Properties

Label 912.2.cc.c.401.2
Level $912$
Weight $2$
Character 912.401
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 401.2
Root \(0.0786547 - 1.73026i\) of defining polynomial
Character \(\chi\) \(=\) 912.401
Dual form 912.2.cc.c.257.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.517874 + 1.65282i) q^{3} +(-0.258510 - 0.710252i) q^{5} +(-0.777943 - 1.34744i) q^{7} +(-2.46361 - 1.71190i) q^{9} +O(q^{10})\) \(q+(-0.517874 + 1.65282i) q^{3} +(-0.258510 - 0.710252i) q^{5} +(-0.777943 - 1.34744i) q^{7} +(-2.46361 - 1.71190i) q^{9} +(-0.832399 - 0.480586i) q^{11} +(0.416982 + 0.496940i) q^{13} +(1.30779 - 0.0594499i) q^{15} +(6.73013 + 1.18670i) q^{17} +(4.14364 - 1.35288i) q^{19} +(2.62994 - 0.587996i) q^{21} +(-0.400647 + 1.10077i) q^{23} +(3.39259 - 2.84672i) q^{25} +(4.10530 - 3.18535i) q^{27} +(1.39666 + 7.92086i) q^{29} +(2.63927 - 1.52379i) q^{31} +(1.22540 - 1.12692i) q^{33} +(-0.755913 + 0.900862i) q^{35} +4.12648i q^{37} +(-1.03729 + 0.431843i) q^{39} +(-4.09755 - 3.43825i) q^{41} +(7.34330 - 2.67274i) q^{43} +(-0.579012 + 2.19233i) q^{45} +(3.11004 - 0.548383i) q^{47} +(2.28961 - 3.96572i) q^{49} +(-5.44676 + 10.5091i) q^{51} +(-13.6276 - 4.96002i) q^{53} +(-0.126153 + 0.715449i) q^{55} +(0.0901766 + 7.54930i) q^{57} +(-2.02192 + 11.4669i) q^{59} +(10.1813 + 3.70568i) q^{61} +(-0.390129 + 4.65133i) q^{63} +(0.245158 - 0.424626i) q^{65} +(9.19012 - 1.62047i) q^{67} +(-1.61189 - 1.23226i) q^{69} +(-0.0322101 + 0.0117235i) q^{71} +(-3.04446 - 2.55461i) q^{73} +(2.94818 + 7.08158i) q^{75} +1.49547i q^{77} +(0.893115 - 1.06437i) q^{79} +(3.13878 + 8.43493i) q^{81} +(10.4856 - 6.05389i) q^{83} +(-0.896950 - 5.08686i) q^{85} +(-13.8150 - 1.79358i) q^{87} +(4.68075 - 3.92762i) q^{89} +(0.345207 - 0.948448i) q^{91} +(1.15173 + 5.15137i) q^{93} +(-2.03206 - 2.59329i) q^{95} +(9.54804 + 1.68358i) q^{97} +(1.22799 + 2.60896i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 3q^{3} - 3q^{9} + O(q^{10}) \) \( 18q - 3q^{3} - 3q^{9} - 12q^{13} - 18q^{15} + 6q^{17} + 6q^{19} - 18q^{25} + 6q^{27} - 6q^{29} - 24q^{33} + 24q^{35} - 6q^{39} + 3q^{41} + 6q^{43} - 54q^{45} - 30q^{47} + 21q^{49} - 42q^{51} - 60q^{53} - 30q^{55} + 12q^{57} - 3q^{59} + 54q^{61} + 18q^{63} + 24q^{65} + 15q^{67} + 30q^{69} - 36q^{71} - 42q^{73} + 6q^{79} - 3q^{81} - 36q^{83} - 60q^{89} + 18q^{91} - 66q^{93} - 6q^{95} + 9q^{97} + 102q^{99} + O(q^{100}) \)

Character values

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

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

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
\(3\) −0.517874 + 1.65282i −0.298995 + 0.954255i
\(4\) 0 0
\(5\) −0.258510 0.710252i −0.115609 0.317634i 0.868370 0.495917i \(-0.165168\pi\)
−0.983979 + 0.178283i \(0.942946\pi\)
\(6\) 0 0
\(7\) −0.777943 1.34744i −0.294035 0.509283i 0.680725 0.732539i \(-0.261665\pi\)
−0.974760 + 0.223256i \(0.928331\pi\)
\(8\) 0 0
\(9\) −2.46361 1.71190i −0.821204 0.570634i
\(10\) 0 0
\(11\) −0.832399 0.480586i −0.250978 0.144902i 0.369234 0.929336i \(-0.379620\pi\)
−0.620212 + 0.784434i \(0.712953\pi\)
\(12\) 0 0
\(13\) 0.416982 + 0.496940i 0.115650 + 0.137826i 0.820763 0.571268i \(-0.193548\pi\)
−0.705113 + 0.709095i \(0.749104\pi\)
\(14\) 0 0
\(15\) 1.30779 0.0594499i 0.337671 0.0153499i
\(16\) 0 0
\(17\) 6.73013 + 1.18670i 1.63230 + 0.287818i 0.913328 0.407226i \(-0.133504\pi\)
0.718968 + 0.695043i \(0.244615\pi\)
\(18\) 0 0
\(19\) 4.14364 1.35288i 0.950615 0.310371i
\(20\) 0 0
\(21\) 2.62994 0.587996i 0.573901 0.128311i
\(22\) 0 0
\(23\) −0.400647 + 1.10077i −0.0835407 + 0.229526i −0.974429 0.224697i \(-0.927861\pi\)
0.890888 + 0.454223i \(0.150083\pi\)
\(24\) 0 0
\(25\) 3.39259 2.84672i 0.678519 0.569345i
\(26\) 0 0
\(27\) 4.10530 3.18535i 0.790066 0.613022i
\(28\) 0 0
\(29\) 1.39666 + 7.92086i 0.259354 + 1.47087i 0.784645 + 0.619945i \(0.212845\pi\)
−0.525292 + 0.850922i \(0.676044\pi\)
\(30\) 0 0
\(31\) 2.63927 1.52379i 0.474028 0.273680i −0.243897 0.969801i \(-0.578426\pi\)
0.717924 + 0.696121i \(0.245092\pi\)
\(32\) 0 0
\(33\) 1.22540 1.12692i 0.213314 0.196172i
\(34\) 0 0
\(35\) −0.755913 + 0.900862i −0.127773 + 0.152273i
\(36\) 0 0
\(37\) 4.12648i 0.678389i 0.940716 + 0.339195i \(0.110154\pi\)
−0.940716 + 0.339195i \(0.889846\pi\)
\(38\) 0 0
\(39\) −1.03729 + 0.431843i −0.166100 + 0.0691502i
\(40\) 0 0
\(41\) −4.09755 3.43825i −0.639929 0.536964i 0.264067 0.964504i \(-0.414936\pi\)
−0.903996 + 0.427540i \(0.859380\pi\)
\(42\) 0 0
