Properties

Label 819.2.fm.e.496.4
Level $819$
Weight $2$
Character 819.496
Analytic conductor $6.540$
Analytic rank $0$
Dimension $32$
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.fm (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 496.4
Character \(\chi\) \(=\) 819.496
Dual form 819.2.fm.e.748.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.604240 - 0.161906i) q^{2} +(-1.39316 - 0.804341i) q^{4} +(-0.965431 - 0.965431i) q^{5} +(2.12303 - 1.57884i) q^{7} +(1.59624 + 1.59624i) q^{8} +O(q^{10})\) \(q+(-0.604240 - 0.161906i) q^{2} +(-1.39316 - 0.804341i) q^{4} +(-0.965431 - 0.965431i) q^{5} +(2.12303 - 1.57884i) q^{7} +(1.59624 + 1.59624i) q^{8} +(0.427043 + 0.739660i) q^{10} +(-1.26706 + 4.72873i) q^{11} +(1.35196 + 3.34249i) q^{13} +(-1.53844 + 0.610269i) q^{14} +(0.902609 + 1.56336i) q^{16} +(2.72530 - 4.72035i) q^{17} +(4.47375 - 1.19874i) q^{19} +(0.568463 + 2.12153i) q^{20} +(1.53121 - 2.65214i) q^{22} +(3.14262 - 1.81439i) q^{23} -3.13589i q^{25} +(-0.275740 - 2.23855i) q^{26} +(-4.22764 + 0.491938i) q^{28} +(-1.00956 - 1.74861i) q^{29} +(-5.91069 - 5.91069i) q^{31} +(-1.46081 - 5.45180i) q^{32} +(-2.41098 + 2.41098i) q^{34} +(-3.57390 - 0.525376i) q^{35} +(-2.84395 + 10.6138i) q^{37} -2.89730 q^{38} -3.08212i q^{40} +(1.08400 - 4.04553i) q^{41} +(-0.669160 - 0.386339i) q^{43} +(5.56872 - 5.56872i) q^{44} +(-2.19266 + 0.587521i) q^{46} +(5.65938 - 5.65938i) q^{47} +(2.01452 - 6.70386i) q^{49} +(-0.507717 + 1.89483i) q^{50} +(0.805003 - 5.74405i) q^{52} +6.72661 q^{53} +(5.78852 - 3.34200i) q^{55} +(5.90909 + 0.868657i) q^{56} +(0.326908 + 1.22004i) q^{58} +(-3.87661 - 14.4677i) q^{59} +(0.210912 + 0.121770i) q^{61} +(2.61450 + 4.52844i) q^{62} -0.0797289i q^{64} +(1.92172 - 4.53216i) q^{65} +(5.55533 + 1.48855i) q^{67} +(-7.59354 + 4.38413i) q^{68} +(2.07443 + 0.896088i) q^{70} +(0.711167 + 2.65411i) q^{71} +(2.17212 - 2.17212i) q^{73} +(3.43686 - 5.95281i) q^{74} +(-7.19684 - 1.92839i) q^{76} +(4.77591 + 12.0397i) q^{77} +8.38955 q^{79} +(0.637914 - 2.38073i) q^{80} +(-1.30999 + 2.26897i) q^{82} +(11.2487 + 11.2487i) q^{83} +(-7.18826 + 1.92609i) q^{85} +(0.341782 + 0.341782i) q^{86} +(-9.57073 + 5.52567i) q^{88} +(-3.25716 - 0.872754i) q^{89} +(8.14751 + 4.96167i) q^{91} -5.83756 q^{92} +(-4.33591 + 2.50334i) q^{94} +(-5.47640 - 3.16180i) q^{95} +(9.46128 - 2.53514i) q^{97} +(-2.30264 + 3.72458i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + O(q^{10}) \) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + 2q^{10} + 4q^{11} + 6q^{13} - 34q^{14} + 14q^{16} + 8q^{17} + 2q^{19} - 44q^{20} - 4q^{22} + 18q^{23} + 28q^{26} - 32q^{28} + 18q^{29} - 14q^{31} + 8q^{32} - 66q^{34} - 22q^{35} - 24q^{37} - 24q^{38} - 6q^{43} + 20q^{44} - 58q^{46} + 28q^{47} + 8q^{49} - 70q^{50} + 28q^{52} + 80q^{53} + 60q^{55} + 54q^{56} - 4q^{58} + 42q^{59} + 36q^{61} - 52q^{62} - 14q^{65} + 26q^{67} + 72q^{68} - 116q^{70} + 4q^{71} + 12q^{73} + 18q^{74} - 48q^{76} - 28q^{77} - 4q^{79} + 98q^{80} + 20q^{82} + 36q^{83} - 10q^{85} + 40q^{86} + 96q^{88} + 54q^{89} + 148q^{91} + 4q^{92} - 60q^{95} - 40q^{97} - 36q^{98} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.604240 0.161906i −0.427262 0.114484i 0.0387787 0.999248i \(-0.487653\pi\)
−0.466041 + 0.884763i \(0.654320\pi\)
\(3\) 0 0
\(4\) −1.39316 0.804341i −0.696579 0.402170i
\(5\) −0.965431 0.965431i −0.431754 0.431754i 0.457471 0.889225i \(-0.348755\pi\)
−0.889225 + 0.457471i \(0.848755\pi\)
\(6\) 0 0
\(7\) 2.12303 1.57884i 0.802430 0.596746i
\(8\) 1.59624 + 1.59624i 0.564357 + 0.564357i
\(9\) 0 0
\(10\) 0.427043 + 0.739660i 0.135043 + 0.233901i
\(11\) −1.26706 + 4.72873i −0.382033 + 1.42577i 0.460759 + 0.887525i \(0.347577\pi\)
−0.842791 + 0.538240i \(0.819089\pi\)
\(12\) 0 0
\(13\) 1.35196 + 3.34249i 0.374966 + 0.927039i
\(14\) −1.53844 + 0.610269i −0.411166 + 0.163101i
\(15\) 0 0
\(16\) 0.902609 + 1.56336i 0.225652 + 0.390841i
\(17\) 2.72530 4.72035i 0.660981 1.14485i −0.319377 0.947628i \(-0.603474\pi\)
0.980358 0.197225i \(-0.0631931\pi\)
\(18\) 0 0
\(19\) 4.47375 1.19874i 1.02635 0.275010i 0.293904 0.955835i \(-0.405045\pi\)
0.732446 + 0.680825i \(0.238379\pi\)
\(20\) 0.568463 + 2.12153i 0.127112 + 0.474389i
\(21\) 0 0
\(22\) 1.53121 2.65214i 0.326456 0.565439i
\(23\) 3.14262 1.81439i 0.655282 0.378327i −0.135195 0.990819i \(-0.543166\pi\)
0.790477 + 0.612492i \(0.209833\pi\)
\(24\) 0 0
\(25\) 3.13589i 0.627177i
\(26\) −0.275740 2.23855i −0.0540771 0.439016i
\(27\) 0 0
\(28\) −4.22764 + 0.491938i −0.798950 + 0.0929676i
\(29\) −1.00956 1.74861i −0.187471 0.324710i 0.756935 0.653490i \(-0.226696\pi\)
−0.944406 + 0.328780i \(0.893362\pi\)
\(30\) 0 0
\(31\) −5.91069 5.91069i −1.06159 1.06159i −0.997974 0.0636160i \(-0.979737\pi\)
−0.0636160 0.997974i \(-0.520263\pi\)
\(32\) −1.46081 5.45180i −0.258236 0.963751i
\(33\) 0 0
\(34\) −2.41098 + 2.41098i −0.413480 + 0.413480i
\(35\) −3.57390 0.525376i −0.604100 0.0888048i
\(36\) 0 0
\(37\) −2.84395 + 10.6138i −0.467543 + 1.74489i 0.180774 + 0.983525i \(0.442140\pi\)
