Properties

Label 1470.2.i.u.361.2
Level $1470$
Weight $2$
Character 1470.361
Analytic conductor $11.738$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1470,2,Mod(361,1470)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1470, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1470.361");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.i (of order \(3\), 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: \(11.7380090971\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1470.361
Dual form 1470.2.i.u.961.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.292893 + 0.507306i) q^{11} +(-0.500000 - 0.866025i) q^{12} +1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.707107 + 1.22474i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(1.41421 + 2.44949i) q^{19} +1.00000 q^{20} +0.585786 q^{22} +(-2.41421 - 4.18154i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{27} +8.24264 q^{29} +(-0.500000 - 0.866025i) q^{30} +(-2.53553 + 4.39167i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.292893 - 0.507306i) q^{33} +1.41421 q^{34} +1.00000 q^{36} +(0.707107 + 1.22474i) q^{37} +(1.41421 - 2.44949i) q^{38} +(-0.500000 - 0.866025i) q^{40} -8.82843 q^{41} +4.58579 q^{43} +(-0.292893 - 0.507306i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-2.41421 + 4.18154i) q^{46} +(4.53553 + 7.85578i) q^{47} +1.00000 q^{48} +1.00000 q^{50} +(-0.707107 - 1.22474i) q^{51} +(4.65685 - 8.06591i) q^{53} +(-0.500000 - 0.866025i) q^{54} +0.585786 q^{55} -2.82843 q^{57} +(-4.12132 - 7.13834i) q^{58} +(-1.24264 + 2.15232i) q^{59} +(-0.500000 + 0.866025i) q^{60} +(5.82843 + 10.0951i) q^{61} +5.07107 q^{62} +1.00000 q^{64} +(-0.292893 + 0.507306i) q^{66} +(-3.94975 + 6.84116i) q^{67} +(-0.707107 - 1.22474i) q^{68} +4.82843 q^{69} +10.8284 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-3.82843 + 6.63103i) q^{73} +(0.707107 - 1.22474i) q^{74} +(-0.500000 - 0.866025i) q^{75} -2.82843 q^{76} +(5.65685 + 9.79796i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.41421 + 7.64564i) q^{82} -5.17157 q^{83} +1.41421 q^{85} +(-2.29289 - 3.97141i) q^{86} +(-4.12132 + 7.13834i) q^{87} +(-0.292893 + 0.507306i) q^{88} +(3.24264 + 5.61642i) q^{89} +1.00000 q^{90} +4.82843 q^{92} +(-2.53553 - 4.39167i) q^{93} +(4.53553 - 7.85578i) q^{94} +(1.41421 - 2.44949i) q^{95} +(-0.500000 - 0.866025i) q^{96} +8.82843 q^{97} +0.585786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 4 q^{6} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 4 q^{6} + 4 q^{8} - 2 q^{9} - 2 q^{10} - 4 q^{11} - 2 q^{12} + 4 q^{15} - 2 q^{16} - 2 q^{18} + 4 q^{20} + 8 q^{22} - 4 q^{23} - 2 q^{24} - 2 q^{25} + 4 q^{27} + 16 q^{29} - 2 q^{30} + 4 q^{31} - 2 q^{32} - 4 q^{33} + 4 q^{36} - 2 q^{40} - 24 q^{41} + 24 q^{43} - 4 q^{44} - 2 q^{45} - 4 q^{46} + 4 q^{47} + 4 q^{48} + 4 q^{50} - 4 q^{53} - 2 q^{54} + 8 q^{55} - 8 q^{58} + 12 q^{59} - 2 q^{60} + 12 q^{61} - 8 q^{62} + 4 q^{64} - 4 q^{66} + 4 q^{67} + 8 q^{69} + 32 q^{71} - 2 q^{72} - 4 q^{73} - 2 q^{75} - 2 q^{80} - 2 q^{81} + 12 q^{82} - 32 q^{83} - 12 q^{86} - 8 q^{87} - 4 q^{88} - 4 q^{89} + 4 q^{90} + 8 q^{92} + 4 q^{93} + 4 q^{94} - 2 q^{96} + 24 q^{97} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) −0.292893 + 0.507306i −0.0883106 + 0.152958i −0.906797 0.421567i \(-0.861480\pi\)
0.818487 + 0.574526i \(0.194813\pi\)
\(12\) −0.500000 0.866025i −0.144338 0.250000i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −0.707107 + 1.22474i −0.171499 + 0.297044i −0.938944 0.344070i \(-0.888194\pi\)
0.767445 + 0.641114i \(0.221528\pi\)
\(18\) −0.500000 + 0.866025i −0.117851 + 0.204124i
\(19\) 1.41421 + 2.44949i 0.324443 + 0.561951i 0.981399 0.191977i \(-0.0614899\pi\)
−0.656957 + 0.753928i \(0.728157\pi\)
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) 0.585786 0.124890
\(23\) −2.41421 4.18154i −0.503398 0.871911i −0.999992 0.00392850i \(-0.998750\pi\)
0.496594 0.867983i \(-0.334584\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 8.24264 1.53062 0.765310 0.643662i \(-0.222586\pi\)
0.765310 + 0.643662i \(0.222586\pi\)
\(30\) −0.500000 0.866025i −0.0912871 0.158114i
\(31\) −2.53553 + 4.39167i −0.455395 + 0.788768i −0.998711 0.0507607i \(-0.983835\pi\)
0.543316 + 0.839529i \(0.317169\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −0.292893 0.507306i −0.0509862 0.0883106i
\(34\) 1.41421 0.242536
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 0.707107 + 1.22474i 0.116248 + 0.201347i 0.918278 0.395937i \(-0.129580\pi\)
−0.802030 + 0.597284i \(0.796247\pi\)
\(38\) 1.41421 2.44949i 0.229416 0.397360i
\(39\) 0 0
\(40\) −0.500000 0.866025i −0.0790569 0.136931i
\(41\) −8.82843 −1.37877 −0.689384 0.724396i \(-0.742119\pi\)
−0.689384 + 0.724396i \(0.742119\pi\)
\(42\) 0 0
\(43\) 4.58579 0.699326 0.349663 0.936876i \(-0.386296\pi\)
0.349663 + 0.936876i \(0.386296\pi\)
\(44\) −0.292893 0.507306i −0.0441553 0.0764792i
\(45\) −0.500000 + 0.866025i −0.0745356 + 0.129099i
\(46\) −2.41421 + 4.18154i −0.355956 + 0.616535i
\(47\) 4.53553 + 7.85578i 0.661576 + 1.14588i 0.980202 + 0.198002i \(0.0634453\pi\)
−0.318626 + 0.947881i \(0.603221\pi\)
\(48\) 1.00000 0.144338
\(49\) 0 0
\(50\) 1.00000 0.141421
\(51\) −0.707107 1.22474i −0.0990148 0.171499i
\(52\) 0 0
\(53\) 4.65685 8.06591i 0.639668 1.10794i −0.345837 0.938294i \(-0.612405\pi\)
0.985506 0.169643i \(-0.0542615\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 0.585786 0.0789874
\(56\) 0 0
\(57\) −2.82843 −0.374634
\(58\) −4.12132 7.13834i −0.541156 0.937309i
\(59\) −1.24264 + 2.15232i −0.161778 + 0.280208i −0.935506 0.353310i \(-0.885056\pi\)
0.773728 + 0.633517i \(0.218390\pi\)
\(60\) −0.500000 + 0.866025i −0.0645497 + 0.111803i
\(61\) 5.82843 + 10.0951i 0.746254 + 1.29255i 0.949607 + 0.313444i \(0.101483\pi\)
−0.203353 + 0.979105i \(0.565184\pi\)
\(62\) 5.07107 0.644026
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −0.292893 + 0.507306i −0.0360527 + 0.0624450i
\(67\) −3.94975 + 6.84116i −0.482538 + 0.835781i −0.999799 0.0200468i \(-0.993618\pi\)
0.517261 + 0.855828i \(0.326952\pi\)
\(68\) −0.707107 1.22474i −0.0857493 0.148522i
\(69\) 4.82843 0.581274
\(70\) 0 0
\(71\) 10.8284 1.28510 0.642549 0.766245i \(-0.277877\pi\)
0.642549 + 0.766245i \(0.277877\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) −3.82843 + 6.63103i −0.448084 + 0.776103i −0.998261 0.0589442i \(-0.981227\pi\)
