Properties

Label 384.3.i.c.161.7
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 161.7
Root \(-1.21144 + 1.59136i\) of defining polynomial
Character \(\chi\) \(=\) 384.161
Dual form 384.3.i.c.353.7

$q$-expansion

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

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
\(3\) 1.14944 + 2.77106i 0.383147 + 0.923687i
\(4\) 0 0
\(5\) −4.80434 4.80434i −0.960868 0.960868i 0.0383950 0.999263i \(-0.487775\pi\)
−0.999263 + 0.0383950i \(0.987775\pi\)
\(6\) 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 0.683325 0.730115i \(-0.260533\pi\)
−0.730115 + 0.683325i \(0.760533\pi\)
\(12\) 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 \(-0.894015\pi\)
0.945079 0.326842i \(-0.105985\pi\)
\(18\) 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
\(21\) −20.4002 + 8.46203i −0.971438 + 0.402954i
\(22\) 0 0
\(23\) 7.80231 0.339231 0.169615 0.985510i \(-0.445747\pi\)
0.169615 + 0.985510i \(0.445747\pi\)
\(24\) 0 0
\(25\) 21.1633i 0.846533i
\(26\) 0 0
\(27\) −24.9603 10.2949i −0.924455 0.381292i
\(28\) 0 0
\(29\) −34.6058 + 34.6058i −1.19330 + 1.19330i −0.217169 + 0.976134i \(0.569682\pi\)
−0.976134 + 0.217169i \(0.930318\pi\)
\(30\) 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 \(-0.786554\pi\)
−0.783473 + 0.621426i \(0.786554\pi\)
\(42\) 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
\(45\) 61.1492 0.0613789i 1.35887 0.00136398i
\(46\) 0 0
\(47\) 23.0508i 0.490442i −0.969467 0.245221i \(-0.921139\pi\)
0.969467 0.245221i \(-0.0788606\pi\)
\(48\) 0 0
\(49\) −5.19710 −0.106063
\(50\) 0 0
\(51\) 30.7938 12.7733i 0.603800 0.250457i
\(52\) 0 0
\(53\) −31.9199 31.9199i −0.602263 0.602263i 0.338650 0.940913i \(-0.390030\pi\)
−0.940913 + 0.338650i \(0.890030\pi\)
\(54\) 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 0.840530 0.541764i \(-0.182244\pi\)
−0.541764 + 0.840530i \(0.682244\pi\)
\(60\) 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
\(69\) 8.96830 + 21.6207i 0.129975 + 0.313343i
\(70\) 0 0
\(71\) 25.6785 0.361669 0.180834 0.983514i \(-0.442120\pi\)
0.180834 + 0.983514i \(0.442120\pi\)
\(72\) 0 0
\(73\) 56.1845i 0.769650i 0.922990 + 0.384825i \(0.125738\pi\)
−0.922990 + 0.384825i \(0.874262\pi\)
\(74\) 0 0
\(75\) −58.6449 + 24.3260i −0.781932 + 0.324347i
\(76\) 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 \(0.549909\pi\)
−0.987733 + 0.156151i \(0.950091\pi\)
\(84\) 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 \(-0.581117\pi\)
−0.252086 + 0.967705i \(0.581117\pi\)
\(90\) 0 0
\(91\) 52.4878 52.4878i 0.576789 0.576789i
\(92\) 0 0
\(93\) −28.5802 68.9008i −0.307314 0.740869i
\(94\) 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
\(99\) 6.55097 0.00657558i 0.0661714 6.64200e-5i
\(100\) 0 0
\(101\) 36.3420 + 36.3420i 0.359822 + 0.359822i 0.863747 0.503925i \(-0.168111\pi\)
−0.503925 + 0.863747i \(0.668111\pi\)
\(102\) 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 0.999805 0.0197471i \(-0.00628610\pi\)
−0.0197471 + 0.999805i \(0.506286\pi\)
\(108\) 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 \(0.0184995\pi\)
−0.998312 + 0.0580853i \(0.981500\pi\)
\(114\) 0 0
\(115\) −37.4849 37.4849i −0.325956 0.325956i
\(116\) 0 0
\(117\) 90.7461 0.0910869i 0.775607 0.000778521i
\(118\) 0 0
\(119\) 81.8098 0.687477
\(120\) 0 0
\(121\) 120.470i 0.995621i
\(122\) 0 0
