Properties

Label 1950.2.y.d.199.2
Level $1950$
Weight $2$
Character 1950.199
Analytic conductor $15.571$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.y (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1950.199
Dual form 1950.2.y.d.49.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-3.23205 - 1.86603i) q^{11} -1.00000i q^{12} +(3.50000 - 0.866025i) q^{13} -3.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.46410 + 2.00000i) q^{17} -1.00000 q^{18} +(1.96410 - 1.13397i) q^{19} +3.00000i q^{21} +(3.23205 - 1.86603i) q^{22} +(3.00000 + 1.73205i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-1.00000 + 3.46410i) q^{26} +1.00000i q^{27} +(1.50000 - 2.59808i) q^{28} +(-2.73205 + 4.73205i) q^{29} +8.92820i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.86603 - 3.23205i) q^{33} -4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(-3.96410 + 6.86603i) q^{37} +2.26795i q^{38} +(3.46410 + 1.00000i) q^{39} +(3.46410 + 2.00000i) q^{41} +(-2.59808 - 1.50000i) q^{42} +(5.19615 - 3.00000i) q^{43} +3.73205i q^{44} +(-3.00000 + 1.73205i) q^{46} -0.464102 q^{47} +(-0.866025 + 0.500000i) q^{48} +(-1.00000 + 1.73205i) q^{49} -4.00000 q^{51} +(-2.50000 - 2.59808i) q^{52} -3.73205i q^{53} +(-0.866025 - 0.500000i) q^{54} +(1.50000 + 2.59808i) q^{56} +2.26795 q^{57} +(-2.73205 - 4.73205i) q^{58} +(-3.92820 + 2.26795i) q^{59} +(3.73205 + 6.46410i) q^{61} +(-7.73205 - 4.46410i) q^{62} +(-1.50000 + 2.59808i) q^{63} +1.00000 q^{64} +3.73205 q^{66} +(2.73205 - 4.73205i) q^{67} +(3.46410 + 2.00000i) q^{68} +(1.73205 + 3.00000i) q^{69} +(-0.803848 + 0.464102i) q^{71} +(0.500000 + 0.866025i) q^{72} +6.92820 q^{73} +(-3.96410 - 6.86603i) q^{74} +(-1.96410 - 1.13397i) q^{76} -11.1962i q^{77} +(-2.59808 + 2.50000i) q^{78} -16.9282 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-3.46410 + 2.00000i) q^{82} +2.53590 q^{83} +(2.59808 - 1.50000i) q^{84} +6.00000i q^{86} +(-4.73205 + 2.73205i) q^{87} +(-3.23205 - 1.86603i) q^{88} +(8.76795 + 5.06218i) q^{89} +(7.50000 + 7.79423i) q^{91} -3.46410i q^{92} +(-4.46410 + 7.73205i) q^{93} +(0.232051 - 0.401924i) q^{94} -1.00000i q^{96} +(-6.19615 - 10.7321i) q^{97} +(-1.00000 - 1.73205i) q^{98} -3.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 2q^{4} + 6q^{7} + 4q^{8} + 2q^{9} + O(q^{10}) \) \( 4q - 2q^{2} - 2q^{4} + 6q^{7} + 4q^{8} + 2q^{9} - 6q^{11} + 14q^{13} - 12q^{14} - 2q^{16} - 4q^{18} - 6q^{19} + 6q^{22} + 12q^{23} - 4q^{26} + 6q^{28} - 4q^{29} - 2q^{32} - 4q^{33} + 2q^{36} - 2q^{37} - 12q^{46} + 12q^{47} - 4q^{49} - 16q^{51} - 10q^{52} + 6q^{56} + 16q^{57} - 4q^{58} + 12q^{59} + 8q^{61} - 24q^{62} - 6q^{63} + 4q^{64} + 8q^{66} + 4q^{67} - 24q^{71} + 2q^{72} - 2q^{74} + 6q^{76} - 40q^{79} - 2q^{81} + 24q^{83} - 12q^{87} - 6q^{88} + 42q^{89} + 30q^{91} - 4q^{93} - 6q^{94} - 4q^{97} - 4q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) −0.866025 + 0.500000i −0.353553 + 0.204124i
\(7\) 1.50000 + 2.59808i 0.566947 + 0.981981i 0.996866 + 0.0791130i \(0.0252088\pi\)
−0.429919 + 0.902867i \(0.641458\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) −3.23205 1.86603i −0.974500 0.562628i −0.0738948 0.997266i \(-0.523543\pi\)
−0.900605 + 0.434638i \(0.856876\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 3.50000 0.866025i 0.970725 0.240192i
\(14\) −3.00000 −0.801784
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.46410 + 2.00000i −0.840168 + 0.485071i −0.857321 0.514782i \(-0.827873\pi\)
0.0171533 + 0.999853i \(0.494540\pi\)
\(18\) −1.00000 −0.235702
\(19\) 1.96410 1.13397i 0.450596 0.260152i −0.257486 0.966282i \(-0.582894\pi\)
0.708082 + 0.706130i \(0.249561\pi\)
\(20\) 0 0
\(21\) 3.00000i 0.654654i
\(22\) 3.23205 1.86603i 0.689076 0.397838i
\(23\) 3.00000 + 1.73205i 0.625543 + 0.361158i 0.779024 0.626994i \(-0.215715\pi\)
−0.153481 + 0.988152i \(0.549048\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) 0 0
\(26\) −1.00000 + 3.46410i −0.196116 + 0.679366i
\(27\) 1.00000i 0.192450i
\(28\) 1.50000 2.59808i 0.283473 0.490990i
\(29\) −2.73205 + 4.73205i −0.507329 + 0.878720i 0.492635 + 0.870236i \(0.336034\pi\)
−0.999964 + 0.00848369i \(0.997300\pi\)
\(30\) 0 0
\(31\) 8.92820i 1.60355i 0.597624 + 0.801776i \(0.296111\pi\)
−0.597624 + 0.801776i \(0.703889\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −1.86603 3.23205i −0.324833 0.562628i
\(34\) 4.00000i 0.685994i
\(35\) 0 0
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) −3.96410 + 6.86603i −0.651694 + 1.12877i 0.331017 + 0.943625i \(0.392608\pi\)
−0.982712 + 0.185143i \(0.940725\pi\)
\(38\) 2.26795i 0.367910i
\(39\) 3.46410 + 1.00000i 0.554700 + 0.160128i
\(40\) 0 0
\(41\) 3.46410 + 2.00000i 0.541002 + 0.312348i 0.745485 0.666523i \(-0.232218\pi\)
−0.204483 + 0.978870i \(0.565551\pi\)
\(42\) −2.59808 1.50000i −0.400892 0.231455i
\(43\) 5.19615 3.00000i 0.792406 0.457496i −0.0484030 0.998828i \(-0.515413\pi\)
0.840809 + 0.541332i \(0.182080\pi\)
\(44\) 3.73205i 0.562628i
\(45\) 0 0
\(46\) −3.00000 + 1.73205i −0.442326 + 0.255377i
\(47\) −0.464102 −0.0676962 −0.0338481 0.999427i \(-0.510776\pi\)
