Properties

Label 504.2.c.f.253.8
Level 504
Weight 2
Character 504.253
Analytic conductor 4.024
Analytic rank 0
Dimension 8
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 504.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.386672896.3
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: no (minimal twist has level 168)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 253.8
Root \(1.40961 - 0.114062i\)
Character \(\chi\) = 504.253
Dual form 504.2.c.f.253.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.40961 + 0.114062i) q^{2} +(1.97398 + 0.321565i) q^{4} -1.12875i q^{5} +1.00000 q^{7} +(2.74586 + 0.678435i) q^{8} +O(q^{10})\) \(q+(1.40961 + 0.114062i) q^{2} +(1.97398 + 0.321565i) q^{4} -1.12875i q^{5} +1.00000 q^{7} +(2.74586 + 0.678435i) q^{8} +(0.128747 - 1.59109i) q^{10} -4.76717i q^{11} -0.456247i q^{13} +(1.40961 + 0.114062i) q^{14} +(3.79319 + 1.26952i) q^{16} -0.415006 q^{17} +7.63843i q^{19} +(0.362965 - 2.22812i) q^{20} +(0.543753 - 6.71984i) q^{22} -1.58499 q^{23} +3.72593 q^{25} +(0.0520404 - 0.643129i) q^{26} +(1.97398 + 0.321565i) q^{28} +6.72593i q^{29} -5.89592 q^{31} +(5.20210 + 2.22219i) q^{32} +(-0.584994 - 0.0473363i) q^{34} -1.12875i q^{35} -5.89592i q^{37} +(-0.871253 + 10.7672i) q^{38} +(0.765782 - 3.09938i) q^{40} +0.415006 q^{41} -9.43967i q^{43} +(1.53295 - 9.41030i) q^{44} +(-2.23422 - 0.180787i) q^{46} -11.2769 q^{47} +1.00000 q^{49} +(5.25209 + 0.424987i) q^{50} +(0.146713 - 0.900623i) q^{52} +7.63843i q^{53} -5.38093 q^{55} +(2.74586 + 0.678435i) q^{56} +(-0.767172 + 9.48091i) q^{58} +4.00000i q^{59} +1.80125i q^{61} +(-8.31092 - 0.672500i) q^{62} +(7.07945 + 3.72577i) q^{64} -0.514988 q^{65} +8.09467i q^{67} +(-0.819213 - 0.133451i) q^{68} +(0.128747 - 1.59109i) q^{70} -10.2068 q^{71} -3.34500 q^{73} +(0.672500 - 8.31092i) q^{74} +(-2.45625 + 15.0781i) q^{76} -4.76717i q^{77} -4.83001 q^{79} +(1.43297 - 4.28155i) q^{80} +(0.584994 + 0.0473363i) q^{82} +5.53434i q^{83} +0.468436i q^{85} +(1.07671 - 13.3062i) q^{86} +(3.23422 - 13.0900i) q^{88} -4.92999 q^{89} -0.456247i q^{91} +(-3.12875 - 0.509678i) q^{92} +(-15.8959 - 1.28626i) q^{94} +8.62185 q^{95} +16.4468 q^{97} +(1.40961 + 0.114062i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{4} + 8q^{7} + 6q^{8} + O(q^{10}) \) \( 8q + 2q^{4} + 8q^{7} + 6q^{8} - 4q^{10} - 6q^{16} - 4q^{17} - 24q^{20} - 12q^{23} - 24q^{25} + 28q^{26} + 2q^{28} + 8q^{31} + 30q^{32} - 4q^{34} - 12q^{38} + 28q^{40} + 4q^{41} - 16q^{44} + 4q^{46} + 8q^{49} + 20q^{50} - 12q^{52} - 8q^{55} + 6q^{56} + 44q^{58} - 12q^{62} + 26q^{64} + 16q^{65} + 16q^{68} - 4q^{70} + 28q^{71} - 8q^{73} - 4q^{74} - 24q^{76} - 40q^{79} + 4q^{80} + 4q^{82} - 24q^{86} + 4q^{88} - 20q^{89} - 20q^{92} - 72q^{94} - 40q^{95} + 40q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.40961 + 0.114062i 0.996742 + 0.0806539i
\(3\) 0 0
\(4\) 1.97398 + 0.321565i 0.986990 + 0.160782i
\(5\) 1.12875i 0.504791i −0.967624 0.252395i \(-0.918782\pi\)
0.967624 0.252395i \(-0.0812184\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 2.74586 + 0.678435i 0.970807 + 0.239863i
\(9\) 0 0
\(10\) 0.128747 1.59109i 0.0407134 0.503146i
\(11\) 4.76717i 1.43736i −0.695343 0.718678i \(-0.744747\pi\)
0.695343 0.718678i \(-0.255253\pi\)
\(12\) 0 0
\(13\) 0.456247i 0.126540i −0.997996 0.0632701i \(-0.979847\pi\)
0.997996 0.0632701i \(-0.0201530\pi\)
\(14\) 1.40961 + 0.114062i 0.376733 + 0.0304843i
\(15\) 0 0
\(16\) 3.79319 + 1.26952i 0.948298 + 0.317381i
\(17\) −0.415006 −0.100654 −0.0503268 0.998733i \(-0.516026\pi\)
−0.0503268 + 0.998733i \(0.516026\pi\)
\(18\) 0 0
\(19\) 7.63843i 1.75237i 0.481970 + 0.876187i \(0.339921\pi\)
−0.481970 + 0.876187i \(0.660079\pi\)
\(20\) 0.362965 2.22812i 0.0811615 0.498224i
\(21\) 0 0
\(22\) 0.543753 6.71984i 0.115928 1.43267i
\(23\) −1.58499 −0.330494 −0.165247 0.986252i \(-0.552842\pi\)
−0.165247 + 0.986252i \(0.552842\pi\)
\(24\) 0 0
\(25\) 3.72593 0.745186
\(26\) 0.0520404 0.643129i 0.0102060 0.126128i
\(27\) 0 0
\(28\) 1.97398 + 0.321565i 0.373047 + 0.0607700i
\(29\) 6.72593i 1.24897i 0.781035 + 0.624487i \(0.214692\pi\)
−0.781035 + 0.624487i \(0.785308\pi\)
\(30\) 0 0
\(31\) −5.89592 −1.05894 −0.529469 0.848329i \(-0.677609\pi\)
−0.529469 + 0.848329i \(0.677609\pi\)
\(32\) 5.20210 + 2.22219i 0.919611 + 0.392831i
\(33\) 0 0
\(34\) −0.584994 0.0473363i −0.100326 0.00811811i
\(35\) 1.12875i 0.190793i
\(36\) 0 0
\(37\) 5.89592i 0.969283i −0.874713 0.484642i \(-0.838950\pi\)
0.874713 0.484642i \(-0.161050\pi\)
