Properties

Label 882.3.n.b.19.1
Level $882$
Weight $3$
Character 882.19
Analytic conductor $24.033$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 882.n (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.0327593166\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.1
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 882.19
Dual form 882.3.n.b.325.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(2.74264 + 1.58346i) q^{5} +2.82843 q^{8} +O(q^{10})\) \(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(2.74264 + 1.58346i) q^{5} +2.82843 q^{8} +(-3.87868 + 2.23936i) q^{10} +(-6.62132 - 11.4685i) q^{11} +5.49333i q^{13} +(-2.00000 + 3.46410i) q^{16} +(-11.7426 + 6.77962i) q^{17} +(0.621320 + 0.358719i) q^{19} -6.33386i q^{20} +18.7279 q^{22} +(-1.13604 + 1.96768i) q^{23} +(-7.48528 - 12.9649i) q^{25} +(-6.72792 - 3.88437i) q^{26} -20.4853 q^{29} +(-21.3198 + 12.3090i) q^{31} +(-2.82843 - 4.89898i) q^{32} -19.1757i q^{34} +(-32.4706 + 56.2407i) q^{37} +(-0.878680 + 0.507306i) q^{38} +(7.75736 + 4.47871i) q^{40} -21.0308i q^{41} +6.48528 q^{43} +(-13.2426 + 22.9369i) q^{44} +(-1.60660 - 2.78272i) q^{46} +(41.3787 + 23.8900i) q^{47} +21.1716 q^{50} +(9.51472 - 5.49333i) q^{52} +(11.0147 + 19.0781i) q^{53} -41.9385i q^{55} +(14.4853 - 25.0892i) q^{58} +(-72.5330 + 41.8770i) q^{59} +(-57.3823 - 33.1297i) q^{61} -34.8151i q^{62} +8.00000 q^{64} +(-8.69848 + 15.0662i) q^{65} +(-46.3198 - 80.2283i) q^{67} +(23.4853 + 13.5592i) q^{68} +48.4264 q^{71} +(-113.441 + 65.4953i) q^{73} +(-45.9203 - 79.5363i) q^{74} -1.43488i q^{76} +(38.1066 - 66.0026i) q^{79} +(-10.9706 + 6.33386i) q^{80} +(25.7574 + 14.8710i) q^{82} +107.981i q^{83} -42.9411 q^{85} +(-4.58579 + 7.94282i) q^{86} +(-18.7279 - 32.4377i) q^{88} +(-145.412 - 83.9535i) q^{89} +4.54416 q^{92} +(-58.5183 + 33.7856i) q^{94} +(1.13604 + 1.96768i) q^{95} -25.5816i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{4} - 6 q^{5} + O(q^{10}) \) \( 4 q - 4 q^{4} - 6 q^{5} - 24 q^{10} - 18 q^{11} - 8 q^{16} - 30 q^{17} - 6 q^{19} + 24 q^{22} - 30 q^{23} + 4 q^{25} + 24 q^{26} - 48 q^{29} + 42 q^{31} - 62 q^{37} - 12 q^{38} + 48 q^{40} - 8 q^{43} - 36 q^{44} + 36 q^{46} + 174 q^{47} + 96 q^{50} + 72 q^{52} + 78 q^{53} + 24 q^{58} - 78 q^{59} + 42 q^{61} + 32 q^{64} + 84 q^{65} - 58 q^{67} + 60 q^{68} + 24 q^{71} - 318 q^{73} - 96 q^{74} + 110 q^{79} + 24 q^{80} + 120 q^{82} - 36 q^{85} - 24 q^{86} - 24 q^{88} - 378 q^{89} + 120 q^{92} + 12 q^{94} + 30 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 1.22474i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −1.00000 1.73205i −0.250000 0.433013i
\(5\) 2.74264 + 1.58346i 0.548528 + 0.316693i 0.748528 0.663103i \(-0.230761\pi\)
−0.200000 + 0.979796i \(0.564094\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.82843 0.353553
\(9\) 0 0
\(10\) −3.87868 + 2.23936i −0.387868 + 0.223936i
\(11\) −6.62132 11.4685i −0.601938 1.04259i −0.992527 0.122022i \(-0.961062\pi\)
0.390589 0.920565i \(-0.372271\pi\)
\(12\) 0 0
\(13\) 5.49333i 0.422563i 0.977425 + 0.211282i \(0.0677638\pi\)
−0.977425 + 0.211282i \(0.932236\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) −11.7426 + 6.77962i −0.690744 + 0.398801i −0.803891 0.594777i \(-0.797240\pi\)
0.113147 + 0.993578i \(0.463907\pi\)
\(18\) 0 0
\(19\) 0.621320 + 0.358719i 0.0327011 + 0.0188800i 0.516261 0.856431i \(-0.327323\pi\)
−0.483560 + 0.875311i \(0.660657\pi\)
\(20\) 6.33386i 0.316693i
\(21\) 0 0
\(22\) 18.7279 0.851269
\(23\) −1.13604 + 1.96768i −0.0493930 + 0.0855512i −0.889665 0.456614i \(-0.849062\pi\)
0.840272 + 0.542165i \(0.182395\pi\)
\(24\) 0 0
\(25\) −7.48528 12.9649i −0.299411 0.518596i
\(26\) −6.72792 3.88437i −0.258766 0.149399i
\(27\) 0 0
\(28\) 0 0
\(29\) −20.4853 −0.706389 −0.353195 0.935550i \(-0.614905\pi\)
−0.353195 + 0.935550i \(0.614905\pi\)
\(30\) 0 0
\(31\) −21.3198 + 12.3090i −0.687736 + 0.397064i −0.802763 0.596298i \(-0.796638\pi\)
0.115028 + 0.993362i \(0.463304\pi\)
\(32\) −2.82843 4.89898i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 19.1757i 0.563990i
\(35\) 0 0
\(36\) 0 0
\(37\) −32.4706 + 56.2407i −0.877583 + 1.52002i −0.0235970 + 0.999722i \(0.507512\pi\)
−0.853986 + 0.520296i \(0.825821\pi\)
\(38\) −0.878680 + 0.507306i −0.0231231 + 0.0133502i
\(39\) 0 0
\(40\) 7.75736 + 4.47871i 0.193934 + 0.111968i
\(41\) 21.0308i 0.512946i −0.966551 0.256473i \(-0.917439\pi\)
0.966551 0.256473i \(-0.0825605\pi\)
\(42\) 0 0
