Properties

Label 3822.2.c.a.883.1
Level $3822$
Weight $2$
Character 3822.883
Analytic conductor $30.519$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3822.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(30.5188236525\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 546)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 883.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 3822.883
Dual form 3822.2.c.a.883.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -3.00000i q^{5} +1.00000i q^{6} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -3.00000i q^{5} +1.00000i q^{6} +1.00000i q^{8} +1.00000 q^{9} -3.00000 q^{10} +5.00000i q^{11} +1.00000 q^{12} +(3.00000 - 2.00000i) q^{13} +3.00000i q^{15} +1.00000 q^{16} -3.00000 q^{17} -1.00000i q^{18} -1.00000i q^{19} +3.00000i q^{20} +5.00000 q^{22} -1.00000 q^{23} -1.00000i q^{24} -4.00000 q^{25} +(-2.00000 - 3.00000i) q^{26} -1.00000 q^{27} +5.00000 q^{29} +3.00000 q^{30} -1.00000i q^{32} -5.00000i q^{33} +3.00000i q^{34} -1.00000 q^{36} +7.00000i q^{37} -1.00000 q^{38} +(-3.00000 + 2.00000i) q^{39} +3.00000 q^{40} -1.00000 q^{43} -5.00000i q^{44} -3.00000i q^{45} +1.00000i q^{46} +8.00000i q^{47} -1.00000 q^{48} +4.00000i q^{50} +3.00000 q^{51} +(-3.00000 + 2.00000i) q^{52} +14.0000 q^{53} +1.00000i q^{54} +15.0000 q^{55} +1.00000i q^{57} -5.00000i q^{58} +14.0000i q^{59} -3.00000i q^{60} +3.00000 q^{61} -1.00000 q^{64} +(-6.00000 - 9.00000i) q^{65} -5.00000 q^{66} -8.00000i q^{67} +3.00000 q^{68} +1.00000 q^{69} +10.0000i q^{71} +1.00000i q^{72} +11.0000i q^{73} +7.00000 q^{74} +4.00000 q^{75} +1.00000i q^{76} +(2.00000 + 3.00000i) q^{78} -3.00000i q^{80} +1.00000 q^{81} +6.00000i q^{83} +9.00000i q^{85} +1.00000i q^{86} -5.00000 q^{87} -5.00000 q^{88} -16.0000i q^{89} -3.00000 q^{90} +1.00000 q^{92} +8.00000 q^{94} -3.00000 q^{95} +1.00000i q^{96} -2.00000i q^{97} +5.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{3} - 2 q^{4} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{3} - 2 q^{4} + 2 q^{9} - 6 q^{10} + 2 q^{12} + 6 q^{13} + 2 q^{16} - 6 q^{17} + 10 q^{22} - 2 q^{23} - 8 q^{25} - 4 q^{26} - 2 q^{27} + 10 q^{29} + 6 q^{30} - 2 q^{36} - 2 q^{38} - 6 q^{39} + 6 q^{40} - 2 q^{43} - 2 q^{48} + 6 q^{51} - 6 q^{52} + 28 q^{53} + 30 q^{55} + 6 q^{61} - 2 q^{64} - 12 q^{65} - 10 q^{66} + 6 q^{68} + 2 q^{69} + 14 q^{74} + 8 q^{75} + 4 q^{78} + 2 q^{81} - 10 q^{87} - 10 q^{88} - 6 q^{90} + 2 q^{92} + 16 q^{94} - 6 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3822\mathbb{Z}\right)^\times\).

\(n\) \(1471\) \(2549\) \(3433\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.00000 −0.577350
\(4\) −1.00000 −0.500000
\(5\) 3.00000i 1.34164i −0.741620 0.670820i \(-0.765942\pi\)
0.741620 0.670820i \(-0.234058\pi\)
\(6\) 1.00000i 0.408248i
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 1.00000 0.333333
\(10\) −3.00000 −0.948683
\(11\) 5.00000i 1.50756i 0.657129 + 0.753778i \(0.271771\pi\)
−0.657129 + 0.753778i \(0.728229\pi\)
\(12\) 1.00000 0.288675
\(13\) 3.00000 2.00000i 0.832050 0.554700i
\(14\) 0 0
\(15\) 3.00000i 0.774597i
\(16\) 1.00000 0.250000
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 1.00000i 0.229416i −0.993399 0.114708i \(-0.963407\pi\)
0.993399 0.114708i \(-0.0365932\pi\)
\(20\) 3.00000i 0.670820i
\(21\) 0 0
\(22\) 5.00000 1.06600
\(23\) −1.00000 −0.208514 −0.104257 0.994550i \(-0.533247\pi\)
−0.104257 + 0.994550i \(0.533247\pi\)
\(24\) 1.00000i 0.204124i
\(25\) −4.00000 −0.800000
\(26\) −2.00000 3.00000i −0.392232 0.588348i
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 5.00000 0.928477 0.464238 0.885710i \(-0.346328\pi\)
0.464238 + 0.885710i \(0.346328\pi\)
\(30\) 3.00000 0.547723
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 5.00000i 0.870388i
\(34\) 3.00000i 0.514496i
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 7.00000i 1.15079i 0.817875 + 0.575396i \(0.195152\pi\)
−0.817875 + 0.575396i \(0.804848\pi\)
\(38\) −1.00000 −0.162221
