Properties

Label 3150.2.bf.f.1151.9
Level 3150
Weight 2
Character 3150.1151
Analytic conductor 25.153
Analytic rank 0
Dimension 32
CM no
Inner twists 8

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Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.bf (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: no (minimal twist has level 630)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1151.9
Character \(\chi\) = 3150.1151
Dual form 3150.2.bf.f.1601.9

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.29693 + 2.30608i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.29693 + 2.30608i) q^{7} -1.00000i q^{8} +(-1.11120 - 0.641550i) q^{11} +6.14864i q^{13} +(0.0298666 + 2.64558i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.26128 - 5.64871i) q^{17} +(-5.22868 + 3.01878i) q^{19} -1.28310 q^{22} +(-2.49343 + 1.43958i) q^{23} +(3.07432 + 5.32488i) q^{26} +(1.34866 + 2.27621i) q^{28} -1.35052i q^{29} +(-7.49558 - 4.32758i) q^{31} +(-0.866025 - 0.500000i) q^{32} -6.52257i q^{34} +(-4.76690 - 8.25652i) q^{37} +(-3.01878 + 5.22868i) q^{38} -8.71759 q^{41} +5.35859 q^{43} +(-1.11120 + 0.641550i) q^{44} +(-1.43958 + 2.49343i) q^{46} +(0.403086 + 0.698165i) q^{47} +(-3.63597 - 5.98162i) q^{49} +(5.32488 + 3.07432i) q^{52} +(-5.77488 - 3.33413i) q^{53} +(2.30608 + 1.29693i) q^{56} +(-0.675260 - 1.16959i) q^{58} +(-0.798110 + 1.38237i) q^{59} +(-5.50239 + 3.17681i) q^{61} -8.65515 q^{62} -1.00000 q^{64} +(2.69731 - 4.67188i) q^{67} +(-3.26128 - 5.64871i) q^{68} +15.6787i q^{71} +(-10.7532 - 6.20837i) q^{73} +(-8.25652 - 4.76690i) q^{74} +6.03756i q^{76} +(2.92060 - 1.73046i) q^{77} +(5.59093 + 9.68377i) q^{79} +(-7.54966 + 4.35880i) q^{82} +3.74493 q^{83} +(4.64067 - 2.67929i) q^{86} +(-0.641550 + 1.11120i) q^{88} +(1.81971 + 3.15183i) q^{89} +(-14.1792 - 7.97433i) q^{91} +2.87917i q^{92} +(0.698165 + 0.403086i) q^{94} +8.76818i q^{97} +(-6.13965 - 3.36225i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 16q^{4} + O(q^{10}) \) \( 32q + 16q^{4} - 16q^{16} - 48q^{19} + 24q^{31} - 16q^{46} + 56q^{49} + 48q^{61} - 32q^{64} - 8q^{79} - 56q^{91} + 120q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) −1.29693 + 2.30608i −0.490192 + 0.871614i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0 0
\(11\) −1.11120 0.641550i −0.335038 0.193435i 0.323037 0.946386i \(-0.395296\pi\)
−0.658076 + 0.752952i \(0.728629\pi\)
\(12\) 0 0
\(13\) 6.14864i 1.70533i 0.522462 + 0.852663i \(0.325014\pi\)
−0.522462 + 0.852663i \(0.674986\pi\)
\(14\) 0.0298666 + 2.64558i 0.00798219 + 0.707062i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.26128 5.64871i 0.790977 1.37001i −0.134385 0.990929i \(-0.542906\pi\)
0.925362 0.379084i \(-0.123761\pi\)
\(18\) 0 0
\(19\) −5.22868 + 3.01878i −1.19954 + 0.692555i −0.960453 0.278443i \(-0.910182\pi\)
−0.239088 + 0.970998i \(0.576848\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.28310 −0.273558
\(23\) −2.49343 + 1.43958i −0.519917 + 0.300174i −0.736901 0.676001i \(-0.763711\pi\)
0.216984 + 0.976175i \(0.430378\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 3.07432 + 5.32488i 0.602923 + 1.04429i
\(27\) 0 0
\(28\) 1.34866 + 2.27621i 0.254872 + 0.430163i
\(29\) 1.35052i 0.250785i −0.992107 0.125393i \(-0.959981\pi\)
0.992107 0.125393i \(-0.0400191\pi\)
\(30\) 0 0
\(31\) −7.49558 4.32758i −1.34625 0.777255i −0.358530 0.933518i \(-0.616722\pi\)
−0.987716 + 0.156263i \(0.950055\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0 0
\(34\) 6.52257i 1.11861i
\(35\) 0 0
\(36\) 0 0
\(37\) −4.76690 8.25652i −0.783674 1.35736i −0.929788 0.368095i \(-0.880010\pi\)
0.146114 0.989268i \(-0.453323\pi\)
\(38\) −3.01878 + 5.22868i −0.489710 + 0.848203i
\(39\) 0 0
\(40\) 0 0
\(41\) −8.71759 −1.36146 −0.680730 0.732535i \(-0.738337\pi\)
−0.680730 + 0.732535i \(0.738337\pi\)
\(42\) 0 0
\(43\) 5.35859 0.817177 0.408588 0.912719i \(-0.366021\pi\)
0.408588 + 0.912719i \(0.366021\pi\)
\(44\) −1.11120 + 0.641550i −0.167519 + 0.0967173i
\(45\) 0 0
\(46\) −1.43958 + 2.49343i −0.212255 + 0.367637i
\(47\) 0.403086 + 0.698165i 0.0587961 + 0.101838i 0.893925 0.448216i \(-0.147940\pi\)
−0.835129 + 0.550054i \(0.814607\pi\)
\(48\) 0 0
\(49\) −3.63597 5.98162i −0.519424 0.854517i
\(50\) 0 0
\(51\) 0 0
\(52\) 5.32488 + 3.07432i 0.738427 + 0.426331i