\(43\) 6.48528 0.150820 0.0754102 0.997153i \(-0.475973\pi\)
0.0754102 + 0.997153i \(0.475973\pi\)
\(44\) −13.2426 + 22.9369i −0.300969 + 0.521294i
\(45\) 0 0
\(46\) −1.60660 2.78272i −0.0349261 0.0604938i
\(47\) 41.3787 + 23.8900i 0.880397 + 0.508298i 0.870789 0.491656i \(-0.163608\pi\)
0.00960801 + 0.999954i \(0.496942\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 21.1716 0.423431
\(51\) 0 0
\(52\) 9.51472 5.49333i 0.182975 0.105641i
\(53\) 11.0147 + 19.0781i 0.207825 + 0.359963i 0.951029 0.309101i \(-0.100028\pi\)
−0.743204 + 0.669065i \(0.766695\pi\)
\(54\) 0 0
\(55\) 41.9385i 0.762518i
\(56\) 0 0
\(57\) 0 0
\(58\) 14.4853 25.0892i 0.249746 0.432573i
\(59\) −72.5330 + 41.8770i −1.22937 + 0.709779i −0.966899 0.255160i \(-0.917872\pi\)
−0.262474 + 0.964939i \(0.584538\pi\)
\(60\) 0 0
\(61\) −57.3823 33.1297i −0.940693 0.543109i −0.0505153 0.998723i \(-0.516086\pi\)
−0.890177 + 0.455614i \(0.849420\pi\)
\(62\) 34.8151i 0.561534i
\(63\) 0 0
\(64\) 8.00000 0.125000
\(65\) −8.69848 + 15.0662i −0.133823 + 0.231788i
\(66\) 0 0
\(67\) −46.3198 80.2283i −0.691340 1.19744i −0.971399 0.237454i \(-0.923687\pi\)
0.280058 0.959983i \(-0.409646\pi\)
\(68\) 23.4853 + 13.5592i 0.345372 + 0.199400i
\(69\) 0 0
\(70\) 0 0
\(71\) 48.4264 0.682062 0.341031 0.940052i \(-0.389224\pi\)
0.341031 + 0.940052i \(0.389224\pi\)
\(72\) 0 0
\(73\) −113.441 + 65.4953i −1.55399 + 0.897195i −0.556177 + 0.831064i \(0.687732\pi\)
−0.997811 + 0.0661316i \(0.978934\pi\)
\(74\) −45.9203 79.5363i −0.620545 1.07482i
\(75\) 0 0
\(76\) 1.43488i 0.0188800i
\(77\) 0 0
\(78\) 0 0
\(79\) 38.1066 66.0026i 0.482362 0.835476i −0.517433 0.855724i \(-0.673112\pi\)
0.999795 + 0.0202482i \(0.00644564\pi\)
\(80\) −10.9706 + 6.33386i −0.137132 + 0.0791732i
\(81\) 0 0
\(82\) 25.7574 + 14.8710i 0.314114 + 0.181354i
\(83\) 107.981i 1.30098i 0.759514 + 0.650491i \(0.225437\pi\)
−0.759514 + 0.650491i \(0.774563\pi\)
\(84\) 0 0
\(85\) −42.9411 −0.505190
\(86\) −4.58579 + 7.94282i −0.0533231 + 0.0923583i
\(87\) 0 0
\(88\) −18.7279 32.4377i −0.212817 0.368610i
\(89\) −145.412 83.9535i −1.63384 0.943297i −0.982894 0.184173i \(-0.941039\pi\)
−0.650945 0.759125i \(-0.725627\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 4.54416 0.0493930
\(93\) 0 0
\(94\) −58.5183 + 33.7856i −0.622535 + 0.359421i
\(95\) 1.13604 + 1.96768i 0.0119583 + 0.0207124i
\(96\) 0 0
\(97\) 25.5816i 0.263728i −0.991268 0.131864i \(-0.957904\pi\)
0.991268 0.131864i \(-0.0420962\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −14.9706 + 25.9298i −0.149706 + 0.259298i
\(101\) 24.6838 14.2512i 0.244394 0.141101i −0.372801 0.927911i \(-0.621603\pi\)
0.617194 + 0.786811i \(0.288269\pi\)
\(102\) 0 0
\(103\) −48.9228 28.2456i −0.474979 0.274229i 0.243343 0.969940i \(-0.421756\pi\)
−0.718322 + 0.695711i \(0.755089\pi\)
\(104\) 15.5375i 0.149399i
\(105\) 0 0
\(106\) −31.1543 −0.293909
\(107\) 23.8051 41.2316i 0.222477 0.385342i −0.733082 0.680140i \(-0.761919\pi\)
0.955560 + 0.294798i \(0.0952523\pi\)
\(108\) 0 0
\(109\) −37.6543 65.2192i −0.345453 0.598341i 0.639983 0.768389i \(-0.278941\pi\)
−0.985436 + 0.170047i \(0.945608\pi\)
\(110\) 51.3640 + 29.6550i 0.466945 + 0.269591i
\(111\) 0 0
\(112\) 0 0
\(113\) −85.4558 −0.756246 −0.378123 0.925755i \(-0.623430\pi\)
−0.378123 + 0.925755i \(0.623430\pi\)
\(114\) 0 0
\(115\) −6.23149 + 3.59775i −0.0541869 + 0.0312848i
\(116\) 20.4853 + 35.4815i 0.176597 + 0.305875i
\(117\) 0 0
\(118\) 118.446i 1.00378i
\(119\) 0 0
\(120\) 0 0
\(121\) −27.1838 + 47.0837i −0.224659 + 0.389121i
\(122\) 81.1508 46.8524i 0.665170 0.384036i
\(123\) 0 0
\(124\) 42.6396 + 24.6180i 0.343868 + 0.198532i
\(125\) 126.584i 1.01267i
\(126\) 0 0
\(127\) −60.6619 −0.477653 −0.238826 0.971062i \(-0.576763\pi\)
−0.238826 + 0.971062i \(0.576763\pi\)
\(128\) −5.65685 + 9.79796i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −12.3015 21.3068i −0.0946270 0.163899i
\(131\) −115.136 66.4738i −0.878901 0.507434i −0.00860515 0.999963i \(-0.502739\pi\)
−0.870296 + 0.492529i \(0.836072\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 131.012 0.977703
\(135\) 0 0
\(136\) −33.2132 + 19.1757i −0.244215 + 0.140997i
\(137\) −58.7132 101.694i −0.428564 0.742294i 0.568182 0.822903i \(-0.307647\pi\)
−0.996746 + 0.0806089i \(0.974314\pi\)
\(138\) 0 0
\(139\) 68.5857i 0.493422i −0.969089 0.246711i \(-0.920650\pi\)
0.969089 0.246711i \(-0.0793499\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −34.2426 + 59.3100i −0.241145 + 0.417676i
