Properties

Label 675.2.r.a.46.14
Level $675$
Weight $2$
Character 675.46
Analytic conductor $5.390$
Analytic rank $0$
Dimension $224$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.r (of order \(15\), degree \(8\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(224\)
Relative dimension: \(28\) over \(\Q(\zeta_{15})\)
Twist minimal: no (minimal twist has level 225)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 46.14
Character \(\chi\) \(=\) 675.46
Dual form 675.2.r.a.631.14

$q$-expansion

\(f(q)\) \(=\) \(q+(0.110043 + 0.122216i) q^{2} +(0.206230 - 1.96215i) q^{4} +(2.06082 + 0.867759i) q^{5} +(2.06663 - 3.57951i) q^{7} +(0.528597 - 0.384048i) q^{8} +O(q^{10})\) \(q+(0.110043 + 0.122216i) q^{2} +(0.206230 - 1.96215i) q^{4} +(2.06082 + 0.867759i) q^{5} +(2.06663 - 3.57951i) q^{7} +(0.528597 - 0.384048i) q^{8} +(0.120726 + 0.347356i) q^{10} +(0.239690 + 0.266203i) q^{11} +(1.23537 - 1.37202i) q^{13} +(0.664892 - 0.141327i) q^{14} +(-3.75457 - 0.798059i) q^{16} +(-3.22940 + 2.34629i) q^{17} +(-0.0599095 + 0.0435268i) q^{19} +(2.12767 - 3.86468i) q^{20} +(-0.00615783 + 0.0585878i) q^{22} +(-4.28234 + 0.910239i) q^{23} +(3.49399 + 3.57660i) q^{25} +0.303627 q^{26} +(-6.59733 - 4.79324i) q^{28} +(5.93713 - 2.64338i) q^{29} +(-4.95171 - 2.20464i) q^{31} +(-0.969013 - 1.67838i) q^{32} +(-0.642128 - 0.136489i) q^{34} +(7.36512 - 5.58341i) q^{35} +(2.37480 + 7.30889i) q^{37} +(-0.0119123 - 0.00253204i) q^{38} +(1.42261 - 0.332761i) q^{40} +(-3.14813 + 3.49635i) q^{41} +(1.55061 - 2.68574i) q^{43} +(0.571760 - 0.415408i) q^{44} +(-0.582489 - 0.423203i) q^{46} +(11.8169 - 5.26122i) q^{47} +(-5.04195 - 8.73292i) q^{49} +(-0.0526256 + 0.820601i) q^{50} +(-2.43733 - 2.70693i) q^{52} +(-1.53179 - 1.11291i) q^{53} +(0.262959 + 0.756591i) q^{55} +(-0.282290 - 2.68581i) q^{56} +(0.976404 + 0.434723i) q^{58} +(-3.31117 + 3.67743i) q^{59} +(6.08932 + 6.76288i) q^{61} +(-0.275461 - 0.847783i) q^{62} +(-2.27380 + 6.99805i) q^{64} +(3.73647 - 1.75549i) q^{65} +(13.1648 + 5.86135i) q^{67} +(3.93777 + 6.82042i) q^{68} +(1.49286 + 0.285716i) q^{70} +(-10.8652 - 7.89400i) q^{71} +(4.15877 - 12.7994i) q^{73} +(-0.631930 + 1.09453i) q^{74} +(0.0730507 + 0.126528i) q^{76} +(1.44823 - 0.307831i) q^{77} +(-5.47332 + 2.43688i) q^{79} +(-7.04499 - 4.90273i) q^{80} -0.773739 q^{82} +(-0.301668 - 2.87018i) q^{83} +(-8.69124 + 2.03296i) q^{85} +(0.498874 - 0.106039i) q^{86} +(0.228934 + 0.0486615i) q^{88} +(-2.21408 + 6.81425i) q^{89} +(-2.35810 - 7.25750i) q^{91} +(0.902876 + 8.59029i) q^{92} +(1.94338 + 0.865246i) q^{94} +(-0.161234 + 0.0377140i) q^{95} +(9.65762 - 4.29985i) q^{97} +(0.512465 - 1.57721i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.110043 + 0.122216i 0.0778125 + 0.0864195i 0.780794 0.624789i \(-0.214815\pi\)
−0.702981 + 0.711208i \(0.748148\pi\)
\(3\) 0 0
\(4\) 0.206230 1.96215i 0.103115 0.981073i
\(5\) 2.06082 + 0.867759i 0.921628 + 0.388074i
\(6\) 0 0
\(7\) 2.06663 3.57951i 0.781114 1.35293i −0.150179 0.988659i \(-0.547985\pi\)
0.931293 0.364271i \(-0.118682\pi\)
\(8\) 0.528597 0.384048i 0.186887 0.135782i
\(9\) 0 0
\(10\) 0.120726 + 0.347356i 0.0381771 + 0.109844i
\(11\) 0.239690 + 0.266203i 0.0722693 + 0.0802632i 0.778195 0.628023i \(-0.216135\pi\)
−0.705926 + 0.708286i \(0.749469\pi\)
\(12\) 0 0
\(13\) 1.23537 1.37202i 0.342631 0.380530i −0.547060 0.837093i \(-0.684253\pi\)
0.889691 + 0.456563i \(0.150920\pi\)
\(14\) 0.664892 0.141327i 0.177700 0.0377713i
\(15\) 0 0
\(16\) −3.75457 0.798059i −0.938644 0.199515i
\(17\) −3.22940 + 2.34629i −0.783244 + 0.569060i −0.905951 0.423383i \(-0.860843\pi\)
0.122707 + 0.992443i \(0.460843\pi\)
\(18\) 0 0
\(19\) −0.0599095 + 0.0435268i −0.0137442 + 0.00998573i −0.594636 0.803995i \(-0.702704\pi\)
0.580892 + 0.813981i \(0.302704\pi\)
\(20\) 2.12767 3.86468i 0.475762 0.864168i
\(21\) 0 0
\(22\) −0.00615783 + 0.0585878i −0.00131285 + 0.0124910i
\(23\) −4.28234 + 0.910239i −0.892929 + 0.189798i −0.631455 0.775413i \(-0.717542\pi\)
−0.261474 + 0.965210i \(0.584209\pi\)
\(24\) 0 0
\(25\) 3.49399 + 3.57660i 0.698798 + 0.715319i
\(26\) 0.303627 0.0595462
\(27\) 0 0
\(28\) −6.59733 4.79324i −1.24678 0.905837i
\(29\) 5.93713 2.64338i 1.10250 0.490863i 0.226906 0.973917i \(-0.427139\pi\)
0.875591 + 0.483054i \(0.160472\pi\)
\(30\) 0 0
\(31\) −4.95171 2.20464i −0.889353 0.395966i −0.0893776 0.995998i \(-0.528488\pi\)
−0.799976 + 0.600032i \(0.795154\pi\)
\(32\) −0.969013 1.67838i −0.171299 0.296698i
\(33\) 0 0
\(34\) −0.642128 0.136489i −0.110124 0.0234076i
\(35\) 7.36512 5.58341i 1.24493 0.943768i
\(36\) 0 0
\(37\) 2.37480 + 7.30889i 0.390415 + 1.20157i 0.932475 + 0.361235i \(0.117645\pi\)
−0.542060 + 0.840340i \(0.682355\pi\)
\(38\) −0.0119123 0.00253204i −0.00193243 0.000410751i
\(39\) 0 0
\(40\) 1.42261 0.332761i 0.224934 0.0526141i
\(41\) −3.14813 + 3.49635i −0.491655 + 0.546038i −0.937004 0.349319i \(-0.886413\pi\)
0.445349 + 0.895357i \(0.353080\pi\)
\(42\) 0 0
\(43\) 1.55061 2.68574i 0.236466 0.409571i −0.723232 0.690605i \(-0.757344\pi\)
0.959698 + 0.281034i \(0.0906775\pi\)
\(44\) 0.571760 0.415408i 0.0861961 0.0626252i
