Properties

Label 108.5.k.a.29.2
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 29.2
Character \(\chi\) \(=\) 108.29
Dual form 108.5.k.a.41.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-8.23149 + 3.63904i) q^{3} +(18.1168 + 21.5908i) q^{5} +(22.9581 - 8.35608i) q^{7} +(54.5147 - 59.9095i) q^{9} +O(q^{10})\) \(q+(-8.23149 + 3.63904i) q^{3} +(18.1168 + 21.5908i) q^{5} +(22.9581 - 8.35608i) q^{7} +(54.5147 - 59.9095i) q^{9} +(-73.4456 + 87.5290i) q^{11} +(-0.427402 - 2.42392i) q^{13} +(-227.698 - 111.797i) q^{15} +(-208.105 + 120.150i) q^{17} +(-246.932 + 427.698i) q^{19} +(-158.572 + 152.329i) q^{21} +(-179.414 + 492.937i) q^{23} +(-29.4131 + 166.810i) q^{25} +(-230.724 + 691.525i) q^{27} +(-95.9782 - 16.9236i) q^{29} +(-1499.65 - 545.827i) q^{31} +(286.044 - 987.765i) q^{33} +(596.344 + 344.299i) q^{35} +(414.251 + 717.504i) q^{37} +(12.3389 + 18.3971i) q^{39} +(2401.19 - 423.394i) q^{41} +(-1294.95 - 1086.59i) q^{43} +(2281.13 + 91.6475i) q^{45} +(-379.164 - 1041.74i) q^{47} +(-1382.02 + 1159.65i) q^{49} +(1275.79 - 1746.31i) q^{51} +3880.06i q^{53} -3220.42 q^{55} +(476.203 - 4419.19i) q^{57} +(2429.52 + 2895.39i) q^{59} +(1823.41 - 663.667i) q^{61} +(750.949 - 1830.94i) q^{63} +(44.5912 - 53.1417i) q^{65} +(-145.480 - 825.059i) q^{67} +(-316.971 - 4710.50i) q^{69} +(1966.62 - 1135.43i) q^{71} +(2940.78 - 5093.57i) q^{73} +(-364.915 - 1480.13i) q^{75} +(-954.774 + 2623.22i) q^{77} +(-988.613 + 5606.70i) q^{79} +(-617.285 - 6531.90i) q^{81} +(7283.42 + 1284.26i) q^{83} +(-6364.34 - 2316.43i) q^{85} +(851.629 - 209.963i) q^{87} +(10189.8 + 5883.10i) q^{89} +(-30.0668 - 52.0773i) q^{91} +(14330.6 - 964.312i) q^{93} +(-13708.0 + 2417.09i) q^{95} +(2197.40 + 1843.84i) q^{97} +(1239.95 + 9171.70i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q + 9q^{5} - 102q^{9} + O(q^{10}) \) \( 72q + 9q^{5} - 102q^{9} + 18q^{11} - 225q^{15} - 282q^{21} - 1278q^{23} + 441q^{25} + 54q^{27} + 1854q^{29} - 1665q^{31} - 45q^{33} - 2673q^{35} + 6951q^{39} - 5472q^{41} + 1260q^{43} + 5553q^{45} + 5103q^{47} - 5904q^{49} + 1899q^{51} + 1107q^{57} - 10944q^{59} + 8352q^{61} - 11985q^{63} + 8757q^{65} + 378q^{67} + 5607q^{69} - 19764q^{71} + 6111q^{73} - 3453q^{75} - 5679q^{77} - 5652q^{79} - 20466q^{81} - 20061q^{83} + 26100q^{85} + 40545q^{87} + 15633q^{89} - 6039q^{91} + 40179q^{93} + 48024q^{95} - 37530q^{97} + 12177q^{99} + O(q^{100}) \)

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
\(3\) −8.23149 + 3.63904i −0.914610 + 0.404338i
\(4\) 0 0
\(5\) 18.1168 + 21.5908i 0.724674 + 0.863632i 0.995076 0.0991149i \(-0.0316011\pi\)
−0.270402 + 0.962747i \(0.587157\pi\)
\(6\) 0 0
\(7\) 22.9581 8.35608i 0.468534 0.170532i −0.0969544 0.995289i \(-0.530910\pi\)
0.565488 + 0.824757i \(0.308688\pi\)
\(8\) 0 0
\(9\) 54.5147 59.9095i 0.673022 0.739623i
\(10\) 0 0
\(11\) −73.4456 + 87.5290i −0.606988 + 0.723380i −0.978775 0.204938i \(-0.934301\pi\)
0.371787 + 0.928318i \(0.378745\pi\)
\(12\) 0 0
\(13\) −0.427402 2.42392i −0.00252901 0.0143427i 0.983517 0.180815i \(-0.0578735\pi\)
−0.986046 + 0.166472i \(0.946762\pi\)
\(14\) 0 0
\(15\) −227.698 111.797i −1.01199 0.496873i
\(16\) 0 0
\(17\) −208.105 + 120.150i −0.720088 + 0.415743i −0.814785 0.579763i \(-0.803145\pi\)
0.0946973 + 0.995506i \(0.469812\pi\)
\(18\) 0 0
\(19\) −246.932 + 427.698i −0.684021 + 1.18476i 0.289722 + 0.957111i \(0.406437\pi\)
−0.973743 + 0.227649i \(0.926896\pi\)
\(20\) 0 0
\(21\) −158.572 + 152.329i −0.359573 + 0.345416i
\(22\) 0 0
\(23\) −179.414 + 492.937i −0.339158 + 0.931828i 0.646477 + 0.762934i \(0.276242\pi\)
−0.985634 + 0.168894i \(0.945980\pi\)
\(24\) 0 0
\(25\) −29.4131 + 166.810i −0.0470609 + 0.266896i
\(26\) 0 0
\(27\) −230.724 + 691.525i −0.316494 + 0.948594i
\(28\) 0 0
\(29\) −95.9782 16.9236i −0.114124 0.0201231i 0.116294 0.993215i \(-0.462898\pi\)
−0.230418 + 0.973092i \(0.574009\pi\)
\(30\) 0 0
\(31\) −1499.65 545.827i −1.56051 0.567978i −0.589654 0.807656i \(-0.700736\pi\)
−0.970852 + 0.239679i \(0.922958\pi\)
\(32\) 0 0
\(33\) 286.044 987.765i 0.262667 0.907039i
\(34\) 0 0
\(35\) 596.344 + 344.299i 0.486811 + 0.281061i
\(36\) 0 0
\(37\) 414.251 + 717.504i 0.302594 + 0.524108i 0.976723 0.214506i \(-0.0688141\pi\)
−0.674129 + 0.738614i \(0.735481\pi\)
\(38\) 0 0
\(39\) 12.3389 + 18.3971i 0.00811236 + 0.0120954i
\(40\) 0 0
\(41\) 2401.19 423.394i 1.42843 0.251870i 0.594656 0.803980i \(-0.297288\pi\)
