Properties

Label 1170.2.bs.d.361.2
Level $1170$
Weight $2$
Character 1170.361
Analytic conductor $9.342$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.bs (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.34249703649\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1170.361
Dual form 1170.2.bs.d.901.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-2.59808 - 1.50000i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-2.59808 - 1.50000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{10} +(3.23205 - 1.86603i) q^{11} +(-0.866025 + 3.50000i) q^{13} -3.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +(-1.96410 - 1.13397i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(1.86603 - 3.23205i) q^{22} +(-1.73205 - 3.00000i) q^{23} -1.00000 q^{25} +(1.00000 + 3.46410i) q^{26} +(-2.59808 + 1.50000i) q^{28} +(-2.73205 - 4.73205i) q^{29} -8.92820i q^{31} +(-0.866025 - 0.500000i) q^{32} -4.00000i q^{34} +(-1.50000 + 2.59808i) q^{35} +(-6.86603 + 3.96410i) q^{37} -2.26795 q^{38} -1.00000 q^{40} +(-3.46410 + 2.00000i) q^{41} +(-3.00000 + 5.19615i) q^{43} -3.73205i q^{44} +(-3.00000 - 1.73205i) q^{46} -0.464102i q^{47} +(1.00000 + 1.73205i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(2.59808 + 2.50000i) q^{52} +3.73205 q^{53} +(-1.86603 - 3.23205i) q^{55} +(-1.50000 + 2.59808i) q^{56} +(-4.73205 - 2.73205i) q^{58} +(-3.92820 - 2.26795i) q^{59} +(3.73205 - 6.46410i) q^{61} +(-4.46410 - 7.73205i) q^{62} -1.00000 q^{64} +(3.50000 + 0.866025i) q^{65} +(4.73205 - 2.73205i) q^{67} +(-2.00000 - 3.46410i) q^{68} +3.00000i q^{70} +(0.803848 + 0.464102i) q^{71} +6.92820i q^{73} +(-3.96410 + 6.86603i) q^{74} +(-1.96410 + 1.13397i) q^{76} -11.1962 q^{77} +16.9282 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-2.00000 + 3.46410i) q^{82} -2.53590i q^{83} +(-3.46410 - 2.00000i) q^{85} +6.00000i q^{86} +(-1.86603 - 3.23205i) q^{88} +(8.76795 - 5.06218i) q^{89} +(7.50000 - 7.79423i) q^{91} -3.46410 q^{92} +(-0.232051 - 0.401924i) q^{94} +(-1.13397 + 1.96410i) q^{95} +(10.7321 + 6.19615i) q^{97} +(1.73205 + 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} + O(q^{10}) \) \( 4q + 2q^{4} - 2q^{10} + 6q^{11} - 12q^{14} - 2q^{16} + 8q^{17} + 6q^{19} + 4q^{22} - 4q^{25} + 4q^{26} - 4q^{29} - 6q^{35} - 24q^{37} - 16q^{38} - 4q^{40} - 12q^{43} - 12q^{46} + 4q^{49} + 8q^{53} - 4q^{55} - 6q^{56} - 12q^{58} + 12q^{59} + 8q^{61} - 4q^{62} - 4q^{64} + 14q^{65} + 12q^{67} - 8q^{68} + 24q^{71} - 2q^{74} + 6q^{76} - 24q^{77} + 40q^{79} - 8q^{82} - 4q^{88} + 42q^{89} + 30q^{91} + 6q^{94} - 8q^{95} + 36q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) −2.59808 1.50000i −0.981981 0.566947i −0.0791130 0.996866i \(-0.525209\pi\)
−0.902867 + 0.429919i \(0.858542\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) 3.23205 1.86603i 0.974500 0.562628i 0.0738948 0.997266i \(-0.476457\pi\)
0.900605 + 0.434638i \(0.143124\pi\)
\(12\) 0 0
\(13\) −0.866025 + 3.50000i −0.240192 + 0.970725i
\(14\) −3.00000 −0.801784
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.00000 3.46410i 0.485071 0.840168i −0.514782 0.857321i \(-0.672127\pi\)
0.999853 + 0.0171533i \(0.00546033\pi\)
\(18\) 0 0
\(19\) −1.96410 1.13397i −0.450596 0.260152i 0.257486 0.966282i \(-0.417106\pi\)
−0.708082 + 0.706130i \(0.750439\pi\)
\(20\) −0.866025 0.500000i −0.193649 0.111803i
\(21\) 0 0
\(22\) 1.86603 3.23205i 0.397838 0.689076i
\(23\) −1.73205 3.00000i −0.361158 0.625543i 0.626994 0.779024i \(-0.284285\pi\)
−0.988152 + 0.153481i \(0.950952\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 1.00000 + 3.46410i 0.196116 + 0.679366i
\(27\) 0 0
\(28\) −2.59808 + 1.50000i −0.490990 + 0.283473i
\(29\) −2.73205 4.73205i −0.507329 0.878720i −0.999964 0.00848369i \(-0.997300\pi\)
0.492635 0.870236i \(-0.336034\pi\)
\(30\) 0 0
\(31\) 8.92820i 1.60355i −0.597624 0.801776i \(-0.703889\pi\)
0.597624 0.801776i \(-0.296111\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0 0
\(34\) 4.00000i 0.685994i
\(35\) −1.50000 + 2.59808i −0.253546 + 0.439155i
\(36\) 0 0
\(37\) −6.86603 + 3.96410i −1.12877 + 0.651694i −0.943625 0.331017i \(-0.892608\pi\)
−0.185143 + 0.982712i \(0.559275\pi\)
\(38\) −2.26795 −0.367910
\(39\) 0 0
\(40\) −1.00000 −0.158114
\(41\) −3.46410 + 2.00000i −0.541002 + 0.312348i −0.745485 0.666523i \(-0.767782\pi\)
0.204483 + 0.978870i \(0.434449\pi\)
\(42\) 0 0
\(43\) −3.00000 + 5.19615i −0.457496 + 0.792406i −0.998828 0.0484030i \(-0.984587\pi\)
0.541332 + 0.840809i \(0.317920\pi\)
\(44\) 3.73205i 0.562628i
\(45\) 0 0
\(46\) −3.00000 1.73205i −0.442326 0.255377i
\(47\) 0.464102i 0.0676962i −0.999427 0.0338481i \(-0.989224\pi\)