\(53\) −5.77488 3.33413i −0.793241 0.457978i 0.0478611 0.998854i \(-0.484760\pi\)
−0.841102 + 0.540876i \(0.818093\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 2.30608 + 1.29693i 0.308162 + 0.173309i
\(57\) 0 0
\(58\) −0.675260 1.16959i −0.0886660 0.153574i
\(59\) −0.798110 + 1.38237i −0.103905 + 0.179969i −0.913290 0.407309i \(-0.866467\pi\)
0.809385 + 0.587278i \(0.199800\pi\)
\(60\) 0 0
\(61\) −5.50239 + 3.17681i −0.704509 + 0.406748i −0.809025 0.587775i \(-0.800004\pi\)
0.104516 + 0.994523i \(0.466671\pi\)
\(62\) −8.65515 −1.09921
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 2.69731 4.67188i 0.329529 0.570761i −0.652889 0.757453i \(-0.726443\pi\)
0.982418 + 0.186692i \(0.0597766\pi\)
\(68\) −3.26128 5.64871i −0.395489 0.685006i
\(69\) 0 0
\(70\) 0 0
\(71\) 15.6787i 1.86072i 0.366650 + 0.930359i \(0.380505\pi\)
−0.366650 + 0.930359i \(0.619495\pi\)
\(72\) 0 0
\(73\) −10.7532 6.20837i −1.25857 0.726635i −0.285772 0.958298i \(-0.592250\pi\)
−0.972796 + 0.231663i \(0.925583\pi\)
\(74\) −8.25652 4.76690i −0.959801 0.554141i
\(75\) 0 0
\(76\) 6.03756i 0.692555i
\(77\) 2.92060 1.73046i 0.332834 0.197204i
\(78\) 0 0
\(79\) 5.59093 + 9.68377i 0.629028 + 1.08951i 0.987747 + 0.156064i \(0.0498805\pi\)
−0.358719 + 0.933446i \(0.616786\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −7.54966 + 4.35880i −0.833720 + 0.481349i
\(83\) 3.74493 0.411059 0.205530 0.978651i \(-0.434108\pi\)
0.205530 + 0.978651i \(0.434108\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 4.64067 2.67929i 0.500417 0.288916i
\(87\) 0 0
\(88\) −0.641550 + 1.11120i −0.0683894 + 0.118454i
\(89\) 1.81971 + 3.15183i 0.192889 + 0.334093i 0.946206 0.323564i \(-0.104881\pi\)
−0.753318 + 0.657657i \(0.771548\pi\)
\(90\) 0 0
\(91\) −14.1792 7.97433i −1.48639 0.835937i
\(92\) 2.87917i 0.300174i
\(93\) 0 0
\(94\) 0.698165 + 0.403086i 0.0720102 + 0.0415751i
\(95\) 0 0
\(96\) 0 0
\(97\) 8.76818i 0.890274i 0.895463 + 0.445137i \(0.146845\pi\)
−0.895463 + 0.445137i \(0.853155\pi\)
\(98\) −6.13965 3.36225i −0.620198 0.339639i
\(99\) 0 0
\(100\) 0 0
\(101\) −0.853270 + 1.47791i −0.0849035 + 0.147057i −0.905350 0.424666i \(-0.860392\pi\)
0.820447 + 0.571723i \(0.193725\pi\)
\(102\) 0 0
\(103\) −8.97583 + 5.18220i −0.884415 + 0.510617i −0.872112 0.489307i \(-0.837250\pi\)
−0.0123035 + 0.999924i \(0.503916\pi\)
\(104\) 6.14864 0.602923
\(105\) 0 0
\(106\) −6.66826 −0.647679
\(107\) −9.97106 + 5.75680i −0.963939 + 0.556531i −0.897383 0.441252i \(-0.854534\pi\)
−0.0665560 + 0.997783i \(0.521201\pi\)
\(108\) 0 0
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.64558 0.0298666i 0.249984 0.00282213i
\(113\) 13.3875i 1.25939i −0.776843 0.629695i \(-0.783180\pi\)
0.776843 0.629695i \(-0.216820\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −1.16959 0.675260i −0.108593 0.0626963i
\(117\) 0 0
\(118\) 1.59622i 0.146944i
\(119\) 8.79670 + 14.8467i 0.806392 + 1.36100i
\(120\) 0 0
\(121\) −4.67683 8.10050i −0.425166 0.736409i
\(122\) −3.17681 + 5.50239i −0.287615 + 0.498163i
\(123\) 0 0
\(124\) −7.49558 + 4.32758i −0.673123 + 0.388628i
\(125\) 0 0
\(126\) 0 0
\(127\) 5.65313 0.501634 0.250817 0.968035i \(-0.419301\pi\)
0.250817 + 0.968035i \(0.419301\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 0 0
\(131\) 6.23366 + 10.7970i 0.544638 + 0.943340i 0.998630 + 0.0523344i \(0.0166662\pi\)
−0.453992 + 0.891006i \(0.650001\pi\)
\(132\) 0 0
\(133\) −0.180321 15.9729i −0.0156358 1.38502i
\(134\) 5.39463i 0.466025i
\(135\) 0 0
\(136\) −5.64871 3.26128i −0.484373 0.279653i
\(137\) 0.0441401 + 0.0254843i 0.00377114 + 0.00217727i 0.501884 0.864935i \(-0.332640\pi\)
−0.498113 + 0.867112i \(0.665974\pi\)
\(138\) 0 0
\(139\) 1.05069i 0.0891184i −0.999007 0.0445592i \(-0.985812\pi\)
0.999007 0.0445592i \(-0.0141883\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 7.83934 + 13.5781i 0.657863 + 1.13945i
\(143\) 3.94466 6.83235i 0.329869 0.571350i
\(144\) 0 0
\(145\) 0 0
\(146\) −12.4167 −1.02762
\(147\) 0 0
\(148\) −9.53381 −0.783674
\(149\) −7.12137 + 4.11153i −0.583406 + 0.336829i −0.762486 0.647005i \(-0.776021\pi\)
0.179080 + 0.983835i \(0.442688\pi\)
\(150\) 0 0
\(151\) 2.13357 3.69546i 0.173628 0.300732i −0.766058 0.642772i \(-0.777784\pi\)
0.939686 + 0.342040i \(0.111118\pi\)
