Properties

Label 912.2.cc.c.497.1
Level $912$
Weight $2$
Character 912.497
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 497.1
Root \(-0.442647 + 1.67453i\) of defining polynomial
Character \(\chi\) \(=\) 912.497
Dual form 912.2.cc.c.545.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.57223 + 0.726702i) q^{3} +(-1.96615 - 0.346685i) q^{5} +(-0.910931 - 1.57778i) q^{7} +(1.94381 - 2.28508i) q^{9} +O(q^{10})\) \(q+(-1.57223 + 0.726702i) q^{3} +(-1.96615 - 0.346685i) q^{5} +(-0.910931 - 1.57778i) q^{7} +(1.94381 - 2.28508i) q^{9} +(4.10844 + 2.37201i) q^{11} +(0.151321 - 0.415752i) q^{13} +(3.34317 - 0.883735i) q^{15} +(-1.07476 + 1.28085i) q^{17} +(3.58212 - 2.48363i) q^{19} +(2.57877 + 1.81865i) q^{21} +(-5.93571 + 1.04663i) q^{23} +(-0.952914 - 0.346832i) q^{25} +(-1.39554 + 5.00524i) q^{27} +(-4.91935 + 4.12783i) q^{29} +(-4.88683 + 2.82141i) q^{31} +(-8.18314 - 0.743731i) q^{33} +(1.24403 + 3.41795i) q^{35} +5.80180i q^{37} +(0.0642158 + 0.763624i) q^{39} +(3.75563 - 1.36694i) q^{41} +(-2.15807 + 12.2390i) q^{43} +(-4.61402 + 3.81892i) q^{45} +(-6.92588 - 8.25394i) q^{47} +(1.84041 - 3.18768i) q^{49} +(0.758974 - 2.79482i) q^{51} +(0.424873 + 2.40957i) q^{53} +(-7.25545 - 6.08805i) q^{55} +(-3.82705 + 6.50797i) q^{57} +(-3.87172 - 3.24876i) q^{59} +(1.80210 + 10.2202i) q^{61} +(-5.37603 - 0.985349i) q^{63} +(-0.441656 + 0.764970i) q^{65} +(-5.27060 - 6.28126i) q^{67} +(8.57172 - 5.95903i) q^{69} +(-0.897109 + 5.08776i) q^{71} +(-13.5869 + 4.94524i) q^{73} +(1.75024 - 0.147184i) q^{75} -8.64294i q^{77} +(3.23544 + 8.88931i) q^{79} +(-1.44321 - 8.88353i) q^{81} +(0.523324 - 0.302141i) q^{83} +(2.55719 - 2.14574i) q^{85} +(4.73465 - 10.0648i) q^{87} +(4.07161 + 1.48195i) q^{89} +(-0.793809 + 0.139970i) q^{91} +(5.63289 - 7.98717i) q^{93} +(-7.90401 + 3.64132i) q^{95} +(1.64505 - 1.96049i) q^{97} +(13.4062 - 4.77739i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 3q^{3} - 3q^{9} + O(q^{10}) \) \( 18q - 3q^{3} - 3q^{9} - 12q^{13} - 18q^{15} + 6q^{17} + 6q^{19} - 18q^{25} + 6q^{27} - 6q^{29} - 24q^{33} + 24q^{35} - 6q^{39} + 3q^{41} + 6q^{43} - 54q^{45} - 30q^{47} + 21q^{49} - 42q^{51} - 60q^{53} - 30q^{55} + 12q^{57} - 3q^{59} + 54q^{61} + 18q^{63} + 24q^{65} + 15q^{67} + 30q^{69} - 36q^{71} - 42q^{73} + 6q^{79} - 3q^{81} - 36q^{83} - 60q^{89} + 18q^{91} - 66q^{93} - 6q^{95} + 9q^{97} + 102q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\) \(1\) \(-1\) \(1\)

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
\(3\) −1.57223 + 0.726702i −0.907727 + 0.419561i
\(4\) 0 0
\(5\) −1.96615 0.346685i −0.879288 0.155042i −0.284260 0.958747i \(-0.591748\pi\)
−0.595028 + 0.803705i \(0.702859\pi\)
\(6\) 0 0
\(7\) −0.910931 1.57778i −0.344300 0.596344i 0.640927 0.767602i \(-0.278550\pi\)
−0.985226 + 0.171258i \(0.945217\pi\)
\(8\) 0 0
\(9\) 1.94381 2.28508i 0.647937 0.761694i
\(10\) 0 0
\(11\) 4.10844 + 2.37201i 1.23874 + 0.715187i 0.968837 0.247701i \(-0.0796749\pi\)
0.269903 + 0.962887i \(0.413008\pi\)
\(12\) 0 0
\(13\) 0.151321 0.415752i 0.0419690 0.115309i −0.916938 0.399030i \(-0.869347\pi\)
0.958907 + 0.283721i \(0.0915691\pi\)
\(14\) 0 0
\(15\) 3.34317 0.883735i 0.863203 0.228179i
\(16\) 0 0
\(17\) −1.07476 + 1.28085i −0.260668 + 0.310652i −0.880466 0.474110i \(-0.842770\pi\)
0.619798 + 0.784761i \(0.287214\pi\)
\(18\) 0 0
\(19\) 3.58212 2.48363i 0.821794 0.569785i
\(20\) 0 0
\(21\) 2.57877 + 1.81865i 0.562733 + 0.396863i
\(22\) 0 0
\(23\) −5.93571 + 1.04663i −1.23768 + 0.218237i −0.753922 0.656964i \(-0.771840\pi\)
−0.483760 + 0.875201i \(0.660729\pi\)
\(24\) 0 0
\(25\) −0.952914 0.346832i −0.190583 0.0693665i
\(26\) 0 0
\(27\) −1.39554 + 5.00524i −0.268572 + 0.963260i
\(28\) 0 0
\(29\) −4.91935 + 4.12783i −0.913501 + 0.766518i −0.972782 0.231723i \(-0.925564\pi\)
0.0592808 + 0.998241i \(0.481119\pi\)
\(30\) 0 0
\(31\) −4.88683 + 2.82141i −0.877700 + 0.506741i −0.869899 0.493229i \(-0.835816\pi\)
−0.00780088 + 0.999970i \(0.502483\pi\)
\(32\) 0 0
\(33\) −8.18314 0.743731i −1.42450 0.129467i
\(34\) 0 0
\(35\) 1.24403 + 3.41795i 0.210280 + 0.577740i
\(36\) 0 0
\(37\) 5.80180i 0.953811i 0.878955 + 0.476905i \(0.158242\pi\)
−0.878955 + 0.476905i \(0.841758\pi\)
\(38\) 0 0
\(39\) 0.0642158 + 0.763624i 0.0102828 + 0.122278i
\(40\) 0 0
\(41\) 3.75563 1.36694i 0.586530 0.213480i −0.0316723 0.999498i \(-0.510083\pi\)
0.618203 + 0.786019i \(0.287861\pi\)
\(42\) 0 0
\(43\) −2.15807 + 12.2390i −0.329102 + 1.86643i 0.150023 + 0.988683i \(0.452065\pi\)
