Properties

Label 546.2.c.a.337.1
Level $546$
Weight $2$
Character 546.337
Analytic conductor $4.360$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 337.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 546.337
Dual form 546.2.c.a.337.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} +1.00000i q^{5} +1.00000i q^{6} -1.00000i q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} +1.00000i q^{5} +1.00000i q^{6} -1.00000i q^{7} +1.00000i q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000i q^{11} +1.00000 q^{12} +(3.00000 + 2.00000i) q^{13} -1.00000 q^{14} -1.00000i q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000i q^{18} -1.00000i q^{19} -1.00000i q^{20} +1.00000i q^{21} +1.00000 q^{22} +3.00000 q^{23} -1.00000i q^{24} +4.00000 q^{25} +(2.00000 - 3.00000i) q^{26} -1.00000 q^{27} +1.00000i q^{28} +9.00000 q^{29} -1.00000 q^{30} -4.00000i q^{31} -1.00000i q^{32} -1.00000i q^{33} -1.00000i q^{34} +1.00000 q^{35} -1.00000 q^{36} -9.00000i q^{37} -1.00000 q^{38} +(-3.00000 - 2.00000i) q^{39} -1.00000 q^{40} +8.00000i q^{41} +1.00000 q^{42} +7.00000 q^{43} -1.00000i q^{44} +1.00000i q^{45} -3.00000i q^{46} +8.00000i q^{47} -1.00000 q^{48} -1.00000 q^{49} -4.00000i q^{50} -1.00000 q^{51} +(-3.00000 - 2.00000i) q^{52} -10.0000 q^{53} +1.00000i q^{54} -1.00000 q^{55} +1.00000 q^{56} +1.00000i q^{57} -9.00000i q^{58} -6.00000i q^{59} +1.00000i q^{60} +11.0000 q^{61} -4.00000 q^{62} -1.00000i q^{63} -1.00000 q^{64} +(-2.00000 + 3.00000i) q^{65} -1.00000 q^{66} -12.0000i q^{67} -1.00000 q^{68} -3.00000 q^{69} -1.00000i q^{70} +6.00000i q^{71} +1.00000i q^{72} +11.0000i q^{73} -9.00000 q^{74} -4.00000 q^{75} +1.00000i q^{76} +1.00000 q^{77} +(-2.00000 + 3.00000i) q^{78} -12.0000 q^{79} +1.00000i q^{80} +1.00000 q^{81} +8.00000 q^{82} +6.00000i q^{83} -1.00000i q^{84} +1.00000i q^{85} -7.00000i q^{86} -9.00000 q^{87} -1.00000 q^{88} +12.0000i q^{89} +1.00000 q^{90} +(2.00000 - 3.00000i) q^{91} -3.00000 q^{92} +4.00000i q^{93} +8.00000 q^{94} +1.00000 q^{95} +1.00000i q^{96} -2.00000i q^{97} +1.00000i q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{3} - 2q^{4} + 2q^{9} + O(q^{10}) \) \( 2q - 2q^{3} - 2q^{4} + 2q^{9} + 2q^{10} + 2q^{12} + 6q^{13} - 2q^{14} + 2q^{16} + 2q^{17} + 2q^{22} + 6q^{23} + 8q^{25} + 4q^{26} - 2q^{27} + 18q^{29} - 2q^{30} + 2q^{35} - 2q^{36} - 2q^{38} - 6q^{39} - 2q^{40} + 2q^{42} + 14q^{43} - 2q^{48} - 2q^{49} - 2q^{51} - 6q^{52} - 20q^{53} - 2q^{55} + 2q^{56} + 22q^{61} - 8q^{62} - 2q^{64} - 4q^{65} - 2q^{66} - 2q^{68} - 6q^{69} - 18q^{74} - 8q^{75} + 2q^{77} - 4q^{78} - 24q^{79} + 2q^{81} + 16q^{82} - 18q^{87} - 2q^{88} + 2q^{90} + 4q^{91} - 6q^{92} + 16q^{94} + 2q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.00000 −0.577350
\(4\) −1.00000 −0.500000
\(5\) 1.00000i 0.447214i 0.974679 + 0.223607i \(0.0717831\pi\)
−0.974679 + 0.223607i \(0.928217\pi\)
\(6\) 1.00000i 0.408248i
\(7\) 1.00000i 0.377964i
\(8\) 1.00000i 0.353553i
\(9\) 1.00000 0.333333
\(10\) 1.00000 0.316228
\(11\) 1.00000i 0.301511i 0.988571 + 0.150756i \(0.0481707\pi\)
−0.988571 + 0.150756i \(0.951829\pi\)
\(12\) 1.00000 0.288675
\(13\) 3.00000 + 2.00000i 0.832050 + 0.554700i
\(14\) −1.00000 −0.267261
\(15\) 1.00000i 0.258199i
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536 0.121268 0.992620i \(-0.461304\pi\)
0.121268 + 0.992620i \(0.461304\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 1.00000i 0.229416i −0.993399 0.114708i \(-0.963407\pi\)
0.993399 0.114708i \(-0.0365932\pi\)
\(20\) 1.00000i 0.223607i
\(21\) 1.00000i 0.218218i
\(22\) 1.00000 0.213201
\(23\) 3.00000 0.625543 0.312772 0.949828i \(-0.398743\pi\)
0.312772 + 0.949828i \(0.398743\pi\)
\(24\) 1.00000i 0.204124i
\(25\) 4.00000 0.800000
\(26\) 2.00000 3.00000i 0.392232 0.588348i
\(27\) −1.00000 −0.192450
\(28\) 1.00000i 0.188982i
\(29\) 9.00000 1.67126 0.835629 0.549294i \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) −1.00000 −0.182574
\(31\) 4.00000i 0.718421i −0.933257 0.359211i \(-0.883046\pi\)
0.933257 0.359211i \(-0.116954\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 1.00000i 0.174078i
\(34\) 1.00000i 0.171499i
\(35\) 1.00000 0.169031
\(36\) −1.00000 −0.166667
\(37\) 9.00000i 1.47959i −0.672832 0.739795i \(-0.734922\pi\)
0.672832 0.739795i \(-0.265078\pi\)
\(38\) −1.00000 −0.162221
\(39\) −3.00000 2.00000i −0.480384 0.320256i
