Properties

Label 91.2.c.a.64.4
Level $91$
Weight $2$
Character 91.64
Analytic conductor $0.727$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
Defining polynomial: \(x^{6} - 2 x^{5} + 2 x^{4} + 2 x^{3} + 4 x^{2} - 4 x + 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 64.4
Root \(1.45161 - 1.45161i\) of defining polynomial
Character \(\chi\) \(=\) 91.64
Dual form 91.2.c.a.64.3

$q$-expansion

\(f(q)\) \(=\) \(q+0.688892i q^{2} -2.21432 q^{3} +1.52543 q^{4} +3.21432i q^{5} -1.52543i q^{6} +1.00000i q^{7} +2.42864i q^{8} +1.90321 q^{9} +O(q^{10})\) \(q+0.688892i q^{2} -2.21432 q^{3} +1.52543 q^{4} +3.21432i q^{5} -1.52543i q^{6} +1.00000i q^{7} +2.42864i q^{8} +1.90321 q^{9} -2.21432 q^{10} -2.68889i q^{11} -3.37778 q^{12} +(3.59210 + 0.311108i) q^{13} -0.688892 q^{14} -7.11753i q^{15} +1.37778 q^{16} -3.59210 q^{17} +1.31111i q^{18} -8.54617i q^{19} +4.90321i q^{20} -2.21432i q^{21} +1.85236 q^{22} +3.28100 q^{23} -5.37778i q^{24} -5.33185 q^{25} +(-0.214320 + 2.47457i) q^{26} +2.42864 q^{27} +1.52543i q^{28} +2.05086 q^{29} +4.90321 q^{30} +5.83654i q^{31} +5.80642i q^{32} +5.95407i q^{33} -2.47457i q^{34} -3.21432 q^{35} +2.90321 q^{36} -3.93332i q^{37} +5.88739 q^{38} +(-7.95407 - 0.688892i) q^{39} -7.80642 q^{40} +0.755569i q^{41} +1.52543 q^{42} -8.80642 q^{43} -4.10171i q^{44} +6.11753i q^{45} +2.26025i q^{46} -1.88247i q^{47} -3.05086 q^{48} -1.00000 q^{49} -3.67307i q^{50} +7.95407 q^{51} +(5.47949 + 0.474572i) q^{52} +2.52543 q^{53} +1.67307i q^{54} +8.64296 q^{55} -2.42864 q^{56} +18.9240i q^{57} +1.41282i q^{58} -7.33185i q^{59} -10.8573i q^{60} +9.05086 q^{61} -4.02074 q^{62} +1.90321i q^{63} -1.24443 q^{64} +(-1.00000 + 11.5462i) q^{65} -4.10171 q^{66} +0.428639i q^{67} -5.47949 q^{68} -7.26517 q^{69} -2.21432i q^{70} +8.98418i q^{71} +4.62222i q^{72} -5.79060i q^{73} +2.70964 q^{74} +11.8064 q^{75} -13.0366i q^{76} +2.68889 q^{77} +(0.474572 - 5.47949i) q^{78} -4.47949 q^{79} +4.42864i q^{80} -11.0874 q^{81} -0.520505 q^{82} -10.8272i q^{83} -3.37778i q^{84} -11.5462i q^{85} -6.06668i q^{86} -4.54125 q^{87} +6.53035 q^{88} -5.36196i q^{89} -4.21432 q^{90} +(-0.311108 + 3.59210i) q^{91} +5.00492 q^{92} -12.9240i q^{93} +1.29682 q^{94} +27.4701 q^{95} -12.8573i q^{96} +9.62867i q^{97} -0.688892i q^{98} -5.11753i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 4q^{4} - 2q^{9} + O(q^{10}) \) \( 6q - 4q^{4} - 2q^{9} - 20q^{12} + 8q^{13} - 4q^{14} + 8q^{16} - 8q^{17} + 24q^{22} + 6q^{23} + 8q^{25} + 12q^{26} - 12q^{27} - 14q^{29} + 16q^{30} - 6q^{35} + 4q^{36} - 4q^{38} - 8q^{39} - 20q^{40} - 4q^{42} - 26q^{43} + 8q^{48} - 6q^{49} + 8q^{51} - 20q^{52} + 2q^{53} + 12q^{55} + 12q^{56} + 28q^{61} + 16q^{62} - 8q^{64} - 6q^{65} + 28q^{66} + 20q^{68} - 4q^{69} - 24q^{74} + 44q^{75} + 16q^{77} + 16q^{78} + 26q^{79} - 26q^{81} - 56q^{82} - 40q^{87} - 40q^{88} - 12q^{90} - 2q^{91} - 36q^{92} + 20q^{94} + 58q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.688892i 0.487120i 0.969886 + 0.243560i \(0.0783153\pi\)
−0.969886 + 0.243560i \(0.921685\pi\)
\(3\) −2.21432 −1.27844 −0.639219 0.769025i \(-0.720742\pi\)
−0.639219 + 0.769025i \(0.720742\pi\)
\(4\) 1.52543 0.762714
\(5\) 3.21432i 1.43749i 0.695275 + 0.718744i \(0.255283\pi\)
−0.695275 + 0.718744i \(0.744717\pi\)
\(6\) 1.52543i 0.622753i
\(7\) 1.00000i 0.377964i
\(8\) 2.42864i 0.858654i
\(9\) 1.90321 0.634404
\(10\) −2.21432 −0.700229
\(11\) 2.68889i 0.810731i −0.914155 0.405366i \(-0.867144\pi\)
0.914155 0.405366i \(-0.132856\pi\)
\(12\) −3.37778 −0.975082
\(13\) 3.59210 + 0.311108i 0.996270 + 0.0862858i
\(14\) −0.688892 −0.184114
\(15\) 7.11753i 1.83774i
\(16\) 1.37778 0.344446
\(17\) −3.59210 −0.871213 −0.435607 0.900137i \(-0.643466\pi\)
−0.435607 + 0.900137i \(0.643466\pi\)
\(18\) 1.31111i 0.309031i
\(19\) 8.54617i 1.96063i −0.197449 0.980313i \(-0.563266\pi\)
0.197449 0.980313i \(-0.436734\pi\)
\(20\) 4.90321i 1.09639i
\(21\) 2.21432i 0.483204i
\(22\) 1.85236 0.394924
\(23\) 3.28100 0.684135 0.342068 0.939675i \(-0.388873\pi\)
0.342068 + 0.939675i \(0.388873\pi\)
\(24\) 5.37778i 1.09774i
\(25\) −5.33185 −1.06637
\(26\) −0.214320 + 2.47457i −0.0420316 + 0.485304i
\(27\) 2.42864 0.467392
\(28\) 1.52543i 0.288279i
\(29\) 2.05086 0.380834 0.190417 0.981703i \(-0.439016\pi\)
0.190417 + 0.981703i \(0.439016\pi\)
\(30\) 4.90321 0.895200
\(31\) 5.83654i 1.04827i 0.851634 + 0.524136i \(0.175612\pi\)
−0.851634 + 0.524136i \(0.824388\pi\)
