Properties

Label 108.5.k.a.41.4
Level 108
Weight 5
Character 108.41
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 41.4
Character \(\chi\) \(=\) 108.41
Dual form 108.5.k.a.29.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.84126 - 8.13909i) q^{3} +(0.0201223 - 0.0239808i) q^{5} +(-60.3934 - 21.9814i) q^{7} +(-51.4895 + 62.5287i) q^{9} +O(q^{10})\) \(q+(-3.84126 - 8.13909i) q^{3} +(0.0201223 - 0.0239808i) q^{5} +(-60.3934 - 21.9814i) q^{7} +(-51.4895 + 62.5287i) q^{9} +(122.535 + 146.032i) q^{11} +(8.21590 - 46.5947i) q^{13} +(-0.272476 - 0.0716604i) q^{15} +(-383.840 - 221.610i) q^{17} +(299.637 + 518.987i) q^{19} +(53.0781 + 575.983i) q^{21} +(158.524 + 435.540i) q^{23} +(108.530 + 615.504i) q^{25} +(706.711 + 178.888i) q^{27} +(-396.668 + 69.9433i) q^{29} +(-1472.40 + 535.909i) q^{31} +(717.877 - 1558.27i) q^{33} +(-1.74238 + 1.00596i) q^{35} +(-532.781 + 922.804i) q^{37} +(-410.798 + 112.112i) q^{39} +(-2327.41 - 410.385i) q^{41} +(1343.05 - 1126.95i) q^{43} +(0.463402 + 2.49298i) q^{45} +(864.494 - 2375.18i) q^{47} +(1324.91 + 1111.73i) q^{49} +(-329.275 + 3975.37i) q^{51} -2410.75i q^{53} +5.96765 q^{55} +(3073.09 - 4432.33i) q^{57} +(165.882 - 197.690i) q^{59} +(-3689.65 - 1342.92i) q^{61} +(4484.09 - 2644.51i) q^{63} +(-0.952054 - 1.13461i) q^{65} +(-702.984 + 3986.82i) q^{67} +(2935.97 - 2963.26i) q^{69} +(-2144.37 - 1238.05i) q^{71} +(761.304 + 1318.62i) q^{73} +(4592.75 - 3247.64i) q^{75} +(-4190.34 - 11512.9i) q^{77} +(1351.07 + 7662.27i) q^{79} +(-1258.67 - 6439.14i) q^{81} +(-12237.2 + 2157.76i) q^{83} +(-13.0381 + 4.74548i) q^{85} +(2092.98 + 2959.85i) q^{87} +(4114.03 - 2375.24i) q^{89} +(-1520.40 + 2633.41i) q^{91} +(10017.7 + 9925.42i) q^{93} +(18.4751 + 3.25765i) q^{95} +(-4423.75 + 3711.97i) q^{97} +(-15440.5 + 142.867i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q + 9q^{5} - 102q^{9} + O(q^{10}) \) \( 72q + 9q^{5} - 102q^{9} + 18q^{11} - 225q^{15} - 282q^{21} - 1278q^{23} + 441q^{25} + 54q^{27} + 1854q^{29} - 1665q^{31} - 45q^{33} - 2673q^{35} + 6951q^{39} - 5472q^{41} + 1260q^{43} + 5553q^{45} + 5103q^{47} - 5904q^{49} + 1899q^{51} + 1107q^{57} - 10944q^{59} + 8352q^{61} - 11985q^{63} + 8757q^{65} + 378q^{67} + 5607q^{69} - 19764q^{71} + 6111q^{73} - 3453q^{75} - 5679q^{77} - 5652q^{79} - 20466q^{81} - 20061q^{83} + 26100q^{85} + 40545q^{87} + 15633q^{89} - 6039q^{91} + 40179q^{93} + 48024q^{95} - 37530q^{97} + 12177q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\) \(1\)

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
\(3\) −3.84126 8.13909i −0.426807 0.904343i
\(4\) 0 0
\(5\) 0.0201223 0.0239808i 0.000804890 0.000959231i −0.765642 0.643267i \(-0.777578\pi\)
0.766447 + 0.642308i \(0.222023\pi\)
\(6\) 0 0
\(7\) −60.3934 21.9814i −1.23252 0.448600i −0.358059 0.933699i \(-0.616561\pi\)
−0.874459 + 0.485099i \(0.838783\pi\)
\(8\) 0 0
\(9\) −51.4895 + 62.5287i −0.635672 + 0.771959i
\(10\) 0 0
\(11\) 122.535 + 146.032i 1.01269 + 1.20688i 0.978242 + 0.207469i \(0.0665226\pi\)
0.0344472 + 0.999407i \(0.489033\pi\)
\(12\) 0 0
\(13\) 8.21590 46.5947i 0.0486148 0.275708i −0.950804 0.309793i \(-0.899740\pi\)
0.999419 + 0.0340844i \(0.0108515\pi\)
\(14\) 0 0
\(15\) −0.272476 0.0716604i −0.00121101 0.000318491i
\(16\) 0 0
\(17\) −383.840 221.610i −1.32817 0.766817i −0.343150 0.939281i \(-0.611494\pi\)
−0.985016 + 0.172464i \(0.944827\pi\)
\(18\) 0 0
\(19\) 299.637 + 518.987i 0.830020 + 1.43764i 0.898022 + 0.439951i \(0.145004\pi\)
−0.0680020 + 0.997685i \(0.521662\pi\)
\(20\) 0 0
\(21\) 53.0781 + 575.983i 0.120359 + 1.30608i
\(22\) 0 0
\(23\) 158.524 + 435.540i 0.299666 + 0.823327i 0.994555 + 0.104210i \(0.0332313\pi\)
−0.694889 + 0.719117i \(0.744546\pi\)
\(24\) 0 0
\(25\) 108.530 + 615.504i 0.173648 + 0.984806i
\(26\) 0 0
\(27\) 706.711 + 178.888i 0.969425 + 0.245389i
\(28\) 0 0
\(29\) −396.668 + 69.9433i −0.471663 + 0.0831668i −0.404427 0.914570i \(-0.632529\pi\)
−0.0672356 + 0.997737i \(0.521418\pi\)
\(30\) 0 0
\(31\) −1472.40 + 535.909i −1.53215 + 0.557658i −0.964148 0.265367i \(-0.914507\pi\)
−0.568005 + 0.823025i \(0.692285\pi\)
\(32\) 0 0
\(33\) 717.877 1558.27i 0.659207 1.43092i
\(34\) 0 0
\(35\) −1.74238 + 1.00596i −0.00142235 + 0.000821196i
\(36\) 0 0
\(37\) −532.781 + 922.804i −0.389175 + 0.674071i −0.992339 0.123546i \(-0.960573\pi\)
0.603163 + 0.797618i \(0.293907\pi\)
\(38\) 0 0
\(39\) −410.798 + 112.112i −0.270084 + 0.0737096i
\(40\) 0 0