\(152\) 3.01878 + 5.22868i 0.244855 + 0.424102i
\(153\) 0 0
\(154\) 1.66409 2.95892i 0.134096 0.238437i
\(155\) 0 0
\(156\) 0 0
\(157\) −4.18466 2.41601i −0.333972 0.192819i 0.323631 0.946183i \(-0.395096\pi\)
−0.657603 + 0.753364i \(0.728430\pi\)
\(158\) 9.68377 + 5.59093i 0.770399 + 0.444790i
\(159\) 0 0
\(160\) 0 0
\(161\) −0.0859910 7.61708i −0.00677704 0.600310i
\(162\) 0 0
\(163\) 5.37661 + 9.31256i 0.421128 + 0.729416i 0.996050 0.0887927i \(-0.0283009\pi\)
−0.574922 + 0.818208i \(0.694968\pi\)
\(164\) −4.35880 + 7.54966i −0.340365 + 0.589529i
\(165\) 0 0
\(166\) 3.24320 1.87246i 0.251721 0.145331i
\(167\) 18.9267 1.46459 0.732295 0.680988i \(-0.238449\pi\)
0.732295 + 0.680988i \(0.238449\pi\)
\(168\) 0 0
\(169\) −24.8057 −1.90813
\(170\) 0 0
\(171\) 0 0
\(172\) 2.67929 4.64067i 0.204294 0.353848i
\(173\) 5.92176 + 10.2568i 0.450223 + 0.779810i 0.998400 0.0565531i \(-0.0180110\pi\)
−0.548176 + 0.836363i \(0.684678\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.28310i 0.0967173i
\(177\) 0 0
\(178\) 3.15183 + 1.81971i 0.236239 + 0.136393i
\(179\) −3.27843 1.89280i −0.245041 0.141475i 0.372450 0.928052i \(-0.378518\pi\)
−0.617492 + 0.786577i \(0.711851\pi\)
\(180\) 0 0
\(181\) 19.0033i 1.41251i 0.707960 + 0.706253i \(0.249616\pi\)
−0.707960 + 0.706253i \(0.750384\pi\)
\(182\) −16.2667 + 0.183639i −1.20577 + 0.0136122i
\(183\) 0 0
\(184\) 1.43958 + 2.49343i 0.106128 + 0.183818i
\(185\) 0 0
\(186\) 0 0
\(187\) −7.24785 + 4.18455i −0.530016 + 0.306005i
\(188\) 0.806172 0.0587961
\(189\) 0 0
\(190\) 0 0
\(191\) 2.44949 1.41421i 0.177239 0.102329i −0.408756 0.912644i \(-0.634037\pi\)
0.585995 + 0.810315i \(0.300704\pi\)
\(192\) 0 0
\(193\) −1.76946 + 3.06479i −0.127368 + 0.220608i −0.922656 0.385623i \(-0.873986\pi\)
0.795288 + 0.606232i \(0.207320\pi\)
\(194\) 4.38409 + 7.59347i 0.314759 + 0.545179i
\(195\) 0 0
\(196\) −6.99822 + 0.158029i −0.499873 + 0.0112878i
\(197\) 2.36728i 0.168662i −0.996438 0.0843308i \(-0.973125\pi\)
0.996438 0.0843308i \(-0.0268752\pi\)
\(198\) 0 0
\(199\) 3.00000 + 1.73205i 0.212664 + 0.122782i 0.602549 0.798082i \(-0.294152\pi\)
−0.389885 + 0.920864i \(0.627485\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 1.70654i 0.120072i
\(203\) 3.11440 + 1.75153i 0.218588 + 0.122933i
\(204\) 0 0
\(205\) 0 0
\(206\) −5.18220 + 8.97583i −0.361061 + 0.625376i
\(207\) 0 0
\(208\) 5.32488 3.07432i 0.369214 0.213166i
\(209\) 7.74679 0.535856
\(210\) 0 0
\(211\) −14.3620 −0.988721 −0.494361 0.869257i \(-0.664598\pi\)
−0.494361 + 0.869257i \(0.664598\pi\)
\(212\) −5.77488 + 3.33413i −0.396621 + 0.228989i
\(213\) 0 0
\(214\) −5.75680 + 9.97106i −0.393527 + 0.681608i
\(215\) 0 0
\(216\) 0 0
\(217\) 19.7009 11.6728i 1.33739 0.792403i
\(218\) 2.00000i 0.135457i
\(219\) 0 0
\(220\) 0 0
\(221\) 34.7319 + 20.0524i 2.33632 + 1.34887i
\(222\) 0 0
\(223\) 13.5975i 0.910557i −0.890349 0.455279i \(-0.849540\pi\)
0.890349 0.455279i \(-0.150460\pi\)
\(224\) 2.27621 1.34866i 0.152086 0.0901109i
\(225\) 0 0
\(226\) −6.69375 11.5939i −0.445261 0.771215i
\(227\) 6.17797 10.7006i 0.410046 0.710221i −0.584848 0.811143i \(-0.698846\pi\)
0.994894 + 0.100922i \(0.0321792\pi\)
\(228\) 0 0
\(229\) 2.09008 1.20671i 0.138116 0.0797414i −0.429350 0.903138i \(-0.641257\pi\)
0.567466 + 0.823397i \(0.307924\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −1.35052 −0.0886660
\(233\) 11.1506 6.43780i 0.730500 0.421754i −0.0881051 0.996111i \(-0.528081\pi\)
0.818605 + 0.574357i \(0.194748\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.798110 + 1.38237i 0.0519525 + 0.0899844i
\(237\) 0 0
\(238\) 15.0415 + 8.45929i 0.974997 + 0.548334i
\(239\) 27.2546i 1.76296i −0.472226 0.881478i \(-0.656549\pi\)
0.472226 0.881478i \(-0.343451\pi\)
\(240\) 0 0
\(241\) 2.26690 + 1.30880i 0.146024 + 0.0843070i 0.571232 0.820789i \(-0.306466\pi\)
−0.425208 + 0.905096i \(0.639799\pi\)
\(242\) −8.10050 4.67683i −0.520720 0.300638i
\(243\) 0 0
\(244\) 6.35361i 0.406748i
\(245\) 0 0
\(246\) 0 0
\(247\) −18.5614 32.1492i −1.18103 2.04561i
\(248\) −4.32758 + 7.49558i −0.274801 + 0.475970i
\(249\) 0 0
\(250\) 0 0
\(251\) −26.7173 −1.68638 −0.843190 0.537615i \(-0.819325\pi\)
−0.843190 + 0.537615i \(0.819325\pi\)
\(252\) 0 0
\(253\) 3.69426 0.232256
