Properties

Label 1638.2.j.e.1171.1
Level $1638$
Weight $2$
Character 1638.1171
Analytic conductor $13.079$
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] = [1638,2,Mod(235,1638)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1638, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1638.235");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.j (of order \(3\), degree \(2\), 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: \(13.0794958511\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 546)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1171.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1638.1171
Dual form 1638.2.j.e.235.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +(-1.50000 - 2.59808i) q^{11} -1.00000 q^{13} +(-2.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} -1.00000 q^{20} +3.00000 q^{22} +(3.00000 - 5.19615i) q^{23} +(2.00000 + 3.46410i) q^{25} +(0.500000 - 0.866025i) q^{26} +(2.50000 - 0.866025i) q^{28} -9.00000 q^{29} +(-2.50000 - 4.33013i) q^{31} +(-0.500000 - 0.866025i) q^{32} +2.00000 q^{34} +(2.00000 + 1.73205i) q^{35} +(4.00000 - 6.92820i) q^{37} +(0.500000 - 0.866025i) q^{40} +4.00000 q^{41} +(-1.50000 + 2.59808i) q^{44} +(3.00000 + 5.19615i) q^{46} +(-6.50000 - 2.59808i) q^{49} -4.00000 q^{50} +(0.500000 + 0.866025i) q^{52} +(0.500000 + 0.866025i) q^{53} -3.00000 q^{55} +(-0.500000 + 2.59808i) q^{56} +(4.50000 - 7.79423i) q^{58} +(-3.50000 - 6.06218i) q^{59} +(2.00000 - 3.46410i) q^{61} +5.00000 q^{62} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-1.00000 + 1.73205i) q^{68} +(-2.50000 + 0.866025i) q^{70} -6.00000 q^{71} +(-3.00000 - 5.19615i) q^{73} +(4.00000 + 6.92820i) q^{74} +(7.50000 - 2.59808i) q^{77} +(6.50000 - 11.2583i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-2.00000 + 3.46410i) q^{82} +3.00000 q^{83} -2.00000 q^{85} +(-1.50000 - 2.59808i) q^{88} +(-4.00000 + 6.92820i) q^{89} +(0.500000 - 2.59808i) q^{91} -6.00000 q^{92} -15.0000 q^{97} +(5.50000 - 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{4} + q^{5} - q^{7} + 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - q^{4} + q^{5} - q^{7} + 2 q^{8} + q^{10} - 3 q^{11} - 2 q^{13} - 4 q^{14} - q^{16} - 2 q^{17} - 2 q^{20} + 6 q^{22} + 6 q^{23} + 4 q^{25} + q^{26} + 5 q^{28} - 18 q^{29} - 5 q^{31} - q^{32} + 4 q^{34} + 4 q^{35} + 8 q^{37} + q^{40} + 8 q^{41} - 3 q^{44} + 6 q^{46} - 13 q^{49} - 8 q^{50} + q^{52} + q^{53} - 6 q^{55} - q^{56} + 9 q^{58} - 7 q^{59} + 4 q^{61} + 10 q^{62} + 2 q^{64} - q^{65} + 4 q^{67} - 2 q^{68} - 5 q^{70} - 12 q^{71} - 6 q^{73} + 8 q^{74} + 15 q^{77} + 13 q^{79} + q^{80} - 4 q^{82} + 6 q^{83} - 4 q^{85} - 3 q^{88} - 8 q^{89} + q^{91} - 12 q^{92} - 30 q^{97} + 11 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).

\(n\) \(379\) \(703\) \(911\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.500000 0.866025i 0.223607 0.387298i −0.732294 0.680989i \(-0.761550\pi\)
0.955901 + 0.293691i \(0.0948835\pi\)
\(6\) 0 0
\(7\) −0.500000 + 2.59808i −0.188982 + 0.981981i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) −2.00000 1.73205i −0.534522 0.462910i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.00000 1.73205i −0.242536 0.420084i 0.718900 0.695113i \(-0.244646\pi\)
−0.961436 + 0.275029i \(0.911312\pi\)
\(18\) 0 0
\(19\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) 3.00000 0.639602
\(23\) 3.00000 5.19615i 0.625543 1.08347i −0.362892 0.931831i \(-0.618211\pi\)
0.988436 0.151642i \(-0.0484560\pi\)
\(24\) 0 0
\(25\) 2.00000 + 3.46410i 0.400000 + 0.692820i
\(26\) 0.500000 0.866025i 0.0980581 0.169842i
\(27\) 0 0
\(28\) 2.50000 0.866025i 0.472456 0.163663i
\(29\) −9.00000 −1.67126 −0.835629 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) 0 0
\(31\) −2.50000 4.33013i −0.449013 0.777714i 0.549309 0.835619i \(-0.314891\pi\)
−0.998322 + 0.0579057i \(0.981558\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) 2.00000 + 1.73205i 0.338062 + 0.292770i
\(36\) 0 0
\(37\) 4.00000 6.92820i 0.657596 1.13899i −0.323640 0.946180i \(-0.604907\pi\)
0.981236 0.192809i \(-0.0617599\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) 4.00000 0.624695 0.312348 0.949968i \(-0.398885\pi\)
0.312348 + 0.949968i \(0.398885\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) −1.50000 + 2.59808i −0.226134 + 0.391675i
\(45\) 0 0
\(46\) 3.00000 + 5.19615i 0.442326 + 0.766131i
