Properties

Label 390.2.e.b.79.2
Level $390$
Weight $2$
Character 390.79
Analytic conductor $3.114$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.11416567883\)
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 79.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 390.79
Dual form 390.2.e.b.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} -1.00000 q^{6} +4.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} -1.00000 q^{6} +4.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(1.00000 + 2.00000i) q^{10} +2.00000 q^{11} -1.00000i q^{12} -1.00000i q^{13} -4.00000 q^{14} +(1.00000 + 2.00000i) q^{15} +1.00000 q^{16} +4.00000i q^{17} -1.00000i q^{18} -2.00000 q^{19} +(-2.00000 + 1.00000i) q^{20} -4.00000 q^{21} +2.00000i q^{22} +6.00000i q^{23} +1.00000 q^{24} +(3.00000 - 4.00000i) q^{25} +1.00000 q^{26} -1.00000i q^{27} -4.00000i q^{28} +2.00000 q^{29} +(-2.00000 + 1.00000i) q^{30} -4.00000 q^{31} +1.00000i q^{32} +2.00000i q^{33} -4.00000 q^{34} +(4.00000 + 8.00000i) q^{35} +1.00000 q^{36} -6.00000i q^{37} -2.00000i q^{38} +1.00000 q^{39} +(-1.00000 - 2.00000i) q^{40} -6.00000 q^{41} -4.00000i q^{42} -8.00000i q^{43} -2.00000 q^{44} +(-2.00000 + 1.00000i) q^{45} -6.00000 q^{46} +8.00000i q^{47} +1.00000i q^{48} -9.00000 q^{49} +(4.00000 + 3.00000i) q^{50} -4.00000 q^{51} +1.00000i q^{52} -10.0000i q^{53} +1.00000 q^{54} +(4.00000 - 2.00000i) q^{55} +4.00000 q^{56} -2.00000i q^{57} +2.00000i q^{58} +14.0000 q^{59} +(-1.00000 - 2.00000i) q^{60} +10.0000 q^{61} -4.00000i q^{62} -4.00000i q^{63} -1.00000 q^{64} +(-1.00000 - 2.00000i) q^{65} -2.00000 q^{66} +4.00000i q^{67} -4.00000i q^{68} -6.00000 q^{69} +(-8.00000 + 4.00000i) q^{70} +8.00000 q^{71} +1.00000i q^{72} -10.0000i q^{73} +6.00000 q^{74} +(4.00000 + 3.00000i) q^{75} +2.00000 q^{76} +8.00000i q^{77} +1.00000i q^{78} +8.00000 q^{79} +(2.00000 - 1.00000i) q^{80} +1.00000 q^{81} -6.00000i q^{82} -12.0000i q^{83} +4.00000 q^{84} +(4.00000 + 8.00000i) q^{85} +8.00000 q^{86} +2.00000i q^{87} -2.00000i q^{88} +18.0000 q^{89} +(-1.00000 - 2.00000i) q^{90} +4.00000 q^{91} -6.00000i q^{92} -4.00000i q^{93} -8.00000 q^{94} +(-4.00000 + 2.00000i) q^{95} -1.00000 q^{96} +6.00000i q^{97} -9.00000i q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{4} + 4q^{5} - 2q^{6} - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{4} + 4q^{5} - 2q^{6} - 2q^{9} + 2q^{10} + 4q^{11} - 8q^{14} + 2q^{15} + 2q^{16} - 4q^{19} - 4q^{20} - 8q^{21} + 2q^{24} + 6q^{25} + 2q^{26} + 4q^{29} - 4q^{30} - 8q^{31} - 8q^{34} + 8q^{35} + 2q^{36} + 2q^{39} - 2q^{40} - 12q^{41} - 4q^{44} - 4q^{45} - 12q^{46} - 18q^{49} + 8q^{50} - 8q^{51} + 2q^{54} + 8q^{55} + 8q^{56} + 28q^{59} - 2q^{60} + 20q^{61} - 2q^{64} - 2q^{65} - 4q^{66} - 12q^{69} - 16q^{70} + 16q^{71} + 12q^{74} + 8q^{75} + 4q^{76} + 16q^{79} + 4q^{80} + 2q^{81} + 8q^{84} + 8q^{85} + 16q^{86} + 36q^{89} - 2q^{90} + 8q^{91} - 16q^{94} - 8q^{95} - 2q^{96} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) 2.00000 1.00000i 0.894427 0.447214i
\(6\) −1.00000 −0.408248
\(7\) 4.00000i 1.51186i 0.654654 + 0.755929i \(0.272814\pi\)
−0.654654 + 0.755929i \(0.727186\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) 1.00000 + 2.00000i 0.316228 + 0.632456i
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 1.00000i 0.277350i
\(14\) −4.00000 −1.06904
\(15\) 1.00000 + 2.00000i 0.258199 + 0.516398i
\(16\) 1.00000 0.250000
\(17\) 4.00000i 0.970143i 0.874475 + 0.485071i \(0.161206\pi\)
−0.874475 + 0.485071i \(0.838794\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) −2.00000 + 1.00000i −0.447214 + 0.223607i
\(21\) −4.00000 −0.872872
\(22\) 2.00000i 0.426401i
\(23\) 6.00000i 1.25109i 0.780189 + 0.625543i \(0.215123\pi\)
−0.780189 + 0.625543i \(0.784877\pi\)
\(24\) 1.00000 0.204124
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) 1.00000 0.196116
\(27\) 1.00000i 0.192450i
\(28\) 4.00000i 0.755929i
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) −2.00000 + 1.00000i −0.365148 + 0.182574i
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.00000i 0.348155i
\(34\) −4.00000 −0.685994
\(35\) 4.00000 + 8.00000i 0.676123 + 1.35225i
\(36\) 1.00000 0.166667
\(37\) 6.00000i 0.986394i −0.869918 0.493197i \(-0.835828\pi\)
0.869918 0.493197i \(-0.164172\pi\)
\(38\) 2.00000i 0.324443i
\(39\) 1.00000 0.160128
\(40\) −1.00000 2.00000i −0.158114 0.316228i
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 4.00000i 0.617213i