\(43\) 7.34330 2.67274i 1.11984 0.407589i 0.285248 0.958454i \(-0.407924\pi\)
0.834595 + 0.550865i \(0.185702\pi\)
\(44\) 0 0
\(45\) −0.579012 + 2.19233i −0.0863139 + 0.326813i
\(46\) 0 0
\(47\) 3.11004 0.548383i 0.453646 0.0799899i 0.0578432 0.998326i \(-0.481578\pi\)
0.395802 + 0.918336i \(0.370467\pi\)
\(48\) 0 0
\(49\) 2.28961 3.96572i 0.327087 0.566531i
\(50\) 0 0
\(51\) −5.44676 + 10.5091i −0.762699 + 1.47157i
\(52\) 0 0
\(53\) −13.6276 4.96002i −1.87189 0.681312i −0.966462 0.256809i \(-0.917329\pi\)
−0.905427 0.424503i \(-0.860449\pi\)
\(54\) 0 0
\(55\) −0.126153 + 0.715449i −0.0170105 + 0.0964711i
\(56\) 0 0
\(57\) 0.0901766 + 7.54930i 0.0119442 + 0.999929i
\(58\) 0 0
\(59\) −2.02192 + 11.4669i −0.263231 + 1.49286i 0.510793 + 0.859704i \(0.329352\pi\)
−0.774024 + 0.633156i \(0.781759\pi\)
\(60\) 0 0
\(61\) 10.1813 + 3.70568i 1.30358 + 0.474464i 0.898161 0.439667i \(-0.144903\pi\)
0.405419 + 0.914131i \(0.367126\pi\)
\(62\) 0 0
\(63\) −0.390129 + 4.65133i −0.0491517 + 0.586012i
\(64\) 0 0
\(65\) 0.245158 0.424626i 0.0304081 0.0526684i
\(66\) 0 0
\(67\) 9.19012 1.62047i 1.12275 0.197972i 0.418703 0.908123i \(-0.362485\pi\)
0.704049 + 0.710151i \(0.251374\pi\)
\(68\) 0 0
\(69\) −1.61189 1.23226i −0.194048 0.148346i
\(70\) 0 0
\(71\) −0.0322101 + 0.0117235i −0.00382263 + 0.00139132i −0.343931 0.938995i \(-0.611759\pi\)
0.340108 + 0.940386i \(0.389536\pi\)
\(72\) 0 0
\(73\) −3.04446 2.55461i −0.356327 0.298994i 0.446998 0.894535i \(-0.352493\pi\)
−0.803325 + 0.595541i \(0.796938\pi\)
\(74\) 0 0
\(75\) 2.94818 + 7.08158i 0.340426 + 0.817711i
\(76\) 0 0
\(77\) 1.49547i 0.170425i
\(78\) 0 0
\(79\) 0.893115 1.06437i 0.100483 0.119751i −0.713459 0.700697i \(-0.752873\pi\)
0.813943 + 0.580945i \(0.197317\pi\)
\(80\) 0 0
\(81\) 3.13878 + 8.43493i 0.348753 + 0.937215i
\(82\) 0 0
\(83\) 10.4856 6.05389i 1.15095 0.664500i 0.201830 0.979421i \(-0.435311\pi\)
0.949118 + 0.314920i \(0.101978\pi\)
\(84\) 0 0
\(85\) −0.896950 5.08686i −0.0972879 0.551747i
\(86\) 0 0
\(87\) −13.8150 1.79358i −1.48113 0.192292i
\(88\) 0 0
\(89\) 4.68075 3.92762i 0.496159 0.416327i −0.360069 0.932926i \(-0.617247\pi\)
0.856227 + 0.516599i \(0.172802\pi\)
\(90\) 0 0
\(91\) 0.345207 0.948448i 0.0361875 0.0994243i
\(92\) 0 0
\(93\) 1.15173 + 5.15137i 0.119429 + 0.534172i
\(94\) 0 0
\(95\) −2.03206 2.59329i −0.208485 0.266066i
\(96\) 0 0
\(97\) 9.54804 + 1.68358i 0.969457 + 0.170941i 0.635885 0.771784i \(-0.280635\pi\)
0.333571 + 0.942725i \(0.391746\pi\)
\(98\) 0 0
\(99\) 1.22799 + 2.60896i 0.123418 + 0.262211i
\(100\) 0 0
\(101\) 12.0945 + 14.4137i 1.20345 + 1.43422i 0.871130 + 0.491053i \(0.163388\pi\)
0.332323 + 0.943166i \(0.392168\pi\)
\(102\) 0 0
\(103\) −9.92876 5.73237i −0.978310 0.564828i −0.0765505 0.997066i \(-0.524391\pi\)
−0.901759 + 0.432238i \(0.857724\pi\)
\(104\) 0 0
\(105\) −1.09749 1.71592i −0.107104 0.167457i
\(106\) 0 0
\(107\) 1.17826 + 2.04080i 0.113906 + 0.197292i 0.917342 0.398100i \(-0.130330\pi\)
−0.803436 + 0.595392i \(0.796997\pi\)
\(108\) 0 0
\(109\) −2.21678 6.09056i −0.212329 0.583370i 0.787111 0.616811i \(-0.211576\pi\)
−0.999441 + 0.0334410i \(0.989353\pi\)
\(110\) 0 0
\(111\) −6.82032 2.13700i −0.647356 0.202835i
\(112\) 0 0
\(113\) −10.0387 −0.944358 −0.472179 0.881503i \(-0.656532\pi\)
−0.472179 + 0.881503i \(0.656532\pi\)
\(114\) 0 0
\(115\) 0.885394 0.0825635
\(116\) 0 0
\(117\) −0.176570 1.93810i −0.0163239 0.179177i
\(118\) 0 0
\(119\) −3.63665 9.99161i −0.333371 0.915929i
\(120\) 0 0
\(121\) −5.03807 8.72620i −0.458007 0.793291i
\(122\) 0 0
\(123\) 7.80481 4.99192i 0.703736 0.450106i
\(124\) 0 0
\(125\) −6.17177 3.56327i −0.552020 0.318709i
\(126\) 0 0
\(127\) −8.95146 10.6679i −0.794313 0.946626i 0.205171 0.978726i \(-0.434225\pi\)
−0.999485 + 0.0321003i \(0.989780\pi\)
\(128\) 0 0
\(129\) 0.614653 + 13.5213i 0.0541172 + 1.19048i
\(130\) 0 0
\(131\) −10.9610 1.93273i −0.957671 0.168863i −0.327096 0.944991i \(-0.606070\pi\)
−0.630575 + 0.776128i \(0.717181\pi\)
\(132\) 0 0
\(133\) −5.04643 4.53083i −0.437581 0.392873i
\(134\) 0 0
\(135\) −3.32367 2.09235i −0.286056 0.180081i
\(136\) 0 0
\(137\) −1.69757 + 4.66403i −0.145033 + 0.398475i −0.990845 0.135007i \(-0.956894\pi\)
0.845812 + 0.533482i \(0.179117\pi\)
\(138\) 0 0
\(139\) 2.76202 2.31761i 0.234272 0.196577i −0.518093 0.855325i \(-0.673358\pi\)
0.752364 + 0.658747i \(0.228913\pi\)
\(140\) 0 0
\(141\) −0.704229 + 5.42432i −0.0593068 + 0.456810i
\(142\) 0 0
\(143\) −0.108273 0.614047i −0.00905425 0.0513492i
