Properties

Label 819.2.et.c.145.4
Level $819$
Weight $2$
Character 819.145
Analytic conductor $6.540$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.et (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 145.4
Character \(\chi\) \(=\) 819.145
Dual form 819.2.et.c.514.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.430820 + 0.430820i) q^{2} +1.62879i q^{4} +(-1.97745 + 0.529856i) q^{5} +(-1.23433 + 2.34018i) q^{7} +(-1.56335 - 1.56335i) q^{8} +O(q^{10})\) \(q+(-0.430820 + 0.430820i) q^{2} +1.62879i q^{4} +(-1.97745 + 0.529856i) q^{5} +(-1.23433 + 2.34018i) q^{7} +(-1.56335 - 1.56335i) q^{8} +(0.623652 - 1.08020i) q^{10} +(0.0981532 - 0.0263001i) q^{11} +(3.09469 + 1.85010i) q^{13} +(-0.476419 - 1.53997i) q^{14} -1.91053 q^{16} -3.63007 q^{17} +(0.374251 - 1.39672i) q^{19} +(-0.863023 - 3.22084i) q^{20} +(-0.0309558 + 0.0536170i) q^{22} +4.80660i q^{23} +(-0.700572 + 0.404476i) q^{25} +(-2.13032 + 0.536194i) q^{26} +(-3.81165 - 2.01047i) q^{28} +(-3.79375 - 6.57097i) q^{29} +(1.73499 - 6.47506i) q^{31} +(3.94980 - 3.94980i) q^{32} +(1.56391 - 1.56391i) q^{34} +(1.20088 - 5.28159i) q^{35} +(-2.15422 - 2.15422i) q^{37} +(0.440501 + 0.762971i) q^{38} +(3.91981 + 2.26310i) q^{40} +(0.872020 - 3.25442i) q^{41} +(-7.21579 - 4.16604i) q^{43} +(0.0428372 + 0.159871i) q^{44} +(-2.07078 - 2.07078i) q^{46} +(0.529965 + 1.97786i) q^{47} +(-3.95284 - 5.77711i) q^{49} +(0.127564 - 0.476077i) q^{50} +(-3.01343 + 5.04060i) q^{52} +(5.27832 + 9.14232i) q^{53} +(-0.180158 + 0.104014i) q^{55} +(5.58823 - 1.72882i) q^{56} +(4.46533 + 1.19648i) q^{58} +(1.58843 - 1.58843i) q^{59} +(-5.15531 + 2.97642i) q^{61} +(2.04212 + 3.53706i) q^{62} -0.417744i q^{64} +(-7.09988 - 2.01874i) q^{65} +(-1.62200 - 6.05338i) q^{67} -5.91262i q^{68} +(1.75806 + 2.79278i) q^{70} +(0.0733605 + 0.273785i) q^{71} +(4.17396 + 1.11841i) q^{73} +1.85616 q^{74} +(2.27496 + 0.609575i) q^{76} +(-0.0596070 + 0.262159i) q^{77} +(-5.01725 + 8.69014i) q^{79} +(3.77797 - 1.01230i) q^{80} +(1.02639 + 1.77775i) q^{82} +(-3.74842 - 3.74842i) q^{83} +(7.17828 - 1.92342i) q^{85} +(4.90352 - 1.31389i) q^{86} +(-0.194565 - 0.112332i) q^{88} +(-5.75005 + 5.75005i) q^{89} +(-8.14945 + 4.95848i) q^{91} -7.82893 q^{92} +(-1.08042 - 0.623781i) q^{94} +2.96025i q^{95} +(16.5697 - 4.43983i) q^{97} +(4.19186 + 0.785934i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 6q^{7} + O(q^{10}) \) \( 36q + 6q^{7} + 8q^{11} - 42q^{14} - 24q^{16} + 8q^{17} - 18q^{19} - 14q^{20} + 4q^{22} + 24q^{25} + 50q^{26} + 34q^{28} - 8q^{29} + 6q^{31} + 50q^{32} - 24q^{34} - 14q^{35} - 14q^{37} + 8q^{38} - 30q^{40} - 34q^{41} + 30q^{43} - 28q^{44} - 32q^{46} + 10q^{47} + 6q^{49} + 20q^{50} + 4q^{52} + 8q^{53} - 30q^{55} + 92q^{56} + 72q^{58} + 70q^{59} - 60q^{61} + 48q^{62} + 44q^{65} - 46q^{67} + 80q^{70} - 42q^{71} - 56q^{73} - 40q^{74} + 12q^{76} - 24q^{77} - 170q^{80} + 24q^{82} + 60q^{83} + 2q^{85} - 12q^{86} + 84q^{88} - 64q^{89} - 86q^{91} + 100q^{92} - 66q^{94} + 36q^{97} + 22q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.430820 + 0.430820i −0.304636 + 0.304636i −0.842824 0.538189i \(-0.819109\pi\)
0.538189 + 0.842824i \(0.319109\pi\)
\(3\) 0 0
\(4\) 1.62879i 0.814394i
\(5\) −1.97745 + 0.529856i −0.884342 + 0.236959i −0.672279 0.740297i \(-0.734685\pi\)
−0.212062 + 0.977256i \(0.568018\pi\)
\(6\) 0 0
\(7\) −1.23433 + 2.34018i −0.466534 + 0.884503i
\(8\) −1.56335 1.56335i −0.552729 0.552729i
\(9\) 0 0
\(10\) 0.623652 1.08020i 0.197216 0.341588i
\(11\) 0.0981532 0.0263001i 0.0295943 0.00792977i −0.243992 0.969777i \(-0.578457\pi\)
0.273586 + 0.961848i \(0.411790\pi\)
\(12\) 0 0
\(13\) 3.09469 + 1.85010i 0.858313 + 0.513126i
\(14\) −0.476419 1.53997i −0.127328 0.411574i
\(15\) 0 0
\(16\) −1.91053 −0.477632
\(17\) −3.63007 −0.880422 −0.440211 0.897894i \(-0.645096\pi\)
−0.440211 + 0.897894i \(0.645096\pi\)
\(18\) 0 0
\(19\) 0.374251 1.39672i 0.0858590 0.320430i −0.909616 0.415449i \(-0.863624\pi\)
0.995475 + 0.0950189i \(0.0302911\pi\)
\(20\) −0.863023 3.22084i −0.192978 0.720203i
\(21\) 0 0
\(22\) −0.0309558 + 0.0536170i −0.00659979 + 0.0114312i
\(23\) 4.80660i 1.00224i 0.865376 + 0.501122i \(0.167079\pi\)
−0.865376 + 0.501122i \(0.832921\pi\)
\(24\) 0 0
\(25\) −0.700572 + 0.404476i −0.140114 + 0.0808951i
\(26\) −2.13032 + 0.536194i −0.417790 + 0.105156i
\(27\) 0 0
\(28\) −3.81165 2.01047i −0.720334 0.379943i
\(29\) −3.79375 6.57097i −0.704482 1.22020i −0.966878 0.255238i \(-0.917846\pi\)
0.262397 0.964960i \(-0.415487\pi\)
\(30\) 0 0
\(31\) 1.73499 6.47506i 0.311613 1.16296i −0.615489 0.788146i \(-0.711041\pi\)
0.927102 0.374810i \(-0.122292\pi\)
\(32\) 3.94980 3.94980i 0.698233 0.698233i
\(33\) 0 0
\(34\) 1.56391 1.56391i 0.268208 0.268208i
\(35\) 1.20088 5.28159i 0.202985 0.892752i
\(36\) 0 0
\(37\) −2.15422 2.15422i −0.354152 0.354152i 0.507500 0.861652i \(-0.330570\pi\)
−0.861652 + 0.507500i \(0.830570\pi\)
\(38\) 0.440501 + 0.762971i 0.0714588 + 0.123770i
\(39\) 0 0
\(40\) 3.91981 + 2.26310i 0.619776 + 0.357828i
