Properties

Label 735.2.q.a.79.2
Level 735
Weight 2
Character 735.79
Analytic conductor 5.869
Analytic rank 0
Dimension 4
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.86900454856\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 79.2
Root \(0.866025 + 0.500000i\) of \(x^{4} - x^{2} + 1\)
Character \(\chi\) \(=\) 735.79
Dual form 735.2.q.a.214.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.23205 - 0.133975i) q^{5} -1.00000 q^{6} -3.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(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} -3.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.86603 - 1.23205i) q^{10} +(3.00000 + 5.19615i) q^{11} +(0.866025 + 0.500000i) q^{12} +2.00000i 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} +6.00000i q^{22} +(1.50000 + 2.59808i) q^{24} +(4.96410 + 0.598076i) q^{25} +(-1.00000 + 1.73205i) q^{26} +1.00000i q^{27} +2.00000 q^{29} +(2.23205 + 0.133975i) q^{30} +(5.00000 + 8.66025i) q^{31} +(-4.33013 + 2.50000i) q^{32} +(-5.19615 - 3.00000i) q^{33} +4.00000 q^{34} -1.00000 q^{36} +(3.46410 + 2.00000i) q^{37} +(-5.19615 + 3.00000i) q^{38} +(-1.00000 - 1.73205i) q^{39} +(-0.401924 + 6.69615i) q^{40} +2.00000 q^{41} +4.00000i q^{43} +(3.00000 - 5.19615i) q^{44} +(-1.23205 + 1.86603i) q^{45} +1.00000i q^{48} +(4.00000 + 3.00000i) q^{50} +(-2.00000 + 3.46410i) q^{51} +(1.73205 - 1.00000i) q^{52} +(-5.19615 + 3.00000i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-6.00000 - 12.0000i) q^{55} -6.00000i q^{57} +(1.73205 + 1.00000i) q^{58} +(-4.00000 - 6.92820i) q^{59} +(-1.86603 - 1.23205i) q^{60} +(1.00000 - 1.73205i) q^{61} +10.0000i q^{62} -7.00000 q^{64} +(0.267949 - 4.46410i) q^{65} +(-3.00000 - 5.19615i) q^{66} +(-13.8564 + 8.00000i) q^{67} +(-3.46410 - 2.00000i) q^{68} +10.0000 q^{71} +(-2.59808 - 1.50000i) q^{72} +(5.19615 - 3.00000i) q^{73} +(2.00000 + 3.46410i) q^{74} +(-4.59808 + 1.96410i) q^{75} +6.00000 q^{76} -2.00000i q^{78} +(2.00000 - 3.46410i) 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} +(-1.73205 + 1.00000i) q^{87} +(15.5885 - 9.00000i) q^{88} +(3.00000 - 5.19615i) q^{89} +(-2.00000 + 1.00000i) q^{90} +(-8.66025 - 5.00000i) q^{93} +(7.39230 - 11.1962i) q^{95} +(2.50000 - 4.33013i) q^{96} -2.00000i q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{4} - 2q^{5} - 4q^{6} + 2q^{9} + O(q^{10}) \) \( 4q - 2q^{4} - 2q^{5} - 4q^{6} + 2q^{9} - 4q^{10} + 12q^{11} + 8q^{15} + 2q^{16} - 12q^{19} + 4q^{20} + 6q^{24} + 6q^{25} - 4q^{26} + 8q^{29} + 2q^{30} + 20q^{31} + 16q^{34} - 4q^{36} - 4q^{39} - 12q^{40} + 8q^{41} + 12q^{44} + 2q^{45} + 16q^{50} - 8q^{51} - 2q^{54} - 24q^{55} - 16q^{59} - 4q^{60} + 4q^{61} - 28q^{64} + 8q^{65} - 12q^{66} + 40q^{71} + 8q^{74} - 8q^{75} + 24q^{76} + 8q^{79} + 2q^{80} - 2q^{81} - 32q^{85} - 8q^{86} + 12q^{89} - 8q^{90} - 12q^{95} + 10q^{96} + 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i 0.773893 0.633316i \(-0.218307\pi\)
−0.161521 + 0.986869i \(0.551640\pi\)
\(3\) −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
\(8\) 3.00000i 1.06066i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) −1.86603 1.23205i −0.590089 0.389609i
\(11\) 3.00000 + 5.19615i 0.904534 + 1.56670i 0.821541 + 0.570149i \(0.193114\pi\)
0.0829925 + 0.996550i \(0.473552\pi\)
\(12\) 0.866025 + 0.500000i 0.250000 + 0.144338i
\(13\) 2.00000i 0.554700i 0.960769 + 0.277350i \(0.0894562\pi\)
−0.960769 + 0.277350i \(0.910544\pi\)
\(14\) 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 \(0.408286\pi\)
−0.972404 + 0.233301i \(0.925047\pi\)
\(20\) 1.00000 + 2.00000i 0.223607 + 0.447214i
\(21\) 0 0
\(22\) 6.00000i 1.27920i
\(23\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) 1.50000 + 2.59808i 0.306186 + 0.530330i
\(25\) 4.96410 + 0.598076i 0.992820 + 0.119615i
\(26\) −1.00000 + 1.73205i −0.196116 + 0.339683i
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 2.23205 + 0.133975i 0.407515 + 0.0244603i
\(31\) 5.00000 + 8.66025i 0.898027 + 1.55543i 0.830014 + 0.557743i \(0.188333\pi\)
0.0680129 + 0.997684i \(0.478334\pi\)
\(32\) −4.33013 + 2.50000i −0.765466 + 0.441942i
\(33\) −5.19615 3.00000i −0.904534 0.522233i
\(34\) 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
\(39\) −1.00000 1.73205i −0.160128 0.277350i
\(40\) −0.401924 + 6.69615i −0.0635497 + 1.05875i
\(41\) 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 \(0.901344\pi\)
\(44\) 3.00000 5.19615i 0.452267 0.783349i
\(45\) −1.23205 + 1.86603i −0.183663 + 0.278171i
\(46\) 0 0
\(47\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(48\) 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
\(52\) 1.73205 1.00000i 0.240192 0.138675i