−0.0338481 + 0.999427i \(0.510776\pi\)
\(48\) −0.866025 + 0.500000i −0.125000 + 0.0721688i
\(49\) −1.00000 + 1.73205i −0.142857 + 0.247436i
\(50\) 0 0
\(51\) −4.00000 −0.560112
\(52\) −2.50000 2.59808i −0.346688 0.360288i
\(53\) 3.73205i 0.512637i −0.966592 0.256318i \(-0.917490\pi\)
0.966592 0.256318i \(-0.0825095\pi\)
\(54\) −0.866025 0.500000i −0.117851 0.0680414i
\(55\) 0 0
\(56\) 1.50000 + 2.59808i 0.200446 + 0.347183i
\(57\) 2.26795 0.300397
\(58\) −2.73205 4.73205i −0.358736 0.621349i
\(59\) −3.92820 + 2.26795i −0.511409 + 0.295262i −0.733412 0.679784i \(-0.762074\pi\)
0.222004 + 0.975046i \(0.428740\pi\)
\(60\) 0 0
\(61\) 3.73205 + 6.46410i 0.477840 + 0.827643i 0.999677 0.0254017i \(-0.00808648\pi\)
−0.521837 + 0.853045i \(0.674753\pi\)
\(62\) −7.73205 4.46410i −0.981971 0.566941i
\(63\) −1.50000 + 2.59808i −0.188982 + 0.327327i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 3.73205 0.459384
\(67\) 2.73205 4.73205i 0.333773 0.578112i −0.649475 0.760383i \(-0.725011\pi\)
0.983248 + 0.182271i \(0.0583447\pi\)
\(68\) 3.46410 + 2.00000i 0.420084 + 0.242536i
\(69\) 1.73205 + 3.00000i 0.208514 + 0.361158i
\(70\) 0 0
\(71\) −0.803848 + 0.464102i −0.0953992 + 0.0550787i −0.546941 0.837171i \(-0.684208\pi\)
0.451541 + 0.892250i \(0.350874\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) 6.92820 0.810885 0.405442 0.914121i \(-0.367117\pi\)
0.405442 + 0.914121i \(0.367117\pi\)
\(74\) −3.96410 6.86603i −0.460817 0.798159i
\(75\) 0 0
\(76\) −1.96410 1.13397i −0.225298 0.130076i
\(77\) 11.1962i 1.27592i
\(78\) −2.59808 + 2.50000i −0.294174 + 0.283069i
\(79\) −16.9282 −1.90457 −0.952286 0.305208i \(-0.901274\pi\)
−0.952286 + 0.305208i \(0.901274\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −3.46410 + 2.00000i −0.382546 + 0.220863i
\(83\) 2.53590 0.278351 0.139176 0.990268i \(-0.455555\pi\)
0.139176 + 0.990268i \(0.455555\pi\)
\(84\) 2.59808 1.50000i 0.283473 0.163663i
\(85\) 0 0
\(86\) 6.00000i 0.646997i
\(87\) −4.73205 + 2.73205i −0.507329 + 0.292907i
\(88\) −3.23205 1.86603i −0.344538 0.198919i
\(89\) 8.76795 + 5.06218i 0.929401 + 0.536590i 0.886622 0.462495i \(-0.153046\pi\)
0.0427788 + 0.999085i \(0.486379\pi\)
\(90\) 0 0
\(91\) 7.50000 + 7.79423i 0.786214 + 0.817057i
\(92\) 3.46410i 0.361158i
\(93\) −4.46410 + 7.73205i −0.462906 + 0.801776i
\(94\) 0.232051 0.401924i 0.0239342 0.0414553i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) −6.19615 10.7321i −0.629124 1.08967i −0.987728 0.156185i \(-0.950080\pi\)
0.358604 0.933490i \(-0.383253\pi\)
\(98\) −1.00000 1.73205i −0.101015 0.174964i
\(99\) 3.73205i 0.375085i
\(100\) 0 0
\(101\) 4.19615 7.26795i 0.417533 0.723188i −0.578158 0.815925i \(-0.696228\pi\)
0.995691 + 0.0927369i \(0.0295616\pi\)
\(102\) 2.00000 3.46410i 0.198030 0.342997i
\(103\) 19.5885i 1.93011i 0.262051 + 0.965054i \(0.415601\pi\)
−0.262051 + 0.965054i \(0.584399\pi\)
\(104\) 3.50000 0.866025i 0.343203 0.0849208i
\(105\) 0 0
\(106\) 3.23205 + 1.86603i 0.313925 + 0.181244i
\(107\) 0.803848 + 0.464102i 0.0777109 + 0.0448664i 0.538352 0.842720i \(-0.319047\pi\)
−0.460641 + 0.887587i \(0.652380\pi\)
\(108\) 0.866025 0.500000i 0.0833333 0.0481125i
\(109\) 10.3923i 0.995402i 0.867349 + 0.497701i \(0.165822\pi\)
−0.867349 + 0.497701i \(0.834178\pi\)
\(110\) 0 0
\(111\) −6.86603 + 3.96410i −0.651694 + 0.376256i
\(112\) −3.00000 −0.283473
\(113\) −10.3923 + 6.00000i −0.977626 + 0.564433i −0.901553 0.432670i \(-0.857572\pi\)
−0.0760733 + 0.997102i \(0.524238\pi\)
\(114\) −1.13397 + 1.96410i −0.106206 + 0.183955i
\(115\) 0 0
\(116\) 5.46410 0.507329
\(117\) 2.50000 + 2.59808i 0.231125 + 0.240192i
\(118\) 4.53590i 0.417563i
\(119\) −10.3923 6.00000i −0.952661 0.550019i
\(120\) 0 0
\(121\) 1.46410 + 2.53590i 0.133100 + 0.230536i
\(122\) −7.46410 −0.675768
\(123\) 2.00000 + 3.46410i 0.180334 + 0.312348i
\(124\) 7.73205 4.46410i 0.694359 0.400888i
\(125\) 0 0
\(126\) −1.50000 2.59808i −0.133631 0.231455i
\(127\) 4.03590 + 2.33013i 0.358128 + 0.206765i 0.668259 0.743928i \(-0.267040\pi\)
−0.310131 + 0.950694i \(0.600373\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 6.00000 0.528271
\(130\) 0 0
\(131\) −20.3205 −1.77541 −0.887706 0.460412i \(-0.847702\pi\)
−0.887706 + 0.460412i \(0.847702\pi\)
\(132\) −1.86603 + 3.23205i −0.162417 + 0.281314i
\(133\) 5.89230 + 3.40192i 0.510928 + 0.294984i
\(134\) 2.73205 + 4.73205i 0.236013 + 0.408787i
\(135\) 0 0
\(136\) −3.46410 + 2.00000i −0.297044 + 0.171499i
\(137\) 3.26795 + 5.66025i 0.279200 + 0.483588i 0.971186 0.238322i \(-0.0765975\pi\)
−0.691986 + 0.721911i \(0.743264\pi\)
\(138\) −3.46410 −0.294884
\(139\) 10.8923 + 18.8660i 0.923873 + 1.60020i 0.793363 + 0.608748i \(0.208328\pi\)
0.130510 + 0.991447i \(0.458339\pi\)
\(140\) 0 0
\(141\) −0.401924 0.232051i −0.0338481 0.0195422i
\(142\) 0.928203i 0.0778931i
\(143\) −12.9282 3.73205i −1.08111 0.312090i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) −3.46410 + 6.00000i −0.286691 + 0.496564i
\(147\) −1.73205 + 1.00000i −0.142857 + 0.0824786i
