Properties

Label 315.2.d.c.64.1
Level $315$
Weight $2$
Character 315.64
Analytic conductor $2.515$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.51528766367\)
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 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 64.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 315.64
Dual form 315.2.d.c.64.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} +1.00000i q^{7} -3.00000i q^{8} +O(q^{10})\) \(q-1.00000i q^{2} +1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} +1.00000i q^{7} -3.00000i q^{8} +(2.00000 + 1.00000i) q^{10} +6.00000 q^{11} -2.00000i q^{13} +1.00000 q^{14} -1.00000 q^{16} +4.00000i q^{17} +6.00000 q^{19} +(-1.00000 + 2.00000i) q^{20} -6.00000i q^{22} +(-3.00000 - 4.00000i) q^{25} -2.00000 q^{26} +1.00000i q^{28} -2.00000 q^{29} -10.0000 q^{31} -5.00000i q^{32} +4.00000 q^{34} +(-2.00000 - 1.00000i) q^{35} +4.00000i q^{37} -6.00000i q^{38} +(6.00000 + 3.00000i) q^{40} -2.00000 q^{41} -4.00000i q^{43} +6.00000 q^{44} -1.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} -2.00000i q^{52} -6.00000i q^{53} +(-6.00000 + 12.0000i) q^{55} +3.00000 q^{56} +2.00000i q^{58} -8.00000 q^{59} -2.00000 q^{61} +10.0000i q^{62} -7.00000 q^{64} +(4.00000 + 2.00000i) q^{65} +16.0000i q^{67} +4.00000i q^{68} +(-1.00000 + 2.00000i) q^{70} -10.0000 q^{71} -6.00000i q^{73} +4.00000 q^{74} +6.00000 q^{76} +6.00000i q^{77} -4.00000 q^{79} +(1.00000 - 2.00000i) q^{80} +2.00000i q^{82} -8.00000i q^{83} +(-8.00000 - 4.00000i) q^{85} -4.00000 q^{86} -18.0000i q^{88} +6.00000 q^{89} +2.00000 q^{91} +(-6.00000 + 12.0000i) q^{95} +2.00000i q^{97} +1.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{4} - 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{4} - 2 q^{5} + 4 q^{10} + 12 q^{11} + 2 q^{14} - 2 q^{16} + 12 q^{19} - 2 q^{20} - 6 q^{25} - 4 q^{26} - 4 q^{29} - 20 q^{31} + 8 q^{34} - 4 q^{35} + 12 q^{40} - 4 q^{41} + 12 q^{44} - 2 q^{49} - 8 q^{50} - 12 q^{55} + 6 q^{56} - 16 q^{59} - 4 q^{61} - 14 q^{64} + 8 q^{65} - 2 q^{70} - 20 q^{71} + 8 q^{74} + 12 q^{76} - 8 q^{79} + 2 q^{80} - 16 q^{85} - 8 q^{86} + 12 q^{89} + 4 q^{91} - 12 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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 −0.935414 0.353553i \(-0.884973\pi\)
0.935414 0.353553i \(-0.115027\pi\)
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −1.00000 + 2.00000i −0.447214 + 0.894427i
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 3.00000i 1.06066i
\(9\) 0 0
\(10\) 2.00000 + 1.00000i 0.632456 + 0.316228i
\(11\) 6.00000 1.80907 0.904534 0.426401i \(-0.140219\pi\)
0.904534 + 0.426401i \(0.140219\pi\)
\(12\) 0 0
\(13\) 2.00000i 0.554700i −0.960769 0.277350i \(-0.910544\pi\)
0.960769 0.277350i \(-0.0894562\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 4.00000i 0.970143i 0.874475 + 0.485071i \(0.161206\pi\)
−0.874475 + 0.485071i \(0.838794\pi\)
\(18\) 0 0
\(19\) 6.00000 1.37649 0.688247 0.725476i \(-0.258380\pi\)
0.688247 + 0.725476i \(0.258380\pi\)
\(20\) −1.00000 + 2.00000i −0.223607 + 0.447214i
\(21\) 0 0
\(22\) 6.00000i 1.27920i
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) −2.00000 −0.392232
\(27\) 0 0
\(28\) 1.00000i 0.188982i
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) −10.0000 −1.79605 −0.898027 0.439941i \(-0.854999\pi\)
−0.898027 + 0.439941i \(0.854999\pi\)
\(32\) 5.00000i 0.883883i
\(33\) 0 0
\(34\) 4.00000 0.685994
\(35\) −2.00000 1.00000i −0.338062 0.169031i
\(36\) 0 0
\(37\) 4.00000i 0.657596i 0.944400 + 0.328798i \(0.106644\pi\)
−0.944400 + 0.328798i \(0.893356\pi\)
\(38\) 6.00000i 0.973329i
\(39\) 0 0
\(40\) 6.00000 + 3.00000i 0.948683 + 0.474342i
