Properties

Label 108.5.k.a.65.11
Level 108
Weight 5
Character 108.65
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 65.11
Character \(\chi\) \(=\) 108.65
Dual form 108.5.k.a.5.11

$q$-expansion

\(f(q)\) \(=\) \(q+(8.08622 - 3.95134i) q^{3} +(-10.7879 + 29.6395i) q^{5} +(15.2291 - 86.3688i) q^{7} +(49.7738 - 63.9028i) q^{9} +O(q^{10})\) \(q+(8.08622 - 3.95134i) q^{3} +(-10.7879 + 29.6395i) q^{5} +(15.2291 - 86.3688i) q^{7} +(49.7738 - 63.9028i) q^{9} +(46.1813 + 126.882i) q^{11} +(215.694 - 180.988i) q^{13} +(29.8824 + 282.298i) q^{15} +(300.316 - 173.387i) q^{17} +(-113.736 + 196.996i) q^{19} +(-218.126 - 758.572i) q^{21} +(-187.562 + 33.0723i) q^{23} +(-283.341 - 237.752i) q^{25} +(149.980 - 713.405i) q^{27} +(429.966 - 512.413i) q^{29} +(-35.8536 - 203.336i) q^{31} +(874.786 + 843.518i) q^{33} +(2395.63 + 1383.12i) q^{35} +(987.943 + 1711.17i) q^{37} +(1029.00 - 2315.79i) q^{39} +(-1257.73 - 1498.90i) q^{41} +(-793.064 + 288.652i) q^{43} +(1357.09 + 2164.64i) q^{45} +(-1802.00 - 317.741i) q^{47} +(-4971.44 - 1809.45i) q^{49} +(1743.31 - 2588.70i) q^{51} +2964.60i q^{53} -4258.91 q^{55} +(-141.294 + 2042.36i) q^{57} +(-1888.83 + 5189.52i) q^{59} +(680.783 - 3860.91i) q^{61} +(-4761.19 - 5272.09i) q^{63} +(3037.52 + 8345.52i) q^{65} +(-3957.28 + 3320.55i) q^{67} +(-1385.99 + 1008.55i) q^{69} +(-1162.57 + 671.209i) q^{71} +(-1153.91 + 1998.62i) q^{73} +(-3230.60 - 802.933i) q^{75} +(11662.0 - 2056.32i) q^{77} +(6080.80 + 5102.39i) q^{79} +(-1606.13 - 6361.37i) q^{81} +(-879.339 + 1047.96i) q^{83} +(1899.34 + 10771.7i) q^{85} +(1452.08 - 5842.43i) q^{87} +(-2800.19 - 1616.69i) q^{89} +(-12346.9 - 21385.5i) q^{91} +(-1093.37 - 1502.55i) q^{93} +(-4611.89 - 5496.24i) q^{95} +(-10325.5 + 3758.17i) q^{97} +(10406.7 + 3364.29i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q + 9q^{5} - 102q^{9} + O(q^{10}) \) \( 72q + 9q^{5} - 102q^{9} + 18q^{11} - 225q^{15} - 282q^{21} - 1278q^{23} + 441q^{25} + 54q^{27} + 1854q^{29} - 1665q^{31} - 45q^{33} - 2673q^{35} + 6951q^{39} - 5472q^{41} + 1260q^{43} + 5553q^{45} + 5103q^{47} - 5904q^{49} + 1899q^{51} + 1107q^{57} - 10944q^{59} + 8352q^{61} - 11985q^{63} + 8757q^{65} + 378q^{67} + 5607q^{69} - 19764q^{71} + 6111q^{73} - 3453q^{75} - 5679q^{77} - 5652q^{79} - 20466q^{81} - 20061q^{83} + 26100q^{85} + 40545q^{87} + 15633q^{89} - 6039q^{91} + 40179q^{93} + 48024q^{95} - 37530q^{97} + 12177q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 8.08622 3.95134i 0.898469 0.439038i
\(4\) 0 0
\(5\) −10.7879 + 29.6395i −0.431515 + 1.18558i 0.513367 + 0.858169i \(0.328398\pi\)
−0.944883 + 0.327409i \(0.893824\pi\)
\(6\) 0 0
\(7\) 15.2291 86.3688i 0.310799 1.76263i −0.284068 0.958804i \(-0.591684\pi\)
0.594867 0.803824i \(-0.297205\pi\)
\(8\) 0 0
\(9\) 49.7738 63.9028i 0.614492 0.788923i
\(10\) 0 0
\(11\) 46.1813 + 126.882i 0.381664 + 1.04861i 0.970656 + 0.240473i \(0.0773027\pi\)
−0.588992 + 0.808139i \(0.700475\pi\)
\(12\) 0 0
\(13\) 215.694 180.988i 1.27629 1.07094i 0.282549 0.959253i \(-0.408820\pi\)
0.993744 0.111684i \(-0.0356245\pi\)
\(14\) 0 0
\(15\) 29.8824 + 282.298i 0.132811 + 1.25466i
\(16\) 0 0
\(17\) 300.316 173.387i 1.03915 0.599956i 0.119561 0.992827i \(-0.461851\pi\)
0.919594 + 0.392871i \(0.128518\pi\)
\(18\) 0 0
\(19\) −113.736 + 196.996i −0.315058 + 0.545696i −0.979450 0.201688i \(-0.935357\pi\)
0.664392 + 0.747384i \(0.268690\pi\)
\(20\) 0 0
\(21\) −218.126 758.572i −0.494617 1.72012i
\(22\) 0 0
\(23\) −187.562 + 33.0723i −0.354560 + 0.0625185i −0.348091 0.937461i \(-0.613170\pi\)
−0.00646861 + 0.999979i \(0.502059\pi\)
\(24\) 0 0
\(25\) −283.341 237.752i −0.453346 0.380403i
\(26\) 0 0
\(27\) 149.980 713.405i 0.205734 0.978608i
\(28\) 0 0
\(29\) 429.966 512.413i 0.511256 0.609291i −0.447234 0.894417i \(-0.647591\pi\)
0.958490 + 0.285126i \(0.0920355\pi\)
\(30\) 0 0
\(31\) −35.8536 203.336i −0.0373087 0.211588i 0.960454 0.278437i \(-0.0898164\pi\)
−0.997763 + 0.0668493i \(0.978705\pi\)
\(32\) 0 0
\(33\) 874.786 + 843.518i 0.803293 + 0.774580i
\(34\) 0 0
\(35\) 2395.63 + 1383.12i 1.95562 + 1.12908i
\(36\) 0 0
\(37\) 987.943 + 1711.17i 0.721653 + 1.24994i 0.960337 + 0.278842i \(0.0899507\pi\)
−0.238684 + 0.971097i \(0.576716\pi\)
\(38\) 0 0
\(39\) 1029.00 2315.79i 0.676528 1.52254i
\(40\) 0 0
\(41\) −1257.73 1498.90i −0.748203 0.891673i 0.248838 0.968545i \(-0.419951\pi\)
−0.997041 + 0.0768719i \(0.975507\pi\)
