Properties

Label 185.2.k.b.117.1
Level $185$
Weight $2$
Character 185.117
Analytic conductor $1.477$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [185,2,Mod(68,185)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(185, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("185.68");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 185 = 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 185.k (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.47723243739\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 117.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 185.117
Dual form 185.2.k.b.68.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +(1.00000 + 1.00000i) q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} +(-1.00000 - 1.00000i) q^{6} +(-3.00000 - 3.00000i) q^{7} +3.00000 q^{8} -1.00000i q^{9} +(1.00000 + 2.00000i) q^{10} -2.00000i q^{11} +(-1.00000 - 1.00000i) q^{12} +2.00000 q^{13} +(3.00000 + 3.00000i) q^{14} +(1.00000 - 3.00000i) q^{15} -1.00000 q^{16} +4.00000i q^{17} +1.00000i q^{18} +(3.00000 - 3.00000i) q^{19} +(1.00000 + 2.00000i) q^{20} -6.00000i q^{21} +2.00000i q^{22} -8.00000 q^{23} +(3.00000 + 3.00000i) q^{24} +(-3.00000 + 4.00000i) q^{25} -2.00000 q^{26} +(4.00000 - 4.00000i) q^{27} +(3.00000 + 3.00000i) q^{28} +(-7.00000 - 7.00000i) q^{29} +(-1.00000 + 3.00000i) q^{30} +(3.00000 - 3.00000i) q^{31} -5.00000 q^{32} +(2.00000 - 2.00000i) q^{33} -4.00000i q^{34} +(-3.00000 + 9.00000i) q^{35} +1.00000i q^{36} +(-1.00000 + 6.00000i) q^{37} +(-3.00000 + 3.00000i) q^{38} +(2.00000 + 2.00000i) q^{39} +(-3.00000 - 6.00000i) q^{40} +6.00000i q^{42} +12.0000 q^{43} +2.00000i q^{44} +(-2.00000 + 1.00000i) q^{45} +8.00000 q^{46} +(5.00000 + 5.00000i) q^{47} +(-1.00000 - 1.00000i) q^{48} +11.0000i q^{49} +(3.00000 - 4.00000i) q^{50} +(-4.00000 + 4.00000i) q^{51} -2.00000 q^{52} +(-3.00000 + 3.00000i) q^{53} +(-4.00000 + 4.00000i) q^{54} +(-4.00000 + 2.00000i) q^{55} +(-9.00000 - 9.00000i) q^{56} +6.00000 q^{57} +(7.00000 + 7.00000i) q^{58} +(7.00000 - 7.00000i) q^{59} +(-1.00000 + 3.00000i) q^{60} +(1.00000 - 1.00000i) q^{61} +(-3.00000 + 3.00000i) q^{62} +(-3.00000 + 3.00000i) q^{63} +7.00000 q^{64} +(-2.00000 - 4.00000i) q^{65} +(-2.00000 + 2.00000i) q^{66} +(3.00000 - 3.00000i) q^{67} -4.00000i q^{68} +(-8.00000 - 8.00000i) q^{69} +(3.00000 - 9.00000i) q^{70} +8.00000 q^{71} -3.00000i q^{72} +(1.00000 + 1.00000i) q^{73} +(1.00000 - 6.00000i) q^{74} +(-7.00000 + 1.00000i) q^{75} +(-3.00000 + 3.00000i) q^{76} +(-6.00000 + 6.00000i) q^{77} +(-2.00000 - 2.00000i) q^{78} +(3.00000 - 3.00000i) q^{79} +(1.00000 + 2.00000i) q^{80} +5.00000 q^{81} +(-5.00000 + 5.00000i) q^{83} +6.00000i q^{84} +(8.00000 - 4.00000i) q^{85} -12.0000 q^{86} -14.0000i q^{87} -6.00000i q^{88} +(5.00000 + 5.00000i) q^{89} +(2.00000 - 1.00000i) q^{90} +(-6.00000 - 6.00000i) q^{91} +8.00000 q^{92} +6.00000 q^{93} +(-5.00000 - 5.00000i) q^{94} +(-9.00000 - 3.00000i) q^{95} +(-5.00000 - 5.00000i) q^{96} -8.00000i q^{97} -11.0000i q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 6 q^{7} + 6 q^{8} + 2 q^{10} - 2 q^{12} + 4 q^{13} + 6 q^{14} + 2 q^{15} - 2 q^{16} + 6 q^{19} + 2 q^{20} - 16 q^{23} + 6 q^{24} - 6 q^{25} - 4 q^{26}+ \cdots - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/185\mathbb{Z}\right)^\times\).

\(n\) \(76\) \(112\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107 −0.353553 0.935414i \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) 1.00000 + 1.00000i 0.577350 + 0.577350i 0.934172 0.356822i \(-0.116140\pi\)
−0.356822 + 0.934172i \(0.616140\pi\)
\(4\) −1.00000 −0.500000
\(5\) −1.00000 2.00000i −0.447214 0.894427i
\(6\) −1.00000 1.00000i −0.408248 0.408248i
\(7\) −3.00000 3.00000i −1.13389 1.13389i −0.989524 0.144370i \(-0.953885\pi\)
−0.144370 0.989524i \(-0.546115\pi\)
\(8\) 3.00000 1.06066
\(9\) 1.00000i 0.333333i
\(10\) 1.00000 + 2.00000i 0.316228 + 0.632456i
\(11\) 2.00000i 0.603023i −0.953463 0.301511i \(-0.902509\pi\)
0.953463 0.301511i \(-0.0974911\pi\)
\(12\) −1.00000 1.00000i −0.288675 0.288675i
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 3.00000 + 3.00000i 0.801784 + 0.801784i
\(15\) 1.00000 3.00000i 0.258199 0.774597i
\(16\) −1.00000 −0.250000
\(17\) 4.00000i 0.970143i 0.874475 + 0.485071i \(0.161206\pi\)
−0.874475 + 0.485071i \(0.838794\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 3.00000 3.00000i 0.688247 0.688247i −0.273597 0.961844i \(-0.588214\pi\)
0.961844 + 0.273597i \(0.0882135\pi\)
\(20\) 1.00000 + 2.00000i 0.223607 + 0.447214i
\(21\) 6.00000i 1.30931i
\(22\) 2.00000i 0.426401i
\(23\) −8.00000 −1.66812 −0.834058 0.551677i \(-0.813988\pi\)
−0.834058 + 0.551677i \(0.813988\pi\)
\(24\) 3.00000 + 3.00000i 0.612372 + 0.612372i
\(25\) −3.00000 + 4.00000i −0.600000 + 0.800000i
\(26\) −2.00000 −0.392232
\(27\) 4.00000 4.00000i 0.769800 0.769800i
\(28\) 3.00000 + 3.00000i 0.566947 + 0.566947i
\(29\) −7.00000 7.00000i −1.29987 1.29987i −0.928477 0.371391i \(-0.878881\pi\)
−0.371391 0.928477i \(-0.621119\pi\)
\(30\) −1.00000 + 3.00000i −0.182574 + 0.547723i
\(31\) 3.00000 3.00000i 0.538816 0.538816i −0.384365 0.923181i \(-0.625580\pi\)
0.923181 + 0.384365i \(0.125580\pi\)
\(32\) −5.00000 −0.883883
\(33\) 2.00000 2.00000i 0.348155 0.348155i
\(34\) 4.00000i 0.685994i
\(35\) −3.00000 + 9.00000i −0.507093 + 1.52128i
\(36\) 1.00000i 0.166667i
\(37\) −1.00000 + 6.00000i −0.164399 + 0.986394i
\(38\) −3.00000 + 3.00000i −0.486664 + 0.486664i
\(39\) 2.00000 + 2.00000i 0.320256 + 0.320256i
\(40\) −3.00000 6.00000i −0.474342 0.948683i
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 6.00000i 0.925820i
\(43\) 12.0000 1.82998 0.914991 0.403473i \(-0.132197\pi\)
0.914991 + 0.403473i \(0.132197\pi\)
\(44\) 2.00000i 0.301511i
\(45\) −2.00000 + 1.00000i −0.298142 + 0.149071i
\(46\) 8.00000 1.17954
\(47\) 5.00000 + 5.00000i 0.729325 + 0.729325i 0.970485 0.241160i \(-0.0775280\pi\)
−0.241160 + 0.970485i \(0.577528\pi\)
\(48\) −1.00000 1.00000i −0.144338 0.144338i
\(49\) 11.0000i 1.57143i
\(50\) 3.00000 4.00000i 0.424264 0.565685i
\(51\) −4.00000 + 4.00000i −0.560112 + 0.560112i
\(52\) −2.00000 −0.277350
\(53\) −3.00000 + 3.00000i −0.412082 + 0.412082i −0.882463 0.470381i \(-0.844116\pi\)
0.470381 + 0.882463i \(0.344116\pi\)
\(54\) −4.00000 + 4.00000i −0.544331 + 0.544331i
\(55\) −4.00000 + 2.00000i −0.539360 + 0.269680i
\(56\) −9.00000 9.00000i −1.20268 1.20268i
\(57\) 6.00000 0.794719
\(58\) 7.00000 + 7.00000i 0.919145 + 0.919145i
\(59\) 7.00000 7.00000i 0.911322 0.911322i −0.0850540 0.996376i \(-0.527106\pi\)
0.996376 + 0.0850540i \(0.0271063\pi\)
\(60\) −1.00000 + 3.00000i −0.129099 + 0.387298i
\(61\) 1.00000 1.00000i 0.128037 0.128037i −0.640184 0.768221i \(-0.721142\pi\)
0.768221 + 0.640184i \(0.221142\pi\)
