Properties

Label 1900.2.i.g.201.7
Level $1900$
Weight $2$
Character 1900.201
Analytic conductor $15.172$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 20 x^{18} + 261 x^{16} + 1994 x^{14} + 11074 x^{12} + 39211 x^{10} + 99376 x^{8} + 134299 x^{6} + 124617 x^{4} + 24768 x^{2} + 4096\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 380)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.7
Root \(-0.628167 - 1.08802i\) of defining polynomial
Character \(\chi\) \(=\) 1900.201
Dual form 1900.2.i.g.501.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.628167 - 1.08802i) q^{3} +4.97100 q^{7} +(0.710812 + 1.23116i) q^{9} +O(q^{10})\) \(q+(0.628167 - 1.08802i) q^{3} +4.97100 q^{7} +(0.710812 + 1.23116i) q^{9} -3.85491 q^{11} +(-1.33470 - 2.31178i) q^{13} +(1.29521 - 2.24337i) q^{17} +(-1.24479 - 4.17738i) q^{19} +(3.12262 - 5.40854i) q^{21} +(-1.08682 - 1.88243i) q^{23} +5.55504 q^{27} +(-1.29432 - 2.24183i) q^{29} +7.76610 q^{31} +(-2.42153 + 4.19421i) q^{33} -2.75768 q^{37} -3.35367 q^{39} +(3.66243 - 6.34351i) q^{41} +(0.895083 - 1.55033i) q^{43} +(0.854141 + 1.47942i) q^{47} +17.7109 q^{49} +(-1.62722 - 2.81842i) q^{51} +(3.98220 + 6.89738i) q^{53} +(-5.32700 - 1.26974i) q^{57} +(0.127300 - 0.220490i) q^{59} +(-1.66702 - 2.88737i) q^{61} +(3.53345 + 6.12011i) q^{63} +(6.60237 + 11.4356i) q^{67} -2.73082 q^{69} +(3.85760 - 6.68156i) q^{71} +(-2.25489 + 3.90558i) q^{73} -19.1628 q^{77} +(-5.52715 + 9.57330i) q^{79} +(1.35706 - 2.35050i) q^{81} -3.04360 q^{83} -3.25221 q^{87} +(-4.76212 - 8.24824i) q^{89} +(-6.63482 - 11.4918i) q^{91} +(4.87841 - 8.44966i) q^{93} +(5.61676 - 9.72851i) q^{97} +(-2.74011 - 4.74601i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 10 q^{9} + O(q^{10}) \) \( 20 q - 10 q^{9} - 14 q^{19} - 8 q^{21} + 16 q^{29} + 8 q^{31} + 8 q^{39} + 26 q^{41} + 44 q^{49} + 26 q^{51} - 4 q^{59} + 2 q^{61} - 48 q^{69} - 2 q^{71} + 16 q^{79} + 26 q^{81} + 40 q^{89} - 4 q^{91} + 20 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\) \(951\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.628167 1.08802i 0.362673 0.628167i −0.625727 0.780042i \(-0.715198\pi\)
0.988400 + 0.151875i \(0.0485310\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 4.97100 1.87886 0.939432 0.342736i \(-0.111354\pi\)
0.939432 + 0.342736i \(0.111354\pi\)
\(8\) 0 0
\(9\) 0.710812 + 1.23116i 0.236937 + 0.410387i
\(10\) 0 0
\(11\) −3.85491 −1.16230 −0.581149 0.813797i \(-0.697397\pi\)
−0.581149 + 0.813797i \(0.697397\pi\)
\(12\) 0 0
\(13\) −1.33470 2.31178i −0.370180 0.641171i 0.619413 0.785066i \(-0.287371\pi\)
−0.989593 + 0.143894i \(0.954037\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.29521 2.24337i 0.314135 0.544097i −0.665118 0.746738i \(-0.731619\pi\)
0.979253 + 0.202641i \(0.0649523\pi\)
\(18\) 0 0
\(19\) −1.24479 4.17738i −0.285574 0.958357i
\(20\) 0 0
\(21\) 3.12262 5.40854i 0.681412 1.18024i
\(22\) 0 0
\(23\) −1.08682 1.88243i −0.226618 0.392514i 0.730186 0.683249i \(-0.239434\pi\)
−0.956804 + 0.290735i \(0.906100\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 5.55504 1.06907
\(28\) 0 0
\(29\) −1.29432 2.24183i −0.240350 0.416298i 0.720464 0.693492i \(-0.243929\pi\)
−0.960814 + 0.277194i \(0.910595\pi\)
\(30\) 0 0
\(31\) 7.76610 1.39483 0.697417 0.716666i \(-0.254333\pi\)
0.697417 + 0.716666i \(0.254333\pi\)
\(32\) 0 0
\(33\) −2.42153 + 4.19421i −0.421533 + 0.730117i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.75768 −0.453359 −0.226680 0.973969i \(-0.572787\pi\)
−0.226680 + 0.973969i \(0.572787\pi\)
\(38\) 0 0
\(39\) −3.35367 −0.537017
\(40\) 0 0
\(41\) 3.66243 6.34351i 0.571975 0.990690i −0.424388 0.905481i \(-0.639511\pi\)
0.996363 0.0852097i \(-0.0271560\pi\)
\(42\) 0 0
\(43\) 0.895083 1.55033i 0.136499 0.236423i −0.789670 0.613532i \(-0.789748\pi\)
0.926169 + 0.377109i \(0.123082\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0.854141 + 1.47942i 0.124589 + 0.215795i 0.921572 0.388207i \(-0.126905\pi\)