\(53\) −5.19615 + 3.00000i −0.713746 + 0.412082i −0.812447 0.583036i \(-0.801865\pi\)
0.0987002 + 0.995117i \(0.468532\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) −6.00000 12.0000i −0.809040 1.61808i
\(56\) 0 0
\(57\) 6.00000i 0.794719i
\(58\) 1.73205 + 1.00000i 0.227429 + 0.131306i
\(59\) −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
\(61\) 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i \(-0.792466\pi\)
0.922916 + 0.385002i \(0.125799\pi\)
\(62\) 10.0000i 1.27000i
\(63\) 0 0
\(64\) −7.00000 −0.875000
\(65\) 0.267949 4.46410i 0.0332350 0.553704i
\(66\) −3.00000 5.19615i −0.369274 0.639602i
\(67\) −13.8564 + 8.00000i −1.69283 + 0.977356i −0.740613 + 0.671932i \(0.765465\pi\)
−0.952217 + 0.305424i \(0.901202\pi\)
\(68\) −3.46410 2.00000i −0.420084 0.242536i
\(69\) 0 0
\(70\) 0 0
\(71\) 10.0000 1.18678 0.593391 0.804914i \(-0.297789\pi\)
0.593391 + 0.804914i \(0.297789\pi\)
\(72\) −2.59808 1.50000i −0.306186 0.176777i
\(73\) 5.19615 3.00000i 0.608164 0.351123i −0.164083 0.986447i \(-0.552466\pi\)
0.772246 + 0.635323i \(0.219133\pi\)
\(74\) 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
\(78\) 2.00000i 0.226455i
\(79\) 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i \(-0.761089\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) −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
\(87\) −1.73205 + 1.00000i −0.185695 + 0.107211i
\(88\) 15.5885 9.00000i 1.66174 0.959403i
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) −2.00000 + 1.00000i −0.210819 + 0.105409i
\(91\) 0 0
\(92\) 0 0
\(93\) −8.66025 5.00000i −0.898027 0.518476i
\(94\) 0 0
\(95\) 7.39230 11.1962i 0.758434 1.14870i
\(96\) 2.50000 4.33013i 0.255155 0.441942i
\(97\) 2.00000i 0.203069i −0.994832 0.101535i \(-0.967625\pi\)
0.994832 0.101535i \(-0.0323753\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) −1.96410 4.59808i −0.196410 0.459808i
\(101\) 3.00000 + 5.19615i 0.298511 + 0.517036i 0.975796 0.218685i \(-0.0701767\pi\)
−0.677284 + 0.735721i \(0.736843\pi\)
\(102\) −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
\(107\) −3.46410 2.00000i −0.334887 0.193347i 0.323122 0.946357i \(-0.395268\pi\)
−0.658009 + 0.753010i \(0.728601\pi\)
\(108\) 0.866025 0.500000i 0.0833333 0.0481125i
\(109\) 1.00000 + 1.73205i 0.0957826 + 0.165900i 0.909935 0.414751i \(-0.136131\pi\)
−0.814152 + 0.580651i \(0.802798\pi\)
\(110\) 0.803848 13.3923i 0.0766439 1.27691i
\(111\) −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
\(115\) 0 0
\(116\) −1.00000 1.73205i −0.0928477 0.160817i
\(117\) 1.73205 + 1.00000i 0.160128 + 0.0924500i
\(118\) 8.00000i 0.736460i
\(119\) 0 0
\(120\) −3.00000 6.00000i −0.273861 0.547723i
\(121\) −12.5000 + 21.6506i −1.13636 + 1.96824i
\(122\) 1.73205 1.00000i 0.156813 0.0905357i
\(123\) −1.73205 + 1.00000i −0.156174 + 0.0901670i
\(124\) 5.00000 8.66025i 0.449013 0.777714i
\(125\) −11.0000 2.00000i −0.983870 0.178885i
\(126\) 0 0
\(127\) 20.0000i 1.77471i 0.461084 + 0.887357i \(0.347461\pi\)
−0.461084 + 0.887357i \(0.652539\pi\)
\(128\) 2.59808 + 1.50000i 0.229640 + 0.132583i
\(129\) −2.00000 3.46410i −0.176090 0.304997i
\(130\) 2.46410 3.73205i 0.216116 0.327323i
\(131\) −2.00000 + 3.46410i −0.174741 + 0.302660i −0.940072 0.340977i \(-0.889242\pi\)
0.765331 + 0.643637i \(0.222575\pi\)
\(132\) 6.00000i 0.522233i
\(133\) 0 0
\(134\) −16.0000 −1.38219
\(135\) 0.133975 2.23205i 0.0115307 0.192104i
\(136\) −6.00000 10.3923i −0.514496 0.891133i
\(137\) −5.19615 + 3.00000i −0.443937 + 0.256307i −0.705266 0.708942i \(-0.749173\pi\)
0.261329 + 0.965250i \(0.415839\pi\)
\(138\) 0 0
\(139\) −2.00000 −0.169638 −0.0848189 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 8.66025 + 5.00000i 0.726752 + 0.419591i
\(143\) −10.3923 + 6.00000i −0.869048 + 0.501745i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −4.46410 0.267949i −0.370723 0.0222520i
\(146\) 6.00000 0.496564
\(147\) 0 0
\(148\) 4.00000i 0.328798i
\(149\) −7.00000 + 12.1244i −0.573462 + 0.993266i 0.422744 + 0.906249i \(0.361067\pi\)
−0.996207 + 0.0870170i \(0.972267\pi\)
\(150\) −4.96410 0.598076i −0.405317 0.0488327i
\(151\) −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i \(-0.272204\pi\)
−0.981617 + 0.190864i \(0.938871\pi\)
\(152\) 15.5885 + 9.00000i 1.26439 + 0.729996i
\(153\) 4.00000i 0.323381i
\(154\) 0 0
\(155\) −10.0000 20.0000i −0.803219 1.60644i
\(156\) −1.00000 + 1.73205i −0.0800641 + 0.138675i
\(157\) 15.5885 9.00000i 1.24409 0.718278i 0.274169 0.961681i \(-0.411597\pi\)
0.969925 + 0.243403i \(0.0782638\pi\)
\(158\) 3.46410 2.00000i 0.275589 0.159111i
\(159\) 3.00000 5.19615i 0.237915 0.412082i
\(160\) 10.0000 5.00000i 0.790569 0.395285i