−0.479125 + 0.877747i \(0.659046\pi\)
\(44\) 0 0
\(45\) −4.61402 + 3.81892i −0.687818 + 0.569291i
\(46\) 0 0
\(47\) −6.92588 8.25394i −1.01024 1.20396i −0.978876 0.204453i \(-0.934459\pi\)
−0.0313665 0.999508i \(-0.509986\pi\)
\(48\) 0 0
\(49\) 1.84041 3.18768i 0.262916 0.455383i
\(50\) 0 0
\(51\) 0.758974 2.79482i 0.106278 0.391353i
\(52\) 0 0
\(53\) 0.424873 + 2.40957i 0.0583608 + 0.330981i 0.999984 0.00568857i \(-0.00181074\pi\)
−0.941623 + 0.336669i \(0.890700\pi\)
\(54\) 0 0
\(55\) −7.25545 6.08805i −0.978325 0.820912i
\(56\) 0 0
\(57\) −3.82705 + 6.50797i −0.506905 + 0.862002i
\(58\) 0 0
\(59\) −3.87172 3.24876i −0.504055 0.422952i 0.354977 0.934875i \(-0.384489\pi\)
−0.859031 + 0.511923i \(0.828933\pi\)
\(60\) 0 0
\(61\) 1.80210 + 10.2202i 0.230735 + 1.30856i 0.851412 + 0.524498i \(0.175747\pi\)
−0.620677 + 0.784067i \(0.713142\pi\)
\(62\) 0 0
\(63\) −5.37603 0.985349i −0.677316 0.124142i
\(64\) 0 0
\(65\) −0.441656 + 0.764970i −0.0547806 + 0.0948828i
\(66\) 0 0
\(67\) −5.27060 6.28126i −0.643906 0.767378i 0.341075 0.940036i \(-0.389209\pi\)
−0.984982 + 0.172658i \(0.944764\pi\)
\(68\) 0 0
\(69\) 8.57172 5.95903i 1.03191 0.717383i
\(70\) 0 0
\(71\) −0.897109 + 5.08776i −0.106467 + 0.603806i 0.884157 + 0.467190i \(0.154734\pi\)
−0.990624 + 0.136616i \(0.956377\pi\)
\(72\) 0 0
\(73\) −13.5869 + 4.94524i −1.59023 + 0.578796i −0.977396 0.211415i \(-0.932193\pi\)
−0.612834 + 0.790212i \(0.709971\pi\)
\(74\) 0 0
\(75\) 1.75024 0.147184i 0.202101 0.0169954i
\(76\) 0 0
\(77\) 8.64294i 0.984954i
\(78\) 0 0
\(79\) 3.23544 + 8.88931i 0.364016 + 1.00013i 0.977595 + 0.210493i \(0.0675068\pi\)
−0.613580 + 0.789633i \(0.710271\pi\)
\(80\) 0 0
\(81\) −1.44321 8.88353i −0.160356 0.987059i
\(82\) 0 0
\(83\) 0.523324 0.302141i 0.0574423 0.0331643i −0.471004 0.882131i \(-0.656108\pi\)
0.528446 + 0.848967i \(0.322775\pi\)
\(84\) 0 0
\(85\) 2.55719 2.14574i 0.277366 0.232738i
\(86\) 0 0
\(87\) 4.73465 10.0648i 0.507608 1.07906i
\(88\) 0 0
\(89\) 4.07161 + 1.48195i 0.431590 + 0.157086i 0.548675 0.836036i \(-0.315133\pi\)
−0.117084 + 0.993122i \(0.537355\pi\)
\(90\) 0 0
\(91\) −0.793809 + 0.139970i −0.0832137 + 0.0146728i
\(92\) 0 0
\(93\) 5.63289 7.98717i 0.584104 0.828231i
\(94\) 0 0
\(95\) −7.90401 + 3.64132i −0.810935 + 0.373592i
\(96\) 0 0
\(97\) 1.64505 1.96049i 0.167029 0.199057i −0.676037 0.736868i \(-0.736304\pi\)
0.843066 + 0.537810i \(0.180748\pi\)
\(98\) 0 0
\(99\) 13.4062 4.77739i 1.34738 0.480145i
\(100\) 0 0
\(101\) −2.72562 + 7.48859i −0.271210 + 0.745142i 0.727073 + 0.686560i \(0.240880\pi\)
−0.998283 + 0.0585821i \(0.981342\pi\)
\(102\) 0 0
\(103\) 13.3041 + 7.68115i 1.31090 + 0.756846i 0.982245 0.187605i \(-0.0600725\pi\)
0.328651 + 0.944451i \(0.393406\pi\)
\(104\) 0 0
\(105\) −4.43974 4.46977i −0.433274 0.436204i
\(106\) 0 0
\(107\) 9.34857 + 16.1922i 0.903760 + 1.56536i 0.822573 + 0.568660i \(0.192538\pi\)
0.0811876 + 0.996699i \(0.474129\pi\)
\(108\) 0 0
\(109\) −11.2420 1.98227i −1.07679 0.189867i −0.392994 0.919541i \(-0.628561\pi\)
−0.683795 + 0.729674i \(0.739672\pi\)
\(110\) 0 0
\(111\) −4.21618 9.12177i −0.400182 0.865800i
\(112\) 0 0
\(113\) −0.594179 −0.0558957 −0.0279478 0.999609i \(-0.508897\pi\)
−0.0279478 + 0.999609i \(0.508897\pi\)
\(114\) 0 0
\(115\) 12.0333 1.12212
\(116\) 0 0
\(117\) −0.655888 1.15393i −0.0606369 0.106680i
\(118\) 0 0
\(119\) 2.99993 + 0.528968i 0.275003 + 0.0484905i
\(120\) 0 0
\(121\) 5.75283 + 9.96419i 0.522984 + 0.905835i
\(122\) 0 0
\(123\) −4.91135 + 4.87836i −0.442842 + 0.439867i
\(124\) 0 0
\(125\) 10.3983 + 6.00348i 0.930056 + 0.536968i
\(126\) 0 0
\(127\) −4.51501 + 12.4049i −0.400642 + 1.10076i 0.561326 + 0.827595i \(0.310291\pi\)
−0.961968 + 0.273161i \(0.911931\pi\)
\(128\) 0 0
\(129\) −5.50112 20.8108i −0.484347 1.83229i
\(130\) 0 0
\(131\) 4.54726 5.41921i 0.397296 0.473479i −0.529898 0.848062i \(-0.677770\pi\)
0.927193 + 0.374583i \(0.122214\pi\)
\(132\) 0 0
\(133\) −7.18169 3.38937i −0.622731 0.293896i
\(134\) 0 0
\(135\) 4.47908 9.35724i 0.385498 0.805343i
\(136\) 0 0
\(137\) −9.23589 + 1.62854i −0.789075 + 0.139135i −0.553641 0.832755i \(-0.686762\pi\)
−0.235434 + 0.971890i \(0.575651\pi\)
\(138\) 0 0
\(139\) −10.1792 3.70494i −0.863392 0.314249i −0.127904 0.991787i \(-0.540825\pi\)
−0.735488 + 0.677538i \(0.763047\pi\)
\(140\) 0 0
\(141\) 16.8872 + 7.94404i 1.42216 + 0.669009i
\(142\) 0 0
\(143\) 1.60786 1.34916i 0.134456 0.112822i
\(144\) 0 0
\(145\) 11.1032 6.41046i 0.922074 0.532359i
