Properties

Label 1900.2.s.c.49.2
Level $1900$
Weight $2$
Character 1900.49
Analytic conductor $15.172$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 9 x^{10} + 59 x^{8} - 180 x^{6} + 403 x^{4} - 198 x^{2} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 380)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.2
Root \(-1.65604 + 0.956115i\) of defining polynomial
Character \(\chi\) \(=\) 1900.49
Dual form 1900.2.s.c.349.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.22469 - 1.28442i) q^{3} -3.56885i q^{7} +(1.79949 + 3.11682i) q^{9} +O(q^{10})\) \(q+(-2.22469 - 1.28442i) q^{3} -3.56885i q^{7} +(1.79949 + 3.11682i) q^{9} +4.56885 q^{11} +(-0.866025 + 0.500000i) q^{13} +(4.96812 + 2.86834i) q^{17} +(4.35327 - 0.221364i) q^{19} +(-4.58392 + 7.93958i) q^{21} +(-4.84887 + 2.79949i) q^{23} -1.53871i q^{27} +(3.38341 + 5.86024i) q^{29} +4.59899 q^{31} +(-10.1643 - 5.86834i) q^{33} -3.56885i q^{37} +2.56885 q^{39} +(-5.35327 + 9.27214i) q^{41} +(9.79088 + 5.65277i) q^{43} +(5.86024 - 3.38341i) q^{47} -5.73669 q^{49} +(-7.36834 - 12.7623i) q^{51} +(-2.94536 + 1.70051i) q^{53} +(-9.96901 - 5.09899i) q^{57} +(-3.38341 + 5.86024i) q^{59} +(-4.06885 - 7.04745i) q^{61} +(11.1234 - 6.42212i) q^{63} +(5.48686 - 3.16784i) q^{67} +14.3830 q^{69} +(0.515069 - 0.892126i) q^{71} +(11.0303 + 6.36834i) q^{73} -16.3055i q^{77} +(2.43115 - 4.21088i) q^{79} +(3.42212 - 5.92729i) q^{81} -9.40101i q^{83} -17.3830i q^{87} +(6.13770 + 10.6308i) q^{89} +(1.78442 + 3.09071i) q^{91} +(-10.2313 - 5.90705i) q^{93} +(2.27689 + 1.31456i) q^{97} +(8.22162 + 14.2403i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 16q^{9} + O(q^{10}) \) \( 12q + 16q^{9} + 20q^{11} - 32q^{21} + 12q^{29} + 44q^{31} - 4q^{39} - 12q^{41} + 12q^{49} - 48q^{51} - 12q^{59} - 14q^{61} - 60q^{69} + 18q^{71} + 64q^{79} - 46q^{81} + 4q^{89} + 4q^{91} + 6q^{99} + O(q^{100}) \)

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
\(3\) −2.22469 1.28442i −1.28442 0.741563i −0.306771 0.951783i \(-0.599249\pi\)
−0.977654 + 0.210220i \(0.932582\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 3.56885i 1.34890i −0.738321 0.674449i \(-0.764381\pi\)
0.738321 0.674449i \(-0.235619\pi\)
\(8\) 0 0
\(9\) 1.79949 + 3.11682i 0.599831 + 1.03894i
\(10\) 0 0
\(11\) 4.56885 1.37756 0.688780 0.724970i \(-0.258147\pi\)
0.688780 + 0.724970i \(0.258147\pi\)
\(12\) 0 0
\(13\) −0.866025 + 0.500000i −0.240192 + 0.138675i −0.615265 0.788320i \(-0.710951\pi\)
0.375073 + 0.926995i \(0.377618\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.96812 + 2.86834i 1.20495 + 0.695676i 0.961651 0.274277i \(-0.0884385\pi\)
0.243295 + 0.969952i \(0.421772\pi\)
\(18\) 0 0
\(19\) 4.35327 0.221364i 0.998710 0.0507843i
\(20\) 0 0
\(21\) −4.58392 + 7.93958i −1.00029 + 1.73256i
\(22\) 0 0
\(23\) −4.84887 + 2.79949i −1.01106 + 0.583735i −0.911501 0.411297i \(-0.865076\pi\)
−0.0995571 + 0.995032i \(0.531743\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 1.53871i 0.296125i
\(28\) 0 0
\(29\) 3.38341 + 5.86024i 0.628284 + 1.08822i 0.987896 + 0.155118i \(0.0495758\pi\)
−0.359612 + 0.933102i \(0.617091\pi\)
\(30\) 0 0
\(31\) 4.59899 0.826003 0.413001 0.910730i \(-0.364480\pi\)
0.413001 + 0.910730i \(0.364480\pi\)
\(32\) 0 0
\(33\) −10.1643 5.86834i −1.76937 1.02155i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.56885i 0.586715i −0.956003 0.293358i \(-0.905227\pi\)
0.956003 0.293358i \(-0.0947727\pi\)
\(38\) 0 0
\(39\) 2.56885 0.411345
\(40\) 0 0
\(41\) −5.35327 + 9.27214i −0.836041 + 1.44807i 0.0571390 + 0.998366i \(0.481802\pi\)
−0.893180 + 0.449699i \(0.851531\pi\)
\(42\) 0 0
\(43\) 9.79088 + 5.65277i 1.49310 + 0.862039i 0.999969 0.00791826i \(-0.00252049\pi\)
0.493127 + 0.869957i \(0.335854\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5.86024 3.38341i 0.854804 0.493522i −0.00746461 0.999972i \(-0.502376\pi\)
0.862269 + 0.506451i \(0.169043\pi\)
\(48\) 0 0