\(148\) 7.92820 0.651694
\(149\) −19.7321 + 11.3923i −1.61651 + 0.933294i −0.628700 + 0.777648i \(0.716413\pi\)
−0.987813 + 0.155646i \(0.950254\pi\)
\(150\) 0 0
\(151\) 18.7846i 1.52867i 0.644819 + 0.764335i \(0.276933\pi\)
−0.644819 + 0.764335i \(0.723067\pi\)
\(152\) 1.96410 1.13397i 0.159310 0.0919775i
\(153\) −3.46410 2.00000i −0.280056 0.161690i
\(154\) 9.69615 + 5.59808i 0.781338 + 0.451106i
\(155\) 0 0
\(156\) −0.866025 3.50000i −0.0693375 0.280224i
\(157\) 10.8038i 0.862241i −0.902294 0.431120i \(-0.858118\pi\)
0.902294 0.431120i \(-0.141882\pi\)
\(158\) 8.46410 14.6603i 0.673368 1.16631i
\(159\) 1.86603 3.23205i 0.147985 0.256318i
\(160\) 0 0
\(161\) 10.3923i 0.819028i
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) −5.46410 9.46410i −0.427981 0.741286i 0.568712 0.822537i \(-0.307442\pi\)
−0.996694 + 0.0812509i \(0.974108\pi\)
\(164\) 4.00000i 0.312348i
\(165\) 0 0
\(166\) −1.26795 + 2.19615i −0.0984119 + 0.170454i
\(167\) −3.23205 + 5.59808i −0.250104 + 0.433192i −0.963554 0.267513i \(-0.913798\pi\)
0.713451 + 0.700706i \(0.247131\pi\)
\(168\) 3.00000i 0.231455i
\(169\) 11.5000 6.06218i 0.884615 0.466321i
\(170\) 0 0
\(171\) 1.96410 + 1.13397i 0.150199 + 0.0867172i
\(172\) −5.19615 3.00000i −0.396203 0.228748i
\(173\) 19.1603 11.0622i 1.45673 0.841042i 0.457879 0.889015i \(-0.348609\pi\)
0.998849 + 0.0479730i \(0.0152761\pi\)
\(174\) 5.46410i 0.414232i
\(175\) 0 0
\(176\) 3.23205 1.86603i 0.243625 0.140657i
\(177\) −4.53590 −0.340939
\(178\) −8.76795 + 5.06218i −0.657186 + 0.379426i
\(179\) 11.4641 19.8564i 0.856867 1.48414i −0.0180347 0.999837i \(-0.505741\pi\)
0.874902 0.484300i \(-0.160926\pi\)
\(180\) 0 0
\(181\) 3.07180 0.228325 0.114162 0.993462i \(-0.463582\pi\)
0.114162 + 0.993462i \(0.463582\pi\)
\(182\) −10.5000 + 2.59808i −0.778312 + 0.192582i
\(183\) 7.46410i 0.551762i
\(184\) 3.00000 + 1.73205i 0.221163 + 0.127688i
\(185\) 0 0
\(186\) −4.46410 7.73205i −0.327324 0.566941i
\(187\) 14.9282 1.09166
\(188\) 0.232051 + 0.401924i 0.0169240 + 0.0293133i
\(189\) −2.59808 + 1.50000i −0.188982 + 0.109109i
\(190\) 0 0
\(191\) −8.66025 15.0000i −0.626634 1.08536i −0.988222 0.153024i \(-0.951099\pi\)
0.361588 0.932338i \(-0.382235\pi\)
\(192\) 0.866025 + 0.500000i 0.0625000 + 0.0360844i
\(193\) 8.92820 15.4641i 0.642666 1.11313i −0.342169 0.939638i \(-0.611162\pi\)
0.984835 0.173492i \(-0.0555051\pi\)
\(194\) 12.3923 0.889716
\(195\) 0 0
\(196\) 2.00000 0.142857
\(197\) −4.69615 + 8.13397i −0.334587 + 0.579522i −0.983405 0.181422i \(-0.941930\pi\)
0.648818 + 0.760943i \(0.275263\pi\)
\(198\) 3.23205 + 1.86603i 0.229692 + 0.132613i
\(199\) −5.53590 9.58846i −0.392429 0.679708i 0.600340 0.799745i \(-0.295032\pi\)
−0.992769 + 0.120037i \(0.961699\pi\)
\(200\) 0 0
\(201\) 4.73205 2.73205i 0.333773 0.192704i
\(202\) 4.19615 + 7.26795i 0.295240 + 0.511371i
\(203\) −16.3923 −1.15051
\(204\) 2.00000 + 3.46410i 0.140028 + 0.242536i
\(205\) 0 0
\(206\) −16.9641 9.79423i −1.18194 0.682396i
\(207\) 3.46410i 0.240772i
\(208\) −1.00000 + 3.46410i −0.0693375 + 0.240192i
\(209\) −8.46410 −0.585474
\(210\) 0 0
\(211\) 10.9641 18.9904i 0.754800 1.30735i −0.190674 0.981653i \(-0.561067\pi\)
0.945474 0.325698i \(-0.105599\pi\)
\(212\) −3.23205 + 1.86603i −0.221978 + 0.128159i
\(213\) −0.928203 −0.0635994
\(214\) −0.803848 + 0.464102i −0.0549499 + 0.0317253i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −23.1962 + 13.3923i −1.57466 + 0.909129i
\(218\) −9.00000 5.19615i −0.609557 0.351928i
\(219\) 6.00000 + 3.46410i 0.405442 + 0.234082i
\(220\) 0 0
\(221\) −10.3923 + 10.0000i −0.699062 + 0.672673i
\(222\) 7.92820i 0.532106i
\(223\) 4.42820 7.66987i 0.296534 0.513613i −0.678806 0.734317i \(-0.737502\pi\)
0.975341 + 0.220705i \(0.0708357\pi\)
\(224\) 1.50000 2.59808i 0.100223 0.173591i
\(225\) 0 0
\(226\) 12.0000i 0.798228i
\(227\) 6.73205 + 11.6603i 0.446822 + 0.773918i 0.998177 0.0603523i \(-0.0192224\pi\)
−0.551355 + 0.834271i \(0.685889\pi\)
\(228\) −1.13397 1.96410i −0.0750993 0.130076i
\(229\) 11.4641i 0.757569i 0.925485 + 0.378785i \(0.123658\pi\)
−0.925485 + 0.378785i \(0.876342\pi\)
\(230\) 0 0
\(231\) 5.59808 9.69615i 0.368326 0.637960i
\(232\) −2.73205 + 4.73205i −0.179368 + 0.310674i
\(233\) 18.0000i 1.17922i 0.807688 + 0.589610i \(0.200718\pi\)
−0.807688 + 0.589610i \(0.799282\pi\)
\(234\) −3.50000 + 0.866025i −0.228802 + 0.0566139i
\(235\) 0 0
\(236\) 3.92820 + 2.26795i 0.255704 + 0.147631i
\(237\) −14.6603 8.46410i −0.952286 0.549802i
\(238\) 10.3923 6.00000i 0.673633 0.388922i
\(239\) 3.46410i 0.224074i 0.993704 + 0.112037i \(0.0357375\pi\)
−0.993704 + 0.112037i \(0.964262\pi\)
\(240\) 0 0
\(241\) 12.8205 7.40192i 0.825842 0.476800i −0.0265852 0.999647i \(-0.508463\pi\)
0.852427 + 0.522847i \(0.175130\pi\)
\(242\) −2.92820 −0.188232
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) 3.73205 6.46410i 0.238920 0.413822i
\(245\) 0 0
\(246\) −4.00000 −0.255031
\(247\) 5.89230 5.66987i 0.374918 0.360765i
\(248\) 8.92820i 0.566941i
\(249\) 2.19615 + 1.26795i 0.139176 + 0.0803530i
\(250\) 0 0
