Properties

Label 280.2.q.e.121.2
Level $280$
Weight $2$
Character 280.121
Analytic conductor $2.236$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.11337408.1
Defining polynomial: \(x^{6} + 18 x^{4} + 81 x^{2} + 12\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 121.2
Root \(-3.17656i\) of defining polynomial
Character \(\chi\) \(=\) 280.121
Dual form 280.2.q.e.81.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.352860 - 0.611171i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.647140 + 2.56539i) q^{7} +(1.25098 - 2.16676i) q^{9} +O(q^{10})\) \(q+(-0.352860 - 0.611171i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.647140 + 2.56539i) q^{7} +(1.25098 - 2.16676i) q^{9} +(2.25098 + 3.89881i) q^{11} +5.09052 q^{13} +0.705720 q^{15} +(-1.00000 - 1.73205i) q^{17} +(1.54526 - 2.67647i) q^{19} +(1.33954 - 1.30074i) q^{21} +(-2.89812 + 5.01969i) q^{23} +(-0.500000 - 0.866025i) q^{25} -3.88284 q^{27} +9.50196 q^{29} +(-2.70572 - 4.68644i) q^{31} +(1.58856 - 2.75147i) q^{33} +(-2.54526 - 0.722254i) q^{35} +(-3.54526 + 6.14057i) q^{37} +(-1.79624 - 3.11118i) q^{39} -6.59248 q^{41} +4.70572 q^{43} +(1.25098 + 2.16676i) q^{45} +(-5.04722 + 8.74204i) q^{47} +(-6.16242 + 3.32033i) q^{49} +(-0.705720 + 1.22234i) q^{51} +(-4.95670 - 8.58526i) q^{53} -4.50196 q^{55} -2.18104 q^{57} +(-4.00000 - 6.92820i) q^{59} +(4.45670 - 7.71923i) q^{61} +(6.36814 + 1.80705i) q^{63} +(-2.54526 + 4.40852i) q^{65} +(0.0585795 + 0.101463i) q^{67} +4.09052 q^{69} +(-4.09052 - 7.08499i) q^{73} +(-0.352860 + 0.611171i) q^{75} +(-8.54526 + 8.29771i) q^{77} +(7.09052 - 12.2811i) q^{79} +(-2.38284 - 4.12720i) q^{81} -10.7057 q^{83} +2.00000 q^{85} +(-3.35286 - 5.80732i) q^{87} +(-2.04526 + 3.54249i) q^{89} +(3.29428 + 13.0592i) q^{91} +(-1.90948 + 3.30732i) q^{93} +(1.54526 + 2.67647i) q^{95} -2.00000 q^{97} +11.2637 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 3q^{5} + 6q^{7} - 9q^{9} + O(q^{10}) \) \( 6q - 3q^{5} + 6q^{7} - 9q^{9} - 3q^{11} + 6q^{13} - 6q^{17} - 3q^{19} - 3q^{23} - 3q^{25} - 36q^{27} + 24q^{29} - 12q^{31} + 18q^{33} - 3q^{35} - 9q^{37} + 18q^{39} + 18q^{41} + 24q^{43} - 9q^{45} + 15q^{47} - 12q^{49} - 9q^{53} + 6q^{55} + 36q^{57} - 24q^{59} + 6q^{61} + 9q^{63} - 3q^{65} - 6q^{67} - 39q^{77} + 18q^{79} - 27q^{81} - 60q^{83} + 12q^{85} - 18q^{87} + 24q^{91} - 36q^{93} - 3q^{95} - 12q^{97} + 126q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.352860 0.611171i −0.203724 0.352860i 0.746002 0.665944i \(-0.231971\pi\)
−0.949725 + 0.313084i \(0.898638\pi\)
\(4\) 0 0
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 0.647140 + 2.56539i 0.244596 + 0.969625i
\(8\) 0 0
\(9\) 1.25098 2.16676i 0.416993 0.722254i
\(10\) 0 0
\(11\) 2.25098 + 3.89881i 0.678696 + 1.17554i 0.975374 + 0.220558i \(0.0707879\pi\)
−0.296678 + 0.954978i \(0.595879\pi\)
\(12\) 0 0
\(13\) 5.09052 1.41186 0.705928 0.708283i \(-0.250530\pi\)
0.705928 + 0.708283i \(0.250530\pi\)
\(14\) 0 0
\(15\) 0.705720 0.182216
\(16\) 0 0
\(17\) −1.00000 1.73205i −0.242536 0.420084i 0.718900 0.695113i \(-0.244646\pi\)
−0.961436 + 0.275029i \(0.911312\pi\)
\(18\) 0 0
\(19\) 1.54526 2.67647i 0.354507 0.614024i −0.632526 0.774539i \(-0.717982\pi\)
0.987033 + 0.160515i \(0.0513154\pi\)
\(20\) 0 0
\(21\) 1.33954 1.30074i 0.292312 0.283844i
\(22\) 0 0
\(23\) −2.89812 + 5.01969i −0.604300 + 1.04668i 0.387862 + 0.921717i \(0.373214\pi\)
−0.992162 + 0.124960i \(0.960120\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) −3.88284 −0.747253
\(28\) 0 0
\(29\) 9.50196 1.76447 0.882235 0.470810i \(-0.156038\pi\)
0.882235 + 0.470810i \(0.156038\pi\)
\(30\) 0 0
\(31\) −2.70572 4.68644i −0.485962 0.841710i 0.513908 0.857845i \(-0.328197\pi\)
−0.999870 + 0.0161350i \(0.994864\pi\)
\(32\) 0 0
\(33\) 1.58856 2.75147i 0.276533 0.478969i
\(34\) 0 0
\(35\) −2.54526 0.722254i −0.430228 0.122083i
\(36\) 0 0
\(37\) −3.54526 + 6.14057i −0.582837 + 1.00950i 0.412304 + 0.911046i \(0.364724\pi\)
−0.995141 + 0.0984573i \(0.968609\pi\)
\(38\) 0 0
\(39\) −1.79624 3.11118i −0.287629 0.498187i
\(40\) 0 0
\(41\) −6.59248 −1.02957 −0.514786 0.857319i \(-0.672129\pi\)
−0.514786 + 0.857319i \(0.672129\pi\)
\(42\) 0 0
