Properties

Label 98.2.c.c.79.2
Level $98$
Weight $2$
Character 98.79
Analytic conductor $0.783$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [98,2,Mod(67,98)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(98, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("98.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 98.c (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: \(0.782533939809\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 98.79
Dual form 98.2.c.c.67.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.707107 + 1.22474i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.41421 + 2.44949i) q^{5} -1.41421 q^{6} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.707107 + 1.22474i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.41421 + 2.44949i) q^{5} -1.41421 q^{6} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.41421 - 2.44949i) q^{10} +(1.00000 + 1.73205i) q^{11} +(0.707107 - 1.22474i) q^{12} -4.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.707107 + 1.22474i) q^{17} +(0.500000 + 0.866025i) q^{18} +(3.53553 - 6.12372i) q^{19} +2.82843 q^{20} -2.00000 q^{22} +(2.00000 - 3.46410i) q^{23} +(0.707107 + 1.22474i) q^{24} +(-1.50000 - 2.59808i) q^{25} +5.65685 q^{27} +2.00000 q^{29} +(2.00000 - 3.46410i) q^{30} +(-4.24264 - 7.34847i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.41421 + 2.44949i) q^{33} -1.41421 q^{34} -1.00000 q^{36} +(-5.00000 + 8.66025i) q^{37} +(3.53553 + 6.12372i) q^{38} +(-1.41421 + 2.44949i) q^{40} -9.89949 q^{41} +2.00000 q^{43} +(1.00000 - 1.73205i) q^{44} +(1.41421 + 2.44949i) q^{45} +(2.00000 + 3.46410i) q^{46} +(-1.41421 + 2.44949i) q^{47} -1.41421 q^{48} +3.00000 q^{50} +(-1.00000 + 1.73205i) q^{51} +(1.00000 + 1.73205i) q^{53} +(-2.82843 + 4.89898i) q^{54} -5.65685 q^{55} +10.0000 q^{57} +(-1.00000 + 1.73205i) q^{58} +(0.707107 + 1.22474i) q^{59} +(2.00000 + 3.46410i) q^{60} +(-1.41421 + 2.44949i) q^{61} +8.48528 q^{62} +1.00000 q^{64} +(-1.41421 - 2.44949i) q^{66} +(-6.00000 - 10.3923i) q^{67} +(0.707107 - 1.22474i) q^{68} +5.65685 q^{69} -12.0000 q^{71} +(0.500000 - 0.866025i) q^{72} +(0.707107 + 1.22474i) q^{73} +(-5.00000 - 8.66025i) q^{74} +(2.12132 - 3.67423i) q^{75} -7.07107 q^{76} +(2.00000 - 3.46410i) q^{79} +(-1.41421 - 2.44949i) q^{80} +(2.50000 + 4.33013i) q^{81} +(4.94975 - 8.57321i) q^{82} +9.89949 q^{83} -4.00000 q^{85} +(-1.00000 + 1.73205i) q^{86} +(1.41421 + 2.44949i) q^{87} +(1.00000 + 1.73205i) q^{88} +(3.53553 - 6.12372i) q^{89} -2.82843 q^{90} -4.00000 q^{92} +(6.00000 - 10.3923i) q^{93} +(-1.41421 - 2.44949i) q^{94} +(10.0000 + 17.3205i) q^{95} +(0.707107 - 1.22474i) q^{96} +9.89949 q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 2 q^{9} + 4 q^{11} - 16 q^{15} - 2 q^{16} + 2 q^{18} - 8 q^{22} + 8 q^{23} - 6 q^{25} + 8 q^{29} + 8 q^{30} - 2 q^{32} - 4 q^{36} - 20 q^{37} + 8 q^{43} + 4 q^{44} + 8 q^{46} + 12 q^{50} - 4 q^{51} + 4 q^{53} + 40 q^{57} - 4 q^{58} + 8 q^{60} + 4 q^{64} - 24 q^{67} - 48 q^{71} + 2 q^{72} - 20 q^{74} + 8 q^{79} + 10 q^{81} - 16 q^{85} - 4 q^{86} + 4 q^{88} - 16 q^{92} + 24 q^{93} + 40 q^{95} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0.707107 + 1.22474i 0.408248 + 0.707107i 0.994694 0.102882i \(-0.0328064\pi\)
−0.586445 + 0.809989i \(0.699473\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.41421 + 2.44949i −0.632456 + 1.09545i 0.354593 + 0.935021i \(0.384620\pi\)
−0.987048 + 0.160424i \(0.948714\pi\)
\(6\) −1.41421 −0.577350
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) −1.41421 2.44949i −0.447214 0.774597i
\(11\) 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i \(-0.0691756\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(12\) 0.707107 1.22474i 0.204124 0.353553i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) −4.00000 −1.03280
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0.707107 + 1.22474i 0.171499 + 0.297044i 0.938944 0.344070i \(-0.111806\pi\)
−0.767445 + 0.641114i \(0.778472\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) 3.53553 6.12372i 0.811107 1.40488i −0.100983 0.994888i \(-0.532199\pi\)
0.912090 0.409991i \(-0.134468\pi\)
\(20\) 2.82843 0.632456
\(21\) 0 0
\(22\) −2.00000 −0.426401
\(23\) 2.00000 3.46410i 0.417029 0.722315i −0.578610 0.815604i \(-0.696405\pi\)
0.995639 + 0.0932891i \(0.0297381\pi\)
\(24\) 0.707107 + 1.22474i 0.144338 + 0.250000i
\(25\) −1.50000 2.59808i −0.300000 0.519615i
\(26\) 0 0
\(27\) 5.65685 1.08866
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 2.00000 3.46410i 0.365148 0.632456i
\(31\) −4.24264 7.34847i −0.762001 1.31982i −0.941818 0.336124i \(-0.890884\pi\)
0.179817 0.983700i \(-0.442449\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −1.41421 + 2.44949i −0.246183 + 0.426401i
\(34\) −1.41421 −0.242536
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) −5.00000 + 8.66025i −0.821995 + 1.42374i 0.0821995 + 0.996616i \(0.473806\pi\)
−0.904194 + 0.427121i \(0.859528\pi\)
\(38\) 3.53553 + 6.12372i 0.573539 + 0.993399i
\(39\) 0 0
\(40\) −1.41421 + 2.44949i −0.223607 + 0.387298i
\(41\) −9.89949 −1.54604 −0.773021 0.634381i \(-0.781255\pi\)
−0.773021 + 0.634381i \(0.781255\pi\)
\(42\) 0 0
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 1.00000 1.73205i 0.150756 0.261116i
\(45\) 1.41421 + 2.44949i 0.210819 + 0.365148i
\(46\) 2.00000 + 3.46410i 0.294884 + 0.510754i
\(47\) −1.41421 + 2.44949i −0.206284 + 0.357295i −0.950541 0.310599i \(-0.899470\pi\)
0.744257 + 0.667893i \(0.232804\pi\)
\(48\) −1.41421 −0.204124
\(49\) 0 0
\(50\) 3.00000 0.424264
\(51\) −1.00000 + 1.73205i −0.140028 + 0.242536i
\(52\) 0 0
\(53\) 1.00000 + 1.73205i 0.137361 + 0.237915i 0.926497 0.376303i \(-0.122805\pi\)
−0.789136 + 0.614218i \(0.789471\pi\)
\(54\) −2.82843 + 4.89898i −0.384900 + 0.666667i
\(55\) −5.65685 −0.762770
\(56\) 0 0
\(57\) 10.0000 1.32453
\(58\) −1.00000 + 1.73205i −0.131306 + 0.227429i
\(59\) 0.707107 + 1.22474i 0.0920575 + 0.159448i 0.908377 0.418153i \(-0.137322\pi\)
−0.816319 + 0.577601i \(0.803989\pi\)
\(60\) 2.00000 + 3.46410i 0.258199 + 0.447214i
\(61\) −1.41421 + 2.44949i −0.181071 + 0.313625i −0.942246 0.334922i \(-0.891290\pi\)
0.761174 + 0.648547i \(0.224623\pi\)
\(62\) 8.48528 1.07763
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −1.41421 2.44949i −0.174078 0.301511i
