Properties

Label 930.2.h.a.371.3
Level $930$
Weight $2$
Character 930.371
Analytic conductor $7.426$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{6})\)
Defining polynomial: \( x^{4} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 371.3
Root \(-1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 930.371
Dual form 930.2.h.a.371.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-1.22474 + 1.22474i) q^{3} -1.00000 q^{4} -1.00000i q^{5} +(-1.22474 - 1.22474i) q^{6} -4.00000 q^{7} -1.00000i q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-1.22474 + 1.22474i) q^{3} -1.00000 q^{4} -1.00000i q^{5} +(-1.22474 - 1.22474i) q^{6} -4.00000 q^{7} -1.00000i q^{8} -3.00000i q^{9} +1.00000 q^{10} -4.89898 q^{11} +(1.22474 - 1.22474i) q^{12} +2.44949i q^{13} -4.00000i q^{14} +(1.22474 + 1.22474i) q^{15} +1.00000 q^{16} +7.34847 q^{17} +3.00000 q^{18} -2.00000 q^{19} +1.00000i q^{20} +(4.89898 - 4.89898i) q^{21} -4.89898i q^{22} +7.34847 q^{23} +(1.22474 + 1.22474i) q^{24} -1.00000 q^{25} -2.44949 q^{26} +(3.67423 + 3.67423i) q^{27} +4.00000 q^{28} +(-1.22474 + 1.22474i) q^{30} +(5.00000 + 2.44949i) q^{31} +1.00000i q^{32} +(6.00000 - 6.00000i) q^{33} +7.34847i q^{34} +4.00000i q^{35} +3.00000i q^{36} -2.44949i q^{37} -2.00000i q^{38} +(-3.00000 - 3.00000i) q^{39} -1.00000 q^{40} -12.0000i q^{41} +(4.89898 + 4.89898i) q^{42} -2.44949i q^{43} +4.89898 q^{44} -3.00000 q^{45} +7.34847i q^{46} -12.0000i q^{47} +(-1.22474 + 1.22474i) q^{48} +9.00000 q^{49} -1.00000i q^{50} +(-9.00000 + 9.00000i) q^{51} -2.44949i q^{52} +2.44949 q^{53} +(-3.67423 + 3.67423i) q^{54} +4.89898i q^{55} +4.00000i q^{56} +(2.44949 - 2.44949i) q^{57} +6.00000i q^{59} +(-1.22474 - 1.22474i) q^{60} +(-2.44949 + 5.00000i) q^{62} +12.0000i q^{63} -1.00000 q^{64} +2.44949 q^{65} +(6.00000 + 6.00000i) q^{66} +4.00000 q^{67} -7.34847 q^{68} +(-9.00000 + 9.00000i) q^{69} -4.00000 q^{70} -3.00000 q^{72} -2.44949i q^{73} +2.44949 q^{74} +(1.22474 - 1.22474i) q^{75} +2.00000 q^{76} +19.5959 q^{77} +(3.00000 - 3.00000i) q^{78} +4.89898i q^{79} -1.00000i q^{80} -9.00000 q^{81} +12.0000 q^{82} -12.2474 q^{83} +(-4.89898 + 4.89898i) q^{84} -7.34847i q^{85} +2.44949 q^{86} +4.89898i q^{88} +4.89898 q^{89} -3.00000i q^{90} -9.79796i q^{91} -7.34847 q^{92} +(-9.12372 + 3.12372i) q^{93} +12.0000 q^{94} +2.00000i q^{95} +(-1.22474 - 1.22474i) q^{96} +14.0000 q^{97} +9.00000i q^{98} +14.6969i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{4} - 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{4} - 16 q^{7} + 4 q^{10} + 4 q^{16} + 12 q^{18} - 8 q^{19} - 4 q^{25} + 16 q^{28} + 20 q^{31} + 24 q^{33} - 12 q^{39} - 4 q^{40} - 12 q^{45} + 36 q^{49} - 36 q^{51} - 4 q^{64} + 24 q^{66} + 16 q^{67} - 36 q^{69} - 16 q^{70} - 12 q^{72} + 8 q^{76} + 12 q^{78} - 36 q^{81} + 48 q^{82} - 12 q^{93} + 48 q^{94} + 56 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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
\(3\) −1.22474 + 1.22474i −0.707107 + 0.707107i
\(4\) −1.00000 −0.500000
\(5\) 1.00000i 0.447214i
\(6\) −1.22474 1.22474i −0.500000 0.500000i
\(7\) −4.00000 −1.51186 −0.755929 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 3.00000i 1.00000i
\(10\) 1.00000 0.316228
\(11\) −4.89898 −1.47710 −0.738549 0.674200i \(-0.764489\pi\)
−0.738549 + 0.674200i \(0.764489\pi\)
\(12\) 1.22474 1.22474i 0.353553 0.353553i
\(13\) 2.44949i 0.679366i 0.940540 + 0.339683i \(0.110320\pi\)
−0.940540 + 0.339683i \(0.889680\pi\)
\(14\) 4.00000i 1.06904i
\(15\) 1.22474 + 1.22474i 0.316228 + 0.316228i
\(16\) 1.00000 0.250000
\(17\) 7.34847 1.78227 0.891133 0.453743i \(-0.149911\pi\)
0.891133 + 0.453743i \(0.149911\pi\)
\(18\) 3.00000 0.707107
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 1.00000i 0.223607i
\(21\) 4.89898 4.89898i 1.06904 1.06904i
\(22\) 4.89898i 1.04447i
\(23\) 7.34847 1.53226 0.766131 0.642685i \(-0.222179\pi\)
0.766131 + 0.642685i \(0.222179\pi\)
\(24\) 1.22474 + 1.22474i 0.250000 + 0.250000i
\(25\) −1.00000 −0.200000
\(26\) −2.44949 −0.480384
\(27\) 3.67423 + 3.67423i 0.707107 + 0.707107i
\(28\) 4.00000 0.755929
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) −1.22474 + 1.22474i −0.223607 + 0.223607i
\(31\) 5.00000 + 2.44949i 0.898027 + 0.439941i
\(32\) 1.00000i 0.176777i
\(33\) 6.00000 6.00000i 1.04447 1.04447i
\(34\) 7.34847i 1.26025i
\(35\) 4.00000i 0.676123i
\(36\) 3.00000i 0.500000i
\(37\) 2.44949i 0.402694i −0.979520 0.201347i \(-0.935468\pi\)
0.979520 0.201347i \(-0.0645318\pi\)
\(38\) 2.00000i 0.324443i
\(39\) −3.00000 3.00000i −0.480384 0.480384i
