Properties

Label 70.2.i.a.9.2
Level 70
Weight 2
Character 70.9
Analytic conductor 0.559
Analytic rank 0
Dimension 4
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 70.i (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.558952814149\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 9.2
Root \(0.866025 + 0.500000i\)
Character \(\chi\) = 70.9
Dual form 70.2.i.a.39.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(-2.59808 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.23205 + 1.86603i) q^{5} -3.00000 q^{6} +(0.866025 - 2.50000i) q^{7} +1.00000i q^{8} +(3.00000 - 5.19615i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(-2.59808 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.23205 + 1.86603i) q^{5} -3.00000 q^{6} +(0.866025 - 2.50000i) q^{7} +1.00000i q^{8} +(3.00000 - 5.19615i) q^{9} +(0.133975 + 2.23205i) q^{10} +(-2.59808 - 1.50000i) q^{12} -2.00000i q^{13} +(2.00000 - 1.73205i) q^{14} +(-6.00000 - 3.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.73205 - 1.00000i) q^{17} +(5.19615 - 3.00000i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(-1.00000 + 2.00000i) q^{20} +(1.50000 + 7.79423i) q^{21} +(0.866025 + 0.500000i) q^{23} +(-1.50000 - 2.59808i) q^{24} +(-1.96410 + 4.59808i) q^{25} +(1.00000 - 1.73205i) q^{26} +9.00000i q^{27} +(2.59808 - 0.500000i) q^{28} +1.00000 q^{29} +(-3.69615 - 5.59808i) q^{30} +(-5.00000 - 8.66025i) q^{31} +(-0.866025 + 0.500000i) q^{32} +2.00000 q^{34} +(5.73205 - 1.46410i) q^{35} +6.00000 q^{36} +(-6.92820 - 4.00000i) q^{37} +(-1.73205 + 1.00000i) q^{38} +(3.00000 + 5.19615i) q^{39} +(-1.86603 + 1.23205i) q^{40} -3.00000 q^{41} +(-2.59808 + 7.50000i) q^{42} +5.00000i q^{43} +(13.3923 - 0.803848i) q^{45} +(0.500000 + 0.866025i) q^{46} +(6.92820 + 4.00000i) q^{47} -3.00000i q^{48} +(-5.50000 - 4.33013i) q^{49} +(-4.00000 + 3.00000i) q^{50} +(-3.00000 + 5.19615i) q^{51} +(1.73205 - 1.00000i) q^{52} +(-5.19615 + 3.00000i) q^{53} +(-4.50000 + 7.79423i) q^{54} +(2.50000 + 0.866025i) q^{56} -6.00000i q^{57} +(0.866025 + 0.500000i) q^{58} +(1.00000 + 1.73205i) q^{59} +(-0.401924 - 6.69615i) q^{60} +(4.50000 - 7.79423i) q^{61} -10.0000i q^{62} +(-10.3923 - 12.0000i) q^{63} -1.00000 q^{64} +(3.73205 - 2.46410i) q^{65} +(6.06218 - 3.50000i) q^{67} +(1.73205 + 1.00000i) q^{68} -3.00000 q^{69} +(5.69615 + 1.59808i) q^{70} +6.00000 q^{71} +(5.19615 + 3.00000i) q^{72} +(-8.66025 + 5.00000i) q^{73} +(-4.00000 - 6.92820i) q^{74} +(-1.79423 - 14.8923i) q^{75} -2.00000 q^{76} +6.00000i q^{78} +(-5.00000 + 8.66025i) q^{79} +(-2.23205 + 0.133975i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-2.59808 - 1.50000i) q^{82} -9.00000i q^{83} +(-6.00000 + 5.19615i) q^{84} +(4.00000 + 2.00000i) q^{85} +(-2.50000 + 4.33013i) q^{86} +(-2.59808 + 1.50000i) q^{87} +(-3.50000 + 6.06218i) q^{89} +(12.0000 + 6.00000i) q^{90} +(-5.00000 - 1.73205i) q^{91} +1.00000i q^{92} +(25.9808 + 15.0000i) q^{93} +(4.00000 + 6.92820i) q^{94} +(-4.46410 + 0.267949i) q^{95} +(1.50000 - 2.59808i) q^{96} +(-2.59808 - 6.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} - 2q^{5} - 12q^{6} + 12q^{9} + O(q^{10}) \) \( 4q + 2q^{4} - 2q^{5} - 12q^{6} + 12q^{9} + 4q^{10} + 8q^{14} - 24q^{15} - 2q^{16} - 4q^{19} - 4q^{20} + 6q^{21} - 6q^{24} + 6q^{25} + 4q^{26} + 4q^{29} + 6q^{30} - 20q^{31} + 8q^{34} + 16q^{35} + 24q^{36} + 12q^{39} - 4q^{40} - 12q^{41} + 12q^{45} + 2q^{46} - 22q^{49} - 16q^{50} - 12q^{51} - 18q^{54} + 10q^{56} + 4q^{59} - 12q^{60} + 18q^{61} - 4q^{64} + 8q^{65} - 12q^{69} + 2q^{70} + 24q^{71} - 16q^{74} + 24q^{75} - 8q^{76} - 20q^{79} - 2q^{80} - 18q^{81} - 24q^{84} + 16q^{85} - 10q^{86} - 14q^{89} + 48q^{90} - 20q^{91} + 16q^{94} - 4q^{95} + 6q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/70\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(57\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) −2.59808 + 1.50000i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(-1.00000\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.23205 + 1.86603i 0.550990 + 0.834512i
\(6\) −3.00000 −1.22474
\(7\) 0.866025 2.50000i 0.327327 0.944911i
\(8\) 1.00000i 0.353553i
\(9\) 3.00000 5.19615i 1.00000 1.73205i
\(10\) 0.133975 + 2.23205i 0.0423665 + 0.705836i
\(11\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) −2.59808 1.50000i −0.750000 0.433013i
\(13\) 2.00000i 0.554700i −0.960769 0.277350i \(-0.910544\pi\)
0.960769 0.277350i \(-0.0894562\pi\)
\(14\) 2.00000 1.73205i 0.534522 0.462910i
\(15\) −6.00000 3.00000i −1.54919 0.774597i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.73205 1.00000i 0.420084 0.242536i −0.275029 0.961436i \(-0.588688\pi\)
0.695113 + 0.718900i \(0.255354\pi\)
\(18\) 5.19615 3.00000i 1.22474 0.707107i
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) −1.00000 + 2.00000i −0.223607 + 0.447214i
\(21\) 1.50000 + 7.79423i 0.327327 + 1.70084i
\(22\) 0 0
\(23\) 0.866025 + 0.500000i 0.180579 + 0.104257i 0.587565 0.809177i \(-0.300087\pi\)
−0.406986 + 0.913434i \(0.633420\pi\)
\(24\) −1.50000 2.59808i −0.306186 0.530330i
\(25\) −1.96410 + 4.59808i −0.392820 + 0.919615i
\(26\) 1.00000 1.73205i 0.196116 0.339683i
\(27\) 9.00000i 1.73205i
\(28\) 2.59808 0.500000i 0.490990 0.0944911i
\(29\) 1.00000 0.185695 0.0928477 0.995680i \(-0.470403\pi\)
0.0928477 + 0.995680i \(0.470403\pi\)
\(30\) −3.69615 5.59808i −0.674822 1.02206i
\(31\) −5.00000 8.66025i −0.898027 1.55543i −0.830014 0.557743i \(-0.811667\pi\)
−0.0680129 0.997684i \(-0.521666\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) 5.73205 1.46410i 0.968893 0.247478i
\(36\) 6.00000 1.00000