\(39\) −3.00000 + 2.00000i −0.480384 + 0.320256i
\(40\) 3.00000 0.474342
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 5.00000i 0.753778i
\(45\) 3.00000i 0.447214i
\(46\) 1.00000i 0.147442i
\(47\) 8.00000i 1.16692i 0.812142 + 0.583460i \(0.198301\pi\)
−0.812142 + 0.583460i \(0.801699\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) 4.00000i 0.565685i
\(51\) 3.00000 0.420084
\(52\) −3.00000 + 2.00000i −0.416025 + 0.277350i
\(53\) 14.0000 1.92305 0.961524 0.274721i \(-0.0885855\pi\)
0.961524 + 0.274721i \(0.0885855\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 15.0000 2.02260
\(56\) 0 0
\(57\) 1.00000i 0.132453i
\(58\) 5.00000i 0.656532i
\(59\) 14.0000i 1.82264i 0.411693 + 0.911322i \(0.364937\pi\)
−0.411693 + 0.911322i \(0.635063\pi\)
\(60\) 3.00000i 0.387298i
\(61\) 3.00000 0.384111 0.192055 0.981384i \(-0.438485\pi\)
0.192055 + 0.981384i \(0.438485\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −6.00000 9.00000i −0.744208 1.11631i
\(66\) −5.00000 −0.615457
\(67\) 8.00000i 0.977356i −0.872464 0.488678i \(-0.837479\pi\)
0.872464 0.488678i \(-0.162521\pi\)
\(68\) 3.00000 0.363803
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) 10.0000i 1.18678i 0.804914 + 0.593391i \(0.202211\pi\)
−0.804914 + 0.593391i \(0.797789\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 11.0000i 1.28745i 0.765256 + 0.643726i \(0.222612\pi\)
−0.765256 + 0.643726i \(0.777388\pi\)
\(74\) 7.00000 0.813733
\(75\) 4.00000 0.461880
\(76\) 1.00000i 0.114708i
\(77\) 0 0
\(78\) 2.00000 + 3.00000i 0.226455 + 0.339683i
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 3.00000i 0.335410i
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 6.00000i 0.658586i 0.944228 + 0.329293i \(0.106810\pi\)
−0.944228 + 0.329293i \(0.893190\pi\)
\(84\) 0 0
\(85\) 9.00000i 0.976187i
\(86\) 1.00000i 0.107833i
\(87\) −5.00000 −0.536056
\(88\) −5.00000 −0.533002
\(89\) 16.0000i 1.69600i −0.529999 0.847998i \(-0.677808\pi\)
0.529999 0.847998i \(-0.322192\pi\)
\(90\) −3.00000 −0.316228
\(91\) 0 0
\(92\) 1.00000 0.104257
\(93\) 0 0
\(94\) 8.00000 0.825137
\(95\) −3.00000 −0.307794
\(96\) 1.00000i 0.102062i
\(97\) 2.00000i 0.203069i −0.994832 0.101535i \(-0.967625\pi\)
0.994832 0.101535i \(-0.0323753\pi\)
\(98\) 0 0
\(99\) 5.00000i 0.502519i
\(100\) 4.00000 0.400000
\(101\) 18.0000 1.79107 0.895533 0.444994i \(-0.146794\pi\)
0.895533 + 0.444994i \(0.146794\pi\)
\(102\) 3.00000i 0.297044i
\(103\) 11.0000 1.08386 0.541931 0.840423i \(-0.317693\pi\)
0.541931 + 0.840423i \(0.317693\pi\)
\(104\) 2.00000 + 3.00000i 0.196116 + 0.294174i
\(105\) 0 0
\(106\) 14.0000i 1.35980i
\(107\) 18.0000 1.74013 0.870063 0.492941i \(-0.164078\pi\)
0.870063 + 0.492941i \(0.164078\pi\)
\(108\) 1.00000 0.0962250
\(109\) 9.00000i 0.862044i −0.902342 0.431022i \(-0.858153\pi\)
0.902342 0.431022i \(-0.141847\pi\)
\(110\) 15.0000i 1.43019i
\(111\) 7.00000i 0.664411i
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 1.00000 0.0936586
\(115\) 3.00000i 0.279751i
\(116\) −5.00000 −0.464238
\(117\) 3.00000 2.00000i 0.277350 0.184900i
\(118\) 14.0000 1.28880
\(119\) 0 0
\(120\) −3.00000 −0.273861
\(121\) −14.0000 −1.27273
\(122\) 3.00000i 0.271607i
\(123\) 0 0
\(124\) 0 0
\(125\) 3.00000i 0.268328i
\(126\) 0 0
\(127\) −12.0000 −1.06483 −0.532414 0.846484i \(-0.678715\pi\)
−0.532414 + 0.846484i \(0.678715\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 1.00000 0.0880451
\(130\) −9.00000 + 6.00000i −0.789352 + 0.526235i
\(131\) −7.00000 −0.611593 −0.305796 0.952097i \(-0.598923\pi\)
−0.305796 + 0.952097i \(0.598923\pi\)
\(132\) 5.00000i 0.435194i
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) 3.00000i 0.258199i
\(136\) 3.00000i 0.257248i
\(137\) 3.00000i 0.256307i −0.991754 0.128154i \(-0.959095\pi\)
0.991754 0.128154i \(-0.0409051\pi\)
\(138\) 1.00000i 0.0851257i
\(139\) −20.0000 −1.69638 −0.848189 0.529694i \(-0.822307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(140\) 0 0
\(141\) 8.00000i 0.673722i
\(142\) 10.0000 0.839181
