Properties

Label 210.2.g.a.169.1
Level $210$
Weight $2$
Character 210.169
Analytic conductor $1.677$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.67685844245\)
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 169.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 210.169
Dual form 210.2.g.a.169.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(-2.00000 + 1.00000i) q^{10} -2.00000 q^{11} +1.00000i q^{12} +2.00000i q^{13} -1.00000 q^{14} +(-2.00000 + 1.00000i) q^{15} +1.00000 q^{16} -8.00000i q^{17} +1.00000i q^{18} +2.00000 q^{19} +(1.00000 + 2.00000i) q^{20} -1.00000 q^{21} +2.00000i q^{22} +1.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} +2.00000 q^{26} +1.00000i q^{27} +1.00000i q^{28} +6.00000 q^{29} +(1.00000 + 2.00000i) q^{30} +6.00000 q^{31} -1.00000i q^{32} +2.00000i q^{33} -8.00000 q^{34} +(-2.00000 + 1.00000i) q^{35} +1.00000 q^{36} -8.00000i q^{37} -2.00000i q^{38} +2.00000 q^{39} +(2.00000 - 1.00000i) q^{40} +6.00000 q^{41} +1.00000i q^{42} +8.00000i q^{43} +2.00000 q^{44} +(1.00000 + 2.00000i) q^{45} -4.00000i q^{47} -1.00000i q^{48} -1.00000 q^{49} +(4.00000 + 3.00000i) q^{50} -8.00000 q^{51} -2.00000i q^{52} -2.00000i q^{53} +1.00000 q^{54} +(2.00000 + 4.00000i) q^{55} +1.00000 q^{56} -2.00000i q^{57} -6.00000i q^{58} +8.00000 q^{59} +(2.00000 - 1.00000i) q^{60} +10.0000 q^{61} -6.00000i q^{62} +1.00000i q^{63} -1.00000 q^{64} +(4.00000 - 2.00000i) q^{65} +2.00000 q^{66} +12.0000i q^{67} +8.00000i q^{68} +(1.00000 + 2.00000i) q^{70} -14.0000 q^{71} -1.00000i q^{72} -10.0000i q^{73} -8.00000 q^{74} +(4.00000 + 3.00000i) q^{75} -2.00000 q^{76} +2.00000i q^{77} -2.00000i q^{78} -4.00000 q^{79} +(-1.00000 - 2.00000i) q^{80} +1.00000 q^{81} -6.00000i q^{82} +16.0000i q^{83} +1.00000 q^{84} +(-16.0000 + 8.00000i) q^{85} +8.00000 q^{86} -6.00000i q^{87} -2.00000i q^{88} -10.0000 q^{89} +(2.00000 - 1.00000i) q^{90} +2.00000 q^{91} -6.00000i q^{93} -4.00000 q^{94} +(-2.00000 - 4.00000i) q^{95} -1.00000 q^{96} -10.0000i q^{97} +1.00000i q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{9} - 4 q^{10} - 4 q^{11} - 2 q^{14} - 4 q^{15} + 2 q^{16} + 4 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{24} - 6 q^{25} + 4 q^{26} + 12 q^{29} + 2 q^{30} + 12 q^{31} - 16 q^{34} - 4 q^{35} + 2 q^{36} + 4 q^{39} + 4 q^{40} + 12 q^{41} + 4 q^{44} + 2 q^{45} - 2 q^{49} + 8 q^{50} - 16 q^{51} + 2 q^{54} + 4 q^{55} + 2 q^{56} + 16 q^{59} + 4 q^{60} + 20 q^{61} - 2 q^{64} + 8 q^{65} + 4 q^{66} + 2 q^{70} - 28 q^{71} - 16 q^{74} + 8 q^{75} - 4 q^{76} - 8 q^{79} - 2 q^{80} + 2 q^{81} + 2 q^{84} - 32 q^{85} + 16 q^{86} - 20 q^{89} + 4 q^{90} + 4 q^{91} - 8 q^{94} - 4 q^{95} - 2 q^{96} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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
\(5\) −1.00000 2.00000i −0.447214 0.894427i
\(6\) −1.00000 −0.408248
\(7\) 1.00000i 0.377964i
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) −2.00000 + 1.00000i −0.632456 + 0.316228i
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 2.00000i 0.554700i 0.960769 + 0.277350i \(0.0894562\pi\)
−0.960769 + 0.277350i \(0.910544\pi\)
\(14\) −1.00000 −0.267261
\(15\) −2.00000 + 1.00000i −0.516398 + 0.258199i
\(16\) 1.00000 0.250000
\(17\) 8.00000i 1.94029i −0.242536 0.970143i \(-0.577979\pi\)
0.242536 0.970143i \(-0.422021\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) 1.00000 + 2.00000i 0.223607 + 0.447214i
\(21\) −1.00000 −0.218218
\(22\) 2.00000i 0.426401i
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 1.00000 0.204124
\(25\) −3.00000 + 4.00000i −0.600000 + 0.800000i
\(26\) 2.00000 0.392232
\(27\) 1.00000i 0.192450i
\(28\) 1.00000i 0.188982i
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 1.00000 + 2.00000i 0.182574 + 0.365148i
\(31\) 6.00000 1.07763 0.538816 0.842424i \(-0.318872\pi\)
0.538816 + 0.842424i \(0.318872\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.00000i 0.348155i
\(34\) −8.00000 −1.37199
\(35\) −2.00000 + 1.00000i −0.338062 + 0.169031i
\(36\) 1.00000 0.166667
\(37\) 8.00000i 1.31519i −0.753371 0.657596i \(-0.771573\pi\)
0.753371 0.657596i \(-0.228427\pi\)
\(38\) 2.00000i 0.324443i
\(39\) 2.00000 0.320256
\(40\) 2.00000 1.00000i 0.316228 0.158114i
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 1.00000i 0.154303i
\(43\) 8.00000i 1.21999i 0.792406 + 0.609994i \(0.208828\pi\)
