Properties

Label 324.5.d.e.163.13
Level 324
Weight 5
Character 324.163
Analytic conductor 33.492
Analytic rank 0
Dimension 22
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 324.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(33.4918680392\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 163.13
Character \(\chi\) \(=\) 324.163
Dual form 324.5.d.e.163.14

$q$-expansion

\(f(q)\) \(=\) \(q+(1.16626 - 3.82620i) q^{2} +(-13.2797 - 8.92473i) q^{4} +39.0789 q^{5} +12.2052i q^{7} +(-49.6354 + 40.4021i) q^{8} +O(q^{10})\) \(q+(1.16626 - 3.82620i) q^{2} +(-13.2797 - 8.92473i) q^{4} +39.0789 q^{5} +12.2052i q^{7} +(-49.6354 + 40.4021i) q^{8} +(45.5763 - 149.524i) q^{10} +111.018i q^{11} +208.982 q^{13} +(46.6996 + 14.2345i) q^{14} +(96.6986 + 237.035i) q^{16} -93.3790 q^{17} +26.8894i q^{19} +(-518.954 - 348.768i) q^{20} +(424.778 + 129.477i) q^{22} +874.774i q^{23} +902.160 q^{25} +(243.728 - 799.608i) q^{26} +(108.928 - 162.081i) q^{28} +1301.62 q^{29} +685.305i q^{31} +(1019.72 - 93.5434i) q^{32} +(-108.905 + 357.287i) q^{34} +476.966i q^{35} -1760.25 q^{37} +(102.884 + 31.3601i) q^{38} +(-1939.70 + 1578.87i) q^{40} -78.0843 q^{41} +1622.88i q^{43} +(990.807 - 1474.28i) q^{44} +(3347.06 + 1020.22i) q^{46} -2308.86i q^{47} +2252.03 q^{49} +(1052.16 - 3451.85i) q^{50} +(-2775.21 - 1865.11i) q^{52} +1313.48 q^{53} +4338.47i q^{55} +(-493.116 - 605.810i) q^{56} +(1518.03 - 4980.25i) q^{58} -5563.78i q^{59} +2180.26 q^{61} +(2622.12 + 799.247i) q^{62} +(831.345 - 4010.75i) q^{64} +8166.79 q^{65} -246.040i q^{67} +(1240.04 + 833.382i) q^{68} +(1824.97 + 556.268i) q^{70} -4608.15i q^{71} +2564.79 q^{73} +(-2052.92 + 6735.08i) q^{74} +(239.980 - 357.082i) q^{76} -1355.00 q^{77} -5180.32i q^{79} +(3778.87 + 9263.05i) q^{80} +(-91.0669 + 298.766i) q^{82} -1873.35i q^{83} -3649.15 q^{85} +(6209.48 + 1892.71i) q^{86} +(-4485.37 - 5510.43i) q^{88} +1167.17 q^{89} +2550.67i q^{91} +(7807.12 - 11616.7i) q^{92} +(-8834.19 - 2692.75i) q^{94} +1050.81i q^{95} -5739.16 q^{97} +(2626.47 - 8616.73i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - q^{2} + q^{4} - 2q^{5} - 61q^{8} + O(q^{10}) \) \( 22q - q^{2} + q^{4} - 2q^{5} - 61q^{8} + 14q^{10} + 2q^{13} + 252q^{14} + q^{16} + 28q^{17} - 140q^{20} + 33q^{22} + 1752q^{25} - 548q^{26} - 258q^{28} + 526q^{29} - 121q^{32} - 385q^{34} - 4q^{37} + 1395q^{38} + 2276q^{40} - 2762q^{41} - 3357q^{44} + 1788q^{46} - 3428q^{49} + 6375q^{50} - 1438q^{52} + 5044q^{53} - 7506q^{56} + 4064q^{58} + 2q^{61} + 9162q^{62} + 4513q^{64} - 2014q^{65} - 11405q^{68} - 3666q^{70} - 1708q^{73} + 14620q^{74} - 1581q^{76} - 3942q^{77} - 22760q^{80} - 4243q^{82} + 1252q^{85} + 22113q^{86} - 1995q^{88} - 6524q^{89} - 30294q^{92} - 7524q^{94} - 5638q^{97} + 46469q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.16626 3.82620i 0.291566 0.956551i
\(3\) 0 0
\(4\) −13.2797 8.92473i −0.829979 0.557795i
\(5\) 39.0789 1.56316 0.781578 0.623808i \(-0.214415\pi\)
0.781578 + 0.623808i \(0.214415\pi\)
\(6\) 0 0
\(7\) 12.2052i 0.249086i 0.992214 + 0.124543i \(0.0397464\pi\)
−0.992214 + 0.124543i \(0.960254\pi\)
\(8\) −49.6354 + 40.4021i −0.775553 + 0.631282i
\(9\) 0 0
\(10\) 45.5763 149.524i 0.455763 1.49524i
\(11\) 111.018i 0.917506i 0.888564 + 0.458753i \(0.151704\pi\)
−0.888564 + 0.458753i \(0.848296\pi\)
\(12\) 0 0
\(13\) 208.982 1.23658 0.618290 0.785950i \(-0.287826\pi\)
0.618290 + 0.785950i \(0.287826\pi\)
\(14\) 46.6996 + 14.2345i 0.238263 + 0.0726250i
\(15\) 0 0
\(16\) 96.6986 + 237.035i 0.377729 + 0.925916i
\(17\) −93.3790 −0.323111 −0.161555 0.986864i \(-0.551651\pi\)
−0.161555 + 0.986864i \(0.551651\pi\)
\(18\) 0 0
\(19\) 26.8894i 0.0744859i 0.999306 + 0.0372429i \(0.0118575\pi\)
−0.999306 + 0.0372429i \(0.988142\pi\)
\(20\) −518.954 348.768i −1.29739 0.871921i
\(21\) 0 0
\(22\) 424.778 + 129.477i 0.877641 + 0.267514i
\(23\) 874.774i 1.65364i 0.562469 + 0.826819i \(0.309852\pi\)
−0.562469 + 0.826819i \(0.690148\pi\)
\(24\) 0 0
\(25\) 902.160 1.44346
\(26\) 243.728 799.608i 0.360545 1.18285i
\(27\) 0 0
\(28\) 108.928 162.081i 0.138939 0.206736i
\(29\) 1301.62 1.54770 0.773851 0.633368i \(-0.218328\pi\)
0.773851 + 0.633368i \(0.218328\pi\)
\(30\) 0 0
\(31\) 685.305i 0.713117i 0.934273 + 0.356558i \(0.116050\pi\)
−0.934273 + 0.356558i \(0.883950\pi\)
\(32\) 1019.72 93.5434i 0.995819 0.0913509i
\(33\) 0 0
\(34\) −108.905 + 357.287i −0.0942081 + 0.309072i
\(35\) 476.966i 0.389360i
\(36\) 0 0
