Properties

Label 108.5.k.a.29.3
Level 108
Weight 5
Character 108.29
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 29.3
Character \(\chi\) \(=\) 108.29
Dual form 108.5.k.a.41.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-6.90497 - 5.77247i) q^{3} +(11.0592 + 13.1798i) q^{5} +(7.77764 - 2.83083i) q^{7} +(14.3573 + 79.7174i) q^{9} +O(q^{10})\) \(q+(-6.90497 - 5.77247i) q^{3} +(11.0592 + 13.1798i) q^{5} +(7.77764 - 2.83083i) q^{7} +(14.3573 + 79.7174i) q^{9} +(44.3220 - 52.8209i) q^{11} +(-4.19703 - 23.8025i) q^{13} +(-0.283269 - 154.845i) q^{15} +(213.549 - 123.293i) q^{17} +(175.684 - 304.294i) q^{19} +(-70.0452 - 25.3494i) q^{21} +(275.524 - 756.995i) q^{23} +(57.1279 - 323.988i) q^{25} +(361.030 - 633.323i) q^{27} +(-348.016 - 61.3646i) q^{29} +(634.917 + 231.091i) q^{31} +(-610.949 + 108.880i) q^{33} +(123.324 + 71.2013i) q^{35} +(870.013 + 1506.91i) q^{37} +(-108.419 + 188.583i) q^{39} +(629.967 - 111.080i) q^{41} +(1149.85 + 964.841i) q^{43} +(-891.882 + 1070.84i) q^{45} +(-649.053 - 1783.26i) q^{47} +(-1786.79 + 1499.30i) q^{49} +(-2186.26 - 381.374i) q^{51} -1728.31i q^{53} +1186.34 q^{55} +(-2969.62 + 1087.01i) q^{57} +(-442.288 - 527.098i) q^{59} +(995.692 - 362.402i) q^{61} +(337.332 + 579.370i) q^{63} +(267.298 - 318.553i) q^{65} +(1019.70 + 5783.02i) q^{67} +(-6272.21 + 3636.58i) q^{69} +(3889.70 - 2245.72i) q^{71} +(-725.679 + 1256.91i) q^{73} +(-2264.68 + 1907.36i) q^{75} +(195.194 - 536.290i) q^{77} +(-173.955 + 986.547i) q^{79} +(-6148.74 + 2289.05i) q^{81} +(-1712.04 - 301.879i) q^{83} +(3986.66 + 1451.03i) q^{85} +(2048.81 + 2432.63i) q^{87} +(-1131.82 - 653.456i) q^{89} +(-100.024 - 173.246i) q^{91} +(-3050.12 - 5260.71i) q^{93} +(5953.47 - 1049.76i) q^{95} +(10494.3 + 8805.79i) q^{97} +(4847.09 + 2774.87i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q + 9q^{5} - 102q^{9} + O(q^{10}) \) \( 72q + 9q^{5} - 102q^{9} + 18q^{11} - 225q^{15} - 282q^{21} - 1278q^{23} + 441q^{25} + 54q^{27} + 1854q^{29} - 1665q^{31} - 45q^{33} - 2673q^{35} + 6951q^{39} - 5472q^{41} + 1260q^{43} + 5553q^{45} + 5103q^{47} - 5904q^{49} + 1899q^{51} + 1107q^{57} - 10944q^{59} + 8352q^{61} - 11985q^{63} + 8757q^{65} + 378q^{67} + 5607q^{69} - 19764q^{71} + 6111q^{73} - 3453q^{75} - 5679q^{77} - 5652q^{79} - 20466q^{81} - 20061q^{83} + 26100q^{85} + 40545q^{87} + 15633q^{89} - 6039q^{91} + 40179q^{93} + 48024q^{95} - 37530q^{97} + 12177q^{99} + O(q^{100}) \)

Character values

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

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

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
\(3\) −6.90497 5.77247i −0.767219 0.641385i
\(4\) 0 0
\(5\) 11.0592 + 13.1798i 0.442368 + 0.527193i 0.940448 0.339938i \(-0.110406\pi\)
−0.498080 + 0.867131i \(0.665962\pi\)
\(6\) 0 0
\(7\) 7.77764 2.83083i 0.158727 0.0577720i −0.261434 0.965221i \(-0.584196\pi\)
0.420162 + 0.907449i \(0.361973\pi\)
\(8\) 0 0
\(9\) 14.3573 + 79.7174i 0.177250 + 0.984166i
\(10\) 0 0
\(11\) 44.3220 52.8209i 0.366298 0.436537i −0.551142 0.834411i \(-0.685808\pi\)
0.917440 + 0.397875i \(0.130252\pi\)
\(12\) 0 0
\(13\) −4.19703 23.8025i −0.0248345 0.140843i 0.969869 0.243625i \(-0.0783367\pi\)
−0.994704 + 0.102782i \(0.967226\pi\)
\(14\) 0 0
\(15\) −0.283269 154.845i −0.00125898 0.688201i
\(16\) 0 0
\(17\) 213.549 123.293i 0.738925 0.426619i −0.0827531 0.996570i \(-0.526371\pi\)
0.821678 + 0.569951i \(0.193038\pi\)
\(18\) 0 0
\(19\) 175.684 304.294i 0.486660 0.842920i −0.513222 0.858256i \(-0.671548\pi\)
0.999882 + 0.0153357i \(0.00488168\pi\)
\(20\) 0 0
\(21\) −70.0452 25.3494i −0.158833 0.0574815i
\(22\) 0 0
\(23\) 275.524 756.995i 0.520839 1.43099i −0.348750 0.937216i \(-0.613394\pi\)
0.869589 0.493777i \(-0.164384\pi\)
\(24\) 0 0
\(25\) 57.1279 323.988i 0.0914047 0.518382i
\(26\) 0 0
\(27\) 361.030 633.323i 0.495240 0.868756i
\(28\) 0 0
\(29\) −348.016 61.3646i −0.413812 0.0729662i −0.0371335 0.999310i \(-0.511823\pi\)
−0.376678 + 0.926344i \(0.622934\pi\)
\(30\) 0 0
\(31\) 634.917 + 231.091i 0.660684 + 0.240469i 0.650531 0.759479i \(-0.274546\pi\)
0.0101521 + 0.999948i \(0.496768\pi\)
\(32\) 0 0
\(33\) −610.949 + 108.880i −0.561019 + 0.0999813i
\(34\) 0 0
\(35\) 123.324 + 71.2013i 0.100673 + 0.0581235i
\(36\) 0 0
\(37\) 870.013 + 1506.91i 0.635510 + 1.10073i 0.986407 + 0.164321i \(0.0525432\pi\)
−0.350897 + 0.936414i \(0.614123\pi\)
\(38\) 0 0
\(39\) −108.419 + 188.583i −0.0712814 + 0.123986i