\(38\) −0.871253 + 10.7672i −0.141336 + 1.74667i
\(39\) 0 0
\(40\) 0.765782 3.09938i 0.121081 0.490054i
\(41\) 0.415006 0.0648130 0.0324065 0.999475i \(-0.489683\pi\)
0.0324065 + 0.999475i \(0.489683\pi\)
\(42\) 0 0
\(43\) 9.43967i 1.43954i −0.694214 0.719768i \(-0.744248\pi\)
0.694214 0.719768i \(-0.255752\pi\)
\(44\) 1.53295 9.41030i 0.231102 1.41866i
\(45\) 0 0
\(46\) −2.23422 0.180787i −0.329417 0.0266557i
\(47\) −11.2769 −1.64490 −0.822449 0.568839i \(-0.807393\pi\)
−0.822449 + 0.568839i \(0.807393\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 5.25209 + 0.424987i 0.742758 + 0.0601022i
\(51\) 0 0
\(52\) 0.146713 0.900623i 0.0203454 0.124894i
\(53\) 7.63843i 1.04922i 0.851343 + 0.524609i \(0.175789\pi\)
−0.851343 + 0.524609i \(0.824211\pi\)
\(54\) 0 0
\(55\) −5.38093 −0.725565
\(56\) 2.74586 + 0.678435i 0.366930 + 0.0906597i
\(57\) 0 0
\(58\) −0.767172 + 9.48091i −0.100735 + 1.24490i
\(59\) 4.00000i 0.520756i 0.965507 + 0.260378i \(0.0838471\pi\)
−0.965507 + 0.260378i \(0.916153\pi\)
\(60\) 0 0
\(61\) 1.80125i 0.230626i 0.993329 + 0.115313i \(0.0367871\pi\)
−0.993329 + 0.115313i \(0.963213\pi\)
\(62\) −8.31092 0.672500i −1.05549 0.0854075i
\(63\) 0 0
\(64\) 7.07945 + 3.72577i 0.884931 + 0.465721i
\(65\) −0.514988 −0.0638764
\(66\) 0 0
\(67\) 8.09467i 0.988922i 0.869200 + 0.494461i \(0.164634\pi\)
−0.869200 + 0.494461i \(0.835366\pi\)
\(68\) −0.819213 0.133451i −0.0993441 0.0161833i
\(69\) 0 0
\(70\) 0.128747 1.59109i 0.0153882 0.190171i
\(71\) −10.2068 −1.21133 −0.605665 0.795720i \(-0.707093\pi\)
−0.605665 + 0.795720i \(0.707093\pi\)
\(72\) 0 0
\(73\) −3.34500 −0.391503 −0.195751 0.980654i \(-0.562715\pi\)
−0.195751 + 0.980654i \(0.562715\pi\)
\(74\) 0.672500 8.31092i 0.0781765 0.966125i
\(75\) 0 0
\(76\) −2.45625 + 15.0781i −0.281751 + 1.72958i
\(77\) 4.76717i 0.543270i
\(78\) 0 0
\(79\) −4.83001 −0.543419 −0.271709 0.962379i \(-0.587589\pi\)
−0.271709 + 0.962379i \(0.587589\pi\)
\(80\) 1.43297 4.28155i 0.160211 0.478692i
\(81\) 0 0
\(82\) 0.584994 + 0.0473363i 0.0646018 + 0.00522742i
\(83\) 5.53434i 0.607473i 0.952756 + 0.303737i \(0.0982343\pi\)
−0.952756 + 0.303737i \(0.901766\pi\)
\(84\) 0 0
\(85\) 0.468436i 0.0508090i
\(86\) 1.07671 13.3062i 0.116104 1.43485i
\(87\) 0 0
\(88\) 3.23422 13.0900i 0.344769 1.39540i
\(89\) −4.92999 −0.522578 −0.261289 0.965261i \(-0.584148\pi\)
−0.261289 + 0.965261i \(0.584148\pi\)
\(90\) 0 0
\(91\) 0.456247i 0.0478277i
\(92\) −3.12875 0.509678i −0.326194 0.0531376i
\(93\) 0 0
\(94\) −15.8959 1.28626i −1.63954 0.132667i
\(95\) 8.62185 0.884583
\(96\) 0 0
\(97\) 16.4468 1.66992 0.834962 0.550308i \(-0.185490\pi\)
0.834962 + 0.550308i \(0.185490\pi\)
\(98\) 1.40961 + 0.114062i 0.142392 + 0.0115220i
\(99\) 0 0
\(100\) 7.35491 + 1.19813i 0.735491 + 0.119813i
\(101\) 16.4056i 1.63242i −0.577757 0.816209i \(-0.696072\pi\)
0.577757 0.816209i \(-0.303928\pi\)
\(102\) 0 0
\(103\) −17.1728 −1.69208 −0.846042 0.533117i \(-0.821021\pi\)
−0.846042 + 0.533117i \(0.821021\pi\)
\(104\) 0.309534 1.25279i 0.0303523 0.122846i
\(105\) 0 0
\(106\) −0.871253 + 10.7672i −0.0846236 + 1.04580i
\(107\) 12.7672i 1.23425i 0.786865 + 0.617125i \(0.211703\pi\)
−0.786865 + 0.617125i \(0.788297\pi\)
\(108\) 0 0
\(109\) 7.27685i 0.696996i −0.937310 0.348498i \(-0.886692\pi\)
0.937310 0.348498i \(-0.113308\pi\)
\(110\) −7.58499 0.613759i −0.723201 0.0585196i
\(111\) 0 0
\(112\) 3.79319 + 1.26952i 0.358423 + 0.119959i
\(113\) 3.34500 0.314671 0.157336 0.987545i \(-0.449710\pi\)
0.157336 + 0.987545i \(0.449710\pi\)
\(114\) 0 0
\(115\) 1.78906i 0.166830i
\(116\) −2.16282 + 13.2769i −0.200813 + 1.23272i
\(117\) 0 0
\(118\) −0.456247 + 5.63843i −0.0420010 + 0.519059i
\(119\) −0.415006 −0.0380435
\(120\) 0 0
\(121\) −11.7259 −1.06599
\(122\) −0.205454 + 2.53905i −0.0186009 + 0.229875i
\(123\) 0 0
\(124\) −11.6384 1.89592i −1.04516 0.170259i
\(125\) 9.84937i 0.880954i
\(126\) 0 0
\(127\) −10.4468 −0.927007 −0.463504 0.886095i \(-0.653408\pi\)
−0.463504 + 0.886095i \(0.653408\pi\)
\(128\) 9.55427 + 6.05937i 0.844486 + 0.535577i
\(129\) 0 0
\(130\) −0.725930 0.0587405i −0.0636683 0.00515188i
\(131\) 6.25749i 0.546720i −0.961912 0.273360i \(-0.911865\pi\)
0.961912 0.273360i \(-0.0881350\pi\)
\(132\) 0 0
\(133\) 7.63843i 0.662335i
\(134\) −0.923293 + 11.4103i −0.0797604 + 0.985700i
\(135\) 0 0
\(136\) −1.13955 0.281554i −0.0977152 0.0241431i
\(137\) 12.9618 1.10740 0.553702 0.832715i \(-0.313215\pi\)
0.553702 + 0.832715i \(0.313215\pi\)
\(138\) 0 0
