Properties

Label 325.2.m.a.199.2
Level $325$
Weight $2$
Character 325.199
Analytic conductor $2.595$
Analytic rank $0$
Dimension $4$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [325,2,Mod(49,325)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(325, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("325.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 325.m (of order \(6\), 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: \(2.59513806569\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 13)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 325.199
Dual form 325.2.m.a.49.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 - 1.50000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.00000 - 1.73205i) q^{6} +1.73205 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 1.50000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.00000 - 1.73205i) q^{6} +1.73205 q^{8} +(0.500000 + 0.866025i) q^{9} -2.00000i q^{12} +(-2.59808 + 2.50000i) q^{13} +(2.50000 - 4.33013i) q^{16} +(-2.59808 + 1.50000i) q^{17} +1.73205 q^{18} +(3.00000 - 1.73205i) q^{19} +(-5.19615 - 3.00000i) q^{23} +(3.00000 + 1.73205i) q^{24} +(1.50000 + 6.06218i) q^{26} -4.00000i q^{27} +(1.50000 - 2.59808i) q^{29} +3.46410i q^{31} +(-2.59808 - 4.50000i) q^{32} +5.19615i q^{34} +(0.500000 - 0.866025i) q^{36} +(-4.33013 + 7.50000i) q^{37} -6.00000i q^{38} +(-7.00000 + 1.73205i) q^{39} +(-4.50000 - 2.59808i) q^{41} +(-6.92820 + 4.00000i) q^{43} +(-9.00000 + 5.19615i) q^{46} +3.46410 q^{47} +(8.66025 - 5.00000i) q^{48} +(3.50000 - 6.06218i) q^{49} -6.00000 q^{51} +(3.46410 + 1.00000i) q^{52} +3.00000i q^{53} +(-6.00000 - 3.46410i) q^{54} +6.92820 q^{57} +(-2.59808 - 4.50000i) q^{58} +(-6.00000 + 3.46410i) q^{59} +(-0.500000 - 0.866025i) q^{61} +(5.19615 + 3.00000i) q^{62} +1.00000 q^{64} +(-1.73205 + 3.00000i) q^{67} +(2.59808 + 1.50000i) q^{68} +(-6.00000 - 10.3923i) q^{69} +(3.00000 - 1.73205i) q^{71} +(0.866025 + 1.50000i) q^{72} +1.73205 q^{73} +(7.50000 + 12.9904i) q^{74} +(-3.00000 - 1.73205i) q^{76} +(-3.46410 + 12.0000i) q^{78} -4.00000 q^{79} +(5.50000 - 9.52628i) q^{81} +(-7.79423 + 4.50000i) q^{82} +13.8564 q^{83} +13.8564i q^{86} +(5.19615 - 3.00000i) q^{87} +(6.00000 + 3.46410i) q^{89} +6.00000i q^{92} +(-3.46410 + 6.00000i) q^{93} +(3.00000 - 5.19615i) q^{94} -10.3923i q^{96} +(3.46410 + 6.00000i) q^{97} +(-6.06218 - 10.5000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{4} + 12 q^{6} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{4} + 12 q^{6} + 2 q^{9} + 10 q^{16} + 12 q^{19} + 12 q^{24} + 6 q^{26} + 6 q^{29} + 2 q^{36} - 28 q^{39} - 18 q^{41} - 36 q^{46} + 14 q^{49} - 24 q^{51} - 24 q^{54} - 24 q^{59} - 2 q^{61} + 4 q^{64} - 24 q^{69} + 12 q^{71} + 30 q^{74} - 12 q^{76} - 16 q^{79} + 22 q^{81} + 24 q^{89} + 12 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(301\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 1.50000i 0.612372 1.06066i −0.378467 0.925615i \(-0.623549\pi\)
0.990839 0.135045i \(-0.0431180\pi\)
\(3\) 1.73205 + 1.00000i 1.00000 + 0.577350i 0.908248 0.418432i \(-0.137420\pi\)
0.0917517 + 0.995782i \(0.470753\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 3.00000 1.73205i 1.22474 0.707107i
\(7\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(8\) 1.73205 0.612372
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(12\) 2.00000i 0.577350i
\(13\) −2.59808 + 2.50000i −0.720577 + 0.693375i
\(14\) 0 0
\(15\) 0 0
\(16\) 2.50000 4.33013i 0.625000 1.08253i
\(17\) −2.59808 + 1.50000i −0.630126 + 0.363803i −0.780801 0.624780i \(-0.785189\pi\)
0.150675 + 0.988583i \(0.451855\pi\)
\(18\) 1.73205 0.408248
\(19\) 3.00000 1.73205i 0.688247 0.397360i −0.114708 0.993399i \(-0.536593\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −5.19615 3.00000i −1.08347 0.625543i −0.151642 0.988436i \(-0.548456\pi\)
−0.931831 + 0.362892i \(0.881789\pi\)
\(24\) 3.00000 + 1.73205i 0.612372 + 0.353553i
\(25\) 0 0
\(26\) 1.50000 + 6.06218i 0.294174 + 1.18889i
\(27\) 4.00000i 0.769800i
\(28\) 0 0
\(29\) 1.50000 2.59808i 0.278543 0.482451i −0.692480 0.721437i \(-0.743482\pi\)
0.971023 + 0.238987i \(0.0768152\pi\)
\(30\) 0 0
\(31\) 3.46410i 0.622171i 0.950382 + 0.311086i \(0.100693\pi\)
−0.950382 + 0.311086i \(0.899307\pi\)
\(32\) −2.59808 4.50000i −0.459279 0.795495i
\(33\) 0 0
\(34\) 5.19615i 0.891133i
\(35\) 0 0
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) −4.33013 + 7.50000i −0.711868 + 1.23299i 0.252286 + 0.967653i \(0.418817\pi\)
−0.964155 + 0.265340i \(0.914516\pi\)
\(38\) 6.00000i 0.973329i
