Properties

Label 260.2.z.a.49.3
Level $260$
Weight $2$
Character 260.49
Analytic conductor $2.076$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.z (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.07611045255\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 7x^{14} + 21x^{12} - 22x^{10} - 26x^{8} - 198x^{6} + 1701x^{4} - 5103x^{2} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.3
Root \(-1.56631 - 0.739379i\) of defining polynomial
Character \(\chi\) \(=\) 260.49
Dual form 260.2.z.a.69.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.28064 + 0.739379i) q^{3} +(-0.494086 - 2.18080i) q^{5} +(-1.56631 + 2.71292i) q^{7} +(-0.406637 + 0.704315i) q^{9} +O(q^{10})\) \(q+(-1.28064 + 0.739379i) q^{3} +(-0.494086 - 2.18080i) q^{5} +(-1.56631 + 2.71292i) q^{7} +(-0.406637 + 0.704315i) q^{9} +(-4.01176 + 2.31619i) q^{11} +(2.44512 + 2.64979i) q^{13} +(2.24518 + 2.42751i) q^{15} +(-5.87021 - 3.38917i) q^{17} +(1.45442 + 0.839708i) q^{19} -4.63238i q^{21} +(-4.79118 + 2.76619i) q^{23} +(-4.51176 + 2.15500i) q^{25} -5.63891i q^{27} +(3.87062 + 6.70410i) q^{29} -1.46127i q^{31} +(3.42509 - 5.93242i) q^{33} +(6.69023 + 2.07538i) q^{35} +(-3.72577 - 6.45322i) q^{37} +(-5.09053 - 1.58556i) q^{39} +(4.78901 - 2.76494i) q^{41} +(10.7707 + 6.21849i) q^{43} +(1.73688 + 0.538800i) q^{45} +1.97634 q^{47} +(-1.40664 - 2.43637i) q^{49} +10.0235 q^{51} -5.65865i q^{53} +(7.03329 + 7.60444i) q^{55} -2.48345 q^{57} +(2.27725 + 1.31477i) q^{59} +(-4.87062 + 8.43615i) q^{61} +(-1.27384 - 2.20635i) q^{63} +(4.57055 - 6.64154i) q^{65} +(0.317776 + 0.550404i) q^{67} +(4.09053 - 7.08500i) q^{69} +(-12.0089 - 6.93335i) q^{71} +4.89025 q^{73} +(4.18459 - 6.09569i) q^{75} -14.5115i q^{77} -6.21024 q^{79} +(2.94938 + 5.10848i) q^{81} -3.33075 q^{83} +(-4.49070 + 14.4763i) q^{85} +(-9.91375 - 5.72371i) q^{87} +(-2.27725 + 1.31477i) q^{89} +(-11.0185 + 2.48305i) q^{91} +(1.08043 + 1.87136i) q^{93} +(1.11263 - 3.58668i) q^{95} +(-3.13942 + 5.43764i) q^{97} -3.76739i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 10 q^{9} - 6 q^{11} + 6 q^{15} - 18 q^{19} - 14 q^{25} + 12 q^{29} + 18 q^{39} - 48 q^{41} + 45 q^{45} - 6 q^{49} + 44 q^{51} + 2 q^{55} - 30 q^{59} - 28 q^{61} - 15 q^{65} - 34 q^{69} - 18 q^{71} - 42 q^{75} - 16 q^{79} - 44 q^{81} - 45 q^{85} + 30 q^{89} - 10 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.28064 + 0.739379i −0.739379 + 0.426881i −0.821844 0.569713i \(-0.807054\pi\)
0.0824643 + 0.996594i \(0.473721\pi\)
\(4\) 0 0
\(5\) −0.494086 2.18080i −0.220962 0.975282i
\(6\) 0 0
\(7\) −1.56631 + 2.71292i −0.592008 + 1.02539i 0.401953 + 0.915660i \(0.368331\pi\)
−0.993962 + 0.109729i \(0.965002\pi\)
\(8\) 0 0
\(9\) −0.406637 + 0.704315i −0.135546 + 0.234772i
\(10\) 0 0
\(11\) −4.01176 + 2.31619i −1.20959 + 0.698358i −0.962670 0.270678i \(-0.912752\pi\)
−0.246921 + 0.969036i \(0.579419\pi\)
\(12\) 0 0
\(13\) 2.44512 + 2.64979i 0.678155 + 0.734919i
\(14\) 0 0
\(15\) 2.24518 + 2.42751i 0.579704 + 0.626779i
\(16\) 0 0
\(17\) −5.87021 3.38917i −1.42373 0.821994i −0.427119 0.904195i \(-0.640471\pi\)
−0.996616 + 0.0822017i \(0.973805\pi\)
\(18\) 0 0
\(19\) 1.45442 + 0.839708i 0.333666 + 0.192642i 0.657468 0.753483i \(-0.271628\pi\)
−0.323802 + 0.946125i \(0.604961\pi\)
\(20\) 0 0
\(21\) 4.63238i 1.01087i
\(22\) 0 0
\(23\) −4.79118 + 2.76619i −0.999030 + 0.576790i −0.907961 0.419054i \(-0.862362\pi\)
−0.0910690 + 0.995845i \(0.529028\pi\)
\(24\) 0 0
\(25\) −4.51176 + 2.15500i −0.902352 + 0.431000i
\(26\) 0 0
\(27\) 5.63891i 1.08521i
\(28\) 0 0
\(29\) 3.87062 + 6.70410i 0.718755 + 1.24492i 0.961493 + 0.274829i \(0.0886212\pi\)
−0.242738 + 0.970092i \(0.578045\pi\)
\(30\) 0 0
\(31\) 1.46127i 0.262451i −0.991353 0.131226i \(-0.958109\pi\)
0.991353 0.131226i \(-0.0418912\pi\)
\(32\) 0 0
\(33\) 3.42509 5.93242i 0.596231 1.03270i
\(34\) 0 0
\(35\) 6.69023 + 2.07538i 1.13085 + 0.350804i
\(36\) 0 0
\(37\) −3.72577 6.45322i −0.612512 1.06090i −0.990816 0.135220i \(-0.956826\pi\)
0.378303 0.925682i \(-0.376508\pi\)
\(38\) 0 0
\(39\) −5.09053 1.58556i −0.815137 0.253892i
\(40\) 0 0
\(41\) 4.78901 2.76494i 0.747918 0.431811i −0.0770232 0.997029i \(-0.524542\pi\)
0.824941 + 0.565219i \(0.191208\pi\)
\(42\) 0 0