\(139\) 18.3644i 1.55764i −0.627245 0.778822i \(-0.715817\pi\)
0.627245 0.778822i \(-0.284183\pi\)
\(140\) 0.362965 2.22812i 0.0306762 0.188311i
\(141\) 0 0
\(142\) −14.3876 1.16421i −1.20738 0.0976985i
\(143\) −2.17501 −0.181883
\(144\) 0 0
\(145\) 7.59187 0.630471
\(146\) −4.71513 0.381537i −0.390227 0.0315762i
\(147\) 0 0
\(148\) 1.89592 11.6384i 0.155844 0.956673i
\(149\) 15.6384i 1.28115i 0.767896 + 0.640575i \(0.221304\pi\)
−0.767896 + 0.640575i \(0.778696\pi\)
\(150\) 0 0
\(151\) 15.2769 1.24321 0.621606 0.783330i \(-0.286480\pi\)
0.621606 + 0.783330i \(0.286480\pi\)
\(152\) −5.18218 + 20.9740i −0.420330 + 1.70122i
\(153\) 0 0
\(154\) 0.543753 6.71984i 0.0438168 0.541500i
\(155\) 6.65500i 0.534543i
\(156\) 0 0
\(157\) 21.7824i 1.73843i 0.494437 + 0.869214i \(0.335374\pi\)
−0.494437 + 0.869214i \(0.664626\pi\)
\(158\) −6.80841 0.550920i −0.541648 0.0438288i
\(159\) 0 0
\(160\) 2.50829 5.87186i 0.198298 0.464211i
\(161\) −1.58499 −0.124915
\(162\) 0 0
\(163\) 4.60966i 0.361056i −0.983570 0.180528i \(-0.942219\pi\)
0.983570 0.180528i \(-0.0577807\pi\)
\(164\) 0.819213 + 0.133451i 0.0639698 + 0.0104208i
\(165\) 0 0
\(166\) −0.631258 + 7.80125i −0.0489951 + 0.605494i
\(167\) 22.9618 1.77684 0.888420 0.459032i \(-0.151804\pi\)
0.888420 + 0.459032i \(0.151804\pi\)
\(168\) 0 0
\(169\) 12.7918 0.983988
\(170\) −0.0534307 + 0.660311i −0.00409795 + 0.0506435i
\(171\) 0 0
\(172\) 3.03546 18.6337i 0.231452 1.42081i
\(173\) 0.216252i 0.0164413i 0.999966 + 0.00822067i \(0.00261675\pi\)
−0.999966 + 0.00822067i \(0.997383\pi\)
\(174\) 0 0
\(175\) 3.72593 0.281654
\(176\) 6.05204 18.0828i 0.456190 1.36304i
\(177\) 0 0
\(178\) −6.94935 0.562324i −0.520876 0.0421480i
\(179\) 22.6165i 1.69044i −0.534419 0.845220i \(-0.679470\pi\)
0.534419 0.845220i \(-0.320530\pi\)
\(180\) 0 0
\(181\) 7.73310i 0.574797i 0.957811 + 0.287398i \(0.0927903\pi\)
−0.957811 + 0.287398i \(0.907210\pi\)
\(182\) 0.0520404 0.643129i 0.00385749 0.0476719i
\(183\) 0 0
\(184\) −4.35217 1.07532i −0.320846 0.0792734i
\(185\) −6.65500 −0.489285
\(186\) 0 0
\(187\) 1.97840i 0.144675i
\(188\) −22.2603 3.62624i −1.62350 0.264470i
\(189\) 0 0
\(190\) 12.1534 + 0.983424i 0.881701 + 0.0713451i
\(191\) −10.2068 −0.738541 −0.369271 0.929322i \(-0.620392\pi\)
−0.369271 + 0.929322i \(0.620392\pi\)
\(192\) 0 0
\(193\) 5.96407 0.429303 0.214651 0.976691i \(-0.431138\pi\)
0.214651 + 0.976691i \(0.431138\pi\)
\(194\) 23.1836 + 1.87596i 1.66448 + 0.134686i
\(195\) 0 0
\(196\) 1.97398 + 0.321565i 0.140999 + 0.0229689i
\(197\) 18.8084i 1.34004i −0.742341 0.670022i \(-0.766285\pi\)
0.742341 0.670022i \(-0.233715\pi\)
\(198\) 0 0
\(199\) 3.27685 0.232290 0.116145 0.993232i \(-0.462946\pi\)
0.116145 + 0.993232i \(0.462946\pi\)
\(200\) 10.2309 + 2.52780i 0.723432 + 0.178743i
\(201\) 0 0
\(202\) 1.87125 23.1254i 0.131661 1.62710i
\(203\) 6.72593i 0.472068i
\(204\) 0 0
\(205\) 0.468436i 0.0327170i
\(206\) −24.2068 1.95876i −1.68657 0.136473i
\(207\) 0 0
\(208\) 0.579217 1.73063i 0.0401615 0.119998i
\(209\) 36.4137 2.51879
\(210\) 0 0
\(211\) 10.1628i 0.699637i 0.936817 + 0.349819i \(0.113757\pi\)
−0.936817 + 0.349819i \(0.886243\pi\)
\(212\) −2.45625 + 15.0781i −0.168696 + 1.03557i
\(213\) 0 0
\(214\) −1.45625 + 17.9967i −0.0995470 + 1.23023i
\(215\) −10.6550 −0.726665
\(216\) 0 0
\(217\) −5.89592 −0.400241
\(218\) 0.830011 10.2575i 0.0562154 0.694725i
\(219\) 0 0
\(220\) −10.6218 1.73032i −0.716125 0.116658i
\(221\) 0.189345i 0.0127367i
\(222\) 0 0
\(223\) 21.9668 1.47101 0.735504 0.677520i \(-0.236945\pi\)
0.735504 + 0.677520i \(0.236945\pi\)
\(224\) 5.20210 + 2.22219i 0.347580 + 0.148476i
\(225\) 0 0
\(226\) 4.71513 + 0.381537i 0.313646 + 0.0253795i
\(227\) 7.91752i 0.525504i −0.964863 0.262752i \(-0.915370\pi\)
0.964863 0.262752i \(-0.0846301\pi\)
\(228\) 0 0
\(229\) 13.1606i 0.869676i −0.900509 0.434838i \(-0.856806\pi\)
0.900509 0.434838i \(-0.143194\pi\)
\(230\) −0.204063 + 2.52187i −0.0134555 + 0.166287i
\(231\) 0 0
\(232\) −4.56311 + 18.4684i −0.299583 + 1.21251i
\(233\) −17.2769 −1.13184 −0.565922 0.824459i \(-0.691480\pi\)
−0.565922 + 0.824459i \(0.691480\pi\)
\(234\) 0 0
\(235\) 12.7287i 0.830330i
\(236\) −1.28626 + 7.89592i −0.0837283 + 0.513981i
\(237\) 0 0
\(238\) −0.584994 0.0473363i −0.0379196 0.00306836i
\(239\) 10.5219 0.680603 0.340301 0.940316i \(-0.389471\pi\)
0.340301 + 0.940316i \(0.389471\pi\)
\(240\) 0 0
\(241\) −6.10686 −0.393378 −0.196689 0.980466i \(-0.563019\pi\)
−0.196689 + 0.980466i \(0.563019\pi\)