\(49\) −5.73669 −0.819527
\(50\) 0 0
\(51\) −7.36834 12.7623i −1.03177 1.78709i
\(52\) 0 0
\(53\) −2.94536 + 1.70051i −0.404577 + 0.233582i −0.688457 0.725277i \(-0.741712\pi\)
0.283880 + 0.958860i \(0.408378\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −9.96901 5.09899i −1.32043 0.675378i
\(58\) 0 0
\(59\) −3.38341 + 5.86024i −0.440483 + 0.762939i −0.997725 0.0674112i \(-0.978526\pi\)
0.557242 + 0.830350i \(0.311859\pi\)
\(60\) 0 0
\(61\) −4.06885 7.04745i −0.520963 0.902334i −0.999703 0.0243773i \(-0.992240\pi\)
0.478740 0.877957i \(-0.341094\pi\)
\(62\) 0 0
\(63\) 11.1234 6.42212i 1.40142 0.809112i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 5.48686 3.16784i 0.670326 0.387013i −0.125874 0.992046i \(-0.540174\pi\)
0.796200 + 0.605033i \(0.206840\pi\)
\(68\) 0 0
\(69\) 14.3830 1.73150
\(70\) 0 0
\(71\) 0.515069 0.892126i 0.0611275 0.105876i −0.833842 0.552003i \(-0.813864\pi\)
0.894970 + 0.446127i \(0.147197\pi\)
\(72\) 0 0
\(73\) 11.0303 + 6.36834i 1.29100 + 0.745358i 0.978831 0.204669i \(-0.0656118\pi\)
0.312167 + 0.950027i \(0.398945\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 16.3055i 1.85819i
\(78\) 0 0
\(79\) 2.43115 4.21088i 0.273526 0.473761i −0.696236 0.717813i \(-0.745143\pi\)
0.969762 + 0.244052i \(0.0784768\pi\)
\(80\) 0 0
\(81\) 3.42212 5.92729i 0.380236 0.658588i
\(82\) 0 0
\(83\) 9.40101i 1.03190i −0.856620 0.515948i \(-0.827440\pi\)
0.856620 0.515948i \(-0.172560\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 17.3830i 1.86365i
\(88\) 0 0
\(89\) 6.13770 + 10.6308i 0.650595 + 1.12686i 0.982979 + 0.183719i \(0.0588137\pi\)
−0.332384 + 0.943144i \(0.607853\pi\)
\(90\) 0 0
\(91\) 1.78442 + 3.09071i 0.187059 + 0.323995i
\(92\) 0 0
\(93\) −10.2313 5.90705i −1.06094 0.612533i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 2.27689 + 1.31456i 0.231183 + 0.133474i 0.611118 0.791540i \(-0.290720\pi\)
−0.379935 + 0.925013i \(0.624053\pi\)
\(98\) 0 0
\(99\) 8.22162 + 14.2403i 0.826304 + 1.43120i
\(100\) 0 0
\(101\) −4.43719 7.68544i −0.441517 0.764730i 0.556285 0.830992i \(-0.312226\pi\)
−0.997802 + 0.0662612i \(0.978893\pi\)
\(102\) 0 0
\(103\) 4.40101i 0.433645i −0.976211 0.216822i \(-0.930431\pi\)
0.976211 0.216822i \(-0.0695692\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 13.9347i 1.34711i 0.739135 + 0.673557i \(0.235235\pi\)
−0.739135 + 0.673557i \(0.764765\pi\)
\(108\) 0 0
\(109\) 1.91608 3.31875i 0.183527 0.317879i −0.759552 0.650447i \(-0.774582\pi\)
0.943079 + 0.332568i \(0.107915\pi\)
\(110\) 0 0
\(111\) −4.58392 + 7.93958i −0.435086 + 0.753592i
\(112\) 0 0
\(113\) 1.70655i 0.160539i −0.996773 0.0802693i \(-0.974422\pi\)
0.996773 0.0802693i \(-0.0255780\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −3.11682 1.79949i −0.288150 0.166363i
\(118\) 0 0
\(119\) 10.2367 17.7305i 0.938396 1.62535i
\(120\) 0 0
\(121\) 9.87439 0.897672
\(122\) 0 0
\(123\) 23.8187 13.7518i 2.14766 1.23995i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −13.0574 + 7.53871i −1.15866 + 0.668952i −0.950982 0.309245i \(-0.899924\pi\)
−0.207677 + 0.978197i \(0.566590\pi\)
\(128\) 0 0
\(129\) −14.5211 25.1513i −1.27851 2.21445i
\(130\) 0 0
\(131\) 6.78442 11.7510i 0.592758 1.02669i −0.401101 0.916034i \(-0.631372\pi\)
0.993859 0.110653i \(-0.0352943\pi\)
\(132\) 0 0
\(133\) −0.790014 15.5362i −0.0685029 1.34716i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −6.08828 + 3.51507i −0.520157 + 0.300313i −0.736999 0.675894i \(-0.763758\pi\)
0.216842 + 0.976207i \(0.430424\pi\)
\(138\) 0 0
\(139\) −6.09899 10.5638i −0.517309 0.896006i −0.999798 0.0201039i \(-0.993600\pi\)
0.482488 0.875902i \(-0.339733\pi\)
\(140\) 0 0
\(141\) −17.3830 −1.46391
\(142\) 0 0
\(143\) −3.95674 + 2.28442i −0.330879 + 0.191033i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 12.7623 + 7.36834i 1.05262 + 0.607731i
\(148\) 0 0
\(149\) 4.76936 8.26077i 0.390721 0.676748i −0.601824 0.798629i \(-0.705559\pi\)