\(37\) −6.92820 4.00000i −1.13899 0.657596i −0.192809 0.981236i \(-0.561760\pi\)
−0.946180 + 0.323640i \(0.895093\pi\)
\(38\) −1.73205 + 1.00000i −0.280976 + 0.162221i
\(39\) 3.00000 + 5.19615i 0.480384 + 0.832050i
\(40\) −1.86603 + 1.23205i −0.295045 + 0.194804i
\(41\) −3.00000 −0.468521 −0.234261 0.972174i \(-0.575267\pi\)
−0.234261 + 0.972174i \(0.575267\pi\)
\(42\) −2.59808 + 7.50000i −0.400892 + 1.15728i
\(43\) 5.00000i 0.762493i 0.924473 + 0.381246i \(0.124505\pi\)
−0.924473 + 0.381246i \(0.875495\pi\)
\(44\) 0 0
\(45\) 13.3923 0.803848i 1.99641 0.119831i
\(46\) 0.500000 + 0.866025i 0.0737210 + 0.127688i
\(47\) 6.92820 + 4.00000i 1.01058 + 0.583460i 0.911362 0.411606i \(-0.135032\pi\)
0.0992202 + 0.995066i \(0.468365\pi\)
\(48\) 3.00000i 0.433013i
\(49\) −5.50000 4.33013i −0.785714 0.618590i
\(50\) −4.00000 + 3.00000i −0.565685 + 0.424264i
\(51\) −3.00000 + 5.19615i −0.420084 + 0.727607i
\(52\) 1.73205 1.00000i 0.240192 0.138675i
\(53\) −5.19615 + 3.00000i −0.713746 + 0.412082i −0.812447 0.583036i \(-0.801865\pi\)
0.0987002 + 0.995117i \(0.468532\pi\)
\(54\) −4.50000 + 7.79423i −0.612372 + 1.06066i
\(55\) 0 0
\(56\) 2.50000 + 0.866025i 0.334077 + 0.115728i
\(57\) 6.00000i 0.794719i
\(58\) 0.866025 + 0.500000i 0.113715 + 0.0656532i
\(59\) 1.00000 + 1.73205i 0.130189 + 0.225494i 0.923749 0.382998i \(-0.125108\pi\)
−0.793560 + 0.608492i \(0.791775\pi\)
\(60\) −0.401924 6.69615i −0.0518881 0.864470i
\(61\) 4.50000 7.79423i 0.576166 0.997949i −0.419748 0.907641i \(-0.637882\pi\)
0.995914 0.0903080i \(-0.0287851\pi\)
\(62\) 10.0000i 1.27000i
\(63\) −10.3923 12.0000i −1.30931 1.51186i
\(64\) −1.00000 −0.125000
\(65\) 3.73205 2.46410i 0.462904 0.305634i
\(66\) 0 0
\(67\) 6.06218 3.50000i 0.740613 0.427593i −0.0816792 0.996659i \(-0.526028\pi\)
0.822292 + 0.569066i \(0.192695\pi\)
\(68\) 1.73205 + 1.00000i 0.210042 + 0.121268i
\(69\) −3.00000 −0.361158
\(70\) 5.69615 + 1.59808i 0.680820 + 0.191007i
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 5.19615 + 3.00000i 0.612372 + 0.353553i
\(73\) −8.66025 + 5.00000i −1.01361 + 0.585206i −0.912245 0.409644i \(-0.865653\pi\)
−0.101361 + 0.994850i \(0.532320\pi\)
\(74\) −4.00000 6.92820i −0.464991 0.805387i
\(75\) −1.79423 14.8923i −0.207180 1.71962i
\(76\) −2.00000 −0.229416
\(77\) 0 0
\(78\) 6.00000i 0.679366i
\(79\) −5.00000 + 8.66025i −0.562544 + 0.974355i 0.434730 + 0.900561i \(0.356844\pi\)
−0.997274 + 0.0737937i \(0.976489\pi\)
\(80\) −2.23205 + 0.133975i −0.249551 + 0.0149788i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) −2.59808 1.50000i −0.286910 0.165647i
\(83\) 9.00000i 0.987878i −0.869496 0.493939i \(-0.835557\pi\)
0.869496 0.493939i \(-0.164443\pi\)
\(84\) −6.00000 + 5.19615i −0.654654 + 0.566947i
\(85\) 4.00000 + 2.00000i 0.433861 + 0.216930i
\(86\) −2.50000 + 4.33013i −0.269582 + 0.466930i
\(87\) −2.59808 + 1.50000i −0.278543 + 0.160817i
\(88\) 0 0
\(89\) −3.50000 + 6.06218i −0.370999 + 0.642590i −0.989720 0.143022i \(-0.954318\pi\)
0.618720 + 0.785611i \(0.287651\pi\)
\(90\) 12.0000 + 6.00000i 1.26491 + 0.632456i
\(91\) −5.00000 1.73205i −0.524142 0.181568i
\(92\) 1.00000i 0.104257i
\(93\) 25.9808 + 15.0000i 2.69408 + 1.55543i
\(94\) 4.00000 + 6.92820i 0.412568 + 0.714590i
\(95\) −4.46410 + 0.267949i −0.458007 + 0.0274910i
\(96\) 1.50000 2.59808i 0.153093 0.265165i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −2.59808 6.50000i −0.262445 0.656599i
\(99\) 0 0
\(100\) −4.96410 + 0.598076i −0.496410 + 0.0598076i
\(101\) 7.50000 + 12.9904i 0.746278 + 1.29259i 0.949595 + 0.313478i \(0.101494\pi\)
−0.203317 + 0.979113i \(0.565172\pi\)
\(102\) −5.19615 + 3.00000i −0.514496 + 0.297044i
\(103\) 9.52628 + 5.50000i 0.938652 + 0.541931i 0.889538 0.456862i \(-0.151027\pi\)
0.0491146 + 0.998793i \(0.484360\pi\)
\(104\) 2.00000 0.196116
\(105\) −12.6962 + 12.4019i −1.23902 + 1.21030i
\(106\) −6.00000 −0.582772
\(107\) −6.06218 3.50000i −0.586053 0.338358i 0.177482 0.984124i \(-0.443205\pi\)
−0.763535 + 0.645766i \(0.776538\pi\)
\(108\) −7.79423 + 4.50000i −0.750000 + 0.433013i
\(109\) 2.50000 + 4.33013i 0.239457 + 0.414751i 0.960558 0.278078i \(-0.0896974\pi\)
−0.721102 + 0.692829i \(0.756364\pi\)
\(110\) 0 0
\(111\) 24.0000 2.27798
\(112\) 1.73205 + 2.00000i 0.163663 + 0.188982i
\(113\) 10.0000i 0.940721i −0.882474 0.470360i \(-0.844124\pi\)
0.882474 0.470360i \(-0.155876\pi\)
\(114\) 3.00000 5.19615i 0.280976 0.486664i
\(115\) 0.133975 + 2.23205i 0.0124932 + 0.208140i
\(116\) 0.500000 + 0.866025i 0.0464238 + 0.0804084i
\(117\) −10.3923 6.00000i −0.960769 0.554700i
\(118\) 2.00000i 0.184115i
\(119\) −1.00000 5.19615i −0.0916698 0.476331i
\(120\) 3.00000 6.00000i 0.273861 0.547723i
\(121\) 5.50000 9.52628i 0.500000 0.866025i
\(122\) 7.79423 4.50000i 0.705656 0.407411i
\(123\) 7.79423 4.50000i 0.702782 0.405751i
\(124\) 5.00000 8.66025i 0.449013 0.777714i
\(125\) −11.0000 + 2.00000i −0.983870 + 0.178885i
\(126\) −3.00000 15.5885i −0.267261 1.38873i
\(127\) 8.00000i 0.709885i 0.934888 + 0.354943i \(0.115500\pi\)
−0.934888 + 0.354943i \(0.884500\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) −7.50000 12.9904i −0.660338 1.14374i
\(130\) 4.46410 0.267949i 0.391528 0.0235007i
\(131\) −10.0000 + 17.3205i −0.873704 + 1.51330i −0.0155672 + 0.999879i \(0.504955\pi\)
−0.858137 + 0.513421i \(0.828378\pi\)
\(132\) 0 0
\(133\) 3.46410 + 4.00000i 0.300376 + 0.346844i
\(134\) 7.00000 0.604708
\(135\) −16.7942 + 11.0885i −1.44542 + 0.954342i
\(136\) 1.00000 + 1.73205i 0.0857493 + 0.148522i
\(137\) −13.8564 + 8.00000i −1.18383 + 0.683486i −0.956898 0.290424i \(-0.906204\pi\)