\(41\) 0.872020 3.25442i 0.136187 0.508256i −0.863804 0.503829i \(-0.831924\pi\)
0.999990 0.00442675i \(-0.00140908\pi\)
\(42\) 0 0
\(43\) −7.21579 4.16604i −1.10040 0.635315i −0.164073 0.986448i \(-0.552463\pi\)
−0.936326 + 0.351133i \(0.885796\pi\)
\(44\) 0.0428372 + 0.159871i 0.00645796 + 0.0241014i
\(45\) 0 0
\(46\) −2.07078 2.07078i −0.305320 0.305320i
\(47\) 0.529965 + 1.97786i 0.0773034 + 0.288500i 0.993746 0.111667i \(-0.0356189\pi\)
−0.916442 + 0.400167i \(0.868952\pi\)
\(48\) 0 0
\(49\) −3.95284 5.77711i −0.564692 0.825302i
\(50\) 0.127564 0.476077i 0.0180403 0.0673275i
\(51\) 0 0
\(52\) −3.01343 + 5.04060i −0.417887 + 0.699005i
\(53\) 5.27832 + 9.14232i 0.725033 + 1.25579i 0.958960 + 0.283540i \(0.0915089\pi\)
−0.233927 + 0.972254i \(0.575158\pi\)
\(54\) 0 0
\(55\) −0.180158 + 0.104014i −0.0242924 + 0.0140252i
\(56\) 5.58823 1.72882i 0.746758 0.231024i
\(57\) 0 0
\(58\) 4.46533 + 1.19648i 0.586326 + 0.157106i
\(59\) 1.58843 1.58843i 0.206796 0.206796i −0.596108 0.802904i \(-0.703287\pi\)
0.802904 + 0.596108i \(0.203287\pi\)
\(60\) 0 0
\(61\) −5.15531 + 2.97642i −0.660070 + 0.381091i −0.792303 0.610127i \(-0.791118\pi\)
0.132234 + 0.991219i \(0.457785\pi\)
\(62\) 2.04212 + 3.53706i 0.259349 + 0.449206i
\(63\) 0 0
\(64\) 0.417744i 0.0522180i
\(65\) −7.09988 2.01874i −0.880632 0.250394i
\(66\) 0 0
\(67\) −1.62200 6.05338i −0.198158 0.739537i −0.991427 0.130665i \(-0.958289\pi\)
0.793268 0.608872i \(-0.208378\pi\)
\(68\) 5.91262i 0.717011i
\(69\) 0 0
\(70\) 1.75806 + 2.79278i 0.210128 + 0.333801i
\(71\) 0.0733605 + 0.273785i 0.00870629 + 0.0324923i 0.970142 0.242536i \(-0.0779793\pi\)
−0.961436 + 0.275029i \(0.911313\pi\)
\(72\) 0 0
\(73\) 4.17396 + 1.11841i 0.488525 + 0.130900i 0.494669 0.869081i \(-0.335289\pi\)
−0.00614434 + 0.999981i \(0.501956\pi\)
\(74\) 1.85616 0.215775
\(75\) 0 0
\(76\) 2.27496 + 0.609575i 0.260956 + 0.0699230i
\(77\) −0.0596070 + 0.262159i −0.00679285 + 0.0298758i
\(78\) 0 0
\(79\) −5.01725 + 8.69014i −0.564485 + 0.977717i 0.432612 + 0.901580i \(0.357592\pi\)
−0.997097 + 0.0761370i \(0.975741\pi\)
\(80\) 3.77797 1.01230i 0.422390 0.113179i
\(81\) 0 0
\(82\) 1.02639 + 1.77775i 0.113346 + 0.196320i
\(83\) −3.74842 3.74842i −0.411442 0.411442i 0.470798 0.882241i \(-0.343966\pi\)
−0.882241 + 0.470798i \(0.843966\pi\)
\(84\) 0 0
\(85\) 7.17828 1.92342i 0.778594 0.208624i
\(86\) 4.90352 1.31389i 0.528760 0.141681i
\(87\) 0 0
\(88\) −0.194565 0.112332i −0.0207407 0.0119746i
\(89\) −5.75005 + 5.75005i −0.609504 + 0.609504i −0.942817 0.333312i \(-0.891834\pi\)
0.333312 + 0.942817i \(0.391834\pi\)
\(90\) 0 0
\(91\) −8.14945 + 4.95848i −0.854294 + 0.519790i
\(92\) −7.82893 −0.816222
\(93\) 0 0
\(94\) −1.08042 0.623781i −0.111437 0.0643381i
\(95\) 2.96025i 0.303715i
\(96\) 0 0
\(97\) 16.5697 4.43983i 1.68239 0.450796i 0.713985 0.700161i \(-0.246889\pi\)
0.968410 + 0.249365i \(0.0802219\pi\)
\(98\) 4.19186 + 0.785934i 0.423442 + 0.0793913i
\(99\) 0 0
\(100\) −0.658805 1.14108i −0.0658805 0.114108i
\(101\) −9.40508 + 16.2901i −0.935840 + 1.62092i −0.162711 + 0.986674i \(0.552024\pi\)
−0.773129 + 0.634249i \(0.781309\pi\)
\(102\) 0 0
\(103\) 0.800311 1.38618i 0.0788569 0.136584i −0.823900 0.566735i \(-0.808206\pi\)
0.902757 + 0.430151i \(0.141540\pi\)
\(104\) −1.94574 7.73047i −0.190795 0.758035i
\(105\) 0 0
\(106\) −6.21270 1.66469i −0.603431 0.161689i
\(107\) −18.1365 −1.75333 −0.876663 0.481105i \(-0.840236\pi\)
−0.876663 + 0.481105i \(0.840236\pi\)
\(108\) 0 0
\(109\) −11.6210 3.11385i −1.11309 0.298252i −0.345008 0.938600i \(-0.612124\pi\)
−0.768085 + 0.640347i \(0.778790\pi\)
\(110\) 0.0328042 0.122427i 0.00312776 0.0116729i
\(111\) 0 0
\(112\) 2.35823 4.47097i 0.222832 0.422467i
\(113\) −5.06433 + 8.77167i −0.476412 + 0.825170i −0.999635 0.0270263i \(-0.991396\pi\)
0.523223 + 0.852196i \(0.324730\pi\)
\(114\) 0 0
\(115\) −2.54680 9.50480i −0.237491 0.886327i
\(116\) 10.7027 6.17921i 0.993722 0.573726i
\(117\) 0 0
\(118\) 1.36865i 0.125995i
\(119\) 4.48072 8.49501i 0.410747 0.778736i
\(120\) 0 0
\(121\) −9.51734 + 5.49484i −0.865212 + 0.499531i
\(122\) 0.938710 3.50331i 0.0849868 0.317175i
\(123\) 0 0
\(124\) 10.5465 + 2.82593i 0.947104 + 0.253776i
\(125\) 8.40900 8.40900i 0.752123 0.752123i
\(126\) 0 0
\(127\) 7.73205 4.46410i 0.686108 0.396125i −0.116044 0.993244i \(-0.537021\pi\)
0.802152 + 0.597119i \(0.203688\pi\)
\(128\) 8.07958 + 8.07958i 0.714141 + 0.714141i
\(129\) 0 0
\(130\) 3.92849 2.18906i 0.344551 0.191993i
\(131\) 16.4911 + 9.52114i 1.44083 + 0.831866i 0.997905 0.0646904i \(-0.0206060\pi\)
0.442929 + 0.896557i \(0.353939\pi\)
\(132\) 0 0
\(133\) 2.80663 + 2.59983i 0.243365 + 0.225434i
\(134\) 3.30670 + 1.90913i 0.285656 + 0.164923i
\(135\) 0 0
\(136\) 5.67509 + 5.67509i 0.486635 + 0.486635i
\(137\) −2.60936 2.60936i −0.222933 0.222933i 0.586800 0.809732i \(-0.300388\pi\)
−0.809732 + 0.586800i \(0.800388\pi\)
\(138\) 0 0
\(139\) −3.25815 1.88110i −0.276353 0.159552i 0.355418 0.934707i \(-0.384338\pi\)
−0.631771 + 0.775155i \(0.717672\pi\)
