Properties

Label 390.2.e.d.79.1
Level $390$
Weight $2$
Character 390.79
Analytic conductor $3.114$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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: \( x^{2} + 1 \) Copy content Toggle raw display
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 79.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 390.79
Dual form 390.2.e.d.79.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} +1.00000 q^{6} +4.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} +1.00000 q^{6} +4.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(1.00000 - 2.00000i) q^{10} -6.00000 q^{11} -1.00000i q^{12} +1.00000i q^{13} +4.00000 q^{14} +(-1.00000 + 2.00000i) q^{15} +1.00000 q^{16} +4.00000i q^{17} +1.00000i q^{18} -2.00000 q^{19} +(-2.00000 - 1.00000i) q^{20} -4.00000 q^{21} +6.00000i q^{22} -6.00000i q^{23} -1.00000 q^{24} +(3.00000 + 4.00000i) q^{25} +1.00000 q^{26} -1.00000i q^{27} -4.00000i q^{28} +10.0000 q^{29} +(2.00000 + 1.00000i) q^{30} +4.00000 q^{31} -1.00000i q^{32} -6.00000i q^{33} +4.00000 q^{34} +(-4.00000 + 8.00000i) q^{35} +1.00000 q^{36} +6.00000i q^{37} +2.00000i q^{38} -1.00000 q^{39} +(-1.00000 + 2.00000i) q^{40} +10.0000 q^{41} +4.00000i q^{42} +6.00000 q^{44} +(-2.00000 - 1.00000i) q^{45} -6.00000 q^{46} -8.00000i q^{47} +1.00000i q^{48} -9.00000 q^{49} +(4.00000 - 3.00000i) q^{50} -4.00000 q^{51} -1.00000i q^{52} -6.00000i q^{53} -1.00000 q^{54} +(-12.0000 - 6.00000i) q^{55} -4.00000 q^{56} -2.00000i q^{57} -10.0000i q^{58} +6.00000 q^{59} +(1.00000 - 2.00000i) q^{60} -6.00000 q^{61} -4.00000i q^{62} -4.00000i q^{63} -1.00000 q^{64} +(-1.00000 + 2.00000i) q^{65} -6.00000 q^{66} +12.0000i q^{67} -4.00000i q^{68} +6.00000 q^{69} +(8.00000 + 4.00000i) q^{70} -1.00000i q^{72} +2.00000i q^{73} +6.00000 q^{74} +(-4.00000 + 3.00000i) q^{75} +2.00000 q^{76} -24.0000i q^{77} +1.00000i q^{78} +8.00000 q^{79} +(2.00000 + 1.00000i) q^{80} +1.00000 q^{81} -10.0000i q^{82} -4.00000i q^{83} +4.00000 q^{84} +(-4.00000 + 8.00000i) q^{85} +10.0000i q^{87} -6.00000i q^{88} -14.0000 q^{89} +(-1.00000 + 2.00000i) q^{90} -4.00000 q^{91} +6.00000i q^{92} +4.00000i q^{93} -8.00000 q^{94} +(-4.00000 - 2.00000i) q^{95} +1.00000 q^{96} -14.0000i q^{97} +9.00000i q^{98} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{9} + 2 q^{10} - 12 q^{11} + 8 q^{14} - 2 q^{15} + 2 q^{16} - 4 q^{19} - 4 q^{20} - 8 q^{21} - 2 q^{24} + 6 q^{25} + 2 q^{26} + 20 q^{29} + 4 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} + 2 q^{36} - 2 q^{39} - 2 q^{40} + 20 q^{41} + 12 q^{44} - 4 q^{45} - 12 q^{46} - 18 q^{49} + 8 q^{50} - 8 q^{51} - 2 q^{54} - 24 q^{55} - 8 q^{56} + 12 q^{59} + 2 q^{60} - 12 q^{61} - 2 q^{64} - 2 q^{65} - 12 q^{66} + 12 q^{69} + 16 q^{70} + 12 q^{74} - 8 q^{75} + 4 q^{76} + 16 q^{79} + 4 q^{80} + 2 q^{81} + 8 q^{84} - 8 q^{85} - 28 q^{89} - 2 q^{90} - 8 q^{91} - 16 q^{94} - 8 q^{95} + 2 q^{96} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(11\) −6.00000 −1.80907 −0.904534 0.426401i \(-0.859781\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) 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
\(22\) 6.00000i 1.27920i
\(23\) 6.00000i 1.25109i −0.780189 0.625543i \(-0.784877\pi\)
0.780189 0.625543i \(-0.215123\pi\)
\(24\) −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
\(29\) 10.0000 1.85695 0.928477 0.371391i \(-0.121119\pi\)
0.928477 + 0.371391i \(0.121119\pi\)
\(30\) 2.00000 + 1.00000i 0.365148 + 0.182574i
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 6.00000i 1.04447i
\(34\) 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 \(0.164172\pi\)
−0.869918 + 0.493197i \(0.835828\pi\)
\(38\) 2.00000i 0.324443i
\(39\) −1.00000 −0.160128
\(40\) −1.00000 + 2.00000i −0.158114 + 0.316228i
\(41\) 10.0000 1.56174 0.780869 0.624695i \(-0.214777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) 4.00000i 0.617213i
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 6.00000 0.904534
\(45\) −2.00000 1.00000i −0.298142 0.149071i
\(46\) −6.00000 −0.884652
\(47\) 8.00000i 1.16692i −0.812142 0.583460i \(-0.801699\pi\)
0.812142 0.583460i \(-0.198301\pi\)