\(123\) −73.8456 178.026i −0.600371 1.44737i
\(124\) 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 −0.890498 0.454988i \(-0.849644\pi\)
0.454988 + 0.890498i \(0.349644\pi\)
\(132\) 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 \(-0.294132\pi\)
0.602599 + 0.798045i \(0.294132\pi\)
\(138\) 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
\(141\) 63.8752 26.4955i 0.453015 0.187912i
\(142\) 0 0
\(143\) 7.33920i 0.0513231i
\(144\) 0 0
\(145\) 332.516 2.29321
\(146\) 0 0
\(147\) −5.97376 14.4015i −0.0406378 0.0979693i
\(148\) 0 0
\(149\) 131.077 + 131.077i 0.879709 + 0.879709i 0.993504 0.113795i \(-0.0363006\pi\)
−0.113795 + 0.993504i \(0.536301\pi\)
\(150\) 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
\(165\) −13.7043 + 5.68458i −0.0830566 + 0.0344520i
\(166\) 0 0
\(167\) −60.3220 −0.361210 −0.180605 0.983556i \(-0.557806\pi\)
−0.180605 + 0.983556i \(0.557806\pi\)
\(168\) 0 0
\(169\) 67.3351i 0.398432i
\(170\) 0 0
\(171\) 269.072 0.270083i 1.57352 0.00157943i
\(172\) 0 0
\(173\) −74.8292 + 74.8292i −0.432539 + 0.432539i −0.889491 0.456952i \(-0.848941\pi\)
0.456952 + 0.889491i \(0.348941\pi\)
\(174\) 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 −0.695943 0.718097i \(-0.745013\pi\)
0.718097 + 0.695943i \(0.245013\pi\)
\(180\) 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
\(189\) 75.7896 183.754i 0.401003 0.972245i
\(190\) 0 0
\(191\) 68.8639i 0.360544i 0.983617 + 0.180272i \(0.0576978\pi\)
−0.983617 + 0.180272i \(0.942302\pi\)
\(192\) 0 0
\(193\) −366.645 −1.89971 −0.949856 0.312686i \(-0.898771\pi\)
−0.949856 + 0.312686i \(0.898771\pi\)
\(194\) 0 0
\(195\) −189.837 + 78.7446i −0.973522 + 0.403819i
\(196\) 0 0
\(197\) −246.744 246.744i −1.25251 1.25251i −0.954593 0.297912i \(-0.903710\pi\)
−0.297912 0.954593i \(-0.596290\pi\)
\(198\) 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
\(213\) 29.5159 + 71.1567i 0.138572 + 0.334069i
\(214\) 0 0
\(215\) −69.5724 −0.323593
\(216\) 0 0
\(217\) 183.048i 0.843541i
\(218\) 0 0
\(219\) −155.691 + 64.5807i −0.710916 + 0.294889i
\(220\) 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 \(-0.363717\pi\)
0.909737 0.415186i \(-0.136283\pi\)
\(228\) 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 \(-0.529292\pi\)
−0.0918923 + 0.995769i \(0.529292\pi\)
\(234\) 0 0
\(235\) −110.744 + 110.744i −0.471250 + 0.471250i
\(236\) 0 0
\(237\) 41.0365 + 98.9305i 0.173150 + 0.417428i
\(238\) 0 0
\(239\) 100.598i 0.420913i −0.977603 0.210456i \(-0.932505\pi\)
0.977603 0.210456i \(-0.0674950\pi\)
\(240\) 0 0
\(241\) −5.23162 −0.0217080 −0.0108540 0.999941i \(-0.503455\pi\)
−0.0108540 + 0.999941i \(0.503455\pi\)
\(242\) 0 0
\(243\) 224.269 93.5551i 0.922916 0.385001i
\(244\) 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 0.740990 0.671516i \(-0.234356\pi\)
−0.671516 + 0.740990i \(0.734356\pi\)
\(252\) 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 \(-0.766881\pi\)
0.743595 0.668630i \(-0.233119\pi\)
\(258\) 0 0
\(259\) 134.545 + 134.545i 0.519480 + 0.519480i
\(260\) 0 0
\(261\) −0.442114 440.460i −0.00169392 1.68758i
\(262\) 0 0
\(263\) −98.0863 −0.372952 −0.186476 0.982460i \(-0.559707\pi\)
−0.186476 + 0.982460i \(0.559707\pi\)
\(264\) 0 0
\(265\) 306.708i 1.15739i
\(266\) 0 0
\(267\) −51.5769 124.341i −0.193172 0.465697i
\(268\) 0 0
\(269\) 126.560 126.560i 0.470482 0.470482i −0.431589 0.902070i \(-0.642047\pi\)