\(254\) 4.89575 2.82656i 0.307187 0.177354i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 5.28063 + 9.14632i 0.329397 + 0.570532i 0.982392 0.186830i \(-0.0598214\pi\)
−0.652996 + 0.757362i \(0.726488\pi\)
\(258\) 0 0
\(259\) 25.2225 0.284743i 1.56725 0.0176930i
\(260\) 0 0
\(261\) 0 0
\(262\) 10.7970 + 6.23366i 0.667042 + 0.385117i
\(263\) −7.21550 4.16587i −0.444927 0.256879i 0.260759 0.965404i \(-0.416027\pi\)
−0.705685 + 0.708526i \(0.749361\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −8.14259 13.7427i −0.499254 0.842621i
\(267\) 0 0
\(268\) −2.69731 4.67188i −0.164765 0.285381i
\(269\) −7.14171 + 12.3698i −0.435438 + 0.754201i −0.997331 0.0730091i \(-0.976740\pi\)
0.561893 + 0.827210i \(0.310073\pi\)
\(270\) 0 0
\(271\) −6.58566 + 3.80223i −0.400050 + 0.230969i −0.686506 0.727125i \(-0.740856\pi\)
0.286456 + 0.958094i \(0.407523\pi\)
\(272\) −6.52257 −0.395489
\(273\) 0 0
\(274\) 0.0509686 0.00307912
\(275\) 0 0
\(276\) 0 0
\(277\) −6.02002 + 10.4270i −0.361708 + 0.626497i −0.988242 0.152897i \(-0.951140\pi\)
0.626534 + 0.779394i \(0.284473\pi\)
\(278\) −0.525345 0.909924i −0.0315081 0.0545736i
\(279\) 0 0
\(280\) 0 0
\(281\) 12.7879i 0.762861i −0.924397 0.381431i \(-0.875431\pi\)
0.924397 0.381431i \(-0.124569\pi\)
\(282\) 0 0
\(283\) 13.4685 + 7.77607i 0.800622 + 0.462239i 0.843689 0.536833i \(-0.180379\pi\)
−0.0430666 + 0.999072i \(0.513713\pi\)
\(284\) 13.5781 + 7.83934i 0.805715 + 0.465180i
\(285\) 0 0
\(286\) 7.88931i 0.466505i
\(287\) 11.3061 20.1034i 0.667376 1.18667i
\(288\) 0 0
\(289\) −12.7719 22.1216i −0.751290 1.30127i
\(290\) 0 0
\(291\) 0 0
\(292\) −10.7532 + 6.20837i −0.629284 + 0.363317i
\(293\) 11.5536 0.674967 0.337483 0.941331i \(-0.390424\pi\)
0.337483 + 0.941331i \(0.390424\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −8.25652 + 4.76690i −0.479900 + 0.277071i
\(297\) 0 0
\(298\) −4.11153 + 7.12137i −0.238174 + 0.412530i
\(299\) −8.85148 15.3312i −0.511894 0.886627i
\(300\) 0 0
\(301\) −6.94969 + 12.3573i −0.400573 + 0.712263i
\(302\) 4.26715i 0.245547i
\(303\) 0 0
\(304\) 5.22868 + 3.01878i 0.299885 + 0.173139i
\(305\) 0 0
\(306\) 0 0
\(307\) 2.57617i 0.147030i 0.997294 + 0.0735150i \(0.0234217\pi\)
−0.997294 + 0.0735150i \(0.976578\pi\)
\(308\) −0.0383219 3.39455i −0.00218359 0.193422i
\(309\) 0 0
\(310\) 0 0
\(311\) −12.3570 + 21.4030i −0.700702 + 1.21365i 0.267519 + 0.963553i \(0.413796\pi\)
−0.968220 + 0.250098i \(0.919537\pi\)
\(312\) 0 0
\(313\) −7.79573 + 4.50087i −0.440641 + 0.254404i −0.703869 0.710329i \(-0.748546\pi\)
0.263229 + 0.964733i \(0.415213\pi\)
\(314\) −4.83203 −0.272687
\(315\) 0 0
\(316\) 11.1819 0.629028
\(317\) 20.7031 11.9529i 1.16280 0.671344i 0.210828 0.977523i \(-0.432384\pi\)
0.951974 + 0.306180i \(0.0990508\pi\)
\(318\) 0 0
\(319\) −0.866426 + 1.50069i −0.0485106 + 0.0840227i
\(320\) 0 0
\(321\) 0 0
\(322\) −3.88301 6.55359i −0.216392 0.365217i
\(323\) 39.3804i 2.19118i
\(324\) 0 0
\(325\) 0 0
\(326\) 9.31256 + 5.37661i 0.515775 + 0.297783i
\(327\) 0 0
\(328\) 8.71759i 0.481349i
\(329\) −2.13279 + 0.0240776i −0.117585 + 0.00132744i
\(330\) 0 0
\(331\) −2.18364 3.78217i −0.120024 0.207887i 0.799753 0.600329i \(-0.204964\pi\)
−0.919777 + 0.392442i \(0.871630\pi\)
\(332\) 1.87246 3.24320i 0.102765 0.177994i
\(333\) 0 0
\(334\) 16.3910 9.46334i 0.896874 0.517811i
\(335\) 0 0
\(336\) 0 0
\(337\) −19.5159 −1.06310 −0.531549 0.847028i \(-0.678390\pi\)
−0.531549 + 0.847028i \(0.678390\pi\)
\(338\) −21.4824 + 12.4029i −1.16849 + 0.674627i
\(339\) 0 0
\(340\) 0 0
\(341\) 5.55271 + 9.61758i 0.300696 + 0.520821i
\(342\) 0 0
\(343\) 18.5096 0.627092i 0.999427 0.0338598i
\(344\) 5.35859i 0.288916i
\(345\) 0 0
\(346\) 10.2568 + 5.92176i 0.551409 + 0.318356i
\(347\) 23.3088 + 13.4574i 1.25128 + 0.722429i 0.971364 0.237595i \(-0.0763591\pi\)
0.279919 + 0.960024i \(0.409692\pi\)
\(348\) 0 0
\(349\) 10.3821i 0.555741i −0.960619 0.277870i \(-0.910371\pi\)
0.960619 0.277870i \(-0.0896286\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.641550 + 1.11120i 0.0341947 + 0.0592270i
\(353\) −0.0844756 + 0.146316i −0.00449618 + 0.00778761i −0.868265 0.496101i \(-0.834765\pi\)
0.863769 + 0.503889i \(0.168098\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 3.63941 0.192889
\(357\) 0 0
\(358\) −3.78561 −0.200075
\(359\) −32.6198 + 18.8330i −1.72161 + 0.993970i −0.805975 + 0.591949i \(0.798359\pi\)