\(43\) 8.00000i 1.21999i −0.792406 0.609994i \(-0.791172\pi\)
0.792406 0.609994i \(-0.208828\pi\)
\(44\) −2.00000 −0.301511
\(45\) −2.00000 + 1.00000i −0.298142 + 0.149071i
\(46\) −6.00000 −0.884652
\(47\) 8.00000i 1.16692i 0.812142 + 0.583460i \(0.198301\pi\)
−0.812142 + 0.583460i \(0.801699\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −9.00000 −1.28571
\(50\) 4.00000 + 3.00000i 0.565685 + 0.424264i
\(51\) −4.00000 −0.560112
\(52\) 1.00000i 0.138675i
\(53\) 10.0000i 1.37361i −0.726844 0.686803i \(-0.759014\pi\)
0.726844 0.686803i \(-0.240986\pi\)
\(54\) 1.00000 0.136083
\(55\) 4.00000 2.00000i 0.539360 0.269680i
\(56\) 4.00000 0.534522
\(57\) 2.00000i 0.264906i
\(58\) 2.00000i 0.262613i
\(59\) 14.0000 1.82264 0.911322 0.411693i \(-0.135063\pi\)
0.911322 + 0.411693i \(0.135063\pi\)
\(60\) −1.00000 2.00000i −0.129099 0.258199i
\(61\) 10.0000 1.28037 0.640184 0.768221i \(-0.278858\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) 4.00000i 0.508001i
\(63\) 4.00000i 0.503953i
\(64\) −1.00000 −0.125000
\(65\) −1.00000 2.00000i −0.124035 0.248069i
\(66\) −2.00000 −0.246183
\(67\) 4.00000i 0.488678i 0.969690 + 0.244339i \(0.0785709\pi\)
−0.969690 + 0.244339i \(0.921429\pi\)
\(68\) 4.00000i 0.485071i
\(69\) −6.00000 −0.722315
\(70\) −8.00000 + 4.00000i −0.956183 + 0.478091i
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 10.0000i 1.17041i −0.810885 0.585206i \(-0.801014\pi\)
0.810885 0.585206i \(-0.198986\pi\)
\(74\) 6.00000 0.697486
\(75\) 4.00000 + 3.00000i 0.461880 + 0.346410i
\(76\) 2.00000 0.229416
\(77\) 8.00000i 0.911685i
\(78\) 1.00000i 0.113228i
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 2.00000 1.00000i 0.223607 0.111803i
\(81\) 1.00000 0.111111
\(82\) 6.00000i 0.662589i
\(83\) 12.0000i 1.31717i −0.752506 0.658586i \(-0.771155\pi\)
0.752506 0.658586i \(-0.228845\pi\)
\(84\) 4.00000 0.436436
\(85\) 4.00000 + 8.00000i 0.433861 + 0.867722i
\(86\) 8.00000 0.862662
\(87\) 2.00000i 0.214423i
\(88\) 2.00000i 0.213201i
\(89\) 18.0000 1.90800 0.953998 0.299813i \(-0.0969242\pi\)
0.953998 + 0.299813i \(0.0969242\pi\)
\(90\) −1.00000 2.00000i −0.105409 0.210819i
\(91\) 4.00000 0.419314
\(92\) 6.00000i 0.625543i
\(93\) 4.00000i 0.414781i
\(94\) −8.00000 −0.825137
\(95\) −4.00000 + 2.00000i −0.410391 + 0.205196i
\(96\) −1.00000 −0.102062
\(97\) 6.00000i 0.609208i 0.952479 + 0.304604i \(0.0985241\pi\)
−0.952479 + 0.304604i \(0.901476\pi\)
\(98\) 9.00000i 0.909137i
\(99\) −2.00000 −0.201008
\(100\) −3.00000 + 4.00000i −0.300000 + 0.400000i
\(101\) −14.0000 −1.39305 −0.696526 0.717532i \(-0.745272\pi\)
−0.696526 + 0.717532i \(0.745272\pi\)
\(102\) 4.00000i 0.396059i
\(103\) 6.00000i 0.591198i −0.955312 0.295599i \(-0.904481\pi\)
0.955312 0.295599i \(-0.0955191\pi\)
\(104\) −1.00000 −0.0980581
\(105\) −8.00000 + 4.00000i −0.780720 + 0.390360i
\(106\) 10.0000 0.971286
\(107\) 8.00000i 0.773389i −0.922208 0.386695i \(-0.873617\pi\)
0.922208 0.386695i \(-0.126383\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) −12.0000 −1.14939 −0.574696 0.818367i \(-0.694880\pi\)
−0.574696 + 0.818367i \(0.694880\pi\)
\(110\) 2.00000 + 4.00000i 0.190693 + 0.381385i
\(111\) 6.00000 0.569495
\(112\) 4.00000i 0.377964i
\(113\) 12.0000i 1.12887i 0.825479 + 0.564433i \(0.190905\pi\)
−0.825479 + 0.564433i \(0.809095\pi\)
\(114\) 2.00000 0.187317
\(115\) 6.00000 + 12.0000i 0.559503 + 1.11901i
\(116\) −2.00000 −0.185695
\(117\) 1.00000i 0.0924500i
\(118\) 14.0000i 1.28880i
\(119\) −16.0000 −1.46672
\(120\) 2.00000 1.00000i 0.182574 0.0912871i
\(121\) −7.00000 −0.636364
\(122\) 10.0000i 0.905357i
\(123\) 6.00000i 0.541002i
\(124\) 4.00000 0.359211
\(125\) 2.00000 11.0000i 0.178885 0.983870i
\(126\) 4.00000 0.356348
\(127\) 18.0000i 1.59724i −0.601834 0.798621i \(-0.705563\pi\)
0.601834 0.798621i \(-0.294437\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 8.00000 0.704361
\(130\) 2.00000 1.00000i 0.175412 0.0877058i
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 2.00000i 0.174078i
\(133\) 8.00000i 0.693688i
\(134\) −4.00000 −0.345547
\(135\) −1.00000 2.00000i −0.0860663 0.172133i
\(136\) 4.00000 0.342997
\(137\) 2.00000i 0.170872i 0.996344 + 0.0854358i \(0.0272282\pi\)
−0.996344 + 0.0854358i \(0.972772\pi\)
\(138\) 6.00000i 0.510754i
\(139\) −16.0000 −1.35710 −0.678551 0.734553i \(-0.737392\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) −4.00000 8.00000i −0.338062 0.676123i
\(141\) −8.00000 −0.673722
\(142\) 8.00000i 0.671345i
