Properties

Label 240.3.c.e.209.12
Level $240$
Weight $3$
Character 240.209
Analytic conductor $6.540$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 240.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53952634465\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 34 x^{10} + 305 x^{8} + 616 x^{6} + 305 x^{4} + 34 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{15}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 120)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 209.12
Root \(4.54164i\) of defining polynomial
Character \(\chi\) \(=\) 240.209
Dual form 240.3.c.e.209.11

$q$-expansion

\(f(q)\) \(=\) \(q+(2.72256 + 1.26002i) q^{3} +(0.689011 + 4.95230i) q^{5} +0.735748i q^{7} +(5.82469 + 6.86097i) q^{9} +O(q^{10})\) \(q+(2.72256 + 1.26002i) q^{3} +(0.689011 + 4.95230i) q^{5} +0.735748i q^{7} +(5.82469 + 6.86097i) q^{9} -10.9451i q^{11} +21.1901i q^{13} +(-4.36412 + 14.3511i) q^{15} +7.03488 q^{17} -23.1529 q^{19} +(-0.927058 + 2.00312i) q^{21} +24.7483 q^{23} +(-24.0505 + 6.82438i) q^{25} +(7.21312 + 26.0187i) q^{27} -32.3284i q^{29} +34.9482 q^{31} +(13.7911 - 29.7987i) q^{33} +(-3.64364 + 0.506939i) q^{35} +37.7818i q^{37} +(-26.6999 + 57.6912i) q^{39} -39.0848i q^{41} -22.6804i q^{43} +(-29.9643 + 33.5729i) q^{45} -39.1076 q^{47} +48.4587 q^{49} +(19.1529 + 8.86409i) q^{51} +60.9179 q^{53} +(54.2034 - 7.54130i) q^{55} +(-63.0352 - 29.1731i) q^{57} -7.79696i q^{59} -11.1529 q^{61} +(-5.04795 + 4.28551i) q^{63} +(-104.939 + 14.6002i) q^{65} -33.3485i q^{67} +(67.3787 + 31.1833i) q^{69} -96.9650i q^{71} -134.535i q^{73} +(-74.0779 - 11.7244i) q^{75} +8.05284 q^{77} -121.049 q^{79} +(-13.1459 + 79.9261i) q^{81} +90.2345 q^{83} +(4.84711 + 34.8388i) q^{85} +(40.7344 - 88.0160i) q^{87} -53.1846i q^{89} -15.5905 q^{91} +(95.1486 + 44.0354i) q^{93} +(-15.9526 - 114.660i) q^{95} -115.001i q^{97} +(75.0940 - 63.7519i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 8 q^{9} + O(q^{10}) \) \( 12 q + 8 q^{9} - 16 q^{15} + 4 q^{21} + 36 q^{25} + 48 q^{31} + 128 q^{39} - 68 q^{45} - 252 q^{49} - 48 q^{51} + 48 q^{55} + 144 q^{61} + 268 q^{69} - 304 q^{75} - 432 q^{79} - 188 q^{81} + 336 q^{85} + 560 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(161\) \(181\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(1\)

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
\(3\) 2.72256 + 1.26002i 0.907521 + 0.420007i
\(4\) 0 0
\(5\) 0.689011 + 4.95230i 0.137802 + 0.990460i
\(6\) 0 0
\(7\) 0.735748i 0.105107i 0.998618 + 0.0525534i \(0.0167360\pi\)
−0.998618 + 0.0525534i \(0.983264\pi\)
\(8\) 0 0
\(9\) 5.82469 + 6.86097i 0.647188 + 0.762330i
\(10\) 0 0
\(11\) 10.9451i 0.995009i −0.867461 0.497505i \(-0.834250\pi\)
0.867461 0.497505i \(-0.165750\pi\)
\(12\) 0 0
\(13\) 21.1901i 1.63000i 0.579458 + 0.815002i \(0.303264\pi\)
−0.579458 + 0.815002i \(0.696736\pi\)
\(14\) 0 0
\(15\) −4.36412 + 14.3511i −0.290942 + 0.956741i
\(16\) 0 0
\(17\) 7.03488 0.413816 0.206908 0.978360i \(-0.433660\pi\)
0.206908 + 0.978360i \(0.433660\pi\)
\(18\) 0 0
\(19\) −23.1529 −1.21857 −0.609287 0.792950i \(-0.708544\pi\)
−0.609287 + 0.792950i \(0.708544\pi\)
\(20\) 0 0
\(21\) −0.927058 + 2.00312i −0.0441456 + 0.0953867i
\(22\) 0 0
\(23\) 24.7483 1.07601 0.538006 0.842941i \(-0.319178\pi\)
0.538006 + 0.842941i \(0.319178\pi\)
\(24\) 0 0
\(25\) −24.0505 + 6.82438i −0.962021 + 0.272975i
\(26\) 0 0
\(27\) 7.21312 + 26.0187i 0.267153 + 0.963654i
\(28\) 0 0
\(29\) 32.3284i 1.11477i −0.830254 0.557386i \(-0.811804\pi\)
0.830254 0.557386i \(-0.188196\pi\)
\(30\) 0 0
\(31\) 34.9482 1.12736 0.563680 0.825993i \(-0.309385\pi\)
0.563680 + 0.825993i \(0.309385\pi\)
\(32\) 0 0
\(33\) 13.7911 29.7987i 0.417911 0.902992i
\(34\) 0 0
\(35\) −3.64364 + 0.506939i −0.104104 + 0.0144840i
\(36\) 0 0
\(37\) 37.7818i 1.02113i 0.859839 + 0.510565i \(0.170564\pi\)
−0.859839 + 0.510565i \(0.829436\pi\)
\(38\) 0 0
\(39\) −26.6999 + 57.6912i −0.684613 + 1.47926i
\(40\) 0 0