\(40\) −1.00000 −0.158114
\(41\) 8.00000i 1.24939i 0.780869 + 0.624695i \(0.214777\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 1.00000 0.154303
\(43\) 7.00000 1.06749 0.533745 0.845645i \(-0.320784\pi\)
0.533745 + 0.845645i \(0.320784\pi\)
\(44\) 1.00000i 0.150756i
\(45\) 1.00000i 0.149071i
\(46\) 3.00000i 0.442326i
\(47\) 8.00000i 1.16692i 0.812142 + 0.583460i \(0.198301\pi\)
−0.812142 + 0.583460i \(0.801699\pi\)
\(48\) −1.00000 −0.144338
\(49\) −1.00000 −0.142857
\(50\) 4.00000i 0.565685i
\(51\) −1.00000 −0.140028
\(52\) −3.00000 2.00000i −0.416025 0.277350i
\(53\) −10.0000 −1.37361 −0.686803 0.726844i \(-0.740986\pi\)
−0.686803 + 0.726844i \(0.740986\pi\)
\(54\) 1.00000i 0.136083i
\(55\) −1.00000 −0.134840
\(56\) 1.00000 0.133631
\(57\) 1.00000i 0.132453i
\(58\) 9.00000i 1.18176i
\(59\) 6.00000i 0.781133i −0.920575 0.390567i \(-0.872279\pi\)
0.920575 0.390567i \(-0.127721\pi\)
\(60\) 1.00000i 0.129099i
\(61\) 11.0000 1.40841 0.704203 0.709999i \(-0.251305\pi\)
0.704203 + 0.709999i \(0.251305\pi\)
\(62\) −4.00000 −0.508001
\(63\) 1.00000i 0.125988i
\(64\) −1.00000 −0.125000
\(65\) −2.00000 + 3.00000i −0.248069 + 0.372104i
\(66\) −1.00000 −0.123091
\(67\) 12.0000i 1.46603i −0.680211 0.733017i \(-0.738112\pi\)
0.680211 0.733017i \(-0.261888\pi\)
\(68\) −1.00000 −0.121268
\(69\) −3.00000 −0.361158
\(70\) 1.00000i 0.119523i
\(71\) 6.00000i 0.712069i 0.934473 + 0.356034i \(0.115871\pi\)
−0.934473 + 0.356034i \(0.884129\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 11.0000i 1.28745i 0.765256 + 0.643726i \(0.222612\pi\)
−0.765256 + 0.643726i \(0.777388\pi\)
\(74\) −9.00000 −1.04623
\(75\) −4.00000 −0.461880
\(76\) 1.00000i 0.114708i
\(77\) 1.00000 0.113961
\(78\) −2.00000 + 3.00000i −0.226455 + 0.339683i
\(79\) −12.0000 −1.35011 −0.675053 0.737769i \(-0.735879\pi\)
−0.675053 + 0.737769i \(0.735879\pi\)
\(80\) 1.00000i 0.111803i
\(81\) 1.00000 0.111111
\(82\) 8.00000 0.883452
\(83\) 6.00000i 0.658586i 0.944228 + 0.329293i \(0.106810\pi\)
−0.944228 + 0.329293i \(0.893190\pi\)
\(84\) 1.00000i 0.109109i
\(85\) 1.00000i 0.108465i
\(86\) 7.00000i 0.754829i
\(87\) −9.00000 −0.964901
\(88\) −1.00000 −0.106600
\(89\) 12.0000i 1.27200i 0.771690 + 0.635999i \(0.219412\pi\)
−0.771690 + 0.635999i \(0.780588\pi\)
\(90\) 1.00000 0.105409
\(91\) 2.00000 3.00000i 0.209657 0.314485i
\(92\) −3.00000 −0.312772
\(93\) 4.00000i 0.414781i
\(94\) 8.00000 0.825137
\(95\) 1.00000 0.102598
\(96\) 1.00000i 0.102062i
\(97\) 2.00000i 0.203069i −0.994832 0.101535i \(-0.967625\pi\)
0.994832 0.101535i \(-0.0323753\pi\)
\(98\) 1.00000i 0.101015i
\(99\) 1.00000i 0.100504i
\(100\) −4.00000 −0.400000
\(101\) −2.00000 −0.199007 −0.0995037 0.995037i \(-0.531726\pi\)
−0.0995037 + 0.995037i \(0.531726\pi\)
\(102\) 1.00000i 0.0990148i
\(103\) −5.00000 −0.492665 −0.246332 0.969185i \(-0.579225\pi\)
−0.246332 + 0.969185i \(0.579225\pi\)
\(104\) −2.00000 + 3.00000i −0.196116 + 0.294174i
\(105\) −1.00000 −0.0975900
\(106\) 10.0000i 0.971286i
\(107\) −2.00000 −0.193347 −0.0966736 0.995316i \(-0.530820\pi\)
−0.0966736 + 0.995316i \(0.530820\pi\)
\(108\) 1.00000 0.0962250
\(109\) 7.00000i 0.670478i 0.942133 + 0.335239i \(0.108817\pi\)
−0.942133 + 0.335239i \(0.891183\pi\)
\(110\) 1.00000i 0.0953463i
\(111\) 9.00000i 0.854242i
\(112\) 1.00000i 0.0944911i
\(113\) −2.00000 −0.188144 −0.0940721 0.995565i \(-0.529988\pi\)
−0.0940721 + 0.995565i \(0.529988\pi\)
\(114\) 1.00000 0.0936586
\(115\) 3.00000i 0.279751i
\(116\) −9.00000 −0.835629
\(117\) 3.00000 + 2.00000i 0.277350 + 0.184900i
\(118\) −6.00000 −0.552345
\(119\) 1.00000i 0.0916698i
\(120\) 1.00000 0.0912871
\(121\) 10.0000 0.909091
\(122\) 11.0000i 0.995893i
\(123\) 8.00000i 0.721336i
\(124\) 4.00000i 0.359211i
\(125\) 9.00000i 0.804984i
\(126\) −1.00000 −0.0890871
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −7.00000 −0.616316
\(130\) 3.00000 + 2.00000i 0.263117 + 0.175412i
\(131\) −3.00000 −0.262111 −0.131056 0.991375i \(-0.541837\pi\)
−0.131056 + 0.991375i \(0.541837\pi\)
\(132\) 1.00000i 0.0870388i
\(133\) −1.00000 −0.0867110
\(134\) −12.0000 −1.03664
\(135\) 1.00000i 0.0860663i
\(136\) 1.00000i 0.0857493i
\(137\) 15.0000i 1.28154i −0.767734 0.640768i \(-0.778616\pi\)
0.767734 0.640768i \(-0.221384\pi\)
\(138\) 3.00000i 0.255377i
