Properties

Label 1470.2.n.f.949.2
Level $1470$
Weight $2$
Character 1470.949
Analytic conductor $11.738$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.n (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.7380090971\)
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 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 949.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1470.949
Dual form 1470.2.n.f.79.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.23205 - 0.133975i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.23205 - 0.133975i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.86603 - 1.23205i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(-0.866025 + 0.500000i) q^{12} +6.00000i q^{13} +(-2.00000 - 1.00000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.46410 + 2.00000i) q^{17} +(0.866025 + 0.500000i) q^{18} +(3.00000 + 5.19615i) q^{19} +(1.00000 - 2.00000i) q^{20} +2.00000i q^{22} +(6.92820 - 4.00000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(4.96410 - 0.598076i) q^{25} +(3.00000 + 5.19615i) q^{26} -1.00000i q^{27} -6.00000 q^{29} +(-2.23205 + 0.133975i) q^{30} +(-1.00000 + 1.73205i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.73205 - 1.00000i) q^{33} +4.00000 q^{34} +1.00000 q^{36} +(3.46410 - 2.00000i) q^{37} +(5.19615 + 3.00000i) q^{38} +(3.00000 - 5.19615i) q^{39} +(-0.133975 - 2.23205i) q^{40} -2.00000 q^{41} -4.00000i q^{43} +(1.00000 + 1.73205i) q^{44} +(1.23205 + 1.86603i) q^{45} +(4.00000 - 6.92820i) q^{46} +(-6.92820 + 4.00000i) q^{47} +1.00000i q^{48} +(4.00000 - 3.00000i) q^{50} +(-2.00000 - 3.46410i) q^{51} +(5.19615 + 3.00000i) q^{52} +(5.19615 + 3.00000i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.00000 + 4.00000i) q^{55} -6.00000i q^{57} +(-5.19615 + 3.00000i) q^{58} +(4.00000 - 6.92820i) q^{59} +(-1.86603 + 1.23205i) q^{60} +(-5.00000 - 8.66025i) q^{61} +2.00000i q^{62} -1.00000 q^{64} +(0.803848 + 13.3923i) q^{65} +(1.00000 - 1.73205i) q^{66} +(-6.92820 - 4.00000i) q^{67} +(3.46410 - 2.00000i) q^{68} -8.00000 q^{69} -6.00000 q^{71} +(0.866025 - 0.500000i) q^{72} +(12.1244 + 7.00000i) q^{73} +(2.00000 - 3.46410i) q^{74} +(-4.59808 - 1.96410i) q^{75} +6.00000 q^{76} -6.00000i q^{78} +(-6.00000 - 10.3923i) q^{79} +(-1.23205 - 1.86603i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.73205 + 1.00000i) q^{82} -8.00000i q^{83} +(8.00000 + 4.00000i) q^{85} +(-2.00000 - 3.46410i) q^{86} +(5.19615 + 3.00000i) q^{87} +(1.73205 + 1.00000i) q^{88} +(5.00000 + 8.66025i) q^{89} +(2.00000 + 1.00000i) q^{90} -8.00000i q^{92} +(1.73205 - 1.00000i) q^{93} +(-4.00000 + 6.92820i) q^{94} +(7.39230 + 11.1962i) q^{95} +(0.500000 + 0.866025i) q^{96} +10.0000i q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} + 2q^{5} - 4q^{6} + 2q^{9} + O(q^{10}) \) \( 4q + 2q^{4} + 2q^{5} - 4q^{6} + 2q^{9} + 4q^{10} - 4q^{11} - 8q^{15} - 2q^{16} + 12q^{19} + 4q^{20} - 2q^{24} + 6q^{25} + 12q^{26} - 24q^{29} - 2q^{30} - 4q^{31} + 16q^{34} + 4q^{36} + 12q^{39} - 4q^{40} - 8q^{41} + 4q^{44} - 2q^{45} + 16q^{46} + 16q^{50} - 8q^{51} - 2q^{54} - 8q^{55} + 16q^{59} - 4q^{60} - 20q^{61} - 4q^{64} + 24q^{65} + 4q^{66} - 32q^{69} - 24q^{71} + 8q^{74} - 8q^{75} + 24q^{76} - 24q^{79} + 2q^{80} - 2q^{81} + 32q^{85} - 8q^{86} + 20q^{89} + 8q^{90} - 16q^{94} - 12q^{95} + 2q^{96} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 2.23205 0.133975i 0.998203 0.0599153i
\(6\) −1.00000 −0.408248
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 1.86603 1.23205i 0.590089 0.389609i
\(11\) −1.00000 + 1.73205i −0.301511 + 0.522233i −0.976478 0.215615i \(-0.930824\pi\)
0.674967 + 0.737848i \(0.264158\pi\)
\(12\) −0.866025 + 0.500000i −0.250000 + 0.144338i
\(13\) 6.00000i 1.66410i 0.554700 + 0.832050i \(0.312833\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 0 0
\(15\) −2.00000 1.00000i −0.516398 0.258199i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.46410 + 2.00000i 0.840168 + 0.485071i 0.857321 0.514782i \(-0.172127\pi\)
−0.0171533 + 0.999853i \(0.505460\pi\)
\(18\) 0.866025 + 0.500000i 0.204124 + 0.117851i
\(19\) 3.00000 + 5.19615i 0.688247 + 1.19208i 0.972404 + 0.233301i \(0.0749529\pi\)
−0.284157 + 0.958778i \(0.591714\pi\)
\(20\) 1.00000 2.00000i 0.223607 0.447214i
\(21\) 0 0
\(22\) 2.00000i 0.426401i
\(23\) 6.92820 4.00000i 1.44463 0.834058i 0.446476 0.894795i \(-0.352679\pi\)
0.998154 + 0.0607377i \(0.0193453\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 4.96410 0.598076i 0.992820 0.119615i
\(26\) 3.00000 + 5.19615i 0.588348 + 1.01905i
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) −2.23205 + 0.133975i −0.407515 + 0.0244603i
\(31\) −1.00000 + 1.73205i −0.179605 + 0.311086i −0.941745 0.336327i \(-0.890815\pi\)
0.762140 + 0.647412i \(0.224149\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 1.73205 1.00000i 0.301511 0.174078i
\(34\) 4.00000 0.685994
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 3.46410 2.00000i 0.569495 0.328798i −0.187453 0.982274i \(-0.560023\pi\)
0.756948 + 0.653476i \(0.226690\pi\)
\(38\) 5.19615 + 3.00000i 0.842927 + 0.486664i
\(39\) 3.00000 5.19615i 0.480384 0.832050i
\(40\) −0.133975 2.23205i −0.0211832 0.352918i