\(40\) −1.00000 −0.158114
\(41\) 12.0000i 1.87409i −0.349215 0.937043i \(-0.613552\pi\)
0.349215 0.937043i \(-0.386448\pi\)
\(42\) 4.89898 + 4.89898i 0.755929 + 0.755929i
\(43\) 2.44949i 0.373544i −0.982403 0.186772i \(-0.940197\pi\)
0.982403 0.186772i \(-0.0598025\pi\)
\(44\) 4.89898 0.738549
\(45\) −3.00000 −0.447214
\(46\) 7.34847i 1.08347i
\(47\) 12.0000i 1.75038i −0.483779 0.875190i \(-0.660736\pi\)
0.483779 0.875190i \(-0.339264\pi\)
\(48\) −1.22474 + 1.22474i −0.176777 + 0.176777i
\(49\) 9.00000 1.28571
\(50\) 1.00000i 0.141421i
\(51\) −9.00000 + 9.00000i −1.26025 + 1.26025i
\(52\) 2.44949i 0.339683i
\(53\) 2.44949 0.336463 0.168232 0.985747i \(-0.446194\pi\)
0.168232 + 0.985747i \(0.446194\pi\)
\(54\) −3.67423 + 3.67423i −0.500000 + 0.500000i
\(55\) 4.89898i 0.660578i
\(56\) 4.00000i 0.534522i
\(57\) 2.44949 2.44949i 0.324443 0.324443i
\(58\) 0 0
\(59\) 6.00000i 0.781133i 0.920575 + 0.390567i \(0.127721\pi\)
−0.920575 + 0.390567i \(0.872279\pi\)
\(60\) −1.22474 1.22474i −0.158114 0.158114i
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) −2.44949 + 5.00000i −0.311086 + 0.635001i
\(63\) 12.0000i 1.51186i
\(64\) −1.00000 −0.125000
\(65\) 2.44949 0.303822
\(66\) 6.00000 + 6.00000i 0.738549 + 0.738549i
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) −7.34847 −0.891133
\(69\) −9.00000 + 9.00000i −1.08347 + 1.08347i
\(70\) −4.00000 −0.478091
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −3.00000 −0.353553
\(73\) 2.44949i 0.286691i −0.989673 0.143346i \(-0.954214\pi\)
0.989673 0.143346i \(-0.0457860\pi\)
\(74\) 2.44949 0.284747
\(75\) 1.22474 1.22474i 0.141421 0.141421i
\(76\) 2.00000 0.229416
\(77\) 19.5959 2.23316
\(78\) 3.00000 3.00000i 0.339683 0.339683i
\(79\) 4.89898i 0.551178i 0.961276 + 0.275589i \(0.0888729\pi\)
−0.961276 + 0.275589i \(0.911127\pi\)
\(80\) 1.00000i 0.111803i
\(81\) −9.00000 −1.00000
\(82\) 12.0000 1.32518
\(83\) −12.2474 −1.34433 −0.672166 0.740400i \(-0.734636\pi\)
−0.672166 + 0.740400i \(0.734636\pi\)
\(84\) −4.89898 + 4.89898i −0.534522 + 0.534522i
\(85\) 7.34847i 0.797053i
\(86\) 2.44949 0.264135
\(87\) 0 0
\(88\) 4.89898i 0.522233i
\(89\) 4.89898 0.519291 0.259645 0.965704i \(-0.416394\pi\)
0.259645 + 0.965704i \(0.416394\pi\)
\(90\) 3.00000i 0.316228i
\(91\) 9.79796i 1.02711i
\(92\) −7.34847 −0.766131
\(93\) −9.12372 + 3.12372i −0.946086 + 0.323915i
\(94\) 12.0000 1.23771
\(95\) 2.00000i 0.205196i
\(96\) −1.22474 1.22474i −0.125000 0.125000i
\(97\) 14.0000 1.42148 0.710742 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 9.00000i 0.909137i
\(99\) 14.6969i 1.47710i
\(100\) 1.00000 0.100000
\(101\) 6.00000i 0.597022i −0.954406 0.298511i \(-0.903510\pi\)
0.954406 0.298511i \(-0.0964900\pi\)
\(102\) −9.00000 9.00000i −0.891133 0.891133i
\(103\) 4.00000 0.394132 0.197066 0.980390i \(-0.436859\pi\)
0.197066 + 0.980390i \(0.436859\pi\)
\(104\) 2.44949 0.240192
\(105\) −4.89898 4.89898i −0.478091 0.478091i
\(106\) 2.44949i 0.237915i
\(107\) 12.0000i 1.16008i −0.814587 0.580042i \(-0.803036\pi\)
0.814587 0.580042i \(-0.196964\pi\)
\(108\) −3.67423 3.67423i −0.353553 0.353553i
\(109\) −16.0000 −1.53252 −0.766261 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) −4.89898 −0.467099
\(111\) 3.00000 + 3.00000i 0.284747 + 0.284747i
\(112\) −4.00000 −0.377964
\(113\) 18.0000i 1.69330i 0.532152 + 0.846649i \(0.321383\pi\)
−0.532152 + 0.846649i \(0.678617\pi\)
\(114\) 2.44949 + 2.44949i 0.229416 + 0.229416i
\(115\) 7.34847i 0.685248i
\(116\) 0 0
\(117\) 7.34847 0.679366
\(118\) −6.00000 −0.552345
\(119\) −29.3939 −2.69453
\(120\) 1.22474 1.22474i 0.111803 0.111803i
\(121\) 13.0000 1.18182
\(122\) 0 0
\(123\) 14.6969 + 14.6969i 1.32518 + 1.32518i
\(124\) −5.00000 2.44949i −0.449013 0.219971i
\(125\) 1.00000i 0.0894427i
\(126\) −12.0000 −1.06904
\(127\) 7.34847i 0.652071i −0.945357 0.326036i \(-0.894287\pi\)
0.945357 0.326036i \(-0.105713\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 3.00000 + 3.00000i 0.264135 + 0.264135i
\(130\) 2.44949i 0.214834i
\(131\) 12.0000i 1.04844i −0.851581 0.524222i \(-0.824356\pi\)
0.851581 0.524222i \(-0.175644\pi\)
\(132\) −6.00000 + 6.00000i −0.522233 + 0.522233i
\(133\) 8.00000 0.693688
\(134\) 4.00000i 0.345547i
\(135\) 3.67423 3.67423i 0.316228 0.316228i
\(136\) 7.34847i 0.630126i
\(137\) −12.2474 −1.04637 −0.523185 0.852219i \(-0.675256\pi\)
−0.523185 + 0.852219i \(0.675256\pi\)
\(138\) −9.00000 9.00000i −0.766131 0.766131i
\(139\) 4.89898i 0.415526i −0.978179 0.207763i \(-0.933382\pi\)
0.978179 0.207763i \(-0.0666183\pi\)
