Properties

Label 637.2.f.a.393.1
Level $637$
Weight $2$
Character 637.393
Analytic conductor $5.086$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 393.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 637.393
Dual form 637.2.f.a.295.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(0.500000 - 0.866025i) q^{4} -3.00000 q^{5} +(-1.50000 + 2.59808i) q^{6} -3.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(0.500000 - 0.866025i) q^{4} -3.00000 q^{5} +(-1.50000 + 2.59808i) q^{6} -3.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(1.50000 + 2.59808i) q^{10} +(1.50000 + 2.59808i) q^{11} -3.00000 q^{12} +(1.00000 - 3.46410i) q^{13} +(4.50000 + 7.79423i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +6.00000 q^{18} +(-0.500000 + 0.866025i) q^{19} +(-1.50000 + 2.59808i) q^{20} +(1.50000 - 2.59808i) q^{22} +(4.50000 + 7.79423i) q^{24} +4.00000 q^{25} +(-3.50000 + 0.866025i) q^{26} +9.00000 q^{27} +(-3.50000 - 6.06218i) q^{29} +(4.50000 - 7.79423i) q^{30} -3.00000 q^{31} +(-2.50000 + 4.33013i) q^{32} +(4.50000 - 7.79423i) q^{33} +2.00000 q^{34} +(3.00000 + 5.19615i) q^{36} +(-1.00000 - 1.73205i) q^{37} +1.00000 q^{38} +(-10.5000 + 2.59808i) q^{39} +9.00000 q^{40} +(1.50000 + 2.59808i) q^{41} +(3.50000 - 6.06218i) q^{43} +3.00000 q^{44} +(9.00000 - 15.5885i) q^{45} -1.00000 q^{47} +(1.50000 - 2.59808i) q^{48} +(-2.00000 - 3.46410i) q^{50} +6.00000 q^{51} +(-2.50000 - 2.59808i) q^{52} +3.00000 q^{53} +(-4.50000 - 7.79423i) q^{54} +(-4.50000 - 7.79423i) q^{55} +3.00000 q^{57} +(-3.50000 + 6.06218i) q^{58} +(-2.00000 + 3.46410i) q^{59} +9.00000 q^{60} +(-6.50000 + 11.2583i) q^{61} +(1.50000 + 2.59808i) q^{62} +7.00000 q^{64} +(-3.00000 + 10.3923i) q^{65} -9.00000 q^{66} +(1.50000 + 2.59808i) q^{67} +(1.00000 + 1.73205i) q^{68} +(-6.50000 + 11.2583i) q^{71} +(9.00000 - 15.5885i) q^{72} +13.0000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(-6.00000 - 10.3923i) q^{75} +(0.500000 + 0.866025i) q^{76} +(7.50000 + 7.79423i) q^{78} -3.00000 q^{79} +(-1.50000 - 2.59808i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(1.50000 - 2.59808i) q^{82} +(3.00000 - 5.19615i) q^{85} -7.00000 q^{86} +(-10.5000 + 18.1865i) q^{87} +(-4.50000 - 7.79423i) q^{88} +(3.00000 + 5.19615i) q^{89} -18.0000 q^{90} +(4.50000 + 7.79423i) q^{93} +(0.500000 + 0.866025i) q^{94} +(1.50000 - 2.59808i) q^{95} +15.0000 q^{96} +(-2.50000 + 4.33013i) q^{97} -18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - 3q^{3} + q^{4} - 6q^{5} - 3q^{6} - 6q^{8} - 6q^{9} + O(q^{10}) \) \( 2q - q^{2} - 3q^{3} + q^{4} - 6q^{5} - 3q^{6} - 6q^{8} - 6q^{9} + 3q^{10} + 3q^{11} - 6q^{12} + 2q^{13} + 9q^{15} + q^{16} - 2q^{17} + 12q^{18} - q^{19} - 3q^{20} + 3q^{22} + 9q^{24} + 8q^{25} - 7q^{26} + 18q^{27} - 7q^{29} + 9q^{30} - 6q^{31} - 5q^{32} + 9q^{33} + 4q^{34} + 6q^{36} - 2q^{37} + 2q^{38} - 21q^{39} + 18q^{40} + 3q^{41} + 7q^{43} + 6q^{44} + 18q^{45} - 2q^{47} + 3q^{48} - 4q^{50} + 12q^{51} - 5q^{52} + 6q^{53} - 9q^{54} - 9q^{55} + 6q^{57} - 7q^{58} - 4q^{59} + 18q^{60} - 13q^{61} + 3q^{62} + 14q^{64} - 6q^{65} - 18q^{66} + 3q^{67} + 2q^{68} - 13q^{71} + 18q^{72} + 26q^{73} - 2q^{74} - 12q^{75} + q^{76} + 15q^{78} - 6q^{79} - 3q^{80} - 9q^{81} + 3q^{82} + 6q^{85} - 14q^{86} - 21q^{87} - 9q^{88} + 6q^{89} - 36q^{90} + 9q^{93} + q^{94} + 3q^{95} + 30q^{96} - 5q^{97} - 36q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i 0.633316 0.773893i \(-0.281693\pi\)
−0.986869 + 0.161521i \(0.948360\pi\)
\(3\) −1.50000 2.59808i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −3.00000 −1.34164 −0.670820 0.741620i \(-0.734058\pi\)
−0.670820 + 0.741620i \(0.734058\pi\)
\(6\) −1.50000 + 2.59808i −0.612372 + 1.06066i
\(7\) 0 0
\(8\) −3.00000 −1.06066
\(9\) −3.00000 + 5.19615i −1.00000 + 1.73205i
\(10\) 1.50000 + 2.59808i 0.474342 + 0.821584i
\(11\) 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) −3.00000 −0.866025
\(13\) 1.00000 3.46410i 0.277350 0.960769i
\(14\) 0 0
\(15\) 4.50000 + 7.79423i 1.16190 + 2.01246i
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i \(-0.911312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) 6.00000 1.41421
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i \(-0.869927\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) −1.50000 + 2.59808i −0.335410 + 0.580948i
\(21\) 0 0
\(22\) 1.50000 2.59808i 0.319801 0.553912i
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 4.50000 + 7.79423i 0.918559 + 1.59099i
\(25\) 4.00000 0.800000
\(26\) −3.50000 + 0.866025i −0.686406 + 0.169842i
\(27\) 9.00000 1.73205
\(28\) 0 0
\(29\) −3.50000 6.06218i −0.649934 1.12572i −0.983138 0.182864i \(-0.941463\pi\)
0.333205 0.942855i \(-0.391870\pi\)
\(30\) 4.50000 7.79423i 0.821584 1.42302i
\(31\) −3.00000 −0.538816 −0.269408 0.963026i \(-0.586828\pi\)
−0.269408 + 0.963026i \(0.586828\pi\)
\(32\) −2.50000 + 4.33013i −0.441942 + 0.765466i
\(33\) 4.50000 7.79423i 0.783349 1.35680i
\(34\) 2.00000 0.342997
\(35\) 0 0
\(36\) 3.00000 + 5.19615i 0.500000 + 0.866025i
\(37\) −1.00000 1.73205i −0.164399 0.284747i 0.772043 0.635571i \(-0.219235\pi\)
