Properties

Label 1470.2.n.b.79.2
Level $1470$
Weight $2$
Character 1470.79
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 79.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1470.79
Dual form 1470.2.n.b.949.2

$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 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 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) 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 \(-0.827873\pi\)
0.0171533 + 0.999853i \(0.494540\pi\)
\(18\) 0.866025 0.500000i 0.204124 0.117851i
\(19\) −3.00000 + 5.19615i −0.688247 + 1.19208i 0.284157 + 0.958778i \(0.408286\pi\)
−0.972404 + 0.233301i \(0.925047\pi\)
\(20\) −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 0.998154 0.0607377i \(-0.0193453\pi\)
0.446476 + 0.894795i \(0.352679\pi\)
\(24\) 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 \(-0.109185\pi\)
−0.762140 + 0.647412i \(0.775851\pi\)
\(32\) −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 0.756948 0.653476i \(-0.226690\pi\)
−0.187453 + 0.982274i \(0.560023\pi\)
\(38\) −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 \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) 4.00000i 0.609994i 0.952353 + 0.304997i \(0.0986555\pi\)
−0.952353 + 0.304997i \(0.901344\pi\)
\(44\) 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 \(-0.135032\pi\)
0.0992202 + 0.995066i \(0.468365\pi\)
\(48\) 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 −0.0987002 0.995117i \(-0.531468\pi\)
0.812447 + 0.583036i \(0.198135\pi\)
\(54\) 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 −0.999709 0.0241347i \(-0.992317\pi\)
0.478953 0.877841i \(-0.341016\pi\)
\(60\) −1.86603 1.23205i −0.240903 0.159057i
\(61\) 5.00000 8.66025i 0.640184 1.10883i −0.345207 0.938527i \(-0.612191\pi\)
0.985391 0.170305i \(-0.0544754\pi\)
\(62\) 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 −0.859440 0.511237i \(-0.829187\pi\)
0.0130248 + 0.999915i \(0.495854\pi\)
\(68\) −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 \(-0.972298\pi\)
−0.422833 + 0.906208i \(0.638964\pi\)
\(74\) 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 0.301401 + 0.953498i \(0.402546\pi\)
−0.976453 + 0.215728i \(0.930788\pi\)
\(80\) 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 0.469389 + 0.882992i \(0.344474\pi\)
−0.999388 + 0.0349934i \(0.988859\pi\)
\(90\) −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 \(-0.332422\pi\)
−0.999996 + 0.00286291i \(0.999089\pi\)
\(102\) −3.46410 + 2.00000i −0.342997 + 0.198030i
\(103\) −6.92820 4.00000i −0.682656 0.394132i 0.118199 0.992990i \(-0.462288\pi\)
−0.800855 + 0.598858i \(0.795621\pi\)
\(104\) −6.00000 −0.588348
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) 10.3923 + 6.00000i 1.00466 + 0.580042i 0.909624 0.415432i \(-0.136370\pi\)
0.0950377 + 0.995474i \(0.469703\pi\)
\(108\) 0.866025 0.500000i 0.0833333 0.0481125i
\(109\) −7.00000 12.1244i −0.670478 1.16130i −0.977769 0.209687i \(-0.932756\pi\)
0.307290 0.951616i \(-0.400578\pi\)
\(110\) −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 \(0.0910696\pi\)
−0.959351 + 0.282216i \(0.908930\pi\)
\(114\) −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 \(-0.943208\pi\)
0.984126 0.177471i \(-0.0567917\pi\)
\(128\) −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 −0.475380 0.879781i \(-0.657689\pi\)
0.999602 0.0281993i \(-0.00897729\pi\)
\(132\) 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 −0.261329 0.965250i \(-0.584161\pi\)
0.705266 + 0.708942i \(0.250827\pi\)
\(138\) 6.92820 + 4.00000i 0.589768 + 0.340503i
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) 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 −0.585231 0.810867i \(-0.698996\pi\)
