533 0.917663 0.397360i \(-0.130073\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.73205 + 1.00000i −0.369274 + 0.213201i
\(23\) 2.59808 1.50000i 0.541736 0.312772i −0.204046 0.978961i \(-0.565409\pi\)
0.745782 + 0.666190i \(0.232076\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 2.00000 0.392232
\(27\) 0 0
\(28\) 3.00000i 0.566947i
\(29\) 0.500000 0.866025i 0.0928477 0.160817i −0.815861 0.578249i \(-0.803736\pi\)
0.908708 + 0.417432i \(0.137070\pi\)
\(30\) 0 0
\(31\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) −4.33013 + 2.50000i −0.765466 + 0.441942i
\(33\) 0 0
\(34\) 2.00000 3.46410i 0.342997 0.594089i
\(35\) 0 0
\(36\) 0 0
\(37\) 4.00000i 0.657596i −0.944400 0.328798i \(-0.893356\pi\)
0.944400 0.328798i \(-0.106644\pi\)
\(38\) 6.92820 + 4.00000i 1.12390 + 0.648886i
\(39\) 0 0
\(40\) 0 0
\(41\) 2.50000 + 4.33013i 0.390434 + 0.676252i 0.992507 0.122189i \(-0.0389915\pi\)
−0.602072 + 0.798441i \(0.705658\pi\)
\(42\) 0 0
\(43\) −6.92820 4.00000i −1.05654 0.609994i −0.132068 0.991241i \(-0.542162\pi\)
−0.924473 + 0.381246i \(0.875495\pi\)
\(44\) 2.00000 0.301511
\(45\) 0 0
\(46\) 3.00000 0.442326
\(47\) 6.06218 + 3.50000i 0.884260 + 0.510527i 0.872060 0.489398i \(-0.162783\pi\)
0.0121990 + 0.999926i \(0.496117\pi\)
\(48\) 0 0
\(49\) 1.00000 + 1.73205i 0.142857 + 0.247436i
\(50\) 0 0
\(51\) 0 0
\(52\) −1.73205 1.00000i −0.240192 0.138675i
\(53\) 2.00000i 0.274721i −0.990521 0.137361i \(-0.956138\pi\)
0.990521 0.137361i \(-0.0438619\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 4.50000 7.79423i 0.601338 1.04155i
\(57\) 0 0
\(58\) 0.866025 0.500000i 0.113715 0.0656532i
\(59\) 7.00000 + 12.1244i 0.911322 + 1.57846i 0.812198 + 0.583382i \(0.198271\pi\)
0.0991242 + 0.995075i \(0.468396\pi\)
\(60\) 0 0
\(61\) −3.50000 + 6.06218i −0.448129 + 0.776182i −0.998264 0.0588933i \(-0.981243\pi\)
0.550135 + 0.835076i \(0.314576\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −7.00000 −0.875000
\(65\) 0 0
\(66\) 0 0
\(67\) −2.59808 + 1.50000i −0.317406 + 0.183254i −0.650236 0.759733i \(-0.725330\pi\)
0.332830 + 0.942987i \(0.391996\pi\)
\(68\) −3.46410 + 2.00000i −0.420084 + 0.242536i
\(69\) 0 0
\(70\) 0 0
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 0 0
\(73\) 4.00000i 0.468165i −0.972217 0.234082i \(-0.924791\pi\)
0.972217 0.234082i \(-0.0752085\pi\)
\(74\) 2.00000 3.46410i 0.232495 0.402694i
\(75\) 0 0
\(76\) −4.00000 6.92820i −0.458831 0.794719i
\(77\) −5.19615 + 3.00000i −0.592157 + 0.341882i
\(78\) 0 0
\(79\) −3.00000 + 5.19615i −0.337526 + 0.584613i −0.983967 0.178352i \(-0.942924\pi\)
0.646440 + 0.762964i \(0.276257\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 5.00000i 0.552158i
\(83\) −7.79423 4.50000i −0.855528 0.493939i 0.00698436 0.999976i \(-0.497777\pi\)
−0.862512 + 0.506036i \(0.831110\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −4.00000 6.92820i −0.431331 0.747087i
\(87\) 0 0
\(88\) 5.19615 + 3.00000i 0.553912 + 0.319801i
\(89\) −15.0000 −1.59000 −0.794998 0.606612i \(-0.792528\pi\)
−0.794998 + 0.606612i \(0.792528\pi\)
\(90\) 0 0
\(91\) 6.00000 0.628971
\(92\) −2.59808 1.50000i −0.270868 0.156386i
\(93\) 0 0
\(94\) 3.50000 + 6.06218i 0.360997 + 0.625266i
\(95\) 0 0
\(96\) 0 0
\(97\) −1.73205 1.00000i −0.175863 0.101535i 0.409484 0.912317i \(-0.365709\pi\)
−0.585348 + 0.810782i \(0.699042\pi\)
\(98\) 2.00000i 0.202031i
\(99\) 0 0
\(100\) 0 0
\(101\) −9.00000 + 15.5885i −0.895533 + 1.55111i −0.0623905 + 0.998052i \(0.519872\pi\)
−0.833143 + 0.553058i \(0.813461\pi\)
\(102\) 0 0
\(103\) −6.92820 + 4.00000i −0.682656 + 0.394132i −0.800855 0.598858i \(-0.795621\pi\)
0.118199 + 0.992990i \(0.462288\pi\)
\(104\) −3.00000 5.19615i −0.294174 0.509525i
\(105\) 0 0
\(106\) 1.00000 1.73205i 0.0971286 0.168232i