0.999427 0.0338481i \(-0.0107762\pi\)
\(48\) 0 0
\(49\) 1.00000 + 1.73205i 0.142857 + 0.247436i
\(50\) −0.866025 + 0.500000i −0.122474 + 0.0707107i
\(51\) 0 0
\(52\) 2.59808 + 2.50000i 0.360288 + 0.346688i
\(53\) 3.73205 0.512637 0.256318 0.966592i \(-0.417490\pi\)
0.256318 + 0.966592i \(0.417490\pi\)
\(54\) 0 0
\(55\) −1.86603 3.23205i −0.251615 0.435810i
\(56\) −1.50000 + 2.59808i −0.200446 + 0.347183i
\(57\) 0 0
\(58\) −4.73205 2.73205i −0.621349 0.358736i
\(59\) −3.92820 2.26795i −0.511409 0.295262i 0.222004 0.975046i \(-0.428740\pi\)
−0.733412 + 0.679784i \(0.762074\pi\)
\(60\) 0 0
\(61\) 3.73205 6.46410i 0.477840 0.827643i −0.521837 0.853045i \(-0.674753\pi\)
0.999677 + 0.0254017i \(0.00808648\pi\)
\(62\) −4.46410 7.73205i −0.566941 0.981971i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 3.50000 + 0.866025i 0.434122 + 0.107417i
\(66\) 0 0
\(67\) 4.73205 2.73205i 0.578112 0.333773i −0.182271 0.983248i \(-0.558345\pi\)
0.760383 + 0.649475i \(0.225011\pi\)
\(68\) −2.00000 3.46410i −0.242536 0.420084i
\(69\) 0 0
\(70\) 3.00000i 0.358569i
\(71\) 0.803848 + 0.464102i 0.0953992 + 0.0550787i 0.546941 0.837171i \(-0.315792\pi\)
−0.451541 + 0.892250i \(0.649126\pi\)
\(72\) 0 0
\(73\) 6.92820i 0.810885i 0.914121 + 0.405442i \(0.132883\pi\)
−0.914121 + 0.405442i \(0.867117\pi\)
\(74\) −3.96410 + 6.86603i −0.460817 + 0.798159i
\(75\) 0 0
\(76\) −1.96410 + 1.13397i −0.225298 + 0.130076i
\(77\) −11.1962 −1.27592
\(78\) 0 0
\(79\) 16.9282 1.90457 0.952286 0.305208i \(-0.0987259\pi\)
0.952286 + 0.305208i \(0.0987259\pi\)
\(80\) −0.866025 + 0.500000i −0.0968246 + 0.0559017i
\(81\) 0 0
\(82\) −2.00000 + 3.46410i −0.220863 + 0.382546i
\(83\) 2.53590i 0.278351i −0.990268 0.139176i \(-0.955555\pi\)
0.990268 0.139176i \(-0.0444452\pi\)
\(84\) 0 0
\(85\) −3.46410 2.00000i −0.375735 0.216930i
\(86\) 6.00000i 0.646997i
\(87\) 0 0
\(88\) −1.86603 3.23205i −0.198919 0.344538i
\(89\) 8.76795 5.06218i 0.929401 0.536590i 0.0427788 0.999085i \(-0.486379\pi\)
0.886622 + 0.462495i \(0.153046\pi\)
\(90\) 0 0
\(91\) 7.50000 7.79423i 0.786214 0.817057i
\(92\) −3.46410 −0.361158
\(93\) 0 0
\(94\) −0.232051 0.401924i −0.0239342 0.0414553i
\(95\) −1.13397 + 1.96410i −0.116343 + 0.201513i
\(96\) 0 0
\(97\) 10.7321 + 6.19615i 1.08967 + 0.629124i 0.933490 0.358604i \(-0.116747\pi\)
0.156185 + 0.987728i \(0.450080\pi\)
\(98\) 1.73205 + 1.00000i 0.174964 + 0.101015i
\(99\) 0 0
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) −4.19615 7.26795i −0.417533 0.723188i 0.578158 0.815925i \(-0.303772\pi\)
−0.995691 + 0.0927369i \(0.970438\pi\)
\(102\) 0 0
\(103\) 19.5885 1.93011 0.965054 0.262051i \(-0.0843989\pi\)
0.965054 + 0.262051i \(0.0843989\pi\)
\(104\) 3.50000 + 0.866025i 0.343203 + 0.0849208i
\(105\) 0 0
\(106\) 3.23205 1.86603i 0.313925 0.181244i
\(107\) 0.464102 + 0.803848i 0.0448664 + 0.0777109i 0.887587 0.460641i \(-0.152380\pi\)
−0.842720 + 0.538352i \(0.819047\pi\)
\(108\) 0 0
\(109\) 10.3923i 0.995402i 0.867349 + 0.497701i \(0.165822\pi\)
−0.867349 + 0.497701i \(0.834178\pi\)
\(110\) −3.23205 1.86603i −0.308164 0.177919i
\(111\) 0 0
\(112\) 3.00000i 0.283473i
\(113\) −6.00000 + 10.3923i −0.564433 + 0.977626i 0.432670 + 0.901553i \(0.357572\pi\)
−0.997102 + 0.0760733i \(0.975762\pi\)
\(114\) 0 0
\(115\) −3.00000 + 1.73205i −0.279751 + 0.161515i
\(116\) −5.46410 −0.507329
\(117\) 0 0
\(118\) −4.53590 −0.417563
\(119\) −10.3923 + 6.00000i −0.952661 + 0.550019i
\(120\) 0 0
\(121\) 1.46410 2.53590i 0.133100 0.230536i
\(122\) 7.46410i 0.675768i
\(123\) 0 0
\(124\) −7.73205 4.46410i −0.694359 0.400888i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) −2.33013 4.03590i −0.206765 0.358128i 0.743928 0.668259i \(-0.232960\pi\)
−0.950694 + 0.310131i \(0.899627\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 3.46410 1.00000i 0.303822 0.0877058i
\(131\) 20.3205 1.77541 0.887706 0.460412i \(-0.152298\pi\)
0.887706 + 0.460412i \(0.152298\pi\)
\(132\) 0 0
\(133\) 3.40192 + 5.89230i 0.294984 + 0.510928i
\(134\) 2.73205 4.73205i 0.236013 0.408787i
\(135\) 0 0
\(136\) −3.46410 2.00000i −0.297044 0.171499i
\(137\) 5.66025 + 3.26795i 0.483588 + 0.279200i 0.721911 0.691986i \(-0.243264\pi\)
−0.238322 + 0.971186i \(0.576598\pi\)
\(138\) 0 0
\(139\) −10.8923 + 18.8660i −0.923873 + 1.60020i −0.130510 + 0.991447i \(0.541661\pi\)
−0.793363 + 0.608748i \(0.791672\pi\)
\(140\) 1.50000 + 2.59808i 0.126773 + 0.219578i
\(141\) 0 0
\(142\) 0.928203 0.0778931
\(143\) 3.73205 + 12.9282i 0.312090 + 1.08111i
\(144\) 0 0
\(145\) −4.73205 + 2.73205i −0.392975 + 0.226884i
\(146\) 3.46410 + 6.00000i 0.286691 + 0.496564i
\(147\) 0 0
