Properties

Label 210.2.g.b.169.2
Level $210$
Weight $2$
Character 210.169
Analytic conductor $1.677$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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: \(x^{2} + 1\)
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 169.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 210.169
Dual form 210.2.g.b.169.1

$q$-expansion

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

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 \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 6.00000i 1.66410i −0.554700 0.832050i \(-0.687167\pi\)
0.554700 0.832050i \(-0.312833\pi\)
\(14\) 1.00000 0.267261
\(15\) −2.00000 1.00000i −0.516398 0.258199i
\(16\) 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
\(19\) 6.00000 1.37649 0.688247 0.725476i \(-0.258380\pi\)
0.688247 + 0.725476i \(0.258380\pi\)
\(20\) −1.00000 + 2.00000i −0.223607 + 0.447214i
\(21\) −1.00000 −0.218218
\(22\) 2.00000i 0.426401i
\(23\) 8.00000i 1.66812i 0.551677 + 0.834058i \(0.313988\pi\)
−0.551677 + 0.834058i \(0.686012\pi\)
\(24\) −1.00000 −0.204124
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) 6.00000 1.17670
\(27\) 1.00000i 0.192450i
\(28\) 1.00000i 0.188982i
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 1.00000 2.00000i 0.182574 0.365148i
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.00000i 0.348155i
\(34\) −4.00000 −0.685994
\(35\) −2.00000 1.00000i −0.338062 0.169031i
\(36\) 1.00000 0.166667
\(37\) 4.00000i 0.657596i 0.944400 + 0.328798i \(0.106644\pi\)
−0.944400 + 0.328798i \(0.893356\pi\)
\(38\) 6.00000i 0.973329i
\(39\) −6.00000 −0.960769
\(40\) −2.00000 1.00000i −0.316228 0.158114i
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 1.00000i 0.154303i
\(43\) 4.00000i 0.609994i −0.952353 0.304997i \(-0.901344\pi\)
0.952353 0.304997i \(-0.0986555\pi\)
\(44\) −2.00000 −0.301511
\(45\) −1.00000 + 2.00000i −0.149071 + 0.298142i
\(46\) −8.00000 −1.17954
\(47\) 8.00000i 1.16692i 0.812142 + 0.583460i \(0.198301\pi\)
−0.812142 + 0.583460i \(0.801699\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −1.00000 −0.142857
\(50\) 4.00000 3.00000i 0.565685 0.424264i
\(51\) 4.00000 0.560112
\(52\) 6.00000i 0.832050i
\(53\) 6.00000i 0.824163i −0.911147 0.412082i \(-0.864802\pi\)
0.911147 0.412082i \(-0.135198\pi\)
\(54\) −1.00000 −0.136083
\(55\) 2.00000 4.00000i 0.269680 0.539360i
\(56\) −1.00000 −0.133631
\(57\) 6.00000i 0.794719i
\(58\) 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 \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 2.00000i 0.254000i
\(63\) 1.00000i 0.125988i
\(64\) −1.00000 −0.125000
\(65\) −12.0000 6.00000i −1.48842 0.744208i
\(66\) 2.00000 0.246183
\(67\) 8.00000i 0.977356i 0.872464 + 0.488678i \(0.162521\pi\)
−0.872464 + 0.488678i \(0.837479\pi\)
\(68\) 4.00000i 0.485071i
\(69\) 8.00000 0.963087
\(70\) 1.00000 2.00000i 0.119523 0.239046i
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 14.0000i 1.63858i 0.573382 + 0.819288i \(0.305631\pi\)
−0.573382 + 0.819288i \(0.694369\pi\)
\(74\) −4.00000 −0.464991
\(75\) −4.00000 + 3.00000i −0.461880 + 0.346410i
\(76\) −6.00000 −0.688247
\(77\) 2.00000i 0.227921i
\(78\) 6.00000i 0.679366i
\(79\) 12.0000 1.35011 0.675053 0.737769i \(-0.264121\pi\)
0.675053 + 0.737769i \(0.264121\pi\)
\(80\) 1.00000 2.00000i 0.111803 0.223607i
\(81\) 1.00000 0.111111
\(82\) 2.00000i 0.220863i
\(83\) 8.00000i 0.878114i 0.898459 + 0.439057i \(0.144687\pi\)
−0.898459 + 0.439057i \(0.855313\pi\)
\(84\) 1.00000 0.109109
\(85\) 8.00000 + 4.00000i 0.867722 + 0.433861i
\(86\) 4.00000 0.431331
\(87\) 6.00000i 0.643268i
\(88\) 2.00000i 0.213201i
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) −2.00000 1.00000i −0.210819 0.105409i
\(91\) −6.00000 −0.628971
\(92\) 8.00000i 0.834058i
\(93\) 2.00000i 0.207390i
\(94\) −8.00000 −0.825137
\(95\) 6.00000 12.0000i 0.615587 1.23117i
\(96\) 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 \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) 4.00000i 0.396059i
