Properties

Label 912.2.cc.c.737.1
Level $912$
Weight $2$
Character 912.737
Analytic conductor $7.282$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.cc (of order \(18\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{18})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Defining polynomial: \(x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + 162 x^{7} + 270 x^{6} + 2916 x^{5} - 4374 x^{4} - 729 x^{3} + 19683\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 114)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 737.1
Root \(1.69944 - 0.334495i\) of defining polynomial
Character \(\chi\) \(=\) 912.737
Dual form 912.2.cc.c.641.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.08684 - 1.34862i) q^{3} +(0.343148 + 0.408948i) q^{5} +(0.716507 - 1.24103i) q^{7} +(-0.637553 + 2.93147i) q^{9} +O(q^{10})\) \(q+(-1.08684 - 1.34862i) q^{3} +(0.343148 + 0.408948i) q^{5} +(0.716507 - 1.24103i) q^{7} +(-0.637553 + 2.93147i) q^{9} +(-1.25645 + 0.725411i) q^{11} +(2.94737 + 0.519701i) q^{13} +(0.178568 - 0.907238i) q^{15} +(1.89590 - 5.20894i) q^{17} +(4.35653 + 0.143752i) q^{19} +(-2.45240 + 0.382503i) q^{21} +(-0.396438 + 0.472456i) q^{23} +(0.818753 - 4.64338i) q^{25} +(4.64636 - 2.32623i) q^{27} +(-4.97822 + 1.81193i) q^{29} +(4.28601 + 2.47453i) q^{31} +(2.34386 + 0.906066i) q^{33} +(0.753384 - 0.132842i) q^{35} -6.41883i q^{37} +(-2.50245 - 4.53972i) q^{39} +(-1.37347 - 7.78933i) q^{41} +(-4.88757 + 4.10116i) q^{43} +(-1.41759 + 0.745203i) q^{45} +(-4.37381 - 12.0169i) q^{47} +(2.47323 + 4.28377i) q^{49} +(-9.08542 + 3.10444i) q^{51} +(-1.41439 - 1.18682i) q^{53} +(-0.727804 - 0.264899i) q^{55} +(-4.54099 - 6.03154i) q^{57} +(1.75650 + 0.639313i) q^{59} +(9.02625 + 7.57392i) q^{61} +(3.18122 + 2.89164i) q^{63} +(0.798855 + 1.38366i) q^{65} +(-3.17216 - 8.71543i) q^{67} +(1.06803 + 0.0211592i) q^{69} +(9.59384 - 8.05019i) q^{71} +(-2.80621 - 15.9148i) q^{73} +(-7.15201 + 3.94243i) q^{75} +2.07905i q^{77} +(7.87896 - 1.38927i) q^{79} +(-8.18705 - 3.73794i) q^{81} +(-4.29627 - 2.48045i) q^{83} +(2.78076 - 1.01211i) q^{85} +(7.85414 + 4.74446i) q^{87} +(-0.832120 + 4.71919i) q^{89} +(2.75678 - 3.28540i) q^{91} +(-1.32101 - 8.46962i) q^{93} +(1.43615 + 1.83092i) q^{95} +(-2.83601 + 7.79188i) q^{97} +(-1.32547 - 4.14573i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 3q^{3} - 3q^{9} + O(q^{10}) \) \( 18q - 3q^{3} - 3q^{9} - 12q^{13} - 18q^{15} + 6q^{17} + 6q^{19} - 18q^{25} + 6q^{27} - 6q^{29} - 24q^{33} + 24q^{35} - 6q^{39} + 3q^{41} + 6q^{43} - 54q^{45} - 30q^{47} + 21q^{49} - 42q^{51} - 60q^{53} - 30q^{55} + 12q^{57} - 3q^{59} + 54q^{61} + 18q^{63} + 24q^{65} + 15q^{67} + 30q^{69} - 36q^{71} - 42q^{73} + 6q^{79} - 3q^{81} - 36q^{83} - 60q^{89} + 18q^{91} - 66q^{93} - 6q^{95} + 9q^{97} + 102q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{11}{18}\right)\) \(1\) \(-1\) \(1\)

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
\(3\) −1.08684 1.34862i −0.627488 0.778626i
\(4\) 0 0
\(5\) 0.343148 + 0.408948i 0.153461 + 0.182887i 0.837297 0.546748i \(-0.184134\pi\)
−0.683837 + 0.729635i \(0.739690\pi\)
\(6\) 0 0
\(7\) 0.716507 1.24103i 0.270814 0.469064i −0.698256 0.715848i \(-0.746040\pi\)
0.969071 + 0.246784i \(0.0793737\pi\)
\(8\) 0 0
\(9\) −0.637553 + 2.93147i −0.212518 + 0.977157i
\(10\) 0 0
\(11\) −1.25645 + 0.725411i −0.378834 + 0.218720i −0.677311 0.735697i \(-0.736855\pi\)
0.298477 + 0.954417i \(0.403521\pi\)
\(12\) 0 0
\(13\) 2.94737 + 0.519701i 0.817454 + 0.144139i 0.566713 0.823915i \(-0.308215\pi\)
0.250741 + 0.968054i \(0.419326\pi\)
\(14\) 0 0
\(15\) 0.178568 0.907238i 0.0461061 0.234248i
\(16\) 0 0
\(17\) 1.89590 5.20894i 0.459823 1.26335i −0.465795 0.884893i \(-0.654232\pi\)
0.925618 0.378460i \(-0.123546\pi\)
\(18\) 0 0
\(19\) 4.35653 + 0.143752i 0.999456 + 0.0329790i
\(20\) 0 0
\(21\) −2.45240 + 0.382503i −0.535158 + 0.0834690i
\(22\) 0 0
\(23\) −0.396438 + 0.472456i −0.0826630 + 0.0985139i −0.805791 0.592200i \(-0.798259\pi\)
0.723128 + 0.690714i \(0.242704\pi\)
\(24\) 0 0
\(25\) 0.818753 4.64338i 0.163751 0.928676i
\(26\) 0 0
\(27\) 4.64636 2.32623i 0.894192 0.447683i
\(28\) 0 0
\(29\) −4.97822 + 1.81193i −0.924433 + 0.336466i −0.760001 0.649922i \(-0.774801\pi\)
−0.164432 + 0.986388i \(0.552579\pi\)
\(30\) 0 0
\(31\) 4.28601 + 2.47453i 0.769790 + 0.444439i 0.832800 0.553574i \(-0.186737\pi\)
−0.0630096 + 0.998013i \(0.520070\pi\)
\(32\) 0 0
\(33\) 2.34386 + 0.906066i 0.408014 + 0.157726i
\(34\) 0 0
\(35\) 0.753384 0.132842i 0.127345 0.0224544i
\(36\) 0 0
