Properties

Label 770.2.m.a.43.2
Level $770$
Weight $2$
Character 770.43
Analytic conductor $6.148$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.14848095564\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.2
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 770.43
Dual form 770.2.m.a.197.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-2.00000 + 1.00000i) q^{5} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-2.00000 + 1.00000i) q^{5} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} -3.00000i q^{9} +(-2.12132 - 0.707107i) q^{10} +(-3.00000 - 1.41421i) q^{11} +(-1.41421 + 1.41421i) q^{13} -1.00000i q^{14} -1.00000 q^{16} +(2.12132 - 2.12132i) q^{18} -4.24264 q^{19} +(-1.00000 - 2.00000i) q^{20} +(-1.12132 - 3.12132i) q^{22} +(-2.00000 - 2.00000i) q^{23} +(3.00000 - 4.00000i) q^{25} -2.00000 q^{26} +(0.707107 - 0.707107i) q^{28} -7.07107 q^{29} +(-0.707107 - 0.707107i) q^{32} +(2.12132 + 0.707107i) q^{35} +3.00000 q^{36} +(6.00000 - 6.00000i) q^{37} +(-3.00000 - 3.00000i) q^{38} +(0.707107 - 2.12132i) q^{40} +1.41421i q^{41} +(-5.65685 + 5.65685i) q^{43} +(1.41421 - 3.00000i) q^{44} +(3.00000 + 6.00000i) q^{45} -2.82843i q^{46} +(7.00000 - 7.00000i) q^{47} +1.00000i q^{49} +(4.94975 - 0.707107i) q^{50} +(-1.41421 - 1.41421i) q^{52} +(-4.00000 - 4.00000i) q^{53} +(7.41421 - 0.171573i) q^{55} +1.00000 q^{56} +(-5.00000 - 5.00000i) q^{58} +4.00000i q^{59} +2.82843i q^{61} +(-2.12132 + 2.12132i) q^{63} -1.00000i q^{64} +(1.41421 - 4.24264i) q^{65} +(-3.00000 + 3.00000i) q^{67} +(1.00000 + 2.00000i) q^{70} -8.00000 q^{71} +(2.12132 + 2.12132i) q^{72} +(-4.24264 + 4.24264i) q^{73} +8.48528 q^{74} -4.24264i q^{76} +(1.12132 + 3.12132i) q^{77} +4.24264 q^{79} +(2.00000 - 1.00000i) q^{80} -9.00000 q^{81} +(-1.00000 + 1.00000i) q^{82} +(-8.48528 + 8.48528i) q^{83} -8.00000 q^{86} +(3.12132 - 1.12132i) q^{88} +14.0000i q^{89} +(-2.12132 + 6.36396i) q^{90} +2.00000 q^{91} +(2.00000 - 2.00000i) q^{92} +9.89949 q^{94} +(8.48528 - 4.24264i) q^{95} +(6.00000 - 6.00000i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(-4.24264 + 9.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 8 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 8 q^{5} - 12 q^{11} - 4 q^{16} - 4 q^{20} + 4 q^{22} - 8 q^{23} + 12 q^{25} - 8 q^{26} + 12 q^{36} + 24 q^{37} - 12 q^{38} + 12 q^{45} + 28 q^{47} - 16 q^{53} + 24 q^{55} + 4 q^{56} - 20 q^{58} - 12 q^{67} + 4 q^{70} - 32 q^{71} - 4 q^{77} + 8 q^{80} - 36 q^{81} - 4 q^{82} - 32 q^{86} + 4 q^{88} + 8 q^{91} + 8 q^{92} + 24 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(617\) \(661\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(4\) 1.00000i 0.500000i
\(5\) −2.00000 + 1.00000i −0.894427 + 0.447214i
\(6\) 0 0
\(7\) −0.707107 0.707107i −0.267261 0.267261i
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 3.00000i 1.00000i
\(10\) −2.12132 0.707107i −0.670820 0.223607i
\(11\) −3.00000 1.41421i −0.904534 0.426401i
\(12\) 0 0
\(13\) −1.41421 + 1.41421i −0.392232 + 0.392232i −0.875482 0.483250i \(-0.839456\pi\)
0.483250 + 0.875482i \(0.339456\pi\)
\(14\) 1.00000i 0.267261i
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) 2.12132 2.12132i 0.500000 0.500000i
\(19\) −4.24264 −0.973329 −0.486664 0.873589i \(-0.661786\pi\)
−0.486664 + 0.873589i \(0.661786\pi\)
\(20\) −1.00000 2.00000i −0.223607 0.447214i
\(21\) 0 0
\(22\) −1.12132 3.12132i −0.239066 0.665468i
\(23\) −2.00000 2.00000i −0.417029 0.417029i 0.467150 0.884178i \(-0.345281\pi\)
−0.884178 + 0.467150i \(0.845281\pi\)
\(24\) 0 0
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) −2.00000 −0.392232
\(27\) 0 0
\(28\) 0.707107 0.707107i 0.133631 0.133631i
\(29\) −7.07107 −1.31306 −0.656532 0.754298i \(-0.727977\pi\)
−0.656532 + 0.754298i \(0.727977\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) 0 0
\(34\) 0 0
\(35\) 2.12132 + 0.707107i 0.358569 + 0.119523i
\(36\) 3.00000 0.500000
\(37\) 6.00000 6.00000i 0.986394 0.986394i −0.0135147 0.999909i \(-0.504302\pi\)
0.999909 + 0.0135147i \(0.00430201\pi\)
\(38\) −3.00000 3.00000i −0.486664 0.486664i
\(39\) 0 0
\(40\) 0.707107 2.12132i 0.111803 0.335410i
\(41\) 1.41421i 0.220863i 0.993884 + 0.110432i \(0.0352233\pi\)
−0.993884 + 0.110432i \(0.964777\pi\)
\(42\) 0 0
\(43\) −5.65685 + 5.65685i −0.862662 + 0.862662i −0.991647 0.128984i \(-0.958828\pi\)
0.128984 + 0.991647i \(0.458828\pi\)
\(44\) 1.41421 3.00000i 0.213201 0.452267i
\(45\) 3.00000 + 6.00000i 0.447214 + 0.894427i
\(46\) 2.82843i 0.417029i
\(47\) 7.00000 7.00000i 1.02105 1.02105i 0.0212814 0.999774i \(-0.493225\pi\)
