Properties

Label 280.2.bo.a.33.6
Level $280$
Weight $2$
Character 280.33
Analytic conductor $2.236$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.bo (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 33.6
Character \(\chi\) \(=\) 280.33
Dual form 280.2.bo.a.17.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0749389 - 0.0200798i) q^{3} +(-0.965007 - 2.01712i) q^{5} +(1.45892 - 2.20716i) q^{7} +(-2.59286 - 1.49699i) q^{9} +O(q^{10})\) \(q+(-0.0749389 - 0.0200798i) q^{3} +(-0.965007 - 2.01712i) q^{5} +(1.45892 - 2.20716i) q^{7} +(-2.59286 - 1.49699i) q^{9} +(-0.390978 - 0.677193i) q^{11} +(-3.28478 + 3.28478i) q^{13} +(0.0318132 + 0.170538i) q^{15} +(1.40637 - 5.24865i) q^{17} +(2.91828 - 5.05461i) q^{19} +(-0.153649 + 0.136108i) q^{21} +(8.39046 - 2.24822i) q^{23} +(-3.13752 + 3.89306i) q^{25} +(0.328824 + 0.328824i) q^{27} +0.303774i q^{29} +(-5.04234 + 2.91120i) q^{31} +(0.0157015 + 0.0585989i) q^{33} +(-5.85997 - 0.812878i) q^{35} +(1.90872 + 7.12345i) q^{37} +(0.312116 - 0.180200i) q^{39} -4.39716i q^{41} +(7.33155 + 7.33155i) q^{43} +(-0.517475 + 6.67472i) q^{45} +(2.28130 - 0.611272i) q^{47} +(-2.74313 - 6.44013i) q^{49} +(-0.210784 + 0.365088i) q^{51} +(-1.61262 + 6.01838i) q^{53} +(-0.988682 + 1.44214i) q^{55} +(-0.320188 + 0.320188i) q^{57} +(2.56228 + 4.43800i) q^{59} +(-8.91983 - 5.14987i) q^{61} +(-7.08687 + 3.53889i) q^{63} +(9.79563 + 3.45595i) q^{65} +(-1.47788 - 0.395996i) q^{67} -0.673916 q^{69} -5.83740 q^{71} +(12.9542 + 3.47108i) q^{73} +(0.313295 - 0.228741i) q^{75} +(-2.06508 - 0.125017i) q^{77} +(8.66781 + 5.00437i) q^{79} +(4.47293 + 7.74735i) q^{81} +(2.94473 - 2.94473i) q^{83} +(-11.9443 + 2.22817i) q^{85} +(0.00609973 - 0.0227645i) q^{87} +(6.43727 - 11.1497i) q^{89} +(2.45783 + 12.0423i) q^{91} +(0.436324 - 0.116913i) q^{93} +(-13.0119 - 1.00878i) q^{95} +(-0.0900545 - 0.0900545i) q^{97} +2.34116i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 4q^{7} + O(q^{10}) \) \( 48q - 4q^{7} + 4q^{11} + 8q^{15} - 4q^{21} - 4q^{23} - 8q^{25} - 36q^{33} + 24q^{35} + 8q^{37} - 16q^{43} + 48q^{45} + 24q^{51} + 16q^{53} - 96q^{57} - 36q^{61} - 68q^{63} + 12q^{65} - 16q^{67} - 64q^{71} - 48q^{73} - 48q^{75} + 4q^{77} - 40q^{85} - 12q^{87} - 80q^{91} + 24q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.0749389 0.0200798i −0.0432660 0.0115931i 0.237121 0.971480i \(-0.423796\pi\)
−0.280387 + 0.959887i \(0.590463\pi\)
\(4\) 0 0
\(5\) −0.965007 2.01712i −0.431564 0.902082i
\(6\) 0 0
\(7\) 1.45892 2.20716i 0.551418 0.834229i
\(8\) 0 0
\(9\) −2.59286 1.49699i −0.864288 0.498997i
\(10\) 0 0
\(11\) −0.390978 0.677193i −0.117884 0.204181i 0.801045 0.598604i \(-0.204278\pi\)
−0.918929 + 0.394423i \(0.870945\pi\)
\(12\) 0 0
\(13\) −3.28478 + 3.28478i −0.911035 + 0.911035i −0.996354 0.0853189i \(-0.972809\pi\)
0.0853189 + 0.996354i \(0.472809\pi\)
\(14\) 0 0
\(15\) 0.0318132 + 0.170538i 0.00821413 + 0.0440327i
\(16\) 0 0
\(17\) 1.40637 5.24865i 0.341095 1.27298i −0.556013 0.831174i \(-0.687670\pi\)
0.897108 0.441811i \(-0.145664\pi\)
\(18\) 0 0
\(19\) 2.91828 5.05461i 0.669499 1.15961i −0.308545 0.951210i \(-0.599842\pi\)
0.978044 0.208397i \(-0.0668245\pi\)
\(20\) 0 0
\(21\) −0.153649 + 0.136108i −0.0335290 + 0.0297011i
\(22\) 0 0
\(23\) 8.39046 2.24822i 1.74953 0.468786i 0.765006 0.644024i \(-0.222736\pi\)
0.984526 + 0.175238i \(0.0560695\pi\)
\(24\) 0 0
\(25\) −3.13752 + 3.89306i −0.627505 + 0.778613i
\(26\) 0 0
\(27\) 0.328824 + 0.328824i 0.0632823 + 0.0632823i
\(28\) 0 0
\(29\) 0.303774i 0.0564094i 0.999602 + 0.0282047i \(0.00897903\pi\)
−0.999602 + 0.0282047i \(0.991021\pi\)
\(30\) 0 0
\(31\) −5.04234 + 2.91120i −0.905632 + 0.522867i −0.879023 0.476779i \(-0.841804\pi\)
−0.0266086 + 0.999646i \(0.508471\pi\)
\(32\) 0 0
\(33\) 0.0157015 + 0.0585989i 0.00273328 + 0.0102008i
\(34\) 0 0
\(35\) −5.85997 0.812878i −0.990515 0.137401i
\(36\) 0 0
\(37\) 1.90872 + 7.12345i 0.313792 + 1.17109i 0.925109 + 0.379702i \(0.123973\pi\)
−0.611317 + 0.791386i \(0.709360\pi\)
\(38\) 0 0
\(39\) 0.312116 0.180200i 0.0499785 0.0288551i
\(40\) 0 0
\(41\) 4.39716i 0.686722i −0.939204 0.343361i \(-0.888435\pi\)
0.939204 0.343361i \(-0.111565\pi\)
\(42\) 0 0
\(43\) 7.33155 + 7.33155i 1.11805 + 1.11805i 0.992027 + 0.126023i \(0.0402214\pi\)
0.126023 + 0.992027i \(0.459779\pi\)
\(44\) 0 0
\(45\) −0.517475 + 6.67472i −0.0771406 + 0.995008i
\(46\) 0 0
\(47\) 2.28130 0.611272i 0.332761 0.0891631i −0.0885698 0.996070i \(-0.528230\pi\)