\(107\) 3.00000i 0.290021i −0.989430 0.145010i \(-0.953678\pi\)
0.989430 0.145010i \(-0.0463216\pi\)
\(108\) 0 0
\(109\) −5.00000 −0.478913 −0.239457 0.970907i \(-0.576969\pi\)
−0.239457 + 0.970907i \(0.576969\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.59808 1.50000i 0.245495 0.141737i
\(113\) −6.92820 + 4.00000i −0.651751 + 0.376288i −0.789127 0.614231i \(-0.789466\pi\)
0.137376 + 0.990519i \(0.456133\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −1.00000 −0.0928477
\(117\) 0 0
\(118\) 14.0000i 1.28880i
\(119\) 6.00000 10.3923i 0.550019 0.952661i
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) −6.06218 + 3.50000i −0.548844 + 0.316875i
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 5.00000i 0.443678i −0.975083 0.221839i \(-0.928794\pi\)
0.975083 0.221839i \(-0.0712060\pi\)
\(128\) 2.59808 + 1.50000i 0.229640 + 0.132583i
\(129\) 0 0
\(130\) 0 0
\(131\) −3.00000 5.19615i −0.262111 0.453990i 0.704692 0.709514i \(-0.251085\pi\)
−0.966803 + 0.255524i \(0.917752\pi\)
\(132\) 0 0
\(133\) 20.7846 + 12.0000i 1.80225 + 1.04053i
\(134\) −3.00000 −0.259161
\(135\) 0 0
\(136\) −12.0000 −1.02899
\(137\) 10.3923 + 6.00000i 0.887875 + 0.512615i 0.873247 0.487278i \(-0.162010\pi\)
0.0146279 + 0.999893i \(0.495344\pi\)
\(138\) 0 0
\(139\) −8.00000 13.8564i −0.678551 1.17529i −0.975417 0.220366i \(-0.929275\pi\)
0.296866 0.954919i \(-0.404058\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1.73205 1.00000i −0.145350 0.0839181i
\(143\) 4.00000i 0.334497i
\(144\) 0 0
\(145\) 0 0
\(146\) 2.00000 3.46410i 0.165521 0.286691i
\(147\) 0 0
\(148\) −3.46410 + 2.00000i −0.284747 + 0.164399i
\(149\) −8.50000 14.7224i −0.696347 1.20611i −0.969724 0.244202i \(-0.921474\pi\)
0.273377 0.961907i \(-0.411859\pi\)
\(150\) 0 0
\(151\) 1.00000 1.73205i 0.0813788 0.140952i −0.822464 0.568818i \(-0.807401\pi\)
0.903842 + 0.427865i \(0.140734\pi\)
\(152\) 24.0000i 1.94666i
\(153\) 0 0
\(154\) −6.00000 −0.483494
\(155\) 0 0
\(156\) 0 0
\(157\) 12.1244 7.00000i 0.967629 0.558661i 0.0691164 0.997609i \(-0.477982\pi\)
0.898513 + 0.438948i \(0.144649\pi\)
\(158\) −5.19615 + 3.00000i −0.413384 + 0.238667i
\(159\) 0 0
\(160\) 0 0
\(161\) 9.00000 0.709299
\(162\) 0 0
\(163\) 4.00000i 0.313304i 0.987654 + 0.156652i \(0.0500701\pi\)
−0.987654 + 0.156652i \(0.949930\pi\)
\(164\) 2.50000 4.33013i 0.195217 0.338126i
\(165\) 0 0
\(166\) −4.50000 7.79423i −0.349268 0.604949i
\(167\) 7.79423 4.50000i 0.603136 0.348220i −0.167139 0.985933i \(-0.553453\pi\)
0.770274 + 0.637713i \(0.220119\pi\)
\(168\) 0 0
\(169\) −4.50000 + 7.79423i −0.346154 + 0.599556i
\(170\) 0 0
\(171\) 0 0
\(172\) 8.00000i 0.609994i
\(173\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.00000 + 1.73205i 0.0753778 + 0.130558i
\(177\) 0 0
\(178\) −12.9904 7.50000i −0.973670 0.562149i
\(179\) −2.00000 −0.149487 −0.0747435 0.997203i \(-0.523814\pi\)
−0.0747435 + 0.997203i \(0.523814\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 5.19615 + 3.00000i 0.385164 + 0.222375i
\(183\) 0 0
\(184\) −4.50000 7.79423i −0.331744 0.574598i
\(185\) 0 0
\(186\) 0 0
\(187\) 6.92820 + 4.00000i 0.506640 + 0.292509i
\(188\) 7.00000i 0.510527i
\(189\) 0 0
\(190\) 0 0
\(191\) 4.00000 6.92820i 0.289430 0.501307i −0.684244 0.729253i \(-0.739868\pi\)
0.973674 + 0.227946i \(0.0732010\pi\)
\(192\) 0 0
\(193\) 8.66025 5.00000i 0.623379 0.359908i −0.154805 0.987945i \(-0.549475\pi\)
0.778183 + 0.628037i \(0.216141\pi\)
\(194\) −1.00000 1.73205i −0.0717958 0.124354i
\(195\) 0 0
\(196\) 1.00000 1.73205i 0.0714286 0.123718i
\(197\) 12.0000i 0.854965i 0.904024 + 0.427482i \(0.140599\pi\)
−0.904024 + 0.427482i \(0.859401\pi\)
\(198\) 0 0
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −15.5885 + 9.00000i −1.09680 + 0.633238i
\(203\) 2.59808 1.50000i 0.182349 0.105279i
