Properties

Label 108.5.k.a.65.12
Level 108
Weight 5
Character 108.65
Analytic conductor 11.164
Analytic rank 0
Dimension 72
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(12\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 65.12
Character \(\chi\) \(=\) 108.65
Dual form 108.5.k.a.5.12

$q$-expansion

\(f(q)\) \(=\) \(q+(8.73547 - 2.16600i) q^{3} +(9.54164 - 26.2154i) q^{5} +(-0.541932 + 3.07345i) q^{7} +(71.6168 - 37.8421i) q^{9} +O(q^{10})\) \(q+(8.73547 - 2.16600i) q^{3} +(9.54164 - 26.2154i) q^{5} +(-0.541932 + 3.07345i) q^{7} +(71.6168 - 37.8421i) q^{9} +(-44.3351 - 121.810i) q^{11} +(-30.3898 + 25.5001i) q^{13} +(26.5679 - 249.671i) q^{15} +(-72.0247 + 41.5835i) q^{17} +(32.6516 - 56.5542i) q^{19} +(1.92308 + 28.0219i) q^{21} +(346.437 - 61.0862i) q^{23} +(-117.428 - 98.5341i) q^{25} +(543.640 - 485.691i) q^{27} +(421.220 - 501.991i) q^{29} +(-18.7225 - 106.181i) q^{31} +(-651.128 - 968.034i) q^{33} +(75.4009 + 43.5328i) q^{35} +(-745.268 - 1290.84i) q^{37} +(-210.236 + 288.580i) q^{39} +(1342.26 + 1599.64i) q^{41} +(-1405.92 + 511.712i) q^{43} +(-308.706 - 2238.54i) q^{45} +(2360.91 + 416.292i) q^{47} +(2247.05 + 817.859i) q^{49} +(-539.100 + 519.257i) q^{51} +2343.67i q^{53} -3616.32 q^{55} +(162.730 - 564.751i) q^{57} +(-978.002 + 2687.04i) q^{59} +(-1139.50 + 6462.44i) q^{61} +(77.4945 + 240.619i) q^{63} +(378.527 + 1040.00i) q^{65} +(-6613.79 + 5549.63i) q^{67} +(2893.98 - 1284.00i) q^{69} +(-426.072 + 245.993i) q^{71} +(-2004.31 + 3471.57i) q^{73} +(-1239.22 - 606.391i) q^{75} +(398.403 - 70.2491i) q^{77} +(-5374.08 - 4509.39i) q^{79} +(3696.94 - 5420.27i) q^{81} +(1605.97 - 1913.93i) q^{83} +(402.895 + 2284.93i) q^{85} +(2592.24 - 5297.49i) q^{87} +(12923.1 + 7461.14i) q^{89} +(-61.9041 - 107.221i) q^{91} +(-393.538 - 886.984i) q^{93} +(-1171.04 - 1395.60i) q^{95} +(15873.9 - 5777.63i) q^{97} +(-7784.68 - 7045.89i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q + 9q^{5} - 102q^{9} + O(q^{10}) \) \( 72q + 9q^{5} - 102q^{9} + 18q^{11} - 225q^{15} - 282q^{21} - 1278q^{23} + 441q^{25} + 54q^{27} + 1854q^{29} - 1665q^{31} - 45q^{33} - 2673q^{35} + 6951q^{39} - 5472q^{41} + 1260q^{43} + 5553q^{45} + 5103q^{47} - 5904q^{49} + 1899q^{51} + 1107q^{57} - 10944q^{59} + 8352q^{61} - 11985q^{63} + 8757q^{65} + 378q^{67} + 5607q^{69} - 19764q^{71} + 6111q^{73} - 3453q^{75} - 5679q^{77} - 5652q^{79} - 20466q^{81} - 20061q^{83} + 26100q^{85} + 40545q^{87} + 15633q^{89} - 6039q^{91} + 40179q^{93} + 48024q^{95} - 37530q^{97} + 12177q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\) \(1\)

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
\(3\) 8.73547 2.16600i 0.970608 0.240667i
\(4\) 0 0
\(5\) 9.54164 26.2154i 0.381666 1.04862i −0.588989 0.808141i \(-0.700474\pi\)
0.970655 0.240477i \(-0.0773037\pi\)
\(6\) 0 0
\(7\) −0.541932 + 3.07345i −0.0110598 + 0.0627235i −0.989838 0.142198i \(-0.954583\pi\)
0.978778 + 0.204922i \(0.0656940\pi\)
\(8\) 0 0
\(9\) 71.6168 37.8421i 0.884159 0.467187i
\(10\) 0 0
\(11\) −44.3351 121.810i −0.366406 1.00669i −0.976717 0.214530i \(-0.931178\pi\)
0.610312 0.792161i \(-0.291044\pi\)
\(12\) 0 0
\(13\) −30.3898 + 25.5001i −0.179821 + 0.150888i −0.728256 0.685306i \(-0.759669\pi\)
0.548434 + 0.836194i \(0.315224\pi\)
\(14\) 0 0
\(15\) 26.5679 249.671i 0.118080 1.10965i
\(16\) 0 0
\(17\) −72.0247 + 41.5835i −0.249220 + 0.143887i −0.619407 0.785070i \(-0.712627\pi\)
0.370187 + 0.928957i \(0.379294\pi\)
\(18\) 0 0
\(19\) 32.6516 56.5542i 0.0904476 0.156660i −0.817252 0.576281i \(-0.804504\pi\)
0.907700 + 0.419621i \(0.137837\pi\)
\(20\) 0 0
\(21\) 1.92308 + 28.0219i 0.00436072 + 0.0635417i
\(22\) 0 0
\(23\) 346.437 61.0862i 0.654890 0.115475i 0.163677 0.986514i \(-0.447665\pi\)
0.491214 + 0.871039i \(0.336553\pi\)
\(24\) 0 0
\(25\) −117.428 98.5341i −0.187885 0.157655i
\(26\) 0 0
\(27\) 543.640 485.691i 0.745735 0.666243i
\(28\) 0 0
\(29\) 421.220 501.991i 0.500856 0.596897i −0.455088 0.890447i \(-0.650392\pi\)
0.955944 + 0.293549i \(0.0948365\pi\)
\(30\) 0 0
\(31\) −18.7225 106.181i −0.0194823 0.110490i 0.973516 0.228620i \(-0.0734212\pi\)
−0.992998 + 0.118130i \(0.962310\pi\)
\(32\) 0 0
\(33\) −651.128 968.034i −0.597914 0.888920i
\(34\) 0 0
\(35\) 75.4009 + 43.5328i 0.0615518 + 0.0355369i
\(36\) 0 0
\(37\) −745.268 1290.84i −0.544389 0.942909i −0.998645 0.0520382i \(-0.983428\pi\)
0.454256 0.890871i \(-0.349905\pi\)
\(38\) 0 0
\(39\) −210.236 + 288.580i −0.138222 + 0.189730i
