Properties

Label 1520.2.q.o.881.1
Level $1520$
Weight $2$
Character 1520.881
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 881.1
Root \(1.07988 + 1.87040i\) of defining polynomial
Character \(\chi\) \(=\) 1520.881
Dual form 1520.2.q.o.961.1

$q$-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 \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).

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

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 0.648652 0.761085i \(-0.275333\pi\)
−0.983445 + 0.181207i \(0.942000\pi\)
\(4\) 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 −0.733981 0.679170i \(-0.762340\pi\)
0.955169 + 0.296061i \(0.0956732\pi\)
\(14\) 0 0
\(15\) −0.579878 + 1.00438i −0.149724 + 0.259329i
\(16\) 0 0
\(17\) 2.99203 + 5.18234i 0.725673 + 1.25690i 0.958696 + 0.284432i \(0.0918050\pi\)
−0.233023 + 0.972471i \(0.574862\pi\)
\(18\) 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 −0.910859 0.412717i \(-0.864580\pi\)
0.812853 + 0.582469i \(0.197913\pi\)
\(24\) 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 −0.961598 0.274463i \(-0.911500\pi\)
0.718491 + 0.695536i \(0.244833\pi\)
\(30\) 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 0.999969 0.00789701i \(-0.00251372\pi\)
−0.506823 + 0.862050i \(0.669180\pi\)
\(42\) 0 0
\(43\) 2.26961 + 3.93108i 0.346113 + 0.599485i 0.985555 0.169354i \(-0.0541682\pi\)
−0.639443 + 0.768839i \(0.720835\pi\)
\(44\) 0 0
\(45\) −1.65497 −0.246708
\(46\) 0 0
\(47\) 4.47718 7.75471i 0.653064 1.13114i −0.329311 0.944221i \(-0.606816\pi\)
0.982375 0.186919i \(-0.0598502\pi\)
\(48\) 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 −0.780691 0.624917i \(-0.785133\pi\)
0.931540 + 0.363640i \(0.118466\pi\)
\(54\) 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 −0.967430 0.253140i \(-0.918537\pi\)
0.264489 0.964389i \(-0.414797\pi\)
\(60\) 0 0
\(61\) 5.26434 9.11811i 0.674030 1.16745i −0.302721 0.953079i \(-0.597895\pi\)
0.976751 0.214375i \(-0.0687716\pi\)
\(62\) 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 −0.833542 0.552456i \(-0.813691\pi\)
0.895212 + 0.445641i \(0.147024\pi\)
\(68\) 0 0
\(69\) 1.09022 0.131247
\(70\) 0 0
\(71\) 4.41694 + 7.65036i 0.524194 + 0.907931i 0.999603 + 0.0281662i \(0.00896677\pi\)
−0.475409 + 0.879765i \(0.657700\pi\)
\(72\) 0 0
\(73\) 5.12499 + 8.87674i 0.599835 + 1.03894i 0.992845 + 0.119410i \(0.0381003\pi\)
−0.393011 + 0.919534i \(0.628566\pi\)
\(74\) 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 0.996677 0.0814604i \(-0.0259584\pi\)
−0.568885 + 0.822417i \(0.692625\pi\)
\(80\) 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 −0.405310 0.914179i \(-0.632837\pi\)
0.994358 0.106081i \(-0.0338302\pi\)
\(90\) 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 0.744450 0.667678i \(-0.232712\pi\)
−0.950451 + 0.310873i \(0.899379\pi\)
\(98\) 0 0
\(99\) 4.76197 8.24798i 0.478596 0.828953i
\(100\) 0 0
\(101\) 5.56503 9.63892i 0.553741 0.959108i −0.444259 0.895898i \(-0.646533\pi\)
0.998000 0.0632098i \(-0.0201337\pi\)
\(102\) 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 0.699326 0.714803i \(-0.253484\pi\)
−0.968700 + 0.248233i \(0.920150\pi\)
\(110\) 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 −0.697726 0.716365i \(-0.745805\pi\)