0.421331 + 0.906907i \(0.361563\pi\)
\(48\) 0 0
\(49\) −2.74313 6.44013i −0.391876 0.920018i
\(50\) 0 0
\(51\) −0.210784 + 0.365088i −0.0295157 + 0.0511226i
\(52\) 0 0
\(53\) −1.61262 + 6.01838i −0.221510 + 0.826688i 0.762262 + 0.647268i \(0.224089\pi\)
−0.983773 + 0.179420i \(0.942578\pi\)
\(54\) 0 0
\(55\) −0.988682 + 1.44214i −0.133314 + 0.194459i
\(56\) 0 0
\(57\) −0.320188 + 0.320188i −0.0424100 + 0.0424100i
\(58\) 0 0
\(59\) 2.56228 + 4.43800i 0.333581 + 0.577779i 0.983211 0.182471i \(-0.0584097\pi\)
−0.649630 + 0.760250i \(0.725076\pi\)
\(60\) 0 0
\(61\) −8.91983 5.14987i −1.14207 0.659373i −0.195126 0.980778i \(-0.562511\pi\)
−0.946942 + 0.321405i \(0.895845\pi\)
\(62\) 0 0
\(63\) −7.08687 + 3.53889i −0.892862 + 0.445858i
\(64\) 0 0
\(65\) 9.79563 + 3.45595i 1.21500 + 0.428658i
\(66\) 0 0
\(67\) −1.47788 0.395996i −0.180551 0.0483786i 0.167410 0.985887i \(-0.446459\pi\)
−0.347962 + 0.937509i \(0.613126\pi\)
\(68\) 0 0
\(69\) −0.673916 −0.0811299
\(70\) 0 0
\(71\) −5.83740 −0.692772 −0.346386 0.938092i \(-0.612591\pi\)
−0.346386 + 0.938092i \(0.612591\pi\)
\(72\) 0 0
\(73\) 12.9542 + 3.47108i 1.51618 + 0.406259i 0.918482 0.395463i \(-0.129416\pi\)
0.597697 + 0.801722i \(0.296082\pi\)
\(74\) 0 0
\(75\) 0.313295 0.228741i 0.0361762 0.0264127i
\(76\) 0 0
\(77\) −2.06508 0.125017i −0.235338 0.0142470i
\(78\) 0 0
\(79\) 8.66781 + 5.00437i 0.975205 + 0.563035i 0.900819 0.434194i \(-0.142967\pi\)
0.0743862 + 0.997230i \(0.476300\pi\)
\(80\) 0 0
\(81\) 4.47293 + 7.74735i 0.496992 + 0.860816i
\(82\) 0 0
\(83\) 2.94473 2.94473i 0.323226 0.323226i −0.526777 0.850003i \(-0.676600\pi\)
0.850003 + 0.526777i \(0.176600\pi\)
\(84\) 0 0
\(85\) −11.9443 + 2.22817i −1.29554 + 0.241678i
\(86\) 0 0
\(87\) 0.00609973 0.0227645i 0.000653959 0.00244061i
\(88\) 0 0
\(89\) 6.43727 11.1497i 0.682350 1.18186i −0.291912 0.956445i \(-0.594292\pi\)
0.974262 0.225419i \(-0.0723751\pi\)
\(90\) 0 0
\(91\) 2.45783 + 12.0423i 0.257650 + 1.26237i
\(92\) 0 0
\(93\) 0.436324 0.116913i 0.0452447 0.0121233i
\(94\) 0 0
\(95\) −13.0119 1.00878i −1.33499 0.103499i
\(96\) 0 0
\(97\) −0.0900545 0.0900545i −0.00914365 0.00914365i 0.702520 0.711664i \(-0.252058\pi\)
−0.711664 + 0.702520i \(0.752058\pi\)
\(98\) 0 0
\(99\) 2.34116i 0.235295i
\(100\) 0 0
\(101\) 5.24945 3.03077i 0.522340 0.301573i −0.215551 0.976492i \(-0.569155\pi\)
0.737892 + 0.674919i \(0.235822\pi\)
\(102\) 0 0
\(103\) 0.666178 + 2.48621i 0.0656405 + 0.244973i 0.990948 0.134243i \(-0.0428602\pi\)
−0.925308 + 0.379216i \(0.876194\pi\)
\(104\) 0 0
\(105\) 0.422817 + 0.178583i 0.0412627 + 0.0174279i
\(106\) 0 0
\(107\) −2.20467 8.22792i −0.213133 0.795423i −0.986815 0.161850i \(-0.948254\pi\)
0.773682 0.633574i \(-0.218413\pi\)
\(108\) 0 0
\(109\) −7.24069 + 4.18042i −0.693533 + 0.400411i −0.804934 0.593364i \(-0.797799\pi\)
0.111401 + 0.993775i \(0.464466\pi\)
\(110\) 0 0
\(111\) 0.572150i 0.0543061i
\(112\) 0 0
\(113\) 0.624674 + 0.624674i 0.0587644 + 0.0587644i 0.735878 0.677114i \(-0.236770\pi\)
−0.677114 + 0.735878i \(0.736770\pi\)
\(114\) 0 0
\(115\) −12.6318 14.7550i −1.17792 1.37591i
\(116\) 0 0
\(117\) 13.4343 3.59970i 1.24200 0.332793i
\(118\) 0 0
\(119\) −9.53284 10.7614i −0.873874 0.986498i
\(120\) 0 0
\(121\) 5.19427 8.99674i 0.472207 0.817886i
\(122\) 0 0
\(123\) −0.0882943 + 0.329519i −0.00796123 + 0.0297117i
\(124\) 0 0
\(125\) 10.8805 + 2.57192i 0.973181 + 0.230040i
\(126\) 0 0
\(127\) 9.47330 9.47330i 0.840620 0.840620i −0.148320 0.988939i \(-0.547387\pi\)
0.988939 + 0.148320i \(0.0473865\pi\)
\(128\) 0 0
\(129\) −0.402202 0.696634i −0.0354119 0.0613352i
\(130\) 0 0
\(131\) −5.71583 3.30004i −0.499394 0.288326i 0.229069 0.973410i \(-0.426432\pi\)
−0.728463 + 0.685085i \(0.759765\pi\)
\(132\) 0 0
\(133\) −6.89881 13.8154i −0.598203 1.19794i
\(134\) 0 0
\(135\) 0.345960 0.980595i 0.0297755 0.0843962i
\(136\) 0 0
\(137\) −0.399466 0.107037i −0.0341287 0.00914475i 0.241714 0.970347i \(-0.422290\pi\)
−0.275843 + 0.961203i \(0.588957\pi\)
\(138\) 0 0
\(139\) −16.1574 −1.37045 −0.685225 0.728332i \(-0.740296\pi\)
−0.685225 + 0.728332i \(0.740296\pi\)
\(140\) 0 0
\(141\) −0.183232 −0.0154309
\(142\) 0 0
\(143\) 3.50871 + 0.940156i 0.293413 + 0.0786198i
\(144\) 0 0
\(145\) 0.612748 0.293144i 0.0508859 0.0243443i
\(146\) 0 0
\(147\) 0.0762506 + 0.537698i 0.00628904 + 0.0443486i
\(148\) 0 0
\(149\) 4.87017 + 2.81179i 0.398979 + 0.230351i 0.686044 0.727560i \(-0.259346\pi\)