\(40\) 0 0
\(41\) 1342.26 + 1599.64i 0.798486 + 0.951599i 0.999609 0.0279673i \(-0.00890341\pi\)
−0.201123 + 0.979566i \(0.564459\pi\)
\(42\) 0 0
\(43\) −1405.92 + 511.712i −0.760366 + 0.276750i −0.692961 0.720975i \(-0.743694\pi\)
−0.0674048 + 0.997726i \(0.521472\pi\)
\(44\) 0 0
\(45\) −308.706 2238.54i −0.152447 1.10545i
\(46\) 0 0
\(47\) 2360.91 + 416.292i 1.06877 + 0.188453i 0.680244 0.732986i \(-0.261874\pi\)
0.388524 + 0.921439i \(0.372985\pi\)
\(48\) 0 0
\(49\) 2247.05 + 817.859i 0.935881 + 0.340633i
\(50\) 0 0
\(51\) −539.100 + 519.257i −0.207266 + 0.199637i
\(52\) 0 0
\(53\) 2343.67i 0.834344i 0.908828 + 0.417172i \(0.136979\pi\)
−0.908828 + 0.417172i \(0.863021\pi\)
\(54\) 0 0
\(55\) −3616.32 −1.19548
\(56\) 0 0
\(57\) 162.730 564.751i 0.0500863 0.173823i
\(58\) 0 0
\(59\) −978.002 + 2687.04i −0.280954 + 0.771916i 0.716295 + 0.697797i \(0.245836\pi\)
−0.997249 + 0.0741183i \(0.976386\pi\)
\(60\) 0 0
\(61\) −1139.50 + 6462.44i −0.306236 + 1.73675i 0.311394 + 0.950281i \(0.399204\pi\)
−0.617630 + 0.786469i \(0.711907\pi\)
\(62\) 0 0
\(63\) 77.4945 + 240.619i 0.0195249 + 0.0606245i
\(64\) 0 0
\(65\) 378.527 + 1040.00i 0.0895923 + 0.246153i
\(66\) 0 0
\(67\) −6613.79 + 5549.63i −1.47333 + 1.23627i −0.560361 + 0.828249i \(0.689337\pi\)
−0.912971 + 0.408024i \(0.866218\pi\)
\(68\) 0 0
\(69\) 2893.98 1284.00i 0.607851 0.269691i
\(70\) 0 0
\(71\) −426.072 + 245.993i −0.0845214 + 0.0487985i −0.541665 0.840594i \(-0.682206\pi\)
0.457144 + 0.889393i \(0.348873\pi\)
\(72\) 0 0
\(73\) −2004.31 + 3471.57i −0.376114 + 0.651449i −0.990493 0.137562i \(-0.956073\pi\)
0.614379 + 0.789011i \(0.289407\pi\)
\(74\) 0 0
\(75\) −1239.22 606.391i −0.220305 0.107803i
\(76\) 0 0
\(77\) 398.403 70.2491i 0.0671956 0.0118484i
\(78\) 0 0
\(79\) −5374.08 4509.39i −0.861093 0.722543i 0.101110 0.994875i \(-0.467761\pi\)
−0.962203 + 0.272332i \(0.912205\pi\)
\(80\) 0 0
\(81\) 3696.94 5420.27i 0.563473 0.826135i
\(82\) 0 0
\(83\) 1605.97 1913.93i 0.233122 0.277823i −0.636784 0.771043i \(-0.719735\pi\)
0.869905 + 0.493219i \(0.164180\pi\)
\(84\) 0 0
\(85\) 402.895 + 2284.93i 0.0557641 + 0.316254i
\(86\) 0 0
\(87\) 2592.24 5297.49i 0.342481 0.699893i
\(88\) 0 0
\(89\) 12923.1 + 7461.14i 1.63150 + 0.941945i 0.983632 + 0.180189i \(0.0576710\pi\)
0.647864 + 0.761756i \(0.275662\pi\)
\(90\) 0 0
\(91\) −61.9041 107.221i −0.00747543 0.0129478i
\(92\) 0 0
\(93\) −393.538 886.984i −0.0455009 0.102553i
\(94\) 0 0
\(95\) −1171.04 1395.60i −0.129756 0.154637i
\(96\) 0 0
\(97\) 15873.9 5777.63i 1.68710 0.614054i 0.692844 0.721088i \(-0.256357\pi\)
0.994255 + 0.107034i \(0.0341352\pi\)
\(98\) 0 0
\(99\) −7784.68 7045.89i −0.794274 0.718895i
\(100\) 0 0
\(101\) 3976.62 + 701.186i 0.389827 + 0.0687370i 0.365127 0.930958i \(-0.381026\pi\)
0.0247004 + 0.999695i \(0.492137\pi\)
\(102\) 0 0
\(103\) −12081.1 4397.16i −1.13876 0.414475i −0.297295 0.954786i \(-0.596084\pi\)
−0.841465 + 0.540311i \(0.818307\pi\)
\(104\) 0 0
\(105\) 752.955 + 216.960i 0.0682952 + 0.0196789i
\(106\) 0 0
\(107\) 6203.55i 0.541842i 0.962602 + 0.270921i \(0.0873283\pi\)
−0.962602 + 0.270921i \(0.912672\pi\)
\(108\) 0 0
\(109\) −6362.04 −0.535480 −0.267740 0.963491i \(-0.586277\pi\)
−0.267740 + 0.963491i \(0.586277\pi\)
\(110\) 0 0
\(111\) −9306.24 9661.86i −0.755315 0.784178i
\(112\) 0 0
\(113\) 2688.37 7386.23i 0.210539 0.578450i −0.788806 0.614642i \(-0.789301\pi\)
0.999345 + 0.0361920i \(0.0115228\pi\)
\(114\) 0 0
\(115\) 1704.18 9664.86i 0.128860 0.730802i
\(116\) 0 0
\(117\) −1211.45 + 2976.25i −0.0884977 + 0.217419i
\(118\) 0 0
\(119\) −88.7723 243.900i −0.00626879 0.0172233i
\(120\) 0 0
\(121\) −1656.33 + 1389.83i −0.113130 + 0.0949271i
\(122\) 0 0
\(123\) 15190.1 + 11066.3i 1.00404 + 0.731460i
\(124\) 0 0
\(125\) 11396.6 6579.83i 0.729382 0.421109i
\(126\) 0 0
\(127\) 2979.36 5160.40i 0.184721 0.319946i −0.758762 0.651368i \(-0.774195\pi\)
0.943482 + 0.331423i \(0.107529\pi\)
\(128\) 0 0
\(129\) −11173.0 + 7515.26i −0.671412 + 0.451611i
\(130\) 0 0
\(131\) −22916.5 + 4040.80i −1.33538 + 0.235464i −0.795335 0.606171i \(-0.792705\pi\)
−0.540048 + 0.841634i \(0.681594\pi\)
\(132\) 0 0
\(133\) 156.122 + 131.002i 0.00882592 + 0.00740583i
\(134\) 0 0
\(135\) −7545.39 18886.1i −0.414013 1.03627i
\(136\) 0 0
\(137\) 8869.93 10570.8i 0.472584 0.563204i −0.476115 0.879383i \(-0.657956\pi\)
0.948700 + 0.316179i \(0.102400\pi\)
\(138\) 0 0