\(139\) −12.0000 −1.01783 −0.508913 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) −1.00000 −0.0845154
\(141\) 8.00000i 0.673722i
\(142\) 6.00000 0.503509
\(143\) −2.00000 + 3.00000i −0.167248 + 0.250873i
\(144\) 1.00000 0.0833333
\(145\) 9.00000i 0.747409i
\(146\) 11.0000 0.910366
\(147\) 1.00000 0.0824786
\(148\) 9.00000i 0.739795i
\(149\) 6.00000i 0.491539i 0.969328 + 0.245770i \(0.0790407\pi\)
−0.969328 + 0.245770i \(0.920959\pi\)
\(150\) 4.00000i 0.326599i
\(151\) 1.00000i 0.0813788i 0.999172 + 0.0406894i \(0.0129554\pi\)
−0.999172 + 0.0406894i \(0.987045\pi\)
\(152\) 1.00000 0.0811107
\(153\) 1.00000 0.0808452
\(154\) 1.00000i 0.0805823i
\(155\) 4.00000 0.321288
\(156\) 3.00000 + 2.00000i 0.240192 + 0.160128i
\(157\) −21.0000 −1.67598 −0.837991 0.545684i \(-0.816270\pi\)
−0.837991 + 0.545684i \(0.816270\pi\)
\(158\) 12.0000i 0.954669i
\(159\) 10.0000 0.793052
\(160\) 1.00000 0.0790569
\(161\) 3.00000i 0.236433i
\(162\) 1.00000i 0.0785674i
\(163\) 20.0000i 1.56652i −0.621694 0.783260i \(-0.713555\pi\)
0.621694 0.783260i \(-0.286445\pi\)
\(164\) 8.00000i 0.624695i
\(165\) 1.00000 0.0778499
\(166\) 6.00000 0.465690
\(167\) 11.0000i 0.851206i −0.904910 0.425603i \(-0.860062\pi\)
0.904910 0.425603i \(-0.139938\pi\)
\(168\) −1.00000 −0.0771517
\(169\) 5.00000 + 12.0000i 0.384615 + 0.923077i
\(170\) 1.00000 0.0766965
\(171\) 1.00000i 0.0764719i
\(172\) −7.00000 −0.533745
\(173\) 14.0000 1.06440 0.532200 0.846619i \(-0.321365\pi\)
0.532200 + 0.846619i \(0.321365\pi\)
\(174\) 9.00000i 0.682288i
\(175\) 4.00000i 0.302372i
\(176\) 1.00000i 0.0753778i
\(177\) 6.00000i 0.450988i
\(178\) 12.0000 0.899438
\(179\) −18.0000 −1.34538 −0.672692 0.739923i \(-0.734862\pi\)
−0.672692 + 0.739923i \(0.734862\pi\)
\(180\) 1.00000i 0.0745356i
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) −3.00000 2.00000i −0.222375 0.148250i
\(183\) −11.0000 −0.813143
\(184\) 3.00000i 0.221163i
\(185\) 9.00000 0.661693
\(186\) 4.00000 0.293294
\(187\) 1.00000i 0.0731272i
\(188\) 8.00000i 0.583460i
\(189\) 1.00000i 0.0727393i
\(190\) 1.00000i 0.0725476i
\(191\) −11.0000 −0.795932 −0.397966 0.917400i \(-0.630284\pi\)
−0.397966 + 0.917400i \(0.630284\pi\)
\(192\) 1.00000 0.0721688
\(193\) 12.0000i 0.863779i −0.901927 0.431889i \(-0.857847\pi\)
0.901927 0.431889i \(-0.142153\pi\)
\(194\) −2.00000 −0.143592
\(195\) 2.00000 3.00000i 0.143223 0.214834i
\(196\) 1.00000 0.0714286
\(197\) 2.00000i 0.142494i −0.997459 0.0712470i \(-0.977302\pi\)
0.997459 0.0712470i \(-0.0226979\pi\)
\(198\) 1.00000 0.0710669
\(199\) 5.00000 0.354441 0.177220 0.984171i \(-0.443289\pi\)
0.177220 + 0.984171i \(0.443289\pi\)
\(200\) 4.00000i 0.282843i
\(201\) 12.0000i 0.846415i
\(202\) 2.00000i 0.140720i
\(203\) 9.00000i 0.631676i
\(204\) 1.00000 0.0700140
\(205\) −8.00000 −0.558744
\(206\) 5.00000i 0.348367i
\(207\) 3.00000 0.208514
\(208\) 3.00000 + 2.00000i 0.208013 + 0.138675i
\(209\) 1.00000 0.0691714
\(210\) 1.00000i 0.0690066i
\(211\) −5.00000 −0.344214 −0.172107 0.985078i \(-0.555058\pi\)
−0.172107 + 0.985078i \(0.555058\pi\)
\(212\) 10.0000 0.686803
\(213\) 6.00000i 0.411113i
\(214\) 2.00000i 0.136717i
\(215\) 7.00000i 0.477396i
\(216\) 1.00000i 0.0680414i
\(217\) −4.00000 −0.271538
\(218\) 7.00000 0.474100
\(219\) 11.0000i 0.743311i
\(220\) 1.00000 0.0674200
\(221\) 3.00000 + 2.00000i 0.201802 + 0.134535i
\(222\) 9.00000 0.604040
\(223\) 8.00000i 0.535720i −0.963458 0.267860i \(-0.913684\pi\)
0.963458 0.267860i \(-0.0863164\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 4.00000 0.266667
\(226\) 2.00000i 0.133038i
\(227\) 12.0000i 0.796468i −0.917284 0.398234i \(-0.869623\pi\)
0.917284 0.398234i \(-0.130377\pi\)
\(228\) 1.00000i 0.0662266i
\(229\) 2.00000i 0.132164i 0.997814 + 0.0660819i \(0.0210498\pi\)
−0.997814 + 0.0660819i \(0.978950\pi\)
\(230\) 3.00000 0.197814
\(231\) −1.00000 −0.0657952
\(232\) 9.00000i 0.590879i
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 2.00000 3.00000i 0.130744 0.196116i
\(235\) −8.00000 −0.521862
\(236\) 6.00000i 0.390567i
\(237\) 12.0000 0.779484
\(238\) −1.00000 −0.0648204
\(239\) 8.00000i 0.517477i −0.965947 0.258738i \(-0.916693\pi\)
0.965947 0.258738i \(-0.0833068\pi\)
\(240\) 1.00000i 0.0645497i
\(241\) 10.0000i 0.644157i 0.946713 + 0.322078i \(0.104381\pi\)
−0.946713 + 0.322078i \(0.895619\pi\)
\(242\) 10.0000i 0.642824i
\(243\) −1.00000 −0.0641500