\(43\) 10.7707 + 6.21849i 1.64252 + 0.948311i 0.979933 + 0.199329i \(0.0638764\pi\)
0.662591 + 0.748982i \(0.269457\pi\)
\(44\) 0 0
\(45\) 1.73688 + 0.538800i 0.258919 + 0.0803196i
\(46\) 0 0
\(47\) 1.97634 0.288279 0.144140 0.989557i \(-0.453959\pi\)
0.144140 + 0.989557i \(0.453959\pi\)
\(48\) 0 0
\(49\) −1.40664 2.43637i −0.200948 0.348052i
\(50\) 0 0
\(51\) 10.0235 1.40357
\(52\) 0 0
\(53\) 5.65865i 0.777276i −0.921391 0.388638i \(-0.872946\pi\)
0.921391 0.388638i \(-0.127054\pi\)
\(54\) 0 0
\(55\) 7.03329 + 7.60444i 0.948369 + 1.02538i
\(56\) 0 0
\(57\) −2.48345 −0.328941
\(58\) 0 0
\(59\) 2.27725 + 1.31477i 0.296473 + 0.171169i 0.640857 0.767660i \(-0.278579\pi\)
−0.344384 + 0.938829i \(0.611912\pi\)
\(60\) 0 0
\(61\) −4.87062 + 8.43615i −0.623618 + 1.08014i 0.365188 + 0.930934i \(0.381005\pi\)
−0.988806 + 0.149205i \(0.952329\pi\)
\(62\) 0 0
\(63\) −1.27384 2.20635i −0.160488 0.277974i
\(64\) 0 0
\(65\) 4.57055 6.64154i 0.566907 0.823782i
\(66\) 0 0
\(67\) 0.317776 + 0.550404i 0.0388225 + 0.0672426i 0.884784 0.466002i \(-0.154306\pi\)
−0.845961 + 0.533244i \(0.820973\pi\)
\(68\) 0 0
\(69\) 4.09053 7.08500i 0.492441 0.852934i
\(70\) 0 0
\(71\) −12.0089 6.93335i −1.42520 0.822838i −0.428460 0.903561i \(-0.640944\pi\)
−0.996737 + 0.0807229i \(0.974277\pi\)
\(72\) 0 0
\(73\) 4.89025 0.572360 0.286180 0.958176i \(-0.407614\pi\)
0.286180 + 0.958176i \(0.407614\pi\)
\(74\) 0 0
\(75\) 4.18459 6.09569i 0.483194 0.703869i
\(76\) 0 0
\(77\) 14.5115i 1.65373i
\(78\) 0 0
\(79\) −6.21024 −0.698707 −0.349354 0.936991i \(-0.613599\pi\)
−0.349354 + 0.936991i \(0.613599\pi\)
\(80\) 0 0
\(81\) 2.94938 + 5.10848i 0.327709 + 0.567609i
\(82\) 0 0
\(83\) −3.33075 −0.365597 −0.182798 0.983150i \(-0.558516\pi\)
−0.182798 + 0.983150i \(0.558516\pi\)
\(84\) 0 0
\(85\) −4.49070 + 14.4763i −0.487085 + 1.57017i
\(86\) 0 0
\(87\) −9.91375 5.72371i −1.06287 0.613646i
\(88\) 0 0
\(89\) −2.27725 + 1.31477i −0.241388 + 0.139366i −0.615815 0.787891i \(-0.711173\pi\)
0.374426 + 0.927257i \(0.377840\pi\)
\(90\) 0 0
\(91\) −11.0185 + 2.48305i −1.15505 + 0.260294i
\(92\) 0 0
\(93\) 1.08043 + 1.87136i 0.112035 + 0.194051i
\(94\) 0 0
\(95\) 1.11263 3.58668i 0.114153 0.367985i
\(96\) 0 0
\(97\) −3.13942 + 5.43764i −0.318760 + 0.552108i −0.980230 0.197864i \(-0.936600\pi\)
0.661470 + 0.749972i \(0.269933\pi\)
\(98\) 0 0
\(99\) 3.76739i 0.378637i
\(100\) 0 0
\(101\) 8.41840 + 14.5811i 0.837662 + 1.45087i 0.891845 + 0.452342i \(0.149411\pi\)
−0.0541831 + 0.998531i \(0.517255\pi\)
\(102\) 0 0
\(103\) 9.86212i 0.971744i 0.874030 + 0.485872i \(0.161498\pi\)
−0.874030 + 0.485872i \(0.838502\pi\)
\(104\) 0 0
\(105\) −10.1023 + 2.28879i −0.985882 + 0.223363i
\(106\) 0 0
\(107\) 3.53096 2.03860i 0.341351 0.197079i −0.319519 0.947580i \(-0.603521\pi\)
0.660869 + 0.750501i \(0.270188\pi\)
\(108\) 0 0
\(109\) 11.6762i 1.11837i −0.829042 0.559186i \(-0.811114\pi\)
0.829042 0.559186i \(-0.188886\pi\)
\(110\) 0 0
\(111\) 9.54275 + 5.50951i 0.905757 + 0.522939i
\(112\) 0 0
\(113\) 3.30892 + 1.91041i 0.311277 + 0.179716i 0.647498 0.762067i \(-0.275815\pi\)
−0.336221 + 0.941783i \(0.609149\pi\)
\(114\) 0 0
\(115\) 8.39975 + 9.08186i 0.783281 + 0.846888i
\(116\) 0 0
\(117\) −2.86056 + 0.644637i −0.264459 + 0.0595967i
\(118\) 0 0
\(119\) 18.3891 10.6170i 1.68573 0.973254i
\(120\) 0 0
\(121\) 5.22947 9.05771i 0.475407 0.823428i
\(122\) 0 0
\(123\) −4.08867 + 7.08179i −0.368663 + 0.638544i
\(124\) 0 0
\(125\) 6.92882 + 8.77448i 0.619732 + 0.784813i
\(126\) 0 0
\(127\) −9.91375 + 5.72371i −0.879703 + 0.507897i −0.870561 0.492061i \(-0.836244\pi\)
−0.00914258 + 0.999958i \(0.502910\pi\)
\(128\) 0 0
\(129\) −18.3913 −1.61926
\(130\) 0 0
\(131\) −4.36778 −0.381615 −0.190807 0.981628i \(-0.561111\pi\)
−0.190807 + 0.981628i \(0.561111\pi\)
\(132\) 0 0
\(133\) −4.55613 + 2.63048i −0.395066 + 0.228092i
\(134\) 0 0
\(135\) −12.2973 + 2.78610i −1.05839 + 0.239790i
\(136\) 0 0
\(137\) −2.76290 + 4.78548i −0.236050 + 0.408851i −0.959577 0.281445i \(-0.909186\pi\)
0.723527 + 0.690296i \(0.242520\pi\)
\(138\) 0 0
\(139\) −5.64787 + 9.78240i −0.479046 + 0.829732i −0.999711 0.0240289i \(-0.992351\pi\)
0.520665 + 0.853761i \(0.325684\pi\)
\(140\) 0 0
\(141\) −2.53099 + 1.46127i −0.213148 + 0.123061i
\(142\) 0 0
\(143\) −15.9467 4.96694i −1.33353 0.415356i
