Properties

Label 108.5.k.a.5.11
Level 108
Weight 5
Character 108.5
Analytic conductor 11.164
Analytic rank 0
Dimension 72
CM no
Inner twists 2

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 5.11
Character \(\chi\) \(=\) 108.5
Dual form 108.5.k.a.65.11

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 8.08622 + 3.95134i 0.898469 + 0.439038i
\(4\) 0 0
\(5\) −10.7879 29.6395i −0.431515 1.18558i −0.944883 0.327409i \(-0.893824\pi\)
0.513367 0.858169i \(-0.328398\pi\)
\(6\) 0 0
\(7\) 15.2291 + 86.3688i 0.310799 + 1.76263i 0.594867 + 0.803824i \(0.297205\pi\)
−0.284068 + 0.958804i \(0.591684\pi\)
\(8\) 0 0
\(9\) 49.7738 + 63.9028i 0.614492 + 0.788923i
\(10\) 0 0
\(11\) 46.1813 126.882i 0.381664 1.04861i −0.588992 0.808139i \(-0.700475\pi\)
0.970656 0.240473i \(-0.0773027\pi\)
\(12\) 0 0
\(13\) 215.694 + 180.988i 1.27629 + 1.07094i 0.993744 + 0.111684i \(0.0356245\pi\)
0.282549 + 0.959253i \(0.408820\pi\)
\(14\) 0 0
\(15\) 29.8824 282.298i 0.132811 1.25466i
\(16\) 0 0
\(17\) 300.316 + 173.387i 1.03915 + 0.599956i 0.919594 0.392871i \(-0.128518\pi\)
0.119561 + 0.992827i \(0.461851\pi\)
\(18\) 0 0
\(19\) −113.736 196.996i −0.315058 0.545696i 0.664392 0.747384i \(-0.268690\pi\)
−0.979450 + 0.201688i \(0.935357\pi\)
\(20\) 0 0
\(21\) −218.126 + 758.572i −0.494617 + 1.72012i
\(22\) 0 0
\(23\) −187.562 33.0723i −0.354560 0.0625185i −0.00646861 0.999979i \(-0.502059\pi\)
−0.348091 + 0.937461i \(0.613170\pi\)
\(24\) 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 0.958490 0.285126i \(-0.0920355\pi\)
−0.447234 + 0.894417i \(0.647591\pi\)
\(30\) 0 0
\(31\) −35.8536 + 203.336i −0.0373087 + 0.211588i −0.997763 0.0668493i \(-0.978705\pi\)
0.960454 + 0.278437i \(0.0898164\pi\)
\(32\) 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 −0.238684 0.971097i \(-0.576716\pi\)
0.960337 0.278842i \(-0.0899507\pi\)
\(38\) 0 0
\(39\) 1029.00 + 2315.79i 0.676528 + 1.52254i
\(40\) 0 0
\(41\) −1257.73 + 1498.90i −0.748203 + 0.891673i −0.997041 0.0768719i \(-0.975507\pi\)
0.248838 + 0.968545i \(0.419951\pi\)
\(42\) 0 0
\(43\) −793.064 288.652i −0.428915 0.156112i 0.118536 0.992950i \(-0.462180\pi\)
−0.547452 + 0.836837i \(0.684402\pi\)
\(44\) 0 0
\(45\) 1357.09 2164.64i 0.670168 1.06896i
\(46\) 0 0
\(47\) −1802.00 + 317.741i −0.815754 + 0.143839i −0.565932 0.824452i \(-0.691483\pi\)
−0.249822 + 0.968292i \(0.580372\pi\)
\(48\) 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 \(-0.823056\pi\)
0.849432 0.527697i \(-0.176944\pi\)
\(54\) 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 −0.843487 0.537150i \(-0.819501\pi\)
0.300875 0.953664i \(-0.402721\pi\)
\(60\) 0 0
\(61\) 680.783 + 3860.91i 0.182957 + 1.03760i 0.928552 + 0.371202i \(0.121054\pi\)
−0.745595 + 0.666399i \(0.767835\pi\)
\(62\) 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 0.0849477 0.996385i \(-0.472928\pi\)
−0.966497 + 0.256678i \(0.917372\pi\)
\(68\) 0 0
\(69\) −1385.99 1008.55i −0.291113 0.211836i
\(70\) 0 0
\(71\) −1162.57 671.209i −0.230622 0.133150i 0.380237 0.924889i \(-0.375843\pi\)
−0.610859 + 0.791739i \(0.709176\pi\)
\(72\) 0 0
\(73\) −1153.91 1998.62i −0.216533 0.375047i 0.737213 0.675661i \(-0.236142\pi\)