\(40\) 0 0
\(41\) 629.967 111.080i 0.374757 0.0660798i 0.0169027 0.999857i \(-0.494619\pi\)
0.357855 + 0.933777i \(0.383508\pi\)
\(42\) 0 0
\(43\) 1149.85 + 964.841i 0.621878 + 0.521818i 0.898393 0.439192i \(-0.144735\pi\)
−0.276515 + 0.961010i \(0.589180\pi\)
\(44\) 0 0
\(45\) −891.882 + 1070.84i −0.440436 + 0.528808i
\(46\) 0 0
\(47\) −649.053 1783.26i −0.293822 0.807270i −0.995499 0.0947744i \(-0.969787\pi\)
0.701676 0.712496i \(-0.252435\pi\)
\(48\) 0 0
\(49\) −1786.79 + 1499.30i −0.744188 + 0.624448i
\(50\) 0 0
\(51\) −2186.26 381.374i −0.840545 0.146626i
\(52\) 0 0
\(53\) 1728.31i 0.615278i −0.951503 0.307639i \(-0.900461\pi\)
0.951503 0.307639i \(-0.0995388\pi\)
\(54\) 0 0
\(55\) 1186.34 0.392177
\(56\) 0 0
\(57\) −2969.62 + 1087.01i −0.914011 + 0.334568i
\(58\) 0 0
\(59\) −442.288 527.098i −0.127058 0.151421i 0.698765 0.715351i \(-0.253733\pi\)
−0.825823 + 0.563930i \(0.809289\pi\)
\(60\) 0 0
\(61\) 995.692 362.402i 0.267587 0.0973938i −0.204742 0.978816i \(-0.565636\pi\)
0.472329 + 0.881422i \(0.343413\pi\)
\(62\) 0 0
\(63\) 337.332 + 579.370i 0.0849917 + 0.145974i
\(64\) 0 0
\(65\) 267.298 318.553i 0.0632657 0.0753971i
\(66\) 0 0
\(67\) 1019.70 + 5783.02i 0.227156 + 1.28826i 0.858521 + 0.512778i \(0.171384\pi\)
−0.631365 + 0.775486i \(0.717505\pi\)
\(68\) 0 0
\(69\) −6272.21 + 3636.58i −1.31741 + 0.763826i
\(70\) 0 0
\(71\) 3889.70 2245.72i 0.771612 0.445491i −0.0618371 0.998086i \(-0.519696\pi\)
0.833450 + 0.552596i \(0.186363\pi\)
\(72\) 0 0
\(73\) −725.679 + 1256.91i −0.136176 + 0.235863i −0.926046 0.377411i \(-0.876814\pi\)
0.789870 + 0.613274i \(0.210148\pi\)
\(74\) 0 0
\(75\) −2264.68 + 1907.36i −0.402610 + 0.339087i
\(76\) 0 0
\(77\) 195.194 536.290i 0.0329219 0.0904520i
\(78\) 0 0
\(79\) −173.955 + 986.547i −0.0278729 + 0.158075i −0.995567 0.0940505i \(-0.970018\pi\)
0.967695 + 0.252126i \(0.0811296\pi\)
\(80\) 0 0
\(81\) −6148.74 + 2289.05i −0.937165 + 0.348887i
\(82\) 0 0
\(83\) −1712.04 301.879i −0.248518 0.0438204i 0.0480014 0.998847i \(-0.484715\pi\)
−0.296519 + 0.955027i \(0.595826\pi\)
\(84\) 0 0
\(85\) 3986.66 + 1451.03i 0.551787 + 0.200834i
\(86\) 0 0
\(87\) 2048.81 + 2432.63i 0.270685 + 0.321394i
\(88\) 0 0
\(89\) −1131.82 653.456i −0.142888 0.0824966i 0.426851 0.904322i \(-0.359623\pi\)
−0.569740 + 0.821825i \(0.692956\pi\)
\(90\) 0 0
\(91\) −100.024 173.246i −0.0120787 0.0209210i
\(92\) 0 0
\(93\) −3050.12 5260.71i −0.352656 0.608245i
\(94\) 0 0
\(95\) 5953.47 1049.76i 0.659664 0.116317i
\(96\) 0 0
\(97\) 10494.3 + 8805.79i 1.11535 + 0.935890i 0.998360 0.0572434i \(-0.0182311\pi\)
0.116990 + 0.993133i \(0.462676\pi\)
\(98\) 0 0
\(99\) 4847.09 + 2774.87i 0.494551 + 0.283122i
\(100\) 0 0
\(101\) −3163.83 8692.56i −0.310149 0.852129i −0.992626 0.121221i \(-0.961319\pi\)
0.682476 0.730908i \(-0.260903\pi\)
\(102\) 0 0
\(103\) 3788.01 3178.52i 0.357057 0.299606i −0.446560 0.894754i \(-0.647351\pi\)
0.803616 + 0.595148i \(0.202906\pi\)
\(104\) 0 0
\(105\) −440.543 1203.53i −0.0399586 0.109163i
\(106\) 0 0
\(107\) 15110.5i 1.31981i −0.751350 0.659904i \(-0.770597\pi\)
0.751350 0.659904i \(-0.229403\pi\)
\(108\) 0 0
\(109\) −15250.4 −1.28360 −0.641798 0.766873i \(-0.721811\pi\)
−0.641798 + 0.766873i \(0.721811\pi\)
\(110\) 0 0
\(111\) 2691.15 15427.3i 0.218420 1.25211i
\(112\) 0 0
\(113\) 1774.06 + 2114.24i 0.138935 + 0.165576i 0.831025 0.556235i \(-0.187754\pi\)
−0.692090 + 0.721811i \(0.743310\pi\)
\(114\) 0 0
\(115\) 13024.1 4740.40i 0.984811 0.358442i
\(116\) 0 0
\(117\) 1837.22 676.316i 0.134211 0.0494058i
\(118\) 0 0
\(119\) 1311.89 1563.45i 0.0926410 0.110405i
\(120\) 0 0
\(121\) 1716.77 + 9736.31i 0.117258 + 0.665003i
\(122\) 0 0
\(123\) −4991.11 2869.46i −0.329904 0.189666i
\(124\) 0 0
\(125\) 14214.4 8206.69i 0.909722 0.525228i
\(126\) 0 0
\(127\) 13768.7 23848.0i 0.853659 1.47858i −0.0242240 0.999707i \(-0.507711\pi\)
0.877883 0.478875i \(-0.158955\pi\)
\(128\) 0 0
\(129\) −2370.19 13299.7i −0.142431 0.799212i
\(130\) 0 0
\(131\) −8139.98 + 22364.4i −0.474330 + 1.30321i 0.439911 + 0.898041i \(0.355010\pi\)
−0.914241 + 0.405170i \(0.867212\pi\)
\(132\) 0 0
\(133\) 505.004 2864.02i 0.0285491 0.161910i
\(134\) 0 0
\(135\) 12339.8 2245.73i 0.677080 0.123223i
\(136\) 0 0
\(137\) −9749.91 1719.17i −0.519469 0.0915964i −0.0922346 0.995737i \(-0.529401\pi\)
−0.427234 + 0.904141i \(0.640512\pi\)
\(138\) 0 0