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 4.00000i 0.609994i −0.952353 0.304997i \(-0.901344\pi\)
0.952353 0.304997i \(-0.0986555\pi\)
\(44\) 1.00000 + 1.73205i 0.150756 + 0.261116i
\(45\) 1.23205 + 1.86603i 0.183663 + 0.278171i
\(46\) 4.00000 6.92820i 0.589768 1.02151i
\(47\) −6.92820 + 4.00000i −1.01058 + 0.583460i −0.911362 0.411606i \(-0.864968\pi\)
−0.0992202 + 0.995066i \(0.531635\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 0 0
\(50\) 4.00000 3.00000i 0.565685 0.424264i
\(51\) −2.00000 3.46410i −0.280056 0.485071i
\(52\) 5.19615 + 3.00000i 0.720577 + 0.416025i
\(53\) 5.19615 + 3.00000i 0.713746 + 0.412082i 0.812447 0.583036i \(-0.198135\pi\)
−0.0987002 + 0.995117i \(0.531468\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) −2.00000 + 4.00000i −0.269680 + 0.539360i
\(56\) 0 0
\(57\) 6.00000i 0.794719i
\(58\) −5.19615 + 3.00000i −0.682288 + 0.393919i
\(59\) 4.00000 6.92820i 0.520756 0.901975i −0.478953 0.877841i \(-0.658984\pi\)
0.999709 0.0241347i \(-0.00768307\pi\)
\(60\) −1.86603 + 1.23205i −0.240903 + 0.159057i
\(61\) −5.00000 8.66025i −0.640184 1.10883i −0.985391 0.170305i \(-0.945525\pi\)
0.345207 0.938527i \(-0.387809\pi\)
\(62\) 2.00000i 0.254000i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0.803848 + 13.3923i 0.0997050 + 1.66111i
\(66\) 1.00000 1.73205i 0.123091 0.213201i
\(67\) −6.92820 4.00000i −0.846415 0.488678i 0.0130248 0.999915i \(-0.495854\pi\)
−0.859440 + 0.511237i \(0.829187\pi\)
\(68\) 3.46410 2.00000i 0.420084 0.242536i
\(69\) −8.00000 −0.963087
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0.866025 0.500000i 0.102062 0.0589256i
\(73\) 12.1244 + 7.00000i 1.41905 + 0.819288i 0.996215 0.0869195i \(-0.0277023\pi\)
0.422833 + 0.906208i \(0.361036\pi\)
\(74\) 2.00000 3.46410i 0.232495 0.402694i
\(75\) −4.59808 1.96410i −0.530940 0.226795i
\(76\) 6.00000 0.688247
\(77\) 0 0
\(78\) 6.00000i 0.679366i
\(79\) −6.00000 10.3923i −0.675053 1.16923i −0.976453 0.215728i \(-0.930788\pi\)
0.301401 0.953498i \(-0.402546\pi\)
\(80\) −1.23205 1.86603i −0.137747 0.208628i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −1.73205 + 1.00000i −0.191273 + 0.110432i
\(83\) 8.00000i 0.878114i −0.898459 0.439057i \(-0.855313\pi\)
0.898459 0.439057i \(-0.144687\pi\)
\(84\) 0 0
\(85\) 8.00000 + 4.00000i 0.867722 + 0.433861i
\(86\) −2.00000 3.46410i −0.215666 0.373544i
\(87\) 5.19615 + 3.00000i 0.557086 + 0.321634i
\(88\) 1.73205 + 1.00000i 0.184637 + 0.106600i
\(89\) 5.00000 + 8.66025i 0.529999 + 0.917985i 0.999388 + 0.0349934i \(0.0111410\pi\)
−0.469389 + 0.882992i \(0.655526\pi\)
\(90\) 2.00000 + 1.00000i 0.210819 + 0.105409i
\(91\) 0 0
\(92\) 8.00000i 0.834058i
\(93\) 1.73205 1.00000i 0.179605 0.103695i
\(94\) −4.00000 + 6.92820i −0.412568 + 0.714590i
\(95\) 7.39230 + 11.1962i 0.758434 + 1.14870i
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 10.0000i 1.01535i 0.861550 + 0.507673i \(0.169494\pi\)
−0.861550 + 0.507673i \(0.830506\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) 1.96410 4.59808i 0.196410 0.459808i
\(101\) 5.00000 8.66025i 0.497519 0.861727i −0.502477 0.864590i \(-0.667578\pi\)
0.999996 + 0.00286291i \(0.000911295\pi\)
\(102\) −3.46410 2.00000i −0.342997 0.198030i
\(103\) 6.92820 4.00000i 0.682656 0.394132i −0.118199 0.992990i \(-0.537712\pi\)
0.800855 + 0.598858i \(0.204379\pi\)
\(104\) 6.00000 0.588348
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) 10.3923 6.00000i 1.00466 0.580042i 0.0950377 0.995474i \(-0.469703\pi\)
0.909624 + 0.415432i \(0.136370\pi\)
\(108\) −0.866025 0.500000i −0.0833333 0.0481125i
\(109\) −7.00000 + 12.1244i −0.670478 + 1.16130i 0.307290 + 0.951616i \(0.400578\pi\)
−0.977769 + 0.209687i \(0.932756\pi\)
\(110\) 0.267949 + 4.46410i 0.0255480 + 0.425635i
\(111\) −4.00000 −0.379663
\(112\) 0 0
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) −3.00000 5.19615i −0.280976 0.486664i
\(115\) 14.9282 9.85641i 1.39206 0.919115i
\(116\) −3.00000 + 5.19615i −0.278543 + 0.482451i
\(117\) −5.19615 + 3.00000i −0.480384 + 0.277350i
\(118\) 8.00000i 0.736460i
\(119\) 0 0
\(120\) −1.00000 + 2.00000i −0.0912871 + 0.182574i
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) −8.66025 5.00000i −0.784063 0.452679i
\(123\) 1.73205 + 1.00000i 0.156174 + 0.0901670i
\(124\) 1.00000 + 1.73205i 0.0898027 + 0.155543i
\(125\) 11.0000 2.00000i 0.983870 0.178885i
\(126\) 0 0
\(127\) 4.00000i 0.354943i 0.984126 + 0.177471i \(0.0567917\pi\)
−0.984126 + 0.177471i \(0.943208\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) −2.00000 + 3.46410i −0.176090 + 0.304997i
\(130\) 7.39230 + 11.1962i 0.648348 + 0.981968i
\(131\) −6.00000 10.3923i −0.524222 0.907980i −0.999602 0.0281993i \(-0.991023\pi\)
0.475380 0.879781i \(-0.342311\pi\)
\(132\) 2.00000i 0.174078i
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) −0.133975 2.23205i −0.0115307 0.192104i
\(136\) 2.00000 3.46410i 0.171499 0.297044i
\(137\) 5.19615 + 3.00000i 0.443937 + 0.256307i 0.705266 0.708942i \(-0.250827\pi\)
−0.261329 + 0.965250i \(0.584161\pi\)
\(138\) −6.92820 + 4.00000i −0.589768 + 0.340503i
\(139\) −14.0000 −1.18746 −0.593732 0.804663i \(-0.702346\pi\)
−0.593732 + 0.804663i \(0.702346\pi\)
\(140\) 0 0
\(141\) 8.00000 0.673722
