Properties

Label 300.2.m.a.61.1
Level $300$
Weight $2$
Character 300.61
Analytic conductor $2.396$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.m (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\Q(\zeta_{15})\)
Defining polynomial: \(x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 61.1
Root \(0.913545 + 0.406737i\) of defining polynomial
Character \(\chi\) \(=\) 300.61
Dual form 300.2.m.a.241.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.309017 - 0.951057i) q^{3} +(-1.49622 - 1.66172i) q^{5} -4.78339 q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(0.309017 - 0.951057i) q^{3} +(-1.49622 - 1.66172i) q^{5} -4.78339 q^{7} +(-0.809017 - 0.587785i) q^{9} +(-1.58268 + 1.14988i) q^{11} +(-0.873619 - 0.634721i) q^{13} +(-2.04275 + 0.909491i) q^{15} +(-1.17603 - 3.61946i) q^{17} +(1.31359 + 4.04280i) q^{19} +(-1.47815 + 4.54927i) q^{21} +(4.74346 - 3.44633i) q^{23} +(-0.522642 + 4.97261i) q^{25} +(-0.809017 + 0.587785i) q^{27} +(3.26015 - 10.0337i) q^{29} +(-1.33369 - 4.10468i) q^{31} +(0.604528 + 1.86055i) q^{33} +(7.15701 + 7.94866i) q^{35} +(-4.57890 - 3.32676i) q^{37} +(-0.873619 + 0.634721i) q^{39} +(-0.694596 - 0.504654i) q^{41} -10.8764 q^{43} +(0.233733 + 2.22382i) q^{45} +(0.927539 - 2.85467i) q^{47} +15.8808 q^{49} -3.80573 q^{51} +(1.30524 - 4.01711i) q^{53} +(4.27882 + 0.909491i) q^{55} +4.25085 q^{57} +(3.85916 + 2.80384i) q^{59} +(-2.93822 + 2.13474i) q^{61} +(3.86984 + 2.81160i) q^{63} +(0.252397 + 2.40140i) q^{65} +(2.14163 + 6.59126i) q^{67} +(-1.81184 - 5.57627i) q^{69} +(-3.70731 + 11.4099i) q^{71} +(13.7177 - 9.96647i) q^{73} +(4.56773 + 2.03368i) q^{75} +(7.57055 - 5.50033i) q^{77} +(-2.04587 + 6.29656i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-0.797847 - 2.45552i) q^{83} +(-4.25493 + 7.36976i) q^{85} +(-8.53519 - 6.20118i) q^{87} +(0.673699 - 0.489471i) q^{89} +(4.17886 + 3.03612i) q^{91} -4.31592 q^{93} +(4.75260 - 8.23174i) q^{95} +(-2.81730 + 8.67076i) q^{97} +1.95630 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{3} + 5q^{5} - 8q^{7} - 2q^{9} + O(q^{10}) \) \( 8q - 2q^{3} + 5q^{5} - 8q^{7} - 2q^{9} - 2q^{11} - 5q^{15} + 7q^{17} + 5q^{19} - 3q^{21} + 7q^{23} + 5q^{25} - 2q^{27} + 27q^{29} - 3q^{31} + 3q^{33} + 20q^{35} - 9q^{37} + 20q^{41} - 68q^{43} - 5q^{45} - 7q^{47} - 8q^{49} - 8q^{51} - 11q^{53} + 5q^{55} - 10q^{57} + 2q^{59} - 14q^{61} + 7q^{63} - 35q^{65} + 28q^{67} + 2q^{69} - 15q^{71} + 6q^{73} + 5q^{75} + 17q^{77} + 24q^{79} - 2q^{81} + 2q^{83} + 10q^{85} - 23q^{87} + 5q^{91} - 18q^{93} + 5q^{95} + 34q^{97} - 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\)

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 0
\(3\) 0.309017 0.951057i 0.178411 0.549093i
\(4\) 0 0
\(5\) −1.49622 1.66172i −0.669131 0.743145i
\(6\) 0 0
\(7\) −4.78339 −1.80795 −0.903975 0.427585i \(-0.859364\pi\)
−0.903975 + 0.427585i \(0.859364\pi\)
\(8\) 0 0
\(9\) −0.809017 0.587785i −0.269672 0.195928i
\(10\) 0 0
\(11\) −1.58268 + 1.14988i −0.477195 + 0.346702i −0.800239 0.599682i \(-0.795294\pi\)
0.323044 + 0.946384i \(0.395294\pi\)
\(12\) 0 0
\(13\) −0.873619 0.634721i −0.242298 0.176040i 0.460008 0.887915i \(-0.347846\pi\)
−0.702307 + 0.711875i \(0.747846\pi\)
\(14\) 0 0
\(15\) −2.04275 + 0.909491i −0.527436 + 0.234830i
\(16\) 0 0
\(17\) −1.17603 3.61946i −0.285230 0.877848i −0.986330 0.164785i \(-0.947307\pi\)
0.701099 0.713064i \(-0.252693\pi\)
\(18\) 0 0
\(19\) 1.31359 + 4.04280i 0.301357 + 0.927482i 0.981012 + 0.193949i \(0.0621298\pi\)
−0.679654 + 0.733533i \(0.737870\pi\)
\(20\) 0 0
\(21\) −1.47815 + 4.54927i −0.322558 + 0.992732i
\(22\) 0 0
\(23\) 4.74346 3.44633i 0.989080 0.718608i 0.0293604 0.999569i \(-0.490653\pi\)
0.959719 + 0.280960i \(0.0906530\pi\)
\(24\) 0 0
\(25\) −0.522642 + 4.97261i −0.104528 + 0.994522i
\(26\) 0 0
\(27\) −0.809017 + 0.587785i −0.155695 + 0.113119i
\(28\) 0 0
\(29\) 3.26015 10.0337i 0.605395 1.86322i 0.111345 0.993782i \(-0.464484\pi\)
0.494050 0.869433i \(-0.335516\pi\)
\(30\) 0 0
\(31\) −1.33369 4.10468i −0.239538 0.737223i −0.996487 0.0837487i \(-0.973311\pi\)
0.756949 0.653474i \(-0.226689\pi\)
\(32\) 0 0
\(33\) 0.604528 + 1.86055i 0.105235 + 0.323880i
\(34\) 0 0
\(35\) 7.15701 + 7.94866i 1.20975 + 1.34357i
\(36\) 0 0
\(37\) −4.57890 3.32676i −0.752766 0.546917i 0.143917 0.989590i \(-0.454030\pi\)
−0.896683 + 0.442673i \(0.854030\pi\)
\(38\) 0 0
