Properties

Label 756.2.ca.a.173.8
Level 756
Weight 2
Character 756.173
Analytic conductor 6.037
Analytic rank 0
Dimension 144
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.ca (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 173.8
Character \(\chi\) \(=\) 756.173
Dual form 756.2.ca.a.437.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.04679 - 1.37994i) q^{3} +(0.700470 - 0.587764i) q^{5} +(-0.673988 + 2.55846i) q^{7} +(-0.808445 + 2.88902i) q^{9} +O(q^{10})\) \(q+(-1.04679 - 1.37994i) q^{3} +(0.700470 - 0.587764i) q^{5} +(-0.673988 + 2.55846i) q^{7} +(-0.808445 + 2.88902i) q^{9} +(2.40709 - 2.86865i) q^{11} +(2.48376 + 2.96003i) q^{13} +(-1.54432 - 0.351336i) q^{15} +(-3.05270 + 5.28743i) q^{17} +(4.82172 - 2.78382i) q^{19} +(4.23604 - 1.74813i) q^{21} +(-0.548926 + 1.50816i) q^{23} +(-0.723049 + 4.10062i) q^{25} +(4.83293 - 1.90860i) q^{27} +(4.21794 - 5.02674i) q^{29} +(1.54773 + 1.84452i) q^{31} +(-6.47828 - 0.318735i) q^{33} +(1.03167 + 2.18827i) q^{35} -2.43591 q^{37} +(1.48467 - 6.52598i) q^{39} +(4.95635 - 4.15887i) q^{41} +(7.68736 - 2.79797i) q^{43} +(1.13177 + 2.49884i) q^{45} +(3.52092 + 2.95440i) q^{47} +(-6.09148 - 3.44875i) q^{49} +(10.4919 - 1.32232i) q^{51} +(9.92435 - 5.72983i) q^{53} -3.42420i q^{55} +(-8.88885 - 3.73958i) q^{57} +(-0.154736 - 0.877551i) q^{59} +(-7.92124 + 9.44017i) q^{61} +(-6.84656 - 4.01554i) q^{63} +(3.47960 + 0.613548i) q^{65} +(-12.2484 - 4.45805i) q^{67} +(2.65578 - 0.821252i) q^{69} +(11.1044 - 6.41115i) q^{71} +4.85770i q^{73} +(6.41547 - 3.29474i) q^{75} +(5.71700 + 8.09188i) q^{77} +(5.29825 - 1.92841i) q^{79} +(-7.69283 - 4.67122i) q^{81} +(6.26479 + 5.25678i) q^{83} +(0.969437 + 5.49795i) q^{85} +(-11.3519 - 0.558520i) q^{87} +(2.04328 + 3.53906i) q^{89} +(-9.24716 + 4.35959i) q^{91} +(0.925156 - 4.06660i) q^{93} +(1.74124 - 4.78402i) q^{95} +(4.13766 + 11.3681i) q^{97} +(6.34159 + 9.27326i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144q - 12q^{9} + O(q^{10}) \) \( 144q - 12q^{9} + 12q^{11} + 12q^{15} - 3q^{21} - 15q^{23} - 6q^{29} - 42q^{39} + 18q^{45} - 54q^{47} - 36q^{49} + 18q^{51} + 45q^{53} + 3q^{57} + 54q^{61} + 39q^{63} - 3q^{65} + 36q^{69} + 36q^{71} + 93q^{77} - 18q^{79} - 36q^{81} + 36q^{85} - 18q^{91} + 60q^{93} + 6q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.04679 1.37994i −0.604367 0.796706i
\(4\) 0 0
\(5\) 0.700470 0.587764i 0.313260 0.262856i −0.472578 0.881289i \(-0.656677\pi\)
0.785838 + 0.618433i \(0.212232\pi\)
\(6\) 0 0
\(7\) −0.673988 + 2.55846i −0.254743 + 0.967009i
\(8\) 0 0
\(9\) −0.808445 + 2.88902i −0.269482 + 0.963006i
\(10\) 0 0
\(11\) 2.40709 2.86865i 0.725764 0.864931i −0.269414 0.963025i \(-0.586830\pi\)
0.995177 + 0.0980932i \(0.0312743\pi\)
\(12\) 0 0
\(13\) 2.48376 + 2.96003i 0.688872 + 0.820965i 0.991219 0.132233i \(-0.0422146\pi\)
−0.302347 + 0.953198i \(0.597770\pi\)
\(14\) 0 0
\(15\) −1.54432 0.351336i −0.398743 0.0907145i
\(16\) 0 0
\(17\) −3.05270 + 5.28743i −0.740388 + 1.28239i 0.211931 + 0.977285i \(0.432025\pi\)
−0.952319 + 0.305105i \(0.901309\pi\)
\(18\) 0 0
\(19\) 4.82172 2.78382i 1.10618 0.638653i 0.168342 0.985729i \(-0.446159\pi\)
0.937837 + 0.347076i \(0.112825\pi\)
\(20\) 0 0
\(21\) 4.23604 1.74813i 0.924380 0.381472i
\(22\) 0 0
\(23\) −0.548926 + 1.50816i −0.114459 + 0.314474i −0.983674 0.179961i \(-0.942403\pi\)
0.869215 + 0.494435i \(0.164625\pi\)
\(24\) 0 0
\(25\) −0.723049 + 4.10062i −0.144610 + 0.820123i
\(26\) 0 0
\(27\) 4.83293 1.90860i 0.930098 0.367311i
\(28\) 0 0
\(29\) 4.21794 5.02674i 0.783251 0.933443i −0.215824 0.976432i \(-0.569244\pi\)
0.999076 + 0.0429895i \(0.0136882\pi\)
\(30\) 0 0
\(31\) 1.54773 + 1.84452i 0.277981 + 0.331285i 0.886912 0.461938i \(-0.152846\pi\)
−0.608931 + 0.793223i \(0.708401\pi\)
\(32\) 0 0
\(33\) −6.47828 0.318735i −1.12772 0.0554846i
\(34\) 0 0
\(35\) 1.03167 + 2.18827i 0.174383 + 0.369886i
\(36\) 0 0
\(37\) −2.43591 −0.400460 −0.200230 0.979749i \(-0.564169\pi\)
−0.200230 + 0.979749i \(0.564169\pi\)
\(38\) 0 0
\(39\) 1.48467 6.52598i 0.237737 1.04499i
\(40\) 0 0
\(41\) 4.95635 4.15887i 0.774052 0.649506i −0.167691 0.985840i \(-0.553631\pi\)
0.941743 + 0.336333i \(0.109187\pi\)
\(42\) 0 0
\(43\) 7.68736 2.79797i 1.17231 0.426686i 0.318831 0.947812i \(-0.396710\pi\)
0.853480 + 0.521125i \(0.174488\pi\)
\(44\) 0 0
\(45\) 1.13177 + 2.49884i 0.168714 + 0.372506i
\(46\) 0 0