\(103\) 8.00000i 0.788263i −0.919054 0.394132i \(-0.871045\pi\)
0.919054 0.394132i \(-0.128955\pi\)
\(104\) −6.00000 −0.588348
\(105\) −1.00000 + 2.00000i −0.0975900 + 0.195180i
\(106\) 6.00000 0.582772
\(107\) 12.0000i 1.16008i 0.814587 + 0.580042i \(0.196964\pi\)
−0.814587 + 0.580042i \(0.803036\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) 4.00000 + 2.00000i 0.381385 + 0.190693i
\(111\) 4.00000 0.379663
\(112\) 1.00000i 0.0944911i
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) 6.00000 0.561951
\(115\) 16.0000 + 8.00000i 1.49201 + 0.746004i
\(116\) 6.00000 0.557086
\(117\) 6.00000i 0.554700i
\(118\) 8.00000i 0.736460i
\(119\) 4.00000 0.366679
\(120\) −1.00000 + 2.00000i −0.0912871 + 0.182574i
\(121\) −7.00000 −0.636364
\(122\) 10.0000i 0.905357i
\(123\) 2.00000i 0.180334i
\(124\) 2.00000 0.179605
\(125\) −11.0000 + 2.00000i −0.983870 + 0.178885i
\(126\) −1.00000 −0.0890871
\(127\) 4.00000i 0.354943i 0.984126 + 0.177471i \(0.0567917\pi\)
−0.984126 + 0.177471i \(0.943208\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −4.00000 −0.352180
\(130\) 6.00000 12.0000i 0.526235 1.05247i
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 2.00000i 0.174078i
\(133\) 6.00000i 0.520266i
\(134\) −8.00000 −0.691095
\(135\) 2.00000 + 1.00000i 0.172133 + 0.0860663i
\(136\) 4.00000 0.342997
\(137\) 6.00000i 0.512615i −0.966595 0.256307i \(-0.917494\pi\)
0.966595 0.256307i \(-0.0825059\pi\)
\(138\) 8.00000i 0.681005i
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) 2.00000 + 1.00000i 0.169031 + 0.0845154i
\(141\) 8.00000 0.673722
\(142\) 6.00000i 0.503509i
\(143\) 12.0000i 1.00349i
\(144\) −1.00000 −0.0833333
\(145\) −6.00000 + 12.0000i −0.498273 + 0.996546i
\(146\) −14.0000 −1.15865
\(147\) 1.00000i 0.0824786i
\(148\) 4.00000i 0.328798i
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) −3.00000 4.00000i −0.244949 0.326599i
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 6.00000i 0.486664i
\(153\) 4.00000i 0.323381i
\(154\) 2.00000 0.161165
\(155\) −2.00000 + 4.00000i −0.160644 + 0.321288i
\(156\) 6.00000 0.480384
\(157\) 22.0000i 1.75579i −0.478852 0.877896i \(-0.658947\pi\)
0.478852 0.877896i \(-0.341053\pi\)
\(158\) 12.0000i 0.954669i
\(159\) −6.00000 −0.475831
\(160\) 2.00000 + 1.00000i 0.158114 + 0.0790569i
\(161\) 8.00000 0.630488
\(162\) 1.00000i 0.0785674i
\(163\) 4.00000i 0.313304i 0.987654 + 0.156652i \(0.0500701\pi\)
−0.987654 + 0.156652i \(0.949930\pi\)
\(164\) −2.00000 −0.156174
\(165\) −4.00000 2.00000i −0.311400 0.155700i
\(166\) −8.00000 −0.620920
\(167\) 12.0000i 0.928588i −0.885681 0.464294i \(-0.846308\pi\)
0.885681 0.464294i \(-0.153692\pi\)
\(168\) 1.00000i 0.0771517i
\(169\) −23.0000 −1.76923
\(170\) −4.00000 + 8.00000i −0.306786 + 0.613572i
\(171\) −6.00000 −0.458831
\(172\) 4.00000i 0.304997i
\(173\) 8.00000i 0.608229i −0.952636 0.304114i \(-0.901639\pi\)
0.952636 0.304114i \(-0.0983605\pi\)
\(174\) −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
\(179\) −10.0000 −0.747435 −0.373718 0.927543i \(-0.621917\pi\)
−0.373718 + 0.927543i \(0.621917\pi\)
\(180\) 1.00000 2.00000i 0.0745356 0.149071i
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 6.00000i 0.444750i
\(183\) 10.0000i 0.739221i
\(184\) 8.00000 0.589768
\(185\) 8.00000 + 4.00000i 0.588172 + 0.294086i
\(186\) −2.00000 −0.146647
\(187\) 8.00000i 0.585018i
\(188\) 8.00000i 0.583460i
\(189\) 1.00000 0.0727393
\(190\) 12.0000 + 6.00000i 0.870572 + 0.435286i
\(191\) −18.0000 −1.30243 −0.651217 0.758891i \(-0.725741\pi\)
−0.651217 + 0.758891i \(0.725741\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 8.00000i 0.575853i 0.957653 + 0.287926i \(0.0929658\pi\)
−0.957653 + 0.287926i \(0.907034\pi\)
\(194\) 10.0000 0.717958
\(195\) −6.00000 + 12.0000i −0.429669 + 0.859338i
\(196\) 1.00000 0.0714286
\(197\) 2.00000i 0.142494i 0.997459 + 0.0712470i \(0.0226979\pi\)
−0.997459 + 0.0712470i \(0.977302\pi\)
\(198\) 2.00000i 0.142134i
\(199\) −6.00000 −0.425329 −0.212664 0.977125i \(-0.568214\pi\)
−0.212664 + 0.977125i \(0.568214\pi\)