\(45\) 0 0
\(46\) −0.582489 0.423203i −0.0858833 0.0623979i
\(47\) 11.8169 5.26122i 1.72367 0.767428i 0.726934 0.686707i \(-0.240945\pi\)
0.996737 0.0807203i \(-0.0257221\pi\)
\(48\) 0 0
\(49\) −5.04195 8.73292i −0.720279 1.24756i
\(50\) −0.0526256 + 0.820601i −0.00744238 + 0.116051i
\(51\) 0 0
\(52\) −2.43733 2.70693i −0.337997 0.375384i
\(53\) −1.53179 1.11291i −0.210408 0.152870i 0.477590 0.878583i \(-0.341510\pi\)
−0.687998 + 0.725712i \(0.741510\pi\)
\(54\) 0 0
\(55\) 0.262959 + 0.756591i 0.0354574 + 0.102019i
\(56\) −0.282290 2.68581i −0.0377225 0.358906i
\(57\) 0 0
\(58\) 0.976404 + 0.434723i 0.128208 + 0.0570820i
\(59\) −3.31117 + 3.67743i −0.431078 + 0.478760i −0.919074 0.394086i \(-0.871061\pi\)
0.487996 + 0.872846i \(0.337728\pi\)
\(60\) 0 0
\(61\) 6.08932 + 6.76288i 0.779658 + 0.865898i 0.993832 0.110898i \(-0.0353726\pi\)
−0.214174 + 0.976796i \(0.568706\pi\)
\(62\) −0.275461 0.847783i −0.0349836 0.107669i
\(63\) 0 0
\(64\) −2.27380 + 6.99805i −0.284226 + 0.874756i
\(65\) 3.73647 1.75549i 0.463452 0.217741i
\(66\) 0 0
\(67\) 13.1648 + 5.86135i 1.60834 + 0.716078i 0.997153 0.0754107i \(-0.0240268\pi\)
0.611184 + 0.791488i \(0.290693\pi\)
\(68\) 3.93777 + 6.82042i 0.477525 + 0.827098i
\(69\) 0 0
\(70\) 1.49286 + 0.285716i 0.178431 + 0.0341496i
\(71\) −10.8652 7.89400i −1.28946 0.936845i −0.289662 0.957129i \(-0.593543\pi\)
−0.999794 + 0.0202841i \(0.993543\pi\)
\(72\) 0 0
\(73\) 4.15877 12.7994i 0.486747 1.49805i −0.342688 0.939449i \(-0.611337\pi\)
0.829435 0.558603i \(-0.188663\pi\)
\(74\) −0.631930 + 1.09453i −0.0734603 + 0.127237i
\(75\) 0 0
\(76\) 0.0730507 + 0.126528i 0.00837950 + 0.0145137i
\(77\) 1.44823 0.307831i 0.165041 0.0350806i
\(78\) 0 0
\(79\) −5.47332 + 2.43688i −0.615797 + 0.274170i −0.690837 0.723010i \(-0.742758\pi\)
0.0750407 + 0.997180i \(0.476091\pi\)
\(80\) −7.04499 4.90273i −0.787654 0.548141i
\(81\) 0 0
\(82\) −0.773739 −0.0854452
\(83\) −0.301668 2.87018i −0.0331123 0.315043i −0.998524 0.0543124i \(-0.982703\pi\)
0.965412 0.260730i \(-0.0839633\pi\)
\(84\) 0 0
\(85\) −8.69124 + 2.03296i −0.942697 + 0.220506i
\(86\) 0.498874 0.106039i 0.0537949 0.0114345i
\(87\) 0 0
\(88\) 0.228934 + 0.0486615i 0.0244045 + 0.00518733i
\(89\) −2.21408 + 6.81425i −0.234692 + 0.722309i 0.762470 + 0.647024i \(0.223987\pi\)
−0.997162 + 0.0752851i \(0.976013\pi\)
\(90\) 0 0
\(91\) −2.35810 7.25750i −0.247196 0.760792i
\(92\) 0.902876 + 8.59029i 0.0941313 + 0.895600i
\(93\) 0 0
\(94\) 1.94338 + 0.865246i 0.200444 + 0.0892434i
\(95\) −0.161234 + 0.0377140i −0.0165422 + 0.00386938i
\(96\) 0 0
\(97\) 9.65762 4.29985i 0.980583 0.436584i 0.147095 0.989122i \(-0.453008\pi\)
0.833487 + 0.552539i \(0.186341\pi\)
\(98\) 0.512465 1.57721i 0.0517668 0.159322i
\(99\) 0 0
\(100\) 7.73837 6.11811i 0.773837 0.611811i
\(101\) −8.75862 + 15.1704i −0.871516 + 1.50951i −0.0110870 + 0.999939i \(0.503529\pi\)
−0.860429 + 0.509571i \(0.829804\pi\)
\(102\) 0 0
\(103\) −1.25065 + 11.8991i −0.123230 + 1.17245i 0.741761 + 0.670665i \(0.233991\pi\)
−0.864990 + 0.501788i \(0.832676\pi\)
\(104\) 0.126092 1.19969i 0.0123644 0.117639i
\(105\) 0 0
\(106\) −0.0325485 0.309678i −0.00316138 0.0300786i
\(107\) 8.49063 0.820820 0.410410 0.911901i \(-0.365386\pi\)
0.410410 + 0.911901i \(0.365386\pi\)
\(108\) 0 0
\(109\) 2.49526 + 7.67961i 0.239002 + 0.735573i 0.996565 + 0.0828110i \(0.0263898\pi\)
−0.757563 + 0.652762i \(0.773610\pi\)
\(110\) −0.0635303 + 0.115396i −0.00605738 + 0.0110025i
\(111\) 0 0
\(112\) −10.6160 + 11.7903i −1.00312 + 1.11407i
\(113\) −5.95046 + 6.60865i −0.559772 + 0.621690i −0.954897 0.296938i \(-0.904035\pi\)
0.395125 + 0.918627i \(0.370701\pi\)
\(114\) 0 0
\(115\) −9.61501 1.84020i −0.896604 0.171599i
\(116\) −3.96228 12.1946i −0.367889 1.13224i
\(117\) 0 0
\(118\) −0.813812 −0.0749175
\(119\) 1.72461 + 16.4086i 0.158095 + 1.50417i
\(120\) 0 0
\(121\) 1.13640 10.8121i 0.103309 0.982921i
\(122\) −0.156439 + 1.48842i −0.0141634 + 0.134755i
\(123\) 0 0
\(124\) −5.34702 + 9.26131i −0.480177 + 0.831691i
\(125\) 4.09687 + 10.4027i 0.366435 + 0.930444i
\(126\) 0 0
\(127\) −1.00273 + 3.08608i −0.0889778 + 0.273845i −0.985637 0.168875i \(-0.945987\pi\)
0.896660 + 0.442720i \(0.145987\pi\)
\(128\) −4.64644 + 2.06873i −0.410691 + 0.182851i
\(129\) 0 0
\(130\) 0.625722 + 0.263475i 0.0548794 + 0.0231083i
\(131\) 7.86032 + 3.49964i 0.686759 + 0.305765i 0.720290 0.693673i \(-0.244009\pi\)
−0.0335311 + 0.999438i \(0.510675\pi\)
\(132\) 0 0
\(133\) 0.0319938 + 0.304401i 0.00277421 + 0.0263949i
\(134\) 0.732352 + 2.25395i 0.0632656 + 0.194711i
\(135\) 0 0
\(136\) −0.805959 + 2.48049i −0.0691105 + 0.212700i
\(137\) −5.60580 1.19155i −0.478936 0.101801i −0.0378831 0.999282i \(-0.512061\pi\)
−0.441053 + 0.897481i \(0.645395\pi\)
\(138\) 0 0
\(139\) −16.2222 + 3.44813i −1.37595 + 0.292466i −0.835767 0.549084i \(-0.814977\pi\)
−0.540179 + 0.841550i \(0.681643\pi\)
\(140\) −9.43655 15.6029i −0.797534 1.31869i
\(141\) 0 0
\(142\) −0.230869 2.19657i −0.0193741 0.184332i
\(143\) 0.661343 0.0553043
\(144\) 0 0
\(145\) 14.5292 0.295542i 1.20658 0.0245434i
\(146\) 2.02193 0.900220i 0.167336 0.0745028i