\(139\) 3753.73 + 21288.5i 0.194283 + 1.10183i 0.913437 + 0.406981i \(0.133418\pi\)
−0.719154 + 0.694850i \(0.755471\pi\)
\(140\) 0 0
\(141\) 21525.3 1477.23i 1.08271 0.0743038i
\(142\) 0 0
\(143\) 4453.49 + 2571.23i 0.217785 + 0.125738i
\(144\) 0 0
\(145\) −9140.77 15832.3i −0.434757 0.753022i
\(146\) 0 0
\(147\) 21400.5 + 2277.26i 0.990352 + 0.105385i
\(148\) 0 0
\(149\) −22455.8 26761.7i −1.01148 1.20543i −0.978558 0.205971i \(-0.933965\pi\)
−0.0329171 0.999458i \(-0.510480\pi\)
\(150\) 0 0
\(151\) 39773.2 14476.3i 1.74436 0.634896i 0.744885 0.667193i \(-0.232505\pi\)
0.999478 + 0.0322972i \(0.0102823\pi\)
\(152\) 0 0
\(153\) −3584.57 + 5703.65i −0.153128 + 0.243652i
\(154\) 0 0
\(155\) −2962.21 522.318i −0.123297 0.0217406i
\(156\) 0 0
\(157\) 15090.4 + 5492.45i 0.612211 + 0.222826i 0.629470 0.777025i \(-0.283272\pi\)
−0.0172596 + 0.999851i \(0.505494\pi\)
\(158\) 0 0
\(159\) 5076.40 + 20473.1i 0.200799 + 0.809820i
\(160\) 0 0
\(161\) 1097.86i 0.0423541i
\(162\) 0 0
\(163\) −10729.0 −0.403815 −0.201908 0.979405i \(-0.564714\pi\)
−0.201908 + 0.979405i \(0.564714\pi\)
\(164\) 0 0
\(165\) −31590.3 + 7832.97i −1.16034 + 0.287712i
\(166\) 0 0
\(167\) −9638.45 + 26481.4i −0.345600 + 0.949529i 0.638138 + 0.769922i \(0.279705\pi\)
−0.983738 + 0.179607i \(0.942517\pi\)
\(168\) 0 0
\(169\) −4686.28 + 26577.2i −0.164080 + 0.930542i
\(170\) 0 0
\(171\) 198.271 5285.84i 0.00678060 0.180768i
\(172\) 0 0
\(173\) −12892.4 35421.5i −0.430765 1.18352i −0.945344 0.326074i \(-0.894274\pi\)
0.514579 0.857443i \(-0.327948\pi\)
\(174\) 0 0
\(175\) 366.478 307.511i 0.0119666 0.0100412i
\(176\) 0 0
\(177\) −2723.17 + 25590.9i −0.0869216 + 0.816844i
\(178\) 0 0
\(179\) −47834.6 + 27617.3i −1.49292 + 0.861938i −0.999967 0.00811870i \(-0.997416\pi\)
−0.492953 + 0.870056i \(0.664082\pi\)
\(180\) 0 0
\(181\) 5248.19 9090.13i 0.160196 0.277468i −0.774743 0.632277i \(-0.782121\pi\)
0.934939 + 0.354809i \(0.115454\pi\)
\(182\) 0 0
\(183\) 4043.59 + 58920.7i 0.120744 + 1.75940i
\(184\) 0 0
\(185\) −40951.1 + 7220.78i −1.19653 + 0.210980i
\(186\) 0 0
\(187\) 8258.49 + 6929.70i 0.236166 + 0.198167i
\(188\) 0 0
\(189\) 1198.13 + 1934.06i 0.0335414 + 0.0541436i
\(190\) 0 0
\(191\) 25833.2 30786.8i 0.708127 0.843913i −0.285293 0.958440i \(-0.592091\pi\)
0.993420 + 0.114527i \(0.0365353\pi\)
\(192\) 0 0
\(193\) 8845.50 + 50165.3i 0.237469 + 1.34676i 0.837350 + 0.546667i \(0.184104\pi\)
−0.599881 + 0.800089i \(0.704785\pi\)
\(194\) 0 0
\(195\) 5559.25 + 8264.95i 0.146200 + 0.217356i
\(196\) 0 0
\(197\) 24425.4 + 14102.0i 0.629376 + 0.363370i 0.780510 0.625143i \(-0.214959\pi\)
−0.151135 + 0.988513i \(0.548293\pi\)
\(198\) 0 0
\(199\) −25117.8 43505.4i −0.634273 1.09859i −0.986669 0.162742i \(-0.947966\pi\)
0.352396 0.935851i \(-0.385367\pi\)
\(200\) 0 0
\(201\) −45754.0 + 62804.1i −1.13250 + 1.55452i
\(202\) 0 0
\(203\) 1314.57 + 1566.64i 0.0319001 + 0.0380170i
\(204\) 0 0
\(205\) 54742.5 19924.6i 1.30262 0.474114i
\(206\) 0 0
\(207\) 22499.1 17484.7i 0.525079 0.408054i
\(208\) 0 0
\(209\) −8336.46 1469.94i −0.190849 0.0336518i
\(210\) 0 0
\(211\) 17352.0 + 6315.62i 0.389749 + 0.141857i 0.529459 0.848335i \(-0.322395\pi\)
−0.139710 + 0.990192i \(0.544617\pi\)
\(212\) 0 0
\(213\) −3189.12 + 3071.74i −0.0702929 + 0.0677057i
\(214\) 0 0
\(215\) 41739.3i 0.902959i
\(216\) 0 0
\(217\) 336.487 0.00714577
\(218\) 0 0
\(219\) −9989.17 + 34667.2i −0.208277 + 0.722820i
\(220\) 0 0
\(221\) 1128.44 3100.35i 0.0231043 0.0634785i
\(222\) 0 0
\(223\) 11371.6 64491.7i 0.228672 1.29686i −0.626868 0.779126i \(-0.715663\pi\)
0.855540 0.517737i \(-0.173226\pi\)
\(224\) 0 0
\(225\) −12138.6 2612.96i −0.239775 0.0516140i
\(226\) 0 0
\(227\) −21863.2 60068.6i −0.424289 1.16572i −0.949229 0.314585i \(-0.898135\pi\)
0.524941 0.851139i \(-0.324088\pi\)
\(228\) 0 0
\(229\) 1269.42 1065.17i 0.0242067 0.0203118i −0.630604 0.776105i \(-0.717193\pi\)
0.654811 + 0.755793i \(0.272748\pi\)
\(230\) 0 0
\(231\) 3328.07 1476.60i 0.0623690 0.0276719i
\(232\) 0 0
\(233\) −18385.1 + 10614.6i −0.338652 + 0.195521i −0.659676 0.751550i \(-0.729306\pi\)
0.321024 + 0.947071i \(0.395973\pi\)
\(234\) 0 0
\(235\) 33440.2 57920.1i 0.605526 1.04880i
\(236\) 0 0
\(237\) −56712.5 27751.3i −1.00968 0.494069i
\(238\) 0 0
\(239\) −18699.3 + 3297.20i −0.327363 + 0.0577230i −0.334915 0.942248i \(-0.608707\pi\)
0.00755117 + 0.999971i \(0.497596\pi\)
\(240\) 0 0
\(241\) 25092.7 + 21055.3i 0.432030 + 0.362516i 0.832717 0.553699i \(-0.186784\pi\)