\(41\) 39.0848i 0.953288i −0.879096 0.476644i \(-0.841853\pi\)
0.879096 0.476644i \(-0.158147\pi\)
\(42\) 0 0
\(43\) 22.6804i 0.527451i −0.964598 0.263725i \(-0.915049\pi\)
0.964598 0.263725i \(-0.0849513\pi\)
\(44\) 0 0
\(45\) −29.9643 + 33.5729i −0.665873 + 0.746065i
\(46\) 0 0
\(47\) −39.1076 −0.832076 −0.416038 0.909347i \(-0.636582\pi\)
−0.416038 + 0.909347i \(0.636582\pi\)
\(48\) 0 0
\(49\) 48.4587 0.988953
\(50\) 0 0
\(51\) 19.1529 + 8.86409i 0.375547 + 0.173806i
\(52\) 0 0
\(53\) 60.9179 1.14939 0.574697 0.818366i \(-0.305120\pi\)
0.574697 + 0.818366i \(0.305120\pi\)
\(54\) 0 0
\(55\) 54.2034 7.54130i 0.985517 0.137115i
\(56\) 0 0
\(57\) −63.0352 29.1731i −1.10588 0.511809i
\(58\) 0 0
\(59\) 7.79696i 0.132152i −0.997815 0.0660759i \(-0.978952\pi\)
0.997815 0.0660759i \(-0.0210480\pi\)
\(60\) 0 0
\(61\) −11.1529 −0.182834 −0.0914171 0.995813i \(-0.529140\pi\)
−0.0914171 + 0.995813i \(0.529140\pi\)
\(62\) 0 0
\(63\) −5.04795 + 4.28551i −0.0801262 + 0.0680239i
\(64\) 0 0
\(65\) −104.939 + 14.6002i −1.61445 + 0.224618i
\(66\) 0 0
\(67\) 33.3485i 0.497739i −0.968537 0.248869i \(-0.919941\pi\)
0.968537 0.248869i \(-0.0800590\pi\)
\(68\) 0 0
\(69\) 67.3787 + 31.1833i 0.976503 + 0.451933i
\(70\) 0 0
\(71\) 96.9650i 1.36570i −0.730557 0.682852i \(-0.760739\pi\)
0.730557 0.682852i \(-0.239261\pi\)
\(72\) 0 0
\(73\) 134.535i 1.84295i −0.388436 0.921476i \(-0.626984\pi\)
0.388436 0.921476i \(-0.373016\pi\)
\(74\) 0 0
\(75\) −74.0779 11.7244i −0.987706 0.156325i
\(76\) 0 0
\(77\) 8.05284 0.104582
\(78\) 0 0
\(79\) −121.049 −1.53227 −0.766134 0.642681i \(-0.777822\pi\)
−0.766134 + 0.642681i \(0.777822\pi\)
\(80\) 0 0
\(81\) −13.1459 + 79.9261i −0.162295 + 0.986742i
\(82\) 0 0
\(83\) 90.2345 1.08716 0.543582 0.839356i \(-0.317068\pi\)
0.543582 + 0.839356i \(0.317068\pi\)
\(84\) 0 0
\(85\) 4.84711 + 34.8388i 0.0570248 + 0.409868i
\(86\) 0 0
\(87\) 40.7344 88.0160i 0.468212 1.01168i
\(88\) 0 0
\(89\) 53.1846i 0.597579i −0.954319 0.298790i \(-0.903417\pi\)
0.954319 0.298790i \(-0.0965829\pi\)
\(90\) 0 0
\(91\) −15.5905 −0.171325
\(92\) 0 0
\(93\) 95.1486 + 44.0354i 1.02310 + 0.473499i
\(94\) 0 0
\(95\) −15.9526 114.660i −0.167922 1.20695i
\(96\) 0 0
\(97\) 115.001i 1.18557i −0.805359 0.592787i \(-0.798028\pi\)
0.805359 0.592787i \(-0.201972\pi\)
\(98\) 0 0
\(99\) 75.0940 63.7519i 0.758526 0.643958i
\(100\) 0 0
\(101\) 29.1802i 0.288913i 0.989511 + 0.144457i \(0.0461434\pi\)
−0.989511 + 0.144457i \(0.953857\pi\)
\(102\) 0 0
\(103\) 89.9481i 0.873283i −0.899636 0.436641i \(-0.856168\pi\)
0.899636 0.436641i \(-0.143832\pi\)
\(104\) 0 0
\(105\) −10.5588 3.21090i −0.100560 0.0305800i
\(106\) 0 0
\(107\) −153.586 −1.43538 −0.717689 0.696363i \(-0.754800\pi\)
−0.717689 + 0.696363i \(0.754800\pi\)
\(108\) 0 0
\(109\) −59.5623 −0.546444 −0.273222 0.961951i \(-0.588089\pi\)
−0.273222 + 0.961951i \(0.588089\pi\)
\(110\) 0 0
\(111\) −47.6059 + 102.863i −0.428882 + 0.926697i
\(112\) 0 0
\(113\) −1.01796 −0.00900851 −0.00450426 0.999990i \(-0.501434\pi\)
−0.00450426 + 0.999990i \(0.501434\pi\)
\(114\) 0 0
\(115\) 17.0518 + 122.561i 0.148277 + 1.06575i
\(116\) 0 0
\(117\) −145.384 + 123.426i −1.24260 + 1.05492i
\(118\) 0 0
\(119\) 5.17590i 0.0434949i
\(120\) 0 0
\(121\) 1.20473 0.00995643
\(122\) 0 0
\(123\) 49.2477 106.411i 0.400388 0.865129i
\(124\) 0 0
\(125\) −50.3674 114.403i −0.402940 0.915227i
\(126\) 0 0
\(127\) 209.731i 1.65142i 0.564091 + 0.825712i \(0.309227\pi\)
−0.564091 + 0.825712i \(0.690773\pi\)
\(128\) 0 0
\(129\) 28.5778 61.7488i 0.221533 0.478672i
\(130\) 0 0
\(131\) 210.051i 1.60344i 0.597698 + 0.801721i \(0.296082\pi\)
−0.597698 + 0.801721i \(0.703918\pi\)
\(132\) 0 0
\(133\) 17.0347i 0.128080i
\(134\) 0 0
\(135\) −123.882 + 53.6487i −0.917646 + 0.397398i
\(136\) 0 0
\(137\) 168.688 1.23130 0.615648 0.788021i \(-0.288894\pi\)
0.615648 + 0.788021i \(0.288894\pi\)
\(138\) 0 0
\(139\) 129.251 0.929866 0.464933 0.885346i \(-0.346078\pi\)
0.464933 + 0.885346i \(0.346078\pi\)
\(140\) 0 0