−0.915631 + 0.402021i \(0.868308\pi\)
\(360\) 0 0
\(361\) 8.72604 15.1139i 0.459265 0.795471i
\(362\) 9.50166 + 16.4574i 0.499396 + 0.864979i
\(363\) 0 0
\(364\) −13.9956 + 8.29240i −0.733568 + 0.434640i
\(365\) 0 0
\(366\) 0 0
\(367\) 13.1253 + 7.57787i 0.685133 + 0.395562i 0.801786 0.597611i \(-0.203883\pi\)
−0.116653 + 0.993173i \(0.537217\pi\)
\(368\) 2.49343 + 1.43958i 0.129979 + 0.0750435i
\(369\) 0 0
\(370\) 0 0
\(371\) 15.1784 8.99319i 0.788021 0.466903i
\(372\) 0 0
\(373\) −6.02002 10.4270i −0.311705 0.539889i 0.667027 0.745034i \(-0.267567\pi\)
−0.978732 + 0.205145i \(0.934233\pi\)
\(374\) −4.18455 + 7.24785i −0.216378 + 0.374778i
\(375\) 0 0
\(376\) 0.698165 0.403086i 0.0360051 0.0207876i
\(377\) 8.30386 0.427671
\(378\) 0 0
\(379\) −18.0918 −0.929312 −0.464656 0.885491i \(-0.653822\pi\)
−0.464656 + 0.885491i \(0.653822\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 1.41421 2.44949i 0.0723575 0.125327i
\(383\) 14.5769 + 25.2480i 0.744846 + 1.29011i 0.950267 + 0.311437i \(0.100810\pi\)
−0.205421 + 0.978674i \(0.565856\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 3.53892i 0.180126i
\(387\) 0 0
\(388\) 7.59347 + 4.38409i 0.385500 + 0.222568i
\(389\) 17.0297 + 9.83207i 0.863438 + 0.498506i 0.865162 0.501493i \(-0.167216\pi\)
−0.00172432 + 0.999999i \(0.500549\pi\)
\(390\) 0 0
\(391\) 18.7796i 0.949723i
\(392\) −5.98162 + 3.63597i −0.302117 + 0.183644i
\(393\) 0 0
\(394\) −1.18364 2.05012i −0.0596309 0.103284i
\(395\) 0 0
\(396\) 0 0
\(397\) 4.92295 2.84227i 0.247076 0.142649i −0.371349 0.928493i \(-0.621105\pi\)
0.618425 + 0.785844i \(0.287771\pi\)
\(398\) 3.46410 0.173640
\(399\) 0 0
\(400\) 0 0
\(401\) 8.84787 5.10832i 0.441842 0.255097i −0.262537 0.964922i \(-0.584559\pi\)
0.704378 + 0.709825i \(0.251226\pi\)
\(402\) 0 0
\(403\) 26.6087 46.0876i 1.32547 2.29579i
\(404\) 0.853270 + 1.47791i 0.0424518 + 0.0735286i
\(405\) 0 0
\(406\) 3.57291 0.0403355i 0.177321 0.00200182i
\(407\) 12.2328i 0.606359i
\(408\) 0 0
\(409\) −12.0969 6.98414i −0.598153 0.345344i 0.170162 0.985416i \(-0.445571\pi\)
−0.768314 + 0.640073i \(0.778904\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 10.3644i 0.510617i
\(413\) −2.15275 3.63333i −0.105930 0.178784i
\(414\) 0 0
\(415\) 0 0
\(416\) 3.07432 5.32488i 0.150731 0.261074i
\(417\) 0 0
\(418\) 6.70891 3.87339i 0.328144 0.189454i
\(419\) 11.3181 0.552924 0.276462 0.961025i \(-0.410838\pi\)
0.276462 + 0.961025i \(0.410838\pi\)
\(420\) 0 0
\(421\) −13.9099 −0.677928 −0.338964 0.940799i \(-0.610077\pi\)
−0.338964 + 0.940799i \(0.610077\pi\)
\(422\) −12.4379 + 7.18100i −0.605466 + 0.349566i
\(423\) 0 0
\(424\) −3.33413 + 5.77488i −0.161920 + 0.280453i
\(425\) 0 0
\(426\) 0 0
\(427\) −0.189761 16.8090i −0.00918318 0.813445i
\(428\) 11.5136i 0.556531i
\(429\) 0 0
\(430\) 0 0
\(431\) −22.5947 13.0451i −1.08835 0.628359i −0.155213 0.987881i \(-0.549606\pi\)
−0.933137 + 0.359522i \(0.882940\pi\)
\(432\) 0 0
\(433\) 8.42614i 0.404935i 0.979289 + 0.202467i \(0.0648960\pi\)
−0.979289 + 0.202467i \(0.935104\pi\)
\(434\) 11.2251 19.9594i 0.538822 0.958083i
\(435\) 0 0
\(436\) −1.00000 1.73205i −0.0478913 0.0829502i
\(437\) 8.69157 15.0542i 0.415774 0.720142i
\(438\) 0 0
\(439\) 23.9529 13.8292i 1.14321 0.660033i 0.195987 0.980606i \(-0.437209\pi\)
0.947224 + 0.320573i \(0.103875\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 40.1049 1.90759
\(443\) −2.04142 + 1.17861i −0.0969906 + 0.0559975i −0.547711 0.836668i \(-0.684501\pi\)
0.450720 + 0.892665i \(0.351167\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −6.79876 11.7758i −0.321931 0.557600i
\(447\) 0 0
\(448\) 1.29693 2.30608i 0.0612740 0.108952i
\(449\) 12.8021i 0.604169i 0.953281 + 0.302084i \(0.0976824\pi\)
−0.953281 + 0.302084i \(0.902318\pi\)
\(450\) 0 0
\(451\) 9.68696 + 5.59277i 0.456141 + 0.263353i
\(452\) −11.5939 6.69375i −0.545332 0.314847i
\(453\) 0 0
\(454\) 12.3559i 0.579893i
\(455\) 0 0
\(456\) 0 0
\(457\) −17.2621 29.8989i −0.807488 1.39861i −0.914599 0.404363i \(-0.867493\pi\)
0.107111 0.994247i \(-0.465840\pi\)
\(458\) 1.20671 2.09008i 0.0563857 0.0976628i
\(459\) 0 0
\(460\) 0 0
\(461\) −20.2692 −0.944032 −0.472016 0.881590i \(-0.656474\pi\)
−0.472016 + 0.881590i \(0.656474\pi\)
\(462\) 0 0
