Properties

Label 3150.2.bf.f.1151.8
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 1151.8
Character \(\chi\) = 3150.1151
Dual form 3150.2.bf.f.1601.8

$q$-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 \(-0.674986\pi\)
0.522462 0.852663i \(-0.325014\pi\)
\(14\) 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 \(0.457094\pi\)
−0.925362 + 0.379084i \(0.876239\pi\)
\(18\) 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 −0.216984 0.976175i \(-0.569622\pi\)
0.736901 + 0.676001i \(0.236289\pi\)
\(24\) 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 \(0.119990\pi\)
−0.146114 + 0.989268i \(0.546677\pi\)
\(38\) 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 \(-0.633979\pi\)
−0.408588 + 0.912719i \(0.633979\pi\)
\(44\) −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 0.835129 0.550054i \(-0.185393\pi\)
−0.893925 + 0.448216i \(0.852060\pi\)
\(48\) 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 0.841102 0.540876i \(-0.181907\pi\)
−0.0478611 + 0.998854i \(0.515240\pi\)
\(54\) 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 −0.982418 0.186692i \(-0.940223\pi\)
0.652889 + 0.757453i \(0.273557\pi\)
\(68\) 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 0.972796 0.231663i \(-0.0744166\pi\)
0.285772 + 0.958298i \(0.407750\pi\)
\(74\) −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 \(-0.565892\pi\)
−0.205530 + 0.978651i \(0.565892\pi\)
\(84\) 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 \(-0.853155\pi\)
0.895463 0.445137i \(-0.146845\pi\)
\(98\) 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 0.0123035 0.999924i \(-0.496084\pi\)
0.872112 + 0.489307i \(0.162750\pi\)
\(104\) 6.14864 0.602923
\(105\) 0 0
\(106\) −6.66826 −0.647679
\(107\) 9.97106 5.75680i 0.963939 0.556531i 0.0665560 0.997783i \(-0.478799\pi\)
0.897383 + 0.441252i \(0.145466\pi\)
\(108\) 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 \(0.216820\pi\)
−0.776843 + 0.629695i \(0.783180\pi\)
\(114\) 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 \(-0.580699\pi\)
−0.250817 + 0.968035i \(0.580699\pi\)
\(128\) 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 0.498113 0.867112i \(-0.334026\pi\)
−0.501884 + 0.864935i \(0.667360\pi\)
\(138\) 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 0.657603 0.753364i \(-0.271570\pi\)
−0.323631 + 0.946183i \(0.604904\pi\)
\(158\) −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 0.574922 0.818208i \(-0.305032\pi\)
−0.996050 + 0.0887927i \(0.971699\pi\)
\(164\) −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 \(-0.761551\pi\)
−0.732295 + 0.680988i \(0.761551\pi\)
\(168\) 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 0.548176 0.836363i \(-0.315322\pi\)
−0.998400 + 0.0565531i \(0.981989\pi\)
\(174\) 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 −0.795288 0.606232i \(-0.792680\pi\)
0.922656 + 0.385623i \(0.126014\pi\)
\(194\) 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 \(0.0268752\pi\)
−0.996438 + 0.0843308i \(0.973125\pi\)
\(198\) 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 \(0.150460\pi\)
−0.890349 + 0.455279i \(0.849540\pi\)
\(224\) 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 −0.994894 0.100922i \(-0.967821\pi\)
0.584848 + 0.811143i \(0.301154\pi\)
\(228\) 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 −0.818605 0.574357i \(-0.805252\pi\)
0.0881051 + 0.996111i \(0.471919\pi\)
\(234\) 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 0.652996 0.757362i \(-0.273512\pi\)
−0.982392 + 0.186830i \(0.940179\pi\)
\(258\) 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 0.705685 0.708526i \(-0.250639\pi\)
−0.260759 + 0.965404i \(0.583973\pi\)
\(264\) 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 −0.626534 0.779394i \(-0.715527\pi\)
0.988242 + 0.152897i \(0.0488604\pi\)
\(278\) 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 0.0430666 0.999072i \(-0.486287\pi\)
−0.843689 + 0.536833i \(0.819621\pi\)
\(284\) 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 \(-0.609576\pi\)
−0.337483 + 0.941331i \(0.609576\pi\)
\(294\) 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 \(-0.976578\pi\)
0.997294 0.0735150i \(-0.0234217\pi\)
\(308\) 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 −0.263229 0.964733i \(-0.584787\pi\)
0.703869 + 0.710329i \(0.251454\pi\)
\(314\) −4.83203 −0.272687
\(315\) 0 0
\(316\) 11.1819 0.629028
\(317\) −20.7031 + 11.9529i −1.16280 + 0.671344i −0.951974 0.306180i \(-0.900949\pi\)
−0.210828 + 0.977523i \(0.567616\pi\)