\(37\) −1760.25 −1.28579 −0.642897 0.765953i \(-0.722268\pi\)
−0.642897 + 0.765953i \(0.722268\pi\)
\(38\) 102.884 + 31.3601i 0.0712495 + 0.0217175i
\(39\) 0 0
\(40\) −1939.70 + 1578.87i −1.21231 + 0.986793i
\(41\) −78.0843 −0.0464511 −0.0232255 0.999730i \(-0.507394\pi\)
−0.0232255 + 0.999730i \(0.507394\pi\)
\(42\) 0 0
\(43\) 1622.88i 0.877709i 0.898558 + 0.438855i \(0.144616\pi\)
−0.898558 + 0.438855i \(0.855384\pi\)
\(44\) 990.807 1474.28i 0.511780 0.761510i
\(45\) 0 0
\(46\) 3347.06 + 1020.22i 1.58179 + 0.482144i
\(47\) 2308.86i 1.04521i −0.852575 0.522604i \(-0.824961\pi\)
0.852575 0.522604i \(-0.175039\pi\)
\(48\) 0 0
\(49\) 2252.03 0.937956
\(50\) 1052.16 3451.85i 0.420863 1.38074i
\(51\) 0 0
\(52\) −2775.21 1865.11i −1.02634 0.689759i
\(53\) 1313.48 0.467598 0.233799 0.972285i \(-0.424884\pi\)
0.233799 + 0.972285i \(0.424884\pi\)
\(54\) 0 0
\(55\) 4338.47i 1.43420i
\(56\) −493.116 605.810i −0.157243 0.193179i
\(57\) 0 0
\(58\) 1518.03 4980.25i 0.451257 1.48046i
\(59\) 5563.78i 1.59833i −0.601113 0.799164i \(-0.705276\pi\)
0.601113 0.799164i \(-0.294724\pi\)
\(60\) 0 0
\(61\) 2180.26 0.585933 0.292967 0.956123i \(-0.405358\pi\)
0.292967 + 0.956123i \(0.405358\pi\)
\(62\) 2622.12 + 799.247i 0.682132 + 0.207921i
\(63\) 0 0
\(64\) 831.345 4010.75i 0.202965 0.979186i
\(65\) 8166.79 1.93297
\(66\) 0 0
\(67\) 246.040i 0.0548096i −0.999624 0.0274048i \(-0.991276\pi\)
0.999624 0.0274048i \(-0.00872430\pi\)
\(68\) 1240.04 + 833.382i 0.268175 + 0.180230i
\(69\) 0 0
\(70\) 1824.97 + 556.268i 0.372443 + 0.113524i
\(71\) 4608.15i 0.914134i −0.889432 0.457067i \(-0.848900\pi\)
0.889432 0.457067i \(-0.151100\pi\)
\(72\) 0 0
\(73\) 2564.79 0.481290 0.240645 0.970613i \(-0.422641\pi\)
0.240645 + 0.970613i \(0.422641\pi\)
\(74\) −2052.92 + 6735.08i −0.374894 + 1.22993i
\(75\) 0 0
\(76\) 239.980 357.082i 0.0415479 0.0618217i
\(77\) −1355.00 −0.228538
\(78\) 0 0
\(79\) 5180.32i 0.830047i −0.909811 0.415023i \(-0.863773\pi\)
0.909811 0.415023i \(-0.136227\pi\)
\(80\) 3778.87 + 9263.05i 0.590449 + 1.44735i
\(81\) 0 0
\(82\) −91.0669 + 298.766i −0.0135436 + 0.0444328i
\(83\) 1873.35i 0.271934i −0.990713 0.135967i \(-0.956586\pi\)
0.990713 0.135967i \(-0.0434141\pi\)
\(84\) 0 0
\(85\) −3649.15 −0.505072
\(86\) 6209.48 + 1892.71i 0.839573 + 0.255910i
\(87\) 0 0
\(88\) −4485.37 5510.43i −0.579205 0.711574i
\(89\) 1167.17 0.147352 0.0736759 0.997282i \(-0.476527\pi\)
0.0736759 + 0.997282i \(0.476527\pi\)
\(90\) 0 0
\(91\) 2550.67i 0.308015i
\(92\) 7807.12 11616.7i 0.922391 1.37248i
\(93\) 0 0
\(94\) −8834.19 2692.75i −0.999795 0.304747i
\(95\) 1050.81i 0.116433i
\(96\) 0 0
\(97\) −5739.16 −0.609965 −0.304983 0.952358i \(-0.598651\pi\)
−0.304983 + 0.952358i \(0.598651\pi\)
\(98\) 2626.47 8616.73i 0.273476 0.897203i
\(99\) 0 0
\(100\) −11980.4 8051.53i −1.19804 0.805153i
\(101\) −15586.7 −1.52796 −0.763981 0.645238i \(-0.776758\pi\)
−0.763981 + 0.645238i \(0.776758\pi\)
\(102\) 0 0
\(103\) 11127.3i 1.04885i 0.851455 + 0.524427i \(0.175720\pi\)
−0.851455 + 0.524427i \(0.824280\pi\)
\(104\) −10372.9 + 8443.31i −0.959034 + 0.780632i
\(105\) 0 0
\(106\) 1531.87 5025.65i 0.136336 0.447281i
\(107\) 4464.91i 0.389983i −0.980805 0.194991i \(-0.937532\pi\)
0.980805 0.194991i \(-0.0624679\pi\)
\(108\) 0 0
\(109\) −4736.05 −0.398624 −0.199312 0.979936i \(-0.563871\pi\)
−0.199312 + 0.979936i \(0.563871\pi\)
\(110\) 16599.9 + 5059.80i 1.37189 + 0.418165i
\(111\) 0 0
\(112\) −2893.06 + 1180.23i −0.230633 + 0.0940869i
\(113\) 18346.1 1.43677 0.718385 0.695645i \(-0.244881\pi\)
0.718385 + 0.695645i \(0.244881\pi\)
\(114\) 0 0
\(115\) 34185.2i 2.58489i
\(116\) −17285.0 11616.6i −1.28456 0.863301i
\(117\) 0 0
\(118\) −21288.2 6488.84i −1.52888 0.466018i
\(119\) 1139.71i 0.0804823i
\(120\) 0 0
\(121\) 2315.96 0.158183
\(122\) 2542.76 8342.10i 0.170838 0.560475i
\(123\) 0 0
\(124\) 6116.16 9100.62i 0.397773 0.591872i
\(125\) 10831.1 0.693190
\(126\) 0 0
\(127\) 8169.42i 0.506505i −0.967400 0.253252i \(-0.918500\pi\)
0.967400 0.253252i \(-0.0815003\pi\)
\(128\) −14376.4 7858.48i −0.877463 0.479644i
\(129\) 0 0
\(130\) 9524.63 31247.8i 0.563588 1.84898i
\(131\) 10543.6i 0.614392i 0.951646 + 0.307196i \(0.0993907\pi\)
−0.951646 + 0.307196i \(0.900609\pi\)
\(132\) 0 0
\(133\) −328.191 −0.0185534
\(134\) −941.399 286.948i −0.0524281 0.0159806i
\(135\) 0 0
\(136\) 4634.90 3772.70i 0.250589 0.203974i
\(137\) −3225.71 −0.171864 −0.0859318 0.996301i \(-0.527387\pi\)