\(42\) 0 0
\(43\) −793.064 + 288.652i −0.428915 + 0.156112i −0.547452 0.836837i \(-0.684402\pi\)
0.118536 + 0.992950i \(0.462180\pi\)
\(44\) 0 0
\(45\) 1357.09 + 2164.64i 0.670168 + 1.06896i
\(46\) 0 0
\(47\) −1802.00 317.741i −0.815754 0.143839i −0.249822 0.968292i \(-0.580372\pi\)
−0.565932 + 0.824452i \(0.691483\pi\)
\(48\) 0 0
\(49\) −4971.44 1809.45i −2.07057 0.753626i
\(50\) 0 0
\(51\) 1743.31 2588.70i 0.670244 0.995270i
\(52\) 0 0
\(53\) 2964.60i 1.05539i 0.849432 + 0.527697i \(0.176944\pi\)
−0.849432 + 0.527697i \(0.823056\pi\)
\(54\) 0 0
\(55\) −4258.91 −1.40791
\(56\) 0 0
\(57\) −141.294 + 2042.36i −0.0434883 + 0.628613i
\(58\) 0 0
\(59\) −1888.83 + 5189.52i −0.542612 + 1.49081i 0.300875 + 0.953664i \(0.402721\pi\)
−0.843487 + 0.537150i \(0.819501\pi\)
\(60\) 0 0
\(61\) 680.783 3860.91i 0.182957 1.03760i −0.745595 0.666399i \(-0.767835\pi\)
0.928552 0.371202i \(-0.121054\pi\)
\(62\) 0 0
\(63\) −4761.19 5272.09i −1.19959 1.32832i
\(64\) 0 0
\(65\) 3037.52 + 8345.52i 0.718940 + 1.97527i
\(66\) 0 0
\(67\) −3957.28 + 3320.55i −0.881549 + 0.739708i −0.966497 0.256678i \(-0.917372\pi\)
0.0849477 + 0.996385i \(0.472928\pi\)
\(68\) 0 0
\(69\) −1385.99 + 1008.55i −0.291113 + 0.211836i
\(70\) 0 0
\(71\) −1162.57 + 671.209i −0.230622 + 0.133150i −0.610859 0.791739i \(-0.709176\pi\)
0.380237 + 0.924889i \(0.375843\pi\)
\(72\) 0 0
\(73\) −1153.91 + 1998.62i −0.216533 + 0.375047i −0.953746 0.300614i \(-0.902808\pi\)
0.737213 + 0.675661i \(0.236142\pi\)
\(74\) 0 0
\(75\) −3230.60 802.933i −0.574328 0.142744i
\(76\) 0 0
\(77\) 11662.0 2056.32i 1.96693 0.346824i
\(78\) 0 0
\(79\) 6080.80 + 5102.39i 0.974330 + 0.817560i 0.983224 0.182400i \(-0.0583867\pi\)
−0.00889403 + 0.999960i \(0.502831\pi\)
\(80\) 0 0
\(81\) −1606.13 6361.37i −0.244800 0.969574i
\(82\) 0 0
\(83\) −879.339 + 1047.96i −0.127644 + 0.152120i −0.826081 0.563551i \(-0.809435\pi\)
0.698437 + 0.715671i \(0.253879\pi\)
\(84\) 0 0
\(85\) 1899.34 + 10771.7i 0.262884 + 1.49089i
\(86\) 0 0
\(87\) 1452.08 5842.43i 0.191846 0.771889i
\(88\) 0 0
\(89\) −2800.19 1616.69i −0.353515 0.204102i 0.312717 0.949846i \(-0.398761\pi\)
−0.666232 + 0.745744i \(0.732094\pi\)
\(90\) 0 0
\(91\) −12346.9 21385.5i −1.49099 2.58248i
\(92\) 0 0
\(93\) −1093.37 1502.55i −0.126416 0.173725i
\(94\) 0 0
\(95\) −4611.89 5496.24i −0.511013 0.609001i
\(96\) 0 0
\(97\) −10325.5 + 3758.17i −1.09741 + 0.399423i −0.826359 0.563143i \(-0.809592\pi\)
−0.271046 + 0.962566i \(0.587370\pi\)
\(98\) 0 0
\(99\) 10406.7 + 3364.29i 1.06180 + 0.343260i
\(100\) 0 0
\(101\) 17983.3 + 3170.94i 1.76289 + 0.310846i 0.958890 0.283777i \(-0.0915876\pi\)
0.804005 + 0.594623i \(0.202699\pi\)
\(102\) 0 0
\(103\) 2539.01 + 924.124i 0.239326 + 0.0871075i 0.458899 0.888489i \(-0.348244\pi\)
−0.219573 + 0.975596i \(0.570466\pi\)
\(104\) 0 0
\(105\) 24836.8 + 1718.25i 2.25277 + 0.155850i
\(106\) 0 0
\(107\) 6516.08i 0.569140i 0.958655 + 0.284570i \(0.0918508\pi\)
−0.958655 + 0.284570i \(0.908149\pi\)
\(108\) 0 0
\(109\) −1020.46 −0.0858901 −0.0429451 0.999077i \(-0.513674\pi\)
−0.0429451 + 0.999077i \(0.513674\pi\)
\(110\) 0 0
\(111\) 14750.1 + 9933.17i 1.19715 + 0.806199i
\(112\) 0 0
\(113\) −6393.36 + 17565.6i −0.500694 + 1.37564i 0.389905 + 0.920855i \(0.372508\pi\)
−0.890599 + 0.454790i \(0.849714\pi\)
\(114\) 0 0
\(115\) 1043.15 5916.02i 0.0788775 0.447336i
\(116\) 0 0
\(117\) −829.767 22791.9i −0.0606156 1.66498i
\(118\) 0 0
\(119\) −10401.7 28578.4i −0.734532 2.01811i
\(120\) 0 0
\(121\) −2750.69 + 2308.10i −0.187876 + 0.157647i
\(122\) 0 0
\(123\) −16092.9 7150.74i −1.06371 0.472651i
\(124\) 0 0
\(125\) −6968.94 + 4023.52i −0.446012 + 0.257505i
\(126\) 0 0
\(127\) 8405.05 14558.0i 0.521114 0.902597i −0.478584 0.878042i \(-0.658850\pi\)
0.999698 0.0245549i \(-0.00781687\pi\)
\(128\) 0 0
\(129\) −5272.33 + 5467.77i −0.316828 + 0.328572i
\(130\) 0 0
\(131\) −14033.3 + 2474.46i −0.817746 + 0.144191i −0.566848 0.823823i \(-0.691837\pi\)
−0.250899 + 0.968013i \(0.580726\pi\)
\(132\) 0 0
\(133\) 15282.2 + 12823.3i 0.863939 + 0.724931i
\(134\) 0 0
\(135\) 19527.0 + 12141.5i 1.07144 + 0.666199i
\(136\) 0 0
\(137\) 23405.4 27893.5i 1.24702 1.48615i 0.437321 0.899306i \(-0.355927\pi\)
0.809703 0.586840i \(-0.199628\pi\)
\(138\) 0 0
\(139\) −1462.43 8293.86i −0.0756913 0.429267i −0.998980 0.0451595i \(-0.985620\pi\)
0.923288 0.384107i \(-0.125491\pi\)
\(140\) 0 0