\(251\) −13.2321 22.9186i −0.835200 1.44661i −0.893868 0.448331i \(-0.852019\pi\)
0.0586681 0.998278i \(-0.481315\pi\)
\(252\) 3.00000 0.188982
\(253\) −6.46410 11.1962i −0.406395 0.703896i
\(254\) −4.03590 + 2.33013i −0.253235 + 0.146205i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 18.5885 + 10.7321i 1.15952 + 0.669447i 0.951188 0.308612i \(-0.0998645\pi\)
0.208328 + 0.978059i \(0.433198\pi\)
\(258\) −3.00000 + 5.19615i −0.186772 + 0.323498i
\(259\) −23.7846 −1.47790
\(260\) 0 0
\(261\) −5.46410 −0.338219
\(262\) 10.1603 17.5981i 0.627703 1.08721i
\(263\) −17.7679 10.2583i −1.09562 0.632556i −0.160552 0.987027i \(-0.551327\pi\)
−0.935067 + 0.354472i \(0.884661\pi\)
\(264\) −1.86603 3.23205i −0.114846 0.198919i
\(265\) 0 0
\(266\) −5.89230 + 3.40192i −0.361280 + 0.208585i
\(267\) 5.06218 + 8.76795i 0.309800 + 0.536590i
\(268\) −5.46410 −0.333773
\(269\) −15.4641 26.7846i −0.942863 1.63309i −0.759975 0.649953i \(-0.774789\pi\)
−0.182888 0.983134i \(-0.558545\pi\)
\(270\) 0 0
\(271\) −3.12436 1.80385i −0.189791 0.109576i 0.402094 0.915599i \(-0.368283\pi\)
−0.591885 + 0.806023i \(0.701616\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 2.59808 + 10.5000i 0.157243 + 0.635489i
\(274\) −6.53590 −0.394848
\(275\) 0 0
\(276\) 1.73205 3.00000i 0.104257 0.180579i
\(277\) 16.9641 9.79423i 1.01927 0.588478i 0.105380 0.994432i \(-0.466394\pi\)
0.913894 + 0.405954i \(0.133061\pi\)
\(278\) −21.7846 −1.30655
\(279\) −7.73205 + 4.46410i −0.462906 + 0.267259i
\(280\) 0 0
\(281\) 6.92820i 0.413302i −0.978415 0.206651i \(-0.933744\pi\)
0.978415 0.206651i \(-0.0662565\pi\)
\(282\) 0.401924 0.232051i 0.0239342 0.0138184i
\(283\) −12.4641 7.19615i −0.740914 0.427767i 0.0814876 0.996674i \(-0.474033\pi\)
−0.822402 + 0.568907i \(0.807366\pi\)
\(284\) 0.803848 + 0.464102i 0.0476996 + 0.0275394i
\(285\) 0 0
\(286\) 9.69615 9.33013i 0.573346 0.551702i
\(287\) 12.0000i 0.708338i
\(288\) 0.500000 0.866025i 0.0294628 0.0510310i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) 12.3923i 0.726450i
\(292\) −3.46410 6.00000i −0.202721 0.351123i
\(293\) 9.62436 + 16.6699i 0.562261 + 0.973864i 0.997299 + 0.0734522i \(0.0234016\pi\)
−0.435038 + 0.900412i \(0.643265\pi\)
\(294\) 2.00000i 0.116642i
\(295\) 0 0
\(296\) −3.96410 + 6.86603i −0.230409 + 0.399080i
\(297\) 1.86603 3.23205i 0.108278 0.187543i
\(298\) 22.7846i 1.31988i
\(299\) 12.0000 + 3.46410i 0.693978 + 0.200334i
\(300\) 0 0
\(301\) 15.5885 + 9.00000i 0.898504 + 0.518751i
\(302\) −16.2679 9.39230i −0.936115 0.540466i
\(303\) 7.26795 4.19615i 0.417533 0.241063i
\(304\) 2.26795i 0.130076i
\(305\) 0 0
\(306\) 3.46410 2.00000i 0.198030 0.114332i
\(307\) 20.2487 1.15565 0.577827 0.816159i \(-0.303901\pi\)
0.577827 + 0.816159i \(0.303901\pi\)
\(308\) −9.69615 + 5.59808i −0.552490 + 0.318980i
\(309\) −9.79423 + 16.9641i −0.557174 + 0.965054i
\(310\) 0 0
\(311\) 5.07180 0.287595 0.143798 0.989607i \(-0.454069\pi\)
0.143798 + 0.989607i \(0.454069\pi\)
\(312\) 3.46410 + 1.00000i 0.196116 + 0.0566139i
\(313\) 1.32051i 0.0746395i 0.999303 + 0.0373198i \(0.0118820\pi\)
−0.999303 + 0.0373198i \(0.988118\pi\)
\(314\) 9.35641 + 5.40192i 0.528013 + 0.304848i
\(315\) 0 0
\(316\) 8.46410 + 14.6603i 0.476143 + 0.824704i
\(317\) 23.5359 1.32191 0.660954 0.750427i \(-0.270152\pi\)
0.660954 + 0.750427i \(0.270152\pi\)
\(318\) 1.86603 + 3.23205i 0.104642 + 0.181244i
\(319\) 17.6603 10.1962i 0.988784 0.570875i
\(320\) 0 0
\(321\) 0.464102 + 0.803848i 0.0259036 + 0.0448664i
\(322\) −9.00000 5.19615i −0.501550 0.289570i
\(323\) −4.53590 + 7.85641i −0.252384 + 0.437142i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 10.9282 0.605257
\(327\) −5.19615 + 9.00000i −0.287348 + 0.497701i
\(328\) 3.46410 + 2.00000i 0.191273 + 0.110432i
\(329\) −0.696152 1.20577i −0.0383801 0.0664763i
\(330\) 0 0
\(331\) 5.53590 3.19615i 0.304280 0.175676i −0.340084 0.940395i \(-0.610455\pi\)
0.644364 + 0.764719i \(0.277122\pi\)
\(332\) −1.26795 2.19615i −0.0695878 0.120530i
\(333\) −7.92820 −0.434463
\(334\) −3.23205 5.59808i −0.176850 0.306313i
\(335\) 0 0
\(336\) −2.59808 1.50000i −0.141737 0.0818317i
\(337\) 5.60770i 0.305471i 0.988267 + 0.152735i \(0.0488082\pi\)
−0.988267 + 0.152735i \(0.951192\pi\)
\(338\) −0.500000 + 12.9904i −0.0271964 + 0.706584i
\(339\) −12.0000 −0.651751
\(340\) 0 0
\(341\) 16.6603 28.8564i 0.902203 1.56266i
\(342\) −1.96410 + 1.13397i −0.106206 + 0.0613183i
\(343\) 15.0000 0.809924
\(344\) 5.19615 3.00000i 0.280158 0.161749i
\(345\) 0 0
\(346\) 22.1244i 1.18941i
\(347\) 14.1962 8.19615i 0.762089 0.439993i −0.0679560 0.997688i \(-0.521648\pi\)
0.830045 + 0.557696i \(0.188314\pi\)
\(348\) 4.73205 + 2.73205i 0.253665 + 0.146453i
\(349\) −15.1244 8.73205i −0.809588 0.467416i 0.0372247 0.999307i \(-0.488148\pi\)
−0.846813 + 0.531891i \(0.821482\pi\)
\(350\) 0 0
\(351\) 0.866025 + 3.50000i 0.0462250 + 0.186816i
\(352\) 3.73205i 0.198919i
\(353\) 14.1962 24.5885i 0.755585 1.30871i −0.189498 0.981881i \(-0.560686\pi\)
0.945083 0.326830i \(-0.105981\pi\)
\(354\) 2.26795 3.92820i 0.120540 0.208782i
