Properties

Label 624.2.cn.f.305.3
Level $624$
Weight $2$
Character 624.305
Analytic conductor $4.983$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 624.cn (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.98266508613\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 312)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 305.3
Character \(\chi\) \(=\) 624.305
Dual form 624.2.cn.f.401.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.52267 + 0.825508i) q^{3} +(1.33870 + 1.33870i) q^{5} +(-0.566234 + 2.11322i) q^{7} +(1.63707 - 2.51396i) q^{9} +O(q^{10})\) \(q+(-1.52267 + 0.825508i) q^{3} +(1.33870 + 1.33870i) q^{5} +(-0.566234 + 2.11322i) q^{7} +(1.63707 - 2.51396i) q^{9} +(0.256724 + 0.958107i) q^{11} +(-3.27036 + 1.51814i) q^{13} +(-3.14352 - 0.933300i) q^{15} +(2.36097 + 4.08932i) q^{17} +(-1.44252 - 0.386521i) q^{19} +(-0.882285 - 3.68517i) q^{21} +(1.71229 - 2.96577i) q^{23} -1.41574i q^{25} +(-0.417438 + 5.17936i) q^{27} +(-0.733696 - 0.423600i) q^{29} +(-3.66157 + 3.66157i) q^{31} +(-1.18183 - 1.24696i) q^{33} +(-3.58699 + 2.07095i) q^{35} +(-10.5491 + 2.82661i) q^{37} +(3.72645 - 5.01134i) q^{39} +(-8.93255 + 2.39347i) q^{41} +(-6.05002 + 3.49298i) q^{43} +(5.55700 - 1.17389i) q^{45} +(0.384064 - 0.384064i) q^{47} +(1.91712 + 1.10685i) q^{49} +(-6.97075 - 4.27770i) q^{51} +10.3968i q^{53} +(-0.938944 + 1.62630i) q^{55} +(2.51556 - 0.602263i) q^{57} +(11.7285 + 3.14264i) q^{59} +(2.83411 + 4.90882i) q^{61} +(4.38557 + 4.88298i) q^{63} +(-6.41038 - 2.34570i) q^{65} +(-1.52023 - 5.67359i) q^{67} +(-0.158991 + 5.92942i) q^{69} +(2.69283 - 10.0498i) q^{71} +(-0.393272 - 0.393272i) q^{73} +(1.16871 + 2.15572i) q^{75} -2.17005 q^{77} +10.0483 q^{79} +(-3.63998 - 8.23107i) q^{81} +(2.25706 + 2.25706i) q^{83} +(-2.31375 + 8.63503i) q^{85} +(1.46686 + 0.0393325i) q^{87} +(-4.60143 - 17.1728i) q^{89} +(-1.35637 - 7.77060i) q^{91} +(2.55273 - 8.59804i) q^{93} +(-1.41367 - 2.44854i) q^{95} +(8.28096 + 2.21888i) q^{97} +(2.82892 + 0.923099i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q - 4q^{7} + O(q^{10}) \) \( 56q - 4q^{7} + 8q^{13} + 8q^{15} - 4q^{19} + 16q^{21} - 24q^{27} + 36q^{31} + 28q^{33} + 20q^{37} - 16q^{39} + 84q^{43} + 12q^{45} - 12q^{49} + 24q^{55} - 36q^{57} - 24q^{61} + 12q^{63} + 32q^{67} - 36q^{69} - 20q^{73} + 60q^{75} + 32q^{79} - 88q^{85} + 16q^{87} - 28q^{91} - 88q^{93} - 36q^{97} - 44q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(1\)

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 0
\(3\) −1.52267 + 0.825508i −0.879116 + 0.476607i
\(4\) 0 0
\(5\) 1.33870 + 1.33870i 0.598687 + 0.598687i 0.939963 0.341276i \(-0.110859\pi\)
−0.341276 + 0.939963i \(0.610859\pi\)
\(6\) 0 0
\(7\) −0.566234 + 2.11322i −0.214016 + 0.798720i 0.772494 + 0.635022i \(0.219009\pi\)
−0.986510 + 0.163698i \(0.947658\pi\)
\(8\) 0 0
\(9\) 1.63707 2.51396i 0.545691 0.837986i
\(10\) 0 0
\(11\) 0.256724 + 0.958107i 0.0774052 + 0.288880i 0.993768 0.111469i \(-0.0355555\pi\)
−0.916363 + 0.400349i \(0.868889\pi\)
\(12\) 0 0
\(13\) −3.27036 + 1.51814i −0.907034 + 0.421057i
\(14\) 0 0
\(15\) −3.14352 0.933300i −0.811653 0.240977i
\(16\) 0 0
\(17\) 2.36097 + 4.08932i 0.572619 + 0.991806i 0.996296 + 0.0859920i \(0.0274060\pi\)
−0.423677 + 0.905814i \(0.639261\pi\)
\(18\) 0 0
\(19\) −1.44252 0.386521i −0.330936 0.0886741i 0.0895251 0.995985i \(-0.471465\pi\)
−0.420461 + 0.907310i \(0.638132\pi\)
\(20\) 0 0
\(21\) −0.882285 3.68517i −0.192530 0.804170i
\(22\) 0 0
\(23\) 1.71229 2.96577i 0.357037 0.618407i −0.630427 0.776248i \(-0.717120\pi\)
0.987464 + 0.157842i \(0.0504536\pi\)
\(24\) 0 0
\(25\) 1.41574i 0.283149i
\(26\) 0 0
\(27\) −0.417438 + 5.17936i −0.0803360 + 0.996768i
\(28\) 0 0
\(29\) −0.733696 0.423600i −0.136244 0.0786605i 0.430329 0.902672i \(-0.358398\pi\)
−0.566573 + 0.824012i \(0.691731\pi\)
\(30\) 0 0
\(31\) −3.66157 + 3.66157i −0.657638 + 0.657638i −0.954821 0.297183i \(-0.903953\pi\)
0.297183 + 0.954821i \(0.403953\pi\)
\(32\) 0 0
\(33\) −1.18183 1.24696i −0.205731 0.217067i
\(34\) 0 0
\(35\) −3.58699 + 2.07095i −0.606312 + 0.350054i
\(36\) 0 0
\(37\) −10.5491 + 2.82661i −1.73425 + 0.464692i −0.981156 0.193217i \(-0.938108\pi\)
−0.753098 + 0.657909i \(0.771441\pi\)
\(38\) 0 0
\(39\) 3.72645 5.01134i 0.596710 0.802457i
\(40\) 0 0
\(41\) −8.93255 + 2.39347i −1.39503 + 0.373797i −0.876558 0.481297i \(-0.840166\pi\)
−0.518473 + 0.855094i \(0.673499\pi\)
\(42\) 0 0