\(200\) −4.00000 + 3.00000i −0.282843 + 0.212132i
\(201\) 8.00000 0.564276
\(202\) 10.0000i 0.703598i
\(203\) 6.00000i 0.421117i
\(204\) −4.00000 −0.280056
\(205\) 2.00000 4.00000i 0.139686 0.279372i
\(206\) 8.00000 0.557386
\(207\) 8.00000i 0.556038i
\(208\) 6.00000i 0.416025i
\(209\) 12.0000 0.830057
\(210\) −2.00000 1.00000i −0.138013 0.0690066i
\(211\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 6.00000i 0.412082i
\(213\) 6.00000i 0.411113i
\(214\) −12.0000 −0.820303
\(215\) −8.00000 4.00000i −0.545595 0.272798i
\(216\) 1.00000 0.0680414
\(217\) 2.00000i 0.135769i
\(218\) 14.0000i 0.948200i
\(219\) 14.0000 0.946032
\(220\) −2.00000 + 4.00000i −0.134840 + 0.269680i
\(221\) 24.0000 1.61441
\(222\) 4.00000i 0.268462i
\(223\) 8.00000i 0.535720i 0.963458 + 0.267860i \(0.0863164\pi\)
−0.963458 + 0.267860i \(0.913684\pi\)
\(224\) 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 \(-0.914466\pi\)
0.964114 0.265489i \(-0.0855335\pi\)
\(228\) 6.00000i 0.397360i
\(229\) −14.0000 −0.925146 −0.462573 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) −8.00000 + 16.0000i −0.527504 + 1.05501i
\(231\) −2.00000 −0.131590
\(232\) 6.00000i 0.393919i
\(233\) 10.0000i 0.655122i 0.944830 + 0.327561i \(0.106227\pi\)
−0.944830 + 0.327561i \(0.893773\pi\)
\(234\) −6.00000 −0.392232
\(235\) 16.0000 + 8.00000i 1.04372 + 0.521862i
\(236\) −8.00000 −0.520756
\(237\) 12.0000i 0.779484i
\(238\) 4.00000i 0.259281i
\(239\) −26.0000 −1.68180 −0.840900 0.541190i \(-0.817974\pi\)
−0.840900 + 0.541190i \(0.817974\pi\)
\(240\) −2.00000 1.00000i −0.129099 0.0645497i
\(241\) −26.0000 −1.67481 −0.837404 0.546585i \(-0.815928\pi\)
−0.837404 + 0.546585i \(0.815928\pi\)
\(242\) 7.00000i 0.449977i
\(243\) 1.00000i 0.0641500i
\(244\) 10.0000 0.640184
\(245\) −1.00000 + 2.00000i −0.0638877 + 0.127775i
\(246\) 2.00000 0.127515
\(247\) 36.0000i 2.29063i
\(248\) 2.00000i 0.127000i
\(249\) 8.00000 0.506979
\(250\) −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
\(253\) 16.0000i 1.00591i
\(254\) −4.00000 −0.250982
\(255\) 4.00000 8.00000i 0.250490 0.500979i
\(256\) 1.00000 0.0625000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 4.00000i 0.249029i
\(259\) 4.00000 0.248548
\(260\) 12.0000 + 6.00000i 0.744208 + 0.372104i
\(261\) 6.00000 0.371391
\(262\) 12.0000i 0.741362i
\(263\) 16.0000i 0.986602i −0.869859 0.493301i \(-0.835790\pi\)
0.869859 0.493301i \(-0.164210\pi\)
\(264\) −2.00000 −0.123091
\(265\) −12.0000 6.00000i −0.737154 0.368577i
\(266\) 6.00000 0.367884
\(267\) 10.0000i 0.611990i
\(268\) 8.00000i 0.488678i
\(269\) −18.0000 −1.09748 −0.548740 0.835993i \(-0.684892\pi\)
−0.548740 + 0.835993i \(0.684892\pi\)
\(270\) −1.00000 + 2.00000i −0.0608581 + 0.121716i
\(271\) 10.0000 0.607457 0.303728 0.952759i \(-0.401768\pi\)
0.303728 + 0.952759i \(0.401768\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 6.00000i 0.363137i
\(274\) 6.00000 0.362473
\(275\) −6.00000 8.00000i −0.361814 0.482418i
\(276\) −8.00000 −0.481543
\(277\) 28.0000i 1.68236i 0.540758 + 0.841178i \(0.318138\pi\)
−0.540758 + 0.841178i \(0.681862\pi\)
\(278\) 14.0000i 0.839664i
\(279\) 2.00000 0.119737
\(280\) −1.00000 + 2.00000i −0.0597614 + 0.119523i
\(281\) 30.0000 1.78965 0.894825 0.446417i \(-0.147300\pi\)
0.894825 + 0.446417i \(0.147300\pi\)
\(282\) 8.00000i 0.476393i
\(283\) 20.0000i 1.18888i −0.804141 0.594438i \(-0.797374\pi\)
0.804141 0.594438i \(-0.202626\pi\)
\(284\) 6.00000 0.356034
\(285\) −12.0000 6.00000i −0.710819 0.355409i
\(286\) 12.0000 0.709575
\(287\) 2.00000i 0.118056i
\(288\) 1.00000i 0.0589256i
\(289\) 1.00000 0.0588235
\(290\) −12.0000 6.00000i −0.704664 0.352332i
\(291\) −10.0000 −0.586210
\(292\) 14.0000i 0.819288i
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) −1.00000 −0.0583212
\(295\) 8.00000 16.0000i 0.465778 0.931556i
\(296\) 4.00000 0.232495
\(297\) 2.00000i 0.116052i
\(298\) 10.0000i 0.579284i
\(299\) 48.0000 2.77591
\(300\) 4.00000 3.00000i 0.230940 0.173205i
\(301\) −4.00000 −0.230556
\(302\) 8.00000i 0.460348i
\(303\) 10.0000i 0.574485i