\(355\) 0 0
\(356\) 10.1244i 0.536590i
\(357\) −6.00000 10.3923i −0.317554 0.550019i
\(358\) 11.4641 + 19.8564i 0.605897 + 1.04944i
\(359\) 12.9282i 0.682324i 0.940004 + 0.341162i \(0.110821\pi\)
−0.940004 + 0.341162i \(0.889179\pi\)
\(360\) 0 0
\(361\) −6.92820 + 12.0000i −0.364642 + 0.631579i
\(362\) −1.53590 + 2.66025i −0.0807250 + 0.139820i
\(363\) 2.92820i 0.153691i
\(364\) 3.00000 10.3923i 0.157243 0.544705i
\(365\) 0 0
\(366\) −6.46410 3.73205i −0.337884 0.195077i
\(367\) −11.5359 6.66025i −0.602169 0.347662i 0.167725 0.985834i \(-0.446358\pi\)
−0.769894 + 0.638171i \(0.779691\pi\)
\(368\) −3.00000 + 1.73205i −0.156386 + 0.0902894i
\(369\) 4.00000i 0.208232i
\(370\) 0 0
\(371\) 9.69615 5.59808i 0.503399 0.290638i
\(372\) 8.92820 0.462906
\(373\) 19.8564 11.4641i 1.02813 0.593589i 0.111679 0.993744i \(-0.464377\pi\)
0.916447 + 0.400156i \(0.131044\pi\)
\(374\) −7.46410 + 12.9282i −0.385960 + 0.668501i
\(375\) 0 0
\(376\) −0.464102 −0.0239342
\(377\) −5.46410 + 18.9282i −0.281416 + 0.974852i
\(378\) 3.00000i 0.154303i
\(379\) −5.42820 3.13397i −0.278828 0.160981i 0.354065 0.935221i \(-0.384799\pi\)
−0.632893 + 0.774239i \(0.718133\pi\)
\(380\) 0 0
\(381\) 2.33013 + 4.03590i 0.119376 + 0.206765i
\(382\) 17.3205 0.886194
\(383\) 18.3923 + 31.8564i 0.939803 + 1.62779i 0.765837 + 0.643035i \(0.222325\pi\)
0.173966 + 0.984752i \(0.444342\pi\)
\(384\) −0.866025 + 0.500000i −0.0441942 + 0.0255155i
\(385\) 0 0
\(386\) 8.92820 + 15.4641i 0.454434 + 0.787102i
\(387\) 5.19615 + 3.00000i 0.264135 + 0.152499i
\(388\) −6.19615 + 10.7321i −0.314562 + 0.544837i
\(389\) 9.85641 0.499740 0.249870 0.968279i \(-0.419612\pi\)
0.249870 + 0.968279i \(0.419612\pi\)
\(390\) 0 0
\(391\) −13.8564 −0.700749
\(392\) −1.00000 + 1.73205i −0.0505076 + 0.0874818i
\(393\) −17.5981 10.1603i −0.887706 0.512517i
\(394\) −4.69615 8.13397i −0.236589 0.409784i
\(395\) 0 0
\(396\) −3.23205 + 1.86603i −0.162417 + 0.0937713i
\(397\) 3.96410 + 6.86603i 0.198953 + 0.344596i 0.948189 0.317707i \(-0.102913\pi\)
−0.749237 + 0.662303i \(0.769579\pi\)
\(398\) 11.0718 0.554979
\(399\) 3.40192 + 5.89230i 0.170309 + 0.294984i
\(400\) 0 0
\(401\) −1.83975 1.06218i −0.0918725 0.0530426i 0.453360 0.891328i \(-0.350225\pi\)
−0.545232 + 0.838285i \(0.683559\pi\)
\(402\) 5.46410i 0.272525i
\(403\) 7.73205 + 31.2487i 0.385161 + 1.55661i
\(404\) −8.39230 −0.417533
\(405\) 0 0
\(406\) 8.19615 14.1962i 0.406768 0.704543i
\(407\) 25.6244 14.7942i 1.27015 0.733323i
\(408\) −4.00000 −0.198030
\(409\) −0.820508 + 0.473721i −0.0405715 + 0.0234240i −0.520149 0.854076i \(-0.674123\pi\)
0.479577 + 0.877500i \(0.340790\pi\)
\(410\) 0 0
\(411\) 6.53590i 0.322392i
\(412\) 16.9641 9.79423i 0.835761 0.482527i
\(413\) −11.7846 6.80385i −0.579883 0.334795i
\(414\) −3.00000 1.73205i −0.147442 0.0851257i
\(415\) 0 0
\(416\) −2.50000 2.59808i −0.122573 0.127381i
\(417\) 21.7846i 1.06680i
\(418\) 4.23205 7.33013i 0.206996 0.358528i
\(419\) −8.92820 + 15.4641i −0.436171 + 0.755471i −0.997390 0.0721964i \(-0.976999\pi\)
0.561219 + 0.827667i \(0.310332\pi\)
\(420\) 0 0
\(421\) 5.85641i 0.285424i −0.989764 0.142712i \(-0.954418\pi\)
0.989764 0.142712i \(-0.0455822\pi\)
\(422\) 10.9641 + 18.9904i 0.533724 + 0.924437i
\(423\) −0.232051 0.401924i −0.0112827 0.0195422i
\(424\) 3.73205i 0.181244i
\(425\) 0 0
\(426\) 0.464102 0.803848i 0.0224858 0.0389465i
\(427\) −11.1962 + 19.3923i −0.541820 + 0.938459i
\(428\) 0.928203i 0.0448664i
\(429\) −9.33013 9.69615i −0.450463 0.468135i
\(430\) 0 0
\(431\) −12.0000 6.92820i −0.578020 0.333720i 0.182326 0.983238i \(-0.441637\pi\)
−0.760346 + 0.649518i \(0.774971\pi\)
\(432\) −0.866025 0.500000i −0.0416667 0.0240563i
\(433\) 28.3923 16.3923i 1.36445 0.787764i 0.374235 0.927334i \(-0.377905\pi\)
0.990212 + 0.139570i \(0.0445720\pi\)
\(434\) 26.7846i 1.28570i
\(435\) 0 0
\(436\) 9.00000 5.19615i 0.431022 0.248851i
\(437\) 7.85641 0.375823
\(438\) −6.00000 + 3.46410i −0.286691 + 0.165521i
\(439\) 10.6603 18.4641i 0.508786 0.881243i −0.491162 0.871068i \(-0.663428\pi\)
0.999948 0.0101753i \(-0.00323895\pi\)
\(440\) 0 0
\(441\) −2.00000 −0.0952381
\(442\) −3.46410 14.0000i −0.164771 0.665912i
\(443\) 7.85641i 0.373269i 0.982429 + 0.186635i \(0.0597580\pi\)
−0.982429 + 0.186635i \(0.940242\pi\)
\(444\) 6.86603 + 3.96410i 0.325847 + 0.188128i
\(445\) 0 0
\(446\) 4.42820 + 7.66987i 0.209682 + 0.363179i
\(447\) −22.7846 −1.07768
\(448\) 1.50000 + 2.59808i 0.0708683 + 0.122748i
\(449\) 15.6962 9.06218i 0.740747 0.427671i −0.0815937 0.996666i \(-0.526001\pi\)
0.822341 + 0.568995i \(0.192668\pi\)
\(450\) 0 0
\(451\) −7.46410 12.9282i −0.351471 0.608765i
\(452\) 10.3923 + 6.00000i 0.488813 + 0.282216i
\(453\) −9.39230 + 16.2679i −0.441289 + 0.764335i
\(454\) −13.4641 −0.631902
\(455\) 0 0
\(456\) 2.26795 0.106206
\(457\) 0.267949 0.464102i 0.0125341 0.0217098i −0.859690 0.510816i \(-0.829343\pi\)
0.872224 + 0.489106i \(0.162677\pi\)
\(458\) −9.92820 5.73205i −0.463914 0.267841i
\(459\) −2.00000 3.46410i −0.0933520 0.161690i
\(460\) 0 0