\(37\) 6.41883i 1.05525i −0.849478 0.527625i \(-0.823083\pi\)
0.849478 0.527625i \(-0.176917\pi\)
\(38\) 0 0
\(39\) −2.50245 4.53972i −0.400712 0.726937i
\(40\) 0 0
\(41\) −1.37347 7.78933i −0.214500 1.21649i −0.881772 0.471675i \(-0.843650\pi\)
0.667273 0.744814i \(-0.267462\pi\)
\(42\) 0 0
\(43\) −4.88757 + 4.10116i −0.745348 + 0.625421i −0.934268 0.356571i \(-0.883946\pi\)
0.188920 + 0.981992i \(0.439501\pi\)
\(44\) 0 0
\(45\) −1.41759 + 0.745203i −0.211323 + 0.111088i
\(46\) 0 0
\(47\) −4.37381 12.0169i −0.637985 1.75285i −0.657963 0.753050i \(-0.728582\pi\)
0.0199780 0.999800i \(-0.493640\pi\)
\(48\) 0 0
\(49\) 2.47323 + 4.28377i 0.353319 + 0.611967i
\(50\) 0 0
\(51\) −9.08542 + 3.10444i −1.27221 + 0.434709i
\(52\) 0 0
\(53\) −1.41439 1.18682i −0.194282 0.163022i 0.540458 0.841371i \(-0.318251\pi\)
−0.734739 + 0.678349i \(0.762696\pi\)
\(54\) 0 0
\(55\) −0.727804 0.264899i −0.0981370 0.0357190i
\(56\) 0 0
\(57\) −4.54099 6.03154i −0.601468 0.798897i
\(58\) 0 0
\(59\) 1.75650 + 0.639313i 0.228676 + 0.0832314i 0.453817 0.891095i \(-0.350062\pi\)
−0.225141 + 0.974326i \(0.572284\pi\)
\(60\) 0 0
\(61\) 9.02625 + 7.57392i 1.15569 + 0.969742i 0.999837 0.0180382i \(-0.00574206\pi\)
0.155856 + 0.987780i \(0.450186\pi\)
\(62\) 0 0
\(63\) 3.18122 + 2.89164i 0.400797 + 0.364313i
\(64\) 0 0
\(65\) 0.798855 + 1.38366i 0.0990857 + 0.171622i
\(66\) 0 0
\(67\) −3.17216 8.71543i −0.387541 1.06476i −0.968105 0.250545i \(-0.919390\pi\)
0.580564 0.814215i \(-0.302832\pi\)
\(68\) 0 0
\(69\) 1.06803 + 0.0211592i 0.128576 + 0.00254727i
\(70\) 0 0
\(71\) 9.59384 8.05019i 1.13858 0.955382i 0.139188 0.990266i \(-0.455551\pi\)
0.999391 + 0.0348843i \(0.0111063\pi\)
\(72\) 0 0
\(73\) −2.80621 15.9148i −0.328442 1.86269i −0.484294 0.874905i \(-0.660923\pi\)
0.155852 0.987780i \(-0.450188\pi\)
\(74\) 0 0
\(75\) −7.15201 + 3.94243i −0.825843 + 0.455232i
\(76\) 0 0
\(77\) 2.07905i 0.236930i
\(78\) 0 0
\(79\) 7.87896 1.38927i 0.886452 0.156305i 0.288159 0.957583i \(-0.406957\pi\)
0.598293 + 0.801277i \(0.295846\pi\)
\(80\) 0 0
\(81\) −8.18705 3.73794i −0.909673 0.415326i
\(82\) 0 0
\(83\) −4.29627 2.48045i −0.471577 0.272265i 0.245323 0.969442i \(-0.421106\pi\)
−0.716900 + 0.697176i \(0.754439\pi\)
\(84\) 0 0
\(85\) 2.78076 1.01211i 0.301616 0.109779i
\(86\) 0 0
\(87\) 7.85414 + 4.74446i 0.842052 + 0.508659i
\(88\) 0 0
\(89\) −0.832120 + 4.71919i −0.0882046 + 0.500233i 0.908414 + 0.418071i \(0.137294\pi\)
−0.996619 + 0.0821621i \(0.973817\pi\)
\(90\) 0 0
\(91\) 2.75678 3.28540i 0.288989 0.344403i
\(92\) 0 0
\(93\) −1.32101 8.46962i −0.136983 0.878259i
\(94\) 0 0
\(95\) 1.43615 + 1.83092i 0.147346 + 0.187849i
\(96\) 0 0
\(97\) −2.83601 + 7.79188i −0.287954 + 0.791146i 0.708399 + 0.705812i \(0.249418\pi\)
−0.996352 + 0.0853335i \(0.972804\pi\)
\(98\) 0 0
\(99\) −1.32547 4.14573i −0.133215 0.416662i
\(100\) 0 0
\(101\) 3.10192 + 0.546953i 0.308653 + 0.0544238i 0.325829 0.945429i \(-0.394357\pi\)
−0.0171763 + 0.999852i \(0.505468\pi\)
\(102\) 0 0
\(103\) 8.85438 5.11208i 0.872448 0.503708i 0.00428731 0.999991i \(-0.498635\pi\)
0.868161 + 0.496282i \(0.165302\pi\)
\(104\) 0 0
\(105\) −0.997962 0.871651i −0.0973911 0.0850644i
\(106\) 0 0
\(107\) −5.80970 + 10.0627i −0.561645 + 0.972798i 0.435708 + 0.900088i \(0.356498\pi\)
−0.997353 + 0.0727101i \(0.976835\pi\)
\(108\) 0 0
\(109\) −0.0205152 0.0244490i −0.00196500 0.00234179i 0.765061 0.643958i \(-0.222709\pi\)
−0.767026 + 0.641616i \(0.778264\pi\)
\(110\) 0 0
\(111\) −8.65657 + 6.97625i −0.821645 + 0.662156i
\(112\) 0 0
\(113\) 10.3475 0.973413 0.486706 0.873566i \(-0.338198\pi\)
0.486706 + 0.873566i \(0.338198\pi\)
\(114\) 0 0
\(115\) −0.329247 −0.0307024
\(116\) 0 0
\(117\) −3.40259 + 8.30880i −0.314570 + 0.768149i
\(118\) 0 0
\(119\) −5.10601 6.08510i −0.468067 0.557820i
\(120\) 0 0
\(121\) −4.44756 + 7.70340i −0.404323 + 0.700309i
\(122\) 0 0
\(123\) −9.01210 + 10.3180i −0.812594 + 0.930347i
\(124\) 0 0
\(125\) 4.49147 2.59315i 0.401729 0.231938i
\(126\) 0 0
\(127\) 0.772141 + 0.136149i 0.0685165 + 0.0120813i 0.207801 0.978171i \(-0.433369\pi\)
−0.139285 + 0.990252i \(0.544480\pi\)
\(128\) 0 0
\(129\) 10.8429 + 2.13417i 0.954666 + 0.187903i
\(130\) 0 0
\(131\) −3.93973 + 10.8243i −0.344216 + 0.945726i 0.639941 + 0.768424i \(0.278959\pi\)
−0.984157 + 0.177301i \(0.943263\pi\)
\(132\) 0 0
\(133\) 3.29988 5.30357i 0.286136 0.459878i
\(134\) 0 0
\(135\) 2.54570 + 1.10188i 0.219099 + 0.0948347i
\(136\) 0 0
\(137\) −8.70595 + 10.3754i −0.743800 + 0.886426i −0.996709 0.0810638i \(-0.974168\pi\)