−0.226935 + 0.973910i \(0.572870\pi\)
\(138\) −2.59808 1.50000i −0.221163 0.127688i
\(139\) 8.00000 0.678551 0.339276 0.940687i \(-0.389818\pi\)
0.339276 + 0.940687i \(0.389818\pi\)
\(140\) 4.13397 + 4.23205i 0.349385 + 0.357674i
\(141\) −24.0000 −2.02116
\(142\) 5.19615 + 3.00000i 0.436051 + 0.251754i
\(143\) 0 0
\(144\) 3.00000 + 5.19615i 0.250000 + 0.433013i
\(145\) 1.23205 + 1.86603i 0.102316 + 0.154965i
\(146\) −10.0000 −0.827606
\(147\) 20.7846 + 3.00000i 1.71429 + 0.247436i
\(148\) 8.00000i 0.657596i
\(149\) −7.50000 + 12.9904i −0.614424 + 1.06421i 0.376061 + 0.926595i \(0.377278\pi\)
−0.990485 + 0.137619i \(0.956055\pi\)
\(150\) 5.89230 13.7942i 0.481105 1.12629i
\(151\) −3.00000 5.19615i −0.244137 0.422857i 0.717752 0.696299i \(-0.245171\pi\)
−0.961888 + 0.273442i \(0.911838\pi\)
\(152\) −1.73205 1.00000i −0.140488 0.0811107i
\(153\) 12.0000i 0.970143i
\(154\) 0 0
\(155\) 10.0000 20.0000i 0.803219 1.60644i
\(156\) −3.00000 + 5.19615i −0.240192 + 0.416025i
\(157\) 10.3923 6.00000i 0.829396 0.478852i −0.0242497 0.999706i \(-0.507720\pi\)
0.853646 + 0.520854i \(0.174386\pi\)
\(158\) −8.66025 + 5.00000i −0.688973 + 0.397779i
\(159\) 9.00000 15.5885i 0.713746 1.23625i
\(160\) −2.00000 1.00000i −0.158114 0.0790569i
\(161\) 2.00000 1.73205i 0.157622 0.136505i
\(162\) 9.00000i 0.707107i
\(163\) −10.3923 6.00000i −0.813988 0.469956i 0.0343508 0.999410i \(-0.489064\pi\)
−0.848339 + 0.529454i \(0.822397\pi\)
\(164\) −1.50000 2.59808i −0.117130 0.202876i
\(165\) 0 0
\(166\) 4.50000 7.79423i 0.349268 0.604949i
\(167\) 9.00000i 0.696441i 0.937413 + 0.348220i \(0.113214\pi\)
−0.937413 + 0.348220i \(0.886786\pi\)
\(168\) −7.79423 + 1.50000i −0.601338 + 0.115728i
\(169\) 9.00000 0.692308
\(170\) 2.46410 + 3.73205i 0.188988 + 0.286235i
\(171\) 6.00000 + 10.3923i 0.458831 + 0.794719i
\(172\) −4.33013 + 2.50000i −0.330169 + 0.190623i
\(173\) −10.3923 6.00000i −0.790112 0.456172i 0.0498898 0.998755i \(-0.484113\pi\)
−0.840002 + 0.542583i \(0.817446\pi\)
\(174\) −3.00000 −0.227429
\(175\) 9.79423 + 8.89230i 0.740374 + 0.672195i
\(176\) 0 0
\(177\) −5.19615 3.00000i −0.390567 0.225494i
\(178\) −6.06218 + 3.50000i −0.454379 + 0.262336i
\(179\) −13.0000 22.5167i −0.971666 1.68297i −0.690526 0.723307i \(-0.742621\pi\)
−0.281139 0.959667i \(-0.590712\pi\)
\(180\) 7.39230 + 11.1962i 0.550990 + 0.834512i
\(181\) 5.00000 0.371647 0.185824 0.982583i \(-0.440505\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(182\) −3.46410 4.00000i −0.256776 0.296500i
\(183\) 27.0000i 1.99590i
\(184\) −0.500000 + 0.866025i −0.0368605 + 0.0638442i
\(185\) −1.07180 17.8564i −0.0788001 1.31283i
\(186\) 15.0000 + 25.9808i 1.09985 + 1.90500i
\(187\) 0 0
\(188\) 8.00000i 0.583460i
\(189\) 22.5000 + 7.79423i 1.63663 + 0.566947i
\(190\) −4.00000 2.00000i −0.290191 0.145095i
\(191\) 10.0000 17.3205i 0.723575 1.25327i −0.235983 0.971757i \(-0.575831\pi\)
0.959558 0.281511i \(-0.0908356\pi\)
\(192\) 2.59808 1.50000i 0.187500 0.108253i
\(193\) 17.3205 10.0000i 1.24676 0.719816i 0.276296 0.961073i \(-0.410893\pi\)
0.970461 + 0.241257i \(0.0775596\pi\)
\(194\) 0 0
\(195\) −6.00000 + 12.0000i −0.429669 + 0.859338i
\(196\) 1.00000 6.92820i 0.0714286 0.494872i
\(197\) 8.00000i 0.569976i 0.958531 + 0.284988i \(0.0919897\pi\)
−0.958531 + 0.284988i \(0.908010\pi\)
\(198\) 0 0
\(199\) 6.00000 + 10.3923i 0.425329 + 0.736691i 0.996451 0.0841740i \(-0.0268252\pi\)
−0.571122 + 0.820865i \(0.693492\pi\)
\(200\) −4.59808 1.96410i −0.325133 0.138883i
\(201\) −10.5000 + 18.1865i −0.740613 + 1.28278i
\(202\) 15.0000i 1.05540i
\(203\) 0.866025 2.50000i 0.0607831 0.175466i
\(204\) −6.00000 −0.420084
\(205\) −3.69615 5.59808i −0.258150 0.390987i
\(206\) 5.50000 + 9.52628i 0.383203 + 0.663727i
\(207\) 5.19615 3.00000i 0.361158 0.208514i
\(208\) 1.73205 + 1.00000i 0.120096 + 0.0693375i
\(209\) 0 0
\(210\) −17.1962 + 4.39230i −1.18665 + 0.303098i
\(211\) −18.0000 −1.23917 −0.619586 0.784929i \(-0.712699\pi\)
−0.619586 + 0.784929i \(0.712699\pi\)
\(212\) −5.19615 3.00000i −0.356873 0.206041i
\(213\) −15.5885 + 9.00000i −1.06810 + 0.616670i
\(214\) −3.50000 6.06218i −0.239255 0.414402i
\(215\) −9.33013 + 6.16025i −0.636309 + 0.420126i
\(216\) −9.00000 −0.612372
\(217\) −25.9808 + 5.00000i −1.76369 + 0.339422i
\(218\) 5.00000i 0.338643i
\(219\) 15.0000 25.9808i 1.01361 1.75562i
\(220\) 0 0
\(221\) −2.00000 3.46410i −0.134535 0.233021i
\(222\) 20.7846 + 12.0000i 1.39497 + 0.805387i
\(223\) 8.00000i 0.535720i −0.963458 0.267860i \(-0.913684\pi\)
0.963458 0.267860i \(-0.0863164\pi\)
\(224\) 0.500000 + 2.59808i 0.0334077 + 0.173591i
\(225\) 18.0000 + 24.0000i 1.20000 + 1.60000i
\(226\) 5.00000 8.66025i 0.332595 0.576072i
\(227\) −10.3923 + 6.00000i −0.689761 + 0.398234i −0.803523 0.595274i \(-0.797043\pi\)
0.113761 + 0.993508i \(0.463710\pi\)
\(228\) 5.19615 3.00000i 0.344124 0.198680i
\(229\) 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i \(-0.726147\pi\)
0.982592 + 0.185776i \(0.0594799\pi\)
\(230\) −1.00000 + 2.00000i −0.0659380 + 0.131876i
\(231\) 0 0
\(232\) 1.00000i 0.0656532i
\(233\) 12.1244 + 7.00000i 0.794293 + 0.458585i 0.841472 0.540301i \(-0.181690\pi\)
−0.0471787 + 0.998886i \(0.515023\pi\)
\(234\) −6.00000 10.3923i −0.392232 0.679366i
\(235\) 1.07180 + 17.8564i 0.0699163 + 1.16482i
\(236\) −1.00000 + 1.73205i −0.0650945 + 0.112747i
\(237\) 30.0000i 1.94871i
\(238\) 1.73205 5.00000i 0.112272 0.324102i
\(239\) 10.0000 0.646846 0.323423 0.946254i \(-0.395166\pi\)
0.323423 + 0.946254i \(0.395166\pi\)
\(240\) 5.59808 3.69615i 0.361354 0.238586i
