Properties

Label 735.2.q.a.79.1
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 79.1
Root \(-0.866025 - 0.500000i\) of \(x^{4} - x^{2} + 1\)
Character \(\chi\) \(=\) 735.79
Dual form 735.2.q.a.214.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.23205 + 1.86603i) q^{5} -1.00000 q^{6} +3.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.23205 + 1.86603i) q^{5} -1.00000 q^{6} +3.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.133975 - 2.23205i) 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} +(-1.96410 + 4.59808i) q^{25} +(-1.00000 + 1.73205i) q^{26} -1.00000i q^{27} +2.00000 q^{29} +(-1.23205 - 1.86603i) 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} +(-5.59808 + 3.69615i) q^{40} +2.00000 q^{41} -4.00000i q^{43} +(3.00000 - 5.19615i) q^{44} +(2.23205 - 0.133975i) 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} +(-0.133975 - 2.23205i) q^{60} +(1.00000 - 1.73205i) q^{61} -10.0000i q^{62} -7.00000 q^{64} +(3.73205 - 2.46410i) 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} +(0.598076 + 4.96410i) q^{75} +6.00000 q^{76} +2.00000i q^{78} +(2.00000 - 3.46410i) q^{79} +(2.23205 - 0.133975i) 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} +(-13.3923 + 0.803848i) 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 0.161521 0.986869i \(-0.448360\pi\)
−0.773893 + 0.633316i \(0.781693\pi\)
\(3\) 0.866025 0.500000i 0.500000 0.288675i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.23205 + 1.86603i 0.550990 + 0.834512i
\(6\) −1.00000 −0.408248
\(7\) 0 0
\(8\) 3.00000i 1.06066i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) −0.133975 2.23205i −0.0423665 0.705836i
\(11\) 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 \(-0.910544\pi\)
0.960769 0.277350i \(-0.0894562\pi\)
\(14\) 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
\(22\) 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
\(25\) −1.96410 + 4.59808i −0.392820 + 0.919615i
\(26\) −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 \(0.440546\pi\)
\(30\) −1.23205 1.86603i −0.224941 0.340688i
\(31\) 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 0.187453 0.982274i \(-0.439977\pi\)
−0.756948 + 0.653476i \(0.773310\pi\)
\(38\) 5.19615 3.00000i 0.842927 0.486664i
\(39\) −1.00000 1.73205i −0.160128 0.277350i
\(40\) −5.59808 + 3.69615i −0.885134 + 0.584413i
\(41\) 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 \(-0.901344\pi\)
0.952353 0.304997i \(-0.0986555\pi\)
\(44\) 3.00000 5.19615i 0.452267 0.783349i
\(45\) 2.23205 0.133975i 0.332734 0.0199718i
\(46\) 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 −0.0987002 0.995117i \(-0.531468\pi\)
0.812447 + 0.583036i \(0.198135\pi\)
\(54\) −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 \(-0.341016\pi\)
\(60\) −0.133975 2.23205i −0.0172960 0.288157i
\(61\) 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
\(65\) 3.73205 2.46410i 0.462904 0.305634i
\(66\) −3.00000 5.19615i −0.369274 0.639602i
\(67\) 13.8564 8.00000i 1.69283 0.977356i 0.740613 0.671932i \(-0.234535\pi\)
0.952217 0.305424i \(-0.0987981\pi\)
\(68\) 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 −0.772246 0.635323i \(-0.780867\pi\)
0.164083 + 0.986447i \(0.447534\pi\)
\(74\) 2.00000 + 3.46410i 0.232495 + 0.402694i
\(75\) 0.598076 + 4.96410i 0.0690599 + 0.573205i