−0.792406 + 0.609994i \(0.791172\pi\)
\(44\) 2.00000 0.301511
\(45\) 1.00000 + 2.00000i 0.149071 + 0.298142i
\(46\) 0 0
\(47\) 4.00000i 0.583460i −0.956501 0.291730i \(-0.905769\pi\)
0.956501 0.291730i \(-0.0942309\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −1.00000 −0.142857
\(50\) 4.00000 + 3.00000i 0.565685 + 0.424264i
\(51\) −8.00000 −1.12022
\(52\) 2.00000i 0.277350i
\(53\) 2.00000i 0.274721i −0.990521 0.137361i \(-0.956138\pi\)
0.990521 0.137361i \(-0.0438619\pi\)
\(54\) 1.00000 0.136083
\(55\) 2.00000 + 4.00000i 0.269680 + 0.539360i
\(56\) 1.00000 0.133631
\(57\) 2.00000i 0.264906i
\(58\) 6.00000i 0.787839i
\(59\) 8.00000 1.04151 0.520756 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) 2.00000 1.00000i 0.258199 0.129099i
\(61\) 10.0000 1.28037 0.640184 0.768221i \(-0.278858\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) 6.00000i 0.762001i
\(63\) 1.00000i 0.125988i
\(64\) −1.00000 −0.125000
\(65\) 4.00000 2.00000i 0.496139 0.248069i
\(66\) 2.00000 0.246183
\(67\) 12.0000i 1.46603i 0.680211 + 0.733017i \(0.261888\pi\)
−0.680211 + 0.733017i \(0.738112\pi\)
\(68\) 8.00000i 0.970143i
\(69\) 0 0
\(70\) 1.00000 + 2.00000i 0.119523 + 0.239046i
\(71\) −14.0000 −1.66149 −0.830747 0.556650i \(-0.812086\pi\)
−0.830747 + 0.556650i \(0.812086\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 10.0000i 1.17041i −0.810885 0.585206i \(-0.801014\pi\)
0.810885 0.585206i \(-0.198986\pi\)
\(74\) −8.00000 −0.929981
\(75\) 4.00000 + 3.00000i 0.461880 + 0.346410i
\(76\) −2.00000 −0.229416
\(77\) 2.00000i 0.227921i
\(78\) 2.00000i 0.226455i
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) −1.00000 2.00000i −0.111803 0.223607i
\(81\) 1.00000 0.111111
\(82\) 6.00000i 0.662589i
\(83\) 16.0000i 1.75623i 0.478451 + 0.878114i \(0.341198\pi\)
−0.478451 + 0.878114i \(0.658802\pi\)
\(84\) 1.00000 0.109109
\(85\) −16.0000 + 8.00000i −1.73544 + 0.867722i
\(86\) 8.00000 0.862662
\(87\) 6.00000i 0.643268i
\(88\) 2.00000i 0.213201i
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 2.00000 1.00000i 0.210819 0.105409i
\(91\) 2.00000 0.209657
\(92\) 0 0
\(93\) 6.00000i 0.622171i
\(94\) −4.00000 −0.412568
\(95\) −2.00000 4.00000i −0.205196 0.410391i
\(96\) −1.00000 −0.102062
\(97\) 10.0000i 1.01535i −0.861550 0.507673i \(-0.830506\pi\)
0.861550 0.507673i \(-0.169494\pi\)
\(98\) 1.00000i 0.101015i
\(99\) 2.00000 0.201008
\(100\) 3.00000 4.00000i 0.300000 0.400000i
\(101\) −10.0000 −0.995037 −0.497519 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 8.00000i 0.792118i
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) −2.00000 −0.196116
\(105\) 1.00000 + 2.00000i 0.0975900 + 0.195180i
\(106\) −2.00000 −0.194257
\(107\) 12.0000i 1.16008i 0.814587 + 0.580042i \(0.196964\pi\)
−0.814587 + 0.580042i \(0.803036\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 6.00000 0.574696 0.287348 0.957826i \(-0.407226\pi\)
0.287348 + 0.957826i \(0.407226\pi\)
\(110\) 4.00000 2.00000i 0.381385 0.190693i
\(111\) −8.00000 −0.759326
\(112\) 1.00000i 0.0944911i
\(113\) 6.00000i 0.564433i 0.959351 + 0.282216i \(0.0910696\pi\)
−0.959351 + 0.282216i \(0.908930\pi\)
\(114\) −2.00000 −0.187317
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) 2.00000i 0.184900i
\(118\) 8.00000i 0.736460i
\(119\) −8.00000 −0.733359
\(120\) −1.00000 2.00000i −0.0912871 0.182574i
\(121\) −7.00000 −0.636364
\(122\) 10.0000i 0.905357i
\(123\) 6.00000i 0.541002i
\(124\) −6.00000 −0.538816
\(125\) 11.0000 + 2.00000i 0.983870 + 0.178885i
\(126\) 1.00000 0.0890871
\(127\) 12.0000i 1.06483i −0.846484 0.532414i \(-0.821285\pi\)
0.846484 0.532414i \(-0.178715\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 8.00000 0.704361
\(130\) −2.00000 4.00000i −0.175412 0.350823i
\(131\) −20.0000 −1.74741 −0.873704 0.486458i \(-0.838289\pi\)
−0.873704 + 0.486458i \(0.838289\pi\)
\(132\) 2.00000i 0.174078i
\(133\) 2.00000i 0.173422i
\(134\) 12.0000 1.03664
\(135\) 2.00000 1.00000i 0.172133 0.0860663i
\(136\) 8.00000 0.685994
\(137\) 14.0000i 1.19610i 0.801459 + 0.598050i \(0.204058\pi\)
−0.801459 + 0.598050i \(0.795942\pi\)
\(138\) 0 0
\(139\) 2.00000 0.169638 0.0848189 0.996396i \(-0.472969\pi\)
0.0848189 + 0.996396i \(0.472969\pi\)
\(140\) 2.00000 1.00000i 0.169031 0.0845154i
\(141\) −4.00000 −0.336861
\(142\) 14.0000i 1.17485i
