Properties

Label 1520.2.q.o.961.1
Level $1520$
Weight $2$
Character 1520.961
Analytic conductor $12.137$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1520.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.1372611072\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.4601315889.1
Defining polynomial: \( x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.1
Root \(1.07988 - 1.87040i\) of defining polynomial
Character \(\chi\) \(=\) 1520.961
Dual form 1520.2.q.o.881.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.579878 + 1.00438i) q^{3} +(-0.500000 + 0.866025i) q^{5} +2.43525 q^{7} +(0.827483 + 1.43324i) q^{9} +O(q^{10})\) \(q+(-0.579878 + 1.00438i) q^{3} +(-0.500000 + 0.866025i) q^{5} +2.43525 q^{7} +(0.827483 + 1.43324i) q^{9} +5.75477 q^{11} +(0.797505 + 1.38132i) q^{13} +(-0.579878 - 1.00438i) q^{15} +(2.99203 - 5.18234i) q^{17} +(-0.149412 - 4.35634i) q^{19} +(-1.41215 + 2.44592i) q^{21} +(-0.470022 - 0.814102i) q^{23} +(-0.500000 - 0.866025i) q^{25} -5.39862 q^{27} +(-1.30917 - 2.26755i) q^{29} +5.26913 q^{31} +(-3.33706 + 5.77996i) q^{33} +(-1.21763 + 2.10899i) q^{35} -2.89384 q^{37} -1.84982 q^{39} +(3.15767 - 5.46925i) q^{41} +(2.26961 - 3.93108i) q^{43} -1.65497 q^{45} +(4.47718 + 7.75471i) q^{47} -1.06953 q^{49} +(3.47002 + 6.01025i) q^{51} +(1.09819 + 1.90213i) q^{53} +(-2.87738 + 4.98377i) q^{55} +(4.46205 + 2.37608i) q^{57} +(-5.39939 + 9.35202i) q^{59} +(5.26434 + 9.11811i) q^{61} +(2.01513 + 3.49031i) q^{63} -1.59501 q^{65} +(0.504789 + 0.874320i) q^{67} +1.09022 q^{69} +(4.41694 - 7.65036i) q^{71} +(5.12499 - 8.87674i) q^{73} +1.15976 q^{75} +14.0143 q^{77} +(3.80229 - 6.58577i) q^{79} +(0.648093 - 1.12253i) q^{81} -3.11355 q^{83} +(2.99203 + 5.18234i) q^{85} +3.03663 q^{87} +(5.55706 + 9.62511i) q^{89} +(1.94213 + 3.36387i) q^{91} +(-3.05545 + 5.29220i) q^{93} +(3.84741 + 2.04877i) q^{95} +(-2.02888 + 3.51412i) q^{97} +(4.76197 + 8.24798i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 3 q^{3} - 4 q^{5} + 8 q^{7} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 3 q^{3} - 4 q^{5} + 8 q^{7} - q^{9} + 4 q^{11} - 7 q^{13} + 3 q^{15} + q^{17} - 5 q^{19} + 4 q^{21} + 2 q^{23} - 4 q^{25} - 24 q^{27} + q^{29} - 19 q^{33} - 4 q^{35} - 4 q^{37} - 30 q^{39} + 8 q^{41} + q^{43} + 2 q^{45} - 12 q^{47} - 20 q^{49} + 22 q^{51} + 5 q^{53} - 2 q^{55} + 7 q^{57} - 5 q^{59} - 3 q^{63} + 14 q^{65} + 4 q^{67} - 18 q^{69} + 20 q^{71} + 20 q^{73} - 6 q^{75} + 28 q^{77} + 17 q^{79} - 12 q^{81} - 2 q^{83} + q^{85} + 32 q^{87} - 11 q^{89} + 6 q^{91} + 8 q^{93} + 4 q^{95} - q^{97} + 38 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(401\) \(1141\) \(1217\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.579878 + 1.00438i −0.334793 + 0.579878i −0.983445 0.181207i \(-0.942000\pi\)
0.648652 + 0.761085i \(0.275333\pi\)
\(4\) 0 0
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 2.43525 0.920440 0.460220 0.887805i \(-0.347771\pi\)
0.460220 + 0.887805i \(0.347771\pi\)
\(8\) 0 0
\(9\) 0.827483 + 1.43324i 0.275828 + 0.477748i
\(10\) 0 0
\(11\) 5.75477 1.73513 0.867564 0.497326i \(-0.165685\pi\)
0.867564 + 0.497326i \(0.165685\pi\)
\(12\) 0 0
\(13\) 0.797505 + 1.38132i 0.221188 + 0.383109i 0.955169 0.296061i \(-0.0956732\pi\)
−0.733981 + 0.679170i \(0.762340\pi\)
\(14\) 0 0
\(15\) −0.579878 1.00438i −0.149724 0.259329i
\(16\) 0 0
\(17\) 2.99203 5.18234i 0.725673 1.25690i −0.233023 0.972471i \(-0.574862\pi\)
0.958696 0.284432i \(-0.0918050\pi\)
\(18\) 0 0
\(19\) −0.149412 4.35634i −0.0342775 0.999412i
\(20\) 0 0
\(21\) −1.41215 + 2.44592i −0.308156 + 0.533743i
\(22\) 0 0
\(23\) −0.470022 0.814102i −0.0980064 0.169752i 0.812853 0.582469i \(-0.197913\pi\)
−0.910859 + 0.412717i \(0.864580\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) −5.39862 −1.03897
\(28\) 0 0
\(29\) −1.30917 2.26755i −0.243106 0.421073i 0.718491 0.695536i \(-0.244833\pi\)
−0.961598 + 0.274463i \(0.911500\pi\)
\(30\) 0 0
\(31\) 5.26913 0.946364 0.473182 0.880965i \(-0.343105\pi\)
0.473182 + 0.880965i \(0.343105\pi\)
\(32\) 0 0
\(33\) −3.33706 + 5.77996i −0.580908 + 1.00616i
\(34\) 0 0
\(35\) −1.21763 + 2.10899i −0.205817 + 0.356485i
\(36\) 0 0
\(37\) −2.89384 −0.475744 −0.237872 0.971297i \(-0.576450\pi\)