\(39\) −7.00000 + 1.73205i −1.12090 + 0.277350i
\(40\) 0 0
\(41\) −4.50000 2.59808i −0.702782 0.405751i 0.105601 0.994409i \(-0.466323\pi\)
−0.808383 + 0.588657i \(0.799657\pi\)
\(42\) 0 0
\(43\) −6.92820 + 4.00000i −1.05654 + 0.609994i −0.924473 0.381246i \(-0.875495\pi\)
−0.132068 + 0.991241i \(0.542162\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −9.00000 + 5.19615i −1.32698 + 0.766131i
\(47\) 3.46410 0.505291 0.252646 0.967559i \(-0.418699\pi\)
0.252646 + 0.967559i \(0.418699\pi\)
\(48\) 8.66025 5.00000i 1.25000 0.721688i
\(49\) 3.50000 6.06218i 0.500000 0.866025i
\(50\) 0 0
\(51\) −6.00000 −0.840168
\(52\) 3.46410 + 1.00000i 0.480384 + 0.138675i
\(53\) 3.00000i 0.412082i 0.978543 + 0.206041i \(0.0660580\pi\)
−0.978543 + 0.206041i \(0.933942\pi\)
\(54\) −6.00000 3.46410i −0.816497 0.471405i
\(55\) 0 0
\(56\) 0 0
\(57\) 6.92820 0.917663
\(58\) −2.59808 4.50000i −0.341144 0.590879i
\(59\) −6.00000 + 3.46410i −0.781133 + 0.450988i −0.836832 0.547460i \(-0.815595\pi\)
0.0556984 + 0.998448i \(0.482261\pi\)
\(60\) 0 0
\(61\) −0.500000 0.866025i −0.0640184 0.110883i 0.832240 0.554416i \(-0.187058\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 5.19615 + 3.00000i 0.659912 + 0.381000i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −1.73205 + 3.00000i −0.211604 + 0.366508i −0.952217 0.305424i \(-0.901202\pi\)
0.740613 + 0.671932i \(0.234535\pi\)
\(68\) 2.59808 + 1.50000i 0.315063 + 0.181902i
\(69\) −6.00000 10.3923i −0.722315 1.25109i
\(70\) 0 0
\(71\) 3.00000 1.73205i 0.356034 0.205557i −0.311305 0.950310i \(-0.600766\pi\)
0.667340 + 0.744753i \(0.267433\pi\)
\(72\) 0.866025 + 1.50000i 0.102062 + 0.176777i
\(73\) 1.73205 0.202721 0.101361 0.994850i \(-0.467680\pi\)
0.101361 + 0.994850i \(0.467680\pi\)
\(74\) 7.50000 + 12.9904i 0.871857 + 1.51010i
\(75\) 0 0
\(76\) −3.00000 1.73205i −0.344124 0.198680i
\(77\) 0 0
\(78\) −3.46410 + 12.0000i −0.392232 + 1.35873i
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 0 0
\(81\) 5.50000 9.52628i 0.611111 1.05848i
\(82\) −7.79423 + 4.50000i −0.860729 + 0.496942i
\(83\) 13.8564 1.52094 0.760469 0.649374i \(-0.224969\pi\)
0.760469 + 0.649374i \(0.224969\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 13.8564i 1.49417i
\(87\) 5.19615 3.00000i 0.557086 0.321634i
\(88\) 0 0
\(89\) 6.00000 + 3.46410i 0.635999 + 0.367194i 0.783072 0.621932i \(-0.213652\pi\)
−0.147073 + 0.989126i \(0.546985\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 6.00000i 0.625543i
\(93\) −3.46410 + 6.00000i −0.359211 + 0.622171i
\(94\) 3.00000 5.19615i 0.309426 0.535942i
\(95\) 0 0
\(96\) 10.3923i 1.06066i
\(97\) 3.46410 + 6.00000i 0.351726 + 0.609208i 0.986552 0.163448i \(-0.0522615\pi\)
−0.634826 + 0.772655i \(0.718928\pi\)
\(98\) −6.06218 10.5000i −0.612372 1.06066i
\(99\) 0 0
\(100\) 0 0
\(101\) 1.50000 2.59808i 0.149256 0.258518i −0.781697 0.623658i \(-0.785646\pi\)
0.930953 + 0.365140i \(0.118979\pi\)
\(102\) −5.19615 + 9.00000i −0.514496 + 0.891133i
\(103\) 10.0000i 0.985329i 0.870219 + 0.492665i \(0.163977\pi\)
−0.870219 + 0.492665i \(0.836023\pi\)
\(104\) −4.50000 + 4.33013i −0.441261 + 0.424604i
\(105\) 0 0
\(106\) 4.50000 + 2.59808i 0.437079 + 0.252347i
\(107\) −5.19615 3.00000i −0.502331 0.290021i 0.227345 0.973814i \(-0.426996\pi\)
−0.729676 + 0.683793i \(0.760329\pi\)
\(108\) −3.46410 + 2.00000i −0.333333 + 0.192450i
\(109\) 13.8564i 1.32720i 0.748086 + 0.663602i \(0.230973\pi\)
−0.748086 + 0.663602i \(0.769027\pi\)
\(110\) 0 0
\(111\) −15.0000 + 8.66025i −1.42374 + 0.821995i
\(112\) 0 0
\(113\) 12.9904 7.50000i 1.22203 0.705541i 0.256681 0.966496i \(-0.417371\pi\)
0.965351 + 0.260955i \(0.0840376\pi\)
\(114\) 6.00000 10.3923i 0.561951 0.973329i
\(115\) 0 0
\(116\) −3.00000 −0.278543
\(117\) −3.46410 1.00000i −0.320256 0.0924500i
\(118\) 12.0000i 1.10469i
\(119\) 0 0
\(120\) 0 0
\(121\) −5.50000 9.52628i −0.500000 0.866025i
\(122\) −1.73205 −0.156813
\(123\) −5.19615 9.00000i −0.468521 0.811503i
\(124\) 3.00000 1.73205i 0.269408 0.155543i
\(125\) 0 0
\(126\) 0 0
\(127\) 1.73205 + 1.00000i 0.153695 + 0.0887357i 0.574875 0.818241i \(-0.305051\pi\)
−0.421180 + 0.906977i \(0.638384\pi\)
\(128\) 6.06218 10.5000i 0.535826 0.928078i
\(129\) −16.0000 −1.40872
\(130\) 0 0
\(131\) 18.0000 1.57267 0.786334 0.617802i \(-0.211977\pi\)
0.786334 + 0.617802i \(0.211977\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 3.00000 + 5.19615i 0.259161 + 0.448879i
\(135\) 0 0
\(136\) −4.50000 + 2.59808i −0.385872 + 0.222783i
\(137\) −7.79423 13.5000i −0.665906 1.15338i −0.979039 0.203674i \(-0.934712\pi\)