\(139\) −5846.34 2127.89i −0.302590 0.110134i 0.186263 0.982500i \(-0.440362\pi\)
−0.488853 + 0.872366i \(0.662585\pi\)
\(140\) 0 0
\(141\) −5812.11 + 16060.0i −0.292345 + 0.807806i
\(142\) 0 0
\(143\) −1443.29 833.286i −0.0705801 0.0407495i
\(144\) 0 0
\(145\) −3040.00 5265.43i −0.144590 0.250437i
\(146\) 0 0
\(147\) 20992.4 38.4030i 0.971466 0.00177717i
\(148\) 0 0
\(149\) 722.838 127.456i 0.0325588 0.00574100i −0.157345 0.987544i \(-0.550293\pi\)
0.189904 + 0.981803i \(0.439182\pi\)
\(150\) 0 0
\(151\) −12154.9 10199.2i −0.533086 0.447312i 0.336080 0.941834i \(-0.390899\pi\)
−0.869165 + 0.494521i \(0.835343\pi\)
\(152\) 0 0
\(153\) 12894.6 + 15253.5i 0.550838 + 0.651607i
\(154\) 0 0
\(155\) 3975.93 + 10923.8i 0.165491 + 0.454684i
\(156\) 0 0
\(157\) −26195.4 + 21980.5i −1.06274 + 0.891741i −0.994375 0.105919i \(-0.966222\pi\)
−0.0683613 + 0.997661i \(0.521777\pi\)
\(158\) 0 0
\(159\) −9976.64 + 11934.0i −0.394630 + 0.472053i
\(160\) 0 0
\(161\) 6667.59i 0.257227i
\(162\) 0 0
\(163\) −45253.0 −1.70322 −0.851612 0.524172i \(-0.824375\pi\)
−0.851612 + 0.524172i \(0.824375\pi\)
\(164\) 0 0
\(165\) −8191.62 6848.09i −0.300886 0.251537i
\(166\) 0 0
\(167\) 31781.8 + 37876.1i 1.13958 + 1.35810i 0.924353 + 0.381539i \(0.124606\pi\)
0.215230 + 0.976563i \(0.430950\pi\)
\(168\) 0 0
\(169\) 26289.6 9568.64i 0.920473 0.335025i
\(170\) 0 0
\(171\) 26779.9 + 9636.27i 0.915834 + 0.329547i
\(172\) 0 0
\(173\) −30120.6 + 35896.3i −1.00640 + 1.19938i −0.0265522 + 0.999647i \(0.508453\pi\)
−0.979850 + 0.199736i \(0.935992\pi\)
\(174\) 0 0
\(175\) −472.836 2681.58i −0.0154395 0.0875619i
\(176\) 0 0
\(177\) 11.3287 + 6192.69i 0.000361605 + 0.197666i
\(178\) 0 0
\(179\) −12684.8 + 7323.59i −0.395894 + 0.228569i −0.684711 0.728815i \(-0.740071\pi\)
0.288817 + 0.957384i \(0.406738\pi\)
\(180\) 0 0
\(181\) −3216.57 + 5571.27i −0.0981830 + 0.170058i −0.910933 0.412555i \(-0.864636\pi\)
0.812750 + 0.582613i \(0.197970\pi\)
\(182\) 0 0
\(183\) −8967.18 3245.22i −0.267765 0.0969041i
\(184\) 0 0
\(185\) −10239.1 + 28131.8i −0.299171 + 0.821965i
\(186\) 0 0
\(187\) 2952.50 16744.5i 0.0844320 0.478837i
\(188\) 0 0
\(189\) 1015.13 5947.77i 0.0284182 0.166506i
\(190\) 0 0
\(191\) −61078.9 10769.9i −1.67427 0.295218i −0.745671 0.666314i \(-0.767871\pi\)
−0.928594 + 0.371096i \(0.878982\pi\)
\(192\) 0 0
\(193\) −9223.47 3357.07i −0.247617 0.0901251i 0.215230 0.976563i \(-0.430950\pi\)
−0.462847 + 0.886438i \(0.653172\pi\)
\(194\) 0 0
\(195\) −3684.52 + 656.632i −0.0968972 + 0.0172684i
\(196\) 0 0
\(197\) 30005.4 + 17323.6i 0.773156 + 0.446382i 0.833999 0.551766i \(-0.186046\pi\)
−0.0608435 + 0.998147i \(0.519379\pi\)
\(198\) 0 0
\(199\) −35471.9 61439.1i −0.895733 1.55145i −0.832895 0.553431i \(-0.813318\pi\)
−0.0628372 0.998024i \(-0.520015\pi\)
\(200\) 0 0
\(201\) 26341.3 45817.8i 0.651995 1.13407i
\(202\) 0 0
\(203\) −2880.45 + 507.902i −0.0698987 + 0.0123250i
\(204\) 0 0
\(205\) 8430.94 + 7074.40i 0.200617 + 0.168338i
\(206\) 0 0
\(207\) 64301.5 + 11095.7i 1.50065 + 0.258948i
\(208\) 0 0
\(209\) −8286.42 22766.7i −0.189703 0.521205i
\(210\) 0 0
\(211\) −48385.5 + 40600.2i −1.08680 + 0.911934i −0.996468 0.0839772i \(-0.973238\pi\)
−0.0903334 + 0.995912i \(0.528793\pi\)
\(212\) 0 0
\(213\) −39821.6 6946.53i −0.877727 0.153112i
\(214\) 0 0
\(215\) 25825.2i 0.558685i
\(216\) 0 0
\(217\) 5592.33 0.118761
\(218\) 0 0
\(219\) 12266.3 4489.99i 0.255755 0.0936176i
\(220\) 0 0
\(221\) −3830.96 4565.55i −0.0784373 0.0934779i
\(222\) 0 0
\(223\) 14199.5 5168.20i 0.285538 0.103927i −0.195281 0.980747i \(-0.562562\pi\)
0.480819 + 0.876820i \(0.340340\pi\)
\(224\) 0 0
\(225\) 26647.7 97.4976i 0.526375 0.00192588i
\(226\) 0 0
\(227\) −40600.0 + 48385.2i −0.787905 + 0.938989i −0.999262 0.0384200i \(-0.987768\pi\)
0.211356 + 0.977409i \(0.432212\pi\)
\(228\) 0 0
\(229\) 11889.2 + 67427.2i 0.226716 + 1.28577i 0.859377 + 0.511343i \(0.170852\pi\)
−0.632660 + 0.774430i \(0.718037\pi\)
\(230\) 0 0
\(231\) −4443.52 + 2576.32i −0.0832729 + 0.0482809i
\(232\) 0 0
\(233\) 81880.6 47273.8i 1.50824 0.870780i 0.508282 0.861191i \(-0.330281\pi\)
0.999954 0.00958931i \(-0.00305242\pi\)
\(234\) 0 0
\(235\) 16325.0 28275.8i 0.295610 0.512011i
\(236\) 0 0
\(237\) 6895.96 5807.93i 0.122772 0.103401i
\(238\) 0 0
\(239\) −33160.0 + 91106.3i −0.580522 + 1.59497i 0.206769 + 0.978390i \(0.433705\pi\)
−0.787291 + 0.616581i \(0.788517\pi\)
\(240\) 0 0
\(241\) 11435.1 64851.9i 0.196883 1.11658i −0.712830 0.701337i \(-0.752587\pi\)