\(143\) 2.00000i 0.167248i
\(144\) −1.00000 −0.0833333
\(145\) 4.00000 2.00000i 0.332182 0.166091i
\(146\) 10.0000 0.827606
\(147\) 9.00000i 0.742307i
\(148\) 6.00000i 0.493197i
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) −3.00000 + 4.00000i −0.244949 + 0.326599i
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 2.00000i 0.162221i
\(153\) 4.00000i 0.323381i
\(154\) −8.00000 −0.644658
\(155\) −8.00000 + 4.00000i −0.642575 + 0.321288i
\(156\) −1.00000 −0.0800641
\(157\) 10.0000i 0.798087i −0.916932 0.399043i \(-0.869342\pi\)
0.916932 0.399043i \(-0.130658\pi\)
\(158\) 8.00000i 0.636446i
\(159\) 10.0000 0.793052
\(160\) 1.00000 + 2.00000i 0.0790569 + 0.158114i
\(161\) −24.0000 −1.89146
\(162\) 1.00000i 0.0785674i
\(163\) 4.00000i 0.313304i 0.987654 + 0.156652i \(0.0500701\pi\)
−0.987654 + 0.156652i \(0.949930\pi\)
\(164\) 6.00000 0.468521
\(165\) 2.00000 + 4.00000i 0.155700 + 0.311400i
\(166\) 12.0000 0.931381
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 4.00000i 0.308607i
\(169\) −1.00000 −0.0769231
\(170\) −8.00000 + 4.00000i −0.613572 + 0.306786i
\(171\) 2.00000 0.152944
\(172\) 8.00000i 0.609994i
\(173\) 10.0000i 0.760286i −0.924928 0.380143i \(-0.875875\pi\)
0.924928 0.380143i \(-0.124125\pi\)
\(174\) −2.00000 −0.151620
\(175\) 16.0000 + 12.0000i 1.20949 + 0.907115i
\(176\) 2.00000 0.150756
\(177\) 14.0000i 1.05230i
\(178\) 18.0000i 1.34916i
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 2.00000 1.00000i 0.149071 0.0745356i
\(181\) 6.00000 0.445976 0.222988 0.974821i \(-0.428419\pi\)
0.222988 + 0.974821i \(0.428419\pi\)
\(182\) 4.00000i 0.296500i
\(183\) 10.0000i 0.739221i
\(184\) 6.00000 0.442326
\(185\) −6.00000 12.0000i −0.441129 0.882258i
\(186\) 4.00000 0.293294
\(187\) 8.00000i 0.585018i
\(188\) 8.00000i 0.583460i
\(189\) 4.00000 0.290957
\(190\) −2.00000 4.00000i −0.145095 0.290191i
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 6.00000i 0.431889i −0.976406 0.215945i \(-0.930717\pi\)
0.976406 0.215945i \(-0.0692831\pi\)
\(194\) −6.00000 −0.430775
\(195\) 2.00000 1.00000i 0.143223 0.0716115i
\(196\) 9.00000 0.642857
\(197\) 26.0000i 1.85242i 0.377004 + 0.926212i \(0.376954\pi\)
−0.377004 + 0.926212i \(0.623046\pi\)
\(198\) 2.00000i 0.142134i
\(199\) −24.0000 −1.70131 −0.850657 0.525720i \(-0.823796\pi\)
−0.850657 + 0.525720i \(0.823796\pi\)
\(200\) −4.00000 3.00000i −0.282843 0.212132i
\(201\) −4.00000 −0.282138
\(202\) 14.0000i 0.985037i
\(203\) 8.00000i 0.561490i
\(204\) 4.00000 0.280056
\(205\) −12.0000 + 6.00000i −0.838116 + 0.419058i
\(206\) 6.00000 0.418040
\(207\) 6.00000i 0.417029i
\(208\) 1.00000i 0.0693375i
\(209\) −4.00000 −0.276686
\(210\) −4.00000 8.00000i −0.276026 0.552052i
\(211\) −28.0000 −1.92760 −0.963800 0.266627i \(-0.914091\pi\)
−0.963800 + 0.266627i \(0.914091\pi\)
\(212\) 10.0000i 0.686803i
\(213\) 8.00000i 0.548151i
\(214\) 8.00000 0.546869
\(215\) −8.00000 16.0000i −0.545595 1.09119i
\(216\) −1.00000 −0.0680414
\(217\) 16.0000i 1.08615i
\(218\) 12.0000i 0.812743i
\(219\) 10.0000 0.675737
\(220\) −4.00000 + 2.00000i −0.269680 + 0.134840i
\(221\) 4.00000 0.269069
\(222\) 6.00000i 0.402694i
\(223\) 16.0000i 1.07144i 0.844396 + 0.535720i \(0.179960\pi\)
−0.844396 + 0.535720i \(0.820040\pi\)
\(224\) −4.00000 −0.267261
\(225\) −3.00000 + 4.00000i −0.200000 + 0.266667i
\(226\) −12.0000 −0.798228
\(227\) 12.0000i 0.796468i 0.917284 + 0.398234i \(0.130377\pi\)
−0.917284 + 0.398234i \(0.869623\pi\)
\(228\) 2.00000i 0.132453i
\(229\) 16.0000 1.05731 0.528655 0.848837i \(-0.322697\pi\)
0.528655 + 0.848837i \(0.322697\pi\)
\(230\) −12.0000 + 6.00000i −0.791257 + 0.395628i
\(231\) −8.00000 −0.526361
\(232\) 2.00000i 0.131306i
\(233\) 4.00000i 0.262049i 0.991379 + 0.131024i \(0.0418266\pi\)
−0.991379 + 0.131024i \(0.958173\pi\)
\(234\) −1.00000 −0.0653720
\(235\) 8.00000 + 16.0000i 0.521862 + 1.04372i
\(236\) −14.0000 −0.911322
\(237\) 8.00000i 0.519656i
\(238\) 16.0000i 1.03713i
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 1.00000 + 2.00000i 0.0645497 + 0.129099i
\(241\) −30.0000 −1.93247 −0.966235 0.257663i \(-0.917048\pi\)
−0.966235 + 0.257663i \(0.917048\pi\)
\(242\) 7.00000i 0.449977i
\(243\) 1.00000i 0.0641500i
\(244\) −10.0000 −0.640184
\(245\) −18.0000 + 9.00000i −1.14998 + 0.574989i
\(246\) 6.00000 0.382546
\(247\) 2.00000i 0.127257i
\(248\) 4.00000i 0.254000i
\(249\) 12.0000 0.760469
\(250\) 11.0000 + 2.00000i 0.695701 + 0.126491i