\(147\) 0 0
\(148\) 14.8309 3.15240i 1.21909 0.259126i
\(149\) 3.50472 + 6.07035i 0.287118 + 0.497302i 0.973120 0.230297i \(-0.0739696\pi\)
−0.686003 + 0.727599i \(0.740636\pi\)
\(150\) 0 0
\(151\) 2.35416 4.07752i 0.191579 0.331824i −0.754195 0.656651i \(-0.771973\pi\)
0.945774 + 0.324827i \(0.105306\pi\)
\(152\) −0.0149516 + 0.0460162i −0.00121273 + 0.00373241i
\(153\) 0 0
\(154\) 0.196990 + 0.143122i 0.0158739 + 0.0115331i
\(155\) −8.29150 8.84027i −0.665989 0.710068i
\(156\) 0 0
\(157\) 8.51816 + 14.7539i 0.679823 + 1.17749i 0.975034 + 0.222057i \(0.0712770\pi\)
−0.295210 + 0.955432i \(0.595390\pi\)
\(158\) −0.900128 0.400763i −0.0716104 0.0318830i
\(159\) 0 0
\(160\) −0.540535 4.29971i −0.0427331 0.339922i
\(161\) −5.59181 + 17.2098i −0.440696 + 1.35632i
\(162\) 0 0
\(163\) 0.313473 + 0.964770i 0.0245531 + 0.0755666i 0.962582 0.270990i \(-0.0873509\pi\)
−0.938029 + 0.346556i \(0.887351\pi\)
\(164\) 6.21111 + 6.89813i 0.485006 + 0.538654i
\(165\) 0 0
\(166\) 0.317584 0.352713i 0.0246493 0.0273758i
\(167\) −3.50153 1.55898i −0.270956 0.120637i 0.266761 0.963763i \(-0.414047\pi\)
−0.537717 + 0.843125i \(0.680713\pi\)
\(168\) 0 0
\(169\) 1.00258 + 9.53887i 0.0771212 + 0.733760i
\(170\) −1.20487 0.838491i −0.0924096 0.0643094i
\(171\) 0 0
\(172\) −4.95002 3.59640i −0.377436 0.274223i
\(173\) −14.8429 16.4847i −1.12849 1.25331i −0.963701 0.266982i \(-0.913974\pi\)
−0.164785 0.986329i \(-0.552693\pi\)
\(174\) 0 0
\(175\) 20.0233 5.11527i 1.51362 0.386678i
\(176\) −0.687489 1.19077i −0.0518215 0.0897574i
\(177\) 0 0
\(178\) −1.07645 + 0.479268i −0.0806836 + 0.0359227i
\(179\) −11.8426 8.60413i −0.885156 0.643103i 0.0494548 0.998776i \(-0.484252\pi\)
−0.934610 + 0.355673i \(0.884252\pi\)
\(180\) 0 0
\(181\) −13.9341 + 10.1237i −1.03571 + 0.752489i −0.969444 0.245313i \(-0.921109\pi\)
−0.0662678 + 0.997802i \(0.521109\pi\)
\(182\) 0.627486 1.08684i 0.0465123 0.0805617i
\(183\) 0 0
\(184\) −1.91405 + 2.12577i −0.141106 + 0.156714i
\(185\) −1.44831 + 17.1231i −0.106482 + 1.25892i
\(186\) 0 0
\(187\) −1.39865 0.297291i −0.102279 0.0217401i
\(188\) −7.88628 24.2715i −0.575166 1.77018i
\(189\) 0 0
\(190\) −0.0223519 0.0155551i −0.00162158 0.00112848i
\(191\) 0.569688 + 0.121091i 0.0412212 + 0.00876184i 0.228476 0.973550i \(-0.426626\pi\)
−0.187255 + 0.982311i \(0.559959\pi\)
\(192\) 0 0
\(193\) −4.64632 8.04765i −0.334449 0.579283i 0.648930 0.760848i \(-0.275217\pi\)
−0.983379 + 0.181565i \(0.941884\pi\)
\(194\) 1.58827 + 0.707142i 0.114031 + 0.0507698i
\(195\) 0 0
\(196\) −18.1751 + 8.09205i −1.29822 + 0.578004i
\(197\) 3.47512 + 2.52482i 0.247592 + 0.179886i 0.704659 0.709546i \(-0.251100\pi\)
−0.457067 + 0.889432i \(0.651100\pi\)
\(198\) 0 0
\(199\) −3.20175 −0.226966 −0.113483 0.993540i \(-0.536201\pi\)
−0.113483 + 0.993540i \(0.536201\pi\)
\(200\) 3.22050 + 0.548719i 0.227723 + 0.0388003i
\(201\) 0 0
\(202\) −2.81789 + 0.598961i −0.198266 + 0.0421427i
\(203\) 2.80785 26.7149i 0.197073 1.87502i
\(204\) 0 0
\(205\) −9.52172 + 4.47354i −0.665026 + 0.312446i
\(206\) −1.59188 + 1.15657i −0.110912 + 0.0805820i
\(207\) 0 0
\(208\) −5.73325 + 4.16545i −0.397529 + 0.288822i
\(209\) −0.0259467 0.00551514i −0.00179477 0.000381490i
\(210\) 0 0
\(211\) 7.09956 1.50906i 0.488754 0.103888i 0.0430586 0.999073i \(-0.486290\pi\)
0.445695 + 0.895185i \(0.352956\pi\)
\(212\) −2.49960 + 2.77608i −0.171673 + 0.190662i
\(213\) 0 0
\(214\) 0.934339 + 1.03769i 0.0638701 + 0.0709349i
\(215\) 5.52611 4.18927i 0.376877 0.285706i
\(216\) 0 0
\(217\) −18.1249 + 13.1685i −1.23040 + 0.893938i
\(218\) −0.663982 + 1.15005i −0.0449705 + 0.0778912i
\(219\) 0 0
\(220\) 1.53877 0.359933i 0.103744 0.0242667i
\(221\) −0.770345 + 7.32935i −0.0518190 + 0.493025i
\(222\) 0 0
\(223\) −0.398119 0.442156i −0.0266600 0.0296090i 0.729667 0.683802i \(-0.239675\pi\)
−0.756327 + 0.654193i \(0.773008\pi\)
\(224\) −8.01038 −0.535216
\(225\) 0 0
\(226\) −1.46249 −0.0972834
\(227\) 6.17937 + 6.86289i 0.410139 + 0.455506i 0.912454 0.409179i \(-0.134185\pi\)
−0.502315 + 0.864685i \(0.667518\pi\)
\(228\) 0 0
\(229\) −0.272928 + 2.59673i −0.0180356 + 0.171597i −0.999832 0.0183402i \(-0.994162\pi\)
0.981796 + 0.189937i \(0.0608285\pi\)
\(230\) −0.833169 1.37761i −0.0549375 0.0908367i
\(231\) 0 0
\(232\) 2.12316 3.67742i 0.139392 0.241435i
\(233\) −5.35177 + 3.88829i −0.350606 + 0.254730i −0.749123 0.662431i \(-0.769525\pi\)
0.398517 + 0.917161i \(0.369525\pi\)
\(234\) 0 0
\(235\) 28.9180 0.588229i 1.88640 0.0383718i
\(236\) 6.53279 + 7.25539i 0.425248 + 0.472286i
\(237\) 0 0
\(238\) −1.81561 + 2.01644i −0.117688 + 0.130706i
\(239\) 16.1587 3.43464i 1.04522 0.222168i 0.346861 0.937917i \(-0.387248\pi\)
0.698358 + 0.715748i \(0.253914\pi\)
\(240\) 0 0
\(241\) −7.35486 1.56332i −0.473768 0.100703i −0.0351616 0.999382i \(-0.511195\pi\)
−0.438607 + 0.898679i \(0.644528\pi\)
\(242\) 1.44646 1.05092i 0.0929823 0.0675556i
\(243\) 0 0
\(244\) 14.5256 10.5534i 0.929903 0.675614i
\(245\) −2.81250 22.3722i −0.179684 1.42931i
\(246\) 0 0
\(247\) −0.0142909 + 0.135969i −0.000909308 + 0.00865148i
\(248\) −3.46415 + 0.736327i −0.219974 + 0.0467568i