−0.400687 + 0.916215i \(0.631228\pi\)
\(242\) 0 0
\(243\) 20554.2 55356.2i 0.348088 0.937462i
\(244\) 0 0
\(245\) 42881.1 51103.7i 0.714387 0.851373i
\(246\) 0 0
\(247\) 449.862 + 2551.29i 0.00737369 + 0.0418183i
\(248\) 0 0
\(249\) 9883.37 20197.6i 0.159407 0.325762i
\(250\) 0 0
\(251\) 27978.7 + 16153.5i 0.444099 + 0.256401i 0.705335 0.708874i \(-0.250797\pi\)
−0.261236 + 0.965275i \(0.584130\pi\)
\(252\) 0 0
\(253\) −22800.2 39491.1i −0.356203 0.616962i
\(254\) 0 0
\(255\) 8468.66 + 19087.3i 0.130237 + 0.293538i
\(256\) 0 0
\(257\) −45702.6 54466.3i −0.691950 0.824634i 0.299640 0.954052i \(-0.403134\pi\)
−0.991590 + 0.129418i \(0.958689\pi\)
\(258\) 0 0
\(259\) 4371.23 1591.00i 0.0651634 0.0237175i
\(260\) 0 0
\(261\) 11170.1 51890.9i 0.163974 0.761745i
\(262\) 0 0
\(263\) 45451.4 + 8014.31i 0.657107 + 0.115866i 0.492253 0.870452i \(-0.336174\pi\)
0.164854 + 0.986318i \(0.447285\pi\)
\(264\) 0 0
\(265\) 61440.4 + 22362.5i 0.874907 + 0.318440i
\(266\) 0 0
\(267\) 129050. + 37185.1i 1.81024 + 0.521611i
\(268\) 0 0
\(269\) 62867.5i 0.868804i −0.900719 0.434402i \(-0.856960\pi\)
0.900719 0.434402i \(-0.143040\pi\)
\(270\) 0 0
\(271\) −89938.3 −1.22463 −0.612317 0.790612i \(-0.709762\pi\)
−0.612317 + 0.790612i \(0.709762\pi\)
\(272\) 0 0
\(273\) −773.002 802.541i −0.0103718 0.0107682i
\(274\) 0 0
\(275\) −6796.21 + 18672.4i −0.0898672 + 0.246908i
\(276\) 0 0
\(277\) 2359.61 13382.0i 0.0307525 0.174406i −0.965563 0.260169i \(-0.916222\pi\)
0.996316 + 0.0857630i \(0.0273328\pi\)
\(278\) 0 0
\(279\) −5358.95 6895.82i −0.0688448 0.0885885i
\(280\) 0 0
\(281\) −12110.1 33272.1i −0.153368 0.421374i 0.839085 0.544000i \(-0.183091\pi\)
−0.992453 + 0.122626i \(0.960869\pi\)
\(282\) 0 0
\(283\) −87306.7 + 73259.0i −1.09012 + 0.914720i −0.996722 0.0809087i \(-0.974218\pi\)
−0.0933993 + 0.995629i \(0.529773\pi\)
\(284\) 0 0
\(285\) −13252.5 9654.70i −0.163158 0.118864i
\(286\) 0 0
\(287\) −5643.82 + 3258.46i −0.0685187 + 0.0395593i
\(288\) 0 0
\(289\) −38302.1 + 66341.2i −0.458593 + 0.794306i
\(290\) 0 0
\(291\) 126152. 84853.3i 1.48973 1.00204i
\(292\) 0 0
\(293\) −70486.8 + 12428.7i −0.821056 + 0.144774i −0.568369 0.822774i \(-0.692425\pi\)
−0.252687 + 0.967548i \(0.581314\pi\)
\(294\) 0 0
\(295\) 61110.1 + 51277.5i 0.702214 + 0.589227i
\(296\) 0 0
\(297\) −83264.2 44687.5i −0.943943 0.506609i
\(298\) 0 0
\(299\) −8970.46 + 10690.6i −0.100340 + 0.119580i
\(300\) 0 0
\(301\) −810.809 4598.33i −0.00894923 0.0507536i
\(302\) 0 0
\(303\) 36256.5 2488.20i 0.394912 0.0271019i
\(304\) 0 0
\(305\) 158543. + 91534.9i 1.70431 + 0.983982i
\(306\) 0 0
\(307\) −8937.59 15480.4i −0.0948296 0.164250i 0.814708 0.579872i \(-0.196897\pi\)
−0.909537 + 0.415622i \(0.863564\pi\)
\(308\) 0 0
\(309\) −115058. 12243.5i −1.20504 0.128230i
\(310\) 0 0
\(311\) −3233.99 3854.12i −0.0334363 0.0398478i 0.749067 0.662494i \(-0.230502\pi\)
−0.782503 + 0.622646i \(0.786058\pi\)
\(312\) 0 0
\(313\) −47171.3 + 17169.0i −0.481493 + 0.175249i −0.571351 0.820706i \(-0.693581\pi\)
0.0898588 + 0.995955i \(0.471358\pi\)
\(314\) 0 0
\(315\) 7047.35 + 264.346i 0.0710239 + 0.00266410i
\(316\) 0 0
\(317\) 43193.0 + 7616.09i 0.429828 + 0.0757903i 0.384377 0.923176i \(-0.374416\pi\)
0.0454512 + 0.998967i \(0.485527\pi\)
\(318\) 0 0
\(319\) −79822.1 29052.9i −0.784408 0.285501i
\(320\) 0 0
\(321\) 13436.9 + 54190.9i 0.130404 + 0.525916i
\(322\) 0 0
\(323\) 5431.07i 0.0520571i
\(324\) 0 0
\(325\) 6081.26 0.0575740
\(326\) 0 0
\(327\) −55575.4 + 13780.2i −0.519741 + 0.128873i
\(328\) 0 0
\(329\) −2558.90 + 7030.53i −0.0236408 + 0.0649526i
\(330\) 0 0
\(331\) 24127.4 136833.i 0.220219 1.24892i −0.651399 0.758735i \(-0.725818\pi\)
0.871618 0.490186i \(-0.163071\pi\)
\(332\) 0 0
\(333\) −102222. 64243.5i −0.921841 0.579350i
\(334\) 0 0
\(335\) 82379.5 + 226336.i 0.734057 + 2.01680i
\(336\) 0 0
\(337\) −103874. + 87160.2i −0.914629 + 0.767465i −0.972994 0.230830i \(-0.925856\pi\)
0.0583648 + 0.998295i \(0.481411\pi\)
\(338\) 0 0
\(339\) 7485.54 70345.2i 0.0651364 0.612118i
\(340\) 0 0
\(341\) −12103.8 + 6988.11i −0.104091 + 0.0600967i
\(342\) 0 0
\(343\) −7478.00 + 12952.3i −0.0635619 + 0.110092i
\(344\) 0 0
\(345\) −6047.36 88118.3i −0.0508075 0.740334i
\(346\) 0 0
\(347\) 23696.0 4178.25i 0.196796 0.0347005i −0.0743812 0.997230i \(-0.523698\pi\)
0.271177 + 0.962529i \(0.412587\pi\)
\(348\) 0 0
\(349\) 39974.2 + 33542.4i 0.328193 + 0.275387i 0.791963 0.610569i \(-0.209059\pi\)