\(67\) −6.00000 10.3923i −0.733017 1.26962i −0.955588 0.294706i \(-0.904778\pi\)
0.222571 0.974916i \(-0.428555\pi\)
\(68\) 0.707107 1.22474i 0.0857493 0.148522i
\(69\) 5.65685 0.681005
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 0.707107 + 1.22474i 0.0827606 + 0.143346i 0.904435 0.426612i \(-0.140293\pi\)
−0.821674 + 0.569958i \(0.806960\pi\)
\(74\) −5.00000 8.66025i −0.581238 1.00673i
\(75\) 2.12132 3.67423i 0.244949 0.424264i
\(76\) −7.07107 −0.811107
\(77\) 0 0
\(78\) 0 0
\(79\) 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i \(-0.761089\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) −1.41421 2.44949i −0.158114 0.273861i
\(81\) 2.50000 + 4.33013i 0.277778 + 0.481125i
\(82\) 4.94975 8.57321i 0.546608 0.946753i
\(83\) 9.89949 1.08661 0.543305 0.839535i \(-0.317173\pi\)
0.543305 + 0.839535i \(0.317173\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.433861
\(86\) −1.00000 + 1.73205i −0.107833 + 0.186772i
\(87\) 1.41421 + 2.44949i 0.151620 + 0.262613i
\(88\) 1.00000 + 1.73205i 0.106600 + 0.184637i
\(89\) 3.53553 6.12372i 0.374766 0.649113i −0.615526 0.788116i \(-0.711056\pi\)
0.990292 + 0.139003i \(0.0443898\pi\)
\(90\) −2.82843 −0.298142
\(91\) 0 0
\(92\) −4.00000 −0.417029
\(93\) 6.00000 10.3923i 0.622171 1.07763i
\(94\) −1.41421 2.44949i −0.145865 0.252646i
\(95\) 10.0000 + 17.3205i 1.02598 + 1.77705i
\(96\) 0.707107 1.22474i 0.0721688 0.125000i
\(97\) 9.89949 1.00514 0.502571 0.864536i \(-0.332388\pi\)
0.502571 + 0.864536i \(0.332388\pi\)
\(98\) 0 0
\(99\) 2.00000 0.201008
\(100\) −1.50000 + 2.59808i −0.150000 + 0.259808i
\(101\) −4.24264 7.34847i −0.422159 0.731200i 0.573992 0.818861i \(-0.305394\pi\)
−0.996150 + 0.0876610i \(0.972061\pi\)
\(102\) −1.00000 1.73205i −0.0990148 0.171499i
\(103\) −1.41421 + 2.44949i −0.139347 + 0.241355i −0.927249 0.374444i \(-0.877834\pi\)
0.787903 + 0.615800i \(0.211167\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −2.00000 −0.194257
\(107\) 2.00000 3.46410i 0.193347 0.334887i −0.753010 0.658009i \(-0.771399\pi\)
0.946357 + 0.323122i \(0.104732\pi\)
\(108\) −2.82843 4.89898i −0.272166 0.471405i
\(109\) 1.00000 + 1.73205i 0.0957826 + 0.165900i 0.909935 0.414751i \(-0.136131\pi\)
−0.814152 + 0.580651i \(0.802798\pi\)
\(110\) 2.82843 4.89898i 0.269680 0.467099i
\(111\) −14.1421 −1.34231
\(112\) 0 0
\(113\) −12.0000 −1.12887 −0.564433 0.825479i \(-0.690905\pi\)
−0.564433 + 0.825479i \(0.690905\pi\)
\(114\) −5.00000 + 8.66025i −0.468293 + 0.811107i
\(115\) 5.65685 + 9.79796i 0.527504 + 0.913664i
\(116\) −1.00000 1.73205i −0.0928477 0.160817i
\(117\) 0 0
\(118\) −1.41421 −0.130189
\(119\) 0 0
\(120\) −4.00000 −0.365148
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) −1.41421 2.44949i −0.128037 0.221766i
\(123\) −7.00000 12.1244i −0.631169 1.09322i
\(124\) −4.24264 + 7.34847i −0.381000 + 0.659912i
\(125\) −5.65685 −0.505964
\(126\) 0 0
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 1.41421 + 2.44949i 0.124515 + 0.215666i
\(130\) 0 0
\(131\) −6.36396 + 11.0227i −0.556022 + 0.963058i 0.441801 + 0.897113i \(0.354340\pi\)
−0.997823 + 0.0659452i \(0.978994\pi\)
\(132\) 2.82843 0.246183
\(133\) 0 0
\(134\) 12.0000 1.03664
\(135\) −8.00000 + 13.8564i −0.688530 + 1.19257i
\(136\) 0.707107 + 1.22474i 0.0606339 + 0.105021i
\(137\) −6.00000 10.3923i −0.512615 0.887875i −0.999893 0.0146279i \(-0.995344\pi\)
0.487278 0.873247i \(-0.337990\pi\)
\(138\) −2.82843 + 4.89898i −0.240772 + 0.417029i
\(139\) 9.89949 0.839664 0.419832 0.907602i \(-0.362089\pi\)
0.419832 + 0.907602i \(0.362089\pi\)
\(140\) 0 0
\(141\) −4.00000 −0.336861
\(142\) 6.00000 10.3923i 0.503509 0.872103i
\(143\) 0 0
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) −2.82843 + 4.89898i −0.234888 + 0.406838i
\(146\) −1.41421 −0.117041
\(147\) 0 0
\(148\) 10.0000 0.821995
\(149\) −5.00000 + 8.66025i −0.409616 + 0.709476i −0.994847 0.101391i \(-0.967671\pi\)
0.585231 + 0.810867i \(0.301004\pi\)
\(150\) 2.12132 + 3.67423i 0.173205 + 0.300000i
\(151\) 8.00000 + 13.8564i 0.651031 + 1.12762i 0.982873 + 0.184284i \(0.0589965\pi\)
−0.331842 + 0.943335i \(0.607670\pi\)
\(152\) 3.53553 6.12372i 0.286770 0.496700i
\(153\) 1.41421 0.114332
\(154\) 0 0
\(155\) 24.0000 1.92773
\(156\) 0 0
\(157\) 5.65685 + 9.79796i 0.451466 + 0.781962i 0.998477 0.0551630i \(-0.0175678\pi\)
−0.547011 + 0.837125i \(0.684235\pi\)
\(158\) 2.00000 + 3.46410i 0.159111 + 0.275589i
\(159\) −1.41421 + 2.44949i −0.112154 + 0.194257i
\(160\) 2.82843 0.223607
\(161\) 0 0
\(162\) −5.00000 −0.392837
\(163\) −5.00000 + 8.66025i −0.391630 + 0.678323i −0.992665 0.120900i \(-0.961422\pi\)
0.601035 + 0.799223i \(0.294755\pi\)
\(164\) 4.94975 + 8.57321i 0.386510 + 0.669456i
\(165\) −4.00000 6.92820i −0.311400 0.539360i
\(166\) −4.94975 + 8.57321i −0.384175 + 0.665410i
\(167\) −19.7990 −1.53209 −0.766046 0.642786i \(-0.777779\pi\)
−0.766046 + 0.642786i \(0.777779\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 2.00000 3.46410i 0.153393 0.265684i
\(171\) −3.53553 6.12372i −0.270369 0.468293i
\(172\) −1.00000 1.73205i −0.0762493 0.132068i
\(173\) 8.48528 14.6969i 0.645124 1.11739i −0.339149 0.940733i \(-0.610139\pi\)
0.984273 0.176655i \(-0.0565276\pi\)
\(174\) −2.82843 −0.214423
\(175\) 0 0
\(176\) −2.00000 −0.150756
\(177\) −1.00000 + 1.73205i −0.0751646 + 0.130189i
\(178\) 3.53553 + 6.12372i 0.264999 + 0.458993i
\(179\) −6.00000 10.3923i −0.448461 0.776757i 0.549825 0.835280i \(-0.314694\pi\)
−0.998286 + 0.0585225i \(0.981361\pi\)
\(180\) 1.41421 2.44949i 0.105409 0.182574i
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) −4.00000 −0.295689
\(184\) 2.00000 3.46410i 0.147442 0.255377i
\(185\) −14.1421 24.4949i −1.03975 1.80090i
\(186\) 6.00000 + 10.3923i 0.439941 + 0.762001i
\(187\) −1.41421 + 2.44949i −0.103418 + 0.179124i
\(188\) 2.82843 0.206284
\(189\) 0 0
\(190\) −20.0000 −1.45095
\(191\) 2.00000 3.46410i 0.144715 0.250654i −0.784552 0.620063i \(-0.787107\pi\)
0.929267 + 0.369410i \(0.120440\pi\)
\(192\) 0.707107 + 1.22474i 0.0510310 + 0.0883883i
\(193\) 8.00000 + 13.8564i 0.575853 + 0.997406i 0.995948 + 0.0899262i \(0.0286631\pi\)
−0.420096 + 0.907480i \(0.638004\pi\)
\(194\) −4.94975 + 8.57321i −0.355371 + 0.615521i
\(195\) 0 0
\(196\) 0 0
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) −1.00000 + 1.73205i −0.0710669 + 0.123091i
\(199\) −4.24264 7.34847i −0.300753 0.520919i 0.675554 0.737311i \(-0.263905\pi\)