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 4.00000i 0.609994i −0.952353 0.304997i \(-0.901344\pi\)
0.952353 0.304997i \(-0.0986555\pi\)
\(44\) 6.00000 0.904534
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) −4.00000 + 3.00000i −0.565685 + 0.424264i
\(51\) 0 0
\(52\) 2.00000i 0.277350i
\(53\) 6.00000i 0.824163i −0.911147 0.412082i \(-0.864802\pi\)
0.911147 0.412082i \(-0.135198\pi\)
\(54\) 0 0
\(55\) −6.00000 + 12.0000i −0.809040 + 1.61808i
\(56\) 3.00000 0.400892
\(57\) 0 0
\(58\) 2.00000i 0.262613i
\(59\) −8.00000 −1.04151 −0.520756 0.853706i \(-0.674350\pi\)
−0.520756 + 0.853706i \(0.674350\pi\)
\(60\) 0 0
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 10.0000i 1.27000i
\(63\) 0 0
\(64\) −7.00000 −0.875000
\(65\) 4.00000 + 2.00000i 0.496139 + 0.248069i
\(66\) 0 0
\(67\) 16.0000i 1.95471i 0.211604 + 0.977356i \(0.432131\pi\)
−0.211604 + 0.977356i \(0.567869\pi\)
\(68\) 4.00000i 0.485071i
\(69\) 0 0
\(70\) −1.00000 + 2.00000i −0.119523 + 0.239046i
\(71\) −10.0000 −1.18678 −0.593391 0.804914i \(-0.702211\pi\)
−0.593391 + 0.804914i \(0.702211\pi\)
\(72\) 0 0
\(73\) 6.00000i 0.702247i −0.936329 0.351123i \(-0.885800\pi\)
0.936329 0.351123i \(-0.114200\pi\)
\(74\) 4.00000 0.464991
\(75\) 0 0
\(76\) 6.00000 0.688247
\(77\) 6.00000i 0.683763i
\(78\) 0 0
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 1.00000 2.00000i 0.111803 0.223607i
\(81\) 0 0
\(82\) 2.00000i 0.220863i
\(83\) 8.00000i 0.878114i −0.898459 0.439057i \(-0.855313\pi\)
0.898459 0.439057i \(-0.144687\pi\)
\(84\) 0 0
\(85\) −8.00000 4.00000i −0.867722 0.433861i
\(86\) −4.00000 −0.431331
\(87\) 0 0
\(88\) 18.0000i 1.91881i
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) 2.00000 0.209657
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −6.00000 + 12.0000i −0.615587 + 1.23117i
\(96\) 0 0
\(97\) 2.00000i 0.203069i 0.994832 + 0.101535i \(0.0323753\pi\)
−0.994832 + 0.101535i \(0.967625\pi\)
\(98\) 1.00000i 0.101015i
\(99\) 0 0
\(100\) −3.00000 4.00000i −0.300000 0.400000i
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 0 0
\(103\) 8.00000i 0.788263i 0.919054 + 0.394132i \(0.128955\pi\)
−0.919054 + 0.394132i \(0.871045\pi\)
\(104\) −6.00000 −0.588348
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 4.00000i 0.386695i 0.981130 + 0.193347i \(0.0619344\pi\)
−0.981130 + 0.193347i \(0.938066\pi\)
\(108\) 0 0
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 12.0000 + 6.00000i 1.14416 + 0.572078i
\(111\) 0 0
\(112\) 1.00000i 0.0944911i
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −2.00000 −0.185695
\(117\) 0 0
\(118\) 8.00000i 0.736460i
\(119\) −4.00000 −0.366679
\(120\) 0 0
\(121\) 25.0000 2.27273
\(122\) 2.00000i 0.181071i
\(123\) 0 0
\(124\) −10.0000 −0.898027
\(125\) 11.0000 2.00000i 0.983870 0.178885i
\(126\) 0 0
\(127\) 20.0000i 1.77471i −0.461084 0.887357i \(-0.652539\pi\)
0.461084 0.887357i \(-0.347461\pi\)
\(128\) 3.00000i 0.265165i
\(129\) 0 0
\(130\) 2.00000 4.00000i 0.175412 0.350823i
\(131\) −4.00000 −0.349482 −0.174741 0.984614i \(-0.555909\pi\)
−0.174741 + 0.984614i \(0.555909\pi\)
\(132\) 0 0
\(133\) 6.00000i 0.520266i
\(134\) 16.0000 1.38219
\(135\) 0 0
\(136\) 12.0000 1.02899
\(137\) 6.00000i 0.512615i −0.966595 0.256307i \(-0.917494\pi\)
0.966595 0.256307i \(-0.0825059\pi\)
\(138\) 0 0
\(139\) −2.00000 −0.169638 −0.0848189 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) −2.00000 1.00000i −0.169031 0.0845154i
\(141\) 0 0
\(142\) 10.0000i 0.839181i
\(143\) 12.0000i 1.00349i
\(144\) 0 0
\(145\) 2.00000 4.00000i 0.166091 0.332182i
\(146\) −6.00000 −0.496564
\(147\) 0 0
\(148\) 4.00000i 0.328798i
\(149\) −14.0000 −1.14692 −0.573462 0.819232i \(-0.694400\pi\)