\(140\) 8.60260 + 1.95597i 0.727052 + 0.165310i
\(141\) 0 0
\(142\) −0.149557 0.0863470i −0.0125506 0.00724608i
\(143\) 0.352412 + 0.100203i 0.0294701 + 0.00837938i
\(144\) 0 0
\(145\) 10.9836 + 10.9836i 0.912139 + 0.912139i
\(146\) −2.28006 + 1.31639i −0.188699 + 0.108945i
\(147\) 0 0
\(148\) 3.50877 3.50877i 0.288419 0.288419i
\(149\) −14.7434 3.95049i −1.20783 0.323636i −0.401918 0.915676i \(-0.631656\pi\)
−0.805909 + 0.592039i \(0.798323\pi\)
\(150\) 0 0
\(151\) −3.29330 + 12.2908i −0.268005 + 1.00021i 0.692380 + 0.721533i \(0.256562\pi\)
−0.960385 + 0.278676i \(0.910105\pi\)
\(152\) −2.76866 + 1.59849i −0.224568 + 0.129654i
\(153\) 0 0
\(154\) −0.0872633 0.138623i −0.00703188 0.0111706i
\(155\) 13.7234i 1.10229i
\(156\) 0 0
\(157\) 15.3520 8.86346i 1.22522 0.707381i 0.259194 0.965825i \(-0.416543\pi\)
0.966026 + 0.258444i \(0.0832096\pi\)
\(158\) −1.58235 5.90542i −0.125885 0.469810i
\(159\) 0 0
\(160\) −5.71771 + 9.90336i −0.452024 + 0.782929i
\(161\) −11.2483 5.93295i −0.886489 0.467582i
\(162\) 0 0
\(163\) −6.17370 + 23.0406i −0.483562 + 1.80468i 0.102891 + 0.994693i \(0.467191\pi\)
−0.586452 + 0.809984i \(0.699476\pi\)
\(164\) 5.30077 + 1.42034i 0.413920 + 0.110910i
\(165\) 0 0
\(166\) 3.22979 0.250680
\(167\) −6.81217 1.82532i −0.527141 0.141247i −0.0145735 0.999894i \(-0.504639\pi\)
−0.512568 + 0.858647i \(0.671306\pi\)
\(168\) 0 0
\(169\) 6.15424 + 11.4510i 0.473403 + 0.880846i
\(170\) −2.26390 + 3.92119i −0.173633 + 0.300742i
\(171\) 0 0
\(172\) 6.78560 11.7530i 0.517397 0.896158i
\(173\) 11.1650 + 19.3383i 0.848859 + 1.47027i 0.882227 + 0.470824i \(0.156043\pi\)
−0.0333684 + 0.999443i \(0.510623\pi\)
\(174\) 0 0
\(175\) −0.0818039 2.13872i −0.00618379 0.161672i
\(176\) −0.187524 + 0.0502470i −0.0141352 + 0.00378751i
\(177\) 0 0
\(178\) 4.95448i 0.371354i
\(179\) −8.47154 4.89104i −0.633192 0.365574i 0.148795 0.988868i \(-0.452461\pi\)
−0.781987 + 0.623294i \(0.785794\pi\)
\(180\) 0 0
\(181\) −14.1944 −1.05506 −0.527530 0.849536i \(-0.676882\pi\)
−0.527530 + 0.849536i \(0.676882\pi\)
\(182\) 1.37473 5.64716i 0.101902 0.418595i
\(183\) 0 0
\(184\) 7.51442 7.51442i 0.553970 0.553970i
\(185\) 5.40128 + 3.11843i 0.397110 + 0.229272i
\(186\) 0 0
\(187\) −0.356303 + 0.0954712i −0.0260555 + 0.00698154i
\(188\) −3.22151 + 0.863201i −0.234953 + 0.0629554i
\(189\) 0 0
\(190\) −1.27533 1.27533i −0.0925224 0.0925224i
\(191\) −2.33347 4.04168i −0.168844 0.292446i 0.769170 0.639044i \(-0.220670\pi\)
−0.938014 + 0.346598i \(0.887337\pi\)
\(192\) 0 0
\(193\) −5.08020 + 1.36124i −0.365681 + 0.0979839i −0.436980 0.899471i \(-0.643952\pi\)
0.0712994 + 0.997455i \(0.477285\pi\)
\(194\) −5.22578 + 9.05131i −0.375189 + 0.649846i
\(195\) 0 0
\(196\) 9.40969 6.43834i 0.672121 0.459881i
\(197\) 11.0378 + 2.95757i 0.786411 + 0.210718i 0.629609 0.776912i \(-0.283215\pi\)
0.156802 + 0.987630i \(0.449882\pi\)
\(198\) 0 0
\(199\) −6.97182 −0.494219 −0.247110 0.968987i \(-0.579481\pi\)
−0.247110 + 0.968987i \(0.579481\pi\)
\(200\) 1.72758 + 0.462904i 0.122159 + 0.0327323i
\(201\) 0 0
\(202\) −2.96619 11.0700i −0.208701 0.778881i
\(203\) 20.0600 0.767273i 1.40793 0.0538520i
\(204\) 0 0
\(205\) 6.89750i 0.481742i
\(206\) 0.252404 + 0.941984i 0.0175858 + 0.0656311i
\(207\) 0 0
\(208\) −5.91249 3.53467i −0.409958 0.245085i
\(209\) 0.146936i 0.0101637i
\(210\) 0 0
\(211\) 3.94886 + 6.83963i 0.271851 + 0.470860i 0.969336 0.245740i \(-0.0790309\pi\)
−0.697485 + 0.716600i \(0.745698\pi\)
\(212\) −14.8909 + 8.59727i −1.02271 + 0.590463i
\(213\) 0 0
\(214\) 7.81359 7.81359i 0.534126 0.534126i
\(215\) 16.4763 + 4.41480i 1.12367 + 0.301087i
\(216\) 0 0
\(217\) 13.0112 + 12.0526i 0.883260 + 0.818181i
\(218\) 6.34808 3.66507i 0.429946 0.248230i
\(219\) 0 0
\(220\) −0.169417 0.293439i −0.0114221 0.0197836i
\(221\) −11.2340 6.71601i −0.755678 0.451768i
\(222\) 0 0
\(223\) −3.02363 + 11.2843i −0.202477 + 0.755654i 0.787727 + 0.616025i \(0.211258\pi\)
−0.990204 + 0.139630i \(0.955409\pi\)
\(224\) 4.36786 + 14.1186i 0.291840 + 0.943339i
\(225\) 0 0
\(226\) −1.59720 5.96083i −0.106244 0.396508i
\(227\) −7.36360 7.36360i −0.488739 0.488739i 0.419169 0.907908i \(-0.362322\pi\)
−0.907908 + 0.419169i \(0.862322\pi\)
\(228\) 0 0
\(229\) −0.194192 0.724734i −0.0128326 0.0478918i 0.959213 0.282685i \(-0.0912252\pi\)
−0.972045 + 0.234794i \(0.924559\pi\)
\(230\) 5.19207 + 2.99764i 0.342355 + 0.197659i
\(231\) 0 0
\(232\) −4.34178 + 16.2037i −0.285052 + 1.06383i
\(233\) 22.2901 + 12.8692i 1.46028 + 0.843091i 0.999024 0.0441785i \(-0.0140670\pi\)
0.461252 + 0.887269i \(0.347400\pi\)
\(234\) 0 0
\(235\) −2.09596 3.63031i −0.136725 0.236815i
\(236\) 2.58721 + 2.58721i 0.168413 + 0.168413i
\(237\) 0 0
\(238\) 1.72944 + 5.59021i 0.112103 + 0.362359i
\(239\) 8.82009 8.82009i 0.570524 0.570524i −0.361751 0.932275i \(-0.617821\pi\)
0.932275 + 0.361751i \(0.117821\pi\)
\(240\) 0 0
\(241\) −20.8684 + 20.8684i −1.34425 + 1.34425i −0.452474 + 0.891777i \(0.649459\pi\)
−0.891777 + 0.452474i \(0.850541\pi\)
\(242\) 1.73297 6.46755i 0.111400 0.415750i
\(243\) 0 0