−0.953746 + 0.300614i \(0.902808\pi\)
\(74\) 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 −0.00889403 0.999960i \(-0.502831\pi\)
0.983224 + 0.182400i \(0.0583867\pi\)
\(80\) 0 0
\(81\) −1606.13 + 6361.37i −0.244800 + 0.969574i
\(82\) 0 0
\(83\) −879.339 1047.96i −0.127644 0.152120i 0.698437 0.715671i \(-0.253879\pi\)
−0.826081 + 0.563551i \(0.809435\pi\)
\(84\) 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 −0.666232 0.745744i \(-0.732094\pi\)
0.312717 + 0.949846i \(0.398761\pi\)
\(90\) 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 −0.271046 0.962566i \(-0.587370\pi\)
−0.826359 + 0.563143i \(0.809592\pi\)
\(98\) 0 0
\(99\) 10406.7 3364.29i 1.06180 0.343260i
\(100\) 0 0
\(101\) 17983.3 3170.94i 1.76289 0.310846i 0.804005 0.594623i \(-0.202699\pi\)
0.958890 + 0.283777i \(0.0915876\pi\)
\(102\) 0 0
\(103\) 2539.01 924.124i 0.239326 0.0871075i −0.219573 0.975596i \(-0.570466\pi\)
0.458899 + 0.888489i \(0.348244\pi\)
\(104\) 0 0
\(105\) 24836.8 1718.25i 2.25277 0.155850i
\(106\) 0 0
\(107\) 6516.08i 0.569140i −0.958655 0.284570i \(-0.908149\pi\)
0.958655 0.284570i \(-0.0918508\pi\)
\(108\) 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 −0.890599 0.454790i \(-0.849714\pi\)
0.389905 0.920855i \(-0.372508\pi\)
\(114\) 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 0.999698 + 0.0245549i \(0.00781687\pi\)
−0.478584 + 0.878042i \(0.658850\pi\)
\(128\) 0 0
\(129\) −5272.33 5467.77i −0.316828 0.328572i
\(130\) 0 0
\(131\) −14033.3 2474.46i −0.817746 0.144191i −0.250899 0.968013i \(-0.580726\pi\)
−0.566848 + 0.823823i \(0.691837\pi\)
\(132\) 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 0.809703 + 0.586840i \(0.199628\pi\)
0.437321 + 0.899306i \(0.355927\pi\)
\(138\) 0 0
\(139\) −1462.43 + 8293.86i −0.0756913 + 0.429267i 0.923288 + 0.384107i \(0.125491\pi\)
−0.998980 + 0.0451595i \(0.985620\pi\)
\(140\) 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 −0.991369 0.131103i \(-0.958148\pi\)
0.301261 + 0.953542i \(0.402593\pi\)
\(150\) 0 0
\(151\) 7165.12 + 2607.89i 0.314246 + 0.114376i 0.494328 0.869275i \(-0.335414\pi\)
−0.180082 + 0.983652i \(0.557636\pi\)
\(152\) 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 0.363678 0.931525i \(-0.381521\pi\)
0.877366 + 0.479821i \(0.159299\pi\)
\(158\) 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 0.973576 0.228365i \(-0.0733380\pi\)
−0.892592 + 0.450864i \(0.851116\pi\)
\(168\) 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 0.604635 + 0.796503i \(0.293319\pi\)
−0.975159 + 0.221505i \(0.928903\pi\)
\(174\) 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 0.136989 0.990573i \(-0.456257\pi\)
−0.789366 + 0.613923i \(0.789591\pi\)
\(180\) 0 0
\(181\) −3335.92 5777.98i −0.101826 0.176368i 0.810611 0.585585i \(-0.199135\pi\)
−0.912437 + 0.409217i \(0.865802\pi\)
\(182\) 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 0.458168 0.888865i \(-0.348506\pi\)
−0.954922 + 0.296858i \(0.904061\pi\)
\(192\) 0 0
\(193\) 5929.51 33627.9i 0.159186 0.902788i −0.795673 0.605727i \(-0.792882\pi\)
0.954859 0.297061i \(-0.0960065\pi\)
\(194\) 0 0
\(195\) 57538.0 55481.4i 1.51316 1.45908i
\(196\) 0 0