\(39\) −0.873619 + 0.634721i −0.139891 + 0.101637i
\(40\) 0 0
\(41\) −0.694596 0.504654i −0.108478 0.0788137i 0.532224 0.846604i \(-0.321356\pi\)
−0.640702 + 0.767790i \(0.721356\pi\)
\(42\) 0 0
\(43\) −10.8764 −1.65864 −0.829321 0.558773i \(-0.811272\pi\)
−0.829321 + 0.558773i \(0.811272\pi\)
\(44\) 0 0
\(45\) 0.233733 + 2.22382i 0.0348428 + 0.331507i
\(46\) 0 0
\(47\) 0.927539 2.85467i 0.135295 0.416397i −0.860340 0.509720i \(-0.829749\pi\)
0.995636 + 0.0933233i \(0.0297490\pi\)
\(48\) 0 0
\(49\) 15.8808 2.26868
\(50\) 0 0
\(51\) −3.80573 −0.532908
\(52\) 0 0
\(53\) 1.30524 4.01711i 0.179288 0.551793i −0.820515 0.571625i \(-0.806313\pi\)
0.999803 + 0.0198323i \(0.00631324\pi\)
\(54\) 0 0
\(55\) 4.27882 + 0.909491i 0.576956 + 0.122636i
\(56\) 0 0
\(57\) 4.25085 0.563039
\(58\) 0 0
\(59\) 3.85916 + 2.80384i 0.502420 + 0.365029i 0.809940 0.586512i \(-0.199499\pi\)
−0.307521 + 0.951541i \(0.599499\pi\)
\(60\) 0 0
\(61\) −2.93822 + 2.13474i −0.376201 + 0.273326i −0.759777 0.650183i \(-0.774692\pi\)
0.383577 + 0.923509i \(0.374692\pi\)
\(62\) 0 0
\(63\) 3.86984 + 2.81160i 0.487554 + 0.354229i
\(64\) 0 0
\(65\) 0.252397 + 2.40140i 0.0313060 + 0.297857i
\(66\) 0 0
\(67\) 2.14163 + 6.59126i 0.261642 + 0.805251i 0.992448 + 0.122666i \(0.0391444\pi\)
−0.730806 + 0.682585i \(0.760856\pi\)
\(68\) 0 0
\(69\) −1.81184 5.57627i −0.218120 0.671304i
\(70\) 0 0
\(71\) −3.70731 + 11.4099i −0.439977 + 1.35411i 0.447922 + 0.894072i \(0.352164\pi\)
−0.887899 + 0.460038i \(0.847836\pi\)
\(72\) 0 0
\(73\) 13.7177 9.96647i 1.60553 1.16649i 0.729836 0.683622i \(-0.239596\pi\)
0.875695 0.482864i \(-0.160404\pi\)
\(74\) 0 0
\(75\) 4.56773 + 2.03368i 0.527436 + 0.234830i
\(76\) 0 0
\(77\) 7.57055 5.50033i 0.862744 0.626820i
\(78\) 0 0
\(79\) −2.04587 + 6.29656i −0.230179 + 0.708418i 0.767546 + 0.640994i \(0.221478\pi\)
−0.997724 + 0.0674234i \(0.978522\pi\)
\(80\) 0 0
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) 0 0
\(83\) −0.797847 2.45552i −0.0875751 0.269528i 0.897673 0.440663i \(-0.145257\pi\)
−0.985248 + 0.171135i \(0.945257\pi\)
\(84\) 0 0
\(85\) −4.25493 + 7.36976i −0.461512 + 0.799362i
\(86\) 0 0
\(87\) −8.53519 6.20118i −0.915069 0.664836i
\(88\) 0 0
\(89\) 0.673699 0.489471i 0.0714120 0.0518838i −0.551507 0.834171i \(-0.685947\pi\)
0.622918 + 0.782287i \(0.285947\pi\)
\(90\) 0 0
\(91\) 4.17886 + 3.03612i 0.438063 + 0.318272i
\(92\) 0 0
\(93\) −4.31592 −0.447540
\(94\) 0 0
\(95\) 4.75260 8.23174i 0.487606 0.844559i
\(96\) 0 0
\(97\) −2.81730 + 8.67076i −0.286054 + 0.880382i 0.700027 + 0.714116i \(0.253171\pi\)
−0.986081 + 0.166266i \(0.946829\pi\)
\(98\) 0 0
\(99\) 1.95630 0.196615
\(100\) 0 0
\(101\) 1.49541 0.148799 0.0743994 0.997229i \(-0.476296\pi\)
0.0743994 + 0.997229i \(0.476296\pi\)
\(102\) 0 0
\(103\) 3.35664 10.3307i 0.330739 1.01791i −0.638044 0.770000i \(-0.720256\pi\)
0.968783 0.247911i \(-0.0797439\pi\)
\(104\) 0 0
\(105\) 9.77126 4.35045i 0.953577 0.424560i
\(106\) 0 0
\(107\) −19.8390 −1.91791 −0.958954 0.283563i \(-0.908484\pi\)
−0.958954 + 0.283563i \(0.908484\pi\)
\(108\) 0 0
\(109\) 1.89626 + 1.37771i 0.181629 + 0.131961i 0.674885 0.737923i \(-0.264193\pi\)
−0.493256 + 0.869884i \(0.664193\pi\)
\(110\) 0 0
\(111\) −4.57890 + 3.32676i −0.434610 + 0.315762i
\(112\) 0 0
\(113\) 2.61192 + 1.89767i 0.245709 + 0.178518i 0.703823 0.710376i \(-0.251475\pi\)
−0.458114 + 0.888893i \(0.651475\pi\)
\(114\) 0 0
\(115\) −12.8241 2.72585i −1.19585 0.254187i
\(116\) 0 0
\(117\) 0.333693 + 1.02700i 0.0308499 + 0.0949463i
\(118\) 0 0
\(119\) 5.62543 + 17.3133i 0.515682 + 1.58711i
\(120\) 0 0
\(121\) −2.21655 + 6.82184i −0.201505 + 0.620167i
\(122\) 0 0
\(123\) −0.694596 + 0.504654i −0.0626296 + 0.0455031i
\(124\) 0 0
\(125\) 9.04508 6.57164i 0.809017 0.587785i
\(126\) 0 0
\(127\) −5.97565 + 4.34156i −0.530253 + 0.385251i −0.820452 0.571715i \(-0.806278\pi\)
0.290199 + 0.956966i \(0.406278\pi\)
\(128\) 0 0
\(129\) −3.36101 + 10.3441i −0.295920 + 0.910748i
\(130\) 0 0
\(131\) −5.21740 16.0575i −0.455847 1.40295i −0.870138 0.492808i \(-0.835971\pi\)
0.414292 0.910144i \(-0.364029\pi\)
\(132\) 0 0
\(133\) −6.28339 19.3383i −0.544839 1.67684i
\(134\) 0 0
\(135\) 2.18720 + 0.464905i 0.188245 + 0.0400126i
\(136\) 0 0
\(137\) −0.679023 0.493339i −0.0580128 0.0421488i 0.558401 0.829571i \(-0.311415\pi\)
−0.616414 + 0.787422i \(0.711415\pi\)
\(138\) 0 0
