Properties

Label 1840.2.m.g.1839.8
Level $1840$
Weight $2$
Character 1840.1839
Analytic conductor $14.692$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.m (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.6924739719\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1839.8
Character \(\chi\) \(=\) 1840.1839
Dual form 1840.2.m.g.1839.5

$q$-expansion

\(f(q)\) \(=\) \(q-2.49894 q^{3} +(-2.19676 - 0.417445i) q^{5} +3.04922i q^{7} +3.24468 q^{9} +O(q^{10})\) \(q-2.49894 q^{3} +(-2.19676 - 0.417445i) q^{5} +3.04922i q^{7} +3.24468 q^{9} -5.87962 q^{11} +6.00311i q^{13} +(5.48956 + 1.04317i) q^{15} -0.968611 q^{17} -1.72585 q^{19} -7.61980i q^{21} +(-3.79127 + 2.93705i) q^{23} +(4.65148 + 1.83405i) q^{25} -0.611451 q^{27} -3.89743 q^{29} +9.01605i q^{31} +14.6928 q^{33} +(1.27288 - 6.69839i) q^{35} +2.15559 q^{37} -15.0014i q^{39} +6.17642 q^{41} +9.08209i q^{43} +(-7.12778 - 1.35448i) q^{45} -9.73942 q^{47} -2.29773 q^{49} +2.42050 q^{51} -9.18153 q^{53} +(12.9161 + 2.45442i) q^{55} +4.31279 q^{57} -1.17122i q^{59} +0.951354i q^{61} +9.89375i q^{63} +(2.50597 - 13.1874i) q^{65} -9.83203i q^{67} +(9.47415 - 7.33950i) q^{69} +8.99828i q^{71} -8.53105i q^{73} +(-11.6238 - 4.58317i) q^{75} -17.9282i q^{77} -5.59242 q^{79} -8.20608 q^{81} -5.97096i q^{83} +(2.12780 + 0.404342i) q^{85} +9.73942 q^{87} -7.22303i q^{89} -18.3048 q^{91} -22.5305i q^{93} +(3.79127 + 0.720447i) q^{95} -7.51772 q^{97} -19.0775 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q + 80q^{9} + O(q^{10}) \) \( 40q + 80q^{9} - 24q^{25} + 24q^{41} - 16q^{49} + 80q^{69} + 40q^{81} - 8q^{85} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).

\(n\) \(737\) \(1151\) \(1201\) \(1381\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(1\)

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
\(3\) −2.49894 −1.44276 −0.721381 0.692539i \(-0.756492\pi\)
−0.721381 + 0.692539i \(0.756492\pi\)
\(4\) 0 0
\(5\) −2.19676 0.417445i −0.982419 0.186687i
\(6\) 0 0
\(7\) 3.04922i 1.15250i 0.817275 + 0.576248i \(0.195484\pi\)
−0.817275 + 0.576248i \(0.804516\pi\)
\(8\) 0 0
\(9\) 3.24468 1.08156
\(10\) 0 0
\(11\) −5.87962 −1.77277 −0.886386 0.462948i \(-0.846792\pi\)
−0.886386 + 0.462948i \(0.846792\pi\)
\(12\) 0 0
\(13\) 6.00311i 1.66496i 0.554052 + 0.832482i \(0.313081\pi\)
−0.554052 + 0.832482i \(0.686919\pi\)
\(14\) 0 0
\(15\) 5.48956 + 1.04317i 1.41740 + 0.269345i
\(16\) 0 0
\(17\) −0.968611 −0.234923 −0.117461 0.993077i \(-0.537476\pi\)
−0.117461 + 0.993077i \(0.537476\pi\)
\(18\) 0 0
\(19\) −1.72585 −0.395937 −0.197969 0.980208i \(-0.563434\pi\)
−0.197969 + 0.980208i \(0.563434\pi\)
\(20\) 0 0
\(21\) 7.61980i 1.66278i
\(22\) 0 0
\(23\) −3.79127 + 2.93705i −0.790535 + 0.612417i
\(24\) 0 0
\(25\) 4.65148 + 1.83405i 0.930296 + 0.366810i
\(26\) 0 0
\(27\) −0.611451 −0.117674
\(28\) 0 0
\(29\) −3.89743 −0.723734 −0.361867 0.932230i \(-0.617861\pi\)
−0.361867 + 0.932230i \(0.617861\pi\)
\(30\) 0 0
\(31\) 9.01605i 1.61933i 0.586892 + 0.809665i \(0.300351\pi\)
−0.586892 + 0.809665i \(0.699649\pi\)
\(32\) 0 0
\(33\) 14.6928 2.55769
\(34\) 0 0
\(35\) 1.27288 6.69839i 0.215156 1.13223i
\(36\) 0 0
\(37\) 2.15559 0.354377 0.177189 0.984177i \(-0.443300\pi\)
0.177189 + 0.984177i \(0.443300\pi\)
\(38\) 0 0
\(39\) 15.0014i 2.40215i
\(40\) 0 0
\(41\) 6.17642 0.964595 0.482297 0.876008i \(-0.339802\pi\)
0.482297 + 0.876008i \(0.339802\pi\)
\(42\) 0 0
\(43\) 9.08209i 1.38501i 0.721415 + 0.692503i \(0.243492\pi\)
−0.721415 + 0.692503i \(0.756508\pi\)
\(44\) 0 0
\(45\) −7.12778 1.35448i −1.06255 0.201914i
\(46\) 0 0
\(47\) −9.73942 −1.42064 −0.710320 0.703879i \(-0.751450\pi\)
−0.710320 + 0.703879i \(0.751450\pi\)
