Properties

Label 108.5.k.a.5.12
Level 108
Weight 5
Character 108.5
Analytic conductor 11.164
Analytic rank 0
Dimension 72
CM no
Inner twists 2

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

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(1\)

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 0.970655 + 0.240477i \(0.0773037\pi\)
−0.588989 + 0.808141i \(0.700474\pi\)
\(6\) 0 0
\(7\) −0.541932 3.07345i −0.0110598 0.0627235i 0.978778 0.204922i \(-0.0656940\pi\)
−0.989838 + 0.142198i \(0.954583\pi\)
\(8\) 0 0
\(9\) 71.6168 + 37.8421i 0.884159 + 0.467187i
\(10\) 0 0
\(11\) −44.3351 + 121.810i −0.366406 + 1.00669i 0.610312 + 0.792161i \(0.291044\pi\)
−0.976717 + 0.214530i \(0.931178\pi\)
\(12\) 0 0
\(13\) −30.3898 25.5001i −0.179821 0.150888i 0.548434 0.836194i \(-0.315224\pi\)
−0.728256 + 0.685306i \(0.759669\pi\)
\(14\) 0 0
\(15\) 26.5679 + 249.671i 0.118080 + 1.10965i
\(16\) 0 0
\(17\) −72.0247 41.5835i −0.249220 0.143887i 0.370187 0.928957i \(-0.379294\pi\)
−0.619407 + 0.785070i \(0.712627\pi\)
\(18\) 0 0
\(19\) 32.6516 + 56.5542i 0.0904476 + 0.156660i 0.907700 0.419621i \(-0.137837\pi\)
−0.817252 + 0.576281i \(0.804504\pi\)
\(20\) 0 0
\(21\) 1.92308 28.0219i 0.00436072 0.0635417i
\(22\) 0 0
\(23\) 346.437 + 61.0862i 0.654890 + 0.115475i 0.491214 0.871039i \(-0.336553\pi\)
0.163677 + 0.986514i \(0.447665\pi\)
\(24\) 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 0.955944 0.293549i \(-0.0948365\pi\)
−0.455088 + 0.890447i \(0.650392\pi\)
\(30\) 0 0
\(31\) −18.7225 + 106.181i −0.0194823 + 0.110490i −0.992998 0.118130i \(-0.962310\pi\)
0.973516 + 0.228620i \(0.0734212\pi\)
\(32\) 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 0.454256 + 0.890871i \(0.349905\pi\)
−0.998645 + 0.0520382i \(0.983428\pi\)
\(38\) 0 0
\(39\) −210.236 288.580i −0.138222 0.189730i
\(40\) 0 0
\(41\) 1342.26 1599.64i 0.798486 0.951599i −0.201123 0.979566i \(-0.564459\pi\)
0.999609 + 0.0279673i \(0.00890341\pi\)
\(42\) 0 0
\(43\) −1405.92 511.712i −0.760366 0.276750i −0.0674048 0.997726i \(-0.521472\pi\)
−0.692961 + 0.720975i \(0.743694\pi\)
\(44\) 0 0
\(45\) −308.706 + 2238.54i −0.152447 + 1.10545i
\(46\) 0 0
\(47\) 2360.91 416.292i 1.06877 0.188453i 0.388524 0.921439i \(-0.372985\pi\)
0.680244 + 0.732986i \(0.261874\pi\)
\(48\) 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 \(-0.863021\pi\)
0.908828 0.417172i \(-0.136979\pi\)
\(54\) 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 −0.997249 0.0741183i \(-0.976386\pi\)
0.716295 0.697797i \(-0.245836\pi\)
\(60\) 0 0
\(61\) −1139.50 6462.44i −0.306236 1.73675i −0.617630 0.786469i \(-0.711907\pi\)
0.311394 0.950281i \(-0.399204\pi\)
\(62\) 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 −0.912971 0.408024i \(-0.866218\pi\)
−0.560361 0.828249i \(-0.689337\pi\)
\(68\) 0 0
\(69\) 2893.98 + 1284.00i 0.607851 + 0.269691i
\(70\) 0 0
\(71\) −426.072 245.993i −0.0845214 0.0487985i 0.457144 0.889393i \(-0.348873\pi\)
−0.541665 + 0.840594i \(0.682206\pi\)
\(72\) 0 0
\(73\) −2004.31 3471.57i −0.376114 0.651449i 0.614379 0.789011i \(-0.289407\pi\)
−0.990493 + 0.137562i \(0.956073\pi\)
\(74\) 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 −0.962203 0.272332i \(-0.912205\pi\)