\(242\) −16.5289 1.33748i −1.06252 0.0859766i
\(243\) 0 0
\(244\) −0.579217 + 3.55562i −0.0370806 + 0.227626i
\(245\) 1.12875i 0.0721130i
\(246\) 0 0
\(247\) 3.48501 0.221746
\(248\) −16.1893 4.00000i −1.02802 0.254000i
\(249\) 0 0
\(250\) 1.12344 13.8837i 0.0710524 0.878084i
\(251\) 19.8743i 1.25446i 0.778836 + 0.627228i \(0.215811\pi\)
−0.778836 + 0.627228i \(0.784189\pi\)
\(252\) 0 0
\(253\) 7.55594i 0.475038i
\(254\) −14.7259 1.19159i −0.923987 0.0747668i
\(255\) 0 0
\(256\) 12.7766 + 9.63110i 0.798539 + 0.601944i
\(257\) 14.7550 0.920391 0.460195 0.887818i \(-0.347779\pi\)
0.460195 + 0.887818i \(0.347779\pi\)
\(258\) 0 0
\(259\) 5.89592i 0.366355i
\(260\) −1.01658 0.165602i −0.0630454 0.0102702i
\(261\) 0 0
\(262\) 0.713741 8.82060i 0.0440951 0.544939i
\(263\) 15.7600 0.971804 0.485902 0.874013i \(-0.338491\pi\)
0.485902 + 0.874013i \(0.338491\pi\)
\(264\) 0 0
\(265\) 8.62185 0.529636
\(266\) −0.871253 + 10.7672i −0.0534199 + 0.660178i
\(267\) 0 0
\(268\) −2.60296 + 15.9787i −0.159001 + 0.976056i
\(269\) 21.8331i 1.33119i 0.746315 + 0.665593i \(0.231821\pi\)
−0.746315 + 0.665593i \(0.768179\pi\)
\(270\) 0 0
\(271\) −18.8328 −1.14401 −0.572005 0.820250i \(-0.693834\pi\)
−0.572005 + 0.820250i \(0.693834\pi\)
\(272\) −1.57420 0.526860i −0.0954496 0.0319456i
\(273\) 0 0
\(274\) 18.2711 + 1.47845i 1.10380 + 0.0893164i
\(275\) 17.7622i 1.07110i
\(276\) 0 0
\(277\) 24.4684i 1.47017i −0.677977 0.735083i \(-0.737143\pi\)
0.677977 0.735083i \(-0.262857\pi\)
\(278\) 2.09467 25.8865i 0.125630 1.55257i
\(279\) 0 0
\(280\) 0.765782 3.09938i 0.0457642 0.185223i
\(281\) −14.5150 −0.865892 −0.432946 0.901420i \(-0.642526\pi\)
−0.432946 + 0.901420i \(0.642526\pi\)
\(282\) 0 0
\(283\) 16.5509i 0.983850i −0.870638 0.491925i \(-0.836293\pi\)
0.870638 0.491925i \(-0.163707\pi\)
\(284\) −20.1481 3.28216i −1.19557 0.194760i
\(285\) 0 0
\(286\) −3.06591 0.248086i −0.181291 0.0146696i
\(287\) 0.415006 0.0244970
\(288\) 0 0
\(289\) −16.8278 −0.989869
\(290\) 10.7016 + 0.865943i 0.628417 + 0.0508499i
\(291\) 0 0
\(292\) −6.60296 1.07563i −0.386409 0.0629467i
\(293\) 9.44377i 0.551711i −0.961199 0.275855i \(-0.911039\pi\)
0.961199 0.275855i \(-0.0889611\pi\)
\(294\) 0 0
\(295\) 4.51499 0.262873
\(296\) 4.00000 16.1893i 0.232495 0.940987i
\(297\) 0 0
\(298\) −1.78375 + 22.0440i −0.103330 + 1.27698i
\(299\) 0.723150i 0.0418208i
\(300\) 0 0
\(301\) 9.43967i 0.544094i
\(302\) 21.5343 + 1.74251i 1.23916 + 0.100270i
\(303\) 0 0
\(304\) −9.69717 + 28.9740i −0.556171 + 1.66177i
\(305\) 2.03315 0.116418
\(306\) 0 0
\(307\) 0.361575i 0.0206362i 0.999947 + 0.0103181i \(0.00328441\pi\)
−0.999947 + 0.0103181i \(0.996716\pi\)
\(308\) 1.53295 9.41030i 0.0873482 0.536202i
\(309\) 0 0
\(310\) −0.759082 + 9.38093i −0.0431130 + 0.532801i
\(311\) 11.2769 0.639452 0.319726 0.947510i \(-0.396409\pi\)
0.319726 + 0.947510i \(0.396409\pi\)
\(312\) 0 0
\(313\) 25.5837 1.44607 0.723037 0.690809i \(-0.242745\pi\)
0.723037 + 0.690809i \(0.242745\pi\)
\(314\) −2.48454 + 30.7047i −0.140211 + 1.73276i
\(315\) 0 0
\(316\) −9.53434 1.55316i −0.536349 0.0873721i
\(317\) 0.361575i 0.0203081i −0.999948 0.0101540i \(-0.996768\pi\)
0.999948 0.0101540i \(-0.00323218\pi\)
\(318\) 0 0
\(319\) 32.0637 1.79522
\(320\) 4.20545 7.99091i 0.235092 0.446705i
\(321\) 0 0
\(322\) −2.23422 0.180787i −0.124508 0.0100749i
\(323\) 3.16999i 0.176383i
\(324\) 0 0
\(325\) 1.69995i 0.0942960i
\(326\) 0.525786 6.49781i 0.0291206 0.359880i
\(327\) 0 0
\(328\) 1.13955 + 0.281554i 0.0629209 + 0.0155462i
\(329\) −11.2769 −0.621713
\(330\) 0 0
\(331\) 7.80403i 0.428948i 0.976730 + 0.214474i \(0.0688037\pi\)
−0.976730 + 0.214474i \(0.931196\pi\)
\(332\) −1.77965 + 10.9247i −0.0976710 + 0.599570i
\(333\) 0 0
\(334\) 32.3671 + 2.61907i 1.77105 + 0.143309i
\(335\) 9.13684 0.499199
\(336\) 0 0
\(337\) 8.76186 0.477289 0.238645 0.971107i \(-0.423297\pi\)
0.238645 + 0.971107i \(0.423297\pi\)
\(338\) 18.0315 + 1.45906i 0.980782 + 0.0793625i
\(339\) 0 0
\(340\) −0.150633 + 0.924684i −0.00816920 + 0.0501480i
\(341\) 28.1069i 1.52207i
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 6.40421 25.9200i 0.345292 1.39751i
\(345\) 0 0
\(346\) −0.0246661 + 0.304830i −0.00132606 + 0.0163878i
\(347\) 2.07717i 0.111509i −0.998445 0.0557543i \(-0.982244\pi\)
0.998445 0.0557543i \(-0.0177563\pi\)
\(348\) 0 0
\(349\) 18.7381i 1.00303i −0.865149 0.501514i \(-0.832776\pi\)
0.865149 0.501514i \(-0.167224\pi\)
\(350\) 5.25209 + 0.424987i 0.280736 + 0.0227165i
\(351\) 0 0
