Properties

Label 35.2.f.a.13.2
Level $35$
Weight $2$
Character 35.13
Analytic conductor $0.279$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [35,2,Mod(13,35)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(35, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("35.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 35.f (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: \(0.279476407074\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 25 \) 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 13.2
Root \(1.58114 - 1.58114i\) of defining polynomial
Character \(\chi\) \(=\) 35.13
Dual form 35.2.f.a.27.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} +(1.58114 - 1.58114i) q^{3} +(-1.58114 + 1.58114i) q^{5} +3.16228i q^{6} +(-0.581139 - 2.58114i) q^{7} +(-2.00000 - 2.00000i) q^{8} -2.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.00000i) q^{2} +(1.58114 - 1.58114i) q^{3} +(-1.58114 + 1.58114i) q^{5} +3.16228i q^{6} +(-0.581139 - 2.58114i) q^{7} +(-2.00000 - 2.00000i) q^{8} -2.00000i q^{9} -3.16228i q^{10} -1.00000 q^{11} +(-1.58114 + 1.58114i) q^{13} +(3.16228 + 2.00000i) q^{14} +5.00000i q^{15} +4.00000 q^{16} +(1.58114 + 1.58114i) q^{17} +(2.00000 + 2.00000i) q^{18} +3.16228 q^{19} +(-5.00000 - 3.16228i) q^{21} +(1.00000 - 1.00000i) q^{22} +(2.00000 + 2.00000i) q^{23} -6.32456 q^{24} -5.00000i q^{25} -3.16228i q^{26} +(1.58114 + 1.58114i) q^{27} -3.00000i q^{29} +(-5.00000 - 5.00000i) q^{30} +3.16228i q^{31} +(-1.58114 + 1.58114i) q^{33} -3.16228 q^{34} +(5.00000 + 3.16228i) q^{35} +(-6.00000 + 6.00000i) q^{37} +(-3.16228 + 3.16228i) q^{38} +5.00000i q^{39} +6.32456 q^{40} -9.48683i q^{41} +(8.16228 - 1.83772i) q^{42} +(-3.00000 - 3.00000i) q^{43} +(3.16228 + 3.16228i) q^{45} -4.00000 q^{46} +(-4.74342 - 4.74342i) q^{47} +(6.32456 - 6.32456i) q^{48} +(-6.32456 + 3.00000i) q^{49} +(5.00000 + 5.00000i) q^{50} +5.00000 q^{51} +(1.00000 + 1.00000i) q^{53} -3.16228 q^{54} +(1.58114 - 1.58114i) q^{55} +(-4.00000 + 6.32456i) q^{56} +(5.00000 - 5.00000i) q^{57} +(3.00000 + 3.00000i) q^{58} +9.48683 q^{59} +6.32456i q^{61} +(-3.16228 - 3.16228i) q^{62} +(-5.16228 + 1.16228i) q^{63} +8.00000i q^{64} -5.00000i q^{65} -3.16228i q^{66} +(-1.00000 + 1.00000i) q^{67} +6.32456 q^{69} +(-8.16228 + 1.83772i) q^{70} -6.00000 q^{71} +(-4.00000 + 4.00000i) q^{72} -12.0000i q^{74} +(-7.90569 - 7.90569i) q^{75} +(0.581139 + 2.58114i) q^{77} +(-5.00000 - 5.00000i) q^{78} -13.0000i q^{79} +(-6.32456 + 6.32456i) q^{80} +11.0000 q^{81} +(9.48683 + 9.48683i) q^{82} +(-3.16228 + 3.16228i) q^{83} -5.00000 q^{85} +6.00000 q^{86} +(-4.74342 - 4.74342i) q^{87} +(2.00000 + 2.00000i) q^{88} -6.32456 q^{89} -6.32456 q^{90} +(5.00000 + 3.16228i) q^{91} +(5.00000 + 5.00000i) q^{93} +9.48683 q^{94} +(-5.00000 + 5.00000i) q^{95} +(-1.58114 - 1.58114i) q^{97} +(3.32456 - 9.32456i) q^{98} +2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} + 4 q^{7} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} + 4 q^{7} - 8 q^{8} - 4 q^{11} + 16 q^{16} + 8 q^{18} - 20 q^{21} + 4 q^{22} + 8 q^{23} - 20 q^{30} + 20 q^{35} - 24 q^{37} + 20 q^{42} - 12 q^{43} - 16 q^{46} + 20 q^{50} + 20 q^{51} + 4 q^{53} - 16 q^{56} + 20 q^{57} + 12 q^{58} - 8 q^{63} - 4 q^{67} - 20 q^{70} - 24 q^{71} - 16 q^{72} - 4 q^{77} - 20 q^{78} + 44 q^{81} - 20 q^{85} + 24 q^{86} + 8 q^{88} + 20 q^{91} + 20 q^{93} - 20 q^{95} - 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.00000i −0.707107 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(3\) 1.58114 1.58114i 0.912871 0.912871i −0.0836263 0.996497i \(-0.526650\pi\)
0.996497 + 0.0836263i \(0.0266502\pi\)
\(4\) 0 0
\(5\) −1.58114 + 1.58114i −0.707107 + 0.707107i
\(6\) 3.16228i 1.29099i
\(7\) −0.581139 2.58114i −0.219650 0.975579i
\(8\) −2.00000 2.00000i −0.707107 0.707107i
\(9\) 2.00000i 0.666667i
\(10\) 3.16228i 1.00000i
\(11\) −1.00000 −0.301511 −0.150756 0.988571i \(-0.548171\pi\)
−0.150756 + 0.988571i \(0.548171\pi\)
\(12\) 0 0
\(13\) −1.58114 + 1.58114i −0.438529 + 0.438529i −0.891517 0.452988i \(-0.850358\pi\)
0.452988 + 0.891517i \(0.350358\pi\)
\(14\) 3.16228 + 2.00000i 0.845154 + 0.534522i
\(15\) 5.00000i 1.29099i
\(16\) 4.00000 1.00000
\(17\) 1.58114 + 1.58114i 0.383482 + 0.383482i 0.872355 0.488873i \(-0.162592\pi\)
−0.488873 + 0.872355i \(0.662592\pi\)
\(18\) 2.00000 + 2.00000i 0.471405 + 0.471405i
\(19\) 3.16228 0.725476 0.362738 0.931891i \(-0.381842\pi\)
0.362738 + 0.931891i \(0.381842\pi\)
\(20\) 0 0
\(21\) −5.00000 3.16228i −1.09109 0.690066i
\(22\) 1.00000 1.00000i 0.213201 0.213201i
\(23\) 2.00000 + 2.00000i 0.417029 + 0.417029i 0.884178 0.467150i \(-0.154719\pi\)
−0.467150 + 0.884178i \(0.654719\pi\)
\(24\) −6.32456 −1.29099
\(25\) 5.00000i 1.00000i
\(26\) 3.16228i 0.620174i
\(27\) 1.58114 + 1.58114i 0.304290 + 0.304290i