0.992545 + 0.121880i \(0.0388925\pi\)
\(150\) 0 0
\(151\) 20.4131 1.66119 0.830597 0.556874i \(-0.187999\pi\)
0.830597 + 0.556874i \(0.187999\pi\)
\(152\) 0 0
\(153\) 20.6463i 1.66915i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −12.3890 7.15277i −0.988747 0.570853i −0.0838472 0.996479i \(-0.526721\pi\)
−0.904899 + 0.425626i \(0.860054\pi\)
\(158\) 0 0
\(159\) 8.73669 0.692864
\(160\) 0 0
\(161\) 9.99097 + 17.3049i 0.787399 + 1.36382i
\(162\) 0 0
\(163\) 2.53871i 0.198847i 0.995045 + 0.0994236i \(0.0316999\pi\)
−0.995045 + 0.0994236i \(0.968300\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 11.7510 6.78442i 0.909317 0.524995i 0.0291058 0.999576i \(-0.490734\pi\)
0.880211 + 0.474582i \(0.157401\pi\)
\(168\) 0 0
\(169\) −6.00000 + 10.3923i −0.461538 + 0.799408i
\(170\) 0 0
\(171\) 8.52364 + 13.1700i 0.651819 + 1.00714i
\(172\) 0 0
\(173\) −2.05324 1.18544i −0.156105 0.0901271i 0.419913 0.907564i \(-0.362061\pi\)
−0.576017 + 0.817437i \(0.695394\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 15.0541 8.69148i 1.13153 0.653292i
\(178\) 0 0
\(179\) −17.8744 −1.33599 −0.667997 0.744164i \(-0.732848\pi\)
−0.667997 + 0.744164i \(0.732848\pi\)
\(180\) 0 0
\(181\) −13.2065 22.8744i −0.981635 1.70024i −0.656028 0.754737i \(-0.727765\pi\)
−0.325607 0.945505i \(-0.605569\pi\)
\(182\) 0 0
\(183\) 20.9045i 1.54531i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 22.6986 + 13.1050i 1.65988 + 0.958335i
\(188\) 0 0
\(189\) −5.49143 −0.399443
\(190\) 0 0
\(191\) 0.526625 0.0381052 0.0190526 0.999818i \(-0.493935\pi\)
0.0190526 + 0.999818i \(0.493935\pi\)
\(192\) 0 0
\(193\) 4.62521 + 2.67037i 0.332930 + 0.192217i 0.657141 0.753767i \(-0.271766\pi\)
−0.324211 + 0.945985i \(0.605099\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4.43115i 0.315706i 0.987463 + 0.157853i \(0.0504573\pi\)
−0.987463 + 0.157853i \(0.949543\pi\)
\(198\) 0 0
\(199\) 6.08392 + 10.5377i 0.431278 + 0.746995i 0.996984 0.0776123i \(-0.0247296\pi\)
−0.565706 + 0.824607i \(0.691396\pi\)
\(200\) 0 0
\(201\) −16.2754 −1.14798
\(202\) 0 0
\(203\) 20.9143 12.0749i 1.46790 0.847491i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −17.4510 10.0753i −1.21293 0.700285i
\(208\) 0 0
\(209\) 19.8895 1.01138i 1.37578 0.0699584i
\(210\) 0 0
\(211\) 10.3357 17.9019i 0.711537 1.23242i −0.252743 0.967534i \(-0.581333\pi\)
0.964280 0.264885i \(-0.0853341\pi\)
\(212\) 0 0
\(213\) −2.29174 + 1.32314i −0.157027 + 0.0906598i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 16.4131i 1.11419i
\(218\) 0 0
\(219\) −16.3593 28.3352i −1.10546 1.91471i
\(220\) 0 0
\(221\) −5.73669 −0.385891
\(222\) 0 0
\(223\) −3.90454 2.25429i −0.261467 0.150958i 0.363536 0.931580i \(-0.381569\pi\)
−0.625004 + 0.780622i \(0.714903\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 16.6714i 1.10652i 0.833010 + 0.553258i \(0.186616\pi\)
−0.833010 + 0.553258i \(0.813384\pi\)
\(228\) 0 0
\(229\) −5.31060 −0.350934 −0.175467 0.984485i \(-0.556144\pi\)
−0.175467 + 0.984485i \(0.556144\pi\)
\(230\) 0 0
\(231\) −20.9432 + 36.2747i −1.37796 + 2.38670i
\(232\) 0 0
\(233\) 2.40052 + 1.38594i 0.157263 + 0.0907961i 0.576566 0.817050i \(-0.304392\pi\)
−0.419303 + 0.907846i \(0.637726\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −10.8171 + 6.24526i −0.702647 + 0.405673i
\(238\) 0 0
\(239\) 8.59899 0.556222 0.278111 0.960549i \(-0.410292\pi\)
0.278111 + 0.960549i \(0.410292\pi\)
\(240\) 0 0
\(241\) −2.83216 4.90545i −0.182436 0.315988i 0.760274 0.649603i \(-0.225065\pi\)
−0.942709 + 0.333615i \(0.891731\pi\)
\(242\) 0 0
\(243\) −19.2240 + 11.0990i −1.23322 + 0.712000i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −3.65936 + 2.36834i −0.232840 + 0.150694i
\(248\) 0 0
\(249\) −12.0749 + 20.9143i −0.765215 + 1.32539i
\(250\) 0 0
\(251\) 11.5598 + 20.0222i 0.729650 + 1.26379i 0.957031 + 0.289984i \(0.0936501\pi\)
−0.227382 + 0.973806i \(0.573017\pi\)
\(252\) 0 0