−0.936442 + 0.350823i \(0.885902\pi\)
\(38\) 1.00000 0.162221
\(39\) −10.5000 + 2.59808i −1.68135 + 0.416025i
\(40\) 9.00000 1.42302
\(41\) 1.50000 + 2.59808i 0.234261 + 0.405751i 0.959058 0.283211i \(-0.0913998\pi\)
−0.724797 + 0.688963i \(0.758066\pi\)
\(42\) 0 0
\(43\) 3.50000 6.06218i 0.533745 0.924473i −0.465478 0.885059i \(-0.654118\pi\)
0.999223 0.0394140i \(-0.0125491\pi\)
\(44\) 3.00000 0.452267
\(45\) 9.00000 15.5885i 1.34164 2.32379i
\(46\) 0 0
\(47\) −1.00000 −0.145865 −0.0729325 0.997337i \(-0.523236\pi\)
−0.0729325 + 0.997337i \(0.523236\pi\)
\(48\) 1.50000 2.59808i 0.216506 0.375000i
\(49\) 0 0
\(50\) −2.00000 3.46410i −0.282843 0.489898i
\(51\) 6.00000 0.840168
\(52\) −2.50000 2.59808i −0.346688 0.360288i
\(53\) 3.00000 0.412082 0.206041 0.978543i \(-0.433942\pi\)
0.206041 + 0.978543i \(0.433942\pi\)
\(54\) −4.50000 7.79423i −0.612372 1.06066i
\(55\) −4.50000 7.79423i −0.606780 1.05097i
\(56\) 0 0
\(57\) 3.00000 0.397360
\(58\) −3.50000 + 6.06218i −0.459573 + 0.796003i
\(59\) −2.00000 + 3.46410i −0.260378 + 0.450988i −0.966342 0.257260i \(-0.917180\pi\)
0.705965 + 0.708247i \(0.250514\pi\)
\(60\) 9.00000 1.16190
\(61\) −6.50000 + 11.2583i −0.832240 + 1.44148i 0.0640184 + 0.997949i \(0.479608\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 1.50000 + 2.59808i 0.190500 + 0.329956i
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) −3.00000 + 10.3923i −0.372104 + 1.28901i
\(66\) −9.00000 −1.10782
\(67\) 1.50000 + 2.59808i 0.183254 + 0.317406i 0.942987 0.332830i \(-0.108004\pi\)
−0.759733 + 0.650236i \(0.774670\pi\)
\(68\) 1.00000 + 1.73205i 0.121268 + 0.210042i
\(69\) 0 0
\(70\) 0 0
\(71\) −6.50000 + 11.2583i −0.771408 + 1.33612i 0.165383 + 0.986229i \(0.447114\pi\)
−0.936791 + 0.349889i \(0.886219\pi\)
\(72\) 9.00000 15.5885i 1.06066 1.83712i
\(73\) 13.0000 1.52153 0.760767 0.649025i \(-0.224823\pi\)
0.760767 + 0.649025i \(0.224823\pi\)
\(74\) −1.00000 + 1.73205i −0.116248 + 0.201347i
\(75\) −6.00000 10.3923i −0.692820 1.20000i
\(76\) 0.500000 + 0.866025i 0.0573539 + 0.0993399i
\(77\) 0 0
\(78\) 7.50000 + 7.79423i 0.849208 + 0.882523i
\(79\) −3.00000 −0.337526 −0.168763 0.985657i \(-0.553977\pi\)
−0.168763 + 0.985657i \(0.553977\pi\)
\(80\) −1.50000 2.59808i −0.167705 0.290474i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 1.50000 2.59808i 0.165647 0.286910i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 3.00000 5.19615i 0.325396 0.563602i
\(86\) −7.00000 −0.754829
\(87\) −10.5000 + 18.1865i −1.12572 + 1.94980i
\(88\) −4.50000 7.79423i −0.479702 0.830868i
\(89\) 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i \(-0.0636557\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(90\) −18.0000 −1.89737
\(91\) 0 0
\(92\) 0 0
\(93\) 4.50000 + 7.79423i 0.466628 + 0.808224i
\(94\) 0.500000 + 0.866025i 0.0515711 + 0.0893237i
\(95\) 1.50000 2.59808i 0.153897 0.266557i
\(96\) 15.0000 1.53093
\(97\) −2.50000 + 4.33013i −0.253837 + 0.439658i −0.964579 0.263795i \(-0.915026\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 0 0
\(99\) −18.0000 −1.80907
\(100\) 2.00000 3.46410i 0.200000 0.346410i
\(101\) −2.50000 4.33013i −0.248759 0.430864i 0.714423 0.699715i \(-0.246689\pi\)
−0.963182 + 0.268851i \(0.913356\pi\)
\(102\) −3.00000 5.19615i −0.297044 0.514496i
\(103\) −5.00000 −0.492665 −0.246332 0.969185i \(-0.579225\pi\)
−0.246332 + 0.969185i \(0.579225\pi\)
\(104\) −3.00000 + 10.3923i −0.294174 + 1.01905i
\(105\) 0 0
\(106\) −1.50000 2.59808i −0.145693 0.252347i
\(107\) −4.00000 6.92820i −0.386695 0.669775i 0.605308 0.795991i \(-0.293050\pi\)
−0.992003 + 0.126217i \(0.959717\pi\)
\(108\) 4.50000 7.79423i 0.433013 0.750000i
\(109\) 7.00000 0.670478 0.335239 0.942133i \(-0.391183\pi\)
0.335239 + 0.942133i \(0.391183\pi\)
\(110\) −4.50000 + 7.79423i −0.429058 + 0.743151i
\(111\) −3.00000 + 5.19615i −0.284747 + 0.493197i
\(112\) 0 0
\(113\) −7.50000 + 12.9904i −0.705541 + 1.22203i 0.260955 + 0.965351i \(0.415962\pi\)
−0.966496 + 0.256681i \(0.917371\pi\)
\(114\) −1.50000 2.59808i −0.140488 0.243332i
\(115\) 0 0
\(116\) −7.00000 −0.649934
\(117\) 15.0000 + 15.5885i 1.38675 + 1.44115i
\(118\) 4.00000 0.368230
\(119\) 0 0
\(120\) −13.5000 23.3827i −1.23238 2.13454i
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 13.0000 1.17696
\(123\) 4.50000 7.79423i 0.405751 0.702782i
\(124\) −1.50000 + 2.59808i −0.134704 + 0.233314i
\(125\) 3.00000 0.268328
\(126\) 0 0
\(127\) −5.50000 9.52628i −0.488046 0.845321i 0.511859 0.859069i \(-0.328957\pi\)
−0.999905 + 0.0137486i \(0.995624\pi\)
\(128\) 1.50000 + 2.59808i 0.132583 + 0.229640i
\(129\) −21.0000 −1.84895
\(130\) 10.5000 2.59808i 0.920911 0.227866i
\(131\) −5.00000 −0.436852 −0.218426 0.975854i \(-0.570092\pi\)
−0.218426 + 0.975854i \(0.570092\pi\)
\(132\) −4.50000 7.79423i −0.391675 0.678401i
\(133\) 0 0
\(134\) 1.50000 2.59808i 0.129580 0.224440i
\(135\) −27.0000 −2.32379
\(136\) 3.00000 5.19615i 0.257248 0.445566i
\(137\) −5.00000 + 8.66025i −0.427179 + 0.739895i −0.996621 0.0821359i \(-0.973826\pi\)