\(304\) 6.00000 0.344124
\(305\) −10.0000 + 20.0000i −0.572598 + 1.14520i
\(306\) 4.00000 0.228665
\(307\) 12.0000i 0.684876i −0.939540 0.342438i \(-0.888747\pi\)
0.939540 0.342438i \(-0.111253\pi\)
\(308\) 2.00000i 0.113961i
\(309\) −8.00000 −0.455104
\(310\) −4.00000 2.00000i −0.227185 0.113592i
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 6.00000i 0.339683i
\(313\) 2.00000i 0.113047i 0.998401 + 0.0565233i \(0.0180015\pi\)
−0.998401 + 0.0565233i \(0.981998\pi\)
\(314\) 22.0000 1.24153
\(315\) 2.00000 + 1.00000i 0.112687 + 0.0563436i
\(316\) −12.0000 −0.675053
\(317\) 2.00000i 0.112331i −0.998421 0.0561656i \(-0.982113\pi\)
0.998421 0.0561656i \(-0.0178875\pi\)
\(318\) 6.00000i 0.336463i
\(319\) −12.0000 −0.671871
\(320\) −1.00000 + 2.00000i −0.0559017 + 0.111803i
\(321\) 12.0000 0.669775
\(322\) 8.00000i 0.445823i
\(323\) 24.0000i 1.33540i
\(324\) −1.00000 −0.0555556
\(325\) −24.0000 + 18.0000i −1.33128 + 0.998460i
\(326\) −4.00000 −0.221540
\(327\) 14.0000i 0.774202i
\(328\) 2.00000i 0.110432i
\(329\) 8.00000 0.441054
\(330\) 2.00000 4.00000i 0.110096 0.220193i
\(331\) −8.00000 −0.439720 −0.219860 0.975531i \(-0.570560\pi\)
−0.219860 + 0.975531i \(0.570560\pi\)
\(332\) 8.00000i 0.439057i
\(333\) 4.00000i 0.219199i
\(334\) 12.0000 0.656611
\(335\) 16.0000 + 8.00000i 0.874173 + 0.437087i
\(336\) −1.00000 −0.0545545
\(337\) 8.00000i 0.435788i −0.975972 0.217894i \(-0.930081\pi\)
0.975972 0.217894i \(-0.0699187\pi\)
\(338\) 23.0000i 1.25104i
\(339\) −6.00000 −0.325875
\(340\) −8.00000 4.00000i −0.433861 0.216930i
\(341\) −4.00000 −0.216612
\(342\) 6.00000i 0.324443i
\(343\) 1.00000i 0.0539949i
\(344\) −4.00000 −0.215666
\(345\) 8.00000 16.0000i 0.430706 0.861411i
\(346\) 8.00000 0.430083
\(347\) 36.0000i 1.93258i 0.257454 + 0.966291i \(0.417117\pi\)
−0.257454 + 0.966291i \(0.582883\pi\)
\(348\) 6.00000i 0.321634i
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) −3.00000 4.00000i −0.160357 0.213809i
\(351\) 6.00000 0.320256
\(352\) 2.00000i 0.106600i
\(353\) 20.0000i 1.06449i −0.846590 0.532246i \(-0.821348\pi\)
0.846590 0.532246i \(-0.178652\pi\)
\(354\) 8.00000 0.425195
\(355\) −6.00000 + 12.0000i −0.318447 + 0.636894i
\(356\) −10.0000 −0.529999
\(357\) 4.00000i 0.211702i
\(358\) 10.0000i 0.528516i
\(359\) −6.00000 −0.316668 −0.158334 0.987386i \(-0.550612\pi\)
−0.158334 + 0.987386i \(0.550612\pi\)
\(360\) 2.00000 + 1.00000i 0.105409 + 0.0527046i
\(361\) 17.0000 0.894737
\(362\) 2.00000i 0.105118i
\(363\) 7.00000i 0.367405i
\(364\) 6.00000 0.314485
\(365\) 28.0000 + 14.0000i 1.46559 + 0.732793i
\(366\) −10.0000 −0.522708
\(367\) 32.0000i 1.67039i −0.549957 0.835193i \(-0.685356\pi\)
0.549957 0.835193i \(-0.314644\pi\)
\(368\) 8.00000i 0.417029i
\(369\) −2.00000 −0.104116
\(370\) −4.00000 + 8.00000i −0.207950 + 0.415900i
\(371\) −6.00000 −0.311504
\(372\) 2.00000i 0.103695i
\(373\) 24.0000i 1.24267i 0.783544 + 0.621336i \(0.213410\pi\)
−0.783544 + 0.621336i \(0.786590\pi\)
\(374\) −8.00000 −0.413670
\(375\) 2.00000 + 11.0000i 0.103280 + 0.568038i
\(376\) 8.00000 0.412568
\(377\) 36.0000i 1.85409i
\(378\) 1.00000i 0.0514344i
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) −6.00000 + 12.0000i −0.307794 + 0.615587i
\(381\) 4.00000 0.204926
\(382\) 18.0000i 0.920960i
\(383\) 20.0000i 1.02195i −0.859595 0.510976i \(-0.829284\pi\)
0.859595 0.510976i \(-0.170716\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −4.00000 2.00000i −0.203859 0.101929i
\(386\) −8.00000 −0.407189
\(387\) 4.00000i 0.203331i
\(388\) 10.0000i 0.507673i
\(389\) −2.00000 −0.101404 −0.0507020 0.998714i \(-0.516146\pi\)
−0.0507020 + 0.998714i \(0.516146\pi\)
\(390\) −12.0000 6.00000i −0.607644 0.303822i
\(391\) −32.0000 −1.61831
\(392\) 1.00000i 0.0505076i
\(393\) 12.0000i 0.605320i
\(394\) −2.00000 −0.100759
\(395\) 12.0000 24.0000i 0.603786 1.20757i
\(396\) 2.00000 0.100504
\(397\) 2.00000i 0.100377i −0.998740 0.0501886i \(-0.984018\pi\)
0.998740 0.0501886i \(-0.0159822\pi\)
\(398\) 6.00000i 0.300753i
\(399\) −6.00000 −0.300376