\(463\) −13.1246 −0.609952 −0.304976 0.952360i \(-0.598648\pi\)
−0.304976 + 0.952360i \(0.598648\pi\)
\(464\) −1.16959 + 0.675260i −0.0542966 + 0.0313482i
\(465\) 0 0
\(466\) 6.43780 11.1506i 0.298225 0.516541i
\(467\) 0.765836 + 1.32647i 0.0354387 + 0.0613816i 0.883201 0.468995i \(-0.155384\pi\)
−0.847762 + 0.530377i \(0.822050\pi\)
\(468\) 0 0
\(469\) 7.27550 + 12.2793i 0.335951 + 0.567005i
\(470\) 0 0
\(471\) 0 0
\(472\) 1.38237 + 0.798110i 0.0636286 + 0.0367360i
\(473\) −5.95444 3.43780i −0.273786 0.158070i
\(474\) 0 0
\(475\) 0 0
\(476\) 17.2560 0.194807i 0.790927 0.00892896i
\(477\) 0 0
\(478\) −13.6273 23.6032i −0.623299 1.07959i
\(479\) 14.6585 25.3893i 0.669764 1.16007i −0.308205 0.951320i \(-0.599728\pi\)
0.977970 0.208746i \(-0.0669382\pi\)
\(480\) 0 0
\(481\) 50.7663 29.3100i 2.31475 1.33642i
\(482\) 2.61759 0.119228
\(483\) 0 0
\(484\) −9.35366 −0.425166
\(485\) 0 0
\(486\) 0 0
\(487\) −4.09770 + 7.09743i −0.185685 + 0.321615i −0.943807 0.330497i \(-0.892784\pi\)
0.758122 + 0.652112i \(0.226117\pi\)
\(488\) 3.17681 + 5.50239i 0.143807 + 0.249082i
\(489\) 0 0
\(490\) 0 0
\(491\) 40.4383i 1.82495i −0.409129 0.912477i \(-0.634167\pi\)
0.409129 0.912477i \(-0.365833\pi\)
\(492\) 0 0
\(493\) −7.62869 4.40443i −0.343579 0.198366i
\(494\) −32.1492 18.5614i −1.44646 0.835116i
\(495\) 0 0
\(496\) 8.65515i 0.388628i
\(497\) −36.1562 20.3341i −1.62183 0.912109i
\(498\) 0 0
\(499\) 8.72450 + 15.1113i 0.390562 + 0.676474i 0.992524 0.122051i \(-0.0389473\pi\)
−0.601961 + 0.798525i \(0.705614\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −23.1379 + 13.3586i −1.03269 + 0.596226i
\(503\) 1.91949 0.0855860 0.0427930 0.999084i \(-0.486374\pi\)
0.0427930 + 0.999084i \(0.486374\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 3.19932 1.84713i 0.142227 0.0821149i
\(507\) 0 0
\(508\) 2.82656 4.89575i 0.125408 0.217214i
\(509\) −5.54549 9.60508i −0.245800 0.425737i 0.716556 0.697529i \(-0.245717\pi\)
−0.962356 + 0.271792i \(0.912384\pi\)
\(510\) 0 0
\(511\) 28.2631 16.7459i 1.25029 0.740796i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 9.14632 + 5.28063i 0.403427 + 0.232919i
\(515\) 0 0
\(516\) 0 0
\(517\) 1.03440i 0.0454928i
\(518\) 21.7009 12.8578i 0.953484 0.564941i
\(519\) 0 0
\(520\) 0 0
\(521\) 19.8706 34.4168i 0.870546 1.50783i 0.00911254 0.999958i \(-0.497099\pi\)
0.861433 0.507871i \(-0.169567\pi\)
\(522\) 0 0
\(523\) −27.0900 + 15.6404i −1.18456 + 0.683907i −0.957065 0.289872i \(-0.906387\pi\)
−0.227496 + 0.973779i \(0.573054\pi\)
\(524\) 12.4673 0.544638
\(525\) 0 0
\(526\) −8.33174 −0.363281
\(527\) −48.8904 + 28.2269i −2.12970 + 1.22958i
\(528\) 0 0
\(529\) −7.35519 + 12.7396i −0.319791 + 0.553894i
\(530\) 0 0
\(531\) 0 0
\(532\) −13.9231 7.83026i −0.603641 0.339485i
\(533\) 53.6013i 2.32173i
\(534\) 0 0
\(535\) 0 0
\(536\) −4.67188 2.69731i −0.201795 0.116506i
\(537\) 0 0
\(538\) 14.2834i 0.615802i
\(539\) 0.202767 + 8.97941i 0.00873380 + 0.386771i
\(540\) 0 0
\(541\) 12.3987 + 21.4752i 0.533061 + 0.923290i 0.999254 + 0.0386065i \(0.0122919\pi\)
−0.466193 + 0.884683i \(0.654375\pi\)
\(542\) −3.80223 + 6.58566i −0.163320 + 0.282878i
\(543\) 0 0
\(544\) −5.64871 + 3.26128i −0.242186 + 0.139826i
\(545\) 0 0
\(546\) 0 0
\(547\) 40.5380 1.73328 0.866640 0.498934i \(-0.166275\pi\)
0.866640 + 0.498934i \(0.166275\pi\)
\(548\) 0.0441401 0.0254843i 0.00188557 0.00108863i
\(549\) 0 0
\(550\) 0 0
\(551\) 4.07692 + 7.06144i 0.173683 + 0.300827i
\(552\) 0 0
\(553\) −29.5825 + 0.333964i −1.25798 + 0.0142016i
\(554\) 12.0400i 0.511532i
\(555\) 0 0
\(556\) −0.909924 0.525345i −0.0385894 0.0222796i
\(557\) 20.5650 + 11.8732i 0.871367 + 0.503084i 0.867802 0.496910i \(-0.165532\pi\)
0.00356477 + 0.999994i \(0.498865\pi\)
\(558\) 0 0
\(559\) 32.9480i 1.39355i
\(560\) 0 0
\(561\) 0 0
\(562\) −6.39394 11.0746i −0.269712 0.467155i
\(563\) 4.21434 7.29944i 0.177613 0.307635i −0.763449 0.645868i \(-0.776496\pi\)
0.941062 + 0.338233i \(0.109829\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 15.5521 0.653705
\(567\) 0 0
\(568\) 15.6787 0.657863
\(569\) 20.3139 11.7283i 0.851605 0.491674i −0.00958727 0.999954i \(-0.503052\pi\)
0.861192 + 0.508280i \(0.169718\pi\)
\(570\) 0 0
\(571\) −7.67946 + 13.3012i −0.321376 + 0.556639i −0.980772 0.195157i \(-0.937479\pi\)
0.659397 + 0.751795i \(0.270812\pi\)