\(241\) −9.00000 15.5885i −0.579741 1.00414i −0.995509 0.0946700i \(-0.969820\pi\)
0.415768 0.909471i \(-0.363513\pi\)
\(242\) 9.52628 5.50000i 0.612372 0.353553i
\(243\) 0 0
\(244\) 9.00000 0.576166
\(245\) 1.30385 15.5981i 0.0832998 0.996525i
\(246\) 9.00000 0.573819
\(247\) 3.46410 + 2.00000i 0.220416 + 0.127257i
\(248\) 8.66025 5.00000i 0.549927 0.317500i
\(249\) 13.5000 + 23.3827i 0.855528 + 1.48182i
\(250\) −10.5263 3.76795i −0.665740 0.238306i
\(251\) −10.0000 −0.631194 −0.315597 0.948893i \(-0.602205\pi\)
−0.315597 + 0.948893i \(0.602205\pi\)
\(252\) 5.19615 15.0000i 0.327327 0.944911i
\(253\) 0 0
\(254\) −4.00000 + 6.92820i −0.250982 + 0.434714i
\(255\) −13.3923 + 0.803848i −0.838659 + 0.0503389i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 10.3923 + 6.00000i 0.648254 + 0.374270i 0.787787 0.615948i \(-0.211227\pi\)
−0.139533 + 0.990217i \(0.544560\pi\)
\(258\) 15.0000i 0.933859i
\(259\) −16.0000 + 13.8564i −0.994192 + 0.860995i
\(260\) 4.00000 + 2.00000i 0.248069 + 0.124035i
\(261\) 3.00000 5.19615i 0.185695 0.321634i
\(262\) −17.3205 + 10.0000i −1.07006 + 0.617802i
\(263\) 18.1865 10.5000i 1.12143 0.647458i 0.179664 0.983728i \(-0.442499\pi\)
0.941766 + 0.336270i \(0.109166\pi\)
\(264\) 0 0
\(265\) −12.0000 6.00000i −0.737154 0.368577i
\(266\) 1.00000 + 5.19615i 0.0613139 + 0.318597i
\(267\) 21.0000i 1.28518i
\(268\) 6.06218 + 3.50000i 0.370306 + 0.213797i
\(269\) 2.50000 + 4.33013i 0.152428 + 0.264013i 0.932119 0.362151i \(-0.117958\pi\)
−0.779692 + 0.626164i \(0.784624\pi\)
\(270\) −20.0885 + 1.20577i −1.22254 + 0.0733809i
\(271\) −3.00000 + 5.19615i −0.182237 + 0.315644i −0.942642 0.333805i \(-0.891667\pi\)
0.760405 + 0.649449i \(0.225000\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 15.5885 3.00000i 0.943456 0.181568i
\(274\) −16.0000 −0.966595
\(275\) 0 0
\(276\) −1.50000 2.59808i −0.0902894 0.156386i
\(277\) 22.5167 13.0000i 1.35290 0.781094i 0.364241 0.931305i \(-0.381328\pi\)
0.988654 + 0.150210i \(0.0479951\pi\)
\(278\) 6.92820 + 4.00000i 0.415526 + 0.239904i
\(279\) −60.0000 −3.59211
\(280\) 1.46410 + 5.73205i 0.0874968 + 0.342556i
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) −20.7846 12.0000i −1.23771 0.714590i
\(283\) 6.92820 4.00000i 0.411839 0.237775i −0.279741 0.960076i \(-0.590248\pi\)
0.691580 + 0.722300i \(0.256915\pi\)
\(284\) 3.00000 + 5.19615i 0.178017 + 0.308335i
\(285\) 11.1962 7.39230i 0.663203 0.437882i
\(286\) 0 0
\(287\) −2.59808 + 7.50000i −0.153360 + 0.442711i
\(288\) 6.00000i 0.353553i
\(289\) −6.50000 + 11.2583i −0.382353 + 0.662255i
\(290\) 0.133975 + 2.23205i 0.00786726 + 0.131071i
\(291\) 0 0
\(292\) −8.66025 5.00000i −0.506803 0.292603i
\(293\) 24.0000i 1.40209i 0.713115 + 0.701047i \(0.247284\pi\)
−0.713115 + 0.701047i \(0.752716\pi\)
\(294\) 16.5000 + 12.9904i 0.962300 + 0.757614i
\(295\) −2.00000 + 4.00000i −0.116445 + 0.232889i
\(296\) 4.00000 6.92820i 0.232495 0.402694i
\(297\) 0 0
\(298\) −12.9904 + 7.50000i −0.752513 + 0.434463i
\(299\) 1.00000 1.73205i 0.0578315 0.100167i
\(300\) 12.0000 9.00000i 0.692820 0.519615i
\(301\) 12.5000 + 4.33013i 0.720488 + 0.249584i
\(302\) 6.00000i 0.345261i
\(303\) −38.9711 22.5000i −2.23883 1.29259i
\(304\) −1.00000 1.73205i −0.0573539 0.0993399i
\(305\) 20.0885 1.20577i 1.15026 0.0690423i
\(306\) 6.00000 10.3923i 0.342997 0.594089i
\(307\) 19.0000i 1.08439i 0.840254 + 0.542194i \(0.182406\pi\)
−0.840254 + 0.542194i \(0.817594\pi\)
\(308\) 0 0
\(309\) −33.0000 −1.87730
\(310\) 18.6603 12.3205i 1.05983 0.699758i
\(311\) −3.00000 5.19615i −0.170114 0.294647i 0.768345 0.640036i \(-0.221080\pi\)
−0.938460 + 0.345389i \(0.887747\pi\)
\(312\) −5.19615 + 3.00000i −0.294174 + 0.169842i
\(313\) −6.92820 4.00000i −0.391605 0.226093i 0.291250 0.956647i \(-0.405929\pi\)
−0.682855 + 0.730554i \(0.739262\pi\)
\(314\) 12.0000 0.677199
\(315\) 9.58846 34.1769i 0.540248 1.92565i
\(316\) −10.0000 −0.562544
\(317\) 19.0526 + 11.0000i 1.07010 + 0.617822i 0.928208 0.372061i \(-0.121349\pi\)
0.141890 + 0.989882i \(0.454682\pi\)
\(318\) 15.5885 9.00000i 0.874157 0.504695i
\(319\) 0 0
\(320\) −1.23205 1.86603i −0.0688737 0.104314i
\(321\) 21.0000 1.17211
\(322\) 2.59808 0.500000i 0.144785 0.0278639i
\(323\) 4.00000i 0.222566i
\(324\) 4.50000 7.79423i 0.250000 0.433013i
\(325\) 9.19615 + 3.92820i 0.510111 + 0.217898i
\(326\) −6.00000 10.3923i −0.332309 0.575577i
\(327\) −12.9904 7.50000i −0.718370 0.414751i
\(328\) 3.00000i 0.165647i
\(329\) 16.0000 13.8564i 0.882109 0.763928i
\(330\) 0 0
\(331\) −7.00000 + 12.1244i −0.384755 + 0.666415i −0.991735 0.128302i \(-0.959047\pi\)
0.606980 + 0.794717i \(0.292381\pi\)
\(332\) 7.79423 4.50000i 0.427764 0.246970i
\(333\) −41.5692 + 24.0000i −2.27798 + 1.31519i
\(334\) −4.50000 + 7.79423i −0.246229 + 0.426481i
\(335\) 14.0000 + 7.00000i 0.764902 + 0.382451i
\(336\) −7.50000 2.59808i −0.409159 0.141737i
\(337\) 2.00000i 0.108947i 0.998515 + 0.0544735i \(0.0173480\pi\)
−0.998515 + 0.0544735i \(0.982652\pi\)
\(338\) 7.79423 + 4.50000i 0.423950 + 0.244768i
\(339\) 15.0000 + 25.9808i 0.814688 + 1.41108i
\(340\) 0.267949 + 4.46410i 0.0145316 + 0.242100i
\(341\) 0 0
\(342\) 12.0000i 0.648886i
\(343\) −15.5885 + 10.0000i −0.841698 + 0.539949i
\(344\) −5.00000 −0.269582
\(345\) −3.69615 5.59808i −0.198994 0.301390i
\(346\) −6.00000 10.3923i −0.322562 0.558694i
\(347\) −18.1865 + 10.5000i −0.976304 + 0.563670i −0.901152 0.433503i \(-0.857278\pi\)
−0.0751519 + 0.997172i \(0.523944\pi\)
\(348\) −2.59808 1.50000i −0.139272 0.0804084i
\(349\) 9.00000 0.481759 0.240879 0.970555i \(-0.422564\pi\)
0.240879 + 0.970555i \(0.422564\pi\)