0.833772 + 0.552110i \(0.186177\pi\)
\(42\) 0 0
\(43\) −1294.95 1086.59i −0.700351 0.587664i 0.221523 0.975155i \(-0.428897\pi\)
−0.921873 + 0.387491i \(0.873342\pi\)
\(44\) 0 0
\(45\) 2281.13 + 91.6475i 1.12648 + 0.0452580i
\(46\) 0 0
\(47\) −379.164 1041.74i −0.171645 0.471591i 0.823805 0.566873i \(-0.191847\pi\)
−0.995450 + 0.0952820i \(0.969625\pi\)
\(48\) 0 0
\(49\) −1382.02 + 1159.65i −0.575602 + 0.482987i
\(50\) 0 0
\(51\) 1275.79 1746.31i 0.490498 0.671401i
\(52\) 0 0
\(53\) 3880.06i 1.38130i 0.723191 + 0.690648i \(0.242675\pi\)
−0.723191 + 0.690648i \(0.757325\pi\)
\(54\) 0 0
\(55\) −3220.42 −1.06460
\(56\) 0 0
\(57\) 476.203 4419.19i 0.146569 1.36017i
\(58\) 0 0
\(59\) 2429.52 + 2895.39i 0.697939 + 0.831771i 0.992291 0.123926i \(-0.0395485\pi\)
−0.294353 + 0.955697i \(0.595104\pi\)
\(60\) 0 0
\(61\) 1823.41 663.667i 0.490032 0.178357i −0.0851732 0.996366i \(-0.527144\pi\)
0.575205 + 0.818009i \(0.304922\pi\)
\(62\) 0 0
\(63\) 750.949 1830.94i 0.189204 0.461310i
\(64\) 0 0
\(65\) 44.5912 53.1417i 0.0105541 0.0125779i
\(66\) 0 0
\(67\) −145.480 825.059i −0.0324082 0.183796i 0.964307 0.264788i \(-0.0853021\pi\)
−0.996715 + 0.0809926i \(0.974191\pi\)
\(68\) 0 0
\(69\) −316.971 4710.50i −0.0665766 0.989393i
\(70\) 0 0
\(71\) 1966.62 1135.43i 0.390126 0.225239i −0.292089 0.956391i \(-0.594350\pi\)
0.682215 + 0.731152i \(0.261017\pi\)
\(72\) 0 0
\(73\) 2940.78 5093.57i 0.551844 0.955822i −0.446298 0.894885i \(-0.647258\pi\)
0.998142 0.0609373i \(-0.0194090\pi\)
\(74\) 0 0
\(75\) −364.915 1480.13i −0.0648737 0.263134i
\(76\) 0 0
\(77\) −954.774 + 2623.22i −0.161035 + 0.442439i
\(78\) 0 0
\(79\) −988.613 + 5606.70i −0.158406 + 0.898366i 0.797199 + 0.603717i \(0.206314\pi\)
−0.955605 + 0.294650i \(0.904797\pi\)
\(80\) 0 0
\(81\) −617.285 6531.90i −0.0940840 0.995564i
\(82\) 0 0
\(83\) 7283.42 + 1284.26i 1.05725 + 0.186422i 0.675137 0.737692i \(-0.264084\pi\)
0.382116 + 0.924114i \(0.375196\pi\)
\(84\) 0 0
\(85\) −6364.34 2316.43i −0.880877 0.320613i
\(86\) 0 0
\(87\) 851.629 209.963i 0.112515 0.0277398i
\(88\) 0 0
\(89\) 10189.8 + 5883.10i 1.28643 + 0.742722i 0.978016 0.208530i \(-0.0668678\pi\)
0.308416 + 0.951252i \(0.400201\pi\)
\(90\) 0 0
\(91\) −30.0668 52.0773i −0.00363082 0.00628877i
\(92\) 0 0
\(93\) 14330.6 964.312i 1.65691 0.111494i
\(94\) 0 0
\(95\) −13708.0 + 2417.09i −1.51889 + 0.267821i
\(96\) 0 0
\(97\) 2197.40 + 1843.84i 0.233542 + 0.195965i 0.752047 0.659110i \(-0.229067\pi\)
−0.518505 + 0.855075i \(0.673511\pi\)
\(98\) 0 0
\(99\) 1239.95 + 9171.70i 0.126513 + 0.935793i
\(100\) 0 0
\(101\) 573.994 + 1577.03i 0.0562684 + 0.154596i 0.964642 0.263563i \(-0.0848977\pi\)
−0.908374 + 0.418159i \(0.862675\pi\)
\(102\) 0 0
\(103\) −11083.9 + 9300.48i −1.04476 + 0.876659i −0.992533 0.121976i \(-0.961077\pi\)
−0.0522289 + 0.998635i \(0.516633\pi\)
\(104\) 0 0
\(105\) −6161.71 663.974i −0.558886 0.0602244i
\(106\) 0 0
\(107\) 6102.13i 0.532983i −0.963837 0.266492i \(-0.914136\pi\)
0.963837 0.266492i \(-0.0858645\pi\)
\(108\) 0 0
\(109\) −19211.9 −1.61703 −0.808513 0.588479i \(-0.799727\pi\)
−0.808513 + 0.588479i \(0.799727\pi\)
\(110\) 0 0
\(111\) −6020.93 4398.65i −0.488672 0.357004i
\(112\) 0 0
\(113\) 176.048 + 209.806i 0.0137871 + 0.0164309i 0.772894 0.634535i \(-0.218808\pi\)
−0.759107 + 0.650966i \(0.774364\pi\)
\(114\) 0 0
\(115\) −13893.3 + 5056.76i −1.05054 + 0.382364i
\(116\) 0 0
\(117\) −168.515 106.534i −0.0123103 0.00778244i
\(118\) 0 0
\(119\) −3773.73 + 4497.36i −0.266488 + 0.317588i
\(120\) 0 0
\(121\) 275.306 + 1561.34i 0.0188037 + 0.106641i
\(122\) 0 0
\(123\) −18224.6 + 12223.2i −1.20461 + 0.807931i
\(124\) 0 0
\(125\) 11121.0 6420.74i 0.711747 0.410927i
\(126\) 0 0
\(127\) 14641.1 25359.1i 0.907749 1.57227i 0.0905660 0.995890i \(-0.471132\pi\)
0.817183 0.576378i \(-0.195534\pi\)
\(128\) 0 0
\(129\) 14613.5 + 4231.88i 0.878162 + 0.254305i
\(130\) 0 0
\(131\) −8692.53 + 23882.5i −0.506528 + 1.39167i 0.378268 + 0.925696i \(0.376520\pi\)
−0.884796 + 0.465979i \(0.845702\pi\)
\(132\) 0 0
\(133\) −2095.21 + 11882.5i −0.118447 + 0.671747i
\(134\) 0 0
\(135\) −19110.6 + 7546.73i −1.04859 + 0.414087i
\(136\) 0 0
\(137\) −12879.6 2271.01i −0.686214 0.120998i −0.180339 0.983605i \(-0.557719\pi\)
−0.505875 + 0.862607i \(0.668830\pi\)
\(138\) 0 0
\(139\) 8423.60 + 3065.94i 0.435982 + 0.158684i 0.550681 0.834716i \(-0.314368\pi\)
−0.114699 + 0.993400i \(0.536590\pi\)