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 0 0
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) −4.00000 −0.565685
\(51\) 0 0
\(52\) 0.500000 + 0.866025i 0.0693375 + 0.120096i
\(53\) 0.500000 + 0.866025i 0.0686803 + 0.118958i 0.898321 0.439340i \(-0.144788\pi\)
−0.829640 + 0.558298i \(0.811454\pi\)
\(54\) 0 0
\(55\) −3.00000 −0.404520
\(56\) −0.500000 + 2.59808i −0.0668153 + 0.347183i
\(57\) 0 0
\(58\) 4.50000 7.79423i 0.590879 1.02343i
\(59\) −3.50000 6.06218i −0.455661 0.789228i 0.543065 0.839691i \(-0.317264\pi\)
−0.998726 + 0.0504625i \(0.983930\pi\)
\(60\) 0 0
\(61\) 2.00000 3.46410i 0.256074 0.443533i −0.709113 0.705095i \(-0.750904\pi\)
0.965187 + 0.261562i \(0.0842377\pi\)
\(62\) 5.00000 0.635001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −0.500000 + 0.866025i −0.0620174 + 0.107417i
\(66\) 0 0
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) −1.00000 + 1.73205i −0.121268 + 0.210042i
\(69\) 0 0
\(70\) −2.50000 + 0.866025i −0.298807 + 0.103510i
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0 0
\(73\) −3.00000 5.19615i −0.351123 0.608164i 0.635323 0.772246i \(-0.280867\pi\)
−0.986447 + 0.164083i \(0.947534\pi\)
\(74\) 4.00000 + 6.92820i 0.464991 + 0.805387i
\(75\) 0 0
\(76\) 0 0
\(77\) 7.50000 2.59808i 0.854704 0.296078i
\(78\) 0 0
\(79\) 6.50000 11.2583i 0.731307 1.26666i −0.225018 0.974355i \(-0.572244\pi\)
0.956325 0.292306i \(-0.0944227\pi\)
\(80\) 0.500000 + 0.866025i 0.0559017 + 0.0968246i
\(81\) 0 0
\(82\) −2.00000 + 3.46410i −0.220863 + 0.382546i
\(83\) 3.00000 0.329293 0.164646 0.986353i \(-0.447352\pi\)
0.164646 + 0.986353i \(0.447352\pi\)
\(84\) 0 0
\(85\) −2.00000 −0.216930
\(86\) 0 0
\(87\) 0 0
\(88\) −1.50000 2.59808i −0.159901 0.276956i
\(89\) −4.00000 + 6.92820i −0.423999 + 0.734388i −0.996326 0.0856373i \(-0.972707\pi\)
0.572327 + 0.820025i \(0.306041\pi\)
\(90\) 0 0
\(91\) 0.500000 2.59808i 0.0524142 0.272352i
\(92\) −6.00000 −0.625543
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −15.0000 −1.52302 −0.761510 0.648154i \(-0.775541\pi\)
−0.761510 + 0.648154i \(0.775541\pi\)
\(98\) 5.50000 4.33013i 0.555584 0.437409i
\(99\) 0 0
\(100\) 2.00000 3.46410i 0.200000 0.346410i
\(101\) −1.00000 1.73205i −0.0995037 0.172345i 0.811976 0.583691i \(-0.198392\pi\)
−0.911479 + 0.411346i \(0.865059\pi\)
\(102\) 0 0
\(103\) 8.00000 13.8564i 0.788263 1.36531i −0.138767 0.990325i \(-0.544314\pi\)
0.927030 0.374987i \(-0.122353\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) −1.00000 −0.0971286
\(107\) 8.50000 14.7224i 0.821726 1.42327i −0.0826699 0.996577i \(-0.526345\pi\)
0.904396 0.426694i \(-0.140322\pi\)
\(108\) 0 0
\(109\) −8.00000 13.8564i −0.766261 1.32720i −0.939577 0.342337i \(-0.888782\pi\)
0.173316 0.984866i \(-0.444552\pi\)
\(110\) 1.50000 2.59808i 0.143019 0.247717i
\(111\) 0 0
\(112\) −2.00000 1.73205i −0.188982 0.163663i
\(113\) −12.0000 −1.12887 −0.564433 0.825479i \(-0.690905\pi\)
−0.564433 + 0.825479i \(0.690905\pi\)
\(114\) 0 0
\(115\) −3.00000 5.19615i −0.279751 0.484544i
\(116\) 4.50000 + 7.79423i 0.417815 + 0.723676i
\(117\) 0 0
\(118\) 7.00000 0.644402
\(119\) 5.00000 1.73205i 0.458349 0.158777i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 2.00000 + 3.46410i 0.181071 + 0.313625i
\(123\) 0 0
\(124\) −2.50000 + 4.33013i −0.224507 + 0.388857i
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) 5.00000 0.443678 0.221839 0.975083i \(-0.428794\pi\)
0.221839 + 0.975083i \(0.428794\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −0.500000 0.866025i −0.0438529 0.0759555i
\(131\) 7.50000 12.9904i 0.655278 1.13497i −0.326546 0.945181i \(-0.605885\pi\)
0.981824 0.189794i \(-0.0607819\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) −1.00000 1.73205i −0.0857493 0.148522i
\(137\) −6.00000 10.3923i −0.512615 0.887875i −0.999893 0.0146279i \(-0.995344\pi\)
0.487278 0.873247i \(-0.337990\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0.500000 2.59808i 0.0422577 0.219578i
\(141\) 0 0
\(142\) 3.00000 5.19615i 0.251754 0.436051i
\(143\) 1.50000 + 2.59808i 0.125436 + 0.217262i
\(144\) 0 0
\(145\) −4.50000 + 7.79423i −0.373705 + 0.647275i
\(146\) 6.00000 0.496564
\(147\) 0 0
\(148\) −8.00000 −0.657596
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) 0 0
\(151\) 5.50000 + 9.52628i 0.447584 + 0.775238i 0.998228 0.0595022i \(-0.0189513\pi\)