0.550178 + 0.835048i \(0.314560\pi\)
\(74\) 0.707107 1.22474i 0.0821995 0.142374i
\(75\) −0.500000 0.866025i −0.0577350 0.100000i
\(76\) −2.82843 −0.324443
\(77\) 0 0
\(78\) 0 0
\(79\) 5.65685 + 9.79796i 0.636446 + 1.10236i 0.986207 + 0.165518i \(0.0529295\pi\)
−0.349761 + 0.936839i \(0.613737\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 4.41421 + 7.64564i 0.487468 + 0.844320i
\(83\) −5.17157 −0.567654 −0.283827 0.958876i \(-0.591604\pi\)
−0.283827 + 0.958876i \(0.591604\pi\)
\(84\) 0 0
\(85\) 1.41421 0.153393
\(86\) −2.29289 3.97141i −0.247249 0.428248i
\(87\) −4.12132 + 7.13834i −0.441852 + 0.765310i
\(88\) −0.292893 + 0.507306i −0.0312225 + 0.0540790i
\(89\) 3.24264 + 5.61642i 0.343719 + 0.595339i 0.985120 0.171867i \(-0.0549798\pi\)
−0.641401 + 0.767206i \(0.721646\pi\)
\(90\) 1.00000 0.105409
\(91\) 0 0
\(92\) 4.82843 0.503398
\(93\) −2.53553 4.39167i −0.262923 0.455395i
\(94\) 4.53553 7.85578i 0.467805 0.810261i
\(95\) 1.41421 2.44949i 0.145095 0.251312i
\(96\) −0.500000 0.866025i −0.0510310 0.0883883i
\(97\) 8.82843 0.896391 0.448195 0.893936i \(-0.352067\pi\)
0.448195 + 0.893936i \(0.352067\pi\)
\(98\) 0 0
\(99\) 0.585786 0.0588738
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 3.17157 5.49333i 0.315583 0.546606i −0.663978 0.747752i \(-0.731133\pi\)
0.979561 + 0.201146i \(0.0644665\pi\)
\(102\) −0.707107 + 1.22474i −0.0700140 + 0.121268i
\(103\) 5.07107 + 8.78335i 0.499667 + 0.865449i 1.00000 0.000384289i \(-0.000122323\pi\)
−0.500333 + 0.865833i \(0.666789\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −9.31371 −0.904627
\(107\) 2.00000 + 3.46410i 0.193347 + 0.334887i 0.946357 0.323122i \(-0.104732\pi\)
−0.753010 + 0.658009i \(0.771399\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) −2.65685 + 4.60181i −0.254480 + 0.440773i −0.964754 0.263152i \(-0.915238\pi\)
0.710274 + 0.703926i \(0.248571\pi\)
\(110\) −0.292893 0.507306i −0.0279263 0.0483697i
\(111\) −1.41421 −0.134231
\(112\) 0 0
\(113\) 9.31371 0.876160 0.438080 0.898936i \(-0.355659\pi\)
0.438080 + 0.898936i \(0.355659\pi\)
\(114\) 1.41421 + 2.44949i 0.132453 + 0.229416i
\(115\) −2.41421 + 4.18154i −0.225127 + 0.389931i
\(116\) −4.12132 + 7.13834i −0.382655 + 0.662778i
\(117\) 0 0
\(118\) 2.48528 0.228789
\(119\) 0 0
\(120\) 1.00000 0.0912871
\(121\) 5.32843 + 9.22911i 0.484402 + 0.839010i
\(122\) 5.82843 10.0951i 0.527681 0.913970i
\(123\) 4.41421 7.64564i 0.398016 0.689384i
\(124\) −2.53553 4.39167i −0.227698 0.394384i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −14.1421 −1.25491 −0.627456 0.778652i \(-0.715904\pi\)
−0.627456 + 0.778652i \(0.715904\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −2.29289 + 3.97141i −0.201878 + 0.349663i
\(130\) 0 0
\(131\) 8.41421 + 14.5738i 0.735153 + 1.27332i 0.954656 + 0.297711i \(0.0962232\pi\)
−0.219503 + 0.975612i \(0.570444\pi\)
\(132\) 0.585786 0.0509862
\(133\) 0 0
\(134\) 7.89949 0.682412
\(135\) −0.500000 0.866025i −0.0430331 0.0745356i
\(136\) −0.707107 + 1.22474i −0.0606339 + 0.105021i
\(137\) 8.00000 13.8564i 0.683486 1.18383i −0.290424 0.956898i \(-0.593796\pi\)
0.973910 0.226935i \(-0.0728704\pi\)
\(138\) −2.41421 4.18154i −0.205512 0.355956i
\(139\) 17.6569 1.49763 0.748817 0.662776i \(-0.230622\pi\)
0.748817 + 0.662776i \(0.230622\pi\)
\(140\) 0 0
\(141\) −9.07107 −0.763922
\(142\) −5.41421 9.37769i −0.454351 0.786959i
\(143\) 0 0
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) −4.12132 7.13834i −0.342257 0.592807i
\(146\) 7.65685 0.633686
\(147\) 0 0
\(148\) −1.41421 −0.116248
\(149\) 6.94975 + 12.0373i 0.569345 + 0.986135i 0.996631 + 0.0820185i \(0.0261367\pi\)
−0.427285 + 0.904117i \(0.640530\pi\)
\(150\) −0.500000 + 0.866025i −0.0408248 + 0.0707107i
\(151\) −8.89949 + 15.4144i −0.724231 + 1.25440i 0.235059 + 0.971981i \(0.424472\pi\)
−0.959290 + 0.282423i \(0.908862\pi\)
\(152\) 1.41421 + 2.44949i 0.114708 + 0.198680i
\(153\) 1.41421 0.114332
\(154\) 0 0
\(155\) 5.07107 0.407318
\(156\) 0 0
\(157\) −0.171573 + 0.297173i −0.0136930 + 0.0237170i −0.872791 0.488095i \(-0.837692\pi\)
0.859098 + 0.511812i \(0.171025\pi\)
\(158\) 5.65685 9.79796i 0.450035 0.779484i
\(159\) 4.65685 + 8.06591i 0.369313 + 0.639668i
\(160\) 1.00000 0.0790569
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) −7.36396 12.7548i −0.576790 0.999029i −0.995845 0.0910685i \(-0.970972\pi\)
0.419055 0.907961i \(-0.362362\pi\)
\(164\) 4.41421 7.64564i 0.344692 0.597024i
\(165\) −0.292893 + 0.507306i −0.0228017 + 0.0394937i
\(166\) 2.58579 + 4.47871i 0.200696 + 0.347616i
\(167\) 1.07107 0.0828817 0.0414409 0.999141i \(-0.486805\pi\)
0.0414409 + 0.999141i \(0.486805\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) −0.707107 1.22474i −0.0542326 0.0939336i
\(171\) 1.41421 2.44949i 0.108148 0.187317i
\(172\) −2.29289 + 3.97141i −0.174831 + 0.302817i
\(173\) −9.24264 16.0087i −0.702705 1.21712i −0.967513 0.252820i \(-0.918642\pi\)
0.264808 0.964301i \(-0.414691\pi\)
\(174\) 8.24264 0.624873
\(175\) 0 0
\(176\) 0.585786 0.0441553
\(177\) −1.24264 2.15232i −0.0934026 0.161778i
\(178\) 3.24264 5.61642i 0.243046 0.420968i
\(179\) −0.292893 + 0.507306i −0.0218919 + 0.0379178i −0.876764 0.480921i \(-0.840302\pi\)
0.854872 + 0.518839i \(0.173636\pi\)
\(180\) −0.500000 0.866025i −0.0372678 0.0645497i
\(181\) −8.82843 −0.656212 −0.328106 0.944641i \(-0.606410\pi\)
−0.328106 + 0.944641i \(0.606410\pi\)
\(182\) 0 0
\(183\) −11.6569 −0.861699
\(184\) −2.41421 4.18154i −0.177978 0.308267i
\(185\) 0.707107 1.22474i 0.0519875 0.0900450i
\(186\) −2.53553 + 4.39167i −0.185914 + 0.322013i
\(187\) −0.414214 0.717439i −0.0302903 0.0524643i
\(188\) −9.07107 −0.661576
\(189\) 0 0
\(190\) −2.82843 −0.205196
\(191\) 5.65685 + 9.79796i 0.409316 + 0.708955i 0.994813 0.101719i \(-0.0324342\pi\)
−0.585498 + 0.810674i \(0.699101\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) 10.8995 18.8785i 0.784563 1.35890i −0.144697 0.989476i \(-0.546221\pi\)
0.929260 0.369427i \(-0.120446\pi\)
\(194\) −4.41421 7.64564i −0.316922 0.548925i
\(195\) 0 0
\(196\) 0 0
\(197\) −20.8284 −1.48396 −0.741982 0.670420i \(-0.766114\pi\)
−0.741982 + 0.670420i \(0.766114\pi\)
\(198\) −0.292893 0.507306i −0.0208150 0.0360527i
\(199\) −1.46447 + 2.53653i −0.103813 + 0.179810i −0.913253 0.407393i \(-0.866438\pi\)
0.809439 + 0.587203i \(0.199771\pi\)