\(43\) 4.70572 0.717616 0.358808 0.933411i \(-0.383183\pi\)
0.358808 + 0.933411i \(0.383183\pi\)
\(44\) 0 0
\(45\) 1.25098 + 2.16676i 0.186485 + 0.323002i
\(46\) 0 0
\(47\) −5.04722 + 8.74204i −0.736213 + 1.27516i 0.217977 + 0.975954i \(0.430054\pi\)
−0.954189 + 0.299204i \(0.903279\pi\)
\(48\) 0 0
\(49\) −6.16242 + 3.32033i −0.880346 + 0.474333i
\(50\) 0 0
\(51\) −0.705720 + 1.22234i −0.0988205 + 0.171162i
\(52\) 0 0
\(53\) −4.95670 8.58526i −0.680855 1.17928i −0.974720 0.223429i \(-0.928275\pi\)
0.293865 0.955847i \(-0.405058\pi\)
\(54\) 0 0
\(55\) −4.50196 −0.607044
\(56\) 0 0
\(57\) −2.18104 −0.288886
\(58\) 0 0
\(59\) −4.00000 6.92820i −0.520756 0.901975i −0.999709 0.0241347i \(-0.992317\pi\)
0.478953 0.877841i \(-0.341016\pi\)
\(60\) 0 0
\(61\) 4.45670 7.71923i 0.570622 0.988346i −0.425880 0.904780i \(-0.640036\pi\)
0.996502 0.0835666i \(-0.0266311\pi\)
\(62\) 0 0
\(63\) 6.36814 + 1.80705i 0.802310 + 0.227667i
\(64\) 0 0
\(65\) −2.54526 + 4.40852i −0.315701 + 0.546810i
\(66\) 0 0
\(67\) 0.0585795 + 0.101463i 0.00715662 + 0.0123956i 0.869582 0.493789i \(-0.164389\pi\)
−0.862425 + 0.506185i \(0.831055\pi\)
\(68\) 0 0
\(69\) 4.09052 0.492441
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −4.09052 7.08499i −0.478759 0.829235i 0.520944 0.853591i \(-0.325580\pi\)
−0.999703 + 0.0243555i \(0.992247\pi\)
\(74\) 0 0
\(75\) −0.352860 + 0.611171i −0.0407447 + 0.0705720i
\(76\) 0 0
\(77\) −8.54526 + 8.29771i −0.973823 + 0.945612i
\(78\) 0 0
\(79\) 7.09052 12.2811i 0.797746 1.38174i −0.123335 0.992365i \(-0.539359\pi\)
0.921081 0.389371i \(-0.127308\pi\)
\(80\) 0 0
\(81\) −2.38284 4.12720i −0.264760 0.458578i
\(82\) 0 0
\(83\) −10.7057 −1.17511 −0.587553 0.809186i \(-0.699909\pi\)
−0.587553 + 0.809186i \(0.699909\pi\)
\(84\) 0 0
\(85\) 2.00000 0.216930
\(86\) 0 0
\(87\) −3.35286 5.80732i −0.359464 0.622610i
\(88\) 0 0
\(89\) −2.04526 + 3.54249i −0.216797 + 0.375504i −0.953827 0.300356i \(-0.902894\pi\)
0.737030 + 0.675860i \(0.236228\pi\)
\(90\) 0 0
\(91\) 3.29428 + 13.0592i 0.345334 + 1.36897i
\(92\) 0 0
\(93\) −1.90948 + 3.30732i −0.198004 + 0.342953i
\(94\) 0 0
\(95\) 1.54526 + 2.67647i 0.158540 + 0.274600i
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 0 0
\(99\) 11.2637 1.13205
\(100\) 0 0
\(101\) 1.66046 + 2.87600i 0.165222 + 0.286173i 0.936734 0.350042i \(-0.113833\pi\)
−0.771512 + 0.636215i \(0.780499\pi\)
\(102\) 0 0
\(103\) 5.44338 9.42821i 0.536352 0.928989i −0.462744 0.886492i \(-0.653135\pi\)
0.999097 0.0424975i \(-0.0135314\pi\)
\(104\) 0 0
\(105\) 0.456700 + 1.81044i 0.0445693 + 0.176681i
\(106\) 0 0
\(107\) −1.94142 + 3.36264i −0.187684 + 0.325079i −0.944478 0.328575i \(-0.893431\pi\)
0.756794 + 0.653654i \(0.226765\pi\)
\(108\) 0 0
\(109\) 5.13578 + 8.89543i 0.491919 + 0.852028i 0.999957 0.00930661i \(-0.00296243\pi\)
−0.508038 + 0.861335i \(0.669629\pi\)
\(110\) 0 0
\(111\) 5.00392 0.474951
\(112\) 0 0
\(113\) 2.82288 0.265554 0.132777 0.991146i \(-0.457611\pi\)
0.132777 + 0.991146i \(0.457611\pi\)
\(114\) 0 0
\(115\) −2.89812 5.01969i −0.270251 0.468089i
\(116\) 0 0
\(117\) 6.36814 11.0299i 0.588735 1.01972i
\(118\) 0 0
\(119\) 3.79624 3.68627i 0.348001 0.337919i
\(120\) 0 0
\(121\) −4.63382 + 8.02601i −0.421256 + 0.729638i
\(122\) 0 0
\(123\) 2.32622 + 4.02913i 0.209748 + 0.363295i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −1.73236 −0.153722 −0.0768610 0.997042i \(-0.524490\pi\)
−0.0768610 + 0.997042i \(0.524490\pi\)
\(128\) 0 0
\(129\) −1.66046 2.87600i −0.146195 0.253218i
\(130\) 0 0
\(131\) 6.36814 11.0299i 0.556387 0.963690i −0.441407 0.897307i \(-0.645521\pi\)
0.997794 0.0663835i \(-0.0211461\pi\)
\(132\) 0 0
\(133\) 7.86618 + 2.23214i 0.682084 + 0.193551i
\(134\) 0 0
\(135\) 1.94142 3.36264i 0.167091 0.289410i
\(136\) 0 0
\(137\) −2.00000 3.46410i −0.170872 0.295958i 0.767853 0.640626i \(-0.221325\pi\)
−0.938725 + 0.344668i \(0.887992\pi\)
\(138\) 0 0
\(139\) −1.41144 −0.119717 −0.0598584 0.998207i \(-0.519065\pi\)
−0.0598584 + 0.998207i \(0.519065\pi\)
\(140\) 0 0
\(141\) 7.12384 0.599936
\(142\) 0 0
\(143\) 11.4587 + 19.8470i 0.958221 + 1.65969i
\(144\) 0 0
\(145\) −4.75098 + 8.22894i −0.394547 + 0.683376i
\(146\) 0 0
