Properties

Label 1764.2.e.h.1079.14
Level 1764
Weight 2
Character 1764.1079
Analytic conductor 14.086
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1764.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.0856109166\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + x^{12} - 10 x^{10} + 4 x^{8} - 40 x^{6} + 16 x^{4} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1079.14
Root \(-1.13008 - 0.850247i\) of defining polynomial
Character \(\chi\) \(=\) 1764.1079
Dual form 1764.2.e.h.1079.13

$q$-expansion

\(f(q)\) \(=\) \(q+(1.13008 + 0.850247i) q^{2} +(0.554161 + 1.92169i) q^{4} +3.87147i q^{5} +(-1.00767 + 2.64284i) q^{8} +O(q^{10})\) \(q+(1.13008 + 0.850247i) q^{2} +(0.554161 + 1.92169i) q^{4} +3.87147i q^{5} +(-1.00767 + 2.64284i) q^{8} +(-3.29170 + 4.37507i) q^{10} +3.46960 q^{11} +0.296538 q^{13} +(-3.38581 + 2.12986i) q^{16} -1.56741i q^{17} +7.07478i q^{19} +(-7.43977 + 2.14542i) q^{20} +(3.92092 + 2.95001i) q^{22} +5.43537 q^{23} -9.98827 q^{25} +(0.335112 + 0.252130i) q^{26} -6.85309i q^{29} +2.81507i q^{31} +(-5.63714 - 0.471866i) q^{32} +(1.33268 - 1.77129i) q^{34} +2.51318 q^{37} +(-6.01531 + 7.99507i) q^{38} +(-10.2317 - 3.90115i) q^{40} -3.55418i q^{41} -0.682082i q^{43} +(1.92272 + 6.66750i) q^{44} +(6.14240 + 4.62140i) q^{46} -2.36931 q^{47} +(-11.2875 - 8.49249i) q^{50} +(0.164330 + 0.569855i) q^{52} -0.623673i q^{53} +13.4324i q^{55} +(5.82681 - 7.74454i) q^{58} -8.85541 q^{59} -2.66536 q^{61} +(-2.39350 + 3.18125i) q^{62} +(-5.96922 - 5.32621i) q^{64} +1.14804i q^{65} -10.6174i q^{67} +(3.01207 - 0.868595i) q^{68} +0.539214 q^{71} -7.39519 q^{73} +(2.84010 + 2.13683i) q^{74} +(-13.5956 + 3.92057i) q^{76} -6.16578i q^{79} +(-8.24567 - 13.1081i) q^{80} +(3.02193 - 4.01651i) q^{82} +6.15982 q^{83} +6.06816 q^{85} +(0.579938 - 0.770808i) q^{86} +(-3.49620 + 9.16959i) q^{88} -11.7165i q^{89} +(3.01207 + 10.4451i) q^{92} +(-2.67751 - 2.01450i) q^{94} -27.3898 q^{95} +6.84782 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 8q^{13} - 4q^{16} - 16q^{22} - 24q^{25} + 8q^{34} - 8q^{37} - 52q^{40} + 24q^{46} - 52q^{52} + 12q^{58} - 16q^{61} + 60q^{64} - 8q^{73} - 36q^{76} + 68q^{82} - 16q^{85} - 44q^{88} + 60q^{94} + 88q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(883\) \(1081\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.13008 + 0.850247i 0.799087 + 0.601215i
\(3\) 0 0
\(4\) 0.554161 + 1.92169i 0.277081 + 0.960847i
\(5\) 3.87147i 1.73137i 0.500586 + 0.865687i \(0.333118\pi\)
−0.500586 + 0.865687i \(0.666882\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00767 + 2.64284i −0.356264 + 0.934385i
\(9\) 0 0
\(10\) −3.29170 + 4.37507i −1.04093 + 1.38352i
\(11\) 3.46960 1.04612 0.523061 0.852295i \(-0.324790\pi\)
0.523061 + 0.852295i \(0.324790\pi\)
\(12\) 0 0
\(13\) 0.296538 0.0822448 0.0411224 0.999154i \(-0.486907\pi\)
0.0411224 + 0.999154i \(0.486907\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −3.38581 + 2.12986i −0.846453 + 0.532464i
\(17\) 1.56741i 0.380152i −0.981769 0.190076i \(-0.939127\pi\)
0.981769 0.190076i \(-0.0608734\pi\)
\(18\) 0 0
\(19\) 7.07478i 1.62307i 0.584307 + 0.811533i \(0.301367\pi\)
−0.584307 + 0.811533i \(0.698633\pi\)
\(20\) −7.43977 + 2.14542i −1.66358 + 0.479730i
\(21\) 0 0
\(22\) 3.92092 + 2.95001i 0.835943 + 0.628945i
\(23\) 5.43537 1.13335 0.566676 0.823940i \(-0.308229\pi\)
0.566676 + 0.823940i \(0.308229\pi\)
\(24\) 0 0
\(25\) −9.98827 −1.99765
\(26\) 0.335112 + 0.252130i 0.0657208 + 0.0494468i
\(27\) 0 0
\(28\) 0 0
\(29\) 6.85309i 1.27259i −0.771447 0.636293i \(-0.780467\pi\)
0.771447 0.636293i \(-0.219533\pi\)
\(30\) 0 0
\(31\) 2.81507i 0.505601i 0.967518 + 0.252800i \(0.0813516\pi\)
−0.967518 + 0.252800i \(0.918648\pi\)
\(32\) −5.63714 0.471866i −0.996515 0.0834149i
\(33\) 0 0
\(34\) 1.33268 1.77129i 0.228553 0.303774i
\(35\) 0 0
\(36\) 0 0
\(37\) 2.51318 0.413165 0.206582 0.978429i \(-0.433766\pi\)
0.206582 + 0.978429i \(0.433766\pi\)
\(38\) −6.01531 + 7.99507i −0.975812 + 1.29697i
\(39\) 0 0
\(40\) −10.2317 3.90115i −1.61777 0.616826i
\(41\) 3.55418i 0.555069i −0.960716 0.277535i \(-0.910483\pi\)
0.960716 0.277535i \(-0.0895173\pi\)
\(42\) 0 0
\(43\) 0.682082i 0.104017i −0.998647 0.0520083i \(-0.983438\pi\)