\(48\) 0 0
\(49\) −2.29773 −0.328247
\(50\) 0 0
\(51\) 2.42050 0.338937
\(52\) 0 0
\(53\) −9.18153 −1.26118 −0.630590 0.776116i \(-0.717187\pi\)
−0.630590 + 0.776116i \(0.717187\pi\)
\(54\) 0 0
\(55\) 12.9161 + 2.45442i 1.74161 + 0.330953i
\(56\) 0 0
\(57\) 4.31279 0.571243
\(58\) 0 0
\(59\) 1.17122i 0.152480i −0.997089 0.0762401i \(-0.975708\pi\)
0.997089 0.0762401i \(-0.0242916\pi\)
\(60\) 0 0
\(61\) 0.951354i 0.121808i 0.998144 + 0.0609042i \(0.0193984\pi\)
−0.998144 + 0.0609042i \(0.980602\pi\)
\(62\) 0 0
\(63\) 9.89375i 1.24650i
\(64\) 0 0
\(65\) 2.50597 13.1874i 0.310827 1.63569i
\(66\) 0 0
\(67\) 9.83203i 1.20117i −0.799559 0.600587i \(-0.794934\pi\)
0.799559 0.600587i \(-0.205066\pi\)
\(68\) 0 0
\(69\) 9.47415 7.33950i 1.14055 0.883572i
\(70\) 0 0
\(71\) 8.99828i 1.06790i 0.845516 + 0.533949i \(0.179293\pi\)
−0.845516 + 0.533949i \(0.820707\pi\)
\(72\) 0 0
\(73\) 8.53105i 0.998483i −0.866463 0.499242i \(-0.833612\pi\)
0.866463 0.499242i \(-0.166388\pi\)
\(74\) 0 0
\(75\) −11.6238 4.58317i −1.34220 0.529219i
\(76\) 0 0
\(77\) 17.9282i 2.04311i
\(78\) 0 0
\(79\) −5.59242 −0.629196 −0.314598 0.949225i \(-0.601870\pi\)
−0.314598 + 0.949225i \(0.601870\pi\)
\(80\) 0 0
\(81\) −8.20608 −0.911786
\(82\) 0 0
\(83\) 5.97096i 0.655397i −0.944782 0.327699i \(-0.893727\pi\)
0.944782 0.327699i \(-0.106273\pi\)
\(84\) 0 0
\(85\) 2.12780 + 0.404342i 0.230793 + 0.0438570i
\(86\) 0 0
\(87\) 9.73942 1.04418
\(88\) 0 0
\(89\) 7.22303i 0.765640i −0.923823 0.382820i \(-0.874953\pi\)
0.923823 0.382820i \(-0.125047\pi\)
\(90\) 0 0
\(91\) −18.3048 −1.91886
\(92\) 0 0
\(93\) 22.5305i 2.33631i
\(94\) 0 0
\(95\) 3.79127 + 0.720447i 0.388976 + 0.0739163i
\(96\) 0 0
\(97\) −7.51772 −0.763309 −0.381654 0.924305i \(-0.624646\pi\)
−0.381654 + 0.924305i \(0.624646\pi\)
\(98\) 0 0
\(99\) −19.0775 −1.91736
\(100\) 0 0
\(101\) 12.8797 1.28158 0.640788 0.767718i \(-0.278608\pi\)
0.640788 + 0.767718i \(0.278608\pi\)
\(102\) 0 0
\(103\) 16.2773i 1.60385i −0.597427 0.801923i \(-0.703810\pi\)
0.597427 0.801923i \(-0.296190\pi\)
\(104\) 0 0
\(105\) −3.18085 + 16.7389i −0.310419 + 1.63354i
\(106\) 0 0
\(107\) 3.07686i 0.297452i 0.988878 + 0.148726i \(0.0475172\pi\)
−0.988878 + 0.148726i \(0.952483\pi\)
\(108\) 0 0
\(109\) 4.89197i 0.468566i 0.972168 + 0.234283i \(0.0752742\pi\)
−0.972168 + 0.234283i \(0.924726\pi\)
\(110\) 0 0
\(111\) −5.38669 −0.511282
\(112\) 0 0
\(113\) −1.92574 −0.181158 −0.0905791 0.995889i \(-0.528872\pi\)
−0.0905791 + 0.995889i \(0.528872\pi\)
\(114\) 0 0
\(115\) 9.55456 4.86933i 0.890967 0.454068i
\(116\) 0 0
\(117\) 19.4782i 1.80076i
\(118\) 0 0
\(119\) 2.95350i 0.270747i
\(120\) 0 0
\(121\) 23.5699 2.14272
\(122\) 0 0
\(123\) −15.4345 −1.39168
\(124\) 0 0
\(125\) −9.45255 5.97070i −0.845462 0.534035i
\(126\) 0 0
\(127\) 13.5081 1.19865 0.599324 0.800506i \(-0.295436\pi\)
0.599324 + 0.800506i \(0.295436\pi\)
\(128\) 0 0
\(129\) 22.6956i 1.99823i
\(130\) 0 0
\(131\) 3.50575i 0.306299i 0.988203 + 0.153149i \(0.0489416\pi\)
−0.988203 + 0.153149i \(0.951058\pi\)
\(132\) 0 0
\(133\) 5.26249i 0.456316i
\(134\) 0 0
\(135\) 1.34321 + 0.255247i 0.115605 + 0.0219682i
\(136\) 0 0
\(137\) −0.570160 −0.0487121 −0.0243560 0.999703i \(-0.507754\pi\)
−0.0243560 + 0.999703i \(0.507754\pi\)
\(138\) 0 0
\(139\) 3.54130i 0.300369i −0.988658 0.150185i \(-0.952013\pi\)
0.988658 0.150185i \(-0.0479868\pi\)
\(140\) 0 0
\(141\) 24.3382 2.04965
\(142\) 0 0
\(143\) 35.2960i 2.95160i
\(144\) 0 0
\(145\) 8.56170 + 1.62696i 0.711010 + 0.135112i
\(146\) 0 0
\(147\) 5.74188 0.473583
\(148\) 0 0
\(149\) 18.0365i 1.47761i 0.673919 + 0.738805i \(0.264610\pi\)
−0.673919 + 0.738805i \(0.735390\pi\)
\(150\) 0 0
