Properties

Label 640.2.j.d.607.5
Level $640$
Weight $2$
Character 640.607
Analytic conductor $5.110$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 640 = 2^{7} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 640.j (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.11042572936\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} + \cdots)\)
Defining polynomial: \(x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + 74 x^{8} + 24 x^{7} - 80 x^{6} - 224 x^{5} - 160 x^{4} - 256 x^{3} + 256 x^{2} + 512\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{13} \)
Twist minimal: no (minimal twist has level 80)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 607.5
Root \(-1.37691 - 0.322680i\) of defining polynomial
Character \(\chi\) \(=\) 640.607
Dual form 640.2.j.d.543.5

$q$-expansion

\(f(q)\) \(=\) \(q+0.614566i q^{3} +(2.07551 + 0.832020i) q^{5} +(2.83610 + 2.83610i) q^{7} +2.62231 q^{9} +O(q^{10})\) \(q+0.614566i q^{3} +(2.07551 + 0.832020i) q^{5} +(2.83610 + 2.83610i) q^{7} +2.62231 q^{9} +(-1.95928 - 1.95928i) q^{11} +2.05493 q^{13} +(-0.511331 + 1.27554i) q^{15} +(-4.06774 - 4.06774i) q^{17} +(-0.683479 - 0.683479i) q^{19} +(-1.74297 + 1.74297i) q^{21} +(-4.95014 + 4.95014i) q^{23} +(3.61549 + 3.45373i) q^{25} +3.45528i q^{27} +(0.835439 - 0.835439i) q^{29} -2.35978i q^{31} +(1.20411 - 1.20411i) q^{33} +(3.52666 + 8.24604i) q^{35} +4.54384 q^{37} +1.26289i q^{39} -5.07255i q^{41} +0.849753 q^{43} +(5.44263 + 2.18181i) q^{45} +(2.72646 - 2.72646i) q^{47} +9.08690i q^{49} +(2.49989 - 2.49989i) q^{51} +5.17605i q^{53} +(-2.43634 - 5.69666i) q^{55} +(0.420043 - 0.420043i) q^{57} +(-4.16328 + 4.16328i) q^{59} +(-5.55706 - 5.55706i) q^{61} +(7.43712 + 7.43712i) q^{63} +(4.26502 + 1.70974i) q^{65} +1.73609 q^{67} +(-3.04219 - 3.04219i) q^{69} +2.33526 q^{71} +(4.39686 + 4.39686i) q^{73} +(-2.12255 + 2.22195i) q^{75} -11.1134i q^{77} -14.0993 q^{79} +5.74343 q^{81} -2.75725i q^{83} +(-5.05819 - 11.8271i) q^{85} +(0.513433 + 0.513433i) q^{87} -11.6448 q^{89} +(5.82797 + 5.82797i) q^{91} +1.45024 q^{93} +(-0.849899 - 1.98724i) q^{95} +(-3.52933 - 3.52933i) q^{97} +(-5.13783 - 5.13783i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 4 q^{5} + 2 q^{7} - 10 q^{9} + O(q^{10}) \) \( 18 q + 4 q^{5} + 2 q^{7} - 10 q^{9} + 2 q^{11} + 20 q^{15} - 6 q^{17} - 2 q^{19} + 16 q^{21} - 2 q^{23} + 6 q^{25} + 14 q^{29} - 8 q^{33} + 6 q^{35} - 8 q^{37} + 44 q^{43} + 4 q^{45} - 38 q^{47} - 8 q^{51} - 6 q^{55} + 24 q^{57} + 10 q^{59} - 14 q^{61} + 6 q^{63} - 12 q^{67} - 32 q^{69} + 24 q^{71} + 14 q^{73} - 64 q^{75} + 16 q^{79} + 2 q^{81} + 10 q^{85} + 24 q^{87} - 12 q^{89} - 16 q^{93} - 34 q^{95} + 18 q^{97} + 22 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/640\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(261\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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 0
\(3\) 0.614566i 0.354820i 0.984137 + 0.177410i \(0.0567718\pi\)
−0.984137 + 0.177410i \(0.943228\pi\)
\(4\) 0 0
\(5\) 2.07551 + 0.832020i 0.928196 + 0.372091i
\(6\) 0 0
\(7\) 2.83610 + 2.83610i 1.07194 + 1.07194i 0.997203 + 0.0747413i \(0.0238131\pi\)
0.0747413 + 0.997203i \(0.476187\pi\)
\(8\) 0 0
\(9\) 2.62231 0.874103
\(10\) 0 0
\(11\) −1.95928 1.95928i −0.590745 0.590745i 0.347088 0.937833i \(-0.387171\pi\)
−0.937833 + 0.347088i \(0.887171\pi\)
\(12\) 0 0
\(13\) 2.05493 0.569934 0.284967 0.958537i \(-0.408017\pi\)
0.284967 + 0.958537i \(0.408017\pi\)
\(14\) 0 0
\(15\) −0.511331 + 1.27554i −0.132025 + 0.329343i
\(16\) 0 0
\(17\) −4.06774 4.06774i −0.986571 0.986571i 0.0133401 0.999911i \(-0.495754\pi\)
−0.999911 + 0.0133401i \(0.995754\pi\)
\(18\) 0 0
\(19\) −0.683479 0.683479i −0.156801 0.156801i 0.624347 0.781147i \(-0.285365\pi\)
−0.781147 + 0.624347i \(0.785365\pi\)
\(20\) 0 0
\(21\) −1.74297 + 1.74297i −0.380347 + 0.380347i
\(22\) 0 0
\(23\) −4.95014 + 4.95014i −1.03218 + 1.03218i −0.0327113 + 0.999465i \(0.510414\pi\)
−0.999465 + 0.0327113i \(0.989586\pi\)
\(24\) 0 0
\(25\) 3.61549 + 3.45373i 0.723097 + 0.690746i
\(26\) 0 0
\(27\) 3.45528i 0.664969i
\(28\) 0 0
\(29\) 0.835439 0.835439i 0.155137 0.155137i −0.625271 0.780408i \(-0.715011\pi\)