\(161\) 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
\(165\) 11.1962 + 7.39230i 0.871619 + 0.575490i
\(166\) 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
\(169\) 9.00000 0.692308
\(170\) −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
\(173\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(174\) −2.00000 −0.151620
\(175\) 0 0
\(176\) 6.00000 0.452267
\(177\) 6.92820 + 4.00000i 0.520756 + 0.300658i
\(178\) 5.19615 3.00000i 0.389468 0.224860i
\(179\) −7.00000 12.1244i −0.523205 0.906217i −0.999635 0.0270049i \(-0.991403\pi\)
0.476431 0.879212i \(-0.341930\pi\)
\(180\) 2.23205 + 0.133975i 0.166367 + 0.00998588i
\(181\) −6.00000 −0.445976 −0.222988 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) 0 0
\(183\) 2.00000i 0.147844i
\(184\) 0 0
\(185\) −7.46410 4.92820i −0.548772 0.362329i
\(186\) −5.00000 8.66025i −0.366618 0.635001i
\(187\) 20.7846 + 12.0000i 1.51992 + 0.877527i
\(188\) 0 0
\(189\) 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 \(-0.0590746\pi\)
\(192\) 6.06218 3.50000i 0.437500 0.252591i
\(193\) 6.92820 4.00000i 0.498703 0.287926i −0.229475 0.973315i \(-0.573701\pi\)
0.728178 + 0.685388i \(0.240368\pi\)
\(194\) 1.00000 1.73205i 0.0717958 0.124354i
\(195\) 2.00000 + 4.00000i 0.143223 + 0.286446i
\(196\) 0 0
\(197\) 2.00000i 0.142494i 0.997459 + 0.0712470i \(0.0226979\pi\)
−0.997459 + 0.0712470i \(0.977302\pi\)
\(198\) 5.19615 + 3.00000i 0.369274 + 0.213201i
\(199\) 7.00000 + 12.1244i 0.496217 + 0.859473i 0.999990 0.00436292i \(-0.00138876\pi\)
−0.503774 + 0.863836i \(0.668055\pi\)
\(200\) 1.79423 14.8923i 0.126871 1.05304i
\(201\) 8.00000 13.8564i 0.564276 0.977356i
\(202\) 6.00000i 0.422159i
\(203\) 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
\(207\) 0 0
\(208\) 1.73205 + 1.00000i 0.120096 + 0.0693375i
\(209\) −36.0000 −2.49017
\(210\) 0 0
\(211\) −16.0000 −1.10149 −0.550743 0.834675i \(-0.685655\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) 5.19615 + 3.00000i 0.356873 + 0.206041i
\(213\) −8.66025 + 5.00000i −0.593391 + 0.342594i
\(214\) −2.00000 3.46410i −0.136717 0.236801i
\(215\) 0.535898 8.92820i 0.0365480 0.608898i
\(216\) 3.00000 0.204124
\(217\) 0 0
\(218\) 2.00000i 0.135457i
\(219\) −3.00000 + 5.19615i −0.202721 + 0.351123i
\(220\) −7.39230 + 11.1962i −0.498389 + 0.754844i
\(221\) 4.00000 + 6.92820i 0.269069 + 0.466041i
\(222\) −3.46410 2.00000i −0.232495 0.134231i
\(223\) 24.0000i 1.60716i 0.595198 + 0.803579i \(0.297074\pi\)
−0.595198 + 0.803579i \(0.702926\pi\)
\(224\) 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
\(229\) −5.00000 + 8.66025i −0.330409 + 0.572286i −0.982592 0.185776i \(-0.940520\pi\)
0.652183 + 0.758062i \(0.273853\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 6.00000i 0.393919i
\(233\) −22.5167 13.0000i −1.47512 0.851658i −0.475509 0.879711i \(-0.657736\pi\)
−0.999606 + 0.0280525i \(0.991069\pi\)
\(234\) 1.00000 + 1.73205i 0.0653720 + 0.113228i
\(235\) 0 0
\(236\) −4.00000 + 6.92820i −0.260378 + 0.450988i
\(237\) 4.00000i 0.259828i
\(238\) 0 0
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 0.133975 2.23205i 0.00864802 0.144078i
\(241\) −11.0000 19.0526i −0.708572 1.22728i −0.965387 0.260822i \(-0.916006\pi\)
0.256814 0.966461i \(-0.417327\pi\)
\(242\) −21.6506 + 12.5000i −1.39176 + 0.803530i
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) −2.00000 −0.128037
\(245\) 0 0
\(246\) −2.00000 −0.127515
\(247\) −10.3923 6.00000i −0.661247 0.381771i
\(248\) 25.9808 15.0000i 1.64978 0.952501i
\(249\) 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
\(253\) 0 0
\(254\) −10.0000 + 17.3205i −0.627456 + 1.08679i
\(255\) 4.92820 7.46410i 0.308616 0.467420i
\(256\) 8.50000 + 14.7224i 0.531250 + 0.920152i
\(257\) −13.8564 8.00000i −0.864339 0.499026i 0.00112398 0.999999i \(-0.499642\pi\)
−0.865463 + 0.500973i \(0.832976\pi\)
\(258\) 4.00000i 0.249029i
\(259\) 0 0
\(260\) −4.00000 + 2.00000i −0.248069 + 0.124035i
\(261\) 1.00000 1.73205i 0.0618984 0.107211i
\(262\) −3.46410 + 2.00000i −0.214013 + 0.123560i
\(263\) 20.7846 12.0000i 1.28163 0.739952i 0.304487 0.952517i \(-0.401515\pi\)
0.977147 + 0.212565i \(0.0681817\pi\)
\(264\) −9.00000 + 15.5885i −0.553912 + 0.959403i
\(265\) 12.0000 6.00000i 0.737154 0.368577i
\(266\) 0 0
\(267\) 6.00000i 0.367194i
\(268\) 13.8564 + 8.00000i 0.846415 + 0.488678i
\(269\) −7.00000 12.1244i −0.426798 0.739235i 0.569789 0.821791i \(-0.307025\pi\)
−0.996586 + 0.0825561i \(0.973692\pi\)
\(270\) 1.23205 1.86603i 0.0749802 0.113563i
\(271\) 7.00000 12.1244i 0.425220 0.736502i −0.571221 0.820796i \(-0.693530\pi\)