0.569442 + 0.822031i \(0.307159\pi\)
\(138\) 0 0
\(139\) −7.50000 + 12.9904i −0.636142 + 1.10183i 0.350130 + 0.936701i \(0.386137\pi\)
−0.986272 + 0.165129i \(0.947196\pi\)
\(140\) 0 0
\(141\) 1.50000 + 2.59808i 0.126323 + 0.218797i
\(142\) 13.0000 1.09094
\(143\) 10.5000 2.59808i 0.878054 0.217262i
\(144\) −6.00000 −0.500000
\(145\) 10.5000 + 18.1865i 0.871978 + 1.51031i
\(146\) −6.50000 11.2583i −0.537944 0.931746i
\(147\) 0 0
\(148\) −2.00000 −0.164399
\(149\) −7.50000 + 12.9904i −0.614424 + 1.06421i 0.376061 + 0.926595i \(0.377278\pi\)
−0.990485 + 0.137619i \(0.956055\pi\)
\(150\) −6.00000 + 10.3923i −0.489898 + 0.848528i
\(151\) −21.0000 −1.70896 −0.854478 0.519488i \(-0.826123\pi\)
−0.854478 + 0.519488i \(0.826123\pi\)
\(152\) 1.50000 2.59808i 0.121666 0.210732i
\(153\) −6.00000 10.3923i −0.485071 0.840168i
\(154\) 0 0
\(155\) 9.00000 0.722897
\(156\) −3.00000 + 10.3923i −0.240192 + 0.832050i
\(157\) −19.0000 −1.51637 −0.758183 0.652042i \(-0.773912\pi\)
−0.758183 + 0.652042i \(0.773912\pi\)
\(158\) 1.50000 + 2.59808i 0.119334 + 0.206692i
\(159\) −4.50000 7.79423i −0.356873 0.618123i
\(160\) 7.50000 12.9904i 0.592927 1.02698i
\(161\) 0 0
\(162\) −4.50000 + 7.79423i −0.353553 + 0.612372i
\(163\) 0.500000 0.866025i 0.0391630 0.0678323i −0.845780 0.533533i \(-0.820864\pi\)
0.884943 + 0.465700i \(0.154198\pi\)
\(164\) 3.00000 0.234261
\(165\) −13.5000 + 23.3827i −1.05097 + 1.82034i
\(166\) 0 0
\(167\) −6.50000 11.2583i −0.502985 0.871196i −0.999994 0.00345033i \(-0.998902\pi\)
0.497009 0.867745i \(-0.334432\pi\)
\(168\) 0 0
\(169\) −11.0000 6.92820i −0.846154 0.532939i
\(170\) −6.00000 −0.460179
\(171\) −3.00000 5.19615i −0.229416 0.397360i
\(172\) −3.50000 6.06218i −0.266872 0.462237i
\(173\) 9.50000 16.4545i 0.722272 1.25101i −0.237816 0.971310i \(-0.576431\pi\)
0.960087 0.279701i \(-0.0902353\pi\)
\(174\) 21.0000 1.59201
\(175\) 0 0
\(176\) −1.50000 + 2.59808i −0.113067 + 0.195837i
\(177\) 12.0000 0.901975
\(178\) 3.00000 5.19615i 0.224860 0.389468i
\(179\) −8.50000 14.7224i −0.635320 1.10041i −0.986447 0.164079i \(-0.947535\pi\)
0.351127 0.936328i \(-0.385798\pi\)
\(180\) −9.00000 15.5885i −0.670820 1.16190i
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) 0 0
\(183\) 39.0000 2.88296
\(184\) 0 0
\(185\) 3.00000 + 5.19615i 0.220564 + 0.382029i
\(186\) 4.50000 7.79423i 0.329956 0.571501i
\(187\) −6.00000 −0.438763
\(188\) −0.500000 + 0.866025i −0.0364662 + 0.0631614i
\(189\) 0 0
\(190\) −3.00000 −0.217643
\(191\) 8.50000 14.7224i 0.615038 1.06528i −0.375339 0.926887i \(-0.622474\pi\)
0.990378 0.138390i \(-0.0441928\pi\)
\(192\) −10.5000 18.1865i −0.757772 1.31250i
\(193\) −3.50000 6.06218i −0.251936 0.436365i 0.712123 0.702055i \(-0.247734\pi\)
−0.964059 + 0.265689i \(0.914400\pi\)
\(194\) 5.00000 0.358979
\(195\) 31.5000 7.79423i 2.25576 0.558156i
\(196\) 0 0
\(197\) 0.500000 + 0.866025i 0.0356235 + 0.0617018i 0.883287 0.468832i \(-0.155325\pi\)
−0.847664 + 0.530534i \(0.821992\pi\)
\(198\) 9.00000 + 15.5885i 0.639602 + 1.10782i
\(199\) −10.0000 + 17.3205i −0.708881 + 1.22782i 0.256391 + 0.966573i \(0.417466\pi\)
−0.965272 + 0.261245i \(0.915867\pi\)
\(200\) −12.0000 −0.848528
\(201\) 4.50000 7.79423i 0.317406 0.549762i
\(202\) −2.50000 + 4.33013i −0.175899 + 0.304667i
\(203\) 0 0
\(204\) 3.00000 5.19615i 0.210042 0.363803i
\(205\) −4.50000 7.79423i −0.314294 0.544373i
\(206\) 2.50000 + 4.33013i 0.174183 + 0.301694i
\(207\) 0 0
\(208\) 3.50000 0.866025i 0.242681 0.0600481i
\(209\) −3.00000 −0.207514
\(210\) 0 0
\(211\) −3.50000 6.06218i −0.240950 0.417338i 0.720035 0.693938i \(-0.244126\pi\)
−0.960985 + 0.276600i \(0.910792\pi\)
\(212\) 1.50000 2.59808i 0.103020 0.178437i
\(213\) 39.0000 2.67224
\(214\) −4.00000 + 6.92820i −0.273434 + 0.473602i
\(215\) −10.5000 + 18.1865i −0.716094 + 1.24031i
\(216\) −27.0000 −1.83712
\(217\) 0 0
\(218\) −3.50000 6.06218i −0.237050 0.410582i
\(219\) −19.5000 33.7750i −1.31769 2.28230i
\(220\) −9.00000 −0.606780
\(221\) 5.00000 + 5.19615i 0.336336 + 0.349531i
\(222\) 6.00000 0.402694
\(223\) −4.50000 7.79423i −0.301342 0.521940i 0.675098 0.737728i \(-0.264101\pi\)
−0.976440 + 0.215788i \(0.930768\pi\)
\(224\) 0 0
\(225\) −12.0000 + 20.7846i −0.800000 + 1.38564i
\(226\) 15.0000 0.997785
\(227\) −2.00000 + 3.46410i −0.132745 + 0.229920i −0.924734 0.380615i \(-0.875712\pi\)
0.791989 + 0.610535i \(0.209046\pi\)
\(228\) 1.50000 2.59808i 0.0993399 0.172062i
\(229\) 13.0000 0.859064 0.429532 0.903052i \(-0.358679\pi\)
0.429532 + 0.903052i \(0.358679\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 10.5000 + 18.1865i 0.689359 + 1.19400i
\(233\) −21.0000 −1.37576 −0.687878 0.725826i \(-0.741458\pi\)
−0.687878 + 0.725826i \(0.741458\pi\)
\(234\) 6.00000 20.7846i 0.392232 1.35873i
\(235\) 3.00000 0.195698
\(236\) 2.00000 + 3.46410i 0.130189 + 0.225494i
\(237\) 4.50000 + 7.79423i 0.292306 + 0.506290i
\(238\) 0 0
\(239\) −4.00000 −0.258738 −0.129369 0.991596i \(-0.541295\pi\)
−0.129369 + 0.991596i \(0.541295\pi\)
\(240\) −4.50000 + 7.79423i −0.290474 + 0.503115i
