Properties

Label 99.2.f.b.91.1
Level 99
Weight 2
Character 99.91
Analytic conductor 0.791
Analytic rank 0
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 99.f (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.790518980011\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 91.1
Root \(0.809017 + 0.587785i\)
Character \(\chi\) = 99.91
Dual form 99.2.f.b.37.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.30902 - 0.951057i) q^{2} +(0.190983 - 0.587785i) q^{4} +(-0.309017 - 0.224514i) q^{5} +(0.927051 - 2.85317i) q^{7} +(0.690983 + 2.12663i) q^{8} +O(q^{10})\) \(q+(1.30902 - 0.951057i) q^{2} +(0.190983 - 0.587785i) q^{4} +(-0.309017 - 0.224514i) q^{5} +(0.927051 - 2.85317i) q^{7} +(0.690983 + 2.12663i) q^{8} -0.618034 q^{10} +(-2.80902 + 1.76336i) q^{11} +(-5.04508 + 3.66547i) q^{13} +(-1.50000 - 4.61653i) q^{14} +(3.92705 + 2.85317i) q^{16} +(-0.500000 - 0.363271i) q^{17} +(-0.263932 - 0.812299i) q^{19} +(-0.190983 + 0.138757i) q^{20} +(-2.00000 + 4.97980i) q^{22} +5.47214 q^{23} +(-1.50000 - 4.61653i) q^{25} +(-3.11803 + 9.59632i) q^{26} +(-1.50000 - 1.08981i) q^{28} +(1.38197 - 4.25325i) q^{29} +(3.11803 - 2.26538i) q^{31} +3.38197 q^{32} -1.00000 q^{34} +(-0.927051 + 0.673542i) q^{35} +(-1.30902 + 4.02874i) q^{37} +(-1.11803 - 0.812299i) q^{38} +(0.263932 - 0.812299i) q^{40} +(-1.83688 - 5.65334i) q^{41} +1.76393 q^{43} +(0.500000 + 1.98787i) q^{44} +(7.16312 - 5.20431i) q^{46} +(0.190983 + 0.587785i) q^{47} +(-1.61803 - 1.17557i) q^{49} +(-6.35410 - 4.61653i) q^{50} +(1.19098 + 3.66547i) q^{52} +(-5.97214 + 4.33901i) q^{53} +(1.26393 + 0.0857567i) q^{55} +6.70820 q^{56} +(-2.23607 - 6.88191i) q^{58} +(1.64590 - 5.06555i) q^{59} +(-0.927051 - 0.673542i) q^{61} +(1.92705 - 5.93085i) q^{62} +(-3.42705 + 2.48990i) q^{64} +2.38197 q^{65} +10.5623 q^{67} +(-0.309017 + 0.224514i) q^{68} +(-0.572949 + 1.76336i) q^{70} +(11.7812 + 8.55951i) q^{71} +(0.381966 - 1.17557i) q^{73} +(2.11803 + 6.51864i) q^{74} -0.527864 q^{76} +(2.42705 + 9.64932i) q^{77} +(-0.427051 + 0.310271i) q^{79} +(-0.572949 - 1.76336i) q^{80} +(-7.78115 - 5.65334i) q^{82} +(-10.2812 - 7.46969i) q^{83} +(0.0729490 + 0.224514i) q^{85} +(2.30902 - 1.67760i) q^{86} +(-5.69098 - 4.75528i) q^{88} -9.47214 q^{89} +(5.78115 + 17.7926i) q^{91} +(1.04508 - 3.21644i) q^{92} +(0.809017 + 0.587785i) q^{94} +(-0.100813 + 0.310271i) q^{95} +(-12.1631 + 8.83702i) q^{97} -3.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 3q^{2} + 3q^{4} + q^{5} - 3q^{7} + 5q^{8} + O(q^{10}) \) \( 4q + 3q^{2} + 3q^{4} + q^{5} - 3q^{7} + 5q^{8} + 2q^{10} - 9q^{11} - 9q^{13} - 6q^{14} + 9q^{16} - 2q^{17} - 10q^{19} - 3q^{20} - 8q^{22} + 4q^{23} - 6q^{25} - 8q^{26} - 6q^{28} + 10q^{29} + 8q^{31} + 18q^{32} - 4q^{34} + 3q^{35} - 3q^{37} + 10q^{40} - 23q^{41} + 16q^{43} + 2q^{44} + 13q^{46} + 3q^{47} - 2q^{49} - 12q^{50} + 7q^{52} - 6q^{53} + 14q^{55} + 20q^{59} + 3q^{61} + q^{62} - 7q^{64} + 14q^{65} + 2q^{67} + q^{68} - 9q^{70} + 27q^{71} + 6q^{73} + 4q^{74} - 20q^{76} + 3q^{77} + 5q^{79} - 9q^{80} - 11q^{82} - 21q^{83} + 7q^{85} + 7q^{86} - 25q^{88} - 20q^{89} + 3q^{91} - 7q^{92} + q^{94} - 25q^{95} - 33q^{97} - 4q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.30902 0.951057i 0.925615 0.672499i −0.0193004 0.999814i \(-0.506144\pi\)
0.944915 + 0.327315i \(0.106144\pi\)
\(3\) 0 0
\(4\) 0.190983 0.587785i 0.0954915 0.293893i
\(5\) −0.309017 0.224514i −0.138197 0.100406i 0.516539 0.856264i \(-0.327220\pi\)
−0.654736 + 0.755858i \(0.727220\pi\)
\(6\) 0 0
\(7\) 0.927051 2.85317i 0.350392 1.07840i −0.608241 0.793752i \(-0.708125\pi\)
0.958633 0.284644i \(-0.0918755\pi\)
\(8\) 0.690983 + 2.12663i 0.244299 + 0.751876i
\(9\) 0 0
\(10\) −0.618034 −0.195440
\(11\) −2.80902 + 1.76336i −0.846950 + 0.531672i
\(12\) 0 0
\(13\) −5.04508 + 3.66547i −1.39925 + 1.01662i −0.404478 + 0.914548i \(0.632547\pi\)
−0.994777 + 0.102070i \(0.967453\pi\)
\(14\) −1.50000 4.61653i −0.400892 1.23382i
\(15\) 0 0
\(16\) 3.92705 + 2.85317i 0.981763 + 0.713292i
\(17\) −0.500000 0.363271i −0.121268 0.0881062i 0.525498 0.850795i \(-0.323879\pi\)
−0.646766 + 0.762688i \(0.723879\pi\)
\(18\) 0 0
\(19\) −0.263932 0.812299i −0.0605502 0.186354i 0.916206 0.400707i \(-0.131236\pi\)
−0.976756 + 0.214353i \(0.931236\pi\)
\(20\) −0.190983 + 0.138757i −0.0427051 + 0.0310271i
\(21\) 0 0
\(22\) −2.00000 + 4.97980i −0.426401 + 1.06170i
\(23\) 5.47214 1.14102 0.570510 0.821291i \(-0.306746\pi\)
0.570510 + 0.821291i \(0.306746\pi\)
\(24\) 0 0
\(25\) −1.50000 4.61653i −0.300000 0.923305i
\(26\) −3.11803 + 9.59632i −0.611497 + 1.88199i
\(27\) 0 0
\(28\) −1.50000 1.08981i −0.283473 0.205955i
\(29\) 1.38197 4.25325i 0.256625 0.789809i −0.736881 0.676023i \(-0.763702\pi\)
0.993505 0.113787i \(-0.0362980\pi\)
\(30\) 0 0
\(31\) 3.11803 2.26538i 0.560015 0.406875i −0.271449 0.962453i \(-0.587503\pi\)
0.831465 + 0.555578i \(0.187503\pi\)
\(32\) 3.38197 0.597853
\(33\) 0 0
\(34\) −1.00000 −0.171499
\(35\) −0.927051 + 0.673542i −0.156700 + 0.113849i