\(204\) 0 0
\(205\) 0 0
\(206\) −8.00000 −0.557386
\(207\) 0 0
\(208\) 2.00000i 0.138675i
\(209\) −8.00000 + 13.8564i −0.553372 + 0.958468i
\(210\) 0 0
\(211\) 11.0000 + 19.0526i 0.757271 + 1.31163i 0.944237 + 0.329266i \(0.106801\pi\)
−0.186966 + 0.982366i \(0.559865\pi\)
\(212\) −1.73205 + 1.00000i −0.118958 + 0.0686803i
\(213\) 0 0
\(214\) 1.50000 2.59808i 0.102538 0.177601i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −4.33013 2.50000i −0.293273 0.169321i
\(219\) 0 0
\(220\) 0 0
\(221\) −4.00000 6.92820i −0.269069 0.466041i
\(222\) 0 0
\(223\) −16.4545 9.50000i −1.10187 0.636167i −0.165161 0.986267i \(-0.552814\pi\)
−0.936713 + 0.350100i \(0.886148\pi\)
\(224\) −15.0000 −1.00223
\(225\) 0 0
\(226\) −8.00000 −0.532152
\(227\) −3.46410 2.00000i −0.229920 0.132745i 0.380615 0.924734i \(-0.375712\pi\)
−0.610535 + 0.791989i \(0.709046\pi\)
\(228\) 0 0
\(229\) 7.50000 + 12.9904i 0.495614 + 0.858429i 0.999987 0.00505719i \(-0.00160976\pi\)
−0.504373 + 0.863486i \(0.668276\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −2.59808 1.50000i −0.170572 0.0984798i
\(233\) 24.0000i 1.57229i 0.618041 + 0.786146i \(0.287927\pi\)
−0.618041 + 0.786146i \(0.712073\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 7.00000 12.1244i 0.455661 0.789228i
\(237\) 0 0
\(238\) 10.3923 6.00000i 0.673633 0.388922i
\(239\) 4.00000 + 6.92820i 0.258738 + 0.448148i 0.965904 0.258900i \(-0.0833599\pi\)
−0.707166 + 0.707048i \(0.750027\pi\)
\(240\) 0 0
\(241\) 5.50000 9.52628i 0.354286 0.613642i −0.632709 0.774389i \(-0.718057\pi\)
0.986996 + 0.160748i \(0.0513906\pi\)
\(242\) 7.00000i 0.449977i
\(243\) 0 0
\(244\) 7.00000 0.448129
\(245\) 0 0
\(246\) 0 0
\(247\) 13.8564 8.00000i 0.881662 0.509028i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 6.00000i 0.377217i
\(254\) 2.50000 4.33013i 0.156864 0.271696i
\(255\) 0 0
\(256\) 8.50000 + 14.7224i 0.531250 + 0.920152i
\(257\) 5.19615 3.00000i 0.324127 0.187135i −0.329104 0.944294i \(-0.606747\pi\)
0.653231 + 0.757159i \(0.273413\pi\)
\(258\) 0 0
\(259\) 6.00000 10.3923i 0.372822 0.645746i
\(260\) 0 0
\(261\) 0 0
\(262\) 6.00000i 0.370681i
\(263\) 13.8564 + 8.00000i 0.854423 + 0.493301i 0.862141 0.506669i \(-0.169123\pi\)
−0.00771799 + 0.999970i \(0.502457\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 12.0000 + 20.7846i 0.735767 + 1.27439i
\(267\) 0 0
\(268\) 2.59808 + 1.50000i 0.158703 + 0.0916271i
\(269\) 25.0000 1.52428 0.762138 0.647414i \(-0.224150\pi\)
0.762138 + 0.647414i \(0.224150\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) −3.46410 2.00000i −0.210042 0.121268i
\(273\) 0 0
\(274\) 6.00000 + 10.3923i 0.362473 + 0.627822i
\(275\) 0 0
\(276\) 0 0
\(277\) −10.3923 6.00000i −0.624413 0.360505i 0.154172 0.988044i \(-0.450729\pi\)
−0.778585 + 0.627539i \(0.784062\pi\)
\(278\) 16.0000i 0.959616i
\(279\) 0 0
\(280\) 0 0
\(281\) −7.50000 + 12.9904i −0.447412 + 0.774941i −0.998217 0.0596933i \(-0.980988\pi\)
0.550804 + 0.834634i \(0.314321\pi\)
\(282\) 0 0
\(283\) −18.1865 + 10.5000i −1.08108 + 0.624160i −0.931187 0.364542i \(-0.881225\pi\)
−0.149890 + 0.988703i \(0.547892\pi\)
\(284\) 1.00000 + 1.73205i 0.0593391 + 0.102778i
\(285\) 0 0
\(286\) −2.00000 + 3.46410i −0.118262 + 0.204837i
\(287\) 15.0000i 0.885422i
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 0 0
\(292\) −3.46410 + 2.00000i −0.202721 + 0.117041i
\(293\) 10.3923 6.00000i 0.607125 0.350524i −0.164714 0.986341i \(-0.552670\pi\)
0.771839 + 0.635818i \(0.219337\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −12.0000 −0.697486
\(297\) 0 0
\(298\) 17.0000i 0.984784i
\(299\) 3.00000 5.19615i 0.173494 0.300501i
\(300\) 0 0
\(301\) −12.0000 20.7846i −0.691669 1.19800i
\(302\) 1.73205 1.00000i 0.0996683 0.0575435i
\(303\) 0 0