−0.237872 + 0.971297i \(0.576450\pi\)
\(38\) 0 0
\(39\) −1.84982 −0.296209
\(40\) 0 0
\(41\) 3.15767 5.46925i 0.493145 0.854153i −0.506823 0.862050i \(-0.669180\pi\)
0.999969 + 0.00789701i \(0.00251372\pi\)
\(42\) 0 0
\(43\) 2.26961 3.93108i 0.346113 0.599485i −0.639443 0.768839i \(-0.720835\pi\)
0.985555 + 0.169354i \(0.0541682\pi\)
\(44\) 0 0
\(45\) −1.65497 −0.246708
\(46\) 0 0
\(47\) 4.47718 + 7.75471i 0.653064 + 1.13114i 0.982375 + 0.186919i \(0.0598502\pi\)
−0.329311 + 0.944221i \(0.606816\pi\)
\(48\) 0 0
\(49\) −1.06953 −0.152791
\(50\) 0 0
\(51\) 3.47002 + 6.01025i 0.485900 + 0.841604i
\(52\) 0 0
\(53\) 1.09819 + 1.90213i 0.150848 + 0.261277i 0.931540 0.363640i \(-0.118466\pi\)
−0.780691 + 0.624917i \(0.785133\pi\)
\(54\) 0 0
\(55\) −2.87738 + 4.98377i −0.387986 + 0.672012i
\(56\) 0 0
\(57\) 4.46205 + 2.37608i 0.591013 + 0.314719i
\(58\) 0 0
\(59\) −5.39939 + 9.35202i −0.702941 + 1.21753i 0.264489 + 0.964389i \(0.414797\pi\)
−0.967430 + 0.253140i \(0.918537\pi\)
\(60\) 0 0
\(61\) 5.26434 + 9.11811i 0.674030 + 1.16745i 0.976751 + 0.214375i \(0.0687716\pi\)
−0.302721 + 0.953079i \(0.597895\pi\)
\(62\) 0 0
\(63\) 2.01513 + 3.49031i 0.253883 + 0.439738i
\(64\) 0 0
\(65\) −1.59501 −0.197837
\(66\) 0 0
\(67\) 0.504789 + 0.874320i 0.0616698 + 0.106815i 0.895212 0.445641i \(-0.147024\pi\)
−0.833542 + 0.552456i \(0.813691\pi\)
\(68\) 0 0
\(69\) 1.09022 0.131247
\(70\) 0 0
\(71\) 4.41694 7.65036i 0.524194 0.907931i −0.475409 0.879765i \(-0.657700\pi\)
0.999603 0.0281662i \(-0.00896677\pi\)
\(72\) 0 0
\(73\) 5.12499 8.87674i 0.599835 1.03894i −0.393011 0.919534i \(-0.628566\pi\)
0.992845 0.119410i \(-0.0381003\pi\)
\(74\) 0 0
\(75\) 1.15976 0.133917
\(76\) 0 0
\(77\) 14.0143 1.59708
\(78\) 0 0
\(79\) 3.80229 6.58577i 0.427792 0.740957i −0.568885 0.822417i \(-0.692625\pi\)
0.996677 + 0.0814604i \(0.0259584\pi\)
\(80\) 0 0
\(81\) 0.648093 1.12253i 0.0720103 0.124726i
\(82\) 0 0
\(83\) −3.11355 −0.341756 −0.170878 0.985292i \(-0.554660\pi\)
−0.170878 + 0.985292i \(0.554660\pi\)
\(84\) 0 0
\(85\) 2.99203 + 5.18234i 0.324531 + 0.562104i
\(86\) 0 0
\(87\) 3.03663 0.325561
\(88\) 0 0
\(89\) 5.55706 + 9.62511i 0.589047 + 1.02026i 0.994358 + 0.106081i \(0.0338302\pi\)
−0.405310 + 0.914179i \(0.632837\pi\)
\(90\) 0 0
\(91\) 1.94213 + 3.36387i 0.203590 + 0.352629i
\(92\) 0 0
\(93\) −3.05545 + 5.29220i −0.316836 + 0.548776i
\(94\) 0 0
\(95\) 3.84741 + 2.04877i 0.394735 + 0.210200i
\(96\) 0 0
\(97\) −2.02888 + 3.51412i −0.206002 + 0.356805i −0.950451 0.310873i \(-0.899379\pi\)
0.744450 + 0.667678i \(0.232712\pi\)
\(98\) 0 0
\(99\) 4.76197 + 8.24798i 0.478596 + 0.828953i
\(100\) 0 0
\(101\) 5.56503 + 9.63892i 0.553741 + 0.959108i 0.998000 + 0.0632098i \(0.0201337\pi\)
−0.444259 + 0.895898i \(0.646533\pi\)
\(102\) 0 0
\(103\) −11.5791 −1.14092 −0.570460 0.821326i \(-0.693235\pi\)
−0.570460 + 0.821326i \(0.693235\pi\)
\(104\) 0 0
\(105\) −1.41215 2.44592i −0.137812 0.238697i
\(106\) 0 0
\(107\) −17.9177 −1.73217 −0.866086 0.499894i \(-0.833372\pi\)
−0.866086 + 0.499894i \(0.833372\pi\)
\(108\) 0 0
\(109\) −2.81235 + 4.87113i −0.269374 + 0.466570i −0.968700 0.248233i \(-0.920150\pi\)
0.699326 + 0.714803i \(0.253484\pi\)
\(110\) 0 0
\(111\) 1.67807 2.90650i 0.159275 0.275873i
\(112\) 0 0
\(113\) −15.6789 −1.47494 −0.737472 0.675378i \(-0.763981\pi\)
−0.737472 + 0.675378i \(0.763981\pi\)
\(114\) 0 0
\(115\) 0.940044 0.0876595
\(116\) 0 0
\(117\) −1.31984 + 2.28604i −0.122020 + 0.211344i
\(118\) 0 0
\(119\) 7.28635 12.6203i 0.667939 1.15690i
\(120\) 0 0
\(121\) 22.1173 2.01067
\(122\) 0 0
\(123\) 3.66213 + 6.34299i 0.330203 + 0.571928i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 3.05996 + 5.30000i 0.271527 + 0.470299i 0.969253 0.246066i \(-0.0791380\pi\)
−0.697726 + 0.716365i \(0.745805\pi\)
\(128\) 0 0
\(129\) 2.63220 + 4.55910i 0.231752 + 0.401406i
\(130\) 0 0
\(131\) −7.44055 + 12.8874i −0.650084 + 1.12598i 0.333018 + 0.942920i \(0.391933\pi\)
−0.983102 + 0.183058i \(0.941400\pi\)
\(132\) 0 0
\(133\) −0.363857 10.6088i −0.0315504 0.919899i
\(134\) 0 0
\(135\) 2.69931 4.67535i 0.232320 0.402390i
\(136\) 0 0
\(137\) −8.67518 15.0258i −0.741170 1.28374i −0.951963 0.306214i \(-0.900938\pi\)
0.210793 0.977531i \(-0.432396\pi\)