−0.287064 + 0.957911i \(0.592679\pi\)
\(150\) 0 0
\(151\) 3.59720 + 6.23053i 0.292736 + 0.507033i 0.974456 0.224580i \(-0.0721010\pi\)
−0.681720 + 0.731613i \(0.738768\pi\)
\(152\) 0 0
\(153\) −11.5037 + 11.5037i −0.930020 + 0.930020i
\(154\) 0 0
\(155\) 10.7381 + 7.36167i 0.862507 + 0.591304i
\(156\) 0 0
\(157\) −0.547542 + 2.04345i −0.0436986 + 0.163085i −0.984327 0.176352i \(-0.943570\pi\)
0.940628 + 0.339438i \(0.110237\pi\)
\(158\) 0 0
\(159\) 0.241696 0.418630i 0.0191677 0.0331995i
\(160\) 0 0
\(161\) 7.27879 21.7991i 0.573649 1.71801i
\(162\) 0 0
\(163\) 0.504944 0.135299i 0.0395503 0.0105975i −0.238990 0.971022i \(-0.576816\pi\)
0.278540 + 0.960425i \(0.410150\pi\)
\(164\) 0 0
\(165\) 0.103049 0.0882201i 0.00802234 0.00686793i
\(166\) 0 0
\(167\) 0.418275 + 0.418275i 0.0323671 + 0.0323671i 0.723105 0.690738i \(-0.242714\pi\)
−0.690738 + 0.723105i \(0.742714\pi\)
\(168\) 0 0
\(169\) 8.57959i 0.659969i
\(170\) 0 0
\(171\) −15.1334 + 8.73727i −1.15728 + 0.668156i
\(172\) 0 0
\(173\) −2.64144 9.85798i −0.200825 0.749488i −0.990682 0.136197i \(-0.956512\pi\)
0.789857 0.613291i \(-0.210155\pi\)
\(174\) 0 0
\(175\) 4.01524 + 12.6047i 0.303523 + 0.952824i
\(176\) 0 0
\(177\) −0.102900 0.384029i −0.00773446 0.0288654i
\(178\) 0 0
\(179\) 18.6482 10.7666i 1.39384 0.804731i 0.400098 0.916472i \(-0.368976\pi\)
0.993737 + 0.111741i \(0.0356427\pi\)
\(180\) 0 0
\(181\) 3.63457i 0.270155i −0.990835 0.135078i \(-0.956872\pi\)
0.990835 0.135078i \(-0.0431284\pi\)
\(182\) 0 0
\(183\) 0.565034 + 0.565034i 0.0417685 + 0.0417685i
\(184\) 0 0
\(185\) 12.5269 10.7243i 0.920996 0.788466i
\(186\) 0 0
\(187\) −4.10421 + 1.09972i −0.300130 + 0.0804195i
\(188\) 0 0
\(189\) 1.20550 0.246042i 0.0876869 0.0178969i
\(190\) 0 0
\(191\) 0.00324409 0.00561893i 0.000234734 0.000406571i −0.865908 0.500203i \(-0.833259\pi\)
0.866143 + 0.499797i \(0.166592\pi\)
\(192\) 0 0
\(193\) 0.678515 2.53225i 0.0488406 0.182275i −0.937196 0.348802i \(-0.886589\pi\)
0.986037 + 0.166527i \(0.0532552\pi\)
\(194\) 0 0
\(195\) −0.664679 0.455680i −0.0475986 0.0326319i
\(196\) 0 0
\(197\) −6.64991 + 6.64991i −0.473786 + 0.473786i −0.903138 0.429351i \(-0.858742\pi\)
0.429351 + 0.903138i \(0.358742\pi\)
\(198\) 0 0
\(199\) 0.846048 + 1.46540i 0.0599747 + 0.103879i 0.894454 0.447160i \(-0.147565\pi\)
−0.834479 + 0.551040i \(0.814231\pi\)
\(200\) 0 0
\(201\) 0.102799 + 0.0593510i 0.00725088 + 0.00418630i
\(202\) 0 0
\(203\) 0.670478 + 0.443180i 0.0470584 + 0.0311052i
\(204\) 0 0
\(205\) −8.86960 + 4.24329i −0.619479 + 0.296364i
\(206\) 0 0
\(207\) −25.1209 6.73112i −1.74602 0.467845i
\(208\) 0 0
\(209\) −4.56393 −0.315693
\(210\) 0 0
\(211\) 9.03597 0.622062 0.311031 0.950400i \(-0.399326\pi\)
0.311031 + 0.950400i \(0.399326\pi\)
\(212\) 0 0
\(213\) 0.437448 + 0.117214i 0.0299735 + 0.00803137i
\(214\) 0 0
\(215\) 7.71360 21.8636i 0.526063 1.49108i
\(216\) 0 0
\(217\) −0.930867 + 15.3765i −0.0631914 + 1.04382i
\(218\) 0 0
\(219\) −0.901078 0.520238i −0.0608892 0.0351544i
\(220\) 0 0
\(221\) 12.6210 + 21.8603i 0.848984 + 1.47048i
\(222\) 0 0
\(223\) 2.08617 2.08617i 0.139700 0.139700i −0.633798 0.773499i \(-0.718505\pi\)
0.773499 + 0.633798i \(0.218505\pi\)
\(224\) 0 0
\(225\) 13.9631 5.39734i 0.930870 0.359822i
\(226\) 0 0
\(227\) 0.121724 0.454280i 0.00807910 0.0301516i −0.961769 0.273863i \(-0.911698\pi\)
0.969848 + 0.243712i \(0.0783651\pi\)
\(228\) 0 0
\(229\) −12.6003 + 21.8244i −0.832651 + 1.44219i 0.0632774 + 0.997996i \(0.479845\pi\)
−0.895929 + 0.444198i \(0.853489\pi\)
\(230\) 0 0
\(231\) 0.152244 + 0.0508350i 0.0100170 + 0.00334470i
\(232\) 0 0
\(233\) −15.0074 + 4.02122i −0.983168 + 0.263439i −0.714378 0.699760i \(-0.753290\pi\)
−0.268790 + 0.963199i \(0.586624\pi\)
\(234\) 0 0
\(235\) −3.43447 4.01176i −0.224040 0.261699i
\(236\) 0 0
\(237\) −0.549070 0.549070i −0.0356659 0.0356659i
\(238\) 0 0
\(239\) 28.2271i 1.82586i 0.408117 + 0.912930i \(0.366186\pi\)
−0.408117 + 0.912930i \(0.633814\pi\)
\(240\) 0 0
\(241\) −11.8212 + 6.82500i −0.761473 + 0.439637i −0.829824 0.558025i \(-0.811559\pi\)
0.0683514 + 0.997661i \(0.478226\pi\)
\(242\) 0 0
\(243\) −0.540706 2.01794i −0.0346863 0.129451i
\(244\) 0 0
\(245\) −10.3434 + 11.7480i −0.660813 + 0.750551i
\(246\) 0 0
\(247\) 7.01737 + 26.1892i 0.446505 + 1.66638i
\(248\) 0 0
\(249\) −0.279804 + 0.161545i −0.0177319 + 0.0102375i
\(250\) 0 0
\(251\) 8.14470i 0.514089i −0.966400 0.257045i \(-0.917251\pi\)
0.966400 0.257045i \(-0.0827487\pi\)