−0.0859318 + 0.996301i \(0.527387\pi\)
\(138\) 0 0
\(139\) 18794.3i 0.972742i 0.873752 + 0.486371i \(0.161680\pi\)
−0.873752 + 0.486371i \(0.838320\pi\)
\(140\) 4256.79 6333.94i 0.217183 0.323160i
\(141\) 0 0
\(142\) −17631.7 5374.32i −0.874415 0.266530i
\(143\) 23200.8i 1.13457i
\(144\) 0 0
\(145\) 50865.8 2.41930
\(146\) 2991.22 9813.41i 0.140328 0.460378i
\(147\) 0 0
\(148\) 23375.5 + 15709.8i 1.06718 + 0.717210i
\(149\) 7650.25 0.344590 0.172295 0.985045i \(-0.444882\pi\)
0.172295 + 0.985045i \(0.444882\pi\)
\(150\) 0 0
\(151\) 1125.80i 0.0493751i 0.999695 + 0.0246876i \(0.00785910\pi\)
−0.999695 + 0.0246876i \(0.992141\pi\)
\(152\) −1086.39 1334.67i −0.0470216 0.0577677i
\(153\) 0 0
\(154\) −1580.29 + 5184.51i −0.0666338 + 0.218608i
\(155\) 26781.0i 1.11471i
\(156\) 0 0
\(157\) −3511.62 −0.142465 −0.0712326 0.997460i \(-0.522693\pi\)
−0.0712326 + 0.997460i \(0.522693\pi\)
\(158\) −19821.0 6041.62i −0.793982 0.242013i
\(159\) 0 0
\(160\) 39849.5 3655.57i 1.55662 0.142796i
\(161\) −10676.8 −0.411898
\(162\) 0 0
\(163\) 41947.9i 1.57883i 0.613861 + 0.789414i \(0.289615\pi\)
−0.613861 + 0.789414i \(0.710385\pi\)
\(164\) 1036.93 + 696.881i 0.0385534 + 0.0259102i
\(165\) 0 0
\(166\) −7167.83 2184.83i −0.260119 0.0792868i
\(167\) 6813.40i 0.244304i −0.992511 0.122152i \(-0.961020\pi\)
0.992511 0.122152i \(-0.0389796\pi\)
\(168\) 0 0
\(169\) 15112.5 0.529131
\(170\) −4255.87 + 13962.4i −0.147262 + 0.483127i
\(171\) 0 0
\(172\) 14483.8 21551.3i 0.489582 0.728480i
\(173\) −15748.3 −0.526189 −0.263095 0.964770i \(-0.584743\pi\)
−0.263095 + 0.964770i \(0.584743\pi\)
\(174\) 0 0
\(175\) 11011.0i 0.359544i
\(176\) −26315.2 + 10735.3i −0.849534 + 0.346568i
\(177\) 0 0
\(178\) 1361.23 4465.85i 0.0429628 0.140950i
\(179\) 22497.6i 0.702151i −0.936347 0.351075i \(-0.885816\pi\)
0.936347 0.351075i \(-0.114184\pi\)
\(180\) 0 0
\(181\) −21847.2 −0.666867 −0.333434 0.942774i \(-0.608207\pi\)
−0.333434 + 0.942774i \(0.608207\pi\)
\(182\) 9759.38 + 2974.75i 0.294632 + 0.0898066i
\(183\) 0 0
\(184\) −35342.7 43419.8i −1.04391 1.28248i
\(185\) −68788.7 −2.00990
\(186\) 0 0
\(187\) 10366.8i 0.296456i
\(188\) −20606.0 + 30660.9i −0.583012 + 0.867500i
\(189\) 0 0
\(190\) 4020.60 + 1225.52i 0.111374 + 0.0339479i
\(191\) 18685.5i 0.512199i 0.966650 + 0.256099i \(0.0824375\pi\)
−0.966650 + 0.256099i \(0.917563\pi\)
\(192\) 0 0
\(193\) 46099.4 1.23760 0.618800 0.785548i \(-0.287619\pi\)
0.618800 + 0.785548i \(0.287619\pi\)
\(194\) −6693.38 + 21959.2i −0.177845 + 0.583462i
\(195\) 0 0
\(196\) −29906.2 20098.8i −0.778484 0.523188i
\(197\) −15934.7 −0.410592 −0.205296 0.978700i \(-0.565816\pi\)
−0.205296 + 0.978700i \(0.565816\pi\)
\(198\) 0 0
\(199\) 73733.8i 1.86192i 0.365124 + 0.930959i \(0.381026\pi\)
−0.365124 + 0.930959i \(0.618974\pi\)
\(200\) −44779.1 + 36449.1i −1.11948 + 0.911228i
\(201\) 0 0
\(202\) −18178.3 + 59638.1i −0.445502 + 1.46157i
\(203\) 15886.5i 0.385511i
\(204\) 0 0
\(205\) −3051.45 −0.0726103
\(206\) 42575.3 + 12977.4i 1.00328 + 0.305810i
\(207\) 0 0
\(208\) 20208.3 + 49536.0i 0.467092 + 1.14497i
\(209\) −2985.21 −0.0683412
\(210\) 0 0
\(211\) 17818.4i 0.400224i 0.979773 + 0.200112i \(0.0641307\pi\)
−0.979773 + 0.200112i \(0.935869\pi\)
\(212\) −17442.6 11722.5i −0.388096 0.260824i
\(213\) 0 0
\(214\) −17083.7 5207.26i −0.373038 0.113706i
\(215\) 63420.5i 1.37200i
\(216\) 0 0
\(217\) −8364.29 −0.177627
\(218\) −5523.49 + 18121.1i −0.116225 + 0.381304i
\(219\) 0 0
\(220\) 38719.6 57613.4i 0.799993 1.19036i
\(221\) −19514.5 −0.399552
\(222\) 0 0
\(223\) 67381.1i 1.35497i 0.735538 + 0.677483i \(0.236929\pi\)
−0.735538 + 0.677483i \(0.763071\pi\)
\(224\) 1141.72 + 12445.9i 0.0227542 + 0.248044i
\(225\) 0 0
\(226\) 21396.4 70196.0i 0.418914 1.37434i
\(227\) 62794.3i 1.21862i −0.792932 0.609310i \(-0.791446\pi\)
0.792932 0.609310i \(-0.208554\pi\)
\(228\) 0 0
\(229\) −40926.3 −0.780426 −0.390213 0.920725i \(-0.627599\pi\)
−0.390213 + 0.920725i \(0.627599\pi\)
\(230\) 130800. + 39869.0i 2.47258 + 0.753667i
\(231\) 0 0
\(232\) −64606.3 + 52588.0i −1.20033 + 0.977037i
\(233\) −79254.5 −1.45986 −0.729932 0.683520i \(-0.760448\pi\)
−0.729932 + 0.683520i \(0.760448\pi\)
\(234\) 0 0
\(235\) 90227.9i 1.63382i
\(236\) −49655.2 + 73885.1i −0.891540 + 1.32658i
\(237\) 0 0
\(238\) −4360.76 1329.20i −0.0769854 0.0234659i
\(239\) 45131.1i 0.790096i −0.918661 0.395048i \(-0.870728\pi\)
0.918661 0.395048i \(-0.129272\pi\)
\(240\) 0 0