\(32\) 5.80642i 1.02644i
\(33\) 5.95407i 1.03647i
\(34\) 2.47457i 0.424386i
\(35\) −3.21432 −0.543319
\(36\) 2.90321 0.483869
\(37\) 3.93332i 0.646634i −0.946291 0.323317i \(-0.895202\pi\)
0.946291 0.323317i \(-0.104798\pi\)
\(38\) 5.88739 0.955061
\(39\) −7.95407 0.688892i −1.27367 0.110311i
\(40\) −7.80642 −1.23430
\(41\) 0.755569i 0.118000i 0.998258 + 0.0590000i \(0.0187912\pi\)
−0.998258 + 0.0590000i \(0.981209\pi\)
\(42\) 1.52543 0.235379
\(43\) −8.80642 −1.34297 −0.671484 0.741019i \(-0.734343\pi\)
−0.671484 + 0.741019i \(0.734343\pi\)
\(44\) 4.10171i 0.618356i
\(45\) 6.11753i 0.911948i
\(46\) 2.26025i 0.333256i
\(47\) 1.88247i 0.274586i −0.990530 0.137293i \(-0.956160\pi\)
0.990530 0.137293i \(-0.0438402\pi\)
\(48\) −3.05086 −0.440353
\(49\) −1.00000 −0.142857
\(50\) 3.67307i 0.519451i
\(51\) 7.95407 1.11379
\(52\) 5.47949 + 0.474572i 0.759869 + 0.0658114i
\(53\) 2.52543 0.346894 0.173447 0.984843i \(-0.444509\pi\)
0.173447 + 0.984843i \(0.444509\pi\)
\(54\) 1.67307i 0.227676i
\(55\) 8.64296 1.16542
\(56\) −2.42864 −0.324541
\(57\) 18.9240i 2.50654i
\(58\) 1.41282i 0.185512i
\(59\) 7.33185i 0.954526i −0.878761 0.477263i \(-0.841629\pi\)
0.878761 0.477263i \(-0.158371\pi\)
\(60\) 10.8573i 1.40167i
\(61\) 9.05086 1.15884 0.579422 0.815028i \(-0.303278\pi\)
0.579422 + 0.815028i \(0.303278\pi\)
\(62\) −4.02074 −0.510635
\(63\) 1.90321i 0.239782i
\(64\) −1.24443 −0.155554
\(65\) −1.00000 + 11.5462i −0.124035 + 1.43213i
\(66\) −4.10171 −0.504886
\(67\) 0.428639i 0.0523666i 0.999657 + 0.0261833i \(0.00833536\pi\)
−0.999657 + 0.0261833i \(0.991665\pi\)
\(68\) −5.47949 −0.664486
\(69\) −7.26517 −0.874624
\(70\) 2.21432i 0.264662i
\(71\) 8.98418i 1.06623i 0.846044 + 0.533113i \(0.178978\pi\)
−0.846044 + 0.533113i \(0.821022\pi\)
\(72\) 4.62222i 0.544733i
\(73\) 5.79060i 0.677739i −0.940833 0.338869i \(-0.889956\pi\)
0.940833 0.338869i \(-0.110044\pi\)
\(74\) 2.70964 0.314989
\(75\) 11.8064 1.36329
\(76\) 13.0366i 1.49540i
\(77\) 2.68889 0.306428
\(78\) 0.474572 5.47949i 0.0537347 0.620431i
\(79\) −4.47949 −0.503983 −0.251991 0.967730i \(-0.581085\pi\)
−0.251991 + 0.967730i \(0.581085\pi\)
\(80\) 4.42864i 0.495137i
\(81\) −11.0874 −1.23194
\(82\) −0.520505 −0.0574802
\(83\) 10.8272i 1.18844i −0.804304 0.594218i \(-0.797462\pi\)
0.804304 0.594218i \(-0.202538\pi\)
\(84\) 3.37778i 0.368546i
\(85\) 11.5462i 1.25236i
\(86\) 6.06668i 0.654187i
\(87\) −4.54125 −0.486873
\(88\) 6.53035 0.696138
\(89\) 5.36196i 0.568367i −0.958770 0.284183i \(-0.908278\pi\)
0.958770 0.284183i \(-0.0917225\pi\)
\(90\) −4.21432 −0.444228
\(91\) −0.311108 + 3.59210i −0.0326130 + 0.376555i
\(92\) 5.00492 0.521799
\(93\) 12.9240i 1.34015i
\(94\) 1.29682 0.133757
\(95\) 27.4701 2.81838
\(96\) 12.8573i 1.31224i
\(97\) 9.62867i 0.977643i 0.872384 + 0.488822i \(0.162573\pi\)
−0.872384 + 0.488822i \(0.837427\pi\)
\(98\) 0.688892i 0.0695886i
\(99\) 5.11753i 0.514331i
\(100\) −8.13335 −0.813335
\(101\) −13.6938 −1.36259 −0.681293 0.732011i \(-0.738582\pi\)
−0.681293 + 0.732011i \(0.738582\pi\)
\(102\) 5.47949i 0.542551i
\(103\) −12.2953 −1.21149 −0.605745 0.795659i \(-0.707125\pi\)
−0.605745 + 0.795659i \(0.707125\pi\)
\(104\) −0.755569 + 8.72393i −0.0740896 + 0.855451i
\(105\) 7.11753 0.694600
\(106\) 1.73975i 0.168979i
\(107\) −18.1891 −1.75841 −0.879205 0.476444i \(-0.841925\pi\)
−0.879205 + 0.476444i \(0.841925\pi\)
\(108\) 3.70471 0.356486
\(109\) 8.36196i 0.800931i 0.916312 + 0.400465i \(0.131152\pi\)
−0.916312 + 0.400465i \(0.868848\pi\)
\(110\) 5.95407i 0.567698i
\(111\) 8.70964i 0.826682i
\(112\) 1.37778i 0.130188i
\(113\) −8.46520 −0.796339 −0.398170 0.917312i \(-0.630354\pi\)
−0.398170 + 0.917312i \(0.630354\pi\)
\(114\) −13.0366 −1.22099
\(115\) 10.5462i 0.983436i
\(116\) 3.12843 0.290468
\(117\) 6.83654 + 0.592104i 0.632038 + 0.0547400i
\(118\) 5.05086 0.464969
\(119\) 3.59210i 0.329288i
\(120\) 17.2859 1.57798
\(121\) 3.76986 0.342714
\(122\) 6.23506i 0.564496i
\(123\) 1.67307i 0.150856i
\(124\) 8.90321i 0.799532i
\(125\) 1.06668i 0.0954065i
\(126\) −1.31111 −0.116803
\(127\) −4.08742 −0.362700 −0.181350 0.983419i \(-0.558047\pi\)
−0.181350 + 0.983419i \(0.558047\pi\)
\(128\) 10.7556i 0.950667i
\(129\) 19.5002 1.71690
\(130\) −7.95407 0.688892i −0.697618 0.0604198i
\(131\) 5.93978 0.518961 0.259480 0.965748i \(-0.416449\pi\)
0.259480 + 0.965748i \(0.416449\pi\)
\(132\) 9.08250i 0.790530i
\(133\) 8.54617 0.741047
\(134\) −0.295286 −0.0255089