\(138\) 0 0
\(139\) −3.35267 5.80700i −0.284370 0.492543i 0.688086 0.725629i \(-0.258451\pi\)
−0.972456 + 0.233086i \(0.925118\pi\)
\(140\) 0 0
\(141\) −10.3849 −0.874564
\(142\) 0 0
\(143\) 4.58946 + 7.94917i 0.383790 + 0.664743i
\(144\) 0 0
\(145\) 2.61834 0.217441
\(146\) 0 0
\(147\) 0.620199 1.07422i 0.0511532 0.0885999i
\(148\) 0 0
\(149\) −7.19642 + 12.4646i −0.589553 + 1.02114i 0.404737 + 0.914433i \(0.367363\pi\)
−0.994291 + 0.106704i \(0.965970\pi\)
\(150\) 0 0
\(151\) −12.7219 −1.03529 −0.517645 0.855595i \(-0.673191\pi\)
−0.517645 + 0.855595i \(0.673191\pi\)
\(152\) 0 0
\(153\) 9.90341 0.800644
\(154\) 0 0
\(155\) −2.63457 + 4.56320i −0.211614 + 0.366525i
\(156\) 0 0
\(157\) 1.68765 2.92309i 0.134689 0.233288i −0.790790 0.612088i \(-0.790330\pi\)
0.925479 + 0.378800i \(0.123663\pi\)
\(158\) 0 0
\(159\) −2.54727 −0.202012
\(160\) 0 0
\(161\) −1.14462 1.98255i −0.0902089 0.156246i
\(162\) 0 0
\(163\) −0.307960 −0.0241213 −0.0120607 0.999927i \(-0.503839\pi\)
−0.0120607 + 0.999927i \(0.503839\pi\)
\(164\) 0 0
\(165\) −3.33706 5.77996i −0.259790 0.449969i
\(166\) 0 0
\(167\) 7.13215 + 12.3532i 0.551902 + 0.955923i 0.998137 + 0.0610070i \(0.0194312\pi\)
−0.446235 + 0.894916i \(0.647235\pi\)
\(168\) 0 0
\(169\) 5.22797 9.05511i 0.402152 0.696547i
\(170\) 0 0
\(171\) 6.12005 3.81894i 0.468012 0.292042i
\(172\) 0 0
\(173\) −6.67357 + 11.5590i −0.507382 + 0.878811i 0.492581 + 0.870266i \(0.336053\pi\)
−0.999963 + 0.00854514i \(0.997280\pi\)
\(174\) 0 0
\(175\) −1.21763 2.10899i −0.0920440 0.159425i
\(176\) 0 0
\(177\) −6.26197 10.8461i −0.470679 0.815239i
\(178\) 0 0
\(179\) 14.2207 1.06291 0.531454 0.847087i \(-0.321646\pi\)
0.531454 + 0.847087i \(0.321646\pi\)
\(180\) 0 0
\(181\) −4.94132 8.55861i −0.367285 0.636157i 0.621855 0.783133i \(-0.286379\pi\)
−0.989140 + 0.146976i \(0.953046\pi\)
\(182\) 0 0
\(183\) −12.2107 −0.902641
\(184\) 0 0
\(185\) 1.44692 2.50613i 0.106379 0.184255i
\(186\) 0 0
\(187\) 17.2184 29.8232i 1.25914 2.18089i
\(188\) 0 0
\(189\) −13.1470 −0.956305
\(190\) 0 0
\(191\) 12.9942 0.940228 0.470114 0.882606i \(-0.344213\pi\)
0.470114 + 0.882606i \(0.344213\pi\)
\(192\) 0 0
\(193\) −7.25795 + 12.5711i −0.522439 + 0.904890i 0.477221 + 0.878784i \(0.341644\pi\)
−0.999659 + 0.0261066i \(0.991689\pi\)
\(194\) 0 0
\(195\) 0.924911 1.60199i 0.0662343 0.114721i
\(196\) 0 0
\(197\) −25.0010 −1.78125 −0.890624 0.454740i \(-0.849732\pi\)
−0.890624 + 0.454740i \(0.849732\pi\)
\(198\) 0 0
\(199\) −1.12769 1.95322i −0.0799401 0.138460i 0.823284 0.567630i \(-0.192140\pi\)
−0.903224 + 0.429170i \(0.858806\pi\)
\(200\) 0 0
\(201\) −1.17086 −0.0825864
\(202\) 0 0
\(203\) −3.18816 5.52205i −0.223765 0.387572i
\(204\) 0 0
\(205\) 3.15767 + 5.46925i 0.220541 + 0.381989i
\(206\) 0 0
\(207\) 0.777871 1.34731i 0.0540657 0.0936446i
\(208\) 0 0
\(209\) −0.859833 25.0697i −0.0594759 1.73411i
\(210\) 0 0
\(211\) 11.1081 19.2397i 0.764710 1.32452i −0.175689 0.984446i \(-0.556215\pi\)
0.940400 0.340071i \(-0.110451\pi\)
\(212\) 0 0
\(213\) 5.12257 + 8.87255i 0.350993 + 0.607937i
\(214\) 0 0
\(215\) 2.26961 + 3.93108i 0.154786 + 0.268098i
\(216\) 0 0
\(217\) 12.8317 0.871071
\(218\) 0 0
\(219\) 5.94373 + 10.2949i 0.401640 + 0.695662i
\(220\) 0 0
\(221\) 9.54463 0.642041
\(222\) 0 0
\(223\) 5.10799 8.84730i 0.342056 0.592459i −0.642758 0.766069i \(-0.722210\pi\)
0.984814 + 0.173610i \(0.0555432\pi\)
\(224\) 0 0
\(225\) 0.827483 1.43324i 0.0551656 0.0955495i
\(226\) 0 0
\(227\) −4.15180 −0.275565 −0.137782 0.990463i \(-0.543997\pi\)
−0.137782 + 0.990463i \(0.543997\pi\)
\(228\) 0 0
\(229\) 6.53286 0.431703 0.215852 0.976426i \(-0.430747\pi\)
0.215852 + 0.976426i \(0.430747\pi\)
\(230\) 0 0
\(231\) −8.12660 + 14.0757i −0.534691 + 0.926111i
\(232\) 0 0
\(233\) −2.57410 + 4.45848i −0.168635 + 0.292084i −0.937940 0.346797i \(-0.887269\pi\)
0.769305 + 0.638882i \(0.220603\pi\)
\(234\) 0 0
\(235\) −8.95437 −0.584118
\(236\) 0 0
\(237\) 4.40973 + 7.63788i 0.286443 + 0.496134i
\(238\) 0 0
\(239\) −13.9962 −0.905338 −0.452669 0.891679i \(-0.649528\pi\)
−0.452669 + 0.891679i \(0.649528\pi\)
\(240\) 0 0
\(241\) −7.61285 13.1858i −0.490387 0.849375i 0.509552 0.860440i \(-0.329811\pi\)
−0.999939 + 0.0110652i \(0.996478\pi\)