0.780408 + 0.625271i \(0.215011\pi\)
\(30\) 0 0
\(31\) 2.35978i 0.423829i −0.977288 0.211915i \(-0.932030\pi\)
0.977288 0.211915i \(-0.0679698\pi\)
\(32\) 0 0
\(33\) 1.20411 1.20411i 0.209608 0.209608i
\(34\) 0 0
\(35\) 3.52666 + 8.24604i 0.596114 + 1.39384i
\(36\) 0 0
\(37\) 4.54384 0.747002 0.373501 0.927630i \(-0.378157\pi\)
0.373501 + 0.927630i \(0.378157\pi\)
\(38\) 0 0
\(39\) 1.26289i 0.202224i
\(40\) 0 0
\(41\) 5.07255i 0.792199i −0.918208 0.396100i \(-0.870364\pi\)
0.918208 0.396100i \(-0.129636\pi\)
\(42\) 0 0
\(43\) 0.849753 0.129586 0.0647930 0.997899i \(-0.479361\pi\)
0.0647930 + 0.997899i \(0.479361\pi\)
\(44\) 0 0
\(45\) 5.44263 + 2.18181i 0.811339 + 0.325245i
\(46\) 0 0
\(47\) 2.72646 2.72646i 0.397696 0.397696i −0.479724 0.877419i \(-0.659263\pi\)
0.877419 + 0.479724i \(0.159263\pi\)
\(48\) 0 0
\(49\) 9.08690i 1.29813i
\(50\) 0 0
\(51\) 2.49989 2.49989i 0.350055 0.350055i
\(52\) 0 0
\(53\) 5.17605i 0.710985i 0.934679 + 0.355492i \(0.115687\pi\)
−0.934679 + 0.355492i \(0.884313\pi\)
\(54\) 0 0
\(55\) −2.43634 5.69666i −0.328517 0.768138i
\(56\) 0 0
\(57\) 0.420043 0.420043i 0.0556360 0.0556360i
\(58\) 0 0
\(59\) −4.16328 + 4.16328i −0.542013 + 0.542013i −0.924119 0.382105i \(-0.875199\pi\)
0.382105 + 0.924119i \(0.375199\pi\)
\(60\) 0 0
\(61\) −5.55706 5.55706i −0.711509 0.711509i 0.255342 0.966851i \(-0.417812\pi\)
−0.966851 + 0.255342i \(0.917812\pi\)
\(62\) 0 0
\(63\) 7.43712 + 7.43712i 0.936990 + 0.936990i
\(64\) 0 0
\(65\) 4.26502 + 1.70974i 0.529011 + 0.212067i
\(66\) 0 0
\(67\) 1.73609 0.212097 0.106048 0.994361i \(-0.466180\pi\)
0.106048 + 0.994361i \(0.466180\pi\)
\(68\) 0 0
\(69\) −3.04219 3.04219i −0.366237 0.366237i
\(70\) 0 0
\(71\) 2.33526 0.277144 0.138572 0.990352i \(-0.455749\pi\)
0.138572 + 0.990352i \(0.455749\pi\)
\(72\) 0 0
\(73\) 4.39686 + 4.39686i 0.514613 + 0.514613i 0.915936 0.401323i \(-0.131450\pi\)
−0.401323 + 0.915936i \(0.631450\pi\)
\(74\) 0 0
\(75\) −2.12255 + 2.22195i −0.245091 + 0.256569i
\(76\) 0 0
\(77\) 11.1134i 1.26649i
\(78\) 0 0
\(79\) −14.0993 −1.58629 −0.793146 0.609032i \(-0.791558\pi\)
−0.793146 + 0.609032i \(0.791558\pi\)
\(80\) 0 0
\(81\) 5.74343 0.638159
\(82\) 0 0
\(83\) 2.75725i 0.302648i −0.988484 0.151324i \(-0.951646\pi\)
0.988484 0.151324i \(-0.0483536\pi\)
\(84\) 0 0
\(85\) −5.05819 11.8271i −0.548638 1.28283i
\(86\) 0 0
\(87\) 0.513433 + 0.513433i 0.0550458 + 0.0550458i
\(88\) 0 0
\(89\) −11.6448 −1.23435 −0.617173 0.786828i \(-0.711722\pi\)
−0.617173 + 0.786828i \(0.711722\pi\)
\(90\) 0 0
\(91\) 5.82797 + 5.82797i 0.610937 + 0.610937i
\(92\) 0 0
\(93\) 1.45024 0.150383
\(94\) 0 0
\(95\) −0.849899 1.98724i −0.0871978 0.203886i
\(96\) 0 0
\(97\) −3.52933 3.52933i −0.358349 0.358349i 0.504855 0.863204i \(-0.331546\pi\)
−0.863204 + 0.504855i \(0.831546\pi\)
\(98\) 0 0
\(99\) −5.13783 5.13783i −0.516372 0.516372i
\(100\) 0 0
\(101\) −7.39467 + 7.39467i −0.735797 + 0.735797i −0.971762 0.235964i \(-0.924175\pi\)
0.235964 + 0.971762i \(0.424175\pi\)
\(102\) 0 0
\(103\) 3.72605 3.72605i 0.367139 0.367139i −0.499294 0.866433i \(-0.666407\pi\)
0.866433 + 0.499294i \(0.166407\pi\)
\(104\) 0 0
\(105\) −5.06774 + 2.16737i −0.494560 + 0.211513i
\(106\) 0 0
\(107\) 16.4605i 1.59130i −0.605758 0.795649i \(-0.707130\pi\)
0.605758 0.795649i \(-0.292870\pi\)
\(108\) 0 0
\(109\) −12.8554 + 12.8554i −1.23133 + 1.23133i −0.267870 + 0.963455i \(0.586320\pi\)
−0.963455 + 0.267870i \(0.913680\pi\)
\(110\) 0 0
\(111\) 2.79249i 0.265051i
\(112\) 0 0
\(113\) 0.863630 0.863630i 0.0812435 0.0812435i −0.665317 0.746561i \(-0.731704\pi\)
0.746561 + 0.665317i \(0.231704\pi\)
\(114\) 0 0
\(115\) −14.3927 + 6.15546i −1.34213 + 0.573999i
\(116\) 0 0
\(117\) 5.38865 0.498181
\(118\) 0 0
\(119\) 23.0730i 2.11510i
\(120\) 0 0
\(121\) 3.32246i 0.302042i
\(122\) 0 0
\(123\) 3.11742 0.281088
\(124\) 0 0
\(125\) 4.63041 + 10.1764i 0.414156 + 0.910206i
\(126\) 0 0
\(127\) 11.7944 11.7944i 1.04659 1.04659i 0.0477265 0.998860i \(-0.484802\pi\)
0.998860 0.0477265i \(-0.0151976\pi\)
\(128\) 0 0
\(129\) 0.522229i 0.0459797i
\(130\) 0 0
\(131\) 15.9756 15.9756i 1.39579 1.39579i 0.584132 0.811659i \(-0.301435\pi\)
0.811659 0.584132i \(-0.198565\pi\)
\(132\) 0 0