\(135\) 7.80642i 0.671870i
\(136\) 8.72393i 0.748070i
\(137\) 16.3620i 1.39790i −0.715172 0.698948i \(-0.753652\pi\)
0.715172 0.698948i \(-0.246348\pi\)
\(138\) 5.00492i 0.426047i
\(139\) 3.03011 0.257011 0.128505 0.991709i \(-0.458982\pi\)
0.128505 + 0.991709i \(0.458982\pi\)
\(140\) −4.90321 −0.414397
\(141\) 4.16839i 0.351041i
\(142\) −6.18913 −0.519380
\(143\) 0.836535 9.65878i 0.0699546 0.807708i
\(144\) 2.62222 0.218518
\(145\) 6.59210i 0.547444i
\(146\) 3.98910 0.330140
\(147\) 2.21432 0.182634
\(148\) 6.00000i 0.493197i
\(149\) 14.5368i 1.19090i −0.803392 0.595451i \(-0.796974\pi\)
0.803392 0.595451i \(-0.203026\pi\)
\(150\) 8.13335i 0.664085i
\(151\) 19.9748i 1.62553i 0.582594 + 0.812764i \(0.302038\pi\)
−0.582594 + 0.812764i \(0.697962\pi\)
\(152\) 20.7556 1.68350
\(153\) −6.83654 −0.552701
\(154\) 1.85236i 0.149267i
\(155\) −18.7605 −1.50688
\(156\) −12.1334 1.05086i −0.971446 0.0841357i
\(157\) 7.39853 0.590467 0.295233 0.955425i \(-0.404603\pi\)
0.295233 + 0.955425i \(0.404603\pi\)
\(158\) 3.08589i 0.245500i
\(159\) −5.59210 −0.443483
\(160\) −18.6637 −1.47550
\(161\) 3.28100i 0.258579i
\(162\) 7.63804i 0.600101i
\(163\) 2.32693i 0.182259i −0.995839 0.0911296i \(-0.970952\pi\)
0.995839 0.0911296i \(-0.0290477\pi\)
\(164\) 1.15257i 0.0900002i
\(165\) −19.1383 −1.48991
\(166\) 7.45875 0.578911
\(167\) 3.42219i 0.264817i 0.991195 + 0.132408i \(0.0422710\pi\)
−0.991195 + 0.132408i \(0.957729\pi\)
\(168\) 5.37778 0.414905
\(169\) 12.8064 + 2.23506i 0.985110 + 0.171928i
\(170\) 7.95407 0.610049
\(171\) 16.2652i 1.24383i
\(172\) −13.4336 −1.02430
\(173\) −8.27454 −0.629102 −0.314551 0.949241i \(-0.601854\pi\)
−0.314551 + 0.949241i \(0.601854\pi\)
\(174\) 3.12843i 0.237166i
\(175\) 5.33185i 0.403050i
\(176\) 3.70471i 0.279253i
\(177\) 16.2351i 1.22030i
\(178\) 3.69381 0.276863
\(179\) 16.2257 1.21277 0.606383 0.795173i \(-0.292620\pi\)
0.606383 + 0.795173i \(0.292620\pi\)
\(180\) 9.33185i 0.695555i
\(181\) 9.20495 0.684199 0.342099 0.939664i \(-0.388862\pi\)
0.342099 + 0.939664i \(0.388862\pi\)
\(182\) −2.47457 0.214320i −0.183428 0.0158864i
\(183\) −20.0415 −1.48151
\(184\) 7.96836i 0.587435i
\(185\) 12.6430 0.929529
\(186\) 8.90321 0.652815
\(187\) 9.65878i 0.706320i
\(188\) 2.87157i 0.209431i
\(189\) 2.42864i 0.176658i
\(190\) 18.9240i 1.37289i
\(191\) −6.66815 −0.482490 −0.241245 0.970464i \(-0.577556\pi\)
−0.241245 + 0.970464i \(0.577556\pi\)
\(192\) 2.75557 0.198866
\(193\) 20.6035i 1.48307i −0.670914 0.741535i \(-0.734098\pi\)
0.670914 0.741535i \(-0.265902\pi\)
\(194\) −6.63311 −0.476230
\(195\) 2.21432 25.5669i 0.158571 1.83088i
\(196\) −1.52543 −0.108959
\(197\) 8.36842i 0.596225i −0.954531 0.298112i \(-0.903643\pi\)
0.954531 0.298112i \(-0.0963571\pi\)
\(198\) 3.52543 0.250541
\(199\) 0.601472 0.0426372 0.0213186 0.999773i \(-0.493214\pi\)
0.0213186 + 0.999773i \(0.493214\pi\)
\(200\) 12.9491i 0.915643i
\(201\) 0.949145i 0.0669475i
\(202\) 9.43356i 0.663743i
\(203\) 2.05086i 0.143942i
\(204\) 12.1334 0.849505
\(205\) −2.42864 −0.169624
\(206\) 8.47013i 0.590142i
\(207\) 6.24443 0.434018
\(208\) 4.94914 + 0.428639i 0.343161 + 0.0297208i
\(209\) −22.9797 −1.58954
\(210\) 4.90321i 0.338354i
\(211\) −1.90321 −0.131023 −0.0655113 0.997852i \(-0.520868\pi\)
−0.0655113 + 0.997852i \(0.520868\pi\)
\(212\) 3.85236 0.264581
\(213\) 19.8938i 1.36310i
\(214\) 12.5303i 0.856557i
\(215\) 28.3067i 1.93050i
\(216\) 5.89829i 0.401328i
\(217\) −5.83654 −0.396210
\(218\) −5.76049 −0.390150
\(219\) 12.8222i 0.866447i
\(220\) 13.1842 0.888879
\(221\) −12.9032 1.11753i −0.867964 0.0751733i
\(222\) −6.00000 −0.402694
\(223\) 10.6336i 0.712078i 0.934471 + 0.356039i \(0.115873\pi\)
−0.934471 + 0.356039i \(0.884127\pi\)
\(224\) −5.80642 −0.387958
\(225\) −10.1476 −0.676510
\(226\) 5.83161i 0.387913i
\(227\) 15.0509i 0.998960i 0.866325 + 0.499480i \(0.166476\pi\)
−0.866325 + 0.499480i \(0.833524\pi\)
\(228\) 28.8671i 1.91177i
\(229\) 6.53480i 0.431831i 0.976412 + 0.215916i \(0.0692736\pi\)
−0.976412 + 0.215916i \(0.930726\pi\)
\(230\) −7.26517 −0.479051
\(231\) −5.95407 −0.391749
\(232\) 4.98079i 0.327005i
\(233\) 27.9590 1.83165 0.915827 0.401573i \(-0.131536\pi\)
0.915827 + 0.401573i \(0.131536\pi\)
\(234\) −0.407896 + 4.70964i −0.0266650 + 0.307879i
\(235\) 6.05086 0.394714
\(236\) 11.1842i 0.728030i
\(237\) 9.91903 0.644310
\(238\) 2.47457 0.160403
\(239\) 19.5812i 1.26660i −0.773905 0.633301i \(-0.781699\pi\)
