Properties

Label 432.2.be.b.191.3
Level $432$
Weight $2$
Character 432.191
Analytic conductor $3.450$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.be (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 191.3
Character \(\chi\) \(=\) 432.191
Dual form 432.2.be.b.95.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.249148 - 1.71404i) q^{3} +(-1.47612 - 1.75917i) q^{5} +(0.590654 + 1.62281i) q^{7} +(-2.87585 - 0.854099i) q^{9} +O(q^{10})\) \(q+(0.249148 - 1.71404i) q^{3} +(-1.47612 - 1.75917i) q^{5} +(0.590654 + 1.62281i) q^{7} +(-2.87585 - 0.854099i) q^{9} +(-0.867802 - 0.728172i) q^{11} +(-1.22373 - 6.94010i) q^{13} +(-3.38306 + 2.09183i) q^{15} +(-1.48526 + 0.857517i) q^{17} +(3.94280 + 2.27638i) q^{19} +(2.92872 - 0.608084i) q^{21} +(-6.51976 - 2.37300i) q^{23} +(-0.0475130 + 0.269460i) q^{25} +(-2.18047 + 4.71652i) q^{27} +(-6.35318 - 1.12024i) q^{29} +(-1.56666 + 4.30438i) q^{31} +(-1.46433 + 1.30602i) q^{33} +(1.98292 - 3.43452i) q^{35} +(1.47273 + 2.55085i) q^{37} +(-12.2005 + 0.368401i) q^{39} +(7.14576 - 1.25999i) q^{41} +(0.337693 - 0.402447i) q^{43} +(2.74260 + 6.31987i) q^{45} +(8.97326 - 3.26600i) q^{47} +(3.07767 - 2.58248i) q^{49} +(1.09977 + 2.75945i) q^{51} -8.57289i q^{53} +2.60148i q^{55} +(4.88414 - 6.19096i) q^{57} +(11.0297 - 9.25501i) q^{59} +(-0.269170 + 0.0979697i) q^{61} +(-0.312594 - 5.17143i) q^{63} +(-10.4025 + 12.3972i) q^{65} +(5.85364 - 1.03215i) q^{67} +(-5.69179 + 10.5839i) q^{69} +(-1.36269 - 2.36024i) q^{71} +(-1.58277 + 2.74144i) q^{73} +(0.450026 + 0.148574i) q^{75} +(0.669113 - 1.83837i) q^{77} +(9.41150 + 1.65950i) q^{79} +(7.54103 + 4.91252i) q^{81} +(-0.731691 + 4.14963i) q^{83} +(3.70095 + 1.34704i) q^{85} +(-3.50301 + 10.6105i) q^{87} +(-5.83560 - 3.36919i) q^{89} +(10.5397 - 6.08507i) q^{91} +(6.98753 + 3.75775i) q^{93} +(-1.81551 - 10.2963i) q^{95} +(-3.21229 - 2.69543i) q^{97} +(1.87374 + 2.83530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{18}\right)\)

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
\(3\) 0.249148 1.71404i 0.143846 0.989600i
\(4\) 0 0
\(5\) −1.47612 1.75917i −0.660141 0.786726i 0.327265 0.944933i \(-0.393873\pi\)
−0.987406 + 0.158207i \(0.949429\pi\)
\(6\) 0 0
\(7\) 0.590654 + 1.62281i 0.223246 + 0.613364i 0.999862 0.0166105i \(-0.00528752\pi\)
−0.776616 + 0.629975i \(0.783065\pi\)
\(8\) 0 0
\(9\) −2.87585 0.854099i −0.958617 0.284700i
\(10\) 0 0
\(11\) −0.867802 0.728172i −0.261652 0.219552i 0.502518 0.864567i \(-0.332407\pi\)
−0.764170 + 0.645014i \(0.776851\pi\)
\(12\) 0 0
\(13\) −1.22373 6.94010i −0.339401 1.92484i −0.378501 0.925601i \(-0.623560\pi\)
0.0391000 0.999235i \(-0.487551\pi\)
\(14\) 0 0
\(15\) −3.38306 + 2.09183i −0.873502 + 0.540109i
\(16\) 0 0
\(17\) −1.48526 + 0.857517i −0.360229 + 0.207979i −0.669181 0.743099i \(-0.733355\pi\)
0.308952 + 0.951078i \(0.400022\pi\)
\(18\) 0 0
\(19\) 3.94280 + 2.27638i 0.904541 + 0.522237i 0.878671 0.477428i \(-0.158431\pi\)
0.0258702 + 0.999665i \(0.491764\pi\)
\(20\) 0 0
\(21\) 2.92872 0.608084i 0.639098 0.132695i
\(22\) 0 0
\(23\) −6.51976 2.37300i −1.35946 0.494804i −0.443575 0.896237i \(-0.646290\pi\)
−0.915889 + 0.401433i \(0.868512\pi\)
\(24\) 0 0
\(25\) −0.0475130 + 0.269460i −0.00950260 + 0.0538919i
\(26\) 0 0
\(27\) −2.18047 + 4.71652i −0.419632 + 0.907694i
\(28\) 0 0
\(29\) −6.35318 1.12024i −1.17976 0.208023i −0.450827 0.892612i \(-0.648871\pi\)
−0.728930 + 0.684589i \(0.759982\pi\)
\(30\) 0 0
\(31\) −1.56666 + 4.30438i −0.281381 + 0.773089i 0.715817 + 0.698288i \(0.246054\pi\)
−0.997198 + 0.0748009i \(0.976168\pi\)
\(32\) 0 0
\(33\) −1.46433 + 1.30602i −0.254906 + 0.227349i
\(34\) 0 0
\(35\) 1.98292 3.43452i 0.335175 0.580540i
\(36\) 0 0
\(37\) 1.47273 + 2.55085i 0.242116 + 0.419357i 0.961317 0.275445i \(-0.0888253\pi\)
−0.719201 + 0.694802i \(0.755492\pi\)
\(38\) 0 0
\(39\) −12.2005 + 0.368401i −1.95364 + 0.0589913i
\(40\) 0 0
\(41\) 7.14576 1.25999i 1.11598 0.196778i 0.414905 0.909865i \(-0.363815\pi\)
0.701076 + 0.713087i \(0.252704\pi\)
\(42\) 0 0
\(43\) 0.337693 0.402447i 0.0514978 0.0613727i −0.739681 0.672958i \(-0.765023\pi\)
0.791178 + 0.611585i \(0.209468\pi\)
\(44\) 0 0
\(45\) 2.74260 + 6.31987i 0.408842 + 0.942110i
\(46\) 0 0
\(47\) 8.97326 3.26600i 1.30888 0.476395i 0.409004 0.912533i \(-0.365876\pi\)
0.899880 + 0.436138i \(0.143654\pi\)
\(48\) 0 0
\(49\) 3.07767 2.58248i 0.439668 0.368925i
\(50\) 0 0