\(41\) −2327.41 410.385i −1.38454 0.244132i −0.568764 0.822501i \(-0.692578\pi\)
−0.815775 + 0.578369i \(0.803689\pi\)
\(42\) 0 0
\(43\) 1343.05 1126.95i 0.726364 0.609491i −0.202774 0.979226i \(-0.564996\pi\)
0.929138 + 0.369734i \(0.120551\pi\)
\(44\) 0 0
\(45\) 0.463402 + 2.49298i 0.000228840 + 0.00123110i
\(46\) 0 0
\(47\) 864.494 2375.18i 0.391351 1.07523i −0.575034 0.818129i \(-0.695011\pi\)
0.966385 0.257099i \(-0.0827665\pi\)
\(48\) 0 0
\(49\) 1324.91 + 1111.73i 0.551814 + 0.463027i
\(50\) 0 0
\(51\) −329.275 + 3975.37i −0.126596 + 1.52840i
\(52\) 0 0
\(53\) 2410.75i 0.858225i −0.903251 0.429112i \(-0.858826\pi\)
0.903251 0.429112i \(-0.141174\pi\)
\(54\) 0 0
\(55\) 5.96765 0.00197278
\(56\) 0 0
\(57\) 3073.09 4432.33i 0.945858 1.36422i
\(58\) 0 0
\(59\) 165.882 197.690i 0.0476535 0.0567912i −0.741691 0.670741i \(-0.765976\pi\)
0.789345 + 0.613950i \(0.210420\pi\)
\(60\) 0 0
\(61\) −3689.65 1342.92i −0.991574 0.360903i −0.205244 0.978711i \(-0.565799\pi\)
−0.786329 + 0.617807i \(0.788021\pi\)
\(62\) 0 0
\(63\) 4484.09 2644.51i 1.12978 0.666291i
\(64\) 0 0
\(65\) −0.952054 1.13461i −0.000225338 0.000268548i
\(66\) 0 0
\(67\) −702.984 + 3986.82i −0.156601 + 0.888131i 0.800706 + 0.599058i \(0.204458\pi\)
−0.957307 + 0.289073i \(0.906653\pi\)
\(68\) 0 0
\(69\) 2935.97 2963.26i 0.616670 0.622403i
\(70\) 0 0
\(71\) −2144.37 1238.05i −0.425385 0.245596i 0.271994 0.962299i \(-0.412317\pi\)
−0.697379 + 0.716703i \(0.745650\pi\)
\(72\) 0 0
\(73\) 761.304 + 1318.62i 0.142861 + 0.247442i 0.928573 0.371150i \(-0.121037\pi\)
−0.785712 + 0.618592i \(0.787703\pi\)
\(74\) 0 0
\(75\) 4592.75 3247.64i 0.816489 0.577359i
\(76\) 0 0
\(77\) −4190.34 11512.9i −0.706753 1.94179i
\(78\) 0 0
\(79\) 1351.07 + 7662.27i 0.216482 + 1.22773i 0.878316 + 0.478081i \(0.158667\pi\)
−0.661834 + 0.749651i \(0.730221\pi\)
\(80\) 0 0
\(81\) −1258.67 6439.14i −0.191841 0.981426i
\(82\) 0 0
\(83\) −12237.2 + 2157.76i −1.77634 + 0.313218i −0.963188 0.268828i \(-0.913364\pi\)
−0.813156 + 0.582045i \(0.802253\pi\)
\(84\) 0 0
\(85\) −13.0381 + 4.74548i −0.00180458 + 0.000656814i
\(86\) 0 0
\(87\) 2092.98 + 2959.85i 0.276520 + 0.391049i
\(88\) 0 0
\(89\) 4114.03 2375.24i 0.519383 0.299866i −0.217299 0.976105i \(-0.569725\pi\)
0.736682 + 0.676239i \(0.236391\pi\)
\(90\) 0 0
\(91\) −1520.40 + 2633.41i −0.183601 + 0.318007i
\(92\) 0 0
\(93\) 10017.7 + 9925.42i 1.15825 + 1.14758i
\(94\) 0 0
\(95\) 18.4751 + 3.25765i 0.00204710 + 0.000360959i
\(96\) 0 0
\(97\) −4423.75 + 3711.97i −0.470162 + 0.394512i −0.846854 0.531826i \(-0.821506\pi\)
0.376692 + 0.926339i \(0.377062\pi\)
\(98\) 0 0
\(99\) −15440.5 + 142.867i −1.57540 + 0.0145767i
\(100\) 0 0
\(101\) 191.499 526.138i 0.0187725 0.0515771i −0.929952 0.367680i \(-0.880152\pi\)
0.948725 + 0.316103i \(0.102374\pi\)
\(102\) 0 0
\(103\) −5058.09 4244.24i −0.476773 0.400060i 0.372485 0.928038i \(-0.378506\pi\)
−0.849258 + 0.527978i \(0.822950\pi\)
\(104\) 0 0
\(105\) 14.8806 + 10.3172i 0.00134971 + 0.000935803i
\(106\) 0 0
\(107\) 4467.37i 0.390198i −0.980784 0.195099i \(-0.937497\pi\)
0.980784 0.195099i \(-0.0625027\pi\)
\(108\) 0 0
\(109\) 9782.65 0.823386 0.411693 0.911323i \(-0.364938\pi\)
0.411693 + 0.911323i \(0.364938\pi\)
\(110\) 0 0
\(111\) 9557.33 + 791.623i 0.775694 + 0.0642499i
\(112\) 0 0
\(113\) −8140.66 + 9701.66i −0.637533 + 0.759782i −0.983978 0.178288i \(-0.942944\pi\)
0.346446 + 0.938070i \(0.387389\pi\)
\(114\) 0 0
\(115\) 13.6344 + 4.96253i 0.00103096 + 0.000375238i
\(116\) 0 0
\(117\) 2490.47 + 2912.86i 0.181932 + 0.212789i
\(118\) 0 0
\(119\) 18310.1 + 21821.1i 1.29299 + 1.54093i
\(120\) 0 0
\(121\) −3768.03 + 21369.6i −0.257362 + 1.45957i
\(122\) 0 0
\(123\) 5600.02 + 20519.4i 0.370152 + 1.35630i
\(124\) 0 0
\(125\) 33.8883 + 19.5654i 0.00216885 + 0.00125219i
\(126\) 0 0
\(127\) 11131.3 + 19280.0i 0.690142 + 1.19536i 0.971791 + 0.235844i \(0.0757853\pi\)
−0.281649 + 0.959518i \(0.590881\pi\)
\(128\) 0 0
\(129\) −14331.3 6602.26i −0.861206 0.396747i
\(130\) 0 0
\(131\) 2326.48 + 6391.94i 0.135568 + 0.372469i 0.988837 0.149001i \(-0.0476059\pi\)
−0.853269 + 0.521470i \(0.825384\pi\)
\(132\) 0 0
\(133\) −6688.05 37929.8i −0.378091 2.14426i
\(134\) 0 0
\(135\) 18.5105 13.3478i 0.00101567 0.000732391i
\(136\) 0 0
\(137\) 6309.25 1112.49i 0.336153 0.0592728i −0.00302422 0.999995i \(-0.500963\pi\)
0.339177 + 0.940723i \(0.389852\pi\)
\(138\) 0 0
\(139\) −21971.8 + 7997.08i −1.13720 + 0.413906i −0.840901 0.541190i \(-0.817974\pi\)
