Properties

Label 1600.2.s.a.943.1
Level $1600$
Weight $2$
Character 1600.943
Analytic conductor $12.776$
Analytic rank $1$
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] = [1600,2,Mod(207,1600)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1600.207");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1600.s (of order \(4\), degree \(2\), not 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: \(12.7760643234\)
Analytic rank: \(1\)
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: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 80)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 943.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1600.943
Dual form 1600.2.s.a.207.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{3} +(-3.00000 + 3.00000i) q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{3} +(-3.00000 + 3.00000i) q^{7} +1.00000 q^{9} +(1.00000 + 1.00000i) q^{11} +2.00000i q^{13} +(-1.00000 + 1.00000i) q^{17} +(3.00000 + 3.00000i) q^{19} +(6.00000 - 6.00000i) q^{21} +(-1.00000 - 1.00000i) q^{23} +4.00000 q^{27} +(-7.00000 + 7.00000i) q^{29} -2.00000i q^{31} +(-2.00000 - 2.00000i) q^{33} -6.00000i q^{37} -4.00000i q^{39} -4.00000i q^{41} +4.00000i q^{43} +(-7.00000 - 7.00000i) q^{47} -11.0000i q^{49} +(2.00000 - 2.00000i) q^{51} +8.00000 q^{53} +(-6.00000 - 6.00000i) q^{57} +(-3.00000 + 3.00000i) q^{59} +(-1.00000 - 1.00000i) q^{61} +(-3.00000 + 3.00000i) q^{63} -4.00000i q^{67} +(2.00000 + 2.00000i) q^{69} +(-3.00000 + 3.00000i) q^{73} -6.00000 q^{77} -8.00000 q^{79} -11.0000 q^{81} -2.00000 q^{83} +(14.0000 - 14.0000i) q^{87} -6.00000 q^{89} +(-6.00000 - 6.00000i) q^{91} +4.00000i q^{93} +(11.0000 - 11.0000i) q^{97} +(1.00000 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 4 q^{3} - 6 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 4 q^{3} - 6 q^{7} + 2 q^{9} + 2 q^{11} - 2 q^{17} + 6 q^{19} + 12 q^{21} - 2 q^{23} + 8 q^{27} - 14 q^{29} - 4 q^{33} - 14 q^{47} + 4 q^{51} + 16 q^{53} - 12 q^{57} - 6 q^{59} - 2 q^{61} - 6 q^{63} + 4 q^{69} - 6 q^{73} - 12 q^{77} - 16 q^{79} - 22 q^{81} - 4 q^{83} + 28 q^{87} - 12 q^{89} - 12 q^{91} + 22 q^{97} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(901\) \(1151\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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 0
\(3\) −2.00000 −1.15470 −0.577350 0.816497i \(-0.695913\pi\)
−0.577350 + 0.816497i \(0.695913\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −3.00000 + 3.00000i −1.13389 + 1.13389i −0.144370 + 0.989524i \(0.546115\pi\)
−0.989524 + 0.144370i \(0.953885\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 1.00000 + 1.00000i 0.301511 + 0.301511i 0.841605 0.540094i \(-0.181611\pi\)
−0.540094 + 0.841605i \(0.681611\pi\)
\(12\) 0 0
\(13\) 2.00000i 0.554700i 0.960769 + 0.277350i \(0.0894562\pi\)
−0.960769 + 0.277350i \(0.910544\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.00000 + 1.00000i −0.242536 + 0.242536i −0.817898 0.575363i \(-0.804861\pi\)
0.575363 + 0.817898i \(0.304861\pi\)
\(18\) 0 0
\(19\) 3.00000 + 3.00000i 0.688247 + 0.688247i 0.961844 0.273597i \(-0.0882135\pi\)
−0.273597 + 0.961844i \(0.588214\pi\)
\(20\) 0 0
\(21\) 6.00000 6.00000i 1.30931 1.30931i
\(22\) 0 0
\(23\) −1.00000 1.00000i −0.208514 0.208514i 0.595121 0.803636i \(-0.297104\pi\)
−0.803636 + 0.595121i \(0.797104\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 4.00000 0.769800
\(28\) 0 0
\(29\) −7.00000 + 7.00000i −1.29987 + 1.29987i −0.371391 + 0.928477i \(0.621119\pi\)
−0.928477 + 0.371391i \(0.878881\pi\)
\(30\) 0 0
\(31\) 2.00000i 0.359211i −0.983739 0.179605i \(-0.942518\pi\)
0.983739 0.179605i \(-0.0574821\pi\)
\(32\) 0 0
