Properties

Label 1900.2.i.f.201.4
Level $1900$
Weight $2$
Character 1900.201
Analytic conductor $15.172$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 3 x^{11} + 15 x^{10} - 16 x^{9} + 79 x^{8} - 65 x^{7} + 298 x^{6} + 13 x^{5} + 233 x^{4} + 14 x^{3} + 145 x^{2} + 33 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.4
Root \(-0.126563 + 0.219213i\) of defining polynomial
Character \(\chi\) \(=\) 1900.201
Dual form 1900.2.i.f.501.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.626563 - 1.08524i) q^{3} -2.18534 q^{7} +(0.714838 + 1.23814i) q^{9} +O(q^{10})\) \(q+(0.626563 - 1.08524i) q^{3} -2.18534 q^{7} +(0.714838 + 1.23814i) q^{9} +2.12964 q^{11} +(-2.58011 - 4.46889i) q^{13} +(-1.31355 + 2.27514i) q^{17} +(2.80353 - 3.33770i) q^{19} +(-1.36925 + 2.37161i) q^{21} +(-1.27261 - 2.20422i) q^{23} +5.55094 q^{27} +(-3.08011 - 5.33491i) q^{29} -1.05063 q^{31} +(1.33435 - 2.31116i) q^{33} -2.25927 q^{37} -6.46641 q^{39} +(5.02728 - 8.70750i) q^{41} +(-0.840080 + 1.45506i) q^{43} +(-3.24455 - 5.61972i) q^{47} -2.22430 q^{49} +(1.64604 + 2.85103i) q^{51} +(-3.63184 - 6.29053i) q^{53} +(-1.86561 - 5.13378i) q^{57} +(3.53663 - 6.12563i) q^{59} +(5.41986 + 9.38748i) q^{61} +(-1.56216 - 2.70574i) q^{63} +(1.41877 + 2.45739i) q^{67} -3.18947 q^{69} +(-3.11236 + 5.39076i) q^{71} +(7.78260 - 13.4799i) q^{73} -4.65397 q^{77} +(2.80671 - 4.86136i) q^{79} +(1.33350 - 2.30969i) q^{81} -7.55136 q^{83} -7.71954 q^{87} +(-7.73341 - 13.3947i) q^{89} +(5.63842 + 9.76603i) q^{91} +(-0.658285 + 1.14018i) q^{93} +(6.63073 - 11.4848i) q^{97} +(1.52234 + 2.63678i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{3} - 3 q^{9} + O(q^{10}) \) \( 12 q + 3 q^{3} - 3 q^{9} + 2 q^{11} + 7 q^{13} - q^{17} + q^{21} - 2 q^{23} - 24 q^{27} + q^{29} + 2 q^{31} + 10 q^{33} + 20 q^{37} + 36 q^{39} - 7 q^{41} + 19 q^{43} - 14 q^{47} + 8 q^{49} + 11 q^{51} + 6 q^{53} - 28 q^{57} - 5 q^{61} - 11 q^{63} + 14 q^{67} - 14 q^{69} + 8 q^{71} - 9 q^{73} + 2 q^{77} + q^{79} + 2 q^{81} - 26 q^{83} + 30 q^{87} - 8 q^{89} + 3 q^{91} + 9 q^{93} - 11 q^{97} - 18 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\) \(951\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.626563 1.08524i 0.361746 0.626563i −0.626502 0.779420i \(-0.715514\pi\)
0.988248 + 0.152857i \(0.0488473\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.18534 −0.825980 −0.412990 0.910736i \(-0.635516\pi\)
−0.412990 + 0.910736i \(0.635516\pi\)
\(8\) 0 0
\(9\) 0.714838 + 1.23814i 0.238279 + 0.412712i
\(10\) 0 0
\(11\) 2.12964 0.642109 0.321055 0.947061i \(-0.395963\pi\)
0.321055 + 0.947061i \(0.395963\pi\)
\(12\) 0 0
\(13\) −2.58011 4.46889i −0.715595 1.23945i −0.962730 0.270465i \(-0.912822\pi\)
0.247135 0.968981i \(-0.420511\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.31355 + 2.27514i −0.318583 + 0.551801i −0.980193 0.198047i \(-0.936540\pi\)
0.661610 + 0.749848i \(0.269874\pi\)
\(18\) 0 0
\(19\) 2.80353 3.33770i 0.643174 0.765720i
\(20\) 0 0
\(21\) −1.36925 + 2.37161i −0.298795 + 0.517528i
\(22\) 0 0
\(23\) −1.27261 2.20422i −0.265357 0.459611i 0.702300 0.711881i \(-0.252156\pi\)
−0.967657 + 0.252269i \(0.918823\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 5.55094 1.06828
\(28\) 0 0
\(29\) −3.08011 5.33491i −0.571963 0.990668i −0.996364 0.0851943i \(-0.972849\pi\)
0.424402 0.905474i \(-0.360484\pi\)
\(30\) 0 0
\(31\) −1.05063 −0.188699 −0.0943493 0.995539i \(-0.530077\pi\)
−0.0943493 + 0.995539i \(0.530077\pi\)
\(32\) 0 0
\(33\) 1.33435 2.31116i 0.232281 0.402322i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.25927 −0.371422 −0.185711 0.982604i \(-0.559459\pi\)
−0.185711 + 0.982604i \(0.559459\pi\)
\(38\) 0 0
\(39\) −6.46641 −1.03545
\(40\) 0 0
\(41\) 5.02728 8.70750i 0.785129 1.35988i −0.143794 0.989608i \(-0.545930\pi\)
0.928922 0.370275i \(-0.120736\pi\)
\(42\) 0 0
\(43\) −0.840080 + 1.45506i −0.128111 + 0.221895i −0.922945 0.384933i \(-0.874225\pi\)