\(143\) 63.0000 36.3731i 0.440559 0.254357i
\(144\) 0 0
\(145\) −56.1838 32.4377i −0.387474 0.223708i
\(146\) 185.249i 1.26883i
\(147\) 0 0
\(148\) 129.882 0.877583
\(149\) −13.1985 + 22.8604i −0.0885804 + 0.153426i −0.906911 0.421322i \(-0.861566\pi\)
0.818331 + 0.574747i \(0.194900\pi\)
\(150\) 0 0
\(151\) 67.1066 + 116.232i 0.444415 + 0.769749i 0.998011 0.0630363i \(-0.0200784\pi\)
−0.553597 + 0.832785i \(0.686745\pi\)
\(152\) 1.75736 + 1.01461i 0.0115616 + 0.00667508i
\(153\) 0 0
\(154\) 0 0
\(155\) −77.9634 −0.502990
\(156\) 0 0
\(157\) 196.323 113.347i 1.25047 0.721958i 0.279265 0.960214i \(-0.409909\pi\)
0.971202 + 0.238256i \(0.0765759\pi\)
\(158\) 53.8909 + 93.3417i 0.341081 + 0.590770i
\(159\) 0 0
\(160\) 17.9149i 0.111968i
\(161\) 0 0
\(162\) 0 0
\(163\) 45.9889 79.6550i 0.282140 0.488681i −0.689771 0.724027i \(-0.742289\pi\)
0.971912 + 0.235346i \(0.0756223\pi\)
\(164\) −36.4264 + 21.0308i −0.222112 + 0.128237i
\(165\) 0 0
\(166\) −132.250 76.3544i −0.796685 0.459967i
\(167\) 203.482i 1.21845i 0.792996 + 0.609227i \(0.208520\pi\)
−0.792996 + 0.609227i \(0.791480\pi\)
\(168\) 0 0
\(169\) 138.823 0.821440
\(170\) 30.3640 52.5919i 0.178612 0.309364i
\(171\) 0 0
\(172\) −6.48528 11.2328i −0.0377051 0.0653072i
\(173\) 61.3234 + 35.4051i 0.354470 + 0.204654i 0.666652 0.745369i \(-0.267727\pi\)
−0.312182 + 0.950022i \(0.601060\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 52.9706 0.300969
\(177\) 0 0
\(178\) 205.643 118.728i 1.15530 0.667012i
\(179\) 54.4081 + 94.2376i 0.303956 + 0.526467i 0.977028 0.213109i \(-0.0683591\pi\)
−0.673072 + 0.739577i \(0.735026\pi\)
\(180\) 0 0
\(181\) 99.6607i 0.550611i 0.961357 + 0.275306i \(0.0887791\pi\)
−0.961357 + 0.275306i \(0.911221\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −3.21320 + 5.56543i −0.0174631 + 0.0302469i
\(185\) −178.110 + 102.832i −0.962758 + 0.555848i
\(186\) 0 0
\(187\) 155.504 + 89.7800i 0.831570 + 0.480107i
\(188\) 95.5600i 0.508298i
\(189\) 0 0
\(190\) −3.21320 −0.0169116
\(191\) 34.9523 60.5391i 0.182996 0.316959i −0.759903 0.650036i \(-0.774754\pi\)
0.942899 + 0.333077i \(0.108087\pi\)
\(192\) 0 0
\(193\) 16.1690 + 28.0056i 0.0837774 + 0.145107i 0.904870 0.425689i \(-0.139968\pi\)
−0.821092 + 0.570796i \(0.806635\pi\)
\(194\) 31.3310 + 18.0889i 0.161500 + 0.0932419i
\(195\) 0 0
\(196\) 0 0
\(197\) −277.103 −1.40661 −0.703306 0.710887i \(-0.748294\pi\)
−0.703306 + 0.710887i \(0.748294\pi\)
\(198\) 0 0
\(199\) −145.011 + 83.7222i −0.728699 + 0.420715i −0.817946 0.575295i \(-0.804887\pi\)
0.0892469 + 0.996010i \(0.471554\pi\)
\(200\) −21.1716 36.6702i −0.105858 0.183351i
\(201\) 0 0
\(202\) 40.3084i 0.199547i
\(203\) 0 0
\(204\) 0 0
\(205\) 33.3015 57.6799i 0.162446 0.281365i
\(206\) 69.1873 39.9453i 0.335861 0.193909i
\(207\) 0 0
\(208\) −19.0294 10.9867i −0.0914877 0.0528204i
\(209\) 9.50079i 0.0454583i
\(210\) 0 0
\(211\) −128.073 −0.606982 −0.303491 0.952834i \(-0.598152\pi\)
−0.303491 + 0.952834i \(0.598152\pi\)
\(212\) 22.0294 38.1561i 0.103912 0.179982i
\(213\) 0 0
\(214\) 33.6655 + 58.3103i 0.157315 + 0.272478i
\(215\) 17.7868 + 10.2692i 0.0827293 + 0.0477638i
\(216\) 0 0
\(217\) 0 0
\(218\) 106.503 0.488544
\(219\) 0 0
\(220\) −72.6396 + 41.9385i −0.330180 + 0.190630i
\(221\) −37.2426 64.5061i −0.168519 0.291883i
\(222\) 0 0
\(223\) 417.169i 1.87071i 0.353705 + 0.935357i \(0.384922\pi\)
−0.353705 + 0.935357i \(0.615078\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 60.4264 104.662i 0.267373 0.463104i
\(227\) 201.143 116.130i 0.886093 0.511586i 0.0134307 0.999910i \(-0.495725\pi\)
0.872663 + 0.488324i \(0.162391\pi\)
\(228\) 0 0
\(229\) 72.4188 + 41.8110i 0.316239 + 0.182581i 0.649715 0.760178i \(-0.274888\pi\)
−0.333476 + 0.942759i \(0.608222\pi\)
\(230\) 10.1760i 0.0442434i
\(231\) 0 0
\(232\) −57.9411 −0.249746
\(233\) 109.537 189.723i 0.470114 0.814261i −0.529302 0.848434i \(-0.677546\pi\)
0.999416 + 0.0341721i \(0.0108794\pi\)
\(234\) 0 0
\(235\) 75.6579 + 131.043i 0.321949 + 0.557631i
\(236\) 145.066 + 83.7539i 0.614687 + 0.354889i
\(237\) 0 0
\(238\) 0 0
\(239\) −193.103 −0.807961 −0.403980 0.914768i \(-0.632374\pi\)
−0.403980 + 0.914768i \(0.632374\pi\)
\(240\) 0 0
\(241\) −42.8970 + 24.7666i −0.177996 + 0.102766i −0.586351 0.810057i \(-0.699436\pi\)
0.408355 + 0.912823i \(0.366103\pi\)
\(242\) −38.4437 66.5864i −0.158858 0.275150i
\(243\) 0 0
\(244\) 132.519i 0.543109i
\(245\) 0 0