\(140\) 0 0
\(141\) 6912.04 + 7195.31i 0.347670 + 0.361919i
\(142\) 0 0
\(143\) 243.554 + 140.616i 0.0119103 + 0.00687642i
\(144\) 0 0
\(145\) −1373.43 2378.85i −0.0653236 0.113144i
\(146\) 0 0
\(147\) 7156.06 14574.9i 0.331161 0.674483i
\(148\) 0 0
\(149\) 2532.71 446.586i 0.114081 0.0201156i −0.116316 0.993212i \(-0.537109\pi\)
0.230397 + 0.973097i \(0.425997\pi\)
\(150\) 0 0
\(151\) 27267.3 + 22880.0i 1.19588 + 1.00347i 0.999738 + 0.0228908i \(0.00728701\pi\)
0.196146 + 0.980575i \(0.437157\pi\)
\(152\) 0 0
\(153\) −4146.71 + 19017.4i −0.177142 + 0.812397i
\(154\) 0 0
\(155\) −15384.0 42267.2i −0.640334 1.75930i
\(156\) 0 0
\(157\) 6637.42 5569.46i 0.269277 0.225951i −0.498143 0.867095i \(-0.665984\pi\)
0.767420 + 0.641144i \(0.221540\pi\)
\(158\) 0 0
\(159\) −14119.7 31938.7i −0.558511 1.26335i
\(160\) 0 0
\(161\) 12816.1i 0.494430i
\(162\) 0 0
\(163\) 44505.1 1.67508 0.837538 0.546380i \(-0.183994\pi\)
0.837538 + 0.546380i \(0.183994\pi\)
\(164\) 0 0
\(165\) 26508.9 11719.3i 0.973696 0.430459i
\(166\) 0 0
\(167\) −20696.9 24665.6i −0.742116 0.884420i 0.254461 0.967083i \(-0.418102\pi\)
−0.996578 + 0.0826633i \(0.973657\pi\)
\(168\) 0 0
\(169\) 26832.9 9766.37i 0.939493 0.341948i
\(170\) 0 0
\(171\) 12161.7 + 38109.4i 0.415914 + 1.30329i
\(172\) 0 0
\(173\) 19826.3 23628.1i 0.662445 0.789472i −0.325289 0.945615i \(-0.605462\pi\)
0.987734 + 0.156143i \(0.0499060\pi\)
\(174\) 0 0
\(175\) 718.607 + 4075.42i 0.0234647 + 0.133075i
\(176\) 0 0
\(177\) −30535.1 14992.3i −0.974658 0.478543i
\(178\) 0 0
\(179\) 26159.6 15103.2i 0.816441 0.471372i −0.0327469 0.999464i \(-0.510426\pi\)
0.849187 + 0.528091i \(0.177092\pi\)
\(180\) 0 0
\(181\) 26379.0 45689.8i 0.805196 1.39464i −0.110963 0.993824i \(-0.535394\pi\)
0.916159 0.400815i \(-0.131273\pi\)
\(182\) 0 0
\(183\) −12594.3 + 12098.4i −0.376072 + 0.361266i
\(184\) 0 0
\(185\) −7986.57 + 21942.9i −0.233355 + 0.641137i
\(186\) 0 0
\(187\) 4767.83 27039.7i 0.136344 0.773248i
\(188\) 0 0
\(189\) 481.439 + 17804.1i 0.0134777 + 0.498421i
\(190\) 0 0
\(191\) −43117.1 7602.71i −1.18191 0.208402i −0.452043 0.891996i \(-0.649305\pi\)
−0.729862 + 0.683594i \(0.760416\pi\)
\(192\) 0 0
\(193\) −65952.9 24004.9i −1.77060 0.644444i −0.999974 0.00715076i \(-0.997724\pi\)
−0.770621 0.637293i \(-0.780054\pi\)
\(194\) 0 0
\(195\) −173.667 + 599.705i −0.00456718 + 0.0157713i
\(196\) 0 0
\(197\) 24057.2 + 13889.5i 0.619888 + 0.357893i 0.776825 0.629716i \(-0.216829\pi\)
−0.156937 + 0.987609i \(0.550162\pi\)
\(198\) 0 0
\(199\) 15512.8 + 26868.9i 0.391727 + 0.678491i 0.992677 0.120795i \(-0.0385445\pi\)
−0.600951 + 0.799286i \(0.705211\pi\)
\(200\) 0 0
\(201\) 4199.94 + 6262.05i 0.103956 + 0.154998i
\(202\) 0 0
\(203\) −2344.90 + 413.469i −0.0569025 + 0.0100335i
\(204\) 0 0
\(205\) 52643.4 + 44173.0i 1.25267 + 1.05111i
\(206\) 0 0
\(207\) 19750.9 + 37620.9i 0.460941 + 0.877989i
\(208\) 0 0
\(209\) −19300.0 53026.2i −0.441839 1.21394i
\(210\) 0 0
\(211\) −19010.7 + 15951.9i −0.427005 + 0.358300i −0.830820 0.556541i \(-0.812128\pi\)
0.403815 + 0.914841i \(0.367684\pi\)
\(212\) 0 0
\(213\) −12056.4 + 16502.9i −0.265740 + 0.363749i
\(214\) 0 0
\(215\) 47644.6i 1.03071i
\(216\) 0 0
\(217\) −38990.1 −0.828008
\(218\) 0 0
\(219\) −5671.23 + 52629.3i −0.118247 + 1.09734i
\(220\) 0 0
\(221\) 380.178 + 453.078i 0.00778399 + 0.00927659i
\(222\) 0 0
\(223\) 74226.5 27016.2i 1.49262 0.543269i 0.538482 0.842637i \(-0.318998\pi\)
0.954138 + 0.299368i \(0.0967760\pi\)
\(224\) 0 0
\(225\) 8390.04 + 10855.7i 0.165729 + 0.214434i
\(226\) 0 0
\(227\) 48220.6 57467.1i 0.935795 1.11524i −0.0573506 0.998354i \(-0.518265\pi\)
0.993146 0.116883i \(-0.0372903\pi\)
\(228\) 0 0
\(229\) −2505.13 14207.3i −0.0477705 0.270920i 0.951562 0.307458i \(-0.0994782\pi\)
−0.999332 + 0.0365377i \(0.988367\pi\)
\(230\) 0 0
\(231\) −1686.80 25067.5i −0.0316111 0.469771i
\(232\) 0 0
\(233\) −21793.0 + 12582.2i −0.401425 + 0.231763i −0.687099 0.726564i \(-0.741116\pi\)
0.285674 + 0.958327i \(0.407783\pi\)
\(234\) 0 0
\(235\) 15622.9 27059.6i 0.282895 0.489988i
\(236\) 0 0
\(237\) −12265.3 49749.1i −0.218364 0.885704i
\(238\) 0 0
\(239\) −12305.3 + 33808.6i −0.215425 + 0.591876i −0.999589 0.0286783i \(-0.990870\pi\)
0.784163 + 0.620554i \(0.213092\pi\)
\(240\) 0 0
\(241\) −11393.0 + 64612.9i −0.196157 + 1.11246i 0.714605 + 0.699529i \(0.246607\pi\)
−0.910762 + 0.412933i \(0.864504\pi\)