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 4.00000i 0.251976i
\(253\) 12.0000i 0.754434i
\(254\) 18.0000 1.12942
\(255\) −8.00000 + 4.00000i −0.500979 + 0.250490i
\(256\) 1.00000 0.0625000
\(257\) 12.0000i 0.748539i −0.927320 0.374270i \(-0.877893\pi\)
0.927320 0.374270i \(-0.122107\pi\)
\(258\) 8.00000i 0.498058i
\(259\) 24.0000 1.49129
\(260\) 1.00000 + 2.00000i 0.0620174 + 0.124035i
\(261\) −2.00000 −0.123797
\(262\) 0 0
\(263\) 10.0000i 0.616626i 0.951285 + 0.308313i \(0.0997645\pi\)
−0.951285 + 0.308313i \(0.900236\pi\)
\(264\) 2.00000 0.123091
\(265\) −10.0000 20.0000i −0.614295 1.22859i
\(266\) 8.00000 0.490511
\(267\) 18.0000i 1.10158i
\(268\) 4.00000i 0.244339i
\(269\) 14.0000 0.853595 0.426798 0.904347i \(-0.359642\pi\)
0.426798 + 0.904347i \(0.359642\pi\)
\(270\) 2.00000 1.00000i 0.121716 0.0608581i
\(271\) 16.0000 0.971931 0.485965 0.873978i \(-0.338468\pi\)
0.485965 + 0.873978i \(0.338468\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 4.00000i 0.242091i
\(274\) −2.00000 −0.120824
\(275\) 6.00000 8.00000i 0.361814 0.482418i
\(276\) 6.00000 0.361158
\(277\) 2.00000i 0.120168i 0.998193 + 0.0600842i \(0.0191369\pi\)
−0.998193 + 0.0600842i \(0.980863\pi\)
\(278\) 16.0000i 0.959616i
\(279\) 4.00000 0.239474
\(280\) 8.00000 4.00000i 0.478091 0.239046i
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 8.00000i 0.476393i
\(283\) 4.00000i 0.237775i 0.992908 + 0.118888i \(0.0379328\pi\)
−0.992908 + 0.118888i \(0.962067\pi\)
\(284\) −8.00000 −0.474713
\(285\) −2.00000 4.00000i −0.118470 0.236940i
\(286\) 2.00000 0.118262
\(287\) 24.0000i 1.41668i
\(288\) 1.00000i 0.0589256i
\(289\) 1.00000 0.0588235
\(290\) 2.00000 + 4.00000i 0.117444 + 0.234888i
\(291\) −6.00000 −0.351726
\(292\) 10.0000i 0.585206i
\(293\) 14.0000i 0.817889i 0.912559 + 0.408944i \(0.134103\pi\)
−0.912559 + 0.408944i \(0.865897\pi\)
\(294\) 9.00000 0.524891
\(295\) 28.0000 14.0000i 1.63022 0.815112i
\(296\) −6.00000 −0.348743
\(297\) 2.00000i 0.116052i
\(298\) 0 0
\(299\) 6.00000 0.346989
\(300\) −4.00000 3.00000i −0.230940 0.173205i
\(301\) 32.0000 1.84445
\(302\) 8.00000i 0.460348i
\(303\) 14.0000i 0.804279i
\(304\) −2.00000 −0.114708
\(305\) 20.0000 10.0000i 1.14520 0.572598i
\(306\) 4.00000 0.228665
\(307\) 28.0000i 1.59804i 0.601302 + 0.799022i \(0.294649\pi\)
−0.601302 + 0.799022i \(0.705351\pi\)
\(308\) 8.00000i 0.455842i
\(309\) 6.00000 0.341328
\(310\) −4.00000 8.00000i −0.227185 0.454369i
\(311\) 8.00000 0.453638 0.226819 0.973937i \(-0.427167\pi\)
0.226819 + 0.973937i \(0.427167\pi\)
\(312\) 1.00000i 0.0566139i
\(313\) 8.00000i 0.452187i −0.974106 0.226093i \(-0.927405\pi\)
0.974106 0.226093i \(-0.0725954\pi\)
\(314\) 10.0000 0.564333
\(315\) −4.00000 8.00000i −0.225374 0.450749i
\(316\) −8.00000 −0.450035
\(317\) 30.0000i 1.68497i −0.538721 0.842484i \(-0.681092\pi\)
0.538721 0.842484i \(-0.318908\pi\)
\(318\) 10.0000i 0.560772i
\(319\) 4.00000 0.223957
\(320\) −2.00000 + 1.00000i −0.111803 + 0.0559017i
\(321\) 8.00000 0.446516
\(322\) 24.0000i 1.33747i
\(323\) 8.00000i 0.445132i
\(324\) −1.00000 −0.0555556
\(325\) −4.00000 3.00000i −0.221880 0.166410i
\(326\) −4.00000 −0.221540
\(327\) 12.0000i 0.663602i
\(328\) 6.00000i 0.331295i
\(329\) −32.0000 −1.76422
\(330\) −4.00000 + 2.00000i −0.220193 + 0.110096i
\(331\) 18.0000 0.989369 0.494685 0.869072i \(-0.335284\pi\)
0.494685 + 0.869072i \(0.335284\pi\)
\(332\) 12.0000i 0.658586i
\(333\) 6.00000i 0.328798i
\(334\) 0 0
\(335\) 4.00000 + 8.00000i 0.218543 + 0.437087i
\(336\) −4.00000 −0.218218
\(337\) 32.0000i 1.74315i −0.490261 0.871576i \(-0.663099\pi\)
0.490261 0.871576i \(-0.336901\pi\)
\(338\) 1.00000i 0.0543928i
\(339\) −12.0000 −0.651751
\(340\) −4.00000 8.00000i −0.216930 0.433861i
\(341\) −8.00000 −0.433224
\(342\) 2.00000i 0.108148i
\(343\) 8.00000i 0.431959i
\(344\) −8.00000 −0.431331
\(345\) −12.0000 + 6.00000i −0.646058 + 0.323029i
\(346\) 10.0000 0.537603
\(347\) 24.0000i 1.28839i −0.764862 0.644194i \(-0.777193\pi\)
0.764862 0.644194i \(-0.222807\pi\)
\(348\) 2.00000i 0.107211i
\(349\) 28.0000 1.49881 0.749403 0.662114i \(-0.230341\pi\)
0.749403 + 0.662114i \(0.230341\pi\)
\(350\) −12.0000 + 16.0000i −0.641427 + 0.855236i
\(351\) −1.00000 −0.0533761
\(352\) 2.00000i 0.106600i
\(353\) 26.0000i 1.38384i 0.721974 + 0.691920i \(0.243235\pi\)
−0.721974 + 0.691920i \(0.756765\pi\)
\(354\) −14.0000 −0.744092
\(355\) 16.0000 8.00000i 0.849192 0.424596i
\(356\) −18.0000 −0.953998
\(357\) 16.0000i 0.846810i