\(140\) 4.00000i 0.338062i
\(141\) 14.6969 + 14.6969i 1.23771 + 1.23771i
\(142\) 0 0
\(143\) 12.0000i 1.00349i
\(144\) 3.00000i 0.250000i
\(145\) 0 0
\(146\) 2.44949 0.202721
\(147\) −11.0227 + 11.0227i −0.909137 + 0.909137i
\(148\) 2.44949i 0.201347i
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 1.22474 + 1.22474i 0.100000 + 0.100000i
\(151\) 14.6969i 1.19602i −0.801489 0.598010i \(-0.795958\pi\)
0.801489 0.598010i \(-0.204042\pi\)
\(152\) 2.00000i 0.162221i
\(153\) 22.0454i 1.78227i
\(154\) 19.5959i 1.57908i
\(155\) 2.44949 5.00000i 0.196748 0.401610i
\(156\) 3.00000 + 3.00000i 0.240192 + 0.240192i
\(157\) 10.0000 0.798087 0.399043 0.916932i \(-0.369342\pi\)
0.399043 + 0.916932i \(0.369342\pi\)
\(158\) −4.89898 −0.389742
\(159\) −3.00000 + 3.00000i −0.237915 + 0.237915i
\(160\) 1.00000 0.0790569
\(161\) −29.3939 −2.31656
\(162\) 9.00000i 0.707107i
\(163\) 20.0000 1.56652 0.783260 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) 12.0000i 0.937043i
\(165\) −6.00000 6.00000i −0.467099 0.467099i
\(166\) 12.2474i 0.950586i
\(167\) 7.34847 0.568642 0.284321 0.958729i \(-0.408232\pi\)
0.284321 + 0.958729i \(0.408232\pi\)
\(168\) −4.89898 4.89898i −0.377964 0.377964i
\(169\) 7.00000 0.538462
\(170\) 7.34847 0.563602
\(171\) 6.00000i 0.458831i
\(172\) 2.44949i 0.186772i
\(173\) 6.00000i 0.456172i 0.973641 + 0.228086i \(0.0732467\pi\)
−0.973641 + 0.228086i \(0.926753\pi\)
\(174\) 0 0
\(175\) 4.00000 0.302372
\(176\) −4.89898 −0.369274
\(177\) −7.34847 7.34847i −0.552345 0.552345i
\(178\) 4.89898i 0.367194i
\(179\) −14.6969 −1.09850 −0.549250 0.835658i \(-0.685087\pi\)
−0.549250 + 0.835658i \(0.685087\pi\)
\(180\) 3.00000 0.223607
\(181\) 24.4949i 1.82069i −0.413849 0.910346i \(-0.635816\pi\)
0.413849 0.910346i \(-0.364184\pi\)
\(182\) 9.79796 0.726273
\(183\) 0 0
\(184\) 7.34847i 0.541736i
\(185\) −2.44949 −0.180090
\(186\) −3.12372 9.12372i −0.229043 0.668984i
\(187\) −36.0000 −2.63258
\(188\) 12.0000i 0.875190i
\(189\) −14.6969 14.6969i −1.06904 1.06904i
\(190\) −2.00000 −0.145095
\(191\) 18.0000i 1.30243i −0.758891 0.651217i \(-0.774259\pi\)
0.758891 0.651217i \(-0.225741\pi\)
\(192\) 1.22474 1.22474i 0.0883883 0.0883883i
\(193\) −2.00000 −0.143963 −0.0719816 0.997406i \(-0.522932\pi\)
−0.0719816 + 0.997406i \(0.522932\pi\)
\(194\) 14.0000i 1.00514i
\(195\) −3.00000 + 3.00000i −0.214834 + 0.214834i
\(196\) −9.00000 −0.642857
\(197\) 22.0454 1.57067 0.785335 0.619071i \(-0.212491\pi\)
0.785335 + 0.619071i \(0.212491\pi\)
\(198\) −14.6969 −1.04447
\(199\) 9.79796i 0.694559i 0.937762 + 0.347279i \(0.112894\pi\)
−0.937762 + 0.347279i \(0.887106\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) −4.89898 + 4.89898i −0.345547 + 0.345547i
\(202\) 6.00000 0.422159
\(203\) 0 0
\(204\) 9.00000 9.00000i 0.630126 0.630126i
\(205\) −12.0000 −0.838116
\(206\) 4.00000i 0.278693i
\(207\) 22.0454i 1.53226i
\(208\) 2.44949i 0.169842i
\(209\) 9.79796 0.677739
\(210\) 4.89898 4.89898i 0.338062 0.338062i
\(211\) 14.0000 0.963800 0.481900 0.876226i \(-0.339947\pi\)
0.481900 + 0.876226i \(0.339947\pi\)
\(212\) −2.44949 −0.168232
\(213\) 0 0
\(214\) 12.0000 0.820303
\(215\) −2.44949 −0.167054
\(216\) 3.67423 3.67423i 0.250000 0.250000i
\(217\) −20.0000 9.79796i −1.35769 0.665129i
\(218\) 16.0000i 1.08366i
\(219\) 3.00000 + 3.00000i 0.202721 + 0.202721i
\(220\) 4.89898i 0.330289i
\(221\) 18.0000i 1.21081i
\(222\) −3.00000 + 3.00000i −0.201347 + 0.201347i
\(223\) 26.9444i 1.80433i 0.431392 + 0.902165i \(0.358023\pi\)
−0.431392 + 0.902165i \(0.641977\pi\)
\(224\) 4.00000i 0.267261i
\(225\) 3.00000i 0.200000i
\(226\) −18.0000 −1.19734
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) −2.44949 + 2.44949i −0.162221 + 0.162221i
\(229\) 9.79796i 0.647467i −0.946148 0.323734i \(-0.895062\pi\)
0.946148 0.323734i \(-0.104938\pi\)
\(230\) 7.34847 0.484544
\(231\) −24.0000 + 24.0000i −1.57908 + 1.57908i
\(232\) 0 0
\(233\) 6.00000i 0.393073i −0.980497 0.196537i \(-0.937031\pi\)
0.980497 0.196537i \(-0.0629694\pi\)
\(234\) 7.34847i 0.480384i
\(235\) −12.0000 −0.782794
\(236\) 6.00000i 0.390567i
\(237\) −6.00000 6.00000i −0.389742 0.389742i
\(238\) 29.3939i 1.90532i
\(239\) −14.6969 −0.950666 −0.475333 0.879806i \(-0.657672\pi\)
−0.475333 + 0.879806i \(0.657672\pi\)
\(240\) 1.22474 + 1.22474i 0.0790569 + 0.0790569i
\(241\) 4.89898i 0.315571i 0.987473 + 0.157786i \(0.0504355\pi\)
−0.987473 + 0.157786i \(0.949565\pi\)
\(242\) 13.0000i 0.835672i
\(243\) 11.0227 11.0227i 0.707107 0.707107i
\(244\) 0 0
\(245\) 9.00000i 0.574989i