\(241\) −13.0000 + 22.5167i −0.837404 + 1.45043i 0.0546547 + 0.998505i \(0.482594\pi\)
−0.892058 + 0.451920i \(0.850739\pi\)
\(242\) −2.00000 −0.128565
\(243\) 0 0
\(244\) 6.50000 + 11.2583i 0.416120 + 0.720741i
\(245\) 0 0
\(246\) −9.00000 −0.573819
\(247\) 2.50000 + 2.59808i 0.159071 + 0.165312i
\(248\) 9.00000 0.571501
\(249\) 0 0
\(250\) −1.50000 2.59808i −0.0948683 0.164317i
\(251\) −11.5000 + 19.9186i −0.725874 + 1.25725i 0.232740 + 0.972539i \(0.425231\pi\)
−0.958613 + 0.284711i \(0.908102\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −5.50000 + 9.52628i −0.345101 + 0.597732i
\(255\) −18.0000 −1.12720
\(256\) 8.50000 14.7224i 0.531250 0.920152i
\(257\) −1.00000 1.73205i −0.0623783 0.108042i 0.833150 0.553047i \(-0.186535\pi\)
−0.895528 + 0.445005i \(0.853202\pi\)
\(258\) 10.5000 + 18.1865i 0.653701 + 1.13224i
\(259\) 0 0
\(260\) 7.50000 + 7.79423i 0.465130 + 0.483378i
\(261\) 42.0000 2.59973
\(262\) 2.50000 + 4.33013i 0.154451 + 0.267516i
\(263\) 13.5000 + 23.3827i 0.832446 + 1.44184i 0.896093 + 0.443866i \(0.146393\pi\)
−0.0636476 + 0.997972i \(0.520273\pi\)
\(264\) −13.5000 + 23.3827i −0.830868 + 1.43910i
\(265\) −9.00000 −0.552866
\(266\) 0 0
\(267\) 9.00000 15.5885i 0.550791 0.953998i
\(268\) 3.00000 0.183254
\(269\) 9.00000 15.5885i 0.548740 0.950445i −0.449622 0.893219i \(-0.648441\pi\)
0.998361 0.0572259i \(-0.0182255\pi\)
\(270\) 13.5000 + 23.3827i 0.821584 + 1.42302i
\(271\) −8.00000 13.8564i −0.485965 0.841717i 0.513905 0.857847i \(-0.328199\pi\)
−0.999870 + 0.0161307i \(0.994865\pi\)
\(272\) −2.00000 −0.121268
\(273\) 0 0
\(274\) 10.0000 0.604122
\(275\) 6.00000 + 10.3923i 0.361814 + 0.626680i
\(276\) 0 0
\(277\) −11.0000 + 19.0526i −0.660926 + 1.14476i 0.319447 + 0.947604i \(0.396503\pi\)
−0.980373 + 0.197153i \(0.936830\pi\)
\(278\) 15.0000 0.899640
\(279\) 9.00000 15.5885i 0.538816 0.933257i
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 1.50000 2.59808i 0.0893237 0.154713i
\(283\) 0.500000 + 0.866025i 0.0297219 + 0.0514799i 0.880504 0.474039i \(-0.157204\pi\)
−0.850782 + 0.525519i \(0.823871\pi\)
\(284\) 6.50000 + 11.2583i 0.385704 + 0.668059i
\(285\) −9.00000 −0.533114
\(286\) −7.50000 7.79423i −0.443484 0.460882i
\(287\) 0 0
\(288\) −15.0000 25.9808i −0.883883 1.53093i
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) 10.5000 18.1865i 0.616581 1.06795i
\(291\) 15.0000 0.879316
\(292\) 6.50000 11.2583i 0.380384 0.658844i
\(293\) 5.50000 9.52628i 0.321313 0.556531i −0.659446 0.751752i \(-0.729209\pi\)
0.980759 + 0.195221i \(0.0625424\pi\)
\(294\) 0 0
\(295\) 6.00000 10.3923i 0.349334 0.605063i
\(296\) 3.00000 + 5.19615i 0.174371 + 0.302020i
\(297\) 13.5000 + 23.3827i 0.783349 + 1.35680i
\(298\) 15.0000 0.868927
\(299\) 0 0
\(300\) −12.0000 −0.692820
\(301\) 0 0
\(302\) 10.5000 + 18.1865i 0.604207 + 1.04652i
\(303\) −7.50000 + 12.9904i −0.430864 + 0.746278i
\(304\) −1.00000 −0.0573539
\(305\) 19.5000 33.7750i 1.11657 1.93395i
\(306\) −6.00000 + 10.3923i −0.342997 + 0.594089i
\(307\) −12.0000 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 0 0
\(309\) 7.50000 + 12.9904i 0.426660 + 0.738997i
\(310\) −4.50000 7.79423i −0.255583 0.442682i
\(311\) 9.00000 0.510343 0.255172 0.966896i \(-0.417868\pi\)
0.255172 + 0.966896i \(0.417868\pi\)
\(312\) 31.5000 7.79423i 1.78334 0.441261i
\(313\) −19.0000 −1.07394 −0.536972 0.843600i \(-0.680432\pi\)
−0.536972 + 0.843600i \(0.680432\pi\)
\(314\) 9.50000 + 16.4545i 0.536116 + 0.928580i
\(315\) 0 0
\(316\) −1.50000 + 2.59808i −0.0843816 + 0.146153i
\(317\) −9.00000 −0.505490 −0.252745 0.967533i \(-0.581333\pi\)
−0.252745 + 0.967533i \(0.581333\pi\)
\(318\) −4.50000 + 7.79423i −0.252347 + 0.437079i
\(319\) 10.5000 18.1865i 0.587887 1.01825i
\(320\) −21.0000 −1.17394
\(321\) −12.0000 + 20.7846i −0.669775 + 1.16008i
\(322\) 0 0
\(323\) −1.00000 1.73205i −0.0556415 0.0963739i
\(324\) −9.00000 −0.500000
\(325\) 4.00000 13.8564i 0.221880 0.768615i
\(326\) −1.00000 −0.0553849
\(327\) −10.5000 18.1865i −0.580651 1.00572i
\(328\) −4.50000 7.79423i −0.248471 0.430364i
\(329\) 0 0
\(330\) 27.0000 1.48630
\(331\) 14.5000 25.1147i 0.796992 1.38043i −0.124574 0.992210i \(-0.539757\pi\)
0.921567 0.388221i \(-0.126910\pi\)
\(332\) 0 0
\(333\) 12.0000 0.657596
\(334\) −6.50000 + 11.2583i −0.355664 + 0.616028i
\(335\) −4.50000 7.79423i −0.245861 0.425844i
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) −0.500000 + 12.9904i −0.0271964 + 0.706584i
\(339\) 45.0000 2.44406
\(340\) −3.00000 5.19615i −0.162698 0.281801i
\(341\) −4.50000 7.79423i −0.243689 0.422081i
\(342\) −3.00000 + 5.19615i −0.162221 + 0.280976i
\(343\) 0 0
\(344\) −10.5000 + 18.1865i −0.566122 + 0.980552i
\(345\) 0 0
\(346\) −19.0000 −1.02145
\(347\) 4.00000 6.92820i 0.214731 0.371925i −0.738458 0.674299i \(-0.764446\pi\)
0.953189 + 0.302374i \(0.0977791\pi\)
\(348\) 10.5000 + 18.1865i 0.562859 + 0.974901i
\(349\) 11.5000 + 19.9186i 0.615581 + 1.06622i 0.990282 + 0.139072i \(0.0444119\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 0 0
\(351\) 9.00000 31.1769i 0.480384 1.66410i
\(352\) −15.0000 −0.799503