\(144\) 0 0
\(145\) 5.26475 3.03961i 0.437214 0.252426i
\(146\) 0 0
\(147\) 5.36888 + 5.83805i 0.442818 + 0.481514i
\(148\) 0 0
\(149\) 12.3170 14.6788i 1.00904 1.20253i 0.0298610 0.999554i \(-0.490494\pi\)
0.979183 0.202978i \(-0.0650620\pi\)
\(150\) 0 0
\(151\) 19.2624i 1.56755i 0.621042 + 0.783777i \(0.286710\pi\)
−0.621042 + 0.783777i \(0.713290\pi\)
\(152\) 0 0
\(153\) −14.5489 14.4449i −1.17621 1.16780i
\(154\) 0 0
\(155\) −1.76455 1.48063i −0.141732 0.118927i
\(156\) 0 0
\(157\) −0.200940 + 0.0731363i −0.0160368 + 0.00583691i −0.350026 0.936740i \(-0.613827\pi\)
0.333989 + 0.942577i \(0.391605\pi\)
\(158\) 0 0
\(159\) 15.2554 19.9552i 1.20983 1.58255i
\(160\) 0 0
\(161\) 1.79490 0.316489i 0.141458 0.0249428i
\(162\) 0 0
\(163\) −7.51668 + 13.0193i −0.588752 + 1.01975i 0.405645 + 0.914031i \(0.367047\pi\)
−0.994396 + 0.105717i \(0.966286\pi\)
\(164\) 0 0
\(165\) −1.11718 0.579020i −0.0869720 0.0450767i
\(166\) 0 0
\(167\) 8.87982 + 3.23199i 0.687141 + 0.250099i 0.661911 0.749583i \(-0.269746\pi\)
0.0252305 + 0.999682i \(0.491968\pi\)
\(168\) 0 0
\(169\) 2.18435 12.3881i 0.168027 0.952929i
\(170\) 0 0
\(171\) −12.5243 3.76054i −0.957758 0.287575i
\(172\) 0 0
\(173\) 2.33529 13.2441i 0.177549 1.00693i −0.757612 0.652705i \(-0.773634\pi\)
0.935161 0.354224i \(-0.115255\pi\)
\(174\) 0 0
\(175\) −6.47502 2.35672i −0.489466 0.178151i
\(176\) 0 0
\(177\) −17.9056 9.28026i −1.34586 0.697547i
\(178\) 0 0
\(179\) −8.34644 + 14.4565i −0.623842 + 1.08053i 0.364921 + 0.931038i \(0.381096\pi\)
−0.988764 + 0.149488i \(0.952237\pi\)
\(180\) 0 0
\(181\) −10.0398 + 1.77029i −0.746251 + 0.131584i −0.533828 0.845593i \(-0.679247\pi\)
−0.212424 + 0.977178i \(0.568136\pi\)
\(182\) 0 0
\(183\) −11.3974 + 14.9087i −0.842523 + 1.10209i
\(184\) 0 0
\(185\) 2.93084 1.06674i 0.215480 0.0784281i
\(186\) 0 0
\(187\) −5.03184 4.22221i −0.367964 0.308759i
\(188\) 0 0
\(189\) −7.48576 3.05361i −0.544509 0.222118i
\(190\) 0 0
\(191\) 12.0667i 0.873115i −0.899676 0.436558i \(-0.856198\pi\)
0.899676 0.436558i \(-0.143802\pi\)
\(192\) 0 0
\(193\) −2.14990 + 2.56215i −0.154753 + 0.184427i −0.837850 0.545900i \(-0.816188\pi\)
0.683098 + 0.730327i \(0.260632\pi\)
\(194\) 0 0
\(195\) 0.574869 + 0.625104i 0.0411672 + 0.0447647i
\(196\) 0 0
\(197\) 5.15098 2.97392i 0.366992 0.211883i −0.305151 0.952304i \(-0.598707\pi\)
0.672144 + 0.740421i \(0.265374\pi\)
\(198\) 0 0
\(199\) −1.94088 11.0073i −0.137585 0.780286i −0.973024 0.230703i \(-0.925898\pi\)
0.835439 0.549583i \(-0.185214\pi\)
\(200\) 0 0
\(201\) −2.08099 + 16.0288i −0.146782 + 1.13058i
\(202\) 0 0
\(203\) 9.58634 8.04389i 0.672829 0.564571i
\(204\) 0 0
\(205\) −1.38276 + 3.79911i −0.0965764 + 0.265342i
\(206\) 0 0
\(207\) 2.87145 2.02600i 0.199579 0.140817i
\(208\) 0 0
\(209\) −4.09933 0.865240i −0.283557 0.0598499i
\(210\) 0 0
\(211\) 20.9377 + 3.69188i 1.44141 + 0.254159i 0.839045 0.544063i \(-0.183115\pi\)
0.602364 + 0.798222i \(0.294226\pi\)
\(212\) 0 0
\(213\) −0.00269607 0.0593087i −0.000184731 0.00406376i
\(214\) 0 0
\(215\) −3.79664 4.52466i −0.258928 0.308579i
\(216\) 0 0
\(217\) −4.10641 2.37084i −0.278761 0.160943i
\(218\) 0 0
\(219\) 5.79895 3.70898i 0.391856 0.250629i
\(220\) 0 0
\(221\) 2.21662 + 3.83930i 0.149106 + 0.258259i
\(222\) 0 0
\(223\) −4.71184 12.9457i −0.315528 0.866907i −0.991515 0.129993i \(-0.958505\pi\)
0.675987 0.736914i \(-0.263718\pi\)
\(224\) 0 0
\(225\) −13.2313 + 1.20544i −0.882090 + 0.0803625i
\(226\) 0 0
\(227\) −16.1886 −1.07448 −0.537238 0.843430i \(-0.680532\pi\)
−0.537238 + 0.843430i \(0.680532\pi\)
\(228\) 0 0
\(229\) −25.6462 −1.69475 −0.847374 0.530997i \(-0.821817\pi\)
−0.847374 + 0.530997i \(0.821817\pi\)
\(230\) 0 0
\(231\) −2.47174 0.774466i −0.162629 0.0509561i
\(232\) 0 0
\(233\) 3.98107 + 10.9379i 0.260808 + 0.716565i 0.999113 + 0.0420981i \(0.0134042\pi\)
−0.738305 + 0.674467i \(0.764374\pi\)
\(234\) 0 0
\(235\) −1.19347 2.06715i −0.0778532 0.134846i
\(236\) 0 0
\(237\) 1.29669 + 2.02737i 0.0842293 + 0.131692i
\(238\) 0 0
\(239\) 13.1831 + 7.61128i 0.852746 + 0.492333i 0.861576 0.507628i \(-0.169478\pi\)
−0.00883069 + 0.999961i \(0.502811\pi\)
\(240\) 0 0
\(241\) 9.76016 + 11.6317i 0.628707 + 0.749264i 0.982541 0.186044i \(-0.0595666\pi\)
−0.353834 + 0.935308i \(0.615122\pi\)
\(242\) 0 0
\(243\) −15.5669 + 0.819603i −0.998617 + 0.0525776i
\(244\) 0 0
\(245\) −3.40855 0.601019i −0.217764 0.0383977i
\(246\) 0 0
\(247\) 2.40012 + 1.49501i 0.152716 + 0.0951254i
\(248\) 0 0