\(143\) 10.0000 + 15.0000i 0.836242 + 1.25436i
\(144\) 1.00000 0.0833333
\(145\) 15.0000i 1.24568i
\(146\) 11.0000 0.910366
\(147\) 0 0
\(148\) 7.00000i 0.575396i
\(149\) 6.00000i 0.491539i 0.969328 + 0.245770i \(0.0790407\pi\)
−0.969328 + 0.245770i \(0.920959\pi\)
\(150\) 4.00000i 0.326599i
\(151\) 15.0000i 1.22068i −0.792139 0.610341i \(-0.791032\pi\)
0.792139 0.610341i \(-0.208968\pi\)
\(152\) 1.00000 0.0811107
\(153\) −3.00000 −0.242536
\(154\) 0 0
\(155\) 0 0
\(156\) 3.00000 2.00000i 0.240192 0.160128i
\(157\) −13.0000 −1.03751 −0.518756 0.854922i \(-0.673605\pi\)
−0.518756 + 0.854922i \(0.673605\pi\)
\(158\) 0 0
\(159\) −14.0000 −1.11027
\(160\) −3.00000 −0.237171
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) 4.00000i 0.313304i 0.987654 + 0.156652i \(0.0500701\pi\)
−0.987654 + 0.156652i \(0.949930\pi\)
\(164\) 0 0
\(165\) −15.0000 −1.16775
\(166\) 6.00000 0.465690
\(167\) 7.00000i 0.541676i −0.962625 0.270838i \(-0.912699\pi\)
0.962625 0.270838i \(-0.0873008\pi\)
\(168\) 0 0
\(169\) 5.00000 12.0000i 0.384615 0.923077i
\(170\) 9.00000 0.690268
\(171\) 1.00000i 0.0764719i
\(172\) 1.00000 0.0762493
\(173\) 26.0000 1.97674 0.988372 0.152057i \(-0.0485898\pi\)
0.988372 + 0.152057i \(0.0485898\pi\)
\(174\) 5.00000i 0.379049i
\(175\) 0 0
\(176\) 5.00000i 0.376889i
\(177\) 14.0000i 1.05230i
\(178\) −16.0000 −1.19925
\(179\) 10.0000 0.747435 0.373718 0.927543i \(-0.378083\pi\)
0.373718 + 0.927543i \(0.378083\pi\)
\(180\) 3.00000i 0.223607i
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) −3.00000 −0.221766
\(184\) 1.00000i 0.0737210i
\(185\) 21.0000 1.54395
\(186\) 0 0
\(187\) 15.0000i 1.09691i
\(188\) 8.00000i 0.583460i
\(189\) 0 0
\(190\) 3.00000i 0.217643i
\(191\) 17.0000 1.23008 0.615038 0.788497i \(-0.289140\pi\)
0.615038 + 0.788497i \(0.289140\pi\)
\(192\) 1.00000 0.0721688
\(193\) 16.0000i 1.15171i −0.817554 0.575853i \(-0.804670\pi\)
0.817554 0.575853i \(-0.195330\pi\)
\(194\) −2.00000 −0.143592
\(195\) 6.00000 + 9.00000i 0.429669 + 0.644503i
\(196\) 0 0
\(197\) 2.00000i 0.142494i 0.997459 + 0.0712470i \(0.0226979\pi\)
−0.997459 + 0.0712470i \(0.977302\pi\)
\(198\) 5.00000 0.355335
\(199\) 5.00000 0.354441 0.177220 0.984171i \(-0.443289\pi\)
0.177220 + 0.984171i \(0.443289\pi\)
\(200\) 4.00000i 0.282843i
\(201\) 8.00000i 0.564276i
\(202\) 18.0000i 1.26648i
\(203\) 0 0
\(204\) −3.00000 −0.210042
\(205\) 0 0
\(206\) 11.0000i 0.766406i
\(207\) −1.00000 −0.0695048
\(208\) 3.00000 2.00000i 0.208013 0.138675i
\(209\) 5.00000 0.345857
\(210\) 0 0
\(211\) −13.0000 −0.894957 −0.447478 0.894295i \(-0.647678\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) −14.0000 −0.961524
\(213\) 10.0000i 0.685189i
\(214\) 18.0000i 1.23045i
\(215\) 3.00000i 0.204598i
\(216\) 1.00000i 0.0680414i
\(217\) 0 0
\(218\) −9.00000 −0.609557
\(219\) 11.0000i 0.743311i
\(220\) −15.0000 −1.01130
\(221\) −9.00000 + 6.00000i −0.605406 + 0.403604i
\(222\) −7.00000 −0.469809
\(223\) 16.0000i 1.07144i 0.844396 + 0.535720i \(0.179960\pi\)
−0.844396 + 0.535720i \(0.820040\pi\)
\(224\) 0 0
\(225\) −4.00000 −0.266667
\(226\) 6.00000i 0.399114i
\(227\) 8.00000i 0.530979i 0.964114 + 0.265489i \(0.0855335\pi\)
−0.964114 + 0.265489i \(0.914466\pi\)
\(228\) 1.00000i 0.0662266i
\(229\) 26.0000i 1.71813i −0.511868 0.859064i \(-0.671046\pi\)
0.511868 0.859064i \(-0.328954\pi\)
\(230\) 3.00000 0.197814
\(231\) 0 0
\(232\) 5.00000i 0.328266i
\(233\) 14.0000 0.917170 0.458585 0.888650i \(-0.348356\pi\)
0.458585 + 0.888650i \(0.348356\pi\)
\(234\) −2.00000 3.00000i −0.130744 0.196116i
\(235\) 24.0000 1.56559
\(236\) 14.0000i 0.911322i
\(237\) 0 0
\(238\) 0 0
\(239\) 4.00000i 0.258738i −0.991596 0.129369i \(-0.958705\pi\)
0.991596 0.129369i \(-0.0412952\pi\)
\(240\) 3.00000i 0.193649i
\(241\) 10.0000i 0.644157i 0.946713 + 0.322078i \(0.104381\pi\)
−0.946713 + 0.322078i \(0.895619\pi\)
\(242\) 14.0000i 0.899954i
\(243\) −1.00000 −0.0641500
\(244\) −3.00000 −0.192055
\(245\) 0 0
\(246\) 0 0