\(242\) 0 0
\(243\) 28851.0 + 51520.9i 0.488595 + 0.872511i
\(244\) 0 0
\(245\) −50075.7 8829.70i −0.834247 0.147100i
\(246\) 0 0
\(247\) 1142.24 + 415.743i 0.0187226 + 0.00681445i
\(248\) 0 0
\(249\) −64626.8 + 15933.3i −1.04235 + 0.256984i
\(250\) 0 0
\(251\) 35938.0 + 20748.8i 0.570435 + 0.329341i 0.757323 0.653040i \(-0.226507\pi\)
−0.186888 + 0.982381i \(0.559840\pi\)
\(252\) 0 0
\(253\) −29969.1 51908.0i −0.468201 0.810948i
\(254\) 0 0
\(255\) 60817.6 4092.44i 0.935295 0.0629364i
\(256\) 0 0
\(257\) −67142.0 + 11838.9i −1.01655 + 0.179245i −0.657007 0.753884i \(-0.728178\pi\)
−0.359541 + 0.933129i \(0.617067\pi\)
\(258\) 0 0
\(259\) 15506.0 + 13011.0i 0.231153 + 0.193960i
\(260\) 0 0
\(261\) −6246.11 + 4827.42i −0.0916914 + 0.0708654i
\(262\) 0 0
\(263\) −10711.9 29430.8i −0.154866 0.425492i 0.837860 0.545885i \(-0.183807\pi\)
−0.992726 + 0.120394i \(0.961584\pi\)
\(264\) 0 0
\(265\) −83773.7 + 70294.5i −1.19293 + 1.00099i
\(266\) 0 0
\(267\) −105286. 11345.4i −1.47689 0.159147i
\(268\) 0 0
\(269\) 136677.i 1.88882i 0.328766 + 0.944411i \(0.393367\pi\)
−0.328766 + 0.944411i \(0.606633\pi\)
\(270\) 0 0
\(271\) 122527. 1.66837 0.834187 0.551481i \(-0.185937\pi\)
0.834187 + 0.551481i \(0.185937\pi\)
\(272\) 0 0
\(273\) 437.006 + 319.259i 0.00586357 + 0.00428369i
\(274\) 0 0
\(275\) −12440.4 14825.9i −0.164502 0.196046i
\(276\) 0 0
\(277\) −39521.0 + 14384.5i −0.515073 + 0.187471i −0.586461 0.809978i \(-0.699479\pi\)
0.0713884 + 0.997449i \(0.477257\pi\)
\(278\) 0 0
\(279\) −114453. + 60087.4i −1.47034 + 0.771925i
\(280\) 0 0
\(281\) −36512.2 + 43513.5i −0.462408 + 0.551076i −0.945979 0.324229i \(-0.894895\pi\)
0.483571 + 0.875305i \(0.339340\pi\)
\(282\) 0 0
\(283\) 1441.88 + 8177.30i 0.0180035 + 0.102103i 0.992485 0.122363i \(-0.0390473\pi\)
−0.974482 + 0.224466i \(0.927936\pi\)
\(284\) 0 0
\(285\) 104041. 69780.1i 1.28090 0.859096i
\(286\) 0 0
\(287\) 51588.9 29784.9i 0.626314 0.361603i
\(288\) 0 0
\(289\) −12888.6 + 22323.7i −0.154316 + 0.267283i
\(290\) 0 0
\(291\) −24797.7 7181.09i −0.292836 0.0848017i
\(292\) 0 0
\(293\) −51954.9 + 142745.i −0.605189 + 1.66274i 0.135404 + 0.990791i \(0.456767\pi\)
−0.740593 + 0.671954i \(0.765455\pi\)
\(294\) 0 0
\(295\) −18498.6 + 104911.i −0.212567 + 1.20553i
\(296\) 0 0
\(297\) −43582.8 70984.5i −0.494086 0.804731i
\(298\) 0 0
\(299\) 1271.52 + 224.203i 0.0142227 + 0.00250784i
\(300\) 0 0
\(301\) −38809.2 14125.4i −0.428353 0.155908i
\(302\) 0 0
\(303\) −10463.7 10892.5i −0.113973 0.118644i
\(304\) 0 0
\(305\) 47363.5 + 27345.3i 0.509148 + 0.293957i
\(306\) 0 0
\(307\) −90294.2 156394.i −0.958039 1.65937i −0.727255 0.686367i \(-0.759204\pi\)
−0.230783 0.973005i \(-0.574129\pi\)
\(308\) 0 0
\(309\) 57392.0 116891.i 0.601083 1.22424i
\(310\) 0 0
\(311\) 71897.1 12677.4i 0.743345 0.131072i 0.210866 0.977515i \(-0.432372\pi\)
0.532479 + 0.846443i \(0.321260\pi\)
\(312\) 0 0
\(313\) −74410.2 62437.5i −0.759528 0.637319i 0.178476 0.983944i \(-0.442883\pi\)
−0.938004 + 0.346625i \(0.887328\pi\)
\(314\) 0 0
\(315\) 53136.3 16957.2i 0.535513 0.170897i
\(316\) 0 0
\(317\) 27314.7 + 75046.5i 0.271818 + 0.746813i 0.998225 + 0.0595488i \(0.0189662\pi\)
−0.726408 + 0.687264i \(0.758812\pi\)
\(318\) 0 0
\(319\) 8530.48 7157.92i 0.0838286 0.0703405i
\(320\) 0 0
\(321\) 22205.9 + 50229.6i 0.215505 + 0.487472i
\(322\) 0 0
\(323\) 118675.i 1.13751i
\(324\) 0 0
\(325\) 416.905 0.00394703
\(326\) 0 0
\(327\) 158142. 69912.8i 1.47895 0.653825i
\(328\) 0 0
\(329\) −17409.8 20748.2i −0.160843 0.191685i
\(330\) 0 0
\(331\) −51094.6 + 18596.9i −0.466357 + 0.169740i −0.564502 0.825432i \(-0.690932\pi\)
0.0981442 + 0.995172i \(0.468709\pi\)
\(332\) 0 0
\(333\) 65568.0 + 14297.0i 0.591294 + 0.128931i
\(334\) 0 0
\(335\) 15178.1 18088.5i 0.135247 0.161181i
\(336\) 0 0
\(337\) 3454.56 + 19591.8i 0.0304181 + 0.172510i 0.996232 0.0867260i \(-0.0276405\pi\)
−0.965814 + 0.259236i \(0.916529\pi\)
\(338\) 0 0
\(339\) −2212.63 1086.37i −0.0192535 0.00945317i
\(340\) 0 0
\(341\) 157918. 91174.0i 1.35807 0.784083i
\(342\) 0 0
\(343\) −51368.5 + 88972.9i −0.436625 + 0.756257i
\(344\) 0 0
\(345\) 95961.0 92183.1i 0.806226 0.774485i
\(346\) 0 0
\(347\) −19743.2 + 54243.9i −0.163967 + 0.450497i −0.994280 0.106801i \(-0.965939\pi\)
0.830313 + 0.557297i \(0.188162\pi\)
\(348\) 0 0
\(349\) 4802.56 27236.6i 0.0394295 0.223616i −0.958725 0.284333i \(-0.908228\pi\)
