Properties

Label 576.2.bb.e.49.18
Level $576$
Weight $2$
Character 576.49
Analytic conductor $4.599$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bb (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 49.18
Character \(\chi\) \(=\) 576.49
Dual form 576.2.bb.e.529.18

$q$-expansion

\(f(q)\) \(=\) \(q+(1.71859 + 0.215523i) q^{3} +(2.73721 - 0.733432i) q^{5} +(1.14487 - 0.660988i) q^{7} +(2.90710 + 0.740791i) q^{9} +O(q^{10})\) \(q+(1.71859 + 0.215523i) q^{3} +(2.73721 - 0.733432i) q^{5} +(1.14487 - 0.660988i) q^{7} +(2.90710 + 0.740791i) q^{9} +(0.343957 - 1.28367i) q^{11} +(-0.902174 - 3.36696i) q^{13} +(4.86220 - 0.670538i) q^{15} -7.60772 q^{17} +(-4.32297 + 4.32297i) q^{19} +(2.11001 - 0.889223i) q^{21} +(3.46087 + 1.99814i) q^{23} +(2.62424 - 1.51511i) q^{25} +(4.83645 + 1.89966i) q^{27} +(-3.54658 - 0.950303i) q^{29} +(-0.569129 + 0.985760i) q^{31} +(0.867781 - 2.13197i) q^{33} +(2.64894 - 2.64894i) q^{35} +(2.26014 + 2.26014i) q^{37} +(-0.824810 - 5.98086i) q^{39} +(-1.42311 - 0.821634i) q^{41} +(-1.65438 + 6.17424i) q^{43} +(8.50065 - 0.104463i) q^{45} +(-4.58731 - 7.94546i) q^{47} +(-2.62619 + 4.54869i) q^{49} +(-13.0746 - 1.63964i) q^{51} +(7.72215 + 7.72215i) q^{53} -3.76593i q^{55} +(-8.36111 + 6.49771i) q^{57} +(4.80982 - 1.28879i) q^{59} +(9.92979 + 2.66068i) q^{61} +(3.81789 - 1.07345i) q^{63} +(-4.93887 - 8.55438i) q^{65} +(3.73189 + 13.9276i) q^{67} +(5.51718 + 4.17987i) q^{69} -7.87498i q^{71} +0.577222i q^{73} +(4.83654 - 2.03826i) q^{75} +(-0.454704 - 1.69698i) q^{77} +(-0.716890 - 1.24169i) q^{79} +(7.90246 + 4.30711i) q^{81} +(-3.30414 - 0.885341i) q^{83} +(-20.8239 + 5.57975i) q^{85} +(-5.89030 - 2.39755i) q^{87} -16.2114i q^{89} +(-3.25839 - 3.25839i) q^{91} +(-1.19055 + 1.57146i) q^{93} +(-8.66225 + 15.0035i) q^{95} +(-0.648931 - 1.12398i) q^{97} +(1.95085 - 3.47695i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q - 2q^{3} + 4q^{5} + O(q^{10}) \) \( 72q - 2q^{3} + 4q^{5} + 2q^{11} - 16q^{13} + 20q^{15} - 16q^{17} - 28q^{19} - 16q^{21} - 8q^{27} + 4q^{29} - 28q^{31} - 32q^{33} + 16q^{35} + 16q^{37} + 10q^{43} + 40q^{45} + 56q^{47} + 4q^{49} + 54q^{51} - 8q^{53} + 14q^{59} - 32q^{61} + 108q^{63} - 64q^{65} + 18q^{67} + 32q^{69} - 86q^{75} - 36q^{77} - 44q^{79} - 44q^{81} - 20q^{83} - 8q^{85} + 80q^{91} - 4q^{93} - 48q^{95} + 40q^{97} - 28q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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 0
\(3\) 1.71859 + 0.215523i 0.992228 + 0.124432i
\(4\) 0 0
\(5\) 2.73721 0.733432i 1.22412 0.328001i 0.411830 0.911261i \(-0.364890\pi\)
0.812286 + 0.583260i \(0.198223\pi\)
\(6\) 0 0
\(7\) 1.14487 0.660988i 0.432718 0.249830i −0.267786 0.963479i \(-0.586292\pi\)
0.700504 + 0.713648i \(0.252959\pi\)
\(8\) 0 0
\(9\) 2.90710 + 0.740791i 0.969033 + 0.246930i
\(10\) 0 0
\(11\) 0.343957 1.28367i 0.103707 0.387040i −0.894488 0.447092i \(-0.852460\pi\)
0.998195 + 0.0600515i \(0.0191265\pi\)
\(12\) 0 0
\(13\) −0.902174 3.36696i −0.250218 0.933827i −0.970689 0.240341i \(-0.922741\pi\)
0.720470 0.693486i \(-0.243926\pi\)
\(14\) 0 0
\(15\) 4.86220 0.670538i 1.25542 0.173132i
\(16\) 0 0
\(17\) −7.60772 −1.84514 −0.922572 0.385825i \(-0.873917\pi\)
−0.922572 + 0.385825i \(0.873917\pi\)
\(18\) 0 0
\(19\) −4.32297 + 4.32297i −0.991757 + 0.991757i −0.999966 0.00820954i \(-0.997387\pi\)
0.00820954 + 0.999966i \(0.497387\pi\)
\(20\) 0 0
\(21\) 2.11001 0.889223i 0.460442 0.194044i
\(22\) 0 0
\(23\) 3.46087 + 1.99814i 0.721642 + 0.416640i 0.815357 0.578959i \(-0.196541\pi\)
−0.0937148 + 0.995599i \(0.529874\pi\)
\(24\) 0 0
\(25\) 2.62424 1.51511i 0.524849 0.303021i
\(26\) 0 0
\(27\) 4.83645 + 1.89966i 0.930776 + 0.365590i
\(28\) 0 0
\(29\) −3.54658 0.950303i −0.658583 0.176467i −0.0859765 0.996297i \(-0.527401\pi\)
−0.572606 + 0.819830i \(0.694068\pi\)
\(30\) 0 0
\(31\) −0.569129 + 0.985760i −0.102219 + 0.177048i −0.912598 0.408857i \(-0.865927\pi\)
0.810380 + 0.585905i \(0.199261\pi\)
\(32\) 0 0
\(33\) 0.867781 2.13197i 0.151061 0.371128i
\(34\) 0 0
\(35\) 2.64894 2.64894i 0.447753 0.447753i
\(36\) 0 0
\(37\) 2.26014 + 2.26014i 0.371565 + 0.371565i 0.868047 0.496482i \(-0.165375\pi\)
−0.496482 + 0.868047i \(0.665375\pi\)
\(38\) 0 0
\(39\) −0.824810 5.98086i −0.132075 0.957704i
\(40\) 0 0
\(41\) −1.42311 0.821634i −0.222253 0.128318i 0.384740 0.923025i \(-0.374291\pi\)
−0.606993 + 0.794707i \(0.707624\pi\)
\(42\) 0 0