0.313133 0.949709i \(-0.398621\pi\)
\(138\) −20.7846 −1.76930
\(139\) −2.00000 3.46410i −0.169638 0.293821i 0.768655 0.639664i \(-0.220926\pi\)
−0.938293 + 0.345843i \(0.887593\pi\)
\(140\) 0 0
\(141\) 6.00000 + 3.46410i 0.505291 + 0.291730i
\(142\) 6.00000i 0.503509i
\(143\) 0 0
\(144\) 5.00000 0.416667
\(145\) 0 0
\(146\) 1.50000 2.59808i 0.124141 0.215018i
\(147\) 12.1244 7.00000i 1.00000 0.577350i
\(148\) 8.66025 0.711868
\(149\) 16.5000 9.52628i 1.35173 0.780423i 0.363241 0.931695i \(-0.381670\pi\)
0.988492 + 0.151272i \(0.0483370\pi\)
\(150\) 0 0
\(151\) 17.3205i 1.40952i 0.709444 + 0.704761i \(0.248946\pi\)
−0.709444 + 0.704761i \(0.751054\pi\)
\(152\) 5.19615 3.00000i 0.421464 0.243332i
\(153\) −2.59808 1.50000i −0.210042 0.121268i
\(154\) 0 0
\(155\) 0 0
\(156\) 5.00000 + 5.19615i 0.400320 + 0.416025i
\(157\) 13.0000i 1.03751i −0.854922 0.518756i \(-0.826395\pi\)
0.854922 0.518756i \(-0.173605\pi\)
\(158\) −3.46410 + 6.00000i −0.275589 + 0.477334i
\(159\) −3.00000 + 5.19615i −0.237915 + 0.412082i
\(160\) 0 0
\(161\) 0 0
\(162\) −9.52628 16.5000i −0.748455 1.29636i
\(163\) −10.3923 18.0000i −0.813988 1.40987i −0.910052 0.414494i \(-0.863959\pi\)
0.0960641 0.995375i \(-0.469375\pi\)
\(164\) 5.19615i 0.405751i
\(165\) 0 0
\(166\) 12.0000 20.7846i 0.931381 1.61320i
\(167\) 6.92820 12.0000i 0.536120 0.928588i −0.462988 0.886365i \(-0.653223\pi\)
0.999108 0.0422232i \(-0.0134441\pi\)
\(168\) 0 0
\(169\) 0.500000 12.9904i 0.0384615 0.999260i
\(170\) 0 0
\(171\) 3.00000 + 1.73205i 0.229416 + 0.132453i
\(172\) 6.92820 + 4.00000i 0.528271 + 0.304997i
\(173\) −5.19615 + 3.00000i −0.395056 + 0.228086i −0.684349 0.729155i \(-0.739913\pi\)
0.289292 + 0.957241i \(0.406580\pi\)
\(174\) 10.3923i 0.787839i
\(175\) 0 0
\(176\) 0 0
\(177\) −13.8564 −1.04151
\(178\) 10.3923 6.00000i 0.778936 0.449719i
\(179\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(180\) 0 0
\(181\) 11.0000 0.817624 0.408812 0.912619i \(-0.365943\pi\)
0.408812 + 0.912619i \(0.365943\pi\)
\(182\) 0 0
\(183\) 2.00000i 0.147844i
\(184\) −9.00000 5.19615i −0.663489 0.383065i
\(185\) 0 0
\(186\) 6.00000 + 10.3923i 0.439941 + 0.762001i
\(187\) 0 0
\(188\) −1.73205 3.00000i −0.126323 0.218797i
\(189\) 0 0
\(190\) 0 0
\(191\) −9.00000 15.5885i −0.651217 1.12794i −0.982828 0.184525i \(-0.940925\pi\)
0.331611 0.943416i \(-0.392408\pi\)
\(192\) 1.73205 + 1.00000i 0.125000 + 0.0721688i
\(193\) −2.59808 + 4.50000i −0.187014 + 0.323917i −0.944253 0.329220i \(-0.893214\pi\)
0.757240 + 0.653137i \(0.226548\pi\)
\(194\) 12.0000 0.861550
\(195\) 0 0
\(196\) −7.00000 −0.500000
\(197\) −6.92820 + 12.0000i −0.493614 + 0.854965i −0.999973 0.00735824i \(-0.997658\pi\)
0.506359 + 0.862323i \(0.330991\pi\)
\(198\) 0 0
\(199\) −1.00000 1.73205i −0.0708881 0.122782i 0.828403 0.560133i \(-0.189250\pi\)
−0.899291 + 0.437351i \(0.855917\pi\)
\(200\) 0 0
\(201\) −6.00000 + 3.46410i −0.423207 + 0.244339i
\(202\) −2.59808 4.50000i −0.182800 0.316619i
\(203\) 0 0
\(204\) 3.00000 + 5.19615i 0.210042 + 0.363803i
\(205\) 0 0
\(206\) 15.0000 + 8.66025i 1.04510 + 0.603388i
\(207\) 6.00000i 0.417029i
\(208\) 4.33013 + 17.5000i 0.300240 + 1.21341i
\(209\) 0 0
\(210\) 0 0
\(211\) −5.00000 + 8.66025i −0.344214 + 0.596196i −0.985211 0.171347i \(-0.945188\pi\)
0.640996 + 0.767544i \(0.278521\pi\)
\(212\) 2.59808 1.50000i 0.178437 0.103020i
\(213\) 6.92820 0.474713
\(214\) −9.00000 + 5.19615i −0.615227 + 0.355202i
\(215\) 0 0
\(216\) 6.92820i 0.471405i
\(217\) 0 0
\(218\) 20.7846 + 12.0000i 1.40771 + 0.812743i
\(219\) 3.00000 + 1.73205i 0.202721 + 0.117041i
\(220\) 0 0
\(221\) 3.00000 10.3923i 0.201802 0.699062i
\(222\) 30.0000i 2.01347i
\(223\) −5.19615 + 9.00000i −0.347960 + 0.602685i −0.985887 0.167412i \(-0.946459\pi\)
0.637927 + 0.770097i \(0.279792\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 25.9808i 1.72821i
\(227\) 12.1244 + 21.0000i 0.804722 + 1.39382i 0.916479 + 0.400083i \(0.131019\pi\)
−0.111757 + 0.993736i \(0.535648\pi\)
\(228\) −3.46410 6.00000i −0.229416 0.397360i
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 2.59808 4.50000i 0.170572 0.295439i
\(233\) 6.00000i 0.393073i −0.980497 0.196537i \(-0.937031\pi\)
0.980497 0.196537i \(-0.0629694\pi\)
\(234\) −4.50000 + 4.33013i −0.294174 + 0.283069i
\(235\) 0 0
\(236\) 6.00000 + 3.46410i 0.390567 + 0.225494i
\(237\) −6.92820 4.00000i −0.450035 0.259828i
\(238\) 0 0
\(239\) 20.7846i 1.34444i 0.740349 + 0.672222i \(0.234660\pi\)
−0.740349 + 0.672222i \(0.765340\pi\)
\(240\) 0 0