\(352\) 10.5936 24.7993i 0.564638 1.32181i
\(353\) 13.2450 0.704961 0.352481 0.935819i \(-0.385338\pi\)
0.352481 + 0.935819i \(0.385338\pi\)
\(354\) 0 0
\(355\) 11.5209i 0.611468i
\(356\) −9.73171 1.58531i −0.515779 0.0840213i
\(357\) 0 0
\(358\) 2.57968 31.8804i 0.136341 1.68493i
\(359\) 5.69186 0.300405 0.150202 0.988655i \(-0.452007\pi\)
0.150202 + 0.988655i \(0.452007\pi\)
\(360\) 0 0
\(361\) −39.3455 −2.07082
\(362\) −0.882052 + 10.9006i −0.0463596 + 0.572924i
\(363\) 0 0
\(364\) 0.146713 0.900623i 0.00768985 0.0472055i
\(365\) 3.77566i 0.197627i
\(366\) 0 0
\(367\) 11.2769 0.588647 0.294323 0.955706i \(-0.404906\pi\)
0.294323 + 0.955706i \(0.404906\pi\)
\(368\) −6.01219 2.01219i −0.313407 0.104893i
\(369\) 0 0
\(370\) −9.38093 0.759082i −0.487691 0.0394628i
\(371\) 7.63843i 0.396567i
\(372\) 0 0
\(373\) 7.08751i 0.366977i −0.983022 0.183489i \(-0.941261\pi\)
0.983022 0.183489i \(-0.0587390\pi\)
\(374\) −0.225660 + 2.78877i −0.0116686 + 0.144204i
\(375\) 0 0
\(376\) −30.9646 7.65061i −1.59688 0.394550i
\(377\) 3.06869 0.158046
\(378\) 0 0
\(379\) 6.67781i 0.343016i −0.985183 0.171508i \(-0.945136\pi\)
0.985183 0.171508i \(-0.0548639\pi\)
\(380\) 17.0194 + 2.77248i 0.873075 + 0.142225i
\(381\) 0 0
\(382\) −14.3876 1.16421i −0.736135 0.0595662i
\(383\) 18.6550 0.953226 0.476613 0.879113i \(-0.341864\pi\)
0.476613 + 0.879113i \(0.341864\pi\)
\(384\) 0 0
\(385\) −5.38093 −0.274238
\(386\) 8.40699 + 0.680273i 0.427904 + 0.0346250i
\(387\) 0 0
\(388\) 32.4657 + 5.28872i 1.64820 + 0.268494i
\(389\) 20.3428i 1.03142i 0.856764 + 0.515709i \(0.172472\pi\)
−0.856764 + 0.515709i \(0.827528\pi\)
\(390\) 0 0
\(391\) 0.657782 0.0332654
\(392\) 2.74586 + 0.678435i 0.138687 + 0.0342662i
\(393\) 0 0
\(394\) 2.14532 26.5125i 0.108080 1.33568i
\(395\) 5.45186i 0.274313i
\(396\) 0 0
\(397\) 10.9031i 0.547210i −0.961842 0.273605i \(-0.911784\pi\)
0.961842 0.273605i \(-0.0882161\pi\)
\(398\) 4.61907 + 0.373764i 0.231533 + 0.0187351i
\(399\) 0 0
\(400\) 14.1332 + 4.73016i 0.706659 + 0.236508i
\(401\) −29.1756 −1.45696 −0.728479 0.685068i \(-0.759772\pi\)
−0.728479 + 0.685068i \(0.759772\pi\)
\(402\) 0 0
\(403\) 2.69000i 0.133998i
\(404\) 5.27546 32.3843i 0.262464 1.61118i
\(405\) 0 0
\(406\) −0.767172 + 9.48091i −0.0380741 + 0.470530i
\(407\) −28.1069 −1.39321
\(408\) 0 0
\(409\) −31.7237 −1.56864 −0.784318 0.620359i \(-0.786987\pi\)
−0.784318 + 0.620359i \(0.786987\pi\)
\(410\) 0.0534307 0.660311i 0.00263875 0.0326104i
\(411\) 0 0
\(412\) −33.8987 5.52216i −1.67007 0.272057i
\(413\) 4.00000i 0.196827i
\(414\) 0 0
\(415\) 6.24687 0.306647
\(416\) 1.01387 2.37345i 0.0497089 0.116368i
\(417\) 0 0
\(418\) 51.3290 + 4.15341i 2.51058 + 0.203150i
\(419\) 19.2769i 0.941736i −0.882204 0.470868i \(-0.843941\pi\)
0.882204 0.470868i \(-0.156059\pi\)
\(420\) 0 0
\(421\) 19.3234i 0.941765i 0.882196 + 0.470882i \(0.156064\pi\)
−0.882196 + 0.470882i \(0.843936\pi\)
\(422\) −1.15919 + 14.3256i −0.0564285 + 0.697358i
\(423\) 0 0
\(424\) −5.18218 + 20.9740i −0.251669 + 1.01859i
\(425\) −1.54628 −0.0750057
\(426\) 0 0
\(427\) 1.80125i 0.0871684i
\(428\) −4.10547 + 25.2021i −0.198445 + 1.21819i
\(429\) 0 0
\(430\) −15.0194 1.21533i −0.724298 0.0586084i
\(431\) −14.4150 −0.694346 −0.347173 0.937801i \(-0.612858\pi\)
−0.347173 + 0.937801i \(0.612858\pi\)
\(432\) 0 0
\(433\) −9.27685 −0.445817 −0.222908 0.974839i \(-0.571555\pi\)
−0.222908 + 0.974839i \(0.571555\pi\)
\(434\) −8.31092 0.672500i −0.398937 0.0322810i
\(435\) 0 0
\(436\) 2.33998 14.3644i 0.112065 0.687928i
\(437\) 12.1069i 0.579150i
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) −14.7753 3.65061i −0.704383 0.174036i
\(441\) 0 0
\(442\) −0.0215971 + 0.266902i −0.00102727 + 0.0126952i
\(443\) 15.6465i 0.743388i −0.928355 0.371694i \(-0.878777\pi\)
0.928355 0.371694i \(-0.121223\pi\)
\(444\) 0 0
\(445\) 5.56472i 0.263793i
\(446\) 30.9646 + 2.50558i 1.46622 + 0.118643i
\(447\) 0 0
\(448\) 7.07945 + 3.72577i 0.334473 + 0.176026i
\(449\) 12.6550 0.597226 0.298613 0.954374i \(-0.403476\pi\)
0.298613 + 0.954374i \(0.403476\pi\)
\(450\) 0 0
\(451\) 1.97840i 0.0931594i
\(452\) 6.60296 + 1.07563i 0.310577 + 0.0505935i
\(453\) 0 0
\(454\) 0.903087 11.1606i 0.0423840 0.523792i
\(455\) −0.514988 −0.0241430
\(456\) 0 0
\(457\) −23.9237 −1.11910 −0.559551 0.828796i \(-0.689026\pi\)
−0.559551 + 0.828796i \(0.689026\pi\)
\(458\) 1.50112 18.5512i 0.0701427 0.866842i
\(459\) 0 0
\(460\) −0.575298 + 3.53156i −0.0268234 + 0.164660i