0.252909 + 0.967490i \(0.418613\pi\)
\(138\) 0 0
\(139\) 1.25656 7.12628i 0.106580 0.604444i −0.883998 0.467491i \(-0.845158\pi\)
0.990578 0.136953i \(-0.0437308\pi\)
\(140\) 0 0
\(141\) −11.4526 + 18.9591i −0.964487 + 1.59664i
\(142\) 0 0
\(143\) −4.08022 + 1.48508i −0.341205 + 0.124188i
\(144\) 0 0
\(145\) −2.44925 1.41408i −0.203399 0.117433i
\(146\) 0 0
\(147\) 3.08916 7.99123i 0.254790 0.659105i
\(148\) 0 0
\(149\) −19.4195 + 3.42419i −1.59091 + 0.280520i −0.897831 0.440341i \(-0.854858\pi\)
−0.693079 + 0.720861i \(0.743746\pi\)
\(150\) 0 0
\(151\) 4.23079i 0.344297i −0.985071 0.172148i \(-0.944929\pi\)
0.985071 0.172148i \(-0.0550709\pi\)
\(152\) 0 0
\(153\) 14.0611 + 8.87874i 1.13677 + 0.717804i
\(154\) 0 0
\(155\) 0.458783 + 2.60189i 0.0368503 + 0.208989i
\(156\) 0 0
\(157\) 7.78482 6.53224i 0.621296 0.521330i −0.276914 0.960895i \(-0.589312\pi\)
0.898211 + 0.439565i \(0.144867\pi\)
\(158\) 0 0
\(159\) −0.0633444 + 3.19736i −0.00502354 + 0.253567i
\(160\) 0 0
\(161\) 0.302280 + 0.830508i 0.0238230 + 0.0654532i
\(162\) 0 0
\(163\) 5.20216 + 9.01041i 0.407465 + 0.705750i 0.994605 0.103735i \(-0.0330795\pi\)
−0.587140 + 0.809485i \(0.699746\pi\)
\(164\) 0 0
\(165\) 0.433759 + 1.26943i 0.0337681 + 0.0988253i
\(166\) 0 0
\(167\) 18.2265 + 15.2939i 1.41041 + 1.18347i 0.956249 + 0.292555i \(0.0945056\pi\)
0.454162 + 0.890919i \(0.349939\pi\)
\(168\) 0 0
\(169\) −3.79909 1.38276i −0.292238 0.106366i
\(170\) 0 0
\(171\) −3.19892 + 12.6794i −0.244628 + 0.969617i
\(172\) 0 0
\(173\) 23.5435 + 8.56912i 1.78998 + 0.651498i 0.999225 + 0.0393612i \(0.0125323\pi\)
0.790752 + 0.612137i \(0.209690\pi\)
\(174\) 0 0
\(175\) −5.17592 4.34311i −0.391263 0.328308i
\(176\) 0 0
\(177\) −1.04684 3.06368i −0.0786856 0.230280i
\(178\) 0 0
\(179\) 7.77173 + 13.4610i 0.580886 + 1.00612i 0.995375 + 0.0960699i \(0.0306272\pi\)
−0.414488 + 0.910055i \(0.636039\pi\)
\(180\) 0 0
\(181\) 7.17064 + 19.7012i 0.532990 + 1.46438i 0.855496 + 0.517810i \(0.173252\pi\)
−0.322506 + 0.946567i \(0.604525\pi\)
\(182\) 0 0
\(183\) 0.404246 20.4046i 0.0298827 1.50835i
\(184\) 0 0
\(185\) 2.62497 2.20261i 0.192992 0.161939i
\(186\) 0 0
\(187\) 1.39652 + 7.92007i 0.102124 + 0.579173i
\(188\) 0 0
\(189\) 0.442240 7.43302i 0.0321682 0.540673i
\(190\) 0 0
\(191\) 1.59398i 0.115336i −0.998336 0.0576682i \(-0.981633\pi\)
0.998336 0.0576682i \(-0.0183665\pi\)
\(192\) 0 0
\(193\) 4.28991 0.756427i 0.308795 0.0544488i −0.0171035 0.999854i \(-0.505444\pi\)
0.325898 + 0.945405i \(0.394333\pi\)
\(194\) 0 0
\(195\) 0.997799 2.58117i 0.0714539 0.184841i
\(196\) 0 0
\(197\) −5.69700 3.28916i −0.405894 0.234343i 0.283130 0.959082i \(-0.408627\pi\)
−0.689024 + 0.724738i \(0.741961\pi\)
\(198\) 0 0
\(199\) −10.2412 + 3.72750i −0.725981 + 0.264235i −0.678463 0.734635i \(-0.737353\pi\)
−0.0475182 + 0.998870i \(0.515131\pi\)
\(200\) 0 0
\(201\) −8.30618 + 13.7503i −0.585873 + 0.969873i
\(202\) 0 0
\(203\) −1.31829 + 7.47637i −0.0925255 + 0.524738i
\(204\) 0 0
\(205\) 2.71413 3.23457i 0.189563 0.225912i
\(206\) 0 0
\(207\) −1.13224 1.46336i −0.0786962 0.101711i
\(208\) 0 0
\(209\) −5.57803 + 2.97966i −0.385841 + 0.206107i
\(210\) 0 0
\(211\) 2.58901 7.11324i 0.178235 0.489695i −0.818116 0.575054i \(-0.804981\pi\)
0.996350 + 0.0853581i \(0.0272034\pi\)
\(212\) 0 0
\(213\) −21.2836 4.18917i −1.45833 0.287037i
\(214\) 0 0
\(215\) −3.35432 0.591458i −0.228763 0.0403371i
\(216\) 0 0
\(217\) 6.14192 3.54604i 0.416940 0.240721i
\(218\) 0 0
\(219\) −18.4131 + 21.0814i −1.24424 + 1.42455i
\(220\) 0 0
\(221\) 8.29501 14.3674i 0.557983 0.966454i
\(222\) 0 0
\(223\) 7.40150 + 8.82076i 0.495641 + 0.590682i 0.954643 0.297753i \(-0.0962373\pi\)
−0.459002 + 0.888435i \(0.651793\pi\)
\(224\) 0 0
\(225\) 13.0899 + 5.36055i 0.872662 + 0.357370i
\(226\) 0 0
\(227\) −1.54291 −0.102407 −0.0512033 0.998688i \(-0.516306\pi\)
−0.0512033 + 0.998688i \(0.516306\pi\)
\(228\) 0 0
\(229\) −8.17334 −0.540110 −0.270055 0.962845i \(-0.587042\pi\)
−0.270055 + 0.962845i \(0.587042\pi\)
\(230\) 0 0
\(231\) 2.80385 2.25960i 0.184480 0.148671i
\(232\) 0 0
\(233\) 5.39612 + 6.43084i 0.353511 + 0.421298i 0.913268 0.407358i \(-0.133550\pi\)
−0.559757 + 0.828657i \(0.689106\pi\)
\(234\) 0 0
\(235\) 3.41344 5.91225i 0.222668 0.385673i
\(236\) 0 0
\(237\) −10.4368 9.11581i −0.677942 0.592135i
\(238\) 0 0
\(239\) 7.60840 4.39271i 0.492147 0.284141i −0.233318 0.972401i \(-0.574958\pi\)
0.725465 + 0.688260i \(0.241625\pi\)
\(240\) 0 0
\(241\) −13.2349 2.33367i −0.852536 0.150325i −0.269730 0.962936i \(-0.586934\pi\)