\(33\) −2.00000 2.00000i −0.348155 0.348155i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 6.00000i 0.986394i −0.869918 0.493197i \(-0.835828\pi\)
0.869918 0.493197i \(-0.164172\pi\)
\(38\) 0 0
\(39\) 4.00000i 0.640513i
\(40\) 0 0
\(41\) 4.00000i 0.624695i −0.949968 0.312348i \(-0.898885\pi\)
0.949968 0.312348i \(-0.101115\pi\)
\(42\) 0 0
\(43\) 4.00000i 0.609994i 0.952353 + 0.304997i \(0.0986555\pi\)
−0.952353 + 0.304997i \(0.901344\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −7.00000 7.00000i −1.02105 1.02105i −0.999774 0.0212814i \(-0.993225\pi\)
−0.0212814 0.999774i \(-0.506775\pi\)
\(48\) 0 0
\(49\) 11.0000i 1.57143i
\(50\) 0 0
\(51\) 2.00000 2.00000i 0.280056 0.280056i
\(52\) 0 0
\(53\) 8.00000 1.09888 0.549442 0.835532i \(-0.314840\pi\)
0.549442 + 0.835532i \(0.314840\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −6.00000 6.00000i −0.794719 0.794719i
\(58\) 0 0
\(59\) −3.00000 + 3.00000i −0.390567 + 0.390567i −0.874889 0.484323i \(-0.839066\pi\)
0.484323 + 0.874889i \(0.339066\pi\)
\(60\) 0 0
\(61\) −1.00000 1.00000i −0.128037 0.128037i 0.640184 0.768221i \(-0.278858\pi\)
−0.768221 + 0.640184i \(0.778858\pi\)
\(62\) 0 0
\(63\) −3.00000 + 3.00000i −0.377964 + 0.377964i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 4.00000i 0.488678i −0.969690 0.244339i \(-0.921429\pi\)
0.969690 0.244339i \(-0.0785709\pi\)
\(68\) 0 0
\(69\) 2.00000 + 2.00000i 0.240772 + 0.240772i
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −3.00000 + 3.00000i −0.351123 + 0.351123i −0.860527 0.509404i \(-0.829866\pi\)
0.509404 + 0.860527i \(0.329866\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −6.00000 −0.683763
\(78\) 0 0
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) −11.0000 −1.22222
\(82\) 0 0
\(83\) −2.00000 −0.219529 −0.109764 0.993958i \(-0.535010\pi\)
−0.109764 + 0.993958i \(0.535010\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 14.0000 14.0000i 1.50096 1.50096i
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) −6.00000 6.00000i −0.628971 0.628971i
\(92\) 0 0
\(93\) 4.00000i 0.414781i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 11.0000 11.0000i 1.11688 1.11688i 0.124684 0.992196i \(-0.460208\pi\)
0.992196 0.124684i \(-0.0397918\pi\)
\(98\) 0 0
\(99\) 1.00000 + 1.00000i 0.100504 + 0.100504i
\(100\) 0 0
\(101\) −5.00000 + 5.00000i −0.497519 + 0.497519i −0.910665 0.413146i \(-0.864430\pi\)
0.413146 + 0.910665i \(0.364430\pi\)
\(102\) 0 0
\(103\) −5.00000 5.00000i −0.492665 0.492665i 0.416480 0.909145i \(-0.363264\pi\)
−0.909145 + 0.416480i \(0.863264\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −6.00000 −0.580042 −0.290021 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(108\) 0 0
\(109\) 5.00000 5.00000i 0.478913 0.478913i −0.425871 0.904784i \(-0.640032\pi\)
0.904784 + 0.425871i \(0.140032\pi\)
\(110\) 0 0
\(111\) 12.0000i 1.13899i
\(112\) 0 0
\(113\) −13.0000 13.0000i −1.22294 1.22294i −0.966583 0.256354i \(-0.917479\pi\)
−0.256354 0.966583i \(-0.582521\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 2.00000i 0.184900i
\(118\) 0 0
\(119\) 6.00000i 0.550019i
\(120\) 0 0
\(121\) 9.00000i 0.818182i
\(122\) 0 0
\(123\) 8.00000i 0.721336i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −7.00000 7.00000i −0.621150 0.621150i 0.324676 0.945825i \(-0.394745\pi\)
−0.945825 + 0.324676i \(0.894745\pi\)
\(128\) 0 0
\(129\) 8.00000i 0.704361i
\(130\) 0 0
\(131\) 7.00000 7.00000i 0.611593 0.611593i −0.331768 0.943361i \(-0.607645\pi\)
0.943361 + 0.331768i \(0.107645\pi\)
\(132\) 0 0
\(133\) −18.0000 −1.56080
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 9.00000 + 9.00000i 0.768922 + 0.768922i 0.977917 0.208995i \(-0.0670192\pi\)
−0.208995 + 0.977917i \(0.567019\pi\)
\(138\) 0 0