\(242\) 0 0
\(243\) −7.34631 12.7242i −0.471266 0.816256i
\(244\) 0 0
\(245\) 0.534767 0.926244i 0.0341650 0.0591756i
\(246\) 0 0
\(247\) 5.89834 3.68059i 0.375302 0.234190i
\(248\) 0 0
\(249\) 1.80548 3.12718i 0.114417 0.198177i
\(250\) 0 0
\(251\) −3.05630 5.29366i −0.192912 0.334133i 0.753302 0.657674i \(-0.228460\pi\)
−0.946214 + 0.323542i \(0.895126\pi\)
\(252\) 0 0
\(253\) −2.70487 4.68497i −0.170053 0.294541i
\(254\) 0 0
\(255\) −6.94004 −0.434602
\(256\) 0 0
\(257\) −0.0613414 0.106246i −0.00382637 0.00662747i 0.864106 0.503310i \(-0.167885\pi\)
−0.867932 + 0.496683i \(0.834551\pi\)
\(258\) 0 0
\(259\) −7.04723 −0.437893
\(260\) 0 0
\(261\) 2.16663 3.75271i 0.134111 0.232287i
\(262\) 0 0
\(263\) −5.03027 + 8.71267i −0.310179 + 0.537247i −0.978401 0.206716i \(-0.933722\pi\)
0.668222 + 0.743962i \(0.267056\pi\)
\(264\) 0 0
\(265\) −2.19639 −0.134923
\(266\) 0 0
\(267\) −12.8897 −0.788835
\(268\) 0 0
\(269\) −2.85614 + 4.94698i −0.174142 + 0.301623i −0.939864 0.341549i \(-0.889049\pi\)
0.765722 + 0.643172i \(0.222382\pi\)
\(270\) 0 0
\(271\) −6.35560 + 11.0082i −0.386075 + 0.668702i −0.991918 0.126883i \(-0.959503\pi\)
0.605843 + 0.795585i \(0.292836\pi\)
\(272\) 0 0
\(273\) −4.50479 −0.272642
\(274\) 0 0
\(275\) −2.87738 4.98377i −0.173513 0.300533i
\(276\) 0 0
\(277\) 17.6019 1.05760 0.528799 0.848747i \(-0.322642\pi\)
0.528799 + 0.848747i \(0.322642\pi\)
\(278\) 0 0
\(279\) 4.36012 + 7.55195i 0.261034 + 0.452123i
\(280\) 0 0
\(281\) 10.2502 + 17.7539i 0.611476 + 1.05911i 0.990992 + 0.133922i \(0.0427571\pi\)
−0.379516 + 0.925185i \(0.623910\pi\)
\(282\) 0 0
\(283\) −5.92805 + 10.2677i −0.352386 + 0.610350i −0.986667 0.162752i \(-0.947963\pi\)
0.634281 + 0.773103i \(0.281296\pi\)
\(284\) 0 0
\(285\) −4.28877 + 2.67621i −0.254045 + 0.158525i
\(286\) 0 0
\(287\) 7.68973 13.3190i 0.453911 0.786196i
\(288\) 0 0
\(289\) −9.40447 16.2890i −0.553204 0.958177i
\(290\) 0 0
\(291\) −2.35301 4.07552i −0.137936 0.238911i
\(292\) 0 0
\(293\) −24.9814 −1.45943 −0.729715 0.683751i \(-0.760347\pi\)
−0.729715 + 0.683751i \(0.760347\pi\)
\(294\) 0 0
\(295\) −5.39939 9.35202i −0.314365 0.544495i
\(296\) 0 0
\(297\) −31.0678 −1.80274
\(298\) 0 0
\(299\) 0.749690 1.29850i 0.0433557 0.0750943i
\(300\) 0 0
\(301\) 5.52708 9.57319i 0.318576 0.551789i
\(302\) 0 0
\(303\) −12.9082 −0.741554
\(304\) 0 0
\(305\) −10.5287 −0.602871
\(306\) 0 0
\(307\) 8.45997 14.6531i 0.482836 0.836296i −0.516970 0.856003i \(-0.672940\pi\)
0.999806 + 0.0197074i \(0.00627348\pi\)
\(308\) 0 0
\(309\) 6.71444 11.6298i 0.381971 0.661594i
\(310\) 0 0
\(311\) 15.2133 0.862670 0.431335 0.902192i \(-0.358043\pi\)
0.431335 + 0.902192i \(0.358043\pi\)
\(312\) 0 0
\(313\) −12.4637 21.5877i −0.704488 1.22021i −0.966876 0.255246i \(-0.917844\pi\)
0.262389 0.964962i \(-0.415490\pi\)
\(314\) 0 0
\(315\) −4.03027 −0.227080
\(316\) 0 0
\(317\) 12.6152 + 21.8502i 0.708541 + 1.22723i 0.965398 + 0.260780i \(0.0839798\pi\)
−0.256857 + 0.966449i \(0.582687\pi\)
\(318\) 0 0
\(319\) −7.53396 13.0492i −0.421821 0.730615i
\(320\) 0 0
\(321\) 10.3901 17.9962i 0.579919 1.00445i
\(322\) 0 0
\(323\) −23.0231 12.2600i −1.28104 0.682163i
\(324\) 0 0
\(325\) 0.797505 1.38132i 0.0442376 0.0766218i
\(326\) 0 0
\(327\) −3.26164 5.64933i −0.180369 0.312408i
\(328\) 0 0
\(329\) 10.9031 + 18.8847i 0.601106 + 1.04115i
\(330\) 0 0
\(331\) 20.2063 1.11064 0.555320 0.831637i \(-0.312596\pi\)
0.555320 + 0.831637i \(0.312596\pi\)
\(332\) 0 0
\(333\) −2.39460 4.14757i −0.131223 0.227285i
\(334\) 0 0
\(335\) −1.00958 −0.0551592
\(336\) 0 0
\(337\) 15.9123 27.5610i 0.866800 1.50134i 0.00155051 0.999999i \(-0.499506\pi\)
0.865249 0.501342i \(-0.167160\pi\)
\(338\) 0 0
\(339\) 9.09183 15.7475i 0.493800 0.855287i
\(340\) 0 0
\(341\) 30.3226 1.64206
\(342\) 0 0
\(343\) −19.6514 −1.06107
\(344\) 0 0
\(345\) −0.545111 + 0.944159i −0.0293478 + 0.0508318i
\(346\) 0 0
\(347\) −1.65128 + 2.86009i −0.0886451 + 0.153538i −0.906939 0.421263i \(-0.861587\pi\)
0.818294 + 0.574801i \(0.194920\pi\)
\(348\) 0 0
\(349\) 17.8486 0.955416 0.477708 0.878519i \(-0.341468\pi\)
0.477708 + 0.878519i \(0.341468\pi\)
\(350\) 0 0
\(351\) −4.30543 7.45723i −0.229807 0.398037i
\(352\) 0 0
\(353\) −8.29523 −0.441511 −0.220755 0.975329i \(-0.570852\pi\)