\(246\) 0 0
\(247\) −1.97056 + 3.41311i −0.00797799 + 0.0138183i
\(248\) −60.3015 + 34.8151i −0.243151 + 0.140383i
\(249\) 0 0
\(250\) 155.033 + 89.5083i 0.620132 + 0.358033i
\(251\) 162.524i 0.647507i 0.946141 + 0.323754i \(0.104945\pi\)
−0.946141 + 0.323754i \(0.895055\pi\)
\(252\) 0 0
\(253\) 30.0883 0.118926
\(254\) 42.8944 74.2954i 0.168876 0.292501i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) −85.8747 49.5798i −0.334143 0.192917i 0.323536 0.946216i \(-0.395128\pi\)
−0.657679 + 0.753298i \(0.728462\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 34.7939 0.133823
\(261\) 0 0
\(262\) 162.827 94.0082i 0.621477 0.358810i
\(263\) 217.173 + 376.154i 0.825751 + 1.43024i 0.901344 + 0.433105i \(0.142582\pi\)
−0.0755923 + 0.997139i \(0.524085\pi\)
\(264\) 0 0
\(265\) 69.7657i 0.263267i
\(266\) 0 0
\(267\) 0 0
\(268\) −92.6396 + 160.457i −0.345670 + 0.598718i
\(269\) −79.1619 + 45.7041i −0.294282 + 0.169904i −0.639871 0.768482i \(-0.721012\pi\)
0.345589 + 0.938386i \(0.387679\pi\)
\(270\) 0 0
\(271\) −14.8051 8.54772i −0.0546313 0.0315414i 0.472436 0.881365i \(-0.343375\pi\)
−0.527067 + 0.849824i \(0.676708\pi\)
\(272\) 54.2369i 0.199400i
\(273\) 0 0
\(274\) 166.066 0.606080
\(275\) −99.1249 + 171.689i −0.360454 + 0.624325i
\(276\) 0 0
\(277\) 200.206 + 346.766i 0.722764 + 1.25186i 0.959888 + 0.280385i \(0.0904620\pi\)
−0.237124 + 0.971479i \(0.576205\pi\)
\(278\) 84.0000 + 48.4974i 0.302158 + 0.174451i
\(279\) 0 0
\(280\) 0 0
\(281\) 538.690 1.91705 0.958524 0.285012i \(-0.0919976\pi\)
0.958524 + 0.285012i \(0.0919976\pi\)
\(282\) 0 0
\(283\) 267.783 154.604i 0.946229 0.546306i 0.0543215 0.998523i \(-0.482700\pi\)
0.891907 + 0.452218i \(0.149367\pi\)
\(284\) −48.4264 83.8770i −0.170516 0.295342i
\(285\) 0 0
\(286\) 102.879i 0.359715i
\(287\) 0 0
\(288\) 0 0
\(289\) −52.5736 + 91.0601i −0.181916 + 0.315087i
\(290\) 79.4558 45.8739i 0.273986 0.158186i
\(291\) 0 0
\(292\) 226.882 + 130.991i 0.776994 + 0.448598i
\(293\) 327.391i 1.11738i 0.829378 + 0.558688i \(0.188695\pi\)
−0.829378 + 0.558688i \(0.811305\pi\)
\(294\) 0 0
\(295\) −265.243 −0.899128
\(296\) −91.8406 + 159.073i −0.310272 + 0.537408i
\(297\) 0 0
\(298\) −18.6655 32.3296i −0.0626358 0.108488i
\(299\) −10.8091 6.24063i −0.0361508 0.0208717i
\(300\) 0 0
\(301\) 0 0
\(302\) −189.806 −0.628497
\(303\) 0 0
\(304\) −2.48528 + 1.43488i −0.00817527 + 0.00471999i
\(305\) −104.919 181.725i −0.343998 0.595821i
\(306\) 0 0
\(307\) 256.140i 0.834331i −0.908831 0.417165i \(-0.863024\pi\)
0.908831 0.417165i \(-0.136976\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 55.1285 95.4853i 0.177834 0.308017i
\(311\) 187.349 108.166i 0.602409 0.347801i −0.167580 0.985859i \(-0.553595\pi\)
0.769989 + 0.638057i \(0.220262\pi\)
\(312\) 0 0
\(313\) −135.809 78.4092i −0.433893 0.250509i 0.267110 0.963666i \(-0.413931\pi\)
−0.701004 + 0.713157i \(0.747264\pi\)
\(314\) 320.595i 1.02100i
\(315\) 0 0
\(316\) −152.426 −0.482362
\(317\) −224.015 + 388.005i −0.706671 + 1.22399i 0.259414 + 0.965766i \(0.416471\pi\)
−0.966085 + 0.258224i \(0.916863\pi\)
\(318\) 0 0
\(319\) 135.640 + 234.935i 0.425203 + 0.736472i
\(320\) 21.9411 + 12.6677i 0.0685660 + 0.0395866i
\(321\) 0 0
\(322\) 0 0
\(323\) −9.72792 −0.0301174
\(324\) 0 0
\(325\) 71.2203 41.1191i 0.219140 0.126520i
\(326\) 65.0381 + 112.649i 0.199503 + 0.345550i
\(327\) 0 0
\(328\) 59.4841i 0.181354i
\(329\) 0 0
\(330\) 0 0
\(331\) 27.5036 47.6376i 0.0830924 0.143920i −0.821484 0.570231i \(-0.806854\pi\)
0.904577 + 0.426311i \(0.140187\pi\)
\(332\) 187.029 107.981i 0.563342 0.325245i
\(333\) 0 0
\(334\) −249.213 143.883i −0.746147 0.430788i
\(335\) 293.383i 0.875770i
\(336\) 0 0
\(337\) −111.632 −0.331254 −0.165627 0.986189i \(-0.552965\pi\)
−0.165627 + 0.986189i \(0.552965\pi\)
\(338\) −98.1630 + 170.023i −0.290423 + 0.503027i
\(339\) 0 0
\(340\) 42.9411 + 74.3762i 0.126297 + 0.218754i
\(341\) 282.331 + 163.004i 0.827949 + 0.478016i
\(342\) 0 0
\(343\) 0 0
\(344\) 18.3431 0.0533231
\(345\) 0 0
\(346\) −86.7244 + 50.0703i −0.250648 + 0.144712i
\(347\) 188.628 + 326.714i 0.543598 + 0.941539i 0.998694 + 0.0510967i \(0.0162717\pi\)
−0.455096 + 0.890442i \(0.650395\pi\)
\(348\) 0 0
\(349\) 204.034i 0.584624i 0.956323 + 0.292312i \(0.0944246\pi\)
−0.956323 + 0.292312i \(0.905575\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −37.4558 + 64.8754i −0.106409 + 0.184305i
\(353\) −361.198 + 208.538i −1.02323 + 0.590759i −0.915036 0.403371i \(-0.867838\pi\)
