Properties

Label 1008.2.r.m.337.1
Level 1008
Weight 2
Character 1008.337
Analytic conductor 8.049
Analytic rank 0
Dimension 8
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.508277025.1
Defining polynomial: \(x^{8} - 3 x^{7} + 5 x^{6} - 15 x^{5} + 21 x^{4} + 3 x^{3} - 22 x^{2} + 3 x + 19\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 337.1
Root \(-0.577806 - 2.22188i\) of defining polynomial
Character \(\chi\) \(=\) 1008.337
Dual form 1008.2.r.m.673.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.71311 + 0.255482i) q^{3} +(1.81197 - 3.13842i) q^{5} +(0.500000 + 0.866025i) q^{7} +(2.86946 - 0.875335i) q^{9} +O(q^{10})\) \(q+(-1.71311 + 0.255482i) q^{3} +(1.81197 - 3.13842i) q^{5} +(0.500000 + 0.866025i) q^{7} +(2.86946 - 0.875335i) q^{9} +(1.95863 + 3.39245i) q^{11} +(-2.53644 + 4.39324i) q^{13} +(-2.30228 + 5.83936i) q^{15} +1.03225 q^{17} +2.50895 q^{19} +(-1.07781 - 1.35585i) q^{21} +(2.47895 - 4.29366i) q^{23} +(-4.06644 - 7.04328i) q^{25} +(-4.69205 + 2.23263i) q^{27} +(4.60288 + 7.97242i) q^{29} +(-0.422194 + 0.731261i) q^{31} +(-4.22205 - 5.31123i) q^{33} +3.62393 q^{35} +4.84439 q^{37} +(3.22279 - 8.17410i) q^{39} +(2.07362 - 3.59161i) q^{41} +(-2.20174 - 3.81352i) q^{43} +(2.45219 - 10.5916i) q^{45} +(-3.93758 - 6.82008i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-1.76835 + 0.263721i) q^{51} +12.2786 q^{53} +14.1959 q^{55} +(-4.29809 + 0.640990i) q^{57} +(-5.60288 + 9.70447i) q^{59} +(-0.208348 - 0.360870i) q^{61} +(2.19279 + 2.04736i) q^{63} +(9.19188 + 15.9208i) q^{65} +(5.02507 - 8.70368i) q^{67} +(-3.14974 + 7.98882i) q^{69} +5.05162 q^{71} +7.20723 q^{73} +(8.76567 + 11.0270i) q^{75} +(-1.95863 + 3.39245i) q^{77} +(7.56570 + 13.1042i) q^{79} +(7.46758 - 5.02347i) q^{81} +(0.932821 + 1.61569i) q^{83} +(1.87040 - 3.23963i) q^{85} +(-9.92202 - 12.4816i) q^{87} -0.669401 q^{89} -5.07288 q^{91} +(0.536438 - 1.36059i) q^{93} +(4.54612 - 7.87412i) q^{95} +(-7.63513 - 13.2244i) q^{97} +(8.58974 + 8.02003i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{3} + 4q^{5} + 4q^{7} + 10q^{9} + O(q^{10}) \) \( 8q + 4q^{3} + 4q^{5} + 4q^{7} + 10q^{9} + 6q^{11} - 3q^{13} - 4q^{15} - 16q^{17} + 4q^{19} - q^{21} + 5q^{23} - 14q^{25} - 5q^{27} + q^{29} - 11q^{31} + 8q^{35} + 54q^{37} + 12q^{39} + 2q^{41} + 11q^{43} + 26q^{45} - 7q^{47} - 4q^{49} - 17q^{51} - 8q^{53} - 12q^{55} - 13q^{57} - 9q^{59} - 7q^{61} + 5q^{63} - 9q^{65} + 12q^{67} + 4q^{69} + 24q^{71} + 26q^{73} + 23q^{75} - 6q^{77} + 22q^{79} + 34q^{81} + 6q^{83} - 11q^{85} - 37q^{87} - 28q^{89} - 6q^{91} - 13q^{93} + 23q^{95} - q^{97} + 42q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) −1.71311 + 0.255482i −0.989062 + 0.147503i
\(4\) 0 0
\(5\) 1.81197 3.13842i 0.810336 1.40354i −0.102294 0.994754i \(-0.532618\pi\)
0.912629 0.408788i \(-0.134049\pi\)
\(6\) 0 0
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i
\(8\) 0 0
\(9\) 2.86946 0.875335i 0.956486 0.291778i
\(10\) 0 0
\(11\) 1.95863 + 3.39245i 0.590550 + 1.02286i 0.994158 + 0.107930i \(0.0344224\pi\)
−0.403609 + 0.914932i \(0.632244\pi\)
\(12\) 0 0
\(13\) −2.53644 + 4.39324i −0.703481 + 1.21847i 0.263755 + 0.964590i \(0.415039\pi\)
−0.967237 + 0.253876i \(0.918295\pi\)
\(14\) 0 0
\(15\) −2.30228 + 5.83936i −0.594446 + 1.50772i
\(16\) 0 0
\(17\) 1.03225 0.250357 0.125178 0.992134i \(-0.460050\pi\)
0.125178 + 0.992134i \(0.460050\pi\)
\(18\) 0 0
\(19\) 2.50895 0.575592 0.287796 0.957692i \(-0.407078\pi\)
0.287796 + 0.957692i \(0.407078\pi\)
\(20\) 0 0
\(21\) −1.07781 1.35585i −0.235197 0.295871i
\(22\) 0 0
\(23\) 2.47895 4.29366i 0.516896 0.895290i −0.482912 0.875669i \(-0.660421\pi\)
0.999807 0.0196209i \(-0.00624592\pi\)
\(24\) 0 0
\(25\) −4.06644 7.04328i −0.813288 1.40866i
\(26\) 0 0
\(27\) −4.69205 + 2.23263i −0.902986 + 0.429671i
\(28\) 0 0
\(29\) 4.60288 + 7.97242i 0.854733 + 1.48044i 0.876893 + 0.480686i \(0.159612\pi\)
−0.0221599 + 0.999754i \(0.507054\pi\)
\(30\) 0 0
\(31\) −0.422194 + 0.731261i −0.0758282 + 0.131338i −0.901446 0.432891i \(-0.857493\pi\)
0.825618 + 0.564230i \(0.190827\pi\)
\(32\) 0 0
\(33\) −4.22205 5.31123i −0.734965 0.924566i
\(34\) 0 0
\(35\) 3.62393 0.612556
\(36\) 0 0
\(37\) 4.84439 0.796412 0.398206 0.917296i \(-0.369633\pi\)
0.398206 + 0.917296i \(0.369633\pi\)
\(38\) 0 0
\(39\) 3.22279 8.17410i 0.516060 1.30890i