\(133\) 3.87683i 0.336163i
\(134\) 0 0
\(135\) −2.87486 + 7.17147i −0.247429 + 0.617222i
\(136\) 0 0
\(137\) −1.29423 + 1.29423i −0.110573 + 0.110573i −0.760229 0.649655i \(-0.774913\pi\)
0.649655 + 0.760229i \(0.274913\pi\)
\(138\) 0 0
\(139\) 8.61413 8.61413i 0.730641 0.730641i −0.240106 0.970747i \(-0.577182\pi\)
0.970747 + 0.240106i \(0.0771821\pi\)
\(140\) 0 0
\(141\) 1.67559 + 1.67559i 0.141110 + 0.141110i
\(142\) 0 0
\(143\) −4.02617 4.02617i −0.336685 0.336685i
\(144\) 0 0
\(145\) 2.42906 1.03886i 0.201723 0.0862727i
\(146\) 0 0
\(147\) −5.58450 −0.460602
\(148\) 0 0
\(149\) 0.0806133 + 0.0806133i 0.00660410 + 0.00660410i 0.710401 0.703797i \(-0.248514\pi\)
−0.703797 + 0.710401i \(0.748514\pi\)
\(150\) 0 0
\(151\) −3.25198 −0.264643 −0.132321 0.991207i \(-0.542243\pi\)
−0.132321 + 0.991207i \(0.542243\pi\)
\(152\) 0 0
\(153\) −10.6669 10.6669i −0.862364 0.862364i
\(154\) 0 0
\(155\) 1.96338 4.89775i 0.157703 0.393397i
\(156\) 0 0
\(157\) 9.06652i 0.723587i 0.932258 + 0.361793i \(0.117835\pi\)
−0.932258 + 0.361793i \(0.882165\pi\)
\(158\) 0 0
\(159\) −3.18102 −0.252271
\(160\) 0 0
\(161\) −28.0782 −2.21287
\(162\) 0 0
\(163\) 3.93313i 0.308067i 0.988066 + 0.154033i \(0.0492263\pi\)
−0.988066 + 0.154033i \(0.950774\pi\)
\(164\) 0 0
\(165\) 3.50097 1.49729i 0.272550 0.116564i
\(166\) 0 0
\(167\) 8.13216 + 8.13216i 0.629285 + 0.629285i 0.947888 0.318603i \(-0.103214\pi\)
−0.318603 + 0.947888i \(0.603214\pi\)
\(168\) 0 0
\(169\) −8.77728 −0.675175
\(170\) 0 0
\(171\) −1.79229 1.79229i −0.137060 0.137060i
\(172\) 0 0
\(173\) −6.86735 −0.522115 −0.261057 0.965323i \(-0.584071\pi\)
−0.261057 + 0.965323i \(0.584071\pi\)
\(174\) 0 0
\(175\) 0.458751 + 20.0490i 0.0346784 + 1.51556i
\(176\) 0 0
\(177\) −2.55861 2.55861i −0.192317 0.192317i
\(178\) 0 0
\(179\) −15.7117 15.7117i −1.17435 1.17435i −0.981163 0.193183i \(-0.938119\pi\)
−0.193183 0.981163i \(-0.561881\pi\)
\(180\) 0 0
\(181\) 13.9112 13.9112i 1.03401 1.03401i 0.0346142 0.999401i \(-0.488980\pi\)
0.999401 0.0346142i \(-0.0110202\pi\)
\(182\) 0 0
\(183\) 3.41518 3.41518i 0.252458 0.252458i
\(184\) 0 0
\(185\) 9.43078 + 3.78056i 0.693365 + 0.277953i
\(186\) 0 0
\(187\) 15.9397i 1.16562i
\(188\) 0 0
\(189\) −9.79951 + 9.79951i −0.712810 + 0.712810i
\(190\) 0 0
\(191\) 10.3393i 0.748123i −0.927404 0.374061i \(-0.877965\pi\)
0.927404 0.374061i \(-0.122035\pi\)
\(192\) 0 0
\(193\) 13.2080 13.2080i 0.950734 0.950734i −0.0481079 0.998842i \(-0.515319\pi\)
0.998842 + 0.0481079i \(0.0153191\pi\)
\(194\) 0 0
\(195\) −1.05075 + 2.62114i −0.0752456 + 0.187704i
\(196\) 0 0
\(197\) −15.2437 −1.08607 −0.543036 0.839709i \(-0.682725\pi\)
−0.543036 + 0.839709i \(0.682725\pi\)
\(198\) 0 0
\(199\) 4.98761i 0.353562i 0.984250 + 0.176781i \(0.0565684\pi\)
−0.984250 + 0.176781i \(0.943432\pi\)
\(200\) 0 0
\(201\) 1.06694i 0.0752561i
\(202\) 0 0
\(203\) 4.73878 0.332597
\(204\) 0 0
\(205\) 4.22046 10.5281i 0.294770 0.735316i
\(206\) 0 0
\(207\) −12.9808 + 12.9808i −0.902228 + 0.902228i
\(208\) 0 0
\(209\) 2.67825i 0.185258i
\(210\) 0 0
\(211\) −10.3803 + 10.3803i −0.714608 + 0.714608i −0.967496 0.252887i \(-0.918620\pi\)
0.252887 + 0.967496i \(0.418620\pi\)
\(212\) 0 0
\(213\) 1.43517i 0.0983362i
\(214\) 0 0
\(215\) 1.76367 + 0.707011i 0.120281 + 0.0482178i
\(216\) 0 0
\(217\) 6.69257 6.69257i 0.454321 0.454321i
\(218\) 0 0
\(219\) −2.70216 + 2.70216i −0.182595 + 0.182595i
\(220\) 0 0
\(221\) −8.35890 8.35890i −0.562280 0.562280i
\(222\) 0 0
\(223\) −1.49853 1.49853i −0.100349 0.100349i 0.655150 0.755499i \(-0.272605\pi\)
−0.755499 + 0.655150i \(0.772605\pi\)
\(224\) 0 0
\(225\) 9.48092 + 9.05675i 0.632061 + 0.603783i
\(226\) 0 0
\(227\) 15.6346 1.03771 0.518853 0.854864i \(-0.326359\pi\)
0.518853 + 0.854864i \(0.326359\pi\)
\(228\) 0 0
\(229\) 9.74097 + 9.74097i 0.643702 + 0.643702i 0.951463 0.307762i \(-0.0995800\pi\)
−0.307762 + 0.951463i \(0.599580\pi\)
\(230\) 0 0
\(231\) 6.82992 0.449376
\(232\) 0 0
\(233\) 0.509123 + 0.509123i 0.0333538 + 0.0333538i 0.723587 0.690233i \(-0.242492\pi\)
−0.690233 + 0.723587i \(0.742492\pi\)
\(234\) 0 0
\(235\) 7.92727 3.39033i 0.517118 0.221161i
\(236\) 0 0
\(237\) 8.66493i 0.562848i
\(238\) 0 0