\(43\) −1.65438 + 6.17424i −0.252291 + 0.941563i 0.717287 + 0.696778i \(0.245384\pi\)
−0.969578 + 0.244784i \(0.921283\pi\)
\(44\) 0 0
\(45\) 8.50065 0.104463i 1.26720 0.0155724i
\(46\) 0 0
\(47\) −4.58731 7.94546i −0.669129 1.15896i −0.978148 0.207909i \(-0.933334\pi\)
0.309020 0.951056i \(-0.399999\pi\)
\(48\) 0 0
\(49\) −2.62619 + 4.54869i −0.375170 + 0.649813i
\(50\) 0 0
\(51\) −13.0746 1.63964i −1.83080 0.229595i
\(52\) 0 0
\(53\) 7.72215 + 7.72215i 1.06072 + 1.06072i 0.998033 + 0.0626852i \(0.0199664\pi\)
0.0626852 + 0.998033i \(0.480034\pi\)
\(54\) 0 0
\(55\) 3.76593i 0.507798i
\(56\) 0 0
\(57\) −8.36111 + 6.49771i −1.10746 + 0.860642i
\(58\) 0 0
\(59\) 4.80982 1.28879i 0.626185 0.167786i 0.0682473 0.997668i \(-0.478259\pi\)
0.557938 + 0.829883i \(0.311593\pi\)
\(60\) 0 0
\(61\) 9.92979 + 2.66068i 1.27138 + 0.340665i 0.830559 0.556931i \(-0.188021\pi\)
0.440820 + 0.897596i \(0.354688\pi\)
\(62\) 0 0
\(63\) 3.81789 1.07345i 0.481009 0.135242i
\(64\) 0 0
\(65\) −4.93887 8.55438i −0.612592 1.06104i
\(66\) 0 0
\(67\) 3.73189 + 13.9276i 0.455923 + 1.70153i 0.685359 + 0.728205i \(0.259645\pi\)
−0.229436 + 0.973324i \(0.573688\pi\)
\(68\) 0 0
\(69\) 5.51718 + 4.17987i 0.664190 + 0.503198i
\(70\) 0 0
\(71\) 7.87498i 0.934588i −0.884102 0.467294i \(-0.845229\pi\)
0.884102 0.467294i \(-0.154771\pi\)
\(72\) 0 0
\(73\) 0.577222i 0.0675588i 0.999429 + 0.0337794i \(0.0107544\pi\)
−0.999429 + 0.0337794i \(0.989246\pi\)
\(74\) 0 0
\(75\) 4.83654 2.03826i 0.558475 0.235358i
\(76\) 0 0
\(77\) −0.454704 1.69698i −0.0518183 0.193389i
\(78\) 0 0
\(79\) −0.716890 1.24169i −0.0806564 0.139701i 0.822876 0.568221i \(-0.192368\pi\)
−0.903532 + 0.428521i \(0.859035\pi\)
\(80\) 0 0
\(81\) 7.90246 + 4.30711i 0.878051 + 0.478567i
\(82\) 0 0
\(83\) −3.30414 0.885341i −0.362676 0.0971788i 0.0728790 0.997341i \(-0.476781\pi\)
−0.435555 + 0.900162i \(0.643448\pi\)
\(84\) 0 0
\(85\) −20.8239 + 5.57975i −2.25867 + 0.605208i
\(86\) 0 0
\(87\) −5.89030 2.39755i −0.631506 0.257044i
\(88\) 0 0
\(89\) 16.2114i 1.71841i −0.511635 0.859203i \(-0.670960\pi\)
0.511635 0.859203i \(-0.329040\pi\)
\(90\) 0 0
\(91\) −3.25839 3.25839i −0.341572 0.341572i
\(92\) 0 0
\(93\) −1.19055 + 1.57146i −0.123455 + 0.162952i
\(94\) 0 0
\(95\) −8.66225 + 15.0035i −0.888728 + 1.53932i
\(96\) 0 0
\(97\) −0.648931 1.12398i −0.0658889 0.114123i 0.831199 0.555975i \(-0.187655\pi\)
−0.897088 + 0.441852i \(0.854322\pi\)
\(98\) 0 0
\(99\) 1.95085 3.47695i 0.196068 0.349446i
\(100\) 0 0
\(101\) 2.60956 9.73900i 0.259661 0.969067i −0.705777 0.708434i \(-0.749402\pi\)
0.965438 0.260633i \(-0.0839313\pi\)
\(102\) 0 0
\(103\) −8.04850 4.64680i −0.793042 0.457863i 0.0479901 0.998848i \(-0.484718\pi\)
−0.841033 + 0.540985i \(0.818052\pi\)
\(104\) 0 0
\(105\) 5.12335 3.98154i 0.499988 0.388558i
\(106\) 0 0
\(107\) −1.89502 1.89502i −0.183199 0.183199i 0.609549 0.792748i \(-0.291350\pi\)
−0.792748 + 0.609549i \(0.791350\pi\)
\(108\) 0 0
\(109\) −8.63272 + 8.63272i −0.826864 + 0.826864i −0.987082 0.160217i \(-0.948780\pi\)
0.160217 + 0.987082i \(0.448780\pi\)
\(110\) 0 0
\(111\) 3.39715 + 4.37137i 0.322443 + 0.414912i
\(112\) 0 0
\(113\) −1.70180 + 2.94761i −0.160092 + 0.277288i −0.934902 0.354907i \(-0.884512\pi\)
0.774809 + 0.632195i \(0.217846\pi\)
\(114\) 0 0
\(115\) 10.9386 + 2.93099i 1.02003 + 0.273317i
\(116\) 0 0
\(117\) −0.128497 10.4564i −0.0118796 0.966695i
\(118\) 0 0
\(119\) −8.70982 + 5.02862i −0.798428 + 0.460972i
\(120\) 0 0
\(121\) 7.99679 + 4.61695i 0.726981 + 0.419722i
\(122\) 0 0
\(123\) −2.26866 1.71877i −0.204559 0.154976i
\(124\) 0 0
\(125\) −3.94700 + 3.94700i −0.353031 + 0.353031i
\(126\) 0 0
\(127\) 5.24504 0.465422 0.232711 0.972546i \(-0.425240\pi\)
0.232711 + 0.972546i \(0.425240\pi\)
\(128\) 0 0
\(129\) −4.17390 + 10.2544i −0.367491 + 0.902852i
\(130\) 0 0
\(131\) −1.68026 6.27080i −0.146805 0.547883i −0.999668 0.0257490i \(-0.991803\pi\)
0.852864 0.522134i \(-0.174864\pi\)
\(132\) 0 0
\(133\) −2.09178 + 7.80665i −0.181381 + 0.676922i
\(134\) 0 0
\(135\) 14.6316 + 1.65256i 1.25929 + 0.142229i
\(136\) 0 0
\(137\) −6.16622 + 3.56007i −0.526816 + 0.304157i −0.739719 0.672916i \(-0.765042\pi\)
0.212903 + 0.977073i \(0.431708\pi\)
\(138\) 0 0
\(139\) −4.07133 + 1.09091i −0.345326 + 0.0925298i −0.427313 0.904104i \(-0.640540\pi\)
0.0819876 + 0.996633i \(0.473873\pi\)
\(140\) 0 0
\(141\) −6.17128 14.6437i −0.519716 1.23322i
\(142\) 0 0
\(143\) −4.63236 −0.387378
\(144\) 0 0