\(36\) 0 0
\(37\) −1.30902 + 4.02874i −0.215201 + 0.662321i 0.783938 + 0.620839i \(0.213208\pi\)
−0.999139 + 0.0414819i \(0.986792\pi\)
\(38\) −1.11803 0.812299i −0.181369 0.131772i
\(39\) 0 0
\(40\) 0.263932 0.812299i 0.0417313 0.128436i
\(41\) −1.83688 5.65334i −0.286873 0.882903i −0.985831 0.167741i \(-0.946353\pi\)
0.698958 0.715162i \(-0.253647\pi\)
\(42\) 0 0
\(43\) 1.76393 0.268997 0.134499 0.990914i \(-0.457058\pi\)
0.134499 + 0.990914i \(0.457058\pi\)
\(44\) 0.500000 + 1.98787i 0.0753778 + 0.299683i
\(45\) 0 0
\(46\) 7.16312 5.20431i 1.05614 0.767334i
\(47\) 0.190983 + 0.587785i 0.0278577 + 0.0857373i 0.964019 0.265834i \(-0.0856474\pi\)
−0.936161 + 0.351572i \(0.885647\pi\)
\(48\) 0 0
\(49\) −1.61803 1.17557i −0.231148 0.167939i
\(50\) −6.35410 4.61653i −0.898606 0.652875i
\(51\) 0 0
\(52\) 1.19098 + 3.66547i 0.165160 + 0.508309i
\(53\) −5.97214 + 4.33901i −0.820336 + 0.596009i −0.916809 0.399327i \(-0.869244\pi\)
0.0964728 + 0.995336i \(0.469244\pi\)
\(54\) 0 0
\(55\) 1.26393 + 0.0857567i 0.170429 + 0.0115634i
\(56\) 6.70820 0.896421
\(57\) 0 0
\(58\) −2.23607 6.88191i −0.293610 0.903639i
\(59\) 1.64590 5.06555i 0.214278 0.659479i −0.784926 0.619589i \(-0.787299\pi\)
0.999204 0.0398899i \(-0.0127007\pi\)
\(60\) 0 0
\(61\) −0.927051 0.673542i −0.118697 0.0862382i 0.526853 0.849956i \(-0.323372\pi\)
−0.645550 + 0.763718i \(0.723372\pi\)
\(62\) 1.92705 5.93085i 0.244736 0.753219i
\(63\) 0 0
\(64\) −3.42705 + 2.48990i −0.428381 + 0.311237i
\(65\) 2.38197 0.295447
\(66\) 0 0
\(67\) 10.5623 1.29039 0.645196 0.764017i \(-0.276776\pi\)
0.645196 + 0.764017i \(0.276776\pi\)
\(68\) −0.309017 + 0.224514i −0.0374738 + 0.0272263i
\(69\) 0 0
\(70\) −0.572949 + 1.76336i −0.0684805 + 0.210761i
\(71\) 11.7812 + 8.55951i 1.39817 + 1.01583i 0.994913 + 0.100738i \(0.0321204\pi\)
0.403253 + 0.915089i \(0.367880\pi\)
\(72\) 0 0
\(73\) 0.381966 1.17557i 0.0447057 0.137590i −0.926212 0.377003i \(-0.876955\pi\)
0.970918 + 0.239412i \(0.0769548\pi\)
\(74\) 2.11803 + 6.51864i 0.246216 + 0.757776i
\(75\) 0 0
\(76\) −0.527864 −0.0605502
\(77\) 2.42705 + 9.64932i 0.276588 + 1.09964i
\(78\) 0 0
\(79\) −0.427051 + 0.310271i −0.0480470 + 0.0349082i −0.611550 0.791206i \(-0.709453\pi\)
0.563503 + 0.826114i \(0.309453\pi\)
\(80\) −0.572949 1.76336i −0.0640576 0.197149i
\(81\) 0 0
\(82\) −7.78115 5.65334i −0.859285 0.624307i
\(83\) −10.2812 7.46969i −1.12850 0.819906i −0.143027 0.989719i \(-0.545684\pi\)
−0.985476 + 0.169813i \(0.945684\pi\)
\(84\) 0 0
\(85\) 0.0729490 + 0.224514i 0.00791243 + 0.0243520i
\(86\) 2.30902 1.67760i 0.248988 0.180900i
\(87\) 0 0
\(88\) −5.69098 4.75528i −0.606661 0.506915i
\(89\) −9.47214 −1.00404 −0.502022 0.864855i \(-0.667410\pi\)
−0.502022 + 0.864855i \(0.667410\pi\)
\(90\) 0 0
\(91\) 5.78115 + 17.7926i 0.606029 + 1.86517i
\(92\) 1.04508 3.21644i 0.108958 0.335337i
\(93\) 0 0
\(94\) 0.809017 + 0.587785i 0.0834437 + 0.0606254i
\(95\) −0.100813 + 0.310271i −0.0103432 + 0.0318331i
\(96\) 0 0
\(97\) −12.1631 + 8.83702i −1.23498 + 0.897264i −0.997253 0.0740689i \(-0.976402\pi\)
−0.237724 + 0.971333i \(0.576402\pi\)
\(98\) −3.23607 −0.326892
\(99\) 0 0
\(100\) −3.00000 −0.300000
\(101\) −2.42705 + 1.76336i −0.241501 + 0.175460i −0.701952 0.712225i \(-0.747688\pi\)
0.460451 + 0.887685i \(0.347688\pi\)
\(102\) 0 0
\(103\) −1.85410 + 5.70634i −0.182690 + 0.562262i −0.999901 0.0140765i \(-0.995519\pi\)
0.817211 + 0.576339i \(0.195519\pi\)
\(104\) −11.2812 8.19624i −1.10621 0.803707i
\(105\) 0 0
\(106\) −3.69098 + 11.3597i −0.358500 + 1.10335i
\(107\) −0.0729490 0.224514i −0.00705225 0.0217046i 0.947468 0.319849i \(-0.103632\pi\)
−0.954521 + 0.298145i \(0.903632\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 1.73607 1.08981i 0.165528 0.103910i
\(111\) 0 0
\(112\) 11.7812 8.55951i 1.11321 0.808798i
\(113\) 3.92705 + 12.0862i 0.369426 + 1.13698i 0.947163 + 0.320753i \(0.103936\pi\)
−0.577737 + 0.816223i \(0.696064\pi\)
\(114\) 0 0
\(115\) −1.69098 1.22857i −0.157685 0.114565i
\(116\) −2.23607 1.62460i −0.207614 0.150840i
\(117\) 0 0
\(118\) −2.66312 8.19624i −0.245160 0.754525i
\(119\) −1.50000 + 1.08981i −0.137505 + 0.0999031i
\(120\) 0 0
\(121\) 4.78115 9.90659i 0.434650 0.900599i
\(122\) −1.85410 −0.167863
\(123\) 0 0
\(124\) −0.736068 2.26538i −0.0661009 0.203438i
\(125\) −1.16312 + 3.57971i −0.104033 + 0.320179i
\(126\) 0 0
\(127\) −7.85410 5.70634i −0.696939 0.506356i 0.181995 0.983299i \(-0.441745\pi\)
−0.878934 + 0.476944i \(0.841745\pi\)
\(128\) −4.20820 + 12.9515i −0.371956 + 1.14476i
\(129\) 0 0
\(130\) 3.11803 2.26538i 0.273470 0.198687i
\(131\) 13.8541 1.21044 0.605219 0.796059i \(-0.293085\pi\)
0.605219 + 0.796059i \(0.293085\pi\)
\(132\) 0 0
\(133\) −2.56231 −0.222180
\(134\) 13.8262 10.0453i 1.19441 0.867786i
\(135\) 0 0
\(136\) 0.427051 1.31433i 0.0366193 0.112703i
\(137\) −1.19098 0.865300i −0.101753 0.0739276i 0.535746 0.844379i \(-0.320031\pi\)
−0.637498 + 0.770452i \(0.720031\pi\)
\(138\) 0 0