−0.796983 + 0.604002i \(0.793572\pi\)
\(48\) 0 0
\(49\) 17.7109 2.53013
\(50\) 0 0
\(51\) −1.62722 2.81842i −0.227856 0.394658i
\(52\) 0 0
\(53\) 3.98220 + 6.89738i 0.546998 + 0.947428i 0.998478 + 0.0551469i \(0.0175627\pi\)
−0.451480 + 0.892281i \(0.649104\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −5.32700 1.26974i −0.705578 0.168182i
\(58\) 0 0
\(59\) 0.127300 0.220490i 0.0165730 0.0287053i −0.857620 0.514284i \(-0.828058\pi\)
0.874193 + 0.485579i \(0.161391\pi\)
\(60\) 0 0
\(61\) −1.66702 2.88737i −0.213441 0.369690i 0.739349 0.673323i \(-0.235134\pi\)
−0.952789 + 0.303633i \(0.901800\pi\)
\(62\) 0 0
\(63\) 3.53345 + 6.12011i 0.445173 + 0.771062i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 6.60237 + 11.4356i 0.806607 + 1.39708i 0.915201 + 0.402999i \(0.132032\pi\)
−0.108593 + 0.994086i \(0.534635\pi\)
\(68\) 0 0
\(69\) −2.73082 −0.328752
\(70\) 0 0
\(71\) 3.85760 6.68156i 0.457813 0.792955i −0.541032 0.841002i \(-0.681966\pi\)
0.998845 + 0.0480468i \(0.0152997\pi\)
\(72\) 0 0
\(73\) −2.25489 + 3.90558i −0.263915 + 0.457114i −0.967279 0.253716i \(-0.918347\pi\)
0.703364 + 0.710830i \(0.251680\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −19.1628 −2.18380
\(78\) 0 0
\(79\) −5.52715 + 9.57330i −0.621852 + 1.07708i 0.367288 + 0.930107i \(0.380286\pi\)
−0.989141 + 0.146973i \(0.953047\pi\)
\(80\) 0 0
\(81\) 1.35706 2.35050i 0.150784 0.261166i
\(82\) 0 0
\(83\) −3.04360 −0.334079 −0.167040 0.985950i \(-0.553421\pi\)
−0.167040 + 0.985950i \(0.553421\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −3.25221 −0.348673
\(88\) 0 0
\(89\) −4.76212 8.24824i −0.504784 0.874311i −0.999985 0.00553277i \(-0.998239\pi\)
0.495201 0.868779i \(-0.335094\pi\)
\(90\) 0 0
\(91\) −6.63482 11.4918i −0.695518 1.20467i
\(92\) 0 0
\(93\) 4.87841 8.44966i 0.505868 0.876189i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 5.61676 9.72851i 0.570295 0.987780i −0.426240 0.904610i \(-0.640162\pi\)
0.996535 0.0831703i \(-0.0265045\pi\)
\(98\) 0 0
\(99\) −2.74011 4.74601i −0.275392 0.476992i
\(100\) 0 0
\(101\) 5.45345 + 9.44564i 0.542638 + 0.939877i 0.998751 + 0.0499550i \(0.0159078\pi\)
−0.456113 + 0.889922i \(0.650759\pi\)
\(102\) 0 0
\(103\) 11.4532 1.12852 0.564260 0.825597i \(-0.309161\pi\)
0.564260 + 0.825597i \(0.309161\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −18.3401 −1.77300 −0.886502 0.462725i \(-0.846872\pi\)
−0.886502 + 0.462725i \(0.846872\pi\)
\(108\) 0 0
\(109\) 6.55467 11.3530i 0.627824 1.08742i −0.360164 0.932889i \(-0.617279\pi\)
0.987988 0.154533i \(-0.0493874\pi\)
\(110\) 0 0
\(111\) −1.73228 + 3.00040i −0.164421 + 0.284785i
\(112\) 0 0
\(113\) 0.696954 0.0655640 0.0327820 0.999463i \(-0.489563\pi\)
0.0327820 + 0.999463i \(0.489563\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.89745 3.28647i 0.175419 0.303835i
\(118\) 0 0
\(119\) 6.43850 11.1518i 0.590216 1.02228i
\(120\) 0 0
\(121\) 3.86029 0.350936
\(122\) 0 0
\(123\) −4.60124 7.96957i −0.414879 0.718592i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 6.92636 + 11.9968i 0.614615 + 1.06454i 0.990452 + 0.137859i \(0.0440220\pi\)
−0.375837 + 0.926686i \(0.622645\pi\)
\(128\) 0 0
\(129\) −1.12452 1.94773i −0.0990088 0.171488i
\(130\) 0 0
\(131\) 6.11533 10.5921i 0.534299 0.925433i −0.464898 0.885364i \(-0.653909\pi\)
0.999197 0.0400690i \(-0.0127578\pi\)
\(132\) 0 0
\(133\) −6.18785 20.7658i −0.536554 1.80062i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −4.59855 7.96493i −0.392881 0.680490i 0.599947 0.800039i \(-0.295188\pi\)
−0.992828 + 0.119550i \(0.961855\pi\)
\(138\) 0 0
\(139\) 3.22178 + 5.58028i 0.273267 + 0.473313i 0.969697 0.244312i \(-0.0785623\pi\)
−0.696429 + 0.717626i \(0.745229\pi\)
\(140\) 0 0
\(141\) 2.14617 0.180741
\(142\) 0 0
\(143\) 5.14516 + 8.91168i 0.430260 + 0.745232i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 11.1254 19.2698i 0.917608 1.58934i
\(148\) 0 0