0.101110 + 0.994875i \(0.467761\pi\)
\(80\) 0 0
\(81\) 3696.94 + 5420.27i 0.563473 + 0.826135i
\(82\) 0 0
\(83\) 1605.97 + 1913.93i 0.233122 + 0.277823i 0.869905 0.493219i \(-0.164180\pi\)
−0.636784 + 0.771043i \(0.719735\pi\)
\(84\) 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 0.647864 0.761756i \(-0.275662\pi\)
0.983632 0.180189i \(-0.0576710\pi\)
\(90\) 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 0.994255 0.107034i \(-0.0341352\pi\)
0.692844 + 0.721088i \(0.256357\pi\)
\(98\) 0 0
\(99\) −7784.68 + 7045.89i −0.794274 + 0.718895i
\(100\) 0 0
\(101\) 3976.62 701.186i 0.389827 0.0687370i 0.0247004 0.999695i \(-0.492137\pi\)
0.365127 + 0.930958i \(0.381026\pi\)
\(102\) 0 0
\(103\) −12081.1 + 4397.16i −1.13876 + 0.414475i −0.841465 0.540311i \(-0.818307\pi\)
−0.297295 + 0.954786i \(0.596084\pi\)
\(104\) 0 0
\(105\) 752.955 216.960i 0.0682952 0.0196789i
\(106\) 0 0
\(107\) 6203.55i 0.541842i −0.962602 0.270921i \(-0.912672\pi\)
0.962602 0.270921i \(-0.0873283\pi\)
\(108\) 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 0.999345 0.0361920i \(-0.0115228\pi\)
−0.788806 + 0.614642i \(0.789301\pi\)
\(114\) 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 0.943482 0.331423i \(-0.107529\pi\)
−0.758762 + 0.651368i \(0.774195\pi\)
\(128\) 0 0
\(129\) −11173.0 7515.26i −0.671412 0.451611i
\(130\) 0 0
\(131\) −22916.5 4040.80i −1.33538 0.235464i −0.540048 0.841634i \(-0.681594\pi\)
−0.795335 + 0.606171i \(0.792705\pi\)
\(132\) 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 0.948700 0.316179i \(-0.102400\pi\)
−0.476115 + 0.879383i \(0.657956\pi\)
\(138\) 0 0
\(139\) 3753.73 21288.5i 0.194283 1.10183i −0.719154 0.694850i \(-0.755471\pi\)
0.913437 0.406981i \(-0.133418\pi\)
\(140\) 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 −0.0329171 + 0.999458i \(0.510480\pi\)
−0.978558 + 0.205971i \(0.933965\pi\)
\(150\) 0 0
\(151\) 39773.2 + 14476.3i 1.74436 + 0.634896i 0.999478 0.0322972i \(-0.0102823\pi\)
0.744885 + 0.667193i \(0.232505\pi\)
\(152\) 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 −0.0172596 0.999851i \(-0.505494\pi\)
0.629470 + 0.777025i \(0.283272\pi\)
\(158\) 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 −0.983738 0.179607i \(-0.942517\pi\)
0.638138 0.769922i \(-0.279705\pi\)
\(168\) 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 0.514579 + 0.857443i \(0.327948\pi\)
−0.945344 + 0.326074i \(0.894274\pi\)
\(174\) 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 −0.492953 0.870056i \(-0.664082\pi\)
−0.999967 + 0.00811870i \(0.997416\pi\)
\(180\) 0 0
\(181\) 5248.19 + 9090.13i 0.160196 + 0.277468i 0.934939 0.354809i \(-0.115454\pi\)
−0.774743 + 0.632277i \(0.782121\pi\)
\(182\) 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 0.993420 0.114527i \(-0.0365353\pi\)
−0.285293 + 0.958440i \(0.592091\pi\)
\(192\) 0 0
\(193\) 8845.50 50165.3i 0.237469 1.34676i −0.599881 0.800089i \(-0.704785\pi\)
0.837350 0.546667i \(-0.184104\pi\)
\(194\) 0 0
\(195\) 5559.25 8264.95i 0.146200 0.217356i
\(196\) 0 0
\(197\) 24425.4 14102.0i 0.629376 0.363370i −0.151135 0.988513i \(-0.548293\pi\)
0.780510 + 0.625143i \(0.214959\pi\)