−0.648317 + 0.761370i \(0.724527\pi\)
\(38\) −2.89730 −0.470004
\(39\) 0 0
\(40\) 3.08212i 0.487327i
\(41\) 1.08400 4.04553i 0.169292 0.631806i −0.828162 0.560489i \(-0.810613\pi\)
0.997454 0.0713169i \(-0.0227201\pi\)
\(42\) 0 0
\(43\) −0.669160 0.386339i −0.102046 0.0589162i 0.448109 0.893979i \(-0.352098\pi\)
−0.550154 + 0.835063i \(0.685431\pi\)
\(44\) 5.56872 5.56872i 0.839517 0.839517i
\(45\) 0 0
\(46\) −2.19266 + 0.587521i −0.323290 + 0.0866252i
\(47\) 5.65938 5.65938i 0.825506 0.825506i −0.161386 0.986891i \(-0.551596\pi\)
0.986891 + 0.161386i \(0.0515964\pi\)
\(48\) 0 0
\(49\) 2.01452 6.70386i 0.287788 0.957694i
\(50\) −0.507717 + 1.89483i −0.0718021 + 0.267969i
\(51\) 0 0
\(52\) 0.805003 5.74405i 0.111634 0.796556i
\(53\) 6.72661 0.923971 0.461986 0.886887i \(-0.347137\pi\)
0.461986 + 0.886887i \(0.347137\pi\)
\(54\) 0 0
\(55\) 5.78852 3.34200i 0.780524 0.450636i
\(56\) 5.90909 + 0.868657i 0.789635 + 0.116079i
\(57\) 0 0
\(58\) 0.326908 + 1.22004i 0.0429251 + 0.160199i
\(59\) −3.87661 14.4677i −0.504692 1.88354i −0.467022 0.884246i \(-0.654673\pi\)
−0.0376705 0.999290i \(-0.511994\pi\)
\(60\) 0 0
\(61\) 0.210912 + 0.121770i 0.0270046 + 0.0155911i 0.513442 0.858125i \(-0.328370\pi\)
−0.486437 + 0.873716i \(0.661704\pi\)
\(62\) 2.61450 + 4.52844i 0.332042 + 0.575113i
\(63\) 0 0
\(64\) 0.0797289i 0.00996611i
\(65\) 1.92172 4.53216i 0.238360 0.562146i
\(66\) 0 0
\(67\) 5.55533 + 1.48855i 0.678691 + 0.181855i 0.581667 0.813427i \(-0.302401\pi\)
0.0970245 + 0.995282i \(0.469067\pi\)
\(68\) −7.59354 + 4.38413i −0.920852 + 0.531654i
\(69\) 0 0
\(70\) 2.07443 + 0.896088i 0.247942 + 0.107103i
\(71\) 0.711167 + 2.65411i 0.0844000 + 0.314985i 0.995200 0.0978630i \(-0.0312007\pi\)
−0.910800 + 0.412848i \(0.864534\pi\)
\(72\) 0 0
\(73\) 2.17212 2.17212i 0.254228 0.254228i −0.568474 0.822701i \(-0.692466\pi\)
0.822701 + 0.568474i \(0.192466\pi\)
\(74\) 3.43686 5.95281i 0.399527 0.692001i
\(75\) 0 0
\(76\) −7.19684 1.92839i −0.825535 0.221201i
\(77\) 4.77591 + 12.0397i 0.544266 + 1.37205i
\(78\) 0 0
\(79\) 8.38955 0.943898 0.471949 0.881626i \(-0.343551\pi\)
0.471949 + 0.881626i \(0.343551\pi\)
\(80\) 0.637914 2.38073i 0.0713209 0.266173i
\(81\) 0 0
\(82\) −1.30999 + 2.26897i −0.144664 + 0.250565i
\(83\) 11.2487 + 11.2487i 1.23470 + 1.23470i 0.962138 + 0.272563i \(0.0878713\pi\)
0.272563 + 0.962138i \(0.412129\pi\)
\(84\) 0 0
\(85\) −7.18826 + 1.92609i −0.779676 + 0.208914i
\(86\) 0.341782 + 0.341782i 0.0368553 + 0.0368553i
\(87\) 0 0
\(88\) −9.57073 + 5.52567i −1.02024 + 0.589038i
\(89\) −3.25716 0.872754i −0.345259 0.0925118i 0.0820228 0.996630i \(-0.473862\pi\)
−0.427281 + 0.904119i \(0.640529\pi\)
\(90\) 0 0
\(91\) 8.14751 + 4.96167i 0.854091 + 0.520124i
\(92\) −5.83756 −0.608608
\(93\) 0 0
\(94\) −4.33591 + 2.50334i −0.447215 + 0.258200i
\(95\) −5.47640 3.16180i −0.561867 0.324394i
\(96\) 0 0
\(97\) 9.46128 2.53514i 0.960648 0.257405i 0.255773 0.966737i \(-0.417670\pi\)
0.704874 + 0.709332i \(0.251003\pi\)
\(98\) −2.30264 + 3.72458i −0.232602 + 0.376239i
\(99\) 0 0
\(100\) −2.52232 + 4.36879i −0.252232 + 0.436879i
\(101\) 1.30615 + 2.26231i 0.129966 + 0.225108i 0.923663 0.383205i \(-0.125180\pi\)
−0.793697 + 0.608313i \(0.791846\pi\)
\(102\) 0 0
\(103\) −16.7503 −1.65046 −0.825230 0.564797i \(-0.808954\pi\)
−0.825230 + 0.564797i \(0.808954\pi\)
\(104\) −3.17736 + 7.49347i −0.311566 + 0.734795i
\(105\) 0 0
\(106\) −4.06449 1.08908i −0.394778 0.105780i
\(107\) −5.79246 10.0328i −0.559978 0.969910i −0.997498 0.0707014i \(-0.977476\pi\)
0.437520 0.899209i \(-0.355857\pi\)
\(108\) 0 0
\(109\) 3.99577 3.99577i 0.382725 0.382725i −0.489358 0.872083i \(-0.662769\pi\)
0.872083 + 0.489358i \(0.162769\pi\)
\(110\) −4.03874 + 1.08218i −0.385079 + 0.103182i
\(111\) 0 0
\(112\) 4.38457 + 1.89399i 0.414303 + 0.178965i
\(113\) −1.65445 + 2.86558i −0.155637 + 0.269571i −0.933291 0.359121i \(-0.883076\pi\)
0.777654 + 0.628693i \(0.216410\pi\)
\(114\) 0 0
\(115\) −4.78566 1.28231i −0.446265 0.119576i
\(116\) 3.24813i 0.301581i
\(117\) 0 0
\(118\) 9.36961i 0.862543i
\(119\) −1.66680 14.3243i −0.152796 1.31310i
\(120\) 0 0
\(121\) −11.2292 6.48316i −1.02083 0.589378i
\(122\) −0.107726 0.107726i −0.00975309 0.00975309i
\(123\) 0 0
\(124\) 3.48032 + 12.9887i 0.312542 + 1.16642i
\(125\) −7.85464 + 7.85464i −0.702540 + 0.702540i
\(126\) 0 0
\(127\) 15.4911 8.94379i 1.37461 0.793633i 0.383108 0.923704i \(-0.374854\pi\)
0.991505 + 0.130071i \(0.0415205\pi\)
\(128\) −2.93452 + 10.9518i −0.259377 + 0.968009i
\(129\) 0 0
\(130\) −1.89496 + 2.42738i −0.166199 + 0.212895i
\(131\) 15.3940i 1.34498i 0.740107 + 0.672489i \(0.234775\pi\)
−0.740107 + 0.672489i \(0.765225\pi\)
\(132\) 0 0
\(133\) 7.60530 9.60831i 0.659463 0.833146i
\(134\) −3.11574 1.79888i −0.269159 0.155399i
\(135\) 0 0
\(136\) 11.8851 3.18459i 1.01914 0.273077i
\(137\) 2.08965 0.559921i 0.178531 0.0478373i −0.168446 0.985711i \(-0.553875\pi\)
0.346977 + 0.937874i \(0.387208\pi\)
\(138\) 0 0