0.902070 + 0.431589i \(0.142047\pi\)
\(270\) 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 \(-0.562213\pi\)
−0.194204 + 0.980961i \(0.562213\pi\)
\(282\) 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
\(285\) −562.888 + 233.487i −1.97504 + 0.819252i
\(286\) 0 0
\(287\) 472.962i 1.64795i
\(288\) 0 0
\(289\) 165.509 0.572697
\(290\) 0 0
\(291\) −94.6721 228.235i −0.325334 0.784311i
\(292\) 0 0
\(293\) −19.4639 19.4639i −0.0664296 0.0664296i 0.673111 0.739541i \(-0.264957\pi\)
−0.739541 + 0.673111i \(0.764957\pi\)
\(294\) 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
\(309\) −242.517 + 100.596i −0.784844 + 0.325554i
\(310\) 0 0
\(311\) 360.965 1.16066 0.580330 0.814381i \(-0.302924\pi\)
0.580330 + 0.814381i \(0.302924\pi\)
\(312\) 0 0
\(313\) 73.9217i 0.236172i 0.993003 + 0.118086i \(0.0376758\pi\)
−0.993003 + 0.118086i \(0.962324\pi\)
\(314\) 0 0
\(315\) 0.451863 + 450.172i 0.00143449 + 1.42912i
\(316\) 0 0
\(317\) 172.709 172.709i 0.544825 0.544825i −0.380115 0.924939i \(-0.624116\pi\)
0.924939 + 0.380115i \(0.124116\pi\)
\(318\) 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
\(333\) 0.233489 + 232.615i 0.000701168 + 0.698544i
\(334\) 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
\(339\) −36.3765 + 15.0890i −0.107305 + 0.0445104i
\(340\) 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 0.411021 0.911626i \(-0.365172\pi\)
−0.911626 + 0.411021i \(0.865172\pi\)
\(348\) 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 \(0.408152\pi\)
−0.284561 + 0.958658i \(0.591848\pi\)
\(354\) 0 0
\(355\) −123.368 123.368i −0.347516 0.347516i
\(356\) 0 0
\(357\) 94.0355 + 226.700i 0.263405 + 0.635014i
\(358\) 0 0
\(359\) −240.896 −0.671020 −0.335510 0.942037i \(-0.608909\pi\)
−0.335510 + 0.942037i \(0.608909\pi\)
\(360\) 0 0
\(361\) 532.827i 1.47598i
\(362\) 0 0
\(363\) 333.830 138.473i 0.919643 0.381469i
\(364\) 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
\(381\) 101.462 + 244.604i 0.266305 + 0.642004i
\(382\) 0 0
\(383\) 69.4683i 0.181379i 0.995879 + 0.0906897i \(0.0289071\pi\)
−0.995879 + 0.0906897i \(0.971093\pi\)
\(384\) 0 0
\(385\) −36.4083 −0.0945669
\(386\) 0 0
\(387\) 0.0925037 + 92.1575i 0.000239028 + 0.238133i
\(388\) 0 0
\(389\) 265.362 + 265.362i 0.682165 + 0.682165i 0.960488 0.278322i \(-0.0897783\pi\)
−0.278322 + 0.960488i \(0.589778\pi\)
\(390\) 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 \(-0.689403\pi\)
0.560531 0.828133i \(-0.310597\pi\)
\(402\) 0 0
\(403\) 177.275 + 177.275i 0.439889 + 0.439889i
\(404\) 0 0
\(405\) −388.369 + 389.932i −0.958937 + 0.962795i
\(406\) 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
\(411\) 189.787 + 457.536i 0.461768 + 1.11323i
\(412\) 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 −0.999393 0.0348367i \(-0.988909\pi\)
0.0348367 + 0.999393i \(0.488909\pi\)
\(420\) 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
\(429\) −20.3374 + 8.43598i −0.0474065 + 0.0196643i
\(430\) 0 0
\(431\) 766.652i 1.77877i 0.457155 + 0.889387i \(0.348868\pi\)
−0.457155 + 0.889387i \(0.651132\pi\)
\(432\) 0 0
\(433\) 151.222 0.349243 0.174622 0.984636i \(-0.444130\pi\)
0.174622 + 0.984636i \(0.444130\pi\)
\(434\) 0 0
\(435\) 382.207 + 921.422i 0.878638 + 2.11821i
\(436\) 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 0.583911 0.811818i \(-0.301522\pi\)