\(151\) 10.5790i 0.860909i −0.902612 0.430454i \(-0.858353\pi\)
0.902612 0.430454i \(-0.141647\pi\)
\(152\) 0 0
\(153\) −3.14284 −0.254083
\(154\) 0 0
\(155\) 3.76371 19.8061i 0.302308 1.59086i
\(156\) 0 0
\(157\) −16.3320 −1.30344 −0.651719 0.758460i \(-0.725952\pi\)
−0.651719 + 0.758460i \(0.725952\pi\)
\(158\) 0 0
\(159\) 22.9441 1.81958
\(160\) 0 0
\(161\) −8.95570 11.5604i −0.705808 0.911089i
\(162\) 0 0
\(163\) 14.1664 1.10959 0.554797 0.831985i \(-0.312796\pi\)
0.554797 + 0.831985i \(0.312796\pi\)
\(164\) 0 0
\(165\) −32.2765 6.13343i −2.51272 0.477487i
\(166\) 0 0
\(167\) −2.54576 −0.196997 −0.0984985 0.995137i \(-0.531404\pi\)
−0.0984985 + 0.995137i \(0.531404\pi\)
\(168\) 0 0
\(169\) −23.0374 −1.77210
\(170\) 0 0
\(171\) −5.59984 −0.428230
\(172\) 0 0
\(173\) 4.52121i 0.343741i −0.985120 0.171870i \(-0.945019\pi\)
0.985120 0.171870i \(-0.0549810\pi\)
\(174\) 0 0
\(175\) −5.59242 + 14.1834i −0.422747 + 1.07216i
\(176\) 0 0
\(177\) 2.92681i 0.219993i
\(178\) 0 0
\(179\) 20.1473i 1.50588i −0.658088 0.752941i \(-0.728635\pi\)
0.658088 0.752941i \(-0.271365\pi\)
\(180\) 0 0
\(181\) 14.1244i 1.04986i 0.851146 + 0.524930i \(0.175908\pi\)
−0.851146 + 0.524930i \(0.824092\pi\)
\(182\) 0 0
\(183\) 2.37737i 0.175741i
\(184\) 0 0
\(185\) −4.73532 0.899842i −0.348147 0.0661577i
\(186\) 0 0
\(187\) 5.69506 0.416464
\(188\) 0 0
\(189\) 1.86445i 0.135619i
\(190\) 0 0
\(191\) −7.52741 −0.544664 −0.272332 0.962203i \(-0.587795\pi\)
−0.272332 + 0.962203i \(0.587795\pi\)
\(192\) 0 0
\(193\) 16.0605i 1.15606i 0.816016 + 0.578030i \(0.196178\pi\)
−0.816016 + 0.578030i \(0.803822\pi\)
\(194\) 0 0
\(195\) −6.26226 + 32.9544i −0.448450 + 2.35992i
\(196\) 0 0
\(197\) 23.6707i 1.68647i 0.537546 + 0.843234i \(0.319351\pi\)
−0.537546 + 0.843234i \(0.680649\pi\)
\(198\) 0 0
\(199\) 20.5976 1.46013 0.730064 0.683379i \(-0.239490\pi\)
0.730064 + 0.683379i \(0.239490\pi\)
\(200\) 0 0
\(201\) 24.5696i 1.73301i
\(202\) 0 0
\(203\) 11.8841i 0.834100i
\(204\) 0 0
\(205\) −13.5681 2.57832i −0.947636 0.180077i
\(206\) 0 0
\(207\) −12.3015 + 9.52979i −0.855012 + 0.662367i
\(208\) 0 0
\(209\) 10.1473 0.701906
\(210\) 0 0
\(211\) 0.254864i 0.0175456i 0.999962 + 0.00877279i \(0.00279250\pi\)
−0.999962 + 0.00877279i \(0.997207\pi\)
\(212\) 0 0
\(213\) 22.4861i 1.54072i
\(214\) 0 0
\(215\) 3.79127 19.9511i 0.258563 1.36066i
\(216\) 0 0
\(217\) −27.4919 −1.86627
\(218\) 0 0
\(219\) 21.3185i 1.44057i
\(220\) 0 0
\(221\) 5.81468i 0.391138i
\(222\) 0 0
\(223\) −3.90122 −0.261245 −0.130623 0.991432i \(-0.541698\pi\)
−0.130623 + 0.991432i \(0.541698\pi\)
\(224\) 0 0
\(225\) 15.0926 + 5.95091i 1.00617 + 0.396728i
\(226\) 0 0
\(227\) 17.6776i 1.17331i 0.809839 + 0.586653i \(0.199555\pi\)
−0.809839 + 0.586653i \(0.800445\pi\)
\(228\) 0 0
\(229\) 26.1981i 1.73122i −0.500722 0.865608i \(-0.666932\pi\)
0.500722 0.865608i \(-0.333068\pi\)
\(230\) 0 0
\(231\) 44.8015i 2.94772i
\(232\) 0 0
\(233\) 13.2589i 0.868618i −0.900764 0.434309i \(-0.856993\pi\)
0.900764 0.434309i \(-0.143007\pi\)
\(234\) 0 0
\(235\) 21.3951 + 4.06567i 1.39566 + 0.265215i
\(236\) 0 0
\(237\) 13.9751 0.907780
\(238\) 0 0
\(239\) 8.29573i 0.536606i 0.963335 + 0.268303i \(0.0864629\pi\)
−0.963335 + 0.268303i \(0.913537\pi\)
\(240\) 0 0
\(241\) 24.9949i 1.61006i 0.593232 + 0.805031i \(0.297852\pi\)
−0.593232 + 0.805031i \(0.702148\pi\)
\(242\) 0 0
\(243\) 22.3408 1.43316
\(244\) 0 0
\(245\) 5.04756 + 0.959176i 0.322477 + 0.0612795i
\(246\) 0 0
\(247\) 10.3605i 0.659221i
\(248\) 0 0
\(249\) 14.9210i 0.945582i
\(250\) 0 0
\(251\) −10.5642 −0.666809 −0.333405 0.942784i \(-0.608197\pi\)
−0.333405 + 0.942784i \(0.608197\pi\)
\(252\) 0 0
\(253\) 22.2912 17.2687i 1.40144 1.08568i