0.909712 0.415239i \(-0.136302\pi\)
\(242\) 0 0
\(243\) 55670.3 + 19687.6i 0.942782 + 0.333411i
\(244\) 0 0
\(245\) −39521.0 6968.62i −0.658409 0.116095i
\(246\) 0 0
\(247\) −7980.33 2904.60i −0.130806 0.0476094i
\(248\) 0 0
\(249\) 10079.0 + 11967.2i 0.162562 + 0.193016i
\(250\) 0 0
\(251\) −21936.7 12665.2i −0.348196 0.201031i 0.315694 0.948861i \(-0.397763\pi\)
−0.663891 + 0.747830i \(0.731096\pi\)
\(252\) 0 0
\(253\) −27773.4 48105.0i −0.433899 0.751534i
\(254\) 0 0
\(255\) −19151.8 33032.2i −0.294530 0.507992i
\(256\) 0 0
\(257\) 124203. 21900.3i 1.88046 0.331576i 0.888579 0.458724i \(-0.151693\pi\)
0.991884 + 0.127148i \(0.0405823\pi\)
\(258\) 0 0
\(259\) 11032.4 + 9257.31i 0.164464 + 0.138002i
\(260\) 0 0
\(261\) −104.728 28624.0i −0.00153738 0.420193i
\(262\) 0 0
\(263\) 895.943 + 2461.58i 0.0129530 + 0.0355880i 0.946001 0.324165i \(-0.105083\pi\)
−0.933048 + 0.359753i \(0.882861\pi\)
\(264\) 0 0
\(265\) 22778.9 19113.8i 0.324370 0.272179i
\(266\) 0 0
\(267\) 4043.12 + 11045.5i 0.0567146 + 0.154939i
\(268\) 0 0
\(269\) 101027.i 1.39616i −0.716021 0.698078i \(-0.754039\pi\)
0.716021 0.698078i \(-0.245961\pi\)
\(270\) 0 0
\(271\) −29168.0 −0.397162 −0.198581 0.980084i \(-0.563633\pi\)
−0.198581 + 0.980084i \(0.563633\pi\)
\(272\) 0 0
\(273\) −309.397 + 1773.65i −0.00415137 + 0.0237981i
\(274\) 0 0
\(275\) −14581.3 17377.4i −0.192811 0.229783i
\(276\) 0 0
\(277\) 79476.1 28926.9i 1.03580 0.377001i 0.232515 0.972593i \(-0.425305\pi\)
0.803287 + 0.595592i \(0.203082\pi\)
\(278\) 0 0
\(279\) −9306.30 + 53931.8i −0.119555 + 0.692845i
\(280\) 0 0
\(281\) 83010.4 98928.0i 1.05128 1.25287i 0.0847312 0.996404i \(-0.472997\pi\)
0.966553 0.256468i \(-0.0825587\pi\)
\(282\) 0 0
\(283\) −3459.59 19620.3i −0.0431968 0.244981i 0.955562 0.294790i \(-0.0952498\pi\)
−0.998759 + 0.0498092i \(0.984139\pi\)
\(284\) 0 0
\(285\) −47168.2 27117.7i −0.580711 0.333859i
\(286\) 0 0
\(287\) 4585.21 2647.27i 0.0556667 0.0321392i
\(288\) 0 0
\(289\) −11358.3 + 19673.1i −0.135993 + 0.235547i
\(290\) 0 0
\(291\) −21631.9 121382.i −0.255452 1.43340i
\(292\) 0 0
\(293\) −14958.8 + 41099.0i −0.174245 + 0.478735i −0.995817 0.0913700i \(-0.970875\pi\)
0.821572 + 0.570105i \(0.193098\pi\)
\(294\) 0 0
\(295\) 2055.72 11658.6i 0.0236222 0.133968i
\(296\) 0 0
\(297\) −17451.2 47140.1i −0.197839 0.534414i
\(298\) 0 0
\(299\) −19174.8 3381.03i −0.214481 0.0378187i
\(300\) 0 0
\(301\) 11674.4 + 4249.15i 0.128855 + 0.0468996i
\(302\) 0 0
\(303\) −28331.3 + 78285.0i −0.308590 + 0.852695i
\(304\) 0 0
\(305\) 15787.9 + 9115.17i 0.169717 + 0.0979863i
\(306\) 0 0
\(307\) 3347.53 + 5798.10i 0.0355180 + 0.0615189i 0.883238 0.468925i \(-0.155359\pi\)
−0.847720 + 0.530444i \(0.822025\pi\)
\(308\) 0 0
\(309\) −44504.0 + 81.4145i −0.466104 + 0.000852677i
\(310\) 0 0
\(311\) 26470.7 4667.50i 0.273681 0.0482574i −0.0351230 0.999383i \(-0.511182\pi\)
0.308804 + 0.951126i \(0.400071\pi\)
\(312\) 0 0
\(313\) 119813. + 100535.i 1.22296 + 1.02619i 0.998664 + 0.0516685i \(0.0164539\pi\)
0.224300 + 0.974520i \(0.427991\pi\)
\(314\) 0 0
\(315\) −3905.38 + 10853.3i −0.0393589 + 0.109381i
\(316\) 0 0
\(317\) −19067.4 52387.3i −0.189746 0.521323i 0.807943 0.589260i \(-0.200581\pi\)
−0.997690 + 0.0679366i \(0.978358\pi\)
\(318\) 0 0
\(319\) −18666.1 + 15662.7i −0.183431 + 0.153917i
\(320\) 0 0
\(321\) −87224.8 + 104337.i −0.846505 + 1.01258i
\(322\) 0 0
\(323\) 86642.5i 0.830473i
\(324\) 0 0
\(325\) −7951.52 −0.0752806
\(326\) 0 0
\(327\) 105304. + 88032.5i 0.984800 + 0.823280i
\(328\) 0 0
\(329\) −10096.2 12032.2i −0.0932752 0.111161i
\(330\) 0 0
\(331\) −37852.5 + 13777.2i −0.345493 + 0.125749i −0.508938 0.860803i \(-0.669962\pi\)
0.163445 + 0.986552i \(0.447739\pi\)
\(332\) 0 0
\(333\) −107636. + 90990.2i −0.970661 + 0.820552i
\(334\) 0 0
\(335\) −64942.1 + 77395.0i −0.578678 + 0.689641i
\(336\) 0 0
\(337\) 36939.7 + 209496.i 0.325262 + 1.84465i 0.507826 + 0.861460i \(0.330449\pi\)
−0.182563 + 0.983194i \(0.558439\pi\)
\(338\) 0 0
\(339\) −45.4407 24839.5i −0.000395408 0.216144i
\(340\) 0 0
\(341\) 40347.2 23294.5i 0.346980 0.200329i
\(342\) 0 0
\(343\) −19589.1 + 33929.3i −0.166504 + 0.288394i
\(344\) 0 0
\(345\) −117295. 42449.1i −0.985465 0.356640i
\(346\) 0 0
\(347\) −12450.0 + 34206.2i −0.103398 + 0.284083i −0.980594 0.196049i \(-0.937189\pi\)
0.877196 + 0.480132i \(0.159411\pi\)
\(348\) 0 0