\(249\) 0 0
\(250\) −0.820536 + 1.64545i −0.0518953 + 0.104067i
\(251\) 19.2136 1.21275 0.606377 0.795177i \(-0.292622\pi\)
0.606377 + 0.795177i \(0.292622\pi\)
\(252\) 0 0
\(253\) −1.26874 0.921796i −0.0797652 0.0579528i
\(254\) −0.487511 + 0.217054i −0.0305892 + 0.0136192i
\(255\) 0 0
\(256\) 12.6799 + 5.64547i 0.792496 + 0.352842i
\(257\) 9.44838 + 16.3651i 0.589374 + 1.02083i 0.994315 + 0.106483i \(0.0339588\pi\)
−0.404941 + 0.914343i \(0.632708\pi\)
\(258\) 0 0
\(259\) 31.0701 + 6.60416i 1.93060 + 0.410363i
\(260\) −2.67395 7.69353i −0.165831 0.477132i
\(261\) 0 0
\(262\) 0.437266 + 1.34577i 0.0270144 + 0.0831417i
\(263\) 15.8269 + 3.36410i 0.975926 + 0.207439i 0.668156 0.744021i \(-0.267084\pi\)
0.307770 + 0.951461i \(0.400417\pi\)
\(264\) 0 0
\(265\) −2.19101 3.62274i −0.134593 0.222543i
\(266\) −0.0336818 + 0.0374075i −0.00206517 + 0.00229360i
\(267\) 0 0
\(268\) 14.2158 24.6225i 0.868368 1.50406i
\(269\) 1.72574 1.25382i 0.105220 0.0764469i −0.533931 0.845528i \(-0.679286\pi\)
0.639151 + 0.769081i \(0.279286\pi\)
\(270\) 0 0
\(271\) −13.1625 9.56310i −0.799563 0.580917i 0.111223 0.993796i \(-0.464523\pi\)
−0.910786 + 0.412879i \(0.864523\pi\)
\(272\) 13.9975 6.23209i 0.848723 0.377876i
\(273\) 0 0
\(274\) −0.471256 0.816239i −0.0284696 0.0493108i
\(275\) −0.114626 + 1.78739i −0.00691221 + 0.107783i
\(276\) 0 0
\(277\) −5.70183 6.33252i −0.342590 0.380484i 0.547087 0.837076i \(-0.315737\pi\)
−0.889676 + 0.456591i \(0.849070\pi\)
\(278\) −2.20656 1.60316i −0.132341 0.0961511i
\(279\) 0 0
\(280\) 1.74888 5.77993i 0.104516 0.345417i
\(281\) −0.868414 8.26241i −0.0518052 0.492894i −0.989405 0.145179i \(-0.953624\pi\)
0.937600 0.347715i \(-0.113042\pi\)
\(282\) 0 0
\(283\) 4.78188 + 2.12903i 0.284253 + 0.126558i 0.543911 0.839143i \(-0.316943\pi\)
−0.259657 + 0.965701i \(0.583610\pi\)
\(284\) −17.7299 + 19.6910i −1.05208 + 1.16845i
\(285\) 0 0
\(286\) 0.0727764 + 0.0808264i 0.00430336 + 0.00477937i
\(287\) 6.00921 + 18.4944i 0.354712 + 1.09169i
\(288\) 0 0
\(289\) −0.329378 + 1.01372i −0.0193752 + 0.0596307i
\(290\) 1.63496 + 1.74317i 0.0960083 + 0.102363i
\(291\) 0 0
\(292\) −24.2566 10.7997i −1.41951 0.632006i
\(293\) 10.1972 + 17.6621i 0.595728 + 1.03183i 0.993444 + 0.114323i \(0.0364698\pi\)
−0.397715 + 0.917509i \(0.630197\pi\)
\(294\) 0 0
\(295\) −10.0149 + 4.70523i −0.583088 + 0.273949i
\(296\) 4.06228 + 2.95142i 0.236115 + 0.171548i
\(297\) 0 0
\(298\) −0.356220 + 1.09633i −0.0206353 + 0.0635089i
\(299\) −4.04142 + 6.99994i −0.233721 + 0.404817i
\(300\) 0 0
\(301\) −6.40909 11.1009i −0.369414 0.639843i
\(302\) 0.757397 0.160990i 0.0435833 0.00926392i
\(303\) 0 0
\(304\) 0.259671 0.115613i 0.0148932 0.00663087i
\(305\) 6.68047 + 19.2212i 0.382523 + 1.10060i
\(306\) 0 0
\(307\) 8.63664 0.492919 0.246459 0.969153i \(-0.420733\pi\)
0.246459 + 0.969153i \(0.420733\pi\)
\(308\) −0.305341 2.90512i −0.0173984 0.165535i
\(309\) 0 0
\(310\) 0.167994 1.98617i 0.00954143 0.112807i
\(311\) −13.1734 + 2.80008i −0.746992 + 0.158778i −0.565654 0.824643i \(-0.691376\pi\)
−0.181338 + 0.983421i \(0.558043\pi\)
\(312\) 0 0
\(313\) 7.14512 + 1.51874i 0.403866 + 0.0858443i 0.405366 0.914155i \(-0.367144\pi\)
−0.00150004 + 0.999999i \(0.500477\pi\)
\(314\) −0.865788 + 2.66462i −0.0488593 + 0.150373i
\(315\) 0 0
\(316\) 3.65275 + 11.2420i 0.205483 + 0.632413i
\(317\) −2.42838 23.1045i −0.136391 1.29768i −0.821908 0.569620i \(-0.807090\pi\)
0.685517 0.728057i \(-0.259576\pi\)
\(318\) 0 0
\(319\) 2.12675 + 0.946889i 0.119075 + 0.0530156i
\(320\) −10.7585 + 12.4486i −0.601420 + 0.695900i
\(321\) 0 0
\(322\) −2.71865 + 1.21042i −0.151505 + 0.0674542i
\(323\) 0.0913448 0.281131i 0.00508256 0.0156425i
\(324\) 0 0
\(325\) 9.22354 0.375392i 0.511630 0.0208230i
\(326\) −0.0834143 + 0.144478i −0.00461989 + 0.00800189i
\(327\) 0 0
\(328\) −0.321324 + 3.05719i −0.0177421 + 0.168805i
\(329\) 5.58858 53.1718i 0.308108 2.93145i
\(330\) 0 0
\(331\) −2.81073 26.7423i −0.154492 1.46989i −0.747267 0.664524i \(-0.768634\pi\)
0.592775 0.805368i \(-0.298032\pi\)
\(332\) −5.69392 −0.312494
\(333\) 0 0
\(334\) −0.194788 0.599497i −0.0106583 0.0328030i
\(335\) 22.0441 + 23.5031i 1.20440 + 1.28411i
\(336\) 0 0
\(337\) 5.77004 6.40828i 0.314314 0.349081i −0.565200 0.824954i \(-0.691201\pi\)
0.879514 + 0.475873i \(0.157868\pi\)
\(338\) −1.05547 + 1.17222i −0.0574102 + 0.0637604i
\(339\) 0 0
\(340\) 2.19657 + 17.4727i 0.119126 + 0.947592i
\(341\) −0.599994 1.84659i −0.0324915 0.0999986i
\(342\) 0 0
\(343\) −12.7466 −0.688251
\(344\) −0.211804 2.01518i −0.0114197 0.108651i
\(345\) 0 0
\(346\) 0.381326 3.62808i 0.0205002 0.195047i
\(347\) 3.67108 34.9280i 0.197074 1.87503i −0.233330 0.972398i \(-0.574962\pi\)
0.430404 0.902636i \(-0.358371\pi\)
\(348\) 0 0
\(349\) 10.5156 18.2135i 0.562886 0.974946i −0.434357 0.900741i \(-0.643025\pi\)
0.997243 0.0742057i \(-0.0236421\pi\)
\(350\) 2.82860 + 1.88426i 0.151195 + 0.100718i
\(351\) 0 0
\(352\) 0.214527 0.660245i 0.0114343 0.0351912i
\(353\) −17.9989 + 8.01363i −0.957985 + 0.426523i −0.825337 0.564641i \(-0.809015\pi\)
−0.132649 + 0.991163i \(0.542348\pi\)