\(249\) 4.57573 + 20.4660i 0.289975 + 1.29698i
\(250\) 0 0
\(251\) 3.71032 10.1940i 0.234193 0.643441i −0.765807 0.643071i \(-0.777660\pi\)
1.00000 0.000369965i \(-0.000117763\pi\)
\(252\) 0 0
\(253\) 0.862512 0.723733i 0.0542257 0.0455007i
\(254\) 0 0
\(255\) 8.87216 + 1.15186i 0.555596 + 0.0721320i
\(256\) 0 0
\(257\) −0.00786014 0.0445771i −0.000490302 0.00278064i 0.984562 0.175038i \(-0.0560049\pi\)
−0.985052 + 0.172258i \(0.944894\pi\)
\(258\) 0 0
\(259\) 5.56017 3.21017i 0.345492 0.199470i
\(260\) 0 0
\(261\) 10.1189 21.9049i 0.626345 1.35588i
\(262\) 0 0
\(263\) 3.52577 4.20185i 0.217408 0.259097i −0.646307 0.763078i \(-0.723687\pi\)
0.863715 + 0.503981i \(0.168132\pi\)
\(264\) 0 0
\(265\) 10.9612i 0.673342i
\(266\) 0 0
\(267\) 4.06760 + 9.77044i 0.248933 + 0.597941i
\(268\) 0 0
\(269\) 1.50432 + 1.26228i 0.0917202 + 0.0769623i 0.687495 0.726189i \(-0.258710\pi\)
−0.595775 + 0.803152i \(0.703155\pi\)
\(270\) 0 0
\(271\) −19.8494 + 7.22458i −1.20576 + 0.438862i −0.865232 0.501371i \(-0.832829\pi\)
−0.340531 + 0.940233i \(0.610607\pi\)
\(272\) 0 0
\(273\) 1.38884 + 1.06174i 0.0840563 + 0.0642594i
\(274\) 0 0
\(275\) −4.19208 + 0.739177i −0.252792 + 0.0445741i
\(276\) 0 0
\(277\) −3.91899 + 6.78789i −0.235469 + 0.407845i −0.959409 0.282018i \(-0.908996\pi\)
0.723940 + 0.689863i \(0.242329\pi\)
\(278\) 0 0
\(279\) −9.11072 0.764161i −0.545445 0.0457491i
\(280\) 0 0
\(281\) −11.0064 4.00600i −0.656587 0.238978i −0.00782495 0.999969i \(-0.502491\pi\)
−0.648762 + 0.760991i \(0.724713\pi\)
\(282\) 0 0
\(283\) −1.21905 + 6.91356i −0.0724648 + 0.410968i 0.926899 + 0.375310i \(0.122464\pi\)
−0.999364 + 0.0356581i \(0.988647\pi\)
\(284\) 0 0
\(285\) 5.33859 2.01562i 0.316231 0.119395i
\(286\) 0 0
\(287\) −1.44517 + 8.19595i −0.0853055 + 0.483791i
\(288\) 0 0
\(289\) 27.9116 + 10.1590i 1.64186 + 0.597587i
\(290\) 0 0
\(291\) −7.72733 + 14.9093i −0.452984 + 0.873998i
\(292\) 0 0
\(293\) −1.29095 + 2.23599i −0.0754180 + 0.130628i −0.901268 0.433262i \(-0.857362\pi\)
0.825850 + 0.563890i \(0.190696\pi\)
\(294\) 0 0
\(295\) 8.66705 1.52824i 0.504615 0.0889773i
\(296\) 0 0
\(297\) −4.94808 + 0.678535i −0.287117 + 0.0393726i
\(298\) 0 0
\(299\) −0.714078 + 0.259903i −0.0412962 + 0.0150306i
\(300\) 0 0
\(301\) −9.31401 7.81539i −0.536851 0.450471i
\(302\) 0 0
\(303\) −30.0867 + 12.5256i −1.72844 + 0.719577i
\(304\) 0 0
\(305\) 8.18923i 0.468914i
\(306\) 0 0
\(307\) 1.26629 1.50910i 0.0722709 0.0861290i −0.728698 0.684836i \(-0.759874\pi\)
0.800968 + 0.598707i \(0.204318\pi\)
\(308\) 0 0
\(309\) 14.6164 13.4418i 0.831499 0.764677i
\(310\) 0 0
\(311\) −22.4909 + 12.9851i −1.27534 + 0.736320i −0.975989 0.217822i \(-0.930105\pi\)
−0.299355 + 0.954142i \(0.596771\pi\)
\(312\) 0 0
\(313\) −2.32842 13.2051i −0.131610 0.746398i −0.977161 0.212502i \(-0.931839\pi\)
0.845551 0.533895i \(-0.179272\pi\)
\(314\) 0 0
\(315\) 3.40446 0.925326i 0.191820 0.0521362i
\(316\) 0 0
\(317\) −23.3056 + 19.5557i −1.30897 + 1.09836i −0.320454 + 0.947264i \(0.603835\pi\)
−0.988519 + 0.151095i \(0.951720\pi\)
\(318\) 0 0
\(319\) 2.64407 7.26453i 0.148040 0.406736i
\(320\) 0 0
\(321\) −3.98326 + 0.890567i −0.222324 + 0.0497066i
\(322\) 0 0
\(323\) 29.4927 4.18776i 1.64102 0.233013i
\(324\) 0 0
\(325\) 2.82930 + 0.498882i 0.156941 + 0.0276730i
\(326\) 0 0
\(327\) 11.2146 0.509796i 0.620169 0.0281918i
\(328\) 0 0
\(329\) −3.15834 3.76397i −0.174125 0.207514i
\(330\) 0 0
\(331\) 9.22014 + 5.32325i 0.506785 + 0.292592i 0.731511 0.681830i \(-0.238815\pi\)
−0.224726 + 0.974422i \(0.572149\pi\)
\(332\) 0 0
\(333\) 7.06413 10.1660i 0.387112 0.557096i
\(334\) 0 0
\(335\) −3.52668 6.10839i −0.192683 0.333737i
\(336\) 0 0
\(337\) −2.38138 6.54278i −0.129722 0.356408i 0.857780 0.514018i \(-0.171843\pi\)
−0.987501 + 0.157610i \(0.949621\pi\)
\(338\) 0 0
\(339\) 5.19876 16.5921i 0.282358 0.901158i
\(340\) 0 0
\(341\) −2.92924 −0.158627
\(342\) 0 0
\(343\) −18.0159 −0.972770
\(344\) 0 0
\(345\) −0.458523 + 1.46340i −0.0246860 + 0.0787866i
\(346\) 0 0
\(347\) 9.63081 + 26.4604i 0.517009 + 1.42047i 0.873799 + 0.486287i \(0.161649\pi\)
−0.356790 + 0.934185i \(0.616129\pi\)
\(348\) 0 0
\(349\) 9.79155 + 16.9595i 0.524130 + 0.907819i 0.999605 + 0.0280904i \(0.00894261\pi\)
−0.475476 + 0.879729i \(0.657724\pi\)
\(350\) 0 0
\(351\) 3.29477 + 0.711853i 0.175862 + 0.0379959i
\(352\) 0 0
\(353\) −3.55050 2.04988i −0.188974 0.109104i 0.402528 0.915408i \(-0.368132\pi\)
−0.591502 + 0.806303i \(0.701465\pi\)
\(354\) 0 0