\(139\) 9.02701 6.55851i 0.765661 0.556285i −0.134980 0.990848i \(-0.543097\pi\)
0.900641 + 0.434563i \(0.143097\pi\)
\(140\) 0 0
\(141\) −2.42833 1.76428i −0.204502 0.148580i
\(142\) 0 0
\(143\) 2.11251 0.176657
\(144\) 0 0
\(145\) −21.5512 + 9.59520i −1.78973 + 0.796838i
\(146\) 0 0
\(147\) 4.90743 15.1035i 0.404758 1.24572i
\(148\) 0 0
\(149\) −22.0277 −1.80458 −0.902288 0.431134i \(-0.858114\pi\)
−0.902288 + 0.431134i \(0.858114\pi\)
\(150\) 0 0
\(151\) 11.7890 0.959378 0.479689 0.877439i \(-0.340750\pi\)
0.479689 + 0.877439i \(0.340750\pi\)
\(152\) 0 0
\(153\) −1.17603 + 3.61946i −0.0950767 + 0.292616i
\(154\) 0 0
\(155\) −4.82535 + 8.35774i −0.387581 + 0.671310i
\(156\) 0 0
\(157\) 11.2769 0.899994 0.449997 0.893030i \(-0.351425\pi\)
0.449997 + 0.893030i \(0.351425\pi\)
\(158\) 0 0
\(159\) −3.41716 2.48271i −0.270998 0.196892i
\(160\) 0 0
\(161\) −22.6898 + 16.4851i −1.78821 + 1.29921i
\(162\) 0 0
\(163\) −8.00627 5.81690i −0.627100 0.455615i 0.228295 0.973592i \(-0.426685\pi\)
−0.855394 + 0.517978i \(0.826685\pi\)
\(164\) 0 0
\(165\) 2.18720 3.78835i 0.170274 0.294923i
\(166\) 0 0
\(167\) −2.32246 7.14780i −0.179717 0.553113i 0.820100 0.572220i \(-0.193918\pi\)
−0.999817 + 0.0191070i \(0.993918\pi\)
\(168\) 0 0
\(169\) −3.65688 11.2547i −0.281299 0.865748i
\(170\) 0 0
\(171\) 1.31359 4.04280i 0.100452 0.309161i
\(172\) 0 0
\(173\) −9.93332 + 7.21698i −0.755217 + 0.548697i −0.897439 0.441138i \(-0.854575\pi\)
0.142223 + 0.989835i \(0.454575\pi\)
\(174\) 0 0
\(175\) 2.50000 23.7859i 0.188982 1.79805i
\(176\) 0 0
\(177\) 3.85916 2.80384i 0.290072 0.210750i
\(178\) 0 0
\(179\) 4.69982 14.4646i 0.351281 1.08113i −0.606854 0.794813i \(-0.707569\pi\)
0.958135 0.286318i \(-0.0924314\pi\)
\(180\) 0 0
\(181\) −6.45087 19.8537i −0.479490 1.47572i −0.839806 0.542887i \(-0.817331\pi\)
0.360316 0.932830i \(-0.382669\pi\)
\(182\) 0 0
\(183\) 1.12230 + 3.45409i 0.0829629 + 0.255333i
\(184\) 0 0
\(185\) 1.32289 + 12.5864i 0.0972606 + 0.925373i
\(186\) 0 0
\(187\) 6.02323 + 4.37613i 0.440462 + 0.320015i
\(188\) 0 0
\(189\) 3.86984 2.81160i 0.281489 0.204514i
\(190\) 0 0
\(191\) 4.24803 + 3.08637i 0.307377 + 0.223322i 0.730770 0.682624i \(-0.239161\pi\)
−0.423393 + 0.905946i \(0.639161\pi\)
\(192\) 0 0
\(193\) 7.94565 0.571940 0.285970 0.958239i \(-0.407684\pi\)
0.285970 + 0.958239i \(0.407684\pi\)
\(194\) 0 0
\(195\) 2.36186 + 0.502029i 0.169136 + 0.0359510i
\(196\) 0 0
\(197\) −4.01905 + 12.3694i −0.286345 + 0.881281i 0.699647 + 0.714489i \(0.253341\pi\)
−0.985992 + 0.166792i \(0.946659\pi\)
\(198\) 0 0
\(199\) 1.06434 0.0754490 0.0377245 0.999288i \(-0.487989\pi\)
0.0377245 + 0.999288i \(0.487989\pi\)
\(200\) 0 0
\(201\) 6.93046 0.488837
\(202\) 0 0
\(203\) −15.5946 + 47.9952i −1.09452 + 3.36860i
\(204\) 0 0
\(205\) 0.200676 + 1.90930i 0.0140158 + 0.133351i
\(206\) 0 0
\(207\) −5.86324 −0.407523
\(208\) 0 0
\(209\) −6.72772 4.88798i −0.465366 0.338108i
\(210\) 0 0
\(211\) 16.5791 12.0454i 1.14135 0.829239i 0.154043 0.988064i \(-0.450771\pi\)
0.987307 + 0.158825i \(0.0507707\pi\)
\(212\) 0 0
\(213\) 9.70587 + 7.05173i 0.665035 + 0.483176i
\(214\) 0 0
\(215\) 16.2736 + 18.0736i 1.10985 + 1.23261i
\(216\) 0 0
\(217\) 6.37957 + 19.6343i 0.433073 + 1.33286i
\(218\) 0 0
\(219\) −5.23968 16.1261i −0.354065 1.08970i
\(220\) 0 0
\(221\) −1.26994 + 3.90848i −0.0854257 + 0.262913i
\(222\) 0 0
\(223\) −8.34266 + 6.06130i −0.558666 + 0.405895i −0.830971 0.556316i \(-0.812214\pi\)
0.272304 + 0.962211i \(0.412214\pi\)
\(224\) 0 0
\(225\) 3.34565 3.71572i 0.223044 0.247715i
\(226\) 0 0
\(227\) 14.6763 10.6630i 0.974100 0.707725i 0.0177176 0.999843i \(-0.494360\pi\)
0.956382 + 0.292118i \(0.0943600\pi\)
\(228\) 0 0
\(229\) −3.00311 + 9.24263i −0.198451 + 0.610770i 0.801468 + 0.598038i \(0.204053\pi\)
−0.999919 + 0.0127320i \(0.995947\pi\)
\(230\) 0 0
\(231\) −2.89169 8.89972i −0.190259 0.585558i
\(232\) 0 0
\(233\) −6.86586 21.1310i −0.449798 1.38433i −0.877136 0.480243i \(-0.840549\pi\)
0.427338 0.904092i \(-0.359451\pi\)
\(234\) 0 0
\(235\) −6.13148 + 2.72991i −0.399973 + 0.178080i
\(236\) 0 0
\(237\) 5.35617 + 3.89149i 0.347921 + 0.252779i
\(238\) 0 0
\(239\) −12.8871 + 9.36300i −0.833595 + 0.605642i −0.920574 0.390568i \(-0.872279\pi\)
0.0869793 + 0.996210i \(0.472279\pi\)
\(240\) 0 0
\(241\) 3.98964 + 2.89864i 0.256995 + 0.186718i 0.708821 0.705388i \(-0.249227\pi\)