\(304\) 4.00000 6.92820i 0.229416 0.397360i
\(305\) 0 0
\(306\) 0 0
\(307\) 7.00000i 0.399511i 0.979846 + 0.199756i \(0.0640148\pi\)
−0.979846 + 0.199756i \(0.935985\pi\)
\(308\) 5.19615 + 3.00000i 0.296078 + 0.170941i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(312\) 0 0
\(313\) 12.1244 + 7.00000i 0.685309 + 0.395663i 0.801852 0.597522i \(-0.203848\pi\)
−0.116543 + 0.993186i \(0.537181\pi\)
\(314\) 14.0000 0.790066
\(315\) 0 0
\(316\) 6.00000 0.337526
\(317\) −29.4449 17.0000i −1.65379 0.954815i −0.975494 0.220024i \(-0.929386\pi\)
−0.678294 0.734791i \(-0.737280\pi\)
\(318\) 0 0
\(319\) 1.00000 + 1.73205i 0.0559893 + 0.0969762i
\(320\) 0 0
\(321\) 0 0
\(322\) 7.79423 + 4.50000i 0.434355 + 0.250775i
\(323\) 32.0000i 1.78053i
\(324\) 0 0
\(325\) 0 0
\(326\) −2.00000 + 3.46410i −0.110770 + 0.191859i
\(327\) 0 0
\(328\) 12.9904 7.50000i 0.717274 0.414118i
\(329\) 10.5000 + 18.1865i 0.578884 + 1.00266i
\(330\) 0 0
\(331\) 3.00000 5.19615i 0.164895 0.285606i −0.771723 0.635959i \(-0.780605\pi\)
0.936618 + 0.350352i \(0.113938\pi\)
\(332\) 9.00000i 0.493939i
\(333\) 0 0
\(334\) 9.00000 0.492458
\(335\) 0 0
\(336\) 0 0
\(337\) −6.92820 + 4.00000i −0.377403 + 0.217894i −0.676688 0.736270i \(-0.736585\pi\)
0.299285 + 0.954164i \(0.403252\pi\)
\(338\) −7.79423 + 4.50000i −0.423950 + 0.244768i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 15.0000i 0.809924i
\(344\) −12.0000 + 20.7846i −0.646997 + 1.12063i
\(345\) 0 0
\(346\) 0 0
\(347\) −3.46410 + 2.00000i −0.185963 + 0.107366i −0.590091 0.807337i \(-0.700908\pi\)
0.404128 + 0.914702i \(0.367575\pi\)
\(348\) 0 0
\(349\) −2.50000 + 4.33013i −0.133822 + 0.231786i −0.925147 0.379610i \(-0.876058\pi\)
0.791325 + 0.611396i \(0.209392\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 10.0000i 0.533002i
\(353\) −20.7846 12.0000i −1.10625 0.638696i −0.168397 0.985719i \(-0.553859\pi\)
−0.937856 + 0.347024i \(0.887192\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 7.50000 + 12.9904i 0.397499 + 0.688489i
\(357\) 0 0
\(358\) −1.73205 1.00000i −0.0915417 0.0528516i
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 0 0
\(361\) 45.0000 2.36842
\(362\) −6.06218 3.50000i −0.318621 0.183956i
\(363\) 0 0
\(364\) −3.00000 5.19615i −0.157243 0.272352i
\(365\) 0 0
\(366\) 0 0
\(367\) −20.7846 12.0000i −1.08495 0.626395i −0.152721 0.988269i \(-0.548804\pi\)
−0.932227 + 0.361874i \(0.882137\pi\)
\(368\) 3.00000i 0.156386i
\(369\) 0 0
\(370\) 0 0
\(371\) 3.00000 5.19615i 0.155752 0.269771i
\(372\) 0 0
\(373\) −8.66025 + 5.00000i −0.448411 + 0.258890i −0.707159 0.707055i \(-0.750023\pi\)
0.258748 + 0.965945i \(0.416690\pi\)
\(374\) 4.00000 + 6.92820i 0.206835 + 0.358249i
\(375\) 0 0
\(376\) 10.5000 18.1865i 0.541496 0.937899i
\(377\) 2.00000i 0.103005i
\(378\) 0 0
\(379\) 26.0000 1.33553 0.667765 0.744372i \(-0.267251\pi\)
0.667765 + 0.744372i \(0.267251\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 6.92820 4.00000i 0.354478 0.204658i
\(383\) 31.1769 18.0000i 1.59307 0.919757i 0.600289 0.799783i \(-0.295052\pi\)
0.992777 0.119974i \(-0.0382810\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 10.0000 0.508987
\(387\) 0 0
\(388\) 2.00000i 0.101535i
\(389\) −16.5000 + 28.5788i −0.836583 + 1.44900i 0.0561516 + 0.998422i \(0.482117\pi\)
−0.892735 + 0.450582i \(0.851216\pi\)
\(390\) 0 0
\(391\) −6.00000 10.3923i −0.303433 0.525561i
\(392\) 5.19615 3.00000i 0.262445 0.151523i
\(393\) 0 0
\(394\) −6.00000 + 10.3923i −0.302276 + 0.523557i
\(395\) 0 0
\(396\) 0 0
\(397\) 34.0000i 1.70641i 0.521575 + 0.853206i \(0.325345\pi\)
−0.521575 + 0.853206i \(0.674655\pi\)
\(398\) −3.46410 2.00000i −0.173640 0.100251i
\(399\) 0 0
\(400\) 0 0
\(401\) −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i \(-0.315043\pi\)