\(350\) 4.03590 + 12.5981i 0.215728 + 0.673395i
\(351\) 18.0000 0.960769
\(352\) 0 0
\(353\) −5.19615 + 3.00000i −0.276563 + 0.159674i −0.631867 0.775077i \(-0.717711\pi\)
0.355303 + 0.934751i \(0.384378\pi\)
\(354\) −3.00000 5.19615i −0.159448 0.276172i
\(355\) 7.39230 + 11.1962i 0.392343 + 0.594230i
\(356\) −7.00000 −0.370999
\(357\) 10.3923 + 12.0000i 0.550019 + 0.635107i
\(358\) 26.0000i 1.37414i
\(359\) −7.00000 + 12.1244i −0.369446 + 0.639899i −0.989479 0.144677i \(-0.953786\pi\)
0.620033 + 0.784576i \(0.287119\pi\)
\(360\) 0.803848 + 13.3923i 0.0423665 + 0.705836i
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 4.33013 + 2.50000i 0.227586 + 0.131397i
\(363\) 33.0000i 1.73205i
\(364\) −1.00000 5.19615i −0.0524142 0.272352i
\(365\) −20.0000 10.0000i −1.04685 0.523424i
\(366\) −13.5000 + 23.3827i −0.705656 + 1.22223i
\(367\) 19.9186 11.5000i 1.03974 0.600295i 0.119982 0.992776i \(-0.461716\pi\)
0.919760 + 0.392481i \(0.128383\pi\)
\(368\) −0.866025 + 0.500000i −0.0451447 + 0.0260643i
\(369\) −9.00000 + 15.5885i −0.468521 + 0.811503i
\(370\) 8.00000 16.0000i 0.415900 0.831800i
\(371\) 3.00000 + 15.5885i 0.155752 + 0.809312i
\(372\) 30.0000i 1.55543i
\(373\) −6.92820 4.00000i −0.358729 0.207112i 0.309794 0.950804i \(-0.399740\pi\)
−0.668523 + 0.743691i \(0.733073\pi\)
\(374\) 0 0
\(375\) 25.5788 21.6962i 1.32089 1.12038i
\(376\) −4.00000 + 6.92820i −0.206284 + 0.357295i
\(377\) 2.00000i 0.103005i
\(378\) 15.5885 + 18.0000i 0.801784 + 0.925820i
\(379\) 2.00000 0.102733 0.0513665 0.998680i \(-0.483642\pi\)
0.0513665 + 0.998680i \(0.483642\pi\)
\(380\) −2.46410 3.73205i −0.126406 0.191450i
\(381\) −12.0000 20.7846i −0.614779 1.06483i
\(382\) 17.3205 10.0000i 0.886194 0.511645i
\(383\) 7.79423 + 4.50000i 0.398266 + 0.229939i 0.685736 0.727851i \(-0.259481\pi\)
−0.287469 + 0.957790i \(0.592814\pi\)
\(384\) 3.00000 0.153093
\(385\) 0 0
\(386\) 20.0000 1.01797
\(387\) 25.9808 + 15.0000i 1.32068 + 0.762493i
\(388\) 0 0
\(389\) −9.00000 15.5885i −0.456318 0.790366i 0.542445 0.840091i \(-0.317499\pi\)
−0.998763 + 0.0497253i \(0.984165\pi\)
\(390\) −11.1962 + 7.39230i −0.566939 + 0.374324i
\(391\) 2.00000 0.101144
\(392\) 4.33013 5.50000i 0.218704 0.277792i
\(393\) 60.0000i 3.02660i
\(394\) −4.00000 + 6.92820i −0.201517 + 0.349038i
\(395\) −22.3205 + 1.33975i −1.12307 + 0.0674099i
\(396\) 0 0
\(397\) −27.7128 16.0000i −1.39087 0.803017i −0.397455 0.917622i \(-0.630107\pi\)
−0.993411 + 0.114605i \(0.963440\pi\)
\(398\) 12.0000i 0.601506i
\(399\) −15.0000 5.19615i −0.750939 0.260133i
\(400\) −3.00000 4.00000i −0.150000 0.200000i
\(401\) −1.50000 + 2.59808i −0.0749064 + 0.129742i −0.901046 0.433724i \(-0.857199\pi\)
0.826139 + 0.563466i \(0.190532\pi\)
\(402\) −18.1865 + 10.5000i −0.907062 + 0.523692i
\(403\) −17.3205 + 10.0000i −0.862796 + 0.498135i
\(404\) −7.50000 + 12.9904i −0.373139 + 0.646296i
\(405\) 9.00000 18.0000i 0.447214 0.894427i
\(406\) 2.00000 1.73205i 0.0992583 0.0859602i
\(407\) 0 0
\(408\) −5.19615 3.00000i −0.257248 0.148522i
\(409\) −8.50000 14.7224i −0.420298 0.727977i 0.575670 0.817682i \(-0.304741\pi\)
−0.995968 + 0.0897044i \(0.971408\pi\)
\(410\) −0.401924 6.69615i −0.0198496 0.330699i
\(411\) 24.0000 41.5692i 1.18383 2.05046i
\(412\) 11.0000i 0.541931i
\(413\) 5.19615 1.00000i 0.255686 0.0492068i
\(414\) 6.00000 0.294884
\(415\) 16.7942 11.0885i 0.824396 0.544311i
\(416\) 1.00000 + 1.73205i 0.0490290 + 0.0849208i
\(417\) −20.7846 + 12.0000i −1.01783 + 0.587643i
\(418\) 0 0
\(419\) 40.0000 1.95413 0.977064 0.212946i \(-0.0683059\pi\)
0.977064 + 0.212946i \(0.0683059\pi\)
\(420\) −17.0885 4.79423i −0.833831 0.233934i
\(421\) 31.0000 1.51085 0.755424 0.655237i \(-0.227431\pi\)
0.755424 + 0.655237i \(0.227431\pi\)
\(422\) −15.5885 9.00000i −0.758834 0.438113i
\(423\) 41.5692 24.0000i 2.02116 1.16692i
\(424\) −3.00000 5.19615i −0.145693 0.252347i
\(425\) 1.19615 + 9.92820i 0.0580219 + 0.481589i
\(426\) −18.0000 −0.872103
\(427\) −15.5885 18.0000i −0.754378 0.871081i
\(428\) 7.00000i 0.338358i
\(429\) 0 0
\(430\) −11.1603 + 0.669873i −0.538195 + 0.0323041i
\(431\) −16.0000 27.7128i −0.770693 1.33488i −0.937184 0.348836i \(-0.886577\pi\)
0.166491 0.986043i \(-0.446756\pi\)
\(432\) −7.79423 4.50000i −0.375000 0.216506i
\(433\) 14.0000i 0.672797i −0.941720 0.336399i \(-0.890791\pi\)
0.941720 0.336399i \(-0.109209\pi\)
\(434\) −25.0000 8.66025i −1.20004 0.415705i
\(435\) −6.00000 3.00000i −0.287678 0.143839i
\(436\) −2.50000 + 4.33013i −0.119728 + 0.207375i
\(437\) −1.73205 + 1.00000i −0.0828552 + 0.0478365i
\(438\) 25.9808 15.0000i 1.24141 0.716728i
\(439\) 4.00000 6.92820i 0.190910 0.330665i −0.754642 0.656136i \(-0.772190\pi\)
0.945552 + 0.325471i \(0.105523\pi\)
\(440\) 0 0
\(441\) −39.0000 + 15.5885i −1.85714 + 0.742307i
\(442\) 4.00000i 0.190261i
\(443\) 2.59808 + 1.50000i 0.123438 + 0.0712672i 0.560448 0.828190i \(-0.310629\pi\)
−0.437009 + 0.899457i \(0.643962\pi\)
\(444\) 12.0000 + 20.7846i 0.569495 + 0.986394i
\(445\) −15.6244 + 0.937822i −0.740665 + 0.0444570i
\(446\) 4.00000 6.92820i 0.189405 0.328060i
\(447\) 45.0000i 2.12843i
\(448\) −0.866025 + 2.50000i −0.0409159 + 0.118114i
\(449\) −23.0000 −1.08544 −0.542719 0.839915i \(-0.682605\pi\)
−0.542719 + 0.839915i \(0.682605\pi\)
\(450\) 3.58846 + 29.7846i 0.169161 + 1.40406i
\(451\) 0 0
\(452\) 8.66025 5.00000i 0.407344 0.235180i
\(453\) 15.5885 + 9.00000i 0.732410 + 0.422857i
\(454\) −12.0000 −0.563188
\(455\) −2.92820 11.4641i −0.137276 0.537445i
\(456\) 6.00000 0.280976
\(457\) 27.7128 + 16.0000i 1.29635 + 0.748448i 0.979772 0.200118i \(-0.0641325\pi\)