\(252\) 0 0
\(253\) −4.80296 4.80296i −0.301960 0.301960i
\(254\) 0 0
\(255\) 0.939834 + 0.0728631i 0.0588547 + 0.00456287i
\(256\) 0 0
\(257\) −10.0007 + 2.67967i −0.623823 + 0.167153i −0.556865 0.830603i \(-0.687996\pi\)
−0.0669581 + 0.997756i \(0.521329\pi\)
\(258\) 0 0
\(259\) 18.5073 + 6.17965i 1.14999 + 0.383985i
\(260\) 0 0
\(261\) 0.454747 0.787644i 0.0281481 0.0487540i
\(262\) 0 0
\(263\) 7.62698 28.4643i 0.470300 1.75518i −0.168391 0.985720i \(-0.553857\pi\)
0.638691 0.769463i \(-0.279476\pi\)
\(264\) 0 0
\(265\) 13.6960 2.55493i 0.841337 0.156948i
\(266\) 0 0
\(267\) −0.706286 + 0.706286i −0.0432240 + 0.0432240i
\(268\) 0 0
\(269\) 10.2431 + 17.7415i 0.624531 + 1.08172i 0.988631 + 0.150360i \(0.0480433\pi\)
−0.364100 + 0.931360i \(0.618623\pi\)
\(270\) 0 0
\(271\) 13.4287 + 7.75309i 0.815738 + 0.470967i 0.848945 0.528482i \(-0.177239\pi\)
−0.0332065 + 0.999449i \(0.510572\pi\)
\(272\) 0 0
\(273\) 0.0576197 0.951787i 0.00348730 0.0576048i
\(274\) 0 0
\(275\) 3.86306 + 0.602610i 0.232951 + 0.0363387i
\(276\) 0 0
\(277\) −2.32259 0.622335i −0.139551 0.0373925i 0.188368 0.982099i \(-0.439680\pi\)
−0.327918 + 0.944706i \(0.606347\pi\)
\(278\) 0 0
\(279\) 17.4321 1.04364
\(280\) 0 0
\(281\) −16.9059 −1.00852 −0.504261 0.863552i \(-0.668235\pi\)
−0.504261 + 0.863552i \(0.668235\pi\)
\(282\) 0 0
\(283\) 5.27738 + 1.41407i 0.313708 + 0.0840578i 0.412238 0.911076i \(-0.364747\pi\)
−0.0985299 + 0.995134i \(0.531414\pi\)
\(284\) 0 0
\(285\) 0.954841 + 0.336873i 0.0565599 + 0.0199547i
\(286\) 0 0
\(287\) −9.70525 6.41509i −0.572883 0.378671i
\(288\) 0 0
\(289\) −10.8480 6.26310i −0.638118 0.368418i
\(290\) 0 0
\(291\) 0.00494031 + 0.00855687i 0.000289606 + 0.000501612i
\(292\) 0 0
\(293\) −9.62258 + 9.62258i −0.562157 + 0.562157i −0.929920 0.367762i \(-0.880124\pi\)
0.367762 + 0.929920i \(0.380124\pi\)
\(294\) 0 0
\(295\) 6.47935 9.45113i 0.377243 0.550266i
\(296\) 0 0
\(297\) 0.0941146 0.351241i 0.00546109 0.0203810i
\(298\) 0 0
\(299\) −20.1759 + 34.9457i −1.16680 + 2.02096i
\(300\) 0 0
\(301\) 26.8780 5.48581i 1.54922 0.316197i
\(302\) 0 0
\(303\) −0.454246 + 0.121715i −0.0260957 + 0.00699233i
\(304\) 0 0
\(305\) −1.78019 + 22.9620i −0.101933 + 1.31480i
\(306\) 0 0
\(307\) 17.8381 + 17.8381i 1.01807 + 1.01807i 0.999834 + 0.0182409i \(0.00580657\pi\)
0.0182409 + 0.999834i \(0.494193\pi\)
\(308\) 0 0
\(309\) 0.199691i 0.0113600i
\(310\) 0 0
\(311\) −10.7681 + 6.21694i −0.610601 + 0.352530i −0.773200 0.634162i \(-0.781345\pi\)
0.162600 + 0.986692i \(0.448012\pi\)
\(312\) 0 0
\(313\) 0.654518 + 2.44269i 0.0369955 + 0.138069i 0.981953 0.189123i \(-0.0605643\pi\)
−0.944958 + 0.327192i \(0.893898\pi\)
\(314\) 0 0
\(315\) 13.9772 + 10.8800i 0.787528 + 0.613018i
\(316\) 0 0
\(317\) −4.12570 15.3973i −0.231722 0.864799i −0.979599 0.200962i \(-0.935593\pi\)
0.747877 0.663837i \(-0.231073\pi\)
\(318\) 0 0
\(319\) 0.205714 0.118769i 0.0115178 0.00664978i
\(320\) 0 0
\(321\) 0.660861i 0.0368857i
\(322\) 0 0
\(323\) −22.4257 22.4257i −1.24780 1.24780i
\(324\) 0 0
\(325\) −2.48178 23.0940i −0.137664 1.28102i
\(326\) 0 0
\(327\) 0.626552 0.167884i 0.0346484 0.00928401i
\(328\) 0 0
\(329\) 1.97904 5.92699i 0.109108 0.326765i
\(330\) 0 0
\(331\) 12.4183 21.5091i 0.682572 1.18225i −0.291621 0.956534i \(-0.594195\pi\)
0.974193 0.225716i \(-0.0724721\pi\)
\(332\) 0 0
\(333\) 5.71468 21.3275i 0.313162 1.16874i
\(334\) 0 0
\(335\) 0.627391 + 3.36319i 0.0342780 + 0.183751i
\(336\) 0 0
\(337\) −20.6822 + 20.6822i −1.12663 + 1.12663i −0.135912 + 0.990721i \(0.543396\pi\)
−0.990721 + 0.135912i \(0.956604\pi\)
\(338\) 0 0
\(339\) −0.0342690 0.0593557i −0.00186124 0.00322376i
\(340\) 0 0
\(341\) 3.94289 + 2.27643i 0.213519 + 0.123275i
\(342\) 0 0
\(343\) −18.2164 3.34107i −0.983593 0.180401i
\(344\) 0 0
\(345\) 0.650333 + 1.35937i 0.0350128 + 0.0731859i
\(346\) 0 0
\(347\) 20.6497 + 5.53308i 1.10854 + 0.297031i 0.766236 0.642560i \(-0.222128\pi\)
0.342300 + 0.939591i \(0.388794\pi\)
\(348\) 0 0
\(349\) −14.6661 −0.785056 −0.392528 0.919740i \(-0.628399\pi\)
−0.392528 + 0.919740i \(0.628399\pi\)
\(350\) 0 0
\(351\) −2.16023 −0.115305
\(352\) 0 0
\(353\) −1.18700 0.318055i −0.0631775 0.0169284i 0.227092 0.973873i \(-0.427078\pi\)
−0.290269 + 0.956945i \(0.593745\pi\)
\(354\) 0 0
\(355\) 5.63313 + 11.7747i 0.298975 + 0.624937i
\(356\) 0 0
\(357\) 0.498293 + 0.997868i 0.0263725 + 0.0528127i
\(358\) 0 0
\(359\) −15.3588 8.86741i −0.810607 0.468004i 0.0365599 0.999331i \(-0.488360\pi\)