\(200\) −0.500000 + 0.866025i −0.0353553 + 0.0612372i
\(201\) −3.94975 6.84116i −0.278594 0.482538i
\(202\) −6.34315 −0.446302
\(203\) 0 0
\(204\) 1.41421 0.0990148
\(205\) 4.41421 + 7.64564i 0.308302 + 0.533995i
\(206\) 5.07107 8.78335i 0.353318 0.611965i
\(207\) −2.41421 + 4.18154i −0.167799 + 0.290637i
\(208\) 0 0
\(209\) −1.65685 −0.114607
\(210\) 0 0
\(211\) −1.65685 −0.114063 −0.0570313 0.998372i \(-0.518163\pi\)
−0.0570313 + 0.998372i \(0.518163\pi\)
\(212\) 4.65685 + 8.06591i 0.319834 + 0.553969i
\(213\) −5.41421 + 9.37769i −0.370976 + 0.642549i
\(214\) 2.00000 3.46410i 0.136717 0.236801i
\(215\) −2.29289 3.97141i −0.156374 0.270848i
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 5.31371 0.359890
\(219\) −3.82843 6.63103i −0.258701 0.448084i
\(220\) −0.292893 + 0.507306i −0.0197469 + 0.0342026i
\(221\) 0 0
\(222\) 0.707107 + 1.22474i 0.0474579 + 0.0821995i
\(223\) 17.6569 1.18239 0.591195 0.806529i \(-0.298656\pi\)
0.591195 + 0.806529i \(0.298656\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) −4.65685 8.06591i −0.309769 0.536536i
\(227\) 6.82843 11.8272i 0.453219 0.784998i −0.545365 0.838199i \(-0.683609\pi\)
0.998584 + 0.0532009i \(0.0169424\pi\)
\(228\) 1.41421 2.44949i 0.0936586 0.162221i
\(229\) −12.8995 22.3426i −0.852423 1.47644i −0.879016 0.476793i \(-0.841799\pi\)
0.0265930 0.999646i \(-0.491534\pi\)
\(230\) 4.82843 0.318377
\(231\) 0 0
\(232\) 8.24264 0.541156
\(233\) −3.48528 6.03668i −0.228328 0.395476i 0.728984 0.684530i \(-0.239993\pi\)
−0.957313 + 0.289054i \(0.906659\pi\)
\(234\) 0 0
\(235\) 4.53553 7.85578i 0.295866 0.512454i
\(236\) −1.24264 2.15232i −0.0808890 0.140104i
\(237\) −11.3137 −0.734904
\(238\) 0 0
\(239\) 23.3137 1.50804 0.754019 0.656852i \(-0.228113\pi\)
0.754019 + 0.656852i \(0.228113\pi\)
\(240\) −0.500000 0.866025i −0.0322749 0.0559017i
\(241\) 8.12132 14.0665i 0.523140 0.906105i −0.476497 0.879176i \(-0.658094\pi\)
0.999637 0.0269294i \(-0.00857294\pi\)
\(242\) 5.32843 9.22911i 0.342524 0.593269i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −11.6569 −0.746254
\(245\) 0 0
\(246\) −8.82843 −0.562880
\(247\) 0 0
\(248\) −2.53553 + 4.39167i −0.161007 + 0.278872i
\(249\) 2.58579 4.47871i 0.163868 0.283827i
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) −17.6569 −1.11449 −0.557245 0.830348i \(-0.688142\pi\)
−0.557245 + 0.830348i \(0.688142\pi\)
\(252\) 0 0
\(253\) 2.82843 0.177822
\(254\) 7.07107 + 12.2474i 0.443678 + 0.768473i
\(255\) −0.707107 + 1.22474i −0.0442807 + 0.0766965i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −0.949747 1.64501i −0.0592436 0.102613i 0.834882 0.550428i \(-0.185536\pi\)
−0.894126 + 0.447815i \(0.852202\pi\)
\(258\) 4.58579 0.285499
\(259\) 0 0
\(260\) 0 0
\(261\) −4.12132 7.13834i −0.255103 0.441852i
\(262\) 8.41421 14.5738i 0.519832 0.900375i
\(263\) 10.8995 18.8785i 0.672092 1.16410i −0.305218 0.952282i \(-0.598729\pi\)
0.977310 0.211814i \(-0.0679373\pi\)
\(264\) −0.292893 0.507306i −0.0180263 0.0312225i
\(265\) −9.31371 −0.572137
\(266\) 0 0
\(267\) −6.48528 −0.396893
\(268\) −3.94975 6.84116i −0.241269 0.417891i
\(269\) −3.82843 + 6.63103i −0.233423 + 0.404301i −0.958813 0.284037i \(-0.908326\pi\)
0.725390 + 0.688338i \(0.241659\pi\)
\(270\) −0.500000 + 0.866025i −0.0304290 + 0.0527046i
\(271\) 7.12132 + 12.3345i 0.432589 + 0.749267i 0.997095 0.0761621i \(-0.0242667\pi\)
−0.564506 + 0.825429i \(0.690933\pi\)
\(272\) 1.41421 0.0857493
\(273\) 0 0
\(274\) −16.0000 −0.966595
\(275\) −0.292893 0.507306i −0.0176621 0.0305917i
\(276\) −2.41421 + 4.18154i −0.145319 + 0.251699i
\(277\) −10.9497 + 18.9655i −0.657907 + 1.13953i 0.323250 + 0.946314i \(0.395225\pi\)
−0.981157 + 0.193214i \(0.938109\pi\)
\(278\) −8.82843 15.2913i −0.529494 0.917110i
\(279\) 5.07107 0.303597
\(280\) 0 0
\(281\) −13.5147 −0.806221 −0.403110 0.915151i \(-0.632071\pi\)
−0.403110 + 0.915151i \(0.632071\pi\)
\(282\) 4.53553 + 7.85578i 0.270087 + 0.467805i
\(283\) −15.2426 + 26.4010i −0.906081 + 1.56938i −0.0866213 + 0.996241i \(0.527607\pi\)
−0.819460 + 0.573137i \(0.805726\pi\)
\(284\) −5.41421 + 9.37769i −0.321274 + 0.556464i
\(285\) 1.41421 + 2.44949i 0.0837708 + 0.145095i
\(286\) 0 0
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) 7.50000 + 12.9904i 0.441176 + 0.764140i
\(290\) −4.12132 + 7.13834i −0.242012 + 0.419178i
\(291\) −4.41421 + 7.64564i −0.258766 + 0.448195i
\(292\) −3.82843 6.63103i −0.224042 0.388052i
\(293\) −28.6274 −1.67243 −0.836216 0.548401i \(-0.815237\pi\)
−0.836216 + 0.548401i \(0.815237\pi\)
\(294\) 0 0
\(295\) 2.48528 0.144699
\(296\) 0.707107 + 1.22474i 0.0410997 + 0.0711868i
\(297\) −0.292893 + 0.507306i −0.0169954 + 0.0294369i
\(298\) 6.94975 12.0373i 0.402588 0.697303i
\(299\) 0 0
\(300\) 1.00000 0.0577350
\(301\) 0 0
\(302\) 17.7990 1.02422
\(303\) 3.17157 + 5.49333i 0.182202 + 0.315583i
\(304\) 1.41421 2.44949i 0.0811107 0.140488i
\(305\) 5.82843 10.0951i 0.333735 0.578046i
\(306\) −0.707107 1.22474i −0.0404226 0.0700140i
\(307\) −7.31371 −0.417415 −0.208708 0.977978i \(-0.566926\pi\)
−0.208708 + 0.977978i \(0.566926\pi\)
\(308\) 0 0
\(309\) −10.1421 −0.576966
\(310\) −2.53553 4.39167i −0.144009 0.249430i
\(311\) 14.5858 25.2633i 0.827084 1.43255i −0.0732320 0.997315i \(-0.523331\pi\)
0.900316 0.435237i \(-0.143335\pi\)
\(312\) 0 0
\(313\) −14.4142 24.9662i −0.814740 1.41117i −0.909515 0.415672i \(-0.863547\pi\)
0.0947753 0.995499i \(-0.469787\pi\)
\(314\) 0.343146 0.0193648
\(315\) 0 0
\(316\) −11.3137 −0.636446
\(317\) 9.00000 + 15.5885i 0.505490 + 0.875535i 0.999980 + 0.00635137i \(0.00202172\pi\)
−0.494489 + 0.869184i \(0.664645\pi\)
\(318\) 4.65685 8.06591i 0.261143 0.452314i
\(319\) −2.41421 + 4.18154i −0.135170 + 0.234121i
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) −4.00000 −0.223258
\(322\) 0 0
\(323\) −4.00000 −0.222566
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) 0 0
\(326\) −7.36396 + 12.7548i −0.407852 + 0.706421i
\(327\) −2.65685 4.60181i −0.146924 0.254480i
\(328\) −8.82843 −0.487468
\(329\) 0 0
\(330\) 0.585786 0.0322465
\(331\) 9.31371 + 16.1318i 0.511928 + 0.886685i 0.999904 + 0.0138281i \(0.00440178\pi\)
−0.487977 + 0.872857i \(0.662265\pi\)
\(332\) 2.58579 4.47871i 0.141913 0.245801i
\(333\) 0.707107 1.22474i 0.0387492 0.0671156i
\(334\) −0.535534 0.927572i −0.0293031 0.0507545i
\(335\) 7.89949 0.431596
\(336\) 0 0