\(76\) 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 \(0.0944227\pi\)
\(80\) 2.23205 0.133975i 0.249551 0.0149788i
\(81\) −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
\(87\) 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
\(95\) −13.3923 + 0.803848i −1.37402 + 0.0824730i
\(96\) 2.50000 4.33013i 0.255155 0.441942i
\(97\) 2.00000i 0.203069i 0.994832 + 0.101535i \(0.0323753\pi\)
−0.994832 + 0.101535i \(0.967625\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) 4.96410 0.598076i 0.496410 0.0598076i
\(101\) 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 0.118199 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
\(107\) 3.46410 + 2.00000i 0.334887 + 0.193347i 0.658009 0.753010i \(-0.271399\pi\)
−0.323122 + 0.946357i \(0.604732\pi\)
\(108\) −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 \(0.802798\pi\)
\(110\) 11.1962 7.39230i 1.06751 0.704829i
\(111\) −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
\(115\) 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 \(-0.652539\pi\)
0.461084 0.887357i \(-0.347461\pi\)
\(128\) −2.59808 1.50000i −0.229640 0.132583i
\(129\) −2.00000 3.46410i −0.176090 0.304997i
\(130\) −4.46410 + 0.267949i −0.391528 + 0.0235007i
\(131\) −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
\(135\) 1.86603 1.23205i 0.160602 0.106038i
\(136\) −6.00000 10.3923i −0.514496 0.891133i
\(137\) 5.19615 3.00000i 0.443937 0.256307i −0.261329 0.965250i \(-0.584161\pi\)
0.705266 + 0.708942i \(0.250827\pi\)
\(138\) 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
\(145\) 2.46410 + 3.73205i 0.204633 + 0.309930i
\(146\) 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 \(0.972267\pi\)
\(150\) 1.96410 4.59808i 0.160368 0.375431i
\(151\) −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 −0.969925 0.243403i \(-0.921736\pi\)
−0.274169 + 0.961681i \(0.588403\pi\)
\(158\) −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 0.358162 0.933659i \(-0.383403\pi\)
−0.629492 + 0.777007i \(0.716737\pi\)
\(164\) −1.00000 1.73205i −0.0780869 0.135250i
\(165\) 0.803848 + 13.3923i 0.0625794 + 1.04259i
\(166\) 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
\(169\) 9.00000 0.692308
\(170\) 4.92820 + 7.46410i 0.377976 + 0.572470i
\(171\) 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 \(-0.341930\pi\)
\(180\) −1.23205 1.86603i −0.0918316 0.139085i
\(181\) −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
\(185\) −0.535898 8.92820i −0.0394000 0.656415i
\(186\) −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 −0.728178 0.685388i \(-0.759632\pi\)
0.229475 + 0.973315i \(0.426299\pi\)
\(194\) 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 \(-0.977302\pi\)
0.997459 0.0712470i \(-0.0226979\pi\)
\(198\) −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 \(0.668055\pi\)
\(200\) −13.7942 5.89230i −0.975399 0.416649i
\(201\) 8.00000 13.8564i 0.564276 0.977356i
\(202\) 6.00000i 0.422159i
\(203\) 0 0
\(204\) 4.00000 0.280056
\(205\) 2.46410 + 3.73205i 0.172100 + 0.260658i
\(206\) 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
\(215\) 7.46410 4.92820i 0.509048 0.336101i
\(216\) 3.00000 0.204124
\(217\) 0 0
\(218\) 2.00000i 0.135457i
\(219\) −3.00000 + 5.19615i −0.202721 + 0.351123i
\(220\) 13.3923 0.803848i 0.902909 0.0541954i
\(221\) 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 \(-0.702926\pi\)