−0.573462 + 0.819232i \(0.694400\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 18.0000i 1.45999i
\(153\) 0 0
\(154\) 6.00000 0.483494
\(155\) 10.0000 20.0000i 0.803219 1.60644i
\(156\) 0 0
\(157\) 18.0000i 1.43656i −0.695756 0.718278i \(-0.744931\pi\)
0.695756 0.718278i \(-0.255069\pi\)
\(158\) 4.00000i 0.318223i
\(159\) 0 0
\(160\) 10.0000 + 5.00000i 0.790569 + 0.395285i
\(161\) 0 0
\(162\) 0 0
\(163\) 4.00000i 0.313304i 0.987654 + 0.156652i \(0.0500701\pi\)
−0.987654 + 0.156652i \(0.949930\pi\)
\(164\) −2.00000 −0.156174
\(165\) 0 0
\(166\) −8.00000 −0.620920
\(167\) 12.0000i 0.928588i 0.885681 + 0.464294i \(0.153692\pi\)
−0.885681 + 0.464294i \(0.846308\pi\)
\(168\) 0 0
\(169\) 9.00000 0.692308
\(170\) −4.00000 + 8.00000i −0.306786 + 0.613572i
\(171\) 0 0
\(172\) 4.00000i 0.304997i
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 4.00000 3.00000i 0.302372 0.226779i
\(176\) −6.00000 −0.452267
\(177\) 0 0
\(178\) 6.00000i 0.449719i
\(179\) −14.0000 −1.04641 −0.523205 0.852207i \(-0.675264\pi\)
−0.523205 + 0.852207i \(0.675264\pi\)
\(180\) 0 0
\(181\) −6.00000 −0.445976 −0.222988 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) 2.00000i 0.148250i
\(183\) 0 0
\(184\) 0 0
\(185\) −8.00000 4.00000i −0.588172 0.294086i
\(186\) 0 0
\(187\) 24.0000i 1.75505i
\(188\) 0 0
\(189\) 0 0
\(190\) 12.0000 + 6.00000i 0.870572 + 0.435286i
\(191\) 18.0000 1.30243 0.651217 0.758891i \(-0.274259\pi\)
0.651217 + 0.758891i \(0.274259\pi\)
\(192\) 0 0
\(193\) 8.00000i 0.575853i −0.957653 0.287926i \(-0.907034\pi\)
0.957653 0.287926i \(-0.0929658\pi\)
\(194\) 2.00000 0.143592
\(195\) 0 0
\(196\) −1.00000 −0.0714286
\(197\) 2.00000i 0.142494i 0.997459 + 0.0712470i \(0.0226979\pi\)
−0.997459 + 0.0712470i \(0.977302\pi\)
\(198\) 0 0
\(199\) −14.0000 −0.992434 −0.496217 0.868199i \(-0.665278\pi\)
−0.496217 + 0.868199i \(0.665278\pi\)
\(200\) −12.0000 + 9.00000i −0.848528 + 0.636396i
\(201\) 0 0
\(202\) 6.00000i 0.422159i
\(203\) 2.00000i 0.140372i
\(204\) 0 0
\(205\) 2.00000 4.00000i 0.139686 0.279372i
\(206\) 8.00000 0.557386
\(207\) 0 0
\(208\) 2.00000i 0.138675i
\(209\) 36.0000 2.49017
\(210\) 0 0
\(211\) −16.0000 −1.10149 −0.550743 0.834675i \(-0.685655\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) 6.00000i 0.412082i
\(213\) 0 0
\(214\) 4.00000 0.273434
\(215\) 8.00000 + 4.00000i 0.545595 + 0.272798i
\(216\) 0 0
\(217\) 10.0000i 0.678844i
\(218\) 2.00000i 0.135457i
\(219\) 0 0
\(220\) −6.00000 + 12.0000i −0.404520 + 0.809040i
\(221\) 8.00000 0.538138
\(222\) 0 0
\(223\) 24.0000i 1.60716i −0.595198 0.803579i \(-0.702926\pi\)
0.595198 0.803579i \(-0.297074\pi\)
\(224\) 5.00000 0.334077
\(225\) 0 0
\(226\) −6.00000 −0.399114
\(227\) 8.00000i 0.530979i 0.964114 + 0.265489i \(0.0855335\pi\)
−0.964114 + 0.265489i \(0.914466\pi\)
\(228\) 0 0
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 6.00000i 0.393919i
\(233\) 26.0000i 1.70332i 0.524097 + 0.851658i \(0.324403\pi\)
−0.524097 + 0.851658i \(0.675597\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −8.00000 −0.520756
\(237\) 0 0
\(238\) 4.00000i 0.259281i
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 0 0
\(241\) 22.0000 1.41714 0.708572 0.705638i \(-0.249340\pi\)
0.708572 + 0.705638i \(0.249340\pi\)
\(242\) 25.0000i 1.60706i
\(243\) 0 0
\(244\) −2.00000 −0.128037
\(245\) 1.00000 2.00000i 0.0638877 0.127775i
\(246\) 0 0
\(247\) 12.0000i 0.763542i
\(248\) 30.0000i 1.90500i
\(249\) 0 0
\(250\) −2.00000 11.0000i −0.126491 0.695701i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −20.0000 −1.25491
\(255\) 0 0
\(256\) −17.0000 −1.06250
\(257\) 16.0000i 0.998053i 0.866587 + 0.499026i \(0.166309\pi\)
−0.866587 + 0.499026i \(0.833691\pi\)
\(258\) 0 0
\(259\) −4.00000 −0.248548