\(139\) 9.00000 9.00000i 0.763370 0.763370i −0.213560 0.976930i \(-0.568506\pi\)
0.976930 + 0.213560i \(0.0685059\pi\)
\(140\) 0 0
\(141\) 14.0000 + 14.0000i 1.17901 + 1.17901i
\(142\) 0 0
\(143\) −2.00000 + 2.00000i −0.167248 + 0.167248i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 22.0000i 1.81453i
\(148\) 0 0
\(149\) 1.00000 + 1.00000i 0.0819232 + 0.0819232i 0.746881 0.664958i \(-0.231550\pi\)
−0.664958 + 0.746881i \(0.731550\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 0 0
\(153\) −1.00000 + 1.00000i −0.0808452 + 0.0808452i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −20.0000 −1.59617 −0.798087 0.602542i \(-0.794154\pi\)
−0.798087 + 0.602542i \(0.794154\pi\)
\(158\) 0 0
\(159\) −16.0000 −1.26888
\(160\) 0 0
\(161\) 6.00000 0.472866
\(162\) 0 0
\(163\) 14.0000 1.09656 0.548282 0.836293i \(-0.315282\pi\)
0.548282 + 0.836293i \(0.315282\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3.00000 + 3.00000i −0.232147 + 0.232147i −0.813588 0.581441i \(-0.802489\pi\)
0.581441 + 0.813588i \(0.302489\pi\)
\(168\) 0 0
\(169\) 9.00000 0.692308
\(170\) 0 0
\(171\) 3.00000 + 3.00000i 0.229416 + 0.229416i
\(172\) 0 0
\(173\) 6.00000i 0.456172i 0.973641 + 0.228086i \(0.0732467\pi\)
−0.973641 + 0.228086i \(0.926753\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 6.00000 6.00000i 0.450988 0.450988i
\(178\) 0 0
\(179\) −5.00000 5.00000i −0.373718 0.373718i 0.495112 0.868829i \(-0.335127\pi\)
−0.868829 + 0.495112i \(0.835127\pi\)
\(180\) 0 0
\(181\) 3.00000 3.00000i 0.222988 0.222988i −0.586767 0.809756i \(-0.699600\pi\)
0.809756 + 0.586767i \(0.199600\pi\)
\(182\) 0 0
\(183\) 2.00000 + 2.00000i 0.147844 + 0.147844i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −2.00000 −0.146254
\(188\) 0 0
\(189\) −12.0000 + 12.0000i −0.872872 + 0.872872i
\(190\) 0 0
\(191\) 18.0000i 1.30243i −0.758891 0.651217i \(-0.774259\pi\)
0.758891 0.651217i \(-0.225741\pi\)
\(192\) 0 0
\(193\) 15.0000 + 15.0000i 1.07972 + 1.07972i 0.996534 + 0.0831899i \(0.0265108\pi\)
0.0831899 + 0.996534i \(0.473489\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 6.00000i 0.427482i 0.976890 + 0.213741i \(0.0685649\pi\)
−0.976890 + 0.213741i \(0.931435\pi\)
\(198\) 0 0
\(199\) 10.0000i 0.708881i 0.935079 + 0.354441i \(0.115329\pi\)
−0.935079 + 0.354441i \(0.884671\pi\)
\(200\) 0 0
\(201\) 8.00000i 0.564276i
\(202\) 0 0
\(203\) 42.0000i 2.94782i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.00000 1.00000i −0.0695048 0.0695048i
\(208\) 0 0
\(209\) 6.00000i 0.415029i
\(210\) 0 0
\(211\) 19.0000 19.0000i 1.30801 1.30801i 0.385167 0.922847i \(-0.374144\pi\)
0.922847 0.385167i \(-0.125856\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 6.00000 + 6.00000i 0.407307 + 0.407307i
\(218\) 0 0
\(219\) 6.00000 6.00000i 0.405442 0.405442i
\(220\) 0 0
\(221\) −2.00000 2.00000i −0.134535 0.134535i
\(222\) 0 0
\(223\) −9.00000 + 9.00000i −0.602685 + 0.602685i −0.941024 0.338340i \(-0.890135\pi\)
0.338340 + 0.941024i \(0.390135\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 12.0000i 0.796468i −0.917284 0.398234i \(-0.869623\pi\)
0.917284 0.398234i \(-0.130377\pi\)
\(228\) 0 0
\(229\) 1.00000 + 1.00000i 0.0660819 + 0.0660819i 0.739375 0.673293i \(-0.235121\pi\)
−0.673293 + 0.739375i \(0.735121\pi\)
\(230\) 0 0
\(231\) 12.0000 0.789542
\(232\) 0 0
\(233\) 9.00000 9.00000i 0.589610 0.589610i −0.347916 0.937526i \(-0.613111\pi\)
0.937526 + 0.347916i \(0.113111\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 16.0000 1.03931
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −14.0000 −0.901819 −0.450910 0.892570i \(-0.648900\pi\)
−0.450910 + 0.892570i \(0.648900\pi\)
\(242\) 0 0
\(243\) 10.0000 0.641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −6.00000 + 6.00000i −0.381771 + 0.381771i
