Properties

Label 1305.2.c.b.784.1
Level $1305$
Weight $2$
Character 1305.784
Analytic conductor $10.420$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1305,2,Mod(784,1305)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1305, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1305.784");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1305.c (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(10.4204774638\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
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 435)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 784.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1305.784
Dual form 1305.2.c.b.784.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} +1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -2.00000i q^{7} -3.00000i q^{8} +O(q^{10})\) \(q-1.00000i q^{2} +1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -2.00000i q^{7} -3.00000i q^{8} +(2.00000 + 1.00000i) q^{10} -4.00000i q^{13} -2.00000 q^{14} -1.00000 q^{16} -2.00000i q^{17} +(-1.00000 + 2.00000i) q^{20} +2.00000i q^{23} +(-3.00000 - 4.00000i) q^{25} -4.00000 q^{26} -2.00000i q^{28} +1.00000 q^{29} +4.00000 q^{31} -5.00000i q^{32} -2.00000 q^{34} +(4.00000 + 2.00000i) q^{35} +2.00000i q^{37} +(6.00000 + 3.00000i) q^{40} -10.0000 q^{41} +2.00000 q^{46} -12.0000i q^{47} +3.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} -4.00000i q^{52} -12.0000i q^{53} -6.00000 q^{56} -1.00000i q^{58} +4.00000 q^{59} +2.00000 q^{61} -4.00000i q^{62} -7.00000 q^{64} +(8.00000 + 4.00000i) q^{65} +2.00000i q^{67} -2.00000i q^{68} +(2.00000 - 4.00000i) q^{70} +8.00000 q^{71} -14.0000i q^{73} +2.00000 q^{74} -8.00000 q^{79} +(1.00000 - 2.00000i) q^{80} +10.0000i q^{82} -6.00000i q^{83} +(4.00000 + 2.00000i) q^{85} +10.0000 q^{89} -8.00000 q^{91} +2.00000i q^{92} -12.0000 q^{94} +10.0000i q^{97} -3.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{4} - 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{4} - 2 q^{5} + 4 q^{10} - 4 q^{14} - 2 q^{16} - 2 q^{20} - 6 q^{25} - 8 q^{26} + 2 q^{29} + 8 q^{31} - 4 q^{34} + 8 q^{35} + 12 q^{40} - 20 q^{41} + 4 q^{46} + 6 q^{49} - 8 q^{50} - 12 q^{56} + 8 q^{59} + 4 q^{61} - 14 q^{64} + 16 q^{65} + 4 q^{70} + 16 q^{71} + 4 q^{74} - 16 q^{79} + 2 q^{80} + 8 q^{85} + 20 q^{89} - 16 q^{91} - 24 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1305\mathbb{Z}\right)^\times\).

\(n\) \(146\) \(262\) \(901\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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
\(7\) 2.00000i 0.755929i −0.925820 0.377964i \(-0.876624\pi\)
0.925820 0.377964i \(-0.123376\pi\)
\(8\) 3.00000i 1.06066i
\(9\) 0 0
\(10\) 2.00000 + 1.00000i 0.632456 + 0.316228i
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) 4.00000i 1.10940i −0.832050 0.554700i \(-0.812833\pi\)
0.832050 0.554700i \(-0.187167\pi\)
\(14\) −2.00000 −0.534522
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 2.00000i 0.485071i −0.970143 0.242536i \(-0.922021\pi\)
0.970143 0.242536i \(-0.0779791\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) −1.00000 + 2.00000i −0.223607 + 0.447214i
\(21\) 0 0
\(22\) 0 0
\(23\) 2.00000i 0.417029i 0.978019 + 0.208514i \(0.0668628\pi\)
−0.978019 + 0.208514i \(0.933137\pi\)
\(24\) 0 0
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) −4.00000 −0.784465
\(27\) 0 0
\(28\) 2.00000i 0.377964i
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 5.00000i 0.883883i
\(33\) 0 0
\(34\) −2.00000 −0.342997
\(35\) 4.00000 + 2.00000i 0.676123 + 0.338062i