−0.811818 + 0.583911i \(0.801522\pi\)
\(444\) 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 \(-0.953139\pi\)
0.989183 0.146687i \(-0.0468611\pi\)
\(450\) 0 0
\(451\) 33.0663 + 33.0663i 0.0733178 + 0.0733178i
\(452\) 0 0
\(453\) 341.034 141.461i 0.752833 0.312277i
\(454\) 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
\(459\) −114.403 + 277.374i −0.249245 + 0.604302i
\(460\) 0 0
\(461\) 303.536 303.536i 0.658430 0.658430i −0.296579 0.955008i \(-0.595846\pi\)
0.955008 + 0.296579i \(0.0958457\pi\)
\(462\) 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 −0.773880 0.633333i \(-0.781687\pi\)
0.633333 + 0.773880i \(0.281687\pi\)
\(468\) 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
\(477\) 406.274 0.407800i 0.851728 0.000854927i
\(478\) 0 0
\(479\) 373.272i 0.779273i −0.920969 0.389636i \(-0.872601\pi\)
0.920969 0.389636i \(-0.127399\pi\)
\(480\) 0 0
\(481\) −260.604 −0.541797
\(482\) 0 0
\(483\) −159.169 + 66.0234i −0.329542 + 0.136694i
\(484\) 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 0.928426 0.371518i \(-0.121163\pi\)
−0.371518 + 0.928426i \(0.621163\pi\)
\(492\) 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
\(501\) −69.3366 167.156i −0.138396 0.333645i
\(502\) 0 0
\(503\) −864.426 −1.71854 −0.859270 0.511522i \(-0.829082\pi\)
−0.859270 + 0.511522i \(0.829082\pi\)
\(504\) 0 0
\(505\) 349.198i 0.691482i
\(506\) 0 0
\(507\) 186.590 77.3977i 0.368027 0.152658i
\(508\) 0 0
\(509\) 171.041 171.041i 0.336033 0.336033i −0.518839 0.854872i \(-0.673635\pi\)
0.854872 + 0.518839i \(0.173635\pi\)
\(510\) 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 \(-0.390452\pi\)
0.337401 + 0.941361i \(0.390452\pi\)
\(522\) 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
\(525\) −179.085 431.736i −0.341114 0.822354i
\(526\) 0 0
\(527\) 276.309i 0.524306i
\(528\) 0 0
\(529\) −468.124 −0.884922
\(530\) 0 0
\(531\) −224.357 + 0.225200i −0.422519 + 0.000424106i
\(532\) 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
\(549\) −157.742 + 0.158334i −0.287325 + 0.000288404i
\(550\) 0 0
\(551\) 1463.16 2.65546
\(552\) 0 0
\(553\) 262.828i 0.475277i
\(554\) 0 0
\(555\) −201.851 486.621i −0.363696 0.876794i
\(556\) 0 0
\(557\) −31.8976 + 31.8976i −0.0572667 + 0.0572667i −0.735160 0.677893i \(-0.762893\pi\)
0.677893 + 0.735160i \(0.262893\pi\)
\(558\) 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 −0.735740 0.677265i \(-0.763165\pi\)
0.677265 + 0.735740i \(0.263165\pi\)
\(564\) 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 \(-0.307476\pi\)
0.568624 + 0.822597i \(0.307476\pi\)
\(570\) 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
\(573\) −190.826 + 79.1550i −0.333030 + 0.138141i
\(574\) 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
\(579\) −421.436 1015.99i −0.727869 1.75474i
\(580\) 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 0.996027 0.0890534i \(-0.0283842\pi\)
−0.0890534 + 0.996027i \(0.528384\pi\)
\(588\) 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 \(0.0689092\pi\)
−0.976659 + 0.214798i \(0.931091\pi\)
\(594\) 0 0
\(595\) −393.042 393.042i −0.660574 0.660574i
\(596\) 0 0
\(597\) 797.517 330.811i 1.33587 0.554123i
\(598\) 0 0
\(599\) −624.772 −1.04303 −0.521513 0.853244i \(-0.674632\pi\)
−0.521513 + 0.853244i \(0.674632\pi\)
\(600\) 0 0
\(601\) 386.910i 0.643777i 0.946778 + 0.321889i \(0.104318\pi\)