\(141\) −106.473 49.2763i −0.755126 0.349478i
\(142\) 0 0
\(143\) 231.927 1.62187
\(144\) 0 0
\(145\) 160.100 22.2746i 1.10414 0.153618i
\(146\) 0 0
\(147\) 131.932 + 61.0590i 0.897495 + 0.415367i
\(148\) 0 0
\(149\) 83.9655i 0.563527i 0.959484 + 0.281763i \(0.0909193\pi\)
−0.959484 + 0.281763i \(0.909081\pi\)
\(150\) 0 0
\(151\) −9.04922 −0.0599286 −0.0299643 0.999551i \(-0.509539\pi\)
−0.0299643 + 0.999551i \(0.509539\pi\)
\(152\) 0 0
\(153\) 40.9760 + 48.2661i 0.267817 + 0.315465i
\(154\) 0 0
\(155\) 24.0797 + 173.074i 0.155353 + 1.11660i
\(156\) 0 0
\(157\) 162.054i 1.03219i 0.856530 + 0.516097i \(0.172616\pi\)
−0.856530 + 0.516097i \(0.827384\pi\)
\(158\) 0 0
\(159\) 165.853 + 76.7578i 1.04310 + 0.482754i
\(160\) 0 0
\(161\) 18.2085i 0.113096i
\(162\) 0 0
\(163\) 136.172i 0.835411i 0.908583 + 0.417705i \(0.137166\pi\)
−0.908583 + 0.417705i \(0.862834\pi\)
\(164\) 0 0
\(165\) 157.074 + 47.7658i 0.951966 + 0.289490i
\(166\) 0 0
\(167\) −140.931 −0.843898 −0.421949 0.906620i \(-0.638654\pi\)
−0.421949 + 0.906620i \(0.638654\pi\)
\(168\) 0 0
\(169\) −280.018 −1.65691
\(170\) 0 0
\(171\) −134.859 158.851i −0.788646 0.928955i
\(172\) 0 0
\(173\) 132.351 0.765032 0.382516 0.923949i \(-0.375058\pi\)
0.382516 + 0.923949i \(0.375058\pi\)
\(174\) 0 0
\(175\) −5.02102 17.6951i −0.0286916 0.101115i
\(176\) 0 0
\(177\) 9.82433 21.2277i 0.0555047 0.119931i
\(178\) 0 0
\(179\) 92.2499i 0.515363i −0.966230 0.257681i \(-0.917042\pi\)
0.966230 0.257681i \(-0.0829585\pi\)
\(180\) 0 0
\(181\) 115.896 0.640311 0.320156 0.947365i \(-0.396265\pi\)
0.320156 + 0.947365i \(0.396265\pi\)
\(182\) 0 0
\(183\) −30.3644 14.0529i −0.165926 0.0767917i
\(184\) 0 0
\(185\) −187.107 + 26.0321i −1.01139 + 0.140714i
\(186\) 0 0
\(187\) 76.9974i 0.411751i
\(188\) 0 0
\(189\) −19.1432 + 5.30704i −0.101287 + 0.0280796i
\(190\) 0 0
\(191\) 53.1183i 0.278106i −0.990285 0.139053i \(-0.955594\pi\)
0.990285 0.139053i \(-0.0444059\pi\)
\(192\) 0 0
\(193\) 271.315i 1.40578i 0.711299 + 0.702890i \(0.248107\pi\)
−0.711299 + 0.702890i \(0.751893\pi\)
\(194\) 0 0
\(195\) −304.101 92.4760i −1.55949 0.474236i
\(196\) 0 0
\(197\) −64.3941 −0.326873 −0.163437 0.986554i \(-0.552258\pi\)
−0.163437 + 0.986554i \(0.552258\pi\)
\(198\) 0 0
\(199\) −72.0308 −0.361964 −0.180982 0.983486i \(-0.557928\pi\)
−0.180982 + 0.983486i \(0.557928\pi\)
\(200\) 0 0
\(201\) 42.0198 90.7933i 0.209054 0.451708i
\(202\) 0 0
\(203\) 23.7855 0.117170
\(204\) 0 0
\(205\) 193.560 26.9299i 0.944194 0.131365i
\(206\) 0 0
\(207\) 144.151 + 169.797i 0.696382 + 0.820276i
\(208\) 0 0
\(209\) 253.411i 1.21249i
\(210\) 0 0
\(211\) −108.583 −0.514613 −0.257307 0.966330i \(-0.582835\pi\)
−0.257307 + 0.966330i \(0.582835\pi\)
\(212\) 0 0
\(213\) 122.178 263.993i 0.573605 1.23940i
\(214\) 0 0
\(215\) 112.320 15.6270i 0.522419 0.0726839i
\(216\) 0 0
\(217\) 25.7130i 0.118493i
\(218\) 0 0
\(219\) 169.518 366.281i 0.774053 1.67252i
\(220\) 0 0
\(221\) 149.069i 0.674522i
\(222\) 0 0
\(223\) 83.6192i 0.374974i 0.982267 + 0.187487i \(0.0600342\pi\)
−0.982267 + 0.187487i \(0.939966\pi\)
\(224\) 0 0
\(225\) −186.909 125.260i −0.830706 0.556712i
\(226\) 0 0
\(227\) −51.6591 −0.227573 −0.113787 0.993505i \(-0.536298\pi\)
−0.113787 + 0.993505i \(0.536298\pi\)
\(228\) 0 0
\(229\) −280.974 −1.22696 −0.613480 0.789710i \(-0.710231\pi\)
−0.613480 + 0.789710i \(0.710231\pi\)
\(230\) 0 0
\(231\) 21.9244 + 10.1467i 0.0949106 + 0.0439253i
\(232\) 0 0
\(233\) −169.192 −0.726148 −0.363074 0.931760i \(-0.618273\pi\)
−0.363074 + 0.931760i \(0.618273\pi\)
\(234\) 0 0
\(235\) −26.9455 193.672i −0.114662 0.824137i
\(236\) 0 0
\(237\) −329.564 152.525i −1.39057 0.643564i
\(238\) 0 0
\(239\) 1.12039i 0.00468782i −0.999997 0.00234391i \(-0.999254\pi\)
0.999997 0.00234391i \(-0.000746090\pi\)
\(240\) 0 0
\(241\) 153.254 0.635908 0.317954 0.948106i \(-0.397004\pi\)
0.317954 + 0.948106i \(0.397004\pi\)
\(242\) 0 0
\(243\) −136.499 + 201.040i −0.561725 + 0.827324i
\(244\) 0 0
\(245\) 33.3886 + 239.982i 0.136280 + 0.979518i