\(247\) −2.00000 3.00000i −0.127257 0.190885i
\(248\) 0 0
\(249\) 6.00000i 0.380235i
\(250\) −3.00000 −0.189737
\(251\) −17.0000 −1.07303 −0.536515 0.843891i \(-0.680260\pi\)
−0.536515 + 0.843891i \(0.680260\pi\)
\(252\) 0 0
\(253\) 5.00000i 0.314347i
\(254\) 12.0000i 0.752947i
\(255\) 9.00000i 0.563602i
\(256\) 1.00000 0.0625000
\(257\) −18.0000 −1.12281 −0.561405 0.827541i \(-0.689739\pi\)
−0.561405 + 0.827541i \(0.689739\pi\)
\(258\) 1.00000i 0.0622573i
\(259\) 0 0
\(260\) 6.00000 + 9.00000i 0.372104 + 0.558156i
\(261\) 5.00000 0.309492
\(262\) 7.00000i 0.432461i
\(263\) 24.0000 1.47990 0.739952 0.672660i \(-0.234848\pi\)
0.739952 + 0.672660i \(0.234848\pi\)
\(264\) 5.00000 0.307729
\(265\) 42.0000i 2.58004i
\(266\) 0 0
\(267\) 16.0000i 0.979184i
\(268\) 8.00000i 0.488678i
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 3.00000 0.182574
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) −3.00000 −0.181902
\(273\) 0 0
\(274\) −3.00000 −0.181237
\(275\) 20.0000i 1.20605i
\(276\) −1.00000 −0.0601929
\(277\) 28.0000 1.68236 0.841178 0.540758i \(-0.181862\pi\)
0.841178 + 0.540758i \(0.181862\pi\)
\(278\) 20.0000i 1.19952i
\(279\) 0 0
\(280\) 0 0
\(281\) 10.0000i 0.596550i 0.954480 + 0.298275i \(0.0964112\pi\)
−0.954480 + 0.298275i \(0.903589\pi\)
\(282\) −8.00000 −0.476393
\(283\) −14.0000 −0.832214 −0.416107 0.909316i \(-0.636606\pi\)
−0.416107 + 0.909316i \(0.636606\pi\)
\(284\) 10.0000i 0.593391i
\(285\) 3.00000 0.177705
\(286\) 15.0000 10.0000i 0.886969 0.591312i
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) −8.00000 −0.470588
\(290\) −15.0000 −0.880830
\(291\) 2.00000i 0.117242i
\(292\) 11.0000i 0.643726i
\(293\) 6.00000i 0.350524i 0.984522 + 0.175262i \(0.0560772\pi\)
−0.984522 + 0.175262i \(0.943923\pi\)
\(294\) 0 0
\(295\) 42.0000 2.44533
\(296\) −7.00000 −0.406867
\(297\) 5.00000i 0.290129i
\(298\) 6.00000 0.347571
\(299\) −3.00000 + 2.00000i −0.173494 + 0.115663i
\(300\) −4.00000 −0.230940
\(301\) 0 0
\(302\) −15.0000 −0.863153
\(303\) −18.0000 −1.03407
\(304\) 1.00000i 0.0573539i
\(305\) 9.00000i 0.515339i
\(306\) 3.00000i 0.171499i
\(307\) 8.00000i 0.456584i 0.973593 + 0.228292i \(0.0733141\pi\)
−0.973593 + 0.228292i \(0.926686\pi\)
\(308\) 0 0
\(309\) −11.0000 −0.625768
\(310\) 0 0
\(311\) 8.00000 0.453638 0.226819 0.973937i \(-0.427167\pi\)
0.226819 + 0.973937i \(0.427167\pi\)
\(312\) −2.00000 3.00000i −0.113228 0.169842i
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) 13.0000i 0.733632i
\(315\) 0 0
\(316\) 0 0
\(317\) 8.00000i 0.449325i −0.974437 0.224662i \(-0.927872\pi\)
0.974437 0.224662i \(-0.0721279\pi\)
\(318\) 14.0000i 0.785081i
\(319\) 25.0000i 1.39973i
\(320\) 3.00000i 0.167705i
\(321\) −18.0000 −1.00466
\(322\) 0 0
\(323\) 3.00000i 0.166924i
\(324\) −1.00000 −0.0555556
\(325\) −12.0000 + 8.00000i −0.665640 + 0.443760i
\(326\) 4.00000 0.221540
\(327\) 9.00000i 0.497701i
\(328\) 0 0
\(329\) 0 0
\(330\) 15.0000i 0.825723i
\(331\) 20.0000i 1.09930i −0.835395 0.549650i \(-0.814761\pi\)
0.835395 0.549650i \(-0.185239\pi\)
\(332\) 6.00000i 0.329293i
\(333\) 7.00000i 0.383598i
\(334\) −7.00000 −0.383023
\(335\) −24.0000 −1.31126
\(336\) 0 0
\(337\) 33.0000 1.79762 0.898812 0.438334i \(-0.144431\pi\)
0.898812 + 0.438334i \(0.144431\pi\)
\(338\) −12.0000 5.00000i −0.652714 0.271964i
\(339\) 6.00000 0.325875
\(340\) 9.00000i 0.488094i
\(341\) 0 0
\(342\) −1.00000 −0.0540738
\(343\) 0 0
\(344\) 1.00000i 0.0539164i
\(345\) 3.00000i 0.161515i
\(346\) 26.0000i 1.39777i
\(347\) 28.0000 1.50312 0.751559 0.659665i \(-0.229302\pi\)
0.751559 + 0.659665i \(0.229302\pi\)
\(348\) 5.00000 0.268028
\(349\) 16.0000i 0.856460i −0.903670 0.428230i \(-0.859137\pi\)
0.903670 0.428230i \(-0.140863\pi\)
\(350\) 0 0
\(351\) −3.00000 + 2.00000i −0.160128 + 0.106752i
\(352\) 5.00000 0.266501
\(353\) 24.0000i 1.27739i −0.769460 0.638696i \(-0.779474\pi\)
0.769460 0.638696i \(-0.220526\pi\)
\(354\) −14.0000 −0.744092
\(355\) 30.0000 1.59223
\(356\) 16.0000i 0.847998i
\(357\) 0 0