\(400\) −3.00000 4.00000i −0.150000 0.200000i
\(401\) −14.0000 −0.699127 −0.349563 0.936913i \(-0.613670\pi\)
−0.349563 + 0.936913i \(0.613670\pi\)
\(402\) 8.00000i 0.399004i
\(403\) 12.0000i 0.597763i
\(404\) −10.0000 −0.497519
\(405\) 1.00000 2.00000i 0.0496904 0.0993808i
\(406\) −6.00000 −0.297775
\(407\) 8.00000i 0.396545i
\(408\) 4.00000i 0.198030i
\(409\) −26.0000 −1.28562 −0.642809 0.766027i \(-0.722231\pi\)
−0.642809 + 0.766027i \(0.722231\pi\)
\(410\) 4.00000 + 2.00000i 0.197546 + 0.0987730i
\(411\) −6.00000 −0.295958
\(412\) 8.00000i 0.394132i
\(413\) 8.00000i 0.393654i
\(414\) 8.00000 0.393179
\(415\) 16.0000 + 8.00000i 0.785409 + 0.392705i
\(416\) 6.00000 0.294174
\(417\) 14.0000i 0.685583i
\(418\) 12.0000i 0.586939i
\(419\) −20.0000 −0.977064 −0.488532 0.872546i \(-0.662467\pi\)
−0.488532 + 0.872546i \(0.662467\pi\)
\(420\) 1.00000 2.00000i 0.0487950 0.0975900i
\(421\) 34.0000 1.65706 0.828529 0.559946i \(-0.189178\pi\)
0.828529 + 0.559946i \(0.189178\pi\)
\(422\) 0 0
\(423\) 8.00000i 0.388973i
\(424\) −6.00000 −0.291386
\(425\) 16.0000 12.0000i 0.776114 0.582086i
\(426\) −6.00000 −0.290701
\(427\) 10.0000i 0.483934i
\(428\) 12.0000i 0.580042i
\(429\) −12.0000 −0.579365
\(430\) 4.00000 8.00000i 0.192897 0.385794i
\(431\) 2.00000 0.0963366 0.0481683 0.998839i \(-0.484662\pi\)
0.0481683 + 0.998839i \(0.484662\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 26.0000i 1.24948i 0.780833 + 0.624740i \(0.214795\pi\)
−0.780833 + 0.624740i \(0.785205\pi\)
\(434\) −2.00000 −0.0960031
\(435\) 12.0000 + 6.00000i 0.575356 + 0.287678i
\(436\) −14.0000 −0.670478
\(437\) 48.0000i 2.29615i
\(438\) 14.0000i 0.668946i
\(439\) 18.0000 0.859093 0.429547 0.903045i \(-0.358673\pi\)
0.429547 + 0.903045i \(0.358673\pi\)
\(440\) −4.00000 2.00000i −0.190693 0.0953463i
\(441\) 1.00000 0.0476190
\(442\) 24.0000i 1.14156i
\(443\) 12.0000i 0.570137i 0.958507 + 0.285069i \(0.0920164\pi\)
−0.958507 + 0.285069i \(0.907984\pi\)
\(444\) −4.00000 −0.189832
\(445\) 10.0000 20.0000i 0.474045 0.948091i
\(446\) −8.00000 −0.378811
\(447\) 10.0000i 0.472984i
\(448\) 1.00000i 0.0472456i
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) −4.00000 + 3.00000i −0.188562 + 0.141421i
\(451\) 4.00000 0.188353
\(452\) 6.00000i 0.282216i
\(453\) 8.00000i 0.375873i
\(454\) 8.00000 0.375459
\(455\) −6.00000 + 12.0000i −0.281284 + 0.562569i
\(456\) −6.00000 −0.280976
\(457\) 28.0000i 1.30978i 0.755722 + 0.654892i \(0.227286\pi\)
−0.755722 + 0.654892i \(0.772714\pi\)
\(458\) 14.0000i 0.654177i
\(459\) −4.00000 −0.186704
\(460\) −16.0000 8.00000i −0.746004 0.373002i
\(461\) −18.0000 −0.838344 −0.419172 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 2.00000i 0.0930484i
\(463\) 36.0000i 1.67306i −0.547920 0.836531i \(-0.684580\pi\)
0.547920 0.836531i \(-0.315420\pi\)
\(464\) −6.00000 −0.278543
\(465\) 4.00000 + 2.00000i 0.185496 + 0.0927478i
\(466\) −10.0000 −0.463241
\(467\) 24.0000i 1.11059i −0.831654 0.555294i \(-0.812606\pi\)
0.831654 0.555294i \(-0.187394\pi\)
\(468\) 6.00000i 0.277350i
\(469\) 8.00000 0.369406
\(470\) −8.00000 + 16.0000i −0.369012 + 0.738025i
\(471\) −22.0000 −1.01371
\(472\) 8.00000i 0.368230i
\(473\) 8.00000i 0.367840i
\(474\) 12.0000 0.551178
\(475\) −18.0000 24.0000i −0.825897 1.10120i
\(476\) −4.00000 −0.183340
\(477\) 6.00000i 0.274721i
\(478\) 26.0000i 1.18921i
\(479\) −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
\(481\) 24.0000 1.09431
\(482\) 26.0000i 1.18427i
\(483\) 8.00000i 0.364013i
\(484\) 7.00000 0.318182
\(485\) −20.0000 10.0000i −0.908153 0.454077i
\(486\) 1.00000 0.0453609
\(487\) 12.0000i 0.543772i 0.962329 + 0.271886i \(0.0876473\pi\)
−0.962329 + 0.271886i \(0.912353\pi\)
\(488\) 10.0000i 0.452679i
\(489\) 4.00000 0.180886
\(490\) −2.00000 1.00000i −0.0903508 0.0451754i
\(491\) −30.0000 −1.35388 −0.676941 0.736038i \(-0.736695\pi\)
−0.676941 + 0.736038i \(0.736695\pi\)
\(492\) 2.00000i 0.0901670i
\(493\) 24.0000i 1.08091i
\(494\) 36.0000 1.61972
\(495\) −2.00000 + 4.00000i −0.0898933 + 0.179787i
\(496\) −2.00000 −0.0898027