\(47\) 3.52092 + 2.95440i 0.513579 + 0.430944i 0.862386 0.506251i \(-0.168969\pi\)
−0.348808 + 0.937194i \(0.613413\pi\)
\(48\) 0 0
\(49\) −6.09148 3.44875i −0.870212 0.492678i
\(50\) 0 0
\(51\) 10.4919 1.32232i 1.46915 0.185162i
\(52\) 0 0
\(53\) 9.92435 5.72983i 1.36321 0.787052i 0.373164 0.927765i \(-0.378273\pi\)
0.990050 + 0.140713i \(0.0449396\pi\)
\(54\) 0 0
\(55\) 3.42420i 0.461720i
\(56\) 0 0
\(57\) −8.88885 3.73958i −1.17736 0.495319i
\(58\) 0 0
\(59\) −0.154736 0.877551i −0.0201449 0.114247i 0.973077 0.230479i \(-0.0740295\pi\)
−0.993222 + 0.116232i \(0.962918\pi\)
\(60\) 0 0
\(61\) −7.92124 + 9.44017i −1.01421 + 1.20869i −0.0363705 + 0.999338i \(0.511580\pi\)
−0.977841 + 0.209351i \(0.932865\pi\)
\(62\) 0 0
\(63\) −6.84656 4.01554i −0.862586 0.505910i
\(64\) 0 0
\(65\) 3.47960 + 0.613548i 0.431592 + 0.0761012i
\(66\) 0 0
\(67\) −12.2484 4.45805i −1.49638 0.544637i −0.541258 0.840856i \(-0.682052\pi\)
−0.955120 + 0.296219i \(0.904274\pi\)
\(68\) 0 0
\(69\) 2.65578 0.821252i 0.319718 0.0988671i
\(70\) 0 0
\(71\) 11.1044 6.41115i 1.31785 0.760864i 0.334471 0.942406i \(-0.391442\pi\)
0.983383 + 0.181542i \(0.0581089\pi\)
\(72\) 0 0
\(73\) 4.85770i 0.568551i 0.958743 + 0.284275i \(0.0917530\pi\)
−0.958743 + 0.284275i \(0.908247\pi\)
\(74\) 0 0
\(75\) 6.41547 3.29474i 0.740795 0.380444i
\(76\) 0 0
\(77\) 5.71700 + 8.09188i 0.651513 + 0.922155i
\(78\) 0 0
\(79\) 5.29825 1.92841i 0.596100 0.216963i −0.0263101 0.999654i \(-0.508376\pi\)
0.622410 + 0.782691i \(0.286154\pi\)
\(80\) 0 0
\(81\) −7.69283 4.67122i −0.854759 0.519025i
\(82\) 0 0
\(83\) 6.26479 + 5.25678i 0.687650 + 0.577006i 0.918230 0.396047i \(-0.129618\pi\)
−0.230581 + 0.973053i \(0.574063\pi\)
\(84\) 0 0
\(85\) 0.969437 + 5.49795i 0.105150 + 0.596336i
\(86\) 0 0
\(87\) −11.3519 0.558520i −1.21705 0.0598796i
\(88\) 0 0
\(89\) 2.04328 + 3.53906i 0.216587 + 0.375139i 0.953762 0.300562i \(-0.0971742\pi\)
−0.737175 + 0.675701i \(0.763841\pi\)
\(90\) 0 0
\(91\) −9.24716 + 4.35959i −0.969366 + 0.457009i
\(92\) 0 0
\(93\) 0.925156 4.06660i 0.0959342 0.421687i
\(94\) 0 0
\(95\) 1.74124 4.78402i 0.178648 0.490830i
\(96\) 0 0
\(97\) 4.13766 + 11.3681i 0.420115 + 1.15426i 0.951640 + 0.307215i \(0.0993971\pi\)
−0.531525 + 0.847043i \(0.678381\pi\)
\(98\) 0 0
\(99\) 6.34159 + 9.27326i 0.637354 + 0.931998i
\(100\) 0 0
\(101\) −2.79081 + 1.01577i −0.277696 + 0.101073i −0.477114 0.878842i \(-0.658317\pi\)
0.199418 + 0.979914i \(0.436095\pi\)
\(102\) 0 0
\(103\) 5.85295 + 6.97527i 0.576708 + 0.687294i 0.972993 0.230834i \(-0.0741453\pi\)
−0.396285 + 0.918127i \(0.629701\pi\)
\(104\) 0 0
\(105\) 1.93974 3.71430i 0.189299 0.362479i
\(106\) 0 0
\(107\) −12.5146 7.22532i −1.20983 0.698498i −0.247111 0.968987i \(-0.579481\pi\)
−0.962723 + 0.270489i \(0.912815\pi\)
\(108\) 0 0
\(109\) 4.51287 + 7.81653i 0.432255 + 0.748688i 0.997067 0.0765319i \(-0.0243847\pi\)
−0.564812 + 0.825220i \(0.691051\pi\)
\(110\) 0 0
\(111\) 2.54989 + 3.36139i 0.242025 + 0.319049i
\(112\) 0 0
\(113\) −3.84867 + 10.5741i −0.362053 + 0.994732i 0.616250 + 0.787551i \(0.288651\pi\)
−0.978303 + 0.207181i \(0.933571\pi\)
\(114\) 0 0
\(115\) 0.501937 + 1.37906i 0.0468059 + 0.128598i
\(116\) 0 0
\(117\) −10.5596 + 4.78261i −0.976233 + 0.442152i
\(118\) 0 0
\(119\) −11.4702 11.3739i −1.05147 1.04264i
\(120\) 0 0
\(121\) −0.524979 2.97730i −0.0477253 0.270664i
\(122\) 0 0
\(123\) −10.9273 2.48596i −0.985277 0.224152i
\(124\) 0 0
\(125\) 4.18972 + 7.25680i 0.374740 + 0.649068i
\(126\) 0 0
\(127\) 1.76290 3.05343i 0.156432 0.270948i −0.777148 0.629318i \(-0.783334\pi\)
0.933579 + 0.358370i \(0.116668\pi\)
\(128\) 0 0
\(129\) −11.9081 7.67916i −1.04845 0.676112i
\(130\) 0 0
\(131\) −10.8842 3.96153i −0.950957 0.346120i −0.180474 0.983580i \(-0.557763\pi\)
−0.770484 + 0.637460i \(0.779985\pi\)
\(132\) 0 0
\(133\) 3.87253 + 14.2125i 0.335791 + 1.23238i
\(134\) 0 0
\(135\) 2.26352 4.17754i 0.194812 0.359546i
\(136\) 0 0
\(137\) −4.58013 0.807600i −0.391307 0.0689980i −0.0254667 0.999676i \(-0.508107\pi\)
−0.365840 + 0.930678i \(0.619218\pi\)
\(138\) 0 0
\(139\) −20.6952 + 3.64913i −1.75535 + 0.309515i −0.956438 0.291935i \(-0.905701\pi\)
−0.798910 + 0.601450i \(0.794590\pi\)
\(140\) 0 0
\(141\) 0.391208 7.95129i 0.0329457 0.669619i
\(142\) 0 0
\(143\) 14.4699 1.21004
\(144\) 0 0
\(145\) 6.00024i 0.498292i
\(146\) 0 0