\(337\) −3.17157 −0.172767 −0.0863833 0.996262i \(-0.527531\pi\)
−0.0863833 + 0.996262i \(0.527531\pi\)
\(338\) 6.50000 + 11.2583i 0.353553 + 0.612372i
\(339\) −4.65685 + 8.06591i −0.252926 + 0.438080i
\(340\) −0.707107 + 1.22474i −0.0383482 + 0.0664211i
\(341\) −1.48528 2.57258i −0.0804325 0.139313i
\(342\) −2.82843 −0.152944
\(343\) 0 0
\(344\) 4.58579 0.247249
\(345\) −2.41421 4.18154i −0.129977 0.225127i
\(346\) −9.24264 + 16.0087i −0.496887 + 0.860634i
\(347\) −0.828427 + 1.43488i −0.0444723 + 0.0770283i −0.887405 0.460991i \(-0.847494\pi\)
0.842932 + 0.538019i \(0.180827\pi\)
\(348\) −4.12132 7.13834i −0.220926 0.382655i
\(349\) −5.79899 −0.310413 −0.155206 0.987882i \(-0.549604\pi\)
−0.155206 + 0.987882i \(0.549604\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.292893 0.507306i −0.0156113 0.0270395i
\(353\) 0.363961 0.630399i 0.0193717 0.0335528i −0.856177 0.516683i \(-0.827167\pi\)
0.875549 + 0.483130i \(0.160500\pi\)
\(354\) −1.24264 + 2.15232i −0.0660456 + 0.114394i
\(355\) −5.41421 9.37769i −0.287357 0.497716i
\(356\) −6.48528 −0.343719
\(357\) 0 0
\(358\) 0.585786 0.0309598
\(359\) −9.41421 16.3059i −0.496863 0.860592i 0.503130 0.864211i \(-0.332182\pi\)
−0.999993 + 0.00361830i \(0.998848\pi\)
\(360\) −0.500000 + 0.866025i −0.0263523 + 0.0456435i
\(361\) 5.50000 9.52628i 0.289474 0.501383i
\(362\) 4.41421 + 7.64564i 0.232006 + 0.401846i
\(363\) −10.6569 −0.559340
\(364\) 0 0
\(365\) 7.65685 0.400778
\(366\) 5.82843 + 10.0951i 0.304657 + 0.527681i
\(367\) −8.24264 + 14.2767i −0.430262 + 0.745236i −0.996896 0.0787338i \(-0.974912\pi\)
0.566633 + 0.823970i \(0.308246\pi\)
\(368\) −2.41421 + 4.18154i −0.125850 + 0.217978i
\(369\) 4.41421 + 7.64564i 0.229795 + 0.398016i
\(370\) −1.41421 −0.0735215
\(371\) 0 0
\(372\) 5.07107 0.262923
\(373\) −5.53553 9.58783i −0.286619 0.496439i 0.686381 0.727242i \(-0.259198\pi\)
−0.973001 + 0.230803i \(0.925865\pi\)
\(374\) −0.414214 + 0.717439i −0.0214185 + 0.0370979i
\(375\) −0.500000 + 0.866025i −0.0258199 + 0.0447214i
\(376\) 4.53553 + 7.85578i 0.233902 + 0.405131i
\(377\) 0 0
\(378\) 0 0
\(379\) −24.4853 −1.25772 −0.628862 0.777517i \(-0.716479\pi\)
−0.628862 + 0.777517i \(0.716479\pi\)
\(380\) 1.41421 + 2.44949i 0.0725476 + 0.125656i
\(381\) 7.07107 12.2474i 0.362262 0.627456i
\(382\) 5.65685 9.79796i 0.289430 0.501307i
\(383\) −7.94975 13.7694i −0.406213 0.703582i 0.588249 0.808680i \(-0.299818\pi\)
−0.994462 + 0.105098i \(0.966484\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −21.7990 −1.10954
\(387\) −2.29289 3.97141i −0.116554 0.201878i
\(388\) −4.41421 + 7.64564i −0.224098 + 0.388149i
\(389\) −13.5355 + 23.4442i −0.686279 + 1.18867i 0.286754 + 0.958004i \(0.407424\pi\)
−0.973033 + 0.230666i \(0.925910\pi\)
\(390\) 0 0
\(391\) 6.82843 0.345328
\(392\) 0 0
\(393\) −16.8284 −0.848882
\(394\) 10.4142 + 18.0379i 0.524660 + 0.908739i
\(395\) 5.65685 9.79796i 0.284627 0.492989i
\(396\) −0.292893 + 0.507306i −0.0147184 + 0.0254931i
\(397\) −10.3137 17.8639i −0.517630 0.896562i −0.999790 0.0204787i \(-0.993481\pi\)
0.482160 0.876083i \(-0.339852\pi\)
\(398\) 2.92893 0.146814
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 12.6569 + 21.9223i 0.632053 + 1.09475i 0.987131 + 0.159912i \(0.0511209\pi\)
−0.355078 + 0.934837i \(0.615546\pi\)
\(402\) −3.94975 + 6.84116i −0.196995 + 0.341206i
\(403\) 0 0
\(404\) 3.17157 + 5.49333i 0.157792 + 0.273303i
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) −0.828427 −0.0410636
\(408\) −0.707107 1.22474i −0.0350070 0.0606339i
\(409\) 9.19239 15.9217i 0.454534 0.787277i −0.544127 0.839003i \(-0.683139\pi\)
0.998661 + 0.0517263i \(0.0164724\pi\)
\(410\) 4.41421 7.64564i 0.218002 0.377591i
\(411\) 8.00000 + 13.8564i 0.394611 + 0.683486i
\(412\) −10.1421 −0.499667
\(413\) 0 0
\(414\) 4.82843 0.237304
\(415\) 2.58579 + 4.47871i 0.126931 + 0.219851i
\(416\) 0 0
\(417\) −8.82843 + 15.2913i −0.432330 + 0.748817i
\(418\) 0.828427 + 1.43488i 0.0405197 + 0.0701822i
\(419\) −17.6569 −0.862594 −0.431297 0.902210i \(-0.641944\pi\)
−0.431297 + 0.902210i \(0.641944\pi\)
\(420\) 0 0
\(421\) 16.6274 0.810371 0.405185 0.914235i \(-0.367207\pi\)
0.405185 + 0.914235i \(0.367207\pi\)
\(422\) 0.828427 + 1.43488i 0.0403272 + 0.0698488i
\(423\) 4.53553 7.85578i 0.220525 0.381961i
\(424\) 4.65685 8.06591i 0.226157 0.391715i
\(425\) −0.707107 1.22474i −0.0342997 0.0594089i
\(426\) 10.8284 0.524639
\(427\) 0 0
\(428\) −4.00000 −0.193347
\(429\) 0 0
\(430\) −2.29289 + 3.97141i −0.110573 + 0.191518i
\(431\) −7.07107 + 12.2474i −0.340601 + 0.589939i −0.984545 0.175134i \(-0.943964\pi\)
0.643943 + 0.765073i \(0.277297\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 8.82843 0.424267 0.212134 0.977241i \(-0.431959\pi\)
0.212134 + 0.977241i \(0.431959\pi\)
\(434\) 0 0
\(435\) 8.24264 0.395204
\(436\) −2.65685 4.60181i −0.127240 0.220387i
\(437\) 6.82843 11.8272i 0.326648 0.565771i
\(438\) −3.82843 + 6.63103i −0.182929 + 0.316843i
\(439\) −16.7782 29.0607i −0.800779 1.38699i −0.919104 0.394014i \(-0.871086\pi\)
0.118326 0.992975i \(-0.462247\pi\)
\(440\) 0.585786 0.0279263
\(441\) 0 0
\(442\) 0 0
\(443\) −6.82843 11.8272i −0.324428 0.561926i 0.656968 0.753918i \(-0.271839\pi\)
−0.981397 + 0.191992i \(0.938505\pi\)
\(444\) 0.707107 1.22474i 0.0335578 0.0581238i
\(445\) 3.24264 5.61642i 0.153716 0.266244i
\(446\) −8.82843 15.2913i −0.418038 0.724063i
\(447\) −13.8995 −0.657424
\(448\) 0 0
\(449\) −25.1127 −1.18514 −0.592571 0.805518i \(-0.701887\pi\)
−0.592571 + 0.805518i \(0.701887\pi\)
\(450\) −0.500000 0.866025i −0.0235702 0.0408248i
\(451\) 2.58579 4.47871i 0.121760 0.210894i
\(452\) −4.65685 + 8.06591i −0.219040 + 0.379388i
\(453\) −8.89949 15.4144i −0.418135 0.724231i
\(454\) −13.6569 −0.640948
\(455\) 0 0
\(456\) −2.82843 −0.132453
\(457\) 4.89949 + 8.48617i 0.229189 + 0.396966i 0.957568 0.288208i \(-0.0930594\pi\)
−0.728379 + 0.685174i \(0.759726\pi\)
\(458\) −12.8995 + 22.3426i −0.602754 + 1.04400i
\(459\) −0.707107 + 1.22474i −0.0330049 + 0.0571662i
\(460\) −2.41421 4.18154i −0.112563 0.194965i
\(461\) −14.0000 −0.652045 −0.326023 0.945362i \(-0.605709\pi\)
−0.326023 + 0.945362i \(0.605709\pi\)
\(462\) 0 0
\(463\) 33.6569 1.56417 0.782083 0.623174i \(-0.214157\pi\)
0.782083 + 0.623174i \(0.214157\pi\)
\(464\) −4.12132 7.13834i −0.191327 0.331389i
\(465\) −2.53553 + 4.39167i −0.117583 + 0.203659i