\(349\) −29968.9 + 169962.i −0.246048 + 1.39541i 0.571997 + 0.820256i \(0.306169\pi\)
−0.818045 + 0.575154i \(0.804942\pi\)
\(350\) 0 0
\(351\) −16590.0 5935.35i −0.134658 0.0481761i
\(352\) 0 0
\(353\) 10299.5 + 1816.08i 0.0826543 + 0.0145742i 0.214822 0.976653i \(-0.431083\pi\)
−0.132168 + 0.991227i \(0.542194\pi\)
\(354\) 0 0
\(355\) 72615.1 + 26429.7i 0.576196 + 0.209718i
\(356\) 0 0
\(357\) −18083.5 + 3222.73i −0.141888 + 0.0252864i
\(358\) 0 0
\(359\) −65698.6 37931.1i −0.509762 0.294311i 0.222974 0.974824i \(-0.428423\pi\)
−0.732736 + 0.680513i \(0.761757\pi\)
\(360\) 0 0
\(361\) 3430.55 + 5941.89i 0.0263238 + 0.0455942i
\(362\) 0 0
\(363\) 44348.2 77139.0i 0.336560 0.585410i
\(364\) 0 0
\(365\) −24591.3 + 4336.11i −0.184585 + 0.0325473i
\(366\) 0 0
\(367\) 22828.4 + 19155.3i 0.169490 + 0.142219i 0.723587 0.690233i \(-0.242492\pi\)
−0.554097 + 0.832452i \(0.686936\pi\)
\(368\) 0 0
\(369\) 17899.6 + 48624.6i 0.131459 + 0.357111i
\(370\) 0 0
\(371\) −4892.56 13442.2i −0.0355458 0.0976614i
\(372\) 0 0
\(373\) 5382.98 4516.86i 0.0386906 0.0324653i −0.623237 0.782033i \(-0.714183\pi\)
0.661928 + 0.749568i \(0.269738\pi\)
\(374\) 0 0
\(375\) −145523. 25385.2i −1.03483 0.180517i
\(376\) 0 0
\(377\) 8541.21i 0.0600948i
\(378\) 0 0
\(379\) 145934. 1.01596 0.507980 0.861369i \(-0.330392\pi\)
0.507980 + 0.861369i \(0.330392\pi\)
\(380\) 0 0
\(381\) −232734. + 85190.8i −1.60328 + 0.586871i
\(382\) 0 0
\(383\) −96300.0 114766.i −0.656491 0.782375i 0.330387 0.943846i \(-0.392821\pi\)
−0.986878 + 0.161470i \(0.948376\pi\)
\(384\) 0 0
\(385\) 9226.89 3358.31i 0.0622492 0.0226569i
\(386\) 0 0
\(387\) −60405.9 + 105516.i −0.403327 + 0.704523i
\(388\) 0 0
\(389\) 63115.2 75217.7i 0.417095 0.497074i −0.516058 0.856553i \(-0.672601\pi\)
0.933153 + 0.359479i \(0.117046\pi\)
\(390\) 0 0
\(391\) −34494.1 195626.i −0.225627 1.27960i
\(392\) 0 0
\(393\) 185304. 107438.i 1.19978 0.695620i
\(394\) 0 0
\(395\) −14926.3 + 8617.71i −0.0956662 + 0.0552329i
\(396\) 0 0
\(397\) −89376.0 + 154804.i −0.567074 + 0.982201i 0.429779 + 0.902934i \(0.358591\pi\)
−0.996853 + 0.0792673i \(0.974742\pi\)
\(398\) 0 0
\(399\) −20019.5 + 16860.9i −0.125750 + 0.105909i
\(400\) 0 0
\(401\) −15740.3 + 43246.2i −0.0978871 + 0.268943i −0.978965 0.204029i \(-0.934596\pi\)
0.881078 + 0.472971i \(0.156819\pi\)
\(402\) 0 0
\(403\) 2835.78 16082.5i 0.0174608 0.0990249i
\(404\) 0 0
\(405\) −98169.3 55724.3i −0.598502 0.339730i
\(406\) 0 0
\(407\) 118157. + 20834.2i 0.713297 + 0.125773i
\(408\) 0 0
\(409\) 99480.0 + 36207.8i 0.594688 + 0.216449i 0.621790 0.783184i \(-0.286406\pi\)
−0.0271021 + 0.999633i \(0.508628\pi\)
\(410\) 0 0
\(411\) 57399.0 + 68151.9i 0.339798 + 0.403454i
\(412\) 0 0
\(413\) −4932.08 2847.54i −0.0289155 0.0166943i
\(414\) 0 0
\(415\) −14955.1 25902.9i −0.0868345 0.150402i
\(416\) 0 0
\(417\) 28085.6 + 48440.9i 0.161515 + 0.278573i
\(418\) 0 0
\(419\) 342282. 60353.5i 1.94965 0.343775i 0.950159 0.311767i \(-0.100921\pi\)
0.999488 0.0320086i \(-0.0101904\pi\)
\(420\) 0 0
\(421\) −124187. 104205.i −0.700668 0.587930i 0.221296 0.975207i \(-0.428971\pi\)
−0.921964 + 0.387277i \(0.873416\pi\)
\(422\) 0 0
\(423\) 132838. 77343.6i 0.742408 0.432259i
\(424\) 0 0
\(425\) −27745.8 76231.0i −0.153610 0.422040i
\(426\) 0 0
\(427\) 6718.23 5637.27i 0.0368468 0.0309181i
\(428\) 0 0
\(429\) 5155.78 + 14085.2i 0.0280143 + 0.0765328i
\(430\) 0 0
\(431\) 68099.8i 0.366599i 0.983057 + 0.183300i \(0.0586778\pi\)
−0.983057 + 0.183300i \(0.941322\pi\)
\(432\) 0 0
\(433\) 115590. 0.616515 0.308257 0.951303i \(-0.400254\pi\)
0.308257 + 0.951303i \(0.400254\pi\)
\(434\) 0 0
\(435\) −9403.42 + 53905.9i −0.0496944 + 0.284877i
\(436\) 0 0
\(437\) −181944. 216832.i −0.952741 1.13543i
\(438\) 0 0
\(439\) −419.769 + 152.783i −0.00217812 + 0.000792770i −0.343109 0.939296i \(-0.611480\pi\)
0.340931 + 0.940088i \(0.389258\pi\)
\(440\) 0 0
\(441\) −145174. 120913.i −0.746467 0.621721i
\(442\) 0 0
\(443\) 20484.1 24412.0i 0.104378 0.124393i −0.711326 0.702862i \(-0.751905\pi\)
0.815704 + 0.578469i \(0.196350\pi\)
\(444\) 0 0
\(445\) −3904.56 22143.9i −0.0197175 0.111824i
\(446\) 0 0
\(447\) −5726.91 3292.48i −0.0286619 0.0164781i
\(448\) 0 0
\(449\) −6386.03 + 3686.98i −0.0316766 + 0.0182885i −0.515755 0.856736i \(-0.672488\pi\)
0.484078 + 0.875025i \(0.339155\pi\)
\(450\) 0 0
\(451\) 22054.1 38198.8i 0.108427 0.187800i
\(452\) 0 0
\(453\) 25054.8 + 140589.i 0.122094 + 0.685100i
\(454\) 0 0