\(40\) 0 0
\(41\) 2.07362 3.59161i 0.323844 0.560915i −0.657433 0.753513i \(-0.728358\pi\)
0.981278 + 0.192598i \(0.0616912\pi\)
\(42\) 0 0
\(43\) −2.20174 3.81352i −0.335762 0.581557i 0.647869 0.761752i \(-0.275660\pi\)
−0.983631 + 0.180195i \(0.942327\pi\)
\(44\) 0 0
\(45\) 2.45219 10.5916i 0.365552 1.57891i
\(46\) 0 0
\(47\) −3.93758 6.82008i −0.574355 0.994812i −0.996111 0.0881025i \(-0.971920\pi\)
0.421757 0.906709i \(-0.361414\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) 0 0
\(51\) −1.76835 + 0.263721i −0.247619 + 0.0369283i
\(52\) 0 0
\(53\) 12.2786 1.68660 0.843300 0.537443i \(-0.180610\pi\)
0.843300 + 0.537443i \(0.180610\pi\)
\(54\) 0 0
\(55\) 14.1959 1.91417
\(56\) 0 0
\(57\) −4.29809 + 0.640990i −0.569296 + 0.0849013i
\(58\) 0 0
\(59\) −5.60288 + 9.70447i −0.729432 + 1.26341i 0.227691 + 0.973733i \(0.426882\pi\)
−0.957123 + 0.289681i \(0.906451\pi\)
\(60\) 0 0
\(61\) −0.208348 0.360870i −0.0266763 0.0462047i 0.852379 0.522924i \(-0.175159\pi\)
−0.879055 + 0.476720i \(0.841826\pi\)
\(62\) 0 0
\(63\) 2.19279 + 2.04736i 0.276266 + 0.257943i
\(64\) 0 0
\(65\) 9.19188 + 15.9208i 1.14011 + 1.97473i
\(66\) 0 0
\(67\) 5.02507 8.70368i 0.613910 1.06332i −0.376665 0.926350i \(-0.622929\pi\)
0.990575 0.136974i \(-0.0437376\pi\)
\(68\) 0 0
\(69\) −3.14974 + 7.98882i −0.379184 + 0.961741i
\(70\) 0 0
\(71\) 5.05162 0.599517 0.299759 0.954015i \(-0.403094\pi\)
0.299759 + 0.954015i \(0.403094\pi\)
\(72\) 0 0
\(73\) 7.20723 0.843543 0.421771 0.906702i \(-0.361408\pi\)
0.421771 + 0.906702i \(0.361408\pi\)
\(74\) 0 0
\(75\) 8.76567 + 11.0270i 1.01217 + 1.27329i
\(76\) 0 0
\(77\) −1.95863 + 3.39245i −0.223207 + 0.386606i
\(78\) 0 0
\(79\) 7.56570 + 13.1042i 0.851208 + 1.47433i 0.880119 + 0.474753i \(0.157463\pi\)
−0.0289116 + 0.999582i \(0.509204\pi\)
\(80\) 0 0
\(81\) 7.46758 5.02347i 0.829731 0.558164i
\(82\) 0 0
\(83\) 0.932821 + 1.61569i 0.102390 + 0.177345i 0.912669 0.408699i \(-0.134018\pi\)
−0.810279 + 0.586045i \(0.800684\pi\)
\(84\) 0 0
\(85\) 1.87040 3.23963i 0.202873 0.351387i
\(86\) 0 0
\(87\) −9.92202 12.4816i −1.06375 1.33817i
\(88\) 0 0
\(89\) −0.669401 −0.0709564 −0.0354782 0.999370i \(-0.511295\pi\)
−0.0354782 + 0.999370i \(0.511295\pi\)
\(90\) 0 0
\(91\) −5.07288 −0.531782
\(92\) 0 0
\(93\) 0.536438 1.36059i 0.0556260 0.141087i
\(94\) 0 0
\(95\) 4.54612 7.87412i 0.466423 0.807868i
\(96\) 0 0
\(97\) −7.63513 13.2244i −0.775230 1.34274i −0.934665 0.355529i \(-0.884301\pi\)
0.159436 0.987208i \(-0.449032\pi\)
\(98\) 0 0
\(99\) 8.58974 + 8.02003i 0.863301 + 0.806044i
\(100\) 0 0
\(101\) 5.87840 + 10.1817i 0.584923 + 1.01312i 0.994885 + 0.101014i \(0.0322087\pi\)
−0.409962 + 0.912103i \(0.634458\pi\)
\(102\) 0 0
\(103\) 5.51538 9.55293i 0.543447 0.941278i −0.455256 0.890361i \(-0.650452\pi\)
0.998703 0.0509171i \(-0.0162144\pi\)
\(104\) 0 0
\(105\) −6.20818 + 0.925849i −0.605856 + 0.0903536i
\(106\) 0 0
\(107\) 0.842907 0.0814869 0.0407434 0.999170i \(-0.487027\pi\)
0.0407434 + 0.999170i \(0.487027\pi\)
\(108\) 0 0
\(109\) −17.1875 −1.64627 −0.823133 0.567849i \(-0.807776\pi\)
−0.823133 + 0.567849i \(0.807776\pi\)
\(110\) 0 0
\(111\) −8.29894 + 1.23765i −0.787701 + 0.117473i
\(112\) 0 0
\(113\) −4.54538 + 7.87284i −0.427594 + 0.740614i −0.996659 0.0816784i \(-0.973972\pi\)
0.569065 + 0.822293i \(0.307305\pi\)
\(114\) 0 0
\(115\) −8.98353 15.5599i −0.837718 1.45097i
\(116\) 0 0
\(117\) −3.43265 + 14.8264i −0.317348 + 1.37071i
\(118\) 0 0
\(119\) 0.516124 + 0.893953i 0.0473130 + 0.0819486i
\(120\) 0 0
\(121\) −2.17248 + 3.76284i −0.197498 + 0.342076i
\(122\) 0 0
\(123\) −2.63473 + 6.68258i −0.237566 + 0.602548i
\(124\) 0 0
\(125\) −11.3533 −1.01547
\(126\) 0 0
\(127\) 14.4859 1.28541 0.642706 0.766113i \(-0.277812\pi\)
0.642706 + 0.766113i \(0.277812\pi\)
\(128\) 0 0
\(129\) 4.74609 + 5.97046i 0.417870 + 0.525670i
\(130\) 0 0
\(131\) 4.03476 6.98840i 0.352518 0.610580i −0.634172 0.773192i \(-0.718659\pi\)
0.986690 + 0.162613i \(0.0519921\pi\)
\(132\) 0 0
\(133\) 1.25447 + 2.17281i 0.108777 + 0.188407i
\(134\) 0 0
\(135\) −1.49490 + 18.7711i −0.128660 + 1.61556i
\(136\) 0 0
\(137\) −9.85792 17.0744i −0.842219 1.45877i −0.888015 0.459815i \(-0.847916\pi\)
0.0457961 0.998951i \(-0.485418\pi\)
\(138\) 0 0
\(139\) 8.35960 14.4792i 0.709052 1.22811i −0.256157 0.966635i \(-0.582457\pi\)