\(358\) 10.0000i 0.528516i
\(359\) 34.0000i 1.79445i −0.441572 0.897226i \(-0.645579\pi\)
0.441572 0.897226i \(-0.354421\pi\)
\(360\) 3.00000 0.158114
\(361\) 18.0000 0.947368
\(362\) 2.00000i 0.105118i
\(363\) 14.0000 0.734809
\(364\) 0 0
\(365\) 33.0000 1.72730
\(366\) 3.00000i 0.156813i
\(367\) 32.0000 1.67039 0.835193 0.549957i \(-0.185356\pi\)
0.835193 + 0.549957i \(0.185356\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 0 0
\(370\) 21.0000i 1.09174i
\(371\) 0 0
\(372\) 0 0
\(373\) −26.0000 −1.34623 −0.673114 0.739538i \(-0.735044\pi\)
−0.673114 + 0.739538i \(0.735044\pi\)
\(374\) −15.0000 −0.775632
\(375\) 3.00000i 0.154919i
\(376\) −8.00000 −0.412568
\(377\) 15.0000 10.0000i 0.772539 0.515026i
\(378\) 0 0
\(379\) 4.00000i 0.205466i −0.994709 0.102733i \(-0.967241\pi\)
0.994709 0.102733i \(-0.0327588\pi\)
\(380\) 3.00000 0.153897
\(381\) 12.0000 0.614779
\(382\) 17.0000i 0.869796i
\(383\) 31.0000i 1.58403i 0.610504 + 0.792013i \(0.290967\pi\)
−0.610504 + 0.792013i \(0.709033\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 0 0
\(386\) −16.0000 −0.814379
\(387\) −1.00000 −0.0508329
\(388\) 2.00000i 0.101535i
\(389\) −30.0000 −1.52106 −0.760530 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) 9.00000 6.00000i 0.455733 0.303822i
\(391\) 3.00000 0.151717
\(392\) 0 0
\(393\) 7.00000 0.353103
\(394\) 2.00000 0.100759
\(395\) 0 0
\(396\) 5.00000i 0.251259i
\(397\) 12.0000i 0.602263i −0.953583 0.301131i \(-0.902636\pi\)
0.953583 0.301131i \(-0.0973643\pi\)
\(398\) 5.00000i 0.250627i
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) 30.0000i 1.49813i 0.662497 + 0.749064i \(0.269497\pi\)
−0.662497 + 0.749064i \(0.730503\pi\)
\(402\) 8.00000 0.399004
\(403\) 0 0
\(404\) −18.0000 −0.895533
\(405\) 3.00000i 0.149071i
\(406\) 0 0
\(407\) −35.0000 −1.73489
\(408\) 3.00000i 0.148522i
\(409\) 19.0000i 0.939490i 0.882802 + 0.469745i \(0.155654\pi\)
−0.882802 + 0.469745i \(0.844346\pi\)
\(410\) 0 0
\(411\) 3.00000i 0.147979i
\(412\) −11.0000 −0.541931
\(413\) 0 0
\(414\) 1.00000i 0.0491473i
\(415\) 18.0000 0.883585
\(416\) −2.00000 3.00000i −0.0980581 0.147087i
\(417\) 20.0000 0.979404
\(418\) 5.00000i 0.244558i
\(419\) 35.0000 1.70986 0.854931 0.518742i \(-0.173599\pi\)
0.854931 + 0.518742i \(0.173599\pi\)
\(420\) 0 0
\(421\) 30.0000i 1.46211i 0.682318 + 0.731055i \(0.260972\pi\)
−0.682318 + 0.731055i \(0.739028\pi\)
\(422\) 13.0000i 0.632830i
\(423\) 8.00000i 0.388973i
\(424\) 14.0000i 0.679900i
\(425\) 12.0000 0.582086
\(426\) −10.0000 −0.484502
\(427\) 0 0
\(428\) −18.0000 −0.870063
\(429\) −10.0000 15.0000i −0.482805 0.724207i
\(430\) 3.00000 0.144673
\(431\) 30.0000i 1.44505i 0.691345 + 0.722525i \(0.257018\pi\)
−0.691345 + 0.722525i \(0.742982\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −4.00000 −0.192228 −0.0961139 0.995370i \(-0.530641\pi\)
−0.0961139 + 0.995370i \(0.530641\pi\)
\(434\) 0 0
\(435\) 15.0000i 0.719195i
\(436\) 9.00000i 0.431022i
\(437\) 1.00000i 0.0478365i
\(438\) −11.0000 −0.525600
\(439\) 15.0000 0.715911 0.357955 0.933739i \(-0.383474\pi\)
0.357955 + 0.933739i \(0.383474\pi\)
\(440\) 15.0000i 0.715097i
\(441\) 0 0
\(442\) 6.00000 + 9.00000i 0.285391 + 0.428086i
\(443\) −6.00000 −0.285069 −0.142534 0.989790i \(-0.545525\pi\)
−0.142534 + 0.989790i \(0.545525\pi\)
\(444\) 7.00000i 0.332205i
\(445\) −48.0000 −2.27542
\(446\) 16.0000 0.757622
\(447\) 6.00000i 0.283790i
\(448\) 0 0
\(449\) 21.0000i 0.991051i 0.868593 + 0.495526i \(0.165025\pi\)
−0.868593 + 0.495526i \(0.834975\pi\)
\(450\) 4.00000i 0.188562i
\(451\) 0 0
\(452\) 6.00000 0.282216
\(453\) 15.0000i 0.704761i
\(454\) 8.00000 0.375459
\(455\) 0 0
\(456\) −1.00000 −0.0468293
\(457\) 8.00000i 0.374224i −0.982339 0.187112i \(-0.940087\pi\)
0.982339 0.187112i \(-0.0599128\pi\)
\(458\) −26.0000 −1.21490
\(459\) 3.00000 0.140028
\(460\) 3.00000i 0.139876i
\(461\) 15.0000i 0.698620i 0.937007 + 0.349310i \(0.113584\pi\)
−0.937007 + 0.349310i \(0.886416\pi\)
\(462\) 0 0