0.996441 + 0.0842940i \(0.0268635\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) 11.7846 + 27.5885i 0.710639 + 1.66365i
\(276\) 0 0
\(277\) −24.2487 + 14.0000i −1.45696 + 0.841178i −0.998861 0.0477206i \(-0.984804\pi\)
−0.458103 + 0.888899i \(0.651471\pi\)
\(278\) −1.73205 1.00000i −0.103882 0.0599760i
\(279\) 10.0000 0.598684
\(280\) 0 0
\(281\) −2.00000 −0.119310 −0.0596550 0.998219i \(-0.519000\pi\)
−0.0596550 + 0.998219i \(0.519000\pi\)
\(282\) 0 0
\(283\) −17.3205 + 10.0000i −1.02960 + 0.594438i −0.916869 0.399188i \(-0.869292\pi\)
−0.112728 + 0.993626i \(0.535959\pi\)
\(284\) −5.00000 8.66025i −0.296695 0.513892i
\(285\) −0.803848 + 13.3923i −0.0476158 + 0.793292i
\(286\) −12.0000 −0.709575
\(287\) 0 0
\(288\) 5.00000i 0.294628i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) −3.73205 2.46410i −0.219154 0.144697i
\(291\) 1.00000 + 1.73205i 0.0586210 + 0.101535i
\(292\) −5.19615 3.00000i −0.304082 0.175562i
\(293\) 24.0000i 1.40209i −0.713115 0.701047i \(-0.752716\pi\)
0.713115 0.701047i \(-0.247284\pi\)
\(294\) 0 0
\(295\) 8.00000 + 16.0000i 0.465778 + 0.931556i
\(296\) 6.00000 10.3923i 0.348743 0.604040i
\(297\) −5.19615 + 3.00000i −0.301511 + 0.174078i
\(298\) −12.1244 + 7.00000i −0.702345 + 0.405499i
\(299\) 0 0
\(300\) 4.00000 + 3.00000i 0.230940 + 0.173205i
\(301\) 0 0
\(302\) 8.00000i 0.460348i
\(303\) −5.19615 3.00000i −0.298511 0.172345i
\(304\) 3.00000 + 5.19615i 0.172062 + 0.298020i
\(305\) −2.46410 + 3.73205i −0.141094 + 0.213697i
\(306\) 2.00000 3.46410i 0.114332 0.198030i
\(307\) 4.00000i 0.228292i 0.993464 + 0.114146i \(0.0364132\pi\)
−0.993464 + 0.114146i \(0.963587\pi\)
\(308\) 0 0
\(309\) −8.00000 −0.455104
\(310\) 1.33975 22.3205i 0.0760925 1.26772i
\(311\) 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
\(313\) 5.19615 + 3.00000i 0.293704 + 0.169570i 0.639611 0.768699i \(-0.279095\pi\)
−0.345907 + 0.938269i \(0.612429\pi\)
\(314\) 18.0000 1.01580
\(315\) 0 0
\(316\) −4.00000 −0.225018
\(317\) 15.5885 + 9.00000i 0.875535 + 0.505490i 0.869184 0.494489i \(-0.164645\pi\)
0.00635137 + 0.999980i \(0.497978\pi\)
\(318\) 5.19615 3.00000i 0.291386 0.168232i
\(319\) 6.00000 + 10.3923i 0.335936 + 0.581857i
\(320\) 15.6244 + 0.937822i 0.873428 + 0.0524259i
\(321\) 4.00000 0.223258
\(322\) 0 0
\(323\) 24.0000i 1.33540i
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −1.19615 + 9.92820i −0.0663506 + 0.550718i
\(326\) 2.00000 + 3.46410i 0.110770 + 0.191859i
\(327\) −1.73205 1.00000i −0.0957826 0.0553001i
\(328\) 6.00000i 0.331295i
\(329\) 0 0
\(330\) 6.00000 + 12.0000i 0.330289 + 0.660578i
\(331\) 12.0000 20.7846i 0.659580 1.14243i −0.321145 0.947030i \(-0.604068\pi\)
0.980725 0.195395i \(-0.0625990\pi\)
\(332\) −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
\(335\) 32.0000 16.0000i 1.74835 0.874173i
\(336\) 0 0
\(337\) 24.0000i 1.30736i −0.756770 0.653682i \(-0.773224\pi\)
0.756770 0.653682i \(-0.226776\pi\)
\(338\) 7.79423 + 4.50000i 0.423950 + 0.244768i
\(339\) 3.00000 + 5.19615i 0.162938 + 0.282216i
\(340\) 7.46410 + 4.92820i 0.404798 + 0.267269i
\(341\) −30.0000 + 51.9615i −1.62459 + 2.81387i
\(342\) 6.00000i 0.324443i
\(343\) 0 0
\(344\) 12.0000 0.646997
\(345\) 0 0
\(346\) 0 0
\(347\) 10.3923 6.00000i 0.557888 0.322097i −0.194409 0.980921i \(-0.562279\pi\)
0.752297 + 0.658824i \(0.228946\pi\)
\(348\) 1.73205 + 1.00000i 0.0928477 + 0.0536056i
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 0 0
\(351\) −2.00000 −0.106752
\(352\) −25.9808 15.0000i −1.38478 0.799503i
\(353\) −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
\(355\) −22.3205 1.33975i −1.18465 0.0711063i
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) 14.0000i 0.739923i
\(359\) 11.0000 19.0526i 0.580558 1.00556i −0.414855 0.909887i \(-0.636168\pi\)
0.995413 0.0956683i \(-0.0304988\pi\)
\(360\) 5.59808 + 3.69615i 0.295045 + 0.194804i
\(361\) −8.50000 14.7224i −0.447368 0.774865i
\(362\) −5.19615 3.00000i −0.273104 0.157676i
\(363\) 25.0000i 1.31216i
\(364\) 0 0
\(365\) −12.0000 + 6.00000i −0.628109 + 0.314054i
\(366\) −1.00000 + 1.73205i −0.0522708 + 0.0905357i
\(367\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(368\) 0 0
\(369\) 1.00000 1.73205i 0.0520579 0.0901670i
\(370\) −4.00000 8.00000i −0.207950 0.415900i
\(371\) 0 0
\(372\) 10.0000i 0.518476i
\(373\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) 12.0000 + 20.7846i 0.620505 + 1.07475i
\(375\) 10.5263 3.76795i 0.543575 0.194576i
\(376\) 0 0
\(377\) 4.00000i 0.206010i
\(378\) 0 0
\(379\) 28.0000 1.43826 0.719132 0.694874i \(-0.244540\pi\)
0.719132 + 0.694874i \(0.244540\pi\)
\(380\) −13.3923 0.803848i −0.687011 0.0412365i
\(381\) −10.0000 17.3205i −0.512316 0.887357i