\(149\) −11.5381 + 19.9846i −0.945239 + 1.63720i −0.189966 + 0.981791i \(0.560838\pi\)
−0.755272 + 0.655411i \(0.772495\pi\)
\(150\) 0 0
\(151\) 20.1613 1.64071 0.820353 0.571858i \(-0.193777\pi\)
0.820353 + 0.571858i \(0.193777\pi\)
\(152\) 0 0
\(153\) 3.68260 0.297721
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −5.93532 + 10.2803i −0.473690 + 0.820456i −0.999546 0.0301179i \(-0.990412\pi\)
0.525856 + 0.850574i \(0.323745\pi\)
\(158\) 0 0
\(159\) 10.0060 0.793524
\(160\) 0 0
\(161\) −5.40259 9.35757i −0.425784 0.737480i
\(162\) 0 0
\(163\) −13.1763 −1.03205 −0.516023 0.856575i \(-0.672588\pi\)
−0.516023 + 0.856575i \(0.672588\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1.83285 3.17459i −0.141830 0.245657i 0.786356 0.617774i \(-0.211965\pi\)
−0.928186 + 0.372117i \(0.878632\pi\)
\(168\) 0 0
\(169\) 2.93713 5.08726i 0.225933 0.391327i
\(170\) 0 0
\(171\) 4.25822 4.50186i 0.325634 0.344266i
\(172\) 0 0
\(173\) −0.0426855 + 0.0739334i −0.00324532 + 0.00562105i −0.867644 0.497187i \(-0.834366\pi\)
0.864398 + 0.502808i \(0.167700\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −0.159931 0.277009i −0.0120212 0.0208212i
\(178\) 0 0
\(179\) −16.2256 −1.21276 −0.606380 0.795175i \(-0.707379\pi\)
−0.606380 + 0.795175i \(0.707379\pi\)
\(180\) 0 0
\(181\) −10.1549 17.5888i −0.754808 1.30737i −0.945470 0.325710i \(-0.894397\pi\)
0.190662 0.981656i \(-0.438937\pi\)
\(182\) 0 0
\(183\) −4.18868 −0.309636
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −4.99291 + 8.64798i −0.365118 + 0.632403i
\(188\) 0 0
\(189\) 27.6141 2.00863
\(190\) 0 0
\(191\) −21.9157 −1.58576 −0.792881 0.609377i \(-0.791420\pi\)
−0.792881 + 0.609377i \(0.791420\pi\)
\(192\) 0 0
\(193\) −2.51480 + 4.35575i −0.181019 + 0.313534i −0.942228 0.334973i \(-0.891273\pi\)
0.761209 + 0.648507i \(0.224606\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 19.1189 1.36217 0.681084 0.732205i \(-0.261509\pi\)
0.681084 + 0.732205i \(0.261509\pi\)
\(198\) 0 0
\(199\) −9.04425 15.6651i −0.641130 1.11047i −0.985181 0.171518i \(-0.945133\pi\)
0.344051 0.938951i \(-0.388201\pi\)
\(200\) 0 0
\(201\) 16.5896 1.17014
\(202\) 0 0
\(203\) −6.43409 11.1442i −0.451584 0.782167i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.54505 2.67611i 0.107388 0.186002i
\(208\) 0 0
\(209\) 4.79854 + 16.1034i 0.331922 + 1.11390i
\(210\) 0 0
\(211\) −8.03757 + 13.9215i −0.553329 + 0.958394i 0.444702 + 0.895678i \(0.353309\pi\)
−0.998031 + 0.0627157i \(0.980024\pi\)
\(212\) 0 0
\(213\) −4.84644 8.39427i −0.332072 0.575166i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 38.6053 2.62070
\(218\) 0 0
\(219\) 2.83289 + 4.90672i 0.191429 + 0.331565i
\(220\) 0 0
\(221\) −6.91489 −0.465146
\(222\) 0 0
\(223\) −8.66036 + 15.0002i −0.579941 + 1.00449i 0.415545 + 0.909573i \(0.363591\pi\)
−0.995485 + 0.0949140i \(0.969742\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −23.7579 −1.57687 −0.788434 0.615120i \(-0.789108\pi\)
−0.788434 + 0.615120i \(0.789108\pi\)
\(228\) 0 0
\(229\) 0.732245 0.0483881 0.0241941 0.999707i \(-0.492298\pi\)
0.0241941 + 0.999707i \(0.492298\pi\)
\(230\) 0 0
\(231\) −12.0374 + 20.8494i −0.792004 + 1.37179i
\(232\) 0 0
\(233\) −9.94933 + 17.2328i −0.651803 + 1.12896i 0.330883 + 0.943672i \(0.392654\pi\)
−0.982685 + 0.185283i \(0.940680\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 6.94394 + 12.0273i 0.451058 + 0.781255i
\(238\) 0 0
\(239\) −28.9063 −1.86979 −0.934897 0.354919i \(-0.884508\pi\)
−0.934897 + 0.354919i \(0.884508\pi\)
\(240\) 0 0
\(241\) 11.8979 + 20.6077i 0.766409 + 1.32746i 0.939499 + 0.342553i \(0.111292\pi\)
−0.173090 + 0.984906i \(0.555375\pi\)
\(242\) 0 0
\(243\) 6.62764 + 11.4794i 0.425163 + 0.736404i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −7.99574 + 8.45324i −0.508757 + 0.537867i
\(248\) 0 0
\(249\) −1.91189 + 3.31150i −0.121161 + 0.209858i
\(250\) 0 0
\(251\) 3.44694 + 5.97028i 0.217569 + 0.376840i 0.954064 0.299602i \(-0.0968540\pi\)
−0.736495 + 0.676443i \(0.763521\pi\)