\(51\) 1.09977 + 2.75945i 0.153998 + 0.386400i
\(52\) 0 0
\(53\) 8.57289i 1.17758i −0.808287 0.588788i \(-0.799605\pi\)
0.808287 0.588788i \(-0.200395\pi\)
\(54\) 0 0
\(55\) 2.60148i 0.350784i
\(56\) 0 0
\(57\) 4.88414 6.19096i 0.646920 0.820012i
\(58\) 0 0
\(59\) 11.0297 9.25501i 1.43594 1.20490i 0.493850 0.869547i \(-0.335589\pi\)
0.942093 0.335352i \(-0.108855\pi\)
\(60\) 0 0
\(61\) −0.269170 + 0.0979697i −0.0344636 + 0.0125437i −0.359194 0.933263i \(-0.616949\pi\)
0.324731 + 0.945806i \(0.394726\pi\)
\(62\) 0 0
\(63\) −0.312594 5.17143i −0.0393832 0.651539i
\(64\) 0 0
\(65\) −10.4025 + 12.3972i −1.29027 + 1.53768i
\(66\) 0 0
\(67\) 5.85364 1.03215i 0.715135 0.126098i 0.195770 0.980650i \(-0.437279\pi\)
0.519365 + 0.854552i \(0.326168\pi\)
\(68\) 0 0
\(69\) −5.69179 + 10.5839i −0.685212 + 1.27415i
\(70\) 0 0
\(71\) −1.36269 2.36024i −0.161721 0.280109i 0.773765 0.633473i \(-0.218371\pi\)
−0.935486 + 0.353364i \(0.885038\pi\)
\(72\) 0 0
\(73\) −1.58277 + 2.74144i −0.185249 + 0.320861i −0.943660 0.330915i \(-0.892643\pi\)
0.758411 + 0.651776i \(0.225976\pi\)
\(74\) 0 0
\(75\) 0.450026 + 0.148574i 0.0519645 + 0.0171559i
\(76\) 0 0
\(77\) 0.669113 1.83837i 0.0762525 0.209502i
\(78\) 0 0
\(79\) 9.41150 + 1.65950i 1.05888 + 0.186709i 0.675858 0.737032i \(-0.263773\pi\)
0.383019 + 0.923741i \(0.374884\pi\)
\(80\) 0 0
\(81\) 7.54103 + 4.91252i 0.837892 + 0.545836i
\(82\) 0 0
\(83\) −0.731691 + 4.14963i −0.0803135 + 0.455481i 0.917956 + 0.396681i \(0.129838\pi\)
−0.998270 + 0.0587991i \(0.981273\pi\)
\(84\) 0 0
\(85\) 3.70095 + 1.34704i 0.401424 + 0.146106i
\(86\) 0 0
\(87\) −3.50301 + 10.6105i −0.375562 + 1.13756i
\(88\) 0 0
\(89\) −5.83560 3.36919i −0.618573 0.357133i 0.157740 0.987481i \(-0.449579\pi\)
−0.776313 + 0.630348i \(0.782912\pi\)
\(90\) 0 0
\(91\) 10.5397 6.08507i 1.10486 0.637889i
\(92\) 0 0
\(93\) 6.98753 + 3.75775i 0.724573 + 0.389660i
\(94\) 0 0
\(95\) −1.81551 10.2963i −0.186267 1.05638i
\(96\) 0 0
\(97\) −3.21229 2.69543i −0.326159 0.273680i 0.464974 0.885324i \(-0.346064\pi\)
−0.791133 + 0.611645i \(0.790508\pi\)
\(98\) 0 0
\(99\) 1.87374 + 2.83530i 0.188318 + 0.284959i
\(100\) 0 0
\(101\) 1.01338 + 2.78424i 0.100835 + 0.277042i 0.979844 0.199763i \(-0.0640171\pi\)
−0.879009 + 0.476805i \(0.841795\pi\)
\(102\) 0 0
\(103\) −8.21708 9.79274i −0.809653 0.964907i 0.190205 0.981744i \(-0.439085\pi\)
−0.999858 + 0.0168372i \(0.994640\pi\)
\(104\) 0 0
\(105\) −5.39286 4.25451i −0.526289 0.415198i
\(106\) 0 0
\(107\) −11.4207 −1.10408 −0.552038 0.833819i \(-0.686150\pi\)
−0.552038 + 0.833819i \(0.686150\pi\)
\(108\) 0 0
\(109\) 18.0047 1.72454 0.862269 0.506451i \(-0.169043\pi\)
0.862269 + 0.506451i \(0.169043\pi\)
\(110\) 0 0
\(111\) 4.73918 1.88878i 0.449823 0.179275i
\(112\) 0 0
\(113\) 7.65099 + 9.11809i 0.719745 + 0.857758i 0.994606 0.103726i \(-0.0330764\pi\)
−0.274861 + 0.961484i \(0.588632\pi\)
\(114\) 0 0
\(115\) 5.44944 + 14.9722i 0.508163 + 1.39617i
\(116\) 0 0
\(117\) −2.40827 + 21.0039i −0.222645 + 1.94181i
\(118\) 0 0
\(119\) −2.26886 1.90380i −0.207986 0.174521i
\(120\) 0 0
\(121\) −1.68728 9.56907i −0.153390 0.869915i
\(122\) 0 0
\(123\) −0.379318 12.5620i −0.0342020 1.13268i
\(124\) 0 0
\(125\) −9.39970 + 5.42692i −0.840734 + 0.485398i
\(126\) 0 0
\(127\) 0.853895 + 0.492997i 0.0757710 + 0.0437464i 0.537407 0.843323i \(-0.319404\pi\)
−0.461636 + 0.887070i \(0.652737\pi\)
\(128\) 0 0
\(129\) −0.605674 0.679088i −0.0533267 0.0597904i
\(130\) 0 0
\(131\) 8.93676 + 3.25271i 0.780808 + 0.284191i 0.701510 0.712660i \(-0.252510\pi\)
0.0792985 + 0.996851i \(0.474732\pi\)
\(132\) 0 0
\(133\) −1.36529 + 7.74297i −0.118386 + 0.671400i
\(134\) 0 0
\(135\) 11.5158 3.12633i 0.991122 0.269072i
\(136\) 0 0
\(137\) 21.5074 + 3.79234i 1.83750 + 0.324001i 0.981277 0.192601i \(-0.0616924\pi\)
0.856225 + 0.516603i \(0.172804\pi\)
\(138\) 0 0
\(139\) −6.57836 + 18.0739i −0.557969 + 1.53301i 0.264609 + 0.964356i \(0.414757\pi\)
−0.822578 + 0.568652i \(0.807465\pi\)
\(140\) 0 0
\(141\) −3.36237 16.1942i −0.283163 1.36380i
\(142\) 0 0
\(143\) −3.99163 + 6.91371i −0.333797 + 0.578153i
\(144\) 0 0
\(145\) 7.40737 + 12.8299i 0.615149 + 1.06547i
\(146\) 0 0
\(147\) −3.65966 5.91867i −0.301844 0.488164i
\(148\) 0 0
\(149\) 2.02217 0.356564i 0.165663 0.0292108i −0.0902014 0.995924i \(-0.528751\pi\)
0.255864 + 0.966713i \(0.417640\pi\)
\(150\) 0 0
\(151\) −6.39929 + 7.62638i −0.520767 + 0.620626i −0.960762 0.277374i \(-0.910536\pi\)