\(43\) −6.05002 + 3.49298i −0.922620 + 0.532675i −0.884470 0.466597i \(-0.845480\pi\)
−0.0381501 + 0.999272i \(0.512146\pi\)
\(44\) 0 0
\(45\) 5.55700 1.17389i 0.828389 0.174993i
\(46\) 0 0
\(47\) 0.384064 0.384064i 0.0560215 0.0560215i −0.678541 0.734563i \(-0.737387\pi\)
0.734563 + 0.678541i \(0.237387\pi\)
\(48\) 0 0
\(49\) 1.91712 + 1.10685i 0.273874 + 0.158121i
\(50\) 0 0
\(51\) −6.97075 4.27770i −0.976100 0.598998i
\(52\) 0 0
\(53\) 10.3968i 1.42811i 0.700090 + 0.714054i \(0.253143\pi\)
−0.700090 + 0.714054i \(0.746857\pi\)
\(54\) 0 0
\(55\) −0.938944 + 1.62630i −0.126607 + 0.219290i
\(56\) 0 0
\(57\) 2.51556 0.602263i 0.333194 0.0797717i
\(58\) 0 0
\(59\) 11.7285 + 3.14264i 1.52692 + 0.409137i 0.922013 0.387159i \(-0.126543\pi\)
0.604908 + 0.796296i \(0.293210\pi\)
\(60\) 0 0
\(61\) 2.83411 + 4.90882i 0.362870 + 0.628510i 0.988432 0.151665i \(-0.0484635\pi\)
−0.625562 + 0.780175i \(0.715130\pi\)
\(62\) 0 0
\(63\) 4.38557 + 4.88298i 0.552530 + 0.615198i
\(64\) 0 0
\(65\) −6.41038 2.34570i −0.795110 0.290948i
\(66\) 0 0
\(67\) −1.52023 5.67359i −0.185726 0.693139i −0.994474 0.104984i \(-0.966521\pi\)
0.808748 0.588155i \(-0.200146\pi\)
\(68\) 0 0
\(69\) −0.158991 + 5.92942i −0.0191403 + 0.713818i
\(70\) 0 0
\(71\) 2.69283 10.0498i 0.319580 1.19269i −0.600069 0.799948i \(-0.704860\pi\)
0.919649 0.392741i \(-0.128473\pi\)
\(72\) 0 0
\(73\) −0.393272 0.393272i −0.0460290 0.0460290i 0.683718 0.729747i \(-0.260362\pi\)
−0.729747 + 0.683718i \(0.760362\pi\)
\(74\) 0 0
\(75\) 1.16871 + 2.15572i 0.134951 + 0.248921i
\(76\) 0 0
\(77\) −2.17005 −0.247300
\(78\) 0 0
\(79\) 10.0483 1.13052 0.565261 0.824912i \(-0.308775\pi\)
0.565261 + 0.824912i \(0.308775\pi\)
\(80\) 0 0
\(81\) −3.63998 8.23107i −0.404442 0.914564i
\(82\) 0 0
\(83\) 2.25706 + 2.25706i 0.247745 + 0.247745i 0.820045 0.572300i \(-0.193949\pi\)
−0.572300 + 0.820045i \(0.693949\pi\)
\(84\) 0 0
\(85\) −2.31375 + 8.63503i −0.250961 + 0.936600i
\(86\) 0 0
\(87\) 1.46686 + 0.0393325i 0.157264 + 0.00421689i
\(88\) 0 0
\(89\) −4.60143 17.1728i −0.487750 1.82031i −0.567342 0.823482i \(-0.692028\pi\)
0.0795919 0.996828i \(-0.474638\pi\)
\(90\) 0 0
\(91\) −1.35637 7.77060i −0.142186 0.814580i
\(92\) 0 0
\(93\) 2.55273 8.59804i 0.264705 0.891575i
\(94\) 0 0
\(95\) −1.41367 2.44854i −0.145039 0.251215i
\(96\) 0 0
\(97\) 8.28096 + 2.21888i 0.840804 + 0.225293i 0.653422 0.756994i \(-0.273333\pi\)
0.187383 + 0.982287i \(0.440000\pi\)
\(98\) 0 0
\(99\) 2.82892 + 0.923099i 0.284317 + 0.0927749i
\(100\) 0 0
\(101\) −1.02109 + 1.76859i −0.101603 + 0.175981i −0.912345 0.409422i \(-0.865730\pi\)
0.810742 + 0.585403i \(0.199064\pi\)
\(102\) 0 0
\(103\) 14.3415i 1.41311i 0.707656 + 0.706557i \(0.249753\pi\)
−0.707656 + 0.706557i \(0.750247\pi\)
\(104\) 0 0
\(105\) 3.75223 6.11447i 0.366180 0.596711i
\(106\) 0 0
\(107\) −0.334916 0.193364i −0.0323776 0.0186932i 0.483724 0.875221i \(-0.339284\pi\)
−0.516101 + 0.856527i \(0.672617\pi\)
\(108\) 0 0
\(109\) −8.24097 + 8.24097i −0.789342 + 0.789342i −0.981386 0.192044i \(-0.938488\pi\)
0.192044 + 0.981386i \(0.438488\pi\)
\(110\) 0 0
\(111\) 13.7294 13.0123i 1.30314 1.23508i
\(112\) 0 0
\(113\) 10.3438 5.97200i 0.973063 0.561798i 0.0728946 0.997340i \(-0.476776\pi\)
0.900169 + 0.435541i \(0.143443\pi\)
\(114\) 0 0
\(115\) 6.26254 1.67804i 0.583985 0.156478i
\(116\) 0 0
\(117\) −1.53727 + 10.7069i −0.142121 + 0.989849i
\(118\) 0 0
\(119\) −9.97847 + 2.67372i −0.914725 + 0.245100i
\(120\) 0 0
\(121\) 8.67422 5.00806i 0.788565 0.455278i
\(122\) 0 0
\(123\) 11.6255 11.0184i 1.04824 0.993493i
\(124\) 0 0
\(125\) 8.58878 8.58878i 0.768204 0.768204i
\(126\) 0 0
\(127\) 0.109854 + 0.0634245i 0.00974800 + 0.00562801i 0.504866 0.863198i \(-0.331542\pi\)
−0.495118 + 0.868826i \(0.664875\pi\)
\(128\) 0 0
\(129\) 6.32873 10.3130i 0.557214 0.908011i
\(130\) 0 0
\(131\) 20.8758i 1.82392i −0.410274 0.911962i \(-0.634567\pi\)
0.410274 0.911962i \(-0.365433\pi\)
\(132\) 0 0
\(133\) 1.63361 2.82949i 0.141652 0.245348i
\(134\) 0 0
\(135\) −7.49245 + 6.37480i −0.644848 + 0.548655i
\(136\) 0 0
\(137\) 12.2978 + 3.29520i 1.05068 + 0.281528i 0.742531 0.669812i \(-0.233625\pi\)
0.308145 + 0.951340i \(0.400292\pi\)
\(138\) 0 0
\(139\) 9.15970 + 15.8651i 0.776915 + 1.34566i 0.933712 + 0.358026i \(0.116550\pi\)
−0.156796 + 0.987631i \(0.550117\pi\)
\(140\) 0 0
\(141\) −0.267757 + 0.901853i −0.0225492 + 0.0759497i
\(142\) 0 0
\(143\) −2.29412 2.74361i −0.191844 0.229432i
\(144\) 0 0