−0.847166 + 0.531328i \(0.821693\pi\)
\(360\) 0 0
\(361\) −7.53269 13.0470i −0.396458 0.686685i
\(362\) 0 0
\(363\) −0.569906 + 0.569906i −0.0299123 + 0.0299123i
\(364\) 0 0
\(365\) −5.49936 29.4798i −0.287849 1.54305i
\(366\) 0 0
\(367\) −2.40926 + 8.99149i −0.125762 + 0.469352i −0.999866 0.0163883i \(-0.994783\pi\)
0.874103 + 0.485740i \(0.161450\pi\)
\(368\) 0 0
\(369\) −6.58251 + 11.4012i −0.342672 + 0.593525i
\(370\) 0 0
\(371\) 10.9309 + 12.3396i 0.567502 + 0.640641i
\(372\) 0 0
\(373\) −14.5351 + 3.89467i −0.752600 + 0.201659i −0.614671 0.788784i \(-0.710711\pi\)
−0.137929 + 0.990442i \(0.544045\pi\)
\(374\) 0 0
\(375\) −0.763729 0.411216i −0.0394388 0.0212351i
\(376\) 0 0
\(377\) −0.997831 0.997831i −0.0513909 0.0513909i
\(378\) 0 0
\(379\) 16.5827i 0.851794i −0.904772 0.425897i \(-0.859959\pi\)
0.904772 0.425897i \(-0.140041\pi\)
\(380\) 0 0
\(381\) −0.900141 + 0.519697i −0.0461156 + 0.0266249i
\(382\) 0 0
\(383\) 7.35797 + 27.4603i 0.375975 + 1.40316i 0.851916 + 0.523679i \(0.175441\pi\)
−0.475941 + 0.879477i \(0.657892\pi\)
\(384\) 0 0
\(385\) 1.74064 + 4.28615i 0.0887113 + 0.218442i
\(386\) 0 0
\(387\) −8.03445 29.9850i −0.408414 1.52422i
\(388\) 0 0
\(389\) 17.2501 9.95935i 0.874614 0.504959i 0.00573552 0.999984i \(-0.498174\pi\)
0.868879 + 0.495025i \(0.164841\pi\)
\(390\) 0 0
\(391\) 47.2004i 2.38703i
\(392\) 0 0
\(393\) 0.362074 + 0.362074i 0.0182642 + 0.0182642i
\(394\) 0 0
\(395\) 1.72989 22.3132i 0.0870404 1.12270i
\(396\) 0 0
\(397\) 10.4715 2.80583i 0.525549 0.140821i 0.0137171 0.999906i \(-0.495634\pi\)
0.511832 + 0.859085i \(0.328967\pi\)
\(398\) 0 0
\(399\) 0.239580 + 1.17383i 0.0119940 + 0.0587652i
\(400\) 0 0
\(401\) −16.8238 + 29.1397i −0.840142 + 1.45517i 0.0496323 + 0.998768i \(0.484195\pi\)
−0.889774 + 0.456401i \(0.849138\pi\)
\(402\) 0 0
\(403\) 7.00035 26.1257i 0.348712 1.30141i
\(404\) 0 0
\(405\) 11.3109 16.4987i 0.562043 0.819825i
\(406\) 0 0
\(407\) 4.07768 4.07768i 0.202123 0.202123i
\(408\) 0 0
\(409\) 5.99488 + 10.3834i 0.296428 + 0.513428i 0.975316 0.220814i \(-0.0708712\pi\)
−0.678888 + 0.734242i \(0.737538\pi\)
\(410\) 0 0
\(411\) 0.0277863 + 0.0160424i 0.00137059 + 0.000791313i
\(412\) 0 0
\(413\) 13.5335 + 0.819300i 0.665942 + 0.0403151i
\(414\) 0 0
\(415\) −8.78155 3.09818i −0.431069 0.152084i
\(416\) 0 0
\(417\) 1.21081 + 0.324437i 0.0592939 + 0.0158877i
\(418\) 0 0
\(419\) −1.15873 −0.0566075 −0.0283037 0.999599i \(-0.509011\pi\)
−0.0283037 + 0.999599i \(0.509011\pi\)
\(420\) 0 0
\(421\) 30.6438 1.49349 0.746744 0.665111i \(-0.231616\pi\)
0.746744 + 0.665111i \(0.231616\pi\)
\(422\) 0 0
\(423\) −6.83016 1.83014i −0.332094 0.0889843i
\(424\) 0 0
\(425\) 16.0208 + 21.9429i 0.777123 + 1.06439i
\(426\) 0 0
\(427\) −24.3799 + 12.1743i −1.17982 + 0.589155i
\(428\) 0 0
\(429\) −0.244061 0.140909i −0.0117834 0.00680313i
\(430\) 0 0
\(431\) 20.2975 + 35.1563i 0.977697 + 1.69342i 0.670731 + 0.741701i \(0.265981\pi\)
0.306967 + 0.951720i \(0.400686\pi\)
\(432\) 0 0
\(433\) 19.1716 19.1716i 0.921327 0.921327i −0.0757959 0.997123i \(-0.524150\pi\)
0.997123 + 0.0757959i \(0.0241498\pi\)
\(434\) 0 0
\(435\) −0.0518049 + 0.00966402i −0.00248386 + 0.000463354i
\(436\) 0 0
\(437\) 13.1218 48.9714i 0.627703 2.34262i
\(438\) 0 0
\(439\) 15.1874 26.3053i 0.724854 1.25548i −0.234179 0.972193i \(-0.575240\pi\)
0.959034 0.283291i \(-0.0914263\pi\)
\(440\) 0 0
\(441\) −2.52825 + 20.8048i −0.120393 + 0.990705i
\(442\) 0 0
\(443\) −35.8429 + 9.60409i −1.70295 + 0.456304i −0.973679 0.227922i \(-0.926807\pi\)
−0.729270 + 0.684226i \(0.760140\pi\)
\(444\) 0 0
\(445\) −28.7022 2.22522i −1.36062 0.105485i
\(446\) 0 0
\(447\) −0.308505 0.308505i −0.0145918 0.0145918i
\(448\) 0 0
\(449\) 16.8567i 0.795516i −0.917490 0.397758i \(-0.869788\pi\)
0.917490 0.397758i \(-0.130212\pi\)
\(450\) 0 0
\(451\) −2.97773 + 1.71919i −0.140216 + 0.0809536i
\(452\) 0 0
\(453\) −0.144462 0.539140i −0.00678742 0.0253310i
\(454\) 0 0
\(455\) 21.9188 16.5786i 1.02757 0.777217i
\(456\) 0 0
\(457\) 1.78496 + 6.66157i 0.0834971 + 0.311615i 0.995025 0.0996221i \(-0.0317634\pi\)
−0.911528 + 0.411237i \(0.865097\pi\)
\(458\) 0 0
\(459\) 2.18833 1.26343i 0.102143 0.0589721i
\(460\) 0 0
\(461\) 0.948800i 0.0441900i −0.999756 0.0220950i \(-0.992966\pi\)
0.999756 0.0220950i \(-0.00703363\pi\)
\(462\) 0 0
\(463\) 4.74202 + 4.74202i 0.220380 + 0.220380i 0.808659 0.588278i \(-0.200194\pi\)
−0.588278 + 0.808659i \(0.700194\pi\)