\(143\) 4.00000i 0.334497i
\(144\) −1.00000 −0.0833333
\(145\) −6.00000 12.0000i −0.498273 0.996546i
\(146\) −10.0000 −0.827606
\(147\) 1.00000i 0.0824786i
\(148\) 8.00000i 0.657596i
\(149\) 18.0000 1.47462 0.737309 0.675556i \(-0.236096\pi\)
0.737309 + 0.675556i \(0.236096\pi\)
\(150\) 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
\(153\) 8.00000i 0.646762i
\(154\) 2.00000 0.161165
\(155\) −6.00000 12.0000i −0.481932 0.963863i
\(156\) −2.00000 −0.160128
\(157\) 10.0000i 0.798087i 0.916932 + 0.399043i \(0.130658\pi\)
−0.916932 + 0.399043i \(0.869342\pi\)
\(158\) 4.00000i 0.318223i
\(159\) −2.00000 −0.158610
\(160\) −2.00000 + 1.00000i −0.158114 + 0.0790569i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) −6.00000 −0.468521
\(165\) 4.00000 2.00000i 0.311400 0.155700i
\(166\) 16.0000 1.24184
\(167\) 8.00000i 0.619059i 0.950890 + 0.309529i \(0.100171\pi\)
−0.950890 + 0.309529i \(0.899829\pi\)
\(168\) 1.00000i 0.0771517i
\(169\) 9.00000 0.692308
\(170\) 8.00000 + 16.0000i 0.613572 + 1.22714i
\(171\) −2.00000 −0.152944
\(172\) 8.00000i 0.609994i
\(173\) 16.0000i 1.21646i −0.793762 0.608229i \(-0.791880\pi\)
0.793762 0.608229i \(-0.208120\pi\)
\(174\) −6.00000 −0.454859
\(175\) 4.00000 + 3.00000i 0.302372 + 0.226779i
\(176\) −2.00000 −0.150756
\(177\) 8.00000i 0.601317i
\(178\) 10.0000i 0.749532i
\(179\) 2.00000 0.149487 0.0747435 0.997203i \(-0.476186\pi\)
0.0747435 + 0.997203i \(0.476186\pi\)
\(180\) −1.00000 2.00000i −0.0745356 0.149071i
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) 2.00000i 0.148250i
\(183\) 10.0000i 0.739221i
\(184\) 0 0
\(185\) −16.0000 + 8.00000i −1.17634 + 0.588172i
\(186\) −6.00000 −0.439941
\(187\) 16.0000i 1.17004i
\(188\) 4.00000i 0.291730i
\(189\) 1.00000 0.0727393
\(190\) −4.00000 + 2.00000i −0.290191 + 0.145095i
\(191\) 14.0000 1.01300 0.506502 0.862239i \(-0.330938\pi\)
0.506502 + 0.862239i \(0.330938\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) −10.0000 −0.717958
\(195\) −2.00000 4.00000i −0.143223 0.286446i
\(196\) 1.00000 0.0714286
\(197\) 6.00000i 0.427482i 0.976890 + 0.213741i \(0.0685649\pi\)
−0.976890 + 0.213741i \(0.931435\pi\)
\(198\) 2.00000i 0.142134i
\(199\) 26.0000 1.84309 0.921546 0.388270i \(-0.126927\pi\)
0.921546 + 0.388270i \(0.126927\pi\)
\(200\) −4.00000 3.00000i −0.282843 0.212132i
\(201\) 12.0000 0.846415
\(202\) 10.0000i 0.703598i
\(203\) 6.00000i 0.421117i
\(204\) 8.00000 0.560112
\(205\) −6.00000 12.0000i −0.419058 0.838116i
\(206\) 0 0
\(207\) 0 0
\(208\) 2.00000i 0.138675i
\(209\) −4.00000 −0.276686
\(210\) 2.00000 1.00000i 0.138013 0.0690066i
\(211\) −8.00000 −0.550743 −0.275371 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) 2.00000i 0.137361i
\(213\) 14.0000i 0.959264i
\(214\) 12.0000 0.820303
\(215\) 16.0000 8.00000i 1.09119 0.545595i
\(216\) −1.00000 −0.0680414
\(217\) 6.00000i 0.407307i
\(218\) 6.00000i 0.406371i
\(219\) −10.0000 −0.675737
\(220\) −2.00000 4.00000i −0.134840 0.269680i
\(221\) 16.0000 1.07628
\(222\) 8.00000i 0.536925i
\(223\) 16.0000i 1.07144i −0.844396 0.535720i \(-0.820040\pi\)
0.844396 0.535720i \(-0.179960\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 3.00000 4.00000i 0.200000 0.266667i
\(226\) 6.00000 0.399114
\(227\) 8.00000i 0.530979i 0.964114 + 0.265489i \(0.0855335\pi\)
−0.964114 + 0.265489i \(0.914466\pi\)
\(228\) 2.00000i 0.132453i
\(229\) −26.0000 −1.71813 −0.859064 0.511868i \(-0.828954\pi\)
−0.859064 + 0.511868i \(0.828954\pi\)
\(230\) 0 0
\(231\) 2.00000 0.131590
\(232\) 6.00000i 0.393919i
\(233\) 6.00000i 0.393073i 0.980497 + 0.196537i \(0.0629694\pi\)
−0.980497 + 0.196537i \(0.937031\pi\)
\(234\) −2.00000 −0.130744
\(235\) −8.00000 + 4.00000i −0.521862 + 0.260931i
\(236\) −8.00000 −0.520756
\(237\) 4.00000i 0.259828i
\(238\) 8.00000i 0.518563i
\(239\) 22.0000 1.42306 0.711531 0.702655i \(-0.248002\pi\)
0.711531 + 0.702655i \(0.248002\pi\)
\(240\) −2.00000 + 1.00000i −0.129099 + 0.0645497i
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) 7.00000i 0.449977i
\(243\) 1.00000i 0.0641500i
\(244\) −10.0000 −0.640184
\(245\) 1.00000 + 2.00000i 0.0638877 + 0.127775i
\(246\) −6.00000 −0.382546
\(247\) 4.00000i 0.254514i
\(248\) 6.00000i 0.381000i
\(249\) 16.0000 1.01396
\(250\) 2.00000 11.0000i 0.126491 0.695701i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 1.00000i 0.0629941i
