Properties

Label 384.3.i.c.161.10
Level $384$
Weight $3$
Character 384.161
Analytic conductor $10.463$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 384.i (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.4632421514\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + 24576 x^{4} - 131072 x^{2} + 1048576\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{23} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 161.10
Root \(1.21144 - 1.59136i\) of defining polynomial
Character \(\chi\) \(=\) 384.161
Dual form 384.3.i.c.353.10

$q$-expansion

\(f(q)\) \(=\) \(q+(2.77106 + 1.14944i) q^{3} +(4.80434 + 4.80434i) q^{5} +7.36187i q^{7} +(6.35757 + 6.37035i) q^{9} +O(q^{10})\) \(q+(2.77106 + 1.14944i) q^{3} +(4.80434 + 4.80434i) q^{5} +7.36187i q^{7} +(6.35757 + 6.37035i) q^{9} +(0.514693 + 0.514693i) q^{11} +(-7.12969 - 7.12969i) q^{13} +(7.79081 + 18.8354i) q^{15} +11.1126i q^{17} +(-21.1403 - 21.1403i) q^{19} +(-8.46203 + 20.4002i) q^{21} -7.80231 q^{23} +21.1633i q^{25} +(10.2949 + 24.9603i) q^{27} +(34.6058 - 34.6058i) q^{29} -24.8644 q^{31} +(0.834637 + 2.01786i) q^{33} +(-35.3689 + 35.3689i) q^{35} +(18.2760 - 18.2760i) q^{37} +(-11.5617 - 27.9520i) q^{39} +64.2448 q^{41} +(7.24058 - 7.24058i) q^{43} +(-0.0613789 + 61.1492i) q^{45} +23.0508i q^{47} -5.19710 q^{49} +(-12.7733 + 30.7938i) q^{51} +(31.9199 + 31.9199i) q^{53} +4.94552i q^{55} +(-34.2816 - 82.8807i) q^{57} +(-17.6272 - 17.6272i) q^{59} +(12.3933 + 12.3933i) q^{61} +(-46.8976 + 46.8036i) q^{63} -68.5069i q^{65} +(41.1425 + 41.1425i) q^{67} +(-21.6207 - 8.96830i) q^{69} -25.6785 q^{71} +56.1845i q^{73} +(-24.3260 + 58.6449i) q^{75} +(-3.78910 + 3.78910i) q^{77} +35.7013 q^{79} +(-0.162608 + 80.9998i) q^{81} +(94.9424 - 94.9424i) q^{83} +(-53.3889 + 53.3889i) q^{85} +(135.672 - 56.1175i) q^{87} +44.8713 q^{89} +(52.4878 - 52.4878i) q^{91} +(-68.9008 - 28.5802i) q^{93} -203.131i q^{95} -82.3636 q^{97} +(-0.00657558 + 6.55097i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 6q^{3} + O(q^{10}) \) \( 20q - 6q^{3} - 92q^{13} + 116q^{15} - 52q^{19} - 48q^{21} + 18q^{27} + 80q^{31} + 60q^{33} + 116q^{37} + 172q^{43} - 60q^{45} - 364q^{49} + 128q^{51} + 244q^{61} - 296q^{63} + 356q^{67} + 20q^{69} - 146q^{75} - 384q^{79} - 188q^{81} - 48q^{85} + 136q^{91} + 132q^{93} + 472q^{97} - 452q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.77106 + 1.14944i 0.923687 + 0.383147i
\(4\) 0 0
\(5\) 4.80434 + 4.80434i 0.960868 + 0.960868i 0.999263 0.0383950i \(-0.0122245\pi\)
−0.0383950 + 0.999263i \(0.512225\pi\)
\(6\) 0 0
\(7\) 7.36187i 1.05170i 0.850579 + 0.525848i \(0.176252\pi\)
−0.850579 + 0.525848i \(0.823748\pi\)
\(8\) 0 0
\(9\) 6.35757 + 6.37035i 0.706397 + 0.707816i
\(10\) 0 0
\(11\) 0.514693 + 0.514693i 0.0467903 + 0.0467903i 0.730115 0.683325i \(-0.239467\pi\)
−0.683325 + 0.730115i \(0.739467\pi\)
\(12\) 0 0
\(13\) −7.12969 7.12969i −0.548438 0.548438i 0.377551 0.925989i \(-0.376766\pi\)
−0.925989 + 0.377551i \(0.876766\pi\)
\(14\) 0 0
\(15\) 7.79081 + 18.8354i 0.519388 + 1.25569i
\(16\) 0 0
\(17\) 11.1126i 0.653684i 0.945079 + 0.326842i \(0.105985\pi\)
−0.945079 + 0.326842i \(0.894015\pi\)
\(18\) 0 0
\(19\) −21.1403 21.1403i −1.11265 1.11265i −0.992791 0.119858i \(-0.961756\pi\)
−0.119858 0.992791i \(-0.538244\pi\)
\(20\) 0 0
\(21\) −8.46203 + 20.4002i −0.402954 + 0.971438i
\(22\) 0 0
\(23\) −7.80231 −0.339231 −0.169615 0.985510i \(-0.554253\pi\)
−0.169615 + 0.985510i \(0.554253\pi\)
\(24\) 0 0
\(25\) 21.1633i 0.846533i
\(26\) 0 0
\(27\) 10.2949 + 24.9603i 0.381292 + 0.924455i
\(28\) 0 0
\(29\) 34.6058 34.6058i 1.19330 1.19330i 0.217169 0.976134i \(-0.430318\pi\)
0.976134 0.217169i \(-0.0696823\pi\)
\(30\) 0 0
\(31\) −24.8644 −0.802078 −0.401039 0.916061i \(-0.631351\pi\)
−0.401039 + 0.916061i \(0.631351\pi\)
\(32\) 0 0
\(33\) 0.834637 + 2.01786i 0.0252920 + 0.0611472i
\(34\) 0 0
\(35\) −35.3689 + 35.3689i −1.01054 + 1.01054i
\(36\) 0 0
\(37\) 18.2760 18.2760i 0.493946 0.493946i −0.415601 0.909547i \(-0.636429\pi\)
0.909547 + 0.415601i \(0.136429\pi\)
\(38\) 0 0
\(39\) −11.5617 27.9520i −0.296453 0.716717i
\(40\) 0 0
\(41\) 64.2448 1.56695 0.783473 0.621426i \(-0.213446\pi\)