0.439995 + 0.898000i \(0.354980\pi\)
\(152\) 0 0
\(153\) 5.00380 1.19753i 0.404533 0.0968146i
\(154\) 0 0
\(155\) 9.88472 3.59774i 0.793960 0.288978i
\(156\) 0 0
\(157\) 7.86613 6.60047i 0.627785 0.526775i −0.272455 0.962169i \(-0.587835\pi\)
0.900240 + 0.435394i \(0.143391\pi\)
\(158\) 0 0
\(159\) −14.6943 2.13592i −1.16533 0.169389i
\(160\) 0 0
\(161\) 11.9819i 0.944310i
\(162\) 0 0
\(163\) 22.6034i 1.77044i −0.465176 0.885218i \(-0.654009\pi\)
0.465176 0.885218i \(-0.345991\pi\)
\(164\) 0 0
\(165\) 4.45904 + 0.648154i 0.347136 + 0.0504587i
\(166\) 0 0
\(167\) −15.1820 + 12.7392i −1.17482 + 0.985787i −0.174816 + 0.984601i \(0.555933\pi\)
−0.999999 + 0.00118593i \(0.999623\pi\)
\(168\) 0 0
\(169\) −34.4514 + 12.5393i −2.65011 + 0.964561i
\(170\) 0 0
\(171\) −9.39466 9.91406i −0.718427 0.758147i
\(172\) 0 0
\(173\) −6.13700 + 7.31379i −0.466587 + 0.556057i −0.947103 0.320929i \(-0.896005\pi\)
0.480516 + 0.876986i \(0.340449\pi\)
\(174\) 0 0
\(175\) −0.465345 + 0.0820529i −0.0351768 + 0.00620262i
\(176\) 0 0
\(177\) −13.1154 21.2112i −0.985814 1.59433i
\(178\) 0 0
\(179\) 2.34317 + 4.05850i 0.175137 + 0.303346i 0.940209 0.340599i \(-0.110630\pi\)
−0.765072 + 0.643945i \(0.777296\pi\)
\(180\) 0 0
\(181\) 5.90627 10.2300i 0.439009 0.760387i −0.558604 0.829435i \(-0.688663\pi\)
0.997613 + 0.0690479i \(0.0219961\pi\)
\(182\) 0 0
\(183\) 0.100861 + 0.485776i 0.00745584 + 0.0359096i
\(184\) 0 0
\(185\) 2.31345 6.35615i 0.170088 0.467313i
\(186\) 0 0
\(187\) 1.91333 + 0.337372i 0.139917 + 0.0246711i
\(188\) 0 0
\(189\) −8.94191 0.752655i −0.650428 0.0547476i
\(190\) 0 0
\(191\) −2.84710 + 16.1467i −0.206009 + 1.16833i 0.689835 + 0.723966i \(0.257683\pi\)
−0.895844 + 0.444368i \(0.853428\pi\)
\(192\) 0 0
\(193\) −1.21489 0.442183i −0.0874495 0.0318290i 0.297925 0.954589i \(-0.403705\pi\)
−0.385374 + 0.922760i \(0.625928\pi\)
\(194\) 0 0
\(195\) 18.6575 + 20.9189i 1.33609 + 1.49804i
\(196\) 0 0
\(197\) −17.7961 10.2746i −1.26792 0.732035i −0.293327 0.956012i \(-0.594763\pi\)
−0.974594 + 0.223977i \(0.928096\pi\)
\(198\) 0 0
\(199\) −6.12484 + 3.53618i −0.434179 + 0.250673i −0.701125 0.713038i \(-0.747319\pi\)
0.266947 + 0.963711i \(0.413985\pi\)
\(200\) 0 0
\(201\) −0.310728 10.2905i −0.0219171 0.725837i
\(202\) 0 0
\(203\) −1.93460 10.9717i −0.135782 0.770060i
\(204\) 0 0
\(205\) −12.7645 10.7107i −0.891515 0.748070i
\(206\) 0 0
\(207\) 16.7231 + 12.3929i 1.16233 + 0.861367i
\(208\) 0 0
\(209\) −1.76398 4.84648i −0.122017 0.335238i
\(210\) 0 0
\(211\) −8.31514 9.90960i −0.572438 0.682205i 0.399692 0.916650i \(-0.369117\pi\)
−0.972129 + 0.234445i \(0.924673\pi\)
\(212\) 0 0
\(213\) −4.38506 + 1.74765i −0.300459 + 0.119747i
\(214\) 0 0
\(215\) −1.20645 −0.0822792
\(216\) 0 0
\(217\) −7.91054 −0.537002
\(218\) 0 0
\(219\) 4.30458 + 3.39595i 0.290877 + 0.229477i
\(220\) 0 0
\(221\) 7.76881 + 9.25851i 0.522587 + 0.622795i
\(222\) 0 0
\(223\) −3.39317 9.32266i −0.227224 0.624292i 0.772722 0.634745i \(-0.218895\pi\)
−0.999945 + 0.0104532i \(0.996673\pi\)
\(224\) 0 0
\(225\) 0.366785 0.734345i 0.0244523 0.0489563i
\(226\) 0 0
\(227\) −6.37742 5.35129i −0.423284 0.355178i 0.406127 0.913817i \(-0.366879\pi\)
−0.829411 + 0.558639i \(0.811324\pi\)
\(228\) 0 0
\(229\) −2.18404 12.3863i −0.144325 0.818508i −0.967907 0.251310i \(-0.919139\pi\)
0.823581 0.567198i \(-0.191973\pi\)
\(230\) 0 0
\(231\) −2.98433 1.60491i −0.196355 0.105596i
\(232\) 0 0
\(233\) 17.7507 10.2484i 1.16289 0.671393i 0.210893 0.977509i \(-0.432363\pi\)
0.951994 + 0.306116i \(0.0990296\pi\)
\(234\) 0 0
\(235\) −18.9911 10.9645i −1.23884 0.715245i
\(236\) 0 0
\(237\) 5.18931 15.7182i 0.337082 1.02101i
\(238\) 0 0
\(239\) 9.90855 + 3.60642i 0.640931 + 0.233280i 0.641982 0.766720i \(-0.278112\pi\)
−0.00105129 + 0.999999i \(0.500335\pi\)
\(240\) 0 0
\(241\) −0.569580 + 3.23025i −0.0366898 + 0.208078i −0.997642 0.0686372i \(-0.978135\pi\)
0.960952 + 0.276716i \(0.0892460\pi\)
\(242\) 0 0
\(243\) 10.2991 11.7017i 0.660686 0.750662i
\(244\) 0 0
\(245\) −9.08604 1.60211i −0.580486 0.102355i
\(246\) 0 0
\(247\) 10.9734 30.1491i 0.698219 1.91834i
\(248\) 0 0
\(249\) 6.93031 + 2.28802i 0.439191 + 0.144997i
\(250\) 0 0
\(251\) −13.5827 + 23.5259i −0.857333 + 1.48494i 0.0171305 + 0.999853i \(0.494547\pi\)
−0.874464 + 0.485091i \(0.838786\pi\)
\(252\) 0 0
\(253\) 3.92991 + 6.80680i 0.247071 + 0.427940i
\(254\) 0 0