\(244\) −4.84796 8.39690i −0.310359 0.537557i
\(245\) 10.8776 + 9.32951i 0.694943 + 0.596040i
\(246\) 0 0
\(247\) 3.74227 3.63002i 0.238115 0.230973i
\(248\) −12.8352 + 7.41042i −0.815038 + 0.470562i
\(249\) 0 0
\(250\) 7.24553i 0.458247i
\(251\) 3.38771 5.86769i 0.213831 0.370365i −0.739080 0.673618i \(-0.764739\pi\)
0.952910 + 0.303253i \(0.0980726\pi\)
\(252\) 0 0
\(253\) 0.126414 + 0.471783i 0.00794757 + 0.0296607i
\(254\) −1.40790 + 5.25435i −0.0883394 + 0.329687i
\(255\) 0 0
\(256\) −6.12620 −0.382888
\(257\) 12.9504 0.807822 0.403911 0.914798i \(-0.367651\pi\)
0.403911 + 0.914798i \(0.367651\pi\)
\(258\) 0 0
\(259\) 7.70028 2.38223i 0.478472 0.148024i
\(260\) 3.28810 11.5642i 0.203919 0.717181i
\(261\) 0 0
\(262\) −11.2066 + 3.00280i −0.692346 + 0.185514i
\(263\) −2.76188 + 4.78372i −0.170305 + 0.294977i −0.938526 0.345207i \(-0.887809\pi\)
0.768222 + 0.640184i \(0.221142\pi\)
\(264\) 0 0
\(265\) −15.2817 15.2817i −0.938748 0.938748i
\(266\) −2.32921 + 0.0890900i −0.142813 + 0.00546246i
\(267\) 0 0
\(268\) 9.85967 2.64189i 0.602275 0.161379i
\(269\) 12.1333i 0.739778i −0.929076 0.369889i \(-0.879396\pi\)
0.929076 0.369889i \(-0.120604\pi\)
\(270\) 0 0
\(271\) −1.61558 + 1.61558i −0.0981395 + 0.0981395i −0.754472 0.656332i \(-0.772107\pi\)
0.656332 + 0.754472i \(0.272107\pi\)
\(272\) 6.93535 0.420518
\(273\) 0 0
\(274\) 2.24833 0.135827
\(275\) −0.0581257 + 0.0581257i −0.00350511 + 0.00350511i
\(276\) 0 0
\(277\) 5.18421i 0.311489i 0.987797 + 0.155745i \(0.0497777\pi\)
−0.987797 + 0.155745i \(0.950222\pi\)
\(278\) 2.21409 0.593264i 0.132792 0.0355816i
\(279\) 0 0
\(280\) −10.1344 + 6.37961i −0.605646 + 0.381255i
\(281\) −13.5499 13.5499i −0.808321 0.808321i 0.176059 0.984380i \(-0.443665\pi\)
−0.984380 + 0.176059i \(0.943665\pi\)
\(282\) 0 0
\(283\) 6.84696 11.8593i 0.407009 0.704961i −0.587544 0.809192i \(-0.699905\pi\)
0.994553 + 0.104232i \(0.0332383\pi\)
\(284\) −0.445938 + 0.119489i −0.0264615 + 0.00709035i
\(285\) 0 0
\(286\) −0.194995 + 0.108657i −0.0115303 + 0.00642500i
\(287\) 6.53956 + 6.05772i 0.386018 + 0.357576i
\(288\) 0 0
\(289\) −3.82256 −0.224857
\(290\) −9.46392 −0.555740
\(291\) 0 0
\(292\) −1.82165 + 6.79850i −0.106604 + 0.397852i
\(293\) 5.35275 + 19.9768i 0.312711 + 1.16705i 0.926102 + 0.377274i \(0.123139\pi\)
−0.613390 + 0.789780i \(0.710195\pi\)
\(294\) 0 0
\(295\) −2.29940 + 3.98267i −0.133876 + 0.231880i
\(296\) 6.73562i 0.391500i
\(297\) 0 0
\(298\) 8.05371 4.64981i 0.466539 0.269356i
\(299\) −8.89270 + 14.8749i −0.514278 + 0.860240i
\(300\) 0 0
\(301\) 18.6560 11.7439i 1.07531 0.676909i
\(302\) −3.87629 6.71393i −0.223055 0.386343i
\(303\) 0 0
\(304\) −0.715016 + 2.66848i −0.0410090 + 0.153048i
\(305\) 8.61728 8.61728i 0.493424 0.493424i
\(306\) 0 0
\(307\) 12.7621 12.7621i 0.728370 0.728370i −0.241925 0.970295i \(-0.577779\pi\)
0.970295 + 0.241925i \(0.0777788\pi\)
\(308\) −0.427001 0.0970872i −0.0243306 0.00553206i
\(309\) 0 0
\(310\) −5.91232 5.91232i −0.335797 0.335797i
\(311\) 3.99213 + 6.91458i 0.226373 + 0.392090i 0.956731 0.290975i \(-0.0939798\pi\)
−0.730357 + 0.683065i \(0.760646\pi\)
\(312\) 0 0
\(313\) −16.6125 9.59123i −0.938994 0.542129i −0.0493493 0.998782i \(-0.515715\pi\)
−0.889645 + 0.456653i \(0.849048\pi\)
\(314\) −2.79538 + 10.4325i −0.157752 + 0.588740i
\(315\) 0 0
\(316\) −14.1544 8.17204i −0.796247 0.459713i
\(317\) −6.86941 25.6370i −0.385824 1.43992i −0.836864 0.547412i \(-0.815613\pi\)
0.451039 0.892504i \(-0.351053\pi\)
\(318\) 0 0
\(319\) −0.545185 0.545185i −0.0305245 0.0305245i
\(320\) 0.221344 + 0.826067i 0.0123735 + 0.0461785i
\(321\) 0 0
\(322\) 7.40202 2.28995i 0.412498 0.127614i
\(323\) −1.35856 + 5.07021i −0.0755922 + 0.282114i
\(324\) 0 0
\(325\) −2.91638 0.0444031i −0.161772 0.00246304i
\(326\) −7.26659 12.5861i −0.402459 0.697079i
\(327\) 0 0
\(328\) −6.45110 + 3.72454i −0.356202 + 0.205653i
\(329\) −5.28269 1.20112i −0.291244 0.0662201i
\(330\) 0 0
\(331\) −32.6825 8.75726i −1.79639 0.481343i −0.802989 0.595994i \(-0.796758\pi\)
−0.993406 + 0.114651i \(0.963425\pi\)
\(332\) 6.10538 6.10538i 0.335076 0.335076i
\(333\) 0 0
\(334\) 3.72120 2.14844i 0.203615 0.117557i
\(335\) 6.41483 + 11.1108i 0.350480 + 0.607049i
\(336\) 0 0
\(337\) 4.82368i 0.262763i −0.991332 0.131381i \(-0.958059\pi\)
0.991332 0.131381i \(-0.0419412\pi\)
\(338\) −7.58469 2.28195i −0.412553 0.124122i
\(339\) 0 0
\(340\) 3.13284 + 11.6919i 0.169902 + 0.634082i
\(341\) 0.681178i 0.0368879i
\(342\) 0 0
\(343\) 18.3986 2.11945i 0.993430 0.114440i
\(344\) 4.76785 + 17.7938i 0.257065 + 0.959380i
\(345\) 0 0
\(346\) −13.1415 3.52124i −0.706489 0.189303i
\(347\) −30.0530 −1.61333 −0.806664 0.591010i \(-0.798729\pi\)
−0.806664 + 0.591010i \(0.798729\pi\)
\(348\) 0 0
\(349\) 29.5463 + 7.91691i 1.58158 + 0.423782i 0.939414 0.342785i \(-0.111370\pi\)
0.642164 + 0.766567i \(0.278037\pi\)
\(350\) 0.956647 + 0.886161i 0.0511349 + 0.0473673i
\(351\) 0 0
\(352\) 0.283806 0.491566i 0.0151269 0.0262005i
\(353\) −30.1693 + 8.08384i −1.60575 + 0.430260i −0.946773 0.321903i \(-0.895678\pi\)