−0.998350 + 0.0574304i \(0.981709\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 18.0000 0.895533
\(405\) 0 0
\(406\) 3.00000 0.148888
\(407\) 6.92820 + 4.00000i 0.343418 + 0.198273i
\(408\) 0 0
\(409\) 7.00000 + 12.1244i 0.346128 + 0.599511i 0.985558 0.169338i \(-0.0541630\pi\)
−0.639430 + 0.768849i \(0.720830\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 6.92820 + 4.00000i 0.341328 + 0.197066i
\(413\) 42.0000i 2.06668i
\(414\) 0 0
\(415\) 0 0
\(416\) −5.00000 + 8.66025i −0.245145 + 0.424604i
\(417\) 0 0
\(418\) −13.8564 + 8.00000i −0.677739 + 0.391293i
\(419\) −13.0000 22.5167i −0.635092 1.10001i −0.986496 0.163787i \(-0.947629\pi\)
0.351404 0.936224i \(-0.385704\pi\)
\(420\) 0 0
\(421\) −17.0000 + 29.4449i −0.828529 + 1.43505i 0.0706626 + 0.997500i \(0.477489\pi\)
−0.899192 + 0.437555i \(0.855845\pi\)
\(422\) 22.0000i 1.07094i
\(423\) 0 0
\(424\) −6.00000 −0.291386
\(425\) 0 0
\(426\) 0 0
\(427\) −18.1865 + 10.5000i −0.880108 + 0.508131i
\(428\) −2.59808 + 1.50000i −0.125583 + 0.0725052i
\(429\) 0 0
\(430\) 0 0
\(431\) 30.0000 1.44505 0.722525 0.691345i \(-0.242982\pi\)
0.722525 + 0.691345i \(0.242982\pi\)
\(432\) 0 0
\(433\) 28.0000i 1.34559i −0.739827 0.672797i \(-0.765093\pi\)
0.739827 0.672797i \(-0.234907\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 2.50000 + 4.33013i 0.119728 + 0.207375i
\(437\) 20.7846 12.0000i 0.994263 0.574038i
\(438\) 0 0
\(439\) 14.0000 24.2487i 0.668184 1.15733i −0.310228 0.950662i \(-0.600405\pi\)
0.978412 0.206666i \(-0.0662612\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 8.00000i 0.380521i
\(443\) −12.9904 7.50000i −0.617192 0.356336i 0.158583 0.987346i \(-0.449307\pi\)
−0.775775 + 0.631010i \(0.782641\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −9.50000 16.4545i −0.449838 0.779142i
\(447\) 0 0
\(448\) −18.1865 10.5000i −0.859233 0.496078i
\(449\) −26.0000 −1.22702 −0.613508 0.789689i \(-0.710242\pi\)
−0.613508 + 0.789689i \(0.710242\pi\)
\(450\) 0 0
\(451\) −10.0000 −0.470882
\(452\) 6.92820 + 4.00000i 0.325875 + 0.188144i
\(453\) 0 0
\(454\) −2.00000 3.46410i −0.0938647 0.162578i
\(455\) 0 0
\(456\) 0 0
\(457\) 17.3205 + 10.0000i 0.810219 + 0.467780i 0.847032 0.531542i \(-0.178387\pi\)
−0.0368128 + 0.999322i \(0.511721\pi\)
\(458\) 15.0000i 0.700904i
\(459\) 0 0
\(460\) 0 0
\(461\) 4.50000 7.79423i 0.209586 0.363013i −0.741998 0.670402i \(-0.766122\pi\)
0.951584 + 0.307388i \(0.0994551\pi\)
\(462\) 0 0
\(463\) 31.1769 18.0000i 1.44891 0.836531i 0.450497 0.892778i \(-0.351247\pi\)
0.998417 + 0.0562469i \(0.0179134\pi\)
\(464\) −0.500000 0.866025i −0.0232119 0.0402042i
\(465\) 0 0
\(466\) −12.0000 + 20.7846i −0.555889 + 0.962828i
\(467\) 20.0000i 0.925490i −0.886492 0.462745i \(-0.846865\pi\)
0.886492 0.462745i \(-0.153135\pi\)
\(468\) 0 0
\(469\) −9.00000 −0.415581
\(470\) 0 0
\(471\) 0 0
\(472\) 36.3731 21.0000i 1.67421 0.966603i
\(473\) 13.8564 8.00000i 0.637118 0.367840i
\(474\) 0 0
\(475\) 0 0
\(476\) −12.0000 −0.550019
\(477\) 0 0
\(478\) 8.00000i 0.365911i
\(479\) 9.00000 15.5885i 0.411220 0.712255i −0.583803 0.811895i \(-0.698436\pi\)
0.995023 + 0.0996406i \(0.0317693\pi\)
\(480\) 0 0
\(481\) −4.00000 6.92820i −0.182384 0.315899i
\(482\) 9.52628 5.50000i 0.433910 0.250518i
\(483\) 0 0
\(484\) 3.50000 6.06218i 0.159091 0.275554i
\(485\) 0 0
\(486\) 0 0
\(487\) 16.0000i 0.725029i −0.931978 0.362515i \(-0.881918\pi\)
0.931978 0.362515i \(-0.118082\pi\)
\(488\) 18.1865 + 10.5000i 0.823266 + 0.475313i
\(489\) 0 0
\(490\) 0 0
\(491\) 10.0000 + 17.3205i 0.451294 + 0.781664i 0.998467 0.0553560i \(-0.0176294\pi\)
−0.547173 + 0.837020i \(0.684296\pi\)
\(492\) 0 0
\(493\) −3.46410 2.00000i −0.156015 0.0900755i
\(494\) 16.0000 0.719874
\(495\) 0 0
\(496\) 0 0
\(497\) −5.19615 3.00000i −0.233079 0.134568i
\(498\) 0 0