\(252\) 0 0
\(253\) 4.18959 + 7.25659i 0.263397 + 0.456218i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.32874 + 10.9617i 0.394776 + 0.683772i 0.993073 0.117502i \(-0.0374888\pi\)
−0.598296 + 0.801275i \(0.704155\pi\)
\(258\) 0 0
\(259\) −13.7084 −0.851800
\(260\) 0 0
\(261\) 1.84004 3.18704i 0.113896 0.197273i
\(262\) 0 0
\(263\) −12.4743 + 21.6062i −0.769200 + 1.33229i 0.168797 + 0.985651i \(0.446012\pi\)
−0.937997 + 0.346643i \(0.887322\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −11.9656 −0.732285
\(268\) 0 0
\(269\) 9.54155 16.5265i 0.581759 1.00764i −0.413512 0.910499i \(-0.635698\pi\)
0.995271 0.0971371i \(-0.0309685\pi\)
\(270\) 0 0
\(271\) −1.48490 + 2.57192i −0.0902012 + 0.156233i −0.907596 0.419845i \(-0.862084\pi\)
0.817395 + 0.576078i \(0.195418\pi\)
\(272\) 0 0
\(273\) −16.6711 −1.00898
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −5.51535 −0.331385 −0.165693 0.986177i \(-0.552986\pi\)
−0.165693 + 0.986177i \(0.552986\pi\)
\(278\) 0 0
\(279\) 5.52024 + 9.56133i 0.330488 + 0.572422i
\(280\) 0 0
\(281\) 12.4800 + 21.6159i 0.744493 + 1.28950i 0.950431 + 0.310934i \(0.100642\pi\)
−0.205939 + 0.978565i \(0.566025\pi\)
\(282\) 0 0
\(283\) 6.72761 11.6526i 0.399915 0.692673i −0.593800 0.804613i \(-0.702373\pi\)
0.993715 + 0.111939i \(0.0357063\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 18.2060 31.5336i 1.07466 1.86137i
\(288\) 0 0
\(289\) 5.14486 + 8.91116i 0.302639 + 0.524186i
\(290\) 0 0
\(291\) −7.05653 12.2223i −0.413661 0.716482i
\(292\) 0 0
\(293\) 23.7710 1.38871 0.694357 0.719630i \(-0.255689\pi\)
0.694357 + 0.719630i \(0.255689\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −21.4141 −1.24257
\(298\) 0 0
\(299\) −2.90117 + 5.02497i −0.167779 + 0.290602i
\(300\) 0 0
\(301\) 4.44946 7.70670i 0.256463 0.444207i
\(302\) 0 0
\(303\) 13.7027 0.787200
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −3.37243 + 5.84122i −0.192475 + 0.333376i −0.946070 0.323963i \(-0.894985\pi\)
0.753595 + 0.657339i \(0.228318\pi\)
\(308\) 0 0
\(309\) 7.19455 12.4613i 0.409284 0.708900i
\(310\) 0 0
\(311\) −11.6908 −0.662924 −0.331462 0.943468i \(-0.607542\pi\)
−0.331462 + 0.943468i \(0.607542\pi\)
\(312\) 0 0
\(313\) −8.78157 15.2101i −0.496364 0.859727i 0.503628 0.863921i \(-0.331998\pi\)
−0.999991 + 0.00419387i \(0.998665\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 16.4775 + 28.5399i 0.925469 + 1.60296i 0.790806 + 0.612067i \(0.209662\pi\)
0.134663 + 0.990891i \(0.457005\pi\)
\(318\) 0 0
\(319\) 4.98949 + 8.64206i 0.279358 + 0.483862i
\(320\) 0 0
\(321\) −11.5206 + 19.9543i −0.643020 + 1.11374i
\(322\) 0 0
\(323\) −10.9837 2.61807i −0.611148 0.145673i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −8.23486 14.2632i −0.455389 0.788757i
\(328\) 0 0
\(329\) 4.24594 + 7.35418i 0.234086 + 0.405449i
\(330\) 0 0
\(331\) −4.54726 −0.249940 −0.124970 0.992161i \(-0.539883\pi\)
−0.124970 + 0.992161i \(0.539883\pi\)
\(332\) 0 0
\(333\) −1.96019 3.39515i −0.107418 0.186053i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 10.9801 19.0180i 0.598122 1.03598i −0.394976 0.918691i \(-0.629247\pi\)
0.993098 0.117286i \(-0.0374195\pi\)
\(338\) 0 0
\(339\) 0.437804 0.758299i 0.0237783 0.0411851i
\(340\) 0 0
\(341\) −29.9376 −1.62121
\(342\) 0 0
\(343\) 53.2439 2.87490
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −3.63104 + 6.28915i −0.194925 + 0.337619i −0.946876 0.321599i \(-0.895780\pi\)
0.751951 + 0.659219i \(0.229113\pi\)
\(348\) 0 0
\(349\) −16.0910 −0.861329 −0.430665 0.902512i \(-0.641721\pi\)
−0.430665 + 0.902512i \(0.641721\pi\)
\(350\) 0 0
\(351\) −7.41433 12.8420i −0.395748 0.685455i
\(352\) 0 0
\(353\) 33.4331 1.77947 0.889733 0.456481i \(-0.150890\pi\)
0.889733 + 0.456481i \(0.150890\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −8.08891 14.0104i −0.428110 0.741509i
\(358\) 0 0
\(359\) −9.97814 + 17.2826i −0.526626 + 0.912143i 0.472893 + 0.881120i \(0.343210\pi\)