0.998647 0.0520083i \(-0.0165622\pi\)
\(44\) 1.92272 + 6.66750i 0.289860 + 1.00516i
\(45\) 0 0
\(46\) 6.14240 + 4.62140i 0.905648 + 0.681389i
\(47\) −2.36931 −0.345600 −0.172800 0.984957i \(-0.555281\pi\)
−0.172800 + 0.984957i \(0.555281\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −11.2875 8.49249i −1.59630 1.20102i
\(51\) 0 0
\(52\) 0.164330 + 0.569855i 0.0227884 + 0.0790247i
\(53\) 0.623673i 0.0856681i −0.999082 0.0428340i \(-0.986361\pi\)
0.999082 0.0428340i \(-0.0136387\pi\)
\(54\) 0 0
\(55\) 13.4324i 1.81123i
\(56\) 0 0
\(57\) 0 0
\(58\) 5.82681 7.74454i 0.765098 1.01691i
\(59\) −8.85541 −1.15288 −0.576438 0.817141i \(-0.695558\pi\)
−0.576438 + 0.817141i \(0.695558\pi\)
\(60\) 0 0
\(61\) −2.66536 −0.341265 −0.170632 0.985335i \(-0.554581\pi\)
−0.170632 + 0.985335i \(0.554581\pi\)
\(62\) −2.39350 + 3.18125i −0.303975 + 0.404019i
\(63\) 0 0
\(64\) −5.96922 5.32621i −0.746152 0.665776i
\(65\) 1.14804i 0.142396i
\(66\) 0 0
\(67\) 10.6174i 1.29712i −0.761165 0.648559i \(-0.775372\pi\)
0.761165 0.648559i \(-0.224628\pi\)
\(68\) 3.01207 0.868595i 0.365267 0.105333i
\(69\) 0 0
\(70\) 0 0
\(71\) 0.539214 0.0639929 0.0319964 0.999488i \(-0.489813\pi\)
0.0319964 + 0.999488i \(0.489813\pi\)
\(72\) 0 0
\(73\) −7.39519 −0.865542 −0.432771 0.901504i \(-0.642464\pi\)
−0.432771 + 0.901504i \(0.642464\pi\)
\(74\) 2.84010 + 2.13683i 0.330155 + 0.248401i
\(75\) 0 0
\(76\) −13.5956 + 3.92057i −1.55952 + 0.449720i
\(77\) 0 0
\(78\) 0 0
\(79\) 6.16578i 0.693705i −0.937920 0.346852i \(-0.887251\pi\)
0.937920 0.346852i \(-0.112749\pi\)
\(80\) −8.24567 13.1081i −0.921894 1.46553i
\(81\) 0 0
\(82\) 3.02193 4.01651i 0.333716 0.443549i
\(83\) 6.15982 0.676128 0.338064 0.941123i \(-0.390228\pi\)
0.338064 + 0.941123i \(0.390228\pi\)
\(84\) 0 0
\(85\) 6.06816 0.658184
\(86\) 0.579938 0.770808i 0.0625363 0.0831183i
\(87\) 0 0
\(88\) −3.49620 + 9.16959i −0.372696 + 0.977482i
\(89\) 11.7165i 1.24194i −0.783832 0.620972i \(-0.786738\pi\)
0.783832 0.620972i \(-0.213262\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 3.01207 + 10.4451i 0.314030 + 1.08898i
\(93\) 0 0
\(94\) −2.67751 2.01450i −0.276164 0.207780i
\(95\) −27.3898 −2.81013
\(96\) 0 0
\(97\) 6.84782 0.695291 0.347645 0.937626i \(-0.386981\pi\)
0.347645 + 0.937626i \(0.386981\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −5.53511 19.1944i −0.553511 1.91944i
\(101\) 3.55418i 0.353654i −0.984242 0.176827i \(-0.943417\pi\)
0.984242 0.176827i \(-0.0565833\pi\)
\(102\) 0 0
\(103\) 2.09794i 0.206716i 0.994644 + 0.103358i \(0.0329588\pi\)
−0.994644 + 0.103358i \(0.967041\pi\)
\(104\) −0.298811 + 0.783703i −0.0293009 + 0.0768484i
\(105\) 0 0
\(106\) 0.530276 0.704801i 0.0515050 0.0684563i
\(107\) 11.0560 1.06882 0.534411 0.845225i \(-0.320534\pi\)
0.534411 + 0.845225i \(0.320534\pi\)
\(108\) 0 0
\(109\) 13.3190 1.27573 0.637864 0.770149i \(-0.279818\pi\)
0.637864 + 0.770149i \(0.279818\pi\)
\(110\) −11.4209 + 15.1797i −1.08894 + 1.44733i
\(111\) 0 0
\(112\) 0 0
\(113\) 6.75101i 0.635082i 0.948245 + 0.317541i \(0.102857\pi\)
−0.948245 + 0.317541i \(0.897143\pi\)
\(114\) 0 0
\(115\) 21.0429i 1.96226i
\(116\) 13.1695 3.79772i 1.22276 0.352609i
\(117\) 0 0
\(118\) −10.0073 7.52928i −0.921248 0.693126i
\(119\) 0 0
\(120\) 0 0
\(121\) 1.03810 0.0943728
\(122\) −3.01207 2.26621i −0.272700 0.205173i
\(123\) 0 0
\(124\) −5.40970 + 1.56000i −0.485805 + 0.140092i
\(125\) 19.3119i 1.72731i
\(126\) 0 0
\(127\) 20.3153i 1.80270i 0.433097 + 0.901348i \(0.357421\pi\)
−0.433097 + 0.901348i \(0.642579\pi\)
\(128\) −2.21710 11.0943i −0.195966 0.980611i
\(129\) 0 0
\(130\) −0.976115 + 1.29737i −0.0856109 + 0.113787i
\(131\) 17.2489 1.50704 0.753520 0.657425i \(-0.228354\pi\)
0.753520 + 0.657425i \(0.228354\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 9.02738 11.9985i 0.779847 1.03651i
\(135\) 0 0
\(136\) 4.14240 + 1.57942i 0.355208 + 0.135434i
\(137\) 16.6310i 1.42088i 0.703757 + 0.710441i \(0.251504\pi\)
−0.703757 + 0.710441i \(0.748496\pi\)
\(138\) 0 0
\(139\) 16.2475i 1.37809i 0.724716 + 0.689047i \(0.241971\pi\)
−0.724716 + 0.689047i \(0.758029\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0.609354 + 0.458465i 0.0511359 + 0.0384735i