\(142\) −5.19615 + 3.00000i −0.436051 + 0.251754i
\(143\) −10.3923 6.00000i −0.869048 0.501745i
\(144\) 0.500000 0.866025i 0.0416667 0.0721688i
\(145\) −13.3923 + 0.803848i −1.11217 + 0.0667559i
\(146\) 14.0000 1.15865
\(147\) 0 0
\(148\) 4.00000i 0.328798i
\(149\) 5.00000 + 8.66025i 0.409616 + 0.709476i 0.994847 0.101391i \(-0.0323294\pi\)
−0.585231 + 0.810867i \(0.698996\pi\)
\(150\) −4.96410 + 0.598076i −0.405317 + 0.0488327i
\(151\) 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i \(-0.727796\pi\)
0.981617 + 0.190864i \(0.0611289\pi\)
\(152\) 5.19615 3.00000i 0.421464 0.243332i
\(153\) 4.00000i 0.323381i
\(154\) 0 0
\(155\) −2.00000 + 4.00000i −0.160644 + 0.321288i
\(156\) −3.00000 5.19615i −0.240192 0.416025i
\(157\) −19.0526 11.0000i −1.52056 0.877896i −0.999706 0.0242497i \(-0.992280\pi\)
−0.520854 0.853646i \(-0.674386\pi\)
\(158\) −10.3923 6.00000i −0.826767 0.477334i
\(159\) −3.00000 5.19615i −0.237915 0.412082i
\(160\) −2.00000 1.00000i −0.158114 0.0790569i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) 3.46410 2.00000i 0.271329 0.156652i −0.358162 0.933659i \(-0.616597\pi\)
0.629492 + 0.777007i \(0.283263\pi\)
\(164\) −1.00000 + 1.73205i −0.0780869 + 0.135250i
\(165\) 3.73205 2.46410i 0.290540 0.191830i
\(166\) −4.00000 6.92820i −0.310460 0.537733i
\(167\) 12.0000i 0.928588i 0.885681 + 0.464294i \(0.153692\pi\)
−0.885681 + 0.464294i \(0.846308\pi\)
\(168\) 0 0
\(169\) −23.0000 −1.76923
\(170\) 8.92820 0.535898i 0.684762 0.0411015i
\(171\) −3.00000 + 5.19615i −0.229416 + 0.397360i
\(172\) −3.46410 2.00000i −0.264135 0.152499i
\(173\) 6.92820 4.00000i 0.526742 0.304114i −0.212947 0.977064i \(-0.568306\pi\)
0.739689 + 0.672949i \(0.234973\pi\)
\(174\) 6.00000 0.454859
\(175\) 0 0
\(176\) 2.00000 0.150756
\(177\) −6.92820 + 4.00000i −0.520756 + 0.300658i
\(178\) 8.66025 + 5.00000i 0.649113 + 0.374766i
\(179\) 5.00000 8.66025i 0.373718 0.647298i −0.616417 0.787420i \(-0.711416\pi\)
0.990134 + 0.140122i \(0.0447496\pi\)
\(180\) 2.23205 0.133975i 0.166367 0.00998588i
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 10.0000i 0.739221i
\(184\) −4.00000 6.92820i −0.294884 0.510754i
\(185\) 7.46410 4.92820i 0.548772 0.362329i
\(186\) 1.00000 1.73205i 0.0733236 0.127000i
\(187\) −6.92820 + 4.00000i −0.506640 + 0.292509i
\(188\) 8.00000i 0.583460i
\(189\) 0 0
\(190\) 12.0000 + 6.00000i 0.870572 + 0.435286i
\(191\) 9.00000 + 15.5885i 0.651217 + 1.12794i 0.982828 + 0.184525i \(0.0590746\pi\)
−0.331611 + 0.943416i \(0.607592\pi\)
\(192\) 0.866025 + 0.500000i 0.0625000 + 0.0360844i
\(193\) −6.92820 4.00000i −0.498703 0.287926i 0.229475 0.973315i \(-0.426299\pi\)
−0.728178 + 0.685388i \(0.759632\pi\)
\(194\) 5.00000 + 8.66025i 0.358979 + 0.621770i
\(195\) 6.00000 12.0000i 0.429669 0.859338i
\(196\) 0 0
\(197\) 2.00000i 0.142494i 0.997459 + 0.0712470i \(0.0226979\pi\)
−0.997459 + 0.0712470i \(0.977302\pi\)
\(198\) −1.73205 + 1.00000i −0.123091 + 0.0710669i
\(199\) −3.00000 + 5.19615i −0.212664 + 0.368345i −0.952548 0.304390i \(-0.901547\pi\)
0.739883 + 0.672735i \(0.234881\pi\)
\(200\) −0.598076 4.96410i −0.0422904 0.351015i
\(201\) 4.00000 + 6.92820i 0.282138 + 0.488678i
\(202\) 10.0000i 0.703598i
\(203\) 0 0
\(204\) −4.00000 −0.280056
\(205\) −4.46410 + 0.267949i −0.311786 + 0.0187144i
\(206\) 4.00000 6.92820i 0.278693 0.482711i
\(207\) 6.92820 + 4.00000i 0.481543 + 0.278019i
\(208\) 5.19615 3.00000i 0.360288 0.208013i
\(209\) −12.0000 −0.830057
\(210\) 0 0
\(211\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 5.19615 3.00000i 0.356873 0.206041i
\(213\) 5.19615 + 3.00000i 0.356034 + 0.205557i
\(214\) 6.00000 10.3923i 0.410152 0.710403i
\(215\) −0.535898 8.92820i −0.0365480 0.608898i
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 14.0000i 0.948200i
\(219\) −7.00000 12.1244i −0.473016 0.819288i
\(220\) 2.46410 + 3.73205i 0.166130 + 0.251615i
\(221\) −12.0000 + 20.7846i −0.807207 + 1.39812i
\(222\) −3.46410 + 2.00000i −0.232495 + 0.134231i
\(223\) 8.00000i 0.535720i −0.963458 0.267860i \(-0.913684\pi\)
0.963458 0.267860i \(-0.0863164\pi\)
\(224\) 0 0
\(225\) 3.00000 + 4.00000i 0.200000 + 0.266667i
\(226\) −3.00000 5.19615i −0.199557 0.345643i
\(227\) −6.92820 4.00000i −0.459841 0.265489i 0.252136 0.967692i \(-0.418867\pi\)
−0.711977 + 0.702202i \(0.752200\pi\)
\(228\) −5.19615 3.00000i −0.344124 0.198680i
\(229\) −7.00000 12.1244i −0.462573 0.801200i 0.536515 0.843891i \(-0.319740\pi\)
−0.999088 + 0.0426906i \(0.986407\pi\)
\(230\) 8.00000 16.0000i 0.527504 1.05501i
\(231\) 0 0
\(232\) 6.00000i 0.393919i
\(233\) 8.66025 5.00000i 0.567352 0.327561i −0.188739 0.982027i \(-0.560440\pi\)
0.756091 + 0.654466i \(0.227107\pi\)
\(234\) −3.00000 + 5.19615i −0.196116 + 0.339683i
\(235\) −14.9282 + 9.85641i −0.973809 + 0.642961i
\(236\) −4.00000 6.92820i −0.260378 0.450988i
\(237\) 12.0000i 0.779484i
\(238\) 0 0
\(239\) −26.0000 −1.68180 −0.840900 0.541190i \(-0.817974\pi\)
−0.840900 + 0.541190i \(0.817974\pi\)
\(240\) 0.133975 + 2.23205i 0.00864802 + 0.144078i
\(241\) −13.0000 + 22.5167i −0.837404 + 1.45043i 0.0546547 + 0.998505i \(0.482594\pi\)
−0.892058 + 0.451920i \(0.850739\pi\)
