Properties

Label 1008.2.r.m.673.1
Level 1008
Weight 2
Character 1008.673
Analytic conductor 8.049
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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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 673.1
Root \(-0.577806 + 2.22188i\) of defining polynomial
Character \(\chi\) \(=\) 1008.673
Dual form 1008.2.r.m.337.1

$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0.912629 + 0.408788i \(0.134049\pi\)
−0.102294 + 0.994754i \(0.532618\pi\)
\(6\) 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 −0.403609 0.914932i \(-0.632244\pi\)
0.994158 0.107930i \(-0.0344224\pi\)
\(12\) 0 0
\(13\) −2.53644 4.39324i −0.703481 1.21847i −0.967237 0.253876i \(-0.918295\pi\)
0.263755 0.964590i \(-0.415039\pi\)
\(14\) 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 0.999807 + 0.0196209i \(0.00624592\pi\)
−0.482912 + 0.875669i \(0.660421\pi\)
\(24\) 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 −0.0221599 0.999754i \(-0.507054\pi\)
0.876893 0.480686i \(-0.159612\pi\)
\(30\) 0 0
\(31\) −0.422194 0.731261i −0.0758282 0.131338i 0.825618 0.564230i \(-0.190827\pi\)
−0.901446 + 0.432891i \(0.857493\pi\)
\(32\) 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 0.981278 0.192598i \(-0.0616912\pi\)
−0.657433 + 0.753513i \(0.728358\pi\)
\(42\) 0 0
\(43\) −2.20174 + 3.81352i −0.335762 + 0.581557i −0.983631 0.180195i \(-0.942327\pi\)
0.647869 + 0.761752i \(0.275660\pi\)
\(44\) 0 0
\(45\) 2.45219 + 10.5916i 0.365552 + 1.57891i
\(46\) 0 0
\(47\) −3.93758 + 6.82008i −0.574355 + 0.994812i 0.421757 + 0.906709i \(0.361414\pi\)
−0.996111 + 0.0881025i \(0.971920\pi\)
\(48\) 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 −0.957123 0.289681i \(-0.906451\pi\)
0.227691 0.973733i \(-0.426882\pi\)
\(60\) 0 0
\(61\) −0.208348 + 0.360870i −0.0266763 + 0.0462047i −0.879055 0.476720i \(-0.841826\pi\)
0.852379 + 0.522924i \(0.175159\pi\)
\(62\) 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 0.990575 + 0.136974i \(0.0437376\pi\)
−0.376665 + 0.926350i \(0.622929\pi\)
\(68\) 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 −0.0289116 0.999582i \(-0.509204\pi\)
0.880119 0.474753i \(-0.157463\pi\)
\(80\) 0 0
\(81\) 7.46758 + 5.02347i 0.829731 + 0.558164i
\(82\) 0 0
\(83\) 0.932821 1.61569i 0.102390 0.177345i −0.810279 0.586045i \(-0.800684\pi\)
0.912669 + 0.408699i \(0.134018\pi\)
\(84\) 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 0.159436 + 0.987208i \(0.449032\pi\)
−0.934665 + 0.355529i \(0.884301\pi\)
\(98\) 0 0
\(99\) 8.58974 8.02003i 0.863301 0.806044i
\(100\) 0 0
\(101\) 5.87840 10.1817i 0.584923 1.01312i −0.409962 0.912103i \(-0.634458\pi\)
0.994885 0.101014i \(-0.0322087\pi\)
\(102\) 0 0
\(103\) 5.51538 + 9.55293i 0.543447 + 0.941278i 0.998703 + 0.0509171i \(0.0162144\pi\)
−0.455256 + 0.890361i \(0.650452\pi\)
\(104\) 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 0.569065 0.822293i \(-0.307305\pi\)
−0.996659 + 0.0816784i \(0.973972\pi\)
\(114\) 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 0.986690 0.162613i \(-0.0519921\pi\)
−0.634172 + 0.773192i \(0.718659\pi\)
\(132\) 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 0.0457961 + 0.998951i \(0.485418\pi\)
−0.888015 + 0.459815i \(0.847916\pi\)
\(138\) 0 0
\(139\) 8.35960 + 14.4792i 0.709052 + 1.22811i 0.965209 + 0.261479i \(0.0842101\pi\)