0.998155 + 0.0607175i \(0.0193389\pi\)
\(350\) 0 0
\(351\) 1774.81 + 263.698i 0.0144058 + 0.00214039i
\(352\) 0 0
\(353\) 163139. + 28765.8i 1.30921 + 0.230848i 0.784337 0.620334i \(-0.213003\pi\)
0.524869 + 0.851183i \(0.324114\pi\)
\(354\) 0 0
\(355\) 60143.9 + 21890.6i 0.477238 + 0.173700i
\(356\) 0 0
\(357\) 14697.3 50752.7i 0.115319 0.398220i
\(358\) 0 0
\(359\) 20895.8 + 12064.2i 0.162133 + 0.0936074i 0.578871 0.815419i \(-0.303493\pi\)
−0.416738 + 0.909027i \(0.636827\pi\)
\(360\) 0 0
\(361\) −56789.9 98363.1i −0.435770 0.754775i
\(362\) 0 0
\(363\) −7947.94 11850.3i −0.0603172 0.0899321i
\(364\) 0 0
\(365\) 163252. 28785.7i 1.22539 0.216069i
\(366\) 0 0
\(367\) 7464.93 + 6263.82i 0.0554235 + 0.0465058i 0.670079 0.742290i \(-0.266260\pi\)
−0.614655 + 0.788796i \(0.710705\pi\)
\(368\) 0 0
\(369\) 105535. 166935.i 0.775074 1.22601i
\(370\) 0 0
\(371\) 32422.1 + 89079.0i 0.235556 + 0.647184i
\(372\) 0 0
\(373\) 19173.2 16088.2i 0.137809 0.115635i −0.571278 0.820757i \(-0.693552\pi\)
0.709086 + 0.705122i \(0.249108\pi\)
\(374\) 0 0
\(375\) −68177.4 + 93322.1i −0.484817 + 0.663624i
\(376\) 0 0
\(377\) 239.877i 0.00168774i
\(378\) 0 0
\(379\) −57436.8 −0.399863 −0.199932 0.979810i \(-0.564072\pi\)
−0.199932 + 0.979810i \(0.564072\pi\)
\(380\) 0 0
\(381\) −28235.1 + 262023.i −0.194509 + 1.80505i
\(382\) 0 0
\(383\) −82991.0 98904.8i −0.565762 0.674249i 0.404994 0.914319i \(-0.367274\pi\)
−0.970755 + 0.240071i \(0.922829\pi\)
\(384\) 0 0
\(385\) −73935.0 + 26910.1i −0.498802 + 0.181549i
\(386\) 0 0
\(387\) −135691. + 18344.4i −0.906001 + 0.122485i
\(388\) 0 0
\(389\) 24505.0 29203.9i 0.161941 0.192993i −0.678972 0.734164i \(-0.737574\pi\)
0.840913 + 0.541171i \(0.182019\pi\)
\(390\) 0 0
\(391\) −21889.1 124139.i −0.143177 0.812000i
\(392\) 0 0
\(393\) −15357.1 228221.i −0.0994315 1.47765i
\(394\) 0 0
\(395\) −138964. + 80230.8i −0.890651 + 0.514218i
\(396\) 0 0
\(397\) 5111.47 8853.33i 0.0324313 0.0561727i −0.849354 0.527823i \(-0.823008\pi\)
0.881786 + 0.471651i \(0.156342\pi\)
\(398\) 0 0
\(399\) −25994.3 105435.i −0.163280 0.662279i
\(400\) 0 0
\(401\) −92985.8 + 255477.i −0.578267 + 1.58877i 0.212834 + 0.977088i \(0.431731\pi\)
−0.791101 + 0.611686i \(0.790492\pi\)
\(402\) 0 0
\(403\) −682.087 + 3868.31i −0.00419981 + 0.0238183i
\(404\) 0 0
\(405\) 129846. 131665.i 0.791621 0.802713i
\(406\) 0 0
\(407\) −93227.3 16438.5i −0.562800 0.0992368i
\(408\) 0 0
\(409\) −236318. 86012.7i −1.41270 0.514181i −0.480779 0.876842i \(-0.659646\pi\)
−0.931921 + 0.362661i \(0.881868\pi\)
\(410\) 0 0
\(411\) 114282. 28175.4i 0.676542 0.166796i
\(412\) 0 0
\(413\) 79971.5 + 46171.6i 0.468851 + 0.270692i
\(414\) 0 0
\(415\) 104224. + 180522.i 0.605163 + 1.04817i
\(416\) 0 0
\(417\) −80495.9 + 5416.60i −0.462915 + 0.0311497i
\(418\) 0 0
\(419\) 226077. 39863.4i 1.28774 0.227063i 0.512476 0.858702i \(-0.328728\pi\)
0.775263 + 0.631638i \(0.217617\pi\)
\(420\) 0 0
\(421\) 34300.2 + 28781.3i 0.193523 + 0.162385i 0.734401 0.678716i \(-0.237463\pi\)
−0.540878 + 0.841101i \(0.681908\pi\)
\(422\) 0 0
\(423\) −83080.4 34074.9i −0.464320 0.190438i
\(424\) 0 0
\(425\) −13921.1 38248.0i −0.0770720 0.211754i
\(426\) 0 0
\(427\) 36316.4 30473.1i 0.199181 0.167133i
\(428\) 0 0
\(429\) −2516.52 271.175i −0.0136737 0.00147345i
\(430\) 0 0
\(431\) 128951.i 0.694176i 0.937833 + 0.347088i \(0.112830\pi\)
−0.937833 + 0.347088i \(0.887170\pi\)
\(432\) 0 0
\(433\) 68399.9 0.364821 0.182410 0.983222i \(-0.441610\pi\)
0.182410 + 0.983222i \(0.441610\pi\)
\(434\) 0 0
\(435\) 19962.1 + 14583.5i 0.105494 + 0.0770696i
\(436\) 0 0
\(437\) −166525. 198457.i −0.872001 1.03921i
\(438\) 0 0
\(439\) 6048.33 2201.41i 0.0313839 0.0114228i −0.326281 0.945273i \(-0.605795\pi\)
0.357664 + 0.933850i \(0.383573\pi\)
\(440\) 0 0
\(441\) −5866.32 + 146014.i −0.0301640 + 0.750789i
\(442\) 0 0
\(443\) −181179. + 215921.i −0.923212 + 1.10024i 0.0714898 + 0.997441i \(0.477225\pi\)
−0.994702 + 0.102800i \(0.967220\pi\)
\(444\) 0 0
\(445\) 57586.6 + 326590.i 0.290805 + 1.64924i
\(446\) 0 0
\(447\) −19222.8 + 12892.7i −0.0962061 + 0.0645252i
\(448\) 0 0
\(449\) −250048. + 144365.i −1.24031 + 0.716094i −0.969158 0.246442i \(-0.920739\pi\)
−0.271154 + 0.962536i \(0.587405\pi\)
\(450\) 0 0
\(451\) −139297. + 241270.i −0.684841 + 1.18618i
\(452\) 0 0
\(453\) −307712. 89109.6i −1.49951 0.434238i
\(454\) 0 0
\(455\) 579.675 1592.64i 0.00280002 0.00769300i