0.783473 + 0.621426i \(0.213446\pi\)
\(42\) 0 0
\(43\) 7.24058 7.24058i 0.168386 0.168386i −0.617884 0.786269i \(-0.712010\pi\)
0.786269 + 0.617884i \(0.212010\pi\)
\(44\) 0 0
\(45\) −0.0613789 + 61.1492i −0.00136398 + 1.35887i
\(46\) 0 0
\(47\) 23.0508i 0.490442i 0.969467 + 0.245221i \(0.0788606\pi\)
−0.969467 + 0.245221i \(0.921139\pi\)
\(48\) 0 0
\(49\) −5.19710 −0.106063
\(50\) 0 0
\(51\) −12.7733 + 30.7938i −0.250457 + 0.603800i
\(52\) 0 0
\(53\) 31.9199 + 31.9199i 0.602263 + 0.602263i 0.940913 0.338650i \(-0.109970\pi\)
−0.338650 + 0.940913i \(0.609970\pi\)
\(54\) 0 0
\(55\) 4.94552i 0.0899185i
\(56\) 0 0
\(57\) −34.2816 82.8807i −0.601432 1.45405i
\(58\) 0 0
\(59\) −17.6272 17.6272i −0.298766 0.298766i 0.541764 0.840530i \(-0.317756\pi\)
−0.840530 + 0.541764i \(0.817756\pi\)
\(60\) 0 0
\(61\) 12.3933 + 12.3933i 0.203170 + 0.203170i 0.801357 0.598187i \(-0.204112\pi\)
−0.598187 + 0.801357i \(0.704112\pi\)
\(62\) 0 0
\(63\) −46.8976 + 46.8036i −0.744407 + 0.742914i
\(64\) 0 0
\(65\) 68.5069i 1.05395i
\(66\) 0 0
\(67\) 41.1425 + 41.1425i 0.614067 + 0.614067i 0.944003 0.329936i \(-0.107027\pi\)
−0.329936 + 0.944003i \(0.607027\pi\)
\(68\) 0 0
\(69\) −21.6207 8.96830i −0.313343 0.129975i
\(70\) 0 0
\(71\) −25.6785 −0.361669 −0.180834 0.983514i \(-0.557880\pi\)
−0.180834 + 0.983514i \(0.557880\pi\)
\(72\) 0 0
\(73\) 56.1845i 0.769650i 0.922990 + 0.384825i \(0.125738\pi\)
−0.922990 + 0.384825i \(0.874262\pi\)
\(74\) 0 0
\(75\) −24.3260 + 58.6449i −0.324347 + 0.781932i
\(76\) 0 0
\(77\) −3.78910 + 3.78910i −0.0492091 + 0.0492091i
\(78\) 0 0
\(79\) 35.7013 0.451915 0.225957 0.974137i \(-0.427449\pi\)
0.225957 + 0.974137i \(0.427449\pi\)
\(80\) 0 0
\(81\) −0.162608 + 80.9998i −0.00200751 + 0.999998i
\(82\) 0 0
\(83\) 94.9424 94.9424i 1.14388 1.14388i 0.156151 0.987733i \(-0.450091\pi\)
0.987733 0.156151i \(-0.0499086\pi\)
\(84\) 0 0
\(85\) −53.3889 + 53.3889i −0.628104 + 0.628104i
\(86\) 0 0
\(87\) 135.672 56.1175i 1.55945 0.645028i
\(88\) 0 0
\(89\) 44.8713 0.504172 0.252086 0.967705i \(-0.418883\pi\)
0.252086 + 0.967705i \(0.418883\pi\)
\(90\) 0 0
\(91\) 52.4878 52.4878i 0.576789 0.576789i
\(92\) 0 0
\(93\) −68.9008 28.5802i −0.740869 0.307314i
\(94\) 0 0
\(95\) 203.131i 2.13822i
\(96\) 0 0
\(97\) −82.3636 −0.849109 −0.424554 0.905402i \(-0.639569\pi\)
−0.424554 + 0.905402i \(0.639569\pi\)
\(98\) 0 0
\(99\) −0.00657558 + 6.55097i −6.64200e−5 + 0.0661714i
\(100\) 0 0
\(101\) −36.3420 36.3420i −0.359822 0.359822i 0.503925 0.863747i \(-0.331889\pi\)
−0.863747 + 0.503925i \(0.831889\pi\)
\(102\) 0 0
\(103\) 87.5176i 0.849685i 0.905267 + 0.424843i \(0.139671\pi\)
−0.905267 + 0.424843i \(0.860329\pi\)
\(104\) 0 0
\(105\) −138.664 + 57.3550i −1.32061 + 0.546238i
\(106\) 0 0
\(107\) −104.866 104.866i −0.980058 0.980058i 0.0197471 0.999805i \(-0.493714\pi\)
−0.999805 + 0.0197471i \(0.993714\pi\)
\(108\) 0 0
\(109\) −7.64006 7.64006i −0.0700923 0.0700923i 0.671192 0.741284i \(-0.265783\pi\)
−0.741284 + 0.671192i \(0.765783\pi\)
\(110\) 0 0
\(111\) 71.6511 29.6367i 0.645505 0.266998i
\(112\) 0 0
\(113\) 13.1273i 0.116171i −0.998312 0.0580853i \(-0.981500\pi\)
0.998312 0.0580853i \(-0.0184995\pi\)
\(114\) 0 0
\(115\) −37.4849 37.4849i −0.325956 0.325956i
\(116\) 0 0
\(117\) 0.0910869 90.7461i 0.000778521 0.775607i
\(118\) 0 0
\(119\) −81.8098 −0.687477
\(120\) 0 0
\(121\) 120.470i 0.995621i
\(122\) 0 0
\(123\) 178.026 + 73.8456i 1.44737 + 0.600371i
\(124\) 0 0
\(125\) 18.4327 18.4327i 0.147461 0.147461i
\(126\) 0 0
\(127\) 88.2707 0.695045 0.347523 0.937672i \(-0.387023\pi\)
0.347523 + 0.937672i \(0.387023\pi\)
\(128\) 0 0
\(129\) 28.3867 11.7415i 0.220052 0.0910192i
\(130\) 0 0
\(131\) 57.0518 57.0518i 0.435510 0.435510i −0.454988 0.890498i \(-0.650356\pi\)
0.890498 + 0.454988i \(0.150356\pi\)
\(132\) 0 0
\(133\) 155.632 155.632i 1.17017 1.17017i
\(134\) 0 0
\(135\) −70.4575 + 169.378i −0.521907 + 1.25465i
\(136\) 0 0
\(137\) −165.112 −1.20520 −0.602599 0.798045i \(-0.705868\pi\)
−0.602599 + 0.798045i \(0.705868\pi\)
\(138\) 0 0
\(139\) −95.0802 + 95.0802i −0.684030 + 0.684030i −0.960906 0.276875i \(-0.910701\pi\)
0.276875 + 0.960906i \(0.410701\pi\)
\(140\) 0 0
\(141\) −26.4955 + 63.8752i −0.187912 + 0.453015i