−0.256157 + 0.966635i \(0.582457\pi\)
\(140\) 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 −0.947447 0.319912i \(-0.896347\pi\)
0.196671 0.980469i \(-0.436987\pi\)
\(150\) 0 0
\(151\) −7.23100 + 12.5245i −0.588450 + 1.01923i 0.405985 + 0.913880i \(0.366928\pi\)
−0.994436 + 0.105346i \(0.966405\pi\)
\(152\) 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 0.778985 0.627042i \(-0.215735\pi\)
−0.932527 + 0.361100i \(0.882401\pi\)
\(158\) 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 0.723805 0.690005i \(-0.242391\pi\)
−0.959464 + 0.281831i \(0.909058\pi\)
\(168\) 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 −0.998286 0.0585258i \(-0.981360\pi\)
0.549828 + 0.835278i \(0.314693\pi\)
\(174\) 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 −0.000163629 1.00000i \(-0.500052\pi\)
0.866107 0.499858i \(-0.166615\pi\)
\(192\) 0 0
\(193\) −6.60707 11.4438i −0.475587 0.823741i 0.524022 0.851705i \(-0.324431\pi\)
−0.999609 + 0.0279638i \(0.991098\pi\)
\(194\) 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 0.921242 0.388989i \(-0.127176\pi\)
−0.797496 + 0.603325i \(0.793842\pi\)
\(212\) 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 −0.643957 0.765062i \(-0.722708\pi\)
0.984541 + 0.175152i \(0.0560417\pi\)
\(224\) 0 0
\(225\) −17.8337 + 16.6509i −1.18891 + 1.11006i
\(226\) 0 0
\(227\) 6.95054 12.0387i 0.461324 0.799036i −0.537704 0.843134i \(-0.680708\pi\)
0.999027 + 0.0440980i \(0.0140414\pi\)
\(228\) 0 0
\(229\) 2.84347 + 4.92504i 0.187902 + 0.325456i 0.944551 0.328366i \(-0.106498\pi\)
−0.756649 + 0.653822i \(0.773165\pi\)
\(230\) 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 0.935483 0.353373i \(-0.114965\pi\)
−0.773771 + 0.633465i \(0.781632\pi\)
\(240\) 0 0
\(241\) −5.14080 + 8.90412i −0.331148 + 0.573565i −0.982737 0.185007i \(-0.940769\pi\)
0.651589 + 0.758572i \(0.274103\pi\)
\(242\) 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 0.996772 0.0802814i \(-0.0255819\pi\)
−0.567912 + 0.823089i \(0.692249\pi\)
\(258\) 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 −0.124219 0.992255i \(-0.539643\pi\)
0.921427 0.388550i \(-0.127024\pi\)
\(264\) 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 −0.672752 0.739868i \(-0.734888\pi\)
0.977120 + 0.212686i \(0.0682213\pi\)
\(278\) 0 0
\(279\) −0.571369 2.46788i −0.0342070 0.147748i
\(280\) 0 0
\(281\) 3.47969 6.02699i 0.207581 0.359540i −0.743371 0.668879i \(-0.766774\pi\)
0.950952 + 0.309339i \(0.100108\pi\)
\(282\) 0 0
\(283\) −3.95920 6.85753i −0.235350 0.407638i 0.724024 0.689774i \(-0.242290\pi\)
−0.959374 + 0.282136i \(0.908957\pi\)
\(284\) 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 0.982310 0.187260i \(-0.0599608\pi\)
−0.653327 + 0.757076i \(0.726627\pi\)
\(294\) 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 0.606829 0.794832i \(-0.292441\pi\)
−0.991760 + 0.128114i \(0.959108\pi\)
\(312\) 0 0
\(313\) 8.92362 15.4562i 0.504393 0.873634i −0.495595 0.868554i \(-0.665050\pi\)
0.999987 0.00507958i \(-0.00161689\pi\)
\(314\) 0 0
\(315\) 10.3987 + 3.17215i 0.585901 + 0.178731i
\(316\) 0 0
\(317\) 9.69755 16.7966i 0.544669 0.943394i −0.453959 0.891022i \(-0.649989\pi\)
0.998628 0.0523711i \(-0.0166779\pi\)
\(318\) 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 −0.593246 0.805021i \(-0.702154\pi\)
0.993792 + 0.111256i \(0.0354873\pi\)