\(572\) −3.94466 6.83235i −0.164934 0.285675i
\(573\) 0 0
\(574\) −0.260365 23.0631i −0.0108674 0.962636i
\(575\) 0 0
\(576\) 0 0
\(577\) 12.3329 + 7.12041i 0.513426 + 0.296426i 0.734241 0.678889i \(-0.237538\pi\)
−0.220815 + 0.975316i \(0.570872\pi\)
\(578\) −22.1216 12.7719i −0.920139 0.531242i
\(579\) 0 0
\(580\) 0 0
\(581\) −4.85690 + 8.63609i −0.201498 + 0.358285i
\(582\) 0 0
\(583\) 4.27802 + 7.40975i 0.177178 + 0.306881i
\(584\) −6.20837 + 10.7532i −0.256904 + 0.444971i
\(585\) 0 0
\(586\) 10.0057 5.77679i 0.413331 0.238637i
\(587\) 12.5249 0.516958 0.258479 0.966017i \(-0.416779\pi\)
0.258479 + 0.966017i \(0.416779\pi\)
\(588\) 0 0
\(589\) 52.2560 2.15317
\(590\) 0 0
\(591\) 0 0
\(592\) −4.76690 + 8.25652i −0.195919 + 0.339341i
\(593\) −7.35750 12.7436i −0.302136 0.523316i 0.674483 0.738290i \(-0.264366\pi\)
−0.976620 + 0.214975i \(0.931033\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 8.22305i 0.336829i
\(597\) 0 0
\(598\) −15.3312 8.85148i −0.626940 0.361964i
\(599\) 23.9304 + 13.8162i 0.977769 + 0.564515i 0.901596 0.432579i \(-0.142396\pi\)
0.0761732 + 0.997095i \(0.475730\pi\)
\(600\) 0 0
\(601\) 8.82137i 0.359831i 0.983682 + 0.179916i \(0.0575825\pi\)
−0.983682 + 0.179916i \(0.942418\pi\)
\(602\) 0.160043 + 14.1766i 0.00652286 + 0.577794i
\(603\) 0 0
\(604\) −2.13357 3.69546i −0.0868139 0.150366i
\(605\) 0 0
\(606\) 0 0
\(607\) −22.9803 + 13.2677i −0.932743 + 0.538519i −0.887678 0.460465i \(-0.847683\pi\)
−0.0450649 + 0.998984i \(0.514349\pi\)
\(608\) 6.03756 0.244855
\(609\) 0 0
\(610\) 0 0
\(611\) −4.29276 + 2.47843i −0.173667 + 0.100266i
\(612\) 0 0
\(613\) −0.456842 + 0.791273i −0.0184517 + 0.0319592i −0.875104 0.483935i \(-0.839207\pi\)
0.856652 + 0.515894i \(0.172540\pi\)
\(614\) 1.28809 + 2.23103i 0.0519830 + 0.0900371i
\(615\) 0 0
\(616\) −1.73046 2.92060i −0.0697223 0.117674i
\(617\) 35.0558i 1.41129i −0.708565 0.705646i \(-0.750657\pi\)
0.708565 0.705646i \(-0.249343\pi\)
\(618\) 0 0
\(619\) −16.5382 9.54835i −0.664727 0.383781i 0.129348 0.991599i \(-0.458711\pi\)
−0.794076 + 0.607819i \(0.792045\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 24.7140i 0.990942i
\(623\) −9.62837 + 0.108697i −0.385753 + 0.00435485i
\(624\) 0 0
\(625\) 0 0
\(626\) −4.50087 + 7.79573i −0.179891 + 0.311580i
\(627\) 0 0
\(628\) −4.18466 + 2.41601i −0.166986 + 0.0964095i
\(629\) −62.1849 −2.47947
\(630\) 0 0
\(631\) 21.5350 0.857296 0.428648 0.903472i \(-0.358990\pi\)
0.428648 + 0.903472i \(0.358990\pi\)
\(632\) 9.68377 5.59093i 0.385200 0.222395i
\(633\) 0 0
\(634\) 11.9529 20.7031i 0.474712 0.822225i
\(635\) 0 0
\(636\) 0 0
\(637\) 36.7788 22.3562i 1.45723 0.885786i
\(638\) 1.73285i 0.0686043i
\(639\) 0 0
\(640\) 0 0
\(641\) −28.6767 16.5565i −1.13266 0.653943i −0.188060 0.982158i \(-0.560220\pi\)
−0.944603 + 0.328214i \(0.893553\pi\)
\(642\) 0 0
\(643\) 3.31191i 0.130609i −0.997865 0.0653044i \(-0.979198\pi\)
0.997865 0.0653044i \(-0.0208018\pi\)
\(644\) −6.63958 3.73407i −0.261636 0.147143i
\(645\) 0 0
\(646\) 19.6902 + 34.1044i 0.774700 + 1.34182i
\(647\) −11.6669 + 20.2077i −0.458674 + 0.794447i −0.998891 0.0470789i \(-0.985009\pi\)
0.540217 + 0.841526i \(0.318342\pi\)
\(648\) 0 0
\(649\) 1.77371 1.02405i 0.0696244 0.0401977i
\(650\) 0 0
\(651\) 0 0
\(652\) 10.7532 0.421128
\(653\) 15.1211 8.73019i 0.591735 0.341639i −0.174048 0.984737i \(-0.555685\pi\)
0.765783 + 0.643099i \(0.222351\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 4.35880 + 7.54966i 0.170182 + 0.294765i
\(657\) 0 0
\(658\) −1.83501 + 1.08725i −0.0715363 + 0.0423854i
\(659\) 1.29864i 0.0505877i −0.999680 0.0252939i \(-0.991948\pi\)
0.999680 0.0252939i \(-0.00805215\pi\)
\(660\) 0 0
\(661\) 4.39869 + 2.53959i 0.171089 + 0.0987785i 0.583099 0.812401i \(-0.301840\pi\)
−0.412010 + 0.911179i \(0.635173\pi\)
\(662\) −3.78217 2.18364i −0.146998 0.0848695i
\(663\) 0 0
\(664\) 3.74493i 0.145331i
\(665\) 0 0
\(666\) 0 0
\(667\) 1.94419 + 3.36743i 0.0752793 + 0.130387i
\(668\) 9.46334 16.3910i 0.366147 0.634186i
\(669\) 0 0
\(670\) 0 0
\(671\) 8.15232 0.314717
\(672\) 0 0
\(673\) 18.4124 0.709747 0.354873 0.934914i \(-0.384524\pi\)
0.354873 + 0.934914i \(0.384524\pi\)
\(674\) −16.9012 + 9.75794i −0.651012 + 0.375862i
\(675\) 0 0
\(676\) −12.4029 + 21.4824i −0.477033 + 0.826246i