\(246\) −14.6969 + 14.6969i −0.937043 + 0.937043i
\(247\) 4.89898i 0.311715i
\(248\) 2.44949 5.00000i 0.155543 0.317500i
\(249\) 15.0000 15.0000i 0.950586 0.950586i
\(250\) −1.00000 −0.0632456
\(251\) 9.79796 0.618442 0.309221 0.950990i \(-0.399932\pi\)
0.309221 + 0.950990i \(0.399932\pi\)
\(252\) 12.0000i 0.755929i
\(253\) −36.0000 −2.26330
\(254\) 7.34847 0.461084
\(255\) 9.00000 + 9.00000i 0.563602 + 0.563602i
\(256\) 1.00000 0.0625000
\(257\) 18.0000i 1.12281i −0.827541 0.561405i \(-0.810261\pi\)
0.827541 0.561405i \(-0.189739\pi\)
\(258\) −3.00000 + 3.00000i −0.186772 + 0.186772i
\(259\) 9.79796i 0.608816i
\(260\) −2.44949 −0.151911
\(261\) 0 0
\(262\) 12.0000 0.741362
\(263\) 31.8434 1.96355 0.981773 0.190057i \(-0.0608673\pi\)
0.981773 + 0.190057i \(0.0608673\pi\)
\(264\) −6.00000 6.00000i −0.369274 0.369274i
\(265\) 2.44949i 0.150471i
\(266\) 8.00000i 0.490511i
\(267\) −6.00000 + 6.00000i −0.367194 + 0.367194i
\(268\) −4.00000 −0.244339
\(269\) 4.89898 0.298696 0.149348 0.988785i \(-0.452283\pi\)
0.149348 + 0.988785i \(0.452283\pi\)
\(270\) 3.67423 + 3.67423i 0.223607 + 0.223607i
\(271\) 9.79796i 0.595184i 0.954693 + 0.297592i \(0.0961834\pi\)
−0.954693 + 0.297592i \(0.903817\pi\)
\(272\) 7.34847 0.445566
\(273\) 12.0000 + 12.0000i 0.726273 + 0.726273i
\(274\) 12.2474i 0.739895i
\(275\) 4.89898 0.295420
\(276\) 9.00000 9.00000i 0.541736 0.541736i
\(277\) 17.1464i 1.03023i −0.857121 0.515115i \(-0.827749\pi\)
0.857121 0.515115i \(-0.172251\pi\)
\(278\) 4.89898 0.293821
\(279\) 7.34847 15.0000i 0.439941 0.898027i
\(280\) 4.00000 0.239046
\(281\) 6.00000i 0.357930i 0.983855 + 0.178965i \(0.0572749\pi\)
−0.983855 + 0.178965i \(0.942725\pi\)
\(282\) −14.6969 + 14.6969i −0.875190 + 0.875190i
\(283\) −4.00000 −0.237775 −0.118888 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) 0 0
\(285\) −2.44949 2.44949i −0.145095 0.145095i
\(286\) 12.0000 0.709575
\(287\) 48.0000i 2.83335i
\(288\) 3.00000 0.176777
\(289\) 37.0000 2.17647
\(290\) 0 0
\(291\) −17.1464 + 17.1464i −1.00514 + 1.00514i
\(292\) 2.44949i 0.143346i
\(293\) 6.00000i 0.350524i 0.984522 + 0.175262i \(0.0560772\pi\)
−0.984522 + 0.175262i \(0.943923\pi\)
\(294\) −11.0227 11.0227i −0.642857 0.642857i
\(295\) 6.00000 0.349334
\(296\) −2.44949 −0.142374
\(297\) −18.0000 18.0000i −1.04447 1.04447i
\(298\) 0 0
\(299\) 18.0000i 1.04097i
\(300\) −1.22474 + 1.22474i −0.0707107 + 0.0707107i
\(301\) 9.79796i 0.564745i
\(302\) 14.6969 0.845714
\(303\) 7.34847 + 7.34847i 0.422159 + 0.422159i
\(304\) −2.00000 −0.114708
\(305\) 0 0
\(306\) 22.0454 1.26025
\(307\) 16.0000 0.913168 0.456584 0.889680i \(-0.349073\pi\)
0.456584 + 0.889680i \(0.349073\pi\)
\(308\) −19.5959 −1.11658
\(309\) −4.89898 + 4.89898i −0.278693 + 0.278693i
\(310\) 5.00000 + 2.44949i 0.283981 + 0.139122i
\(311\) 6.00000i 0.340229i −0.985424 0.170114i \(-0.945586\pi\)
0.985424 0.170114i \(-0.0544137\pi\)
\(312\) −3.00000 + 3.00000i −0.169842 + 0.169842i
\(313\) 17.1464i 0.969173i 0.874743 + 0.484587i \(0.161030\pi\)
−0.874743 + 0.484587i \(0.838970\pi\)
\(314\) 10.0000i 0.564333i
\(315\) 12.0000 0.676123
\(316\) 4.89898i 0.275589i
\(317\) 6.00000i 0.336994i −0.985702 0.168497i \(-0.946109\pi\)
0.985702 0.168497i \(-0.0538913\pi\)
\(318\) −3.00000 3.00000i −0.168232 0.168232i
\(319\) 0 0
\(320\) 1.00000i 0.0559017i
\(321\) 14.6969 + 14.6969i 0.820303 + 0.820303i
\(322\) 29.3939i 1.63806i
\(323\) −14.6969 −0.817760
\(324\) 9.00000 0.500000
\(325\) 2.44949i 0.135873i
\(326\) 20.0000i 1.10770i
\(327\) 19.5959 19.5959i 1.08366 1.08366i
\(328\) −12.0000 −0.662589
\(329\) 48.0000i 2.64633i
\(330\) 6.00000 6.00000i 0.330289 0.330289i
\(331\) 24.4949i 1.34636i 0.739478 + 0.673181i \(0.235072\pi\)
−0.739478 + 0.673181i \(0.764928\pi\)
\(332\) 12.2474 0.672166
\(333\) −7.34847 −0.402694
\(334\) 7.34847i 0.402090i
\(335\) 4.00000i 0.218543i
\(336\) 4.89898 4.89898i 0.267261 0.267261i
\(337\) 26.9444i 1.46775i 0.679282 + 0.733877i \(0.262291\pi\)
−0.679282 + 0.733877i \(0.737709\pi\)
\(338\) 7.00000i 0.380750i
\(339\) −22.0454 22.0454i −1.19734 1.19734i
\(340\) 7.34847i 0.398527i
\(341\) −24.4949 12.0000i −1.32647 0.649836i
\(342\) −6.00000 −0.324443
\(343\) −8.00000 −0.431959
\(344\) −2.44949 −0.132068
\(345\) 9.00000 + 9.00000i 0.484544 + 0.484544i
\(346\) −6.00000 −0.322562
\(347\) −17.1464 −0.920468 −0.460234 0.887798i \(-0.652235\pi\)
−0.460234 + 0.887798i \(0.652235\pi\)
\(348\) 0 0
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 4.00000i 0.213809i
\(351\) −9.00000 + 9.00000i −0.480384 + 0.480384i