0.794834 + 0.606827i \(0.207558\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.24455 5.61972i −0.473266 0.819720i 0.526266 0.850320i \(-0.323592\pi\)
−0.999532 + 0.0305997i \(0.990258\pi\)
\(48\) 0 0
\(49\) −2.22430 −0.317757
\(50\) 0 0
\(51\) 1.64604 + 2.85103i 0.230492 + 0.399224i
\(52\) 0 0
\(53\) −3.63184 6.29053i −0.498871 0.864071i 0.501128 0.865373i \(-0.332919\pi\)
−0.999999 + 0.00130277i \(0.999585\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −1.86561 5.13378i −0.247106 0.679985i
\(58\) 0 0
\(59\) 3.53663 6.12563i 0.460430 0.797489i −0.538552 0.842592i \(-0.681028\pi\)
0.998982 + 0.0451035i \(0.0143618\pi\)
\(60\) 0 0
\(61\) 5.41986 + 9.38748i 0.693943 + 1.20194i 0.970536 + 0.240957i \(0.0774612\pi\)
−0.276593 + 0.960987i \(0.589205\pi\)
\(62\) 0 0
\(63\) −1.56216 2.70574i −0.196814 0.340892i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 1.41877 + 2.45739i 0.173331 + 0.300218i 0.939582 0.342323i \(-0.111214\pi\)
−0.766251 + 0.642541i \(0.777880\pi\)
\(68\) 0 0
\(69\) −3.18947 −0.383967
\(70\) 0 0
\(71\) −3.11236 + 5.39076i −0.369369 + 0.639766i −0.989467 0.144759i \(-0.953759\pi\)
0.620098 + 0.784524i \(0.287093\pi\)
\(72\) 0 0
\(73\) 7.78260 13.4799i 0.910885 1.57770i 0.0980678 0.995180i \(-0.468734\pi\)
0.812817 0.582519i \(-0.197933\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.65397 −0.530370
\(78\) 0 0
\(79\) 2.80671 4.86136i 0.315779 0.546946i −0.663823 0.747889i \(-0.731067\pi\)
0.979603 + 0.200943i \(0.0644007\pi\)
\(80\) 0 0
\(81\) 1.33350 2.30969i 0.148167 0.256632i
\(82\) 0 0
\(83\) −7.55136 −0.828869 −0.414435 0.910079i \(-0.636021\pi\)
−0.414435 + 0.910079i \(0.636021\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −7.71954 −0.827621
\(88\) 0 0
\(89\) −7.73341 13.3947i −0.819740 1.41983i −0.905874 0.423548i \(-0.860784\pi\)
0.0861333 0.996284i \(-0.472549\pi\)
\(90\) 0 0
\(91\) 5.63842 + 9.76603i 0.591067 + 1.02376i
\(92\) 0 0
\(93\) −0.658285 + 1.14018i −0.0682610 + 0.118232i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 6.63073 11.4848i 0.673248 1.16610i −0.303729 0.952758i \(-0.598232\pi\)
0.976978 0.213342i \(-0.0684348\pi\)
\(98\) 0 0
\(99\) 1.52234 + 2.63678i 0.153001 + 0.265006i
\(100\) 0 0
\(101\) 2.08748 + 3.61562i 0.207712 + 0.359767i 0.950993 0.309211i \(-0.100065\pi\)
−0.743282 + 0.668979i \(0.766732\pi\)
\(102\) 0 0
\(103\) −15.8667 −1.56340 −0.781699 0.623656i \(-0.785646\pi\)
−0.781699 + 0.623656i \(0.785646\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.02114 −0.388739 −0.194369 0.980928i \(-0.562266\pi\)
−0.194369 + 0.980928i \(0.562266\pi\)
\(108\) 0 0
\(109\) −2.21086 + 3.82932i −0.211762 + 0.366783i −0.952266 0.305269i \(-0.901254\pi\)
0.740504 + 0.672052i \(0.234587\pi\)
\(110\) 0 0
\(111\) −1.41558 + 2.45185i −0.134361 + 0.232719i
\(112\) 0 0
\(113\) 6.04226 0.568408 0.284204 0.958764i \(-0.408271\pi\)
0.284204 + 0.958764i \(0.408271\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 3.68873 6.38906i 0.341023 0.590669i
\(118\) 0 0
\(119\) 2.87055 4.97194i 0.263143 0.455777i
\(120\) 0 0
\(121\) −6.46465 −0.587695
\(122\) 0 0
\(123\) −6.29981 10.9116i −0.568035 0.983865i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 3.88488 + 6.72881i 0.344727 + 0.597085i 0.985304 0.170809i \(-0.0546380\pi\)
−0.640577 + 0.767894i \(0.721305\pi\)
\(128\) 0 0
\(129\) 1.05273 + 1.82338i 0.0926874 + 0.160539i
\(130\) 0 0
\(131\) −8.18596 + 14.1785i −0.715211 + 1.23878i 0.247667 + 0.968845i \(0.420336\pi\)
−0.962878 + 0.269937i \(0.912997\pi\)
\(132\) 0 0
\(133\) −6.12666 + 7.29399i −0.531249 + 0.632470i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −0.255662 0.442820i −0.0218427 0.0378326i 0.854897 0.518797i \(-0.173620\pi\)
−0.876740 + 0.480964i \(0.840287\pi\)
\(138\) 0 0
\(139\) 3.83289 + 6.63877i 0.325102 + 0.563093i 0.981533 0.191293i \(-0.0612681\pi\)
−0.656431 + 0.754386i \(0.727935\pi\)
\(140\) 0 0
\(141\) −8.13165 −0.684808
\(142\) 0 0