\(318\) 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 \(-0.321610\pi\)
0.531549 + 0.847028i \(0.321610\pi\)
\(338\) 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 −0.279919 0.960024i \(-0.590308\pi\)
−0.971364 + 0.237595i \(0.923641\pi\)
\(348\) 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 −0.863769 0.503889i \(-0.831902\pi\)
0.868265 + 0.496101i \(0.165235\pi\)
\(354\) 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 0.116653 0.993173i \(-0.462783\pi\)
−0.801786 + 0.597611i \(0.796117\pi\)
\(368\) −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 0.978732 0.205145i \(-0.0657667\pi\)
−0.667027 + 0.745034i \(0.732433\pi\)
\(374\) −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 \(-0.899190\pi\)
0.205421 0.978674i \(-0.434144\pi\)
\(384\) 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 −0.618425 0.785844i \(-0.712229\pi\)
0.371349 + 0.928493i \(0.378895\pi\)
\(398\) −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 \(-0.935104\pi\)
0.979289 0.202467i \(-0.0648960\pi\)
\(434\) 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 −0.450720 0.892665i \(-0.648833\pi\)
0.547711 + 0.836668i \(0.315499\pi\)
\(444\) 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 \(0.132507\pi\)
−0.107111 + 0.994247i \(0.534160\pi\)
\(458\) −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 \(-0.401352\pi\)
0.304976 + 0.952360i \(0.401352\pi\)
\(464\) −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 0.847762 0.530377i \(-0.177950\pi\)
−0.883201 + 0.468995i \(0.844616\pi\)
\(468\) 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 −0.758122 0.652112i \(-0.773883\pi\)
0.943807 + 0.330497i \(0.107216\pi\)
\(488\) −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 \(-0.513626\pi\)
−0.0427930 + 0.999084i \(0.513626\pi\)
\(504\) 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 0.227496 0.973779i \(-0.426946\pi\)
0.957065 + 0.289872i \(0.0936129\pi\)
\(524\) 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 \(-0.833725\pi\)
−0.866640 + 0.498934i \(0.833725\pi\)
\(548\) −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 −0.00356477 0.999994i \(-0.501135\pi\)
−0.867802 + 0.496910i \(0.834468\pi\)
\(558\) 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 −0.941062 0.338233i \(-0.890171\pi\)
0.763449 + 0.645868i \(0.223504\pi\)
\(564\) 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 0.220815 0.975316i \(-0.429128\pi\)
−0.734241 + 0.678889i \(0.762462\pi\)
\(578\) 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 \(-0.583221\pi\)
−0.258479 + 0.966017i \(0.583221\pi\)
\(588\) 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 0.976620 0.214975i \(-0.0689669\pi\)
−0.674483 + 0.738290i \(0.735634\pi\)
\(594\) 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 0.0450649 0.998984i \(-0.485651\pi\)
0.887678 + 0.460465i \(0.152317\pi\)
\(608\) −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 −0.856652 0.515894i \(-0.827460\pi\)
0.875104 + 0.483935i \(0.160793\pi\)
\(614\) 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 \(0.249343\pi\)
−0.708565 + 0.705646i \(0.750657\pi\)
\(618\) 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 \(0.0208018\pi\)
−0.997865 + 0.0653044i \(0.979198\pi\)
\(644\) −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 −0.540217 0.841526i \(-0.681658\pi\)
0.998891 + 0.0470789i \(0.0149912\pi\)
\(648\) 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 −0.765783 0.643099i \(-0.777649\pi\)
0.174048 + 0.984737i \(0.444315\pi\)
\(654\) 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 \(-0.615476\pi\)
−0.354873 + 0.934914i \(0.615476\pi\)
\(674\) −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 \(-0.875054\pi\)
0.130695 0.991423i \(-0.458279\pi\)
\(678\) 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 0.0683485 0.997662i \(-0.478227\pi\)
−0.829826 + 0.558022i \(0.811560\pi\)
\(684\) 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 \(-0.863304\pi\)
0.909197 0.416365i \(-0.136696\pi\)
\(728\) 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 0.0100750 0.999949i \(-0.496793\pi\)
0.871019 + 0.491249i \(0.163460\pi\)
\(734\) 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 \(0.00657559\pi\)
−0.999787 + 0.0206564i \(0.993424\pi\)
\(744\) 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 \(-0.294065\pi\)
0.602768 + 0.797917i \(0.294065\pi\)
\(758\) 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 −0.981156 0.193216i \(-0.938108\pi\)
0.657908 + 0.753098i \(0.271442\pi\)
\(774\) 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