\(141\) −15826.9 + 4550.99i −0.796080 + 0.228912i
\(142\) 0 0
\(143\) 32925.2 + 19009.4i 1.61011 + 0.929599i
\(144\) 0 0
\(145\) 10549.2 + 18271.8i 0.501747 + 0.869052i
\(146\) 0 0
\(147\) −47349.9 + 5012.19i −2.19121 + 0.231949i
\(148\) 0 0
\(149\) −15321.1 18259.0i −0.690108 0.822439i 0.301261 0.953542i \(-0.402593\pi\)
−0.991369 + 0.131103i \(0.958148\pi\)
\(150\) 0 0
\(151\) 7165.12 2607.89i 0.314246 0.114376i −0.180082 0.983652i \(-0.557636\pi\)
0.494328 + 0.869275i \(0.335414\pi\)
\(152\) 0 0
\(153\) 3867.93 27821.2i 0.165233 1.18848i
\(154\) 0 0
\(155\) 6413.55 + 1130.88i 0.266953 + 0.0470711i
\(156\) 0 0
\(157\) 30590.5 + 11134.0i 1.24104 + 0.451703i 0.877366 0.479821i \(-0.159299\pi\)
0.363678 + 0.931525i \(0.381521\pi\)
\(158\) 0 0
\(159\) 11714.2 + 23972.4i 0.463358 + 0.948239i
\(160\) 0 0
\(161\) 16703.2i 0.644388i
\(162\) 0 0
\(163\) −11743.8 −0.442013 −0.221007 0.975272i \(-0.570934\pi\)
−0.221007 + 0.975272i \(0.570934\pi\)
\(164\) 0 0
\(165\) −34438.5 + 16828.4i −1.26496 + 0.618124i
\(166\) 0 0
\(167\) 2258.54 6205.28i 0.0809830 0.222499i −0.892592 0.450864i \(-0.851116\pi\)
0.973576 + 0.228365i \(0.0733380\pi\)
\(168\) 0 0
\(169\) 8807.35 49948.9i 0.308370 1.74885i
\(170\) 0 0
\(171\) 6927.54 + 17073.3i 0.236912 + 0.583882i
\(172\) 0 0
\(173\) −11089.4 30467.9i −0.370524 1.01801i −0.975159 0.221505i \(-0.928903\pi\)
0.604635 0.796503i \(-0.293319\pi\)
\(174\) 0 0
\(175\) −24849.4 + 20851.1i −0.811408 + 0.680852i
\(176\) 0 0
\(177\) 5232.06 + 49427.0i 0.167004 + 1.57768i
\(178\) 0 0
\(179\) −20902.8 + 12068.2i −0.652377 + 0.376650i −0.789366 0.613923i \(-0.789591\pi\)
0.136989 + 0.990573i \(0.456257\pi\)
\(180\) 0 0
\(181\) −3335.92 + 5777.98i −0.101826 + 0.176368i −0.912437 0.409217i \(-0.865802\pi\)
0.810611 + 0.585585i \(0.199135\pi\)
\(182\) 0 0
\(183\) −9750.82 33910.2i −0.291165 1.01258i
\(184\) 0 0
\(185\) −61375.9 + 10822.2i −1.79331 + 0.316208i
\(186\) 0 0
\(187\) 35868.7 + 30097.4i 1.02573 + 0.860689i
\(188\) 0 0
\(189\) −59331.9 23818.2i −1.66098 0.666784i
\(190\) 0 0
\(191\) −18122.1 + 21597.0i −0.496753 + 0.592008i −0.954922 0.296858i \(-0.904061\pi\)
0.458168 + 0.888865i \(0.348506\pi\)
\(192\) 0 0
\(193\) 5929.51 + 33627.9i 0.159186 + 0.902788i 0.954859 + 0.297061i \(0.0960065\pi\)
−0.795673 + 0.605727i \(0.792882\pi\)
\(194\) 0 0
\(195\) 57538.0 + 55481.4i 1.51316 + 1.45908i
\(196\) 0 0
\(197\) −4567.28 2636.92i −0.117686 0.0679461i 0.440001 0.897997i \(-0.354978\pi\)
−0.557688 + 0.830051i \(0.688311\pi\)
\(198\) 0 0
\(199\) −24297.3 42084.1i −0.613553 1.06270i −0.990637 0.136525i \(-0.956407\pi\)
0.377084 0.926179i \(-0.376927\pi\)
\(200\) 0 0
\(201\) −18878.8 + 42487.2i −0.467285 + 1.05164i
\(202\) 0 0
\(203\) −37708.5 44939.3i −0.915055 1.09052i
\(204\) 0 0
\(205\) 57994.9 21108.4i 1.38001 0.502282i
\(206\) 0 0
\(207\) −7222.28 + 13631.9i −0.168552 + 0.318138i
\(208\) 0 0
\(209\) −30247.7 5333.49i −0.692469 0.122101i
\(210\) 0 0
\(211\) −14002.0 5096.30i −0.314503 0.114470i 0.179946 0.983677i \(-0.442408\pi\)
−0.494449 + 0.869207i \(0.664630\pi\)
\(212\) 0 0
\(213\) −6748.60 + 10021.2i −0.148749 + 0.220883i
\(214\) 0 0
\(215\) 26619.9i 0.575878i
\(216\) 0 0
\(217\) −18107.9 −0.384546
\(218\) 0 0
\(219\) −1433.49 + 20720.8i −0.0298887 + 0.432034i
\(220\) 0 0
\(221\) 33395.1 91752.2i 0.683751 1.87859i
\(222\) 0 0
\(223\) −1567.49 + 8889.65i −0.0315206 + 0.178762i −0.996504 0.0835505i \(-0.973374\pi\)
0.964983 + 0.262312i \(0.0844851\pi\)
\(224\) 0 0
\(225\) −29296.0 + 6272.49i −0.578686 + 0.123901i
\(226\) 0 0
\(227\) 20863.3 + 57321.4i 0.404885 + 1.11241i 0.959844 + 0.280534i \(0.0905115\pi\)
−0.554960 + 0.831877i \(0.687266\pi\)
\(228\) 0 0
\(229\) −45065.7 + 37814.6i −0.859361 + 0.721089i −0.961830 0.273647i \(-0.911770\pi\)
0.102470 + 0.994736i \(0.467326\pi\)
\(230\) 0 0
\(231\) 86175.9 62708.2i 1.61496 1.17517i
\(232\) 0 0
\(233\) 25541.4 14746.3i 0.470470 0.271626i −0.245966 0.969278i \(-0.579105\pi\)
0.716437 + 0.697652i \(0.245772\pi\)
\(234\) 0 0
\(235\) 28857.4 49982.6i 0.522543 0.905071i
\(236\) 0 0
\(237\) 69331.9 + 17231.8i 1.23435 + 0.306784i
\(238\) 0 0
\(239\) −91549.5 + 16142.6i −1.60273 + 0.282604i −0.902297 0.431115i \(-0.858120\pi\)
−0.700432 + 0.713719i \(0.747009\pi\)
\(240\) 0 0
\(241\) 75263.3 + 63153.4i 1.29583 + 1.08733i 0.990849 + 0.134976i \(0.0430957\pi\)
0.304985 + 0.952357i \(0.401349\pi\)
\(242\) 0 0