\(499\) −16.0000 27.7128i −0.716258 1.24060i −0.962472 0.271380i \(-0.912520\pi\)
0.246214 0.969216i \(-0.420813\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 7.00000i 0.312115i −0.987748 0.156057i \(-0.950122\pi\)
0.987748 0.156057i \(-0.0498784\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −3.00000 + 5.19615i −0.133366 + 0.230997i
\(507\) 0 0
\(508\) −4.33013 + 2.50000i −0.192118 + 0.110920i
\(509\) −21.5000 37.2391i −0.952971 1.65059i −0.738945 0.673766i \(-0.764676\pi\)
−0.214026 0.976828i \(-0.568658\pi\)
\(510\) 0 0
\(511\) 6.00000 10.3923i 0.265424 0.459728i
\(512\) 11.0000i 0.486136i
\(513\) 0 0
\(514\) 6.00000 0.264649
\(515\) 0 0
\(516\) 0 0
\(517\) −12.1244 + 7.00000i −0.533229 + 0.307860i
\(518\) 10.3923 6.00000i 0.456612 0.263625i
\(519\) 0 0
\(520\) 0 0
\(521\) −11.0000 −0.481919 −0.240959 0.970535i \(-0.577462\pi\)
−0.240959 + 0.970535i \(0.577462\pi\)
\(522\) 0 0
\(523\) 29.0000i 1.26808i 0.773300 + 0.634041i \(0.218605\pi\)
−0.773300 + 0.634041i \(0.781395\pi\)
\(524\) −3.00000 + 5.19615i −0.131056 + 0.226995i
\(525\) 0 0
\(526\) 8.00000 + 13.8564i 0.348817 + 0.604168i
\(527\) 0 0
\(528\) 0 0
\(529\) −7.00000 + 12.1244i −0.304348 + 0.527146i
\(530\) 0 0
\(531\) 0 0
\(532\) 24.0000i 1.04053i
\(533\) 8.66025 + 5.00000i 0.375117 + 0.216574i
\(534\) 0 0
\(535\) 0 0
\(536\) 4.50000 + 7.79423i 0.194370 + 0.336659i
\(537\) 0 0
\(538\) 21.6506 + 12.5000i 0.933425 + 0.538913i
\(539\) −4.00000 −0.172292
\(540\) 0 0
\(541\) −39.0000 −1.67674 −0.838370 0.545101i \(-0.816491\pi\)
−0.838370 + 0.545101i \(0.816491\pi\)
\(542\) −6.92820 4.00000i −0.297592 0.171815i
\(543\) 0 0
\(544\) 10.0000 + 17.3205i 0.428746 + 0.742611i
\(545\) 0 0
\(546\) 0 0
\(547\) 25.1147 + 14.5000i 1.07383 + 0.619975i 0.929225 0.369514i \(-0.120476\pi\)
0.144604 + 0.989490i \(0.453809\pi\)
\(548\) 12.0000i 0.512615i
\(549\) 0 0
\(550\) 0 0
\(551\) 4.00000 6.92820i 0.170406 0.295151i
\(552\) 0 0
\(553\) −15.5885 + 9.00000i −0.662889 + 0.382719i
\(554\) −6.00000 10.3923i −0.254916 0.441527i
\(555\) 0 0
\(556\) −8.00000 + 13.8564i −0.339276 + 0.587643i
\(557\) 30.0000i 1.27114i 0.772043 + 0.635570i \(0.219235\pi\)
−0.772043 + 0.635570i \(0.780765\pi\)
\(558\) 0 0
\(559\) −16.0000 −0.676728
\(560\) 0 0
\(561\) 0 0
\(562\) −12.9904 + 7.50000i −0.547966 + 0.316368i
\(563\) −18.1865 + 10.5000i −0.766471 + 0.442522i −0.831614 0.555354i \(-0.812583\pi\)
0.0651433 + 0.997876i \(0.479250\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −21.0000 −0.882696
\(567\) 0 0
\(568\) 6.00000i 0.251754i
\(569\) 3.00000 5.19615i 0.125767 0.217834i −0.796266 0.604947i \(-0.793194\pi\)
0.922032 + 0.387113i \(0.126528\pi\)
\(570\) 0 0
\(571\) −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i \(-0.933141\pi\)
0.308443 0.951243i \(-0.400192\pi\)
\(572\) 3.46410 2.00000i 0.144841 0.0836242i
\(573\) 0 0
\(574\) −7.50000 + 12.9904i −0.313044 + 0.542208i
\(575\) 0 0
\(576\) 0 0
\(577\) 10.0000i 0.416305i −0.978096 0.208153i \(-0.933255\pi\)
0.978096 0.208153i \(-0.0667451\pi\)
\(578\) 0.866025 + 0.500000i 0.0360219 + 0.0207973i
\(579\) 0 0
\(580\) 0 0
\(581\) −13.5000 23.3827i −0.560074 0.970077i
\(582\) 0 0
\(583\) 3.46410 + 2.00000i 0.143468 + 0.0828315i
\(584\) −12.0000 −0.496564
\(585\) 0 0
\(586\) 12.0000 0.495715
\(587\) −28.5788 16.5000i −1.17957 0.681028i −0.223659 0.974668i \(-0.571800\pi\)
−0.955916 + 0.293640i \(0.905133\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −3.46410 2.00000i −0.142374 0.0821995i
\(593\) 20.0000i 0.821302i 0.911793 + 0.410651i \(0.134698\pi\)
−0.911793 + 0.410651i \(0.865302\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −8.50000 + 14.7224i −0.348174 + 0.603054i
\(597\) 0 0
\(598\) 5.19615 3.00000i 0.212486 0.122679i