\(139\) 1.11782 + 0.645374i 0.0948124 + 0.0547399i 0.546657 0.837357i \(-0.315900\pi\)
−0.451844 + 0.892097i \(0.649234\pi\)
\(140\) 4.55643 + 3.60657i 0.385089 + 0.304811i
\(141\) 0 0
\(142\) 1.71886i 0.144244i
\(143\) −17.5187 + 2.15792i −1.46499 + 0.180454i
\(144\) 0 0
\(145\) −0.713503 + 2.66283i −0.0592532 + 0.221136i
\(146\) −1.66416 + 0.960803i −0.137727 + 0.0795166i
\(147\) 0 0
\(148\) 12.4992 12.4992i 1.02743 1.02743i
\(149\) 0.326352 + 1.21796i 0.0267358 + 0.0997793i 0.978004 0.208584i \(-0.0668854\pi\)
−0.951269 + 0.308363i \(0.900219\pi\)
\(150\) 0 0
\(151\) 5.35713 + 5.35713i 0.435957 + 0.435957i 0.890649 0.454692i \(-0.150251\pi\)
−0.454692 + 0.890649i \(0.650251\pi\)
\(152\) 9.05468 + 5.22772i 0.734431 + 0.424024i
\(153\) 0 0
\(154\) −0.936497 8.04812i −0.0754651 0.648536i
\(155\) 11.4127i 0.916692i
\(156\) 0 0
\(157\) 7.45263i 0.594785i −0.954755 0.297392i \(-0.903883\pi\)
0.954755 0.297392i \(-0.0961169\pi\)
\(158\) −5.06930 1.35831i −0.403292 0.108062i
\(159\) 0 0
\(160\) −3.85303 + 6.67364i −0.304609 + 0.527598i
\(161\) 3.80724 8.81372i 0.300053 0.694618i
\(162\) 0 0
\(163\) −11.3293 + 3.03568i −0.887379 + 0.237773i −0.673588 0.739107i \(-0.735248\pi\)
−0.213791 + 0.976879i \(0.568581\pi\)
\(164\) −4.76417 + 4.76417i −0.372019 + 0.372019i
\(165\) 0 0
\(166\) −4.97567 8.61811i −0.386187 0.668895i
\(167\) 6.94320 + 1.86042i 0.537281 + 0.143964i 0.517248 0.855835i \(-0.326956\pi\)
0.0200325 + 0.999799i \(0.493623\pi\)
\(168\) 0 0
\(169\) −9.34441 + 9.03780i −0.718801 + 0.695216i
\(170\) 4.65527 0.357043
\(171\) 0 0
\(172\) 0.621497 + 1.07646i 0.0473887 + 0.0820796i
\(173\) 7.63293 13.2206i 0.580321 1.00515i −0.415120 0.909767i \(-0.636260\pi\)
0.995441 0.0953789i \(-0.0304063\pi\)
\(174\) 0 0
\(175\) −4.95107 6.65758i −0.374266 0.503266i
\(176\) −8.53638 + 2.28732i −0.643454 + 0.172413i
\(177\) 0 0
\(178\) 1.82680 + 1.05471i 0.136925 + 0.0790535i
\(179\) −19.5943 + 11.3128i −1.46455 + 0.845557i −0.999216 0.0395805i \(-0.987398\pi\)
−0.465330 + 0.885137i \(0.654065\pi\)
\(180\) 0 0
\(181\) −1.46318 −0.108758 −0.0543788 0.998520i \(-0.517318\pi\)
−0.0543788 + 0.998520i \(0.517318\pi\)
\(182\) −4.11972 4.31716i −0.305374 0.320009i
\(183\) 0 0
\(184\) 7.91260 + 2.12018i 0.583325 + 0.156301i
\(185\) 12.9925 7.50123i 0.955229 0.551502i
\(186\) 0 0
\(187\) 18.8682 + 18.8682i 1.37978 + 1.37978i
\(188\) −12.4365 + 3.33235i −0.907024 + 0.243036i
\(189\) 0 0
\(190\) 2.79715 + 2.79715i 0.202926 + 0.202926i
\(191\) 2.07125 3.58751i 0.149870 0.259583i −0.781309 0.624144i \(-0.785448\pi\)
0.931179 + 0.364561i \(0.118781\pi\)
\(192\) 0 0
\(193\) 0.316568 1.18145i 0.0227871 0.0850425i −0.953596 0.301089i \(-0.902650\pi\)
0.976383 + 0.216047i \(0.0693164\pi\)
\(194\) −6.12733 −0.439917
\(195\) 0 0
\(196\) −8.19873 + 7.71918i −0.585623 + 0.551370i
\(197\) 11.1850 + 2.99702i 0.796901 + 0.213529i 0.634223 0.773150i \(-0.281320\pi\)
0.162678 + 0.986679i \(0.447987\pi\)
\(198\) 0 0
\(199\) 1.08128 1.87283i 0.0766498 0.132761i −0.825153 0.564910i \(-0.808911\pi\)
0.901803 + 0.432148i \(0.142244\pi\)
\(200\) 5.00563 5.00563i 0.353952 0.353952i
\(201\) 0 0
\(202\) −0.422944 1.57845i −0.0297583 0.111059i
\(203\) −4.90412 2.11842i −0.344202 0.148684i
\(204\) 0 0
\(205\) −4.95221 + 2.85916i −0.345877 + 0.199692i
\(206\) 10.1212 + 2.71197i 0.705179 + 0.188952i
\(207\) 0 0
\(208\) −4.00523 + 5.13056i −0.277713 + 0.355740i
\(209\) 22.6741i 1.56840i
\(210\) 0 0
\(211\) −9.04131 15.6600i −0.622429 1.07808i −0.989032 0.147701i \(-0.952813\pi\)
0.366603 0.930378i \(-0.380521\pi\)
\(212\) −9.37124 5.41049i −0.643619 0.371594i
\(213\) 0 0
\(214\) 1.87566 + 7.00006i 0.128218 + 0.478515i
\(215\) 0.273043 + 1.01901i 0.0186214 + 0.0694960i
\(216\) 0 0
\(217\) −21.8806 3.21653i −1.48535 0.218352i
\(218\) −3.06134 + 1.76746i −0.207340 + 0.119708i
\(219\) 0 0
\(220\) −10.7524 −0.724929
\(221\) 19.4622 + 2.72754i 1.30917 + 0.183474i
\(222\) 0 0
\(223\) −5.56628 + 20.7736i −0.372746 + 1.39111i 0.483865 + 0.875142i \(0.339232\pi\)
−0.856611 + 0.515963i \(0.827434\pi\)
\(224\) −11.7089 9.26796i −0.782331 0.619241i
\(225\) 0 0
\(226\) 1.46363 1.46363i 0.0973595 0.0973595i
\(227\) −2.73398 + 0.732566i −0.181460 + 0.0486221i −0.348405 0.937344i \(-0.613277\pi\)
0.166945 + 0.985966i \(0.446610\pi\)
\(228\) 0 0
\(229\) −0.121782 + 0.121782i −0.00804759 + 0.00804759i −0.711119 0.703072i \(-0.751811\pi\)
0.703072 + 0.711119i \(0.251811\pi\)
\(230\) 2.68407 + 1.54965i 0.176982 + 0.102181i
\(231\) 0 0
\(232\) 1.17971 4.40272i 0.0774514 0.289053i
\(233\) 8.72869i 0.571835i −0.958254 0.285918i \(-0.907702\pi\)
0.958254 0.285918i \(-0.0922984\pi\)
\(234\) 0 0
\(235\) −10.9275 −0.712830
\(236\) −6.23623 + 23.2739i −0.405944 + 1.51500i
\(237\) 0 0
\(238\) −1.31203 + 8.92515i −0.0850462 + 0.578532i
\(239\) 15.9007 15.9007i 1.02853 1.02853i 0.0289485 0.999581i \(-0.490784\pi\)
0.999581 0.0289485i \(-0.00921587\pi\)
\(240\) 0 0
\(241\) 2.48430 + 9.27155i 0.160028 + 0.597233i 0.998622 + 0.0524761i \(0.0167113\pi\)
−0.838594 + 0.544757i \(0.816622\pi\)