\(254\) 0 0
\(255\) −5.31724 1.01042i −0.332979 0.0632752i
\(256\) 0 0
\(257\) 12.9404i 0.807202i 0.914935 + 0.403601i \(0.132242\pi\)
−0.914935 + 0.403601i \(0.867758\pi\)
\(258\) 0 0
\(259\) 6.57288i 0.408419i
\(260\) 0 0
\(261\) −12.6459 −0.782763
\(262\) 0 0
\(263\) 22.5116i 1.38813i 0.719914 + 0.694063i \(0.244181\pi\)
−0.719914 + 0.694063i \(0.755819\pi\)
\(264\) 0 0
\(265\) 20.1696 + 3.83279i 1.23901 + 0.235446i
\(266\) 0 0
\(267\) 18.0499i 1.10464i
\(268\) 0 0
\(269\) 27.1013 1.65240 0.826199 0.563379i \(-0.190499\pi\)
0.826199 + 0.563379i \(0.190499\pi\)
\(270\) 0 0
\(271\) 18.3787i 1.11643i −0.829697 0.558214i \(-0.811487\pi\)
0.829697 0.558214i \(-0.188513\pi\)
\(272\) 0 0
\(273\) 45.7425 2.76846
\(274\) 0 0
\(275\) −27.3489 10.7835i −1.64920 0.650270i
\(276\) 0 0
\(277\) 4.28386i 0.257392i −0.991684 0.128696i \(-0.958921\pi\)
0.991684 0.128696i \(-0.0410792\pi\)
\(278\) 0 0
\(279\) 29.2542i 1.75141i
\(280\) 0 0
\(281\) 20.2609i 1.20866i 0.796733 + 0.604332i \(0.206560\pi\)
−0.796733 + 0.604332i \(0.793440\pi\)
\(282\) 0 0
\(283\) 7.40056i 0.439918i −0.975509 0.219959i \(-0.929408\pi\)
0.975509 0.219959i \(-0.0705923\pi\)
\(284\) 0 0
\(285\) −9.47415 1.80035i −0.561200 0.106644i
\(286\) 0 0
\(287\) 18.8332i 1.11169i
\(288\) 0 0
\(289\) −16.0618 −0.944811
\(290\) 0 0
\(291\) 18.7863 1.10127
\(292\) 0 0
\(293\) 25.0574 1.46387 0.731933 0.681376i \(-0.238618\pi\)
0.731933 + 0.681376i \(0.238618\pi\)
\(294\) 0 0
\(295\) −0.488921 + 2.57289i −0.0284661 + 0.149800i
\(296\) 0 0
\(297\) 3.59510 0.208609
\(298\) 0 0
\(299\) −17.6314 22.7594i −1.01965 1.31621i
\(300\) 0 0
\(301\) −27.6933 −1.59621
\(302\) 0 0
\(303\) −32.1855 −1.84901
\(304\) 0 0
\(305\) 0.397138 2.08989i 0.0227401 0.119667i
\(306\) 0 0
\(307\) −8.46339 −0.483031 −0.241515 0.970397i \(-0.577644\pi\)
−0.241515 + 0.970397i \(0.577644\pi\)
\(308\) 0 0
\(309\) 40.6759i 2.31397i
\(310\) 0 0
\(311\) 21.5882i 1.22416i 0.790798 + 0.612078i \(0.209666\pi\)
−0.790798 + 0.612078i \(0.790334\pi\)
\(312\) 0 0
\(313\) −12.7441 −0.720338 −0.360169 0.932887i \(-0.617281\pi\)
−0.360169 + 0.932887i \(0.617281\pi\)
\(314\) 0 0
\(315\) 4.13010 21.7342i 0.232705 1.22458i
\(316\) 0 0
\(317\) 20.3313i 1.14192i 0.820978 + 0.570960i \(0.193429\pi\)
−0.820978 + 0.570960i \(0.806571\pi\)
\(318\) 0 0
\(319\) 22.9154 1.28301
\(320\) 0 0
\(321\) 7.68889i 0.429152i
\(322\) 0 0
\(323\) 1.67168 0.0930146
\(324\) 0 0
\(325\) −11.0100 + 27.9234i −0.610725 + 1.54891i
\(326\) 0 0
\(327\) 12.2247i 0.676029i
\(328\) 0 0
\(329\) 29.6976i 1.63728i
\(330\) 0 0
\(331\) 0.989723i 0.0544001i 0.999630 + 0.0272000i \(0.00865911\pi\)
−0.999630 + 0.0272000i \(0.991341\pi\)
\(332\) 0 0
\(333\) 6.99422 0.383281
\(334\) 0 0
\(335\) −4.10433 + 21.5986i −0.224244 + 1.18006i
\(336\) 0 0
\(337\) 25.4823 1.38811 0.694056 0.719921i \(-0.255822\pi\)
0.694056 + 0.719921i \(0.255822\pi\)
\(338\) 0 0
\(339\) 4.81230 0.261368
\(340\) 0 0
\(341\) 53.0109i 2.87070i
\(342\) 0 0
\(343\) 14.3382i 0.774192i
\(344\) 0 0
\(345\) −23.8762 + 12.1682i −1.28545 + 0.655111i
\(346\) 0 0
\(347\) 19.9535 1.07116 0.535579 0.844485i \(-0.320093\pi\)
0.535579 + 0.844485i \(0.320093\pi\)
\(348\) 0 0
\(349\) −22.9641 −1.22924 −0.614620 0.788823i \(-0.710691\pi\)
−0.614620 + 0.788823i \(0.710691\pi\)
\(350\) 0 0
\(351\) 3.67061i 0.195923i
\(352\) 0 0
\(353\) 13.0078i 0.692337i −0.938172 0.346168i \(-0.887483\pi\)
0.938172 0.346168i \(-0.112517\pi\)
\(354\) 0 0
\(355\) 3.75628 19.7670i 0.199363 1.04912i
\(356\) 0 0
\(357\) 7.38062i 0.390624i
\(358\) 0 0
\(359\) 24.2551 1.28013 0.640066 0.768320i \(-0.278907\pi\)
0.640066 + 0.768320i \(0.278907\pi\)
\(360\) 0 0