\(198\) 0 0
\(199\) −25117.8 + 43505.4i −0.634273 + 1.09859i 0.352396 + 0.935851i \(0.385367\pi\)
−0.986669 + 0.162742i \(0.947966\pi\)
\(200\) 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 −0.139710 0.990192i \(-0.544617\pi\)
0.529459 + 0.848335i \(0.322395\pi\)
\(212\) 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 0.855540 + 0.517737i \(0.173226\pi\)
−0.626868 + 0.779126i \(0.715663\pi\)
\(224\) 0 0
\(225\) −12138.6 + 2612.96i −0.239775 + 0.0516140i
\(226\) 0 0
\(227\) −21863.2 + 60068.6i −0.424289 + 1.16572i 0.524941 + 0.851139i \(0.324088\pi\)
−0.949229 + 0.314585i \(0.898135\pi\)
\(228\) 0 0
\(229\) 1269.42 + 1065.17i 0.0242067 + 0.0203118i 0.654811 0.755793i \(-0.272748\pi\)
−0.630604 + 0.776105i \(0.717193\pi\)
\(230\) 0 0
\(231\) 3328.07 + 1476.60i 0.0623690 + 0.0276719i
\(232\) 0 0
\(233\) −18385.1 10614.6i −0.338652 0.195521i 0.321024 0.947071i \(-0.395973\pi\)
−0.659676 + 0.751550i \(0.729306\pi\)
\(234\) 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 0.00755117 0.999971i \(-0.497596\pi\)
−0.334915 + 0.942248i \(0.608707\pi\)
\(240\) 0 0
\(241\) 25092.7 21055.3i 0.432030 0.362516i −0.400687 0.916215i \(-0.631228\pi\)
0.832717 + 0.553699i \(0.186784\pi\)
\(242\) 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 −0.261236 0.965275i \(-0.584130\pi\)
0.705335 + 0.708874i \(0.250797\pi\)
\(252\) 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 −0.991590 0.129418i \(-0.958689\pi\)
0.299640 + 0.954052i \(0.403134\pi\)
\(258\) 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 0.164854 0.986318i \(-0.447285\pi\)
0.492253 + 0.870452i \(0.336174\pi\)
\(264\) 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 \(0.143040\pi\)
−0.900719 + 0.434402i \(0.856960\pi\)
\(270\) 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 0.996316 0.0857630i \(-0.0273328\pi\)
−0.965563 + 0.260169i \(0.916222\pi\)
\(278\) 0 0
\(279\) −5358.95 + 6895.82i −0.0688448 + 0.0885885i
\(280\) 0 0
\(281\) −12110.1 + 33272.1i −0.153368 + 0.421374i −0.992453 0.122626i \(-0.960869\pi\)
0.839085 + 0.544000i \(0.183091\pi\)
\(282\) 0 0
\(283\) −87306.7 73259.0i −1.09012 0.914720i −0.0933993 0.995629i \(-0.529773\pi\)
−0.996722 + 0.0809087i \(0.974218\pi\)
\(284\) 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 −0.252687 0.967548i \(-0.581314\pi\)
−0.568369 + 0.822774i \(0.692425\pi\)
\(294\) 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 −0.909537 0.415622i \(-0.863564\pi\)
0.814708 + 0.579872i \(0.196897\pi\)
\(308\) 0 0
\(309\) −115058. + 12243.5i −1.20504 + 0.128230i
\(310\) 0 0
\(311\) −3233.99 + 3854.12i −0.0334363 + 0.0398478i −0.782503 0.622646i \(-0.786058\pi\)
0.749067 + 0.662494i \(0.230502\pi\)
\(312\) 0 0
\(313\) −47171.3 17169.0i −0.481493 0.175249i 0.0898588 0.995955i \(-0.471358\pi\)
−0.571351 + 0.820706i \(0.693581\pi\)
\(314\) 0 0
\(315\) 7047.35 264.346i 0.0710239 0.00266410i
\(316\) 0 0
\(317\) 43193.0 7616.09i 0.429828 0.0757903i 0.0454512 0.998967i \(-0.485527\pi\)
0.384377 + 0.923176i \(0.374416\pi\)
\(318\) 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 0.871618 + 0.490186i \(0.163071\pi\)
−0.651399 + 0.758735i \(0.725818\pi\)