−0.451826 + 0.892106i \(0.649227\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −23.7612 26.3895i −1.51805 1.68596i
\(246\) 0 0
\(247\) 1.41848 4.36563i 0.0902556 0.277778i
\(248\) 0 0
\(249\) −2.58189 −0.163620
\(250\) 0 0
\(251\) 15.4351 0.974252 0.487126 0.873332i \(-0.338045\pi\)
0.487126 + 0.873332i \(0.338045\pi\)
\(252\) 0 0
\(253\) −3.54449 + 10.9088i −0.222840 + 0.685832i
\(254\) 0 0
\(255\) 5.69421 + 6.32406i 0.356585 + 0.396028i
\(256\) 0 0
\(257\) 21.1828 1.32134 0.660672 0.750674i \(-0.270271\pi\)
0.660672 + 0.750674i \(0.270271\pi\)
\(258\) 0 0
\(259\) 21.9026 + 15.9132i 1.36096 + 0.988798i
\(260\) 0 0
\(261\) −8.53519 + 6.20118i −0.528315 + 0.383843i
\(262\) 0 0
\(263\) 16.9298 + 12.3002i 1.04394 + 0.758465i 0.971050 0.238876i \(-0.0767788\pi\)
0.0728867 + 0.997340i \(0.476779\pi\)
\(264\) 0 0
\(265\) −8.62825 + 3.84154i −0.530029 + 0.235984i
\(266\) 0 0
\(267\) −0.257330 0.791981i −0.0157483 0.0484684i
\(268\) 0 0
\(269\) −4.25938 13.1090i −0.259699 0.799272i −0.992867 0.119225i \(-0.961959\pi\)
0.733168 0.680048i \(-0.238041\pi\)
\(270\) 0 0
\(271\) 3.25998 10.0332i 0.198029 0.609472i −0.801898 0.597460i \(-0.796177\pi\)
0.999928 0.0120115i \(-0.00382346\pi\)
\(272\) 0 0
\(273\) 4.17886 3.03612i 0.252916 0.183754i
\(274\) 0 0
\(275\) −4.89074 8.47101i −0.294923 0.510821i
\(276\) 0 0
\(277\) −14.5317 + 10.5579i −0.873127 + 0.634364i −0.931424 0.363935i \(-0.881433\pi\)
0.0582969 + 0.998299i \(0.481433\pi\)
\(278\) 0 0
\(279\) −1.33369 + 4.10468i −0.0798461 + 0.245741i
\(280\) 0 0
\(281\) −0.286375 0.881371i −0.0170837 0.0525782i 0.942151 0.335188i \(-0.108800\pi\)
−0.959235 + 0.282610i \(0.908800\pi\)
\(282\) 0 0
\(283\) −2.03256 6.25556i −0.120823 0.371855i 0.872294 0.488982i \(-0.162632\pi\)
−0.993117 + 0.117127i \(0.962632\pi\)
\(284\) 0 0
\(285\) −6.36022 7.06374i −0.376747 0.418420i
\(286\) 0 0
\(287\) 3.32252 + 2.41395i 0.196122 + 0.142491i
\(288\) 0 0
\(289\) 2.03585 1.47913i 0.119756 0.0870076i
\(290\) 0 0
\(291\) 7.37579 + 5.35882i 0.432376 + 0.314140i
\(292\) 0 0
\(293\) 25.6208 1.49678 0.748391 0.663257i \(-0.230827\pi\)
0.748391 + 0.663257i \(0.230827\pi\)
\(294\) 0 0
\(295\) −1.11495 10.6080i −0.0649148 0.617623i
\(296\) 0 0
\(297\) 0.604528 1.86055i 0.0350783 0.107960i
\(298\) 0 0
\(299\) −6.33143 −0.366156
\(300\) 0 0
\(301\) 52.0262 2.99874
\(302\) 0 0
\(303\) 0.462107 1.42222i 0.0265474 0.0817044i
\(304\) 0 0
\(305\) 7.94358 + 1.68846i 0.454848 + 0.0966809i
\(306\) 0 0
\(307\) −6.18420 −0.352951 −0.176476 0.984305i \(-0.556470\pi\)
−0.176476 + 0.984305i \(0.556470\pi\)
\(308\) 0 0
\(309\) −8.78779 6.38470i −0.499920 0.363213i
\(310\) 0 0
\(311\) 19.6091 14.2468i 1.11193 0.807864i 0.128963 0.991649i \(-0.458835\pi\)
0.982966 + 0.183785i \(0.0588351\pi\)
\(312\) 0 0
\(313\) 24.2392 + 17.6108i 1.37008 + 0.995420i 0.997731 + 0.0673262i \(0.0214468\pi\)
0.372347 + 0.928094i \(0.378553\pi\)
\(314\) 0 0
\(315\) −1.11803 10.6374i −0.0629941 0.599349i
\(316\) 0 0
\(317\) 0.761007 + 2.34214i 0.0427424 + 0.131548i 0.970151 0.242503i \(-0.0779685\pi\)
−0.927408 + 0.374051i \(0.877969\pi\)
\(318\) 0 0
\(319\) 6.37782 + 19.6289i 0.357090 + 1.09901i
\(320\) 0 0
\(321\) −6.13058 + 18.8680i −0.342176 + 1.05311i
\(322\) 0 0
\(323\) 13.0879 9.50894i 0.728232 0.529092i
\(324\) 0 0
\(325\) 3.61281 4.01243i 0.200403 0.222570i
\(326\) 0 0
\(327\) 1.89626 1.37771i 0.104863 0.0761878i
\(328\) 0 0
\(329\) −4.43678 + 13.6550i −0.244607 + 0.752824i
\(330\) 0 0
\(331\) −8.27755 25.4757i −0.454975 1.40027i −0.871164 0.490992i \(-0.836634\pi\)
0.416189 0.909278i \(-0.363366\pi\)
\(332\) 0 0
\(333\) 1.74898 + 5.38282i 0.0958437 + 0.294977i
\(334\) 0 0
\(335\) 7.74850 13.4208i 0.423346 0.733256i
\(336\) 0 0
\(337\) −1.97124 1.43219i −0.107381 0.0780165i 0.532799 0.846242i \(-0.321140\pi\)
−0.640180 + 0.768225i \(0.721140\pi\)
\(338\) 0 0
\(339\) 2.61192 1.89767i 0.141860 0.103067i
\(340\) 0 0
\(341\) 6.83070 + 4.96280i 0.369903 + 0.268751i
\(342\) 0 0
\(343\) −42.4802 −2.29372
\(344\) 0 0
\(345\) −6.55530 + 11.3541i −0.352925 + 0.611285i
\(346\) 0 0
\(347\) −2.36011 + 7.26368i −0.126698 + 0.389935i −0.994207 0.107487i \(-0.965720\pi\)
0.867509 + 0.497421i \(0.165720\pi\)
\(348\) 0 0
\(349\) −20.2283 −1.08280 −0.541398 0.840766i \(-0.682105\pi\)
−0.541398 + 0.840766i \(0.682105\pi\)
\(350\) 0 0
\(351\) 1.07985 0.0576383
\(352\) 0 0
\(353\) −8.74279 + 26.9075i −0.465331 + 1.43214i 0.393234 + 0.919439i \(0.371356\pi\)