0.595198 0.803579i \(-0.297074\pi\)
\(224\) 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
\(229\) −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 0.999606 0.0280525i \(-0.00893057\pi\)
0.475509 + 0.879711i \(0.342264\pi\)
\(234\) 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 \(0.437836\pi\)
\(240\) 1.86603 1.23205i 0.120451 0.0795285i
\(241\) −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
\(250\) 10.5263 + 3.76795i 0.665740 + 0.238306i
\(251\) 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
\(255\) −8.92820 + 0.535898i −0.559106 + 0.0335593i
\(256\) 8.50000 + 14.7224i 0.531250 + 0.920152i
\(257\) 13.8564 + 8.00000i 0.864339 + 0.499026i 0.865463 0.500973i \(-0.167024\pi\)
−0.00112398 + 0.999999i \(0.500358\pi\)
\(258\) 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 −0.977147 0.212565i \(-0.931818\pi\)
−0.304487 + 0.952517i \(0.598485\pi\)
\(264\) −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 \(0.973692\pi\)
\(270\) −2.23205 + 0.133975i −0.135838 + 0.00815343i
\(271\) 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
\(275\) −29.7846 + 3.58846i −1.79608 + 0.216392i
\(276\) 0 0
\(277\) 24.2487 14.0000i 1.45696 0.841178i 0.458103 0.888899i \(-0.348529\pi\)
0.998861 + 0.0477206i \(0.0151957\pi\)
\(278\) 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 0.112728 0.993626i \(-0.464041\pi\)
0.916869 + 0.399188i \(0.130708\pi\)
\(284\) −5.00000 8.66025i −0.296695 0.513892i
\(285\) −11.1962 + 7.39230i −0.663203 + 0.437882i
\(286\) −12.0000 −0.709575
\(287\) 0 0
\(288\) 5.00000i 0.294628i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) −0.267949 4.46410i −0.0157345 0.262141i
\(291\) 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 \(0.247284\pi\)
−0.713115 + 0.701047i \(0.752716\pi\)
\(294\) 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
\(305\) 4.46410 0.267949i 0.255614 0.0153427i
\(306\) 2.00000 3.46410i 0.114332 0.198030i
\(307\) 4.00000i 0.228292i −0.993464 0.114146i \(-0.963587\pi\)
0.993464 0.114146i \(-0.0364132\pi\)
\(308\) 0 0
\(309\) −8.00000 −0.455104
\(310\) 18.6603 12.3205i 1.05983 0.699758i
\(311\) 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 0.345907 0.938269i \(-0.387571\pi\)
−0.639611 + 0.768699i \(0.720905\pi\)
\(314\) 18.0000 1.01580
\(315\) 0 0
\(316\) −4.00000 −0.225018
\(317\) −15.5885 9.00000i −0.875535 0.505490i −0.00635137 0.999980i \(-0.502022\pi\)
−0.869184 + 0.494489i \(0.835355\pi\)
\(318\) −5.19615 + 3.00000i −0.291386 + 0.168232i
\(319\) 6.00000 + 10.3923i 0.335936 + 0.581857i
\(320\) −8.62436 13.0622i −0.482116 0.730198i
\(321\) 4.00000 0.223258
\(322\) 0 0
\(323\) 24.0000i 1.33540i
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 9.19615 + 3.92820i 0.510111 + 0.217898i
\(326\) 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 \(0.226776\pi\)
−0.756770 + 0.653682i \(0.773224\pi\)
\(338\) −7.79423 4.50000i −0.423950 0.244768i
\(339\) 3.00000 + 5.19615i 0.162938 + 0.282216i
\(340\) 0.535898 + 8.92820i 0.0290632 + 0.484200i
\(341\) −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 −0.752297 0.658824i \(-0.771054\pi\)
0.194409 + 0.980921i \(0.437721\pi\)
\(348\) −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 0.0376440 0.999291i \(-0.488015\pi\)
0.884234 + 0.467045i \(0.154681\pi\)
\(354\) 4.00000 + 6.92820i 0.212598 + 0.368230i