−0.296297 + 0.955096i \(0.595752\pi\)
\(140\) 0 0
\(141\) −22652.5 + 2087.48i −1.13941 + 0.104999i
\(142\) 0 0
\(143\) 7811.05 4509.71i 0.381977 0.220535i
\(144\) 0 0
\(145\) −6.30457 + 10.9198i −0.000299860 + 0.000519373i
\(146\) 0 0
\(147\) 3959.14 15054.0i 0.183217 0.696652i
\(148\) 0 0
\(149\) −33711.6 5944.26i −1.51847 0.267747i −0.648639 0.761096i \(-0.724662\pi\)
−0.869832 + 0.493348i \(0.835773\pi\)
\(150\) 0 0
\(151\) 22011.9 18470.2i 0.965390 0.810059i −0.0164311 0.999865i \(-0.505230\pi\)
0.981822 + 0.189806i \(0.0607860\pi\)
\(152\) 0 0
\(153\) 33620.7 12590.4i 1.43623 0.537845i
\(154\) 0 0
\(155\) −16.7765 + 46.0930i −0.000698292 + 0.00191854i
\(156\) 0 0
\(157\) −5881.23 4934.94i −0.238599 0.200208i 0.515645 0.856802i \(-0.327552\pi\)
−0.754244 + 0.656594i \(0.771997\pi\)
\(158\) 0 0
\(159\) −19621.3 + 9260.33i −0.776130 + 0.366296i
\(160\) 0 0
\(161\) 29788.3i 1.14920i
\(162\) 0 0
\(163\) 9213.77 0.346786 0.173393 0.984853i \(-0.444527\pi\)
0.173393 + 0.984853i \(0.444527\pi\)
\(164\) 0 0
\(165\) −22.9233 48.5712i −0.000841994 0.00178407i
\(166\) 0 0
\(167\) −9340.18 + 11131.2i −0.334905 + 0.399125i −0.907047 0.421030i \(-0.861669\pi\)
0.572141 + 0.820155i \(0.306113\pi\)
\(168\) 0 0
\(169\) 24735.0 + 9002.80i 0.866041 + 0.315213i
\(170\) 0 0
\(171\) −47879.7 7986.44i −1.63742 0.273125i
\(172\) 0 0
\(173\) 14480.8 + 17257.6i 0.483839 + 0.576617i 0.951639 0.307217i \(-0.0993979\pi\)
−0.467800 + 0.883834i \(0.654953\pi\)
\(174\) 0 0
\(175\) 6975.14 39558.0i 0.227760 1.29169i
\(176\) 0 0
\(177\) −2246.21 590.747i −0.0716975 0.0188562i
\(178\) 0 0
\(179\) 35962.9 + 20763.2i 1.12240 + 0.648020i 0.942013 0.335576i \(-0.108931\pi\)
0.180390 + 0.983595i \(0.442264\pi\)
\(180\) 0 0
\(181\) 896.024 + 1551.96i 0.0273503 + 0.0473721i 0.879377 0.476127i \(-0.157960\pi\)
−0.852026 + 0.523499i \(0.824626\pi\)
\(182\) 0 0
\(183\) 3242.73 + 35188.9i 0.0968298 + 1.05076i
\(184\) 0 0
\(185\) 11.4088 + 31.3454i 0.000333347 + 0.000915863i
\(186\) 0 0
\(187\) −14671.8 83208.0i −0.419566 2.37948i
\(188\) 0 0
\(189\) −38748.4 26338.2i −1.08475 0.737330i
\(190\) 0 0
\(191\) 55200.3 9733.31i 1.51313 0.266805i 0.645399 0.763846i \(-0.276691\pi\)
0.867727 + 0.497041i \(0.165580\pi\)
\(192\) 0 0
\(193\) −39783.2 + 14479.9i −1.06803 + 0.388733i −0.815441 0.578840i \(-0.803506\pi\)
−0.252593 + 0.967573i \(0.581283\pi\)
\(194\) 0 0
\(195\) −5.57764 + 12.1072i −0.000146683 + 0.000318401i
\(196\) 0 0
\(197\) 51989.7 30016.3i 1.33963 0.773436i 0.352878 0.935669i \(-0.385203\pi\)
0.986752 + 0.162233i \(0.0518696\pi\)
\(198\) 0 0
\(199\) 29053.9 50322.8i 0.733665 1.27074i −0.221642 0.975128i \(-0.571142\pi\)
0.955307 0.295616i \(-0.0955250\pi\)
\(200\) 0 0
\(201\) 35149.4 9592.76i 0.870013 0.237439i
\(202\) 0 0
\(203\) 25493.6 + 4495.21i 0.618641 + 0.109083i
\(204\) 0 0
\(205\) −56.6741 + 47.5552i −0.00134858 + 0.00113159i
\(206\) 0 0
\(207\) −35396.0 12513.4i −0.826064 0.292036i
\(208\) 0 0
\(209\) −39072.5 + 107351.i −0.894496 + 2.45761i
\(210\) 0 0
\(211\) −7858.30 6593.90i −0.176508 0.148108i 0.550254 0.834998i \(-0.314531\pi\)
−0.726761 + 0.686890i \(0.758975\pi\)
\(212\) 0 0
\(213\) −1839.53 + 22208.8i −0.0405460 + 0.489516i
\(214\) 0 0
\(215\) 54.8841i 0.00118732i
\(216\) 0 0
\(217\) 100703. 2.13857
\(218\) 0 0
\(219\) 7807.98 11261.5i 0.162798 0.234805i
\(220\) 0 0
\(221\) −13479.4 + 16064.2i −0.275986 + 0.328908i
\(222\) 0 0
\(223\) −74762.5 27211.3i −1.50340 0.547192i −0.546460 0.837485i \(-0.684025\pi\)
−0.956938 + 0.290293i \(0.906247\pi\)
\(224\) 0 0
\(225\) −44074.8 24905.7i −0.870613 0.491965i
\(226\) 0 0
\(227\) 14091.0 + 16793.0i 0.273458 + 0.325895i 0.885242 0.465130i \(-0.153992\pi\)
−0.611784 + 0.791025i \(0.709548\pi\)
\(228\) 0 0
\(229\) −4457.80 + 25281.5i −0.0850061 + 0.482093i 0.912349 + 0.409413i \(0.134266\pi\)
−0.997355 + 0.0726804i \(0.976845\pi\)
\(230\) 0 0
\(231\) −77608.0 + 78329.4i −1.45440 + 1.46791i
\(232\) 0 0
\(233\) −42121.6 24318.9i −0.775877 0.447953i 0.0590903 0.998253i \(-0.481180\pi\)
−0.834967 + 0.550300i \(0.814513\pi\)
\(234\) 0 0
\(235\) −39.5630 68.5252i −0.000716397 0.00124084i
\(236\) 0 0
\(237\) 57174.1 40429.2i 1.01789 0.719778i
\(238\) 0 0
\(239\) −34021.3 93472.8i −0.595601 1.63640i −0.759938 0.649996i \(-0.774771\pi\)
0.164337 0.986404i \(-0.447452\pi\)
\(240\) 0 0
\(241\) 8476.64 + 48073.4i 0.145945 + 0.827696i 0.966603 + 0.256277i \(0.0824958\pi\)