\(456\) 0 0
\(457\) 56283.2 319198.i 0.269492 1.52837i −0.486438 0.873715i \(-0.661704\pi\)
0.755930 0.654652i \(-0.227185\pi\)
\(458\) 0 0
\(459\) −35071.6 171632.i −0.166468 0.814651i
\(460\) 0 0
\(461\) 254561. + 44886.0i 1.19782 + 0.211207i 0.736754 0.676161i \(-0.236358\pi\)
0.461062 + 0.887368i \(0.347469\pi\)
\(462\) 0 0
\(463\) 249634. + 90859.5i 1.16451 + 0.423846i 0.850706 0.525642i \(-0.176175\pi\)
0.313802 + 0.949488i \(0.398397\pi\)
\(464\) 0 0
\(465\) 280446. + 291939.i 1.29701 + 1.35016i
\(466\) 0 0
\(467\) −234369. 135313.i −1.07465 0.620448i −0.145200 0.989402i \(-0.546383\pi\)
−0.929448 + 0.368954i \(0.879716\pi\)
\(468\) 0 0
\(469\) −10234.2 17726.2i −0.0465274 0.0805878i
\(470\) 0 0
\(471\) −34368.3 + 69998.7i −0.154923 + 0.315536i
\(472\) 0 0
\(473\) 190216. 33540.3i 0.850209 0.149915i
\(474\) 0 0
\(475\) −64081.2 53770.5i −0.284017 0.238318i
\(476\) 0 0
\(477\) 232452. + 211521.i 1.02164 + 0.929643i
\(478\) 0 0
\(479\) −43361.6 119135.i −0.188988 0.519240i 0.808623 0.588328i \(-0.200213\pi\)
−0.997611 + 0.0690874i \(0.977991\pi\)
\(480\) 0 0
\(481\) 1562.12 1310.77i 0.00675187 0.00566549i
\(482\) 0 0
\(483\) −46638.4 105496.i −0.199917 0.452210i
\(484\) 0 0
\(485\) 80848.2i 0.343706i
\(486\) 0 0
\(487\) −99411.6 −0.419159 −0.209580 0.977792i \(-0.567210\pi\)
−0.209580 + 0.977792i \(0.567210\pi\)
\(488\) 0 0
\(489\) −366343. + 161956.i −1.53204 + 0.677297i
\(490\) 0 0
\(491\) 59612.1 + 71043.0i 0.247270 + 0.294685i 0.875376 0.483443i \(-0.160614\pi\)
−0.628106 + 0.778128i \(0.716169\pi\)
\(492\) 0 0
\(493\) 22006.9 8009.87i 0.0905453 0.0329558i
\(494\) 0 0
\(495\) −175561. + 192934.i −0.716501 + 0.787405i
\(496\) 0 0
\(497\) 35662.3 42500.7i 0.144376 0.172061i
\(498\) 0 0
\(499\) −58901.1 334045.i −0.236550 1.34154i −0.839326 0.543629i \(-0.817050\pi\)
0.602776 0.797910i \(-0.294061\pi\)
\(500\) 0 0
\(501\) 260125. + 127718.i 1.03635 + 0.508833i
\(502\) 0 0
\(503\) −22048.1 + 12729.5i −0.0871435 + 0.0503123i −0.542939 0.839772i \(-0.682688\pi\)
0.455795 + 0.890085i \(0.349355\pi\)
\(504\) 0 0
\(505\) −23650.5 + 40963.9i −0.0927380 + 0.160627i
\(506\) 0 0
\(507\) −185334. + 178038.i −0.721007 + 0.692621i
\(508\) 0 0
\(509\) 149571. 410944.i 0.577315 1.58616i −0.215373 0.976532i \(-0.569097\pi\)
0.792688 0.609628i \(-0.208681\pi\)
\(510\) 0 0
\(511\) 24952.5 141512.i 0.0955590 0.541942i
\(512\) 0 0
\(513\) −238791. 269440.i −0.907367 1.02383i
\(514\) 0 0
\(515\) −401610. 70814.6i −1.51422 0.266998i
\(516\) 0 0
\(517\) 119031. + 43323.7i 0.445326 + 0.162085i
\(518\) 0 0
\(519\) −77216.5 + 266643.i −0.286666 + 0.989910i
\(520\) 0 0
\(521\) −389228. 224721.i −1.43393 0.827882i −0.436515 0.899697i \(-0.643787\pi\)
−0.997418 + 0.0718152i \(0.977121\pi\)
\(522\) 0 0
\(523\) 179231. + 310437.i 0.655254 + 1.13493i 0.981830 + 0.189762i \(0.0607717\pi\)
−0.326576 + 0.945171i \(0.605895\pi\)
\(524\) 0 0
\(525\) −20745.8 30931.7i −0.0752683 0.112224i
\(526\) 0 0
\(527\) 377665. 66592.6i 1.35983 0.239775i
\(528\) 0 0
\(529\) 3573.37 + 2998.41i 0.0127693 + 0.0107147i
\(530\) 0 0
\(531\) 305906. + 12290.2i 1.08492 + 0.0435883i
\(532\) 0 0
\(533\) −2052.55 5639.32i −0.00722501 0.0198506i
\(534\) 0 0
\(535\) 131750. 110551.i 0.460302 0.386239i
\(536\) 0 0
\(537\) −160371. + 219518.i −0.556131 + 0.761240i
\(538\) 0 0
\(539\) 206138.i 0.709547i
\(540\) 0 0
\(541\) 116585. 0.398333 0.199167 0.979966i \(-0.436177\pi\)
0.199167 + 0.979966i \(0.436177\pi\)
\(542\) 0 0
\(543\) −50871.4 + 472089.i −0.172534 + 1.60112i
\(544\) 0 0
\(545\) −348059. 414800.i −1.17182 1.39652i
\(546\) 0 0
\(547\) −51478.9 + 18736.8i −0.172050 + 0.0626210i −0.426609 0.904436i \(-0.640292\pi\)
0.254559 + 0.967057i \(0.418070\pi\)
\(548\) 0 0
\(549\) 59642.8 145419.i 0.197885 0.482477i
\(550\) 0 0
\(551\) 30938.2 36870.8i 0.101904 0.121445i
\(552\) 0 0
\(553\) 24153.4 + 136980.i 0.0789818 + 0.447928i
\(554\) 0 0
\(555\) −14109.9 209686.i −0.0458075 0.680744i
\(556\) 0 0
\(557\) −30508.0 + 17613.8i −0.0983339 + 0.0567731i −0.548360 0.836242i \(-0.684748\pi\)
0.450027 + 0.893015i \(0.351414\pi\)
\(558\) 0 0
\(559\) −2080.34 + 3603.26i −0.00665750 + 0.0115311i
\(560\) 0 0
\(561\) 59152.3 + 239927.i 0.187952 + 0.762349i
\(562\) 0 0
\(563\) −61925.1 + 170138.i −0.195366 + 0.536765i −0.998235 0.0593917i \(-0.981084\pi\)
0.802868 + 0.596156i \(0.203306\pi\)
\(564\) 0 0
\(565\) −1340.44 + 7602.04i −0.00419906 + 0.0238140i