\(145\) −0.415127 1.54928i −0.0344744 0.128660i
\(146\) 0 0
\(147\) −3.83286 0.102774i −0.316129 0.00847669i
\(148\) 0 0
\(149\) 0.550277 2.05366i 0.0450804 0.168242i −0.939716 0.341957i \(-0.888910\pi\)
0.984796 + 0.173714i \(0.0555770\pi\)
\(150\) 0 0
\(151\) −2.93665 2.93665i −0.238981 0.238981i 0.577447 0.816428i \(-0.304049\pi\)
−0.816428 + 0.577447i \(0.804049\pi\)
\(152\) 0 0
\(153\) 14.1455 + 0.759138i 1.14359 + 0.0613727i
\(154\) 0 0
\(155\) −9.80352 −0.787438
\(156\) 0 0
\(157\) 16.1940 1.29242 0.646211 0.763159i \(-0.276353\pi\)
0.646211 + 0.763159i \(0.276353\pi\)
\(158\) 0 0
\(159\) −8.58263 15.8309i −0.680647 1.25547i
\(160\) 0 0
\(161\) 5.29776 + 5.29776i 0.417522 + 0.417522i
\(162\) 0 0
\(163\) −0.995027 + 3.71349i −0.0779365 + 0.290863i −0.993883 0.110437i \(-0.964775\pi\)
0.915947 + 0.401300i \(0.131442\pi\)
\(164\) 0 0
\(165\) 0.0871838 3.25143i 0.00678725 0.253123i
\(166\) 0 0
\(167\) 6.12521 + 22.8596i 0.473983 + 1.76893i 0.625238 + 0.780434i \(0.285002\pi\)
−0.151255 + 0.988495i \(0.548332\pi\)
\(168\) 0 0
\(169\) 8.39049 9.92974i 0.645422 0.763826i
\(170\) 0 0
\(171\) −3.33321 + 2.99367i −0.254897 + 0.228931i
\(172\) 0 0
\(173\) 7.36150 + 12.7505i 0.559684 + 0.969401i 0.997523 + 0.0703477i \(0.0224109\pi\)
−0.437838 + 0.899054i \(0.644256\pi\)
\(174\) 0 0
\(175\) 2.99177 + 0.801643i 0.226157 + 0.0605985i
\(176\) 0 0
\(177\) −20.4530 + 4.89675i −1.53734 + 0.368062i
\(178\) 0 0
\(179\) −8.53187 + 14.7776i −0.637702 + 1.10453i 0.348234 + 0.937408i \(0.386782\pi\)
−0.985936 + 0.167125i \(0.946552\pi\)
\(180\) 0 0
\(181\) 3.51901i 0.261566i −0.991411 0.130783i \(-0.958251\pi\)
0.991411 0.130783i \(-0.0417491\pi\)
\(182\) 0 0
\(183\) −8.36769 5.13495i −0.618557 0.379587i
\(184\) 0 0
\(185\) −17.9061 10.3381i −1.31648 0.760070i
\(186\) 0 0
\(187\) −3.31189 + 3.31189i −0.242189 + 0.242189i
\(188\) 0 0
\(189\) −10.7087 3.81487i −0.778945 0.277491i
\(190\) 0 0
\(191\) −18.6177 + 10.7490i −1.34713 + 0.777767i −0.987842 0.155459i \(-0.950314\pi\)
−0.359290 + 0.933226i \(0.616981\pi\)
\(192\) 0 0
\(193\) −3.88032 + 1.03973i −0.279312 + 0.0748413i −0.395755 0.918356i \(-0.629517\pi\)
0.116444 + 0.993197i \(0.462851\pi\)
\(194\) 0 0
\(195\) 11.6973 1.72009i 0.837662 0.123178i
\(196\) 0 0
\(197\) 7.74656 2.07569i 0.551920 0.147886i 0.0279283 0.999610i \(-0.491109\pi\)
0.523992 + 0.851723i \(0.324442\pi\)
\(198\) 0 0
\(199\) −9.75011 + 5.62923i −0.691167 + 0.399046i −0.804049 0.594563i \(-0.797325\pi\)
0.112882 + 0.993608i \(0.463992\pi\)
\(200\) 0 0
\(201\) 6.99841 + 7.38406i 0.493630 + 0.520831i
\(202\) 0 0
\(203\) 1.31060 1.31060i 0.0919862 0.0919862i
\(204\) 0 0
\(205\) −15.1622 8.75390i −1.05897 0.611399i
\(206\) 0 0
\(207\) −4.65269 9.15982i −0.323384 0.636651i
\(208\) 0 0
\(209\) 1.48132i 0.102465i
\(210\) 0 0
\(211\) 11.9794 20.7489i 0.824696 1.42842i −0.0774545 0.996996i \(-0.524679\pi\)
0.902151 0.431420i \(-0.141987\pi\)
\(212\) 0 0
\(213\) 4.19587 + 17.5255i 0.287496 + 1.20083i
\(214\) 0 0
\(215\) −12.7753 3.42312i −0.871266 0.233455i
\(216\) 0 0
\(217\) −5.66438 9.81100i −0.384523 0.666014i
\(218\) 0 0
\(219\) 0.923475 + 0.274176i 0.0624027 + 0.0185271i
\(220\) 0 0
\(221\) −13.9294 9.78925i −0.936992 0.658496i
\(222\) 0 0
\(223\) 0.495422 + 1.84894i 0.0331759 + 0.123814i 0.980528 0.196380i \(-0.0629185\pi\)
−0.947352 + 0.320194i \(0.896252\pi\)
\(224\) 0 0
\(225\) −3.55912 2.31768i −0.237275 0.154512i
\(226\) 0 0
\(227\) 2.83237 10.5705i 0.187991 0.701591i −0.805980 0.591943i \(-0.798361\pi\)
0.993970 0.109648i \(-0.0349723\pi\)
\(228\) 0 0
\(229\) 2.18006 + 2.18006i 0.144063 + 0.144063i 0.775460 0.631397i \(-0.217518\pi\)
−0.631397 + 0.775460i \(0.717518\pi\)
\(230\) 0 0
\(231\) 3.30428 1.79140i 0.217406 0.117865i
\(232\) 0 0
\(233\) 7.80150 0.511093 0.255546 0.966797i \(-0.417745\pi\)
0.255546 + 0.966797i \(0.417745\pi\)
\(234\) 0 0
\(235\) 1.02830 0.0670787
\(236\) 0 0
\(237\) −15.3003 + 8.29495i −0.993861 + 0.538815i
\(238\) 0 0
\(239\) 14.8365 + 14.8365i 0.959695 + 0.959695i 0.999219 0.0395239i \(-0.0125841\pi\)
−0.0395239 + 0.999219i \(0.512584\pi\)
\(240\) 0 0
\(241\) −4.24837 + 15.8551i −0.273661 + 1.02132i 0.683072 + 0.730351i \(0.260644\pi\)
−0.956733 + 0.290967i \(0.906023\pi\)
\(242\) 0 0
\(243\) 12.3373 + 9.52841i 0.791439 + 0.611248i
\(244\) 0 0
\(245\) 1.08471 + 4.04820i 0.0692997 + 0.258630i
\(246\) 0 0
\(247\) 5.30434 0.925883i 0.337507 0.0589125i
\(248\) 0 0
\(249\) −5.29999 1.57355i −0.335873 0.0997196i