\(242\) 6.06218 + 3.50000i 0.389692 + 0.224989i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) −10.0000 −0.640184
\(245\) 0 0
\(246\) 2.00000 0.127515
\(247\) −31.1769 + 18.0000i −1.98374 + 1.14531i
\(248\) 1.73205 + 1.00000i 0.109985 + 0.0635001i
\(249\) −4.00000 + 6.92820i −0.253490 + 0.439057i
\(250\) 8.52628 7.23205i 0.539249 0.457395i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 16.0000i 1.00591i
\(254\) 2.00000 + 3.46410i 0.125491 + 0.217357i
\(255\) −4.92820 7.46410i −0.308616 0.467420i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(258\) 4.00000i 0.249029i
\(259\) 0 0
\(260\) 12.0000 + 6.00000i 0.744208 + 0.372104i
\(261\) −3.00000 5.19615i −0.185695 0.321634i
\(262\) −10.3923 6.00000i −0.642039 0.370681i
\(263\) 13.8564 + 8.00000i 0.854423 + 0.493301i 0.862141 0.506669i \(-0.169123\pi\)
−0.00771799 + 0.999970i \(0.502457\pi\)
\(264\) −1.00000 1.73205i −0.0615457 0.106600i
\(265\) 12.0000 + 6.00000i 0.737154 + 0.368577i
\(266\) 0 0
\(267\) 10.0000i 0.611990i
\(268\) −6.92820 + 4.00000i −0.423207 + 0.244339i
\(269\) −9.00000 + 15.5885i −0.548740 + 0.950445i 0.449622 + 0.893219i \(0.351559\pi\)
−0.998361 + 0.0572259i \(0.981774\pi\)
\(270\) −1.23205 1.86603i −0.0749802 0.113563i
\(271\) 5.00000 + 8.66025i 0.303728 + 0.526073i 0.976977 0.213343i \(-0.0684351\pi\)
−0.673249 + 0.739416i \(0.735102\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) −3.92820 + 9.19615i −0.236880 + 0.554549i
\(276\) −4.00000 + 6.92820i −0.240772 + 0.417029i
\(277\) −24.2487 14.0000i −1.45696 0.841178i −0.458103 0.888899i \(-0.651471\pi\)
−0.998861 + 0.0477206i \(0.984804\pi\)
\(278\) −12.1244 + 7.00000i −0.727171 + 0.419832i
\(279\) −2.00000 −0.119737
\(280\) 0 0
\(281\) 30.0000 1.78965 0.894825 0.446417i \(-0.147300\pi\)
0.894825 + 0.446417i \(0.147300\pi\)
\(282\) 6.92820 4.00000i 0.412568 0.238197i
\(283\) −17.3205 10.0000i −1.02960 0.594438i −0.112728 0.993626i \(-0.535959\pi\)
−0.916869 + 0.399188i \(0.869292\pi\)
\(284\) −3.00000 + 5.19615i −0.178017 + 0.308335i
\(285\) −0.803848 13.3923i −0.0476158 0.793292i
\(286\) −12.0000 −0.709575
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) −0.500000 0.866025i −0.0294118 0.0509427i
\(290\) −11.1962 + 7.39230i −0.657461 + 0.434091i
\(291\) 5.00000 8.66025i 0.293105 0.507673i
\(292\) 12.1244 7.00000i 0.709524 0.409644i
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 8.00000 16.0000i 0.465778 0.931556i
\(296\) −2.00000 3.46410i −0.116248 0.201347i
\(297\) 1.73205 + 1.00000i 0.100504 + 0.0580259i
\(298\) 8.66025 + 5.00000i 0.501675 + 0.289642i
\(299\) 24.0000 + 41.5692i 1.38796 + 2.40401i
\(300\) −4.00000 + 3.00000i −0.230940 + 0.173205i
\(301\) 0 0
\(302\) 8.00000i 0.460348i
\(303\) −8.66025 + 5.00000i −0.497519 + 0.287242i
\(304\) 3.00000 5.19615i 0.172062 0.298020i
\(305\) −12.3205 18.6603i −0.705470 1.06848i
\(306\) 2.00000 + 3.46410i 0.114332 + 0.198030i
\(307\) 12.0000i 0.684876i 0.939540 + 0.342438i \(0.111253\pi\)
−0.939540 + 0.342438i \(0.888747\pi\)
\(308\) 0 0
\(309\) −8.00000 −0.455104
\(310\) 0.267949 + 4.46410i 0.0152185 + 0.253544i
\(311\) 12.0000 20.7846i 0.680458 1.17859i −0.294384 0.955687i \(-0.595114\pi\)
0.974841 0.222900i \(-0.0715523\pi\)
\(312\) −5.19615 3.00000i −0.294174 0.169842i
\(313\) −1.73205 + 1.00000i −0.0979013 + 0.0565233i −0.548151 0.836379i \(-0.684668\pi\)
0.450250 + 0.892903i \(0.351335\pi\)
\(314\) −22.0000 −1.24153
\(315\) 0 0
\(316\) −12.0000 −0.675053
\(317\) −1.73205 + 1.00000i −0.0972817 + 0.0561656i −0.547852 0.836576i \(-0.684554\pi\)
0.450570 + 0.892741i \(0.351221\pi\)
\(318\) −5.19615 3.00000i −0.291386 0.168232i
\(319\) 6.00000 10.3923i 0.335936 0.581857i
\(320\) −2.23205 + 0.133975i −0.124775 + 0.00748941i
\(321\) −12.0000 −0.669775
\(322\) 0 0
\(323\) 24.0000i 1.33540i
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 3.58846 + 29.7846i 0.199052 + 1.65215i
\(326\) 2.00000 3.46410i 0.110770 0.191859i
\(327\) 12.1244 7.00000i 0.670478 0.387101i
\(328\) 2.00000i 0.110432i
\(329\) 0 0
\(330\) 2.00000 4.00000i 0.110096 0.220193i
\(331\) 4.00000 + 6.92820i 0.219860 + 0.380808i 0.954765 0.297361i \(-0.0961066\pi\)
−0.734905 + 0.678170i \(0.762773\pi\)
\(332\) −6.92820 4.00000i −0.380235 0.219529i
\(333\) 3.46410 + 2.00000i 0.189832 + 0.109599i
\(334\) 6.00000 + 10.3923i 0.328305 + 0.568642i
\(335\) −16.0000 8.00000i −0.874173 0.437087i
\(336\) 0 0
\(337\) 8.00000i 0.435788i −0.975972 0.217894i \(-0.930081\pi\)
0.975972 0.217894i \(-0.0699187\pi\)
\(338\) −19.9186 + 11.5000i −1.08343 + 0.625518i
\(339\) −3.00000 + 5.19615i −0.162938 + 0.282216i
\(340\) 7.46410 4.92820i 0.404798 0.267269i
\(341\) −2.00000 3.46410i −0.108306 0.187592i
\(342\) 6.00000i 0.324443i
\(343\) 0 0
\(344\) −4.00000 −0.215666
\(345\) −17.8564 + 1.07180i −0.961357 + 0.0577036i
\(346\) 4.00000 6.92820i 0.215041 0.372463i
\(347\) −31.1769 18.0000i −1.67366 0.966291i −0.965559 0.260184i \(-0.916217\pi\)
−0.708105 0.706107i \(-0.750450\pi\)
\(348\) 5.19615 3.00000i 0.278543 0.160817i
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 0 0
\(351\) 6.00000 0.320256
\(352\) 1.73205 1.00000i 0.0923186 0.0533002i
\(353\) −17.3205 10.0000i −0.921878 0.532246i −0.0376440 0.999291i \(-0.511985\pi\)
−0.884234 + 0.467045i \(0.845319\pi\)