\(62\) −3.00000 + 3.00000i −0.381000 + 0.381000i
\(63\) −3.00000 + 3.00000i −0.377964 + 0.377964i
\(64\) 7.00000 0.875000
\(65\) −2.00000 4.00000i −0.248069 0.496139i
\(66\) −2.00000 + 2.00000i −0.246183 + 0.246183i
\(67\) 3.00000 3.00000i 0.366508 0.366508i −0.499694 0.866202i \(-0.666554\pi\)
0.866202 + 0.499694i \(0.166554\pi\)
\(68\) 4.00000i 0.485071i
\(69\) −8.00000 8.00000i −0.963087 0.963087i
\(70\) 3.00000 9.00000i 0.358569 1.07571i
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 3.00000i 0.353553i
\(73\) 1.00000 + 1.00000i 0.117041 + 0.117041i 0.763202 0.646160i \(-0.223626\pi\)
−0.646160 + 0.763202i \(0.723626\pi\)
\(74\) 1.00000 6.00000i 0.116248 0.697486i
\(75\) −7.00000 + 1.00000i −0.808290 + 0.115470i
\(76\) −3.00000 + 3.00000i −0.344124 + 0.344124i
\(77\) −6.00000 + 6.00000i −0.683763 + 0.683763i
\(78\) −2.00000 2.00000i −0.226455 0.226455i
\(79\) 3.00000 3.00000i 0.337526 0.337526i −0.517909 0.855436i \(-0.673290\pi\)
0.855436 + 0.517909i \(0.173290\pi\)
\(80\) 1.00000 + 2.00000i 0.111803 + 0.223607i
\(81\) 5.00000 0.555556
\(82\) 0 0
\(83\) −5.00000 + 5.00000i −0.548821 + 0.548821i −0.926100 0.377279i \(-0.876860\pi\)
0.377279 + 0.926100i \(0.376860\pi\)
\(84\) 6.00000i 0.654654i
\(85\) 8.00000 4.00000i 0.867722 0.433861i
\(86\) −12.0000 −1.29399
\(87\) 14.0000i 1.50096i
\(88\) 6.00000i 0.639602i
\(89\) 5.00000 + 5.00000i 0.529999 + 0.529999i 0.920572 0.390573i \(-0.127723\pi\)
−0.390573 + 0.920572i \(0.627723\pi\)
\(90\) 2.00000 1.00000i 0.210819 0.105409i
\(91\) −6.00000 6.00000i −0.628971 0.628971i
\(92\) 8.00000 0.834058
\(93\) 6.00000 0.622171
\(94\) −5.00000 5.00000i −0.515711 0.515711i
\(95\) −9.00000 3.00000i −0.923381 0.307794i
\(96\) −5.00000 5.00000i −0.510310 0.510310i
\(97\) 8.00000i 0.812277i −0.913812 0.406138i \(-0.866875\pi\)
0.913812 0.406138i \(-0.133125\pi\)
\(98\) 11.0000i 1.11117i
\(99\) −2.00000 −0.201008
\(100\) 3.00000 4.00000i 0.300000 0.400000i
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 4.00000 4.00000i 0.396059 0.396059i
\(103\) 14.0000i 1.37946i −0.724066 0.689730i \(-0.757729\pi\)
0.724066 0.689730i \(-0.242271\pi\)
\(104\) 6.00000 0.588348
\(105\) −12.0000 + 6.00000i −1.17108 + 0.585540i
\(106\) 3.00000 3.00000i 0.291386 0.291386i
\(107\) −3.00000 3.00000i −0.290021 0.290021i 0.547068 0.837088i \(-0.315744\pi\)
−0.837088 + 0.547068i \(0.815744\pi\)
\(108\) −4.00000 + 4.00000i −0.384900 + 0.384900i
\(109\) −3.00000 + 3.00000i −0.287348 + 0.287348i −0.836031 0.548683i \(-0.815129\pi\)
0.548683 + 0.836031i \(0.315129\pi\)
\(110\) 4.00000 2.00000i 0.381385 0.190693i
\(111\) −7.00000 + 5.00000i −0.664411 + 0.474579i
\(112\) 3.00000 + 3.00000i 0.283473 + 0.283473i
\(113\) 4.00000i 0.376288i −0.982141 0.188144i \(-0.939753\pi\)
0.982141 0.188144i \(-0.0602472\pi\)
\(114\) −6.00000 −0.561951
\(115\) 8.00000 + 16.0000i 0.746004 + 1.49201i
\(116\) 7.00000 + 7.00000i 0.649934 + 0.649934i
\(117\) 2.00000i 0.184900i
\(118\) −7.00000 + 7.00000i −0.644402 + 0.644402i
\(119\) 12.0000 12.0000i 1.10004 1.10004i
\(120\) 3.00000 9.00000i 0.273861 0.821584i
\(121\) 7.00000 0.636364
\(122\) −1.00000 + 1.00000i −0.0905357 + 0.0905357i
\(123\) 0 0
\(124\) −3.00000 + 3.00000i −0.269408 + 0.269408i
\(125\) 11.0000 + 2.00000i 0.983870 + 0.178885i
\(126\) 3.00000 3.00000i 0.267261 0.267261i
\(127\) 9.00000 + 9.00000i 0.798621 + 0.798621i 0.982878 0.184257i \(-0.0589879\pi\)
−0.184257 + 0.982878i \(0.558988\pi\)
\(128\) 3.00000 0.265165
\(129\) 12.0000 + 12.0000i 1.05654 + 1.05654i
\(130\) 2.00000 + 4.00000i 0.175412 + 0.350823i
\(131\) −5.00000 + 5.00000i −0.436852 + 0.436852i −0.890951 0.454099i \(-0.849961\pi\)
0.454099 + 0.890951i \(0.349961\pi\)
\(132\) −2.00000 + 2.00000i −0.174078 + 0.174078i
\(133\) −18.0000 −1.56080
\(134\) −3.00000 + 3.00000i −0.259161 + 0.259161i
\(135\) −12.0000 4.00000i −1.03280 0.344265i
\(136\) 12.0000i 1.02899i
\(137\) −7.00000 7.00000i −0.598050 0.598050i 0.341743 0.939793i \(-0.388983\pi\)
−0.939793 + 0.341743i \(0.888983\pi\)
\(138\) 8.00000 + 8.00000i 0.681005 + 0.681005i
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 3.00000 9.00000i 0.253546 0.760639i
\(141\) 10.0000i 0.842152i
\(142\) −8.00000 −0.671345
\(143\) 4.00000i 0.334497i
\(144\) 1.00000i 0.0833333i
\(145\) −7.00000 + 21.0000i −0.581318 + 1.74396i
\(146\) −1.00000 1.00000i −0.0827606 0.0827606i
\(147\) −11.0000 + 11.0000i −0.907265 + 0.907265i
\(148\) 1.00000 6.00000i 0.0821995 0.493197i
\(149\) 16.0000i 1.31077i 0.755295 + 0.655386i \(0.227494\pi\)
−0.755295 + 0.655386i \(0.772506\pi\)
\(150\) 7.00000 1.00000i 0.571548 0.0816497i
\(151\) 2.00000i 0.162758i 0.996683 + 0.0813788i \(0.0259324\pi\)
−0.996683 + 0.0813788i \(0.974068\pi\)
\(152\) 9.00000 9.00000i 0.729996 0.729996i
\(153\) 4.00000 0.323381
\(154\) 6.00000 6.00000i 0.483494 0.483494i
\(155\) −9.00000 3.00000i −0.722897 0.240966i
\(156\) −2.00000 2.00000i −0.160128 0.160128i
\(157\) −3.00000 3.00000i −0.239426 0.239426i 0.577186 0.816612i \(-0.304151\pi\)
−0.816612 + 0.577186i \(0.804151\pi\)
\(158\) −3.00000 + 3.00000i −0.238667 + 0.238667i
\(159\) −6.00000 −0.475831
\(160\) 5.00000 + 10.0000i 0.395285 + 0.790569i
\(161\) 24.0000 + 24.0000i 1.89146 + 1.89146i
\(162\) −5.00000 −0.392837
\(163\) 10.0000i 0.783260i −0.920123 0.391630i \(-0.871911\pi\)
0.920123 0.391630i \(-0.128089\pi\)
\(164\) 0 0
\(165\) −6.00000 2.00000i −0.467099 0.155700i
\(166\) 5.00000 5.00000i 0.388075 0.388075i
\(167\) 6.00000i 0.464294i −0.972681 0.232147i \(-0.925425\pi\)
0.972681 0.232147i \(-0.0745750\pi\)
\(168\) 18.0000i 1.38873i
\(169\) −9.00000 −0.692308
\(170\) −8.00000 + 4.00000i −0.613572 + 0.306786i
\(171\) −3.00000 3.00000i −0.229416 0.229416i
\(172\) −12.0000 −0.914991
\(173\) 1.00000 + 1.00000i 0.0760286 + 0.0760286i 0.744099 0.668070i \(-0.232879\pi\)
−0.668070 + 0.744099i \(0.732879\pi\)
\(174\) 14.0000i 1.06134i
\(175\) 21.0000 3.00000i 1.58745 0.226779i
\(176\) 2.00000i 0.150756i
\(177\) 14.0000 1.05230
\(178\) −5.00000 5.00000i −0.374766 0.374766i
\(179\) −7.00000 7.00000i −0.523205 0.523205i 0.395333 0.918538i \(-0.370629\pi\)
−0.918538 + 0.395333i \(0.870629\pi\)
\(180\) 2.00000 1.00000i 0.149071 0.0745356i
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 6.00000 + 6.00000i 0.444750 + 0.444750i
\(183\) 2.00000 0.147844
\(184\) −24.0000 −1.76930
\(185\) 13.0000 4.00000i 0.955779 0.294086i
\(186\) −6.00000 −0.439941
\(187\) 8.00000 0.585018
\(188\) −5.00000 5.00000i −0.364662 0.364662i
\(189\) −24.0000 −1.74574
\(190\) 9.00000 + 3.00000i 0.652929 + 0.217643i
\(191\) −11.0000 11.0000i −0.795932 0.795932i 0.186519 0.982451i \(-0.440279\pi\)
−0.982451 + 0.186519i \(0.940279\pi\)
\(192\) 7.00000 + 7.00000i 0.505181 + 0.505181i
\(193\) 2.00000 0.143963 0.0719816 0.997406i \(-0.477068\pi\)