−0.220755 + 0.975329i \(0.570852\pi\)
\(354\) 0 0
\(355\) 4.41694 + 7.65036i 0.234427 + 0.406039i
\(356\) 0 0
\(357\) 8.45039 + 14.6365i 0.447242 + 0.774646i
\(358\) 0 0
\(359\) 4.17511 7.23150i 0.220354 0.381664i −0.734562 0.678542i \(-0.762612\pi\)
0.954915 + 0.296878i \(0.0959455\pi\)
\(360\) 0 0
\(361\) −18.9554 + 1.30178i −0.997650 + 0.0685148i
\(362\) 0 0
\(363\) −12.8254 + 22.2142i −0.673156 + 1.16594i
\(364\) 0 0
\(365\) 5.12499 + 8.87674i 0.268254 + 0.464630i
\(366\) 0 0
\(367\) 7.20988 + 12.4879i 0.376353 + 0.651862i 0.990528 0.137307i \(-0.0438448\pi\)
−0.614176 + 0.789169i \(0.710511\pi\)
\(368\) 0 0
\(369\) 10.4517 0.544093
\(370\) 0 0
\(371\) 2.67438 + 4.63216i 0.138847 + 0.240490i
\(372\) 0 0
\(373\) −24.1157 −1.24866 −0.624332 0.781159i \(-0.714629\pi\)
−0.624332 + 0.781159i \(0.714629\pi\)
\(374\) 0 0
\(375\) −0.579878 + 1.00438i −0.0299448 + 0.0518659i
\(376\) 0 0
\(377\) 2.08814 3.61676i 0.107545 0.186273i
\(378\) 0 0
\(379\) −16.6757 −0.856571 −0.428285 0.903644i \(-0.640882\pi\)
−0.428285 + 0.903644i \(0.640882\pi\)
\(380\) 0 0
\(381\) −7.09760 −0.363621
\(382\) 0 0
\(383\) −5.43895 + 9.42053i −0.277917 + 0.481367i −0.970867 0.239619i \(-0.922977\pi\)
0.692950 + 0.720986i \(0.256311\pi\)
\(384\) 0 0
\(385\) −7.00716 + 12.1368i −0.357118 + 0.618546i
\(386\) 0 0
\(387\) 7.51226 0.381870
\(388\) 0 0
\(389\) −18.2272 31.5704i −0.924154 1.60068i −0.792917 0.609330i \(-0.791438\pi\)
−0.131237 0.991351i \(-0.541895\pi\)
\(390\) 0 0
\(391\) −5.62528 −0.284482
\(392\) 0 0
\(393\) −8.62922 14.9463i −0.435287 0.753939i
\(394\) 0 0
\(395\) 3.80229 + 6.58577i 0.191314 + 0.331366i
\(396\) 0 0
\(397\) −4.29191 + 7.43380i −0.215405 + 0.373092i −0.953398 0.301717i \(-0.902440\pi\)
0.737993 + 0.674808i \(0.235774\pi\)
\(398\) 0 0
\(399\) 10.8662 + 5.78635i 0.543992 + 0.289680i
\(400\) 0 0
\(401\) 8.52785 14.7707i 0.425860 0.737612i −0.570640 0.821200i \(-0.693305\pi\)
0.996500 + 0.0835885i \(0.0266381\pi\)
\(402\) 0 0
\(403\) 4.20216 + 7.27836i 0.209325 + 0.362561i
\(404\) 0 0
\(405\) 0.648093 + 1.12253i 0.0322040 + 0.0557790i
\(406\) 0 0
\(407\) −16.6533 −0.825476
\(408\) 0 0
\(409\) 5.89702 + 10.2139i 0.291589 + 0.505047i 0.974186 0.225749i \(-0.0724828\pi\)
−0.682597 + 0.730795i \(0.739149\pi\)
\(410\) 0 0
\(411\) 20.1222 0.992553
\(412\) 0 0
\(413\) −13.1489 + 22.7745i −0.647015 + 1.12066i
\(414\) 0 0
\(415\) 1.55677 2.69641i 0.0764190 0.132362i
\(416\) 0 0
\(417\) 7.77656 0.380820
\(418\) 0 0
\(419\) −1.14280 −0.0558292 −0.0279146 0.999610i \(-0.508887\pi\)
−0.0279146 + 0.999610i \(0.508887\pi\)
\(420\) 0 0
\(421\) −9.75944 + 16.9039i −0.475646 + 0.823843i −0.999611 0.0278967i \(-0.991119\pi\)
0.523965 + 0.851740i \(0.324452\pi\)
\(422\) 0 0
\(423\) −7.40959 + 12.8338i −0.360266 + 0.624000i
\(424\) 0 0
\(425\) −5.98406 −0.290269
\(426\) 0 0
\(427\) 12.8200 + 22.2049i 0.620404 + 1.07457i
\(428\) 0 0
\(429\) −10.6453 −0.513960
\(430\) 0 0
\(431\) −18.4392 31.9377i −0.888187 1.53838i −0.842017 0.539451i \(-0.818632\pi\)
−0.0461694 0.998934i \(-0.514701\pi\)
\(432\) 0 0
\(433\) −0.184467 0.319506i −0.00886490 0.0153545i 0.861559 0.507658i \(-0.169488\pi\)
−0.870424 + 0.492303i \(0.836155\pi\)
\(434\) 0 0
\(435\) −1.51832 + 2.62980i −0.0727976 + 0.126089i
\(436\) 0 0
\(437\) −3.47628 + 2.16921i −0.166293 + 0.103767i
\(438\) 0 0
\(439\) −1.13220 + 1.96102i −0.0540367 + 0.0935944i −0.891778 0.452472i \(-0.850542\pi\)
0.837742 + 0.546067i \(0.183875\pi\)
\(440\) 0 0
\(441\) −0.885022 1.53290i −0.0421439 0.0729954i
\(442\) 0 0
\(443\) −8.23137 14.2572i −0.391084 0.677378i 0.601508 0.798866i \(-0.294567\pi\)
−0.992593 + 0.121488i \(0.961233\pi\)
\(444\) 0 0
\(445\) −11.1141 −0.526860
\(446\) 0 0
\(447\) −8.34609 14.4558i −0.394756 0.683738i
\(448\) 0 0
\(449\) 14.1613 0.668315 0.334158 0.942517i \(-0.391548\pi\)
0.334158 + 0.942517i \(0.391548\pi\)
\(450\) 0 0
\(451\) 18.1717 31.4742i 0.855670 1.48206i
\(452\) 0 0
\(453\) 7.37713 12.7776i 0.346608 0.600342i
\(454\) 0 0
\(455\) −3.88426 −0.182097
\(456\) 0 0
\(457\) 1.22073 0.0571033 0.0285516 0.999592i \(-0.490910\pi\)
0.0285516 + 0.999592i \(0.490910\pi\)
\(458\) 0 0
\(459\) −16.1528 + 27.9775i −0.753950 + 1.30588i
\(460\) 0 0