\(36\) 0 0
\(37\) 2.00000i 0.328798i 0.986394 + 0.164399i \(0.0525685\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 6.00000 + 3.00000i 0.948683 + 0.474342i
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 2.00000 0.294884
\(47\) 12.0000i 1.75038i −0.483779 0.875190i \(-0.660736\pi\)
0.483779 0.875190i \(-0.339264\pi\)
\(48\) 0 0
\(49\) 3.00000 0.428571
\(50\) −4.00000 + 3.00000i −0.565685 + 0.424264i
\(51\) 0 0
\(52\) 4.00000i 0.554700i
\(53\) 12.0000i 1.64833i −0.566352 0.824163i \(-0.691646\pi\)
0.566352 0.824163i \(-0.308354\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −6.00000 −0.801784
\(57\) 0 0
\(58\) 1.00000i 0.131306i
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) 0 0
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 4.00000i 0.508001i
\(63\) 0 0
\(64\) −7.00000 −0.875000
\(65\) 8.00000 + 4.00000i 0.992278 + 0.496139i
\(66\) 0 0
\(67\) 2.00000i 0.244339i 0.992509 + 0.122169i \(0.0389851\pi\)
−0.992509 + 0.122169i \(0.961015\pi\)
\(68\) 2.00000i 0.242536i
\(69\) 0 0
\(70\) 2.00000 4.00000i 0.239046 0.478091i
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 0 0
\(73\) 14.0000i 1.63858i −0.573382 0.819288i \(-0.694369\pi\)
0.573382 0.819288i \(-0.305631\pi\)
\(74\) 2.00000 0.232495
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 1.00000 2.00000i 0.111803 0.223607i
\(81\) 0 0
\(82\) 10.0000i 1.10432i
\(83\) 6.00000i 0.658586i −0.944228 0.329293i \(-0.893190\pi\)
0.944228 0.329293i \(-0.106810\pi\)
\(84\) 0 0
\(85\) 4.00000 + 2.00000i 0.433861 + 0.216930i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) 0 0
\(91\) −8.00000 −0.838628
\(92\) 2.00000i 0.208514i
\(93\) 0 0
\(94\) −12.0000 −1.23771
\(95\) 0 0
\(96\) 0 0
\(97\) 10.0000i 1.01535i 0.861550 + 0.507673i \(0.169494\pi\)
−0.861550 + 0.507673i \(0.830506\pi\)
\(98\) 3.00000i 0.303046i
\(99\) 0 0
\(100\) −3.00000 4.00000i −0.300000 0.400000i
\(101\) −2.00000 −0.199007 −0.0995037 0.995037i \(-0.531726\pi\)
−0.0995037 + 0.995037i \(0.531726\pi\)
\(102\) 0 0
\(103\) 2.00000i 0.197066i 0.995134 + 0.0985329i \(0.0314150\pi\)
−0.995134 + 0.0985329i \(0.968585\pi\)
\(104\) −12.0000 −1.17670
\(105\) 0 0
\(106\) −12.0000 −1.16554
\(107\) 6.00000i 0.580042i −0.957020 0.290021i \(-0.906338\pi\)
0.957020 0.290021i \(-0.0936623\pi\)
\(108\) 0 0
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.00000i 0.188982i
\(113\) 14.0000i 1.31701i 0.752577 + 0.658505i \(0.228811\pi\)
−0.752577 + 0.658505i \(0.771189\pi\)
\(114\) 0 0
\(115\) −4.00000 2.00000i −0.373002 0.186501i
\(116\) 1.00000 0.0928477
\(117\) 0 0
\(118\) 4.00000i 0.368230i
\(119\) −4.00000 −0.366679
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 2.00000i 0.181071i
\(123\) 0 0
\(124\) 4.00000 0.359211
\(125\) 11.0000 2.00000i 0.983870 0.178885i
\(126\) 0 0
\(127\) 12.0000i 1.06483i 0.846484 + 0.532414i \(0.178715\pi\)
−0.846484 + 0.532414i \(0.821285\pi\)
\(128\) 3.00000i 0.265165i
\(129\) 0 0
\(130\) 4.00000 8.00000i 0.350823 0.701646i
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 2.00000 0.172774
\(135\) 0 0
\(136\) −6.00000 −0.514496
\(137\) 14.0000i 1.19610i 0.801459 + 0.598050i \(0.204058\pi\)
−0.801459 + 0.598050i \(0.795942\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 4.00000 + 2.00000i 0.338062 + 0.169031i
\(141\) 0 0
\(142\) 8.00000i 0.671345i
\(143\) 0 0
\(144\) 0 0
\(145\) −1.00000 + 2.00000i −0.0830455 + 0.166091i
\(146\) −14.0000 −1.15865
\(147\) 0 0
\(148\) 2.00000i 0.164399i
\(149\) −6.00000 −0.491539 −0.245770 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) 0 0