\(28\) 0 0
\(29\) 3.00000i 0.557086i −0.960424 0.278543i \(-0.910149\pi\)
0.960424 0.278543i \(-0.0898515\pi\)
\(30\) −5.00000 5.00000i −0.912871 0.912871i
\(31\) 3.16228i 0.567962i 0.958830 + 0.283981i \(0.0916552\pi\)
−0.958830 + 0.283981i \(0.908345\pi\)
\(32\) 0 0
\(33\) −1.58114 + 1.58114i −0.275241 + 0.275241i
\(34\) −3.16228 −0.542326
\(35\) 5.00000 + 3.16228i 0.845154 + 0.534522i
\(36\) 0 0
\(37\) −6.00000 + 6.00000i −0.986394 + 0.986394i −0.999909 0.0135147i \(-0.995698\pi\)
0.0135147 + 0.999909i \(0.495698\pi\)
\(38\) −3.16228 + 3.16228i −0.512989 + 0.512989i
\(39\) 5.00000i 0.800641i
\(40\) 6.32456 1.00000
\(41\) 9.48683i 1.48159i −0.671729 0.740797i \(-0.734448\pi\)
0.671729 0.740797i \(-0.265552\pi\)
\(42\) 8.16228 1.83772i 1.25947 0.283567i
\(43\) −3.00000 3.00000i −0.457496 0.457496i 0.440337 0.897833i \(-0.354859\pi\)
−0.897833 + 0.440337i \(0.854859\pi\)
\(44\) 0 0
\(45\) 3.16228 + 3.16228i 0.471405 + 0.471405i
\(46\) −4.00000 −0.589768
\(47\) −4.74342 4.74342i −0.691898 0.691898i 0.270751 0.962649i \(-0.412728\pi\)
−0.962649 + 0.270751i \(0.912728\pi\)
\(48\) 6.32456 6.32456i 0.912871 0.912871i
\(49\) −6.32456 + 3.00000i −0.903508 + 0.428571i
\(50\) 5.00000 + 5.00000i 0.707107 + 0.707107i
\(51\) 5.00000 0.700140
\(52\) 0 0
\(53\) 1.00000 + 1.00000i 0.137361 + 0.137361i 0.772444 0.635083i \(-0.219034\pi\)
−0.635083 + 0.772444i \(0.719034\pi\)
\(54\) −3.16228 −0.430331
\(55\) 1.58114 1.58114i 0.213201 0.213201i
\(56\) −4.00000 + 6.32456i −0.534522 + 0.845154i
\(57\) 5.00000 5.00000i 0.662266 0.662266i
\(58\) 3.00000 + 3.00000i 0.393919 + 0.393919i
\(59\) 9.48683 1.23508 0.617540 0.786539i \(-0.288129\pi\)
0.617540 + 0.786539i \(0.288129\pi\)
\(60\) 0 0
\(61\) 6.32456i 0.809776i 0.914366 + 0.404888i \(0.132690\pi\)
−0.914366 + 0.404888i \(0.867310\pi\)
\(62\) −3.16228 3.16228i −0.401610 0.401610i
\(63\) −5.16228 + 1.16228i −0.650386 + 0.146433i
\(64\) 8.00000i 1.00000i
\(65\) 5.00000i 0.620174i
\(66\) 3.16228i 0.389249i
\(67\) −1.00000 + 1.00000i −0.122169 + 0.122169i −0.765548 0.643379i \(-0.777532\pi\)
0.643379 + 0.765548i \(0.277532\pi\)
\(68\) 0 0
\(69\) 6.32456 0.761387
\(70\) −8.16228 + 1.83772i −0.975579 + 0.219650i
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) −4.00000 + 4.00000i −0.471405 + 0.471405i
\(73\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(74\) 12.0000i 1.39497i
\(75\) −7.90569 7.90569i −0.912871 0.912871i
\(76\) 0 0
\(77\) 0.581139 + 2.58114i 0.0662269 + 0.294148i
\(78\) −5.00000 5.00000i −0.566139 0.566139i
\(79\) 13.0000i 1.46261i −0.682048 0.731307i \(-0.738911\pi\)
0.682048 0.731307i \(-0.261089\pi\)
\(80\) −6.32456 + 6.32456i −0.707107 + 0.707107i
\(81\) 11.0000 1.22222
\(82\) 9.48683 + 9.48683i 1.04765 + 1.04765i
\(83\) −3.16228 + 3.16228i −0.347105 + 0.347105i −0.859030 0.511925i \(-0.828933\pi\)
0.511925 + 0.859030i \(0.328933\pi\)
\(84\) 0 0
\(85\) −5.00000 −0.542326
\(86\) 6.00000 0.646997
\(87\) −4.74342 4.74342i −0.508548 0.508548i
\(88\) 2.00000 + 2.00000i 0.213201 + 0.213201i
\(89\) −6.32456 −0.670402 −0.335201 0.942147i \(-0.608804\pi\)
−0.335201 + 0.942147i \(0.608804\pi\)
\(90\) −6.32456 −0.666667
\(91\) 5.00000 + 3.16228i 0.524142 + 0.331497i
\(92\) 0 0
\(93\) 5.00000 + 5.00000i 0.518476 + 0.518476i
\(94\) 9.48683 0.978492
\(95\) −5.00000 + 5.00000i −0.512989 + 0.512989i
\(96\) 0 0
\(97\) −1.58114 1.58114i −0.160540 0.160540i 0.622266 0.782806i \(-0.286212\pi\)
−0.782806 + 0.622266i \(0.786212\pi\)
\(98\) 3.32456 9.32456i 0.335831 0.941922i
\(99\) 2.00000i 0.201008i
\(100\) 0 0
\(101\) 3.16228i 0.314658i −0.987546 0.157329i \(-0.949712\pi\)
0.987546 0.157329i \(-0.0502884\pi\)
\(102\) −5.00000 + 5.00000i −0.495074 + 0.495074i
\(103\) 11.0680 11.0680i 1.09056 1.09056i 0.0950911 0.995469i \(-0.469686\pi\)
0.995469 0.0950911i \(-0.0303142\pi\)
\(104\) 6.32456 0.620174
\(105\) 12.9057 2.90569i 1.25947 0.283567i
\(106\) −2.00000 −0.194257
\(107\) −3.00000 + 3.00000i −0.290021 + 0.290021i −0.837088 0.547068i \(-0.815744\pi\)
0.547068 + 0.837088i \(0.315744\pi\)
\(108\) 0 0
\(109\) 7.00000i 0.670478i 0.942133 + 0.335239i \(0.108817\pi\)
−0.942133 + 0.335239i \(0.891183\pi\)
\(110\) 3.16228i 0.301511i
\(111\) 18.9737i 1.80090i
\(112\) −2.32456 10.3246i −0.219650 0.975579i
\(113\) 12.0000 + 12.0000i 1.12887 + 1.12887i 0.990362 + 0.138503i \(0.0442291\pi\)
0.138503 + 0.990362i \(0.455771\pi\)
\(114\) 10.0000i 0.936586i
\(115\) −6.32456 −0.589768
\(116\) 0 0
\(117\) 3.16228 + 3.16228i 0.292353 + 0.292353i
\(118\) −9.48683 + 9.48683i −0.873334 + 0.873334i
\(119\) 3.16228 5.00000i 0.289886 0.458349i
\(120\) 10.0000 10.0000i 0.912871 0.912871i
\(121\) −10.0000 −0.909091
\(122\) −6.32456 6.32456i −0.572598 0.572598i
\(123\) −15.0000 15.0000i −1.35250 1.35250i
\(124\) 0 0
\(125\) 7.90569 + 7.90569i 0.707107 + 0.707107i