\(250\) 0 0
\(251\) 2.11649 + 3.66588i 0.133592 + 0.231388i 0.925059 0.379824i \(-0.124016\pi\)
−0.791467 + 0.611212i \(0.790682\pi\)
\(252\) 0 0
\(253\) 3.28112 + 0.879172i 0.206282 + 0.0552731i
\(254\) 0 0
\(255\) −3.60520 15.0583i −0.225766 0.942990i
\(256\) 0 0
\(257\) −3.01424 + 5.22082i −0.188023 + 0.325666i −0.944591 0.328249i \(-0.893541\pi\)
0.756568 + 0.653915i \(0.226875\pi\)
\(258\) 0 0
\(259\) 23.8929i 1.48464i
\(260\) 0 0
\(261\) −2.26603 + 1.15102i −0.140264 + 0.0712462i
\(262\) 0 0
\(263\) 16.9076 + 9.76159i 1.04257 + 0.601925i 0.920559 0.390604i \(-0.127734\pi\)
0.122006 + 0.992529i \(0.461067\pi\)
\(264\) 0 0
\(265\) −13.9182 + 13.9182i −0.854989 + 0.854989i
\(266\) 0 0
\(267\) 21.1827 + 22.3500i 1.29636 + 1.36780i
\(268\) 0 0
\(269\) 22.7011 13.1065i 1.38411 0.799118i 0.391469 0.920191i \(-0.371967\pi\)
0.992644 + 0.121074i \(0.0386337\pi\)
\(270\) 0 0
\(271\) −13.9542 + 3.73902i −0.847657 + 0.227129i −0.656402 0.754411i \(-0.727923\pi\)
−0.191255 + 0.981540i \(0.561256\pi\)
\(272\) 0 0
\(273\) 8.48000 + 10.7124i 0.513233 + 0.648343i
\(274\) 0 0
\(275\) 1.35643 0.363456i 0.0817961 0.0219172i
\(276\) 0 0
\(277\) −4.00445 + 2.31197i −0.240604 + 0.138913i −0.615454 0.788172i \(-0.711028\pi\)
0.374850 + 0.927085i \(0.377694\pi\)
\(278\) 0 0
\(279\) 3.21078 + 15.1993i 0.192224 + 0.909959i
\(280\) 0 0
\(281\) −2.83565 + 2.83565i −0.169161 + 0.169161i −0.786611 0.617450i \(-0.788166\pi\)
0.617450 + 0.786611i \(0.288166\pi\)
\(282\) 0 0
\(283\) −21.9372 12.6654i −1.30403 0.752883i −0.322938 0.946420i \(-0.604671\pi\)
−0.981093 + 0.193537i \(0.938004\pi\)
\(284\) 0 0
\(285\) 4.17384 + 2.56134i 0.247237 + 0.151721i
\(286\) 0 0
\(287\) 20.2317i 1.19424i
\(288\) 0 0
\(289\) −2.64835 + 4.58708i −0.155785 + 0.269828i
\(290\) 0 0
\(291\) −14.4409 + 3.45737i −0.846541 + 0.202675i
\(292\) 0 0
\(293\) −17.0816 4.57700i −0.997917 0.267391i −0.277345 0.960770i \(-0.589454\pi\)
−0.720573 + 0.693379i \(0.756121\pi\)
\(294\) 0 0
\(295\) 11.4939 + 19.9081i 0.669202 + 1.15909i
\(296\) 0 0
\(297\) −5.06955 + 0.929715i −0.294165 + 0.0539475i
\(298\) 0 0
\(299\) −1.09734 + 12.2986i −0.0634607 + 0.711249i
\(300\) 0 0
\(301\) −3.95569 14.7628i −0.228002 0.850917i
\(302\) 0 0
\(303\) 0.0948117 3.53591i 0.00544679 0.203132i
\(304\) 0 0
\(305\) −2.77742 + 10.3655i −0.159035 + 0.593526i
\(306\) 0 0
\(307\) −16.5562 16.5562i −0.944910 0.944910i 0.0536497 0.998560i \(-0.482915\pi\)
−0.998560 + 0.0536497i \(0.982915\pi\)
\(308\) 0 0
\(309\) −11.8390 21.8375i −0.673500 1.24229i
\(310\) 0 0
\(311\) 27.9565 1.58527 0.792635 0.609697i \(-0.208709\pi\)
0.792635 + 0.609697i \(0.208709\pi\)
\(312\) 0 0
\(313\) 22.1801 1.25369 0.626846 0.779144i \(-0.284346\pi\)
0.626846 + 0.779144i \(0.284346\pi\)
\(314\) 0 0
\(315\) −0.665886 + 12.4078i −0.0375184 + 0.699103i
\(316\) 0 0
\(317\) 5.44471 + 5.44471i 0.305805 + 0.305805i 0.843280 0.537475i \(-0.180622\pi\)
−0.537475 + 0.843280i \(0.680622\pi\)
\(318\) 0 0
\(319\) 0.217496 0.811708i 0.0121775 0.0454469i
\(320\) 0 0
\(321\) 0.669592 + 0.0179544i 0.0373730 + 0.00100212i
\(322\) 0 0
\(323\) −1.82513 6.81148i −0.101553 0.379001i
\(324\) 0 0
\(325\) 2.14930 + 4.62999i 0.119222 + 0.256826i
\(326\) 0 0
\(327\) 5.74533 19.3513i 0.317717 1.07013i
\(328\) 0 0
\(329\) 0.594140 + 1.02908i 0.0327560 + 0.0567350i
\(330\) 0 0
\(331\) −5.61987 1.50584i −0.308896 0.0827684i 0.101041 0.994882i \(-0.467783\pi\)
−0.409937 + 0.912114i \(0.634449\pi\)
\(332\) 0 0
\(333\) −10.1636 + 31.1473i −0.556962 + 1.70686i
\(334\) 0 0
\(335\) 5.56011 9.63039i 0.303781 0.526165i
\(336\) 0 0
\(337\) 15.0629i 0.820528i −0.911967 0.410264i \(-0.865436\pi\)
0.911967 0.410264i \(-0.134564\pi\)
\(338\) 0 0
\(339\) −10.8203 + 17.6323i −0.587679 + 0.957655i
\(340\) 0 0
\(341\) −4.44819 2.56817i −0.240883 0.139074i
\(342\) 0 0
\(343\) −14.2534 + 14.2534i −0.769612 + 0.769612i
\(344\) 0 0
\(345\) −8.15058 + 7.72489i −0.438812 + 0.415894i
\(346\) 0 0
\(347\) −6.58502 + 3.80186i −0.353502 + 0.204095i −0.666227 0.745749i \(-0.732092\pi\)
0.312724 + 0.949844i \(0.398758\pi\)
\(348\) 0 0
\(349\) −13.2155 + 3.54107i −0.707407 + 0.189549i −0.594546 0.804062i \(-0.702668\pi\)
−0.112861 + 0.993611i \(0.536002\pi\)
\(350\) 0 0
\(351\) −6.49783 17.5721i −0.346828 0.937929i
\(352\) 0 0
\(353\) −6.31893 + 1.69315i −0.336323 + 0.0901174i −0.423028 0.906117i \(-0.639033\pi\)
0.0867052 + 0.996234i \(0.472366\pi\)
\(354\) 0 0
\(355\) 17.0586 9.84877i 0.905375 0.522719i