\(246\) 0 0
\(247\) 490.611i 1.98628i
\(248\) 0 0
\(249\) 245.669 + 113.697i 0.986623 + 0.456616i
\(250\) 0 0
\(251\) 126.692i 0.504751i 0.967629 + 0.252375i \(0.0812118\pi\)
−0.967629 + 0.252375i \(0.918788\pi\)
\(252\) 0 0
\(253\) 270.872i 1.07064i
\(254\) 0 0
\(255\) −30.7011 + 100.958i −0.120396 + 0.395915i
\(256\) 0 0
\(257\) 396.692 1.54355 0.771774 0.635897i \(-0.219370\pi\)
0.771774 + 0.635897i \(0.219370\pi\)
\(258\) 0 0
\(259\) −27.7979 −0.107328
\(260\) 0 0
\(261\) 221.804 188.303i 0.849824 0.721467i
\(262\) 0 0
\(263\) −394.431 −1.49974 −0.749868 0.661587i \(-0.769883\pi\)
−0.749868 + 0.661587i \(0.769883\pi\)
\(264\) 0 0
\(265\) 41.9731 + 301.684i 0.158389 + 1.13843i
\(266\) 0 0
\(267\) 67.0137 144.798i 0.250987 0.542316i
\(268\) 0 0
\(269\) 104.802i 0.389597i −0.980843 0.194798i \(-0.937595\pi\)
0.980843 0.194798i \(-0.0624053\pi\)
\(270\) 0 0
\(271\) 335.355 1.23747 0.618736 0.785599i \(-0.287645\pi\)
0.618736 + 0.785599i \(0.287645\pi\)
\(272\) 0 0
\(273\) −42.4462 19.6444i −0.155481 0.0719576i
\(274\) 0 0
\(275\) 74.6935 + 263.235i 0.271613 + 0.957220i
\(276\) 0 0
\(277\) 167.790i 0.605739i −0.953032 0.302870i \(-0.902055\pi\)
0.953032 0.302870i \(-0.0979447\pi\)
\(278\) 0 0
\(279\) 203.562 + 239.778i 0.729614 + 0.859421i
\(280\) 0 0
\(281\) 99.4601i 0.353950i −0.984215 0.176975i \(-0.943369\pi\)
0.984215 0.176975i \(-0.0566312\pi\)
\(282\) 0 0
\(283\) 487.022i 1.72093i −0.509512 0.860464i \(-0.670174\pi\)
0.509512 0.860464i \(-0.329826\pi\)
\(284\) 0 0
\(285\) 101.042 332.270i 0.354534 1.16586i
\(286\) 0 0
\(287\) 28.7566 0.100197
\(288\) 0 0
\(289\) −239.511 −0.828756
\(290\) 0 0
\(291\) 144.903 313.097i 0.497950 1.07593i
\(292\) 0 0
\(293\) −343.107 −1.17101 −0.585507 0.810667i \(-0.699105\pi\)
−0.585507 + 0.810667i \(0.699105\pi\)
\(294\) 0 0
\(295\) 38.6129 5.37219i 0.130891 0.0182108i
\(296\) 0 0
\(297\) 284.777 78.9484i 0.958845 0.265819i
\(298\) 0 0
\(299\) 524.417i 1.75390i
\(300\) 0 0
\(301\) 16.6870 0.0554387
\(302\) 0 0
\(303\) −36.7677 + 79.4450i −0.121346 + 0.262195i
\(304\) 0 0
\(305\) −7.68447 55.2325i −0.0251950 0.181090i
\(306\) 0 0
\(307\) 364.627i 1.18771i 0.804573 + 0.593854i \(0.202394\pi\)
−0.804573 + 0.593854i \(0.797606\pi\)
\(308\) 0 0
\(309\) 113.337 244.889i 0.366785 0.792522i
\(310\) 0 0
\(311\) 121.963i 0.392164i −0.980587 0.196082i \(-0.937178\pi\)
0.980587 0.196082i \(-0.0628219\pi\)
\(312\) 0 0
\(313\) 94.8060i 0.302895i 0.988465 + 0.151447i \(0.0483934\pi\)
−0.988465 + 0.151447i \(0.951607\pi\)
\(314\) 0 0
\(315\) −24.7012 22.0462i −0.0784165 0.0699879i
\(316\) 0 0
\(317\) −511.282 −1.61288 −0.806438 0.591318i \(-0.798608\pi\)
−0.806438 + 0.591318i \(0.798608\pi\)
\(318\) 0 0
\(319\) −353.837 −1.10921
\(320\) 0 0
\(321\) −418.146 193.521i −1.30264 0.602869i
\(322\) 0 0
\(323\) −162.878 −0.504265
\(324\) 0 0
\(325\) −144.609 509.632i −0.444951 1.56810i
\(326\) 0 0
\(327\) −162.162 75.0498i −0.495909 0.229510i
\(328\) 0 0
\(329\) 28.7733i 0.0874569i
\(330\) 0 0
\(331\) 182.682 0.551909 0.275954 0.961171i \(-0.411006\pi\)
0.275954 + 0.961171i \(0.411006\pi\)
\(332\) 0 0
\(333\) −259.220 + 220.067i −0.778438 + 0.660863i
\(334\) 0 0
\(335\) 165.152 22.9775i 0.492990 0.0685895i
\(336\) 0 0
\(337\) 89.0617i 0.264278i 0.991231 + 0.132139i \(0.0421845\pi\)
−0.991231 + 0.132139i \(0.957815\pi\)
\(338\) 0 0
\(339\) −2.77147 1.28265i −0.00817541 0.00378364i
\(340\) 0 0
\(341\) 382.511i 1.12173i
\(342\) 0 0
\(343\) 71.7050i 0.209053i
\(344\) 0 0
\(345\) −108.005 + 355.165i −0.313057 + 1.02946i
\(346\) 0 0
\(347\) −17.7180 −0.0510605 −0.0255303 0.999674i \(-0.508127\pi\)
−0.0255303 + 0.999674i \(0.508127\pi\)
\(348\) 0 0
\(349\) 229.114 0.656488 0.328244 0.944593i \(-0.393543\pi\)
0.328244 + 0.944593i \(0.393543\pi\)
\(350\) 0 0
\(351\) −551.337 + 152.846i −1.57076 + 0.435460i
\(352\) 0 0
\(353\) −183.760 −0.520566 −0.260283 0.965532i \(-0.583816\pi\)
−0.260283 + 0.965532i \(0.583816\pi\)
\(354\) 0 0