−0.550645 + 0.834740i \(0.685618\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −1.50000 + 7.79423i −0.120873 + 0.628077i
\(155\) −5.00000 −0.401610
\(156\) 0 0
\(157\) 7.00000 + 12.1244i 0.558661 + 0.967629i 0.997609 + 0.0691164i \(0.0220180\pi\)
−0.438948 + 0.898513i \(0.644649\pi\)
\(158\) 6.50000 + 11.2583i 0.517112 + 0.895665i
\(159\) 0 0
\(160\) −1.00000 −0.0790569
\(161\) 12.0000 + 10.3923i 0.945732 + 0.819028i
\(162\) 0 0
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) −2.00000 3.46410i −0.156174 0.270501i
\(165\) 0 0
\(166\) −1.50000 + 2.59808i −0.116423 + 0.201650i
\(167\) 4.00000 0.309529 0.154765 0.987951i \(-0.450538\pi\)
0.154765 + 0.987951i \(0.450538\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 1.00000 1.73205i 0.0766965 0.132842i
\(171\) 0 0
\(172\) 0 0
\(173\) −7.00000 + 12.1244i −0.532200 + 0.921798i 0.467093 + 0.884208i \(0.345301\pi\)
−0.999293 + 0.0375896i \(0.988032\pi\)
\(174\) 0 0
\(175\) −10.0000 + 3.46410i −0.755929 + 0.261861i
\(176\) 3.00000 0.226134
\(177\) 0 0
\(178\) −4.00000 6.92820i −0.299813 0.519291i
\(179\) 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i \(-0.0186389\pi\)
−0.549825 + 0.835280i \(0.685306\pi\)
\(180\) 0 0
\(181\) −8.00000 −0.594635 −0.297318 0.954779i \(-0.596092\pi\)
−0.297318 + 0.954779i \(0.596092\pi\)
\(182\) 2.00000 + 1.73205i 0.148250 + 0.128388i
\(183\) 0 0
\(184\) 3.00000 5.19615i 0.221163 0.383065i
\(185\) −4.00000 6.92820i −0.294086 0.509372i
\(186\) 0 0
\(187\) −3.00000 + 5.19615i −0.219382 + 0.379980i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3.00000 + 5.19615i −0.217072 + 0.375980i −0.953912 0.300088i \(-0.902984\pi\)
0.736839 + 0.676068i \(0.236317\pi\)
\(192\) 0 0
\(193\) −9.50000 16.4545i −0.683825 1.18442i −0.973805 0.227387i \(-0.926982\pi\)
0.289980 0.957033i \(-0.406351\pi\)
\(194\) 7.50000 12.9904i 0.538469 0.932655i
\(195\) 0 0
\(196\) 1.00000 + 6.92820i 0.0714286 + 0.494872i
\(197\) 22.0000 1.56744 0.783718 0.621117i \(-0.213321\pi\)
0.783718 + 0.621117i \(0.213321\pi\)
\(198\) 0 0
\(199\) 12.0000 + 20.7846i 0.850657 + 1.47338i 0.880616 + 0.473831i \(0.157129\pi\)
−0.0299585 + 0.999551i \(0.509538\pi\)
\(200\) 2.00000 + 3.46410i 0.141421 + 0.244949i
\(201\) 0 0
\(202\) 2.00000 0.140720
\(203\) 4.50000 23.3827i 0.315838 1.64114i
\(204\) 0 0
\(205\) 2.00000 3.46410i 0.139686 0.241943i
\(206\) 8.00000 + 13.8564i 0.557386 + 0.965422i
\(207\) 0 0
\(208\) 0.500000 0.866025i 0.0346688 0.0600481i
\(209\) 0 0
\(210\) 0 0
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) 0.500000 0.866025i 0.0343401 0.0594789i
\(213\) 0 0
\(214\) 8.50000 + 14.7224i 0.581048 + 1.00640i
\(215\) 0 0
\(216\) 0 0
\(217\) 12.5000 4.33013i 0.848555 0.293948i
\(218\) 16.0000 1.08366
\(219\) 0 0
\(220\) 1.50000 + 2.59808i 0.101130 + 0.175162i
\(221\) 1.00000 + 1.73205i 0.0672673 + 0.116510i
\(222\) 0 0
\(223\) −1.00000 −0.0669650 −0.0334825 0.999439i \(-0.510660\pi\)
−0.0334825 + 0.999439i \(0.510660\pi\)
\(224\) 2.50000 0.866025i 0.167038 0.0578638i
\(225\) 0 0
\(226\) 6.00000 10.3923i 0.399114 0.691286i
\(227\) −6.50000 11.2583i −0.431420 0.747242i 0.565576 0.824696i \(-0.308654\pi\)
−0.996996 + 0.0774548i \(0.975321\pi\)
\(228\) 0 0
\(229\) 7.00000 12.1244i 0.462573 0.801200i −0.536515 0.843891i \(-0.680260\pi\)
0.999088 + 0.0426906i \(0.0135930\pi\)
\(230\) 6.00000 0.395628
\(231\) 0 0
\(232\) −9.00000 −0.590879
\(233\) −7.00000 + 12.1244i −0.458585 + 0.794293i −0.998886 0.0471787i \(-0.984977\pi\)
0.540301 + 0.841472i \(0.318310\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −3.50000 + 6.06218i −0.227831 + 0.394614i
\(237\) 0 0
\(238\) −1.00000 + 5.19615i −0.0648204 + 0.336817i
\(239\) −22.0000 −1.42306 −0.711531 0.702655i \(-0.751998\pi\)
−0.711531 + 0.702655i \(0.751998\pi\)
\(240\) 0 0
\(241\) 13.5000 + 23.3827i 0.869611 + 1.50621i 0.862394 + 0.506237i \(0.168964\pi\)
0.00721719 + 0.999974i \(0.497703\pi\)
\(242\) 1.00000 + 1.73205i 0.0642824 + 0.111340i
\(243\) 0 0
\(244\) −4.00000 −0.256074
\(245\) −5.50000 + 4.33013i −0.351382 + 0.276642i
\(246\) 0 0
\(247\) 0 0
\(248\) −2.50000 4.33013i −0.158750 0.274963i
\(249\) 0 0
\(250\) −4.50000 + 7.79423i −0.284605 + 0.492950i
\(251\) −23.0000 −1.45175 −0.725874 0.687828i \(-0.758564\pi\)
−0.725874 + 0.687828i \(0.758564\pi\)
\(252\) 0 0
\(253\) −18.0000 −1.13165