\(461\) 4.34580 7.52714i 0.202404 0.350574i −0.746898 0.664938i \(-0.768458\pi\)
0.949303 + 0.314364i \(0.101791\pi\)
\(462\) 0 0
\(463\) 19.7149 0.916229 0.458114 0.888893i \(-0.348525\pi\)
0.458114 + 0.888893i \(0.348525\pi\)
\(464\) 0 0
\(465\) −3.05545 5.29220i −0.141693 0.245420i
\(466\) 0 0
\(467\) 11.4795 0.531207 0.265604 0.964082i \(-0.414429\pi\)
0.265604 + 0.964082i \(0.414429\pi\)
\(468\) 0 0
\(469\) 1.22929 + 2.12919i 0.0567633 + 0.0983170i
\(470\) 0 0
\(471\) 1.95726 + 3.39008i 0.0901858 + 0.156206i
\(472\) 0 0
\(473\) 13.0611 22.6225i 0.600549 1.04018i
\(474\) 0 0
\(475\) −3.69799 + 2.30756i −0.169676 + 0.105878i
\(476\) 0 0
\(477\) −1.81747 + 3.14796i −0.0832164 + 0.144135i
\(478\) 0 0
\(479\) 19.6316 + 34.0029i 0.896989 + 1.55363i 0.831324 + 0.555789i \(0.187584\pi\)
0.0656652 + 0.997842i \(0.479083\pi\)
\(480\) 0 0
\(481\) −2.30785 3.99731i −0.105229 0.182262i
\(482\) 0 0
\(483\) 2.65497 0.120805
\(484\) 0 0
\(485\) −2.02888 3.51412i −0.0921267 0.159568i
\(486\) 0 0
\(487\) −31.5943 −1.43168 −0.715838 0.698266i \(-0.753955\pi\)
−0.715838 + 0.698266i \(0.753955\pi\)
\(488\) 0 0
\(489\) 0.178579 0.309309i 0.00807564 0.0139874i
\(490\) 0 0
\(491\) −5.53187 + 9.58148i −0.249650 + 0.432406i −0.963429 0.267965i \(-0.913649\pi\)
0.713779 + 0.700371i \(0.246982\pi\)
\(492\) 0 0
\(493\) −15.6683 −0.705663
\(494\) 0 0
\(495\) −9.52395 −0.428070
\(496\) 0 0
\(497\) 10.7564 18.6306i 0.482489 0.835696i
\(498\) 0 0
\(499\) −10.1868 + 17.6440i −0.456023 + 0.789854i −0.998746 0.0500570i \(-0.984060\pi\)
0.542724 + 0.839911i \(0.317393\pi\)
\(500\) 0 0
\(501\) −16.5431 −0.739091
\(502\) 0 0
\(503\) −6.83622 11.8407i −0.304812 0.527950i 0.672407 0.740181i \(-0.265260\pi\)
−0.977219 + 0.212231i \(0.931927\pi\)
\(504\) 0 0
\(505\) −11.1301 −0.495281
\(506\) 0 0
\(507\) 6.06317 + 10.5017i 0.269275 + 0.466398i
\(508\) 0 0
\(509\) 3.86196 + 6.68912i 0.171179 + 0.296490i 0.938832 0.344375i \(-0.111909\pi\)
−0.767654 + 0.640865i \(0.778576\pi\)
\(510\) 0 0
\(511\) 12.4807 21.6171i 0.552112 0.956285i
\(512\) 0 0
\(513\) 0.806621 + 23.5182i 0.0356132 + 1.03836i
\(514\) 0 0
\(515\) 5.78953 10.0278i 0.255117 0.441876i
\(516\) 0 0
\(517\) 25.7651 + 44.6265i 1.13315 + 1.96267i
\(518\) 0 0
\(519\) −7.73971 13.4056i −0.339736 0.588439i
\(520\) 0 0
\(521\) −2.16876 −0.0950151 −0.0475075 0.998871i \(-0.515128\pi\)
−0.0475075 + 0.998871i \(0.515128\pi\)
\(522\) 0 0
\(523\) −11.9466 20.6921i −0.522389 0.904804i −0.999661 0.0260485i \(-0.991708\pi\)
0.477272 0.878756i \(-0.341626\pi\)
\(524\) 0 0
\(525\) 2.82430 0.123263
\(526\) 0 0
\(527\) 15.7654 27.3065i 0.686751 1.18949i
\(528\) 0 0
\(529\) 11.0582 19.1533i 0.480790 0.832752i
\(530\) 0 0
\(531\) −17.8716 −0.775562
\(532\) 0 0
\(533\) 10.0730 0.436312
\(534\) 0 0
\(535\) 8.95887 15.5172i 0.387326 0.670868i
\(536\) 0 0
\(537\) −8.24629 + 14.2830i −0.355854 + 0.616356i
\(538\) 0 0
\(539\) −6.15492 −0.265111
\(540\) 0 0
\(541\) −21.2275 36.7671i −0.912641 1.58074i −0.810319 0.585990i \(-0.800706\pi\)
−0.102323 0.994751i \(-0.532627\pi\)
\(542\) 0 0
\(543\) 11.4614 0.491858
\(544\) 0 0
\(545\) −2.81235 4.87113i −0.120468 0.208656i
\(546\) 0 0
\(547\) 6.01535 + 10.4189i 0.257198 + 0.445480i 0.965490 0.260439i \(-0.0838674\pi\)
−0.708292 + 0.705919i \(0.750534\pi\)
\(548\) 0 0
\(549\) −8.71231 + 15.0902i −0.371833 + 0.644033i
\(550\) 0 0
\(551\) −9.68259 + 6.04198i −0.412492 + 0.257397i
\(552\) 0 0
\(553\) 9.25956 16.0380i 0.393756 0.682006i
\(554\) 0 0
\(555\) 1.67807 + 2.90650i 0.0712301 + 0.123374i
\(556\) 0 0
\(557\) 4.37635 + 7.58006i 0.185432 + 0.321178i 0.943722 0.330740i \(-0.107298\pi\)
−0.758290 + 0.651917i \(0.773965\pi\)
\(558\) 0 0
\(559\) 7.24011 0.306224
\(560\) 0 0
\(561\) 19.9692 + 34.5876i 0.843099 + 1.46029i
\(562\) 0 0
\(563\) 35.9707 1.51598 0.757991 0.652265i \(-0.226181\pi\)
0.757991 + 0.652265i \(0.226181\pi\)
\(564\) 0 0
\(565\) 7.83943 13.5783i 0.329807 0.571243i
\(566\) 0 0
\(567\) 1.57827 2.73365i 0.0662812 0.114802i
\(568\) 0 0
\(569\) −20.3125 −0.851543 −0.425772 0.904831i \(-0.639997\pi\)
−0.425772 + 0.904831i \(0.639997\pi\)
\(570\) 0 0
\(571\) −10.1773 −0.425906 −0.212953 0.977062i \(-0.568308\pi\)
−0.212953 + 0.977062i \(0.568308\pi\)
\(572\) 0 0