\(147\) 4.20376 + 2.59468i 0.346720 + 0.214006i
\(148\) 0 0
\(149\) −11.5472 + 20.0004i −0.945985 + 1.63849i −0.192218 + 0.981352i \(0.561568\pi\)
−0.753767 + 0.657142i \(0.771765\pi\)
\(150\) 0 0
\(151\) 0.203760 + 0.352922i 0.0165817 + 0.0287204i 0.874197 0.485571i \(-0.161388\pi\)
−0.857615 + 0.514291i \(0.828055\pi\)
\(152\) 0 0
\(153\) −5.00392 −0.404543
\(154\) 0 0
\(155\) 5.41144 0.434657
\(156\) 0 0
\(157\) 7.04722 + 12.2061i 0.562429 + 0.974156i 0.997284 + 0.0736555i \(0.0234665\pi\)
−0.434854 + 0.900501i \(0.643200\pi\)
\(158\) 0 0
\(159\) −3.49804 + 6.05878i −0.277413 + 0.480493i
\(160\) 0 0
\(161\) −14.7529 4.18636i −1.16269 0.329931i
\(162\) 0 0
\(163\) 8.09052 14.0132i 0.633698 1.09760i −0.353091 0.935589i \(-0.614869\pi\)
0.986789 0.162009i \(-0.0517973\pi\)
\(164\) 0 0
\(165\) 1.58856 + 2.75147i 0.123669 + 0.214201i
\(166\) 0 0
\(167\) 7.79624 0.603291 0.301646 0.953420i \(-0.402464\pi\)
0.301646 + 0.953420i \(0.402464\pi\)
\(168\) 0 0
\(169\) 12.9134 0.993338
\(170\) 0 0
\(171\) −3.86618 6.69642i −0.295654 0.512088i
\(172\) 0 0
\(173\) 4.45474 7.71584i 0.338688 0.586624i −0.645499 0.763762i \(-0.723350\pi\)
0.984186 + 0.177137i \(0.0566837\pi\)
\(174\) 0 0
\(175\) 1.89812 1.84313i 0.143484 0.139328i
\(176\) 0 0
\(177\) −2.82288 + 4.88937i −0.212181 + 0.367507i
\(178\) 0 0
\(179\) −0.839541 1.45413i −0.0627502 0.108687i 0.832944 0.553358i \(-0.186654\pi\)
−0.895694 + 0.444671i \(0.853320\pi\)
\(180\) 0 0
\(181\) 12.5059 0.929555 0.464777 0.885428i \(-0.346134\pi\)
0.464777 + 0.885428i \(0.346134\pi\)
\(182\) 0 0
\(183\) −6.29036 −0.464997
\(184\) 0 0
\(185\) −3.54526 6.14057i −0.260653 0.451464i
\(186\) 0 0
\(187\) 4.50196 7.79762i 0.329216 0.570219i
\(188\) 0 0
\(189\) −2.51274 9.96099i −0.182775 0.724555i
\(190\) 0 0
\(191\) −3.29428 + 5.70586i −0.238366 + 0.412862i −0.960245 0.279157i \(-0.909945\pi\)
0.721880 + 0.692019i \(0.243278\pi\)
\(192\) 0 0
\(193\) −8.91340 15.4385i −0.641601 1.11128i −0.985075 0.172123i \(-0.944937\pi\)
0.343475 0.939162i \(-0.388396\pi\)
\(194\) 0 0
\(195\) 3.59248 0.257263
\(196\) 0 0
\(197\) 5.09052 0.362685 0.181342 0.983420i \(-0.441956\pi\)
0.181342 + 0.983420i \(0.441956\pi\)
\(198\) 0 0
\(199\) −12.1810 21.0982i −0.863491 1.49561i −0.868538 0.495623i \(-0.834940\pi\)
0.00504654 0.999987i \(-0.498394\pi\)
\(200\) 0 0
\(201\) 0.0413407 0.0716041i 0.00291595 0.00505057i
\(202\) 0 0
\(203\) 6.14910 + 24.3762i 0.431582 + 1.71087i
\(204\) 0 0
\(205\) 3.29624 5.70926i 0.230219 0.398752i
\(206\) 0 0
\(207\) 7.25098 + 12.5591i 0.503978 + 0.872915i
\(208\) 0 0
\(209\) 13.9134 0.962410
\(210\) 0 0
\(211\) −8.26764 −0.569168 −0.284584 0.958651i \(-0.591855\pi\)
−0.284584 + 0.958651i \(0.591855\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2.35286 + 4.07527i −0.160464 + 0.277931i
\(216\) 0 0
\(217\) 10.2716 9.97400i 0.697279 0.677079i
\(218\) 0 0
\(219\) −2.88676 + 5.00002i −0.195069 + 0.337870i
\(220\) 0 0
\(221\) −5.09052 8.81704i −0.342425 0.593098i
\(222\) 0 0
\(223\) −17.8268 −1.19377 −0.596885 0.802327i \(-0.703595\pi\)
−0.596885 + 0.802327i \(0.703595\pi\)
\(224\) 0 0
\(225\) −2.50196 −0.166797
\(226\) 0 0
\(227\) −2.67908 4.64030i −0.177817 0.307988i 0.763316 0.646026i \(-0.223570\pi\)
−0.941133 + 0.338038i \(0.890237\pi\)
\(228\) 0 0
\(229\) −12.0905 + 20.9414i −0.798964 + 1.38385i 0.121327 + 0.992613i \(0.461285\pi\)
−0.920291 + 0.391234i \(0.872048\pi\)
\(230\) 0 0
\(231\) 8.08660 + 2.29469i 0.532059 + 0.150979i
\(232\) 0 0
\(233\) −9.00000 + 15.5885i −0.589610 + 1.02123i 0.404674 + 0.914461i \(0.367385\pi\)
−0.994283 + 0.106773i \(0.965948\pi\)
\(234\) 0 0
\(235\) −5.04722 8.74204i −0.329244 0.570268i
\(236\) 0 0
\(237\) −10.0078 −0.650079
\(238\) 0 0
\(239\) −12.7696 −0.825997 −0.412998 0.910732i \(-0.635519\pi\)
−0.412998 + 0.910732i \(0.635519\pi\)
\(240\) 0 0
\(241\) 11.0472 + 19.1343i 0.711614 + 1.23255i 0.964251 + 0.264990i \(0.0853688\pi\)
−0.252637 + 0.967561i \(0.581298\pi\)
\(242\) 0 0
\(243\) −7.50588 + 13.0006i −0.481502 + 0.833987i
\(244\) 0 0
\(245\) 0.205720 6.99698i 0.0131429 0.447020i
\(246\) 0 0
\(247\) 7.86618 13.6246i 0.500513 0.866914i
\(248\) 0 0
\(249\) 3.77762 + 6.54303i 0.239397 + 0.414647i
\(250\) 0 0