0.999774 0.0212814i \(-0.00677460\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 4.94975 0.707107i 0.700000 0.100000i
\(51\) 0 0
\(52\) −1.41421 1.41421i −0.196116 0.196116i
\(53\) −4.00000 4.00000i −0.549442 0.549442i 0.376837 0.926279i \(-0.377012\pi\)
−0.926279 + 0.376837i \(0.877012\pi\)
\(54\) 0 0
\(55\) 7.41421 0.171573i 0.999732 0.0231349i
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) −5.00000 5.00000i −0.656532 0.656532i
\(59\) 4.00000i 0.520756i 0.965507 + 0.260378i \(0.0838471\pi\)
−0.965507 + 0.260378i \(0.916153\pi\)
\(60\) 0 0
\(61\) 2.82843i 0.362143i 0.983470 + 0.181071i \(0.0579565\pi\)
−0.983470 + 0.181071i \(0.942043\pi\)
\(62\) 0 0
\(63\) −2.12132 + 2.12132i −0.267261 + 0.267261i
\(64\) 1.00000i 0.125000i
\(65\) 1.41421 4.24264i 0.175412 0.526235i
\(66\) 0 0
\(67\) −3.00000 + 3.00000i −0.366508 + 0.366508i −0.866202 0.499694i \(-0.833446\pi\)
0.499694 + 0.866202i \(0.333446\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 1.00000 + 2.00000i 0.119523 + 0.239046i
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 2.12132 + 2.12132i 0.250000 + 0.250000i
\(73\) −4.24264 + 4.24264i −0.496564 + 0.496564i −0.910366 0.413803i \(-0.864200\pi\)
0.413803 + 0.910366i \(0.364200\pi\)
\(74\) 8.48528 0.986394
\(75\) 0 0
\(76\) 4.24264i 0.486664i
\(77\) 1.12132 + 3.12132i 0.127786 + 0.355707i
\(78\) 0 0
\(79\) 4.24264 0.477334 0.238667 0.971101i \(-0.423290\pi\)
0.238667 + 0.971101i \(0.423290\pi\)
\(80\) 2.00000 1.00000i 0.223607 0.111803i
\(81\) −9.00000 −1.00000
\(82\) −1.00000 + 1.00000i −0.110432 + 0.110432i
\(83\) −8.48528 + 8.48528i −0.931381 + 0.931381i −0.997792 0.0664117i \(-0.978845\pi\)
0.0664117 + 0.997792i \(0.478845\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −8.00000 −0.862662
\(87\) 0 0
\(88\) 3.12132 1.12132i 0.332734 0.119533i
\(89\) 14.0000i 1.48400i 0.670402 + 0.741999i \(0.266122\pi\)
−0.670402 + 0.741999i \(0.733878\pi\)
\(90\) −2.12132 + 6.36396i −0.223607 + 0.670820i
\(91\) 2.00000 0.209657
\(92\) 2.00000 2.00000i 0.208514 0.208514i
\(93\) 0 0
\(94\) 9.89949 1.02105
\(95\) 8.48528 4.24264i 0.870572 0.435286i
\(96\) 0 0
\(97\) 6.00000 6.00000i 0.609208 0.609208i −0.333531 0.942739i \(-0.608240\pi\)
0.942739 + 0.333531i \(0.108240\pi\)
\(98\) −0.707107 + 0.707107i −0.0714286 + 0.0714286i
\(99\) −4.24264 + 9.00000i −0.426401 + 0.904534i
\(100\) 4.00000 + 3.00000i 0.400000 + 0.300000i
\(101\) 5.65685i 0.562878i 0.959579 + 0.281439i \(0.0908117\pi\)
−0.959579 + 0.281439i \(0.909188\pi\)
\(102\) 0 0
\(103\) 3.00000 + 3.00000i 0.295599 + 0.295599i 0.839287 0.543688i \(-0.182973\pi\)
−0.543688 + 0.839287i \(0.682973\pi\)
\(104\) 2.00000i 0.196116i
\(105\) 0 0
\(106\) 5.65685i 0.549442i
\(107\) −8.48528 8.48528i −0.820303 0.820303i 0.165848 0.986151i \(-0.446964\pi\)
−0.986151 + 0.165848i \(0.946964\pi\)
\(108\) 0 0
\(109\) 12.7279 1.21911 0.609557 0.792742i \(-0.291347\pi\)
0.609557 + 0.792742i \(0.291347\pi\)
\(110\) 5.36396 + 5.12132i 0.511434 + 0.488299i
\(111\) 0 0
\(112\) 0.707107 + 0.707107i 0.0668153 + 0.0668153i
\(113\) −9.00000 9.00000i −0.846649 0.846649i 0.143065 0.989713i \(-0.454304\pi\)
−0.989713 + 0.143065i \(0.954304\pi\)
\(114\) 0 0
\(115\) 6.00000 + 2.00000i 0.559503 + 0.186501i
\(116\) 7.07107i 0.656532i
\(117\) 4.24264 + 4.24264i 0.392232 + 0.392232i
\(118\) −2.82843 + 2.82843i −0.260378 + 0.260378i
\(119\) 0 0
\(120\) 0 0
\(121\) 7.00000 + 8.48528i 0.636364 + 0.771389i
\(122\) −2.00000 + 2.00000i −0.181071 + 0.181071i
\(123\) 0 0
\(124\) 0 0
\(125\) −2.00000 + 11.0000i −0.178885 + 0.983870i
\(126\) −3.00000 −0.267261
\(127\) 9.89949 + 9.89949i 0.878438 + 0.878438i 0.993373 0.114935i \(-0.0366659\pi\)
−0.114935 + 0.993373i \(0.536666\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 0 0
\(130\) 4.00000 2.00000i 0.350823 0.175412i
\(131\) 1.41421i 0.123560i −0.998090 0.0617802i \(-0.980322\pi\)
0.998090 0.0617802i \(-0.0196778\pi\)
\(132\) 0 0
\(133\) 3.00000 + 3.00000i 0.260133 + 0.260133i
\(134\) −4.24264 −0.366508
\(135\) 0 0
\(136\) 0 0
\(137\) 5.00000 5.00000i 0.427179 0.427179i −0.460487 0.887666i \(-0.652325\pi\)
0.887666 + 0.460487i \(0.152325\pi\)
\(138\) 0 0
\(139\) −18.3848 −1.55938 −0.779688 0.626168i \(-0.784622\pi\)
−0.779688 + 0.626168i \(0.784622\pi\)
\(140\) −0.707107 + 2.12132i −0.0597614 + 0.179284i
\(141\) 0 0
\(142\) −5.65685 5.65685i −0.474713 0.474713i
\(143\) 6.24264 2.24264i 0.522036 0.187539i
\(144\) 3.00000i 0.250000i
\(145\) 14.1421 7.07107i 1.17444 0.587220i
\(146\) −6.00000 −0.496564
\(147\) 0 0
\(148\) 6.00000 + 6.00000i 0.493197 + 0.493197i