\(139\) 1.80902 5.56758i 0.153439 0.472236i −0.844561 0.535460i \(-0.820138\pi\)
0.997999 + 0.0632239i \(0.0201382\pi\)
\(140\) 0.218847 + 0.673542i 0.0184960 + 0.0569247i
\(141\) 0 0
\(142\) 23.5623 1.97730
\(143\) 7.70820 19.1926i 0.644592 1.60497i
\(144\) 0 0
\(145\) −1.38197 + 1.00406i −0.114766 + 0.0833824i
\(146\) −0.618034 1.90211i −0.0511489 0.157420i
\(147\) 0 0
\(148\) 2.11803 + 1.53884i 0.174101 + 0.126492i
\(149\) 12.1353 + 8.81678i 0.994159 + 0.722299i 0.960828 0.277146i \(-0.0893885\pi\)
0.0333309 + 0.999444i \(0.489388\pi\)
\(150\) 0 0
\(151\) 0.618034 + 1.90211i 0.0502949 + 0.154792i 0.973050 0.230596i \(-0.0740676\pi\)
−0.922755 + 0.385388i \(0.874068\pi\)
\(152\) 1.54508 1.12257i 0.125323 0.0910524i
\(153\) 0 0
\(154\) 12.3541 + 10.3229i 0.995522 + 0.831840i
\(155\) −1.47214 −0.118245
\(156\) 0 0
\(157\) 3.00000 + 9.23305i 0.239426 + 0.736878i 0.996503 + 0.0835524i \(0.0266266\pi\)
−0.757077 + 0.653325i \(0.773373\pi\)
\(158\) −0.263932 + 0.812299i −0.0209973 + 0.0646231i
\(159\) 0 0
\(160\) −1.04508 0.759299i −0.0826212 0.0600278i
\(161\) 5.07295 15.6129i 0.399804 1.23047i
\(162\) 0 0
\(163\) 12.3541 8.97578i 0.967648 0.703037i 0.0127336 0.999919i \(-0.495947\pi\)
0.954914 + 0.296882i \(0.0959467\pi\)
\(164\) −3.67376 −0.286873
\(165\) 0 0
\(166\) −20.5623 −1.59594
\(167\) −15.3992 + 11.1882i −1.19162 + 0.865766i −0.993435 0.114398i \(-0.963506\pi\)
−0.198190 + 0.980164i \(0.563506\pi\)
\(168\) 0 0
\(169\) 8.00000 24.6215i 0.615385 1.89396i
\(170\) 0.309017 + 0.224514i 0.0237005 + 0.0172194i
\(171\) 0 0
\(172\) 0.336881 1.03681i 0.0256869 0.0790563i
\(173\) −5.44427 16.7557i −0.413920 1.27392i −0.913213 0.407482i \(-0.866407\pi\)
0.499293 0.866433i \(-0.333593\pi\)
\(174\) 0 0
\(175\) −14.5623 −1.10081
\(176\) −16.0623 1.08981i −1.21074 0.0821478i
\(177\) 0 0
\(178\) −12.3992 + 9.00854i −0.929358 + 0.675218i
\(179\) −0.690983 2.12663i −0.0516465 0.158952i 0.921907 0.387412i \(-0.126631\pi\)
−0.973553 + 0.228460i \(0.926631\pi\)
\(180\) 0 0
\(181\) 6.89919 + 5.01255i 0.512813 + 0.372580i 0.813889 0.581020i \(-0.197346\pi\)
−0.301077 + 0.953600i \(0.597346\pi\)
\(182\) 24.4894 + 17.7926i 1.81527 + 1.31887i
\(183\) 0 0
\(184\) 3.78115 + 11.6372i 0.278750 + 0.857905i
\(185\) 1.30902 0.951057i 0.0962408 0.0699231i
\(186\) 0 0
\(187\) 2.04508 + 0.138757i 0.149551 + 0.0101469i
\(188\) 0.381966 0.0278577
\(189\) 0 0
\(190\) 0.163119 + 0.502029i 0.0118339 + 0.0364210i
\(191\) −0.454915 + 1.40008i −0.0329165 + 0.101307i −0.966165 0.257925i \(-0.916961\pi\)
0.933248 + 0.359232i \(0.116961\pi\)
\(192\) 0 0
\(193\) −1.26393 0.918300i −0.0909798 0.0661007i 0.541365 0.840787i \(-0.317908\pi\)
−0.632345 + 0.774687i \(0.717908\pi\)
\(194\) −7.51722 + 23.1356i −0.539705 + 1.66104i
\(195\) 0 0
\(196\) −1.00000 + 0.726543i −0.0714286 + 0.0518959i
\(197\) −26.6180 −1.89646 −0.948228 0.317590i \(-0.897127\pi\)
−0.948228 + 0.317590i \(0.897127\pi\)
\(198\) 0 0
\(199\) −3.29180 −0.233349 −0.116675 0.993170i \(-0.537223\pi\)
−0.116675 + 0.993170i \(0.537223\pi\)
\(200\) 8.78115 6.37988i 0.620921 0.451126i
\(201\) 0 0
\(202\) −1.50000 + 4.61653i −0.105540 + 0.324818i
\(203\) −10.8541 7.88597i −0.761809 0.553486i
\(204\) 0 0
\(205\) −0.701626 + 2.15938i −0.0490037 + 0.150818i
\(206\) 3.00000 + 9.23305i 0.209020 + 0.643297i
\(207\) 0 0
\(208\) −30.2705 −2.09888
\(209\) 2.17376 + 1.81636i 0.150362 + 0.125640i
\(210\) 0 0
\(211\) −9.11803 + 6.62464i −0.627711 + 0.456059i −0.855607 0.517627i \(-0.826816\pi\)
0.227895 + 0.973686i \(0.426816\pi\)
\(212\) 1.40983 + 4.33901i 0.0968275 + 0.298004i
\(213\) 0 0
\(214\) −0.309017 0.224514i −0.0211240 0.0153475i
\(215\) −0.545085 0.396027i −0.0371745 0.0270088i
\(216\) 0 0
\(217\) −3.57295 10.9964i −0.242548 0.746485i
\(218\) 0 0
\(219\) 0 0
\(220\) 0.291796 0.726543i 0.0196729 0.0489835i
\(221\) 3.85410 0.259255
\(222\) 0 0
\(223\) −3.92705 12.0862i −0.262975 0.809353i −0.992153 0.125029i \(-0.960097\pi\)
0.729178 0.684324i \(-0.239903\pi\)
\(224\) 3.13525 9.64932i 0.209483 0.644722i
\(225\) 0 0
\(226\) 16.6353 + 12.0862i 1.10656 + 0.803963i
\(227\) −3.36475 + 10.3556i −0.223326 + 0.687327i 0.775131 + 0.631800i \(0.217684\pi\)
−0.998457 + 0.0555264i \(0.982316\pi\)
\(228\) 0 0
\(229\) −8.09017 + 5.87785i −0.534613 + 0.388419i −0.822081 0.569371i \(-0.807187\pi\)
0.287467 + 0.957790i \(0.407187\pi\)
\(230\) −3.38197 −0.223000
\(231\) 0 0
\(232\) 10.0000 0.656532
\(233\) 7.01722 5.09831i 0.459713 0.334001i −0.333705 0.942677i \(-0.608299\pi\)
0.793419 + 0.608676i \(0.208299\pi\)
\(234\) 0 0
\(235\) 0.0729490 0.224514i 0.00475867 0.0146457i
\(236\) −2.66312 1.93487i −0.173354 0.125949i
\(237\) 0 0
\(238\) −0.927051 + 2.85317i −0.0600918 + 0.184944i
\(239\) 5.42705 + 16.7027i 0.351047 + 1.08041i 0.958266 + 0.285877i \(0.0922848\pi\)
−0.607220 + 0.794534i \(0.707715\pi\)
\(240\) 0 0
\(241\) 17.1246 1.10309 0.551547 0.834144i \(-0.314038\pi\)
0.551547 + 0.834144i \(0.314038\pi\)
\(242\) −3.16312 17.5150i −0.203333 1.12591i