\(142\) 0 0
\(143\) 7.33920i 0.0513231i
\(144\) 0 0
\(145\) 332.516 2.29321
\(146\) 0 0
\(147\) −14.4015 5.97376i −0.0979693 0.0406378i
\(148\) 0 0
\(149\) −131.077 131.077i −0.879709 0.879709i 0.113795 0.993504i \(-0.463699\pi\)
−0.993504 + 0.113795i \(0.963699\pi\)
\(150\) 0 0
\(151\) 123.070i 0.815031i −0.913198 0.407515i \(-0.866395\pi\)
0.913198 0.407515i \(-0.133605\pi\)
\(152\) 0 0
\(153\) −70.7913 + 70.6494i −0.462688 + 0.461761i
\(154\) 0 0
\(155\) −119.457 119.457i −0.770690 0.770690i
\(156\) 0 0
\(157\) −139.181 139.181i −0.886503 0.886503i 0.107683 0.994185i \(-0.465657\pi\)
−0.994185 + 0.107683i \(0.965657\pi\)
\(158\) 0 0
\(159\) 51.7620 + 125.142i 0.325547 + 0.787058i
\(160\) 0 0
\(161\) 57.4396i 0.356768i
\(162\) 0 0
\(163\) −19.9311 19.9311i −0.122277 0.122277i 0.643320 0.765597i \(-0.277556\pi\)
−0.765597 + 0.643320i \(0.777556\pi\)
\(164\) 0 0
\(165\) −5.68458 + 13.7043i −0.0344520 + 0.0830566i
\(166\) 0 0
\(167\) 60.3220 0.361210 0.180605 0.983556i \(-0.442194\pi\)
0.180605 + 0.983556i \(0.442194\pi\)
\(168\) 0 0
\(169\) 67.3351i 0.398432i
\(170\) 0 0
\(171\) 0.270083 269.072i 0.00157943 1.57352i
\(172\) 0 0
\(173\) 74.8292 74.8292i 0.432539 0.432539i −0.456952 0.889491i \(-0.651059\pi\)
0.889491 + 0.456952i \(0.151059\pi\)
\(174\) 0 0
\(175\) −155.802 −0.890295
\(176\) 0 0
\(177\) −28.5846 69.1074i −0.161495 0.390438i
\(178\) 0 0
\(179\) −3.96558 + 3.96558i −0.0221541 + 0.0221541i −0.718097 0.695943i \(-0.754987\pi\)
0.695943 + 0.718097i \(0.254987\pi\)
\(180\) 0 0
\(181\) −158.820 + 158.820i −0.877457 + 0.877457i −0.993271 0.115814i \(-0.963052\pi\)
0.115814 + 0.993271i \(0.463052\pi\)
\(182\) 0 0
\(183\) 20.0973 + 48.5882i 0.109821 + 0.265509i
\(184\) 0 0
\(185\) 175.608 0.949233
\(186\) 0 0
\(187\) −5.71960 + 5.71960i −0.0305861 + 0.0305861i
\(188\) 0 0
\(189\) −183.754 + 75.7896i −0.972245 + 0.401003i
\(190\) 0 0
\(191\) 68.8639i 0.360544i −0.983617 0.180272i \(-0.942302\pi\)
0.983617 0.180272i \(-0.0576978\pi\)
\(192\) 0 0
\(193\) −366.645 −1.89971 −0.949856 0.312686i \(-0.898771\pi\)
−0.949856 + 0.312686i \(0.898771\pi\)
\(194\) 0 0
\(195\) 78.7446 189.837i 0.403819 0.973522i
\(196\) 0 0
\(197\) 246.744 + 246.744i 1.25251 + 1.25251i 0.954593 + 0.297912i \(0.0962901\pi\)
0.297912 + 0.954593i \(0.403710\pi\)
\(198\) 0 0
\(199\) 287.802i 1.44624i −0.690722 0.723120i \(-0.742707\pi\)
0.690722 0.723120i \(-0.257293\pi\)
\(200\) 0 0
\(201\) 66.7176 + 161.299i 0.331928 + 0.802484i
\(202\) 0 0
\(203\) 254.763 + 254.763i 1.25499 + 1.25499i
\(204\) 0 0
\(205\) 308.654 + 308.654i 1.50563 + 1.50563i
\(206\) 0 0
\(207\) −49.6037 49.7034i −0.239632 0.240113i
\(208\) 0 0
\(209\) 21.7616i 0.104122i
\(210\) 0 0
\(211\) 156.146 + 156.146i 0.740027 + 0.740027i 0.972583 0.232556i \(-0.0747089\pi\)
−0.232556 + 0.972583i \(0.574709\pi\)
\(212\) 0 0
\(213\) −71.1567 29.5159i −0.334069 0.138572i
\(214\) 0 0
\(215\) 69.5724 0.323593
\(216\) 0 0
\(217\) 183.048i 0.843541i
\(218\) 0 0
\(219\) −64.5807 + 155.691i −0.294889 + 0.710916i
\(220\) 0 0
\(221\) 79.2296 79.2296i 0.358505 0.358505i
\(222\) 0 0
\(223\) −45.2998 −0.203138 −0.101569 0.994828i \(-0.532386\pi\)
−0.101569 + 0.994828i \(0.532386\pi\)
\(224\) 0 0
\(225\) −134.818 + 134.547i −0.599190 + 0.597988i
\(226\) 0 0
\(227\) −300.757 + 300.757i −1.32492 + 1.32492i −0.415186 + 0.909737i \(0.636283\pi\)
−0.909737 + 0.415186i \(0.863717\pi\)
\(228\) 0 0
\(229\) −65.7088 + 65.7088i −0.286938 + 0.286938i −0.835868 0.548930i \(-0.815035\pi\)
0.548930 + 0.835868i \(0.315035\pi\)
\(230\) 0 0
\(231\) −14.8552 + 6.14449i −0.0643082 + 0.0265995i
\(232\) 0 0
\(233\) 42.8218 0.183785 0.0918923 0.995769i \(-0.470708\pi\)
0.0918923 + 0.995769i \(0.470708\pi\)
\(234\) 0 0
\(235\) −110.744 + 110.744i −0.471250 + 0.471250i
\(236\) 0 0
\(237\) 98.9305 + 41.0365i 0.417428 + 0.173150i
\(238\) 0 0
\(239\) 100.598i 0.420913i 0.977603 + 0.210456i \(0.0674950\pi\)
−0.977603 + 0.210456i \(0.932505\pi\)
\(240\) 0 0
\(241\) −5.23162 −0.0217080 −0.0108540 0.999941i \(-0.503455\pi\)
−0.0108540 + 0.999941i \(0.503455\pi\)
\(242\) 0 0
\(243\) −93.5551 + 224.269i −0.385001 + 0.922916i
\(244\) 0 0
\(245\) −24.9686 24.9686i −0.101913 0.101913i