\(143\) 1.02887 0.0860382
\(144\) 0 0
\(145\) 26.5315 2.20332
\(146\) −8.35716 6.28774i −0.691643 0.520377i
\(147\) 0 0
\(148\) 1.39271 + 4.82957i 0.114480 + 0.396988i
\(149\) 5.65685i 0.463428i −0.972784 0.231714i \(-0.925567\pi\)
0.972784 0.231714i \(-0.0744333\pi\)
\(150\) 0 0
\(151\) 3.99775i 0.325332i 0.986681 + 0.162666i \(0.0520094\pi\)
−0.986681 + 0.162666i \(0.947991\pi\)
\(152\) −18.6975 7.12902i −1.51657 0.578240i
\(153\) 0 0
\(154\) 0 0
\(155\) −10.8984 −0.875384
\(156\) 0 0
\(157\) 10.9502 0.873918 0.436959 0.899481i \(-0.356055\pi\)
0.436959 + 0.899481i \(0.356055\pi\)
\(158\) 5.24244 6.96783i 0.417066 0.554331i
\(159\) 0 0
\(160\) 1.82681 21.8240i 0.144422 1.72534i
\(161\) 0 0
\(162\) 0 0
\(163\) 21.0429i 1.64820i 0.566441 + 0.824102i \(0.308320\pi\)
−0.566441 + 0.824102i \(0.691680\pi\)
\(164\) 6.83004 1.96959i 0.533337 0.153799i
\(165\) 0 0
\(166\) 6.96109 + 5.23736i 0.540285 + 0.406498i
\(167\) −8.39346 −0.649505 −0.324753 0.945799i \(-0.605281\pi\)
−0.324753 + 0.945799i \(0.605281\pi\)
\(168\) 0 0
\(169\) −12.9121 −0.993236
\(170\) 6.85750 + 5.15943i 0.525947 + 0.395710i
\(171\) 0 0
\(172\) 1.31075 0.377984i 0.0999440 0.0288210i
\(173\) 15.0211i 1.14203i −0.820939 0.571016i \(-0.806550\pi\)
0.820939 0.571016i \(-0.193450\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −11.7474 + 7.38974i −0.885493 + 0.557023i
\(177\) 0 0
\(178\) 9.96190 13.2406i 0.746676 0.992422i
\(179\) −2.57640 −0.192569 −0.0962847 0.995354i \(-0.530696\pi\)
−0.0962847 + 0.995354i \(0.530696\pi\)
\(180\) 0 0
\(181\) 22.3412 1.66061 0.830305 0.557309i \(-0.188166\pi\)
0.830305 + 0.557309i \(0.188166\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −5.47704 + 14.3648i −0.403773 + 1.05899i
\(185\) 9.72971i 0.715342i
\(186\) 0 0
\(187\) 5.43826i 0.397685i
\(188\) −1.31298 4.55309i −0.0957590 0.332068i
\(189\) 0 0
\(190\) −30.9526 23.2881i −2.24554 1.68949i
\(191\) 8.29434 0.600157 0.300079 0.953914i \(-0.402987\pi\)
0.300079 + 0.953914i \(0.402987\pi\)
\(192\) 0 0
\(193\) −21.3530 −1.53702 −0.768510 0.639838i \(-0.779002\pi\)
−0.768510 + 0.639838i \(0.779002\pi\)
\(194\) 7.73859 + 5.82234i 0.555598 + 0.418019i
\(195\) 0 0
\(196\) 0 0
\(197\) 0.572559i 0.0407932i 0.999792 + 0.0203966i \(0.00649288\pi\)
−0.999792 + 0.0203966i \(0.993507\pi\)
\(198\) 0 0
\(199\) 17.5003i 1.24056i −0.784380 0.620281i \(-0.787019\pi\)
0.784380 0.620281i \(-0.212981\pi\)
\(200\) 10.0648 26.3974i 0.711692 1.86658i
\(201\) 0 0
\(202\) 3.02193 4.01651i 0.212622 0.282600i
\(203\) 0 0
\(204\) 0 0
\(205\) 13.7599 0.961032
\(206\) −1.78377 + 2.37084i −0.124281 + 0.165184i
\(207\) 0 0
\(208\) −1.00402 + 0.631583i −0.0696163 + 0.0437924i
\(209\) 24.5466i 1.69793i
\(210\) 0 0
\(211\) 7.94873i 0.547213i 0.961842 + 0.273607i \(0.0882167\pi\)
−0.961842 + 0.273607i \(0.911783\pi\)
\(212\) 1.19851 0.345616i 0.0823139 0.0237370i
\(213\) 0 0
\(214\) 12.4941 + 9.40030i 0.854081 + 0.642592i
\(215\) 2.64066 0.180092
\(216\) 0 0
\(217\) 0 0
\(218\) 15.0515 + 11.3244i 1.01942 + 0.766987i
\(219\) 0 0
\(220\) −25.8130 + 7.44374i −1.74031 + 0.501857i
\(221\) 0.464795i 0.0312655i
\(222\) 0 0
\(223\) 1.17855i 0.0789216i −0.999221 0.0394608i \(-0.987436\pi\)
0.999221 0.0394608i \(-0.0125640\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −5.74002 + 7.62918i −0.381821 + 0.507486i
\(227\) −4.54802 −0.301863 −0.150931 0.988544i \(-0.548227\pi\)
−0.150931 + 0.988544i \(0.548227\pi\)
\(228\) 0 0
\(229\) −16.1287 −1.06582 −0.532908 0.846173i \(-0.678901\pi\)
−0.532908 + 0.846173i \(0.678901\pi\)
\(230\) −17.8916 + 23.7801i −1.17974 + 1.56801i
\(231\) 0 0
\(232\) 18.1116 + 6.90563i 1.18909 + 0.453377i
\(233\) 8.27821i 0.542323i 0.962534 + 0.271162i \(0.0874078\pi\)
−0.962534 + 0.271162i \(0.912592\pi\)
\(234\) 0 0
\(235\) 9.17272i 0.598362i
\(236\) −4.90732 17.0174i −0.319440 1.10774i
\(237\) 0 0
\(238\) 0 0
\(239\) 18.1308 1.17279 0.586393 0.810027i \(-0.300547\pi\)
0.586393 + 0.810027i \(0.300547\pi\)
\(240\) 0 0
\(241\) 19.4216 1.25105 0.625526 0.780203i \(-0.284884\pi\)
0.625526 + 0.780203i \(0.284884\pi\)
\(242\) 1.17314 + 0.882641i 0.0754121 + 0.0567383i
\(243\) 0 0
\(244\) −1.47704 5.12201i −0.0945578 0.327903i
\(245\) 0 0
\(246\) 0 0