\(126\) 4.00000 6.32456i 0.356348 0.563436i
\(127\) 9.00000 9.00000i 0.798621 0.798621i −0.184257 0.982878i \(-0.558988\pi\)
0.982878 + 0.184257i \(0.0589879\pi\)
\(128\) −8.00000 8.00000i −0.707107 0.707107i
\(129\) −9.48683 −0.835269
\(130\) 5.00000 + 5.00000i 0.438529 + 0.438529i
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) −1.83772 8.16228i −0.159351 0.707759i
\(134\) 2.00000i 0.172774i
\(135\) −5.00000 −0.430331
\(136\) 6.32456i 0.542326i
\(137\) 2.00000 2.00000i 0.170872 0.170872i −0.616491 0.787362i \(-0.711446\pi\)
0.787362 + 0.616491i \(0.211446\pi\)
\(138\) −6.32456 + 6.32456i −0.538382 + 0.538382i
\(139\) −18.9737 −1.60933 −0.804663 0.593732i \(-0.797654\pi\)
−0.804663 + 0.593732i \(0.797654\pi\)
\(140\) 0 0
\(141\) −15.0000 −1.26323
\(142\) 6.00000 6.00000i 0.503509 0.503509i
\(143\) 1.58114 1.58114i 0.132221 0.132221i
\(144\) 8.00000i 0.666667i
\(145\) 4.74342 + 4.74342i 0.393919 + 0.393919i
\(146\) 0 0
\(147\) −5.25658 + 14.7434i −0.433556 + 1.21602i
\(148\) 0 0
\(149\) 12.0000i 0.983078i 0.870855 + 0.491539i \(0.163566\pi\)
−0.870855 + 0.491539i \(0.836434\pi\)
\(150\) 15.8114 1.29099
\(151\) 9.00000 0.732410 0.366205 0.930534i \(-0.380657\pi\)
0.366205 + 0.930534i \(0.380657\pi\)
\(152\) −6.32456 6.32456i −0.512989 0.512989i
\(153\) 3.16228 3.16228i 0.255655 0.255655i
\(154\) −3.16228 2.00000i −0.254824 0.161165i
\(155\) −5.00000 5.00000i −0.401610 0.401610i
\(156\) 0 0
\(157\) 6.32456 + 6.32456i 0.504754 + 0.504754i 0.912912 0.408157i \(-0.133828\pi\)
−0.408157 + 0.912912i \(0.633828\pi\)
\(158\) 13.0000 + 13.0000i 1.03422 + 1.03422i
\(159\) 3.16228 0.250785
\(160\) 0 0
\(161\) 4.00000 6.32456i 0.315244 0.498445i
\(162\) −11.0000 + 11.0000i −0.864242 + 0.864242i
\(163\) 6.00000 + 6.00000i 0.469956 + 0.469956i 0.901900 0.431944i \(-0.142172\pi\)
−0.431944 + 0.901900i \(0.642172\pi\)
\(164\) 0 0
\(165\) 5.00000i 0.389249i
\(166\) 6.32456i 0.490881i
\(167\) 11.0680 + 11.0680i 0.856465 + 0.856465i 0.990920 0.134454i \(-0.0429282\pi\)
−0.134454 + 0.990920i \(0.542928\pi\)
\(168\) 3.67544 + 16.3246i 0.283567 + 1.25947i
\(169\) 8.00000i 0.615385i
\(170\) 5.00000 5.00000i 0.383482 0.383482i
\(171\) 6.32456i 0.483651i
\(172\) 0 0
\(173\) −11.0680 + 11.0680i −0.841482 + 0.841482i −0.989052 0.147569i \(-0.952855\pi\)
0.147569 + 0.989052i \(0.452855\pi\)
\(174\) 9.48683 0.719195
\(175\) −12.9057 + 2.90569i −0.975579 + 0.219650i
\(176\) −4.00000 −0.301511
\(177\) 15.0000 15.0000i 1.12747 1.12747i
\(178\) 6.32456 6.32456i 0.474045 0.474045i
\(179\) 6.00000i 0.448461i 0.974536 + 0.224231i \(0.0719869\pi\)
−0.974536 + 0.224231i \(0.928013\pi\)
\(180\) 0 0
\(181\) 22.1359i 1.64535i −0.568511 0.822676i \(-0.692480\pi\)
0.568511 0.822676i \(-0.307520\pi\)
\(182\) −8.16228 + 1.83772i −0.605028 + 0.136221i
\(183\) 10.0000 + 10.0000i 0.739221 + 0.739221i
\(184\) 8.00000i 0.589768i
\(185\) 18.9737i 1.39497i
\(186\) −10.0000 −0.733236
\(187\) −1.58114 1.58114i −0.115624 0.115624i
\(188\) 0 0
\(189\) 3.16228 5.00000i 0.230022 0.363696i
\(190\) 10.0000i 0.725476i
\(191\) −3.00000 −0.217072 −0.108536 0.994092i \(-0.534616\pi\)
−0.108536 + 0.994092i \(0.534616\pi\)
\(192\) 12.6491 + 12.6491i 0.912871 + 0.912871i
\(193\) −8.00000 8.00000i −0.575853 0.575853i 0.357905 0.933758i \(-0.383491\pi\)
−0.933758 + 0.357905i \(0.883491\pi\)
\(194\) 3.16228 0.227038
\(195\) −7.90569 7.90569i −0.566139 0.566139i
\(196\) 0 0
\(197\) −1.00000 + 1.00000i −0.0712470 + 0.0712470i −0.741832 0.670585i \(-0.766043\pi\)
0.670585 + 0.741832i \(0.266043\pi\)
\(198\) −2.00000 2.00000i −0.142134 0.142134i
\(199\) −9.48683 −0.672504 −0.336252 0.941772i \(-0.609159\pi\)
−0.336252 + 0.941772i \(0.609159\pi\)
\(200\) −10.0000 + 10.0000i −0.707107 + 0.707107i
\(201\) 3.16228i 0.223050i
\(202\) 3.16228 + 3.16228i 0.222497 + 0.222497i
\(203\) −7.74342 + 1.74342i −0.543481 + 0.122364i
\(204\) 0 0
\(205\) 15.0000 + 15.0000i 1.04765 + 1.04765i
\(206\) 22.1359i 1.54228i
\(207\) 4.00000 4.00000i 0.278019 0.278019i
\(208\) −6.32456 + 6.32456i −0.438529 + 0.438529i
\(209\) −3.16228 −0.218739
\(210\) −10.0000 + 15.8114i −0.690066 + 1.09109i
\(211\) 17.0000 1.17033 0.585164 0.810915i \(-0.301030\pi\)
0.585164 + 0.810915i \(0.301030\pi\)
\(212\) 0 0
\(213\) −9.48683 + 9.48683i −0.650027 + 0.650027i
\(214\) 6.00000i 0.410152i
\(215\) 9.48683 0.646997
\(216\) 6.32456i 0.430331i
\(217\) 8.16228 1.83772i 0.554092 0.124753i
\(218\) −7.00000 7.00000i −0.474100 0.474100i
\(219\) 0 0
\(220\) 0 0
\(221\) −5.00000 −0.336336
\(222\) −18.9737 18.9737i −1.27343 1.27343i
\(223\) 14.2302 14.2302i 0.952928 0.952928i −0.0460129 0.998941i \(-0.514652\pi\)
0.998941 + 0.0460129i \(0.0146515\pi\)
\(224\) 0 0
\(225\) −10.0000 −0.666667
\(226\) −24.0000 −1.59646
\(227\) −1.58114 1.58114i −0.104944 0.104944i 0.652685 0.757629i \(-0.273642\pi\)