\(145\) −10.4047 −0.864063
\(146\) 0 0
\(147\) −5.49369 + 7.25133i −0.453112 + 0.598080i
\(148\) 0 0
\(149\) −8.40971 + 2.25338i −0.688950 + 0.184604i −0.586276 0.810111i \(-0.699407\pi\)
−0.102674 + 0.994715i \(0.532740\pi\)
\(150\) 0 0
\(151\) −17.8103 + 10.2828i −1.44938 + 0.836803i −0.998445 0.0557515i \(-0.982245\pi\)
−0.450940 + 0.892554i \(0.648911\pi\)
\(152\) 0 0
\(153\) −22.1164 5.63573i −1.78801 0.455622i
\(154\) 0 0
\(155\) −0.834834 + 3.11564i −0.0670555 + 0.250255i
\(156\) 0 0
\(157\) −2.38710 8.90879i −0.190512 0.710999i −0.993383 0.114847i \(-0.963362\pi\)
0.802872 0.596152i \(-0.203304\pi\)
\(158\) 0 0
\(159\) 11.6069 + 14.9355i 0.920487 + 1.18446i
\(160\) 0 0
\(161\) 5.28298 0.416357
\(162\) 0 0
\(163\) 10.4053 10.4053i 0.815004 0.815004i −0.170375 0.985379i \(-0.554498\pi\)
0.985379 + 0.170375i \(0.0544981\pi\)
\(164\) 0 0
\(165\) 0.811644 6.47209i 0.0631864 0.503851i
\(166\) 0 0
\(167\) 5.95392 + 3.43750i 0.460728 + 0.266001i 0.712350 0.701824i \(-0.247631\pi\)
−0.251622 + 0.967826i \(0.580964\pi\)
\(168\) 0 0
\(169\) 0.735830 0.424832i 0.0566023 0.0326794i
\(170\) 0 0
\(171\) −15.7697 + 9.36488i −1.20594 + 0.716150i
\(172\) 0 0
\(173\) −3.07494 0.823927i −0.233783 0.0626420i 0.140025 0.990148i \(-0.455282\pi\)
−0.373808 + 0.927506i \(0.621948\pi\)
\(174\) 0 0
\(175\) 2.00294 3.46919i 0.151408 0.262246i
\(176\) 0 0
\(177\) 8.54387 1.17827i 0.642197 0.0885642i
\(178\) 0 0
\(179\) 3.73648 3.73648i 0.279278 0.279278i −0.553543 0.832821i \(-0.686725\pi\)
0.832821 + 0.553543i \(0.186725\pi\)
\(180\) 0 0
\(181\) 0.169132 + 0.169132i 0.0125715 + 0.0125715i 0.713365 0.700793i \(-0.247170\pi\)
−0.700793 + 0.713365i \(0.747170\pi\)
\(182\) 0 0
\(183\) 16.4918 + 6.71271i 1.21911 + 0.496218i
\(184\) 0 0
\(185\) 7.84414 + 4.52882i 0.576713 + 0.332965i
\(186\) 0 0
\(187\) −2.61673 + 9.76578i −0.191354 + 0.714145i
\(188\) 0 0
\(189\) 6.79274 1.02198i 0.494099 0.0743383i
\(190\) 0 0
\(191\) −11.0451 19.1306i −0.799194 1.38424i −0.920142 0.391586i \(-0.871927\pi\)
0.120947 0.992659i \(-0.461407\pi\)
\(192\) 0 0
\(193\) 7.90683 13.6950i 0.569146 0.985790i −0.427505 0.904013i \(-0.640607\pi\)
0.996651 0.0817767i \(-0.0260594\pi\)
\(194\) 0 0
\(195\) −6.64423 15.7659i −0.475803 1.12902i
\(196\) 0 0
\(197\) 1.19611 + 1.19611i 0.0852196 + 0.0852196i 0.748432 0.663212i \(-0.230807\pi\)
−0.663212 + 0.748432i \(0.730807\pi\)
\(198\) 0 0
\(199\) 6.39170i 0.453095i −0.974000 0.226548i \(-0.927256\pi\)
0.974000 0.226548i \(-0.0727439\pi\)
\(200\) 0 0
\(201\) 3.41187 + 24.7402i 0.240655 + 1.74504i
\(202\) 0 0
\(203\) −4.68849 + 1.25628i −0.329068 + 0.0881734i
\(204\) 0 0
\(205\) −4.49796 1.20523i −0.314151 0.0841766i
\(206\) 0 0
\(207\) 8.58090 + 8.37256i 0.596414 + 0.581933i
\(208\) 0 0
\(209\) 4.06233 + 7.03617i 0.280997 + 0.486702i
\(210\) 0 0
\(211\) −0.539586 2.01376i −0.0371466 0.138633i 0.944862 0.327468i \(-0.106195\pi\)
−0.982009 + 0.188835i \(0.939529\pi\)
\(212\) 0 0
\(213\) 1.69724 13.5339i 0.116293 0.927324i
\(214\) 0 0
\(215\) 18.1135i 1.23533i
\(216\) 0 0
\(217\) 1.50475i 0.102149i
\(218\) 0 0
\(219\) −0.124405 + 0.992008i −0.00840649 + 0.0670337i
\(220\) 0 0
\(221\) 6.86349 + 25.6149i 0.461688 + 1.72304i
\(222\) 0 0
\(223\) −13.6496 23.6417i −0.914042 1.58317i −0.808297 0.588775i \(-0.799611\pi\)
−0.105745 0.994393i \(-0.533723\pi\)
\(224\) 0 0
\(225\) 8.75131 2.46055i 0.583421 0.164037i
\(226\) 0 0
\(227\) −2.80787 0.752368i −0.186365 0.0499364i 0.164429 0.986389i \(-0.447422\pi\)
−0.350794 + 0.936452i \(0.614088\pi\)
\(228\) 0 0
\(229\) −6.48583 + 1.73787i −0.428596 + 0.114842i −0.466667 0.884433i \(-0.654545\pi\)
0.0380710 + 0.999275i \(0.487879\pi\)
\(230\) 0 0
\(231\) −0.415712 3.01441i −0.0273518 0.198333i
\(232\) 0 0
\(233\) 11.8159i 0.774086i −0.922062 0.387043i \(-0.873497\pi\)
0.922062 0.387043i \(-0.126503\pi\)
\(234\) 0 0
\(235\) −18.3839 18.3839i −1.19923 1.19923i
\(236\) 0 0
\(237\) −0.964426 2.28846i −0.0626462 0.148651i
\(238\) 0 0
\(239\) 1.75364 3.03739i 0.113433 0.196472i −0.803719 0.595009i \(-0.797148\pi\)
0.917152 + 0.398537i \(0.130482\pi\)
\(240\) 0 0
\(241\) −4.35635 7.54543i −0.280617 0.486044i 0.690920 0.722932i \(-0.257206\pi\)
−0.971537 + 0.236888i \(0.923873\pi\)
\(242\) 0 0
\(243\) 12.6528 + 9.10531i 0.811678 + 0.584106i
\(244\) 0 0
\(245\) −3.85226 + 14.3768i −0.246112 + 0.918502i
\(246\) 0 0
\(247\) 18.4553 + 10.6552i 1.17428 + 0.677973i
\(248\) 0 0