\(332\) 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 0.0583648 0.998295i \(-0.481411\pi\)
−0.972994 + 0.230830i \(0.925856\pi\)
\(338\) 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 0.271177 0.962529i \(-0.412587\pi\)
−0.0743812 + 0.997230i \(0.523698\pi\)
\(348\) 0 0
\(349\) 39974.2 33542.4i 0.328193 0.275387i −0.463770 0.885956i \(-0.653504\pi\)
0.791963 + 0.610569i \(0.209059\pi\)
\(350\) 0 0
\(351\) −4135.97 28623.0i −0.0335709 0.232327i
\(352\) 0 0
\(353\) 6742.14 + 8034.97i 0.0541064 + 0.0644814i 0.792419 0.609977i \(-0.208821\pi\)
−0.738313 + 0.674459i \(0.764377\pi\)
\(354\) 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 0.500766 0.865583i \(-0.333052\pi\)
1.00000 0.000884863i \(-0.000281661\pi\)
\(360\) 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 −0.121113 0.992639i \(-0.538646\pi\)
−0.730834 + 0.682556i \(0.760868\pi\)
\(368\) 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 −0.629969 0.776620i \(-0.716933\pi\)
0.0166172 + 0.999862i \(0.494710\pi\)
\(374\) 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 0.933042 0.359767i \(-0.117144\pi\)
−0.946006 + 0.324150i \(0.894922\pi\)
\(384\) 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 0.695534 + 0.718493i \(0.255168\pi\)
−0.994649 + 0.103317i \(0.967054\pi\)
\(390\) 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 −0.984605 0.174791i \(-0.944075\pi\)
0.340929 0.940089i \(-0.389258\pi\)
\(398\) 0 0
\(399\) 1647.55 806.200i 0.0103488 0.00506404i
\(400\) 0 0
\(401\) 168219. + 29661.5i 1.04613 + 0.184461i 0.670195 0.742185i \(-0.266211\pi\)
0.375935 + 0.926646i \(0.377322\pi\)
\(402\) 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 −0.922552 0.385872i \(-0.873901\pi\)
0.998892 0.0470691i \(-0.0149881\pi\)
\(410\) 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 −0.806472 0.591272i \(-0.798626\pi\)
0.722332 + 0.691547i \(0.243070\pi\)
\(420\) 0 0
\(421\) −143751. 52321.0i −0.811046 0.295197i −0.0969904 0.995285i \(-0.530922\pi\)
−0.714056 + 0.700089i \(0.753144\pi\)
\(422\) 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 \(0.393139\pi\)
−0.329444 + 0.944175i \(0.606861\pi\)
\(432\) 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 −0.960882 0.276958i \(-0.910674\pi\)
0.808208 0.588897i \(-0.200438\pi\)
\(440\) 0 0
\(441\) 191876. + 26460.7i 0.986606 + 0.136058i
\(442\) 0 0
\(443\) 15829.7 43491.8i 0.0806614 0.221615i −0.892806 0.450442i \(-0.851267\pi\)
0.973467 + 0.228826i \(0.0734888\pi\)
\(444\) 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 0.334813 0.942285i \(-0.391327\pi\)
−0.648636 + 0.761099i \(0.724660\pi\)
\(450\) 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 −0.848108 0.529824i \(-0.822258\pi\)
0.374503 + 0.927226i \(0.377813\pi\)
\(458\) 0 0
\(459\) −18958.8 57588.2i −0.0899882 0.273343i
\(460\) 0 0
\(461\) 228366. + 272156.i 1.07456 + 1.28061i 0.957796 + 0.287450i \(0.0928074\pi\)
0.116763 + 0.993160i \(0.462748\pi\)
\(462\) 0 0
\(463\) −5698.10 + 32315.6i −0.0265808 + 0.150747i −0.995210 0.0977652i \(-0.968831\pi\)
0.968629 + 0.248512i \(0.0799417\pi\)
\(464\) 0 0
\(465\) −27007.7 1853.48i −0.124905 0.00857198i
\(466\) 0 0