\(151\) −24.0000 −1.95309 −0.976546 0.215308i \(-0.930924\pi\)
−0.976546 + 0.215308i \(0.930924\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −4.00000 + 8.00000i −0.321288 + 0.642575i
\(156\) 0 0
\(157\) 22.0000i 1.75579i 0.478852 + 0.877896i \(0.341053\pi\)
−0.478852 + 0.877896i \(0.658947\pi\)
\(158\) 8.00000i 0.636446i
\(159\) 0 0
\(160\) 10.0000 + 5.00000i 0.790569 + 0.395285i
\(161\) 4.00000 0.315244
\(162\) 0 0
\(163\) 4.00000i 0.313304i 0.987654 + 0.156652i \(0.0500701\pi\)
−0.987654 + 0.156652i \(0.949930\pi\)
\(164\) −10.0000 −0.780869
\(165\) 0 0
\(166\) −6.00000 −0.465690
\(167\) 2.00000i 0.154765i −0.997001 0.0773823i \(-0.975344\pi\)
0.997001 0.0773823i \(-0.0246562\pi\)
\(168\) 0 0
\(169\) −3.00000 −0.230769
\(170\) 2.00000 4.00000i 0.153393 0.306786i
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) −8.00000 + 6.00000i −0.604743 + 0.453557i
\(176\) 0 0
\(177\) 0 0
\(178\) 10.0000i 0.749532i
\(179\) −20.0000 −1.49487 −0.747435 0.664335i \(-0.768715\pi\)
−0.747435 + 0.664335i \(0.768715\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 8.00000i 0.592999i
\(183\) 0 0
\(184\) 6.00000 0.442326
\(185\) −4.00000 2.00000i −0.294086 0.147043i
\(186\) 0 0
\(187\) 0 0
\(188\) 12.0000i 0.875190i
\(189\) 0 0
\(190\) 0 0
\(191\) −12.0000 −0.868290 −0.434145 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) 0 0
\(193\) 6.00000i 0.431889i −0.976406 0.215945i \(-0.930717\pi\)
0.976406 0.215945i \(-0.0692831\pi\)
\(194\) 10.0000 0.717958
\(195\) 0 0
\(196\) 3.00000 0.214286
\(197\) 8.00000i 0.569976i 0.958531 + 0.284988i \(0.0919897\pi\)
−0.958531 + 0.284988i \(0.908010\pi\)
\(198\) 0 0
\(199\) 16.0000 1.13421 0.567105 0.823646i \(-0.308063\pi\)
0.567105 + 0.823646i \(0.308063\pi\)
\(200\) −12.0000 + 9.00000i −0.848528 + 0.636396i
\(201\) 0 0
\(202\) 2.00000i 0.140720i
\(203\) 2.00000i 0.140372i
\(204\) 0 0
\(205\) 10.0000 20.0000i 0.698430 1.39686i
\(206\) 2.00000 0.139347
\(207\) 0 0
\(208\) 4.00000i 0.277350i
\(209\) 0 0
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) 12.0000i 0.824163i
\(213\) 0 0
\(214\) −6.00000 −0.410152
\(215\) 0 0
\(216\) 0 0
\(217\) 8.00000i 0.543075i
\(218\) 14.0000i 0.948200i
\(219\) 0 0
\(220\) 0 0
\(221\) −8.00000 −0.538138
\(222\) 0 0
\(223\) 18.0000i 1.20537i 0.797980 + 0.602685i \(0.205902\pi\)
−0.797980 + 0.602685i \(0.794098\pi\)
\(224\) −10.0000 −0.668153
\(225\) 0 0
\(226\) 14.0000 0.931266
\(227\) 6.00000i 0.398234i 0.979976 + 0.199117i \(0.0638074\pi\)
−0.979976 + 0.199117i \(0.936193\pi\)
\(228\) 0 0
\(229\) 22.0000 1.45380 0.726900 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) −2.00000 + 4.00000i −0.131876 + 0.263752i
\(231\) 0 0
\(232\) 3.00000i 0.196960i
\(233\) 20.0000i 1.31024i 0.755523 + 0.655122i \(0.227383\pi\)
−0.755523 + 0.655122i \(0.772617\pi\)
\(234\) 0 0
\(235\) 24.0000 + 12.0000i 1.56559 + 0.782794i
\(236\) 4.00000 0.260378
\(237\) 0 0
\(238\) 4.00000i 0.259281i
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) 30.0000 1.93247 0.966235 0.257663i \(-0.0829523\pi\)
0.966235 + 0.257663i \(0.0829523\pi\)
\(242\) 11.0000i 0.707107i
\(243\) 0 0
\(244\) 2.00000 0.128037
\(245\) −3.00000 + 6.00000i −0.191663 + 0.383326i
\(246\) 0 0
\(247\) 0 0
\(248\) 12.0000i 0.762001i
\(249\) 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
\(254\) 12.0000 0.752947
\(255\) 0 0
\(256\) −17.0000 −1.06250
\(257\) 8.00000i 0.499026i −0.968371 0.249513i \(-0.919729\pi\)
0.968371 0.249513i \(-0.0802706\pi\)
\(258\) 0 0