\(361\) −16.0214 −0.843234
\(362\) 0 0
\(363\) −58.8997 −3.09143
\(364\) 0 0
\(365\) −3.56124 + 18.7406i −0.186404 + 0.980929i
\(366\) 0 0
\(367\) 25.0126i 1.30565i −0.757511 0.652823i \(-0.773585\pi\)
0.757511 0.652823i \(-0.226415\pi\)
\(368\) 0 0
\(369\) 20.0405 1.04327
\(370\) 0 0
\(371\) 27.9965i 1.45351i
\(372\) 0 0
\(373\) −5.79181 −0.299889 −0.149944 0.988694i \(-0.547909\pi\)
−0.149944 + 0.988694i \(0.547909\pi\)
\(374\) 0 0
\(375\) 23.6213 + 14.9204i 1.21980 + 0.770486i
\(376\) 0 0
\(377\) 23.3967i 1.20499i
\(378\) 0 0
\(379\) 37.1025 1.90583 0.952914 0.303240i \(-0.0980682\pi\)
0.952914 + 0.303240i \(0.0980682\pi\)
\(380\) 0 0
\(381\) −33.7558 −1.72936
\(382\) 0 0
\(383\) 9.75029i 0.498216i −0.968476 0.249108i \(-0.919863\pi\)
0.968476 0.249108i \(-0.0801375\pi\)
\(384\) 0 0
\(385\) −7.48405 + 39.3840i −0.381423 + 2.00719i
\(386\) 0 0
\(387\) 29.4685i 1.49797i
\(388\) 0 0
\(389\) 12.3075i 0.624014i −0.950080 0.312007i \(-0.898999\pi\)
0.950080 0.312007i \(-0.101001\pi\)
\(390\) 0 0
\(391\) 3.67227 2.84486i 0.185715 0.143871i
\(392\) 0 0
\(393\) 8.76065i 0.441916i
\(394\) 0 0
\(395\) 12.2852 + 2.33453i 0.618135 + 0.117463i
\(396\) 0 0
\(397\) 8.73767i 0.438531i −0.975665 0.219266i \(-0.929634\pi\)
0.975665 0.219266i \(-0.0703661\pi\)
\(398\) 0 0
\(399\) 13.1506i 0.658355i
\(400\) 0 0
\(401\) 1.58414i 0.0791083i −0.999217 0.0395541i \(-0.987406\pi\)
0.999217 0.0395541i \(-0.0125938\pi\)
\(402\) 0 0
\(403\) −54.1244 −2.69613
\(404\) 0 0
\(405\) 18.0268 + 3.42559i 0.895757 + 0.170219i
\(406\) 0 0
\(407\) −12.6741 −0.628230
\(408\) 0 0
\(409\) −20.0682 −0.992306 −0.496153 0.868235i \(-0.665255\pi\)
−0.496153 + 0.868235i \(0.665255\pi\)
\(410\) 0 0
\(411\) 1.42479 0.0702799
\(412\) 0 0
\(413\) 3.57131 0.175733
\(414\) 0 0
\(415\) −2.49255 + 13.1167i −0.122354 + 0.643875i
\(416\) 0 0
\(417\) 8.84949i 0.433361i
\(418\) 0 0
\(419\) −22.4700 −1.09773 −0.548865 0.835911i \(-0.684940\pi\)
−0.548865 + 0.835911i \(0.684940\pi\)
\(420\) 0 0
\(421\) 10.3190i 0.502917i 0.967868 + 0.251458i \(0.0809102\pi\)
−0.967868 + 0.251458i \(0.919090\pi\)
\(422\) 0 0
\(423\) −31.6013 −1.53651
\(424\) 0 0
\(425\) −4.50547 1.77648i −0.218548 0.0861719i
\(426\) 0 0
\(427\) −2.90089 −0.140384
\(428\) 0 0
\(429\) 88.2025i 4.25846i
\(430\) 0 0
\(431\) 27.5506 1.32707 0.663534 0.748146i \(-0.269056\pi\)
0.663534 + 0.748146i \(0.269056\pi\)
\(432\) 0 0
\(433\) 9.84191 0.472972 0.236486 0.971635i \(-0.424004\pi\)
0.236486 + 0.971635i \(0.424004\pi\)
\(434\) 0 0
\(435\) −21.3951 4.06567i −1.02582 0.194934i
\(436\) 0 0
\(437\) 6.54317 5.06890i 0.313002 0.242479i
\(438\) 0 0
\(439\) 22.5128i 1.07448i 0.843431 + 0.537238i \(0.180532\pi\)
−0.843431 + 0.537238i \(0.819468\pi\)
\(440\) 0 0
\(441\) −7.45541 −0.355020
\(442\) 0 0
\(443\) 31.0216 1.47388 0.736941 0.675957i \(-0.236270\pi\)
0.736941 + 0.675957i \(0.236270\pi\)
\(444\) 0 0
\(445\) −3.01522 + 15.8672i −0.142935 + 0.752180i
\(446\) 0 0
\(447\) 45.0721i 2.13184i
\(448\) 0 0
\(449\) −22.2768 −1.05131 −0.525654 0.850698i \(-0.676179\pi\)
−0.525654 + 0.850698i \(0.676179\pi\)
\(450\) 0 0
\(451\) −36.3150 −1.71001
\(452\) 0 0
\(453\) 26.4363i 1.24209i
\(454\) 0 0
\(455\) 40.2112 + 7.64125i 1.88513 + 0.358227i
\(456\) 0 0
\(457\) −16.0377 −0.750210 −0.375105 0.926982i \(-0.622393\pi\)
−0.375105 + 0.926982i \(0.622393\pi\)
\(458\) 0 0
\(459\) 0.592258 0.0276442
\(460\) 0 0
\(461\) 12.8075 0.596507 0.298253 0.954487i \(-0.403596\pi\)
0.298253 + 0.954487i \(0.403596\pi\)
\(462\) 0 0
\(463\) 12.0225 0.558735 0.279368 0.960184i \(-0.409875\pi\)
0.279368 + 0.960184i \(0.409875\pi\)
\(464\) 0 0
\(465\) −9.40526 + 49.4941i −0.436159 + 2.29523i
\(466\) 0 0