\(255\) 3.23095 6.00795i 0.202330 0.376233i
\(256\) 0 0
\(257\) 17.8463 3.14678i 1.11322 0.196291i 0.413358 0.910569i \(-0.364356\pi\)
0.699862 + 0.714278i \(0.253245\pi\)
\(258\) 0 0
\(259\) −3.26966 + 3.89663i −0.203167 + 0.242125i
\(260\) 0 0
\(261\) 17.3140 + 8.64788i 1.07171 + 0.535290i
\(262\) 0 0
\(263\) 22.9414 8.34997i 1.41463 0.514881i 0.482141 0.876093i \(-0.339859\pi\)
0.932484 + 0.361212i \(0.117637\pi\)
\(264\) 0 0
\(265\) −15.0812 + 12.6546i −0.926430 + 0.777367i
\(266\) 0 0
\(267\) −7.22884 + 9.16302i −0.442398 + 0.560767i
\(268\) 0 0
\(269\) 17.9539i 1.09467i −0.836913 0.547336i \(-0.815642\pi\)
0.836913 0.547336i \(-0.184358\pi\)
\(270\) 0 0
\(271\) 12.9608i 0.787315i 0.919257 + 0.393658i \(0.128790\pi\)
−0.919257 + 0.393658i \(0.871210\pi\)
\(272\) 0 0
\(273\) −7.80411 19.5814i −0.472326 1.18512i
\(274\) 0 0
\(275\) 0.237445 0.199240i 0.0143185 0.0120146i
\(276\) 0 0
\(277\) 12.5757 4.57718i 0.755600 0.275016i 0.0646398 0.997909i \(-0.479410\pi\)
0.690960 + 0.722893i \(0.257188\pi\)
\(278\) 0 0
\(279\) 8.18185 11.0407i 0.489835 0.660987i
\(280\) 0 0
\(281\) −12.6425 + 15.0667i −0.754188 + 0.898806i −0.997466 0.0711505i \(-0.977333\pi\)
0.243278 + 0.969957i \(0.421777\pi\)
\(282\) 0 0
\(283\) −32.5889 + 5.74630i −1.93721 + 0.341582i −0.999975 0.00711797i \(-0.997734\pi\)
−0.937234 + 0.348700i \(0.886623\pi\)
\(284\) 0 0
\(285\) −18.1005 + 0.546557i −1.07218 + 0.0323752i
\(286\) 0 0
\(287\) 6.26540 + 10.8520i 0.369835 + 0.640573i
\(288\) 0 0
\(289\) −7.02933 + 12.1752i −0.413490 + 0.716185i
\(290\) 0 0
\(291\) −5.42041 + 4.83443i −0.317750 + 0.283399i
\(292\) 0 0
\(293\) 2.70081 7.42041i 0.157783 0.433505i −0.835461 0.549550i \(-0.814799\pi\)
0.993244 + 0.116045i \(0.0370216\pi\)
\(294\) 0 0
\(295\) −32.5623 5.74161i −1.89585 0.334289i
\(296\) 0 0
\(297\) 5.32665 2.50525i 0.309084 0.145369i
\(298\) 0 0
\(299\) −8.49044 + 48.1517i −0.491015 + 2.78468i
\(300\) 0 0
\(301\) 0.852555 + 0.310305i 0.0491405 + 0.0178857i
\(302\) 0 0
\(303\) 5.02477 1.04328i 0.288665 0.0599351i
\(304\) 0 0
\(305\) 0.569672 + 0.328901i 0.0326193 + 0.0188328i
\(306\) 0 0
\(307\) 4.34321 2.50755i 0.247880 0.143114i −0.370913 0.928668i \(-0.620955\pi\)
0.618793 + 0.785554i \(0.287622\pi\)
\(308\) 0 0
\(309\) −18.8324 + 11.6445i −1.07134 + 0.662435i
\(310\) 0 0
\(311\) 1.21509 + 6.89111i 0.0689014 + 0.390759i 0.999683 + 0.0251831i \(0.00801689\pi\)
−0.930781 + 0.365576i \(0.880872\pi\)
\(312\) 0 0
\(313\) 7.39378 + 6.20412i 0.417921 + 0.350678i 0.827372 0.561655i \(-0.189835\pi\)
−0.409450 + 0.912332i \(0.634280\pi\)
\(314\) 0 0
\(315\) −8.63601 + 8.18356i −0.486584 + 0.461092i
\(316\) 0 0
\(317\) 0.807269 + 2.21795i 0.0453408 + 0.124573i 0.960296 0.278982i \(-0.0899969\pi\)
−0.914956 + 0.403554i \(0.867775\pi\)
\(318\) 0 0
\(319\) 4.69758 + 5.59835i 0.263014 + 0.313448i
\(320\) 0 0
\(321\) −2.84544 + 19.5754i −0.158817 + 1.09259i
\(322\) 0 0
\(323\) −7.80813 −0.434456
\(324\) 0 0
\(325\) 1.92822 0.106958
\(326\) 0 0
\(327\) 4.48584 30.8607i 0.248067 1.70660i
\(328\) 0 0
\(329\) 10.6002 + 12.6328i 0.584407 + 0.696469i
\(330\) 0 0
\(331\) −2.95113 8.10818i −0.162209 0.445666i 0.831785 0.555098i \(-0.187319\pi\)
−0.993994 + 0.109432i \(0.965097\pi\)
\(332\) 0 0
\(333\) −2.05668 8.59371i −0.112706 0.470933i
\(334\) 0 0
\(335\) −10.4564 8.77397i −0.571294 0.479373i
\(336\) 0 0
\(337\) 0.218162 + 1.23726i 0.0118840 + 0.0673977i 0.990173 0.139848i \(-0.0446613\pi\)
−0.978289 + 0.207245i \(0.933550\pi\)
\(338\) 0 0
\(339\) 17.5350 10.8423i 0.952370 0.588874i
\(340\) 0 0
\(341\) 4.49388 2.59454i 0.243357 0.140502i
\(342\) 0 0
\(343\) 16.4778 + 9.51348i 0.889719 + 0.513680i
\(344\) 0 0
\(345\) 27.0206 5.61024i 1.45474 0.302045i
\(346\) 0 0
\(347\) −19.5931 7.13131i −1.05181 0.382829i −0.242466 0.970160i \(-0.577956\pi\)
−0.809347 + 0.587331i \(0.800179\pi\)
\(348\) 0 0
\(349\) −3.21404 + 18.2277i −0.172043 + 0.975707i 0.769458 + 0.638698i \(0.220526\pi\)
−0.941501 + 0.337009i \(0.890585\pi\)
\(350\) 0 0
\(351\) 35.4014 + 9.36094i 1.88959 + 0.499650i
\(352\) 0 0
\(353\) 10.6452 + 1.87704i 0.566588 + 0.0999048i 0.449602 0.893229i \(-0.351566\pi\)
0.116986 + 0.993134i \(0.462677\pi\)
\(354\) 0 0
\(355\) −2.14058 + 5.88120i −0.113610 + 0.312142i
\(356\) 0 0
\(357\) −3.82847 + 3.41459i −0.202624 + 0.180719i
\(358\) 0 0
\(359\) 0.479687 0.830842i 0.0253169 0.0438502i −0.853089 0.521765i \(-0.825274\pi\)
0.878406 + 0.477915i \(0.158607\pi\)