\(143\) −5.49470 9.51710i −0.459490 0.795860i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −1.39366 + 2.41390i −0.114947 + 0.199095i
\(148\) 0 0
\(149\) −6.96176 + 12.0581i −0.570330 + 0.987840i 0.426202 + 0.904628i \(0.359851\pi\)
−0.996532 + 0.0832122i \(0.973482\pi\)
\(150\) 0 0
\(151\) 0.617238 0.0502301 0.0251151 0.999685i \(-0.492005\pi\)
0.0251151 + 0.999685i \(0.492005\pi\)
\(152\) 0 0
\(153\) −3.75590 −0.303647
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 9.52408 16.4962i 0.760104 1.31654i −0.182692 0.983170i \(-0.558481\pi\)
0.942796 0.333369i \(-0.108185\pi\)
\(158\) 0 0
\(159\) −9.10230 −0.721859
\(160\) 0 0
\(161\) 2.78107 + 4.81696i 0.219179 + 0.379630i
\(162\) 0 0
\(163\) −0.523410 −0.0409967 −0.0204983 0.999790i \(-0.506525\pi\)
−0.0204983 + 0.999790i \(0.506525\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 10.4720 + 18.1381i 0.810349 + 1.40357i 0.912620 + 0.408810i \(0.134056\pi\)
−0.102270 + 0.994757i \(0.532611\pi\)
\(168\) 0 0
\(169\) −6.81397 + 11.8021i −0.524151 + 0.907857i
\(170\) 0 0
\(171\) 6.13659 + 1.08524i 0.469277 + 0.0829903i
\(172\) 0 0
\(173\) 0.896215 1.55229i 0.0681380 0.118018i −0.829944 0.557847i \(-0.811628\pi\)
0.898082 + 0.439829i \(0.144961\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −4.43185 7.67618i −0.333118 0.576977i
\(178\) 0 0
\(179\) 26.6492 1.99186 0.995928 0.0901537i \(-0.0287358\pi\)
0.995928 + 0.0901537i \(0.0287358\pi\)
\(180\) 0 0
\(181\) −5.21515 9.03290i −0.387639 0.671410i 0.604492 0.796611i \(-0.293376\pi\)
−0.992131 + 0.125200i \(0.960043\pi\)
\(182\) 0 0
\(183\) 13.5835 1.00412
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −2.79738 + 4.84521i −0.204565 + 0.354317i
\(188\) 0 0
\(189\) −12.1307 −0.882377
\(190\) 0 0
\(191\) 5.07372 0.367122 0.183561 0.983008i \(-0.441238\pi\)
0.183561 + 0.983008i \(0.441238\pi\)
\(192\) 0 0
\(193\) −3.25345 + 5.63515i −0.234189 + 0.405627i −0.959037 0.283282i \(-0.908577\pi\)
0.724848 + 0.688909i \(0.241910\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −6.78955 −0.483735 −0.241868 0.970309i \(-0.577760\pi\)
−0.241868 + 0.970309i \(0.577760\pi\)
\(198\) 0 0
\(199\) −6.90024 11.9516i −0.489145 0.847224i 0.510777 0.859713i \(-0.329358\pi\)
−0.999922 + 0.0124890i \(0.996025\pi\)
\(200\) 0 0
\(201\) 3.55581 0.250807
\(202\) 0 0
\(203\) 6.73109 + 11.6586i 0.472430 + 0.818272i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.81941 3.15132i 0.126458 0.219032i
\(208\) 0 0
\(209\) 5.97050 7.10808i 0.412988 0.491676i
\(210\) 0 0
\(211\) −2.06131 + 3.57030i −0.141907 + 0.245789i −0.928215 0.372045i \(-0.878657\pi\)
0.786308 + 0.617835i \(0.211990\pi\)
\(212\) 0 0
\(213\) 3.90018 + 6.75530i 0.267236 + 0.462866i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 2.29598 0.155861
\(218\) 0 0
\(219\) −9.75258 16.8920i −0.659018 1.14145i
\(220\) 0 0
\(221\) 13.5564 0.911904
\(222\) 0 0
\(223\) 2.53146 4.38462i 0.169519 0.293616i −0.768732 0.639571i \(-0.779112\pi\)
0.938251 + 0.345956i \(0.112445\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.05466 0.335489 0.167745 0.985830i \(-0.446352\pi\)
0.167745 + 0.985830i \(0.446352\pi\)
\(228\) 0 0
\(229\) 1.01317 0.0669523 0.0334761 0.999440i \(-0.489342\pi\)
0.0334761 + 0.999440i \(0.489342\pi\)
\(230\) 0 0
\(231\) −2.91601 + 5.05067i −0.191859 + 0.332310i
\(232\) 0 0
\(233\) 5.73375 9.93114i 0.375630 0.650611i −0.614791 0.788690i \(-0.710760\pi\)
0.990421 + 0.138079i \(0.0440929\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −3.51716 6.09190i −0.228464 0.395711i
\(238\) 0 0
\(239\) 18.0027 1.16450 0.582250 0.813010i \(-0.302172\pi\)
0.582250 + 0.813010i \(0.302172\pi\)
\(240\) 0 0
\(241\) −1.52915 2.64856i −0.0985012 0.170609i 0.812563 0.582873i \(-0.198071\pi\)
−0.911064 + 0.412264i \(0.864738\pi\)
\(242\) 0 0
\(243\) 6.65537 + 11.5274i 0.426942 + 0.739485i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −22.1492 3.91703i −1.40932 0.249234i
\(248\) 0 0
\(249\) −4.73140 + 8.19503i −0.299840 + 0.519339i
\(250\) 0 0