0.773905 0.633301i \(-0.218301\pi\)
\(240\) 9.80642i 0.633002i
\(241\) 13.3575i 0.860433i 0.902726 + 0.430217i \(0.141563\pi\)
−0.902726 + 0.430217i \(0.858437\pi\)
\(242\) 2.59703i 0.166943i
\(243\) 17.2652 1.10756
\(244\) 13.8064 0.883866
\(245\) 3.21432i 0.205355i
\(246\) 1.15257 0.0734849
\(247\) 2.65878 30.6987i 0.169174 1.95331i
\(248\) −14.1748 −0.900103
\(249\) 23.9748i 1.51934i
\(250\) 0.734825 0.0464744
\(251\) −3.29682 −0.208093 −0.104047 0.994572i \(-0.533179\pi\)
−0.104047 + 0.994572i \(0.533179\pi\)
\(252\) 2.90321i 0.182885i
\(253\) 8.82225i 0.554650i
\(254\) 2.81579i 0.176678i
\(255\) 25.5669i 1.60106i
\(256\) −9.89829 −0.618643
\(257\) 23.6938 1.47798 0.738990 0.673717i \(-0.235303\pi\)
0.738990 + 0.673717i \(0.235303\pi\)
\(258\) 13.4336i 0.836337i
\(259\) 3.93332 0.244405
\(260\) −1.52543 + 17.6128i −0.0946030 + 1.09230i
\(261\) 3.90321 0.241603
\(262\) 4.09187i 0.252796i
\(263\) 9.99063 0.616049 0.308024 0.951378i \(-0.400332\pi\)
0.308024 + 0.951378i \(0.400332\pi\)
\(264\) −14.4603 −0.889969
\(265\) 8.11753i 0.498656i
\(266\) 5.88739i 0.360979i
\(267\) 11.8731i 0.726622i
\(268\) 0.653858i 0.0399408i
\(269\) −18.2034 −1.10988 −0.554941 0.831890i \(-0.687259\pi\)
−0.554941 + 0.831890i \(0.687259\pi\)
\(270\) −5.37778 −0.327282
\(271\) 24.1748i 1.46852i 0.678870 + 0.734258i \(0.262470\pi\)
−0.678870 + 0.734258i \(0.737530\pi\)
\(272\) −4.94914 −0.300086
\(273\) 0.688892 7.95407i 0.0416937 0.481402i
\(274\) 11.2716 0.680944
\(275\) 14.3368i 0.864540i
\(276\) −11.0825 −0.667088
\(277\) −1.69535 −0.101863 −0.0509317 0.998702i \(-0.516219\pi\)
−0.0509317 + 0.998702i \(0.516219\pi\)
\(278\) 2.08742i 0.125195i
\(279\) 11.1082i 0.665028i
\(280\) 7.80642i 0.466523i
\(281\) 11.6479i 0.694854i −0.937707 0.347427i \(-0.887055\pi\)
0.937707 0.347427i \(-0.112945\pi\)
\(282\) −2.87157 −0.170999
\(283\) −12.1334 −0.721253 −0.360626 0.932710i \(-0.617437\pi\)
−0.360626 + 0.932710i \(0.617437\pi\)
\(284\) 13.7047i 0.813225i
\(285\) −60.8276 −3.60312
\(286\) 6.65386 + 0.576283i 0.393451 + 0.0340763i
\(287\) −0.755569 −0.0445998
\(288\) 11.0509i 0.651178i
\(289\) −4.09679 −0.240988
\(290\) −4.54125 −0.266671
\(291\) 21.3210i 1.24986i
\(292\) 8.83314i 0.516921i
\(293\) 11.4538i 0.669140i −0.942371 0.334570i \(-0.891409\pi\)
0.942371 0.334570i \(-0.108591\pi\)
\(294\) 1.52543i 0.0889647i
\(295\) 23.5669 1.37212
\(296\) 9.55262 0.555235
\(297\) 6.53035i 0.378929i
\(298\) 10.0143 0.580112
\(299\) 11.7857 + 1.02074i 0.681583 + 0.0590311i
\(300\) 18.0098 1.03980
\(301\) 8.80642i 0.507594i
\(302\) −13.7605 −0.791827
\(303\) 30.3225 1.74198
\(304\) 11.7748i 0.675330i
\(305\) 29.0923i 1.66582i
\(306\) 4.70964i 0.269232i
\(307\) 3.96989i 0.226574i −0.993562 0.113287i \(-0.963862\pi\)
0.993562 0.113287i \(-0.0361379\pi\)
\(308\) 4.10171 0.233717
\(309\) 27.2257 1.54882
\(310\) 12.9240i 0.734031i
\(311\) −27.3481 −1.55077 −0.775386 0.631488i \(-0.782444\pi\)
−0.775386 + 0.631488i \(0.782444\pi\)
\(312\) 1.67307 19.3176i 0.0947190 1.09364i
\(313\) −19.1032 −1.07978 −0.539890 0.841736i \(-0.681534\pi\)
−0.539890 + 0.841736i \(0.681534\pi\)
\(314\) 5.09679i 0.287628i
\(315\) −6.11753 −0.344684
\(316\) −6.83314 −0.384394
\(317\) 9.90813i 0.556496i 0.960509 + 0.278248i \(0.0897538\pi\)
−0.960509 + 0.278248i \(0.910246\pi\)
\(318\) 3.85236i 0.216029i
\(319\) 5.51453i 0.308754i
\(320\) 4.00000i 0.223607i
\(321\) 40.2766 2.24802
\(322\) −2.26025 −0.125959
\(323\) 30.6987i 1.70812i
\(324\) −16.9131 −0.939614
\(325\) −19.1526 1.65878i −1.06239 0.0920126i
\(326\) 1.60300 0.0887821
\(327\) 18.5161i 1.02394i
\(328\) −1.83500 −0.101321
\(329\) 1.88247 0.103784
\(330\) 13.1842i 0.725767i
\(331\) 23.4193i 1.28724i 0.765345 + 0.643620i \(0.222568\pi\)
−0.765345 + 0.643620i \(0.777432\pi\)
\(332\) 16.5161i 0.906437i
\(333\) 7.48595i 0.410227i
\(334\) −2.35752 −0.128998
\(335\) −1.37778 −0.0752764
\(336\) 3.05086i 0.166438i
\(337\) 7.51606 0.409426 0.204713 0.978822i \(-0.434374\pi\)
0.204713 + 0.978822i \(0.434374\pi\)
\(338\) −1.53972 + 8.82225i −0.0837496 + 0.479867i
\(339\) 18.7447 1.01807
\(340\) 17.6128i 0.955191i
\(341\) 15.6938 0.849868
\(342\) 11.2050 0.605894
\(343\) 1.00000i 0.0539949i
\(344\) 21.3876i 1.15314i
\(345\) 23.3526i 1.25726i
\(346\) 5.70027i 0.306448i
\(347\) 5.64449 0.303012 0.151506 0.988456i \(-0.451588\pi\)
0.151506 + 0.988456i \(0.451588\pi\)
\(348\) −6.92735 −0.371345
\(349\) 24.1590i 1.29320i −0.762828 0.646601i \(-0.776190\pi\)