\(241\) 75653.5 1.30255 0.651276 0.758841i \(-0.274234\pi\)
0.651276 + 0.758841i \(0.274234\pi\)
\(242\) 2701.02 8861.32i 0.0461208 0.151310i
\(243\) 0 0
\(244\) −28953.1 19458.2i −0.486312 0.326831i
\(245\) 88007.0 1.46617
\(246\) 0 0
\(247\) 5619.40i 0.0921078i
\(248\) −27687.7 34015.4i −0.450178 0.553060i
\(249\) 0 0
\(250\) 12631.9 41442.0i 0.202111 0.663072i
\(251\) 78270.9i 1.24238i −0.783662 0.621188i \(-0.786650\pi\)
0.783662 0.621188i \(-0.213350\pi\)
\(252\) 0 0
\(253\) −97115.9 −1.51722
\(254\) −31257.8 9527.70i −0.484498 0.147680i
\(255\) 0 0
\(256\) −46834.8 + 45841.8i −0.714642 + 0.699490i
\(257\) 23012.7 0.348418 0.174209 0.984709i \(-0.444263\pi\)
0.174209 + 0.984709i \(0.444263\pi\)
\(258\) 0 0
\(259\) 21484.2i 0.320273i
\(260\) −108452. 72886.4i −1.60432 1.07820i
\(261\) 0 0
\(262\) 40341.9 + 12296.6i 0.587697 + 0.179136i
\(263\) 86877.1i 1.25601i −0.778209 0.628006i \(-0.783871\pi\)
0.778209 0.628006i \(-0.216129\pi\)
\(264\) 0 0
\(265\) 51329.5 0.730929
\(266\) −382.757 + 1255.72i −0.00540953 + 0.0177472i
\(267\) 0 0
\(268\) −2195.84 + 3267.33i −0.0305725 + 0.0454908i
\(269\) 54083.3 0.747409 0.373705 0.927548i \(-0.378087\pi\)
0.373705 + 0.927548i \(0.378087\pi\)
\(270\) 0 0
\(271\) 47957.3i 0.653004i −0.945197 0.326502i \(-0.894130\pi\)
0.945197 0.326502i \(-0.105870\pi\)
\(272\) −9029.61 22134.0i −0.122048 0.299173i
\(273\) 0 0
\(274\) −3762.03 + 12342.2i −0.0501096 + 0.164396i
\(275\) 100156.i 1.32438i
\(276\) 0 0
\(277\) −73723.5 −0.960830 −0.480415 0.877041i \(-0.659514\pi\)
−0.480415 + 0.877041i \(0.659514\pi\)
\(278\) 71911.0 + 21919.2i 0.930477 + 0.283618i
\(279\) 0 0
\(280\) −19270.4 23674.4i −0.245796 0.301969i
\(281\) −56123.9 −0.710780 −0.355390 0.934718i \(-0.615652\pi\)
−0.355390 + 0.934718i \(0.615652\pi\)
\(282\) 0 0
\(283\) 152766.i 1.90746i −0.300666 0.953730i \(-0.597209\pi\)
0.300666 0.953730i \(-0.402791\pi\)
\(284\) −41126.5 + 61194.6i −0.509900 + 0.758711i
\(285\) 0 0
\(286\) 88771.0 + 27058.3i 1.08527 + 0.330802i
\(287\) 953.034i 0.0115703i
\(288\) 0 0
\(289\) −74801.4 −0.895600
\(290\) 59322.9 194623.i 0.705385 2.31418i
\(291\) 0 0
\(292\) −34059.6 22890.1i −0.399460 0.268461i
\(293\) 38840.3 0.452426 0.226213 0.974078i \(-0.427366\pi\)
0.226213 + 0.974078i \(0.427366\pi\)
\(294\) 0 0
\(295\) 217426.i 2.49844i
\(296\) 87370.8 71117.8i 0.997201 0.811699i
\(297\) 0 0
\(298\) 8922.21 29271.4i 0.100471 0.329618i
\(299\) 182812.i 2.04486i
\(300\) 0 0
\(301\) −19807.6 −0.218625
\(302\) 4307.55 + 1312.98i 0.0472298 + 0.0143961i
\(303\) 0 0
\(304\) −6373.72 + 2600.17i −0.0689677 + 0.0281354i
\(305\) 85202.0 0.915905
\(306\) 0 0
\(307\) 457.528i 0.00485446i −0.999997 0.00242723i \(-0.999227\pi\)
0.999997 0.00242723i \(-0.000772612\pi\)
\(308\) 17993.9 + 12093.0i 0.189681 + 0.127477i
\(309\) 0 0
\(310\) 102469. + 31233.7i 1.06628 + 0.325012i
\(311\) 10722.3i 0.110858i 0.998463 + 0.0554292i \(0.0176527\pi\)
−0.998463 + 0.0554292i \(0.982347\pi\)
\(312\) 0 0
\(313\) 17952.2 0.183244 0.0916218 0.995794i \(-0.470795\pi\)
0.0916218 + 0.995794i \(0.470795\pi\)
\(314\) −4095.48 + 13436.2i −0.0415380 + 0.136275i
\(315\) 0 0
\(316\) −46232.9 + 68792.9i −0.462996 + 0.688921i
\(317\) 61371.8 0.610732 0.305366 0.952235i \(-0.401221\pi\)
0.305366 + 0.952235i \(0.401221\pi\)
\(318\) 0 0
\(319\) 144503.i 1.42003i
\(320\) 32488.0 156735.i 0.317266 1.53062i
\(321\) 0 0
\(322\) −12452.0 + 40851.6i −0.120095 + 0.394001i
\(323\) 2510.90i 0.0240672i
\(324\) 0 0
\(325\) 188535. 1.78495
\(326\) 160501. + 48922.3i 1.51023 + 0.460333i
\(327\) 0 0
\(328\) 3875.74 3154.77i 0.0360253 0.0293237i
\(329\) 28180.2 0.260347
\(330\) 0 0
\(331\) 185899.i 1.69676i 0.529389 + 0.848379i \(0.322421\pi\)
−0.529389 + 0.848379i \(0.677579\pi\)
\(332\) −16719.2 + 24877.5i −0.151684 + 0.225700i
\(333\) 0 0
\(334\) −26069.4 7946.22i −0.233689 0.0712308i
\(335\) 9614.98i 0.0856759i
\(336\) 0 0
\(337\) −147998. −1.30315 −0.651576 0.758584i \(-0.725892\pi\)
−0.651576 + 0.758584i \(0.725892\pi\)
\(338\) 17625.2 57823.6i 0.154277 0.506141i
\(339\) 0 0
\(340\) 48459.4 + 32567.6i 0.419199 + 0.281727i
\(341\) −76081.3 −0.654289
\(342\) 0 0
\(343\) 56791.2i 0.482717i
\(344\) −65567.9 80552.5i −0.554082 0.680710i
\(345\) 0 0
\(346\) −18366.7 + 60256.2i −0.153419 + 0.503326i
\(347\) 144980.i 1.20406i −0.798472 0.602031i \(-0.794358\pi\)
0.798472 0.602031i \(-0.205642\pi\)
\(348\) 0 0
\(349\) −178952. −1.46921 −0.734606 0.678494i \(-0.762633\pi\)