\(147\) 1.61748 + 12.0160i 0.133407 + 0.991061i
\(148\) 0 0
\(149\) −13.2104 + 2.32935i −1.08224 + 0.190827i −0.686204 0.727409i \(-0.740724\pi\)
−0.396032 + 0.918237i \(0.629613\pi\)
\(150\) 0 0
\(151\) −8.01271 6.72346i −0.652065 0.547148i 0.255632 0.966774i \(-0.417717\pi\)
−0.907697 + 0.419627i \(0.862161\pi\)
\(152\) 0 0
\(153\) −12.8075 13.0939i −1.03543 1.05858i
\(154\) 0 0
\(155\) 2.16828 + 0.382326i 0.174160 + 0.0307092i
\(156\) 0 0
\(157\) −19.5690 + 3.45055i −1.56178 + 0.275384i −0.886694 0.462357i \(-0.847004\pi\)
−0.675084 + 0.737741i \(0.735893\pi\)
\(158\) 0 0
\(159\) −18.2955 7.69702i −1.45093 0.610413i
\(160\) 0 0
\(161\) −3.48861 2.42089i −0.274941 0.190793i
\(162\) 0 0
\(163\) 7.01252 12.1460i 0.549263 0.951352i −0.449062 0.893501i \(-0.648242\pi\)
0.998325 0.0578512i \(-0.0184249\pi\)
\(164\) 0 0
\(165\) −4.72518 + 3.58444i −0.367855 + 0.279048i
\(166\) 0 0
\(167\) 2.12777 + 0.774444i 0.164652 + 0.0599283i 0.423031 0.906115i \(-0.360966\pi\)
−0.258379 + 0.966044i \(0.583188\pi\)
\(168\) 0 0
\(169\) −0.335292 + 1.90154i −0.0257917 + 0.146272i
\(170\) 0 0
\(171\) 4.14441 + 16.1806i 0.316931 + 1.23736i
\(172\) 0 0
\(173\) 4.40574 24.9862i 0.334962 1.89967i −0.0926401 0.995700i \(-0.529531\pi\)
0.427603 0.903967i \(-0.359358\pi\)
\(174\) 0 0
\(175\) −10.0040 4.61366i −0.756228 0.348760i
\(176\) 0 0
\(177\) −1.04899 + 1.13214i −0.0788467 + 0.0850969i
\(178\) 0 0
\(179\) 3.76744 + 2.17513i 0.281591 + 0.162577i 0.634144 0.773215i \(-0.281353\pi\)
−0.352552 + 0.935792i \(0.614686\pi\)
\(180\) 0 0
\(181\) 2.32397 + 1.34175i 0.172740 + 0.0997313i 0.583877 0.811842i \(-0.301535\pi\)
−0.411137 + 0.911573i \(0.634868\pi\)
\(182\) 0 0
\(183\) 21.3187 + 1.04889i 1.57593 + 0.0775364i
\(184\) 0 0
\(185\) −1.70628 + 1.43174i −0.125448 + 0.105263i
\(186\) 0 0
\(187\) 7.81969 + 21.4844i 0.571832 + 1.57110i
\(188\) 0 0
\(189\) 1.62576 + 13.6513i 0.118256 + 0.992983i
\(190\) 0 0
\(191\) 5.63477 + 15.4814i 0.407717 + 1.12019i 0.958387 + 0.285471i \(0.0921501\pi\)
−0.550670 + 0.834723i \(0.685628\pi\)
\(192\) 0 0
\(193\) 7.76210 6.51318i 0.558728 0.468829i −0.319156 0.947702i \(-0.603399\pi\)
0.877884 + 0.478874i \(0.158955\pi\)
\(194\) 0 0
\(195\) −2.79577 5.44389i −0.200209 0.389845i
\(196\) 0 0
\(197\) 23.3394 + 13.4750i 1.66286 + 0.960054i 0.971338 + 0.237701i \(0.0763939\pi\)
0.691524 + 0.722353i \(0.256939\pi\)
\(198\) 0 0
\(199\) −10.8742 6.27825i −0.770855 0.445053i 0.0623246 0.998056i \(-0.480149\pi\)
−0.833180 + 0.553003i \(0.813482\pi\)
\(200\) 0 0
\(201\) 6.66972 + 21.5686i 0.470445 + 1.52133i
\(202\) 0 0
\(203\) 10.0179 + 14.1794i 0.703119 + 0.995199i
\(204\) 0 0
\(205\) 1.02734 5.82633i 0.0717525 0.406928i
\(206\) 0 0
\(207\) −3.91333 2.80512i −0.271995 0.194969i
\(208\) 0 0
\(209\) 3.62048 20.5328i 0.250434 1.42028i
\(210\) 0 0
\(211\) 4.63971 + 1.68871i 0.319411 + 0.116256i 0.496750 0.867894i \(-0.334527\pi\)
−0.177339 + 0.984150i \(0.556749\pi\)
\(212\) 0 0
\(213\) −20.4710 8.61226i −1.40265 0.590102i
\(214\) 0 0
\(215\) 3.74022 6.47825i 0.255081 0.441813i
\(216\) 0 0
\(217\) −5.76228 + 2.71664i −0.391169 + 0.184417i
\(218\) 0 0
\(219\) 6.70331 5.08501i 0.452968 0.343613i
\(220\) 0 0
\(221\) −23.2331 + 4.09663i −1.56283 + 0.275569i
\(222\) 0 0
\(223\) −12.8650 2.26844i −0.861502 0.151906i −0.274595 0.961560i \(-0.588544\pi\)
−0.586908 + 0.809654i \(0.699655\pi\)
\(224\) 0 0
\(225\) −11.2622 5.40402i −0.750814 0.360268i
\(226\) 0 0
\(227\) −11.7375 9.84892i −0.779044 0.653696i 0.163963 0.986466i \(-0.447572\pi\)
−0.943008 + 0.332770i \(0.892017\pi\)
\(228\) 0 0
\(229\) 9.15063 1.61350i 0.604691 0.106623i 0.137083 0.990560i \(-0.456227\pi\)
0.467608 + 0.883936i \(0.345116\pi\)
\(230\) 0 0
\(231\) 5.18175 16.3596i 0.340934 1.07638i
\(232\) 0 0
\(233\) 9.39194i 0.615286i −0.951502 0.307643i \(-0.900460\pi\)
0.951502 0.307643i \(-0.0995403\pi\)
\(234\) 0 0
\(235\) 4.20279 0.274160
\(236\) 0 0
\(237\) −8.20726 5.29261i −0.533119 0.343792i
\(238\) 0 0
\(239\) −8.59351 + 1.51527i −0.555868 + 0.0980145i −0.444523 0.895767i \(-0.646627\pi\)
−0.111345 + 0.993782i \(0.535516\pi\)
\(240\) 0 0
\(241\) −5.56319 0.980941i −0.358357 0.0631880i −0.00842855 0.999964i \(-0.502683\pi\)
−0.349928 + 0.936777i \(0.613794\pi\)
\(242\) 0 0
\(243\) 1.60682 + 15.5054i 0.103078 + 0.994673i
\(244\) 0 0
\(245\) −6.29395 + 1.16461i −0.402106 + 0.0744043i
\(246\) 0 0