−0.757629 + 0.652685i \(0.773642\pi\)
\(228\) 0 0
\(229\) 15.8114 1.04485 0.522423 0.852686i \(-0.325028\pi\)
0.522423 + 0.852686i \(0.325028\pi\)
\(230\) 6.32456 6.32456i 0.417029 0.417029i
\(231\) 5.00000 + 3.16228i 0.328976 + 0.208063i
\(232\) −6.00000 + 6.00000i −0.393919 + 0.393919i
\(233\) −18.0000 18.0000i −1.17922 1.17922i −0.979943 0.199276i \(-0.936141\pi\)
−0.199276 0.979943i \(-0.563859\pi\)
\(234\) −6.32456 −0.413449
\(235\) 15.0000 0.978492
\(236\) 0 0
\(237\) −20.5548 20.5548i −1.33518 1.33518i
\(238\) 1.83772 + 8.16228i 0.119122 + 0.529082i
\(239\) 19.0000i 1.22901i −0.788914 0.614504i \(-0.789356\pi\)
0.788914 0.614504i \(-0.210644\pi\)
\(240\) 20.0000i 1.29099i
\(241\) 25.2982i 1.62960i 0.579741 + 0.814801i \(0.303154\pi\)
−0.579741 + 0.814801i \(0.696846\pi\)
\(242\) 10.0000 10.0000i 0.642824 0.642824i
\(243\) 12.6491 12.6491i 0.811441 0.811441i
\(244\) 0 0
\(245\) 5.25658 14.7434i 0.335831 0.941922i
\(246\) 30.0000 1.91273
\(247\) −5.00000 + 5.00000i −0.318142 + 0.318142i
\(248\) 6.32456 6.32456i 0.401610 0.401610i
\(249\) 10.0000i 0.633724i
\(250\) −15.8114 −1.00000
\(251\) 12.6491i 0.798405i 0.916863 + 0.399202i \(0.130713\pi\)
−0.916863 + 0.399202i \(0.869287\pi\)
\(252\) 0 0
\(253\) −2.00000 2.00000i −0.125739 0.125739i
\(254\) 18.0000i 1.12942i
\(255\) −7.90569 + 7.90569i −0.495074 + 0.495074i
\(256\) 0 0
\(257\) 12.6491 + 12.6491i 0.789030 + 0.789030i 0.981335 0.192305i \(-0.0615964\pi\)
−0.192305 + 0.981335i \(0.561596\pi\)
\(258\) 9.48683 9.48683i 0.590624 0.590624i
\(259\) 18.9737 + 12.0000i 1.17897 + 0.745644i
\(260\) 0 0
\(261\) −6.00000 −0.371391
\(262\) 0 0
\(263\) 7.00000 + 7.00000i 0.431638 + 0.431638i 0.889185 0.457547i \(-0.151272\pi\)
−0.457547 + 0.889185i \(0.651272\pi\)
\(264\) 6.32456 0.389249
\(265\) −3.16228 −0.194257
\(266\) 10.0000 + 6.32456i 0.613139 + 0.387783i
\(267\) −10.0000 + 10.0000i −0.611990 + 0.611990i
\(268\) 0 0
\(269\) −18.9737 −1.15684 −0.578422 0.815737i \(-0.696331\pi\)
−0.578422 + 0.815737i \(0.696331\pi\)
\(270\) 5.00000 5.00000i 0.304290 0.304290i
\(271\) 12.6491i 0.768379i −0.923254 0.384189i \(-0.874481\pi\)
0.923254 0.384189i \(-0.125519\pi\)
\(272\) 6.32456 + 6.32456i 0.383482 + 0.383482i
\(273\) 12.9057 2.90569i 0.781088 0.175861i
\(274\) 4.00000i 0.241649i
\(275\) 5.00000i 0.301511i
\(276\) 0 0
\(277\) −18.0000 + 18.0000i −1.08152 + 1.08152i −0.0851468 + 0.996368i \(0.527136\pi\)
−0.996368 + 0.0851468i \(0.972864\pi\)
\(278\) 18.9737 18.9737i 1.13796 1.13796i
\(279\) 6.32456 0.378641
\(280\) −3.67544 16.3246i −0.219650 0.975579i
\(281\) 9.00000 0.536895 0.268447 0.963294i \(-0.413489\pi\)
0.268447 + 0.963294i \(0.413489\pi\)
\(282\) 15.0000 15.0000i 0.893237 0.893237i
\(283\) −4.74342 + 4.74342i −0.281967 + 0.281967i −0.833893 0.551926i \(-0.813893\pi\)
0.551926 + 0.833893i \(0.313893\pi\)
\(284\) 0 0
\(285\) 15.8114i 0.936586i
\(286\) 3.16228i 0.186989i
\(287\) −24.4868 + 5.51317i −1.44541 + 0.325432i
\(288\) 0 0
\(289\) 12.0000i 0.705882i
\(290\) −9.48683 −0.557086
\(291\) −5.00000 −0.293105
\(292\) 0 0
\(293\) −7.90569 + 7.90569i −0.461856 + 0.461856i −0.899263 0.437408i \(-0.855897\pi\)
0.437408 + 0.899263i \(0.355897\pi\)
\(294\) −9.48683 20.0000i −0.553283 1.16642i
\(295\) −15.0000 + 15.0000i −0.873334 + 0.873334i
\(296\) 24.0000 1.39497
\(297\) −1.58114 1.58114i −0.0917470 0.0917470i
\(298\) −12.0000 12.0000i −0.695141 0.695141i
\(299\) −6.32456 −0.365758
\(300\) 0 0
\(301\) −6.00000 + 9.48683i −0.345834 + 0.546812i
\(302\) −9.00000 + 9.00000i −0.517892 + 0.517892i
\(303\) −5.00000 5.00000i −0.287242 0.287242i
\(304\) 12.6491 0.725476
\(305\) −10.0000 10.0000i −0.572598 0.572598i
\(306\) 6.32456i 0.361551i
\(307\) −4.74342 4.74342i −0.270721 0.270721i 0.558669 0.829390i \(-0.311312\pi\)
−0.829390 + 0.558669i \(0.811312\pi\)
\(308\) 0 0
\(309\) 35.0000i 1.99108i
\(310\) 10.0000 0.567962
\(311\) 22.1359i 1.25521i −0.778530 0.627607i \(-0.784034\pi\)
0.778530 0.627607i \(-0.215966\pi\)
\(312\) 10.0000 10.0000i 0.566139 0.566139i
\(313\) −14.2302 + 14.2302i −0.804341 + 0.804341i −0.983771 0.179430i \(-0.942575\pi\)
0.179430 + 0.983771i \(0.442575\pi\)
\(314\) −12.6491 −0.713831
\(315\) 6.32456 10.0000i 0.356348 0.563436i
\(316\) 0 0
\(317\) 19.0000 19.0000i 1.06715 1.06715i 0.0695692 0.997577i \(-0.477838\pi\)
0.997577 0.0695692i \(-0.0221625\pi\)
\(318\) −3.16228 + 3.16228i −0.177332 + 0.177332i
\(319\) 3.00000i 0.167968i
\(320\) −12.6491 12.6491i −0.707107 0.707107i
\(321\) 9.48683i 0.529503i
\(322\) 2.32456 + 10.3246i 0.129542 + 0.575365i
\(323\) 5.00000 + 5.00000i 0.278207 + 0.278207i
\(324\) 0 0
\(325\) 7.90569 + 7.90569i 0.438529 + 0.438529i
\(326\) −12.0000 −0.664619
\(327\) 11.0680 + 11.0680i 0.612060 + 0.612060i
\(328\) −18.9737 + 18.9737i −1.04765 + 1.04765i
\(329\) −9.48683 + 15.0000i −0.523026 + 0.826977i