\(241\) −1.50000 + 0.866025i −0.0966235 + 0.0557856i −0.547533 0.836784i \(-0.684433\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) −19.0526 −1.22474
\(243\) 8.66025 5.00000i 0.555556 0.320750i
\(244\) −0.500000 + 0.866025i −0.0320092 + 0.0554416i
\(245\) 0 0
\(246\) −18.0000 −1.14764
\(247\) −3.46410 + 12.0000i −0.220416 + 0.763542i
\(248\) 6.00000i 0.381000i
\(249\) 24.0000 + 13.8564i 1.52094 + 0.878114i
\(250\) 0 0
\(251\) 9.00000 + 15.5885i 0.568075 + 0.983935i 0.996756 + 0.0804789i \(0.0256450\pi\)
−0.428681 + 0.903456i \(0.641022\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 3.00000 1.73205i 0.188237 0.108679i
\(255\) 0 0
\(256\) −9.50000 16.4545i −0.593750 1.02841i
\(257\) −2.59808 1.50000i −0.162064 0.0935674i 0.416775 0.909010i \(-0.363160\pi\)
−0.578838 + 0.815442i \(0.696494\pi\)
\(258\) −13.8564 + 24.0000i −0.862662 + 1.49417i
\(259\) 0 0
\(260\) 0 0
\(261\) 3.00000 0.185695
\(262\) 15.5885 27.0000i 0.963058 1.66807i
\(263\) 10.3923 + 6.00000i 0.640817 + 0.369976i 0.784929 0.619586i \(-0.212699\pi\)
−0.144112 + 0.989561i \(0.546033\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 6.92820 + 12.0000i 0.423999 + 0.734388i
\(268\) 3.46410 0.211604
\(269\) −3.00000 5.19615i −0.182913 0.316815i 0.759958 0.649972i \(-0.225219\pi\)
−0.942871 + 0.333157i \(0.891886\pi\)
\(270\) 0 0
\(271\) 18.0000 + 10.3923i 1.09342 + 0.631288i 0.934485 0.356001i \(-0.115860\pi\)
0.158937 + 0.987289i \(0.449193\pi\)
\(272\) 15.0000i 0.909509i
\(273\) 0 0
\(274\) −27.0000 −1.63113
\(275\) 0 0
\(276\) −6.00000 + 10.3923i −0.361158 + 0.625543i
\(277\) −6.06218 + 3.50000i −0.364241 + 0.210295i −0.670940 0.741512i \(-0.734109\pi\)
0.306699 + 0.951807i \(0.400776\pi\)
\(278\) −6.92820 −0.415526
\(279\) −3.00000 + 1.73205i −0.179605 + 0.103695i
\(280\) 0 0
\(281\) 22.5167i 1.34323i −0.740900 0.671616i \(-0.765601\pi\)
0.740900 0.671616i \(-0.234399\pi\)
\(282\) 10.3923 6.00000i 0.618853 0.357295i
\(283\) 3.46410 + 2.00000i 0.205919 + 0.118888i 0.599414 0.800439i \(-0.295400\pi\)
−0.393494 + 0.919327i \(0.628734\pi\)
\(284\) −3.00000 1.73205i −0.178017 0.102778i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 2.59808 4.50000i 0.153093 0.265165i
\(289\) −4.00000 + 6.92820i −0.235294 + 0.407541i
\(290\) 0 0
\(291\) 13.8564i 0.812277i
\(292\) −0.866025 1.50000i −0.0506803 0.0877809i
\(293\) −2.59808 4.50000i −0.151781 0.262893i 0.780101 0.625653i \(-0.215168\pi\)
−0.931882 + 0.362761i \(0.881834\pi\)
\(294\) 24.2487i 1.41421i
\(295\) 0 0
\(296\) −7.50000 + 12.9904i −0.435929 + 0.755051i
\(297\) 0 0
\(298\) 33.0000i 1.91164i
\(299\) 21.0000 5.19615i 1.21446 0.300501i
\(300\) 0 0
\(301\) 0 0
\(302\) 25.9808 + 15.0000i 1.49502 + 0.863153i
\(303\) 5.19615 3.00000i 0.298511 0.172345i
\(304\) 17.3205i 0.993399i
\(305\) 0 0
\(306\) −4.50000 + 2.59808i −0.257248 + 0.148522i
\(307\) 17.3205 0.988534 0.494267 0.869310i \(-0.335437\pi\)
0.494267 + 0.869310i \(0.335437\pi\)
\(308\) 0 0
\(309\) −10.0000 + 17.3205i −0.568880 + 0.985329i
\(310\) 0 0
\(311\) −30.0000 −1.70114 −0.850572 0.525859i \(-0.823744\pi\)
−0.850572 + 0.525859i \(0.823744\pi\)
\(312\) −12.1244 + 3.00000i −0.686406 + 0.169842i
\(313\) 10.0000i 0.565233i −0.959233 0.282617i \(-0.908798\pi\)
0.959233 0.282617i \(-0.0912024\pi\)
\(314\) −19.5000 11.2583i −1.10045 0.635344i
\(315\) 0 0
\(316\) 2.00000 + 3.46410i 0.112509 + 0.194871i
\(317\) 5.19615 0.291845 0.145922 0.989296i \(-0.453385\pi\)
0.145922 + 0.989296i \(0.453385\pi\)
\(318\) 5.19615 + 9.00000i 0.291386 + 0.504695i
\(319\) 0 0
\(320\) 0 0
\(321\) −6.00000 10.3923i −0.334887 0.580042i
\(322\) 0 0
\(323\) −5.19615 + 9.00000i −0.289122 + 0.500773i
\(324\) −11.0000 −0.611111
\(325\) 0 0
\(326\) −36.0000 −1.99386
\(327\) −13.8564 + 24.0000i −0.766261 + 1.32720i
\(328\) −7.79423 4.50000i −0.430364 0.248471i
\(329\) 0 0
\(330\) 0 0
\(331\) −24.0000 + 13.8564i −1.31916 + 0.761617i −0.983593 0.180400i \(-0.942261\pi\)
−0.335566 + 0.942017i \(0.608928\pi\)
\(332\) −6.92820 12.0000i −0.380235 0.658586i
\(333\) −8.66025 −0.474579
\(334\) −12.0000 20.7846i −0.656611 1.13728i
\(335\) 0 0
\(336\) 0 0
\(337\) 23.0000i 1.25289i −0.779466 0.626445i \(-0.784509\pi\)
0.779466 0.626445i \(-0.215491\pi\)
\(338\) −19.0526 12.0000i −1.03632 0.652714i
\(339\) 30.0000 1.62938
\(340\) 0 0
\(341\) 0 0
\(342\) 5.19615 3.00000i 0.280976 0.162221i
\(343\) 0 0
\(344\) −12.0000 + 6.92820i −0.646997 + 0.373544i
\(345\) 0 0
\(346\) 10.3923i 0.558694i
\(347\) −25.9808 + 15.0000i −1.39472 + 0.805242i −0.993833 0.110885i \(-0.964631\pi\)
−0.400887 + 0.916127i \(0.631298\pi\)
\(348\) −5.19615 3.00000i −0.278543 0.160817i