\(197\) −4567.28 + 2636.92i −0.117686 + 0.0679461i −0.557688 0.830051i \(-0.688311\pi\)
0.440001 + 0.897997i \(0.354978\pi\)
\(198\) 0 0
\(199\) −24297.3 + 42084.1i −0.613553 + 1.06270i 0.377084 + 0.926179i \(0.376927\pi\)
−0.990637 + 0.136525i \(0.956407\pi\)
\(200\) 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 −0.494449 0.869207i \(-0.664630\pi\)
0.179946 + 0.983677i \(0.442408\pi\)
\(212\) 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 0.964983 0.262312i \(-0.0844851\pi\)
−0.996504 + 0.0835505i \(0.973374\pi\)
\(224\) 0 0
\(225\) −29296.0 6272.49i −0.578686 0.123901i
\(226\) 0 0
\(227\) 20863.3 57321.4i 0.404885 1.11241i −0.554960 0.831877i \(-0.687266\pi\)
0.959844 0.280534i \(-0.0905115\pi\)
\(228\) 0 0
\(229\) −45065.7 37814.6i −0.859361 0.721089i 0.102470 0.994736i \(-0.467326\pi\)
−0.961830 + 0.273647i \(0.911770\pi\)
\(230\) 0 0
\(231\) 86175.9 + 62708.2i 1.61496 + 1.17517i
\(232\) 0 0
\(233\) 25541.4 + 14746.3i 0.470470 + 0.271626i 0.716437 0.697652i \(-0.245772\pi\)
−0.245966 + 0.969278i \(0.579105\pi\)
\(234\) 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 −0.700432 0.713719i \(-0.747009\pi\)
−0.902297 + 0.431115i \(0.858120\pi\)
\(240\) 0 0
\(241\) 75263.3 63153.4i 1.29583 1.08733i 0.304985 0.952357i \(-0.401349\pi\)
0.990849 0.134976i \(-0.0430957\pi\)
\(242\) 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 0.144527 0.989501i \(-0.453834\pi\)
0.929196 + 0.369587i \(0.120501\pi\)
\(252\) 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 −0.424277 0.905533i \(-0.639472\pi\)
0.965450 + 0.260587i \(0.0839160\pi\)
\(258\) 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 0.108331 0.994115i \(-0.465449\pi\)
0.441805 + 0.897111i \(0.354338\pi\)
\(264\) 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 \(-0.940329\pi\)
0.982480 0.186367i \(-0.0596715\pi\)
\(270\) 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 0.970245 0.242126i \(-0.0778448\pi\)
−0.994544 + 0.104319i \(0.966734\pi\)
\(278\) 0 0
\(279\) −14778.3 + 7829.67i −0.189853 + 0.100585i
\(280\) 0 0
\(281\) −3060.57 + 8408.86i −0.0387606 + 0.106494i −0.957563 0.288224i \(-0.906935\pi\)
0.918803 + 0.394718i \(0.129158\pi\)
\(282\) 0 0
\(283\) 47874.3 + 40171.3i 0.597764 + 0.501584i 0.890726 0.454540i \(-0.150196\pi\)
−0.292962 + 0.956124i \(0.594641\pi\)
\(284\) 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 0.0617628 0.998091i \(-0.480328\pi\)
−0.283329 + 0.959023i \(0.591439\pi\)
\(294\) 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 0.156704 + 0.987646i \(0.449913\pi\)
−0.933678 + 0.358113i \(0.883420\pi\)
\(308\) 0 0
\(309\) 24182.5 + 2559.82i 0.253270 + 0.0268098i
\(310\) 0 0
\(311\) 76390.5 91038.6i 0.789802 0.941250i −0.209529 0.977802i \(-0.567193\pi\)
0.999332 + 0.0365526i \(0.0116377\pi\)
\(312\) 0 0
\(313\) −128096. 46623.1i −1.30752 0.475897i −0.408078 0.912947i \(-0.633801\pi\)
−0.899437 + 0.437050i \(0.856023\pi\)
\(314\) 0 0
\(315\) 207625. + 84244.5i 2.09247 + 0.849025i
\(316\) 0 0
\(317\) 2046.11 360.784i 0.0203615 0.00359028i −0.163458 0.986550i \(-0.552265\pi\)
0.183820 + 0.982960i \(0.441154\pi\)
\(318\) 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 −0.980039 0.198807i \(-0.936293\pi\)