\(244\) −11.0000 −0.704203
\(245\) 1.00000i 0.0638877i
\(246\) −8.00000 −0.510061
\(247\) 2.00000 3.00000i 0.127257 0.190885i
\(248\) 4.00000 0.254000
\(249\) 6.00000i 0.380235i
\(250\) 9.00000 0.569210
\(251\) 11.0000 0.694314 0.347157 0.937807i \(-0.387147\pi\)
0.347157 + 0.937807i \(0.387147\pi\)
\(252\) 1.00000i 0.0629941i
\(253\) 3.00000i 0.188608i
\(254\) 16.0000i 1.00393i
\(255\) 1.00000i 0.0626224i
\(256\) 1.00000 0.0625000
\(257\) 14.0000 0.873296 0.436648 0.899632i \(-0.356166\pi\)
0.436648 + 0.899632i \(0.356166\pi\)
\(258\) 7.00000i 0.435801i
\(259\) −9.00000 −0.559233
\(260\) 2.00000 3.00000i 0.124035 0.186052i
\(261\) 9.00000 0.557086
\(262\) 3.00000i 0.185341i
\(263\) 16.0000 0.986602 0.493301 0.869859i \(-0.335790\pi\)
0.493301 + 0.869859i \(0.335790\pi\)
\(264\) 1.00000 0.0615457
\(265\) 10.0000i 0.614295i
\(266\) 1.00000i 0.0613139i
\(267\) 12.0000i 0.734388i
\(268\) 12.0000i 0.733017i
\(269\) −20.0000 −1.21942 −0.609711 0.792624i \(-0.708714\pi\)
−0.609711 + 0.792624i \(0.708714\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 4.00000i 0.242983i −0.992592 0.121491i \(-0.961232\pi\)
0.992592 0.121491i \(-0.0387677\pi\)
\(272\) 1.00000 0.0606339
\(273\) −2.00000 + 3.00000i −0.121046 + 0.181568i
\(274\) −15.0000 −0.906183
\(275\) 4.00000i 0.241209i
\(276\) 3.00000 0.180579
\(277\) 16.0000 0.961347 0.480673 0.876900i \(-0.340392\pi\)
0.480673 + 0.876900i \(0.340392\pi\)
\(278\) 12.0000i 0.719712i
\(279\) 4.00000i 0.239474i
\(280\) 1.00000i 0.0597614i
\(281\) 22.0000i 1.31241i −0.754583 0.656205i \(-0.772161\pi\)
0.754583 0.656205i \(-0.227839\pi\)
\(282\) −8.00000 −0.476393
\(283\) −14.0000 −0.832214 −0.416107 0.909316i \(-0.636606\pi\)
−0.416107 + 0.909316i \(0.636606\pi\)
\(284\) 6.00000i 0.356034i
\(285\) −1.00000 −0.0592349
\(286\) 3.00000 + 2.00000i 0.177394 + 0.118262i
\(287\) 8.00000 0.472225
\(288\) 1.00000i 0.0589256i
\(289\) −16.0000 −0.941176
\(290\) 9.00000 0.528498
\(291\) 2.00000i 0.117242i
\(292\) 11.0000i 0.643726i
\(293\) 26.0000i 1.51894i −0.650545 0.759468i \(-0.725459\pi\)
0.650545 0.759468i \(-0.274541\pi\)
\(294\) 1.00000i 0.0583212i
\(295\) 6.00000 0.349334
\(296\) 9.00000 0.523114
\(297\) 1.00000i 0.0580259i
\(298\) 6.00000 0.347571
\(299\) 9.00000 + 6.00000i 0.520483 + 0.346989i
\(300\) 4.00000 0.230940
\(301\) 7.00000i 0.403473i
\(302\) 1.00000 0.0575435
\(303\) 2.00000 0.114897
\(304\) 1.00000i 0.0573539i
\(305\) 11.0000i 0.629858i
\(306\) 1.00000i 0.0571662i
\(307\) 8.00000i 0.456584i −0.973593 0.228292i \(-0.926686\pi\)
0.973593 0.228292i \(-0.0733141\pi\)
\(308\) −1.00000 −0.0569803
\(309\) 5.00000 0.284440
\(310\) 4.00000i 0.227185i
\(311\) 8.00000 0.453638 0.226819 0.973937i \(-0.427167\pi\)
0.226819 + 0.973937i \(0.427167\pi\)
\(312\) 2.00000 3.00000i 0.113228 0.169842i
\(313\) −14.0000 −0.791327 −0.395663 0.918396i \(-0.629485\pi\)
−0.395663 + 0.918396i \(0.629485\pi\)
\(314\) 21.0000i 1.18510i
\(315\) 1.00000 0.0563436
\(316\) 12.0000 0.675053
\(317\) 12.0000i 0.673987i −0.941507 0.336994i \(-0.890590\pi\)
0.941507 0.336994i \(-0.109410\pi\)
\(318\) 10.0000i 0.560772i
\(319\) 9.00000i 0.503903i
\(320\) 1.00000i 0.0559017i
\(321\) 2.00000 0.111629
\(322\) −3.00000 −0.167183
\(323\) 1.00000i 0.0556415i
\(324\) −1.00000 −0.0555556
\(325\) 12.0000 + 8.00000i 0.665640 + 0.443760i
\(326\) −20.0000 −1.10770
\(327\) 7.00000i 0.387101i
\(328\) −8.00000 −0.441726
\(329\) 8.00000 0.441054
\(330\) 1.00000i 0.0550482i
\(331\) 8.00000i 0.439720i −0.975531 0.219860i \(-0.929440\pi\)
0.975531 0.219860i \(-0.0705600\pi\)
\(332\) 6.00000i 0.329293i
\(333\) 9.00000i 0.493197i
\(334\) −11.0000 −0.601893
\(335\) 12.0000 0.655630
\(336\) 1.00000i 0.0545545i
\(337\) 17.0000 0.926049 0.463025 0.886345i \(-0.346764\pi\)
0.463025 + 0.886345i \(0.346764\pi\)
\(338\) 12.0000 5.00000i 0.652714 0.271964i
\(339\) 2.00000 0.108625
\(340\) 1.00000i 0.0542326i
\(341\) 4.00000 0.216612
\(342\) −1.00000 −0.0540738
\(343\) 1.00000i 0.0539949i
\(344\) 7.00000i 0.377415i
\(345\) 3.00000i 0.161515i
\(346\) 14.0000i 0.752645i
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 9.00000 0.482451
\(349\) 4.00000i 0.214115i −0.994253 0.107058i \(-0.965857\pi\)
0.994253 0.107058i \(-0.0341429\pi\)
\(350\) −4.00000 −0.213809
\(351\) −3.00000 2.00000i −0.160128 0.106752i
\(352\) 1.00000 0.0533002