\(355\) 12.3205 + 18.6603i 0.653905 + 0.990383i
\(356\) −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 \(-0.0304988\pi\)
\(360\) 0.401924 + 6.69615i 0.0211832 + 0.352918i
\(361\) −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
\(375\) −8.52628 + 7.23205i −0.440295 + 0.373461i
\(376\) 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 \(0.244540\pi\)
\(380\) 7.39230 + 11.1962i 0.379217 + 0.574351i
\(381\) −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 0.872316 0.488943i \(-0.162617\pi\)
0.0127209 + 0.999919i \(0.495951\pi\)
\(384\) −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 \(0.604260\pi\)
\(390\) −3.73205 + 2.46410i −0.188980 + 0.124775i
\(391\) 0 0
\(392\) 0 0
\(393\) 4.00000i 0.201773i
\(394\) −1.00000 + 1.73205i −0.0503793 + 0.0872595i
\(395\) 8.92820 0.535898i 0.449227 0.0269640i
\(396\) −3.00000 5.19615i −0.150756 0.261116i
\(397\) 19.0526 + 11.0000i 0.956221 + 0.552074i 0.895008 0.446051i \(-0.147170\pi\)
0.0612128 + 0.998125i \(0.480503\pi\)
\(398\) 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 \(-0.349725\pi\)
\(410\) −0.267949 4.46410i −0.0132331 0.220466i
\(411\) 3.00000 5.19615i 0.147979 0.256307i
\(412\) 8.00000i 0.394132i
\(413\) 0 0
\(414\) 0 0
\(415\) −14.9282 + 9.85641i −0.732797 + 0.483832i
\(416\) −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
\(425\) −2.39230 19.8564i −0.116044 0.963177i
\(426\) −10.0000 −0.484502
\(427\) 0 0
\(428\) 4.00000i 0.193347i
\(429\) 6.00000 10.3923i 0.289683 0.501745i
\(430\) −8.92820 + 0.535898i −0.430556 + 0.0258433i
\(431\) 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 \(-0.695653\pi\)
0.576683 0.816968i \(-0.304347\pi\)
\(434\) 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 0.580030 0.814595i \(-0.303041\pi\)
−0.415445 + 0.909618i \(0.636374\pi\)
\(444\) 2.00000 + 3.46410i 0.0949158 + 0.164399i
\(445\) 13.3923 0.803848i 0.634856 0.0381060i
\(446\) −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 \(0.575825\pi\)
\(450\) −0.598076 4.96410i −0.0281936 0.234010i
\(451\) 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 0.0368128 0.999322i \(-0.488279\pi\)
−0.847032 + 0.531542i \(0.821613\pi\)
\(458\) 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 \(0.315420\pi\)
−0.547920 + 0.836531i \(0.684580\pi\)
\(464\) 1.00000 1.73205i 0.0464238 0.0804084i
\(465\) 1.33975 + 22.3205i 0.0621292 + 1.03509i
\(466\) −13.0000 22.5167i −0.602213 1.04306i
\(467\) −20.7846 12.0000i −0.961797 0.555294i −0.0650714 0.997881i \(-0.520728\pi\)
−0.896726 + 0.442587i \(0.854061\pi\)
\(468\) 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 \(0.648611\pi\)
\(480\) 11.1603 0.669873i 0.509394 0.0305754i
\(481\) −4.00000 + 6.92820i −0.182384 + 0.315899i
\(482\) 22.0000i 1.00207i
\(483\) 0 0
\(484\) 25.0000 1.13636
\(485\) −3.73205 + 2.46410i −0.169464 + 0.111889i
\(486\) 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 \(0.420981\pi\)
\(488\) 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
\(495\) 7.39230 + 11.1962i 0.332259 + 0.503230i
\(496\) 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 \(0.138129\pi\)
\(500\) 7.23205 + 8.52628i 0.323427 + 0.381307i
\(501\) −6.00000 10.3923i −0.268060 0.464294i
\(502\) 0 0
\(503\) 36.0000i 1.60516i −0.596544 0.802580i \(-0.703460\pi\)
0.596544 0.802580i \(-0.296540\pi\)
\(504\) 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