\(48\) 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
\(53\) 6.00000i 0.824163i −0.911147 0.412082i \(-0.864802\pi\)
0.911147 0.412082i \(-0.135198\pi\)
\(54\) −1.00000 −0.136083
\(55\) −12.0000 6.00000i −1.61808 0.809040i
\(56\) −4.00000 −0.534522
\(57\) 2.00000i 0.264906i
\(58\) 10.0000i 1.31306i
\(59\) 6.00000 0.781133 0.390567 0.920575i \(-0.372279\pi\)
0.390567 + 0.920575i \(0.372279\pi\)
\(60\) 1.00000 2.00000i 0.129099 0.258199i
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 4.00000i 0.508001i
\(63\) 4.00000i 0.503953i
\(64\) −1.00000 −0.125000
\(65\) −1.00000 + 2.00000i −0.124035 + 0.248069i
\(66\) −6.00000 −0.738549
\(67\) 12.0000i 1.46603i 0.680211 + 0.733017i \(0.261888\pi\)
−0.680211 + 0.733017i \(0.738112\pi\)
\(68\) 4.00000i 0.485071i
\(69\) 6.00000 0.722315
\(70\) 8.00000 + 4.00000i 0.956183 + 0.478091i
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 2.00000i 0.234082i 0.993127 + 0.117041i \(0.0373409\pi\)
−0.993127 + 0.117041i \(0.962659\pi\)
\(74\) 6.00000 0.697486
\(75\) −4.00000 + 3.00000i −0.461880 + 0.346410i
\(76\) 2.00000 0.229416
\(77\) 24.0000i 2.73505i
\(78\) 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
\(82\) 10.0000i 1.10432i
\(83\) 4.00000i 0.439057i −0.975606 0.219529i \(-0.929548\pi\)
0.975606 0.219529i \(-0.0704519\pi\)
\(84\) 4.00000 0.436436
\(85\) −4.00000 + 8.00000i −0.433861 + 0.867722i
\(86\) 0 0
\(87\) 10.0000i 1.07211i
\(88\) 6.00000i 0.639602i
\(89\) −14.0000 −1.48400 −0.741999 0.670402i \(-0.766122\pi\)
−0.741999 + 0.670402i \(0.766122\pi\)
\(90\) −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
\(97\) 14.0000i 1.42148i −0.703452 0.710742i \(-0.748359\pi\)
0.703452 0.710742i \(-0.251641\pi\)
\(98\) 9.00000i 0.909137i
\(99\) 6.00000 0.603023
\(100\) −3.00000 4.00000i −0.300000 0.400000i
\(101\) 10.0000 0.995037 0.497519 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) 4.00000i 0.396059i
\(103\) 2.00000i 0.197066i −0.995134 0.0985329i \(-0.968585\pi\)
0.995134 0.0985329i \(-0.0314150\pi\)
\(104\) −1.00000 −0.0980581
\(105\) −8.00000 4.00000i −0.780720 0.390360i
\(106\) −6.00000 −0.582772
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) −4.00000 −0.383131 −0.191565 0.981480i \(-0.561356\pi\)
−0.191565 + 0.981480i \(0.561356\pi\)
\(110\) −6.00000 + 12.0000i −0.572078 + 1.14416i
\(111\) −6.00000 −0.569495
\(112\) 4.00000i 0.377964i
\(113\) 4.00000i 0.376288i −0.982141 0.188144i \(-0.939753\pi\)
0.982141 0.188144i \(-0.0602472\pi\)
\(114\) −2.00000 −0.187317
\(115\) 6.00000 12.0000i 0.559503 1.11901i
\(116\) −10.0000 −0.928477
\(117\) 1.00000i 0.0924500i
\(118\) 6.00000i 0.552345i
\(119\) −16.0000 −1.46672
\(120\) −2.00000 1.00000i −0.182574 0.0912871i
\(121\) 25.0000 2.27273
\(122\) 6.00000i 0.543214i
\(123\) 10.0000i 0.901670i
\(124\) −4.00000 −0.359211
\(125\) 2.00000 + 11.0000i 0.178885 + 0.983870i
\(126\) −4.00000 −0.356348
\(127\) 10.0000i 0.887357i 0.896186 + 0.443678i \(0.146327\pi\)
−0.896186 + 0.443678i \(0.853673\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) 2.00000 + 1.00000i 0.175412 + 0.0877058i
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) 6.00000i 0.522233i
\(133\) 8.00000i 0.693688i
\(134\) 12.0000 1.03664
\(135\) 1.00000 2.00000i 0.0860663 0.172133i
\(136\) −4.00000 −0.342997
\(137\) 14.0000i 1.19610i 0.801459 + 0.598050i \(0.204058\pi\)
−0.801459 + 0.598050i \(0.795942\pi\)
\(138\) 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
\(142\) 0 0
\(143\) 6.00000i 0.501745i
\(144\) −1.00000 −0.0833333
\(145\) 20.0000 + 10.0000i 1.66091 + 0.830455i
\(146\) 2.00000 0.165521
\(147\) 9.00000i 0.742307i
\(148\) 6.00000i 0.493197i
\(149\) −16.0000 −1.31077 −0.655386 0.755295i \(-0.727494\pi\)
−0.655386 + 0.755295i \(0.727494\pi\)
\(150\) 3.00000 + 4.00000i 0.244949 + 0.326599i
\(151\) 16.0000 1.30206 0.651031 0.759051i \(-0.274337\pi\)
0.651031 + 0.759051i \(0.274337\pi\)
\(152\) 2.00000i 0.162221i
\(153\) 4.00000i 0.323381i
\(154\) −24.0000 −1.93398
\(155\) 8.00000 + 4.00000i 0.642575 + 0.321288i
\(156\) 1.00000 0.0800641
\(157\) 6.00000i 0.478852i −0.970915 0.239426i \(-0.923041\pi\)
0.970915 0.239426i \(-0.0769593\pi\)