\(146\) 0 0
\(147\) −0.577052 + 6.34920i −0.0475944 + 0.523673i
\(148\) 0 0
\(149\) −3.85231 10.5841i −0.315594 0.867086i −0.991501 0.130100i \(-0.958470\pi\)
0.675907 0.736987i \(-0.263752\pi\)
\(150\) 0 0
\(151\) 3.54669i 0.288625i −0.989532 0.144313i \(-0.953903\pi\)
0.989532 0.144313i \(-0.0460971\pi\)
\(152\) 0 0
\(153\) 0.837717 + 4.94564i 0.0677254 + 0.399832i
\(154\) 0 0
\(155\) 10.5864 3.85312i 0.850318 0.309490i
\(156\) 0 0
\(157\) −0.0548481 + 0.311059i −0.00437736 + 0.0248252i −0.986918 0.161222i \(-0.948457\pi\)
0.982541 + 0.186047i \(0.0595677\pi\)
\(158\) 0 0
\(159\) −2.41904 3.47965i −0.191842 0.275954i
\(160\) 0 0
\(161\) 7.05837 + 8.41184i 0.556277 + 0.662946i
\(162\) 0 0
\(163\) −0.624535 + 1.08173i −0.0489174 + 0.0847274i −0.889447 0.457038i \(-0.848910\pi\)
0.840530 + 0.541765i \(0.182244\pi\)
\(164\) 0 0
\(165\) 15.8314 + 4.29926i 1.23248 + 0.334697i
\(166\) 0 0
\(167\) −0.177553 1.00695i −0.0137395 0.0779205i 0.977167 0.212472i \(-0.0681516\pi\)
−0.990907 + 0.134552i \(0.957040\pi\)
\(168\) 0 0
\(169\) 9.80863 + 8.23041i 0.754510 + 0.633109i
\(170\) 0 0
\(171\) 1.28765 13.0131i 0.0984689 0.995140i
\(172\) 0 0
\(173\) −11.5762 9.71361i −0.880124 0.738512i 0.0860802 0.996288i \(-0.472566\pi\)
−0.966205 + 0.257776i \(0.917010\pi\)
\(174\) 0 0
\(175\) 0.320814 + 1.81943i 0.0242513 + 0.137536i
\(176\) 0 0
\(177\) 8.44811 + 2.29421i 0.634998 + 0.172443i
\(178\) 0 0
\(179\) −2.97218 + 5.14797i −0.222151 + 0.384777i −0.955461 0.295118i \(-0.904641\pi\)
0.733310 + 0.679895i \(0.237974\pi\)
\(180\) 0 0
\(181\) −4.17230 4.97236i −0.310125 0.369593i 0.588358 0.808600i \(-0.299774\pi\)
−0.898483 + 0.439008i \(0.855330\pi\)
\(182\) 0 0
\(183\) −10.2604 14.7589i −0.758468 1.09101i
\(184\) 0 0
\(185\) 2.01140 11.4072i 0.147881 0.838675i
\(186\) 0 0
\(187\) −7.45377 + 2.71295i −0.545073 + 0.198390i
\(188\) 0 0
\(189\) 9.16841 2.35758i 0.666904 0.171488i
\(190\) 0 0
\(191\) 23.8639i 1.72673i −0.504577 0.863367i \(-0.668352\pi\)
0.504577 0.863367i \(-0.331648\pi\)
\(192\) 0 0
\(193\) −0.726280 1.99544i −0.0522788 0.143635i 0.910805 0.412837i \(-0.135462\pi\)
−0.963084 + 0.269202i \(0.913240\pi\)
\(194\) 0 0
\(195\) 0.138479 1.52366i 0.00991669 0.109112i
\(196\) 0 0
\(197\) 3.27574 1.89125i 0.233387 0.134746i −0.378747 0.925500i \(-0.623645\pi\)
0.612133 + 0.790755i \(0.290312\pi\)
\(198\) 0 0
\(199\) 10.5692 8.86860i 0.749230 0.628679i −0.186069 0.982537i \(-0.559575\pi\)
0.935299 + 0.353858i \(0.115130\pi\)
\(200\) 0 0
\(201\) 12.8512 + 6.04542i 0.906453 + 0.426411i
\(202\) 0 0
\(203\) 10.9940 + 4.00149i 0.771627 + 0.280849i
\(204\) 0 0
\(205\) −7.85802 + 1.38558i −0.548828 + 0.0967731i
\(206\) 0 0
\(207\) −9.14627 + 15.5980i −0.635710 + 1.08414i
\(208\) 0 0
\(209\) 20.6081 1.70704i 1.42549 0.118078i
\(210\) 0 0
\(211\) −10.3613 + 12.3481i −0.713299 + 0.850077i −0.993961 0.109730i \(-0.965002\pi\)
0.280662 + 0.959807i \(0.409446\pi\)
\(212\) 0 0
\(213\) −2.28682 8.65106i −0.156690 0.592761i
\(214\) 0 0
\(215\) 8.48615 23.3155i 0.578751 1.59010i
\(216\) 0 0
\(217\) 8.90313 + 5.14022i 0.604384 + 0.348941i
\(218\) 0 0
\(219\) 17.7681 17.6487i 1.20065 1.19259i
\(220\) 0 0
\(221\) 0.369882 + 0.640654i 0.0248809 + 0.0430951i
\(222\) 0 0
\(223\) −1.05803 0.186559i −0.0708508 0.0124929i 0.138110 0.990417i \(-0.455897\pi\)
−0.208961 + 0.977924i \(0.567008\pi\)
\(224\) 0 0
\(225\) −2.64482 + 1.50331i −0.176322 + 0.100221i
\(226\) 0 0
\(227\) 18.7633 1.24536 0.622682 0.782475i \(-0.286043\pi\)
0.622682 + 0.782475i \(0.286043\pi\)
\(228\) 0 0
\(229\) −11.6264 −0.768296 −0.384148 0.923271i \(-0.625505\pi\)
−0.384148 + 0.923271i \(0.625505\pi\)
\(230\) 0 0
\(231\) 6.28083 + 13.5887i 0.413249 + 0.894069i
\(232\) 0 0
\(233\) −16.0133 2.82357i −1.04907 0.184979i −0.377565 0.925983i \(-0.623239\pi\)
−0.671500 + 0.741004i \(0.734350\pi\)
\(234\) 0 0
\(235\) 10.7558 + 18.6296i 0.701630 + 1.21526i
\(236\) 0 0
\(237\) −11.5467 11.6248i −0.750041 0.755114i
\(238\) 0 0
\(239\) −5.90043 3.40661i −0.381667 0.220356i 0.296876 0.954916i \(-0.404055\pi\)
−0.678543 + 0.734560i \(0.737388\pi\)
\(240\) 0 0
\(241\) −6.63839 + 18.2388i −0.427616 + 1.17487i 0.519639 + 0.854386i \(0.326066\pi\)
−0.947255 + 0.320480i \(0.896156\pi\)
\(242\) 0 0
\(243\) 8.72473 + 12.9182i 0.559692 + 0.828701i
\(244\) 0 0
\(245\) −4.72364 + 5.62942i −0.301782 + 0.359650i
\(246\) 0 0
\(247\) −0.490525 1.86510i −0.0312114 0.118674i
\(248\) 0 0
\(249\) −0.603219 + 0.855336i −0.0382274 + 0.0542047i