0.969253 + 0.246066i \(0.0791380\pi\)
\(128\) 0 0
\(129\) 2.63220 4.55910i 0.231752 0.401406i
\(130\) 0 0
\(131\) −7.44055 12.8874i −0.650084 1.12598i −0.983102 0.183058i \(-0.941400\pi\)
0.333018 0.942920i \(-0.391933\pi\)
\(132\) 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 0.210793 + 0.977531i \(0.432396\pi\)
−0.951963 + 0.306214i \(0.900938\pi\)
\(138\) 0 0
\(139\) −3.35267 + 5.80700i −0.284370 + 0.492543i −0.972456 0.233086i \(-0.925118\pi\)
0.688086 + 0.725629i \(0.258451\pi\)
\(140\) 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 −0.994291 0.106704i \(-0.965970\pi\)
0.404737 0.914433i \(-0.367363\pi\)
\(150\) 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 0.925479 0.378800i \(-0.123663\pi\)
−0.790790 + 0.612088i \(0.790330\pi\)
\(158\) 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 −0.446235 0.894916i \(-0.647235\pi\)
0.998137 0.0610070i \(-0.0194312\pi\)
\(168\) 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 −0.999963 0.00854514i \(-0.997280\pi\)
0.492581 0.870266i \(-0.336053\pi\)
\(174\) 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 −0.989140 0.146976i \(-0.953046\pi\)
0.621855 + 0.783133i \(0.286379\pi\)
\(182\) 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 −0.999659 0.0261066i \(-0.991689\pi\)
0.477221 0.878784i \(-0.341644\pi\)
\(194\) 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 −0.903224 0.429170i \(-0.858806\pi\)
0.823284 + 0.567630i \(0.192140\pi\)
\(200\) 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 0.940400 + 0.340071i \(0.110451\pi\)
−0.175689 + 0.984446i \(0.556215\pi\)
\(212\) 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 0.984814 0.173610i \(-0.0555432\pi\)
−0.642758 + 0.766069i \(0.722210\pi\)
\(224\) 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 0.769305 0.638882i \(-0.220603\pi\)
−0.937940 + 0.346797i \(0.887269\pi\)
\(234\) 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 −0.999939 0.0110652i \(-0.996478\pi\)
0.509552 + 0.860440i \(0.329811\pi\)
\(242\) 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 −0.946214 0.323542i \(-0.895126\pi\)
0.753302 + 0.657674i \(0.228460\pi\)
\(252\) 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 −0.867932 0.496683i \(-0.834551\pi\)
0.864106 + 0.503310i \(0.167885\pi\)
\(258\) 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 0.668222 0.743962i \(-0.267056\pi\)
−0.978401 + 0.206716i \(0.933722\pi\)
\(264\) 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 0.765722 0.643172i \(-0.222382\pi\)
−0.939864 + 0.341549i \(0.889049\pi\)
\(270\) 0 0
\(271\) −6.35560 11.0082i −0.386075 0.668702i 0.605843 0.795585i \(-0.292836\pi\)
−0.991918 + 0.126883i \(0.959503\pi\)
\(272\) 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 −0.379516 0.925185i \(-0.623910\pi\)
0.990992 0.133922i \(-0.0427571\pi\)
\(282\) 0 0
\(283\) −5.92805 10.2677i −0.352386 0.610350i 0.634281 0.773103i \(-0.281296\pi\)
−0.986667 + 0.162752i \(0.947963\pi\)
\(284\) 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 0.999806 0.0197074i \(-0.00627348\pi\)
−0.516970 + 0.856003i \(0.672940\pi\)
\(308\) 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 0.262389 + 0.964962i \(0.415490\pi\)
−0.966876 + 0.255246i \(0.917844\pi\)
\(314\) 0 0
\(315\) −4.03027 −0.227080