\(358\) 0 0
\(359\) −20.0000 −1.05556 −0.527780 0.849381i \(-0.676975\pi\)
−0.527780 + 0.849381i \(0.676975\pi\)
\(360\) 1.00000 + 2.00000i 0.0527046 + 0.105409i
\(361\) −15.0000 −0.789474
\(362\) 6.00000i 0.315353i
\(363\) 7.00000i 0.367405i
\(364\) −4.00000 −0.209657
\(365\) −10.0000 20.0000i −0.523424 1.04685i
\(366\) −10.0000 −0.522708
\(367\) 22.0000i 1.14839i 0.818718 + 0.574195i \(0.194685\pi\)
−0.818718 + 0.574195i \(0.805315\pi\)
\(368\) 6.00000i 0.312772i
\(369\) 6.00000 0.312348
\(370\) 12.0000 6.00000i 0.623850 0.311925i
\(371\) 40.0000 2.07670
\(372\) 4.00000i 0.207390i
\(373\) 2.00000i 0.103556i 0.998659 + 0.0517780i \(0.0164888\pi\)
−0.998659 + 0.0517780i \(0.983511\pi\)
\(374\) −8.00000 −0.413670
\(375\) 11.0000 + 2.00000i 0.568038 + 0.103280i
\(376\) 8.00000 0.412568
\(377\) 2.00000i 0.103005i
\(378\) 4.00000i 0.205738i
\(379\) −26.0000 −1.33553 −0.667765 0.744372i \(-0.732749\pi\)
−0.667765 + 0.744372i \(0.732749\pi\)
\(380\) 4.00000 2.00000i 0.205196 0.102598i
\(381\) 18.0000 0.922168
\(382\) 0 0
\(383\) 12.0000i 0.613171i 0.951843 + 0.306586i \(0.0991866\pi\)
−0.951843 + 0.306586i \(0.900813\pi\)
\(384\) 1.00000 0.0510310
\(385\) 8.00000 + 16.0000i 0.407718 + 0.815436i
\(386\) 6.00000 0.305392
\(387\) 8.00000i 0.406663i
\(388\) 6.00000i 0.304604i
\(389\) 26.0000 1.31825 0.659126 0.752032i \(-0.270926\pi\)
0.659126 + 0.752032i \(0.270926\pi\)
\(390\) 1.00000 + 2.00000i 0.0506370 + 0.101274i
\(391\) −24.0000 −1.21373
\(392\) 9.00000i 0.454569i
\(393\) 0 0
\(394\) −26.0000 −1.30986
\(395\) 16.0000 8.00000i 0.805047 0.402524i
\(396\) 2.00000 0.100504
\(397\) 6.00000i 0.301131i 0.988600 + 0.150566i \(0.0481095\pi\)
−0.988600 + 0.150566i \(0.951890\pi\)
\(398\) 24.0000i 1.20301i
\(399\) 8.00000 0.400501
\(400\) 3.00000 4.00000i 0.150000 0.200000i
\(401\) −18.0000 −0.898877 −0.449439 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) 4.00000i 0.199502i
\(403\) 4.00000i 0.199254i
\(404\) 14.0000 0.696526
\(405\) 2.00000 1.00000i 0.0993808 0.0496904i
\(406\) −8.00000 −0.397033
\(407\) 12.0000i 0.594818i
\(408\) 4.00000i 0.198030i
\(409\) 2.00000 0.0988936 0.0494468 0.998777i \(-0.484254\pi\)
0.0494468 + 0.998777i \(0.484254\pi\)
\(410\) −6.00000 12.0000i −0.296319 0.592638i
\(411\) −2.00000 −0.0986527
\(412\) 6.00000i 0.295599i
\(413\) 56.0000i 2.75558i
\(414\) 6.00000 0.294884
\(415\) −12.0000 24.0000i −0.589057 1.17811i
\(416\) 1.00000 0.0490290
\(417\) 16.0000i 0.783523i
\(418\) 4.00000i 0.195646i
\(419\) −16.0000 −0.781651 −0.390826 0.920465i \(-0.627810\pi\)
−0.390826 + 0.920465i \(0.627810\pi\)
\(420\) 8.00000 4.00000i 0.390360 0.195180i
\(421\) 28.0000 1.36464 0.682318 0.731055i \(-0.260972\pi\)
0.682318 + 0.731055i \(0.260972\pi\)
\(422\) 28.0000i 1.36302i
\(423\) 8.00000i 0.388973i
\(424\) −10.0000 −0.485643
\(425\) 16.0000 + 12.0000i 0.776114 + 0.582086i
\(426\) −8.00000 −0.387601
\(427\) 40.0000i 1.93574i
\(428\) 8.00000i 0.386695i
\(429\) 2.00000 0.0965609
\(430\) 16.0000 8.00000i 0.771589 0.385794i
\(431\) −8.00000 −0.385346 −0.192673 0.981263i \(-0.561716\pi\)
−0.192673 + 0.981263i \(0.561716\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 16.0000 0.768025
\(435\) 2.00000 + 4.00000i 0.0958927 + 0.191785i
\(436\) 12.0000 0.574696
\(437\) 12.0000i 0.574038i
\(438\) 10.0000i 0.477818i
\(439\) −32.0000 −1.52728 −0.763638 0.645644i \(-0.776589\pi\)
−0.763638 + 0.645644i \(0.776589\pi\)
\(440\) −2.00000 4.00000i −0.0953463 0.190693i
\(441\) 9.00000 0.428571
\(442\) 4.00000i 0.190261i
\(443\) 8.00000i 0.380091i −0.981775 0.190046i \(-0.939136\pi\)
0.981775 0.190046i \(-0.0608636\pi\)
\(444\) −6.00000 −0.284747
\(445\) 36.0000 18.0000i 1.70656 0.853282i
\(446\) −16.0000 −0.757622
\(447\) 0 0
\(448\) 4.00000i 0.188982i
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) −4.00000 3.00000i −0.188562 0.141421i
\(451\) −12.0000 −0.565058
\(452\) 12.0000i 0.564433i
\(453\) 8.00000i 0.375873i
\(454\) −12.0000 −0.563188
\(455\) 8.00000 4.00000i 0.375046 0.187523i
\(456\) −2.00000 −0.0936586
\(457\) 26.0000i 1.21623i −0.793849 0.608114i \(-0.791926\pi\)
0.793849 0.608114i \(-0.208074\pi\)
\(458\) 16.0000i 0.747631i
\(459\) 4.00000 0.186704
\(460\) −6.00000 12.0000i −0.279751 0.559503i
\(461\) −4.00000 −0.186299 −0.0931493 0.995652i \(-0.529693\pi\)
−0.0931493 + 0.995652i \(0.529693\pi\)
\(462\) 8.00000i 0.372194i
\(463\) 36.0000i 1.67306i 0.547920 + 0.836531i \(0.315420\pi\)
−0.547920 + 0.836531i \(0.684580\pi\)