\(330\) 5.00000 + 5.00000i 0.275241 + 0.275241i
\(331\) −6.00000 −0.329790 −0.164895 0.986311i \(-0.552728\pi\)
−0.164895 + 0.986311i \(0.552728\pi\)
\(332\) 0 0
\(333\) 12.0000 + 12.0000i 0.657596 + 0.657596i
\(334\) −22.1359 −1.21122
\(335\) 3.16228i 0.172774i
\(336\) −20.0000 12.6491i −1.09109 0.690066i
\(337\) −8.00000 + 8.00000i −0.435788 + 0.435788i −0.890592 0.454804i \(-0.849709\pi\)
0.454804 + 0.890592i \(0.349709\pi\)
\(338\) −8.00000 8.00000i −0.435143 0.435143i
\(339\) 37.9473 2.06102
\(340\) 0 0
\(341\) 3.16228i 0.171247i
\(342\) 6.32456 + 6.32456i 0.341993 + 0.341993i
\(343\) 11.4189 + 14.5811i 0.616561 + 0.787307i
\(344\) 12.0000i 0.646997i
\(345\) −10.0000 + 10.0000i −0.538382 + 0.538382i
\(346\) 22.1359i 1.19004i
\(347\) 24.0000 24.0000i 1.28839 1.28839i 0.352621 0.935766i \(-0.385290\pi\)
0.935766 0.352621i \(-0.114710\pi\)
\(348\) 0 0
\(349\) 34.7851 1.86200 0.931001 0.365018i \(-0.118937\pi\)
0.931001 + 0.365018i \(0.118937\pi\)
\(350\) 10.0000 15.8114i 0.534522 0.845154i
\(351\) −5.00000 −0.266880
\(352\) 0 0
\(353\) 14.2302 14.2302i 0.757400 0.757400i −0.218449 0.975848i \(-0.570100\pi\)
0.975848 + 0.218449i \(0.0700996\pi\)
\(354\) 30.0000i 1.59448i
\(355\) 9.48683 9.48683i 0.503509 0.503509i
\(356\) 0 0
\(357\) −2.90569 12.9057i −0.153786 0.683042i
\(358\) −6.00000 6.00000i −0.317110 0.317110i
\(359\) 22.0000i 1.16112i 0.814219 + 0.580558i \(0.197165\pi\)
−0.814219 + 0.580558i \(0.802835\pi\)
\(360\) 12.6491i 0.666667i
\(361\) −9.00000 −0.473684
\(362\) 22.1359 + 22.1359i 1.16344 + 1.16344i
\(363\) −15.8114 + 15.8114i −0.829883 + 0.829883i
\(364\) 0 0
\(365\) 0 0
\(366\) −20.0000 −1.04542
\(367\) −17.3925 17.3925i −0.907883 0.907883i 0.0882186 0.996101i \(-0.471883\pi\)
−0.996101 + 0.0882186i \(0.971883\pi\)
\(368\) 8.00000 + 8.00000i 0.417029 + 0.417029i
\(369\) −18.9737 −0.987730
\(370\) 18.9737 + 18.9737i 0.986394 + 0.986394i
\(371\) 2.00000 3.16228i 0.103835 0.164177i
\(372\) 0 0
\(373\) 12.0000 + 12.0000i 0.621336 + 0.621336i 0.945873 0.324537i \(-0.105208\pi\)
−0.324537 + 0.945873i \(0.605208\pi\)
\(374\) 3.16228 0.163517
\(375\) 25.0000 1.29099
\(376\) 18.9737i 0.978492i
\(377\) 4.74342 + 4.74342i 0.244298 + 0.244298i
\(378\) 1.83772 + 8.16228i 0.0945222 + 0.419822i
\(379\) 8.00000i 0.410932i −0.978664 0.205466i \(-0.934129\pi\)
0.978664 0.205466i \(-0.0658711\pi\)
\(380\) 0 0
\(381\) 28.4605i 1.45808i
\(382\) 3.00000 3.00000i 0.153493 0.153493i
\(383\) −15.8114 + 15.8114i −0.807924 + 0.807924i −0.984319 0.176395i \(-0.943556\pi\)
0.176395 + 0.984319i \(0.443556\pi\)
\(384\) −25.2982 −1.29099
\(385\) −5.00000 3.16228i −0.254824 0.161165i
\(386\) 16.0000 0.814379
\(387\) −6.00000 + 6.00000i −0.304997 + 0.304997i
\(388\) 0 0
\(389\) 23.0000i 1.16615i −0.812420 0.583073i \(-0.801850\pi\)
0.812420 0.583073i \(-0.198150\pi\)
\(390\) 15.8114 0.800641
\(391\) 6.32456i 0.319847i
\(392\) 18.6491 + 6.64911i 0.941922 + 0.335831i
\(393\) 0 0
\(394\) 2.00000i 0.100759i
\(395\) 20.5548 + 20.5548i 1.03422 + 1.03422i
\(396\) 0 0
\(397\) −23.7171 23.7171i −1.19033 1.19033i −0.976976 0.213351i \(-0.931562\pi\)
−0.213351 0.976976i \(-0.568438\pi\)
\(398\) 9.48683 9.48683i 0.475532 0.475532i
\(399\) −15.8114 10.0000i −0.791559 0.500626i
\(400\) 20.0000i 1.00000i
\(401\) −1.00000 −0.0499376 −0.0249688 0.999688i \(-0.507949\pi\)
−0.0249688 + 0.999688i \(0.507949\pi\)
\(402\) −3.16228 3.16228i −0.157720 0.157720i
\(403\) −5.00000 5.00000i −0.249068 0.249068i
\(404\) 0 0
\(405\) −17.3925 + 17.3925i −0.864242 + 0.864242i
\(406\) 6.00000 9.48683i 0.297775 0.470824i
\(407\) 6.00000 6.00000i 0.297409 0.297409i
\(408\) −10.0000 10.0000i −0.495074 0.495074i
\(409\) 3.16228 0.156365 0.0781823 0.996939i \(-0.475088\pi\)
0.0781823 + 0.996939i \(0.475088\pi\)
\(410\) −30.0000 −1.48159
\(411\) 6.32456i 0.311967i
\(412\) 0 0
\(413\) −5.51317 24.4868i −0.271285 1.20492i
\(414\) 8.00000i 0.393179i
\(415\) 10.0000i 0.490881i
\(416\) 0 0
\(417\) −30.0000 + 30.0000i −1.46911 + 1.46911i
\(418\) 3.16228 3.16228i 0.154672 0.154672i
\(419\) −15.8114 −0.772437 −0.386218 0.922407i \(-0.626219\pi\)
−0.386218 + 0.922407i \(0.626219\pi\)
\(420\) 0 0
\(421\) 19.0000 0.926003 0.463002 0.886357i \(-0.346772\pi\)
0.463002 + 0.886357i \(0.346772\pi\)
\(422\) −17.0000 + 17.0000i −0.827547 + 0.827547i
\(423\) −9.48683 + 9.48683i −0.461266 + 0.461266i
\(424\) 4.00000i 0.194257i
\(425\) 7.90569 7.90569i 0.383482 0.383482i
\(426\) 18.9737i 0.919277i
\(427\) 16.3246 3.67544i 0.790001 0.177867i
\(428\) 0 0
\(429\) 5.00000i 0.241402i
\(430\) −9.48683 + 9.48683i −0.457496 + 0.457496i
\(431\) −23.0000 −1.10787 −0.553936 0.832560i \(-0.686875\pi\)
−0.553936 + 0.832560i \(0.686875\pi\)
\(432\) 6.32456 + 6.32456i 0.304290 + 0.304290i
\(433\) 9.48683 9.48683i 0.455908 0.455908i −0.441402 0.897310i \(-0.645519\pi\)