\(467\) −154413. + 89150.2i −0.708026 + 0.408779i −0.810330 0.585974i \(-0.800712\pi\)
0.102304 + 0.994753i \(0.467379\pi\)
\(468\) 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 −0.387524 0.921860i \(-0.626670\pi\)
−0.0488591 + 0.998806i \(0.515559\pi\)
\(480\) 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 0.993732 0.111790i \(-0.0356585\pi\)
−0.833100 + 0.553122i \(0.813436\pi\)
\(492\) 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 0.999993 + 0.00372771i \(0.00118657\pi\)
0.177318 + 0.984154i \(0.443258\pi\)
\(500\) 0 0
\(501\) −26837.5 252204.i −0.106922 1.00479i
\(502\) 0 0
\(503\) −357988. 206684.i −1.41492 0.816905i −0.419074 0.907952i \(-0.637645\pi\)
−0.995847 + 0.0910468i \(0.970979\pi\)
\(504\) 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 0.250956 0.967999i \(-0.419255\pi\)
−0.0952539 + 0.995453i \(0.530366\pi\)
\(510\) 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 −0.149664 0.988737i \(-0.547819\pi\)
0.781439 + 0.623982i \(0.214486\pi\)
\(522\) 0 0
\(523\) 54197.2 93872.3i 0.198141 0.343190i −0.749785 0.661682i \(-0.769843\pi\)
0.947926 + 0.318492i \(0.103176\pi\)
\(524\) 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 −0.992606 0.121379i \(-0.961268\pi\)
0.891231 0.453550i \(-0.149843\pi\)
\(548\) 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 −0.262398 0.964960i \(-0.584513\pi\)
−0.966879 + 0.255237i \(0.917847\pi\)
\(558\) 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 0.814687 0.579901i \(-0.196909\pi\)
0.567218 + 0.823568i \(0.308020\pi\)
\(564\) 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 −0.876374 0.481632i \(-0.840044\pi\)
−0.322134 0.946694i \(-0.604400\pi\)
\(570\) 0 0
\(571\) −31098.8 + 176370.i −0.0953831 + 0.540944i 0.899246 + 0.437443i \(0.144116\pi\)
−0.994629 + 0.103502i \(0.966995\pi\)
\(572\) 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 −0.0256315 0.999671i \(-0.508160\pi\)
0.878557 0.477638i \(-0.158507\pi\)
\(578\) 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 −0.585592 0.810606i \(-0.699138\pi\)
−0.273033 + 0.962005i \(0.588027\pi\)
\(588\) 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 \(0.222490\pi\)
−0.765503 + 0.643432i \(0.777510\pi\)
\(594\) 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 0.704520 + 0.709684i \(0.251162\pi\)
−0.0835172 + 0.996506i \(0.526615\pi\)
\(600\) 0 0
\(601\) 22312.8 + 126542.i 0.0617739 + 0.350337i 0.999991 + 0.00428948i \(0.00136539\pi\)
−0.938217 + 0.346048i \(0.887524\pi\)
\(602\) 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 0.127696 0.991813i \(-0.459242\pi\)
−0.954571 + 0.297983i \(0.903686\pi\)
\(608\) 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 −0.964581 0.263785i \(-0.915029\pi\)
0.253846 0.967245i \(-0.418304\pi\)
\(614\) 0 0
\(615\) 435045. + 292624.i 1.15023 + 0.773676i
\(616\) 0 0
\(617\) −528258. 93146.1i −1.38764 0.244678i −0.570582 0.821240i \(-0.693283\pi\)
−0.817053 + 0.576563i \(0.804394\pi\)
\(618\) 0 0
\(619\) −71460.3 + 59962.3i −0.186502 + 0.156494i −0.731258 0.682101i \(-0.761067\pi\)
0.544756 + 0.838594i \(0.316622\pi\)
\(620\) 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 −0.336001 0.941862i \(-0.609074\pi\)