\(497\) 6.00000i 0.269137i
\(498\) 8.00000i 0.358489i
\(499\) 12.0000 0.537194 0.268597 0.963253i \(-0.413440\pi\)
0.268597 + 0.963253i \(0.413440\pi\)
\(500\) 11.0000 2.00000i 0.491935 0.0894427i
\(501\) −12.0000 −0.536120
\(502\) 0 0
\(503\) 12.0000i 0.535054i 0.963550 + 0.267527i \(0.0862064\pi\)
−0.963550 + 0.267527i \(0.913794\pi\)
\(504\) 1.00000 0.0445435
\(505\) 10.0000 20.0000i 0.444994 0.889988i
\(506\) −16.0000 −0.711287
\(507\) 23.0000i 1.02147i
\(508\) 4.00000i 0.177471i
\(509\) −30.0000 −1.32973 −0.664863 0.746965i \(-0.731510\pi\)
−0.664863 + 0.746965i \(0.731510\pi\)
\(510\) 8.00000 + 4.00000i 0.354246 + 0.177123i
\(511\) 14.0000 0.619324
\(512\) 1.00000i 0.0441942i
\(513\) 6.00000i 0.264906i
\(514\) 0 0
\(515\) −16.0000 8.00000i −0.705044 0.352522i
\(516\) 4.00000 0.176090
\(517\) 16.0000i 0.703679i
\(518\) 4.00000i 0.175750i
\(519\) −8.00000 −0.351161
\(520\) −6.00000 + 12.0000i −0.263117 + 0.526235i
\(521\) −26.0000 −1.13908 −0.569540 0.821963i \(-0.692879\pi\)
−0.569540 + 0.821963i \(0.692879\pi\)
\(522\) 6.00000i 0.262613i
\(523\) 28.0000i 1.22435i 0.790721 + 0.612177i \(0.209706\pi\)
−0.790721 + 0.612177i \(0.790294\pi\)
\(524\) 12.0000 0.524222
\(525\) 3.00000 + 4.00000i 0.130931 + 0.174574i
\(526\) 16.0000 0.697633
\(527\) 8.00000i 0.348485i
\(528\) 2.00000i 0.0870388i
\(529\) −41.0000 −1.78261
\(530\) 6.00000 12.0000i 0.260623 0.521247i
\(531\) −8.00000 −0.347170
\(532\) 6.00000i 0.260133i
\(533\) 12.0000i 0.519778i
\(534\) 10.0000 0.432742
\(535\) 24.0000 + 12.0000i 1.03761 + 0.518805i
\(536\) 8.00000 0.345547
\(537\) 10.0000i 0.431532i
\(538\) 18.0000i 0.776035i
\(539\) −2.00000 −0.0861461
\(540\) −2.00000 1.00000i −0.0860663 0.0430331i
\(541\) 22.0000 0.945854 0.472927 0.881102i \(-0.343197\pi\)
0.472927 + 0.881102i \(0.343197\pi\)
\(542\) 10.0000i 0.429537i
\(543\) 2.00000i 0.0858282i
\(544\) −4.00000 −0.171499
\(545\) 14.0000 28.0000i 0.599694 1.19939i
\(546\) −6.00000 −0.256776
\(547\) 40.0000i 1.71028i 0.518400 + 0.855138i \(0.326528\pi\)
−0.518400 + 0.855138i \(0.673472\pi\)
\(548\) 6.00000i 0.256307i
\(549\) 10.0000 0.426790
\(550\) 8.00000 6.00000i 0.341121 0.255841i
\(551\) −36.0000 −1.53365
\(552\) 8.00000i 0.340503i
\(553\) 12.0000i 0.510292i
\(554\) −28.0000 −1.18961
\(555\) 4.00000 8.00000i 0.169791 0.339581i
\(556\) −14.0000 −0.593732
\(557\) 42.0000i 1.77960i −0.456354 0.889799i \(-0.650845\pi\)
0.456354 0.889799i \(-0.349155\pi\)
\(558\) 2.00000i 0.0846668i
\(559\) −24.0000 −1.01509
\(560\) −2.00000 1.00000i −0.0845154 0.0422577i
\(561\) 8.00000 0.337760
\(562\) 30.0000i 1.26547i
\(563\) 4.00000i 0.168580i 0.996441 + 0.0842900i \(0.0268622\pi\)
−0.996441 + 0.0842900i \(0.973138\pi\)
\(564\) −8.00000 −0.336861
\(565\) −12.0000 6.00000i −0.504844 0.252422i
\(566\) 20.0000 0.840663
\(567\) 1.00000i 0.0419961i
\(568\) 6.00000i 0.251754i
\(569\) 46.0000 1.92842 0.964210 0.265139i \(-0.0854179\pi\)
0.964210 + 0.265139i \(0.0854179\pi\)
\(570\) 6.00000 12.0000i 0.251312 0.502625i
\(571\) 4.00000 0.167395 0.0836974 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) 12.0000i 0.501745i
\(573\) 18.0000i 0.751961i
\(574\) 2.00000 0.0834784
\(575\) 32.0000 24.0000i 1.33449 1.00087i
\(576\) 1.00000 0.0416667
\(577\) 26.0000i 1.08239i −0.840896 0.541197i \(-0.817971\pi\)
0.840896 0.541197i \(-0.182029\pi\)
\(578\) 1.00000i 0.0415945i
\(579\) 8.00000 0.332469
\(580\) 6.00000 12.0000i 0.249136 0.498273i
\(581\) 8.00000 0.331896
\(582\) 10.0000i 0.414513i
\(583\) 12.0000i 0.496989i
\(584\) 14.0000 0.579324
\(585\) 12.0000 + 6.00000i 0.496139 + 0.248069i
\(586\) 0 0
\(587\) 12.0000i 0.495293i −0.968850 0.247647i \(-0.920343\pi\)
0.968850 0.247647i \(-0.0796572\pi\)
\(588\) 1.00000i 0.0412393i
\(589\) −12.0000 −0.494451
\(590\) 16.0000 + 8.00000i 0.658710 + 0.329355i
\(591\) 2.00000 0.0822690
\(592\) 4.00000i 0.164399i
\(593\) 12.0000i 0.492781i −0.969171 0.246390i \(-0.920755\pi\)
0.969171 0.246390i \(-0.0792446\pi\)
\(594\) −2.00000 −0.0820610
\(595\) 4.00000 8.00000i 0.163984 0.327968i