\(247\) 20.2162 + 7.35811i 1.28633 + 0.468185i
\(248\) 0 0
\(249\) 0.696078 14.1478i 0.0441121 0.896578i
\(250\) 0 0
\(251\) −0.593298 + 1.02762i −0.0374487 + 0.0648630i −0.884142 0.467218i \(-0.845256\pi\)
0.846694 + 0.532081i \(0.178590\pi\)
\(252\) 0 0
\(253\) 3.00508 + 5.20495i 0.188928 + 0.327233i
\(254\) 0 0
\(255\) 6.57202 7.09298i 0.411556 0.444180i
\(256\) 0 0
\(257\) 2.10237 + 11.9231i 0.131142 + 0.743743i 0.977469 + 0.211080i \(0.0676979\pi\)
−0.846327 + 0.532664i \(0.821191\pi\)
\(258\) 0 0
\(259\) 1.64177 6.23218i 0.102015 0.387249i
\(260\) 0 0
\(261\) 11.1124 + 16.2495i 0.687839 + 1.00582i
\(262\) 0 0
\(263\) −0.490567 1.34782i −0.0302497 0.0831103i 0.923649 0.383241i \(-0.125192\pi\)
−0.953898 + 0.300130i \(0.902970\pi\)
\(264\) 0 0
\(265\) 3.58392 9.84675i 0.220159 0.604881i
\(266\) 0 0
\(267\) 2.74478 6.52425i 0.167978 0.399278i
\(268\) 0 0
\(269\) −5.22031 9.04184i −0.318288 0.551291i 0.661843 0.749642i \(-0.269775\pi\)
−0.980131 + 0.198352i \(0.936441\pi\)
\(270\) 0 0
\(271\) 11.2170 + 6.47615i 0.681386 + 0.393398i 0.800377 0.599497i \(-0.204633\pi\)
−0.118991 + 0.992895i \(0.537966\pi\)
\(272\) 0 0
\(273\) 15.6958 + 8.19690i 0.949955 + 0.496099i
\(274\) 0 0
\(275\) 10.0228 + 11.9447i 0.604398 + 0.720293i
\(276\) 0 0
\(277\) 19.0041 6.91693i 1.14185 0.415598i 0.299267 0.954169i \(-0.403258\pi\)
0.842580 + 0.538571i \(0.181036\pi\)
\(278\) 0 0
\(279\) −6.58009 + 2.98024i −0.393940 + 0.178422i
\(280\) 0 0
\(281\) −9.35867 25.7127i −0.558291 1.53389i −0.822115 0.569322i \(-0.807206\pi\)
0.263824 0.964571i \(-0.415016\pi\)
\(282\) 0 0
\(283\) −7.50273 + 20.6136i −0.445991 + 1.22535i 0.489501 + 0.872003i \(0.337179\pi\)
−0.935492 + 0.353347i \(0.885043\pi\)
\(284\) 0 0
\(285\) −8.42436 + 2.60508i −0.499016 + 0.154312i
\(286\) 0 0
\(287\) 7.29981 + 15.4837i 0.430894 + 0.913972i
\(288\) 0 0
\(289\) −10.1379 17.5594i −0.596348 1.03291i
\(290\) 0 0
\(291\) 11.3560 17.6098i 0.665701 1.03230i
\(292\) 0 0
\(293\) −2.68082 15.2037i −0.156615 0.888209i −0.957294 0.289116i \(-0.906639\pi\)
0.800679 0.599094i \(-0.204472\pi\)
\(294\) 0 0
\(295\) −0.624181 0.523750i −0.0363412 0.0304939i
\(296\) 0 0
\(297\) 6.15816 18.4582i 0.357333 1.07105i
\(298\) 0 0
\(299\) −5.82761 + 2.12108i −0.337019 + 0.122665i
\(300\) 0 0
\(301\) 1.97732 + 21.5536i 0.113971 + 1.24233i
\(302\) 0 0
\(303\) 4.32310 + 2.78783i 0.248355 + 0.160157i
\(304\) 0 0
\(305\) 11.2684i 0.645225i
\(306\) 0 0
\(307\) 22.4632 12.9691i 1.28204 0.740187i 0.304820 0.952410i \(-0.401404\pi\)
0.977221 + 0.212223i \(0.0680704\pi\)
\(308\) 0 0
\(309\) 3.49860 15.3784i 0.199028 0.874844i
\(310\) 0 0
\(311\) −0.873505 0.317930i −0.0495319 0.0180281i 0.317135 0.948380i \(-0.397279\pi\)
−0.366667 + 0.930352i \(0.619501\pi\)
\(312\) 0 0
\(313\) 4.73809 + 0.835452i 0.267812 + 0.0472226i 0.305942 0.952050i \(-0.401029\pi\)
−0.0381292 + 0.999273i \(0.512140\pi\)
\(314\) 0 0
\(315\) −7.15600 + 1.21140i −0.403195 + 0.0682547i
\(316\) 0 0
\(317\) 8.42285 10.0380i 0.473074 0.563788i −0.475755 0.879578i \(-0.657825\pi\)
0.948829 + 0.315790i \(0.102269\pi\)
\(318\) 0 0
\(319\) −4.26704 24.1996i −0.238909 1.35492i
\(320\) 0 0
\(321\) 3.12975 + 24.8328i 0.174686 + 1.38603i
\(322\) 0 0
\(323\) 33.9927i 1.89140i
\(324\) 0 0
\(325\) −13.9338 + 8.04471i −0.772910 + 0.446240i
\(326\) 0 0
\(327\) 6.06226 14.4098i 0.335244 0.796862i
\(328\) 0 0
\(329\) −9.93179 + 7.01692i −0.547557 + 0.386855i
\(330\) 0 0
\(331\) −14.0616 11.7991i −0.772897 0.648537i 0.168552 0.985693i \(-0.446091\pi\)
−0.941449 + 0.337156i \(0.890535\pi\)
\(332\) 0 0
\(333\) 1.96930 7.03737i 0.107917 0.385646i
\(334\) 0 0
\(335\) −11.1999 + 4.07643i −0.611916 + 0.222719i
\(336\) 0 0
\(337\) −19.7150 + 16.5428i −1.07394 + 0.901145i −0.995404 0.0957659i \(-0.969470\pi\)
−0.0785390 + 0.996911i \(0.525026\pi\)
\(338\) 0 0
\(339\) 18.6204 5.75803i 1.01132 0.312733i
\(340\) 0 0
\(341\) 9.01680 0.488287
\(342\) 0 0
\(343\) 12.9291 13.2604i 0.698105 0.715996i
\(344\) 0 0
\(345\) 1.37759 2.13623i 0.0741670 0.115011i
\(346\) 0 0
\(347\) −12.4203 14.8019i −0.666756 0.794609i 0.321582 0.946882i \(-0.395785\pi\)
−0.988339 + 0.152272i \(0.951341\pi\)
\(348\) 0 0
\(349\) 5.91691 7.05150i 0.316725 0.377458i −0.584070 0.811704i \(-0.698541\pi\)
0.900795 + 0.434245i \(0.142985\pi\)
\(350\) 0 0
\(351\) 17.6534 + 9.56512i 0.942268 + 0.510548i
\(352\) 0 0