\(332\) 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 −0.944387 0.328837i \(-0.893343\pi\)
0.187412 0.982281i \(-0.439990\pi\)
\(338\) 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 0.993757 0.111564i \(-0.0355861\pi\)
−0.593496 + 0.804837i \(0.702253\pi\)
\(348\) 0 0
\(349\) 10.9579 18.9796i 0.586562 1.01596i −0.408116 0.912930i \(-0.633814\pi\)
0.994679 0.103026i \(-0.0328525\pi\)
\(350\) 0 0
\(351\) 2.09260 + 26.2762i 0.111695 + 1.40252i
\(352\) 0 0
\(353\) −7.73100 + 13.3905i −0.411480 + 0.712703i −0.995052 0.0993578i \(-0.968321\pi\)
0.583572 + 0.812061i \(0.301654\pi\)
\(354\) 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 0.187174 + 0.982327i \(0.440067\pi\)
−0.944307 + 0.329066i \(0.893266\pi\)
\(368\) 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 0.848556 0.529106i \(-0.177473\pi\)
−0.882497 + 0.470317i \(0.844139\pi\)
\(374\) 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 −0.999138 0.0415148i \(-0.986782\pi\)
0.463616 0.886036i \(-0.346552\pi\)
\(384\) 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 −0.974879 0.222733i \(-0.928502\pi\)
0.680333 + 0.732904i \(0.261835\pi\)
\(390\) 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 0.920769 0.390108i \(-0.127562\pi\)
−0.798228 + 0.602355i \(0.794229\pi\)
\(402\) 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 0.806035 0.591868i \(-0.201609\pi\)
−0.915590 + 0.402113i \(0.868276\pi\)
\(410\) 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 0.863818 + 0.503803i \(0.168066\pi\)
0.00439727 + 0.999990i \(0.498600\pi\)
\(420\) 0 0
\(421\) 1.81923 3.15100i 0.0886639 0.153570i −0.818283 0.574816i \(-0.805074\pi\)
0.906947 + 0.421246i \(0.138407\pi\)
\(422\) 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 −0.711343 0.702846i \(-0.751913\pi\)
0.964353 + 0.264618i \(0.0852458\pi\)
\(440\) 0 0
\(441\) −0.676667 2.92269i −0.0322222 0.139176i
\(442\) 0 0
\(443\) −10.0680 + 17.4383i −0.478347 + 0.828521i −0.999692 0.0248251i \(-0.992097\pi\)
0.521345 + 0.853346i \(0.325430\pi\)
\(444\) 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 0.395777 + 0.918347i \(0.370475\pi\)
−0.993200 + 0.116421i \(0.962858\pi\)
\(458\) 0 0
\(459\) −4.84336 2.30463i −0.226069 0.107571i
\(460\) 0 0
\(461\) 8.82316 15.2822i 0.410936 0.711761i −0.584057 0.811713i \(-0.698535\pi\)
0.994992 + 0.0999516i \(0.0318688\pi\)
\(462\) 0 0
\(463\) 13.2501 + 22.9499i 0.615785 + 1.06657i 0.990246 + 0.139328i \(0.0444943\pi\)
−0.374461 + 0.927242i \(0.622172\pi\)
\(464\) 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 −0.956324 0.292309i \(-0.905577\pi\)
0.731309 + 0.682047i \(0.238910\pi\)
\(480\) 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 0.851931 0.523653i \(-0.175431\pi\)
−0.879463 + 0.475968i \(0.842098\pi\)
\(492\) 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 0.999065 0.0432393i \(-0.0137678\pi\)
−0.536979 + 0.843596i \(0.680434\pi\)
\(500\) 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 0.996627 + 0.0820702i \(0.0261532\pi\)
−0.427238 + 0.904139i \(0.640513\pi\)
\(510\) 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 −0.963032 0.269388i \(-0.913179\pi\)
0.714813 + 0.699316i \(0.246512\pi\)
\(548\) 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 0.543696 0.839282i \(-0.317024\pi\)
−0.998688 + 0.0512136i \(0.983691\pi\)
\(564\) 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 −0.992369 0.123307i \(-0.960650\pi\)