\(242\) 5.73545 + 5.73545i 0.368689 + 0.368689i
\(243\) 0 0
\(244\) −0.195890 0.339291i −0.0125406 0.0217209i
\(245\) −8.41699 + 4.52724i −0.537742 + 0.289235i
\(246\) 0 0
\(247\) 10.0551 + 13.3328i 0.639791 + 0.848347i
\(248\) 18.8698i 1.19823i
\(249\) 0 0
\(250\) 6.01779 3.47437i 0.380599 0.219739i
\(251\) −2.87929 + 4.98708i −0.181739 + 0.314782i −0.942473 0.334282i \(-0.891506\pi\)
0.760734 + 0.649064i \(0.224839\pi\)
\(252\) 0 0
\(253\) 4.59789 + 17.1596i 0.289067 + 1.07881i
\(254\) −10.8084 + 2.89610i −0.678178 + 0.181717i
\(255\) 0 0
\(256\) 3.46658 6.00429i 0.216661 0.375268i
\(257\) 11.1749 + 19.3555i 0.697071 + 1.20736i 0.969477 + 0.245181i \(0.0788473\pi\)
−0.272406 + 0.962182i \(0.587819\pi\)
\(258\) 0 0
\(259\) 10.7197 + 27.0235i 0.666089 + 1.67916i
\(260\) −6.32266 + 4.76831i −0.392115 + 0.295718i
\(261\) 0 0
\(262\) 2.49237 9.30166i 0.153979 0.574658i
\(263\) −8.93301 15.4724i −0.550833 0.954071i −0.998215 0.0597277i \(-0.980977\pi\)
0.447382 0.894343i \(-0.352357\pi\)
\(264\) 0 0
\(265\) −6.49408 6.49408i −0.398928 0.398928i
\(266\) −6.15106 + 4.57438i −0.377146 + 0.280473i
\(267\) 0 0
\(268\) −6.54216 6.54216i −0.399626 0.399626i
\(269\) 7.06977 + 4.08173i 0.431051 + 0.248868i 0.699794 0.714344i \(-0.253275\pi\)
−0.268743 + 0.963212i \(0.586608\pi\)
\(270\) 0 0
\(271\) 17.9820 + 4.81826i 1.09233 + 0.292688i 0.759637 0.650348i \(-0.225377\pi\)
0.332691 + 0.943036i \(0.392044\pi\)
\(272\) 9.83950 0.596607
\(273\) 0 0
\(274\) −1.35331 −0.0817562
\(275\) 14.8288 + 3.97335i 0.894208 + 0.239602i
\(276\) 0 0
\(277\) −4.63889 2.67826i −0.278724 0.160921i 0.354122 0.935199i \(-0.384780\pi\)
−0.632846 + 0.774278i \(0.718113\pi\)
\(278\) −0.570942 0.570942i −0.0342428 0.0342428i
\(279\) 0 0
\(280\) −4.86619 6.54344i −0.290810 0.391046i
\(281\) 11.1684 + 11.1684i 0.666249 + 0.666249i 0.956846 0.290597i \(-0.0938539\pi\)
−0.290597 + 0.956846i \(0.593854\pi\)
\(282\) 0 0
\(283\) −10.7122 18.5541i −0.636775 1.10293i −0.986136 0.165938i \(-0.946935\pi\)
0.349361 0.936988i \(-0.386399\pi\)
\(284\) 1.14404 4.26962i 0.0678863 0.253355i
\(285\) 0 0
\(286\) 10.9349 + 1.53248i 0.646593 + 0.0906172i
\(287\) −4.08590 10.3002i −0.241183 0.608004i
\(288\) 0 0
\(289\) −6.35448 11.0063i −0.373793 0.647428i
\(290\) 0.862254 1.49347i 0.0506333 0.0876994i
\(291\) 0 0
\(292\) −4.77324 + 1.27898i −0.279332 + 0.0748469i
\(293\) 1.33426 + 4.97953i 0.0779484 + 0.290907i 0.993886 0.110414i \(-0.0352177\pi\)
−0.915937 + 0.401321i \(0.868551\pi\)
\(294\) 0 0
\(295\) −10.2250 + 17.7102i −0.595321 + 1.03113i
\(296\) −21.4818 + 12.4025i −1.24860 + 0.720882i
\(297\) 0 0
\(298\) 0.788779i 0.0456927i
\(299\) 10.3133 + 8.05119i 0.596433 + 0.465612i
\(300\) 0 0
\(301\) −2.03061 + 0.236287i −0.117043 + 0.0136193i
\(302\) −2.36964 4.10434i −0.136357 0.236178i
\(303\) 0 0
\(304\) 5.91212 + 5.91212i 0.339083 + 0.339083i
\(305\) −0.0860606 0.321182i −0.00492781 0.0183908i
\(306\) 0 0
\(307\) −17.9644 + 17.9644i −1.02528 + 1.02528i −0.0256108 + 0.999672i \(0.508153\pi\)
−0.999672 + 0.0256108i \(0.991847\pi\)
\(308\) 3.03043 20.6147i 0.172675 1.17463i
\(309\) 0 0
\(310\) 1.84778 6.89602i 0.104947 0.391667i
\(311\) −7.22402 −0.409637 −0.204818 0.978800i \(-0.565660\pi\)
−0.204818 + 0.978800i \(0.565660\pi\)
\(312\) 0 0
\(313\) 20.9613i 1.18480i −0.805643 0.592401i \(-0.798180\pi\)
0.805643 0.592401i \(-0.201820\pi\)
\(314\) −1.20662 + 4.50318i −0.0680936 + 0.254129i
\(315\) 0 0
\(316\) −11.6880 6.74806i −0.657500 0.379608i
\(317\) −0.207227 + 0.207227i −0.0116390 + 0.0116390i −0.712902 0.701263i \(-0.752620\pi\)
0.701263 + 0.712902i \(0.252620\pi\)
\(318\) 0 0
\(319\) 9.54790 2.55835i 0.534580 0.143240i
\(320\) −0.0769727 + 0.0769727i −0.00430291 + 0.00430291i
\(321\) 0 0
\(322\) −3.72748 + 4.70919i −0.207724 + 0.262433i
\(323\) 6.53384 24.3846i 0.363552 1.35680i
\(324\) 0 0
\(325\) 10.4817 4.23959i 0.581417 0.235170i
\(326\) 7.33711 0.406365
\(327\) 0 0
\(328\) 8.18797 4.72733i 0.452105 0.261023i
\(329\) 3.07977 20.9503i 0.169793 1.15503i
\(330\) 0 0
\(331\) −3.35420 12.5180i −0.184363 0.688054i −0.994766 0.102180i \(-0.967418\pi\)
0.810403 0.585873i \(-0.199248\pi\)
\(332\) −6.62342 24.7189i −0.363507 1.35663i
\(333\) 0 0
\(334\) −3.89414 2.24828i −0.213078 0.123021i
\(335\) −3.92620 6.80037i −0.214511 0.371544i
\(336\) 0 0
\(337\) 25.0887i 1.36667i 0.730105 + 0.683335i \(0.239471\pi\)
−0.730105 + 0.683335i \(0.760529\pi\)
\(338\) 7.10954 3.94809i 0.386708 0.214748i
\(339\) 0 0
\(340\) 11.5636 + 3.09846i 0.627125 + 0.168038i
\(341\) 35.4392 20.4608i 1.91914 1.10802i
\(342\) 0 0
\(343\) −6.30746 17.4131i −0.340571 0.940219i
\(344\) −0.451449 1.68483i −0.0243405 0.0908401i
\(345\) 0 0
\(346\) −6.75261 + 6.75261i −0.363023 + 0.363023i
\(347\) −6.71302 + 11.6273i −0.360374 + 0.624185i −0.988022 0.154311i \(-0.950684\pi\)
0.627649 + 0.778497i \(0.284017\pi\)
\(348\) 0 0
\(349\) 5.30405 + 1.42122i 0.283919 + 0.0760760i 0.397968 0.917399i \(-0.369715\pi\)
−0.114049 + 0.993475i \(0.536382\pi\)