0.965209 0.261479i \(-0.0842101\pi\)
\(140\) 0 0
\(141\) 8.48789 + 10.6775i 0.714809 + 0.899211i
\(142\) 0 0
\(143\) −19.8718 −1.66176
\(144\) 0 0
\(145\) 33.3610 2.77048
\(146\) 0 0
\(147\) 0.635299 1.61133i 0.0523986 0.132901i
\(148\) 0 0
\(149\) −9.16439 + 15.8732i −0.750776 + 1.30038i 0.196671 + 0.980469i \(0.436987\pi\)
−0.947447 + 0.319912i \(0.896347\pi\)
\(150\) 0 0
\(151\) −7.23100 12.5245i −0.588450 1.01923i −0.994436 0.105346i \(-0.966405\pi\)
0.405985 0.913880i \(-0.366928\pi\)
\(152\) 0 0
\(153\) 2.96199 0.903563i 0.239463 0.0730487i
\(154\) 0 0
\(155\) 1.53000 + 2.65004i 0.122893 + 0.212856i
\(156\) 0 0
\(157\) −1.92387 + 3.33225i −0.153542 + 0.265942i −0.932527 0.361100i \(-0.882401\pi\)
0.778985 + 0.627042i \(0.215735\pi\)
\(158\) 0 0
\(159\) −21.0346 + 3.13697i −1.66815 + 0.248778i
\(160\) 0 0
\(161\) 4.95789 0.390737
\(162\) 0 0
\(163\) −13.0322 −1.02076 −0.510382 0.859948i \(-0.670496\pi\)
−0.510382 + 0.859948i \(0.670496\pi\)
\(164\) 0 0
\(165\) −24.3191 + 3.62679i −1.89324 + 0.282346i
\(166\) 0 0
\(167\) −3.04538 + 5.27476i −0.235659 + 0.408173i −0.959464 0.281831i \(-0.909058\pi\)
0.723805 + 0.690005i \(0.242391\pi\)
\(168\) 0 0
\(169\) −6.36704 11.0280i −0.489772 0.848310i
\(170\) 0 0
\(171\) 7.19932 2.19617i 0.550546 0.167945i
\(172\) 0 0
\(173\) −5.89855 10.2166i −0.448458 0.776752i 0.549828 0.835278i \(-0.314693\pi\)
−0.998286 + 0.0585258i \(0.981360\pi\)
\(174\) 0 0
\(175\) 4.06644 7.04328i 0.307394 0.532422i
\(176\) 0 0
\(177\) 7.11900 18.0562i 0.535097 1.35719i
\(178\) 0 0
\(179\) −1.06148 −0.0793389 −0.0396694 0.999213i \(-0.512630\pi\)
−0.0396694 + 0.999213i \(0.512630\pi\)
\(180\) 0 0
\(181\) −16.0384 −1.19212 −0.596062 0.802938i \(-0.703269\pi\)
−0.596062 + 0.802938i \(0.703269\pi\)
\(182\) 0 0
\(183\) 0.449118 + 0.564979i 0.0331998 + 0.0417644i
\(184\) 0 0
\(185\) 8.77786 15.2037i 0.645361 1.11780i
\(186\) 0 0
\(187\) 2.02179 + 3.50185i 0.147848 + 0.256081i
\(188\) 0 0
\(189\) −4.27954 2.94712i −0.311291 0.214371i
\(190\) 0 0
\(191\) 11.9676 + 20.7285i 0.865944 + 1.49986i 0.866107 + 0.499858i \(0.166615\pi\)
−0.000163629 1.00000i \(0.500052\pi\)
\(192\) 0 0
\(193\) −6.60707 + 11.4438i −0.475587 + 0.823741i −0.999609 0.0279638i \(-0.991098\pi\)
0.524022 + 0.851705i \(0.324431\pi\)
\(194\) 0 0
\(195\) −19.8141 24.9256i −1.41892 1.78496i
\(196\) 0 0
\(197\) −25.0403 −1.78405 −0.892023 0.451990i \(-0.850714\pi\)
−0.892023 + 0.451990i \(0.850714\pi\)
\(198\) 0 0
\(199\) −8.28159 −0.587066 −0.293533 0.955949i \(-0.594831\pi\)
−0.293533 + 0.955949i \(0.594831\pi\)
\(200\) 0 0
\(201\) −6.38484 + 16.1941i −0.450352 + 1.14225i
\(202\) 0 0
\(203\) −4.60288 + 7.97242i −0.323059 + 0.559554i
\(204\) 0 0
\(205\) −7.51464 13.0157i −0.524845 0.909059i
\(206\) 0 0
\(207\) 3.35484 14.4904i 0.233178 1.00715i
\(208\) 0 0
\(209\) 4.91410 + 8.51148i 0.339916 + 0.588751i
\(210\) 0 0
\(211\) 1.79752 3.11340i 0.123747 0.214335i −0.797496 0.603325i \(-0.793842\pi\)
0.921242 + 0.388989i \(0.127176\pi\)
\(212\) 0 0
\(213\) −8.65396 + 1.29060i −0.592959 + 0.0884303i
\(214\) 0 0
\(215\) −15.9579 −1.08832
\(216\) 0 0
\(217\) −0.844387 −0.0573207
\(218\) 0 0
\(219\) −12.3468 + 1.84132i −0.834316 + 0.124425i
\(220\) 0 0
\(221\) −2.61823 + 4.53491i −0.176121 + 0.305051i
\(222\) 0 0
\(223\) 5.08601 + 8.80923i 0.340585 + 0.589910i 0.984541 0.175152i \(-0.0560417\pi\)
−0.643957 + 0.765062i \(0.722708\pi\)
\(224\) 0 0
\(225\) −17.8337 16.6509i −1.18891 1.11006i
\(226\) 0 0
\(227\) 6.95054 + 12.0387i 0.461324 + 0.799036i 0.999027 0.0440980i \(-0.0140414\pi\)
−0.537704 + 0.843134i \(0.680708\pi\)
\(228\) 0 0
\(229\) 2.84347 4.92504i 0.187902 0.325456i −0.756649 0.653822i \(-0.773165\pi\)
0.944551 + 0.328366i \(0.106498\pi\)
\(230\) 0 0
\(231\) 2.48863 6.31202i 0.163740 0.415300i
\(232\) 0 0
\(233\) 19.4775 1.27601 0.638006 0.770031i \(-0.279759\pi\)
0.638006 + 0.770031i \(0.279759\pi\)
\(234\) 0 0
\(235\) −28.5390 −1.86168
\(236\) 0 0
\(237\) −16.3087 20.5159i −1.05936 1.33265i
\(238\) 0 0
\(239\) 2.50000 4.33013i 0.161712 0.280093i −0.773771 0.633465i \(-0.781632\pi\)
0.935483 + 0.353373i \(0.114965\pi\)
\(240\) 0 0
\(241\) −5.14080 8.90412i −0.331148 0.573565i 0.651589 0.758572i \(-0.274103\pi\)
−0.982737 + 0.185007i \(0.940769\pi\)
\(242\) 0 0
\(243\) −11.5093 + 10.5136i −0.738325 + 0.674446i
\(244\) 0 0