\(254\) −2.50000 + 4.33013i −0.156864 + 0.271696i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −13.0000 + 22.5167i −0.810918 + 1.40455i 0.101305 + 0.994855i \(0.467698\pi\)
−0.912222 + 0.409695i \(0.865635\pi\)
\(258\) 0 0
\(259\) 16.0000 + 13.8564i 0.994192 + 0.860995i
\(260\) 1.00000 0.0620174
\(261\) 0 0
\(262\) 7.50000 + 12.9904i 0.463352 + 0.802548i
\(263\) −13.0000 22.5167i −0.801614 1.38844i −0.918553 0.395298i \(-0.870641\pi\)
0.116939 0.993139i \(-0.462692\pi\)
\(264\) 0 0
\(265\) 1.00000 0.0614295
\(266\) 0 0
\(267\) 0 0
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) −1.50000 2.59808i −0.0914566 0.158408i 0.816668 0.577108i \(-0.195819\pi\)
−0.908124 + 0.418701i \(0.862486\pi\)
\(270\) 0 0
\(271\) −4.50000 + 7.79423i −0.273356 + 0.473466i −0.969719 0.244224i \(-0.921467\pi\)
0.696363 + 0.717689i \(0.254800\pi\)
\(272\) 2.00000 0.121268
\(273\) 0 0
\(274\) 12.0000 0.724947
\(275\) 6.00000 10.3923i 0.361814 0.626680i
\(276\) 0 0
\(277\) 11.0000 + 19.0526i 0.660926 + 1.14476i 0.980373 + 0.197153i \(0.0631696\pi\)
−0.319447 + 0.947604i \(0.603497\pi\)
\(278\) −2.00000 + 3.46410i −0.119952 + 0.207763i
\(279\) 0 0
\(280\) 2.00000 + 1.73205i 0.119523 + 0.103510i
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) −7.00000 12.1244i −0.416107 0.720718i 0.579437 0.815017i \(-0.303272\pi\)
−0.995544 + 0.0942988i \(0.969939\pi\)
\(284\) 3.00000 + 5.19615i 0.178017 + 0.308335i
\(285\) 0 0
\(286\) −3.00000 −0.177394
\(287\) −2.00000 + 10.3923i −0.118056 + 0.613438i
\(288\) 0 0
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) −4.50000 7.79423i −0.264249 0.457693i
\(291\) 0 0
\(292\) −3.00000 + 5.19615i −0.175562 + 0.304082i
\(293\) −15.0000 −0.876309 −0.438155 0.898900i \(-0.644368\pi\)
−0.438155 + 0.898900i \(0.644368\pi\)
\(294\) 0 0
\(295\) −7.00000 −0.407556
\(296\) 4.00000 6.92820i 0.232495 0.402694i
\(297\) 0 0
\(298\) −3.00000 5.19615i −0.173785 0.301005i
\(299\) −3.00000 + 5.19615i −0.173494 + 0.300501i
\(300\) 0 0
\(301\) 0 0
\(302\) −11.0000 −0.632979
\(303\) 0 0
\(304\) 0 0
\(305\) −2.00000 3.46410i −0.114520 0.198354i
\(306\) 0 0
\(307\) −18.0000 −1.02731 −0.513657 0.857996i \(-0.671710\pi\)
−0.513657 + 0.857996i \(0.671710\pi\)
\(308\) −6.00000 5.19615i −0.341882 0.296078i
\(309\) 0 0
\(310\) 2.50000 4.33013i 0.141990 0.245935i
\(311\) 1.00000 + 1.73205i 0.0567048 + 0.0982156i 0.892984 0.450088i \(-0.148607\pi\)
−0.836280 + 0.548303i \(0.815274\pi\)
\(312\) 0 0
\(313\) −6.50000 + 11.2583i −0.367402 + 0.636358i −0.989158 0.146852i \(-0.953086\pi\)
0.621757 + 0.783210i \(0.286419\pi\)
\(314\) −14.0000 −0.790066
\(315\) 0 0
\(316\) −13.0000 −0.731307
\(317\) 1.50000 2.59808i 0.0842484 0.145922i −0.820822 0.571184i \(-0.806484\pi\)
0.905071 + 0.425261i \(0.139818\pi\)
\(318\) 0 0
\(319\) 13.5000 + 23.3827i 0.755855 + 1.30918i
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) 0 0
\(322\) −15.0000 + 5.19615i −0.835917 + 0.289570i
\(323\) 0 0
\(324\) 0 0
\(325\) −2.00000 3.46410i −0.110940 0.192154i
\(326\) 2.00000 + 3.46410i 0.110770 + 0.191859i
\(327\) 0 0
\(328\) 4.00000 0.220863
\(329\) 0 0
\(330\) 0 0
\(331\) −4.00000 + 6.92820i −0.219860 + 0.380808i −0.954765 0.297361i \(-0.903893\pi\)
0.734905 + 0.678170i \(0.237227\pi\)
\(332\) −1.50000 2.59808i −0.0823232 0.142588i
\(333\) 0 0
\(334\) −2.00000 + 3.46410i −0.109435 + 0.189547i
\(335\) 4.00000 0.218543
\(336\) 0 0
\(337\) 1.00000 0.0544735 0.0272367 0.999629i \(-0.491329\pi\)
0.0272367 + 0.999629i \(0.491329\pi\)
\(338\) −0.500000 + 0.866025i −0.0271964 + 0.0471056i
\(339\) 0 0
\(340\) 1.00000 + 1.73205i 0.0542326 + 0.0939336i
\(341\) −7.50000 + 12.9904i −0.406148 + 0.703469i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) −7.00000 12.1244i −0.376322 0.651809i
\(347\) −14.0000 24.2487i −0.751559 1.30174i −0.947067 0.321037i \(-0.895969\pi\)
0.195507 0.980702i \(-0.437365\pi\)
\(348\) 0 0
\(349\) −34.0000 −1.81998 −0.909989 0.414632i \(-0.863910\pi\)
−0.909989 + 0.414632i \(0.863910\pi\)
\(350\) 2.00000 10.3923i 0.106904 0.555492i
\(351\) 0 0
\(352\) −1.50000 + 2.59808i −0.0799503 + 0.138478i
\(353\) 3.00000 + 5.19615i 0.159674 + 0.276563i 0.934751 0.355303i \(-0.115622\pi\)
−0.775077 + 0.631867i \(0.782289\pi\)
\(354\) 0 0
\(355\) −3.00000 + 5.19615i −0.159223 + 0.275783i
\(356\) 8.00000 0.423999
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) −1.00000 + 1.73205i −0.0527780 + 0.0914141i −0.891207 0.453596i \(-0.850141\pi\)