\(353\) −12.5000 21.6506i −0.665308 1.15235i −0.979202 0.202889i \(-0.934967\pi\)
0.313894 0.949458i \(-0.398366\pi\)
\(354\) −6.00000 10.3923i −0.318896 0.552345i
\(355\) 19.5000 33.7750i 1.03495 1.79259i
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) −8.50000 + 14.7224i −0.449239 + 0.778105i
\(359\) 17.0000 0.897226 0.448613 0.893726i \(-0.351918\pi\)
0.448613 + 0.893726i \(0.351918\pi\)
\(360\) −27.0000 + 46.7654i −1.42302 + 2.46475i
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) −11.0000 19.0526i −0.578147 1.00138i
\(363\) −6.00000 −0.314918
\(364\) 0 0
\(365\) −39.0000 −2.04135
\(366\) −19.5000 33.7750i −1.01928 1.76545i
\(367\) −15.5000 26.8468i −0.809093 1.40139i −0.913493 0.406855i \(-0.866625\pi\)
0.104399 0.994535i \(-0.466708\pi\)
\(368\) 0 0
\(369\) −18.0000 −0.937043
\(370\) 3.00000 5.19615i 0.155963 0.270135i
\(371\) 0 0
\(372\) 9.00000 0.466628
\(373\) 4.50000 7.79423i 0.233001 0.403570i −0.725689 0.688023i \(-0.758479\pi\)
0.958690 + 0.284453i \(0.0918121\pi\)
\(374\) 3.00000 + 5.19615i 0.155126 + 0.268687i
\(375\) −4.50000 7.79423i −0.232379 0.402492i
\(376\) 3.00000 0.154713
\(377\) −24.5000 + 6.06218i −1.26181 + 0.312218i
\(378\) 0 0
\(379\) 16.5000 + 28.5788i 0.847548 + 1.46800i 0.883390 + 0.468639i \(0.155255\pi\)
−0.0358418 + 0.999357i \(0.511411\pi\)
\(380\) −1.50000 2.59808i −0.0769484 0.133278i
\(381\) −16.5000 + 28.5788i −0.845321 + 1.46414i
\(382\) −17.0000 −0.869796
\(383\) −10.5000 + 18.1865i −0.536525 + 0.929288i 0.462563 + 0.886586i \(0.346930\pi\)
−0.999088 + 0.0427020i \(0.986403\pi\)
\(384\) 4.50000 7.79423i 0.229640 0.397748i
\(385\) 0 0
\(386\) −3.50000 + 6.06218i −0.178145 + 0.308557i
\(387\) 21.0000 + 36.3731i 1.06749 + 1.84895i
\(388\) 2.50000 + 4.33013i 0.126918 + 0.219829i
\(389\) −33.0000 −1.67317 −0.836583 0.547840i \(-0.815450\pi\)
−0.836583 + 0.547840i \(0.815450\pi\)
\(390\) −22.5000 23.3827i −1.13933 1.18403i
\(391\) 0 0
\(392\) 0 0
\(393\) 7.50000 + 12.9904i 0.378325 + 0.655278i
\(394\) 0.500000 0.866025i 0.0251896 0.0436297i
\(395\) 9.00000 0.452839
\(396\) −9.00000 + 15.5885i −0.452267 + 0.783349i
\(397\) −0.500000 + 0.866025i −0.0250943 + 0.0434646i −0.878300 0.478110i \(-0.841322\pi\)
0.853206 + 0.521575i \(0.174655\pi\)
\(398\) 20.0000 1.00251
\(399\) 0 0
\(400\) 2.00000 + 3.46410i 0.100000 + 0.173205i
\(401\) 1.00000 + 1.73205i 0.0499376 + 0.0864945i 0.889914 0.456129i \(-0.150764\pi\)
−0.839976 + 0.542623i \(0.817431\pi\)
\(402\) −9.00000 −0.448879
\(403\) −3.00000 + 10.3923i −0.149441 + 0.517678i
\(404\) −5.00000 −0.248759
\(405\) 13.5000 + 23.3827i 0.670820 + 1.16190i
\(406\) 0 0
\(407\) 3.00000 5.19615i 0.148704 0.257564i
\(408\) −18.0000 −0.891133
\(409\) 7.00000 12.1244i 0.346128 0.599511i −0.639430 0.768849i \(-0.720830\pi\)
0.985558 + 0.169338i \(0.0541630\pi\)
\(410\) −4.50000 + 7.79423i −0.222239 + 0.384930i
\(411\) 30.0000 1.47979
\(412\) −2.50000 + 4.33013i −0.123166 + 0.213330i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 12.5000 + 12.9904i 0.612863 + 0.636906i
\(417\) 45.0000 2.20366
\(418\) 1.50000 + 2.59808i 0.0733674 + 0.127076i
\(419\) −12.5000 21.6506i −0.610665 1.05770i −0.991129 0.132907i \(-0.957569\pi\)
0.380464 0.924796i \(-0.375764\pi\)
\(420\) 0 0
\(421\) 18.0000 0.877266 0.438633 0.898666i \(-0.355463\pi\)
0.438633 + 0.898666i \(0.355463\pi\)
\(422\) −3.50000 + 6.06218i −0.170377 + 0.295102i
\(423\) 3.00000 5.19615i 0.145865 0.252646i
\(424\) −9.00000 −0.437079
\(425\) −4.00000 + 6.92820i −0.194029 + 0.336067i
\(426\) −19.5000 33.7750i −0.944778 1.63640i
\(427\) 0 0
\(428\) −8.00000 −0.386695
\(429\) −22.5000 23.3827i −1.08631 1.12893i
\(430\) 21.0000 1.01271
\(431\) −4.50000 7.79423i −0.216757 0.375435i 0.737057 0.675830i \(-0.236215\pi\)
−0.953815 + 0.300395i \(0.902881\pi\)
\(432\) 4.50000 + 7.79423i 0.216506 + 0.375000i
\(433\) 13.5000 23.3827i 0.648769 1.12370i −0.334649 0.942343i \(-0.608618\pi\)
0.983417 0.181357i \(-0.0580490\pi\)
\(434\) 0 0
\(435\) 31.5000 54.5596i 1.51031 2.61593i
\(436\) 3.50000 6.06218i 0.167620 0.290326i
\(437\) 0 0
\(438\) −19.5000 + 33.7750i −0.931746 + 1.61383i
\(439\) −8.00000 13.8564i −0.381819 0.661330i 0.609503 0.792784i \(-0.291369\pi\)
−0.991322 + 0.131453i \(0.958036\pi\)
\(440\) 13.5000 + 23.3827i 0.643587 + 1.11473i
\(441\) 0 0
\(442\) 2.00000 6.92820i 0.0951303 0.329541i
\(443\) −11.0000 −0.522626 −0.261313 0.965254i \(-0.584155\pi\)
−0.261313 + 0.965254i \(0.584155\pi\)
\(444\) 3.00000 + 5.19615i 0.142374 + 0.246598i
\(445\) −9.00000 15.5885i −0.426641 0.738964i
\(446\) −4.50000 + 7.79423i −0.213081 + 0.369067i
\(447\) 45.0000 2.12843
\(448\) 0 0
\(449\) −7.50000 + 12.9904i −0.353947 + 0.613054i −0.986937 0.161106i \(-0.948494\pi\)
0.632990 + 0.774160i \(0.281827\pi\)
\(450\) 24.0000 1.13137
\(451\) −4.50000 + 7.79423i −0.211897 + 0.367016i
\(452\) 7.50000 + 12.9904i 0.352770 + 0.611016i
\(453\) 31.5000 + 54.5596i 1.48000 + 2.56343i
\(454\) 4.00000 0.187729
\(455\) 0 0
\(456\) −9.00000 −0.421464
\(457\) 9.00000 + 15.5885i 0.421002 + 0.729197i 0.996038 0.0889312i \(-0.0283451\pi\)