\(144\) 0 0
\(145\) 12.7079 11.7534i 1.05533 0.976069i
\(146\) 0 0
\(147\) 3.60280 + 2.08008i 0.297154 + 0.171562i
\(148\) 0 0
\(149\) −5.25802 3.03572i −0.430754 0.248696i 0.268914 0.963164i \(-0.413335\pi\)
−0.699668 + 0.714468i \(0.746669\pi\)
\(150\) 0 0
\(151\) 15.1403i 1.23210i −0.787708 0.616048i \(-0.788733\pi\)
0.787708 0.616048i \(-0.211267\pi\)
\(152\) 0 0
\(153\) 4.77408 2.75632i 0.385962 0.222835i
\(154\) 0 0
\(155\) −3.18673 + 0.721991i −0.255964 + 0.0579917i
\(156\) 0 0
\(157\) 19.3218i 1.54205i 0.636804 + 0.771026i \(0.280256\pi\)
−0.636804 + 0.771026i \(0.719744\pi\)
\(158\) 0 0
\(159\) 4.18389 + 7.24671i 0.331804 + 0.574701i
\(160\) 0 0
\(161\) 17.3308i 1.36586i
\(162\) 0 0
\(163\) 0.278858 0.482997i 0.0218419 0.0378312i −0.854898 0.518796i \(-0.826380\pi\)
0.876740 + 0.480965i \(0.159714\pi\)
\(164\) 0 0
\(165\) −14.6297 4.53830i −1.13892 0.353306i
\(166\) 0 0
\(167\) −3.16473 5.48147i −0.244894 0.424169i 0.717208 0.696859i \(-0.245420\pi\)
−0.962102 + 0.272691i \(0.912086\pi\)
\(168\) 0 0
\(169\) −1.04275 + 12.9581i −0.0802113 + 0.996778i
\(170\) 0 0
\(171\) −1.18284 + 0.682912i −0.0904539 + 0.0522236i
\(172\) 0 0
\(173\) 6.62192 + 3.82317i 0.503455 + 0.290670i 0.730139 0.683298i \(-0.239455\pi\)
−0.226684 + 0.973968i \(0.572788\pi\)
\(174\) 0 0
\(175\) 1.22045 15.6155i 0.0922571 1.18042i
\(176\) 0 0
\(177\) −3.88846 −0.292275
\(178\) 0 0
\(179\) 2.27725 + 3.94432i 0.170210 + 0.294812i 0.938493 0.345298i \(-0.112222\pi\)
−0.768283 + 0.640110i \(0.778889\pi\)
\(180\) 0 0
\(181\) −7.76475 −0.577149 −0.288575 0.957457i \(-0.593181\pi\)
−0.288575 + 0.957457i \(0.593181\pi\)
\(182\) 0 0
\(183\) 14.4049i 1.06484i
\(184\) 0 0
\(185\) −12.2323 + 11.3136i −0.899337 + 0.831791i
\(186\) 0 0
\(187\) 31.3998 2.29618
\(188\) 0 0
\(189\) 15.2979 + 8.83227i 1.11276 + 0.642453i
\(190\) 0 0
\(191\) −5.71991 + 9.90717i −0.413878 + 0.716858i −0.995310 0.0967371i \(-0.969159\pi\)
0.581432 + 0.813595i \(0.302493\pi\)
\(192\) 0 0
\(193\) 1.58132 + 2.73893i 0.113826 + 0.197153i 0.917310 0.398174i \(-0.130356\pi\)
−0.803484 + 0.595327i \(0.797023\pi\)
\(194\) 0 0
\(195\) −0.942624 + 11.8848i −0.0675027 + 0.851089i
\(196\) 0 0
\(197\) 11.5791 + 20.0556i 0.824978 + 1.42890i 0.901936 + 0.431870i \(0.142146\pi\)
−0.0769575 + 0.997034i \(0.524521\pi\)
\(198\) 0 0
\(199\) 3.01176 5.21652i 0.213498 0.369789i −0.739309 0.673366i \(-0.764848\pi\)
0.952807 + 0.303577i \(0.0981810\pi\)
\(200\) 0 0
\(201\) −0.813915 0.469914i −0.0574091 0.0331452i
\(202\) 0 0
\(203\) −24.2503 −1.70204
\(204\) 0 0
\(205\) −8.39595 9.07775i −0.586399 0.634018i
\(206\) 0 0
\(207\) 4.49934i 0.312725i
\(208\) 0 0
\(209\) −7.77969 −0.538132
\(210\) 0 0
\(211\) 2.56910 + 4.44981i 0.176864 + 0.306338i 0.940805 0.338949i \(-0.110071\pi\)
−0.763941 + 0.645287i \(0.776738\pi\)
\(212\) 0 0
\(213\) 20.5055 1.40501
\(214\) 0 0
\(215\) 8.23961 26.5613i 0.561936 1.81146i
\(216\) 0 0
\(217\) 3.96430 + 2.28879i 0.269115 + 0.155373i
\(218\) 0 0
\(219\) −6.26266 + 3.61575i −0.423191 + 0.244330i
\(220\) 0 0
\(221\) −5.37281 23.8417i −0.361414 1.60377i
\(222\) 0 0
\(223\) −8.31533 14.4026i −0.556836 0.964468i −0.997758 0.0669227i \(-0.978682\pi\)
0.440922 0.897545i \(-0.354651\pi\)
\(224\) 0 0
\(225\) 0.316846 4.05400i 0.0211231 0.270267i
\(226\) 0 0
\(227\) 7.22129 12.5076i 0.479294 0.830161i −0.520424 0.853908i \(-0.674226\pi\)
0.999718 + 0.0237467i \(0.00755951\pi\)
\(228\) 0 0
\(229\) 4.00567i 0.264702i −0.991203 0.132351i \(-0.957747\pi\)
0.991203 0.132351i \(-0.0422526\pi\)
\(230\) 0 0
\(231\) 10.7295 + 18.5840i 0.705948 + 1.22274i
\(232\) 0 0
\(233\) 3.48148i 0.228079i 0.993476 + 0.114040i \(0.0363791\pi\)
−0.993476 + 0.114040i \(0.963621\pi\)
\(234\) 0 0
\(235\) −0.976482 4.31000i −0.0636987 0.281154i
\(236\) 0 0
\(237\) 7.95310 4.59173i 0.516610 0.298265i
\(238\) 0 0
\(239\) 19.1155i 1.23648i 0.785990 + 0.618239i \(0.212154\pi\)
−0.785990 + 0.618239i \(0.787846\pi\)
\(240\) 0 0
\(241\) 19.3464 + 11.1696i 1.24621 + 0.719499i 0.970351 0.241700i \(-0.0777050\pi\)
0.275857 + 0.961199i \(0.411038\pi\)
\(242\) 0 0
\(243\) 7.09611 + 4.09694i 0.455216 + 0.262819i
\(244\) 0 0
\(245\) −4.61822 + 4.27136i −0.295047 + 0.272887i
\(246\) 0 0
\(247\) 1.33118 + 5.90708i 0.0847010 + 0.375859i