\(573\) −7.53505 + 13.0511i −0.314781 + 0.545217i
\(574\) 0 0
\(575\) −0.470022 + 0.814102i −0.0196013 + 0.0339504i
\(576\) 0 0
\(577\) −32.7441 −1.36316 −0.681578 0.731745i \(-0.738706\pi\)
−0.681578 + 0.731745i \(0.738706\pi\)
\(578\) 0 0
\(579\) −8.41745 14.5794i −0.349817 0.605901i
\(580\) 0 0
\(581\) −7.58228 −0.314566
\(582\) 0 0
\(583\) 6.31984 + 10.9463i 0.261741 + 0.453349i
\(584\) 0 0
\(585\) −1.31984 2.28604i −0.0545689 0.0945160i
\(586\) 0 0
\(587\) 4.38663 7.59786i 0.181056 0.313597i −0.761185 0.648535i \(-0.775382\pi\)
0.942240 + 0.334938i \(0.108715\pi\)
\(588\) 0 0
\(589\) −0.787274 22.9541i −0.0324390 0.945808i
\(590\) 0 0
\(591\) 14.4975 25.1105i 0.596349 1.03291i
\(592\) 0 0
\(593\) 16.1603 + 27.9905i 0.663625 + 1.14943i 0.979656 + 0.200684i \(0.0643163\pi\)
−0.316031 + 0.948749i \(0.602350\pi\)
\(594\) 0 0
\(595\) 7.28635 + 12.6203i 0.298711 + 0.517383i
\(596\) 0 0
\(597\) 2.61570 0.107053
\(598\) 0 0
\(599\) −9.77520 16.9311i −0.399404 0.691787i 0.594249 0.804281i \(-0.297449\pi\)
−0.993652 + 0.112494i \(0.964116\pi\)
\(600\) 0 0
\(601\) −0.401837 −0.0163913 −0.00819564 0.999966i \(-0.502609\pi\)
−0.00819564 + 0.999966i \(0.502609\pi\)
\(602\) 0 0
\(603\) −0.835409 + 1.44697i −0.0340205 + 0.0589252i
\(604\) 0 0
\(605\) −11.0587 + 19.1542i −0.449599 + 0.778728i
\(606\) 0 0
\(607\) −13.4453 −0.545727 −0.272863 0.962053i \(-0.587971\pi\)
−0.272863 + 0.962053i \(0.587971\pi\)
\(608\) 0 0
\(609\) 7.39497 0.299659
\(610\) 0 0
\(611\) −7.14115 + 12.3688i −0.288900 + 0.500390i
\(612\) 0 0
\(613\) 10.3527 17.9313i 0.418140 0.724239i −0.577613 0.816311i \(-0.696016\pi\)
0.995752 + 0.0920716i \(0.0293489\pi\)
\(614\) 0 0
\(615\) −7.32425 −0.295342
\(616\) 0 0
\(617\) 4.63936 + 8.03560i 0.186773 + 0.323501i 0.944173 0.329451i \(-0.106864\pi\)
−0.757399 + 0.652952i \(0.773530\pi\)
\(618\) 0 0
\(619\) 2.89129 0.116211 0.0581053 0.998310i \(-0.481494\pi\)
0.0581053 + 0.998310i \(0.481494\pi\)
\(620\) 0 0
\(621\) 2.53747 + 4.39503i 0.101825 + 0.176366i
\(622\) 0 0
\(623\) 13.5329 + 23.4396i 0.542183 + 0.939088i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 25.6781 + 13.6738i 1.02548 + 0.546078i
\(628\) 0 0
\(629\) −8.65844 + 14.9969i −0.345234 + 0.597964i
\(630\) 0 0
\(631\) 15.2270 + 26.3740i 0.606178 + 1.04993i 0.991864 + 0.127301i \(0.0406314\pi\)
−0.385686 + 0.922630i \(0.626035\pi\)
\(632\) 0 0
\(633\) 12.8826 + 22.3134i 0.512039 + 0.886877i
\(634\) 0 0
\(635\) −6.11991 −0.242861
\(636\) 0 0
\(637\) −0.852959 1.47737i −0.0337955 0.0585355i
\(638\) 0 0
\(639\) 14.6198 0.578349
\(640\) 0 0
\(641\) 10.0369 17.3845i 0.396434 0.686645i −0.596849 0.802354i \(-0.703581\pi\)
0.993283 + 0.115709i \(0.0369141\pi\)
\(642\) 0 0
\(643\) −1.04457 + 1.80924i −0.0411937 + 0.0713496i −0.885887 0.463901i \(-0.846449\pi\)
0.844693 + 0.535250i \(0.179783\pi\)
\(644\) 0 0
\(645\) −5.26439 −0.207285
\(646\) 0 0
\(647\) 2.10623 0.0828043 0.0414021 0.999143i \(-0.486818\pi\)
0.0414021 + 0.999143i \(0.486818\pi\)
\(648\) 0 0
\(649\) −31.0722 + 53.8187i −1.21969 + 2.11257i
\(650\) 0 0
\(651\) −7.44081 + 12.8879i −0.291628 + 0.505115i
\(652\) 0 0
\(653\) 1.83067 0.0716395 0.0358197 0.999358i \(-0.488596\pi\)
0.0358197 + 0.999358i \(0.488596\pi\)
\(654\) 0 0
\(655\) −7.44055 12.8874i −0.290726 0.503553i
\(656\) 0 0
\(657\) 16.9634 0.661804
\(658\) 0 0
\(659\) 12.0268 + 20.8310i 0.468497 + 0.811460i 0.999352 0.0360024i \(-0.0114624\pi\)
−0.530855 + 0.847463i \(0.678129\pi\)
\(660\) 0 0
\(661\) 8.72110 + 15.1054i 0.339211 + 0.587531i 0.984285 0.176589i \(-0.0565065\pi\)
−0.645073 + 0.764121i \(0.723173\pi\)
\(662\) 0 0
\(663\) −5.53472 + 9.58642i −0.214951 + 0.372306i
\(664\) 0 0
\(665\) 9.36941 + 4.98929i 0.363330 + 0.193476i
\(666\) 0 0
\(667\) −1.23068 + 2.13159i −0.0476519 + 0.0825356i
\(668\) 0 0
\(669\) 5.92402 + 10.2607i 0.229036 + 0.396702i
\(670\) 0 0
\(671\) 30.2951 + 52.4726i 1.16953 + 2.02568i
\(672\) 0 0
\(673\) 47.5187 1.83171 0.915856 0.401506i \(-0.131513\pi\)
0.915856 + 0.401506i \(0.131513\pi\)
\(674\) 0 0
\(675\) 2.69931 + 4.67535i 0.103897 + 0.179954i
\(676\) 0 0
\(677\) 14.5531 0.559321 0.279661 0.960099i \(-0.409778\pi\)
0.279661 + 0.960099i \(0.409778\pi\)
\(678\) 0 0
\(679\) −4.94084 + 8.55778i −0.189612 + 0.328418i