−0.658978 + 0.752162i \(0.729011\pi\)
\(354\) 0 0
\(355\) −0.290133 0.502525i −0.0153987 0.0266713i
\(356\) −9.36562 9.36562i −0.496377 0.496377i
\(357\) 0 0
\(358\) 5.75687 1.54255i 0.304260 0.0815262i
\(359\) −12.8721 + 3.44908i −0.679366 + 0.182035i −0.581970 0.813210i \(-0.697718\pi\)
−0.0973957 + 0.995246i \(0.531051\pi\)
\(360\) 0 0
\(361\) 14.6437 + 8.45455i 0.770722 + 0.444976i
\(362\) 6.11523 6.11523i 0.321409 0.321409i
\(363\) 0 0
\(364\) −8.07631 13.2737i −0.423314 0.695732i
\(365\) −8.84639 −0.463041
\(366\) 0 0
\(367\) −20.0733 11.5893i −1.04782 0.604957i −0.125779 0.992058i \(-0.540143\pi\)
−0.922037 + 0.387101i \(0.873476\pi\)
\(368\) 9.18313i 0.478704i
\(369\) 0 0
\(370\) −3.67047 + 0.983498i −0.190818 + 0.0511296i
\(371\) −27.9098 + 1.06752i −1.44901 + 0.0554230i
\(372\) 0 0
\(373\) −0.724254 1.25444i −0.0375004 0.0649527i 0.846666 0.532125i \(-0.178606\pi\)
−0.884166 + 0.467172i \(0.845273\pi\)
\(374\) 0.112372 0.194634i 0.00581060 0.0100643i
\(375\) 0 0
\(376\) 2.26357 3.92062i 0.116735 0.202190i
\(377\) 0.416476 27.3539i 0.0214496 1.40880i
\(378\) 0 0
\(379\) −2.31805 0.621121i −0.119070 0.0319048i 0.198792 0.980042i \(-0.436298\pi\)
−0.317862 + 0.948137i \(0.602965\pi\)
\(380\) −4.82161 −0.247343
\(381\) 0 0
\(382\) 2.74654 + 0.735934i 0.140525 + 0.0376537i
\(383\) 7.48482 27.9337i 0.382456 1.42735i −0.459681 0.888084i \(-0.652036\pi\)
0.842137 0.539263i \(-0.181297\pi\)
\(384\) 0 0
\(385\) −0.0210365 0.549988i −0.00107212 0.0280300i
\(386\) 1.60221 2.77510i 0.0815501 0.141249i
\(387\) 0 0
\(388\) 7.23154 + 26.9885i 0.367126 + 1.37013i
\(389\) 26.2815 15.1736i 1.33252 0.769332i 0.346837 0.937925i \(-0.387256\pi\)
0.985686 + 0.168593i \(0.0539223\pi\)
\(390\) 0 0
\(391\) 17.4483i 0.882399i
\(392\) −2.85199 + 15.2114i −0.144047 + 0.768290i
\(393\) 0 0
\(394\) −6.02949 + 3.48113i −0.303761 + 0.175377i
\(395\) 5.31684 19.8427i 0.267519 0.998396i
\(396\) 0 0
\(397\) 16.6187 + 4.45296i 0.834068 + 0.223488i 0.650488 0.759517i \(-0.274565\pi\)
0.183580 + 0.983005i \(0.441231\pi\)
\(398\) 3.00360 3.00360i 0.150557 0.150557i
\(399\) 0 0
\(400\) 1.33846 0.772762i 0.0669231 0.0386381i
\(401\) 10.6544 + 10.6544i 0.532056 + 0.532056i 0.921184 0.389128i \(-0.127224\pi\)
−0.389128 + 0.921184i \(0.627224\pi\)
\(402\) 0 0
\(403\) 17.3488 16.8284i 0.864205 0.838283i
\(404\) −26.5331 15.3189i −1.32007 0.762143i
\(405\) 0 0
\(406\) −8.31168 + 8.97279i −0.412502 + 0.445312i
\(407\) −0.268100 0.154787i −0.0132892 0.00767253i
\(408\) 0 0
\(409\) 12.7272 + 12.7272i 0.629320 + 0.629320i 0.947897 0.318577i \(-0.103205\pi\)
−0.318577 + 0.947897i \(0.603205\pi\)
\(410\) −2.97158 2.97158i −0.146756 0.146756i
\(411\) 0 0
\(412\) 2.25779 + 1.30354i 0.111233 + 0.0642206i
\(413\) 1.75655 + 5.67785i 0.0864341 + 0.279389i
\(414\) 0 0
\(415\) 9.39842 + 5.42618i 0.461351 + 0.266361i
\(416\) 19.5310 4.91588i 0.957584 0.241021i
\(417\) 0 0
\(418\) 0.0633028 + 0.0633028i 0.00309624 + 0.00309624i
\(419\) −13.0716 + 7.54692i −0.638592 + 0.368691i −0.784072 0.620670i \(-0.786861\pi\)
0.145480 + 0.989361i \(0.453527\pi\)
\(420\) 0 0
\(421\) −13.2298 + 13.2298i −0.644780 + 0.644780i −0.951727 0.306947i \(-0.900693\pi\)
0.306947 + 0.951727i \(0.400693\pi\)
\(422\) −4.64790 1.24540i −0.226256 0.0606252i
\(423\) 0 0
\(424\) 6.04080 22.5446i 0.293367 1.09486i
\(425\) 2.54313 1.46828i 0.123360 0.0712219i
\(426\) 0 0
\(427\) −0.601971 15.7382i −0.0291314 0.761626i
\(428\) 29.5406i 1.42790i
\(429\) 0 0
\(430\) −9.00029 + 5.19632i −0.434032 + 0.250589i
\(431\) −10.5271 39.2876i −0.507072 1.89242i −0.447701 0.894183i \(-0.647757\pi\)
−0.0593708 0.998236i \(-0.518909\pi\)
\(432\) 0 0
\(433\) −1.94157 + 3.36289i −0.0933058 + 0.161610i −0.908900 0.417014i \(-0.863077\pi\)
0.815594 + 0.578624i \(0.196410\pi\)
\(434\) −10.7980 + 0.413012i −0.518320 + 0.0198252i
\(435\) 0 0
\(436\) 5.07180 18.9282i 0.242895 0.906496i
\(437\) 6.71348 + 1.79887i 0.321149 + 0.0860517i
\(438\) 0 0
\(439\) −23.3601 −1.11491 −0.557457 0.830206i \(-0.688223\pi\)
−0.557457 + 0.830206i \(0.688223\pi\)
\(440\) 0.444261 + 0.119039i 0.0211793 + 0.00567498i
\(441\) 0 0
\(442\) 7.73321 1.94642i 0.367831 0.0925820i
\(443\) 7.62370 13.2046i 0.362213 0.627371i −0.626112 0.779733i \(-0.715355\pi\)
0.988325 + 0.152362i \(0.0486880\pi\)
\(444\) 0 0
\(445\) 8.32374 14.4171i 0.394583 0.683438i
\(446\) −3.55888 6.16415i −0.168518 0.291881i
\(447\) 0 0
\(448\) 0.977594 + 0.515635i 0.0461870 + 0.0243615i
\(449\) −22.2529 + 5.96266i −1.05018 + 0.281395i −0.742327 0.670038i \(-0.766278\pi\)
−0.307855 + 0.951433i \(0.599611\pi\)
\(450\) 0 0
\(451\) 0.342366i 0.0161214i
\(452\) −14.2872 8.24872i −0.672013 0.387987i
\(453\) 0 0
\(454\) 6.34478 0.297775
\(455\) 13.4878 14.1232i 0.632319 0.662104i
\(456\) 0 0
\(457\) −2.86607 + 2.86607i −0.134069 + 0.134069i −0.770957 0.636887i \(-0.780222\pi\)
0.636887 + 0.770957i \(0.280222\pi\)
\(458\) 0.395892 + 0.228568i 0.0184988 + 0.0106803i
\(459\) 0 0
\(460\) 15.4813 4.14820i 0.721819 0.193411i