0.0719816 + 0.997406i \(0.477068\pi\)
\(194\) 8.00000i 0.574367i
\(195\) 2.00000 6.00000i 0.143223 0.429669i
\(196\) 11.0000i 0.785714i
\(197\) 1.00000 + 1.00000i 0.0712470 + 0.0712470i 0.741832 0.670585i \(-0.233957\pi\)
−0.670585 + 0.741832i \(0.733957\pi\)
\(198\) 2.00000 0.142134
\(199\) −15.0000 15.0000i −1.06332 1.06332i −0.997855 0.0654671i \(-0.979146\pi\)
−0.0654671 0.997855i \(-0.520854\pi\)
\(200\) −9.00000 + 12.0000i −0.636396 + 0.848528i
\(201\) 6.00000 0.423207
\(202\) 0 0
\(203\) 42.0000i 2.94782i
\(204\) 4.00000 4.00000i 0.280056 0.280056i
\(205\) 0 0
\(206\) 14.0000i 0.975426i
\(207\) 8.00000i 0.556038i
\(208\) −2.00000 −0.138675
\(209\) −6.00000 6.00000i −0.415029 0.415029i
\(210\) 12.0000 6.00000i 0.828079 0.414039i
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) 3.00000 3.00000i 0.206041 0.206041i
\(213\) 8.00000 + 8.00000i 0.548151 + 0.548151i
\(214\) 3.00000 + 3.00000i 0.205076 + 0.205076i
\(215\) −12.0000 24.0000i −0.818393 1.63679i
\(216\) 12.0000 12.0000i 0.816497 0.816497i
\(217\) −18.0000 −1.22192
\(218\) 3.00000 3.00000i 0.203186 0.203186i
\(219\) 2.00000i 0.135147i
\(220\) 4.00000 2.00000i 0.269680 0.134840i
\(221\) 8.00000i 0.538138i
\(222\) 7.00000 5.00000i 0.469809 0.335578i
\(223\) −1.00000 + 1.00000i −0.0669650 + 0.0669650i −0.739796 0.672831i \(-0.765078\pi\)
0.672831 + 0.739796i \(0.265078\pi\)
\(224\) 15.0000 + 15.0000i 1.00223 + 1.00223i
\(225\) 4.00000 + 3.00000i 0.266667 + 0.200000i
\(226\) 4.00000i 0.266076i
\(227\) 2.00000i 0.132745i −0.997795 0.0663723i \(-0.978857\pi\)
0.997795 0.0663723i \(-0.0211425\pi\)
\(228\) −6.00000 −0.397360
\(229\) 4.00000i 0.264327i 0.991228 + 0.132164i \(0.0421925\pi\)
−0.991228 + 0.132164i \(0.957808\pi\)
\(230\) −8.00000 16.0000i −0.527504 1.05501i
\(231\) −12.0000 −0.789542
\(232\) −21.0000 21.0000i −1.37872 1.37872i
\(233\) 1.00000 + 1.00000i 0.0655122 + 0.0655122i 0.739104 0.673592i \(-0.235249\pi\)
−0.673592 + 0.739104i \(0.735249\pi\)
\(234\) 2.00000i 0.130744i
\(235\) 5.00000 15.0000i 0.326164 0.978492i
\(236\) −7.00000 + 7.00000i −0.455661 + 0.455661i
\(237\) 6.00000 0.389742
\(238\) −12.0000 + 12.0000i −0.777844 + 0.777844i
\(239\) 7.00000 7.00000i 0.452792 0.452792i −0.443488 0.896280i \(-0.646259\pi\)
0.896280 + 0.443488i \(0.146259\pi\)
\(240\) −1.00000 + 3.00000i −0.0645497 + 0.193649i
\(241\) 1.00000 + 1.00000i 0.0644157 + 0.0644157i 0.738581 0.674165i \(-0.235496\pi\)
−0.674165 + 0.738581i \(0.735496\pi\)
\(242\) −7.00000 −0.449977
\(243\) −7.00000 7.00000i −0.449050 0.449050i
\(244\) −1.00000 + 1.00000i −0.0640184 + 0.0640184i
\(245\) 22.0000 11.0000i 1.40553 0.702764i
\(246\) 0 0
\(247\) 6.00000 6.00000i 0.381771 0.381771i
\(248\) 9.00000 9.00000i 0.571501 0.571501i
\(249\) −10.0000 −0.633724
\(250\) −11.0000 2.00000i −0.695701 0.126491i
\(251\) −5.00000 + 5.00000i −0.315597 + 0.315597i −0.847073 0.531476i \(-0.821638\pi\)
0.531476 + 0.847073i \(0.321638\pi\)
\(252\) 3.00000 3.00000i 0.188982 0.188982i
\(253\) 16.0000i 1.00591i
\(254\) −9.00000 9.00000i −0.564710 0.564710i
\(255\) 12.0000 + 4.00000i 0.751469 + 0.250490i
\(256\) −17.0000 −1.06250
\(257\) 28.0000i 1.74659i 0.487190 + 0.873296i \(0.338022\pi\)
−0.487190 + 0.873296i \(0.661978\pi\)
\(258\) −12.0000 12.0000i −0.747087 0.747087i
\(259\) 21.0000 15.0000i 1.30488 0.932055i
\(260\) 2.00000 + 4.00000i 0.124035 + 0.248069i
\(261\) −7.00000 + 7.00000i −0.433289 + 0.433289i
\(262\) 5.00000 5.00000i 0.308901 0.308901i
\(263\) −7.00000 7.00000i −0.431638 0.431638i 0.457547 0.889185i \(-0.348728\pi\)
−0.889185 + 0.457547i \(0.848728\pi\)
\(264\) 6.00000 6.00000i 0.369274 0.369274i
\(265\) 9.00000 + 3.00000i 0.552866 + 0.184289i
\(266\) 18.0000 1.10365
\(267\) 10.0000i 0.611990i
\(268\) −3.00000 + 3.00000i −0.183254 + 0.183254i
\(269\) 16.0000i 0.975537i −0.872973 0.487769i \(-0.837811\pi\)
0.872973 0.487769i \(-0.162189\pi\)
\(270\) 12.0000 + 4.00000i 0.730297 + 0.243432i
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 12.0000i 0.726273i
\(274\) 7.00000 + 7.00000i 0.422885 + 0.422885i
\(275\) 8.00000 + 6.00000i 0.482418 + 0.361814i
\(276\) 8.00000 + 8.00000i 0.481543 + 0.481543i
\(277\) 26.0000 1.56219 0.781094 0.624413i \(-0.214662\pi\)
0.781094 + 0.624413i \(0.214662\pi\)
\(278\) −4.00000 −0.239904
\(279\) −3.00000 3.00000i −0.179605 0.179605i
\(280\) −9.00000 + 27.0000i −0.537853 + 1.61356i
\(281\) 9.00000 + 9.00000i 0.536895 + 0.536895i 0.922616 0.385721i \(-0.126047\pi\)
−0.385721 + 0.922616i \(0.626047\pi\)
\(282\) 10.0000i 0.595491i
\(283\) 22.0000i 1.30776i 0.756596 + 0.653882i \(0.226861\pi\)
−0.756596 + 0.653882i \(0.773139\pi\)
\(284\) −8.00000 −0.474713
\(285\) −6.00000 12.0000i −0.355409 0.710819i
\(286\) 4.00000i 0.236525i
\(287\) 0 0
\(288\) 5.00000i 0.294628i
\(289\) 1.00000 0.0588235
\(290\) 7.00000 21.0000i 0.411054 1.23316i
\(291\) 8.00000 8.00000i 0.468968 0.468968i
\(292\) −1.00000 1.00000i −0.0585206 0.0585206i
\(293\) 1.00000 1.00000i 0.0584206 0.0584206i −0.677293 0.735714i \(-0.736847\pi\)
0.735714 + 0.677293i \(0.236847\pi\)
\(294\) 11.0000 11.0000i 0.641533 0.641533i
\(295\) −21.0000 7.00000i −1.22267 0.407556i
\(296\) −3.00000 + 18.0000i −0.174371 + 1.04623i
\(297\) −8.00000 8.00000i −0.464207 0.464207i
\(298\) 16.0000i 0.926855i
\(299\) −16.0000 −0.925304
\(300\) 7.00000 1.00000i 0.404145 0.0577350i
\(301\) −36.0000 36.0000i −2.07501 2.07501i
\(302\) 2.00000i 0.115087i
\(303\) 0 0
\(304\) −3.00000 + 3.00000i −0.172062 + 0.172062i
\(305\) −3.00000 1.00000i −0.171780 0.0572598i
\(306\) −4.00000 −0.228665
\(307\) −9.00000 + 9.00000i −0.513657 + 0.513657i −0.915645 0.401988i \(-0.868319\pi\)
0.401988 + 0.915645i \(0.368319\pi\)
\(308\) 6.00000 6.00000i 0.341882 0.341882i
\(309\) 14.0000 14.0000i 0.796432 0.796432i
\(310\) 9.00000 + 3.00000i 0.511166 + 0.170389i
\(311\) 3.00000 3.00000i 0.170114 0.170114i −0.616915 0.787030i \(-0.711618\pi\)
0.787030 + 0.616915i \(0.211618\pi\)
\(312\) 6.00000 + 6.00000i 0.339683 + 0.339683i
\(313\) −30.0000 −1.69570 −0.847850 0.530236i \(-0.822103\pi\)
−0.847850 + 0.530236i \(0.822103\pi\)
\(314\) 3.00000 + 3.00000i 0.169300 + 0.169300i
\(315\) 9.00000 + 3.00000i 0.507093 + 0.169031i
\(316\) −3.00000 + 3.00000i −0.168763 + 0.168763i
\(317\) 17.0000 17.0000i 0.954815 0.954815i −0.0442073 0.999022i \(-0.514076\pi\)
0.999022 + 0.0442073i \(0.0140762\pi\)
\(318\) 6.00000 0.336463
\(319\) −14.0000 + 14.0000i −0.783850 + 0.783850i
\(320\) −7.00000 14.0000i −0.391312 0.782624i
\(321\) 6.00000i 0.334887i
\(322\) −24.0000 24.0000i −1.33747 1.33747i
\(323\) 12.0000 + 12.0000i 0.667698 + 0.667698i
\(324\) −5.00000 −0.277778
\(325\) −6.00000 + 8.00000i −0.332820 + 0.443760i
\(326\) 10.0000i 0.553849i
\(327\) −6.00000 −0.331801
\(328\) 0 0
\(329\) 30.0000i 1.65395i
\(330\) 6.00000 + 2.00000i 0.330289 + 0.110096i