\(354\) −4.00000 + 6.92820i −0.212598 + 0.368230i
\(355\) −13.3923 + 0.803848i −0.710790 + 0.0426638i
\(356\) 10.0000 0.529999
\(357\) 0 0
\(358\) 10.0000i 0.528516i
\(359\) 3.00000 + 5.19615i 0.158334 + 0.274242i 0.934268 0.356572i \(-0.116054\pi\)
−0.775934 + 0.630814i \(0.782721\pi\)
\(360\) 1.86603 1.23205i 0.0983482 0.0649348i
\(361\) −8.50000 + 14.7224i −0.447368 + 0.774865i
\(362\) −1.73205 + 1.00000i −0.0910346 + 0.0525588i
\(363\) 7.00000i 0.367405i
\(364\) 0 0
\(365\) 28.0000 + 14.0000i 1.46559 + 0.732793i
\(366\) 5.00000 + 8.66025i 0.261354 + 0.452679i
\(367\) −27.7128 16.0000i −1.44660 0.835193i −0.448320 0.893873i \(-0.647978\pi\)
−0.998277 + 0.0586798i \(0.981311\pi\)
\(368\) −6.92820 4.00000i −0.361158 0.208514i
\(369\) −1.00000 1.73205i −0.0520579 0.0901670i
\(370\) 4.00000 8.00000i 0.207950 0.415900i
\(371\) 0 0
\(372\) 2.00000i 0.103695i
\(373\) 20.7846 12.0000i 1.07619 0.621336i 0.146321 0.989237i \(-0.453257\pi\)
0.929865 + 0.367901i \(0.119923\pi\)
\(374\) −4.00000 + 6.92820i −0.206835 + 0.358249i
\(375\) −10.5263 3.76795i −0.543575 0.194576i
\(376\) 4.00000 + 6.92820i 0.206284 + 0.357295i
\(377\) 36.0000i 1.85409i
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 13.3923 0.803848i 0.687011 0.0412365i
\(381\) 2.00000 3.46410i 0.102463 0.177471i
\(382\) 15.5885 + 9.00000i 0.797575 + 0.460480i
\(383\) 17.3205 10.0000i 0.885037 0.510976i 0.0127209 0.999919i \(-0.495951\pi\)
0.872316 + 0.488943i \(0.162617\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −8.00000 −0.407189
\(387\) 3.46410 2.00000i 0.176090 0.101666i
\(388\) 8.66025 + 5.00000i 0.439658 + 0.253837i
\(389\) 1.00000 1.73205i 0.0507020 0.0878185i −0.839561 0.543266i \(-0.817187\pi\)
0.890263 + 0.455448i \(0.150521\pi\)
\(390\) −0.803848 13.3923i −0.0407044 0.678146i
\(391\) 32.0000 1.61831
\(392\) 0 0
\(393\) 12.0000i 0.605320i
\(394\) 1.00000 + 1.73205i 0.0503793 + 0.0872595i
\(395\) −14.7846 22.3923i −0.743894 1.12668i
\(396\) −1.00000 + 1.73205i −0.0502519 + 0.0870388i
\(397\) 1.73205 1.00000i 0.0869291 0.0501886i −0.455905 0.890028i \(-0.650684\pi\)
0.542834 + 0.839840i \(0.317351\pi\)
\(398\) 6.00000i 0.300753i
\(399\) 0 0
\(400\) −3.00000 4.00000i −0.150000 0.200000i
\(401\) 7.00000 + 12.1244i 0.349563 + 0.605461i 0.986172 0.165726i \(-0.0529966\pi\)
−0.636609 + 0.771187i \(0.719663\pi\)
\(402\) 6.92820 + 4.00000i 0.345547 + 0.199502i
\(403\) −10.3923 6.00000i −0.517678 0.298881i
\(404\) −5.00000 8.66025i −0.248759 0.430864i
\(405\) −1.00000 + 2.00000i −0.0496904 + 0.0993808i
\(406\) 0 0
\(407\) 8.00000i 0.396545i
\(408\) −3.46410 + 2.00000i −0.171499 + 0.0990148i
\(409\) −13.0000 + 22.5167i −0.642809 + 1.11338i 0.341994 + 0.939702i \(0.388898\pi\)
−0.984803 + 0.173675i \(0.944436\pi\)
\(410\) −3.73205 + 2.46410i −0.184313 + 0.121693i
\(411\) −3.00000 5.19615i −0.147979 0.256307i
\(412\) 8.00000i 0.394132i
\(413\) 0 0
\(414\) 8.00000 0.393179
\(415\) −1.07180 17.8564i −0.0526124 0.876537i
\(416\) 3.00000 5.19615i 0.147087 0.254762i
\(417\) 12.1244 + 7.00000i 0.593732 + 0.342791i
\(418\) −10.3923 + 6.00000i −0.508304 + 0.293470i
\(419\) 20.0000 0.977064 0.488532 0.872546i \(-0.337533\pi\)
0.488532 + 0.872546i \(0.337533\pi\)
\(420\) 0 0
\(421\) 34.0000 1.65706 0.828529 0.559946i \(-0.189178\pi\)
0.828529 + 0.559946i \(0.189178\pi\)
\(422\) 0 0
\(423\) −6.92820 4.00000i −0.336861 0.194487i
\(424\) 3.00000 5.19615i 0.145693 0.252347i
\(425\) 18.3923 + 7.85641i 0.892158 + 0.381092i
\(426\) 6.00000 0.290701
\(427\) 0 0
\(428\) 12.0000i 0.580042i
\(429\) 6.00000 + 10.3923i 0.289683 + 0.501745i
\(430\) −4.92820 7.46410i −0.237659 0.359951i
\(431\) −1.00000 + 1.73205i −0.0481683 + 0.0834300i −0.889104 0.457705i \(-0.848672\pi\)
0.840936 + 0.541135i \(0.182005\pi\)
\(432\) −0.866025 + 0.500000i −0.0416667 + 0.0240563i
\(433\) 26.0000i 1.24948i −0.780833 0.624740i \(-0.785205\pi\)
0.780833 0.624740i \(-0.214795\pi\)
\(434\) 0 0
\(435\) 12.0000 + 6.00000i 0.575356 + 0.287678i
\(436\) 7.00000 + 12.1244i 0.335239 + 0.580651i
\(437\) 41.5692 + 24.0000i 1.98853 + 1.14808i
\(438\) −12.1244 7.00000i −0.579324 0.334473i
\(439\) 9.00000 + 15.5885i 0.429547 + 0.743996i 0.996833 0.0795241i \(-0.0253401\pi\)
−0.567286 + 0.823521i \(0.692007\pi\)
\(440\) 4.00000 + 2.00000i 0.190693 + 0.0953463i
\(441\) 0 0
\(442\) 24.0000i 1.14156i
\(443\) 10.3923 6.00000i 0.493753 0.285069i −0.232377 0.972626i \(-0.574650\pi\)
0.726130 + 0.687557i \(0.241317\pi\)
\(444\) −2.00000 + 3.46410i −0.0949158 + 0.164399i
\(445\) 12.3205 + 18.6603i 0.584048 + 0.884581i
\(446\) −4.00000 6.92820i −0.189405 0.328060i
\(447\) 10.0000i 0.472984i
\(448\) 0 0
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 4.59808 + 1.96410i 0.216755 + 0.0925886i
\(451\) 2.00000 3.46410i 0.0941763 0.163118i
\(452\) −5.19615 3.00000i −0.244406 0.141108i
\(453\) −6.92820 + 4.00000i −0.325515 + 0.187936i
\(454\) −8.00000 −0.375459
\(455\) 0 0
\(456\) −6.00000 −0.280976
\(457\) 24.2487 14.0000i 1.13431 0.654892i 0.189292 0.981921i \(-0.439381\pi\)
0.945015 + 0.327028i \(0.106047\pi\)
\(458\) −12.1244 7.00000i −0.566534 0.327089i
\(459\) 2.00000 3.46410i 0.0933520 0.161690i
\(460\) −1.07180 17.8564i −0.0499728 0.832559i