\(350\) 1.91373 + 4.82438i 0.102293 + 0.257874i
\(351\) 0 0
\(352\) 27.6310 1.47274
\(353\) −0.756952 + 2.82498i −0.0402885 + 0.150359i −0.983140 0.182855i \(-0.941466\pi\)
0.942851 + 0.333213i \(0.108133\pi\)
\(354\) 0 0
\(355\) 1.87578 3.24894i 0.0995560 0.172436i
\(356\) 3.83575 + 3.83575i 0.203295 + 0.203295i
\(357\) 0 0
\(358\) 13.6713 3.66320i 0.722548 0.193606i
\(359\) 19.7266 + 19.7266i 1.04113 + 1.04113i 0.999117 + 0.0420147i \(0.0133776\pi\)
0.0420147 + 0.999117i \(0.486622\pi\)
\(360\) 0 0
\(361\) 2.12302 1.22573i 0.111738 0.0645120i
\(362\) 0.884114 + 0.236898i 0.0464680 + 0.0124511i
\(363\) 0 0
\(364\) −7.35990 13.4658i −0.385763 0.705798i
\(365\) −4.19407 −0.219527
\(366\) 0 0
\(367\) −14.4392 + 8.33648i −0.753720 + 0.435161i −0.827037 0.562148i \(-0.809975\pi\)
0.0733163 + 0.997309i \(0.476642\pi\)
\(368\) 5.67312 + 3.27538i 0.295732 + 0.170741i
\(369\) 0 0
\(370\) −9.06508 + 2.42898i −0.471271 + 0.126277i
\(371\) 14.2808 10.6203i 0.741422 0.551376i
\(372\) 0 0
\(373\) 17.1121 29.6390i 0.886030 1.53465i 0.0415014 0.999138i \(-0.486786\pi\)
0.844529 0.535511i \(-0.179881\pi\)
\(374\) −8.34603 14.4557i −0.431563 0.747489i
\(375\) 0 0
\(376\) 18.0675 0.931760
\(377\) 4.47983 5.73850i 0.230723 0.295548i
\(378\) 0 0
\(379\) −11.6824 3.13028i −0.600082 0.160792i −0.0540253 0.998540i \(-0.517205\pi\)
−0.546057 + 0.837748i \(0.683872\pi\)
\(380\) 5.08633 + 8.80978i 0.260923 + 0.451932i
\(381\) 0 0
\(382\) −1.83237 + 1.83237i −0.0937521 + 0.0937521i
\(383\) −32.0791 + 8.59556i −1.63916 + 0.439213i −0.956550 0.291567i \(-0.905823\pi\)
−0.682614 + 0.730780i \(0.739157\pi\)
\(384\) 0 0
\(385\) 7.01271 16.2343i 0.357401 0.827378i
\(386\) −0.382566 + 0.662623i −0.0194721 + 0.0337266i
\(387\) 0 0
\(388\) −15.2202 4.07824i −0.772688 0.207041i
\(389\) 25.6927i 1.30267i 0.758789 + 0.651337i \(0.225791\pi\)
−0.758789 + 0.651337i \(0.774209\pi\)
\(390\) 0 0
\(391\) 19.7790i 1.00027i
\(392\) 13.9166 7.48533i 0.702897 0.378066i
\(393\) 0 0
\(394\) −6.27321 3.62184i −0.316040 0.182466i
\(395\) −8.09953 8.09953i −0.407532 0.407532i
\(396\) 0 0
\(397\) 3.00423 + 11.2120i 0.150778 + 0.562712i 0.999430 + 0.0337600i \(0.0107482\pi\)
−0.848652 + 0.528952i \(0.822585\pi\)
\(398\) −0.956572 + 0.956572i −0.0479486 + 0.0479486i
\(399\) 0 0
\(400\) 4.90253 2.83048i 0.245127 0.141524i
\(401\) −7.55225 + 28.1854i −0.377141 + 1.40751i 0.473049 + 0.881036i \(0.343153\pi\)
−0.850191 + 0.526475i \(0.823513\pi\)
\(402\) 0 0
\(403\) 11.7654 27.7474i 0.586075 1.38220i
\(404\) 4.20234i 0.209074i
\(405\) 0 0
\(406\) 2.62028 + 2.07404i 0.130042 + 0.102933i
\(407\) −46.5862 26.8966i −2.30919 1.33321i
\(408\) 0 0
\(409\) 2.36962 0.634939i 0.117170 0.0313957i −0.199757 0.979845i \(-0.564015\pi\)
0.316928 + 0.948450i \(0.397349\pi\)
\(410\) 3.45523 0.925827i 0.170642 0.0457233i
\(411\) 0 0
\(412\) 23.3359 + 13.4730i 1.14968 + 0.663766i
\(413\) −31.0724 24.5948i −1.52897 1.21023i
\(414\) 0 0
\(415\) 21.7196i 1.06617i
\(416\) 16.2476 12.2533i 0.796605 0.600769i
\(417\) 0 0
\(418\) 3.67105 13.7006i 0.179557 0.670116i
\(419\) −19.8935 + 11.4855i −0.971861 + 0.561104i −0.899803 0.436296i \(-0.856290\pi\)
−0.0720579 + 0.997400i \(0.522957\pi\)
\(420\) 0 0
\(421\) 1.61471 1.61471i 0.0786962 0.0786962i −0.666663 0.745359i \(-0.732278\pi\)
0.745359 + 0.666663i \(0.232278\pi\)
\(422\) 2.92767 + 10.9262i 0.142517 + 0.531881i
\(423\) 0 0
\(424\) 10.7373 + 10.7373i 0.521450 + 0.521450i
\(425\) −14.8025 8.54622i −0.718026 0.414552i
\(426\) 0 0
\(427\) 0.640030 0.0744753i 0.0309732 0.00360411i
\(428\) 18.6364i 0.900826i
\(429\) 0 0
\(430\) 0.659934i 0.0318249i
\(431\) −18.1238 4.85625i −0.872991 0.233917i −0.205610 0.978634i \(-0.565918\pi\)
−0.667381 + 0.744717i \(0.732585\pi\)
\(432\) 0 0
\(433\) 2.29346 3.97239i 0.110217 0.190901i −0.805641 0.592404i \(-0.798179\pi\)
0.915858 + 0.401503i \(0.131512\pi\)
\(434\) 12.7004 + 5.48614i 0.609636 + 0.263343i
\(435\) 0 0
\(436\) −8.78070 + 2.35278i −0.420519 + 0.112678i
\(437\) 11.8843 11.8843i 0.568505 0.568505i
\(438\) 0 0
\(439\) −0.747446 1.29461i −0.0356737 0.0617886i 0.847637 0.530576i \(-0.178024\pi\)
−0.883311 + 0.468787i \(0.844691\pi\)
\(440\) 14.5745 + 3.90523i 0.694814 + 0.186175i
\(441\) 0 0
\(442\) −11.3182 4.79912i −0.538353 0.228271i
\(443\) −5.15152 −0.244756 −0.122378 0.992484i \(-0.539052\pi\)
−0.122378 + 0.992484i \(0.539052\pi\)
\(444\) 0 0
\(445\) 2.30198 + 3.98715i 0.109124 + 0.189009i
\(446\) 6.72673 11.6510i 0.318520 0.551693i
\(447\) 0 0
\(448\) −0.125879 0.169267i −0.00594724 0.00799711i
\(449\) 18.3337 4.91250i 0.865221 0.231835i 0.201201 0.979550i \(-0.435516\pi\)
0.664020 + 0.747715i \(0.268849\pi\)
\(450\) 0 0
\(451\) 17.7567 + 10.2519i 0.836132 + 0.482741i
\(452\) 4.60981 2.66147i 0.216827 0.125185i
\(453\) 0 0
\(454\) 1.77058 0.0830976
\(455\) −3.07571 12.6560i −0.144191 0.593323i
\(456\) 0 0
\(457\) 9.41753 + 2.52342i 0.440533 + 0.118041i 0.472267 0.881456i \(-0.343436\pi\)
−0.0317331 + 0.999496i \(0.510103\pi\)
\(458\) 0.0933028 0.0538684i 0.00435975 0.00251710i