\(331\) −7.00000 7.00000i −0.384755 0.384755i 0.488057 0.872812i \(-0.337706\pi\)
−0.872812 + 0.488057i \(0.837706\pi\)
\(332\) 5.00000 5.00000i 0.274411 0.274411i
\(333\) 6.00000 + 1.00000i 0.328798 + 0.0547997i
\(334\) 6.00000i 0.328305i
\(335\) −9.00000 3.00000i −0.491723 0.163908i
\(336\) 6.00000i 0.327327i
\(337\) −15.0000 + 15.0000i −0.817102 + 0.817102i −0.985687 0.168585i \(-0.946080\pi\)
0.168585 + 0.985687i \(0.446080\pi\)
\(338\) 9.00000 0.489535
\(339\) 4.00000 4.00000i 0.217250 0.217250i
\(340\) −8.00000 + 4.00000i −0.433861 + 0.216930i
\(341\) −6.00000 6.00000i −0.324918 0.324918i
\(342\) 3.00000 + 3.00000i 0.162221 + 0.162221i
\(343\) 12.0000 12.0000i 0.647939 0.647939i
\(344\) 36.0000 1.94099
\(345\) −8.00000 + 24.0000i −0.430706 + 1.29212i
\(346\) −1.00000 1.00000i −0.0537603 0.0537603i
\(347\) 4.00000 0.214731 0.107366 0.994220i \(-0.465758\pi\)
0.107366 + 0.994220i \(0.465758\pi\)
\(348\) 14.0000i 0.750479i
\(349\) 32.0000i 1.71292i 0.516213 + 0.856460i \(0.327341\pi\)
−0.516213 + 0.856460i \(0.672659\pi\)
\(350\) −21.0000 + 3.00000i −1.12250 + 0.160357i
\(351\) 8.00000 8.00000i 0.427008 0.427008i
\(352\) 10.0000i 0.533002i
\(353\) 32.0000i 1.70319i −0.524202 0.851594i \(-0.675636\pi\)
0.524202 0.851594i \(-0.324364\pi\)
\(354\) −14.0000 −0.744092
\(355\) −8.00000 16.0000i −0.424596 0.849192i
\(356\) −5.00000 5.00000i −0.264999 0.264999i
\(357\) 24.0000 1.27021
\(358\) 7.00000 + 7.00000i 0.369961 + 0.369961i
\(359\) 34.0000i 1.79445i 0.441572 + 0.897226i \(0.354421\pi\)
−0.441572 + 0.897226i \(0.645579\pi\)
\(360\) −6.00000 + 3.00000i −0.316228 + 0.158114i
\(361\) 1.00000i 0.0526316i
\(362\) −10.0000 −0.525588
\(363\) 7.00000 + 7.00000i 0.367405 + 0.367405i
\(364\) 6.00000 + 6.00000i 0.314485 + 0.314485i
\(365\) 1.00000 3.00000i 0.0523424 0.157027i
\(366\) −2.00000 −0.104542
\(367\) 17.0000 + 17.0000i 0.887393 + 0.887393i 0.994272 0.106879i \(-0.0340858\pi\)
−0.106879 + 0.994272i \(0.534086\pi\)
\(368\) 8.00000 0.417029
\(369\) 0 0
\(370\) −13.0000 + 4.00000i −0.675838 + 0.207950i
\(371\) 18.0000 0.934513
\(372\) −6.00000 −0.311086
\(373\) −3.00000 3.00000i −0.155334 0.155334i 0.625161 0.780496i \(-0.285033\pi\)
−0.780496 + 0.625161i \(0.785033\pi\)
\(374\) −8.00000 −0.413670
\(375\) 9.00000 + 13.0000i 0.464758 + 0.671317i
\(376\) 15.0000 + 15.0000i 0.773566 + 0.773566i
\(377\) −14.0000 14.0000i −0.721037 0.721037i
\(378\) 24.0000 1.23443
\(379\) 14.0000i 0.719132i 0.933120 + 0.359566i \(0.117075\pi\)
−0.933120 + 0.359566i \(0.882925\pi\)
\(380\) 9.00000 + 3.00000i 0.461690 + 0.153897i
\(381\) 18.0000i 0.922168i
\(382\) 11.0000 + 11.0000i 0.562809 + 0.562809i
\(383\) 8.00000 0.408781 0.204390 0.978889i \(-0.434479\pi\)
0.204390 + 0.978889i \(0.434479\pi\)
\(384\) 3.00000 + 3.00000i 0.153093 + 0.153093i
\(385\) 18.0000 + 6.00000i 0.917365 + 0.305788i
\(386\) −2.00000 −0.101797
\(387\) 12.0000i 0.609994i
\(388\) 8.00000i 0.406138i
\(389\) 5.00000 5.00000i 0.253510 0.253510i −0.568898 0.822408i \(-0.692630\pi\)
0.822408 + 0.568898i \(0.192630\pi\)
\(390\) −2.00000 + 6.00000i −0.101274 + 0.303822i
\(391\) 32.0000i 1.61831i
\(392\) 33.0000i 1.66675i
\(393\) −10.0000 −0.504433
\(394\) −1.00000 1.00000i −0.0503793 0.0503793i
\(395\) −9.00000 3.00000i −0.452839 0.150946i
\(396\) 2.00000 0.100504
\(397\) 5.00000 5.00000i 0.250943 0.250943i −0.570414 0.821357i \(-0.693217\pi\)
0.821357 + 0.570414i \(0.193217\pi\)
\(398\) 15.0000 + 15.0000i 0.751882 + 0.751882i
\(399\) −18.0000 18.0000i −0.901127 0.901127i
\(400\) 3.00000 4.00000i 0.150000 0.200000i
\(401\) 1.00000 1.00000i 0.0499376 0.0499376i −0.681697 0.731635i \(-0.738758\pi\)
0.731635 + 0.681697i \(0.238758\pi\)
\(402\) −6.00000 −0.299253
\(403\) 6.00000 6.00000i 0.298881 0.298881i
\(404\) 0 0
\(405\) −5.00000 10.0000i −0.248452 0.496904i
\(406\) 42.0000i 2.08443i
\(407\) 12.0000 + 2.00000i 0.594818 + 0.0991363i
\(408\) −12.0000 + 12.0000i −0.594089 + 0.594089i
\(409\) −3.00000 3.00000i −0.148340 0.148340i 0.629036 0.777376i \(-0.283450\pi\)
−0.777376 + 0.629036i \(0.783450\pi\)
\(410\) 0 0
\(411\) 14.0000i 0.690569i
\(412\) 14.0000i 0.689730i
\(413\) −42.0000 −2.06668
\(414\) 8.00000i 0.393179i
\(415\) 15.0000 + 5.00000i 0.736321 + 0.245440i
\(416\) −10.0000 −0.490290
\(417\) 4.00000 + 4.00000i 0.195881 + 0.195881i
\(418\) 6.00000 + 6.00000i 0.293470 + 0.293470i
\(419\) 22.0000i 1.07477i 0.843337 + 0.537385i \(0.180588\pi\)
−0.843337 + 0.537385i \(0.819412\pi\)
\(420\) 12.0000 6.00000i 0.585540 0.292770i
\(421\) −27.0000 + 27.0000i −1.31590 + 1.31590i −0.398909 + 0.916991i \(0.630611\pi\)
−0.916991 + 0.398909i \(0.869389\pi\)
\(422\) −20.0000 −0.973585
\(423\) 5.00000 5.00000i 0.243108 0.243108i
\(424\) −9.00000 + 9.00000i −0.437079 + 0.437079i
\(425\) −16.0000 12.0000i −0.776114 0.582086i
\(426\) −8.00000 8.00000i −0.387601 0.387601i
\(427\) −6.00000 −0.290360
\(428\) 3.00000 + 3.00000i 0.145010 + 0.145010i
\(429\) 4.00000 4.00000i 0.193122 0.193122i
\(430\) 12.0000 + 24.0000i 0.578691 + 1.15738i
\(431\) 11.0000 11.0000i 0.529851 0.529851i −0.390677 0.920528i \(-0.627759\pi\)
0.920528 + 0.390677i \(0.127759\pi\)
\(432\) −4.00000 + 4.00000i −0.192450 + 0.192450i
\(433\) 5.00000 5.00000i 0.240285 0.240285i −0.576683 0.816968i \(-0.695653\pi\)
0.816968 + 0.576683i \(0.195653\pi\)
\(434\) 18.0000 0.864028
\(435\) −28.0000 + 14.0000i −1.34250 + 0.671249i
\(436\) 3.00000 3.00000i 0.143674 0.143674i
\(437\) −24.0000 + 24.0000i −1.14808 + 1.14808i
\(438\) 2.00000i 0.0955637i
\(439\) 17.0000 + 17.0000i 0.811366 + 0.811366i 0.984839 0.173473i \(-0.0554989\pi\)
−0.173473 + 0.984839i \(0.555499\pi\)
\(440\) −12.0000 + 6.00000i −0.572078 + 0.286039i
\(441\) 11.0000 0.523810
\(442\) 8.00000i 0.380521i
\(443\) −11.0000 11.0000i −0.522626 0.522626i 0.395738 0.918364i \(-0.370489\pi\)
−0.918364 + 0.395738i \(0.870489\pi\)
\(444\) 7.00000 5.00000i 0.332205 0.237289i
\(445\) 5.00000 15.0000i 0.237023 0.711068i
\(446\) 1.00000 1.00000i 0.0473514 0.0473514i
\(447\) −16.0000 + 16.0000i −0.756774 + 0.756774i
\(448\) −21.0000 21.0000i −0.992157 0.992157i
\(449\) 5.00000 5.00000i 0.235965 0.235965i −0.579212 0.815177i \(-0.696640\pi\)
0.815177 + 0.579212i \(0.196640\pi\)
\(450\) −4.00000 3.00000i −0.188562 0.141421i
\(451\) 0 0
\(452\) 4.00000i 0.188144i
\(453\) −2.00000 + 2.00000i −0.0939682 + 0.0939682i
\(454\) 2.00000i 0.0938647i
\(455\) −6.00000 + 18.0000i −0.281284 + 0.843853i
\(456\) 18.0000 0.842927
\(457\) 32.0000i 1.49690i −0.663193 0.748448i \(-0.730799\pi\)
0.663193 0.748448i \(-0.269201\pi\)
\(458\) 4.00000i 0.186908i
\(459\) 16.0000 + 16.0000i 0.746816 + 0.746816i
\(460\) −8.00000 16.0000i −0.373002 0.746004i
\(461\) 21.0000 + 21.0000i 0.978068 + 0.978068i 0.999765 0.0216971i \(-0.00690694\pi\)