\(245\) 1.81197 + 3.13842i 0.115762 + 0.200506i
\(246\) 0 0
\(247\) −6.36379 + 11.0224i −0.404918 + 0.701339i
\(248\) 0 0
\(249\) −2.01080 2.52953i −0.127429 0.160303i
\(250\) 0 0
\(251\) 0.829685 0.0523693 0.0261846 0.999657i \(-0.491664\pi\)
0.0261846 + 0.999657i \(0.491664\pi\)
\(252\) 0 0
\(253\) 19.4214 1.22101
\(254\) 0 0
\(255\) −2.37652 + 6.02767i −0.148824 + 0.377467i
\(256\) 0 0
\(257\) 6.87516 11.9081i 0.428860 0.742808i −0.567912 0.823089i \(-0.692249\pi\)
0.996772 + 0.0802814i \(0.0255819\pi\)
\(258\) 0 0
\(259\) 2.42219 + 4.19536i 0.150508 + 0.260687i
\(260\) 0 0
\(261\) 20.1863 + 18.8475i 1.24950 + 1.16663i
\(262\) 0 0
\(263\) 12.9285 + 22.3929i 0.797208 + 1.38081i 0.921427 + 0.388550i \(0.127024\pi\)
−0.124219 + 0.992255i \(0.539643\pi\)
\(264\) 0 0
\(265\) 22.2485 38.5355i 1.36671 2.36721i
\(266\) 0 0
\(267\) 1.14675 0.171020i 0.0701802 0.0104662i
\(268\) 0 0
\(269\) 9.32410 0.568500 0.284250 0.958750i \(-0.408255\pi\)
0.284250 + 0.958750i \(0.408255\pi\)
\(270\) 0 0
\(271\) −25.7421 −1.56372 −0.781861 0.623453i \(-0.785729\pi\)
−0.781861 + 0.623453i \(0.785729\pi\)
\(272\) 0 0
\(273\) 8.69037 1.29603i 0.525965 0.0784392i
\(274\) 0 0
\(275\) 15.9293 27.5904i 0.960574 1.66376i
\(276\) 0 0
\(277\) 5.06570 + 8.77405i 0.304368 + 0.527181i 0.977120 0.212686i \(-0.0682213\pi\)
−0.672752 + 0.739868i \(0.734888\pi\)
\(278\) 0 0
\(279\) −0.571369 + 2.46788i −0.0342070 + 0.147748i
\(280\) 0 0
\(281\) 3.47969 + 6.02699i 0.207581 + 0.359540i 0.950952 0.309339i \(-0.100108\pi\)
−0.743371 + 0.668879i \(0.766774\pi\)
\(282\) 0 0
\(283\) −3.95920 + 6.85753i −0.235350 + 0.407638i −0.959374 0.282136i \(-0.908957\pi\)
0.724024 + 0.689774i \(0.242290\pi\)
\(284\) 0 0
\(285\) −5.77629 + 14.6506i −0.342158 + 0.867829i
\(286\) 0 0
\(287\) 4.14723 0.244803
\(288\) 0 0
\(289\) −15.9345 −0.937321
\(290\) 0 0
\(291\) 16.4584 + 20.7042i 0.964807 + 1.21370i
\(292\) 0 0
\(293\) 5.63128 9.75367i 0.328983 0.569815i −0.653327 0.757076i \(-0.726627\pi\)
0.982310 + 0.187260i \(0.0599608\pi\)
\(294\) 0 0
\(295\) 20.3044 + 35.1683i 1.18217 + 2.04758i
\(296\) 0 0
\(297\) −16.7641 11.5446i −0.972752 0.669888i
\(298\) 0 0
\(299\) 12.5754 + 21.7812i 0.727253 + 1.25964i
\(300\) 0 0
\(301\) 2.20174 3.81352i 0.126906 0.219808i
\(302\) 0 0
\(303\) −12.6716 15.9405i −0.727962 0.915757i
\(304\) 0 0
\(305\) −1.51008 −0.0864669
\(306\) 0 0
\(307\) −23.0142 −1.31349 −0.656744 0.754113i \(-0.728067\pi\)
−0.656744 + 0.754113i \(0.728067\pi\)
\(308\) 0 0
\(309\) −7.00783 + 17.7742i −0.398662 + 1.01114i
\(310\) 0 0
\(311\) −6.78832 + 11.7577i −0.384930 + 0.666719i −0.991760 0.128114i \(-0.959108\pi\)
0.606829 + 0.794832i \(0.292441\pi\)
\(312\) 0 0
\(313\) 8.92362 + 15.4562i 0.504393 + 0.873634i 0.999987 + 0.00507958i \(0.00161689\pi\)
−0.495595 + 0.868554i \(0.665050\pi\)
\(314\) 0 0
\(315\) 10.3987 3.17215i 0.585901 0.178731i
\(316\) 0 0
\(317\) 9.69755 + 16.7966i 0.544669 + 0.943394i 0.998628 + 0.0523711i \(0.0166779\pi\)
−0.453959 + 0.891022i \(0.649989\pi\)
\(318\) 0 0
\(319\) −18.0307 + 31.2301i −1.00952 + 1.74855i
\(320\) 0 0
\(321\) −1.44399 + 0.215347i −0.0805956 + 0.0120195i
\(322\) 0 0
\(323\) 2.58986 0.144103
\(324\) 0 0
\(325\) 41.2571 2.28853
\(326\) 0 0
\(327\) 29.4440 4.39110i 1.62826 0.242828i
\(328\) 0 0
\(329\) 3.93758 6.82008i 0.217086 0.376003i
\(330\) 0 0
\(331\) 7.28729 + 12.6220i 0.400546 + 0.693765i 0.993792 0.111256i \(-0.0354873\pi\)
−0.593246 + 0.805021i \(0.702154\pi\)
\(332\) 0 0
\(333\) 13.9008 4.24046i 0.761757 0.232376i
\(334\) 0 0
\(335\) −18.2105 31.5415i −0.994946 1.72330i
\(336\) 0 0
\(337\) −13.8962 + 24.0689i −0.756975 + 1.31112i 0.187412 + 0.982281i \(0.439990\pi\)
−0.944387 + 0.328837i \(0.893343\pi\)
\(338\) 0 0
\(339\) 5.77535 14.6483i 0.313674 0.795584i
\(340\) 0 0
\(341\) −3.30769 −0.179121
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 19.3650 + 24.3607i 1.04258 + 1.31153i
\(346\) 0 0
\(347\) 7.45604 12.9142i 0.400261 0.693273i −0.593496 0.804837i \(-0.702253\pi\)
0.993757 + 0.111564i \(0.0355861\pi\)
\(348\) 0 0
\(349\) 10.9579 + 18.9796i 0.586562 + 1.01596i 0.994679 + 0.103026i \(0.0328525\pi\)
−0.408116 + 0.912930i \(0.633814\pi\)
\(350\) 0 0
\(351\) 2.09260 26.2762i 0.111695 1.40252i
\(352\) 0 0
\(353\) −7.73100 13.3905i −0.411480 0.712703i 0.583572 0.812061i \(-0.301654\pi\)