\(250\) 0 0
\(251\) −16.8226 + 2.96628i −1.06183 + 0.187230i −0.677170 0.735827i \(-0.736794\pi\)
−0.384664 + 0.923057i \(0.625683\pi\)
\(252\) 0 0
\(253\) −26.8691 9.77955i −1.68925 0.614835i
\(254\) 0 0
\(255\) −2.46118 + 5.23190i −0.154125 + 0.327635i
\(256\) 0 0
\(257\) 12.1113 10.1626i 0.755485 0.633927i −0.181462 0.983398i \(-0.558083\pi\)
0.936947 + 0.349471i \(0.113639\pi\)
\(258\) 0 0
\(259\) 9.15396 5.28504i 0.568800 0.328397i
\(260\) 0 0
\(261\) −0.129859 + 19.2648i −0.00803808 + 1.19246i
\(262\) 0 0
\(263\) −0.888930 2.44232i −0.0548138 0.150600i 0.909264 0.416220i \(-0.136645\pi\)
−0.964078 + 0.265620i \(0.914423\pi\)
\(264\) 0 0
\(265\) 4.88488i 0.300076i
\(266\) 0 0
\(267\) −7.47844 + 0.628889i −0.457673 + 0.0384874i
\(268\) 0 0
\(269\) 29.9875 10.9146i 1.82837 0.665473i 0.835039 0.550191i \(-0.185445\pi\)
0.993333 0.115281i \(-0.0367769\pi\)
\(270\) 0 0
\(271\) 3.48942 19.7895i 0.211967 1.20212i −0.674126 0.738617i \(-0.735479\pi\)
0.886093 0.463508i \(-0.153410\pi\)
\(272\) 0 0
\(273\) 1.14633 0.796927i 0.0693792 0.0482322i
\(274\) 0 0
\(275\) −3.09230 3.68526i −0.186473 0.222229i
\(276\) 0 0
\(277\) 4.04017 6.99778i 0.242750 0.420456i −0.718746 0.695272i \(-0.755284\pi\)
0.961497 + 0.274816i \(0.0886171\pi\)
\(278\) 0 0
\(279\) −3.05191 + 16.6511i −0.182713 + 0.996875i
\(280\) 0 0
\(281\) 2.05091 + 11.6313i 0.122347 + 0.693866i 0.982848 + 0.184417i \(0.0590396\pi\)
−0.860501 + 0.509449i \(0.829849\pi\)
\(282\) 0 0
\(283\) −11.0055 9.23472i −0.654210 0.548947i 0.254135 0.967169i \(-0.418209\pi\)
−0.908345 + 0.418221i \(0.862654\pi\)
\(284\) 0 0
\(285\) 9.78076 11.4689i 0.579363 0.679356i
\(286\) 0 0
\(287\) −5.57784 4.68036i −0.329249 0.276273i
\(288\) 0 0
\(289\) 2.46655 + 13.9885i 0.145091 + 0.822854i
\(290\) 0 0
\(291\) −1.16170 + 4.27779i −0.0681000 + 0.250769i
\(292\) 0 0
\(293\) −0.00324263 + 0.00561639i −0.000189436 + 0.000328113i −0.866120 0.499836i \(-0.833394\pi\)
0.865931 + 0.500164i \(0.166727\pi\)
\(294\) 0 0
\(295\) 6.48608 + 7.72981i 0.377634 + 0.450047i
\(296\) 0 0
\(297\) −17.6060 + 17.2535i −1.02160 + 1.00115i
\(298\) 0 0
\(299\) −0.463063 + 2.62616i −0.0267797 + 0.151875i
\(300\) 0 0
\(301\) 21.2763 7.74393i 1.22634 0.446353i
\(302\) 0 0
\(303\) −1.15666 13.7545i −0.0664486 0.790175i
\(304\) 0 0
\(305\) 20.7192i 1.18638i
\(306\) 0 0
\(307\) −4.66013 12.8036i −0.265968 0.730741i −0.998736 0.0502623i \(-0.983994\pi\)
0.732768 0.680478i \(-0.238228\pi\)
\(308\) 0 0
\(309\) −26.4991 2.40839i −1.50748 0.137008i
\(310\) 0 0
\(311\) −10.1422 + 5.85560i −0.575111 + 0.332041i −0.759188 0.650871i \(-0.774404\pi\)
0.184077 + 0.982912i \(0.441070\pi\)
\(312\) 0 0
\(313\) 1.34587 1.12932i 0.0760730 0.0638328i −0.603958 0.797016i \(-0.706411\pi\)
0.680031 + 0.733183i \(0.261966\pi\)
\(314\) 0 0
\(315\) 10.2285 + 3.80113i 0.576309 + 0.214170i
\(316\) 0 0
\(317\) −6.59148 2.39910i −0.370214 0.134747i 0.150211 0.988654i \(-0.452005\pi\)
−0.520426 + 0.853907i \(0.674227\pi\)
\(318\) 0 0
\(319\) −30.0021 + 5.29018i −1.67979 + 0.296193i
\(320\) 0 0
\(321\) −26.4650 18.6642i −1.47713 1.04174i
\(322\) 0 0
\(323\) −0.668758 + 7.25746i −0.0372107 + 0.403816i
\(324\) 0 0
\(325\) −0.288393 + 0.343693i −0.0159971 + 0.0190647i
\(326\) 0 0
\(327\) 19.1155 5.05300i 1.05709 0.279431i
\(328\) 0 0
\(329\) −6.71389 + 18.4463i −0.370149 + 1.01698i
\(330\) 0 0
\(331\) 1.36720 + 0.789353i 0.0751481 + 0.0433868i 0.537103 0.843517i \(-0.319519\pi\)
−0.461955 + 0.886903i \(0.652852\pi\)
\(332\) 0 0
\(333\) 13.2576 + 11.2776i 0.726512 + 0.618009i
\(334\) 0 0
\(335\) 8.18517 + 14.1771i 0.447203 + 0.774579i
\(336\) 0 0
\(337\) 32.2083 + 5.67918i 1.75450 + 0.309365i 0.956159 0.292847i \(-0.0946028\pi\)
0.798336 + 0.602212i \(0.205714\pi\)
\(338\) 0 0
\(339\) 0.934186 0.431791i 0.0507380 0.0234517i
\(340\) 0 0
\(341\) −26.7696 −1.44966
\(342\) 0 0
\(343\) −19.4590 −1.05069
\(344\) 0 0
\(345\) −18.9192 + 8.74465i −1.01857 + 0.470796i
\(346\) 0 0
\(347\) −2.28496 0.402900i −0.122663 0.0216288i 0.111980 0.993711i \(-0.464281\pi\)
−0.234643 + 0.972082i \(0.575392\pi\)
\(348\) 0 0
\(349\) 6.90604 + 11.9616i 0.369672 + 0.640291i 0.989514 0.144436i \(-0.0461367\pi\)
−0.619842 + 0.784727i \(0.712803\pi\)
\(350\) 0 0
\(351\) 1.86977 + 1.33760i 0.0998007 + 0.0713958i
\(352\) 0 0
\(353\) −12.6233 7.28806i −0.671870 0.387904i 0.124915 0.992167i \(-0.460134\pi\)
−0.796785 + 0.604263i \(0.793468\pi\)
\(354\) 0 0
\(355\) 3.52770 9.69228i 0.187231 0.514413i