\(251\) −13.5059 −0.852484 −0.426242 0.904609i \(-0.640163\pi\)
−0.426242 + 0.904609i \(0.640163\pi\)
\(252\) 0 0
\(253\) −26.0944 −1.64054
\(254\) 0 0
\(255\) −0.705720 1.22234i −0.0441939 0.0765460i
\(256\) 0 0
\(257\) 8.18104 14.1700i 0.510319 0.883899i −0.489609 0.871942i \(-0.662861\pi\)
0.999929 0.0119570i \(-0.00380612\pi\)
\(258\) 0 0
\(259\) −18.0472 5.12115i −1.12140 0.318213i
\(260\) 0 0
\(261\) 11.8868 20.5885i 0.735772 1.27439i
\(262\) 0 0
\(263\) −4.55662 7.89230i −0.280973 0.486660i 0.690651 0.723188i \(-0.257324\pi\)
−0.971625 + 0.236528i \(0.923991\pi\)
\(264\) 0 0
\(265\) 9.91340 0.608975
\(266\) 0 0
\(267\) 2.88676 0.176667
\(268\) 0 0
\(269\) −4.45670 7.71923i −0.271730 0.470650i 0.697575 0.716512i \(-0.254262\pi\)
−0.969305 + 0.245862i \(0.920929\pi\)
\(270\) 0 0
\(271\) −8.18104 + 14.1700i −0.496963 + 0.860765i −0.999994 0.00350346i \(-0.998885\pi\)
0.503031 + 0.864268i \(0.332218\pi\)
\(272\) 0 0
\(273\) 6.81896 6.62142i 0.412702 0.400747i
\(274\) 0 0
\(275\) 2.25098 3.89881i 0.135739 0.235107i
\(276\) 0 0
\(277\) −5.58856 9.67967i −0.335784 0.581595i 0.647851 0.761767i \(-0.275668\pi\)
−0.983635 + 0.180172i \(0.942335\pi\)
\(278\) 0 0
\(279\) −13.5392 −0.810571
\(280\) 0 0
\(281\) −28.2755 −1.68677 −0.843387 0.537307i \(-0.819442\pi\)
−0.843387 + 0.537307i \(0.819442\pi\)
\(282\) 0 0
\(283\) 6.41144 + 11.1049i 0.381121 + 0.660120i 0.991223 0.132203i \(-0.0422050\pi\)
−0.610102 + 0.792323i \(0.708872\pi\)
\(284\) 0 0
\(285\) 1.09052 1.88884i 0.0645969 0.111885i
\(286\) 0 0
\(287\) −4.26626 16.9123i −0.251829 0.998299i
\(288\) 0 0
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) 0 0
\(291\) 0.705720 + 1.22234i 0.0413700 + 0.0716550i
\(292\) 0 0
\(293\) 8.90948 0.520497 0.260249 0.965542i \(-0.416195\pi\)
0.260249 + 0.965542i \(0.416195\pi\)
\(294\) 0 0
\(295\) 8.00000 0.465778
\(296\) 0 0
\(297\) −8.74020 15.1385i −0.507158 0.878423i
\(298\) 0 0
\(299\) −14.7529 + 25.5528i −0.853185 + 1.47776i
\(300\) 0 0
\(301\) 3.04526 + 12.0720i 0.175526 + 0.695818i
\(302\) 0 0
\(303\) 1.17182 2.02965i 0.0673192 0.116600i
\(304\) 0 0
\(305\) 4.45670 + 7.71923i 0.255190 + 0.442002i
\(306\) 0 0
\(307\) −9.12108 −0.520567 −0.260284 0.965532i \(-0.583816\pi\)
−0.260284 + 0.965532i \(0.583816\pi\)
\(308\) 0 0
\(309\) −7.68300 −0.437071
\(310\) 0 0
\(311\) 6.58856 + 11.4117i 0.373603 + 0.647099i 0.990117 0.140245i \(-0.0447889\pi\)
−0.616514 + 0.787344i \(0.711456\pi\)
\(312\) 0 0
\(313\) 8.76960 15.1894i 0.495687 0.858555i −0.504300 0.863528i \(-0.668250\pi\)
0.999988 + 0.00497286i \(0.00158292\pi\)
\(314\) 0 0
\(315\) −4.74902 + 4.61145i −0.267577 + 0.259826i
\(316\) 0 0
\(317\) 6.59248 11.4185i 0.370271 0.641327i −0.619336 0.785126i \(-0.712598\pi\)
0.989607 + 0.143798i \(0.0459316\pi\)
\(318\) 0 0
\(319\) 21.3887 + 37.0464i 1.19754 + 2.07420i
\(320\) 0 0
\(321\) 2.74020 0.152943
\(322\) 0 0
\(323\) −6.18104 −0.343922
\(324\) 0 0
\(325\) −2.54526 4.40852i −0.141186 0.244541i
\(326\) 0 0
\(327\) 3.62442 6.27768i 0.200431 0.347157i
\(328\) 0 0
\(329\) −25.6930 7.29075i −1.41650 0.401952i
\(330\) 0 0
\(331\) −4.25098 + 7.36291i −0.233655 + 0.404702i −0.958881 0.283809i \(-0.908402\pi\)
0.725226 + 0.688511i \(0.241735\pi\)
\(332\) 0 0
\(333\) 8.87010 + 15.3635i 0.486078 + 0.841913i
\(334\) 0 0
\(335\) −0.117159 −0.00640108
\(336\) 0 0
\(337\) 28.1889 1.53555 0.767773 0.640722i \(-0.221365\pi\)
0.767773 + 0.640722i \(0.221365\pi\)
\(338\) 0 0
\(339\) −0.996080 1.72526i −0.0540997 0.0937034i
\(340\) 0 0
\(341\) 12.1810 21.0982i 0.659640 1.14253i
\(342\) 0 0
\(343\) −12.5059 13.6603i −0.675254 0.737585i
\(344\) 0 0
\(345\) −2.04526 + 3.54249i −0.110113 + 0.190722i
\(346\) 0 0
\(347\) −1.35286 2.34322i −0.0726253 0.125791i 0.827426 0.561575i \(-0.189804\pi\)
−0.900051 + 0.435784i \(0.856471\pi\)
\(348\) 0 0
\(349\) −13.6830 −0.732434 −0.366217 0.930529i \(-0.619347\pi\)
−0.366217 + 0.930529i \(0.619347\pi\)
\(350\) 0 0
\(351\) −19.7657 −1.05501
\(352\) 0 0
\(353\) 10.1810 + 17.6341i 0.541882 + 0.938567i 0.998796 + 0.0490565i \(0.0156214\pi\)
−0.456914 + 0.889511i \(0.651045\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −3.59248 1.01942i −0.190134 0.0539533i