−0.995052 + 0.0993578i \(0.968321\pi\)
\(354\) 0 0
\(355\) 9.15337 15.8541i 0.485810 0.841448i
\(356\) 0 0
\(357\) −1.11256 1.39958i −0.0588831 0.0740734i
\(358\) 0 0
\(359\) −7.56506 −0.399269 −0.199634 0.979870i \(-0.563975\pi\)
−0.199634 + 0.979870i \(0.563975\pi\)
\(360\) 0 0
\(361\) −12.7052 −0.668694
\(362\) 0 0
\(363\) 2.76034 7.00117i 0.144880 0.367466i
\(364\) 0 0
\(365\) 13.0593 22.6193i 0.683553 1.18395i
\(366\) 0 0
\(367\) −14.5046 25.1227i −0.757133 1.31139i −0.944307 0.329066i \(-0.893266\pi\)
0.187174 0.982327i \(-0.440067\pi\)
\(368\) 0 0
\(369\) 2.80630 12.1211i 0.146090 0.630998i
\(370\) 0 0
\(371\) 6.13932 + 10.6336i 0.318737 + 0.552069i
\(372\) 0 0
\(373\) −0.655525 + 1.13540i −0.0339418 + 0.0587889i −0.882497 0.470317i \(-0.844139\pi\)
0.848556 + 0.529106i \(0.177473\pi\)
\(374\) 0 0
\(375\) 19.4495 2.90057i 1.00437 0.149785i
\(376\) 0 0
\(377\) −46.6997 −2.40515
\(378\) 0 0
\(379\) 15.7015 0.806531 0.403265 0.915083i \(-0.367875\pi\)
0.403265 + 0.915083i \(0.367875\pi\)
\(380\) 0 0
\(381\) −24.8158 + 3.70088i −1.27135 + 0.189602i
\(382\) 0 0
\(383\) −10.4804 + 18.1525i −0.535522 + 0.927551i 0.463616 + 0.886036i \(0.346552\pi\)
−0.999138 + 0.0415148i \(0.986782\pi\)
\(384\) 0 0
\(385\) 7.09795 + 12.2940i 0.361745 + 0.626561i
\(386\) 0 0
\(387\) −9.65590 9.01548i −0.490837 0.458283i
\(388\) 0 0
\(389\) −5.80937 10.0621i −0.294547 0.510170i 0.680333 0.732904i \(-0.261835\pi\)
−0.974879 + 0.222733i \(0.928502\pi\)
\(390\) 0 0
\(391\) 2.55889 4.43212i 0.129409 0.224142i
\(392\) 0 0
\(393\) −5.12655 + 13.0027i −0.258600 + 0.655898i
\(394\) 0 0
\(395\) 54.8351 2.75906
\(396\) 0 0
\(397\) −35.5217 −1.78278 −0.891390 0.453237i \(-0.850269\pi\)
−0.891390 + 0.453237i \(0.850269\pi\)
\(398\) 0 0
\(399\) −2.70416 3.40176i −0.135377 0.170301i
\(400\) 0 0
\(401\) 2.45388 4.25024i 0.122541 0.212247i −0.798228 0.602355i \(-0.794229\pi\)
0.920769 + 0.390108i \(0.127562\pi\)
\(402\) 0 0
\(403\) −2.14174 3.70960i −0.106687 0.184788i
\(404\) 0 0
\(405\) −2.23475 32.5387i −0.111046 1.61686i
\(406\) 0 0
\(407\) 9.48837 + 16.4343i 0.470321 + 0.814620i
\(408\) 0 0
\(409\) −2.21561 + 3.83756i −0.109555 + 0.189755i −0.915590 0.402113i \(-0.868276\pi\)
0.806035 + 0.591868i \(0.201609\pi\)
\(410\) 0 0
\(411\) 21.2499 + 26.7317i 1.04818 + 1.31858i
\(412\) 0 0
\(413\) −11.2058 −0.551399
\(414\) 0 0
\(415\) 6.76096 0.331882
\(416\) 0 0
\(417\) −10.6217 + 26.9402i −0.520146 + 1.31927i
\(418\) 0 0
\(419\) 17.7719 30.7819i 0.868216 1.50379i 0.00439727 0.999990i \(-0.498600\pi\)
0.863818 0.503803i \(-0.168066\pi\)
\(420\) 0 0
\(421\) 1.81923 + 3.15100i 0.0886639 + 0.153570i 0.906947 0.421246i \(-0.138407\pi\)
−0.818283 + 0.574816i \(0.805074\pi\)
\(422\) 0 0
\(423\) −17.2686 16.1232i −0.839627 0.783939i
\(424\) 0 0
\(425\) −4.19757 7.27041i −0.203612 0.352667i
\(426\) 0 0
\(427\) 0.208348 0.360870i 0.0100827 0.0174637i
\(428\) 0 0
\(429\) 34.0425 5.07688i 1.64359 0.245114i
\(430\) 0 0
\(431\) −10.9303 −0.526495 −0.263247 0.964728i \(-0.584794\pi\)
−0.263247 + 0.964728i \(0.584794\pi\)
\(432\) 0 0
\(433\) 15.3189 0.736180 0.368090 0.929790i \(-0.380012\pi\)
0.368090 + 0.929790i \(0.380012\pi\)
\(434\) 0 0
\(435\) −57.1509 + 8.52314i −2.74018 + 0.408653i
\(436\) 0 0
\(437\) 6.21954 10.7726i 0.297521 0.515322i
\(438\) 0 0
\(439\) 5.30117 + 9.18189i 0.253011 + 0.438228i 0.964353 0.264618i \(-0.0852458\pi\)
−0.711343 + 0.702846i \(0.751913\pi\)
\(440\) 0 0
\(441\) −0.676667 + 2.92269i −0.0322222 + 0.139176i
\(442\) 0 0
\(443\) −10.0680 17.4383i −0.478347 0.828521i 0.521345 0.853346i \(-0.325430\pi\)
−0.999692 + 0.0248251i \(0.992097\pi\)
\(444\) 0 0
\(445\) −1.21293 + 2.10086i −0.0574985 + 0.0995903i
\(446\) 0 0
\(447\) 11.6442 29.5338i 0.550754 1.39690i
\(448\) 0 0
\(449\) −2.74616 −0.129599 −0.0647997 0.997898i \(-0.520641\pi\)
−0.0647997 + 0.997898i \(0.520641\pi\)
\(450\) 0 0
\(451\) 16.2458 0.764985
\(452\) 0 0
\(453\) 15.5872 + 19.6083i 0.732352 + 0.921279i
\(454\) 0 0
\(455\) −9.19188 + 15.9208i −0.430922 + 0.746379i
\(456\) 0 0
\(457\) −12.7715 22.1208i −0.597423 1.03477i −0.993200 0.116421i \(-0.962858\pi\)
0.395777 0.918347i \(-0.370475\pi\)
\(458\) 0 0
\(459\) −4.84336 + 2.30463i −0.226069 + 0.107571i
\(460\) 0 0
\(461\) 8.82316 + 15.2822i 0.410936 + 0.711761i 0.994992 0.0999516i \(-0.0318688\pi\)