\(461\) 18.0000 0.838344 0.419172 0.907907i \(-0.362320\pi\)
0.419172 + 0.907907i \(0.362320\pi\)
\(462\) 0 0
\(463\) 36.0000i 1.67306i −0.547920 0.836531i \(-0.684580\pi\)
0.547920 0.836531i \(-0.315420\pi\)
\(464\) 3.00000 + 5.19615i 0.139272 + 0.241225i
\(465\) 3.73205 2.46410i 0.173070 0.114270i
\(466\) 5.00000 8.66025i 0.231621 0.401179i
\(467\) 20.7846 12.0000i 0.961797 0.555294i 0.0650714 0.997881i \(-0.479272\pi\)
0.896726 + 0.442587i \(0.145939\pi\)
\(468\) 6.00000i 0.277350i
\(469\) 0 0
\(470\) −8.00000 + 16.0000i −0.369012 + 0.738025i
\(471\) 11.0000 + 19.0526i 0.506853 + 0.877896i
\(472\) −6.92820 4.00000i −0.318896 0.184115i
\(473\) 6.92820 + 4.00000i 0.318559 + 0.183920i
\(474\) 6.00000 + 10.3923i 0.275589 + 0.477334i
\(475\) 18.0000 + 24.0000i 0.825897 + 1.10120i
\(476\) 0 0
\(477\) 6.00000i 0.274721i
\(478\) −22.5167 + 13.0000i −1.02989 + 0.594606i
\(479\) −4.00000 + 6.92820i −0.182765 + 0.316558i −0.942821 0.333300i \(-0.891838\pi\)
0.760056 + 0.649857i \(0.225171\pi\)
\(480\) 1.23205 + 1.86603i 0.0562352 + 0.0851720i
\(481\) 12.0000 + 20.7846i 0.547153 + 0.947697i
\(482\) 26.0000i 1.18427i
\(483\) 0 0
\(484\) 7.00000 0.318182
\(485\) 1.33975 + 22.3205i 0.0608347 + 1.01352i
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) −10.3923 6.00000i −0.470920 0.271886i 0.245705 0.969345i \(-0.420981\pi\)
−0.716625 + 0.697459i \(0.754314\pi\)
\(488\) −8.66025 + 5.00000i −0.392031 + 0.226339i
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) −30.0000 −1.35388 −0.676941 0.736038i \(-0.736695\pi\)
−0.676941 + 0.736038i \(0.736695\pi\)
\(492\) 1.73205 1.00000i 0.0780869 0.0450835i
\(493\) −20.7846 12.0000i −0.936092 0.540453i
\(494\) −18.0000 + 31.1769i −0.809858 + 1.40272i
\(495\) −4.46410 + 0.267949i −0.200646 + 0.0120434i
\(496\) 2.00000 0.0898027
\(497\) 0 0
\(498\) 8.00000i 0.358489i
\(499\) −6.00000 10.3923i −0.268597 0.465223i 0.699903 0.714238i \(-0.253227\pi\)
−0.968500 + 0.249015i \(0.919893\pi\)
\(500\) 3.76795 10.5263i 0.168508 0.470750i
\(501\) 6.00000 10.3923i 0.268060 0.464294i
\(502\) 0 0
\(503\) 12.0000i 0.535054i −0.963550 0.267527i \(-0.913794\pi\)
0.963550 0.267527i \(-0.0862064\pi\)
\(504\) 0 0
\(505\) 10.0000 20.0000i 0.444994 0.889988i
\(506\) 8.00000 + 13.8564i 0.355643 + 0.615992i
\(507\) 19.9186 + 11.5000i 0.884615 + 0.510733i
\(508\) 3.46410 + 2.00000i 0.153695 + 0.0887357i
\(509\) −15.0000 25.9808i −0.664863 1.15158i −0.979322 0.202306i \(-0.935156\pi\)
0.314459 0.949271i \(-0.398177\pi\)
\(510\) −8.00000 4.00000i −0.354246 0.177123i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 5.19615 3.00000i 0.229416 0.132453i
\(514\) 0 0
\(515\) 14.9282 9.85641i 0.657815 0.434325i
\(516\) 2.00000 + 3.46410i 0.0880451 + 0.152499i
\(517\) 16.0000i 0.703679i
\(518\) 0 0
\(519\) −8.00000 −0.351161
\(520\) 13.3923 0.803848i 0.587291 0.0352510i
\(521\) −13.0000 + 22.5167i −0.569540 + 0.986473i 0.427071 + 0.904218i \(0.359545\pi\)
−0.996611 + 0.0822547i \(0.973788\pi\)
\(522\) −5.19615 3.00000i −0.227429 0.131306i
\(523\) −24.2487 + 14.0000i −1.06032 + 0.612177i −0.925521 0.378695i \(-0.876373\pi\)
−0.134801 + 0.990873i \(0.543039\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) 16.0000 0.697633
\(527\) −6.92820 + 4.00000i −0.301797 + 0.174243i
\(528\) −1.73205 1.00000i −0.0753778 0.0435194i
\(529\) 20.5000 35.5070i 0.891304 1.54378i
\(530\) 13.3923 0.803848i 0.581725 0.0349169i
\(531\) 8.00000 0.347170
\(532\) 0 0
\(533\) 12.0000i 0.519778i
\(534\) −5.00000 8.66025i −0.216371 0.374766i
\(535\) 22.3923 14.7846i 0.968104 0.639194i
\(536\) −4.00000 + 6.92820i −0.172774 + 0.299253i
\(537\) −8.66025 + 5.00000i −0.373718 + 0.215766i
\(538\) 18.0000i 0.776035i
\(539\) 0 0
\(540\) −2.00000 1.00000i −0.0860663 0.0430331i
\(541\) −11.0000 19.0526i −0.472927 0.819133i 0.526593 0.850118i \(-0.323469\pi\)
−0.999520 + 0.0309841i \(0.990136\pi\)
\(542\) 8.66025 + 5.00000i 0.371990 + 0.214768i
\(543\) 1.73205 + 1.00000i 0.0743294 + 0.0429141i
\(544\) −2.00000 3.46410i −0.0857493 0.148522i
\(545\) −14.0000 + 28.0000i −0.599694 + 1.19939i
\(546\) 0 0
\(547\) 40.0000i 1.71028i 0.518400 + 0.855138i \(0.326528\pi\)
−0.518400 + 0.855138i \(0.673472\pi\)
\(548\) 5.19615 3.00000i 0.221969 0.128154i
\(549\) 5.00000 8.66025i 0.213395 0.369611i
\(550\) 1.19615 + 9.92820i 0.0510041 + 0.423340i
\(551\) −18.0000 31.1769i −0.766826 1.32818i
\(552\) 8.00000i 0.340503i
\(553\) 0 0
\(554\) −28.0000 −1.18961
\(555\) −8.92820 + 0.535898i −0.378981 + 0.0227476i
\(556\) −7.00000 + 12.1244i −0.296866 + 0.514187i
\(557\) 36.3731 + 21.0000i 1.54118 + 0.889799i 0.998765 + 0.0496855i \(0.0158219\pi\)
0.542411 + 0.840113i \(0.317511\pi\)
\(558\) −1.73205 + 1.00000i −0.0733236 + 0.0423334i
\(559\) 24.0000 1.01509
\(560\) 0 0
\(561\) 8.00000 0.337760
\(562\) 25.9808 15.0000i 1.09593 0.632737i
\(563\) 3.46410 + 2.00000i 0.145994 + 0.0842900i 0.571218 0.820798i \(-0.306471\pi\)
−0.425223 + 0.905088i \(0.639804\pi\)
\(564\) 4.00000 6.92820i 0.168430 0.291730i
\(565\) −0.803848 13.3923i −0.0338181 0.563418i
\(566\) −20.0000 −0.840663
\(567\) 0 0
\(568\) 6.00000i 0.251754i
\(569\) −23.0000 39.8372i −0.964210 1.67006i −0.711722 0.702461i \(-0.752085\pi\)