−0.734606 + 0.678494i \(0.762633\pi\)
\(350\) 42130.5 + 12841.8i 0.343922 + 0.104831i
\(351\) 0 0
\(352\) 10385.0 + 113207.i 0.0838150 + 0.913670i
\(353\) −26395.4 −0.211826 −0.105913 0.994375i \(-0.533776\pi\)
−0.105913 + 0.994375i \(0.533776\pi\)
\(354\) 0 0
\(355\) 180081.i 1.42893i
\(356\) −15499.7 10416.7i −0.122299 0.0821922i
\(357\) 0 0
\(358\) −86080.4 26238.2i −0.671643 0.204723i
\(359\) 181364.i 1.40722i 0.710587 + 0.703609i \(0.248429\pi\)
−0.710587 + 0.703609i \(0.751571\pi\)
\(360\) 0 0
\(361\) 129598. 0.994452
\(362\) −25479.6 + 83592.0i −0.194436 + 0.637892i
\(363\) 0 0
\(364\) 22764.0 33872.0i 0.171809 0.255646i
\(365\) 100229. 0.752331
\(366\) 0 0
\(367\) 209000.i 1.55173i −0.630901 0.775863i \(-0.717315\pi\)
0.630901 0.775863i \(-0.282685\pi\)
\(368\) −207352. + 84589.4i −1.53113 + 0.624626i
\(369\) 0 0
\(370\) −80225.8 + 263199.i −0.586017 + 1.92257i
\(371\) 16031.3i 0.116472i
\(372\) 0 0
\(373\) −76595.9 −0.550539 −0.275269 0.961367i \(-0.588767\pi\)
−0.275269 + 0.961367i \(0.588767\pi\)
\(374\) −39665.4 12090.4i −0.283575 0.0864365i
\(375\) 0 0
\(376\) 93282.9 + 114601.i 0.659822 + 0.810614i
\(377\) 272015. 1.91386
\(378\) 0 0
\(379\) 232118.i 1.61596i −0.589211 0.807979i \(-0.700561\pi\)
0.589211 0.807979i \(-0.299439\pi\)
\(380\) 9378.17 13954.4i 0.0649458 0.0966369i
\(381\) 0 0
\(382\) 71494.6 + 21792.3i 0.489944 + 0.149340i
\(383\) 85585.3i 0.583447i −0.956503 0.291724i \(-0.905771\pi\)
0.956503 0.291724i \(-0.0942288\pi\)
\(384\) 0 0
\(385\) −52951.9 −0.357240
\(386\) 53764.1 176386.i 0.360842 1.18383i
\(387\) 0 0
\(388\) 76214.1 + 51220.4i 0.506258 + 0.340236i
\(389\) −121738. −0.804504 −0.402252 0.915529i \(-0.631772\pi\)
−0.402252 + 0.915529i \(0.631772\pi\)
\(390\) 0 0
\(391\) 81685.5i 0.534308i
\(392\) −111781. + 90986.8i −0.727435 + 0.592115i
\(393\) 0 0
\(394\) −18584.0 + 60969.2i −0.119715 + 0.392752i
\(395\) 202441.i 1.29749i
\(396\) 0 0
\(397\) −71690.8 −0.454865 −0.227432 0.973794i \(-0.573033\pi\)
−0.227432 + 0.973794i \(0.573033\pi\)
\(398\) 282120. + 85993.1i 1.78102 + 0.542872i
\(399\) 0 0
\(400\) 87237.5 + 213843.i 0.545235 + 1.33652i
\(401\) 86280.5 0.536567 0.268283 0.963340i \(-0.413544\pi\)
0.268283 + 0.963340i \(0.413544\pi\)
\(402\) 0 0
\(403\) 143217.i 0.881826i
\(404\) 206987. + 139107.i 1.26818 + 0.852291i
\(405\) 0 0
\(406\) 60785.0 + 18527.9i 0.368761 + 0.112402i
\(407\) 195420.i 1.17972i
\(408\) 0 0
\(409\) 230461. 1.37769 0.688844 0.724910i \(-0.258118\pi\)
0.688844 + 0.724910i \(0.258118\pi\)
\(410\) −3558.79 + 11675.5i −0.0211707 + 0.0694554i
\(411\) 0 0
\(412\) 99308.0 147767.i 0.585046 0.870526i
\(413\) 67907.1 0.398121
\(414\) 0 0
\(415\) 73208.6i 0.425075i
\(416\) 213103. 19548.9i 1.23141 0.112963i
\(417\) 0 0
\(418\) −3481.55 + 11422.0i −0.0199260 + 0.0653718i
\(419\) 55624.6i 0.316839i −0.987372 0.158420i \(-0.949360\pi\)
0.987372 0.158420i \(-0.0506399\pi\)
\(420\) 0 0
\(421\) 140971. 0.795366 0.397683 0.917523i \(-0.369814\pi\)
0.397683 + 0.917523i \(0.369814\pi\)
\(422\) 68176.8 + 20781.0i 0.382835 + 0.116692i
\(423\) 0 0
\(424\) −65195.3 + 53067.4i −0.362647 + 0.295186i
\(425\) −84242.8 −0.466396
\(426\) 0 0
\(427\) 26610.5i 0.145948i
\(428\) −39848.1 + 59292.5i −0.217530 + 0.323677i
\(429\) 0 0
\(430\) 242660. + 73965.1i 1.31238 + 0.400027i
\(431\) 191015.i 1.02828i −0.857705 0.514142i \(-0.828111\pi\)
0.857705 0.514142i \(-0.171889\pi\)
\(432\) 0 0
\(433\) 48243.4 0.257313 0.128657 0.991689i \(-0.458933\pi\)
0.128657 + 0.991689i \(0.458933\pi\)
\(434\) −9754.97 + 32003.5i −0.0517901 + 0.169909i
\(435\) 0 0
\(436\) 62893.1 + 42268.0i 0.330849 + 0.222351i
\(437\) −23522.1 −0.123173
\(438\) 0 0
\(439\) 262210.i 1.36057i −0.732948 0.680285i \(-0.761856\pi\)
0.732948 0.680285i \(-0.238144\pi\)
\(440\) −175283. 215342.i −0.905388 1.11230i
\(441\) 0 0
\(442\) −22759.1 + 74666.6i −0.116496 + 0.382192i
\(443\) 90983.0i 0.463610i −0.972762 0.231805i \(-0.925537\pi\)
0.972762 0.231805i \(-0.0744631\pi\)
\(444\) 0 0
\(445\) 45611.9 0.230334
\(446\) 257814. + 78584.2i 1.29609 + 0.395062i
\(447\) 0 0
\(448\) 48952.0 + 10146.7i 0.243901 + 0.0505557i
\(449\) −283350. −1.40550 −0.702748 0.711438i \(-0.748044\pi\)
−0.702748 + 0.711438i \(0.748044\pi\)
\(450\) 0 0
\(451\) 8668.77i 0.0426191i
\(452\) −243630. 163734.i −1.19249 0.801424i
\(453\) 0 0
\(454\) −240264. 73234.7i −1.16567 0.355308i
\(455\) 99677.3i 0.481475i
\(456\) 0 0