\(461\) 14.2239 3.81128i 0.662473 0.177509i 0.0881113 0.996111i \(-0.471917\pi\)
0.574362 + 0.818601i \(0.305250\pi\)
\(462\) 0 0
\(463\) 3.88913 + 3.88913i 0.180743 + 0.180743i 0.791680 0.610936i \(-0.209207\pi\)
−0.610936 + 0.791680i \(0.709207\pi\)
\(464\) 7.24806 + 12.5540i 0.336483 + 0.582805i
\(465\) 0 0
\(466\) −15.1474 + 4.05872i −0.701688 + 0.188017i
\(467\) −2.18755 + 3.78894i −0.101228 + 0.175331i −0.912191 0.409766i \(-0.865610\pi\)
0.810963 + 0.585097i \(0.198944\pi\)
\(468\) 0 0
\(469\) 16.1680 + 3.67613i 0.746571 + 0.169748i
\(470\) 2.46699 + 0.661028i 0.113794 + 0.0304909i
\(471\) 0 0
\(472\) −4.96655 −0.228604
\(473\) −0.817820 0.219134i −0.0376034 0.0100758i
\(474\) 0 0
\(475\) 0.302751 + 1.12988i 0.0138912 + 0.0518425i
\(476\) 13.8366 + 7.29815i 0.634198 + 0.334510i
\(477\) 0 0
\(478\) 7.59974i 0.347604i
\(479\) −8.19394 30.5802i −0.374391 1.39724i −0.854233 0.519890i \(-0.825973\pi\)
0.479843 0.877355i \(-0.340694\pi\)
\(480\) 0 0
\(481\) −2.68112 10.6522i −0.122249 0.485697i
\(482\) 17.9811i 0.819015i
\(483\) 0 0
\(484\) −8.94993 15.5017i −0.406815 0.704624i
\(485\) −30.4132 + 17.5591i −1.38099 + 0.797316i
\(486\) 0 0
\(487\) −22.4600 + 22.4600i −1.01776 + 1.01776i −0.0179183 + 0.999839i \(0.505704\pi\)
−0.999839 + 0.0179183i \(0.994296\pi\)
\(488\) 12.7128 + 3.40638i 0.575480 + 0.154199i
\(489\) 0 0
\(490\) −8.70562 + 0.666938i −0.393280 + 0.0301292i
\(491\) −3.19371 + 1.84389i −0.144130 + 0.0832136i −0.570331 0.821415i \(-0.693185\pi\)
0.426201 + 0.904629i \(0.359852\pi\)
\(492\) 0 0
\(493\) 13.7716 + 23.8531i 0.620241 + 1.07429i
\(494\) −0.0483580 + 3.17613i −0.00217573 + 0.142901i
\(495\) 0 0
\(496\) −3.31474 + 12.3708i −0.148836 + 0.555464i
\(497\) −0.731257 0.166266i −0.0328013 0.00745804i
\(498\) 0 0
\(499\) −7.61668 28.4258i −0.340969 1.27252i −0.897251 0.441521i \(-0.854439\pi\)
0.556281 0.830994i \(-0.312228\pi\)
\(500\) 13.6965 + 13.6965i 0.612525 + 0.612525i
\(501\) 0 0
\(502\) 1.06842 + 3.98741i 0.0476861 + 0.177967i
\(503\) 12.1149 + 6.99455i 0.540178 + 0.311872i 0.745151 0.666896i \(-0.232377\pi\)
−0.204973 + 0.978768i \(0.565711\pi\)
\(504\) 0 0
\(505\) 9.96667 37.1961i 0.443511 1.65520i
\(506\) −0.257715 0.148792i −0.0114568 0.00661461i
\(507\) 0 0
\(508\) 7.27107 + 12.5939i 0.322602 + 0.558763i
\(509\) 26.6190 + 26.6190i 1.17987 + 1.17987i 0.979777 + 0.200090i \(0.0641235\pi\)
0.200090 + 0.979777i \(0.435877\pi\)
\(510\) 0 0
\(511\) −7.76933 + 8.38731i −0.343695 + 0.371033i
\(512\) −13.5199 + 13.5199i −0.597499 + 0.597499i
\(513\) 0 0
\(514\) −5.57928 + 5.57928i −0.246092 + 0.246092i
\(515\) −0.848098 + 3.16515i −0.0373717 + 0.139473i
\(516\) 0 0
\(517\) 0.104036 + 0.180195i 0.00457548 + 0.00792496i
\(518\) −2.29112 + 4.34375i −0.100666 + 0.190853i
\(519\) 0 0
\(520\) 7.94362 + 14.2556i 0.348351 + 0.625151i
\(521\) 6.79737 3.92446i 0.297798 0.171934i −0.343655 0.939096i \(-0.611665\pi\)
0.641453 + 0.767162i \(0.278332\pi\)
\(522\) 0 0
\(523\) 13.2423i 0.579043i 0.957171 + 0.289522i \(0.0934962\pi\)
−0.957171 + 0.289522i \(0.906504\pi\)
\(524\) −15.5079 + 26.8605i −0.677467 + 1.17341i
\(525\) 0 0
\(526\) −0.871048 3.25079i −0.0379795 0.141741i
\(527\) −6.29813 + 23.5050i −0.274351 + 1.02389i
\(528\) 0 0
\(529\) −0.103385 −0.00449500
\(530\) 13.1673 0.571953
\(531\) 0 0
\(532\) −4.23458 + 4.57140i −0.183592 + 0.198195i
\(533\) 8.71965 8.45811i 0.377690 0.366362i
\(534\) 0 0
\(535\) 35.8641 9.60975i 1.55054 0.415466i
\(536\) −6.92782 + 11.9993i −0.299236 + 0.518292i
\(537\) 0 0
\(538\) 5.22726 + 5.22726i 0.225363 + 0.225363i
\(539\) −0.539922 0.463082i −0.0232561 0.0199464i
\(540\) 0 0
\(541\) 23.6349 6.33296i 1.01614 0.272275i 0.287950 0.957645i \(-0.407026\pi\)
0.728195 + 0.685370i \(0.240360\pi\)
\(542\) 1.39205i 0.0597936i
\(543\) 0 0
\(544\) −14.3381 + 14.3381i −0.614740 + 0.614740i
\(545\) 24.6299 1.05503
\(546\) 0 0
\(547\) −39.7857 −1.70111 −0.850557 0.525883i \(-0.823735\pi\)
−0.850557 + 0.525883i \(0.823735\pi\)
\(548\) 4.25009 4.25009i 0.181555 0.181555i
\(549\) 0 0
\(550\) 0.0500834i 0.00213556i
\(551\) −10.5976 + 2.83963i −0.451474 + 0.120972i
\(552\) 0 0
\(553\) −14.1435 22.4678i −0.601442 0.955428i
\(554\) −2.23346 2.23346i −0.0948908 0.0948908i
\(555\) 0 0
\(556\) 3.06391 5.30684i 0.129939 0.225060i
\(557\) 0.380110 0.101850i 0.0161058 0.00431553i −0.250757 0.968050i \(-0.580680\pi\)
0.266863 + 0.963734i \(0.414013\pi\)
\(558\) 0 0
\(559\) −14.6231 26.2426i −0.618489 1.10994i
\(560\) −2.29431 + 10.0906i −0.0969521 + 0.426407i
\(561\) 0 0
\(562\) 11.6752 0.492487
\(563\) −27.7772 −1.17067 −0.585335 0.810792i \(-0.699037\pi\)
−0.585335 + 0.810792i \(0.699037\pi\)
\(564\) 0 0
\(565\) 5.36673 20.0289i 0.225780 0.842622i
\(566\) 2.15941 + 8.05902i 0.0907667 + 0.338746i
\(567\) 0 0
\(568\) 0.313335 0.542712i 0.0131472 0.0227717i
\(569\) 0.573198i 0.0240297i −0.999928 0.0120149i \(-0.996175\pi\)
0.999928 0.0120149i \(-0.00382454\pi\)
\(570\) 0 0
\(571\) 26.2481 15.1543i 1.09845 0.634189i 0.162635 0.986686i \(-0.448001\pi\)