\(352\) 4.89898i 0.261116i
\(353\) −2.44949 −0.130373 −0.0651866 0.997873i \(-0.520764\pi\)
−0.0651866 + 0.997873i \(0.520764\pi\)
\(354\) 7.34847 7.34847i 0.390567 0.390567i
\(355\) 0 0
\(356\) −4.89898 −0.259645
\(357\) 36.0000 36.0000i 1.90532 1.90532i
\(358\) 14.6969i 0.776757i
\(359\) 24.0000i 1.26667i −0.773877 0.633336i \(-0.781685\pi\)
0.773877 0.633336i \(-0.218315\pi\)
\(360\) 3.00000i 0.158114i
\(361\) −15.0000 −0.789474
\(362\) 24.4949 1.28742
\(363\) −15.9217 + 15.9217i −0.835672 + 0.835672i
\(364\) 9.79796i 0.513553i
\(365\) −2.44949 −0.128212
\(366\) 0 0
\(367\) 26.9444i 1.40649i −0.710950 0.703243i \(-0.751735\pi\)
0.710950 0.703243i \(-0.248265\pi\)
\(368\) 7.34847 0.383065
\(369\) −36.0000 −1.87409
\(370\) 2.44949i 0.127343i
\(371\) −9.79796 −0.508685
\(372\) 9.12372 3.12372i 0.473043 0.161958i
\(373\) 2.00000 0.103556 0.0517780 0.998659i \(-0.483511\pi\)
0.0517780 + 0.998659i \(0.483511\pi\)
\(374\) 36.0000i 1.86152i
\(375\) −1.22474 1.22474i −0.0632456 0.0632456i
\(376\) −12.0000 −0.618853
\(377\) 0 0
\(378\) 14.6969 14.6969i 0.755929 0.755929i
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 2.00000i 0.102598i
\(381\) 9.00000 + 9.00000i 0.461084 + 0.461084i
\(382\) 18.0000 0.920960
\(383\) −26.9444 −1.37679 −0.688397 0.725334i \(-0.741685\pi\)
−0.688397 + 0.725334i \(0.741685\pi\)
\(384\) 1.22474 + 1.22474i 0.0625000 + 0.0625000i
\(385\) 19.5959i 0.998700i
\(386\) 2.00000i 0.101797i
\(387\) −7.34847 −0.373544
\(388\) −14.0000 −0.710742
\(389\) 4.89898 0.248388 0.124194 0.992258i \(-0.460365\pi\)
0.124194 + 0.992258i \(0.460365\pi\)
\(390\) −3.00000 3.00000i −0.151911 0.151911i
\(391\) 54.0000 2.73090
\(392\) 9.00000i 0.454569i
\(393\) 14.6969 + 14.6969i 0.741362 + 0.741362i
\(394\) 22.0454i 1.11063i
\(395\) 4.89898 0.246494
\(396\) 14.6969i 0.738549i
\(397\) −34.0000 −1.70641 −0.853206 0.521575i \(-0.825345\pi\)
−0.853206 + 0.521575i \(0.825345\pi\)
\(398\) −9.79796 −0.491127
\(399\) −9.79796 + 9.79796i −0.490511 + 0.490511i
\(400\) −1.00000 −0.0500000
\(401\) 19.5959 0.978573 0.489287 0.872123i \(-0.337257\pi\)
0.489287 + 0.872123i \(0.337257\pi\)
\(402\) −4.89898 4.89898i −0.244339 0.244339i
\(403\) −6.00000 + 12.2474i −0.298881 + 0.610089i
\(404\) 6.00000i 0.298511i
\(405\) 9.00000i 0.447214i
\(406\) 0 0
\(407\) 12.0000i 0.594818i
\(408\) 9.00000 + 9.00000i 0.445566 + 0.445566i
\(409\) 19.5959i 0.968956i −0.874804 0.484478i \(-0.839010\pi\)
0.874804 0.484478i \(-0.160990\pi\)
\(410\) 12.0000i 0.592638i
\(411\) 15.0000 15.0000i 0.739895 0.739895i
\(412\) −4.00000 −0.197066
\(413\) 24.0000i 1.18096i
\(414\) 22.0454 1.08347
\(415\) 12.2474i 0.601204i
\(416\) −2.44949 −0.120096
\(417\) 6.00000 + 6.00000i 0.293821 + 0.293821i
\(418\) 9.79796i 0.479234i
\(419\) 30.0000i 1.46560i 0.680446 + 0.732798i \(0.261786\pi\)
−0.680446 + 0.732798i \(0.738214\pi\)
\(420\) 4.89898 + 4.89898i 0.239046 + 0.239046i
\(421\) −26.0000 −1.26716 −0.633581 0.773676i \(-0.718416\pi\)
−0.633581 + 0.773676i \(0.718416\pi\)
\(422\) 14.0000i 0.681509i
\(423\) −36.0000 −1.75038
\(424\) 2.44949i 0.118958i
\(425\) −7.34847 −0.356453
\(426\) 0 0
\(427\) 0 0
\(428\) 12.0000i 0.580042i
\(429\) 14.6969 + 14.6969i 0.709575 + 0.709575i
\(430\) 2.44949i 0.118125i
\(431\) 24.0000i 1.15604i −0.816023 0.578020i \(-0.803826\pi\)
0.816023 0.578020i \(-0.196174\pi\)
\(432\) 3.67423 + 3.67423i 0.176777 + 0.176777i
\(433\) 17.1464i 0.824005i 0.911183 + 0.412002i \(0.135170\pi\)
−0.911183 + 0.412002i \(0.864830\pi\)
\(434\) 9.79796 20.0000i 0.470317 0.960031i
\(435\) 0 0
\(436\) 16.0000 0.766261
\(437\) −14.6969 −0.703050
\(438\) −3.00000 + 3.00000i −0.143346 + 0.143346i
\(439\) −8.00000 −0.381819 −0.190910 0.981608i \(-0.561144\pi\)
−0.190910 + 0.981608i \(0.561144\pi\)
\(440\) 4.89898 0.233550
\(441\) 27.0000i 1.28571i
\(442\) −18.0000 −0.856173
\(443\) 24.0000i 1.14027i −0.821549 0.570137i \(-0.806890\pi\)
0.821549 0.570137i \(-0.193110\pi\)
\(444\) −3.00000 3.00000i −0.142374 0.142374i
\(445\) 4.89898i 0.232234i
\(446\) −26.9444 −1.27585
\(447\) 0 0
\(448\) 4.00000 0.188982
\(449\) 29.3939 1.38718 0.693591 0.720369i \(-0.256027\pi\)
0.693591 + 0.720369i \(0.256027\pi\)
\(450\) −3.00000 −0.141421
\(451\) 58.7878i 2.76821i
\(452\) 18.0000i 0.846649i
\(453\) 18.0000 + 18.0000i 0.845714 + 0.845714i
\(454\) 0 0
\(455\) −9.79796 −0.459335
\(456\) −2.44949 2.44949i −0.114708 0.114708i
\(457\) 7.34847i 0.343747i −0.985119 0.171873i \(-0.945018\pi\)
0.985119 0.171873i \(-0.0549820\pi\)
\(458\) 9.79796 0.457829