\(247\) 2.09794i 0.133489i
\(248\) −7.43977 2.83665i −0.472426 0.180127i
\(249\) 0 0
\(250\) 16.4199 21.8240i 1.03849 1.38027i
\(251\) 13.8654 0.875175 0.437587 0.899176i \(-0.355833\pi\)
0.437587 + 0.899176i \(0.355833\pi\)
\(252\) 0 0
\(253\) 18.8585 1.18563
\(254\) −17.2731 + 22.9580i −1.08381 + 1.44051i
\(255\) 0 0
\(256\) 6.92742 14.4226i 0.432964 0.901411i
\(257\) 7.69751i 0.480157i 0.970753 + 0.240079i \(0.0771733\pi\)
−0.970753 + 0.240079i \(0.922827\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −2.20618 + 0.636198i −0.136821 + 0.0394553i
\(261\) 0 0
\(262\) 19.4926 + 14.6658i 1.20426 + 0.906055i
\(263\) 10.0548 0.620006 0.310003 0.950736i \(-0.399670\pi\)
0.310003 + 0.950736i \(0.399670\pi\)
\(264\) 0 0
\(265\) 2.41453 0.148323
\(266\) 0 0
\(267\) 0 0
\(268\) 20.4033 5.88373i 1.24633 0.359406i
\(269\) 28.1088i 1.71382i −0.515463 0.856912i \(-0.672380\pi\)
0.515463 0.856912i \(-0.327620\pi\)
\(270\) 0 0
\(271\) 25.3026i 1.53702i 0.639837 + 0.768511i \(0.279002\pi\)
−0.639837 + 0.768511i \(0.720998\pi\)
\(272\) 3.33835 + 5.30694i 0.202417 + 0.321780i
\(273\) 0 0
\(274\) −14.1404 + 18.7944i −0.854255 + 1.13541i
\(275\) −34.6553 −2.08979
\(276\) 0 0
\(277\) 2.52861 0.151929 0.0759647 0.997111i \(-0.475796\pi\)
0.0759647 + 0.997111i \(0.475796\pi\)
\(278\) −13.8144 + 18.3610i −0.828532 + 1.10122i
\(279\) 0 0
\(280\) 0 0
\(281\) 8.00911i 0.477784i 0.971046 + 0.238892i \(0.0767841\pi\)
−0.971046 + 0.238892i \(0.923216\pi\)
\(282\) 0 0
\(283\) 7.07478i 0.420552i −0.977642 0.210276i \(-0.932564\pi\)
0.977642 0.210276i \(-0.0674363\pi\)
\(284\) 0.298811 + 1.03620i 0.0177312 + 0.0614873i
\(285\) 0 0
\(286\) 1.16270 + 0.874791i 0.0687520 + 0.0517275i
\(287\) 0 0
\(288\) 0 0
\(289\) 14.5432 0.855485
\(290\) 29.9827 + 22.5583i 1.76065 + 1.32467i
\(291\) 0 0
\(292\) −4.09813 14.2113i −0.239825 0.831653i
\(293\) 19.9465i 1.16529i −0.812728 0.582643i \(-0.802018\pi\)
0.812728 0.582643i \(-0.197982\pi\)
\(294\) 0 0
\(295\) 34.2834i 1.99606i
\(296\) −2.53245 + 6.64194i −0.147196 + 0.386055i
\(297\) 0 0
\(298\) 4.80972 6.39270i 0.278620 0.370319i
\(299\) 1.61179 0.0932124
\(300\) 0 0
\(301\) 0 0
\(302\) −3.39908 + 4.51778i −0.195595 + 0.259969i
\(303\) 0 0
\(304\) −15.0683 23.9539i −0.864224 1.37385i
\(305\) 10.3189i 0.590856i
\(306\) 0 0
\(307\) 10.4255i 0.595014i 0.954720 + 0.297507i \(0.0961552\pi\)
−0.954720 + 0.297507i \(0.903845\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −12.3161 9.26636i −0.699508 0.526294i
\(311\) 22.7061 1.28754 0.643772 0.765217i \(-0.277368\pi\)
0.643772 + 0.765217i \(0.277368\pi\)
\(312\) 0 0
\(313\) 22.3835 1.26519 0.632594 0.774484i \(-0.281990\pi\)
0.632594 + 0.774484i \(0.281990\pi\)
\(314\) 12.3746 + 9.31034i 0.698337 + 0.525413i
\(315\) 0 0
\(316\) 11.8487 3.41684i 0.666544 0.192212i
\(317\) 29.1409i 1.63672i −0.574707 0.818359i \(-0.694884\pi\)
0.574707 0.818359i \(-0.305116\pi\)
\(318\) 0 0
\(319\) 23.7774i 1.33128i
\(320\) 20.6202 23.1096i 1.15271 1.29187i
\(321\) 0 0
\(322\) 0 0
\(323\) 11.0890 0.617011
\(324\) 0 0
\(325\) −2.96190 −0.164297
\(326\) −17.8916 + 23.7801i −0.990925 + 1.31706i
\(327\) 0 0
\(328\) 9.39313 + 3.58143i 0.518649 + 0.197751i
\(329\) 0 0
\(330\) 0 0
\(331\) 20.4309i 1.12298i −0.827483 0.561491i \(-0.810228\pi\)
0.827483 0.561491i \(-0.189772\pi\)
\(332\) 3.41353 + 11.8373i 0.187342 + 0.649655i
\(333\) 0 0
\(334\) −9.48528 7.13651i −0.519011 0.390492i
\(335\) 41.1048 2.24579
\(336\) 0 0
\(337\) −6.16681 −0.335928 −0.167964 0.985793i \(-0.553719\pi\)
−0.167964 + 0.985793i \(0.553719\pi\)
\(338\) −14.5917 10.9784i −0.793682 0.597148i
\(339\) 0 0
\(340\) 3.36274 + 11.6611i 0.182370 + 0.632414i
\(341\) 9.76715i 0.528921i
\(342\) 0 0
\(343\) 0 0
\(344\) 1.80264 + 0.687312i 0.0971916 + 0.0370574i
\(345\) 0 0
\(346\) 12.7716 16.9750i 0.686607 0.912583i
\(347\) 15.1197 0.811669 0.405834 0.913947i \(-0.366981\pi\)
0.405834 + 0.913947i \(0.366981\pi\)
\(348\) 0 0
\(349\) −18.8933 −1.01134 −0.505668 0.862728i \(-0.668754\pi\)
−0.505668 + 0.862728i \(0.668754\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −19.5586 1.63718i −1.04248 0.0872622i
\(353\) 10.6282i 0.565680i 0.959167 + 0.282840i \(0.0912766\pi\)
−0.959167 + 0.282840i \(0.908723\pi\)