\(149\) −9.89949 −0.810998 −0.405499 0.914095i \(-0.632902\pi\)
−0.405499 + 0.914095i \(0.632902\pi\)
\(150\) 0 0
\(151\) 18.3848i 1.49613i −0.663624 0.748066i \(-0.730983\pi\)
0.663624 0.748066i \(-0.269017\pi\)
\(152\) 3.00000 3.00000i 0.243332 0.243332i
\(153\) 0 0
\(154\) −1.41421 + 3.00000i −0.113961 + 0.241747i
\(155\) 0 0
\(156\) 0 0
\(157\) 7.00000 7.00000i 0.558661 0.558661i −0.370265 0.928926i \(-0.620733\pi\)
0.928926 + 0.370265i \(0.120733\pi\)
\(158\) 3.00000 + 3.00000i 0.238667 + 0.238667i
\(159\) 0 0
\(160\) 2.12132 + 0.707107i 0.167705 + 0.0559017i
\(161\) 2.82843i 0.222911i
\(162\) −6.36396 6.36396i −0.500000 0.500000i
\(163\) 1.00000 + 1.00000i 0.0783260 + 0.0783260i 0.745184 0.666858i \(-0.232361\pi\)
−0.666858 + 0.745184i \(0.732361\pi\)
\(164\) −1.41421 −0.110432
\(165\) 0 0
\(166\) −12.0000 −0.931381
\(167\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(168\) 0 0
\(169\) 9.00000i 0.692308i
\(170\) 0 0
\(171\) 12.7279i 0.973329i
\(172\) −5.65685 5.65685i −0.431331 0.431331i
\(173\) 12.7279 12.7279i 0.967686 0.967686i −0.0318080 0.999494i \(-0.510127\pi\)
0.999494 + 0.0318080i \(0.0101265\pi\)
\(174\) 0 0
\(175\) −4.94975 + 0.707107i −0.374166 + 0.0534522i
\(176\) 3.00000 + 1.41421i 0.226134 + 0.106600i
\(177\) 0 0
\(178\) −9.89949 + 9.89949i −0.741999 + 0.741999i
\(179\) 2.00000i 0.149487i −0.997203 0.0747435i \(-0.976186\pi\)
0.997203 0.0747435i \(-0.0238138\pi\)
\(180\) −6.00000 + 3.00000i −0.447214 + 0.223607i
\(181\) 4.00000 0.297318 0.148659 0.988889i \(-0.452504\pi\)
0.148659 + 0.988889i \(0.452504\pi\)
\(182\) 1.41421 + 1.41421i 0.104828 + 0.104828i
\(183\) 0 0
\(184\) 2.82843 0.208514
\(185\) −6.00000 + 18.0000i −0.441129 + 1.32339i
\(186\) 0 0
\(187\) 0 0
\(188\) 7.00000 + 7.00000i 0.510527 + 0.510527i
\(189\) 0 0
\(190\) 9.00000 + 3.00000i 0.652929 + 0.217643i
\(191\) −16.0000 −1.15772 −0.578860 0.815427i \(-0.696502\pi\)
−0.578860 + 0.815427i \(0.696502\pi\)
\(192\) 0 0
\(193\) 7.07107 7.07107i 0.508987 0.508987i −0.405229 0.914215i \(-0.632808\pi\)
0.914215 + 0.405229i \(0.132808\pi\)
\(194\) 8.48528 0.609208
\(195\) 0 0
\(196\) −1.00000 −0.0714286
\(197\) 8.48528 + 8.48528i 0.604551 + 0.604551i 0.941517 0.336966i \(-0.109401\pi\)
−0.336966 + 0.941517i \(0.609401\pi\)
\(198\) −9.36396 + 3.36396i −0.665468 + 0.239066i
\(199\) 22.0000i 1.55954i 0.626067 + 0.779769i \(0.284664\pi\)
−0.626067 + 0.779769i \(0.715336\pi\)
\(200\) 0.707107 + 4.94975i 0.0500000 + 0.350000i
\(201\) 0 0
\(202\) −4.00000 + 4.00000i −0.281439 + 0.281439i
\(203\) 5.00000 + 5.00000i 0.350931 + 0.350931i
\(204\) 0 0
\(205\) −1.41421 2.82843i −0.0987730 0.197546i
\(206\) 4.24264i 0.295599i
\(207\) −6.00000 + 6.00000i −0.417029 + 0.417029i
\(208\) 1.41421 1.41421i 0.0980581 0.0980581i
\(209\) 12.7279 + 6.00000i 0.880409 + 0.415029i
\(210\) 0 0
\(211\) 5.65685i 0.389434i −0.980859 0.194717i \(-0.937621\pi\)
0.980859 0.194717i \(-0.0623788\pi\)
\(212\) 4.00000 4.00000i 0.274721 0.274721i
\(213\) 0 0
\(214\) 12.0000i 0.820303i
\(215\) 5.65685 16.9706i 0.385794 1.15738i
\(216\) 0 0
\(217\) 0 0
\(218\) 9.00000 + 9.00000i 0.609557 + 0.609557i
\(219\) 0 0
\(220\) 0.171573 + 7.41421i 0.0115674 + 0.499866i
\(221\) 0 0
\(222\) 0 0
\(223\) −7.00000 7.00000i −0.468755 0.468755i 0.432756 0.901511i \(-0.357541\pi\)
−0.901511 + 0.432756i \(0.857541\pi\)
\(224\) 1.00000i 0.0668153i
\(225\) −12.0000 9.00000i −0.800000 0.600000i
\(226\) 12.7279i 0.846649i
\(227\) −15.5563 15.5563i −1.03251 1.03251i −0.999453 0.0330577i \(-0.989475\pi\)
−0.0330577 0.999453i \(-0.510525\pi\)
\(228\) 0 0
\(229\) 2.00000i 0.132164i −0.997814 0.0660819i \(-0.978950\pi\)
0.997814 0.0660819i \(-0.0210498\pi\)
\(230\) 2.82843 + 5.65685i 0.186501 + 0.373002i
\(231\) 0 0
\(232\) 5.00000 5.00000i 0.328266 0.328266i
\(233\) 18.3848 18.3848i 1.20443 1.20443i 0.231621 0.972806i \(-0.425597\pi\)
0.972806 0.231621i \(-0.0744028\pi\)
\(234\) 6.00000i 0.392232i
\(235\) −7.00000 + 21.0000i −0.456630 + 1.36989i
\(236\) −4.00000 −0.260378
\(237\) 0 0
\(238\) 0 0
\(239\) −12.7279 −0.823301 −0.411650 0.911342i \(-0.635048\pi\)
−0.411650 + 0.911342i \(0.635048\pi\)
\(240\) 0 0
\(241\) 21.2132i 1.36646i 0.730202 + 0.683231i \(0.239426\pi\)
−0.730202 + 0.683231i \(0.760574\pi\)
\(242\) −1.05025 + 10.9497i −0.0675128 + 0.703876i
\(243\) 0 0
\(244\) −2.82843 −0.181071
\(245\) −1.00000 2.00000i −0.0638877 0.127775i
\(246\) 0 0
\(247\) 6.00000 6.00000i 0.381771 0.381771i
\(248\) 0 0
\(249\) 0 0
\(250\) −9.19239 + 6.36396i −0.581378 + 0.402492i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) −2.12132 2.12132i −0.133631 0.133631i