\(464\) 0 0
\(465\) −0.656882 0.767295i −0.0304622 0.0355825i
\(466\) 0 0
\(467\) −26.6857 + 7.15041i −1.23487 + 0.330882i −0.816473 0.577384i \(-0.804074\pi\)
−0.418394 + 0.908266i \(0.637407\pi\)
\(468\) 0 0
\(469\) −3.03013 + 2.68419i −0.139918 + 0.123944i
\(470\) 0 0
\(471\) 0.0820644 0.142140i 0.00378133 0.00654945i
\(472\) 0 0
\(473\) 2.09840 7.83135i 0.0964847 0.360086i
\(474\) 0 0
\(475\) 10.5217 + 27.2200i 0.482770 + 1.24894i
\(476\) 0 0
\(477\) 13.1908 13.1908i 0.603964 0.603964i
\(478\) 0 0
\(479\) −2.54289 4.40442i −0.116188 0.201243i 0.802066 0.597235i \(-0.203734\pi\)
−0.918254 + 0.395992i \(0.870401\pi\)
\(480\) 0 0
\(481\) −29.6687 17.1292i −1.35278 0.781026i
\(482\) 0 0
\(483\) −0.983186 + 1.48744i −0.0447365 + 0.0676809i
\(484\) 0 0
\(485\) −0.0947473 + 0.268554i −0.00430225 + 0.0121944i
\(486\) 0 0
\(487\) −18.4260 4.93722i −0.834961 0.223727i −0.184084 0.982911i \(-0.558932\pi\)
−0.650877 + 0.759184i \(0.725598\pi\)
\(488\) 0 0
\(489\) −0.0405567 −0.00183404
\(490\) 0 0
\(491\) −21.7497 −0.981548 −0.490774 0.871287i \(-0.663286\pi\)
−0.490774 + 0.871287i \(0.663286\pi\)
\(492\) 0 0
\(493\) 1.59440 + 0.427219i 0.0718083 + 0.0192410i
\(494\) 0 0
\(495\) 4.72239 2.25923i 0.212256 0.101545i
\(496\) 0 0
\(497\) −8.51627 + 12.8841i −0.382007 + 0.577930i
\(498\) 0 0
\(499\) −28.7858 16.6195i −1.28863 0.743992i −0.310221 0.950664i \(-0.600403\pi\)
−0.978410 + 0.206673i \(0.933736\pi\)
\(500\) 0 0
\(501\) −0.0229462 0.0397440i −0.00102516 0.00177563i
\(502\) 0 0
\(503\) −25.2173 + 25.2173i −1.12438 + 1.12438i −0.133307 + 0.991075i \(0.542560\pi\)
−0.991075 + 0.133307i \(0.957440\pi\)
\(504\) 0 0
\(505\) −11.1792 7.66405i −0.497467 0.341046i
\(506\) 0 0
\(507\) −0.172277 + 0.642945i −0.00765108 + 0.0285542i
\(508\) 0 0
\(509\) −7.44191 + 12.8898i −0.329857 + 0.571329i −0.982483 0.186351i \(-0.940334\pi\)
0.652626 + 0.757680i \(0.273667\pi\)
\(510\) 0 0
\(511\) 26.5604 23.5281i 1.17496 1.04082i
\(512\) 0 0
\(513\) 2.62168 0.702477i 0.115750 0.0310151i
\(514\) 0 0
\(515\) 4.37211 3.74297i 0.192658 0.164935i
\(516\) 0 0
\(517\) −1.30589 1.30589i −0.0574328 0.0574328i
\(518\) 0 0
\(519\) 0.791786i 0.0347555i
\(520\) 0 0
\(521\) −23.3131 + 13.4598i −1.02137 + 0.589686i −0.914500 0.404587i \(-0.867415\pi\)
−0.106867 + 0.994273i \(0.534082\pi\)
\(522\) 0 0
\(523\) 7.74842 + 28.9175i 0.338815 + 1.26447i 0.899674 + 0.436563i \(0.143804\pi\)
−0.560859 + 0.827911i \(0.689529\pi\)
\(524\) 0 0
\(525\) −0.0477979 1.02521i −0.00208607 0.0447437i
\(526\) 0 0
\(527\) 8.18845 + 30.5597i 0.356695 + 1.33120i
\(528\) 0 0
\(529\) 45.4268 26.2271i 1.97508 1.14031i
\(530\) 0 0
\(531\) 15.3429i 0.665823i
\(532\) 0 0
\(533\) 14.4437 + 14.4437i 0.625627 + 0.625627i
\(534\) 0 0
\(535\) −14.4692 + 12.3871i −0.625557 + 0.535540i
\(536\) 0 0
\(537\) −1.61367 + 0.432382i −0.0696350 + 0.0186586i
\(538\) 0 0
\(539\) −3.28871 + 4.37558i −0.141655 + 0.188469i
\(540\) 0 0
\(541\) 12.1822 21.1003i 0.523755 0.907171i −0.475862 0.879520i \(-0.657864\pi\)
0.999618 0.0276510i \(-0.00880272\pi\)
\(542\) 0 0
\(543\) −0.0729815 + 0.272371i −0.00313194 + 0.0116885i
\(544\) 0 0
\(545\) 15.4197 + 10.5712i 0.660508 + 0.452820i
\(546\) 0 0
\(547\) 27.6642 27.6642i 1.18283 1.18283i 0.203827 0.979007i \(-0.434662\pi\)
0.979007 0.203827i \(-0.0653379\pi\)
\(548\) 0 0
\(549\) 15.4186 + 26.7058i 0.658050 + 1.13978i
\(550\) 0 0
\(551\) 1.53546 + 0.886497i 0.0654127 + 0.0377660i
\(552\) 0 0
\(553\) 23.6911 11.8303i 1.00745 0.503077i
\(554\) 0 0
\(555\) −1.15409 + 0.552129i −0.0489886 + 0.0234366i
\(556\) 0 0
\(557\) 13.3251 + 3.57044i 0.564601 + 0.151284i 0.529819 0.848111i \(-0.322260\pi\)
0.0347817 + 0.999395i \(0.488926\pi\)
\(558\) 0 0
\(559\) −48.1651 −2.03717
\(560\) 0 0
\(561\) 0.329647 0.0139177
\(562\) 0 0
\(563\) 19.1580 + 5.13338i 0.807415 + 0.216346i 0.638837 0.769342i \(-0.279416\pi\)
0.168578 + 0.985688i \(0.446083\pi\)
\(564\) 0 0
\(565\) 0.657226 1.86285i 0.0276497 0.0783709i
\(566\) 0 0
\(567\) 23.6253 + 1.43024i 0.992169 + 0.0600643i
\(568\) 0 0
\(569\) 10.4442 + 6.02994i 0.437842 + 0.252788i 0.702682 0.711504i \(-0.251986\pi\)
−0.264840 + 0.964292i \(0.585319\pi\)
\(570\) 0 0
\(571\) 1.69675 + 2.93885i 0.0710067 + 0.122987i 0.899343 0.437244i \(-0.144046\pi\)
−0.828336 + 0.560232i \(0.810712\pi\)
\(572\) 0 0
\(573\) −0.000355935 0 0.000355935i −1.48694e−5 0 1.48694e-5i
\(574\) 0 0
\(575\) −17.5728 + 39.7184i −0.732837 + 1.65637i
\(576\) 0 0