\(677\) 20.6397 + 35.7491i 0.793250 + 1.37395i 0.923945 + 0.382526i \(0.124946\pi\)
−0.130695 + 0.991423i \(0.541721\pi\)
\(678\) 0 0
\(679\) −20.2201 11.3717i −0.775976 0.436405i
\(680\) 0 0
\(681\) 0 0
\(682\) 9.61758 + 5.55271i 0.368276 + 0.212624i
\(683\) 19.9007 + 11.4896i 0.761477 + 0.439639i 0.829826 0.558022i \(-0.188440\pi\)
−0.0683485 + 0.997662i \(0.521773\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 15.7163 9.79790i 0.600050 0.374085i
\(687\) 0 0
\(688\) −2.67929 4.64067i −0.102147 0.176924i
\(689\) 20.5004 35.5077i 0.781001 1.35273i
\(690\) 0 0
\(691\) 11.0048 6.35361i 0.418642 0.241703i −0.275854 0.961199i \(-0.588961\pi\)
0.694496 + 0.719497i \(0.255627\pi\)
\(692\) 11.8435 0.450223
\(693\) 0 0
\(694\) 26.9147 1.02167
\(695\) 0 0
\(696\) 0 0
\(697\) −28.4305 + 49.2431i −1.07688 + 1.86522i
\(698\) −5.19105 8.99116i −0.196484 0.340320i
\(699\) 0 0
\(700\) 0 0
\(701\) 26.5441i 1.00256i −0.865286 0.501279i \(-0.832863\pi\)
0.865286 0.501279i \(-0.167137\pi\)
\(702\) 0 0
\(703\) 49.8492 + 28.7804i 1.88010 + 1.08548i
\(704\) 1.11120 + 0.641550i 0.0418798 + 0.0241793i
\(705\) 0 0
\(706\) 0.168951i 0.00635856i
\(707\) −2.30154 3.88444i −0.0865582 0.146089i
\(708\) 0 0
\(709\) 21.1766 + 36.6789i 0.795303 + 1.37751i 0.922646 + 0.385647i \(0.126022\pi\)
−0.127343 + 0.991859i \(0.540645\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 3.15183 1.81971i 0.118120 0.0681964i
\(713\) 24.9196 0.933248
\(714\) 0 0
\(715\) 0 0
\(716\) −3.27843 + 1.89280i −0.122521 + 0.0707374i
\(717\) 0 0
\(718\) −18.8330 + 32.6198i −0.702843 + 1.21736i
\(719\) 11.9507 + 20.6992i 0.445686 + 0.771951i 0.998100 0.0616189i \(-0.0196263\pi\)
−0.552413 + 0.833570i \(0.686293\pi\)
\(720\) 0 0
\(721\) −0.309550 27.4199i −0.0115282 1.02117i
\(722\) 17.4521i 0.649499i
\(723\) 0 0
\(724\) 16.4574 + 9.50166i 0.611633 + 0.353126i
\(725\) 0 0
\(726\) 0 0
\(727\) 22.4529i 0.832731i 0.909197 + 0.416365i \(0.136696\pi\)
−0.909197 + 0.416365i \(0.863304\pi\)
\(728\) −7.97433 + 14.1792i −0.295548 + 0.525517i
\(729\) 0 0
\(730\) 0 0
\(731\) 17.4759 30.2691i 0.646368 1.11954i
\(732\) 0 0
\(733\) −23.8547 + 13.7725i −0.881094 + 0.508700i −0.871019 0.491249i \(-0.836540\pi\)
−0.0100750 + 0.999949i \(0.503207\pi\)
\(734\) 15.1557 0.559409
\(735\) 0 0
\(736\) 2.87917 0.106128
\(737\) −5.99449 + 3.46092i −0.220810 + 0.127485i
\(738\) 0 0
\(739\) 15.5456 26.9258i 0.571856 0.990483i −0.424520 0.905419i \(-0.639557\pi\)
0.996375 0.0850646i \(-0.0271097\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 8.64824 15.3775i 0.317487 0.564526i
\(743\) 1.12610i 0.0413127i −0.999787 0.0206564i \(-0.993424\pi\)
0.999787 0.0206564i \(-0.00657559\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −10.4270 6.02002i −0.381759 0.220409i
\(747\) 0 0
\(748\) 8.36910i 0.306005i
\(749\) −0.343872 30.4602i −0.0125648 1.11299i
\(750\) 0 0
\(751\) 4.77108 + 8.26375i 0.174099 + 0.301549i 0.939849 0.341590i \(-0.110965\pi\)
−0.765750 + 0.643138i \(0.777632\pi\)
\(752\) 0.403086 0.698165i 0.0146990 0.0254595i
\(753\) 0 0
\(754\) 7.19135 4.15193i 0.261894 0.151204i
\(755\) 0 0
\(756\) 0 0
\(757\) −33.1687 −1.20554 −0.602768 0.797917i \(-0.705935\pi\)
−0.602768 + 0.797917i \(0.705935\pi\)
\(758\) −15.6679 + 9.04589i −0.569085 + 0.328562i
\(759\) 0 0
\(760\) 0 0
\(761\) 2.17122 + 3.76067i 0.0787068 + 0.136324i 0.902692 0.430287i \(-0.141588\pi\)
−0.823985 + 0.566611i \(0.808254\pi\)
\(762\) 0 0
\(763\) 2.69731 + 4.55242i 0.0976493 + 0.164809i
\(764\) 2.82843i 0.102329i
\(765\) 0 0
\(766\) 25.2480 + 14.5769i 0.912246 + 0.526685i
\(767\) −8.49967 4.90729i −0.306905 0.177192i
\(768\) 0 0
\(769\) 46.1795i 1.66528i 0.553818 + 0.832638i \(0.313170\pi\)
−0.553818 + 0.832638i \(0.686830\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1.76946 + 3.06479i 0.0636842 + 0.110304i
\(773\) 8.98723 15.5663i 0.323248 0.559883i −0.657908 0.753098i \(-0.728558\pi\)
0.981156 + 0.193216i \(0.0618917\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 8.76818 0.314759
\(777\) 0 0
\(778\) 19.6641 0.704994
\(779\) 45.5815 26.3165i 1.63313 0.942886i
\(780\) 0 0
\(781\) 10.0587 17.4221i 0.359927 0.623412i
\(782\) 9.38978 + 16.2636i 0.335778 + 0.581584i
\(783\) 0 0
\(784\) −3.36225 + 6.13965i −0.120080 + 0.219273i
\(785\) 0 0
\(786\) 0 0