\(253\) 3.17157 + 8.82843i 0.199395 + 0.555038i
\(254\) 14.0000i 0.878438i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 8.00000 8.00000i 0.499026 0.499026i −0.412108 0.911135i \(-0.635208\pi\)
0.911135 + 0.412108i \(0.135208\pi\)
\(258\) 0 0
\(259\) −8.48528 −0.527250
\(260\) 4.24264 + 1.41421i 0.263117 + 0.0877058i
\(261\) 21.2132i 1.31306i
\(262\) 1.00000 1.00000i 0.0617802 0.0617802i
\(263\) 9.89949 9.89949i 0.610429 0.610429i −0.332629 0.943058i \(-0.607936\pi\)
0.943058 + 0.332629i \(0.107936\pi\)
\(264\) 0 0
\(265\) 12.0000 + 4.00000i 0.737154 + 0.245718i
\(266\) 4.24264i 0.260133i
\(267\) 0 0
\(268\) −3.00000 3.00000i −0.183254 0.183254i
\(269\) 18.0000i 1.09748i −0.835993 0.548740i \(-0.815108\pi\)
0.835993 0.548740i \(-0.184892\pi\)
\(270\) 0 0
\(271\) 31.1127i 1.88996i −0.327125 0.944981i \(-0.606080\pi\)
0.327125 0.944981i \(-0.393920\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 7.07107 0.427179
\(275\) −14.6569 + 7.75736i −0.883842 + 0.467786i
\(276\) 0 0
\(277\) −5.65685 5.65685i −0.339887 0.339887i 0.516437 0.856325i \(-0.327258\pi\)
−0.856325 + 0.516437i \(0.827258\pi\)
\(278\) −13.0000 13.0000i −0.779688 0.779688i
\(279\) 0 0
\(280\) −2.00000 + 1.00000i −0.119523 + 0.0597614i
\(281\) 28.2843i 1.68730i 0.536895 + 0.843649i \(0.319597\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 0 0
\(283\) −4.24264 + 4.24264i −0.252199 + 0.252199i −0.821872 0.569673i \(-0.807070\pi\)
0.569673 + 0.821872i \(0.307070\pi\)
\(284\) 8.00000i 0.474713i
\(285\) 0 0
\(286\) 6.00000 + 2.82843i 0.354787 + 0.167248i
\(287\) 1.00000 1.00000i 0.0590281 0.0590281i
\(288\) −2.12132 + 2.12132i −0.125000 + 0.125000i
\(289\) 17.0000i 1.00000i
\(290\) 15.0000 + 5.00000i 0.880830 + 0.293610i
\(291\) 0 0
\(292\) −4.24264 4.24264i −0.248282 0.248282i
\(293\) −21.2132 + 21.2132i −1.23929 + 1.23929i −0.278996 + 0.960292i \(0.590002\pi\)
−0.960292 + 0.278996i \(0.909998\pi\)
\(294\) 0 0
\(295\) −4.00000 8.00000i −0.232889 0.465778i
\(296\) 8.48528i 0.493197i
\(297\) 0 0
\(298\) −7.00000 7.00000i −0.405499 0.405499i
\(299\) 5.65685 0.327144
\(300\) 0 0
\(301\) 8.00000 0.461112
\(302\) 13.0000 13.0000i 0.748066 0.748066i
\(303\) 0 0
\(304\) 4.24264 0.243332
\(305\) −2.82843 5.65685i −0.161955 0.323911i
\(306\) 0 0
\(307\) −18.3848 18.3848i −1.04927 1.04927i −0.998721 0.0505532i \(-0.983902\pi\)
−0.0505532 0.998721i \(-0.516098\pi\)
\(308\) −3.12132 + 1.12132i −0.177854 + 0.0638932i
\(309\) 0 0
\(310\) 0 0
\(311\) −30.0000 −1.70114 −0.850572 0.525859i \(-0.823744\pi\)
−0.850572 + 0.525859i \(0.823744\pi\)
\(312\) 0 0
\(313\) −12.0000 12.0000i −0.678280 0.678280i 0.281331 0.959611i \(-0.409224\pi\)
−0.959611 + 0.281331i \(0.909224\pi\)
\(314\) 9.89949 0.558661
\(315\) 2.12132 6.36396i 0.119523 0.358569i
\(316\) 4.24264i 0.238667i
\(317\) 8.00000 8.00000i 0.449325 0.449325i −0.445805 0.895130i \(-0.647083\pi\)
0.895130 + 0.445805i \(0.147083\pi\)
\(318\) 0 0
\(319\) 21.2132 + 10.0000i 1.18771 + 0.559893i
\(320\) 1.00000 + 2.00000i 0.0559017 + 0.111803i
\(321\) 0 0
\(322\) −2.00000 + 2.00000i −0.111456 + 0.111456i
\(323\) 0 0
\(324\) 9.00000i 0.500000i
\(325\) 1.41421 + 9.89949i 0.0784465 + 0.549125i
\(326\) 1.41421i 0.0783260i
\(327\) 0 0
\(328\) −1.00000 1.00000i −0.0552158 0.0552158i
\(329\) −9.89949 −0.545777
\(330\) 0 0
\(331\) 4.00000 0.219860 0.109930 0.993939i \(-0.464937\pi\)
0.109930 + 0.993939i \(0.464937\pi\)
\(332\) −8.48528 8.48528i −0.465690 0.465690i
\(333\) −18.0000 18.0000i −0.986394 0.986394i
\(334\) 0 0
\(335\) 3.00000 9.00000i 0.163908 0.491723i
\(336\) 0 0
\(337\) 15.5563 + 15.5563i 0.847408 + 0.847408i 0.989809 0.142401i \(-0.0454822\pi\)
−0.142401 + 0.989809i \(0.545482\pi\)
\(338\) −6.36396 + 6.36396i −0.346154 + 0.346154i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) −9.00000 + 9.00000i −0.486664 + 0.486664i
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) 8.00000i 0.431331i
\(345\) 0 0
\(346\) 18.0000 0.967686
\(347\) 2.82843 + 2.82843i 0.151838 + 0.151838i 0.778938 0.627100i \(-0.215758\pi\)
−0.627100 + 0.778938i \(0.715758\pi\)
\(348\) 0 0
\(349\) 33.9411 1.81683 0.908413 0.418073i \(-0.137294\pi\)
0.908413 + 0.418073i \(0.137294\pi\)
\(350\) −4.00000 3.00000i −0.213809 0.160357i
\(351\) 0 0
\(352\) 1.12132 + 3.12132i 0.0597666 + 0.166367i
\(353\) −4.00000 4.00000i −0.212899 0.212899i 0.592599 0.805498i \(-0.298102\pi\)
−0.805498 + 0.592599i \(0.798102\pi\)
\(354\) 0 0
\(355\) 16.0000 8.00000i 0.849192 0.424596i
\(356\) −14.0000 −0.741999