\(253\) 0 0
\(254\) −12.0000 −0.752947
\(255\) 8.00000 + 16.0000i 0.500979 + 1.00196i
\(256\) 1.00000 0.0625000
\(257\) 20.0000i 1.24757i 0.781598 + 0.623783i \(0.214405\pi\)
−0.781598 + 0.623783i \(0.785595\pi\)
\(258\) 8.00000i 0.498058i
\(259\) −8.00000 −0.497096
\(260\) −4.00000 + 2.00000i −0.248069 + 0.124035i
\(261\) −6.00000 −0.371391
\(262\) 20.0000i 1.23560i
\(263\) 24.0000i 1.47990i −0.672660 0.739952i \(-0.734848\pi\)
0.672660 0.739952i \(-0.265152\pi\)
\(264\) −2.00000 −0.123091
\(265\) −4.00000 + 2.00000i −0.245718 + 0.122859i
\(266\) −2.00000 −0.122628
\(267\) 10.0000i 0.611990i
\(268\) 12.0000i 0.733017i
\(269\) −14.0000 −0.853595 −0.426798 0.904347i \(-0.640358\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) −1.00000 2.00000i −0.0608581 0.121716i
\(271\) 2.00000 0.121491 0.0607457 0.998153i \(-0.480652\pi\)
0.0607457 + 0.998153i \(0.480652\pi\)
\(272\) 8.00000i 0.485071i
\(273\) 2.00000i 0.121046i
\(274\) 14.0000 0.845771
\(275\) 6.00000 8.00000i 0.361814 0.482418i
\(276\) 0 0
\(277\) 8.00000i 0.480673i 0.970690 + 0.240337i \(0.0772579\pi\)
−0.970690 + 0.240337i \(0.922742\pi\)
\(278\) 2.00000i 0.119952i
\(279\) −6.00000 −0.359211
\(280\) −1.00000 2.00000i −0.0597614 0.119523i
\(281\) 22.0000 1.31241 0.656205 0.754583i \(-0.272161\pi\)
0.656205 + 0.754583i \(0.272161\pi\)
\(282\) 4.00000i 0.238197i
\(283\) 4.00000i 0.237775i 0.992908 + 0.118888i \(0.0379328\pi\)
−0.992908 + 0.118888i \(0.962067\pi\)
\(284\) 14.0000 0.830747
\(285\) −4.00000 + 2.00000i −0.236940 + 0.118470i
\(286\) −4.00000 −0.236525
\(287\) 6.00000i 0.354169i
\(288\) 1.00000i 0.0589256i
\(289\) −47.0000 −2.76471
\(290\) −12.0000 + 6.00000i −0.704664 + 0.352332i
\(291\) −10.0000 −0.586210
\(292\) 10.0000i 0.585206i
\(293\) 16.0000i 0.934730i −0.884064 0.467365i \(-0.845203\pi\)
0.884064 0.467365i \(-0.154797\pi\)
\(294\) 1.00000 0.0583212
\(295\) −8.00000 16.0000i −0.465778 0.931556i
\(296\) 8.00000 0.464991
\(297\) 2.00000i 0.116052i
\(298\) 18.0000i 1.04271i
\(299\) 0 0
\(300\) −4.00000 3.00000i −0.230940 0.173205i
\(301\) 8.00000 0.461112
\(302\) 8.00000i 0.460348i
\(303\) 10.0000i 0.574485i
\(304\) 2.00000 0.114708
\(305\) −10.0000 20.0000i −0.572598 1.14520i
\(306\) 8.00000 0.457330
\(307\) 28.0000i 1.59804i −0.601302 0.799022i \(-0.705351\pi\)
0.601302 0.799022i \(-0.294649\pi\)
\(308\) 2.00000i 0.113961i
\(309\) 0 0
\(310\) −12.0000 + 6.00000i −0.681554 + 0.340777i
\(311\) −8.00000 −0.453638 −0.226819 0.973937i \(-0.572833\pi\)
−0.226819 + 0.973937i \(0.572833\pi\)
\(312\) 2.00000i 0.113228i
\(313\) 10.0000i 0.565233i 0.959233 + 0.282617i \(0.0912024\pi\)
−0.959233 + 0.282617i \(0.908798\pi\)
\(314\) 10.0000 0.564333
\(315\) 2.00000 1.00000i 0.112687 0.0563436i
\(316\) 4.00000 0.225018
\(317\) 2.00000i 0.112331i 0.998421 + 0.0561656i \(0.0178875\pi\)
−0.998421 + 0.0561656i \(0.982113\pi\)
\(318\) 2.00000i 0.112154i
\(319\) −12.0000 −0.671871
\(320\) 1.00000 + 2.00000i 0.0559017 + 0.111803i
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) 16.0000i 0.890264i
\(324\) −1.00000 −0.0555556
\(325\) −8.00000 6.00000i −0.443760 0.332820i
\(326\) 0 0
\(327\) 6.00000i 0.331801i
\(328\) 6.00000i 0.331295i
\(329\) −4.00000 −0.220527
\(330\) −2.00000 4.00000i −0.110096 0.220193i
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 16.0000i 0.878114i
\(333\) 8.00000i 0.438397i
\(334\) 8.00000 0.437741
\(335\) 24.0000 12.0000i 1.31126 0.655630i
\(336\) −1.00000 −0.0545545
\(337\) 32.0000i 1.74315i −0.490261 0.871576i \(-0.663099\pi\)
0.490261 0.871576i \(-0.336901\pi\)
\(338\) 9.00000i 0.489535i
\(339\) 6.00000 0.325875
\(340\) 16.0000 8.00000i 0.867722 0.433861i
\(341\) −12.0000 −0.649836
\(342\) 2.00000i 0.108148i
\(343\) 1.00000i 0.0539949i
\(344\) −8.00000 −0.431331
\(345\) 0 0
\(346\) −16.0000 −0.860165
\(347\) 4.00000i 0.214731i −0.994220 0.107366i \(-0.965758\pi\)
0.994220 0.107366i \(-0.0342415\pi\)
\(348\) 6.00000i 0.321634i
\(349\) −18.0000 −0.963518 −0.481759 0.876304i \(-0.660002\pi\)
−0.481759 + 0.876304i \(0.660002\pi\)
\(350\) 3.00000 4.00000i 0.160357 0.213809i
\(351\) −2.00000 −0.106752
\(352\) 2.00000i 0.106600i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) −8.00000 −0.425195
\(355\) 14.0000 + 28.0000i 0.743043 + 1.48609i
\(356\) 10.0000 0.529999
\(357\) 8.00000i 0.423405i
\(358\) 2.00000i 0.105703i