\(148\) 7.92820i 0.651694i
\(149\) −19.7321 11.3923i −1.61651 0.933294i −0.987813 0.155646i \(-0.950254\pi\)
−0.628700 0.777648i \(-0.716413\pi\)
\(150\) 0 0
\(151\) 18.7846i 1.52867i −0.644819 0.764335i \(-0.723067\pi\)
0.644819 0.764335i \(-0.276933\pi\)
\(152\) −1.13397 + 1.96410i −0.0919775 + 0.159310i
\(153\) 0 0
\(154\) −9.69615 + 5.59808i −0.781338 + 0.451106i
\(155\) −8.92820 −0.717131
\(156\) 0 0
\(157\) 10.8038 0.862241 0.431120 0.902294i \(-0.358118\pi\)
0.431120 + 0.902294i \(0.358118\pi\)
\(158\) 14.6603 8.46410i 1.16631 0.673368i
\(159\) 0 0
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) 10.3923i 0.819028i
\(162\) 0 0
\(163\) −9.46410 5.46410i −0.741286 0.427981i 0.0812509 0.996694i \(-0.474108\pi\)
−0.822537 + 0.568712i \(0.807442\pi\)
\(164\) 4.00000i 0.312348i
\(165\) 0 0
\(166\) −1.26795 2.19615i −0.0984119 0.170454i
\(167\) 5.59808 3.23205i 0.433192 0.250104i −0.267513 0.963554i \(-0.586202\pi\)
0.700706 + 0.713451i \(0.252869\pi\)
\(168\) 0 0
\(169\) −11.5000 6.06218i −0.884615 0.466321i
\(170\) −4.00000 −0.306786
\(171\) 0 0
\(172\) 3.00000 + 5.19615i 0.228748 + 0.396203i
\(173\) 11.0622 19.1603i 0.841042 1.45673i −0.0479730 0.998849i \(-0.515276\pi\)
0.889015 0.457879i \(-0.151391\pi\)
\(174\) 0 0
\(175\) 2.59808 + 1.50000i 0.196396 + 0.113389i
\(176\) −3.23205 1.86603i −0.243625 0.140657i
\(177\) 0 0
\(178\) 5.06218 8.76795i 0.379426 0.657186i
\(179\) 11.4641 + 19.8564i 0.856867 + 1.48414i 0.874902 + 0.484300i \(0.160926\pi\)
−0.0180347 + 0.999837i \(0.505741\pi\)
\(180\) 0 0
\(181\) 3.07180 0.228325 0.114162 0.993462i \(-0.463582\pi\)
0.114162 + 0.993462i \(0.463582\pi\)
\(182\) 2.59808 10.5000i 0.192582 0.778312i
\(183\) 0 0
\(184\) −3.00000 + 1.73205i −0.221163 + 0.127688i
\(185\) 3.96410 + 6.86603i 0.291447 + 0.504800i
\(186\) 0 0
\(187\) 14.9282i 1.09166i
\(188\) −0.401924 0.232051i −0.0293133 0.0169240i
\(189\) 0 0
\(190\) 2.26795i 0.164534i
\(191\) 8.66025 15.0000i 0.626634 1.08536i −0.361588 0.932338i \(-0.617765\pi\)
0.988222 0.153024i \(-0.0489012\pi\)
\(192\) 0 0
\(193\) −15.4641 + 8.92820i −1.11313 + 0.642666i −0.939638 0.342169i \(-0.888838\pi\)
−0.173492 + 0.984835i \(0.555505\pi\)
\(194\) 12.3923 0.889716
\(195\) 0 0
\(196\) 2.00000 0.142857
\(197\) 8.13397 4.69615i 0.579522 0.334587i −0.181422 0.983405i \(-0.558070\pi\)
0.760943 + 0.648818i \(0.224737\pi\)
\(198\) 0 0
\(199\) 5.53590 9.58846i 0.392429 0.679708i −0.600340 0.799745i \(-0.704968\pi\)
0.992769 + 0.120037i \(0.0383014\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 0 0
\(202\) −7.26795 4.19615i −0.511371 0.295240i
\(203\) 16.3923i 1.15051i
\(204\) 0 0
\(205\) 2.00000 + 3.46410i 0.139686 + 0.241943i
\(206\) 16.9641 9.79423i 1.18194 0.682396i
\(207\) 0 0
\(208\) 3.46410 1.00000i 0.240192 0.0693375i
\(209\) −8.46410 −0.585474
\(210\) 0 0
\(211\) 10.9641 + 18.9904i 0.754800 + 1.30735i 0.945474 + 0.325698i \(0.105599\pi\)
−0.190674 + 0.981653i \(0.561067\pi\)
\(212\) 1.86603 3.23205i 0.128159 0.221978i
\(213\) 0 0
\(214\) 0.803848 + 0.464102i 0.0549499 + 0.0317253i
\(215\) 5.19615 + 3.00000i 0.354375 + 0.204598i
\(216\) 0 0
\(217\) −13.3923 + 23.1962i −0.909129 + 1.57466i
\(218\) 5.19615 + 9.00000i 0.351928 + 0.609557i
\(219\) 0 0
\(220\) −3.73205 −0.251615
\(221\) 10.3923 + 10.0000i 0.699062 + 0.672673i
\(222\) 0 0
\(223\) −7.66987 + 4.42820i −0.513613 + 0.296534i −0.734317 0.678806i \(-0.762498\pi\)
0.220705 + 0.975341i \(0.429164\pi\)
\(224\) 1.50000 + 2.59808i 0.100223 + 0.173591i
\(225\) 0 0
\(226\) 12.0000i 0.798228i
\(227\) 11.6603 + 6.73205i 0.773918 + 0.446822i 0.834271 0.551355i \(-0.185889\pi\)
−0.0603523 + 0.998177i \(0.519222\pi\)
\(228\) 0 0
\(229\) 11.4641i 0.757569i 0.925485 + 0.378785i \(0.123658\pi\)
−0.925485 + 0.378785i \(0.876342\pi\)
\(230\) −1.73205 + 3.00000i −0.114208 + 0.197814i
\(231\) 0 0
\(232\) −4.73205 + 2.73205i −0.310674 + 0.179368i
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 0 0
\(235\) −0.464102 −0.0302747
\(236\) −3.92820 + 2.26795i −0.255704 + 0.147631i
\(237\) 0 0
\(238\) −6.00000 + 10.3923i −0.388922 + 0.673633i
\(239\) 3.46410i 0.224074i −0.993704 0.112037i \(-0.964262\pi\)
0.993704 0.112037i \(-0.0357375\pi\)
\(240\) 0 0
\(241\) 12.8205 + 7.40192i 0.825842 + 0.476800i 0.852427 0.522847i \(-0.175130\pi\)
−0.0265852 + 0.999647i \(0.508463\pi\)
\(242\) 2.92820i 0.188232i
\(243\) 0 0
\(244\) −3.73205 6.46410i −0.238920 0.413822i
\(245\) 1.73205 1.00000i 0.110657 0.0638877i
\(246\) 0 0
\(247\) 5.66987 5.89230i 0.360765 0.374918i
\(248\) −8.92820 −0.566941
\(249\) 0 0
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 13.2321 22.9186i 0.835200 1.44661i −0.0586681 0.998278i \(-0.518685\pi\)