\(243\) 0 0
\(244\) −0.572949 + 0.416272i −0.0366793 + 0.0266491i
\(245\) 0.236068 + 0.726543i 0.0150818 + 0.0464171i
\(246\) 0 0
\(247\) 4.30902 + 3.13068i 0.274176 + 0.199201i
\(248\) 6.97214 + 5.06555i 0.442731 + 0.321663i
\(249\) 0 0
\(250\) 1.88197 + 5.79210i 0.119026 + 0.366324i
\(251\) 13.5902 9.87384i 0.857804 0.623231i −0.0694827 0.997583i \(-0.522135\pi\)
0.927287 + 0.374352i \(0.122135\pi\)
\(252\) 0 0
\(253\) −15.3713 + 9.64932i −0.966387 + 0.606648i
\(254\) −15.7082 −0.985620
\(255\) 0 0
\(256\) 4.19098 + 12.8985i 0.261936 + 0.806157i
\(257\) 8.44427 25.9888i 0.526739 1.62114i −0.234112 0.972210i \(-0.575218\pi\)
0.760851 0.648927i \(-0.224782\pi\)
\(258\) 0 0
\(259\) 10.2812 + 7.46969i 0.638840 + 0.464144i
\(260\) 0.454915 1.40008i 0.0282126 0.0868296i
\(261\) 0 0
\(262\) 18.1353 13.1760i 1.12040 0.814018i
\(263\) 0.673762 0.0415459 0.0207730 0.999784i \(-0.493387\pi\)
0.0207730 + 0.999784i \(0.493387\pi\)
\(264\) 0 0
\(265\) 2.81966 0.173210
\(266\) −3.35410 + 2.43690i −0.205653 + 0.149416i
\(267\) 0 0
\(268\) 2.01722 6.20837i 0.123221 0.379236i
\(269\) 19.7984 + 14.3844i 1.20713 + 0.877030i 0.994967 0.100205i \(-0.0319498\pi\)
0.212161 + 0.977235i \(0.431950\pi\)
\(270\) 0 0
\(271\) 1.93769 5.96361i 0.117707 0.362263i −0.874795 0.484493i \(-0.839004\pi\)
0.992502 + 0.122229i \(0.0390043\pi\)
\(272\) −0.927051 2.85317i −0.0562107 0.172999i
\(273\) 0 0
\(274\) −2.38197 −0.143900
\(275\) 12.3541 + 10.3229i 0.744980 + 0.622492i
\(276\) 0 0
\(277\) −8.44427 + 6.13512i −0.507367 + 0.368624i −0.811824 0.583902i \(-0.801525\pi\)
0.304457 + 0.952526i \(0.401525\pi\)
\(278\) −2.92705 9.00854i −0.175553 0.540296i
\(279\) 0 0
\(280\) −2.07295 1.50609i −0.123882 0.0900058i
\(281\) −4.23607 3.07768i −0.252703 0.183599i 0.454221 0.890889i \(-0.349918\pi\)
−0.706924 + 0.707290i \(0.749918\pi\)
\(282\) 0 0
\(283\) −6.85410 21.0948i −0.407434 1.25395i −0.918846 0.394617i \(-0.870877\pi\)
0.511412 0.859336i \(-0.329123\pi\)
\(284\) 7.28115 5.29007i 0.432057 0.313908i
\(285\) 0 0
\(286\) −8.16312 32.4544i −0.482695 1.91907i
\(287\) −17.8328 −1.05264
\(288\) 0 0
\(289\) −5.13525 15.8047i −0.302074 0.929688i
\(290\) −0.854102 + 2.62866i −0.0501546 + 0.154360i
\(291\) 0 0
\(292\) −0.618034 0.449028i −0.0361677 0.0262774i
\(293\) −5.54508 + 17.0660i −0.323947 + 0.997007i 0.647966 + 0.761669i \(0.275620\pi\)
−0.971914 + 0.235338i \(0.924380\pi\)
\(294\) 0 0
\(295\) −1.64590 + 1.19581i −0.0958279 + 0.0696230i
\(296\) −9.47214 −0.550557
\(297\) 0 0
\(298\) 24.2705 1.40595
\(299\) −27.6074 + 20.0579i −1.59658 + 1.15998i
\(300\) 0 0
\(301\) 1.63525 5.03280i 0.0942545 0.290086i
\(302\) 2.61803 + 1.90211i 0.150651 + 0.109454i
\(303\) 0 0
\(304\) 1.28115 3.94298i 0.0734792 0.226146i
\(305\) 0.135255 + 0.416272i 0.00774467 + 0.0238357i
\(306\) 0 0
\(307\) −19.5623 −1.11648 −0.558240 0.829680i \(-0.688523\pi\)
−0.558240 + 0.829680i \(0.688523\pi\)
\(308\) 6.13525 + 0.416272i 0.349589 + 0.0237193i
\(309\) 0 0
\(310\) −1.92705 + 1.40008i −0.109449 + 0.0795195i
\(311\) −3.54508 10.9106i −0.201023 0.618686i −0.999853 0.0171293i \(-0.994547\pi\)
0.798830 0.601557i \(-0.205453\pi\)
\(312\) 0 0
\(313\) 22.5172 + 16.3597i 1.27275 + 0.924706i 0.999308 0.0371831i \(-0.0118385\pi\)
0.273440 + 0.961889i \(0.411838\pi\)
\(314\) 12.7082 + 9.23305i 0.717165 + 0.521051i
\(315\) 0 0
\(316\) 0.100813 + 0.310271i 0.00567118 + 0.0174541i
\(317\) 20.5172 14.9066i 1.15236 0.837240i 0.163569 0.986532i \(-0.447699\pi\)
0.988793 + 0.149292i \(0.0476994\pi\)
\(318\) 0 0
\(319\) 3.61803 + 14.3844i 0.202571 + 0.805370i
\(320\) 1.61803 0.0904508
\(321\) 0 0
\(322\) −8.20820 25.2623i −0.457425 1.40781i
\(323\) −0.163119 + 0.502029i −0.00907618 + 0.0279336i
\(324\) 0 0
\(325\) 24.4894 + 17.7926i 1.35843 + 0.986954i
\(326\) 7.63525 23.4989i 0.422878 1.30148i
\(327\) 0 0
\(328\) 10.7533 7.81272i 0.593751 0.431385i
\(329\) 1.85410 0.102220
\(330\) 0 0
\(331\) −22.5967 −1.24203 −0.621015 0.783799i \(-0.713279\pi\)
−0.621015 + 0.783799i \(0.713279\pi\)
\(332\) −6.35410 + 4.61653i −0.348727 + 0.253365i
\(333\) 0 0
\(334\) −9.51722 + 29.2910i −0.520759 + 1.60273i
\(335\) −3.26393 2.37139i −0.178328 0.129563i
\(336\) 0 0
\(337\) −4.23607 + 13.0373i −0.230753 + 0.710186i 0.766903 + 0.641763i \(0.221797\pi\)
−0.997656 + 0.0684228i \(0.978203\pi\)
\(338\) −12.9443 39.8384i −0.704076 2.16692i
\(339\) 0 0
\(340\) 0.145898 0.00791243
\(341\) −4.76393 + 11.8617i −0.257981 + 0.642347i
\(342\) 0 0
\(343\) 12.1353 8.81678i 0.655242 0.476061i
\(344\) 1.21885 + 3.75123i 0.0657158 + 0.202253i
\(345\) 0 0
\(346\) −23.0623 16.7557i −1.23984 0.900794i
\(347\) −2.47214 1.79611i −0.132711 0.0964203i 0.519449 0.854501i \(-0.326137\pi\)
−0.652160 + 0.758081i \(0.726137\pi\)
\(348\) 0 0
\(349\) 9.30902 + 28.6502i 0.498300 + 1.53361i 0.811750 + 0.584006i \(0.198515\pi\)
−0.313449 + 0.949605i \(0.601485\pi\)
\(350\) −19.0623 + 13.8496i −1.01892 + 0.740291i
\(351\) 0 0