\(354\) 0 0
\(355\) 2.08755i 0.110796i
\(356\) 22.5155 6.49282i 1.19332 0.344119i
\(357\) 0 0
\(358\) −2.91154 2.19058i −0.153880 0.115776i
\(359\) −2.80941 −0.148275 −0.0741374 0.997248i \(-0.523620\pi\)
−0.0741374 + 0.997248i \(0.523620\pi\)
\(360\) 0 0
\(361\) −31.0525 −1.63434
\(362\) 25.2474 + 18.9956i 1.32697 + 0.998384i
\(363\) 0 0
\(364\) 0 0
\(365\) 28.6302i 1.49858i
\(366\) 0 0
\(367\) 18.8811i 0.985585i −0.870147 0.492792i \(-0.835976\pi\)
0.870147 0.492792i \(-0.164024\pi\)
\(368\) −18.4031 + 11.5766i −0.959329 + 0.603470i
\(369\) 0 0
\(370\) −8.27265 + 10.9953i −0.430075 + 0.571621i
\(371\) 0 0
\(372\) 0 0
\(373\) −33.5884 −1.73914 −0.869570 0.493810i \(-0.835604\pi\)
−0.869570 + 0.493810i \(0.835604\pi\)
\(374\) 4.62386 6.14567i 0.239094 0.317785i
\(375\) 0 0
\(376\) 2.38748 6.26172i 0.123125 0.322923i
\(377\) 2.03220i 0.104664i
\(378\) 0 0
\(379\) 7.57538i 0.389121i 0.980890 + 0.194561i \(0.0623281\pi\)
−0.980890 + 0.194561i \(0.937672\pi\)
\(380\) −15.1784 52.6348i −0.778633 2.70011i
\(381\) 0 0
\(382\) 9.37326 + 7.05223i 0.479578 + 0.360824i
\(383\) −36.3809 −1.85898 −0.929488 0.368853i \(-0.879751\pi\)
−0.929488 + 0.368853i \(0.879751\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −24.1306 18.1553i −1.22821 0.924080i
\(387\) 0 0
\(388\) 3.79480 + 13.1594i 0.192652 + 0.668068i
\(389\) 3.41758i 0.173278i 0.996240 + 0.0866391i \(0.0276127\pi\)
−0.996240 + 0.0866391i \(0.972387\pi\)
\(390\) 0 0
\(391\) 8.51943i 0.430846i
\(392\) 0 0
\(393\) 0 0
\(394\) −0.486817 + 0.647038i −0.0245255 + 0.0325973i
\(395\) 23.8706 1.20106
\(396\) 0 0
\(397\) −19.7716 −0.992309 −0.496155 0.868234i \(-0.665255\pi\)
−0.496155 + 0.868234i \(0.665255\pi\)
\(398\) 14.8795 19.7767i 0.745844 0.991317i
\(399\) 0 0
\(400\) 33.8184 21.2736i 1.69092 1.06368i
\(401\) 3.80960i 0.190242i −0.995466 0.0951211i \(-0.969676\pi\)
0.995466 0.0951211i \(-0.0303238\pi\)
\(402\) 0 0
\(403\) 0.834774i 0.0415831i
\(404\) 6.83004 1.96959i 0.339807 0.0979907i
\(405\) 0 0
\(406\) 0 0
\(407\) 8.71973 0.432221
\(408\) 0 0
\(409\) −29.4934 −1.45836 −0.729178 0.684325i \(-0.760097\pi\)
−0.729178 + 0.684325i \(0.760097\pi\)
\(410\) 15.5498 + 11.6993i 0.767949 + 0.577787i
\(411\) 0 0
\(412\) −4.03160 + 1.16260i −0.198623 + 0.0572771i
\(413\) 0 0
\(414\) 0 0
\(415\) 23.8475i 1.17063i
\(416\) −1.67163 0.139926i −0.0819582 0.00686044i
\(417\) 0 0
\(418\) −20.8707 + 27.7397i −1.02082 + 1.35679i
\(419\) 4.99528 0.244035 0.122018 0.992528i \(-0.461064\pi\)
0.122018 + 0.992528i \(0.461064\pi\)
\(420\) 0 0
\(421\) −4.51318 −0.219959 −0.109980 0.993934i \(-0.535079\pi\)
−0.109980 + 0.993934i \(0.535079\pi\)
\(422\) −6.75838 + 8.98270i −0.328993 + 0.437271i
\(423\) 0 0
\(424\) 1.64827 + 0.628455i 0.0800470 + 0.0305205i
\(425\) 15.6557i 0.759411i
\(426\) 0 0
\(427\) 0 0
\(428\) 6.12679 + 21.2462i 0.296150 + 1.02697i
\(429\) 0 0
\(430\) 2.98416 + 2.24521i 0.143909 + 0.108274i
\(431\) 20.2872 0.977201 0.488600 0.872508i \(-0.337508\pi\)
0.488600 + 0.872508i \(0.337508\pi\)
\(432\) 0 0
\(433\) −8.34123 −0.400854 −0.200427 0.979709i \(-0.564233\pi\)
−0.200427 + 0.979709i \(0.564233\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 7.38087 + 25.5950i 0.353480 + 1.22578i
\(437\) 38.4540i 1.83951i
\(438\) 0 0
\(439\) 23.8683i 1.13917i −0.821931 0.569586i \(-0.807103\pi\)
0.821931 0.569586i \(-0.192897\pi\)
\(440\) −35.4998 13.5354i −1.69239 0.645276i
\(441\) 0 0
\(442\) 0.395190 0.525256i 0.0187973 0.0249839i
\(443\) 6.00229 0.285177 0.142589 0.989782i \(-0.454457\pi\)
0.142589 + 0.989782i \(0.454457\pi\)
\(444\) 0 0
\(445\) 45.3600 2.15027
\(446\) 1.00206 1.33186i 0.0474488 0.0630652i
\(447\) 0 0
\(448\) 0 0
\(449\) 4.92296i 0.232329i 0.993230 + 0.116165i \(0.0370600\pi\)
−0.993230 + 0.116165i \(0.962940\pi\)
\(450\) 0 0
\(451\) 12.3316i 0.580671i
\(452\) −12.9734 + 3.74115i −0.610216 + 0.175969i
\(453\) 0 0
\(454\) −5.13963 3.86694i −0.241215 0.181485i
\(455\) 0 0
\(456\) 0 0
\(457\) −26.4436 −1.23698 −0.618489 0.785793i \(-0.712255\pi\)
−0.618489 + 0.785793i \(0.712255\pi\)
\(458\) −18.2267 13.7134i −0.851679 0.640784i
\(459\) 0 0
\(460\) −40.4379 + 11.6611i −1.88543 + 0.543703i
\(461\) 8.92124i 0.415504i −0.978182 0.207752i \(-0.933385\pi\)