\(260\) 4.00000 + 2.00000i 0.248069 + 0.124035i
\(261\) 0 0
\(262\) 4.00000i 0.247121i
\(263\) 24.0000i 1.47990i 0.672660 + 0.739952i \(0.265152\pi\)
−0.672660 + 0.739952i \(0.734848\pi\)
\(264\) 0 0
\(265\) 12.0000 + 6.00000i 0.737154 + 0.368577i
\(266\) 6.00000 0.367884
\(267\) 0 0
\(268\) 16.0000i 0.977356i
\(269\) −14.0000 −0.853595 −0.426798 0.904347i \(-0.640358\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) 0 0
\(271\) −14.0000 −0.850439 −0.425220 0.905090i \(-0.639803\pi\)
−0.425220 + 0.905090i \(0.639803\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) −18.0000 24.0000i −1.08544 1.44725i
\(276\) 0 0
\(277\) 28.0000i 1.68236i 0.540758 + 0.841178i \(0.318138\pi\)
−0.540758 + 0.841178i \(0.681862\pi\)
\(278\) 2.00000i 0.119952i
\(279\) 0 0
\(280\) −3.00000 + 6.00000i −0.179284 + 0.358569i
\(281\) 2.00000 0.119310 0.0596550 0.998219i \(-0.481000\pi\)
0.0596550 + 0.998219i \(0.481000\pi\)
\(282\) 0 0
\(283\) 20.0000i 1.18888i 0.804141 + 0.594438i \(0.202626\pi\)
−0.804141 + 0.594438i \(0.797374\pi\)
\(284\) −10.0000 −0.593391
\(285\) 0 0
\(286\) −12.0000 −0.709575
\(287\) 2.00000i 0.118056i
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) −4.00000 2.00000i −0.234888 0.117444i
\(291\) 0 0
\(292\) 6.00000i 0.351123i
\(293\) 24.0000i 1.40209i −0.713115 0.701047i \(-0.752716\pi\)
0.713115 0.701047i \(-0.247284\pi\)
\(294\) 0 0
\(295\) 8.00000 16.0000i 0.465778 0.931556i
\(296\) 12.0000 0.697486
\(297\) 0 0
\(298\) 14.0000i 0.810998i
\(299\) 0 0
\(300\) 0 0
\(301\) 4.00000 0.230556
\(302\) 8.00000i 0.460348i
\(303\) 0 0
\(304\) −6.00000 −0.344124
\(305\) 2.00000 4.00000i 0.114520 0.229039i
\(306\) 0 0
\(307\) 4.00000i 0.228292i −0.993464 0.114146i \(-0.963587\pi\)
0.993464 0.114146i \(-0.0364132\pi\)
\(308\) 6.00000i 0.341882i
\(309\) 0 0
\(310\) −20.0000 10.0000i −1.13592 0.567962i
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) 6.00000i 0.339140i 0.985518 + 0.169570i \(0.0542379\pi\)
−0.985518 + 0.169570i \(0.945762\pi\)
\(314\) −18.0000 −1.01580
\(315\) 0 0
\(316\) −4.00000 −0.225018
\(317\) 18.0000i 1.01098i −0.862832 0.505490i \(-0.831312\pi\)
0.862832 0.505490i \(-0.168688\pi\)
\(318\) 0 0
\(319\) −12.0000 −0.671871
\(320\) 7.00000 14.0000i 0.391312 0.782624i
\(321\) 0 0
\(322\) 0 0
\(323\) 24.0000i 1.33540i
\(324\) 0 0
\(325\) −8.00000 + 6.00000i −0.443760 + 0.332820i
\(326\) 4.00000 0.221540
\(327\) 0 0
\(328\) 6.00000i 0.331295i
\(329\) 0 0
\(330\) 0 0
\(331\) −24.0000 −1.31916 −0.659580 0.751635i \(-0.729266\pi\)
−0.659580 + 0.751635i \(0.729266\pi\)
\(332\) 8.00000i 0.439057i
\(333\) 0 0
\(334\) 12.0000 0.656611
\(335\) −32.0000 16.0000i −1.74835 0.874173i
\(336\) 0 0
\(337\) 24.0000i 1.30736i 0.756770 + 0.653682i \(0.226776\pi\)
−0.756770 + 0.653682i \(0.773224\pi\)
\(338\) 9.00000i 0.489535i
\(339\) 0 0
\(340\) −8.00000 4.00000i −0.433861 0.216930i
\(341\) −60.0000 −3.24918
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) −12.0000 −0.646997
\(345\) 0 0
\(346\) 0 0
\(347\) 12.0000i 0.644194i 0.946707 + 0.322097i \(0.104388\pi\)
−0.946707 + 0.322097i \(0.895612\pi\)
\(348\) 0 0
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) −3.00000 4.00000i −0.160357 0.213809i
\(351\) 0 0
\(352\) 30.0000i 1.59901i
\(353\) 20.0000i 1.06449i −0.846590 0.532246i \(-0.821348\pi\)
0.846590 0.532246i \(-0.178652\pi\)
\(354\) 0 0
\(355\) 10.0000 20.0000i 0.530745 1.06149i
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) 14.0000i 0.739923i
\(359\) 22.0000 1.16112 0.580558 0.814219i \(-0.302835\pi\)
0.580558 + 0.814219i \(0.302835\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) 6.00000i 0.315353i
\(363\) 0 0
\(364\) 2.00000 0.104828
\(365\) 12.0000 + 6.00000i 0.628109 + 0.314054i