−0.582806 + 0.812611i \(0.698045\pi\)
\(242\) 0 0
\(243\) 3.85697 + 15.1038i 0.247425 + 0.968907i
\(244\) 0 0
\(245\) −0.903153 + 2.48139i −0.0577003 + 0.158530i
\(246\) 0 0
\(247\) 12.7656 + 2.68778i 0.812256 + 0.171020i
\(248\) 0 0
\(249\) 1.32418 + 8.48990i 0.0839162 + 0.538026i
\(250\) 0 0
\(251\) −5.05003 + 6.01839i −0.318755 + 0.379877i −0.901501 0.432777i \(-0.857534\pi\)
0.582746 + 0.812654i \(0.301978\pi\)
\(252\) 0 0
\(253\) 0.155379 0.881197i 0.00976858 0.0554004i
\(254\) 0 0
\(255\) −4.38720 2.65018i −0.274737 0.165961i
\(256\) 0 0
\(257\) −11.5445 + 4.20184i −0.720123 + 0.262103i −0.675978 0.736922i \(-0.736279\pi\)
−0.0441451 + 0.999025i \(0.514056\pi\)
\(258\) 0 0
\(259\) −7.96595 4.59914i −0.494980 0.285777i
\(260\) 0 0
\(261\) −2.13773 15.7487i −0.132322 0.974821i
\(262\) 0 0
\(263\) 23.4707 4.13852i 1.44727 0.255192i 0.605849 0.795579i \(-0.292833\pi\)
0.841416 + 0.540387i \(0.181722\pi\)
\(264\) 0 0
\(265\) 0.985668i 0.0605491i
\(266\) 0 0
\(267\) 7.26877 4.00679i 0.444842 0.245212i
\(268\) 0 0
\(269\) −3.30229 18.7282i −0.201344 1.14188i −0.903090 0.429452i \(-0.858707\pi\)
0.701745 0.712428i \(-0.252404\pi\)
\(270\) 0 0
\(271\) −4.13554 + 3.47013i −0.251216 + 0.210795i −0.759696 0.650279i \(-0.774652\pi\)
0.508480 + 0.861074i \(0.330208\pi\)
\(272\) 0 0
\(273\) −7.42693 0.147138i −0.449499 0.00890522i
\(274\) 0 0
\(275\) 2.33964 + 6.42810i 0.141085 + 0.387629i
\(276\) 0 0
\(277\) 0.0466956 + 0.0808791i 0.00280567 + 0.00485956i 0.867425 0.497568i \(-0.165774\pi\)
−0.864619 + 0.502428i \(0.832440\pi\)
\(278\) 0 0
\(279\) −9.98657 + 10.9867i −0.597880 + 0.657755i
\(280\) 0 0
\(281\) 7.81505 + 6.55760i 0.466207 + 0.391194i 0.845409 0.534120i \(-0.179357\pi\)
−0.379202 + 0.925314i \(0.623801\pi\)
\(282\) 0 0
\(283\) −18.1732 6.61449i −1.08028 0.393190i −0.260269 0.965536i \(-0.583811\pi\)
−0.820013 + 0.572346i \(0.806034\pi\)
\(284\) 0 0
\(285\) 0.908354 3.92674i 0.0538063 0.232600i
\(286\) 0 0
\(287\) −10.6509 3.87660i −0.628701 0.228828i
\(288\) 0 0
\(289\) −10.5158 8.82384i −0.618579 0.519049i
\(290\) 0 0
\(291\) 13.5906 4.64383i 0.796694 0.272226i
\(292\) 0 0
\(293\) 8.09268 + 14.0169i 0.472780 + 0.818878i 0.999515 0.0311512i \(-0.00991734\pi\)
−0.526735 + 0.850030i \(0.676584\pi\)
\(294\) 0 0
\(295\) 0.341293 + 0.937695i 0.0198709 + 0.0545947i
\(296\) 0 0
\(297\) −4.15044 + 6.29331i −0.240833 + 0.365175i
\(298\) 0 0
\(299\) −1.41399 + 1.18647i −0.0817729 + 0.0686156i
\(300\) 0 0
\(301\) 1.58767 + 9.00413i 0.0915118 + 0.518989i
\(302\) 0 0
\(303\) −2.63367 4.77777i −0.151300 0.274476i
\(304\) 0 0
\(305\) 6.29025i 0.360179i
\(306\) 0 0
\(307\) −17.5661 + 3.09738i −1.00255 + 0.176777i −0.650745 0.759296i \(-0.725543\pi\)
−0.351806 + 0.936073i \(0.614432\pi\)
\(308\) 0 0
\(309\) −16.5176 6.38518i −0.939651 0.363240i
\(310\) 0 0
\(311\) −28.3493 16.3675i −1.60754 0.928114i −0.989918 0.141639i \(-0.954763\pi\)
−0.617622 0.786475i \(-0.711904\pi\)
\(312\) 0 0
\(313\) −24.8285 + 9.03684i −1.40339 + 0.510792i −0.929183 0.369621i \(-0.879488\pi\)
−0.474208 + 0.880413i \(0.657265\pi\)
\(314\) 0 0
\(315\) −0.0908997 + 2.29322i −0.00512162 + 0.129208i
\(316\) 0 0
\(317\) −2.32840 + 13.2050i −0.130776 + 0.741669i 0.846932 + 0.531701i \(0.178447\pi\)
−0.977708 + 0.209968i \(0.932664\pi\)
\(318\) 0 0
\(319\) 4.94049 5.88785i 0.276614 0.329656i
\(320\) 0 0
\(321\) 19.8850 3.10148i 1.10987 0.173107i
\(322\) 0 0
\(323\) 9.00833 22.4203i 0.501237 1.24750i
\(324\) 0 0
\(325\) 4.82634 13.2603i 0.267717 0.735547i
\(326\) 0 0
\(327\) −0.0106757 + 0.0542394i −0.000590369 + 0.00299945i
\(328\) 0 0
\(329\) −18.0472 3.18221i −0.994975 0.175441i
\(330\) 0 0
\(331\) −21.6450 + 12.4967i −1.18971 + 0.686882i −0.958242 0.285959i \(-0.907688\pi\)
−0.231473 + 0.972841i \(0.574355\pi\)
\(332\) 0 0
\(333\) 18.8166 + 4.09234i 1.03114 + 0.224259i
\(334\) 0 0
\(335\) 2.47564 4.28793i 0.135259 0.234275i
\(336\) 0 0
\(337\) 10.7174 + 12.7725i 0.583815 + 0.695764i 0.974405 0.224801i \(-0.0721732\pi\)
−0.390589 + 0.920565i \(0.627729\pi\)
\(338\) 0 0
\(339\) −11.2461 13.9549i −0.610805 0.757925i
\(340\) 0 0
\(341\) −7.18020 −0.388830
\(342\) 0 0
\(343\) 17.1195 0.924364
\(344\) 0 0
\(345\) 0.357839 + 0.444029i 0.0192654 + 0.0239057i
\(346\) 0 0
\(347\) −23.0175 27.4312i −1.23564 1.47258i −0.829244 0.558886i \(-0.811229\pi\)
−0.406399 0.913696i \(-0.633216\pi\)
\(348\) 0 0
\(349\) 9.77902 16.9378i 0.523459 0.906657i −0.476168 0.879354i \(-0.657975\pi\)
0.999627 0.0273031i \(-0.00869193\pi\)
\(350\) 0 0