−0.0216971 + 0.999765i \(0.506907\pi\)
\(462\) 12.0000 0.558291
\(463\) 40.0000 1.85896 0.929479 0.368875i \(-0.120257\pi\)
0.929479 + 0.368875i \(0.120257\pi\)
\(464\) 7.00000 + 7.00000i 0.324967 + 0.324967i
\(465\) −6.00000 12.0000i −0.278243 0.556487i
\(466\) −1.00000 1.00000i −0.0463241 0.0463241i
\(467\) 38.0000i 1.75843i 0.476425 + 0.879215i \(0.341932\pi\)
−0.476425 + 0.879215i \(0.658068\pi\)
\(468\) 2.00000i 0.0924500i
\(469\) −18.0000 −0.831163
\(470\) −5.00000 + 15.0000i −0.230633 + 0.691898i
\(471\) 6.00000i 0.276465i
\(472\) 21.0000 21.0000i 0.966603 0.966603i
\(473\) 24.0000i 1.10352i
\(474\) −6.00000 −0.275589
\(475\) 3.00000 + 21.0000i 0.137649 + 0.963546i
\(476\) −12.0000 + 12.0000i −0.550019 + 0.550019i
\(477\) 3.00000 + 3.00000i 0.137361 + 0.137361i
\(478\) −7.00000 + 7.00000i −0.320173 + 0.320173i
\(479\) 23.0000 23.0000i 1.05090 1.05090i 0.0522635 0.998633i \(-0.483356\pi\)
0.998633 0.0522635i \(-0.0166436\pi\)
\(480\) −5.00000 + 15.0000i −0.228218 + 0.684653i
\(481\) −2.00000 + 12.0000i −0.0911922 + 0.547153i
\(482\) −1.00000 1.00000i −0.0455488 0.0455488i
\(483\) 48.0000i 2.18408i
\(484\) −7.00000 −0.318182
\(485\) −16.0000 + 8.00000i −0.726523 + 0.363261i
\(486\) 7.00000 + 7.00000i 0.317526 + 0.317526i
\(487\) 2.00000i 0.0906287i 0.998973 + 0.0453143i \(0.0144289\pi\)
−0.998973 + 0.0453143i \(0.985571\pi\)
\(488\) 3.00000 3.00000i 0.135804 0.135804i
\(489\) 10.0000 10.0000i 0.452216 0.452216i
\(490\) −22.0000 + 11.0000i −0.993859 + 0.496929i
\(491\) −4.00000 −0.180517 −0.0902587 0.995918i \(-0.528769\pi\)
−0.0902587 + 0.995918i \(0.528769\pi\)
\(492\) 0 0
\(493\) 28.0000 28.0000i 1.26106 1.26106i
\(494\) −6.00000 + 6.00000i −0.269953 + 0.269953i
\(495\) 2.00000 + 4.00000i 0.0898933 + 0.179787i
\(496\) −3.00000 + 3.00000i −0.134704 + 0.134704i
\(497\) −24.0000 24.0000i −1.07655 1.07655i
\(498\) 10.0000 0.448111
\(499\) −27.0000 27.0000i −1.20869 1.20869i −0.971453 0.237233i \(-0.923759\pi\)
−0.237233 0.971453i \(-0.576241\pi\)
\(500\) −11.0000 2.00000i −0.491935 0.0894427i
\(501\) 6.00000 6.00000i 0.268060 0.268060i
\(502\) 5.00000 5.00000i 0.223161 0.223161i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) −9.00000 + 9.00000i −0.400892 + 0.400892i
\(505\) 0 0
\(506\) 16.0000i 0.711287i
\(507\) −9.00000 9.00000i −0.399704 0.399704i
\(508\) −9.00000 9.00000i −0.399310 0.399310i
\(509\) 30.0000 1.32973 0.664863 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) −12.0000 4.00000i −0.531369 0.177123i
\(511\) 6.00000i 0.265424i
\(512\) 11.0000 0.486136
\(513\) 24.0000i 1.05963i
\(514\) 28.0000i 1.23503i
\(515\) −28.0000 + 14.0000i −1.23383 + 0.616914i
\(516\) −12.0000 12.0000i −0.528271 0.528271i
\(517\) 10.0000 10.0000i 0.439799 0.439799i
\(518\) −21.0000 + 15.0000i −0.922687 + 0.659062i
\(519\) 2.00000i 0.0877903i
\(520\) −6.00000 12.0000i −0.263117 0.526235i
\(521\) 44.0000i 1.92767i −0.266491 0.963837i \(-0.585864\pi\)
0.266491 0.963837i \(-0.414136\pi\)
\(522\) 7.00000 7.00000i 0.306382 0.306382i
\(523\) −4.00000 −0.174908 −0.0874539 0.996169i \(-0.527873\pi\)
−0.0874539 + 0.996169i \(0.527873\pi\)
\(524\) 5.00000 5.00000i 0.218426 0.218426i
\(525\) 24.0000 + 18.0000i 1.04745 + 0.785584i
\(526\) 7.00000 + 7.00000i 0.305215 + 0.305215i
\(527\) 12.0000 + 12.0000i 0.522728 + 0.522728i
\(528\) −2.00000 + 2.00000i −0.0870388 + 0.0870388i
\(529\) 41.0000 1.78261
\(530\) −9.00000 3.00000i −0.390935 0.130312i
\(531\) −7.00000 7.00000i −0.303774 0.303774i
\(532\) 18.0000 0.780399
\(533\) 0 0
\(534\) 10.0000i 0.432742i
\(535\) −3.00000 + 9.00000i −0.129701 + 0.389104i
\(536\) 9.00000 9.00000i 0.388741 0.388741i
\(537\) 14.0000i 0.604145i
\(538\) 16.0000i 0.689809i
\(539\) 22.0000 0.947607
\(540\) 12.0000 + 4.00000i 0.516398 + 0.172133i
\(541\) 1.00000 + 1.00000i 0.0429934 + 0.0429934i 0.728277 0.685283i \(-0.240322\pi\)
−0.685283 + 0.728277i \(0.740322\pi\)
\(542\) 8.00000 0.343629
\(543\) 10.0000 + 10.0000i 0.429141 + 0.429141i
\(544\) 20.0000i 0.857493i
\(545\) 9.00000 + 3.00000i 0.385518 + 0.128506i
\(546\) 12.0000i 0.513553i
\(547\) 20.0000 0.855138 0.427569 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) 7.00000 + 7.00000i 0.299025 + 0.299025i
\(549\) −1.00000 1.00000i −0.0426790 0.0426790i
\(550\) −8.00000 6.00000i −0.341121 0.255841i
\(551\) −42.0000 −1.78926
\(552\) −24.0000 24.0000i −1.02151 1.02151i
\(553\) −18.0000 −0.765438
\(554\) −26.0000 −1.10463
\(555\) 17.0000 + 9.00000i 0.721610 + 0.382029i
\(556\) −4.00000 −0.169638
\(557\) −14.0000 −0.593199 −0.296600 0.955002i \(-0.595853\pi\)
−0.296600 + 0.955002i \(0.595853\pi\)
\(558\) 3.00000 + 3.00000i 0.127000 + 0.127000i
\(559\) 24.0000 1.01509
\(560\) 3.00000 9.00000i 0.126773 0.380319i
\(561\) 8.00000 + 8.00000i 0.337760 + 0.337760i
\(562\) −9.00000 9.00000i −0.379642 0.379642i
\(563\) −12.0000 −0.505740 −0.252870 0.967500i \(-0.581374\pi\)
−0.252870 + 0.967500i \(0.581374\pi\)
\(564\) 10.0000i 0.421076i
\(565\) −8.00000 + 4.00000i −0.336563 + 0.168281i
\(566\) 22.0000i 0.924729i
\(567\) −15.0000 15.0000i −0.629941 0.629941i
\(568\) 24.0000 1.00702
\(569\) 25.0000 + 25.0000i 1.04805 + 1.04805i 0.998786 + 0.0492690i \(0.0156892\pi\)
0.0492690 + 0.998786i \(0.484311\pi\)
\(570\) 6.00000 + 12.0000i 0.251312 + 0.502625i
\(571\) −28.0000 −1.17176 −0.585882 0.810397i \(-0.699252\pi\)
−0.585882 + 0.810397i \(0.699252\pi\)
\(572\) 4.00000i 0.167248i
\(573\) 22.0000i 0.919063i
\(574\) 0 0
\(575\) 24.0000 32.0000i 1.00087 1.33449i
\(576\) 7.00000i 0.291667i
\(577\) 12.0000i 0.499567i 0.968302 + 0.249783i \(0.0803594\pi\)
−0.968302 + 0.249783i \(0.919641\pi\)
\(578\) −1.00000 −0.0415945
\(579\) 2.00000 + 2.00000i 0.0831172 + 0.0831172i
\(580\) 7.00000 21.0000i 0.290659 0.871978i
\(581\) 30.0000 1.24461
\(582\) −8.00000 + 8.00000i −0.331611 + 0.331611i
\(583\) 6.00000 + 6.00000i 0.248495 + 0.248495i
\(584\) 3.00000 + 3.00000i 0.124141 + 0.124141i
\(585\) −4.00000 + 2.00000i −0.165380 + 0.0826898i
\(586\) −1.00000 + 1.00000i −0.0413096 + 0.0413096i
\(587\) −36.0000 −1.48588 −0.742940 0.669359i \(-0.766569\pi\)
−0.742940 + 0.669359i \(0.766569\pi\)
\(588\) 11.0000 11.0000i 0.453632 0.453632i
\(589\) 18.0000i 0.741677i
\(590\) 21.0000 + 7.00000i 0.864556 + 0.288185i
\(591\) 2.00000i 0.0822690i
\(592\) 1.00000 6.00000i 0.0410997 0.246598i
\(593\) −3.00000 + 3.00000i −0.123195 + 0.123195i −0.766016 0.642821i \(-0.777764\pi\)
0.642821 + 0.766016i \(0.277764\pi\)
\(594\) 8.00000 + 8.00000i 0.328244 + 0.328244i
\(595\) −36.0000 12.0000i −1.47586 0.491952i
\(596\) 16.0000i 0.655386i
\(597\) 30.0000i 1.22782i
\(598\) 16.0000 0.654289
\(599\) 6.00000i 0.245153i −0.992459 0.122577i \(-0.960884\pi\)
0.992459 0.122577i \(-0.0391157\pi\)
\(600\) −21.0000 + 3.00000i −0.857321 + 0.122474i