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −4.00000 + 8.00000i −0.207950 + 0.415900i
\(371\) 6.00000 0.311504
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 24.0000 1.24101
\(375\) 0 0
\(376\) 0 0
\(377\) 4.00000i 0.206010i
\(378\) 0 0
\(379\) 28.0000 1.43826 0.719132 0.694874i \(-0.244540\pi\)
0.719132 + 0.694874i \(0.244540\pi\)
\(380\) −6.00000 + 12.0000i −0.307794 + 0.615587i
\(381\) 0 0
\(382\) 18.0000i 0.920960i
\(383\) 20.0000i 1.02195i 0.859595 + 0.510976i \(0.170716\pi\)
−0.859595 + 0.510976i \(0.829284\pi\)
\(384\) 0 0
\(385\) −12.0000 6.00000i −0.611577 0.305788i
\(386\) −8.00000 −0.407189
\(387\) 0 0
\(388\) 2.00000i 0.101535i
\(389\) 26.0000 1.31825 0.659126 0.752032i \(-0.270926\pi\)
0.659126 + 0.752032i \(0.270926\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 3.00000i 0.151523i
\(393\) 0 0
\(394\) 2.00000 0.100759
\(395\) 4.00000 8.00000i 0.201262 0.402524i
\(396\) 0 0
\(397\) 22.0000i 1.10415i −0.833795 0.552074i \(-0.813837\pi\)
0.833795 0.552074i \(-0.186163\pi\)
\(398\) 14.0000i 0.701757i
\(399\) 0 0
\(400\) 3.00000 + 4.00000i 0.150000 + 0.200000i
\(401\) 30.0000 1.49813 0.749064 0.662497i \(-0.230503\pi\)
0.749064 + 0.662497i \(0.230503\pi\)
\(402\) 0 0
\(403\) 20.0000i 0.996271i
\(404\) 6.00000 0.298511
\(405\) 0 0
\(406\) −2.00000 −0.0992583
\(407\) 24.0000i 1.18964i
\(408\) 0 0
\(409\) 22.0000 1.08783 0.543915 0.839140i \(-0.316941\pi\)
0.543915 + 0.839140i \(0.316941\pi\)
\(410\) −4.00000 2.00000i −0.197546 0.0987730i
\(411\) 0 0
\(412\) 8.00000i 0.394132i
\(413\) 8.00000i 0.393654i
\(414\) 0 0
\(415\) 16.0000 + 8.00000i 0.785409 + 0.392705i
\(416\) −10.0000 −0.490290
\(417\) 0 0
\(418\) 36.0000i 1.76082i
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) 18.0000 0.877266 0.438633 0.898666i \(-0.355463\pi\)
0.438633 + 0.898666i \(0.355463\pi\)
\(422\) 16.0000i 0.778868i
\(423\) 0 0
\(424\) −18.0000 −0.874157
\(425\) 16.0000 12.0000i 0.776114 0.582086i
\(426\) 0 0
\(427\) 2.00000i 0.0967868i
\(428\) 4.00000i 0.193347i
\(429\) 0 0
\(430\) 4.00000 8.00000i 0.192897 0.385794i
\(431\) 14.0000 0.674356 0.337178 0.941441i \(-0.390528\pi\)
0.337178 + 0.941441i \(0.390528\pi\)
\(432\) 0 0
\(433\) 34.0000i 1.63394i −0.576683 0.816968i \(-0.695653\pi\)
0.576683 0.816968i \(-0.304347\pi\)
\(434\) −10.0000 −0.480015
\(435\) 0 0
\(436\) −2.00000 −0.0957826
\(437\) 0 0
\(438\) 0 0
\(439\) −6.00000 −0.286364 −0.143182 0.989696i \(-0.545733\pi\)
−0.143182 + 0.989696i \(0.545733\pi\)
\(440\) 36.0000 + 18.0000i 1.71623 + 0.858116i
\(441\) 0 0
\(442\) 8.00000i 0.380521i
\(443\) 4.00000i 0.190046i 0.995475 + 0.0950229i \(0.0302924\pi\)
−0.995475 + 0.0950229i \(0.969708\pi\)
\(444\) 0 0
\(445\) −6.00000 + 12.0000i −0.284427 + 0.568855i
\(446\) −24.0000 −1.13643
\(447\) 0 0
\(448\) 7.00000i 0.330719i
\(449\) 10.0000 0.471929 0.235965 0.971762i \(-0.424175\pi\)
0.235965 + 0.971762i \(0.424175\pi\)
\(450\) 0 0
\(451\) −12.0000 −0.565058
\(452\) 6.00000i 0.282216i
\(453\) 0 0
\(454\) 8.00000 0.375459
\(455\) −2.00000 + 4.00000i −0.0937614 + 0.187523i
\(456\) 0 0
\(457\) 20.0000i 0.935561i 0.883845 + 0.467780i \(0.154946\pi\)
−0.883845 + 0.467780i \(0.845054\pi\)
\(458\) 10.0000i 0.467269i
\(459\) 0 0
\(460\) 0 0
\(461\) −30.0000 −1.39724 −0.698620 0.715493i \(-0.746202\pi\)
−0.698620 + 0.715493i \(0.746202\pi\)
\(462\) 0 0
\(463\) 36.0000i 1.67306i 0.547920 + 0.836531i \(0.315420\pi\)
−0.547920 + 0.836531i \(0.684580\pi\)
\(464\) 2.00000 0.0928477
\(465\) 0 0
\(466\) 26.0000 1.20443
\(467\) 24.0000i 1.11059i −0.831654 0.555294i \(-0.812606\pi\)
0.831654 0.555294i \(-0.187394\pi\)
\(468\) 0 0
\(469\) −16.0000 −0.738811
\(470\) 0 0
\(471\) 0 0
\(472\) 24.0000i 1.10469i