\(246\) 0 0
\(247\) 301.448i 1.22044i
\(248\) 0 0
\(249\) 372.222 153.961i 1.49487 0.618315i
\(250\) 0 0
\(251\) −17.4381 17.4381i −0.0694747 0.0694747i 0.671516 0.740990i \(-0.265644\pi\)
−0.740990 + 0.671516i \(0.765644\pi\)
\(252\) 0 0
\(253\) −4.01579 4.01579i −0.0158727 0.0158727i
\(254\) 0 0
\(255\) −209.311 + 86.5765i −0.820828 + 0.339516i
\(256\) 0 0
\(257\) 343.676i 1.33726i 0.743595 + 0.668630i \(0.233119\pi\)
−0.743595 + 0.668630i \(0.766881\pi\)
\(258\) 0 0
\(259\) 134.545 + 134.545i 0.519480 + 0.519480i
\(260\) 0 0
\(261\) 440.460 + 0.442114i 1.68758 + 0.00169392i
\(262\) 0 0
\(263\) 98.0863 0.372952 0.186476 0.982460i \(-0.440293\pi\)
0.186476 + 0.982460i \(0.440293\pi\)
\(264\) 0 0
\(265\) 306.708i 1.15739i
\(266\) 0 0
\(267\) 124.341 + 51.5769i 0.465697 + 0.193172i
\(268\) 0 0
\(269\) −126.560 + 126.560i −0.470482 + 0.470482i −0.902070 0.431589i \(-0.857953\pi\)
0.431589 + 0.902070i \(0.357953\pi\)
\(270\) 0 0
\(271\) 206.487 0.761945 0.380972 0.924586i \(-0.375589\pi\)
0.380972 + 0.924586i \(0.375589\pi\)
\(272\) 0 0
\(273\) 205.779 85.1154i 0.753768 0.311778i
\(274\) 0 0
\(275\) −10.8926 + 10.8926i −0.0396095 + 0.0396095i
\(276\) 0 0
\(277\) −183.416 + 183.416i −0.662153 + 0.662153i −0.955887 0.293734i \(-0.905102\pi\)
0.293734 + 0.955887i \(0.405102\pi\)
\(278\) 0 0
\(279\) −158.077 158.395i −0.566585 0.567723i
\(280\) 0 0
\(281\) 109.143 0.388409 0.194204 0.980961i \(-0.437787\pi\)
0.194204 + 0.980961i \(0.437787\pi\)
\(282\) 0 0
\(283\) 60.4623 60.4623i 0.213648 0.213648i −0.592167 0.805815i \(-0.701728\pi\)
0.805815 + 0.592167i \(0.201728\pi\)
\(284\) 0 0
\(285\) 233.487 562.888i 0.819252 1.97504i
\(286\) 0 0
\(287\) 472.962i 1.64795i
\(288\) 0 0
\(289\) 165.509 0.572697
\(290\) 0 0
\(291\) −228.235 94.6721i −0.784311 0.325334i
\(292\) 0 0
\(293\) 19.4639 + 19.4639i 0.0664296 + 0.0664296i 0.739541 0.673111i \(-0.235043\pi\)
−0.673111 + 0.739541i \(0.735043\pi\)
\(294\) 0 0
\(295\) 169.374i 0.574149i
\(296\) 0 0
\(297\) −7.54818 + 18.1456i −0.0254147 + 0.0610963i
\(298\) 0 0
\(299\) 55.6280 + 55.6280i 0.186047 + 0.186047i
\(300\) 0 0
\(301\) 53.3042 + 53.3042i 0.177090 + 0.177090i
\(302\) 0 0
\(303\) −58.9329 142.479i −0.194498 0.470227i
\(304\) 0 0
\(305\) 119.084i 0.390438i
\(306\) 0 0
\(307\) −408.201 408.201i −1.32964 1.32964i −0.905677 0.423967i \(-0.860637\pi\)
−0.423967 0.905677i \(-0.639363\pi\)
\(308\) 0 0
\(309\) −100.596 + 242.517i −0.325554 + 0.784844i
\(310\) 0 0
\(311\) −360.965 −1.16066 −0.580330 0.814381i \(-0.697076\pi\)
−0.580330 + 0.814381i \(0.697076\pi\)
\(312\) 0 0
\(313\) 73.9217i 0.236172i 0.993003 + 0.118086i \(0.0376758\pi\)
−0.993003 + 0.118086i \(0.962324\pi\)
\(314\) 0 0
\(315\) −450.172 0.451863i −1.42912 0.00143449i
\(316\) 0 0
\(317\) −172.709 + 172.709i −0.544825 + 0.544825i −0.924939 0.380115i \(-0.875884\pi\)
0.380115 + 0.924939i \(0.375884\pi\)
\(318\) 0 0
\(319\) 35.6227 0.111670
\(320\) 0 0
\(321\) −170.053 411.128i −0.529761 1.28077i
\(322\) 0 0
\(323\) 234.925 234.925i 0.727321 0.727321i
\(324\) 0 0
\(325\) 150.888 150.888i 0.464271 0.464271i
\(326\) 0 0
\(327\) −12.3893 29.9529i −0.0378877 0.0915990i
\(328\) 0 0
\(329\) −169.697 −0.515796
\(330\) 0 0
\(331\) 261.507 261.507i 0.790051 0.790051i −0.191451 0.981502i \(-0.561319\pi\)
0.981502 + 0.191451i \(0.0613194\pi\)
\(332\) 0 0
\(333\) 232.615 + 0.233489i 0.698544 + 0.000701168i
\(334\) 0 0
\(335\) 395.325i 1.18007i
\(336\) 0 0
\(337\) 18.2211 0.0540684 0.0270342 0.999635i \(-0.491394\pi\)
0.0270342 + 0.999635i \(0.491394\pi\)
\(338\) 0 0
\(339\) 15.0890 36.3765i 0.0445104 0.107305i
\(340\) 0 0
\(341\) −12.7975 12.7975i −0.0375294 0.0375294i
\(342\) 0 0
\(343\) 322.471i 0.940149i
\(344\) 0 0
\(345\) −60.7863 146.960i −0.176192 0.425970i
\(346\) 0 0
\(347\) 173.710 + 173.710i 0.500605 + 0.500605i 0.911626 0.411021i \(-0.134828\pi\)
−0.411021 + 0.911626i \(0.634828\pi\)
\(348\) 0 0
\(349\) −387.899 387.899i −1.11146 1.11146i −0.992953 0.118506i \(-0.962189\pi\)
−0.118506 0.992953i \(-0.537811\pi\)
\(350\) 0 0
\(351\) 104.560 251.358i 0.297891 0.716121i
\(352\) 0 0
\(353\) 676.812i 1.91732i −0.284561 0.958658i \(-0.591848\pi\)