−0.252488 0.967600i \(-0.581249\pi\)
\(570\) −7.39230 11.1962i −0.309630 0.468955i
\(571\) −2.00000 + 3.46410i −0.0836974 + 0.144968i −0.904835 0.425762i \(-0.860006\pi\)
0.821138 + 0.570730i \(0.193340\pi\)
\(572\) −10.3923 + 6.00000i −0.434524 + 0.250873i
\(573\) 18.0000i 0.751961i
\(574\) 0 0
\(575\) 32.0000 24.0000i 1.33449 1.00087i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −22.5167 13.0000i −0.937381 0.541197i −0.0482425 0.998836i \(-0.515362\pi\)
−0.889138 + 0.457639i \(0.848695\pi\)
\(578\) −0.866025 0.500000i −0.0360219 0.0207973i
\(579\) 4.00000 + 6.92820i 0.166234 + 0.287926i
\(580\) −6.00000 + 12.0000i −0.249136 + 0.498273i
\(581\) 0 0
\(582\) 10.0000i 0.414513i
\(583\) −10.3923 + 6.00000i −0.430405 + 0.248495i
\(584\) 7.00000 12.1244i 0.289662 0.501709i
\(585\) −11.1962 + 7.39230i −0.462904 + 0.305634i
\(586\) 0 0
\(587\) 12.0000i 0.495293i 0.968850 + 0.247647i \(0.0796572\pi\)
−0.968850 + 0.247647i \(0.920343\pi\)
\(588\) 0 0
\(589\) −12.0000 −0.494451
\(590\) −1.07180 17.8564i −0.0441252 0.735137i
\(591\) 1.00000 1.73205i 0.0411345 0.0712470i
\(592\) −3.46410 2.00000i −0.142374 0.0821995i
\(593\) 10.3923 6.00000i 0.426761 0.246390i −0.271205 0.962522i \(-0.587422\pi\)
0.697966 + 0.716131i \(0.254089\pi\)
\(594\) 2.00000 0.0820610
\(595\) 0 0
\(596\) 10.0000 0.409616
\(597\) 5.19615 3.00000i 0.212664 0.122782i
\(598\) 41.5692 + 24.0000i 1.69989 + 0.981433i
\(599\) 15.0000 25.9808i 0.612883 1.06155i −0.377869 0.925859i \(-0.623343\pi\)
0.990752 0.135686i \(-0.0433238\pi\)
\(600\) −1.96410 + 4.59808i −0.0801841 + 0.187716i
\(601\) −38.0000 −1.55005 −0.775026 0.631929i \(-0.782263\pi\)
−0.775026 + 0.631929i \(0.782263\pi\)
\(602\) 0 0
\(603\) 8.00000i 0.325785i
\(604\) −4.00000 6.92820i −0.162758 0.281905i
\(605\) 8.62436 + 13.0622i 0.350630 + 0.531053i
\(606\) −5.00000 + 8.66025i −0.203111 + 0.351799i
\(607\) −6.92820 + 4.00000i −0.281207 + 0.162355i −0.633970 0.773358i \(-0.718576\pi\)
0.352763 + 0.935713i \(0.385242\pi\)
\(608\) 6.00000i 0.243332i
\(609\) 0 0
\(610\) −20.0000 10.0000i −0.809776 0.404888i
\(611\) −24.0000 41.5692i −0.970936 1.68171i
\(612\) 3.46410 + 2.00000i 0.140028 + 0.0808452i
\(613\) 24.2487 + 14.0000i 0.979396 + 0.565455i 0.902088 0.431553i \(-0.142034\pi\)
0.0773084 + 0.997007i \(0.475367\pi\)
\(614\) 6.00000 + 10.3923i 0.242140 + 0.419399i
\(615\) 4.00000 + 2.00000i 0.161296 + 0.0806478i
\(616\) 0 0
\(617\) 26.0000i 1.04672i −0.852111 0.523360i \(-0.824678\pi\)
0.852111 0.523360i \(-0.175322\pi\)
\(618\) −6.92820 + 4.00000i −0.278693 + 0.160904i
\(619\) 11.0000 19.0526i 0.442127 0.765787i −0.555720 0.831370i \(-0.687557\pi\)
0.997847 + 0.0655827i \(0.0208906\pi\)
\(620\) 2.46410 + 3.73205i 0.0989607 + 0.149883i
\(621\) −4.00000 6.92820i −0.160514 0.278019i
\(622\) 24.0000i 0.962312i
\(623\) 0 0
\(624\) −6.00000 −0.240192
\(625\) 24.2846 5.93782i 0.971384 0.237513i
\(626\) −1.00000 + 1.73205i −0.0399680 + 0.0692267i
\(627\) 10.3923 + 6.00000i 0.415029 + 0.239617i
\(628\) −19.0526 + 11.0000i −0.760280 + 0.438948i
\(629\) 16.0000 0.637962
\(630\) 0 0
\(631\) −4.00000 −0.159237 −0.0796187 0.996825i \(-0.525370\pi\)
−0.0796187 + 0.996825i \(0.525370\pi\)
\(632\) −10.3923 + 6.00000i −0.413384 + 0.238667i
\(633\) 0 0
\(634\) −1.00000 + 1.73205i −0.0397151 + 0.0687885i
\(635\) 0.535898 + 8.92820i 0.0212665 + 0.354305i
\(636\) −6.00000 −0.237915
\(637\) 0 0
\(638\) 12.0000i 0.475085i
\(639\) −3.00000 5.19615i −0.118678 0.205557i
\(640\) −1.86603 + 1.23205i −0.0737611 + 0.0487011i
\(641\) −7.00000 + 12.1244i −0.276483 + 0.478883i −0.970508 0.241068i \(-0.922502\pi\)
0.694025 + 0.719951i \(0.255836\pi\)
\(642\) −10.3923 + 6.00000i −0.410152 + 0.236801i
\(643\) 12.0000i 0.473234i 0.971603 + 0.236617i \(0.0760386\pi\)
−0.971603 + 0.236617i \(0.923961\pi\)
\(644\) 0 0
\(645\) −4.00000 + 8.00000i −0.157500 + 0.315000i
\(646\) 12.0000 + 20.7846i 0.472134 + 0.817760i
\(647\) 31.1769 + 18.0000i 1.22569 + 0.707653i 0.966126 0.258073i \(-0.0830873\pi\)
0.259565 + 0.965726i \(0.416421\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) 8.00000 + 13.8564i 0.314027 + 0.543912i
\(650\) 18.0000 + 24.0000i 0.706018 + 0.941357i
\(651\) 0 0
\(652\) 4.00000i 0.156652i
\(653\) −29.4449 + 17.0000i −1.15227 + 0.665261i −0.949439 0.313953i \(-0.898347\pi\)
−0.202828 + 0.979214i \(0.565013\pi\)
\(654\) 7.00000 12.1244i 0.273722 0.474100i
\(655\) −14.7846 22.3923i −0.577683 0.874940i
\(656\) 1.00000 + 1.73205i 0.0390434 + 0.0676252i
\(657\) 14.0000i 0.546192i
\(658\) 0 0
\(659\) 26.0000 1.01282 0.506408 0.862294i \(-0.330973\pi\)
0.506408 + 0.862294i \(0.330973\pi\)
\(660\) −0.267949 4.46410i −0.0104299 0.173765i
\(661\) 19.0000 32.9090i 0.739014 1.28001i −0.213925 0.976850i \(-0.568625\pi\)
0.952940 0.303160i \(-0.0980418\pi\)
\(662\) 6.92820 + 4.00000i 0.269272 + 0.155464i
\(663\) 20.7846 12.0000i 0.807207 0.466041i
\(664\) −8.00000 −0.310460
\(665\) 0 0
\(666\) 4.00000 0.154997
\(667\) −41.5692 + 24.0000i −1.60957 + 0.929284i
\(668\) 10.3923 + 6.00000i 0.402090 + 0.232147i
\(669\) −4.00000 + 6.92820i −0.154649 + 0.267860i
\(670\) −17.8564 + 1.07180i −0.689853 + 0.0414071i
\(671\) 20.0000 0.772091
\(672\) 0 0