\(349\) −12.0000 6.92820i −0.642345 0.370858i 0.143172 0.989698i \(-0.454270\pi\)
−0.785517 + 0.618840i \(0.787603\pi\)
\(350\) 0 0
\(351\) 10.0000 + 10.3923i 0.533761 + 0.554700i
\(352\) 0 0
\(353\) 16.4545 28.5000i 0.875784 1.51690i 0.0198582 0.999803i \(-0.493679\pi\)
0.855926 0.517099i \(-0.172988\pi\)
\(354\) −12.0000 + 20.7846i −0.637793 + 1.10469i
\(355\) 0 0
\(356\) 6.92820i 0.367194i
\(357\) 0 0
\(358\) 0 0
\(359\) 6.92820i 0.365657i 0.983145 + 0.182828i \(0.0585252\pi\)
−0.983145 + 0.182828i \(0.941475\pi\)
\(360\) 0 0
\(361\) −3.50000 + 6.06218i −0.184211 + 0.319062i
\(362\) 9.52628 16.5000i 0.500690 0.867221i
\(363\) 22.0000i 1.15470i
\(364\) 0 0
\(365\) 0 0
\(366\) −3.00000 1.73205i −0.156813 0.0905357i
\(367\) 19.0526 + 11.0000i 0.994535 + 0.574195i 0.906627 0.421933i \(-0.138648\pi\)
0.0879086 + 0.996129i \(0.471982\pi\)
\(368\) −25.9808 + 15.0000i −1.35434 + 0.781929i
\(369\) 5.19615i 0.270501i
\(370\) 0 0
\(371\) 0 0
\(372\) 6.92820 0.359211
\(373\) −16.4545 + 9.50000i −0.851981 + 0.491891i −0.861319 0.508065i \(-0.830361\pi\)
0.00933789 + 0.999956i \(0.497028\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 6.00000 0.309426
\(377\) 2.59808 + 10.5000i 0.133808 + 0.540778i
\(378\) 0 0
\(379\) 21.0000 + 12.1244i 1.07870 + 0.622786i 0.930545 0.366178i \(-0.119334\pi\)
0.148153 + 0.988964i \(0.452667\pi\)
\(380\) 0 0
\(381\) 2.00000 + 3.46410i 0.102463 + 0.177471i
\(382\) −31.1769 −1.59515
\(383\) 10.3923 + 18.0000i 0.531022 + 0.919757i 0.999345 + 0.0361995i \(0.0115252\pi\)
−0.468323 + 0.883558i \(0.655141\pi\)
\(384\) 21.0000 12.1244i 1.07165 0.618718i
\(385\) 0 0
\(386\) 4.50000 + 7.79423i 0.229044 + 0.396716i
\(387\) −6.92820 4.00000i −0.352180 0.203331i
\(388\) 3.46410 6.00000i 0.175863 0.304604i
\(389\) 9.00000 0.456318 0.228159 0.973624i \(-0.426729\pi\)
0.228159 + 0.973624i \(0.426729\pi\)
\(390\) 0 0
\(391\) 18.0000 0.910299
\(392\) 6.06218 10.5000i 0.306186 0.530330i
\(393\) 31.1769 + 18.0000i 1.57267 + 0.907980i
\(394\) 12.0000 + 20.7846i 0.604551 + 1.04711i
\(395\) 0 0
\(396\) 0 0
\(397\) −6.92820 12.0000i −0.347717 0.602263i 0.638127 0.769931i \(-0.279710\pi\)
−0.985843 + 0.167668i \(0.946376\pi\)
\(398\) −3.46410 −0.173640
\(399\) 0 0
\(400\) 0 0
\(401\) −1.50000 0.866025i −0.0749064 0.0432472i 0.462079 0.886839i \(-0.347104\pi\)
−0.536985 + 0.843592i \(0.680437\pi\)
\(402\) 12.0000i 0.598506i
\(403\) −8.66025 9.00000i −0.431398 0.448322i
\(404\) −3.00000 −0.149256
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −10.3923 −0.514496
\(409\) −13.5000 + 7.79423i −0.667532 + 0.385400i −0.795141 0.606425i \(-0.792603\pi\)
0.127609 + 0.991825i \(0.459270\pi\)
\(410\) 0 0
\(411\) 31.1769i 1.53784i
\(412\) 8.66025 5.00000i 0.426660 0.246332i
\(413\) 0 0
\(414\) −9.00000 5.19615i −0.442326 0.255377i
\(415\) 0 0
\(416\) 18.0000 + 5.19615i 0.882523 + 0.254762i
\(417\) 8.00000i 0.391762i
\(418\) 0 0
\(419\) 9.00000 15.5885i 0.439679 0.761546i −0.557986 0.829851i \(-0.688426\pi\)
0.997665 + 0.0683046i \(0.0217590\pi\)
\(420\) 0 0
\(421\) 15.5885i 0.759735i 0.925041 + 0.379867i \(0.124030\pi\)
−0.925041 + 0.379867i \(0.875970\pi\)
\(422\) 8.66025 + 15.0000i 0.421575 + 0.730189i
\(423\) 1.73205 + 3.00000i 0.0842152 + 0.145865i
\(424\) 5.19615i 0.252347i
\(425\) 0 0
\(426\) 6.00000 10.3923i 0.290701 0.503509i
\(427\) 0 0
\(428\) 6.00000i 0.290021i
\(429\) 0 0
\(430\) 0 0
\(431\) −6.00000 3.46410i −0.289010 0.166860i 0.348485 0.937314i \(-0.386696\pi\)
−0.637495 + 0.770454i \(0.720029\pi\)
\(432\) −17.3205 10.0000i −0.833333 0.481125i
\(433\) 14.7224 8.50000i 0.707515 0.408484i −0.102625 0.994720i \(-0.532724\pi\)
0.810140 + 0.586236i \(0.199391\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 12.0000 6.92820i 0.574696 0.331801i
\(437\) −20.7846 −0.994263
\(438\) 5.19615 3.00000i 0.248282 0.143346i
\(439\) −14.0000 + 24.2487i −0.668184 + 1.15733i 0.310228 + 0.950662i \(0.399595\pi\)
−0.978412 + 0.206666i \(0.933739\pi\)
\(440\) 0 0
\(441\) 7.00000 0.333333
\(442\) −12.9904 13.5000i −0.617889 0.642130i
\(443\) 12.0000i 0.570137i 0.958507 + 0.285069i \(0.0920164\pi\)
−0.958507 + 0.285069i \(0.907984\pi\)
\(444\) 15.0000 + 8.66025i 0.711868 + 0.410997i
\(445\) 0 0
\(446\) 9.00000 + 15.5885i 0.426162 + 0.738135i
\(447\) 38.1051 1.80231
\(448\) 0 0
\(449\) 6.00000 3.46410i 0.283158 0.163481i −0.351694 0.936115i \(-0.614394\pi\)
0.634852 + 0.772634i \(0.281061\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −12.9904 7.50000i −0.611016 0.352770i
\(453\) −17.3205 + 30.0000i −0.813788 + 1.40952i
\(454\) 42.0000 1.97116
\(455\) 0 0