0.852939 0.522010i \(-0.174818\pi\)
\(332\) 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 0.440105 0.897946i \(-0.354941\pi\)
−0.807881 + 0.589345i \(0.799386\pi\)
\(338\) 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 0.0746448 0.997210i \(-0.476218\pi\)
−0.270923 + 0.962601i \(0.587329\pi\)
\(348\) 0 0
\(349\) −124185. + 104204.i −1.01957 + 0.855524i −0.989574 0.144025i \(-0.953995\pi\)
−0.0300003 + 0.999550i \(0.509551\pi\)
\(350\) 0 0
\(351\) −96768.2 + 181022.i −0.785450 + 1.46932i
\(352\) 0 0
\(353\) 67927.0 + 80952.2i 0.545121 + 0.649650i 0.966328 0.257315i \(-0.0828378\pi\)
−0.421207 + 0.906965i \(0.638393\pi\)
\(354\) 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 −0.496266 0.868170i \(-0.665296\pi\)
0.503724 + 0.863864i \(0.331963\pi\)
\(360\) 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 0.0470672 0.998892i \(-0.485013\pi\)
−0.606020 + 0.795450i \(0.707235\pi\)
\(368\) 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 −0.252633 0.967562i \(-0.581297\pi\)
0.428409 + 0.903585i \(0.359074\pi\)
\(374\) 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 −0.896554 0.442934i \(-0.853937\pi\)
0.402087 0.915601i \(-0.368285\pi\)
\(384\) 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 −0.735519 0.677505i \(-0.763061\pi\)
0.998931 0.0462165i \(-0.0147164\pi\)
\(390\) 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 0.978301 + 0.207187i \(0.0664307\pi\)
−0.309722 + 0.950827i \(0.600236\pi\)
\(398\) 0 0
\(399\) 174245. 43306.8i 1.09449 0.272026i
\(400\) 0 0
\(401\) 18741.2 + 3304.59i 0.116549 + 0.0205508i 0.231619 0.972807i \(-0.425598\pi\)
−0.115069 + 0.993357i \(0.536709\pi\)
\(402\) 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 0.888685 + 0.458518i \(0.151619\pi\)
−0.991913 + 0.126918i \(0.959492\pi\)
\(410\) 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 −0.940882 0.338736i \(-0.890001\pi\)
0.496972 + 0.867767i \(0.334445\pi\)
\(420\) 0 0
\(421\) 203870. + 74202.8i 1.15024 + 0.418655i 0.845603 0.533812i \(-0.179241\pi\)
0.304641 + 0.952467i \(0.401463\pi\)
\(422\) 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 \(0.217850\pi\)
−0.774802 + 0.632204i \(0.782150\pi\)
\(432\) 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 0.379726 + 0.925099i \(0.376018\pi\)
−0.0404229 + 0.999183i \(0.512871\pi\)
\(440\) 0 0
\(441\) −363077. 227625.i −1.86690 1.17042i
\(442\) 0 0
\(443\) 31232.3 85809.9i 0.159146 0.437250i −0.834334 0.551260i \(-0.814147\pi\)
0.993480 + 0.114010i \(0.0363695\pi\)
\(444\) 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 0.208407 0.978042i \(-0.433172\pi\)
−0.742806 + 0.669507i \(0.766505\pi\)
\(450\) 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 −0.360437 0.932783i \(-0.617372\pi\)
0.856023 + 0.516938i \(0.172928\pi\)
\(458\) 0 0
\(459\) −78653.9 + 240251.i −0.373332 + 1.14036i
\(460\) 0 0
\(461\) −168200. 200453.i −0.791450 0.943213i 0.207940 0.978142i \(-0.433324\pi\)
−0.999390 + 0.0349284i \(0.988880\pi\)
\(462\) 0 0
\(463\) −26468.5 + 150110.i −0.123472 + 0.700242i 0.858732 + 0.512424i \(0.171253\pi\)
−0.982204 + 0.187818i \(0.939859\pi\)
\(464\) 0 0
\(465\) 56329.9 + 16197.6i 0.260515 + 0.0749107i
\(466\) 0 0