0.284561 0.958658i \(-0.408152\pi\)
\(354\) 0 0
\(355\) −123.368 123.368i −0.347516 0.347516i
\(356\) 0 0
\(357\) −226.700 94.0355i −0.635014 0.263405i
\(358\) 0 0
\(359\) 240.896 0.671020 0.335510 0.942037i \(-0.391091\pi\)
0.335510 + 0.942037i \(0.391091\pi\)
\(360\) 0 0
\(361\) 532.827i 1.47598i
\(362\) 0 0
\(363\) 138.473 333.830i 0.381469 0.919643i
\(364\) 0 0
\(365\) −269.929 + 269.929i −0.739532 + 0.739532i
\(366\) 0 0
\(367\) −666.702 −1.81663 −0.908313 0.418291i \(-0.862629\pi\)
−0.908313 + 0.418291i \(0.862629\pi\)
\(368\) 0 0
\(369\) 408.441 + 409.261i 1.10689 + 1.10911i
\(370\) 0 0
\(371\) −234.990 + 234.990i −0.633397 + 0.633397i
\(372\) 0 0
\(373\) 358.513 358.513i 0.961160 0.961160i −0.0381137 0.999273i \(-0.512135\pi\)
0.999273 + 0.0381137i \(0.0121349\pi\)
\(374\) 0 0
\(375\) 72.2653 29.8908i 0.192708 0.0797088i
\(376\) 0 0
\(377\) −493.457 −1.30890
\(378\) 0 0
\(379\) −140.959 + 140.959i −0.371925 + 0.371925i −0.868178 0.496253i \(-0.834709\pi\)
0.496253 + 0.868178i \(0.334709\pi\)
\(380\) 0 0
\(381\) 244.604 + 101.462i 0.642004 + 0.266305i
\(382\) 0 0
\(383\) 69.4683i 0.181379i −0.995879 0.0906897i \(-0.971093\pi\)
0.995879 0.0906897i \(-0.0289071\pi\)
\(384\) 0 0
\(385\) −36.4083 −0.0945669
\(386\) 0 0
\(387\) 92.1575 + 0.0925037i 0.238133 + 0.000239028i
\(388\) 0 0
\(389\) −265.362 265.362i −0.682165 0.682165i 0.278322 0.960488i \(-0.410222\pi\)
−0.960488 + 0.278322i \(0.910222\pi\)
\(390\) 0 0
\(391\) 86.7042i 0.221750i
\(392\) 0 0
\(393\) 223.672 92.5164i 0.569139 0.235411i
\(394\) 0 0
\(395\) 171.521 + 171.521i 0.434230 + 0.434230i
\(396\) 0 0
\(397\) −259.123 259.123i −0.652703 0.652703i 0.300940 0.953643i \(-0.402700\pi\)
−0.953643 + 0.300940i \(0.902700\pi\)
\(398\) 0 0
\(399\) 610.157 252.377i 1.52922 0.632523i
\(400\) 0 0
\(401\) 664.163i 1.65627i 0.560531 + 0.828133i \(0.310597\pi\)
−0.560531 + 0.828133i \(0.689403\pi\)
\(402\) 0 0
\(403\) 177.275 + 177.275i 0.439889 + 0.439889i
\(404\) 0 0
\(405\) −389.932 + 388.369i −0.962795 + 0.958937i
\(406\) 0 0
\(407\) 18.8131 0.0462237
\(408\) 0 0
\(409\) 530.421i 1.29687i −0.761269 0.648437i \(-0.775423\pi\)
0.761269 0.648437i \(-0.224577\pi\)
\(410\) 0 0
\(411\) −457.536 189.787i −1.11323 0.461768i
\(412\) 0 0
\(413\) 129.769 129.769i 0.314211 0.314211i
\(414\) 0 0
\(415\) 912.271 2.19824
\(416\) 0 0
\(417\) −372.762 + 154.184i −0.893914 + 0.369746i
\(418\) 0 0
\(419\) 404.149 404.149i 0.964556 0.964556i −0.0348367 0.999393i \(-0.511091\pi\)
0.999393 + 0.0348367i \(0.0110911\pi\)
\(420\) 0 0
\(421\) 264.630 264.630i 0.628575 0.628575i −0.319134 0.947710i \(-0.603392\pi\)
0.947710 + 0.319134i \(0.103392\pi\)
\(422\) 0 0
\(423\) −146.842 + 146.547i −0.347143 + 0.346447i
\(424\) 0 0
\(425\) −235.180 −0.553366
\(426\) 0 0
\(427\) −91.2382 + 91.2382i −0.213673 + 0.213673i
\(428\) 0 0
\(429\) 8.43598 20.3374i 0.0196643 0.0474065i
\(430\) 0 0
\(431\) 766.652i 1.77877i −0.457155 0.889387i \(-0.651132\pi\)
0.457155 0.889387i \(-0.348868\pi\)
\(432\) 0 0
\(433\) 151.222 0.349243 0.174622 0.984636i \(-0.444130\pi\)
0.174622 + 0.984636i \(0.444130\pi\)
\(434\) 0 0
\(435\) 921.422 + 382.207i 2.11821 + 0.878638i
\(436\) 0 0
\(437\) 164.943 + 164.943i 0.377445 + 0.377445i
\(438\) 0 0
\(439\) 565.007i 1.28703i 0.765433 + 0.643516i \(0.222525\pi\)
−0.765433 + 0.643516i \(0.777475\pi\)
\(440\) 0 0
\(441\) −33.0409 33.1073i −0.0749228 0.0750733i
\(442\) 0 0
\(443\) 100.963 + 100.963i 0.227907 + 0.227907i 0.811818 0.583911i \(-0.198478\pi\)
−0.583911 + 0.811818i \(0.698478\pi\)
\(444\) 0 0
\(445\) 215.577 + 215.577i 0.484442 + 0.484442i
\(446\) 0 0
\(447\) −212.557 513.887i −0.475518 1.14963i
\(448\) 0 0
\(449\) 131.725i 0.293375i 0.989183 + 0.146687i \(0.0468611\pi\)
−0.989183 + 0.146687i \(0.953139\pi\)
\(450\) 0 0
\(451\) 33.0663 + 33.0663i 0.0733178 + 0.0733178i
\(452\) 0 0
\(453\) 141.461 341.034i 0.312277 0.752833i
\(454\) 0 0
\(455\) 504.339 1.10844
\(456\) 0 0
\(457\) 137.963i 0.301888i −0.988542 0.150944i \(-0.951769\pi\)
0.988542 0.150944i \(-0.0482313\pi\)
\(458\) 0 0
\(459\) −277.374 + 114.403i −0.604302 + 0.249245i
\(460\) 0 0
\(461\) −303.536 + 303.536i −0.658430 + 0.658430i −0.955008 0.296579i \(-0.904154\pi\)