\(243\) −38123.5 45093.1i −0.645624 0.763655i
\(244\) 0 0
\(245\) 107263. 127831.i 1.78696 2.12962i
\(246\) 0 0
\(247\) 11121.9 + 63075.6i 0.182300 + 1.03387i
\(248\) 0 0
\(249\) −2969.70 + 11948.6i −0.0478976 + 0.192716i
\(250\) 0 0
\(251\) 67645.6 + 39055.2i 1.07372 + 0.619914i 0.929196 0.369587i \(-0.120501\pi\)
0.144527 + 0.989501i \(0.453834\pi\)
\(252\) 0 0
\(253\) −12858.2 22271.0i −0.200880 0.347935i
\(254\) 0 0
\(255\) 57921.0 + 79597.2i 0.890750 + 1.22410i
\(256\) 0 0
\(257\) 35744.0 + 42598.0i 0.541174 + 0.644946i 0.965450 0.260587i \(-0.0839160\pi\)
−0.424277 + 0.905533i \(0.639472\pi\)
\(258\) 0 0
\(259\) 162837. 59267.8i 2.42747 0.883526i
\(260\) 0 0
\(261\) −11343.6 52980.8i −0.166521 0.777746i
\(262\) 0 0
\(263\) 38052.4 + 6709.66i 0.550136 + 0.0970038i 0.441805 0.897111i \(-0.354338\pi\)
0.108331 + 0.994115i \(0.465449\pi\)
\(264\) 0 0
\(265\) −87869.3 31981.8i −1.25125 0.455419i
\(266\) 0 0
\(267\) −29031.0 2008.41i −0.407230 0.0281728i
\(268\) 0 0
\(269\) 26971.5i 0.372735i 0.982480 + 0.186367i \(0.0596715\pi\)
−0.982480 + 0.186367i \(0.940329\pi\)
\(270\) 0 0
\(271\) 15106.5 0.205696 0.102848 0.994697i \(-0.467204\pi\)
0.102848 + 0.994697i \(0.467204\pi\)
\(272\) 0 0
\(273\) −184341. 124141.i −2.47342 1.66567i
\(274\) 0 0
\(275\) 17081.3 46930.6i 0.225869 0.620570i
\(276\) 0 0
\(277\) −1864.45 + 10573.8i −0.0242991 + 0.137807i −0.994544 0.104319i \(-0.966734\pi\)
0.970245 + 0.242126i \(0.0778448\pi\)
\(278\) 0 0
\(279\) −14778.3 7829.67i −0.189853 0.100585i
\(280\) 0 0
\(281\) −3060.57 8408.86i −0.0387606 0.106494i 0.918803 0.394718i \(-0.129158\pi\)
−0.957563 + 0.288224i \(0.906935\pi\)
\(282\) 0 0
\(283\) 47874.3 40171.3i 0.597764 0.501584i −0.292962 0.956124i \(-0.594641\pi\)
0.890726 + 0.454540i \(0.150196\pi\)
\(284\) 0 0
\(285\) −59010.3 26220.6i −0.726504 0.322815i
\(286\) 0 0
\(287\) −148613. + 85801.5i −1.80423 + 1.04167i
\(288\) 0 0
\(289\) 18365.8 31810.6i 0.219895 0.380869i
\(290\) 0 0
\(291\) −68644.4 + 71188.9i −0.810623 + 0.840672i
\(292\) 0 0
\(293\) −19021.2 + 3353.96i −0.221566 + 0.0390681i −0.283329 0.959023i \(-0.591439\pi\)
0.0617628 + 0.998091i \(0.480328\pi\)
\(294\) 0 0
\(295\) −133438. 111968.i −1.53333 1.28662i
\(296\) 0 0
\(297\) 97444.6 13916.1i 1.10470 0.157763i
\(298\) 0 0
\(299\) −34470.3 + 41080.1i −0.385569 + 0.459503i
\(300\) 0 0
\(301\) 12852.8 + 72891.9i 0.141862 + 0.804538i
\(302\) 0 0
\(303\) 157946. 45417.2i 1.72038 0.494692i
\(304\) 0 0
\(305\) 107091. + 61829.1i 1.15121 + 0.664651i
\(306\) 0 0
\(307\) −73229.0 126836.i −0.776974 1.34576i −0.933678 0.358113i \(-0.883420\pi\)
0.156704 0.987646i \(-0.449913\pi\)
\(308\) 0 0
\(309\) 24182.5 2559.82i 0.253270 0.0268098i
\(310\) 0 0
\(311\) 76390.5 + 91038.6i 0.789802 + 0.941250i 0.999332 0.0365526i \(-0.0116377\pi\)
−0.209529 + 0.977802i \(0.567193\pi\)
\(312\) 0 0
\(313\) −128096. + 46623.1i −1.30752 + 0.475897i −0.899437 0.437050i \(-0.856023\pi\)
−0.408078 + 0.912947i \(0.633801\pi\)
\(314\) 0 0
\(315\) 207625. 84244.5i 2.09247 0.849025i
\(316\) 0 0
\(317\) 2046.11 + 360.784i 0.0203615 + 0.00359028i 0.183820 0.982960i \(-0.441154\pi\)
−0.163458 + 0.986550i \(0.552265\pi\)
\(318\) 0 0
\(319\) 84872.5 + 30891.1i 0.834037 + 0.303565i
\(320\) 0 0
\(321\) 25747.2 + 52690.4i 0.249874 + 0.511354i
\(322\) 0 0
\(323\) 78881.4i 0.756083i
\(324\) 0 0
\(325\) −104145. −0.985990
\(326\) 0 0
\(327\) −8251.66 + 4032.19i −0.0771696 + 0.0377090i
\(328\) 0 0
\(329\) −54885.9 + 150798.i −0.507071 + 1.39317i
\(330\) 0 0
\(331\) −13925.1 + 78973.4i −0.127099 + 0.720817i 0.852939 + 0.522010i \(0.174818\pi\)
−0.980039 + 0.198807i \(0.936293\pi\)
\(332\) 0 0
\(333\) 158522. + 22039.1i 1.42956 + 0.198749i
\(334\) 0 0
\(335\) −55728.6 153113.i −0.496579 1.36434i
\(336\) 0 0
\(337\) −41768.0 + 35047.5i −0.367777 + 0.308601i −0.807881 0.589345i \(-0.799386\pi\)
0.440105 + 0.897946i \(0.354941\pi\)
\(338\) 0 0
\(339\) 17709.6 + 167302.i 0.154102 + 1.45580i
\(340\) 0 0
\(341\) 24143.9 13939.5i 0.207634 0.119878i
\(342\) 0 0
\(343\) −126706. + 219461.i −1.07698 + 1.86539i
\(344\) 0 0
\(345\) −14941.0 51960.1i −0.125529 0.436548i
\(346\) 0 0
\(347\) −23633.6 + 4167.25i −0.196278 + 0.0346091i −0.270923 0.962601i \(-0.587329\pi\)
0.0746448 + 0.997210i \(0.476218\pi\)
\(348\) 0 0
\(349\) −124185. 104204.i −1.01957 0.855524i −0.0300003 0.999550i \(-0.509551\pi\)
−0.989574 + 0.144025i \(0.953995\pi\)
\(350\) 0 0