0.762828 0.646601i \(-0.223810\pi\)
\(350\) 3.67307 0.196334
\(351\) 8.72393 + 0.755569i 0.465649 + 0.0403293i
\(352\) 15.6128 0.832168
\(353\) 36.1289i 1.92295i 0.274896 + 0.961474i \(0.411356\pi\)
−0.274896 + 0.961474i \(0.588644\pi\)
\(354\) −11.1842 −0.594434
\(355\) −28.8780 −1.53269
\(356\) 8.17929i 0.433501i
\(357\) 7.95407i 0.420974i
\(358\) 11.1778i 0.590763i
\(359\) 17.4128i 0.919013i −0.888174 0.459507i \(-0.848026\pi\)
0.888174 0.459507i \(-0.151974\pi\)
\(360\) −14.8573 −0.783047
\(361\) −54.0370 −2.84405
\(362\) 6.34122i 0.333287i
\(363\) −8.34767 −0.438139
\(364\) −0.474572 + 5.47949i −0.0248744 + 0.287204i
\(365\) 18.6128 0.974241
\(366\) 13.8064i 0.721673i
\(367\) 2.93825 0.153375 0.0766876 0.997055i \(-0.475566\pi\)
0.0766876 + 0.997055i \(0.475566\pi\)
\(368\) 4.52051 0.235648
\(369\) 1.43801i 0.0748597i
\(370\) 8.70964i 0.452792i
\(371\) 2.52543i 0.131114i
\(372\) 19.7146i 1.02215i
\(373\) −18.7699 −0.971866 −0.485933 0.873996i \(-0.661520\pi\)
−0.485933 + 0.873996i \(0.661520\pi\)
\(374\) −6.65386 −0.344063
\(375\) 2.36196i 0.121971i
\(376\) 4.57184 0.235774
\(377\) 7.36689 + 0.638037i 0.379414 + 0.0328606i
\(378\) −1.67307 −0.0860535
\(379\) 23.6894i 1.21684i 0.793615 + 0.608421i \(0.208197\pi\)
−0.793615 + 0.608421i \(0.791803\pi\)
\(380\) 41.9037 2.14961
\(381\) 9.05086 0.463689
\(382\) 4.59364i 0.235031i
\(383\) 31.6128i 1.61534i 0.589634 + 0.807671i \(0.299272\pi\)
−0.589634 + 0.807671i \(0.700728\pi\)
\(384\) 23.8163i 1.21537i
\(385\) 8.64296i 0.440486i
\(386\) 14.1936 0.722434
\(387\) −16.7605 −0.851984
\(388\) 14.6878i 0.745662i
\(389\) 20.0558 1.01687 0.508434 0.861101i \(-0.330225\pi\)
0.508434 + 0.861101i \(0.330225\pi\)
\(390\) 17.6128 + 1.52543i 0.891861 + 0.0772430i
\(391\) −11.7857 −0.596027
\(392\) 2.42864i 0.122665i
\(393\) −13.1526 −0.663459
\(394\) 5.76494 0.290433
\(395\) 14.3985i 0.724469i
\(396\) 7.80642i 0.392288i
\(397\) 22.8731i 1.14797i −0.818867 0.573984i \(-0.805397\pi\)
0.818867 0.573984i \(-0.194603\pi\)
\(398\) 0.414349i 0.0207695i
\(399\) −18.9240 −0.947383
\(400\) −7.34614 −0.367307
\(401\) 5.61285i 0.280292i 0.990131 + 0.140146i \(0.0447572\pi\)
−0.990131 + 0.140146i \(0.955243\pi\)
\(402\) 0.653858 0.0326115
\(403\) −1.81579 + 20.9654i −0.0904510 + 1.04436i
\(404\) −20.8889 −1.03926
\(405\) 35.6385i 1.77089i
\(406\) −1.41282 −0.0701170
\(407\) −10.5763 −0.524247
\(408\) 19.3176i 0.956362i
\(409\) 26.1175i 1.29143i −0.763579 0.645714i \(-0.776560\pi\)
0.763579 0.645714i \(-0.223440\pi\)
\(410\) 1.67307i 0.0826271i
\(411\) 36.2306i 1.78712i
\(412\) −18.7556 −0.924021
\(413\) 7.33185 0.360777
\(414\) 4.30174i 0.211419i
\(415\) 34.8020 1.70836
\(416\) −1.80642 + 20.8573i −0.0885672 + 1.02261i
\(417\) −6.70964 −0.328572
\(418\) 15.8306i 0.774298i
\(419\) −25.2464 −1.23337 −0.616685 0.787210i \(-0.711525\pi\)
−0.616685 + 0.787210i \(0.711525\pi\)
\(420\) 10.8573 0.529781
\(421\) 8.22861i 0.401038i −0.979690 0.200519i \(-0.935737\pi\)
0.979690 0.200519i \(-0.0642628\pi\)
\(422\) 1.31111i 0.0638237i
\(423\) 3.58274i 0.174199i
\(424\) 6.13335i 0.297862i
\(425\) 19.1526 0.929036
\(426\) 13.7047 0.663996
\(427\) 9.05086i 0.438002i
\(428\) −27.7462 −1.34116
\(429\) −1.85236 + 21.3876i −0.0894326 + 1.03260i
\(430\) 19.5002 0.940385
\(431\) 1.43801i 0.0692664i −0.999400 0.0346332i \(-0.988974\pi\)
0.999400 0.0346332i \(-0.0110263\pi\)
\(432\) 3.34614 0.160991
\(433\) 16.5018 0.793024 0.396512 0.918029i \(-0.370220\pi\)
0.396512 + 0.918029i \(0.370220\pi\)
\(434\) 4.02074i 0.193002i
\(435\) 14.5970i 0.699874i
\(436\) 12.7556i 0.610881i
\(437\) 28.0400i 1.34133i
\(438\) −8.83314 −0.422064
\(439\) 10.1619 0.485003 0.242501 0.970151i \(-0.422032\pi\)
0.242501 + 0.970151i \(0.422032\pi\)
\(440\) 20.9906i 1.00069i
\(441\) −1.90321 −0.0906291
\(442\) 0.769859 8.88892i 0.0366185 0.422803i
\(443\) 3.20787 0.152410 0.0762052 0.997092i \(-0.475720\pi\)
0.0762052 + 0.997092i \(0.475720\pi\)
\(444\) 13.2859i 0.630522i
\(445\) 17.2351 0.817020
\(446\) −7.32540 −0.346868
\(447\) 32.1891i 1.52249i
\(448\) 1.24443i 0.0587939i
\(449\) 18.4099i 0.868817i 0.900716 + 0.434409i \(0.143043\pi\)
−0.900716 + 0.434409i \(0.856957\pi\)
\(450\) 6.99063i 0.329542i
\(451\) 2.03164 0.0956663
\(452\) −12.9131 −0.607379
\(453\) 44.2306i 2.07814i
\(454\) −10.3684 −0.486614
\(455\) −11.5462 1.00000i −0.541293 0.0468807i
\(456\) −45.9595 −2.15225