−0.976307 + 0.216391i \(0.930571\pi\)
\(200\) −1.50000 2.59808i −0.106066 0.183712i
\(201\) 8.48528 14.6969i 0.598506 1.03664i
\(202\) 8.48528 0.597022
\(203\) 0 0
\(204\) 2.00000 0.140028
\(205\) 14.0000 24.2487i 0.977802 1.69360i
\(206\) −1.41421 2.44949i −0.0985329 0.170664i
\(207\) −2.00000 3.46410i −0.139010 0.240772i
\(208\) 0 0
\(209\) 14.1421 0.978232
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) 1.00000 1.73205i 0.0686803 0.118958i
\(213\) −8.48528 14.6969i −0.581402 1.00702i
\(214\) 2.00000 + 3.46410i 0.136717 + 0.236801i
\(215\) −2.82843 + 4.89898i −0.192897 + 0.334108i
\(216\) 5.65685 0.384900
\(217\) 0 0
\(218\) −2.00000 −0.135457
\(219\) −1.00000 + 1.73205i −0.0675737 + 0.117041i
\(220\) 2.82843 + 4.89898i 0.190693 + 0.330289i
\(221\) 0 0
\(222\) 7.07107 12.2474i 0.474579 0.821995i
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) −3.00000 −0.200000
\(226\) 6.00000 10.3923i 0.399114 0.691286i
\(227\) 10.6066 + 18.3712i 0.703985 + 1.21934i 0.967057 + 0.254561i \(0.0819311\pi\)
−0.263072 + 0.964776i \(0.584736\pi\)
\(228\) −5.00000 8.66025i −0.331133 0.573539i
\(229\) 8.48528 14.6969i 0.560723 0.971201i −0.436710 0.899602i \(-0.643857\pi\)
0.997434 0.0715988i \(-0.0228101\pi\)
\(230\) −11.3137 −0.746004
\(231\) 0 0
\(232\) 2.00000 0.131306
\(233\) −12.0000 + 20.7846i −0.786146 + 1.36165i 0.142166 + 0.989843i \(0.454593\pi\)
−0.928312 + 0.371802i \(0.878740\pi\)
\(234\) 0 0
\(235\) −4.00000 6.92820i −0.260931 0.451946i
\(236\) 0.707107 1.22474i 0.0460287 0.0797241i
\(237\) 5.65685 0.367452
\(238\) 0 0
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 2.00000 3.46410i 0.129099 0.223607i
\(241\) 10.6066 + 18.3712i 0.683231 + 1.18339i 0.973989 + 0.226595i \(0.0727593\pi\)
−0.290758 + 0.956797i \(0.593907\pi\)
\(242\) 3.50000 + 6.06218i 0.224989 + 0.389692i
\(243\) 4.94975 8.57321i 0.317526 0.549972i
\(244\) 2.82843 0.181071
\(245\) 0 0
\(246\) 14.0000 0.892607
\(247\) 0 0
\(248\) −4.24264 7.34847i −0.269408 0.466628i
\(249\) 7.00000 + 12.1244i 0.443607 + 0.768350i
\(250\) 2.82843 4.89898i 0.178885 0.309839i
\(251\) 9.89949 0.624851 0.312425 0.949942i \(-0.398859\pi\)
0.312425 + 0.949942i \(0.398859\pi\)
\(252\) 0 0
\(253\) 8.00000 0.502956
\(254\) −8.00000 + 13.8564i −0.501965 + 0.869428i
\(255\) −2.82843 4.89898i −0.177123 0.306786i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −6.36396 + 11.0227i −0.396973 + 0.687577i −0.993351 0.115126i \(-0.963273\pi\)
0.596378 + 0.802704i \(0.296606\pi\)
\(258\) −2.82843 −0.176090
\(259\) 0 0
\(260\) 0 0
\(261\) 1.00000 1.73205i 0.0618984 0.107211i
\(262\) −6.36396 11.0227i −0.393167 0.680985i
\(263\) −6.00000 10.3923i −0.369976 0.640817i 0.619586 0.784929i \(-0.287301\pi\)
−0.989561 + 0.144112i \(0.953967\pi\)
\(264\) −1.41421 + 2.44949i −0.0870388 + 0.150756i
\(265\) −5.65685 −0.347498
\(266\) 0 0
\(267\) 10.0000 0.611990
\(268\) −6.00000 + 10.3923i −0.366508 + 0.634811i
\(269\) 5.65685 + 9.79796i 0.344904 + 0.597392i 0.985336 0.170623i \(-0.0545780\pi\)
−0.640432 + 0.768015i \(0.721245\pi\)
\(270\) −8.00000 13.8564i −0.486864 0.843274i
\(271\) −11.3137 + 19.5959i −0.687259 + 1.19037i 0.285462 + 0.958390i \(0.407853\pi\)
−0.972721 + 0.231977i \(0.925480\pi\)
\(272\) −1.41421 −0.0857493
\(273\) 0 0
\(274\) 12.0000 0.724947
\(275\) 3.00000 5.19615i 0.180907 0.313340i
\(276\) −2.82843 4.89898i −0.170251 0.294884i
\(277\) 1.00000 + 1.73205i 0.0600842 + 0.104069i 0.894503 0.447062i \(-0.147530\pi\)
−0.834419 + 0.551131i \(0.814196\pi\)
\(278\) −4.94975 + 8.57321i −0.296866 + 0.514187i
\(279\) −8.48528 −0.508001
\(280\) 0 0
\(281\) 16.0000 0.954480 0.477240 0.878773i \(-0.341637\pi\)
0.477240 + 0.878773i \(0.341637\pi\)
\(282\) 2.00000 3.46410i 0.119098 0.206284i
\(283\) 0.707107 + 1.22474i 0.0420331 + 0.0728035i 0.886277 0.463156i \(-0.153283\pi\)
−0.844243 + 0.535960i \(0.819950\pi\)
\(284\) 6.00000 + 10.3923i 0.356034 + 0.616670i
\(285\) −14.1421 + 24.4949i −0.837708 + 1.45095i
\(286\) 0 0
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) 7.50000 12.9904i 0.441176 0.764140i
\(290\) −2.82843 4.89898i −0.166091 0.287678i
\(291\) 7.00000 + 12.1244i 0.410347 + 0.710742i
\(292\) 0.707107 1.22474i 0.0413803 0.0716728i
\(293\) −19.7990 −1.15667 −0.578335 0.815800i \(-0.696297\pi\)
−0.578335 + 0.815800i \(0.696297\pi\)
\(294\) 0 0
\(295\) −4.00000 −0.232889
\(296\) −5.00000 + 8.66025i −0.290619 + 0.503367i
\(297\) 5.65685 + 9.79796i 0.328244 + 0.568535i
\(298\) −5.00000 8.66025i −0.289642 0.501675i
\(299\) 0 0
\(300\) −4.24264 −0.244949
\(301\) 0 0
\(302\) −16.0000 −0.920697
\(303\) 6.00000 10.3923i 0.344691 0.597022i
\(304\) 3.53553 + 6.12372i 0.202777 + 0.351220i
\(305\) −4.00000 6.92820i −0.229039 0.396708i
\(306\) −0.707107 + 1.22474i −0.0404226 + 0.0700140i
\(307\) −9.89949 −0.564994 −0.282497 0.959268i \(-0.591163\pi\)
−0.282497 + 0.959268i \(0.591163\pi\)
\(308\) 0 0
\(309\) −4.00000 −0.227552
\(310\) −12.0000 + 20.7846i −0.681554 + 1.18049i
\(311\) 5.65685 + 9.79796i 0.320771 + 0.555591i 0.980647 0.195783i \(-0.0627248\pi\)
−0.659877 + 0.751374i \(0.729391\pi\)
\(312\) 0 0
\(313\) −6.36396 + 11.0227i −0.359712 + 0.623040i −0.987913 0.155012i \(-0.950459\pi\)
0.628200 + 0.778052i \(0.283792\pi\)
\(314\) −11.3137 −0.638470
\(315\) 0 0
\(316\) −4.00000 −0.225018
\(317\) −5.00000 + 8.66025i −0.280828 + 0.486408i −0.971589 0.236675i \(-0.923942\pi\)
0.690761 + 0.723083i \(0.257276\pi\)
\(318\) −1.41421 2.44949i −0.0793052 0.137361i
\(319\) 2.00000 + 3.46410i 0.111979 + 0.193952i
\(320\) −1.41421 + 2.44949i −0.0790569 + 0.136931i
\(321\) 5.65685 0.315735
\(322\) 0 0
\(323\) 10.0000 0.556415
\(324\) 2.50000 4.33013i 0.138889 0.240563i
\(325\) 0 0
\(326\) −5.00000 8.66025i −0.276924 0.479647i
\(327\) −1.41421 + 2.44949i −0.0782062 + 0.135457i
\(328\) −9.89949 −0.546608
\(329\) 0 0
\(330\) 8.00000 0.440386
\(331\) −5.00000 + 8.66025i −0.274825 + 0.476011i −0.970091 0.242742i \(-0.921953\pi\)
0.695266 + 0.718752i \(0.255287\pi\)
\(332\) −4.94975 8.57321i −0.271653 0.470516i
\(333\) 5.00000 + 8.66025i 0.273998 + 0.474579i
\(334\) 9.89949 17.1464i 0.541676 0.938211i
\(335\) 33.9411 1.85440
\(336\) 0 0
\(337\) 2.00000 0.108947 0.0544735 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) 6.50000 11.2583i 0.353553 0.612372i
\(339\) −8.48528 14.6969i −0.460857 0.798228i