\(239\) 8.19486 0.530081 0.265041 0.964237i \(-0.414615\pi\)
0.265041 + 0.964237i \(0.414615\pi\)
\(240\) 0 0
\(241\) 5.66775 0.365092 0.182546 0.983197i \(-0.441566\pi\)
0.182546 + 0.983197i \(0.441566\pi\)
\(242\) 0 0
\(243\) 13.8956i 0.891400i
\(244\) 0 0
\(245\) −7.56048 + 18.8600i −0.483022 + 1.20492i
\(246\) 0 0
\(247\) −1.40450 1.40450i −0.0893661 0.0893661i
\(248\) 0 0
\(249\) 1.69451 0.107385
\(250\) 0 0
\(251\) −14.7484 14.7484i −0.930911 0.930911i 0.0668521 0.997763i \(-0.478704\pi\)
−0.997763 + 0.0668521i \(0.978704\pi\)
\(252\) 0 0
\(253\) 19.3974 1.21951
\(254\) 0 0
\(255\) 7.26851 3.10859i 0.455172 0.194668i
\(256\) 0 0
\(257\) 3.61143 + 3.61143i 0.225275 + 0.225275i 0.810715 0.585440i \(-0.199078\pi\)
−0.585440 + 0.810715i \(0.699078\pi\)
\(258\) 0 0
\(259\) 12.8868 + 12.8868i 0.800745 + 0.800745i
\(260\) 0 0
\(261\) 2.19078 2.19078i 0.135606 0.135606i
\(262\) 0 0
\(263\) −6.80041 + 6.80041i −0.419331 + 0.419331i −0.884973 0.465642i \(-0.845823\pi\)
0.465642 + 0.884973i \(0.345823\pi\)
\(264\) 0 0
\(265\) −4.30657 + 10.7429i −0.264551 + 0.659933i
\(266\) 0 0
\(267\) 7.15650i 0.437970i
\(268\) 0 0
\(269\) 1.20010 1.20010i 0.0731711 0.0731711i −0.669574 0.742745i \(-0.733523\pi\)
0.742745 + 0.669574i \(0.233523\pi\)
\(270\) 0 0
\(271\) 2.79591i 0.169840i −0.996388 0.0849199i \(-0.972937\pi\)
0.996388 0.0849199i \(-0.0270634\pi\)
\(272\) 0 0
\(273\) −3.58167 + 3.58167i −0.216773 + 0.216773i
\(274\) 0 0
\(275\) −0.316922 13.8506i −0.0191111 0.835220i
\(276\) 0 0
\(277\) −13.8115 −0.829852 −0.414926 0.909855i \(-0.636193\pi\)
−0.414926 + 0.909855i \(0.636193\pi\)
\(278\) 0 0
\(279\) 6.18807i 0.370470i
\(280\) 0 0
\(281\) 7.21718i 0.430541i 0.976554 + 0.215270i \(0.0690633\pi\)
−0.976554 + 0.215270i \(0.930937\pi\)
\(282\) 0 0
\(283\) −25.2988 −1.50386 −0.751930 0.659243i \(-0.770877\pi\)
−0.751930 + 0.659243i \(0.770877\pi\)
\(284\) 0 0
\(285\) 1.22129 0.522319i 0.0723428 0.0309395i
\(286\) 0 0
\(287\) 14.3862 14.3862i 0.849193 0.849193i
\(288\) 0 0
\(289\) 16.0930i 0.946644i
\(290\) 0 0
\(291\) 2.16901 2.16901i 0.127149 0.127149i
\(292\) 0 0
\(293\) 14.1276i 0.825344i −0.910880 0.412672i \(-0.864596\pi\)
0.910880 0.412672i \(-0.135404\pi\)
\(294\) 0 0
\(295\) −12.1049 + 5.17700i −0.704773 + 0.301417i
\(296\) 0 0
\(297\) 6.76985 6.76985i 0.392827 0.392827i
\(298\) 0 0
\(299\) −10.1722 + 10.1722i −0.588272 + 0.588272i
\(300\) 0 0
\(301\) 2.40998 + 2.40998i 0.138909 + 0.138909i
\(302\) 0 0
\(303\) −4.54451 4.54451i −0.261076 0.261076i
\(304\) 0 0
\(305\) −6.91016 16.1573i −0.395674 0.925166i
\(306\) 0 0
\(307\) 22.6081 1.29031 0.645156 0.764051i \(-0.276792\pi\)
0.645156 + 0.764051i \(0.276792\pi\)
\(308\) 0 0
\(309\) 2.28990 + 2.28990i 0.130268 + 0.130268i
\(310\) 0 0
\(311\) −10.7903 −0.611859 −0.305929 0.952054i \(-0.598967\pi\)
−0.305929 + 0.952054i \(0.598967\pi\)
\(312\) 0 0
\(313\) 20.6842 + 20.6842i 1.16914 + 1.16914i 0.982412 + 0.186727i \(0.0597879\pi\)
0.186727 + 0.982412i \(0.440212\pi\)
\(314\) 0 0
\(315\) 9.24799 + 21.6237i 0.521065 + 1.21836i
\(316\) 0 0
\(317\) 23.8207i 1.33791i −0.743305 0.668953i \(-0.766743\pi\)
0.743305 0.668953i \(-0.233257\pi\)
\(318\) 0 0
\(319\) −3.27372 −0.183293
\(320\) 0 0
\(321\) 10.1161 0.564624
\(322\) 0 0
\(323\) 5.56042i 0.309390i
\(324\) 0 0
\(325\) 7.42956 + 7.09716i 0.412118 + 0.393680i
\(326\) 0 0
\(327\) −7.90050 7.90050i −0.436899 0.436899i
\(328\) 0 0
\(329\) 15.4650 0.852615
\(330\) 0 0
\(331\) 19.7688 + 19.7688i 1.08659 + 1.08659i 0.995877 + 0.0907155i \(0.0289154\pi\)
0.0907155 + 0.995877i \(0.471085\pi\)
\(332\) 0 0
\(333\) 11.9153 0.652957
\(334\) 0 0
\(335\) 3.60326 + 1.44446i 0.196867 + 0.0789191i
\(336\) 0 0
\(337\) 7.26955 + 7.26955i 0.395998 + 0.395998i 0.876819 0.480821i \(-0.159661\pi\)
−0.480821 + 0.876819i \(0.659661\pi\)
\(338\) 0 0
\(339\) 0.530758 + 0.530758i 0.0288268 + 0.0288268i
\(340\) 0 0
\(341\) −4.62347 + 4.62347i −0.250375 + 0.250375i
\(342\) 0 0
\(343\) −5.91866 + 5.91866i −0.319578 + 0.319578i
\(344\) 0 0
\(345\) −3.78293 8.84526i −0.203666 0.476213i
\(346\) 0 0
\(347\) 23.4667i 1.25976i 0.776692 + 0.629880i \(0.216896\pi\)
−0.776692 + 0.629880i \(0.783104\pi\)
\(348\) 0 0