−0.108189 + 0.994130i \(0.534505\pi\)
\(354\) 0 0
\(355\) 132.816 + 76.6815i 0.374130 + 0.216004i
\(356\) 335.814i 0.943297i
\(357\) 0 0
\(358\) −153.889 −0.429859
\(359\) −89.4153 + 154.872i −0.249068 + 0.431398i −0.963267 0.268544i \(-0.913457\pi\)
0.714200 + 0.699942i \(0.246791\pi\)
\(360\) 0 0
\(361\) −180.243 312.189i −0.499287 0.864791i
\(362\) −122.059 70.4707i −0.337179 0.194671i
\(363\) 0 0
\(364\) 0 0
\(365\) −414.838 −1.13654
\(366\) 0 0
\(367\) 544.724 314.497i 1.48426 0.856939i 0.484422 0.874835i \(-0.339030\pi\)
0.999840 + 0.0178960i \(0.00569679\pi\)
\(368\) −4.54416 7.87071i −0.0123482 0.0213878i
\(369\) 0 0
\(370\) 290.853i 0.786088i
\(371\) 0 0
\(372\) 0 0
\(373\) 127.779 221.320i 0.342572 0.593351i −0.642338 0.766422i \(-0.722035\pi\)
0.984910 + 0.173070i \(0.0553687\pi\)
\(374\) −219.915 + 126.968i −0.588009 + 0.339487i
\(375\) 0 0
\(376\) 117.037 + 67.5711i 0.311267 + 0.179710i
\(377\) 112.532i 0.298494i
\(378\) 0 0
\(379\) 219.750 0.579816 0.289908 0.957055i \(-0.406375\pi\)
0.289908 + 0.957055i \(0.406375\pi\)
\(380\) 2.27208 3.93535i 0.00597915 0.0103562i
\(381\) 0 0
\(382\) 49.4300 + 85.6152i 0.129398 + 0.224124i
\(383\) −14.7534 8.51785i −0.0385205 0.0222398i 0.480616 0.876931i \(-0.340413\pi\)
−0.519137 + 0.854691i \(0.673746\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −45.7330 −0.118479
\(387\) 0 0
\(388\) −44.3087 + 25.5816i −0.114198 + 0.0659320i
\(389\) −76.1102 131.827i −0.195656 0.338886i 0.751459 0.659779i \(-0.229350\pi\)
−0.947115 + 0.320893i \(0.896017\pi\)
\(390\) 0 0
\(391\) 30.8076i 0.0787919i
\(392\) 0 0
\(393\) 0 0
\(394\) 195.941 339.380i 0.497313 0.861371i
\(395\) 209.025 120.681i 0.529178 0.305521i
\(396\) 0 0
\(397\) 322.786 + 186.361i 0.813064 + 0.469423i 0.848019 0.529966i \(-0.177795\pi\)
−0.0349549 + 0.999389i \(0.511129\pi\)
\(398\) 236.802i 0.594980i
\(399\) 0 0
\(400\) 59.8823 0.149706
\(401\) 325.786 564.279i 0.812435 1.40718i −0.0987205 0.995115i \(-0.531475\pi\)
0.911155 0.412063i \(-0.135192\pi\)
\(402\) 0 0
\(403\) −67.6173 117.117i −0.167785 0.290612i
\(404\) −49.3675 28.5024i −0.122197 0.0705504i
\(405\) 0 0
\(406\) 0 0
\(407\) 859.992 2.11300
\(408\) 0 0
\(409\) −462.081 + 266.782i −1.12978 + 0.652280i −0.943880 0.330289i \(-0.892854\pi\)
−0.185902 + 0.982568i \(0.559521\pi\)
\(410\) 47.0955 + 81.5717i 0.114867 + 0.198955i
\(411\) 0 0
\(412\) 112.982i 0.274229i
\(413\) 0 0
\(414\) 0 0
\(415\) −170.985 + 296.154i −0.412012 + 0.713625i
\(416\) 26.9117 15.5375i 0.0646916 0.0373497i
\(417\) 0 0
\(418\) 11.6360 + 6.71807i 0.0278374 + 0.0160719i
\(419\) 534.252i 1.27507i 0.770423 + 0.637533i \(0.220045\pi\)
−0.770423 + 0.637533i \(0.779955\pi\)
\(420\) 0 0
\(421\) 157.220 0.373445 0.186723 0.982413i \(-0.440213\pi\)
0.186723 + 0.982413i \(0.440213\pi\)
\(422\) 90.5614 156.857i 0.214600 0.371699i
\(423\) 0 0
\(424\) 31.1543 + 53.9609i 0.0734772 + 0.127266i
\(425\) 175.794 + 101.495i 0.413633 + 0.238811i
\(426\) 0 0
\(427\) 0 0
\(428\) −95.2203 −0.222477
\(429\) 0 0
\(430\) −25.1543 + 14.5229i −0.0584984 + 0.0337741i
\(431\) −114.268 197.918i −0.265123 0.459207i 0.702473 0.711711i \(-0.252079\pi\)
−0.967596 + 0.252504i \(0.918746\pi\)
\(432\) 0 0
\(433\) 47.5549i 0.109827i 0.998491 + 0.0549133i \(0.0174882\pi\)
−0.998491 + 0.0549133i \(0.982512\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −75.3087 + 130.438i −0.172726 + 0.299171i
\(437\) −1.41169 + 0.815039i −0.00323041 + 0.00186508i
\(438\) 0 0
\(439\) 63.9594 + 36.9270i 0.145693 + 0.0841161i 0.571075 0.820898i \(-0.306527\pi\)
−0.425381 + 0.905014i \(0.639860\pi\)
\(440\) 118.620i 0.269591i
\(441\) 0 0
\(442\) 105.338 0.238321
\(443\) 117.320 203.204i 0.264830 0.458699i −0.702689 0.711497i \(-0.748017\pi\)
0.967519 + 0.252798i \(0.0813507\pi\)
\(444\) 0 0
\(445\) −265.875 460.508i −0.597471 1.03485i
\(446\) −510.926 294.983i −1.14557 0.661397i
\(447\) 0 0
\(448\) 0 0
\(449\) 255.161 0.568288 0.284144 0.958782i \(-0.408291\pi\)
0.284144 + 0.958782i \(0.408291\pi\)
\(450\) 0 0
\(451\) −241.191 + 139.252i −0.534791 + 0.308762i
\(452\) 85.4558 + 148.014i 0.189062 + 0.327464i
\(453\) 0 0
\(454\) 328.465i 0.723492i
\(455\) 0 0
\(456\) 0 0
\(457\) 72.8675 126.210i 0.159448 0.276171i −0.775222 0.631689i \(-0.782362\pi\)
0.934670 + 0.355518i \(0.115695\pi\)
\(458\) −102.416 + 59.1297i −0.223615 + 0.129104i
\(459\) 0 0
\(460\) 12.4630 + 7.19551i 0.0270934 + 0.0156424i