\(357\) 0 0
\(358\) 1.41421 1.41421i 0.0747435 0.0747435i
\(359\) −9.89949 −0.522475 −0.261238 0.965275i \(-0.584131\pi\)
−0.261238 + 0.965275i \(0.584131\pi\)
\(360\) −6.36396 2.12132i −0.335410 0.111803i
\(361\) −1.00000 −0.0526316
\(362\) 2.82843 + 2.82843i 0.148659 + 0.148659i
\(363\) 0 0
\(364\) 2.00000i 0.104828i
\(365\) 4.24264 12.7279i 0.222070 0.666210i
\(366\) 0 0
\(367\) 25.0000 25.0000i 1.30499 1.30499i 0.380005 0.924984i \(-0.375922\pi\)
0.924984 0.380005i \(-0.124078\pi\)
\(368\) 2.00000 + 2.00000i 0.104257 + 0.104257i
\(369\) 4.24264 0.220863
\(370\) −16.9706 + 8.48528i −0.882258 + 0.441129i
\(371\) 5.65685i 0.293689i
\(372\) 0 0
\(373\) 14.1421 14.1421i 0.732252 0.732252i −0.238813 0.971065i \(-0.576758\pi\)
0.971065 + 0.238813i \(0.0767584\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 9.89949i 0.510527i
\(377\) 10.0000 10.0000i 0.515026 0.515026i
\(378\) 0 0
\(379\) 30.0000i 1.54100i −0.637442 0.770498i \(-0.720007\pi\)
0.637442 0.770498i \(-0.279993\pi\)
\(380\) 4.24264 + 8.48528i 0.217643 + 0.435286i
\(381\) 0 0
\(382\) −11.3137 11.3137i −0.578860 0.578860i
\(383\) −9.00000 9.00000i −0.459879 0.459879i 0.438737 0.898616i \(-0.355426\pi\)
−0.898616 + 0.438737i \(0.855426\pi\)
\(384\) 0 0
\(385\) −5.36396 5.12132i −0.273373 0.261007i
\(386\) 10.0000 0.508987
\(387\) 16.9706 + 16.9706i 0.862662 + 0.862662i
\(388\) 6.00000 + 6.00000i 0.304604 + 0.304604i
\(389\) 30.0000i 1.52106i −0.649303 0.760530i \(-0.724939\pi\)
0.649303 0.760530i \(-0.275061\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.707107 0.707107i −0.0357143 0.0357143i
\(393\) 0 0
\(394\) 12.0000i 0.604551i
\(395\) −8.48528 + 4.24264i −0.426941 + 0.213470i
\(396\) −9.00000 4.24264i −0.452267 0.213201i
\(397\) −9.00000 + 9.00000i −0.451697 + 0.451697i −0.895918 0.444220i \(-0.853481\pi\)
0.444220 + 0.895918i \(0.353481\pi\)
\(398\) −15.5563 + 15.5563i −0.779769 + 0.779769i
\(399\) 0 0
\(400\) −3.00000 + 4.00000i −0.150000 + 0.200000i
\(401\) 22.0000 1.09863 0.549314 0.835616i \(-0.314889\pi\)
0.549314 + 0.835616i \(0.314889\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −5.65685 −0.281439
\(405\) 18.0000 9.00000i 0.894427 0.447214i
\(406\) 7.07107i 0.350931i
\(407\) −26.4853 + 9.51472i −1.31283 + 0.471627i
\(408\) 0 0
\(409\) −9.89949 −0.489499 −0.244749 0.969586i \(-0.578706\pi\)
−0.244749 + 0.969586i \(0.578706\pi\)
\(410\) 1.00000 3.00000i 0.0493865 0.148159i
\(411\) 0 0
\(412\) −3.00000 + 3.00000i −0.147799 + 0.147799i
\(413\) 2.82843 2.82843i 0.139178 0.139178i
\(414\) −8.48528 −0.417029
\(415\) 8.48528 25.4558i 0.416526 1.24958i
\(416\) 2.00000 0.0980581
\(417\) 0 0
\(418\) 4.75736 + 13.2426i 0.232690 + 0.647719i
\(419\) 8.00000i 0.390826i 0.980721 + 0.195413i \(0.0626047\pi\)
−0.980721 + 0.195413i \(0.937395\pi\)
\(420\) 0 0
\(421\) 6.00000 0.292422 0.146211 0.989253i \(-0.453292\pi\)
0.146211 + 0.989253i \(0.453292\pi\)
\(422\) 4.00000 4.00000i 0.194717 0.194717i
\(423\) −21.0000 21.0000i −1.02105 1.02105i
\(424\) 5.65685 0.274721
\(425\) 0 0
\(426\) 0 0
\(427\) 2.00000 2.00000i 0.0967868 0.0967868i
\(428\) 8.48528 8.48528i 0.410152 0.410152i
\(429\) 0 0
\(430\) 16.0000 8.00000i 0.771589 0.385794i
\(431\) 9.89949i 0.476842i −0.971162 0.238421i \(-0.923370\pi\)
0.971162 0.238421i \(-0.0766298\pi\)
\(432\) 0 0
\(433\) 20.0000 + 20.0000i 0.961139 + 0.961139i 0.999273 0.0381340i \(-0.0121414\pi\)
−0.0381340 + 0.999273i \(0.512141\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 12.7279i 0.609557i
\(437\) 8.48528 + 8.48528i 0.405906 + 0.405906i
\(438\) 0 0
\(439\) −31.1127 −1.48493 −0.742464 0.669886i \(-0.766343\pi\)
−0.742464 + 0.669886i \(0.766343\pi\)
\(440\) −5.12132 + 5.36396i −0.244149 + 0.255717i
\(441\) 3.00000 0.142857
\(442\) 0 0
\(443\) −15.0000 15.0000i −0.712672 0.712672i 0.254422 0.967093i \(-0.418115\pi\)
−0.967093 + 0.254422i \(0.918115\pi\)
\(444\) 0 0
\(445\) −14.0000 28.0000i −0.663664 1.32733i
\(446\) 9.89949i 0.468755i
\(447\) 0 0
\(448\) −0.707107 + 0.707107i −0.0334077 + 0.0334077i
\(449\) 24.0000i 1.13263i 0.824189 + 0.566315i \(0.191631\pi\)
−0.824189 + 0.566315i \(0.808369\pi\)
\(450\) −2.12132 14.8492i −0.100000 0.700000i
\(451\) 2.00000 4.24264i 0.0941763 0.199778i
\(452\) 9.00000 9.00000i 0.423324 0.423324i
\(453\) 0 0
\(454\) 22.0000i 1.03251i
\(455\) −4.00000 + 2.00000i −0.187523 + 0.0937614i
\(456\) 0 0
\(457\) −1.41421 1.41421i −0.0661541 0.0661541i 0.673256 0.739410i \(-0.264895\pi\)
−0.739410 + 0.673256i \(0.764895\pi\)
\(458\) 1.41421 1.41421i 0.0660819 0.0660819i
\(459\) 0 0