0.838429 + 0.545010i \(0.183474\pi\)
\(360\) 0 0
\(361\) 9.50000 + 16.4545i 0.500000 + 0.866025i
\(362\) 4.00000 6.92820i 0.210235 0.364138i
\(363\) 0 0
\(364\) −2.50000 + 0.866025i −0.131036 + 0.0453921i
\(365\) −6.00000 −0.314054
\(366\) 0 0
\(367\) 1.50000 + 2.59808i 0.0782994 + 0.135618i 0.902516 0.430656i \(-0.141718\pi\)
−0.824217 + 0.566274i \(0.808384\pi\)
\(368\) 3.00000 + 5.19615i 0.156386 + 0.270868i
\(369\) 0 0
\(370\) 8.00000 0.415900
\(371\) −2.50000 + 0.866025i −0.129794 + 0.0449618i
\(372\) 0 0
\(373\) 13.0000 22.5167i 0.673114 1.16587i −0.303902 0.952703i \(-0.598289\pi\)
0.977016 0.213165i \(-0.0683772\pi\)
\(374\) −3.00000 5.19615i −0.155126 0.268687i
\(375\) 0 0
\(376\) 0 0
\(377\) 9.00000 0.463524
\(378\) 0 0
\(379\) −24.0000 −1.23280 −0.616399 0.787434i \(-0.711409\pi\)
−0.616399 + 0.787434i \(0.711409\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −3.00000 5.19615i −0.153493 0.265858i
\(383\) −13.0000 + 22.5167i −0.664269 + 1.15055i 0.315214 + 0.949021i \(0.397924\pi\)
−0.979483 + 0.201527i \(0.935410\pi\)
\(384\) 0 0
\(385\) 1.50000 7.79423i 0.0764471 0.397231i
\(386\) 19.0000 0.967075
\(387\) 0 0
\(388\) 7.50000 + 12.9904i 0.380755 + 0.659487i
\(389\) 17.0000 + 29.4449i 0.861934 + 1.49291i 0.870059 + 0.492947i \(0.164080\pi\)
−0.00812520 + 0.999967i \(0.502586\pi\)
\(390\) 0 0
\(391\) −12.0000 −0.606866
\(392\) −6.50000 2.59808i −0.328300 0.131223i
\(393\) 0 0
\(394\) −11.0000 + 19.0526i −0.554172 + 0.959854i
\(395\) −6.50000 11.2583i −0.327050 0.566468i
\(396\) 0 0
\(397\) −17.0000 + 29.4449i −0.853206 + 1.47780i 0.0250943 + 0.999685i \(0.492011\pi\)
−0.878300 + 0.478110i \(0.841322\pi\)
\(398\) −24.0000 −1.20301
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) 3.00000 5.19615i 0.149813 0.259483i −0.781345 0.624099i \(-0.785466\pi\)
0.931158 + 0.364615i \(0.118800\pi\)
\(402\) 0 0
\(403\) 2.50000 + 4.33013i 0.124534 + 0.215699i
\(404\) −1.00000 + 1.73205i −0.0497519 + 0.0861727i
\(405\) 0 0
\(406\) 18.0000 + 15.5885i 0.893325 + 0.773642i
\(407\) −24.0000 −1.18964
\(408\) 0 0
\(409\) 5.50000 + 9.52628i 0.271957 + 0.471044i 0.969363 0.245633i \(-0.0789957\pi\)
−0.697406 + 0.716677i \(0.745662\pi\)
\(410\) 2.00000 + 3.46410i 0.0987730 + 0.171080i
\(411\) 0 0
\(412\) −16.0000 −0.788263
\(413\) 17.5000 6.06218i 0.861119 0.298300i
\(414\) 0 0
\(415\) 1.50000 2.59808i 0.0736321 0.127535i
\(416\) 0.500000 + 0.866025i 0.0245145 + 0.0424604i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) −12.0000 −0.584844 −0.292422 0.956289i \(-0.594461\pi\)
−0.292422 + 0.956289i \(0.594461\pi\)
\(422\) −10.0000 + 17.3205i −0.486792 + 0.843149i
\(423\) 0 0
\(424\) 0.500000 + 0.866025i 0.0242821 + 0.0420579i
\(425\) 4.00000 6.92820i 0.194029 0.336067i
\(426\) 0 0
\(427\) 8.00000 + 6.92820i 0.387147 + 0.335279i
\(428\) −17.0000 −0.821726
\(429\) 0 0
\(430\) 0 0
\(431\) 13.0000 + 22.5167i 0.626188 + 1.08459i 0.988310 + 0.152459i \(0.0487191\pi\)
−0.362122 + 0.932131i \(0.617948\pi\)
\(432\) 0 0
\(433\) −38.0000 −1.82616 −0.913082 0.407777i \(-0.866304\pi\)
−0.913082 + 0.407777i \(0.866304\pi\)
\(434\) −2.50000 + 12.9904i −0.120004 + 0.623558i
\(435\) 0 0
\(436\) −8.00000 + 13.8564i −0.383131 + 0.663602i
\(437\) 0 0
\(438\) 0 0
\(439\) 14.5000 25.1147i 0.692047 1.19866i −0.279119 0.960257i \(-0.590042\pi\)
0.971166 0.238404i \(-0.0766244\pi\)
\(440\) −3.00000 −0.143019
\(441\) 0 0
\(442\) −2.00000 −0.0951303
\(443\) 19.5000 33.7750i 0.926473 1.60470i 0.137298 0.990530i \(-0.456158\pi\)
0.789175 0.614168i \(-0.210508\pi\)
\(444\) 0 0
\(445\) 4.00000 + 6.92820i 0.189618 + 0.328428i
\(446\) 0.500000 0.866025i 0.0236757 0.0410075i
\(447\) 0 0
\(448\) −0.500000 + 2.59808i −0.0236228 + 0.122748i
\(449\) −8.00000 −0.377543 −0.188772 0.982021i \(-0.560451\pi\)
−0.188772 + 0.982021i \(0.560451\pi\)
\(450\) 0 0
\(451\) −6.00000 10.3923i −0.282529 0.489355i
\(452\) 6.00000 + 10.3923i 0.282216 + 0.488813i
\(453\) 0 0
\(454\) 13.0000 0.610120
\(455\) −2.00000 1.73205i −0.0937614 0.0811998i
\(456\) 0 0
\(457\) −0.500000 + 0.866025i −0.0233890 + 0.0405110i −0.877483 0.479608i \(-0.840779\pi\)
0.854094 + 0.520119i \(0.174112\pi\)
\(458\) 7.00000 + 12.1244i 0.327089 + 0.566534i
\(459\) 0 0
\(460\) −3.00000 + 5.19615i −0.139876 + 0.242272i
\(461\) 26.0000 1.21094 0.605470 0.795868i \(-0.292985\pi\)
0.605470 + 0.795868i \(0.292985\pi\)
\(462\) 0 0