\(351\) 14.9035 4.44154i 0.795490 0.237072i
\(352\) 0 0
\(353\) 27.9356 16.1286i 1.48686 0.858441i 0.486976 0.873416i \(-0.338100\pi\)
0.999888 + 0.0149745i \(0.00476672\pi\)
\(354\) 0 0
\(355\) 6.58422 + 1.16098i 0.349454 + 0.0616182i
\(356\) 0 0
\(357\) −2.65707 + 13.4996i −0.140627 + 0.714475i
\(358\) 0 0
\(359\) 5.99057 16.4590i 0.316170 0.868671i −0.675206 0.737629i \(-0.735945\pi\)
0.991377 0.131042i \(-0.0418323\pi\)
\(360\) 0 0
\(361\) 18.9587 + 1.25252i 0.997825 + 0.0659220i
\(362\) 0 0
\(363\) 15.2227 2.37430i 0.798987 0.124619i
\(364\) 0 0
\(365\) 5.54538 6.60873i 0.290258 0.345917i
\(366\) 0 0
\(367\) −3.59236 + 20.3733i −0.187520 + 1.06348i 0.735155 + 0.677899i \(0.237109\pi\)
−0.922675 + 0.385578i \(0.874002\pi\)
\(368\) 0 0
\(369\) 23.7099 + 0.939823i 1.23429 + 0.0489252i
\(370\) 0 0
\(371\) −2.48630 + 0.904938i −0.129082 + 0.0469820i
\(372\) 0 0
\(373\) 2.46819 + 1.42501i 0.127798 + 0.0737843i 0.562536 0.826773i \(-0.309826\pi\)
−0.434738 + 0.900557i \(0.643159\pi\)
\(374\) 0 0
\(375\) −8.37868 3.23894i −0.432673 0.167258i
\(376\) 0 0
\(377\) −15.6143 + 2.75323i −0.804179 + 0.141798i
\(378\) 0 0
\(379\) 15.1648i 0.778963i −0.921034 0.389482i \(-0.872654\pi\)
0.921034 0.389482i \(-0.127346\pi\)
\(380\) 0 0
\(381\) −0.655581 1.18930i −0.0335864 0.0609296i
\(382\) 0 0
\(383\) −0.366876 2.08066i −0.0187465 0.106317i 0.973999 0.226553i \(-0.0727458\pi\)
−0.992745 + 0.120237i \(0.961635\pi\)
\(384\) 0 0
\(385\) −0.850223 + 0.713422i −0.0433314 + 0.0363594i
\(386\) 0 0
\(387\) −8.90635 16.9425i −0.452735 0.861235i
\(388\) 0 0
\(389\) 1.43738 + 3.94918i 0.0728783 + 0.200231i 0.970783 0.239958i \(-0.0771336\pi\)
−0.897905 + 0.440189i \(0.854911\pi\)
\(390\) 0 0
\(391\) 1.70939 + 2.96075i 0.0864475 + 0.149731i
\(392\) 0 0
\(393\) 18.8798 6.45112i 0.952358 0.325416i
\(394\) 0 0
\(395\) 3.27179 + 2.74536i 0.164622 + 0.138134i
\(396\) 0 0
\(397\) 0.284948 + 0.103713i 0.0143011 + 0.00520518i 0.349161 0.937063i \(-0.386467\pi\)
−0.334860 + 0.942268i \(0.608689\pi\)
\(398\) 0 0
\(399\) −10.7390 + 1.31385i −0.537620 + 0.0657747i
\(400\) 0 0
\(401\) 11.8640 + 4.31814i 0.592460 + 0.215638i 0.620811 0.783960i \(-0.286803\pi\)
−0.0283512 + 0.999598i \(0.509026\pi\)
\(402\) 0 0
\(403\) 11.3464 + 9.52080i 0.565207 + 0.474265i
\(404\) 0 0
\(405\) −1.28075 4.63075i −0.0636410 0.230104i
\(406\) 0 0
\(407\) 4.65629 + 8.06493i 0.230804 + 0.399764i
\(408\) 0 0
\(409\) −6.63505 18.2296i −0.328082 0.901398i −0.988597 0.150585i \(-0.951884\pi\)
0.660515 0.750813i \(-0.270338\pi\)
\(410\) 0 0
\(411\) 23.4544 + 0.464666i 1.15692 + 0.0229203i
\(412\) 0 0
\(413\) 2.05195 1.72179i 0.100970 0.0847237i
\(414\) 0 0
\(415\) −0.459881 2.60812i −0.0225747 0.128027i
\(416\) 0 0
\(417\) −10.9763 + 6.05052i −0.537513 + 0.296295i
\(418\) 0 0
\(419\) 15.4879i 0.756633i 0.925676 + 0.378316i \(0.123497\pi\)
−0.925676 + 0.378316i \(0.876503\pi\)
\(420\) 0 0
\(421\) 13.7766 2.42919i 0.671431 0.118391i 0.172468 0.985015i \(-0.444826\pi\)
0.498962 + 0.866624i \(0.333715\pi\)
\(422\) 0 0
\(423\) 38.0158 5.16026i 1.84839 0.250901i
\(424\) 0 0
\(425\) −22.6348 13.0682i −1.09795 0.633901i
\(426\) 0 0
\(427\) 15.8668 5.77505i 0.767849 0.279474i
\(428\) 0 0
\(429\) 6.43736 + 3.88862i 0.310798 + 0.187744i
\(430\) 0 0
\(431\) −4.86245 + 27.5763i −0.234216 + 1.32831i 0.610042 + 0.792369i \(0.291152\pi\)
−0.844258 + 0.535936i \(0.819959\pi\)
\(432\) 0 0
\(433\) −3.78152 + 4.50664i −0.181728 + 0.216575i −0.849216 0.528045i \(-0.822925\pi\)
0.667488 + 0.744621i \(0.267370\pi\)
\(434\) 0 0
\(435\) 0.754896 + 4.83999i 0.0361945 + 0.232060i
\(436\) 0 0
\(437\) −1.79501 + 2.00128i −0.0858669 + 0.0957342i
\(438\) 0 0
\(439\) −7.65568 + 21.0338i −0.365386 + 1.00389i 0.611709 + 0.791083i \(0.290482\pi\)
−0.977094 + 0.212806i \(0.931740\pi\)
\(440\) 0 0
\(441\) −14.1346 + 4.51909i −0.673074 + 0.215195i
\(442\) 0 0
\(443\) 14.6859 + 2.58952i 0.697748 + 0.123032i 0.511261 0.859426i \(-0.329179\pi\)
0.186487 + 0.982457i \(0.440290\pi\)
\(444\) 0 0
\(445\) −2.21544 + 1.27909i −0.105022 + 0.0606345i
\(446\) 0 0
\(447\) 25.7239 + 22.4680i 1.21670 + 1.06270i
\(448\) 0 0
\(449\) 2.44541 4.23557i 0.115406 0.199889i −0.802536 0.596604i \(-0.796516\pi\)
0.917942 + 0.396715i \(0.129850\pi\)
\(450\) 0 0
\(451\) 7.37616 + 8.79056i 0.347330 + 0.413931i
\(452\) 0 0
\(453\) −5.70573 + 4.59820i −0.268078 + 0.216042i
\(454\) 0 0
\(455\) 2.28954 0.107335
\(456\) 0 0
\(457\) −30.3578 −1.42008 −0.710039 0.704162i \(-0.751323\pi\)
−0.710039 + 0.704162i \(0.751323\pi\)
\(458\) 0 0
\(459\) −3.30815 28.6129i −0.154411 1.33554i