\(249\) −5.48765 2.23366i −0.347766 0.141552i
\(250\) 0 0
\(251\) 9.70213 + 9.70213i 0.612393 + 0.612393i 0.943569 0.331176i \(-0.107445\pi\)
−0.331176 + 0.943569i \(0.607445\pi\)
\(252\) 0 0
\(253\) 3.75533 3.75533i 0.236096 0.236096i
\(254\) 0 0
\(255\) −36.9903 + 5.10127i −2.31642 + 0.319454i
\(256\) 0 0
\(257\) −9.26857 + 16.0536i −0.578158 + 1.00140i 0.417533 + 0.908662i \(0.362895\pi\)
−0.995691 + 0.0927366i \(0.970439\pi\)
\(258\) 0 0
\(259\) 4.08149 + 1.09363i 0.253611 + 0.0679550i
\(260\) 0 0
\(261\) −9.60628 5.38990i −0.594614 0.333626i
\(262\) 0 0
\(263\) −3.42692 + 1.97853i −0.211313 + 0.122002i −0.601922 0.798555i \(-0.705598\pi\)
0.390608 + 0.920557i \(0.372265\pi\)
\(264\) 0 0
\(265\) 26.8008 + 15.4734i 1.64636 + 0.950525i
\(266\) 0 0
\(267\) 3.49393 27.8608i 0.213825 1.70505i
\(268\) 0 0
\(269\) 17.6742 17.6742i 1.07762 1.07762i 0.0808951 0.996723i \(-0.474222\pi\)
0.996723 0.0808951i \(-0.0257779\pi\)
\(270\) 0 0
\(271\) 26.9563 1.63748 0.818738 0.574167i \(-0.194674\pi\)
0.818738 + 0.574167i \(0.194674\pi\)
\(272\) 0 0
\(273\) −4.89758 6.30209i −0.296415 0.381420i
\(274\) 0 0
\(275\) −1.04226 3.88979i −0.0628509 0.234563i
\(276\) 0 0
\(277\) 2.47723 9.24514i 0.148842 0.555487i −0.850712 0.525632i \(-0.823829\pi\)
0.999554 0.0298548i \(-0.00950449\pi\)
\(278\) 0 0
\(279\) −2.38476 + 2.44410i −0.142772 + 0.146324i
\(280\) 0 0
\(281\) 8.51476 4.91600i 0.507948 0.293264i −0.224042 0.974580i \(-0.571925\pi\)
0.731990 + 0.681316i \(0.238592\pi\)
\(282\) 0 0
\(283\) 30.0988 8.06496i 1.78919 0.479412i 0.796982 0.604003i \(-0.206428\pi\)
0.992208 + 0.124591i \(0.0397617\pi\)
\(284\) 0 0
\(285\) −18.1204 + 23.9179i −1.07336 + 1.41677i
\(286\) 0 0
\(287\) −2.17236 −0.128231
\(288\) 0 0
\(289\) 40.8774 2.40456
\(290\) 0 0
\(291\) −0.873002 2.07152i −0.0511763 0.121435i
\(292\) 0 0
\(293\) 30.6204 8.20472i 1.78886 0.479325i 0.796711 0.604360i \(-0.206571\pi\)
0.992152 + 0.125035i \(0.0399044\pi\)
\(294\) 0 0
\(295\) 12.2202 7.05535i 0.711489 0.410778i
\(296\) 0 0
\(297\) 4.10207 5.55499i 0.238026 0.322333i
\(298\) 0 0
\(299\) 3.60533 13.4553i 0.208502 0.778139i
\(300\) 0 0
\(301\) 2.18706 + 8.16220i 0.126060 + 0.470462i
\(302\) 0 0
\(303\) 6.58374 16.1749i 0.378226 0.929225i
\(304\) 0 0
\(305\) 29.1313 1.66805
\(306\) 0 0
\(307\) −17.2513 + 17.2513i −0.984581 + 0.984581i −0.999883 0.0153018i \(-0.995129\pi\)
0.0153018 + 0.999883i \(0.495129\pi\)
\(308\) 0 0
\(309\) −12.8306 9.72059i −0.729906 0.552985i
\(310\) 0 0
\(311\) 8.53625 + 4.92841i 0.484046 + 0.279464i 0.722101 0.691787i \(-0.243176\pi\)
−0.238055 + 0.971252i \(0.576510\pi\)
\(312\) 0 0
\(313\) −8.45774 + 4.88308i −0.478060 + 0.276008i −0.719608 0.694381i \(-0.755678\pi\)
0.241548 + 0.970389i \(0.422345\pi\)
\(314\) 0 0
\(315\) 9.66305 5.73843i 0.544451 0.323324i
\(316\) 0 0
\(317\) −12.8098 3.43237i −0.719469 0.192781i −0.119534 0.992830i \(-0.538140\pi\)
−0.599935 + 0.800049i \(0.704807\pi\)
\(318\) 0 0
\(319\) −2.43974 + 4.22576i −0.136599 + 0.236597i
\(320\) 0 0
\(321\) −2.84834 3.66519i −0.158979 0.204571i
\(322\) 0 0
\(323\) 32.8879 32.8879i 1.82993 1.82993i
\(324\) 0 0
\(325\) −7.46883 7.46883i −0.414296 0.414296i
\(326\) 0 0
\(327\) −16.6966 + 12.9756i −0.923327 + 0.717550i
\(328\) 0 0
\(329\) −10.5037 6.06432i −0.579089 0.334337i
\(330\) 0 0
\(331\) −0.274151 + 1.02314i −0.0150687 + 0.0562371i −0.973051 0.230591i \(-0.925934\pi\)
0.957982 + 0.286828i \(0.0926008\pi\)
\(332\) 0 0
\(333\) 4.89617 + 8.24476i 0.268308 + 0.451810i
\(334\) 0 0
\(335\) 20.4299 + 35.3857i 1.11621 + 1.93332i
\(336\) 0 0
\(337\) −2.50387 + 4.33683i −0.136395 + 0.236242i −0.926129 0.377206i \(-0.876885\pi\)
0.789735 + 0.613448i \(0.210218\pi\)
\(338\) 0 0
\(339\) −3.55998 + 4.69895i −0.193351 + 0.255212i
\(340\) 0 0
\(341\) 1.06963 + 1.06963i 0.0579238 + 0.0579238i
\(342\) 0 0
\(343\) 16.1974i 0.874575i
\(344\) 0 0
\(345\) 18.1673 + 7.39470i 0.978094 + 0.398117i
\(346\) 0 0
\(347\) −5.88711 + 1.57745i −0.316036 + 0.0846817i −0.413350 0.910572i \(-0.635642\pi\)
0.0973140 + 0.995254i \(0.468975\pi\)
\(348\) 0 0
\(349\) −5.42227 1.45289i −0.290247 0.0777715i 0.110758 0.993847i \(-0.464672\pi\)
−0.401005 + 0.916076i \(0.631339\pi\)
\(350\) 0 0
\(351\) 2.03276 17.9980i 0.108501 0.960661i
\(352\) 0 0
\(353\) −5.06146 8.76671i −0.269395 0.466605i 0.699311 0.714817i \(-0.253490\pi\)
−0.968706 + 0.248212i \(0.920157\pi\)
\(354\) 0 0
\(355\) −5.77576 21.5554i −0.306546 1.14404i
\(356\) 0 0