\(566\) 0 0
\(567\) −68752.8 144802.i −0.213857 0.450411i
\(568\) 0 0
\(569\) 368377. + 64954.7i 1.13780 + 0.200626i 0.710645 0.703551i \(-0.248403\pi\)
0.427159 + 0.904176i \(0.359514\pi\)
\(570\) 0 0
\(571\) 459788. + 167349.i 1.41022 + 0.513277i 0.931193 0.364526i \(-0.118769\pi\)
0.479023 + 0.877803i \(0.340991\pi\)
\(572\) 0 0
\(573\) 382584. 94323.3i 1.16525 0.287283i
\(574\) 0 0
\(575\) −76949.6 44426.9i −0.232740 0.134372i
\(576\) 0 0
\(577\) 113291. + 196225.i 0.340285 + 0.589390i 0.984485 0.175466i \(-0.0561433\pi\)
−0.644201 + 0.764856i \(0.722810\pi\)
\(578\) 0 0
\(579\) 630245. 42409.4i 1.87998 0.126504i
\(580\) 0 0
\(581\) 177945. 31376.5i 0.527149 0.0929507i
\(582\) 0 0
\(583\) −339618. 284973.i −0.999203 0.838431i
\(584\) 0 0
\(585\) −752.814 5568.44i −0.00219976 0.0162713i
\(586\) 0 0
\(587\) 136938. + 376234.i 0.397418 + 1.09190i 0.963538 + 0.267573i \(0.0862217\pi\)
−0.566120 + 0.824323i \(0.691556\pi\)
\(588\) 0 0
\(589\) 603759. 506614.i 1.74034 1.46032i
\(590\) 0 0
\(591\) −248571. 26785.5i −0.711665 0.0766877i
\(592\) 0 0
\(593\) 332164.i 0.944590i −0.881441 0.472295i \(-0.843426\pi\)
0.881441 0.472295i \(-0.156574\pi\)
\(594\) 0 0
\(595\) −165470. −0.467396
\(596\) 0 0
\(597\) −225470. 164719.i −0.632617 0.462164i
\(598\) 0 0
\(599\) −403032. 480315.i −1.12327 1.33867i −0.934219 0.356700i \(-0.883902\pi\)
−0.189056 0.981966i \(-0.560543\pi\)
\(600\) 0 0
\(601\) 565600. 205862.i 1.56589 0.569936i 0.593811 0.804604i \(-0.297623\pi\)
0.972076 + 0.234668i \(0.0754003\pi\)
\(602\) 0 0
\(603\) −57359.7 36262.2i −0.157751 0.0997287i
\(604\) 0 0
\(605\) −28722.8 + 34230.6i −0.0784724 + 0.0935197i
\(606\) 0 0
\(607\) −72553.0 411469.i −0.196915 1.11676i −0.909665 0.415342i \(-0.863662\pi\)
0.712751 0.701417i \(-0.247449\pi\)
\(608\) 0 0
\(609\) 17797.4 11936.6i 0.0479867 0.0321846i
\(610\) 0 0
\(611\) −2363.05 + 1364.31i −0.00632980 + 0.00365451i
\(612\) 0 0
\(613\) 165625. 286871.i 0.440764 0.763425i −0.556983 0.830524i \(-0.688041\pi\)
0.997746 + 0.0670991i \(0.0213744\pi\)
\(614\) 0 0
\(615\) −594081. 172038.i −1.57071 0.454857i
\(616\) 0 0
\(617\) −182752. + 502108.i −0.480057 + 1.31895i 0.429387 + 0.903120i \(0.358730\pi\)
−0.909444 + 0.415826i \(0.863493\pi\)
\(618\) 0 0
\(619\) 18382.4 104252.i 0.0479756 0.272083i −0.951378 0.308025i \(-0.900332\pi\)
0.999354 + 0.0359418i \(0.0114431\pi\)
\(620\) 0 0
\(621\) −299483. 237802.i −0.776585 0.616641i
\(622\) 0 0
\(623\) 283099. + 49918.0i 0.729395 + 0.128612i
\(624\) 0 0
\(625\) 439587. + 159997.i 1.12534 + 0.409591i
\(626\) 0 0
\(627\) 351832. + 366251.i 0.894953 + 0.931631i
\(628\) 0 0
\(629\) −172416. 99544.2i −0.435788 0.251602i
\(630\) 0 0
\(631\) 288702. + 500047.i 0.725089 + 1.25589i 0.958937 + 0.283618i \(0.0915348\pi\)
−0.233848 + 0.972273i \(0.575132\pi\)
\(632\) 0 0
\(633\) 98436.7 200488.i 0.245669 0.500359i
\(634\) 0 0
\(635\) 812774. 143314.i 2.01568 0.355419i
\(636\) 0 0
\(637\) 3401.58 + 2854.27i 0.00838305 + 0.00703422i
\(638\) 0 0
\(639\) 39187.0 179717.i 0.0959710 0.440137i
\(640\) 0 0
\(641\) 181206. + 497859.i 0.441018 + 1.21169i 0.938824 + 0.344397i \(0.111917\pi\)
−0.497806 + 0.867288i \(0.665861\pi\)
\(642\) 0 0
\(643\) 68330.7 57336.3i 0.165270 0.138678i −0.556402 0.830913i \(-0.687818\pi\)
0.721672 + 0.692235i \(0.243374\pi\)
\(644\) 0 0
\(645\) 173381. + 392186.i 0.416755 + 0.942697i
\(646\) 0 0
\(647\) 690108.i 1.64857i −0.566172 0.824287i \(-0.691576\pi\)
0.566172 0.824287i \(-0.308424\pi\)
\(648\) 0 0
\(649\) −431869. −1.02533
\(650\) 0 0
\(651\) 320946. 141886.i 0.757304 0.334795i
\(652\) 0 0
\(653\) −360793. 429977.i −0.846121 1.00837i −0.999795 0.0202458i \(-0.993555\pi\)
0.153674 0.988122i \(-0.450889\pi\)
\(654\) 0 0
\(655\) −673125. + 244997.i −1.56896 + 0.571056i
\(656\) 0 0
\(657\) −144838. 453855.i −0.335545 1.05145i
\(658\) 0 0
\(659\) −470549. + 560778.i −1.08351 + 1.29128i −0.129479 + 0.991582i \(0.541330\pi\)
−0.954034 + 0.299698i \(0.903114\pi\)
\(660\) 0 0
\(661\) 118352. + 671209.i 0.270878 + 1.53623i 0.751758 + 0.659439i \(0.229206\pi\)
−0.480880 + 0.876786i \(0.659683\pi\)
\(662\) 0 0
\(663\) −4778.20 2346.02i −0.0108702 0.00533710i
\(664\) 0 0
\(665\) −294512. + 170037.i −0.665978 + 0.384503i
\(666\) 0 0
\(667\) 25562.1 44274.9i 0.0574573 0.0995190i
\(668\) 0 0
\(669\) −512681. + 492497.i −1.14550 + 1.10040i
\(670\) 0 0
\(671\) −75831.2 + 208345.i −0.168424 + 0.462740i