−0.820658 + 0.571419i \(0.806393\pi\)
\(242\) 0 0
\(243\) −47573.8 + 34978.8i −0.805667 + 0.592369i
\(244\) 0 0
\(245\) 53.3202 9.40178i 0.000888299 0.000156631i
\(246\) 0 0
\(247\) 26643.8 9697.56i 0.436719 0.158953i
\(248\) 0 0
\(249\) 64568.6 + 91311.4i 1.04141 + 1.47274i
\(250\) 0 0
\(251\) 35448.9 20466.5i 0.562673 0.324859i −0.191545 0.981484i \(-0.561350\pi\)
0.754217 + 0.656625i \(0.228016\pi\)
\(252\) 0 0
\(253\) −44178.0 + 76518.5i −0.690184 + 1.19543i
\(254\) 0 0
\(255\) 88.7066 + 87.8896i 0.00136419 + 0.00135163i
\(256\) 0 0
\(257\) −432.210 76.2102i −0.00654377 0.00115384i 0.170375 0.985379i \(-0.445502\pi\)
−0.176919 + 0.984225i \(0.556613\pi\)
\(258\) 0 0
\(259\) 52461.0 44020.0i 0.782054 0.656221i
\(260\) 0 0
\(261\) 16050.8 28404.5i 0.235621 0.416971i
\(262\) 0 0
\(263\) −26508.2 + 72830.8i −0.383239 + 1.05294i 0.586745 + 0.809772i \(0.300409\pi\)
−0.969984 + 0.243168i \(0.921813\pi\)
\(264\) 0 0
\(265\) −57.8117 48.5098i −0.000823236 0.000690777i
\(266\) 0 0
\(267\) −35135.3 24360.5i −0.492857 0.341715i
\(268\) 0 0
\(269\) 46665.4i 0.644897i 0.946587 + 0.322449i \(0.104506\pi\)
−0.946587 + 0.322449i \(0.895494\pi\)
\(270\) 0 0
\(271\) −64614.8 −0.879819 −0.439910 0.898042i \(-0.644989\pi\)
−0.439910 + 0.898042i \(0.644989\pi\)
\(272\) 0 0
\(273\) 27273.8 + 2259.06i 0.365949 + 0.0303112i
\(274\) 0 0
\(275\) −76584.5 + 91269.8i −1.01269 + 1.20687i
\(276\) 0 0
\(277\) −23345.1 8496.92i −0.304254 0.110739i 0.185382 0.982667i \(-0.440648\pi\)
−0.489635 + 0.871927i \(0.662870\pi\)
\(278\) 0 0
\(279\) 42303.3 119661.i 0.543458 1.53725i
\(280\) 0 0
\(281\) −10338.9 12321.4i −0.130937 0.156044i 0.696592 0.717467i \(-0.254699\pi\)
−0.827529 + 0.561423i \(0.810254\pi\)
\(282\) 0 0
\(283\) −23776.7 + 134845.i −0.296879 + 1.68368i 0.362588 + 0.931950i \(0.381893\pi\)
−0.659467 + 0.751734i \(0.729218\pi\)
\(284\) 0 0
\(285\) −44.4532 162.884i −0.000547285 0.00200534i
\(286\) 0 0
\(287\) 131539. + 75944.3i 1.59695 + 0.922001i
\(288\) 0 0
\(289\) 56461.5 + 97794.3i 0.676016 + 1.17089i
\(290\) 0 0
\(291\) 47204.8 + 21746.7i 0.557443 + 0.256807i
\(292\) 0 0
\(293\) −20530.8 56407.8i −0.239150 0.657058i −0.999967 0.00809254i \(-0.997424\pi\)
0.760818 0.648966i \(-0.224798\pi\)
\(294\) 0 0
\(295\) −1.40285 7.95594i −1.61200e−5 9.14213e-5i
\(296\) 0 0
\(297\) 60473.6 + 125122.i 0.685572 + 1.41848i
\(298\) 0 0
\(299\) 21596.3 3808.00i 0.241566 0.0425946i
\(300\) 0 0
\(301\) −105883. + 38538.3i −1.16867 + 0.425362i
\(302\) 0 0
\(303\) −5017.88 + 462.409i −0.0546556 + 0.00503664i
\(304\) 0 0
\(305\) −106.448 + 61.4580i −0.00114430 + 0.000660661i
\(306\) 0 0
\(307\) 57552.3 99683.5i 0.610641 1.05766i −0.380492 0.924784i \(-0.624245\pi\)
0.991133 0.132877i \(-0.0424215\pi\)
\(308\) 0 0
\(309\) −15114.8 + 57471.4i −0.158302 + 0.601915i
\(310\) 0 0
\(311\) −34145.6 6020.79i −0.353032 0.0622491i −0.00567992 0.999984i \(-0.501808\pi\)
−0.347352 + 0.937735i \(0.612919\pi\)
\(312\) 0 0
\(313\) 89576.8 75163.9i 0.914339 0.767221i −0.0586009 0.998281i \(-0.518664\pi\)
0.972939 + 0.231060i \(0.0742195\pi\)
\(314\) 0 0
\(315\) 26.8127 160.745i 0.000270221 0.00162001i
\(316\) 0 0
\(317\) 53640.5 147376.i 0.533795 1.46659i −0.320726 0.947172i \(-0.603927\pi\)
0.854521 0.519418i \(-0.173851\pi\)
\(318\) 0 0
\(319\) −58819.8 49355.7i −0.578019 0.485016i
\(320\) 0 0
\(321\) −36360.3 + 17160.3i −0.352872 + 0.166539i
\(322\) 0 0
\(323\) 265610.i 2.54589i
\(324\) 0 0
\(325\) 29570.9 0.279961
\(326\) 0 0
\(327\) −37577.7 79621.9i −0.351427 0.744624i
\(328\) 0 0
\(329\) −104419. + 124442.i −0.964694 + 1.14968i
\(330\) 0 0
\(331\) −2040.65 742.736i −0.0186257 0.00677920i 0.332690 0.943036i \(-0.392044\pi\)
−0.351316 + 0.936257i \(0.614266\pi\)
\(332\) 0 0
\(333\) −30269.1 80828.8i −0.272967 0.728916i
\(334\) 0 0
\(335\) 81.4614 + 97.0819i 0.000725876 + 0.000865065i
\(336\) 0 0
\(337\) −10362.9 + 58770.8i −0.0912474 + 0.517490i 0.904585 + 0.426292i \(0.140181\pi\)
−0.995833 + 0.0911974i \(0.970931\pi\)
\(338\) 0 0
\(339\) 110233. + 28990.9i 0.959207 + 0.252268i
\(340\) 0 0
\(341\) −258681. 149349.i −2.22462 1.28438i
\(342\) 0 0
\(343\) 21577.1 + 37372.6i 0.183402 + 0.317662i
\(344\) 0 0
\(345\) −11.9829 130.034i −0.000100676 0.00109249i
\(346\) 0 0
\(347\) −31580.8 86767.6i −0.262280 0.720607i −0.999013 0.0444237i \(-0.985855\pi\)
0.736733 0.676184i \(-0.236367\pi\)
\(348\) 0 0
\(349\) −4641.37 26322.5i −0.0381062 0.216111i 0.959809 0.280655i \(-0.0905517\pi\)