\(466\) −3.48528 + 6.03668i −0.161453 + 0.279644i
\(467\) 10.2426 + 17.7408i 0.473973 + 0.820945i 0.999556 0.0297972i \(-0.00948613\pi\)
−0.525583 + 0.850742i \(0.676153\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −9.07107 −0.418417
\(471\) −0.171573 0.297173i −0.00790566 0.0136930i
\(472\) −1.24264 + 2.15232i −0.0571972 + 0.0990684i
\(473\) −1.34315 + 2.32640i −0.0617579 + 0.106968i
\(474\) 5.65685 + 9.79796i 0.259828 + 0.450035i
\(475\) −2.82843 −0.129777
\(476\) 0 0
\(477\) −9.31371 −0.426445
\(478\) −11.6569 20.1903i −0.533172 0.923481i
\(479\) −8.24264 + 14.2767i −0.376616 + 0.652318i −0.990567 0.137026i \(-0.956246\pi\)
0.613952 + 0.789344i \(0.289579\pi\)
\(480\) −0.500000 + 0.866025i −0.0228218 + 0.0395285i
\(481\) 0 0
\(482\) −16.2426 −0.739832
\(483\) 0 0
\(484\) −10.6569 −0.484402
\(485\) −4.41421 7.64564i −0.200439 0.347171i
\(486\) −0.500000 + 0.866025i −0.0226805 + 0.0392837i
\(487\) −12.2426 + 21.2049i −0.554767 + 0.960885i 0.443155 + 0.896445i \(0.353859\pi\)
−0.997922 + 0.0644394i \(0.979474\pi\)
\(488\) 5.82843 + 10.0951i 0.263840 + 0.456985i
\(489\) 14.7279 0.666020
\(490\) 0 0
\(491\) 11.8995 0.537017 0.268508 0.963277i \(-0.413469\pi\)
0.268508 + 0.963277i \(0.413469\pi\)
\(492\) 4.41421 + 7.64564i 0.199008 + 0.344692i
\(493\) −5.82843 + 10.0951i −0.262499 + 0.454662i
\(494\) 0 0
\(495\) −0.292893 0.507306i −0.0131646 0.0228017i
\(496\) 5.07107 0.227698
\(497\) 0 0
\(498\) −5.17157 −0.231744
\(499\) −7.89949 13.6823i −0.353630 0.612505i 0.633253 0.773945i \(-0.281719\pi\)
−0.986883 + 0.161440i \(0.948386\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) −0.535534 + 0.927572i −0.0239259 + 0.0414409i
\(502\) 8.82843 + 15.2913i 0.394032 + 0.682483i
\(503\) 23.8995 1.06563 0.532813 0.846233i \(-0.321135\pi\)
0.532813 + 0.846233i \(0.321135\pi\)
\(504\) 0 0
\(505\) −6.34315 −0.282266
\(506\) −1.41421 2.44949i −0.0628695 0.108893i
\(507\) 6.50000 11.2583i 0.288675 0.500000i
\(508\) 7.07107 12.2474i 0.313728 0.543393i
\(509\) 9.17157 + 15.8856i 0.406523 + 0.704118i 0.994497 0.104761i \(-0.0334078\pi\)
−0.587975 + 0.808879i \(0.700074\pi\)
\(510\) 1.41421 0.0626224
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 1.41421 + 2.44949i 0.0624391 + 0.108148i
\(514\) −0.949747 + 1.64501i −0.0418916 + 0.0725583i
\(515\) 5.07107 8.78335i 0.223458 0.387041i
\(516\) −2.29289 3.97141i −0.100939 0.174831i
\(517\) −5.31371 −0.233697
\(518\) 0 0
\(519\) 18.4853 0.811414
\(520\) 0 0
\(521\) 6.07107 10.5154i 0.265978 0.460688i −0.701841 0.712333i \(-0.747638\pi\)
0.967819 + 0.251646i \(0.0809717\pi\)
\(522\) −4.12132 + 7.13834i −0.180385 + 0.312436i
\(523\) 10.5563 + 18.2841i 0.461597 + 0.799509i 0.999041 0.0437902i \(-0.0139433\pi\)
−0.537444 + 0.843300i \(0.680610\pi\)
\(524\) −16.8284 −0.735153
\(525\) 0 0
\(526\) −21.7990 −0.950481
\(527\) −3.58579 6.21076i −0.156199 0.270545i
\(528\) −0.292893 + 0.507306i −0.0127465 + 0.0220777i
\(529\) −0.156854 + 0.271680i −0.00681975 + 0.0118122i
\(530\) 4.65685 + 8.06591i 0.202281 + 0.350361i
\(531\) 2.48528 0.107852
\(532\) 0 0
\(533\) 0 0
\(534\) 3.24264 + 5.61642i 0.140323 + 0.243046i
\(535\) 2.00000 3.46410i 0.0864675 0.149766i
\(536\) −3.94975 + 6.84116i −0.170603 + 0.295493i
\(537\) −0.292893 0.507306i −0.0126393 0.0218919i
\(538\) 7.65685 0.330110
\(539\) 0 0
\(540\) 1.00000 0.0430331
\(541\) 1.24264 + 2.15232i 0.0534253 + 0.0925353i 0.891501 0.453018i \(-0.149653\pi\)
−0.838076 + 0.545554i \(0.816319\pi\)
\(542\) 7.12132 12.3345i 0.305887 0.529812i
\(543\) 4.41421 7.64564i 0.189432 0.328106i
\(544\) −0.707107 1.22474i −0.0303170 0.0525105i
\(545\) 5.31371 0.227614
\(546\) 0 0
\(547\) 27.4142 1.17215 0.586074 0.810258i \(-0.300673\pi\)
0.586074 + 0.810258i \(0.300673\pi\)
\(548\) 8.00000 + 13.8564i 0.341743 + 0.591916i
\(549\) 5.82843 10.0951i 0.248751 0.430850i
\(550\) −0.292893 + 0.507306i −0.0124890 + 0.0216316i
\(551\) 11.6569 + 20.1903i 0.496599 + 0.860134i
\(552\) 4.82843 0.205512
\(553\) 0 0
\(554\) 21.8995 0.930420
\(555\) 0.707107 + 1.22474i 0.0300150 + 0.0519875i
\(556\) −8.82843 + 15.2913i −0.374409 + 0.648495i
\(557\) −6.31371 + 10.9357i −0.267520 + 0.463359i −0.968221 0.250097i \(-0.919538\pi\)
0.700700 + 0.713456i \(0.252871\pi\)
\(558\) −2.53553 4.39167i −0.107338 0.185914i
\(559\) 0 0
\(560\) 0 0
\(561\) 0.828427 0.0349762
\(562\) 6.75736 + 11.7041i 0.285042 + 0.493707i
\(563\) 13.0711 22.6398i 0.550880 0.954152i −0.447332 0.894368i \(-0.647626\pi\)
0.998211 0.0597836i \(-0.0190411\pi\)
\(564\) 4.53553 7.85578i 0.190980 0.330788i
\(565\) −4.65685 8.06591i −0.195915 0.339335i
\(566\) 30.4853 1.28139
\(567\) 0 0
\(568\) 10.8284 0.454351
\(569\) −17.4853 30.2854i −0.733021 1.26963i −0.955586 0.294712i \(-0.904776\pi\)
0.222565 0.974918i \(-0.428557\pi\)
\(570\) 1.41421 2.44949i 0.0592349 0.102598i
\(571\) −2.34315 + 4.05845i −0.0980576 + 0.169841i −0.910881 0.412670i \(-0.864596\pi\)
0.812823 + 0.582511i \(0.197930\pi\)
\(572\) 0 0
\(573\) −11.3137 −0.472637
\(574\) 0 0
\(575\) 4.82843 0.201359
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 6.07107 10.5154i 0.252742 0.437762i −0.711538 0.702648i \(-0.752001\pi\)
0.964280 + 0.264886i \(0.0853343\pi\)
\(578\) 7.50000 12.9904i 0.311959 0.540329i
\(579\) 10.8995 + 18.8785i 0.452968 + 0.784563i
\(580\) 8.24264 0.342257
\(581\) 0 0
\(582\) 8.82843 0.365950
\(583\) 2.72792 + 4.72490i 0.112979 + 0.195685i
\(584\) −3.82843 + 6.63103i −0.158421 + 0.274394i
\(585\) 0 0
\(586\) 14.3137 + 24.7921i 0.591294 + 1.02415i
\(587\) 19.7990 0.817192 0.408596 0.912715i \(-0.366019\pi\)
0.408596 + 0.912715i \(0.366019\pi\)
\(588\) 0 0
\(589\) −14.3431 −0.590999
\(590\) −1.24264 2.15232i −0.0511587 0.0886095i
\(591\) 10.4142 18.0379i 0.428384 0.741982i
\(592\) 0.707107 1.22474i 0.0290619 0.0503367i
\(593\) −18.6066 32.2276i −0.764082 1.32343i −0.940731 0.339154i \(-0.889859\pi\)
0.176649 0.984274i \(-0.443474\pi\)
\(594\) 0.585786 0.0240351
\(595\) 0 0
\(596\) −13.8995 −0.569345
\(597\) −1.46447 2.53653i −0.0599366 0.103813i
\(598\) 0 0
\(599\) −2.34315 + 4.05845i −0.0957383 + 0.165824i −0.909917 0.414791i \(-0.863855\pi\)
0.814178 + 0.580615i \(0.197188\pi\)
\(600\) −0.500000 0.866025i −0.0204124 0.0353553i
\(601\) 42.1838 1.72071 0.860356 0.509694i \(-0.170241\pi\)
0.860356 + 0.509694i \(0.170241\pi\)
\(602\) 0 0
\(603\) 7.89949 0.321692