\(340\) 2.00000 + 3.46410i 0.108465 + 0.187867i
\(341\) 8.48528 14.6969i 0.459504 0.795884i
\(342\) 7.07107 0.382360
\(343\) 0 0
\(344\) 2.00000 0.107833
\(345\) −8.00000 + 13.8564i −0.430706 + 0.746004i
\(346\) 8.48528 + 14.6969i 0.456172 + 0.790112i
\(347\) 15.0000 + 25.9808i 0.805242 + 1.39472i 0.916127 + 0.400887i \(0.131298\pi\)
−0.110885 + 0.993833i \(0.535369\pi\)
\(348\) 1.41421 2.44949i 0.0758098 0.131306i
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.00000 1.73205i 0.0533002 0.0923186i
\(353\) 0.707107 + 1.22474i 0.0376355 + 0.0651866i 0.884230 0.467052i \(-0.154684\pi\)
−0.846594 + 0.532239i \(0.821351\pi\)
\(354\) −1.00000 1.73205i −0.0531494 0.0920575i
\(355\) 16.9706 29.3939i 0.900704 1.56007i
\(356\) −7.07107 −0.374766
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) 16.0000 27.7128i 0.844448 1.46263i −0.0416523 0.999132i \(-0.513262\pi\)
0.886100 0.463494i \(-0.153404\pi\)
\(360\) 1.41421 + 2.44949i 0.0745356 + 0.129099i
\(361\) −15.5000 26.8468i −0.815789 1.41299i
\(362\) 0 0
\(363\) 9.89949 0.519589
\(364\) 0 0
\(365\) −4.00000 −0.209370
\(366\) 2.00000 3.46410i 0.104542 0.181071i
\(367\) −14.1421 24.4949i −0.738213 1.27862i −0.953299 0.302028i \(-0.902336\pi\)
0.215086 0.976595i \(-0.430997\pi\)
\(368\) 2.00000 + 3.46410i 0.104257 + 0.180579i
\(369\) −4.94975 + 8.57321i −0.257674 + 0.446304i
\(370\) 28.2843 1.47043
\(371\) 0 0
\(372\) −12.0000 −0.622171
\(373\) −5.00000 + 8.66025i −0.258890 + 0.448411i −0.965945 0.258748i \(-0.916690\pi\)
0.707055 + 0.707159i \(0.250023\pi\)
\(374\) −1.41421 2.44949i −0.0731272 0.126660i
\(375\) −4.00000 6.92820i −0.206559 0.357771i
\(376\) −1.41421 + 2.44949i −0.0729325 + 0.126323i
\(377\) 0 0
\(378\) 0 0
\(379\) −26.0000 −1.33553 −0.667765 0.744372i \(-0.732749\pi\)
−0.667765 + 0.744372i \(0.732749\pi\)
\(380\) 10.0000 17.3205i 0.512989 0.888523i
\(381\) 11.3137 + 19.5959i 0.579619 + 1.00393i
\(382\) 2.00000 + 3.46410i 0.102329 + 0.177239i
\(383\) 18.3848 31.8434i 0.939418 1.62712i 0.172859 0.984947i \(-0.444700\pi\)
0.766559 0.642173i \(-0.221967\pi\)
\(384\) −1.41421 −0.0721688
\(385\) 0 0
\(386\) −16.0000 −0.814379
\(387\) 1.00000 1.73205i 0.0508329 0.0880451i
\(388\) −4.94975 8.57321i −0.251285 0.435239i
\(389\) −13.0000 22.5167i −0.659126 1.14164i −0.980842 0.194804i \(-0.937593\pi\)
0.321716 0.946836i \(-0.395740\pi\)
\(390\) 0 0
\(391\) 5.65685 0.286079
\(392\) 0 0
\(393\) −18.0000 −0.907980
\(394\) −1.00000 + 1.73205i −0.0503793 + 0.0872595i
\(395\) 5.65685 + 9.79796i 0.284627 + 0.492989i
\(396\) −1.00000 1.73205i −0.0502519 0.0870388i
\(397\) −11.3137 + 19.5959i −0.567819 + 0.983491i 0.428963 + 0.903322i \(0.358879\pi\)
−0.996781 + 0.0801687i \(0.974454\pi\)
\(398\) 8.48528 0.425329
\(399\) 0 0
\(400\) 3.00000 0.150000
\(401\) 9.00000 15.5885i 0.449439 0.778450i −0.548911 0.835881i \(-0.684957\pi\)
0.998350 + 0.0574304i \(0.0182907\pi\)
\(402\) 8.48528 + 14.6969i 0.423207 + 0.733017i
\(403\) 0 0
\(404\) −4.24264 + 7.34847i −0.211079 + 0.365600i
\(405\) −14.1421 −0.702728
\(406\) 0 0
\(407\) −20.0000 −0.991363
\(408\) −1.00000 + 1.73205i −0.0495074 + 0.0857493i
\(409\) −19.0919 33.0681i −0.944033 1.63511i −0.757676 0.652631i \(-0.773665\pi\)
−0.186357 0.982482i \(-0.559668\pi\)
\(410\) 14.0000 + 24.2487i 0.691411 + 1.19756i
\(411\) 8.48528 14.6969i 0.418548 0.724947i
\(412\) 2.82843 0.139347
\(413\) 0 0
\(414\) 4.00000 0.196589
\(415\) −14.0000 + 24.2487i −0.687233 + 1.19032i
\(416\) 0 0
\(417\) 7.00000 + 12.1244i 0.342791 + 0.593732i
\(418\) −7.07107 + 12.2474i −0.345857 + 0.599042i
\(419\) −9.89949 −0.483622 −0.241811 0.970323i \(-0.577741\pi\)
−0.241811 + 0.970323i \(0.577741\pi\)
\(420\) 0 0
\(421\) 30.0000 1.46211 0.731055 0.682318i \(-0.239028\pi\)
0.731055 + 0.682318i \(0.239028\pi\)
\(422\) 6.00000 10.3923i 0.292075 0.505889i
\(423\) 1.41421 + 2.44949i 0.0687614 + 0.119098i
\(424\) 1.00000 + 1.73205i 0.0485643 + 0.0841158i
\(425\) 2.12132 3.67423i 0.102899 0.178227i
\(426\) 16.9706 0.822226
\(427\) 0 0
\(428\) −4.00000 −0.193347
\(429\) 0 0
\(430\) −2.82843 4.89898i −0.136399 0.236250i
\(431\) −6.00000 10.3923i −0.289010 0.500580i 0.684564 0.728953i \(-0.259993\pi\)
−0.973574 + 0.228373i \(0.926659\pi\)
\(432\) −2.82843 + 4.89898i −0.136083 + 0.235702i
\(433\) −29.6985 −1.42722 −0.713609 0.700544i \(-0.752941\pi\)
−0.713609 + 0.700544i \(0.752941\pi\)
\(434\) 0 0
\(435\) −8.00000 −0.383571
\(436\) 1.00000 1.73205i 0.0478913 0.0829502i
\(437\) −14.1421 24.4949i −0.676510 1.17175i
\(438\) −1.00000 1.73205i −0.0477818 0.0827606i
\(439\) 8.48528 14.6969i 0.404980 0.701447i −0.589339 0.807886i \(-0.700612\pi\)
0.994319 + 0.106439i \(0.0339450\pi\)
\(440\) −5.65685 −0.269680
\(441\) 0 0
\(442\) 0 0
\(443\) 2.00000 3.46410i 0.0950229 0.164584i −0.814595 0.580030i \(-0.803041\pi\)
0.909618 + 0.415445i \(0.136374\pi\)
\(444\) 7.07107 + 12.2474i 0.335578 + 0.581238i
\(445\) 10.0000 + 17.3205i 0.474045 + 0.821071i
\(446\) 0 0
\(447\) −14.1421 −0.668900
\(448\) 0 0
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 1.50000 2.59808i 0.0707107 0.122474i
\(451\) −9.89949 17.1464i −0.466149 0.807394i
\(452\) 6.00000 + 10.3923i 0.282216 + 0.488813i
\(453\) −11.3137 + 19.5959i −0.531564 + 0.920697i
\(454\) −21.2132 −0.995585
\(455\) 0 0
\(456\) 10.0000 0.468293
\(457\) −12.0000 + 20.7846i −0.561336 + 0.972263i 0.436044 + 0.899925i \(0.356379\pi\)
−0.997380 + 0.0723376i \(0.976954\pi\)
\(458\) 8.48528 + 14.6969i 0.396491 + 0.686743i
\(459\) 4.00000 + 6.92820i 0.186704 + 0.323381i
\(460\) 5.65685 9.79796i 0.263752 0.456832i
\(461\) 39.5980 1.84426 0.922131 0.386878i \(-0.126447\pi\)
0.922131 + 0.386878i \(0.126447\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) −1.00000 + 1.73205i −0.0464238 + 0.0804084i
\(465\) 16.9706 + 29.3939i 0.786991 + 1.36311i
\(466\) −12.0000 20.7846i −0.555889 0.962828i
\(467\) −16.2635 + 28.1691i −0.752583 + 1.30351i 0.193984 + 0.981005i \(0.437859\pi\)
−0.946567 + 0.322507i \(0.895474\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 8.00000 0.369012
\(471\) −8.00000 + 13.8564i −0.368621 + 0.638470i
\(472\) 0.707107 + 1.22474i 0.0325472 + 0.0563735i
\(473\) 2.00000 + 3.46410i 0.0919601 + 0.159280i
\(474\) −2.82843 + 4.89898i −0.129914 + 0.225018i
\(475\) −21.2132 −0.973329
\(476\) 0 0
\(477\) 2.00000 0.0915737
\(478\) 6.00000 10.3923i 0.274434 0.475333i