0.897310 + 0.441402i \(0.145519\pi\)
\(434\) −6.32456 + 10.0000i −0.303588 + 0.480015i
\(435\) 15.0000 0.719195
\(436\) 0 0
\(437\) 6.32456 + 6.32456i 0.302545 + 0.302545i
\(438\) 0 0
\(439\) −12.6491 −0.603709 −0.301855 0.953354i \(-0.597606\pi\)
−0.301855 + 0.953354i \(0.597606\pi\)
\(440\) −6.32456 −0.301511
\(441\) 6.00000 + 12.6491i 0.285714 + 0.602339i
\(442\) 5.00000 5.00000i 0.237826 0.237826i
\(443\) 1.00000 + 1.00000i 0.0475114 + 0.0475114i 0.730463 0.682952i \(-0.239304\pi\)
−0.682952 + 0.730463i \(0.739304\pi\)
\(444\) 0 0
\(445\) 10.0000 10.0000i 0.474045 0.474045i
\(446\) 28.4605i 1.34764i
\(447\) 18.9737 + 18.9737i 0.897424 + 0.897424i
\(448\) 20.6491 4.64911i 0.975579 0.219650i
\(449\) 17.0000i 0.802280i 0.916017 + 0.401140i \(0.131386\pi\)
−0.916017 + 0.401140i \(0.868614\pi\)
\(450\) 10.0000 10.0000i 0.471405 0.471405i
\(451\) 9.48683i 0.446718i
\(452\) 0 0
\(453\) 14.2302 14.2302i 0.668595 0.668595i
\(454\) 3.16228 0.148413
\(455\) −12.9057 + 2.90569i −0.605028 + 0.136221i
\(456\) −20.0000 −0.936586
\(457\) −1.00000 + 1.00000i −0.0467780 + 0.0467780i −0.730109 0.683331i \(-0.760531\pi\)
0.683331 + 0.730109i \(0.260531\pi\)
\(458\) −15.8114 + 15.8114i −0.738818 + 0.738818i
\(459\) 5.00000i 0.233380i
\(460\) 0 0
\(461\) 6.32456i 0.294564i −0.989095 0.147282i \(-0.952948\pi\)
0.989095 0.147282i \(-0.0470525\pi\)
\(462\) −8.16228 + 1.83772i −0.379744 + 0.0854986i
\(463\) −4.00000 4.00000i −0.185896 0.185896i 0.608023 0.793919i \(-0.291963\pi\)
−0.793919 + 0.608023i \(0.791963\pi\)
\(464\) 12.0000i 0.557086i
\(465\) −15.8114 −0.733236
\(466\) 36.0000 1.66767
\(467\) −11.0680 11.0680i −0.512165 0.512165i 0.403025 0.915189i \(-0.367959\pi\)
−0.915189 + 0.403025i \(0.867959\pi\)
\(468\) 0 0
\(469\) 3.16228 + 2.00000i 0.146020 + 0.0923514i
\(470\) −15.0000 + 15.0000i −0.691898 + 0.691898i
\(471\) 20.0000 0.921551
\(472\) −18.9737 18.9737i −0.873334 0.873334i
\(473\) 3.00000 + 3.00000i 0.137940 + 0.137940i
\(474\) 41.1096 1.88823
\(475\) 15.8114i 0.725476i
\(476\) 0 0
\(477\) 2.00000 2.00000i 0.0915737 0.0915737i
\(478\) 19.0000 + 19.0000i 0.869040 + 0.869040i
\(479\) −6.32456 −0.288976 −0.144488 0.989507i \(-0.546154\pi\)
−0.144488 + 0.989507i \(0.546154\pi\)
\(480\) 0 0
\(481\) 18.9737i 0.865125i
\(482\) −25.2982 25.2982i −1.15230 1.15230i
\(483\) −3.67544 16.3246i −0.167239 0.742793i
\(484\) 0 0
\(485\) 5.00000 0.227038
\(486\) 25.2982i 1.14755i
\(487\) 4.00000 4.00000i 0.181257 0.181257i −0.610646 0.791904i \(-0.709090\pi\)
0.791904 + 0.610646i \(0.209090\pi\)
\(488\) 12.6491 12.6491i 0.572598 0.572598i
\(489\) 18.9737 0.858019
\(490\) 9.48683 + 20.0000i 0.428571 + 0.903508i
\(491\) −41.0000 −1.85030 −0.925152 0.379597i \(-0.876063\pi\)
−0.925152 + 0.379597i \(0.876063\pi\)
\(492\) 0 0
\(493\) 4.74342 4.74342i 0.213633 0.213633i
\(494\) 10.0000i 0.449921i
\(495\) −3.16228 3.16228i −0.142134 0.142134i
\(496\) 12.6491i 0.567962i
\(497\) 3.48683 + 15.4868i 0.156406 + 0.694679i
\(498\) −10.0000 10.0000i −0.448111 0.448111i
\(499\) 19.0000i 0.850557i −0.905063 0.425278i \(-0.860176\pi\)
0.905063 0.425278i \(-0.139824\pi\)
\(500\) 0 0
\(501\) 35.0000 1.56368
\(502\) −12.6491 12.6491i −0.564557 0.564557i
\(503\) 7.90569 7.90569i 0.352497 0.352497i −0.508541 0.861038i \(-0.669815\pi\)
0.861038 + 0.508541i \(0.169815\pi\)
\(504\) 12.6491 + 8.00000i 0.563436 + 0.356348i
\(505\) 5.00000 + 5.00000i 0.222497 + 0.222497i
\(506\) 4.00000 0.177822
\(507\) 12.6491 + 12.6491i 0.561767 + 0.561767i
\(508\) 0 0
\(509\) 18.9737 0.840993 0.420496 0.907294i \(-0.361856\pi\)
0.420496 + 0.907294i \(0.361856\pi\)
\(510\) 15.8114i 0.700140i
\(511\) 0 0
\(512\) 16.0000 16.0000i 0.707107 0.707107i
\(513\) 5.00000 + 5.00000i 0.220755 + 0.220755i
\(514\) −25.2982 −1.11586
\(515\) 35.0000i 1.54228i
\(516\) 0 0
\(517\) 4.74342 + 4.74342i 0.208615 + 0.208615i
\(518\) −30.9737 + 6.97367i −1.36090 + 0.306405i
\(519\) 35.0000i 1.53633i
\(520\) −10.0000 + 10.0000i −0.438529 + 0.438529i
\(521\) 41.1096i 1.80104i 0.434810 + 0.900522i \(0.356816\pi\)
−0.434810 + 0.900522i \(0.643184\pi\)
\(522\) 6.00000 6.00000i 0.262613 0.262613i
\(523\) −18.9737 + 18.9737i −0.829660 + 0.829660i −0.987470 0.157809i \(-0.949557\pi\)
0.157809 + 0.987470i \(0.449557\pi\)
\(524\) 0 0
\(525\) −15.8114 + 25.0000i −0.690066 + 1.09109i
\(526\) −14.0000 −0.610429
\(527\) −5.00000 + 5.00000i −0.217803 + 0.217803i
\(528\) −6.32456 + 6.32456i −0.275241 + 0.275241i
\(529\) 15.0000i 0.652174i
\(530\) 3.16228 3.16228i 0.137361 0.137361i
\(531\) 18.9737i 0.823387i
\(532\) 0 0
\(533\) 15.0000 + 15.0000i 0.649722 + 0.649722i
\(534\) 20.0000i 0.865485i
\(535\) 9.48683i 0.410152i
\(536\) 4.00000 0.172774
\(537\) 9.48683 + 9.48683i 0.409387 + 0.409387i
\(538\) 18.9737 18.9737i 0.818013 0.818013i