\(599\) 5.00000 + 8.66025i 0.204294 + 0.353848i 0.949908 0.312531i \(-0.101177\pi\)
−0.745613 + 0.666379i \(0.767843\pi\)
\(600\) 0 0
\(601\) −1.00000 + 1.73205i −0.0407909 + 0.0706518i −0.885700 0.464258i \(-0.846321\pi\)
0.844909 + 0.534910i \(0.179654\pi\)
\(602\) 24.0000i 0.978167i
\(603\) 0 0
\(604\) −2.00000 −0.0813788
\(605\) 0 0
\(606\) 0 0
\(607\) −35.5070 + 20.5000i −1.44119 + 0.832069i −0.997929 0.0643251i \(-0.979511\pi\)
−0.443257 + 0.896394i \(0.646177\pi\)
\(608\) −34.6410 + 20.0000i −1.40488 + 0.811107i
\(609\) 0 0
\(610\) 0 0
\(611\) 14.0000 0.566379
\(612\) 0 0
\(613\) 44.0000i 1.77714i 0.458738 + 0.888572i \(0.348302\pi\)
−0.458738 + 0.888572i \(0.651698\pi\)
\(614\) −3.50000 + 6.06218i −0.141249 + 0.244650i
\(615\) 0 0
\(616\) 9.00000 + 15.5885i 0.362620 + 0.628077i
\(617\) 31.1769 18.0000i 1.25514 0.724653i 0.283011 0.959117i \(-0.408667\pi\)
0.972125 + 0.234464i \(0.0753335\pi\)
\(618\) 0 0
\(619\) −2.00000 + 3.46410i −0.0803868 + 0.139234i −0.903416 0.428765i \(-0.858949\pi\)
0.823029 + 0.567999i \(0.192282\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −38.9711 22.5000i −1.56135 0.901443i
\(624\) 0 0
\(625\) 0 0
\(626\) 7.00000 + 12.1244i 0.279776 + 0.484587i
\(627\) 0 0
\(628\) −12.1244 7.00000i −0.483814 0.279330i
\(629\) −16.0000 −0.637962
\(630\) 0 0
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) 15.5885 + 9.00000i 0.620076 + 0.358001i
\(633\) 0 0
\(634\) −17.0000 29.4449i −0.675156 1.16940i
\(635\) 0 0
\(636\) 0 0
\(637\) 3.46410 + 2.00000i 0.137253 + 0.0792429i
\(638\) 2.00000i 0.0791808i
\(639\) 0 0
\(640\) 0 0
\(641\) 16.5000 28.5788i 0.651711 1.12880i −0.330997 0.943632i \(-0.607385\pi\)
0.982708 0.185164i \(-0.0592817\pi\)
\(642\) 0 0
\(643\) 7.79423 4.50000i 0.307374 0.177463i −0.338377 0.941011i \(-0.609878\pi\)
0.645751 + 0.763548i \(0.276544\pi\)
\(644\) −4.50000 7.79423i −0.177325 0.307136i
\(645\) 0 0
\(646\) 16.0000 27.7128i 0.629512 1.09035i
\(647\) 17.0000i 0.668339i 0.942513 + 0.334169i \(0.108456\pi\)
−0.942513 + 0.334169i \(0.891544\pi\)
\(648\) 0 0
\(649\) −28.0000 −1.09910
\(650\) 0 0
\(651\) 0 0
\(652\) 3.46410 2.00000i 0.135665 0.0783260i
\(653\) −3.46410 + 2.00000i −0.135561 + 0.0782660i −0.566247 0.824236i \(-0.691605\pi\)
0.430686 + 0.902502i \(0.358272\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 5.00000 0.195217
\(657\) 0 0
\(658\) 21.0000i 0.818665i
\(659\) 4.00000 6.92820i 0.155818 0.269884i −0.777539 0.628835i \(-0.783532\pi\)
0.933357 + 0.358951i \(0.116865\pi\)
\(660\) 0 0
\(661\) 7.00000 + 12.1244i 0.272268 + 0.471583i 0.969442 0.245319i \(-0.0788928\pi\)
−0.697174 + 0.716902i \(0.745559\pi\)
\(662\) 5.19615 3.00000i 0.201954 0.116598i
\(663\) 0 0
\(664\) −13.5000 + 23.3827i −0.523902 + 0.907424i
\(665\) 0 0
\(666\) 0 0
\(667\) 3.00000i 0.116160i
\(668\) −7.79423 4.50000i −0.301568 0.174110i
\(669\) 0 0
\(670\) 0 0
\(671\) −7.00000 12.1244i −0.270232 0.468056i
\(672\) 0 0
\(673\) 5.19615 + 3.00000i 0.200297 + 0.115642i 0.596794 0.802395i \(-0.296441\pi\)
−0.396497 + 0.918036i \(0.629774\pi\)
\(674\) −8.00000 −0.308148
\(675\) 0 0
\(676\) 9.00000 0.346154
\(677\) −36.3731 21.0000i −1.39793 0.807096i −0.403755 0.914867i \(-0.632295\pi\)
−0.994176 + 0.107772i \(0.965628\pi\)
\(678\) 0 0
\(679\) −3.00000 5.19615i −0.115129 0.199410i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 12.0000i 0.459167i 0.973289 + 0.229584i \(0.0737364\pi\)
−0.973289 + 0.229584i \(0.926264\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 7.50000 12.9904i 0.286351 0.495975i
\(687\) 0 0
\(688\) −6.92820 + 4.00000i −0.264135 + 0.152499i
\(689\) −2.00000 3.46410i −0.0761939 0.131972i
\(690\) 0 0
\(691\) 7.00000 12.1244i 0.266293 0.461232i −0.701609 0.712562i \(-0.747535\pi\)
0.967901 + 0.251330i \(0.0808679\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −4.00000 −0.151838