\(460\) −2.00000 + 6.00000i −0.0932505 + 0.279751i
\(461\) 2.82843i 0.131733i −0.997828 0.0658665i \(-0.979019\pi\)
0.997828 0.0658665i \(-0.0209811\pi\)
\(462\) 0 0
\(463\) −10.0000 10.0000i −0.464739 0.464739i 0.435466 0.900205i \(-0.356584\pi\)
−0.900205 + 0.435466i \(0.856584\pi\)
\(464\) 7.07107 0.328266
\(465\) 0 0
\(466\) 26.0000 1.20443
\(467\) −2.00000 + 2.00000i −0.0925490 + 0.0925490i −0.751865 0.659317i \(-0.770846\pi\)
0.659317 + 0.751865i \(0.270846\pi\)
\(468\) −4.24264 + 4.24264i −0.196116 + 0.196116i
\(469\) 4.24264 0.195907
\(470\) −19.7990 + 9.89949i −0.913259 + 0.456630i
\(471\) 0 0
\(472\) −2.82843 2.82843i −0.130189 0.130189i
\(473\) 24.9706 8.97056i 1.14815 0.412467i
\(474\) 0 0
\(475\) −12.7279 + 16.9706i −0.583997 + 0.778663i
\(476\) 0 0
\(477\) −12.0000 + 12.0000i −0.549442 + 0.549442i
\(478\) −9.00000 9.00000i −0.411650 0.411650i
\(479\) −8.48528 −0.387702 −0.193851 0.981031i \(-0.562098\pi\)
−0.193851 + 0.981031i \(0.562098\pi\)
\(480\) 0 0
\(481\) 16.9706i 0.773791i
\(482\) −15.0000 + 15.0000i −0.683231 + 0.683231i
\(483\) 0 0
\(484\) −8.48528 + 7.00000i −0.385695 + 0.318182i
\(485\) −6.00000 + 18.0000i −0.272446 + 0.817338i
\(486\) 0 0
\(487\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(488\) −2.00000 2.00000i −0.0905357 0.0905357i
\(489\) 0 0
\(490\) 0.707107 2.12132i 0.0319438 0.0958315i
\(491\) 2.82843i 0.127645i 0.997961 + 0.0638226i \(0.0203292\pi\)
−0.997961 + 0.0638226i \(0.979671\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 8.48528 0.381771
\(495\) −0.514719 22.2426i −0.0231349 0.999732i
\(496\) 0 0
\(497\) 5.65685 + 5.65685i 0.253745 + 0.253745i
\(498\) 0 0
\(499\) 44.0000i 1.96971i 0.173379 + 0.984855i \(0.444532\pi\)
−0.173379 + 0.984855i \(0.555468\pi\)
\(500\) −11.0000 2.00000i −0.491935 0.0894427i
\(501\) 0 0
\(502\) 0 0
\(503\) 19.7990 19.7990i 0.882793 0.882793i −0.111024 0.993818i \(-0.535413\pi\)
0.993818 + 0.111024i \(0.0354132\pi\)
\(504\) 3.00000i 0.133631i
\(505\) −5.65685 11.3137i −0.251727 0.503453i
\(506\) −4.00000 + 8.48528i −0.177822 + 0.377217i
\(507\) 0 0
\(508\) −9.89949 + 9.89949i −0.439219 + 0.439219i
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 6.00000 0.265424
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) 11.3137 0.499026
\(515\) −9.00000 3.00000i −0.396587 0.132196i
\(516\) 0 0
\(517\) −30.8995 + 11.1005i −1.35896 + 0.488200i
\(518\) −6.00000 6.00000i −0.263625 0.263625i
\(519\) 0 0
\(520\) 2.00000 + 4.00000i 0.0877058 + 0.175412i
\(521\) −30.0000 −1.31432 −0.657162 0.753749i \(-0.728243\pi\)
−0.657162 + 0.753749i \(0.728243\pi\)
\(522\) −15.0000 + 15.0000i −0.656532 + 0.656532i
\(523\) −9.89949 + 9.89949i −0.432875 + 0.432875i −0.889605 0.456730i \(-0.849020\pi\)
0.456730 + 0.889605i \(0.349020\pi\)
\(524\) 1.41421 0.0617802
\(525\) 0 0
\(526\) 14.0000 0.610429
\(527\) 0 0
\(528\) 0 0
\(529\) 15.0000i 0.652174i
\(530\) 5.65685 + 11.3137i 0.245718 + 0.491436i
\(531\) 12.0000 0.520756
\(532\) −3.00000 + 3.00000i −0.130066 + 0.130066i
\(533\) −2.00000 2.00000i −0.0866296 0.0866296i
\(534\) 0 0
\(535\) 25.4558 + 8.48528i 1.10055 + 0.366851i
\(536\) 4.24264i 0.183254i
\(537\) 0 0
\(538\) 12.7279 12.7279i 0.548740 0.548740i
\(539\) 1.41421 3.00000i 0.0609145 0.129219i
\(540\) 0 0
\(541\) 41.0122i 1.76325i −0.471949 0.881626i \(-0.656449\pi\)
0.471949 0.881626i \(-0.343551\pi\)
\(542\) 22.0000 22.0000i 0.944981 0.944981i
\(543\) 0 0
\(544\) 0 0
\(545\) −25.4558 + 12.7279i −1.09041 + 0.545204i
\(546\) 0 0
\(547\) 2.82843 + 2.82843i 0.120935 + 0.120935i 0.764984 0.644049i \(-0.222747\pi\)
−0.644049 + 0.764984i \(0.722747\pi\)
\(548\) 5.00000 + 5.00000i 0.213589 + 0.213589i
\(549\) 8.48528 0.362143
\(550\) −15.8492 4.87868i −0.675814 0.208028i
\(551\) 30.0000 1.27804
\(552\) 0 0
\(553\) −3.00000 3.00000i −0.127573 0.127573i
\(554\) 8.00000i 0.339887i
\(555\) 0 0
\(556\) 18.3848i 0.779688i
\(557\) −1.41421 1.41421i −0.0599222 0.0599222i 0.676511 0.736433i \(-0.263491\pi\)
−0.736433 + 0.676511i \(0.763491\pi\)
\(558\) 0 0
\(559\) 16.0000i 0.676728i
\(560\) −2.12132 0.707107i −0.0896421 0.0298807i
\(561\) 0 0
\(562\) −20.0000 + 20.0000i −0.843649 + 0.843649i
\(563\) −14.1421 + 14.1421i −0.596020 + 0.596020i −0.939251 0.343231i \(-0.888479\pi\)
0.343231 + 0.939251i \(0.388479\pi\)
\(564\) 0 0
\(565\) 27.0000 + 9.00000i 1.13590 + 0.378633i
\(566\) −6.00000 −0.252199
\(567\) 6.36396 + 6.36396i 0.267261 + 0.267261i
\(568\) 5.65685 5.65685i 0.237356 0.237356i
\(569\) −28.2843 −1.18574 −0.592869 0.805299i \(-0.702005\pi\)
−0.592869 + 0.805299i \(0.702005\pi\)
\(570\) 0 0