0.296579 + 0.955008i \(0.404154\pi\)
\(462\) 0 0
\(463\) −280.379 −0.605570 −0.302785 0.953059i \(-0.597916\pi\)
−0.302785 + 0.953059i \(0.597916\pi\)
\(464\) 0 0
\(465\) −193.714 468.332i −0.416589 1.00716i
\(466\) 0 0
\(467\) 65.6355 65.6355i 0.140547 0.140547i −0.633333 0.773880i \(-0.718313\pi\)
0.773880 + 0.633333i \(0.218313\pi\)
\(468\) 0 0
\(469\) −302.886 + 302.886i −0.645812 + 0.645812i
\(470\) 0 0
\(471\) −225.699 545.659i −0.479190 1.15851i
\(472\) 0 0
\(473\) 7.45335 0.0157576
\(474\) 0 0
\(475\) 447.400 447.400i 0.941894 0.941894i
\(476\) 0 0
\(477\) −0.407800 + 406.274i −0.000854927 + 0.851728i
\(478\) 0 0
\(479\) 373.272i 0.779273i 0.920969 + 0.389636i \(0.127399\pi\)
−0.920969 + 0.389636i \(0.872601\pi\)
\(480\) 0 0
\(481\) −260.604 −0.541797
\(482\) 0 0
\(483\) 66.0234 159.169i 0.136694 0.329542i
\(484\) 0 0
\(485\) −395.702 395.702i −0.815881 0.815881i
\(486\) 0 0
\(487\) 0.0470526i 9.66171e-5i 1.00000 4.83086e-5i \(1.53771e-5\pi\)
−1.00000 4.83086e-5i \(0.999985\pi\)
\(488\) 0 0
\(489\) −32.3206 78.1398i −0.0660954 0.159795i
\(490\) 0 0
\(491\) −273.442 273.442i −0.556908 0.556908i 0.371518 0.928426i \(-0.378837\pi\)
−0.928426 + 0.371518i \(0.878837\pi\)
\(492\) 0 0
\(493\) 384.562 + 384.562i 0.780044 + 0.780044i
\(494\) 0 0
\(495\) −31.5047 + 31.4415i −0.0636458 + 0.0635182i
\(496\) 0 0
\(497\) 189.042i 0.380365i
\(498\) 0 0
\(499\) −46.2637 46.2637i −0.0927129 0.0927129i 0.659229 0.751942i \(-0.270883\pi\)
−0.751942 + 0.659229i \(0.770883\pi\)
\(500\) 0 0
\(501\) 167.156 + 69.3366i 0.333645 + 0.138396i
\(502\) 0 0
\(503\) 864.426 1.71854 0.859270 0.511522i \(-0.170918\pi\)
0.859270 + 0.511522i \(0.170918\pi\)
\(504\) 0 0
\(505\) 349.198i 0.691482i
\(506\) 0 0
\(507\) 77.3977 186.590i 0.152658 0.368027i
\(508\) 0 0
\(509\) −171.041 + 171.041i −0.336033 + 0.336033i −0.854872 0.518839i \(-0.826365\pi\)
0.518839 + 0.854872i \(0.326365\pi\)
\(510\) 0 0
\(511\) −413.623 −0.809438
\(512\) 0 0
\(513\) 310.031 745.306i 0.604349 1.45284i
\(514\) 0 0
\(515\) −420.464 + 420.464i −0.816435 + 0.816435i
\(516\) 0 0
\(517\) −11.8641 + 11.8641i −0.0229479 + 0.0229479i
\(518\) 0 0
\(519\) 293.368 121.345i 0.565257 0.233805i
\(520\) 0 0
\(521\) −351.572 −0.674802 −0.337401 0.941361i \(-0.609548\pi\)
−0.337401 + 0.941361i \(0.609548\pi\)
\(522\) 0 0
\(523\) −287.638 + 287.638i −0.549977 + 0.549977i −0.926434 0.376457i \(-0.877142\pi\)
0.376457 + 0.926434i \(0.377142\pi\)
\(524\) 0 0
\(525\) −431.736 179.085i −0.822354 0.341114i
\(526\) 0 0
\(527\) 276.309i 0.524306i
\(528\) 0 0
\(529\) −468.124 −0.884922
\(530\) 0 0
\(531\) 0.225200 224.357i 0.000424106 0.422519i
\(532\) 0 0
\(533\) −458.045 458.045i −0.859372 0.859372i
\(534\) 0 0
\(535\) 1007.63i 1.88341i
\(536\) 0 0
\(537\) −15.5471 + 6.43067i −0.0289517 + 0.0119752i
\(538\) 0 0
\(539\) −2.67491 2.67491i −0.00496273 0.00496273i
\(540\) 0 0
\(541\) −419.846 419.846i −0.776056 0.776056i 0.203102 0.979158i \(-0.434898\pi\)
−0.979158 + 0.203102i \(0.934898\pi\)
\(542\) 0 0
\(543\) −622.654 + 257.545i −1.14669 + 0.474301i
\(544\) 0 0
\(545\) 73.4108i 0.134699i
\(546\) 0 0
\(547\) 517.346 + 517.346i 0.945789 + 0.945789i 0.998604 0.0528155i \(-0.0168195\pi\)
−0.0528155 + 0.998604i \(0.516820\pi\)
\(548\) 0 0
\(549\) −0.158334 + 157.742i −0.000288404 + 0.287325i
\(550\) 0 0
\(551\) −1463.16 −2.65546
\(552\) 0 0
\(553\) 262.828i 0.475277i
\(554\) 0 0
\(555\) 486.621 + 201.851i 0.876794 + 0.363696i
\(556\) 0 0
\(557\) 31.8976 31.8976i 0.0572667 0.0572667i −0.677893 0.735160i \(-0.737107\pi\)
0.735160 + 0.677893i \(0.237107\pi\)
\(558\) 0 0
\(559\) −103.246 −0.184698
\(560\) 0 0
\(561\) −22.4237 + 9.27502i −0.0399709 + 0.0165330i
\(562\) 0 0
\(563\) 32.9214 32.9214i 0.0584750 0.0584750i −0.677265 0.735740i \(-0.736835\pi\)
0.735740 + 0.677265i \(0.236835\pi\)
\(564\) 0 0
\(565\) 63.0679 63.0679i 0.111625 0.111625i
\(566\) 0 0
\(567\) −596.310 1.19710i −1.05169 0.00211129i
\(568\) 0 0
\(569\) −647.095 −1.13725 −0.568624 0.822597i \(-0.692524\pi\)
−0.568624 + 0.822597i \(0.692524\pi\)
\(570\) 0 0
\(571\) 451.861 451.861i 0.791350 0.791350i −0.190363 0.981714i \(-0.560967\pi\)
0.981714 + 0.190363i \(0.0609666\pi\)
\(572\) 0 0