\(352\) −9.50000 + 5.96361i −0.506352 + 0.317861i
\(353\) 1.52786 0.0813200 0.0406600 0.999173i \(-0.487054\pi\)
0.0406600 + 0.999173i \(0.487054\pi\)
\(354\) 0 0
\(355\) −1.71885 5.29007i −0.0912269 0.280768i
\(356\) −1.80902 + 5.56758i −0.0958777 + 0.295081i
\(357\) 0 0
\(358\) −2.92705 2.12663i −0.154699 0.112396i
\(359\) 5.32624 16.3925i 0.281108 0.865162i −0.706430 0.707783i \(-0.749696\pi\)
0.987538 0.157379i \(-0.0503044\pi\)
\(360\) 0 0
\(361\) 14.7812 10.7391i 0.777955 0.565218i
\(362\) 13.7984 0.725226
\(363\) 0 0
\(364\) 11.5623 0.606029
\(365\) −0.381966 + 0.277515i −0.0199930 + 0.0145258i
\(366\) 0 0
\(367\) −4.50000 + 13.8496i −0.234898 + 0.722942i 0.762237 + 0.647298i \(0.224101\pi\)
−0.997135 + 0.0756437i \(0.975899\pi\)
\(368\) 21.4894 + 15.6129i 1.12021 + 0.813880i
\(369\) 0 0
\(370\) 0.809017 2.48990i 0.0420588 0.129444i
\(371\) 6.84346 + 21.0620i 0.355295 + 1.09348i
\(372\) 0 0
\(373\) 22.4164 1.16068 0.580339 0.814375i \(-0.302920\pi\)
0.580339 + 0.814375i \(0.302920\pi\)
\(374\) 2.80902 1.76336i 0.145251 0.0911810i
\(375\) 0 0
\(376\) −1.11803 + 0.812299i −0.0576582 + 0.0418911i
\(377\) 8.61803 + 26.5236i 0.443851 + 1.36603i
\(378\) 0 0
\(379\) −22.9894 16.7027i −1.18088 0.857962i −0.188613 0.982052i \(-0.560399\pi\)
−0.992271 + 0.124089i \(0.960399\pi\)
\(380\) 0.163119 + 0.118513i 0.00836783 + 0.00607958i
\(381\) 0 0
\(382\) 0.736068 + 2.26538i 0.0376605 + 0.115907i
\(383\) −7.19098 + 5.22455i −0.367442 + 0.266962i −0.756149 0.654399i \(-0.772922\pi\)
0.388707 + 0.921361i \(0.372922\pi\)
\(384\) 0 0
\(385\) 1.41641 3.52671i 0.0721868 0.179738i
\(386\) −2.52786 −0.128665
\(387\) 0 0
\(388\) 2.87132 + 8.83702i 0.145769 + 0.448632i
\(389\) 2.86475 8.81678i 0.145248 0.447028i −0.851795 0.523876i \(-0.824485\pi\)
0.997043 + 0.0768476i \(0.0244855\pi\)
\(390\) 0 0
\(391\) −2.73607 1.98787i −0.138369 0.100531i
\(392\) 1.38197 4.25325i 0.0697998 0.214822i
\(393\) 0 0
\(394\) −34.8435 + 25.3153i −1.75539 + 1.27536i
\(395\) 0.201626 0.0101449
\(396\) 0 0
\(397\) −25.2918 −1.26936 −0.634679 0.772776i \(-0.718868\pi\)
−0.634679 + 0.772776i \(0.718868\pi\)
\(398\) −4.30902 + 3.13068i −0.215992 + 0.156927i
\(399\) 0 0
\(400\) 7.28115 22.4091i 0.364058 1.12045i
\(401\) −12.0623 8.76378i −0.602363 0.437642i 0.244354 0.969686i \(-0.421424\pi\)
−0.846717 + 0.532044i \(0.821424\pi\)
\(402\) 0 0
\(403\) −7.42705 + 22.8581i −0.369968 + 1.13864i
\(404\) 0.572949 + 1.76336i 0.0285053 + 0.0877302i
\(405\) 0 0
\(406\) −21.7082 −1.07736
\(407\) −3.42705 13.6251i −0.169873 0.675369i
\(408\) 0 0
\(409\) 23.4164 17.0130i 1.15787 0.841240i 0.168360 0.985726i \(-0.446153\pi\)
0.989507 + 0.144486i \(0.0461529\pi\)
\(410\) 1.13525 + 3.49396i 0.0560662 + 0.172554i
\(411\) 0 0
\(412\) 3.00000 + 2.17963i 0.147799 + 0.107383i
\(413\) −12.9271 9.39205i −0.636099 0.462153i
\(414\) 0 0
\(415\) 1.50000 + 4.61653i 0.0736321 + 0.226616i
\(416\) −17.0623 + 12.3965i −0.836548 + 0.607788i
\(417\) 0 0
\(418\) 4.57295 + 0.310271i 0.223670 + 0.0151758i
\(419\) 21.5066 1.05067 0.525333 0.850897i \(-0.323941\pi\)
0.525333 + 0.850897i \(0.323941\pi\)
\(420\) 0 0
\(421\) −1.15248 3.54696i −0.0561682 0.172868i 0.919037 0.394172i \(-0.128969\pi\)
−0.975205 + 0.221304i \(0.928969\pi\)
\(422\) −5.63525 + 17.3435i −0.274320 + 0.844270i
\(423\) 0 0
\(424\) −13.3541 9.70232i −0.648533 0.471186i
\(425\) −0.927051 + 2.85317i −0.0449686 + 0.138399i
\(426\) 0 0
\(427\) −2.78115 + 2.02063i −0.134589 + 0.0977849i
\(428\) −0.145898 −0.00705225
\(429\) 0 0
\(430\) −1.09017 −0.0525727
\(431\) −1.20820 + 0.877812i −0.0581971 + 0.0422827i −0.616503 0.787352i \(-0.711451\pi\)
0.558306 + 0.829635i \(0.311451\pi\)
\(432\) 0 0
\(433\) −1.85410 + 5.70634i −0.0891025 + 0.274229i −0.985672 0.168674i \(-0.946051\pi\)
0.896569 + 0.442903i \(0.146051\pi\)
\(434\) −15.1353 10.9964i −0.726515 0.527844i
\(435\) 0 0
\(436\) 0 0
\(437\) −1.44427 4.44501i −0.0690889 0.212634i
\(438\) 0 0
\(439\) 16.7082 0.797439 0.398720 0.917073i \(-0.369455\pi\)
0.398720 + 0.917073i \(0.369455\pi\)
\(440\) 0.690983 + 2.74717i 0.0329413 + 0.130966i
\(441\) 0 0
\(442\) 5.04508 3.66547i 0.239970 0.174349i
\(443\) 0.270510 + 0.832544i 0.0128523 + 0.0395553i 0.957277 0.289172i \(-0.0933801\pi\)
−0.944425 + 0.328728i \(0.893380\pi\)
\(444\) 0 0
\(445\) 2.92705 + 2.12663i 0.138756 + 0.100812i
\(446\) −16.6353 12.0862i −0.787702 0.572299i
\(447\) 0 0
\(448\) 3.92705 + 12.0862i 0.185536 + 0.571020i
\(449\) −12.5623 + 9.12705i −0.592852 + 0.430732i −0.843334 0.537389i \(-0.819411\pi\)
0.250483 + 0.968121i \(0.419411\pi\)
\(450\) 0 0
\(451\) 15.1287 + 12.6412i 0.712382 + 0.595253i
\(452\) 7.85410 0.369426
\(453\) 0 0
\(454\) 5.44427 + 16.7557i 0.255512 + 0.786386i
\(455\) 2.20820 6.79615i 0.103522 0.318609i
\(456\) 0 0
\(457\) −26.5344 19.2784i −1.24123 0.901806i −0.243549 0.969889i \(-0.578312\pi\)
−0.997680 + 0.0680830i \(0.978312\pi\)
\(458\) −5.00000 + 15.3884i −0.233635 + 0.719054i
\(459\) 0 0
\(460\) −1.04508 + 0.759299i −0.0487273 + 0.0354025i