\(460\) 0 0
\(461\) −16.0576 19.1367i −0.747879 0.891287i 0.249138 0.968468i \(-0.419853\pi\)
−0.997017 + 0.0771808i \(0.975408\pi\)
\(462\) 0 0
\(463\) 2.94958 5.10883i 0.137079 0.237427i −0.789311 0.613994i \(-0.789562\pi\)
0.926390 + 0.376566i \(0.122895\pi\)
\(464\) 0 0
\(465\) 3.01033 3.44656i 0.139601 0.159830i
\(466\) 0 0
\(467\) 4.76849 2.75309i 0.220659 0.127398i −0.385596 0.922668i \(-0.626004\pi\)
0.606256 + 0.795270i \(0.292671\pi\)
\(468\) 0 0
\(469\) −13.0890 2.30794i −0.604392 0.106571i
\(470\) 0 0
\(471\) −17.2704 3.39926i −0.795777 0.156630i
\(472\) 0 0
\(473\) 3.16596 8.69840i 0.145571 0.399953i
\(474\) 0 0
\(475\) 4.23442 20.1113i 0.194288 0.922770i
\(476\) 0 0
\(477\) 4.38087 3.38960i 0.200586 0.155199i
\(478\) 0 0
\(479\) −21.4896 + 25.6103i −0.981884 + 1.17016i 0.00353081 + 0.999994i \(0.498876\pi\)
−0.985415 + 0.170170i \(0.945568\pi\)
\(480\) 0 0
\(481\) 3.33588 18.9187i 0.152103 0.862618i
\(482\) 0 0
\(483\) 0.791510 1.31029i 0.0360149 0.0596204i
\(484\) 0 0
\(485\) −4.15965 + 1.51399i −0.188880 + 0.0687467i
\(486\) 0 0
\(487\) −21.9456 12.6703i −0.994448 0.574145i −0.0878470 0.996134i \(-0.527999\pi\)
−0.906601 + 0.421989i \(0.861332\pi\)
\(488\) 0 0
\(489\) 6.49770 16.8086i 0.293836 0.760112i
\(490\) 0 0
\(491\) 7.76474 1.36913i 0.350418 0.0617881i 0.00433112 0.999991i \(-0.498621\pi\)
0.346087 + 0.938202i \(0.387510\pi\)
\(492\) 0 0
\(493\) 29.3665i 1.32260i
\(494\) 0 0
\(495\) 1.24056 1.96465i 0.0557589 0.0883044i
\(496\) 0 0
\(497\) −3.11645 17.6742i −0.139792 0.792798i
\(498\) 0 0
\(499\) 9.89069 8.29927i 0.442768 0.371526i −0.393976 0.919121i \(-0.628901\pi\)
0.836744 + 0.547594i \(0.184456\pi\)
\(500\) 0 0
\(501\) 0.816285 41.2026i 0.0364689 1.84080i
\(502\) 0 0
\(503\) −2.85952 7.85647i −0.127500 0.350303i 0.859475 0.511178i \(-0.170791\pi\)
−0.986975 + 0.160875i \(0.948568\pi\)
\(504\) 0 0
\(505\) 0.840744 + 1.45621i 0.0374126 + 0.0648006i
\(506\) 0 0
\(507\) 2.26420 + 6.62637i 0.100556 + 0.294287i
\(508\) 0 0
\(509\) 5.11088 + 4.28853i 0.226536 + 0.190086i 0.748990 0.662581i \(-0.230539\pi\)
−0.522454 + 0.852667i \(0.674984\pi\)
\(510\) 0 0
\(511\) −21.7614 7.92049i −0.962666 0.350382i
\(512\) 0 0
\(513\) 20.5764 9.46635i 0.908470 0.417950i
\(514\) 0 0
\(515\) 5.12894 + 1.86678i 0.226008 + 0.0822603i
\(516\) 0 0
\(517\) 14.2127 + 11.9259i 0.625073 + 0.524499i
\(518\) 0 0
\(519\) −14.0315 41.0645i −0.615915 1.80253i
\(520\) 0 0
\(521\) 7.75609 + 13.4339i 0.339800 + 0.588552i 0.984395 0.175973i \(-0.0563071\pi\)
−0.644595 + 0.764525i \(0.722974\pi\)
\(522\) 0 0
\(523\) 7.60779 + 20.9022i 0.332666 + 0.913991i 0.987416 + 0.158146i \(0.0505516\pi\)
−0.654750 + 0.755845i \(0.727226\pi\)
\(524\) 0 0
\(525\) −0.231806 + 11.7006i −0.0101169 + 0.510657i
\(526\) 0 0
\(527\) 21.0155 17.6341i 0.915450 0.768154i
\(528\) 0 0
\(529\) 3.92786 + 22.2760i 0.170776 + 0.968521i
\(530\) 0 0
\(531\) −2.99399 + 4.74153i −0.129928 + 0.205765i
\(532\) 0 0
\(533\) 23.6718i 1.02534i
\(534\) 0 0
\(535\) −6.10871 + 1.07713i −0.264103 + 0.0465684i
\(536\) 0 0
\(537\) 9.70718 25.1111i 0.418896 1.08362i
\(538\) 0 0
\(539\) −6.21498 3.58822i −0.267698 0.154556i
\(540\) 0 0
\(541\) 7.24376 2.63651i 0.311433 0.113352i −0.181575 0.983377i \(-0.558119\pi\)
0.493008 + 0.870025i \(0.335897\pi\)
\(542\) 0 0
\(543\) 18.7761 31.0825i 0.805758 1.33388i
\(544\) 0 0
\(545\) 0.00295864 0.0167793i 0.000126734 0.000718746i
\(546\) 0 0
\(547\) −18.1301 + 21.6066i −0.775188 + 0.923833i −0.998705 0.0508673i \(-0.983801\pi\)
0.223518 + 0.974700i \(0.428246\pi\)
\(548\) 0 0
\(549\) −27.9575 + 21.6314i −1.19320 + 0.923207i
\(550\) 0 0
\(551\) −21.9482 + 7.17807i −0.935026 + 0.305796i
\(552\) 0 0
\(553\) 3.92121 10.7734i 0.166747 0.458133i
\(554\) 0 0
\(555\) −5.82341 1.14620i −0.247190 0.0486534i
\(556\) 0 0
\(557\) 30.7949 + 5.42997i 1.30482 + 0.230075i 0.782487 0.622666i \(-0.213951\pi\)
0.522333 + 0.852741i \(0.325062\pi\)
\(558\) 0 0
\(559\) −16.5369 + 9.54757i −0.699435 + 0.403819i
\(560\) 0 0
\(561\) 9.16337 10.4912i 0.386878 0.442940i
\(562\) 0 0
\(563\) 4.37942 7.58538i 0.184571 0.319686i −0.758861 0.651252i \(-0.774244\pi\)
0.943432 + 0.331567i \(0.107577\pi\)
\(564\) 0 0
\(565\) 3.55073 + 4.23160i 0.149380 + 0.178025i
\(566\) 0 0
\(567\) −10.5050 + 7.48210i −0.441167 + 0.314219i
\(568\) 0 0
\(569\) −39.4950 −1.65572 −0.827859 0.560936i \(-0.810441\pi\)
−0.827859 + 0.560936i \(0.810441\pi\)
\(570\) 0 0
\(571\) 1.49689 0.0626431 0.0313215 0.999509i \(-0.490028\pi\)
0.0313215 + 0.999509i \(0.490028\pi\)