\(463\) 11.0000i 0.511213i −0.966781 0.255607i \(-0.917725\pi\)
0.966781 0.255607i \(-0.0822752\pi\)
\(464\) 5.00000 0.232119
\(465\) 0 0
\(466\) 14.0000i 0.648537i
\(467\) 7.00000 0.323921 0.161961 0.986797i \(-0.448218\pi\)
0.161961 + 0.986797i \(0.448218\pi\)
\(468\) −3.00000 + 2.00000i −0.138675 + 0.0924500i
\(469\) 0 0
\(470\) 24.0000i 1.10704i
\(471\) 13.0000 0.599008
\(472\) −14.0000 −0.644402
\(473\) 5.00000i 0.229900i
\(474\) 0 0
\(475\) 4.00000i 0.183533i
\(476\) 0 0
\(477\) 14.0000 0.641016
\(478\) −4.00000 −0.182956
\(479\) 21.0000i 0.959514i −0.877401 0.479757i \(-0.840725\pi\)
0.877401 0.479757i \(-0.159275\pi\)
\(480\) 3.00000 0.136931
\(481\) 14.0000 + 21.0000i 0.638345 + 0.957518i
\(482\) 10.0000 0.455488
\(483\) 0 0
\(484\) 14.0000 0.636364
\(485\) −6.00000 −0.272446
\(486\) 1.00000i 0.0453609i
\(487\) 32.0000i 1.45006i 0.688718 + 0.725029i \(0.258174\pi\)
−0.688718 + 0.725029i \(0.741826\pi\)
\(488\) 3.00000i 0.135804i
\(489\) 4.00000i 0.180886i
\(490\) 0 0
\(491\) −28.0000 −1.26362 −0.631811 0.775122i \(-0.717688\pi\)
−0.631811 + 0.775122i \(0.717688\pi\)
\(492\) 0 0
\(493\) −15.0000 −0.675566
\(494\) −3.00000 + 2.00000i −0.134976 + 0.0899843i
\(495\) 15.0000 0.674200
\(496\) 0 0
\(497\) 0 0
\(498\) −6.00000 −0.268866
\(499\) 14.0000i 0.626726i −0.949633 0.313363i \(-0.898544\pi\)
0.949633 0.313363i \(-0.101456\pi\)
\(500\) 3.00000i 0.134164i
\(501\) 7.00000i 0.312737i
\(502\) 17.0000i 0.758747i
\(503\) 6.00000 0.267527 0.133763 0.991013i \(-0.457294\pi\)
0.133763 + 0.991013i \(0.457294\pi\)
\(504\) 0 0
\(505\) 54.0000i 2.40297i
\(506\) −5.00000 −0.222277
\(507\) −5.00000 + 12.0000i −0.222058 + 0.532939i
\(508\) 12.0000 0.532414
\(509\) 1.00000i 0.0443242i −0.999754 0.0221621i \(-0.992945\pi\)
0.999754 0.0221621i \(-0.00705500\pi\)
\(510\) −9.00000 −0.398527
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 1.00000i 0.0441511i
\(514\) 18.0000i 0.793946i
\(515\) 33.0000i 1.45415i
\(516\) −1.00000 −0.0440225
\(517\) −40.0000 −1.75920
\(518\) 0 0
\(519\) −26.0000 −1.14127
\(520\) 9.00000 6.00000i 0.394676 0.263117i
\(521\) −27.0000 −1.18289 −0.591446 0.806345i \(-0.701443\pi\)
−0.591446 + 0.806345i \(0.701443\pi\)
\(522\) 5.00000i 0.218844i
\(523\) 16.0000 0.699631 0.349816 0.936819i \(-0.386244\pi\)
0.349816 + 0.936819i \(0.386244\pi\)
\(524\) 7.00000 0.305796
\(525\) 0 0
\(526\) 24.0000i 1.04645i
\(527\) 0 0
\(528\) 5.00000i 0.217597i
\(529\) −22.0000 −0.956522
\(530\) −42.0000 −1.82436
\(531\) 14.0000i 0.607548i
\(532\) 0 0
\(533\) 0 0
\(534\) 16.0000 0.692388
\(535\) 54.0000i 2.33462i
\(536\) 8.00000 0.345547
\(537\) −10.0000 −0.431532
\(538\) 0 0
\(539\) 0 0
\(540\) 3.00000i 0.129099i
\(541\) 15.0000i 0.644900i −0.946586 0.322450i \(-0.895494\pi\)
0.946586 0.322450i \(-0.104506\pi\)
\(542\) 0 0
\(543\) 2.00000 0.0858282
\(544\) 3.00000i 0.128624i
\(545\) −27.0000 −1.15655
\(546\) 0 0
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) 3.00000i 0.128154i
\(549\) 3.00000 0.128037
\(550\) −20.0000 −0.852803
\(551\) 5.00000i 0.213007i
\(552\) 1.00000i 0.0425628i
\(553\) 0 0
\(554\) 28.0000i 1.18961i
\(555\) −21.0000 −0.891400
\(556\) 20.0000 0.848189
\(557\) 22.0000i 0.932170i 0.884740 + 0.466085i \(0.154336\pi\)
−0.884740 + 0.466085i \(0.845664\pi\)
\(558\) 0 0
\(559\) −3.00000 + 2.00000i −0.126886 + 0.0845910i
\(560\) 0 0
\(561\) 15.0000i 0.633300i
\(562\) 10.0000 0.421825
\(563\) −9.00000 −0.379305 −0.189652 0.981851i \(-0.560736\pi\)
−0.189652 + 0.981851i \(0.560736\pi\)
\(564\) 8.00000i 0.336861i
\(565\) 18.0000i 0.757266i
\(566\) 14.0000i 0.588464i
\(567\) 0 0
\(568\) −10.0000 −0.419591
\(569\) −30.0000 −1.25767 −0.628833 0.777541i \(-0.716467\pi\)
−0.628833 + 0.777541i \(0.716467\pi\)
\(570\) 3.00000i 0.125656i
\(571\) 32.0000 1.33916 0.669579 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) −10.0000 15.0000i −0.418121 0.627182i
\(573\) −17.0000 −0.710185
\(574\) 0 0
\(575\) 4.00000 0.166812
\(576\) −1.00000 −0.0416667
\(577\) 38.0000i 1.58196i 0.611842 + 0.790980i \(0.290429\pi\)