−0.997915 + 0.0645444i \(0.979441\pi\)
\(350\) 0 0
\(351\) 14141.5 31459.2i 0.114784 0.255349i
\(352\) 0 0
\(353\) 51899.9 9151.35i 0.416502 0.0734405i 0.0385297 0.999257i \(-0.487733\pi\)
0.377972 + 0.925817i \(0.376621\pi\)
\(354\) 0 0
\(355\) −72.8389 + 26.5112i −0.000577972 + 0.000210364i
\(356\) 0 0
\(357\) 107270. 232848.i 0.841671 1.82699i
\(358\) 0 0
\(359\) −31426.2 + 18143.9i −0.243839 + 0.140781i −0.616940 0.787010i \(-0.711628\pi\)
0.373101 + 0.927791i \(0.378295\pi\)
\(360\) 0 0
\(361\) −114404. + 198154.i −0.877865 + 1.52051i
\(362\) 0 0
\(363\) 188403. 51417.7i 1.42980 0.390211i
\(364\) 0 0
\(365\) 46.9406 + 8.27690i 0.000352341 + 6.21272e-5i
\(366\) 0 0
\(367\) −160886. + 135000.i −1.19450 + 1.00231i −0.194733 + 0.980856i \(0.562384\pi\)
−0.999770 + 0.0214507i \(0.993172\pi\)
\(368\) 0 0
\(369\) 145498. 124399.i 1.06857 0.913620i
\(370\) 0 0
\(371\) −52991.7 + 145594.i −0.385000 + 1.05778i
\(372\) 0 0
\(373\) 10634.3 + 8923.25i 0.0764350 + 0.0641366i 0.680205 0.733022i \(-0.261891\pi\)
−0.603770 + 0.797159i \(0.706335\pi\)
\(374\) 0 0
\(375\) 29.0709 350.975i 0.000206726 0.00249583i
\(376\) 0 0
\(377\) 19057.3i 0.134084i
\(378\) 0 0
\(379\) 123341. 0.858677 0.429338 0.903144i \(-0.358747\pi\)
0.429338 + 0.903144i \(0.358747\pi\)
\(380\) 0 0
\(381\) 114163. 164658.i 0.786459 1.13431i
\(382\) 0 0
\(383\) 158981. 189467.i 1.08380 1.29162i 0.129889 0.991529i \(-0.458538\pi\)
0.953910 0.300093i \(-0.0970176\pi\)
\(384\) 0 0
\(385\) −360.406 131.177i −0.00243148 0.000884987i
\(386\) 0 0
\(387\) 1313.94 + 142005.i 0.00877308 + 0.948160i
\(388\) 0 0
\(389\) −45832.1 54620.6i −0.302880 0.360958i 0.593041 0.805173i \(-0.297927\pi\)
−0.895921 + 0.444214i \(0.853483\pi\)
\(390\) 0 0
\(391\) 35672.4 202308.i 0.233334 1.32330i
\(392\) 0 0
\(393\) 43088.0 43488.5i 0.278979 0.281572i
\(394\) 0 0
\(395\) 210.934 + 121.783i 0.00135192 + 0.000780533i
\(396\) 0 0
\(397\) 35045.3 + 60700.3i 0.222356 + 0.385132i 0.955523 0.294917i \(-0.0952919\pi\)
−0.733167 + 0.680049i \(0.761959\pi\)
\(398\) 0 0
\(399\) −283023. + 200133.i −1.77777 + 1.25711i
\(400\) 0 0
\(401\) −51680.5 141991.i −0.321394 0.883023i −0.990209 0.139594i \(-0.955420\pi\)
0.668815 0.743429i \(-0.266802\pi\)
\(402\) 0 0
\(403\) 12873.4 + 73009.0i 0.0792656 + 0.449538i
\(404\) 0 0
\(405\) −179.743 99.3861i −0.00109583 0.000605920i
\(406\) 0 0
\(407\) −200043. + 35273.0i −1.20763 + 0.212938i
\(408\) 0 0
\(409\) −35042.7 + 12754.5i −0.209484 + 0.0762460i −0.444631 0.895714i \(-0.646665\pi\)
0.235147 + 0.971960i \(0.424443\pi\)
\(410\) 0 0
\(411\) −33290.1 47078.1i −0.197075 0.278699i
\(412\) 0 0
\(413\) −14363.7 + 8292.86i −0.0842102 + 0.0486188i
\(414\) 0 0
\(415\) −194.496 + 336.877i −0.00112931 + 0.00195603i
\(416\) 0 0
\(417\) 149488. + 148112.i 0.859677 + 0.851759i
\(418\) 0 0
\(419\) 242548. + 42767.8i 1.38156 + 0.243607i 0.814545 0.580100i \(-0.196986\pi\)
0.567017 + 0.823706i \(0.308098\pi\)
\(420\) 0 0
\(421\) −13777.8 + 11560.9i −0.0777348 + 0.0652272i −0.680827 0.732444i \(-0.738379\pi\)
0.603092 + 0.797671i \(0.293935\pi\)
\(422\) 0 0
\(423\) 104004. + 176352.i 0.581261 + 0.985600i
\(424\) 0 0
\(425\) 94743.7 260306.i 0.524533 1.44114i
\(426\) 0 0
\(427\) 193311. + 162207.i 1.06023 + 0.889640i
\(428\) 0 0
\(429\) −66709.2 46251.8i −0.362469 0.251313i
\(430\) 0 0
\(431\) 314703.i 1.69413i 0.531490 + 0.847064i \(0.321632\pi\)
−0.531490 + 0.847064i \(0.678368\pi\)
\(432\) 0 0
\(433\) −208556. −1.11236 −0.556182 0.831060i \(-0.687734\pi\)
−0.556182 + 0.831060i \(0.687734\pi\)
\(434\) 0 0
\(435\) 113.095 + 9.36752i 0.000597674 + 4.95047e-5i
\(436\) 0 0
\(437\) −178540. + 212776.i −0.934916 + 1.11419i
\(438\) 0 0
\(439\) 175311. + 63807.9i 0.909661 + 0.331090i 0.754118 0.656739i \(-0.228065\pi\)
0.155544 + 0.987829i \(0.450287\pi\)
\(440\) 0 0
\(441\) −137734. + 25602.3i −0.708211 + 0.131644i
\(442\) 0 0
\(443\) 44298.3 + 52792.7i 0.225725 + 0.269009i 0.867006 0.498297i \(-0.166041\pi\)
−0.641281 + 0.767306i \(0.721597\pi\)
\(444\) 0 0
\(445\) 25.8236 146.453i 0.000130406 0.000739567i
\(446\) 0 0
\(447\) 81114.0 + 297215.i 0.405958 + 1.48750i
\(448\) 0 0
\(449\) 174409. + 100695.i 0.865117 + 0.499476i 0.865723 0.500524i \(-0.166859\pi\)
−0.000605245 1.00000i \(0.500193\pi\)
\(450\) 0 0
\(451\) −225261. 390163.i −1.10747 1.91820i
\(452\) 0 0
\(453\) −234883. 108208.i −1.14461 0.527306i
\(454\) 0 0
\(455\) 32.5574 + 89.4506i 0.000157263 + 0.000432077i
