Properties

Label 1470.2.n.f.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.f.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 \(-0.687167\pi\)
0.554700 0.832050i \(-0.312833\pi\)
\(14\) 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 −0.0171533 0.999853i \(-0.505460\pi\)
0.857321 + 0.514782i \(0.172127\pi\)
\(18\) 0.866025 0.500000i 0.204124 0.117851i
\(19\) 3.00000 5.19615i 0.688247 1.19208i −0.284157 0.958778i \(-0.591714\pi\)
0.972404 0.233301i \(-0.0749529\pi\)
\(20\) 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 0.762140 0.647412i \(-0.224149\pi\)
−0.941745 + 0.336327i \(0.890815\pi\)
\(32\) −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 \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 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 −0.0992202 0.995066i \(-0.531635\pi\)
−0.911362 + 0.411606i \(0.864968\pi\)
\(48\) 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 \(0.00768307\pi\)
−0.478953 + 0.877841i \(0.658984\pi\)
\(60\) −1.86603 1.23205i −0.240903 0.159057i
\(61\) −5.00000 + 8.66025i −0.640184 + 1.10883i 0.345207 + 0.938527i \(0.387809\pi\)
−0.985391 + 0.170305i \(0.945525\pi\)
\(62\) 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 0.422833 0.906208i \(-0.361036\pi\)
0.996215 + 0.0869195i \(0.0277023\pi\)
\(74\) 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 \(0.144687\pi\)
−0.898459 + 0.439057i \(0.855313\pi\)
\(84\) 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 \(-0.655526\pi\)
0.999388 0.0349934i \(-0.0111410\pi\)
\(90\) 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 \(-0.830506\pi\)
0.861550 0.507673i \(-0.169494\pi\)
\(98\) 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 0.999996 0.00286291i \(-0.000911295\pi\)
−0.502477 + 0.864590i \(0.667578\pi\)
\(102\) −3.46410 + 2.00000i −0.342997 + 0.198030i
\(103\) 6.92820 + 4.00000i 0.682656 + 0.394132i 0.800855 0.598858i \(-0.204379\pi\)
−0.118199 + 0.992990i \(0.537712\pi\)
\(104\) 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 \(0.342311\pi\)
−0.999602 + 0.0281993i \(0.991023\pi\)
\(132\) 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 \(-0.702346\pi\)
−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 −0.585231 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 \(0.674386\pi\)
−0.999706 + 0.0242497i \(0.992280\pi\)
\(158\) −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 \(-0.846308\pi\)
0.885681 0.464294i \(-0.153692\pi\)
\(168\) 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 0.739689 0.672949i \(-0.234973\pi\)
−0.212947 + 0.977064i \(0.568306\pi\)
\(174\) 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 \(-0.523682\pi\)
−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 −0.331611 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 0.739883 0.672735i \(-0.234881\pi\)
−0.952548 + 0.304390i \(0.901547\pi\)
\(200\) −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 \(0.0863164\pi\)
−0.963458 + 0.267860i \(0.913684\pi\)
\(224\) 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 −0.711977 0.702202i \(-0.752200\pi\)
0.252136 + 0.967692i \(0.418867\pi\)
\(228\) −5.19615 + 3.00000i −0.344124 + 0.198680i
\(229\) −7.00000 + 12.1244i −0.462573 + 0.801200i −0.999088 0.0426906i \(-0.986407\pi\)
0.536515 + 0.843891i \(0.319740\pi\)
\(230\) 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 \(-0.850739\pi\)
0.0546547 0.998505i \(-0.482594\pi\)
\(242\) 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 \(-0.981774\pi\)
0.449622 0.893219i \(-0.351559\pi\)
\(270\) −1.23205 + 1.86603i −0.0749802 + 0.113563i
\(271\) 5.00000 8.66025i 0.303728 0.526073i −0.673249 0.739416i \(-0.735102\pi\)
0.976977 + 0.213343i \(0.0684351\pi\)
\(272\) 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 −0.916869 0.399188i \(-0.869292\pi\)
−0.112728 + 0.993626i \(0.535959\pi\)
\(284\) −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 \(-0.888747\pi\)
0.939540 0.342438i \(-0.111253\pi\)
\(308\) 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 \(0.0715523\pi\)
−0.294384 + 0.955687i \(0.595114\pi\)
\(312\) −5.19615 + 3.00000i −0.294174 + 0.169842i
\(313\) −1.73205 1.00000i −0.0979013 0.0565233i 0.450250 0.892903i \(-0.351335\pi\)