\(456\) 12.0000 0.561951
\(457\) −0.866025 + 1.50000i −0.0405110 + 0.0701670i −0.885570 0.464506i \(-0.846232\pi\)
0.845059 + 0.534673i \(0.179565\pi\)
\(458\) 0 0
\(459\) 6.00000 + 10.3923i 0.280056 + 0.485071i
\(460\) 0 0
\(461\) 19.5000 11.2583i 0.908206 0.524353i 0.0283522 0.999598i \(-0.490974\pi\)
0.879853 + 0.475245i \(0.157641\pi\)
\(462\) 0 0
\(463\) 13.8564 0.643962 0.321981 0.946746i \(-0.395651\pi\)
0.321981 + 0.946746i \(0.395651\pi\)
\(464\) −7.50000 12.9904i −0.348179 0.603063i
\(465\) 0 0
\(466\) −9.00000 5.19615i −0.416917 0.240707i
\(467\) 12.0000i 0.555294i 0.960683 + 0.277647i \(0.0895545\pi\)
−0.960683 + 0.277647i \(0.910445\pi\)
\(468\) 0.866025 + 3.50000i 0.0400320 + 0.161788i
\(469\) 0 0
\(470\) 0 0
\(471\) 13.0000 22.5167i 0.599008 1.03751i
\(472\) −10.3923 + 6.00000i −0.478345 + 0.276172i
\(473\) 0 0
\(474\) −12.0000 + 6.92820i −0.551178 + 0.318223i
\(475\) 0 0
\(476\) 0 0
\(477\) −2.59808 + 1.50000i −0.118958 + 0.0686803i
\(478\) 31.1769 + 18.0000i 1.42600 + 0.823301i
\(479\) −21.0000 12.1244i −0.959514 0.553976i −0.0634909 0.997982i \(-0.520223\pi\)
−0.896024 + 0.444006i \(0.853557\pi\)
\(480\) 0 0
\(481\) −7.50000 30.3109i −0.341971 1.38206i
\(482\) 3.00000i 0.136646i
\(483\) 0 0
\(484\) −5.50000 + 9.52628i −0.250000 + 0.433013i
\(485\) 0 0
\(486\) 17.3205i 0.785674i
\(487\) −3.46410 6.00000i −0.156973 0.271886i 0.776802 0.629744i \(-0.216840\pi\)
−0.933776 + 0.357858i \(0.883507\pi\)
\(488\) −0.866025 1.50000i −0.0392031 0.0679018i
\(489\) 41.5692i 1.87983i
\(490\) 0 0
\(491\) −6.00000 + 10.3923i −0.270776 + 0.468998i −0.969061 0.246822i \(-0.920614\pi\)
0.698285 + 0.715820i \(0.253947\pi\)
\(492\) −5.19615 + 9.00000i −0.234261 + 0.405751i
\(493\) 9.00000i 0.405340i
\(494\) 15.0000 + 15.5885i 0.674882 + 0.701358i
\(495\) 0 0
\(496\) 15.0000 + 8.66025i 0.673520 + 0.388857i
\(497\) 0 0
\(498\) 41.5692 24.0000i 1.86276 1.07547i
\(499\) 31.1769i 1.39567i −0.716258 0.697835i \(-0.754147\pi\)
0.716258 0.697835i \(-0.245853\pi\)
\(500\) 0 0
\(501\) 24.0000 13.8564i 1.07224 0.619059i
\(502\) 31.1769 1.39149
\(503\) −31.1769 + 18.0000i −1.39011 + 0.802580i −0.993327 0.115332i \(-0.963207\pi\)
−0.396783 + 0.917912i \(0.629873\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 13.8564 22.0000i 0.615385 0.977054i
\(508\) 2.00000i 0.0887357i
\(509\) −16.5000 9.52628i −0.731350 0.422245i 0.0875661 0.996159i \(-0.472091\pi\)
−0.818916 + 0.573914i \(0.805424\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −8.66025 −0.382733
\(513\) −6.92820 12.0000i −0.305888 0.529813i
\(514\) −4.50000 + 2.59808i −0.198486 + 0.114596i
\(515\) 0 0
\(516\) 8.00000 + 13.8564i 0.352180 + 0.609994i
\(517\) 0 0
\(518\) 0 0
\(519\) −12.0000 −0.526742
\(520\) 0 0
\(521\) 9.00000 0.394297 0.197149 0.980374i \(-0.436832\pi\)
0.197149 + 0.980374i \(0.436832\pi\)
\(522\) 2.59808 4.50000i 0.113715 0.196960i
\(523\) −13.8564 8.00000i −0.605898 0.349816i 0.165460 0.986216i \(-0.447089\pi\)
−0.771358 + 0.636401i \(0.780422\pi\)
\(524\) −9.00000 15.5885i −0.393167 0.680985i
\(525\) 0 0
\(526\) 18.0000 10.3923i 0.784837 0.453126i
\(527\) −5.19615 9.00000i −0.226348 0.392046i
\(528\) 0 0
\(529\) 6.50000 + 11.2583i 0.282609 + 0.489493i
\(530\) 0 0
\(531\) −6.00000 3.46410i −0.260378 0.150329i
\(532\) 0 0
\(533\) 18.1865 4.50000i 0.787746 0.194917i
\(534\) 24.0000 1.03858
\(535\) 0 0
\(536\) −3.00000 + 5.19615i −0.129580 + 0.224440i
\(537\) 0 0
\(538\) −10.3923 −0.448044
\(539\) 0 0
\(540\) 0 0
\(541\) 29.4449i 1.26593i 0.774179 + 0.632967i \(0.218163\pi\)
−0.774179 + 0.632967i \(0.781837\pi\)
\(542\) 31.1769 18.0000i 1.33916 0.773166i
\(543\) 19.0526 + 11.0000i 0.817624 + 0.472055i
\(544\) 13.5000 + 7.79423i 0.578808 + 0.334175i
\(545\) 0 0
\(546\) 0 0
\(547\) 22.0000i 0.940652i −0.882493 0.470326i \(-0.844136\pi\)
0.882493 0.470326i \(-0.155864\pi\)
\(548\) −7.79423 + 13.5000i −0.332953 + 0.576691i
\(549\) 0.500000 0.866025i 0.0213395 0.0369611i
\(550\) 0 0
\(551\) 10.3923i 0.442727i
\(552\) −10.3923 18.0000i −0.442326 0.766131i
\(553\) 0 0
\(554\) 12.1244i 0.515115i
\(555\) 0 0
\(556\) −2.00000 + 3.46410i −0.0848189 + 0.146911i
\(557\) 7.79423 13.5000i 0.330252 0.572013i −0.652309 0.757953i \(-0.726200\pi\)
0.982561 + 0.185940i \(0.0595329\pi\)
\(558\) 6.00000i 0.254000i
\(559\) 8.00000 27.7128i 0.338364 1.17213i
\(560\) 0 0
\(561\) 0 0
\(562\) −33.7750 19.5000i −1.42471 0.822558i
\(563\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(564\) 6.92820i 0.291730i
\(565\) 0 0
\(566\) 6.00000 3.46410i 0.252199 0.145607i
\(567\) 0 0