\(358\) 0 0
\(359\) 9.20768 15.9482i 0.485963 0.841712i −0.513907 0.857846i \(-0.671802\pi\)
0.999870 + 0.0161337i \(0.00513574\pi\)
\(360\) 0 0
\(361\) 4.72434 + 8.18280i 0.248650 + 0.430674i
\(362\) 0 0
\(363\) 6.54036 0.343280
\(364\) 0 0
\(365\) 8.18104 0.428215
\(366\) 0 0
\(367\) 12.8115 + 22.1902i 0.668756 + 1.15832i 0.978252 + 0.207419i \(0.0665062\pi\)
−0.309496 + 0.950901i \(0.600160\pi\)
\(368\) 0 0
\(369\) −8.24706 + 14.2843i −0.429325 + 0.743612i
\(370\) 0 0
\(371\) 18.8168 18.2717i 0.976921 0.948620i
\(372\) 0 0
\(373\) −14.0944 + 24.4123i −0.729782 + 1.26402i 0.227193 + 0.973850i \(0.427045\pi\)
−0.956975 + 0.290170i \(0.906288\pi\)
\(374\) 0 0
\(375\) −0.352860 0.611171i −0.0182216 0.0315607i
\(376\) 0 0
\(377\) 48.3699 2.49118
\(378\) 0 0
\(379\) 21.7402 1.11672 0.558359 0.829599i \(-0.311431\pi\)
0.558359 + 0.829599i \(0.311431\pi\)
\(380\) 0 0
\(381\) 0.611280 + 1.05877i 0.0313168 + 0.0542423i
\(382\) 0 0
\(383\) 10.1058 17.5038i 0.516382 0.894400i −0.483437 0.875379i \(-0.660612\pi\)
0.999819 0.0190210i \(-0.00605495\pi\)
\(384\) 0 0
\(385\) −2.91340 11.5493i −0.148481 0.588605i
\(386\) 0 0
\(387\) 5.88676 10.1962i 0.299241 0.518300i
\(388\) 0 0
\(389\) −6.91340 11.9744i −0.350523 0.607124i 0.635818 0.771839i \(-0.280663\pi\)
−0.986341 + 0.164715i \(0.947330\pi\)
\(390\) 0 0
\(391\) 11.5925 0.586257
\(392\) 0 0
\(393\) −8.98824 −0.453397
\(394\) 0 0
\(395\) 7.09052 + 12.2811i 0.356763 + 0.617931i
\(396\) 0 0
\(397\) −18.1850 + 31.4973i −0.912677 + 1.58080i −0.102410 + 0.994742i \(0.532655\pi\)
−0.810267 + 0.586061i \(0.800678\pi\)
\(398\) 0 0
\(399\) −1.41144 5.59521i −0.0706603 0.280111i
\(400\) 0 0
\(401\) 3.40948 5.90539i 0.170261 0.294901i −0.768250 0.640150i \(-0.778872\pi\)
0.938511 + 0.345249i \(0.112205\pi\)
\(402\) 0 0
\(403\) −13.7735 23.8564i −0.686108 1.18837i
\(404\) 0 0
\(405\) 4.76568 0.236809
\(406\) 0 0
\(407\) −31.9212 −1.58228
\(408\) 0 0
\(409\) 8.93202 + 15.4707i 0.441660 + 0.764978i 0.997813 0.0661025i \(-0.0210564\pi\)
−0.556153 + 0.831080i \(0.687723\pi\)
\(410\) 0 0
\(411\) −1.41144 + 2.44468i −0.0696212 + 0.120587i
\(412\) 0 0
\(413\) 15.1850 14.7451i 0.747203 0.725557i
\(414\) 0 0
\(415\) 5.35286 9.27143i 0.262762 0.455116i
\(416\) 0 0
\(417\) 0.498040 + 0.862631i 0.0243891 + 0.0422432i
\(418\) 0 0
\(419\) 18.4487 0.901277 0.450639 0.892706i \(-0.351196\pi\)
0.450639 + 0.892706i \(0.351196\pi\)
\(420\) 0 0
\(421\) −10.7324 −0.523063 −0.261532 0.965195i \(-0.584228\pi\)
−0.261532 + 0.965195i \(0.584228\pi\)
\(422\) 0 0
\(423\) 12.6279 + 21.8722i 0.613992 + 1.06346i
\(424\) 0 0
\(425\) −1.00000 + 1.73205i −0.0485071 + 0.0840168i
\(426\) 0 0
\(427\) 22.6869 + 6.43773i 1.09790 + 0.311544i
\(428\) 0 0
\(429\) 8.08660 14.0064i 0.390425 0.676236i
\(430\) 0 0
\(431\) −3.29428 5.70586i −0.158680 0.274842i 0.775713 0.631086i \(-0.217390\pi\)
−0.934393 + 0.356244i \(0.884057\pi\)
\(432\) 0 0
\(433\) 5.17712 0.248797 0.124398 0.992232i \(-0.460300\pi\)
0.124398 + 0.992232i \(0.460300\pi\)
\(434\) 0 0
\(435\) 6.70572 0.321515
\(436\) 0 0
\(437\) 8.95670 + 15.5135i 0.428457 + 0.742109i
\(438\) 0 0
\(439\) −15.5059 + 26.8570i −0.740055 + 1.28181i 0.212414 + 0.977180i \(0.431867\pi\)
−0.952470 + 0.304634i \(0.901466\pi\)
\(440\) 0 0
\(441\) −0.514702 + 17.5062i −0.0245096 + 0.833626i
\(442\) 0 0
\(443\) −2.43946 + 4.22527i −0.115902 + 0.200749i −0.918140 0.396256i \(-0.870309\pi\)
0.802238 + 0.597005i \(0.203643\pi\)
\(444\) 0 0
\(445\) −2.04526 3.54249i −0.0969546 0.167930i
\(446\) 0 0
\(447\) 16.2982 0.770878
\(448\) 0 0
\(449\) 27.7696 1.31053 0.655264 0.755400i \(-0.272557\pi\)
0.655264 + 0.755400i \(0.272557\pi\)
\(450\) 0 0
\(451\) −14.8395 25.7028i −0.698767 1.21030i
\(452\) 0 0
\(453\) 0.143797 0.249064i 0.00675619 0.0117021i
\(454\) 0 0
\(455\) −12.9567 3.67665i −0.607419 0.172364i
\(456\) 0 0
\(457\) 12.5020 21.6540i 0.584817 1.01293i −0.410081 0.912049i \(-0.634500\pi\)
0.994898 0.100884i \(-0.0321670\pi\)
\(458\) 0 0
\(459\) 3.88284 + 6.72528i 0.181236 + 0.313909i
\(460\) 0 0
\(461\) −4.00784 −0.186664 −0.0933318 0.995635i \(-0.529752\pi\)
−0.0933318 + 0.995635i \(0.529752\pi\)
\(462\) 0 0
\(463\) −36.8002 −1.71025 −0.855124 0.518423i \(-0.826519\pi\)