0.994847 + 0.101391i \(0.0323294\pi\)
\(150\) 4.96410 + 0.598076i 0.405317 + 0.0488327i
\(151\) 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i \(-0.0611289\pi\)
−0.656101 + 0.754673i \(0.727796\pi\)
\(152\) −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 0.520854 0.853646i \(-0.325614\pi\)
0.999706 0.0242497i \(-0.00771967\pi\)
\(158\) −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 0.629492 0.777007i \(-0.283263\pi\)
−0.358162 + 0.933659i \(0.616597\pi\)
\(164\) 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 \(-0.431694\pi\)
−0.739689 + 0.672949i \(0.765027\pi\)
\(174\) −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 0.990134 0.140122i \(-0.0447496\pi\)
−0.616417 + 0.787420i \(0.711416\pi\)
\(180\) −2.23205 0.133975i −0.166367 0.00998588i
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 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 −0.331611 0.943416i \(-0.607592\pi\)
0.982828 0.184525i \(-0.0590746\pi\)
\(192\) −0.866025 + 0.500000i −0.0625000 + 0.0360844i
\(193\) −6.92820 + 4.00000i −0.498703 + 0.287926i −0.728178 0.685388i \(-0.759632\pi\)
0.229475 + 0.973315i \(0.426299\pi\)
\(194\) −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 \(-0.977302\pi\)
0.997459 0.0712470i \(-0.0226979\pi\)
\(198\) −1.73205 1.00000i −0.123091 0.0710669i
\(199\) 3.00000 + 5.19615i 0.212664 + 0.368345i 0.952548 0.304390i \(-0.0984526\pi\)
−0.739883 + 0.672735i \(0.765119\pi\)
\(200\) −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 \(-0.581133\pi\)
0.711977 + 0.702202i \(0.247800\pi\)
\(228\) −5.19615 + 3.00000i −0.344124 + 0.198680i
\(229\) 7.00000 12.1244i 0.462573 0.801200i −0.536515 0.843891i \(-0.680260\pi\)
0.999088 + 0.0426906i \(0.0135930\pi\)
\(230\) −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 0.756091 0.654466i \(-0.227107\pi\)
−0.188739 + 0.982027i \(0.560440\pi\)
\(234\) 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 0.892058 + 0.451920i \(0.149261\pi\)
−0.0546547 + 0.998505i \(0.517406\pi\)
\(242\) 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 \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) 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 −0.00771799 0.999970i \(-0.502457\pi\)
0.862141 + 0.506669i \(0.169123\pi\)
\(264\) 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 0.998361 + 0.0572259i \(0.0182255\pi\)
−0.449622 + 0.893219i \(0.648441\pi\)
\(270\) −1.23205 + 1.86603i −0.0749802 + 0.113563i
\(271\) −5.00000 + 8.66025i −0.303728 + 0.526073i −0.976977 0.213343i \(-0.931565\pi\)
0.673249 + 0.739416i \(0.264898\pi\)
\(272\) 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 −0.998861 0.0477206i \(-0.984804\pi\)
−0.458103 + 0.888899i \(0.651471\pi\)
\(278\) 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 \(-0.464041\pi\)
0.916869 + 0.399188i \(0.130708\pi\)
\(284\) −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 −0.974841 0.222900i \(-0.928448\pi\)
0.294384 0.955687i \(-0.404886\pi\)
\(312\) −5.19615 + 3.00000i −0.294174 + 0.169842i
\(313\) 1.73205 + 1.00000i 0.0979013 + 0.0565233i 0.548151 0.836379i \(-0.315332\pi\)
−0.450250 + 0.892903i \(0.648665\pi\)
\(314\) 22.0000 1.24153
\(315\) 0 0
\(316\) −12.0000 −0.675053
\(317\) −1.73205 1.00000i −0.0972817 0.0561656i 0.450570 0.892741i \(-0.351221\pi\)
−0.547852 + 0.836576i \(0.684554\pi\)
\(318\) 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 −0.734905 0.678170i \(-0.762773\pi\)
0.954765 + 0.297361i \(0.0961066\pi\)
\(332\) 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 \(0.0699187\pi\)
−0.975972 + 0.217894i \(0.930081\pi\)
\(338\) −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 −0.708105 + 0.706107i \(0.750450\pi\)