−0.999519 + 0.0310231i \(0.990123\pi\)
\(360\) 0 0
\(361\) −15.9010 + 10.3999i −0.836895 + 0.547363i
\(362\) 0 0
\(363\) 2.42491 4.20007i 0.127275 0.220446i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −3.81476 6.60735i −0.199129 0.344901i 0.749117 0.662437i \(-0.230478\pi\)
−0.948246 + 0.317536i \(0.897144\pi\)
\(368\) 0 0
\(369\) 10.4132 0.542089
\(370\) 0 0
\(371\) 19.7956 + 34.2869i 1.02773 + 1.78009i
\(372\) 0 0
\(373\) −2.22095 −0.114996 −0.0574982 0.998346i \(-0.518312\pi\)
−0.0574982 + 0.998346i \(0.518312\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −3.45508 + 5.98437i −0.177946 + 0.308211i
\(378\) 0 0
\(379\) 6.92717 0.355825 0.177912 0.984046i \(-0.443066\pi\)
0.177912 + 0.984046i \(0.443066\pi\)
\(380\) 0 0
\(381\) 17.4037 0.891616
\(382\) 0 0
\(383\) 9.60631 16.6386i 0.490859 0.850193i −0.509085 0.860716i \(-0.670016\pi\)
0.999945 + 0.0105227i \(0.00334956\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2.54494 0.129367
\(388\) 0 0
\(389\) −13.4261 23.2547i −0.680730 1.17906i −0.974758 0.223262i \(-0.928329\pi\)
0.294029 0.955797i \(-0.405004\pi\)
\(390\) 0 0
\(391\) −5.63065 −0.284754
\(392\) 0 0
\(393\) −7.68291 13.3072i −0.387551 0.671259i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −3.70839 + 6.42312i −0.186119 + 0.322367i −0.943953 0.330080i \(-0.892924\pi\)
0.757834 + 0.652447i \(0.226258\pi\)
\(398\) 0 0
\(399\) −26.4805 6.31190i −1.32568 0.315990i
\(400\) 0 0
\(401\) 2.66556 4.61689i 0.133112 0.230557i −0.791763 0.610829i \(-0.790836\pi\)
0.924875 + 0.380272i \(0.124170\pi\)
\(402\) 0 0
\(403\) −10.3655 17.9535i −0.516340 0.894327i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 10.6306 0.526938
\(408\) 0 0
\(409\) 5.70960 + 9.88933i 0.282322 + 0.488996i 0.971956 0.235162i \(-0.0755621\pi\)
−0.689634 + 0.724158i \(0.742229\pi\)
\(410\) 0 0
\(411\) −11.5546 −0.569948
\(412\) 0 0
\(413\) 0.632807 1.09605i 0.0311384 0.0539333i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 8.09526 0.396426
\(418\) 0 0
\(419\) −12.2311 −0.597529 −0.298765 0.954327i \(-0.596575\pi\)
−0.298765 + 0.954327i \(0.596575\pi\)
\(420\) 0 0
\(421\) 6.63359 11.4897i 0.323301 0.559974i −0.657866 0.753135i \(-0.728541\pi\)
0.981167 + 0.193161i \(0.0618739\pi\)
\(422\) 0 0
\(423\) −1.21427 + 2.10317i −0.0590397 + 0.102260i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −8.28678 14.3531i −0.401026 0.694597i
\(428\) 0 0
\(429\) 12.9281 0.624174
\(430\) 0 0
\(431\) −8.19094 14.1871i −0.394544 0.683370i 0.598499 0.801124i \(-0.295764\pi\)
−0.993043 + 0.117754i \(0.962431\pi\)
\(432\) 0 0
\(433\) 7.50864 + 13.0054i 0.360842 + 0.624997i 0.988100 0.153815i \(-0.0491559\pi\)
−0.627257 + 0.778812i \(0.715823\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −6.51076 + 6.88329i −0.311452 + 0.329272i
\(438\) 0 0
\(439\) −7.68192 + 13.3055i −0.366638 + 0.635035i −0.989038 0.147664i \(-0.952825\pi\)
0.622400 + 0.782700i \(0.286158\pi\)
\(440\) 0 0
\(441\) 12.5891 + 21.8050i 0.599481 + 1.03833i
\(442\) 0 0
\(443\) 12.1180 + 20.9890i 0.575745 + 0.997219i 0.995960 + 0.0897946i \(0.0286211\pi\)
−0.420216 + 0.907424i \(0.638046\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 14.4957 + 25.1073i 0.685624 + 1.18754i
\(448\) 0 0
\(449\) 16.8854 0.796873 0.398436 0.917196i \(-0.369553\pi\)
0.398436 + 0.917196i \(0.369553\pi\)
\(450\) 0 0
\(451\) −14.1183 + 24.4536i −0.664805 + 1.15148i
\(452\) 0 0
\(453\) 12.6647 21.9359i 0.595039 1.03064i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −29.1914 −1.36551 −0.682757 0.730645i \(-0.739219\pi\)
−0.682757 + 0.730645i \(0.739219\pi\)
\(458\) 0 0
\(459\) 7.19495 12.4620i 0.335831 0.581677i
\(460\) 0 0
\(461\) −1.87254 + 3.24333i −0.0872127 + 0.151057i −0.906332 0.422566i \(-0.861129\pi\)
0.819119 + 0.573623i \(0.194463\pi\)
\(462\) 0 0
\(463\) −21.4714 −0.997860 −0.498930 0.866642i \(-0.666273\pi\)
−0.498930 + 0.866642i \(0.666273\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 29.1079 1.34695 0.673476 0.739209i \(-0.264800\pi\)