\(479\) 15.5563 + 26.9444i 0.710788 + 1.23112i 0.964562 + 0.263857i \(0.0849947\pi\)
−0.253774 + 0.967264i \(0.581672\pi\)
\(480\) 2.00000 + 3.46410i 0.0912871 + 0.158114i
\(481\) 0 0
\(482\) −21.2132 −0.966235
\(483\) 0 0
\(484\) −7.00000 −0.318182
\(485\) −14.0000 + 24.2487i −0.635707 + 1.10108i
\(486\) 4.94975 + 8.57321i 0.224525 + 0.388889i
\(487\) −6.00000 10.3923i −0.271886 0.470920i 0.697459 0.716625i \(-0.254314\pi\)
−0.969345 + 0.245705i \(0.920981\pi\)
\(488\) −1.41421 + 2.44949i −0.0640184 + 0.110883i
\(489\) −14.1421 −0.639529
\(490\) 0 0
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) −7.00000 + 12.1244i −0.315584 + 0.546608i
\(493\) 1.41421 + 2.44949i 0.0636930 + 0.110319i
\(494\) 0 0
\(495\) −2.82843 + 4.89898i −0.127128 + 0.220193i
\(496\) 8.48528 0.381000
\(497\) 0 0
\(498\) −14.0000 −0.627355
\(499\) 2.00000 3.46410i 0.0895323 0.155074i −0.817781 0.575529i \(-0.804796\pi\)
0.907314 + 0.420455i \(0.138129\pi\)
\(500\) 2.82843 + 4.89898i 0.126491 + 0.219089i
\(501\) −14.0000 24.2487i −0.625474 1.08335i
\(502\) −4.94975 + 8.57321i −0.220918 + 0.382641i
\(503\) 39.5980 1.76559 0.882793 0.469762i \(-0.155660\pi\)
0.882793 + 0.469762i \(0.155660\pi\)
\(504\) 0 0
\(505\) 24.0000 1.06799
\(506\) −4.00000 + 6.92820i −0.177822 + 0.307996i
\(507\) −9.19239 15.9217i −0.408248 0.707107i
\(508\) −8.00000 13.8564i −0.354943 0.614779i
\(509\) −11.3137 + 19.5959i −0.501471 + 0.868574i 0.498527 + 0.866874i \(0.333874\pi\)
−0.999999 + 0.00169976i \(0.999459\pi\)
\(510\) 5.65685 0.250490
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 20.0000 34.6410i 0.883022 1.52944i
\(514\) −6.36396 11.0227i −0.280702 0.486191i
\(515\) −4.00000 6.92820i −0.176261 0.305293i
\(516\) 1.41421 2.44949i 0.0622573 0.107833i
\(517\) −5.65685 −0.248788
\(518\) 0 0
\(519\) 24.0000 1.05348
\(520\) 0 0
\(521\) 0.707107 + 1.22474i 0.0309789 + 0.0536570i 0.881099 0.472931i \(-0.156804\pi\)
−0.850120 + 0.526589i \(0.823471\pi\)
\(522\) 1.00000 + 1.73205i 0.0437688 + 0.0758098i
\(523\) −6.36396 + 11.0227i −0.278277 + 0.481989i −0.970957 0.239256i \(-0.923097\pi\)
0.692680 + 0.721245i \(0.256430\pi\)
\(524\) 12.7279 0.556022
\(525\) 0 0
\(526\) 12.0000 0.523225
\(527\) 6.00000 10.3923i 0.261364 0.452696i
\(528\) −1.41421 2.44949i −0.0615457 0.106600i
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) 2.82843 4.89898i 0.122859 0.212798i
\(531\) 1.41421 0.0613716
\(532\) 0 0
\(533\) 0 0
\(534\) −5.00000 + 8.66025i −0.216371 + 0.374766i
\(535\) 5.65685 + 9.79796i 0.244567 + 0.423603i
\(536\) −6.00000 10.3923i −0.259161 0.448879i
\(537\) 8.48528 14.6969i 0.366167 0.634220i
\(538\) −11.3137 −0.487769
\(539\) 0 0
\(540\) 16.0000 0.688530
\(541\) −5.00000 + 8.66025i −0.214967 + 0.372333i −0.953262 0.302144i \(-0.902298\pi\)
0.738296 + 0.674477i \(0.235631\pi\)
\(542\) −11.3137 19.5959i −0.485965 0.841717i
\(543\) 0 0
\(544\) 0.707107 1.22474i 0.0303170 0.0525105i
\(545\) −5.65685 −0.242313
\(546\) 0 0
\(547\) −26.0000 −1.11168 −0.555840 0.831289i \(-0.687603\pi\)
−0.555840 + 0.831289i \(0.687603\pi\)
\(548\) −6.00000 + 10.3923i −0.256307 + 0.443937i
\(549\) 1.41421 + 2.44949i 0.0603572 + 0.104542i
\(550\) 3.00000 + 5.19615i 0.127920 + 0.221565i
\(551\) 7.07107 12.2474i 0.301238 0.521759i
\(552\) 5.65685 0.240772
\(553\) 0 0
\(554\) −2.00000 −0.0849719
\(555\) 20.0000 34.6410i 0.848953 1.47043i
\(556\) −4.94975 8.57321i −0.209916 0.363585i
\(557\) 15.0000 + 25.9808i 0.635570 + 1.10084i 0.986394 + 0.164399i \(0.0525683\pi\)
−0.350824 + 0.936442i \(0.614098\pi\)
\(558\) 4.24264 7.34847i 0.179605 0.311086i
\(559\) 0 0
\(560\) 0 0
\(561\) −4.00000 −0.168880
\(562\) −8.00000 + 13.8564i −0.337460 + 0.584497i
\(563\) 0.707107 + 1.22474i 0.0298010 + 0.0516168i 0.880541 0.473970i \(-0.157179\pi\)
−0.850740 + 0.525586i \(0.823846\pi\)
\(564\) 2.00000 + 3.46410i 0.0842152 + 0.145865i
\(565\) 16.9706 29.3939i 0.713957 1.23661i
\(566\) −1.41421 −0.0594438
\(567\) 0 0
\(568\) −12.0000 −0.503509
\(569\) −5.00000 + 8.66025i −0.209611 + 0.363057i −0.951592 0.307364i \(-0.900553\pi\)
0.741981 + 0.670421i \(0.233886\pi\)
\(570\) −14.1421 24.4949i −0.592349 1.02598i
\(571\) 1.00000 + 1.73205i 0.0418487 + 0.0724841i 0.886191 0.463320i \(-0.153342\pi\)
−0.844342 + 0.535804i \(0.820009\pi\)
\(572\) 0 0
\(573\) 5.65685 0.236318
\(574\) 0 0
\(575\) −12.0000 −0.500435
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 10.6066 + 18.3712i 0.441559 + 0.764802i 0.997805 0.0662152i \(-0.0210924\pi\)
−0.556247 + 0.831017i \(0.687759\pi\)
\(578\) 7.50000 + 12.9904i 0.311959 + 0.540329i
\(579\) −11.3137 + 19.5959i −0.470182 + 0.814379i
\(580\) 5.65685 0.234888
\(581\) 0 0
\(582\) −14.0000 −0.580319
\(583\) −2.00000 + 3.46410i −0.0828315 + 0.143468i
\(584\) 0.707107 + 1.22474i 0.0292603 + 0.0506803i
\(585\) 0 0
\(586\) 9.89949 17.1464i 0.408944 0.708312i
\(587\) −29.6985 −1.22579 −0.612894 0.790165i \(-0.709995\pi\)
−0.612894 + 0.790165i \(0.709995\pi\)
\(588\) 0 0
\(589\) −60.0000 −2.47226
\(590\) 2.00000 3.46410i 0.0823387 0.142615i
\(591\) 1.41421 + 2.44949i 0.0581730 + 0.100759i
\(592\) −5.00000 8.66025i −0.205499 0.355934i
\(593\) 3.53553 6.12372i 0.145187 0.251471i −0.784256 0.620438i \(-0.786955\pi\)
0.929443 + 0.368967i \(0.120288\pi\)
\(594\) −11.3137 −0.464207
\(595\) 0 0
\(596\) 10.0000 0.409616
\(597\) 6.00000 10.3923i 0.245564 0.425329i
\(598\) 0 0
\(599\) 8.00000 + 13.8564i 0.326871 + 0.566157i 0.981889 0.189456i \(-0.0606724\pi\)
−0.655018 + 0.755613i \(0.727339\pi\)
\(600\) 2.12132 3.67423i 0.0866025 0.150000i
\(601\) 29.6985 1.21143 0.605713 0.795683i \(-0.292888\pi\)
0.605713 + 0.795683i \(0.292888\pi\)
\(602\) 0 0
\(603\) −12.0000 −0.488678
\(604\) 8.00000 13.8564i 0.325515 0.563809i
\(605\) 9.89949 + 17.1464i 0.402472 + 0.697101i
\(606\) 6.00000 + 10.3923i 0.243733 + 0.422159i
\(607\) 8.48528 14.6969i 0.344407 0.596530i −0.640839 0.767675i \(-0.721413\pi\)
0.985246 + 0.171145i \(0.0547467\pi\)
\(608\) −7.07107 −0.286770
\(609\) 0 0
\(610\) 8.00000 0.323911
\(611\) 0 0
\(612\) −0.707107 1.22474i −0.0285831 0.0495074i
\(613\) 15.0000 + 25.9808i 0.605844 + 1.04935i 0.991917 + 0.126885i \(0.0404979\pi\)
−0.386073 + 0.922468i \(0.626169\pi\)
\(614\) 4.94975 8.57321i 0.199756 0.345987i
\(615\) 39.5980 1.59674
\(616\) 0 0
\(617\) −26.0000 −1.04672 −0.523360 0.852111i \(-0.675322\pi\)