\(473\) 24.0000i 1.10352i
\(474\) 0 0
\(475\) −18.0000 24.0000i −0.825897 1.10120i
\(476\) −4.00000 −0.183340
\(477\) 0 0
\(478\) 6.00000i 0.274434i
\(479\) 24.0000 1.09659 0.548294 0.836286i \(-0.315277\pi\)
0.548294 + 0.836286i \(0.315277\pi\)
\(480\) 0 0
\(481\) 8.00000 0.364769
\(482\) 22.0000i 1.00207i
\(483\) 0 0
\(484\) 25.0000 1.13636
\(485\) −4.00000 2.00000i −0.181631 0.0908153i
\(486\) 0 0
\(487\) 12.0000i 0.543772i −0.962329 0.271886i \(-0.912353\pi\)
0.962329 0.271886i \(-0.0876473\pi\)
\(488\) 6.00000i 0.271607i
\(489\) 0 0
\(490\) −2.00000 1.00000i −0.0903508 0.0451754i
\(491\) −10.0000 −0.451294 −0.225647 0.974209i \(-0.572450\pi\)
−0.225647 + 0.974209i \(0.572450\pi\)
\(492\) 0 0
\(493\) 8.00000i 0.360302i
\(494\) −12.0000 −0.539906
\(495\) 0 0
\(496\) 10.0000 0.449013
\(497\) 10.0000i 0.448561i
\(498\) 0 0
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) 11.0000 2.00000i 0.491935 0.0894427i
\(501\) 0 0
\(502\) 0 0
\(503\) 36.0000i 1.60516i 0.596544 + 0.802580i \(0.296540\pi\)
−0.596544 + 0.802580i \(0.703460\pi\)
\(504\) 0 0
\(505\) −6.00000 + 12.0000i −0.266996 + 0.533993i
\(506\) 0 0
\(507\) 0 0
\(508\) 20.0000i 0.887357i
\(509\) 30.0000 1.32973 0.664863 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) 0 0
\(511\) 6.00000 0.265424
\(512\) 11.0000i 0.486136i
\(513\) 0 0
\(514\) 16.0000 0.705730
\(515\) −16.0000 8.00000i −0.705044 0.352522i
\(516\) 0 0
\(517\) 0 0
\(518\) 4.00000i 0.175750i
\(519\) 0 0
\(520\) 6.00000 12.0000i 0.263117 0.526235i
\(521\) −38.0000 −1.66481 −0.832405 0.554168i \(-0.813037\pi\)
−0.832405 + 0.554168i \(0.813037\pi\)
\(522\) 0 0
\(523\) 20.0000i 0.874539i 0.899331 + 0.437269i \(0.144054\pi\)
−0.899331 + 0.437269i \(0.855946\pi\)
\(524\) −4.00000 −0.174741
\(525\) 0 0
\(526\) 24.0000 1.04645
\(527\) 40.0000i 1.74243i
\(528\) 0 0
\(529\) 23.0000 1.00000
\(530\) 6.00000 12.0000i 0.260623 0.521247i
\(531\) 0 0
\(532\) 6.00000i 0.260133i
\(533\) 4.00000i 0.173259i
\(534\) 0 0
\(535\) −8.00000 4.00000i −0.345870 0.172935i
\(536\) 48.0000 2.07328
\(537\) 0 0
\(538\) 14.0000i 0.603583i
\(539\) −6.00000 −0.258438
\(540\) 0 0
\(541\) 6.00000 0.257960 0.128980 0.991647i \(-0.458830\pi\)
0.128980 + 0.991647i \(0.458830\pi\)
\(542\) 14.0000i 0.601351i
\(543\) 0 0
\(544\) 20.0000 0.857493
\(545\) 2.00000 4.00000i 0.0856706 0.171341i
\(546\) 0 0
\(547\) 16.0000i 0.684111i 0.939680 + 0.342055i \(0.111123\pi\)
−0.939680 + 0.342055i \(0.888877\pi\)
\(548\) 6.00000i 0.256307i
\(549\) 0 0
\(550\) −24.0000 + 18.0000i −1.02336 + 0.767523i
\(551\) −12.0000 −0.511217
\(552\) 0 0
\(553\) 4.00000i 0.170097i
\(554\) 28.0000 1.18961
\(555\) 0 0
\(556\) −2.00000 −0.0848189
\(557\) 38.0000i 1.61011i 0.593199 + 0.805056i \(0.297865\pi\)
−0.593199 + 0.805056i \(0.702135\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 2.00000 + 1.00000i 0.0845154 + 0.0422577i
\(561\) 0 0
\(562\) 2.00000i 0.0843649i
\(563\) 36.0000i 1.51722i 0.651546 + 0.758610i \(0.274121\pi\)
−0.651546 + 0.758610i \(0.725879\pi\)
\(564\) 0 0
\(565\) 12.0000 + 6.00000i 0.504844 + 0.252422i
\(566\) 20.0000 0.840663
\(567\) 0 0
\(568\) 30.0000i 1.25877i
\(569\) −30.0000 −1.25767 −0.628833 0.777541i \(-0.716467\pi\)
−0.628833 + 0.777541i \(0.716467\pi\)
\(570\) 0 0
\(571\) 36.0000 1.50655 0.753277 0.657704i \(-0.228472\pi\)
0.753277 + 0.657704i \(0.228472\pi\)
\(572\) 12.0000i 0.501745i
\(573\) 0 0
\(574\) −2.00000 −0.0834784
\(575\) 0 0
\(576\) 0 0
\(577\) 14.0000i 0.582828i −0.956597 0.291414i \(-0.905874\pi\)
0.956597 0.291414i \(-0.0941257\pi\)
\(578\) 1.00000i 0.0415945i
\(579\) 0 0
\(580\) 2.00000 4.00000i 0.0830455 0.166091i
\(581\) 8.00000 0.331896
\(582\) 0 0
\(583\) 36.0000i 1.49097i