\(577\) −6.53624 + 24.3936i −0.272107 + 1.01552i 0.685648 + 0.727933i \(0.259519\pi\)
−0.957755 + 0.287585i \(0.907148\pi\)
\(578\) 0 0
\(579\) −0.101694 + 0.176140i −0.00422627 + 0.00732012i
\(580\) 0 0
\(581\) −2.20338 10.7956i −0.0914117 0.447877i
\(582\) 0 0
\(583\) 4.70611 1.26100i 0.194907 0.0522252i
\(584\) 0 0
\(585\) −20.2252 23.6248i −0.836209 0.976765i
\(586\) 0 0
\(587\) 19.6875 + 19.6875i 0.812589 + 0.812589i 0.985021 0.172433i \(-0.0551627\pi\)
−0.172433 + 0.985021i \(0.555163\pi\)
\(588\) 0 0
\(589\) 33.9828i 1.40023i
\(590\) 0 0
\(591\) 0.631866 0.364808i 0.0259915 0.0150062i
\(592\) 0 0
\(593\) 4.42647 + 16.5198i 0.181773 + 0.678387i 0.995298 + 0.0968573i \(0.0308790\pi\)
−0.813525 + 0.581530i \(0.802454\pi\)
\(594\) 0 0
\(595\) −12.5078 + 29.6137i −0.512770 + 1.21404i
\(596\) 0 0
\(597\) −0.0339770 0.126804i −0.00139058 0.00518973i
\(598\) 0 0
\(599\) −16.8012 + 9.70017i −0.686478 + 0.396338i −0.802291 0.596933i \(-0.796386\pi\)
0.115813 + 0.993271i \(0.463053\pi\)
\(600\) 0 0
\(601\) 26.7561i 1.09141i 0.837979 + 0.545703i \(0.183737\pi\)
−0.837979 + 0.545703i \(0.816263\pi\)
\(602\) 0 0
\(603\) 3.23913 + 3.23913i 0.131908 + 0.131908i
\(604\) 0 0
\(605\) −23.1600 1.79554i −0.941588 0.0729991i
\(606\) 0 0
\(607\) −8.62113 + 2.31003i −0.349921 + 0.0937611i −0.429498 0.903068i \(-0.641310\pi\)
0.0795773 + 0.996829i \(0.474643\pi\)
\(608\) 0 0
\(609\) −0.0413459 0.0466745i −0.00167542 0.00189135i
\(610\) 0 0
\(611\) −5.48567 + 9.50146i −0.221926 + 0.384388i
\(612\) 0 0
\(613\) 5.02936 18.7698i 0.203134 0.758107i −0.786876 0.617111i \(-0.788303\pi\)
0.990010 0.140996i \(-0.0450304\pi\)
\(614\) 0 0
\(615\) 0.749882 0.139888i 0.0302382 0.00564082i
\(616\) 0 0
\(617\) −12.8763 + 12.8763i −0.518381 + 0.518381i −0.917081 0.398700i \(-0.869461\pi\)
0.398700 + 0.917081i \(0.369461\pi\)
\(618\) 0 0
\(619\) 5.08338 + 8.80468i 0.204318 + 0.353890i 0.949915 0.312507i \(-0.101169\pi\)
−0.745597 + 0.666397i \(0.767836\pi\)
\(620\) 0 0
\(621\) 3.49826 + 2.01972i 0.140380 + 0.0810485i
\(622\) 0 0
\(623\) −15.2177 30.4746i −0.609685 1.22094i
\(624\) 0 0
\(625\) −5.31188 24.4292i −0.212475 0.977166i
\(626\) 0 0
\(627\) 0.342016 + 0.0916428i 0.0136588 + 0.00365986i
\(628\) 0 0
\(629\) 40.0729 1.59781
\(630\) 0 0
\(631\) −30.9143 −1.23068 −0.615339 0.788262i \(-0.710981\pi\)
−0.615339 + 0.788262i \(0.710981\pi\)
\(632\) 0 0
\(633\) −0.677146 0.181441i −0.0269141 0.00721162i
\(634\) 0 0
\(635\) −28.2506 9.96696i −1.12109 0.395527i
\(636\) 0 0
\(637\) 30.1650 + 12.1438i 1.19518 + 0.481156i
\(638\) 0 0
\(639\) 15.1356 + 8.73853i 0.598754 + 0.345691i
\(640\) 0 0
\(641\) 9.22748 + 15.9825i 0.364463 + 0.631269i 0.988690 0.149974i \(-0.0479191\pi\)
−0.624226 + 0.781243i \(0.714586\pi\)
\(642\) 0 0
\(643\) 15.3634 15.3634i 0.605874 0.605874i −0.335991 0.941865i \(-0.609071\pi\)
0.941865 + 0.335991i \(0.109071\pi\)
\(644\) 0 0
\(645\) −1.01707 + 1.48355i −0.0400469 + 0.0584145i
\(646\) 0 0
\(647\) 10.5915 39.5282i 0.416396 1.55401i −0.365626 0.930762i \(-0.619145\pi\)
0.782022 0.623250i \(-0.214188\pi\)
\(648\) 0 0
\(649\) 2.00359 3.47032i 0.0786478 0.136222i
\(650\) 0 0
\(651\) 0.378515 1.13360i 0.0148352 0.0444294i
\(652\) 0 0
\(653\) 7.32658 1.96315i 0.286711 0.0768240i −0.112597 0.993641i \(-0.535917\pi\)
0.399308 + 0.916817i \(0.369250\pi\)
\(654\) 0 0
\(655\) −1.14075 + 14.7141i −0.0445726 + 0.574926i
\(656\) 0 0
\(657\) −28.3924 28.3924i −1.10769 1.10769i
\(658\) 0 0
\(659\) 4.25711i 0.165834i −0.996556 0.0829168i \(-0.973576\pi\)
0.996556 0.0829168i \(-0.0264236\pi\)
\(660\) 0 0
\(661\) −36.1264 + 20.8576i −1.40515 + 0.811266i −0.994916 0.100713i \(-0.967888\pi\)
−0.410238 + 0.911979i \(0.634554\pi\)
\(662\) 0 0
\(663\) −0.506857 1.89162i −0.0196847 0.0734643i
\(664\) 0 0
\(665\) −21.2098 + 27.2476i −0.822481 + 1.05662i
\(666\) 0 0
\(667\) 0.682950 + 2.54880i 0.0264439 + 0.0986900i
\(668\) 0 0
\(669\) −0.198225 + 0.114445i −0.00766384 + 0.00442472i
\(670\) 0 0
\(671\) 8.05393i 0.310919i
\(672\) 0 0
\(673\) 28.2067 + 28.2067i 1.08729 + 1.08729i 0.995807 + 0.0914807i \(0.0291600\pi\)
0.0914807 + 0.995807i \(0.470840\pi\)
\(674\) 0 0
\(675\) −2.31183 + 0.248439i −0.0889823 + 0.00956244i
\(676\) 0 0
\(677\) 19.7132 5.28215i 0.757641 0.203009i 0.140736 0.990047i \(-0.455053\pi\)
0.616905 + 0.787038i \(0.288386\pi\)
\(678\) 0 0
\(679\) −0.330147 + 0.0673830i −0.0126699 + 0.00258592i
\(680\) 0 0
\(681\) −0.0182437 + 0.0315990i −0.000699100 + 0.00121088i