\(680\) 0 0
\(681\) 2.40754 4.16998i 0.0922570 0.159794i
\(682\) 0 0
\(683\) −3.33714 −0.127692 −0.0638460 0.997960i \(-0.520337\pi\)
−0.0638460 + 0.997960i \(0.520337\pi\)
\(684\) 0 0
\(685\) 17.3504 0.662923
\(686\) 0 0
\(687\) −3.78826 + 6.56146i −0.144531 + 0.250335i
\(688\) 0 0
\(689\) −1.75163 + 3.03391i −0.0667318 + 0.115583i
\(690\) 0 0
\(691\) 19.3318 0.735415 0.367708 0.929941i \(-0.380143\pi\)
0.367708 + 0.929941i \(0.380143\pi\)
\(692\) 0 0
\(693\) 11.5966 + 20.0859i 0.440519 + 0.763001i
\(694\) 0 0
\(695\) 6.70534 0.254348
\(696\) 0 0
\(697\) −18.8957 32.7283i −0.715725 1.23967i
\(698\) 0 0
\(699\) −2.98533 5.17074i −0.112916 0.195575i
\(700\) 0 0
\(701\) −4.96892 + 8.60643i −0.187674 + 0.325060i −0.944474 0.328586i \(-0.893428\pi\)
0.756801 + 0.653646i \(0.226761\pi\)
\(702\) 0 0
\(703\) 0.432375 + 12.6065i 0.0163073 + 0.475464i
\(704\) 0 0
\(705\) 5.19244 8.99357i 0.195559 0.338717i
\(706\) 0 0
\(707\) 13.5523 + 23.4732i 0.509686 + 0.882801i
\(708\) 0 0
\(709\) −18.6059 32.2264i −0.698760 1.21029i −0.968897 0.247466i \(-0.920402\pi\)
0.270136 0.962822i \(-0.412931\pi\)
\(710\) 0 0
\(711\) 12.5853 0.471987
\(712\) 0 0
\(713\) −2.47661 4.28961i −0.0927497 0.160647i
\(714\) 0 0
\(715\) −9.17891 −0.343272
\(716\) 0 0
\(717\) 8.11608 14.0575i 0.303100 0.524985i
\(718\) 0 0
\(719\) −1.32109 + 2.28819i −0.0492683 + 0.0853351i −0.889608 0.456725i \(-0.849022\pi\)
0.840340 + 0.542060i \(0.182356\pi\)
\(720\) 0 0
\(721\) −28.1980 −1.05015
\(722\) 0 0
\(723\) 17.6581 0.656711
\(724\) 0 0
\(725\) −1.30917 + 2.26755i −0.0486213 + 0.0842145i
\(726\) 0 0
\(727\) −5.08653 + 8.81013i −0.188649 + 0.326750i −0.944800 0.327647i \(-0.893744\pi\)
0.756151 + 0.654397i \(0.227077\pi\)
\(728\) 0 0
\(729\) 20.9284 0.775126
\(730\) 0 0
\(731\) −13.5815 23.5238i −0.502329 0.870060i
\(732\) 0 0
\(733\) 14.8222 0.547472 0.273736 0.961805i \(-0.411741\pi\)
0.273736 + 0.961805i \(0.411741\pi\)
\(734\) 0 0
\(735\) 0.620199 + 1.07422i 0.0228764 + 0.0396231i
\(736\) 0 0
\(737\) 2.90494 + 5.03151i 0.107005 + 0.185338i
\(738\) 0 0
\(739\) 17.7433 30.7323i 0.652697 1.13050i −0.329769 0.944062i \(-0.606971\pi\)
0.982466 0.186443i \(-0.0596959\pi\)
\(740\) 0 0
\(741\) 0.276386 + 8.05845i 0.0101533 + 0.296035i
\(742\) 0 0
\(743\) −4.36941 + 7.56804i −0.160298 + 0.277645i −0.934976 0.354712i \(-0.884579\pi\)
0.774677 + 0.632357i \(0.217912\pi\)
\(744\) 0 0
\(745\) −7.19642 12.4646i −0.263656 0.456666i
\(746\) 0 0
\(747\) −2.57641 4.46247i −0.0942658 0.163273i
\(748\) 0 0
\(749\) −43.6342 −1.59436
\(750\) 0 0
\(751\) 6.54957 + 11.3442i 0.238997 + 0.413955i 0.960427 0.278533i \(-0.0898480\pi\)
−0.721430 + 0.692488i \(0.756515\pi\)
\(752\) 0 0
\(753\) 7.08911 0.258342
\(754\) 0 0
\(755\) 6.36093 11.0175i 0.231498 0.400966i
\(756\) 0 0
\(757\) 8.21901 14.2357i 0.298725 0.517407i −0.677119 0.735873i \(-0.736772\pi\)
0.975845 + 0.218466i \(0.0701053\pi\)
\(758\) 0 0
\(759\) 6.27397 0.227731
\(760\) 0 0
\(761\) 16.3918 0.594203 0.297101 0.954846i \(-0.403980\pi\)
0.297101 + 0.954846i \(0.403980\pi\)
\(762\) 0 0
\(763\) −6.84879 + 11.8625i −0.247943 + 0.429450i
\(764\) 0 0
\(765\) −4.95171 + 8.57661i −0.179029 + 0.310088i
\(766\) 0 0
\(767\) −17.2242 −0.621929
\(768\) 0 0
\(769\) 25.0210 + 43.3377i 0.902282 + 1.56280i 0.824525 + 0.565825i \(0.191442\pi\)
0.0777564 + 0.996972i \(0.475224\pi\)
\(770\) 0 0
\(771\) 0.142282 0.00512416
\(772\) 0 0
\(773\) −24.3436 42.1644i −0.875580 1.51655i −0.856144 0.516737i \(-0.827146\pi\)
−0.0194356 0.999811i \(-0.506187\pi\)
\(774\) 0 0
\(775\) −2.63457 4.56320i −0.0946364 0.163915i
\(776\) 0 0
\(777\) 4.08653 7.07808i 0.146603 0.253925i
\(778\) 0 0
\(779\) −24.2977 12.9387i −0.870555 0.463577i
\(780\) 0 0
\(781\) 25.4185 44.0261i 0.909544 1.57538i
\(782\) 0 0
\(783\) 7.06771 + 12.2416i 0.252579 + 0.437480i
\(784\) 0 0
\(785\) 1.68765 + 2.92309i 0.0602348 + 0.104330i
\(786\) 0 0
\(787\) −6.51678 −0.232298 −0.116149 0.993232i \(-0.537055\pi\)
−0.116149 + 0.993232i \(0.537055\pi\)
\(788\) 0 0
\(789\) −5.83388 10.1046i −0.207692 0.359732i
\(790\) 0 0
\(791\) −38.1820 −1.35760
\(792\) 0 0
\(793\) −8.39668 + 14.5435i −0.298175 + 0.516454i
\(794\) 0 0
\(795\) 1.27364 2.20600i 0.0451712 0.0782388i
\(796\) 0