\(455\) 1177.18 3234.26i 0.00568615 0.0156226i
\(456\) 0 0
\(457\) 16663.8 94505.3i 0.0797889 0.452505i −0.918571 0.395256i \(-0.870656\pi\)
0.998360 0.0572493i \(-0.0182330\pi\)
\(458\) 0 0
\(459\) −986.543 179758.i −0.00468264 0.853225i
\(460\) 0 0
\(461\) 7688.93 + 1355.77i 0.0361796 + 0.00637944i 0.191709 0.981452i \(-0.438597\pi\)
−0.155529 + 0.987831i \(0.549708\pi\)
\(462\) 0 0
\(463\) −140479. 51130.3i −0.655315 0.238515i −0.00710280 0.999975i \(-0.502261\pi\)
−0.648212 + 0.761460i \(0.724483\pi\)
\(464\) 0 0
\(465\) 35603.4 98379.2i 0.164659 0.454986i
\(466\) 0 0
\(467\) 174259. + 100609.i 0.799029 + 0.461319i 0.843131 0.537708i \(-0.180710\pi\)
−0.0441027 + 0.999027i \(0.514043\pi\)
\(468\) 0 0
\(469\) 24301.6 + 42091.6i 0.110481 + 0.191359i
\(470\) 0 0
\(471\) 307760. 563.008i 1.38730 0.00253789i
\(472\) 0 0
\(473\) 101928. 17972.6i 0.455585 0.0803319i
\(474\) 0 0
\(475\) −88551.3 74303.4i −0.392471 0.329322i
\(476\) 0 0
\(477\) 137777. 24813.9i 0.605535 0.109058i
\(478\) 0 0
\(479\) 78432.5 + 215492.i 0.341842 + 0.939203i 0.984860 + 0.173352i \(0.0554597\pi\)
−0.643018 + 0.765851i \(0.722318\pi\)
\(480\) 0 0
\(481\) 32216.7 27033.0i 0.139249 0.116844i
\(482\) 0 0
\(483\) −38488.5 + 46039.5i −0.164982 + 0.197350i
\(484\) 0 0
\(485\) 235698.i 1.00201i
\(486\) 0 0
\(487\) 225927. 0.952600 0.476300 0.879283i \(-0.341978\pi\)
0.476300 + 0.879283i \(0.341978\pi\)
\(488\) 0 0
\(489\) 312470. + 261221.i 1.30675 + 1.09242i
\(490\) 0 0
\(491\) −259155. 308848.i −1.07497 1.28110i −0.957628 0.288007i \(-0.907008\pi\)
−0.117341 0.993092i \(-0.537437\pi\)
\(492\) 0 0
\(493\) −81884.4 + 29803.5i −0.336905 + 0.122623i
\(494\) 0 0
\(495\) 17032.5 + 94571.7i 0.0695135 + 0.385967i
\(496\) 0 0
\(497\) 23895.4 28477.5i 0.0967391 0.115289i
\(498\) 0 0
\(499\) −52018.8 295013.i −0.208910 1.18479i −0.891167 0.453675i \(-0.850113\pi\)
0.682257 0.731112i \(-0.260999\pi\)
\(500\) 0 0
\(501\) −814.058 444993.i −0.00324325 1.77287i
\(502\) 0 0
\(503\) −275570. + 159100.i −1.08917 + 0.628833i −0.933356 0.358953i \(-0.883134\pi\)
−0.155815 + 0.987786i \(0.549800\pi\)
\(504\) 0 0
\(505\) 79577.0 137831.i 0.312036 0.540463i
\(506\) 0 0
\(507\) −236764. 85684.8i −0.921084 0.333340i
\(508\) 0 0
\(509\) −149917. + 411893.i −0.578648 + 1.58982i 0.211814 + 0.977310i \(0.432063\pi\)
−0.790461 + 0.612512i \(0.790159\pi\)
\(510\) 0 0
\(511\) −2085.96 + 11830.1i −0.00798850 + 0.0453050i
\(512\) 0 0
\(513\) −129289. 221124.i −0.491279 0.840237i
\(514\) 0 0
\(515\) 83784.7 + 14773.5i 0.315901 + 0.0557018i
\(516\) 0 0
\(517\) −122961. 44754.1i −0.460029 0.167437i
\(518\) 0 0
\(519\) 415192. 73993.0i 1.54140 0.274698i
\(520\) 0 0
\(521\) −76314.7 44060.3i −0.281146 0.162320i 0.352796 0.935700i \(-0.385231\pi\)
−0.633942 + 0.773380i \(0.718564\pi\)
\(522\) 0 0
\(523\) 205191. + 355401.i 0.750162 + 1.29932i 0.947744 + 0.319033i \(0.103358\pi\)
−0.197581 + 0.980286i \(0.563309\pi\)
\(524\) 0 0
\(525\) −12214.4 + 21245.7i −0.0443154 + 0.0770819i
\(526\) 0 0
\(527\) 164078. 28931.4i 0.590785 0.104171i
\(528\) 0 0
\(529\) −282757. 237262.i −1.01042 0.847845i
\(530\) 0 0
\(531\) 35668.9 42825.7i 0.126503 0.151885i
\(532\) 0 0
\(533\) −5287.98 14528.6i −0.0186138 0.0511411i
\(534\) 0 0
\(535\) 199154. 167110.i 0.695794 0.583840i
\(536\) 0 0
\(537\) 129864. + 22653.6i 0.450338 + 0.0785576i
\(538\) 0 0
\(539\) 160832.i 0.553599i
\(540\) 0 0
\(541\) −492919. −1.68415 −0.842075 0.539361i \(-0.818666\pi\)
−0.842075 + 0.539361i \(0.818666\pi\)
\(542\) 0 0
\(543\) 54370.3 19901.9i 0.184400 0.0674986i
\(544\) 0 0
\(545\) −168657. 200998.i −0.567821 0.676703i
\(546\) 0 0
\(547\) −371903. + 135361.i −1.24295 + 0.452398i −0.878014 0.478634i \(-0.841132\pi\)
−0.364938 + 0.931032i \(0.618910\pi\)
\(548\) 0 0
\(549\) 43185.2 + 74170.9i 0.143282 + 0.246087i
\(550\) 0 0
\(551\) −79813.8 + 95118.4i −0.262890 + 0.313301i
\(552\) 0 0
\(553\) 1439.79 + 8165.44i 0.00470813 + 0.0267011i
\(554\) 0 0
\(555\) 233091. 135144.i 0.756726 0.438744i
\(556\) 0 0
\(557\) −359117. + 207336.i −1.15751 + 0.668291i −0.950707 0.310091i \(-0.899640\pi\)
−0.206806 + 0.978382i \(0.566307\pi\)
\(558\) 0 0
\(559\) 18139.7 31418.9i 0.0580505 0.100546i
\(560\) 0 0
\(561\) −117044. + 98576.9i −0.371897 + 0.313220i
\(562\) 0 0
\(563\) −16738.4 + 45988.4i −0.0528077 + 0.145088i −0.963292 0.268455i \(-0.913487\pi\)
0.910484 + 0.413543i \(0.135709\pi\)
\(564\) 0 0