−0.858565 + 0.512705i \(0.828644\pi\)
\(354\) 0 0
\(355\) 24.5071 10.9113i 1.30070 0.579110i
\(356\) 0 0
\(357\) 18.2043 0.963472
\(358\) 0 0
\(359\) −18.4713 13.4202i −0.974880 0.708292i −0.0183215 0.999832i \(-0.505832\pi\)
−0.956559 + 0.291540i \(0.905832\pi\)
\(360\) 0 0
\(361\) 0.752597 0.546793i 0.0396103 0.0287786i
\(362\) 0 0
\(363\) 5.80301 + 4.21613i 0.304579 + 0.221289i
\(364\) 0 0
\(365\) −37.0862 7.88291i −1.94118 0.412610i
\(366\) 0 0
\(367\) −0.778091 2.39472i −0.0406160 0.125003i 0.928693 0.370851i \(-0.120934\pi\)
−0.969309 + 0.245847i \(0.920934\pi\)
\(368\) 0 0
\(369\) 0.265312 + 0.816547i 0.0138116 + 0.0425077i
\(370\) 0 0
\(371\) −6.24346 + 19.2154i −0.324144 + 0.997614i
\(372\) 0 0
\(373\) −4.57416 + 3.32332i −0.236841 + 0.172075i −0.699875 0.714265i \(-0.746761\pi\)
0.463034 + 0.886341i \(0.346761\pi\)
\(374\) 0 0
\(375\) −3.45492 10.6331i −0.178411 0.549093i
\(376\) 0 0
\(377\) −9.21675 + 6.69636i −0.474687 + 0.344880i
\(378\) 0 0
\(379\) −4.44729 + 13.6874i −0.228442 + 0.703073i 0.769482 + 0.638669i \(0.220515\pi\)
−0.997924 + 0.0644039i \(0.979485\pi\)
\(380\) 0 0
\(381\) 2.28249 + 7.02479i 0.116936 + 0.359891i
\(382\) 0 0
\(383\) −2.53391 7.79859i −0.129477 0.398489i 0.865213 0.501404i \(-0.167183\pi\)
−0.994690 + 0.102915i \(0.967183\pi\)
\(384\) 0 0
\(385\) −20.4672 4.35045i −1.04311 0.221719i
\(386\) 0 0
\(387\) 8.79923 + 6.39301i 0.447290 + 0.324975i
\(388\) 0 0
\(389\) −3.82719 + 2.78062i −0.194046 + 0.140983i −0.680566 0.732687i \(-0.738266\pi\)
0.486520 + 0.873670i \(0.338266\pi\)
\(390\) 0 0
\(391\) −18.0523 13.1158i −0.912945 0.663293i
\(392\) 0 0
\(393\) −16.8839 −0.851679
\(394\) 0 0
\(395\) 13.5242 6.02137i 0.680477 0.302968i
\(396\) 0 0
\(397\) −2.34336 + 7.21211i −0.117610 + 0.361965i −0.992482 0.122387i \(-0.960945\pi\)
0.874873 + 0.484353i \(0.160945\pi\)
\(398\) 0 0
\(399\) −20.3335 −1.01795
\(400\) 0 0
\(401\) 10.1128 0.505011 0.252506 0.967595i \(-0.418745\pi\)
0.252506 + 0.967595i \(0.418745\pi\)
\(402\) 0 0
\(403\) −1.44019 + 4.43245i −0.0717411 + 0.220796i
\(404\) 0 0
\(405\) 1.11803 1.93649i 0.0555556 0.0962250i
\(406\) 0 0
\(407\) 11.0723 0.548833
\(408\) 0 0
\(409\) −3.21927 2.33894i −0.159183 0.115653i 0.505342 0.862919i \(-0.331366\pi\)
−0.664525 + 0.747266i \(0.731366\pi\)
\(410\) 0 0
\(411\) −0.679023 + 0.493339i −0.0334937 + 0.0243346i
\(412\) 0 0
\(413\) −18.4598 13.4119i −0.908350 0.659955i
\(414\) 0 0
\(415\) −2.88664 + 4.99980i −0.141699 + 0.245431i
\(416\) 0 0
\(417\) −3.44801 10.6119i −0.168850 0.519666i
\(418\) 0 0
\(419\) 0.555164 + 1.70862i 0.0271215 + 0.0834714i 0.963701 0.266984i \(-0.0860269\pi\)
−0.936580 + 0.350455i \(0.886027\pi\)
\(420\) 0 0
\(421\) 4.84234 14.9032i 0.236001 0.726337i −0.760986 0.648769i \(-0.775284\pi\)
0.996987 0.0775686i \(-0.0247157\pi\)
\(422\) 0 0
\(423\) −2.42833 + 1.76428i −0.118069 + 0.0857824i
\(424\) 0 0
\(425\) 18.6128 3.95628i 0.902854 0.191908i
\(426\) 0 0
\(427\) 14.0546 10.2113i 0.680152 0.494159i
\(428\) 0 0
\(429\) 0.652802 2.00912i 0.0315176 0.0970011i
\(430\) 0 0
\(431\) −11.9206 36.6880i −0.574197 1.76720i −0.638896 0.769293i \(-0.720609\pi\)
0.0646985 0.997905i \(-0.479391\pi\)
\(432\) 0 0
\(433\) 2.83353 + 8.72070i 0.136171 + 0.419090i 0.995770 0.0918780i \(-0.0292870\pi\)
−0.859600 + 0.510968i \(0.829287\pi\)
\(434\) 0 0
\(435\) 2.46590 + 23.4615i 0.118231 + 1.12489i
\(436\) 0 0
\(437\) 20.1637 + 14.6498i 0.964563 + 0.700796i
\(438\) 0 0
\(439\) −14.3101 + 10.3969i −0.682982 + 0.496216i −0.874346 0.485304i \(-0.838709\pi\)
0.191363 + 0.981519i \(0.438709\pi\)
\(440\) 0 0
\(441\) −12.8478 9.33449i −0.611801 0.444500i
\(442\) 0 0
\(443\) −18.6673 −0.886912 −0.443456 0.896296i \(-0.646248\pi\)
−0.443456 + 0.896296i \(0.646248\pi\)
\(444\) 0 0
\(445\) −1.82137 0.387144i −0.0863411 0.0183524i
\(446\) 0 0
\(447\) −6.80692 + 20.9495i −0.321956 + 0.990880i
\(448\) 0 0
\(449\) 41.2111 1.94487 0.972436 0.233171i \(-0.0749102\pi\)
0.972436 + 0.233171i \(0.0749102\pi\)
\(450\) 0 0
\(451\) 1.67961 0.0790899
\(452\) 0 0
\(453\) 3.64301 11.2120i 0.171164 0.526787i
\(454\) 0 0
\(455\) −1.20731 11.4868i −0.0565997 0.538510i
\(456\) 0 0
\(457\) −5.56092 −0.260129 −0.130064 0.991506i \(-0.541518\pi\)
−0.130064 + 0.991506i \(0.541518\pi\)
\(458\) 0 0
\(459\) 3.07890 + 2.23695i 0.143711 + 0.104412i
\(460\) 0 0
\(461\) −17.1210 + 12.4391i −0.797404 + 0.579348i −0.910151 0.414276i \(-0.864035\pi\)