\(461\) 28.0526 16.1962i 1.30654 0.754330i 0.325021 0.945707i \(-0.394629\pi\)
0.981517 + 0.191377i \(0.0612952\pi\)
\(462\) 5.59808 + 9.69615i 0.260446 + 0.451106i
\(463\) −0.784610 −0.0364639 −0.0182320 0.999834i \(-0.505804\pi\)
−0.0182320 + 0.999834i \(0.505804\pi\)
\(464\) −2.73205 4.73205i −0.126832 0.219680i
\(465\) 0 0
\(466\) −15.5885 9.00000i −0.722121 0.416917i
\(467\) 3.60770i 0.166944i −0.996510 0.0834721i \(-0.973399\pi\)
0.996510 0.0834721i \(-0.0266010\pi\)
\(468\) 1.00000 3.46410i 0.0462250 0.160128i
\(469\) 16.3923 0.756926
\(470\) 0 0
\(471\) 5.40192 9.35641i 0.248908 0.431120i
\(472\) −3.92820 + 2.26795i −0.180810 + 0.104391i
\(473\) −22.3923 −1.02960
\(474\) 14.6603 8.46410i 0.673368 0.388769i
\(475\) 0 0
\(476\) 12.0000i 0.550019i
\(477\) 3.23205 1.86603i 0.147985 0.0854394i
\(478\) −3.00000 1.73205i −0.137217 0.0792222i
\(479\) 22.7321 + 13.1244i 1.03865 + 0.599667i 0.919452 0.393203i \(-0.128633\pi\)
0.119202 + 0.992870i \(0.461966\pi\)
\(480\) 0 0
\(481\) −7.92820 + 27.4641i −0.361495 + 1.25226i
\(482\) 14.8038i 0.674297i
\(483\) −5.19615 + 9.00000i −0.236433 + 0.409514i
\(484\) 1.46410 2.53590i 0.0665501 0.115268i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 10.5000 + 18.1865i 0.475800 + 0.824110i 0.999616 0.0277214i \(-0.00882512\pi\)
−0.523815 + 0.851832i \(0.675492\pi\)
\(488\) 3.73205 + 6.46410i 0.168942 + 0.292616i
\(489\) 10.9282i 0.494190i
\(490\) 0 0
\(491\) 7.69615 13.3301i 0.347322 0.601580i −0.638450 0.769663i \(-0.720424\pi\)
0.985773 + 0.168083i \(0.0537576\pi\)
\(492\) 2.00000 3.46410i 0.0901670 0.156174i
\(493\) 21.8564i 0.984363i
\(494\) 1.96410 + 7.93782i 0.0883691 + 0.357140i
\(495\) 0 0
\(496\) −7.73205 4.46410i −0.347179 0.200444i
\(497\) −2.41154 1.39230i −0.108172 0.0624534i
\(498\) −2.19615 + 1.26795i −0.0984119 + 0.0568182i
\(499\) 1.32051i 0.0591141i 0.999563 + 0.0295570i \(0.00940967\pi\)
−0.999563 + 0.0295570i \(0.990590\pi\)
\(500\) 0 0
\(501\) −5.59808 + 3.23205i −0.250104 + 0.144397i
\(502\) 26.4641 1.18115
\(503\) 0.232051 0.133975i 0.0103466 0.00597363i −0.494818 0.868997i \(-0.664765\pi\)
0.505164 + 0.863023i \(0.331432\pi\)
\(504\) −1.50000 + 2.59808i −0.0668153 + 0.115728i
\(505\) 0 0
\(506\) 12.9282 0.574729
\(507\) 12.9904 + 0.500000i 0.576923 + 0.0222058i
\(508\) 4.66025i 0.206765i
\(509\) −4.60770 2.66025i −0.204232 0.117914i 0.394396 0.918941i \(-0.370954\pi\)
−0.598628 + 0.801027i \(0.704287\pi\)
\(510\) 0 0
\(511\) 10.3923 + 18.0000i 0.459728 + 0.796273i
\(512\) 1.00000 0.0441942
\(513\) 1.13397 + 1.96410i 0.0500662 + 0.0867172i
\(514\) −18.5885 + 10.7321i −0.819902 + 0.473370i
\(515\) 0 0
\(516\) −3.00000 5.19615i −0.132068 0.228748i
\(517\) 1.50000 + 0.866025i 0.0659699 + 0.0380878i
\(518\) 11.8923 20.5981i 0.522518 0.905028i
\(519\) 22.1244 0.971151
\(520\) 0 0
\(521\) −27.3923 −1.20008 −0.600039 0.799970i \(-0.704848\pi\)
−0.600039 + 0.799970i \(0.704848\pi\)
\(522\) 2.73205 4.73205i 0.119579 0.207116i
\(523\) −11.8756 6.85641i −0.519286 0.299810i 0.217357 0.976092i \(-0.430257\pi\)
−0.736642 + 0.676283i \(0.763590\pi\)
\(524\) 10.1603 + 17.5981i 0.443853 + 0.768776i
\(525\) 0 0
\(526\) 17.7679 10.2583i 0.774719 0.447284i
\(527\) −17.8564 30.9282i −0.777837 1.34725i
\(528\) 3.73205 0.162417
\(529\) −5.50000 9.52628i −0.239130 0.414186i
\(530\) 0 0
\(531\) −3.92820 2.26795i −0.170470 0.0984206i
\(532\) 6.80385i 0.294984i
\(533\) 13.8564 + 4.00000i 0.600188 + 0.173259i
\(534\) −10.1244 −0.438124
\(535\) 0 0
\(536\) 2.73205 4.73205i 0.118007 0.204393i
\(537\) 19.8564 11.4641i 0.856867 0.494713i
\(538\) 30.9282 1.33341
\(539\) 6.46410 3.73205i 0.278429 0.160751i
\(540\) 0 0
\(541\) 26.7846i 1.15156i −0.817605 0.575780i \(-0.804698\pi\)
0.817605 0.575780i \(-0.195302\pi\)
\(542\) 3.12436 1.80385i 0.134203 0.0774819i
\(543\) 2.66025 + 1.53590i 0.114162 + 0.0659117i
\(544\) 3.46410 + 2.00000i 0.148522 + 0.0857493i
\(545\) 0 0
\(546\) −10.3923 3.00000i −0.444750 0.128388i
\(547\) 29.3205i 1.25365i −0.779158 0.626827i \(-0.784353\pi\)
0.779158 0.626827i \(-0.215647\pi\)
\(548\) 3.26795 5.66025i 0.139600 0.241794i
\(549\) −3.73205 + 6.46410i −0.159280 + 0.275881i
\(550\) 0 0
\(551\) 12.3923i 0.527930i
\(552\) 1.73205 + 3.00000i 0.0737210 + 0.127688i
\(553\) −25.3923 43.9808i −1.07979 1.87025i
\(554\) 19.5885i 0.832234i
\(555\) 0 0
\(556\) 10.8923 18.8660i 0.461937 0.800098i
\(557\) 21.6962 37.5788i 0.919295 1.59227i 0.118808 0.992917i \(-0.462093\pi\)
0.800488 0.599349i \(-0.204574\pi\)
\(558\) 8.92820i 0.377961i
\(559\) 15.5885 15.0000i 0.659321 0.634432i
\(560\) 0 0
\(561\) 12.9282 + 7.46410i 0.545829 + 0.315135i
\(562\) 6.00000 + 3.46410i 0.253095 + 0.146124i
\(563\) 16.7321 9.66025i 0.705172 0.407131i −0.104099 0.994567i \(-0.533196\pi\)
0.809271 + 0.587436i \(0.199863\pi\)
\(564\) 0.464102i 0.0195422i
\(565\) 0 0
\(566\) 12.4641 7.19615i 0.523905 0.302477i
\(567\) −3.00000 −0.125988
\(568\) −0.803848 + 0.464102i −0.0337287 + 0.0194733i
\(569\) 9.16025 15.8660i 0.384018 0.665138i −0.607615 0.794232i \(-0.707873\pi\)
0.991632 + 0.129094i \(0.0412068\pi\)