\(461\) 888.329i 1.92696i −0.267777 0.963481i \(-0.586289\pi\)
0.267777 0.963481i \(-0.413711\pi\)
\(462\) 0 0
\(463\) 234.014 0.505430 0.252715 0.967541i \(-0.418676\pi\)
0.252715 + 0.967541i \(0.418676\pi\)
\(464\) 40.9706 70.9631i 0.0882986 0.152938i
\(465\) 0 0
\(466\) 154.908 + 268.309i 0.332421 + 0.575770i
\(467\) 681.231 + 393.309i 1.45874 + 0.842204i 0.998950 0.0458237i \(-0.0145912\pi\)
0.459790 + 0.888028i \(0.347925\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −213.993 −0.455304
\(471\) 0 0
\(472\) −205.154 + 118.446i −0.434649 + 0.250945i
\(473\) −42.9411 74.3762i −0.0907846 0.157244i
\(474\) 0 0
\(475\) 10.7405i 0.0226115i
\(476\) 0 0
\(477\) 0 0
\(478\) 136.544 236.501i 0.285657 0.494773i
\(479\) 638.202 368.466i 1.33236 0.769240i 0.346702 0.937975i \(-0.387302\pi\)
0.985661 + 0.168735i \(0.0539682\pi\)
\(480\) 0 0
\(481\) −308.948 178.371i −0.642304 0.370834i
\(482\) 70.0505i 0.145333i
\(483\) 0 0
\(484\) 108.735 0.224659
\(485\) 40.5076 70.1612i 0.0835208 0.144662i
\(486\) 0 0
\(487\) −135.349 234.432i −0.277925 0.481379i 0.692944 0.720991i \(-0.256313\pi\)
−0.970869 + 0.239612i \(0.922980\pi\)
\(488\) −162.302 93.7048i −0.332585 0.192018i
\(489\) 0 0
\(490\) 0 0
\(491\) −760.161 −1.54819 −0.774094 0.633070i \(-0.781794\pi\)
−0.774094 + 0.633070i \(0.781794\pi\)
\(492\) 0 0
\(493\) 240.551 138.882i 0.487934 0.281709i
\(494\) −2.78680 4.82687i −0.00564129 0.00977100i
\(495\) 0 0
\(496\) 98.4720i 0.198532i
\(497\) 0 0
\(498\) 0 0
\(499\) −62.7462 + 108.680i −0.125744 + 0.217795i −0.922023 0.387134i \(-0.873465\pi\)
0.796280 + 0.604929i \(0.206798\pi\)
\(500\) −219.250 + 126.584i −0.438500 + 0.253168i
\(501\) 0 0
\(502\) −199.051 114.922i −0.396516 0.228928i
\(503\) 117.083i 0.232770i −0.993204 0.116385i \(-0.962869\pi\)
0.993204 0.116385i \(-0.0371306\pi\)
\(504\) 0 0
\(505\) 90.2649 0.178742
\(506\) −21.2756 + 36.8505i −0.0420467 + 0.0728271i
\(507\) 0 0
\(508\) 60.6619 + 105.070i 0.119413 + 0.206830i
\(509\) −574.110 331.463i −1.12792 0.651204i −0.184507 0.982831i \(-0.559069\pi\)
−0.943410 + 0.331627i \(0.892402\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 22.6274 0.0441942
\(513\) 0 0
\(514\) 121.445 70.1164i 0.236275 0.136413i
\(515\) −89.4518 154.935i −0.173693 0.300845i
\(516\) 0 0
\(517\) 632.733i 1.22386i
\(518\) 0 0
\(519\) 0 0
\(520\) −24.6030 + 42.6137i −0.0473135 + 0.0819494i
\(521\) −40.8229 + 23.5691i −0.0783550 + 0.0452383i −0.538666 0.842520i \(-0.681071\pi\)
0.460311 + 0.887758i \(0.347738\pi\)
\(522\) 0 0
\(523\) −432.554 249.735i −0.827064 0.477506i 0.0257824 0.999668i \(-0.491792\pi\)
−0.852846 + 0.522162i \(0.825126\pi\)
\(524\) 265.895i 0.507434i
\(525\) 0 0
\(526\) −614.257 −1.16779
\(527\) 166.901 289.080i 0.316699 0.548539i
\(528\) 0 0
\(529\) 261.919 + 453.657i 0.495121 + 0.857574i
\(530\) −85.4451 49.3318i −0.161217 0.0930788i
\(531\) 0 0
\(532\) 0 0
\(533\) 115.529 0.216752
\(534\) 0 0
\(535\) 130.578 75.3890i 0.244070 0.140914i
\(536\) −131.012 226.920i −0.244426 0.423358i
\(537\) 0 0
\(538\) 129.271i 0.240280i
\(539\) 0 0
\(540\) 0 0
\(541\) −249.405 + 431.981i −0.461007 + 0.798487i −0.999011 0.0444550i \(-0.985845\pi\)
0.538005 + 0.842942i \(0.319178\pi\)
\(542\) 20.9376 12.0883i 0.0386302 0.0223031i
\(543\) 0 0
\(544\) 66.4264 + 38.3513i 0.122107 + 0.0704987i
\(545\) 238.497i 0.437609i
\(546\) 0 0
\(547\) −279.897 −0.511694 −0.255847 0.966717i \(-0.582354\pi\)
−0.255847 + 0.966717i \(0.582354\pi\)
\(548\) −117.426 + 203.389i −0.214282 + 0.371147i
\(549\) 0 0
\(550\) −140.184 242.805i −0.254880 0.441464i
\(551\) −12.7279 7.34847i −0.0230997 0.0133366i
\(552\) 0 0
\(553\) 0 0
\(554\) −566.267 −1.02214
\(555\) 0 0
\(556\) −118.794 + 68.5857i −0.213658 + 0.123356i
\(557\) −130.890 226.708i −0.234991 0.407016i 0.724279 0.689507i \(-0.242173\pi\)
−0.959270 + 0.282491i \(0.908839\pi\)
\(558\) 0 0
\(559\) 35.6258i 0.0637312i
\(560\) 0 0
\(561\) 0 0
\(562\) −380.912 + 659.758i −0.677779 + 1.17395i
\(563\) −420.076 + 242.531i −0.746139 + 0.430784i −0.824297 0.566157i \(-0.808429\pi\)
0.0781581 + 0.996941i \(0.475096\pi\)
\(564\) 0 0
\(565\) −234.375 135.316i −0.414822 0.239498i
\(566\) 437.287i 0.772593i
\(567\) 0 0
\(568\) 136.971 0.241145
\(569\) −227.000 + 393.175i −0.398945 + 0.690993i −0.993596 0.112991i \(-0.963957\pi\)
0.594651 + 0.803984i \(0.297290\pi\)
\(570\) 0 0
\(571\) 115.769 + 200.517i 0.202747 + 0.351168i 0.949413 0.314032i \(-0.101680\pi\)