0.316579 + 0.948566i \(0.397466\pi\)
\(458\) 8.66025 5.00000i 0.404667 0.233635i
\(459\) 9.00000 + 15.5885i 0.420084 + 0.727607i
\(460\) −1.86603 + 1.23205i −0.0870039 + 0.0574447i
\(461\) −14.0000 −0.652045 −0.326023 0.945362i \(-0.605709\pi\)
−0.326023 + 0.945362i \(0.605709\pi\)
\(462\) 0 0
\(463\) 25.0000i 1.16185i 0.813958 + 0.580924i \(0.197309\pi\)
−0.813958 + 0.580924i \(0.802691\pi\)
\(464\) −0.500000 + 0.866025i −0.0232119 + 0.0402042i
\(465\) 4.01924 + 66.9615i 0.186388 + 3.10527i
\(466\) 7.00000 + 12.1244i 0.324269 + 0.561650i
\(467\) 0.866025 + 0.500000i 0.0400749 + 0.0231372i 0.519904 0.854225i \(-0.325968\pi\)
−0.479829 + 0.877362i \(0.659301\pi\)
\(468\) 12.0000i 0.554700i
\(469\) −3.50000 18.1865i −0.161615 0.839776i
\(470\) −8.00000 + 16.0000i −0.369012 + 0.738025i
\(471\) −18.0000 + 31.1769i −0.829396 + 1.43656i
\(472\) −1.73205 + 1.00000i −0.0797241 + 0.0460287i
\(473\) 0 0
\(474\) 15.0000 25.9808i 0.688973 1.19334i
\(475\) −6.00000 8.00000i −0.275299 0.367065i
\(476\) 4.00000 3.46410i 0.183340 0.158777i
\(477\) 36.0000i 1.64833i
\(478\) 8.66025 + 5.00000i 0.396111 + 0.228695i
\(479\) 9.00000 + 15.5885i 0.411220 + 0.712255i 0.995023 0.0996406i \(-0.0317693\pi\)
−0.583803 + 0.811895i \(0.698436\pi\)
\(480\) 6.69615 0.401924i 0.305636 0.0183452i
\(481\) −8.00000 + 13.8564i −0.364769 + 0.631798i
\(482\) 18.0000i 0.819878i
\(483\) −2.59808 + 7.50000i −0.118217 + 0.341262i
\(484\) 11.0000 0.500000
\(485\) 0 0
\(486\) 0 0
\(487\) −3.46410 + 2.00000i −0.156973 + 0.0906287i −0.576429 0.817147i \(-0.695554\pi\)
0.419456 + 0.907776i \(0.362221\pi\)
\(488\) 7.79423 + 4.50000i 0.352828 + 0.203705i
\(489\) 36.0000 1.62798
\(490\) 8.92820 12.8564i 0.403335 0.580793i
\(491\) −18.0000 −0.812329 −0.406164 0.913800i \(-0.633134\pi\)
−0.406164 + 0.913800i \(0.633134\pi\)
\(492\) 7.79423 + 4.50000i 0.351391 + 0.202876i
\(493\) 1.73205 1.00000i 0.0780076 0.0450377i
\(494\) 2.00000 + 3.46410i 0.0899843 + 0.155857i
\(495\) 0 0
\(496\) 10.0000 0.449013
\(497\) 5.19615 15.0000i 0.233079 0.672842i
\(498\) 27.0000i 1.20990i
\(499\) 8.00000 13.8564i 0.358129 0.620298i −0.629519 0.776985i \(-0.716748\pi\)
0.987648 + 0.156687i \(0.0500814\pi\)
\(500\) −7.23205 8.52628i −0.323427 0.381307i
\(501\) −13.5000 23.3827i −0.603136 1.04466i
\(502\) −8.66025 5.00000i −0.386526 0.223161i
\(503\) 5.00000i 0.222939i −0.993768 0.111469i \(-0.964444\pi\)
0.993768 0.111469i \(-0.0355557\pi\)
\(504\) 12.0000 10.3923i 0.534522 0.462910i
\(505\) −15.0000 + 30.0000i −0.667491 + 1.33498i
\(506\) 0 0
\(507\) −23.3827 + 13.5000i −1.03846 + 0.599556i
\(508\) −6.92820 + 4.00000i −0.307389 + 0.177471i
\(509\) 17.5000 30.3109i 0.775674 1.34351i −0.158741 0.987320i \(-0.550744\pi\)
0.934415 0.356186i \(-0.115923\pi\)
\(510\) −12.0000 6.00000i −0.531369 0.265684i
\(511\) 5.00000 + 25.9808i 0.221187 + 1.14932i
\(512\) 1.00000i 0.0441942i
\(513\) −15.5885 9.00000i −0.688247 0.397360i
\(514\) 6.00000 + 10.3923i 0.264649 + 0.458385i
\(515\) 1.47372 + 24.5526i 0.0649399 + 1.08192i
\(516\) 7.50000 12.9904i 0.330169 0.571870i
\(517\) 0 0
\(518\) −20.7846 + 4.00000i −0.913223 + 0.175750i
\(519\) 36.0000 1.58022
\(520\) 2.46410 + 3.73205i 0.108058 + 0.163661i
\(521\) 9.00000 + 15.5885i 0.394297 + 0.682943i 0.993011 0.118020i \(-0.0376547\pi\)
−0.598714 + 0.800963i \(0.704321\pi\)
\(522\) 5.19615 3.00000i 0.227429 0.131306i
\(523\) −3.46410 2.00000i −0.151475 0.0874539i 0.422347 0.906434i \(-0.361206\pi\)
−0.573822 + 0.818980i \(0.694540\pi\)
\(524\) −20.0000 −0.873704
\(525\) −38.7846 8.41154i −1.69270 0.367110i
\(526\) 21.0000 0.915644
\(527\) −17.3205 10.0000i −0.754493 0.435607i
\(528\) 0 0
\(529\) −11.0000 19.0526i −0.478261 0.828372i
\(530\) −7.39230 11.1962i −0.321101 0.486330i
\(531\) 12.0000 0.520756
\(532\) −1.73205 + 5.00000i −0.0750939 + 0.216777i
\(533\) 6.00000i 0.259889i
\(534\) 10.5000 18.1865i 0.454379 0.787008i
\(535\) −0.937822 15.6244i −0.0405456 0.675500i
\(536\) 3.50000 + 6.06218i 0.151177 + 0.261846i
\(537\) 67.5500 + 39.0000i 2.91500 + 1.68297i
\(538\) 5.00000i 0.215565i
\(539\) 0 0
\(540\) −18.0000 9.00000i −0.774597 0.387298i
\(541\) −2.50000 + 4.33013i −0.107483 + 0.186167i −0.914750 0.404020i \(-0.867613\pi\)
0.807267 + 0.590187i \(0.200946\pi\)
\(542\) −5.19615 + 3.00000i −0.223194 + 0.128861i
\(543\) −12.9904 + 7.50000i −0.557471 + 0.321856i
\(544\) −1.00000 + 1.73205i −0.0428746 + 0.0742611i
\(545\) −5.00000 + 10.0000i −0.214176 + 0.428353i
\(546\) 15.0000 + 5.19615i 0.641941 + 0.222375i
\(547\) 37.0000i 1.58201i −0.611812 0.791003i \(-0.709559\pi\)
0.611812 0.791003i \(-0.290441\pi\)
\(548\) −13.8564 8.00000i −0.591916 0.341743i
\(549\) −27.0000 46.7654i −1.15233 1.99590i
\(550\) 0 0
\(551\) −1.00000 + 1.73205i −0.0426014 + 0.0737878i
\(552\) 3.00000i 0.127688i
\(553\) 17.3205 + 20.0000i 0.736543 + 0.850487i
\(554\) 26.0000 1.10463
\(555\) 29.5692 + 44.7846i 1.25514 + 1.90100i
\(556\) 4.00000 + 6.92820i 0.169638 + 0.293821i
\(557\) 3.46410 2.00000i 0.146779 0.0847427i −0.424812 0.905282i \(-0.639660\pi\)
0.571591 + 0.820539i \(0.306326\pi\)
\(558\) −51.9615 30.0000i −2.19971 1.27000i
\(559\) 10.0000 0.422955
\(560\) −1.59808 + 5.69615i −0.0675310 + 0.240706i
\(561\) 0 0
\(562\) 15.5885 + 9.00000i 0.657559 + 0.379642i
\(563\) 9.52628 5.50000i 0.401485 0.231797i −0.285640 0.958337i \(-0.592206\pi\)
0.687124 + 0.726540i \(0.258873\pi\)
\(564\) −12.0000 20.7846i −0.505291 0.875190i
\(565\) 18.6603 12.3205i 0.785043 0.518328i
\(566\) 8.00000 0.336265
\(567\) −23.3827 + 4.50000i −0.981981 + 0.188982i
\(568\) 6.00000i 0.251754i