\(158\) 8.00000i 0.636446i
\(159\) 6.00000 0.475831
\(160\) 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 \(-0.949930\pi\)
0.987654 0.156652i \(-0.0500701\pi\)
\(164\) −10.0000 −0.780869
\(165\) 6.00000 12.0000i 0.467099 0.934199i
\(166\) −4.00000 −0.310460
\(167\) 16.0000i 1.23812i 0.785345 + 0.619059i \(0.212486\pi\)
−0.785345 + 0.619059i \(0.787514\pi\)
\(168\) 4.00000i 0.308607i
\(169\) −1.00000 −0.0769231
\(170\) 8.00000 + 4.00000i 0.613572 + 0.306786i
\(171\) 2.00000 0.152944
\(172\) 0 0
\(173\) 22.0000i 1.67263i −0.548250 0.836315i \(-0.684706\pi\)
0.548250 0.836315i \(-0.315294\pi\)
\(174\) 10.0000 0.758098
\(175\) −16.0000 + 12.0000i −1.20949 + 0.907115i
\(176\) −6.00000 −0.452267
\(177\) 6.00000i 0.450988i
\(178\) 14.0000i 1.04934i
\(179\) 24.0000 1.79384 0.896922 0.442189i \(-0.145798\pi\)
0.896922 + 0.442189i \(0.145798\pi\)
\(180\) 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
\(183\) 6.00000i 0.443533i
\(184\) 6.00000 0.442326
\(185\) −6.00000 + 12.0000i −0.441129 + 0.882258i
\(186\) 4.00000 0.293294
\(187\) 24.0000i 1.75505i
\(188\) 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
\(193\) 2.00000i 0.143963i −0.997406 0.0719816i \(-0.977068\pi\)
0.997406 0.0719816i \(-0.0229323\pi\)
\(194\) −14.0000 −1.00514
\(195\) −2.00000 1.00000i −0.143223 0.0716115i
\(196\) 9.00000 0.642857
\(197\) 6.00000i 0.427482i 0.976890 + 0.213741i \(0.0685649\pi\)
−0.976890 + 0.213741i \(0.931435\pi\)
\(198\) 6.00000i 0.426401i
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) −4.00000 + 3.00000i −0.282843 + 0.212132i
\(201\) −12.0000 −0.846415
\(202\) 10.0000i 0.703598i
\(203\) 40.0000i 2.80745i
\(204\) 4.00000 0.280056
\(205\) 20.0000 + 10.0000i 1.39686 + 0.698430i
\(206\) −2.00000 −0.139347
\(207\) 6.00000i 0.417029i
\(208\) 1.00000i 0.0693375i
\(209\) 12.0000 0.830057
\(210\) −4.00000 + 8.00000i −0.276026 + 0.552052i
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 6.00000i 0.412082i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 16.0000i 1.08615i
\(218\) 4.00000i 0.270914i
\(219\) −2.00000 −0.135147
\(220\) 12.0000 + 6.00000i 0.809040 + 0.404520i
\(221\) −4.00000 −0.269069
\(222\) 6.00000i 0.402694i
\(223\) 8.00000i 0.535720i 0.963458 + 0.267860i \(0.0863164\pi\)
−0.963458 + 0.267860i \(0.913684\pi\)
\(224\) 4.00000 0.267261
\(225\) −3.00000 4.00000i −0.200000 0.266667i
\(226\) −4.00000 −0.266076
\(227\) 4.00000i 0.265489i 0.991150 + 0.132745i \(0.0423790\pi\)
−0.991150 + 0.132745i \(0.957621\pi\)
\(228\) 2.00000i 0.132453i
\(229\) −8.00000 −0.528655 −0.264327 0.964433i \(-0.585150\pi\)
−0.264327 + 0.964433i \(0.585150\pi\)
\(230\) −12.0000 6.00000i −0.791257 0.395628i
\(231\) 24.0000 1.57908
\(232\) 10.0000i 0.656532i
\(233\) 12.0000i 0.786146i −0.919507 0.393073i \(-0.871412\pi\)
0.919507 0.393073i \(-0.128588\pi\)
\(234\) −1.00000 −0.0653720
\(235\) 8.00000 16.0000i 0.521862 1.04372i
\(236\) −6.00000 −0.390567
\(237\) 8.00000i 0.519656i
\(238\) 16.0000i 1.03713i
\(239\) 4.00000 0.258738 0.129369 0.991596i \(-0.458705\pi\)
0.129369 + 0.991596i \(0.458705\pi\)
\(240\) −1.00000 + 2.00000i −0.0645497 + 0.129099i
\(241\) 18.0000 1.15948 0.579741 0.814801i \(-0.303154\pi\)
0.579741 + 0.814801i \(0.303154\pi\)
\(242\) 25.0000i 1.60706i
\(243\) 1.00000i 0.0641500i
\(244\) 6.00000 0.384111
\(245\) −18.0000 9.00000i −1.14998 0.574989i
\(246\) 10.0000 0.637577
\(247\) 2.00000i 0.127257i
\(248\) 4.00000i 0.254000i
\(249\) 4.00000 0.253490
\(250\) 11.0000 2.00000i 0.695701 0.126491i
\(251\) −20.0000 −1.26239 −0.631194 0.775625i \(-0.717435\pi\)
−0.631194 + 0.775625i \(0.717435\pi\)
\(252\) 4.00000i 0.251976i
\(253\) 36.0000i 2.26330i
\(254\) 10.0000 0.627456
\(255\) −8.00000 4.00000i −0.500979 0.250490i
\(256\) 1.00000 0.0625000
\(257\) 28.0000i 1.74659i −0.487190 0.873296i \(-0.661978\pi\)
0.487190 0.873296i \(-0.338022\pi\)
\(258\) 0 0
\(259\) −24.0000 −1.49129
\(260\) 1.00000 2.00000i 0.0620174 0.124035i
\(261\) −10.0000 −0.618984
\(262\) 8.00000i 0.494242i
\(263\) 10.0000i 0.616626i −0.951285 0.308313i \(-0.900236\pi\)
0.951285 0.308313i \(-0.0997645\pi\)
\(264\) 6.00000 0.369274
\(265\) 6.00000 12.0000i 0.368577 0.737154i