\(355\) 480.199 66.8099i 1.35267 0.188197i
\(356\) 0 0
\(357\) −6.52174 + 14.0917i −0.0182682 + 0.0394726i
\(358\) 0 0
\(359\) 537.837i 1.49815i −0.662484 0.749076i \(-0.730498\pi\)
0.662484 0.749076i \(-0.269502\pi\)
\(360\) 0 0
\(361\) 175.056 0.484921
\(362\) 0 0
\(363\) 3.27995 + 1.51798i 0.00903567 + 0.00418177i
\(364\) 0 0
\(365\) 666.260 92.6964i 1.82537 0.253963i
\(366\) 0 0
\(367\) 153.740i 0.418909i 0.977818 + 0.209455i \(0.0671689\pi\)
−0.977818 + 0.209455i \(0.932831\pi\)
\(368\) 0 0
\(369\) 268.160 227.657i 0.726721 0.616957i
\(370\) 0 0
\(371\) 44.8202i 0.120809i
\(372\) 0 0
\(373\) 211.056i 0.565833i 0.959145 + 0.282917i \(0.0913020\pi\)
−0.959145 + 0.282917i \(0.908698\pi\)
\(374\) 0 0
\(375\) 7.02209 374.934i 0.0187256 0.999825i
\(376\) 0 0
\(377\) 685.040 1.81708
\(378\) 0 0
\(379\) −699.345 −1.84524 −0.922618 0.385715i \(-0.873955\pi\)
−0.922618 + 0.385715i \(0.873955\pi\)
\(380\) 0 0
\(381\) −264.265 + 571.006i −0.693610 + 1.49870i
\(382\) 0 0
\(383\) 186.008 0.485662 0.242831 0.970069i \(-0.421924\pi\)
0.242831 + 0.970069i \(0.421924\pi\)
\(384\) 0 0
\(385\) 5.54850 + 39.8801i 0.0144117 + 0.103585i
\(386\) 0 0
\(387\) 155.609 132.106i 0.402092 0.341360i
\(388\) 0 0
\(389\) 288.194i 0.740858i 0.928861 + 0.370429i \(0.120789\pi\)
−0.928861 + 0.370429i \(0.879211\pi\)
\(390\) 0 0
\(391\) 174.101 0.445271
\(392\) 0 0
\(393\) −264.669 + 571.877i −0.673457 + 1.45516i
\(394\) 0 0
\(395\) −83.4043 599.472i −0.211150 1.51765i
\(396\) 0 0
\(397\) 64.3054i 0.161978i −0.996715 0.0809892i \(-0.974192\pi\)
0.996715 0.0809892i \(-0.0258079\pi\)
\(398\) 0 0
\(399\) 21.4641 46.3780i 0.0537947 0.116236i
\(400\) 0 0
\(401\) 659.774i 1.64532i 0.568533 + 0.822661i \(0.307511\pi\)
−0.568533 + 0.822661i \(0.692489\pi\)
\(402\) 0 0
\(403\) 740.553i 1.83760i
\(404\) 0 0
\(405\) −404.876 10.0324i −0.999693 0.0247712i
\(406\) 0 0
\(407\) 413.526 1.01603
\(408\) 0 0
\(409\) 217.863 0.532672 0.266336 0.963880i \(-0.414187\pi\)
0.266336 + 0.963880i \(0.414187\pi\)
\(410\) 0 0
\(411\) 459.263 + 212.550i 1.11743 + 0.517153i
\(412\) 0 0
\(413\) 5.73660 0.0138901
\(414\) 0 0
\(415\) 62.1726 + 446.868i 0.149814 + 1.07679i
\(416\) 0 0
\(417\) 351.895 + 162.859i 0.843872 + 0.390550i
\(418\) 0 0
\(419\) 407.129i 0.971668i 0.874051 + 0.485834i \(0.161484\pi\)
−0.874051 + 0.485834i \(0.838516\pi\)
\(420\) 0 0
\(421\) −69.1949 −0.164359 −0.0821793 0.996618i \(-0.526188\pi\)
−0.0821793 + 0.996618i \(0.526188\pi\)
\(422\) 0 0
\(423\) −227.790 268.316i −0.538510 0.634316i
\(424\) 0 0
\(425\) −169.192 + 48.0087i −0.398100 + 0.112962i
\(426\) 0 0
\(427\) 8.20572i 0.0192171i
\(428\) 0 0
\(429\) 631.437 + 292.233i 1.47188 + 0.681197i
\(430\) 0 0
\(431\) 452.663i 1.05026i −0.851021 0.525132i \(-0.824016\pi\)
0.851021 0.525132i \(-0.175984\pi\)
\(432\) 0 0
\(433\) 226.323i 0.522686i 0.965246 + 0.261343i \(0.0841654\pi\)
−0.965246 + 0.261343i \(0.915835\pi\)
\(434\) 0 0
\(435\) 463.948 + 141.085i 1.06655 + 0.324333i
\(436\) 0 0
\(437\) −572.994 −1.31120
\(438\) 0 0
\(439\) −188.642 −0.429709 −0.214855 0.976646i \(-0.568928\pi\)
−0.214855 + 0.976646i \(0.568928\pi\)
\(440\) 0 0
\(441\) 282.257 + 332.474i 0.640038 + 0.753908i
\(442\) 0 0
\(443\) −499.705 −1.12800 −0.564001 0.825774i \(-0.690739\pi\)
−0.564001 + 0.825774i \(0.690739\pi\)
\(444\) 0 0
\(445\) 263.386 36.6448i 0.591878 0.0823478i
\(446\) 0 0
\(447\) −105.798 + 228.601i −0.236685 + 0.511412i
\(448\) 0 0
\(449\) 818.928i 1.82389i −0.410310 0.911946i \(-0.634579\pi\)
0.410310 0.911946i \(-0.365421\pi\)
\(450\) 0 0
\(451\) −427.787 −0.948531
\(452\) 0 0
\(453\) −24.6371 11.4022i −0.0543864 0.0251704i
\(454\) 0 0
\(455\) −10.7421 77.2090i −0.0236089 0.169690i
\(456\) 0 0
\(457\) 311.602i 0.681842i −0.940092 0.340921i \(-0.889261\pi\)
0.940092 0.340921i \(-0.110739\pi\)
\(458\) 0 0
\(459\) 50.7434 + 183.038i 0.110552 + 0.398776i
\(460\) 0 0
\(461\) 7.18351i 0.0155825i 0.999970 + 0.00779123i \(0.00248005\pi\)
−0.999970 + 0.00779123i \(0.997520\pi\)
\(462\) 0 0