\(382\) 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 \(0.837383\pi\)
\(384\) −3.00000 −0.153093
\(385\) 0 0
\(386\) 8.00000 0.407189
\(387\) 3.46410 + 2.00000i 0.176090 + 0.101666i
\(388\) −1.73205 + 1.00000i −0.0879316 + 0.0507673i
\(389\) 13.0000 + 22.5167i 0.659126 + 1.14164i 0.980842 + 0.194804i \(0.0624070\pi\)
−0.321716 + 0.946836i \(0.604260\pi\)
\(390\) −0.267949 + 4.46410i −0.0135681 + 0.226049i
\(391\) 0 0
\(392\) 0 0
\(393\) 4.00000i 0.201773i
\(394\) −1.00000 + 1.73205i −0.0503793 + 0.0872595i
\(395\) −4.92820 + 7.46410i −0.247965 + 0.375560i
\(396\) −3.00000 5.19615i −0.150756 0.261116i
\(397\) −19.0526 11.0000i −0.956221 0.552074i −0.0612128 0.998125i \(-0.519497\pi\)
−0.895008 + 0.446051i \(0.852830\pi\)
\(398\) 14.0000i 0.701757i
\(399\) 0 0
\(400\) 3.00000 4.00000i 0.150000 0.200000i
\(401\) 15.0000 25.9808i 0.749064 1.29742i −0.199207 0.979957i \(-0.563837\pi\)
0.948272 0.317460i \(-0.102830\pi\)
\(402\) 13.8564 8.00000i 0.691095 0.399004i
\(403\) −17.3205 + 10.0000i −0.862796 + 0.498135i
\(404\) 3.00000 5.19615i 0.149256 0.258518i
\(405\) 1.00000 + 2.00000i 0.0496904 + 0.0993808i
\(406\) 0 0
\(407\) 24.0000i 1.18964i
\(408\) 10.3923 + 6.00000i 0.514496 + 0.297044i
\(409\) −11.0000 19.0526i −0.543915 0.942088i −0.998674 0.0514740i \(-0.983608\pi\)
0.454759 0.890614i \(-0.349725\pi\)
\(410\) −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
\(414\) 0 0
\(415\) −1.07180 + 17.8564i −0.0526124 + 0.876537i
\(416\) −5.00000 8.66025i −0.245145 0.424604i
\(417\) 1.73205 1.00000i 0.0848189 0.0489702i
\(418\) −31.1769 18.0000i −1.52491 0.880409i
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) 18.0000 0.877266 0.438633 0.898666i \(-0.355463\pi\)
0.438633 + 0.898666i \(0.355463\pi\)
\(422\) −13.8564 8.00000i −0.674519 0.389434i
\(423\) 0 0
\(424\) 9.00000 + 15.5885i 0.437079 + 0.757042i
\(425\) 18.3923 7.85641i 0.892158 0.381092i
\(426\) −10.0000 −0.484502
\(427\) 0 0
\(428\) 4.00000i 0.193347i
\(429\) 6.00000 10.3923i 0.289683 0.501745i
\(430\) 4.92820 7.46410i 0.237659 0.359951i
\(431\) 7.00000 + 12.1244i 0.337178 + 0.584010i 0.983901 0.178716i \(-0.0571942\pi\)
−0.646723 + 0.762725i \(0.723861\pi\)
\(432\) 0.866025 + 0.500000i 0.0416667 + 0.0240563i
\(433\) 34.0000i 1.63394i 0.576683 + 0.816968i \(0.304347\pi\)
−0.576683 + 0.816968i \(0.695653\pi\)
\(434\) 0 0
\(435\) 4.00000 2.00000i 0.191785 0.0958927i
\(436\) 1.00000 1.73205i 0.0478913 0.0829502i
\(437\) 0 0
\(438\) −5.19615 + 3.00000i −0.248282 + 0.143346i
\(439\) 3.00000 5.19615i 0.143182 0.247999i −0.785511 0.618848i \(-0.787600\pi\)
0.928693 + 0.370849i \(0.120933\pi\)
\(440\) −36.0000 + 18.0000i −1.71623 + 0.858116i
\(441\) 0 0
\(442\) 8.00000i 0.380521i
\(443\) −3.46410 2.00000i −0.164584 0.0950229i 0.415445 0.909618i \(-0.363626\pi\)
−0.580030 + 0.814595i \(0.696959\pi\)
\(444\) 2.00000 + 3.46410i 0.0949158 + 0.164399i
\(445\) −7.39230 + 11.1962i −0.350429 + 0.530749i
\(446\) −12.0000 + 20.7846i −0.568216 + 0.984180i
\(447\) 14.0000i 0.662177i
\(448\) 0 0
\(449\) −10.0000 −0.471929 −0.235965 0.971762i \(-0.575825\pi\)
−0.235965 + 0.971762i \(0.575825\pi\)
\(450\) 4.59808 1.96410i 0.216755 0.0925886i
\(451\) 6.00000 + 10.3923i 0.282529 + 0.489355i
\(452\) −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
\(456\) −18.0000 −0.842927
\(457\) 17.3205 + 10.0000i 0.810219 + 0.467780i 0.847032 0.531542i \(-0.178387\pi\)
−0.0368128 + 0.999322i \(0.511721\pi\)
\(458\) −8.66025 + 5.00000i −0.404667 + 0.233635i
\(459\) 2.00000 + 3.46410i 0.0933520 + 0.161690i
\(460\) 0 0
\(461\) 30.0000 1.39724 0.698620 0.715493i \(-0.253798\pi\)
0.698620 + 0.715493i \(0.253798\pi\)
\(462\) 0 0
\(463\) 36.0000i 1.67306i −0.547920 0.836531i \(-0.684580\pi\)
0.547920 0.836531i \(-0.315420\pi\)
\(464\) 1.00000 1.73205i 0.0464238 0.0804084i
\(465\) 18.6603 + 12.3205i 0.865349 + 0.571350i
\(466\) −13.0000 22.5167i −0.602213 1.04306i
\(467\) 20.7846 + 12.0000i 0.961797 + 0.555294i 0.896726 0.442587i \(-0.145939\pi\)
0.0650714 + 0.997881i \(0.479272\pi\)
\(468\) 2.00000i 0.0924500i
\(469\) 0 0
\(470\) 0 0
\(471\) −9.00000 + 15.5885i −0.414698 + 0.718278i
\(472\) −20.7846 + 12.0000i −0.956689 + 0.552345i
\(473\) −20.7846 + 12.0000i −0.955677 + 0.551761i
\(474\) −2.00000 + 3.46410i −0.0918630 + 0.159111i
\(475\) −18.0000 + 24.0000i −0.825897 + 1.10120i
\(476\) 0 0
\(477\) 6.00000i 0.274721i
\(478\) 5.19615 + 3.00000i 0.237666 + 0.137217i
\(479\) 12.0000 + 20.7846i 0.548294 + 0.949673i 0.998392 + 0.0566937i \(0.0180558\pi\)
−0.450098 + 0.892979i \(0.648611\pi\)
\(480\) −6.16025 + 9.33013i −0.281176 + 0.425860i
\(481\) −4.00000 + 6.92820i −0.182384 + 0.315899i