\(357\) −16.0524 + 6.76496i −0.849582 + 0.358040i
\(358\) 0 0
\(359\) 5.28081i 0.278710i 0.990242 + 0.139355i \(0.0445030\pi\)
−0.990242 + 0.139355i \(0.955497\pi\)
\(360\) 0 0
\(361\) 18.3761i 0.967163i
\(362\) 0 0
\(363\) 12.7481 + 9.65813i 0.669104 + 0.506920i
\(364\) 0 0
\(365\) 0.423353 + 1.57998i 0.0221593 + 0.0826997i
\(366\) 0 0
\(367\) −5.01941 8.69388i −0.262011 0.453817i 0.704765 0.709441i \(-0.251052\pi\)
−0.966776 + 0.255624i \(0.917719\pi\)
\(368\) 0 0
\(369\) −3.52847 3.44280i −0.183685 0.179225i
\(370\) 0 0
\(371\) 13.9451 + 3.73657i 0.723992 + 0.193993i
\(372\) 0 0
\(373\) 25.1865 6.74869i 1.30411 0.349434i 0.461105 0.887346i \(-0.347453\pi\)
0.843001 + 0.537912i \(0.180787\pi\)
\(374\) 0 0
\(375\) −7.63395 + 5.93261i −0.394215 + 0.306359i
\(376\) 0 0
\(377\) 12.7985i 0.659157i
\(378\) 0 0
\(379\) 11.3259 + 11.3259i 0.581771 + 0.581771i 0.935390 0.353619i \(-0.115049\pi\)
−0.353619 + 0.935390i \(0.615049\pi\)
\(380\) 0 0
\(381\) 9.01407 + 1.13043i 0.461805 + 0.0579135i
\(382\) 0 0
\(383\) −2.50076 + 4.33145i −0.127783 + 0.221327i −0.922817 0.385238i \(-0.874119\pi\)
0.795034 + 0.606564i \(0.207453\pi\)
\(384\) 0 0
\(385\) −2.48924 4.31148i −0.126863 0.219733i
\(386\) 0 0
\(387\) −9.38328 + 16.7236i −0.476979 + 0.850107i
\(388\) 0 0
\(389\) −3.45749 + 12.9035i −0.175302 + 0.654235i 0.821198 + 0.570643i \(0.193306\pi\)
−0.996500 + 0.0835921i \(0.973361\pi\)
\(390\) 0 0
\(391\) −26.3294 15.2013i −1.33153 0.768761i
\(392\) 0 0
\(393\) −1.53617 11.1391i −0.0774895 0.561892i
\(394\) 0 0
\(395\) −2.87297 2.87297i −0.144555 0.144555i
\(396\) 0 0
\(397\) −18.7165 + 18.7165i −0.939356 + 0.939356i −0.998263 0.0589078i \(-0.981238\pi\)
0.0589078 + 0.998263i \(0.481238\pi\)
\(398\) 0 0
\(399\) −5.27743 + 12.9656i −0.264202 + 0.649092i
\(400\) 0 0
\(401\) 6.66124 11.5376i 0.332647 0.576161i −0.650383 0.759606i \(-0.725392\pi\)
0.983030 + 0.183445i \(0.0587250\pi\)
\(402\) 0 0
\(403\) 3.83247 + 1.02691i 0.190909 + 0.0511538i
\(404\) 0 0
\(405\) 24.7896 + 5.99352i 1.23181 + 0.297820i
\(406\) 0 0
\(407\) 3.67866 2.12388i 0.182345 0.105277i
\(408\) 0 0
\(409\) −10.6037 6.12206i −0.524320 0.302717i 0.214380 0.976750i \(-0.431227\pi\)
−0.738701 + 0.674034i \(0.764560\pi\)
\(410\) 0 0
\(411\) −11.3645 + 4.78934i −0.560568 + 0.236241i
\(412\) 0 0
\(413\) 4.65472 4.65472i 0.229044 0.229044i
\(414\) 0 0
\(415\) −9.69344 −0.475832
\(416\) 0 0
\(417\) −7.23206 + 0.997361i −0.354156 + 0.0488410i
\(418\) 0 0
\(419\) 8.58573 + 32.0424i 0.419440 + 1.56537i 0.775772 + 0.631013i \(0.217361\pi\)
−0.356332 + 0.934360i \(0.615973\pi\)
\(420\) 0 0
\(421\) 6.61930 24.7035i 0.322605 1.20398i −0.594093 0.804396i \(-0.702489\pi\)
0.916698 0.399581i \(-0.130844\pi\)
\(422\) 0 0
\(423\) −7.44985 26.4965i −0.362224 1.28830i
\(424\) 0 0
\(425\) −19.9645 + 11.5265i −0.968421 + 0.559118i
\(426\) 0 0
\(427\) 13.1269 3.51736i 0.635258 0.170217i
\(428\) 0 0
\(429\) −7.96113 0.998381i −0.384367 0.0482023i
\(430\) 0 0
\(431\) 10.3041 0.496332 0.248166 0.968717i \(-0.420172\pi\)
0.248166 + 0.968717i \(0.420172\pi\)
\(432\) 0 0
\(433\) −11.7692 −0.565591 −0.282795 0.959180i \(-0.591262\pi\)
−0.282795 + 0.959180i \(0.591262\pi\)
\(434\) 0 0
\(435\) −17.8814 2.24245i −0.857347 0.107517i
\(436\) 0 0
\(437\) −23.5991 + 6.32337i −1.12890 + 0.302488i
\(438\) 0 0
\(439\) 23.9893 13.8502i 1.14494 0.661034i 0.197294 0.980344i \(-0.436785\pi\)
0.947650 + 0.319310i \(0.103451\pi\)
\(440\) 0 0
\(441\) −11.0042 + 11.2780i −0.524011 + 0.537050i
\(442\) 0 0
\(443\) −6.50677 + 24.2836i −0.309146 + 1.15375i 0.620172 + 0.784466i \(0.287063\pi\)
−0.929317 + 0.369282i \(0.879604\pi\)
\(444\) 0 0
\(445\) −11.8900 44.3739i −0.563638 2.10353i
\(446\) 0 0
\(447\) −14.9385 + 2.06014i −0.706567 + 0.0974413i
\(448\) 0 0
\(449\) −20.0988 −0.948522 −0.474261 0.880384i \(-0.657285\pi\)
−0.474261 + 0.880384i \(0.657285\pi\)
\(450\) 0 0
\(451\) −1.54419 + 1.54419i −0.0727133 + 0.0727133i
\(452\) 0 0
\(453\) −32.8248 + 13.8334i −1.54225 + 0.649949i
\(454\) 0 0
\(455\) −11.3087 6.52907i −0.530159 0.306088i
\(456\) 0 0
\(457\) −20.8270 + 12.0245i −0.974244 + 0.562480i −0.900527 0.434799i \(-0.856819\pi\)
−0.0737167 + 0.997279i \(0.523486\pi\)
\(458\) 0 0
\(459\) −36.7944 14.4521i −1.71742 0.674566i
\(460\) 0 0
\(461\) −3.90967 1.04759i −0.182092 0.0487913i 0.166621 0.986021i \(-0.446714\pi\)
−0.348713 + 0.937230i \(0.613381\pi\)
\(462\) 0 0