−0.523360 + 0.852111i \(0.675322\pi\)
\(618\) 2.00000 3.46410i 0.0804518 0.139347i
\(619\) −9.19239 15.9217i −0.369473 0.639946i 0.620010 0.784594i \(-0.287129\pi\)
−0.989483 + 0.144647i \(0.953795\pi\)
\(620\) −12.0000 20.7846i −0.481932 0.834730i
\(621\) 11.3137 19.5959i 0.454003 0.786357i
\(622\) −11.3137 −0.453638
\(623\) 0 0
\(624\) 0 0
\(625\) 15.5000 26.8468i 0.620000 1.07387i
\(626\) −6.36396 11.0227i −0.254355 0.440556i
\(627\) 10.0000 + 17.3205i 0.399362 + 0.691714i
\(628\) 5.65685 9.79796i 0.225733 0.390981i
\(629\) −14.1421 −0.563884
\(630\) 0 0
\(631\) 44.0000 1.75161 0.875806 0.482663i \(-0.160330\pi\)
0.875806 + 0.482663i \(0.160330\pi\)
\(632\) 2.00000 3.46410i 0.0795557 0.137795i
\(633\) −8.48528 14.6969i −0.337260 0.584151i
\(634\) −5.00000 8.66025i −0.198575 0.343943i
\(635\) −22.6274 + 39.1918i −0.897942 + 1.55528i
\(636\) 2.82843 0.112154
\(637\) 0 0
\(638\) −4.00000 −0.158362
\(639\) −6.00000 + 10.3923i −0.237356 + 0.411113i
\(640\) −1.41421 2.44949i −0.0559017 0.0968246i
\(641\) −13.0000 22.5167i −0.513469 0.889355i −0.999878 0.0156233i \(-0.995027\pi\)
0.486409 0.873731i \(-0.338307\pi\)
\(642\) −2.82843 + 4.89898i −0.111629 + 0.193347i
\(643\) 9.89949 0.390398 0.195199 0.980764i \(-0.437465\pi\)
0.195199 + 0.980764i \(0.437465\pi\)
\(644\) 0 0
\(645\) −8.00000 −0.315000
\(646\) −5.00000 + 8.66025i −0.196722 + 0.340733i
\(647\) −4.24264 7.34847i −0.166795 0.288898i 0.770496 0.637445i \(-0.220009\pi\)
−0.937291 + 0.348547i \(0.886675\pi\)
\(648\) 2.50000 + 4.33013i 0.0982093 + 0.170103i
\(649\) −1.41421 + 2.44949i −0.0555127 + 0.0961509i
\(650\) 0 0
\(651\) 0 0
\(652\) 10.0000 0.391630
\(653\) 9.00000 15.5885i 0.352197 0.610023i −0.634437 0.772975i \(-0.718768\pi\)
0.986634 + 0.162951i \(0.0521013\pi\)
\(654\) −1.41421 2.44949i −0.0553001 0.0957826i
\(655\) −18.0000 31.1769i −0.703318 1.21818i
\(656\) 4.94975 8.57321i 0.193255 0.334728i
\(657\) 1.41421 0.0551737
\(658\) 0 0
\(659\) 30.0000 1.16863 0.584317 0.811525i \(-0.301362\pi\)
0.584317 + 0.811525i \(0.301362\pi\)
\(660\) −4.00000 + 6.92820i −0.155700 + 0.269680i
\(661\) −4.24264 7.34847i −0.165020 0.285822i 0.771643 0.636056i \(-0.219435\pi\)
−0.936662 + 0.350234i \(0.886102\pi\)
\(662\) −5.00000 8.66025i −0.194331 0.336590i
\(663\) 0 0
\(664\) 9.89949 0.384175
\(665\) 0 0
\(666\) −10.0000 −0.387492
\(667\) 4.00000 6.92820i 0.154881 0.268261i
\(668\) 9.89949 + 17.1464i 0.383023 + 0.663415i
\(669\) 0 0
\(670\) −16.9706 + 29.3939i −0.655630 + 1.13558i
\(671\) −5.65685 −0.218380
\(672\) 0 0
\(673\) −12.0000 −0.462566 −0.231283 0.972887i \(-0.574292\pi\)
−0.231283 + 0.972887i \(0.574292\pi\)
\(674\) −1.00000 + 1.73205i −0.0385186 + 0.0667161i
\(675\) −8.48528 14.6969i −0.326599 0.565685i
\(676\) 6.50000 + 11.2583i 0.250000 + 0.433013i
\(677\) 8.48528 14.6969i 0.326116 0.564849i −0.655622 0.755090i \(-0.727593\pi\)
0.981738 + 0.190240i \(0.0609267\pi\)
\(678\) 16.9706 0.651751
\(679\) 0 0
\(680\) −4.00000 −0.153393
\(681\) −15.0000 + 25.9808i −0.574801 + 0.995585i
\(682\) 8.48528 + 14.6969i 0.324918 + 0.562775i
\(683\) −6.00000 10.3923i −0.229584 0.397650i 0.728101 0.685470i \(-0.240403\pi\)
−0.957685 + 0.287819i \(0.907070\pi\)
\(684\) −3.53553 + 6.12372i −0.135185 + 0.234146i
\(685\) 33.9411 1.29682
\(686\) 0 0
\(687\) 24.0000 0.915657
\(688\) −1.00000 + 1.73205i −0.0381246 + 0.0660338i
\(689\) 0 0
\(690\) −8.00000 13.8564i −0.304555 0.527504i
\(691\) −6.36396 + 11.0227i −0.242096 + 0.419323i −0.961311 0.275464i \(-0.911168\pi\)
0.719215 + 0.694788i \(0.244502\pi\)
\(692\) −16.9706 −0.645124
\(693\) 0 0
\(694\) −30.0000 −1.13878
\(695\) −14.0000 + 24.2487i −0.531050 + 0.919806i
\(696\) 1.41421 + 2.44949i 0.0536056 + 0.0928477i
\(697\) −7.00000 12.1244i −0.265144 0.459243i
\(698\) 0 0
\(699\) −33.9411 −1.28377
\(700\) 0 0
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0 0
\(703\) 35.3553 + 61.2372i 1.33345 + 2.30961i
\(704\) 1.00000 + 1.73205i 0.0376889 + 0.0652791i
\(705\) 5.65685 9.79796i 0.213049 0.369012i
\(706\) −1.41421 −0.0532246
\(707\) 0 0
\(708\) 2.00000 0.0751646
\(709\) −5.00000 + 8.66025i −0.187779 + 0.325243i −0.944509 0.328484i \(-0.893462\pi\)
0.756730 + 0.653727i \(0.226796\pi\)
\(710\) 16.9706 + 29.3939i 0.636894 + 1.10313i
\(711\) −2.00000 3.46410i −0.0750059 0.129914i
\(712\) 3.53553 6.12372i 0.132500 0.229496i
\(713\) −33.9411 −1.27111
\(714\) 0 0
\(715\) 0 0
\(716\) −6.00000 + 10.3923i −0.224231 + 0.388379i
\(717\) −8.48528 14.6969i −0.316889 0.548867i
\(718\) 16.0000 + 27.7128i 0.597115 + 1.03423i
\(719\) −1.41421 + 2.44949i −0.0527413 + 0.0913506i −0.891191 0.453629i \(-0.850129\pi\)
0.838449 + 0.544979i \(0.183463\pi\)
\(720\) −2.82843 −0.105409
\(721\) 0 0
\(722\) 31.0000 1.15370
\(723\) −15.0000 + 25.9808i −0.557856 + 0.966235i
\(724\) 0 0
\(725\) −3.00000 5.19615i −0.111417 0.192980i
\(726\) −4.94975 + 8.57321i −0.183702 + 0.318182i
\(727\) −19.7990 −0.734304 −0.367152 0.930161i \(-0.619667\pi\)
−0.367152 + 0.930161i \(0.619667\pi\)
\(728\) 0 0
\(729\) 29.0000 1.07407
\(730\) 2.00000 3.46410i 0.0740233 0.128212i
\(731\) 1.41421 + 2.44949i 0.0523066 + 0.0905977i
\(732\) 2.00000 + 3.46410i 0.0739221 + 0.128037i
\(733\) −21.2132 + 36.7423i −0.783528 + 1.35711i 0.146347 + 0.989233i \(0.453248\pi\)
−0.929875 + 0.367876i \(0.880085\pi\)
\(734\) 28.2843 1.04399
\(735\) 0 0
\(736\) −4.00000 −0.147442
\(737\) 12.0000 20.7846i 0.442026 0.765611i
\(738\) −4.94975 8.57321i −0.182203 0.315584i
\(739\) 15.0000 + 25.9808i 0.551784 + 0.955718i 0.998146 + 0.0608653i \(0.0193860\pi\)
−0.446362 + 0.894852i \(0.647281\pi\)
\(740\) −14.1421 + 24.4949i −0.519875 + 0.900450i
\(741\) 0 0
\(742\) 0 0
\(743\) 16.0000 0.586983 0.293492 0.955962i \(-0.405183\pi\)
0.293492 + 0.955962i \(0.405183\pi\)
\(744\) 6.00000 10.3923i 0.219971 0.381000i
\(745\) −14.1421 24.4949i −0.518128 0.897424i
\(746\) −5.00000 8.66025i −0.183063 0.317074i
\(747\) 4.94975 8.57321i 0.181102 0.313678i
\(748\) 2.82843 0.103418
\(749\) 0 0
\(750\) 8.00000 0.292119
\(751\) 2.00000 3.46410i 0.0729810 0.126407i −0.827225 0.561870i \(-0.810082\pi\)
0.900207 + 0.435463i \(0.143415\pi\)
\(752\) −1.41421 2.44949i −0.0515711 0.0893237i
\(753\) 7.00000 + 12.1244i 0.255094 + 0.441836i
\(754\) 0 0
\(755\) −45.2548 −1.64699
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 13.0000 22.5167i 0.472181 0.817842i