0.112747 + 0.993624i \(0.464035\pi\)
\(462\) 0 0
\(463\) 6.26637 + 4.55278i 0.291223 + 0.211586i 0.723798 0.690012i \(-0.242395\pi\)
−0.432575 + 0.901598i \(0.642395\pi\)
\(464\) 0 0
\(465\) 6.45757 + 7.17186i 0.299463 + 0.332587i
\(466\) 0 0
\(467\) −0.751544 2.31301i −0.0347773 0.107034i 0.932161 0.362044i \(-0.117921\pi\)
−0.966938 + 0.255011i \(0.917921\pi\)
\(468\) 0 0
\(469\) −10.2442 31.5286i −0.473036 1.45585i
\(470\) 0 0
\(471\) 3.48475 10.7250i 0.160569 0.494180i
\(472\) 0 0
\(473\) 17.2139 12.5066i 0.791495 0.575055i
\(474\) 0 0
\(475\) −20.7898 + 4.41901i −0.953902 + 0.202758i
\(476\) 0 0
\(477\) −3.41716 + 2.48271i −0.156461 + 0.113676i
\(478\) 0 0
\(479\) 10.5465 32.4587i 0.481880 1.48308i −0.354569 0.935030i \(-0.615372\pi\)
0.836449 0.548045i \(-0.184628\pi\)
\(480\) 0 0
\(481\) 1.88864 + 5.81265i 0.0861148 + 0.265034i
\(482\) 0 0
\(483\) 8.66673 + 26.6735i 0.394350 + 1.21368i
\(484\) 0 0
\(485\) 18.6237 8.29181i 0.845659 0.376512i
\(486\) 0 0
\(487\) 25.9175 + 18.8302i 1.17443 + 0.853277i 0.991533 0.129854i \(-0.0414509\pi\)
0.182902 + 0.983131i \(0.441451\pi\)
\(488\) 0 0
\(489\) −8.00627 + 5.81690i −0.362056 + 0.263049i
\(490\) 0 0
\(491\) −23.7860 17.2815i −1.07345 0.779904i −0.0969178 0.995292i \(-0.530898\pi\)
−0.976529 + 0.215388i \(0.930898\pi\)
\(492\) 0 0
\(493\) −40.1507 −1.80830
\(494\) 0 0
\(495\) −2.92705 3.25082i −0.131561 0.146113i
\(496\) 0 0
\(497\) 17.7335 54.5781i 0.795456 2.44816i
\(498\) 0 0
\(499\) −9.04298 −0.404819 −0.202410 0.979301i \(-0.564877\pi\)
−0.202410 + 0.979301i \(0.564877\pi\)
\(500\) 0 0
\(501\) −7.51564 −0.335774
\(502\) 0 0
\(503\) 0.950848 2.92641i 0.0423962 0.130482i −0.927618 0.373530i \(-0.878147\pi\)
0.970014 + 0.243048i \(0.0781473\pi\)
\(504\) 0 0
\(505\) −2.23747 2.48496i −0.0995659 0.110579i
\(506\) 0 0
\(507\) −11.8339 −0.525563
\(508\) 0 0
\(509\) −21.2410 15.4325i −0.941491 0.684033i 0.00728833 0.999973i \(-0.497680\pi\)
−0.948779 + 0.315940i \(0.897680\pi\)
\(510\) 0 0
\(511\) −65.6169 + 47.6735i −2.90272 + 2.10895i
\(512\) 0 0
\(513\) −3.43901 2.49859i −0.151836 0.110315i
\(514\) 0 0
\(515\) −22.1890 + 9.87917i −0.977763 + 0.435328i
\(516\) 0 0
\(517\) 1.81454 + 5.58458i 0.0798034 + 0.245610i
\(518\) 0 0
\(519\) 3.79419 + 11.6773i 0.166547 + 0.512578i
\(520\) 0 0
\(521\) 6.41127 19.7319i 0.280883 0.864469i −0.706720 0.707494i \(-0.749826\pi\)
0.987603 0.156975i \(-0.0501742\pi\)
\(522\) 0 0
\(523\) 18.1623 13.1957i 0.794182 0.577007i −0.115020 0.993363i \(-0.536693\pi\)
0.909202 + 0.416356i \(0.136693\pi\)
\(524\) 0 0
\(525\) −21.8492 9.72789i −0.953577 0.424560i
\(526\) 0 0
\(527\) −13.2883 + 9.65450i −0.578846 + 0.420557i
\(528\) 0 0
\(529\) 3.51586 10.8207i 0.152864 0.470466i
\(530\) 0 0
\(531\) −1.47407 4.53671i −0.0639691 0.196877i
\(532\) 0 0
\(533\) 0.286498 + 0.881750i 0.0124096 + 0.0381928i
\(534\) 0 0
\(535\) 29.6835 + 32.9669i 1.28333 + 1.42528i
\(536\) 0 0
\(537\) −12.3043 8.93959i −0.530969 0.385772i
\(538\) 0 0
\(539\) −25.1341 + 18.2610i −1.08260 + 0.786558i
\(540\) 0 0
\(541\) 20.4954 + 14.8908i 0.881166 + 0.640205i 0.933560 0.358422i \(-0.116685\pi\)
−0.0523936 + 0.998627i \(0.516685\pi\)
\(542\) 0 0
\(543\) −20.8755 −0.895852
\(544\) 0 0
\(545\) −0.547848 5.21243i −0.0234672 0.223276i
\(546\) 0 0
\(547\) −3.64866 + 11.2294i −0.156005 + 0.480135i −0.998261 0.0589426i \(-0.981227\pi\)
0.842256 + 0.539078i \(0.181227\pi\)
\(548\) 0 0
\(549\) 3.63184 0.155003
\(550\) 0 0
\(551\) 44.8468 1.91054
\(552\) 0 0
\(553\) 9.78621 30.1189i 0.416152 1.28078i
\(554\) 0 0
\(555\) 12.3792 + 2.63128i 0.525468 + 0.111692i
\(556\) 0 0
\(557\) 5.93356 0.251413 0.125706 0.992067i \(-0.459880\pi\)
0.125706 + 0.992067i \(0.459880\pi\)
\(558\) 0 0
\(559\) 9.50187 + 6.90351i 0.401886 + 0.291987i
\(560\) 0 0
\(561\) 6.02323 4.37613i 0.254301 0.184761i
\(562\) 0 0
\(563\) −11.1180 8.07772i −0.468569 0.340435i 0.328314 0.944569i \(-0.393520\pi\)
−0.796883 + 0.604133i \(0.793520\pi\)
\(564\) 0 0
\(565\) −0.754609 7.17962i −0.0317466 0.302049i
\(566\) 0 0
\(567\) −1.47815 4.54927i −0.0620764 0.191051i
\(568\) 0 0
\(569\) 10.2309 + 31.4874i 0.428900 + 1.32002i 0.899210 + 0.437518i \(0.144142\pi\)
−0.470309 + 0.882502i \(0.655858\pi\)
\(570\) 0 0
\(571\) −7.91367 + 24.3558i −0.331177 + 1.01926i 0.637398 + 0.770535i \(0.280011\pi\)
−0.968575 + 0.248722i \(0.919989\pi\)