\(356\) 0 0
\(357\) −5.10098 + 1.34839i −0.269972 + 0.0713645i
\(358\) 0 0
\(359\) −12.4925 + 14.8880i −0.659331 + 0.785760i −0.987290 0.158932i \(-0.949195\pi\)
0.327959 + 0.944692i \(0.393639\pi\)
\(360\) 0 0
\(361\) 6.66313 17.7933i 0.350691 0.936491i
\(362\) 0 0
\(363\) −16.2858 11.4854i −0.854780 0.602827i
\(364\) 0 0
\(365\) 28.4284 5.01269i 1.48801 0.262376i
\(366\) 0 0
\(367\) 7.10474 + 2.58591i 0.370865 + 0.134984i 0.520727 0.853723i \(-0.325661\pi\)
−0.149863 + 0.988707i \(0.547883\pi\)
\(368\) 0 0
\(369\) 4.17666 11.2390i 0.217428 0.585078i
\(370\) 0 0
\(371\) 3.41475 2.86531i 0.177285 0.148760i
\(372\) 0 0
\(373\) −5.00566 + 2.89002i −0.259183 + 0.149640i −0.623962 0.781455i \(-0.714478\pi\)
0.364779 + 0.931094i \(0.381145\pi\)
\(374\) 0 0
\(375\) −20.7113 1.88236i −1.06953 0.0972049i
\(376\) 0 0
\(377\) 0.971750 + 2.66986i 0.0500477 + 0.137505i
\(378\) 0 0
\(379\) 31.0884i 1.59690i 0.602058 + 0.798452i \(0.294347\pi\)
−0.602058 + 0.798452i \(0.705653\pi\)
\(380\) 0 0
\(381\) −1.91602 22.7844i −0.0981607 1.16728i
\(382\) 0 0
\(383\) 6.29971 2.29291i 0.321900 0.117162i −0.176016 0.984387i \(-0.556321\pi\)
0.497916 + 0.867225i \(0.334099\pi\)
\(384\) 0 0
\(385\) −2.99638 + 16.9933i −0.152709 + 0.866058i
\(386\) 0 0
\(387\) 23.7722 + 28.7216i 1.20841 + 1.46000i
\(388\) 0 0
\(389\) 22.9366 + 27.3348i 1.16293 + 1.38593i 0.908000 + 0.418971i \(0.137609\pi\)
0.254933 + 0.966959i \(0.417947\pi\)
\(390\) 0 0
\(391\) 5.03890 8.72763i 0.254828 0.441375i
\(392\) 0 0
\(393\) −3.21118 + 11.8247i −0.161983 + 0.596479i
\(394\) 0 0
\(395\) −3.27957 18.5994i −0.165013 0.935837i
\(396\) 0 0
\(397\) −23.1763 19.4472i −1.16319 0.976029i −0.163242 0.986586i \(-0.552195\pi\)
−0.999944 + 0.0105571i \(0.996640\pi\)
\(398\) 0 0
\(399\) 13.7543 + 0.109926i 0.688577 + 0.00550318i
\(400\) 0 0
\(401\) −14.3394 12.0322i −0.716074 0.600858i 0.210222 0.977654i \(-0.432581\pi\)
−0.926296 + 0.376796i \(0.877026\pi\)
\(402\) 0 0
\(403\) 0.433526 + 2.45865i 0.0215955 + 0.122474i
\(404\) 0 0
\(405\) −0.242228 + 17.9667i −0.0120364 + 0.892772i
\(406\) 0 0
\(407\) −13.7619 + 23.8363i −0.682153 + 1.18152i
\(408\) 0 0
\(409\) −9.76955 11.6429i −0.483073 0.575704i 0.468369 0.883533i \(-0.344842\pi\)
−0.951442 + 0.307829i \(0.900398\pi\)
\(410\) 0 0
\(411\) 13.3375 9.27216i 0.657889 0.457362i
\(412\) 0 0
\(413\) −1.59895 + 9.06811i −0.0786793 + 0.446212i
\(414\) 0 0
\(415\) −1.13368 + 0.412626i −0.0556502 + 0.0202550i
\(416\) 0 0
\(417\) 18.6965 1.57225i 0.915571 0.0769936i
\(418\) 0 0
\(419\) 6.74268i 0.329402i −0.986344 0.164701i \(-0.947334\pi\)
0.986344 0.164701i \(-0.0526659\pi\)
\(420\) 0 0
\(421\) 5.11036 + 14.0406i 0.249064 + 0.684297i 0.999721 + 0.0236056i \(0.00751459\pi\)
−0.750658 + 0.660691i \(0.770263\pi\)
\(422\) 0 0
\(423\) −32.3235 0.217884i −1.57162 0.0105939i
\(424\) 0 0
\(425\) 1.46839 0.847778i 0.0712276 0.0411233i
\(426\) 0 0
\(427\) 14.4836 12.1532i 0.700913 0.588136i
\(428\) 0 0
\(429\) −1.54749 + 3.28962i −0.0747137 + 0.158824i
\(430\) 0 0
\(431\) 12.6508 + 4.60452i 0.609368 + 0.221792i 0.628227 0.778030i \(-0.283781\pi\)
−0.0188586 + 0.999822i \(0.506003\pi\)
\(432\) 0 0
\(433\) 16.6663 2.93872i 0.800933 0.141226i 0.241824 0.970320i \(-0.422254\pi\)
0.559109 + 0.829094i \(0.311143\pi\)
\(434\) 0 0
\(435\) −12.7983 + 18.1474i −0.613634 + 0.870103i
\(436\) 0 0
\(437\) −18.6630 + 18.4913i −0.892772 + 0.884558i
\(438\) 0 0
\(439\) 9.65722 11.5090i 0.460914 0.549296i −0.484660 0.874702i \(-0.661057\pi\)
0.945574 + 0.325407i \(0.105501\pi\)
\(440\) 0 0
\(441\) −3.70671 10.4017i −0.176510 0.495321i
\(442\) 0 0
\(443\) −12.6699 + 34.8103i −0.601966 + 1.65389i 0.145320 + 0.989385i \(0.453579\pi\)
−0.747286 + 0.664503i \(0.768643\pi\)
\(444\) 0 0
\(445\) −7.49163 4.32529i −0.355137 0.205039i
\(446\) 0 0
\(447\) 13.7482 + 13.8412i 0.650269 + 0.654667i
\(448\) 0 0
\(449\) −5.81501 10.0719i −0.274427 0.475322i 0.695563 0.718465i \(-0.255155\pi\)
−0.969991 + 0.243143i \(0.921822\pi\)
\(450\) 0 0
\(451\) 18.6721 + 3.29240i 0.879236 + 0.155033i
\(452\) 0 0
\(453\) 2.57738 + 5.57621i 0.121096 + 0.261993i
\(454\) 0 0
\(455\) 1.60927 0.0754438
\(456\) 0 0
\(457\) 15.7379 0.736189 0.368094 0.929788i \(-0.380010\pi\)
0.368094 + 0.929788i \(0.380010\pi\)
\(458\) 0 0
\(459\) −4.91109 7.16692i −0.229230 0.334523i
\(460\) 0 0
\(461\) −5.96078 1.05105i −0.277621 0.0489521i 0.0331039 0.999452i \(-0.489461\pi\)
−0.310725 + 0.950500i \(0.600572\pi\)
\(462\) 0 0