0.602971 + 0.797763i \(0.293983\pi\)
\(570\) 0 0
\(571\) −4.42902 7.67130i −0.185349 0.321034i 0.758345 0.651853i \(-0.226008\pi\)
−0.943694 + 0.330820i \(0.892675\pi\)
\(572\) 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 −0.639763 0.768572i \(-0.720968\pi\)
0.985484 + 0.169766i \(0.0543010\pi\)
\(588\) 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 0.989054 0.147555i \(-0.0471403\pi\)
−0.622313 + 0.782768i \(0.713807\pi\)
\(600\) 0 0
\(601\) 2.66678 4.61900i 0.108780 0.188413i −0.806496 0.591239i \(-0.798639\pi\)
0.915276 + 0.402826i \(0.131972\pi\)
\(602\) 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 0.619482 0.785011i \(-0.287343\pi\)
−0.989580 + 0.143981i \(0.954010\pi\)
\(608\) 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 0.922540 0.385901i \(-0.126109\pi\)
−0.795470 + 0.605993i \(0.792776\pi\)
\(618\) 0 0
\(619\) 7.03450 12.1841i 0.282740 0.489721i −0.689318 0.724459i \(-0.742090\pi\)
0.972059 + 0.234738i \(0.0754232\pi\)
\(620\) 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 0.457964 + 0.888971i \(0.348579\pi\)
−0.998853 + 0.0478765i \(0.984755\pi\)
\(642\) 0 0
\(643\) −21.3323 36.9486i −0.841263 1.45711i −0.888827 0.458242i \(-0.848479\pi\)
0.0475644 0.998868i \(-0.484854\pi\)
\(644\) 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 0.873522 0.486784i \(-0.161830\pi\)
−0.858328 + 0.513101i \(0.828497\pi\)
\(654\) 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 −0.958667 0.284531i \(-0.908162\pi\)
0.725745 + 0.687964i \(0.241495\pi\)
\(660\) 0 0
\(661\) −6.31373 10.9357i −0.245576 0.425350i 0.716718 0.697364i \(-0.245644\pi\)
−0.962293 + 0.272014i \(0.912310\pi\)
\(662\) 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 0.435574 + 0.900153i \(0.356545\pi\)
−0.997342 + 0.0728584i \(0.976788\pi\)
\(674\) 0 0
\(675\) 34.8050 23.9685i 1.33965 0.922550i
\(676\) 0 0
\(677\) 3.92732 6.80232i 0.150939 0.261435i −0.780634 0.624989i \(-0.785104\pi\)
0.931573 + 0.363554i \(0.118437\pi\)
\(678\) 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 −0.898567 0.438837i \(-0.855391\pi\)
0.829327 + 0.558763i \(0.188724\pi\)
\(692\) 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 0.321155 + 0.947027i \(0.395929\pi\)
−0.980727 + 0.195385i \(0.937404\pi\)
\(710\) 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 −0.841062 0.540939i \(-0.818069\pi\)
0.888998 + 0.457911i \(0.151402\pi\)
\(728\) 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 0.997211 0.0746325i \(-0.0237784\pi\)
−0.563239 + 0.826294i \(0.690445\pi\)
\(734\) 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 0.935268 0.353940i \(-0.115158\pi\)
−0.774155 + 0.632996i \(0.781825\pi\)
\(744\) 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 0.883418 0.468585i \(-0.155236\pi\)
−0.847516 + 0.530770i \(0.821903\pi\)
\(752\) 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 0.972785 0.231711i \(-0.0744325\pi\)
−0.687060 + 0.726600i \(0.741099\pi\)
\(762\) 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 0.919502 + 0.393084i \(0.128592\pi\)
−0.119330 + 0.992855i \(0.538075\pi\)
\(770\) 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 0.997526 0.0702995i \(-0.0223955\pi\)
−0.559644 + 0.828733i \(0.689062\pi\)
\(788\) 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 0.980002 + 0.198986i \(0.0637649\pi\)
−0.317674 + 0.948200i \(0.602902\pi\)
\(798\) 0 <