\(248\) 0 0
\(249\) 4.00000 0.253490
\(250\) 0 0
\(251\) −11.0000 11.0000i −0.694314 0.694314i 0.268864 0.963178i \(-0.413352\pi\)
−0.963178 + 0.268864i \(0.913352\pi\)
\(252\) 0 0
\(253\) 2.00000i 0.125739i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −13.0000 + 13.0000i −0.810918 + 0.810918i −0.984771 0.173854i \(-0.944378\pi\)
0.173854 + 0.984771i \(0.444378\pi\)
\(258\) 0 0
\(259\) 18.0000 + 18.0000i 1.11847 + 1.11847i
\(260\) 0 0
\(261\) −7.00000 + 7.00000i −0.433289 + 0.433289i
\(262\) 0 0
\(263\) 7.00000 + 7.00000i 0.431638 + 0.431638i 0.889185 0.457547i \(-0.151272\pi\)
−0.457547 + 0.889185i \(0.651272\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 12.0000 0.734388
\(268\) 0 0
\(269\) 1.00000 1.00000i 0.0609711 0.0609711i −0.675964 0.736935i \(-0.736272\pi\)
0.736935 + 0.675964i \(0.236272\pi\)
\(270\) 0 0
\(271\) 30.0000i 1.82237i 0.411997 + 0.911185i \(0.364831\pi\)
−0.411997 + 0.911185i \(0.635169\pi\)
\(272\) 0 0
\(273\) 12.0000 + 12.0000i 0.726273 + 0.726273i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 18.0000i 1.08152i 0.841178 + 0.540758i \(0.181862\pi\)
−0.841178 + 0.540758i \(0.818138\pi\)
\(278\) 0 0
\(279\) 2.00000i 0.119737i
\(280\) 0 0
\(281\) 16.0000i 0.954480i 0.878773 + 0.477240i \(0.158363\pi\)
−0.878773 + 0.477240i \(0.841637\pi\)
\(282\) 0 0
\(283\) 12.0000i 0.713326i 0.934233 + 0.356663i \(0.116086\pi\)
−0.934233 + 0.356663i \(0.883914\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 12.0000 + 12.0000i 0.708338 + 0.708338i
\(288\) 0 0
\(289\) 15.0000i 0.882353i
\(290\) 0 0
\(291\) −22.0000 + 22.0000i −1.28966 + 1.28966i
\(292\) 0 0
\(293\) 12.0000 0.701047 0.350524 0.936554i \(-0.386004\pi\)
0.350524 + 0.936554i \(0.386004\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 4.00000 + 4.00000i 0.232104 + 0.232104i
\(298\) 0 0
\(299\) 2.00000 2.00000i 0.115663 0.115663i
\(300\) 0 0
\(301\) −12.0000 12.0000i −0.691669 0.691669i
\(302\) 0 0
\(303\) 10.0000 10.0000i 0.574485 0.574485i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 4.00000i 0.228292i 0.993464 + 0.114146i \(0.0364132\pi\)
−0.993464 + 0.114146i \(0.963587\pi\)
\(308\) 0 0
\(309\) 10.0000 + 10.0000i 0.568880 + 0.568880i
\(310\) 0 0
\(311\) −16.0000 −0.907277 −0.453638 0.891186i \(-0.649874\pi\)
−0.453638 + 0.891186i \(0.649874\pi\)
\(312\) 0 0
\(313\) 13.0000 13.0000i 0.734803 0.734803i −0.236764 0.971567i \(-0.576087\pi\)
0.971567 + 0.236764i \(0.0760868\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8.00000 −0.449325 −0.224662 0.974437i \(-0.572128\pi\)
−0.224662 + 0.974437i \(0.572128\pi\)
\(318\) 0 0
\(319\) −14.0000 −0.783850
\(320\) 0 0
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) −6.00000 −0.333849
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −10.0000 + 10.0000i −0.553001 + 0.553001i
\(328\) 0 0
\(329\) 42.0000 2.31553
\(330\) 0 0
\(331\) 21.0000 + 21.0000i 1.15426 + 1.15426i 0.985689 + 0.168576i \(0.0539168\pi\)
0.168576 + 0.985689i \(0.446083\pi\)
\(332\) 0 0
\(333\) 6.00000i 0.328798i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 11.0000 11.0000i 0.599208 0.599208i −0.340894 0.940102i \(-0.610730\pi\)
0.940102 + 0.340894i \(0.110730\pi\)
\(338\) 0 0
\(339\) 26.0000 + 26.0000i 1.41213 + 1.41213i
\(340\) 0 0
\(341\) 2.00000 2.00000i 0.108306 0.108306i
\(342\) 0 0
\(343\) 12.0000 + 12.0000i 0.647939 + 0.647939i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.00000 0.107366 0.0536828 0.998558i \(-0.482904\pi\)
0.0536828 + 0.998558i \(0.482904\pi\)
\(348\) 0 0
\(349\) −3.00000 + 3.00000i −0.160586 + 0.160586i −0.782826 0.622240i \(-0.786223\pi\)
0.622240 + 0.782826i \(0.286223\pi\)
\(350\) 0 0
\(351\) 8.00000i 0.427008i
\(352\) 0 0