\(349\) 23.2089 23.2089i 1.24234 1.24234i 0.283315 0.959027i \(-0.408566\pi\)
0.959027 0.283315i \(-0.0914342\pi\)
\(350\) 0 0
\(351\) 7.10035i 0.378988i
\(352\) 0 0
\(353\) −13.3220 + 13.3220i −0.709059 + 0.709059i −0.966337 0.257278i \(-0.917174\pi\)
0.257278 + 0.966337i \(0.417174\pi\)
\(354\) 0 0
\(355\) 4.84685 + 1.94298i 0.257244 + 0.103123i
\(356\) 0 0
\(357\) 14.1799 0.750479
\(358\) 0 0
\(359\) 26.9902i 1.42449i 0.701932 + 0.712244i \(0.252321\pi\)
−0.701932 + 0.712244i \(0.747679\pi\)
\(360\) 0 0
\(361\) 18.0657i 0.950827i
\(362\) 0 0
\(363\) 2.04187 0.107170
\(364\) 0 0
\(365\) 5.46745 + 12.7840i 0.286179 + 0.669145i
\(366\) 0 0
\(367\) −19.4758 + 19.4758i −1.01663 + 1.01663i −0.0167684 + 0.999859i \(0.505338\pi\)
−0.999859 + 0.0167684i \(0.994662\pi\)
\(368\) 0 0
\(369\) 13.3018i 0.692464i
\(370\) 0 0
\(371\) −14.6798 + 14.6798i −0.762136 + 0.762136i
\(372\) 0 0
\(373\) 4.87069i 0.252195i 0.992018 + 0.126097i \(0.0402452\pi\)
−0.992018 + 0.126097i \(0.959755\pi\)
\(374\) 0 0
\(375\) −6.25408 + 2.84569i −0.322959 + 0.146951i
\(376\) 0 0
\(377\) 1.71677 1.71677i 0.0884180 0.0884180i
\(378\) 0 0
\(379\) −2.54450 + 2.54450i −0.130702 + 0.130702i −0.769432 0.638729i \(-0.779460\pi\)
0.638729 + 0.769432i \(0.279460\pi\)
\(380\) 0 0
\(381\) 7.24846 + 7.24846i 0.371350 + 0.371350i
\(382\) 0 0
\(383\) 0.193238 + 0.193238i 0.00987399 + 0.00987399i 0.712027 0.702153i \(-0.247778\pi\)
−0.702153 + 0.712027i \(0.747778\pi\)
\(384\) 0 0
\(385\) 9.24658 23.0660i 0.471249 1.17555i
\(386\) 0 0
\(387\) 2.22831 0.113272
\(388\) 0 0
\(389\) −2.01528 2.01528i −0.102179 0.102179i 0.654169 0.756348i \(-0.273018\pi\)
−0.756348 + 0.654169i \(0.773018\pi\)
\(390\) 0 0
\(391\) 40.2718 2.03663
\(392\) 0 0
\(393\) 9.81803 + 9.81803i 0.495254 + 0.495254i
\(394\) 0 0
\(395\) −29.2632 11.7309i −1.47239 0.590244i
\(396\) 0 0
\(397\) 21.5509i 1.08161i 0.841149 + 0.540804i \(0.181880\pi\)
−0.841149 + 0.540804i \(0.818120\pi\)
\(398\) 0 0
\(399\) 2.38257 0.119277
\(400\) 0 0
\(401\) −10.3965 −0.519176 −0.259588 0.965719i \(-0.583587\pi\)
−0.259588 + 0.965719i \(0.583587\pi\)
\(402\) 0 0
\(403\) 4.84917i 0.241555i
\(404\) 0 0
\(405\) 11.9205 + 4.77865i 0.592337 + 0.237453i
\(406\) 0 0
\(407\) −8.90264 8.90264i −0.441288 0.441288i
\(408\) 0 0
\(409\) −0.330732 −0.0163536 −0.00817682 0.999967i \(-0.502603\pi\)
−0.00817682 + 0.999967i \(0.502603\pi\)
\(410\) 0 0
\(411\) −0.795389 0.795389i −0.0392337 0.0392337i
\(412\) 0 0
\(413\) −23.6150 −1.16202
\(414\) 0 0
\(415\) 2.29409 5.72270i 0.112612 0.280917i
\(416\) 0 0
\(417\) 5.29395 + 5.29395i 0.259246 + 0.259246i
\(418\) 0 0
\(419\) 6.71354 + 6.71354i 0.327978 + 0.327978i 0.851817 0.523839i \(-0.175501\pi\)
−0.523839 + 0.851817i \(0.675501\pi\)
\(420\) 0 0
\(421\) −2.99831 + 2.99831i −0.146129 + 0.146129i −0.776386 0.630258i \(-0.782949\pi\)
0.630258 + 0.776386i \(0.282949\pi\)
\(422\) 0 0
\(423\) 7.14963 7.14963i 0.347627 0.347627i
\(424\) 0 0
\(425\) −0.657974 28.7557i −0.0319164 1.39486i
\(426\) 0 0
\(427\) 31.5208i 1.52540i
\(428\) 0 0
\(429\) 2.47435 2.47435i 0.119463 0.119463i
\(430\) 0 0
\(431\) 19.9548i 0.961191i −0.876942 0.480596i \(-0.840420\pi\)
0.876942 0.480596i \(-0.159580\pi\)
\(432\) 0 0
\(433\) −16.1910 + 16.1910i −0.778092 + 0.778092i −0.979506 0.201414i \(-0.935446\pi\)
0.201414 + 0.979506i \(0.435446\pi\)
\(434\) 0 0
\(435\) 0.638449 + 1.49282i 0.0306113 + 0.0715753i
\(436\) 0 0
\(437\) 6.76664 0.323692
\(438\) 0 0
\(439\) 29.3734i 1.40191i 0.713204 + 0.700957i \(0.247243\pi\)
−0.713204 + 0.700957i \(0.752757\pi\)
\(440\) 0 0
\(441\) 23.8287i 1.13470i
\(442\) 0 0
\(443\) 19.8713 0.944115 0.472057 0.881568i \(-0.343511\pi\)
0.472057 + 0.881568i \(0.343511\pi\)
\(444\) 0 0
\(445\) −24.1689 9.68870i −1.14572 0.459288i
\(446\) 0 0
\(447\) −0.0495422 + 0.0495422i −0.00234326 + 0.00234326i
\(448\) 0 0
\(449\) 16.7577i 0.790844i −0.918500 0.395422i \(-0.870598\pi\)
0.918500 0.395422i \(-0.129402\pi\)
\(450\) 0 0
\(451\) −9.93854 + 9.93854i −0.467987 + 0.467987i
\(452\) 0 0
\(453\) 1.99856i 0.0939005i
\(454\) 0 0
\(455\) 7.24703 + 16.9450i 0.339746 + 0.794394i
\(456\) 0 0
\(457\) −5.00267 + 5.00267i −0.234015 + 0.234015i −0.814366 0.580351i \(-0.802915\pi\)