\(457\) 3.40297i 0.159184i 0.996828 + 0.0795922i \(0.0253618\pi\)
−0.996828 + 0.0795922i \(0.974638\pi\)
\(458\) −4.50177 −0.210354
\(459\) −8.72393 −0.407198
\(460\) 16.0874i 0.750080i
\(461\) 17.5714i 0.818380i 0.912449 + 0.409190i \(0.134189\pi\)
−0.912449 + 0.409190i \(0.865811\pi\)
\(462\) 4.10171i 0.190829i
\(463\) 15.7714i 0.732959i −0.930426 0.366479i \(-0.880563\pi\)
0.930426 0.366479i \(-0.119437\pi\)
\(464\) 2.82564 0.131177
\(465\) 41.5417 1.92645
\(466\) 19.2607i 0.892236i
\(467\) 3.76694 0.174313 0.0871567 0.996195i \(-0.472222\pi\)
0.0871567 + 0.996195i \(0.472222\pi\)
\(468\) 10.4286 + 0.903212i 0.482064 + 0.0417510i
\(469\) −0.428639 −0.0197927
\(470\) 4.16839i 0.192273i
\(471\) −16.3827 −0.754875
\(472\) 17.8064 0.819607
\(473\) 23.6795i 1.08879i
\(474\) 6.83314i 0.313857i
\(475\) 45.5669i 2.09075i
\(476\) 5.47949i 0.251152i
\(477\) 4.80642 0.220071
\(478\) 13.4893 0.616988
\(479\) 12.1032i 0.553011i 0.961012 + 0.276506i \(0.0891764\pi\)
−0.961012 + 0.276506i \(0.910824\pi\)
\(480\) 41.3274 1.88633
\(481\) 1.22369 14.1289i 0.0557954 0.644223i
\(482\) −9.20189 −0.419135
\(483\) 7.26517i 0.330577i
\(484\) 5.75065 0.261393
\(485\) −30.9496 −1.40535
\(486\) 11.8938i 0.539516i
\(487\) 17.3778i 0.787463i −0.919226 0.393731i \(-0.871184\pi\)
0.919226 0.393731i \(-0.128816\pi\)
\(488\) 21.9813i 0.995045i
\(489\) 5.15257i 0.233007i
\(490\) 2.21432 0.100033
\(491\) 19.3921 0.875152 0.437576 0.899181i \(-0.355837\pi\)
0.437576 + 0.899181i \(0.355837\pi\)
\(492\) 2.55215i 0.115060i
\(493\) −7.36689 −0.331788
\(494\) 21.1481 + 1.83161i 0.951499 + 0.0824082i
\(495\) 16.4494 0.739345
\(496\) 8.04149i 0.361073i
\(497\) −8.98418 −0.402995
\(498\) −16.5161 −0.740102
\(499\) 10.6702i 0.477662i −0.971061 0.238831i \(-0.923236\pi\)
0.971061 0.238831i \(-0.0767642\pi\)
\(500\) 1.62714i 0.0727678i
\(501\) 7.57781i 0.338552i
\(502\) 2.27115i 0.101366i
\(503\) −4.27655 −0.190682 −0.0953410 0.995445i \(-0.530394\pi\)
−0.0953410 + 0.995445i \(0.530394\pi\)
\(504\) −4.62222 −0.205890
\(505\) 44.0163i 1.95870i
\(506\) 6.07758 0.270181
\(507\) −28.3575 4.94914i −1.25940 0.219799i
\(508\) −6.23506 −0.276636
\(509\) 33.0765i 1.46609i 0.680180 + 0.733046i \(0.261902\pi\)
−0.680180 + 0.733046i \(0.738098\pi\)
\(510\) −17.6128 −0.779910
\(511\) 5.79060 0.256161
\(512\) 14.6923i 0.649313i
\(513\) 20.7556i 0.916381i
\(514\) 16.3225i 0.719954i
\(515\) 39.5210i 1.74150i
\(516\) 29.7462 1.30950
\(517\) −5.06175 −0.222616
\(518\) 2.70964i 0.119055i
\(519\) 18.3225 0.804268
\(520\) −28.0415 2.42864i −1.22970 0.106503i
\(521\) 24.3783 1.06803 0.534015 0.845475i \(-0.320682\pi\)
0.534015 + 0.845475i \(0.320682\pi\)
\(522\) 2.68889i 0.117690i
\(523\) 34.9403 1.52783 0.763915 0.645317i \(-0.223275\pi\)
0.763915 + 0.645317i \(0.223275\pi\)
\(524\) 9.06070 0.395818
\(525\) 11.8064i 0.515275i
\(526\) 6.88247i 0.300090i
\(527\) 20.9654i 0.913269i
\(528\) 8.20342i 0.357008i
\(529\) −12.2351 −0.531959
\(530\) −5.59210 −0.242905
\(531\) 13.9541i 0.605555i
\(532\) 13.0366 0.565207
\(533\) −0.235063 + 2.71408i −0.0101817 + 0.117560i
\(534\) −8.17929 −0.353952
\(535\) 58.4657i 2.52769i
\(536\) −1.04101 −0.0449648
\(537\) −35.9289 −1.55045
\(538\) 12.5402i 0.540646i
\(539\) 2.68889i 0.115819i
\(540\) 11.9081i 0.512445i
\(541\) 30.4953i 1.31110i 0.755153 + 0.655548i \(0.227562\pi\)
−0.755153 + 0.655548i \(0.772438\pi\)
\(542\) −16.6539 −0.715344
\(543\) −20.3827 −0.874706
\(544\) 20.8573i 0.894248i
\(545\) −26.8780 −1.15133
\(546\) 5.47949 + 0.474572i 0.234501 + 0.0203098i
\(547\) −10.0049 −0.427780 −0.213890 0.976858i \(-0.568613\pi\)
−0.213890 + 0.976858i \(0.568613\pi\)
\(548\) 24.9590i 1.06620i
\(549\) 17.2257 0.735175
\(550\) −9.87649 −0.421135
\(551\) 17.5270i 0.746674i
\(552\) 17.6445i 0.750999i
\(553\) 4.47949i 0.190487i
\(554\) 1.16791i 0.0496198i
\(555\) −27.9956 −1.18835
\(556\) 4.62222 0.196026
\(557\) 14.1936i 0.601401i −0.953719 0.300701i \(-0.902780\pi\)
0.953719 0.300701i \(-0.0972205\pi\)
\(558\) −7.65233 −0.323949
\(559\) −31.6336 2.73975i −1.33796 0.115879i
\(560\) −4.42864 −0.187144
\(561\) 21.3876i 0.902986i
\(562\) 8.02413 0.338478
\(563\) 21.3590 0.900177 0.450088 0.892984i \(-0.351393\pi\)
0.450088 + 0.892984i \(0.351393\pi\)
\(564\) 6.35857i 0.267744i
\(565\) 27.2099i 1.14473i
\(566\) 8.35857i 0.351337i
\(567\) 11.0874i 0.465628i
\(568\) −21.8193 −0.915519
\(569\) −34.2672 −1.43656 −0.718278 0.695757i \(-0.755069\pi\)
−0.718278 + 0.695757i \(0.755069\pi\)