0.978182 0.207752i \(-0.0666147\pi\)
\(462\) 0 0
\(463\) 14.3310i 0.666020i −0.942923 0.333010i \(-0.891936\pi\)
0.942923 0.333010i \(-0.108064\pi\)
\(464\) 14.5961 + 23.2033i 0.677606 + 1.07718i
\(465\) 0 0
\(466\) −7.03852 + 9.35504i −0.326053 + 0.433364i
\(467\) 21.3656 0.988684 0.494342 0.869268i \(-0.335409\pi\)
0.494342 + 0.869268i \(0.335409\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 7.79907 10.3659i 0.359744 0.478144i
\(471\) 0 0
\(472\) 8.92330 23.4034i 0.410728 1.07723i
\(473\) 2.36655i 0.108814i
\(474\) 0 0
\(475\) 70.6648i 3.24232i
\(476\) 0 0
\(477\) 0 0
\(478\) 20.4893 + 15.4157i 0.937159 + 0.705097i
\(479\) 32.3851 1.47971 0.739856 0.672766i \(-0.234894\pi\)
0.739856 + 0.672766i \(0.234894\pi\)
\(480\) 0 0
\(481\) 0.745254 0.0339807
\(482\) 21.9479 + 16.5131i 0.999700 + 0.752152i
\(483\) 0 0
\(484\) 0.575275 + 1.99491i 0.0261489 + 0.0906778i
\(485\) 26.5111i 1.20381i
\(486\) 0 0
\(487\) 2.88516i 0.130739i 0.997861 + 0.0653695i \(0.0208226\pi\)
−0.997861 + 0.0653695i \(0.979177\pi\)
\(488\) 2.68580 7.04413i 0.121580 0.318873i
\(489\) 0 0
\(490\) 0 0
\(491\) 16.6547 0.751617 0.375808 0.926697i \(-0.377365\pi\)
0.375808 + 0.926697i \(0.377365\pi\)
\(492\) 0 0
\(493\) −10.7416 −0.483776
\(494\) −1.78377 + 2.37084i −0.0802555 + 0.106669i
\(495\) 0 0
\(496\) −5.99569 9.53128i −0.269214 0.427967i
\(497\) 0 0
\(498\) 0 0
\(499\) 26.0610i 1.16665i 0.812239 + 0.583325i \(0.198249\pi\)
−0.812239 + 0.583325i \(0.801751\pi\)
\(500\) 37.1116 10.7019i 1.65968 0.478604i
\(501\) 0 0
\(502\) 15.6690 + 11.7890i 0.699341 + 0.526168i
\(503\) −28.7302 −1.28102 −0.640509 0.767951i \(-0.721277\pi\)
−0.640509 + 0.767951i \(0.721277\pi\)
\(504\) 0 0
\(505\) 13.7599 0.612307
\(506\) 21.3117 + 16.0344i 0.947419 + 0.712816i
\(507\) 0 0
\(508\) −39.0399 + 11.2580i −1.73211 + 0.499492i
\(509\) 15.7921i 0.699973i 0.936755 + 0.349986i \(0.113814\pi\)
−0.936755 + 0.349986i \(0.886186\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 20.0913 10.4086i 0.887918 0.460002i
\(513\) 0 0
\(514\) −6.54478 + 8.69880i −0.288678 + 0.383688i
\(515\) −8.12211 −0.357903
\(516\) 0 0
\(517\) −8.22056 −0.361540
\(518\) 0 0
\(519\) 0 0
\(520\) −3.03408 1.15684i −0.133053 0.0507307i
\(521\) 3.41466i 0.149599i −0.997199 0.0747995i \(-0.976168\pi\)
0.997199 0.0747995i \(-0.0238317\pi\)
\(522\) 0 0
\(523\) 6.61336i 0.289182i −0.989492 0.144591i \(-0.953813\pi\)
0.989492 0.144591i \(-0.0461866\pi\)
\(524\) 9.55865 + 33.1470i 0.417572 + 1.44803i
\(525\) 0 0
\(526\) 11.3627 + 8.54907i 0.495439 + 0.372757i
\(527\) 4.41235 0.192205
\(528\) 0 0
\(529\) 6.54324 0.284489
\(530\) 2.72861 + 2.05295i 0.118523 + 0.0891743i
\(531\) 0 0
\(532\) 0 0
\(533\) 1.05395i 0.0456516i
\(534\) 0 0
\(535\) 42.8028i 1.85053i
\(536\) 28.0600 + 10.6988i 1.21201 + 0.462116i
\(537\) 0 0
\(538\) 23.8994 31.7652i 1.03038 1.36949i
\(539\) 0 0
\(540\) 0 0
\(541\) 9.39128 0.403762 0.201881 0.979410i \(-0.435295\pi\)
0.201881 + 0.979410i \(0.435295\pi\)
\(542\) −21.5134 + 28.5939i −0.924081 + 1.22821i
\(543\) 0 0
\(544\) −0.739605 + 8.83568i −0.0317103 + 0.378827i
\(545\) 51.5640i 2.20876i
\(546\) 0 0
\(547\) 14.8029i 0.632924i −0.948605 0.316462i \(-0.897505\pi\)
0.948605 0.316462i \(-0.102495\pi\)
\(548\) −31.9597 + 9.21625i −1.36525 + 0.393699i
\(549\) 0 0
\(550\) −39.1632 29.4655i −1.66992 1.25641i
\(551\) 48.4841 2.06549
\(552\) 0 0
\(553\) 0 0
\(554\) 2.85753 + 2.14994i 0.121405 + 0.0913422i
\(555\) 0 0
\(556\) −31.2227 + 9.00374i −1.32414 + 0.381843i
\(557\) 3.59946i 0.152514i −0.997088 0.0762569i \(-0.975703\pi\)
0.997088 0.0762569i \(-0.0242969\pi\)
\(558\) 0 0
\(559\) 0.202263i 0.00855482i
\(560\) 0 0
\(561\) 0 0
\(562\) −6.80972 + 9.05094i −0.287251 + 0.381791i
\(563\) −19.1320 −0.806318 −0.403159 0.915130i \(-0.632088\pi\)
−0.403159 + 0.915130i \(0.632088\pi\)
\(564\) 0 0
\(565\) −26.1363 −1.09956
\(566\) 6.01531 7.99507i 0.252842 0.336058i
\(567\) 0 0
\(568\) −0.543348 + 1.42506i −0.0227984 + 0.0597940i
\(569\) 31.8810i 1.33652i 0.743928 + 0.668260i \(0.232960\pi\)
−0.743928 + 0.668260i \(0.767040\pi\)
\(570\) 0 0
\(571\) 22.6794i 0.949102i 0.880228 + 0.474551i \(0.157390\pi\)
−0.880228 + 0.474551i \(0.842610\pi\)