\(463\) −8.00000 −0.371792 −0.185896 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) 4.50000 7.79423i 0.208907 0.361838i
\(465\) 0 0
\(466\) −7.00000 12.1244i −0.324269 0.561650i
\(467\) 6.00000 10.3923i 0.277647 0.480899i −0.693153 0.720791i \(-0.743779\pi\)
0.970799 + 0.239892i \(0.0771121\pi\)
\(468\) 0 0
\(469\) −10.0000 + 3.46410i −0.461757 + 0.159957i
\(470\) 0 0
\(471\) 0 0
\(472\) −3.50000 6.06218i −0.161101 0.279034i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) −4.00000 3.46410i −0.183340 0.158777i
\(477\) 0 0
\(478\) 11.0000 19.0526i 0.503128 0.871444i
\(479\) 15.0000 + 25.9808i 0.685367 + 1.18709i 0.973321 + 0.229447i \(0.0736918\pi\)
−0.287954 + 0.957644i \(0.592975\pi\)
\(480\) 0 0
\(481\) −4.00000 + 6.92820i −0.182384 + 0.315899i
\(482\) −27.0000 −1.22982
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) −7.50000 + 12.9904i −0.340557 + 0.589863i
\(486\) 0 0
\(487\) 4.50000 + 7.79423i 0.203914 + 0.353190i 0.949786 0.312899i \(-0.101300\pi\)
−0.745872 + 0.666089i \(0.767967\pi\)
\(488\) 2.00000 3.46410i 0.0905357 0.156813i
\(489\) 0 0
\(490\) −1.00000 6.92820i −0.0451754 0.312984i
\(491\) 29.0000 1.30875 0.654376 0.756169i \(-0.272931\pi\)
0.654376 + 0.756169i \(0.272931\pi\)
\(492\) 0 0
\(493\) 9.00000 + 15.5885i 0.405340 + 0.702069i
\(494\) 0 0
\(495\) 0 0
\(496\) 5.00000 0.224507
\(497\) 3.00000 15.5885i 0.134568 0.699238i
\(498\) 0 0
\(499\) −8.00000 + 13.8564i −0.358129 + 0.620298i −0.987648 0.156687i \(-0.949919\pi\)
0.629519 + 0.776985i \(0.283252\pi\)
\(500\) −4.50000 7.79423i −0.201246 0.348569i
\(501\) 0 0
\(502\) 11.5000 19.9186i 0.513270 0.889010i
\(503\) 26.0000 1.15928 0.579641 0.814872i \(-0.303193\pi\)
0.579641 + 0.814872i \(0.303193\pi\)
\(504\) 0 0
\(505\) −2.00000 −0.0889988
\(506\) 9.00000 15.5885i 0.400099 0.692991i
\(507\) 0 0
\(508\) −2.50000 4.33013i −0.110920 0.192118i
\(509\) −10.5000 + 18.1865i −0.465404 + 0.806104i −0.999220 0.0394971i \(-0.987424\pi\)
0.533815 + 0.845601i \(0.320758\pi\)
\(510\) 0 0
\(511\) 15.0000 5.19615i 0.663561 0.229864i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −13.0000 22.5167i −0.573405 0.993167i
\(515\) −8.00000 13.8564i −0.352522 0.610586i
\(516\) 0 0
\(517\) 0 0
\(518\) −20.0000 + 6.92820i −0.878750 + 0.304408i
\(519\) 0 0
\(520\) −0.500000 + 0.866025i −0.0219265 + 0.0379777i
\(521\) 14.0000 + 24.2487i 0.613351 + 1.06236i 0.990671 + 0.136272i \(0.0435123\pi\)
−0.377320 + 0.926083i \(0.623154\pi\)
\(522\) 0 0
\(523\) 6.00000 10.3923i 0.262362 0.454424i −0.704507 0.709697i \(-0.748832\pi\)
0.966869 + 0.255273i \(0.0821653\pi\)
\(524\) −15.0000 −0.655278
\(525\) 0 0
\(526\) 26.0000 1.13365
\(527\) −5.00000 + 8.66025i −0.217803 + 0.377247i
\(528\) 0 0
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) −0.500000 + 0.866025i −0.0217186 + 0.0376177i
\(531\) 0 0
\(532\) 0 0
\(533\) −4.00000 −0.173259
\(534\) 0 0
\(535\) −8.50000 14.7224i −0.367487 0.636506i
\(536\) 2.00000 + 3.46410i 0.0863868 + 0.149626i
\(537\) 0 0
\(538\) 3.00000 0.129339
\(539\) 3.00000 + 20.7846i 0.129219 + 0.895257i
\(540\) 0 0
\(541\) 16.0000 27.7128i 0.687894 1.19147i −0.284624 0.958639i \(-0.591869\pi\)
0.972518 0.232828i \(-0.0747978\pi\)
\(542\) −4.50000 7.79423i −0.193292 0.334791i
\(543\) 0 0
\(544\) −1.00000 + 1.73205i −0.0428746 + 0.0742611i
\(545\) −16.0000 −0.685365
\(546\) 0 0
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) −6.00000 + 10.3923i −0.256307 + 0.443937i
\(549\) 0 0
\(550\) 6.00000 + 10.3923i 0.255841 + 0.443129i
\(551\) 0 0
\(552\) 0 0
\(553\) 26.0000 + 22.5167i 1.10563 + 0.957506i
\(554\) −22.0000 −0.934690
\(555\) 0 0
\(556\) −2.00000 3.46410i −0.0848189 0.146911i
\(557\) 8.50000 + 14.7224i 0.360157 + 0.623809i 0.987986 0.154541i \(-0.0493899\pi\)
−0.627830 + 0.778351i \(0.716057\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −2.50000 + 0.866025i −0.105644 + 0.0365963i
\(561\) 0 0
\(562\) 0 0
\(563\) 1.50000 + 2.59808i 0.0632175 + 0.109496i 0.895902 0.444252i \(-0.146530\pi\)
−0.832684 + 0.553748i \(0.813197\pi\)
\(564\) 0 0
\(565\) −6.00000 + 10.3923i −0.252422 + 0.437208i
\(566\) 14.0000 0.588464
\(567\) 0 0
\(568\) −6.00000 −0.251754
\(569\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(570\) 0 0
\(571\) −10.0000 17.3205i −0.418487 0.724841i 0.577301 0.816532i \(-0.304106\pi\)
−0.995788 + 0.0916910i \(0.970773\pi\)
\(572\) 1.50000 2.59808i 0.0627182 0.108631i
\(573\) 0 0