\(604\) −8.89949 15.4144i −0.362115 0.627202i
\(605\) 5.32843 9.22911i 0.216631 0.375217i
\(606\) 3.17157 5.49333i 0.128836 0.223151i
\(607\) 2.48528 + 4.30463i 0.100874 + 0.174720i 0.912045 0.410090i \(-0.134503\pi\)
−0.811171 + 0.584809i \(0.801169\pi\)
\(608\) −2.82843 −0.114708
\(609\) 0 0
\(610\) −11.6569 −0.471972
\(611\) 0 0
\(612\) −0.707107 + 1.22474i −0.0285831 + 0.0495074i
\(613\) 2.60660 4.51477i 0.105280 0.182350i −0.808573 0.588396i \(-0.799760\pi\)
0.913852 + 0.406046i \(0.133093\pi\)
\(614\) 3.65685 + 6.33386i 0.147579 + 0.255614i
\(615\) −8.82843 −0.355997
\(616\) 0 0
\(617\) −44.2843 −1.78282 −0.891409 0.453200i \(-0.850282\pi\)
−0.891409 + 0.453200i \(0.850282\pi\)
\(618\) 5.07107 + 8.78335i 0.203988 + 0.353318i
\(619\) −0.928932 + 1.60896i −0.0373369 + 0.0646695i −0.884090 0.467317i \(-0.845221\pi\)
0.846753 + 0.531986i \(0.178554\pi\)
\(620\) −2.53553 + 4.39167i −0.101829 + 0.176374i
\(621\) −2.41421 4.18154i −0.0968791 0.167799i
\(622\) −29.1716 −1.16967
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −14.4142 + 24.9662i −0.576108 + 0.997848i
\(627\) 0.828427 1.43488i 0.0330842 0.0573035i
\(628\) −0.171573 0.297173i −0.00684650 0.0118585i
\(629\) −2.00000 −0.0797452
\(630\) 0 0
\(631\) 24.8284 0.988404 0.494202 0.869347i \(-0.335460\pi\)
0.494202 + 0.869347i \(0.335460\pi\)
\(632\) 5.65685 + 9.79796i 0.225018 + 0.389742i
\(633\) 0.828427 1.43488i 0.0329270 0.0570313i
\(634\) 9.00000 15.5885i 0.357436 0.619097i
\(635\) 7.07107 + 12.2474i 0.280607 + 0.486025i
\(636\) −9.31371 −0.369313
\(637\) 0 0
\(638\) 4.82843 0.191159
\(639\) −5.41421 9.37769i −0.214183 0.370976i
\(640\) −0.500000 + 0.866025i −0.0197642 + 0.0342327i
\(641\) 15.0000 25.9808i 0.592464 1.02618i −0.401435 0.915888i \(-0.631488\pi\)
0.993899 0.110291i \(-0.0351782\pi\)
\(642\) 2.00000 + 3.46410i 0.0789337 + 0.136717i
\(643\) 48.4264 1.90975 0.954876 0.297006i \(-0.0959882\pi\)
0.954876 + 0.297006i \(0.0959882\pi\)
\(644\) 0 0
\(645\) 4.58579 0.180565
\(646\) 2.00000 + 3.46410i 0.0786889 + 0.136293i
\(647\) −16.5355 + 28.6404i −0.650079 + 1.12597i 0.333024 + 0.942918i \(0.391931\pi\)
−0.983103 + 0.183052i \(0.941402\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) −0.727922 1.26080i −0.0285734 0.0494907i
\(650\) 0 0
\(651\) 0 0
\(652\) 14.7279 0.576790
\(653\) −16.4142 28.4303i −0.642338 1.11256i −0.984910 0.173070i \(-0.944631\pi\)
0.342572 0.939492i \(-0.388702\pi\)
\(654\) −2.65685 + 4.60181i −0.103891 + 0.179945i
\(655\) 8.41421 14.5738i 0.328771 0.569447i
\(656\) 4.41421 + 7.64564i 0.172346 + 0.298512i
\(657\) 7.65685 0.298722
\(658\) 0 0
\(659\) 20.1005 0.783005 0.391502 0.920177i \(-0.371956\pi\)
0.391502 + 0.920177i \(0.371956\pi\)
\(660\) −0.292893 0.507306i −0.0114009 0.0197469i
\(661\) 13.8284 23.9515i 0.537863 0.931607i −0.461155 0.887319i \(-0.652565\pi\)
0.999019 0.0442875i \(-0.0141017\pi\)
\(662\) 9.31371 16.1318i 0.361988 0.626981i
\(663\) 0 0
\(664\) −5.17157 −0.200696
\(665\) 0 0
\(666\) −1.41421 −0.0547997
\(667\) −19.8995 34.4669i −0.770512 1.33457i
\(668\) −0.535534 + 0.927572i −0.0207204 + 0.0358888i
\(669\) −8.82843 + 15.2913i −0.341327 + 0.591195i
\(670\) −3.94975 6.84116i −0.152592 0.264297i
\(671\) −6.82843 −0.263609
\(672\) 0 0
\(673\) 41.5980 1.60348 0.801742 0.597670i \(-0.203907\pi\)
0.801742 + 0.597670i \(0.203907\pi\)
\(674\) 1.58579 + 2.74666i 0.0610822 + 0.105797i
\(675\) −0.500000 + 0.866025i −0.0192450 + 0.0333333i
\(676\) 6.50000 11.2583i 0.250000 0.433013i
\(677\) −5.58579 9.67487i −0.214679 0.371835i 0.738494 0.674260i \(-0.235537\pi\)
−0.953173 + 0.302425i \(0.902204\pi\)
\(678\) 9.31371 0.357691
\(679\) 0 0
\(680\) 1.41421 0.0542326
\(681\) 6.82843 + 11.8272i 0.261666 + 0.453219i
\(682\) −1.48528 + 2.57258i −0.0568744 + 0.0985093i
\(683\) −15.8995 + 27.5387i −0.608377 + 1.05374i 0.383131 + 0.923694i \(0.374846\pi\)
−0.991508 + 0.130046i \(0.958487\pi\)
\(684\) 1.41421 + 2.44949i 0.0540738 + 0.0936586i
\(685\) −16.0000 −0.611329
\(686\) 0 0
\(687\) 25.7990 0.984293
\(688\) −2.29289 3.97141i −0.0874157 0.151408i
\(689\) 0 0
\(690\) −2.41421 + 4.18154i −0.0919075 + 0.159189i
\(691\) 6.14214 + 10.6385i 0.233658 + 0.404707i 0.958882 0.283806i \(-0.0915971\pi\)
−0.725224 + 0.688513i \(0.758264\pi\)
\(692\) 18.4853 0.702705
\(693\) 0 0
\(694\) 1.65685 0.0628933
\(695\) −8.82843 15.2913i −0.334881 0.580031i
\(696\) −4.12132 + 7.13834i −0.156218 + 0.270578i
\(697\) 6.24264 10.8126i 0.236457 0.409555i
\(698\) 2.89949 + 5.02207i 0.109748 + 0.190088i
\(699\) 6.97056 0.263651
\(700\) 0 0
\(701\) −11.5563 −0.436477 −0.218239 0.975895i \(-0.570031\pi\)
−0.218239 + 0.975895i \(0.570031\pi\)
\(702\) 0 0
\(703\) −2.00000 + 3.46410i −0.0754314 + 0.130651i
\(704\) −0.292893 + 0.507306i −0.0110388 + 0.0191198i
\(705\) 4.53553 + 7.85578i 0.170818 + 0.295866i
\(706\) −0.727922 −0.0273957
\(707\) 0 0
\(708\) 2.48528 0.0934026
\(709\) 22.5563 + 39.0687i 0.847121 + 1.46726i 0.883766 + 0.467929i \(0.155000\pi\)
−0.0366445 + 0.999328i \(0.511667\pi\)
\(710\) −5.41421 + 9.37769i −0.203192 + 0.351939i
\(711\) 5.65685 9.79796i 0.212149 0.367452i
\(712\) 3.24264 + 5.61642i 0.121523 + 0.210484i
\(713\) 24.4853 0.916981
\(714\) 0 0
\(715\) 0 0
\(716\) −0.292893 0.507306i −0.0109459 0.0189589i
\(717\) −11.6569 + 20.1903i −0.435333 + 0.754019i
\(718\) −9.41421 + 16.3059i −0.351335 + 0.608531i
\(719\) 6.14214 + 10.6385i 0.229063 + 0.396749i 0.957531 0.288331i \(-0.0931005\pi\)
−0.728468 + 0.685080i \(0.759767\pi\)
\(720\) 1.00000 0.0372678
\(721\) 0 0
\(722\) −11.0000 −0.409378
\(723\) 8.12132 + 14.0665i 0.302035 + 0.523140i
\(724\) 4.41421 7.64564i 0.164053 0.284148i
\(725\) −4.12132 + 7.13834i −0.153062 + 0.265111i
\(726\) 5.32843 + 9.22911i 0.197756 + 0.342524i
\(727\) 45.6569 1.69332 0.846659 0.532135i \(-0.178610\pi\)
0.846659 + 0.532135i \(0.178610\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −3.82843 6.63103i −0.141696 0.245425i
\(731\) −3.24264 + 5.61642i −0.119933 + 0.207731i
\(732\) 5.82843 10.0951i 0.215425 0.373127i
\(733\) 7.97056 + 13.8054i 0.294399 + 0.509915i 0.974845 0.222884i \(-0.0715471\pi\)
−0.680446 + 0.732799i \(0.738214\pi\)
\(734\) 16.4853 0.608483
\(735\) 0 0
\(736\) 4.82843 0.177978
\(737\) −2.31371 4.00746i −0.0852265 0.147617i
\(738\) 4.41421 7.64564i 0.162489 0.281440i
\(739\) 21.5563 37.3367i 0.792963 1.37345i −0.131161 0.991361i \(-0.541871\pi\)