\(253\) −22.1537 + 12.7905i −1.39279 + 0.804130i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 9.15289 5.28442i 0.570942 0.329633i −0.186584 0.982439i \(-0.559742\pi\)
0.757525 + 0.652806i \(0.226408\pi\)
\(258\) 0 0
\(259\) −12.7367 −0.791419
\(260\) 0 0
\(261\) −12.1769 + 21.0909i −0.753729 + 1.30550i
\(262\) 0 0
\(263\) −7.67498 4.43115i −0.473259 0.273236i 0.244344 0.969689i \(-0.421427\pi\)
−0.717603 + 0.696452i \(0.754761\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 31.5337i 1.92983i
\(268\) 0 0
\(269\) 2.66784 4.62083i 0.162661 0.281737i −0.773161 0.634210i \(-0.781326\pi\)
0.935822 + 0.352472i \(0.114659\pi\)
\(270\) 0 0
\(271\) −2.23064 + 3.86359i −0.135502 + 0.234696i −0.925789 0.378040i \(-0.876598\pi\)
0.790287 + 0.612737i \(0.209931\pi\)
\(272\) 0 0
\(273\) 9.16784i 0.554863i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 23.0774i 1.38659i 0.720655 + 0.693294i \(0.243841\pi\)
−0.720655 + 0.693294i \(0.756159\pi\)
\(278\) 0 0
\(279\) 8.27585 + 14.3342i 0.495462 + 0.858166i
\(280\) 0 0
\(281\) −2.01507 3.49020i −0.120209 0.208208i 0.799641 0.600478i \(-0.205023\pi\)
−0.919850 + 0.392270i \(0.871690\pi\)
\(282\) 0 0
\(283\) −27.5735 15.9196i −1.63908 0.946322i −0.981152 0.193239i \(-0.938101\pi\)
−0.657925 0.753083i \(-0.728566\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 33.0909 + 19.1050i 1.95329 + 1.12773i
\(288\) 0 0
\(289\) 7.95479 + 13.7781i 0.467929 + 0.810477i
\(290\) 0 0
\(291\) −3.37692 5.84899i −0.197958 0.342874i
\(292\) 0 0
\(293\) 18.6764i 1.09109i −0.838082 0.545544i \(-0.816323\pi\)
0.838082 0.545544i \(-0.183677\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 7.03014i 0.407930i
\(298\) 0 0
\(299\) 2.79949 4.84887i 0.161899 0.280417i
\(300\) 0 0
\(301\) 20.1739 34.9422i 1.16280 2.01403i
\(302\) 0 0
\(303\) 22.7970i 1.30965i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −27.5318 15.8955i −1.57132 0.907204i −0.996007 0.0892730i \(-0.971546\pi\)
−0.575316 0.817931i \(-0.695121\pi\)
\(308\) 0 0
\(309\) −5.65277 + 9.79088i −0.321575 + 0.556984i
\(310\) 0 0
\(311\) 2.37087 0.134440 0.0672199 0.997738i \(-0.478587\pi\)
0.0672199 + 0.997738i \(0.478587\pi\)
\(312\) 0 0
\(313\) −10.5742 + 6.10503i −0.597691 + 0.345077i −0.768132 0.640291i \(-0.778814\pi\)
0.170442 + 0.985368i \(0.445480\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −24.6326 + 14.2216i −1.38350 + 0.798766i −0.992572 0.121655i \(-0.961180\pi\)
−0.390930 + 0.920420i \(0.627847\pi\)
\(318\) 0 0
\(319\) 15.4583 + 26.7746i 0.865499 + 1.49909i
\(320\) 0 0
\(321\) 17.8980 31.0003i 0.998971 1.73027i
\(322\) 0 0
\(323\) 22.2625 + 11.3869i 1.23872 + 0.633586i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −8.52537 + 4.92212i −0.471454 + 0.272194i
\(328\) 0 0
\(329\) −12.0749 20.9143i −0.665710 1.15304i
\(330\) 0 0
\(331\) −32.5930 −1.79147 −0.895737 0.444584i \(-0.853352\pi\)
−0.895737 + 0.444584i \(0.853352\pi\)
\(332\) 0 0
\(333\) 11.1234 6.42212i 0.609561 0.351930i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 10.1016 + 5.83216i 0.550269 + 0.317698i 0.749231 0.662309i \(-0.230423\pi\)
−0.198961 + 0.980007i \(0.563757\pi\)
\(338\) 0 0
\(339\) −2.19193 + 3.79654i −0.119049 + 0.206200i
\(340\) 0 0
\(341\) 21.0121 1.13787
\(342\) 0 0
\(343\) 4.50857i 0.243440i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 26.2602 + 15.1613i 1.40972 + 0.813903i 0.995361 0.0962092i \(-0.0306718\pi\)
0.414361 + 0.910113i \(0.364005\pi\)
\(348\) 0 0
\(349\) −3.44324 −0.184312 −0.0921561 0.995745i \(-0.529376\pi\)
−0.0921561 + 0.995745i \(0.529376\pi\)
\(350\) 0 0
\(351\) 0.769355 + 1.33256i 0.0410652 + 0.0711269i
\(352\) 0 0
\(353\) 6.53871i 0.348020i −0.984744 0.174010i \(-0.944327\pi\)
0.984744 0.174010i \(-0.0556726\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −45.5469 + 26.2965i −2.41060 + 1.39176i
\(358\) 0 0
\(359\) −11.2392 + 19.4669i −0.593183 + 1.02742i 0.400617 + 0.916245i \(0.368796\pi\)