\(574\) −8.00000 6.92820i −0.333914 0.289178i
\(575\) 24.0000 1.00087
\(576\) 0 0
\(577\) 1.50000 + 2.59808i 0.0624458 + 0.108159i 0.895558 0.444945i \(-0.146777\pi\)
−0.833112 + 0.553104i \(0.813443\pi\)
\(578\) 6.50000 + 11.2583i 0.270364 + 0.468285i
\(579\) 0 0
\(580\) 9.00000 0.373705
\(581\) −1.50000 + 7.79423i −0.0622305 + 0.323359i
\(582\) 0 0
\(583\) 1.50000 2.59808i 0.0621237 0.107601i
\(584\) −3.00000 5.19615i −0.124141 0.215018i
\(585\) 0 0
\(586\) 7.50000 12.9904i 0.309822 0.536628i
\(587\) 9.00000 0.371470 0.185735 0.982600i \(-0.440533\pi\)
0.185735 + 0.982600i \(0.440533\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 3.50000 6.06218i 0.144093 0.249576i
\(591\) 0 0
\(592\) 4.00000 + 6.92820i 0.164399 + 0.284747i
\(593\) −20.0000 + 34.6410i −0.821302 + 1.42254i 0.0834118 + 0.996515i \(0.473418\pi\)
−0.904713 + 0.426021i \(0.859915\pi\)
\(594\) 0 0
\(595\) 1.00000 5.19615i 0.0409960 0.213021i
\(596\) 6.00000 0.245770
\(597\) 0 0
\(598\) −3.00000 5.19615i −0.122679 0.212486i
\(599\) 9.00000 + 15.5885i 0.367730 + 0.636927i 0.989210 0.146503i \(-0.0468017\pi\)
−0.621480 + 0.783430i \(0.713468\pi\)
\(600\) 0 0
\(601\) 19.0000 0.775026 0.387513 0.921864i \(-0.373334\pi\)
0.387513 + 0.921864i \(0.373334\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 5.50000 9.52628i 0.223792 0.387619i
\(605\) −1.00000 1.73205i −0.0406558 0.0704179i
\(606\) 0 0
\(607\) −0.500000 + 0.866025i −0.0202944 + 0.0351509i −0.875994 0.482322i \(-0.839794\pi\)
0.855700 + 0.517472i \(0.173127\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 4.00000 0.161955
\(611\) 0 0
\(612\) 0 0
\(613\) 14.0000 + 24.2487i 0.565455 + 0.979396i 0.997007 + 0.0773084i \(0.0246326\pi\)
−0.431553 + 0.902088i \(0.642034\pi\)
\(614\) 9.00000 15.5885i 0.363210 0.629099i
\(615\) 0 0
\(616\) 7.50000 2.59808i 0.302184 0.104679i
\(617\) −4.00000 −0.161034 −0.0805170 0.996753i \(-0.525657\pi\)
−0.0805170 + 0.996753i \(0.525657\pi\)
\(618\) 0 0
\(619\) −16.0000 27.7128i −0.643094 1.11387i −0.984738 0.174042i \(-0.944317\pi\)
0.341644 0.939829i \(-0.389016\pi\)
\(620\) 2.50000 + 4.33013i 0.100402 + 0.173902i
\(621\) 0 0
\(622\) −2.00000 −0.0801927
\(623\) −16.0000 13.8564i −0.641026 0.555145i
\(624\) 0 0
\(625\) −5.50000 + 9.52628i −0.220000 + 0.381051i
\(626\) −6.50000 11.2583i −0.259792 0.449973i
\(627\) 0 0
\(628\) 7.00000 12.1244i 0.279330 0.483814i
\(629\) −16.0000 −0.637962
\(630\) 0 0
\(631\) −13.0000 −0.517522 −0.258761 0.965941i \(-0.583314\pi\)
−0.258761 + 0.965941i \(0.583314\pi\)
\(632\) 6.50000 11.2583i 0.258556 0.447832i
\(633\) 0 0
\(634\) 1.50000 + 2.59808i 0.0595726 + 0.103183i
\(635\) 2.50000 4.33013i 0.0992095 0.171836i
\(636\) 0 0
\(637\) 6.50000 + 2.59808i 0.257539 + 0.102940i
\(638\) −27.0000 −1.06894
\(639\) 0 0
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) 6.00000 + 10.3923i 0.236986 + 0.410471i 0.959848 0.280521i \(-0.0905072\pi\)
−0.722862 + 0.690992i \(0.757174\pi\)
\(642\) 0 0
\(643\) −32.0000 −1.26196 −0.630978 0.775800i \(-0.717346\pi\)
−0.630978 + 0.775800i \(0.717346\pi\)
\(644\) 3.00000 15.5885i 0.118217 0.614271i
\(645\) 0 0
\(646\) 0 0
\(647\) 18.0000 + 31.1769i 0.707653 + 1.22569i 0.965726 + 0.259565i \(0.0835793\pi\)
−0.258073 + 0.966126i \(0.583087\pi\)
\(648\) 0 0
\(649\) −10.5000 + 18.1865i −0.412161 + 0.713884i
\(650\) 4.00000 0.156893
\(651\) 0 0
\(652\) −4.00000 −0.156652
\(653\) 19.5000 33.7750i 0.763094 1.32172i −0.178154 0.984003i \(-0.557013\pi\)
0.941248 0.337715i \(-0.109654\pi\)
\(654\) 0 0
\(655\) −7.50000 12.9904i −0.293049 0.507576i
\(656\) −2.00000 + 3.46410i −0.0780869 + 0.135250i
\(657\) 0 0
\(658\) 0 0
\(659\) 12.0000 0.467454 0.233727 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) 0 0
\(661\) −13.0000 22.5167i −0.505641 0.875797i −0.999979 0.00652642i \(-0.997923\pi\)
0.494337 0.869270i \(-0.335411\pi\)
\(662\) −4.00000 6.92820i −0.155464 0.269272i
\(663\) 0 0
\(664\) 3.00000 0.116423
\(665\) 0 0
\(666\) 0 0
\(667\) −27.0000 + 46.7654i −1.04544 + 1.81076i
\(668\) −2.00000 3.46410i −0.0773823 0.134030i
\(669\) 0 0
\(670\) −2.00000 + 3.46410i −0.0772667 + 0.133830i
\(671\) −12.0000 −0.463255
\(672\) 0 0
\(673\) 17.0000 0.655302 0.327651 0.944799i \(-0.393743\pi\)
0.327651 + 0.944799i \(0.393743\pi\)
\(674\) −0.500000 + 0.866025i −0.0192593 + 0.0333581i
\(675\) 0 0
\(676\) −0.500000 0.866025i −0.0192308 0.0333087i