\(463\) −5.16489 + 8.94585i −0.240033 + 0.415749i −0.960723 0.277508i \(-0.910492\pi\)
0.720691 + 0.693257i \(0.243825\pi\)
\(464\) 0 0
\(465\) −2.10623 + 5.17459i −0.0976741 + 0.239966i
\(466\) 0 0
\(467\) −11.8966 + 11.8966i −0.550509 + 0.550509i −0.926588 0.376079i \(-0.877272\pi\)
0.376079 + 0.926588i \(0.377272\pi\)
\(468\) 0 0
\(469\) 13.4785 + 13.4785i 0.622380 + 0.622380i
\(470\) 0 0
\(471\) −2.18240 15.8250i −0.100560 0.729179i
\(472\) 0 0
\(473\) 7.35663 + 4.24735i 0.338258 + 0.195293i
\(474\) 0 0
\(475\) −4.79476 + 17.8943i −0.219999 + 0.821046i
\(476\) 0 0
\(477\) 16.7286 + 28.1695i 0.765948 + 1.28980i
\(478\) 0 0
\(479\) 7.47878 + 12.9536i 0.341714 + 0.591866i 0.984751 0.173969i \(-0.0556593\pi\)
−0.643037 + 0.765835i \(0.722326\pi\)
\(480\) 0 0
\(481\) 5.57077 9.64886i 0.254005 0.439950i
\(482\) 0 0
\(483\) 9.07927 + 1.13860i 0.413121 + 0.0518082i
\(484\) 0 0
\(485\) −2.60062 2.60062i −0.118088 0.118088i
\(486\) 0 0
\(487\) 27.0362i 1.22513i 0.790420 + 0.612565i \(0.209862\pi\)
−0.790420 + 0.612565i \(0.790138\pi\)
\(488\) 0 0
\(489\) 20.1250 15.6398i 0.910082 0.707257i
\(490\) 0 0
\(491\) −5.41853 + 1.45189i −0.244535 + 0.0655229i −0.379005 0.925395i \(-0.623734\pi\)
0.134470 + 0.990918i \(0.457067\pi\)
\(492\) 0 0
\(493\) 26.9814 + 7.22964i 1.21518 + 0.325607i
\(494\) 0 0
\(495\) 2.78977 10.9479i 0.125391 0.492073i
\(496\) 0 0
\(497\) −5.20527 9.01579i −0.233488 0.404413i
\(498\) 0 0
\(499\) −5.68146 21.2035i −0.254337 0.949198i −0.968458 0.249176i \(-0.919840\pi\)
0.714121 0.700022i \(-0.246826\pi\)
\(500\) 0 0
\(501\) 9.49148 + 7.19085i 0.424048 + 0.321264i
\(502\) 0 0
\(503\) 23.1955i 1.03423i −0.855915 0.517117i \(-0.827005\pi\)
0.855915 0.517117i \(-0.172995\pi\)
\(504\) 0 0
\(505\) 28.5716i 1.27142i
\(506\) 0 0
\(507\) 1.35615 0.571523i 0.0602288 0.0253822i
\(508\) 0 0
\(509\) −3.37049 12.5788i −0.149394 0.557547i −0.999520 0.0309681i \(-0.990141\pi\)
0.850126 0.526579i \(-0.176526\pi\)
\(510\) 0 0
\(511\) 0.381537 + 0.660842i 0.0168782 + 0.0292339i
\(512\) 0 0
\(513\) −29.1200 + 12.6957i −1.28568 + 0.560527i
\(514\) 0 0
\(515\) −25.4385 6.81623i −1.12095 0.300359i
\(516\) 0 0
\(517\) −11.7772 + 3.15568i −0.517959 + 0.138787i
\(518\) 0 0
\(519\) −5.10698 2.07871i −0.224171 0.0912453i
\(520\) 0 0
\(521\) 21.4547i 0.939949i 0.882680 + 0.469974i \(0.155737\pi\)
−0.882680 + 0.469974i \(0.844263\pi\)
\(522\) 0 0
\(523\) −2.07495 2.07495i −0.0907314 0.0907314i 0.660284 0.751016i \(-0.270436\pi\)
−0.751016 + 0.660284i \(0.770436\pi\)
\(524\) 0 0
\(525\) 4.18992 5.53043i 0.182863 0.241368i
\(526\) 0 0
\(527\) 4.32977 7.49939i 0.188608 0.326678i
\(528\) 0 0
\(529\) −3.51490 6.08799i −0.152822 0.264695i
\(530\) 0 0
\(531\) 14.9374 0.183562i 0.648226 0.00796593i
\(532\) 0 0
\(533\) −1.48251 + 5.53282i −0.0642148 + 0.239653i
\(534\) 0 0
\(535\) −6.57693 3.79719i −0.284346 0.164167i
\(536\) 0 0
\(537\) 7.22677 5.61618i 0.311858 0.242356i
\(538\) 0 0
\(539\) 4.93571 + 4.93571i 0.212596 + 0.212596i
\(540\) 0 0
\(541\) 22.7947 22.7947i 0.980022 0.980022i −0.0197819 0.999804i \(-0.506297\pi\)
0.999804 + 0.0197819i \(0.00629719\pi\)
\(542\) 0 0
\(543\) 0.254217 + 0.327121i 0.0109095 + 0.0140381i
\(544\) 0 0
\(545\) −17.2980 + 29.9610i −0.740965 + 1.28339i
\(546\) 0 0
\(547\) −13.3804 3.58528i −0.572106 0.153295i −0.0388438 0.999245i \(-0.512367\pi\)
−0.533262 + 0.845950i \(0.679034\pi\)
\(548\) 0 0
\(549\) 26.8959 + 15.0908i 1.14789 + 0.644058i
\(550\) 0 0
\(551\) 19.4399 11.2236i 0.828166 0.478142i
\(552\) 0 0
\(553\) −1.64148 0.947711i −0.0698030 0.0403008i
\(554\) 0 0
\(555\) 12.5048 + 9.47377i 0.530799 + 0.402139i
\(556\) 0 0
\(557\) −8.62660 + 8.62660i −0.365521 + 0.365521i −0.865841 0.500320i \(-0.833216\pi\)
0.500320 + 0.865841i \(0.333216\pi\)
\(558\) 0 0
\(559\) 22.2810 0.942384
\(560\) 0 0
\(561\) −6.60184 + 16.2194i −0.278730 + 0.684784i
\(562\) 0 0
\(563\) 5.46409 + 20.3923i 0.230284 + 0.859432i 0.980218 + 0.197920i \(0.0634185\pi\)
−0.749934 + 0.661513i \(0.769915\pi\)
\(564\) 0 0
\(565\) −2.49631 + 9.31636i −0.105021 + 0.391942i
\(566\) 0 0
\(567\) 11.8942 0.292376i 0.499509 0.0122786i
\(568\) 0 0
\(569\) 21.4776 12.4001i 0.900389 0.519840i 0.0230625 0.999734i \(-0.492658\pi\)
0.877326 + 0.479894i \(0.159325\pi\)
\(570\) 0 0
\(571\) −17.7063 + 4.74438i −0.740985 + 0.198546i −0.609516 0.792774i \(-0.708636\pi\)
−0.131469 + 0.991320i \(0.541969\pi\)
\(572\) 0 0
\(573\) −14.8589 35.2582i −0.620738 1.47293i
\(574\) 0 0