\(515\) −1.07180 17.8564i −0.0472290 0.786847i
\(516\) −2.00000 + 3.46410i −0.0880451 + 0.152499i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 7.39230 + 11.1962i 0.324174 + 0.490984i
\(521\) −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 0.0709788 0.997478i \(-0.477388\pi\)
−0.828352 + 0.560208i \(0.810721\pi\)
\(524\) 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
\(530\) −7.39230 11.1962i −0.321101 0.486330i
\(531\) −8.00000 −0.347170
\(532\) 0 0
\(533\) 4.00000i 0.173259i
\(534\) −3.00000 + 5.19615i −0.129823 + 0.224860i
\(535\) 0.535898 + 8.92820i 0.0231689 + 0.386000i
\(536\) 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 \(0.111123\pi\)
−0.939680 + 0.342055i \(0.888877\pi\)
\(548\) −5.19615 3.00000i −0.221969 0.128154i
\(549\) −1.00000 1.73205i −0.0426790 0.0739221i
\(550\) 27.5885 + 11.7846i 1.17638 + 0.502497i
\(551\) −6.00000 + 10.3923i −0.255609 + 0.442727i
\(552\) 0 0
\(553\) 0 0
\(554\) −28.0000 −1.18961
\(555\) −4.92820 7.46410i −0.209191 0.316833i
\(556\) 1.00000 + 1.73205i 0.0424094 + 0.0734553i
\(557\) −32.9090 + 19.0000i −1.39440 + 0.805056i −0.993798 0.111198i \(-0.964531\pi\)
−0.400599 + 0.916253i \(0.631198\pi\)
\(558\) −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 −0.982748 0.184950i \(-0.940788\pi\)
−0.331202 + 0.943560i \(0.607454\pi\)
\(564\) 0 0
\(565\) −11.1962 + 7.39230i −0.471026 + 0.310997i
\(566\) −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 \(0.950200\pi\)
\(570\) 13.3923 0.803848i 0.560942 0.0336695i
\(571\) −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 −0.730670 0.682730i \(-0.760792\pi\)
0.225927 + 0.974144i \(0.427459\pi\)
\(578\) 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
\(585\) −0.267949 4.46410i −0.0110783 0.184568i
\(586\) 12.0000 20.7846i 0.495715 0.858604i
\(587\) 12.0000i 0.495293i 0.968850 + 0.247647i \(0.0796572\pi\)
−0.968850 + 0.247647i \(0.920343\pi\)
\(588\) 0 0
\(589\) −60.0000 −2.47226
\(590\) −14.9282 + 9.85641i −0.614584 + 0.405782i
\(591\) −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 \(-0.974373\pi\)
−0.568029 0.823009i \(-0.692294\pi\)
\(594\) −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 \(0.846343\pi\)
\(600\) −14.8923 + 1.79423i −0.607976 + 0.0732491i
\(601\) −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
\(605\) −55.8013 + 3.34936i −2.26864 + 0.136171i
\(606\) −3.00000 5.19615i −0.121867 0.211079i
\(607\) 20.7846 + 12.0000i 0.843621 + 0.487065i 0.858494 0.512824i \(-0.171401\pi\)
−0.0148722 + 0.999889i \(0.504734\pi\)
\(608\) 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 −0.428409 0.903585i \(-0.640926\pi\)
0.568323 + 0.822806i \(0.307592\pi\)
\(614\) −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 \(0.175322\pi\)
−0.852111 + 0.523360i \(0.824678\pi\)
\(618\) 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 \(0.768925\pi\)
\(620\) 22.3205 1.33975i 0.896413 0.0538055i
\(621\) 0 0
\(622\) 24.0000i 0.962312i
\(623\) 0 0
\(624\) −2.00000 −0.0800641
\(625\) −17.2846 18.0622i −0.691384 0.722487i
\(626\) 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
\(635\) 37.3205 24.6410i 1.48102 0.977849i
\(636\) −6.00000 −0.237915
\(637\) 0 0
\(638\) 12.0000i 0.475085i
\(639\) 5.00000 8.66025i 0.197797 0.342594i
\(640\) −0.401924 6.69615i −0.0158874 0.264689i