−0.463770 + 0.885956i \(0.653504\pi\)
\(350\) 0 0
\(351\) −4135.97 + 28623.0i −0.0335709 + 0.232327i
\(352\) 0 0
\(353\) 6742.14 8034.97i 0.0541064 0.0644814i −0.738313 0.674459i \(-0.764377\pi\)
0.792419 + 0.609977i \(0.208821\pi\)
\(354\) 0 0
\(355\) 2383.39 + 13516.8i 0.0189120 + 0.107255i
\(356\) 0 0
\(357\) −1303.76 1938.30i −0.0102296 0.0152084i
\(358\) 0 0
\(359\) 193420. + 111671.i 1.50077 + 0.866467i 1.00000 0.000884863i \(0.000281661\pi\)
0.500766 + 0.865583i \(0.333052\pi\)
\(360\) 0 0
\(361\) 63028.2 + 109168.i 0.483638 + 0.837686i
\(362\) 0 0
\(363\) −11458.5 + 15728.4i −0.0869587 + 0.119364i
\(364\) 0 0
\(365\) 71884.3 + 85668.4i 0.539571 + 0.643035i
\(366\) 0 0
\(367\) −114748. + 41764.8i −0.851946 + 0.310083i −0.730834 0.682556i \(-0.760868\pi\)
−0.121113 + 0.992639i \(0.538646\pi\)
\(368\) 0 0
\(369\) 156662. + 63767.2i 1.15056 + 0.468322i
\(370\) 0 0
\(371\) −7203.16 1270.11i −0.0523329 0.00922771i
\(372\) 0 0
\(373\) −85335.1 31059.4i −0.613352 0.223242i 0.0166172 0.999862i \(-0.494710\pi\)
−0.629969 + 0.776620i \(0.716933\pi\)
\(374\) 0 0
\(375\) 85302.7 82163.0i 0.606597 0.584270i
\(376\) 0 0
\(377\) 25996.6i 0.182908i
\(378\) 0 0
\(379\) −122906. −0.855645 −0.427823 0.903863i \(-0.640719\pi\)
−0.427823 + 0.903863i \(0.640719\pi\)
\(380\) 0 0
\(381\) 14848.7 51531.9i 0.102291 0.354998i
\(382\) 0 0
\(383\) −1901.62 + 5224.66i −0.0129636 + 0.0356173i −0.946006 0.324150i \(-0.894922\pi\)
0.933042 + 0.359767i \(0.117144\pi\)
\(384\) 0 0
\(385\) 1959.80 11114.6i 0.0132218 0.0749846i
\(386\) 0 0
\(387\) −81323.0 + 89850.0i −0.542990 + 0.599924i
\(388\) 0 0
\(389\) −45262.3 124357.i −0.299114 0.821810i −0.994649 0.103317i \(-0.967054\pi\)
0.695534 0.718493i \(-0.255168\pi\)
\(390\) 0 0
\(391\) −22411.8 + 18805.8i −0.146597 + 0.123009i
\(392\) 0 0
\(393\) −191434. + 84935.5i −1.23946 + 0.549926i
\(394\) 0 0
\(395\) −169493. + 97856.9i −1.08632 + 0.627187i
\(396\) 0 0
\(397\) −101449. + 175715.i −0.643676 + 1.11488i 0.340929 + 0.940089i \(0.389258\pi\)
−0.984605 + 0.174791i \(0.944075\pi\)
\(398\) 0 0
\(399\) 1647.55 + 806.200i 0.0103488 + 0.00506404i
\(400\) 0 0
\(401\) 168219. 29661.5i 1.04613 0.184461i 0.375935 0.926646i \(-0.377322\pi\)
0.670195 + 0.742185i \(0.266211\pi\)
\(402\) 0 0
\(403\) 3276.59 + 2749.39i 0.0201749 + 0.0169288i
\(404\) 0 0
\(405\) −106820. 148635.i −0.651241 0.906174i
\(406\) 0 0
\(407\) −124196. + 148011.i −0.749751 + 0.893519i
\(408\) 0 0
\(409\) 12770.1 + 72422.8i 0.0763391 + 0.432941i 0.998892 + 0.0470691i \(0.0149881\pi\)
−0.922552 + 0.385872i \(0.873901\pi\)
\(410\) 0 0
\(411\) 54586.7 111553.i 0.323149 0.660386i
\(412\) 0 0
\(413\) −7728.47 4462.04i −0.0453099 0.0261597i
\(414\) 0 0
\(415\) −34850.8 60363.3i −0.202356 0.350491i
\(416\) 0 0
\(417\) 78901.6 + 177834.i 0.453747 + 1.02269i
\(418\) 0 0
\(419\) −14771.8 17604.3i −0.0841404 0.100275i 0.722332 0.691547i \(-0.243070\pi\)
−0.806472 + 0.591272i \(0.798626\pi\)
\(420\) 0 0
\(421\) −143751. + 52321.0i −0.811046 + 0.295197i −0.714056 0.700089i \(-0.753144\pi\)
−0.0969904 + 0.995285i \(0.530922\pi\)
\(422\) 0 0
\(423\) 184834. 59528.3i 1.03300 0.332692i
\(424\) 0 0
\(425\) 12555.1 + 2213.81i 0.0695094 + 0.0122564i
\(426\) 0 0
\(427\) −19244.5 7004.42i −0.105548 0.0384164i
\(428\) 0 0
\(429\) 44472.6 + 12814.6i 0.241645 + 0.0696289i
\(430\) 0 0
\(431\) 350782.i 1.88835i −0.329444 0.944175i \(-0.606861\pi\)
0.329444 0.944175i \(-0.393139\pi\)
\(432\) 0 0
\(433\) 262879. 1.40210 0.701051 0.713111i \(-0.252715\pi\)
0.701051 + 0.713111i \(0.252715\pi\)
\(434\) 0 0
\(435\) −114142. 118503.i −0.603206 0.626257i
\(436\) 0 0
\(437\) 7857.04 21587.0i 0.0411430 0.113039i
\(438\) 0 0
\(439\) −29423.4 + 166868.i −0.152674 + 0.865855i 0.808208 + 0.588897i \(0.200438\pi\)
−0.960882 + 0.276958i \(0.910674\pi\)
\(440\) 0 0
\(441\) 191876. 26460.7i 0.986606 0.136058i
\(442\) 0 0
\(443\) 15829.7 + 43491.8i 0.0806614 + 0.221615i 0.973467 0.228826i \(-0.0734888\pi\)
−0.892806 + 0.450442i \(0.851267\pi\)
\(444\) 0 0
\(445\) 318905. 267593.i 1.61043 1.35131i
\(446\) 0 0
\(447\) −254128. 185137.i −1.27185 0.926570i
\(448\) 0 0
\(449\) −63267.2 + 36527.3i −0.313824 + 0.181186i −0.648636 0.761099i \(-0.724660\pi\)
0.334813 + 0.942285i \(0.391327\pi\)
\(450\) 0 0
\(451\) 135342. 234420.i 0.665396 1.15250i
\(452\) 0 0
\(453\) 316082. 212606.i 1.54029 1.03605i
\(454\) 0 0
\(455\) −3401.51 + 599.778i −0.0164304 + 0.00289713i