0.580351 + 0.814366i \(0.302915\pi\)
\(458\) 0 0
\(459\) 14.0552 14.0552i 0.656039 0.656039i
\(460\) 0 0
\(461\) −2.71518 2.71518i −0.126459 0.126459i 0.641045 0.767503i \(-0.278501\pi\)
−0.767503 + 0.641045i \(0.778501\pi\)
\(462\) 0 0
\(463\) 9.18551 + 9.18551i 0.426887 + 0.426887i 0.887566 0.460680i \(-0.152394\pi\)
−0.460680 + 0.887566i \(0.652394\pi\)
\(464\) 0 0
\(465\) 3.00999 + 1.20663i 0.139585 + 0.0559561i
\(466\) 0 0
\(467\) 1.06405 0.0492385 0.0246193 0.999697i \(-0.492163\pi\)
0.0246193 + 0.999697i \(0.492163\pi\)
\(468\) 0 0
\(469\) 4.92371 + 4.92371i 0.227356 + 0.227356i
\(470\) 0 0
\(471\) −5.57197 −0.256743
\(472\) 0 0
\(473\) −1.66490 1.66490i −0.0765523 0.0765523i
\(474\) 0 0
\(475\) −0.110556 4.83166i −0.00507265 0.221692i
\(476\) 0 0
\(477\) 13.5732i 0.621474i
\(478\) 0 0
\(479\) 15.8658 0.724926 0.362463 0.931998i \(-0.381936\pi\)
0.362463 + 0.931998i \(0.381936\pi\)
\(480\) 0 0
\(481\) 9.33725 0.425742
\(482\) 0 0
\(483\) 17.2559i 0.785170i
\(484\) 0 0
\(485\) −4.38869 10.2616i −0.199280 0.465957i
\(486\) 0 0
\(487\) −13.7947 13.7947i −0.625099 0.625099i 0.321732 0.946831i \(-0.395735\pi\)
−0.946831 + 0.321732i \(0.895735\pi\)
\(488\) 0 0
\(489\) −2.41717 −0.109308
\(490\) 0 0
\(491\) −19.4471 19.4471i −0.877637 0.877637i 0.115652 0.993290i \(-0.463104\pi\)
−0.993290 + 0.115652i \(0.963104\pi\)
\(492\) 0 0
\(493\) −6.79669 −0.306108
\(494\) 0 0
\(495\) −6.38885 14.9384i −0.287157 0.671431i
\(496\) 0 0
\(497\) 6.62302 + 6.62302i 0.297083 + 0.297083i
\(498\) 0 0
\(499\) −23.0141 23.0141i −1.03025 1.03025i −0.999528 0.0307258i \(-0.990218\pi\)
−0.0307258 0.999528i \(-0.509782\pi\)
\(500\) 0 0
\(501\) −4.99775 + 4.99775i −0.223283 + 0.223283i
\(502\) 0 0
\(503\) 6.63364 6.63364i 0.295780 0.295780i −0.543579 0.839358i \(-0.682931\pi\)
0.839358 + 0.543579i \(0.182931\pi\)
\(504\) 0 0
\(505\) −21.5002 + 9.19520i −0.956748 + 0.409181i
\(506\) 0 0
\(507\) 5.39422i 0.239566i
\(508\) 0 0
\(509\) −8.04140 + 8.04140i −0.356429 + 0.356429i −0.862495 0.506066i \(-0.831099\pi\)
0.506066 + 0.862495i \(0.331099\pi\)
\(510\) 0 0
\(511\) 24.9398i 1.10327i
\(512\) 0 0
\(513\) 2.36161 2.36161i 0.104268 0.104268i
\(514\) 0 0
\(515\) 10.8336 4.63331i 0.477386 0.204168i
\(516\) 0 0
\(517\) −10.6838 −0.469873
\(518\) 0 0
\(519\) 4.22044i 0.185257i
\(520\) 0 0
\(521\) 32.8549i 1.43940i 0.694285 + 0.719700i \(0.255721\pi\)
−0.694285 + 0.719700i \(0.744279\pi\)
\(522\) 0 0
\(523\) 2.46341 0.107717 0.0538587 0.998549i \(-0.482848\pi\)
0.0538587 + 0.998549i \(0.482848\pi\)
\(524\) 0 0
\(525\) −12.3214 + 0.281933i −0.537751 + 0.0123046i
\(526\) 0 0
\(527\) −9.59896 + 9.59896i −0.418137 + 0.418137i
\(528\) 0 0
\(529\) 26.0078i 1.13078i
\(530\) 0 0
\(531\) −10.9174 + 10.9174i −0.473775 + 0.473775i
\(532\) 0 0
\(533\) 10.4237i 0.451501i
\(534\) 0 0
\(535\) 13.6955 34.1640i 0.592107 1.47704i
\(536\) 0 0
\(537\) 9.65586 9.65586i 0.416681 0.416681i
\(538\) 0 0
\(539\) 17.8038 17.8038i 0.766863 0.766863i
\(540\) 0 0
\(541\) 18.0772 + 18.0772i 0.777198 + 0.777198i 0.979353 0.202156i \(-0.0647947\pi\)
−0.202156 + 0.979353i \(0.564795\pi\)
\(542\) 0 0
\(543\) 8.54938 + 8.54938i 0.366889 + 0.366889i
\(544\) 0 0
\(545\) −37.3775 + 15.9856i −1.60108 + 0.684747i
\(546\) 0 0
\(547\) −43.6742 −1.86738 −0.933688 0.358089i \(-0.883428\pi\)
−0.933688 + 0.358089i \(0.883428\pi\)
\(548\) 0 0
\(549\) −14.5723 14.5723i −0.621932 0.621932i
\(550\) 0 0
\(551\) −1.14201 −0.0486513
\(552\) 0 0
\(553\) −39.9869 39.9869i −1.70042 1.70042i
\(554\) 0 0
\(555\) −2.32341 + 5.79584i −0.0986231 + 0.246020i
\(556\) 0 0
\(557\) 5.18948i 0.219885i 0.993938 + 0.109943i \(0.0350667\pi\)
−0.993938 + 0.109943i \(0.964933\pi\)
\(558\) 0 0
\(559\) 1.74618 0.0738555
\(560\) 0 0
\(561\) −9.79597 −0.413586
\(562\) 0 0
\(563\) 11.3756i 0.479423i 0.970844 + 0.239711i \(0.0770528\pi\)
−0.970844 + 0.239711i \(0.922947\pi\)
\(564\) 0 0
\(565\) 2.51103 1.07392i 0.105640 0.0451800i
\(566\) 0 0
\(567\) 16.2889 + 16.2889i 0.684071 + 0.684071i
\(568\) 0 0
\(569\) −7.51787 −0.315165 −0.157583 0.987506i \(-0.550370\pi\)
−0.157583 + 0.987506i \(0.550370\pi\)
\(570\) 0 0
\(571\) 7.76889 + 7.76889i 0.325118 + 0.325118i 0.850726 0.525609i \(-0.176162\pi\)