\(248\) 0 0
\(249\) 4.26549 2.46268i 0.270315 0.156066i
\(250\) 0 0
\(251\) 8.37281 14.5021i 0.528487 0.915367i −0.470961 0.882154i \(-0.656093\pi\)
0.999448 0.0332127i \(-0.0105739\pi\)
\(252\) 0 0
\(253\) 12.8140 22.1946i 0.805612 1.39536i
\(254\) 0 0
\(255\) −4.95248 21.8593i −0.310136 1.36888i
\(256\) 0 0
\(257\) 13.6560 7.88431i 0.851839 0.491810i −0.00943181 0.999956i \(-0.503002\pi\)
0.861271 + 0.508146i \(0.169669\pi\)
\(258\) 0 0
\(259\) 23.3428 1.45045
\(260\) 0 0
\(261\) −6.29574 −0.389696
\(262\) 0 0
\(263\) −10.6443 + 6.14549i −0.656355 + 0.378947i −0.790887 0.611962i \(-0.790380\pi\)
0.134532 + 0.990909i \(0.457047\pi\)
\(264\) 0 0
\(265\) −12.3404 + 2.79586i −0.758063 + 0.171748i
\(266\) 0 0
\(267\) 1.94423 3.36751i 0.118985 0.206088i
\(268\) 0 0
\(269\) 6.82503 11.8213i 0.416130 0.720758i −0.579417 0.815031i \(-0.696720\pi\)
0.995546 + 0.0942739i \(0.0300529\pi\)
\(270\) 0 0
\(271\) −1.54558 + 0.892343i −0.0938875 + 0.0542060i −0.546209 0.837649i \(-0.683929\pi\)
0.452321 + 0.891855i \(0.350596\pi\)
\(272\) 0 0
\(273\) 12.2748 11.3267i 0.742906 0.685525i
\(274\) 0 0
\(275\) 13.1087 19.0954i 0.790484 1.15150i
\(276\) 0 0
\(277\) −16.9723 9.79899i −1.01977 0.588764i −0.105732 0.994395i \(-0.533719\pi\)
−0.914037 + 0.405631i \(0.867052\pi\)
\(278\) 0 0
\(279\) 1.02919 + 0.594204i 0.0616161 + 0.0355741i
\(280\) 0 0
\(281\) 18.0710i 1.07803i 0.842297 + 0.539013i \(0.181203\pi\)
−0.842297 + 0.539013i \(0.818797\pi\)
\(282\) 0 0
\(283\) 6.31095 3.64363i 0.375147 0.216591i −0.300558 0.953764i \(-0.597173\pi\)
0.675705 + 0.737172i \(0.263839\pi\)
\(284\) 0 0
\(285\) 1.22704 + 5.41590i 0.0726834 + 0.320810i
\(286\) 0 0
\(287\) 17.3230i 1.02254i
\(288\) 0 0
\(289\) 14.4729 + 25.0678i 0.851347 + 1.47458i
\(290\) 0 0
\(291\) 9.28489i 0.544290i
\(292\) 0 0
\(293\) −6.14226 + 10.6387i −0.358835 + 0.621520i −0.987766 0.155941i \(-0.950159\pi\)
0.628932 + 0.777461i \(0.283492\pi\)
\(294\) 0 0
\(295\) 1.74210 5.61584i 0.101429 0.326967i
\(296\) 0 0
\(297\) 13.0608 + 22.6219i 0.757864 + 1.31266i
\(298\) 0 0
\(299\) −19.0448 5.93194i −1.10139 0.343053i
\(300\) 0 0
\(301\) −33.7406 + 19.4801i −1.94478 + 1.12282i
\(302\) 0 0
\(303\) −21.5619 12.4488i −1.23870 0.715163i
\(304\) 0 0
\(305\) 20.8040 + 6.45365i 1.19124 + 0.369535i
\(306\) 0 0
\(307\) 31.1511 1.77789 0.888943 0.458018i \(-0.151440\pi\)
0.888943 + 0.458018i \(0.151440\pi\)
\(308\) 0 0
\(309\) −7.29185 12.6299i −0.414819 0.718487i
\(310\) 0 0
\(311\) 0.694196 0.0393643 0.0196821 0.999806i \(-0.493735\pi\)
0.0196821 + 0.999806i \(0.493735\pi\)
\(312\) 0 0
\(313\) 14.5944i 0.824925i 0.910975 + 0.412463i \(0.135331\pi\)
−0.910975 + 0.412463i \(0.864669\pi\)
\(314\) 0 0
\(315\) −4.18222 + 3.86810i −0.235641 + 0.217943i
\(316\) 0 0
\(317\) 14.5641 0.817999 0.408999 0.912535i \(-0.365878\pi\)
0.408999 + 0.912535i \(0.365878\pi\)
\(318\) 0 0
\(319\) −31.0560 17.9302i −1.73880 1.00390i
\(320\) 0 0
\(321\) −3.01460 + 5.22143i −0.168258 + 0.291432i
\(322\) 0 0
\(323\) −5.69182 9.85852i −0.316701 0.548543i
\(324\) 0 0
\(325\) −16.7421 6.68596i −0.928685 0.370870i
\(326\) 0 0
\(327\) 8.63311 + 14.9530i 0.477412 + 0.826902i
\(328\) 0 0
\(329\) −3.09556 + 5.36167i −0.170664 + 0.295598i
\(330\) 0 0
\(331\) −8.71991 5.03444i −0.479290 0.276718i 0.240831 0.970567i \(-0.422580\pi\)
−0.720120 + 0.693849i \(0.755913\pi\)
\(332\) 0 0
\(333\) 6.06013 0.332093
\(334\) 0 0
\(335\) 1.04331 0.964952i 0.0570022 0.0527210i
\(336\) 0 0
\(337\) 0.974536i 0.0530863i −0.999648 0.0265432i \(-0.991550\pi\)
0.999648 0.0265432i \(-0.00844995\pi\)
\(338\) 0 0
\(339\) −5.65006 −0.306869
\(340\) 0 0
\(341\) 3.38457 + 5.86225i 0.183285 + 0.317459i
\(342\) 0 0
\(343\) −13.1154 −0.708165
\(344\) 0 0
\(345\) −17.4720 5.42002i −0.940662 0.291804i
\(346\) 0 0
\(347\) −7.29440 4.21142i −0.391584 0.226081i 0.291262 0.956643i \(-0.405925\pi\)
−0.682846 + 0.730562i \(0.739258\pi\)
\(348\) 0 0
\(349\) 3.51639 2.03019i 0.188228 0.108674i −0.402925 0.915233i \(-0.632006\pi\)
0.591153 + 0.806560i \(0.298673\pi\)
\(350\) 0 0
\(351\) 14.9419 13.7878i 0.797540 0.735940i
\(352\) 0 0
\(353\) −1.95925 3.39351i −0.104280 0.180618i 0.809164 0.587583i \(-0.199921\pi\)
−0.913444 + 0.406965i \(0.866587\pi\)
\(354\) 0 0