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 36.0000 + 36.0000i 1.46725 + 1.46725i
\(603\) −3.00000 3.00000i −0.122169 0.122169i
\(604\) 2.00000i 0.0813788i
\(605\) −7.00000 14.0000i −0.284590 0.569181i
\(606\) 0 0
\(607\) −32.0000 −1.29884 −0.649420 0.760430i \(-0.724988\pi\)
−0.649420 + 0.760430i \(0.724988\pi\)
\(608\) −15.0000 + 15.0000i −0.608330 + 0.608330i
\(609\) −42.0000 + 42.0000i −1.70193 + 1.70193i
\(610\) 3.00000 + 1.00000i 0.121466 + 0.0404888i
\(611\) 10.0000 + 10.0000i 0.404557 + 0.404557i
\(612\) −4.00000 −0.161690
\(613\) 21.0000 + 21.0000i 0.848182 + 0.848182i 0.989906 0.141724i \(-0.0452646\pi\)
−0.141724 + 0.989906i \(0.545265\pi\)
\(614\) 9.00000 9.00000i 0.363210 0.363210i
\(615\) 0 0
\(616\) −18.0000 + 18.0000i −0.725241 + 0.725241i
\(617\) 17.0000 17.0000i 0.684394 0.684394i −0.276593 0.960987i \(-0.589205\pi\)
0.960987 + 0.276593i \(0.0892054\pi\)
\(618\) −14.0000 + 14.0000i −0.563163 + 0.563163i
\(619\) −20.0000 −0.803868 −0.401934 0.915669i \(-0.631662\pi\)
−0.401934 + 0.915669i \(0.631662\pi\)
\(620\) 9.00000 + 3.00000i 0.361449 + 0.120483i
\(621\) −32.0000 + 32.0000i −1.28412 + 1.28412i
\(622\) −3.00000 + 3.00000i −0.120289 + 0.120289i
\(623\) 30.0000i 1.20192i
\(624\) −2.00000 2.00000i −0.0800641 0.0800641i
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 30.0000 1.19904
\(627\) 12.0000i 0.479234i
\(628\) 3.00000 + 3.00000i 0.119713 + 0.119713i
\(629\) −24.0000 4.00000i −0.956943 0.159490i
\(630\) −9.00000 3.00000i −0.358569 0.119523i
\(631\) 23.0000 23.0000i 0.915616 0.915616i −0.0810911 0.996707i \(-0.525840\pi\)
0.996707 + 0.0810911i \(0.0258405\pi\)
\(632\) 9.00000 9.00000i 0.358001 0.358001i
\(633\) 20.0000 + 20.0000i 0.794929 + 0.794929i
\(634\) −17.0000 + 17.0000i −0.675156 + 0.675156i
\(635\) 9.00000 27.0000i 0.357154 1.07146i
\(636\) 6.00000 0.237915
\(637\) 22.0000i 0.871672i
\(638\) 14.0000 14.0000i 0.554265 0.554265i
\(639\) 8.00000i 0.316475i
\(640\) −3.00000 6.00000i −0.118585 0.237171i
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) 6.00000i 0.236801i
\(643\) 10.0000i 0.394362i −0.980367 0.197181i \(-0.936821\pi\)
0.980367 0.197181i \(-0.0631786\pi\)
\(644\) −24.0000 24.0000i −0.945732 0.945732i
\(645\) 12.0000 36.0000i 0.472500 1.41750i
\(646\) −12.0000 12.0000i −0.472134 0.472134i
\(647\) −24.0000 −0.943537 −0.471769 0.881722i \(-0.656384\pi\)
−0.471769 + 0.881722i \(0.656384\pi\)
\(648\) 15.0000 0.589256
\(649\) −14.0000 14.0000i −0.549548 0.549548i
\(650\) 6.00000 8.00000i 0.235339 0.313786i
\(651\) −18.0000 18.0000i −0.705476 0.705476i
\(652\) 10.0000i 0.391630i
\(653\) 36.0000i 1.40879i 0.709809 + 0.704394i \(0.248781\pi\)
−0.709809 + 0.704394i \(0.751219\pi\)
\(654\) 6.00000 0.234619
\(655\) 15.0000 + 5.00000i 0.586098 + 0.195366i
\(656\) 0 0
\(657\) 1.00000 1.00000i 0.0390137 0.0390137i
\(658\) 30.0000i 1.16952i
\(659\) 20.0000 0.779089 0.389545 0.921008i \(-0.372632\pi\)
0.389545 + 0.921008i \(0.372632\pi\)
\(660\) 6.00000 + 2.00000i 0.233550 + 0.0778499i
\(661\) 33.0000 33.0000i 1.28355 1.28355i 0.344919 0.938633i \(-0.387906\pi\)
0.938633 0.344919i \(-0.112094\pi\)
\(662\) 7.00000 + 7.00000i 0.272063 + 0.272063i
\(663\) −8.00000 + 8.00000i −0.310694 + 0.310694i
\(664\) −15.0000 + 15.0000i −0.582113 + 0.582113i
\(665\) 18.0000 + 36.0000i 0.698010 + 1.39602i
\(666\) −6.00000 1.00000i −0.232495 0.0387492i
\(667\) 56.0000 + 56.0000i 2.16833 + 2.16833i
\(668\) 6.00000i 0.232147i
\(669\) −2.00000 −0.0773245
\(670\) 9.00000 + 3.00000i 0.347700 + 0.115900i
\(671\) −2.00000 2.00000i −0.0772091 0.0772091i
\(672\) 30.0000i 1.15728i
\(673\) −15.0000 + 15.0000i −0.578208 + 0.578208i −0.934409 0.356202i \(-0.884072\pi\)
0.356202 + 0.934409i \(0.384072\pi\)
\(674\) 15.0000 15.0000i 0.577778 0.577778i
\(675\) 4.00000 + 28.0000i 0.153960 + 1.07772i
\(676\) 9.00000 0.346154
\(677\) −23.0000 + 23.0000i −0.883962 + 0.883962i −0.993935 0.109973i \(-0.964924\pi\)
0.109973 + 0.993935i \(0.464924\pi\)
\(678\) −4.00000 + 4.00000i −0.153619 + 0.153619i
\(679\) −24.0000 + 24.0000i −0.921035 + 0.921035i
\(680\) 24.0000 12.0000i 0.920358 0.460179i
\(681\) 2.00000 2.00000i 0.0766402 0.0766402i
\(682\) 6.00000 + 6.00000i 0.229752 + 0.229752i
\(683\) 4.00000 0.153056 0.0765279 0.997067i \(-0.475617\pi\)
0.0765279 + 0.997067i \(0.475617\pi\)
\(684\) 3.00000 + 3.00000i 0.114708 + 0.114708i
\(685\) −7.00000 + 21.0000i −0.267456 + 0.802369i
\(686\) −12.0000 + 12.0000i −0.458162 + 0.458162i
\(687\) −4.00000 + 4.00000i −0.152610 + 0.152610i
\(688\) −12.0000 −0.457496
\(689\) −6.00000 + 6.00000i −0.228582 + 0.228582i
\(690\) 8.00000 24.0000i 0.304555 0.913664i
\(691\) 46.0000i 1.74992i 0.484193 + 0.874961i \(0.339113\pi\)
−0.484193 + 0.874961i \(0.660887\pi\)
\(692\) −1.00000 1.00000i −0.0380143 0.0380143i
\(693\) 6.00000 + 6.00000i 0.227921 + 0.227921i
\(694\) −4.00000 −0.151838
\(695\) −4.00000 8.00000i −0.151729 0.303457i
\(696\) 42.0000i 1.59201i
\(697\) 0 0
\(698\) 32.0000i 1.21122i
\(699\) 2.00000i 0.0756469i
\(700\) −21.0000 + 3.00000i −0.793725 + 0.113389i
\(701\) 9.00000 + 9.00000i 0.339925 + 0.339925i 0.856339 0.516414i \(-0.172733\pi\)
−0.516414 + 0.856339i \(0.672733\pi\)
\(702\) −8.00000 + 8.00000i −0.301941 + 0.301941i
\(703\) 15.0000 + 21.0000i 0.565736 + 0.792030i
\(704\) 14.0000i 0.527645i
\(705\) 20.0000 10.0000i 0.753244 0.376622i
\(706\) 32.0000i 1.20434i
\(707\) 0 0
\(708\) −14.0000 −0.526152
\(709\) −15.0000 + 15.0000i −0.563337 + 0.563337i −0.930254 0.366917i \(-0.880413\pi\)
0.366917 + 0.930254i \(0.380413\pi\)
\(710\) 8.00000 + 16.0000i 0.300235 + 0.600469i
\(711\) −3.00000 3.00000i −0.112509 0.112509i
\(712\) 15.0000 + 15.0000i 0.562149 + 0.562149i
\(713\) −24.0000 + 24.0000i −0.898807 + 0.898807i
\(714\) −24.0000 −0.898177
\(715\) −8.00000 + 4.00000i −0.299183 + 0.149592i
\(716\) 7.00000 + 7.00000i 0.261602 + 0.261602i
\(717\) 14.0000 0.522840
\(718\) 34.0000i 1.26887i
\(719\) 26.0000i 0.969636i 0.874615 + 0.484818i \(0.161114\pi\)
−0.874615 + 0.484818i \(0.838886\pi\)
\(720\) 2.00000 1.00000i 0.0745356 0.0372678i
\(721\) −42.0000 + 42.0000i −1.56416 + 1.56416i
\(722\) 1.00000i 0.0372161i
\(723\) 2.00000i 0.0743808i
\(724\) −10.0000 −0.371647
\(725\) 49.0000 7.00000i 1.81981 0.259973i
\(726\) −7.00000 7.00000i −0.259794 0.259794i
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) −18.0000 18.0000i −0.667124 0.667124i
\(729\) 29.0000i 1.07407i
\(730\) −1.00000 + 3.00000i −0.0370117 + 0.111035i
\(731\) 48.0000i 1.77534i
\(732\) −2.00000 −0.0739221
\(733\) −3.00000 3.00000i −0.110808 0.110808i 0.649529 0.760337i \(-0.274966\pi\)
−0.760337 + 0.649529i \(0.774966\pi\)
\(734\) −17.0000 17.0000i −0.627481 0.627481i
\(735\) 33.0000 + 11.0000i 1.21722 + 0.405741i
\(736\) 40.0000 1.47442
\(737\) −6.00000 6.00000i −0.221013 0.221013i
\(738\) 0 0