\(565\) −8245.69 + 46763.6i −0.0258303 + 0.146491i
\(566\) 0 0
\(567\) −41342.8 + 35209.4i −0.128598 + 0.109520i
\(568\) 0 0
\(569\) 415714. + 73301.6i 1.28401 + 0.226406i 0.773684 0.633572i \(-0.218412\pi\)
0.510331 + 0.859978i \(0.329523\pi\)
\(570\) 0 0
\(571\) −238847. 86933.2i −0.732567 0.266633i −0.0513161 0.998682i \(-0.516342\pi\)
−0.681251 + 0.732050i \(0.738564\pi\)
\(572\) 0 0
\(573\) 359579. + 426941.i 1.09518 + 1.30035i
\(574\) 0 0
\(575\) −229518. 132512.i −0.694193 0.400793i
\(576\) 0 0
\(577\) 72698.7 + 125918.i 0.218361 + 0.378212i 0.954307 0.298828i \(-0.0965957\pi\)
−0.735946 + 0.677040i \(0.763262\pi\)
\(578\) 0 0
\(579\) 44309.2 + 76422.6i 0.132171 + 0.227963i
\(580\) 0 0
\(581\) −14170.2 + 2498.59i −0.0419782 + 0.00740189i
\(582\) 0 0
\(583\) −91291.2 76602.4i −0.268591 0.225375i
\(584\) 0 0
\(585\) 29231.9 + 16734.7i 0.0854171 + 0.0488998i
\(586\) 0 0
\(587\) 201839. + 554549.i 0.585773 + 1.60940i 0.778151 + 0.628077i \(0.216158\pi\)
−0.192378 + 0.981321i \(0.561620\pi\)
\(588\) 0 0
\(589\) 181865. 152602.i 0.524225 0.439877i
\(590\) 0 0
\(591\) −107186. 292824.i −0.306877 0.838363i
\(592\) 0 0
\(593\) 632321.i 1.79816i 0.437786 + 0.899079i \(0.355763\pi\)
−0.437786 + 0.899079i \(0.644237\pi\)
\(594\) 0 0
\(595\) 35114.4 0.0991863
\(596\) 0 0
\(597\) −109723. + 628996.i −0.307857 + 1.76481i
\(598\) 0 0
\(599\) −258279. 307805.i −0.719840 0.857872i 0.274775 0.961509i \(-0.411397\pi\)
−0.994615 + 0.103636i \(0.966952\pi\)
\(600\) 0 0
\(601\) −338819. + 123320.i −0.938034 + 0.341417i −0.765389 0.643568i \(-0.777454\pi\)
−0.172645 + 0.984984i \(0.555231\pi\)
\(602\) 0 0
\(603\) −446367. + 164316.i −1.22760 + 0.451904i
\(604\) 0 0
\(605\) −109337. + 130302.i −0.298714 + 0.355993i
\(606\) 0 0
\(607\) −63002.8 357306.i −0.170995 0.969758i −0.942666 0.333737i \(-0.891690\pi\)
0.771672 0.636021i \(-0.219421\pi\)
\(608\) 0 0
\(609\) 22821.3 + 13120.3i 0.0615327 + 0.0353760i
\(610\) 0 0
\(611\) −39722.0 + 22933.5i −0.106402 + 0.0614311i
\(612\) 0 0
\(613\) 51114.3 88532.6i 0.136026 0.235604i −0.789963 0.613155i \(-0.789900\pi\)
0.925989 + 0.377551i \(0.123234\pi\)
\(614\) 0 0
\(615\) −17378.7 97515.9i −0.0459480 0.257825i
\(616\) 0 0
\(617\) −174957. + 480690.i −0.459580 + 1.26268i 0.466220 + 0.884669i \(0.345616\pi\)
−0.925799 + 0.378015i \(0.876607\pi\)
\(618\) 0 0
\(619\) −92539.8 + 524819.i −0.241517 + 1.36971i 0.586929 + 0.809639i \(0.300337\pi\)
−0.828445 + 0.560070i \(0.810774\pi\)
\(620\) 0 0
\(621\) −379950. 447793.i −0.985244 1.16117i
\(622\) 0 0
\(623\) −10652.7 1878.36i −0.0274463 0.00483952i
\(624\) 0 0
\(625\) 72146.1 + 26259.0i 0.184694 + 0.0672231i
\(626\) 0 0
\(627\) −74202.8 + 205037.i −0.188749 + 0.521551i
\(628\) 0 0
\(629\) 371581. + 214533.i 0.939188 + 0.542241i
\(630\) 0 0
\(631\) 54673.1 + 94696.5i 0.137314 + 0.237835i 0.926479 0.376346i \(-0.122820\pi\)
−0.789165 + 0.614181i \(0.789486\pi\)
\(632\) 0 0
\(633\) 568464. 1039.93i 1.41872 0.00259536i
\(634\) 0 0
\(635\) 466583. 82271.2i 1.15713 0.204033i
\(636\) 0 0
\(637\) 43186.3 + 36237.6i 0.106431 + 0.0893061i
\(638\) 0 0
\(639\) 234868. + 277834.i 0.575205 + 0.680431i
\(640\) 0 0
\(641\) −56474.2 155162.i −0.137447 0.377631i 0.851804 0.523860i \(-0.175509\pi\)
−0.989251 + 0.146229i \(0.953286\pi\)
\(642\) 0 0
\(643\) 174635. 146536.i 0.422386 0.354424i −0.406684 0.913569i \(-0.633315\pi\)
0.829070 + 0.559145i \(0.188871\pi\)
\(644\) 0 0
\(645\) 149075. 178322.i 0.358332 0.428634i
\(646\) 0 0
\(647\) 167904.i 0.401101i −0.979683 0.200550i \(-0.935727\pi\)
0.979683 0.200550i \(-0.0642730\pi\)
\(648\) 0 0
\(649\) −47444.9 −0.112642
\(650\) 0 0
\(651\) −38614.9 32281.6i −0.0911156 0.0761715i
\(652\) 0 0
\(653\) −381636. 454816.i −0.894999 1.06662i −0.997414 0.0718765i \(-0.977101\pi\)
0.102415 0.994742i \(-0.467343\pi\)
\(654\) 0 0
\(655\) −384780. + 140049.i −0.896872 + 0.326435i
\(656\) 0 0
\(657\) −110617. 39803.5i −0.256265 0.0922125i
\(658\) 0 0
\(659\) 346989. 413526.i 0.798997 0.952207i −0.200626 0.979668i \(-0.564298\pi\)
0.999623 + 0.0274604i \(0.00874203\pi\)
\(660\) 0 0
\(661\) −63023.7 357425.i −0.144245 0.818054i −0.967970 0.251065i \(-0.919219\pi\)
0.823725 0.566989i \(-0.191892\pi\)
\(662\) 0 0
\(663\) 98.1259 + 53639.1i 0.000223232 + 0.122027i
\(664\) 0 0
\(665\) 43332.2 25017.9i 0.0979869 0.0565728i
\(666\) 0 0
\(667\) −142339. + 246539.i −0.319943 + 0.554158i
\(668\) 0 0
\(669\) −127880. 46279.9i −0.285727 0.103405i