0.673476 + 0.739209i \(0.264800\pi\)
\(468\) 0 0
\(469\) 32.8204 + 56.8466i 1.51550 + 2.62493i
\(470\) 0 0
\(471\) 7.45675 + 12.9155i 0.343589 + 0.595114i
\(472\) 0 0
\(473\) −3.45046 + 5.97637i −0.158652 + 0.274794i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −5.66119 + 9.80547i −0.259208 + 0.448962i
\(478\) 0 0
\(479\) 0.258348 + 0.447471i 0.0118042 + 0.0204455i 0.871867 0.489742i \(-0.162909\pi\)
−0.860063 + 0.510188i \(0.829576\pi\)
\(480\) 0 0
\(481\) 3.68068 + 6.37513i 0.167825 + 0.290681i
\(482\) 0 0
\(483\) −13.5749 −0.617681
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −10.6668 −0.483358 −0.241679 0.970356i \(-0.577698\pi\)
−0.241679 + 0.970356i \(0.577698\pi\)
\(488\) 0 0
\(489\) −8.27691 + 14.3360i −0.374295 + 0.648298i
\(490\) 0 0
\(491\) −12.0852 + 20.9322i −0.545398 + 0.944656i 0.453184 + 0.891417i \(0.350288\pi\)
−0.998582 + 0.0532395i \(0.983045\pi\)
\(492\) 0 0
\(493\) −6.70569 −0.302009
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 19.1761 33.2141i 0.860168 1.48985i
\(498\) 0 0
\(499\) 2.38934 4.13846i 0.106962 0.185263i −0.807576 0.589763i \(-0.799221\pi\)
0.914538 + 0.404500i \(0.132554\pi\)
\(500\) 0 0
\(501\) −4.60535 −0.205752
\(502\) 0 0
\(503\) −8.92453 15.4577i −0.397925 0.689227i 0.595545 0.803322i \(-0.296936\pi\)
−0.993470 + 0.114096i \(0.963603\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −3.69002 6.39130i −0.163879 0.283847i
\(508\) 0 0
\(509\) −3.57492 6.19194i −0.158455 0.274453i 0.775856 0.630909i \(-0.217318\pi\)
−0.934312 + 0.356457i \(0.883985\pi\)
\(510\) 0 0
\(511\) −11.2091 + 19.4147i −0.495860 + 0.858854i
\(512\) 0 0
\(513\) −6.91484 23.2055i −0.305298 1.02455i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −3.29263 5.70301i −0.144810 0.250818i
\(518\) 0 0
\(519\) 0.0536272 + 0.0928851i 0.00235397 + 0.00407720i
\(520\) 0 0
\(521\) −19.7280 −0.864301 −0.432151 0.901801i \(-0.642245\pi\)
−0.432151 + 0.901801i \(0.642245\pi\)
\(522\) 0 0
\(523\) 18.1328 + 31.4070i 0.792894 + 1.37333i 0.924168 + 0.381986i \(0.124760\pi\)
−0.131274 + 0.991346i \(0.541907\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 10.0587 17.4222i 0.438166 0.758925i
\(528\) 0 0
\(529\) 9.13764 15.8269i 0.397289 0.688124i
\(530\) 0 0
\(531\) 0.361944 0.0157070
\(532\) 0 0
\(533\) −19.5530 −0.846936
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −10.1924 + 17.6538i −0.439835 + 0.761816i
\(538\) 0 0
\(539\) −68.2738 −2.94076
\(540\) 0 0
\(541\) 11.4419 + 19.8180i 0.491927 + 0.852043i 0.999957 0.00929658i \(-0.00295924\pi\)
−0.508029 + 0.861340i \(0.669626\pi\)
\(542\) 0 0
\(543\) −25.5159 −1.09499
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 6.35861 + 11.0134i 0.271875 + 0.470901i 0.969342 0.245716i \(-0.0790230\pi\)
−0.697467 + 0.716617i \(0.745690\pi\)
\(548\) 0 0
\(549\) 2.36988 4.10475i 0.101144 0.175187i
\(550\) 0 0
\(551\) −7.75383 + 8.19749i −0.330324 + 0.349225i
\(552\) 0 0
\(553\) −27.4755 + 47.5889i −1.16838 + 2.02369i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 11.1803 + 19.3648i 0.473722 + 0.820511i 0.999547 0.0300814i \(-0.00957665\pi\)
−0.525825 + 0.850593i \(0.676243\pi\)
\(558\) 0 0
\(559\) −4.77869 −0.202117
\(560\) 0 0
\(561\) 6.27277 + 10.8648i 0.264837 + 0.458710i
\(562\) 0 0
\(563\) 10.6447 0.448619 0.224310 0.974518i \(-0.427987\pi\)
0.224310 + 0.974518i \(0.427987\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 6.74595 11.6843i 0.283303 0.490696i
\(568\) 0 0
\(569\) −3.13498 −0.131425 −0.0657126 0.997839i \(-0.520932\pi\)
−0.0657126 + 0.997839i \(0.520932\pi\)
\(570\) 0 0
\(571\) 1.29260 0.0540938 0.0270469 0.999634i \(-0.491390\pi\)
0.0270469 + 0.999634i \(0.491390\pi\)
\(572\) 0 0
\(573\) −13.7667 + 23.8446i −0.575112 + 0.996124i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −8.18544 −0.340764 −0.170382 0.985378i \(-0.554500\pi\)
−0.170382 + 0.985378i \(0.554500\pi\)