−0.993801 + 0.111178i \(0.964538\pi\)
\(360\) 0 0
\(361\) 18.9020 1.92731i 0.994842 0.101438i
\(362\) 0 0
\(363\) −21.9674 12.6829i −1.15299 0.665680i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −7.44256 + 4.29696i −0.388499 + 0.224300i −0.681509 0.731809i \(-0.738676\pi\)
0.293011 + 0.956109i \(0.405343\pi\)
\(368\) 0 0
\(369\) −38.5327 −2.00593
\(370\) 0 0
\(371\) 6.06885 + 10.5116i 0.315079 + 0.545733i
\(372\) 0 0
\(373\) 37.2453i 1.92849i 0.265019 + 0.964243i \(0.414622\pi\)
−0.265019 + 0.964243i \(0.585378\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −5.86024 3.38341i −0.301818 0.174255i
\(378\) 0 0
\(379\) −12.1678 −0.625020 −0.312510 0.949914i \(-0.601170\pi\)
−0.312510 + 0.949914i \(0.601170\pi\)
\(380\) 0 0
\(381\) 38.7316 1.98428
\(382\) 0 0
\(383\) 21.6977 + 12.5272i 1.10870 + 0.640108i 0.938492 0.345301i \(-0.112223\pi\)
0.170207 + 0.985408i \(0.445556\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 40.6885i 2.06831i
\(388\) 0 0
\(389\) 11.0211 + 19.0891i 0.558793 + 0.967857i 0.997598 + 0.0692748i \(0.0220685\pi\)
−0.438805 + 0.898582i \(0.644598\pi\)
\(390\) 0 0
\(391\) −32.1196 −1.62436
\(392\) 0 0
\(393\) −30.1865 + 17.4282i −1.52271 + 0.879135i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 31.3327 + 18.0900i 1.57254 + 0.907909i 0.995856 + 0.0909453i \(0.0289889\pi\)
0.576689 + 0.816964i \(0.304344\pi\)
\(398\) 0 0
\(399\) −18.1975 + 35.5779i −0.911016 + 1.78112i
\(400\) 0 0
\(401\) −13.9583 + 24.1765i −0.697045 + 1.20732i 0.272442 + 0.962172i \(0.412169\pi\)
−0.969487 + 0.245144i \(0.921165\pi\)
\(402\) 0 0
\(403\) −3.98284 + 2.29949i −0.198399 + 0.114546i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 16.3055i 0.808235i
\(408\) 0 0
\(409\) 4.06281 + 7.03699i 0.200893 + 0.347957i 0.948816 0.315828i \(-0.102282\pi\)
−0.747924 + 0.663785i \(0.768949\pi\)
\(410\) 0 0
\(411\) 18.0594 0.890803
\(412\) 0 0
\(413\) 20.9143 + 12.0749i 1.02913 + 0.594167i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 31.3348i 1.53447i
\(418\) 0 0
\(419\) 2.87439 0.140423 0.0702115 0.997532i \(-0.477633\pi\)
0.0702115 + 0.997532i \(0.477633\pi\)
\(420\) 0 0
\(421\) 3.48240 6.03170i 0.169722 0.293967i −0.768600 0.639729i \(-0.779046\pi\)
0.938322 + 0.345763i \(0.112380\pi\)
\(422\) 0 0
\(423\) 21.0909 + 12.1769i 1.02548 + 0.592059i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −25.1513 + 14.5211i −1.21716 + 0.702726i
\(428\) 0 0
\(429\) 11.7367 0.566653
\(430\) 0 0
\(431\) 5.08996 + 8.81607i 0.245175 + 0.424655i 0.962181 0.272412i \(-0.0878213\pi\)
−0.717006 + 0.697067i \(0.754488\pi\)
\(432\) 0 0
\(433\) −17.1186 + 9.88341i −0.822666 + 0.474967i −0.851335 0.524622i \(-0.824207\pi\)
0.0286689 + 0.999589i \(0.490873\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −20.4887 + 13.2603i −0.980109 + 0.634328i
\(438\) 0 0
\(439\) 19.3266 33.4747i 0.922411 1.59766i 0.126737 0.991936i \(-0.459550\pi\)
0.795673 0.605726i \(-0.207117\pi\)
\(440\) 0 0
\(441\) −10.3231 17.8802i −0.491578 0.851438i
\(442\) 0 0
\(443\) 9.27214 5.35327i 0.440533 0.254342i −0.263291 0.964717i \(-0.584808\pi\)
0.703824 + 0.710375i \(0.251475\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −21.2207 + 12.2518i −1.00370 + 0.579488i
\(448\) 0 0
\(449\) −23.0724 −1.08885 −0.544426 0.838809i \(-0.683253\pi\)
−0.544426 + 0.838809i \(0.683253\pi\)
\(450\) 0 0
\(451\) −24.4583 + 42.3630i −1.15170 + 1.99480i
\(452\) 0 0
\(453\) −45.4128 26.2191i −2.13368 1.23188i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 6.87439i 0.321570i 0.986989 + 0.160785i \(0.0514026\pi\)
−0.986989 + 0.160785i \(0.948597\pi\)
\(458\) 0 0
\(459\) 4.41355 7.64450i 0.206007 0.356815i
\(460\) 0 0
\(461\) 1.41355 2.44834i 0.0658357 0.114031i −0.831229 0.555931i \(-0.812362\pi\)
0.897064 + 0.441900i \(0.145695\pi\)
\(462\) 0 0
\(463\) 23.9347i 1.11234i −0.831069 0.556169i \(-0.812271\pi\)