\(355\) −9.18681 + 29.6147i −0.487585 + 1.57179i
\(356\) 0 0
\(357\) −15.6999 + 27.1930i −0.830927 + 1.43921i
\(358\) 0 0
\(359\) 4.23682i 0.223611i −0.993730 0.111805i \(-0.964337\pi\)
0.993730 0.111805i \(-0.0356633\pi\)
\(360\) 0 0
\(361\) −8.08978 14.0119i −0.425778 0.737469i
\(362\) 0 0
\(363\) 15.4663i 0.811768i
\(364\) 0 0
\(365\) −2.41620 10.6646i −0.126470 0.558213i
\(366\) 0 0
\(367\) −19.9499 + 11.5181i −1.04138 + 0.601238i −0.920222 0.391396i \(-0.871992\pi\)
−0.121153 + 0.992634i \(0.538659\pi\)
\(368\) 0 0
\(369\) 4.49730i 0.234120i
\(370\) 0 0
\(371\) 15.3515 + 8.86319i 0.797010 + 0.460154i
\(372\) 0 0
\(373\) −20.2984 11.7193i −1.05101 0.606801i −0.128078 0.991764i \(-0.540881\pi\)
−0.922932 + 0.384964i \(0.874214\pi\)
\(374\) 0 0
\(375\) −15.3610 6.11395i −0.793239 0.315723i
\(376\) 0 0
\(377\) −8.30032 + 26.6487i −0.427488 + 1.37248i
\(378\) 0 0
\(379\) 18.8942 10.9086i 0.970532 0.560337i 0.0711334 0.997467i \(-0.477338\pi\)
0.899398 + 0.437130i \(0.144005\pi\)
\(380\) 0 0
\(381\) 8.46398 14.6600i 0.433623 0.751057i
\(382\) 0 0
\(383\) −6.94924 + 12.0364i −0.355089 + 0.615033i −0.987133 0.159900i \(-0.948883\pi\)
0.632044 + 0.774933i \(0.282216\pi\)
\(384\) 0 0
\(385\) −31.6466 + 7.16990i −1.61286 + 0.365412i
\(386\) 0 0
\(387\) −8.75956 + 5.05733i −0.445273 + 0.257079i
\(388\) 0 0
\(389\) −6.66919 −0.338141 −0.169071 0.985604i \(-0.554077\pi\)
−0.169071 + 0.985604i \(0.554077\pi\)
\(390\) 0 0
\(391\) 37.5003 1.89647
\(392\) 0 0
\(393\) 5.59356 3.22945i 0.282158 0.162904i
\(394\) 0 0
\(395\) 3.06839 + 13.5433i 0.154388 + 0.681437i
\(396\) 0 0
\(397\) 1.66745 2.88812i 0.0836871 0.144950i −0.821144 0.570721i \(-0.806664\pi\)
0.904831 + 0.425771i \(0.139997\pi\)
\(398\) 0 0
\(399\) 3.88984 6.73741i 0.194736 0.337292i
\(400\) 0 0
\(401\) −17.1405 + 9.89607i −0.855956 + 0.494186i −0.862656 0.505791i \(-0.831201\pi\)
0.00670012 + 0.999978i \(0.497867\pi\)
\(402\) 0 0
\(403\) 3.87205 3.57298i 0.192880 0.177983i
\(404\) 0 0
\(405\) 9.68332 8.95604i 0.481168 0.445029i
\(406\) 0 0
\(407\) 29.8937 + 17.2592i 1.48178 + 0.855505i
\(408\) 0 0
\(409\) 5.06018 + 2.92150i 0.250210 + 0.144459i 0.619860 0.784712i \(-0.287189\pi\)
−0.369651 + 0.929171i \(0.620523\pi\)
\(410\) 0 0
\(411\) 8.17132i 0.403062i
\(412\) 0 0
\(413\) −7.13375 + 4.11868i −0.351029 + 0.202667i
\(414\) 0 0
\(415\) 1.64567 + 7.26368i 0.0807829 + 0.356560i
\(416\) 0 0
\(417\) 16.7037i 0.817982i
\(418\) 0 0
\(419\) −17.8553 30.9262i −0.872287 1.51085i −0.859625 0.510926i \(-0.829303\pi\)
−0.0126627 0.999920i \(-0.504031\pi\)
\(420\) 0 0
\(421\) 24.9384i 1.21542i −0.794159 0.607711i \(-0.792088\pi\)
0.794159 0.607711i \(-0.207912\pi\)
\(422\) 0 0
\(423\) −0.803653 + 1.39197i −0.0390750 + 0.0676798i
\(424\) 0 0
\(425\) 33.7886 + 2.64079i 1.63899 + 0.128097i
\(426\) 0 0
\(427\) −15.2578 26.4272i −0.738375 1.27890i
\(428\) 0 0
\(429\) 24.0944 5.42975i 1.16329 0.262151i
\(430\) 0 0
\(431\) −26.2773 + 15.1712i −1.26573 + 0.730770i −0.974177 0.225785i \(-0.927505\pi\)
−0.291553 + 0.956555i \(0.594172\pi\)
\(432\) 0 0
\(433\) 10.1016 + 5.83216i 0.485452 + 0.280276i 0.722686 0.691177i \(-0.242907\pi\)
−0.237234 + 0.971453i \(0.576241\pi\)
\(434\) 0 0
\(435\) −7.58401 + 24.4479i −0.363625 + 1.17219i
\(436\) 0 0
\(437\) −9.29116 −0.444457
\(438\) 0 0
\(439\) 1.74627 + 3.02462i 0.0833447 + 0.144357i 0.904685 0.426082i \(-0.140106\pi\)
−0.821340 + 0.570439i \(0.806773\pi\)
\(440\) 0 0
\(441\) 2.28796 0.108950
\(442\) 0 0
\(443\) 27.7833i 1.32002i 0.751255 + 0.660012i \(0.229449\pi\)
−0.751255 + 0.660012i \(0.770551\pi\)
\(444\) 0 0
\(445\) 3.99241 + 4.31662i 0.189258 + 0.204627i
\(446\) 0 0
\(447\) 8.97820 0.424654
\(448\) 0 0
\(449\) −3.16257 1.82591i −0.149251 0.0861700i 0.423515 0.905889i \(-0.360796\pi\)
−0.572766 + 0.819719i \(0.694129\pi\)
\(450\) 0 0
\(451\) −12.8082 + 22.1845i −0.603116 + 1.04463i
\(452\) 0 0
\(453\) 11.1944 + 19.3893i 0.525958 + 0.910987i
\(454\) 0 0
\(455\) 10.8591 + 22.8022i 0.509083 + 1.06899i
\(456\) 0 0
\(457\) −21.1718 36.6706i −0.990374 1.71538i −0.615061 0.788480i \(-0.710869\pi\)
−0.375313 0.926898i \(-0.622465\pi\)
\(458\) 0 0
\(459\) −19.1112 + 33.1016i −0.892035 + 1.54505i
\(460\) 0 0
\(461\) 2.87450 + 1.65960i 0.133879 + 0.0772951i 0.565444 0.824787i \(-0.308705\pi\)