\(464\) 2.00000 0.0928477
\(465\) −4.00000 8.00000i −0.185496 0.370991i
\(466\) −4.00000 −0.185296
\(467\) 16.0000i 0.740392i −0.928954 0.370196i \(-0.879291\pi\)
0.928954 0.370196i \(-0.120709\pi\)
\(468\) 1.00000i 0.0462250i
\(469\) −16.0000 −0.738811
\(470\) −16.0000 + 8.00000i −0.738025 + 0.369012i
\(471\) 10.0000 0.460776
\(472\) 14.0000i 0.644402i
\(473\) 16.0000i 0.735681i
\(474\) −8.00000 −0.367452
\(475\) −6.00000 + 8.00000i −0.275299 + 0.367065i
\(476\) 16.0000 0.733359
\(477\) 10.0000i 0.457869i
\(478\) 12.0000i 0.548867i
\(479\) 12.0000 0.548294 0.274147 0.961688i \(-0.411605\pi\)
0.274147 + 0.961688i \(0.411605\pi\)
\(480\) −2.00000 + 1.00000i −0.0912871 + 0.0456435i
\(481\) −6.00000 −0.273576
\(482\) 30.0000i 1.36646i
\(483\) 24.0000i 1.09204i
\(484\) 7.00000 0.318182
\(485\) 6.00000 + 12.0000i 0.272446 + 0.544892i
\(486\) −1.00000 −0.0453609
\(487\) 40.0000i 1.81257i −0.422664 0.906287i \(-0.638905\pi\)
0.422664 0.906287i \(-0.361095\pi\)
\(488\) 10.0000i 0.452679i
\(489\) −4.00000 −0.180886
\(490\) −9.00000 18.0000i −0.406579 0.813157i
\(491\) 8.00000 0.361035 0.180517 0.983572i \(-0.442223\pi\)
0.180517 + 0.983572i \(0.442223\pi\)
\(492\) 6.00000i 0.270501i
\(493\) 8.00000i 0.360302i
\(494\) −2.00000 −0.0899843
\(495\) −4.00000 + 2.00000i −0.179787 + 0.0898933i
\(496\) −4.00000 −0.179605
\(497\) 32.0000i 1.43540i
\(498\) 12.0000i 0.537733i
\(499\) −30.0000 −1.34298 −0.671492 0.741012i \(-0.734346\pi\)
−0.671492 + 0.741012i \(0.734346\pi\)
\(500\) −2.00000 + 11.0000i −0.0894427 + 0.491935i
\(501\) 0 0
\(502\) 12.0000i 0.535586i
\(503\) 18.0000i 0.802580i −0.915951 0.401290i \(-0.868562\pi\)
0.915951 0.401290i \(-0.131438\pi\)
\(504\) −4.00000 −0.178174
\(505\) −28.0000 + 14.0000i −1.24598 + 0.622992i
\(506\) −12.0000 −0.533465
\(507\) 1.00000i 0.0444116i
\(508\) 18.0000i 0.798621i
\(509\) 16.0000 0.709188 0.354594 0.935020i \(-0.384619\pi\)
0.354594 + 0.935020i \(0.384619\pi\)
\(510\) −4.00000 8.00000i −0.177123 0.354246i
\(511\) 40.0000 1.76950
\(512\) 1.00000i 0.0441942i
\(513\) 2.00000i 0.0883022i
\(514\) 12.0000 0.529297
\(515\) −6.00000 12.0000i −0.264392 0.528783i
\(516\) −8.00000 −0.352180
\(517\) 16.0000i 0.703679i
\(518\) 24.0000i 1.05450i
\(519\) 10.0000 0.438951
\(520\) −2.00000 + 1.00000i −0.0877058 + 0.0438529i
\(521\) 38.0000 1.66481 0.832405 0.554168i \(-0.186963\pi\)
0.832405 + 0.554168i \(0.186963\pi\)
\(522\) 2.00000i 0.0875376i
\(523\) 8.00000i 0.349816i −0.984585 0.174908i \(-0.944037\pi\)
0.984585 0.174908i \(-0.0559627\pi\)
\(524\) 0 0
\(525\) −12.0000 + 16.0000i −0.523723 + 0.698297i
\(526\) −10.0000 −0.436021
\(527\) 16.0000i 0.696971i
\(528\) 2.00000i 0.0870388i
\(529\) −13.0000 −0.565217
\(530\) 20.0000 10.0000i 0.868744 0.434372i
\(531\) −14.0000 −0.607548
\(532\) 8.00000i 0.346844i
\(533\) 6.00000i 0.259889i
\(534\) −18.0000 −0.778936
\(535\) −8.00000 16.0000i −0.345870 0.691740i
\(536\) 4.00000 0.172774
\(537\) 0 0
\(538\) 14.0000i 0.603583i
\(539\) −18.0000 −0.775315
\(540\) 1.00000 + 2.00000i 0.0430331 + 0.0860663i
\(541\) −8.00000 −0.343947 −0.171973 0.985102i \(-0.555014\pi\)
−0.171973 + 0.985102i \(0.555014\pi\)
\(542\) 16.0000i 0.687259i
\(543\) 6.00000i 0.257485i
\(544\) −4.00000 −0.171499
\(545\) −24.0000 + 12.0000i −1.02805 + 0.514024i
\(546\) −4.00000 −0.171184
\(547\) 44.0000i 1.88130i 0.339372 + 0.940652i \(0.389785\pi\)
−0.339372 + 0.940652i \(0.610215\pi\)
\(548\) 2.00000i 0.0854358i
\(549\) −10.0000 −0.426790
\(550\) 8.00000 + 6.00000i 0.341121 + 0.255841i
\(551\) −4.00000 −0.170406
\(552\) 6.00000i 0.255377i
\(553\) 32.0000i 1.36078i
\(554\) −2.00000 −0.0849719
\(555\) 12.0000 6.00000i 0.509372 0.254686i
\(556\) 16.0000 0.678551
\(557\) 14.0000i 0.593199i 0.955002 + 0.296600i \(0.0958526\pi\)
−0.955002 + 0.296600i \(0.904147\pi\)
\(558\) 4.00000i 0.169334i
\(559\) −8.00000 −0.338364
\(560\) 4.00000 + 8.00000i 0.169031 + 0.338062i
\(561\) −8.00000 −0.337760
\(562\) 18.0000i 0.759284i
\(563\) 16.0000i 0.674320i 0.941447 + 0.337160i \(0.109466\pi\)
−0.941447 + 0.337160i \(0.890534\pi\)
\(564\) 8.00000 0.336861
\(565\) 12.0000 + 24.0000i 0.504844 + 1.00969i
\(566\) −4.00000 −0.168133
\(567\) 4.00000i 0.167984i
\(568\) 8.00000i 0.335673i
\(569\) 42.0000 1.76073 0.880366 0.474295i \(-0.157297\pi\)
0.880366 + 0.474295i \(0.157297\pi\)
\(570\) 4.00000 2.00000i 0.167542 0.0837708i
\(571\) −36.0000 −1.50655 −0.753277 0.657704i \(-0.771528\pi\)
−0.753277 + 0.657704i \(0.771528\pi\)