\(351\) −96768.2 181022.i −0.785450 1.46932i
\(352\) 0 0
\(353\) 67927.0 80952.2i 0.545121 0.649650i −0.421207 0.906965i \(-0.638393\pi\)
0.966328 + 0.257315i \(0.0828378\pi\)
\(354\) 0 0
\(355\) −7352.62 41698.8i −0.0583426 0.330877i
\(356\) 0 0
\(357\) −197034. 189991.i −1.54598 1.49072i
\(358\) 0 0
\(359\) 961.228 + 554.965i 0.00745826 + 0.00430603i 0.503724 0.863864i \(-0.331963\pi\)
−0.496266 + 0.868170i \(0.665296\pi\)
\(360\) 0 0
\(361\) 39288.8 + 68050.3i 0.301477 + 0.522174i
\(362\) 0 0
\(363\) −13122.6 + 29532.8i −0.0995878 + 0.224125i
\(364\) 0 0
\(365\) −46789.9 55762.1i −0.351210 0.418555i
\(366\) 0 0
\(367\) −75284.8 + 27401.4i −0.558952 + 0.203442i −0.606020 0.795450i \(-0.707235\pi\)
0.0470672 + 0.998892i \(0.485013\pi\)
\(368\) 0 0
\(369\) −158386. + 5766.23i −1.16323 + 0.0423486i
\(370\) 0 0
\(371\) 256049. + 45148.4i 1.86027 + 0.328016i
\(372\) 0 0
\(373\) 24455.5 + 8901.06i 0.175776 + 0.0639771i 0.428409 0.903585i \(-0.359074\pi\)
−0.252633 + 0.967562i \(0.581297\pi\)
\(374\) 0 0
\(375\) −40454.1 + 60071.7i −0.287673 + 0.427176i
\(376\) 0 0
\(377\) 188343.i 1.32516i
\(378\) 0 0
\(379\) −33218.9 −0.231263 −0.115632 0.993292i \(-0.536889\pi\)
−0.115632 + 0.993292i \(0.536889\pi\)
\(380\) 0 0
\(381\) 10441.6 150930.i 0.0719310 1.03974i
\(382\) 0 0
\(383\) −72532.8 + 199282.i −0.494467 + 1.35854i 0.402087 + 0.915601i \(0.368285\pi\)
−0.896554 + 0.442934i \(0.853937\pi\)
\(384\) 0 0
\(385\) −64859.6 + 367837.i −0.437575 + 2.48161i
\(386\) 0 0
\(387\) −21028.2 + 65046.3i −0.140404 + 0.434311i
\(388\) 0 0
\(389\) 39859.9 + 109514.i 0.263413 + 0.723721i 0.998931 + 0.0462165i \(0.0147164\pi\)
−0.735519 + 0.677505i \(0.763061\pi\)
\(390\) 0 0
\(391\) −50593.6 + 42453.1i −0.330934 + 0.277687i
\(392\) 0 0
\(393\) −103699. + 75459.5i −0.671414 + 0.488572i
\(394\) 0 0
\(395\) −216831. + 125187.i −1.38972 + 0.802355i
\(396\) 0 0
\(397\) 105374. 182513.i 0.668580 1.15801i −0.309722 0.950827i \(-0.600236\pi\)
0.978301 0.207187i \(-0.0664307\pi\)
\(398\) 0 0
\(399\) 174245. + 43306.8i 1.09449 + 0.272026i
\(400\) 0 0
\(401\) 18741.2 3304.59i 0.116549 0.0205508i −0.115069 0.993357i \(-0.536709\pi\)
0.231619 + 0.972807i \(0.425598\pi\)
\(402\) 0 0
\(403\) −44534.8 37369.2i −0.274214 0.230093i
\(404\) 0 0
\(405\) 205874. + 21020.9i 1.25514 + 0.128156i
\(406\) 0 0
\(407\) −171492. + 204376.i −1.03527 + 1.23379i
\(408\) 0 0
\(409\) −17268.1 97932.2i −0.103228 0.585435i −0.991913 0.126918i \(-0.959492\pi\)
0.888685 0.458518i \(-0.151619\pi\)
\(410\) 0 0
\(411\) 79044.6 318035.i 0.467938 1.88275i
\(412\) 0 0
\(413\) 419448. + 242168.i 2.45911 + 1.41977i
\(414\) 0 0
\(415\) −21574.6 37368.4i −0.125270 0.216974i
\(416\) 0 0
\(417\) −44597.4 61287.4i −0.256471 0.352451i
\(418\) 0 0
\(419\) −77933.2 92877.2i −0.443910 0.529031i 0.496972 0.867767i \(-0.334445\pi\)
−0.940882 + 0.338736i \(0.890001\pi\)
\(420\) 0 0
\(421\) 203870. 74202.8i 1.15024 0.418655i 0.304641 0.952467i \(-0.401463\pi\)
0.845603 + 0.533812i \(0.179241\pi\)
\(422\) 0 0
\(423\) −109997. + 99337.6i −0.614752 + 0.555179i
\(424\) 0 0
\(425\) −126315. 22272.7i −0.699322 0.123309i
\(426\) 0 0
\(427\) −323095. 117597.i −1.77204 0.644971i
\(428\) 0 0
\(429\) 341353. + 23615.3i 1.85476 + 0.128315i
\(430\) 0 0
\(431\) 234878.i 1.26441i −0.774802 0.632204i \(-0.782150\pi\)
0.774802 0.632204i \(-0.217850\pi\)
\(432\) 0 0
\(433\) −21782.0 −0.116177 −0.0580887 0.998311i \(-0.518501\pi\)
−0.0580887 + 0.998311i \(0.518501\pi\)
\(434\) 0 0
\(435\) 157502. + 106066.i 0.832351 + 0.560530i
\(436\) 0 0
\(437\) 14817.4 40710.6i 0.0775908 0.213179i
\(438\) 0 0
\(439\) 65390.8 370850.i 0.339303 1.92428i −0.0404229 0.999183i \(-0.512871\pi\)
0.379726 0.925099i \(-0.376018\pi\)
\(440\) 0 0
\(441\) −363077. + 227625.i −1.86690 + 1.17042i
\(442\) 0 0
\(443\) 31232.3 + 85809.9i 0.159146 + 0.437250i 0.993480 0.114010i \(-0.0363695\pi\)
−0.834334 + 0.551260i \(0.814147\pi\)
\(444\) 0 0
\(445\) 78125.9 65555.4i 0.394526 0.331046i
\(446\) 0 0
\(447\) −196037. 87107.1i −0.981122 0.435952i
\(448\) 0 0
\(449\) −107735. + 62201.0i −0.534399 + 0.308535i −0.742806 0.669507i \(-0.766505\pi\)
0.208407 + 0.978042i \(0.433172\pi\)
\(450\) 0 0
\(451\) 132100. 228804.i 0.649458 1.12489i
\(452\) 0 0
\(453\) 47634.1 49399.8i 0.232125 0.240729i
\(454\) 0 0
\(455\) 767051. 135252.i 3.70511 0.653312i
\(456\) 0 0
\(457\) 103503. + 86849.0i 0.495586 + 0.415846i 0.856023 0.516938i \(-0.172928\pi\)