\(266\) −8.00000 −0.490511
\(267\) 14.0000i 0.856786i
\(268\) 12.0000i 0.733017i
\(269\) −10.0000 −0.609711 −0.304855 0.952399i \(-0.598608\pi\)
−0.304855 + 0.952399i \(0.598608\pi\)
\(270\) −2.00000 1.00000i −0.121716 0.0608581i
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 4.00000i 0.242091i
\(274\) 14.0000 0.845771
\(275\) −18.0000 24.0000i −1.08544 1.44725i
\(276\) −6.00000 −0.361158
\(277\) 14.0000i 0.841178i 0.907251 + 0.420589i \(0.138177\pi\)
−0.907251 + 0.420589i \(0.861823\pi\)
\(278\) 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
\(283\) 12.0000i 0.713326i −0.934233 0.356663i \(-0.883914\pi\)
0.934233 0.356663i \(-0.116086\pi\)
\(284\) 0 0
\(285\) 2.00000 4.00000i 0.118470 0.236940i
\(286\) −6.00000 −0.354787
\(287\) 40.0000i 2.36113i
\(288\) 1.00000i 0.0589256i
\(289\) 1.00000 0.0588235
\(290\) 10.0000 20.0000i 0.587220 1.17444i
\(291\) 14.0000 0.820695
\(292\) 2.00000i 0.117041i
\(293\) 18.0000i 1.05157i 0.850617 + 0.525786i \(0.176229\pi\)
−0.850617 + 0.525786i \(0.823771\pi\)
\(294\) −9.00000 −0.524891
\(295\) 12.0000 + 6.00000i 0.698667 + 0.349334i
\(296\) −6.00000 −0.348743
\(297\) 6.00000i 0.348155i
\(298\) 16.0000i 0.926855i
\(299\) 6.00000 0.346989
\(300\) 4.00000 3.00000i 0.230940 0.173205i
\(301\) 0 0
\(302\) 16.0000i 0.920697i
\(303\) 10.0000i 0.574485i
\(304\) −2.00000 −0.114708
\(305\) −12.0000 6.00000i −0.687118 0.343559i
\(306\) −4.00000 −0.228665
\(307\) 4.00000i 0.228292i 0.993464 + 0.114146i \(0.0364132\pi\)
−0.993464 + 0.114146i \(0.963587\pi\)
\(308\) 24.0000i 1.36753i
\(309\) 2.00000 0.113776
\(310\) 4.00000 8.00000i 0.227185 0.454369i
\(311\) −8.00000 −0.453638 −0.226819 0.973937i \(-0.572833\pi\)
−0.226819 + 0.973937i \(0.572833\pi\)
\(312\) 1.00000i 0.0566139i
\(313\) 8.00000i 0.452187i −0.974106 0.226093i \(-0.927405\pi\)
0.974106 0.226093i \(-0.0725954\pi\)
\(314\) −6.00000 −0.338600
\(315\) 4.00000 8.00000i 0.225374 0.450749i
\(316\) −8.00000 −0.450035
\(317\) 2.00000i 0.112331i −0.998421 0.0561656i \(-0.982113\pi\)
0.998421 0.0561656i \(-0.0178875\pi\)
\(318\) 6.00000i 0.336463i
\(319\) −60.0000 −3.35936
\(320\) −2.00000 1.00000i −0.111803 0.0559017i
\(321\) 0 0
\(322\) 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
\(327\) 4.00000i 0.221201i
\(328\) 10.0000i 0.552158i
\(329\) 32.0000 1.76422
\(330\) −12.0000 6.00000i −0.660578 0.330289i
\(331\) 2.00000 0.109930 0.0549650 0.998488i \(-0.482495\pi\)
0.0549650 + 0.998488i \(0.482495\pi\)
\(332\) 4.00000i 0.219529i
\(333\) 6.00000i 0.328798i
\(334\) 16.0000 0.875481
\(335\) −12.0000 + 24.0000i −0.655630 + 1.31126i
\(336\) −4.00000 −0.218218
\(337\) 16.0000i 0.871576i −0.900049 0.435788i \(-0.856470\pi\)
0.900049 0.435788i \(-0.143530\pi\)
\(338\) 1.00000i 0.0543928i
\(339\) 4.00000 0.217250
\(340\) 4.00000 8.00000i 0.216930 0.433861i
\(341\) −24.0000 −1.29967
\(342\) 2.00000i 0.108148i
\(343\) 8.00000i 0.431959i
\(344\) 0 0
\(345\) 12.0000 + 6.00000i 0.646058 + 0.323029i
\(346\) −22.0000 −1.18273
\(347\) 16.0000i 0.858925i −0.903085 0.429463i \(-0.858703\pi\)
0.903085 0.429463i \(-0.141297\pi\)
\(348\) 10.0000i 0.536056i
\(349\) 4.00000 0.214115 0.107058 0.994253i \(-0.465857\pi\)
0.107058 + 0.994253i \(0.465857\pi\)
\(350\) 12.0000 + 16.0000i 0.641427 + 0.855236i
\(351\) 1.00000 0.0533761
\(352\) 6.00000i 0.319801i
\(353\) 26.0000i 1.38384i −0.721974 0.691920i \(-0.756765\pi\)
0.721974 0.691920i \(-0.243235\pi\)
\(354\) 6.00000 0.318896
\(355\) 0 0
\(356\) 14.0000 0.741999
\(357\) 16.0000i 0.846810i
\(358\) 24.0000i 1.26844i
\(359\) 20.0000 1.05556 0.527780 0.849381i \(-0.323025\pi\)
0.527780 + 0.849381i \(0.323025\pi\)
\(360\) 1.00000 2.00000i 0.0527046 0.105409i
\(361\) −15.0000 −0.789474
\(362\) 6.00000i 0.315353i
\(363\) 25.0000i 1.31216i
\(364\) 4.00000 0.209657
\(365\) −2.00000 + 4.00000i −0.104685 + 0.209370i
\(366\) −6.00000 −0.313625
\(367\) 18.0000i 0.939592i 0.882775 + 0.469796i \(0.155673\pi\)
−0.882775 + 0.469796i \(0.844327\pi\)
\(368\) 6.00000i 0.312772i
\(369\) −10.0000 −0.520579
\(370\) 12.0000 + 6.00000i 0.623850 + 0.311925i
\(371\) 24.0000 1.24602
\(372\) 4.00000i 0.207390i