\(316\) 0 0
\(317\) 12.6152 21.8502i 0.708541 1.22723i −0.256857 0.966449i \(-0.582687\pi\)
0.965398 0.260780i \(-0.0839798\pi\)
\(318\) 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 0.865249 + 0.501342i \(0.167160\pi\)
0.00155051 + 0.999999i \(0.499506\pi\)
\(338\) 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 0.818294 0.574801i \(-0.194920\pi\)
−0.906939 + 0.421263i \(0.861587\pi\)
\(348\) 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 0.954915 0.296878i \(-0.0959455\pi\)
−0.734562 + 0.678542i \(0.762612\pi\)
\(360\) 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 −0.614176 0.789169i \(-0.710511\pi\)
0.990528 + 0.137307i \(0.0438448\pi\)
\(368\) 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 0.692950 0.720986i \(-0.256311\pi\)
−0.970867 + 0.239619i \(0.922977\pi\)
\(384\) 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 −0.131237 + 0.991351i \(0.541895\pi\)
−0.792917 + 0.609330i \(0.791438\pi\)
\(390\) 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 0.737993 0.674808i \(-0.235774\pi\)
−0.953398 + 0.301717i \(0.902440\pi\)
\(398\) 0 0
\(399\) 10.8662 5.78635i 0.543992 0.289680i
\(400\) 0 0
\(401\) 8.52785 + 14.7707i 0.425860 + 0.737612i 0.996500 0.0835885i \(-0.0266381\pi\)
−0.570640 + 0.821200i \(0.693305\pi\)
\(402\) 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 −0.682597 0.730795i \(-0.739149\pi\)
0.974186 + 0.225749i \(0.0724828\pi\)
\(410\) 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 0.523965 0.851740i \(-0.324452\pi\)
−0.999611 + 0.0278967i \(0.991119\pi\)
\(422\) 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 −0.0461694 + 0.998934i \(0.514701\pi\)
−0.842017 + 0.539451i \(0.818632\pi\)
\(432\) 0 0
\(433\) −0.184467 + 0.319506i −0.00886490 + 0.0153545i −0.870424 0.492303i \(-0.836155\pi\)
0.861559 + 0.507658i \(0.169488\pi\)
\(434\) 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 0.837742 0.546067i \(-0.183875\pi\)
−0.891778 + 0.452472i \(0.850542\pi\)
\(440\) 0 0
\(441\) −0.885022 + 1.53290i −0.0421439 + 0.0729954i
\(442\) 0 0
\(443\) −8.23137 + 14.2572i −0.391084 + 0.677378i −0.992593 0.121488i \(-0.961233\pi\)
0.601508 + 0.798866i \(0.294567\pi\)
\(444\) 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 0.949303 0.314364i \(-0.101791\pi\)
−0.746898 + 0.664938i \(0.768458\pi\)
\(462\) 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 0.0656652 0.997842i \(-0.479083\pi\)
0.831324 0.555789i \(-0.187584\pi\)
\(480\) 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 0.713779 0.700371i \(-0.246982\pi\)
−0.963429 + 0.267965i \(0.913649\pi\)
\(492\) 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 0.542724 0.839911i \(-0.317393\pi\)
−0.998746 + 0.0500570i \(0.984060\pi\)
\(500\) 0 0
\(501\) −16.5431 −0.739091
\(502\) 0 0
\(503\) −6.83622 + 11.8407i −0.304812 + 0.527950i −0.977219 0.212231i \(-0.931927\pi\)
0.672407 + 0.740181i \(0.265260\pi\)
\(504\) 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 −0.767654 0.640865i \(-0.778576\pi\)
0.938832 + 0.344375i \(0.111909\pi\)
\(510\) 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 0.477272 + 0.878756i \(0.341626\pi\)
−0.999661 + 0.0260485i \(0.991708\pi\)
\(524\) 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 −0.102323 + 0.994751i \(0.532627\pi\)