\(459\) 27.0000 + 27.0000i 1.26025 + 1.26025i
\(460\) 7.34847i 0.342624i
\(461\) 14.6969 0.684505 0.342252 0.939608i \(-0.388810\pi\)
0.342252 + 0.939608i \(0.388810\pi\)
\(462\) −24.0000 24.0000i −1.11658 1.11658i
\(463\) 2.44949i 0.113837i 0.998379 + 0.0569187i \(0.0181276\pi\)
−0.998379 + 0.0569187i \(0.981872\pi\)
\(464\) 0 0
\(465\) 3.12372 + 9.12372i 0.144859 + 0.423103i
\(466\) 6.00000 0.277945
\(467\) 36.0000i 1.66588i 0.553362 + 0.832941i \(0.313345\pi\)
−0.553362 + 0.832941i \(0.686655\pi\)
\(468\) −7.34847 −0.339683
\(469\) −16.0000 −0.738811
\(470\) 12.0000i 0.553519i
\(471\) −12.2474 + 12.2474i −0.564333 + 0.564333i
\(472\) 6.00000 0.276172
\(473\) 12.0000i 0.551761i
\(474\) 6.00000 6.00000i 0.275589 0.275589i
\(475\) 2.00000 0.0917663
\(476\) 29.3939 1.34727
\(477\) 7.34847i 0.336463i
\(478\) 14.6969i 0.672222i
\(479\) 30.0000i 1.37073i −0.728197 0.685367i \(-0.759642\pi\)
0.728197 0.685367i \(-0.240358\pi\)
\(480\) −1.22474 + 1.22474i −0.0559017 + 0.0559017i
\(481\) 6.00000 0.273576
\(482\) −4.89898 −0.223142
\(483\) 36.0000 36.0000i 1.63806 1.63806i
\(484\) −13.0000 −0.590909
\(485\) 14.0000i 0.635707i
\(486\) 11.0227 + 11.0227i 0.500000 + 0.500000i
\(487\) 31.8434i 1.44296i 0.692435 + 0.721480i \(0.256538\pi\)
−0.692435 + 0.721480i \(0.743462\pi\)
\(488\) 0 0
\(489\) −24.4949 + 24.4949i −1.10770 + 1.10770i
\(490\) 9.00000 0.406579
\(491\) 19.5959 0.884351 0.442176 0.896928i \(-0.354207\pi\)
0.442176 + 0.896928i \(0.354207\pi\)
\(492\) −14.6969 14.6969i −0.662589 0.662589i
\(493\) 0 0
\(494\) 4.89898 0.220416
\(495\) 14.6969 0.660578
\(496\) 5.00000 + 2.44949i 0.224507 + 0.109985i
\(497\) 0 0
\(498\) 15.0000 + 15.0000i 0.672166 + 0.672166i
\(499\) 9.79796i 0.438617i −0.975656 0.219308i \(-0.929620\pi\)
0.975656 0.219308i \(-0.0703801\pi\)
\(500\) 1.00000i 0.0447214i
\(501\) −9.00000 + 9.00000i −0.402090 + 0.402090i
\(502\) 9.79796i 0.437304i
\(503\) 24.0000i 1.07011i −0.844818 0.535054i \(-0.820291\pi\)
0.844818 0.535054i \(-0.179709\pi\)
\(504\) 12.0000 0.534522
\(505\) −6.00000 −0.266996
\(506\) 36.0000i 1.60040i
\(507\) −8.57321 + 8.57321i −0.380750 + 0.380750i
\(508\) 7.34847i 0.326036i
\(509\) −39.1918 −1.73715 −0.868574 0.495560i \(-0.834963\pi\)
−0.868574 + 0.495560i \(0.834963\pi\)
\(510\) −9.00000 + 9.00000i −0.398527 + 0.398527i
\(511\) 9.79796i 0.433436i
\(512\) 1.00000i 0.0441942i
\(513\) −7.34847 7.34847i −0.324443 0.324443i
\(514\) 18.0000 0.793946
\(515\) 4.00000i 0.176261i
\(516\) −3.00000 3.00000i −0.132068 0.132068i
\(517\) 58.7878i 2.58548i
\(518\) −9.79796 −0.430498
\(519\) −7.34847 7.34847i −0.322562 0.322562i
\(520\) 2.44949i 0.107417i
\(521\) 18.0000i 0.788594i −0.918983 0.394297i \(-0.870988\pi\)
0.918983 0.394297i \(-0.129012\pi\)
\(522\) 0 0
\(523\) 22.0454i 0.963978i 0.876177 + 0.481989i \(0.160086\pi\)
−0.876177 + 0.481989i \(0.839914\pi\)
\(524\) 12.0000i 0.524222i
\(525\) −4.89898 + 4.89898i −0.213809 + 0.213809i
\(526\) 31.8434i 1.38844i
\(527\) 36.7423 + 18.0000i 1.60052 + 0.784092i
\(528\) 6.00000 6.00000i 0.261116 0.261116i
\(529\) 31.0000 1.34783
\(530\) 2.44949 0.106399
\(531\) 18.0000 0.781133
\(532\) −8.00000 −0.346844
\(533\) 29.3939 1.27319
\(534\) −6.00000 6.00000i −0.259645 0.259645i
\(535\) −12.0000 −0.518805
\(536\) 4.00000i 0.172774i
\(537\) 18.0000 18.0000i 0.776757 0.776757i
\(538\) 4.89898i 0.211210i
\(539\) −44.0908 −1.89913
\(540\) −3.67423 + 3.67423i −0.158114 + 0.158114i
\(541\) −8.00000 −0.343947 −0.171973 0.985102i \(-0.555014\pi\)
−0.171973 + 0.985102i \(0.555014\pi\)
\(542\) −9.79796 −0.420858
\(543\) 30.0000 + 30.0000i 1.28742 + 1.28742i
\(544\) 7.34847i 0.315063i
\(545\) 16.0000i 0.685365i
\(546\) −12.0000 + 12.0000i −0.513553 + 0.513553i
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) 12.2474 0.523185
\(549\) 0 0
\(550\) 4.89898i 0.208893i
\(551\) 0 0
\(552\) 9.00000 + 9.00000i 0.383065 + 0.383065i
\(553\) 19.5959i 0.833303i
\(554\) 17.1464 0.728482
\(555\) 3.00000 3.00000i 0.127343 0.127343i
\(556\) 4.89898i 0.207763i
\(557\) 26.9444 1.14167 0.570835 0.821065i \(-0.306620\pi\)
0.570835 + 0.821065i \(0.306620\pi\)
\(558\) 15.0000 + 7.34847i 0.635001 + 0.311086i
\(559\) 6.00000 0.253773
\(560\) 4.00000i 0.169031i
\(561\) 44.0908 44.0908i 1.86152 1.86152i
\(562\) −6.00000 −0.253095
\(563\) 12.0000i 0.505740i −0.967500 0.252870i \(-0.918626\pi\)
0.967500 0.252870i \(-0.0813744\pi\)
\(564\) −14.6969 14.6969i −0.618853 0.618853i
\(565\) 18.0000 0.757266
\(566\) 4.00000i 0.168133i
\(567\) 36.0000 1.51186
\(568\) 0 0
\(569\) 19.5959 0.821504 0.410752 0.911747i \(-0.365266\pi\)