\(572\) 0 0
\(573\) −2.14967 + 1.73240i −0.0898039 + 0.0723722i
\(574\) 0 0
\(575\) 1.86921 + 2.22764i 0.0779514 + 0.0928988i
\(576\) 0 0
\(577\) −5.32793 + 9.22825i −0.221805 + 0.384177i −0.955356 0.295457i \(-0.904528\pi\)
0.733551 + 0.679634i \(0.237861\pi\)
\(578\) 0 0
\(579\) −5.68259 4.96335i −0.236160 0.206270i
\(580\) 0 0
\(581\) −6.15662 + 3.55453i −0.255420 + 0.147467i
\(582\) 0 0
\(583\) 2.63804 + 0.465158i 0.109257 + 0.0192649i
\(584\) 0 0
\(585\) −4.56546 + 1.45967i −0.188759 + 0.0603497i
\(586\) 0 0
\(587\) −0.0214414 + 0.0589098i −0.000884983 + 0.00243147i −0.940134 0.340804i \(-0.889301\pi\)
0.939249 + 0.343236i \(0.111523\pi\)
\(588\) 0 0
\(589\) 18.3164 + 11.3965i 0.754714 + 0.469584i
\(590\) 0 0
\(591\) 1.75590 + 11.2579i 0.0722280 + 0.463087i
\(592\) 0 0
\(593\) 10.0616 11.9910i 0.413181 0.492409i −0.518811 0.854889i \(-0.673625\pi\)
0.931992 + 0.362479i \(0.118070\pi\)
\(594\) 0 0
\(595\) 0.736374 4.17618i 0.0301884 0.171207i
\(596\) 0 0
\(597\) 16.1576 + 9.76032i 0.661285 + 0.399463i
\(598\) 0 0
\(599\) 2.10138 0.764839i 0.0858600 0.0312505i −0.298733 0.954337i \(-0.596564\pi\)
0.384593 + 0.923086i \(0.374342\pi\)
\(600\) 0 0
\(601\) −16.1749 9.33861i −0.659790 0.380930i 0.132407 0.991195i \(-0.457729\pi\)
−0.792197 + 0.610266i \(0.791063\pi\)
\(602\) 0 0
\(603\) 27.5715 3.74254i 1.12280 0.152408i
\(604\) 0 0
\(605\) −4.67646 + 0.824586i −0.190125 + 0.0335242i
\(606\) 0 0
\(607\) 43.2872i 1.75697i −0.477766 0.878487i \(-0.658553\pi\)
0.477766 0.878487i \(-0.341447\pi\)
\(608\) 0 0
\(609\) 11.5155 6.34776i 0.466634 0.257224i
\(610\) 0 0
\(611\) −6.64602 37.6915i −0.268869 1.52483i
\(612\) 0 0
\(613\) −6.84929 + 5.74724i −0.276640 + 0.232129i −0.770542 0.637389i \(-0.780015\pi\)
0.493902 + 0.869518i \(0.335570\pi\)
\(614\) 0 0
\(615\) −7.31203 0.144862i −0.294850 0.00584140i
\(616\) 0 0
\(617\) 8.89796 + 24.4469i 0.358218 + 0.984197i 0.979647 + 0.200726i \(0.0643302\pi\)
−0.621429 + 0.783470i \(0.713448\pi\)
\(618\) 0 0
\(619\) 9.72654 + 16.8469i 0.390943 + 0.677133i 0.992574 0.121641i \(-0.0388157\pi\)
−0.601631 + 0.798774i \(0.705482\pi\)
\(620\) 0 0
\(621\) −0.742952 + 3.11741i −0.0298136 + 0.125097i
\(622\) 0 0
\(623\) 5.26042 + 4.41402i 0.210754 + 0.176844i
\(624\) 0 0
\(625\) −19.5516 7.11620i −0.782064 0.284648i
\(626\) 0 0
\(627\) 10.0809 + 4.28423i 0.402591 + 0.171096i
\(628\) 0 0
\(629\) −33.4353 12.1695i −1.33315 0.485228i
\(630\) 0 0
\(631\) 11.6007 + 9.73414i 0.461816 + 0.387510i 0.843799 0.536660i \(-0.180314\pi\)
−0.381982 + 0.924170i \(0.624759\pi\)
\(632\) 0 0
\(633\) −12.4069 + 4.23937i −0.493130 + 0.168500i
\(634\) 0 0
\(635\) 0.209281 + 0.362485i 0.00830506 + 0.0143848i
\(636\) 0 0
\(637\) 5.06326 + 13.9112i 0.200614 + 0.551182i
\(638\) 0 0
\(639\) 17.4823 + 33.2565i 0.691590 + 1.31561i
\(640\) 0 0
\(641\) 28.6682 24.0555i 1.13233 0.950135i 0.133166 0.991094i \(-0.457486\pi\)
0.999161 + 0.0409586i \(0.0130412\pi\)
\(642\) 0 0
\(643\) −1.81700 10.3047i −0.0716554 0.406378i −0.999446 0.0332769i \(-0.989406\pi\)
0.927791 0.373101i \(-0.121705\pi\)
\(644\) 0 0
\(645\) 2.84797 + 5.16653i 0.112139 + 0.203432i
\(646\) 0 0
\(647\) 15.2706i 0.600348i 0.953884 + 0.300174i \(0.0970448\pi\)
−0.953884 + 0.300174i \(0.902955\pi\)
\(648\) 0 0
\(649\) −2.67071 + 0.470919i −0.104835 + 0.0184852i
\(650\) 0 0
\(651\) −11.4575 4.42913i −0.449057 0.173591i
\(652\) 0 0
\(653\) 2.32583 + 1.34282i 0.0910168 + 0.0525486i 0.544818 0.838555i \(-0.316599\pi\)
−0.453801 + 0.891103i \(0.649932\pi\)
\(654\) 0 0
\(655\) −5.77850 + 2.10320i −0.225785 + 0.0821789i
\(656\) 0 0
\(657\) 48.4429 + 1.92020i 1.88994 + 0.0749142i
\(658\) 0 0
\(659\) 5.97002 33.8577i 0.232559 1.31891i −0.615134 0.788422i \(-0.710898\pi\)
0.847694 0.530486i \(-0.177991\pi\)
\(660\) 0 0
\(661\) 11.2236 13.3757i 0.436546 0.520256i −0.502253 0.864721i \(-0.667495\pi\)
0.938799 + 0.344465i \(0.111940\pi\)
\(662\) 0 0
\(663\) −28.3915 + 4.42824i −1.10263 + 0.171979i
\(664\) 0 0
\(665\) 3.30123 0.470429i 0.128016 0.0182425i
\(666\) 0 0
\(667\) 1.11750 3.07031i 0.0432698 0.118883i
\(668\) 0 0
\(669\) 3.85160 19.5686i 0.148912 0.756565i
\(670\) 0 0
\(671\) −16.8352 2.96851i −0.649917 0.114598i
\(672\) 0 0
\(673\) −38.2505 + 22.0839i −1.47445 + 0.851273i −0.999586 0.0287864i \(-0.990836\pi\)
−0.474863 + 0.880060i \(0.657502\pi\)
\(674\) 0 0
\(675\) −6.99733 23.4794i −0.269328 0.903723i
\(676\) 0 0
\(677\) 9.28464 16.0815i 0.356838 0.618061i −0.630593 0.776114i \(-0.717188\pi\)
0.987431 + 0.158053i \(0.0505216\pi\)
\(678\) 0 0