−0.611842 + 0.790980i \(0.709571\pi\)
\(578\) 8.00000i 0.332756i
\(579\) 16.0000i 0.664937i
\(580\) 15.0000i 0.622841i
\(581\) 0 0
\(582\) 2.00000 0.0829027
\(583\) 70.0000i 2.89910i
\(584\) −11.0000 −0.455183
\(585\) −6.00000 9.00000i −0.248069 0.372104i
\(586\) 6.00000 0.247858
\(587\) 8.00000i 0.330195i 0.986277 + 0.165098i \(0.0527939\pi\)
−0.986277 + 0.165098i \(0.947206\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 42.0000i 1.72911i
\(591\) 2.00000i 0.0822690i
\(592\) 7.00000i 0.287698i
\(593\) 24.0000i 0.985562i −0.870153 0.492781i \(-0.835980\pi\)
0.870153 0.492781i \(-0.164020\pi\)
\(594\) −5.00000 −0.205152
\(595\) 0 0
\(596\) 6.00000i 0.245770i
\(597\) −5.00000 −0.204636
\(598\) 2.00000 + 3.00000i 0.0817861 + 0.122679i
\(599\) −45.0000 −1.83865 −0.919325 0.393499i \(-0.871265\pi\)
−0.919325 + 0.393499i \(0.871265\pi\)
\(600\) 4.00000i 0.163299i
\(601\) 48.0000 1.95796 0.978980 0.203954i \(-0.0653794\pi\)
0.978980 + 0.203954i \(0.0653794\pi\)
\(602\) 0 0
\(603\) 8.00000i 0.325785i
\(604\) 15.0000i 0.610341i
\(605\) 42.0000i 1.70754i
\(606\) 18.0000i 0.731200i
\(607\) −23.0000 −0.933541 −0.466771 0.884378i \(-0.654583\pi\)
−0.466771 + 0.884378i \(0.654583\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 0 0
\(610\) −9.00000 −0.364399
\(611\) 16.0000 + 24.0000i 0.647291 + 0.970936i
\(612\) 3.00000 0.121268
\(613\) 39.0000i 1.57520i 0.616190 + 0.787598i \(0.288675\pi\)
−0.616190 + 0.787598i \(0.711325\pi\)
\(614\) 8.00000 0.322854
\(615\) 0 0
\(616\) 0 0
\(617\) 17.0000i 0.684394i 0.939628 + 0.342197i \(0.111171\pi\)
−0.939628 + 0.342197i \(0.888829\pi\)
\(618\) 11.0000i 0.442485i
\(619\) 11.0000i 0.442127i −0.975259 0.221064i \(-0.929047\pi\)
0.975259 0.221064i \(-0.0709529\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 8.00000i 0.320771i
\(623\) 0 0
\(624\) −3.00000 + 2.00000i −0.120096 + 0.0800641i
\(625\) −29.0000 −1.16000
\(626\) 6.00000i 0.239808i
\(627\) −5.00000 −0.199681
\(628\) 13.0000 0.518756
\(629\) 21.0000i 0.837325i
\(630\) 0 0
\(631\) 35.0000i 1.39333i −0.717398 0.696664i \(-0.754667\pi\)
0.717398 0.696664i \(-0.245333\pi\)
\(632\) 0 0
\(633\) 13.0000 0.516704
\(634\) −8.00000 −0.317721
\(635\) 36.0000i 1.42862i
\(636\) 14.0000 0.555136
\(637\) 0 0
\(638\) 25.0000 0.989759
\(639\) 10.0000i 0.395594i
\(640\) 3.00000 0.118585
\(641\) −8.00000 −0.315981 −0.157991 0.987441i \(-0.550502\pi\)
−0.157991 + 0.987441i \(0.550502\pi\)
\(642\) 18.0000i 0.710403i
\(643\) 19.0000i 0.749287i −0.927169 0.374643i \(-0.877765\pi\)
0.927169 0.374643i \(-0.122235\pi\)
\(644\) 0 0
\(645\) 3.00000i 0.118125i
\(646\) 3.00000 0.118033
\(647\) 2.00000 0.0786281 0.0393141 0.999227i \(-0.487483\pi\)
0.0393141 + 0.999227i \(0.487483\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −70.0000 −2.74774
\(650\) 8.00000 + 12.0000i 0.313786 + 0.470679i
\(651\) 0 0
\(652\) 4.00000i 0.156652i
\(653\) −1.00000 −0.0391330 −0.0195665 0.999809i \(-0.506229\pi\)
−0.0195665 + 0.999809i \(0.506229\pi\)
\(654\) 9.00000 0.351928
\(655\) 21.0000i 0.820538i
\(656\) 0 0
\(657\) 11.0000i 0.429151i
\(658\) 0 0
\(659\) −30.0000 −1.16863 −0.584317 0.811525i \(-0.698638\pi\)
−0.584317 + 0.811525i \(0.698638\pi\)
\(660\) 15.0000 0.583874
\(661\) 50.0000i 1.94477i 0.233373 + 0.972387i \(0.425024\pi\)
−0.233373 + 0.972387i \(0.574976\pi\)
\(662\) −20.0000 −0.777322
\(663\) 9.00000 6.00000i 0.349531 0.233021i
\(664\) −6.00000 −0.232845
\(665\) 0 0
\(666\) 7.00000 0.271244
\(667\) −5.00000 −0.193601
\(668\) 7.00000i 0.270838i
\(669\) 16.0000i 0.618596i
\(670\) 24.0000i 0.927201i
\(671\) 15.0000i 0.579069i
\(672\) 0 0
\(673\) −11.0000 −0.424019 −0.212009 0.977268i \(-0.568001\pi\)
−0.212009 + 0.977268i \(0.568001\pi\)
\(674\) 33.0000i 1.27111i
\(675\) 4.00000 0.153960
\(676\) −5.00000 + 12.0000i −0.192308 + 0.461538i
\(677\) −8.00000 −0.307465 −0.153732 0.988113i \(-0.549129\pi\)
−0.153732 + 0.988113i \(0.549129\pi\)
\(678\) 6.00000i 0.230429i
\(679\) 0 0