\(570\) 41.9037i 1.75515i
\(571\) 37.6494 1.57558 0.787789 0.615945i \(-0.211226\pi\)
0.787789 + 0.615945i \(0.211226\pi\)
\(572\) 1.27607 14.7338i 0.0533553 0.616050i
\(573\) 14.7654 0.616834
\(574\) 0.520505i 0.0217255i
\(575\) −17.4938 −0.729541
\(576\) −2.36842 −0.0986840
\(577\) 28.3970i 1.18218i 0.806605 + 0.591091i \(0.201303\pi\)
−0.806605 + 0.591091i \(0.798697\pi\)
\(578\) 2.82225i 0.117390i
\(579\) 45.6227i 1.89601i
\(580\) 10.0558i 0.417543i
\(581\) 10.8272 0.449187
\(582\) 14.6878 0.608830
\(583\) 6.79060i 0.281238i
\(584\) 14.0633 0.581943
\(585\) −1.90321 + 21.9748i −0.0786881 + 0.908547i
\(586\) 7.89045 0.325952
\(587\) 6.23659i 0.257412i −0.991683 0.128706i \(-0.958918\pi\)
0.991683 0.128706i \(-0.0410823\pi\)
\(588\) 3.37778 0.139297
\(589\) 49.8800 2.05527
\(590\) 16.2351i 0.668387i
\(591\) 18.5303i 0.762237i
\(592\) 5.41927i 0.222731i
\(593\) 17.5698i 0.721506i −0.932661 0.360753i \(-0.882520\pi\)
0.932661 0.360753i \(-0.117480\pi\)
\(594\) 4.49871 0.184584
\(595\) 11.5462 0.473347
\(596\) 22.1748i 0.908317i
\(597\) −1.33185 −0.0545090
\(598\) −0.703182 + 8.11906i −0.0287553 + 0.332013i
\(599\) 16.9813 0.693836 0.346918 0.937896i \(-0.387228\pi\)
0.346918 + 0.937896i \(0.387228\pi\)
\(600\) 28.6735i 1.17059i
\(601\) −18.7052 −0.763001 −0.381500 0.924369i \(-0.624592\pi\)
−0.381500 + 0.924369i \(0.624592\pi\)
\(602\) 6.06668 0.247259
\(603\) 0.815792i 0.0332216i
\(604\) 30.4701i 1.23981i
\(605\) 12.1175i 0.492648i
\(606\) 20.8889i 0.848554i
\(607\) −10.3575 −0.420399 −0.210199 0.977659i \(-0.567411\pi\)
−0.210199 + 0.977659i \(0.567411\pi\)
\(608\) 49.6227 2.01247
\(609\) 4.54125i 0.184021i
\(610\) −20.0415 −0.811456
\(611\) 0.585651 6.76202i 0.0236929 0.273562i
\(612\) −10.4286 −0.421553
\(613\) 7.02227i 0.283627i −0.989893 0.141814i \(-0.954707\pi\)
0.989893 0.141814i \(-0.0452933\pi\)
\(614\) 2.73483 0.110369
\(615\) 5.37778 0.216853
\(616\) 6.53035i 0.263115i
\(617\) 29.9813i 1.20700i 0.797363 + 0.603500i \(0.206228\pi\)
−0.797363 + 0.603500i \(0.793772\pi\)
\(618\) 18.7556i 0.754460i
\(619\) 0.0285802i 0.00114874i −1.00000 0.000574368i \(-0.999817\pi\)
1.00000 0.000574368i \(-0.000182827\pi\)
\(620\) −28.6178 −1.14932
\(621\) 7.96836 0.319759
\(622\) 18.8399i 0.755412i
\(623\) 5.36196 0.214823
\(624\) −10.9590 0.949145i −0.438711 0.0379962i
\(625\) −23.2306 −0.929225
\(626\) 13.1601i 0.525982i
\(627\) 50.8845 2.03213
\(628\) 11.2859 0.450357
\(629\) 14.1289i 0.563356i
\(630\) 4.21432i 0.167903i
\(631\) 12.1936i 0.485419i 0.970099 + 0.242709i \(0.0780361\pi\)
−0.970099 + 0.242709i \(0.921964\pi\)
\(632\) 10.8791i 0.432746i
\(633\) 4.21432 0.167504
\(634\) −6.82564 −0.271081
\(635\) 13.1383i 0.521377i
\(636\) −8.53035 −0.338250
\(637\) −3.59210 0.311108i −0.142324 0.0123265i
\(638\) 3.79892 0.150401
\(639\) 17.0988i 0.676418i
\(640\) −34.5718 −1.36657
\(641\) 2.82516 0.111587 0.0557935 0.998442i \(-0.482231\pi\)
0.0557935 + 0.998442i \(0.482231\pi\)
\(642\) 27.7462i 1.09506i
\(643\) 37.7275i 1.48783i −0.668276 0.743913i \(-0.732968\pi\)
0.668276 0.743913i \(-0.267032\pi\)
\(644\) 5.00492i 0.197222i
\(645\) 62.6800i 2.46802i
\(646\) −21.1481 −0.832062
\(647\) −12.3664 −0.486174 −0.243087 0.970005i \(-0.578160\pi\)
−0.243087 + 0.970005i \(0.578160\pi\)
\(648\) 26.9273i 1.05781i
\(649\) −19.7146 −0.773864
\(650\) 1.14272 13.1941i 0.0448212 0.517513i
\(651\) 12.9240 0.506530
\(652\) 3.54956i 0.139012i
\(653\) −33.0005 −1.29141 −0.645704 0.763588i \(-0.723436\pi\)
−0.645704 + 0.763588i \(0.723436\pi\)
\(654\) 12.7556 0.498782
\(655\) 19.0923i 0.746000i
\(656\) 1.04101i 0.0406446i
\(657\) 11.0207i 0.429960i
\(658\) 1.29682i 0.0505552i
\(659\) 32.8118 1.27817 0.639084 0.769137i \(-0.279314\pi\)
0.639084 + 0.769137i \(0.279314\pi\)
\(660\) −29.1941 −1.13638
\(661\) 14.7067i 0.572025i 0.958226 + 0.286013i \(0.0923299\pi\)
−0.958226 + 0.286013i \(0.907670\pi\)
\(662\) −16.1334 −0.627041
\(663\) 28.5718 + 2.47457i 1.10964 + 0.0961044i
\(664\) 26.2953 1.02046
\(665\) 27.4701i 1.06525i
\(666\) 5.15701 0.199830
\(667\) 6.72885 0.260542
\(668\) 5.22030i 0.201979i
\(669\) 23.5462i 0.910348i
\(670\) 0.949145i 0.0366687i
\(671\) 24.3368i 0.939511i
\(672\) 12.8573 0.495980
\(673\) −21.2908 −0.820702 −0.410351 0.911928i \(-0.634594\pi\)
−0.410351 + 0.911928i \(0.634594\pi\)
\(674\) 5.17775i 0.199440i
\(675\) −12.9491 −0.498413
\(676\) 19.5353 + 3.40943i 0.751357 + 0.131132i