0.410752 + 0.911747i \(0.365266\pi\)
\(570\) 2.44949 2.44949i 0.102598 0.102598i
\(571\) 44.0908i 1.84514i −0.385826 0.922572i \(-0.626083\pi\)
0.385826 0.922572i \(-0.373917\pi\)
\(572\) 12.0000i 0.501745i
\(573\) 22.0454 + 22.0454i 0.920960 + 0.920960i
\(574\) −48.0000 −2.00348
\(575\) −7.34847 −0.306452
\(576\) 3.00000i 0.125000i
\(577\) −26.0000 −1.08239 −0.541197 0.840896i \(-0.682029\pi\)
−0.541197 + 0.840896i \(0.682029\pi\)
\(578\) 37.0000i 1.53900i
\(579\) 2.44949 2.44949i 0.101797 0.101797i
\(580\) 0 0
\(581\) 48.9898 2.03244
\(582\) −17.1464 17.1464i −0.710742 0.710742i
\(583\) −12.0000 −0.496989
\(584\) −2.44949 −0.101361
\(585\) 7.34847i 0.303822i
\(586\) −6.00000 −0.247858
\(587\) −12.2474 −0.505506 −0.252753 0.967531i \(-0.581336\pi\)
−0.252753 + 0.967531i \(0.581336\pi\)
\(588\) 11.0227 11.0227i 0.454569 0.454569i
\(589\) −10.0000 4.89898i −0.412043 0.201859i
\(590\) 6.00000i 0.247016i
\(591\) −27.0000 + 27.0000i −1.11063 + 1.11063i
\(592\) 2.44949i 0.100673i
\(593\) 6.00000i 0.246390i −0.992382 0.123195i \(-0.960686\pi\)
0.992382 0.123195i \(-0.0393141\pi\)
\(594\) 18.0000 18.0000i 0.738549 0.738549i
\(595\) 29.3939i 1.20503i
\(596\) 0 0
\(597\) −12.0000 12.0000i −0.491127 0.491127i
\(598\) −18.0000 −0.736075
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) −1.22474 1.22474i −0.0500000 0.0500000i
\(601\) 4.89898i 0.199834i 0.994996 + 0.0999168i \(0.0318577\pi\)
−0.994996 + 0.0999168i \(0.968142\pi\)
\(602\) −9.79796 −0.399335
\(603\) 12.0000i 0.488678i
\(604\) 14.6969i 0.598010i
\(605\) 13.0000i 0.528525i
\(606\) −7.34847 + 7.34847i −0.298511 + 0.298511i
\(607\) 4.00000 0.162355 0.0811775 0.996700i \(-0.474132\pi\)
0.0811775 + 0.996700i \(0.474132\pi\)
\(608\) 2.00000i 0.0811107i
\(609\) 0 0
\(610\) 0 0
\(611\) 29.3939 1.18915
\(612\) 22.0454i 0.891133i
\(613\) 41.6413i 1.68188i −0.541130 0.840939i \(-0.682003\pi\)
0.541130 0.840939i \(-0.317997\pi\)
\(614\) 16.0000i 0.645707i
\(615\) 14.6969 14.6969i 0.592638 0.592638i
\(616\) 19.5959i 0.789542i
\(617\) 18.0000i 0.724653i 0.932051 + 0.362326i \(0.118017\pi\)
−0.932051 + 0.362326i \(0.881983\pi\)
\(618\) −4.89898 4.89898i −0.197066 0.197066i
\(619\) 29.3939i 1.18144i −0.806877 0.590720i \(-0.798844\pi\)
0.806877 0.590720i \(-0.201156\pi\)
\(620\) −2.44949 + 5.00000i −0.0983739 + 0.200805i
\(621\) 27.0000 + 27.0000i 1.08347 + 1.08347i
\(622\) 6.00000 0.240578
\(623\) −19.5959 −0.785094
\(624\) −3.00000 3.00000i −0.120096 0.120096i
\(625\) 1.00000 0.0400000
\(626\) −17.1464 −0.685309
\(627\) −12.0000 + 12.0000i −0.479234 + 0.479234i
\(628\) −10.0000 −0.399043
\(629\) 18.0000i 0.717707i
\(630\) 12.0000i 0.478091i
\(631\) 9.79796i 0.390051i −0.980798 0.195025i \(-0.937521\pi\)
0.980798 0.195025i \(-0.0624789\pi\)
\(632\) 4.89898 0.194871
\(633\) −17.1464 + 17.1464i −0.681509 + 0.681509i
\(634\) 6.00000 0.238290
\(635\) −7.34847 −0.291615
\(636\) 3.00000 3.00000i 0.118958 0.118958i
\(637\) 22.0454i 0.873471i
\(638\) 0 0
\(639\) 0 0
\(640\) −1.00000 −0.0395285
\(641\) 4.89898 0.193498 0.0967490 0.995309i \(-0.469156\pi\)
0.0967490 + 0.995309i \(0.469156\pi\)
\(642\) −14.6969 + 14.6969i −0.580042 + 0.580042i
\(643\) 22.0454i 0.869386i 0.900579 + 0.434693i \(0.143143\pi\)
−0.900579 + 0.434693i \(0.856857\pi\)
\(644\) 29.3939 1.15828
\(645\) 3.00000 3.00000i 0.118125 0.118125i
\(646\) 14.6969i 0.578243i
\(647\) −36.7423 −1.44449 −0.722245 0.691637i \(-0.756890\pi\)
−0.722245 + 0.691637i \(0.756890\pi\)
\(648\) 9.00000i 0.353553i
\(649\) 29.3939i 1.15381i
\(650\) 2.44949 0.0960769
\(651\) 36.4949 12.4949i 1.43035 0.489714i
\(652\) −20.0000 −0.783260
\(653\) 42.0000i 1.64359i −0.569785 0.821794i \(-0.692974\pi\)
0.569785 0.821794i \(-0.307026\pi\)
\(654\) 19.5959 + 19.5959i 0.766261 + 0.766261i
\(655\) −12.0000 −0.468879
\(656\) 12.0000i 0.468521i
\(657\) −7.34847 −0.286691
\(658\) −48.0000 −1.87123
\(659\) 36.0000i 1.40236i −0.712984 0.701180i \(-0.752657\pi\)
0.712984 0.701180i \(-0.247343\pi\)
\(660\) 6.00000 + 6.00000i 0.233550 + 0.233550i
\(661\) −4.00000 −0.155582 −0.0777910 0.996970i \(-0.524787\pi\)
−0.0777910 + 0.996970i \(0.524787\pi\)
\(662\) −24.4949 −0.952021
\(663\) −22.0454 22.0454i −0.856173 0.856173i
\(664\) 12.2474i 0.475293i
\(665\) 8.00000i 0.310227i
\(666\) 7.34847i 0.284747i
\(667\) 0 0
\(668\) −7.34847 −0.284321
\(669\) −33.0000 33.0000i −1.27585 1.27585i
\(670\) 4.00000 0.154533
\(671\) 0 0
\(672\) 4.89898 + 4.89898i 0.188982 + 0.188982i
\(673\) 26.9444i 1.03863i 0.854583 + 0.519315i \(0.173813\pi\)