\(463\) 557.563i 1.20424i 0.798406 + 0.602120i \(0.205677\pi\)
−0.798406 + 0.602120i \(0.794323\pi\)
\(464\) 0 0
\(465\) −152.518 + 501.545i −0.327996 + 1.07859i
\(466\) 0 0
\(467\) 659.257 1.41168 0.705842 0.708369i \(-0.250569\pi\)
0.705842 + 0.708369i \(0.250569\pi\)
\(468\) 0 0
\(469\) 24.5361 0.0523157
\(470\) 0 0
\(471\) −204.192 + 441.203i −0.433529 + 0.936738i
\(472\) 0 0
\(473\) −248.239 −0.524818
\(474\) 0 0
\(475\) 556.839 158.004i 1.17229 0.332640i
\(476\) 0 0
\(477\) 354.828 + 417.956i 0.743875 + 0.876218i
\(478\) 0 0
\(479\) 30.3870i 0.0634384i 0.999497 + 0.0317192i \(0.0100982\pi\)
−0.999497 + 0.0317192i \(0.989902\pi\)
\(480\) 0 0
\(481\) −800.598 −1.66445
\(482\) 0 0
\(483\) −22.9431 + 49.5738i −0.0475012 + 0.102637i
\(484\) 0 0
\(485\) 569.518 79.2368i 1.17426 0.163375i
\(486\) 0 0
\(487\) 26.5618i 0.0545416i 0.999628 + 0.0272708i \(0.00868164\pi\)
−0.999628 + 0.0272708i \(0.991318\pi\)
\(488\) 0 0
\(489\) −171.580 + 370.737i −0.350878 + 0.758153i
\(490\) 0 0
\(491\) 19.3354i 0.0393796i 0.999806 + 0.0196898i \(0.00626786\pi\)
−0.999806 + 0.0196898i \(0.993732\pi\)
\(492\) 0 0
\(493\) 227.426i 0.461311i
\(494\) 0 0
\(495\) 367.459 + 327.962i 0.742341 + 0.662550i
\(496\) 0 0
\(497\) 71.3418 0.143545
\(498\) 0 0
\(499\) −313.190 −0.627635 −0.313817 0.949483i \(-0.601608\pi\)
−0.313817 + 0.949483i \(0.601608\pi\)
\(500\) 0 0
\(501\) −383.693 177.576i −0.765855 0.354443i
\(502\) 0 0
\(503\) −551.684 −1.09679 −0.548394 0.836220i \(-0.684760\pi\)
−0.548394 + 0.836220i \(0.684760\pi\)
\(504\) 0 0
\(505\) −144.509 + 20.1055i −0.286157 + 0.0398129i
\(506\) 0 0
\(507\) −762.368 352.829i −1.50368 0.695915i
\(508\) 0 0
\(509\) 567.057i 1.11406i −0.830492 0.557031i \(-0.811941\pi\)
0.830492 0.557031i \(-0.188059\pi\)
\(510\) 0 0
\(511\) 98.9842 0.193707
\(512\) 0 0
\(513\) −167.005 602.407i −0.325545 1.17428i
\(514\) 0 0
\(515\) 445.450 61.9753i 0.864951 0.120340i
\(516\) 0 0
\(517\) 428.036i 0.827923i
\(518\) 0 0
\(519\) 360.333 + 166.764i 0.694283 + 0.321319i
\(520\) 0 0
\(521\) 740.223i 1.42077i −0.703811 0.710387i \(-0.748520\pi\)
0.703811 0.710387i \(-0.251480\pi\)
\(522\) 0 0
\(523\) 2.11805i 0.00404981i −0.999998 0.00202491i \(-0.999355\pi\)
0.999998 0.00202491i \(-0.000644548\pi\)
\(524\) 0 0
\(525\) 8.62619 54.5027i 0.0164308 0.103815i
\(526\) 0 0
\(527\) 245.856 0.466520
\(528\) 0 0
\(529\) 83.4771 0.157802
\(530\) 0 0
\(531\) 53.4947 45.4149i 0.100743 0.0855271i
\(532\) 0 0
\(533\) 828.210 1.55386
\(534\) 0 0
\(535\) −105.822 760.602i −0.197798 1.42169i
\(536\) 0 0
\(537\) 116.237 251.156i 0.216456 0.467702i
\(538\) 0 0
\(539\) 530.385i 0.984017i
\(540\) 0 0
\(541\) 6.61681 0.0122307 0.00611535 0.999981i \(-0.498053\pi\)
0.00611535 + 0.999981i \(0.498053\pi\)
\(542\) 0 0
\(543\) 315.535 + 146.032i 0.581096 + 0.268935i
\(544\) 0 0
\(545\) −41.0391 294.971i −0.0753011 0.541230i
\(546\) 0 0
\(547\) 230.092i 0.420644i −0.977632 0.210322i \(-0.932549\pi\)
0.977632 0.210322i \(-0.0674512\pi\)
\(548\) 0 0
\(549\) −64.9622 76.5197i −0.118328 0.139380i
\(550\) 0 0
\(551\) 748.495i 1.35843i
\(552\) 0 0
\(553\) 89.0617i 0.161052i
\(554\) 0 0
\(555\) −542.211 164.885i −0.976957 0.297089i
\(556\) 0 0
\(557\) −529.620 −0.950844 −0.475422 0.879758i \(-0.657705\pi\)
−0.475422 + 0.879758i \(0.657705\pi\)
\(558\) 0 0
\(559\) 480.598 0.859747
\(560\) 0 0
\(561\) 97.0184 209.630i 0.172938 0.373673i
\(562\) 0 0
\(563\) −131.530 −0.233623 −0.116812 0.993154i \(-0.537267\pi\)
−0.116812 + 0.993154i \(0.537267\pi\)
\(564\) 0 0
\(565\) −0.701387 5.04125i −0.00124139 0.00892257i
\(566\) 0 0
\(567\) −58.8055 9.67206i −0.103713 0.0170583i
\(568\) 0 0
\(569\) 172.534i 0.303224i 0.988440 + 0.151612i \(0.0484464\pi\)
−0.988440 + 0.151612i \(0.951554\pi\)
\(570\) 0 0
\(571\) −197.935 −0.346646 −0.173323 0.984865i \(-0.555450\pi\)
−0.173323 + 0.984865i \(0.555450\pi\)
\(572\) 0 0
\(573\) 66.9302 144.618i 0.116807 0.252387i
\(574\) 0 0
\(575\) −595.209 + 168.892i −1.03515 + 0.293724i