\(360\) 0 0
\(361\) 0.863791 + 1.49613i 0.0454627 + 0.0787437i
\(362\) 0 0
\(363\) −16.8221 + 0.507954i −0.882933 + 0.0266607i
\(364\) 0 0
\(365\) 7.15902 1.26233i 0.374720 0.0660733i
\(366\) 0 0
\(367\) 12.8294 15.2895i 0.669688 0.798103i −0.319054 0.947737i \(-0.603365\pi\)
0.988741 + 0.149634i \(0.0478095\pi\)
\(368\) 0 0
\(369\) −21.6263 2.47964i −1.12582 0.129085i
\(370\) 0 0
\(371\) 13.9122 5.06361i 0.722283 0.262890i
\(372\) 0 0
\(373\) 18.8836 15.8452i 0.977754 0.820433i −0.00599498 0.999982i \(-0.501908\pi\)
0.983749 + 0.179549i \(0.0574638\pi\)
\(374\) 0 0
\(375\) 6.96002 + 17.4635i 0.359414 + 0.901813i
\(376\) 0 0
\(377\) 45.4626i 2.34144i
\(378\) 0 0
\(379\) 8.36788i 0.429829i −0.976633 0.214915i \(-0.931053\pi\)
0.976633 0.214915i \(-0.0689473\pi\)
\(380\) 0 0
\(381\) 1.05776 1.34078i 0.0541908 0.0686902i
\(382\) 0 0
\(383\) 0.716215 0.600976i 0.0365969 0.0307084i −0.624306 0.781180i \(-0.714618\pi\)
0.660903 + 0.750472i \(0.270174\pi\)
\(384\) 0 0
\(385\) −4.22171 + 1.53658i −0.215158 + 0.0783112i
\(386\) 0 0
\(387\) −1.31489 + 0.868955i −0.0668394 + 0.0441715i
\(388\) 0 0
\(389\) −8.06355 + 9.60976i −0.408838 + 0.487234i −0.930694 0.365800i \(-0.880796\pi\)
0.521855 + 0.853034i \(0.325240\pi\)
\(390\) 0 0
\(391\) 11.7185 2.06628i 0.592627 0.104496i
\(392\) 0 0
\(393\) 7.80185 14.5075i 0.393551 0.731808i
\(394\) 0 0
\(395\) −10.9732 19.0061i −0.552120 0.956299i
\(396\) 0 0
\(397\) −10.5305 + 18.2393i −0.528509 + 0.915404i 0.470939 + 0.882166i \(0.343915\pi\)
−0.999447 + 0.0332380i \(0.989418\pi\)
\(398\) 0 0
\(399\) 12.9316 + 4.26931i 0.647388 + 0.213733i
\(400\) 0 0
\(401\) −1.15588 + 3.17576i −0.0577220 + 0.158590i −0.965202 0.261505i \(-0.915781\pi\)
0.907480 + 0.420095i \(0.138003\pi\)
\(402\) 0 0
\(403\) 31.7899 + 5.60543i 1.58357 + 0.279226i
\(404\) 0 0
\(405\) −2.48950 20.5174i −0.123704 1.01952i
\(406\) 0 0
\(407\) 0.579416 3.28603i 0.0287206 0.162883i
\(408\) 0 0
\(409\) −24.3709 8.87029i −1.20506 0.438607i −0.340075 0.940398i \(-0.610452\pi\)
−0.864989 + 0.501791i \(0.832675\pi\)
\(410\) 0 0
\(411\) 11.8587 35.9197i 0.584949 1.77179i
\(412\) 0 0
\(413\) 21.5338 + 12.4326i 1.05961 + 0.611767i
\(414\) 0 0
\(415\) 8.37997 4.83818i 0.411356 0.237497i
\(416\) 0 0
\(417\) 29.3404 + 15.7786i 1.43680 + 0.772683i
\(418\) 0 0
\(419\) 5.30706 + 30.0979i 0.259267 + 1.47038i 0.784877 + 0.619651i \(0.212726\pi\)
−0.525610 + 0.850725i \(0.676163\pi\)
\(420\) 0 0
\(421\) 3.65610 + 3.06783i 0.178187 + 0.149517i 0.727519 0.686087i \(-0.240673\pi\)
−0.549332 + 0.835604i \(0.685118\pi\)
\(422\) 0 0
\(423\) −28.5952 + 1.72848i −1.39035 + 0.0840414i
\(424\) 0 0
\(425\) −0.160497 0.440962i −0.00778524 0.0213898i
\(426\) 0 0
\(427\) −0.317972 0.378945i −0.0153878 0.0183384i
\(428\) 0 0
\(429\) 10.8559 + 8.56435i 0.524125 + 0.413491i
\(430\) 0 0
\(431\) 32.3238 1.55698 0.778491 0.627656i \(-0.215985\pi\)
0.778491 + 0.627656i \(0.215985\pi\)
\(432\) 0 0
\(433\) 14.6596 0.704497 0.352249 0.935907i \(-0.385417\pi\)
0.352249 + 0.935907i \(0.385417\pi\)
\(434\) 0 0
\(435\) 23.8365 9.49996i 1.14287 0.455488i
\(436\) 0 0
\(437\) −20.3043 24.1977i −0.971285 1.15753i
\(438\) 0 0
\(439\) 2.75846 + 7.57882i 0.131654 + 0.361717i 0.987951 0.154767i \(-0.0494627\pi\)
−0.856297 + 0.516484i \(0.827240\pi\)
\(440\) 0 0
\(441\) −11.0566 + 4.79818i −0.526506 + 0.228485i
\(442\) 0 0
\(443\) −17.3346 14.5455i −0.823593 0.691076i 0.130218 0.991485i \(-0.458432\pi\)
−0.953810 + 0.300409i \(0.902877\pi\)
\(444\) 0 0
\(445\) 2.68707 + 15.2392i 0.127380 + 0.722405i
\(446\) 0 0
\(447\) −0.107343 3.55492i −0.00507715 0.168142i
\(448\) 0 0
\(449\) 5.54560 3.20175i 0.261713 0.151100i −0.363403 0.931632i \(-0.618385\pi\)
0.625116 + 0.780532i \(0.285052\pi\)
\(450\) 0 0
\(451\) −7.11860 4.10992i −0.335202 0.193529i
\(452\) 0 0
\(453\) 11.4775 + 12.8687i 0.539261 + 0.604625i
\(454\) 0 0
\(455\) −26.2625 9.55876i −1.23120 0.448122i
\(456\) 0 0
\(457\) 1.41804 8.04210i 0.0663331 0.376194i −0.933511 0.358548i \(-0.883272\pi\)
0.999844 0.0176455i \(-0.00561702\pi\)
\(458\) 0 0
\(459\) −0.805924 8.87507i −0.0376173 0.414253i
\(460\) 0 0
\(461\) 21.5599 + 3.80159i 1.00414 + 0.177058i 0.651459 0.758684i \(-0.274157\pi\)
0.352686 + 0.935742i \(0.385269\pi\)
\(462\) 0 0
\(463\) −2.20720 + 6.06423i −0.102577 + 0.281829i −0.980356 0.197238i \(-0.936803\pi\)
0.877778 + 0.479067i \(0.159025\pi\)
\(464\) 0 0