\(570\) 0 0
\(571\) −16.8564 −0.705419 −0.352709 0.935733i \(-0.614740\pi\)
−0.352709 + 0.935733i \(0.614740\pi\)
\(572\) 3.23205 + 13.0622i 0.135139 + 0.546157i
\(573\) 17.3205i 0.723575i
\(574\) −10.3923 6.00000i −0.433766 0.250435i
\(575\) 0 0
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 25.3205 1.05411 0.527053 0.849832i \(-0.323297\pi\)
0.527053 + 0.849832i \(0.323297\pi\)
\(578\) −0.500000 0.866025i −0.0207973 0.0360219i
\(579\) 15.4641 8.92820i 0.642666 0.371043i
\(580\) 0 0
\(581\) 3.80385 + 6.58846i 0.157810 + 0.273335i
\(582\) 10.7321 + 6.19615i 0.444858 + 0.256839i
\(583\) −6.96410 + 12.0622i −0.288424 + 0.499564i
\(584\) 6.92820 0.286691
\(585\) 0 0
\(586\) −19.2487 −0.795157
\(587\) −2.46410 + 4.26795i −0.101704 + 0.176157i −0.912387 0.409329i \(-0.865763\pi\)
0.810683 + 0.585486i \(0.199096\pi\)
\(588\) 1.73205 + 1.00000i 0.0714286 + 0.0412393i
\(589\) 10.1244 + 17.5359i 0.417167 + 0.722554i
\(590\) 0 0
\(591\) −8.13397 + 4.69615i −0.334587 + 0.193174i
\(592\) −3.96410 6.86603i −0.162924 0.282192i
\(593\) 3.21539 0.132040 0.0660201 0.997818i \(-0.478970\pi\)
0.0660201 + 0.997818i \(0.478970\pi\)
\(594\) 1.86603 + 3.23205i 0.0765639 + 0.132613i
\(595\) 0 0
\(596\) 19.7321 + 11.3923i 0.808256 + 0.466647i
\(597\) 11.0718i 0.453138i
\(598\) −9.00000 + 8.66025i −0.368037 + 0.354144i
\(599\) −15.0718 −0.615817 −0.307908 0.951416i \(-0.599629\pi\)
−0.307908 + 0.951416i \(0.599629\pi\)
\(600\) 0 0
\(601\) 12.3564 21.4019i 0.504028 0.873003i −0.495961 0.868345i \(-0.665184\pi\)
0.999989 0.00465778i \(-0.00148262\pi\)
\(602\) −15.5885 + 9.00000i −0.635338 + 0.366813i
\(603\) 5.46410 0.222515
\(604\) 16.2679 9.39230i 0.661933 0.382167i
\(605\) 0 0
\(606\) 8.39230i 0.340914i
\(607\) −32.4282 + 18.7224i −1.31622 + 0.759920i −0.983118 0.182971i \(-0.941429\pi\)
−0.333102 + 0.942891i \(0.608095\pi\)
\(608\) −1.96410 1.13397i −0.0796548 0.0459887i
\(609\) −14.1962 8.19615i −0.575257 0.332125i
\(610\) 0 0
\(611\) −1.62436 + 0.401924i −0.0657144 + 0.0162601i
\(612\) 4.00000i 0.161690i
\(613\) 22.5000 38.9711i 0.908766 1.57403i 0.0929864 0.995667i \(-0.470359\pi\)
0.815780 0.578362i \(-0.196308\pi\)
\(614\) −10.1244 + 17.5359i −0.408586 + 0.707691i
\(615\) 0 0
\(616\) 11.1962i 0.451106i
\(617\) −14.2679 24.7128i −0.574406 0.994900i −0.996106 0.0881649i \(-0.971900\pi\)
0.421700 0.906735i \(-0.361434\pi\)
\(618\) −9.79423 16.9641i −0.393982 0.682396i
\(619\) 42.5167i 1.70889i 0.519543 + 0.854444i \(0.326102\pi\)
−0.519543 + 0.854444i \(0.673898\pi\)
\(620\) 0 0
\(621\) −1.73205 + 3.00000i −0.0695048 + 0.120386i
\(622\) −2.53590 + 4.39230i −0.101680 + 0.176115i
\(623\) 30.3731i 1.21687i
\(624\) −2.59808 + 2.50000i −0.104006 + 0.100080i
\(625\) 0 0
\(626\) −1.14359 0.660254i −0.0457072 0.0263891i
\(627\) −7.33013 4.23205i −0.292737 0.169012i
\(628\) −9.35641 + 5.40192i −0.373361 + 0.215560i
\(629\) 31.7128i 1.26447i
\(630\) 0 0
\(631\) 6.92820 4.00000i 0.275807 0.159237i −0.355716 0.934594i \(-0.615763\pi\)
0.631524 + 0.775356i \(0.282430\pi\)
\(632\) −16.9282 −0.673368
\(633\) 18.9904 10.9641i 0.754800 0.435784i
\(634\) −11.7679 + 20.3827i −0.467365 + 0.809500i
\(635\) 0 0
\(636\) −3.73205 −0.147985
\(637\) −2.00000 + 6.92820i −0.0792429 + 0.274505i
\(638\) 20.3923i 0.807339i
\(639\) −0.803848 0.464102i −0.0317997 0.0183596i
\(640\) 0 0
\(641\) −3.76795 6.52628i −0.148825 0.257773i 0.781968 0.623318i \(-0.214216\pi\)
−0.930793 + 0.365546i \(0.880882\pi\)
\(642\) −0.928203 −0.0366333
\(643\) 14.3923 + 24.9282i 0.567577 + 0.983072i 0.996805 + 0.0798761i \(0.0254525\pi\)
−0.429228 + 0.903196i \(0.641214\pi\)
\(644\) 9.00000 5.19615i 0.354650 0.204757i
\(645\) 0 0
\(646\) −4.53590 7.85641i −0.178463 0.309106i
\(647\) −27.9449 16.1340i −1.09863 0.634292i −0.162766 0.986665i \(-0.552042\pi\)
−0.935860 + 0.352373i \(0.885375\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 16.9282 0.664490
\(650\) 0 0
\(651\) −26.7846 −1.04977
\(652\) −5.46410 + 9.46410i −0.213991 + 0.370643i
\(653\) −25.6244 14.7942i −1.00276 0.578943i −0.0936952 0.995601i \(-0.529868\pi\)
−0.909063 + 0.416658i \(0.863201\pi\)
\(654\) −5.19615 9.00000i −0.203186 0.351928i
\(655\) 0 0
\(656\) −3.46410 + 2.00000i −0.135250 + 0.0780869i
\(657\) 3.46410 + 6.00000i 0.135147 + 0.234082i
\(658\) 1.39230 0.0542777
\(659\) 7.85641 + 13.6077i 0.306042 + 0.530081i 0.977493 0.210969i \(-0.0676618\pi\)
−0.671451 + 0.741049i \(0.734328\pi\)
\(660\) 0 0
\(661\) 36.7128 + 21.1962i 1.42796 + 0.824435i 0.996960 0.0779157i \(-0.0248265\pi\)
0.431003 + 0.902351i \(0.358160\pi\)
\(662\) 6.39230i 0.248444i
\(663\) −14.0000 + 3.46410i −0.543715 + 0.134535i
\(664\) 2.53590 0.0984119
\(665\) 0 0
\(666\) 3.96410 6.86603i 0.153606 0.266053i
\(667\) −16.3923 + 9.46410i −0.634713 + 0.366451i
\(668\) 6.46410 0.250104
\(669\) 7.66987 4.42820i 0.296534 0.171204i
\(670\) 0 0
\(671\) 27.8564i 1.07538i
\(672\) 2.59808 1.50000i 0.100223 0.0578638i
\(673\) −21.4641 12.3923i −0.827380 0.477688i 0.0255746 0.999673i \(-0.491858\pi\)
−0.852955 + 0.521985i \(0.825192\pi\)