\(373\) 18.0000i 0.932005i −0.884783 0.466002i \(-0.845694\pi\)
0.884783 0.466002i \(-0.154306\pi\)
\(374\) −24.0000 −1.24101
\(375\) −11.0000 + 2.00000i −0.568038 + 0.103280i
\(376\) 8.00000 0.412568
\(377\) 10.0000i 0.515026i
\(378\) 4.00000i 0.205738i
\(379\) −10.0000 −0.513665 −0.256833 0.966456i \(-0.582679\pi\)
−0.256833 + 0.966456i \(0.582679\pi\)
\(380\) 4.00000 + 2.00000i 0.205196 + 0.102598i
\(381\) −10.0000 −0.512316
\(382\) 0 0
\(383\) 20.0000i 1.02195i 0.859595 + 0.510976i \(0.170716\pi\)
−0.859595 + 0.510976i \(0.829284\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 24.0000 48.0000i 1.22315 2.44631i
\(386\) −2.00000 −0.101797
\(387\) 0 0
\(388\) 14.0000i 0.710742i
\(389\) −30.0000 −1.52106 −0.760530 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) −1.00000 + 2.00000i −0.0506370 + 0.101274i
\(391\) 24.0000 1.21373
\(392\) 9.00000i 0.454569i
\(393\) 8.00000i 0.403547i
\(394\) 6.00000 0.302276
\(395\) 16.0000 + 8.00000i 0.805047 + 0.402524i
\(396\) −6.00000 −0.301511
\(397\) 10.0000i 0.501886i 0.968002 + 0.250943i \(0.0807406\pi\)
−0.968002 + 0.250943i \(0.919259\pi\)
\(398\) 8.00000i 0.401004i
\(399\) 8.00000 0.400501
\(400\) 3.00000 + 4.00000i 0.150000 + 0.200000i
\(401\) 30.0000 1.49813 0.749064 0.662497i \(-0.230503\pi\)
0.749064 + 0.662497i \(0.230503\pi\)
\(402\) 12.0000i 0.598506i
\(403\) 4.00000i 0.199254i
\(404\) −10.0000 −0.497519
\(405\) 2.00000 + 1.00000i 0.0993808 + 0.0496904i
\(406\) 40.0000 1.98517
\(407\) 36.0000i 1.78445i
\(408\) 4.00000i 0.198030i
\(409\) 34.0000 1.68119 0.840596 0.541663i \(-0.182205\pi\)
0.840596 + 0.541663i \(0.182205\pi\)
\(410\) 10.0000 20.0000i 0.493865 0.987730i
\(411\) −14.0000 −0.690569
\(412\) 2.00000i 0.0985329i
\(413\) 24.0000i 1.18096i
\(414\) 6.00000 0.294884
\(415\) 4.00000 8.00000i 0.196352 0.392705i
\(416\) 1.00000 0.0490290
\(417\) 16.0000i 0.783523i
\(418\) 12.0000i 0.586939i
\(419\) −8.00000 −0.390826 −0.195413 0.980721i \(-0.562605\pi\)
−0.195413 + 0.980721i \(0.562605\pi\)
\(420\) 8.00000 + 4.00000i 0.390360 + 0.195180i
\(421\) 4.00000 0.194948 0.0974740 0.995238i \(-0.468924\pi\)
0.0974740 + 0.995238i \(0.468924\pi\)
\(422\) 4.00000i 0.194717i
\(423\) 8.00000i 0.388973i
\(424\) 6.00000 0.291386
\(425\) −16.0000 + 12.0000i −0.776114 + 0.582086i
\(426\) 0 0
\(427\) 24.0000i 1.16144i
\(428\) 0 0
\(429\) 6.00000 0.289683
\(430\) 0 0
\(431\) −16.0000 −0.770693 −0.385346 0.922772i \(-0.625918\pi\)
−0.385346 + 0.922772i \(0.625918\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 16.0000i 0.768911i 0.923144 + 0.384455i \(0.125611\pi\)
−0.923144 + 0.384455i \(0.874389\pi\)
\(434\) 16.0000 0.768025
\(435\) −10.0000 + 20.0000i −0.479463 + 0.958927i
\(436\) 4.00000 0.191565
\(437\) 12.0000i 0.574038i
\(438\) 2.00000i 0.0955637i
\(439\) 32.0000 1.52728 0.763638 0.645644i \(-0.223411\pi\)
0.763638 + 0.645644i \(0.223411\pi\)
\(440\) 6.00000 12.0000i 0.286039 0.572078i
\(441\) 9.00000 0.428571
\(442\) 4.00000i 0.190261i
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 6.00000 0.284747
\(445\) −28.0000 14.0000i −1.32733 0.663664i
\(446\) 8.00000 0.378811
\(447\) 16.0000i 0.756774i
\(448\) 4.00000i 0.188982i
\(449\) −38.0000 −1.79333 −0.896665 0.442709i \(-0.854018\pi\)
−0.896665 + 0.442709i \(0.854018\pi\)
\(450\) −4.00000 + 3.00000i −0.188562 + 0.141421i
\(451\) −60.0000 −2.82529
\(452\) 4.00000i 0.188144i
\(453\) 16.0000i 0.751746i
\(454\) 4.00000 0.187729
\(455\) −8.00000 4.00000i −0.375046 0.187523i
\(456\) 2.00000 0.0936586
\(457\) 14.0000i 0.654892i −0.944870 0.327446i \(-0.893812\pi\)
0.944870 0.327446i \(-0.106188\pi\)
\(458\) 8.00000i 0.373815i
\(459\) 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 \(0.529693\pi\)
\(462\) 24.0000i 1.11658i
\(463\) 4.00000i 0.185896i 0.995671 + 0.0929479i \(0.0296290\pi\)
−0.995671 + 0.0929479i \(0.970371\pi\)
\(464\) 10.0000 0.464238
\(465\) −4.00000 + 8.00000i −0.185496 + 0.370991i
\(466\) −12.0000 −0.555889
\(467\) 8.00000i 0.370196i −0.982720 0.185098i \(-0.940740\pi\)
0.982720 0.185098i \(-0.0592602\pi\)
\(468\) 1.00000i 0.0462250i
\(469\) −48.0000 −2.21643
\(470\) −16.0000 8.00000i −0.738025 0.369012i