−0.584057 + 0.811713i \(0.698535\pi\)
\(462\) 0 0
\(463\) 13.2501 22.9499i 0.615785 1.06657i −0.374461 0.927242i \(-0.622172\pi\)
0.990246 0.139328i \(-0.0444943\pi\)
\(464\) 0 0
\(465\) −3.29809 4.14891i −0.152945 0.192401i
\(466\) 0 0
\(467\) −20.1735 −0.933519 −0.466759 0.884384i \(-0.654579\pi\)
−0.466759 + 0.884384i \(0.654579\pi\)
\(468\) 0 0
\(469\) 10.0501 0.464072
\(470\) 0 0
\(471\) 2.44447 6.20001i 0.112635 0.285681i
\(472\) 0 0
\(473\) 8.62479 14.9386i 0.396568 0.686876i
\(474\) 0 0
\(475\) −10.2025 17.6712i −0.468122 0.810811i
\(476\) 0 0
\(477\) 35.2330 10.7479i 1.61321 0.492113i
\(478\) 0 0
\(479\) −4.92470 8.52984i −0.225015 0.389738i 0.731309 0.682047i \(-0.238910\pi\)
−0.956324 + 0.292309i \(0.905577\pi\)
\(480\) 0 0
\(481\) −12.2875 + 21.2826i −0.560261 + 0.970401i
\(482\) 0 0
\(483\) −8.49339 + 1.26665i −0.386463 + 0.0576346i
\(484\) 0 0
\(485\) −55.3383 −2.51278
\(486\) 0 0
\(487\) −10.0278 −0.454403 −0.227202 0.973848i \(-0.572958\pi\)
−0.227202 + 0.973848i \(0.572958\pi\)
\(488\) 0 0
\(489\) 22.3256 3.32950i 1.00960 0.150565i
\(490\) 0 0
\(491\) −0.610055 + 1.05665i −0.0275314 + 0.0476858i −0.879463 0.475968i \(-0.842098\pi\)
0.851931 + 0.523653i \(0.175431\pi\)
\(492\) 0 0
\(493\) 4.75131 + 8.22951i 0.213988 + 0.370639i
\(494\) 0 0
\(495\) 40.7345 12.4262i 1.83088 0.558514i
\(496\) 0 0
\(497\) 2.52581 + 4.37483i 0.113298 + 0.196238i
\(498\) 0 0
\(499\) 10.3222 17.8786i 0.462086 0.800356i −0.536979 0.843596i \(-0.680434\pi\)
0.999065 + 0.0432393i \(0.0137678\pi\)
\(500\) 0 0
\(501\) 3.86946 9.81426i 0.172875 0.438469i
\(502\) 0 0
\(503\) −8.85094 −0.394644 −0.197322 0.980339i \(-0.563224\pi\)
−0.197322 + 0.980339i \(0.563224\pi\)
\(504\) 0 0
\(505\) 42.6059 1.89594
\(506\) 0 0
\(507\) 13.7249 + 17.2655i 0.609543 + 0.766788i
\(508\) 0 0
\(509\) 12.8460 22.2499i 0.569388 0.986209i −0.427238 0.904139i \(-0.640513\pi\)
0.996627 0.0820702i \(-0.0261532\pi\)
\(510\) 0 0
\(511\) 3.60362 + 6.24165i 0.159415 + 0.276114i
\(512\) 0 0
\(513\) −11.7721 + 5.60156i −0.519751 + 0.247315i
\(514\) 0 0
\(515\) −19.9874 34.6191i −0.880749 1.52550i
\(516\) 0 0
\(517\) 15.4245 26.7161i 0.678370 1.17497i
\(518\) 0 0
\(519\) 12.7150 + 15.9951i 0.558126 + 0.702107i
\(520\) 0 0
\(521\) −14.6797 −0.643129 −0.321565 0.946888i \(-0.604209\pi\)
−0.321565 + 0.946888i \(0.604209\pi\)
\(522\) 0 0
\(523\) −20.7922 −0.909182 −0.454591 0.890700i \(-0.650214\pi\)
−0.454591 + 0.890700i \(0.650214\pi\)
\(524\) 0 0
\(525\) −5.16681 + 13.1048i −0.225498 + 0.571939i
\(526\) 0 0
\(527\) −0.435809 + 0.754843i −0.0189841 + 0.0328815i
\(528\) 0 0
\(529\) −0.790345 1.36892i −0.0343628 0.0595181i
\(530\) 0 0
\(531\) −7.58256 + 32.7510i −0.329055 + 1.42127i
\(532\) 0 0
\(533\) 10.5192 + 18.2198i 0.455637 + 0.789187i
\(534\) 0 0
\(535\) 1.52732 2.64539i 0.0660317 0.114370i
\(536\) 0 0
\(537\) 1.81843 0.271189i 0.0784710 0.0117027i
\(538\) 0 0
\(539\) −3.91726 −0.168728
\(540\) 0 0
\(541\) −30.9593 −1.33104 −0.665521 0.746379i \(-0.731791\pi\)
−0.665521 + 0.746379i \(0.731791\pi\)
\(542\) 0 0
\(543\) 27.4755 4.09752i 1.17909 0.175841i
\(544\) 0 0
\(545\) −31.1432 + 53.9416i −1.33403 + 2.31060i
\(546\) 0 0
\(547\) −5.80535 10.0552i −0.248219 0.429928i 0.714813 0.699316i \(-0.246512\pi\)
−0.963032 + 0.269388i \(0.913179\pi\)
\(548\) 0 0
\(549\) −0.913729 0.853127i −0.0389970 0.0364106i
\(550\) 0 0
\(551\) 11.5484 + 20.0024i 0.491977 + 0.852130i
\(552\) 0 0
\(553\) −7.56570 + 13.1042i −0.321726 + 0.557246i
\(554\) 0 0
\(555\) −11.1531 + 28.2881i −0.473424 + 1.20076i
\(556\) 0 0
\(557\) 19.0116 0.805546 0.402773 0.915300i \(-0.368046\pi\)
0.402773 + 0.915300i \(0.368046\pi\)
\(558\) 0 0
\(559\) 22.3383 0.944809
\(560\) 0 0
\(561\) −4.35821 5.48251i −0.184004 0.231472i
\(562\) 0 0
\(563\) −10.7959 + 18.6990i −0.454992 + 0.788069i −0.998688 0.0512136i \(-0.983691\pi\)
0.543696 + 0.839282i \(0.317024\pi\)
\(564\) 0 0
\(565\) 16.4722 + 28.5306i 0.692989 + 1.20029i
\(566\) 0 0
\(567\) 8.08424 + 3.95538i 0.339506 + 0.166110i
\(568\) 0 0
\(569\) −9.28858 16.0883i −0.389397 0.674456i 0.602971 0.797763i \(-0.293983\pi\)
−0.992369 + 0.123307i \(0.960650\pi\)
\(570\) 0 0
\(571\) −4.42902 + 7.67130i −0.185349 + 0.321034i −0.943694 0.330820i \(-0.892675\pi\)
0.758345 + 0.651853i \(0.226008\pi\)
\(572\) 0 0
\(573\) −25.7975 32.4525i −1.07770 1.35572i
\(574\) 0 0