\(356\) 0 0
\(357\) 12.9868 12.3085i 0.687334 0.651436i
\(358\) 0 0
\(359\) −11.5879 + 11.5879i −0.611588 + 0.611588i −0.943360 0.331772i \(-0.892354\pi\)
0.331772 + 0.943360i \(0.392354\pi\)
\(360\) 0 0
\(361\) −14.5230 8.38487i −0.764370 0.441309i
\(362\) 0 0
\(363\) −9.07381 + 14.7863i −0.476252 + 0.776078i
\(364\) 0 0
\(365\) 1.05295i 0.0551139i
\(366\) 0 0
\(367\) 10.4529 18.1049i 0.545635 0.945068i −0.452931 0.891545i \(-0.649622\pi\)
0.998567 0.0535227i \(-0.0170449\pi\)
\(368\) 0 0
\(369\) −8.60617 + 26.3744i −0.448019 + 1.37299i
\(370\) 0 0
\(371\) −21.9707 5.88702i −1.14066 0.305639i
\(372\) 0 0
\(373\) 11.5708 + 20.0412i 0.599114 + 1.03770i 0.992952 + 0.118516i \(0.0378138\pi\)
−0.393838 + 0.919180i \(0.628853\pi\)
\(374\) 0 0
\(375\) −5.98781 + 20.1680i −0.309209 + 1.04147i
\(376\) 0 0
\(377\) 3.04253 + 0.271468i 0.156698 + 0.0139813i
\(378\) 0 0
\(379\) 3.41564 + 12.7474i 0.175450 + 0.654788i 0.996475 + 0.0838951i \(0.0267361\pi\)
−0.821025 + 0.570893i \(0.806597\pi\)
\(380\) 0 0
\(381\) −0.219630 0.00588915i −0.0112520 0.000301710i
\(382\) 0 0
\(383\) 2.61140 9.74587i 0.133436 0.497991i −0.866563 0.499067i \(-0.833676\pi\)
0.999999 + 0.00107658i \(0.000342686\pi\)
\(384\) 0 0
\(385\) −2.90506 2.90506i −0.148055 0.148055i
\(386\) 0 0
\(387\) −1.12312 + 20.9278i −0.0570915 + 1.06382i
\(388\) 0 0
\(389\) −21.6943 −1.09994 −0.549971 0.835184i \(-0.685361\pi\)
−0.549971 + 0.835184i \(0.685361\pi\)
\(390\) 0 0
\(391\) 16.1707 0.817786
\(392\) 0 0
\(393\) 17.2331 + 31.7870i 0.869295 + 1.60344i
\(394\) 0 0
\(395\) 13.4517 + 13.4517i 0.676829 + 0.676829i
\(396\) 0 0
\(397\) 4.57617 17.0785i 0.229672 0.857146i −0.750807 0.660521i \(-0.770335\pi\)
0.980479 0.196625i \(-0.0629980\pi\)
\(398\) 0 0
\(399\) −0.151685 + 5.65694i −0.00759376 + 0.283201i
\(400\) 0 0
\(401\) 1.42326 + 5.31167i 0.0710741 + 0.265252i 0.992314 0.123742i \(-0.0394894\pi\)
−0.921240 + 0.388994i \(0.872823\pi\)
\(402\) 0 0
\(403\) 6.41587 17.5334i 0.319597 0.873403i
\(404\) 0 0
\(405\) 6.14612 15.8918i 0.305403 0.789671i
\(406\) 0 0
\(407\) −5.41639 9.38147i −0.268481 0.465022i
\(408\) 0 0
\(409\) −19.7035 5.27954i −0.974275 0.261056i −0.263643 0.964620i \(-0.584924\pi\)
−0.710632 + 0.703564i \(0.751591\pi\)
\(410\) 0 0
\(411\) −21.4458 + 5.13445i −1.05784 + 0.253264i
\(412\) 0 0
\(413\) −13.2822 + 23.0054i −0.653572 + 1.13202i
\(414\) 0 0
\(415\) 6.04308i 0.296643i
\(416\) 0 0
\(417\) −27.0440 16.5959i −1.32435 0.812706i
\(418\) 0 0
\(419\) 30.6973 + 17.7231i 1.49966 + 0.865831i 1.00000 0.000389131i \(-0.000123864\pi\)
0.499663 + 0.866220i \(0.333457\pi\)
\(420\) 0 0
\(421\) 26.7150 26.7150i 1.30201 1.30201i 0.374972 0.927036i \(-0.377652\pi\)
0.927036 0.374972i \(-0.122348\pi\)
\(422\) 0 0
\(423\) −0.336780 1.59426i −0.0163748 0.0775157i
\(424\) 0 0
\(425\) 5.78943 3.34253i 0.280829 0.162136i
\(426\) 0 0
\(427\) −11.9782 + 3.20954i −0.579664 + 0.155320i
\(428\) 0 0
\(429\) 5.75807 + 2.28381i 0.278002 + 0.110263i
\(430\) 0 0
\(431\) −25.5938 + 6.85785i −1.23281 + 0.330331i −0.815674 0.578512i \(-0.803634\pi\)
−0.417138 + 0.908843i \(0.636967\pi\)
\(432\) 0 0
\(433\) −22.5129 + 12.9978i −1.08190 + 0.624636i −0.931409 0.363975i \(-0.881419\pi\)
−0.150493 + 0.988611i \(0.548086\pi\)
\(434\) 0 0
\(435\) 1.91104 + 2.01635i 0.0916275 + 0.0966767i
\(436\) 0 0
\(437\) −3.61634 + 3.61634i −0.172993 + 0.172993i
\(438\) 0 0
\(439\) 21.2539 + 12.2710i 1.01440 + 0.585661i 0.912476 0.409131i \(-0.134168\pi\)
0.101920 + 0.994793i \(0.467501\pi\)
\(440\) 0 0
\(441\) 5.92104 3.00757i 0.281955 0.143217i
\(442\) 0 0
\(443\) 24.7493i 1.17587i −0.808907 0.587937i \(-0.799940\pi\)
0.808907 0.587937i \(-0.200060\pi\)
\(444\) 0 0
\(445\) 16.8293 29.1492i 0.797785 1.38180i
\(446\) 0 0
\(447\) 0.857420 + 3.58131i 0.0405546 + 0.169390i
\(448\) 0 0
\(449\) 18.0387 + 4.83346i 0.851300 + 0.228105i 0.657985 0.753031i \(-0.271409\pi\)
0.193316 + 0.981137i \(0.438076\pi\)
\(450\) 0 0
\(451\) −4.58640 7.94388i −0.215965 0.374063i
\(452\) 0 0
\(453\) 6.89579 + 2.04733i 0.323992 + 0.0961921i
\(454\) 0 0
\(455\) 8.58675 12.2183i 0.402553 0.572803i
\(456\) 0 0
\(457\) 0.610148 + 2.27710i 0.0285415 + 0.106518i 0.978727 0.205166i \(-0.0657735\pi\)
−0.950186 + 0.311685i \(0.899107\pi\)
\(458\) 0 0
\(459\) −22.1656 + 10.5213i −1.03460 + 0.491091i
\(460\) 0 0
\(461\) 3.36375 12.5537i 0.156665 0.584683i −0.842292 0.539022i \(-0.818794\pi\)
0.998957 0.0456608i \(-0.0145393\pi\)