\(482\) 22.0000i 1.00207i
\(483\) 0 0
\(484\) 25.0000 1.13636
\(485\) −0.267949 + 4.46410i −0.0121669 + 0.202704i
\(486\) 0.500000 + 0.866025i 0.0226805 + 0.0392837i
\(487\) 10.3923 6.00000i 0.470920 0.271886i −0.245705 0.969345i \(-0.579019\pi\)
0.716625 + 0.697459i \(0.245686\pi\)
\(488\) −5.19615 3.00000i −0.235219 0.135804i
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) 10.0000 0.451294 0.225647 0.974209i \(-0.427550\pi\)
0.225647 + 0.974209i \(0.427550\pi\)
\(492\) 1.73205 + 1.00000i 0.0780869 + 0.0450835i
\(493\) 6.92820 4.00000i 0.312031 0.180151i
\(494\) −6.00000 10.3923i −0.269953 0.467572i
\(495\) −13.3923 0.803848i −0.601939 0.0361303i
\(496\) 10.0000 0.449013
\(497\) 0 0
\(498\) 8.00000i 0.358489i
\(499\) 2.00000 3.46410i 0.0895323 0.155074i −0.817781 0.575529i \(-0.804796\pi\)
0.907314 + 0.420455i \(0.138129\pi\)
\(500\) 3.76795 + 10.5263i 0.168508 + 0.470750i
\(501\) −6.00000 10.3923i −0.268060 0.464294i
\(502\) 0 0
\(503\) 36.0000i 1.60516i 0.596544 + 0.802580i \(0.296540\pi\)
−0.596544 + 0.802580i \(0.703460\pi\)
\(504\) 0 0
\(505\) −6.00000 12.0000i −0.266996 0.533993i
\(506\) 0 0
\(507\) −7.79423 + 4.50000i −0.346154 + 0.199852i
\(508\) 17.3205 10.0000i 0.768473 0.443678i
\(509\) 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
\(512\) 11.0000i 0.486136i
\(513\) −5.19615 3.00000i −0.229416 0.132453i
\(514\) −8.00000 13.8564i −0.352865 0.611180i
\(515\) −14.9282 9.85641i −0.657815 0.434325i
\(516\) −2.00000 + 3.46410i −0.0880451 + 0.152499i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) −13.3923 0.803848i −0.587291 0.0352510i
\(521\) −19.0000 32.9090i −0.832405 1.44177i −0.896126 0.443800i \(-0.853630\pi\)
0.0637207 0.997968i \(-0.479703\pi\)
\(522\) 1.73205 1.00000i 0.0758098 0.0437688i
\(523\) 17.3205 + 10.0000i 0.757373 + 0.437269i 0.828352 0.560208i \(-0.189279\pi\)
−0.0709788 + 0.997478i \(0.522612\pi\)
\(524\) 4.00000 0.174741
\(525\) 0 0
\(526\) 24.0000 1.04645
\(527\) 34.6410 + 20.0000i 1.50899 + 0.871214i
\(528\) −5.19615 + 3.00000i −0.226134 + 0.130558i
\(529\) −11.5000 19.9186i −0.500000 0.866025i
\(530\) 13.3923 + 0.803848i 0.581725 + 0.0349169i
\(531\) −8.00000 −0.347170
\(532\) 0 0
\(533\) 4.00000i 0.173259i
\(534\) −3.00000 + 5.19615i −0.129823 + 0.224860i
\(535\) 7.46410 + 4.92820i 0.322701 + 0.213065i
\(536\) 24.0000 + 41.5692i 1.03664 + 1.79552i
\(537\) 12.1244 + 7.00000i 0.523205 + 0.302072i
\(538\) 14.0000i 0.603583i
\(539\) 0 0
\(540\) −2.00000 + 1.00000i −0.0860663 + 0.0430331i
\(541\) −3.00000 + 5.19615i −0.128980 + 0.223400i −0.923282 0.384124i \(-0.874504\pi\)
0.794302 + 0.607524i \(0.207837\pi\)
\(542\) 12.1244 7.00000i 0.520786 0.300676i
\(543\) 5.19615 3.00000i 0.222988 0.128742i
\(544\) −10.0000 + 17.3205i −0.428746 + 0.742611i
\(545\) −2.00000 4.00000i −0.0856706 0.171341i
\(546\) 0 0
\(547\) 16.0000i 0.684111i −0.939680 0.342055i \(-0.888877\pi\)
0.939680 0.342055i \(-0.111123\pi\)
\(548\) 5.19615 + 3.00000i 0.221969 + 0.128154i
\(549\) −1.00000 1.73205i −0.0426790 0.0739221i
\(550\) −3.58846 + 29.7846i −0.153012 + 1.27002i
\(551\) −6.00000 + 10.3923i −0.255609 + 0.442727i
\(552\) 0 0
\(553\) 0 0
\(554\) −28.0000 −1.18961
\(555\) 8.92820 + 0.535898i 0.378981 + 0.0227476i
\(556\) 1.00000 + 1.73205i 0.0424094 + 0.0734553i
\(557\) 32.9090 19.0000i 1.39440 0.805056i 0.400599 0.916253i \(-0.368802\pi\)
0.993798 + 0.111198i \(0.0354686\pi\)
\(558\) 8.66025 + 5.00000i 0.366618 + 0.211667i
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) −24.0000 −1.01328
\(562\) −1.73205 1.00000i −0.0730622 0.0421825i
\(563\) 31.1769 18.0000i 1.31395 0.758610i 0.331202 0.943560i \(-0.392546\pi\)
0.982748 + 0.184950i \(0.0592124\pi\)
\(564\) 0 0
\(565\) −0.803848 + 13.3923i −0.0338181 + 0.563418i
\(566\) −20.0000 −0.840663
\(567\) 0 0
\(568\) 30.0000i 1.25877i
\(569\) −15.0000 + 25.9808i −0.628833 + 1.08917i 0.358954 + 0.933355i \(0.383134\pi\)
−0.987786 + 0.155815i \(0.950200\pi\)
\(570\) −7.39230 + 11.1962i −0.309630 + 0.468955i
\(571\) −18.0000 31.1769i −0.753277 1.30471i −0.946227 0.323505i \(-0.895139\pi\)
0.192950 0.981209i \(-0.438194\pi\)
\(572\) 10.3923 + 6.00000i 0.434524 + 0.250873i
\(573\) 18.0000i 0.751961i
\(574\) 0 0
\(575\) 0 0
\(576\) −3.50000 + 6.06218i −0.145833 + 0.252591i
\(577\) 12.1244 7.00000i 0.504744 0.291414i −0.225927 0.974144i \(-0.572541\pi\)
0.730670 + 0.682730i \(0.239208\pi\)
\(578\) −0.866025 + 0.500000i −0.0360219 + 0.0207973i
\(579\) −4.00000 + 6.92820i −0.166234 + 0.287926i
\(580\) 2.00000 + 4.00000i 0.0830455 + 0.166091i
\(581\) 0 0
\(582\) 2.00000i 0.0829027i
\(583\) −31.1769 18.0000i −1.29122 0.745484i