−0.431565 + 0.902082i \(0.642038\pi\)
\(462\) 0 0
\(463\) 26.2130 1.21822 0.609111 0.793085i \(-0.291526\pi\)
0.609111 + 0.793085i \(0.291526\pi\)
\(464\) 0 0
\(465\) 3.54723 3.28081i 0.164499 0.152144i
\(466\) 0 0
\(467\) 2.45243i 0.113485i −0.998389 0.0567424i \(-0.981929\pi\)
0.998389 0.0567424i \(-0.0180714\pi\)
\(468\) 0 0
\(469\) −1.99094 −0.0919330
\(470\) 0 0
\(471\) −14.2862 24.7444i −0.658272 1.14016i
\(472\) 0 0
\(473\) −57.6128 −2.64904
\(474\) 0 0
\(475\) −8.37155 0.654289i −0.384113 0.0300208i
\(476\) 0 0
\(477\) 3.98548 + 2.30102i 0.182482 + 0.105356i
\(478\) 0 0
\(479\) 1.89707 1.09528i 0.0866795 0.0500444i −0.456034 0.889962i \(-0.650730\pi\)
0.542713 + 0.839918i \(0.317397\pi\)
\(480\) 0 0
\(481\) 7.98969 25.6514i 0.364299 1.16960i
\(482\) 0 0
\(483\) 12.8140 + 22.1946i 0.583059 + 1.00989i
\(484\) 0 0
\(485\) 13.4095 + 4.15979i 0.608895 + 0.188886i
\(486\) 0 0
\(487\) −9.75727 + 16.9001i −0.442144 + 0.765816i −0.997848 0.0655640i \(-0.979115\pi\)
0.555704 + 0.831380i \(0.312449\pi\)
\(488\) 0 0
\(489\) 0.824728i 0.0372955i
\(490\) 0 0
\(491\) 15.6383 + 27.0863i 0.705747 + 1.22239i 0.966421 + 0.256963i \(0.0827217\pi\)
−0.260674 + 0.965427i \(0.583945\pi\)
\(492\) 0 0
\(493\) 52.4727i 2.36325i
\(494\) 0 0
\(495\) −8.21592 + 1.86141i −0.369278 + 0.0836643i
\(496\) 0 0
\(497\) 37.6193 21.7195i 1.68746 0.974254i
\(498\) 0 0
\(499\) 31.5312i 1.41153i −0.708445 0.705766i \(-0.750603\pi\)
0.708445 0.705766i \(-0.249397\pi\)
\(500\) 0 0
\(501\) 8.10576 + 4.67986i 0.362139 + 0.209081i
\(502\) 0 0
\(503\) 4.86709 + 2.81002i 0.217013 + 0.125293i 0.604566 0.796555i \(-0.293346\pi\)
−0.387553 + 0.921847i \(0.626680\pi\)
\(504\) 0 0
\(505\) 27.6390 25.5631i 1.22992 1.13754i
\(506\) 0 0
\(507\) −8.24557 17.3657i −0.366199 0.771238i
\(508\) 0 0
\(509\) −13.7002 + 7.90980i −0.607250 + 0.350596i −0.771888 0.635758i \(-0.780688\pi\)
0.164639 + 0.986354i \(0.447354\pi\)
\(510\) 0 0
\(511\) −7.65963 + 13.2669i −0.338842 + 0.586892i
\(512\) 0 0
\(513\) 4.73504 8.20132i 0.209057 0.362097i
\(514\) 0 0
\(515\) 21.5073 4.87273i 0.947725 0.214718i
\(516\) 0 0
\(517\) −7.92861 + 4.57758i −0.348700 + 0.201322i
\(518\) 0 0
\(519\) −11.3071 −0.496326
\(520\) 0 0
\(521\) 12.6030 0.552149 0.276074 0.961136i \(-0.410966\pi\)
0.276074 + 0.961136i \(0.410966\pi\)
\(522\) 0 0
\(523\) 23.8881 13.7918i 1.04456 0.603074i 0.123435 0.992353i \(-0.460609\pi\)
0.921120 + 0.389278i \(0.127276\pi\)
\(524\) 0 0
\(525\) 9.98279 + 20.9002i 0.435685 + 0.912159i
\(526\) 0 0
\(527\) −4.95248 + 8.57794i −0.215733 + 0.373661i
\(528\) 0 0
\(529\) 3.80361 6.58804i 0.165374 0.286437i
\(530\) 0 0
\(531\) −1.85203 + 1.06927i −0.0803712 + 0.0464023i
\(532\) 0 0
\(533\) 19.0362 + 5.92925i 0.824550 + 0.256824i
\(534\) 0 0
\(535\) −6.19037 6.69306i −0.267633 0.289366i
\(536\) 0 0
\(537\) −5.83269 3.36751i −0.251699 0.145319i
\(538\) 0 0
\(539\) 11.2862 + 6.51608i 0.486130 + 0.280667i
\(540\) 0 0
\(541\) 27.6835i 1.19021i 0.803650 + 0.595103i \(0.202889\pi\)
−0.803650 + 0.595103i \(0.797111\pi\)
\(542\) 0 0
\(543\) 9.94387 5.74110i 0.426732 0.246374i
\(544\) 0 0
\(545\) −25.4633 + 5.76902i −1.09073 + 0.247118i
\(546\) 0 0
\(547\) 24.7863i 1.05979i −0.848064 0.529893i \(-0.822232\pi\)
0.848064 0.529893i \(-0.177768\pi\)
\(548\) 0 0
\(549\) −3.96114 6.86090i −0.169057 0.292816i
\(550\) 0 0
\(551\) 13.0007i 0.553850i
\(552\) 0 0
\(553\) 9.72715 16.8479i 0.413641 0.716446i
\(554\) 0 0
\(555\) 7.30019 23.5330i 0.309876 0.998919i
\(556\) 0 0
\(557\) −16.3096 28.2490i −0.691058 1.19695i −0.971491 0.237075i \(-0.923811\pi\)
0.280433 0.959874i \(-0.409522\pi\)
\(558\) 0 0
\(559\) 9.85811 + 43.7452i 0.416954 + 1.85022i
\(560\) 0 0
\(561\) −40.2119 + 23.2164i −1.69775 + 0.980196i
\(562\) 0 0
\(563\) −29.6082 17.0943i −1.24783 0.720438i −0.277158 0.960824i \(-0.589392\pi\)
−0.970677 + 0.240387i \(0.922726\pi\)
\(564\) 0 0
\(565\) 2.53132 8.16000i 0.106494 0.343294i
\(566\) 0 0
\(567\) −18.4786 −0.776027
\(568\) 0 0
\(569\) −10.1721 17.6186i −0.426438 0.738612i 0.570116 0.821564i \(-0.306898\pi\)
−0.996554 + 0.0829524i \(0.973565\pi\)
\(570\) 0 0
\(571\) 46.7490 1.95639 0.978193 0.207700i \(-0.0665978\pi\)
0.978193 + 0.207700i \(0.0665978\pi\)
\(572\) 0 0