\(461\) 6.74558i 0.314173i −0.987585 0.157086i \(-0.949790\pi\)
0.987585 0.157086i \(-0.0502101\pi\)
\(462\) 0 0
\(463\) −11.1700 −0.519113 −0.259557 0.965728i \(-0.583576\pi\)
−0.259557 + 0.965728i \(0.583576\pi\)
\(464\) −8.53873 + 25.5127i −0.396401 + 1.18440i
\(465\) 0 0
\(466\) −24.3536 1.97063i −1.12816 0.0912877i
\(467\) 3.70935i 0.171648i −0.996310 0.0858242i \(-0.972648\pi\)
0.996310 0.0858242i \(-0.0273523\pi\)
\(468\) 0 0
\(469\) 8.09467i 0.373777i
\(470\) −1.45186 + 17.9425i −0.0669693 + 0.827624i
\(471\) 0 0
\(472\) −2.71374 + 10.9834i −0.124910 + 0.505553i
\(473\) −45.0005 −2.06913
\(474\) 0 0
\(475\) 28.4602i 1.30585i
\(476\) −0.819213 0.133451i −0.0375485 0.00611672i
\(477\) 0 0
\(478\) 14.8317 + 1.20014i 0.678386 + 0.0548933i
\(479\) 2.17501 0.0993788 0.0496894 0.998765i \(-0.484177\pi\)
0.0496894 + 0.998765i \(0.484177\pi\)
\(480\) 0 0
\(481\) −2.69000 −0.122653
\(482\) −8.60827 0.696560i −0.392096 0.0317274i
\(483\) 0 0
\(484\) −23.1467 3.77064i −1.05212 0.171393i
\(485\) 18.5643i 0.842962i
\(486\) 0 0
\(487\) −4.51499 −0.204594 −0.102297 0.994754i \(-0.532619\pi\)
−0.102297 + 0.994754i \(0.532619\pi\)
\(488\) −1.22203 + 4.94596i −0.0553187 + 0.223893i
\(489\) 0 0
\(490\) 0.128747 1.59109i 0.00581620 0.0718781i
\(491\) 1.91221i 0.0862967i 0.999069 + 0.0431483i \(0.0137388\pi\)
−0.999069 + 0.0431483i \(0.986261\pi\)
\(492\) 0 0
\(493\) 2.79130i 0.125714i
\(494\) 4.91249 + 0.397507i 0.221024 + 0.0178847i
\(495\) 0 0
\(496\) −22.3644 7.48501i −1.00419 0.336087i
\(497\) −10.2068 −0.457840
\(498\) 0 0
\(499\) 27.4065i 1.22688i 0.789740 + 0.613442i \(0.210216\pi\)
−0.789740 + 0.613442i \(0.789784\pi\)
\(500\) 3.16721 19.4425i 0.141642 0.869493i
\(501\) 0 0
\(502\) −2.26690 + 28.0150i −0.101177 + 1.25037i
\(503\) −17.1368 −0.764094 −0.382047 0.924143i \(-0.624781\pi\)
−0.382047 + 0.924143i \(0.624781\pi\)
\(504\) 0 0
\(505\) −18.5178 −0.824030
\(506\) −0.861845 + 10.6509i −0.0383137 + 0.473490i
\(507\) 0 0
\(508\) −20.6218 3.35933i −0.914947 0.149046i
\(509\) 21.6437i 0.959342i −0.877449 0.479671i \(-0.840756\pi\)
0.877449 0.479671i \(-0.159244\pi\)
\(510\) 0 0
\(511\) −3.34500 −0.147974
\(512\) 16.9115 + 15.0334i 0.747388 + 0.664388i
\(513\) 0 0
\(514\) 20.7987 + 1.68298i 0.917392 + 0.0742331i
\(515\) 19.3837i 0.854148i
\(516\) 0 0
\(517\) 53.7587i 2.36430i
\(518\) 0.672500 8.31092i 0.0295479 0.365161i
\(519\) 0 0
\(520\) −1.41408 0.349386i −0.0620116 0.0153216i
\(521\) −28.3137 −1.24045 −0.620223 0.784426i \(-0.712958\pi\)
−0.620223 + 0.784426i \(0.712958\pi\)
\(522\) 0 0
\(523\) 15.0687i 0.658908i −0.944172 0.329454i \(-0.893135\pi\)
0.944172 0.329454i \(-0.106865\pi\)
\(524\) 2.01219 12.3522i 0.0879029 0.539607i
\(525\) 0 0
\(526\) 22.2154 + 1.79762i 0.968638 + 0.0783798i
\(527\) 2.44684 0.106586
\(528\) 0 0
\(529\) −20.4878 −0.890774
\(530\) 12.1534 + 0.983424i 0.527911 + 0.0427172i
\(531\) 0 0
\(532\) −2.45625 + 15.0781i −0.106492 + 0.653718i
\(533\) 0.189345i 0.00820145i
\(534\) 0 0
\(535\) 14.4109 0.623038
\(536\) −5.49171 + 22.2268i −0.237206 + 0.960052i
\(537\) 0 0
\(538\) −2.49032 + 30.7760i −0.107365 + 1.32685i
\(539\) 4.76717i 0.205337i
\(540\) 0 0
\(541\) 46.2990i 1.99055i 0.0971017 + 0.995274i \(0.469043\pi\)
−0.0971017 + 0.995274i \(0.530957\pi\)
\(542\) −26.5468 2.14810i −1.14028 0.0922689i
\(543\) 0 0
\(544\) −2.15890 0.922220i −0.0925622 0.0395399i
\(545\) −8.21372 −0.351837
\(546\) 0 0
\(547\) 2.03714i 0.0871020i 0.999051 + 0.0435510i \(0.0138671\pi\)
−0.999051 + 0.0435510i \(0.986133\pi\)
\(548\) 25.5864 + 4.16807i 1.09300 + 0.178051i
\(549\) 0 0
\(550\) 2.02598 25.0376i 0.0863882 1.06761i
\(551\) −51.3755 −2.18867
\(552\) 0 0
\(553\) −4.83001 −0.205393
\(554\) 2.79092 34.4909i 0.118575 1.46538i
\(555\) 0 0
\(556\) 5.90533 36.2509i 0.250442 1.53738i
\(557\) 11.1234i 0.471315i −0.971836 0.235658i \(-0.924276\pi\)
0.971836 0.235658i \(-0.0757244\pi\)
\(558\) 0 0
\(559\) −4.30683 −0.182159
\(560\) 1.43297 4.28155i 0.0605541 0.180929i
\(561\) 0 0
\(562\) −20.4604 1.65561i −0.863071 0.0698375i
\(563\) 37.2437i 1.56963i 0.619727 + 0.784817i \(0.287243\pi\)
−0.619727 + 0.784817i \(0.712757\pi\)
\(564\) 0 0
\(565\) 3.77566i 0.158843i
\(566\) 1.88783 23.3303i 0.0793514 0.980645i
\(567\) 0 0
\(568\) −28.0265 6.92468i −1.17597 0.290553i
\(569\) −22.9369 −0.961564 −0.480782 0.876840i \(-0.659647\pi\)
−0.480782 + 0.876840i \(0.659647\pi\)
\(570\) 0 0
\(571\) 35.1634i 1.47154i −0.677231 0.735770i \(-0.736820\pi\)
0.677231 0.735770i \(-0.263180\pi\)