\(467\) 0.645389i 0.0298650i 0.999889 + 0.0149325i \(0.00475334\pi\)
−0.999889 + 0.0149325i \(0.995247\pi\)
\(468\) 0 0
\(469\) 29.9800 1.38435
\(470\) 0 0
\(471\) 40.8127 1.88055
\(472\) 0 0
\(473\) 53.3992i 2.45530i
\(474\) 0 0
\(475\) −8.02776 3.16530i −0.368339 0.145234i
\(476\) 0 0
\(477\) −29.7912 −1.36404
\(478\) 0 0
\(479\) −32.9225 −1.50427 −0.752134 0.659011i \(-0.770975\pi\)
−0.752134 + 0.659011i \(0.770975\pi\)
\(480\) 0 0
\(481\) 12.9403i 0.590026i
\(482\) 0 0
\(483\) 22.3797 + 28.8888i 1.01831 + 1.31448i
\(484\) 0 0
\(485\) 16.5146 + 3.13823i 0.749889 + 0.142500i
\(486\) 0 0
\(487\) 4.57008 0.207090 0.103545 0.994625i \(-0.466981\pi\)
0.103545 + 0.994625i \(0.466981\pi\)
\(488\) 0 0
\(489\) −35.4008 −1.60088
\(490\) 0 0
\(491\) 26.5326i 1.19740i 0.800974 + 0.598700i \(0.204316\pi\)
−0.800974 + 0.598700i \(0.795684\pi\)
\(492\) 0 0
\(493\) 3.77509 0.170021
\(494\) 0 0
\(495\) 41.9086 + 7.96381i 1.88365 + 0.357947i
\(496\) 0 0
\(497\) −27.4377 −1.23075
\(498\) 0 0
\(499\) 4.30379i 0.192664i 0.995349 + 0.0963322i \(0.0307111\pi\)
−0.995349 + 0.0963322i \(0.969289\pi\)
\(500\) 0 0
\(501\) 6.36170 0.284220
\(502\) 0 0
\(503\) 3.17002i 0.141344i 0.997500 + 0.0706720i \(0.0225144\pi\)
−0.997500 + 0.0706720i \(0.977486\pi\)
\(504\) 0 0
\(505\) −28.2935 5.37656i −1.25905 0.239254i
\(506\) 0 0
\(507\) 57.5689 2.55673
\(508\) 0 0
\(509\) 26.0671 1.15540 0.577702 0.816248i \(-0.303950\pi\)
0.577702 + 0.816248i \(0.303950\pi\)
\(510\) 0 0
\(511\) 26.0130 1.15075
\(512\) 0 0
\(513\) 1.05527 0.0465914
\(514\) 0 0
\(515\) −6.79486 + 35.7572i −0.299417 + 1.57565i
\(516\) 0 0
\(517\) 57.2641 2.51847
\(518\) 0 0
\(519\) 11.2982i 0.495936i
\(520\) 0 0
\(521\) 20.7148i 0.907532i 0.891121 + 0.453766i \(0.149920\pi\)
−0.891121 + 0.453766i \(0.850080\pi\)
\(522\) 0 0
\(523\) 2.82308i 0.123445i 0.998093 + 0.0617223i \(0.0196593\pi\)
−0.998093 + 0.0617223i \(0.980341\pi\)
\(524\) 0 0
\(525\) 13.9751 35.4434i 0.609923 1.54687i
\(526\) 0 0
\(527\) 8.73304i 0.380417i
\(528\) 0 0
\(529\) 5.74750 22.2703i 0.249891 0.968274i
\(530\) 0 0
\(531\) 3.80025i 0.164917i
\(532\) 0 0
\(533\) 37.0777i 1.60602i
\(534\) 0 0
\(535\) 1.28442 6.75912i 0.0555304 0.292222i
\(536\) 0 0
\(537\) 50.3469i 2.17263i
\(538\) 0 0
\(539\) 13.5098 0.581907
\(540\) 0 0
\(541\) −26.8743 −1.15542 −0.577709 0.816243i \(-0.696053\pi\)
−0.577709 + 0.816243i \(0.696053\pi\)
\(542\) 0 0
\(543\) 35.2960i 1.51470i
\(544\) 0 0
\(545\) 2.04213 10.7465i 0.0874751 0.460328i
\(546\) 0 0
\(547\) −1.62485 −0.0694737 −0.0347368 0.999396i \(-0.511059\pi\)
−0.0347368 + 0.999396i \(0.511059\pi\)
\(548\) 0 0
\(549\) 3.08684i 0.131743i
\(550\) 0 0
\(551\) 6.72637 0.286553
\(552\) 0 0
\(553\) 17.0525i 0.725146i
\(554\) 0 0
\(555\) 11.8333 + 2.24865i 0.502294 + 0.0954498i
\(556\) 0 0
\(557\) −11.8048 −0.500186 −0.250093 0.968222i \(-0.580461\pi\)
−0.250093 + 0.968222i \(0.580461\pi\)
\(558\) 0 0
\(559\) −54.5208 −2.30598
\(560\) 0 0
\(561\) −14.2316 −0.600858
\(562\) 0 0
\(563\) 7.58816i 0.319803i 0.987133 + 0.159901i \(0.0511176\pi\)
−0.987133 + 0.159901i \(0.948882\pi\)
\(564\) 0 0
\(565\) 4.23038 + 0.803889i 0.177973 + 0.0338199i
\(566\) 0 0
\(567\) 25.0221i 1.05083i
\(568\) 0 0
\(569\) 4.86024i 0.203752i 0.994797 + 0.101876i \(0.0324844\pi\)
−0.994797 + 0.101876i \(0.967516\pi\)
\(570\) 0 0
\(571\) −5.68775 −0.238025 −0.119012 0.992893i \(-0.537973\pi\)
−0.119012 + 0.992893i \(0.537973\pi\)
\(572\) 0 0
\(573\) 18.8105 0.785821
\(574\) 0 0
\(575\) −23.0217 + 6.70824i −0.960072 + 0.279753i
\(576\) 0 0
\(577\) 44.1269i 1.83703i −0.395391 0.918513i \(-0.629391\pi\)
0.395391 0.918513i \(-0.370609\pi\)
\(578\) 0 0
\(579\) 40.1341i 1.66792i