0.893868 0.448331i \(-0.147981\pi\)
\(252\) 0 0
\(253\) −11.1962 6.46410i −0.703896 0.406395i
\(254\) −4.03590 2.33013i −0.253235 0.146205i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 10.7321 + 18.5885i 0.669447 + 1.15952i 0.978059 + 0.208328i \(0.0668022\pi\)
−0.308612 + 0.951188i \(0.599864\pi\)
\(258\) 0 0
\(259\) 23.7846 1.47790
\(260\) 2.50000 2.59808i 0.155043 0.161126i
\(261\) 0 0
\(262\) 17.5981 10.1603i 1.08721 0.627703i
\(263\) 10.2583 + 17.7679i 0.632556 + 1.09562i 0.987027 + 0.160552i \(0.0513274\pi\)
−0.354472 + 0.935067i \(0.615339\pi\)
\(264\) 0 0
\(265\) 3.73205i 0.229258i
\(266\) 5.89230 + 3.40192i 0.361280 + 0.208585i
\(267\) 0 0
\(268\) 5.46410i 0.333773i
\(269\) −15.4641 + 26.7846i −0.942863 + 1.63309i −0.182888 + 0.983134i \(0.558545\pi\)
−0.759975 + 0.649953i \(0.774789\pi\)
\(270\) 0 0
\(271\) −3.12436 + 1.80385i −0.189791 + 0.109576i −0.591885 0.806023i \(-0.701616\pi\)
0.402094 + 0.915599i \(0.368283\pi\)
\(272\) −4.00000 −0.242536
\(273\) 0 0
\(274\) 6.53590 0.394848
\(275\) −3.23205 + 1.86603i −0.194900 + 0.112526i
\(276\) 0 0
\(277\) 9.79423 16.9641i 0.588478 1.01927i −0.405954 0.913894i \(-0.633061\pi\)
0.994432 0.105380i \(-0.0336060\pi\)
\(278\) 21.7846i 1.30655i
\(279\) 0 0
\(280\) 2.59808 + 1.50000i 0.155265 + 0.0896421i
\(281\) 6.92820i 0.413302i −0.978415 0.206651i \(-0.933744\pi\)
0.978415 0.206651i \(-0.0662565\pi\)
\(282\) 0 0
\(283\) −7.19615 12.4641i −0.427767 0.740914i 0.568907 0.822402i \(-0.307366\pi\)
−0.996674 + 0.0814876i \(0.974033\pi\)
\(284\) 0.803848 0.464102i 0.0476996 0.0275394i
\(285\) 0 0
\(286\) 9.69615 + 9.33013i 0.573346 + 0.551702i
\(287\) 12.0000 0.708338
\(288\) 0 0
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) −2.73205 + 4.73205i −0.160432 + 0.277876i
\(291\) 0 0
\(292\) 6.00000 + 3.46410i 0.351123 + 0.202721i
\(293\) −16.6699 9.62436i −0.973864 0.562261i −0.0734522 0.997299i \(-0.523402\pi\)
−0.900412 + 0.435038i \(0.856735\pi\)
\(294\) 0 0
\(295\) −2.26795 + 3.92820i −0.132045 + 0.228709i
\(296\) 3.96410 + 6.86603i 0.230409 + 0.399080i
\(297\) 0 0
\(298\) −22.7846 −1.31988
\(299\) 12.0000 3.46410i 0.693978 0.200334i
\(300\) 0 0
\(301\) 15.5885 9.00000i 0.898504 0.518751i
\(302\) −9.39230 16.2679i −0.540466 0.936115i
\(303\) 0 0
\(304\) 2.26795i 0.130076i
\(305\) −6.46410 3.73205i −0.370133 0.213697i
\(306\) 0 0
\(307\) 20.2487i 1.15565i −0.816159 0.577827i \(-0.803901\pi\)
0.816159 0.577827i \(-0.196099\pi\)
\(308\) −5.59808 + 9.69615i −0.318980 + 0.552490i
\(309\) 0 0
\(310\) −7.73205 + 4.46410i −0.439151 + 0.253544i
\(311\) −5.07180 −0.287595 −0.143798 0.989607i \(-0.545931\pi\)
−0.143798 + 0.989607i \(0.545931\pi\)
\(312\) 0 0
\(313\) 1.32051 0.0746395 0.0373198 0.999303i \(-0.488118\pi\)
0.0373198 + 0.999303i \(0.488118\pi\)
\(314\) 9.35641 5.40192i 0.528013 0.304848i
\(315\) 0 0
\(316\) 8.46410 14.6603i 0.476143 0.824704i
\(317\) 23.5359i 1.32191i 0.750427 + 0.660954i \(0.229848\pi\)
−0.750427 + 0.660954i \(0.770152\pi\)
\(318\) 0 0
\(319\) −17.6603 10.1962i −0.988784 0.570875i
\(320\) 1.00000i 0.0559017i
\(321\) 0 0
\(322\) 5.19615 + 9.00000i 0.289570 + 0.501550i
\(323\) −7.85641 + 4.53590i −0.437142 + 0.252384i
\(324\) 0 0
\(325\) 0.866025 3.50000i 0.0480384 0.194145i
\(326\) −10.9282 −0.605257
\(327\) 0 0
\(328\) 2.00000 + 3.46410i 0.110432 + 0.191273i
\(329\) −0.696152 + 1.20577i −0.0383801 + 0.0664763i
\(330\) 0 0
\(331\) 5.53590 + 3.19615i 0.304280 + 0.175676i 0.644364 0.764719i \(-0.277122\pi\)
−0.340084 + 0.940395i \(0.610455\pi\)
\(332\) −2.19615 1.26795i −0.120530 0.0695878i
\(333\) 0 0
\(334\) 3.23205 5.59808i 0.176850 0.306313i
\(335\) −2.73205 4.73205i −0.149268 0.258540i
\(336\) 0 0
\(337\) −5.60770 −0.305471 −0.152735 0.988267i \(-0.548808\pi\)
−0.152735 + 0.988267i \(0.548808\pi\)
\(338\) −12.9904 + 0.500000i −0.706584 + 0.0271964i
\(339\) 0 0
\(340\) −3.46410 + 2.00000i −0.187867 + 0.108465i
\(341\) −16.6603 28.8564i −0.902203 1.56266i
\(342\) 0 0
\(343\) 15.0000i 0.809924i
\(344\) 5.19615 + 3.00000i 0.280158 + 0.161749i
\(345\) 0 0
\(346\) 22.1244i 1.18941i
\(347\) −8.19615 + 14.1962i −0.439993 + 0.762089i −0.997688 0.0679560i \(-0.978352\pi\)
0.557696 + 0.830045i \(0.311686\pi\)
\(348\) 0 0
\(349\) 15.1244 8.73205i 0.809588 0.467416i −0.0372247 0.999307i \(-0.511852\pi\)
0.846813 + 0.531891i \(0.178518\pi\)
\(350\) 3.00000 0.160357
\(351\) 0 0
\(352\) −3.73205 −0.198919
\(353\) 24.5885 14.1962i 1.30871 0.755585i 0.326830 0.945083i \(-0.394019\pi\)
0.981881 + 0.189498i \(0.0606861\pi\)
\(354\) 0 0
\(355\) 0.464102 0.803848i 0.0246320 0.0426638i