\(467\) −310052. + 179009.i −1.42168 + 0.820806i −0.996442 0.0842767i \(-0.973142\pi\)
−0.425235 + 0.905083i \(0.639809\pi\)
\(468\) 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 −0.486092 0.873908i \(-0.661578\pi\)
−0.157883 + 0.987458i \(0.550467\pi\)
\(480\) 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 0.961472 + 0.274903i \(0.0886457\pi\)
−0.559826 + 0.828610i \(0.689132\pi\)
\(492\) 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 0.0929533 0.995670i \(-0.470369\pi\)
−0.964403 + 0.264437i \(0.914814\pi\)
\(500\) 0 0
\(501\) −6256.14 + 59101.5i −0.0249248 + 0.235463i
\(502\) 0 0
\(503\) 176203. + 101731.i 0.696429 + 0.402083i 0.806016 0.591894i \(-0.201620\pi\)
−0.109587 + 0.993977i \(0.534953\pi\)
\(504\) 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 0.277597 0.960698i \(-0.410462\pi\)
−0.0677222 + 0.997704i \(0.521573\pi\)
\(510\) 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 −0.456603 0.889670i \(-0.650934\pi\)
0.542175 + 0.840265i \(0.317601\pi\)
\(522\) 0 0
\(523\) 25930.8 44913.4i 0.0948009 0.164200i −0.814725 0.579848i \(-0.803112\pi\)
0.909525 + 0.415648i \(0.136445\pi\)
\(524\) 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 −0.850282 0.526327i \(-0.823569\pi\)
0.618989 0.785399i \(-0.287542\pi\)
\(548\) 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 −0.156797 0.987631i \(-0.550117\pi\)
−0.933712 + 0.358026i \(0.883450\pi\)
\(558\) 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 −0.689203 0.724569i \(-0.742039\pi\)
−0.895456 + 0.445151i \(0.853150\pi\)
\(564\) 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 0.968209 + 0.250143i \(0.0804776\pi\)
0.0782149 + 0.996937i \(0.475078\pi\)
\(570\) 0 0
\(571\) 13409.5 76049.2i 0.0411284 0.233250i −0.957314 0.289051i \(-0.906660\pi\)
0.998442 + 0.0558010i \(0.0177712\pi\)
\(572\) 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 −0.715304 0.698813i \(-0.753712\pi\)
0.962842 + 0.270065i \(0.0870452\pi\)
\(578\) 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 −0.382793 0.923834i \(-0.625038\pi\)
−0.0437382 + 0.999043i \(0.513927\pi\)
\(588\) 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 \(0.0399170\pi\)
−0.992147 + 0.125075i \(0.960083\pi\)
\(594\) 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 −0.576585 0.817037i \(-0.695615\pi\)
−0.0834914 0.996508i \(-0.526607\pi\)
\(600\) 0 0
\(601\) 8308.99 + 47122.6i 0.0230038 + 0.130461i 0.994147 0.108036i \(-0.0344563\pi\)
−0.971143 + 0.238497i \(0.923345\pi\)
\(602\) 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 0.934188 + 0.356782i \(0.116126\pi\)
0.513582 + 0.858041i \(0.328318\pi\)
\(608\) 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 0.984383 + 0.176040i \(0.0563287\pi\)
−0.339737 + 0.940521i \(0.610338\pi\)
\(614\) 0 0
\(615\) 385553. + 399845.i 1.01937 + 1.05716i
\(616\) 0 0
\(617\) −15518.7 2736.36i −0.0407647 0.00718792i 0.153229 0.988191i \(-0.451033\pi\)
−0.193993 + 0.981003i \(0.562144\pi\)
\(618\) 0 0
\(619\) 534132. 448190.i 1.39402 1.16972i 0.430332 0.902671i \(-0.358396\pi\)
0.963683 0.267047i \(-0.0860480\pi\)
\(620\) 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 −0.979414 0.201860i \(-0.935302\pi\)