\(568\) 5.19615 3.00000i 0.218026 0.125877i
\(569\) −21.0000 + 36.3731i −0.880366 + 1.52484i −0.0294311 + 0.999567i \(0.509370\pi\)
−0.850935 + 0.525271i \(0.823964\pi\)
\(570\) 0 0
\(571\) 40.0000 1.67395 0.836974 0.547243i \(-0.184323\pi\)
0.836974 + 0.547243i \(0.184323\pi\)
\(572\) 0 0
\(573\) 36.0000i 1.50392i
\(574\) 0 0
\(575\) 0 0
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 19.0526 0.793168 0.396584 0.917998i \(-0.370195\pi\)
0.396584 + 0.917998i \(0.370195\pi\)
\(578\) 6.92820 + 12.0000i 0.288175 + 0.499134i
\(579\) −9.00000 + 5.19615i −0.374027 + 0.215945i
\(580\) 0 0
\(581\) 0 0
\(582\) 20.7846 + 12.0000i 0.861550 + 0.497416i
\(583\) 0 0
\(584\) 3.00000 0.124141
\(585\) 0 0
\(586\) −9.00000 −0.371787
\(587\) 10.3923 18.0000i 0.428936 0.742940i −0.567843 0.823137i \(-0.692222\pi\)
0.996779 + 0.0801976i \(0.0255551\pi\)
\(588\) −12.1244 7.00000i −0.500000 0.288675i
\(589\) 6.00000 + 10.3923i 0.247226 + 0.428207i
\(590\) 0 0
\(591\) −24.0000 + 13.8564i −0.987228 + 0.569976i
\(592\) 21.6506 + 37.5000i 0.889836 + 1.54124i
\(593\) −25.9808 −1.06690 −0.533451 0.845831i \(-0.679105\pi\)
−0.533451 + 0.845831i \(0.679105\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −16.5000 9.52628i −0.675866 0.390212i
\(597\) 4.00000i 0.163709i
\(598\) 10.3923 36.0000i 0.424973 1.47215i
\(599\) −30.0000 −1.22577 −0.612883 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) 0 0
\(601\) −12.5000 + 21.6506i −0.509886 + 0.883148i 0.490049 + 0.871695i \(0.336979\pi\)
−0.999934 + 0.0114528i \(0.996354\pi\)
\(602\) 0 0
\(603\) −3.46410 −0.141069
\(604\) 15.0000 8.66025i 0.610341 0.352381i
\(605\) 0 0
\(606\) 10.3923i 0.422159i
\(607\) −29.4449 + 17.0000i −1.19513 + 0.690009i −0.959466 0.281826i \(-0.909060\pi\)
−0.235665 + 0.971834i \(0.575727\pi\)
\(608\) −15.5885 9.00000i −0.632195 0.364998i
\(609\) 0 0
\(610\) 0 0
\(611\) −9.00000 + 8.66025i −0.364101 + 0.350356i
\(612\) 3.00000i 0.121268i
\(613\) −6.06218 + 10.5000i −0.244849 + 0.424091i −0.962089 0.272735i \(-0.912072\pi\)
0.717240 + 0.696826i \(0.245405\pi\)
\(614\) 15.0000 25.9808i 0.605351 1.04850i
\(615\) 0 0
\(616\) 0 0
\(617\) −11.2583 19.5000i −0.453243 0.785040i 0.545342 0.838214i \(-0.316400\pi\)
−0.998585 + 0.0531732i \(0.983066\pi\)
\(618\) 17.3205 + 30.0000i 0.696733 + 1.20678i
\(619\) 20.7846i 0.835404i 0.908584 + 0.417702i \(0.137164\pi\)
−0.908584 + 0.417702i \(0.862836\pi\)
\(620\) 0 0
\(621\) −12.0000 + 20.7846i −0.481543 + 0.834058i
\(622\) −25.9808 + 45.0000i −1.04173 + 1.80434i
\(623\) 0 0
\(624\) −10.0000 + 34.6410i −0.400320 + 1.38675i
\(625\) 0 0
\(626\) −15.0000 8.66025i −0.599521 0.346133i
\(627\) 0 0
\(628\) −11.2583 + 6.50000i −0.449256 + 0.259378i
\(629\) 25.9808i 1.03592i
\(630\) 0 0
\(631\) −42.0000 + 24.2487i −1.67199 + 0.965326i −0.705473 + 0.708737i \(0.749265\pi\)
−0.966521 + 0.256589i \(0.917401\pi\)
\(632\) −6.92820 −0.275589
\(633\) −17.3205 + 10.0000i −0.688428 + 0.397464i
\(634\) 4.50000 7.79423i 0.178718 0.309548i
\(635\) 0 0
\(636\) 6.00000 0.237915
\(637\) 6.06218 + 24.5000i 0.240192 + 0.970725i
\(638\) 0 0
\(639\) 3.00000 + 1.73205i 0.118678 + 0.0685189i
\(640\) 0 0
\(641\) −16.5000 28.5788i −0.651711 1.12880i −0.982708 0.185164i \(-0.940718\pi\)
0.330997 0.943632i \(-0.392615\pi\)
\(642\) −20.7846 −0.820303
\(643\) −6.92820 12.0000i −0.273222 0.473234i 0.696463 0.717592i \(-0.254756\pi\)
−0.969685 + 0.244359i \(0.921423\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 9.00000 + 15.5885i 0.354100 + 0.613320i
\(647\) −15.5885 9.00000i −0.612845 0.353827i 0.161233 0.986916i \(-0.448453\pi\)
−0.774078 + 0.633090i \(0.781786\pi\)
\(648\) 9.52628 16.5000i 0.374228 0.648181i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −10.3923 + 18.0000i −0.406994 + 0.704934i
\(653\) −25.9808 15.0000i −1.01671 0.586995i −0.103558 0.994623i \(-0.533023\pi\)
−0.913148 + 0.407628i \(0.866356\pi\)
\(654\) 24.0000 + 41.5692i 0.938474 + 1.62549i
\(655\) 0 0
\(656\) −22.5000 + 12.9904i −0.878477 + 0.507189i
\(657\) 0.866025 + 1.50000i 0.0337869 + 0.0585206i
\(658\) 0 0
\(659\) −6.00000 10.3923i −0.233727 0.404827i 0.725175 0.688565i \(-0.241759\pi\)
−0.958902 + 0.283738i \(0.908425\pi\)
\(660\) 0 0
\(661\) −40.5000 23.3827i −1.57527 0.909481i −0.995506 0.0946945i \(-0.969813\pi\)
−0.579761 0.814787i \(-0.696854\pi\)
\(662\) 48.0000i 1.86557i
\(663\) 15.5885 15.0000i 0.605406 0.582552i
\(664\) 24.0000 0.931381
\(665\) 0 0
\(666\) −7.50000 + 12.9904i −0.290619 + 0.503367i
\(667\) −15.5885 + 9.00000i −0.603587 + 0.348481i
\(668\) −13.8564 −0.536120