\(459\) 0 0
\(460\) 5.63577 + 5.63577i 0.262769 + 0.262769i
\(461\) 15.3121 4.10288i 0.713157 0.191090i 0.116041 0.993244i \(-0.462980\pi\)
0.597117 + 0.802154i \(0.296313\pi\)
\(462\) 0 0
\(463\) 18.1402 + 18.1402i 0.843045 + 0.843045i 0.989254 0.146209i \(-0.0467071\pi\)
−0.146209 + 0.989254i \(0.546707\pi\)
\(464\) 1.82248 3.15663i 0.0846065 0.146543i
\(465\) 0 0
\(466\) −1.41322 + 5.27422i −0.0654663 + 0.244323i
\(467\) −15.9305 −0.737174 −0.368587 0.929593i \(-0.620158\pi\)
−0.368587 + 0.929593i \(0.620158\pi\)
\(468\) 0 0
\(469\) 14.1443 5.61076i 0.653123 0.259081i
\(470\) 6.60282 + 1.76922i 0.304565 + 0.0816080i
\(471\) 0 0
\(472\) 16.9060 29.2820i 0.778160 1.34781i
\(473\) 2.67476 2.67476i 0.122986 0.122986i
\(474\) 0 0
\(475\) −3.75911 14.0292i −0.172480 0.643703i
\(476\) −9.19946 + 21.2966i −0.421657 + 0.976130i
\(477\) 0 0
\(478\) −12.1822 + 7.03341i −0.557202 + 0.321701i
\(479\) −8.19612 2.19614i −0.374490 0.100344i 0.0666644 0.997775i \(-0.478764\pi\)
−0.441155 + 0.897431i \(0.645431\pi\)
\(480\) 0 0
\(481\) −39.3213 + 4.84352i −1.79290 + 0.220845i
\(482\) 6.00446i 0.273496i
\(483\) 0 0
\(484\) 10.4293 + 18.0641i 0.474061 + 0.821098i
\(485\) −11.5817 6.68671i −0.525899 0.303628i
\(486\) 0 0
\(487\) −0.212412 0.792734i −0.00962533 0.0359222i 0.960946 0.276735i \(-0.0892526\pi\)
−0.970571 + 0.240813i \(0.922586\pi\)
\(488\) 0.142292 + 0.531043i 0.00644128 + 0.0240392i
\(489\) 0 0
\(490\) 5.81886 1.37278i 0.262869 0.0620158i
\(491\) 28.7764 16.6141i 1.29866 0.749782i 0.318488 0.947927i \(-0.396825\pi\)
0.980173 + 0.198145i \(0.0634917\pi\)
\(492\) 0 0
\(493\) −11.0054 −0.495660
\(494\) −3.91703 9.68419i −0.176236 0.435712i
\(495\) 0 0
\(496\) 3.90552 14.5756i 0.175363 0.654463i
\(497\) 5.70025 + 4.51194i 0.255691 + 0.202388i
\(498\) 0 0
\(499\) −2.26621 + 2.26621i −0.101449 + 0.101449i −0.756010 0.654560i \(-0.772854\pi\)
0.654560 + 0.756010i \(0.272854\pi\)
\(500\) 17.2606 4.62495i 0.771916 0.206834i
\(501\) 0 0
\(502\) 2.54722 2.54722i 0.113688 0.113688i
\(503\) −9.09104 5.24871i −0.405349 0.234028i 0.283440 0.958990i \(-0.408524\pi\)
−0.688789 + 0.724961i \(0.741858\pi\)
\(504\) 0 0
\(505\) 0.923111 3.44510i 0.0410779 0.153305i
\(506\) 11.1129i 0.494029i
\(507\) 0 0
\(508\) −28.7754 −1.27670
\(509\) 3.18662 11.8926i 0.141244 0.527131i −0.858649 0.512563i \(-0.828696\pi\)
0.999894 0.0145680i \(-0.00463731\pi\)
\(510\) 0 0
\(511\) 1.18204 8.04092i 0.0522905 0.355709i
\(512\) 12.9677 12.9677i 0.573099 0.573099i
\(513\) 0 0
\(514\) −3.61856 13.5046i −0.159608 0.595664i
\(515\) 16.1713 + 16.1713i 0.712592 + 0.712592i
\(516\) 0 0
\(517\) 19.5909 + 33.9325i 0.861607 + 1.49235i
\(518\) −2.10200 18.0643i −0.0923565 0.793698i
\(519\) 0 0
\(520\) 10.3020 4.16691i 0.451771 0.182731i
\(521\) 10.4773i 0.459019i 0.973306 + 0.229509i \(0.0737122\pi\)
−0.973306 + 0.229509i \(0.926288\pi\)
\(522\) 0 0
\(523\) −31.3912 + 18.1237i −1.37264 + 0.792495i −0.991260 0.131923i \(-0.957885\pi\)
−0.381381 + 0.924418i \(0.624552\pi\)
\(524\) 12.3820 21.4463i 0.540911 0.936885i
\(525\) 0 0
\(526\) 2.89261 + 10.7954i 0.126124 + 0.470700i
\(527\) −44.0089 + 11.7921i −1.91706 + 0.513674i
\(528\) 0 0
\(529\) −4.91595 + 8.51467i −0.213737 + 0.370203i
\(530\) 2.87255 + 4.97541i 0.124776 + 0.216118i
\(531\) 0 0
\(532\) −18.3237 + 7.26865i −0.794435 + 0.315136i
\(533\) 14.9876 1.84615i 0.649187 0.0799656i
\(534\) 0 0
\(535\) −4.09379 + 15.2782i −0.176990 + 0.660535i
\(536\) 6.49157 + 11.2437i 0.280393 + 0.485655i
\(537\) 0 0
\(538\) −3.61098 3.61098i −0.155680 0.155680i
\(539\) 29.1482 + 18.0203i 1.25550 + 0.776189i
\(540\) 0 0
\(541\) 15.3940 + 15.3940i 0.661840 + 0.661840i 0.955813 0.293974i \(-0.0949778\pi\)
−0.293974 + 0.955813i \(0.594978\pi\)
\(542\) −10.0853 5.82276i −0.433202 0.250109i
\(543\) 0 0
\(544\) −29.7155 7.96225i −1.27404 0.341379i
\(545\) −7.71528 −0.330486
\(546\) 0 0
\(547\) −1.98911 −0.0850480 −0.0425240 0.999095i \(-0.513540\pi\)
−0.0425240 + 0.999095i \(0.513540\pi\)
\(548\) −3.36159 0.900735i −0.143600 0.0384775i
\(549\) 0 0
\(550\) −8.31681 4.80171i −0.354630 0.204746i
\(551\) −6.61267 6.61267i −0.281709 0.281709i
\(552\) 0 0
\(553\) 17.8113 13.2458i 0.757412 0.563268i
\(554\) 2.36938 + 2.36938i 0.100665 + 0.100665i
\(555\) 0 0
\(556\) −1.03820 1.79822i −0.0440296 0.0762614i
\(557\) 6.80662 25.4027i 0.288406 1.07634i −0.657909 0.753098i \(-0.728559\pi\)
0.946315 0.323247i \(-0.104775\pi\)
\(558\) 0 0
\(559\) 0.386658 2.75897i 0.0163539 0.116692i
\(560\) −2.40448 6.06152i −0.101608 0.256146i
\(561\) 0 0
\(562\) −4.94015 8.55659i −0.208388 0.360938i
\(563\) −23.3973 + 40.5252i −0.986077 + 1.70794i −0.349027 + 0.937113i \(0.613488\pi\)
−0.637050 + 0.770822i \(0.719846\pi\)
\(564\) 0 0
\(565\) 4.36378 1.16927i 0.183585 0.0491916i
\(566\) 3.46873 + 12.9455i 0.145802 + 0.544139i
\(567\) 0 0
\(568\) −3.10141 + 5.37180i −0.130132 + 0.225396i
\(569\) 5.67847 3.27847i 0.238054 0.137441i −0.376228 0.926527i \(-0.622779\pi\)
0.614282 + 0.789087i \(0.289446\pi\)