\(573\) 16.9167i 0.706707i
\(574\) 0 0
\(575\) 15.6555 22.8054i 0.652880 0.951050i
\(576\) 0 0
\(577\) −11.8607 −0.493768 −0.246884 0.969045i \(-0.579407\pi\)
−0.246884 + 0.969045i \(0.579407\pi\)
\(578\) 0 0
\(579\) −4.05022 2.33839i −0.168321 0.0971803i
\(580\) 0 0
\(581\) 5.21697 9.03606i 0.216436 0.374879i
\(582\) 0 0
\(583\) 13.1065 + 22.7011i 0.542816 + 0.940185i
\(584\) 0 0
\(585\) 2.81919 + 5.91980i 0.116559 + 0.244754i
\(586\) 0 0
\(587\) 5.59483 + 9.69054i 0.230924 + 0.399971i 0.958080 0.286500i \(-0.0924920\pi\)
−0.727157 + 0.686472i \(0.759159\pi\)
\(588\) 0 0
\(589\) 1.22704 2.12529i 0.0505592 0.0875710i
\(590\) 0 0
\(591\) −29.6574 17.1227i −1.21994 0.704335i
\(592\) 0 0
\(593\) 27.6058 1.13363 0.566817 0.823844i \(-0.308175\pi\)
0.566817 + 0.823844i \(0.308175\pi\)
\(594\) 0 0
\(595\) −32.2392 34.8572i −1.32168 1.42901i
\(596\) 0 0
\(597\) 8.90733i 0.364553i
\(598\) 0 0
\(599\) 29.3193 1.19795 0.598976 0.800767i \(-0.295574\pi\)
0.598976 + 0.800767i \(0.295574\pi\)
\(600\) 0 0
\(601\) −16.1764 28.0184i −0.659850 1.14289i −0.980654 0.195748i \(-0.937287\pi\)
0.320804 0.947146i \(-0.396047\pi\)
\(602\) 0 0
\(603\) −0.516878 −0.0210489
\(604\) 0 0
\(605\) −22.3368 6.92914i −0.908122 0.281710i
\(606\) 0 0
\(607\) 15.4492 + 8.91963i 0.627066 + 0.362036i 0.779615 0.626259i \(-0.215415\pi\)
−0.152549 + 0.988296i \(0.548748\pi\)
\(608\) 0 0
\(609\) 31.0560 17.9302i 1.25845 0.726567i
\(610\) 0 0
\(611\) 4.83240 + 5.23689i 0.195498 + 0.211862i
\(612\) 0 0
\(613\) 13.8288 + 23.9523i 0.558542 + 0.967423i 0.997619 + 0.0689733i \(0.0219723\pi\)
−0.439077 + 0.898450i \(0.644694\pi\)
\(614\) 0 0
\(615\) 17.4641 + 5.41756i 0.704221 + 0.218457i
\(616\) 0 0
\(617\) 15.8577 27.4664i 0.638408 1.10575i −0.347374 0.937727i \(-0.612927\pi\)
0.985782 0.168028i \(-0.0537400\pi\)
\(618\) 0 0
\(619\) 47.4958i 1.90902i 0.298186 + 0.954508i \(0.403618\pi\)
−0.298186 + 0.954508i \(0.596382\pi\)
\(620\) 0 0
\(621\) 15.5983 + 27.0170i 0.625938 + 1.08416i
\(622\) 0 0
\(623\) 8.23735i 0.330022i
\(624\) 0 0
\(625\) 15.7119 19.4457i 0.628478 0.777828i
\(626\) 0 0
\(627\) 9.96300 5.75214i 0.397884 0.229718i
\(628\) 0 0
\(629\) 50.5090i 2.01392i
\(630\) 0 0
\(631\) −7.47459 4.31546i −0.297559 0.171796i 0.343787 0.939048i \(-0.388290\pi\)
−0.641346 + 0.767252i \(0.721624\pi\)
\(632\) 0 0
\(633\) −6.58020 3.79908i −0.261540 0.151000i
\(634\) 0 0
\(635\) 17.3805 + 18.7919i 0.689724 + 0.745733i
\(636\) 0 0
\(637\) 3.01645 9.68450i 0.119516 0.383714i
\(638\) 0 0
\(639\) 9.76654 5.63871i 0.386358 0.223064i
\(640\) 0 0
\(641\) 7.59556 13.1559i 0.300007 0.519627i −0.676131 0.736782i \(-0.736344\pi\)
0.976137 + 0.217155i \(0.0696778\pi\)
\(642\) 0 0
\(643\) 6.80445 11.7856i 0.268341 0.464781i −0.700092 0.714052i \(-0.746858\pi\)
0.968434 + 0.249272i \(0.0801912\pi\)
\(644\) 0 0
\(645\) 9.08687 + 40.1077i 0.357795 + 1.57924i
\(646\) 0 0
\(647\) −6.95677 + 4.01649i −0.273499 + 0.157905i −0.630477 0.776208i \(-0.717140\pi\)
0.356978 + 0.934113i \(0.383807\pi\)
\(648\) 0 0
\(649\) −12.1811 −0.478148
\(650\) 0 0
\(651\) −6.76914 −0.265304
\(652\) 0 0
\(653\) −32.3286 + 18.6649i −1.26512 + 0.730415i −0.974060 0.226292i \(-0.927340\pi\)
−0.291055 + 0.956706i \(0.594006\pi\)
\(654\) 0 0
\(655\) 2.15806 + 9.52524i 0.0843222 + 0.372182i
\(656\) 0 0
\(657\) −1.98855 + 3.44428i −0.0775809 + 0.134374i
\(658\) 0 0
\(659\) 3.72275 6.44799i 0.145018 0.251178i −0.784362 0.620303i \(-0.787009\pi\)
0.929380 + 0.369126i \(0.120343\pi\)
\(660\) 0 0
\(661\) 43.5907 25.1671i 1.69548 0.978888i 0.745542 0.666459i \(-0.232191\pi\)
0.949941 0.312429i \(-0.101142\pi\)
\(662\) 0 0
\(663\) 24.5087 + 26.5602i 0.951840 + 1.03151i
\(664\) 0 0
\(665\) 7.98766 + 8.63631i 0.309748 + 0.334902i
\(666\) 0 0
\(667\) −37.0896 21.4137i −1.43612 0.829142i
\(668\) 0 0
\(669\) 21.2979 + 12.2964i 0.823426 + 0.475405i
\(670\) 0 0
\(671\) 45.1251i 1.74203i
\(672\) 0 0
\(673\) 12.7485 7.36034i 0.491418 0.283720i −0.233744 0.972298i \(-0.575098\pi\)
0.725163 + 0.688578i \(0.241765\pi\)
\(674\) 0 0
\(675\) 12.1519 + 25.4414i 0.467725 + 0.979240i
\(676\) 0 0
\(677\) 22.0788i 0.848559i −0.905531 0.424279i \(-0.860527\pi\)
0.905531 0.424279i \(-0.139473\pi\)
\(678\) 0 0
\(679\) −9.83460 17.0340i −0.377417 0.653706i
\(680\) 0 0