\(573\) 79.1550 190.826i 0.138141 0.333030i
\(574\) 0 0
\(575\) 165.123i 0.287170i
\(576\) 0 0
\(577\) 532.176 0.922315 0.461157 0.887318i \(-0.347434\pi\)
0.461157 + 0.887318i \(0.347434\pi\)
\(578\) 0 0
\(579\) −1015.99 421.436i −1.75474 0.727869i
\(580\) 0 0
\(581\) 698.953 + 698.953i 1.20302 + 1.20302i
\(582\) 0 0
\(583\) 32.8579i 0.0563601i
\(584\) 0 0
\(585\) 436.412 435.537i 0.746004 0.744508i
\(586\) 0 0
\(587\) −532.393 532.393i −0.906973 0.906973i 0.0890534 0.996027i \(-0.471616\pi\)
−0.996027 + 0.0890534i \(0.971616\pi\)
\(588\) 0 0
\(589\) 525.642 + 525.642i 0.892431 + 0.892431i
\(590\) 0 0
\(591\) 400.124 + 967.359i 0.677029 + 1.63682i
\(592\) 0 0
\(593\) 254.750i 0.429595i −0.976659 0.214798i \(-0.931091\pi\)
0.976659 0.214798i \(-0.0689092\pi\)
\(594\) 0 0
\(595\) −393.042 393.042i −0.660574 0.660574i
\(596\) 0 0
\(597\) 330.811 797.517i 0.554123 1.33587i
\(598\) 0 0
\(599\) 624.772 1.04303 0.521513 0.853244i \(-0.325368\pi\)
0.521513 + 0.853244i \(0.325368\pi\)
\(600\) 0 0
\(601\) 386.910i 0.643777i 0.946778 + 0.321889i \(0.104318\pi\)
−0.946778 + 0.321889i \(0.895682\pi\)
\(602\) 0 0
\(603\) −0.525625 + 523.658i −0.000871684 + 0.868422i
\(604\) 0 0
\(605\) 578.779 578.779i 0.956660 0.956660i
\(606\) 0 0
\(607\) 951.141 1.56695 0.783477 0.621421i \(-0.213444\pi\)
0.783477 + 0.621421i \(0.213444\pi\)
\(608\) 0 0
\(609\) 413.129 + 998.800i 0.678373 + 1.64007i
\(610\) 0 0
\(611\) 164.345 164.345i 0.268977 0.268977i
\(612\) 0 0
\(613\) −387.896 + 387.896i −0.632783 + 0.632783i −0.948765 0.315982i \(-0.897666\pi\)
0.315982 + 0.948765i \(0.397666\pi\)
\(614\) 0 0
\(615\) 500.519 + 1210.08i 0.813852 + 1.96761i
\(616\) 0 0
\(617\) 882.945 1.43103 0.715514 0.698598i \(-0.246192\pi\)
0.715514 + 0.698598i \(0.246192\pi\)
\(618\) 0 0
\(619\) −694.731 + 694.731i −1.12234 + 1.12234i −0.130955 + 0.991388i \(0.541804\pi\)
−0.991388 + 0.130955i \(0.958196\pi\)
\(620\) 0 0
\(621\) −80.3239 194.748i −0.129346 0.313604i
\(622\) 0 0
\(623\) 330.337i 0.530235i
\(624\) 0 0
\(625\) 706.197 1.12991
\(626\) 0 0
\(627\) 25.0136 60.3027i 0.0398942 0.0961765i
\(628\) 0 0
\(629\) 203.094 + 203.094i 0.322885 + 0.322885i
\(630\) 0 0
\(631\) 927.845i 1.47044i 0.677831 + 0.735218i \(0.262920\pi\)
−0.677831 + 0.735218i \(0.737080\pi\)
\(632\) 0 0
\(633\) 253.209 + 612.170i 0.400014 + 0.967093i
\(634\) 0 0
\(635\) 424.082 + 424.082i 0.667846 + 0.667846i
\(636\) 0 0
\(637\) 37.0537 + 37.0537i 0.0581691 + 0.0581691i
\(638\) 0 0
\(639\) −163.253 163.581i −0.255482 0.255995i
\(640\) 0 0
\(641\) 759.287i 1.18453i 0.805741 + 0.592267i \(0.201767\pi\)
−0.805741 + 0.592267i \(0.798233\pi\)
\(642\) 0 0
\(643\) 274.424 + 274.424i 0.426787 + 0.426787i 0.887532 0.460746i \(-0.152418\pi\)
−0.460746 + 0.887532i \(0.652418\pi\)
\(644\) 0 0
\(645\) 192.789 + 79.9694i 0.298898 + 0.123984i
\(646\) 0 0
\(647\) −747.683 −1.15561 −0.577807 0.816173i \(-0.696092\pi\)
−0.577807 + 0.816173i \(0.696092\pi\)
\(648\) 0 0
\(649\) 18.1452i 0.0279587i
\(650\) 0 0
\(651\) 210.403 507.239i 0.323200 0.779168i
\(652\) 0 0
\(653\) 605.127 605.127i 0.926688 0.926688i −0.0708022 0.997490i \(-0.522556\pi\)
0.997490 + 0.0708022i \(0.0225559\pi\)
\(654\) 0 0
\(655\) 548.192 0.836935
\(656\) 0 0
\(657\) −357.914 + 357.197i −0.544771 + 0.543678i
\(658\) 0 0
\(659\) −588.767 + 588.767i −0.893425 + 0.893425i −0.994844 0.101418i \(-0.967662\pi\)
0.101418 + 0.994844i \(0.467662\pi\)
\(660\) 0 0
\(661\) −3.60334 + 3.60334i −0.00545135 + 0.00545135i −0.709827 0.704376i \(-0.751227\pi\)
0.704376 + 0.709827i \(0.251227\pi\)
\(662\) 0 0
\(663\) 310.620 128.480i 0.468507 0.193786i
\(664\) 0 0
\(665\) 1495.42 2.24875
\(666\) 0 0
\(667\) −270.005 + 270.005i −0.404805 + 0.404805i
\(668\) 0 0
\(669\) −125.529 52.0695i −0.187636 0.0778319i
\(670\) 0 0
\(671\) 12.7575i 0.0190127i
\(672\) 0 0
\(673\) −460.445 −0.684167 −0.342084 0.939670i \(-0.611133\pi\)
−0.342084 + 0.939670i \(0.611133\pi\)
\(674\) 0 0
\(675\) −528.242 + 217.874i −0.782581 + 0.322776i
\(676\) 0 0
\(677\) 150.713 + 150.713i 0.222618 + 0.222618i 0.809600 0.586982i \(-0.199684\pi\)
−0.586982 + 0.809600i \(0.699684\pi\)
\(678\) 0 0
\(679\) 606.350i 0.893004i
\(680\) 0 0