\(570\) 0 0
\(571\) 12.2503i 0.512659i −0.966590 0.256329i \(-0.917487\pi\)
0.966590 0.256329i \(-0.0825132\pi\)
\(572\) 26.1421 + 11.0847i 1.09305 + 0.463474i
\(573\) 0 0
\(574\) 0.801194 + 6.88535i 0.0334412 + 0.287389i
\(575\) −5.68973 9.85491i −0.237278 0.410978i
\(576\) 0 0
\(577\) 25.5329 + 25.5329i 1.06295 + 1.06295i 0.997881 + 0.0650684i \(0.0207266\pi\)
0.0650684 + 0.997881i \(0.479273\pi\)
\(578\) 2.05765 + 7.67925i 0.0855869 + 0.319415i
\(579\) 0 0
\(580\) 3.13585 3.13585i 0.130209 0.130209i
\(581\) 41.6411 + 6.12139i 1.72756 + 0.253958i
\(582\) 0 0
\(583\) −8.52302 + 31.8083i −0.352987 + 1.31737i
\(584\) 6.93447 0.286950
\(585\) 0 0
\(586\) 3.22485i 0.133217i
\(587\) −1.99568 + 7.44800i −0.0823707 + 0.307412i −0.994803 0.101815i \(-0.967535\pi\)
0.912433 + 0.409227i \(0.134202\pi\)
\(588\) 0 0
\(589\) −33.5283 19.3576i −1.38151 0.797616i
\(590\) 9.04571 9.04571i 0.372406 0.372406i
\(591\) 0 0
\(592\) −19.1602 + 5.13395i −0.787479 + 0.211004i
\(593\) −5.94198 + 5.94198i −0.244008 + 0.244008i −0.818506 0.574498i \(-0.805197\pi\)
0.574498 + 0.818506i \(0.305197\pi\)
\(594\) 0 0
\(595\) −12.2199 + 15.4383i −0.500967 + 0.632907i
\(596\) 0.524996 1.95931i 0.0215047 0.0802566i
\(597\) 0 0
\(598\) −4.92816 6.53462i −0.201528 0.267221i
\(599\) −28.6135 −1.16912 −0.584558 0.811352i \(-0.698732\pi\)
−0.584558 + 0.811352i \(0.698732\pi\)
\(600\) 0 0
\(601\) 5.37026 3.10052i 0.219058 0.126473i −0.386456 0.922308i \(-0.626301\pi\)
0.605514 + 0.795835i \(0.292968\pi\)
\(602\) 1.26523 + 0.185994i 0.0515671 + 0.00758054i
\(603\) 0 0
\(604\) −3.15437 11.7723i −0.128350 0.479007i
\(605\) 4.58194 + 17.1000i 0.186282 + 0.695215i
\(606\) 0 0
\(607\) −19.0001 10.9697i −0.771192 0.445248i 0.0621079 0.998069i \(-0.480218\pi\)
−0.833300 + 0.552822i \(0.813551\pi\)
\(608\) −13.0706 22.6389i −0.530082 0.918128i
\(609\) 0 0
\(610\) 0.208005i 0.00842187i
\(611\) 26.5676 + 11.2651i 1.07481 + 0.455739i
\(612\) 0 0
\(613\) −3.56397 0.954962i −0.143947 0.0385706i 0.186126 0.982526i \(-0.440407\pi\)
−0.330073 + 0.943955i \(0.607073\pi\)
\(614\) 13.7633 7.94627i 0.555443 0.320685i
\(615\) 0 0
\(616\) −11.5948 + 26.8418i −0.467168 + 1.08149i
\(617\) −1.16293 4.34013i −0.0468180 0.174727i 0.938558 0.345122i \(-0.112162\pi\)
−0.985376 + 0.170395i \(0.945496\pi\)
\(618\) 0 0
\(619\) −6.43883 + 6.43883i −0.258798 + 0.258798i −0.824565 0.565767i \(-0.808580\pi\)
0.565767 + 0.824565i \(0.308580\pi\)
\(620\) 9.17971 15.8997i 0.368666 0.638548i
\(621\) 0 0
\(622\) 4.36504 + 1.16961i 0.175022 + 0.0468970i
\(623\) −8.29300 + 3.28966i −0.332252 + 0.131798i
\(624\) 0 0
\(625\) −0.513208 −0.0205283
\(626\) −3.39375 + 12.6656i −0.135641 + 0.506221i
\(627\) 0 0
\(628\) −5.99445 + 10.3827i −0.239205 + 0.414315i
\(629\) 42.3502 + 42.3502i 1.68861 + 1.68861i
\(630\) 0 0
\(631\) −24.5144 + 6.56863i −0.975905 + 0.261493i −0.711319 0.702869i \(-0.751902\pi\)
−0.264586 + 0.964362i \(0.585235\pi\)
\(632\) 13.3918 + 13.3918i 0.532696 + 0.532696i
\(633\) 0 0
\(634\) 0.158766 0.0916634i 0.00630539 0.00364042i
\(635\) −23.5902 6.32097i −0.936148 0.250840i
\(636\) 0 0
\(637\) 25.1311 2.32985i 0.995730 0.0923121i
\(638\) −6.18343 −0.244804
\(639\) 0 0
\(640\) 13.4063 7.74011i 0.529929 0.305955i
\(641\) −26.7633 15.4518i −1.05709 0.610309i −0.132461 0.991188i \(-0.542288\pi\)
−0.924625 + 0.380879i \(0.875621\pi\)
\(642\) 0 0
\(643\) −22.1486 + 5.93469i −0.873454 + 0.234041i −0.667581 0.744537i \(-0.732670\pi\)
−0.205873 + 0.978579i \(0.566004\pi\)
\(644\) −12.3933 + 9.21659i −0.488365 + 0.363185i
\(645\) 0 0
\(646\) −7.89601 + 13.6763i −0.310664 + 0.538086i
\(647\) 9.66194 + 16.7350i 0.379850 + 0.657919i 0.991040 0.133564i \(-0.0426423\pi\)
−0.611190 + 0.791484i \(0.709309\pi\)
\(648\) 0 0
\(649\) 73.3258 2.87829
\(650\) −7.01984 + 0.864690i −0.275341 + 0.0339159i
\(651\) 0 0
\(652\) 18.2252 + 4.88344i 0.713755 + 0.191250i
\(653\) −10.3312 17.8942i −0.404291 0.700253i 0.589947 0.807442i \(-0.299148\pi\)
−0.994239 + 0.107189i \(0.965815\pi\)
\(654\) 0 0
\(655\) 14.8618 14.8618i 0.580700 0.580700i
\(656\) 7.30306 1.95685i 0.285137 0.0764022i
\(657\) 0 0
\(658\) −5.25289 + 12.1604i −0.204779 + 0.474061i
\(659\) −11.5048 + 19.9270i −0.448165 + 0.776245i −0.998267 0.0588532i \(-0.981256\pi\)
0.550102 + 0.835098i \(0.314589\pi\)
\(660\) 0 0
\(661\) 27.9076 + 7.47783i 1.08548 + 0.290854i 0.756839 0.653601i \(-0.226743\pi\)
0.328642 + 0.944455i \(0.393409\pi\)
\(662\) 8.10696i 0.315086i
\(663\) 0 0
\(664\) 35.9112i 1.39362i
\(665\) −16.6186 + 1.93377i −0.644440 + 0.0749884i
\(666\) 0 0
\(667\) −6.34535 3.66349i −0.245693 0.141851i
\(668\) −8.17656 8.17656i −0.316361 0.316361i
\(669\) 0 0
\(670\) 1.27135 + 4.74473i 0.0491164 + 0.183305i
\(671\) −0.843058 + 0.843058i −0.0325459 + 0.0325459i
\(672\) 0 0
\(673\) −4.00219 + 2.31066i −0.154273 + 0.0890695i −0.575149 0.818049i \(-0.695056\pi\)
0.420876 + 0.907118i \(0.361723\pi\)
\(674\) 4.06200 15.1596i 0.156462 0.583926i
\(675\) 0 0
\(676\) 20.2877 5.07500i 0.780297 0.195192i