\(575\) 12.1096 0.505004
\(576\) 0 0
\(577\) −23.4462 −0.976078 −0.488039 0.872822i \(-0.662288\pi\)
−0.488039 + 0.872822i \(0.662288\pi\)
\(578\) 0 0
\(579\) 16.5402 21.8320i 0.687387 0.907308i
\(580\) 0 0
\(581\) −4.36800 + 1.17040i −0.181215 + 0.0485564i
\(582\) 0 0
\(583\) 12.5688 7.25657i 0.520545 0.300537i
\(584\) 0 0
\(585\) −8.02079 28.5271i −0.331619 1.17945i
\(586\) 0 0
\(587\) −4.33159 + 16.1657i −0.178784 + 0.667230i 0.817092 + 0.576507i \(0.195585\pi\)
−0.995876 + 0.0907235i \(0.971082\pi\)
\(588\) 0 0
\(589\) −1.80108 6.72173i −0.0742123 0.276964i
\(590\) 0 0
\(591\) 1.79784 + 2.31342i 0.0739532 + 0.0951613i
\(592\) 0 0
\(593\) 6.18675 0.254059 0.127030 0.991899i \(-0.459456\pi\)
0.127030 + 0.991899i \(0.459456\pi\)
\(594\) 0 0
\(595\) −20.1524 + 20.1524i −0.826168 + 0.826168i
\(596\) 0 0
\(597\) 1.37756 10.9847i 0.0563797 0.449574i
\(598\) 0 0
\(599\) −7.98730 4.61147i −0.326352 0.188420i 0.327868 0.944723i \(-0.393670\pi\)
−0.654220 + 0.756304i \(0.727003\pi\)
\(600\) 0 0
\(601\) −15.0097 + 8.66586i −0.612259 + 0.353488i −0.773849 0.633370i \(-0.781671\pi\)
0.161590 + 0.986858i \(0.448338\pi\)
\(602\) 0 0
\(603\) 0.531535 + 43.2535i 0.0216458 + 1.76142i
\(604\) 0 0
\(605\) 25.2751 + 6.77243i 1.02758 + 0.275339i
\(606\) 0 0
\(607\) −11.8418 + 20.5106i −0.480643 + 0.832498i −0.999753 0.0222090i \(-0.992930\pi\)
0.519110 + 0.854707i \(0.326263\pi\)
\(608\) 0 0
\(609\) −8.32835 + 1.14855i −0.337482 + 0.0465415i
\(610\) 0 0
\(611\) −22.6135 + 22.6135i −0.914844 + 0.914844i
\(612\) 0 0
\(613\) 15.4110 + 15.4110i 0.622445 + 0.622445i 0.946156 0.323711i \(-0.104930\pi\)
−0.323711 + 0.946156i \(0.604930\pi\)
\(614\) 0 0
\(615\) −7.47040 3.04070i −0.301236 0.122613i
\(616\) 0 0
\(617\) −11.9979 6.92700i −0.483018 0.278870i 0.238655 0.971104i \(-0.423293\pi\)
−0.721673 + 0.692234i \(0.756627\pi\)
\(618\) 0 0
\(619\) 10.3518 38.6333i 0.416072 1.55280i −0.366606 0.930376i \(-0.619480\pi\)
0.782678 0.622427i \(-0.213853\pi\)
\(620\) 0 0
\(621\) 12.9426 + 16.2384i 0.519367 + 0.651624i
\(622\) 0 0
\(623\) −10.7156 18.5599i −0.429310 0.743586i
\(624\) 0 0
\(625\) −15.4844 + 26.8198i −0.619377 + 1.07279i
\(626\) 0 0
\(627\) 5.46503 + 12.9678i 0.218252 + 0.517884i
\(628\) 0 0
\(629\) −17.1945 17.1945i −0.685591 0.685591i
\(630\) 0 0
\(631\) 16.7956i 0.668624i −0.942462 0.334312i \(-0.891496\pi\)
0.942462 0.334312i \(-0.108504\pi\)
\(632\) 0 0
\(633\) −0.493315 3.57712i −0.0196075 0.142178i
\(634\) 0 0
\(635\) 14.3567 3.84688i 0.569730 0.152659i
\(636\) 0 0
\(637\) 17.6845 + 4.73856i 0.700687 + 0.187749i
\(638\) 0 0
\(639\) 5.83371 22.8933i 0.230778 0.905647i
\(640\) 0 0
\(641\) 20.0246 + 34.6837i 0.790925 + 1.36992i 0.925395 + 0.379005i \(0.123734\pi\)
−0.134470 + 0.990918i \(0.542933\pi\)
\(642\) 0 0
\(643\) 0.289008 + 1.07859i 0.0113974 + 0.0425356i 0.971390 0.237489i \(-0.0763242\pi\)
−0.959993 + 0.280024i \(0.909658\pi\)
\(644\) 0 0
\(645\) −3.90388 + 31.1297i −0.153715 + 1.22573i
\(646\) 0 0
\(647\) 31.9272i 1.25519i −0.778541 0.627594i \(-0.784040\pi\)
0.778541 0.627594i \(-0.215960\pi\)
\(648\) 0 0
\(649\) 6.61750i 0.259759i
\(650\) 0 0
\(651\) −0.324308 + 2.58605i −0.0127106 + 0.101355i
\(652\) 0 0
\(653\) −3.36682 12.5651i −0.131754 0.491712i 0.868236 0.496151i \(-0.165254\pi\)
−0.999990 + 0.00443888i \(0.998587\pi\)
\(654\) 0 0
\(655\) −9.19841 15.9321i −0.359412 0.622519i
\(656\) 0 0
\(657\) −0.427601 + 1.67804i −0.0166823 + 0.0654667i
\(658\) 0 0
\(659\) −15.4883 4.15007i −0.603337 0.161664i −0.0557954 0.998442i \(-0.517769\pi\)
−0.547541 + 0.836779i \(0.684436\pi\)
\(660\) 0 0
\(661\) 21.9923 5.89283i 0.855403 0.229204i 0.195637 0.980676i \(-0.437322\pi\)
0.659765 + 0.751472i \(0.270656\pi\)
\(662\) 0 0
\(663\) 6.27493 + 45.5007i 0.243698 + 1.76710i
\(664\) 0 0
\(665\) 22.9026i 0.888124i
\(666\) 0 0
\(667\) −10.3754 10.3754i −0.401738 0.401738i
\(668\) 0 0
\(669\) −18.3627 43.5722i −0.709941 1.68460i
\(670\) 0 0
\(671\) 6.83085 11.8314i 0.263702 0.456745i
\(672\) 0 0
\(673\) 16.3212 + 28.2692i 0.629136 + 1.08970i 0.987725 + 0.156201i \(0.0499246\pi\)
−0.358589 + 0.933496i \(0.616742\pi\)
\(674\) 0 0
\(675\) 15.5702 2.34257i 0.599298 0.0901656i
\(676\) 0 0
\(677\) 3.84993 14.3681i 0.147965 0.552212i −0.851641 0.524126i \(-0.824392\pi\)
0.999606 0.0280861i \(-0.00894127\pi\)
\(678\) 0 0
\(679\) −1.48588 0.857871i −0.0570227 0.0329221i
\(680\) 0 0
\(681\) −4.66343 1.89817i −0.178703 0.0727381i