0.831069 0.556169i \(-0.187729\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 33.5508i 1.55255i −0.630397 0.776273i \(-0.717108\pi\)
0.630397 0.776273i \(-0.282892\pi\)
\(468\) 0 0
\(469\) −11.3055 19.5818i −0.522041 0.904202i
\(470\) 0 0
\(471\) 18.3744 + 31.8254i 0.846647 + 1.46644i
\(472\) 0 0
\(473\) 44.7331 + 25.8266i 2.05683 + 1.18751i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −10.6003 6.12010i −0.485356 0.280220i
\(478\) 0 0
\(479\) −18.4583 31.9707i −0.843382 1.46078i −0.887019 0.461732i \(-0.847228\pi\)
0.0436379 0.999047i \(-0.486105\pi\)
\(480\) 0 0
\(481\) 1.78442 + 3.09071i 0.0813628 + 0.140924i
\(482\) 0 0
\(483\) 51.3306i 2.33562i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 12.8744i 0.583394i 0.956511 + 0.291697i \(0.0942199\pi\)
−0.956511 + 0.291697i \(0.905780\pi\)
\(488\) 0 0
\(489\) 3.26078 5.64784i 0.147458 0.255404i
\(490\) 0 0
\(491\) 12.3382 21.3704i 0.556815 0.964433i −0.440944 0.897534i \(-0.645356\pi\)
0.997760 0.0668981i \(-0.0213103\pi\)
\(492\) 0 0
\(493\) 38.8192i 1.74833i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −3.18386 1.83821i −0.142816 0.0824548i
\(498\) 0 0
\(499\) 15.7603 27.2977i 0.705529 1.22201i −0.260971 0.965347i \(-0.584043\pi\)
0.966500 0.256666i \(-0.0826240\pi\)
\(500\) 0 0
\(501\) −34.8563 −1.55727
\(502\) 0 0
\(503\) 10.5420 6.08645i 0.470046 0.271381i −0.246213 0.969216i \(-0.579186\pi\)
0.716259 + 0.697834i \(0.245853\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 26.6963 15.4131i 1.18562 0.684520i
\(508\) 0 0
\(509\) −4.70051 8.14151i −0.208346 0.360866i 0.742847 0.669461i \(-0.233475\pi\)
−0.951194 + 0.308594i \(0.900141\pi\)
\(510\) 0 0
\(511\) 22.7277 39.3655i 1.00541 1.74143i
\(512\) 0 0
\(513\) −0.340615 6.69843i −0.0150385 0.295743i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 26.7746 15.4583i 1.17754 0.679856i
\(518\) 0 0
\(519\) 3.04521 + 5.27446i 0.133670 + 0.231523i
\(520\) 0 0
\(521\) 8.49649 0.372238 0.186119 0.982527i \(-0.440409\pi\)
0.186119 + 0.982527i \(0.440409\pi\)
\(522\) 0 0
\(523\) 19.4320 11.2191i 0.849703 0.490577i −0.0108473 0.999941i \(-0.503453\pi\)
0.860551 + 0.509365i \(0.170120\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 22.8483 + 13.1915i 0.995288 + 0.574630i
\(528\) 0 0
\(529\) 4.17434 7.23016i 0.181493 0.314355i
\(530\) 0 0
\(531\) −24.3537 −1.05686
\(532\) 0 0
\(533\) 10.7065i 0.463752i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 39.7650 + 22.9583i 1.71598 + 0.990724i
\(538\) 0 0
\(539\) −26.2101 −1.12895
\(540\) 0 0
\(541\) 13.7603 + 23.8336i 0.591603 + 1.02469i 0.994017 + 0.109228i \(0.0348379\pi\)
−0.402414 + 0.915458i \(0.631829\pi\)
\(542\) 0 0
\(543\) 67.8513i 2.91178i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.736308 0.425107i 0.0314822 0.0181763i −0.484176 0.874970i \(-0.660881\pi\)
0.515659 + 0.856794i \(0.327547\pi\)
\(548\) 0 0
\(549\) 14.6437 25.3637i 0.624980 1.08250i
\(550\) 0 0
\(551\) 16.0262 + 24.7623i 0.682738 + 1.05491i
\(552\) 0 0
\(553\) −15.0280 8.67641i −0.639055 0.368958i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 34.1127 19.6950i 1.44540 0.834504i 0.447200 0.894434i \(-0.352421\pi\)
0.998203 + 0.0599303i \(0.0190878\pi\)
\(558\) 0 0
\(559\) −11.3055 −0.478173
\(560\) 0 0
\(561\) −33.6649 58.3092i −1.42133 2.46182i
\(562\) 0 0
\(563\) 22.0774i 0.930452i −0.885192 0.465226i \(-0.845973\pi\)
0.885192 0.465226i \(-0.154027\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −21.1536 12.2130i −0.888368 0.512900i
\(568\) 0 0
\(569\) 7.53365 0.315827 0.157914 0.987453i \(-0.449523\pi\)
0.157914 + 0.987453i \(0.449523\pi\)
\(570\) 0 0
\(571\) −38.2824 −1.60207 −0.801035 0.598618i \(-0.795717\pi\)
−0.801035 + 0.598618i \(0.795717\pi\)
\(572\) 0 0
\(573\) −1.17158 0.676410i −0.0489433 0.0282574i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 3.21006i 0.133637i 0.997765 + 0.0668183i \(0.0212848\pi\)
−0.997765 + 0.0668183i \(0.978715\pi\)
\(578\) 0 0