\(354\) 0 0
\(355\) −15.5411 25.6965i −0.824835 1.36383i
\(356\) 12.9139 + 5.74966i 0.684438 + 0.304731i
\(357\) 0 0
\(358\) −0.251638 2.39418i −0.0132995 0.126536i
\(359\) 0.938606 + 2.88873i 0.0495377 + 0.152461i 0.972765 0.231792i \(-0.0744589\pi\)
−0.923228 + 0.384253i \(0.874459\pi\)
\(360\) 0 0
\(361\) −5.86963 + 18.0649i −0.308928 + 0.950782i
\(362\) −2.77063 0.588915i −0.145621 0.0309527i
\(363\) 0 0
\(364\) −14.7266 + 3.13023i −0.771882 + 0.164069i
\(365\) 19.6773 22.7684i 1.02995 1.19175i
\(366\) 0 0
\(367\) 0.759260 + 7.22388i 0.0396330 + 0.377083i 0.996303 + 0.0859088i \(0.0273794\pi\)
−0.956670 + 0.291175i \(0.905954\pi\)
\(368\) 16.8048 0.876010
\(369\) 0 0
\(370\) −2.25209 + 1.70728i −0.117080 + 0.0887572i
\(371\) −7.14934 + 3.18309i −0.371175 + 0.165258i
\(372\) 0 0
\(373\) −10.3292 + 2.19554i −0.534825 + 0.113681i −0.467404 0.884044i \(-0.654810\pi\)
−0.0674212 + 0.997725i \(0.521477\pi\)
\(374\) −0.117578 0.203651i −0.00607983 0.0105306i
\(375\) 0 0
\(376\) 4.22581 7.31932i 0.217930 0.377465i
\(377\) 3.70779 11.4114i 0.190961 0.587718i
\(378\) 0 0
\(379\) −28.5159 20.7180i −1.46476 1.06421i −0.982090 0.188412i \(-0.939666\pi\)
−0.482673 0.875801i \(-0.660334\pi\)
\(380\) 0.0407492 + 0.324142i 0.00209039 + 0.0166281i
\(381\) 0 0
\(382\) 0.0478913 + 0.0829501i 0.00245033 + 0.00424410i
\(383\) 5.70095 + 2.53823i 0.291305 + 0.129697i 0.547186 0.837011i \(-0.315699\pi\)
−0.255881 + 0.966708i \(0.582366\pi\)
\(384\) 0 0
\(385\) 3.25167 + 0.622330i 0.165720 + 0.0317169i
\(386\) 0.472253 1.45344i 0.0240370 0.0739784i
\(387\) 0 0
\(388\) −6.44524 19.8364i −0.327208 1.00704i
\(389\) −19.0702 21.1796i −0.966899 1.07385i −0.997235 0.0743103i \(-0.976324\pi\)
0.0303363 0.999540i \(-0.490342\pi\)
\(390\) 0 0
\(391\) 11.6937 12.9872i 0.591375 0.656788i
\(392\) −6.01902 2.67984i −0.304006 0.135352i
\(393\) 0 0
\(394\) 0.0738414 + 0.702554i 0.00372008 + 0.0353942i
\(395\) −13.3942 + 0.272455i −0.673934 + 0.0137087i
\(396\) 0 0
\(397\) −4.87063 3.53872i −0.244450 0.177603i 0.458814 0.888533i \(-0.348275\pi\)
−0.703263 + 0.710929i \(0.748275\pi\)
\(398\) −0.352332 0.391304i −0.0176608 0.0196143i
\(399\) 0 0
\(400\) −10.2641 16.2170i −0.513205 0.810851i
\(401\) −13.2682 22.9812i −0.662583 1.14763i −0.979934 0.199320i \(-0.936127\pi\)
0.317351 0.948308i \(-0.397207\pi\)
\(402\) 0 0
\(403\) −9.14202 + 4.07029i −0.455396 + 0.202756i
\(404\) 27.9602 + 20.3143i 1.39107 + 1.01067i
\(405\) 0 0
\(406\) 3.57397 2.59664i 0.177373 0.128869i
\(407\) −1.37643 + 2.38405i −0.0682272 + 0.118173i
\(408\) 0 0
\(409\) −18.2716 + 20.2927i −0.903475 + 1.00341i 0.0964928 + 0.995334i \(0.469238\pi\)
−0.999967 + 0.00807647i \(0.997429\pi\)
\(410\) −1.59454 0.671419i −0.0787487 0.0331590i
\(411\) 0 0
\(412\) 23.0898 + 4.90790i 1.13755 + 0.241795i
\(413\) 6.32043 + 19.4523i 0.311008 + 0.957184i
\(414\) 0 0
\(415\) 1.86894 6.17670i 0.0917425 0.303202i
\(416\) −3.49986 0.743918i −0.171595 0.0364736i
\(417\) 0 0
\(418\) −0.00218123 0.00377800i −0.000106687 0.000184788i
\(419\) 10.8046 + 4.81054i 0.527841 + 0.235010i 0.653314 0.757087i \(-0.273378\pi\)
−0.125473 + 0.992097i \(0.540045\pi\)
\(420\) 0 0
\(421\) 1.67084 0.743904i 0.0814316 0.0362557i −0.365617 0.930766i \(-0.619142\pi\)
0.447048 + 0.894510i \(0.352475\pi\)
\(422\) 0.965691 + 0.701616i 0.0470091 + 0.0341541i
\(423\) 0 0
\(424\) −1.23711 −0.0600795
\(425\) −19.6752 3.35233i −0.954389 0.162612i
\(426\) 0 0
\(427\) 36.7922 7.82043i 1.78050 0.378457i
\(428\) 1.75102 16.6599i 0.0846388 0.805285i
\(429\) 0 0
\(430\) 1.12011 + 0.214375i 0.0540163 + 0.0103381i
\(431\) −28.5016 + 20.7076i −1.37288 + 0.997452i −0.375369 + 0.926876i \(0.622484\pi\)
−0.997506 + 0.0705766i \(0.977516\pi\)
\(432\) 0 0
\(433\) 3.17805 2.30899i 0.152727 0.110963i −0.508797 0.860886i \(-0.669910\pi\)
0.661525 + 0.749923i \(0.269910\pi\)
\(434\) −3.60393 0.766039i −0.172994 0.0367711i
\(435\) 0 0
\(436\) 15.5831 3.31229i 0.746295 0.158630i
\(437\) 0.216933 0.240928i 0.0103773 0.0115252i
\(438\) 0 0
\(439\) 12.9252 + 14.3549i 0.616887 + 0.685123i 0.967925 0.251238i \(-0.0808378\pi\)
−0.351038 + 0.936361i \(0.614171\pi\)
\(440\) 0.429567 + 0.298943i 0.0204788 + 0.0142515i
\(441\) 0 0
\(442\) −0.980532 + 0.712398i −0.0466392 + 0.0338853i
\(443\) 2.24077 3.88113i 0.106462 0.184398i −0.807872 0.589357i \(-0.799381\pi\)
0.914335 + 0.404959i \(0.132714\pi\)
\(444\) 0 0
\(445\) −10.4760 + 12.1217i −0.496608 + 0.574623i
\(446\) 0.0102280 0.0973128i 0.000484309 0.00460790i
\(447\) 0 0
\(448\) 20.3505 + 22.6015i 0.961471 + 1.06782i
\(449\) 11.2399 0.530445 0.265222 0.964187i \(-0.414555\pi\)
0.265222 + 0.964187i \(0.414555\pi\)
\(450\) 0 0
\(451\) −1.68531 −0.0793583
\(452\) 11.7400 + 13.0386i 0.552202 + 0.613283i
\(453\) 0 0
\(454\) −0.158753 + 1.51043i −0.00745064 + 0.0708881i
\(455\) 1.43812 17.0027i 0.0674203 0.797098i
\(456\) 0 0
\(457\) 7.48417 12.9630i 0.350095 0.606381i −0.636171 0.771548i \(-0.719483\pi\)
0.986266 + 0.165166i \(0.0528161\pi\)
\(458\) −0.347396 + 0.252398i −0.0162327 + 0.0117938i
\(459\) 0 0
\(460\) −5.59363 + 18.4866i −0.260805 + 0.861940i