\(471\) 6.00000 0.276465
\(472\) 6.00000i 0.276172i
\(473\) 0 0
\(474\) 8.00000 0.367452
\(475\) −6.00000 8.00000i −0.275299 0.367065i
\(476\) 16.0000 0.733359
\(477\) 6.00000i 0.274721i
\(478\) 4.00000i 0.182956i
\(479\) 20.0000 0.913823 0.456912 0.889512i \(-0.348956\pi\)
0.456912 + 0.889512i \(0.348956\pi\)
\(480\) 2.00000 + 1.00000i 0.0912871 + 0.0456435i
\(481\) −6.00000 −0.273576
\(482\) 18.0000i 0.819878i
\(483\) 24.0000i 1.09204i
\(484\) −25.0000 −1.13636
\(485\) 14.0000 28.0000i 0.635707 1.27141i
\(486\) 1.00000 0.0453609
\(487\) 32.0000i 1.45006i −0.688718 0.725029i \(-0.741826\pi\)
0.688718 0.725029i \(-0.258174\pi\)
\(488\) 6.00000i 0.271607i
\(489\) 4.00000 0.180886
\(490\) −9.00000 + 18.0000i −0.406579 + 0.813157i
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 10.0000i 0.450835i
\(493\) 40.0000i 1.80151i
\(494\) −2.00000 −0.0899843
\(495\) 12.0000 + 6.00000i 0.539360 + 0.269680i
\(496\) 4.00000 0.179605
\(497\) 0 0
\(498\) 4.00000i 0.179244i
\(499\) 18.0000 0.805791 0.402895 0.915246i \(-0.368004\pi\)
0.402895 + 0.915246i \(0.368004\pi\)
\(500\) −2.00000 11.0000i −0.0894427 0.491935i
\(501\) −16.0000 −0.714827
\(502\) 20.0000i 0.892644i
\(503\) 14.0000i 0.624229i −0.950044 0.312115i \(-0.898963\pi\)
0.950044 0.312115i \(-0.101037\pi\)
\(504\) 4.00000 0.178174
\(505\) 20.0000 + 10.0000i 0.889988 + 0.444994i
\(506\) 36.0000 1.60040
\(507\) 1.00000i 0.0444116i
\(508\) 10.0000i 0.443678i
\(509\) −16.0000 −0.709188 −0.354594 0.935020i \(-0.615381\pi\)
−0.354594 + 0.935020i \(0.615381\pi\)
\(510\) −4.00000 + 8.00000i −0.177123 + 0.354246i
\(511\) −8.00000 −0.353899
\(512\) 1.00000i 0.0441942i
\(513\) 2.00000i 0.0883022i
\(514\) −28.0000 −1.23503
\(515\) 2.00000 4.00000i 0.0881305 0.176261i
\(516\) 0 0
\(517\) 48.0000i 2.11104i
\(518\) 24.0000i 1.05450i
\(519\) 22.0000 0.965693
\(520\) −2.00000 1.00000i −0.0877058 0.0438529i
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 10.0000i 0.437688i
\(523\) 16.0000i 0.699631i 0.936819 + 0.349816i \(0.113756\pi\)
−0.936819 + 0.349816i \(0.886244\pi\)
\(524\) 8.00000 0.349482
\(525\) −12.0000 16.0000i −0.523723 0.698297i
\(526\) −10.0000 −0.436021
\(527\) 16.0000i 0.696971i
\(528\) 6.00000i 0.261116i
\(529\) −13.0000 −0.565217
\(530\) −12.0000 6.00000i −0.521247 0.260623i
\(531\) −6.00000 −0.260378
\(532\) 8.00000i 0.346844i
\(533\) 10.0000i 0.433148i
\(534\) −14.0000 −0.605839
\(535\) 0 0
\(536\) −12.0000 −0.518321
\(537\) 24.0000i 1.03568i
\(538\) 10.0000i 0.431131i
\(539\) 54.0000 2.32594
\(540\) −1.00000 + 2.00000i −0.0430331 + 0.0860663i
\(541\) −32.0000 −1.37579 −0.687894 0.725811i \(-0.741464\pi\)
−0.687894 + 0.725811i \(0.741464\pi\)
\(542\) 8.00000i 0.343629i
\(543\) 6.00000i 0.257485i
\(544\) 4.00000 0.171499
\(545\) −8.00000 4.00000i −0.342682 0.171341i
\(546\) −4.00000 −0.171184
\(547\) 36.0000i 1.53925i −0.638497 0.769624i \(-0.720443\pi\)
0.638497 0.769624i \(-0.279557\pi\)
\(548\) 14.0000i 0.598050i
\(549\) 6.00000 0.256074
\(550\) −24.0000 + 18.0000i −1.02336 + 0.767523i
\(551\) −20.0000 −0.852029
\(552\) 6.00000i 0.255377i
\(553\) 32.0000i 1.36078i
\(554\) 14.0000 0.594803
\(555\) −12.0000 6.00000i −0.509372 0.254686i
\(556\) 16.0000 0.678551
\(557\) 18.0000i 0.762684i 0.924434 + 0.381342i \(0.124538\pi\)
−0.924434 + 0.381342i \(0.875462\pi\)
\(558\) 4.00000i 0.169334i
\(559\) 0 0
\(560\) −4.00000 + 8.00000i −0.169031 + 0.338062i
\(561\) 24.0000 1.01328
\(562\) 18.0000i 0.759284i
\(563\) 24.0000i 1.01148i 0.862686 + 0.505740i \(0.168780\pi\)
−0.862686 + 0.505740i \(0.831220\pi\)
\(564\) −8.00000 −0.336861
\(565\) 4.00000 8.00000i 0.168281 0.336563i
\(566\) −12.0000 −0.504398
\(567\) 4.00000i 0.167984i
\(568\) 0 0
\(569\) 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
\(571\) 12.0000 0.502184 0.251092 0.967963i \(-0.419210\pi\)
0.251092 + 0.967963i \(0.419210\pi\)
\(572\) 6.00000i 0.250873i
\(573\) 0 0
\(574\) 40.0000 1.66957
\(575\) 24.0000 18.0000i 1.00087 0.750652i
\(576\) 1.00000 0.0416667
\(577\) 2.00000i 0.0832611i −0.999133 0.0416305i \(-0.986745\pi\)
0.999133 0.0416305i \(-0.0132552\pi\)
\(578\) 1.00000i 0.0415945i
\(579\) 2.00000 0.0831172