\(356\) 10.1244i 0.536590i
\(357\) 0 0
\(358\) 19.8564 + 11.4641i 1.04944 + 0.605897i
\(359\) 12.9282i 0.682324i −0.940004 0.341162i \(-0.889179\pi\)
0.940004 0.341162i \(-0.110821\pi\)
\(360\) 0 0
\(361\) −6.92820 12.0000i −0.364642 0.631579i
\(362\) 2.66025 1.53590i 0.139820 0.0807250i
\(363\) 0 0
\(364\) −3.00000 10.3923i −0.157243 0.544705i
\(365\) 6.92820 0.362639
\(366\) 0 0
\(367\) 6.66025 + 11.5359i 0.347662 + 0.602169i 0.985834 0.167725i \(-0.0536422\pi\)
−0.638171 + 0.769894i \(0.720309\pi\)
\(368\) −1.73205 + 3.00000i −0.0902894 + 0.156386i
\(369\) 0 0
\(370\) 6.86603 + 3.96410i 0.356948 + 0.206084i
\(371\) −9.69615 5.59808i −0.503399 0.290638i
\(372\) 0 0
\(373\) −11.4641 + 19.8564i −0.593589 + 1.02813i 0.400156 + 0.916447i \(0.368956\pi\)
−0.993744 + 0.111679i \(0.964377\pi\)
\(374\) −7.46410 12.9282i −0.385960 0.668501i
\(375\) 0 0
\(376\) −0.464102 −0.0239342
\(377\) 18.9282 5.46410i 0.974852 0.281416i
\(378\) 0 0
\(379\) 5.42820 3.13397i 0.278828 0.160981i −0.354065 0.935221i \(-0.615201\pi\)
0.632893 + 0.774239i \(0.281867\pi\)
\(380\) 1.13397 + 1.96410i 0.0581717 + 0.100756i
\(381\) 0 0
\(382\) 17.3205i 0.886194i
\(383\) −31.8564 18.3923i −1.62779 0.939803i −0.984752 0.173966i \(-0.944342\pi\)
−0.643035 0.765837i \(-0.722325\pi\)
\(384\) 0 0
\(385\) 11.1962i 0.570609i
\(386\) −8.92820 + 15.4641i −0.454434 + 0.787102i
\(387\) 0 0
\(388\) 10.7321 6.19615i 0.544837 0.314562i
\(389\) 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
\(392\) 1.73205 1.00000i 0.0874818 0.0505076i
\(393\) 0 0
\(394\) 4.69615 8.13397i 0.236589 0.409784i
\(395\) 16.9282i 0.851750i
\(396\) 0 0
\(397\) −6.86603 3.96410i −0.344596 0.198953i 0.317707 0.948189i \(-0.397087\pi\)
−0.662303 + 0.749237i \(0.730421\pi\)
\(398\) 11.0718i 0.554979i
\(399\) 0 0
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) 1.83975 1.06218i 0.0918725 0.0530426i −0.453360 0.891328i \(-0.649775\pi\)
0.545232 + 0.838285i \(0.316441\pi\)
\(402\) 0 0
\(403\) 31.2487 + 7.73205i 1.55661 + 0.385161i
\(404\) −8.39230 −0.417533
\(405\) 0 0
\(406\) 8.19615 + 14.1962i 0.406768 + 0.704543i
\(407\) −14.7942 + 25.6244i −0.733323 + 1.27015i
\(408\) 0 0
\(409\) 0.820508 + 0.473721i 0.0405715 + 0.0234240i 0.520149 0.854076i \(-0.325877\pi\)
−0.479577 + 0.877500i \(0.659210\pi\)
\(410\) 3.46410 + 2.00000i 0.171080 + 0.0987730i
\(411\) 0 0
\(412\) 9.79423 16.9641i 0.482527 0.835761i
\(413\) 6.80385 + 11.7846i 0.334795 + 0.579883i
\(414\) 0 0
\(415\) −2.53590 −0.124482
\(416\) 2.50000 2.59808i 0.122573 0.127381i
\(417\) 0 0
\(418\) −7.33013 + 4.23205i −0.358528 + 0.206996i
\(419\) −8.92820 15.4641i −0.436171 0.755471i 0.561219 0.827667i \(-0.310332\pi\)
−0.997390 + 0.0721964i \(0.976999\pi\)
\(420\) 0 0
\(421\) 5.85641i 0.285424i 0.989764 + 0.142712i \(0.0455822\pi\)
−0.989764 + 0.142712i \(0.954418\pi\)
\(422\) 18.9904 + 10.9641i 0.924437 + 0.533724i
\(423\) 0 0
\(424\) 3.73205i 0.181244i
\(425\) −2.00000 + 3.46410i −0.0970143 + 0.168034i
\(426\) 0 0
\(427\) −19.3923 + 11.1962i −0.938459 + 0.541820i
\(428\) 0.928203 0.0448664
\(429\) 0 0
\(430\) 6.00000 0.289346
\(431\) 12.0000 6.92820i 0.578020 0.333720i −0.182326 0.983238i \(-0.558363\pi\)
0.760346 + 0.649518i \(0.225029\pi\)
\(432\) 0 0
\(433\) −16.3923 + 28.3923i −0.787764 + 1.36445i 0.139570 + 0.990212i \(0.455428\pi\)
−0.927334 + 0.374235i \(0.877905\pi\)
\(434\) 26.7846i 1.28570i
\(435\) 0 0
\(436\) 9.00000 + 5.19615i 0.431022 + 0.248851i
\(437\) 7.85641i 0.375823i
\(438\) 0 0
\(439\) −10.6603 18.4641i −0.508786 0.881243i −0.999948 0.0101753i \(-0.996761\pi\)
0.491162 0.871068i \(-0.336572\pi\)
\(440\) −3.23205 + 1.86603i −0.154082 + 0.0889593i
\(441\) 0 0
\(442\) 14.0000 + 3.46410i 0.665912 + 0.164771i
\(443\) −7.85641 −0.373269 −0.186635 0.982429i \(-0.559758\pi\)
−0.186635 + 0.982429i \(0.559758\pi\)
\(444\) 0 0
\(445\) −5.06218 8.76795i −0.239970 0.415641i
\(446\) −4.42820 + 7.66987i −0.209682 + 0.363179i
\(447\) 0 0
\(448\) 2.59808 + 1.50000i 0.122748 + 0.0708683i
\(449\) 15.6962 + 9.06218i 0.740747 + 0.427671i 0.822341 0.568995i \(-0.192668\pi\)
−0.0815937 + 0.996666i \(0.526001\pi\)
\(450\) 0 0
\(451\) −7.46410 + 12.9282i −0.351471 + 0.608765i
\(452\) 6.00000 + 10.3923i 0.282216 + 0.488813i
\(453\) 0 0
\(454\) 13.4641 0.631902
\(455\) −7.79423 7.50000i −0.365399 0.351605i
\(456\) 0 0
\(457\) 0.464102 0.267949i 0.0217098 0.0125341i −0.489106 0.872224i \(-0.662677\pi\)
0.510816 + 0.859690i \(0.329343\pi\)
\(458\) 5.73205 + 9.92820i 0.267841 + 0.463914i
\(459\) 0 0
\(460\) 3.46410i 0.161515i
\(461\) −28.0526 16.1962i −1.30654 0.754330i −0.325021 0.945707i \(-0.605371\pi\)
−0.981517 + 0.191377i \(0.938705\pi\)