\(579\) −6.85977 11.8815i −0.285082 0.493777i
\(580\) 0 0
\(581\) −33.5508 −1.39192
\(582\) 0 0
\(583\) −13.4569 + 7.76936i −0.557329 + 0.321774i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −2.16202 1.24824i −0.0892361 0.0515205i 0.454718 0.890636i \(-0.349740\pi\)
−0.543954 + 0.839115i \(0.683073\pi\)
\(588\) 0 0
\(589\) 20.0207 1.01805i 0.824937 0.0419480i
\(590\) 0 0
\(591\) 5.69148 9.85793i 0.234116 0.405501i
\(592\) 0 0
\(593\) 12.1766 7.03014i 0.500031 0.288693i −0.228695 0.973498i \(-0.573446\pi\)
0.728726 + 0.684805i \(0.240113\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 31.2573i 1.27928i
\(598\) 0 0
\(599\) −11.6678 20.2093i −0.476735 0.825729i 0.522910 0.852388i \(-0.324847\pi\)
−0.999645 + 0.0266590i \(0.991513\pi\)
\(600\) 0 0
\(601\) 46.6111 1.90131 0.950653 0.310257i \(-0.100415\pi\)
0.950653 + 0.310257i \(0.100415\pi\)
\(602\) 0 0
\(603\) 19.7471 + 11.4010i 0.804165 + 0.464285i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 11.1929i 0.454307i −0.973859 0.227153i \(-0.927058\pi\)
0.973859 0.227153i \(-0.0729418\pi\)
\(608\) 0 0
\(609\) −62.0372 −2.51387
\(610\) 0 0
\(611\) −3.38341 + 5.86024i −0.136878 + 0.237080i
\(612\) 0 0
\(613\) −29.4092 16.9794i −1.18783 0.685792i −0.230015 0.973187i \(-0.573877\pi\)
−0.957812 + 0.287395i \(0.907211\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −14.3290 + 8.27287i −0.576865 + 0.333053i −0.759887 0.650056i \(-0.774746\pi\)
0.183022 + 0.983109i \(0.441412\pi\)
\(618\) 0 0
\(619\) −21.4312 −0.861391 −0.430695 0.902497i \(-0.641732\pi\)
−0.430695 + 0.902497i \(0.641732\pi\)
\(620\) 0 0
\(621\) 4.30761 + 7.46100i 0.172859 + 0.299400i
\(622\) 0 0
\(623\) 37.9398 21.9045i 1.52002 0.877586i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −45.5469 23.2965i −1.81897 0.930373i
\(628\) 0 0
\(629\) 10.2367 17.7305i 0.408163 0.706960i
\(630\) 0 0
\(631\) −10.5035 18.1926i −0.418138 0.724237i 0.577614 0.816310i \(-0.303984\pi\)
−0.995752 + 0.0920733i \(0.970651\pi\)
\(632\) 0 0
\(633\) −45.9873 + 26.5508i −1.82783 + 1.05530i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 4.96812 2.86834i 0.196844 0.113648i
\(638\) 0 0
\(639\) 3.70746 0.146665
\(640\) 0 0
\(641\) 15.9106 27.5579i 0.628430 1.08847i −0.359437 0.933169i \(-0.617031\pi\)
0.987867 0.155303i \(-0.0496353\pi\)
\(642\) 0 0
\(643\) 7.69670 + 4.44369i 0.303528 + 0.175242i 0.644027 0.765003i \(-0.277263\pi\)
−0.340499 + 0.940245i \(0.610596\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.37593i 0.0540934i −0.999634 0.0270467i \(-0.991390\pi\)
0.999634 0.0270467i \(-0.00861029\pi\)
\(648\) 0 0
\(649\) −15.4583 + 26.7746i −0.606792 + 1.05099i
\(650\) 0 0
\(651\) −21.0814 + 36.5140i −0.826245 + 1.43110i
\(652\) 0 0
\(653\) 24.7237i 0.967513i −0.875203 0.483756i \(-0.839272\pi\)
0.875203 0.483756i \(-0.160728\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 45.8392i 1.78836i
\(658\) 0 0
\(659\) −20.9020 36.2033i −0.814226 1.41028i −0.909882 0.414867i \(-0.863828\pi\)
0.0956561 0.995414i \(-0.469505\pi\)
\(660\) 0 0
\(661\) 11.5211 + 19.9552i 0.448119 + 0.776165i 0.998264 0.0589041i \(-0.0187606\pi\)
−0.550144 + 0.835070i \(0.685427\pi\)
\(662\) 0 0
\(663\) 12.7623 + 7.36834i 0.495648 + 0.286163i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −32.8114 18.9437i −1.27046 0.733503i
\(668\) 0 0
\(669\) 5.79092 + 10.0302i 0.223890 + 0.387789i
\(670\) 0 0
\(671\) −18.5900 32.1988i −0.717658 1.24302i
\(672\) 0 0
\(673\) 29.5156i 1.13774i 0.822427 + 0.568871i \(0.192620\pi\)
−0.822427 + 0.568871i \(0.807380\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 12.5035i 0.480549i −0.970705 0.240275i \(-0.922763\pi\)
0.970705 0.240275i \(-0.0772375\pi\)
\(678\) 0 0
\(679\) 4.69148 8.12588i 0.180042 0.311843i
\(680\) 0 0
\(681\) 21.4131 37.0886i 0.820552 1.42124i
\(682\) 0 0
\(683\) 12.9045i 0.493778i 0.969044 + 0.246889i \(0.0794083\pi\)