\(669\) −18.0000 + 10.3923i −0.695920 + 0.401790i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −16.4545 9.50000i −0.634274 0.366198i 0.148132 0.988968i \(-0.452674\pi\)
−0.782405 + 0.622770i \(0.786007\pi\)
\(674\) −34.5000 19.9186i −1.32889 0.767235i
\(675\) 0 0
\(676\) −11.5000 + 6.06218i −0.442308 + 0.233161i
\(677\) 6.00000i 0.230599i −0.993331 0.115299i \(-0.963217\pi\)
0.993331 0.115299i \(-0.0367827\pi\)
\(678\) 25.9808 45.0000i 0.997785 1.72821i
\(679\) 0 0
\(680\) 0 0
\(681\) 48.4974i 1.85843i
\(682\) 0 0
\(683\) −12.1244 21.0000i −0.463926 0.803543i 0.535227 0.844708i \(-0.320226\pi\)
−0.999152 + 0.0411658i \(0.986893\pi\)
\(684\) 3.46410i 0.132453i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 40.0000i 1.52499i
\(689\) −7.50000 7.79423i −0.285727 0.296936i
\(690\) 0 0
\(691\) 12.0000 + 6.92820i 0.456502 + 0.263561i 0.710572 0.703624i \(-0.248436\pi\)
−0.254071 + 0.967186i \(0.581770\pi\)
\(692\) 5.19615 + 3.00000i 0.197528 + 0.114043i
\(693\) 0 0
\(694\) 51.9615i 1.97243i
\(695\) 0 0
\(696\) 9.00000 5.19615i 0.341144 0.196960i
\(697\) 15.5885 0.590455
\(698\) −20.7846 + 12.0000i −0.786709 + 0.454207i
\(699\) 6.00000 10.3923i 0.226941 0.393073i
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 24.2487 6.00000i 0.915209 0.226455i
\(703\) 30.0000i 1.13147i
\(704\) 0 0
\(705\) 0 0
\(706\) −28.5000 49.3634i −1.07261 1.85782i
\(707\) 0 0
\(708\) 6.92820 + 12.0000i 0.260378 + 0.450988i
\(709\) 4.50000 2.59808i 0.169001 0.0975728i −0.413114 0.910679i \(-0.635559\pi\)
0.582115 + 0.813107i \(0.302225\pi\)
\(710\) 0 0
\(711\) −2.00000 3.46410i −0.0750059 0.129914i
\(712\) 10.3923 + 6.00000i 0.389468 + 0.224860i
\(713\) 10.3923 18.0000i 0.389195 0.674105i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −20.7846 + 36.0000i −0.776215 + 1.34444i
\(718\) 10.3923 + 6.00000i 0.387837 + 0.223918i
\(719\) −24.0000 41.5692i −0.895049 1.55027i −0.833744 0.552151i \(-0.813807\pi\)
−0.0613050 0.998119i \(-0.519526\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 6.06218 + 10.5000i 0.225611 + 0.390770i
\(723\) −3.46410 −0.128831
\(724\) −5.50000 9.52628i −0.204406 0.354041i
\(725\) 0 0
\(726\) −33.0000 19.0526i −1.22474 0.707107i
\(727\) 32.0000i 1.18681i −0.804902 0.593407i \(-0.797782\pi\)
0.804902 0.593407i \(-0.202218\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) 0 0
\(731\) 12.0000 20.7846i 0.443836 0.768747i
\(732\) −1.73205 + 1.00000i −0.0640184 + 0.0369611i
\(733\) 12.1244 0.447823 0.223912 0.974609i \(-0.428117\pi\)
0.223912 + 0.974609i \(0.428117\pi\)
\(734\) 33.0000 19.0526i 1.21805 0.703243i
\(735\) 0 0
\(736\) 31.1769i 1.14920i
\(737\) 0 0
\(738\) −7.79423 4.50000i −0.286910 0.165647i
\(739\) 18.0000 + 10.3923i 0.662141 + 0.382287i 0.793092 0.609102i \(-0.208470\pi\)
−0.130951 + 0.991389i \(0.541803\pi\)
\(740\) 0 0
\(741\) −18.0000 + 17.3205i −0.661247 + 0.636285i
\(742\) 0 0
\(743\) −17.3205 + 30.0000i −0.635428 + 1.10059i 0.350997 + 0.936377i \(0.385843\pi\)
−0.986424 + 0.164216i \(0.947490\pi\)
\(744\) −6.00000 + 10.3923i −0.219971 + 0.381000i
\(745\) 0 0
\(746\) 32.9090i 1.20488i
\(747\) 6.92820 + 12.0000i 0.253490 + 0.439057i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 8.00000 13.8564i 0.291924 0.505627i −0.682341 0.731034i \(-0.739038\pi\)
0.974265 + 0.225407i \(0.0723712\pi\)
\(752\) 8.66025 15.0000i 0.315807 0.546994i
\(753\) 36.0000i 1.31191i
\(754\) 18.0000 + 5.19615i 0.655521 + 0.189233i
\(755\) 0 0
\(756\) 0 0
\(757\) 22.5167 + 13.0000i 0.818382 + 0.472493i 0.849858 0.527011i \(-0.176688\pi\)
−0.0314762 + 0.999505i \(0.510021\pi\)
\(758\) 36.3731 21.0000i 1.32113 0.762754i
\(759\) 0 0
\(760\) 0 0
\(761\) 30.0000 17.3205i 1.08750 0.627868i 0.154590 0.987979i \(-0.450594\pi\)
0.932910 + 0.360111i \(0.117261\pi\)
\(762\) 6.92820 0.250982
\(763\) 0 0
\(764\) −9.00000 + 15.5885i −0.325609 + 0.563971i
\(765\) 0 0
\(766\) 36.0000 1.30073
\(767\) 6.92820 24.0000i 0.250163 0.866590i
\(768\) 38.0000i 1.37121i
\(769\) −6.00000 3.46410i −0.216366 0.124919i 0.387901 0.921701i \(-0.373200\pi\)
−0.604266 + 0.796782i \(0.706534\pi\)
\(770\) 0 0
\(771\) −3.00000 5.19615i −0.108042 0.187135i
\(772\) 5.19615 0.187014
\(773\) 17.3205 + 30.0000i 0.622975 + 1.07903i 0.988929 + 0.148392i \(0.0474097\pi\)
−0.365953 + 0.930633i \(0.619257\pi\)
\(774\) −12.0000 + 6.92820i −0.431331 + 0.249029i
\(775\) 0 0
\(776\) 6.00000 + 10.3923i 0.215387 + 0.373062i
\(777\) 0 0
\(778\) 7.79423 13.5000i 0.279437 0.483998i
\(779\) −18.0000 −0.644917
\(780\) 0 0
\(781\) 0 0
\(782\) 15.5885 27.0000i 0.557442 0.965518i
\(783\) −10.3923 6.00000i −0.371391