\(677\) 15.5000 26.8468i 0.595713 1.03181i −0.397732 0.917501i \(-0.630203\pi\)
0.993446 0.114304i \(-0.0364639\pi\)
\(678\) 0 0
\(679\) 7.50000 38.9711i 0.287824 1.49558i
\(680\) −2.00000 −0.0766965
\(681\) 0 0
\(682\) −7.50000 12.9904i −0.287190 0.497427i
\(683\) −20.5000 35.5070i −0.784411 1.35864i −0.929350 0.369199i \(-0.879632\pi\)
0.144940 0.989440i \(-0.453701\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 8.50000 + 16.4545i 0.324532 + 0.628235i
\(687\) 0 0
\(688\) 0 0
\(689\) −0.500000 0.866025i −0.0190485 0.0329929i
\(690\) 0 0
\(691\) −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i \(-0.881959\pi\)
0.779857 + 0.625958i \(0.215292\pi\)
\(692\) 14.0000 0.532200
\(693\) 0 0
\(694\) 28.0000 1.06287
\(695\) 2.00000 3.46410i 0.0758643 0.131401i
\(696\) 0 0
\(697\) −4.00000 6.92820i −0.151511 0.262424i
\(698\) 17.0000 29.4449i 0.643459 1.11450i
\(699\) 0 0
\(700\) 8.00000 + 6.92820i 0.302372 + 0.261861i
\(701\) 39.0000 1.47301 0.736505 0.676432i \(-0.236475\pi\)
0.736505 + 0.676432i \(0.236475\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −1.50000 2.59808i −0.0565334 0.0979187i
\(705\) 0 0
\(706\) −6.00000 −0.225813
\(707\) 5.00000 1.73205i 0.188044 0.0651405i
\(708\) 0 0
\(709\) 13.0000 22.5167i 0.488225 0.845631i −0.511683 0.859174i \(-0.670978\pi\)
0.999908 + 0.0135434i \(0.00431112\pi\)
\(710\) −3.00000 5.19615i −0.112588 0.195008i
\(711\) 0 0
\(712\) −4.00000 + 6.92820i −0.149906 + 0.259645i
\(713\) −30.0000 −1.12351
\(714\) 0 0
\(715\) 3.00000 0.112194
\(716\) 6.00000 10.3923i 0.224231 0.388379i
\(717\) 0 0
\(718\) −1.00000 1.73205i −0.0373197 0.0646396i
\(719\) 1.00000 1.73205i 0.0372937 0.0645946i −0.846776 0.531949i \(-0.821460\pi\)
0.884070 + 0.467355i \(0.154793\pi\)
\(720\) 0 0
\(721\) 32.0000 + 27.7128i 1.19174 + 1.03208i
\(722\) −19.0000 −0.707107
\(723\) 0 0
\(724\) 4.00000 + 6.92820i 0.148659 + 0.257485i
\(725\) −18.0000 31.1769i −0.668503 1.15788i
\(726\) 0 0
\(727\) −9.00000 −0.333792 −0.166896 0.985975i \(-0.553374\pi\)
−0.166896 + 0.985975i \(0.553374\pi\)
\(728\) 0.500000 2.59808i 0.0185312 0.0962911i
\(729\) 0 0
\(730\) 3.00000 5.19615i 0.111035 0.192318i
\(731\) 0 0
\(732\) 0 0
\(733\) −11.0000 + 19.0526i −0.406294 + 0.703722i −0.994471 0.105010i \(-0.966513\pi\)
0.588177 + 0.808732i \(0.299846\pi\)
\(734\) −3.00000 −0.110732
\(735\) 0 0
\(736\) −6.00000 −0.221163
\(737\) 6.00000 10.3923i 0.221013 0.382805i
\(738\) 0 0
\(739\) 9.00000 + 15.5885i 0.331070 + 0.573431i 0.982722 0.185088i \(-0.0592569\pi\)
−0.651652 + 0.758518i \(0.725924\pi\)
\(740\) −4.00000 + 6.92820i −0.147043 + 0.254686i
\(741\) 0 0
\(742\) 0.500000 2.59808i 0.0183556 0.0953784i
\(743\) 20.0000 0.733729 0.366864 0.930274i \(-0.380431\pi\)
0.366864 + 0.930274i \(0.380431\pi\)
\(744\) 0 0
\(745\) 3.00000 + 5.19615i 0.109911 + 0.190372i
\(746\) 13.0000 + 22.5167i 0.475964 + 0.824394i
\(747\) 0 0
\(748\) 6.00000 0.219382
\(749\) 34.0000 + 29.4449i 1.24233 + 1.07589i
\(750\) 0 0
\(751\) −6.50000 + 11.2583i −0.237188 + 0.410822i −0.959906 0.280321i \(-0.909559\pi\)
0.722718 + 0.691143i \(0.242893\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −4.50000 + 7.79423i −0.163880 + 0.283849i
\(755\) 11.0000 0.400331
\(756\) 0 0
\(757\) 22.0000 0.799604 0.399802 0.916602i \(-0.369079\pi\)
0.399802 + 0.916602i \(0.369079\pi\)
\(758\) 12.0000 20.7846i 0.435860 0.754931i
\(759\) 0 0
\(760\) 0 0
\(761\) −16.0000 + 27.7128i −0.580000 + 1.00459i 0.415479 + 0.909603i \(0.363614\pi\)
−0.995479 + 0.0949859i \(0.969719\pi\)
\(762\) 0 0
\(763\) 40.0000 13.8564i 1.44810 0.501636i
\(764\) 6.00000 0.217072
\(765\) 0 0
\(766\) −13.0000 22.5167i −0.469709 0.813560i
\(767\) 3.50000 + 6.06218i 0.126378 + 0.218893i
\(768\) 0 0
\(769\) −13.0000 −0.468792 −0.234396 0.972141i \(-0.575311\pi\)
−0.234396 + 0.972141i \(0.575311\pi\)
\(770\) 6.00000 + 5.19615i 0.216225 + 0.187256i
\(771\) 0 0
\(772\) −9.50000 + 16.4545i −0.341912 + 0.592210i
\(773\) 9.00000 + 15.5885i 0.323708 + 0.560678i 0.981250 0.192740i \(-0.0617373\pi\)
−0.657542 + 0.753418i \(0.728404\pi\)
\(774\) 0 0
\(775\) 10.0000 17.3205i 0.359211 0.622171i
\(776\) −15.0000 −0.538469
\(777\) 0 0
\(778\) −34.0000 −1.21896
\(779\) 0 0
\(780\) 0 0
\(781\) 9.00000 + 15.5885i 0.322045 + 0.557799i
\(782\) 6.00000 10.3923i 0.214560 0.371628i
\(783\) 0 0
\(784\) 5.50000 4.33013i 0.196429 0.154647i
\(785\) 14.0000 0.499681
\(786\) 0 0