\(259\) 4.00000 0.248548
\(260\) 8.00000 + 4.00000i 0.496139 + 0.248069i
\(261\) 0 0
\(262\) 12.0000i 0.741362i
\(263\) 16.0000i 0.986602i 0.869859 + 0.493301i \(0.164210\pi\)
−0.869859 + 0.493301i \(0.835790\pi\)
\(264\) 0 0
\(265\) 24.0000 + 12.0000i 1.47431 + 0.737154i
\(266\) 0 0
\(267\) 0 0
\(268\) 2.00000i 0.122169i
\(269\) 26.0000 1.58525 0.792624 0.609711i \(-0.208714\pi\)
0.792624 + 0.609711i \(0.208714\pi\)
\(270\) 0 0
\(271\) −24.0000 −1.45790 −0.728948 0.684569i \(-0.759990\pi\)
−0.728948 + 0.684569i \(0.759990\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 0 0
\(274\) 14.0000 0.845771
\(275\) 0 0
\(276\) 0 0
\(277\) 8.00000i 0.480673i −0.970690 0.240337i \(-0.922742\pi\)
0.970690 0.240337i \(-0.0772579\pi\)
\(278\) 4.00000i 0.239904i
\(279\) 0 0
\(280\) 6.00000 12.0000i 0.358569 0.717137i
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) 10.0000i 0.594438i 0.954809 + 0.297219i \(0.0960592\pi\)
−0.954809 + 0.297219i \(0.903941\pi\)
\(284\) 8.00000 0.474713
\(285\) 0 0
\(286\) 0 0
\(287\) 20.0000i 1.18056i
\(288\) 0 0
\(289\) 13.0000 0.764706
\(290\) 2.00000 + 1.00000i 0.117444 + 0.0587220i
\(291\) 0 0
\(292\) 14.0000i 0.819288i
\(293\) 6.00000i 0.350524i 0.984522 + 0.175262i \(0.0560772\pi\)
−0.984522 + 0.175262i \(0.943923\pi\)
\(294\) 0 0
\(295\) −4.00000 + 8.00000i −0.232889 + 0.465778i
\(296\) 6.00000 0.348743
\(297\) 0 0
\(298\) 6.00000i 0.347571i
\(299\) 8.00000 0.462652
\(300\) 0 0
\(301\) 0 0
\(302\) 24.0000i 1.38104i
\(303\) 0 0
\(304\) 0 0
\(305\) −2.00000 + 4.00000i −0.114520 + 0.229039i
\(306\) 0 0
\(307\) 8.00000i 0.456584i −0.973593 0.228292i \(-0.926686\pi\)
0.973593 0.228292i \(-0.0733141\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 8.00000 + 4.00000i 0.454369 + 0.227185i
\(311\) −8.00000 −0.453638 −0.226819 0.973937i \(-0.572833\pi\)
−0.226819 + 0.973937i \(0.572833\pi\)
\(312\) 0 0
\(313\) 28.0000i 1.58265i −0.611393 0.791327i \(-0.709391\pi\)
0.611393 0.791327i \(-0.290609\pi\)
\(314\) 22.0000 1.24153
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) 6.00000i 0.336994i 0.985702 + 0.168497i \(0.0538913\pi\)
−0.985702 + 0.168497i \(0.946109\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 7.00000 14.0000i 0.391312 0.782624i
\(321\) 0 0
\(322\) 4.00000i 0.222911i
\(323\) 0 0
\(324\) 0 0
\(325\) −16.0000 + 12.0000i −0.887520 + 0.665640i
\(326\) 4.00000 0.221540
\(327\) 0 0
\(328\) 30.0000i 1.65647i
\(329\) −24.0000 −1.32316
\(330\) 0 0
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) 6.00000i 0.329293i
\(333\) 0 0
\(334\) −2.00000 −0.109435
\(335\) −4.00000 2.00000i −0.218543 0.109272i
\(336\) 0 0
\(337\) 2.00000i 0.108947i 0.998515 + 0.0544735i \(0.0173480\pi\)
−0.998515 + 0.0544735i \(0.982652\pi\)
\(338\) 3.00000i 0.163178i
\(339\) 0 0
\(340\) 4.00000 + 2.00000i 0.216930 + 0.108465i
\(341\) 0 0
\(342\) 0 0
\(343\) 20.0000i 1.07990i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6.00000i 0.322097i 0.986947 + 0.161048i \(0.0514875\pi\)
−0.986947 + 0.161048i \(0.948512\pi\)
\(348\) 0 0
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 6.00000 + 8.00000i 0.320713 + 0.427618i
\(351\) 0 0
\(352\) 0 0
\(353\) 28.0000i 1.49029i 0.666903 + 0.745145i \(0.267620\pi\)
−0.666903 + 0.745145i \(0.732380\pi\)
\(354\) 0 0
\(355\) −8.00000 + 16.0000i −0.424596 + 0.849192i
\(356\) 10.0000 0.529999
\(357\) 0 0
\(358\) 20.0000i 1.05703i
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) 2.00000i 0.105118i
\(363\) 0 0
\(364\) −8.00000 −0.419314
\(365\) 28.0000 + 14.0000i 1.46559 + 0.732793i