\(456\) 0 0
\(457\) 12388.7 + 70259.5i 0.0593187 + 0.336413i 0.999996 0.00288993i \(-0.000919895\pi\)
−0.940677 + 0.339303i \(0.889809\pi\)
\(458\) 0 0
\(459\) −231620. 225279.i −1.09939 1.06929i
\(460\) 0 0
\(461\) −284665. + 50194.1i −1.33947 + 0.236184i −0.797044 0.603921i \(-0.793604\pi\)
−0.542423 + 0.840105i \(0.682493\pi\)
\(462\) 0 0
\(463\) 68653.9 24988.0i 0.320260 0.116565i −0.176888 0.984231i \(-0.556603\pi\)
0.497148 + 0.867666i \(0.334381\pi\)
\(464\) 0 0
\(465\) 439.597 40.5099i 0.00203306 0.000187351i
\(466\) 0 0
\(467\) −79976.9 + 46174.7i −0.366717 + 0.211724i −0.672023 0.740530i \(-0.734574\pi\)
0.305306 + 0.952254i \(0.401241\pi\)
\(468\) 0 0
\(469\) 130091. 225325.i 0.591429 1.02439i
\(470\) 0 0
\(471\) −17574.6 + 66824.2i −0.0792214 + 0.301226i
\(472\) 0 0
\(473\) 329141. + 58036.5i 1.47116 + 0.259405i
\(474\) 0 0
\(475\) −286919. + 240753.i −1.27166 + 1.06705i
\(476\) 0 0
\(477\) 150741. + 124128.i 0.662514 + 0.545550i
\(478\) 0 0
\(479\) 94771.9 260384.i 0.413056 1.13486i −0.542501 0.840055i \(-0.682523\pi\)
0.955557 0.294806i \(-0.0952551\pi\)
\(480\) 0 0
\(481\) 38620.5 + 32406.4i 0.166927 + 0.140069i
\(482\) 0 0
\(483\) −242450. + 114425.i −1.03927 + 0.490484i
\(484\) 0 0
\(485\) 180.778i 0.000768533i
\(486\) 0 0
\(487\) −231576. −0.976416 −0.488208 0.872727i \(-0.662349\pi\)
−0.488208 + 0.872727i \(0.662349\pi\)
\(488\) 0 0
\(489\) −35392.5 74991.7i −0.148011 0.313614i
\(490\) 0 0
\(491\) −271099. + 323083.i −1.12451 + 1.34014i −0.191003 + 0.981589i \(0.561174\pi\)
−0.933509 + 0.358553i \(0.883270\pi\)
\(492\) 0 0
\(493\) 167757. + 61058.6i 0.690220 + 0.251219i
\(494\) 0 0
\(495\) −307.271 + 373.149i −0.00125404 + 0.00152290i
\(496\) 0 0
\(497\) 102291. + 121906.i 0.414120 + 0.493529i
\(498\) 0 0
\(499\) −12436.4 + 70530.2i −0.0499451 + 0.283253i −0.999543 0.0302167i \(-0.990380\pi\)
0.949598 + 0.313470i \(0.101491\pi\)
\(500\) 0 0
\(501\) 126476. + 33262.7i 0.503886 + 0.132520i
\(502\) 0 0
\(503\) 259012. + 149541.i 1.02373 + 0.591048i 0.915181 0.403043i \(-0.132048\pi\)
0.108545 + 0.994092i \(0.465381\pi\)
\(504\) 0 0
\(505\) −8.76382 15.1794i −3.43645e−5 5.95211e-5i
\(506\) 0 0
\(507\) −21738.9 235902.i −0.0845712 0.917733i
\(508\) 0 0
\(509\) −108249. 297413.i −0.417820 1.14795i −0.952936 0.303173i \(-0.901954\pi\)
0.535115 0.844779i \(-0.320268\pi\)
\(510\) 0 0
\(511\) −16992.7 96370.3i −0.0650759 0.369064i
\(512\) 0 0
\(513\) 118916. + 420375.i 0.451862 + 1.59736i
\(514\) 0 0
\(515\) −203.560 + 35.8932i −0.000767500 + 0.000135331i
\(516\) 0 0
\(517\) 452783. 164800.i 1.69398 0.616559i
\(518\) 0 0
\(519\) 84836.2 184151.i 0.314954 0.683660i
\(520\) 0 0
\(521\) −175042. + 101061.i −0.644862 + 0.372311i −0.786485 0.617609i \(-0.788101\pi\)
0.141623 + 0.989921i \(0.454768\pi\)
\(522\) 0 0
\(523\) −53298.1 + 92314.9i −0.194853 + 0.337496i −0.946852 0.321668i \(-0.895756\pi\)
0.751999 + 0.659164i \(0.229090\pi\)
\(524\) 0 0
\(525\) −348759. + 95181.2i −1.26534 + 0.345329i
\(526\) 0 0
\(527\) 683928. + 120595.i 2.46257 + 0.434218i
\(528\) 0 0
\(529\) 49805.3 41791.6i 0.177977 0.149341i
\(530\) 0 0
\(531\) 3820.14 + 20551.3i 0.0135485 + 0.0728871i
\(532\) 0 0
\(533\) −38243.5 + 105073.i −0.134618 + 0.369860i
\(534\) 0 0
\(535\) −107.131 89.8936i −0.000374290 0.000314066i
\(536\) 0 0
\(537\) 30850.6 372462.i 0.106983 1.29162i
\(538\) 0 0
\(539\) 329704.i 1.13487i
\(540\) 0 0
\(541\) −53821.8 −0.183892 −0.0919462 0.995764i \(-0.529309\pi\)
−0.0919462 + 0.995764i \(0.529309\pi\)
\(542\) 0 0
\(543\) 9189.67 13254.3i 0.0311674 0.0449528i
\(544\) 0 0
\(545\) 196.849 234.596i 0.000662736 0.000789818i
\(546\) 0 0
\(547\) −35772.0 13019.9i −0.119555 0.0435145i 0.281550 0.959547i \(-0.409152\pi\)
−0.401105 + 0.916032i \(0.631374\pi\)
\(548\) 0 0
\(549\) 273949. 161562.i 0.908919 0.536038i
\(550\) 0 0
\(551\) −155156. 184908.i −0.511053 0.609049i
\(552\) 0 0
\(553\) 86832.0 492449.i 0.283942 1.61032i
\(554\) 0 0
\(555\) 211.299 213.263i 0.000685979 0.000692356i
\(556\) 0 0
\(557\) −369490. 213325.i −1.19095 0.687594i −0.232426 0.972614i \(-0.574666\pi\)
−0.958522 + 0.285020i \(0.908000\pi\)
\(558\) 0 0
\(559\) −41475.5 71837.7i −0.132730 0.229895i
\(560\) 0 0
\(561\) −620879. + 439038.i −1.97279 + 1.39501i
\(562\) 0 0
\(563\) −77677.9 213418.i −0.245065 0.673310i −0.999850 0.0173374i \(-0.994481\pi\)
0.754785 0.655972i \(-0.227741\pi\)
\(564\) 0 0
\(565\) 68.8448 + 390.438i 0.000215662 + 0.00122308i