0.924125 0.382091i \(-0.124796\pi\)
\(740\) 0.707107 + 1.22474i 0.0259938 + 0.0450225i
\(741\) 0 0
\(742\) 0 0
\(743\) 5.65685 0.207530 0.103765 0.994602i \(-0.466911\pi\)
0.103765 + 0.994602i \(0.466911\pi\)
\(744\) −2.53553 4.39167i −0.0929572 0.161007i
\(745\) 6.94975 12.0373i 0.254619 0.441013i
\(746\) −5.53553 + 9.58783i −0.202670 + 0.351035i
\(747\) 2.58579 + 4.47871i 0.0946090 + 0.163868i
\(748\) 0.828427 0.0302903
\(749\) 0 0
\(750\) 1.00000 0.0365148
\(751\) −12.7574 22.0964i −0.465523 0.806309i 0.533702 0.845672i \(-0.320800\pi\)
−0.999225 + 0.0393635i \(0.987467\pi\)
\(752\) 4.53553 7.85578i 0.165394 0.286471i
\(753\) 8.82843 15.2913i 0.321726 0.557245i
\(754\) 0 0
\(755\) 17.7990 0.647772
\(756\) 0 0
\(757\) 23.7574 0.863476 0.431738 0.901999i \(-0.357901\pi\)
0.431738 + 0.901999i \(0.357901\pi\)
\(758\) 12.2426 + 21.2049i 0.444673 + 0.770196i
\(759\) −1.41421 + 2.44949i −0.0513327 + 0.0889108i
\(760\) 1.41421 2.44949i 0.0512989 0.0888523i
\(761\) 9.48528 + 16.4290i 0.343841 + 0.595550i 0.985143 0.171739i \(-0.0549385\pi\)
−0.641301 + 0.767289i \(0.721605\pi\)
\(762\) −14.1421 −0.512316
\(763\) 0 0
\(764\) −11.3137 −0.409316
\(765\) −0.707107 1.22474i −0.0255655 0.0442807i
\(766\) −7.94975 + 13.7694i −0.287236 + 0.497507i
\(767\) 0 0
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) −30.5858 −1.10295 −0.551476 0.834191i \(-0.685935\pi\)
−0.551476 + 0.834191i \(0.685935\pi\)
\(770\) 0 0
\(771\) 1.89949 0.0684086
\(772\) 10.8995 + 18.8785i 0.392281 + 0.679451i
\(773\) −14.1716 + 24.5459i −0.509716 + 0.882854i 0.490221 + 0.871598i \(0.336916\pi\)
−0.999937 + 0.0112557i \(0.996417\pi\)
\(774\) −2.29289 + 3.97141i −0.0824163 + 0.142749i
\(775\) −2.53553 4.39167i −0.0910791 0.157754i
\(776\) 8.82843 0.316922
\(777\) 0 0
\(778\) 27.0711 0.970545
\(779\) −12.4853 21.6251i −0.447332 0.774801i
\(780\) 0 0
\(781\) −3.17157 + 5.49333i −0.113488 + 0.196567i
\(782\) −3.41421 5.91359i −0.122092 0.211470i
\(783\) 8.24264 0.294568
\(784\) 0 0
\(785\) 0.343146 0.0122474
\(786\) 8.41421 + 14.5738i 0.300125 + 0.519832i
\(787\) −14.4853 + 25.0892i −0.516345 + 0.894335i 0.483475 + 0.875358i \(0.339374\pi\)
−0.999820 + 0.0189770i \(0.993959\pi\)
\(788\) 10.4142 18.0379i 0.370991 0.642575i
\(789\) 10.8995 + 18.8785i 0.388032 + 0.672092i
\(790\) −11.3137 −0.402524
\(791\) 0 0
\(792\) 0.585786 0.0208150
\(793\) 0 0
\(794\) −10.3137 + 17.8639i −0.366020 + 0.633965i
\(795\) 4.65685 8.06591i 0.165162 0.286068i
\(796\) −1.46447 2.53653i −0.0519066 0.0899049i
\(797\) 26.4853 0.938157 0.469078 0.883157i \(-0.344586\pi\)
0.469078 + 0.883157i \(0.344586\pi\)
\(798\) 0 0
\(799\) −12.8284 −0.453837
\(800\) −0.500000 0.866025i −0.0176777 0.0306186i
\(801\) 3.24264 5.61642i 0.114573 0.198446i
\(802\) 12.6569 21.9223i 0.446929 0.774104i
\(803\) −2.24264 3.88437i −0.0791411 0.137076i
\(804\) 7.89949 0.278594
\(805\) 0 0
\(806\) 0 0
\(807\) −3.82843 6.63103i −0.134767 0.233423i
\(808\) 3.17157 5.49333i 0.111576 0.193255i
\(809\) −12.5563 + 21.7482i −0.441458 + 0.764627i −0.997798 0.0663274i \(-0.978872\pi\)
0.556340 + 0.830955i \(0.312205\pi\)
\(810\) −0.500000 0.866025i −0.0175682 0.0304290i
\(811\) −3.02944 −0.106378 −0.0531890 0.998584i \(-0.516939\pi\)
−0.0531890 + 0.998584i \(0.516939\pi\)
\(812\) 0 0
\(813\) −14.2426 −0.499511
\(814\) 0.414214 + 0.717439i 0.0145182 + 0.0251462i
\(815\) −7.36396 + 12.7548i −0.257948 + 0.446780i
\(816\) −0.707107 + 1.22474i −0.0247537 + 0.0428746i
\(817\) 6.48528 + 11.2328i 0.226891 + 0.392987i
\(818\) −18.3848 −0.642809
\(819\) 0 0
\(820\) −8.82843 −0.308302
\(821\) 2.22183 + 3.84831i 0.0775422 + 0.134307i 0.902189 0.431341i \(-0.141959\pi\)
−0.824647 + 0.565648i \(0.808626\pi\)
\(822\) 8.00000 13.8564i 0.279032 0.483298i
\(823\) −8.14214 + 14.1026i −0.283817 + 0.491585i −0.972322 0.233646i \(-0.924934\pi\)
0.688505 + 0.725232i \(0.258267\pi\)
\(824\) 5.07107 + 8.78335i 0.176659 + 0.305982i
\(825\) 0.585786 0.0203945
\(826\) 0 0
\(827\) −11.1127 −0.386426 −0.193213 0.981157i \(-0.561891\pi\)
−0.193213 + 0.981157i \(0.561891\pi\)
\(828\) −2.41421 4.18154i −0.0838997 0.145319i
\(829\) 22.6569 39.2428i 0.786905 1.36296i −0.140949 0.990017i \(-0.545015\pi\)
0.927854 0.372943i \(-0.121651\pi\)
\(830\) 2.58579 4.47871i 0.0897540 0.155458i
\(831\) −10.9497 18.9655i −0.379843 0.657907i
\(832\) 0 0
\(833\) 0 0
\(834\) 17.6569 0.611407
\(835\) −0.535534 0.927572i −0.0185329 0.0321000i
\(836\) 0.828427 1.43488i 0.0286518 0.0496263i
\(837\) −2.53553 + 4.39167i −0.0876409 + 0.151798i
\(838\) 8.82843 + 15.2913i 0.304973 + 0.528229i
\(839\) 5.17157 0.178543 0.0892713 0.996007i \(-0.471546\pi\)
0.0892713 + 0.996007i \(0.471546\pi\)
\(840\) 0 0
\(841\) 38.9411 1.34280
\(842\) −8.31371 14.3998i −0.286509 0.496249i
\(843\) 6.75736 11.7041i 0.232736 0.403110i
\(844\) 0.828427 1.43488i 0.0285156 0.0493905i
\(845\) 6.50000 + 11.2583i 0.223607 + 0.387298i
\(846\) −9.07107 −0.311870
\(847\) 0 0
\(848\) −9.31371 −0.319834
\(849\) −15.2426 26.4010i −0.523126 0.906081i
\(850\) −0.707107 + 1.22474i −0.0242536 + 0.0420084i
\(851\) 3.41421 5.91359i 0.117038 0.202715i
\(852\) −5.41421 9.37769i −0.185488 0.321274i
\(853\) 6.68629 0.228934 0.114467 0.993427i \(-0.463484\pi\)
0.114467 + 0.993427i \(0.463484\pi\)
\(854\) 0 0
\(855\) −2.82843 −0.0967302
\(856\) 2.00000 + 3.46410i 0.0683586 + 0.118401i
\(857\) −13.6360 + 23.6183i −0.465798 + 0.806786i −0.999237 0.0390524i \(-0.987566\pi\)
0.533439 + 0.845839i \(0.320899\pi\)
\(858\) 0 0
\(859\) −8.48528 14.6969i −0.289514 0.501453i 0.684180 0.729313i \(-0.260160\pi\)
−0.973694 + 0.227860i \(0.926827\pi\)
\(860\) 4.58579 0.156374
\(861\) 0 0
\(862\) 14.1421 0.481683
\(863\) 0.485281 + 0.840532i 0.0165192 + 0.0286120i 0.874167 0.485626i \(-0.161408\pi\)
−0.857648 + 0.514238i \(0.828075\pi\)
\(864\) −0.500000 + 0.866025i −0.0170103 + 0.0294628i
\(865\) −9.24264 + 16.0087i −0.314259 + 0.544313i
\(866\) −4.41421 7.64564i −0.150001 0.259809i
\(867\) −15.0000 −0.509427
\(868\) 0 0
\(869\) −6.62742 −0.224820
\(870\) −4.12132 7.13834i −0.139726 0.242012i
\(871\) 0 0
\(872\) −2.65685 + 4.60181i −0.0899724 + 0.155837i
\(873\) −4.41421 7.64564i −0.149398 0.258766i
\(874\) −13.6569 −0.461950
\(875\) 0 0
\(876\) 7.65685 0.258701
\(877\) −10.7071 18.5453i −0.361553 0.626229i 0.626663 0.779290i \(-0.284420\pi\)