\(569\) −9.00000 + 15.5885i −0.377300 + 0.653502i −0.990668 0.136295i \(-0.956481\pi\)
0.613369 + 0.789797i \(0.289814\pi\)
\(570\) 13.3923 0.803848i 0.560942 0.0336695i
\(571\) 5.00000 + 8.66025i 0.209243 + 0.362420i 0.951476 0.307722i \(-0.0995665\pi\)
−0.742233 + 0.670142i \(0.766233\pi\)
\(572\) 0 0
\(573\) 60.0000i 2.50654i
\(574\) −6.00000 + 5.19615i −0.250435 + 0.216883i
\(575\) −4.00000 + 3.00000i −0.166812 + 0.125109i
\(576\) −3.00000 + 5.19615i −0.125000 + 0.216506i
\(577\) 13.8564 8.00000i 0.576850 0.333044i −0.183031 0.983107i \(-0.558591\pi\)
0.759880 + 0.650063i \(0.225257\pi\)
\(578\) −11.2583 + 6.50000i −0.468285 + 0.270364i
\(579\) −30.0000 + 51.9615i −1.24676 + 2.15945i
\(580\) −1.00000 + 2.00000i −0.0415227 + 0.0830455i
\(581\) −22.5000 7.79423i −0.933457 0.323359i
\(582\) 0 0
\(583\) 0 0
\(584\) −5.00000 8.66025i −0.206901 0.358364i
\(585\) −1.60770 26.7846i −0.0664700 1.10741i
\(586\) −12.0000 + 20.7846i −0.495715 + 0.858604i
\(587\) 28.0000i 1.15568i −0.816149 0.577842i \(-0.803895\pi\)
0.816149 0.577842i \(-0.196105\pi\)
\(588\) 7.79423 + 19.5000i 0.321429 + 0.804166i
\(589\) 20.0000 0.824086
\(590\) −3.73205 + 2.46410i −0.153646 + 0.101445i
\(591\) −12.0000 20.7846i −0.493614 0.854965i
\(592\) 6.92820 4.00000i 0.284747 0.164399i
\(593\) −36.3731 21.0000i −1.49366 0.862367i −0.493689 0.869638i \(-0.664352\pi\)
−0.999974 + 0.00727173i \(0.997685\pi\)
\(594\) 0 0
\(595\) 8.46410 8.26795i 0.346994 0.338953i
\(596\) −15.0000 −0.614424
\(597\) −31.1769 18.0000i −1.27599 0.736691i
\(598\) 1.73205 1.00000i 0.0708288 0.0408930i
\(599\) 18.0000 + 31.1769i 0.735460 + 1.27385i 0.954521 + 0.298143i \(0.0963673\pi\)
−0.219061 + 0.975711i \(0.570299\pi\)
\(600\) 14.8923 1.79423i 0.607976 0.0732491i
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 8.66025 + 10.0000i 0.352966 + 0.407570i
\(603\) 42.0000i 1.71037i
\(604\) 3.00000 5.19615i 0.122068 0.211428i
\(605\) 24.5526 1.47372i 0.998203 0.0599153i
\(606\) −22.5000 38.9711i −0.914000 1.58309i
\(607\) 4.33013 + 2.50000i 0.175754 + 0.101472i 0.585296 0.810819i \(-0.300978\pi\)
−0.409542 + 0.912291i \(0.634311\pi\)
\(608\) 2.00000i 0.0811107i
\(609\) 1.50000 + 7.79423i 0.0607831 + 0.315838i
\(610\) 18.0000 + 9.00000i 0.728799 + 0.364399i
\(611\) 8.00000 13.8564i 0.323645 0.560570i
\(612\) 10.3923 6.00000i 0.420084 0.242536i
\(613\) 15.5885 9.00000i 0.629612 0.363507i −0.150990 0.988535i \(-0.548246\pi\)
0.780602 + 0.625029i \(0.214913\pi\)
\(614\) −9.50000 + 16.4545i −0.383389 + 0.664049i
\(615\) 18.0000 + 9.00000i 0.725830 + 0.362915i
\(616\) 0 0
\(617\) 20.0000i 0.805170i −0.915383 0.402585i \(-0.868112\pi\)
0.915383 0.402585i \(-0.131888\pi\)
\(618\) −28.5788 16.5000i −1.14961 0.663727i
\(619\) −10.0000 17.3205i −0.401934 0.696170i 0.592025 0.805919i \(-0.298329\pi\)
−0.993959 + 0.109749i \(0.964995\pi\)
\(620\) 22.3205 1.33975i 0.896413 0.0538055i
\(621\) −4.50000 + 7.79423i −0.180579 + 0.312772i
\(622\) 6.00000i 0.240578i
\(623\) 12.1244 + 14.0000i 0.485752 + 0.560898i
\(624\) −6.00000 −0.240192
\(625\) −17.2846 18.0622i −0.691384 0.722487i
\(626\) −4.00000 6.92820i −0.159872 0.276907i
\(627\) 0 0
\(628\) 10.3923 + 6.00000i 0.414698 + 0.239426i
\(629\) −16.0000 −0.637962
\(630\) 25.3923 24.8038i 1.01165 0.988209i
\(631\) −24.0000 −0.955425 −0.477712 0.878516i \(-0.658534\pi\)
−0.477712 + 0.878516i \(0.658534\pi\)
\(632\) −8.66025 5.00000i −0.344486 0.198889i
\(633\) 46.7654 27.0000i 1.85876 1.07315i
\(634\) 11.0000 + 19.0526i 0.436866 + 0.756674i
\(635\) −14.9282 + 9.85641i −0.592408 + 0.391140i
\(636\) 18.0000 0.713746
\(637\) −8.66025 + 11.0000i −0.343132 + 0.435836i
\(638\) 0 0
\(639\) 18.0000 31.1769i 0.712069 1.23334i
\(640\) −0.133975 2.23205i −0.00529581 0.0882296i
\(641\) 17.5000 + 30.3109i 0.691208 + 1.19721i 0.971442 + 0.237276i \(0.0762547\pi\)
−0.280234 + 0.959932i \(0.590412\pi\)
\(642\) 18.1865 + 10.5000i 0.717765 + 0.414402i
\(643\) 20.0000i 0.788723i −0.918955 0.394362i \(-0.870966\pi\)
0.918955 0.394362i \(-0.129034\pi\)
\(644\) 2.50000 + 0.866025i 0.0985138 + 0.0341262i
\(645\) 15.0000 30.0000i 0.590624 1.18125i
\(646\) −2.00000 + 3.46410i −0.0786889 + 0.136293i
\(647\) −18.1865 + 10.5000i −0.714986 + 0.412798i −0.812905 0.582397i \(-0.802115\pi\)
0.0979182 + 0.995194i \(0.468782\pi\)
\(648\) 7.79423 4.50000i 0.306186 0.176777i
\(649\) 0 0
\(650\) 6.00000 + 8.00000i 0.235339 + 0.313786i
\(651\) 60.0000 51.9615i 2.35159 2.03653i
\(652\) 12.0000i 0.469956i
\(653\) −36.3731 21.0000i −1.42339 0.821794i −0.426801 0.904345i \(-0.640360\pi\)
−0.996587 + 0.0825519i \(0.973693\pi\)
\(654\) −7.50000 12.9904i −0.293273 0.507964i
\(655\) −44.6410 + 2.67949i −1.74427 + 0.104696i
\(656\) 1.50000 2.59808i 0.0585652 0.101438i
\(657\) 60.0000i 2.34082i
\(658\) 20.7846 4.00000i 0.810268 0.155936i
\(659\) −30.0000 −1.16863 −0.584317 0.811525i \(-0.698638\pi\)
−0.584317 + 0.811525i \(0.698638\pi\)
\(660\) 0 0
\(661\) 20.5000 + 35.5070i 0.797358 + 1.38106i 0.921331 + 0.388778i \(0.127103\pi\)
−0.123974 + 0.992286i \(0.539564\pi\)
\(662\) −12.1244 + 7.00000i −0.471226 + 0.272063i
\(663\) 10.3923 + 6.00000i 0.403604 + 0.233021i
\(664\) 9.00000 0.349268
\(665\) −3.19615 + 11.3923i −0.123941 + 0.441775i
\(666\) −48.0000 −1.85996
\(667\) 0.866025 + 0.500000i 0.0335326 + 0.0193601i
\(668\) −7.79423 + 4.50000i −0.301568 + 0.174110i
\(669\) 12.0000 + 20.7846i 0.463947 + 0.803579i
\(670\) 8.62436 + 13.0622i 0.333188 + 0.504636i
\(671\) 0 0
\(672\) −5.19615 6.00000i −0.200446 0.231455i
\(673\) 20.0000i 0.770943i 0.922720 + 0.385472i \(0.125961\pi\)
−0.922720 + 0.385472i \(0.874039\pi\)