\(584\) −9.00000 15.5885i −0.372423 0.645055i
\(585\) −3.73205 2.46410i −0.154301 0.101878i
\(586\) 12.0000 20.7846i 0.495715 0.858604i
\(587\) 12.0000i 0.495293i −0.968850 0.247647i \(-0.920343\pi\)
0.968850 0.247647i \(-0.0796572\pi\)
\(588\) 0 0
\(589\) −60.0000 −2.47226
\(590\) −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
\(593\) 38.1051 + 22.0000i 1.56479 + 0.903432i 0.996761 + 0.0804231i \(0.0256271\pi\)
0.568029 + 0.823009i \(0.307706\pi\)
\(594\) −6.00000 −0.246183
\(595\) 0 0
\(596\) 14.0000 0.573462
\(597\) −12.1244 7.00000i −0.496217 0.286491i
\(598\) 0 0
\(599\) −1.00000 1.73205i −0.0408589 0.0707697i 0.844873 0.534967i \(-0.179676\pi\)
−0.885732 + 0.464198i \(0.846343\pi\)
\(600\) 5.89230 + 13.7942i 0.240552 + 0.563147i
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 0 0
\(603\) 16.0000i 0.651570i
\(604\) −4.00000 + 6.92820i −0.162758 + 0.281905i
\(605\) 30.8013 46.6506i 1.25225 1.89662i
\(606\) −3.00000 5.19615i −0.121867 0.211079i
\(607\) −20.7846 12.0000i −0.843621 0.487065i 0.0148722 0.999889i \(-0.495266\pi\)
−0.858494 + 0.512824i \(0.828599\pi\)
\(608\) 30.0000i 1.21666i
\(609\) 0 0
\(610\) −4.00000 + 2.00000i −0.161955 + 0.0809776i
\(611\) 0 0
\(612\) −3.46410 + 2.00000i −0.140028 + 0.0808452i
\(613\) −3.46410 + 2.00000i −0.139914 + 0.0807792i −0.568323 0.822806i \(-0.692408\pi\)
0.428409 + 0.903585i \(0.359074\pi\)
\(614\) −2.00000 + 3.46410i −0.0807134 + 0.139800i
\(615\) 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
\(619\) 5.00000 + 8.66025i 0.200967 + 0.348085i 0.948840 0.315757i \(-0.102258\pi\)
−0.747873 + 0.663842i \(0.768925\pi\)
\(620\) −12.3205 + 18.6603i −0.494804 + 0.749414i
\(621\) 0 0
\(622\) 24.0000i 0.962312i
\(623\) 0 0
\(624\) −2.00000 −0.0800641
\(625\) 24.2846 + 5.93782i 0.971384 + 0.237513i
\(626\) 3.00000 + 5.19615i 0.119904 + 0.207680i
\(627\) 31.1769 18.0000i 1.24509 0.718851i
\(628\) −15.5885 9.00000i −0.622047 0.359139i
\(629\) 16.0000 0.637962
\(630\) 0 0
\(631\) −20.0000 −0.796187 −0.398094 0.917345i \(-0.630328\pi\)
−0.398094 + 0.917345i \(0.630328\pi\)
\(632\) −10.3923 6.00000i −0.413384 0.238667i
\(633\) 13.8564 8.00000i 0.550743 0.317971i
\(634\) 9.00000 + 15.5885i 0.357436 + 0.619097i
\(635\) 2.67949 44.6410i 0.106332 1.77152i
\(636\) −6.00000 −0.237915
\(637\) 0 0
\(638\) 12.0000i 0.475085i
\(639\) 5.00000 8.66025i 0.197797 0.342594i
\(640\) −5.59808 3.69615i −0.221283 0.146103i
\(641\) 1.00000 + 1.73205i 0.0394976 + 0.0684119i 0.885098 0.465404i \(-0.154091\pi\)
−0.845601 + 0.533816i \(0.820758\pi\)
\(642\) 3.46410 + 2.00000i 0.136717 + 0.0789337i
\(643\) 20.0000i 0.788723i 0.918955 + 0.394362i \(0.129034\pi\)
−0.918955 + 0.394362i \(0.870966\pi\)
\(644\) 0 0
\(645\) 4.00000 + 8.00000i 0.157500 + 0.315000i
\(646\) −12.0000 + 20.7846i −0.472134 + 0.817760i
\(647\) −17.3205 + 10.0000i −0.680939 + 0.393141i −0.800209 0.599721i \(-0.795278\pi\)
0.119269 + 0.992862i \(0.461945\pi\)
\(648\) −2.59808 + 1.50000i −0.102062 + 0.0589256i
\(649\) 24.0000 41.5692i 0.942082 1.63173i
\(650\) −6.00000 + 8.00000i −0.235339 + 0.313786i
\(651\) 0 0
\(652\) 4.00000i 0.156652i
\(653\) 1.73205 + 1.00000i 0.0677804 + 0.0391330i 0.533507 0.845796i \(-0.320874\pi\)
−0.465727 + 0.884929i \(0.654207\pi\)
\(654\) −1.00000 1.73205i −0.0391031 0.0677285i
\(655\) 4.92820 7.46410i 0.192561 0.291647i
\(656\) 1.00000 1.73205i 0.0390434 0.0676252i
\(657\) 6.00000i 0.234082i
\(658\) 0 0
\(659\) 18.0000 0.701180 0.350590 0.936529i \(-0.385981\pi\)
0.350590 + 0.936529i \(0.385981\pi\)
\(660\) 0.803848 13.3923i 0.0312897 0.521295i
\(661\) 9.00000 + 15.5885i 0.350059 + 0.606321i 0.986260 0.165203i \(-0.0528281\pi\)
−0.636200 + 0.771524i \(0.719495\pi\)
\(662\) 20.7846 12.0000i 0.807817 0.466393i
\(663\) −6.92820 4.00000i −0.269069 0.155347i
\(664\) −24.0000 −0.931381
\(665\) 0 0
\(666\) 4.00000 0.154997
\(667\) 0 0
\(668\) 10.3923 6.00000i 0.402090 0.232147i
\(669\) −12.0000 20.7846i −0.463947 0.803579i
\(670\) 35.7128 + 2.14359i 1.37971 + 0.0828142i
\(671\) 12.0000 0.463255
\(672\) 0 0
\(673\) 36.0000i 1.38770i 0.720121 + 0.693849i \(0.244086\pi\)
−0.720121 + 0.693849i \(0.755914\pi\)
\(674\) 12.0000 20.7846i 0.462223 0.800593i
\(675\) −0.598076 + 4.96410i −0.0230200 + 0.191068i
\(676\) −4.50000 7.79423i −0.173077 0.299778i
\(677\) −27.7128 16.0000i −1.06509 0.614930i −0.138254 0.990397i \(-0.544149\pi\)
−0.926836 + 0.375467i \(0.877482\pi\)
\(678\) 6.00000i 0.230429i
\(679\) 0 0
\(680\) 12.0000 + 24.0000i 0.460179 + 0.920358i
\(681\) −4.00000 + 6.92820i −0.153280 + 0.265489i
\(682\) −51.9615 + 30.0000i −1.98971 + 1.14876i
\(683\) −24.2487 + 14.0000i −0.927851 + 0.535695i −0.886131 0.463434i \(-0.846617\pi\)