\(457\) 198453. 0.950224 0.475112 0.879925i \(-0.342407\pi\)
0.475112 + 0.879925i \(0.342407\pi\)
\(458\) −47730.9 + 156592.i −0.227546 + 0.746517i
\(459\) 0 0
\(460\) 305094. 453968.i 1.44184 2.14541i
\(461\) 208695. 0.981996 0.490998 0.871161i \(-0.336632\pi\)
0.490998 + 0.871161i \(0.336632\pi\)
\(462\) 0 0
\(463\) 26197.8i 0.122209i −0.998131 0.0611044i \(-0.980538\pi\)
0.998131 0.0611044i \(-0.0194622\pi\)
\(464\) 125865. + 308528.i 0.584612 + 1.43304i
\(465\) 0 0
\(466\) −92431.7 + 303244.i −0.425647 + 1.39643i
\(467\) 96607.8i 0.442974i −0.975163 0.221487i \(-0.928909\pi\)
0.975163 0.221487i \(-0.0710911\pi\)
\(468\) 0 0
\(469\) 3002.97 0.0136523
\(470\) −345230. 105230.i −1.56283 0.476367i
\(471\) 0 0
\(472\) 224788. + 276160.i 1.00900 + 1.23959i
\(473\) −180170. −0.805303
\(474\) 0 0
\(475\) 24258.5i 0.107517i
\(476\) −10171.6 + 15135.0i −0.0448926 + 0.0667986i
\(477\) 0 0
\(478\) −172681. 52634.7i −0.755767 0.230365i
\(479\) 34253.4i 0.149291i −0.997210 0.0746453i \(-0.976218\pi\)
0.997210 0.0746453i \(-0.0237825\pi\)
\(480\) 0 0
\(481\) −367861. −1.58999
\(482\) 88232.0 289466.i 0.379780 1.24596i
\(483\) 0 0
\(484\) −30755.1 20669.3i −0.131288 0.0882337i
\(485\) −224280. −0.953470
\(486\) 0 0
\(487\) 69521.4i 0.293130i −0.989201 0.146565i \(-0.953178\pi\)
0.989201 0.146565i \(-0.0468218\pi\)
\(488\) −108218. + 88086.9i −0.454422 + 0.369889i
\(489\) 0 0
\(490\) 102639. 336732.i 0.427486 1.40247i
\(491\) 201271.i 0.834867i 0.908707 + 0.417433i \(0.137070\pi\)
−0.908707 + 0.417433i \(0.862930\pi\)
\(492\) 0 0
\(493\) −121544. −0.500079
\(494\) 21501.0 + 6553.71i 0.0881057 + 0.0268555i
\(495\) 0 0
\(496\) −162441. + 66268.0i −0.660286 + 0.269365i
\(497\) 56243.4 0.227698
\(498\) 0 0
\(499\) 54098.6i 0.217263i 0.994082 + 0.108631i \(0.0346468\pi\)
−0.994082 + 0.108631i \(0.965353\pi\)
\(500\) −143833. 96664.6i −0.575333 0.386658i
\(501\) 0 0
\(502\) −299480. 91284.6i −1.18840 0.362235i
\(503\) 239548.i 0.946795i 0.880849 + 0.473397i \(0.156973\pi\)
−0.880849 + 0.473397i \(0.843027\pi\)
\(504\) 0 0
\(505\) −609113. −2.38844
\(506\) −113263. + 371585.i −0.442370 + 1.45130i
\(507\) 0 0
\(508\) −72909.8 + 108487.i −0.282526 + 0.420388i
\(509\) −115476. −0.445714 −0.222857 0.974851i \(-0.571538\pi\)
−0.222857 + 0.974851i \(0.571538\pi\)
\(510\) 0 0
\(511\) 31303.8i 0.119882i
\(512\) 120778. + 232663.i 0.460733 + 0.887539i
\(513\) 0 0
\(514\) 26838.8 88051.1i 0.101587 0.333279i
\(515\) 434842.i 1.63952i
\(516\) 0 0
\(517\) 256326. 0.958985
\(518\) −82203.0 25056.3i −0.306357 0.0933807i
\(519\) 0 0
\(520\) −405362. + 329955.i −1.49912 + 1.22025i
\(521\) −217267. −0.800420 −0.400210 0.916424i \(-0.631063\pi\)
−0.400210 + 0.916424i \(0.631063\pi\)
\(522\) 0 0
\(523\) 39683.4i 0.145079i 0.997366 + 0.0725397i \(0.0231104\pi\)
−0.997366 + 0.0725397i \(0.976890\pi\)
\(524\) 94098.5 140015.i 0.342705 0.509932i
\(525\) 0 0
\(526\) −332409. 101322.i −1.20144 0.366210i
\(527\) 63993.1i 0.230416i
\(528\) 0 0
\(529\) −485389. −1.73452
\(530\) 59863.7 196397.i 0.213114 0.699170i
\(531\) 0 0
\(532\) 4358.26 + 2929.01i 0.0153989 + 0.0103490i
\(533\) −16318.2 −0.0574405
\(534\) 0 0
\(535\) 174484.i 0.609603i
\(536\) 9940.53 + 12212.3i 0.0346003 + 0.0425077i
\(537\) 0 0
\(538\) 63075.4 206934.i 0.217919 0.714935i
\(539\) 250017.i 0.860580i
\(540\) 0 0
\(541\) −194992. −0.666228 −0.333114 0.942887i \(-0.608099\pi\)
−0.333114 + 0.942887i \(0.608099\pi\)
\(542\) −183494. 55930.8i −0.624631 0.190394i
\(543\) 0 0
\(544\) −95220.3 + 8734.98i −0.321760 + 0.0295165i
\(545\) −185080. −0.623111
\(546\) 0 0
\(547\) 94267.3i 0.315055i −0.987515 0.157527i \(-0.949648\pi\)
0.987515 0.157527i \(-0.0503523\pi\)
\(548\) 42836.3 + 28788.5i 0.142643 + 0.0958647i
\(549\) 0 0
\(550\) 383218. + 116809.i 1.26684 + 0.386144i
\(551\) 34999.7i 0.115282i
\(552\) 0 0
\(553\) 63226.9 0.206753
\(554\) −85981.1 + 282081.i −0.280145 + 0.919083i
\(555\) 0 0
\(556\) 167734. 249582.i 0.542591 0.807355i
\(557\) 563587. 1.81656 0.908282 0.418358i \(-0.137394\pi\)
0.908282 + 0.418358i \(0.137394\pi\)
\(558\) 0 0
\(559\) 339154.i 1.08536i
\(560\) −113057. + 46121.9i −0.360515 + 0.147072i
\(561\) 0 0
\(562\) −65455.3 + 214741.i −0.207239 + 0.679897i
\(563\) 627590.i 1.97997i 0.141165 + 0.989986i \(0.454915\pi\)
−0.141165 + 0.989986i \(0.545085\pi\)
\(564\) 0 0
\(565\) 716946. 2.24590
\(566\) −584516. 178166.i −1.82458 0.556150i
\(567\) 0 0
\(568\) 186179. + 228727.i 0.577077 + 0.708959i