−0.360437 + 0.932783i \(0.617372\pi\)
\(458\) 0 0
\(459\) −78653.9 240251.i −0.373332 1.14036i
\(460\) 0 0
\(461\) −168200. + 200453.i −0.791450 + 0.943213i −0.999390 0.0349284i \(-0.988880\pi\)
0.207940 + 0.978142i \(0.433324\pi\)
\(462\) 0 0
\(463\) −26468.5 150110.i −0.123472 0.700242i −0.982204 0.187818i \(-0.939859\pi\)
0.858732 0.512424i \(-0.171253\pi\)
\(464\) 0 0
\(465\) 56329.9 16197.6i 0.260515 0.0749107i
\(466\) 0 0
\(467\) −310052. 179009.i −1.42168 0.820806i −0.425235 0.905083i \(-0.639809\pi\)
−0.996442 + 0.0842767i \(0.973142\pi\)
\(468\) 0 0
\(469\) 226526. + 392354.i 1.02985 + 1.78374i
\(470\) 0 0
\(471\) 291356. 30841.3i 1.31335 0.139024i
\(472\) 0 0
\(473\) −73249.5 87295.3i −0.327403 0.390183i
\(474\) 0 0
\(475\) 79062.2 28776.3i 0.350414 0.127540i
\(476\) 0 0
\(477\) 189446. + 147560.i 0.832626 + 0.648531i
\(478\) 0 0
\(479\) −147754. 26053.1i −0.643976 0.113550i −0.157883 0.987458i \(-0.550467\pi\)
−0.486092 + 0.873908i \(0.661578\pi\)
\(480\) 0 0
\(481\) 522794. + 190282.i 2.25965 + 0.822444i
\(482\) 0 0
\(483\) 66000.0 + 135066.i 0.282911 + 0.578963i
\(484\) 0 0
\(485\) 346585.i 1.47342i
\(486\) 0 0
\(487\) 191423. 0.807117 0.403559 0.914954i \(-0.367773\pi\)
0.403559 + 0.914954i \(0.367773\pi\)
\(488\) 0 0
\(489\) −94963.3 + 46403.9i −0.397135 + 0.194060i
\(490\) 0 0
\(491\) 96829.2 266036.i 0.401646 1.10351i −0.559826 0.828610i \(-0.689132\pi\)
0.961472 0.274903i \(-0.0886457\pi\)
\(492\) 0 0
\(493\) 40279.5 228436.i 0.165726 0.939878i
\(494\) 0 0
\(495\) −211982. + 272156.i −0.865146 + 1.11073i
\(496\) 0 0
\(497\) 40266.6 + 110631.i 0.163017 + 0.447884i
\(498\) 0 0
\(499\) −216992. + 182078.i −0.871450 + 0.731233i −0.964403 0.264437i \(-0.914814\pi\)
0.0929533 + 0.995670i \(0.470369\pi\)
\(500\) 0 0
\(501\) −6256.14 59101.5i −0.0249248 0.235463i
\(502\) 0 0
\(503\) 176203. 101731.i 0.696429 0.402083i −0.109587 0.993977i \(-0.534953\pi\)
0.806016 + 0.591894i \(0.201620\pi\)
\(504\) 0 0
\(505\) −287986. + 498807.i −1.12925 + 1.95592i
\(506\) 0 0
\(507\) −126147. 438699.i −0.490751 1.70667i
\(508\) 0 0
\(509\) 54374.6 9587.70i 0.209875 0.0370066i −0.0677222 0.997704i \(-0.521573\pi\)
0.277597 + 0.960698i \(0.410462\pi\)
\(510\) 0 0
\(511\) 155046. + 130099.i 0.593769 + 0.498232i
\(512\) 0 0
\(513\) 123480. + 110685.i 0.469204 + 0.420586i
\(514\) 0 0
\(515\) −54781.1 + 65285.5i −0.206546 + 0.246151i
\(516\) 0 0
\(517\) −42903.0 243315.i −0.160512 0.910308i
\(518\) 0 0
\(519\) −210061. 202552.i −0.779848 0.751973i
\(520\) 0 0
\(521\) 23227.7 + 13410.5i 0.0855719 + 0.0494050i 0.542175 0.840265i \(-0.317601\pi\)
−0.456603 + 0.889670i \(0.650934\pi\)
\(522\) 0 0
\(523\) 25930.8 + 44913.4i 0.0948009 + 0.164200i 0.909525 0.415648i \(-0.136445\pi\)
−0.814725 + 0.579848i \(0.803112\pi\)
\(524\) 0 0
\(525\) −118548. + 266795.i −0.430105 + 0.967963i
\(526\) 0 0
\(527\) −46023.3 54848.4i −0.165713 0.197489i
\(528\) 0 0
\(529\) −228879. + 83305.0i −0.817888 + 0.297687i
\(530\) 0 0
\(531\) 237611. + 379004.i 0.842707 + 1.34417i
\(532\) 0 0
\(533\) −542568. 95669.3i −1.90985 0.336758i
\(534\) 0 0
\(535\) −193133. 70294.7i −0.674760 0.245592i
\(536\) 0 0
\(537\) −121339. + 180181.i −0.420777 + 0.624826i
\(538\) 0 0
\(539\) 714349.i 2.45886i
\(540\) 0 0
\(541\) 237828. 0.812585 0.406292 0.913743i \(-0.366821\pi\)
0.406292 + 0.913743i \(0.366821\pi\)
\(542\) 0 0
\(543\) −4144.20 + 59903.4i −0.0140553 + 0.203166i
\(544\) 0 0
\(545\) 11008.6 30245.9i 0.0370629 0.101829i
\(546\) 0 0
\(547\) −69204.9 + 392480.i −0.231293 + 1.31173i 0.618989 + 0.785399i \(0.287542\pi\)
−0.850282 + 0.526327i \(0.823569\pi\)
\(548\) 0 0
\(549\) −212838. 235676.i −0.706162 0.781937i
\(550\) 0 0
\(551\) 52041.0 + 142981.i 0.171412 + 0.470952i
\(552\) 0 0
\(553\) 533293. 447486.i 1.74388 1.46329i
\(554\) 0 0
\(555\) −453537. + 330028.i −1.47240 + 1.07143i
\(556\) 0 0
\(557\) −338329. + 195334.i −1.09051 + 0.629605i −0.933712 0.358026i \(-0.883450\pi\)
−0.156797 + 0.987631i \(0.550117\pi\)
\(558\) 0 0
\(559\) −118816. + 205796.i −0.380235 + 0.658587i
\(560\) 0 0
\(561\) 408967. + 101645.i 1.29946 + 0.322968i
\(562\) 0 0
\(563\) −502288. + 88566.9i −1.58466 + 0.279418i −0.895456 0.445151i \(-0.853150\pi\)
−0.689203 + 0.724569i \(0.742039\pi\)
\(564\) 0 0
\(565\) −451664. 378991.i −1.41488 1.18722i
\(566\) 0 0
\(567\) −573884. + 41841.3i −1.78508 + 0.130149i