−0.855124 + 0.518423i \(0.826519\pi\)
\(464\) 0 0
\(465\) −1.90948 3.30732i −0.0885500 0.153373i
\(466\) 0 0
\(467\) 11.7377 20.3302i 0.543154 0.940771i −0.455566 0.890202i \(-0.650563\pi\)
0.998721 0.0505688i \(-0.0161034\pi\)
\(468\) 0 0
\(469\) −0.222382 + 0.215939i −0.0102686 + 0.00997116i
\(470\) 0 0
\(471\) 4.97336 8.61411i 0.229160 0.396917i
\(472\) 0 0
\(473\) 10.5925 + 18.3467i 0.487043 + 0.843583i
\(474\) 0 0
\(475\) −3.09052 −0.141803
\(476\) 0 0
\(477\) −24.8029 −1.13565
\(478\) 0 0
\(479\) 18.8868 + 32.7128i 0.862958 + 1.49469i 0.869060 + 0.494706i \(0.164724\pi\)
−0.00610232 + 0.999981i \(0.501942\pi\)
\(480\) 0 0
\(481\) −18.0472 + 31.2587i −0.822882 + 1.42527i
\(482\) 0 0
\(483\) 2.64714 + 10.4938i 0.120449 + 0.477483i
\(484\) 0 0
\(485\) 1.00000 1.73205i 0.0454077 0.0786484i
\(486\) 0 0
\(487\) 3.08660 + 5.34615i 0.139867 + 0.242257i 0.927446 0.373957i \(-0.121999\pi\)
−0.787579 + 0.616214i \(0.788666\pi\)
\(488\) 0 0
\(489\) −11.4193 −0.516398
\(490\) 0 0
\(491\) 39.7814 1.79531 0.897654 0.440701i \(-0.145270\pi\)
0.897654 + 0.440701i \(0.145270\pi\)
\(492\) 0 0
\(493\) −9.50196 16.4579i −0.427947 0.741226i
\(494\) 0 0
\(495\) −5.63186 + 9.75467i −0.253133 + 0.438440i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −1.88284 + 3.26118i −0.0842875 + 0.145990i −0.905087 0.425226i \(-0.860195\pi\)
0.820800 + 0.571216i \(0.193528\pi\)
\(500\) 0 0
\(501\) −2.75098 4.76484i −0.122905 0.212877i
\(502\) 0 0
\(503\) 18.7057 0.834047 0.417023 0.908896i \(-0.363073\pi\)
0.417023 + 0.908896i \(0.363073\pi\)
\(504\) 0 0
\(505\) −3.32092 −0.147779
\(506\) 0 0
\(507\) −4.55662 7.89230i −0.202367 0.350509i
\(508\) 0 0
\(509\) −6.16242 + 10.6736i −0.273144 + 0.473100i −0.969665 0.244437i \(-0.921397\pi\)
0.696521 + 0.717537i \(0.254730\pi\)
\(510\) 0 0
\(511\) 15.5286 15.0787i 0.686945 0.667045i
\(512\) 0 0
\(513\) −6.00000 + 10.3923i −0.264906 + 0.458831i
\(514\) 0 0
\(515\) 5.44338 + 9.42821i 0.239864 + 0.415457i
\(516\) 0 0
\(517\) −45.4448 −1.99866
\(518\) 0 0
\(519\) −6.28759 −0.275995
\(520\) 0 0
\(521\) 14.7796 + 25.5990i 0.647505 + 1.12151i 0.983717 + 0.179725i \(0.0575209\pi\)
−0.336212 + 0.941786i \(0.609146\pi\)
\(522\) 0 0
\(523\) 21.5020 37.2425i 0.940215 1.62850i 0.175155 0.984541i \(-0.443957\pi\)
0.765060 0.643959i \(-0.222709\pi\)
\(524\) 0 0
\(525\) −1.79624 0.509709i −0.0783943 0.0222455i
\(526\) 0 0
\(527\) −5.41144 + 9.37289i −0.235726 + 0.408289i
\(528\) 0 0
\(529\) −5.29820 9.17675i −0.230357 0.398989i
\(530\) 0 0
\(531\) −20.0157 −0.868606
\(532\) 0 0
\(533\) −33.5592 −1.45361
\(534\) 0 0
\(535\) −1.94142 3.36264i −0.0839349 0.145380i
\(536\) 0 0
\(537\) −0.592480 + 1.02621i −0.0255674 + 0.0442841i
\(538\) 0 0
\(539\) −26.8168 16.5521i −1.15508 0.712950i
\(540\) 0 0
\(541\) 2.48334 4.30127i 0.106767 0.184926i −0.807692 0.589605i \(-0.799283\pi\)
0.914459 + 0.404679i \(0.132617\pi\)
\(542\) 0 0
\(543\) −4.41282 7.64323i −0.189372 0.328003i
\(544\) 0 0
\(545\) −10.2716 −0.439985
\(546\) 0 0
\(547\) −22.1250 −0.945997 −0.472998 0.881063i \(-0.656828\pi\)
−0.472998 + 0.881063i \(0.656828\pi\)
\(548\) 0 0
\(549\) −11.1505 19.3132i −0.475891 0.824267i
\(550\) 0 0
\(551\) 14.6830 25.4317i 0.625517 1.08343i
\(552\) 0 0
\(553\) 36.0944 + 10.2423i 1.53489 + 0.435547i
\(554\) 0 0
\(555\) −2.50196 + 4.33352i −0.106202 + 0.183948i
\(556\) 0 0
\(557\) −2.77958 4.81437i −0.117775 0.203991i 0.801111 0.598516i \(-0.204243\pi\)
−0.918885 + 0.394524i \(0.870909\pi\)
\(558\) 0 0
\(559\) 23.9546 1.01317
\(560\) 0 0
\(561\) −6.35424 −0.268276
\(562\) 0 0
\(563\) −4.74158 8.21266i −0.199834 0.346122i 0.748641 0.662976i \(-0.230707\pi\)
−0.948474 + 0.316854i \(0.897374\pi\)
\(564\) 0 0
\(565\) −1.41144 + 2.44468i −0.0593797 + 0.102849i
\(566\) 0 0
\(567\) 9.04584 8.78379i 0.379889 0.368884i
\(568\) 0 0
\(569\) 17.1417 29.6902i 0.718616 1.24468i −0.242933 0.970043i \(-0.578109\pi\)
0.961548 0.274636i \(-0.0885573\pi\)
\(570\) 0 0
\(571\) 15.7735 + 27.3205i 0.660101 + 1.14333i 0.980589 + 0.196076i \(0.0628200\pi\)
−0.320487 + 0.947253i \(0.603847\pi\)
\(572\) 0 0
\(573\) 4.64968 0.194243
\(574\) 0 0
\(575\) 5.79624 0.241720
\(576\) 0 0