\(462\) 0 0
\(463\) 0.784610i 0.0364639i −0.999834 0.0182320i \(-0.994196\pi\)
0.999834 0.0182320i \(-0.00580373\pi\)
\(464\) −2.73205 + 4.73205i −0.126832 + 0.219680i
\(465\) 0 0
\(466\) −15.5885 + 9.00000i −0.722121 + 0.416917i
\(467\) −3.60770 −0.166944 −0.0834721 0.996510i \(-0.526601\pi\)
−0.0834721 + 0.996510i \(0.526601\pi\)
\(468\) 0 0
\(469\) −16.3923 −0.756926
\(470\) −0.401924 + 0.232051i −0.0185394 + 0.0107037i
\(471\) 0 0
\(472\) −2.26795 + 3.92820i −0.104391 + 0.180810i
\(473\) 22.3923i 1.02960i
\(474\) 0 0
\(475\) 1.96410 + 1.13397i 0.0901192 + 0.0520303i
\(476\) 12.0000i 0.550019i
\(477\) 0 0
\(478\) −1.73205 3.00000i −0.0792222 0.137217i
\(479\) 22.7321 13.1244i 1.03865 0.599667i 0.119202 0.992870i \(-0.461966\pi\)
0.919452 + 0.393203i \(0.128633\pi\)
\(480\) 0 0
\(481\) −7.92820 27.4641i −0.361495 1.25226i
\(482\) 14.8038 0.674297
\(483\) 0 0
\(484\) −1.46410 2.53590i −0.0665501 0.115268i
\(485\) 6.19615 10.7321i 0.281353 0.487317i
\(486\) 0 0
\(487\) −18.1865 10.5000i −0.824110 0.475800i 0.0277214 0.999616i \(-0.491175\pi\)
−0.851832 + 0.523815i \(0.824508\pi\)
\(488\) −6.46410 3.73205i −0.292616 0.168942i
\(489\) 0 0
\(490\) 1.00000 1.73205i 0.0451754 0.0782461i
\(491\) −7.69615 13.3301i −0.347322 0.601580i 0.638450 0.769663i \(-0.279576\pi\)
−0.985773 + 0.168083i \(0.946242\pi\)
\(492\) 0 0
\(493\) −21.8564 −0.984363
\(494\) 1.96410 7.93782i 0.0883691 0.357140i
\(495\) 0 0
\(496\) −7.73205 + 4.46410i −0.347179 + 0.200444i
\(497\) −1.39230 2.41154i −0.0624534 0.108172i
\(498\) 0 0
\(499\) 1.32051i 0.0591141i 0.999563 + 0.0295570i \(0.00940967\pi\)
−0.999563 + 0.0295570i \(0.990590\pi\)
\(500\) 0.866025 + 0.500000i 0.0387298 + 0.0223607i
\(501\) 0 0
\(502\) 26.4641i 1.18115i
\(503\) 0.133975 0.232051i 0.00597363 0.0103466i −0.863023 0.505164i \(-0.831432\pi\)
0.868997 + 0.494818i \(0.164765\pi\)
\(504\) 0 0
\(505\) −7.26795 + 4.19615i −0.323419 + 0.186726i
\(506\) −12.9282 −0.574729
\(507\) 0 0
\(508\) −4.66025 −0.206765
\(509\) −4.60770 + 2.66025i −0.204232 + 0.117914i −0.598628 0.801027i \(-0.704287\pi\)
0.394396 + 0.918941i \(0.370954\pi\)
\(510\) 0 0
\(511\) 10.3923 18.0000i 0.459728 0.796273i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 18.5885 + 10.7321i 0.819902 + 0.473370i
\(515\) 19.5885i 0.863171i
\(516\) 0 0
\(517\) −0.866025 1.50000i −0.0380878 0.0659699i
\(518\) 20.5981 11.8923i 0.905028 0.522518i
\(519\) 0 0
\(520\) 0.866025 3.50000i 0.0379777 0.153485i
\(521\) 27.3923 1.20008 0.600039 0.799970i \(-0.295152\pi\)
0.600039 + 0.799970i \(0.295152\pi\)
\(522\) 0 0
\(523\) −6.85641 11.8756i −0.299810 0.519286i 0.676283 0.736642i \(-0.263590\pi\)
−0.976092 + 0.217357i \(0.930257\pi\)
\(524\) 10.1603 17.5981i 0.443853 0.768776i
\(525\) 0 0
\(526\) 17.7679 + 10.2583i 0.774719 + 0.447284i
\(527\) −30.9282 17.8564i −1.34725 0.777837i
\(528\) 0 0
\(529\) 5.50000 9.52628i 0.239130 0.414186i
\(530\) −1.86603 3.23205i −0.0810550 0.140391i
\(531\) 0 0
\(532\) 6.80385 0.294984
\(533\) −4.00000 13.8564i −0.173259 0.600188i
\(534\) 0 0
\(535\) 0.803848 0.464102i 0.0347534 0.0200649i
\(536\) −2.73205 4.73205i −0.118007 0.204393i
\(537\) 0 0
\(538\) 30.9282i 1.33341i
\(539\) 6.46410 + 3.73205i 0.278429 + 0.160751i
\(540\) 0 0
\(541\) 26.7846i 1.15156i 0.817605 + 0.575780i \(0.195302\pi\)
−0.817605 + 0.575780i \(0.804698\pi\)
\(542\) −1.80385 + 3.12436i −0.0774819 + 0.134203i
\(543\) 0 0
\(544\) −3.46410 + 2.00000i −0.148522 + 0.0857493i
\(545\) 10.3923 0.445157
\(546\) 0 0
\(547\) 29.3205 1.25365 0.626827 0.779158i \(-0.284353\pi\)
0.626827 + 0.779158i \(0.284353\pi\)
\(548\) 5.66025 3.26795i 0.241794 0.139600i
\(549\) 0 0
\(550\) −1.86603 + 3.23205i −0.0795676 + 0.137815i
\(551\) 12.3923i 0.527930i
\(552\) 0 0
\(553\) −43.9808 25.3923i −1.87025 1.07979i
\(554\) 19.5885i 0.832234i
\(555\) 0 0
\(556\) 10.8923 + 18.8660i 0.461937 + 0.800098i
\(557\) −37.5788 + 21.6962i −1.59227 + 0.919295i −0.599349 + 0.800488i \(0.704574\pi\)
−0.992917 + 0.118808i \(0.962093\pi\)
\(558\) 0 0
\(559\) −15.5885 15.0000i −0.659321 0.634432i
\(560\) 3.00000 0.126773
\(561\) 0 0
\(562\) −3.46410 6.00000i −0.146124 0.253095i
\(563\) 9.66025 16.7321i 0.407131 0.705172i −0.587436 0.809271i \(-0.699863\pi\)
0.994567 + 0.104099i \(0.0331959\pi\)
\(564\) 0 0
\(565\) 10.3923 + 6.00000i 0.437208 + 0.252422i
\(566\) −12.4641 7.19615i −0.523905 0.302477i
\(567\) 0 0
\(568\) 0.464102 0.803848i 0.0194733 0.0337287i
\(569\) 9.16025 + 15.8660i 0.384018 + 0.665138i 0.991632 0.129094i \(-0.0412068\pi\)
−0.607615 + 0.794232i \(0.707873\pi\)
\(570\) 0 0
\(571\) −16.8564 −0.705419 −0.352709 0.935733i \(-0.614740\pi\)