\(739\) 44.0000 1.61857 0.809283 0.587419i \(-0.199856\pi\)
0.809283 + 0.587419i \(0.199856\pi\)
\(740\) −13.0000 + 4.00000i −0.477890 + 0.147043i
\(741\) 12.0000 0.440831
\(742\) −18.0000 −0.660801
\(743\) 5.00000 + 5.00000i 0.183432 + 0.183432i 0.792850 0.609417i \(-0.208597\pi\)
−0.609417 + 0.792850i \(0.708597\pi\)
\(744\) 18.0000 0.659912
\(745\) 32.0000 16.0000i 1.17239 0.586195i
\(746\) 3.00000 + 3.00000i 0.109838 + 0.109838i
\(747\) 5.00000 + 5.00000i 0.182940 + 0.182940i
\(748\) −8.00000 −0.292509
\(749\) 18.0000i 0.657706i
\(750\) −9.00000 13.0000i −0.328634 0.474693i
\(751\) 22.0000i 0.802791i −0.915905 0.401396i \(-0.868525\pi\)
0.915905 0.401396i \(-0.131475\pi\)
\(752\) −5.00000 5.00000i −0.182331 0.182331i
\(753\) −10.0000 −0.364420
\(754\) 14.0000 + 14.0000i 0.509850 + 0.509850i
\(755\) 4.00000 2.00000i 0.145575 0.0727875i
\(756\) 24.0000 0.872872
\(757\) 36.0000i 1.30844i −0.756303 0.654221i \(-0.772997\pi\)
0.756303 0.654221i \(-0.227003\pi\)
\(758\) 14.0000i 0.508503i
\(759\) −16.0000 + 16.0000i −0.580763 + 0.580763i
\(760\) −27.0000 9.00000i −0.979393 0.326464i
\(761\) 8.00000i 0.290000i 0.989432 + 0.145000i \(0.0463182\pi\)
−0.989432 + 0.145000i \(0.953682\pi\)
\(762\) 18.0000i 0.652071i
\(763\) 18.0000 0.651644
\(764\) 11.0000 + 11.0000i 0.397966 + 0.397966i
\(765\) −4.00000 8.00000i −0.144620 0.289241i
\(766\) −8.00000 −0.289052
\(767\) 14.0000 14.0000i 0.505511 0.505511i
\(768\) −17.0000 17.0000i −0.613435 0.613435i
\(769\) −15.0000 15.0000i −0.540914 0.540914i 0.382883 0.923797i \(-0.374931\pi\)
−0.923797 + 0.382883i \(0.874931\pi\)
\(770\) −18.0000 6.00000i −0.648675 0.216225i
\(771\) −28.0000 + 28.0000i −1.00840 + 1.00840i
\(772\) −2.00000 −0.0719816
\(773\) −11.0000 + 11.0000i −0.395643 + 0.395643i −0.876693 0.481050i \(-0.840255\pi\)
0.481050 + 0.876693i \(0.340255\pi\)
\(774\) 12.0000i 0.431331i
\(775\) 3.00000 + 21.0000i 0.107763 + 0.754342i
\(776\) 24.0000i 0.861550i
\(777\) 36.0000 + 6.00000i 1.29149 + 0.215249i
\(778\) −5.00000 + 5.00000i −0.179259 + 0.179259i
\(779\) 0 0
\(780\) −2.00000 + 6.00000i −0.0716115 + 0.214834i
\(781\) 16.0000i 0.572525i
\(782\) 32.0000i 1.14432i
\(783\) −56.0000 −2.00128
\(784\) 11.0000i 0.392857i
\(785\) −3.00000 + 9.00000i −0.107075 + 0.321224i
\(786\) 10.0000 0.356688
\(787\) −27.0000 27.0000i −0.962446 0.962446i 0.0368739 0.999320i \(-0.488260\pi\)
−0.999320 + 0.0368739i \(0.988260\pi\)
\(788\) −1.00000 1.00000i −0.0356235 0.0356235i
\(789\) 14.0000i 0.498413i
\(790\) 9.00000 + 3.00000i 0.320206 + 0.106735i
\(791\) −12.0000 + 12.0000i −0.426671 + 0.426671i
\(792\) −6.00000 −0.213201
\(793\) 2.00000 2.00000i 0.0710221 0.0710221i
\(794\) −5.00000 + 5.00000i −0.177443 + 0.177443i
\(795\) 6.00000 + 12.0000i 0.212798 + 0.425596i
\(796\) 15.0000 + 15.0000i 0.531661 + 0.531661i
\(797\) −46.0000 −1.62940 −0.814702 0.579880i \(-0.803099\pi\)
−0.814702 + 0.579880i \(0.803099\pi\)
\(798\) 18.0000 + 18.0000i 0.637193 + 0.637193i
\(799\) −20.0000 + 20.0000i −0.707549 + 0.707549i
\(800\) 15.0000 20.0000i 0.530330 0.707107i
\(801\) 5.00000 5.00000i 0.176666 0.176666i
\(802\) −1.00000 + 1.00000i −0.0353112 + 0.0353112i
\(803\) 2.00000 2.00000i 0.0705785 0.0705785i
\(804\) −6.00000 −0.211604
\(805\) 24.0000 72.0000i 0.845889 2.53767i
\(806\) −6.00000 + 6.00000i −0.211341 + 0.211341i
\(807\) 16.0000 16.0000i 0.563227 0.563227i
\(808\) 0 0
\(809\) 25.0000 + 25.0000i 0.878953 + 0.878953i 0.993426 0.114473i \(-0.0365180\pi\)
−0.114473 + 0.993426i \(0.536518\pi\)
\(810\) 5.00000 + 10.0000i 0.175682 + 0.351364i
\(811\) 20.0000 0.702295 0.351147 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) 42.0000i 1.47391i
\(813\) −8.00000 8.00000i −0.280572 0.280572i
\(814\) −12.0000 2.00000i −0.420600 0.0701000i
\(815\) −20.0000 + 10.0000i −0.700569 + 0.350285i
\(816\) 4.00000 4.00000i 0.140028 0.140028i
\(817\) 36.0000 36.0000i 1.25948 1.25948i
\(818\) 3.00000 + 3.00000i 0.104893 + 0.104893i
\(819\) −6.00000 + 6.00000i −0.209657 + 0.209657i
\(820\) 0 0
\(821\) −18.0000 −0.628204 −0.314102 0.949389i \(-0.601703\pi\)
−0.314102 + 0.949389i \(0.601703\pi\)
\(822\) 14.0000i 0.488306i
\(823\) 11.0000 11.0000i 0.383436 0.383436i −0.488903 0.872338i \(-0.662603\pi\)
0.872338 + 0.488903i \(0.162603\pi\)
\(824\) 42.0000i 1.46314i
\(825\) 2.00000 + 14.0000i 0.0696311 + 0.487417i
\(826\) 42.0000 1.46137
\(827\) 38.0000i 1.32139i 0.750655 + 0.660695i \(0.229738\pi\)
−0.750655 + 0.660695i \(0.770262\pi\)
\(828\) 8.00000i 0.278019i
\(829\) 21.0000 + 21.0000i 0.729360 + 0.729360i 0.970492 0.241132i \(-0.0775187\pi\)
−0.241132 + 0.970492i \(0.577519\pi\)
\(830\) −15.0000 5.00000i −0.520658 0.173553i
\(831\) 26.0000 + 26.0000i 0.901930 + 0.901930i
\(832\) 14.0000 0.485363
\(833\) −44.0000 −1.52451
\(834\) −4.00000 4.00000i −0.138509 0.138509i
\(835\) −12.0000 + 6.00000i −0.415277 + 0.207639i
\(836\) 6.00000 + 6.00000i 0.207514 + 0.207514i
\(837\) 24.0000i 0.829561i
\(838\) 22.0000i 0.759977i
\(839\) 24.0000 0.828572 0.414286 0.910147i \(-0.364031\pi\)
0.414286 + 0.910147i \(0.364031\pi\)
\(840\) −36.0000 + 18.0000i −1.24212 + 0.621059i
\(841\) 69.0000i 2.37931i
\(842\) 27.0000 27.0000i 0.930481 0.930481i
\(843\) 18.0000i 0.619953i
\(844\) −20.0000 −0.688428
\(845\) 9.00000 + 18.0000i 0.309609 + 0.619219i
\(846\) −5.00000 + 5.00000i −0.171904 + 0.171904i
\(847\) −21.0000 21.0000i −0.721569 0.721569i
\(848\) 3.00000 3.00000i 0.103020 0.103020i
\(849\) −22.0000 + 22.0000i −0.755038 + 0.755038i
\(850\) 16.0000 + 12.0000i 0.548795 + 0.411597i
\(851\) 8.00000 48.0000i 0.274236 1.64542i
\(852\) −8.00000 8.00000i −0.274075 0.274075i
\(853\) 44.0000i 1.50653i −0.657716 0.753266i \(-0.728477\pi\)
0.657716 0.753266i \(-0.271523\pi\)
\(854\) 6.00000 0.205316
\(855\) −3.00000 + 9.00000i −0.102598 + 0.307794i
\(856\) −9.00000 9.00000i −0.307614 0.307614i
\(857\) 32.0000i 1.09310i −0.837427 0.546550i \(-0.815941\pi\)
0.837427 0.546550i \(-0.184059\pi\)
\(858\) −4.00000 + 4.00000i −0.136558 + 0.136558i
\(859\) 7.00000 7.00000i 0.238837 0.238837i −0.577531 0.816368i \(-0.695984\pi\)
0.816368 + 0.577531i \(0.195984\pi\)
\(860\) 12.0000 + 24.0000i 0.409197 + 0.818393i
\(861\) 0 0
\(862\) −11.0000 + 11.0000i −0.374661 + 0.374661i
\(863\) 15.0000 15.0000i 0.510606 0.510606i −0.404106 0.914712i \(-0.632417\pi\)
0.914712 + 0.404106i \(0.132417\pi\)
\(864\) −20.0000 + 20.0000i −0.680414 + 0.680414i
\(865\) 1.00000 3.00000i 0.0340010 0.102003i
\(866\) −5.00000 + 5.00000i −0.169907 + 0.169907i
\(867\) 1.00000 + 1.00000i 0.0339618 + 0.0339618i
\(868\) 18.0000 0.610960
\(869\) −6.00000 6.00000i −0.203536 0.203536i
\(870\) 28.0000 14.0000i 0.949289 0.474644i
\(871\) 6.00000 6.00000i 0.203302 0.203302i
\(872\) −9.00000 + 9.00000i −0.304778 + 0.304778i
\(873\) −8.00000 −0.270759
\(874\) 24.0000 24.0000i 0.811812 0.811812i