\(569\) 77719.7 0.240053 0.120026 0.992771i \(-0.461702\pi\)
0.120026 + 0.992771i \(0.461702\pi\)
\(570\) 0 0
\(571\) 318806.i 0.977811i −0.872337 0.488905i \(-0.837396\pi\)
0.872337 0.488905i \(-0.162604\pi\)
\(572\) 207061. 308099.i 0.632858 0.941669i
\(573\) 0 0
\(574\) −3646.50 1111.49i −0.0110676 0.00337351i
\(575\) 789186.i 2.38695i
\(576\) 0 0
\(577\) 40053.7 0.120307 0.0601534 0.998189i \(-0.480841\pi\)
0.0601534 + 0.998189i \(0.480841\pi\)
\(578\) −87238.1 + 286205.i −0.261126 + 0.856686i
\(579\) 0 0
\(580\) −675480. 453963.i −2.00797 1.34947i
\(581\) 22864.7 0.0677349
\(582\) 0 0
\(583\) 145821.i 0.429024i
\(584\) −127304. + 103623.i −0.373266 + 0.303830i
\(585\) 0 0
\(586\) 45298.0 148611.i 0.131912 0.432768i
\(587\) 13734.6i 0.0398601i −0.999801 0.0199301i \(-0.993656\pi\)
0.999801 0.0199301i \(-0.00634436\pi\)
\(588\) 0 0
\(589\) −18427.4 −0.0531171
\(590\) −831917. 253577.i −2.38988 0.728459i
\(591\) 0 0
\(592\) −170214. 417240.i −0.485681 1.19054i
\(593\) −537582. −1.52875 −0.764373 0.644775i \(-0.776951\pi\)
−0.764373 + 0.644775i \(0.776951\pi\)
\(594\) 0 0
\(595\) 44538.6i 0.125806i
\(596\) −101593. 68276.4i −0.286003 0.192211i
\(597\) 0 0
\(598\) 699476. + 213207.i 1.95601 + 0.596210i
\(599\) 455415.i 1.26927i −0.772812 0.634635i \(-0.781151\pi\)
0.772812 0.634635i \(-0.218849\pi\)
\(600\) 0 0
\(601\) −237993. −0.658892 −0.329446 0.944174i \(-0.606862\pi\)
−0.329446 + 0.944174i \(0.606862\pi\)
\(602\) −23100.9 + 75788.0i −0.0637436 + 0.209126i
\(603\) 0 0
\(604\) 10047.5 14950.3i 0.0275412 0.0409803i
\(605\) 90505.0 0.247265
\(606\) 0 0
\(607\) 595989.i 1.61756i 0.588109 + 0.808781i \(0.299873\pi\)
−0.588109 + 0.808781i \(0.700127\pi\)
\(608\) 2515.32 + 27419.6i 0.00680435 + 0.0741744i
\(609\) 0 0
\(610\) 99368.1 326000.i 0.267047 0.876109i
\(611\) 482511.i 1.29248i
\(612\) 0 0
\(613\) 547275. 1.45641 0.728206 0.685358i \(-0.240354\pi\)
0.728206 + 0.685358i \(0.240354\pi\)
\(614\) −1750.60 533.599i −0.00464354 0.00141540i
\(615\) 0 0
\(616\) 67256.0 54744.8i 0.177243 0.144272i
\(617\) −518155. −1.36110 −0.680549 0.732703i \(-0.738259\pi\)
−0.680549 + 0.732703i \(0.738259\pi\)
\(618\) 0 0
\(619\) 204231.i 0.533016i −0.963833 0.266508i \(-0.914130\pi\)
0.963833 0.266508i \(-0.0858698\pi\)
\(620\) 239013. 355642.i 0.621781 0.925187i
\(621\) 0 0
\(622\) 41025.8 + 12505.1i 0.106042 + 0.0323226i
\(623\) 14245.6i 0.0367033i
\(624\) 0 0
\(625\) −140583. −0.359891
\(626\) 20937.0 68688.8i 0.0534276 0.175282i
\(627\) 0 0
\(628\) 46633.1 + 31340.3i 0.118243 + 0.0794664i
\(629\) 164370. 0.415454
\(630\) 0 0
\(631\) 177036.i 0.444633i −0.974975 0.222317i \(-0.928638\pi\)
0.974975 0.222317i \(-0.0713618\pi\)
\(632\) 209296. + 257127.i 0.523994 + 0.643745i
\(633\) 0 0
\(634\) 71575.8 234821.i 0.178069 0.584196i
\(635\) 319252.i 0.791746i
\(636\) 0 0
\(637\) 470635. 1.15986
\(638\) 552899. + 168529.i 1.35833 + 0.414031i
\(639\) 0 0
\(640\) −561812. 307101.i −1.37161 0.749758i
\(641\) −218888. −0.532728 −0.266364 0.963873i \(-0.585822\pi\)
−0.266364 + 0.963873i \(0.585822\pi\)
\(642\) 0 0
\(643\) 345184.i 0.834889i 0.908702 + 0.417445i \(0.137074\pi\)
−0.908702 + 0.417445i \(0.862926\pi\)
\(644\) 141784. + 95287.5i 0.341866 + 0.229755i
\(645\) 0 0
\(646\) −9607.23 2928.38i −0.0230215 0.00701717i
\(647\) 398251.i 0.951366i −0.879617 0.475683i \(-0.842201\pi\)
0.879617 0.475683i \(-0.157799\pi\)
\(648\) 0 0
\(649\) 617681. 1.46648
\(650\) 219882. 721374.i 0.520431 1.70739i
\(651\) 0 0
\(652\) 374373. 557053.i 0.880663 1.31039i
\(653\) 342288. 0.802722 0.401361 0.915920i \(-0.368537\pi\)
0.401361 + 0.915920i \(0.368537\pi\)
\(654\) 0 0
\(655\) 412031.i 0.960390i
\(656\) −7550.63 18508.7i −0.0175459 0.0430098i
\(657\) 0 0
\(658\) 32865.5 107823.i 0.0759082 0.249035i
\(659\) 522927.i 1.20412i −0.798450 0.602061i \(-0.794346\pi\)
0.798450 0.602061i \(-0.205654\pi\)
\(660\) 0 0
\(661\) 308588. 0.706279 0.353140 0.935571i \(-0.385114\pi\)
0.353140 + 0.935571i \(0.385114\pi\)
\(662\) 711286. + 216807.i 1.62304 + 0.494717i
\(663\) 0 0
\(664\) 75687.4 + 92984.7i 0.171667 + 0.210899i
\(665\) −12825.3 −0.0290018
\(666\) 0 0
\(667\) 1.13862e6i 2.55934i
\(668\) −60807.7 + 90479.6i −0.136272 + 0.202767i
\(669\) 0 0
\(670\) −36788.8 11213.6i −0.0819533 0.0249802i
\(671\) 242048.i 0.537597i
\(672\) 0 0
\(673\) −248520. −0.548695 −0.274348 0.961631i \(-0.588462\pi\)
−0.274348 + 0.961631i \(0.588462\pi\)
\(674\) −172604. + 566269.i −0.379955 + 1.24653i