\(572\) −4.29343 0.699406i −0.179517 0.0292436i
\(573\) 0 0
\(574\) 0.584994 + 0.0473363i 0.0244172 + 0.00197578i
\(575\) −5.90558 −0.246280
\(576\) 0 0
\(577\) 13.7918 0.574162 0.287081 0.957906i \(-0.407315\pi\)
0.287081 + 0.957906i \(0.407315\pi\)
\(578\) −23.7205 1.91941i −0.986644 0.0798368i
\(579\) 0 0
\(580\) 14.9862 + 2.44128i 0.622268 + 0.101369i
\(581\) 5.53434i 0.229603i
\(582\) 0 0
\(583\) 36.4137 1.50810
\(584\) −9.18489 2.26937i −0.380073 0.0939070i
\(585\) 0 0
\(586\) 1.07717 13.3120i 0.0444976 0.549914i
\(587\) 26.9862i 1.11384i −0.830566 0.556920i \(-0.811983\pi\)
0.830566 0.556920i \(-0.188017\pi\)
\(588\) 0 0
\(589\) 45.0355i 1.85566i
\(590\) 6.36436 + 0.514988i 0.262016 + 0.0212017i
\(591\) 0 0
\(592\) 7.48501 22.3644i 0.307632 0.919169i
\(593\) 31.8337 1.30725 0.653627 0.756817i \(-0.273247\pi\)
0.653627 + 0.756817i \(0.273247\pi\)
\(594\) 0 0
\(595\) 0.468436i 0.0192040i
\(596\) −5.02876 + 30.8699i −0.205986 + 1.26448i
\(597\) 0 0
\(598\) −0.0824838 + 1.01936i −0.00337301 + 0.0416846i
\(599\) 34.9006 1.42600 0.712999 0.701165i \(-0.247336\pi\)
0.712999 + 0.701165i \(0.247336\pi\)
\(600\) 0 0
\(601\) −0.175010 −0.00713881 −0.00356941 0.999994i \(-0.501136\pi\)
−0.00356941 + 0.999994i \(0.501136\pi\)
\(602\) 1.07671 13.3062i 0.0438833 0.542321i
\(603\) 0 0
\(604\) 30.1562 + 4.91249i 1.22704 + 0.199887i
\(605\) 13.2356i 0.538104i
\(606\) 0 0
\(607\) −32.1705 −1.30576 −0.652881 0.757461i \(-0.726440\pi\)
−0.652881 + 0.757461i \(0.726440\pi\)
\(608\) −16.9740 + 39.7359i −0.688387 + 1.61150i
\(609\) 0 0
\(610\) 2.86594 + 0.231905i 0.116039 + 0.00938956i
\(611\) 5.14503i 0.208146i
\(612\) 0 0
\(613\) 8.37869i 0.338412i 0.985581 + 0.169206i \(0.0541203\pi\)
−0.985581 + 0.169206i \(0.945880\pi\)
\(614\) −0.0412419 + 0.509678i −0.00166439 + 0.0205689i
\(615\) 0 0
\(616\) 3.23422 13.0900i 0.130310 0.527410i
\(617\) −28.9618 −1.16596 −0.582980 0.812487i \(-0.698113\pi\)
−0.582980 + 0.812487i \(0.698113\pi\)
\(618\) 0 0
\(619\) 6.85497i 0.275524i −0.990465 0.137762i \(-0.956009\pi\)
0.990465 0.137762i \(-0.0439910\pi\)
\(620\) −2.14001 + 13.1368i −0.0859450 + 0.527588i
\(621\) 0 0
\(622\) 15.8959 + 1.28626i 0.637368 + 0.0515743i
\(623\) −4.92999 −0.197516
\(624\) 0 0
\(625\) 7.51221 0.300488
\(626\) 36.0629 + 2.91812i 1.44136 + 0.116632i
\(627\) 0 0
\(628\) −7.00446 + 42.9981i −0.279508 + 1.71581i
\(629\) 2.44684i 0.0975619i
\(630\) 0 0
\(631\) −40.2055 −1.60056 −0.800278 0.599629i \(-0.795315\pi\)
−0.800278 + 0.599629i \(0.795315\pi\)
\(632\) −13.2625 3.27685i −0.527555 0.130346i
\(633\) 0 0
\(634\) 0.0412419 0.509678i 0.00163793 0.0202419i
\(635\) 11.7918i 0.467945i
\(636\) 0 0
\(637\) 0.456247i 0.0180772i
\(638\) 45.1971 + 3.65724i 1.78937 + 0.144792i
\(639\) 0 0
\(640\) 6.83949 10.7844i 0.270355 0.426289i
\(641\) 24.0737 0.950854 0.475427 0.879755i \(-0.342294\pi\)
0.475427 + 0.879755i \(0.342294\pi\)
\(642\) 0 0
\(643\) 23.7559i 0.936841i −0.883506 0.468421i \(-0.844823\pi\)
0.883506 0.468421i \(-0.155177\pi\)
\(644\) −3.12875 0.509678i −0.123290 0.0200841i
\(645\) 0 0
\(646\) 0.361575 4.46844i 0.0142260 0.175808i
\(647\) 32.6218 1.28250 0.641249 0.767333i \(-0.278417\pi\)
0.641249 + 0.767333i \(0.278417\pi\)
\(648\) 0 0
\(649\) 19.0687 0.748512
\(650\) 0.193899 2.39625i 0.00760535 0.0939888i
\(651\) 0 0
\(652\) 1.48230 9.09938i 0.0580515 0.356359i
\(653\) 14.4109i 0.563942i −0.959423 0.281971i \(-0.909012\pi\)
0.959423 0.281971i \(-0.0909883\pi\)
\(654\) 0 0
\(655\) −7.06313 −0.275979
\(656\) 1.57420 + 0.526860i 0.0614620 + 0.0205704i
\(657\) 0 0
\(658\) −15.8959 1.28626i −0.619687 0.0501436i
\(659\) 23.3315i 0.908866i 0.890781 + 0.454433i \(0.150158\pi\)
−0.890781 + 0.454433i \(0.849842\pi\)
\(660\) 0 0
\(661\) 44.1468i 1.71711i −0.512721 0.858555i \(-0.671362\pi\)
0.512721 0.858555i \(-0.328638\pi\)
\(662\) −0.890142 + 11.0006i −0.0345963 + 0.427551i
\(663\) 0 0
\(664\) −3.75469 + 15.1965i −0.145710 + 0.589739i
\(665\) 8.62185 0.334341
\(666\) 0 0
\(667\) 10.6606i 0.412779i
\(668\) 45.3262 + 7.38371i 1.75372 + 0.285684i
\(669\) 0 0
\(670\) 12.8793 + 1.04216i 0.497572 + 0.0402623i
\(671\) 8.58685 0.331492
\(672\) 0 0
\(673\) 11.6960 0.450846 0.225423 0.974261i \(-0.427624\pi\)
0.225423 + 0.974261i \(0.427624\pi\)
\(674\) 12.3508 + 0.999394i 0.475734 + 0.0384952i
\(675\) 0 0
\(676\) 25.2508 + 4.11340i 0.971186 + 0.158208i
\(677\) 0.648756i 0.0249337i 0.999922 + 0.0124669i \(0.00396843\pi\)
−0.999922 + 0.0124669i \(0.996032\pi\)
\(678\) 0 0
\(679\) 16.4468 0.631172