\(584\) −18.0000 −0.744845
\(585\) 0 0
\(586\) −24.0000 −0.991431
\(587\) 12.0000i 0.495293i −0.968850 0.247647i \(-0.920343\pi\)
0.968850 0.247647i \(-0.0796572\pi\)
\(588\) 0 0
\(589\) −60.0000 −2.47226
\(590\) −16.0000 8.00000i −0.658710 0.329355i
\(591\) 0 0
\(592\) 4.00000i 0.164399i
\(593\) 44.0000i 1.80686i −0.428732 0.903432i \(-0.641040\pi\)
0.428732 0.903432i \(-0.358960\pi\)
\(594\) 0 0
\(595\) 4.00000 8.00000i 0.163984 0.327968i
\(596\) −14.0000 −0.573462
\(597\) 0 0
\(598\) 0 0
\(599\) −2.00000 −0.0817178 −0.0408589 0.999165i \(-0.513009\pi\)
−0.0408589 + 0.999165i \(0.513009\pi\)
\(600\) 0 0
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 4.00000i 0.163028i
\(603\) 0 0
\(604\) 8.00000 0.325515
\(605\) −25.0000 + 50.0000i −1.01639 + 2.03279i
\(606\) 0 0
\(607\) 24.0000i 0.974130i −0.873366 0.487065i \(-0.838067\pi\)
0.873366 0.487065i \(-0.161933\pi\)
\(608\) 30.0000i 1.21666i
\(609\) 0 0
\(610\) −4.00000 2.00000i −0.161955 0.0809776i
\(611\) 0 0
\(612\) 0 0
\(613\) 4.00000i 0.161558i 0.996732 + 0.0807792i \(0.0257409\pi\)
−0.996732 + 0.0807792i \(0.974259\pi\)
\(614\) −4.00000 −0.161427
\(615\) 0 0
\(616\) 18.0000 0.725241
\(617\) 26.0000i 1.04672i −0.852111 0.523360i \(-0.824678\pi\)
0.852111 0.523360i \(-0.175322\pi\)
\(618\) 0 0
\(619\) −10.0000 −0.401934 −0.200967 0.979598i \(-0.564408\pi\)
−0.200967 + 0.979598i \(0.564408\pi\)
\(620\) 10.0000 20.0000i 0.401610 0.803219i
\(621\) 0 0
\(622\) 24.0000i 0.962312i
\(623\) 6.00000i 0.240385i
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 6.00000 0.239808
\(627\) 0 0
\(628\) 18.0000i 0.718278i
\(629\) −16.0000 −0.637962
\(630\) 0 0
\(631\) −20.0000 −0.796187 −0.398094 0.917345i \(-0.630328\pi\)
−0.398094 + 0.917345i \(0.630328\pi\)
\(632\) 12.0000i 0.477334i
\(633\) 0 0
\(634\) −18.0000 −0.714871
\(635\) 40.0000 + 20.0000i 1.58735 + 0.793676i
\(636\) 0 0
\(637\) 2.00000i 0.0792429i
\(638\) 12.0000i 0.475085i
\(639\) 0 0
\(640\) 6.00000 + 3.00000i 0.237171 + 0.118585i
\(641\) 2.00000 0.0789953 0.0394976 0.999220i \(-0.487424\pi\)
0.0394976 + 0.999220i \(0.487424\pi\)
\(642\) 0 0
\(643\) 20.0000i 0.788723i −0.918955 0.394362i \(-0.870966\pi\)
0.918955 0.394362i \(-0.129034\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 24.0000 0.944267
\(647\) 20.0000i 0.786281i −0.919478 0.393141i \(-0.871389\pi\)
0.919478 0.393141i \(-0.128611\pi\)
\(648\) 0 0
\(649\) −48.0000 −1.88416
\(650\) 6.00000 + 8.00000i 0.235339 + 0.313786i
\(651\) 0 0
\(652\) 4.00000i 0.156652i
\(653\) 2.00000i 0.0782660i −0.999234 0.0391330i \(-0.987540\pi\)
0.999234 0.0391330i \(-0.0124596\pi\)
\(654\) 0 0
\(655\) 4.00000 8.00000i 0.156293 0.312586i
\(656\) 2.00000 0.0780869
\(657\) 0 0
\(658\) 0 0
\(659\) −18.0000 −0.701180 −0.350590 0.936529i \(-0.614019\pi\)
−0.350590 + 0.936529i \(0.614019\pi\)
\(660\) 0 0
\(661\) −18.0000 −0.700119 −0.350059 0.936727i \(-0.613839\pi\)
−0.350059 + 0.936727i \(0.613839\pi\)
\(662\) 24.0000i 0.932786i
\(663\) 0 0
\(664\) −24.0000 −0.931381
\(665\) −12.0000 6.00000i −0.465340 0.232670i
\(666\) 0 0
\(667\) 0 0
\(668\) 12.0000i 0.464294i
\(669\) 0 0
\(670\) −16.0000 + 32.0000i −0.618134 + 1.23627i
\(671\) −12.0000 −0.463255
\(672\) 0 0
\(673\) 36.0000i 1.38770i −0.720121 0.693849i \(-0.755914\pi\)
0.720121 0.693849i \(-0.244086\pi\)
\(674\) 24.0000 0.924445
\(675\) 0 0
\(676\) 9.00000 0.346154
\(677\) 32.0000i 1.22986i 0.788582 + 0.614930i \(0.210816\pi\)
−0.788582 + 0.614930i \(0.789184\pi\)
\(678\) 0 0
\(679\) −2.00000 −0.0767530
\(680\) −12.0000 + 24.0000i −0.460179 + 0.920358i
\(681\) 0 0
\(682\) 60.0000i 2.29752i
\(683\) 28.0000i 1.07139i −0.844411 0.535695i \(-0.820050\pi\)
0.844411 0.535695i \(-0.179950\pi\)
\(684\) 0 0