\(580\) 0 0
\(581\) 18.2067 0.755343
\(582\) 0 0
\(583\) 53.9839 2.23578
\(584\) 0 0
\(585\) 8.13108 42.7889i 0.336179 1.76910i
\(586\) 0 0
\(587\) −11.8106 −0.487474 −0.243737 0.969841i \(-0.578373\pi\)
−0.243737 + 0.969841i \(0.578373\pi\)
\(588\) 0 0
\(589\) 15.5604i 0.641153i
\(590\) 0 0
\(591\) 59.1516i 2.43317i
\(592\) 0 0
\(593\) 19.7606i 0.811472i −0.913990 0.405736i \(-0.867015\pi\)
0.913990 0.405736i \(-0.132985\pi\)
\(594\) 0 0
\(595\) −1.23293 + 6.48813i −0.0505450 + 0.265987i
\(596\) 0 0
\(597\) −51.4722 −2.10662
\(598\) 0 0
\(599\) 22.0799i 0.902160i −0.892483 0.451080i \(-0.851039\pi\)
0.892483 0.451080i \(-0.148961\pi\)
\(600\) 0 0
\(601\) −21.2764 −0.867883 −0.433941 0.900941i \(-0.642877\pi\)
−0.433941 + 0.900941i \(0.642877\pi\)
\(602\) 0 0
\(603\) 31.9019i 1.29914i
\(604\) 0 0
\(605\) −51.7773 9.83914i −2.10505 0.400018i
\(606\) 0 0
\(607\) 5.66921 0.230106 0.115053 0.993359i \(-0.463296\pi\)
0.115053 + 0.993359i \(0.463296\pi\)
\(608\) 0 0
\(609\) 29.6976i 1.20341i
\(610\) 0 0
\(611\) 58.4668i 2.36532i
\(612\) 0 0
\(613\) 12.4953 0.504678 0.252339 0.967639i \(-0.418800\pi\)
0.252339 + 0.967639i \(0.418800\pi\)
\(614\) 0 0
\(615\) 33.9058 + 6.44305i 1.36721 + 0.259809i
\(616\) 0 0
\(617\) 14.4637 0.582286 0.291143 0.956680i \(-0.405965\pi\)
0.291143 + 0.956680i \(0.405965\pi\)
\(618\) 0 0
\(619\) −16.0292 −0.644270 −0.322135 0.946694i \(-0.604400\pi\)
−0.322135 + 0.946694i \(0.604400\pi\)
\(620\) 0 0
\(621\) 2.31818 1.79586i 0.0930253 0.0720654i
\(622\) 0 0
\(623\) 22.0246 0.882397
\(624\) 0 0
\(625\) 18.2725 + 17.0621i 0.730901 + 0.682484i
\(626\) 0 0
\(627\) −25.3576 −1.01268
\(628\) 0 0
\(629\) −2.08793 −0.0832513
\(630\) 0 0
\(631\) 17.9112 0.713034 0.356517 0.934289i \(-0.383964\pi\)
0.356517 + 0.934289i \(0.383964\pi\)
\(632\) 0 0
\(633\) 0.636889i 0.0253141i
\(634\) 0 0
\(635\) −29.6740 5.63888i −1.17758 0.223772i
\(636\) 0 0
\(637\) 13.7935i 0.546520i
\(638\) 0 0
\(639\) 29.1966i 1.15500i
\(640\) 0 0
\(641\) 12.2324i 0.483150i −0.970382 0.241575i \(-0.922336\pi\)
0.970382 0.241575i \(-0.0776639\pi\)
\(642\) 0 0
\(643\) 40.2616i 1.58776i −0.608072 0.793882i \(-0.708057\pi\)
0.608072 0.793882i \(-0.291943\pi\)
\(644\) 0 0
\(645\) −9.47415 + 49.8566i −0.373044 + 1.96310i
\(646\) 0 0
\(647\) 0.217415 0.00854748 0.00427374 0.999991i \(-0.498640\pi\)
0.00427374 + 0.999991i \(0.498640\pi\)
\(648\) 0 0
\(649\) 6.88634i 0.270313i
\(650\) 0 0
\(651\) 68.7005 2.69259
\(652\) 0 0
\(653\) 1.08204i 0.0423434i −0.999776 0.0211717i \(-0.993260\pi\)
0.999776 0.0211717i \(-0.00673966\pi\)
\(654\) 0 0
\(655\) 1.46346 7.70128i 0.0571820 0.300914i
\(656\) 0 0
\(657\) 27.6806i 1.07992i
\(658\) 0 0
\(659\) 10.7166 0.417460 0.208730 0.977973i \(-0.433067\pi\)
0.208730 + 0.977973i \(0.433067\pi\)
\(660\) 0 0
\(661\) 46.7678i 1.81905i 0.415644 + 0.909527i \(0.363556\pi\)
−0.415644 + 0.909527i \(0.636444\pi\)
\(662\) 0 0
\(663\) 14.5305i 0.564318i
\(664\) 0 0
\(665\) −2.19680 + 11.5604i −0.0851883 + 0.448294i
\(666\) 0 0
\(667\) 14.7762 11.4469i 0.572137 0.443227i
\(668\) 0 0
\(669\) 9.74891 0.376915
\(670\) 0 0
\(671\) 5.59360i 0.215938i
\(672\) 0 0
\(673\) 22.4945i 0.867100i 0.901129 + 0.433550i \(0.142739\pi\)
−0.901129 + 0.433550i \(0.857261\pi\)
\(674\) 0 0
\(675\) −2.84415 1.12143i −0.109471 0.0431639i
\(676\) 0 0
\(677\) 21.4298 0.823614 0.411807 0.911271i \(-0.364898\pi\)
0.411807 + 0.911271i \(0.364898\pi\)
\(678\) 0 0
\(679\) 22.9232i 0.879710i
\(680\) 0 0
\(681\) 44.1753i 1.69280i
\(682\) 0 0
\(683\) −23.7273 −0.907899 −0.453949 0.891027i \(-0.649985\pi\)
−0.453949 + 0.891027i \(0.649985\pi\)
\(684\) 0 0
\(685\) 1.25250 + 0.238011i 0.0478557 + 0.00909392i