\(462\) 0 0
\(463\) −1.03011 1.03011i −0.0478733 0.0478733i 0.682765 0.730638i \(-0.260777\pi\)
−0.730638 + 0.682765i \(0.760777\pi\)
\(464\) 0 0
\(465\) 14.9276 8.09288i 0.692250 0.375298i
\(466\) 0 0
\(467\) −36.9118 −1.70808 −0.854038 0.520211i \(-0.825853\pi\)
−0.854038 + 0.520211i \(0.825853\pi\)
\(468\) 0 0
\(469\) 12.8503 0.593373
\(470\) 0 0
\(471\) −24.6582 + 13.3683i −1.13619 + 0.615977i
\(472\) 0 0
\(473\) −4.89984 4.89984i −0.225295 0.225295i
\(474\) 0 0
\(475\) −0.547215 + 2.04224i −0.0251080 + 0.0937042i
\(476\) 0 0
\(477\) 26.1371 + 17.0203i 1.19674 + 0.779307i
\(478\) 0 0
\(479\) −2.40863 8.98914i −0.110053 0.410724i 0.888816 0.458264i \(-0.151529\pi\)
−0.998869 + 0.0475398i \(0.984862\pi\)
\(480\) 0 0
\(481\) 30.2080 25.2590i 1.37737 1.15171i
\(482\) 0 0
\(483\) −12.4401 3.69342i −0.566045 0.168057i
\(484\) 0 0
\(485\) 8.11534 + 14.0562i 0.368498 + 0.638258i
\(486\) 0 0
\(487\) −16.0328 4.29597i −0.726515 0.194669i −0.123438 0.992352i \(-0.539392\pi\)
−0.603077 + 0.797683i \(0.706059\pi\)
\(488\) 0 0
\(489\) −1.55041 6.47584i −0.0701121 0.292848i
\(490\) 0 0
\(491\) 12.3545 21.3987i 0.557553 0.965709i −0.440147 0.897926i \(-0.645074\pi\)
0.997700 0.0677839i \(-0.0215928\pi\)
\(492\) 0 0
\(493\) 4.00042i 0.180170i
\(494\) 0 0
\(495\) 2.55133 + 5.02284i 0.114674 + 0.225760i
\(496\) 0 0
\(497\) 19.7126 + 11.3811i 0.884229 + 0.510510i
\(498\) 0 0
\(499\) 4.69214 4.69214i 0.210049 0.210049i −0.594239 0.804288i \(-0.702547\pi\)
0.804288 + 0.594239i \(0.202547\pi\)
\(500\) 0 0
\(501\) −28.1975 29.7513i −1.25977 1.32919i
\(502\) 0 0
\(503\) 31.1321 17.9741i 1.38811 0.801427i 0.395010 0.918677i \(-0.370741\pi\)
0.993102 + 0.117249i \(0.0374077\pi\)
\(504\) 0 0
\(505\) −3.73456 + 1.00067i −0.166186 + 0.0445293i
\(506\) 0 0
\(507\) −4.57891 + 22.0462i −0.203357 + 0.979105i
\(508\) 0 0
\(509\) −17.0359 + 4.56477i −0.755105 + 0.202330i −0.615781 0.787917i \(-0.711160\pi\)
−0.139324 + 0.990247i \(0.544493\pi\)
\(510\) 0 0
\(511\) 1.05375 0.608385i 0.0466153 0.0269134i
\(512\) 0 0
\(513\) 2.60409 7.30996i 0.114974 0.322743i
\(514\) 0 0
\(515\) −19.1991 + 19.1991i −0.846012 + 0.846012i
\(516\) 0 0
\(517\) 0.466573 + 0.269376i 0.0205199 + 0.0118472i
\(518\) 0 0
\(519\) −21.7348 13.3379i −0.954051 0.585467i
\(520\) 0 0
\(521\) 22.9129i 1.00383i 0.864917 + 0.501915i \(0.167371\pi\)
−0.864917 + 0.501915i \(0.832629\pi\)
\(522\) 0 0
\(523\) −6.11740 + 10.5957i −0.267495 + 0.463316i −0.968214 0.250122i \(-0.919529\pi\)
0.700719 + 0.713437i \(0.252863\pi\)
\(524\) 0 0
\(525\) −5.21726 + 1.24909i −0.227700 + 0.0545147i
\(526\) 0 0
\(527\) −23.6182 6.32848i −1.02882 0.275673i
\(528\) 0 0
\(529\) 5.63612 + 9.76205i 0.245049 + 0.424437i
\(530\) 0 0
\(531\) 27.1009 24.3402i 1.17608 1.05628i
\(532\) 0 0
\(533\) 25.5790 21.3884i 1.10795 0.926434i
\(534\) 0 0
\(535\) −0.189497 0.707211i −0.00819266 0.0305754i
\(536\) 0 0
\(537\) 0.792210 29.5447i 0.0341864 1.27495i
\(538\) 0 0
\(539\) −0.568310 + 2.12096i −0.0244789 + 0.0913563i
\(540\) 0 0
\(541\) −17.8177 17.8177i −0.766042 0.766042i 0.211365 0.977407i \(-0.432209\pi\)
−0.977407 + 0.211365i \(0.932209\pi\)
\(542\) 0 0
\(543\) 2.90497 + 5.35831i 0.124664 + 0.229947i
\(544\) 0 0
\(545\) −22.0644 −0.945137
\(546\) 0 0
\(547\) 19.4843 0.833087 0.416543 0.909116i \(-0.363241\pi\)
0.416543 + 0.909116i \(0.363241\pi\)
\(548\) 0 0
\(549\) 16.9802 + 0.911269i 0.724698 + 0.0388920i
\(550\) 0 0
\(551\) 0.894639 + 0.894639i 0.0381129 + 0.0381129i
\(552\) 0 0
\(553\) −5.68970 + 21.2342i −0.241950 + 0.902971i
\(554\) 0 0
\(555\) 35.7992 + 0.959920i 1.51959 + 0.0407463i
\(556\) 0 0
\(557\) 1.33172 + 4.97004i 0.0564267 + 0.210587i 0.988383 0.151983i \(-0.0485659\pi\)
−0.931956 + 0.362570i \(0.881899\pi\)
\(558\) 0 0
\(559\) 14.4829 20.6081i 0.612562 0.871630i
\(560\) 0 0
\(561\) 2.30894 7.77692i 0.0974834 0.328342i
\(562\) 0 0
\(563\) 1.28809 + 2.23104i 0.0542866 + 0.0940271i 0.891892 0.452249i \(-0.149378\pi\)
−0.837605 + 0.546276i \(0.816045\pi\)
\(564\) 0 0
\(565\) 21.8420 + 5.85255i 0.918901 + 0.246219i
\(566\) 0 0
\(567\) 19.4551 3.03134i 0.817038 0.127304i
\(568\) 0 0
\(569\) 2.81100 4.86880i 0.117843 0.204111i −0.801069 0.598572i \(-0.795735\pi\)
0.918913 + 0.394461i \(0.129069\pi\)
\(570\) 0 0
\(571\) 33.8079i 1.41482i −0.706806 0.707408i \(-0.749864\pi\)
0.706806 0.707408i \(-0.250136\pi\)
\(572\) 0 0
\(573\) 19.4754 31.7362i 0.813597 1.32580i
\(574\) 0 0
\(575\) −4.19878 2.42417i −0.175101 0.101095i