0.935813 + 0.352497i \(0.114667\pi\)
\(572\) −0.163209 + 0.574004i −0.00682412 + 0.0240003i
\(573\) 0 0
\(574\) −5.42716 + 0.207583i −0.226525 + 0.00866437i
\(575\) −1.94415 3.36737i −0.0810768 0.140429i
\(576\) 0 0
\(577\) −10.1337 + 37.8193i −0.421870 + 1.57444i 0.348795 + 0.937199i \(0.386591\pi\)
−0.770665 + 0.637240i \(0.780076\pi\)
\(578\) 1.64684 1.64684i 0.0684994 0.0684994i
\(579\) 0 0
\(580\) −17.8900 + 17.8900i −0.742841 + 0.742841i
\(581\) 13.3988 4.14516i 0.555874 0.171970i
\(582\) 0 0
\(583\) 0.758528 + 0.758528i 0.0314150 + 0.0314150i
\(584\) −4.77691 8.27385i −0.197670 0.342374i
\(585\) 0 0
\(586\) −10.9125 6.30031i −0.450790 0.260264i
\(587\) −4.30312 + 16.0595i −0.177609 + 0.662845i 0.818484 + 0.574530i \(0.194815\pi\)
−0.996093 + 0.0883156i \(0.971852\pi\)
\(588\) 0 0
\(589\) −8.39455 4.84659i −0.345891 0.199700i
\(590\) −0.725188 2.70644i −0.0298555 0.111422i
\(591\) 0 0
\(592\) 4.11569 + 4.11569i 0.169154 + 0.169154i
\(593\) 1.93471 + 7.22043i 0.0794489 + 0.296507i 0.994205 0.107499i \(-0.0342841\pi\)
−0.914756 + 0.404006i \(0.867617\pi\)
\(594\) 0 0
\(595\) −4.35927 + 19.1726i −0.178713 + 0.785999i
\(596\) 6.43450 24.0139i 0.263568 0.983647i
\(597\) 0 0
\(598\) −2.57727 10.2396i −0.105392 0.418727i
\(599\) −2.38287 4.12725i −0.0973613 0.168635i 0.813230 0.581942i \(-0.197707\pi\)
−0.910592 + 0.413307i \(0.864374\pi\)
\(600\) 0 0
\(601\) −15.7639 + 9.10131i −0.643024 + 0.371250i −0.785778 0.618508i \(-0.787737\pi\)
0.142754 + 0.989758i \(0.454404\pi\)
\(602\) −2.97784 + 13.0969i −0.121368 + 0.533789i
\(603\) 0 0
\(604\) −20.0191 5.36409i −0.814564 0.218262i
\(605\) 15.9086 15.9086i 0.646775 0.646775i
\(606\) 0 0
\(607\) −25.1421 + 14.5158i −1.02048 + 0.589177i −0.914244 0.405163i \(-0.867215\pi\)
−0.106240 + 0.994340i \(0.533881\pi\)
\(608\) −4.03856 6.99499i −0.163785 0.283685i
\(609\) 0 0
\(610\) 7.42500i 0.300629i
\(611\) −2.01916 + 7.10135i −0.0816865 + 0.287290i
\(612\) 0 0
\(613\) 2.94070 + 10.9749i 0.118774 + 0.443270i 0.999542 0.0302784i \(-0.00963940\pi\)
−0.880768 + 0.473549i \(0.842973\pi\)
\(614\) 10.9963i 0.443775i
\(615\) 0 0
\(616\) 0.503034 0.316660i 0.0202678 0.0127586i
\(617\) 5.32917 + 19.8887i 0.214544 + 0.800690i 0.986327 + 0.164803i \(0.0526988\pi\)
−0.771782 + 0.635887i \(0.780635\pi\)
\(618\) 0 0
\(619\) −0.198576 0.0532082i −0.00798143 0.00213862i 0.254826 0.966987i \(-0.417982\pi\)
−0.262808 + 0.964848i \(0.584648\pi\)
\(620\) −22.3525 −0.897698
\(621\) 0 0
\(622\) −4.69883 1.25905i −0.188406 0.0504832i
\(623\) −6.35865 20.5536i −0.254754 0.823463i
\(624\) 0 0
\(625\) −10.1504 + 17.5810i −0.406017 + 0.703242i
\(626\) 11.2891 3.02490i 0.451203 0.120899i
\(627\) 0 0
\(628\) 14.4367 + 25.0051i 0.576087 + 0.997812i
\(629\) 7.81998 + 7.81998i 0.311803 + 0.311803i
\(630\) 0 0
\(631\) 28.5113 7.63958i 1.13502 0.304127i 0.358071 0.933694i \(-0.383435\pi\)
0.776946 + 0.629568i \(0.216768\pi\)
\(632\) 21.4295 5.74202i 0.852421 0.228405i
\(633\) 0 0
\(634\) 14.0044 + 8.08544i 0.556186 + 0.321114i
\(635\) −12.9244 + 12.9244i −0.512889 + 0.512889i
\(636\) 0 0
\(637\) −1.54457 25.1916i −0.0611982 0.998126i
\(638\) 0.469754 0.0185977
\(639\) 0 0
\(640\) −20.2580 11.6959i −0.800766 0.462323i
\(641\) 47.3075i 1.86853i 0.356575 + 0.934267i \(0.383944\pi\)
−0.356575 + 0.934267i \(0.616056\pi\)
\(642\) 0 0
\(643\) 19.6736 5.27154i 0.775853 0.207889i 0.150897 0.988549i \(-0.451784\pi\)
0.624955 + 0.780660i \(0.285117\pi\)
\(644\) 9.66351 18.3211i 0.380796 0.721951i
\(645\) 0 0
\(646\) −1.59905 2.76964i −0.0629139 0.108970i
\(647\) 1.56833 2.71643i 0.0616576 0.106794i −0.833549 0.552446i \(-0.813695\pi\)
0.895206 + 0.445652i \(0.147028\pi\)
\(648\) 0 0
\(649\) 0.114133 0.197685i 0.00448013 0.00775981i
\(650\) 1.27556 1.23730i 0.0500317 0.0485311i
\(651\) 0 0
\(652\) −37.5282 10.0557i −1.46972 0.393810i
\(653\) 4.18468 0.163759 0.0818795 0.996642i \(-0.473908\pi\)
0.0818795 + 0.996642i \(0.473908\pi\)
\(654\) 0 0
\(655\) −37.6551 10.0897i −1.47131 0.394236i
\(656\) −1.66602 + 6.21766i −0.0650471 + 0.242759i
\(657\) 0 0
\(658\) 2.79336 1.75842i 0.108896 0.0685503i
\(659\) 8.69927 15.0676i 0.338875 0.586949i −0.645346 0.763890i \(-0.723287\pi\)
0.984221 + 0.176941i \(0.0566202\pi\)
\(660\) 0 0
\(661\) −7.68938 28.6972i −0.299082 1.11619i −0.937921 0.346849i \(-0.887252\pi\)
0.638839 0.769341i \(-0.279415\pi\)
\(662\) 17.8531 10.3075i 0.693880 0.400612i
\(663\) 0 0
\(664\) 11.7202i 0.454833i
\(665\) −6.92749 3.65393i −0.268637 0.141693i
\(666\) 0 0
\(667\) 31.5840 18.2350i 1.22294 0.706063i
\(668\) 2.97305 11.0956i 0.115031 0.429301i
\(669\) 0 0
\(670\) −7.55040 2.02312i −0.291697 0.0781601i
\(671\) −0.427730 + 0.427730i −0.0165123 + 0.0165123i
\(672\) 0 0
\(673\) −22.9048 + 13.2241i −0.882917 + 0.509752i −0.871619 0.490184i \(-0.836930\pi\)
−0.0112978 + 0.999936i \(0.503596\pi\)
\(674\) 2.07814 + 2.07814i 0.0800469 + 0.0800469i
\(675\) 0 0
\(676\) −18.6512 + 10.0240i −0.717356 + 0.385537i
\(677\) 8.72930 + 5.03986i 0.335494 + 0.193698i 0.658278 0.752775i \(-0.271285\pi\)