\(677\) 21.5334i 0.827596i −0.910369 0.413798i \(-0.864202\pi\)
0.910369 0.413798i \(-0.135798\pi\)
\(678\) 0 0
\(679\) 16.0840 20.3201i 0.617247 0.779812i
\(680\) −14.5487 8.39970i −0.557918 0.322114i
\(681\) 0 0
\(682\) −24.7265 + 6.62545i −0.946827 + 0.253701i
\(683\) −26.5081 + 7.10282i −1.01430 + 0.271782i −0.727426 0.686186i \(-0.759284\pi\)
−0.286877 + 0.957967i \(0.592617\pi\)
\(684\) 0 0
\(685\) −2.55798 1.47685i −0.0977355 0.0564276i
\(686\) 0.991938 + 11.5429i 0.0378724 + 0.440710i
\(687\) 0 0
\(688\) 1.39485i 0.0531783i
\(689\) 9.09410 + 22.4836i 0.346458 + 0.856557i
\(690\) 0 0
\(691\) 10.4368 38.9506i 0.397033 1.48175i −0.421255 0.906942i \(-0.638410\pi\)
0.818289 0.574807i \(-0.194923\pi\)
\(692\) −21.2678 + 12.2790i −0.808479 + 0.466776i
\(693\) 0 0
\(694\) 5.93879 5.93879i 0.225433 0.225433i
\(695\) −0.456115 1.70224i −0.0173014 0.0645698i
\(696\) 0 0
\(697\) −16.1421 16.1421i −0.611426 0.611426i
\(698\) −2.97482 1.71751i −0.112598 0.0650087i
\(699\) 0 0
\(700\) 1.54266 + 13.2574i 0.0583071 + 0.501083i
\(701\) 17.7693i 0.671135i 0.942016 + 0.335568i \(0.108928\pi\)
−0.942016 + 0.335568i \(0.891072\pi\)
\(702\) 0 0
\(703\) 50.8926i 1.91945i
\(704\) 0.377016 + 0.101021i 0.0142093 + 0.00380738i
\(705\) 0 0
\(706\) 0.914760 1.58441i 0.0344275 0.0596301i
\(707\) 6.34482 + 2.74076i 0.238621 + 0.103077i
\(708\) 0 0
\(709\) 13.1479 3.52297i 0.493780 0.132308i −0.00333188 0.999994i \(-0.501061\pi\)
0.497112 + 0.867687i \(0.334394\pi\)
\(710\) −1.65944 + 1.65944i −0.0622777 + 0.0622777i
\(711\) 0 0
\(712\) −3.80610 6.59235i −0.142639 0.247059i
\(713\) −29.2994 7.85074i −1.09727 0.294013i
\(714\) 0 0
\(715\) 18.9964 + 14.8298i 0.710427 + 0.554603i
\(716\) 36.3973 1.36023
\(717\) 0 0
\(718\) −8.72576 15.1135i −0.325642 0.564029i
\(719\) −14.3958 + 24.9343i −0.536873 + 0.929892i 0.462197 + 0.886777i \(0.347061\pi\)
−0.999070 + 0.0431147i \(0.986272\pi\)
\(720\) 0 0
\(721\) −35.5615 + 26.4461i −1.32438 + 0.984905i
\(722\) −1.48127 + 0.396904i −0.0551271 + 0.0147713i
\(723\) 0 0
\(724\) 2.03845 + 1.17690i 0.0757583 + 0.0437391i
\(725\) −5.48345 + 3.16587i −0.203650 + 0.117578i
\(726\) 0 0
\(727\) −35.7112 −1.32445 −0.662227 0.749303i \(-0.730389\pi\)
−0.662227 + 0.749303i \(0.730389\pi\)
\(728\) 5.08537 + 20.9254i 0.188476 + 0.775548i
\(729\) 0 0
\(730\) 2.53422 + 0.679043i 0.0937957 + 0.0251325i
\(731\) −3.64732 + 2.10578i −0.134901 + 0.0778850i
\(732\) 0 0
\(733\) −5.08991 5.08991i −0.188000 0.188000i 0.606831 0.794831i \(-0.292441\pi\)
−0.794831 + 0.606831i \(0.792441\pi\)
\(734\) 10.0745 2.69944i 0.371855 0.0996383i
\(735\) 0 0
\(736\) −14.4825 14.4825i −0.533831 0.533831i
\(737\) −14.0779 + 24.3836i −0.518565 + 0.898180i
\(738\) 0 0
\(739\) −2.23899 + 8.35601i −0.0823624 + 0.307381i −0.994802 0.101831i \(-0.967530\pi\)
0.912439 + 0.409212i \(0.134196\pi\)
\(740\) −24.1342 −0.887190
\(741\) 0 0
\(742\) −10.3485 + 4.10504i −0.379906 + 0.150701i
\(743\) −0.167623 0.0449143i −0.00614947 0.00164775i 0.255743 0.966745i \(-0.417680\pi\)
−0.261892 + 0.965097i \(0.584347\pi\)
\(744\) 0 0
\(745\) 0.860788 1.49093i 0.0315368 0.0546234i
\(746\) −15.1385 + 15.1385i −0.554260 + 0.554260i
\(747\) 0 0
\(748\) −11.1099 41.4628i −0.406219 1.51603i
\(749\) −28.1378 12.1546i −1.02813 0.444120i
\(750\) 0 0
\(751\) 5.40946 3.12315i 0.197394 0.113965i −0.398045 0.917366i \(-0.630311\pi\)
0.595439 + 0.803400i \(0.296978\pi\)
\(752\) 13.9559 + 3.73947i 0.508919 + 0.136364i
\(753\) 0 0
\(754\) −3.63599 + 2.74212i −0.132415 + 0.0998622i
\(755\) 10.3439i 0.376452i
\(756\) 0 0
\(757\) 5.42762 + 9.40091i 0.197270 + 0.341682i 0.947642 0.319334i \(-0.103459\pi\)
−0.750372 + 0.661016i \(0.770126\pi\)
\(758\) 6.55213 + 3.78288i 0.237984 + 0.137400i
\(759\) 0 0
\(760\) −3.69466 13.7887i −0.134020 0.500168i
\(761\) −5.34573 19.9505i −0.193783 0.723206i −0.992579 0.121604i \(-0.961196\pi\)
0.798796 0.601602i \(-0.205471\pi\)
\(762\) 0 0
\(763\) 2.17445 14.7918i 0.0787204 0.535500i
\(764\) −5.77116 + 3.33198i −0.208793 + 0.120547i
\(765\) 0 0
\(766\) 20.7751 0.750635
\(767\) 43.1171 32.5173i 1.55687 1.17413i
\(768\) 0 0
\(769\) −7.59897 + 28.3597i −0.274026 + 1.02268i 0.682466 + 0.730918i \(0.260908\pi\)
−0.956491 + 0.291760i \(0.905759\pi\)
\(770\) −6.86579 + 8.67403i −0.247426 + 0.312590i
\(771\) 0 0
\(772\) −1.39132 + 1.39132i −0.0500745 + 0.0500745i
\(773\) −14.8539 + 3.98008i −0.534257 + 0.143154i −0.515853 0.856677i \(-0.672525\pi\)
−0.0184036 + 0.999831i \(0.505858\pi\)
\(774\) 0 0
\(775\) −18.5352 + 18.5352i −0.665805 + 0.665805i
\(776\) 19.1492 + 11.0558i 0.687416 + 0.396880i
\(777\) 0 0
\(778\) 4.15980 15.5246i 0.149136 0.556583i
\(779\) 19.3981i 0.695011i
\(780\) 0 0
\(781\) −13.4517 −0.481338
\(782\) −3.20234 + 11.9513i −0.114515 + 0.427377i
\(783\) 0 0
\(784\) 12.2989 2.90154i 0.439246 0.103626i
\(785\) −7.19500 + 7.19500i −0.256801 + 0.256801i
\(786\) 0 0
\(787\) −8.72193 32.5507i −0.310903 1.16031i −0.927744 0.373218i \(-0.878254\pi\)
0.616841 0.787088i \(-0.288412\pi\)
\(788\) −13.1719