\(759\) 5.65685 + 9.79796i 0.205331 + 0.355643i
\(760\) 10.0000 + 17.3205i 0.362738 + 0.628281i
\(761\) 3.53553 6.12372i 0.128163 0.221985i −0.794802 0.606869i \(-0.792425\pi\)
0.922965 + 0.384884i \(0.125759\pi\)
\(762\) −22.6274 −0.819705
\(763\) 0 0
\(764\) −4.00000 −0.144715
\(765\) −2.00000 + 3.46410i −0.0723102 + 0.125245i
\(766\) 18.3848 + 31.8434i 0.664269 + 1.15055i
\(767\) 0 0
\(768\) 0.707107 1.22474i 0.0255155 0.0441942i
\(769\) 29.6985 1.07095 0.535477 0.844550i \(-0.320132\pi\)
0.535477 + 0.844550i \(0.320132\pi\)
\(770\) 0 0
\(771\) −18.0000 −0.648254
\(772\) 8.00000 13.8564i 0.287926 0.498703i
\(773\) −24.0416 41.6413i −0.864717 1.49773i −0.867328 0.497738i \(-0.834164\pi\)
0.00261021 0.999997i \(-0.499169\pi\)
\(774\) 1.00000 + 1.73205i 0.0359443 + 0.0622573i
\(775\) −12.7279 + 22.0454i −0.457200 + 0.791894i
\(776\) 9.89949 0.355371
\(777\) 0 0
\(778\) 26.0000 0.932145
\(779\) −35.0000 + 60.6218i −1.25401 + 2.17200i
\(780\) 0 0
\(781\) −12.0000 20.7846i −0.429394 0.743732i
\(782\) −2.82843 + 4.89898i −0.101144 + 0.175187i
\(783\) 11.3137 0.404319
\(784\) 0 0
\(785\) −32.0000 −1.14213
\(786\) 9.00000 15.5885i 0.321019 0.556022i
\(787\) 0.707107 + 1.22474i 0.0252056 + 0.0436574i 0.878353 0.478012i \(-0.158643\pi\)
−0.853147 + 0.521670i \(0.825309\pi\)
\(788\) −1.00000 1.73205i −0.0356235 0.0617018i
\(789\) 8.48528 14.6969i 0.302084 0.523225i
\(790\) −11.3137 −0.402524
\(791\) 0 0
\(792\) 2.00000 0.0710669
\(793\) 0 0
\(794\) −11.3137 19.5959i −0.401508 0.695433i
\(795\) −4.00000 6.92820i −0.141865 0.245718i
\(796\) −4.24264 + 7.34847i −0.150376 + 0.260460i
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) −4.00000 −0.141510
\(800\) −1.50000 + 2.59808i −0.0530330 + 0.0918559i
\(801\) −3.53553 6.12372i −0.124922 0.216371i
\(802\) 9.00000 + 15.5885i 0.317801 + 0.550448i
\(803\) −1.41421 + 2.44949i −0.0499065 + 0.0864406i
\(804\) −16.9706 −0.598506
\(805\) 0 0
\(806\) 0 0
\(807\) −8.00000 + 13.8564i −0.281613 + 0.487769i
\(808\) −4.24264 7.34847i −0.149256 0.258518i
\(809\) 8.00000 + 13.8564i 0.281265 + 0.487165i 0.971697 0.236232i \(-0.0759127\pi\)
−0.690432 + 0.723398i \(0.742579\pi\)
\(810\) 7.07107 12.2474i 0.248452 0.430331i
\(811\) −29.6985 −1.04285 −0.521427 0.853296i \(-0.674600\pi\)
−0.521427 + 0.853296i \(0.674600\pi\)
\(812\) 0 0
\(813\) −32.0000 −1.12229
\(814\) 10.0000 17.3205i 0.350500 0.607083i
\(815\) −14.1421 24.4949i −0.495377 0.858019i
\(816\) −1.00000 1.73205i −0.0350070 0.0606339i
\(817\) 7.07107 12.2474i 0.247385 0.428484i
\(818\) 38.1838 1.33506
\(819\) 0 0
\(820\) −28.0000 −0.977802
\(821\) 9.00000 15.5885i 0.314102 0.544041i −0.665144 0.746715i \(-0.731630\pi\)
0.979246 + 0.202674i \(0.0649632\pi\)
\(822\) 8.48528 + 14.6969i 0.295958 + 0.512615i
\(823\) −20.0000 34.6410i −0.697156 1.20751i −0.969448 0.245295i \(-0.921115\pi\)
0.272292 0.962215i \(-0.412218\pi\)
\(824\) −1.41421 + 2.44949i −0.0492665 + 0.0853320i
\(825\) 8.48528 0.295420
\(826\) 0 0
\(827\) −12.0000 −0.417281 −0.208640 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) −2.00000 + 3.46410i −0.0695048 + 0.120386i
\(829\) 15.5563 + 26.9444i 0.540294 + 0.935817i 0.998887 + 0.0471706i \(0.0150204\pi\)
−0.458593 + 0.888647i \(0.651646\pi\)
\(830\) −14.0000 24.2487i −0.485947 0.841685i
\(831\) −1.41421 + 2.44949i −0.0490585 + 0.0849719i
\(832\) 0 0
\(833\) 0 0
\(834\) −14.0000 −0.484780
\(835\) 28.0000 48.4974i 0.968980 1.67832i
\(836\) −7.07107 12.2474i −0.244558 0.423587i
\(837\) −24.0000 41.5692i −0.829561 1.43684i
\(838\) 4.94975 8.57321i 0.170986 0.296157i
\(839\) 19.7990 0.683537 0.341769 0.939784i \(-0.388974\pi\)
0.341769 + 0.939784i \(0.388974\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) −15.0000 + 25.9808i −0.516934 + 0.895356i
\(843\) 11.3137 + 19.5959i 0.389665 + 0.674919i
\(844\) 6.00000 + 10.3923i 0.206529 + 0.357718i
\(845\) 18.3848 31.8434i 0.632456 1.09545i
\(846\) −2.82843 −0.0972433
\(847\) 0 0
\(848\) −2.00000 −0.0686803
\(849\) −1.00000 + 1.73205i −0.0343199 + 0.0594438i
\(850\) 2.12132 + 3.67423i 0.0727607 + 0.126025i
\(851\) 20.0000 + 34.6410i 0.685591 + 1.18748i
\(852\) −8.48528 + 14.6969i −0.290701 + 0.503509i
\(853\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(854\) 0 0
\(855\) 20.0000 0.683986
\(856\) 2.00000 3.46410i 0.0683586 0.118401i
\(857\) −9.19239 15.9217i −0.314006 0.543874i 0.665220 0.746648i \(-0.268338\pi\)
−0.979226 + 0.202773i \(0.935005\pi\)
\(858\) 0 0
\(859\) 13.4350 23.2702i 0.458397 0.793967i −0.540479 0.841357i \(-0.681757\pi\)
0.998876 + 0.0473900i \(0.0150904\pi\)
\(860\) 5.65685 0.192897
\(861\) 0 0
\(862\) 12.0000 0.408722
\(863\) 2.00000 3.46410i 0.0680808 0.117919i −0.829976 0.557800i \(-0.811646\pi\)
0.898056 + 0.439880i \(0.144979\pi\)
\(864\) −2.82843 4.89898i −0.0962250 0.166667i
\(865\) 24.0000 + 41.5692i 0.816024 + 1.41340i
\(866\) 14.8492 25.7196i 0.504598 0.873989i
\(867\) 21.2132 0.720438
\(868\) 0 0
\(869\) 8.00000 0.271381
\(870\) 4.00000 6.92820i 0.135613 0.234888i
\(871\) 0 0
\(872\) 1.00000 + 1.73205i 0.0338643 + 0.0586546i
\(873\) 4.94975 8.57321i 0.167524 0.290159i
\(874\) 28.2843 0.956730
\(875\) 0 0
\(876\) 2.00000 0.0675737
\(877\) 23.0000 39.8372i 0.776655 1.34521i −0.157205 0.987566i \(-0.550248\pi\)
0.933860 0.357640i \(-0.116418\pi\)
\(878\) 8.48528 + 14.6969i 0.286364 + 0.495998i
\(879\) −14.0000 24.2487i −0.472208 0.817889i
\(880\) 2.82843 4.89898i 0.0953463 0.165145i
\(881\) 29.6985 1.00057 0.500284 0.865862i \(-0.333229\pi\)
0.500284 + 0.865862i \(0.333229\pi\)
\(882\) 0 0
\(883\) 44.0000 1.48072 0.740359 0.672212i \(-0.234656\pi\)
0.740359 + 0.672212i \(0.234656\pi\)
\(884\) 0 0
\(885\) −2.82843 4.89898i −0.0950765 0.164677i
\(886\) 2.00000 + 3.46410i 0.0671913 + 0.116379i
\(887\) 18.3848 31.8434i 0.617300 1.06920i −0.372676 0.927962i \(-0.621560\pi\)
0.989976 0.141234i \(-0.0451070\pi\)
\(888\) −14.1421 −0.474579
\(889\) 0 0
\(890\) −20.0000 −0.670402
\(891\) −5.00000 + 8.66025i −0.167506 + 0.290129i
\(892\) 0 0
\(893\) 10.0000 + 17.3205i 0.334637 + 0.579609i
\(894\) 7.07107 12.2474i 0.236492 0.409616i
\(895\) 33.9411 1.13453
\(896\) 0 0
\(897\) 0 0
\(898\) −15.0000 + 25.9808i −0.500556 + 0.866989i
\(899\) −8.48528 14.6969i −0.283000 0.490170i
\(900\) 1.50000 + 2.59808i 0.0500000 + 0.0866025i
\(901\) −1.41421 + 2.44949i −0.0471143 + 0.0816043i
\(902\) 19.7990 0.659234