\(580\) −20.0000 10.0000i −0.830455 0.415227i
\(581\) 16.0000 0.663792
\(582\) 14.0000i 0.580319i
\(583\) 36.0000i 1.49097i
\(584\) −2.00000 −0.0827606
\(585\) 1.00000 2.00000i 0.0413449 0.0826898i
\(586\) 18.0000 0.743573
\(587\) 28.0000i 1.15568i 0.816149 + 0.577842i \(0.196105\pi\)
−0.816149 + 0.577842i \(0.803895\pi\)
\(588\) 9.00000i 0.371154i
\(589\) −8.00000 −0.329634
\(590\) 6.00000 12.0000i 0.247016 0.494032i
\(591\) −6.00000 −0.246807
\(592\) 6.00000i 0.246598i
\(593\) 14.0000i 0.574911i 0.957794 + 0.287456i \(0.0928094\pi\)
−0.957794 + 0.287456i \(0.907191\pi\)
\(594\) 6.00000 0.246183
\(595\) −32.0000 16.0000i −1.31187 0.655936i
\(596\) 16.0000 0.655386
\(597\) 8.00000i 0.327418i
\(598\) 6.00000i 0.245358i
\(599\) 32.0000 1.30748 0.653742 0.756717i \(-0.273198\pi\)
0.653742 + 0.756717i \(0.273198\pi\)
\(600\) −3.00000 4.00000i −0.122474 0.163299i
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) 0 0
\(603\) 12.0000i 0.488678i
\(604\) −16.0000 −0.651031
\(605\) 50.0000 + 25.0000i 2.03279 + 1.01639i
\(606\) 10.0000 0.406222
\(607\) 42.0000i 1.70473i −0.522949 0.852364i \(-0.675168\pi\)
0.522949 0.852364i \(-0.324832\pi\)
\(608\) 2.00000i 0.0811107i
\(609\) −40.0000 −1.62088
\(610\) −6.00000 + 12.0000i −0.242933 + 0.485866i
\(611\) 8.00000 0.323645
\(612\) 4.00000i 0.161690i
\(613\) 38.0000i 1.53481i −0.641165 0.767403i \(-0.721549\pi\)
0.641165 0.767403i \(-0.278451\pi\)
\(614\) 4.00000 0.161427
\(615\) −10.0000 + 20.0000i −0.403239 + 0.806478i
\(616\) 24.0000 0.966988
\(617\) 18.0000i 0.724653i 0.932051 + 0.362326i \(0.118017\pi\)
−0.932051 + 0.362326i \(0.881983\pi\)
\(618\) 2.00000i 0.0804518i
\(619\) 22.0000 0.884255 0.442127 0.896952i \(-0.354224\pi\)
0.442127 + 0.896952i \(0.354224\pi\)
\(620\) −8.00000 4.00000i −0.321288 0.160644i
\(621\) −6.00000 −0.240772
\(622\) 8.00000i 0.320771i
\(623\) 56.0000i 2.24359i
\(624\) −1.00000 −0.0400320
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) −8.00000 −0.319744
\(627\) 12.0000i 0.479234i
\(628\) 6.00000i 0.239426i
\(629\) −24.0000 −0.956943
\(630\) −8.00000 4.00000i −0.318728 0.159364i
\(631\) 40.0000 1.59237 0.796187 0.605050i \(-0.206847\pi\)
0.796187 + 0.605050i \(0.206847\pi\)
\(632\) 8.00000i 0.318223i
\(633\) 4.00000i 0.158986i
\(634\) −2.00000 −0.0794301
\(635\) −10.0000 + 20.0000i −0.396838 + 0.793676i
\(636\) −6.00000 −0.237915
\(637\) 9.00000i 0.356593i
\(638\) 60.0000i 2.37542i
\(639\) 0 0
\(640\) −1.00000 + 2.00000i −0.0395285 + 0.0790569i
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) 0 0
\(643\) 20.0000i 0.788723i −0.918955 0.394362i \(-0.870966\pi\)
0.918955 0.394362i \(-0.129034\pi\)
\(644\) −24.0000 −0.945732
\(645\) 0 0
\(646\) −8.00000 −0.314756
\(647\) 6.00000i 0.235884i 0.993020 + 0.117942i \(0.0376297\pi\)
−0.993020 + 0.117942i \(0.962370\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −36.0000 −1.41312
\(650\) 3.00000 + 4.00000i 0.117670 + 0.156893i
\(651\) −16.0000 −0.627089
\(652\) 4.00000i 0.156652i
\(653\) 10.0000i 0.391330i −0.980671 0.195665i \(-0.937313\pi\)
0.980671 0.195665i \(-0.0626866\pi\)
\(654\) −4.00000 −0.156412
\(655\) −16.0000 8.00000i −0.625172 0.312586i
\(656\) 10.0000 0.390434
\(657\) 2.00000i 0.0780274i
\(658\) 32.0000i 1.24749i
\(659\) 32.0000 1.24654 0.623272 0.782006i \(-0.285803\pi\)
0.623272 + 0.782006i \(0.285803\pi\)
\(660\) −6.00000 + 12.0000i −0.233550 + 0.467099i
\(661\) −32.0000 −1.24466 −0.622328 0.782757i \(-0.713813\pi\)
−0.622328 + 0.782757i \(0.713813\pi\)
\(662\) 2.00000i 0.0777322i
\(663\) 4.00000i 0.155347i
\(664\) 4.00000 0.155230
\(665\) 8.00000 16.0000i 0.310227 0.620453i
\(666\) −6.00000 −0.232495
\(667\) 60.0000i 2.32321i
\(668\) 16.0000i 0.619059i
\(669\) −8.00000 −0.309298
\(670\) 24.0000 + 12.0000i 0.927201 + 0.463600i
\(671\) 36.0000 1.38976
\(672\) 4.00000i 0.154303i
\(673\) 44.0000i 1.69608i 0.529936 + 0.848038i \(0.322216\pi\)
−0.529936 + 0.848038i \(0.677784\pi\)
\(674\) −16.0000 −0.616297
\(675\) 4.00000 3.00000i 0.153960 0.115470i
\(676\) 1.00000 0.0384615
\(677\) 6.00000i 0.230599i −0.993331 0.115299i \(-0.963217\pi\)
0.993331 0.115299i \(-0.0367827\pi\)
\(678\) 4.00000i 0.153619i