\(576\) 0 0
\(577\) 865.374i 1.49978i −0.661562 0.749891i \(-0.730106\pi\)
0.661562 0.749891i \(-0.269894\pi\)
\(578\) 0 0
\(579\) −341.863 + 738.673i −0.590437 + 1.27577i
\(580\) 0 0
\(581\) 66.3899i 0.114268i
\(582\) 0 0
\(583\) 666.753i 1.14366i
\(584\) 0 0
\(585\) −711.412 634.945i −1.21609 1.08538i
\(586\) 0 0
\(587\) 30.8886 0.0526211 0.0263105 0.999654i \(-0.491624\pi\)
0.0263105 + 0.999654i \(0.491624\pi\)
\(588\) 0 0
\(589\) −809.151 −1.37377
\(590\) 0 0
\(591\) −175.317 81.1379i −0.296644 0.137289i
\(592\) 0 0
\(593\) −511.286 −0.862202 −0.431101 0.902304i \(-0.641875\pi\)
−0.431101 + 0.902304i \(0.641875\pi\)
\(594\) 0 0
\(595\) −25.6326 + 3.56625i −0.0430800 + 0.00599370i
\(596\) 0 0
\(597\) −196.108 90.7603i −0.328490 0.152027i
\(598\) 0 0
\(599\) 514.866i 0.859543i −0.902938 0.429772i \(-0.858594\pi\)
0.902938 0.429772i \(-0.141406\pi\)
\(600\) 0 0
\(601\) 853.532 1.42019 0.710093 0.704107i \(-0.248653\pi\)
0.710093 + 0.704107i \(0.248653\pi\)
\(602\) 0 0
\(603\) 228.803 194.245i 0.379441 0.322131i
\(604\) 0 0
\(605\) 0.830071 + 5.96618i 0.00137202 + 0.00986145i
\(606\) 0 0
\(607\) 88.0713i 0.145093i −0.997365 0.0725464i \(-0.976887\pi\)
0.997365 0.0725464i \(-0.0231125\pi\)
\(608\) 0 0
\(609\) 64.7576 + 29.9703i 0.106334 + 0.0492123i
\(610\) 0 0
\(611\) 828.691i 1.35629i
\(612\) 0 0
\(613\) 403.346i 0.657987i 0.944332 + 0.328994i \(0.106709\pi\)
−0.944332 + 0.328994i \(0.893291\pi\)
\(614\) 0 0
\(615\) 560.911 + 170.571i 0.912050 + 0.277351i
\(616\) 0 0
\(617\) −365.738 −0.592769 −0.296384 0.955069i \(-0.595781\pi\)
−0.296384 + 0.955069i \(0.595781\pi\)
\(618\) 0 0
\(619\) 399.495 0.645389 0.322694 0.946503i \(-0.395411\pi\)
0.322694 + 0.946503i \(0.395411\pi\)
\(620\) 0 0
\(621\) 178.512 + 643.917i 0.287460 + 1.03690i
\(622\) 0 0
\(623\) 39.1304 0.0628097
\(624\) 0 0
\(625\) 531.856 328.260i 0.850969 0.525216i
\(626\) 0 0
\(627\) −319.303 + 689.927i −0.509255 + 1.10036i
\(628\) 0 0
\(629\) 265.790i 0.422560i
\(630\) 0 0
\(631\) 715.762 1.13433 0.567165 0.823604i \(-0.308040\pi\)
0.567165 + 0.823604i \(0.308040\pi\)
\(632\) 0 0
\(633\) −295.625 136.817i −0.467022 0.216141i
\(634\) 0 0
\(635\) −1038.65 + 144.507i −1.63567 + 0.227570i
\(636\) 0 0
\(637\) 1026.84i 1.61200i
\(638\) 0 0
\(639\) 665.274 564.791i 1.04112 0.883867i
\(640\) 0 0
\(641\) 627.158i 0.978406i 0.872170 + 0.489203i \(0.162712\pi\)
−0.872170 + 0.489203i \(0.837288\pi\)
\(642\) 0 0
\(643\) 802.039i 1.24734i −0.781688 0.623669i \(-0.785641\pi\)
0.781688 0.623669i \(-0.214359\pi\)
\(644\) 0 0
\(645\) 325.489 + 98.9800i 0.504634 + 0.153457i
\(646\) 0 0
\(647\) −19.9275 −0.0307998 −0.0153999 0.999881i \(-0.504902\pi\)
−0.0153999 + 0.999881i \(0.504902\pi\)
\(648\) 0 0
\(649\) −85.3385 −0.131492
\(650\) 0 0
\(651\) −32.3990 + 70.0054i −0.0497680 + 0.107535i
\(652\) 0 0
\(653\) 78.4638 0.120159 0.0600795 0.998194i \(-0.480865\pi\)
0.0600795 + 0.998194i \(0.480865\pi\)
\(654\) 0 0
\(655\) −1040.23 + 144.727i −1.58815 + 0.220958i
\(656\) 0 0
\(657\) 923.044 783.628i 1.40494 1.19274i
\(658\) 0 0
\(659\) 371.793i 0.564178i −0.959388 0.282089i \(-0.908973\pi\)
0.959388 0.282089i \(-0.0910274\pi\)
\(660\) 0 0
\(661\) 782.868 1.18437 0.592185 0.805802i \(-0.298266\pi\)
0.592185 + 0.805802i \(0.298266\pi\)
\(662\) 0 0
\(663\) −187.831 + 405.851i −0.283304 + 0.612143i
\(664\) 0 0
\(665\) 84.3609 11.7371i 0.126859 0.0176498i
\(666\) 0 0
\(667\) 800.071i 1.19951i
\(668\) 0 0
\(669\) −105.362 + 227.658i −0.157492 + 0.340297i
\(670\) 0 0
\(671\) 122.070i 0.181922i
\(672\) 0 0
\(673\) 221.323i 0.328860i −0.986389 0.164430i \(-0.947421\pi\)
0.986389 0.164430i \(-0.0525785\pi\)
\(674\) 0 0
\(675\) −351.041 576.537i −0.520060 0.854130i
\(676\) 0 0
\(677\) −576.855 −0.852076 −0.426038 0.904705i \(-0.640091\pi\)
−0.426038 + 0.904705i \(0.640091\pi\)
\(678\) 0 0
\(679\) 84.6116 0.124612
\(680\) 0 0
\(681\) −140.645 65.0916i −0.206527 0.0955824i
\(682\) 0 0
\(683\) 1272.02 1.86239 0.931197 0.364516i \(-0.118766\pi\)