−0.969044 + 0.246889i \(0.920592\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 11.8144 + 6.82106i 0.450748 + 0.260240i
\(688\) 0 0
\(689\) 1.70051 2.94536i 0.0647841 0.112209i
\(690\) 0 0
\(691\) 23.3779 0.889337 0.444669 0.895695i \(-0.353321\pi\)
0.444669 + 0.895695i \(0.353321\pi\)
\(692\) 0 0
\(693\) 50.8213 29.3417i 1.93054 1.11460i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −53.1914 + 30.7101i −2.01477 + 1.16323i
\(698\) 0 0
\(699\) −3.56028 6.16658i −0.134662 0.233242i
\(700\) 0 0
\(701\) 5.82314 10.0860i 0.219937 0.380942i −0.734852 0.678228i \(-0.762748\pi\)
0.954788 + 0.297286i \(0.0960816\pi\)
\(702\) 0 0
\(703\) −0.790014 15.5362i −0.0297959 0.585958i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −27.4282 + 15.8357i −1.03154 + 0.595562i
\(708\) 0 0
\(709\) −6.58645 11.4081i −0.247359 0.428439i 0.715433 0.698681i \(-0.246229\pi\)
−0.962792 + 0.270243i \(0.912896\pi\)
\(710\) 0 0
\(711\) 17.4994 0.656277
\(712\) 0 0
\(713\) −22.2999 + 12.8748i −0.835137 + 0.482167i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −19.1301 11.0448i −0.714426 0.412474i
\(718\) 0 0
\(719\) −2.43972 + 4.22572i −0.0909863 + 0.157593i −0.907926 0.419130i \(-0.862335\pi\)
0.816940 + 0.576723i \(0.195669\pi\)
\(720\) 0 0
\(721\) −15.7065 −0.584942
\(722\) 0 0
\(723\) 14.5508i 0.541150i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 43.2813 + 24.9884i 1.60521 + 0.926770i 0.990421 + 0.138081i \(0.0440934\pi\)
0.614792 + 0.788689i \(0.289240\pi\)
\(728\) 0 0
\(729\) 36.4905 1.35150
\(730\) 0 0
\(731\) 32.4282 + 56.1672i 1.19940 + 2.07742i
\(732\) 0 0
\(733\) 39.0493i 1.44232i −0.692770 0.721159i \(-0.743610\pi\)
0.692770 0.721159i \(-0.256390\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 25.0686 14.4734i 0.923415 0.533134i
\(738\) 0 0
\(739\) −12.4020 + 21.4809i −0.456215 + 0.790187i −0.998757 0.0498412i \(-0.984128\pi\)
0.542542 + 0.840028i \(0.317462\pi\)
\(740\) 0 0
\(741\) 11.1829 0.568650i 0.410814 0.0208899i
\(742\) 0 0
\(743\) 17.1961 + 9.92817i 0.630863 + 0.364229i 0.781086 0.624423i \(-0.214666\pi\)
−0.150223 + 0.988652i \(0.547999\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 29.3012 16.9171i 1.07208 0.618963i
\(748\) 0 0
\(749\) 49.7307 1.81712
\(750\) 0 0
\(751\) 13.7191 + 23.7622i 0.500617 + 0.867094i 1.00000 0.000712212i \(0.000226704\pi\)
−0.499383 + 0.866381i \(0.666440\pi\)
\(752\) 0 0
\(753\) 59.3909i 2.16432i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 10.0033 + 5.77540i 0.363576 + 0.209910i 0.670648 0.741776i \(-0.266016\pi\)
−0.307073 + 0.951686i \(0.599349\pi\)
\(758\) 0 0
\(759\) 65.7136 2.38525
\(760\) 0 0
\(761\) −46.9940 −1.70353 −0.851766 0.523922i \(-0.824468\pi\)
−0.851766 + 0.523922i \(0.824468\pi\)
\(762\) 0 0
\(763\) −11.8441 6.83821i −0.428786 0.247560i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 6.76683i 0.244336i
\(768\) 0 0
\(769\) −6.43719 11.1495i −0.232131 0.402063i 0.726304 0.687374i \(-0.241237\pi\)
−0.958435 + 0.285311i \(0.907903\pi\)
\(770\) 0 0
\(771\) −27.1498 −0.977776
\(772\) 0 0
\(773\) −24.2748 + 14.0151i −0.873104 + 0.504087i −0.868379 0.495902i \(-0.834838\pi\)
−0.00472572 + 0.999989i \(0.501504\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 28.3352 + 16.3593i 1.01652 + 0.586887i
\(778\) 0 0
\(779\) −21.2518 + 41.5492i −0.761423 + 1.48865i
\(780\) 0 0
\(781\) 2.35327 4.07599i 0.0842068 0.145850i
\(782\) 0 0
\(783\) 9.01722 5.20609i 0.322249 0.186051i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 22.3478i 0.796612i −0.917253 0.398306i \(-0.869598\pi\)
0.917253 0.398306i \(-0.130402\pi\)
\(788\) 0 0
\(789\) 11.3830 + 19.7159i 0.405244 + 0.701903i
\(790\) 0 0
\(791\) −6.09042 −0.216550
\(792\) 0 0
\(793\) 7.04745 + 4.06885i 0.250262 + 0.144489i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 16.3176i 0.578000i −0.957329 0.289000i \(-0.906677\pi\)
0.957329 0.289000i \(-0.0933227\pi\)
\(798\) 0 0
\(799\) 38.8192 1.37332
\(800\) 0 0