\(572\) 0 0
\(573\) 4.24803 3.08637i 0.177464 0.128935i
\(574\) 0 0
\(575\) 14.6581 + 25.3886i 0.611285 + 1.05878i
\(576\) 0 0
\(577\) −2.82151 + 2.04995i −0.117461 + 0.0853405i −0.644965 0.764212i \(-0.723128\pi\)
0.527504 + 0.849553i \(0.323128\pi\)
\(578\) 0 0
\(579\) 2.45534 7.55676i 0.102040 0.314048i
\(580\) 0 0
\(581\) 3.81641 + 11.7457i 0.158331 + 0.487294i
\(582\) 0 0
\(583\) 2.55343 + 7.85866i 0.105752 + 0.325472i
\(584\) 0 0
\(585\) 1.20731 2.09113i 0.0499162 0.0864574i
\(586\) 0 0
\(587\) −27.8690 20.2480i −1.15028 0.835724i −0.161758 0.986831i \(-0.551716\pi\)
−0.988517 + 0.151107i \(0.951716\pi\)
\(588\) 0 0
\(589\) 14.8425 10.7837i 0.611575 0.444335i
\(590\) 0 0
\(591\) 10.5220 + 7.64469i 0.432818 + 0.314460i
\(592\) 0 0
\(593\) 35.7248 1.46704 0.733522 0.679666i \(-0.237875\pi\)
0.733522 + 0.679666i \(0.237875\pi\)
\(594\) 0 0
\(595\) 20.3530 35.2524i 0.834391 1.44521i
\(596\) 0 0
\(597\) 0.328899 1.01225i 0.0134609 0.0414285i
\(598\) 0 0
\(599\) 39.7697 1.62495 0.812473 0.582998i \(-0.198121\pi\)
0.812473 + 0.582998i \(0.198121\pi\)
\(600\) 0 0
\(601\) −15.5134 −0.632805 −0.316402 0.948625i \(-0.602475\pi\)
−0.316402 + 0.948625i \(0.602475\pi\)
\(602\) 0 0
\(603\) 2.14163 6.59126i 0.0872140 0.268417i
\(604\) 0 0
\(605\) 14.6525 6.52369i 0.595707 0.265226i
\(606\) 0 0
\(607\) 15.1855 0.616358 0.308179 0.951328i \(-0.400280\pi\)
0.308179 + 0.951328i \(0.400280\pi\)
\(608\) 0 0
\(609\) 40.8271 + 29.6626i 1.65440 + 1.20199i
\(610\) 0 0
\(611\) −2.62224 + 1.90517i −0.106084 + 0.0770748i
\(612\) 0 0
\(613\) 25.9974 + 18.8882i 1.05002 + 0.762887i 0.972217 0.234081i \(-0.0752082\pi\)
0.0778070 + 0.996968i \(0.475208\pi\)
\(614\) 0 0
\(615\) 1.87786 + 0.399152i 0.0757228 + 0.0160954i
\(616\) 0 0
\(617\) 1.33569 + 4.11082i 0.0537727 + 0.165495i 0.974336 0.225097i \(-0.0722700\pi\)
−0.920564 + 0.390593i \(0.872270\pi\)
\(618\) 0 0
\(619\) 10.3201 + 31.7621i 0.414801 + 1.27663i 0.912428 + 0.409236i \(0.134205\pi\)
−0.497627 + 0.867391i \(0.665795\pi\)
\(620\) 0 0
\(621\) −1.81184 + 5.57627i −0.0727067 + 0.223768i
\(622\) 0 0
\(623\) −3.22256 + 2.34133i −0.129109 + 0.0938034i
\(624\) 0 0
\(625\) −24.4537 5.19779i −0.978148 0.207912i
\(626\) 0 0
\(627\) −6.72772 + 4.88798i −0.268679 + 0.195207i
\(628\) 0 0
\(629\) −6.65615 + 20.4855i −0.265398 + 0.816812i
\(630\) 0 0
\(631\) 3.39726 + 10.4557i 0.135243 + 0.416234i 0.995628 0.0934106i \(-0.0297769\pi\)
−0.860385 + 0.509645i \(0.829777\pi\)
\(632\) 0 0
\(633\) −6.33264 19.4898i −0.251700 0.774652i
\(634\) 0 0
\(635\) 16.1554 + 3.43393i 0.641106 + 0.136271i
\(636\) 0 0
\(637\) −13.8738 10.0799i −0.549698 0.399379i
\(638\) 0 0
\(639\) 9.70587 7.05173i 0.383958 0.278962i
\(640\) 0 0
\(641\) 5.55031 + 4.03253i 0.219224 + 0.159276i 0.691977 0.721919i \(-0.256740\pi\)
−0.472753 + 0.881195i \(0.656740\pi\)
\(642\) 0 0
\(643\) 23.1923 0.914615 0.457308 0.889309i \(-0.348814\pi\)
0.457308 + 0.889309i \(0.348814\pi\)
\(644\) 0 0
\(645\) 22.2179 9.89202i 0.874827 0.389498i
\(646\) 0 0
\(647\) −9.51298 + 29.2779i −0.373994 + 1.15103i 0.570161 + 0.821533i \(0.306881\pi\)
−0.944155 + 0.329502i \(0.893119\pi\)
\(648\) 0 0
\(649\) −9.33188 −0.366309
\(650\) 0 0
\(651\) 20.6447 0.809130
\(652\) 0 0
\(653\) −2.41245 + 7.42477i −0.0944066 + 0.290554i −0.987099 0.160114i \(-0.948814\pi\)
0.892692 + 0.450667i \(0.148814\pi\)
\(654\) 0 0
\(655\) −18.8767 + 32.6955i −0.737575 + 1.27752i
\(656\) 0 0
\(657\) −16.9560 −0.661515
\(658\) 0 0
\(659\) −4.26388 3.09789i −0.166097 0.120677i 0.501632 0.865081i \(-0.332733\pi\)
−0.667729 + 0.744405i \(0.732733\pi\)
\(660\) 0 0
\(661\) 29.8490 21.6865i 1.16099 0.843509i 0.171088 0.985256i \(-0.445272\pi\)
0.989903 + 0.141747i \(0.0452719\pi\)
\(662\) 0 0
\(663\) 3.32476 + 2.41558i 0.129123 + 0.0938132i
\(664\) 0 0
\(665\) −22.7335 + 39.3756i −0.881567 + 1.52692i
\(666\) 0 0
\(667\) −19.1151 58.8301i −0.740138 2.27791i
\(668\) 0 0
\(669\) 3.18661 + 9.80739i 0.123202 + 0.379176i
\(670\) 0 0
\(671\) 2.19555 6.75721i 0.0847583 0.260859i
\(672\) 0 0
\(673\) 36.4227 26.4626i 1.40399 1.02006i 0.409829 0.912162i \(-0.365588\pi\)
0.994162 0.107897i \(-0.0344116\pi\)
\(674\) 0 0
\(675\) −2.50000 4.33013i −0.0962250 0.166667i
\(676\) 0 0
\(677\) −25.5161 + 18.5385i −0.980662 + 0.712493i −0.957856 0.287247i \(-0.907260\pi\)
−0.0228056 + 0.999740i \(0.507260\pi\)
\(678\) 0 0
\(679\) 13.4762 41.4756i 0.517171 1.59169i