\(353\) −4.49925 + 25.5165i −0.239471 + 1.35811i 0.593520 + 0.804820i \(0.297738\pi\)
−0.832990 + 0.553287i \(0.813373\pi\)
\(354\) 0 0
\(355\) 4.01008 11.0176i 0.212833 0.584754i
\(356\) 0 0
\(357\) −3.68827 + 27.7343i −0.195204 + 1.46785i
\(358\) 0 0
\(359\) −18.8538 + 10.8853i −0.995068 + 0.574503i −0.906785 0.421593i \(-0.861471\pi\)
−0.0882827 + 0.996095i \(0.528138\pi\)
\(360\) 0 0
\(361\) 5.99935 10.3912i 0.315755 0.546904i
\(362\) 0 0
\(363\) −3.55894 + 3.84106i −0.186796 + 0.201603i
\(364\) 0 0
\(365\) 2.85518 + 3.40267i 0.149447 + 0.178104i
\(366\) 0 0
\(367\) −10.0506 + 11.9778i −0.524635 + 0.625235i −0.961670 0.274209i \(-0.911584\pi\)
0.437035 + 0.899444i \(0.356028\pi\)
\(368\) 0 0
\(369\) 8.00811 + 17.6812i 0.416886 + 0.920446i
\(370\) 0 0
\(371\) 7.97067 + 29.2529i 0.413816 + 1.51874i
\(372\) 0 0
\(373\) −18.2009 + 15.2724i −0.942409 + 0.790775i −0.978003 0.208591i \(-0.933112\pi\)
0.0355936 + 0.999366i \(0.488668\pi\)
\(374\) 0 0
\(375\) 5.62815 13.3779i 0.290636 0.690833i
\(376\) 0 0
\(377\) 25.3557 1.30588
\(378\) 0 0
\(379\) −2.22199 −0.114136 −0.0570680 0.998370i \(-0.518175\pi\)
−0.0570680 + 0.998370i \(0.518175\pi\)
\(380\) 0 0
\(381\) −6.05892 + 0.763625i −0.310408 + 0.0391217i
\(382\) 0 0
\(383\) 15.8539 13.3030i 0.810095 0.679751i −0.140535 0.990076i \(-0.544882\pi\)
0.950631 + 0.310325i \(0.100438\pi\)
\(384\) 0 0
\(385\) 8.76070 + 2.30787i 0.446487 + 0.117620i
\(386\) 0 0
\(387\) 1.86857 + 24.4709i 0.0949849 + 1.24393i
\(388\) 0 0
\(389\) 18.8479 22.4621i 0.955626 1.13887i −0.0345999 0.999401i \(-0.511016\pi\)
0.990226 0.139470i \(-0.0445399\pi\)
\(390\) 0 0
\(391\) −6.29859 7.50637i −0.318533 0.379613i
\(392\) 0 0
\(393\) 5.92687 + 19.1664i 0.298971 + 0.966817i
\(394\) 0 0
\(395\) 2.57782 4.46492i 0.129704 0.224654i
\(396\) 0 0
\(397\) 27.6163 15.9443i 1.38602 0.800220i 0.393158 0.919471i \(-0.371383\pi\)
0.992864 + 0.119251i \(0.0380494\pi\)
\(398\) 0 0
\(399\) 15.5586 20.2214i 0.778902 1.01234i
\(400\) 0 0
\(401\) 3.57887 9.83286i 0.178720 0.491030i −0.817693 0.575655i \(-0.804747\pi\)
0.996413 + 0.0846254i \(0.0269694\pi\)
\(402\) 0 0
\(403\) −1.61563 + 9.16268i −0.0804801 + 0.456426i
\(404\) 0 0
\(405\) −8.13418 + 1.24952i −0.404190 + 0.0620892i
\(406\) 0 0
\(407\) −5.86343 + 6.98777i −0.290640 + 0.346371i
\(408\) 0 0
\(409\) −0.632612 0.753918i −0.0312807 0.0372788i 0.750177 0.661237i \(-0.229968\pi\)
−0.781458 + 0.623958i \(0.785524\pi\)
\(410\) 0 0
\(411\) 3.68001 + 7.16567i 0.181522 + 0.353457i
\(412\) 0 0
\(413\) 2.34947 + 0.195572i 0.115610 + 0.00962347i
\(414\) 0 0
\(415\) 7.47804 0.367083
\(416\) 0 0
\(417\) 26.6992 + 24.7382i 1.30747 + 1.21144i
\(418\) 0 0
\(419\) −10.6223 + 8.91314i −0.518931 + 0.435435i −0.864259 0.503047i \(-0.832212\pi\)
0.345328 + 0.938482i \(0.387768\pi\)
\(420\) 0 0
\(421\) 6.03019 2.19481i 0.293893 0.106968i −0.190866 0.981616i \(-0.561130\pi\)
0.484759 + 0.874648i \(0.338907\pi\)
\(422\) 0 0
\(423\) −11.3818 + 7.78352i −0.553401 + 0.378448i
\(424\) 0 0
\(425\) −19.4745 16.3410i −0.944650 0.792655i
\(426\) 0 0
\(427\) −18.8135 26.6288i −0.910450 1.28866i
\(428\) 0 0
\(429\) −15.1470 19.9676i −0.731306 0.964044i
\(430\) 0 0
\(431\) −8.73432 + 5.04276i −0.420717 + 0.242901i −0.695384 0.718638i \(-0.744766\pi\)
0.274667 + 0.961539i \(0.411432\pi\)
\(432\) 0 0
\(433\) 15.6232i 0.750805i 0.926862 + 0.375403i \(0.122496\pi\)
−0.926862 + 0.375403i \(0.877504\pi\)
\(434\) 0 0
\(435\) −8.27994 + 6.28101i −0.396993 + 0.301151i
\(436\) 0 0
\(437\) 1.55169 + 8.80005i 0.0742273 + 0.420964i
\(438\) 0 0
\(439\) 17.3026 20.6205i 0.825809 0.984161i −0.174191 0.984712i \(-0.555731\pi\)
1.00000 0.000551317i \(0.000175490\pi\)
\(440\) 0 0
\(441\) 14.8881 14.8103i 0.708958 0.705251i
\(442\) 0 0
\(443\) −33.6691 5.93677i −1.59967 0.282064i −0.698524 0.715587i \(-0.746159\pi\)
−0.901143 + 0.433522i \(0.857270\pi\)
\(444\) 0 0
\(445\) 3.51138 + 1.27804i 0.166456 + 0.0605849i
\(446\) 0 0
\(447\) 17.0429 + 15.7911i 0.806101 + 0.746895i
\(448\) 0 0
\(449\) 21.9379 12.6659i 1.03531 0.597739i 0.116812 0.993154i \(-0.462733\pi\)
0.918502 + 0.395415i \(0.129399\pi\)
\(450\) 0 0
\(451\) 24.2288i 1.14089i
\(452\) 0 0
\(453\) −0.890289 + 18.0951i −0.0418294 + 0.850182i
\(454\) 0 0
\(455\) −3.91495 + 8.48892i −0.183536 + 0.397966i
\(456\) 0 0
\(457\) 28.2998 10.3003i 1.32381 0.481828i 0.419133 0.907925i \(-0.362334\pi\)
0.904677 + 0.426097i \(0.140112\pi\)