\(456\) 0 0
\(457\) −98911.9 82997.0i −0.473605 0.397402i 0.374503 0.927226i \(-0.377813\pi\)
−0.848108 + 0.529824i \(0.822258\pi\)
\(458\) 0 0
\(459\) −18958.8 + 57588.2i −0.0899882 + 0.273343i
\(460\) 0 0
\(461\) 228366. 272156.i 1.07456 1.28061i 0.116763 0.993160i \(-0.462748\pi\)
0.957796 0.287450i \(-0.0928074\pi\)
\(462\) 0 0
\(463\) −5698.10 32315.6i −0.0265808 0.150747i 0.968629 0.248512i \(-0.0799417\pi\)
−0.995210 + 0.0977652i \(0.968831\pi\)
\(464\) 0 0
\(465\) −27007.7 + 1853.48i −0.124905 + 0.00857198i
\(466\) 0 0
\(467\) −154413. 89150.2i −0.708026 0.408779i 0.102304 0.994753i \(-0.467379\pi\)
−0.810330 + 0.585974i \(0.800712\pi\)
\(468\) 0 0
\(469\) −13472.3 23334.7i −0.0612485 0.106086i
\(470\) 0 0
\(471\) 143718. + 15293.3i 0.647843 + 0.0689380i
\(472\) 0 0
\(473\) 124663. + 148567.i 0.557204 + 0.664050i
\(474\) 0 0
\(475\) −9406.74 + 3423.77i −0.0416919 + 0.0151746i
\(476\) 0 0
\(477\) 88689.5 + 167846.i 0.389794 + 0.737692i
\(478\) 0 0
\(479\) −100124. 17654.6i −0.436383 0.0769462i −0.0488591 0.998806i \(-0.515559\pi\)
−0.387524 + 0.921860i \(0.626670\pi\)
\(480\) 0 0
\(481\) 55565.2 + 20224.1i 0.240167 + 0.0874135i
\(482\) 0 0
\(483\) 2377.97 + 9590.34i 0.0101933 + 0.0411093i
\(484\) 0 0
\(485\) 471270.i 2.00348i
\(486\) 0 0
\(487\) −126703. −0.534229 −0.267115 0.963665i \(-0.586070\pi\)
−0.267115 + 0.963665i \(0.586070\pi\)
\(488\) 0 0
\(489\) −93722.6 + 23239.0i −0.391946 + 0.0971851i
\(490\) 0 0
\(491\) 38725.2 106397.i 0.160632 0.441332i −0.833100 0.553122i \(-0.813436\pi\)
0.993732 + 0.111790i \(0.0356585\pi\)
\(492\) 0 0
\(493\) −9463.74 + 53671.5i −0.0389376 + 0.220826i
\(494\) 0 0
\(495\) −258990. + 136849.i −1.05699 + 0.558512i
\(496\) 0 0
\(497\) −525.145 1442.82i −0.00212602 0.00584118i
\(498\) 0 0
\(499\) 293152. 245983.i 1.17731 0.987881i 0.177318 0.984154i \(-0.443258\pi\)
0.999993 0.00372771i \(-0.00118657\pi\)
\(500\) 0 0
\(501\) −26837.5 + 252204.i −0.106922 + 1.00479i
\(502\) 0 0
\(503\) −357988. + 206684.i −1.41492 + 0.816905i −0.995847 0.0910468i \(-0.970979\pi\)
−0.419074 + 0.907952i \(0.637645\pi\)
\(504\) 0 0
\(505\) 56325.4 97558.5i 0.220862 0.382545i
\(506\) 0 0
\(507\) 16629.5 + 242315.i 0.0646940 + 0.942680i
\(508\) 0 0
\(509\) 40339.3 7112.92i 0.155702 0.0274544i −0.0952539 0.995453i \(-0.530366\pi\)
0.250956 + 0.967999i \(0.419255\pi\)
\(510\) 0 0
\(511\) −9583.50 8041.51i −0.0367014 0.0307961i
\(512\) 0 0
\(513\) −9717.16 46603.8i −0.0369237 0.177087i
\(514\) 0 0
\(515\) −230547. + 274755.i −0.869251 + 1.03593i
\(516\) 0 0
\(517\) −53962.7 306038.i −0.201889 1.14497i
\(518\) 0 0
\(519\) −189344. 281498.i −0.702937 1.04506i
\(520\) 0 0
\(521\) 171490. + 99009.5i 0.631775 + 0.364755i 0.781439 0.623982i \(-0.214486\pi\)
−0.149664 + 0.988737i \(0.547819\pi\)
\(522\) 0 0
\(523\) 54197.2 + 93872.3i 0.198141 + 0.343190i 0.947926 0.318492i \(-0.103176\pi\)
−0.749785 + 0.661682i \(0.769843\pi\)
\(524\) 0 0
\(525\) 2535.29 3480.05i 0.00919831 0.0126260i
\(526\) 0 0
\(527\) 5763.84 + 6869.08i 0.0207535 + 0.0247330i
\(528\) 0 0
\(529\) −146677. + 53386.2i −0.524146 + 0.190773i
\(530\) 0 0
\(531\) 31641.9 + 229447.i 0.112221 + 0.813754i
\(532\) 0 0
\(533\) −81581.8 14385.1i −0.287170 0.0506358i
\(534\) 0 0
\(535\) 162629. + 59192.0i 0.568185 + 0.206803i
\(536\) 0 0
\(537\) −358039. + 344860.i −1.24160 + 1.19590i
\(538\) 0 0
\(539\) 309972.i 1.06695i
\(540\) 0 0
\(541\) 570303. 1.94855 0.974274 0.225368i \(-0.0723584\pi\)
0.974274 + 0.225368i \(0.0723584\pi\)
\(542\) 0 0
\(543\) 26156.1 90774.2i 0.0887103 0.307867i
\(544\) 0 0
\(545\) −60704.3 + 166784.i −0.204374 + 0.561514i
\(546\) 0 0
\(547\) −30332.4 + 172024.i −0.101375 + 0.574929i 0.891231 + 0.453550i \(0.149843\pi\)
−0.992606 + 0.121379i \(0.961268\pi\)
\(548\) 0 0
\(549\) 162945. + 505941.i 0.540626 + 1.67863i
\(550\) 0 0
\(551\) −14636.2 40212.6i −0.0482086 0.132452i
\(552\) 0 0
\(553\) 16771.8 14073.2i 0.0548440 0.0460196i
\(554\) 0 0
\(555\) −342087. + 151777.i −1.11058 + 0.492743i
\(556\) 0 0
\(557\) −381382. + 220191.i −1.22928 + 0.709723i −0.966879 0.255237i \(-0.917847\pi\)
−0.262398 + 0.964960i \(0.584513\pi\)
\(558\) 0 0
\(559\) 29676.9 51401.8i 0.0949717 0.164496i
\(560\) 0 0
\(561\) 87151.5 + 42646.2i 0.276917 + 0.135505i
\(562\) 0 0
\(563\) 438021. 77234.9i 1.38190 0.243667i 0.567218 0.823568i \(-0.308020\pi\)
0.814687 + 0.579901i \(0.196909\pi\)
\(564\) 0 0
\(565\) −167982. 140953.i −0.526217 0.441549i