\(251\) −0.789341 1.36718i −0.0498228 0.0862956i 0.840038 0.542527i \(-0.182532\pi\)
−0.889861 + 0.456231i \(0.849199\pi\)
\(252\) 0 0
\(253\) −2.71019 4.69418i −0.170388 0.295121i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 7.07800 + 12.2595i 0.441513 + 0.764724i 0.997802 0.0662654i \(-0.0211084\pi\)
−0.556289 + 0.830989i \(0.687775\pi\)
\(258\) 0 0
\(259\) 4.93727 0.306787
\(260\) 0 0
\(261\) 4.40356 7.62719i 0.272574 0.472112i
\(262\) 0 0
\(263\) −9.04170 + 15.6607i −0.557535 + 0.965679i 0.440166 + 0.897916i \(0.354919\pi\)
−0.997701 + 0.0677628i \(0.978414\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −19.3819 −1.18615
\(268\) 0 0
\(269\) 3.29767 5.71172i 0.201062 0.348250i −0.747809 0.663914i \(-0.768894\pi\)
0.948871 + 0.315664i \(0.102227\pi\)
\(270\) 0 0
\(271\) 12.4587 21.5791i 0.756811 1.31084i −0.187657 0.982235i \(-0.560089\pi\)
0.944469 0.328601i \(-0.106577\pi\)
\(272\) 0 0
\(273\) 14.1313 0.855265
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 17.5130 1.05226 0.526128 0.850406i \(-0.323643\pi\)
0.526128 + 0.850406i \(0.323643\pi\)
\(278\) 0 0
\(279\) −0.751029 1.30082i −0.0449630 0.0778781i
\(280\) 0 0
\(281\) −8.43050 14.6021i −0.502922 0.871086i −0.999994 0.00337702i \(-0.998925\pi\)
0.497073 0.867709i \(-0.334408\pi\)
\(282\) 0 0
\(283\) −1.90656 + 3.30226i −0.113333 + 0.196299i −0.917112 0.398629i \(-0.869486\pi\)
0.803779 + 0.594928i \(0.202819\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −10.9863 + 19.0288i −0.648501 + 1.12324i
\(288\) 0 0
\(289\) 5.04917 + 8.74542i 0.297010 + 0.514437i
\(290\) 0 0
\(291\) −8.30913 14.3918i −0.487090 0.843665i
\(292\) 0 0
\(293\) −12.6667 −0.739996 −0.369998 0.929033i \(-0.620642\pi\)
−0.369998 + 0.929033i \(0.620642\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 11.8215 0.685952
\(298\) 0 0
\(299\) −6.56694 + 11.3743i −0.379776 + 0.657791i
\(300\) 0 0
\(301\) 1.83586 3.17980i 0.105817 0.183281i
\(302\) 0 0
\(303\) 5.23174 0.300556
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 7.64480 13.2412i 0.436312 0.755714i −0.561090 0.827755i \(-0.689618\pi\)
0.997402 + 0.0720410i \(0.0229512\pi\)
\(308\) 0 0
\(309\) −9.94152 + 17.2192i −0.565553 + 0.979567i
\(310\) 0 0
\(311\) −27.9152 −1.58292 −0.791462 0.611218i \(-0.790680\pi\)
−0.791462 + 0.611218i \(0.790680\pi\)
\(312\) 0 0
\(313\) 1.95539 + 3.38684i 0.110525 + 0.191436i 0.915982 0.401219i \(-0.131413\pi\)
−0.805457 + 0.592654i \(0.798080\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4.70175 + 8.14366i 0.264076 + 0.457394i 0.967321 0.253554i \(-0.0815996\pi\)
−0.703245 + 0.710948i \(0.748266\pi\)
\(318\) 0 0
\(319\) −6.55952 11.3614i −0.367263 0.636118i
\(320\) 0 0
\(321\) −2.51950 + 4.36390i −0.140625 + 0.243569i
\(322\) 0 0
\(323\) 3.91113 + 10.7626i 0.217621 + 0.598849i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 2.77049 + 4.79863i 0.153208 + 0.265365i
\(328\) 0 0
\(329\) 7.09043 + 12.2810i 0.390908 + 0.677073i
\(330\) 0 0
\(331\) 1.46413 0.0804757 0.0402379 0.999190i \(-0.487188\pi\)
0.0402379 + 0.999190i \(0.487188\pi\)
\(332\) 0 0
\(333\) −1.61501 2.79729i −0.0885022 0.153290i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 15.6121 27.0410i 0.850447 1.47302i −0.0303589 0.999539i \(-0.509665\pi\)
0.880806 0.473478i \(-0.157002\pi\)
\(338\) 0 0
\(339\) 3.78585 6.55729i 0.205619 0.356143i
\(340\) 0 0
\(341\) −2.23746 −0.121165
\(342\) 0 0
\(343\) 20.1582 1.08844
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −15.1197 + 26.1882i −0.811670 + 1.40585i 0.100024 + 0.994985i \(0.468108\pi\)
−0.911694 + 0.410869i \(0.865225\pi\)
\(348\) 0 0
\(349\) 17.1752 0.919367 0.459683 0.888083i \(-0.347963\pi\)
0.459683 + 0.888083i \(0.347963\pi\)
\(350\) 0 0
\(351\) −14.3221 24.8065i −0.764455 1.32407i
\(352\) 0 0
\(353\) 10.6712 0.567970 0.283985 0.958829i \(-0.408343\pi\)
0.283985 + 0.958829i \(0.408343\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −3.59716 6.23047i −0.190382 0.329751i
\(358\) 0 0