\(366\) 0 0
\(367\) 24.0000i 1.25279i −0.779506 0.626395i \(-0.784530\pi\)
0.779506 0.626395i \(-0.215470\pi\)
\(368\) 2.00000i 0.104257i
\(369\) 0 0
\(370\) −2.00000 + 4.00000i −0.103975 + 0.207950i
\(371\) −24.0000 −1.24602
\(372\) 0 0
\(373\) 4.00000i 0.207112i −0.994624 0.103556i \(-0.966978\pi\)
0.994624 0.103556i \(-0.0330221\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −36.0000 −1.85656
\(377\) 4.00000i 0.206010i
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 12.0000i 0.613973i
\(383\) 18.0000i 0.919757i 0.887982 + 0.459879i \(0.152107\pi\)
−0.887982 + 0.459879i \(0.847893\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −6.00000 −0.305392
\(387\) 0 0
\(388\) 10.0000i 0.507673i
\(389\) 2.00000 0.101404 0.0507020 0.998714i \(-0.483854\pi\)
0.0507020 + 0.998714i \(0.483854\pi\)
\(390\) 0 0
\(391\) 4.00000 0.202289
\(392\) 9.00000i 0.454569i
\(393\) 0 0
\(394\) 8.00000 0.403034
\(395\) 8.00000 16.0000i 0.402524 0.805047i
\(396\) 0 0
\(397\) 20.0000i 1.00377i 0.864934 + 0.501886i \(0.167360\pi\)
−0.864934 + 0.501886i \(0.832640\pi\)
\(398\) 16.0000i 0.802008i
\(399\) 0 0
\(400\) 3.00000 + 4.00000i 0.150000 + 0.200000i
\(401\) 34.0000 1.69788 0.848939 0.528490i \(-0.177242\pi\)
0.848939 + 0.528490i \(0.177242\pi\)
\(402\) 0 0
\(403\) 16.0000i 0.797017i
\(404\) −2.00000 −0.0995037
\(405\) 0 0
\(406\) −2.00000 −0.0992583
\(407\) 0 0
\(408\) 0 0
\(409\) 22.0000 1.08783 0.543915 0.839140i \(-0.316941\pi\)
0.543915 + 0.839140i \(0.316941\pi\)
\(410\) −20.0000 10.0000i −0.987730 0.493865i
\(411\) 0 0
\(412\) 2.00000i 0.0985329i
\(413\) 8.00000i 0.393654i
\(414\) 0 0
\(415\) 12.0000 + 6.00000i 0.589057 + 0.294528i
\(416\) −20.0000 −0.980581
\(417\) 0 0
\(418\) 0 0
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) −22.0000 −1.07221 −0.536107 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) 12.0000i 0.584151i
\(423\) 0 0
\(424\) −36.0000 −1.74831
\(425\) −8.00000 + 6.00000i −0.388057 + 0.291043i
\(426\) 0 0
\(427\) 4.00000i 0.193574i
\(428\) 6.00000i 0.290021i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 14.0000i 0.672797i 0.941720 + 0.336399i \(0.109209\pi\)
−0.941720 + 0.336399i \(0.890791\pi\)
\(434\) −8.00000 −0.384012
\(435\) 0 0
\(436\) 14.0000 0.670478
\(437\) 0 0
\(438\) 0 0
\(439\) 16.0000 0.763638 0.381819 0.924237i \(-0.375298\pi\)
0.381819 + 0.924237i \(0.375298\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 8.00000i 0.380521i
\(443\) 24.0000i 1.14027i −0.821549 0.570137i \(-0.806890\pi\)
0.821549 0.570137i \(-0.193110\pi\)
\(444\) 0 0
\(445\) −10.0000 + 20.0000i −0.474045 + 0.948091i
\(446\) 18.0000 0.852325
\(447\) 0 0
\(448\) 14.0000i 0.661438i
\(449\) −34.0000 −1.60456 −0.802280 0.596948i \(-0.796380\pi\)
−0.802280 + 0.596948i \(0.796380\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 14.0000i 0.658505i
\(453\) 0 0
\(454\) 6.00000 0.281594
\(455\) 8.00000 16.0000i 0.375046 0.750092i
\(456\) 0 0
\(457\) 8.00000i 0.374224i −0.982339 0.187112i \(-0.940087\pi\)
0.982339 0.187112i \(-0.0599128\pi\)
\(458\) 22.0000i 1.02799i
\(459\) 0 0
\(460\) −4.00000 2.00000i −0.186501 0.0932505i
\(461\) −26.0000 −1.21094 −0.605470 0.795868i \(-0.707015\pi\)
−0.605470 + 0.795868i \(0.707015\pi\)
\(462\) 0 0
\(463\) 30.0000i 1.39422i 0.716965 + 0.697109i \(0.245531\pi\)
−0.716965 + 0.697109i \(0.754469\pi\)
\(464\) −1.00000 −0.0464238
\(465\) 0 0
\(466\) 20.0000 0.926482
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) 4.00000 0.184703
\(470\) 12.0000 24.0000i 0.553519 1.10704i
\(471\) 0 0