\(463\) −4.59401 7.95705i −0.213502 0.369796i 0.739306 0.673369i \(-0.235154\pi\)
−0.952808 + 0.303574i \(0.901820\pi\)
\(464\) 0 0
\(465\) −13.8441 + 13.7511i −0.642006 + 0.637693i
\(466\) 0 0
\(467\) −0.179338 0.103541i −0.00829879 0.00479131i 0.495845 0.868411i \(-0.334858\pi\)
−0.504144 + 0.863620i \(0.668192\pi\)
\(468\) 0 0
\(469\) −5.10928 + 14.0376i −0.235925 + 0.648198i
\(470\) 0 0
\(471\) −0.139813 0.528915i −0.00644226 0.0243711i
\(472\) 0 0
\(473\) −37.8972 + 45.1642i −1.74252 + 2.07665i
\(474\) 0 0
\(475\) −4.27485 + 1.12429i −0.196144 + 0.0515862i
\(476\) 0 0
\(477\) 6.33195 + 3.71288i 0.289920 + 0.170001i
\(478\) 0 0
\(479\) −4.92232 + 0.867938i −0.224907 + 0.0396571i −0.284966 0.958538i \(-0.591982\pi\)
0.0600591 + 0.998195i \(0.480871\pi\)
\(480\) 0 0
\(481\) 2.41211 + 0.877937i 0.109983 + 0.0400305i
\(482\) 0 0
\(483\) −17.2103 8.09601i −0.783094 0.368381i
\(484\) 0 0
\(485\) −3.91408 + 3.28430i −0.177729 + 0.149132i
\(486\) 0 0
\(487\) 23.4422 13.5344i 1.06227 0.613300i 0.136209 0.990680i \(-0.456508\pi\)
0.926059 + 0.377380i \(0.123175\pi\)
\(488\) 0 0
\(489\) 0.195820 2.15457i 0.00885529 0.0974332i
\(490\) 0 0
\(491\) −2.14701 5.89886i −0.0968931 0.266212i 0.881771 0.471677i \(-0.156351\pi\)
−0.978664 + 0.205466i \(0.934129\pi\)
\(492\) 0 0
\(493\) 10.7374i 0.483587i
\(494\) 0 0
\(495\) −28.0149 + 4.74531i −1.25918 + 0.213286i
\(496\) 0 0
\(497\) 8.84457 3.21916i 0.396733 0.144399i
\(498\) 0 0
\(499\) 3.81949 21.6614i 0.170984 0.969699i −0.771694 0.635994i \(-0.780590\pi\)
0.942678 0.333704i \(-0.108299\pi\)
\(500\) 0 0
\(501\) 1.01091 + 1.45414i 0.0451641 + 0.0649660i
\(502\) 0 0
\(503\) 6.51623 + 7.76574i 0.290544 + 0.346257i 0.891496 0.453028i \(-0.149656\pi\)
−0.600952 + 0.799285i \(0.705212\pi\)
\(504\) 0 0
\(505\) 7.95516 13.7787i 0.354000 0.613146i
\(506\) 0 0
\(507\) −21.4025 5.81216i −0.950517 0.258127i
\(508\) 0 0
\(509\) −1.94826 11.0492i −0.0863553 0.489745i −0.997056 0.0766782i \(-0.975569\pi\)
0.910701 0.413067i \(-0.135543\pi\)
\(510\) 0 0
\(511\) 20.1793 + 16.9324i 0.892678 + 0.749045i
\(512\) 0 0
\(513\) 7.43220 + 21.3954i 0.328139 + 0.944629i
\(514\) 0 0
\(515\) −23.4950 19.7146i −1.03531 0.868730i
\(516\) 0 0
\(517\) −8.87612 50.3390i −0.390371 2.21391i
\(518\) 0 0
\(519\) 25.2594 + 6.85956i 1.10876 + 0.301101i
\(520\) 0 0
\(521\) −22.3984 + 38.7951i −0.981290 + 1.69964i −0.323904 + 0.946090i \(0.604995\pi\)
−0.657386 + 0.753554i \(0.728338\pi\)
\(522\) 0 0
\(523\) −25.4174 30.2913i −1.11143 1.32455i −0.940705 0.339226i \(-0.889835\pi\)
−0.170721 0.985319i \(-0.554610\pi\)
\(524\) 0 0
\(525\) −1.82657 2.62742i −0.0797182 0.114670i
\(526\) 0 0
\(527\) 1.63837 9.29163i 0.0713683 0.404750i
\(528\) 0 0
\(529\) 12.5243 4.55849i 0.544536 0.198195i
\(530\) 0 0
\(531\) −14.9496 + 2.53223i −0.648756 + 0.109889i
\(532\) 0 0
\(533\) 1.76826i 0.0765917i
\(534\) 0 0
\(535\) −12.7671 35.0773i −0.551969 1.51652i
\(536\) 0 0
\(537\) 0.931913 10.2537i 0.0402150 0.442479i
\(538\) 0 0
\(539\) 15.1224 8.73093i 0.651368 0.376068i
\(540\) 0 0
\(541\) 9.00083 7.55259i 0.386976 0.324711i −0.428458 0.903562i \(-0.640943\pi\)
0.815434 + 0.578850i \(0.196499\pi\)
\(542\) 0 0
\(543\) 10.1732 + 4.78567i 0.436576 + 0.205373i
\(544\) 0 0
\(545\) 21.4162 + 7.79487i 0.917370 + 0.333895i
\(546\) 0 0
\(547\) −3.60851 + 0.636278i −0.154289 + 0.0272053i −0.250259 0.968179i \(-0.580516\pi\)
0.0959702 + 0.995384i \(0.469405\pi\)
\(548\) 0 0
\(549\) 26.8570 + 15.7482i 1.14623 + 0.672117i
\(550\) 0 0
\(551\) −7.36969 + 27.0042i −0.313959 + 1.15042i
\(552\) 0 0
\(553\) 11.0781 13.2024i 0.471089 0.561422i
\(554\) 0 0
\(555\) 5.12726 + 19.3964i 0.217640 + 0.823333i
\(556\) 0 0
\(557\) 4.53013 12.4464i 0.191948 0.527372i −0.805964 0.591965i \(-0.798353\pi\)
0.997912 + 0.0645925i \(0.0205747\pi\)
\(558\) 0 0
\(559\) 4.76183 + 2.74924i 0.201404 + 0.116281i
\(560\) 0 0
\(561\) 9.74752 9.68204i 0.411541 0.408776i
\(562\) 0 0
\(563\) 2.30395 + 3.99056i 0.0970999 + 0.168182i 0.910483 0.413546i \(-0.135710\pi\)
−0.813383 + 0.581728i \(0.802377\pi\)
\(564\) 0 0
\(565\) 1.16824 + 0.205993i 0.0491484 + 0.00866619i
\(566\) 0 0
\(567\) −12.7016 + 10.3693i −0.533416 + 0.435472i
\(568\) 0 0
\(569\) 24.3659 1.02147 0.510736 0.859738i \(-0.329373\pi\)
0.510736 + 0.859738i \(0.329373\pi\)
\(570\) 0 0
\(571\) 20.9944 0.878589 0.439294 0.898343i \(-0.355228\pi\)
0.439294 + 0.898343i \(0.355228\pi\)
\(572\) 0 0
\(573\) 17.3420 + 37.5196i 0.724470 + 1.56740i
\(574\) 0 0