−0.525609 + 0.850726i \(0.676162\pi\)
\(572\) 0 0
\(573\) 6.35416 0.265449
\(574\) 0 0
\(575\) −34.9936 + 0.800708i −1.45934 + 0.0333918i
\(576\) 0 0
\(577\) −9.84819 9.84819i −0.409986 0.409986i 0.471748 0.881733i \(-0.343623\pi\)
−0.881733 + 0.471748i \(0.843623\pi\)
\(578\) 0 0
\(579\) 8.11720 + 8.11720i 0.337339 + 0.337339i
\(580\) 0 0
\(581\) 7.81984 7.81984i 0.324421 0.324421i
\(582\) 0 0
\(583\) 10.1413 10.1413i 0.420010 0.420010i
\(584\) 0 0
\(585\) 11.1842 + 4.48346i 0.462410 + 0.185368i
\(586\) 0 0
\(587\) 33.0447i 1.36390i 0.731398 + 0.681951i \(0.238868\pi\)
−0.731398 + 0.681951i \(0.761132\pi\)
\(588\) 0 0
\(589\) −1.61286 + 1.61286i −0.0664567 + 0.0664567i
\(590\) 0 0
\(591\) 9.36829i 0.385360i
\(592\) 0 0
\(593\) 18.5424 18.5424i 0.761445 0.761445i −0.215139 0.976584i \(-0.569020\pi\)
0.976584 + 0.215139i \(0.0690203\pi\)
\(594\) 0 0
\(595\) 19.1972 47.8882i 0.787008 1.96323i
\(596\) 0 0
\(597\) −3.06521 −0.125451
\(598\) 0 0
\(599\) 28.3117i 1.15678i −0.815759 0.578392i \(-0.803681\pi\)
0.815759 0.578392i \(-0.196319\pi\)
\(600\) 0 0
\(601\) 41.7630i 1.70355i −0.523909 0.851774i \(-0.675527\pi\)
0.523909 0.851774i \(-0.324473\pi\)
\(602\) 0 0
\(603\) 4.55255 0.185394
\(604\) 0 0
\(605\) 2.76435 6.89579i 0.112387 0.280354i
\(606\) 0 0
\(607\) 4.01973 4.01973i 0.163156 0.163156i −0.620807 0.783963i \(-0.713195\pi\)
0.783963 + 0.620807i \(0.213195\pi\)
\(608\) 0 0
\(609\) 2.91229i 0.118012i
\(610\) 0 0
\(611\) 5.60268 5.60268i 0.226660 0.226660i
\(612\) 0 0
\(613\) 21.5230i 0.869305i 0.900598 + 0.434652i \(0.143129\pi\)
−0.900598 + 0.434652i \(0.856871\pi\)
\(614\) 0 0
\(615\) 6.47023 + 2.59375i 0.260905 + 0.104590i
\(616\) 0 0
\(617\) −26.4655 + 26.4655i −1.06546 + 1.06546i −0.0677580 + 0.997702i \(0.521585\pi\)
−0.997702 + 0.0677580i \(0.978415\pi\)
\(618\) 0 0
\(619\) −21.7935 + 21.7935i −0.875955 + 0.875955i −0.993113 0.117158i \(-0.962622\pi\)
0.117158 + 0.993113i \(0.462622\pi\)
\(620\) 0 0
\(621\) −17.1041 17.1041i −0.686365 0.686365i
\(622\) 0 0
\(623\) −33.0258 33.0258i −1.32315 1.32315i
\(624\) 0 0
\(625\) 1.14348 + 24.9738i 0.0457391 + 0.998953i
\(626\) 0 0
\(627\) −1.64596 −0.0657334
\(628\) 0 0
\(629\) −18.4831 18.4831i −0.736971 0.736971i
\(630\) 0 0
\(631\) −42.7412 −1.70150 −0.850751 0.525570i \(-0.823852\pi\)
−0.850751 + 0.525570i \(0.823852\pi\)
\(632\) 0 0
\(633\) −6.37937 6.37937i −0.253557 0.253557i
\(634\) 0 0
\(635\) 34.2927 14.6663i 1.36086 0.582013i
\(636\) 0 0
\(637\) 18.6729i 0.739848i
\(638\) 0 0
\(639\) 6.12376 0.242252
\(640\) 0 0
\(641\) 45.4930 1.79687 0.898433 0.439110i \(-0.144706\pi\)
0.898433 + 0.439110i \(0.144706\pi\)
\(642\) 0 0
\(643\) 31.3531i 1.23645i −0.786002 0.618224i \(-0.787853\pi\)
0.786002 0.618224i \(-0.212147\pi\)
\(644\) 0 0
\(645\) −0.434505 + 1.08389i −0.0171086 + 0.0426782i
\(646\) 0 0
\(647\) −24.0355 24.0355i −0.944932 0.944932i 0.0536292 0.998561i \(-0.482921\pi\)
−0.998561 + 0.0536292i \(0.982921\pi\)
\(648\) 0 0
\(649\) 16.3141 0.640383
\(650\) 0 0
\(651\) 4.11303 + 4.11303i 0.161202 + 0.161202i
\(652\) 0 0
\(653\) −15.4153 −0.603248 −0.301624 0.953427i \(-0.597529\pi\)
−0.301624 + 0.953427i \(0.597529\pi\)
\(654\) 0 0
\(655\) 46.4494 19.8654i 1.81493 0.776207i
\(656\) 0 0
\(657\) 11.5299 + 11.5299i 0.449825 + 0.449825i
\(658\) 0 0
\(659\) 30.4355 + 30.4355i 1.18560 + 1.18560i 0.978272 + 0.207327i \(0.0664763\pi\)
0.207327 + 0.978272i \(0.433524\pi\)
\(660\) 0 0
\(661\) 11.2208 11.2208i 0.436437 0.436437i −0.454374 0.890811i \(-0.650137\pi\)
0.890811 + 0.454374i \(0.150137\pi\)
\(662\) 0 0
\(663\) 5.13709 5.13709i 0.199508 0.199508i
\(664\) 0 0
\(665\) 3.22560 8.04639i 0.125083 0.312026i
\(666\) 0 0
\(667\) 8.27109i 0.320258i
\(668\) 0 0
\(669\) 0.920946 0.920946i 0.0356058 0.0356058i
\(670\) 0 0
\(671\) 21.7757i 0.840640i
\(672\) 0 0
\(673\) −29.2965 + 29.2965i −1.12930 + 1.12930i −0.139006 + 0.990291i \(0.544391\pi\)
−0.990291 + 0.139006i \(0.955609\pi\)
\(674\) 0 0
\(675\) −11.9336 + 12.4925i −0.459325 + 0.480837i
\(676\) 0 0
\(677\) −2.74511 −0.105503 −0.0527516 0.998608i \(-0.516799\pi\)
−0.0527516 + 0.998608i \(0.516799\pi\)
\(678\) 0 0
\(679\) 20.0191i 0.768261i
\(680\) 0 0
\(681\) 9.60850i 0.368199i
\(682\) 0 0