\(578\) 0 0
\(579\) 3.15943 + 5.47229i 0.131301 + 0.227420i
\(580\) 0 0
\(581\) −15.1298 −0.627689
\(582\) 0 0
\(583\) −15.3510 26.5887i −0.635774 1.10119i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −9.08512 + 15.7359i −0.374983 + 0.649490i −0.990325 0.138771i \(-0.955685\pi\)
0.615341 + 0.788261i \(0.289018\pi\)
\(588\) 0 0
\(589\) −9.66715 32.4420i −0.398328 1.33675i
\(590\) 0 0
\(591\) 12.0099 20.8017i 0.494021 0.855669i
\(592\) 0 0
\(593\) 4.44341 + 7.69621i 0.182469 + 0.316046i 0.942721 0.333583i \(-0.108258\pi\)
−0.760252 + 0.649629i \(0.774924\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −22.7252 −0.930081
\(598\) 0 0
\(599\) 2.18264 + 3.78044i 0.0891801 + 0.154465i 0.907165 0.420775i \(-0.138242\pi\)
−0.817985 + 0.575240i \(0.804909\pi\)
\(600\) 0 0
\(601\) −4.25303 −0.173485 −0.0867424 0.996231i \(-0.527646\pi\)
−0.0867424 + 0.996231i \(0.527646\pi\)
\(602\) 0 0
\(603\) −9.38608 + 16.2572i −0.382231 + 0.662043i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −23.5995 −0.957876 −0.478938 0.877849i \(-0.658978\pi\)
−0.478938 + 0.877849i \(0.658978\pi\)
\(608\) 0 0
\(609\) −16.1667 −0.655109
\(610\) 0 0
\(611\) 2.28005 3.94917i 0.0922410 0.159766i
\(612\) 0 0
\(613\) −10.1665 + 17.6090i −0.410623 + 0.711220i −0.994958 0.100293i \(-0.968022\pi\)
0.584335 + 0.811512i \(0.301355\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 15.6422 + 27.0932i 0.629733 + 1.09073i 0.987605 + 0.156959i \(0.0501691\pi\)
−0.357872 + 0.933771i \(0.616498\pi\)
\(618\) 0 0
\(619\) 25.7635 1.03552 0.517761 0.855525i \(-0.326766\pi\)
0.517761 + 0.855525i \(0.326766\pi\)
\(620\) 0 0
\(621\) −6.03733 10.4570i −0.242270 0.419624i
\(622\) 0 0
\(623\) −23.6725 41.0020i −0.948420 1.64271i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 20.5351 + 4.89474i 0.820092 + 0.195477i
\(628\) 0 0
\(629\) −3.57177 + 6.18649i −0.142416 + 0.246671i
\(630\) 0 0
\(631\) −10.6458 18.4391i −0.423804 0.734050i 0.572504 0.819902i \(-0.305972\pi\)
−0.996308 + 0.0858517i \(0.972639\pi\)
\(632\) 0 0
\(633\) 10.0979 + 17.4900i 0.401355 + 0.695167i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −23.6388 40.9436i −0.936603 1.62224i
\(638\) 0 0
\(639\) 10.9681 0.433891
\(640\) 0 0
\(641\) 16.5525 28.6698i 0.653785 1.13239i −0.328412 0.944535i \(-0.606513\pi\)
0.982197 0.187854i \(-0.0601533\pi\)
\(642\) 0 0
\(643\) −15.0702 + 26.1024i −0.594311 + 1.02938i 0.399333 + 0.916806i \(0.369242\pi\)
−0.993644 + 0.112570i \(0.964092\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 10.5273 0.413870 0.206935 0.978355i \(-0.433651\pi\)
0.206935 + 0.978355i \(0.433651\pi\)
\(648\) 0 0
\(649\) −0.490728 + 0.849966i −0.0192628 + 0.0333641i
\(650\) 0 0
\(651\) 24.2506 42.0033i 0.950456 1.64624i
\(652\) 0 0
\(653\) 14.9511 0.585081 0.292540 0.956253i \(-0.405499\pi\)
0.292540 + 0.956253i \(0.405499\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −6.41120 −0.250125
\(658\) 0 0
\(659\) 16.6909 + 28.9094i 0.650184 + 1.12615i 0.983078 + 0.183187i \(0.0586414\pi\)
−0.332894 + 0.942964i \(0.608025\pi\)
\(660\) 0 0
\(661\) −12.7433 22.0720i −0.495655 0.858501i 0.504332 0.863510i \(-0.331739\pi\)
−0.999987 + 0.00500935i \(0.998405\pi\)
\(662\) 0 0
\(663\) −4.34371 + 7.52353i −0.168696 + 0.292190i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −2.81340 + 4.87295i −0.108935 + 0.188681i
\(668\) 0 0
\(669\) 10.8803 + 18.8453i 0.420657 + 0.728600i
\(670\) 0 0
\(671\) 6.42622 + 11.1305i 0.248081 + 0.429690i
\(672\) 0 0
\(673\) 9.87133 0.380512 0.190256 0.981735i \(-0.439068\pi\)
0.190256 + 0.981735i \(0.439068\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 11.8367 0.454922 0.227461 0.973787i \(-0.426958\pi\)
0.227461 + 0.973787i \(0.426958\pi\)
\(678\) 0 0
\(679\) 27.9209 48.3605i 1.07151 1.85590i
\(680\) 0 0
\(681\) −14.9239 + 25.8490i −0.571887 + 0.990537i
\(682\) 0 0
\(683\) −29.6716 −1.13535 −0.567675 0.823253i \(-0.692157\pi\)