\(355\) 0.0166533 + 0.0198466i 0.000883864 + 0.00105335i
\(356\) 0 0
\(357\) 18.3976 0.836324i 0.973706 0.0442629i
\(358\) 0 0
\(359\) 5.52450 + 0.974118i 0.291572 + 0.0514120i 0.317521 0.948251i \(-0.397150\pi\)
−0.0259490 + 0.999663i \(0.508261\pi\)
\(360\) 0 0
\(361\) 15.3395 11.2117i 0.807340 0.590087i
\(362\) 0 0
\(363\) 17.0319 3.80795i 0.893943 0.199865i
\(364\) 0 0
\(365\) −1.02739 + 2.82273i −0.0537760 + 0.147748i
\(366\) 0 0
\(367\) 2.28539 1.91767i 0.119296 0.100101i −0.581188 0.813769i \(-0.697412\pi\)
0.700484 + 0.713668i \(0.252967\pi\)
\(368\) 0 0
\(369\) 4.20882 + 15.4851i 0.219103 + 0.806123i
\(370\) 0 0
\(371\) 3.91814 + 22.2209i 0.203420 + 1.15365i
\(372\) 0 0
\(373\) −18.2415 + 10.5317i −0.944510 + 0.545313i −0.891371 0.453274i \(-0.850256\pi\)
−0.0531391 + 0.998587i \(0.516923\pi\)
\(374\) 0 0
\(375\) 9.08564 8.35548i 0.469180 0.431475i
\(376\) 0 0
\(377\) −3.35381 + 3.99691i −0.172730 + 0.205852i
\(378\) 0 0
\(379\) 9.54057i 0.490066i 0.969515 + 0.245033i \(0.0787988\pi\)
−0.969515 + 0.245033i \(0.921201\pi\)
\(380\) 0 0
\(381\) 22.2679 9.27048i 1.14082 0.474941i
\(382\) 0 0
\(383\) −5.96084 5.00173i −0.304584 0.255577i 0.477665 0.878542i \(-0.341483\pi\)
−0.782249 + 0.622965i \(0.785928\pi\)
\(384\) 0 0
\(385\) 1.06216 0.386595i 0.0541328 0.0197027i
\(386\) 0 0
\(387\) −22.6665 5.98640i −1.15220 0.304306i
\(388\) 0 0
\(389\) 9.63724 1.69931i 0.488627 0.0861582i 0.0760939 0.997101i \(-0.475755\pi\)
0.412533 + 0.910942i \(0.364644\pi\)
\(390\) 0 0
\(391\) −4.00269 + 6.93287i −0.202425 + 0.350610i
\(392\) 0 0
\(393\) 8.87089 17.1157i 0.447477 0.863373i
\(394\) 0 0
\(395\) −0.986853 0.359185i −0.0496539 0.0180726i
\(396\) 0 0
\(397\) −2.05329 + 11.6448i −0.103052 + 0.584435i 0.888929 + 0.458045i \(0.151450\pi\)
−0.991981 + 0.126390i \(0.959661\pi\)
\(398\) 0 0
\(399\) 10.1020 5.99443i 0.505735 0.300097i
\(400\) 0 0
\(401\) −3.59086 + 20.3648i −0.179319 + 1.01697i 0.753720 + 0.657195i \(0.228257\pi\)
−0.933039 + 0.359774i \(0.882854\pi\)
\(402\) 0 0
\(403\) 1.85776 + 0.676169i 0.0925416 + 0.0336824i
\(404\) 0 0
\(405\) 5.17952 4.40984i 0.257372 0.219127i
\(406\) 0 0
\(407\) 1.98313 3.43488i 0.0982999 0.170260i
\(408\) 0 0
\(409\) 3.39761 0.599090i 0.168001 0.0296231i −0.0890148 0.996030i \(-0.528372\pi\)
0.257016 + 0.966407i \(0.417261\pi\)
\(410\) 0 0
\(411\) −6.82966 5.22115i −0.336882 0.257540i
\(412\) 0 0
\(413\) 17.0238 6.19617i 0.837688 0.304893i
\(414\) 0 0
\(415\) −7.01043 5.88245i −0.344128 0.288758i
\(416\) 0 0
\(417\) 2.40021 + 5.76535i 0.117539 + 0.282331i
\(418\) 0 0
\(419\) 25.3156i 1.23675i −0.785884 0.618374i \(-0.787792\pi\)
0.785884 0.618374i \(-0.212208\pi\)
\(420\) 0 0
\(421\) 20.4536 24.3756i 0.996845 1.18799i 0.0146955 0.999892i \(-0.495322\pi\)
0.982150 0.188102i \(-0.0602334\pi\)
\(422\) 0 0
\(423\) −8.60071 3.97307i −0.418181 0.193178i
\(424\) 0 0
\(425\) 26.2108 15.1328i 1.27141 0.734049i
\(426\) 0 0
\(427\) −2.92728 16.6014i −0.141661 0.803400i
\(428\) 0 0
\(429\) 1.07098 + 0.139043i 0.0517074 + 0.00671308i
\(430\) 0 0
\(431\) 25.2345 21.1742i 1.21550 1.01993i 0.216455 0.976293i \(-0.430551\pi\)
0.999048 0.0436350i \(-0.0138938\pi\)
\(432\) 0 0
\(433\) −5.46188 + 15.0064i −0.262481 + 0.721161i 0.736517 + 0.676419i \(0.236469\pi\)
−0.998999 + 0.0447423i \(0.985753\pi\)
\(434\) 0 0
\(435\) 2.29744 + 10.2758i 0.110154 + 0.492688i
\(436\) 0 0
\(437\) −0.170932 + 5.10321i −0.00817679 + 0.244120i
\(438\) 0 0
\(439\) 30.5401 + 5.38505i 1.45760 + 0.257014i 0.845589 0.533835i \(-0.179250\pi\)
0.612011 + 0.790849i \(0.290361\pi\)
\(440\) 0 0
\(441\) −12.4296 + 5.85041i −0.591887 + 0.278591i
\(442\) 0 0
\(443\) −12.5287 14.9311i −0.595257 0.709400i 0.381350 0.924431i \(-0.375459\pi\)
−0.976607 + 0.215031i \(0.931015\pi\)
\(444\) 0 0
\(445\) −3.99962 2.30918i −0.189600 0.109466i
\(446\) 0 0
\(447\) 17.8827 + 27.9594i 0.845823 + 1.32244i
\(448\) 0 0
\(449\) 6.61607 + 11.4594i 0.312232 + 0.540801i 0.978845 0.204602i \(-0.0655901\pi\)
−0.666613 + 0.745404i \(0.732257\pi\)
\(450\) 0 0
\(451\) 1.75842 + 4.83122i 0.0828007 + 0.227493i
\(452\) 0 0
\(453\) −31.8373 9.97551i −1.49585 0.468690i
\(454\) 0 0
\(455\) −0.762876 −0.0357642
\(456\) 0 0
\(457\) −15.4038 −0.720559 −0.360279 0.932844i \(-0.617319\pi\)
−0.360279 + 0.932844i \(0.617319\pi\)
\(458\) 0 0
\(459\) 31.4093 16.5661i 1.46606 0.773238i
\(460\) 0 0
\(461\) −5.65076 15.5253i −0.263182 0.723087i −0.998948 0.0458511i \(-0.985400\pi\)
0.735766 0.677236i \(-0.236822\pi\)
\(462\) 0 0