\(575\) −40.3219 −1.68154
\(576\) 0 0
\(577\) −3.76684 −0.156816 −0.0784078 0.996921i \(-0.524984\pi\)
−0.0784078 + 0.996921i \(0.524984\pi\)
\(578\) 0 0
\(579\) 8.39492 21.2924i 0.348881 0.884881i
\(580\) 0 0
\(581\) −0.932821 + 1.61569i −0.0386999 + 0.0670302i
\(582\) 0 0
\(583\) 24.0493 + 41.6546i 0.996021 + 1.72516i
\(584\) 0 0
\(585\) 40.3117 + 37.6381i 1.66669 + 1.55614i
\(586\) 0 0
\(587\) 8.37616 + 14.5079i 0.345721 + 0.598806i 0.985484 0.169766i \(-0.0543010\pi\)
−0.639763 + 0.768572i \(0.720968\pi\)
\(588\) 0 0
\(589\) −1.05926 + 1.83469i −0.0436461 + 0.0755973i
\(590\) 0 0
\(591\) 42.8966 6.39734i 1.76453 0.263151i
\(592\) 0 0
\(593\) 30.3776 1.24746 0.623729 0.781640i \(-0.285617\pi\)
0.623729 + 0.781640i \(0.285617\pi\)
\(594\) 0 0
\(595\) 3.74080 0.153358
\(596\) 0 0
\(597\) 14.1872 2.11580i 0.580645 0.0865938i
\(598\) 0 0
\(599\) 8.97578 15.5465i 0.366741 0.635213i −0.622313 0.782768i \(-0.713807\pi\)
0.989054 + 0.147555i \(0.0471403\pi\)
\(600\) 0 0
\(601\) 2.66678 + 4.61900i 0.108780 + 0.188413i 0.915276 0.402826i \(-0.131972\pi\)
−0.806496 + 0.591239i \(0.798639\pi\)
\(602\) 0 0
\(603\) 6.80060 29.3735i 0.276942 1.19618i
\(604\) 0 0
\(605\) 7.87291 + 13.6363i 0.320079 + 0.554393i
\(606\) 0 0
\(607\) −9.11826 + 15.7933i −0.370099 + 0.641030i −0.989580 0.143981i \(-0.954010\pi\)
0.619482 + 0.785011i \(0.287343\pi\)
\(608\) 0 0
\(609\) 5.84840 14.8335i 0.236989 0.601085i
\(610\) 0 0
\(611\) 39.9497 1.61619
\(612\) 0 0
\(613\) 24.2030 0.977550 0.488775 0.872410i \(-0.337444\pi\)
0.488775 + 0.872410i \(0.337444\pi\)
\(614\) 0 0
\(615\) 16.1987 + 20.3775i 0.653193 + 0.821699i
\(616\) 0 0
\(617\) 3.15635 5.46696i 0.127070 0.220092i −0.795470 0.605993i \(-0.792776\pi\)
0.922540 + 0.385901i \(0.126109\pi\)
\(618\) 0 0
\(619\) 7.03450 + 12.1841i 0.282740 + 0.489721i 0.972059 0.234738i \(-0.0754232\pi\)
−0.689318 + 0.724459i \(0.742090\pi\)
\(620\) 0 0
\(621\) −2.04516 + 25.6807i −0.0820696 + 1.03053i
\(622\) 0 0
\(623\) −0.334701 0.579718i −0.0134095 0.0232259i
\(624\) 0 0
\(625\) −0.239656 + 0.415097i −0.00958625 + 0.0166039i
\(626\) 0 0
\(627\) −10.5929 13.3256i −0.423040 0.532173i
\(628\) 0 0
\(629\) 5.00061 0.199387
\(630\) 0 0
\(631\) 1.75345 0.0698036 0.0349018 0.999391i \(-0.488888\pi\)
0.0349018 + 0.999391i \(0.488888\pi\)
\(632\) 0 0
\(633\) −2.28393 + 5.79282i −0.0907780 + 0.230244i
\(634\) 0 0
\(635\) 26.2479 45.4627i 1.04162 1.80413i
\(636\) 0 0
\(637\) −2.53644 4.39324i −0.100497 0.174066i
\(638\) 0 0
\(639\) 14.4954 4.42186i 0.573430 0.174926i
\(640\) 0 0
\(641\) −13.6942 23.7191i −0.540889 0.936847i −0.998853 0.0478765i \(-0.984755\pi\)
0.457964 0.888971i \(-0.348579\pi\)
\(642\) 0 0
\(643\) −21.3323 + 36.9486i −0.841263 + 1.45711i 0.0475644 + 0.998868i \(0.484854\pi\)
−0.888827 + 0.458242i \(0.848479\pi\)
\(644\) 0 0
\(645\) 27.3375 4.07695i 1.07641 0.160530i
\(646\) 0 0
\(647\) −45.7615 −1.79907 −0.899536 0.436847i \(-0.856095\pi\)
−0.899536 + 0.436847i \(0.856095\pi\)
\(648\) 0 0
\(649\) −43.8959 −1.72306
\(650\) 0 0
\(651\) 1.44652 0.215726i 0.0566938 0.00845496i
\(652\) 0 0
\(653\) 0.388265 0.672494i 0.0151940 0.0263167i −0.858328 0.513101i \(-0.828497\pi\)
0.873522 + 0.486784i \(0.161830\pi\)
\(654\) 0 0
\(655\) −14.6217 25.3255i −0.571316 0.989549i
\(656\) 0 0
\(657\) 20.6809 6.30874i 0.806837 0.246127i
\(658\) 0 0
\(659\) −5.97934 10.3565i −0.232922 0.403433i 0.725745 0.687964i \(-0.241495\pi\)
−0.958667 + 0.284531i \(0.908162\pi\)
\(660\) 0 0
\(661\) −6.31373 + 10.9357i −0.245576 + 0.425350i −0.962293 0.272014i \(-0.912310\pi\)
0.716718 + 0.697364i \(0.245644\pi\)
\(662\) 0 0
\(663\) 3.32672 8.43770i 0.129199 0.327693i
\(664\) 0 0
\(665\) 9.09225 0.352582
\(666\) 0 0
\(667\) 45.6411 1.76723
\(668\) 0 0
\(669\) −10.9635 13.7918i −0.423872 0.533220i
\(670\) 0 0
\(671\) 0.816155 1.41362i 0.0315073 0.0545723i
\(672\) 0 0
\(673\) −14.5735 25.2421i −0.561768 0.973011i −0.997342 0.0728584i \(-0.976788\pi\)
0.435574 0.900153i \(-0.356545\pi\)
\(674\) 0 0
\(675\) 34.8050 + 23.9685i 1.33965 + 0.922550i
\(676\) 0 0
\(677\) 3.92732 + 6.80232i 0.150939 + 0.261435i 0.931573 0.363554i \(-0.118437\pi\)
−0.780634 + 0.624989i \(0.785104\pi\)
\(678\) 0 0
\(679\) 7.63513 13.2244i 0.293009 0.507507i
\(680\) 0 0
\(681\) −14.9827 18.8478i −0.574137 0.722249i
\(682\) 0 0