−0.746666 + 0.665200i \(0.768346\pi\)
\(572\) −126.000 72.7461i −0.220280 0.127179i
\(573\) 0 0
\(574\) 0 0
\(575\) 34.0143 0.0591553
\(576\) 0 0
\(577\) −564.014 + 325.634i −0.977494 + 0.564356i −0.901513 0.432753i \(-0.857542\pi\)
−0.0759812 + 0.997109i \(0.524209\pi\)
\(578\) −74.3503 128.778i −0.128634 0.222800i
\(579\) 0 0
\(580\) 129.751i 0.223708i
\(581\) 0 0
\(582\) 0 0
\(583\) 145.864 252.644i 0.250195 0.433351i
\(584\) −320.860 + 185.249i −0.549418 + 0.317206i
\(585\) 0 0
\(586\) −400.971 231.500i −0.684250 0.395052i
\(587\) 823.029i 1.40209i −0.713116 0.701046i \(-0.752717\pi\)
0.713116 0.701046i \(-0.247283\pi\)
\(588\) 0 0
\(589\) −17.6619 −0.0299863
\(590\) 187.555 324.855i 0.317890 0.550601i
\(591\) 0 0
\(592\) −129.882 224.963i −0.219396 0.380004i
\(593\) −700.110 404.209i −1.18062 0.681634i −0.224465 0.974482i \(-0.572064\pi\)
−0.956159 + 0.292848i \(0.905397\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 52.7939 0.0885804
\(597\) 0 0
\(598\) 15.2864 8.82559i 0.0255625 0.0147585i
\(599\) 265.422 + 459.725i 0.443109 + 0.767488i 0.997918 0.0644900i \(-0.0205421\pi\)
−0.554809 + 0.831978i \(0.687209\pi\)
\(600\) 0 0
\(601\) 936.503i 1.55824i −0.626874 0.779121i \(-0.715666\pi\)
0.626874 0.779121i \(-0.284334\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 134.213 232.464i 0.222207 0.384874i
\(605\) −149.111 + 86.0890i −0.246464 + 0.142296i
\(606\) 0 0
\(607\) −521.452 301.060i −0.859064 0.495981i 0.00463474 0.999989i \(-0.498525\pi\)
−0.863699 + 0.504008i \(0.831858\pi\)
\(608\) 4.05845i 0.00667508i
\(609\) 0 0
\(610\) 296.756 0.486486
\(611\) −131.235 + 227.307i −0.214788 + 0.372024i
\(612\) 0 0
\(613\) −548.448 949.940i −0.894695 1.54966i −0.834181 0.551491i \(-0.814059\pi\)
−0.0605142 0.998167i \(-0.519274\pi\)
\(614\) 313.706 + 181.118i 0.510921 + 0.294981i
\(615\) 0 0
\(616\) 0 0
\(617\) 432.956 0.701712 0.350856 0.936429i \(-0.385891\pi\)
0.350856 + 0.936429i \(0.385891\pi\)
\(618\) 0 0
\(619\) −194.951 + 112.555i −0.314946 + 0.181834i −0.649137 0.760671i \(-0.724870\pi\)
0.334192 + 0.942505i \(0.391537\pi\)
\(620\) 77.9634 + 135.037i 0.125747 + 0.217801i
\(621\) 0 0
\(622\) 305.940i 0.491865i
\(623\) 0 0
\(624\) 0 0
\(625\) 13.3091 23.0520i 0.0212945 0.0368832i
\(626\) 192.062 110.887i 0.306809 0.177136i
\(627\) 0 0
\(628\) −392.647 226.695i −0.625234 0.360979i
\(629\) 880.552i 1.39992i
\(630\) 0 0
\(631\) 750.514 1.18940 0.594702 0.803946i \(-0.297270\pi\)
0.594702 + 0.803946i \(0.297270\pi\)
\(632\) 107.782 186.683i 0.170541 0.295385i
\(633\) 0 0
\(634\) −316.805 548.722i −0.499692 0.865492i
\(635\) −166.374 96.0560i −0.262006 0.151269i
\(636\) 0 0
\(637\) 0 0
\(638\) −383.647 −0.601327
\(639\) 0 0
\(640\) −31.0294 + 17.9149i −0.0484835 + 0.0279920i
\(641\) −580.926 1006.19i −0.906281 1.56973i −0.819188 0.573525i \(-0.805575\pi\)
−0.0870937 0.996200i \(-0.527758\pi\)
\(642\) 0 0
\(643\) 121.957i 0.189669i 0.995493 + 0.0948347i \(0.0302322\pi\)
−0.995493 + 0.0948347i \(0.969768\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 6.87868 11.9142i 0.0106481 0.0184431i
\(647\) −137.504 + 79.3877i −0.212525 + 0.122701i −0.602484 0.798131i \(-0.705822\pi\)
0.389959 + 0.920832i \(0.372489\pi\)
\(648\) 0 0
\(649\) 960.529 + 554.561i 1.48001 + 0.854486i
\(650\) 116.302i 0.178927i
\(651\) 0 0
\(652\) −183.955 −0.282140
\(653\) −195.471 + 338.565i −0.299342 + 0.518476i −0.975986 0.217835i \(-0.930101\pi\)
0.676643 + 0.736311i \(0.263434\pi\)
\(654\) 0 0
\(655\) −210.518 364.628i −0.321401 0.556683i
\(656\) 72.8528 + 42.0616i 0.111056 + 0.0641183i
\(657\) 0 0
\(658\) 0 0
\(659\) 331.955 0.503726 0.251863 0.967763i \(-0.418957\pi\)
0.251863 + 0.967763i \(0.418957\pi\)
\(660\) 0 0
\(661\) −561.029 + 323.910i −0.848758 + 0.490031i −0.860232 0.509904i \(-0.829681\pi\)
0.0114736 + 0.999934i \(0.496348\pi\)
\(662\) 38.8959 + 67.3697i 0.0587552 + 0.101767i
\(663\) 0 0
\(664\) 305.418i 0.459967i
\(665\) 0 0
\(666\) 0 0
\(667\) 23.2721 40.3084i 0.0348907 0.0604324i
\(668\) 352.441 203.482i 0.527606 0.304613i
\(669\) 0 0
\(670\) 359.319 + 207.453i 0.536298 + 0.309632i
\(671\) 877.448i 1.30767i
\(672\) 0 0
\(673\) 100.956 0.150009 0.0750047 0.997183i \(-0.476103\pi\)
0.0750047 + 0.997183i \(0.476103\pi\)
\(674\) 78.9361 136.721i 0.117116 0.202851i
\(675\) 0 0
\(676\) −138.823 240.449i −0.205360 0.355694i
\(677\) 643.610 + 371.588i 0.950679 + 0.548875i 0.893292 0.449477i \(-0.148390\pi\)