\(359\) −0.751774 + 1.30211i −0.0396771 + 0.0687228i −0.885182 0.465245i \(-0.845966\pi\)
0.845505 + 0.533968i \(0.179300\pi\)
\(360\) 0 0
\(361\) −3.28043 18.7147i −0.172654 0.984982i
\(362\) 0 0
\(363\) −4.05051 + 7.01569i −0.212597 + 0.368228i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 17.9857 + 31.1522i 0.938846 + 1.62613i 0.767628 + 0.640896i \(0.221437\pi\)
0.171218 + 0.985233i \(0.445230\pi\)
\(368\) 0 0
\(369\) 14.3747 0.748320
\(370\) 0 0
\(371\) 7.93679 + 13.7469i 0.412058 + 0.713705i
\(372\) 0 0
\(373\) 18.0175 0.932911 0.466455 0.884545i \(-0.345531\pi\)
0.466455 + 0.884545i \(0.345531\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −15.8941 + 27.5294i −0.818587 + 1.41783i
\(378\) 0 0
\(379\) −14.1538 −0.727032 −0.363516 0.931588i \(-0.618424\pi\)
−0.363516 + 0.931588i \(0.618424\pi\)
\(380\) 0 0
\(381\) 9.73649 0.498815
\(382\) 0 0
\(383\) −8.80446 + 15.2498i −0.449887 + 0.779227i −0.998378 0.0569291i \(-0.981869\pi\)
0.548491 + 0.836156i \(0.315202\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −2.40208 −0.122105
\(388\) 0 0
\(389\) 5.72023 + 9.90774i 0.290027 + 0.502342i 0.973816 0.227338i \(-0.0730023\pi\)
−0.683789 + 0.729680i \(0.739669\pi\)
\(390\) 0 0
\(391\) 6.68653 0.338152
\(392\) 0 0
\(393\) 10.2580 + 17.7674i 0.517450 + 0.896249i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −8.97852 + 15.5513i −0.450619 + 0.780495i −0.998425 0.0561107i \(-0.982130\pi\)
0.547806 + 0.836606i \(0.315463\pi\)
\(398\) 0 0
\(399\) 4.07699 + 11.2190i 0.204105 + 0.561654i
\(400\) 0 0
\(401\) −4.69150 + 8.12592i −0.234282 + 0.405789i −0.959064 0.283190i \(-0.908607\pi\)
0.724782 + 0.688979i \(0.241941\pi\)
\(402\) 0 0
\(403\) 2.71074 + 4.69514i 0.135032 + 0.233882i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −4.81143 −0.238494
\(408\) 0 0
\(409\) 19.4232 + 33.6420i 0.960415 + 1.66349i 0.721459 + 0.692457i \(0.243472\pi\)
0.238956 + 0.971030i \(0.423195\pi\)
\(410\) 0 0
\(411\) −0.640753 −0.0316060
\(412\) 0 0
\(413\) −7.72874 + 13.3866i −0.380306 + 0.658710i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 9.60620 0.470418
\(418\) 0 0
\(419\) 40.0512 1.95663 0.978314 0.207128i \(-0.0664118\pi\)
0.978314 + 0.207128i \(0.0664118\pi\)
\(420\) 0 0
\(421\) 18.7255 32.4336i 0.912627 1.58072i 0.102289 0.994755i \(-0.467383\pi\)
0.810339 0.585962i \(-0.199283\pi\)
\(422\) 0 0
\(423\) 4.63865 8.03438i 0.225539 0.390645i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −11.8442 20.5148i −0.573183 0.992782i
\(428\) 0 0
\(429\) −13.7711 −0.664875
\(430\) 0 0
\(431\) 7.38909 + 12.7983i 0.355920 + 0.616472i 0.987275 0.159022i \(-0.0508342\pi\)
−0.631355 + 0.775494i \(0.717501\pi\)
\(432\) 0 0
\(433\) 4.84501 + 8.39180i 0.232836 + 0.403284i 0.958642 0.284616i \(-0.0918661\pi\)
−0.725805 + 0.687900i \(0.758533\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −10.9248 1.93202i −0.522604 0.0924211i
\(438\) 0 0
\(439\) −2.80499 + 4.85838i −0.133875 + 0.231878i −0.925167 0.379560i \(-0.876075\pi\)
0.791292 + 0.611438i \(0.209409\pi\)
\(440\) 0 0
\(441\) −1.59001 2.75398i −0.0757149 0.131142i
\(442\) 0 0
\(443\) 2.68171 + 4.64485i 0.127412 + 0.220684i 0.922673 0.385583i \(-0.126000\pi\)
−0.795261 + 0.606267i \(0.792666\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 8.72396 + 15.1103i 0.412629 + 0.714695i
\(448\) 0 0
\(449\) 6.14784 0.290134 0.145067 0.989422i \(-0.453660\pi\)
0.145067 + 0.989422i \(0.453660\pi\)
\(450\) 0 0
\(451\) 10.7063 18.5438i 0.504138 0.873193i
\(452\) 0 0
\(453\) 0.386738 0.669851i 0.0181706 0.0314723i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 31.6775 1.48181 0.740906 0.671608i \(-0.234396\pi\)
0.740906 + 0.671608i \(0.234396\pi\)
\(458\) 0 0
\(459\) −7.29144 + 12.6291i −0.340335 + 0.589478i
\(460\) 0 0
\(461\) 4.34077 7.51844i 0.202170 0.350169i −0.747057 0.664760i \(-0.768534\pi\)
0.949227 + 0.314591i \(0.101867\pi\)
\(462\) 0 0
\(463\) 0.258854 0.0120300 0.00601499 0.999982i \(-0.498085\pi\)