\(685\) 12.0000 + 6.00000i 0.458496 + 0.229248i
\(686\) −1.00000 −0.0381802
\(687\) 0 0
\(688\) 4.00000i 0.152499i
\(689\) −12.0000 −0.457164
\(690\) 0 0
\(691\) −50.0000 −1.90209 −0.951045 0.309053i \(-0.899988\pi\)
−0.951045 + 0.309053i \(0.899988\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) 2.00000 4.00000i 0.0758643 0.151729i
\(696\) 0 0
\(697\) 8.00000i 0.303022i
\(698\) 2.00000i 0.0757011i
\(699\) 0 0
\(700\) 4.00000 3.00000i 0.151186 0.113389i
\(701\) 10.0000 0.377695 0.188847 0.982006i \(-0.439525\pi\)
0.188847 + 0.982006i \(0.439525\pi\)
\(702\) 0 0
\(703\) 24.0000i 0.905177i
\(704\) −42.0000 −1.58293
\(705\) 0 0
\(706\) −20.0000 −0.752710
\(707\) 6.00000i 0.225653i
\(708\) 0 0
\(709\) −26.0000 −0.976450 −0.488225 0.872718i \(-0.662356\pi\)
−0.488225 + 0.872718i \(0.662356\pi\)
\(710\) −20.0000 10.0000i −0.750587 0.375293i
\(711\) 0 0
\(712\) 18.0000i 0.674579i
\(713\) 0 0
\(714\) 0 0
\(715\) 24.0000 + 12.0000i 0.897549 + 0.448775i
\(716\) −14.0000 −0.523205
\(717\) 0 0
\(718\) 22.0000i 0.821033i
\(719\) 12.0000 0.447524 0.223762 0.974644i \(-0.428166\pi\)
0.223762 + 0.974644i \(0.428166\pi\)
\(720\) 0 0
\(721\) −8.00000 −0.297936
\(722\) 17.0000i 0.632674i
\(723\) 0 0
\(724\) −6.00000 −0.222988
\(725\) 6.00000 + 8.00000i 0.222834 + 0.297113i
\(726\) 0 0
\(727\) 40.0000i 1.48352i 0.670667 + 0.741759i \(0.266008\pi\)
−0.670667 + 0.741759i \(0.733992\pi\)
\(728\) 6.00000i 0.222375i
\(729\) 0 0
\(730\) 6.00000 12.0000i 0.222070 0.444140i
\(731\) 16.0000 0.591781
\(732\) 0 0
\(733\) 22.0000i 0.812589i 0.913742 + 0.406294i \(0.133179\pi\)
−0.913742 + 0.406294i \(0.866821\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 96.0000i 3.53621i
\(738\) 0 0
\(739\) 44.0000 1.61857 0.809283 0.587419i \(-0.199856\pi\)
0.809283 + 0.587419i \(0.199856\pi\)
\(740\) −8.00000 4.00000i −0.294086 0.147043i
\(741\) 0 0
\(742\) 6.00000i 0.220267i
\(743\) 40.0000i 1.46746i −0.679442 0.733729i \(-0.737778\pi\)
0.679442 0.733729i \(-0.262222\pi\)
\(744\) 0 0
\(745\) 14.0000 28.0000i 0.512920 1.02584i
\(746\) 0 0
\(747\) 0 0
\(748\) 24.0000i 0.877527i
\(749\) −4.00000 −0.146157
\(750\) 0 0
\(751\) −12.0000 −0.437886 −0.218943 0.975738i \(-0.570261\pi\)
−0.218943 + 0.975738i \(0.570261\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 4.00000 0.145671
\(755\) −8.00000 + 16.0000i −0.291150 + 0.582300i
\(756\) 0 0
\(757\) 40.0000i 1.45382i 0.686730 + 0.726912i \(0.259045\pi\)
−0.686730 + 0.726912i \(0.740955\pi\)
\(758\) 28.0000i 1.01701i
\(759\) 0 0
\(760\) 36.0000 + 18.0000i 1.30586 + 0.652929i
\(761\) 22.0000 0.797499 0.398750 0.917060i \(-0.369444\pi\)
0.398750 + 0.917060i \(0.369444\pi\)
\(762\) 0 0
\(763\) 2.00000i 0.0724049i
\(764\) 18.0000 0.651217
\(765\) 0 0
\(766\) 20.0000 0.722629
\(767\) 16.0000i 0.577727i
\(768\) 0 0
\(769\) 18.0000 0.649097 0.324548 0.945869i \(-0.394788\pi\)
0.324548 + 0.945869i \(0.394788\pi\)
\(770\) −6.00000 + 12.0000i −0.216225 + 0.432450i
\(771\) 0 0
\(772\) 8.00000i 0.287926i
\(773\) 24.0000i 0.863220i −0.902060 0.431610i \(-0.857946\pi\)
0.902060 0.431610i \(-0.142054\pi\)
\(774\) 0 0
\(775\) 30.0000 + 40.0000i 1.07763 + 1.43684i
\(776\) 6.00000 0.215387
\(777\) 0 0
\(778\) 26.0000i 0.932145i
\(779\) −12.0000 −0.429945
\(780\) 0 0
\(781\) −60.0000 −2.14697
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 36.0000 + 18.0000i 1.28490 + 0.642448i
\(786\) 0 0
\(787\) 4.00000i 0.142585i 0.997455 + 0.0712923i \(0.0227123\pi\)
−0.997455 + 0.0712923i \(0.977288\pi\)
\(788\) 2.00000i 0.0712470i
\(789\) 0 0
\(790\) −8.00000 4.00000i −0.284627 0.142314i
\(791\) 6.00000 0.213335
\(792\) 0 0
\(793\) 4.00000i 0.142044i
\(794\) −22.0000 −0.780751
\(795\) 0 0
\(796\) −14.0000 −0.496217