\(463\) 4.69170 + 8.12625i 0.218042 + 0.377659i 0.954209 0.299140i \(-0.0966998\pi\)
−0.736168 + 0.676799i \(0.763366\pi\)
\(464\) 0 0
\(465\) 3.36103 2.14970i 0.155864 0.0996899i
\(466\) 0 0
\(467\) −18.5458 10.7074i −0.858196 0.495480i 0.00521153 0.999986i \(-0.498341\pi\)
−0.863408 + 0.504507i \(0.831674\pi\)
\(468\) 0 0
\(469\) −9.33287 11.1225i −0.430952 0.513588i
\(470\) 0 0
\(471\) −0.0168192 0.369993i −0.000774989 0.0170484i
\(472\) 0 0
\(473\) −7.39703 1.30430i −0.340116 0.0599716i
\(474\) 0 0
\(475\) 10.2064 16.3855i 0.468302 0.751820i
\(476\) 0 0
\(477\) 25.0820 + 35.5486i 1.14842 + 1.62766i
\(478\) 0 0
\(479\) −11.4165 + 31.3665i −0.521632 + 1.43317i 0.347071 + 0.937839i \(0.387176\pi\)
−0.868703 + 0.495333i \(0.835046\pi\)
\(480\) 0 0
\(481\) −2.05061 + 1.72067i −0.0934998 + 0.0784557i
\(482\) 0 0
\(483\) −0.406432 + 3.13054i −0.0184933 + 0.142444i
\(484\) 0 0
\(485\) −1.27250 7.21673i −0.0577815 0.327695i
\(486\) 0 0
\(487\) 28.9750 16.7288i 1.31298 0.758052i 0.330395 0.943843i \(-0.392818\pi\)
0.982589 + 0.185791i \(0.0594846\pi\)
\(488\) 0 0
\(489\) −17.6258 19.1660i −0.797066 0.866718i
\(490\) 0 0
\(491\) −0.635055 + 0.756829i −0.0286596 + 0.0341552i −0.780184 0.625550i \(-0.784875\pi\)
0.751524 + 0.659705i \(0.229319\pi\)
\(492\) 0 0
\(493\) 54.9658i 2.47554i
\(494\) 0 0
\(495\) 1.53557 1.54663i 0.0690188 0.0695158i
\(496\) 0 0
\(497\) 0.0408543 + 0.0342808i 0.00183256 + 0.00153770i
\(498\) 0 0
\(499\) 4.11402 1.49738i 0.184169 0.0670319i −0.248290 0.968686i \(-0.579868\pi\)
0.432458 + 0.901654i \(0.357646\pi\)
\(500\) 0 0
\(501\) −9.94052 + 13.0030i −0.444110 + 0.580930i
\(502\) 0 0
\(503\) −31.7905 + 5.60552i −1.41747 + 0.249938i −0.829301 0.558802i \(-0.811261\pi\)
−0.588167 + 0.808740i \(0.700150\pi\)
\(504\) 0 0
\(505\) 7.11080 12.3163i 0.316426 0.548067i
\(506\) 0 0
\(507\) 19.3440 + 10.0258i 0.859097 + 0.445261i
\(508\) 0 0
\(509\) 21.2608 + 7.73831i 0.942370 + 0.342994i 0.767101 0.641526i \(-0.221698\pi\)
0.175268 + 0.984521i \(0.443921\pi\)
\(510\) 0 0
\(511\) −1.07375 + 6.08956i −0.0475000 + 0.269386i
\(512\) 0 0
\(513\) 12.7015 18.7529i 0.560785 0.827962i
\(514\) 0 0
\(515\) −1.50474 + 8.53380i −0.0663067 + 0.376044i
\(516\) 0 0
\(517\) −2.85234 1.03817i −0.125446 0.0456585i
\(518\) 0 0
\(519\) 20.6807 + 10.7186i 0.907781 + 0.470493i
\(520\) 0 0
\(521\) 4.86213 8.42145i 0.213014 0.368950i −0.739643 0.673000i \(-0.765005\pi\)
0.952656 + 0.304049i \(0.0983388\pi\)
\(522\) 0 0
\(523\) −33.5671 + 5.91879i −1.46779 + 0.258810i −0.849686 0.527288i \(-0.823209\pi\)
−0.618101 + 0.786099i \(0.712098\pi\)
\(524\) 0 0
\(525\) 7.24847 9.48155i 0.316349 0.413809i
\(526\) 0 0
\(527\) 19.5709 7.12324i 0.852523 0.310293i
\(528\) 0 0
\(529\) 16.5678 + 13.9021i 0.720341 + 0.604438i
\(530\) 0 0
\(531\) 24.6114 24.7886i 1.06804 1.07573i
\(532\) 0 0
\(533\) 3.46992i 0.150299i
\(534\) 0 0
\(535\) 1.14489 1.36443i 0.0494980 0.0589894i
\(536\) 0 0
\(537\) −19.5715 21.2818i −0.844572 0.918376i
\(538\) 0 0
\(539\) −3.81174 + 2.20071i −0.164183 + 0.0947911i
\(540\) 0 0
\(541\) 0.180608 + 1.02428i 0.00776495 + 0.0440372i 0.988444 0.151586i \(-0.0484381\pi\)
−0.980679 + 0.195623i \(0.937327\pi\)
\(542\) 0 0
\(543\) 2.27338 17.5107i 0.0975603 0.751457i
\(544\) 0 0
\(545\) −3.75277 + 3.14895i −0.160751 + 0.134886i
\(546\) 0 0
\(547\) −8.86889 + 24.3671i −0.379207 + 1.04186i 0.592480 + 0.805586i \(0.298149\pi\)
−0.971686 + 0.236276i \(0.924073\pi\)
\(548\) 0 0
\(549\) −18.7390 26.5587i −0.799760 1.13350i
\(550\) 0 0
\(551\) 16.5032 + 30.9317i 0.703060 + 1.31773i
\(552\) 0 0
\(553\) −2.12897 0.375395i −0.0905330 0.0159634i
\(554\) 0 0
\(555\) 0.245319 + 5.39658i 0.0104132 + 0.229072i
\(556\) 0 0
\(557\) −2.42914 2.89494i −0.102926 0.122662i 0.712122 0.702055i \(-0.247734\pi\)
−0.815048 + 0.579393i \(0.803290\pi\)
\(558\) 0 0
\(559\) 4.39021 + 2.53469i 0.185686 + 0.107206i
\(560\) 0 0
\(561\) 9.58440 6.13013i 0.404654 0.258814i
\(562\) 0 0
\(563\) −5.99208 10.3786i −0.252536 0.437406i 0.711687 0.702496i \(-0.247931\pi\)
−0.964223 + 0.265091i \(0.914598\pi\)
\(564\) 0 0
\(565\) 2.59510 + 7.12998i 0.109177 + 0.299960i
\(566\) 0 0
\(567\) 8.92374 10.7912i 0.374762 0.453188i
\(568\) 0 0
\(569\) 11.2148 0.470147 0.235074 0.971978i \(-0.424467\pi\)
0.235074 + 0.971978i \(0.424467\pi\)
\(570\) 0 0
\(571\) −16.2525 −0.680144 −0.340072 0.940399i \(-0.610452\pi\)
−0.340072 + 0.940399i \(0.610452\pi\)
\(572\) 0 0
\(573\) 19.9440 + 6.24902i 0.833174 + 0.261057i
\(574\) 0 0