\(359\) −14.0000 −0.738892 −0.369446 0.929252i \(-0.620452\pi\)
−0.369446 + 0.929252i \(0.620452\pi\)
\(360\) −2.00000 + 1.00000i −0.105409 + 0.0527046i
\(361\) −15.0000 −0.789474
\(362\) 22.0000i 1.15629i
\(363\) 7.00000i 0.367405i
\(364\) −2.00000 −0.104828
\(365\) −20.0000 + 10.0000i −1.04685 + 0.523424i
\(366\) −10.0000 −0.522708
\(367\) 32.0000i 1.67039i 0.549957 + 0.835193i \(0.314644\pi\)
−0.549957 + 0.835193i \(0.685356\pi\)
\(368\) 0 0
\(369\) −6.00000 −0.312348
\(370\) 8.00000 + 16.0000i 0.415900 + 0.831800i
\(371\) −2.00000 −0.103835
\(372\) 6.00000i 0.311086i
\(373\) 36.0000i 1.86401i 0.362446 + 0.932005i \(0.381942\pi\)
−0.362446 + 0.932005i \(0.618058\pi\)
\(374\) 16.0000 0.827340
\(375\) 2.00000 11.0000i 0.103280 0.568038i
\(376\) 4.00000 0.206284
\(377\) 12.0000i 0.618031i
\(378\) 1.00000i 0.0514344i
\(379\) 28.0000 1.43826 0.719132 0.694874i \(-0.244540\pi\)
0.719132 + 0.694874i \(0.244540\pi\)
\(380\) 2.00000 + 4.00000i 0.102598 + 0.205196i
\(381\) −12.0000 −0.614779
\(382\) 14.0000i 0.716302i
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 1.00000 0.0510310
\(385\) 4.00000 2.00000i 0.203859 0.101929i
\(386\) 0 0
\(387\) 8.00000i 0.406663i
\(388\) 10.0000i 0.507673i
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) −4.00000 + 2.00000i −0.202548 + 0.101274i
\(391\) 0 0
\(392\) 1.00000i 0.0505076i
\(393\) 20.0000i 1.00887i
\(394\) 6.00000 0.302276
\(395\) 4.00000 + 8.00000i 0.201262 + 0.402524i
\(396\) −2.00000 −0.100504
\(397\) 2.00000i 0.100377i −0.998740 0.0501886i \(-0.984018\pi\)
0.998740 0.0501886i \(-0.0159822\pi\)
\(398\) 26.0000i 1.30326i
\(399\) −2.00000 −0.100125
\(400\) −3.00000 + 4.00000i −0.150000 + 0.200000i
\(401\) 18.0000 0.898877 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) 12.0000i 0.598506i
\(403\) 12.0000i 0.597763i
\(404\) 10.0000 0.497519
\(405\) −1.00000 2.00000i −0.0496904 0.0993808i
\(406\) −6.00000 −0.297775
\(407\) 16.0000i 0.793091i
\(408\) 8.00000i 0.396059i
\(409\) −10.0000 −0.494468 −0.247234 0.968956i \(-0.579522\pi\)
−0.247234 + 0.968956i \(0.579522\pi\)
\(410\) −12.0000 + 6.00000i −0.592638 + 0.296319i
\(411\) 14.0000 0.690569
\(412\) 0 0
\(413\) 8.00000i 0.393654i
\(414\) 0 0
\(415\) 32.0000 16.0000i 1.57082 0.785409i
\(416\) 2.00000 0.0980581
\(417\) 2.00000i 0.0979404i
\(418\) 4.00000i 0.195646i
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) −1.00000 2.00000i −0.0487950 0.0975900i
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 8.00000i 0.389434i
\(423\) 4.00000i 0.194487i
\(424\) 2.00000 0.0971286
\(425\) 32.0000 + 24.0000i 1.55223 + 1.16417i
\(426\) 14.0000 0.678302
\(427\) 10.0000i 0.483934i
\(428\) 12.0000i 0.580042i
\(429\) −4.00000 −0.193122
\(430\) −8.00000 16.0000i −0.385794 0.771589i
\(431\) −6.00000 −0.289010 −0.144505 0.989504i \(-0.546159\pi\)
−0.144505 + 0.989504i \(0.546159\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 26.0000i 1.24948i 0.780833 + 0.624740i \(0.214795\pi\)
−0.780833 + 0.624740i \(0.785205\pi\)
\(434\) −6.00000 −0.288009
\(435\) −12.0000 + 6.00000i −0.575356 + 0.287678i
\(436\) −6.00000 −0.287348
\(437\) 0 0
\(438\) 10.0000i 0.477818i
\(439\) −6.00000 −0.286364 −0.143182 0.989696i \(-0.545733\pi\)
−0.143182 + 0.989696i \(0.545733\pi\)
\(440\) −4.00000 + 2.00000i −0.190693 + 0.0953463i
\(441\) 1.00000 0.0476190
\(442\) 16.0000i 0.761042i
\(443\) 36.0000i 1.71041i 0.518289 + 0.855206i \(0.326569\pi\)
−0.518289 + 0.855206i \(0.673431\pi\)
\(444\) 8.00000 0.379663
\(445\) 10.0000 + 20.0000i 0.474045 + 0.948091i
\(446\) −16.0000 −0.757622
\(447\) 18.0000i 0.851371i
\(448\) 1.00000i 0.0472456i
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) −4.00000 3.00000i −0.188562 0.141421i
\(451\) −12.0000 −0.565058
\(452\) 6.00000i 0.282216i
\(453\) 8.00000i 0.375873i
\(454\) 8.00000 0.375459
\(455\) −2.00000 4.00000i −0.0937614 0.187523i
\(456\) 2.00000 0.0936586
\(457\) 28.0000i 1.30978i 0.755722 + 0.654892i \(0.227286\pi\)
−0.755722 + 0.654892i \(0.772714\pi\)
\(458\) 26.0000i 1.21490i
\(459\) 8.00000 0.373408
\(460\) 0 0
\(461\) 18.0000 0.838344 0.419172 0.907907i \(-0.362320\pi\)
0.419172 + 0.907907i \(0.362320\pi\)
\(462\) 2.00000i 0.0930484i
\(463\) 12.0000i 0.557687i −0.960337 0.278844i \(-0.910049\pi\)
0.960337 0.278844i \(-0.0899511\pi\)
\(464\) 6.00000 0.278543