\(682\) 0 0
\(683\) −21.4912 21.4912i −0.822338 0.822338i 0.164105 0.986443i \(-0.447526\pi\)
−0.986443 + 0.164105i \(0.947526\pi\)
\(684\) 0 0
\(685\) −14.2671 + 14.2671i −0.545120 + 0.545120i
\(686\) 0 0
\(687\) −11.5210 + 1.58885i −0.439555 + 0.0606183i
\(688\) 0 0
\(689\) 19.0334 32.9669i 0.725116 1.25594i
\(690\) 0 0
\(691\) 8.83775 + 2.36807i 0.336204 + 0.0900855i 0.422971 0.906143i \(-0.360987\pi\)
−0.0867676 + 0.996229i \(0.527654\pi\)
\(692\) 0 0
\(693\) −0.0647636 5.27012i −0.00246017 0.200195i
\(694\) 0 0
\(695\) −10.3440 + 5.97209i −0.392369 + 0.226534i
\(696\) 0 0
\(697\) 10.8266 + 6.25077i 0.410088 + 0.236765i
\(698\) 0 0
\(699\) 2.54660 20.3067i 0.0963212 0.768070i
\(700\) 0 0
\(701\) −4.05144 + 4.05144i −0.153021 + 0.153021i −0.779466 0.626445i \(-0.784509\pi\)
0.626445 + 0.779466i \(0.284509\pi\)
\(702\) 0 0
\(703\) −19.5411 −0.737005
\(704\) 0 0
\(705\) −27.6322 35.5565i −1.04069 1.33913i
\(706\) 0 0
\(707\) −3.44978 12.8747i −0.129742 0.484204i
\(708\) 0 0
\(709\) −1.00775 + 3.76098i −0.0378469 + 0.141247i −0.982264 0.187503i \(-0.939961\pi\)
0.944417 + 0.328750i \(0.106627\pi\)
\(710\) 0 0
\(711\) −1.16424 4.14078i −0.0436623 0.155291i
\(712\) 0 0
\(713\) −3.93936 + 2.27439i −0.147530 + 0.0851767i
\(714\) 0 0
\(715\) −12.6797 + 3.39752i −0.474195 + 0.127060i
\(716\) 0 0
\(717\) 3.66841 4.84208i 0.136999 0.180831i
\(718\) 0 0
\(719\) 37.0063 1.38010 0.690050 0.723761i \(-0.257588\pi\)
0.690050 + 0.723761i \(0.257588\pi\)
\(720\) 0 0
\(721\) −12.2859 −0.457552
\(722\) 0 0
\(723\) −5.86057 13.9064i −0.217957 0.517184i
\(724\) 0 0
\(725\) −10.7469 + 2.87962i −0.399129 + 0.106946i
\(726\) 0 0
\(727\) −28.4066 + 16.4006i −1.05354 + 0.608264i −0.923640 0.383262i \(-0.874801\pi\)
−0.129905 + 0.991526i \(0.541467\pi\)
\(728\) 0 0
\(729\) 19.7826 + 18.3753i 0.732688 + 0.680565i
\(730\) 0 0
\(731\) 12.5861 46.9719i 0.465513 1.73732i
\(732\) 0 0
\(733\) 10.9743 + 40.9566i 0.405345 + 1.51277i 0.803419 + 0.595413i \(0.203012\pi\)
−0.398075 + 0.917353i \(0.630322\pi\)
\(734\) 0 0
\(735\) −9.71899 + 23.8776i −0.358490 + 0.880740i
\(736\) 0 0
\(737\) 19.1620 0.705842
\(738\) 0 0
\(739\) 15.3761 15.3761i 0.565620 0.565620i −0.365278 0.930898i \(-0.619026\pi\)
0.930898 + 0.365278i \(0.119026\pi\)
\(740\) 0 0
\(741\) 29.4207 + 22.2894i 1.08080 + 0.818823i
\(742\) 0 0
\(743\) −40.4824 23.3725i −1.48516 0.857456i −0.485299 0.874348i \(-0.661289\pi\)
−0.999857 + 0.0168926i \(0.994623\pi\)
\(744\) 0 0
\(745\) −21.3664 + 12.3359i −0.782805 + 0.451952i
\(746\) 0 0
\(747\) −8.94961 5.02145i −0.327449 0.183725i
\(748\) 0 0
\(749\) −3.42213 0.916958i −0.125042 0.0335049i
\(750\) 0 0
\(751\) −25.7074 + 44.5265i −0.938077 + 1.62480i −0.169023 + 0.985612i \(0.554061\pi\)
−0.769054 + 0.639184i \(0.779272\pi\)
\(752\) 0 0
\(753\) 14.5829 + 18.7650i 0.531432 + 0.683835i
\(754\) 0 0
\(755\) −41.2088 + 41.2088i −1.49974 + 1.49974i
\(756\) 0 0
\(757\) 25.4143 + 25.4143i 0.923698 + 0.923698i 0.997289 0.0735910i \(-0.0234459\pi\)
−0.0735910 + 0.997289i \(0.523446\pi\)
\(758\) 0 0
\(759\) 7.26324 5.64452i 0.263639 0.204883i
\(760\) 0 0
\(761\) 20.2336 + 11.6819i 0.733467 + 0.423467i 0.819689 0.572808i \(-0.194146\pi\)
−0.0862220 + 0.996276i \(0.527479\pi\)
\(762\) 0 0
\(763\) −4.17717 + 15.5894i −0.151224 + 0.564375i
\(764\) 0 0
\(765\) −64.6706 + 0.794725i −2.33817 + 0.0287334i
\(766\) 0 0
\(767\) −8.67859 15.0318i −0.313366 0.542765i
\(768\) 0 0
\(769\) −12.7645 + 22.1087i −0.460299 + 0.797261i −0.998976 0.0452513i \(-0.985591\pi\)
0.538677 + 0.842513i \(0.318924\pi\)
\(770\) 0 0
\(771\) −19.3888 + 25.5920i −0.698270 + 0.921674i
\(772\) 0 0
\(773\) −19.2256 19.2256i −0.691496 0.691496i 0.271065 0.962561i \(-0.412624\pi\)
−0.962561 + 0.271065i \(0.912624\pi\)
\(774\) 0 0
\(775\) 3.44916i 0.123898i
\(776\) 0 0
\(777\) 6.77870 + 2.75916i 0.243185 + 0.0989843i
\(778\) 0 0
\(779\) 9.70397 2.60017i 0.347681 0.0931608i
\(780\) 0 0
\(781\) −10.1088 2.70866i −0.361723 0.0969234i
\(782\) 0 0
\(783\) −15.3476 11.3334i −0.548479 0.405022i
\(784\) 0 0
\(785\) −13.0680 22.6344i −0.466416 0.807857i
\(786\) 0 0
\(787\) −5.16260 19.2671i −0.184027 0.686797i −0.994837 0.101488i \(-0.967640\pi\)
0.810810 0.585309i \(-0.199027\pi\)
\(788\) 0 0
\(789\) −6.31589 + 2.66171i −0.224852 + 0.0947593i
\(790\) 0 0
\(791\) 4.49949i 0.159983i
\(792\) 0 0
\(793\) 35.8336i 1.27249i
\(794\) 0 0
\(795\) 42.7246 + 32.3687i 1.51529 + 1.14800i
\(796\) 0 0