\(875\) −27.0000 39.0000i −0.912767 1.31844i
\(876\) 2.00000i 0.0675737i
\(877\) 37.0000 + 37.0000i 1.24940 + 1.24940i 0.955985 + 0.293417i \(0.0947923\pi\)
0.293417 + 0.955985i \(0.405208\pi\)
\(878\) −17.0000 17.0000i −0.573722 0.573722i
\(879\) 2.00000 0.0674583
\(880\) 4.00000 2.00000i 0.134840 0.0674200i
\(881\) 12.0000i 0.404290i 0.979356 + 0.202145i \(0.0647913\pi\)
−0.979356 + 0.202145i \(0.935209\pi\)
\(882\) −11.0000 −0.370389
\(883\) 2.00000i 0.0673054i −0.999434 0.0336527i \(-0.989286\pi\)
0.999434 0.0336527i \(-0.0107140\pi\)
\(884\) 8.00000i 0.269069i
\(885\) −14.0000 28.0000i −0.470605 0.941210i
\(886\) 11.0000 + 11.0000i 0.369552 + 0.369552i
\(887\) −5.00000 + 5.00000i −0.167884 + 0.167884i −0.786048 0.618165i \(-0.787876\pi\)
0.618165 + 0.786048i \(0.287876\pi\)
\(888\) −21.0000 + 15.0000i −0.704714 + 0.503367i
\(889\) 54.0000i 1.81110i
\(890\) −5.00000 + 15.0000i −0.167600 + 0.502801i
\(891\) 10.0000i 0.335013i
\(892\) 1.00000 1.00000i 0.0334825 0.0334825i
\(893\) 30.0000 1.00391
\(894\) 16.0000 16.0000i 0.535120 0.535120i
\(895\) −7.00000 + 21.0000i −0.233984 + 0.701953i
\(896\) −9.00000 9.00000i −0.300669 0.300669i
\(897\) −16.0000 16.0000i −0.534224 0.534224i
\(898\) −5.00000 + 5.00000i −0.166852 + 0.166852i
\(899\) −42.0000 −1.40078
\(900\) −4.00000 3.00000i −0.133333 0.100000i
\(901\) −12.0000 12.0000i −0.399778 0.399778i
\(902\) 0 0
\(903\) 72.0000i 2.39601i
\(904\) 12.0000i 0.399114i
\(905\) −10.0000 20.0000i −0.332411 0.664822i
\(906\) 2.00000 2.00000i 0.0664455 0.0664455i
\(907\) 14.0000i 0.464862i 0.972613 + 0.232431i \(0.0746680\pi\)
−0.972613 + 0.232431i \(0.925332\pi\)
\(908\) 2.00000i 0.0663723i
\(909\) 0 0
\(910\) 6.00000 18.0000i 0.198898 0.596694i
\(911\) −11.0000 11.0000i −0.364446 0.364446i 0.501001 0.865447i \(-0.332965\pi\)
−0.865447 + 0.501001i \(0.832965\pi\)
\(912\) −6.00000 −0.198680
\(913\) 10.0000 + 10.0000i 0.330952 + 0.330952i
\(914\) 32.0000i 1.05847i
\(915\) −2.00000 4.00000i −0.0661180 0.132236i
\(916\) 4.00000i 0.132164i
\(917\) 30.0000 0.990687
\(918\) −16.0000 16.0000i −0.528079 0.528079i
\(919\) −3.00000 3.00000i −0.0989609 0.0989609i 0.655893 0.754854i \(-0.272292\pi\)
−0.754854 + 0.655893i \(0.772292\pi\)
\(920\) 24.0000 + 48.0000i 0.791257 + 1.58251i
\(921\) −18.0000 −0.593120
\(922\) −21.0000 21.0000i −0.691598 0.691598i
\(923\) 16.0000 0.526646
\(924\) 12.0000 0.394771
\(925\) −21.0000 22.0000i −0.690476 0.723356i
\(926\) −40.0000 −1.31448
\(927\) −14.0000 −0.459820
\(928\) 35.0000 + 35.0000i 1.14893 + 1.14893i
\(929\) 34.0000 1.11550 0.557752 0.830008i \(-0.311664\pi\)
0.557752 + 0.830008i \(0.311664\pi\)
\(930\) 6.00000 + 12.0000i 0.196748 + 0.393496i
\(931\) 33.0000 + 33.0000i 1.08153 + 1.08153i
\(932\) −1.00000 1.00000i −0.0327561 0.0327561i
\(933\) 6.00000 0.196431
\(934\) 38.0000i 1.24340i
\(935\) −8.00000 16.0000i −0.261628 0.523256i
\(936\) 6.00000i 0.196116i
\(937\) −35.0000 35.0000i −1.14340 1.14340i −0.987824 0.155576i \(-0.950277\pi\)
−0.155576 0.987824i \(-0.549723\pi\)
\(938\) 18.0000 0.587721
\(939\) −30.0000 30.0000i −0.979013 0.979013i
\(940\) −5.00000 + 15.0000i −0.163082 + 0.489246i
\(941\) −30.0000 −0.977972 −0.488986 0.872292i \(-0.662633\pi\)
−0.488986 + 0.872292i \(0.662633\pi\)
\(942\) 6.00000i 0.195491i
\(943\) 0 0
\(944\) −7.00000 + 7.00000i −0.227831 + 0.227831i
\(945\) 24.0000 + 48.0000i 0.780720 + 1.56144i
\(946\) 24.0000i 0.780307i
\(947\) 18.0000i 0.584921i −0.956278 0.292461i \(-0.905526\pi\)
0.956278 0.292461i \(-0.0944741\pi\)
\(948\) −6.00000 −0.194871
\(949\) 2.00000 + 2.00000i 0.0649227 + 0.0649227i
\(950\) −3.00000 21.0000i −0.0973329 0.681330i
\(951\) 34.0000 1.10253
\(952\) 36.0000 36.0000i 1.16677 1.16677i
\(953\) −7.00000 7.00000i −0.226752 0.226752i 0.584582 0.811334i \(-0.301258\pi\)
−0.811334 + 0.584582i \(0.801258\pi\)
\(954\) −3.00000 3.00000i −0.0971286 0.0971286i
\(955\) −11.0000 + 33.0000i −0.355952 + 1.06785i
\(956\) −7.00000 + 7.00000i −0.226396 + 0.226396i
\(957\) −28.0000 −0.905111
\(958\) −23.0000 + 23.0000i −0.743096 + 0.743096i
\(959\) 42.0000i 1.35625i
\(960\) 7.00000 21.0000i 0.225924 0.677772i
\(961\) 13.0000i 0.419355i
\(962\) 2.00000 12.0000i 0.0644826 0.386896i
\(963\) −3.00000 + 3.00000i −0.0966736 + 0.0966736i
\(964\) −1.00000 1.00000i −0.0322078 0.0322078i
\(965\) −2.00000 4.00000i −0.0643823 0.128765i
\(966\) 48.0000i 1.54437i
\(967\) 2.00000i 0.0643157i 0.999483 + 0.0321578i \(0.0102379\pi\)
−0.999483 + 0.0321578i \(0.989762\pi\)
\(968\) 21.0000 0.674966
\(969\) 24.0000i 0.770991i
\(970\) 16.0000 8.00000i 0.513729 0.256865i
\(971\) 36.0000 1.15529 0.577647 0.816286i \(-0.303971\pi\)
0.577647 + 0.816286i \(0.303971\pi\)
\(972\) 7.00000 + 7.00000i 0.224525 + 0.224525i
\(973\) −12.0000 12.0000i −0.384702 0.384702i
\(974\) 2.00000i 0.0640841i
\(975\) −14.0000 + 2.00000i −0.448359 + 0.0640513i
\(976\) −1.00000 + 1.00000i −0.0320092 + 0.0320092i
\(977\) 18.0000 0.575871 0.287936 0.957650i \(-0.407031\pi\)
0.287936 + 0.957650i \(0.407031\pi\)
\(978\) −10.0000 + 10.0000i −0.319765 + 0.319765i
\(979\) 10.0000 10.0000i 0.319601 0.319601i
\(980\) −22.0000 + 11.0000i −0.702764 + 0.351382i
\(981\) 3.00000 + 3.00000i 0.0957826 + 0.0957826i
\(982\) 4.00000 0.127645
\(983\) −15.0000 15.0000i −0.478426 0.478426i 0.426202 0.904628i \(-0.359851\pi\)
−0.904628 + 0.426202i \(0.859851\pi\)
\(984\) 0 0
\(985\) 1.00000 3.00000i 0.0318626 0.0955879i
\(986\) −28.0000 + 28.0000i −0.891702 + 0.891702i
\(987\) 30.0000 30.0000i 0.954911 0.954911i
\(988\) −6.00000 + 6.00000i −0.190885 + 0.190885i
\(989\) −96.0000 −3.05262
\(990\) −2.00000 4.00000i −0.0635642 0.127128i
\(991\) 39.0000 39.0000i 1.23888 1.23888i 0.278415 0.960461i \(-0.410191\pi\)
0.960461 0.278415i \(-0.0898090\pi\)
\(992\) −15.0000 + 15.0000i −0.476250 + 0.476250i
\(993\) 14.0000i 0.444277i
\(994\) 24.0000 + 24.0000i 0.761234 + 0.761234i
\(995\) −15.0000 + 45.0000i −0.475532 + 1.42660i
\(996\) 10.0000 0.316862
\(997\) 28.0000i 0.886769i 0.896332 + 0.443384i \(0.146222\pi\)
−0.896332 + 0.443384i \(0.853778\pi\)
\(998\) 27.0000 + 27.0000i 0.854670 + 0.854670i
\(999\) 20.0000 + 28.0000i 0.632772 + 0.885881i
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 185.2.k.b.117.1 yes 2
5.2 odd 4 925.2.f.b.43.1 2
5.3 odd 4 185.2.f.a.43.1 2
5.4 even 2 925.2.k.a.857.1 2
37.31 odd 4 185.2.f.a.142.1 yes 2
185.68 even 4 inner 185.2.k.b.68.1 yes 2
185.142 even 4 925.2.k.a.68.1 2
185.179 odd 4 925.2.f.b.882.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
185.2.f.a.43.1 2 5.3 odd 4
185.2.f.a.142.1 yes 2 37.31 odd 4
185.2.k.b.68.1 yes 2 185.68 even 4 inner
185.2.k.b.117.1 yes 2 1.1 even 1 trivial
925.2.f.b.43.1 2 5.2 odd 4
925.2.f.b.882.1 2 185.179 odd 4
925.2.k.a.68.1 2 185.142 even 4
925.2.k.a.857.1 2 5.4 even 2