−0.352709 + 0.935733i \(0.614740\pi\)
\(572\) 13.0622 + 3.23205i 0.546157 + 0.135139i
\(573\) 0 0
\(574\) 10.3923 6.00000i 0.433766 0.250435i
\(575\) 1.73205 + 3.00000i 0.0722315 + 0.125109i
\(576\) 0 0
\(577\) 25.3205i 1.05411i −0.849832 0.527053i \(-0.823297\pi\)
0.849832 0.527053i \(-0.176703\pi\)
\(578\) 0.866025 + 0.500000i 0.0360219 + 0.0207973i
\(579\) 0 0
\(580\) 5.46410i 0.226884i
\(581\) −3.80385 + 6.58846i −0.157810 + 0.273335i
\(582\) 0 0
\(583\) 12.0622 6.96410i 0.499564 0.288424i
\(584\) 6.92820 0.286691
\(585\) 0 0
\(586\) −19.2487 −0.795157
\(587\) 4.26795 2.46410i 0.176157 0.101704i −0.409329 0.912387i \(-0.634237\pi\)
0.585486 + 0.810683i \(0.300904\pi\)
\(588\) 0 0
\(589\) −10.1244 + 17.5359i −0.417167 + 0.722554i
\(590\) 4.53590i 0.186740i
\(591\) 0 0
\(592\) 6.86603 + 3.96410i 0.282192 + 0.162924i
\(593\) 3.21539i 0.132040i −0.997818 0.0660201i \(-0.978970\pi\)
0.997818 0.0660201i \(-0.0210302\pi\)
\(594\) 0 0
\(595\) 6.00000 + 10.3923i 0.245976 + 0.426043i
\(596\) −19.7321 + 11.3923i −0.808256 + 0.466647i
\(597\) 0 0
\(598\) 8.66025 9.00000i 0.354144 0.368037i
\(599\) −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 0.999989 + 0.00465778i \(0.00148262\pi\)
−0.495961 + 0.868345i \(0.665184\pi\)
\(602\) 9.00000 15.5885i 0.366813 0.635338i
\(603\) 0 0
\(604\) −16.2679 9.39230i −0.661933 0.382167i
\(605\) −2.53590 1.46410i −0.103099 0.0595242i
\(606\) 0 0
\(607\) −18.7224 + 32.4282i −0.759920 + 1.31622i 0.182971 + 0.983118i \(0.441429\pi\)
−0.942891 + 0.333102i \(0.891905\pi\)
\(608\) 1.13397 + 1.96410i 0.0459887 + 0.0796548i
\(609\) 0 0
\(610\) −7.46410 −0.302213
\(611\) 1.62436 + 0.401924i 0.0657144 + 0.0162601i
\(612\) 0 0
\(613\) −38.9711 + 22.5000i −1.57403 + 0.908766i −0.578362 + 0.815780i \(0.696308\pi\)
−0.995667 + 0.0929864i \(0.970359\pi\)
\(614\) −10.1244 17.5359i −0.408586 0.707691i
\(615\) 0 0
\(616\) 11.1962i 0.451106i
\(617\) −24.7128 14.2679i −0.994900 0.574406i −0.0881649 0.996106i \(-0.528100\pi\)
−0.906735 + 0.421700i \(0.861434\pi\)
\(618\) 0 0
\(619\) 42.5167i 1.70889i 0.519543 + 0.854444i \(0.326102\pi\)
−0.519543 + 0.854444i \(0.673898\pi\)
\(620\) −4.46410 + 7.73205i −0.179283 + 0.310527i
\(621\) 0 0
\(622\) −4.39230 + 2.53590i −0.176115 + 0.101680i
\(623\) −30.3731 −1.21687
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 1.14359 0.660254i 0.0457072 0.0263891i
\(627\) 0 0
\(628\) 5.40192 9.35641i 0.215560 0.373361i
\(629\) 31.7128i 1.26447i
\(630\) 0 0
\(631\) 6.92820 + 4.00000i 0.275807 + 0.159237i 0.631524 0.775356i \(-0.282430\pi\)
−0.355716 + 0.934594i \(0.615763\pi\)
\(632\) 16.9282i 0.673368i
\(633\) 0 0
\(634\) 11.7679 + 20.3827i 0.467365 + 0.809500i
\(635\) −4.03590 + 2.33013i −0.160160 + 0.0924683i
\(636\) 0 0
\(637\) −6.92820 + 2.00000i −0.274505 + 0.0792429i
\(638\) −20.3923 −0.807339
\(639\) 0 0
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) 3.76795 6.52628i 0.148825 0.257773i −0.781968 0.623318i \(-0.785784\pi\)
0.930793 + 0.365546i \(0.119118\pi\)
\(642\) 0 0
\(643\) 24.9282 + 14.3923i 0.983072 + 0.567577i 0.903196 0.429228i \(-0.141214\pi\)
0.0798761 + 0.996805i \(0.474548\pi\)
\(644\) 9.00000 + 5.19615i 0.354650 + 0.204757i
\(645\) 0 0
\(646\) −4.53590 + 7.85641i −0.178463 + 0.309106i
\(647\) −16.1340 27.9449i −0.634292 1.09863i −0.986665 0.162766i \(-0.947958\pi\)
0.352373 0.935860i \(-0.385375\pi\)
\(648\) 0 0
\(649\) −16.9282 −0.664490
\(650\) −1.00000 3.46410i −0.0392232 0.135873i
\(651\) 0 0
\(652\) −9.46410 + 5.46410i −0.370643 + 0.213991i
\(653\) 14.7942 + 25.6244i 0.578943 + 1.00276i 0.995601 + 0.0936952i \(0.0298679\pi\)
−0.416658 + 0.909063i \(0.636799\pi\)
\(654\) 0 0
\(655\) 20.3205i 0.793988i
\(656\) 3.46410 + 2.00000i 0.135250 + 0.0780869i
\(657\) 0 0
\(658\) 1.39230i 0.0542777i
\(659\) 7.85641 13.6077i 0.306042 0.530081i −0.671451 0.741049i \(-0.734328\pi\)
0.977493 + 0.210969i \(0.0676618\pi\)
\(660\) 0 0
\(661\) 36.7128 21.1962i 1.42796 0.824435i 0.431003 0.902351i \(-0.358160\pi\)
0.996960 + 0.0779157i \(0.0248265\pi\)
\(662\) 6.39230 0.248444
\(663\) 0 0
\(664\) −2.53590 −0.0984119
\(665\) 5.89230 3.40192i 0.228494 0.131921i
\(666\) 0 0
\(667\) −9.46410 + 16.3923i −0.366451 + 0.634713i
\(668\) 6.46410i 0.250104i
\(669\) 0 0
\(670\) −4.73205 2.73205i −0.182815 0.105548i
\(671\) 27.8564i 1.07538i
\(672\) 0 0
\(673\) −12.3923 21.4641i −0.477688 0.827380i 0.521985 0.852955i \(-0.325192\pi\)
−0.999673 + 0.0255746i \(0.991858\pi\)
\(674\) −4.85641 + 2.80385i −0.187062 + 0.108000i
\(675\) 0 0
\(676\) −11.0000 + 6.92820i −0.423077 + 0.266469i
\(677\) 2.92820 0.112540 0.0562700 0.998416i \(-0.482079\pi\)