\(568\) 0 0
\(569\) 338791. 403756.i 1.04642 1.24708i 0.0782149 0.996937i \(-0.475078\pi\)
0.968209 0.250143i \(-0.0804776\pi\)
\(570\) 0 0
\(571\) 13409.5 + 76049.2i 0.0411284 + 0.233250i 0.998442 0.0558010i \(-0.0177712\pi\)
−0.957314 + 0.289051i \(0.906660\pi\)
\(572\) 0 0
\(573\) −61201.7 + 246245.i −0.186404 + 0.749994i
\(574\) 0 0
\(575\) 61007.1 + 35222.5i 0.184521 + 0.106533i
\(576\) 0 0
\(577\) 82412.6 + 142743.i 0.247538 + 0.428748i 0.962842 0.270065i \(-0.0870452\pi\)
−0.715304 + 0.698813i \(0.753712\pi\)
\(578\) 0 0
\(579\) 180823. + 248493.i 0.539381 + 0.741238i
\(580\) 0 0
\(581\) 77119.1 + 91906.9i 0.228460 + 0.272268i
\(582\) 0 0
\(583\) −376155. + 136909.i −1.10670 + 0.402806i
\(584\) 0 0
\(585\) 684491. + 221282.i 2.00012 + 0.646599i
\(586\) 0 0
\(587\) −146970. 25914.7i −0.426532 0.0752090i −0.0437382 0.999043i \(-0.513927\pi\)
−0.382793 + 0.923834i \(0.625038\pi\)
\(588\) 0 0
\(589\) 44134.2 + 16063.6i 0.127217 + 0.0463032i
\(590\) 0 0
\(591\) −47351.4 3275.84i −0.135568 0.00937880i
\(592\) 0 0
\(593\) 87964.7i 0.250149i −0.992147 0.125075i \(-0.960083\pi\)
0.992147 0.125075i \(-0.0399170\pi\)
\(594\) 0 0
\(595\) 959262. 2.70959
\(596\) 0 0
\(597\) −362762. 244295.i −1.01782 0.685434i
\(598\) 0 0
\(599\) −236836. + 650702.i −0.660077 + 1.81355i −0.0834914 + 0.996508i \(0.526607\pi\)
−0.576585 + 0.817037i \(0.695615\pi\)
\(600\) 0 0
\(601\) 8308.99 47122.6i 0.0230038 0.130461i −0.971143 0.238497i \(-0.923345\pi\)
0.994147 + 0.108036i \(0.0344563\pi\)
\(602\) 0 0
\(603\) 15223.5 + 418157.i 0.0418678 + 1.15002i
\(604\) 0 0
\(605\) −38736.8 106429.i −0.105831 0.290769i
\(606\) 0 0
\(607\) 533429. 447600.i 1.44777 1.21482i 0.513582 0.858041i \(-0.328318\pi\)
0.934188 0.356782i \(-0.116126\pi\)
\(608\) 0 0
\(609\) −482489. 214389.i −1.30093 0.578055i
\(610\) 0 0
\(611\) −446187. + 257606.i −1.19518 + 0.690040i
\(612\) 0 0
\(613\) 242238. 419569.i 0.644646 1.11656i −0.339737 0.940521i \(-0.610338\pi\)
0.984383 0.176040i \(-0.0563287\pi\)
\(614\) 0 0
\(615\) 385553. 399845.i 1.01937 1.05716i
\(616\) 0 0
\(617\) −15518.7 + 2736.36i −0.0407647 + 0.00718792i −0.193993 0.981003i \(-0.562144\pi\)
0.153229 + 0.988191i \(0.451033\pi\)
\(618\) 0 0
\(619\) 534132. + 448190.i 1.39402 + 1.16972i 0.963683 + 0.267047i \(0.0860480\pi\)
0.430332 + 0.902671i \(0.358396\pi\)
\(620\) 0 0
\(621\) −4536.73 + 138768.i −0.0117641 + 0.359838i
\(622\) 0 0
\(623\) −182276. + 217228.i −0.469628 + 0.559680i
\(624\) 0 0
\(625\) −84217.5 477621.i −0.215597 1.22271i
\(626\) 0 0
\(627\) −265664. + 76391.3i −0.675769 + 0.194316i
\(628\) 0 0
\(629\) 593390. + 342594.i 1.49982 + 0.865921i
\(630\) 0 0
\(631\) −125378. 217160.i −0.314892 0.545408i 0.664523 0.747268i \(-0.268635\pi\)
−0.979414 + 0.201860i \(0.935302\pi\)
\(632\) 0 0
\(633\) −133360. + 14116.8i −0.332827 + 0.0352312i
\(634\) 0 0
\(635\) 340818. + 406171.i 0.845230 + 1.00731i
\(636\) 0 0
\(637\) −1.39980e6 + 509484.i −3.44974 + 1.25560i
\(638\) 0 0
\(639\) −14973.3 + 107700.i −0.0366705 + 0.263763i
\(640\) 0 0
\(641\) 128403. + 22641.0i 0.312507 + 0.0551034i 0.327702 0.944781i \(-0.393726\pi\)
−0.0151950 + 0.999885i \(0.504837\pi\)
\(642\) 0 0
\(643\) 508983. + 185255.i 1.23107 + 0.448072i 0.873963 0.485993i \(-0.161542\pi\)
0.357104 + 0.934065i \(0.383764\pi\)
\(644\) 0 0
\(645\) −105184. 215255.i −0.252832 0.517408i
\(646\) 0 0
\(647\) 667818.i 1.59533i −0.603102 0.797664i \(-0.706069\pi\)
0.603102 0.797664i \(-0.293931\pi\)
\(648\) 0 0
\(649\) −745686. −1.77038
\(650\) 0 0
\(651\) −146424. + 71550.5i −0.345503 + 0.168830i
\(652\) 0 0
\(653\) 121288. 333237.i 0.284441 0.781496i −0.712378 0.701796i \(-0.752382\pi\)
0.996819 0.0796995i \(-0.0253961\pi\)
\(654\) 0 0
\(655\) 78048.5 442635.i 0.181921 1.03172i
\(656\) 0 0
\(657\) 70283.3 + 173217.i 0.162825 + 0.401291i
\(658\) 0 0
\(659\) −177897. 488767.i −0.409635 1.12546i −0.957384 0.288819i \(-0.906737\pi\)
0.547749 0.836643i \(-0.315485\pi\)
\(660\) 0 0
\(661\) 432970. 363305.i 0.990957 0.831512i 0.00525099 0.999986i \(-0.498329\pi\)
0.985706 + 0.168475i \(0.0538841\pi\)
\(662\) 0 0
\(663\) −92504.3 873883.i −0.210443 1.98805i
\(664\) 0 0
\(665\) −544938. + 314620.i −1.23227 + 0.711449i
\(666\) 0 0
\(667\) −63698.7 + 110329.i −0.143179 + 0.247993i
\(668\) 0 0
\(669\) 22451.0 + 78077.3i 0.0501630 + 0.174451i
\(670\) 0 0
\(671\) 521320. 91922.8i 1.15787 0.204164i