\(465\) −3.70391 17.8392i −0.171765 0.827271i
\(466\) 0 0
\(467\) 12.0625 20.8929i 0.558188 0.966810i −0.439460 0.898262i \(-0.644830\pi\)
0.997648 0.0685478i \(-0.0218366\pi\)
\(468\) 0 0
\(469\) 5.13246 + 8.88969i 0.236995 + 0.410488i
\(470\) 0 0
\(471\) −9.35362 15.1273i −0.430992 0.697031i
\(472\) 0 0
\(473\) −0.586102 + 0.103346i −0.0269490 + 0.00475183i
\(474\) 0 0
\(475\) −0.800726 + 0.954268i −0.0367398 + 0.0437848i
\(476\) 0 0
\(477\) −7.32209 + 24.6543i −0.335256 + 1.12884i
\(478\) 0 0
\(479\) 20.6931 7.53168i 0.945493 0.344131i 0.177160 0.984182i \(-0.443309\pi\)
0.768333 + 0.640051i \(0.221087\pi\)
\(480\) 0 0
\(481\) 15.9009 13.3424i 0.725019 0.608363i
\(482\) 0 0
\(483\) −20.5375 2.98528i −0.934489 0.135835i
\(484\) 0 0
\(485\) 9.62976i 0.437265i
\(486\) 0 0
\(487\) 2.57215i 0.116555i 0.998300 + 0.0582777i \(0.0185609\pi\)
−0.998300 + 0.0582777i \(0.981439\pi\)
\(488\) 0 0
\(489\) −38.7431 5.63160i −1.75202 0.254670i
\(490\) 0 0
\(491\) 24.4783 20.5398i 1.10469 0.926946i 0.106960 0.994263i \(-0.465888\pi\)
0.997732 + 0.0673168i \(0.0214438\pi\)
\(492\) 0 0
\(493\) 10.3968 3.78412i 0.468247 0.170428i
\(494\) 0 0
\(495\) 2.22192 7.48147i 0.0998680 0.336267i
\(496\) 0 0
\(497\) 3.02535 3.60547i 0.135705 0.161727i
\(498\) 0 0
\(499\) −25.8045 + 4.55003i −1.15517 + 0.203687i −0.718231 0.695805i \(-0.755048\pi\)
−0.436937 + 0.899492i \(0.643937\pi\)
\(500\) 0 0
\(501\) 18.0529 + 29.1964i 0.806543 + 1.30440i
\(502\) 0 0
\(503\) 13.4076 + 23.2226i 0.597814 + 1.03544i 0.993143 + 0.116905i \(0.0372972\pi\)
−0.395329 + 0.918540i \(0.629369\pi\)
\(504\) 0 0
\(505\) 3.40208 5.89258i 0.151391 0.262216i
\(506\) 0 0
\(507\) 12.9093 + 62.1752i 0.573323 + 2.76130i
\(508\) 0 0
\(509\) −3.39845 + 9.33715i −0.150633 + 0.413862i −0.991942 0.126693i \(-0.959564\pi\)
0.841308 + 0.540555i \(0.181786\pi\)
\(510\) 0 0
\(511\) −5.38370 0.949292i −0.238161 0.0419942i
\(512\) 0 0
\(513\) −19.3337 + 13.6327i −0.853605 + 0.601900i
\(514\) 0 0
\(515\) −5.09771 + 28.9105i −0.224632 + 1.27395i
\(516\) 0 0
\(517\) −10.1652 3.69984i −0.447066 0.162719i
\(518\) 0 0
\(519\) 11.0071 + 12.3413i 0.483158 + 0.541721i
\(520\) 0 0
\(521\) −9.45901 5.46116i −0.414407 0.239258i 0.278275 0.960502i \(-0.410237\pi\)
−0.692681 + 0.721244i \(0.743571\pi\)
\(522\) 0 0
\(523\) −5.09476 + 2.94146i −0.222778 + 0.128621i −0.607236 0.794521i \(-0.707722\pi\)
0.384458 + 0.923143i \(0.374388\pi\)
\(524\) 0 0
\(525\) 0.0247019 + 0.818062i 0.00107808 + 0.0357032i
\(526\) 0 0
\(527\) −1.36417 7.73657i −0.0594240 0.337010i
\(528\) 0 0
\(529\) 19.2571 + 16.1586i 0.837266 + 0.702550i
\(530\) 0 0
\(531\) −39.6244 + 17.1956i −1.71955 + 0.746224i
\(532\) 0 0
\(533\) −17.4889 48.0504i −0.757529 2.08129i
\(534\) 0 0
\(535\) 16.8583 + 20.0909i 0.728846 + 0.868605i
\(536\) 0 0
\(537\) 7.54021 3.00512i 0.325384 0.129681i
\(538\) 0 0
\(539\) −4.55130 −0.196038
\(540\) 0 0
\(541\) −31.3090 −1.34608 −0.673039 0.739607i \(-0.735011\pi\)
−0.673039 + 0.739607i \(0.735011\pi\)
\(542\) 0 0
\(543\) −16.0630 12.6723i −0.689329 0.543822i
\(544\) 0 0
\(545\) −26.5771 31.6734i −1.13844 1.35674i
\(546\) 0 0
\(547\) 1.77952 + 4.88920i 0.0760870 + 0.209047i 0.971905 0.235374i \(-0.0756315\pi\)
−0.895818 + 0.444421i \(0.853409\pi\)
\(548\) 0 0
\(549\) 0.857767 0.0518489i 0.0366086 0.00221286i
\(550\) 0 0
\(551\) −22.4993 18.8791i −0.958500 0.804277i
\(552\) 0 0
\(553\) 2.86589 + 16.2533i 0.121870 + 0.691159i
\(554\) 0 0
\(555\) −10.3183 5.54896i −0.437987 0.235540i
\(556\) 0 0
\(557\) −24.3579 + 14.0631i −1.03208 + 0.595871i −0.917580 0.397552i \(-0.869860\pi\)
−0.114499 + 0.993423i \(0.536526\pi\)
\(558\) 0 0
\(559\) −3.20627 1.85114i −0.135611 0.0782949i
\(560\) 0 0
\(561\) 1.05497 3.19547i 0.0445410 0.134913i
\(562\) 0 0
\(563\) 25.1504 + 9.15398i 1.05996 + 0.385794i 0.812414 0.583081i \(-0.198153\pi\)
0.247547 + 0.968876i \(0.420375\pi\)
\(564\) 0 0
\(565\) 4.74651 26.9188i 0.199687 1.13248i
\(566\) 0 0
\(567\) −3.51794 + 15.1393i −0.147740 + 0.635789i
\(568\) 0 0
\(569\) 2.77648 + 0.489568i 0.116396 + 0.0205238i 0.231543 0.972825i \(-0.425623\pi\)
−0.115147 + 0.993348i \(0.536734\pi\)
\(570\) 0 0
\(571\) 9.98909 27.4448i 0.418031 1.14853i −0.534787 0.844987i \(-0.679608\pi\)
0.952818 0.303543i \(-0.0981695\pi\)
\(572\) 0 0
\(573\) 26.9667 + 8.90296i 1.12655 + 0.371926i
\(574\) 0 0
\(575\) 0.949200 1.64406i 0.0395844 0.0685622i
\(576\) 0 0