\(679\) 7.63791 + 9.10251i 0.293116 + 0.349322i
\(680\) 0 0
\(681\) 1.67690 + 2.08080i 0.0642589 + 0.0797364i
\(682\) 0 0
\(683\) −18.9873 −0.726527 −0.363264 0.931686i \(-0.618338\pi\)
−0.363264 + 0.931686i \(0.618338\pi\)
\(684\) 0 0
\(685\) −7.23041 −0.276260
\(686\) 0 0
\(687\) 8.88312 + 11.0227i 0.338912 + 0.420544i
\(688\) 0 0
\(689\) −3.55195 4.23305i −0.135319 0.161266i
\(690\) 0 0
\(691\) −7.53839 + 13.0569i −0.286774 + 0.496707i −0.973038 0.230646i \(-0.925916\pi\)
0.686264 + 0.727352i \(0.259249\pi\)
\(692\) 0 0
\(693\) −6.09467 1.32550i −0.231518 0.0503517i
\(694\) 0 0
\(695\) 3.34547 1.93151i 0.126901 0.0732662i
\(696\) 0 0
\(697\) −43.1781 7.61346i −1.63549 0.288380i
\(698\) 0 0
\(699\) 2.80804 14.2666i 0.106210 0.539613i
\(700\) 0 0
\(701\) −4.16179 + 11.4344i −0.157189 + 0.431872i −0.993140 0.116931i \(-0.962694\pi\)
0.835951 + 0.548804i \(0.184917\pi\)
\(702\) 0 0
\(703\) 0.922720 27.9638i 0.0348010 1.05468i
\(704\) 0 0
\(705\) −11.6832 + 1.82224i −0.440017 + 0.0686297i
\(706\) 0 0
\(707\) 2.90133 3.45768i 0.109116 0.130039i
\(708\) 0 0
\(709\) −6.71310 + 38.0719i −0.252116 + 1.42982i 0.551253 + 0.834338i \(0.314150\pi\)
−0.803369 + 0.595481i \(0.796961\pi\)
\(710\) 0 0
\(711\) −0.950637 + 23.9827i −0.0356517 + 0.899421i
\(712\) 0 0
\(713\) −2.86824 + 1.04395i −0.107417 + 0.0390964i
\(714\) 0 0
\(715\) −2.00744 1.15900i −0.0750740 0.0433440i
\(716\) 0 0
\(717\) −14.1932 5.48666i −0.530056 0.204903i
\(718\) 0 0
\(719\) −26.0696 + 4.59678i −0.972233 + 0.171431i −0.637135 0.770752i \(-0.719881\pi\)
−0.335098 + 0.942183i \(0.608769\pi\)
\(720\) 0 0
\(721\) 14.6514i 0.545646i
\(722\) 0 0
\(723\) 11.2370 + 20.3852i 0.417909 + 0.758134i
\(724\) 0 0
\(725\) 4.33752 + 24.5993i 0.161091 + 0.913595i
\(726\) 0 0
\(727\) −23.0429 + 19.3353i −0.854614 + 0.717107i −0.960801 0.277240i \(-0.910580\pi\)
0.106187 + 0.994346i \(0.466136\pi\)
\(728\) 0 0
\(729\) 16.1773 21.6170i 0.599160 0.800629i
\(730\) 0 0
\(731\) 12.0964 + 33.2345i 0.447400 + 1.22922i
\(732\) 0 0
\(733\) 4.85445 + 8.40816i 0.179303 + 0.310563i 0.941642 0.336616i \(-0.109282\pi\)
−0.762339 + 0.647178i \(0.775949\pi\)
\(734\) 0 0
\(735\) 4.32804 1.47887i 0.159642 0.0545489i
\(736\) 0 0
\(737\) 10.3079 + 8.64938i 0.379697 + 0.318604i
\(738\) 0 0
\(739\) 46.3353 + 16.8647i 1.70447 + 0.620377i 0.996322 0.0856846i \(-0.0273078\pi\)
0.708150 + 0.706062i \(0.249530\pi\)
\(740\) 0 0
\(741\) −10.2494 20.1371i −0.376520 0.739756i
\(742\) 0 0
\(743\) 6.36036 + 2.31498i 0.233339 + 0.0849285i 0.456043 0.889958i \(-0.349266\pi\)
−0.222704 + 0.974886i \(0.571488\pi\)
\(744\) 0 0
\(745\) −8.06409 6.76658i −0.295445 0.247908i
\(746\) 0 0
\(747\) 10.0105 11.0130i 0.366264 0.402944i
\(748\) 0 0
\(749\) 8.32539 + 14.4200i 0.304203 + 0.526895i
\(750\) 0 0
\(751\) −7.71871 21.2070i −0.281660 0.773853i −0.997165 0.0752462i \(-0.976026\pi\)
0.715505 0.698607i \(-0.246196\pi\)
\(752\) 0 0
\(753\) 13.6051 + 0.269537i 0.495797 + 0.00982247i
\(754\) 0 0
\(755\) 1.73017 1.45179i 0.0629675 0.0528360i
\(756\) 0 0
\(757\) −9.07767 51.4820i −0.329933 1.87115i −0.472457 0.881354i \(-0.656633\pi\)
0.142523 0.989791i \(-0.454478\pi\)
\(758\) 0 0
\(759\) −1.35727 + 0.748174i −0.0492659 + 0.0271570i
\(760\) 0 0
\(761\) 16.8329i 0.610193i 0.952321 + 0.305097i \(0.0986888\pi\)
−0.952321 + 0.305097i \(0.901311\pi\)
\(762\) 0 0
\(763\) −0.0450412 + 0.00794198i −0.00163060 + 0.000287519i
\(764\) 0 0
\(765\) 1.19410 + 8.79699i 0.0431728 + 0.318056i
\(766\) 0 0
\(767\) 4.84480 + 2.79715i 0.174936 + 0.100999i
\(768\) 0 0
\(769\) 2.83204 1.03078i 0.102126 0.0371708i −0.290452 0.956890i \(-0.593806\pi\)
0.392578 + 0.919719i \(0.371583\pi\)
\(770\) 0 0
\(771\) 18.2137 + 11.0024i 0.655949 + 0.396240i
\(772\) 0 0
\(773\) −8.98386 + 50.9500i −0.323127 + 1.83254i 0.199396 + 0.979919i \(0.436102\pi\)
−0.522523 + 0.852625i \(0.675009\pi\)
\(774\) 0 0
\(775\) 14.9994 17.8755i 0.538793 0.642108i
\(776\) 0 0
\(777\) 2.45522 + 15.7416i 0.0880806 + 0.564726i
\(778\) 0 0
\(779\) −4.86382 34.1319i −0.174265 1.22290i
\(780\) 0 0
\(781\) −6.21447 + 17.0741i −0.222371 + 0.610960i
\(782\) 0 0
\(783\) −18.9157 + 19.9993i −0.675991 + 0.714718i
\(784\) 0 0
\(785\) 5.34270 + 0.942061i 0.190689 + 0.0336236i
\(786\) 0 0
\(787\) −14.8092 + 8.55010i −0.527891 + 0.304778i −0.740157 0.672434i \(-0.765249\pi\)
0.212266 + 0.977212i \(0.431916\pi\)
\(788\) 0 0
\(789\) −31.0902 27.1552i −1.10684 0.966749i
\(790\) 0 0
\(791\) 7.41407 12.8416i 0.263614 0.456593i
\(792\) 0 0
\(793\) 22.6675 + 27.0141i 0.804948 + 0.959300i
\