\(575\) 6.01923 + 1.06135i 0.251019 + 0.0442614i
\(576\) 0 0
\(577\) −2.59042 4.48675i −0.107841 0.186786i 0.807055 0.590477i \(-0.201060\pi\)
−0.914895 + 0.403691i \(0.867727\pi\)
\(578\) 0 0
\(579\) 2.59197 + 2.60950i 0.107718 + 0.108447i
\(580\) 0 0
\(581\) −0.953424 0.550460i −0.0395547 0.0228369i
\(582\) 0 0
\(583\) −3.96996 + 10.9074i −0.164419 + 0.451738i
\(584\) 0 0
\(585\) 0.889525 + 2.49618i 0.0367773 + 0.103204i
\(586\) 0 0
\(587\) −19.9370 + 23.7599i −0.822887 + 0.980678i −0.999994 0.00351357i \(-0.998882\pi\)
0.177107 + 0.984192i \(0.443326\pi\)
\(588\) 0 0
\(589\) −10.4978 + 22.2437i −0.432556 + 0.916536i
\(590\) 0 0
\(591\) −3.77584 + 5.35396i −0.155317 + 0.220232i
\(592\) 0 0
\(593\) −19.0316 + 3.35579i −0.781536 + 0.137806i −0.550161 0.835059i \(-0.685434\pi\)
−0.231375 + 0.972865i \(0.574322\pi\)
\(594\) 0 0
\(595\) −5.71492 2.08006i −0.234289 0.0852742i
\(596\) 0 0
\(597\) −10.1724 + 21.6241i −0.416327 + 0.885016i
\(598\) 0 0
\(599\) 14.4631 12.1360i 0.590946 0.495863i −0.297575 0.954698i \(-0.596178\pi\)
0.888521 + 0.458836i \(0.151733\pi\)
\(600\) 0 0
\(601\) −9.35958 + 5.40376i −0.381785 + 0.220424i −0.678595 0.734513i \(-0.737411\pi\)
0.296809 + 0.954937i \(0.404077\pi\)
\(602\) 0 0
\(603\) −24.5982 0.165810i −1.00172 0.00675231i
\(604\) 0 0
\(605\) −7.85648 21.5855i −0.319411 0.877575i
\(606\) 0 0
\(607\) 7.06408i 0.286722i 0.989670 + 0.143361i \(0.0457910\pi\)
−0.989670 + 0.143361i \(0.954209\pi\)
\(608\) 0 0
\(609\) −20.1930 + 1.69810i −0.818260 + 0.0688104i
\(610\) 0 0
\(611\) −4.47963 + 1.63045i −0.181226 + 0.0659610i
\(612\) 0 0
\(613\) −5.48141 + 31.0866i −0.221392 + 1.25558i 0.648071 + 0.761580i \(0.275576\pi\)
−0.869463 + 0.493998i \(0.835535\pi\)
\(614\) 0 0
\(615\) 11.3477 7.88888i 0.457583 0.318110i
\(616\) 0 0
\(617\) −19.6647 23.4355i −0.791672 0.943478i 0.207725 0.978187i \(-0.433394\pi\)
−0.999397 + 0.0347092i \(0.988950\pi\)
\(618\) 0 0
\(619\) −21.8906 + 37.9157i −0.879859 + 1.52396i −0.0283650 + 0.999598i \(0.509030\pi\)
−0.851494 + 0.524364i \(0.824303\pi\)
\(620\) 0 0
\(621\) 3.04491 31.1703i 0.122188 1.25082i
\(622\) 0 0
\(623\) −1.37078 7.77406i −0.0549190 0.311461i
\(624\) 0 0
\(625\) −14.4792 12.1495i −0.579170 0.485981i
\(626\) 0 0
\(627\) −31.1601 + 17.6598i −1.24442 + 0.705264i
\(628\) 0 0
\(629\) −7.43124 6.23555i −0.296303 0.248628i
\(630\) 0 0
\(631\) −0.0934107 0.529758i −0.00371862 0.0210893i 0.982892 0.184183i \(-0.0589639\pi\)
−0.986611 + 0.163094i \(0.947853\pi\)
\(632\) 0 0
\(633\) 7.31692 26.9436i 0.290822 1.07091i
\(634\) 0 0
\(635\) 13.1778 22.8246i 0.522944 0.905765i
\(636\) 0 0
\(637\) −1.04679 1.24752i −0.0414755 0.0494285i
\(638\) 0 0
\(639\) 9.88214 + 11.9396i 0.390932 + 0.472324i
\(640\) 0 0
\(641\) 4.01897 22.7927i 0.158740 0.900259i −0.796547 0.604577i \(-0.793342\pi\)
0.955287 0.295682i \(-0.0955467\pi\)
\(642\) 0 0
\(643\) 8.18931 2.98066i 0.322955 0.117546i −0.175455 0.984487i \(-0.556140\pi\)
0.498410 + 0.866941i \(0.333917\pi\)
\(644\) 0 0
\(645\) 3.60124 + 42.8242i 0.141799 + 1.68620i
\(646\) 0 0
\(647\) 39.9441i 1.57037i −0.619264 0.785183i \(-0.712569\pi\)
0.619264 0.785183i \(-0.287431\pi\)
\(648\) 0 0
\(649\) −8.20063 22.5310i −0.321903 0.884421i
\(650\) 0 0
\(651\) −17.7332 1.61169i −0.695018 0.0631672i
\(652\) 0 0
\(653\) 1.49337 0.862200i 0.0584402 0.0337405i −0.470495 0.882403i \(-0.655925\pi\)
0.528935 + 0.848662i \(0.322591\pi\)
\(654\) 0 0
\(655\) −10.8193 + 9.07851i −0.422747 + 0.354727i
\(656\) 0 0
\(657\) −15.1101 + 40.6599i −0.589502 + 1.58629i
\(658\) 0 0
\(659\) 22.0705 + 8.03300i 0.859744 + 0.312921i 0.734006 0.679142i \(-0.237648\pi\)
0.125737 + 0.992064i \(0.459870\pi\)
\(660\) 0 0
\(661\) 10.0686 1.77536i 0.391622 0.0690535i 0.0256300 0.999671i \(-0.491841\pi\)
0.365992 + 0.930618i \(0.380730\pi\)
\(662\) 0 0
\(663\) −1.04710 0.738461i −0.0406661 0.0286795i
\(664\) 0 0
\(665\) 12.9452 + 9.15379i 0.501994 + 0.354969i
\(666\) 0 0
\(667\) 24.8796 29.6503i 0.963341 1.14807i
\(668\) 0 0
\(669\) 1.79904 0.475558i 0.0695548 0.0183861i
\(670\) 0 0
\(671\) −16.8386 + 46.2637i −0.650047 + 1.78599i
\(672\) 0 0
\(673\) −32.9000 18.9948i −1.26820 0.732197i −0.293555 0.955942i \(-0.594838\pi\)
−0.974648 + 0.223745i \(0.928172\pi\)
\(674\) 0 0
\(675\) 3.06581 4.28555i 0.118003 0.164951i
\(676\) 0 0
\(677\) 16.1698 + 28.0070i 0.621457 + 1.07640i 0.989215 + 0.146474i \(0.0467925\pi\)
−0.367757 + 0.929922i \(0.619874\pi\)
\(678\) 0 0
\(679\) −4.59174 0.809648i −0.176215 0.0310714i