\(539\) 6.32456 3.00000i 0.272418 0.129219i
\(540\) 0 0
\(541\) 9.00000 0.386940 0.193470 0.981106i \(-0.438026\pi\)
0.193470 + 0.981106i \(0.438026\pi\)
\(542\) 12.6491 + 12.6491i 0.543326 + 0.543326i
\(543\) −35.0000 35.0000i −1.50199 1.50199i
\(544\) 0 0
\(545\) −11.0680 11.0680i −0.474100 0.474100i
\(546\) −10.0000 + 15.8114i −0.427960 + 0.676665i
\(547\) 14.0000 14.0000i 0.598597 0.598597i −0.341342 0.939939i \(-0.610882\pi\)
0.939939 + 0.341342i \(0.110882\pi\)
\(548\) 0 0
\(549\) 12.6491 0.539851
\(550\) −5.00000 5.00000i −0.213201 0.213201i
\(551\) 9.48683i 0.404153i
\(552\) −12.6491 12.6491i −0.538382 0.538382i
\(553\) −33.5548 + 7.55480i −1.42690 + 0.321263i
\(554\) 36.0000i 1.52949i
\(555\) −30.0000 30.0000i −1.27343 1.27343i
\(556\) 0 0
\(557\) −6.00000 + 6.00000i −0.254228 + 0.254228i −0.822702 0.568473i \(-0.807534\pi\)
0.568473 + 0.822702i \(0.307534\pi\)
\(558\) −6.32456 + 6.32456i −0.267740 + 0.267740i
\(559\) 9.48683 0.401250
\(560\) 20.0000 + 12.6491i 0.845154 + 0.534522i
\(561\) −5.00000 −0.211100
\(562\) −9.00000 + 9.00000i −0.379642 + 0.379642i
\(563\) 9.48683 9.48683i 0.399822 0.399822i −0.478348 0.878170i \(-0.658764\pi\)
0.878170 + 0.478348i \(0.158764\pi\)
\(564\) 0 0
\(565\) −37.9473 −1.59646
\(566\) 9.48683i 0.398761i
\(567\) −6.39253 28.3925i −0.268461 1.19237i
\(568\) 12.0000 + 12.0000i 0.503509 + 0.503509i
\(569\) 32.0000i 1.34151i 0.741679 + 0.670755i \(0.234030\pi\)
−0.741679 + 0.670755i \(0.765970\pi\)
\(570\) −15.8114 15.8114i −0.662266 0.662266i
\(571\) −26.0000 −1.08807 −0.544033 0.839064i \(-0.683103\pi\)
−0.544033 + 0.839064i \(0.683103\pi\)
\(572\) 0 0
\(573\) −4.74342 + 4.74342i −0.198159 + 0.198159i
\(574\) 18.9737 30.0000i 0.791946 1.25218i
\(575\) 10.0000 10.0000i 0.417029 0.417029i
\(576\) 16.0000 0.666667
\(577\) 20.5548 + 20.5548i 0.855708 + 0.855708i 0.990829 0.135121i \(-0.0431424\pi\)
−0.135121 + 0.990829i \(0.543142\pi\)
\(578\) 12.0000 + 12.0000i 0.499134 + 0.499134i
\(579\) −25.2982 −1.05136
\(580\) 0 0
\(581\) 10.0000 + 6.32456i 0.414870 + 0.262387i
\(582\) 5.00000 5.00000i 0.207257 0.207257i
\(583\) −1.00000 1.00000i −0.0414158 0.0414158i
\(584\) 0 0
\(585\) −10.0000 −0.413449
\(586\) 15.8114i 0.653162i
\(587\) −15.8114 15.8114i −0.652606 0.652606i 0.301014 0.953620i \(-0.402675\pi\)
−0.953620 + 0.301014i \(0.902675\pi\)
\(588\) 0 0
\(589\) 10.0000i 0.412043i
\(590\) 30.0000i 1.23508i
\(591\) 3.16228i 0.130079i
\(592\) −24.0000 + 24.0000i −0.986394 + 0.986394i
\(593\) 20.5548 20.5548i 0.844085 0.844085i −0.145303 0.989387i \(-0.546416\pi\)
0.989387 + 0.145303i \(0.0464156\pi\)
\(594\) 3.16228 0.129750
\(595\) 2.90569 + 12.9057i 0.119122 + 0.529082i
\(596\) 0 0
\(597\) −15.0000 + 15.0000i −0.613909 + 0.613909i
\(598\) 6.32456 6.32456i 0.258630 0.258630i
\(599\) 13.0000i 0.531166i −0.964088 0.265583i \(-0.914436\pi\)
0.964088 0.265583i \(-0.0855644\pi\)
\(600\) 31.6228i 1.29099i
\(601\) 22.1359i 0.902944i 0.892285 + 0.451472i \(0.149101\pi\)
−0.892285 + 0.451472i \(0.850899\pi\)
\(602\) −3.48683 15.4868i −0.142113 0.631196i
\(603\) 2.00000 + 2.00000i 0.0814463 + 0.0814463i
\(604\) 0 0
\(605\) 15.8114 15.8114i 0.642824 0.642824i
\(606\) 10.0000 0.406222
\(607\) 14.2302 + 14.2302i 0.577588 + 0.577588i 0.934238 0.356650i \(-0.116081\pi\)
−0.356650 + 0.934238i \(0.616081\pi\)
\(608\) 0 0
\(609\) −9.48683 + 15.0000i −0.384426 + 0.607831i
\(610\) 20.0000 0.809776
\(611\) 15.0000 0.606835
\(612\) 0 0
\(613\) 17.0000 + 17.0000i 0.686624 + 0.686624i 0.961484 0.274861i \(-0.0886317\pi\)
−0.274861 + 0.961484i \(0.588632\pi\)
\(614\) 9.48683 0.382857
\(615\) 47.4342 1.91273
\(616\) 4.00000 6.32456i 0.161165 0.254824i
\(617\) 4.00000 4.00000i 0.161034 0.161034i −0.621991 0.783025i \(-0.713676\pi\)
0.783025 + 0.621991i \(0.213676\pi\)
\(618\) 35.0000 + 35.0000i 1.40791 + 1.40791i
\(619\) −25.2982 −1.01682 −0.508411 0.861115i \(-0.669767\pi\)
−0.508411 + 0.861115i \(0.669767\pi\)
\(620\) 0 0
\(621\) 6.32456i 0.253796i
\(622\) 22.1359 + 22.1359i 0.887570 + 0.887570i
\(623\) 3.67544 + 16.3246i 0.147254 + 0.654029i
\(624\) 20.0000i 0.800641i
\(625\) −25.0000 −1.00000
\(626\) 28.4605i 1.13751i
\(627\) −5.00000 + 5.00000i −0.199681 + 0.199681i
\(628\) 0 0
\(629\) −18.9737 −0.756530
\(630\) 3.67544 + 16.3246i 0.146433 + 0.650386i
\(631\) −31.0000 −1.23409 −0.617045 0.786928i \(-0.711670\pi\)
−0.617045 + 0.786928i \(0.711670\pi\)
\(632\) −26.0000 + 26.0000i −1.03422 + 1.03422i
\(633\) 26.8794 26.8794i 1.06836 1.06836i
\(634\) 38.0000i 1.50917i
\(635\) 28.4605i 1.12942i
\(636\) 0 0
\(637\) 5.25658 14.7434i 0.208273 0.584155i
\(638\) −3.00000 3.00000i −0.118771 0.118771i
\(639\) 12.0000i 0.474713i
\(640\) 25.2982 1.00000
\(641\) 44.0000 1.73790 0.868948 0.494904i \(-0.164797\pi\)
0.868948 + 0.494904i \(0.164797\pi\)
\(642\) −9.48683 9.48683i −0.374415 0.374415i