\(458\) 0 0
\(459\) −4.66188 + 31.3802i −0.217598 + 1.46470i
\(460\) 0 0
\(461\) −16.9479 14.2210i −0.789344 0.662338i 0.156239 0.987719i \(-0.450063\pi\)
−0.945583 + 0.325381i \(0.894507\pi\)
\(462\) 0 0
\(463\) −6.48204 36.7614i −0.301246 1.70845i −0.640670 0.767816i \(-0.721343\pi\)
0.339425 0.940633i \(-0.389768\pi\)
\(464\) 0 0
\(465\) −1.74216 3.39230i −0.0807906 0.157314i
\(466\) 0 0
\(467\) −8.81347 15.2654i −0.407839 0.706397i 0.586809 0.809726i \(-0.300384\pi\)
−0.994647 + 0.103328i \(0.967051\pi\)
\(468\) 0 0
\(469\) 19.6610 28.3324i 0.907861 1.30827i
\(470\) 0 0
\(471\) 25.2463 + 23.3920i 1.16329 + 1.07785i
\(472\) 0 0
\(473\) 10.4777 28.7873i 0.481766 1.32364i
\(474\) 0 0
\(475\) 7.92905 + 21.7849i 0.363810 + 0.999559i
\(476\) 0 0
\(477\) 8.53027 + 33.3039i 0.390574 + 1.52488i
\(478\) 0 0
\(479\) 24.5142 8.92243i 1.12008 0.407676i 0.285399 0.958409i \(-0.407874\pi\)
0.834682 + 0.550733i \(0.185652\pi\)
\(480\) 0 0
\(481\) −6.05021 7.21036i −0.275866 0.328764i
\(482\) 0 0
\(483\) 0.311182 + 7.34823i 0.0141593 + 0.334356i
\(484\) 0 0
\(485\) 9.58008 + 5.53106i 0.435009 + 0.251153i
\(486\) 0 0
\(487\) 1.88377 + 3.26279i 0.0853619 + 0.147851i 0.905545 0.424249i \(-0.139462\pi\)
−0.820183 + 0.572101i \(0.806129\pi\)
\(488\) 0 0
\(489\) −24.1014 + 3.03758i −1.08990 + 0.137364i
\(490\) 0 0
\(491\) −10.2584 + 28.1847i −0.462955 + 1.27196i 0.460298 + 0.887764i \(0.347743\pi\)
−0.923253 + 0.384193i \(0.874480\pi\)
\(492\) 0 0
\(493\) 13.7024 + 37.6472i 0.617127 + 1.69554i
\(494\) 0 0
\(495\) 9.89258 + 2.76828i 0.444638 + 0.124425i
\(496\) 0 0
\(497\) 8.91845 + 32.7314i 0.400047 + 1.46820i
\(498\) 0 0
\(499\) −3.23287 18.3345i −0.144723 0.820766i −0.967589 0.252530i \(-0.918737\pi\)
0.822866 0.568236i \(-0.192374\pi\)
\(500\) 0 0
\(501\) −1.15865 3.74686i −0.0517647 0.167398i
\(502\) 0 0
\(503\) −21.0298 36.4246i −0.937670 1.62409i −0.769801 0.638284i \(-0.779645\pi\)
−0.167869 0.985809i \(-0.553689\pi\)
\(504\) 0 0
\(505\) −1.35784 + 2.35185i −0.0604232 + 0.104656i
\(506\) 0 0
\(507\) 2.97498 1.52783i 0.132123 0.0678535i
\(508\) 0 0
\(509\) −22.9472 8.35211i −1.01712 0.370201i −0.220956 0.975284i \(-0.570918\pi\)
−0.796162 + 0.605083i \(0.793140\pi\)
\(510\) 0 0
\(511\) −12.4283 3.27403i −0.549794 0.144835i
\(512\) 0 0
\(513\) 17.9899 22.6568i 0.794271 1.00032i
\(514\) 0 0
\(515\) 8.19963 + 1.44582i 0.361319 + 0.0637102i
\(516\) 0 0
\(517\) 16.9503 2.98880i 0.745474 0.131447i
\(518\) 0 0
\(519\) −39.0913 + 20.0758i −1.71592 + 0.881229i
\(520\) 0 0
\(521\) 16.6726 0.730441 0.365220 0.930921i \(-0.380994\pi\)
0.365220 + 0.930921i \(0.380994\pi\)
\(522\) 0 0
\(523\) 9.76741i 0.427099i −0.976932 0.213549i \(-0.931498\pi\)
0.976932 0.213549i \(-0.0685024\pi\)
\(524\) 0 0
\(525\) 4.10552 + 18.6344i 0.179180 + 0.813270i
\(526\) 0 0
\(527\) −14.4775 + 2.55277i −0.630650 + 0.111201i
\(528\) 0 0
\(529\) 15.6458 + 13.1284i 0.680252 + 0.570799i
\(530\) 0 0
\(531\) 2.66035 + 0.262417i 0.115450 + 0.0113879i
\(532\) 0 0
\(533\) 24.6208 + 4.34131i 1.06644 + 0.188043i
\(534\) 0 0
\(535\) −13.0129 + 2.29453i −0.562597 + 0.0992010i
\(536\) 0 0
\(537\) −0.942189 7.47573i −0.0406585 0.322602i
\(538\) 0 0
\(539\) −24.5560 + 9.17292i −1.05770 + 0.395106i
\(540\) 0 0
\(541\) 15.0773 26.1147i 0.648224 1.12276i −0.335322 0.942103i \(-0.608845\pi\)
0.983547 0.180654i \(-0.0578214\pi\)
\(542\) 0 0
\(543\) −0.581197 4.61147i −0.0249416 0.197897i
\(544\) 0 0
\(545\) 7.75541 + 2.82274i 0.332205 + 0.120913i
\(546\) 0 0
\(547\) −8.06550 + 45.7417i −0.344856 + 1.95578i −0.0558860 + 0.998437i \(0.517798\pi\)
−0.288970 + 0.957338i \(0.593313\pi\)
\(548\) 0 0
\(549\) −20.8689 30.5165i −0.890663 1.30241i
\(550\) 0 0
\(551\) 6.34417 35.9796i 0.270271 1.53278i
\(552\) 0 0
\(553\) 1.36280 + 14.8551i 0.0579523 + 0.631704i
\(554\) 0 0
\(555\) 3.76183 + 0.855820i 0.159681 + 0.0363276i
\(556\) 0 0
\(557\) −29.5500 17.0607i −1.25207 0.722886i −0.280554 0.959838i \(-0.590518\pi\)
−0.971521 + 0.236953i \(0.923851\pi\)
\(558\) 0 0
\(559\) 27.3756 + 15.8053i 1.15787 + 0.668494i
\(560\) 0 0
\(561\) 21.4615 33.2804i 0.906106 1.40510i
\(562\) 0 0
\(563\) −4.17263 + 3.50125i −0.175855 + 0.147560i −0.726467 0.687201i \(-0.758839\pi\)
0.550612 + 0.834762i \(0.314395\pi\)
\(564\) 0 0
\(565\) 3.51922 + 9.66898i 0.148055 + 0.406777i
\(566\) 0 0
\(567\) 17.1360 16.5335i 0.719646 0.694342i