\(465\) −12.0000 + 6.00000i −0.556487 + 0.278243i
\(466\) 6.00000 0.277945
\(467\) 16.0000i 0.740392i −0.928954 0.370196i \(-0.879291\pi\)
0.928954 0.370196i \(-0.120709\pi\)
\(468\) 2.00000i 0.0924500i
\(469\) 12.0000 0.554109
\(470\) 4.00000 + 8.00000i 0.184506 + 0.369012i
\(471\) 10.0000 0.460776
\(472\) 8.00000i 0.368230i
\(473\) 16.0000i 0.735681i
\(474\) 4.00000 0.183726
\(475\) −6.00000 + 8.00000i −0.275299 + 0.367065i
\(476\) 8.00000 0.366679
\(477\) 2.00000i 0.0915737i
\(478\) 22.0000i 1.00626i
\(479\) −8.00000 −0.365529 −0.182765 0.983157i \(-0.558505\pi\)
−0.182765 + 0.983157i \(0.558505\pi\)
\(480\) 1.00000 + 2.00000i 0.0456435 + 0.0912871i
\(481\) 16.0000 0.729537
\(482\) 10.0000i 0.455488i
\(483\) 0 0
\(484\) 7.00000 0.318182
\(485\) −20.0000 + 10.0000i −0.908153 + 0.454077i
\(486\) −1.00000 −0.0453609
\(487\) 36.0000i 1.63132i −0.578535 0.815658i \(-0.696375\pi\)
0.578535 0.815658i \(-0.303625\pi\)
\(488\) 10.0000i 0.452679i
\(489\) 0 0
\(490\) 2.00000 1.00000i 0.0903508 0.0451754i
\(491\) −42.0000 −1.89543 −0.947717 0.319113i \(-0.896615\pi\)
−0.947717 + 0.319113i \(0.896615\pi\)
\(492\) 6.00000i 0.270501i
\(493\) 48.0000i 2.16181i
\(494\) 4.00000 0.179969
\(495\) −2.00000 4.00000i −0.0898933 0.179787i
\(496\) 6.00000 0.269408
\(497\) 14.0000i 0.627986i
\(498\) 16.0000i 0.716977i
\(499\) 28.0000 1.25345 0.626726 0.779240i \(-0.284395\pi\)
0.626726 + 0.779240i \(0.284395\pi\)
\(500\) −11.0000 2.00000i −0.491935 0.0894427i
\(501\) 8.00000 0.357414
\(502\) 0 0
\(503\) 24.0000i 1.07011i 0.844818 + 0.535054i \(0.179709\pi\)
−0.844818 + 0.535054i \(0.820291\pi\)
\(504\) −1.00000 −0.0445435
\(505\) 10.0000 + 20.0000i 0.444994 + 0.889988i
\(506\) 0 0
\(507\) 9.00000i 0.399704i
\(508\) 12.0000i 0.532414i
\(509\) −2.00000 −0.0886484 −0.0443242 0.999017i \(-0.514113\pi\)
−0.0443242 + 0.999017i \(0.514113\pi\)
\(510\) 16.0000 8.00000i 0.708492 0.354246i
\(511\) −10.0000 −0.442374
\(512\) 1.00000i 0.0441942i
\(513\) 2.00000i 0.0883022i
\(514\) 20.0000 0.882162
\(515\) 0 0
\(516\) −8.00000 −0.352180
\(517\) 8.00000i 0.351840i
\(518\) 8.00000i 0.351500i
\(519\) −16.0000 −0.702322
\(520\) 2.00000 + 4.00000i 0.0877058 + 0.175412i
\(521\) −6.00000 −0.262865 −0.131432 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) 6.00000i 0.262613i
\(523\) 12.0000i 0.524723i −0.964970 0.262362i \(-0.915499\pi\)
0.964970 0.262362i \(-0.0845013\pi\)
\(524\) 20.0000 0.873704
\(525\) 3.00000 4.00000i 0.130931 0.174574i
\(526\) −24.0000 −1.04645
\(527\) 48.0000i 2.09091i
\(528\) 2.00000i 0.0870388i
\(529\) 23.0000 1.00000
\(530\) 2.00000 + 4.00000i 0.0868744 + 0.173749i
\(531\) −8.00000 −0.347170
\(532\) 2.00000i 0.0867110i
\(533\) 12.0000i 0.519778i
\(534\) 10.0000 0.432742
\(535\) 24.0000 12.0000i 1.03761 0.518805i
\(536\) −12.0000 −0.518321
\(537\) 2.00000i 0.0863064i
\(538\) 14.0000i 0.603583i
\(539\) 2.00000 0.0861461
\(540\) −2.00000 + 1.00000i −0.0860663 + 0.0430331i
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) 2.00000i 0.0859074i
\(543\) 22.0000i 0.944110i
\(544\) −8.00000 −0.342997
\(545\) −6.00000 12.0000i −0.257012 0.514024i
\(546\) −2.00000 −0.0855921
\(547\) 20.0000i 0.855138i −0.903983 0.427569i \(-0.859370\pi\)
0.903983 0.427569i \(-0.140630\pi\)
\(548\) 14.0000i 0.598050i
\(549\) −10.0000 −0.426790
\(550\) −8.00000 6.00000i −0.341121 0.255841i
\(551\) 12.0000 0.511217
\(552\) 0 0
\(553\) 4.00000i 0.170097i
\(554\) 8.00000 0.339887
\(555\) 8.00000 + 16.0000i 0.339581 + 0.679162i
\(556\) −2.00000 −0.0848189
\(557\) 6.00000i 0.254228i −0.991888 0.127114i \(-0.959429\pi\)
0.991888 0.127114i \(-0.0405714\pi\)
\(558\) 6.00000i 0.254000i
\(559\) −16.0000 −0.676728
\(560\) −2.00000 + 1.00000i −0.0845154 + 0.0422577i
\(561\) 16.0000 0.675521
\(562\) 22.0000i 0.928014i
\(563\) 12.0000i 0.505740i 0.967500 + 0.252870i \(0.0813744\pi\)
−0.967500 + 0.252870i \(0.918626\pi\)
\(564\) 4.00000 0.168430
\(565\) 12.0000 6.00000i 0.504844 0.252422i
\(566\) 4.00000 0.168133
\(567\) 1.00000i 0.0419961i
\(568\) 14.0000i 0.587427i
\(569\) −18.0000 −0.754599 −0.377300 0.926091i \(-0.623147\pi\)
−0.377300 + 0.926091i \(0.623147\pi\)
\(570\) 2.00000 + 4.00000i 0.0837708 + 0.167542i
\(571\) −44.0000 −1.84134 −0.920671 0.390339i \(-0.872358\pi\)
−0.920671 + 0.390339i \(0.872358\pi\)
\(572\) 4.00000i 0.167248i
\(573\) 14.0000i 0.584858i
\(574\) −6.00000 −0.250435