\(681\) 21.3571i 0.818405i
\(682\) 0 0
\(683\) −19.9013 + 34.4700i −0.761501 + 1.31896i 0.180576 + 0.983561i \(0.442204\pi\)
−0.942077 + 0.335397i \(0.891130\pi\)
\(684\) 0 0
\(685\) 11.8013 + 3.66089i 0.450904 + 0.139875i
\(686\) 0 0
\(687\) 2.96171 + 5.12983i 0.112996 + 0.195715i
\(688\) 0 0
\(689\) 14.9942 13.8361i 0.571234 0.527113i
\(690\) 0 0
\(691\) −34.6907 + 20.0287i −1.31970 + 0.761927i −0.983680 0.179928i \(-0.942413\pi\)
−0.336017 + 0.941856i \(0.609080\pi\)
\(692\) 0 0
\(693\) 10.2206 + 5.90089i 0.388250 + 0.224156i
\(694\) 0 0
\(695\) 24.1240 + 7.48352i 0.915074 + 0.283866i
\(696\) 0 0
\(697\) −37.4833 −1.41978
\(698\) 0 0
\(699\) −2.57413 4.45853i −0.0973627 0.168637i
\(700\) 0 0
\(701\) 12.1911 0.460452 0.230226 0.973137i \(-0.426053\pi\)
0.230226 + 0.973137i \(0.426053\pi\)
\(702\) 0 0
\(703\) 12.5142i 0.471983i
\(704\) 0 0
\(705\) 4.43725 + 4.79758i 0.167117 + 0.180687i
\(706\) 0 0
\(707\) −52.7432 −1.98361
\(708\) 0 0
\(709\) −18.7237 10.8101i −0.703183 0.405983i 0.105349 0.994435i \(-0.466404\pi\)
−0.808532 + 0.588452i \(0.799737\pi\)
\(710\) 0 0
\(711\) 2.52531 4.37397i 0.0947066 0.164037i
\(712\) 0 0
\(713\) 4.04214 + 7.00119i 0.151379 + 0.262197i
\(714\) 0 0
\(715\) −2.95288 + 37.2305i −0.110431 + 1.39234i
\(716\) 0 0
\(717\) −14.1336 24.4801i −0.527829 0.914227i
\(718\) 0 0
\(719\) −1.39194 + 2.41091i −0.0519105 + 0.0899117i −0.890813 0.454370i \(-0.849864\pi\)
0.838903 + 0.544282i \(0.183198\pi\)
\(720\) 0 0
\(721\) −26.7552 15.4471i −0.996415 0.575281i
\(722\) 0 0
\(723\) −33.0343 −1.22856
\(724\) 0 0
\(725\) −31.9106 21.9061i −1.18513 0.813573i
\(726\) 0 0
\(727\) 22.5075i 0.834756i −0.908733 0.417378i \(-0.862949\pi\)
0.908733 0.417378i \(-0.137051\pi\)
\(728\) 0 0
\(729\) −29.8131 −1.10419
\(730\) 0 0
\(731\) −42.1510 73.0077i −1.55901 2.70029i
\(732\) 0 0
\(733\) 8.58058 0.316931 0.158465 0.987365i \(-0.449345\pi\)
0.158465 + 0.987365i \(0.449345\pi\)
\(734\) 0 0
\(735\) 2.75614 8.88471i 0.101662 0.327717i
\(736\) 0 0
\(737\) −2.54968 1.47206i −0.0939187 0.0542240i
\(738\) 0 0
\(739\) −4.98591 + 2.87861i −0.183410 + 0.105892i −0.588894 0.808211i \(-0.700436\pi\)
0.405484 + 0.914102i \(0.367103\pi\)
\(740\) 0 0
\(741\) −6.07234 6.58061i −0.223073 0.241745i
\(742\) 0 0
\(743\) −13.3320 23.0918i −0.489105 0.847154i 0.510817 0.859690i \(-0.329343\pi\)
−0.999921 + 0.0125354i \(0.996010\pi\)
\(744\) 0 0
\(745\) −4.02238 + 12.9666i −0.147369 + 0.475059i
\(746\) 0 0
\(747\) 1.35440 2.34590i 0.0495550 0.0858318i
\(748\) 0 0
\(749\) 12.7723i 0.466689i
\(750\) 0 0
\(751\) 21.8390 + 37.8262i 0.796916 + 1.38030i 0.921615 + 0.388104i \(0.126870\pi\)
−0.124699 + 0.992195i \(0.539797\pi\)
\(752\) 0 0
\(753\) 24.7627i 0.902404i
\(754\) 0 0
\(755\) −33.0178 + 7.48058i −1.20164 + 0.272246i
\(756\) 0 0
\(757\) −27.9105 + 16.1141i −1.01442 + 0.585678i −0.912484 0.409112i \(-0.865838\pi\)
−0.101941 + 0.994790i \(0.532505\pi\)
\(758\) 0 0
\(759\) 37.8977i 1.37560i
\(760\) 0 0
\(761\) 10.4017 + 6.00543i 0.377062 + 0.217697i 0.676539 0.736407i \(-0.263479\pi\)
−0.299477 + 0.954103i \(0.596812\pi\)
\(762\) 0 0
\(763\) 31.6765 + 18.2884i 1.14677 + 0.662086i
\(764\) 0 0
\(765\) −8.36978 9.04946i −0.302610 0.327184i
\(766\) 0 0
\(767\) 2.08430 + 9.24902i 0.0752596 + 0.333963i
\(768\) 0 0
\(769\) −43.3628 + 25.0355i −1.56370 + 0.902804i −0.566826 + 0.823838i \(0.691829\pi\)
−0.996877 + 0.0789667i \(0.974838\pi\)
\(770\) 0 0
\(771\) −11.6590 + 20.1940i −0.419888 + 0.727268i
\(772\) 0 0
\(773\) −24.3030 + 42.0940i −0.874118 + 1.51402i −0.0164180 + 0.999865i \(0.505226\pi\)
−0.857700 + 0.514151i \(0.828107\pi\)
\(774\) 0 0
\(775\) 3.14903 + 6.59288i 0.113117 + 0.236823i
\(776\) 0 0
\(777\) −29.8937 + 17.2592i −1.07243 + 0.619169i
\(778\) 0 0
\(779\) 9.28695 0.332740
\(780\) 0 0
\(781\) 64.2359 2.29854
\(782\) 0 0
\(783\) 37.8038 21.8261i 1.35100 0.780000i
\(784\) 0 0
\(785\) 42.1370 9.54665i 1.50394 0.340734i
\(786\) 0 0
\(787\) 20.3298 35.2122i 0.724679 1.25518i −0.234427 0.972134i \(-0.575321\pi\)
0.959106 0.283047i \(-0.0913452\pi\)
\(788\) 0 0
\(789\) 9.08769 15.7403i 0.323530 0.560371i
\(790\) 0 0
\(791\) −10.3656 + 5.98457i −0.368558 + 0.212787i
\(792\) 0 0
\(793\) −34.2633 + 7.72134i −1.21672 + 0.274193i
\(794\) 0 0
\(795\) 13.7364