\(677\) −3.07160 −0.118051 −0.0590256 0.998256i \(-0.518799\pi\)
−0.0590256 + 0.998256i \(0.518799\pi\)
\(678\) 12.9131i 0.495923i
\(679\) −9.62867 −0.369514
\(680\) 28.0415 1.07534
\(681\) 33.3274i 1.27711i
\(682\) 10.8113i 0.413988i
\(683\) 24.7971i 0.948833i 0.880301 + 0.474416i \(0.157341\pi\)
−0.880301 + 0.474416i \(0.842659\pi\)
\(684\) 24.8113i 0.948686i
\(685\) 52.5926 2.00946
\(686\) 0.688892 0.0263020
\(687\) 14.4701i 0.552070i
\(688\) −12.1334 −0.462580
\(689\) 9.07160 + 0.785680i 0.345600 + 0.0299320i
\(690\) 16.0874 0.612438
\(691\) 27.0953i 1.03075i −0.856964 0.515376i \(-0.827652\pi\)
0.856964 0.515376i \(-0.172348\pi\)
\(692\) −12.6222 −0.479825
\(693\) 5.11753 0.194399
\(694\) 3.88845i 0.147603i
\(695\) 9.73975i 0.369450i
\(696\) 11.0291i 0.418055i
\(697\) 2.71408i 0.102803i
\(698\) 16.6430 0.629945
\(699\) −61.9101 −2.34166
\(700\) 8.13335i 0.307412i
\(701\) −13.5205 −0.510662 −0.255331 0.966854i \(-0.582185\pi\)
−0.255331 + 0.966854i \(0.582185\pi\)
\(702\) −0.520505 + 6.00984i −0.0196452 + 0.226827i
\(703\) −33.6149 −1.26781
\(704\) 3.34614i 0.126112i
\(705\) −13.3985 −0.504618
\(706\) −24.8889 −0.936707
\(707\) 13.6938i 0.515009i
\(708\) 24.7654i 0.930741i
\(709\) 50.9753i 1.91442i 0.289399 + 0.957209i \(0.406545\pi\)
−0.289399 + 0.957209i \(0.593455\pi\)
\(710\) 19.8938i 0.746603i
\(711\) −8.52543 −0.319729
\(712\) 13.0223 0.488030
\(713\) 19.1497i 0.717160i
\(714\) −5.47949 −0.205065
\(715\) 31.0464 + 2.68889i 1.16107 + 0.100559i
\(716\) 24.7511 0.924993
\(717\) 43.3590i 1.61927i
\(718\) 11.9956 0.447670
\(719\) −41.5417 −1.54924 −0.774622 0.632424i \(-0.782060\pi\)
−0.774622 + 0.632424i \(0.782060\pi\)
\(720\) 8.42864i 0.314117i
\(721\) 12.2953i 0.457900i
\(722\) 37.2257i 1.38540i
\(723\) 29.5778i 1.10001i
\(724\) 14.0415 0.521848
\(725\) −10.9349 −0.406110
\(726\) 5.75065i 0.213427i
\(727\) 20.8988 0.775092 0.387546 0.921850i \(-0.373323\pi\)
0.387546 + 0.921850i \(0.373323\pi\)
\(728\) −8.72393 0.755569i −0.323330 0.0280032i
\(729\) −4.96836 −0.184013
\(730\) 12.8222i 0.474573i
\(731\) 31.6336 1.17001
\(732\) −30.5718 −1.12997
\(733\) 19.3575i 0.714986i 0.933916 + 0.357493i \(0.116368\pi\)
−0.933916 + 0.357493i \(0.883632\pi\)
\(734\) 2.02413i 0.0747122i
\(735\) 7.11753i 0.262534i
\(736\) 19.0509i 0.702224i
\(737\) 1.15257 0.0424553
\(738\) −0.990632 −0.0364657
\(739\) 1.31111i 0.0482299i 0.999709 + 0.0241149i \(0.00767677\pi\)
−0.999709 + 0.0241149i \(0.992323\pi\)
\(740\) 19.2859 0.708964
\(741\) −5.88739 + 67.9768i −0.216279 + 2.49719i
\(742\) −1.73975 −0.0638681
\(743\) 21.5210i 0.789528i −0.918783 0.394764i \(-0.870826\pi\)
0.918783 0.394764i \(-0.129174\pi\)
\(744\) 31.3876 1.15073
\(745\) 46.7259 1.71191
\(746\) 12.9304i 0.473416i
\(747\) 20.6064i 0.753949i
\(748\) 14.7338i 0.538720i
\(749\) 18.1891i 0.664616i
\(750\) −1.62714 −0.0594147
\(751\) 16.3176 0.595436 0.297718 0.954654i \(-0.403774\pi\)
0.297718 + 0.954654i \(0.403774\pi\)
\(752\) 2.59364i 0.0945802i
\(753\) 7.30021 0.266034
\(754\) −0.439539 + 5.07499i −0.0160071 + 0.184820i
\(755\) −64.2054 −2.33667
\(756\) 3.70471i 0.134739i
\(757\) −18.7462 −0.681342 −0.340671 0.940183i \(-0.610654\pi\)
−0.340671 + 0.940183i \(0.610654\pi\)
\(758\) −16.3194 −0.592748
\(759\) 19.5353i 0.709085i
\(760\) 66.7150i 2.42001i
\(761\) 10.2968i 0.373259i 0.982430 + 0.186630i \(0.0597564\pi\)
−0.982430 + 0.186630i \(0.940244\pi\)
\(762\) 6.23506i 0.225873i
\(763\) −8.36196 −0.302723
\(764\) −10.1718 −0.368002
\(765\) 21.9748i 0.794501i
\(766\) −21.7778 −0.786865
\(767\) 2.28100 26.3368i 0.0823620 0.950966i
\(768\) 21.9180 0.790897
\(769\) 9.36641i 0.337761i 0.985637 + 0.168881i \(0.0540153\pi\)
−0.985637 + 0.168881i \(0.945985\pi\)
\(770\) −5.95407 −0.214570
\(771\) −52.4657 −1.88951
\(772\) 31.4291i 1.13116i
\(773\) 3.71456i 0.133603i −0.997766 0.0668017i \(-0.978721\pi\)
0.997766 0.0668017i \(-0.0212795\pi\)
\(774\) 11.5462i 0.415019i
\(775\) 31.1195i 1.11785i
\(776\) −23.3846 −0.839457
\(777\) −8.70964 −0.312456
\(778\) 13.8163i 0.495337i
\(779\) 6.45722 0.231354
\(780\) 3.37778 39.0005i 0.120944 1.39644i
\(781\) 24.1575 0.864423
\(782\) 8.11906i 0.290337i
\(783\) 4.98079 0.177999
\(784\) −1.37778 −0.0492066
\(785\) 23.7812i 0.848789i
\(786\) 9.06070i 0.323184i
\(787\) 6.23659i 0.222311i −0.993803 0.111155i \(-0.964545\pi\)
0.993803 0.111155i \(-0.0354551\pi\)
\(788\) 12.7654i 0.454749i
\(789\) −22.1225 −0.787580
\(790\) 9.91903 0.352903
\(791\) 8.46520i