\(672\) 0 0
\(673\) −289892. 243249.i −0.640039 0.537057i 0.263991 0.964525i \(-0.414961\pi\)
−0.904030 + 0.427468i \(0.859406\pi\)
\(674\) 0 0
\(675\) −212109. + 166479.i −0.465534 + 0.365386i
\(676\) 0 0
\(677\) −241740. + 288095.i −0.527438 + 0.628576i −0.962323 0.271910i \(-0.912345\pi\)
0.434884 + 0.900486i \(0.356789\pi\)
\(678\) 0 0
\(679\) 167340. + 949034.i 0.362962 + 2.05846i
\(680\) 0 0
\(681\) 395202. + 381076.i 0.852167 + 0.821707i
\(682\) 0 0
\(683\) −56691.2 32730.7i −0.121527 0.0701639i 0.438004 0.898973i \(-0.355686\pi\)
−0.559531 + 0.828809i \(0.689019\pi\)
\(684\) 0 0
\(685\) 574252. + 994634.i 1.22383 + 2.11974i
\(686\) 0 0
\(687\) −214993. + 483847.i −0.455523 + 1.02517i
\(688\) 0 0
\(689\) 536559. + 639446.i 1.13026 + 1.34699i
\(690\) 0 0
\(691\) 353222. 128562.i 0.739761 0.269251i 0.0554705 0.998460i \(-0.482334\pi\)
0.684291 + 0.729209i \(0.260112\pi\)
\(692\) 0 0
\(693\) 449056. 847582.i 0.935048 1.76488i
\(694\) 0 0
\(695\) 261602. + 46127.5i 0.541591 + 0.0954972i
\(696\) 0 0
\(697\) −637606. 232070.i −1.31246 0.477697i
\(698\) 0 0
\(699\) 148265. 220165.i 0.303449 0.450602i
\(700\) 0 0
\(701\) 960237.i 1.95408i −0.213055 0.977040i \(-0.568341\pi\)
0.213055 0.977040i \(-0.431659\pi\)
\(702\) 0 0
\(703\) −449458. −0.909449
\(704\) 0 0
\(705\) 35849.5 518195.i 0.0721282 1.04259i
\(706\) 0 0
\(707\) 547740. 1.50490e6i 1.09581 3.01072i
\(708\) 0 0
\(709\) 28749.5 163047.i 0.0571924 0.324354i −0.942766 0.333455i \(-0.891786\pi\)
0.999959 + 0.00910028i \(0.00289675\pi\)
\(710\) 0 0
\(711\) 628722. 134614.i 1.24371 0.266288i
\(712\) 0 0
\(713\) 13449.6 + 36952.4i 0.0264563 + 0.0726882i
\(714\) 0 0
\(715\) −918620. + 770814.i −1.79690 + 1.50778i
\(716\) 0 0
\(717\) −676504. + 492276.i −1.31593 + 0.957570i
\(718\) 0 0
\(719\) 243132. 140372.i 0.470310 0.271534i −0.246059 0.969255i \(-0.579136\pi\)
0.716370 + 0.697721i \(0.245802\pi\)
\(720\) 0 0
\(721\) 118482. 205218.i 0.227920 0.394770i
\(722\) 0 0
\(723\) 858136. + 213281.i 1.64165 + 0.408015i
\(724\) 0 0
\(725\) −243654. + 42962.8i −0.463552 + 0.0817366i
\(726\) 0 0
\(727\) 299480. + 251294.i 0.566630 + 0.475459i 0.880526 0.473998i \(-0.157190\pi\)
−0.313896 + 0.949458i \(0.601634\pi\)
\(728\) 0 0
\(729\) −486453. 213994.i −0.915347 0.402667i
\(730\) 0 0
\(731\) −188121. + 224194.i −0.352049 + 0.419555i
\(732\) 0 0
\(733\) −63621.7 360816.i −0.118412 0.671550i −0.985004 0.172532i \(-0.944805\pi\)
0.866592 0.499018i \(-0.166306\pi\)
\(734\) 0 0
\(735\) 362246. 1.45750e6i 0.670547 2.69794i
\(736\) 0 0
\(737\) −604070. 348760.i −1.11212 0.642084i
\(738\) 0 0
\(739\) −269023. 465962.i −0.492607 0.853221i 0.507356 0.861736i \(-0.330623\pi\)
−0.999964 + 0.00851547i \(0.997289\pi\)
\(740\) 0 0
\(741\) 339168. + 466097.i 0.617701 + 0.848867i
\(742\) 0 0
\(743\) 569499. + 678702.i 1.03161 + 1.22942i 0.972919 + 0.231147i \(0.0742479\pi\)
0.0586901 + 0.998276i \(0.481308\pi\)
\(744\) 0 0
\(745\) 706468. 257133.i 1.27286 0.463282i
\(746\) 0 0
\(747\) 23199.2 + 108353.i 0.0415750 + 0.194178i
\(748\) 0 0
\(749\) 562786. + 99234.3i 1.00318 + 0.176888i
\(750\) 0 0
\(751\) −321565. 117040.i −0.570149 0.207517i 0.0408271 0.999166i \(-0.487001\pi\)
−0.610976 + 0.791649i \(0.709223\pi\)
\(752\) 0 0
\(753\) 701317. + 48518.2i 1.23687 + 0.0855686i
\(754\) 0 0
\(755\) 240504.i 0.421918i
\(756\) 0 0
\(757\) 360278. 0.628704 0.314352 0.949307i \(-0.398213\pi\)
0.314352 + 0.949307i \(0.398213\pi\)
\(758\) 0 0
\(759\) −191974. 129281.i −0.333241 0.224415i
\(760\) 0 0
\(761\) −212386. + 583525.i −0.366738 + 1.00761i 0.609855 + 0.792513i \(0.291228\pi\)
−0.976594 + 0.215093i \(0.930995\pi\)
\(762\) 0 0
\(763\) −15540.7 + 88135.9i −0.0266945 + 0.151392i
\(764\) 0 0
\(765\) 782877. + 414775.i 1.33774 + 0.708744i
\(766\) 0 0
\(767\) 531835. + 1.46120e6i 0.904036 + 2.48382i
\(768\) 0 0
\(769\) 296424. 248729.i 0.501257 0.420604i −0.356783 0.934187i \(-0.616127\pi\)
0.858040 + 0.513583i \(0.171682\pi\)
\(770\) 0 0
\(771\) 457353. + 203220.i 0.769383 + 0.341868i
\(772\) 0 0
\(773\) −599094. + 345887.i −1.00262 + 0.578862i −0.909022 0.416748i \(-0.863170\pi\)
−0.0935968 + 0.995610i \(0.529836\pi\)
\(774\) 0 0
\(775\) −38184.6 + 66137.8i −0.0635749 + 0.110115i
\(776\) 0 0
\(777\) 1.08255e6 1.12268e6i 1.79310 1.85957i
\(778\) 0 0
\(779\) 438327. 77288.8i 0.722309 0.127363i
\(780\) 0 0
\(781\) −138853. 116512.i −0.227643 0.191015i
\(782\) 0