0.664523 + 0.747268i \(0.268635\pi\)
\(632\) 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 −0.0151950 0.999885i \(-0.504837\pi\)
0.327702 + 0.944781i \(0.393726\pi\)
\(642\) 0 0
\(643\) 508983. 185255.i 1.23107 0.448072i 0.357104 0.934065i \(-0.383764\pi\)
0.873963 + 0.485993i \(0.161542\pi\)
\(644\) 0 0
\(645\) −105184. + 215255.i −0.252832 + 0.517408i
\(646\) 0 0
\(647\) 667818.i 1.59533i 0.603102 + 0.797664i \(0.293931\pi\)
−0.603102 + 0.797664i \(0.706069\pi\)
\(648\) 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 0.996819 + 0.0796995i \(0.0253961\pi\)
−0.712378 + 0.701796i \(0.752382\pi\)
\(654\) 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 0.547749 + 0.836643i \(0.315485\pi\)
−0.957384 + 0.288819i \(0.906737\pi\)
\(660\) 0 0
\(661\) 432970. + 363305.i 0.990957 + 0.831512i 0.985706 0.168475i \(-0.0538841\pi\)
0.00525099 + 0.999986i \(0.498329\pi\)
\(662\) 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 −0.904030 0.427468i \(-0.859406\pi\)
0.263991 + 0.964525i \(0.414961\pi\)
\(674\) 0 0
\(675\) −212109. 166479.i −0.465534 0.365386i
\(676\) 0 0
\(677\) −241740. 288095.i −0.527438 0.628576i 0.434884 0.900486i \(-0.356789\pi\)
−0.962323 + 0.271910i \(0.912345\pi\)
\(678\) 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 −0.559531 0.828809i \(-0.689019\pi\)
0.438004 + 0.898973i \(0.355686\pi\)
\(684\) 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 0.684291 0.729209i \(-0.260112\pi\)
0.0554705 + 0.998460i \(0.482334\pi\)
\(692\) 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 \(0.431659\pi\)
−0.213055 + 0.977040i \(0.568341\pi\)
\(702\) 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 0.999959 0.00910028i \(-0.00289675\pi\)
−0.942766 + 0.333455i \(0.891786\pi\)
\(710\) 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 0.716370 0.697721i \(-0.245802\pi\)
−0.246059 + 0.969255i \(0.579136\pi\)
\(720\) 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 −0.313896 0.949458i \(-0.601634\pi\)
0.880526 + 0.473998i \(0.157190\pi\)
\(728\) 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 0.866592 + 0.499018i \(0.166306\pi\)
−0.985004 + 0.172532i \(0.944805\pi\)
\(734\) 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 −0.999964 0.00851547i \(-0.997289\pi\)
0.507356 + 0.861736i \(0.330623\pi\)
\(740\) 0 0
\(741\) 339168. 466097.i 0.617701 0.848867i
\(742\) 0 0
\(743\) 569499. 678702.i 1.03161 1.22942i 0.0586901 0.998276i \(-0.481308\pi\)
0.972919 0.231147i \(-0.0742479\pi\)
\(744\) 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 −0.610976 0.791649i \(-0.709223\pi\)
0.0408271 + 0.999166i \(0.487001\pi\)
\(752\) 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 −0.976594 0.215093i \(-0.930995\pi\)
0.609855 0.792513i \(-0.291228\pi\)
\(762\) 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 0.858040 0.513583i \(-0.171682\pi\)
−0.356783 + 0.934187i \(0.616127\pi\)
\(770\) 0 0
\(771\) 457353. 203220.i 0.769383 0.341868i
\(772\) 0 0
\(773\) −599094. 345887.i −1.00262 0.578862i −0.0935968 0.995610i \(-0.529836\pi\)
−0.909022 + 0.416748i \(0.863170\pi\)
\(774\) 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
\(782\)