0.00601499 + 0.999982i \(0.498085\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 22.8060 1.05534 0.527668 0.849451i \(-0.323066\pi\)
0.527668 + 0.849451i \(0.323066\pi\)
\(468\) 0 0
\(469\) −3.10050 5.37023i −0.143168 0.247974i
\(470\) 0 0
\(471\) −11.9349 20.6718i −0.549930 0.952506i
\(472\) 0 0
\(473\) −1.78907 + 3.09875i −0.0822613 + 0.142481i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 5.19235 8.99342i 0.237741 0.411780i
\(478\) 0 0
\(479\) −3.10389 5.37609i −0.141820 0.245640i 0.786362 0.617766i \(-0.211962\pi\)
−0.928182 + 0.372126i \(0.878629\pi\)
\(480\) 0 0
\(481\) 5.82918 + 10.0964i 0.265788 + 0.460358i
\(482\) 0 0
\(483\) 6.97007 0.317149
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −21.5698 −0.977420 −0.488710 0.872446i \(-0.662532\pi\)
−0.488710 + 0.872446i \(0.662532\pi\)
\(488\) 0 0
\(489\) −0.327950 + 0.568025i −0.0148304 + 0.0256870i
\(490\) 0 0
\(491\) −18.2548 + 31.6182i −0.823828 + 1.42691i 0.0789841 + 0.996876i \(0.474832\pi\)
−0.902812 + 0.430036i \(0.858501\pi\)
\(492\) 0 0
\(493\) 16.1835 0.728870
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 6.80155 11.7806i 0.305091 0.528434i
\(498\) 0 0
\(499\) −18.5178 + 32.0737i −0.828969 + 1.43582i 0.0698794 + 0.997555i \(0.477739\pi\)
−0.898848 + 0.438260i \(0.855595\pi\)
\(500\) 0 0
\(501\) 26.2455 1.17256
\(502\) 0 0
\(503\) 17.0971 + 29.6130i 0.762321 + 1.32038i 0.941651 + 0.336590i \(0.109274\pi\)
−0.179330 + 0.983789i \(0.557393\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 8.53876 + 14.7896i 0.379220 + 0.656827i
\(508\) 0 0
\(509\) −17.0016 29.4476i −0.753581 1.30524i −0.946077 0.323943i \(-0.894991\pi\)
0.192495 0.981298i \(-0.438342\pi\)
\(510\) 0 0
\(511\) −17.0076 + 29.4581i −0.752373 + 1.30315i
\(512\) 0 0
\(513\) 15.5622 18.5274i 0.687089 0.818003i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −6.90970 11.9680i −0.303888 0.526350i
\(518\) 0 0
\(519\) −1.12307 1.94522i −0.0492973 0.0853855i
\(520\) 0 0
\(521\) −33.6165 −1.47277 −0.736383 0.676565i \(-0.763468\pi\)
−0.736383 + 0.676565i \(0.763468\pi\)
\(522\) 0 0
\(523\) 11.6947 + 20.2557i 0.511372 + 0.885722i 0.999913 + 0.0131810i \(0.00419577\pi\)
−0.488541 + 0.872541i \(0.662471\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.38005 2.39032i 0.0601161 0.104124i
\(528\) 0 0
\(529\) 8.26095 14.3084i 0.359172 0.622103i
\(530\) 0 0
\(531\) 10.1125 0.438844
\(532\) 0 0
\(533\) −51.8838 −2.24734
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 16.6974 28.9208i 0.720546 1.24802i
\(538\) 0 0
\(539\) −4.73695 −0.204035
\(540\) 0 0
\(541\) −18.0050 31.1856i −0.774097 1.34077i −0.935301 0.353854i \(-0.884871\pi\)
0.161204 0.986921i \(-0.448462\pi\)
\(542\) 0 0
\(543\) −13.0705 −0.560908
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −6.61701 11.4610i −0.282923 0.490037i 0.689180 0.724590i \(-0.257971\pi\)
−0.972103 + 0.234553i \(0.924637\pi\)
\(548\) 0 0
\(549\) −7.74865 + 13.4211i −0.330704 + 0.572797i
\(550\) 0 0
\(551\) −26.4415 4.67611i −1.12645 0.199209i
\(552\) 0 0
\(553\) −6.13361 + 10.6237i −0.260827 + 0.451766i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 9.03385 + 15.6471i 0.382776 + 0.662988i 0.991458 0.130427i \(-0.0416347\pi\)
−0.608682 + 0.793415i \(0.708301\pi\)
\(558\) 0 0
\(559\) 8.67001 0.366702
\(560\) 0 0
\(561\) 3.50547 + 6.07166i 0.148001 + 0.256346i
\(562\) 0 0
\(563\) −24.4686 −1.03123 −0.515613 0.856821i \(-0.672436\pi\)
−0.515613 + 0.856821i \(0.672436\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −2.91415 + 5.04745i −0.122383 + 0.211973i
\(568\) 0 0
\(569\) −18.4580 −0.773801 −0.386900 0.922122i \(-0.626454\pi\)
−0.386900 + 0.922122i \(0.626454\pi\)
\(570\) 0 0
\(571\) −19.5131 −0.816598 −0.408299 0.912848i \(-0.633878\pi\)
−0.408299 + 0.912848i \(0.633878\pi\)
\(572\) 0 0
\(573\) 3.17901 5.50620i 0.132805 0.230025i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −5.03750 −0.209714 −0.104857 0.994487i \(-0.533438\pi\)