\(353\) −13.0000 13.0000i −0.691920 0.691920i 0.270734 0.962654i \(-0.412734\pi\)
−0.962654 + 0.270734i \(0.912734\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 12.0000i 0.635107i
\(358\) 0 0
\(359\) 14.0000i 0.738892i −0.929252 0.369446i \(-0.879548\pi\)
0.929252 0.369446i \(-0.120452\pi\)
\(360\) 0 0
\(361\) 1.00000i 0.0526316i
\(362\) 0 0
\(363\) 18.0000i 0.944755i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 21.0000 + 21.0000i 1.09619 + 1.09619i 0.994852 + 0.101339i \(0.0323127\pi\)
0.101339 + 0.994852i \(0.467687\pi\)
\(368\) 0 0
\(369\) 4.00000i 0.208232i
\(370\) 0 0
\(371\) −24.0000 + 24.0000i −1.24602 + 1.24602i
\(372\) 0 0
\(373\) 4.00000 0.207112 0.103556 0.994624i \(-0.466978\pi\)
0.103556 + 0.994624i \(0.466978\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −14.0000 14.0000i −0.721037 0.721037i
\(378\) 0 0
\(379\) −15.0000 + 15.0000i −0.770498 + 0.770498i −0.978194 0.207695i \(-0.933404\pi\)
0.207695 + 0.978194i \(0.433404\pi\)
\(380\) 0 0
\(381\) 14.0000 + 14.0000i 0.717242 + 0.717242i
\(382\) 0 0
\(383\) −5.00000 + 5.00000i −0.255488 + 0.255488i −0.823216 0.567728i \(-0.807823\pi\)
0.567728 + 0.823216i \(0.307823\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 4.00000i 0.203331i
\(388\) 0 0
\(389\) −23.0000 23.0000i −1.16615 1.16615i −0.983105 0.183041i \(-0.941406\pi\)
−0.183041 0.983105i \(-0.558594\pi\)
\(390\) 0 0
\(391\) 2.00000 0.101144
\(392\) 0 0
\(393\) −14.0000 + 14.0000i −0.706207 + 0.706207i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 32.0000 1.60603 0.803017 0.595956i \(-0.203227\pi\)
0.803017 + 0.595956i \(0.203227\pi\)
\(398\) 0 0
\(399\) 36.0000 1.80225
\(400\) 0 0
\(401\) −2.00000 −0.0998752 −0.0499376 0.998752i \(-0.515902\pi\)
−0.0499376 + 0.998752i \(0.515902\pi\)
\(402\) 0 0
\(403\) 4.00000 0.199254
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 6.00000 6.00000i 0.297409 0.297409i
\(408\) 0 0
\(409\) −38.0000 −1.87898 −0.939490 0.342578i \(-0.888700\pi\)
−0.939490 + 0.342578i \(0.888700\pi\)
\(410\) 0 0
\(411\) −18.0000 18.0000i −0.887875 0.887875i
\(412\) 0 0
\(413\) 18.0000i 0.885722i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −18.0000 + 18.0000i −0.881464 + 0.881464i
\(418\) 0 0
\(419\) −17.0000 17.0000i −0.830504 0.830504i 0.157081 0.987586i \(-0.449792\pi\)
−0.987586 + 0.157081i \(0.949792\pi\)
\(420\) 0 0
\(421\) −5.00000 + 5.00000i −0.243685 + 0.243685i −0.818373 0.574688i \(-0.805124\pi\)
0.574688 + 0.818373i \(0.305124\pi\)
\(422\) 0 0
\(423\) −7.00000 7.00000i −0.340352 0.340352i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 6.00000 0.290360
\(428\) 0 0
\(429\) 4.00000 4.00000i 0.193122 0.193122i
\(430\) 0 0
\(431\) 2.00000i 0.0963366i −0.998839 0.0481683i \(-0.984662\pi\)
0.998839 0.0481683i \(-0.0153384\pi\)
\(432\) 0 0
\(433\) −5.00000 5.00000i −0.240285 0.240285i 0.576683 0.816968i \(-0.304347\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.00000i 0.287019i
\(438\) 0 0
\(439\) 26.0000i 1.24091i 0.784241 + 0.620456i \(0.213053\pi\)
−0.784241 + 0.620456i \(0.786947\pi\)
\(440\) 0 0
\(441\) 11.0000i 0.523810i
\(442\) 0 0
\(443\) 4.00000i 0.190046i −0.995475 0.0950229i \(-0.969708\pi\)
0.995475 0.0950229i \(-0.0302924\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −2.00000 2.00000i −0.0945968 0.0945968i
\(448\) 0 0
\(449\) 24.0000i 1.13263i −0.824189 0.566315i \(-0.808369\pi\)
0.824189 0.566315i \(-0.191631\pi\)
\(450\) 0 0
\(451\) 4.00000 4.00000i 0.188353 0.188353i
\(452\) 0 0
\(453\) 16.0000 0.751746
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −7.00000 7.00000i −0.327446 0.327446i 0.524168 0.851615i \(-0.324376\pi\)
−0.851615 + 0.524168i \(0.824376\pi\)
\(458\) 0 0
\(459\) −4.00000 + 4.00000i −0.186704 + 0.186704i