\(577\) −19.3591 33.5310i −0.805930 1.39591i −0.915661 0.401951i \(-0.868332\pi\)
0.109731 0.993961i \(-0.465001\pi\)
\(578\) 0 0
\(579\) −1.06060 + 1.97219i −0.0440772 + 0.0819616i
\(580\) 0 0
\(581\) −7.16622 + 1.26360i −0.297305 + 0.0524229i
\(582\) 0 0
\(583\) −6.24254 + 7.43957i −0.258539 + 0.308115i
\(584\) 0 0
\(585\) 40.5043 26.7677i 1.67465 1.10671i
\(586\) 0 0
\(587\) −10.2093 + 3.71586i −0.421381 + 0.153370i −0.544003 0.839083i \(-0.683092\pi\)
0.122622 + 0.992453i \(0.460870\pi\)
\(588\) 0 0
\(589\) −15.9754 + 13.4050i −0.658256 + 0.552343i
\(590\) 0 0
\(591\) −22.0449 + 27.9433i −0.906807 + 1.14944i
\(592\) 0 0
\(593\) 10.1060i 0.415003i −0.978235 0.207501i \(-0.933467\pi\)
0.978235 0.207501i \(-0.0665332\pi\)
\(594\) 0 0
\(595\) 6.80156i 0.278837i
\(596\) 0 0
\(597\) 4.53515 + 11.3792i 0.185611 + 0.465722i
\(598\) 0 0
\(599\) −0.142727 + 0.119762i −0.00583168 + 0.00489336i −0.645699 0.763592i \(-0.723434\pi\)
0.639867 + 0.768486i \(0.278989\pi\)
\(600\) 0 0
\(601\) 28.1284 10.2379i 1.14738 0.417612i 0.302806 0.953052i \(-0.402076\pi\)
0.844573 + 0.535440i \(0.179854\pi\)
\(602\) 0 0
\(603\) −17.7157 2.03126i −0.721441 0.0827194i
\(604\) 0 0
\(605\) −14.3430 + 17.0933i −0.583126 + 0.694942i
\(606\) 0 0
\(607\) 16.7567 2.95465i 0.680132 0.119926i 0.177099 0.984193i \(-0.443329\pi\)
0.503033 + 0.864267i \(0.332217\pi\)
\(608\) 0 0
\(609\) −19.2879 + 0.582409i −0.781584 + 0.0236004i
\(610\) 0 0
\(611\) −33.6472 58.2786i −1.36122 2.35770i
\(612\) 0 0
\(613\) 14.6554 25.3840i 0.591928 1.02525i −0.402045 0.915620i \(-0.631700\pi\)
0.993973 0.109629i \(-0.0349662\pi\)
\(614\) 0 0
\(615\) −21.5389 + 19.2104i −0.868530 + 0.774636i
\(616\) 0 0
\(617\) −6.62643 + 18.2060i −0.266770 + 0.732945i 0.731901 + 0.681411i \(0.238633\pi\)
−0.998671 + 0.0515338i \(0.983589\pi\)
\(618\) 0 0
\(619\) −0.171532 0.0302457i −0.00689445 0.00121568i 0.170200 0.985410i \(-0.445559\pi\)
−0.177094 + 0.984194i \(0.556670\pi\)
\(620\) 0 0
\(621\) 25.4084 25.5763i 1.01961 1.02634i
\(622\) 0 0
\(623\) 2.02072 11.4601i 0.0809586 0.459139i
\(624\) 0 0
\(625\) 24.7075 + 8.99281i 0.988302 + 0.359712i
\(626\) 0 0
\(627\) −8.74654 + 1.81603i −0.349303 + 0.0725252i
\(628\) 0 0
\(629\) −4.37479 2.52579i −0.174434 0.100710i
\(630\) 0 0
\(631\) −19.9875 + 11.5398i −0.795691 + 0.459392i −0.841962 0.539537i \(-0.818599\pi\)
0.0462714 + 0.998929i \(0.485266\pi\)
\(632\) 0 0
\(633\) −19.0571 + 11.7835i −0.757453 + 0.468352i
\(634\) 0 0
\(635\) −0.393186 2.22987i −0.0156031 0.0884897i
\(636\) 0 0
\(637\) −21.6889 18.1991i −0.859344 0.721075i
\(638\) 0 0
\(639\) 1.90300 + 7.95157i 0.0752816 + 0.314559i
\(640\) 0 0
\(641\) −10.1866 27.9876i −0.402348 1.10544i −0.961123 0.276122i \(-0.910951\pi\)
0.558775 0.829320i \(-0.311272\pi\)
\(642\) 0 0
\(643\) 27.1310 + 32.3334i 1.06994 + 1.27511i 0.959647 + 0.281207i \(0.0907348\pi\)
0.110294 + 0.993899i \(0.464821\pi\)
\(644\) 0 0
\(645\) −0.300585 + 2.06790i −0.0118355 + 0.0814235i
\(646\) 0 0
\(647\) −22.3033 −0.876834 −0.438417 0.898772i \(-0.644461\pi\)
−0.438417 + 0.898772i \(0.644461\pi\)
\(648\) 0 0
\(649\) −16.3108 −0.640256
\(650\) 0 0
\(651\) −1.97090 + 13.5590i −0.0772455 + 0.531417i
\(652\) 0 0
\(653\) 12.2527 + 14.6022i 0.479487 + 0.571430i 0.950511 0.310690i \(-0.100560\pi\)
−0.471025 + 0.882120i \(0.656116\pi\)
\(654\) 0 0
\(655\) −7.46965 20.5227i −0.291863 0.801888i
\(656\) 0 0
\(657\) 6.89327 6.53212i 0.268932 0.254842i
\(658\) 0 0
\(659\) 1.06327 + 0.892192i 0.0414193 + 0.0347549i 0.663262 0.748387i \(-0.269171\pi\)
−0.621843 + 0.783142i \(0.713616\pi\)
\(660\) 0 0
\(661\) 6.42078 + 36.4141i 0.249739 + 1.41634i 0.809223 + 0.587502i \(0.199888\pi\)
−0.559484 + 0.828841i \(0.689000\pi\)
\(662\) 0 0
\(663\) 17.8050 11.0093i 0.691489 0.427565i
\(664\) 0 0
\(665\) 15.6365 9.02776i 0.606359 0.350082i
\(666\) 0 0
\(667\) 38.7629 + 22.3798i 1.50091 + 0.866548i
\(668\) 0 0
\(669\) −16.8248 + 3.49330i −0.650484 + 0.135059i
\(670\) 0 0
\(671\) 0.304925 + 0.110984i 0.0117715 + 0.00428447i
\(672\) 0 0
\(673\) 4.93462 27.9856i 0.190215 1.07877i −0.728854 0.684669i \(-0.759947\pi\)
0.919069 0.394096i \(-0.128942\pi\)
\(674\) 0 0
\(675\) −1.16731 0.811644i −0.0449298 0.0312402i
\(676\) 0 0
\(677\) 34.8917 + 6.15234i 1.34100 + 0.236454i 0.797683 0.603077i \(-0.206059\pi\)
0.543313 + 0.839530i \(0.317170\pi\)
\(678\) 0 0
\(679\) 2.47682 6.80500i 0.0950516 0.261152i
\(680\) 0 0
\(681\) −10.7612 + 9.59787i −0.412371 + 0.367791i