\(572\) 0.570158 + 1.97717i 0.0238395 + 0.0826695i
\(573\) 0 0
\(574\) 0 0
\(575\) −54.2899 −2.26405
\(576\) 0 0
\(577\) 1.38056 0.0574734 0.0287367 0.999587i \(-0.490852\pi\)
0.0287367 + 0.999587i \(0.490852\pi\)
\(578\) 16.4350 + 12.3653i 0.683607 + 0.514330i
\(579\) 0 0
\(580\) 14.7027 + 50.9854i 0.610498 + 2.11705i
\(581\) 0 0
\(582\) 0 0
\(583\) 2.16389i 0.0896193i
\(584\) 7.45189 19.5443i 0.308361 0.808749i
\(585\) 0 0
\(586\) 16.9594 22.5411i 0.700588 0.931166i
\(587\) −39.5737 −1.63338 −0.816692 0.577074i \(-0.804194\pi\)
−0.816692 + 0.577074i \(0.804194\pi\)
\(588\) 0 0
\(589\) −19.9160 −0.820624
\(590\) 29.1494 38.7430i 1.20006 1.59502i
\(591\) 0 0
\(592\) −8.50916 + 5.35272i −0.349724 + 0.219995i
\(593\) 22.7337i 0.933563i −0.884373 0.466781i \(-0.845413\pi\)
0.884373 0.466781i \(-0.154587\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 10.8707 3.13481i 0.445283 0.128407i
\(597\) 0 0
\(598\) 1.82146 + 1.37042i 0.0744848 + 0.0560407i
\(599\) 13.0276 0.532293 0.266147 0.963933i \(-0.414249\pi\)
0.266147 + 0.963933i \(0.414249\pi\)
\(600\) 0 0
\(601\) 43.6907 1.78218 0.891091 0.453825i \(-0.149941\pi\)
0.891091 + 0.453825i \(0.149941\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −7.68245 + 2.21540i −0.312595 + 0.0901433i
\(605\) 4.01897i 0.163394i
\(606\) 0 0
\(607\) 9.05507i 0.367534i 0.982970 + 0.183767i \(0.0588292\pi\)
−0.982970 + 0.183767i \(0.941171\pi\)
\(608\) 3.33835 39.8815i 0.135388 1.61741i
\(609\) 0 0
\(610\) 8.77358 11.6611i 0.355232 0.472146i
\(611\) −0.702591 −0.0284238
\(612\) 0 0
\(613\) 11.6275 0.469630 0.234815 0.972040i \(-0.424552\pi\)
0.234815 + 0.972040i \(0.424552\pi\)
\(614\) −8.86424 + 11.7816i −0.357732 + 0.475468i
\(615\) 0 0
\(616\) 0 0
\(617\) 18.3734i 0.739685i 0.929094 + 0.369843i \(0.120588\pi\)
−0.929094 + 0.369843i \(0.879412\pi\)
\(618\) 0 0
\(619\) 22.6794i 0.911561i −0.890092 0.455781i \(-0.849360\pi\)
0.890092 0.455781i \(-0.150640\pi\)
\(620\) −6.03950 20.9435i −0.242552 0.841110i
\(621\) 0 0
\(622\) 25.6597 + 19.3058i 1.02886 + 0.774091i
\(623\) 0 0
\(624\) 0 0
\(625\) 24.8241 0.992965
\(626\) 25.2951 + 19.0315i 1.01100 + 0.760650i
\(627\) 0 0
\(628\) 6.06816 + 21.0429i 0.242146 + 0.839702i
\(629\) 3.93918i 0.157065i
\(630\) 0 0
\(631\) 27.5820i 1.09802i 0.835815 + 0.549011i \(0.184995\pi\)
−0.835815 + 0.549011i \(0.815005\pi\)
\(632\) 16.2952 + 6.21305i 0.648187 + 0.247142i
\(633\) 0 0
\(634\) 24.7770 32.9316i 0.984020 1.30788i
\(635\) −78.6502 −3.12114
\(636\) 0 0
\(637\) 0 0
\(638\) 20.2167 26.8704i 0.800387 1.06381i
\(639\) 0 0
\(640\) 42.9514 8.58345i 1.69780 0.339290i
\(641\) 28.7971i 1.13742i −0.822539 0.568709i \(-0.807443\pi\)
0.822539 0.568709i \(-0.192557\pi\)
\(642\) 0 0
\(643\) 38.1698i 1.50527i 0.658438 + 0.752635i \(0.271217\pi\)
−0.658438 + 0.752635i \(0.728783\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 12.5315 + 9.42842i 0.493046 + 0.370956i
\(647\) −45.7885 −1.80013 −0.900066 0.435754i \(-0.856482\pi\)
−0.900066 + 0.435754i \(0.856482\pi\)
\(648\) 0 0
\(649\) −30.7247 −1.20605
\(650\) −3.34718 2.51835i −0.131287 0.0987776i
\(651\) 0 0
\(652\) −40.4379 + 11.6611i −1.58367 + 0.456685i
\(653\) 6.01957i 0.235564i −0.993039 0.117782i \(-0.962422\pi\)
0.993039 0.117782i \(-0.0375784\pi\)
\(654\) 0 0
\(655\) 66.7784i 2.60925i
\(656\) 7.56989 + 12.0338i 0.295554 + 0.469840i
\(657\) 0 0
\(658\) 0 0
\(659\) −8.45187 −0.329238 −0.164619 0.986357i \(-0.552639\pi\)
−0.164619 + 0.986357i \(0.552639\pi\)
\(660\) 0 0
\(661\) 19.3229 0.751574 0.375787 0.926706i \(-0.377372\pi\)
0.375787 + 0.926706i \(0.377372\pi\)
\(662\) 17.3713 23.0885i 0.675154 0.897361i
\(663\) 0 0
\(664\) −6.20704 + 16.2794i −0.240880 + 0.631764i
\(665\) 0 0
\(666\) 0 0
\(667\) 37.2491i 1.44229i
\(668\) −4.65133 16.1296i −0.179965 0.624075i
\(669\) 0 0
\(670\) 46.4517 + 34.9492i 1.79459 + 1.35021i
\(671\) −9.24773 −0.357005
\(672\) 0 0
\(673\) 30.5239 1.17661 0.588305 0.808639i \(-0.299795\pi\)
0.588305 + 0.808639i \(0.299795\pi\)
\(674\) −6.96899 5.24331i −0.268435 0.201965i
\(675\) 0 0
\(676\) −7.15537 24.8130i −0.275206 0.954347i
\(677\) 19.9465i 0.766606i −0.923623 0.383303i \(-0.874786\pi\)