\(675\) 0 0
\(676\) −200689. 134875.i −0.439168 0.295147i
\(677\) −269522. −0.588054 −0.294027 0.955797i \(-0.594996\pi\)
−0.294027 + 0.955797i \(0.594996\pi\)
\(678\) 0 0
\(679\) 70047.6i 0.151934i
\(680\) 181127. 147433.i 0.391710 0.318843i
\(681\) 0 0
\(682\) −88730.9 + 291103.i −0.190768 + 0.625860i
\(683\) 124482.i 0.266848i −0.991059 0.133424i \(-0.957403\pi\)
0.991059 0.133424i \(-0.0425972\pi\)
\(684\) 0 0
\(685\) −126057. −0.268649
\(686\) 217295. + 66233.6i 0.461744 + 0.140744i
\(687\) 0 0
\(688\) −384680. + 156931.i −0.812685 + 0.331536i
\(689\) 274495. 0.578223
\(690\) 0 0
\(691\) 890738.i 1.86549i 0.360531 + 0.932747i \(0.382596\pi\)
−0.360531 + 0.932747i \(0.617404\pi\)
\(692\) 209132. + 140549.i 0.436726 + 0.293506i
\(693\) 0 0
\(694\) −554723. 169085.i −1.15175 0.351064i
\(695\) 734462.i 1.52055i
\(696\) 0 0
\(697\) 7291.43 0.0150088
\(698\) −208705. + 684705.i −0.428372 + 1.40538i
\(699\) 0 0
\(700\) 98270.6 146223.i 0.200552 0.298414i
\(701\) 170934. 0.347851 0.173925 0.984759i \(-0.444355\pi\)
0.173925 + 0.984759i \(0.444355\pi\)
\(702\) 0 0
\(703\) 47332.1i 0.0957734i
\(704\) 445266. + 92294.4i 0.898409 + 0.186222i
\(705\) 0 0
\(706\) −30784.0 + 100994.i −0.0617611 + 0.202622i
\(707\) 190239.i 0.380594i
\(708\) 0 0
\(709\) −701926. −1.39637 −0.698183 0.715920i \(-0.746008\pi\)
−0.698183 + 0.715920i \(0.746008\pi\)
\(710\) −689028. 210022.i −1.36685 0.416628i
\(711\) 0 0
\(712\) −57933.2 + 47156.3i −0.114279 + 0.0930206i
\(713\) −599487. −1.17924
\(714\) 0 0
\(715\) 906662.i 1.77351i
\(716\) −200785. + 298761.i −0.391657 + 0.582770i
\(717\) 0 0
\(718\) 693934. + 211518.i 1.34608 + 0.410297i
\(719\) 768366.i 1.48631i −0.669117 0.743157i \(-0.733328\pi\)
0.669117 0.743157i \(-0.266672\pi\)
\(720\) 0 0
\(721\) −135811. −0.261255
\(722\) 151145. 495868.i 0.289948 0.951244i
\(723\) 0 0
\(724\) 290124. + 194981.i 0.553486 + 0.371975i
\(725\) 1.17427e6 2.23404
\(726\) 0 0
\(727\) 255758.i 0.483905i 0.970288 + 0.241952i \(0.0777878\pi\)
−0.970288 + 0.241952i \(0.922212\pi\)
\(728\) −103052. 126604.i −0.194444 0.238882i
\(729\) 0 0
\(730\) 116894. 383497.i 0.219354 0.719642i
\(731\) 151543.i 0.283597i
\(732\) 0 0
\(733\) 369658. 0.688006 0.344003 0.938968i \(-0.388217\pi\)
0.344003 + 0.938968i \(0.388217\pi\)
\(734\) −799678. 243750.i −1.48430 0.452431i
\(735\) 0 0
\(736\) 81829.3 + 892023.i 0.151061 + 1.64672i
\(737\) 27314.9 0.0502881
\(738\) 0 0
\(739\) 1.03557e6i 1.89623i −0.317932 0.948114i \(-0.602988\pi\)
0.317932 0.948114i \(-0.397012\pi\)
\(740\) 913490. + 613920.i 1.66817 + 1.12111i
\(741\) 0 0
\(742\) 61339.1 + 18696.8i 0.111411 + 0.0339593i
\(743\) 561187.i 1.01655i −0.861194 0.508276i \(-0.830283\pi\)
0.861194 0.508276i \(-0.169717\pi\)
\(744\) 0 0
\(745\) 298963. 0.538648
\(746\) −89331.1 + 293072.i −0.160518 + 0.526618i
\(747\) 0 0
\(748\) −92520.5 + 137667.i −0.165362 + 0.246052i
\(749\) 54495.1 0.0971391
\(750\) 0 0
\(751\) 190408.i 0.337603i −0.985650 0.168801i \(-0.946010\pi\)
0.985650 0.168801i \(-0.0539896\pi\)
\(752\) 547281. 223264.i 0.967775 0.394805i
\(753\) 0 0
\(754\) 317241. 1.04078e6i 0.558016 1.83070i
\(755\) 43995.1i 0.0771810i
\(756\) 0 0
\(757\) 523077. 0.912797 0.456398 0.889776i \(-0.349139\pi\)
0.456398 + 0.889776i \(0.349139\pi\)
\(758\) −888130. 270711.i −1.54575 0.471159i
\(759\) 0 0
\(760\) −42454.8 52157.3i −0.0735021 0.0903000i
\(761\) 160897. 0.277830 0.138915 0.990304i \(-0.455638\pi\)
0.138915 + 0.990304i \(0.455638\pi\)
\(762\) 0 0
\(763\) 57804.5i 0.0992916i
\(764\) 166763. 248137.i 0.285702 0.425114i
\(765\) 0 0
\(766\) −327467. 99815.1i −0.558097 0.170113i
\(767\) 1.16273e6i 1.97646i
\(768\) 0 0
\(769\) −595609. −1.00718 −0.503591 0.863942i \(-0.667988\pi\)
−0.503591 + 0.863942i \(0.667988\pi\)
\(770\) −61755.9 + 202605.i −0.104159 + 0.341718i
\(771\) 0 0
\(772\) −612184. 411424.i −1.02718 0.690328i
\(773\) 583394. 0.976345 0.488172 0.872747i \(-0.337664\pi\)
0.488172 + 0.872747i \(0.337664\pi\)
\(774\) 0 0
\(775\) 618255.i 1.02935i
\(776\) 284866. 231874.i 0.473060 0.385060i
\(777\) 0 0
\(778\) −141979. + 465796.i −0.234566 + 0.769549i
\(779\) 2099.64i 0.00345995i
\(780\) 0 0
\(781\) 511588. 0.838723
\(782\) −312545. 95266.9i −0.511092 0.155786i
\(783\) 0 0
\(784\) 217768. + 533810.i 0.354293 + 0.868469i
\(785\) −137230. −0.222695
\(786\) 0 0
\(787\) 174412.i 0.281597i 0.990038 + 0.140798i \(0.0449669\pi\)
−0.990038 + 0.140798i \(0.955033\pi\)