\(577\) 5.32092 + 9.21610i 0.221513 + 0.383671i 0.955268 0.295743i \(-0.0955672\pi\)
−0.733755 + 0.679414i \(0.762234\pi\)
\(578\) 0 0
\(579\) −6.29036 + 10.8952i −0.261418 + 0.452790i
\(580\) 0 0
\(581\) −6.92810 27.4643i −0.287426 1.13941i
\(582\) 0 0
\(583\) 22.3149 38.6505i 0.924187 1.60074i
\(584\) 0 0
\(585\) 6.36814 + 11.0299i 0.263290 + 0.456032i
\(586\) 0 0
\(587\) 6.64184 0.274138 0.137069 0.990562i \(-0.456232\pi\)
0.137069 + 0.990562i \(0.456232\pi\)
\(588\) 0 0
\(589\) −16.7242 −0.689107
\(590\) 0 0
\(591\) −1.79624 3.11118i −0.0738874 0.127977i
\(592\) 0 0
\(593\) −6.76960 + 11.7253i −0.277994 + 0.481500i −0.970886 0.239541i \(-0.923003\pi\)
0.692892 + 0.721041i \(0.256336\pi\)
\(594\) 0 0
\(595\) 1.29428 + 5.13077i 0.0530603 + 0.210341i
\(596\) 0 0
\(597\) −8.59640 + 14.8894i −0.351827 + 0.609383i
\(598\) 0 0
\(599\) −13.0905 22.6734i −0.534864 0.926412i −0.999170 0.0407369i \(-0.987029\pi\)
0.464306 0.885675i \(-0.346304\pi\)
\(600\) 0 0
\(601\) −36.0078 −1.46879 −0.734395 0.678722i \(-0.762534\pi\)
−0.734395 + 0.678722i \(0.762534\pi\)
\(602\) 0 0
\(603\) 0.293127 0.0119371
\(604\) 0 0
\(605\) −4.63382 8.02601i −0.188392 0.326304i
\(606\) 0 0
\(607\) −11.8715 + 20.5620i −0.481849 + 0.834586i −0.999783 0.0208341i \(-0.993368\pi\)
0.517934 + 0.855420i \(0.326701\pi\)
\(608\) 0 0
\(609\) 12.7283 12.3595i 0.515775 0.500834i
\(610\) 0 0
\(611\) −25.6930 + 44.5015i −1.03943 + 1.80034i
\(612\) 0 0
\(613\) 4.77958 + 8.27847i 0.193045 + 0.334364i 0.946258 0.323413i \(-0.104830\pi\)
−0.753213 + 0.657777i \(0.771497\pi\)
\(614\) 0 0
\(615\) −4.65244 −0.187605
\(616\) 0 0
\(617\) −19.8268 −0.798197 −0.399098 0.916908i \(-0.630677\pi\)
−0.399098 + 0.916908i \(0.630677\pi\)
\(618\) 0 0
\(619\) −13.5758 23.5140i −0.545658 0.945108i −0.998565 0.0535500i \(-0.982946\pi\)
0.452907 0.891558i \(-0.350387\pi\)
\(620\) 0 0
\(621\) 11.2529 19.4907i 0.451565 0.782133i
\(622\) 0 0
\(623\) −10.4114 2.95439i −0.417126 0.118365i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) −4.90948 8.50347i −0.196066 0.339596i
\(628\) 0 0
\(629\) 14.1810 0.565435
\(630\) 0 0
\(631\) −49.7735 −1.98145 −0.990726 0.135873i \(-0.956616\pi\)
−0.990726 + 0.135873i \(0.956616\pi\)
\(632\) 0 0
\(633\) 2.91732 + 5.05294i 0.115953 + 0.200836i
\(634\) 0 0
\(635\) 0.866179 1.50027i 0.0343733 0.0595362i
\(636\) 0 0
\(637\) −31.3699 + 16.9022i −1.24292 + 0.669690i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −10.1152 17.5200i −0.399526 0.692000i 0.594141 0.804361i \(-0.297492\pi\)
−0.993667 + 0.112361i \(0.964159\pi\)
\(642\) 0 0
\(643\) −25.1850 −0.993198 −0.496599 0.867980i \(-0.665418\pi\)
−0.496599 + 0.867980i \(0.665418\pi\)
\(644\) 0 0
\(645\) 3.32092 0.130761
\(646\) 0 0
\(647\) −9.78488 16.9479i −0.384683 0.666291i 0.607042 0.794670i \(-0.292356\pi\)
−0.991725 + 0.128379i \(0.959023\pi\)
\(648\) 0 0
\(649\) 18.0078 31.1905i 0.706870 1.22433i
\(650\) 0 0
\(651\) −9.72024 2.75826i −0.380966 0.108105i
\(652\) 0 0
\(653\) −9.13382 + 15.8202i −0.357434 + 0.619094i −0.987531 0.157422i \(-0.949682\pi\)
0.630097 + 0.776516i \(0.283015\pi\)
\(654\) 0 0
\(655\) 6.36814 + 11.0299i 0.248824 + 0.430975i
\(656\) 0 0
\(657\) −20.4686 −0.798558
\(658\) 0 0
\(659\) 46.0078 1.79221 0.896105 0.443841i \(-0.146385\pi\)
0.896105 + 0.443841i \(0.146385\pi\)
\(660\) 0 0
\(661\) 24.2302 + 41.9680i 0.942446 + 1.63236i 0.760785 + 0.649004i \(0.224814\pi\)
0.181661 + 0.983361i \(0.441853\pi\)
\(662\) 0 0
\(663\) −3.59248 + 6.22236i −0.139520 + 0.241656i
\(664\) 0 0
\(665\) −5.86618 + 5.69624i −0.227481 + 0.220891i
\(666\) 0 0
\(667\) −27.5378 + 47.6969i −1.06627 + 1.84683i
\(668\) 0 0
\(669\) 6.29036 + 10.8952i 0.243199 + 0.421234i
\(670\) 0 0
\(671\) 40.1278 1.54912
\(672\) 0 0
\(673\) −15.0118 −0.578661 −0.289330 0.957229i \(-0.593433\pi\)
−0.289330 + 0.957229i \(0.593433\pi\)
\(674\) 0 0
\(675\) 1.94142 + 3.36264i 0.0747253 + 0.129428i
\(676\) 0 0
\(677\) −3.95670 + 6.85320i −0.152068 + 0.263390i −0.931988 0.362490i \(-0.881927\pi\)
0.779919 + 0.625880i \(0.215260\pi\)
\(678\) 0 0
\(679\) −1.29428 5.13077i −0.0496699 0.196901i
\(680\) 0 0
\(681\) −1.89068 + 3.27475i −0.0724510 + 0.125489i
\(682\) 0 0