0.0562700 + 0.998416i \(0.482079\pi\)
\(678\) 0 0
\(679\) −18.5885 32.1962i −0.713360 1.23557i
\(680\) −2.00000 + 3.46410i −0.0766965 + 0.132842i
\(681\) 0 0
\(682\) −28.8564 16.6603i −1.10497 0.637954i
\(683\) 5.78461 + 3.33975i 0.221342 + 0.127792i 0.606571 0.795029i \(-0.292544\pi\)
−0.385230 + 0.922821i \(0.625878\pi\)
\(684\) 0 0
\(685\) 3.26795 5.66025i 0.124862 0.216267i
\(686\) 7.50000 + 12.9904i 0.286351 + 0.495975i
\(687\) 0 0
\(688\) 6.00000 0.228748
\(689\) −3.23205 + 13.0622i −0.123131 + 0.497629i
\(690\) 0 0
\(691\) 19.9641 11.5263i 0.759470 0.438480i −0.0696353 0.997573i \(-0.522184\pi\)
0.829106 + 0.559092i \(0.188850\pi\)
\(692\) −11.0622 19.1603i −0.420521 0.728364i
\(693\) 0 0
\(694\) 16.3923i 0.622243i
\(695\) 18.8660 + 10.8923i 0.715629 + 0.413169i
\(696\) 0 0
\(697\) 16.0000i 0.606043i
\(698\) 8.73205 15.1244i 0.330513 0.572465i
\(699\) 0 0
\(700\) 2.59808 1.50000i 0.0981981 0.0566947i
\(701\) −16.3923 −0.619129 −0.309564 0.950878i \(-0.600183\pi\)
−0.309564 + 0.950878i \(0.600183\pi\)
\(702\) 0 0
\(703\) 17.9808 0.678157
\(704\) −3.23205 + 1.86603i −0.121812 + 0.0703285i
\(705\) 0 0
\(706\) 14.1962 24.5885i 0.534279 0.925399i
\(707\) 25.1769i 0.946875i
\(708\) 0 0
\(709\) −6.33975 3.66025i −0.238094 0.137464i 0.376206 0.926536i \(-0.377228\pi\)
−0.614300 + 0.789072i \(0.710562\pi\)
\(710\) 0.928203i 0.0348348i
\(711\) 0 0
\(712\) −5.06218 8.76795i −0.189713 0.328593i
\(713\) −26.7846 + 15.4641i −1.00309 + 0.579135i
\(714\) 0 0
\(715\) 12.9282 3.73205i 0.483487 0.139571i
\(716\) 22.9282 0.856867
\(717\) 0 0
\(718\) −6.46410 11.1962i −0.241238 0.417837i
\(719\) 8.00000 13.8564i 0.298350 0.516757i −0.677409 0.735607i \(-0.736897\pi\)
0.975759 + 0.218850i \(0.0702305\pi\)
\(720\) 0 0
\(721\) −50.8923 29.3827i −1.89533 1.09427i
\(722\) −12.0000 6.92820i −0.446594 0.257841i
\(723\) 0 0
\(724\) 1.53590 2.66025i 0.0570812 0.0988676i
\(725\) 2.73205 + 4.73205i 0.101466 + 0.175744i
\(726\) 0 0
\(727\) 12.6603 0.469543 0.234771 0.972051i \(-0.424566\pi\)
0.234771 + 0.972051i \(0.424566\pi\)
\(728\) −7.79423 7.50000i −0.288873 0.277968i
\(729\) 0 0
\(730\) 6.00000 3.46410i 0.222070 0.128212i
\(731\) 12.0000 + 20.7846i 0.443836 + 0.768747i
\(732\) 0 0
\(733\) 6.85641i 0.253247i 0.991951 + 0.126624i \(0.0404140\pi\)
−0.991951 + 0.126624i \(0.959586\pi\)
\(734\) 11.5359 + 6.66025i 0.425798 + 0.245834i
\(735\) 0 0
\(736\) 3.46410i 0.127688i
\(737\) 10.1962 17.6603i 0.375580 0.650524i
\(738\) 0 0
\(739\) 37.9641 21.9186i 1.39653 0.806288i 0.402505 0.915418i \(-0.368140\pi\)
0.994028 + 0.109130i \(0.0348064\pi\)
\(740\) 7.92820 0.291447
\(741\) 0 0
\(742\) −11.1962 −0.411024
\(743\) 2.53590 1.46410i 0.0930331 0.0537127i −0.452762 0.891632i \(-0.649561\pi\)
0.545795 + 0.837919i \(0.316228\pi\)
\(744\) 0 0
\(745\) −11.3923 + 19.7321i −0.417382 + 0.722926i
\(746\) 22.9282i 0.839461i
\(747\) 0 0
\(748\) −12.9282 7.46410i −0.472702 0.272915i
\(749\) 2.78461i 0.101747i
\(750\) 0 0
\(751\) −20.5885 35.6603i −0.751283 1.30126i −0.947201 0.320641i \(-0.896102\pi\)
0.195917 0.980620i \(-0.437232\pi\)
\(752\) −0.401924 + 0.232051i −0.0146567 + 0.00846202i
\(753\) 0 0
\(754\) 13.6603 14.1962i 0.497477 0.516993i
\(755\) −18.7846 −0.683642
\(756\) 0 0
\(757\) −9.13397 15.8205i −0.331980 0.575006i 0.650920 0.759146i \(-0.274383\pi\)
−0.982900 + 0.184140i \(0.941050\pi\)
\(758\) 3.13397 5.42820i 0.113831 0.197161i
\(759\) 0 0
\(760\) 1.96410 + 1.13397i 0.0712455 + 0.0411336i
\(761\) −38.0885 21.9904i −1.38071 0.797151i −0.388463 0.921465i \(-0.626994\pi\)
−0.992243 + 0.124314i \(0.960327\pi\)
\(762\) 0 0
\(763\) 15.5885 27.0000i 0.564340 0.977466i
\(764\) −8.66025 15.0000i −0.313317 0.542681i
\(765\) 0 0
\(766\) −36.7846 −1.32908
\(767\) 11.3397 11.7846i 0.409454 0.425518i
\(768\) 0 0
\(769\) 34.3923 19.8564i 1.24022 0.716040i 0.271080 0.962557i \(-0.412619\pi\)
0.969139 + 0.246517i \(0.0792860\pi\)
\(770\) 5.59808 + 9.69615i 0.201741 + 0.349425i
\(771\) 0 0
\(772\) 17.8564i 0.642666i
\(773\) −46.2391 26.6962i −1.66310 0.960194i −0.971220 0.238186i \(-0.923447\pi\)
−0.691885 0.722008i \(-0.743220\pi\)
\(774\) 0 0
\(775\) 8.92820i 0.320711i
\(776\) 6.19615 10.7321i 0.222429 0.385258i
\(777\) 0 0
\(778\) 8.53590 4.92820i 0.306027 0.176685i
\(779\) 9.07180 0.325031
\(780\) 0 0
\(781\) 3.46410 0.123955
\(782\) −12.0000 + 6.92820i −0.429119 + 0.247752i
\(783\) 0 0
\(784\) 1.00000 1.73205i 0.0357143 0.0618590i
\(785\) 10.8038i 0.385606i
\(786\) 0 0
\(787\) 4.73205 + 2.73205i 0.168679 + 0.0973871i 0.581963 0.813215i \(-0.302285\pi\)
−0.413284 + 0.910602i \(0.635618\pi\)
\(788\) 9.39230i 0.334587i
\(789\) 0