\(568\) 0 0
\(569\) −0.348275 0.956878i −0.0146005 0.0401144i 0.932178 0.361999i \(-0.117906\pi\)
−0.946779 + 0.321885i \(0.895684\pi\)
\(570\) 0 0
\(571\) 2.74392 2.30242i 0.114830 0.0963534i −0.583565 0.812067i \(-0.698343\pi\)
0.698394 + 0.715713i \(0.253898\pi\)
\(572\) 0 0
\(573\) 15.4649 23.9814i 0.646055 1.00184i
\(574\) 0 0
\(575\) −5.78749 3.34141i −0.241355 0.139346i
\(576\) 0 0
\(577\) −19.9959 11.5446i −0.832440 0.480609i 0.0222476 0.999752i \(-0.492918\pi\)
−0.854687 + 0.519143i \(0.826251\pi\)
\(578\) 0 0
\(579\) −17.1131 3.89325i −0.711196 0.161798i
\(580\) 0 0
\(581\) −17.6717 + 12.4852i −0.733144 + 0.517974i
\(582\) 0 0
\(583\) 7.45188 42.2617i 0.308625 1.75030i
\(584\) 0 0
\(585\) −4.58562 + 9.55661i −0.189592 + 0.395117i
\(586\) 0 0
\(587\) 0.0818717 0.464317i 0.00337921 0.0191644i −0.983072 0.183222i \(-0.941347\pi\)
0.986451 + 0.164058i \(0.0524583\pi\)
\(588\) 0 0
\(589\) 12.5975 + 4.58513i 0.519073 + 0.188927i
\(590\) 0 0
\(591\) −5.83689 46.3124i −0.240098 1.90504i
\(592\) 0 0
\(593\) −19.0760 + 33.0406i −0.783357 + 1.35681i 0.146619 + 0.989193i \(0.453161\pi\)
−0.929976 + 0.367621i \(0.880172\pi\)
\(594\) 0 0
\(595\) −14.7197 1.22528i −0.603449 0.0502316i
\(596\) 0 0
\(597\) 2.71951 + 21.5778i 0.111302 + 0.883120i
\(598\) 0 0
\(599\) −26.2990 + 4.63723i −1.07455 + 0.189472i −0.682804 0.730602i \(-0.739240\pi\)
−0.391745 + 0.920074i \(0.628128\pi\)
\(600\) 0 0
\(601\) −26.0201 4.58804i −1.06138 0.187150i −0.384412 0.923162i \(-0.625596\pi\)
−0.676969 + 0.736012i \(0.736707\pi\)
\(602\) 0 0
\(603\) 22.7815 31.7817i 0.927735 1.29425i
\(604\) 0 0
\(605\) −2.11768 1.77695i −0.0860960 0.0722432i
\(606\) 0 0
\(607\) −6.92812 + 1.22162i −0.281204 + 0.0495838i −0.312471 0.949927i \(-0.601157\pi\)
0.0312673 + 0.999511i \(0.490046\pi\)
\(608\) 0 0
\(609\) 9.07999 28.6670i 0.367940 1.16164i
\(610\) 0 0
\(611\) 17.7601i 0.718495i
\(612\) 0 0
\(613\) −21.2303 −0.857485 −0.428743 0.903427i \(-0.641043\pi\)
−0.428743 + 0.903427i \(0.641043\pi\)
\(614\) 0 0
\(615\) −9.11537 + 4.68130i −0.367567 + 0.188768i
\(616\) 0 0
\(617\) −16.1973 + 2.85602i −0.652079 + 0.114979i −0.489895 0.871782i \(-0.662965\pi\)
−0.162184 + 0.986761i \(0.551854\pi\)
\(618\) 0 0
\(619\) 28.5343 + 5.03136i 1.14689 + 0.202227i 0.714617 0.699516i \(-0.246601\pi\)
0.432272 + 0.901743i \(0.357712\pi\)
\(620\) 0 0
\(621\) 0.225560 + 8.33653i 0.00905139 + 0.334533i
\(622\) 0 0
\(623\) −10.4317 + 2.84237i −0.417937 + 0.113877i
\(624\) 0 0
\(625\) −12.3638 4.50004i −0.494550 0.180002i
\(626\) 0 0
\(627\) −32.1238 + 16.4975i −1.28290 + 0.658848i
\(628\) 0 0
\(629\) 7.43608 12.8797i 0.296496 0.513546i
\(630\) 0 0
\(631\) −7.51188 13.0110i −0.299043 0.517958i 0.676874 0.736099i \(-0.263334\pi\)
−0.975917 + 0.218141i \(0.930001\pi\)
\(632\) 0 0
\(633\) −2.52650 8.17023i −0.100419 0.324738i
\(634\) 0 0
\(635\) −0.559839 3.17500i −0.0222165 0.125996i
\(636\) 0 0
\(637\) −4.92139 26.5969i −0.194993 1.05381i
\(638\) 0 0
\(639\) 9.54459 + 37.2640i 0.377578 + 1.47414i
\(640\) 0 0
\(641\) 2.72963 + 7.49959i 0.107814 + 0.296216i 0.981854 0.189637i \(-0.0607312\pi\)
−0.874040 + 0.485853i \(0.838509\pi\)
\(642\) 0 0
\(643\) 10.8529 29.8181i 0.427996 1.17591i −0.519031 0.854756i \(-0.673707\pi\)
0.947027 0.321154i \(-0.104071\pi\)
\(644\) 0 0
\(645\) −12.8548 + 1.62013i −0.506157 + 0.0637925i
\(646\) 0 0
\(647\) 0.285978 + 0.495329i 0.0112430 + 0.0194734i 0.871592 0.490232i \(-0.163088\pi\)
−0.860349 + 0.509705i \(0.829755\pi\)
\(648\) 0 0
\(649\) −2.88985 1.66846i −0.113437 0.0654926i
\(650\) 0 0
\(651\) 9.78071 + 5.10782i 0.383336 + 0.200191i
\(652\) 0 0
\(653\) −26.4290 31.4968i −1.03425 1.23257i −0.972116 0.234499i \(-0.924655\pi\)
−0.0621301 0.998068i \(-0.519789\pi\)
\(654\) 0 0
\(655\) −9.95250 + 3.62241i −0.388876 + 0.141539i
\(656\) 0 0
\(657\) −14.0340 3.92718i −0.547518 0.153214i
\(658\) 0 0
\(659\) −4.33314 11.9052i −0.168795 0.463761i 0.826236 0.563324i \(-0.190478\pi\)
−0.995031 + 0.0995628i \(0.968256\pi\)
\(660\) 0 0
\(661\) 2.80824 7.71557i 0.109228 0.300101i −0.873021 0.487682i \(-0.837843\pi\)
0.982249 + 0.187581i \(0.0600648\pi\)
\(662\) 0 0
\(663\) 29.9734 + 27.7719i 1.16407 + 1.07857i
\(664\) 0 0
\(665\) 11.0662 + 7.67928i 0.429128 + 0.297790i
\(666\) 0 0
\(667\) 5.26581 + 9.12064i 0.203893 + 0.353153i
\(668\) 0 0
\(669\) 10.3367 + 20.1274i 0.399639 + 0.778171i