\(461\) −20.1758 22.4075i −0.939679 1.04362i −0.998970 0.0453786i \(-0.985551\pi\)
0.0592908 0.998241i \(-0.481116\pi\)
\(462\) 0 0
\(463\) −18.4989 + 20.5451i −0.859718 + 0.954814i −0.999374 0.0353863i \(-0.988734\pi\)
0.139655 + 0.990200i \(0.455401\pi\)
\(464\) −24.4010 + 5.18658i −1.13279 + 0.240781i
\(465\) 0 0
\(466\) −1.06414 0.226189i −0.0492952 0.0104780i
\(467\) 23.9054 17.3683i 1.10621 0.803709i 0.124147 0.992264i \(-0.460380\pi\)
0.982063 + 0.188555i \(0.0603805\pi\)
\(468\) 0 0
\(469\) 48.1876 35.0103i 2.22510 1.61663i
\(470\) 3.25413 + 3.46950i 0.150102 + 0.160036i
\(471\) 0 0
\(472\) −0.337965 + 3.21552i −0.0155561 + 0.148007i
\(473\) 1.08662 0.230968i 0.0499627 0.0106199i
\(474\) 0 0
\(475\) −0.365001 0.0621900i −0.0167474 0.00285347i
\(476\) 32.5517 1.49201
\(477\) 0 0
\(478\) 2.19793 + 1.59689i 0.100531 + 0.0730399i
\(479\) 12.2428 5.45085i 0.559389 0.249056i −0.107510 0.994204i \(-0.534288\pi\)
0.666899 + 0.745148i \(0.267621\pi\)
\(480\) 0 0
\(481\) 12.9617 + 5.77093i 0.591003 + 0.263132i
\(482\) −0.618292 1.07091i −0.0281624 0.0487788i
\(483\) 0 0
\(484\) −20.9806 4.45957i −0.953664 0.202708i
\(485\) 23.6339 0.480743i 1.07316 0.0218294i
\(486\) 0 0
\(487\) 0.825534 + 2.54073i 0.0374085 + 0.115132i 0.968017 0.250885i \(-0.0807215\pi\)
−0.930608 + 0.366016i \(0.880721\pi\)
\(488\) 5.81607 + 1.23624i 0.263281 + 0.0559621i
\(489\) 0 0
\(490\) 2.42474 2.80565i 0.109538 0.126746i
\(491\) 11.9826 13.3080i 0.540767 0.600582i −0.409388 0.912360i \(-0.634258\pi\)
0.950155 + 0.311778i \(0.100925\pi\)
\(492\) 0 0
\(493\) −12.9712 + 22.4668i −0.584193 + 1.01185i
\(494\) −0.0181901 + 0.0132159i −0.000818413 + 0.000594612i
\(495\) 0 0
\(496\) 16.8321 + 12.2293i 0.755785 + 0.549110i
\(497\) −50.7110 + 22.5780i −2.27470 + 1.01276i
\(498\) 0 0
\(499\) −10.2734 17.7940i −0.459899 0.796568i 0.539057 0.842270i \(-0.318781\pi\)
−0.998955 + 0.0457019i \(0.985448\pi\)
\(500\) 21.2565 5.89331i 0.950618 0.263557i
\(501\) 0 0
\(502\) 2.11433 + 2.34821i 0.0943674 + 0.104806i
\(503\) 32.2593 + 23.4377i 1.43837 + 1.04504i 0.988380 + 0.152003i \(0.0485724\pi\)
0.449990 + 0.893034i \(0.351428\pi\)
\(504\) 0 0
\(505\) −31.2142 + 23.6631i −1.38901 + 1.05299i
\(506\) −0.0269590 0.256498i −0.00119847 0.0114027i
\(507\) 0 0
\(508\) 5.84855 + 2.60394i 0.259487 + 0.115531i
\(509\) −13.2868 + 14.7564i −0.588925 + 0.654068i −0.961780 0.273822i \(-0.911712\pi\)
0.372855 + 0.927890i \(0.378379\pi\)
\(510\) 0 0
\(511\) −37.2209 41.3380i −1.64655 1.82868i
\(512\) 3.84880 + 11.8454i 0.170094 + 0.523497i
\(513\) 0 0
\(514\) −0.960336 + 2.95561i −0.0423586 + 0.130366i
\(515\) −12.9029 + 23.4367i −0.568570 + 1.03274i
\(516\) 0 0
\(517\) 4.23295 + 1.88463i 0.186165 + 0.0828859i
\(518\) 2.61193 + 4.52400i 0.114762 + 0.198773i
\(519\) 0 0
\(520\) 1.30089 2.36293i 0.0570480 0.103621i
\(521\) −8.76012 6.36460i −0.383788 0.278838i 0.379117 0.925349i \(-0.376228\pi\)
−0.762905 + 0.646510i \(0.776228\pi\)
\(522\) 0 0
\(523\) 4.62026 14.2197i 0.202030 0.621785i −0.797792 0.602932i \(-0.793999\pi\)
0.999822 0.0188521i \(-0.00600116\pi\)
\(524\) 8.48783 14.7014i 0.370793 0.642232i
\(525\) 0 0
\(526\) 1.33050 + 2.30449i 0.0580124 + 0.100480i
\(527\) 21.1638 4.49850i 0.921909 0.195958i
\(528\) 0 0
\(529\) −3.50166 + 1.55904i −0.152246 + 0.0677844i
\(530\) 0.201649 0.666436i 0.00875908 0.0289481i
\(531\) 0 0
\(532\) 0.603877 0.0261814
\(533\) 0.907952 + 8.63858i 0.0393278 + 0.374179i
\(534\) 0 0
\(535\) 17.4977 + 7.36782i 0.756491 + 0.318539i
\(536\) 9.20991 1.95763i 0.397808 0.0845566i
\(537\) 0 0
\(538\) 0.343143 + 0.0729373i 0.0147939 + 0.00314455i
\(539\) 1.11622 3.43538i 0.0480791 0.147972i
\(540\) 0 0
\(541\) 11.4490 + 35.2363i 0.492230 + 1.51493i 0.821230 + 0.570597i \(0.193288\pi\)
−0.329000 + 0.944330i \(0.606712\pi\)
\(542\) −0.279684 2.66102i −0.0120135 0.114300i
\(543\) 0 0
\(544\) 7.06730 + 3.14656i 0.303008 + 0.134908i
\(545\) −1.52177 + 17.9916i −0.0651854 + 0.770675i
\(546\) 0 0
\(547\) −19.4966 + 8.68045i −0.833615 + 0.371149i −0.778742 0.627344i \(-0.784142\pi\)
−0.0548729 + 0.998493i \(0.517475\pi\)
\(548\) −3.49408 + 10.7537i −0.149260 + 0.459374i
\(549\) 0 0
\(550\) −0.231060 + 0.182681i −0.00985245 + 0.00778955i
\(551\) −0.240632 + 0.416787i −0.0102513 + 0.0177557i
\(552\) 0 0
\(553\) −2.58850 + 24.6280i −0.110074 + 1.04729i
\(554\) 0.146484 1.39371i 0.00622352 0.0592129i
\(555\) 0 0
\(556\) 3.42023 + 32.5414i 0.145050 + 1.38006i
\(557\) −38.6947 −1.63955 −0.819773 0.572689i \(-0.805900\pi\)
−0.819773 + 0.572689i \(0.805900\pi\)
\(558\) 0 0
\(559\) −1.76930 5.44535i −0.0748335 0.230314i
\(560\) −32.1088 + 15.0855i −1.35684 + 0.637479i
\(561\) 0 0
\(562\) 0.914232 1.01536i 0.0385646 0.0428303i
\(563\) −9.13347 + 10.1437i −0.384930 + 0.427508i −0.904205 0.427100i \(-0.859535\pi\)
0.519275 + 0.854607i \(0.326202\pi\)
\(564\) 0 0
\(565\) −17.9976 + 8.45570i −0.757163 + 0.355734i
\(566\) 0.266014 + 0.818707i 0.0111814 + 0.0344128i
\(567\) 0 0
\(568\) −8.77496 −0.368189
\(569\) 2.42745 + 23.0956i 0.101764 + 0.968218i 0.919624 + 0.392801i \(0.128494\pi\)
−0.817860 + 0.575417i \(0.804840\pi\)