\(572\) 2.00000i 0.0836242i
\(573\) 0 0
\(574\) 24.0000 1.00174
\(575\) 24.0000 + 18.0000i 1.00087 + 0.750652i
\(576\) 1.00000 0.0416667
\(577\) 26.0000i 1.08239i 0.840896 + 0.541197i \(0.182029\pi\)
−0.840896 + 0.541197i \(0.817971\pi\)
\(578\) 1.00000i 0.0415945i
\(579\) 6.00000 0.249351
\(580\) −4.00000 + 2.00000i −0.166091 + 0.0830455i
\(581\) 48.0000 1.99138
\(582\) 6.00000i 0.248708i
\(583\) 20.0000i 0.828315i
\(584\) −10.0000 −0.413803
\(585\) 1.00000 + 2.00000i 0.0413449 + 0.0826898i
\(586\) −14.0000 −0.578335
\(587\) 36.0000i 1.48588i 0.669359 + 0.742940i \(0.266569\pi\)
−0.669359 + 0.742940i \(0.733431\pi\)
\(588\) 9.00000i 0.371154i
\(589\) 8.00000 0.329634
\(590\) 14.0000 + 28.0000i 0.576371 + 1.15274i
\(591\) −26.0000 −1.06950
\(592\) 6.00000i 0.246598i
\(593\) 14.0000i 0.574911i −0.957794 0.287456i \(-0.907191\pi\)
0.957794 0.287456i \(-0.0928094\pi\)
\(594\) 2.00000 0.0820610
\(595\) −32.0000 + 16.0000i −1.31187 + 0.655936i
\(596\) 0 0
\(597\) 24.0000i 0.982255i
\(598\) 6.00000i 0.245358i
\(599\) 16.0000 0.653742 0.326871 0.945069i \(-0.394006\pi\)
0.326871 + 0.945069i \(0.394006\pi\)
\(600\) 3.00000 4.00000i 0.122474 0.163299i
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 32.0000i 1.30422i
\(603\) 4.00000i 0.162893i
\(604\) −8.00000 −0.325515
\(605\) −14.0000 + 7.00000i −0.569181 + 0.284590i
\(606\) 14.0000 0.568711
\(607\) 18.0000i 0.730597i 0.930890 + 0.365299i \(0.119033\pi\)
−0.930890 + 0.365299i \(0.880967\pi\)
\(608\) 2.00000i 0.0811107i
\(609\) −8.00000 −0.324176
\(610\) 10.0000 + 20.0000i 0.404888 + 0.809776i
\(611\) 8.00000 0.323645
\(612\) 4.00000i 0.161690i
\(613\) 26.0000i 1.05013i −0.851062 0.525065i \(-0.824041\pi\)
0.851062 0.525065i \(-0.175959\pi\)
\(614\) −28.0000 −1.12999
\(615\) −6.00000 12.0000i −0.241943 0.483887i
\(616\) 8.00000 0.322329
\(617\) 34.0000i 1.36879i −0.729112 0.684394i \(-0.760067\pi\)
0.729112 0.684394i \(-0.239933\pi\)
\(618\) 6.00000i 0.241355i
\(619\) −42.0000 −1.68812 −0.844061 0.536247i \(-0.819842\pi\)
−0.844061 + 0.536247i \(0.819842\pi\)
\(620\) 8.00000 4.00000i 0.321288 0.160644i
\(621\) 6.00000 0.240772
\(622\) 8.00000i 0.320771i
\(623\) 72.0000i 2.88462i
\(624\) 1.00000 0.0400320
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 8.00000 0.319744
\(627\) 4.00000i 0.159745i
\(628\) 10.0000i 0.399043i
\(629\) 24.0000 0.956943
\(630\) 8.00000 4.00000i 0.318728 0.159364i
\(631\) −32.0000 −1.27390 −0.636950 0.770905i \(-0.719804\pi\)
−0.636950 + 0.770905i \(0.719804\pi\)
\(632\) 8.00000i 0.318223i
\(633\) 28.0000i 1.11290i
\(634\) 30.0000 1.19145
\(635\) −18.0000 36.0000i −0.714308 1.42862i
\(636\) −10.0000 −0.396526
\(637\) 9.00000i 0.356593i
\(638\) 4.00000i 0.158362i
\(639\) −8.00000 −0.316475
\(640\) −1.00000 2.00000i −0.0395285 0.0790569i
\(641\) −2.00000 −0.0789953 −0.0394976 0.999220i \(-0.512576\pi\)
−0.0394976 + 0.999220i \(0.512576\pi\)
\(642\) 8.00000i 0.315735i
\(643\) 20.0000i 0.788723i 0.918955 + 0.394362i \(0.129034\pi\)
−0.918955 + 0.394362i \(0.870966\pi\)
\(644\) 24.0000 0.945732
\(645\) 16.0000 8.00000i 0.629999 0.315000i
\(646\) 8.00000 0.314756
\(647\) 6.00000i 0.235884i −0.993020 0.117942i \(-0.962370\pi\)
0.993020 0.117942i \(-0.0376297\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 28.0000 1.09910
\(650\) 3.00000 4.00000i 0.117670 0.156893i
\(651\) 16.0000 0.627089
\(652\) 4.00000i 0.156652i
\(653\) 26.0000i 1.01746i 0.860927 + 0.508729i \(0.169885\pi\)
−0.860927 + 0.508729i \(0.830115\pi\)
\(654\) 12.0000 0.469237
\(655\) 0 0
\(656\) −6.00000 −0.234261
\(657\) 10.0000i 0.390137i
\(658\) 32.0000i 1.24749i
\(659\) −40.0000 −1.55818 −0.779089 0.626913i \(-0.784318\pi\)
−0.779089 + 0.626913i \(0.784318\pi\)
\(660\) −2.00000 4.00000i −0.0778499 0.155700i
\(661\) 24.0000 0.933492 0.466746 0.884391i \(-0.345426\pi\)
0.466746 + 0.884391i \(0.345426\pi\)
\(662\) 18.0000i 0.699590i
\(663\) 4.00000i 0.155347i
\(664\) −12.0000 −0.465690
\(665\) −8.00000 16.0000i −0.310227 0.620453i
\(666\) −6.00000 −0.232495
\(667\) 12.0000i 0.464642i
\(668\) 0 0
\(669\) −16.0000 −0.618596
\(670\) −8.00000 + 4.00000i −0.309067 + 0.154533i
\(671\) 20.0000 0.772091
\(672\) 4.00000i 0.154303i
\(673\) 12.0000i 0.462566i −0.972887 0.231283i \(-0.925708\pi\)
0.972887 0.231283i \(-0.0742923\pi\)
\(674\) 32.0000 1.23259
\(675\) −4.00000 3.00000i −0.153960 0.115470i
\(676\) 1.00000 0.0384615
\(677\) 22.0000i 0.845529i 0.906240 + 0.422764i \(0.138940\pi\)
−0.906240 + 0.422764i \(0.861060\pi\)