\(670\) 0 0
\(671\) 8.01346 + 45.4466i 0.309356 + 1.75445i
\(672\) 0 0
\(673\) −33.8139 28.3732i −1.30343 1.09371i −0.989542 0.144248i \(-0.953924\pi\)
−0.313889 0.949460i \(-0.601632\pi\)
\(674\) 0 0
\(675\) 4.33200 + 21.1980i 0.166739 + 0.815912i
\(676\) 0 0
\(677\) −21.2078 + 7.71902i −0.815084 + 0.296666i −0.715722 0.698385i \(-0.753902\pi\)
−0.0993616 + 0.995051i \(0.531680\pi\)
\(678\) 0 0
\(679\) −31.8737 + 2.92408i −1.22320 + 0.112216i
\(680\) 0 0
\(681\) −1.30415 + 26.5068i −0.0499751 + 1.01574i
\(682\) 0 0
\(683\) 11.7561i 0.449836i 0.974378 + 0.224918i \(0.0722114\pi\)
−0.974378 + 0.224918i \(0.927789\pi\)
\(684\) 0 0
\(685\) −3.68292 + 2.12634i −0.140717 + 0.0812431i
\(686\) 0 0
\(687\) −11.8054 10.9383i −0.450403 0.417321i
\(688\) 0 0
\(689\) 41.6102 + 15.1449i 1.58522 + 0.576974i
\(690\) 0 0
\(691\) 17.9020 + 3.15660i 0.681023 + 0.120083i 0.503449 0.864025i \(-0.332064\pi\)
0.177574 + 0.984107i \(0.443175\pi\)
\(692\) 0 0
\(693\) −27.9995 + 9.97467i −1.06361 + 0.378906i
\(694\) 0 0
\(695\) −12.3516 + 14.7200i −0.468522 + 0.558363i
\(696\) 0 0
\(697\) 6.85949 + 38.9021i 0.259822 + 1.47352i
\(698\) 0 0
\(699\) −12.9603 + 9.83142i −0.490202 + 0.371859i
\(700\) 0 0
\(701\) 10.7142i 0.404669i −0.979317 0.202334i \(-0.935147\pi\)
0.979317 0.202334i \(-0.0648527\pi\)
\(702\) 0 0
\(703\) −11.7453 + 6.78113i −0.442981 + 0.255755i
\(704\) 0 0
\(705\) −4.39945 5.79958i −0.165693 0.218425i
\(706\) 0 0
\(707\) −0.717844 7.82480i −0.0269973 0.294282i
\(708\) 0 0
\(709\) 5.48560 + 4.60297i 0.206016 + 0.172868i 0.739958 0.672653i \(-0.234845\pi\)
−0.533942 + 0.845521i \(0.679290\pi\)
\(710\) 0 0
\(711\) 1.28785 + 16.8658i 0.0482982 + 0.632515i
\(712\) 0 0
\(713\) −3.63142 + 1.32173i −0.135998 + 0.0494991i
\(714\) 0 0
\(715\) 10.1358 8.50491i 0.379056 0.318066i
\(716\) 0 0
\(717\) 11.0866 + 10.2723i 0.414037 + 0.383627i
\(718\) 0 0
\(719\) 12.8506 0.479247 0.239624 0.970866i \(-0.422976\pi\)
0.239624 + 0.970866i \(0.422976\pi\)
\(720\) 0 0
\(721\) −21.7908 + 10.2733i −0.811532 + 0.382598i
\(722\) 0 0
\(723\) 4.46988 + 8.70369i 0.166237 + 0.323694i
\(724\) 0 0
\(725\) 17.5630 + 20.9307i 0.652272 + 0.777348i
\(726\) 0 0
\(727\) −25.2662 + 30.1111i −0.937071 + 1.11676i 0.0559043 + 0.998436i \(0.482196\pi\)
−0.992975 + 0.118322i \(0.962249\pi\)
\(728\) 0 0
\(729\) 19.7145 18.4483i 0.730166 0.683270i
\(730\) 0 0
\(731\) −8.67311 + 49.1877i −0.320787 + 1.81927i
\(732\) 0 0
\(733\) −2.35387 + 6.46721i −0.0869422 + 0.238872i −0.975543 0.219810i \(-0.929456\pi\)
0.888600 + 0.458682i \(0.151678\pi\)
\(734\) 0 0
\(735\) 8.19556 + 7.46614i 0.302298 + 0.275393i
\(736\) 0 0
\(737\) −42.2715 + 24.4055i −1.55709 + 0.898987i
\(738\) 0 0
\(739\) −8.13308 + 14.0869i −0.299180 + 0.518195i −0.975949 0.218001i \(-0.930046\pi\)
0.676768 + 0.736196i \(0.263380\pi\)
\(740\) 0 0
\(741\) −11.0085 35.5995i −0.404408 1.30778i
\(742\) 0 0
\(743\) −4.66918 5.56451i −0.171296 0.204142i 0.673566 0.739127i \(-0.264762\pi\)
−0.844862 + 0.534985i \(0.820317\pi\)
\(744\) 0 0
\(745\) −7.88437 + 9.39622i −0.288861 + 0.344251i
\(746\) 0 0
\(747\) −20.2517 + 13.8493i −0.740969 + 0.506718i
\(748\) 0 0
\(749\) 26.9204 27.1484i 0.983651 0.991982i
\(750\) 0 0
\(751\) 22.4704 18.8549i 0.819956 0.688024i −0.133006 0.991115i \(-0.542463\pi\)
0.952962 + 0.303091i \(0.0980185\pi\)
\(752\) 0 0
\(753\) 2.03911 0.256996i 0.0743095 0.00936545i
\(754\) 0 0
\(755\) −9.56447 −0.348087
\(756\) 0 0
\(757\) 20.1619 0.732796 0.366398 0.930458i \(-0.380591\pi\)
0.366398 + 0.930458i \(0.380591\pi\)
\(758\) 0 0
\(759\) 4.03680 9.59533i 0.146527 0.348288i
\(760\) 0 0
\(761\) −34.3005 + 28.7816i −1.24339 + 1.04333i −0.246143 + 0.969234i \(0.579163\pi\)
−0.997251 + 0.0740978i \(0.976392\pi\)
\(762\) 0 0
\(763\) −23.0399 + 6.27779i −0.834102 + 0.227271i
\(764\) 0 0
\(765\) −16.6674 1.64407i −0.602611 0.0594415i
\(766\) 0 0
\(767\) 2.21325 2.63765i 0.0799159 0.0952400i
\(768\) 0 0
\(769\) 7.23057 + 8.61705i 0.260741 + 0.310739i 0.880493 0.474058i \(-0.157211\pi\)
−0.619752 + 0.784797i \(0.712767\pi\)
\(770\) 0 0
\(771\) 14.2524 15.3822i 0.513287 0.553976i
\(772\) 0 0
\(773\) 10.1685 17.6124i 0.365737 0.633476i −0.623157 0.782097i \(-0.714150\pi\)
0.988894 + 0.148621i \(0.0474835\pi\)
\(774\) 0 0
\(775\) −8.68274 + 5.01298i −0.311893 + 0.180072i
\(776\) 0 0
\(777\) −10.3186 + 4.25827i −0.370178 + 0.152765i
\(778\) 0