−0.104857 + 0.994487i \(0.533438\pi\)
\(578\) 0 0
\(579\) 4.07699 + 7.06155i 0.169434 + 0.293468i
\(580\) 0 0
\(581\) 16.5023 0.684630
\(582\) 0 0
\(583\) −7.73449 13.3965i −0.320330 0.554828i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −14.8436 + 25.7099i −0.612662 + 1.06116i 0.378128 + 0.925754i \(0.376568\pi\)
−0.990790 + 0.135409i \(0.956765\pi\)
\(588\) 0 0
\(589\) −2.94547 + 3.50668i −0.121366 + 0.144490i
\(590\) 0 0
\(591\) −4.25408 + 7.36828i −0.174989 + 0.303091i
\(592\) 0 0
\(593\) 17.2178 + 29.8222i 0.707052 + 1.22465i 0.965946 + 0.258744i \(0.0833085\pi\)
−0.258894 + 0.965906i \(0.583358\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −17.2937 −0.707786
\(598\) 0 0
\(599\) −0.909784 1.57579i −0.0371728 0.0643851i 0.846840 0.531847i \(-0.178502\pi\)
−0.884013 + 0.467462i \(0.845169\pi\)
\(600\) 0 0
\(601\) −9.14106 −0.372872 −0.186436 0.982467i \(-0.559694\pi\)
−0.186436 + 0.982467i \(0.559694\pi\)
\(602\) 0 0
\(603\) −2.02839 + 3.51327i −0.0826023 + 0.143071i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 27.7363 1.12578 0.562890 0.826532i \(-0.309689\pi\)
0.562890 + 0.826532i \(0.309689\pi\)
\(608\) 0 0
\(609\) 16.8698 0.683599
\(610\) 0 0
\(611\) −16.7426 + 28.9990i −0.677333 + 1.17317i
\(612\) 0 0
\(613\) 11.1937 19.3881i 0.452109 0.783076i −0.546407 0.837519i \(-0.684005\pi\)
0.998517 + 0.0544430i \(0.0173383\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −21.8234 37.7993i −0.878578 1.52174i −0.852902 0.522071i \(-0.825160\pi\)
−0.0256759 0.999670i \(-0.508174\pi\)
\(618\) 0 0
\(619\) 27.7258 1.11440 0.557198 0.830380i \(-0.311876\pi\)
0.557198 + 0.830380i \(0.311876\pi\)
\(620\) 0 0
\(621\) −7.06416 12.2355i −0.283475 0.490993i
\(622\) 0 0
\(623\) 16.9001 + 29.2719i 0.677089 + 1.17275i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −3.97307 10.9331i −0.158669 0.436625i
\(628\) 0 0
\(629\) 2.96767 5.14015i 0.118329 0.204951i
\(630\) 0 0
\(631\) −5.83973 10.1147i −0.232476 0.402660i 0.726060 0.687631i \(-0.241349\pi\)
−0.958536 + 0.284971i \(0.908016\pi\)
\(632\) 0 0
\(633\) 2.58308 + 4.47403i 0.102668 + 0.177827i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 5.73894 + 9.94014i 0.227385 + 0.393843i
\(638\) 0 0
\(639\) −8.89932 −0.352052
\(640\) 0 0
\(641\) −9.87218 + 17.0991i −0.389928 + 0.675374i −0.992439 0.122736i \(-0.960833\pi\)
0.602512 + 0.798110i \(0.294167\pi\)
\(642\) 0 0
\(643\) −9.48677 + 16.4316i −0.374122 + 0.647998i −0.990195 0.139691i \(-0.955389\pi\)
0.616073 + 0.787689i \(0.288722\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −6.83157 −0.268577 −0.134288 0.990942i \(-0.542875\pi\)
−0.134288 + 0.990942i \(0.542875\pi\)
\(648\) 0 0
\(649\) 7.53174 13.0454i 0.295647 0.512075i
\(650\) 0 0
\(651\) 1.43858 2.49169i 0.0563822 0.0976569i
\(652\) 0 0
\(653\) −18.7904 −0.735325 −0.367663 0.929959i \(-0.619842\pi\)
−0.367663 + 0.929959i \(0.619842\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 22.2532 0.868180
\(658\) 0 0
\(659\) −17.7289 30.7073i −0.690619 1.19619i −0.971635 0.236485i \(-0.924005\pi\)
0.281016 0.959703i \(-0.409329\pi\)
\(660\) 0 0
\(661\) 11.8550 + 20.5335i 0.461108 + 0.798662i 0.999016 0.0443412i \(-0.0141189\pi\)
−0.537909 + 0.843003i \(0.680786\pi\)
\(662\) 0 0
\(663\) 8.49396 14.7120i 0.329878 0.571365i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −7.83954 + 13.5785i −0.303548 + 0.525761i
\(668\) 0 0
\(669\) −3.17224 5.49448i −0.122646 0.212429i
\(670\) 0 0
\(671\) 11.5423 + 19.9919i 0.445587 + 0.771779i
\(672\) 0 0
\(673\) −2.76230 −0.106479 −0.0532394 0.998582i \(-0.516955\pi\)
−0.0532394 + 0.998582i \(0.516955\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −17.0981 −0.657132 −0.328566 0.944481i \(-0.606565\pi\)
−0.328566 + 0.944481i \(0.606565\pi\)
\(678\) 0 0
\(679\) −14.4904 + 25.0981i −0.556090 + 0.963175i
\(680\) 0 0
\(681\) 3.16706 5.48551i 0.121362 0.210205i
\(682\) 0 0
\(683\) 17.4864 0.669098 0.334549 0.942378i \(-0.391416\pi\)