\(682\) 0 0
\(683\) 17.7063 30.6681i 0.677511 1.17348i −0.298217 0.954498i \(-0.596392\pi\)
0.975728 0.218986i \(-0.0702749\pi\)
\(684\) 0 0
\(685\) −25.0762 43.4332i −0.958111 1.65950i
\(686\) 0 0
\(687\) −21.7747 + 0.657500i −0.830756 + 0.0250852i
\(688\) 0 0
\(689\) −59.4967 + 10.4909i −2.26664 + 0.399670i
\(690\) 0 0
\(691\) 3.47685 4.14355i 0.132266 0.157628i −0.695847 0.718191i \(-0.744971\pi\)
0.828112 + 0.560563i \(0.189415\pi\)
\(692\) 0 0
\(693\) −3.49442 + 4.71540i −0.132742 + 0.179123i
\(694\) 0 0
\(695\) 41.5056 15.1068i 1.57440 0.573033i
\(696\) 0 0
\(697\) −9.53288 + 7.99904i −0.361084 + 0.302985i
\(698\) 0 0
\(699\) −13.1435 32.9787i −0.497134 1.24737i
\(700\) 0 0
\(701\) 35.4485i 1.33887i −0.742870 0.669436i \(-0.766536\pi\)
0.742870 0.669436i \(-0.233464\pi\)
\(702\) 0 0
\(703\) 13.4100i 0.505767i
\(704\) 0 0
\(705\) −23.5251 + 29.8196i −0.886008 + 1.12307i
\(706\) 0 0
\(707\) −3.91973 + 3.28904i −0.147417 + 0.123697i
\(708\) 0 0
\(709\) 17.5781 6.39792i 0.660161 0.240279i 0.00985524 0.999951i \(-0.496863\pi\)
0.650306 + 0.759672i \(0.274641\pi\)
\(710\) 0 0
\(711\) −25.6487 12.8108i −0.961901 0.480444i
\(712\) 0 0
\(713\) 20.4286 24.3458i 0.765055 0.911757i
\(714\) 0 0
\(715\) 18.0545 3.18350i 0.675201 0.119056i
\(716\) 0 0
\(717\) 8.65023 16.0851i 0.323049 0.600709i
\(718\) 0 0
\(719\) 17.9949 + 31.1681i 0.671097 + 1.16237i 0.977593 + 0.210503i \(0.0675101\pi\)
−0.306496 + 0.951872i \(0.599157\pi\)
\(720\) 0 0
\(721\) 11.0383 19.1189i 0.411087 0.712024i
\(722\) 0 0
\(723\) 5.39485 + 1.78109i 0.200637 + 0.0662395i
\(724\) 0 0
\(725\) 0.603717 1.65870i 0.0224215 0.0616026i
\(726\) 0 0
\(727\) −7.82609 1.37995i −0.290254 0.0511796i 0.0266254 0.999645i \(-0.491524\pi\)
−0.316879 + 0.948466i \(0.602635\pi\)
\(728\) 0 0
\(729\) −17.4911 20.5685i −0.647819 0.761795i
\(730\) 0 0
\(731\) −0.156458 + 0.887319i −0.00578682 + 0.0328187i
\(732\) 0 0
\(733\) 8.97374 + 3.26618i 0.331453 + 0.120639i 0.502385 0.864644i \(-0.332456\pi\)
−0.170933 + 0.985283i \(0.554678\pi\)
\(734\) 0 0
\(735\) −5.00985 + 15.1746i −0.184791 + 0.559725i
\(736\) 0 0
\(737\) −5.83138 3.36675i −0.214802 0.124016i
\(738\) 0 0
\(739\) −23.3163 + 13.4617i −0.857704 + 0.495195i −0.863243 0.504789i \(-0.831570\pi\)
0.00553893 + 0.999985i \(0.498237\pi\)
\(740\) 0 0
\(741\) −48.9427 26.3204i −1.79795 0.966903i
\(742\) 0 0
\(743\) −2.09650 11.8899i −0.0769132 0.436196i −0.998810 0.0487619i \(-0.984472\pi\)
0.921897 0.387434i \(-0.126639\pi\)
\(744\) 0 0
\(745\) −3.61223 3.03102i −0.132342 0.111048i
\(746\) 0 0
\(747\) 5.64842 11.3088i 0.206665 0.413766i
\(748\) 0 0
\(749\) −6.74566 18.5335i −0.246481 0.677201i
\(750\) 0 0
\(751\) 25.0832 + 29.8929i 0.915297 + 1.09081i 0.995569 + 0.0940360i \(0.0299769\pi\)
−0.0802713 + 0.996773i \(0.525579\pi\)
\(752\) 0 0
\(753\) 36.9402 + 29.1427i 1.34618 + 1.06202i
\(754\) 0 0
\(755\) 22.8622 0.832042
\(756\) 0 0
\(757\) 14.8793 0.540797 0.270398 0.962749i \(-0.412845\pi\)
0.270398 + 0.962749i \(0.412845\pi\)
\(758\) 0 0
\(759\) 12.6462 5.04011i 0.459029 0.182944i
\(760\) 0 0
\(761\) 9.15327 + 10.9084i 0.331806 + 0.395431i 0.905993 0.423294i \(-0.139126\pi\)
−0.574187 + 0.818724i \(0.694682\pi\)
\(762\) 0 0
\(763\) 10.6346 + 29.2182i 0.384997 + 1.05777i
\(764\) 0 0
\(765\) −9.49287 7.03485i −0.343216 0.254345i
\(766\) 0 0
\(767\) −77.7280 65.2215i −2.80659 2.35501i
\(768\) 0 0
\(769\) −0.349200 1.98041i −0.0125925 0.0714154i 0.977864 0.209242i \(-0.0670995\pi\)
−0.990456 + 0.137826i \(0.955988\pi\)
\(770\) 0 0
\(771\) −0.947333 31.3732i −0.0341174 1.12988i
\(772\) 0 0
\(773\) −21.2389 + 12.2623i −0.763910 + 0.441044i −0.830698 0.556724i \(-0.812058\pi\)
0.0667878 + 0.997767i \(0.478725\pi\)
\(774\) 0 0
\(775\) −1.08542 0.626666i −0.0389894 0.0225105i
\(776\) 0 0
\(777\) 5.86434 + 6.57516i 0.210382 + 0.235883i
\(778\) 0 0
\(779\) 31.0425 + 11.2986i 1.11221 + 0.404813i
\(780\) 0 0
\(781\) −0.536121 + 3.04049i −0.0191839 + 0.108797i
\(782\) 0 0
\(783\) 19.1365 27.5223i 0.683884 0.983565i
\(784\) 0 0
\(785\) −23.2227 4.09479i −0.828854 0.146149i
\(786\) 0 0
\(787\) −3.81446 + 10.4801i −0.135971 + 0.373577i −0.988926 0.148407i \(-0.952586\pi\)
0.852956 + 0.521984i \(0.174808\pi\)
\(788\) 0 0
\(789\) −8.59637 41.4027i −0.306039 1.47398i
\(790\) 0 0
\(791\) −10.2778 + 17.8017i −0.365438 + 0.632957i
\(792\) 0 0
\(793\) 1.00931 + 1.74818i 0.0358416 + 0.0620795i
\(794\) 0 0