\(576\) 0 0
\(577\) −5.78457 + 5.78457i −0.240815 + 0.240815i −0.817187 0.576372i \(-0.804468\pi\)
0.576372 + 0.817187i \(0.304468\pi\)
\(578\) 0 0
\(579\) 5.05016 4.78640i 0.209877 0.198916i
\(580\) 0 0
\(581\) −6.04769 + 3.49163i −0.250900 + 0.144857i
\(582\) 0 0
\(583\) −9.96124 + 2.66911i −0.412552 + 0.110543i
\(584\) 0 0
\(585\) −16.3913 + 12.2754i −0.677695 + 0.507524i
\(586\) 0 0
\(587\) 39.0455 10.4622i 1.61158 0.431822i 0.663068 0.748559i \(-0.269254\pi\)
0.948514 + 0.316737i \(0.102587\pi\)
\(588\) 0 0
\(589\) 6.69716 3.86661i 0.275952 0.159321i
\(590\) 0 0
\(591\) −10.0820 + 9.55544i −0.414718 + 0.393058i
\(592\) 0 0
\(593\) 8.23055 8.23055i 0.337988 0.337988i −0.517621 0.855610i \(-0.673182\pi\)
0.855610 + 0.517621i \(0.173182\pi\)
\(594\) 0 0
\(595\) −16.9375 9.77890i −0.694372 0.400896i
\(596\) 0 0
\(597\) 10.1993 16.6203i 0.417428 0.680223i
\(598\) 0 0
\(599\) 7.22852i 0.295349i 0.989036 + 0.147675i \(0.0471789\pi\)
−0.989036 + 0.147675i \(0.952821\pi\)
\(600\) 0 0
\(601\) −1.92099 + 3.32725i −0.0783587 + 0.135721i −0.902542 0.430602i \(-0.858301\pi\)
0.824183 + 0.566323i \(0.191635\pi\)
\(602\) 0 0
\(603\) −16.7519 5.46628i −0.682190 0.222604i
\(604\) 0 0
\(605\) 18.3165 + 4.90790i 0.744672 + 0.199534i
\(606\) 0 0
\(607\) 6.01621 + 10.4204i 0.244190 + 0.422950i 0.961904 0.273389i \(-0.0881445\pi\)
−0.717713 + 0.696339i \(0.754811\pi\)
\(608\) 0 0
\(609\) −0.913707 + 3.07753i −0.0370253 + 0.124708i
\(610\) 0 0
\(611\) −0.672964 + 1.83909i −0.0272252 + 0.0744017i
\(612\) 0 0
\(613\) 6.43463 + 24.0144i 0.259892 + 0.969931i 0.965303 + 0.261133i \(0.0840960\pi\)
−0.705411 + 0.708799i \(0.749237\pi\)
\(614\) 0 0
\(615\) 30.3135 + 0.812825i 1.22236 + 0.0327763i
\(616\) 0 0
\(617\) −11.6729 + 43.5637i −0.469932 + 1.75381i 0.170066 + 0.985433i \(0.445602\pi\)
−0.639997 + 0.768377i \(0.721065\pi\)
\(618\) 0 0
\(619\) 24.4865 + 24.4865i 0.984197 + 0.984197i 0.999877 0.0156805i \(-0.00499147\pi\)
−0.0156805 + 0.999877i \(0.504991\pi\)
\(620\) 0 0
\(621\) 14.6460 + 10.1066i 0.587725 + 0.405564i
\(622\) 0 0
\(623\) 38.8952 1.55830
\(624\) 0 0
\(625\) 15.9169 0.636678
\(626\) 0 0
\(627\) 1.22284 + 2.25556i 0.0488354 + 0.0900784i
\(628\) 0 0
\(629\) −36.4649 36.4649i −1.45395 1.45395i
\(630\) 0 0
\(631\) −3.56833 + 13.3172i −0.142053 + 0.530149i 0.857816 + 0.513957i \(0.171821\pi\)
−0.999869 + 0.0161917i \(0.994846\pi\)
\(632\) 0 0
\(633\) −1.11232 + 41.4830i −0.0442109 + 1.64880i
\(634\) 0 0
\(635\) 0.0621559 + 0.231969i 0.00246658 + 0.00920541i
\(636\) 0 0
\(637\) −7.95003 0.709336i −0.314992 0.0281049i
\(638\) 0 0
\(639\) −20.8564 23.2219i −0.825065 0.918644i
\(640\) 0 0
\(641\) −18.7773 32.5233i −0.741659 1.28459i −0.951739 0.306908i \(-0.900706\pi\)
0.210080 0.977684i \(-0.432628\pi\)
\(642\) 0 0
\(643\) 33.9096 + 9.08605i 1.33726 + 0.358319i 0.855418 0.517937i \(-0.173300\pi\)
0.481845 + 0.876256i \(0.339967\pi\)
\(644\) 0 0
\(645\) 22.2784 5.33378i 0.877210 0.210017i
\(646\) 0 0
\(647\) 4.67261 8.09319i 0.183699 0.318176i −0.759438 0.650579i \(-0.774526\pi\)
0.943137 + 0.332403i \(0.107859\pi\)
\(648\) 0 0
\(649\) 12.0440i 0.472767i
\(650\) 0 0
\(651\) 16.7241 + 10.2630i 0.655468 + 0.402237i
\(652\) 0 0
\(653\) −4.78580 2.76309i −0.187283 0.108128i 0.403427 0.915012i \(-0.367819\pi\)
−0.590710 + 0.806884i \(0.701152\pi\)
\(654\) 0 0
\(655\) 27.9465 27.9465i 1.09196 1.09196i
\(656\) 0 0
\(657\) −1.63249 + 0.344855i −0.0636894 + 0.0134541i
\(658\) 0 0
\(659\) 30.1079 17.3828i 1.17284 0.677138i 0.218491 0.975839i \(-0.429887\pi\)
0.954347 + 0.298701i \(0.0965533\pi\)
\(660\) 0 0
\(661\) −10.7464 + 2.87948i −0.417985 + 0.111999i −0.461681 0.887046i \(-0.652753\pi\)
0.0436959 + 0.999045i \(0.486087\pi\)
\(662\) 0 0
\(663\) 29.2910 + 3.40703i 1.13757 + 0.132318i
\(664\) 0 0
\(665\) 5.97476 1.60093i 0.231691 0.0620815i
\(666\) 0 0
\(667\) −2.51260 + 1.45065i −0.0972883 + 0.0561694i
\(668\) 0 0
\(669\) −2.28068 2.40636i −0.0881763 0.0930353i
\(670\) 0 0
\(671\) −3.97559 + 3.97559i −0.153476 + 0.153476i
\(672\) 0 0
\(673\) 38.4396 + 22.1931i 1.48174 + 0.855482i 0.999785 0.0207144i \(-0.00659408\pi\)
0.481954 + 0.876197i \(0.339927\pi\)
\(674\) 0 0
\(675\) 7.33265 + 0.590986i 0.282234 + 0.0227470i
\(676\) 0 0
\(677\) 20.7036i 0.795704i −0.917450 0.397852i \(-0.869756\pi\)
0.917450 0.397852i \(-0.130244\pi\)
\(678\) 0 0
\(679\) −9.37793 + 16.2430i −0.359892 + 0.623351i
\(680\) 0 0
\(681\) 4.41329 + 18.4336i 0.169117 + 0.706378i