\(472\) 12.0000i 0.552345i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) −4.00000 −0.183340
\(477\) 0 0
\(478\) 24.0000i 1.09773i
\(479\) 36.0000 1.64488 0.822441 0.568850i \(-0.192612\pi\)
0.822441 + 0.568850i \(0.192612\pi\)
\(480\) 0 0
\(481\) 8.00000 0.364769
\(482\) 30.0000i 1.36646i
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) −20.0000 10.0000i −0.908153 0.454077i
\(486\) 0 0
\(487\) 14.0000i 0.634401i 0.948359 + 0.317200i \(0.102743\pi\)
−0.948359 + 0.317200i \(0.897257\pi\)
\(488\) 6.00000i 0.271607i
\(489\) 0 0
\(490\) 6.00000 + 3.00000i 0.271052 + 0.135526i
\(491\) 4.00000 0.180517 0.0902587 0.995918i \(-0.471231\pi\)
0.0902587 + 0.995918i \(0.471231\pi\)
\(492\) 0 0
\(493\) 2.00000i 0.0900755i
\(494\) 0 0
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 16.0000i 0.717698i
\(498\) 0 0
\(499\) 4.00000 0.179065 0.0895323 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) 11.0000 2.00000i 0.491935 0.0894427i
\(501\) 0 0
\(502\) 0 0
\(503\) 4.00000i 0.178351i 0.996016 + 0.0891756i \(0.0284232\pi\)
−0.996016 + 0.0891756i \(0.971577\pi\)
\(504\) 0 0
\(505\) 2.00000 4.00000i 0.0889988 0.177998i
\(506\) 0 0
\(507\) 0 0
\(508\) 12.0000i 0.532414i
\(509\) 26.0000 1.15243 0.576215 0.817298i \(-0.304529\pi\)
0.576215 + 0.817298i \(0.304529\pi\)
\(510\) 0 0
\(511\) −28.0000 −1.23865
\(512\) 11.0000i 0.486136i
\(513\) 0 0
\(514\) −8.00000 −0.352865
\(515\) −4.00000 2.00000i −0.176261 0.0881305i
\(516\) 0 0
\(517\) 0 0
\(518\) 4.00000i 0.175750i
\(519\) 0 0
\(520\) 12.0000 24.0000i 0.526235 1.05247i
\(521\) −10.0000 −0.438108 −0.219054 0.975713i \(-0.570297\pi\)
−0.219054 + 0.975713i \(0.570297\pi\)
\(522\) 0 0
\(523\) 34.0000i 1.48672i −0.668894 0.743358i \(-0.733232\pi\)
0.668894 0.743358i \(-0.266768\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) 16.0000 0.697633
\(527\) 8.00000i 0.348485i
\(528\) 0 0
\(529\) 19.0000 0.826087
\(530\) 12.0000 24.0000i 0.521247 1.04249i
\(531\) 0 0
\(532\) 0 0
\(533\) 40.0000i 1.73259i
\(534\) 0 0
\(535\) 12.0000 + 6.00000i 0.518805 + 0.259403i
\(536\) 6.00000 0.259161
\(537\) 0 0
\(538\) 26.0000i 1.12094i
\(539\) 0 0
\(540\) 0 0
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) 24.0000i 1.03089i
\(543\) 0 0
\(544\) −10.0000 −0.428746
\(545\) −14.0000 + 28.0000i −0.599694 + 1.19939i
\(546\) 0 0
\(547\) 46.0000i 1.96682i −0.181402 0.983409i \(-0.558064\pi\)
0.181402 0.983409i \(-0.441936\pi\)
\(548\) 14.0000i 0.598050i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 16.0000i 0.680389i
\(554\) −8.00000 −0.339887
\(555\) 0 0
\(556\) 4.00000 0.169638
\(557\) 20.0000i 0.847427i 0.905796 + 0.423714i \(0.139274\pi\)
−0.905796 + 0.423714i \(0.860726\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −4.00000 2.00000i −0.169031 0.0845154i
\(561\) 0 0
\(562\) 6.00000i 0.253095i
\(563\) 28.0000i 1.18006i −0.807382 0.590030i \(-0.799116\pi\)
0.807382 0.590030i \(-0.200884\pi\)
\(564\) 0 0
\(565\) −28.0000 14.0000i −1.17797 0.588984i
\(566\) 10.0000 0.420331
\(567\) 0 0
\(568\) 24.0000i 1.00702i
\(569\) 14.0000 0.586911 0.293455 0.955973i \(-0.405195\pi\)
0.293455 + 0.955973i \(0.405195\pi\)
\(570\) 0 0
\(571\) 4.00000 0.167395 0.0836974 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 20.0000 0.834784
\(575\) 8.00000 6.00000i 0.333623 0.250217i
\(576\) 0 0
\(577\) 6.00000i 0.249783i 0.992170 + 0.124892i \(0.0398583\pi\)
−0.992170 + 0.124892i \(0.960142\pi\)
\(578\) 13.0000i 0.540729i
\(579\) 0 0
\(580\) −1.00000 + 2.00000i −0.0415227 + 0.0830455i
\(581\) −12.0000 −0.497844
\(582\) 0 0