−0.965559 + 0.260184i \(0.916217\pi\)
\(348\) −5.19615 3.00000i −0.278543 0.160817i
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 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 \(-0.488015\pi\)
0.884234 + 0.467045i \(0.154681\pi\)
\(354\) −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 −0.775934 0.630814i \(-0.782721\pi\)
0.934268 + 0.356572i \(0.116054\pi\)
\(360\) −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 \(-0.352022\pi\)
0.998277 + 0.0586798i \(0.0186891\pi\)
\(368\) −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 0.929865 0.367901i \(-0.119923\pi\)
0.146321 + 0.989237i \(0.453257\pi\)
\(374\) 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 \(-0.504049\pi\)
−0.872316 + 0.488943i \(0.837383\pi\)
\(384\) −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 0.890263 0.455448i \(-0.150521\pi\)
−0.839561 + 0.543266i \(0.817187\pi\)
\(390\) 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 \(-0.349316\pi\)
−0.542834 + 0.839840i \(0.682649\pi\)
\(398\) 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 −0.636609 0.771187i \(-0.719663\pi\)
0.986172 + 0.165726i \(0.0529966\pi\)
\(402\) −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 0.984803 + 0.173675i \(0.0555643\pi\)
−0.341994 + 0.939702i \(0.611102\pi\)
\(410\) −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 \(-0.662467\pi\)
−0.488532 + 0.872546i \(0.662467\pi\)
\(420\) 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 0.840936 0.541135i \(-0.182005\pi\)
−0.889104 + 0.457705i \(0.848672\pi\)
\(432\) 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 \(-0.974660\pi\)
0.567286 + 0.823521i \(0.307993\pi\)
\(440\) −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 0.726130 0.687557i \(-0.241317\pi\)
−0.232377 + 0.972626i \(0.574650\pi\)
\(444\) 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 0.945015 0.327028i \(-0.106047\pi\)
0.189292 + 0.981921i \(0.439381\pi\)
\(458\) 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 \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 0 0
\(463\) 36.0000i 1.67306i 0.547920 + 0.836531i \(0.315420\pi\)
−0.547920 + 0.836531i \(0.684580\pi\)
\(464\) 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 \(-0.520728\pi\)
−0.896726 + 0.442587i \(0.854061\pi\)
\(468\) 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 \(-0.108162\pi\)
−0.760056 + 0.649857i \(0.774829\pi\)
\(480\) 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 −0.716625 0.697459i \(-0.754314\pi\)
0.245705 + 0.969345i \(0.420981\pi\)
\(488\) 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 −0.968500 0.249015i \(-0.919893\pi\)
0.699903 + 0.714238i \(0.253227\pi\)
\(500\) −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 −0.314459 0.949271i \(-0.601823\pi\)
0.979322 0.202306i \(-0.0648436\pi\)
\(510\) 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 0.996611 + 0.0822547i \(0.0262121\pi\)
−0.427071 + 0.904218i \(0.640455\pi\)
\(522\) −5.19615 + 3.00000i −0.227429 + 0.131306i
\(523\) 24.2487 + 14.0000i 1.06032 + 0.612177i 0.925521 0.378695i \(-0.123627\pi\)
0.134801 + 0.990873i \(0.456961\pi\)
\(524\) 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 −0.999520 0.0309841i \(-0.990136\pi\)
0.526593 + 0.850118i \(0.323469\pi\)
\(542\) −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 \(-0.673472\pi\)
0.518400 0.855138i \(-0.326528\pi\)
\(548\) 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 0.542411 0.840113i \(-0.317511\pi\)
0.998765 0.0496855i \(-0.0158219\pi\)
\(558\) 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 \(-0.693529\pi\)
0.425223 + 0.905088i \(0.360196\pi\)