\(641\) 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 \(-0.870966\pi\)
0.918955 0.394362i \(-0.129034\pi\)
\(644\) 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 −0.119269 0.992862i \(-0.538055\pi\)
0.800209 + 0.599721i \(0.204722\pi\)
\(648\) 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 0.465727 0.884929i \(-0.345793\pi\)
−0.533507 + 0.845796i \(0.679126\pi\)
\(654\) −1.00000 1.73205i −0.0391031 0.0677285i
\(655\) −8.92820 + 0.535898i −0.348854 + 0.0209393i
\(656\) 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 \(0.385981\pi\)
\(660\) 11.1962 7.39230i 0.435810 0.287745i
\(661\) 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
\(670\) −19.7128 29.8564i −0.761572 1.15345i
\(671\) 12.0000 0.463255
\(672\) 0 0
\(673\) 36.0000i 1.38770i −0.720121 0.693849i \(-0.755914\pi\)
0.720121 0.693849i \(-0.244086\pi\)
\(674\) 12.0000 20.7846i 0.462223 0.800593i
\(675\) 4.59808 + 1.96410i 0.176980 + 0.0755983i
\(676\) −4.50000 7.79423i −0.173077 0.299778i
\(677\) 27.7128 + 16.0000i 1.06509 + 0.614930i 0.926836 0.375467i \(-0.122518\pi\)
0.138254 + 0.990397i \(0.455851\pi\)
\(678\) 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 0.0417198 0.999129i \(-0.486716\pi\)
0.886131 + 0.463434i \(0.153383\pi\)
\(684\) 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
\(695\) −2.46410 3.73205i −0.0934687 0.141565i
\(696\) 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 \(0.00431112\pi\)
\(710\) −1.33975 22.3205i −0.0502798 0.837674i
\(711\) −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
\(725\) −3.92820 + 9.19615i −0.145890 + 0.341537i
\(726\) 12.5000 21.6506i 0.463919 0.803530i
\(727\) 40.0000i 1.48352i 0.670667 + 0.741759i \(0.266008\pi\)
−0.670667 + 0.741759i \(0.733992\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 7.39230 + 11.1962i 0.273601 + 0.414388i
\(731\) 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 0.105010 0.994471i \(-0.466513\pi\)
−0.808732 + 0.588177i \(0.799846\pi\)
\(734\) 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 \(-0.466811\pi\)
\(740\) −7.46410 + 4.92820i −0.274386 + 0.181164i
\(741\) 12.0000 0.440831
\(742\) 0 0
\(743\) 40.0000i 1.46746i 0.679442 + 0.733729i \(0.262222\pi\)
−0.679442 + 0.733729i \(0.737778\pi\)
\(744\) −15.0000 + 25.9808i −0.549927 + 0.952501i
\(745\) −31.2487 + 1.87564i −1.14486 + 0.0687183i
\(746\) 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 \(0.259045\pi\)
−0.686730 + 0.726912i \(0.740955\pi\)
\(758\) −24.2487 14.0000i −0.880753 0.508503i
\(759\) 0 0
\(760\) −2.41154 40.1769i −0.0874758 1.45737i
\(761\) 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
\(765\) −7.46410 + 4.92820i −0.269865 + 0.178180i
\(766\) −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 −0.0772449 0.997012i \(-0.524612\pi\)
0.824815 + 0.565402i \(0.191279\pi\)
\(774\) 2.00000 + 3.46410i 0.0718885 + 0.124515i
\(775\) −49.6410 + 5.98076i −1.78316 + 0.214835i
\(776\) −6.00000 −0.215387
\(777\) 0 0
\(778\) 26.0000i 0.932145i
\(779\) −6.00000 + 10.3923i −0.214972 + 0.372343i
\(780\) −4.46410 + 0.267949i −0.159840 + 0.00959412i
\(781\) 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 −0.436987 0.899468i \(-0.643954\pi\)
0.560469 + 0.828176i \(0.310621\pi\)
\(788\) −1.73205 + 1.00000i −0.0617018 + 0.0356235i
\(789\) −12.0000 + 20.7846i −0.427211 + 0.739952i
\(790\) −8.00000 4.00000i −0.284627