\(686\) 0 0
\(687\) 65.4673i 2.49773i
\(688\) 0 0
\(689\) 55.1178i 2.09982i
\(690\) 0 0
\(691\) 13.4839i 0.512952i −0.966551 0.256476i \(-0.917439\pi\)
0.966551 0.256476i \(-0.0825615\pi\)
\(692\) 0 0
\(693\) 58.1715i 2.20975i
\(694\) 0 0
\(695\) −1.47830 + 7.77938i −0.0560751 + 0.295089i
\(696\) 0 0
\(697\) −5.98255 −0.226605
\(698\) 0 0
\(699\) 33.1331i 1.25321i
\(700\) 0 0
\(701\) 5.04107i 0.190399i −0.995458 0.0951993i \(-0.969651\pi\)
0.995458 0.0951993i \(-0.0303489\pi\)
\(702\) 0 0
\(703\) −3.72023 −0.140311
\(704\) 0 0
\(705\) −53.4651 10.1599i −2.01361 0.382642i
\(706\) 0 0
\(707\) 39.2730i 1.47701i
\(708\) 0 0
\(709\) 20.7675i 0.779938i 0.920828 + 0.389969i \(0.127514\pi\)
−0.920828 + 0.389969i \(0.872486\pi\)
\(710\) 0 0
\(711\) −18.1456 −0.680514
\(712\) 0 0
\(713\) −26.4806 34.1823i −0.991705 1.28014i
\(714\) 0 0
\(715\) −14.7341 + 77.5367i −0.551026 + 2.89971i
\(716\) 0 0
\(717\) 20.7305i 0.774195i
\(718\) 0 0
\(719\) 39.1171i 1.45882i −0.684077 0.729410i \(-0.739795\pi\)
0.684077 0.729410i \(-0.260205\pi\)
\(720\) 0 0
\(721\) 49.6329 1.84843
\(722\) 0 0
\(723\) 62.4607i 2.32294i
\(724\) 0 0
\(725\) −18.1288 7.14807i −0.673287 0.265473i
\(726\) 0 0
\(727\) 17.8782i 0.663065i −0.943444 0.331533i \(-0.892434\pi\)
0.943444 0.331533i \(-0.107566\pi\)
\(728\) 0 0
\(729\) −31.2101 −1.15593
\(730\) 0 0
\(731\) 8.79701i 0.325369i
\(732\) 0 0
\(733\) −12.7920 −0.472482 −0.236241 0.971694i \(-0.575916\pi\)
−0.236241 + 0.971694i \(0.575916\pi\)
\(734\) 0 0
\(735\) −12.6135 2.39692i −0.465257 0.0884118i
\(736\) 0 0
\(737\) 57.8086i 2.12941i
\(738\) 0 0
\(739\) 5.81963i 0.214079i 0.994255 + 0.107039i \(0.0341371\pi\)
−0.994255 + 0.107039i \(0.965863\pi\)
\(740\) 0 0
\(741\) 25.8902i 0.951099i
\(742\) 0 0
\(743\) 0.0511796i 0.00187760i 1.00000 0.000938799i \(0.000298829\pi\)
−1.00000 0.000938799i \(0.999701\pi\)
\(744\) 0 0
\(745\) 7.52926 39.6219i 0.275851 1.45163i
\(746\) 0 0
\(747\) 19.3739i 0.708853i
\(748\) 0 0
\(749\) −9.38203 −0.342812
\(750\) 0 0
\(751\) −35.4547 −1.29376 −0.646881 0.762591i \(-0.723927\pi\)
−0.646881 + 0.762591i \(0.723927\pi\)
\(752\) 0 0
\(753\) 26.3994 0.962047
\(754\) 0 0
\(755\) −4.41616 + 23.2395i −0.160721 + 0.845773i
\(756\) 0 0
\(757\) 47.5666 1.72884 0.864418 0.502773i \(-0.167687\pi\)
0.864418 + 0.502773i \(0.167687\pi\)
\(758\) 0 0
\(759\) −55.7044 + 43.1534i −2.02194 + 1.56637i
\(760\) 0 0
\(761\) 18.2647 0.662095 0.331047 0.943614i \(-0.392598\pi\)
0.331047 + 0.943614i \(0.392598\pi\)
\(762\) 0 0
\(763\) −14.9167 −0.540020
\(764\) 0 0
\(765\) 6.90405 + 1.31196i 0.249616 + 0.0474340i
\(766\) 0 0
\(767\) 7.03098 0.253874
\(768\) 0 0
\(769\) 31.5027i 1.13602i 0.823022 + 0.568009i \(0.192286\pi\)
−0.823022 + 0.568009i \(0.807714\pi\)
\(770\) 0 0
\(771\) 32.3373i 1.16460i
\(772\) 0 0
\(773\) 16.3913 0.589554 0.294777 0.955566i \(-0.404755\pi\)
0.294777 + 0.955566i \(0.404755\pi\)
\(774\) 0 0
\(775\) −16.5359 + 41.9380i −0.593987 + 1.50646i
\(776\) 0 0
\(777\) 16.4252i 0.589251i
\(778\) 0 0
\(779\) −10.6596 −0.381919
\(780\) 0 0
\(781\) 52.9064i 1.89314i
\(782\) 0 0
\(783\) 2.38309 0.0851645
\(784\) 0 0
\(785\) 35.8775 + 6.81773i 1.28052 + 0.243335i
\(786\) 0 0
\(787\) 38.6427i 1.37746i −0.725017 0.688731i \(-0.758168\pi\)
0.725017 0.688731i \(-0.241832\pi\)
\(788\) 0 0
\(789\) 56.2551i 2.00273i
\(790\) 0 0
\(791\) 5.87199i 0.208784i
\(792\) 0 0
\(793\) −5.71109 −0.202807
\(794\) 0 0
\(795\) −50.4025 9.57789i −1.78759 0.339693i
\(796\) 0 0
\(797\) −47.5892 −1.68569 −0.842847 0.538153i \(-0.819122\pi\)
−0.842847 + 0.538153i \(0.819122\pi\)
\(798\) 0 0
\(799\) 9.43371 0.333741
\(800\) 0 0
\(801\) 23.4365i 0.828087i
\(802\) 0 0
\(803\) 50.1593i