\(460\) 0 0
\(461\) −21.0000 21.0000i −0.978068 0.978068i 0.0216971 0.999765i \(-0.493093\pi\)
−0.999765 + 0.0216971i \(0.993093\pi\)
\(462\) 0 0
\(463\) 19.0000 19.0000i 0.883005 0.883005i −0.110834 0.993839i \(-0.535352\pi\)
0.993839 + 0.110834i \(0.0353522\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 28.0000i 1.29569i 0.761774 + 0.647843i \(0.224329\pi\)
−0.761774 + 0.647843i \(0.775671\pi\)
\(468\) 0 0
\(469\) 12.0000 + 12.0000i 0.554109 + 0.554109i
\(470\) 0 0
\(471\) 40.0000 1.84310
\(472\) 0 0
\(473\) −4.00000 + 4.00000i −0.183920 + 0.183920i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 8.00000 0.366295
\(478\) 0 0
\(479\) 32.0000 1.46212 0.731059 0.682315i \(-0.239027\pi\)
0.731059 + 0.682315i \(0.239027\pi\)
\(480\) 0 0
\(481\) 12.0000 0.547153
\(482\) 0 0
\(483\) −12.0000 −0.546019
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −15.0000 + 15.0000i −0.679715 + 0.679715i −0.959936 0.280221i \(-0.909592\pi\)
0.280221 + 0.959936i \(0.409592\pi\)
\(488\) 0 0
\(489\) −28.0000 −1.26620
\(490\) 0 0
\(491\) 9.00000 + 9.00000i 0.406164 + 0.406164i 0.880399 0.474234i \(-0.157275\pi\)
−0.474234 + 0.880399i \(0.657275\pi\)
\(492\) 0 0
\(493\) 14.0000i 0.630528i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −29.0000 29.0000i −1.29822 1.29822i −0.929568 0.368650i \(-0.879820\pi\)
−0.368650 0.929568i \(-0.620180\pi\)
\(500\) 0 0
\(501\) 6.00000 6.00000i 0.268060 0.268060i
\(502\) 0 0
\(503\) −29.0000 29.0000i −1.29305 1.29305i −0.932893 0.360153i \(-0.882725\pi\)
−0.360153 0.932893i \(-0.617275\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −18.0000 −0.799408
\(508\) 0 0
\(509\) 17.0000 17.0000i 0.753512 0.753512i −0.221621 0.975133i \(-0.571135\pi\)
0.975133 + 0.221621i \(0.0711348\pi\)
\(510\) 0 0
\(511\) 18.0000i 0.796273i
\(512\) 0 0
\(513\) 12.0000 + 12.0000i 0.529813 + 0.529813i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 14.0000i 0.615719i
\(518\) 0 0
\(519\) 12.0000i 0.526742i
\(520\) 0 0
\(521\) 16.0000i 0.700973i −0.936568 0.350486i \(-0.886016\pi\)
0.936568 0.350486i \(-0.113984\pi\)
\(522\) 0 0
\(523\) 20.0000i 0.874539i 0.899331 + 0.437269i \(0.144054\pi\)
−0.899331 + 0.437269i \(0.855946\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.00000 + 2.00000i 0.0871214 + 0.0871214i
\(528\) 0 0
\(529\) 21.0000i 0.913043i
\(530\) 0 0
\(531\) −3.00000 + 3.00000i −0.130189 + 0.130189i
\(532\) 0 0
\(533\) 8.00000 0.346518
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 10.0000 + 10.0000i 0.431532 + 0.431532i
\(538\) 0 0
\(539\) 11.0000 11.0000i 0.473804 0.473804i
\(540\) 0 0
\(541\) 15.0000 + 15.0000i 0.644900 + 0.644900i 0.951756 0.306856i \(-0.0992769\pi\)
−0.306856 + 0.951756i \(0.599277\pi\)
\(542\) 0 0
\(543\) −6.00000 + 6.00000i −0.257485 + 0.257485i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 28.0000i 1.19719i −0.801050 0.598597i \(-0.795725\pi\)
0.801050 0.598597i \(-0.204275\pi\)
\(548\) 0 0
\(549\) −1.00000 1.00000i −0.0426790 0.0426790i
\(550\) 0 0
\(551\) −42.0000 −1.78926
\(552\) 0 0
\(553\) 24.0000 24.0000i 1.02058 1.02058i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −28.0000 −1.18640 −0.593199 0.805056i \(-0.702135\pi\)
−0.593199 + 0.805056i \(0.702135\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 4.00000 0.168880
\(562\) 0 0
\(563\) −18.0000 −0.758610 −0.379305 0.925272i \(-0.623837\pi\)
−0.379305 + 0.925272i \(0.623837\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 33.0000 33.0000i 1.38587 1.38587i
\(568\) 0 0
\(569\) −6.00000 −0.251533 −0.125767 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) 0 0
\(571\) 25.0000 + 25.0000i 1.04622 + 1.04622i 0.998879 + 0.0473385i \(0.0150740\pi\)
0.0473385 + 0.998879i \(0.484926\pi\)
\(572\) 0 0