−0.946778 + 0.321889i \(0.895682\pi\)
\(602\) 0 0
\(603\) −523.658 + 0.525625i −0.868422 + 0.000871684i
\(604\) 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 \(-0.753808\pi\)
−0.715514 + 0.698598i \(0.753808\pi\)
\(618\) 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
\(621\) −194.748 80.3239i −0.313604 0.129346i
\(622\) 0 0
\(623\) 330.337i 0.530235i
\(624\) 0 0
\(625\) 706.197 1.12991
\(626\) 0 0
\(627\) −60.3027 + 25.0136i −0.0961765 + 0.0398942i
\(628\) 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 \(-0.798233\pi\)
0.805741 0.592267i \(-0.201767\pi\)
\(642\) 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
\(645\) −79.9694 192.789i −0.123984 0.298898i
\(646\) 0 0
\(647\) 747.683 1.15561 0.577807 0.816173i \(-0.303908\pi\)
0.577807 + 0.816173i \(0.303908\pi\)
\(648\) 0 0
\(649\) 18.1452i 0.0279587i
\(650\) 0 0
\(651\) 507.239 210.403i 0.779168 0.323200i
\(652\) 0 0
\(653\) −605.127 + 605.127i −0.926688 + 0.926688i −0.997490 0.0708022i \(-0.977444\pi\)
0.0708022 + 0.997490i \(0.477444\pi\)
\(654\) 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 −0.101418 0.994844i \(-0.532338\pi\)
0.994844 + 0.101418i \(0.0323381\pi\)
\(660\) 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
\(669\) −52.0695 125.529i −0.0778319 0.187636i
\(670\) 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
\(675\) 217.874 528.242i 0.322776 0.782581i
\(676\) 0 0
\(677\) −150.713 150.713i −0.222618 0.222618i 0.586982 0.809600i \(-0.300316\pi\)
−0.809600 + 0.586982i \(0.800316\pi\)
\(678\) 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 0.143536 0.989645i \(-0.454153\pi\)
−0.989645 + 0.143536i \(0.954153\pi\)
\(684\) 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
\(693\) 0.0484085 + 48.2274i 6.98536e−5 + 0.0695922i
\(694\) 0 0
\(695\) 913.595 1.31453
\(696\) 0 0
\(697\) 713.929i 1.02429i
\(698\) 0 0
\(699\) −49.2212 118.662i −0.0704165 0.169760i
\(700\) 0 0
\(701\) 413.745 413.745i 0.590221 0.590221i −0.347470 0.937691i \(-0.612959\pi\)
0.937691 + 0.347470i \(0.112959\pi\)
\(702\) 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
\(717\) 278.764 115.632i 0.388792 0.161272i
\(718\) 0 0
\(719\) 567.983i 0.789963i −0.918689 0.394981i \(-0.870751\pi\)
0.918689 0.394981i \(-0.129249\pi\)
\(720\) 0 0
\(721\) −644.293 −0.893610
\(722\) 0 0
\(723\) −6.01344 14.4972i −0.00831735 0.0200514i
\(724\) 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
\(741\) −835.331 + 346.497i −1.12730 + 0.467607i
\(742\) 0 0
\(743\) −1160.78 −1.56229 −0.781145 0.624349i \(-0.785364\pi\)
−0.781145 + 0.624349i \(0.785364\pi\)
\(744\) 0 0
\(745\) 1259.47i 1.69057i
\(746\) 0 0
\(747\) −1.21296 1208.42i −0.00162377 1.61770i
\(748\) 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 \(-0.650819\pi\)
−0.456282 + 0.889835i \(0.650819\pi\)
\(762\) 0 0
\(763\) 56.2451 56.2451i 0.0737157 0.0737157i
\(764\) 0 0
\(765\) −0.682081 679.529i −0.000891610 0.888273i
\(766\) 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
\(771\) 952.347 395.035i 1.23521 0.512367i
\(772\) 0 0
\(773\) −142.479 142.479i −0.184320 0.184320i 0.608916 0.793235i \(-0.291605\pi\)
−0.793235 + 0.608916i \(0.791605\pi\)
\(774\) 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
\(789\) −112.744 271.803i −0.142895 0.344491i
\(790\) 0 0
\(791\) −96.6413 −0.122176
\(792\) 0 0
\(793\) 176.721i 0.222852i
\(794\) 0 0