\(683\) −8.87441 −0.339570 −0.169785 0.985481i \(-0.554307\pi\)
−0.169785 + 0.985481i \(0.554307\pi\)
\(684\) 0 0
\(685\) −71.4488 −2.72992
\(686\) 0 0
\(687\) −3.61291 + 9.16357i −0.137841 + 0.349612i
\(688\) 0 0
\(689\) −31.1440 + 53.9430i −1.18649 + 2.05506i
\(690\) 0 0
\(691\) −1.82008 3.15248i −0.0692392 0.119926i 0.829327 0.558763i \(-0.188724\pi\)
−0.898567 + 0.438837i \(0.855391\pi\)
\(692\) 0 0
\(693\) −2.65068 + 11.4490i −0.100691 + 0.434910i
\(694\) 0 0
\(695\) −30.2946 52.4718i −1.14914 1.99037i
\(696\) 0 0
\(697\) 2.14049 3.70743i 0.0810767 0.140429i
\(698\) 0 0
\(699\) −33.3670 + 4.97615i −1.26206 + 0.188215i
\(700\) 0 0
\(701\) 18.1003 0.683638 0.341819 0.939766i \(-0.388957\pi\)
0.341819 + 0.939766i \(0.388957\pi\)
\(702\) 0 0
\(703\) 12.1543 0.458408
\(704\) 0 0
\(705\) 48.8903 7.29120i 1.84132 0.274603i
\(706\) 0 0
\(707\) −5.87840 + 10.1817i −0.221080 + 0.382922i
\(708\) 0 0
\(709\) −17.5624 30.4191i −0.659572 1.14241i −0.980727 0.195385i \(-0.937404\pi\)
0.321155 0.947027i \(-0.395929\pi\)
\(710\) 0 0
\(711\) 33.1800 + 30.9794i 1.24435 + 1.16182i
\(712\) 0 0
\(713\) 2.09319 + 3.62551i 0.0783906 + 0.135776i
\(714\) 0 0
\(715\) −36.0070 + 62.3660i −1.34659 + 2.33235i
\(716\) 0 0
\(717\) −3.17649 + 8.05667i −0.118628 + 0.300882i
\(718\) 0 0
\(719\) 23.8092 0.887933 0.443966 0.896044i \(-0.353571\pi\)
0.443966 + 0.896044i \(0.353571\pi\)
\(720\) 0 0
\(721\) 11.0308 0.410807
\(722\) 0 0
\(723\) 11.0816 + 13.9403i 0.412128 + 0.518446i
\(724\) 0 0
\(725\) 37.4346 64.8387i 1.39029 2.40805i
\(726\) 0 0
\(727\) 1.29251 + 2.23869i 0.0479364 + 0.0830283i 0.888998 0.457911i \(-0.151402\pi\)
−0.841062 + 0.540939i \(0.818069\pi\)
\(728\) 0 0
\(729\) 17.0307 20.9513i 0.630766 0.775973i
\(730\) 0 0
\(731\) −2.27274 3.93650i −0.0840603 0.145597i
\(732\) 0 0
\(733\) 11.7493 20.3505i 0.433972 0.751661i −0.563239 0.826294i \(-0.690445\pi\)
0.997211 + 0.0746325i \(0.0237784\pi\)
\(734\) 0 0
\(735\) −3.90590 4.91351i −0.144071 0.181238i
\(736\) 0 0
\(737\) 39.3691 1.45018
\(738\) 0 0
\(739\) −16.9236 −0.622544 −0.311272 0.950321i \(-0.600755\pi\)
−0.311272 + 0.950321i \(0.600755\pi\)
\(740\) 0 0
\(741\) 8.08581 20.5084i 0.297040 0.753394i
\(742\) 0 0
\(743\) 4.39163 7.60652i 0.161113 0.279056i −0.774155 0.632996i \(-0.781825\pi\)
0.935268 + 0.353940i \(0.115158\pi\)
\(744\) 0 0
\(745\) 33.2111 + 57.5233i 1.21676 + 2.10749i
\(746\) 0 0
\(747\) 4.09096 + 3.81963i 0.149680 + 0.139753i
\(748\) 0 0
\(749\) 0.421453 + 0.729979i 0.0153996 + 0.0266728i
\(750\) 0 0
\(751\) 0.983876 1.70412i 0.0359021 0.0621843i −0.847516 0.530770i \(-0.821903\pi\)
0.883418 + 0.468585i \(0.155236\pi\)
\(752\) 0 0
\(753\) −1.42134 + 0.211970i −0.0517964 + 0.00772460i
\(754\) 0 0
\(755\) −52.4093 −1.90737
\(756\) 0 0
\(757\) −10.3423 −0.375899 −0.187949 0.982179i \(-0.560184\pi\)
−0.187949 + 0.982179i \(0.560184\pi\)
\(758\) 0 0
\(759\) −33.2708 + 4.96181i −1.20766 + 0.180102i
\(760\) 0 0
\(761\) 7.88205 13.6521i 0.285724 0.494889i −0.687060 0.726600i \(-0.741099\pi\)
0.972785 + 0.231711i \(0.0744325\pi\)
\(762\) 0 0
\(763\) −8.59376 14.8848i −0.311115 0.538867i
\(764\) 0 0
\(765\) 2.53127 10.9332i 0.0915184 0.395290i
\(766\) 0 0
\(767\) −28.4227 49.2296i −1.02628 1.77758i
\(768\) 0 0
\(769\) 22.1895 38.4333i 0.800172 1.38594i −0.119330 0.992855i \(-0.538075\pi\)
0.919502 0.393084i \(-0.128592\pi\)
\(770\) 0 0
\(771\) −8.73555 + 22.1563i −0.314603 + 0.797941i
\(772\) 0 0
\(773\) −25.5222 −0.917969 −0.458984 0.888444i \(-0.651787\pi\)
−0.458984 + 0.888444i \(0.651787\pi\)
\(774\) 0 0
\(775\) 6.86730 0.246681
\(776\) 0 0
\(777\) −5.22131 6.56827i −0.187314 0.235635i
\(778\) 0 0
\(779\) 5.20259 9.01116i 0.186402 0.322858i
\(780\) 0 0
\(781\) 9.89427 + 17.1374i 0.354045 + 0.613223i
\(782\) 0 0
\(783\) −39.3964 27.1304i −1.40791 0.969563i
\(784\) 0 0
\(785\) 6.97199 + 12.0758i 0.248841 + 0.431005i
\(786\) 0 0
\(787\) 12.2841 21.2767i 0.437882 0.758434i −0.559644 0.828733i \(-0.689062\pi\)
0.997526 + 0.0702995i \(0.0223955\pi\)
\(788\) 0 0
\(789\) −27.8689 35.0584i −0.992160 1.24811i
\(790\) 0 0
\(791\) −9.09077 −0.323231
\(792\) 0 0
\(793\) 2.11385 0.0750650
\(794\) 0 0
\(795\) −28.2688 + 71.6994i −1.00259 + 2.54291i
\(796\) 0 0
\(797\) 18.6983 32.3864i 0.662328 1.14719i −0.317674 0.948200i \(-0.602902\pi\)
0.980002 0.198986i \(-0.0637649\pi\)
\(798\) 0