\(695\) 0 0
\(696\) 0 0
\(697\) 17.3205 10.0000i 0.656061 0.378777i
\(698\) −4.33013 + 2.50000i −0.163898 + 0.0946264i
\(699\) 0 0
\(700\) 0 0
\(701\) −23.0000 −0.868698 −0.434349 0.900745i \(-0.643022\pi\)
−0.434349 + 0.900745i \(0.643022\pi\)
\(702\) 0 0
\(703\) 32.0000i 1.20690i
\(704\) 7.00000 12.1244i 0.263822 0.456954i
\(705\) 0 0
\(706\) −12.0000 20.7846i −0.451626 0.782239i
\(707\) −46.7654 + 27.0000i −1.75879 + 1.01544i
\(708\) 0 0
\(709\) −20.5000 + 35.5070i −0.769894 + 1.33349i 0.167727 + 0.985834i \(0.446357\pi\)
−0.937620 + 0.347661i \(0.886976\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 45.0000i 1.68645i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 1.00000 + 1.73205i 0.0373718 + 0.0647298i
\(717\) 0 0
\(718\) 20.7846 + 12.0000i 0.775675 + 0.447836i
\(719\) 6.00000 0.223762 0.111881 0.993722i \(-0.464312\pi\)
0.111881 + 0.993722i \(0.464312\pi\)
\(720\) 0 0
\(721\) −24.0000 −0.893807
\(722\) 38.9711 + 22.5000i 1.45036 + 0.837363i
\(723\) 0 0
\(724\) 3.50000 + 6.06218i 0.130076 + 0.225299i
\(725\) 0 0
\(726\) 0 0
\(727\) −19.9186 11.5000i −0.738739 0.426511i 0.0828714 0.996560i \(-0.473591\pi\)
−0.821611 + 0.570049i \(0.806924\pi\)
\(728\) 18.0000i 0.667124i
\(729\) 0 0
\(730\) 0 0
\(731\) −16.0000 + 27.7128i −0.591781 + 1.02500i
\(732\) 0 0
\(733\) 29.4449 17.0000i 1.08757 0.627909i 0.154642 0.987971i \(-0.450578\pi\)
0.932929 + 0.360061i \(0.117244\pi\)
\(734\) −12.0000 20.7846i −0.442928 0.767174i
\(735\) 0 0
\(736\) −7.50000 + 12.9904i −0.276454 + 0.478832i
\(737\) 6.00000i 0.221013i
\(738\) 0 0
\(739\) 2.00000 0.0735712 0.0367856 0.999323i \(-0.488288\pi\)
0.0367856 + 0.999323i \(0.488288\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 5.19615 3.00000i 0.190757 0.110133i
\(743\) −25.1147 + 14.5000i −0.921370 + 0.531953i −0.884072 0.467351i \(-0.845209\pi\)
−0.0372984 + 0.999304i \(0.511875\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −10.0000 −0.366126
\(747\) 0 0
\(748\) 8.00000i 0.292509i
\(749\) 4.50000 7.79423i 0.164426 0.284795i
\(750\) 0 0
\(751\) −5.00000 8.66025i −0.182453 0.316017i 0.760263 0.649616i \(-0.225070\pi\)
−0.942715 + 0.333599i \(0.891737\pi\)
\(752\) 6.06218 3.50000i 0.221065 0.127632i
\(753\) 0 0
\(754\) 1.00000 1.73205i 0.0364179 0.0630776i
\(755\) 0 0
\(756\) 0 0
\(757\) 26.0000i 0.944986i −0.881334 0.472493i \(-0.843354\pi\)
0.881334 0.472493i \(-0.156646\pi\)
\(758\) 22.5167 + 13.0000i 0.817842 + 0.472181i
\(759\) 0 0
\(760\) 0 0
\(761\) 7.50000 + 12.9904i 0.271875 + 0.470901i 0.969342 0.245716i \(-0.0790230\pi\)
−0.697467 + 0.716617i \(0.745690\pi\)
\(762\) 0 0
\(763\) −12.9904 7.50000i −0.470283 0.271518i
\(764\) −8.00000 −0.289430
\(765\) 0 0
\(766\) 36.0000 1.30073
\(767\) 24.2487 + 14.0000i 0.875570 + 0.505511i
\(768\) 0 0
\(769\) 2.50000 + 4.33013i 0.0901523 + 0.156148i 0.907575 0.419890i \(-0.137931\pi\)
−0.817423 + 0.576038i \(0.804598\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −8.66025 5.00000i −0.311689 0.179954i
\(773\) 24.0000i 0.863220i −0.902060 0.431610i \(-0.857946\pi\)
0.902060 0.431610i \(-0.142054\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −3.00000 + 5.19615i −0.107694 + 0.186531i
\(777\) 0 0
\(778\) −28.5788 + 16.5000i −1.02460 + 0.591554i
\(779\) 20.0000 + 34.6410i 0.716574 + 1.24114i
\(780\) 0 0
\(781\) 2.00000 3.46410i 0.0715656 0.123955i
\(782\) 12.0000i 0.429119i
\(783\) 0 0
\(784\) 2.00000 0.0714286
\(785\) 0 0
\(786\) 0 0
\(787\) 24.2487 14.0000i 0.864373 0.499046i −0.00110111 0.999999i \(-0.500350\pi\)
0.865474 + 0.500953i \(0.167017\pi\)
\(788\) 10.3923 6.00000i 0.370211 0.213741i
\(789\) 0 0
\(790\) 0 0
\(791\) −24.0000 −0.853342
\(792\) 0 0
\(793\) 14.0000i 0.497155i
\(794\) −17.0000 + 29.4449i −0.603307 +