\(571\) 33.9411i 1.42039i 0.704004 + 0.710196i \(0.251394\pi\)
−0.704004 + 0.710196i \(0.748606\pi\)
\(572\) 2.24264 + 6.24264i 0.0937695 + 0.261018i
\(573\) 0 0
\(574\) 1.41421 0.0590281
\(575\) −14.0000 + 2.00000i −0.583840 + 0.0834058i
\(576\) −3.00000 −0.125000
\(577\) 2.00000 2.00000i 0.0832611 0.0832611i −0.664250 0.747511i \(-0.731249\pi\)
0.747511 + 0.664250i \(0.231249\pi\)
\(578\) 12.0208 12.0208i 0.500000 0.500000i
\(579\) 0 0
\(580\) 7.07107 + 14.1421i 0.293610 + 0.587220i
\(581\) 12.0000 0.497844
\(582\) 0 0
\(583\) 6.34315 + 17.6569i 0.262706 + 0.731272i
\(584\) 6.00000i 0.248282i
\(585\) −12.7279 4.24264i −0.526235 0.175412i
\(586\) −30.0000 −1.23929
\(587\) 14.0000 14.0000i 0.577842 0.577842i −0.356466 0.934308i \(-0.616019\pi\)
0.934308 + 0.356466i \(0.116019\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 2.82843 8.48528i 0.116445 0.349334i
\(591\) 0 0
\(592\) −6.00000 + 6.00000i −0.246598 + 0.246598i
\(593\) −24.0416 + 24.0416i −0.987271 + 0.987271i −0.999920 0.0126486i \(-0.995974\pi\)
0.0126486 + 0.999920i \(0.495974\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 9.89949i 0.405499i
\(597\) 0 0
\(598\) 4.00000 + 4.00000i 0.163572 + 0.163572i
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 29.6985i 1.21143i −0.795683 0.605713i \(-0.792888\pi\)
0.795683 0.605713i \(-0.207112\pi\)
\(602\) 5.65685 + 5.65685i 0.230556 + 0.230556i
\(603\) 9.00000 + 9.00000i 0.366508 + 0.366508i
\(604\) 18.3848 0.748066
\(605\) −22.4853 9.97056i −0.914157 0.405361i
\(606\) 0 0
\(607\) 5.65685 + 5.65685i 0.229605 + 0.229605i 0.812527 0.582923i \(-0.198091\pi\)
−0.582923 + 0.812527i \(0.698091\pi\)
\(608\) 3.00000 + 3.00000i 0.121666 + 0.121666i
\(609\) 0 0
\(610\) 2.00000 6.00000i 0.0809776 0.242933i
\(611\) 19.7990i 0.800981i
\(612\) 0 0
\(613\) 7.07107 7.07107i 0.285598 0.285598i −0.549739 0.835337i \(-0.685273\pi\)
0.835337 + 0.549739i \(0.185273\pi\)
\(614\) 26.0000i 1.04927i
\(615\) 0 0
\(616\) −3.00000 1.41421i −0.120873 0.0569803i
\(617\) −17.0000 + 17.0000i −0.684394 + 0.684394i −0.960987 0.276593i \(-0.910795\pi\)
0.276593 + 0.960987i \(0.410795\pi\)
\(618\) 0 0
\(619\) 12.0000i 0.482321i −0.970485 0.241160i \(-0.922472\pi\)
0.970485 0.241160i \(-0.0775280\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −21.2132 21.2132i −0.850572 0.850572i
\(623\) 9.89949 9.89949i 0.396615 0.396615i
\(624\) 0 0
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 16.9706i 0.678280i
\(627\) 0 0
\(628\) 7.00000 + 7.00000i 0.279330 + 0.279330i
\(629\) 0 0
\(630\) 6.00000 3.00000i 0.239046 0.119523i
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) −3.00000 + 3.00000i −0.119334 + 0.119334i
\(633\) 0 0
\(634\) 11.3137 0.449325
\(635\) −29.6985 9.89949i −1.17855 0.392849i
\(636\) 0 0
\(637\) −1.41421 1.41421i −0.0560332 0.0560332i
\(638\) 7.92893 + 22.0711i 0.313909 + 0.873802i
\(639\) 24.0000i 0.949425i
\(640\) −0.707107 + 2.12132i −0.0279508 + 0.0838525i
\(641\) 8.00000 0.315981 0.157991 0.987441i \(-0.449498\pi\)
0.157991 + 0.987441i \(0.449498\pi\)
\(642\) 0 0
\(643\) 28.0000 + 28.0000i 1.10421 + 1.10421i 0.993897 + 0.110316i \(0.0351862\pi\)
0.110316 + 0.993897i \(0.464814\pi\)
\(644\) −2.82843 −0.111456
\(645\) 0 0
\(646\) 0 0
\(647\) −19.0000 + 19.0000i −0.746967 + 0.746967i −0.973908 0.226941i \(-0.927127\pi\)
0.226941 + 0.973908i \(0.427127\pi\)
\(648\) 6.36396 6.36396i 0.250000 0.250000i
\(649\) 5.65685 12.0000i 0.222051 0.471041i
\(650\) −6.00000 + 8.00000i −0.235339 + 0.313786i
\(651\) 0 0
\(652\) −1.00000 + 1.00000i −0.0391630 + 0.0391630i
\(653\) 4.00000 + 4.00000i 0.156532 + 0.156532i 0.781028 0.624496i \(-0.214696\pi\)
−0.624496 + 0.781028i \(0.714696\pi\)
\(654\) 0 0
\(655\) 1.41421 + 2.82843i 0.0552579 + 0.110516i
\(656\) 1.41421i 0.0552158i
\(657\) 12.7279 + 12.7279i 0.496564 + 0.496564i
\(658\) −7.00000 7.00000i −0.272888 0.272888i
\(659\) −31.1127 −1.21198 −0.605989 0.795473i \(-0.707223\pi\)
−0.605989 + 0.795473i \(0.707223\pi\)
\(660\) 0 0
\(661\) −22.0000 −0.855701 −0.427850 0.903850i \(-0.640729\pi\)
−0.427850 + 0.903850i \(0.640729\pi\)
\(662\) 2.82843 + 2.82843i 0.109930 + 0.109930i
\(663\) 0 0
\(664\) 12.0000i 0.465690i
\(665\) −9.00000 3.00000i −0.349005 0.116335i
\(666\) 25.4558i 0.986394i
\(667\) 14.1421 + 14.1421i 0.547586 + 0.547586i
\(668\) 0 0
\(669\) 0 0
\(670\) 8.48528 4.24264i 0.327815 0.163908i
\(671\) 4.00000 8.48528i 0.154418 0.327571i
\(672\) 0 0
\(673\) 15.5563 15.5563i 0.599653 0.599653i −0.340567 0.940220i \(-0.610619\pi\)
0.940220 + 0.340567i \(0.110619\pi\)