−0.575036 + 0.818128i \(0.695012\pi\)
\(458\) −6.50000 11.2583i −0.303725 0.526067i
\(459\) −9.00000 + 15.5885i −0.420084 + 0.727607i
\(460\) 0 0
\(461\) 17.5000 30.3109i 0.815056 1.41172i −0.0942312 0.995550i \(-0.530039\pi\)
0.909288 0.416169i \(-0.136627\pi\)
\(462\) 0 0
\(463\) −8.00000 −0.371792 −0.185896 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) 3.50000 6.06218i 0.162483 0.281430i
\(465\) −13.5000 23.3827i −0.626048 1.08435i
\(466\) 10.5000 + 18.1865i 0.486403 + 0.842475i
\(467\) 7.00000 0.323921 0.161961 0.986797i \(-0.448218\pi\)
0.161961 + 0.986797i \(0.448218\pi\)
\(468\) 21.0000 5.19615i 0.970725 0.240192i
\(469\) 0 0
\(470\) −1.50000 2.59808i −0.0691898 0.119840i
\(471\) 28.5000 + 49.3634i 1.31321 + 2.27455i
\(472\) 6.00000 10.3923i 0.276172 0.478345i
\(473\) 21.0000 0.965581
\(474\) 4.50000 7.79423i 0.206692 0.358001i
\(475\) −2.00000 + 3.46410i −0.0917663 + 0.158944i
\(476\) 0 0
\(477\) −9.00000 + 15.5885i −0.412082 + 0.713746i
\(478\) 2.00000 + 3.46410i 0.0914779 + 0.158444i
\(479\) −17.5000 30.3109i −0.799595 1.38494i −0.919880 0.392200i \(-0.871714\pi\)
0.120284 0.992739i \(-0.461619\pi\)
\(480\) −45.0000 −2.05396
\(481\) −7.00000 + 1.73205i −0.319173 + 0.0789747i
\(482\) 26.0000 1.18427
\(483\) 0 0
\(484\) −1.00000 1.73205i −0.0454545 0.0787296i
\(485\) 7.50000 12.9904i 0.340557 0.589863i
\(486\) 0 0
\(487\) −8.00000 + 13.8564i −0.362515 + 0.627894i −0.988374 0.152042i \(-0.951415\pi\)
0.625859 + 0.779936i \(0.284748\pi\)
\(488\) 19.5000 33.7750i 0.882724 1.52892i
\(489\) −3.00000 −0.135665
\(490\) 0 0
\(491\) −7.50000 12.9904i −0.338470 0.586248i 0.645675 0.763612i \(-0.276576\pi\)
−0.984145 + 0.177365i \(0.943243\pi\)
\(492\) −4.50000 7.79423i −0.202876 0.351391i
\(493\) 14.0000 0.630528
\(494\) 1.00000 3.46410i 0.0449921 0.155857i
\(495\) 54.0000 2.42712
\(496\) −1.50000 2.59808i −0.0673520 0.116657i
\(497\) 0 0
\(498\) 0 0
\(499\) −31.0000 −1.38775 −0.693875 0.720095i \(-0.744098\pi\)
−0.693875 + 0.720095i \(0.744098\pi\)
\(500\) 1.50000 2.59808i 0.0670820 0.116190i
\(501\) −19.5000 + 33.7750i −0.871196 + 1.50896i
\(502\) 23.0000 1.02654
\(503\) −15.5000 + 26.8468i −0.691111 + 1.19704i 0.280363 + 0.959894i \(0.409545\pi\)
−0.971474 + 0.237145i \(0.923788\pi\)
\(504\) 0 0
\(505\) 7.50000 + 12.9904i 0.333746 + 0.578064i
\(506\) 0 0
\(507\) −1.50000 + 38.9711i −0.0666173 + 1.73077i
\(508\) −11.0000 −0.488046
\(509\) −17.0000 29.4449i −0.753512 1.30512i −0.946111 0.323843i \(-0.895025\pi\)
0.192599 0.981278i \(-0.438308\pi\)
\(510\) 9.00000 + 15.5885i 0.398527 + 0.690268i
\(511\) 0 0
\(512\) −11.0000 −0.486136
\(513\) −4.50000 + 7.79423i −0.198680 + 0.344124i
\(514\) −1.00000 + 1.73205i −0.0441081 + 0.0763975i
\(515\) 15.0000 0.660979
\(516\) −10.5000 + 18.1865i −0.462237 + 0.800617i
\(517\) −1.50000 2.59808i −0.0659699 0.114263i
\(518\) 0 0
\(519\) −57.0000 −2.50202
\(520\) 9.00000 31.1769i 0.394676 1.36720i
\(521\) 17.0000 0.744784 0.372392 0.928076i \(-0.378538\pi\)
0.372392 + 0.928076i \(0.378538\pi\)
\(522\) −21.0000 36.3731i −0.919145 1.59201i
\(523\) 2.00000 + 3.46410i 0.0874539 + 0.151475i 0.906434 0.422347i \(-0.138794\pi\)
−0.818980 + 0.573822i \(0.805460\pi\)
\(524\) −2.50000 + 4.33013i −0.109213 + 0.189162i
\(525\) 0 0
\(526\) 13.5000 23.3827i 0.588628 1.01953i
\(527\) 3.00000 5.19615i 0.130682 0.226348i
\(528\) 9.00000 0.391675
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) 4.50000 + 7.79423i 0.195468 + 0.338560i
\(531\) −12.0000 20.7846i −0.520756 0.901975i
\(532\) 0 0
\(533\) 10.5000 2.59808i 0.454805 0.112535i
\(534\) −18.0000 −0.778936
\(535\) 12.0000 + 20.7846i 0.518805 + 0.898597i
\(536\) −4.50000 7.79423i −0.194370 0.336659i
\(537\) −25.5000 + 44.1673i −1.10041 + 1.90596i
\(538\) −18.0000 −0.776035
\(539\) 0 0
\(540\) −13.5000 + 23.3827i −0.580948 + 1.00623i
\(541\) −37.0000 −1.59075 −0.795377 0.606115i \(-0.792727\pi\)
−0.795377 + 0.606115i \(0.792727\pi\)
\(542\) −8.00000 + 13.8564i −0.343629 + 0.595184i
\(543\) −33.0000 57.1577i −1.41617 2.45287i
\(544\) −5.00000 8.66025i −0.214373 0.371305i
\(545\) −21.0000 −0.899541
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 5.00000 + 8.66025i 0.213589 + 0.369948i
\(549\) −39.0000 67.5500i −1.66448 2.88296i
\(550\) 6.00000 10.3923i 0.255841 0.443129i
\(551\) 7.00000 0.298210
\(552\) 0 0
\(553\) 0 0
\(554\) 22.0000 0.934690
\(555\) 9.00000 15.5885i 0.382029 0.661693i
\(556\) 7.50000 + 12.9904i 0.318071 + 0.550915i
\(557\) −1.50000 2.59808i −0.0635570 0.110084i 0.832496 0.554031i \(-0.186911\pi\)
−0.896053 + 0.443947i \(0.853578\pi\)
\(558\) −18.0000 −0.762001
\(559\) −17.5000 18.1865i −0.740171 0.769208i
\(560\) 0 0
\(561\) 9.00000 + 15.5885i 0.379980 + 0.658145i
\(562\) 9.00000 + 15.5885i 0.379642 + 0.657559i
\(563\) 2.00000 3.46410i 0.0842900 0.145994i −0.820798 0.571218i \(-0.806471\pi\)
0.905088 + 0.425223i \(0.139804\pi\)
\(564\) 3.00000 0.126323
\(565\) 22.5000 38.9711i 0.946582 1.63953i
\(566\) 0.500000 0.866025i 0.0210166 0.0364018i
\(567\) 0 0
\(568\) 19.5000 33.7750i 0.818202 1.41717i