\(573\) 36.0000i 1.50392i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −9.00000 + 9.00000i −0.374675 + 0.374675i −0.869177 0.494502i \(-0.835351\pi\)
0.494502 + 0.869177i \(0.335351\pi\)
\(578\) 0 0
\(579\) −30.0000 30.0000i −1.24676 1.24676i
\(580\) 0 0
\(581\) 6.00000 6.00000i 0.248922 0.248922i
\(582\) 0 0
\(583\) 8.00000 + 8.00000i 0.331326 + 0.331326i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 2.00000 0.0825488 0.0412744 0.999148i \(-0.486858\pi\)
0.0412744 + 0.999148i \(0.486858\pi\)
\(588\) 0 0
\(589\) 6.00000 6.00000i 0.247226 0.247226i
\(590\) 0 0
\(591\) 12.0000i 0.493614i
\(592\) 0 0
\(593\) −17.0000 17.0000i −0.698106 0.698106i 0.265896 0.964002i \(-0.414332\pi\)
−0.964002 + 0.265896i \(0.914332\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 20.0000i 0.818546i
\(598\) 0 0
\(599\) 30.0000i 1.22577i −0.790173 0.612883i \(-0.790010\pi\)
0.790173 0.612883i \(-0.209990\pi\)
\(600\) 0 0
\(601\) 16.0000i 0.652654i 0.945257 + 0.326327i \(0.105811\pi\)
−0.945257 + 0.326327i \(0.894189\pi\)
\(602\) 0 0
\(603\) 4.00000i 0.162893i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −23.0000 23.0000i −0.933541 0.933541i 0.0643840 0.997925i \(-0.479492\pi\)
−0.997925 + 0.0643840i \(0.979492\pi\)
\(608\) 0 0
\(609\) 84.0000i 3.40385i
\(610\) 0 0
\(611\) 14.0000 14.0000i 0.566379 0.566379i
\(612\) 0 0
\(613\) −8.00000 −0.323117 −0.161558 0.986863i \(-0.551652\pi\)
−0.161558 + 0.986863i \(0.551652\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 25.0000 + 25.0000i 1.00646 + 1.00646i 0.999979 + 0.00648312i \(0.00206366\pi\)
0.00648312 + 0.999979i \(0.497936\pi\)
\(618\) 0 0
\(619\) −7.00000 + 7.00000i −0.281354 + 0.281354i −0.833649 0.552295i \(-0.813752\pi\)
0.552295 + 0.833649i \(0.313752\pi\)
\(620\) 0 0
\(621\) −4.00000 4.00000i −0.160514 0.160514i
\(622\) 0 0
\(623\) 18.0000 18.0000i 0.721155 0.721155i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 12.0000i 0.479234i
\(628\) 0 0
\(629\) 6.00000 + 6.00000i 0.239236 + 0.239236i
\(630\) 0 0
\(631\) −24.0000 −0.955425 −0.477712 0.878516i \(-0.658534\pi\)
−0.477712 + 0.878516i \(0.658534\pi\)
\(632\) 0 0
\(633\) −38.0000 + 38.0000i −1.51036 + 1.51036i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 22.0000 0.871672
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −30.0000 −1.18493 −0.592464 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) 0 0
\(643\) −26.0000 −1.02534 −0.512670 0.858586i \(-0.671344\pi\)
−0.512670 + 0.858586i \(0.671344\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −15.0000 + 15.0000i −0.589711 + 0.589711i −0.937553 0.347842i \(-0.886914\pi\)
0.347842 + 0.937553i \(0.386914\pi\)
\(648\) 0 0
\(649\) −6.00000 −0.235521
\(650\) 0 0
\(651\) −12.0000 12.0000i −0.470317 0.470317i
\(652\) 0 0
\(653\) 2.00000i 0.0782660i 0.999234 + 0.0391330i \(0.0124596\pi\)
−0.999234 + 0.0391330i \(0.987540\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −3.00000 + 3.00000i −0.117041 + 0.117041i
\(658\) 0 0
\(659\) 11.0000 + 11.0000i 0.428499 + 0.428499i 0.888117 0.459618i \(-0.152014\pi\)
−0.459618 + 0.888117i \(0.652014\pi\)
\(660\) 0 0
\(661\) −25.0000 + 25.0000i −0.972387 + 0.972387i −0.999629 0.0272416i \(-0.991328\pi\)
0.0272416 + 0.999629i \(0.491328\pi\)
\(662\) 0 0
\(663\) 4.00000 + 4.00000i 0.155347 + 0.155347i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 14.0000 0.542082
\(668\) 0 0
\(669\) 18.0000 18.0000i 0.695920 0.695920i
\(670\) 0 0
\(671\) 2.00000i 0.0772091i
\(672\) 0 0
\(673\) −1.00000 1.00000i −0.0385472 0.0385472i 0.687570 0.726118i \(-0.258677\pi\)
−0.726118 + 0.687570i \(0.758677\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 42.0000i 1.61419i −0.590421 0.807096i \(-0.701038\pi\)