\(674\) 22.0000i 0.847408i
\(675\) 0 0
\(676\) −9.00000 −0.346154
\(677\) −18.3848 18.3848i −0.706584 0.706584i 0.259231 0.965815i \(-0.416531\pi\)
−0.965815 + 0.259231i \(0.916531\pi\)
\(678\) 0 0
\(679\) −8.48528 −0.325635
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 33.0000 + 33.0000i 1.26271 + 1.26271i 0.949774 + 0.312936i \(0.101312\pi\)
0.312936 + 0.949774i \(0.398688\pi\)
\(684\) −12.7279 −0.486664
\(685\) −5.00000 + 15.0000i −0.191040 + 0.573121i
\(686\) 1.00000 0.0381802
\(687\) 0 0
\(688\) 5.65685 5.65685i 0.215666 0.215666i
\(689\) 11.3137 0.431018
\(690\) 0 0
\(691\) 12.0000 0.456502 0.228251 0.973602i \(-0.426699\pi\)
0.228251 + 0.973602i \(0.426699\pi\)
\(692\) 12.7279 + 12.7279i 0.483843 + 0.483843i
\(693\) 9.36396 3.36396i 0.355707 0.127786i
\(694\) 4.00000i 0.151838i
\(695\) 36.7696 18.3848i 1.39475 0.697374i
\(696\) 0 0
\(697\) 0 0
\(698\) 24.0000 + 24.0000i 0.908413 + 0.908413i
\(699\) 0 0
\(700\) −0.707107 4.94975i −0.0267261 0.187083i
\(701\) 38.1838i 1.44218i 0.692841 + 0.721090i \(0.256359\pi\)
−0.692841 + 0.721090i \(0.743641\pi\)
\(702\) 0 0
\(703\) −25.4558 + 25.4558i −0.960085 + 0.960085i
\(704\) −1.41421 + 3.00000i −0.0533002 + 0.113067i
\(705\) 0 0
\(706\) 5.65685i 0.212899i
\(707\) 4.00000 4.00000i 0.150435 0.150435i
\(708\) 0 0
\(709\) 10.0000i 0.375558i 0.982211 + 0.187779i \(0.0601289\pi\)
−0.982211 + 0.187779i \(0.939871\pi\)
\(710\) 16.9706 + 5.65685i 0.636894 + 0.212298i
\(711\) 12.7279i 0.477334i
\(712\) −9.89949 9.89949i −0.370999 0.370999i
\(713\) 0 0
\(714\) 0 0
\(715\) −10.2426 + 10.7279i −0.383053 + 0.401202i
\(716\) 2.00000 0.0747435
\(717\) 0 0
\(718\) −7.00000 7.00000i −0.261238 0.261238i
\(719\) 24.0000i 0.895049i 0.894272 + 0.447524i \(0.147694\pi\)
−0.894272 + 0.447524i \(0.852306\pi\)
\(720\) −3.00000 6.00000i −0.111803 0.223607i
\(721\) 4.24264i 0.158004i
\(722\) −0.707107 0.707107i −0.0263158 0.0263158i
\(723\) 0 0
\(724\) 4.00000i 0.148659i
\(725\) −21.2132 + 28.2843i −0.787839 + 1.05045i
\(726\) 0 0
\(727\) −31.0000 + 31.0000i −1.14973 + 1.14973i −0.163120 + 0.986606i \(0.552156\pi\)
−0.986606 + 0.163120i \(0.947844\pi\)
\(728\) −1.41421 + 1.41421i −0.0524142 + 0.0524142i
\(729\) 27.0000i 1.00000i
\(730\) 12.0000 6.00000i 0.444140 0.222070i
\(731\) 0 0
\(732\) 0 0
\(733\) 9.89949 9.89949i 0.365646 0.365646i −0.500240 0.865887i \(-0.666755\pi\)
0.865887 + 0.500240i \(0.166755\pi\)
\(734\) 35.3553 1.30499
\(735\) 0 0
\(736\) 2.82843i 0.104257i
\(737\) 13.2426 4.75736i 0.487799 0.175240i
\(738\) 3.00000 + 3.00000i 0.110432 + 0.110432i
\(739\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) −18.0000 6.00000i −0.661693 0.220564i
\(741\) 0 0
\(742\) −4.00000 + 4.00000i −0.146845 + 0.146845i
\(743\) 1.41421 1.41421i 0.0518825 0.0518825i −0.680690 0.732572i \(-0.738320\pi\)
0.732572 + 0.680690i \(0.238320\pi\)
\(744\) 0 0
\(745\) 19.7990 9.89949i 0.725379 0.362689i
\(746\) 20.0000 0.732252
\(747\) 25.4558 + 25.4558i 0.931381 + 0.931381i
\(748\) 0 0
\(749\) 12.0000i 0.438470i
\(750\) 0 0
\(751\) 4.00000 0.145962 0.0729810 0.997333i \(-0.476749\pi\)
0.0729810 + 0.997333i \(0.476749\pi\)
\(752\) −7.00000 + 7.00000i −0.255264 + 0.255264i
\(753\) 0 0
\(754\) 14.1421 0.515026
\(755\) 18.3848 + 36.7696i 0.669091 + 1.33818i
\(756\) 0 0
\(757\) −14.0000 + 14.0000i −0.508839 + 0.508839i −0.914170 0.405331i \(-0.867156\pi\)
0.405331 + 0.914170i \(0.367156\pi\)
\(758\) 21.2132 21.2132i 0.770498 0.770498i
\(759\) 0 0
\(760\) −3.00000 + 9.00000i −0.108821 + 0.326464i
\(761\) 9.89949i 0.358856i 0.983771 + 0.179428i \(0.0574248\pi\)
−0.983771 + 0.179428i \(0.942575\pi\)
\(762\) 0 0
\(763\) −9.00000 9.00000i −0.325822 0.325822i
\(764\) 16.0000i 0.578860i
\(765\) 0 0
\(766\) 12.7279i 0.459879i
\(767\) −5.65685 5.65685i −0.204257 0.204257i
\(768\) 0 0
\(769\) 43.8406 1.58093 0.790467 0.612505i \(-0.209838\pi\)
0.790467 + 0.612505i \(0.209838\pi\)
\(770\) −0.171573 7.41421i −0.00618306 0.267190i
\(771\) 0 0
\(772\) 7.07107 + 7.07107i 0.254493 + 0.254493i
\(773\) 15.0000 + 15.0000i 0.539513 + 0.539513i 0.923386 0.383873i \(-0.125410\pi\)
−0.383873 + 0.923386i \(0.625410\pi\)
\(774\) 24.0000i 0.862662i
\(775\) 0 0
\(776\) 8.48528i 0.304604i
\(777\) 0 0
\(778\) 21.2132 21.2132i 0.760530 0.760530i
\(779\) 6.00000i 0.214972i
\(780\) 0 0
\(781\) 24.0000 + 11.3137i 0.858788 + 0.404836i
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000i 0.0357143i
\(785\) −7.00000 + 21.0000i −0.249841 + 0.749522i
\(786\) 0 0
\(787\) 8.48528 + 8.48528i 0.302468 + 0.302468i 0.841979 0.539511i \(-0.181391\pi\)
−0.539511 + 0.84197