\(683\) −14.8548 25.7293i −0.568404 0.984504i −0.996724 0.0808774i \(-0.974228\pi\)
0.428320 0.903627i \(-0.359106\pi\)
\(684\) 0 0
\(685\) 4.00000 0.152832
\(686\) 0 0
\(687\) 17.0650 0.651072
\(688\) 0 0
\(689\) −25.2322 43.7034i −0.961270 1.66497i
\(690\) 0 0
\(691\) 10.8868 18.8564i 0.414152 0.717332i −0.581187 0.813770i \(-0.697412\pi\)
0.995339 + 0.0964378i \(0.0307449\pi\)
\(692\) 0 0
\(693\) 7.28921 + 28.8958i 0.276894 + 1.09766i
\(694\) 0 0
\(695\) 0.705720 1.22234i 0.0267695 0.0463661i
\(696\) 0 0
\(697\) 6.59248 + 11.4185i 0.249708 + 0.432507i
\(698\) 0 0
\(699\) 12.7030 0.480470
\(700\) 0 0
\(701\) 24.0905 0.909886 0.454943 0.890520i \(-0.349660\pi\)
0.454943 + 0.890520i \(0.349660\pi\)
\(702\) 0 0
\(703\) 10.9567 + 18.9776i 0.413240 + 0.715752i
\(704\) 0 0
\(705\) −3.56192 + 6.16943i −0.134150 + 0.232354i
\(706\) 0 0
\(707\) −6.30350 + 6.12090i −0.237068 + 0.230200i
\(708\) 0 0
\(709\) 12.0186 20.8169i 0.451369 0.781794i −0.547103 0.837066i \(-0.684269\pi\)
0.998471 + 0.0552719i \(0.0176026\pi\)
\(710\) 0 0
\(711\) −17.7402 30.7269i −0.665309 1.15235i
\(712\) 0 0
\(713\) 31.3660 1.17467
\(714\) 0 0
\(715\) −22.9173 −0.857059
\(716\) 0 0
\(717\) 4.50588 + 7.80441i 0.168275 + 0.291461i
\(718\) 0 0
\(719\) 0.117159 0.202925i 0.00436929 0.00756783i −0.863832 0.503779i \(-0.831943\pi\)
0.868202 + 0.496211i \(0.165276\pi\)
\(720\) 0 0
\(721\) 27.7096 + 7.86300i 1.03196 + 0.292833i
\(722\) 0 0
\(723\) 7.79624 13.5035i 0.289945 0.502200i
\(724\) 0 0
\(725\) −4.75098 8.22894i −0.176447 0.305615i
\(726\) 0 0
\(727\) 9.44200 0.350184 0.175092 0.984552i \(-0.443978\pi\)
0.175092 + 0.984552i \(0.443978\pi\)
\(728\) 0 0
\(729\) −3.70295 −0.137146
\(730\) 0 0
\(731\) −4.70572 8.15055i −0.174047 0.301459i
\(732\) 0 0
\(733\) 14.3721 24.8931i 0.530844 0.919449i −0.468508 0.883459i \(-0.655208\pi\)
0.999352 0.0359897i \(-0.0114584\pi\)
\(734\) 0 0
\(735\) −4.34894 + 2.34322i −0.160413 + 0.0864310i
\(736\) 0 0
\(737\) −0.263722 + 0.456781i −0.00971434 + 0.0168257i
\(738\) 0 0
\(739\) 13.0739 + 22.6446i 0.480930 + 0.832995i 0.999761 0.0218823i \(-0.00696591\pi\)
−0.518831 + 0.854877i \(0.673633\pi\)
\(740\) 0 0
\(741\) −11.1026 −0.407865
\(742\) 0 0
\(743\) 32.7547 1.20165 0.600827 0.799379i \(-0.294838\pi\)
0.600827 + 0.799379i \(0.294838\pi\)
\(744\) 0 0
\(745\) −11.5472 20.0004i −0.423057 0.732757i
\(746\) 0 0
\(747\) −13.3926 + 23.1967i −0.490011 + 0.848724i
\(748\) 0 0
\(749\) −9.88284 2.80440i −0.361111 0.102470i
\(750\) 0 0
\(751\) −13.0905 + 22.6734i −0.477680 + 0.827366i −0.999673 0.0255841i \(-0.991855\pi\)
0.521993 + 0.852950i \(0.325189\pi\)
\(752\) 0 0
\(753\) 4.76568 + 8.25440i 0.173671 + 0.300807i
\(754\) 0 0
\(755\) −0.407520 −0.0148312
\(756\) 0 0
\(757\) 16.8229 0.611438 0.305719 0.952122i \(-0.401103\pi\)
0.305719 + 0.952122i \(0.401103\pi\)
\(758\) 0 0
\(759\) 9.20768 + 15.9482i 0.334218 + 0.578882i
\(760\) 0 0
\(761\) 2.95278 5.11436i 0.107038 0.185396i −0.807531 0.589825i \(-0.799197\pi\)
0.914569 + 0.404430i \(0.132530\pi\)
\(762\) 0 0
\(763\) −19.4967 + 18.9319i −0.705826 + 0.685379i
\(764\) 0 0
\(765\) 2.50196 4.33352i 0.0904585 0.156679i
\(766\) 0 0
\(767\) −20.3621 35.2682i −0.735232 1.27346i
\(768\) 0 0
\(769\) 0.275481 0.00993410 0.00496705 0.999988i \(-0.498419\pi\)
0.00496705 + 0.999988i \(0.498419\pi\)
\(770\) 0 0
\(771\) −11.5470 −0.415857
\(772\) 0 0
\(773\) −3.68906 6.38964i −0.132686 0.229819i 0.792025 0.610489i \(-0.209027\pi\)
−0.924711 + 0.380669i \(0.875694\pi\)
\(774\) 0 0
\(775\) −2.70572 + 4.68644i −0.0971923 + 0.168342i
\(776\) 0 0
\(777\) 3.23824 + 12.8370i 0.116171 + 0.460524i
\(778\) 0 0
\(779\) −10.1871 + 17.6446i −0.364991 + 0.632182i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −36.8946 −1.31851
\(784\) 0 0
\(785\) −14.0944 −0.503052
\(786\) 0 0
\(787\) 9.33014 + 16.1603i 0.332584 + 0.576052i 0.983018 0.183511i \(-0.0587463\pi\)
−0.650434 + 0.759563i \(0.725413\pi\)
\(788\) 0 0
\(789\) −3.21570 + 5.56975i −0.114482 + 0.198288i
\(790\) 0 0
\(791\) 1.82680 + 7.24178i 0.0649535 + 0.257488i
\(792\) 0 0
\(793\) 22.6869 39.2949i 0.805636 1.39540i
\(794\) 0 0
\(795\) −3.49804 6.05878i −0.124063 0.214883i
\(796\) 0 0
\(797\) 9.81896