\(682\) 0 0
\(683\) −11.6682 + 43.5462i −0.446470 + 1.66625i 0.265555 + 0.964096i \(0.414445\pi\)
−0.712025 + 0.702154i \(0.752222\pi\)
\(684\) 0 0
\(685\) 0.169582 + 0.909060i 0.00647939 + 0.0347334i
\(686\) 0 0
\(687\) 1.38248 1.38248i 0.0527450 0.0527450i
\(688\) 0 0
\(689\) −14.4720 25.0662i −0.551338 0.954945i
\(690\) 0 0
\(691\) −6.73905 3.89079i −0.256366 0.148013i 0.366310 0.930493i \(-0.380621\pi\)
−0.622676 + 0.782480i \(0.713954\pi\)
\(692\) 0 0
\(693\) 5.16732 + 3.41555i 0.196290 + 0.129746i
\(694\) 0 0
\(695\) 15.5920 + 32.5913i 0.591437 + 1.23626i
\(696\) 0 0
\(697\) −23.0792 6.18405i −0.874186 0.234237i
\(698\) 0 0
\(699\) 1.20538 0.0455918
\(700\) 0 0
\(701\) −11.0999 −0.419237 −0.209618 0.977783i \(-0.567222\pi\)
−0.209618 + 0.977783i \(0.567222\pi\)
\(702\) 0 0
\(703\) 41.5764 + 11.1404i 1.56808 + 0.420167i
\(704\) 0 0
\(705\) 0.176820 + 0.369601i 0.00665944 + 0.0139200i
\(706\) 0 0
\(707\) 0.969101 16.0080i 0.0364468 0.602044i
\(708\) 0 0
\(709\) −34.2204 19.7572i −1.28517 0.741996i −0.307385 0.951585i \(-0.599454\pi\)
−0.977790 + 0.209589i \(0.932787\pi\)
\(710\) 0 0
\(711\) −14.9830 25.9513i −0.561905 0.973249i
\(712\) 0 0
\(713\) −35.7626 + 35.7626i −1.33932 + 1.33932i
\(714\) 0 0
\(715\) −1.48952 7.98474i −0.0557050 0.298612i
\(716\) 0 0
\(717\) 0.566795 2.11531i 0.0211674 0.0789976i
\(718\) 0 0
\(719\) 19.8400 34.3639i 0.739908 1.28156i −0.212628 0.977133i \(-0.568202\pi\)
0.952536 0.304425i \(-0.0984643\pi\)
\(720\) 0 0
\(721\) 6.45936 + 2.15681i 0.240559 + 0.0803237i
\(722\) 0 0
\(723\) 1.02292 0.274089i 0.0380426 0.0101935i
\(724\) 0 0
\(725\) −1.18261 0.953098i −0.0439211 0.0353972i
\(726\) 0 0
\(727\) 23.2801 + 23.2801i 0.863410 + 0.863410i 0.991733 0.128322i \(-0.0409591\pi\)
−0.128322 + 0.991733i \(0.540959\pi\)
\(728\) 0 0
\(729\) 26.6755i 0.987982i
\(730\) 0 0
\(731\) 48.7916 28.1698i 1.80462 1.04190i
\(732\) 0 0
\(733\) 4.27364 + 15.9494i 0.157850 + 0.589106i 0.998844 + 0.0480612i \(0.0153043\pi\)
−0.840994 + 0.541044i \(0.818029\pi\)
\(734\) 0 0
\(735\) 1.01102 0.672688i 0.0372919 0.0248125i
\(736\) 0 0
\(737\) 0.309651 + 1.15563i 0.0114062 + 0.0425683i
\(738\) 0 0
\(739\) 37.3385 21.5574i 1.37352 0.793001i 0.382149 0.924101i \(-0.375184\pi\)
0.991369 + 0.131099i \(0.0418507\pi\)
\(740\) 0 0
\(741\) 2.10350i 0.0772739i
\(742\) 0 0
\(743\) −8.79757 8.79757i −0.322751 0.322751i 0.527070 0.849822i \(-0.323290\pi\)
−0.849822 + 0.527070i \(0.823290\pi\)
\(744\) 0 0
\(745\) 0.971971 12.5371i 0.0356103 0.459324i
\(746\) 0 0
\(747\) −12.0435 + 3.22705i −0.440649 + 0.118072i
\(748\) 0 0
\(749\) −21.3768 7.13779i −0.781091 0.260809i
\(750\) 0 0
\(751\) −1.89233 + 3.27761i −0.0690521 + 0.119602i −0.898484 0.439006i \(-0.855331\pi\)
0.829432 + 0.558607i \(0.188664\pi\)
\(752\) 0 0
\(753\) −0.163544 + 0.610355i −0.00595988 + 0.0222426i
\(754\) 0 0
\(755\) 9.09639 13.2685i 0.331051 0.482889i
\(756\) 0 0
\(757\) 14.6751 14.6751i 0.533375 0.533375i −0.388200 0.921575i \(-0.626903\pi\)
0.921575 + 0.388200i \(0.126903\pi\)
\(758\) 0 0
\(759\) 0.263486 + 0.456371i 0.00956394 + 0.0165652i
\(760\) 0 0
\(761\) −30.3893 17.5453i −1.10161 0.636016i −0.164968 0.986299i \(-0.552752\pi\)
−0.936644 + 0.350283i \(0.886085\pi\)
\(762\) 0 0
\(763\) −1.33670 + 22.0803i −0.0483919 + 0.799359i
\(764\) 0 0
\(765\) 34.3055 + 12.1032i 1.24032 + 0.437591i
\(766\) 0 0
\(767\) −22.9944 6.16134i −0.830280 0.222473i
\(768\) 0 0
\(769\) 17.2197 0.620959 0.310479 0.950580i \(-0.399510\pi\)
0.310479 + 0.950580i \(0.399510\pi\)
\(770\) 0 0
\(771\) 0.803245 0.0289282
\(772\) 0 0
\(773\) 19.0628 + 5.10786i 0.685641 + 0.183717i 0.584790 0.811185i \(-0.301177\pi\)
0.100851 + 0.994902i \(0.467844\pi\)
\(774\) 0 0
\(775\) 4.48700 28.7641i 0.161178 1.03324i
\(776\) 0 0
\(777\) −1.26283 0.834719i −0.0453037 0.0299454i
\(778\) 0 0
\(779\) −22.2259 12.8321i −0.796327 0.459759i
\(780\) 0 0
\(781\) 2.28229 + 3.95305i 0.0816669 + 0.141451i
\(782\) 0 0
\(783\) −0.0998883 + 0.0998883i −0.00356972 + 0.00356972i
\(784\) 0 0
\(785\) 4.65027 0.867490i 0.165975 0.0309621i
\(786\) 0 0
\(787\) −8.85989 + 33.0656i −0.315821 + 1.17866i 0.607402 + 0.794395i \(0.292212\pi\)
−0.923223 + 0.384265i \(0.874455\pi\)
\(788\) 0 0
\(789\) −1.14312 + 1.97993i −0.0406960 + 0.0704875i
\(790\) 0 0
\(791\) 2.29010 0.467410i 0.0814267 0.0166192i
\(792\) 0 0
\(793\) 46.2159 12.3835i 1.64117 0.439751i
\(794\) 0 0
\(795\) −1.07766 0.0835487i −0.0382208 0.00296317i
\(796\) 0 0