\(570\) 0 0
\(571\) −2.66000 + 25.3082i −0.111317 + 1.05911i 0.786151 + 0.618035i \(0.212071\pi\)
−0.897468 + 0.441079i \(0.854596\pi\)
\(572\) 0.136389 1.29765i 0.00570269 0.0542575i
\(573\) 0 0
\(574\) −1.59904 + 2.76961i −0.0667425 + 0.115601i
\(575\) −18.2180 12.1358i −0.759743 0.506099i
\(576\) 0 0
\(577\) 9.47834 29.1713i 0.394588 1.21442i −0.534693 0.845046i \(-0.679573\pi\)
0.929282 0.369372i \(-0.120427\pi\)
\(578\) −0.160139 + 0.0712983i −0.00666089 + 0.00296562i
\(579\) 0 0
\(580\) 2.41645 28.5693i 0.100338 1.18628i
\(581\) −10.8973 4.85178i −0.452095 0.201286i
\(582\) 0 0
\(583\) −0.0708951 0.674522i −0.00293618 0.0279359i
\(584\) −2.71726 8.36287i −0.112441 0.346058i
\(585\) 0 0
\(586\) −1.03645 + 3.18986i −0.0428153 + 0.131772i
\(587\) −14.4830 3.07845i −0.597777 0.127061i −0.100921 0.994894i \(-0.532179\pi\)
−0.496856 + 0.867833i \(0.665512\pi\)
\(588\) 0 0
\(589\) 0.392615 0.0834530i 0.0161774 0.00343862i
\(590\) −1.67712 0.706193i −0.0690460 0.0290735i
\(591\) 0 0
\(592\) −3.08345 29.3370i −0.126729 1.20574i
\(593\) −29.3262 −1.20428 −0.602140 0.798390i \(-0.705685\pi\)
−0.602140 + 0.798390i \(0.705685\pi\)
\(594\) 0 0
\(595\) −10.6846 + 35.3118i −0.438026 + 1.44764i
\(596\) 12.6337 5.62488i 0.517496 0.230404i
\(597\) 0 0
\(598\) −1.30023 + 0.276373i −0.0531705 + 0.0113017i
\(599\) −2.03948 3.53249i −0.0833310 0.144334i 0.821348 0.570428i \(-0.193223\pi\)
−0.904679 + 0.426094i \(0.859889\pi\)
\(600\) 0 0
\(601\) −8.15219 + 14.1200i −0.332535 + 0.575967i −0.983008 0.183562i \(-0.941237\pi\)
0.650474 + 0.759529i \(0.274570\pi\)
\(602\) 0.651421 2.00487i 0.0265500 0.0817124i
\(603\) 0 0
\(604\) −7.51520 5.46011i −0.305789 0.222169i
\(605\) 11.7242 21.2958i 0.476658 0.865796i
\(606\) 0 0
\(607\) 9.93751 + 17.2123i 0.403351 + 0.698625i 0.994128 0.108210i \(-0.0345120\pi\)
−0.590777 + 0.806835i \(0.701179\pi\)
\(608\) 0.131107 + 0.0583728i 0.00531711 + 0.00236733i
\(609\) 0 0
\(610\) −1.61398 + 2.93162i −0.0653483 + 0.118698i
\(611\) 7.37976 22.7126i 0.298553 0.918852i
\(612\) 0 0
\(613\) 1.01670 + 3.12907i 0.0410639 + 0.126382i 0.969487 0.245143i \(-0.0788350\pi\)
−0.928423 + 0.371525i \(0.878835\pi\)
\(614\) 0.950406 + 1.05553i 0.0383552 + 0.0425978i
\(615\) 0 0
\(616\) 0.647308 0.718908i 0.0260808 0.0289656i
\(617\) −40.1863 17.8921i −1.61784 0.720308i −0.619912 0.784671i \(-0.712832\pi\)
−0.997927 + 0.0643626i \(0.979499\pi\)
\(618\) 0 0
\(619\) 1.18396 + 11.2646i 0.0475873 + 0.452763i 0.992207 + 0.124597i \(0.0397638\pi\)
−0.944620 + 0.328166i \(0.893570\pi\)
\(620\) −19.0559 + 14.4460i −0.765302 + 0.580166i
\(621\) 0 0
\(622\) −1.79186 1.30186i −0.0718469 0.0521998i
\(623\) 19.8160 + 22.0079i 0.793912 + 0.881728i
\(624\) 0 0
\(625\) −0.584094 + 24.9932i −0.0233638 + 0.999727i
\(626\) 0.600659 + 1.04037i 0.0240072 + 0.0415817i
\(627\) 0 0
\(628\) 30.7060 13.6712i 1.22530 0.545540i
\(629\) −24.8180 18.0313i −0.989559 0.718956i
\(630\) 0 0
\(631\) 19.7944 14.3815i 0.788005 0.572519i −0.119366 0.992850i \(-0.538086\pi\)
0.907371 + 0.420331i \(0.138086\pi\)
\(632\) −1.95730 + 3.39015i −0.0778573 + 0.134853i
\(633\) 0 0
\(634\) 2.55650 2.83928i 0.101532 0.112762i
\(635\) −4.74442 + 5.48974i −0.188277 + 0.217854i
\(636\) 0 0
\(637\) −18.2104 3.87074i −0.721523 0.153364i
\(638\) 0.118310 + 0.364121i 0.00468394 + 0.0144157i
\(639\) 0 0
\(640\) −11.3706 + 0.231293i −0.449464 + 0.00914267i
\(641\) 28.6247 + 6.08438i 1.13061 + 0.240318i 0.734978 0.678091i \(-0.237192\pi\)
0.395631 + 0.918409i \(0.370526\pi\)
\(642\) 0 0
\(643\) −3.57430 6.19087i −0.140957 0.244144i 0.786900 0.617080i \(-0.211685\pi\)
−0.927857 + 0.372936i \(0.878351\pi\)
\(644\) 32.6150 + 14.5211i 1.28521 + 0.572213i
\(645\) 0 0
\(646\) 0.0444105 0.0197728i 0.00174731 0.000777951i
\(647\) −25.5288 18.5478i −1.00364 0.729188i −0.0407758 0.999168i \(-0.512983\pi\)
−0.962866 + 0.269980i \(0.912983\pi\)
\(648\) 0 0
\(649\) −1.77260 −0.0695805
\(650\) 1.06087 + 1.08595i 0.0416107 + 0.0425945i
\(651\) 0 0
\(652\) 1.95767 0.416115i 0.0766681 0.0162963i
\(653\) −0.244296 + 2.32432i −0.00956003 + 0.0909576i −0.998262 0.0589403i \(-0.981228\pi\)
0.988701 + 0.149898i \(0.0478945\pi\)
\(654\) 0 0
\(655\) 13.1619 + 14.0330i 0.514277 + 0.548315i
\(656\) 14.6102 10.6149i 0.570431 0.414443i
\(657\) 0 0
\(658\) 7.11341 5.16819i 0.277309 0.201477i
\(659\) −41.8091 8.88679i −1.62865 0.346180i −0.699142 0.714983i \(-0.746435\pi\)
−0.929508 + 0.368802i \(0.879768\pi\)
\(660\) 0 0
\(661\) −5.59291 + 1.18881i −0.217539 + 0.0462393i −0.315392 0.948962i \(-0.602136\pi\)
0.0978528 + 0.995201i \(0.468803\pi\)
\(662\) 2.95903 3.28634i 0.115006 0.127727i
\(663\) 0 0
\(664\) −1.26175 1.40131i −0.0489652 0.0543814i
\(665\) −0.198213 + 0.655079i −0.00768637 + 0.0254029i
\(666\) 0 0
\(667\) −23.0187 + 16.7240i −0.891287 + 0.647558i
\(668\) −3.78106 + 6.54900i −0.146294 + 0.253388i
\(669\) 0 0
\(670\) −0.446636 + 5.28050i −0.0172550 + 0.204003i
\(671\) −0.340747 + 3.24199i −0.0131544 + 0.125156i
\(672\) 0 0
\(673\) −1.32261 1.46890i −0.0509827 0.0566221i 0.717114 0.696956i \(-0.245463\pi\)
−0.768097 + 0.640334i \(0.778796\pi\)