\(583\) 0 0
\(584\) −42.0000 −1.73797
\(585\) 0 0
\(586\) 6.00000 0.247858
\(587\) 42.0000i 1.73353i −0.498721 0.866763i \(-0.666197\pi\)
0.498721 0.866763i \(-0.333803\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 8.00000 + 4.00000i 0.329355 + 0.164677i
\(591\) 0 0
\(592\) 2.00000i 0.0821995i
\(593\) 36.0000i 1.47834i 0.673517 + 0.739171i \(0.264783\pi\)
−0.673517 + 0.739171i \(0.735217\pi\)
\(594\) 0 0
\(595\) 4.00000 8.00000i 0.163984 0.327968i
\(596\) −6.00000 −0.245770
\(597\) 0 0
\(598\) 8.00000i 0.327144i
\(599\) −36.0000 −1.47092 −0.735460 0.677568i \(-0.763034\pi\)
−0.735460 + 0.677568i \(0.763034\pi\)
\(600\) 0 0
\(601\) −2.00000 −0.0815817 −0.0407909 0.999168i \(-0.512988\pi\)
−0.0407909 + 0.999168i \(0.512988\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −24.0000 −0.976546
\(605\) 11.0000 22.0000i 0.447214 0.894427i
\(606\) 0 0
\(607\) 28.0000i 1.13648i −0.822861 0.568242i \(-0.807624\pi\)
0.822861 0.568242i \(-0.192376\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 4.00000 + 2.00000i 0.161955 + 0.0809776i
\(611\) −48.0000 −1.94187
\(612\) 0 0
\(613\) 40.0000i 1.61558i −0.589467 0.807792i \(-0.700662\pi\)
0.589467 0.807792i \(-0.299338\pi\)
\(614\) −8.00000 −0.322854
\(615\) 0 0
\(616\) 0 0
\(617\) 18.0000i 0.724653i −0.932051 0.362326i \(-0.881983\pi\)
0.932051 0.362326i \(-0.118017\pi\)
\(618\) 0 0
\(619\) −36.0000 −1.44696 −0.723481 0.690344i \(-0.757459\pi\)
−0.723481 + 0.690344i \(0.757459\pi\)
\(620\) −4.00000 + 8.00000i −0.160644 + 0.321288i
\(621\) 0 0
\(622\) 8.00000i 0.320771i
\(623\) 20.0000i 0.801283i
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) −28.0000 −1.11911
\(627\) 0 0
\(628\) 22.0000i 0.877896i
\(629\) 4.00000 0.159490
\(630\) 0 0
\(631\) −8.00000 −0.318475 −0.159237 0.987240i \(-0.550904\pi\)
−0.159237 + 0.987240i \(0.550904\pi\)
\(632\) 24.0000i 0.954669i
\(633\) 0 0
\(634\) 6.00000 0.238290
\(635\) −24.0000 12.0000i −0.952411 0.476205i
\(636\) 0 0
\(637\) 12.0000i 0.475457i
\(638\) 0 0
\(639\) 0 0
\(640\) 6.00000 + 3.00000i 0.237171 + 0.118585i
\(641\) −50.0000 −1.97488 −0.987441 0.157991i \(-0.949498\pi\)
−0.987441 + 0.157991i \(0.949498\pi\)
\(642\) 0 0
\(643\) 10.0000i 0.394362i 0.980367 + 0.197181i \(0.0631786\pi\)
−0.980367 + 0.197181i \(0.936821\pi\)
\(644\) 4.00000 0.157622
\(645\) 0 0
\(646\) 0 0
\(647\) 18.0000i 0.707653i 0.935311 + 0.353827i \(0.115120\pi\)
−0.935311 + 0.353827i \(0.884880\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 12.0000 + 16.0000i 0.470679 + 0.627572i
\(651\) 0 0
\(652\) 4.00000i 0.156652i
\(653\) 6.00000i 0.234798i −0.993085 0.117399i \(-0.962544\pi\)
0.993085 0.117399i \(-0.0374557\pi\)
\(654\) 0 0
\(655\) −12.0000 + 24.0000i −0.468879 + 0.937758i
\(656\) 10.0000 0.390434
\(657\) 0 0
\(658\) 24.0000i 0.935617i
\(659\) 28.0000 1.09073 0.545363 0.838200i \(-0.316392\pi\)
0.545363 + 0.838200i \(0.316392\pi\)
\(660\) 0 0
\(661\) 26.0000 1.01128 0.505641 0.862744i \(-0.331256\pi\)
0.505641 + 0.862744i \(0.331256\pi\)
\(662\) 8.00000i 0.310929i
\(663\) 0 0
\(664\) −18.0000 −0.698535
\(665\) 0 0
\(666\) 0 0
\(667\) 2.00000i 0.0774403i
\(668\) 2.00000i 0.0773823i
\(669\) 0 0
\(670\) −2.00000 + 4.00000i −0.0772667 + 0.154533i
\(671\) 0 0
\(672\) 0 0
\(673\) 12.0000i 0.462566i 0.972887 + 0.231283i \(0.0742923\pi\)
−0.972887 + 0.231283i \(0.925708\pi\)
\(674\) 2.00000 0.0770371
\(675\) 0 0
\(676\) −3.00000 −0.115385
\(677\) 14.0000i 0.538064i −0.963131 0.269032i \(-0.913296\pi\)
0.963131 0.269032i \(-0.0867037\pi\)
\(678\) 0 0
\(679\) 20.0000 0.767530