0.0573873 + 0.998352i \(0.481723\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −121.456 −0.178612
\(681\) 0 0
\(682\) −399.276 + 230.522i −0.585448 + 0.338009i
\(683\) 2.21721 + 3.84032i 0.00324628 + 0.00562272i 0.867644 0.497186i \(-0.165633\pi\)
−0.864398 + 0.502809i \(0.832300\pi\)
\(684\) 0 0
\(685\) 371.881i 0.542892i
\(686\) 0 0
\(687\) 0 0
\(688\) −12.9706 + 22.4657i −0.0188526 + 0.0326536i
\(689\) −104.802 + 60.5074i −0.152107 + 0.0878192i
\(690\) 0 0
\(691\) 846.253 + 488.584i 1.22468 + 0.707069i 0.965912 0.258871i \(-0.0833506\pi\)
0.258767 + 0.965940i \(0.416684\pi\)
\(692\) 141.620i 0.204654i
\(693\) 0 0
\(694\) −533.522 −0.768763
\(695\) 108.603 188.106i 0.156263 0.270656i
\(696\) 0 0
\(697\) 142.581 + 246.957i 0.204563 + 0.354314i
\(698\) −249.889 144.274i −0.358008 0.206696i
\(699\) 0 0
\(700\) 0 0
\(701\) 840.177 1.19854 0.599270 0.800547i \(-0.295458\pi\)
0.599270 + 0.800547i \(0.295458\pi\)
\(702\) 0 0
\(703\) −40.3492 + 23.2956i −0.0573958 + 0.0331375i
\(704\) −52.9706 91.7477i −0.0752423 0.130323i
\(705\) 0 0
\(706\) 589.835i 0.835460i
\(707\) 0 0
\(708\) 0 0
\(709\) −341.279 + 591.112i −0.481352 + 0.833727i −0.999771 0.0214003i \(-0.993188\pi\)
0.518419 + 0.855127i \(0.326521\pi\)
\(710\) −187.831 + 108.444i −0.264550 + 0.152738i
\(711\) 0 0
\(712\) −411.286 237.456i −0.577649 0.333506i
\(713\) 55.9340i 0.0784488i
\(714\) 0 0
\(715\) 230.382 0.322212
\(716\) 108.816 188.475i 0.151978 0.263234i
\(717\) 0 0
\(718\) −126.452 219.022i −0.176117 0.305044i
\(719\) 119.187 + 68.8126i 0.165768 + 0.0957060i 0.580589 0.814197i \(-0.302822\pi\)
−0.414821 + 0.909903i \(0.636156\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 509.803 0.706099
\(723\) 0 0
\(724\) 172.617 99.6607i 0.238422 0.137653i
\(725\) 153.338 + 265.589i 0.211501 + 0.366330i
\(726\) 0 0
\(727\) 264.137i 0.363325i 0.983361 + 0.181662i \(0.0581478\pi\)
−0.983361 + 0.181662i \(0.941852\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 293.335 508.070i 0.401828 0.695987i
\(731\) −76.1543 + 43.9677i −0.104178 + 0.0601474i
\(732\) 0 0
\(733\) −501.705 289.660i −0.684455 0.395170i 0.117077 0.993123i \(-0.462648\pi\)
−0.801531 + 0.597953i \(0.795981\pi\)
\(734\) 889.530i 1.21189i
\(735\) 0 0
\(736\) 12.8528 0.0174631
\(737\) −613.397 + 1062.43i −0.832288 + 1.44157i
\(738\) 0 0
\(739\) 99.0477 + 171.556i 0.134029 + 0.232146i 0.925226 0.379416i \(-0.123875\pi\)
−0.791197 + 0.611562i \(0.790542\pi\)
\(740\) 356.220 + 205.664i 0.481379 + 0.277924i
\(741\) 0 0
\(742\) 0 0
\(743\) −976.690 −1.31452 −0.657261 0.753663i \(-0.728285\pi\)
−0.657261 + 0.753663i \(0.728285\pi\)
\(744\) 0 0
\(745\) −72.3974 + 41.7987i −0.0971777 + 0.0561056i
\(746\) 180.707 + 312.994i 0.242235 + 0.419563i
\(747\) 0 0
\(748\) 359.120i 0.480107i
\(749\) 0 0
\(750\) 0 0
\(751\) 417.665 723.417i 0.556145 0.963272i −0.441668 0.897178i \(-0.645613\pi\)
0.997813 0.0660933i \(-0.0210535\pi\)
\(752\) −165.515 + 95.5600i −0.220099 + 0.127074i
\(753\) 0 0
\(754\) 137.823 + 79.5724i 0.182790 + 0.105534i
\(755\) 425.044i 0.562972i
\(756\) 0 0
\(757\) 104.221 0.137677 0.0688383 0.997628i \(-0.478071\pi\)
0.0688383 + 0.997628i \(0.478071\pi\)
\(758\) −155.387 + 269.138i −0.204996 + 0.355063i
\(759\) 0 0
\(760\) 3.21320 + 5.56543i 0.00422790 + 0.00732294i
\(761\) −473.785 273.540i −0.622583 0.359448i 0.155291 0.987869i \(-0.450368\pi\)
−0.777874 + 0.628420i \(0.783702\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −139.809 −0.182996
\(765\) 0 0
\(766\) 20.8644 12.0461i 0.0272381 0.0157259i
\(767\) −230.044 398.447i −0.299927 0.519488i
\(768\) 0 0
\(769\) 341.205i 0.443700i −0.975081 0.221850i \(-0.928790\pi\)
0.975081 0.221850i \(-0.0712095\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 32.3381 56.0112i 0.0418887 0.0725534i
\(773\) −425.213 + 245.497i −0.550081 + 0.317590i −0.749155 0.662395i \(-0.769540\pi\)
0.199074 + 0.979985i \(0.436207\pi\)
\(774\) 0 0
\(775\) 319.169 + 184.273i 0.411832 + 0.237771i
\(776\) 72.3557i 0.0932419i
\(777\) 0 0
\(778\) 215.272 0.276699
\(779\) 7.54416 13.0669i 0.00968441 0.0167739i
\(780\) 0 0
\(781\) −320.647 555.376i −0.410559 0.711109i
\(782\) 37.7315 + 21.7843i 0.0482500 + 0.0278571i
\(783\) 0 0
\(784\) 0 0
\(785\) 717.926 0.914555
\(786\) 0 0
\(787\) −260.202 + 150.228i −0.330625 + 0.190887i −0.656119 0.754658i \(-0.727803\pi\)
0.325493 + 0.945544i \(0.394470\pi\)
\(788\) 277.103 + 479.956i 0.351653 + 0.609081i
\(789\) 0 0
\(790\) 341.337i 0.432072i
\(791\) 0 0