\(673\) 12.0000i 0.462566i −0.972887 0.231283i \(-0.925708\pi\)
0.972887 0.231283i \(-0.0742923\pi\)
\(674\) −4.00000 6.92820i −0.154074 0.266864i
\(675\) −0.598076 4.96410i −0.0230200 0.191068i
\(676\) −11.5000 + 19.9186i −0.442308 + 0.766099i
\(677\) −34.6410 + 20.0000i −1.33136 + 0.768662i −0.985509 0.169626i \(-0.945744\pi\)
−0.345854 + 0.938288i \(0.612411\pi\)
\(678\) 6.00000i 0.230429i
\(679\) 0 0
\(680\) 4.00000 8.00000i 0.153393 0.306786i
\(681\) 4.00000 + 6.92820i 0.153280 + 0.265489i
\(682\) −3.46410 2.00000i −0.132647 0.0765840i
\(683\) 3.46410 + 2.00000i 0.132550 + 0.0765279i 0.564809 0.825222i \(-0.308950\pi\)
−0.432259 + 0.901750i \(0.642283\pi\)
\(684\) 3.00000 + 5.19615i 0.114708 + 0.198680i
\(685\) 12.0000 + 6.00000i 0.458496 + 0.229248i
\(686\) 0 0
\(687\) 14.0000i 0.534133i
\(688\) −3.46410 + 2.00000i −0.132068 + 0.0762493i
\(689\) −18.0000 + 31.1769i −0.685745 + 1.18775i
\(690\) −14.9282 + 9.85641i −0.568307 + 0.375227i
\(691\) −1.00000 1.73205i −0.0380418 0.0658903i 0.846378 0.532583i \(-0.178779\pi\)
−0.884419 + 0.466693i \(0.845445\pi\)
\(692\) 8.00000i 0.304114i
\(693\) 0 0
\(694\) −36.0000 −1.36654
\(695\) −31.2487 + 1.87564i −1.18533 + 0.0711472i
\(696\) 3.00000 5.19615i 0.113715 0.196960i
\(697\) −6.92820 4.00000i −0.262424 0.151511i
\(698\) −22.5167 + 13.0000i −0.852268 + 0.492057i
\(699\) −10.0000 −0.378235
\(700\) 0 0
\(701\) −34.0000 −1.28416 −0.642081 0.766637i \(-0.721929\pi\)
−0.642081 + 0.766637i \(0.721929\pi\)
\(702\) 5.19615 3.00000i 0.196116 0.113228i
\(703\) 20.7846 + 12.0000i 0.783906 + 0.452589i
\(704\) 1.00000 1.73205i 0.0376889 0.0652791i
\(705\) 17.8564 1.07180i 0.672511 0.0403662i
\(706\) −20.0000 −0.752710
\(707\) 0 0
\(708\) 8.00000i 0.300658i
\(709\) −3.00000 5.19615i −0.112667 0.195146i 0.804178 0.594389i \(-0.202606\pi\)
−0.916845 + 0.399244i \(0.869273\pi\)
\(710\) −11.1962 + 7.39230i −0.420184 + 0.277428i
\(711\) 6.00000 10.3923i 0.225018 0.389742i
\(712\) 8.66025 5.00000i 0.324557 0.187383i
\(713\) 16.0000i 0.599205i
\(714\) 0 0
\(715\) −24.0000 12.0000i −0.897549 0.448775i
\(716\) −5.00000 8.66025i −0.186859 0.323649i
\(717\) 22.5167 + 13.0000i 0.840900 + 0.485494i
\(718\) 5.19615 + 3.00000i 0.193919 + 0.111959i
\(719\) 2.00000 + 3.46410i 0.0745874 + 0.129189i 0.900907 0.434013i \(-0.142903\pi\)
−0.826319 + 0.563202i \(0.809569\pi\)
\(720\) 1.00000 2.00000i 0.0372678 0.0745356i
\(721\) 0 0
\(722\) 17.0000i 0.632674i
\(723\) 22.5167 13.0000i 0.837404 0.483475i
\(724\) −1.00000 + 1.73205i −0.0371647 + 0.0643712i
\(725\) −29.7846 + 3.58846i −1.10617 + 0.133272i
\(726\) −3.50000 6.06218i −0.129897 0.224989i
\(727\) 24.0000i 0.890111i −0.895503 0.445055i \(-0.853184\pi\)
0.895503 0.445055i \(-0.146816\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 31.2487 1.87564i 1.15657 0.0694207i
\(731\) 8.00000 13.8564i 0.295891 0.512498i
\(732\) 8.66025 + 5.00000i 0.320092 + 0.184805i
\(733\) 12.1244 7.00000i 0.447823 0.258551i −0.259087 0.965854i \(-0.583422\pi\)
0.706910 + 0.707303i \(0.250088\pi\)
\(734\) −32.0000 −1.18114
\(735\) 0 0
\(736\) −8.00000 −0.294884
\(737\) 13.8564 8.00000i 0.510407 0.294684i
\(738\) −1.73205 1.00000i −0.0637577 0.0368105i
\(739\) −22.0000 + 38.1051i −0.809283 + 1.40172i 0.104078 + 0.994569i \(0.466811\pi\)
−0.913361 + 0.407150i \(0.866523\pi\)
\(740\) −0.535898 8.92820i −0.0197000 0.328207i
\(741\) 36.0000 1.32249
\(742\) 0 0
\(743\) 48.0000i 1.76095i 0.474093 + 0.880475i \(0.342776\pi\)
−0.474093 + 0.880475i \(0.657224\pi\)
\(744\) −1.00000 1.73205i −0.0366618 0.0635001i
\(745\) 12.3205 + 18.6603i 0.451388 + 0.683659i
\(746\) 12.0000 20.7846i 0.439351 0.760979i
\(747\) 6.92820 4.00000i 0.253490 0.146352i
\(748\) 8.00000i 0.292509i
\(749\) 0 0
\(750\) −11.0000 + 2.00000i −0.401663 + 0.0730297i
\(751\) −10.0000 17.3205i −0.364905 0.632034i 0.623856 0.781540i \(-0.285565\pi\)
−0.988761 + 0.149505i \(0.952232\pi\)
\(752\) 6.92820 + 4.00000i 0.252646 + 0.145865i
\(753\) 0 0
\(754\) −18.0000 31.1769i −0.655521 1.13540i
\(755\) 8.00000 16.0000i 0.291150 0.582300i
\(756\) 0 0
\(757\) 32.0000i 1.16306i −0.813525 0.581530i \(-0.802454\pi\)
0.813525 0.581530i \(-0.197546\pi\)
\(758\) −17.3205 + 10.0000i −0.629109 + 0.363216i
\(759\) 8.00000 13.8564i 0.290382 0.502956i
\(760\) 11.1962 7.39230i 0.406127 0.268147i
\(761\) −3.00000 5.19615i −0.108750 0.188360i 0.806514 0.591215i \(-0.201351\pi\)
−0.915264 + 0.402854i \(0.868018\pi\)
\(762\) 4.00000i 0.144905i
\(763\) 0 0
\(764\) 18.0000 0.651217
\(765\) 0.535898 + 8.92820i 0.0193754 + 0.322800i
\(766\) 10.0000 17.3205i 0.361315 0.625815i
\(767\) 41.5692 + 24.0000i 1.50098 + 0.866590i
\(768\) 0.866025 0.500000i 0.0312500 0.0180422i
\(769\) 30.0000 1.08183 0.540914 0.841078i \(-0.318079\pi\)
0.540914 + 0.841078i \(0.318079\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −6.92820 + 4.00000i −0.249351 + 0.143963i
\(773\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(774\) 2.00000 3.46410i 0.0718885 0.124515i
\(775\) −3.92820 + 9.19615i −0.141105 + 0.330336i
\(776\) 10.0000 0.358979
\(777\) 0 0
\(778\) 2.00000i 0.0717035i
\(779\) −6.00000 10.3923i −0.214972 0.372343i
\(780\) −7.39230 11.1962i −0.264687 0.400887i
\(781\) 6.00000 10.3923i 0.214697 0.371866i