\(682\) 0 0
\(683\) 3.10117 + 0.830957i 0.118663 + 0.0317957i 0.317662 0.948204i \(-0.397102\pi\)
−0.198999 + 0.980000i \(0.563769\pi\)
\(684\) 0 0
\(685\) 12.0519 + 20.8745i 0.460478 + 0.797572i
\(686\) 0 0
\(687\) −5.11918 1.51987i −0.195309 0.0579865i
\(688\) 0 0
\(689\) −15.7838 34.0012i −0.601315 1.29534i
\(690\) 0 0
\(691\) 0.553429 + 2.06543i 0.0210534 + 0.0785725i 0.975653 0.219319i \(-0.0703834\pi\)
−0.954600 + 0.297891i \(0.903717\pi\)
\(692\) 0 0
\(693\) −3.55254 + 5.45542i −0.134950 + 0.207234i
\(694\) 0 0
\(695\) −8.97649 + 33.5007i −0.340498 + 1.27076i
\(696\) 0 0
\(697\) −30.8772 30.8772i −1.16956 1.16956i
\(698\) 0 0
\(699\) −11.8791 + 6.44019i −0.449310 + 0.243591i
\(700\) 0 0
\(701\) −21.3084 −0.804808 −0.402404 0.915462i \(-0.631825\pi\)
−0.402404 + 0.915462i \(0.631825\pi\)
\(702\) 0 0
\(703\) 16.3097 0.615133
\(704\) 0 0
\(705\) −1.56576 + 0.848867i −0.0589700 + 0.0319702i
\(706\) 0 0
\(707\) −3.15923 3.15923i −0.118815 0.118815i
\(708\) 0 0
\(709\) 7.30917 27.2782i 0.274502 1.02445i −0.681673 0.731657i \(-0.738747\pi\)
0.956175 0.292797i \(-0.0945859\pi\)
\(710\) 0 0
\(711\) 16.4498 25.2610i 0.616917 0.947363i
\(712\) 0 0
\(713\) 4.58972 + 17.1291i 0.171886 + 0.641489i
\(714\) 0 0
\(715\) 0.601732 6.74403i 0.0225035 0.252213i
\(716\) 0 0
\(717\) −34.8389 10.3435i −1.30108 0.386286i
\(718\) 0 0
\(719\) −2.67277 4.62937i −0.0996774 0.172646i 0.811874 0.583833i \(-0.198448\pi\)
−0.911551 + 0.411187i \(0.865114\pi\)
\(720\) 0 0
\(721\) −30.3068 8.12067i −1.12868 0.302430i
\(722\) 0 0
\(723\) −6.61964 27.6492i −0.246187 1.02829i
\(724\) 0 0
\(725\) −0.599709 + 1.03873i −0.0222726 + 0.0385773i
\(726\) 0 0
\(727\) 3.49159i 0.129496i 0.997902 + 0.0647480i \(0.0206244\pi\)
−0.997902 + 0.0647480i \(0.979376\pi\)
\(728\) 0 0
\(729\) −26.6515 4.32412i −0.987092 0.160153i
\(730\) 0 0
\(731\) −28.5678 16.4937i −1.05662 0.610040i
\(732\) 0 0
\(733\) −1.07662 + 1.07662i −0.0397658 + 0.0397658i −0.726710 0.686944i \(-0.758952\pi\)
0.686944 + 0.726710i \(0.258952\pi\)
\(734\) 0 0
\(735\) −4.99349 5.26865i −0.184187 0.194337i
\(736\) 0 0
\(737\) 5.04562 2.91309i 0.185858 0.107305i
\(738\) 0 0
\(739\) −32.6118 + 8.73832i −1.19965 + 0.321444i −0.802692 0.596394i \(-0.796599\pi\)
−0.396954 + 0.917838i \(0.629933\pi\)
\(740\) 0 0
\(741\) −7.31246 + 5.78859i −0.268630 + 0.212649i
\(742\) 0 0
\(743\) 9.87756 2.64668i 0.362372 0.0970974i −0.0730388 0.997329i \(-0.523270\pi\)
0.435411 + 0.900232i \(0.356603\pi\)
\(744\) 0 0
\(745\) 3.48590 2.01259i 0.127713 0.0737354i
\(746\) 0 0
\(747\) 9.36914 1.97918i 0.342799 0.0724146i
\(748\) 0 0
\(749\) 0.598261 0.598261i 0.0218600 0.0218600i
\(750\) 0 0
\(751\) −29.4768 17.0185i −1.07563 0.621012i −0.145912 0.989298i \(-0.546612\pi\)
−0.929713 + 0.368285i \(0.879945\pi\)
\(752\) 0 0
\(753\) −6.24894 3.83475i −0.227724 0.139746i
\(754\) 0 0
\(755\) 7.86261i 0.286150i
\(756\) 0 0
\(757\) 4.15573 7.19794i 0.151043 0.261614i −0.780568 0.625070i \(-0.785070\pi\)
0.931611 + 0.363457i \(0.118404\pi\)
\(758\) 0 0
\(759\) −5.72183 + 1.36989i −0.207689 + 0.0497240i
\(760\) 0 0
\(761\) 30.3530 + 8.13305i 1.10029 + 0.294823i 0.762884 0.646535i \(-0.223783\pi\)
0.337409 + 0.941358i \(0.390449\pi\)
\(762\) 0 0
\(763\) −12.7486 22.0813i −0.461531 0.799395i
\(764\) 0 0
\(765\) 17.9203 + 19.9528i 0.647911 + 0.721397i
\(766\) 0 0
\(767\) −43.1274 + 7.52796i −1.55724 + 0.271819i
\(768\) 0 0
\(769\) 12.2950 + 45.8856i 0.443370 + 1.65468i 0.720205 + 0.693761i \(0.244048\pi\)
−0.276835 + 0.960917i \(0.589286\pi\)
\(770\) 0 0
\(771\) 0.279882 10.4379i 0.0100797 0.375912i
\(772\) 0 0
\(773\) 2.09638 7.82380i 0.0754015 0.281402i −0.917923 0.396760i \(-0.870135\pi\)
0.993324 + 0.115357i \(0.0368013\pi\)
\(774\) 0 0
\(775\) 5.18385 + 5.18385i 0.186209 + 0.186209i
\(776\) 0 0
\(777\) 19.7238 + 36.3812i 0.707588 + 1.30517i
\(778\) 0 0
\(779\) 13.8105 0.494812
\(780\) 0 0
\(781\) 10.3201 0.369281
\(782\) 0 0
\(783\) 2.50025 3.62325i 0.0893515 0.129484i
\(784\) 0 0
\(785\) 21.6790 + 21.6790i 0.773755 + 0.773755i
\(786\) 0 0
\(787\) 5.53321 20.6502i 0.197238 0.736101i −0.794439 0.607344i \(-0.792235\pi\)
0.991676 0.128756i \(-0.0410985\pi\)
\(788\) 0 0
\(789\) −33.8030 0.906392i −1.20342 0.0322684i
\(790\) 0 0
\(791\) 6.76310 + 25.2402i 0.240468 + 0.897439i
\(792\) 0 0
\(793\) −16.7208 11.7510i −0.593774 0.417291i
\(794\) 0 0
\(795\) 9.70332 32.6825i 0.344141 1.15913i
\(796\) 0 0
\(797\) −7.33180