\(566\) 0 0
\(567\) −65525.8 + 416548.i −0.203820 + 1.29568i
\(568\) 0 0
\(569\) 508866. 89726.9i 1.57173 0.277139i 0.681215 0.732084i \(-0.261452\pi\)
0.890520 + 0.454945i \(0.150341\pi\)
\(570\) 0 0
\(571\) 470667. 171309.i 1.44358 0.525421i 0.502791 0.864408i \(-0.332306\pi\)
0.940791 + 0.338987i \(0.110084\pi\)
\(572\) 0 0
\(573\) −291259. 411892.i −0.887095 1.25451i
\(574\) 0 0
\(575\) −250872. + 144841.i −0.758781 + 0.438082i
\(576\) 0 0
\(577\) 139405. 241457.i 0.418723 0.725250i −0.577088 0.816682i \(-0.695811\pi\)
0.995811 + 0.0914318i \(0.0291444\pi\)
\(578\) 0 0
\(579\) 270671. + 268178.i 0.807392 + 0.799956i
\(580\) 0 0
\(581\) 786479. + 138677.i 2.32989 + 0.410822i
\(582\) 0 0
\(583\) 352047. 295403.i 1.03577 0.869115i
\(584\) 0 0
\(585\) 119.967 1.11002i 0.000350549 3.24354e-6i
\(586\) 0 0
\(587\) 107700. 295904.i 0.312565 0.858764i −0.679572 0.733608i \(-0.737835\pi\)
0.992137 0.125156i \(-0.0399431\pi\)
\(588\) 0 0
\(589\) −719315. 603577.i −2.07343 1.73981i
\(590\) 0 0
\(591\) −444011. 307849.i −1.27121 0.881378i
\(592\) 0 0
\(593\) 36185.2i 0.102902i −0.998676 0.0514508i \(-0.983615\pi\)
0.998676 0.0514508i \(-0.0163845\pi\)
\(594\) 0 0
\(595\) 891.727 0.00251883
\(596\) 0 0
\(597\) −521185. 43169.1i −1.46232 0.121122i
\(598\) 0 0
\(599\) 65094.9 77577.1i 0.181424 0.216212i −0.667666 0.744461i \(-0.732707\pi\)
0.849090 + 0.528249i \(0.177151\pi\)
\(600\) 0 0
\(601\) −267323. 97297.5i −0.740094 0.269372i −0.0556627 0.998450i \(-0.517727\pi\)
−0.684431 + 0.729077i \(0.739949\pi\)
\(602\) 0 0
\(603\) −213094. 249236.i −0.586053 0.685450i
\(604\) 0 0
\(605\) 436.638 + 520.364i 0.00119292 + 0.00142166i
\(606\) 0 0
\(607\) 71270.1 404193.i 0.193433 1.09701i −0.721201 0.692726i \(-0.756409\pi\)
0.914633 0.404285i \(-0.132480\pi\)
\(608\) 0 0
\(609\) −61340.6 224762.i −0.165392 0.606021i
\(610\) 0 0
\(611\) −103568. 59795.1i −0.277424 0.160171i
\(612\) 0 0
\(613\) −163074. 282453.i −0.433974 0.751666i 0.563237 0.826295i \(-0.309556\pi\)
−0.997211 + 0.0746297i \(0.976223\pi\)
\(614\) 0 0
\(615\) 604.756 + 278.604i 0.00159893 + 0.000736608i
\(616\) 0 0
\(617\) 249596. + 685760.i 0.655643 + 1.80137i 0.595764 + 0.803160i \(0.296849\pi\)
0.0598795 + 0.998206i \(0.480928\pi\)
\(618\) 0 0
\(619\) 119433. + 677338.i 0.311705 + 1.76776i 0.590131 + 0.807307i \(0.299076\pi\)
−0.278427 + 0.960457i \(0.589813\pi\)
\(620\) 0 0
\(621\) 34117.3 + 336159.i 0.0884690 + 0.871688i
\(622\) 0 0
\(623\) −300671. + 53016.4i −0.774668 + 0.136595i
\(624\) 0 0
\(625\) −367066. + 133601.i −0.939688 + 0.342019i
\(626\) 0 0
\(627\) 1.02383e6 94347.8i 2.60430 0.239992i
\(628\) 0 0
\(629\) 409005. 236139.i 1.03378 0.596852i
\(630\) 0 0
\(631\) −43866.1 + 75978.2i −0.110172 + 0.190823i −0.915839 0.401545i \(-0.868473\pi\)
0.805668 + 0.592368i \(0.201807\pi\)
\(632\) 0 0
\(633\) −23482.5 + 89288.3i −0.0586054 + 0.222837i
\(634\) 0 0
\(635\) 686.336 + 121.020i 0.00170212 + 0.000300129i
\(636\) 0 0
\(637\) 62685.9 52599.7i 0.154487 0.129630i
\(638\) 0 0
\(639\) 187826. 70337.8i 0.459996 0.172261i
\(640\) 0 0
\(641\) −95751.6 + 263075.i −0.233040 + 0.640272i −0.999999 0.00142423i \(-0.999547\pi\)
0.766959 + 0.641696i \(0.221769\pi\)
\(642\) 0 0
\(643\) 395316. + 331709.i 0.956142 + 0.802298i 0.980321 0.197409i \(-0.0632528\pi\)
−0.0241793 + 0.999708i \(0.507697\pi\)
\(644\) 0 0
\(645\) −446.706 + 210.824i −0.00107375 + 0.000506758i
\(646\) 0 0
\(647\) 230598.i 0.550868i 0.961320 + 0.275434i \(0.0888215\pi\)
−0.961320 + 0.275434i \(0.911178\pi\)
\(648\) 0 0
\(649\) 49195.4 0.116798
\(650\) 0 0
\(651\) −386827. 819632.i −0.912756 1.93400i
\(652\) 0 0
\(653\) −344862. + 410991.i −0.808760 + 0.963842i −0.999843 0.0177317i \(-0.994356\pi\)
0.191083 + 0.981574i \(0.438800\pi\)
\(654\) 0 0
\(655\) 200.098 + 72.8296i 0.000466401 + 0.000169756i
\(656\) 0 0
\(657\) −121651. 20291.6i −0.281828 0.0470094i
\(658\) 0 0
\(659\) −432211. 515089.i −0.995234 1.18607i −0.982521 0.186154i \(-0.940398\pi\)
−0.0127133 0.999919i \(-0.504047\pi\)
\(660\) 0 0
\(661\) −90978.6 + 515965.i −0.208227 + 1.18091i 0.684054 + 0.729431i \(0.260215\pi\)
−0.892281 + 0.451481i \(0.850896\pi\)
\(662\) 0 0
\(663\) 182526. + 48003.7i 0.415238 + 0.109206i
\(664\) 0 0
\(665\) −1044.16 602.849i −0.00236116 0.00136322i
\(666\) 0 0
\(667\) −93344.4 161677.i −0.209815 0.363410i
\(668\) 0 0
\(669\) 65706.8 + 713024.i 0.146811 + 1.59313i
\(670\) 0 0