\(596\) 10.0000 0.409616
\(597\) 6.00000i 0.245564i
\(598\) 48.0000i 1.96287i
\(599\) −30.0000 −1.22577 −0.612883 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) 3.00000 + 4.00000i 0.122474 + 0.163299i
\(601\) 38.0000 1.55005 0.775026 0.631929i \(-0.217737\pi\)
0.775026 + 0.631929i \(0.217737\pi\)
\(602\) 4.00000i 0.163028i
\(603\) 8.00000i 0.325785i
\(604\) 8.00000 0.325515
\(605\) −7.00000 + 14.0000i −0.284590 + 0.569181i
\(606\) 10.0000 0.406222
\(607\) 8.00000i 0.324710i 0.986732 + 0.162355i \(0.0519090\pi\)
−0.986732 + 0.162355i \(0.948091\pi\)
\(608\) 6.00000i 0.243332i
\(609\) 6.00000 0.243132
\(610\) −20.0000 10.0000i −0.809776 0.404888i
\(611\) 48.0000 1.94187
\(612\) 4.00000i 0.161690i
\(613\) 28.0000i 1.13091i −0.824779 0.565455i \(-0.808701\pi\)
0.824779 0.565455i \(-0.191299\pi\)
\(614\) 12.0000 0.484281
\(615\) −4.00000 2.00000i −0.161296 0.0806478i
\(616\) −2.00000 −0.0805823
\(617\) 26.0000i 1.04672i −0.852111 0.523360i \(-0.824678\pi\)
0.852111 0.523360i \(-0.175322\pi\)
\(618\) 8.00000i 0.321807i
\(619\) 22.0000 0.884255 0.442127 0.896952i \(-0.354224\pi\)
0.442127 + 0.896952i \(0.354224\pi\)
\(620\) 2.00000 4.00000i 0.0803219 0.160644i
\(621\) −8.00000 −0.321029
\(622\) 24.0000i 0.962312i
\(623\) 10.0000i 0.400642i
\(624\) −6.00000 −0.240192
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) −2.00000 −0.0799361
\(627\) 12.0000i 0.479234i
\(628\) 22.0000i 0.877896i
\(629\) −16.0000 −0.637962
\(630\) −1.00000 + 2.00000i −0.0398410 + 0.0796819i
\(631\) −4.00000 −0.159237 −0.0796187 0.996825i \(-0.525370\pi\)
−0.0796187 + 0.996825i \(0.525370\pi\)
\(632\) 12.0000i 0.477334i
\(633\) 0 0
\(634\) 2.00000 0.0794301
\(635\) 8.00000 + 4.00000i 0.317470 + 0.158735i
\(636\) 6.00000 0.237915
\(637\) 6.00000i 0.237729i
\(638\) 12.0000i 0.475085i
\(639\) 6.00000 0.237356
\(640\) −2.00000 1.00000i −0.0790569 0.0395285i
\(641\) 14.0000 0.552967 0.276483 0.961019i \(-0.410831\pi\)
0.276483 + 0.961019i \(0.410831\pi\)
\(642\) 12.0000i 0.473602i
\(643\) 12.0000i 0.473234i −0.971603 0.236617i \(-0.923961\pi\)
0.971603 0.236617i \(-0.0760386\pi\)
\(644\) −8.00000 −0.315244
\(645\) −4.00000 + 8.00000i −0.157500 + 0.315000i
\(646\) −24.0000 −0.944267
\(647\) 36.0000i 1.41531i 0.706560 + 0.707653i \(0.250246\pi\)
−0.706560 + 0.707653i \(0.749754\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 16.0000 0.628055
\(650\) −18.0000 24.0000i −0.706018 0.941357i
\(651\) 2.00000 0.0783862
\(652\) 4.00000i 0.156652i
\(653\) 34.0000i 1.33052i −0.746611 0.665261i \(-0.768320\pi\)
0.746611 0.665261i \(-0.231680\pi\)
\(654\) 14.0000 0.547443
\(655\) −12.0000 + 24.0000i −0.468879 + 0.937758i
\(656\) 2.00000 0.0780869
\(657\) 14.0000i 0.546192i
\(658\) 8.00000i 0.311872i
\(659\) 26.0000 1.01282 0.506408 0.862294i \(-0.330973\pi\)
0.506408 + 0.862294i \(0.330973\pi\)
\(660\) 4.00000 + 2.00000i 0.155700 + 0.0778499i
\(661\) 38.0000 1.47803 0.739014 0.673690i \(-0.235292\pi\)
0.739014 + 0.673690i \(0.235292\pi\)
\(662\) 8.00000i 0.310929i
\(663\) 24.0000i 0.932083i
\(664\) 8.00000 0.310460
\(665\) −12.0000 6.00000i −0.465340 0.232670i
\(666\) 4.00000 0.154997
\(667\) 48.0000i 1.85857i
\(668\) 12.0000i 0.464294i
\(669\) 8.00000 0.309298
\(670\) −8.00000 + 16.0000i −0.309067 + 0.618134i
\(671\) −20.0000 −0.772091
\(672\) 1.00000i 0.0385758i
\(673\) 12.0000i 0.462566i −0.972887 0.231283i \(-0.925708\pi\)
0.972887 0.231283i \(-0.0742923\pi\)
\(674\) 8.00000 0.308148
\(675\) 4.00000 3.00000i 0.153960 0.115470i
\(676\) 23.0000 0.884615
\(677\) 40.0000i 1.53732i 0.639655 + 0.768662i \(0.279077\pi\)
−0.639655 + 0.768662i \(0.720923\pi\)
\(678\) 6.00000i 0.230429i
\(679\) −10.0000 −0.383765
\(680\) 4.00000 8.00000i 0.153393 0.306786i
\(681\) −8.00000 −0.306561
\(682\) 4.00000i 0.153168i
\(683\) 4.00000i 0.153056i −0.997067 0.0765279i \(-0.975617\pi\)
0.997067 0.0765279i \(-0.0243834\pi\)
\(684\) 6.00000 0.229416
\(685\) −12.0000 6.00000i −0.458496 0.229248i
\(686\) −1.00000 −0.0381802
\(687\) 14.0000i 0.534133i
\(688\) 4.00000i 0.152499i