−0.567675 + 0.823253i \(0.692157\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0.459972 0.796696i 0.0175490 0.0303958i
\(688\) 0 0
\(689\) 10.6301 18.4119i 0.404976 0.701438i
\(690\) 0 0
\(691\) 9.73437 0.370313 0.185156 0.982709i \(-0.440721\pi\)
0.185156 + 0.982709i \(0.440721\pi\)
\(692\) 0 0
\(693\) −13.6211 23.5924i −0.517423 0.896203i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −9.48723 16.4324i −0.359355 0.622420i
\(698\) 0 0
\(699\) 12.4997 + 21.6501i 0.472782 + 0.818882i
\(700\) 0 0
\(701\) 10.3345 17.8999i 0.390329 0.676070i −0.602164 0.798373i \(-0.705695\pi\)
0.992493 + 0.122303i \(0.0390279\pi\)
\(702\) 0 0
\(703\) 3.43272 + 11.5199i 0.129468 + 0.434480i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 27.1091 + 46.9543i 1.01954 + 1.76590i
\(708\) 0 0
\(709\) −10.0066 17.3319i −0.375806 0.650915i 0.614641 0.788807i \(-0.289301\pi\)
−0.990447 + 0.137892i \(0.955967\pi\)
\(710\) 0 0
\(711\) −15.7150 −0.589360
\(712\) 0 0
\(713\) −8.44037 14.6191i −0.316094 0.547491i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −18.1580 + 31.4506i −0.678123 + 1.17454i
\(718\) 0 0
\(719\) −11.2807 + 19.5387i −0.420698 + 0.728671i −0.996008 0.0892647i \(-0.971548\pi\)
0.575309 + 0.817936i \(0.304882\pi\)
\(720\) 0 0
\(721\) 56.9341 2.12034
\(722\) 0 0
\(723\) 29.8954 1.11182
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 2.77735 4.81051i 0.103006 0.178412i −0.809916 0.586546i \(-0.800487\pi\)
0.912922 + 0.408134i \(0.133821\pi\)
\(728\) 0 0
\(729\) 24.7954 0.918349
\(730\) 0 0
\(731\) −2.31864 4.01601i −0.0857581 0.148537i
\(732\) 0 0
\(733\) 45.3490 1.67500 0.837501 0.546436i \(-0.184016\pi\)
0.837501 + 0.546436i \(0.184016\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −25.4515 44.0833i −0.937518 1.62383i
\(738\) 0 0
\(739\) 9.01081 15.6072i 0.331468 0.574119i −0.651332 0.758793i \(-0.725789\pi\)
0.982800 + 0.184674i \(0.0591228\pi\)
\(740\) 0 0
\(741\) 4.17461 + 14.0096i 0.153358 + 0.514654i
\(742\) 0 0
\(743\) 21.3235 36.9333i 0.782282 1.35495i −0.148328 0.988938i \(-0.547389\pi\)
0.930610 0.366013i \(-0.119277\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −2.16343 3.74717i −0.0791557 0.137102i
\(748\) 0 0
\(749\) −91.1687 −3.33123
\(750\) 0 0
\(751\) −2.45338 4.24938i −0.0895252 0.155062i 0.817785 0.575523i \(-0.195202\pi\)
−0.907311 + 0.420461i \(0.861868\pi\)
\(752\) 0 0
\(753\) 8.66102 0.315625
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 13.9842 24.2213i 0.508264 0.880339i −0.491690 0.870770i \(-0.663621\pi\)
0.999954 0.00956884i \(-0.00304590\pi\)
\(758\) 0 0
\(759\) 10.5271 0.382108
\(760\) 0 0
\(761\) −11.7443 −0.425731 −0.212866 0.977081i \(-0.568280\pi\)
−0.212866 + 0.977081i \(0.568280\pi\)
\(762\) 0 0
\(763\) 32.5833 56.4359i 1.17959 2.04312i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −0.679630 −0.0245400
\(768\) 0 0
\(769\) −8.22905 14.2531i −0.296747 0.513981i 0.678643 0.734469i \(-0.262568\pi\)
−0.975390 + 0.220488i \(0.929235\pi\)
\(770\) 0 0
\(771\) 15.9020 0.572698
\(772\) 0 0
\(773\) 22.9542 + 39.7578i 0.825605 + 1.42999i 0.901456 + 0.432871i \(0.142499\pi\)
−0.0758511 + 0.997119i \(0.524167\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −8.61118 + 14.9150i −0.308924 + 0.535073i
\(778\) 0 0
\(779\) −31.0582 7.40303i −1.11278 0.265241i
\(780\) 0 0
\(781\) −14.8707 + 25.7568i −0.532115 + 0.921650i
\(782\) 0 0
\(783\) −7.19002 12.4535i −0.256950 0.445051i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −28.1763 −1.00438 −0.502189 0.864758i \(-0.667472\pi\)
−0.502189 + 0.864758i \(0.667472\pi\)
\(788\) 0 0
\(789\) 15.6719 + 27.1446i 0.557936 + 0.966373i
\(790\) 0 0
\(791\) 3.46456 0.123186
\(792\) 0 0
\(793\) −4.44997 + 7.70757i −0.158023 + 0.273704i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.18117 0.0418394 0.0209197 0.999781i \(-0.493341\pi\)
0.0209197 + 0.999781i \(0.493341\pi\)
\(798\) 0 0
\(799\) 4.42517 0.156551
\(800\) 0 0
\(801\) 6.76994 11.7259i 0.239204 0.414314i
\(802\) 0