\(670\) 0 0
\(671\) 24988.7 68655.8i 0.0555006 0.152487i
\(672\) 0 0
\(673\) 139117. 788974.i 0.307151 1.74194i −0.306054 0.952014i \(-0.599009\pi\)
0.613205 0.789924i \(-0.289880\pi\)
\(674\) 0 0
\(675\) −184565. 153150.i −0.405080 0.336132i
\(676\) 0 0
\(677\) 318018. + 56075.2i 0.693865 + 0.122347i 0.509448 0.860501i \(-0.329849\pi\)
0.184416 + 0.982848i \(0.440961\pi\)
\(678\) 0 0
\(679\) 106549. + 38780.6i 0.231105 + 0.0841152i
\(680\) 0 0
\(681\) 559643. 99736.2i 1.20675 0.215060i
\(682\) 0 0
\(683\) −638191. 368460.i −1.36807 0.789858i −0.377392 0.926054i \(-0.623179\pi\)
−0.990682 + 0.136196i \(0.956512\pi\)
\(684\) 0 0
\(685\) −85167.7 147515.i −0.181507 0.314380i
\(686\) 0 0
\(687\) 307126. 534213.i 0.650734 1.13188i
\(688\) 0 0
\(689\) −41138.3 + 7253.79i −0.0866578 + 0.0152801i
\(690\) 0 0
\(691\) 320796. + 269180.i 0.671852 + 0.563751i 0.913613 0.406585i \(-0.133281\pi\)
−0.241761 + 0.970336i \(0.577725\pi\)
\(692\) 0 0
\(693\) 45554.1 + 7860.68i 0.0948552 + 0.0163679i
\(694\) 0 0
\(695\) −36610.5 100587.i −0.0757942 0.208243i
\(696\) 0 0
\(697\) 120834. 101392.i 0.248727 0.208707i
\(698\) 0 0
\(699\) −838270. 146229.i −1.71565 0.299281i
\(700\) 0 0
\(701\) 396026.i 0.805911i −0.915220 0.402956i \(-0.867983\pi\)
0.915220 0.402956i \(-0.132017\pi\)
\(702\) 0 0
\(703\) 611390. 1.23711
\(704\) 0 0
\(705\) −275945. + 101008.i −0.555194 + 0.203225i
\(706\) 0 0
\(707\) −49214.3 58651.3i −0.0984584 0.117338i
\(708\) 0 0
\(709\) 471516. 171618.i 0.938002 0.341405i 0.172625 0.984988i \(-0.444775\pi\)
0.765376 + 0.643583i \(0.222553\pi\)
\(710\) 0 0
\(711\) −81142.5 + 296.881i −0.160513 + 0.000587277i
\(712\) 0 0
\(713\) 349869. 416958.i 0.688219 0.820188i
\(714\) 0 0
\(715\) −4979.09 28237.8i −0.00973953 0.0552356i
\(716\) 0 0
\(717\) 754877. 437672.i 1.46838 0.851354i
\(718\) 0 0
\(719\) −397408. + 229444.i −0.768739 + 0.443832i −0.832425 0.554138i \(-0.813048\pi\)
0.0636853 + 0.997970i \(0.479715\pi\)
\(720\) 0 0
\(721\) 20464.0 35444.6i 0.0393658 0.0681836i
\(722\) 0 0
\(723\) −453314. + 381791.i −0.867207 + 0.730381i
\(724\) 0 0
\(725\) −39762.8 + 109247.i −0.0756487 + 0.207843i
\(726\) 0 0
\(727\) −103524. + 587115.i −0.195872 + 1.11085i 0.715299 + 0.698819i \(0.246291\pi\)
−0.911171 + 0.412028i \(0.864821\pi\)
\(728\) 0 0
\(729\) −270756. 457297.i −0.509475 0.860485i
\(730\) 0 0
\(731\) 364508. + 64272.6i 0.682139 + 0.120279i
\(732\) 0 0
\(733\) 321783. + 117119.i 0.598901 + 0.217982i 0.623640 0.781712i \(-0.285653\pi\)
−0.0247390 + 0.999694i \(0.507875\pi\)
\(734\) 0 0
\(735\) 232665. + 276252.i 0.430682 + 0.511364i
\(736\) 0 0
\(737\) 350660. + 202453.i 0.645581 + 0.372726i
\(738\) 0 0
\(739\) 467974. + 810555.i 0.856905 + 1.48420i 0.874866 + 0.484365i \(0.160949\pi\)
−0.0179608 + 0.999839i \(0.505717\pi\)
\(740\) 0 0
\(741\) 38337.2 + 66122.3i 0.0698207 + 0.120424i
\(742\) 0 0
\(743\) 630777. 111223.i 1.14261 0.201473i 0.429864 0.902894i \(-0.358562\pi\)
0.712747 + 0.701421i \(0.247451\pi\)
\(744\) 0 0
\(745\) 9673.85 + 8117.32i 0.0174296 + 0.0146252i
\(746\) 0 0
\(747\) −515.203 140814.i −0.000923288 0.252350i
\(748\) 0 0
\(749\) −42775.2 117524.i −0.0762480 0.209490i
\(750\) 0 0
\(751\) −280016. + 234962.i −0.496482 + 0.416598i −0.856342 0.516408i \(-0.827269\pi\)
0.359861 + 0.933006i \(0.382824\pi\)
\(752\) 0 0
\(753\) 78363.2 + 214082.i 0.138204 + 0.377563i
\(754\) 0 0
\(755\) 272994.i 0.478915i
\(756\) 0 0
\(757\) −24716.3 −0.0431312 −0.0215656 0.999767i \(-0.506865\pi\)
−0.0215656 + 0.999767i \(0.506865\pi\)
\(758\) 0 0
\(759\) −85909.7 + 492485.i −0.149128 + 0.854888i
\(760\) 0 0
\(761\) −492900. 587416.i −0.851118 1.01432i −0.999677 0.0254195i \(-0.991908\pi\)
0.148559 0.988904i \(-0.452537\pi\)
\(762\) 0 0
\(763\) −118612. + 43171.3i −0.203742 + 0.0741560i
\(764\) 0 0
\(765\) −58434.5 + 338639.i −0.0998497 + 0.578648i
\(766\) 0 0
\(767\) −10690.0 + 12739.8i −0.0181713 + 0.0216557i
\(768\) 0 0
\(769\) 116072. + 658279.i 0.196280 + 1.11316i 0.910584 + 0.413324i \(0.135632\pi\)
−0.714304 + 0.699836i \(0.753257\pi\)
\(770\) 0 0
\(771\) −984034. 565735.i −1.65539 0.951709i
\(772\) 0 0
\(773\) 542163. 313018.i 0.907342 0.523854i 0.0277668 0.999614i \(-0.491160\pi\)
0.879575 + 0.475760i \(0.157827\pi\)
\(774\) 0 0
\(775\) 111142. 192504.i 0.185044 0.320506i
\(776\) 0 0
\(777\) −22741.1 127606.i −0.0376678 0.211363i
\(778\) 0 0
\(779\) 76874.3 211210.i 0.126679 0.348049i
\(780\) 0 0