\(353\) 16.0000i 0.851594i −0.904819 0.425797i \(-0.859994\pi\)
0.904819 0.425797i \(-0.140006\pi\)
\(354\) 6.00000 0.318896
\(355\) −6.00000 −0.318447
\(356\) 12.0000i 0.635999i
\(357\) 1.00000i 0.0529256i
\(358\) 18.0000i 0.951330i
\(359\) 30.0000i 1.58334i 0.610949 + 0.791670i \(0.290788\pi\)
−0.610949 + 0.791670i \(0.709212\pi\)
\(360\) −1.00000 −0.0527046
\(361\) 18.0000 0.947368
\(362\) 2.00000i 0.105118i
\(363\) −10.0000 −0.524864
\(364\) −2.00000 + 3.00000i −0.104828 + 0.157243i
\(365\) −11.0000 −0.575766
\(366\) 11.0000i 0.574979i
\(367\) −8.00000 −0.417597 −0.208798 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) 3.00000 0.156386
\(369\) 8.00000i 0.416463i
\(370\) 9.00000i 0.467888i
\(371\) 10.0000i 0.519174i
\(372\) 4.00000i 0.207390i
\(373\) −14.0000 −0.724893 −0.362446 0.932005i \(-0.618058\pi\)
−0.362446 + 0.932005i \(0.618058\pi\)
\(374\) 1.00000 0.0517088
\(375\) 9.00000i 0.464758i
\(376\) −8.00000 −0.412568
\(377\) 27.0000 + 18.0000i 1.39057 + 0.927047i
\(378\) 1.00000 0.0514344
\(379\) 16.0000i 0.821865i 0.911666 + 0.410932i \(0.134797\pi\)
−0.911666 + 0.410932i \(0.865203\pi\)
\(380\) −1.00000 −0.0512989
\(381\) −16.0000 −0.819705
\(382\) 11.0000i 0.562809i
\(383\) 35.0000i 1.78842i 0.447651 + 0.894208i \(0.352261\pi\)
−0.447651 + 0.894208i \(0.647739\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 1.00000i 0.0509647i
\(386\) −12.0000 −0.610784
\(387\) 7.00000 0.355830
\(388\) 2.00000i 0.101535i
\(389\) 2.00000 0.101404 0.0507020 0.998714i \(-0.483854\pi\)
0.0507020 + 0.998714i \(0.483854\pi\)
\(390\) −3.00000 2.00000i −0.151911 0.101274i
\(391\) 3.00000 0.151717
\(392\) 1.00000i 0.0505076i
\(393\) 3.00000 0.151330
\(394\) −2.00000 −0.100759
\(395\) 12.0000i 0.603786i
\(396\) 1.00000i 0.0502519i
\(397\) 4.00000i 0.200754i 0.994949 + 0.100377i \(0.0320049\pi\)
−0.994949 + 0.100377i \(0.967995\pi\)
\(398\) 5.00000i 0.250627i
\(399\) 1.00000 0.0500626
\(400\) 4.00000 0.200000
\(401\) 14.0000i 0.699127i 0.936913 + 0.349563i \(0.113670\pi\)
−0.936913 + 0.349563i \(0.886330\pi\)
\(402\) 12.0000 0.598506
\(403\) 8.00000 12.0000i 0.398508 0.597763i
\(404\) 2.00000 0.0995037
\(405\) 1.00000i 0.0496904i
\(406\) −9.00000 −0.446663
\(407\) 9.00000 0.446113
\(408\) 1.00000i 0.0495074i
\(409\) 27.0000i 1.33506i 0.744581 + 0.667532i \(0.232649\pi\)
−0.744581 + 0.667532i \(0.767351\pi\)
\(410\) 8.00000i 0.395092i
\(411\) 15.0000i 0.739895i
\(412\) 5.00000 0.246332
\(413\) −6.00000 −0.295241
\(414\) 3.00000i 0.147442i
\(415\) −6.00000 −0.294528
\(416\) 2.00000 3.00000i 0.0980581 0.147087i
\(417\) 12.0000 0.587643
\(418\) 1.00000i 0.0489116i
\(419\) 23.0000 1.12362 0.561812 0.827265i \(-0.310105\pi\)
0.561812 + 0.827265i \(0.310105\pi\)
\(420\) 1.00000 0.0487950
\(421\) 22.0000i 1.07221i 0.844150 + 0.536107i \(0.180106\pi\)
−0.844150 + 0.536107i \(0.819894\pi\)
\(422\) 5.00000i 0.243396i
\(423\) 8.00000i 0.388973i
\(424\) 10.0000i 0.485643i
\(425\) 4.00000 0.194029
\(426\) −6.00000 −0.290701
\(427\) 11.0000i 0.532327i
\(428\) 2.00000 0.0966736
\(429\) 2.00000 3.00000i 0.0965609 0.144841i
\(430\) 7.00000 0.337570
\(431\) 18.0000i 0.867029i −0.901146 0.433515i \(-0.857273\pi\)
0.901146 0.433515i \(-0.142727\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 4.00000 0.192228 0.0961139 0.995370i \(-0.469359\pi\)
0.0961139 + 0.995370i \(0.469359\pi\)
\(434\) 4.00000i 0.192006i
\(435\) 9.00000i 0.431517i
\(436\) 7.00000i 0.335239i
\(437\) 3.00000i 0.143509i
\(438\) −11.0000 −0.525600
\(439\) −33.0000 −1.57500 −0.787502 0.616312i \(-0.788626\pi\)
−0.787502 + 0.616312i \(0.788626\pi\)
\(440\) 1.00000i 0.0476731i
\(441\) −1.00000 −0.0476190
\(442\) 2.00000 3.00000i 0.0951303 0.142695i
\(443\) −6.00000 −0.285069 −0.142534 0.989790i \(-0.545525\pi\)
−0.142534 + 0.989790i \(0.545525\pi\)
\(444\) 9.00000i 0.427121i
\(445\) −12.0000 −0.568855
\(446\) −8.00000 −0.378811
\(447\) 6.00000i 0.283790i
\(448\) 1.00000i 0.0472456i
\(449\) 15.0000i 0.707894i −0.935266 0.353947i \(-0.884839\pi\)
0.935266 0.353947i \(-0.115161\pi\)
\(450\) 4.00000i 0.188562i
\(451\) −8.00000 −0.376705
\(452\) 2.00000 0.0940721
\(453\) 1.00000i 0.0469841i
\(454\) −12.0000 −0.563188
\(455\) 3.00000 + 2.00000i 0.140642 + 0.0937614i
\(456\) −1.00000 −0.0468293
\(457\) 4.00000i 0.187112i 0.995614 + 0.0935561i \(0.0298234\pi\)
−0.995614 + 0.0935561i \(0.970177\pi\)