\(461\) 9.90983 0.461547 0.230773 0.973008i \(-0.425874\pi\)
0.230773 + 0.973008i \(0.425874\pi\)
\(462\) 0 0
\(463\) 8.79837 0.408895 0.204448 0.978878i \(-0.434460\pi\)
0.204448 + 0.978878i \(0.434460\pi\)
\(464\) 17.5623 12.7598i 0.815310 0.592357i
\(465\) 0 0
\(466\) 4.33688 13.3475i 0.200902 0.618313i
\(467\) −11.5172 8.36775i −0.532953 0.387213i 0.288508 0.957478i \(-0.406841\pi\)
−0.821461 + 0.570264i \(0.806841\pi\)
\(468\) 0 0
\(469\) 9.79180 30.1360i 0.452143 1.39155i
\(470\) −0.118034 0.363271i −0.00544450 0.0167565i
\(471\) 0 0
\(472\) 11.9098 0.548194
\(473\) −4.95492 + 3.11044i −0.227827 + 0.143018i
\(474\) 0 0
\(475\) −3.35410 + 2.43690i −0.153897 + 0.111813i
\(476\) 0.354102 + 1.08981i 0.0162302 + 0.0499515i
\(477\) 0 0
\(478\) 22.9894 + 16.7027i 1.05151 + 0.763966i
\(479\) −13.6803 9.93935i −0.625071 0.454140i 0.229618 0.973281i \(-0.426252\pi\)
−0.854689 + 0.519140i \(0.826252\pi\)
\(480\) 0 0
\(481\) −8.16312 25.1235i −0.372206 1.14553i
\(482\) 22.4164 16.2865i 1.02104 0.741829i
\(483\) 0 0
\(484\) −4.90983 4.70228i −0.223174 0.213740i
\(485\) 5.74265 0.260760
\(486\) 0 0
\(487\) 12.1074 + 37.2627i 0.548638 + 1.68853i 0.712179 + 0.701998i \(0.247709\pi\)
−0.163540 + 0.986537i \(0.552291\pi\)
\(488\) 0.791796 2.43690i 0.0358429 0.110313i
\(489\) 0 0
\(490\) 1.00000 + 0.726543i 0.0451754 + 0.0328218i
\(491\) 8.10081 24.9317i 0.365585 1.12515i −0.584030 0.811732i \(-0.698525\pi\)
0.949614 0.313421i \(-0.101475\pi\)
\(492\) 0 0
\(493\) −2.23607 + 1.62460i −0.100707 + 0.0731682i
\(494\) 8.61803 0.387744
\(495\) 0 0
\(496\) 18.7082 0.840023
\(497\) 35.3435 25.6785i 1.58537 1.15184i
\(498\) 0 0
\(499\) 0.791796 2.43690i 0.0354457 0.109091i −0.931768 0.363054i \(-0.881734\pi\)
0.967214 + 0.253963i \(0.0817342\pi\)
\(500\) 1.88197 + 1.36733i 0.0841641 + 0.0611488i
\(501\) 0 0
\(502\) 8.39919 25.8500i 0.374874 1.15374i
\(503\) 9.29180 + 28.5972i 0.414301 + 1.27509i 0.912875 + 0.408239i \(0.133857\pi\)
−0.498574 + 0.866847i \(0.666143\pi\)
\(504\) 0 0
\(505\) 1.14590 0.0509918
\(506\) −10.9443 + 27.2501i −0.486532 + 1.21142i
\(507\) 0 0
\(508\) −4.85410 + 3.52671i −0.215366 + 0.156473i
\(509\) −6.60739 20.3355i −0.292867 0.901353i −0.983929 0.178558i \(-0.942857\pi\)
0.691062 0.722796i \(-0.257143\pi\)
\(510\) 0 0
\(511\) −3.00000 2.17963i −0.132712 0.0964210i
\(512\) −4.28115 3.11044i −0.189202 0.137463i
\(513\) 0 0
\(514\) −13.6631 42.0508i −0.602654 1.85478i
\(515\) 1.85410 1.34708i 0.0817015 0.0593596i
\(516\) 0 0
\(517\) −1.57295 1.31433i −0.0691782 0.0578041i
\(518\) 20.5623 0.903456
\(519\) 0 0
\(520\) 1.64590 + 5.06555i 0.0721774 + 0.222139i
\(521\) −12.0000 + 36.9322i −0.525730 + 1.61803i 0.237139 + 0.971476i \(0.423790\pi\)
−0.762869 + 0.646553i \(0.776210\pi\)
\(522\) 0 0
\(523\) −28.2984 20.5600i −1.23740 0.899025i −0.239979 0.970778i \(-0.577141\pi\)
−0.997422 + 0.0717533i \(0.977141\pi\)
\(524\) 2.64590 8.14324i 0.115587 0.355739i
\(525\) 0 0
\(526\) 0.881966 0.640786i 0.0384555 0.0279396i
\(527\) −2.38197 −0.103760
\(528\) 0 0
\(529\) 6.94427 0.301925
\(530\) 3.69098 2.68166i 0.160326 0.116484i
\(531\) 0 0
\(532\) −0.489357 + 1.50609i −0.0212163 + 0.0652971i
\(533\) 29.9894 + 21.7885i 1.29898 + 0.943767i
\(534\) 0 0
\(535\) −0.0278640 + 0.0857567i −0.00120467 + 0.00370759i
\(536\) 7.29837 + 22.4621i 0.315242 + 0.970214i
\(537\) 0 0
\(538\) 39.5967 1.70714
\(539\) 6.61803 + 0.449028i 0.285059 + 0.0193410i
\(540\) 0 0
\(541\) 0.454915 0.330515i 0.0195583 0.0142100i −0.577963 0.816063i \(-0.696152\pi\)
0.597521 + 0.801853i \(0.296152\pi\)
\(542\) −3.13525 9.64932i −0.134671 0.414474i
\(543\) 0 0
\(544\) −1.69098 1.22857i −0.0725003 0.0526745i
\(545\) 0 0
\(546\) 0 0
\(547\) 5.98936 + 18.4333i 0.256086 + 0.788153i 0.993614 + 0.112836i \(0.0359933\pi\)
−0.737527 + 0.675317i \(0.764007\pi\)
\(548\) −0.736068 + 0.534785i −0.0314433 + 0.0228449i
\(549\) 0 0
\(550\) 25.9894 + 1.76336i 1.10819 + 0.0751897i
\(551\) −3.81966 −0.162723
\(552\) 0 0
\(553\) 0.489357 + 1.50609i 0.0208096 + 0.0640453i
\(554\) −5.21885 + 16.0620i −0.221728 + 0.682407i
\(555\) 0 0
\(556\) −2.92705 2.12663i −0.124135 0.0901891i
\(557\) −8.06231 + 24.8132i −0.341611 + 1.05137i 0.621762 + 0.783206i \(0.286417\pi\)
−0.963373 + 0.268164i \(0.913583\pi\)
\(558\) 0 0
\(559\) −8.89919 + 6.46564i −0.376396 + 0.273467i
\(560\) −5.56231 −0.235050
\(561\) 0 0
\(562\) −8.47214 −0.357375
\(563\) 21.7533 15.8047i 0.916792 0.666088i −0.0259316 0.999664i \(-0.508255\pi\)
0.942723 + 0.333575i \(0.108255\pi\)
\(564\) 0 0
\(565\) 1.50000 4.61653i 0.0631055 0.194219i
\(566\) −29.0344 21.0948i −1.22041 0.886679i
\(567\) 0 0
\(568\) −10.0623 + 30.9686i −0.422205 + 1.29941i
\(569\) −10.5279 32.4014i −0.441351 1.35834i −0.886436 0.462851i \(-0.846827\pi\)
0.445085 0.895488i \(-0.353173\pi\)
\(570\) 0 0
\(571\) −25.6869 −1.07496 −0.537482 0.843275i \(-0.680624\pi\)
−0.537482 + 0.843275i \(0.680624\pi\)
\(572\) −9.80902 8.19624i −0.410136 0.342702i