\(680\) 6.00000 12.0000i 0.230089 0.460179i
\(681\) 0 0
\(682\) 0 0
\(683\) 18.0000i 0.688751i −0.938832 0.344375i \(-0.888091\pi\)
0.938832 0.344375i \(-0.111909\pi\)
\(684\) 0 0
\(685\) −28.0000 14.0000i −1.06983 0.534913i
\(686\) −20.0000 −0.763604
\(687\) 0 0
\(688\) 0 0
\(689\) −48.0000 −1.82865
\(690\) 0 0
\(691\) −44.0000 −1.67384 −0.836919 0.547326i \(-0.815646\pi\)
−0.836919 + 0.547326i \(0.815646\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 6.00000 0.227757
\(695\) −4.00000 + 8.00000i −0.151729 + 0.303457i
\(696\) 0 0
\(697\) 20.0000i 0.757554i
\(698\) 2.00000i 0.0757011i
\(699\) 0 0
\(700\) −8.00000 + 6.00000i −0.302372 + 0.226779i
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 28.0000 1.05379
\(707\) 4.00000i 0.150435i
\(708\) 0 0
\(709\) 6.00000 0.225335 0.112667 0.993633i \(-0.464061\pi\)
0.112667 + 0.993633i \(0.464061\pi\)
\(710\) 16.0000 + 8.00000i 0.600469 + 0.300235i
\(711\) 0 0
\(712\) 30.0000i 1.12430i
\(713\) 8.00000i 0.299602i
\(714\) 0 0
\(715\) 0 0
\(716\) −20.0000 −0.747435
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 4.00000 0.148968
\(722\) 19.0000i 0.707107i
\(723\) 0 0
\(724\) 2.00000 0.0743294
\(725\) −3.00000 4.00000i −0.111417 0.148556i
\(726\) 0 0
\(727\) 40.0000i 1.48352i −0.670667 0.741759i \(-0.733992\pi\)
0.670667 0.741759i \(-0.266008\pi\)
\(728\) 24.0000i 0.889499i
\(729\) 0 0
\(730\) 14.0000 28.0000i 0.518163 1.03633i
\(731\) 0 0
\(732\) 0 0
\(733\) 50.0000i 1.84679i 0.383849 + 0.923396i \(0.374598\pi\)
−0.383849 + 0.923396i \(0.625402\pi\)
\(734\) −24.0000 −0.885856
\(735\) 0 0
\(736\) 10.0000 0.368605
\(737\) 0 0
\(738\) 0 0
\(739\) 40.0000 1.47142 0.735712 0.677295i \(-0.236848\pi\)
0.735712 + 0.677295i \(0.236848\pi\)
\(740\) −4.00000 2.00000i −0.147043 0.0735215i
\(741\) 0 0
\(742\) 24.0000i 0.881068i
\(743\) 20.0000i 0.733729i 0.930274 + 0.366864i \(0.119569\pi\)
−0.930274 + 0.366864i \(0.880431\pi\)
\(744\) 0 0
\(745\) 6.00000 12.0000i 0.219823 0.439646i
\(746\) −4.00000 −0.146450
\(747\) 0 0
\(748\) 0 0
\(749\) −12.0000 −0.438470
\(750\) 0 0
\(751\) −20.0000 −0.729810 −0.364905 0.931045i \(-0.618899\pi\)
−0.364905 + 0.931045i \(0.618899\pi\)
\(752\) 12.0000i 0.437595i
\(753\) 0 0
\(754\) −4.00000 −0.145671
\(755\) 24.0000 48.0000i 0.873449 1.74690i
\(756\) 0 0
\(757\) 42.0000i 1.52652i 0.646094 + 0.763258i \(0.276401\pi\)
−0.646094 + 0.763258i \(0.723599\pi\)
\(758\) 20.0000i 0.726433i
\(759\) 0 0
\(760\) 0 0
\(761\) 42.0000 1.52250 0.761249 0.648459i \(-0.224586\pi\)
0.761249 + 0.648459i \(0.224586\pi\)
\(762\) 0 0
\(763\) 28.0000i 1.01367i
\(764\) −12.0000 −0.434145
\(765\) 0 0
\(766\) 18.0000 0.650366
\(767\) 16.0000i 0.577727i
\(768\) 0 0
\(769\) −38.0000 −1.37032 −0.685158 0.728395i \(-0.740267\pi\)
−0.685158 + 0.728395i \(0.740267\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 6.00000i 0.215945i
\(773\) 30.0000i 1.07903i −0.841978 0.539513i \(-0.818609\pi\)
0.841978 0.539513i \(-0.181391\pi\)
\(774\) 0 0
\(775\) −12.0000 16.0000i −0.431053 0.574737i
\(776\) 30.0000 1.07694
\(777\) 0 0
\(778\) 2.00000i 0.0717035i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 4.00000i 0.143040i
\(783\) 0 0
\(784\) −3.00000 −0.107143
\(785\) −44.0000 22.0000i −1.57043 0.785214i
\(786\) 0 0
\(787\) 34.0000i 1.21197i −0.795476 0.605985i \(-0.792779\pi\)
0.795476 0.605985i \(-0.207221\pi\)
\(788\) 8.00000i 0.284988i
\(789\) 0 0
\(790\) −16.0000 8.00000i −0.569254 0.284627i
\(791\) 28.0000 0.995565
\(792\) 0 0
\(793\) 8.00000i 0.284088i
\(794\) 20.0000 0.709773