\(458\) 2.00000 0.0934539
\(459\) −1.00000 −0.0466760
\(460\) 3.00000i 0.139876i
\(461\) 3.00000i 0.139724i 0.997557 + 0.0698620i \(0.0222559\pi\)
−0.997557 + 0.0698620i \(0.977744\pi\)
\(462\) 1.00000i 0.0465242i
\(463\) 29.0000i 1.34774i 0.738848 + 0.673872i \(0.235370\pi\)
−0.738848 + 0.673872i \(0.764630\pi\)
\(464\) 9.00000 0.417815
\(465\) −4.00000 −0.185496
\(466\) 18.0000i 0.833834i
\(467\) −37.0000 −1.71216 −0.856078 0.516847i \(-0.827106\pi\)
−0.856078 + 0.516847i \(0.827106\pi\)
\(468\) −3.00000 2.00000i −0.138675 0.0924500i
\(469\) −12.0000 −0.554109
\(470\) 8.00000i 0.369012i
\(471\) 21.0000 0.967629
\(472\) 6.00000 0.276172
\(473\) 7.00000i 0.321860i
\(474\) 12.0000i 0.551178i
\(475\) 4.00000i 0.183533i
\(476\) 1.00000i 0.0458349i
\(477\) −10.0000 −0.457869
\(478\) −8.00000 −0.365911
\(479\) 39.0000i 1.78196i 0.454047 + 0.890978i \(0.349980\pi\)
−0.454047 + 0.890978i \(0.650020\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 18.0000 27.0000i 0.820729 1.23109i
\(482\) 10.0000 0.455488
\(483\) 3.00000i 0.136505i
\(484\) −10.0000 −0.454545
\(485\) 2.00000 0.0908153
\(486\) 1.00000i 0.0453609i
\(487\) 32.0000i 1.45006i 0.688718 + 0.725029i \(0.258174\pi\)
−0.688718 + 0.725029i \(0.741826\pi\)
\(488\) 11.0000i 0.497947i
\(489\) 20.0000i 0.904431i
\(490\) −1.00000 −0.0451754
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 8.00000i 0.360668i
\(493\) 9.00000 0.405340
\(494\) −3.00000 2.00000i −0.134976 0.0899843i
\(495\) −1.00000 −0.0449467
\(496\) 4.00000i 0.179605i
\(497\) 6.00000 0.269137
\(498\) −6.00000 −0.268866
\(499\) 10.0000i 0.447661i −0.974628 0.223831i \(-0.928144\pi\)
0.974628 0.223831i \(-0.0718563\pi\)
\(500\) 9.00000i 0.402492i
\(501\) 11.0000i 0.491444i
\(502\) 11.0000i 0.490954i
\(503\) −38.0000 −1.69434 −0.847168 0.531325i \(-0.821694\pi\)
−0.847168 + 0.531325i \(0.821694\pi\)
\(504\) 1.00000 0.0445435
\(505\) 2.00000i 0.0889988i
\(506\) 3.00000 0.133366
\(507\) −5.00000 12.0000i −0.222058 0.532939i
\(508\) −16.0000 −0.709885
\(509\) 37.0000i 1.64000i −0.572366 0.819998i \(-0.693974\pi\)
0.572366 0.819998i \(-0.306026\pi\)
\(510\) −1.00000 −0.0442807
\(511\) 11.0000 0.486611
\(512\) 1.00000i 0.0441942i
\(513\) 1.00000i 0.0441511i
\(514\) 14.0000i 0.617514i
\(515\) 5.00000i 0.220326i
\(516\) 7.00000 0.308158
\(517\) −8.00000 −0.351840
\(518\) 9.00000i 0.395437i
\(519\) −14.0000 −0.614532
\(520\) −3.00000 2.00000i −0.131559 0.0877058i
\(521\) −31.0000 −1.35813 −0.679067 0.734076i \(-0.737616\pi\)
−0.679067 + 0.734076i \(0.737616\pi\)
\(522\) 9.00000i 0.393919i
\(523\) −36.0000 −1.57417 −0.787085 0.616844i \(-0.788411\pi\)
−0.787085 + 0.616844i \(0.788411\pi\)
\(524\) 3.00000 0.131056
\(525\) 4.00000i 0.174574i
\(526\) 16.0000i 0.697633i
\(527\) 4.00000i 0.174243i
\(528\) 1.00000i 0.0435194i
\(529\) −14.0000 −0.608696
\(530\) −10.0000 −0.434372
\(531\) 6.00000i 0.260378i
\(532\) 1.00000 0.0433555
\(533\) −16.0000 + 24.0000i −0.693037 + 1.03956i
\(534\) −12.0000 −0.519291
\(535\) 2.00000i 0.0864675i
\(536\) 12.0000 0.518321
\(537\) 18.0000 0.776757
\(538\) 20.0000i 0.862261i
\(539\) 1.00000i 0.0430730i
\(540\) 1.00000i 0.0430331i
\(541\) 41.0000i 1.76273i 0.472438 + 0.881364i \(0.343374\pi\)
−0.472438 + 0.881364i \(0.656626\pi\)
\(542\) −4.00000 −0.171815
\(543\) 2.00000 0.0858282
\(544\) 1.00000i 0.0428746i
\(545\) −7.00000 −0.299847
\(546\) 3.00000 + 2.00000i 0.128388 + 0.0855921i
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 15.0000i 0.640768i
\(549\) 11.0000 0.469469
\(550\) 4.00000 0.170561
\(551\) 9.00000i 0.383413i
\(552\) 3.00000i 0.127688i
\(553\) 12.0000i 0.510292i
\(554\) 16.0000i 0.679775i
\(555\) −9.00000 −0.382029
\(556\) 12.0000 0.508913
\(557\) 2.00000i 0.0847427i −0.999102 0.0423714i \(-0.986509\pi\)
0.999102 0.0423714i \(-0.0134913\pi\)
\(558\) −4.00000 −0.169334
\(559\) 21.0000 + 14.0000i 0.888205 + 0.592137i
\(560\) 1.00000 0.0422577
\(561\) 1.00000i 0.0422200i
\(562\) −22.0000 −0.928014
\(563\) 11.0000 0.463595 0.231797 0.972764i \(-0.425539\pi\)
0.231797 + 0.972764i \(0.425539\pi\)
\(564\) 8.00000i 0.336861i
\(565\) 2.00000i 0.0841406i
\(566\) 14.0000i 0.588464i
\(567\) 1.00000i 0.0419961i
\(568\) −6.00000 −0.251754
\(569\) −30.0000 −1.25767 −0.628833 0.777541i \(-0.716467\pi\)
−0.628833 + 0.777541i \(0.716467\pi\)
\(570\) 1.00000i 0.0418854i