\(689\) −36.0000 −1.37149
\(690\) 16.0000 + 8.00000i 0.609110 + 0.304555i
\(691\) −2.00000 −0.0760836 −0.0380418 0.999276i \(-0.512112\pi\)
−0.0380418 + 0.999276i \(0.512112\pi\)
\(692\) 8.00000i 0.304114i
\(693\) 2.00000i 0.0759737i
\(694\) −36.0000 −1.36654
\(695\) 14.0000 28.0000i 0.531050 1.06210i
\(696\) 6.00000 0.227429
\(697\) 8.00000i 0.303022i
\(698\) 26.0000i 0.984115i
\(699\) 10.0000 0.378235
\(700\) 4.00000 3.00000i 0.151186 0.113389i
\(701\) −34.0000 −1.28416 −0.642081 0.766637i \(-0.721929\pi\)
−0.642081 + 0.766637i \(0.721929\pi\)
\(702\) 6.00000i 0.226455i
\(703\) 24.0000i 0.905177i
\(704\) −2.00000 −0.0753778
\(705\) 8.00000 16.0000i 0.301297 0.602595i
\(706\) 20.0000 0.752710
\(707\) 10.0000i 0.376089i
\(708\) 8.00000i 0.300658i
\(709\) 6.00000 0.225335 0.112667 0.993633i \(-0.464061\pi\)
0.112667 + 0.993633i \(0.464061\pi\)
\(710\) −12.0000 6.00000i −0.450352 0.225176i
\(711\) −12.0000 −0.450035
\(712\) 10.0000i 0.374766i
\(713\) 16.0000i 0.599205i
\(714\) 4.00000 0.149696
\(715\) −24.0000 12.0000i −0.897549 0.448775i
\(716\) 10.0000 0.373718
\(717\) 26.0000i 0.970988i
\(718\) 6.00000i 0.223918i
\(719\) 4.00000 0.149175 0.0745874 0.997214i \(-0.476236\pi\)
0.0745874 + 0.997214i \(0.476236\pi\)
\(720\) −1.00000 + 2.00000i −0.0372678 + 0.0745356i
\(721\) −8.00000 −0.297936
\(722\) 17.0000i 0.632674i
\(723\) 26.0000i 0.966950i
\(724\) −2.00000 −0.0743294
\(725\) 18.0000 + 24.0000i 0.668503 + 0.891338i
\(726\) −7.00000 −0.259794
\(727\) 24.0000i 0.890111i 0.895503 + 0.445055i \(0.146816\pi\)
−0.895503 + 0.445055i \(0.853184\pi\)
\(728\) 6.00000i 0.222375i
\(729\) −1.00000 −0.0370370
\(730\) −14.0000 + 28.0000i −0.518163 + 1.03633i
\(731\) 16.0000 0.591781
\(732\) 10.0000i 0.369611i
\(733\) 14.0000i 0.517102i −0.965998 0.258551i \(-0.916755\pi\)
0.965998 0.258551i \(-0.0832450\pi\)
\(734\) 32.0000 1.18114
\(735\) 2.00000 + 1.00000i 0.0737711 + 0.0368856i
\(736\) −8.00000 −0.294884
\(737\) 16.0000i 0.589368i
\(738\) 2.00000i 0.0736210i
\(739\) 44.0000 1.61857 0.809283 0.587419i \(-0.199856\pi\)
0.809283 + 0.587419i \(0.199856\pi\)
\(740\) −8.00000 4.00000i −0.294086 0.147043i
\(741\) −36.0000 −1.32249
\(742\) 6.00000i 0.220267i
\(743\) 48.0000i 1.76095i 0.474093 + 0.880475i \(0.342776\pi\)
−0.474093 + 0.880475i \(0.657224\pi\)
\(744\) 2.00000 0.0733236
\(745\) −10.0000 + 20.0000i −0.366372 + 0.732743i
\(746\) −24.0000 −0.878702
\(747\) 8.00000i 0.292705i
\(748\) 8.00000i 0.292509i
\(749\) 12.0000 0.438470
\(750\) −11.0000 + 2.00000i −0.401663 + 0.0730297i
\(751\) 20.0000 0.729810 0.364905 0.931045i \(-0.381101\pi\)
0.364905 + 0.931045i \(0.381101\pi\)
\(752\) 8.00000i 0.291730i
\(753\) 0 0
\(754\) −36.0000 −1.31104
\(755\) −8.00000 + 16.0000i −0.291150 + 0.582300i
\(756\) −1.00000 −0.0363696
\(757\) 32.0000i 1.16306i −0.813525 0.581530i \(-0.802454\pi\)
0.813525 0.581530i \(-0.197546\pi\)
\(758\) 20.0000i 0.726433i
\(759\) 16.0000 0.580763
\(760\) −12.0000 6.00000i −0.435286 0.217643i
\(761\) −6.00000 −0.217500 −0.108750 0.994069i \(-0.534685\pi\)
−0.108750 + 0.994069i \(0.534685\pi\)
\(762\) 4.00000i 0.144905i
\(763\) 14.0000i 0.506834i
\(764\) 18.0000 0.651217
\(765\) −8.00000 4.00000i −0.289241 0.144620i
\(766\) 20.0000 0.722629
\(767\) 48.0000i 1.73318i
\(768\) 1.00000i 0.0360844i
\(769\) −30.0000 −1.08183 −0.540914 0.841078i \(-0.681921\pi\)
−0.540914 + 0.841078i \(0.681921\pi\)
\(770\) 2.00000 4.00000i 0.0720750 0.144150i
\(771\) 0 0
\(772\) 8.00000i 0.287926i
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) −4.00000 −0.143777
\(775\) 6.00000 + 8.00000i 0.215526 + 0.287368i
\(776\) −10.0000 −0.358979
\(777\) 4.00000i 0.143499i
\(778\) 2.00000i 0.0717035i
\(779\) 12.0000 0.429945
\(780\) 6.00000 12.0000i 0.214834 0.429669i
\(781\) −12.0000 −0.429394
\(782\) 32.0000i 1.14432i
\(783\) 6.00000i 0.214423i
\(784\) −1.00000 −0.0357143
\(785\) −44.0000 22.0000i −1.57043 0.785214i
\(786\) −12.0000 −0.428026
\(787\) 28.0000i 0.998092i 0.866575 + 0.499046i \(0.166316\pi\)
−0.866575 + 0.499046i \(0.833684\pi\)
\(788\)