\(569\) −5.00000 8.66025i −0.209611 0.363057i 0.741981 0.670421i \(-0.233886\pi\)
−0.951592 + 0.307364i \(0.900553\pi\)
\(570\) 4.50000 + 7.79423i 0.188484 + 0.326464i
\(571\) 43.0000 1.79949 0.899747 0.436412i \(-0.143751\pi\)
0.899747 + 0.436412i \(0.143751\pi\)
\(572\) 3.00000 10.3923i 0.125436 0.434524i
\(573\) −51.0000 −2.13056
\(574\) 0 0
\(575\) 0 0
\(576\) −21.0000 + 36.3731i −0.875000 + 1.51554i
\(577\) 1.00000 0.0416305 0.0208153 0.999783i \(-0.493374\pi\)
0.0208153 + 0.999783i \(0.493374\pi\)
\(578\) 6.50000 11.2583i 0.270364 0.468285i
\(579\) −10.5000 + 18.1865i −0.436365 + 0.755807i
\(580\) 21.0000 0.871978
\(581\) 0 0
\(582\) −7.50000 12.9904i −0.310885 0.538469i
\(583\) 4.50000 + 7.79423i 0.186371 + 0.322804i
\(584\) −39.0000 −1.61383
\(585\) −45.0000 46.7654i −1.86052 1.93351i
\(586\) −11.0000 −0.454406
\(587\) −16.5000 28.5788i −0.681028 1.17957i −0.974668 0.223659i \(-0.928200\pi\)
0.293640 0.955916i \(-0.405133\pi\)
\(588\) 0 0
\(589\) 1.50000 2.59808i 0.0618064 0.107052i
\(590\) −12.0000 −0.494032
\(591\) 1.50000 2.59808i 0.0617018 0.106871i
\(592\) 1.00000 1.73205i 0.0410997 0.0711868i
\(593\) −27.0000 −1.10876 −0.554379 0.832265i \(-0.687044\pi\)
−0.554379 + 0.832265i \(0.687044\pi\)
\(594\) 13.5000 23.3827i 0.553912 0.959403i
\(595\) 0 0
\(596\) 7.50000 + 12.9904i 0.307212 + 0.532107i
\(597\) 60.0000 2.45564
\(598\) 0 0
\(599\) −25.0000 −1.02147 −0.510736 0.859738i \(-0.670627\pi\)
−0.510736 + 0.859738i \(0.670627\pi\)
\(600\) 18.0000 + 31.1769i 0.734847 + 1.27279i
\(601\) 17.5000 + 30.3109i 0.713840 + 1.23641i 0.963405 + 0.268049i \(0.0863789\pi\)
−0.249565 + 0.968358i \(0.580288\pi\)
\(602\) 0 0
\(603\) −18.0000 −0.733017
\(604\) −10.5000 + 18.1865i −0.427239 + 0.740000i
\(605\) −3.00000 + 5.19615i −0.121967 + 0.211254i
\(606\) 15.0000 0.609333
\(607\) 5.50000 9.52628i 0.223238 0.386660i −0.732551 0.680712i \(-0.761671\pi\)
0.955789 + 0.294052i \(0.0950039\pi\)
\(608\) −2.50000 4.33013i −0.101388 0.175610i
\(609\) 0 0
\(610\) −39.0000 −1.57906
\(611\) −1.00000 + 3.46410i −0.0404557 + 0.140143i
\(612\) −12.0000 −0.485071
\(613\) 12.5000 + 21.6506i 0.504870 + 0.874461i 0.999984 + 0.00563283i \(0.00179300\pi\)
−0.495114 + 0.868828i \(0.664874\pi\)
\(614\) 6.00000 + 10.3923i 0.242140 + 0.419399i
\(615\) −13.5000 + 23.3827i −0.544373 + 0.942881i
\(616\) 0 0
\(617\) 16.5000 28.5788i 0.664265 1.15054i −0.315219 0.949019i \(-0.602078\pi\)
0.979484 0.201522i \(-0.0645887\pi\)
\(618\) 7.50000 12.9904i 0.301694 0.522550i
\(619\) −11.0000 −0.442127 −0.221064 0.975259i \(-0.570953\pi\)
−0.221064 + 0.975259i \(0.570953\pi\)
\(620\) 4.50000 7.79423i 0.180724 0.313024i
\(621\) 0 0
\(622\) −4.50000 7.79423i −0.180434 0.312520i
\(623\) 0 0
\(624\) −7.50000 7.79423i −0.300240 0.312019i
\(625\) −29.0000 −1.16000
\(626\) 9.50000 + 16.4545i 0.379696 + 0.657653i
\(627\) 4.50000 + 7.79423i 0.179713 + 0.311272i
\(628\) −9.50000 + 16.4545i −0.379091 + 0.656605i
\(629\) 4.00000 0.159490
\(630\) 0 0
\(631\) −12.5000 + 21.6506i −0.497617 + 0.861898i −0.999996 0.00274930i \(-0.999125\pi\)
0.502379 + 0.864647i \(0.332458\pi\)
\(632\) 9.00000 0.358001
\(633\) −10.5000 + 18.1865i −0.417338 + 0.722850i
\(634\) 4.50000 + 7.79423i 0.178718 + 0.309548i
\(635\) 16.5000 + 28.5788i 0.654783 + 1.13412i
\(636\) −9.00000 −0.356873
\(637\) 0 0
\(638\) −21.0000 −0.831398
\(639\) −39.0000 67.5500i −1.54282 2.67224i
\(640\) −4.50000 7.79423i −0.177878 0.308094i
\(641\) 9.00000 15.5885i 0.355479 0.615707i −0.631721 0.775196i \(-0.717651\pi\)
0.987200 + 0.159489i \(0.0509845\pi\)
\(642\) 24.0000 0.947204
\(643\) −9.50000 + 16.4545i −0.374643 + 0.648901i −0.990274 0.139134i \(-0.955568\pi\)
0.615630 + 0.788035i \(0.288902\pi\)
\(644\) 0 0
\(645\) 63.0000 2.48062
\(646\) −1.00000 + 1.73205i −0.0393445 + 0.0681466i
\(647\) 4.50000 + 7.79423i 0.176913 + 0.306423i 0.940822 0.338902i \(-0.110055\pi\)
−0.763908 + 0.645325i \(0.776722\pi\)
\(648\) 13.5000 + 23.3827i 0.530330 + 0.918559i
\(649\) −12.0000 −0.471041
\(650\) −14.0000 + 3.46410i −0.549125 + 0.135873i
\(651\) 0 0
\(652\) −0.500000 0.866025i −0.0195815 0.0339162i
\(653\) −9.00000 15.5885i −0.352197 0.610023i 0.634437 0.772975i \(-0.281232\pi\)
−0.986634 + 0.162951i \(0.947899\pi\)
\(654\) −10.5000 + 18.1865i −0.410582 + 0.711150i
\(655\) 15.0000 0.586098
\(656\) −1.50000 + 2.59808i −0.0585652 + 0.101438i
\(657\) −39.0000 + 67.5500i −1.52153 + 2.63538i
\(658\) 0 0
\(659\) −14.5000 + 25.1147i −0.564840 + 0.978331i 0.432225 + 0.901766i \(0.357729\pi\)
−0.997065 + 0.0765653i \(0.975605\pi\)
\(660\) 13.5000 + 23.3827i 0.525487 + 0.910170i
\(661\) −4.50000 7.79423i −0.175030 0.303160i 0.765142 0.643862i \(-0.222669\pi\)
−0.940172 + 0.340701i \(0.889335\pi\)
\(662\) −29.0000 −1.12712
\(663\) 6.00000 20.7846i 0.233021 0.807207i
\(664\) 0 0
\(665\) 0 0
\(666\) −6.00000 10.3923i −0.232495 0.402694i
\(667\) 0 0
\(668\) −13.0000 −0.502985
\(669\) −13.5000 + 23.3827i −0.521940 + 0.904027i
\(670\) −4.50000 + 7.79423i −0.173850 + 0.301117i
\(671\) −39.0000 −1.50558
\(672\) 0 0