\(674\) 1.41815 0.0546250
\(675\) 0 0
\(676\) 18.9234 0.727824
\(677\) 6.94407 + 7.71217i 0.266882 + 0.296403i 0.861659 0.507488i \(-0.169426\pi\)
−0.594776 + 0.803891i \(0.702759\pi\)
\(678\) 0 0
\(679\) 4.56739 43.4558i 0.175280 1.66768i
\(680\) −3.81341 + 4.41247i −0.146237 + 0.169210i
\(681\) 0 0
\(682\) 0.159657 0.276534i 0.00611358 0.0105890i
\(683\) −19.2932 + 14.0174i −0.738235 + 0.536359i −0.892158 0.451724i \(-0.850809\pi\)
0.153923 + 0.988083i \(0.450809\pi\)
\(684\) 0 0
\(685\) −10.5186 7.32006i −0.401894 0.279685i
\(686\) −1.40268 1.55783i −0.0535545 0.0594783i
\(687\) 0 0
\(688\) −7.96526 + 8.84632i −0.303673 + 0.337263i
\(689\) −3.41927 + 0.726789i −0.130264 + 0.0276884i
\(690\) 0 0
\(691\) 1.00613 + 0.213859i 0.0382748 + 0.00813556i 0.227009 0.973893i \(-0.427105\pi\)
−0.188734 + 0.982028i \(0.560439\pi\)
\(692\) −35.4065 + 25.7243i −1.34595 + 0.977893i
\(693\) 0 0
\(694\) 4.67273 3.39494i 0.177374 0.128870i
\(695\) −36.4232 6.97095i −1.38161 0.264423i
\(696\) 0 0
\(697\) 1.96309 18.6775i 0.0743573 0.707462i
\(698\) 3.38314 0.719110i 0.128054 0.0272187i
\(699\) 0 0
\(700\) −5.90750 40.3435i −0.223283 1.52484i
\(701\) −14.7743 −0.558019 −0.279009 0.960288i \(-0.590006\pi\)
−0.279009 + 0.960288i \(0.590006\pi\)
\(702\) 0 0
\(703\) −0.460406 0.334504i −0.0173645 0.0126161i
\(704\) −2.40791 + 1.07207i −0.0907516 + 0.0404052i
\(705\) 0 0
\(706\) −2.96005 1.31790i −0.111403 0.0495999i
\(707\) 36.2017 + 62.7032i 1.36151 + 2.35820i
\(708\) 0 0
\(709\) 11.5131 + 2.44719i 0.432384 + 0.0919062i 0.418962 0.908004i \(-0.362394\pi\)
0.0134224 + 0.999910i \(0.495727\pi\)
\(710\) 1.43032 4.72709i 0.0536788 0.177405i
\(711\) 0 0
\(712\) 1.44664 + 4.45231i 0.0542152 + 0.166857i
\(713\) 23.2117 + 4.93379i 0.869283 + 0.184772i
\(714\) 0 0
\(715\) 1.36291 + 0.573886i 0.0509700 + 0.0214621i
\(716\) −19.3249 + 21.4624i −0.722204 + 0.802089i
\(717\) 0 0
\(718\) −0.249761 + 0.432599i −0.00932099 + 0.0161444i
\(719\) 37.9326 27.5596i 1.41465 1.02780i 0.422019 0.906587i \(-0.361321\pi\)
0.992626 0.121213i \(-0.0386785\pi\)
\(720\) 0 0
\(721\) 40.0084 + 29.0678i 1.48999 + 1.08254i
\(722\) −2.85372 + 1.27056i −0.106205 + 0.0472853i
\(723\) 0 0
\(724\) 16.9905 + 29.4285i 0.631449 + 1.09370i
\(725\) 30.1985 + 11.9988i 1.12155 + 0.445623i
\(726\) 0 0
\(727\) −21.0528 23.3815i −0.780806 0.867173i 0.213142 0.977021i \(-0.431630\pi\)
−0.993948 + 0.109848i \(0.964964\pi\)
\(728\) −4.03371 2.93066i −0.149499 0.108618i
\(729\) 0 0
\(730\) 4.94801 0.100649i 0.183134 0.00372518i
\(731\) 1.29399 + 12.3115i 0.0478600 + 0.455357i
\(732\) 0 0
\(733\) −41.4138 18.4386i −1.52965 0.681045i −0.542388 0.840128i \(-0.682480\pi\)
−0.987265 + 0.159083i \(0.949146\pi\)
\(734\) −0.799319 + 0.887734i −0.0295034 + 0.0327669i
\(735\) 0 0
\(736\) 5.67737 + 6.30535i 0.209271 + 0.232418i
\(737\) 1.59517 + 4.90942i 0.0587587 + 0.180841i
\(738\) 0 0
\(739\) 12.0961 37.2280i 0.444963 1.36945i −0.437562 0.899188i \(-0.644158\pi\)
0.882524 0.470267i \(-0.155842\pi\)
\(740\) 33.2993 + 6.37309i 1.22411 + 0.234279i
\(741\) 0 0
\(742\) −1.17576 0.523483i −0.0431636 0.0192177i
\(743\) −24.2958 42.0815i −0.891325 1.54382i −0.838288 0.545228i \(-0.816443\pi\)
−0.0530375 0.998593i \(-0.516890\pi\)
\(744\) 0 0
\(745\) 1.95500 + 15.5512i 0.0716258 + 0.569750i
\(746\) −1.40499 1.02078i −0.0514403 0.0373735i
\(747\) 0 0
\(748\) −0.871772 + 2.68304i −0.0318751 + 0.0981016i
\(749\) 17.5470 30.3923i 0.641154 1.11051i
\(750\) 0 0
\(751\) 9.62073 + 16.6636i 0.351066 + 0.608063i 0.986436 0.164144i \(-0.0524861\pi\)
−0.635371 + 0.772207i \(0.719153\pi\)
\(752\) −48.5662 + 10.3231i −1.77103 + 0.376443i
\(753\) 0 0
\(754\) 1.80267 0.802601i 0.0656494 0.0292290i
\(755\) 8.38982 6.36021i 0.305337 0.231472i
\(756\) 0 0
\(757\) −21.2374 −0.771886 −0.385943 0.922523i \(-0.626124\pi\)
−0.385943 + 0.922523i \(0.626124\pi\)
\(758\) −0.605923 5.76497i −0.0220081 0.209393i
\(759\) 0 0
\(760\) −0.0707436 + 0.0818570i −0.00256614 + 0.00296926i
\(761\) 33.1709 7.05068i 1.20244 0.255587i 0.437221 0.899354i \(-0.355963\pi\)
0.765221 + 0.643767i \(0.222629\pi\)
\(762\) 0 0
\(763\) 32.6460 + 6.93913i 1.18187 + 0.251213i
\(764\) 0.355085 1.09284i 0.0128465 0.0395375i
\(765\) 0 0
\(766\) 0.317141 + 0.976061i 0.0114588 + 0.0352665i
\(767\) 0.954975 + 9.08598i 0.0344822 + 0.328076i
\(768\) 0 0
\(769\) 32.2891 + 14.3760i 1.16437 + 0.518413i 0.895631 0.444799i \(-0.146725\pi\)
0.268744 + 0.963212i \(0.413391\pi\)
\(770\) 0.281767 + 0.465888i 0.0101542 + 0.0167894i
\(771\) 0 0
\(772\) −16.7489 + 7.45708i −0.602805 + 0.268386i
\(773\) −2.89307 + 8.90395i −0.104056 + 0.320253i −0.989508 0.144479i \(-0.953849\pi\)
0.885451 + 0.464732i \(0.153849\pi\)
\(774\) 0 0
\(775\) −9.41610 25.4133i −0.338236 0.912872i
\(776\) 3.45364 5.98188i 0.123978 0.214737i
\(777\) 0 0
\(778\) 0.489929 4.66136i 0.0175648 0.167118i
\(779\) 0.0364178 0.346492i 0.00130480 0.0124144i
\(780\) 0 0
\(781\) −0.502866 4.78445i −0.0179940 0.171201i
\(782\) 2.87405 0.102776
\(783\) 0 0
\(784\) 11.9610 + 36.8122i 0.427178 + 1.31472i
\(785\) 4.75161 + 37.7969i 0.169592 + 1.34903i
\(786\) 0 0