\(674\) −1.00000 + 1.73205i −0.0385186 + 0.0667161i
\(675\) −41.3827 17.6769i −1.59282 0.680385i
\(676\) 4.50000 + 7.79423i 0.173077 + 0.299778i
\(677\) −1.73205 1.00000i −0.0665681 0.0384331i 0.466347 0.884602i \(-0.345570\pi\)
−0.532915 + 0.846169i \(0.678903\pi\)
\(678\) 30.0000i 1.15214i
\(679\) 0 0
\(680\) −2.00000 + 4.00000i −0.0766965 + 0.153393i
\(681\) 18.0000 31.1769i 0.689761 1.19470i
\(682\) 0 0
\(683\) 21.6506 12.5000i 0.828439 0.478299i −0.0248792 0.999690i \(-0.507920\pi\)
0.853318 + 0.521391i \(0.174587\pi\)
\(684\) −6.00000 + 10.3923i −0.229416 + 0.397360i
\(685\) −32.0000 16.0000i −1.22266 0.611329i
\(686\) −18.5000 + 0.866025i −0.706333 + 0.0330650i
\(687\) 30.0000i 1.14457i
\(688\) −4.33013 2.50000i −0.165085 0.0953116i
\(689\) 6.00000 + 10.3923i 0.228582 + 0.395915i
\(690\) −0.401924 6.69615i −0.0153010 0.254918i
\(691\) 10.0000 17.3205i 0.380418 0.658903i −0.610704 0.791859i \(-0.709113\pi\)
0.991122 + 0.132956i \(0.0424468\pi\)
\(692\) 12.0000i 0.456172i
\(693\) 0 0
\(694\) −21.0000 −0.797149
\(695\) 9.85641 + 14.9282i 0.373875 + 0.566259i
\(696\) −1.50000 2.59808i −0.0568574 0.0984798i
\(697\) −5.19615 + 3.00000i −0.196818 + 0.113633i
\(698\) 7.79423 + 4.50000i 0.295016 + 0.170328i
\(699\) −42.0000 −1.58859
\(700\) −2.80385 + 12.9282i −0.105975 + 0.488640i
\(701\) −1.00000 −0.0377695 −0.0188847 0.999822i \(-0.506012\pi\)
−0.0188847 + 0.999822i \(0.506012\pi\)
\(702\) 15.5885 + 9.00000i 0.588348 + 0.339683i
\(703\) 13.8564 8.00000i 0.522604 0.301726i
\(704\) 0 0
\(705\) −29.5692 44.7846i −1.11364 1.68669i
\(706\) −6.00000 −0.225813
\(707\) 38.9711 7.50000i 1.46566 0.282067i
\(708\) 6.00000i 0.225494i
\(709\) −4.50000 + 7.79423i −0.169001 + 0.292718i −0.938069 0.346449i \(-0.887387\pi\)
0.769068 + 0.639167i \(0.220721\pi\)
\(710\) 0.803848 + 13.3923i 0.0301679 + 0.502604i
\(711\) 30.0000 + 51.9615i 1.12509 + 1.94871i
\(712\) −6.06218 3.50000i −0.227190 0.131168i
\(713\) 10.0000i 0.374503i
\(714\) 3.00000 + 15.5885i 0.112272 + 0.583383i
\(715\) 0 0
\(716\) 13.0000 22.5167i 0.485833 0.841487i
\(717\) −25.9808 + 15.0000i −0.970269 + 0.560185i
\(718\) −12.1244 + 7.00000i −0.452477 + 0.261238i
\(719\) 10.0000 17.3205i 0.372937 0.645946i −0.617079 0.786901i \(-0.711684\pi\)
0.990016 + 0.140955i \(0.0450174\pi\)
\(720\) −6.00000 + 12.0000i −0.223607 + 0.447214i
\(721\) 22.0000 19.0526i 0.819323 0.709554i
\(722\) 15.0000i 0.558242i
\(723\) 46.7654 + 27.0000i 1.73922 + 1.00414i
\(724\) 2.50000 + 4.33013i 0.0929118 + 0.160928i
\(725\) −1.96410 + 4.59808i −0.0729449 + 0.170768i
\(726\) −16.5000 + 28.5788i −0.612372 + 1.06066i
\(727\) 29.0000i 1.07555i 0.843088 + 0.537775i \(0.180735\pi\)
−0.843088 + 0.537775i \(0.819265\pi\)
\(728\) 1.73205 5.00000i 0.0641941 0.185312i
\(729\) 27.0000 1.00000
\(730\) −12.3205 18.6603i −0.456002 0.690647i
\(731\) 5.00000 + 8.66025i 0.184932 + 0.320311i
\(732\) −23.3827 + 13.5000i −0.864249 + 0.498974i
\(733\) 13.8564 + 8.00000i 0.511798 + 0.295487i 0.733572 0.679611i \(-0.237852\pi\)
−0.221774 + 0.975098i \(0.571185\pi\)
\(734\) 23.0000 0.848945
\(735\) 20.0096 + 42.4808i 0.738066 + 1.56693i
\(736\) −1.00000 −0.0368605
\(737\) 0 0
\(738\) −15.5885 + 9.00000i −0.573819 + 0.331295i
\(739\) −16.0000 27.7128i −0.588570 1.01943i −0.994420 0.105493i \(-0.966358\pi\)
0.405851 0.913939i \(-0.366975\pi\)
\(740\) 14.9282 9.85641i 0.548772 0.362329i
\(741\) −12.0000 −0.440831
\(742\) −5.19615 + 15.0000i −0.190757 + 0.550667i
\(743\) 3.00000i 0.110059i −0.998485 0.0550297i \(-0.982475\pi\)
0.998485 0.0550297i \(-0.0175253\pi\)
\(744\) −15.0000 + 25.9808i −0.549927 + 0.952501i
\(745\) −33.4808 + 2.00962i −1.22664 + 0.0736267i
\(746\) −4.00000 6.92820i −0.146450 0.253660i
\(747\) −46.7654 27.0000i −1.71106 0.987878i
\(748\) 0 0
\(749\) −14.0000 + 12.1244i −0.511549 + 0.443014i
\(750\) 33.0000 6.00000i 1.20499 0.219089i
\(751\) −2.00000 + 3.46410i −0.0729810 + 0.126407i −0.900207 0.435463i \(-0.856585\pi\)
0.827225 + 0.561870i \(0.189918\pi\)
\(752\) −6.92820 + 4.00000i −0.252646 + 0.145865i
\(753\) 25.9808 15.0000i 0.946792 0.546630i
\(754\) 1.00000 1.73205i 0.0364179 0.0630776i
\(755\) 6.00000 12.0000i 0.218362 0.436725i
\(756\) 4.50000 + 23.3827i 0.163663 + 0.850420i
\(757\) 6.00000i 0.218074i 0.994038 + 0.109037i \(0.0347767\pi\)
−0.994038 + 0.109037i \(0.965223\pi\)
\(758\) 1.73205 + 1.00000i 0.0629109 + 0.0363216i
\(759\) 0 0
\(760\) −0.267949 4.46410i −0.00971954 0.161930i
\(761\) 25.0000 43.3013i 0.906249 1.56967i 0.0870179 0.996207i \(-0.472266\pi\)
0.819231 0.573463i \(-0.194400\pi\)
\(762\) 24.0000i 0.869428i
\(763\) 12.9904 2.50000i 0.470283 0.0905061i
\(764\) 20.0000 0.723575
\(765\) 22.3923 14.7846i 0.809595 0.534539i
\(766\) 4.50000 + 7.79423i 0.162592 + 0.281617i
\(767\) 3.46410 2.00000i 0.125081 0.0722158i
\(768\) 2.59808 + 1.50000i 0.0937500 + 0.0541266i
\(769\) −34.0000 −1.22607 −0.613036 0.790055i \(-0.710052\pi\)
−0.613036 + 0.790055i \(0.710052\pi\)
\(770\) 0 0
\(771\) −36.0000 −1.29651
\(772\) 17.3205 + 10.0000i 0.623379 + 0.359908i
\(773\) −15.5885 + 9.00000i −0.560678 + 0.323708i −0.753418 0.657542i \(-0.771596\pi\)
0.192740 + 0.981250i \(0.438263\pi\)
\(774\) 15.0000 + 25.9808i 0.539164 + 0.933859i
\(775\) 49.6410 5.98076i 1.78316 0.214835i
\(776\) 0 0
\(777\) 20.7846 60.0000i 0.745644 2.15249i
\(778\) 18.0000i 0.645331i
\(779\) 3.00000 5.19615i 0.107486 0.186171i
\(780\) −13.3923 + 0.803848i −0.479521 + 0.0287824i
\(781\) 0 0
\(782\) 1.73205 + 1.00000i 0.0619380 + 0.0357599i
\(783\) 9.00000i 0.321634i
\(784\) 6.50000 2.59808i 0.232143 0.0927884i
\(785\) 24.0000 + 12.0000i