\(680\) −9.00000 −0.345134
\(681\) 8.00000i 0.306561i
\(682\) 0 0
\(683\) 1.00000i 0.0382639i −0.999817 0.0191320i \(-0.993910\pi\)
0.999817 0.0191320i \(-0.00609027\pi\)
\(684\) 1.00000i 0.0382360i
\(685\) −9.00000 −0.343872
\(686\) 0 0
\(687\) 26.0000i 0.991962i
\(688\) −1.00000 −0.0381246
\(689\) 42.0000 28.0000i 1.60007 1.06672i
\(690\) −3.00000 −0.114208
\(691\) 40.0000i 1.52167i −0.648944 0.760836i \(-0.724789\pi\)
0.648944 0.760836i \(-0.275211\pi\)
\(692\) −26.0000 −0.988372
\(693\) 0 0
\(694\) 28.0000i 1.06287i
\(695\) 60.0000i 2.27593i
\(696\) 5.00000i 0.189525i
\(697\) 0 0
\(698\) −16.0000 −0.605609
\(699\) −14.0000 −0.529529
\(700\) 0 0
\(701\) 2.00000 0.0755390 0.0377695 0.999286i \(-0.487975\pi\)
0.0377695 + 0.999286i \(0.487975\pi\)
\(702\) 2.00000 + 3.00000i 0.0754851 + 0.113228i
\(703\) 7.00000 0.264010
\(704\) 5.00000i 0.188445i
\(705\) −24.0000 −0.903892
\(706\) −24.0000 −0.903252
\(707\) 0 0
\(708\) 14.0000i 0.526152i
\(709\) 26.0000i 0.976450i 0.872718 + 0.488225i \(0.162356\pi\)
−0.872718 + 0.488225i \(0.837644\pi\)
\(710\) 30.0000i 1.12588i
\(711\) 0 0
\(712\) 16.0000 0.599625
\(713\) 0 0
\(714\) 0 0
\(715\) 45.0000 30.0000i 1.68290 1.12194i
\(716\) −10.0000 −0.373718
\(717\) 4.00000i 0.149383i
\(718\) −34.0000 −1.26887
\(719\) 20.0000 0.745874 0.372937 0.927857i \(-0.378351\pi\)
0.372937 + 0.927857i \(0.378351\pi\)
\(720\) 3.00000i 0.111803i
\(721\) 0 0
\(722\) 18.0000i 0.669891i
\(723\) 10.0000i 0.371904i
\(724\) 2.00000 0.0743294
\(725\) −20.0000 −0.742781
\(726\) 14.0000i 0.519589i
\(727\) 7.00000 0.259616 0.129808 0.991539i \(-0.458564\pi\)
0.129808 + 0.991539i \(0.458564\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 33.0000i 1.22138i
\(731\) 3.00000 0.110959
\(732\) 3.00000 0.110883
\(733\) 36.0000i 1.32969i 0.746981 + 0.664845i \(0.231502\pi\)
−0.746981 + 0.664845i \(0.768498\pi\)
\(734\) 32.0000i 1.18114i
\(735\) 0 0
\(736\) 1.00000i 0.0368605i
\(737\) 40.0000 1.47342
\(738\) 0 0
\(739\) 24.0000i 0.882854i −0.897297 0.441427i \(-0.854472\pi\)
0.897297 0.441427i \(-0.145528\pi\)
\(740\) −21.0000 −0.771975
\(741\) 2.00000 + 3.00000i 0.0734718 + 0.110208i
\(742\) 0 0
\(743\) 4.00000i 0.146746i 0.997305 + 0.0733729i \(0.0233763\pi\)
−0.997305 + 0.0733729i \(0.976624\pi\)
\(744\) 0 0
\(745\) 18.0000 0.659469
\(746\) 26.0000i 0.951928i
\(747\) 6.00000i 0.219529i
\(748\) 15.0000i 0.548454i
\(749\) 0 0
\(750\) 3.00000 0.109545
\(751\) −48.0000 −1.75154 −0.875772 0.482724i \(-0.839647\pi\)
−0.875772 + 0.482724i \(0.839647\pi\)
\(752\) 8.00000i 0.291730i
\(753\) 17.0000 0.619514
\(754\) −10.0000 15.0000i −0.364179 0.546268i
\(755\) −45.0000 −1.63772
\(756\) 0 0
\(757\) 18.0000 0.654221 0.327111 0.944986i \(-0.393925\pi\)
0.327111 + 0.944986i \(0.393925\pi\)
\(758\) −4.00000 −0.145287
\(759\) 5.00000i 0.181489i
\(760\) 3.00000i 0.108821i
\(761\) 30.0000i 1.08750i 0.839248 + 0.543750i \(0.182996\pi\)
−0.839248 + 0.543750i \(0.817004\pi\)
\(762\) 12.0000i 0.434714i
\(763\) 0 0
\(764\) −17.0000 −0.615038
\(765\) 9.00000i 0.325396i
\(766\) 31.0000 1.12008
\(767\) 28.0000 + 42.0000i 1.01102 + 1.51653i
\(768\) −1.00000 −0.0360844
\(769\) 1.00000i 0.0360609i −0.999837 0.0180305i \(-0.994260\pi\)
0.999837 0.0180305i \(-0.00573959\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) 16.0000i 0.575853i
\(773\) 9.00000i 0.323708i −0.986815 0.161854i \(-0.948253\pi\)
0.986815 0.161854i \(-0.0517473\pi\)
\(774\) 1.00000i 0.0359443i
\(775\) 0 0
\(776\) 2.00000 0.0717958
\(777\) 0 0
\(778\) 30.0000i 1.07555i
\(779\) 0 0
\(780\) −6.00000 9.00000i −0.214834 0.322252i
\(781\) −50.0000 −1.78914
\(782\) 3.00000i 0.107280i
\(783\) −5.00000 −0.178685
\(784\) 0 0
\(785\) 39.0000i 1.39197i
\(786\) 7.00000i 0.249682i
\(787\) 13.0000i 0.463400i 0.972787 + 0.231700i \(0.0744288\pi\)
−0.972787 + 0.231700i \(0.925571\pi\)
\(788\) 2.00000i 0.0712470i
\(789\) −24.0000 −0.854423
\(790\) 0 0
\(791\) 0 0
\(792\) −5.00000 −0.177667
\(793\) 9.00000 6.00000i 0.319599 0.213066i
\(794\) −12.0000