\(575\) 1.77435 + 4.87499i 0.0739956 + 0.203301i
\(576\) 0 0
\(577\) −4.02000 6.96284i −0.167355 0.289867i 0.770134 0.637882i \(-0.220189\pi\)
−0.937489 + 0.348015i \(0.886856\pi\)
\(578\) 0 0
\(579\) −3.12138 4.88025i −0.129720 0.202816i
\(580\) 0 0
\(581\) −16.3145 9.41916i −0.676838 0.390772i
\(582\) 0 0
\(583\) 8.95984 + 10.6779i 0.371079 + 0.442234i
\(584\) 0 0
\(585\) −1.33089 + 0.626428i −0.0550257 + 0.0258996i
\(586\) 0 0
\(587\) 19.5628 + 3.44945i 0.807444 + 0.142374i 0.562108 0.827064i \(-0.309991\pi\)
0.245336 + 0.969438i \(0.421102\pi\)
\(588\) 0 0
\(589\) 8.87470 9.88463i 0.365676 0.407289i
\(590\) 0 0
\(591\) 2.24779 + 10.0537i 0.0924617 + 0.413556i
\(592\) 0 0
\(593\) −7.64203 + 20.9963i −0.313821 + 0.862215i 0.678056 + 0.735010i \(0.262823\pi\)
−0.991876 + 0.127205i \(0.959399\pi\)
\(594\) 0 0
\(595\) −6.15644 + 5.16587i −0.252390 + 0.211780i
\(596\) 0 0
\(597\) 19.1982 + 2.49246i 0.785729 + 0.102010i
\(598\) 0 0
\(599\) −2.89198 16.4012i −0.118163 0.670136i −0.985135 0.171780i \(-0.945048\pi\)
0.866972 0.498356i \(-0.166063\pi\)
\(600\) 0 0
\(601\) 17.9204 10.3464i 0.730990 0.422037i −0.0877940 0.996139i \(-0.527982\pi\)
0.818784 + 0.574101i \(0.194648\pi\)
\(602\) 0 0
\(603\) −25.4150 11.7404i −1.03498 0.478106i
\(604\) 0 0
\(605\) −4.89540 + 5.83411i −0.199026 + 0.237191i
\(606\) 0 0
\(607\) 39.3916i 1.59886i 0.600761 + 0.799428i \(0.294864\pi\)
−0.600761 + 0.799428i \(0.705136\pi\)
\(608\) 0 0
\(609\) 8.33058 + 20.0102i 0.337572 + 0.810854i
\(610\) 0 0
\(611\) 1.56934 + 1.31683i 0.0634888 + 0.0532734i
\(612\) 0 0
\(613\) −26.4005 + 9.60900i −1.06631 + 0.388104i −0.814794 0.579750i \(-0.803150\pi\)
−0.251512 + 0.967854i \(0.580928\pi\)
\(614\) 0 0
\(615\) −5.56314 4.25292i −0.224328 0.171494i
\(616\) 0 0
\(617\) 20.3648 3.59086i 0.819854 0.144562i 0.252038 0.967717i \(-0.418899\pi\)
0.567817 + 0.823155i \(0.307788\pi\)
\(618\) 0 0
\(619\) −16.8830 + 29.2423i −0.678586 + 1.17535i 0.296821 + 0.954933i \(0.404074\pi\)
−0.975407 + 0.220412i \(0.929260\pi\)
\(620\) 0 0
\(621\) 1.86156 + 5.79519i 0.0747019 + 0.232553i
\(622\) 0 0
\(623\) −8.93358 3.25156i −0.357916 0.130271i
\(624\) 0 0
\(625\) 2.90984 16.5025i 0.116394 0.660101i
\(626\) 0 0
\(627\) 3.55302 6.32736i 0.141894 0.252690i
\(628\) 0 0
\(629\) −4.89690 + 27.7717i −0.195252 + 1.10733i
\(630\) 0 0
\(631\) 35.0060 + 12.7411i 1.39357 + 0.507217i 0.926262 0.376880i \(-0.123003\pi\)
0.467304 + 0.884096i \(0.345225\pi\)
\(632\) 0 0
\(633\) −16.9451 + 32.6942i −0.673506 + 1.29948i
\(634\) 0 0
\(635\) −5.26287 + 9.11556i −0.208851 + 0.361740i
\(636\) 0 0
\(637\) 2.92545 0.515836i 0.115911 0.0204382i
\(638\) 0 0
\(639\) 0.0994226 + 0.0262583i 0.00393310 + 0.00103876i
\(640\) 0 0
\(641\) −7.37099 + 2.68282i −0.291137 + 0.105965i −0.483460 0.875367i \(-0.660620\pi\)
0.192323 + 0.981332i \(0.438398\pi\)
\(642\) 0 0
\(643\) −29.9819 25.1578i −1.18237 0.992126i −0.999960 0.00890393i \(-0.997166\pi\)
−0.182410 0.983223i \(-0.558390\pi\)
\(644\) 0 0
\(645\) 9.44461 3.93195i 0.371881 0.154820i
\(646\) 0 0
\(647\) 6.21339i 0.244274i 0.992513 + 0.122137i \(0.0389747\pi\)
−0.992513 + 0.122137i \(0.961025\pi\)
\(648\) 0 0
\(649\) 7.19386 8.57331i 0.282384 0.336532i
\(650\) 0 0
\(651\) 6.04516 5.55935i 0.236929 0.217888i
\(652\) 0 0
\(653\) −23.3831 + 13.5002i −0.915050 + 0.528304i −0.882053 0.471151i \(-0.843839\pi\)
−0.0329976 + 0.999455i \(0.510505\pi\)
\(654\) 0 0
\(655\) 1.46082 + 8.28473i 0.0570790 + 0.323711i
\(656\) 0 0
\(657\) 3.12714 + 11.5054i 0.122001 + 0.448868i
\(658\) 0 0
\(659\) −23.3482 + 19.5915i −0.909517 + 0.763176i −0.972027 0.234869i \(-0.924534\pi\)
0.0625097 + 0.998044i \(0.480090\pi\)
\(660\) 0 0
\(661\) −11.2133 + 30.8082i −0.436146 + 1.19830i 0.505834 + 0.862631i \(0.331185\pi\)
−0.941980 + 0.335670i \(0.891037\pi\)
\(662\) 0 0
\(663\) −7.49360 + 1.67540i −0.291027 + 0.0650671i
\(664\) 0 0
\(665\) −1.91347 + 4.75550i −0.0742013 + 0.184410i
\(666\) 0 0
\(667\) −9.27861 1.63607i −0.359269 0.0633489i
\(668\) 0 0
\(669\) 23.8370 1.08359i 0.921591 0.0418939i
\(670\) 0 0
\(671\) −6.69399 7.97759i −0.258419 0.307971i
\(672\) 0 0
\(673\) 26.7750 + 15.4586i 1.03210 + 0.595884i 0.917586 0.397537i \(-0.130135\pi\)
0.114516 + 0.993421i \(0.463468\pi\)
\(674\) 0 0
\(675\) 4.85980 22.4933i 0.187054 0.865766i
\(676\) 0 0
\(677\) −19.6720 34.0729i −0.756057 1.30953i −0.944847 0.327511i \(-0.893790\pi\)
0.188791 0.982017i \(-0.439543\pi\)
\(678\) 0 0
\(679\) −5.15932 14.1751i −0.197996 0.543991i