−0.810319 + 0.585990i \(0.800706\pi\)
\(542\) 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 −0.708292 0.705919i \(-0.750534\pi\)
0.965490 + 0.260439i \(0.0838674\pi\)
\(548\) 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 −0.758290 0.651917i \(-0.773965\pi\)
0.943722 + 0.330740i \(0.107298\pi\)
\(558\) 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 0.942240 0.334938i \(-0.108715\pi\)
−0.761185 + 0.648535i \(0.775382\pi\)
\(588\) 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 −0.316031 0.948749i \(-0.602350\pi\)
0.979656 0.200684i \(-0.0643163\pi\)
\(594\) 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 −0.993652 0.112494i \(-0.964116\pi\)
0.594249 + 0.804281i \(0.297449\pi\)
\(600\) 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 0.995752 0.0920716i \(-0.0293489\pi\)
−0.577613 + 0.816311i \(0.696016\pi\)
\(614\) 0 0
\(615\) −7.32425 −0.295342
\(616\) 0 0
\(617\) 4.63936 8.03560i 0.186773 0.323501i −0.757399 0.652952i \(-0.773530\pi\)
0.944173 + 0.329451i \(0.106864\pi\)
\(618\) 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 −0.385686 0.922630i \(-0.626035\pi\)
0.991864 0.127301i \(-0.0406314\pi\)
\(632\) 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 0.993283 0.115709i \(-0.0369141\pi\)
−0.596849 + 0.802354i \(0.703581\pi\)
\(642\) 0 0
\(643\) −1.04457 1.80924i −0.0411937 0.0713496i 0.844693 0.535250i \(-0.179783\pi\)
−0.885887 + 0.463901i \(0.846449\pi\)
\(644\) 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 −0.530855 0.847463i \(-0.678129\pi\)
0.999352 + 0.0360024i \(0.0114624\pi\)
\(660\) 0 0
\(661\) 8.72110 15.1054i 0.339211 0.587531i −0.645073 0.764121i \(-0.723173\pi\)
0.984285 + 0.176589i \(0.0565065\pi\)
\(662\) 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 0.756801 0.653646i \(-0.226761\pi\)
−0.944474 + 0.328586i \(0.893428\pi\)
\(702\) 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 0.270136 + 0.962822i \(0.412931\pi\)
−0.968897 + 0.247466i \(0.920402\pi\)
\(710\) 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 0.840340 0.542060i \(-0.182356\pi\)
−0.889608 + 0.456725i \(0.849022\pi\)
\(720\) 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 0.756151 0.654397i \(-0.227077\pi\)
−0.944800 + 0.327647i \(0.893744\pi\)
\(728\) 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 0.982466 + 0.186443i \(0.0596959\pi\)
−0.329769 + 0.944062i \(0.606971\pi\)
\(740\) 0 0
\(741\) 0.276386 8.05845i 0.0101533 0.296035i
\(742\) 0 0
\(743\) −4.36941 7.56804i −0.160298 0.277645i 0.774677 0.632357i \(-0.217912\pi\)
−0.934976 + 0.354712i \(0.884579\pi\)
\(744\) 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 −0.721430 0.692488i \(-0.756515\pi\)
0.960427 + 0.278533i \(0.0898480\pi\)
\(752\) 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 0.975845 0.218466i \(-0.0701053\pi\)
−0.677119 + 0.735873i \(0.736772\pi\)
\(758\) 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 0.0777564 0.996972i \(-0.475224\pi\)
0.824525 0.565825i \(-0.191442\pi\)
\(770\) 0 0
\(771\) 0.142282 0.00512416
\(772\) 0 0
\(773\) −24.3436 + 42.1644i −0.875580 + 1.51655i −0.0194356 + 0.999811i \(0.506187\pi\)
−0.856144 + 0.516737i \(0.827146\pi\)
\(774\) 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
\(796\)