\(679\) 56.0000 2.14908
\(680\) −8.00000 4.00000i −0.306786 0.153393i
\(681\) −4.00000 −0.153280
\(682\) 24.0000i 0.919007i
\(683\) 20.0000i 0.765279i −0.923898 0.382639i \(-0.875015\pi\)
0.923898 0.382639i \(-0.124985\pi\)
\(684\) −2.00000 −0.0764719
\(685\) −14.0000 + 28.0000i −0.534913 + 1.06983i
\(686\) −8.00000 −0.305441
\(687\) 8.00000i 0.305219i
\(688\) 0 0
\(689\) 6.00000 0.228582
\(690\) 6.00000 12.0000i 0.228416 0.456832i
\(691\) 18.0000 0.684752 0.342376 0.939563i \(-0.388768\pi\)
0.342376 + 0.939563i \(0.388768\pi\)
\(692\) 22.0000i 0.836315i
\(693\) 24.0000i 0.911685i
\(694\) −16.0000 −0.607352
\(695\) −32.0000 16.0000i −1.21383 0.606915i
\(696\) −10.0000 −0.379049
\(697\) 40.0000i 1.51511i
\(698\) 4.00000i 0.151402i
\(699\) 12.0000 0.453882
\(700\) 16.0000 12.0000i 0.604743 0.453557i
\(701\) −6.00000 −0.226617 −0.113308 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(702\) 1.00000i 0.0377426i
\(703\) 12.0000i 0.452589i
\(704\) 6.00000 0.226134
\(705\) 16.0000 + 8.00000i 0.602595 + 0.301297i
\(706\) −26.0000 −0.978523
\(707\) 40.0000i 1.50435i
\(708\) 6.00000i 0.225494i
\(709\) 8.00000 0.300446 0.150223 0.988652i \(-0.452001\pi\)
0.150223 + 0.988652i \(0.452001\pi\)
\(710\) 0 0
\(711\) −8.00000 −0.300023
\(712\) 14.0000i 0.524672i
\(713\) 24.0000i 0.898807i
\(714\) −16.0000 −0.598785
\(715\) 6.00000 12.0000i 0.224387 0.448775i
\(716\) −24.0000 −0.896922
\(717\) 4.00000i 0.149383i
\(718\) 20.0000i 0.746393i
\(719\) −8.00000 −0.298350 −0.149175 0.988811i \(-0.547662\pi\)
−0.149175 + 0.988811i \(0.547662\pi\)
\(720\) −2.00000 1.00000i −0.0745356 0.0372678i
\(721\) 8.00000 0.297936
\(722\) 15.0000i 0.558242i
\(723\) 18.0000i 0.669427i
\(724\) −6.00000 −0.222988
\(725\) 30.0000 + 40.0000i 1.11417 + 1.48556i
\(726\) 25.0000 0.927837
\(727\) 38.0000i 1.40934i −0.709534 0.704671i \(-0.751095\pi\)
0.709534 0.704671i \(-0.248905\pi\)
\(728\) 4.00000i 0.148250i
\(729\) −1.00000 −0.0370370
\(730\) 4.00000 + 2.00000i 0.148047 + 0.0740233i
\(731\) 0 0
\(732\) 6.00000i 0.221766i
\(733\) 18.0000i 0.664845i −0.943131 0.332423i \(-0.892134\pi\)
0.943131 0.332423i \(-0.107866\pi\)
\(734\) 18.0000 0.664392
\(735\) 9.00000 18.0000i 0.331970 0.663940i
\(736\) −6.00000 −0.221163
\(737\) 72.0000i 2.65215i
\(738\) 10.0000i 0.368105i
\(739\) 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
\(742\) 24.0000i 0.881068i
\(743\) 36.0000i 1.32071i −0.750953 0.660356i \(-0.770405\pi\)
0.750953 0.660356i \(-0.229595\pi\)
\(744\) −4.00000 −0.146647
\(745\) −32.0000 16.0000i −1.17239 0.586195i
\(746\) −18.0000 −0.659027
\(747\) 4.00000i 0.146352i
\(748\) 24.0000i 0.877527i
\(749\) 0 0
\(750\) 2.00000 + 11.0000i 0.0730297 + 0.401663i
\(751\) −48.0000 −1.75154 −0.875772 0.482724i \(-0.839647\pi\)
−0.875772 + 0.482724i \(0.839647\pi\)
\(752\) 8.00000i 0.291730i
\(753\) 20.0000i 0.728841i
\(754\) 10.0000 0.364179
\(755\) 32.0000 + 16.0000i 1.16460 + 0.582300i
\(756\) −4.00000 −0.145479
\(757\) 22.0000i 0.799604i 0.916602 + 0.399802i \(0.130921\pi\)
−0.916602 + 0.399802i \(0.869079\pi\)
\(758\) 10.0000i 0.363216i
\(759\) −36.0000 −1.30672
\(760\) 2.00000 4.00000i 0.0725476 0.145095i
\(761\) 30.0000 1.08750 0.543750 0.839248i \(-0.317004\pi\)
0.543750 + 0.839248i \(0.317004\pi\)
\(762\) 10.0000i 0.362262i
\(763\) 16.0000i 0.579239i
\(764\) 0 0
\(765\) 4.00000 8.00000i 0.144620 0.289241i
\(766\) 20.0000 0.722629
\(767\) 6.00000i 0.216647i
\(768\) 1.00000i 0.0360844i
\(769\) −10.0000 −0.360609 −0.180305 0.983611i \(-0.557708\pi\)
−0.180305 + 0.983611i \(0.557708\pi\)
\(770\) −48.0000 24.0000i −1.72980 0.864900i
\(771\) 28.0000 1.00840
\(772\) 2.00000i 0.0719816i
\(773\) 18.0000i 0.647415i −0.946157 0.323708i \(-0.895071\pi\)
0.946157 0.323708i \(-0.104929\pi\)
\(774\) 0 0
\(775\) 12.0000 + 16.0000i 0.431053 + 0.574737i
\(776\) 14.0000 0.502571
\(777\) 24.0000i 0.860995i
\(778\) 30.0000i 1.07555i
\(779\) −20.0000 −0.716574
\(780\) 2.00000 + 1.00000i 0.0716115 + 0.0358057i
\(781\) 0 0
\(782\) 24.0000i 0.858238i
\(783\) 10.0000i 0.357371i
\(784\) −9.00000 −0.321429
\(785\) 6.00000 12.0000i 0.214149 0.428298i
\(786\) −8.00000 −0.285351
\(787\) 12.0000i