\(573\) 0 0
\(574\) −23.3435 + 16.9600i −0.974337 + 0.707897i
\(575\) −8.20820 25.2623i −0.342306 1.05351i
\(576\) 0 0
\(577\) −12.3262 8.95554i −0.513148 0.372824i 0.300868 0.953666i \(-0.402723\pi\)
−0.814016 + 0.580842i \(0.802723\pi\)
\(578\) −21.7533 15.8047i −0.904818 0.657388i
\(579\) 0 0
\(580\) 0.326238 + 1.00406i 0.0135463 + 0.0416912i
\(581\) −30.8435 + 22.4091i −1.27960 + 0.929685i
\(582\) 0 0
\(583\) 9.12461 22.7194i 0.377903 0.940940i
\(584\) 2.76393 0.114372
\(585\) 0 0
\(586\) 8.97214 + 27.6134i 0.370636 + 1.14070i
\(587\) −7.51064 + 23.1154i −0.309997 + 0.954074i 0.667767 + 0.744370i \(0.267250\pi\)
−0.977765 + 0.209704i \(0.932750\pi\)
\(588\) 0 0
\(589\) −2.66312 1.93487i −0.109732 0.0797249i
\(590\) −1.01722 + 3.13068i −0.0418783 + 0.128888i
\(591\) 0 0
\(592\) −16.6353 + 12.0862i −0.683705 + 0.496741i
\(593\) 29.2148 1.19971 0.599854 0.800110i \(-0.295225\pi\)
0.599854 + 0.800110i \(0.295225\pi\)
\(594\) 0 0
\(595\) 0.708204 0.0290335
\(596\) 7.50000 5.44907i 0.307212 0.223203i
\(597\) 0 0
\(598\) −17.0623 + 52.5124i −0.697730 + 2.14739i
\(599\) −17.5623 12.7598i −0.717576 0.521350i 0.168033 0.985781i \(-0.446259\pi\)
−0.885609 + 0.464432i \(0.846259\pi\)
\(600\) 0 0
\(601\) −6.12868 + 18.8621i −0.249994 + 0.769402i 0.744781 + 0.667309i \(0.232554\pi\)
−0.994775 + 0.102093i \(0.967446\pi\)
\(602\) −2.64590 8.14324i −0.107839 0.331894i
\(603\) 0 0
\(604\) 1.23607 0.0502949
\(605\) −3.70163 + 1.98787i −0.150493 + 0.0808184i
\(606\) 0 0
\(607\) 1.88197 1.36733i 0.0763866 0.0554981i −0.548937 0.835864i \(-0.684967\pi\)
0.625323 + 0.780366i \(0.284967\pi\)
\(608\) −0.892609 2.74717i −0.0362001 0.111412i
\(609\) 0 0
\(610\) 0.572949 + 0.416272i 0.0231980 + 0.0168544i
\(611\) −3.11803 2.26538i −0.126142 0.0916476i
\(612\) 0 0
\(613\) 1.03444 + 3.18368i 0.0417807 + 0.128588i 0.969771 0.244016i \(-0.0784650\pi\)
−0.927990 + 0.372604i \(0.878465\pi\)
\(614\) −25.6074 + 18.6049i −1.03343 + 0.750831i
\(615\) 0 0
\(616\) −18.8435 + 11.8290i −0.759225 + 0.476602i
\(617\) −46.4164 −1.86865 −0.934327 0.356417i \(-0.883998\pi\)
−0.934327 + 0.356417i \(0.883998\pi\)
\(618\) 0 0
\(619\) −9.63525 29.6543i −0.387274 1.19191i −0.934817 0.355129i \(-0.884437\pi\)
0.547544 0.836777i \(-0.315563\pi\)
\(620\) −0.281153 + 0.865300i −0.0112914 + 0.0347513i
\(621\) 0 0
\(622\) −15.0172 10.9106i −0.602136 0.437477i
\(623\) −8.78115 + 27.0256i −0.351809 + 1.08276i
\(624\) 0 0
\(625\) −18.4721 + 13.4208i −0.738885 + 0.536832i
\(626\) 45.0344 1.79994
\(627\) 0 0
\(628\) 6.00000 0.239426
\(629\) 2.11803 1.53884i 0.0844515 0.0613576i
\(630\) 0 0
\(631\) 3.93363 12.1065i 0.156595 0.481951i −0.841724 0.539908i \(-0.818459\pi\)
0.998319 + 0.0579577i \(0.0184589\pi\)
\(632\) −0.954915 0.693786i −0.0379845 0.0275973i
\(633\) 0 0
\(634\) 12.6803 39.0261i 0.503601 1.54992i
\(635\) 1.14590 + 3.52671i 0.0454736 + 0.139953i
\(636\) 0 0
\(637\) 12.4721 0.494164
\(638\) 18.4164 + 15.3884i 0.729113 + 0.609233i
\(639\) 0 0
\(640\) 4.20820 3.05744i 0.166344 0.120856i
\(641\) 2.08359 + 6.41264i 0.0822969 + 0.253284i 0.983736 0.179623i \(-0.0574878\pi\)
−0.901439 + 0.432907i \(0.857488\pi\)
\(642\) 0 0
\(643\) 14.9164 + 10.8374i 0.588246 + 0.427386i 0.841687 0.539965i \(-0.181563\pi\)
−0.253442 + 0.967351i \(0.581563\pi\)
\(644\) −8.20820 5.96361i −0.323449 0.234999i
\(645\) 0 0
\(646\) 0.263932 + 0.812299i 0.0103843 + 0.0319595i
\(647\) 2.59017 1.88187i 0.101830 0.0739839i −0.535705 0.844405i \(-0.679954\pi\)
0.637535 + 0.770421i \(0.279954\pi\)
\(648\) 0 0
\(649\) 4.30902 + 17.1315i 0.169144 + 0.672471i
\(650\) 48.9787 1.92110
\(651\) 0 0
\(652\) −2.91641 8.97578i −0.114215 0.351519i
\(653\) −6.78773 + 20.8905i −0.265624 + 0.817508i 0.725924 + 0.687774i \(0.241412\pi\)
−0.991549 + 0.129734i \(0.958588\pi\)
\(654\) 0 0
\(655\) −4.28115 3.11044i −0.167278 0.121535i
\(656\) 8.91641 27.4419i 0.348127 1.07143i
\(657\) 0 0
\(658\) 2.42705 1.76336i 0.0946163 0.0687428i
\(659\) −20.6525 −0.804506 −0.402253 0.915528i \(-0.631773\pi\)
−0.402253 + 0.915528i \(0.631773\pi\)
\(660\) 0 0
\(661\) −21.0902 −0.820313 −0.410156 0.912015i \(-0.634526\pi\)
−0.410156 + 0.912015i \(0.634526\pi\)
\(662\) −29.5795 + 21.4908i −1.14964 + 0.835263i
\(663\) 0 0
\(664\) 8.78115 27.0256i 0.340775 1.04880i
\(665\) 0.791796 + 0.575274i 0.0307045 + 0.0223082i
\(666\) 0 0
\(667\) 7.56231 23.2744i 0.292814 0.901188i
\(668\) 3.63525 + 11.1882i 0.140652 + 0.432883i
\(669\) 0 0
\(670\) −6.52786 −0.252193
\(671\) 3.79180 + 0.257270i 0.146381 + 0.00993180i
\(672\) 0 0
\(673\) 11.6631 8.47375i 0.449580 0.326639i −0.339850 0.940480i \(-0.610376\pi\)
0.789430 + 0.613841i \(0.210376\pi\)
\(674\) 6.85410 + 21.0948i 0.264010 + 0.812540i
\(675\) 0 0
\(676\) −12.9443 9.40456i −0.497857 0.361714i
\(677\) 18.1803 + 13.2088i 0.698727 + 0.507655i 0.879517 0.475867i \(-0.157866\pi\)
−0.180790 + 0.983522i \(0.557866\pi\)
\(678\) 0 0
\(679\) 13.9377 + 42.8958i 0.534880 + 1.64619i
\(680\) −0.427051 + 0.310271i −0.0163767 + 0.0118983i