\(672\) 0 0
\(673\) −50789.8 + 288043.i −0.112136 + 0.635957i 0.875992 + 0.482326i \(0.160208\pi\)
−0.988128 + 0.153631i \(0.950903\pi\)
\(674\) 0 0
\(675\) −108567. 58827.0i −0.238281 0.129113i
\(676\) 0 0
\(677\) −547224. 96490.4i −1.19396 0.210527i −0.458871 0.888503i \(-0.651746\pi\)
−0.735084 + 0.677976i \(0.762857\pi\)
\(678\) 0 0
\(679\) 65855.5 + 23969.4i 0.142841 + 0.0519898i
\(680\) 0 0
\(681\) −187802. + 648516.i −0.404954 + 1.39838i
\(682\) 0 0
\(683\) −8476.38 4893.84i −0.0181706 0.0104908i 0.490887 0.871223i \(-0.336673\pi\)
−0.509058 + 0.860732i \(0.670006\pi\)
\(684\) 0 0
\(685\) −184304. 319224.i −0.392783 0.680321i
\(686\) 0 0
\(687\) 72321.9 + 107831.i 0.153235 + 0.228470i
\(688\) 0 0
\(689\) 9404.96 1658.35i 0.0198115 0.00349331i
\(690\) 0 0
\(691\) −604854. 507533.i −1.26676 1.06294i −0.994928 0.100594i \(-0.967926\pi\)
−0.271833 0.962344i \(-0.587630\pi\)
\(692\) 0 0
\(693\) 105106. + 200204.i 0.218858 + 0.416876i
\(694\) 0 0
\(695\) 86412.9 + 237418.i 0.178900 + 0.491522i
\(696\) 0 0
\(697\) −448829. + 376612.i −0.923880 + 0.775227i
\(698\) 0 0
\(699\) 133601. 182876.i 0.273437 0.374284i
\(700\) 0 0
\(701\) 765720.i 1.55824i 0.626876 + 0.779119i \(0.284333\pi\)
−0.626876 + 0.779119i \(0.715667\pi\)
\(702\) 0 0
\(703\) −409167. −0.827922
\(704\) 0 0
\(705\) −30128.4 + 279593.i −0.0606174 + 0.562533i
\(706\) 0 0
\(707\) 26355.6 + 31409.4i 0.0527272 + 0.0628379i
\(708\) 0 0
\(709\) −132595. + 48260.7i −0.263776 + 0.0960066i −0.470523 0.882388i \(-0.655935\pi\)
0.206747 + 0.978394i \(0.433712\pi\)
\(710\) 0 0
\(711\) 282001. + 364875.i 0.557842 + 0.721781i
\(712\) 0 0
\(713\) 538116. 641302.i 1.05851 1.26149i
\(714\) 0 0
\(715\) 1376.42 + 7806.05i 0.00269239 + 0.0152693i
\(716\) 0 0
\(717\) −21739.8 323074.i −0.0422880 0.628440i
\(718\) 0 0
\(719\) 76955.1 44430.1i 0.148861 0.0859447i −0.423720 0.905793i \(-0.639276\pi\)
0.572580 + 0.819849i \(0.305942\pi\)
\(720\) 0 0
\(721\) −176750. + 306140.i −0.340007 + 0.588910i
\(722\) 0 0
\(723\) −141348. 573319.i −0.270403 1.09678i
\(724\) 0 0
\(725\) 5646.03 15512.3i 0.0107416 0.0295122i
\(726\) 0 0
\(727\) −2153.14 + 12211.1i −0.00407384 + 0.0231039i −0.986777 0.162084i \(-0.948178\pi\)
0.982703 + 0.185188i \(0.0592895\pi\)
\(728\) 0 0
\(729\) −424974. 319103.i −0.799663 0.600449i
\(730\) 0 0
\(731\) 400039. + 70537.7i 0.748631 + 0.132004i
\(732\) 0 0
\(733\) −405994. 147770.i −0.755634 0.275028i −0.0646595 0.997907i \(-0.520596\pi\)
−0.690975 + 0.722879i \(0.742818\pi\)
\(734\) 0 0
\(735\) 444329. 109546.i 0.822489 0.202779i
\(736\) 0 0
\(737\) 82901.5 + 47863.2i 0.152626 + 0.0881184i
\(738\) 0 0
\(739\) 95170.2 + 164840.i 0.174266 + 0.301837i 0.939907 0.341431i \(-0.110911\pi\)
−0.765641 + 0.643268i \(0.777578\pi\)
\(740\) 0 0
\(741\) −10915.3 + 734.493i −0.0198792 + 0.00133768i
\(742\) 0 0
\(743\) 920487. 162307.i 1.66740 0.294008i 0.741269 0.671208i \(-0.234224\pi\)
0.926132 + 0.377200i \(0.123113\pi\)
\(744\) 0 0
\(745\) 55526.9 + 46592.6i 0.100044 + 0.0839469i
\(746\) 0 0
\(747\) 473993. 366334.i 0.849436 0.656502i
\(748\) 0 0
\(749\) −50989.9 140093.i −0.0908908 0.249721i
\(750\) 0 0
\(751\) 193215. 162126.i 0.342578 0.287457i −0.455223 0.890377i \(-0.650441\pi\)
0.797802 + 0.602920i \(0.205996\pi\)
\(752\) 0 0
\(753\) −371329. 40013.7i −0.654890 0.0705697i
\(754\) 0 0
\(755\) 1.00324e6i 1.75999i
\(756\) 0 0
\(757\) −449009. −0.783544 −0.391772 0.920062i \(-0.628138\pi\)
−0.391772 + 0.920062i \(0.628138\pi\)
\(758\) 0 0
\(759\) 435586. + 318221.i 0.756119 + 0.552390i
\(760\) 0 0
\(761\) −380749. 453759.i −0.657460 0.783530i 0.329559 0.944135i \(-0.393100\pi\)
−0.987019 + 0.160605i \(0.948656\pi\)
\(762\) 0 0
\(763\) −441069. + 160536.i −0.757631 + 0.275755i
\(764\) 0 0
\(765\) −485726. + 255005.i −0.829982 + 0.435738i
\(766\) 0 0
\(767\) 5979.82 7126.47i 0.0101648 0.0121139i
\(768\) 0 0
\(769\) −35286.0 200117.i −0.0596692 0.338401i 0.940329 0.340267i \(-0.110517\pi\)
−0.999998 + 0.00186555i \(0.999406\pi\)
\(770\) 0 0
\(771\) 509596. 341785.i 0.857269 0.574968i
\(772\) 0 0
\(773\) −93598.2 + 54039.0i −0.156642 + 0.0904374i −0.576272 0.817258i \(-0.695493\pi\)
0.419630 + 0.907695i \(0.362160\pi\)
\(774\) 0 0
\(775\) 135158. 234101.i 0.225030 0.389763i
\(776\) 0 0
\(777\) −174985. 50673.4i −0.289840 0.0839340i
\(778\) 0 0
\(779\) −411844. + 1.13153e6i −0.678669 + 1.86463i
\(780\) 0 0