0.983677 0.179946i \(-0.0575923\pi\)
\(632\) 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 −0.552713 0.833371i \(-0.686408\pi\)
−0.234351 + 0.972152i \(0.575296\pi\)
\(642\) 0 0
\(643\) −122155. + 44460.8i −0.295454 + 0.107536i −0.485494 0.874240i \(-0.661360\pi\)
0.190040 + 0.981776i \(0.439138\pi\)
\(644\) 0 0
\(645\) 90407.4 364612.i 0.217313 0.876419i
\(646\) 0 0
\(647\) 667031.i 1.59345i 0.604345 + 0.796723i \(0.293435\pi\)
−0.604345 + 0.796723i \(0.706565\pi\)
\(648\) 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 −0.993734 0.111771i \(-0.964348\pi\)
0.689399 0.724382i \(-0.257875\pi\)
\(654\) 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 −0.339257 0.940694i \(-0.610176\pi\)
0.864552 0.502543i \(-0.167602\pi\)
\(660\) 0 0
\(661\) 254247. + 213339.i 0.581906 + 0.488277i 0.885572 0.464501i \(-0.153766\pi\)
−0.303666 + 0.952778i \(0.598211\pi\)
\(662\) 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 −0.234203 + 0.972188i \(0.575248\pi\)
−0.998087 + 0.0618264i \(0.980307\pi\)
\(674\) 0 0
\(675\) −111696. 3466.81i −0.245149 0.00760891i
\(676\) 0 0
\(677\) −148547. 177031.i −0.324105 0.386254i 0.579248 0.815152i \(-0.303346\pi\)
−0.903353 + 0.428898i \(0.858902\pi\)
\(678\) 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 −0.279593 0.960119i \(-0.590199\pi\)
0.691691 + 0.722194i \(0.256866\pi\)
\(684\) 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 0.923127 0.384494i \(-0.125624\pi\)
0.460008 + 0.887915i \(0.347846\pi\)
\(692\) 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 \(-0.994514\pi\)
0.999851 0.0172355i \(-0.00548649\pi\)
\(702\) 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 −0.999993 0.00364447i \(-0.998840\pi\)
0.938440 0.345443i \(-0.112271\pi\)
\(710\) 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 0.307110 0.951674i \(-0.400638\pi\)
−0.670619 + 0.741802i \(0.733971\pi\)
\(720\) 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 −0.743470 0.668770i \(-0.766821\pi\)
0.529507 + 0.848305i \(0.322377\pi\)
\(728\) 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 0.616073 + 0.787689i \(0.288723\pi\)
−0.848325 + 0.529476i \(0.822388\pi\)
\(734\) 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 −0.896018 0.444017i \(-0.853553\pi\)
0.832539 + 0.553966i \(0.186886\pi\)
\(740\) 0 0
\(741\) 9455.86 21312.3i 0.0172213 0.0388145i
\(742\) 0 0
\(743\) 349329. 416315.i 0.632787 0.754126i −0.350425 0.936591i \(-0.613963\pi\)
0.983212 + 0.182464i \(0.0584074\pi\)
\(744\) 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 −0.221262 0.975214i \(-0.571018\pi\)
0.457359 + 0.889282i \(0.348795\pi\)
\(752\) 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 0.999924 0.0123215i \(-0.00392215\pi\)
−0.773906 + 0.633300i \(0.781700\pi\)
\(762\) 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 0.656301 0.754499i \(-0.272120\pi\)
−0.629071 + 0.777348i \(0.716564\pi\)
\(770\) 0 0
\(771\) −517208. + 376796.i −0.870075 + 0.633867i
\(772\) 0 0
\(773\) −337649. 194942.i −0.565076 0.326247i 0.190104 0.981764i \(-0.439117\pi\)
−0.755180 + 0.655517i \(0.772451\pi\)
\(774\) 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