\(680\) 0 0
\(681\) −29.5002 + 13.6353i −1.13045 + 0.522506i
\(682\) 0 0
\(683\) −27.4952 −1.05208 −0.526038 0.850461i \(-0.676323\pi\)
−0.526038 + 0.850461i \(0.676323\pi\)
\(684\) 0 0
\(685\) 18.7237 0.715396
\(686\) 0 0
\(687\) 18.2794 8.44895i 0.697403 0.322347i
\(688\) 0 0
\(689\) 1.06608 + 0.187978i 0.0406144 + 0.00716141i
\(690\) 0 0
\(691\) −8.55714 14.8214i −0.325529 0.563833i 0.656090 0.754682i \(-0.272209\pi\)
−0.981619 + 0.190850i \(0.938876\pi\)
\(692\) 0 0
\(693\) −19.7498 16.8002i −0.750234 0.638188i
\(694\) 0 0
\(695\) 18.7294 + 10.8134i 0.710448 + 0.410178i
\(696\) 0 0
\(697\) −2.28556 + 6.27952i −0.0865717 + 0.237854i
\(698\) 0 0
\(699\) 27.2285 7.19757i 1.02987 0.272237i
\(700\) 0 0
\(701\) −24.3781 + 29.0527i −0.920748 + 1.09730i 0.0742333 + 0.997241i \(0.476349\pi\)
−0.994981 + 0.100064i \(0.968095\pi\)
\(702\) 0 0
\(703\) 14.4096 + 20.7827i 0.543467 + 0.783836i
\(704\) 0 0
\(705\) −30.4487 21.4737i −1.14676 0.808746i
\(706\) 0 0
\(707\) 14.2982 2.52116i 0.537739 0.0948178i
\(708\) 0 0
\(709\) −18.3247 6.66963i −0.688197 0.250483i −0.0258338 0.999666i \(-0.508224\pi\)
−0.662363 + 0.749183i \(0.730446\pi\)
\(710\) 0 0
\(711\) 26.6019 + 9.88587i 0.997649 + 0.370749i
\(712\) 0 0
\(713\) 26.0539 21.8618i 0.975724 0.818730i
\(714\) 0 0
\(715\) −3.62903 + 2.09522i −0.135718 + 0.0783568i
\(716\) 0 0
\(717\) 11.7524 + 1.06813i 0.438902 + 0.0398900i
\(718\) 0 0
\(719\) 0.618865 + 1.70032i 0.0230798 + 0.0634111i 0.950697 0.310120i \(-0.100369\pi\)
−0.927618 + 0.373531i \(0.878147\pi\)
\(720\) 0 0
\(721\) 27.9880i 1.04233i
\(722\) 0 0
\(723\) −2.81711 33.4997i −0.104769 1.24587i
\(724\) 0 0
\(725\) 6.11938 2.22727i 0.227268 0.0827189i
\(726\) 0 0
\(727\) −2.39063 + 13.5580i −0.0886637 + 0.502837i 0.907842 + 0.419312i \(0.137729\pi\)
−0.996506 + 0.0835244i \(0.973382\pi\)
\(728\) 0 0
\(729\) −23.1049 13.9700i −0.855738 0.517409i
\(730\) 0 0
\(731\) −13.3569 15.9181i −0.494023 0.588754i
\(732\) 0 0
\(733\) 3.00825 5.21044i 0.111112 0.192452i −0.805107 0.593130i \(-0.797892\pi\)
0.916219 + 0.400678i \(0.131225\pi\)
\(734\) 0 0
\(735\) 3.33574 12.2834i 0.123041 0.453080i
\(736\) 0 0
\(737\) −6.75474 38.3080i −0.248814 1.41109i
\(738\) 0 0
\(739\) −16.5397 13.8784i −0.608421 0.510526i 0.285719 0.958313i \(-0.407768\pi\)
−0.894140 + 0.447788i \(0.852212\pi\)
\(740\) 0 0
\(741\) 2.12659 + 2.57590i 0.0781222 + 0.0946281i
\(742\) 0 0
\(743\) 18.9259 + 15.8807i 0.694322 + 0.582606i 0.920152 0.391561i \(-0.128065\pi\)
−0.225830 + 0.974167i \(0.572509\pi\)
\(744\) 0 0
\(745\) 3.90485 + 22.1455i 0.143063 + 0.811349i
\(746\) 0 0
\(747\) 0.326825 1.78314i 0.0119579 0.0652418i
\(748\) 0 0
\(749\) 17.0318 29.4999i 0.622329 1.07790i
\(750\) 0 0
\(751\) 14.8918 + 17.7473i 0.543409 + 0.647609i 0.965948 0.258735i \(-0.0833057\pi\)
−0.422540 + 0.906344i \(0.638861\pi\)
\(752\) 0 0
\(753\) 24.2934 16.8887i 0.885300 0.615458i
\(754\) 0 0
\(755\) −1.22958 + 6.97331i −0.0447491 + 0.253785i
\(756\) 0 0
\(757\) −11.1562 + 4.06054i −0.405480 + 0.147583i −0.536705 0.843770i \(-0.680331\pi\)
0.131225 + 0.991353i \(0.458109\pi\)
\(758\) 0 0
\(759\) 49.3512 4.15012i 1.79134 0.150640i
\(760\) 0 0
\(761\) 6.51835i 0.236290i −0.992996 0.118145i \(-0.962305\pi\)
0.992996 0.118145i \(-0.0376948\pi\)
\(762\) 0 0
\(763\) 7.11311 + 19.5431i 0.257512 + 0.707508i
\(764\) 0 0
\(765\) 0.0675037 10.0143i 0.00244060 0.362068i
\(766\) 0 0
\(767\) −1.93655 + 1.11807i −0.0699249 + 0.0403711i
\(768\) 0 0
\(769\) 6.42301 5.38954i 0.231620 0.194352i −0.519590 0.854416i \(-0.673915\pi\)
0.751209 + 0.660064i \(0.229471\pi\)
\(770\) 0 0
\(771\) −11.6566 + 24.7793i −0.419803 + 0.892405i
\(772\) 0 0
\(773\) 15.1689 + 5.52103i 0.545588 + 0.198578i 0.600085 0.799936i \(-0.295133\pi\)
−0.0544971 + 0.998514i \(0.517356\pi\)
\(774\) 0 0
\(775\) 5.63528 0.993653i 0.202425 0.0356931i
\(776\) 0 0
\(777\) −10.5515 + 14.9615i −0.378532 + 0.536741i
\(778\) 0 0
\(779\) 10.0581 14.2241i 0.360370 0.509632i
\(780\) 0 0
\(781\) −15.7539 + 18.7748i −0.563719 + 0.671815i
\(782\) 0 0
\(783\) −13.7956 30.3831i −0.493015 1.08580i
\(784\) 0 0
\(785\) 0.215679 0.592574i 0.00769792 0.0211499i
\(786\) 0 0
\(787\) −19.4065 11.2044i −0.691768 0.399392i 0.112506 0.993651i \(-0.464112\pi\)
−0.804274 + 0.594259i \(0.797446\pi\)
\(788\) 0 0
\(789\) 3.17244 + 3.19389i 0.112942 + 0.113706i
\(790\) 0 0
\(791\) 0.541256 + 0.937483i 0.0192449 + 0.0333331i
\(792\) 0 0
\(793\) 4.52177 + 0.797311i 0.160573 + 0.0283133i