0.923623 0.383303i \(-0.125214\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −6.11468 + 16.0372i −0.234487 + 0.614998i
\(681\) 0 0
\(682\) −8.30448 + 11.0377i −0.317995 + 0.422654i
\(683\) −27.3733 −1.04741 −0.523705 0.851900i \(-0.675451\pi\)
−0.523705 + 0.851900i \(0.675451\pi\)
\(684\) 0 0
\(685\) −64.3864 −2.46008
\(686\) 0 0
\(687\) 0 0
\(688\) 1.45274 + 2.30940i 0.0553851 + 0.0880451i
\(689\) 0.184943i 0.00704576i
\(690\) 0 0
\(691\) 48.3588i 1.83965i −0.392324 0.919827i \(-0.628329\pi\)
0.392324 0.919827i \(-0.371671\pi\)
\(692\) 28.8659 8.32410i 1.09732 0.316435i
\(693\) 0 0
\(694\) 17.0865 + 12.8555i 0.648594 + 0.487987i
\(695\) −62.9017 −2.38600
\(696\) 0 0
\(697\) −5.57084 −0.211010
\(698\) −21.3509 16.0640i −0.808145 0.608030i
\(699\) 0 0
\(700\) 0 0
\(701\) 17.0447i 0.643768i 0.946779 + 0.321884i \(0.104316\pi\)
−0.946779 + 0.321884i \(0.895684\pi\)
\(702\) 0 0
\(703\) 17.7802i 0.670594i
\(704\) −20.7108 18.4798i −0.780567 0.696483i
\(705\) 0 0
\(706\) −9.03656 + 12.0107i −0.340095 + 0.452028i
\(707\) 0 0
\(708\) 0 0
\(709\) −26.4407 −0.993000 −0.496500 0.868037i \(-0.665382\pi\)
−0.496500 + 0.868037i \(0.665382\pi\)
\(710\) −1.77493 + 2.35910i −0.0666120 + 0.0885353i
\(711\) 0 0
\(712\) 30.9648 + 11.8063i 1.16045 + 0.442460i
\(713\) 15.3009i 0.573024i
\(714\) 0 0
\(715\) 3.98323i 0.148964i
\(716\) −1.42774 4.95106i −0.0533573 0.185030i
\(717\) 0 0
\(718\) −3.17485 2.38869i −0.118484 0.0891450i
\(719\) 34.7544 1.29612 0.648060 0.761590i \(-0.275581\pi\)
0.648060 + 0.761590i \(0.275581\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −35.0918 26.4023i −1.30598 0.982592i
\(723\) 0 0
\(724\) 12.3806 + 42.9330i 0.460123 + 1.59559i
\(725\) 68.4505i 2.54219i
\(726\) 0 0
\(727\) 22.9785i 0.852226i −0.904670 0.426113i \(-0.859883\pi\)
0.904670 0.426113i \(-0.140117\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 24.3428 32.3545i 0.900966 1.19749i
\(731\) −1.06910 −0.0395421
\(732\) 0 0
\(733\) 20.8777 0.771134 0.385567 0.922680i \(-0.374006\pi\)
0.385567 + 0.922680i \(0.374006\pi\)
\(734\) 16.0536 21.3371i 0.592548 0.787568i
\(735\) 0 0
\(736\) −30.6399 2.56477i −1.12940 0.0945385i
\(737\) 36.8380i 1.35694i
\(738\) 0 0
\(739\) 6.90369i 0.253956i 0.991906 + 0.126978i \(0.0405278\pi\)
−0.991906 + 0.126978i \(0.959472\pi\)
\(740\) −18.6975 + 5.39183i −0.687334 + 0.198208i
\(741\) 0 0
\(742\) 0 0
\(743\) 12.7592 0.468091 0.234046 0.972226i \(-0.424803\pi\)
0.234046 + 0.972226i \(0.424803\pi\)
\(744\) 0 0
\(745\) 21.9003 0.802366
\(746\) −37.9575 28.5584i −1.38972 1.04560i
\(747\) 0 0
\(748\) 10.4507 3.01368i 0.382114 0.110191i
\(749\) 0 0
\(750\) 0 0
\(751\) 51.7473i 1.88829i −0.329535 0.944143i \(-0.606892\pi\)
0.329535 0.944143i \(-0.393108\pi\)
\(752\) 8.02204 5.04630i 0.292534 0.184019i
\(753\) 0 0
\(754\) 1.72787 2.29655i 0.0629254 0.0836354i
\(755\) −15.4772 −0.563272
\(756\) 0 0
\(757\) −24.2613 −0.881793 −0.440897 0.897558i \(-0.645339\pi\)
−0.440897 + 0.897558i \(0.645339\pi\)
\(758\) −6.44094 + 8.56079i −0.233946 + 0.310942i
\(759\) 0 0
\(760\) 27.5998 72.3868i 1.00115 2.62575i
\(761\) 48.1383i 1.74501i 0.488603 + 0.872506i \(0.337507\pi\)
−0.488603 + 0.872506i \(0.662493\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 4.59640 + 15.9392i 0.166292 + 0.576659i
\(765\) 0 0
\(766\) −41.1133 30.9327i −1.48548 1.11764i
\(767\) −2.62596 −0.0948180
\(768\) 0 0
\(769\) −32.1961 −1.16102 −0.580510 0.814253i \(-0.697147\pi\)
−0.580510 + 0.814253i \(0.697147\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −11.8330 41.0338i −0.425879 1.47684i
\(773\) 40.1610i 1.44449i −0.691638 0.722245i \(-0.743110\pi\)
0.691638 0.722245i \(-0.256890\pi\)
\(774\) 0 0
\(775\) 28.1176i 1.01002i
\(776\) −6.90032 + 18.0977i −0.247707 + 0.649670i
\(777\) 0 0
\(778\) −2.90579 + 3.86214i −0.104177 + 0.138464i
\(779\) 25.1450 0.900914
\(780\) 0 0
\(781\) 1.87085 0.0669444
\(782\) 7.24361 9.62763i 0.259031 0.344283i
\(783\) 0 0
\(784\) 0 0
\(785\) 42.3932i 1.51308i
\(786\) 0 0
\(787\) 35.1924i 1.25447i −0.778828 0.627237i \(-0.784186\pi\)
0.778828 0.627237i \(-0.215814\pi\)
\(788\) −1.10028 + 0.317290i −0.0391960 + 0.0113030i
\(789\) 0 0
\(790\) 26.9757 + 20.2959i 0.959753 + 0.722096i
\(791\) 0 0
\(792\) 0 0
\(793\) −0.790381 −0.0280672