0.931197 + 0.364516i \(0.118766\pi\)
\(684\) 0 0
\(685\) 116.228 + 835.392i 0.169675 + 1.21955i
\(686\) 0 0
\(687\) −764.969 354.033i −1.11349 0.515332i
\(688\) 0 0
\(689\) 1290.85i 1.87352i
\(690\) 0 0
\(691\) −1.61487 −0.00233701 −0.00116851 0.999999i \(-0.500372\pi\)
−0.00116851 + 0.999999i \(0.500372\pi\)
\(692\) 0 0
\(693\) 46.9053 + 55.2503i 0.0676844 + 0.0797263i
\(694\) 0 0
\(695\) 89.0556 + 640.091i 0.128138 + 0.920995i
\(696\) 0 0
\(697\) 274.957i 0.394486i
\(698\) 0 0
\(699\) −460.637 213.186i −0.658994 0.304987i
\(700\) 0 0
\(701\) 550.235i 0.784929i −0.919767 0.392465i \(-0.871623\pi\)
0.919767 0.392465i \(-0.128377\pi\)
\(702\) 0 0
\(703\) 874.758i 1.24432i
\(704\) 0 0
\(705\) 170.670 561.237i 0.242085 0.796081i
\(706\) 0 0
\(707\) −21.4693 −0.0303668
\(708\) 0 0
\(709\) −430.539 −0.607249 −0.303624 0.952792i \(-0.598197\pi\)
−0.303624 + 0.952792i \(0.598197\pi\)
\(710\) 0 0
\(711\) −705.075 830.515i −0.991666 1.16809i
\(712\) 0 0
\(713\) 864.907 1.21305
\(714\) 0 0
\(715\) 159.801 + 1148.57i 0.223497 + 1.60640i
\(716\) 0 0
\(717\) 1.41171 3.05033i 0.00196892 0.00425429i
\(718\) 0 0
\(719\) 460.561i 0.640558i 0.947323 + 0.320279i \(0.103777\pi\)
−0.947323 + 0.320279i \(0.896223\pi\)
\(720\) 0 0
\(721\) 66.1792 0.0917880
\(722\) 0 0
\(723\) 417.243 + 193.103i 0.577100 + 0.267086i
\(724\) 0 0
\(725\) 220.621 + 777.514i 0.304305 + 1.07243i
\(726\) 0 0
\(727\) 413.275i 0.568467i 0.958755 + 0.284233i \(0.0917390\pi\)
−0.958755 + 0.284233i \(0.908261\pi\)
\(728\) 0 0
\(729\) −624.942 + 375.352i −0.857259 + 0.514886i
\(730\) 0 0
\(731\) 159.554i 0.218268i
\(732\) 0 0
\(733\) 307.003i 0.418831i −0.977827 0.209416i \(-0.932844\pi\)
0.977827 0.209416i \(-0.0671562\pi\)
\(734\) 0 0
\(735\) −211.480 + 695.436i −0.287727 + 0.946171i
\(736\) 0 0
\(737\) −365.003 −0.495255
\(738\) 0 0
\(739\) 988.511 1.33763 0.668817 0.743427i \(-0.266801\pi\)
0.668817 + 0.743427i \(0.266801\pi\)
\(740\) 0 0
\(741\) 618.180 1335.72i 0.834251 1.80259i
\(742\) 0 0
\(743\) 652.187 0.877775 0.438887 0.898542i \(-0.355373\pi\)
0.438887 + 0.898542i \(0.355373\pi\)
\(744\) 0 0
\(745\) −415.822 + 57.8532i −0.558151 + 0.0776552i
\(746\) 0 0
\(747\) 525.589 + 619.097i 0.703599 + 0.828777i
\(748\) 0 0
\(749\) 113.000i 0.150868i
\(750\) 0 0
\(751\) −554.876 −0.738850 −0.369425 0.929261i \(-0.620445\pi\)
−0.369425 + 0.929261i \(0.620445\pi\)
\(752\) 0 0
\(753\) −159.635 + 344.928i −0.211999 + 0.458072i
\(754\) 0 0
\(755\) −6.23501 44.8144i −0.00825829 0.0593569i
\(756\) 0 0
\(757\) 547.156i 0.722795i 0.932412 + 0.361397i \(0.117700\pi\)
−0.932412 + 0.361397i \(0.882300\pi\)
\(758\) 0 0
\(759\) 341.305 737.467i 0.449677 0.971630i
\(760\) 0 0
\(761\) 1361.34i 1.78888i −0.447184 0.894442i \(-0.647573\pi\)
0.447184 0.894442i \(-0.352427\pi\)
\(762\) 0 0
\(763\) 43.8229i 0.0574350i
\(764\) 0 0
\(765\) −210.795 + 236.181i −0.275549 + 0.308734i
\(766\) 0 0
\(767\) 165.218 0.215408
\(768\) 0 0
\(769\) −396.180 −0.515188 −0.257594 0.966253i \(-0.582930\pi\)
−0.257594 + 0.966253i \(0.582930\pi\)
\(770\) 0 0
\(771\) 1080.02 + 499.840i 1.40080 + 0.648301i
\(772\) 0 0
\(773\) 664.286 0.859361 0.429681 0.902981i \(-0.358626\pi\)
0.429681 + 0.902981i \(0.358626\pi\)
\(774\) 0 0
\(775\) −840.522 + 238.499i −1.08454 + 0.307741i
\(776\) 0 0
\(777\) −75.6815 35.0259i −0.0974022 0.0450784i
\(778\) 0 0
\(779\) 904.927i 1.16165i
\(780\) 0 0
\(781\) −1061.29 −1.35889
\(782\) 0 0
\(783\) 841.141 233.189i 1.07425 0.297814i
\(784\) 0 0
\(785\) −802.542 + 111.657i −1.02235 + 0.142239i
\(786\) 0 0
\(787\) 957.551i 1.21671i 0.793665 + 0.608355i \(0.208170\pi\)
−0.793665 + 0.608355i \(0.791830\pi\)
\(788\) 0 0
\(789\) −1073.86 496.991i −1.36104 0.629900i
\(790\) 0 0
\(791\) 0.748964i 0.000946857i
\(792\) 0 0
\(793\) 236.330i 0.298021i
\(794\) 0 0
\(795\) −265.853 + 874.240i −0.334407 + 1.09967i
\(796\) 0 0
\(797\) 643.860 0.807854 0.403927 0.914791i \(-0.367645\pi\)
0.403927 + 0.914791i \(0.367645\pi\)
\(798\) 0 0
\(799\) −275.117