−0.0417198 + 0.999129i \(0.513284\pi\)
\(684\) 3.00000 5.19615i 0.114708 0.198680i
\(685\) 12.0000 6.00000i 0.458496 0.229248i
\(686\) 0 0
\(687\) 10.0000i 0.381524i
\(688\) 3.46410 + 2.00000i 0.132068 + 0.0762493i
\(689\) −6.00000 10.3923i −0.228582 0.395915i
\(690\) 0 0
\(691\) 25.0000 43.3013i 0.951045 1.64726i 0.207875 0.978155i \(-0.433345\pi\)
0.743170 0.669102i \(-0.233321\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) 4.46410 + 0.267949i 0.169333 + 0.0101639i
\(696\) 3.00000 + 5.19615i 0.113715 + 0.196960i
\(697\) 6.92820 4.00000i 0.262424 0.151511i
\(698\) 1.73205 + 1.00000i 0.0655591 + 0.0378506i
\(699\) 26.0000 0.983410
\(700\) 0 0
\(701\) −10.0000 −0.377695 −0.188847 0.982006i \(-0.560475\pi\)
−0.188847 + 0.982006i \(0.560475\pi\)
\(702\) −1.73205 1.00000i −0.0653720 0.0377426i
\(703\) −20.7846 + 12.0000i −0.783906 + 0.452589i
\(704\) −21.0000 36.3731i −0.791467 1.37086i
\(705\) 0 0
\(706\) −20.0000 −0.752710
\(707\) 0 0
\(708\) 8.00000i 0.300658i
\(709\) 13.0000 22.5167i 0.488225 0.845631i −0.511683 0.859174i \(-0.670978\pi\)
0.999908 + 0.0135434i \(0.00431112\pi\)
\(710\) −18.6603 12.3205i −0.700307 0.462380i
\(711\) −2.00000 3.46410i −0.0750059 0.129914i
\(712\) −15.5885 9.00000i −0.584202 0.337289i
\(713\) 0 0
\(714\) 0 0
\(715\) 24.0000 12.0000i 0.897549 0.448775i
\(716\) −7.00000 + 12.1244i −0.261602 + 0.453108i
\(717\) −5.19615 + 3.00000i −0.194054 + 0.112037i
\(718\) 19.0526 11.0000i 0.711035 0.410516i
\(719\) 6.00000 10.3923i 0.223762 0.387568i −0.732185 0.681106i \(-0.761499\pi\)
0.955947 + 0.293538i \(0.0948328\pi\)
\(720\) 1.00000 + 2.00000i 0.0372678 + 0.0745356i
\(721\) 0 0
\(722\) 17.0000i 0.632674i
\(723\) 19.0526 + 11.0000i 0.708572 + 0.409094i
\(724\) 3.00000 + 5.19615i 0.111494 + 0.193113i
\(725\) 9.92820 + 1.19615i 0.368724 + 0.0444240i
\(726\) 12.5000 21.6506i 0.463919 0.803530i
\(727\) 40.0000i 1.48352i −0.670667 0.741759i \(-0.733992\pi\)
0.670667 0.741759i \(-0.266008\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) −13.3923 0.803848i −0.495671 0.0297517i
\(731\) 8.00000 + 13.8564i 0.295891 + 0.512498i
\(732\) 1.73205 1.00000i 0.0640184 0.0369611i
\(733\) 19.0526 + 11.0000i 0.703722 + 0.406294i 0.808732 0.588177i \(-0.200154\pi\)
−0.105010 + 0.994471i \(0.533487\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −83.1384 48.0000i −3.06244 1.76810i
\(738\) 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
\(741\) 12.0000 0.440831
\(742\) 0 0
\(743\) 40.0000i 1.46746i −0.679442 0.733729i \(-0.737778\pi\)
0.679442 0.733729i \(-0.262222\pi\)
\(744\) −15.0000 + 25.9808i −0.549927 + 0.952501i
\(745\) 17.2487 26.1244i 0.631944 0.957122i
\(746\) 0 0
\(747\) −6.92820 4.00000i −0.253490 0.146352i
\(748\) 24.0000i 0.877527i
\(749\) 0 0
\(750\) 11.0000 + 2.00000i 0.401663 + 0.0730297i
\(751\) 6.00000 10.3923i 0.218943 0.379221i −0.735542 0.677479i \(-0.763072\pi\)
0.954485 + 0.298259i \(0.0964058\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −2.00000 + 3.46410i −0.0728357 + 0.126155i
\(755\) 8.00000 + 16.0000i 0.291150 + 0.582300i
\(756\) 0 0
\(757\) 40.0000i 1.45382i −0.686730 0.726912i \(-0.740955\pi\)
0.686730 0.726912i \(-0.259045\pi\)
\(758\) 24.2487 + 14.0000i 0.880753 + 0.508503i
\(759\) 0 0
\(760\) −33.5885 22.1769i −1.21838 0.804441i
\(761\) 11.0000 19.0526i 0.398750 0.690655i −0.594822 0.803857i \(-0.702778\pi\)
0.993572 + 0.113203i \(0.0361109\pi\)
\(762\) 20.0000i 0.724524i
\(763\) 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
\(767\) 13.8564 8.00000i 0.500326 0.288863i
\(768\) −14.7224 8.50000i −0.531250 0.306717i
\(769\) 18.0000 0.649097 0.324548 0.945869i \(-0.394788\pi\)
0.324548 + 0.945869i \(0.394788\pi\)
\(770\) 0 0
\(771\) 16.0000 0.576226
\(772\) −6.92820 4.00000i −0.249351 0.143963i
\(773\) −20.7846 + 12.0000i −0.747570 + 0.431610i −0.824815 0.565402i \(-0.808721\pi\)
0.0772449 + 0.997012i \(0.475388\pi\)
\(774\) 2.00000 + 3.46410i 0.0718885 + 0.124515i
\(775\) 19.6410 + 45.9808i 0.705526 + 1.65168i
\(776\) −6.00000 −0.215387
\(777\) 0 0
\(778\) 26.0000i 0.932145i
\(779\) −6.00000 + 10.3923i −0.214972 + 0.372343i
\(780\) 2.46410 3.73205i 0.0882290 0.133629i
\(781\) 30.0000 + 51.9615i 1.07348 + 1.85933i
\(782\) 0 0
\(783\) 2.00000i 0.0714742i
\(784\) 0 0
\(785\) −36.0000 + 18.0000i −1.28490 + 0.642448i
\(786\) 2.00000 3.46410i 0.0713376 0.123560i
\(787\) −3.46410 + 2.00000i −0.123482 + 0.0712923i −0.560469 0.828176i \(-0.689379\pi\)
0.436987 + 0.899468i \(0.356046\pi\)
\(788\) 1.73205 1.00000i 0.0617018 0.0356235i
\(789\) −12.0000 + 20.7846i −0.427211 + 0.739952i
\(790\) −8.00000 + 4.00000i −0.284627 + 0.142314i