\(681\) −1179.12 + 487.714i −1.73145 + 0.716174i
\(682\) 0 0
\(683\) 577.893 + 577.893i 0.846109 + 0.846109i 0.989645 0.143536i \(-0.0458473\pi\)
−0.143536 + 0.989645i \(0.545847\pi\)
\(684\) 0 0
\(685\) −793.254 793.254i −1.15803 1.15803i
\(686\) 0 0
\(687\) −257.612 + 106.555i −0.374981 + 0.155102i
\(688\) 0 0
\(689\) 455.158i 0.660607i
\(690\) 0 0
\(691\) −545.023 545.023i −0.788745 0.788745i 0.192544 0.981288i \(-0.438326\pi\)
−0.981288 + 0.192544i \(0.938326\pi\)
\(692\) 0 0
\(693\) −48.2274 0.0484085i −0.0695922 6.98536e-5i
\(694\) 0 0
\(695\) −913.595 −1.31453
\(696\) 0 0
\(697\) 713.929i 1.02429i
\(698\) 0 0
\(699\) 118.662 + 49.2212i 0.169760 + 0.0704165i
\(700\) 0 0
\(701\) −413.745 + 413.745i −0.590221 + 0.590221i −0.937691 0.347470i \(-0.887041\pi\)
0.347470 + 0.937691i \(0.387041\pi\)
\(702\) 0 0
\(703\) −772.721 −1.09918
\(704\) 0 0
\(705\) −434.171 + 179.584i −0.615846 + 0.254730i
\(706\) 0 0
\(707\) 267.545 267.545i 0.378423 0.378423i
\(708\) 0 0
\(709\) −521.959 + 521.959i −0.736191 + 0.736191i −0.971839 0.235648i \(-0.924279\pi\)
0.235648 + 0.971839i \(0.424279\pi\)
\(710\) 0 0
\(711\) 226.973 + 227.429i 0.319231 + 0.319873i
\(712\) 0 0
\(713\) 194.000 0.272089
\(714\) 0 0
\(715\) 35.2600 35.2600i 0.0493147 0.0493147i
\(716\) 0 0
\(717\) −115.632 + 278.764i −0.161272 + 0.388792i
\(718\) 0 0
\(719\) 567.983i 0.789963i 0.918689 + 0.394981i \(0.129249\pi\)
−0.918689 + 0.394981i \(0.870751\pi\)
\(720\) 0 0
\(721\) −644.293 −0.893610
\(722\) 0 0
\(723\) −14.4972 6.01344i −0.0200514 0.00831735i
\(724\) 0 0
\(725\) 732.374 + 732.374i 1.01017 + 1.01017i
\(726\) 0 0
\(727\) 635.396i 0.873998i −0.899462 0.436999i \(-0.856041\pi\)
0.899462 0.436999i \(-0.143959\pi\)
\(728\) 0 0
\(729\) −517.031 + 513.926i −0.709233 + 0.704974i
\(730\) 0 0
\(731\) 80.4619 + 80.4619i 0.110071 + 0.110071i
\(732\) 0 0
\(733\) 637.378 + 637.378i 0.869547 + 0.869547i 0.992422 0.122875i \(-0.0392116\pi\)
−0.122875 + 0.992422i \(0.539212\pi\)
\(734\) 0 0
\(735\) −40.4897 97.8896i −0.0550880 0.133183i
\(736\) 0 0
\(737\) 42.3515i 0.0574648i
\(738\) 0 0
\(739\) 397.296 + 397.296i 0.537613 + 0.537613i 0.922827 0.385214i \(-0.125872\pi\)
−0.385214 + 0.922827i \(0.625872\pi\)
\(740\) 0 0
\(741\) −346.497 + 835.331i −0.467607 + 1.12730i
\(742\) 0 0
\(743\) 1160.78 1.56229 0.781145 0.624349i \(-0.214636\pi\)
0.781145 + 0.624349i \(0.214636\pi\)
\(744\) 0 0
\(745\) 1259.47i 1.69057i
\(746\) 0 0
\(747\) 1208.42 + 1.21296i 1.61770 + 0.00162377i
\(748\) 0 0
\(749\) 772.011 772.011i 1.03072 1.03072i
\(750\) 0 0
\(751\) −1220.14 −1.62469 −0.812343 0.583181i \(-0.801808\pi\)
−0.812343 + 0.583181i \(0.801808\pi\)
\(752\) 0 0
\(753\) −28.2781 68.3663i −0.0375539 0.0907919i
\(754\) 0 0
\(755\) 591.268 591.268i 0.783136 0.783136i
\(756\) 0 0
\(757\) −202.623 + 202.623i −0.267666 + 0.267666i −0.828159 0.560493i \(-0.810612\pi\)
0.560493 + 0.828159i \(0.310612\pi\)
\(758\) 0 0
\(759\) −6.51210 15.7439i −0.00857984 0.0207430i
\(760\) 0 0
\(761\) 694.461 0.912563 0.456282 0.889835i \(-0.349181\pi\)
0.456282 + 0.889835i \(0.349181\pi\)
\(762\) 0 0
\(763\) 56.2451 56.2451i 0.0737157 0.0737157i
\(764\) 0 0
\(765\) −679.529 0.682081i −0.888273 0.000891610i
\(766\) 0 0
\(767\) 251.353i 0.327709i
\(768\) 0 0
\(769\) 405.268 0.527007 0.263503 0.964658i \(-0.415122\pi\)
0.263503 + 0.964658i \(0.415122\pi\)
\(770\) 0 0
\(771\) −395.035 + 952.347i −0.512367 + 1.23521i
\(772\) 0 0
\(773\) 142.479 + 142.479i 0.184320 + 0.184320i 0.793235 0.608916i \(-0.208395\pi\)
−0.608916 + 0.793235i \(0.708395\pi\)
\(774\) 0 0
\(775\) 526.214i 0.678985i
\(776\) 0 0
\(777\) 218.182 + 527.486i 0.280800 + 0.678875i
\(778\) 0 0
\(779\) −1358.16 1358.16i −1.74346 1.74346i
\(780\) 0 0
\(781\) −13.2165 13.2165i −0.0169226 0.0169226i
\(782\) 0 0
\(783\) 1220.03 + 507.507i 1.55815 + 0.648158i
\(784\) 0 0
\(785\) 1337.34i 1.70362i
\(786\) 0 0
\(787\) −482.883 482.883i −0.613574 0.613574i 0.330301 0.943876i \(-0.392850\pi\)
−0.943876 + 0.330301i \(0.892850\pi\)
\(788\) 0 0
\(789\) 271.803 + 112.744i 0.344491 + 0.142895i
\(790\) 0 0
\(791\) 96.6413 0.122176
\(792\) 0 0
\(793\) 176.721i 0.222852i
\(794\) 0 0
\(795\) −352.543 + 849.908i −0.443451 + 1.06907i