\(566\) 0 0
\(567\) 14655.4 + 14299.8i 0.0455861 + 0.0444799i
\(568\) 0 0
\(569\) −388030. + 462436.i −1.19851 + 1.42833i −0.322134 + 0.946694i \(0.604400\pi\)
−0.876374 + 0.481632i \(0.840044\pi\)
\(570\) 0 0
\(571\) −31098.8 176370.i −0.0953831 0.540944i −0.994629 0.103502i \(-0.966995\pi\)
0.899246 0.437443i \(-0.144116\pi\)
\(572\) 0 0
\(573\) 158981. 324892.i 0.484212 0.989532i
\(574\) 0 0
\(575\) −46700.6 26962.6i −0.141249 0.0815504i
\(576\) 0 0
\(577\) 283964. + 491839.i 0.852925 + 1.47731i 0.878557 + 0.477638i \(0.158507\pi\)
−0.0256315 + 0.999671i \(0.508160\pi\)
\(578\) 0 0
\(579\) 185928. + 419058.i 0.554610 + 1.25002i
\(580\) 0 0
\(581\) 5012.03 + 5973.10i 0.0148478 + 0.0176949i
\(582\) 0 0
\(583\) 285482. 103907.i 0.839926 0.305708i
\(584\) 0 0
\(585\) 66464.6 + 60156.9i 0.194213 + 0.175782i
\(586\) 0 0
\(587\) −295856. 52167.4i −0.858626 0.151399i −0.273033 0.962005i \(-0.588027\pi\)
−0.585592 + 0.810606i \(0.699138\pi\)
\(588\) 0 0
\(589\) −6616.28 2408.13i −0.0190714 0.00694143i
\(590\) 0 0
\(591\) 243913. + 70282.3i 0.698328 + 0.201220i
\(592\) 0 0
\(593\) 452524.i 1.28686i −0.765503 0.643432i \(-0.777510\pi\)
0.765503 0.643432i \(-0.222490\pi\)
\(594\) 0 0
\(595\) −7240.97 −0.0204533
\(596\) 0 0
\(597\) −313649. 325635.i −0.880026 0.913654i
\(598\) 0 0
\(599\) 222816. 612183.i 0.621003 1.70619i −0.0835172 0.996506i \(-0.526615\pi\)
0.704520 0.709684i \(-0.251162\pi\)
\(600\) 0 0
\(601\) 22312.8 126542.i 0.0617739 0.350337i −0.938217 0.346048i \(-0.887524\pi\)
0.999991 0.00428948i \(-0.00136539\pi\)
\(602\) 0 0
\(603\) −263649. + 647727.i −0.725089 + 1.78138i
\(604\) 0 0
\(605\) 20630.8 + 56682.7i 0.0563645 + 0.154860i
\(606\) 0 0
\(607\) −304661. + 255641.i −0.826875 + 0.693831i −0.954571 0.297983i \(-0.903686\pi\)
0.127696 + 0.991813i \(0.459242\pi\)
\(608\) 0 0
\(609\) 14876.8 + 10838.0i 0.0401119 + 0.0292223i
\(610\) 0 0
\(611\) −82363.0 + 47552.3i −0.220623 + 0.127376i
\(612\) 0 0
\(613\) −267072. + 462583.i −0.710736 + 1.23103i 0.253846 + 0.967245i \(0.418304\pi\)
−0.964581 + 0.263785i \(0.915029\pi\)
\(614\) 0 0
\(615\) 435045. 292624.i 1.15023 0.773676i
\(616\) 0 0
\(617\) −528258. + 93146.1i −1.38764 + 0.244678i −0.817053 0.576563i \(-0.804394\pi\)
−0.570582 + 0.821240i \(0.693283\pi\)
\(618\) 0 0
\(619\) −71460.3 59962.3i −0.186502 0.156494i 0.544756 0.838594i \(-0.316622\pi\)
−0.731258 + 0.682101i \(0.761067\pi\)
\(620\) 0 0
\(621\) 158668. 201470.i 0.411440 0.522430i
\(622\) 0 0
\(623\) −29934.9 + 35675.0i −0.0771262 + 0.0919154i
\(624\) 0 0
\(625\) −80387.6 455901.i −0.205792 1.16711i
\(626\) 0 0
\(627\) −76006.8 + 5216.17i −0.193338 + 0.0132684i
\(628\) 0 0
\(629\) 107355. + 61981.7i 0.271346 + 0.156661i
\(630\) 0 0
\(631\) 257879. + 446660.i 0.647676 + 1.12181i 0.983677 + 0.179946i \(0.0575923\pi\)
−0.336001 + 0.941862i \(0.609074\pi\)
\(632\) 0 0
\(633\) 165258. + 17585.3i 0.412434 + 0.0438877i
\(634\) 0 0
\(635\) −106854. 127344.i −0.264999 0.315814i
\(636\) 0 0
\(637\) −89142.9 + 32445.4i −0.219689 + 0.0799602i
\(638\) 0 0
\(639\) −21205.1 + 33740.7i −0.0519323 + 0.0826329i
\(640\) 0 0
\(641\) −323390. 57022.3i −0.787064 0.138781i −0.234351 0.972152i \(-0.575296\pi\)
−0.552713 + 0.833371i \(0.686408\pi\)
\(642\) 0 0
\(643\) −122155. 44460.8i −0.295454 0.107536i 0.190040 0.981776i \(-0.439138\pi\)
−0.485494 + 0.874240i \(0.661360\pi\)
\(644\) 0 0
\(645\) 90407.4 + 364612.i 0.217313 + 0.876419i
\(646\) 0 0
\(647\) 667031.i 1.59345i −0.604345 0.796723i \(-0.706565\pi\)
0.604345 0.796723i \(-0.293435\pi\)
\(648\) 0 0
\(649\) 370667. 0.880024
\(650\) 0 0
\(651\) 2939.37 728.833i 0.00693574 0.00171975i
\(652\) 0 0
\(653\) −129771. + 356543.i −0.304335 + 0.836153i 0.689399 + 0.724382i \(0.257875\pi\)
−0.993734 + 0.111771i \(0.964348\pi\)
\(654\) 0 0
\(655\) −112730. + 639322.i −0.262758 + 1.49017i
\(656\) 0 0
\(657\) −12170.9 + 324470.i −0.0281962 + 0.751700i
\(658\) 0 0
\(659\) 228126. + 626770.i 0.525295 + 1.44324i 0.864552 + 0.502543i \(0.167602\pi\)
−0.339257 + 0.940694i \(0.610176\pi\)
\(660\) 0 0
\(661\) 254247. 213339.i 0.581906 0.488277i −0.303666 0.952778i \(-0.598211\pi\)
0.885572 + 0.464501i \(0.153766\pi\)
\(662\) 0 0
\(663\) 3142.04 29527.2i 0.00714800 0.0671731i
\(664\) 0 0
\(665\) 4923.92 2842.83i 0.0111344 0.00642846i
\(666\) 0 0
\(667\) 115262. 199639.i 0.259079 0.448738i
\(668\) 0 0
\(669\) −40352.8 587996.i −0.0901617 1.31378i
\(670\) 0 0
\(671\) 837708. 147711.i 1.86058 0.328070i