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) 18.0000i 0.749350i −0.927156 0.374675i \(-0.877754\pi\)
0.927156 0.374675i \(-0.122246\pi\)
\(578\) 47.0000i 1.95494i
\(579\) 0 0
\(580\) 6.00000 + 12.0000i 0.249136 + 0.498273i
\(581\) 16.0000 0.663792
\(582\) 10.0000i 0.414513i
\(583\) 4.00000i 0.165663i
\(584\) 10.0000 0.413803
\(585\) −4.00000 + 2.00000i −0.165380 + 0.0826898i
\(586\) −16.0000 −0.660954
\(587\) 4.00000i 0.165098i −0.996587 0.0825488i \(-0.973694\pi\)
0.996587 0.0825488i \(-0.0263060\pi\)
\(588\) 1.00000i 0.0412393i
\(589\) 12.0000 0.494451
\(590\) −16.0000 + 8.00000i −0.658710 + 0.329355i
\(591\) 6.00000 0.246807
\(592\) 8.00000i 0.328798i
\(593\) 32.0000i 1.31408i −0.753855 0.657041i \(-0.771808\pi\)
0.753855 0.657041i \(-0.228192\pi\)
\(594\) −2.00000 −0.0820610
\(595\) 8.00000 + 16.0000i 0.327968 + 0.655936i
\(596\) −18.0000 −0.737309
\(597\) 26.0000i 1.06411i
\(598\) 0 0
\(599\) −14.0000 −0.572024 −0.286012 0.958226i \(-0.592330\pi\)
−0.286012 + 0.958226i \(0.592330\pi\)
\(600\) −3.00000 + 4.00000i −0.122474 + 0.163299i
\(601\) −42.0000 −1.71322 −0.856608 0.515968i \(-0.827432\pi\)
−0.856608 + 0.515968i \(0.827432\pi\)
\(602\) 8.00000i 0.326056i
\(603\) 12.0000i 0.488678i
\(604\) −8.00000 −0.325515
\(605\) 7.00000 + 14.0000i 0.284590 + 0.569181i
\(606\) 10.0000 0.406222
\(607\) 16.0000i 0.649420i 0.945814 + 0.324710i \(0.105267\pi\)
−0.945814 + 0.324710i \(0.894733\pi\)
\(608\) 2.00000i 0.0811107i
\(609\) −6.00000 −0.243132
\(610\) −20.0000 + 10.0000i −0.809776 + 0.404888i
\(611\) 8.00000 0.323645
\(612\) 8.00000i 0.323381i
\(613\) 32.0000i 1.29247i 0.763139 + 0.646234i \(0.223657\pi\)
−0.763139 + 0.646234i \(0.776343\pi\)
\(614\) −28.0000 −1.12999
\(615\) −12.0000 + 6.00000i −0.483887 + 0.241943i
\(616\) −2.00000 −0.0805823
\(617\) 18.0000i 0.724653i 0.932051 + 0.362326i \(0.118017\pi\)
−0.932051 + 0.362326i \(0.881983\pi\)
\(618\) 0 0
\(619\) 18.0000 0.723481 0.361741 0.932279i \(-0.382183\pi\)
0.361741 + 0.932279i \(0.382183\pi\)
\(620\) 6.00000 + 12.0000i 0.240966 + 0.481932i
\(621\) 0 0
\(622\) 8.00000i 0.320771i
\(623\) 10.0000i 0.400642i
\(624\) 2.00000 0.0800641
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 10.0000 0.399680
\(627\) 4.00000i 0.159745i
\(628\) 10.0000i 0.399043i
\(629\) −64.0000 −2.55185
\(630\) −1.00000 2.00000i −0.0398410 0.0796819i
\(631\) 12.0000 0.477712 0.238856 0.971055i \(-0.423228\pi\)
0.238856 + 0.971055i \(0.423228\pi\)
\(632\) 4.00000i 0.159111i
\(633\) 8.00000i 0.317971i
\(634\) 2.00000 0.0794301
\(635\) −24.0000 + 12.0000i −0.952411 + 0.476205i
\(636\) 2.00000 0.0793052
\(637\) 2.00000i 0.0792429i
\(638\) 12.0000i 0.475085i
\(639\) 14.0000 0.553831
\(640\) 2.00000 1.00000i 0.0790569 0.0395285i
\(641\) 30.0000 1.18493 0.592464 0.805597i \(-0.298155\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(642\) 12.0000i 0.473602i
\(643\) 20.0000i 0.788723i −0.918955 0.394362i \(-0.870966\pi\)
0.918955 0.394362i \(-0.129034\pi\)
\(644\) 0 0
\(645\) −8.00000 16.0000i −0.315000 0.629999i
\(646\) −16.0000 −0.629512
\(647\) 16.0000i 0.629025i −0.949253 0.314512i \(-0.898159\pi\)
0.949253 0.314512i \(-0.101841\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −16.0000 −0.628055
\(650\) −6.00000 + 8.00000i −0.235339 + 0.313786i
\(651\) −6.00000 −0.235159
\(652\) 0 0
\(653\) 14.0000i 0.547862i −0.961749 0.273931i \(-0.911676\pi\)
0.961749 0.273931i \(-0.0883240\pi\)
\(654\) −6.00000 −0.234619
\(655\) 20.0000 + 40.0000i 0.781465 + 1.56293i
\(656\) 6.00000 0.234261
\(657\) 10.0000i 0.390137i
\(658\) 4.00000i 0.155936i
\(659\) 6.00000 0.233727 0.116863 0.993148i \(-0.462716\pi\)
0.116863 + 0.993148i \(0.462716\pi\)
\(660\) −4.00000 + 2.00000i −0.155700 + 0.0778499i
\(661\) 10.0000 0.388955 0.194477 0.980907i \(-0.437699\pi\)
0.194477 + 0.980907i \(0.437699\pi\)
\(662\) 0 0
\(663\) 16.0000i 0.621389i
\(664\) −16.0000 −0.620920
\(665\) −4.00000 + 2.00000i −0.155113 + 0.0775567i
\(666\) 8.00000 0.309994
\(667\) 0 0
\(668\) 8.00000i 0.309529i
\(669\) −16.0000 −0.618596
\(670\) −12.0000 24.0000i −0.463600 0.927201i
\(671\) −20.0000 −0.772091
\(672\) 1.00000i 0.0385758i
\(673\) 12.0000i 0.462566i 0.972887 + 0.231283i \(0.0742923\pi\)
−0.972887 + 0.231283i \(0.925708\pi\)
\(674\) −32.0000 −1.23259
\(675\) −4.00000 3.00000i −0.153960 0.115470i