\(681\) 0 0
\(682\) 5.04508 + 20.0579i 0.193186 + 0.768058i
\(683\) 38.8885 1.48803 0.744014 0.668164i \(-0.232919\pi\)
0.744014 + 0.668164i \(0.232919\pi\)
\(684\) 0 0
\(685\) 0.173762 + 0.534785i 0.00663911 + 0.0204331i
\(686\) 7.50000 23.0826i 0.286351 0.881299i
\(687\) 0 0
\(688\) 6.92705 + 5.03280i 0.264091 + 0.191874i
\(689\) 14.2254 43.7814i 0.541946 1.66794i
\(690\) 0 0
\(691\) 32.1246 23.3399i 1.22208 0.887892i 0.225807 0.974172i \(-0.427498\pi\)
0.996271 + 0.0862806i \(0.0274981\pi\)
\(692\) −10.8885 −0.413920
\(693\) 0 0
\(694\) −4.94427 −0.187682
\(695\) −1.80902 + 1.31433i −0.0686199 + 0.0498553i
\(696\) 0 0
\(697\) −1.13525 + 3.49396i −0.0430008 + 0.132343i
\(698\) 39.4336 + 28.6502i 1.49258 + 1.08443i
\(699\) 0 0
\(700\) −2.78115 + 8.55951i −0.105118 + 0.323519i
\(701\) −15.3541 47.2551i −0.579916 1.78480i −0.618792 0.785555i \(-0.712377\pi\)
0.0388752 0.999244i \(-0.487623\pi\)
\(702\) 0 0
\(703\) 3.61803 0.136457
\(704\) 5.23607 13.0373i 0.197342 0.491361i
\(705\) 0 0
\(706\) 2.00000 1.45309i 0.0752710 0.0546876i
\(707\) 2.78115 + 8.55951i 0.104596 + 0.321913i
\(708\) 0 0
\(709\) −5.06231 3.67798i −0.190119 0.138129i 0.488654 0.872478i \(-0.337488\pi\)
−0.678773 + 0.734348i \(0.737488\pi\)
\(710\) −7.28115 5.29007i −0.273257 0.198533i
\(711\) 0 0
\(712\) −6.54508 20.1437i −0.245287 0.754917i
\(713\) 17.0623 12.3965i 0.638988 0.464252i
\(714\) 0 0
\(715\) −6.69098 + 4.20025i −0.250229 + 0.157081i
\(716\) −1.38197 −0.0516465
\(717\) 0 0
\(718\) −8.61803 26.5236i −0.321622 0.989851i
\(719\) 8.78115 27.0256i 0.327482 1.00789i −0.642826 0.766012i \(-0.722238\pi\)
0.970308 0.241873i \(-0.0777618\pi\)
\(720\) 0 0
\(721\) 14.5623 + 10.5801i 0.542329 + 0.394025i
\(722\) 9.13525 28.1154i 0.339979 1.04635i
\(723\) 0 0
\(724\) 4.26393 3.09793i 0.158468 0.115134i
\(725\) −21.7082 −0.806222
\(726\) 0 0
\(727\) 32.1459 1.19223 0.596113 0.802901i \(-0.296711\pi\)
0.596113 + 0.802901i \(0.296711\pi\)
\(728\) −33.8435 + 24.5887i −1.25432 + 0.911318i
\(729\) 0 0
\(730\) −0.236068 + 0.726543i −0.00873727 + 0.0268905i
\(731\) −0.881966 0.640786i −0.0326207 0.0237003i
\(732\) 0 0
\(733\) −7.50658 + 23.1029i −0.277262 + 0.853324i 0.711350 + 0.702838i \(0.248084\pi\)
−0.988612 + 0.150486i \(0.951916\pi\)
\(734\) 7.28115 + 22.4091i 0.268752 + 0.827134i
\(735\) 0 0
\(736\) 18.5066 0.682162
\(737\) −29.6697 + 18.6251i −1.09290 + 0.686064i
\(738\) 0 0
\(739\) 20.2254 14.6946i 0.744004 0.540551i −0.149958 0.988692i \(-0.547914\pi\)
0.893963 + 0.448142i \(0.147914\pi\)
\(740\) −0.309017 0.951057i −0.0113597 0.0349615i
\(741\) 0 0
\(742\) 28.9894 + 21.0620i 1.06423 + 0.773210i
\(743\) 10.3713 + 7.53521i 0.380487 + 0.276440i 0.761546 0.648111i \(-0.224441\pi\)
−0.381059 + 0.924551i \(0.624441\pi\)
\(744\) 0 0
\(745\) −1.77051 5.44907i −0.0648665 0.199638i
\(746\) 29.3435 21.3193i 1.07434 0.780554i
\(747\) 0 0
\(748\) 0.472136 1.17557i 0.0172630 0.0429831i
\(749\) −0.708204 −0.0258772
\(750\) 0 0
\(751\) −16.3541 50.3328i −0.596770 1.83667i −0.545713 0.837972i \(-0.683741\pi\)
−0.0510571 0.998696i \(-0.516259\pi\)
\(752\) −0.927051 + 2.85317i −0.0338061 + 0.104044i
\(753\) 0 0
\(754\) 36.5066 + 26.5236i 1.32949 + 0.965932i
\(755\) 0.236068 0.726543i 0.00859139 0.0264416i
\(756\) 0 0
\(757\) 12.8992 9.37181i 0.468829 0.340624i −0.328156 0.944624i \(-0.606427\pi\)
0.796985 + 0.603999i \(0.206427\pi\)
\(758\) −45.9787 −1.67002
\(759\) 0 0
\(760\) −0.729490 −0.0264614
\(761\) 3.95492 2.87341i 0.143366 0.104161i −0.513791 0.857916i \(-0.671759\pi\)
0.657156 + 0.753754i \(0.271759\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0.736068 + 0.534785i 0.0266300 + 0.0193478i
\(765\) 0 0
\(766\) −4.44427 + 13.6781i −0.160578 + 0.494208i
\(767\) 10.2639 + 31.5891i 0.370609 + 1.14062i
\(768\) 0 0
\(769\) −47.6869 −1.71963 −0.859817 0.510602i \(-0.829423\pi\)
−0.859817 + 0.510602i \(0.829423\pi\)
\(770\) −1.50000 5.96361i −0.0540562 0.214914i
\(771\) 0 0
\(772\) −0.781153 + 0.567541i −0.0281143 + 0.0204262i
\(773\) −15.2188 46.8388i −0.547384 1.68467i −0.715253 0.698865i \(-0.753689\pi\)
0.167870 0.985809i \(-0.446311\pi\)
\(774\) 0 0
\(775\) −15.1353 10.9964i −0.543674 0.395003i
\(776\) −27.1976 19.7602i −0.976336 0.709349i
\(777\) 0 0
\(778\) −4.63525 14.2658i −0.166182 0.511455i
\(779\) −4.10739 + 2.98419i −0.147163 + 0.106920i
\(780\) 0 0
\(781\) −48.1869 3.26944i −1.72426 0.116990i
\(782\) −5.47214 −0.195683
\(783\) 0 0
\(784\) −3.00000 9.23305i −0.107143 0.329752i
\(785\) 1.14590 3.52671i 0.0408989 0.125874i
\(786\) 0 0
\(787\) 19.1803 + 13.9353i 0.683705 + 0.496741i 0.874585 0.484873i \(-0.161134\pi\)
−0.190880 + 0.981613i \(0.561134\pi\)
\(788\) −5.08359 + 15.6457i −0.181095 + 0.557355i
\(789\) 0 0
\(790\) 0.263932 0.191758i 0.00939028 0.00682244i
\(791\) 38.1246 1.35556
\(792\) 0 0
\(793\) 7.14590 0.253758
\(794\) −33.1074 + 24.0539i −1.17494 + 0.853642i
\(795\) 0 0
\(796\) −0.628677 + 1.93487i −0.0222829 + 0.0685796i
\(797\)