\(673\) 20.5000 + 35.5070i 0.790217 + 1.36870i 0.925832 + 0.377934i \(0.123365\pi\)
−0.135615 + 0.990762i \(0.543301\pi\)
\(674\) −7.00000 12.1244i −0.269630 0.467013i
\(675\) 36.0000 1.38564
\(676\) −11.5000 + 6.06218i −0.442308 + 0.233161i
\(677\) −7.00000 −0.269032 −0.134516 0.990911i \(-0.542948\pi\)
−0.134516 + 0.990911i \(0.542948\pi\)
\(678\) −22.5000 38.9711i −0.864107 1.49668i
\(679\) 0 0
\(680\) −9.00000 + 15.5885i −0.345134 + 0.597790i
\(681\) 12.0000 0.459841
\(682\) −4.50000 + 7.79423i −0.172314 + 0.298456i
\(683\) −6.00000 + 10.3923i −0.229584 + 0.397650i −0.957685 0.287819i \(-0.907070\pi\)
0.728101 + 0.685470i \(0.240403\pi\)
\(684\) −6.00000 −0.229416
\(685\) 15.0000 25.9808i 0.573121 0.992674i
\(686\) 0 0
\(687\) −19.5000 33.7750i −0.743971 1.28860i
\(688\) 7.00000 0.266872
\(689\) 3.00000 10.3923i 0.114291 0.395915i
\(690\) 0 0
\(691\) −2.00000 3.46410i −0.0760836 0.131781i 0.825473 0.564441i \(-0.190908\pi\)
−0.901557 + 0.432660i \(0.857575\pi\)
\(692\) −9.50000 16.4545i −0.361136 0.625506i
\(693\) 0 0
\(694\) −8.00000 −0.303676
\(695\) 22.5000 38.9711i 0.853474 1.47826i
\(696\) 31.5000 54.5596i 1.19400 2.06808i
\(697\) −6.00000 −0.227266
\(698\) 11.5000 19.9186i 0.435281 0.753930i
\(699\) 31.5000 + 54.5596i 1.19144 + 2.06363i
\(700\) 0 0
\(701\) 42.0000 1.58632 0.793159 0.609015i \(-0.208435\pi\)
0.793159 + 0.609015i \(0.208435\pi\)
\(702\) −31.5000 + 7.79423i −1.18889 + 0.294174i
\(703\) 2.00000 0.0754314
\(704\) 10.5000 + 18.1865i 0.395734 + 0.685431i
\(705\) −4.50000 7.79423i −0.169480 0.293548i
\(706\) −12.5000 + 21.6506i −0.470444 + 0.814832i
\(707\) 0 0
\(708\) 6.00000 10.3923i 0.225494 0.390567i
\(709\) −5.50000 + 9.52628i −0.206557 + 0.357767i −0.950628 0.310334i \(-0.899559\pi\)
0.744071 + 0.668101i \(0.232892\pi\)
\(710\) −39.0000 −1.46364
\(711\) 9.00000 15.5885i 0.337526 0.584613i
\(712\) −9.00000 15.5885i −0.337289 0.584202i
\(713\) 0 0
\(714\) 0 0
\(715\) −31.5000 + 7.79423i −1.17803 + 0.291488i
\(716\) −17.0000 −0.635320
\(717\) 6.00000 + 10.3923i 0.224074 + 0.388108i
\(718\) −8.50000 14.7224i −0.317217 0.549436i
\(719\) −4.50000 + 7.79423i −0.167822 + 0.290676i −0.937654 0.347571i \(-0.887007\pi\)
0.769832 + 0.638247i \(0.220340\pi\)
\(720\) 18.0000 0.670820
\(721\) 0 0
\(722\) 9.00000 15.5885i 0.334945 0.580142i
\(723\) 78.0000 2.90085
\(724\) 11.0000 19.0526i 0.408812 0.708083i
\(725\) −14.0000 24.2487i −0.519947 0.900575i
\(726\) 3.00000 + 5.19615i 0.111340 + 0.192847i
\(727\) 8.00000 0.296704 0.148352 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 19.5000 + 33.7750i 0.721727 + 1.25007i
\(731\) 7.00000 + 12.1244i 0.258904 + 0.448435i
\(732\) 19.5000 33.7750i 0.720741 1.24836i
\(733\) 9.00000 0.332423 0.166211 0.986090i \(-0.446847\pi\)
0.166211 + 0.986090i \(0.446847\pi\)
\(734\) −15.5000 + 26.8468i −0.572115 + 0.990933i
\(735\) 0 0
\(736\) 0 0
\(737\) −4.50000 + 7.79423i −0.165760 + 0.287104i
\(738\) 9.00000 + 15.5885i 0.331295 + 0.573819i
\(739\) −0.500000 0.866025i −0.0183928 0.0318573i 0.856683 0.515844i \(-0.172522\pi\)
−0.875075 + 0.483987i \(0.839188\pi\)
\(740\) 6.00000 0.220564
\(741\) 3.00000 10.3923i 0.110208 0.381771i
\(742\) 0 0
\(743\) −25.5000 44.1673i −0.935504 1.62034i −0.773732 0.633513i \(-0.781612\pi\)
−0.161772 0.986828i \(-0.551721\pi\)
\(744\) −13.5000 23.3827i −0.494934 0.857251i
\(745\) 22.5000 38.9711i 0.824336 1.42779i
\(746\) −9.00000 −0.329513
\(747\) 0 0
\(748\) −3.00000 + 5.19615i −0.109691 + 0.189990i
\(749\) 0 0
\(750\) −4.50000 + 7.79423i −0.164317 + 0.284605i
\(751\) −14.0000 24.2487i −0.510867 0.884848i −0.999921 0.0125942i \(-0.995991\pi\)
0.489053 0.872254i \(-0.337342\pi\)
\(752\) −0.500000 0.866025i −0.0182331 0.0315807i
\(753\) 69.0000 2.51450
\(754\) 17.5000 + 18.1865i 0.637312 + 0.662314i
\(755\) 63.0000 2.29280
\(756\) 0 0
\(757\) −1.50000 2.59808i −0.0545184 0.0944287i 0.837478 0.546471i \(-0.184029\pi\)
−0.891997 + 0.452042i \(0.850696\pi\)
\(758\) 16.5000 28.5788i 0.599307 1.03803i
\(759\) 0 0
\(760\) −4.50000 + 7.79423i −0.163232 + 0.282726i
\(761\) −4.50000 + 7.79423i −0.163125 + 0.282541i −0.935988 0.352032i \(-0.885491\pi\)
0.772863 + 0.634573i \(0.218824\pi\)
\(762\) 33.0000 1.19546
\(763\) 0 0
\(764\) −8.50000 14.7224i −0.307519 0.532639i
\(765\) 18.0000 + 31.1769i 0.650791 + 1.12720i
\(766\) 21.0000 0.758761
\(767\) 10.0000 + 10.3923i 0.361079 + 0.375244i
\(768\) −51.0000 −1.84030
\(769\) 9.50000 + 16.4545i 0.342579 + 0.593364i 0.984911 0.173063i \(-0.0553663\pi\)
−0.642332 + 0.766426i \(0.722033\pi\)
\(770\) 0 0
\(771\) −3.00000 + 5.19615i −0.108042 + 0.187135i
\(772\) −7.00000 −0.251936
\(773\) −3.00000 + 5.19615i −0.107903 + 0.186893i −0.914920 0.403634i \(-0.867747\pi\)
0.807018 + 0.590527i \(0.201080\pi\)
\(774\) 21.0000 36.3731i 0.754829 1.30740i
\(775\) −12.0000 −0.431053
\(776\) 7.50000 12.9904i 0.269234 0.466328i
\(777\) 0 0
\(778\) 16.5000 + 28.5788i 0.591554 + 1.02460i
\(779\) −3.00000 −0.107486
\(780\) 9.00000 31.1769i 0.322252 1.11631i
\(781\) −39.0000 −1.39553
\(782\) 0 0
\(783\) −31.5000 54.5596i