\(674\) −4.85641 2.80385i −0.187062 0.108000i
\(675\) 0 0
\(676\) −11.0000 6.92820i −0.423077 0.266469i
\(677\) 2.92820i 0.112540i 0.998416 + 0.0562700i \(0.0179208\pi\)
−0.998416 + 0.0562700i \(0.982079\pi\)
\(678\) 6.00000 10.3923i 0.230429 0.399114i
\(679\) 18.5885 32.1962i 0.713360 1.23557i
\(680\) 0 0
\(681\) 13.4641i 0.515945i
\(682\) 16.6603 + 28.8564i 0.637954 + 1.10497i
\(683\) −3.33975 5.78461i −0.127792 0.221342i 0.795029 0.606571i \(-0.207456\pi\)
−0.922821 + 0.385230i \(0.874122\pi\)
\(684\) 2.26795i 0.0867172i
\(685\) 0 0
\(686\) −7.50000 + 12.9904i −0.286351 + 0.495975i
\(687\) −5.73205 + 9.92820i −0.218691 + 0.378785i
\(688\) 6.00000i 0.228748i
\(689\) −3.23205 13.0622i −0.123131 0.497629i
\(690\) 0 0
\(691\) 19.9641 + 11.5263i 0.759470 + 0.438480i 0.829106 0.559092i \(-0.188850\pi\)
−0.0696353 + 0.997573i \(0.522184\pi\)
\(692\) −19.1603 11.0622i −0.728364 0.420521i
\(693\) 9.69615 5.59808i 0.368326 0.212653i
\(694\) 16.3923i 0.622243i
\(695\) 0 0
\(696\) −4.73205 + 2.73205i −0.179368 + 0.103558i
\(697\) −16.0000 −0.606043
\(698\) 15.1244 8.73205i 0.572465 0.330513i
\(699\) −9.00000 + 15.5885i −0.340411 + 0.589610i
\(700\) 0 0
\(701\) 16.3923 0.619129 0.309564 0.950878i \(-0.399817\pi\)
0.309564 + 0.950878i \(0.399817\pi\)
\(702\) −3.46410 1.00000i −0.130744 0.0377426i
\(703\) 17.9808i 0.678157i
\(704\) −3.23205 1.86603i −0.121812 0.0703285i
\(705\) 0 0
\(706\) 14.1962 + 24.5885i 0.534279 + 0.925399i
\(707\) 25.1769 0.946875
\(708\) 2.26795 + 3.92820i 0.0852348 + 0.147631i
\(709\) 6.33975 3.66025i 0.238094 0.137464i −0.376206 0.926536i \(-0.622772\pi\)
0.614300 + 0.789072i \(0.289438\pi\)
\(710\) 0 0
\(711\) −8.46410 14.6603i −0.317429 0.549802i
\(712\) 8.76795 + 5.06218i 0.328593 + 0.189713i
\(713\) −15.4641 + 26.7846i −0.579135 + 1.00309i
\(714\) 12.0000 0.449089
\(715\) 0 0
\(716\) −22.9282 −0.856867
\(717\) −1.73205 + 3.00000i −0.0646846 + 0.112037i
\(718\) −11.1962 6.46410i −0.417837 0.241238i
\(719\) 8.00000 + 13.8564i 0.298350 + 0.516757i 0.975759 0.218850i \(-0.0702305\pi\)
−0.677409 + 0.735607i \(0.736897\pi\)
\(720\) 0 0
\(721\) −50.8923 + 29.3827i −1.89533 + 1.09427i
\(722\) −6.92820 12.0000i −0.257841 0.446594i
\(723\) 14.8038 0.550561
\(724\) −1.53590 2.66025i −0.0570812 0.0988676i
\(725\) 0 0
\(726\) −2.53590 1.46410i −0.0941160 0.0543379i
\(727\) 12.6603i 0.469543i −0.972051 0.234771i \(-0.924566\pi\)
0.972051 0.234771i \(-0.0754342\pi\)
\(728\) 7.50000 + 7.79423i 0.277968 + 0.288873i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −12.0000 + 20.7846i −0.443836 + 0.768747i
\(732\) 6.46410 3.73205i 0.238920 0.137941i
\(733\) 6.85641 0.253247 0.126624 0.991951i \(-0.459586\pi\)
0.126624 + 0.991951i \(0.459586\pi\)
\(734\) 11.5359 6.66025i 0.425798 0.245834i
\(735\) 0 0
\(736\) 3.46410i 0.127688i
\(737\) −17.6603 + 10.1962i −0.650524 + 0.375580i
\(738\) −3.46410 2.00000i −0.127515 0.0736210i
\(739\) −37.9641 21.9186i −1.39653 0.806288i −0.402505 0.915418i \(-0.631860\pi\)
−0.994028 + 0.109130i \(0.965194\pi\)
\(740\) 0 0
\(741\) 7.93782 1.96410i 0.291603 0.0721531i
\(742\) 11.1962i 0.411024i
\(743\) 1.46410 2.53590i 0.0537127 0.0930331i −0.837919 0.545795i \(-0.816228\pi\)
0.891632 + 0.452762i \(0.149561\pi\)
\(744\) −4.46410 + 7.73205i −0.163662 + 0.283471i
\(745\) 0 0
\(746\) 22.9282i 0.839461i
\(747\) 1.26795 + 2.19615i 0.0463918 + 0.0803530i
\(748\) −7.46410 12.9282i −0.272915 0.472702i
\(749\) 2.78461i 0.101747i
\(750\) 0 0
\(751\) −20.5885 + 35.6603i −0.751283 + 1.30126i 0.195917 + 0.980620i \(0.437232\pi\)
−0.947201 + 0.320641i \(0.896102\pi\)
\(752\) 0.232051 0.401924i 0.00846202 0.0146567i
\(753\) 26.4641i 0.964405i
\(754\) −13.6603 14.1962i −0.497477 0.516993i
\(755\) 0 0
\(756\) 2.59808 + 1.50000i 0.0944911 + 0.0545545i
\(757\) 15.8205 + 9.13397i 0.575006 + 0.331980i 0.759146 0.650920i \(-0.225617\pi\)
−0.184140 + 0.982900i \(0.558950\pi\)
\(758\) 5.42820 3.13397i 0.197161 0.113831i
\(759\) 12.9282i 0.469264i
\(760\) 0 0
\(761\) 38.0885 21.9904i 1.38071 0.797151i 0.388463 0.921465i \(-0.373006\pi\)
0.992243 + 0.124314i \(0.0396730\pi\)
\(762\) −4.66025 −0.168823
\(763\) −27.0000 + 15.5885i −0.977466 + 0.564340i
\(764\) −8.66025 + 15.0000i −0.313317 + 0.542681i
\(765\) 0 0
\(766\) −36.7846 −1.32908
\(767\) −11.7846 + 11.3397i −0.425518 + 0.409454i
\(768\) 1.00000i 0.0360844i
\(769\) −34.3923 19.8564i −1.24022 0.716040i −0.271080 0.962557i \(-0.587381\pi\)
−0.969139 + 0.246517i \(0.920714\pi\)
\(770\) 0 0
\(771\) 10.7321 + 18.5885i 0.386505 + 0.669447i
\(772\) −17.8564 −0.642666
\(773\) 26.6962 + 46.2391i 0.960194 + 1.66310i 0.722008 + 0.691885i \(0.243220\pi\)
0.238186 + 0.971220i \(0.423447\pi\)
\(774\) −5.19615 + 3.00000i −0.186772 + 0.107833i
\(775\) 0 0
\(776\) −6.19615 10.7321i −0.222429 0.385258i
\(777\) −20.5981 11.8923i −0.738952 0.426634i
\(778\) −4.92820 + 8.53590i −0.176685 + 0.306027i
\(779\) 9.07180 0.325031
\(780\) 0 0
\(781\) 3.46410 0.123955
\(782\) 6.92820 12.0000i 0.247752 0.429119i
\(783\) −4.73205 2.73205i −0.169110 0.0976355i