\(680\) 0 0
\(681\) 8.38366 26.7568i 0.321263 1.02532i
\(682\) 0 0
\(683\) −12.0176 −0.459840 −0.229920 0.973210i \(-0.573846\pi\)
−0.229920 + 0.973210i \(0.573846\pi\)
\(684\) 0 0
\(685\) 3.75147 0.143336
\(686\) 0 0
\(687\) 13.2815 42.3885i 0.506720 1.61722i
\(688\) 0 0
\(689\) −3.21761 8.84031i −0.122581 0.336789i
\(690\) 0 0
\(691\) 17.5214 + 30.3479i 0.666544 + 1.15449i 0.978864 + 0.204512i \(0.0655606\pi\)
−0.312320 + 0.949977i \(0.601106\pi\)
\(692\) 0 0
\(693\) 2.56010 3.68427i 0.0972503 0.139954i
\(694\) 0 0
\(695\) −2.36010 1.36260i −0.0895237 0.0516865i
\(696\) 0 0
\(697\) −23.4968 28.0024i −0.890006 1.06067i
\(698\) 0 0
\(699\) −20.1400 + 0.915530i −0.761766 + 0.0346285i
\(700\) 0 0
\(701\) −2.95841 0.521647i −0.111738 0.0197023i 0.117500 0.993073i \(-0.462512\pi\)
−0.229237 + 0.973371i \(0.573623\pi\)
\(702\) 0 0
\(703\) 5.58262 + 17.0986i 0.210552 + 0.644887i
\(704\) 0 0
\(705\) 4.03468 0.902063i 0.151955 0.0339737i
\(706\) 0 0
\(707\) 10.0127 27.5097i 0.376567 1.03461i
\(708\) 0 0
\(709\) 2.36012 1.98037i 0.0886360 0.0743744i −0.597393 0.801949i \(-0.703797\pi\)
0.686029 + 0.727574i \(0.259352\pi\)
\(710\) 0 0
\(711\) −4.02239 + 1.09328i −0.150852 + 0.0410011i
\(712\) 0 0
\(713\) 0.619918 + 3.51573i 0.0232161 + 0.131665i
\(714\) 0 0
\(715\) −0.408138 + 0.235639i −0.0152635 + 0.00881239i
\(716\) 0 0
\(717\) −19.4073 + 17.8476i −0.724777 + 0.666532i
\(718\) 0 0
\(719\) −7.13781 + 8.50651i −0.266195 + 0.317239i −0.882540 0.470237i \(-0.844168\pi\)
0.616345 + 0.787476i \(0.288613\pi\)
\(720\) 0 0
\(721\) 17.8378i 0.664316i
\(722\) 0 0
\(723\) −24.2796 + 10.1080i −0.902969 + 0.375921i
\(724\) 0 0
\(725\) 27.2868 + 22.8964i 1.01341 + 0.850349i
\(726\) 0 0
\(727\) −13.8709 + 5.04860i −0.514444 + 0.187242i −0.586179 0.810182i \(-0.699368\pi\)
0.0717355 + 0.997424i \(0.477146\pi\)
\(728\) 0 0
\(729\) 6.70703 26.1537i 0.248409 0.968655i
\(730\) 0 0
\(731\) 52.5931 9.27357i 1.94522 0.342996i
\(732\) 0 0
\(733\) −18.1447 + 31.4276i −0.670191 + 1.16080i 0.307659 + 0.951497i \(0.400454\pi\)
−0.977850 + 0.209308i \(0.932879\pi\)
\(734\) 0 0
\(735\) 2.75857 5.32245i 0.101751 0.196322i
\(736\) 0 0
\(737\) −8.42862 3.06777i −0.310472 0.113003i
\(738\) 0 0
\(739\) 2.94942 16.7270i 0.108496 0.615312i −0.881270 0.472613i \(-0.843311\pi\)
0.989766 0.142699i \(-0.0455780\pi\)
\(740\) 0 0
\(741\) −3.71394 + 3.19273i −0.136435 + 0.117288i
\(742\) 0 0
\(743\) 4.59818 26.0776i 0.168691 0.956693i −0.776486 0.630134i \(-0.783000\pi\)
0.945177 0.326559i \(-0.105889\pi\)
\(744\) 0 0
\(745\) −13.6097 4.95352i −0.498620 0.181483i
\(746\) 0 0
\(747\) −36.1962 3.03595i −1.32435 0.111080i
\(748\) 0 0
\(749\) 1.83324 3.17526i 0.0669850 0.116021i
\(750\) 0 0
\(751\) −46.8929 + 8.26849i −1.71115 + 0.301722i −0.941566 0.336827i \(-0.890646\pi\)
−0.769581 + 0.638549i \(0.779535\pi\)
\(752\) 0 0
\(753\) 14.9274 + 11.4117i 0.543984 + 0.415866i
\(754\) 0 0
\(755\) 13.6812 4.97954i 0.497909 0.181224i
\(756\) 0 0
\(757\) −12.6519 10.6162i −0.459843 0.385854i 0.383230 0.923653i \(-0.374812\pi\)
−0.843073 + 0.537799i \(0.819256\pi\)
\(758\) 0 0
\(759\) 0.749527 + 1.80038i 0.0272061 + 0.0653496i
\(760\) 0 0
\(761\) 19.1974i 0.695906i 0.937512 + 0.347953i \(0.113123\pi\)
−0.937512 + 0.347953i \(0.886877\pi\)
\(762\) 0 0
\(763\) −6.48211 + 7.72508i −0.234668 + 0.279667i
\(764\) 0 0
\(765\) −6.49847 + 14.0675i −0.234953 + 0.508613i
\(766\) 0 0
\(767\) −6.54145 + 3.77671i −0.236198 + 0.136369i
\(768\) 0 0
\(769\) −5.25863 29.8231i −0.189631 1.07545i −0.919860 0.392248i \(-0.871698\pi\)
0.730229 0.683203i \(-0.239413\pi\)
\(770\) 0 0
\(771\) 0.0777483 + 0.0100939i 0.00280004 + 0.000363524i
\(772\) 0 0
\(773\) 21.9958 18.4567i 0.791134 0.663840i −0.154892 0.987931i \(-0.549503\pi\)
0.946026 + 0.324091i \(0.105058\pi\)
\(774\) 0 0
\(775\) 4.61619 12.6829i 0.165818 0.455582i
\(776\) 0 0
\(777\) 2.42635 + 10.8524i 0.0870449 + 0.389328i
\(778\) 0 0
\(779\) −21.6303 8.70339i −0.774985 0.311831i
\(780\) 0 0
\(781\) 0.0324458 + 0.00572106i 0.00116100 + 0.000204716i
\(782\) 0 0
\(783\) 30.9645 + 28.0687i 1.10658 + 1.00309i
\(784\) 0 0
\(785\) 0.103890 + 0.123812i 0.00370800 + 0.00441903i
\(786\) 0 0
\(787\) −22.1812 12.8063i −0.790673 0.456495i 0.0495262 0.998773i \(-0.484229\pi\)
−0.840200 + 0.542277i \(0.817562\pi\)
\(788\) 0 0
\(789\) 5.11899 + 8.00348i 0.182241 + 0.284932i
\(790\) 0 0
\(791\) 7.80951 + 13.5265i 0.277674 + 0.480946i
\(792\) 0 0
\(793\) 2.40391 + 6.60469i 0.0853653 + 0.234539i