\(903\) 0 0
\(904\) −12.0000 −0.399114
\(905\) 0 0
\(906\) −11.3137 19.5959i −0.375873 0.651031i
\(907\) 22.0000 + 38.1051i 0.730498 + 1.26526i 0.956671 + 0.291172i \(0.0940453\pi\)
−0.226173 + 0.974087i \(0.572621\pi\)
\(908\) 10.6066 18.3712i 0.351992 0.609669i
\(909\) −8.48528 −0.281439
\(910\) 0 0
\(911\) −40.0000 −1.32526 −0.662630 0.748947i \(-0.730560\pi\)
−0.662630 + 0.748947i \(0.730560\pi\)
\(912\) −5.00000 + 8.66025i −0.165567 + 0.286770i
\(913\) 9.89949 + 17.1464i 0.327625 + 0.567464i
\(914\) −12.0000 20.7846i −0.396925 0.687494i
\(915\) 5.65685 9.79796i 0.187010 0.323911i
\(916\) −16.9706 −0.560723
\(917\) 0 0
\(918\) −8.00000 −0.264039
\(919\) 16.0000 27.7128i 0.527791 0.914161i −0.471684 0.881768i \(-0.656354\pi\)
0.999475 0.0323936i \(-0.0103130\pi\)
\(920\) 5.65685 + 9.79796i 0.186501 + 0.323029i
\(921\) −7.00000 12.1244i −0.230658 0.399511i
\(922\) −19.7990 + 34.2929i −0.652045 + 1.12938i
\(923\) 0 0
\(924\) 0 0
\(925\) 30.0000 0.986394
\(926\) −8.00000 + 13.8564i −0.262896 + 0.455350i
\(927\) 1.41421 + 2.44949i 0.0464489 + 0.0804518i
\(928\) −1.00000 1.73205i −0.0328266 0.0568574i
\(929\) −16.2635 + 28.1691i −0.533587 + 0.924199i 0.465644 + 0.884972i \(0.345823\pi\)
−0.999230 + 0.0392269i \(0.987510\pi\)
\(930\) −33.9411 −1.11297
\(931\) 0 0
\(932\) 24.0000 0.786146
\(933\) −8.00000 + 13.8564i −0.261908 + 0.453638i
\(934\) −16.2635 28.1691i −0.532157 0.921722i
\(935\) −4.00000 6.92820i −0.130814 0.226576i
\(936\) 0 0
\(937\) 9.89949 0.323402 0.161701 0.986840i \(-0.448302\pi\)
0.161701 + 0.986840i \(0.448302\pi\)
\(938\) 0 0
\(939\) −18.0000 −0.587408
\(940\) −4.00000 + 6.92820i −0.130466 + 0.225973i
\(941\) 15.5563 + 26.9444i 0.507122 + 0.878362i 0.999966 + 0.00824396i \(0.00262416\pi\)
−0.492844 + 0.870118i \(0.664043\pi\)
\(942\) −8.00000 13.8564i −0.260654 0.451466i
\(943\) −19.7990 + 34.2929i −0.644744 + 1.11673i
\(944\) −1.41421 −0.0460287
\(945\) 0 0
\(946\) −4.00000 −0.130051
\(947\) 9.00000 15.5885i 0.292461 0.506557i −0.681930 0.731417i \(-0.738859\pi\)
0.974391 + 0.224860i \(0.0721926\pi\)
\(948\) −2.82843 4.89898i −0.0918630 0.159111i
\(949\) 0 0
\(950\) 10.6066 18.3712i 0.344124 0.596040i
\(951\) −14.1421 −0.458590
\(952\) 0 0
\(953\) −26.0000 −0.842223 −0.421111 0.907009i \(-0.638360\pi\)
−0.421111 + 0.907009i \(0.638360\pi\)
\(954\) −1.00000 + 1.73205i −0.0323762 + 0.0560772i
\(955\) 5.65685 + 9.79796i 0.183052 + 0.317055i
\(956\) 6.00000 + 10.3923i 0.194054 + 0.336111i
\(957\) −2.82843 + 4.89898i −0.0914301 + 0.158362i
\(958\) −31.1127 −1.00521
\(959\) 0 0
\(960\) −4.00000 −0.129099
\(961\) −20.5000 + 35.5070i −0.661290 + 1.14539i
\(962\) 0 0
\(963\) −2.00000 3.46410i −0.0644491 0.111629i
\(964\) 10.6066 18.3712i 0.341616 0.591696i
\(965\) −45.2548 −1.45680
\(966\) 0 0
\(967\) −12.0000 −0.385894 −0.192947 0.981209i \(-0.561805\pi\)
−0.192947 + 0.981209i \(0.561805\pi\)
\(968\) 3.50000 6.06218i 0.112494 0.194846i
\(969\) 7.07107 + 12.2474i 0.227155 + 0.393445i
\(970\) −14.0000 24.2487i −0.449513 0.778579i
\(971\) −16.2635 + 28.1691i −0.521919 + 0.903990i 0.477756 + 0.878493i \(0.341450\pi\)
−0.999675 + 0.0254978i \(0.991883\pi\)
\(972\) −9.89949 −0.317526
\(973\) 0 0
\(974\) 12.0000 0.384505
\(975\) 0 0
\(976\) −1.41421 2.44949i −0.0452679 0.0784063i
\(977\) −6.00000 10.3923i −0.191957 0.332479i 0.753942 0.656941i \(-0.228150\pi\)
−0.945899 + 0.324462i \(0.894817\pi\)
\(978\) 7.07107 12.2474i 0.226108 0.391630i
\(979\) 14.1421 0.451985
\(980\) 0 0
\(981\) 2.00000 0.0638551
\(982\) 6.00000 10.3923i 0.191468 0.331632i
\(983\) −24.0416 41.6413i −0.766809 1.32815i −0.939285 0.343138i \(-0.888510\pi\)
0.172476 0.985014i \(-0.444823\pi\)
\(984\) −7.00000 12.1244i −0.223152 0.386510i
\(985\) −2.82843 + 4.89898i −0.0901212 + 0.156094i
\(986\) −2.82843 −0.0900755
\(987\) 0 0
\(988\) 0 0
\(989\) 4.00000 6.92820i 0.127193 0.220304i
\(990\) −2.82843 4.89898i −0.0898933 0.155700i
\(991\) 8.00000 + 13.8564i 0.254128 + 0.440163i 0.964658 0.263504i \(-0.0848781\pi\)
−0.710530 + 0.703667i \(0.751545\pi\)
\(992\) −4.24264 + 7.34847i −0.134704 + 0.233314i
\(993\) −14.1421 −0.448787
\(994\) 0 0
\(995\) 24.0000 0.760851
\(996\) 7.00000 12.1244i 0.221803 0.384175i
\(997\) 15.5563 + 26.9444i 0.492675 + 0.853337i 0.999964 0.00843818i \(-0.00268599\pi\)
−0.507290 + 0.861775i \(0.669353\pi\)
\(998\) 2.00000 + 3.46410i 0.0633089 + 0.109654i
\(999\) −28.2843 + 48.9898i −0.894875 + 1.54997i
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 98.2.c.c.79.2 4
3.2 odd 2 882.2.g.l.667.2 4
4.3 odd 2 784.2.i.m.177.1 4
7.2 even 3 98.2.a.b.1.1 2
7.3 odd 6 inner 98.2.c.c.67.1 4
7.4 even 3 inner 98.2.c.c.67.2 4
7.5 odd 6 98.2.a.b.1.2 yes 2
7.6 odd 2 inner 98.2.c.c.79.1 4
21.2 odd 6 882.2.a.n.1.1 2
21.5 even 6 882.2.a.n.1.2 2
21.11 odd 6 882.2.g.l.361.2 4
21.17 even 6 882.2.g.l.361.1 4
21.20 even 2 882.2.g.l.667.1 4
28.3 even 6 784.2.i.m.753.2 4
28.11 odd 6 784.2.i.m.753.1 4
28.19 even 6 784.2.a.l.1.1 2
28.23 odd 6 784.2.a.l.1.2 2
28.27 even 2 784.2.i.m.177.2 4
35.2 odd 12 2450.2.c.v.99.4 4
35.9 even 6 2450.2.a.bj.1.2 2
35.12 even 12 2450.2.c.v.99.3 4
35.19 odd 6 2450.2.a.bj.1.1 2
35.23 odd 12 2450.2.c.v.99.1 4
35.33 even 12 2450.2.c.v.99.2 4
56.5 odd 6 3136.2.a.bn.1.1 2
56.19 even 6 3136.2.a.bm.1.2 2
56.37 even 6 3136.2.a.bn.1.2 2
56.51 odd 6 3136.2.a.bm.1.1 2
84.23 even 6 7056.2.a.cl.1.1 2
84.47 odd 6 7056.2.a.cl.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
98.2.a.b.1.1 2 7.2 even 3
98.2.a.b.1.2 yes 2 7.5 odd 6
98.2.c.c.67.1 4 7.3 odd 6 inner
98.2.c.c.67.2 4 7.4 even 3 inner
98.2.c.c.79.1 4 7.6 odd 2 inner
98.2.c.c.79.2 4 1.1 even 1 trivial
784.2.a.l.1.1 2 28.19 even 6
784.2.a.l.1.2 2 28.23 odd 6
784.2.i.m.177.1 4 4.3 odd 2
784.2.i.m.177.2 4 28.27 even 2
784.2.i.m.753.1 4 28.11 odd 6
784.2.i.m.753.2 4 28.3 even 6
882.2.a.n.1.1 2 21.2 odd 6
882.2.a.n.1.2 2 21.5 even 6
882.2.g.l.361.1 4 21.17 even 6
882.2.g.l.361.2 4 21.11 odd 6
882.2.g.l.667.1 4 21.20 even 2
882.2.g.l.667.2 4 3.2 odd 2
2450.2.a.bj.1.1 2 35.19 odd 6
2450.2.a.bj.1.2 2 35.9 even 6
2450.2.c.v.99.1 4 35.23 odd 12
2450.2.c.v.99.2 4 35.33 even 12
2450.2.c.v.99.3 4 35.12 even 12
2450.2.c.v.99.4 4 35.2 odd 12
3136.2.a.bm.1.1 2 56.51 odd 6
3136.2.a.bm.1.2 2 56.19 even 6
3136.2.a.bn.1.1 2 56.5 odd 6
3136.2.a.bn.1.2 2 56.37 even 6
7056.2.a.cl.1.1 2 84.23 even 6
7056.2.a.cl.1.2 2 84.47 odd 6