\(571\) 32.0000 1.33916 0.669579 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) 2.00000 3.00000i 0.0836242 0.125436i
\(573\) 11.0000 0.459532
\(574\) 8.00000i 0.333914i
\(575\) 12.0000 0.500435
\(576\) −1.00000 −0.0416667
\(577\) 18.0000i 0.749350i −0.927156 0.374675i \(-0.877754\pi\)
0.927156 0.374675i \(-0.122246\pi\)
\(578\) 16.0000i 0.665512i
\(579\) 12.0000i 0.498703i
\(580\) 9.00000i 0.373705i
\(581\) 6.00000 0.248922
\(582\) 2.00000 0.0829027
\(583\) 10.0000i 0.414158i
\(584\) −11.0000 −0.455183
\(585\) −2.00000 + 3.00000i −0.0826898 + 0.124035i
\(586\) −26.0000 −1.07405
\(587\) 16.0000i 0.660391i −0.943913 0.330195i \(-0.892885\pi\)
0.943913 0.330195i \(-0.107115\pi\)
\(588\) −1.00000 −0.0412393
\(589\) −4.00000 −0.164817
\(590\) 6.00000i 0.247016i
\(591\) 2.00000i 0.0822690i
\(592\) 9.00000i 0.369898i
\(593\) 28.0000i 1.14982i −0.818216 0.574911i \(-0.805037\pi\)
0.818216 0.574911i \(-0.194963\pi\)
\(594\) −1.00000 −0.0410305
\(595\) 1.00000 0.0409960
\(596\) 6.00000i 0.245770i
\(597\) −5.00000 −0.204636
\(598\) 6.00000 9.00000i 0.245358 0.368037i
\(599\) 39.0000 1.59350 0.796748 0.604311i \(-0.206552\pi\)
0.796748 + 0.604311i \(0.206552\pi\)
\(600\) 4.00000i 0.163299i
\(601\) −16.0000 −0.652654 −0.326327 0.945257i \(-0.605811\pi\)
−0.326327 + 0.945257i \(0.605811\pi\)
\(602\) −7.00000 −0.285299
\(603\) 12.0000i 0.488678i
\(604\) 1.00000i 0.0406894i
\(605\) 10.0000i 0.406558i
\(606\) 2.00000i 0.0812444i
\(607\) 1.00000 0.0405887 0.0202944 0.999794i \(-0.493540\pi\)
0.0202944 + 0.999794i \(0.493540\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 9.00000i 0.364698i
\(610\) 11.0000 0.445377
\(611\) −16.0000 + 24.0000i −0.647291 + 0.970936i
\(612\) −1.00000 −0.0404226
\(613\) 17.0000i 0.686624i −0.939222 0.343312i \(-0.888451\pi\)
0.939222 0.343312i \(-0.111549\pi\)
\(614\) −8.00000 −0.322854
\(615\) 8.00000 0.322591
\(616\) 1.00000i 0.0402911i
\(617\) 19.0000i 0.764911i −0.923974 0.382456i \(-0.875078\pi\)
0.923974 0.382456i \(-0.124922\pi\)
\(618\) 5.00000i 0.201129i
\(619\) 21.0000i 0.844061i 0.906582 + 0.422031i \(0.138683\pi\)
−0.906582 + 0.422031i \(0.861317\pi\)
\(620\) −4.00000 −0.160644
\(621\) −3.00000 −0.120386
\(622\) 8.00000i 0.320771i
\(623\) 12.0000 0.480770
\(624\) −3.00000 2.00000i −0.120096 0.0800641i
\(625\) 11.0000 0.440000
\(626\) 14.0000i 0.559553i
\(627\) −1.00000 −0.0399362
\(628\) 21.0000 0.837991
\(629\) 9.00000i 0.358854i
\(630\) 1.00000i 0.0398410i
\(631\) 29.0000i 1.15447i 0.816577 + 0.577236i \(0.195869\pi\)
−0.816577 + 0.577236i \(0.804131\pi\)
\(632\) 12.0000i 0.477334i
\(633\) 5.00000 0.198732
\(634\) −12.0000 −0.476581
\(635\) 16.0000i 0.634941i
\(636\) −10.0000 −0.396526
\(637\) −3.00000 2.00000i −0.118864 0.0792429i
\(638\) 9.00000 0.356313
\(639\) 6.00000i 0.237356i
\(640\) −1.00000 −0.0395285
\(641\) −44.0000 −1.73790 −0.868948 0.494904i \(-0.835203\pi\)
−0.868948 + 0.494904i \(0.835203\pi\)
\(642\) 2.00000i 0.0789337i
\(643\) 19.0000i 0.749287i −0.927169 0.374643i \(-0.877765\pi\)
0.927169 0.374643i \(-0.122235\pi\)
\(644\) 3.00000i 0.118217i
\(645\) 7.00000i 0.275625i
\(646\) −1.00000 −0.0393445
\(647\) 42.0000 1.65119 0.825595 0.564263i \(-0.190840\pi\)
0.825595 + 0.564263i \(0.190840\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 6.00000 0.235521
\(650\) 8.00000 12.0000i 0.313786 0.470679i
\(651\) 4.00000 0.156772
\(652\) 20.0000i 0.783260i
\(653\) −13.0000 −0.508729 −0.254365 0.967108i \(-0.581866\pi\)
−0.254365 + 0.967108i \(0.581866\pi\)
\(654\) −7.00000 −0.273722
\(655\) 3.00000i 0.117220i
\(656\) 8.00000i 0.312348i
\(657\) 11.0000i 0.429151i
\(658\) 8.00000i 0.311872i
\(659\) −30.0000 −1.16863 −0.584317 0.811525i \(-0.698638\pi\)
−0.584317 + 0.811525i \(0.698638\pi\)
\(660\) −1.00000 −0.0389249
\(661\) 26.0000i 1.01128i 0.862744 + 0.505641i \(0.168744\pi\)
−0.862744 + 0.505641i \(0.831256\pi\)
\(662\) −8.00000 −0.310929
\(663\) −3.00000 2.00000i −0.116510 0.0776736i
\(664\) −6.00000 −0.232845
\(665\) 1.00000i 0.0387783i
\(666\) −9.00000 −0.348743
\(667\) 27.0000 1.04544
\(668\) 11.0000i 0.425603i
\(669\) 8.00000i 0.309298i
\(670\) 12.0000i 0.463600i
\(671\) 11.0000i 0.424650i
\(672\) 1.00000 0.0385758
\(673\) 29.0000 1.11787 0.558934 0.829212i \(-0.311211\pi\)
0.558934 + 0.829212i \(0.311211\pi\)
\(674\) 17.0000i 0.654816i
\(675\) −4.00000 −0.153960