\(564\) 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 −0.252488 + 0.967600i \(0.581249\pi\)
−0.711722 + 0.702461i \(0.752085\pi\)
\(570\) 7.39230 11.1962i 0.309630 0.468955i
\(571\) −2.00000 3.46410i −0.0836974 0.144968i 0.821138 0.570730i \(-0.193340\pi\)
−0.904835 + 0.425762i \(0.860006\pi\)
\(572\) 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 \(-0.484638\pi\)
0.889138 + 0.457639i \(0.151305\pi\)
\(578\) −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 \(-0.412578\pi\)
−0.697966 + 0.716131i \(0.745911\pi\)
\(594\) −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 0.990752 + 0.135686i \(0.0433238\pi\)
−0.377869 + 0.925859i \(0.623343\pi\)
\(600\) 1.96410 + 4.59808i 0.0801841 + 0.187716i
\(601\) 38.0000 1.55005 0.775026 0.631929i \(-0.217737\pi\)
0.775026 + 0.631929i \(0.217737\pi\)
\(602\) 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 \(-0.281424\pi\)
−0.352763 + 0.935713i \(0.614758\pi\)
\(608\) 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 0.0773084 0.997007i \(-0.475367\pi\)
0.902088 + 0.431553i \(0.142034\pi\)
\(614\) −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 \(0.175322\pi\)
−0.852111 + 0.523360i \(0.824678\pi\)
\(618\) −6.92820 4.00000i −0.278693 0.160904i
\(619\) −11.0000 19.0526i −0.442127 0.765787i 0.555720 0.831370i \(-0.312443\pi\)
−0.997847 + 0.0655827i \(0.979109\pi\)
\(620\) 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 0.694025 0.719951i \(-0.255836\pi\)
−0.970508 + 0.241068i \(0.922502\pi\)
\(642\) 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 \(-0.916913\pi\)
−0.259565 + 0.965726i \(0.583579\pi\)
\(648\) 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 −0.202828 0.979214i \(-0.565013\pi\)
−0.949439 + 0.313953i \(0.898347\pi\)
\(654\) −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 −0.952940 0.303160i \(-0.901958\pi\)
0.213925 0.976850i \(-0.431375\pi\)
\(662\) 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 \(0.0742923\pi\)
−0.972887 + 0.231283i \(0.925708\pi\)
\(674\) −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 \(-0.0542560\pi\)
0.345854 + 0.938288i \(0.387589\pi\)
\(678\) 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 −0.432259 0.901750i \(-0.642283\pi\)
0.564809 + 0.825222i \(0.308950\pi\)
\(684\) −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 \(-0.821221\pi\)
0.884419 + 0.466693i \(0.154555\pi\)
\(692\) 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 −0.916845 0.399244i \(-0.869273\pi\)
0.804178 + 0.594389i \(0.202606\pi\)
\(710\) 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 \(-0.857097\pi\)
0.826319 + 0.563202i \(0.190431\pi\)
\(720\) −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 \(-0.416578\pi\)
−0.706910 + 0.707303i \(0.749912\pi\)
\(734\) 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 −0.913361 0.407150i \(-0.866523\pi\)
0.104078 0.994569i \(-0.466811\pi\)
\(740\) 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 \(-0.657224\pi\)
0.474093 0.880475i \(-0.342776\pi\)
\(744\) −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 −0.988761 0.149505i \(-0.952232\pi\)
0.623856 + 0.781540i \(0.285565\pi\)
\(752\) −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 \(0.197546\pi\)
−0.813525 + 0.581530i \(0.802454\pi\)
\(758\) −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 \(-0.798649\pi\)
0.915264 + 0.402854i \(0.131982\pi\)
\(762\) 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 \(-0.681921\pi\)
−0.540914 + 0.841078i \(0.681921\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −6.92820 4.00000i −0.249351 0.143963i
\(773\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(774\) 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