0.590421 0.807096i \(-0.298962\pi\)
\(678\) 0 0
\(679\) 66.0000i 2.53285i
\(680\) 0 0
\(681\) 24.0000i 0.919682i
\(682\) 0 0
\(683\) 4.00000i 0.153056i −0.997067 0.0765279i \(-0.975617\pi\)
0.997067 0.0765279i \(-0.0243834\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −2.00000 2.00000i −0.0763048 0.0763048i
\(688\) 0 0
\(689\) 16.0000i 0.609551i
\(690\) 0 0
\(691\) −21.0000 + 21.0000i −0.798878 + 0.798878i −0.982919 0.184041i \(-0.941082\pi\)
0.184041 + 0.982919i \(0.441082\pi\)
\(692\) 0 0
\(693\) −6.00000 −0.227921
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 4.00000 + 4.00000i 0.151511 + 0.151511i
\(698\) 0 0
\(699\) −18.0000 + 18.0000i −0.680823 + 0.680823i
\(700\) 0 0
\(701\) −13.0000 13.0000i −0.491003 0.491003i 0.417619 0.908622i \(-0.362865\pi\)
−0.908622 + 0.417619i \(0.862865\pi\)
\(702\) 0 0
\(703\) 18.0000 18.0000i 0.678883 0.678883i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 30.0000i 1.12827i
\(708\) 0 0
\(709\) 1.00000 + 1.00000i 0.0375558 + 0.0375558i 0.725635 0.688080i \(-0.241546\pi\)
−0.688080 + 0.725635i \(0.741546\pi\)
\(710\) 0 0
\(711\) −8.00000 −0.300023
\(712\) 0 0
\(713\) −2.00000 + 2.00000i −0.0749006 + 0.0749006i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 32.0000 1.19340 0.596699 0.802465i \(-0.296479\pi\)
0.596699 + 0.802465i \(0.296479\pi\)
\(720\) 0 0
\(721\) 30.0000 1.11726
\(722\) 0 0
\(723\) 28.0000 1.04133
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −7.00000 + 7.00000i −0.259616 + 0.259616i −0.824898 0.565282i \(-0.808767\pi\)
0.565282 + 0.824898i \(0.308767\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −4.00000 4.00000i −0.147945 0.147945i
\(732\) 0 0
\(733\) 30.0000i 1.10808i 0.832492 + 0.554038i \(0.186914\pi\)
−0.832492 + 0.554038i \(0.813086\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.00000 4.00000i 0.147342 0.147342i
\(738\) 0 0
\(739\) −21.0000 21.0000i −0.772497 0.772497i 0.206045 0.978543i \(-0.433941\pi\)
−0.978543 + 0.206045i \(0.933941\pi\)
\(740\) 0 0
\(741\) 12.0000 12.0000i 0.440831 0.440831i
\(742\) 0 0
\(743\) 31.0000 + 31.0000i 1.13728 + 1.13728i 0.988936 + 0.148344i \(0.0473942\pi\)
0.148344 + 0.988936i \(0.452606\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −2.00000 −0.0731762
\(748\) 0 0
\(749\) 18.0000 18.0000i 0.657706 0.657706i
\(750\) 0 0
\(751\) 50.0000i 1.82453i −0.409605 0.912263i \(-0.634333\pi\)
0.409605 0.912263i \(-0.365667\pi\)
\(752\) 0 0
\(753\) 22.0000 + 22.0000i 0.801725 + 0.801725i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 2.00000i 0.0726912i 0.999339 + 0.0363456i \(0.0115717\pi\)
−0.999339 + 0.0363456i \(0.988428\pi\)
\(758\) 0 0
\(759\) 4.00000i 0.145191i
\(760\) 0 0
\(761\) 40.0000i 1.45000i 0.688749 + 0.724999i \(0.258160\pi\)
−0.688749 + 0.724999i \(0.741840\pi\)
\(762\) 0 0
\(763\) 30.0000i 1.08607i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −6.00000 6.00000i −0.216647 0.216647i
\(768\) 0 0
\(769\) 4.00000i 0.144244i −0.997396 0.0721218i \(-0.977023\pi\)
0.997396 0.0721218i \(-0.0229770\pi\)
\(770\) 0 0
\(771\) 26.0000 26.0000i 0.936367 0.936367i
\(772\) 0 0
\(773\) −48.0000 −1.72644 −0.863220 0.504828i \(-0.831556\pi\)
−0.863220 + 0.504828i \(0.831556\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −36.0000 36.0000i −1.29149 1.29149i
\(778\) 0 0
\(779\) 12.0000 12.0000i 0.429945 0.429945i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −28.0000 + 28.0000i −1.00064 + 1.00064i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 4.00000i 0.142585i 0.997455 + 0.0712923i \(0.0227123\pi\)
−0.997455 + 0.0712923i \(0.977288\pi\)
\(788\) 0 0
\(789\) −14.0000 14.0000i −0.498413 0.498413i
\(790\) 0 0
\(791\) 78.0000 2.77336
\(792\) 0 0
\(793\) 2.00000 2.00000i 0.0710221 0.0710221i