\(676\) −5.00000 12.0000i −0.192308 0.461538i
\(677\) 32.0000 1.22986 0.614930 0.788582i \(-0.289184\pi\)
0.614930 + 0.788582i \(0.289184\pi\)
\(678\) 2.00000i 0.0768095i
\(679\) −2.00000 −0.0767530
\(680\) −1.00000 −0.0383482
\(681\) 12.0000i 0.459841i
\(682\) 4.00000i 0.153168i
\(683\) 19.0000i 0.727015i 0.931591 + 0.363507i \(0.118421\pi\)
−0.931591 + 0.363507i \(0.881579\pi\)
\(684\) 1.00000i 0.0382360i
\(685\) 15.0000 0.573121
\(686\) 1.00000 0.0381802
\(687\) 2.00000i 0.0763048i
\(688\) 7.00000 0.266872
\(689\) −30.0000 20.0000i −1.14291 0.761939i
\(690\) −3.00000 −0.114208
\(691\) 40.0000i 1.52167i −0.648944 0.760836i \(-0.724789\pi\)
0.648944 0.760836i \(-0.275211\pi\)
\(692\) −14.0000 −0.532200
\(693\) 1.00000 0.0379869
\(694\) 0 0
\(695\) 12.0000i 0.455186i
\(696\) 9.00000i 0.341144i
\(697\) 8.00000i 0.303022i
\(698\) −4.00000 −0.151402
\(699\) 18.0000 0.680823
\(700\) 4.00000i 0.151186i
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) −2.00000 + 3.00000i −0.0754851 + 0.113228i
\(703\) −9.00000 −0.339441
\(704\) 1.00000i 0.0376889i
\(705\) 8.00000 0.301297
\(706\) −16.0000 −0.602168
\(707\) 2.00000i 0.0752177i
\(708\) 6.00000i 0.225494i
\(709\) 14.0000i 0.525781i −0.964826 0.262891i \(-0.915324\pi\)
0.964826 0.262891i \(-0.0846758\pi\)
\(710\) 6.00000i 0.225176i
\(711\) −12.0000 −0.450035
\(712\) −12.0000 −0.449719
\(713\) 12.0000i 0.449404i
\(714\) 1.00000 0.0374241
\(715\) −3.00000 2.00000i −0.112194 0.0747958i
\(716\) 18.0000 0.672692
\(717\) 8.00000i 0.298765i
\(718\) 30.0000 1.11959
\(719\) −8.00000 −0.298350 −0.149175 0.988811i \(-0.547662\pi\)
−0.149175 + 0.988811i \(0.547662\pi\)
\(720\) 1.00000i 0.0372678i
\(721\) 5.00000i 0.186210i
\(722\) 18.0000i 0.669891i
\(723\) 10.0000i 0.371904i
\(724\) 2.00000 0.0743294
\(725\) 36.0000 1.33701
\(726\) 10.0000i 0.371135i
\(727\) 23.0000 0.853023 0.426511 0.904482i \(-0.359742\pi\)
0.426511 + 0.904482i \(0.359742\pi\)
\(728\) 3.00000 + 2.00000i 0.111187 + 0.0741249i
\(729\) 1.00000 0.0370370
\(730\) 11.0000i 0.407128i
\(731\) 7.00000 0.258904
\(732\) 11.0000 0.406572
\(733\) 40.0000i 1.47743i −0.674016 0.738717i \(-0.735432\pi\)
0.674016 0.738717i \(-0.264568\pi\)
\(734\) 8.00000i 0.295285i
\(735\) 1.00000i 0.0368856i
\(736\) 3.00000i 0.110581i
\(737\) 12.0000 0.442026
\(738\) 8.00000 0.294484
\(739\) 8.00000i 0.294285i 0.989115 + 0.147142i \(0.0470076\pi\)
−0.989115 + 0.147142i \(0.952992\pi\)
\(740\) −9.00000 −0.330847
\(741\) −2.00000 + 3.00000i −0.0734718 + 0.110208i
\(742\) 10.0000 0.367112
\(743\) 36.0000i 1.32071i −0.750953 0.660356i \(-0.770405\pi\)
0.750953 0.660356i \(-0.229595\pi\)
\(744\) −4.00000 −0.146647
\(745\) −6.00000 −0.219823
\(746\) 14.0000i 0.512576i
\(747\) 6.00000i 0.219529i
\(748\) 1.00000i 0.0365636i
\(749\) 2.00000i 0.0730784i
\(750\) −9.00000 −0.328634
\(751\) 20.0000 0.729810 0.364905 0.931045i \(-0.381101\pi\)
0.364905 + 0.931045i \(0.381101\pi\)
\(752\) 8.00000i 0.291730i
\(753\) −11.0000 −0.400862
\(754\) 18.0000 27.0000i 0.655521 0.983282i
\(755\) −1.00000 −0.0363937
\(756\) 1.00000i 0.0363696i
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) 16.0000 0.581146
\(759\) 3.00000i 0.108893i
\(760\) 1.00000i 0.0362738i
\(761\) 42.0000i 1.52250i −0.648459 0.761249i \(-0.724586\pi\)
0.648459 0.761249i \(-0.275414\pi\)
\(762\) 16.0000i 0.579619i
\(763\) 7.00000 0.253417
\(764\) 11.0000 0.397966
\(765\) 1.00000i 0.0361551i
\(766\) 35.0000 1.26460
\(767\) 12.0000 18.0000i 0.433295 0.649942i
\(768\) −1.00000 −0.0360844
\(769\) 31.0000i 1.11789i 0.829205 + 0.558944i \(0.188793\pi\)
−0.829205 + 0.558944i \(0.811207\pi\)
\(770\) 1.00000 0.0360375
\(771\) −14.0000 −0.504198
\(772\) 12.0000i 0.431889i
\(773\) 19.0000i 0.683383i 0.939812 + 0.341691i \(0.111000\pi\)
−0.939812 + 0.341691i \(0.889000\pi\)
\(774\) 7.00000i 0.251610i
\(775\) 16.0000i 0.574737i
\(776\) 2.00000 0.0717958
\(777\) 9.00000 0.322873
\(778\) 2.00000i 0.0717035i
\(779\) 8.00000 0.286630
\(780\) −2.00000 + 3.00000i −0.0716115 + 0.107417i
\(781\) −6.00000 −0.214697
\(782\) 3.00000i 0.107280i
\(783\) −9.00000 −0.321634
\(784\) −1.00000 −0.0357143
\(785\) 21.0000i 0.749522i
\(786\) 3.00000i 0.107006i
\(787\) 53.0000i 1.88925i 0.328158 + 0.944623i \(0.393572\pi\)
−0.328158 + 0.944623i \(0.606428\pi\)
\(788\) 2.00000i 0.0712470i
\(789\) −16.0000 −0.569615
\(790\) −12.0000 −0.426941
\(791\)