−0.854583 + 0.519315i \(0.826187\pi\)
\(674\) −26.9444 −1.03786
\(675\) −3.67423 3.67423i −0.141421 0.141421i
\(676\) −7.00000 −0.269231
\(677\) −31.8434 −1.22384 −0.611920 0.790920i \(-0.709603\pi\)
−0.611920 + 0.790920i \(0.709603\pi\)
\(678\) 22.0454 22.0454i 0.846649 0.846649i
\(679\) −56.0000 −2.14908
\(680\) −7.34847 −0.281801
\(681\) 0 0
\(682\) 12.0000 24.4949i 0.459504 0.937958i
\(683\) 48.0000i 1.83667i 0.395805 + 0.918334i \(0.370466\pi\)
−0.395805 + 0.918334i \(0.629534\pi\)
\(684\) 6.00000i 0.229416i
\(685\) 12.2474i 0.467951i
\(686\) 8.00000i 0.305441i
\(687\) 12.0000 + 12.0000i 0.457829 + 0.457829i
\(688\) 2.44949i 0.0933859i
\(689\) 6.00000i 0.228582i
\(690\) −9.00000 + 9.00000i −0.342624 + 0.342624i
\(691\) −4.00000 −0.152167 −0.0760836 0.997101i \(-0.524242\pi\)
−0.0760836 + 0.997101i \(0.524242\pi\)
\(692\) 6.00000i 0.228086i
\(693\) 58.7878i 2.23316i
\(694\) 17.1464i 0.650870i
\(695\) −4.89898 −0.185829
\(696\) 0 0
\(697\) 88.1816i 3.34012i
\(698\) 2.00000i 0.0757011i
\(699\) 7.34847 + 7.34847i 0.277945 + 0.277945i
\(700\) −4.00000 −0.151186
\(701\) 36.0000i 1.35970i 0.733351 + 0.679851i \(0.237955\pi\)
−0.733351 + 0.679851i \(0.762045\pi\)
\(702\) −9.00000 9.00000i −0.339683 0.339683i
\(703\) 4.89898i 0.184769i
\(704\) 4.89898 0.184637
\(705\) 14.6969 14.6969i 0.553519 0.553519i
\(706\) 2.44949i 0.0921878i
\(707\) 24.0000i 0.902613i
\(708\) 7.34847 + 7.34847i 0.276172 + 0.276172i
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 14.6969 0.551178
\(712\) 4.89898i 0.183597i
\(713\) 36.7423 + 18.0000i 1.37601 + 0.674105i
\(714\) 36.0000 + 36.0000i 1.34727 + 1.34727i
\(715\) −12.0000 −0.448775
\(716\) 14.6969 0.549250
\(717\) 18.0000 18.0000i 0.672222 0.672222i
\(718\) 24.0000 0.895672
\(719\) 4.89898 0.182701 0.0913506 0.995819i \(-0.470882\pi\)
0.0913506 + 0.995819i \(0.470882\pi\)
\(720\) −3.00000 −0.111803
\(721\) −16.0000 −0.595871
\(722\) 15.0000i 0.558242i
\(723\) −6.00000 6.00000i −0.223142 0.223142i
\(724\) 24.4949i 0.910346i
\(725\) 0 0
\(726\) −15.9217 15.9217i −0.590909 0.590909i
\(727\) 8.00000 0.296704 0.148352 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) −9.79796 −0.363137
\(729\) 27.0000i 1.00000i
\(730\) 2.44949i 0.0906597i
\(731\) 18.0000i 0.665754i
\(732\) 0 0
\(733\) 22.0000 0.812589 0.406294 0.913742i \(-0.366821\pi\)
0.406294 + 0.913742i \(0.366821\pi\)
\(734\) 26.9444 0.994535
\(735\) 11.0227 + 11.0227i 0.406579 + 0.406579i
\(736\) 7.34847i 0.270868i
\(737\) −19.5959 −0.721825
\(738\) 36.0000i 1.32518i
\(739\) 14.6969i 0.540636i 0.962771 + 0.270318i \(0.0871288\pi\)
−0.962771 + 0.270318i \(0.912871\pi\)
\(740\) 2.44949 0.0900450
\(741\) 6.00000 + 6.00000i 0.220416 + 0.220416i
\(742\) 9.79796i 0.359694i
\(743\) −2.44949 −0.0898631 −0.0449315 0.998990i \(-0.514307\pi\)
−0.0449315 + 0.998990i \(0.514307\pi\)
\(744\) 3.12372 + 9.12372i 0.114521 + 0.334492i
\(745\) 0 0
\(746\) 2.00000i 0.0732252i
\(747\) 36.7423i 1.34433i
\(748\) 36.0000 1.31629
\(749\) 48.0000i 1.75388i
\(750\) 1.22474 1.22474i 0.0447214 0.0447214i
\(751\) 10.0000 0.364905 0.182453 0.983215i \(-0.441596\pi\)
0.182453 + 0.983215i \(0.441596\pi\)
\(752\) 12.0000i 0.437595i
\(753\) −12.0000 + 12.0000i −0.437304 + 0.437304i
\(754\) 0 0
\(755\) −14.6969 −0.534876
\(756\) 14.6969 + 14.6969i 0.534522 + 0.534522i
\(757\) 51.4393i 1.86959i 0.355184 + 0.934796i \(0.384418\pi\)
−0.355184 + 0.934796i \(0.615582\pi\)
\(758\) 20.0000i 0.726433i
\(759\) 44.0908 44.0908i 1.60040 1.60040i
\(760\) 2.00000 0.0725476
\(761\) −29.3939 −1.06553 −0.532764 0.846264i \(-0.678847\pi\)
−0.532764 + 0.846264i \(0.678847\pi\)
\(762\) −9.00000 + 9.00000i −0.326036 + 0.326036i
\(763\) 64.0000 2.31696
\(764\) 18.0000i 0.651217i
\(765\) −22.0454 −0.797053
\(766\) 26.9444i 0.973540i
\(767\) −14.6969 −0.530676
\(768\) −1.22474 + 1.22474i −0.0441942 + 0.0441942i
\(769\) −50.0000 −1.80305 −0.901523 0.432731i \(-0.857550\pi\)
−0.901523 + 0.432731i \(0.857550\pi\)
\(770\) 19.5959 0.706188
\(771\) 22.0454 + 22.0454i 0.793946 + 0.793946i
\(772\) 2.00000 0.0719816
\(773\) −46.5403 −1.67394 −0.836969 0.547250i \(-0.815675\pi\)
−0.836969 + 0.547250i \(0.815675\pi\)
\(774\) 7.34847i 0.264135i
\(775\) −5.00000 2.44949i −0.179605 0.0879883i
\(776\) 14.0000i 0.502571i
\(777\) −12.0000 12.0000i −0.430498 0.430498i
\(778\) 4.89898i 0.175637i
\(779\) 24.0000i 0.859889i
\(780\) 3.00000 3.00000i 0.107417 0.107417i
\(781\) 0 0
\(782\) 54.0000i 1.93104i
\(783\) 0 0
\(784\) 9.00000 0.321429
\(785\) 10.0000i 0.356915i
\(786\) −14.6969 + 14.6969i −0.524222 + 0.524222i