\(676\) −9.00000 −0.346154
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 6.00000i 0.230429i
\(679\) −10.0000 −0.383765
\(680\) −8.00000 16.0000i −0.306786 0.613572i
\(681\) 8.00000 0.306561
\(682\) 12.0000i 0.459504i
\(683\) 28.0000i 1.07139i 0.844411 + 0.535695i \(0.179950\pi\)
−0.844411 + 0.535695i \(0.820050\pi\)
\(684\) 2.00000 0.0764719
\(685\) 28.0000 14.0000i 1.06983 0.534913i
\(686\) 1.00000 0.0381802
\(687\) 26.0000i 0.991962i
\(688\) 8.00000i 0.304997i
\(689\) 4.00000 0.152388
\(690\) 0 0
\(691\) −14.0000 −0.532585 −0.266293 0.963892i \(-0.585799\pi\)
−0.266293 + 0.963892i \(0.585799\pi\)
\(692\) 16.0000i 0.608229i
\(693\) 2.00000i 0.0759737i
\(694\) −4.00000 −0.151838
\(695\) −2.00000 4.00000i −0.0758643 0.151729i
\(696\) 6.00000 0.227429
\(697\) 48.0000i 1.81813i
\(698\) 18.0000i 0.681310i
\(699\) 6.00000 0.226941
\(700\) −4.00000 3.00000i −0.151186 0.113389i
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 2.00000i 0.0754851i
\(703\) 16.0000i 0.603451i
\(704\) 2.00000 0.0753778
\(705\) 4.00000 + 8.00000i 0.150649 + 0.301297i
\(706\) 0 0
\(707\) 10.0000i 0.376089i
\(708\) 8.00000i 0.300658i
\(709\) 38.0000 1.42712 0.713560 0.700594i \(-0.247082\pi\)
0.713560 + 0.700594i \(0.247082\pi\)
\(710\) 28.0000 14.0000i 1.05082 0.525411i
\(711\) 4.00000 0.150012
\(712\) 10.0000i 0.374766i
\(713\) 0 0
\(714\) 8.00000 0.299392
\(715\) −8.00000 + 4.00000i −0.299183 + 0.149592i
\(716\) −2.00000 −0.0747435
\(717\) 22.0000i 0.821605i
\(718\) 14.0000i 0.522475i
\(719\) 20.0000 0.745874 0.372937 0.927857i \(-0.378351\pi\)
0.372937 + 0.927857i \(0.378351\pi\)
\(720\) 1.00000 + 2.00000i 0.0372678 + 0.0745356i
\(721\) 0 0
\(722\) 15.0000i 0.558242i
\(723\) 10.0000i 0.371904i
\(724\) −22.0000 −0.817624
\(725\) −18.0000 + 24.0000i −0.668503 + 0.891338i
\(726\) 7.00000 0.259794
\(727\) 16.0000i 0.593407i −0.954970 0.296704i \(-0.904113\pi\)
0.954970 0.296704i \(-0.0958873\pi\)
\(728\) 2.00000i 0.0741249i
\(729\) −1.00000 −0.0370370
\(730\) 10.0000 + 20.0000i 0.370117 + 0.740233i
\(731\) 64.0000 2.36713
\(732\) 10.0000i 0.369611i
\(733\) 30.0000i 1.10808i −0.832492 0.554038i \(-0.813086\pi\)
0.832492 0.554038i \(-0.186914\pi\)
\(734\) 32.0000 1.18114
\(735\) 2.00000 1.00000i 0.0737711 0.0368856i
\(736\) 0 0
\(737\) 24.0000i 0.884051i
\(738\) 6.00000i 0.220863i
\(739\) −20.0000 −0.735712 −0.367856 0.929883i \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) 16.0000 8.00000i 0.588172 0.294086i
\(741\) 4.00000 0.146944
\(742\) 2.00000i 0.0734223i
\(743\) 16.0000i 0.586983i 0.955962 + 0.293492i \(0.0948173\pi\)
−0.955962 + 0.293492i \(0.905183\pi\)
\(744\) 6.00000 0.219971
\(745\) −18.0000 36.0000i −0.659469 1.31894i
\(746\) 36.0000 1.31805
\(747\) 16.0000i 0.585409i
\(748\) 16.0000i 0.585018i
\(749\) 12.0000 0.438470
\(750\) −11.0000 2.00000i −0.401663 0.0730297i
\(751\) 4.00000 0.145962 0.0729810 0.997333i \(-0.476749\pi\)
0.0729810 + 0.997333i \(0.476749\pi\)
\(752\) 4.00000i 0.145865i
\(753\) 0 0
\(754\) 12.0000 0.437014
\(755\) −8.00000 16.0000i −0.291150 0.582300i
\(756\) −1.00000 −0.0363696
\(757\) 4.00000i 0.145382i 0.997354 + 0.0726912i \(0.0231588\pi\)
−0.997354 + 0.0726912i \(0.976841\pi\)
\(758\) 28.0000i 1.01701i
\(759\) 0 0
\(760\) 4.00000 2.00000i 0.145095 0.0725476i
\(761\) 6.00000 0.217500 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) 12.0000i 0.434714i
\(763\) 6.00000i 0.217215i
\(764\) −14.0000 −0.506502
\(765\) 16.0000 8.00000i 0.578481 0.289241i
\(766\) 0 0
\(767\) 16.0000i 0.577727i
\(768\) 1.00000i 0.0360844i
\(769\) 42.0000 1.51456 0.757279 0.653091i \(-0.226528\pi\)
0.757279 + 0.653091i \(0.226528\pi\)
\(770\) −2.00000 4.00000i −0.0720750 0.144150i
\(771\) 20.0000 0.720282
\(772\) 0 0
\(773\) 32.0000i 1.15096i −0.817816 0.575480i \(-0.804815\pi\)
0.817816 0.575480i \(-0.195185\pi\)
\(774\) −8.00000 −0.287554
\(775\) −18.0000 + 24.0000i −0.646579 + 0.862105i
\(776\) 10.0000 0.358979
\(777\) 8.00000i 0.286998i
\(778\) 6.00000i 0.215110i
\(779\) 12.0000 0.429945
\(780\) 2.00000 + 4.00000i 0.0716115 + 0.143223i
\(781\) 28.0000 1.00192
\(782\) 0 0
\(783\) 6.00000i 0.214423i
\(784\) −1.00000 −0.0357143
\(785\) 20.0000 10.0000i 0.713831 0.356915i
\(786\) 20.0000 0.713376
\(787\) 44.0000i 1.56843i 0.620489 + 0.784215i \(0.286934\pi\)
−0.620489 + 0.784215i \(0.713066\pi\)
\(788\) 6.00000i 0.213741i