−0.548151 + 0.836379i \(0.684668\pi\)
\(314\) −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 \(-0.744983\pi\)
−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 −0.884234 0.467045i \(-0.845319\pi\)
−0.0376440 + 0.999291i \(0.511985\pi\)
\(354\) −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 −0.998277 0.0586798i \(-0.981311\pi\)
−0.448320 + 0.893873i \(0.647978\pi\)
\(368\) −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 0.872316 0.488943i \(-0.162617\pi\)
0.0127209 + 0.999919i \(0.495951\pi\)
\(384\) 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 0.542834 0.839840i \(-0.317351\pi\)
−0.455905 + 0.890028i \(0.650684\pi\)
\(398\) 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 \(-0.944436\pi\)
0.341994 0.939702i \(-0.388898\pi\)
\(410\) −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 0.840936 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 \(0.214795\pi\)
−0.780833 + 0.624740i \(0.785205\pi\)
\(434\) 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 −0.567286 0.823521i \(-0.692007\pi\)
0.996833 + 0.0795241i \(0.0253401\pi\)
\(440\) 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 \(-0.362320\pi\)
0.419172 + 0.907907i \(0.362320\pi\)
\(462\) 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 0.896726 0.442587i \(-0.145939\pi\)
0.0650714 + 0.997881i \(0.479272\pi\)
\(468\) 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 0.760056 0.649857i \(-0.225171\pi\)
−0.942821 + 0.333300i \(0.891838\pi\)
\(480\) 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 \(0.0862064\pi\)
−0.963550 + 0.267527i \(0.913794\pi\)
\(504\) 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 \(0.398177\pi\)
−0.979322 + 0.202306i \(0.935156\pi\)
\(510\) −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 \(-0.973788\pi\)
0.427071 0.904218i \(-0.359545\pi\)
\(522\) −5.19615 + 3.00000i −0.227429 + 0.131306i
\(523\) −24.2487 14.0000i −1.06032 0.612177i −0.134801 0.990873i \(-0.543039\pi\)
−0.925521 + 0.378695i \(0.876373\pi\)
\(524\) −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 −0.425223 0.905088i \(-0.639804\pi\)
0.571218 + 0.820798i \(0.306471\pi\)
\(564\) 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 −0.889138 0.457639i \(-0.848695\pi\)
−0.0482425 + 0.998836i \(0.515362\pi\)
\(578\) −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 \(-0.920343\pi\)
0.968850 0.247647i \(-0.0796572\pi\)
\(588\) 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 0.697966 0.716131i \(-0.254089\pi\)
−0.271205 + 0.962522i \(0.587422\pi\)
\(594\) 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 \(-0.782263\pi\)
−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 0.352763 0.935713i \(-0.385242\pi\)
−0.633970 + 0.773358i \(0.718576\pi\)
\(608\) 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 0.997847 0.0655827i \(-0.0208906\pi\)
−0.555720 + 0.831370i \(0.687557\pi\)
\(620\) 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 \(-0.923961\pi\)
0.971603 0.236617i \(-0.0760386\pi\)
\(644\) 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 0.259565 0.965726i \(-0.416421\pi\)
0.966126 + 0.258073i \(0.0830873\pi\)
\(648\) 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 \(0.0980418\pi\)
−0.213925 + 0.976850i \(0.568625\pi\)
\(662\) 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 −0.345854 0.938288i \(-0.612411\pi\)
−0.985509 + 0.169626i \(0.945744\pi\)
\(678\) 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 −0.884419 0.466693i \(-0.845445\pi\)
0.846378 + 0.532583i \(0.178779\pi\)
\(692\) 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 −0.826319 0.563202i \(-0.809569\pi\)
0.900907 + 0.434013i \(0.142903\pi\)
\(720\) 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 \(0.146816\pi\)
−0.895503 + 0.445055i \(0.853184\pi\)
\(728\) 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 0.706910 0.707303i \(-0.250088\pi\)
−0.259087 + 0.965854i \(0.583422\pi\)
\(734\) −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 −0.915264 0.402854i \(-0.868018\pi\)
0.806514 + 0.591215i \(0.201351\pi\)
\(762\) 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 \(-0.666667\pi\)
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