−0.322783 + 0.946473i \(0.604619\pi\)
\(678\) 0 0
\(679\) −10.0625 + 44.2561i −0.386164 + 1.69839i
\(680\) −14.2292 8.21522i −0.545664 0.315039i
\(681\) 0 0
\(682\) 0.293465 + 0.293465i 0.0112374 + 0.0112374i
\(683\) 31.5016 + 31.5016i 1.20537 + 1.20537i 0.972509 + 0.232864i \(0.0748097\pi\)
0.232864 + 0.972509i \(0.425190\pi\)
\(684\) 0 0
\(685\) 6.54246 + 3.77729i 0.249974 + 0.144323i
\(686\) −7.01338 + 8.83958i −0.267772 + 0.337497i
\(687\) 0 0
\(688\) 13.7860 + 7.95933i 0.525585 + 0.303447i
\(689\) −0.579451 + 38.0581i −0.0220753 + 1.44990i
\(690\) 0 0
\(691\) −2.87952 2.87952i −0.109542 0.109542i 0.650211 0.759753i \(-0.274680\pi\)
−0.759753 + 0.650211i \(0.774680\pi\)
\(692\) −31.4981 + 18.1854i −1.19738 + 0.691306i
\(693\) 0 0
\(694\) 12.9474 12.9474i 0.491478 0.491478i
\(695\) 7.43954 + 1.99342i 0.282198 + 0.0756146i
\(696\) 0 0
\(697\) −3.16550 + 11.8138i −0.119902 + 0.447479i
\(698\) −16.1399 + 9.31838i −0.610905 + 0.352706i
\(699\) 0 0
\(700\) 3.48352 0.133241i 0.131665 0.00503604i
\(701\) 19.7829i 0.747191i 0.927592 + 0.373596i \(0.121875\pi\)
−0.927592 + 0.373596i \(0.878125\pi\)
\(702\) 0 0
\(703\) −3.81507 + 2.20263i −0.143888 + 0.0830737i
\(704\) −0.0109867 0.0410029i −0.000414076 0.00154535i
\(705\) 0 0
\(706\) 9.51487 16.4802i 0.358097 0.620242i
\(707\) −26.5126 42.1169i −0.997110 1.58397i
\(708\) 0 0
\(709\) −1.08628 + 4.05405i −0.0407960 + 0.152253i −0.983319 0.181888i \(-0.941779\pi\)
0.942523 + 0.334140i \(0.108446\pi\)
\(710\) 0.341493 + 0.0915029i 0.0128160 + 0.00343404i
\(711\) 0 0
\(712\) 17.9787 0.673782
\(713\) 31.1230 + 8.33939i 1.16557 + 0.312313i
\(714\) 0 0
\(715\) −0.749969 0.0114186i −0.0280472 0.000427032i
\(716\) 7.96647 13.7983i 0.297721 0.515668i
\(717\) 0 0
\(718\) 4.05964 7.03151i 0.151505 0.262414i
\(719\) −10.3212 17.8769i −0.384918 0.666697i 0.606840 0.794824i \(-0.292437\pi\)
−0.991758 + 0.128127i \(0.959103\pi\)
\(720\) 0 0
\(721\) 2.25605 + 3.58387i 0.0840197 + 0.133470i
\(722\) −9.95120 + 2.66642i −0.370345 + 0.0992337i
\(723\) 0 0
\(724\) 23.1196i 0.859235i
\(725\) 5.31559 + 3.06896i 0.197416 + 0.113978i
\(726\) 0 0
\(727\) 14.8265 0.549885 0.274942 0.961461i \(-0.411341\pi\)
0.274942 + 0.961461i \(0.411341\pi\)
\(728\) 20.4923 + 4.98862i 0.759497 + 0.184890i
\(729\) 0 0
\(730\) 3.81120 3.81120i 0.141059 0.141059i
\(731\) 26.1939 + 15.1230i 0.968815 + 0.559346i
\(732\) 0 0
\(733\) 38.1303 10.2170i 1.40838 0.377373i 0.527031 0.849846i \(-0.323305\pi\)
0.881345 + 0.472473i \(0.156639\pi\)
\(734\) 13.6409 3.65506i 0.503494 0.134911i
\(735\) 0 0
\(736\) 18.9851 + 18.9851i 0.699801 + 0.699801i
\(737\) −0.318408 0.551499i −0.0117287 0.0203147i
\(738\) 0 0
\(739\) 10.3718 2.77912i 0.381533 0.102232i −0.0629547 0.998016i \(-0.520052\pi\)
0.444488 + 0.895785i \(0.353386\pi\)
\(740\) −5.07927 + 8.79755i −0.186718 + 0.323404i
\(741\) 0 0
\(742\) 11.5642 12.4840i 0.424536 0.458303i
\(743\) 23.5602 + 6.31294i 0.864340 + 0.231599i 0.663639 0.748053i \(-0.269011\pi\)
0.200701 + 0.979652i \(0.435678\pi\)
\(744\) 0 0
\(745\) 31.2475 1.14482
\(746\) 0.852463 + 0.228417i 0.0312109 + 0.00836293i
\(747\) 0 0
\(748\) −0.155502 0.580343i −0.00568573 0.0212194i
\(749\) 22.3865 42.4427i 0.817987 1.55082i
\(750\) 0 0
\(751\) 44.0350i 1.60686i 0.595398 + 0.803431i \(0.296994\pi\)
−0.595398 + 0.803431i \(0.703006\pi\)
\(752\) −1.01251 3.77875i −0.0369225 0.137797i
\(753\) 0 0
\(754\) 11.6052 + 11.9641i 0.422637 + 0.435705i
\(755\) 26.0493i 0.948032i
\(756\) 0 0
\(757\) 15.1721 + 26.2788i 0.551438 + 0.955119i 0.998171 + 0.0604518i \(0.0192542\pi\)
−0.446733 + 0.894667i \(0.647413\pi\)
\(758\) 1.26626 0.731073i 0.0459925 0.0265538i
\(759\) 0 0
\(760\) 4.62791 4.62791i 0.167872 0.167872i
\(761\) −30.3847 8.14155i −1.10144 0.295131i −0.338092 0.941113i \(-0.609781\pi\)
−0.763353 + 0.645982i \(0.776448\pi\)
\(762\) 0 0
\(763\) 21.6312 23.3517i 0.783101 0.845389i
\(764\) 6.58305 3.80072i 0.238166 0.137505i
\(765\) 0 0
\(766\) 8.80980 + 15.2590i 0.318311 + 0.551331i
\(767\) 7.85445 1.97694i 0.283608 0.0713832i
\(768\) 0 0
\(769\) −6.01297 + 22.4407i −0.216833 + 0.809232i 0.768680 + 0.639633i \(0.220914\pi\)
−0.985513 + 0.169599i \(0.945753\pi\)
\(770\) 0.246009 + 0.227883i 0.00886555 + 0.00821234i
\(771\) 0 0
\(772\) −2.21717 8.27457i −0.0797975 0.297808i
\(773\) 38.0766 + 38.0766i 1.36952 + 1.36952i 0.861125 + 0.508394i \(0.169761\pi\)
0.508394 + 0.861125i \(0.330239\pi\)
\(774\) 0 0
\(775\) 1.40352 + 5.23801i 0.0504160 + 0.188155i
\(776\) −32.8453 18.9632i −1.17908 0.680741i
\(777\) 0 0
\(778\) −4.78549 + 17.8597i −0.171568 + 0.640300i
\(779\) −4.21917 2.43594i −0.151168 0.0872766i
\(780\) 0 0
\(781\) 0.0144011 + 0.0249435i 0.000515313 + 0.000892548i
\(782\) 7.51708 + 7.51708i 0.268810 + 0.268810i
\(783\) 0 0
\(784\) 7.55201 + 11.0373i 0.269715 + 0.394190i
\(785\) −25.6614 + 25.6614i −0.915894 + 0.915894i
\(786\) 0 0
\(787\) 14.8317 14.8317i 0.528695 0.528695i −0.391488 0.920183i \(-0.628040\pi\)
0.920183 + 0.391488i \(0.128040\pi\)
\(788\) −4.81726 + 17.9783i