\(680\) −0.317804 + 1.28626i −0.0121872 + 0.0493258i
\(681\) 0 0
\(682\) −3.20592 + 39.6196i −0.122761 + 1.51711i
\(683\) 22.4909i 0.860589i 0.902689 + 0.430294i \(0.141590\pi\)
−0.902689 + 0.430294i \(0.858410\pi\)
\(684\) 0 0
\(685\) 14.6306i 0.559007i
\(686\) 1.40961 + 0.114062i 0.0538190 + 0.00435490i
\(687\) 0 0
\(688\) 11.9839 35.8065i 0.456882 1.36511i
\(689\) 3.48501 0.132768
\(690\) 0 0
\(691\) 45.2681i 1.72208i −0.508538 0.861039i \(-0.669814\pi\)
0.508538 0.861039i \(-0.330186\pi\)
\(692\) −0.0695390 + 0.426877i −0.00264348 + 0.0162274i
\(693\) 0 0
\(694\) 0.236926 2.92800i 0.00899360 0.111145i
\(695\) −20.7287 −0.786285
\(696\) 0 0
\(697\) −0.172230 −0.00652366
\(698\) 2.13730 26.4134i 0.0808982 0.999761i
\(699\) 0 0
\(700\) 7.35491 + 1.19813i 0.277990 + 0.0452850i
\(701\) 1.03091i 0.0389370i −0.999810 0.0194685i \(-0.993803\pi\)
0.999810 0.0194685i \(-0.00619740\pi\)
\(702\) 0 0
\(703\) 45.0355 1.69855
\(704\) 17.7614 33.7490i 0.669408 1.27196i
\(705\) 0 0
\(706\) 18.6703 + 1.51075i 0.702664 + 0.0568579i
\(707\) 16.4056i 0.616996i
\(708\) 0 0
\(709\) 10.5481i 0.396144i 0.980188 + 0.198072i \(0.0634679\pi\)
−0.980188 + 0.198072i \(0.936532\pi\)
\(710\) −1.31410 + 16.2400i −0.0493173 + 0.609476i
\(711\) 0 0
\(712\) −13.5371 3.34468i −0.507322 0.125347i
\(713\) 9.34500 0.349973
\(714\) 0 0
\(715\) 2.45504i 0.0918131i
\(716\) 7.27268 44.6446i 0.271793 1.66845i
\(717\) 0 0
\(718\) 8.02328 + 0.649224i 0.299426 + 0.0242288i
\(719\) 7.00502 0.261243 0.130622 0.991432i \(-0.458303\pi\)
0.130622 + 0.991432i \(0.458303\pi\)
\(720\) 0 0
\(721\) −17.1728 −0.639547
\(722\) −55.4617 4.48783i −2.06407 0.167020i
\(723\) 0 0
\(724\) −2.48669 + 15.2650i −0.0924171 + 0.567318i
\(725\) 25.0603i 0.930718i
\(726\) 0 0
\(727\) −17.8028 −0.660270 −0.330135 0.943934i \(-0.607094\pi\)
−0.330135 + 0.943934i \(0.607094\pi\)
\(728\) 0.309534 1.25279i 0.0114721 0.0464315i
\(729\) 0 0
\(730\) −0.430659 + 5.32219i −0.0159394 + 0.196983i
\(731\) 3.91752i 0.144895i
\(732\) 0 0
\(733\) 34.3300i 1.26801i 0.773330 + 0.634004i \(0.218590\pi\)
−0.773330 + 0.634004i \(0.781410\pi\)
\(734\) 15.8959 + 1.28626i 0.586729 + 0.0474767i
\(735\) 0 0
\(736\) −8.24531 3.52216i −0.303926 0.129828i
\(737\) 38.5887 1.42143
\(738\) 0 0
\(739\) 0.0946726i 0.00348259i −0.999998 0.00174129i \(-0.999446\pi\)
0.999998 0.00174129i \(-0.000554271\pi\)
\(740\) −13.1368 2.14001i −0.482920 0.0786684i
\(741\) 0 0
\(742\) −0.871253 + 10.7672i −0.0319847 + 0.395275i
\(743\) 13.2755 0.487032 0.243516 0.969897i \(-0.421699\pi\)
0.243516 + 0.969897i \(0.421699\pi\)
\(744\) 0 0
\(745\) 17.6518 0.646713
\(746\) 0.808414 9.99059i 0.0295981 0.365782i
\(747\) 0 0
\(748\) −0.636184 + 3.90533i −0.0232612 + 0.142793i
\(749\) 12.7672i 0.466502i
\(750\) 0 0
\(751\) 15.4187 0.562637 0.281318 0.959615i \(-0.409228\pi\)
0.281318 + 0.959615i \(0.409228\pi\)
\(752\) −42.7753 14.3162i −1.55985 0.522059i
\(753\) 0 0
\(754\) 4.32564 + 0.350020i 0.157531 + 0.0127470i
\(755\) 17.2437i 0.627562i
\(756\) 0 0
\(757\) 9.96685i 0.362251i 0.983460 + 0.181126i \(0.0579741\pi\)
−0.983460 + 0.181126i \(0.942026\pi\)
\(758\) 0.761683 9.41308i 0.0276656 0.341899i
\(759\) 0 0
\(760\) 23.6744 + 5.84937i 0.858759 + 0.212179i
\(761\) −23.4837 −0.851283 −0.425642 0.904892i \(-0.639952\pi\)
−0.425642 + 0.904892i \(0.639952\pi\)
\(762\) 0 0
\(763\) 7.27685i 0.263440i
\(764\) −20.1481 3.28216i −0.728933 0.118744i
\(765\) 0 0
\(766\) 26.2962 + 2.12782i 0.950121 + 0.0768814i
\(767\) 1.82499 0.0658966
\(768\) 0 0
\(769\) 22.9369 0.827125 0.413562 0.910476i \(-0.364284\pi\)
0.413562 + 0.910476i \(0.364284\pi\)
\(770\) −7.58499 0.613759i −0.273344 0.0221183i
\(771\) 0 0
\(772\) 11.7729 + 1.91783i 0.423718 + 0.0690243i
\(773\) 35.0956i 1.26230i −0.775660 0.631150i \(-0.782583\pi\)
0.775660 0.631150i \(-0.217417\pi\)
\(774\) 0 0
\(775\) −21.9678 −0.789106
\(776\) 45.1607 + 11.1581i 1.62117 + 0.400553i
\(777\) 0 0
\(778\) −2.32033 + 28.6753i −0.0831880 + 1.02806i
\(779\) 3.16999i 0.113577i
\(780\) 0 0
\(781\) 48.6578i 1.74111i
\(782\) 0.927213 + 0.0750278i 0.0331571 + 0.00268299i
\(783\) 0 0
\(784\) 3.79319 + 1.26952i 0.135471 + 0.0453402i
\(785\) 24.5869 0.877542
\(786\) 0 0
\(787\) 17.9480i 0.639778i 0.947455 + 0.319889i \(0.103646\pi\)
−0.947455 + 0.319889i \(0.896354\pi\)
\(788\) 6.04812 37.1274i 0.215455 1.32261i
\(789\) 0 0
\(790\) −0.621849 + 7.68498i −0.0221244 + 0.273419i
\(791\) 3.34500 0.118934
\(792\) 0 0
\(793\) 0.821814 0.0291835
\(794\) 1.24363