0.334549 + 0.942378i \(0.391416\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0.634816 1.09953i 0.0242197 0.0419498i
\(688\) 0 0
\(689\) −18.7411 + 32.4605i −0.713979 + 1.23665i
\(690\) 0 0
\(691\) 20.2781 0.771416 0.385708 0.922621i \(-0.373957\pi\)
0.385708 + 0.922621i \(0.373957\pi\)
\(692\) 0 0
\(693\) −3.32684 5.76225i −0.126376 0.218890i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 13.2072 + 22.8755i 0.500257 + 0.866470i
\(698\) 0 0
\(699\) −7.18511 12.4450i −0.271766 0.470712i
\(700\) 0 0
\(701\) 24.2078 41.9292i 0.914317 1.58364i 0.106418 0.994322i \(-0.466062\pi\)
0.807899 0.589321i \(-0.200605\pi\)
\(702\) 0 0
\(703\) −6.33394 + 7.54077i −0.238889 + 0.284405i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4.56184 7.90134i −0.171566 0.297161i
\(708\) 0 0
\(709\) 9.60392 + 16.6345i 0.360683 + 0.624721i 0.988073 0.153984i \(-0.0492104\pi\)
−0.627391 + 0.778705i \(0.715877\pi\)
\(710\) 0 0
\(711\) 8.02537 0.300975
\(712\) 0 0
\(713\) 1.33704 + 2.31582i 0.0500724 + 0.0867280i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 11.2799 19.5373i 0.421254 0.729633i
\(718\) 0 0
\(719\) 25.0395 43.3698i 0.933817 1.61742i 0.157088 0.987585i \(-0.449789\pi\)
0.776729 0.629835i \(-0.216877\pi\)
\(720\) 0 0
\(721\) 34.6742 1.29133
\(722\) 0 0
\(723\) −3.83243 −0.142530
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 22.2320 38.5070i 0.824540 1.42815i −0.0777303 0.996974i \(-0.524767\pi\)
0.902270 0.431171i \(-0.141899\pi\)
\(728\) 0 0
\(729\) 24.6810 0.914112
\(730\) 0 0
\(731\) −2.20697 3.82259i −0.0816279 0.141384i
\(732\) 0 0
\(733\) −40.6973 −1.50319 −0.751594 0.659626i \(-0.770715\pi\)
−0.751594 + 0.659626i \(0.770715\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3.02147 + 5.23335i 0.111297 + 0.192773i
\(738\) 0 0
\(739\) −20.0899 + 34.7967i −0.739019 + 1.28002i 0.213919 + 0.976851i \(0.431377\pi\)
−0.952938 + 0.303167i \(0.901956\pi\)
\(740\) 0 0
\(741\) −18.1288 + 21.5829i −0.665978 + 0.792868i
\(742\) 0 0
\(743\) 14.7584 25.5623i 0.541432 0.937788i −0.457390 0.889266i \(-0.651216\pi\)
0.998822 0.0485220i \(-0.0154511\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −5.39800 9.34961i −0.197502 0.342084i
\(748\) 0 0
\(749\) 8.78756 0.321090
\(750\) 0 0
\(751\) −0.886284 1.53509i −0.0323410 0.0560162i 0.849402 0.527747i \(-0.176963\pi\)
−0.881743 + 0.471730i \(0.843630\pi\)
\(752\) 0 0
\(753\) −1.97829 −0.0720928
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −5.33238 + 9.23595i −0.193809 + 0.335686i −0.946509 0.322677i \(-0.895417\pi\)
0.752701 + 0.658363i \(0.228751\pi\)
\(758\) 0 0
\(759\) −6.79241 −0.246549
\(760\) 0 0
\(761\) −26.5852 −0.963713 −0.481856 0.876250i \(-0.660037\pi\)
−0.481856 + 0.876250i \(0.660037\pi\)
\(762\) 0 0
\(763\) 4.83148 8.36837i 0.174911 0.302955i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −36.4997 −1.31793
\(768\) 0 0
\(769\) −3.28351 5.68721i −0.118406 0.205086i 0.800730 0.599026i \(-0.204445\pi\)
−0.919136 + 0.393940i \(0.871112\pi\)
\(770\) 0 0
\(771\) 17.7392 0.638863
\(772\) 0 0
\(773\) 10.8126 + 18.7279i 0.388902 + 0.673597i 0.992302 0.123841i \(-0.0395213\pi\)
−0.603400 + 0.797438i \(0.706188\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 3.09351 5.35812i 0.110979 0.192222i
\(778\) 0 0
\(779\) −14.9689 41.1913i −0.536315 1.47583i
\(780\) 0 0
\(781\) −6.62819 + 11.4804i −0.237175 + 0.410800i
\(782\) 0 0
\(783\) −17.0975 29.6138i −0.611016 1.05831i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −46.4649 −1.65630 −0.828148 0.560509i \(-0.810605\pi\)
−0.828148 + 0.560509i \(0.810605\pi\)
\(788\) 0 0
\(789\) 11.3304 + 19.6248i 0.403372 + 0.698662i
\(790\) 0 0
\(791\) −13.2044 −0.469494
\(792\) 0 0
\(793\) 27.9677 48.4415i 0.993163 1.72021i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 36.8012 1.30357 0.651783 0.758405i \(-0.274021\pi\)
0.651783 + 0.758405i \(0.274021\pi\)
\(798\) 0 0
\(799\) 17.0475 0.603097
\(800\) 0 0
\(801\) 11.0563 19.1500i 0.390654 0.676633i
\(802\) 0