\(683\) 33.0796 1.26576 0.632878 0.774251i \(-0.281873\pi\)
0.632878 + 0.774251i \(0.281873\pi\)
\(684\) 0 0
\(685\) −3.76301 + 1.60936i −0.143777 + 0.0614905i
\(686\) 0 0
\(687\) −5.98647 + 5.98647i −0.228398 + 0.228398i
\(688\) 0 0
\(689\) 10.6364i 0.405214i
\(690\) 0 0
\(691\) 30.8216 30.8216i 1.17251 1.17251i 0.190899 0.981610i \(-0.438860\pi\)
0.981610 0.190899i \(-0.0611404\pi\)
\(692\) 0 0
\(693\) 29.1428i 1.10704i
\(694\) 0 0
\(695\) 25.0458 10.7116i 0.950043 0.406314i
\(696\) 0 0
\(697\) −20.6338 + 20.6338i −0.781561 + 0.781561i
\(698\) 0 0
\(699\) −0.312890 + 0.312890i −0.0118346 + 0.0118346i
\(700\) 0 0
\(701\) 22.1242 + 22.1242i 0.835619 + 0.835619i 0.988279 0.152660i \(-0.0487838\pi\)
−0.152660 + 0.988279i \(0.548784\pi\)
\(702\) 0 0
\(703\) −3.10562 3.10562i −0.117131 0.117131i
\(704\) 0 0
\(705\) 2.08358 + 4.87183i 0.0784723 + 0.183484i
\(706\) 0 0
\(707\) −41.9440 −1.57747
\(708\) 0 0
\(709\) 7.09244 + 7.09244i 0.266362 + 0.266362i 0.827632 0.561270i \(-0.189687\pi\)
−0.561270 + 0.827632i \(0.689687\pi\)
\(710\) 0 0
\(711\) −36.9726 −1.38658
\(712\) 0 0
\(713\) 11.6812 + 11.6812i 0.437466 + 0.437466i
\(714\) 0 0
\(715\) −5.00651 11.7062i −0.187233 0.437788i
\(716\) 0 0
\(717\) 5.03628i 0.188083i
\(718\) 0 0
\(719\) 30.2949 1.12981 0.564905 0.825156i \(-0.308913\pi\)
0.564905 + 0.825156i \(0.308913\pi\)
\(720\) 0 0
\(721\) 21.1349 0.787104
\(722\) 0 0
\(723\) 3.48320i 0.129542i
\(724\) 0 0
\(725\) 5.90590 0.135136i 0.219340 0.00501883i
\(726\) 0 0
\(727\) 15.9503 + 15.9503i 0.591566 + 0.591566i 0.938054 0.346489i \(-0.112626\pi\)
−0.346489 + 0.938054i \(0.612626\pi\)
\(728\) 0 0
\(729\) 8.69055 0.321872
\(730\) 0 0
\(731\) −3.45657 3.45657i −0.127846 0.127846i
\(732\) 0 0
\(733\) −35.8535 −1.32428 −0.662140 0.749380i \(-0.730352\pi\)
−0.662140 + 0.749380i \(0.730352\pi\)
\(734\) 0 0
\(735\) −11.5907 4.64642i −0.427529 0.171386i
\(736\) 0 0
\(737\) −3.40147 3.40147i −0.125295 0.125295i
\(738\) 0 0
\(739\) 21.4532 + 21.4532i 0.789168 + 0.789168i 0.981358 0.192190i \(-0.0615590\pi\)
−0.192190 + 0.981358i \(0.561559\pi\)
\(740\) 0 0
\(741\) 0.863157 0.863157i 0.0317089 0.0317089i
\(742\) 0 0
\(743\) 13.0311 13.0311i 0.478063 0.478063i −0.426449 0.904512i \(-0.640235\pi\)
0.904512 + 0.426449i \(0.140235\pi\)
\(744\) 0 0
\(745\) 0.100242 + 0.234385i 0.00367258 + 0.00858722i
\(746\) 0 0
\(747\) 7.23036i 0.264545i
\(748\) 0 0
\(749\) 46.6836 46.6836i 1.70578 1.70578i
\(750\) 0 0
\(751\) 22.4879i 0.820595i 0.911952 + 0.410297i \(0.134575\pi\)
−0.911952 + 0.410297i \(0.865425\pi\)
\(752\) 0 0
\(753\) 9.06387 9.06387i 0.330306 0.330306i
\(754\) 0 0
\(755\) −6.74952 2.70571i −0.245640 0.0984710i
\(756\) 0 0
\(757\) −15.8781 −0.577100 −0.288550 0.957465i \(-0.593173\pi\)
−0.288550 + 0.957465i \(0.593173\pi\)
\(758\) 0 0
\(759\) 11.9210i 0.432705i
\(760\) 0 0
\(761\) 19.5227i 0.707696i −0.935303 0.353848i \(-0.884873\pi\)
0.935303 0.353848i \(-0.115127\pi\)
\(762\) 0 0
\(763\) −72.9184 −2.63982
\(764\) 0 0
\(765\) −13.2641 31.0142i −0.479566 1.12132i
\(766\) 0 0
\(767\) −8.55524 + 8.55524i −0.308912 + 0.308912i
\(768\) 0 0
\(769\) 8.03843i 0.289873i −0.989441 0.144937i \(-0.953702\pi\)
0.989441 0.144937i \(-0.0462978\pi\)
\(770\) 0 0
\(771\) −2.21946 + 2.21946i −0.0799320 + 0.0799320i
\(772\) 0 0
\(773\) 40.5118i 1.45711i 0.684988 + 0.728554i \(0.259807\pi\)
−0.684988 + 0.728554i \(0.740193\pi\)
\(774\) 0 0
\(775\) 8.15005 8.53175i 0.292758 0.306470i
\(776\) 0 0
\(777\) −7.91977 + 7.91977i −0.284120 + 0.284120i
\(778\) 0 0
\(779\) −3.46698 + 3.46698i −0.124217 + 0.124217i
\(780\) 0 0
\(781\) −4.57542 4.57542i −0.163721 0.163721i
\(782\) 0 0
\(783\) 2.88668 + 2.88668i 0.103161 + 0.103161i
\(784\) 0 0
\(785\) −7.54352 + 18.8176i −0.269240 + 0.671631i
\(786\) 0 0
\(787\) −15.8333 −0.564396 −0.282198 0.959356i \(-0.591063\pi\)
−0.282198 + 0.959356i \(0.591063\pi\)
\(788\) 0 0
\(789\) −4.17930 4.17930i −0.148787 0.148787i
\(790\) 0 0
\(791\) 4.89868 0.174177
\(792\) 0 0
\(793\) −11.4194 11.4194i −0.405513 0.405513i
\(794\) 0 0
\(795\) −6.60224 2.64667i −0.234157 0.0938678i
\(796\) 0 0
\(797\) 10.2670i 0.363674i 0.983329 + 0.181837i \(0.0582044\pi\)
−0.983329 + 0.181837i \(0.941796\pi\)