\(680\) 0 0
\(681\) −5.60585 17.2530i −0.214816 0.661137i
\(682\) 0 0
\(683\) −6.39320 19.6762i −0.244629 0.752891i −0.995697 0.0926660i \(-0.970461\pi\)
0.751068 0.660225i \(-0.229539\pi\)
\(684\) 0 0
\(685\) 0.196176 + 1.86649i 0.00749551 + 0.0713150i
\(686\) 0 0
\(687\) 7.86225 + 5.71226i 0.299964 + 0.217936i
\(688\) 0 0
\(689\) −3.69003 + 2.68096i −0.140579 + 0.102137i
\(690\) 0 0
\(691\) 27.6523 + 20.0906i 1.05194 + 0.764282i 0.972581 0.232564i \(-0.0747116\pi\)
0.0793624 + 0.996846i \(0.474712\pi\)
\(692\) 0 0
\(693\) −9.35772 −0.355470
\(694\) 0 0
\(695\) −24.4048 5.18741i −0.925728 0.196770i
\(696\) 0 0
\(697\) −1.00971 + 3.10755i −0.0382453 + 0.117707i
\(698\) 0 0
\(699\) −22.2184 −0.840377
\(700\) 0 0
\(701\) −16.6859 −0.630216 −0.315108 0.949056i \(-0.602041\pi\)
−0.315108 + 0.949056i \(0.602041\pi\)
\(702\) 0 0
\(703\) 7.43467 22.8816i 0.280404 0.862994i
\(704\) 0 0
\(705\) 0.701568 + 6.67497i 0.0264226 + 0.251394i
\(706\) 0 0
\(707\) −7.15312 −0.269021
\(708\) 0 0
\(709\) −38.2796 27.8118i −1.43762 1.04449i −0.988533 0.151007i \(-0.951749\pi\)
−0.449089 0.893487i \(-0.648251\pi\)
\(710\) 0 0
\(711\) 5.35617 3.89149i 0.200872 0.145942i
\(712\) 0 0
\(713\) −20.4724 14.8741i −0.766697 0.557038i
\(714\) 0 0
\(715\) −3.16078 3.51041i −0.118207 0.131282i
\(716\) 0 0
\(717\) 4.92242 + 15.1496i 0.183831 + 0.565774i
\(718\) 0 0
\(719\) 1.73431 + 5.33767i 0.0646790 + 0.199062i 0.978174 0.207789i \(-0.0666268\pi\)
−0.913495 + 0.406851i \(0.866627\pi\)
\(720\) 0 0
\(721\) −16.0561 + 49.4156i −0.597960 + 1.84033i
\(722\) 0 0
\(723\) 3.98964 2.89864i 0.148376 0.107802i
\(724\) 0 0
\(725\) 48.1899 + 21.4555i 1.78973 + 0.796838i
\(726\) 0 0
\(727\) 11.8412 8.60317i 0.439167 0.319074i −0.346137 0.938184i \(-0.612507\pi\)
0.785304 + 0.619110i \(0.212507\pi\)
\(728\) 0 0
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) 0 0
\(731\) 12.7911 + 39.3669i 0.473095 + 1.45604i
\(732\) 0 0
\(733\) 9.96818 + 30.6789i 0.368183 + 1.13315i 0.947964 + 0.318378i \(0.103138\pi\)
−0.579781 + 0.814773i \(0.696862\pi\)
\(734\) 0 0
\(735\) −32.4405 + 14.4434i −1.19658 + 0.532754i
\(736\) 0 0
\(737\) −10.9687 7.96921i −0.404037 0.293550i
\(738\) 0 0
\(739\) 19.2956 14.0191i 0.709800 0.515700i −0.173309 0.984867i \(-0.555446\pi\)
0.883109 + 0.469168i \(0.155446\pi\)
\(740\) 0 0
\(741\) −3.71363 2.69811i −0.136423 0.0991174i
\(742\) 0 0
\(743\) 7.48188 0.274483 0.137242 0.990538i \(-0.456176\pi\)
0.137242 + 0.990538i \(0.456176\pi\)
\(744\) 0 0
\(745\) 32.9583 + 36.6039i 1.20750 + 1.34106i
\(746\) 0 0
\(747\) −0.797847 + 2.45552i −0.0291917 + 0.0898428i
\(748\) 0 0
\(749\) 94.8975 3.46748
\(750\) 0 0
\(751\) −32.3687 −1.18115 −0.590576 0.806982i \(-0.701099\pi\)
−0.590576 + 0.806982i \(0.701099\pi\)
\(752\) 0 0
\(753\) 4.76969 14.6796i 0.173817 0.534955i
\(754\) 0 0
\(755\) −17.6390 19.5901i −0.641949 0.712957i
\(756\) 0 0
\(757\) −10.2847 −0.373804 −0.186902 0.982379i \(-0.559845\pi\)
−0.186902 + 0.982379i \(0.559845\pi\)
\(758\) 0 0
\(759\) 9.27961 + 6.74203i 0.336828 + 0.244720i
\(760\) 0 0
\(761\) −23.3033 + 16.9308i −0.844743 + 0.613742i −0.923691 0.383137i \(-0.874844\pi\)
0.0789487 + 0.996879i \(0.474844\pi\)
\(762\) 0 0
\(763\) −9.07055 6.59014i −0.328376 0.238579i
\(764\) 0 0
\(765\) 7.77415 3.46127i 0.281075 0.125143i
\(766\) 0 0
\(767\) −1.59178 4.89898i −0.0574757 0.176892i
\(768\) 0 0
\(769\) −12.1673 37.4472i −0.438765 1.35038i −0.889179 0.457560i \(-0.848724\pi\)
0.450414 0.892820i \(-0.351276\pi\)
\(770\) 0 0
\(771\) 6.54584 20.1460i 0.235743 0.725541i
\(772\) 0 0
\(773\) −4.09692 + 2.97658i −0.147356 + 0.107060i −0.659021 0.752125i \(-0.729029\pi\)
0.511665 + 0.859185i \(0.329029\pi\)
\(774\) 0 0
\(775\) 21.1080 4.48665i 0.758223 0.161165i
\(776\) 0 0
\(777\) 21.9026 15.9132i 0.785753 0.570883i
\(778\) 0 0
\(779\) 1.12780 3.47102i 0.0404077 0.124362i
\(780\) 0 0
\(781\) −7.25260 22.3212i −0.259518 0.798715i
\(782\) 0 0
\(783\) 3.26015 + 10.0337i 0.116508 + 0.358576i
\(784\) 0 0
\(785\) −16.8727 18.7391i −0.602213 0.668826i
\(786\) 0 0
\(787\) −4.31328 3.13378i −0.153752 0.111707i 0.508250 0.861210i \(-0.330293\pi\)
−0.662001 + 0.749503i \(0.730293\pi\)
\(788\) 0 0
\(789\) 16.9298 12.3002i 0.602717 0.437900i
\(790\) 0 0
\(791\) −12.4938 9.07729i −0.444229 0.322751i
\(792\) 0 0
\(793\) 3.92185 0.139269
\(794\) 0 0
\(795\) 0.987250 + 9.39306i 0.0350141 +