\(678\) 12.0000i 0.460857i
\(679\) −24.0000 −0.921035
\(680\) 8.00000 4.00000i 0.306786 0.153393i
\(681\) −12.0000 −0.459841
\(682\) 8.00000i 0.306336i
\(683\) 12.0000i 0.459167i −0.973289 0.229584i \(-0.926264\pi\)
0.973289 0.229584i \(-0.0737364\pi\)
\(684\) −2.00000 −0.0764719
\(685\) 2.00000 + 4.00000i 0.0764161 + 0.152832i
\(686\) 8.00000 0.305441
\(687\) 16.0000i 0.610438i
\(688\) 8.00000i 0.304997i
\(689\) −10.0000 −0.380970
\(690\) −6.00000 12.0000i −0.228416 0.456832i
\(691\) 2.00000 0.0760836 0.0380418 0.999276i \(-0.487888\pi\)
0.0380418 + 0.999276i \(0.487888\pi\)
\(692\) 10.0000i 0.380143i
\(693\) 8.00000i 0.303895i
\(694\) 24.0000 0.911028
\(695\) −32.0000 + 16.0000i −1.21383 + 0.606915i
\(696\) 2.00000 0.0758098
\(697\) 24.0000i 0.909065i
\(698\) 28.0000i 1.05982i
\(699\) −4.00000 −0.151294
\(700\) −16.0000 12.0000i −0.604743 0.453557i
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 1.00000i 0.0377426i
\(703\) 12.0000i 0.452589i
\(704\) −2.00000 −0.0753778
\(705\) −16.0000 + 8.00000i −0.602595 + 0.301297i
\(706\) −26.0000 −0.978523
\(707\) 56.0000i 2.10610i
\(708\) 14.0000i 0.526152i
\(709\) 32.0000 1.20179 0.600893 0.799330i \(-0.294812\pi\)
0.600893 + 0.799330i \(0.294812\pi\)
\(710\) 8.00000 + 16.0000i 0.300235 + 0.600469i
\(711\) −8.00000 −0.300023
\(712\) 18.0000i 0.674579i
\(713\) 24.0000i 0.898807i
\(714\) 16.0000 0.598785
\(715\) −2.00000 4.00000i −0.0747958 0.149592i
\(716\) 0 0
\(717\) 12.0000i 0.448148i
\(718\) 20.0000i 0.746393i
\(719\) −24.0000 −0.895049 −0.447524 0.894272i \(-0.647694\pi\)
−0.447524 + 0.894272i \(0.647694\pi\)
\(720\) −2.00000 + 1.00000i −0.0745356 + 0.0372678i
\(721\) 24.0000 0.893807
\(722\) 15.0000i 0.558242i
\(723\) 30.0000i 1.11571i
\(724\) −6.00000 −0.222988
\(725\) 6.00000 8.00000i 0.222834 0.297113i
\(726\) 7.00000 0.259794
\(727\) 14.0000i 0.519231i 0.965712 + 0.259616i \(0.0835959\pi\)
−0.965712 + 0.259616i \(0.916404\pi\)
\(728\) 4.00000i 0.148250i
\(729\) −1.00000 −0.0370370
\(730\) 20.0000 10.0000i 0.740233 0.370117i
\(731\) 32.0000 1.18356
\(732\) 10.0000i 0.369611i
\(733\) 2.00000i 0.0738717i 0.999318 + 0.0369358i \(0.0117597\pi\)
−0.999318 + 0.0369358i \(0.988240\pi\)
\(734\) −22.0000 −0.812035
\(735\) −9.00000 18.0000i −0.331970 0.663940i
\(736\) −6.00000 −0.221163
\(737\) 8.00000i 0.294684i
\(738\) 6.00000i 0.220863i
\(739\) 2.00000 0.0735712 0.0367856 0.999323i \(-0.488288\pi\)
0.0367856 + 0.999323i \(0.488288\pi\)
\(740\) 6.00000 + 12.0000i 0.220564 + 0.441129i
\(741\) −2.00000 −0.0734718
\(742\) 40.0000i 1.46845i
\(743\) 4.00000i 0.146746i 0.997305 + 0.0733729i \(0.0233763\pi\)
−0.997305 + 0.0733729i \(0.976624\pi\)
\(744\) −4.00000 −0.146647
\(745\) 0 0
\(746\) −2.00000 −0.0732252
\(747\) 12.0000i 0.439057i
\(748\) 8.00000i 0.292509i
\(749\) 32.0000 1.16925
\(750\) −2.00000 + 11.0000i −0.0730297 + 0.401663i
\(751\) 48.0000 1.75154 0.875772 0.482724i \(-0.160353\pi\)
0.875772 + 0.482724i \(0.160353\pi\)
\(752\) 8.00000i 0.291730i
\(753\) 12.0000i 0.437304i
\(754\) 2.00000 0.0728357
\(755\) 16.0000 8.00000i 0.582300 0.291150i
\(756\) −4.00000 −0.145479
\(757\) 22.0000i 0.799604i −0.916602 0.399802i \(-0.869079\pi\)
0.916602 0.399802i \(-0.130921\pi\)
\(758\) 26.0000i 0.944363i
\(759\) −12.0000 −0.435572
\(760\) 2.00000 + 4.00000i 0.0725476 + 0.145095i
\(761\) 14.0000 0.507500 0.253750 0.967270i \(-0.418336\pi\)
0.253750 + 0.967270i \(0.418336\pi\)
\(762\) 18.0000i 0.652071i
\(763\) 48.0000i 1.73772i
\(764\) 0 0
\(765\) −4.00000 8.00000i −0.144620 0.289241i
\(766\) −12.0000 −0.433578
\(767\) 14.0000i 0.505511i
\(768\) 1.00000i 0.0360844i
\(769\) 22.0000 0.793340 0.396670 0.917961i \(-0.370166\pi\)
0.396670 + 0.917961i \(0.370166\pi\)
\(770\) −16.0000 + 8.00000i −0.576600 + 0.288300i
\(771\) 12.0000 0.432169
\(772\) 6.00000i 0.215945i
\(773\) 14.0000i 0.503545i −0.967786 0.251773i \(-0.918987\pi\)
0.967786 0.251773i \(-0.0810135\pi\)
\(774\) −8.00000 −0.287554
\(775\) −12.0000 + 16.0000i −0.431053 + 0.574737i
\(776\) 6.00000 0.215387
\(777\) 24.0000i 0.860995i
\(778\) 26.0000i 0.932145i
\(779\) 12.0000 0.429945
\(780\) −2.00000 + 1.00000i −0.0716115 + 0.0358057i
\(781\) 16.0000 0.572525
\(782\) 24.0000i 0.858238i
\(783\) 2.00000i 0.0714742i
\(784\) −9.00000 −0.321429
\(785\) −10.0000 20.0000i −0.356915 0.713831i
\(786\) 0 0
\(787\) 28.0000i 0.998092i −0.866575 0.499046i \(-0.833684\pi\)
0.866575 0.499046i \(-0.166316\pi\)
\(788\) 26.0000i 0.926212i