−0.988217 + 0.153061i \(0.951087\pi\)
\(878\) −16.7782 + 29.0607i −0.566236 + 0.980749i
\(879\) 14.3137 24.7921i 0.482789 0.836216i
\(880\) −0.292893 0.507306i −0.00987343 0.0171013i
\(881\) 31.6569 1.06655 0.533273 0.845943i \(-0.320962\pi\)
0.533273 + 0.845943i \(0.320962\pi\)
\(882\) 0 0
\(883\) −10.0416 −0.337928 −0.168964 0.985622i \(-0.554042\pi\)
−0.168964 + 0.985622i \(0.554042\pi\)
\(884\) 0 0
\(885\) −1.24264 + 2.15232i −0.0417709 + 0.0723493i
\(886\) −6.82843 + 11.8272i −0.229405 + 0.397342i
\(887\) 11.8492 + 20.5235i 0.397859 + 0.689111i 0.993461 0.114168i \(-0.0364201\pi\)
−0.595603 + 0.803279i \(0.703087\pi\)
\(888\) −1.41421 −0.0474579
\(889\) 0 0
\(890\) −6.48528 −0.217387
\(891\) −0.292893 0.507306i −0.00981229 0.0169954i
\(892\) −8.82843 + 15.2913i −0.295598 + 0.511990i
\(893\) −12.8284 + 22.2195i −0.429287 + 0.743547i
\(894\) 6.94975 + 12.0373i 0.232434 + 0.402588i
\(895\) 0.585786 0.0195807
\(896\) 0 0
\(897\) 0 0
\(898\) 12.5563 + 21.7482i 0.419011 + 0.725748i
\(899\) −20.8995 + 36.1990i −0.697037 + 1.20730i
\(900\) −0.500000 + 0.866025i −0.0166667 + 0.0288675i
\(901\) 6.58579 + 11.4069i 0.219404 + 0.380019i
\(902\) −5.17157 −0.172195
\(903\) 0 0
\(904\) 9.31371 0.309769
\(905\) 4.41421 + 7.64564i 0.146733 + 0.254150i
\(906\) −8.89949 + 15.4144i −0.295666 + 0.512108i
\(907\) −21.6066 + 37.4237i −0.717435 + 1.24263i 0.244577 + 0.969630i \(0.421351\pi\)
−0.962013 + 0.273005i \(0.911983\pi\)
\(908\) 6.82843 + 11.8272i 0.226609 + 0.392499i
\(909\) −6.34315 −0.210389
\(910\) 0 0
\(911\) 5.65685 0.187420 0.0937100 0.995600i \(-0.470127\pi\)
0.0937100 + 0.995600i \(0.470127\pi\)
\(912\) 1.41421 + 2.44949i 0.0468293 + 0.0811107i
\(913\) 1.51472 2.62357i 0.0501299 0.0868275i
\(914\) 4.89949 8.48617i 0.162061 0.280698i
\(915\) 5.82843 + 10.0951i 0.192682 + 0.333735i
\(916\) 25.7990 0.852423
\(917\) 0 0
\(918\) 1.41421 0.0466760
\(919\) −13.3848 23.1831i −0.441523 0.764740i 0.556280 0.830995i \(-0.312228\pi\)
−0.997803 + 0.0662548i \(0.978895\pi\)
\(920\) −2.41421 + 4.18154i −0.0795943 + 0.137861i
\(921\) 3.65685 6.33386i 0.120497 0.208708i
\(922\) 7.00000 + 12.1244i 0.230533 + 0.399294i
\(923\) 0 0
\(924\) 0 0
\(925\) −1.41421 −0.0464991
\(926\) −16.8284 29.1477i −0.553016 0.957853i
\(927\) 5.07107 8.78335i 0.166556 0.288483i
\(928\) −4.12132 + 7.13834i −0.135289 + 0.234327i
\(929\) 5.82843 + 10.0951i 0.191224 + 0.331211i 0.945656 0.325168i \(-0.105421\pi\)
−0.754432 + 0.656378i \(0.772087\pi\)
\(930\) 5.07107 0.166287
\(931\) 0 0
\(932\) 6.97056 0.228328
\(933\) 14.5858 + 25.2633i 0.477517 + 0.827084i
\(934\) 10.2426 17.7408i 0.335149 0.580496i
\(935\) −0.414214 + 0.717439i −0.0135462 + 0.0234628i
\(936\) 0 0
\(937\) −17.0294 −0.556327 −0.278164 0.960534i \(-0.589726\pi\)
−0.278164 + 0.960534i \(0.589726\pi\)
\(938\) 0 0
\(939\) 28.8284 0.940780
\(940\) 4.53553 + 7.85578i 0.147933 + 0.256227i
\(941\) −18.1421 + 31.4231i −0.591417 + 1.02436i 0.402625 + 0.915365i \(0.368098\pi\)
−0.994042 + 0.108999i \(0.965236\pi\)
\(942\) −0.171573 + 0.297173i −0.00559015 + 0.00968242i
\(943\) 21.3137 + 36.9164i 0.694070 + 1.20216i
\(944\) 2.48528 0.0808890
\(945\) 0 0
\(946\) 2.68629 0.0873389
\(947\) −18.2426 31.5972i −0.592806 1.02677i −0.993852 0.110713i \(-0.964687\pi\)
0.401046 0.916058i \(-0.368647\pi\)
\(948\) 5.65685 9.79796i 0.183726 0.318223i
\(949\) 0 0
\(950\) 1.41421 + 2.44949i 0.0458831 + 0.0794719i
\(951\) −18.0000 −0.583690
\(952\) 0 0
\(953\) −23.5980 −0.764414 −0.382207 0.924077i \(-0.624836\pi\)
−0.382207 + 0.924077i \(0.624836\pi\)
\(954\) 4.65685 + 8.06591i 0.150771 + 0.261143i
\(955\) 5.65685 9.79796i 0.183052 0.317055i
\(956\) −11.6569 + 20.1903i −0.377010 + 0.653000i
\(957\) −2.41421 4.18154i −0.0780404 0.135170i
\(958\) 16.4853 0.532615
\(959\) 0 0
\(960\) 1.00000 0.0322749
\(961\) 2.64214 + 4.57631i 0.0852302 + 0.147623i
\(962\) 0 0
\(963\) 2.00000 3.46410i 0.0644491 0.111629i
\(964\) 8.12132 + 14.0665i 0.261570 + 0.453053i
\(965\) −21.7990 −0.701734
\(966\) 0 0
\(967\) −44.2843 −1.42409 −0.712043 0.702136i \(-0.752230\pi\)
−0.712043 + 0.702136i \(0.752230\pi\)
\(968\) 5.32843 + 9.22911i 0.171262 + 0.296635i
\(969\) 2.00000 3.46410i 0.0642493 0.111283i
\(970\) −4.41421 + 7.64564i −0.141732 + 0.245487i
\(971\) −22.4853 38.9456i −0.721587 1.24983i −0.960363 0.278751i \(-0.910080\pi\)
0.238776 0.971075i \(-0.423254\pi\)
\(972\) 1.00000 0.0320750
\(973\) 0 0
\(974\) 24.4853 0.784559
\(975\) 0 0
\(976\) 5.82843 10.0951i 0.186563 0.323137i
\(977\) −2.65685 + 4.60181i −0.0850003 + 0.147225i −0.905391 0.424578i \(-0.860422\pi\)
0.820391 + 0.571803i \(0.193756\pi\)
\(978\) −7.36396 12.7548i −0.235474 0.407852i
\(979\) −3.79899 −0.121416
\(980\) 0 0
\(981\) 5.31371 0.169654
\(982\) −5.94975 10.3053i −0.189864 0.328854i
\(983\) 8.43503 14.6099i 0.269036 0.465983i −0.699577 0.714557i \(-0.746628\pi\)
0.968613 + 0.248573i \(0.0799617\pi\)
\(984\) 4.41421 7.64564i 0.140720 0.243734i
\(985\) 10.4142 + 18.0379i 0.331824 + 0.574737i
\(986\) 11.6569 0.371230
\(987\) 0 0
\(988\) 0 0
\(989\) −11.0711 19.1757i −0.352039 0.609750i
\(990\) −0.292893 + 0.507306i −0.00930876 + 0.0161232i
\(991\) −10.4142 + 18.0379i −0.330818 + 0.572994i −0.982673 0.185350i \(-0.940658\pi\)
0.651854 + 0.758344i \(0.273991\pi\)
\(992\) −2.53553 4.39167i −0.0805033 0.139436i
\(993\) −18.6274 −0.591123
\(994\) 0 0
\(995\) 2.92893 0.0928534
\(996\) 2.58579 + 4.47871i 0.0819338 + 0.141913i
\(997\) 1.34315 2.32640i 0.0425379 0.0736777i −0.843973 0.536386i \(-0.819789\pi\)
0.886510 + 0.462709i \(0.153122\pi\)
\(998\) −7.89949 + 13.6823i −0.250054 + 0.433106i
\(999\) 0.707107 + 1.22474i 0.0223719 + 0.0387492i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1470.2.i.u.361.2 4
7.2 even 3 inner 1470.2.i.u.961.2 4
7.3 odd 6 1470.2.a.u.1.1 2
7.4 even 3 1470.2.a.v.1.1 yes 2
7.5 odd 6 1470.2.i.v.961.2 4
7.6 odd 2 1470.2.i.v.361.2 4
21.11 odd 6 4410.2.a.bn.1.2 2
21.17 even 6 4410.2.a.br.1.2 2
35.4 even 6 7350.2.a.dd.1.1 2
35.24 odd 6 7350.2.a.df.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1470.2.a.u.1.1 2 7.3 odd 6
1470.2.a.v.1.1 yes 2 7.4 even 3
1470.2.i.u.361.2 4 1.1 even 1 trivial
1470.2.i.u.961.2 4 7.2 even 3 inner
1470.2.i.v.361.2 4 7.6 odd 2
1470.2.i.v.961.2 4 7.5 odd 6
4410.2.a.bn.1.2 2 21.11 odd 6
4410.2.a.br.1.2 2 21.17 even 6
7350.2.a.dd.1.1 2 35.4 even 6
7350.2.a.df.1.1 2 35.24 odd 6