\(672\) 0 0
\(673\) −558140. 468335.i −1.23229 1.03401i −0.998087 0.0618264i \(-0.980307\pi\)
−0.234203 0.972188i \(-0.575248\pi\)
\(674\) 0 0
\(675\) −111696. + 3466.81i −0.245149 + 0.00760891i
\(676\) 0 0
\(677\) −148547. + 177031.i −0.324105 + 0.386254i −0.903353 0.428898i \(-0.858902\pi\)
0.579248 + 0.815152i \(0.303346\pi\)
\(678\) 0 0
\(679\) 9154.69 + 51918.8i 0.0198566 + 0.112612i
\(680\) 0 0
\(681\) −321094. 477372.i −0.692369 1.02935i
\(682\) 0 0
\(683\) 192239. + 110989.i 0.412098 + 0.237925i 0.691691 0.722194i \(-0.256866\pi\)
−0.279593 + 0.960119i \(0.590199\pi\)
\(684\) 0 0
\(685\) −192484. 333392.i −0.410216 0.710516i
\(686\) 0 0
\(687\) 8781.82 12054.3i 0.0186068 0.0255405i
\(688\) 0 0
\(689\) −59763.8 71223.8i −0.125893 0.150033i
\(690\) 0 0
\(691\) 660421. 240374.i 1.38314 0.503420i 0.460008 0.887915i \(-0.347846\pi\)
0.923127 + 0.384494i \(0.125624\pi\)
\(692\) 0 0
\(693\) 25874.0 20107.4i 0.0538761 0.0418688i
\(694\) 0 0
\(695\) 593903. + 104721.i 1.22955 + 0.216803i
\(696\) 0 0
\(697\) −163194. 59397.8i −0.335922 0.122266i
\(698\) 0 0
\(699\) −137611. + 132546.i −0.281643 + 0.271277i
\(700\) 0 0
\(701\) 16939.1i 0.0344710i 0.999851 + 0.0172355i \(0.00548649\pi\)
−0.999851 + 0.0172355i \(0.994514\pi\)
\(702\) 0 0
\(703\) −97336.8 −0.196955
\(704\) 0 0
\(705\) 166660. 578391.i 0.335316 1.16371i
\(706\) 0 0
\(707\) −4310.12 + 11842.0i −0.00862285 + 0.0236911i
\(708\) 0 0
\(709\) −30941.8 + 175479.i −0.0615535 + 0.349087i 0.938440 + 0.345443i \(0.112271\pi\)
−0.999993 + 0.00364447i \(0.998840\pi\)
\(710\) 0 0
\(711\) −555520. 119582.i −1.09891 0.236551i
\(712\) 0 0
\(713\) −12972.3 35641.2i −0.0255176 0.0701089i
\(714\) 0 0
\(715\) 109899. 92216.5i 0.214973 0.180383i
\(716\) 0 0
\(717\) −156206. + 69305.4i −0.303849 + 0.134812i
\(718\) 0 0
\(719\) −187920. + 108496.i −0.363509 + 0.209872i −0.670619 0.741802i \(-0.733971\pi\)
0.307110 + 0.951674i \(0.400638\pi\)
\(720\) 0 0
\(721\) 20061.6 34747.7i 0.0385918 0.0668430i
\(722\) 0 0
\(723\) 264803. + 129577.i 0.506578 + 0.247886i
\(724\) 0 0
\(725\) −98926.4 + 17443.4i −0.188207 + 0.0331860i
\(726\) 0 0
\(727\) −113085. 94889.8i −0.213962 0.179536i 0.529507 0.848305i \(-0.322377\pi\)
−0.743470 + 0.668770i \(0.766821\pi\)
\(728\) 0 0
\(729\) 59649.0 528083.i 0.112240 0.993681i
\(730\) 0 0
\(731\) 79981.9 95318.7i 0.149678 0.178379i
\(732\) 0 0
\(733\) −124786. 707699.i −0.232252 1.31717i −0.848325 0.529476i \(-0.822388\pi\)
0.616073 0.787689i \(-0.288723\pi\)
\(734\) 0 0
\(735\) 263895. 539295.i 0.488492 0.998279i
\(736\) 0 0
\(737\) 969221. + 559580.i 1.78438 + 1.03021i
\(738\) 0 0
\(739\) −34667.1 60045.2i −0.0634788 0.109948i 0.832539 0.553966i \(-0.186886\pi\)
−0.896018 + 0.444017i \(0.853553\pi\)
\(740\) 0 0
\(741\) 9455.86 + 21312.3i 0.0172213 + 0.0388145i
\(742\) 0 0
\(743\) 349329. + 416315.i 0.632787 + 0.754126i 0.983212 0.182464i \(-0.0584074\pi\)
−0.350425 + 0.936591i \(0.613963\pi\)
\(744\) 0 0
\(745\) −915835. + 333337.i −1.65008 + 0.600580i
\(746\) 0 0
\(747\) 42587.8 197843.i 0.0763210 0.354551i
\(748\) 0 0
\(749\) −19066.3 3361.91i −0.0339862 0.00599269i
\(750\) 0 0
\(751\) 133159. + 48466.0i 0.236097 + 0.0859324i 0.457359 0.889282i \(-0.348795\pi\)
−0.221262 + 0.975214i \(0.571018\pi\)
\(752\) 0 0
\(753\) 279396. + 80506.5i 0.492754 + 0.141985i
\(754\) 0 0
\(755\) 1.18080e6i 2.07149i
\(756\) 0 0
\(757\) −497775. −0.868643 −0.434322 0.900758i \(-0.643012\pi\)
−0.434322 + 0.900758i \(0.643012\pi\)
\(758\) 0 0
\(759\) −284708. 295588.i −0.494216 0.513101i
\(760\) 0 0
\(761\) 130892. 359622.i 0.226018 0.620979i −0.773906 0.633300i \(-0.781700\pi\)
0.999924 + 0.0123215i \(0.00392215\pi\)
\(762\) 0 0
\(763\) 3447.80 19553.4i 0.00592233 0.0335872i
\(764\) 0 0
\(765\) 115321. + 148393.i 0.197054 + 0.253566i
\(766\) 0 0
\(767\) −38798.4 106598.i −0.0659513 0.181200i
\(768\) 0 0
\(769\) 16103.1 13512.1i 0.0272305 0.0228491i −0.629071 0.777348i \(-0.716564\pi\)
0.656301 + 0.754499i \(0.272120\pi\)
\(770\) 0 0
\(771\) −517208. 376796.i −0.870075 0.633867i
\(772\) 0 0
\(773\) −337649. + 194942.i −0.565076 + 0.326247i −0.755180 0.655517i \(-0.772451\pi\)
0.190104 + 0.981764i \(0.439117\pi\)
\(774\) 0 0
\(775\) −8263.86 + 14313.4i −0.0137588 + 0.0238309i
\(776\) 0 0
\(777\) 34738.6 23366.2i 0.0575401 0.0387031i
\(778\) 0 0
\(779\) 134293. 23679.5i 0.221299 0.0390209i
\(780\) 0 0
\(781\) 48854.3 + 40993.6i 0.0800941 + 0.0672069i