\(671\) −256003. 703362.i −0.568590 1.56219i
\(672\) 0 0
\(673\) 2915.44 + 16534.3i 0.00643685 + 0.0365052i 0.987857 0.155366i \(-0.0496556\pi\)
−0.981420 + 0.191871i \(0.938544\pi\)
\(674\) 0 0
\(675\) −33407.2 + 454398.i −0.0733218 + 0.997307i
\(676\) 0 0
\(677\) 886585. 156329.i 1.93438 0.341084i 0.934495 0.355975i \(-0.115851\pi\)
0.999889 + 0.0148909i \(0.00474009\pi\)
\(678\) 0 0
\(679\) 348759. 126938.i 0.756461 0.275329i
\(680\) 0 0
\(681\) 82552.6 179194.i 0.178007 0.386394i
\(682\) 0 0
\(683\) −515809. + 297802.i −1.10573 + 0.638391i −0.937719 0.347395i \(-0.887066\pi\)
−0.168007 + 0.985786i \(0.553733\pi\)
\(684\) 0 0
\(685\) 100.278 173.686i 0.000213710 0.000370156i
\(686\) 0 0
\(687\) 222892. 60830.2i 0.472259 0.128886i
\(688\) 0 0
\(689\) −112328. 19806.5i −0.236620 0.0417224i
\(690\) 0 0
\(691\) −285792. + 239808.i −0.598541 + 0.502236i −0.890976 0.454050i \(-0.849979\pi\)
0.292435 + 0.956285i \(0.405534\pi\)
\(692\) 0 0
\(693\) 935642. + 330775.i 1.94824 + 0.688757i
\(694\) 0 0
\(695\) −250.346 + 687.820i −0.000518288 + 0.00142398i
\(696\) 0 0
\(697\) 802407. + 673300.i 1.65169 + 1.38594i
\(698\) 0 0
\(699\) −36133.8 + 436246.i −0.0739536 + 0.892848i
\(700\) 0 0
\(701\) 182277.i 0.370934i 0.982650 + 0.185467i \(0.0593798\pi\)
−0.982650 + 0.185467i \(0.940620\pi\)
\(702\) 0 0
\(703\) −638564. −1.29209
\(704\) 0 0
\(705\) −405.761 + 585.230i −0.000816379 + 0.00117747i
\(706\) 0 0
\(707\) −23130.5 + 27565.9i −0.0462750 + 0.0551484i
\(708\) 0 0
\(709\) 219638. + 79941.7i 0.436933 + 0.159031i 0.551115 0.834429i \(-0.314202\pi\)
−0.114182 + 0.993460i \(0.536425\pi\)
\(710\) 0 0
\(711\) −548677. 310046.i −1.08537 0.613320i
\(712\) 0 0
\(713\) −466820. 556334.i −0.918270 1.09435i
\(714\) 0 0
\(715\) 49.0296 278.061i 9.59061e−5 0.000543910i
\(716\) 0 0
\(717\) −630099. + 635956.i −1.22566 + 1.23705i
\(718\) 0 0
\(719\) 355326. + 205148.i 0.687336 + 0.396834i 0.802613 0.596500i \(-0.203442\pi\)
−0.115277 + 0.993333i \(0.536776\pi\)
\(720\) 0 0
\(721\) 212181. + 367508.i 0.408164 + 0.706962i
\(722\) 0 0
\(723\) 358713. 253654.i 0.686231 0.485250i
\(724\) 0 0
\(725\) −86100.8 236560.i −0.163806 0.450054i
\(726\) 0 0
\(727\) 167973. + 952624.i 0.317813 + 1.80241i 0.555996 + 0.831185i \(0.312337\pi\)
−0.238183 + 0.971220i \(0.576552\pi\)
\(728\) 0 0
\(729\) 467439. + 252845.i 0.879569 + 0.475772i
\(730\) 0 0
\(731\) −765258. + 134936.i −1.43210 + 0.252518i
\(732\) 0 0
\(733\) −165250. + 60146.2i −0.307563 + 0.111944i −0.491191 0.871052i \(-0.663438\pi\)
0.183628 + 0.982996i \(0.441216\pi\)
\(734\) 0 0
\(735\) −281.339 397.863i −0.000520780 0.000736476i
\(736\) 0 0
\(737\) −668343. + 385868.i −1.23045 + 0.710402i
\(738\) 0 0
\(739\) −366610. + 634988.i −0.671299 + 1.16272i 0.306237 + 0.951955i \(0.400930\pi\)
−0.977536 + 0.210769i \(0.932403\pi\)
\(740\) 0 0
\(741\) −181275. 179605.i −0.330143 0.327102i
\(742\) 0 0
\(743\) 730405. + 128790.i 1.32308 + 0.233295i 0.790175 0.612881i \(-0.209989\pi\)
0.532904 + 0.846176i \(0.321101\pi\)
\(744\) 0 0
\(745\) −820.901 + 688.818i −0.00147903 + 0.00124106i
\(746\) 0 0
\(747\) 495167. 876280.i 0.887382 1.57037i
\(748\) 0 0
\(749\) −98199.0 + 269800.i −0.175043 + 0.480925i
\(750\) 0 0
\(751\) −72745.4 61040.7i −0.128981 0.108228i 0.576015 0.817439i \(-0.304607\pi\)
−0.704996 + 0.709211i \(0.749051\pi\)
\(752\) 0 0
\(753\) −302747. 209905.i −0.533936 0.370197i
\(754\) 0 0
\(755\) 899.523i 0.00157804i
\(756\) 0 0
\(757\) −499006. −0.870791 −0.435396 0.900239i \(-0.643391\pi\)
−0.435396 + 0.900239i \(0.643391\pi\)
\(758\) 0 0
\(759\) 792490. + 65641.1i 1.37566 + 0.113944i
\(760\) 0 0
\(761\) −314122. + 374356.i −0.542412 + 0.646421i −0.965727 0.259561i \(-0.916422\pi\)
0.423315 + 0.905983i \(0.360866\pi\)
\(762\) 0 0
\(763\) −590807. 215036.i −1.01484 0.369371i
\(764\) 0 0
\(765\) 374.596 1059.60i 0.000640089 0.00181058i
\(766\) 0 0
\(767\) −7848.44 9353.41i −0.0133411 0.0158993i
\(768\) 0 0
\(769\) 96572.4 547689.i 0.163305 0.926150i −0.787489 0.616328i \(-0.788619\pi\)
0.950795 0.309822i \(-0.100269\pi\)
\(770\) 0 0
\(771\) 1039.95 + 3810.53i 0.00174945 + 0.00641028i
\(772\) 0 0
\(773\) 297119. + 171542.i 0.497247 + 0.287086i 0.727576 0.686027i \(-0.240647\pi\)
−0.230329 + 0.973113i \(0.573980\pi\)
\(774\) 0 0
\(775\) −489654. 848105.i −0.815240 1.41204i
\(776\) 0 0
\(777\) −559798. 257892.i −0.927235 0.427165i
\(778\) 0 0
\(779\) −484394. 1.33086e6i −0.798222 2.19310i
\(780\) 0 0