\(643\) 4.74342 4.74342i 0.187062 0.187062i −0.607363 0.794425i \(-0.707772\pi\)
0.794425 + 0.607363i \(0.207772\pi\)
\(644\) 0 0
\(645\) 15.0000 15.0000i 0.590624 0.590624i
\(646\) −10.0000 −0.393445
\(647\) 12.6491 + 12.6491i 0.497288 + 0.497288i 0.910593 0.413305i \(-0.135626\pi\)
−0.413305 + 0.910593i \(0.635626\pi\)
\(648\) −22.0000 22.0000i −0.864242 0.864242i
\(649\) −9.48683 −0.372391
\(650\) −15.8114 −0.620174
\(651\) 10.0000 15.8114i 0.391931 0.619697i
\(652\) 0 0
\(653\) −19.0000 19.0000i −0.743527 0.743527i 0.229728 0.973255i \(-0.426216\pi\)
−0.973255 + 0.229728i \(0.926216\pi\)
\(654\) −22.1359 −0.865584
\(655\) 0 0
\(656\) 37.9473i 1.48159i
\(657\) 0 0
\(658\) −5.51317 24.4868i −0.214926 0.954596i
\(659\) 1.00000i 0.0389545i 0.999810 + 0.0194772i \(0.00620019\pi\)
−0.999810 + 0.0194772i \(0.993800\pi\)
\(660\) 0 0
\(661\) 12.6491i 0.491993i −0.969271 0.245997i \(-0.920885\pi\)
0.969271 0.245997i \(-0.0791152\pi\)
\(662\) 6.00000 6.00000i 0.233197 0.233197i
\(663\) −7.90569 + 7.90569i −0.307032 + 0.307032i
\(664\) 12.6491 0.490881
\(665\) 15.8114 + 10.0000i 0.613139 + 0.387783i
\(666\) −24.0000 −0.929981
\(667\) 6.00000 6.00000i 0.232321 0.232321i
\(668\) 0 0
\(669\) 45.0000i 1.73980i
\(670\) 3.16228 + 3.16228i 0.122169 + 0.122169i
\(671\) 6.32456i 0.244157i
\(672\) 0 0
\(673\) −24.0000 24.0000i −0.925132 0.925132i 0.0722542 0.997386i \(-0.476981\pi\)
−0.997386 + 0.0722542i \(0.976981\pi\)
\(674\) 16.0000i 0.616297i
\(675\) 7.90569 7.90569i 0.304290 0.304290i
\(676\) 0 0
\(677\) −14.2302 14.2302i −0.546913 0.546913i 0.378634 0.925547i \(-0.376394\pi\)
−0.925547 + 0.378634i \(0.876394\pi\)
\(678\) −37.9473 + 37.9473i −1.45736 + 1.45736i
\(679\) −3.16228 + 5.00000i −0.121357 + 0.191882i
\(680\) 10.0000 + 10.0000i 0.383482 + 0.383482i
\(681\) −5.00000 −0.191600
\(682\) 3.16228 + 3.16228i 0.121090 + 0.121090i
\(683\) 32.0000 + 32.0000i 1.22445 + 1.22445i 0.966035 + 0.258411i \(0.0831988\pi\)
0.258411 + 0.966035i \(0.416801\pi\)
\(684\) 0 0
\(685\) 6.32456i 0.241649i
\(686\) −26.0000 3.16228i −0.992685 0.120736i
\(687\) 25.0000 25.0000i 0.953809 0.953809i
\(688\) −12.0000 12.0000i −0.457496 0.457496i
\(689\) −3.16228 −0.120473
\(690\) 20.0000i 0.761387i
\(691\) 31.6228i 1.20299i 0.798878 + 0.601494i \(0.205427\pi\)
−0.798878 + 0.601494i \(0.794573\pi\)
\(692\) 0 0
\(693\) 5.16228 1.16228i 0.196099 0.0441513i
\(694\) 48.0000i 1.82206i
\(695\) 30.0000 30.0000i 1.13796 1.13796i
\(696\) 18.9737i 0.719195i
\(697\) 15.0000 15.0000i 0.568166 0.568166i
\(698\) −34.7851 + 34.7851i −1.31663 + 1.31663i
\(699\) −56.9210 −2.15295
\(700\) 0 0
\(701\) −13.0000 −0.491003 −0.245502 0.969396i \(-0.578953\pi\)
−0.245502 + 0.969396i \(0.578953\pi\)
\(702\) 5.00000 5.00000i 0.188713 0.188713i
\(703\) −18.9737 + 18.9737i −0.715605 + 0.715605i
\(704\) 8.00000i 0.301511i
\(705\) 23.7171 23.7171i 0.893237 0.893237i
\(706\) 28.4605i 1.07113i
\(707\) −8.16228 + 1.83772i −0.306974 + 0.0691147i
\(708\) 0 0
\(709\) 9.00000i 0.338002i −0.985616 0.169001i \(-0.945946\pi\)
0.985616 0.169001i \(-0.0540541\pi\)
\(710\) 18.9737i 0.712069i
\(711\) −26.0000 −0.975076
\(712\) 12.6491 + 12.6491i 0.474045 + 0.474045i
\(713\) −6.32456 + 6.32456i −0.236856 + 0.236856i
\(714\) 15.8114 + 10.0000i 0.591726 + 0.374241i
\(715\) 5.00000i 0.186989i
\(716\) 0 0
\(717\) −30.0416 30.0416i −1.12193 1.12193i
\(718\) −22.0000 22.0000i −0.821033 0.821033i
\(719\) 31.6228 1.17933 0.589665 0.807648i \(-0.299260\pi\)
0.589665 + 0.807648i \(0.299260\pi\)
\(720\) 12.6491 + 12.6491i 0.471405 + 0.471405i
\(721\) −35.0000 22.1359i −1.30347 0.824386i
\(722\) 9.00000 9.00000i 0.334945 0.334945i
\(723\) 40.0000 + 40.0000i 1.48762 + 1.48762i
\(724\) 0 0
\(725\) −15.0000 −0.557086
\(726\) 31.6228i 1.17363i
\(727\) 9.48683 + 9.48683i 0.351847 + 0.351847i 0.860796 0.508949i \(-0.169966\pi\)
−0.508949 + 0.860796i \(0.669966\pi\)
\(728\) −3.67544 16.3246i −0.136221 0.605028i
\(729\) 7.00000i 0.259259i
\(730\) 0 0
\(731\) 9.48683i 0.350883i
\(732\) 0 0
\(733\) 17.3925 17.3925i 0.642408 0.642408i −0.308739 0.951147i \(-0.599907\pi\)
0.951147 + 0.308739i \(0.0999070\pi\)
\(734\) 34.7851 1.28394
\(735\) −15.0000 31.6228i −0.553283 1.16642i
\(736\) 0 0
\(737\) 1.00000 1.00000i 0.0368355 0.0368355i
\(738\) 18.9737 18.9737i 0.698430 0.698430i
\(739\) 37.0000i 1.36107i 0.732717 + 0.680534i \(0.238252\pi\)
−0.732717 + 0.680534i \(0.761748\pi\)
\(740\) 0 0
\(741\) 15.8114i 0.580846i
\(742\) 1.16228 + 5.16228i 0.0426686 + 0.189513i
\(743\) −9.00000 9.00000i −0.330178 0.330178i 0.522476 0.852654i \(-0.325008\pi\)
−0.852654 + 0.522476i \(0.825008\pi\)
\(744\) 20.0000i 0.733236i
\(745\) −18.9737 18.9737i −0.695141 0.695141i
\(746\) −24.0000 −0.878702
\(747\) 6.32456 + 6.32456i 0.231403 + 0.231403i
\(748\) 0 0
\(749\) 9.48683 + 6.00000i 0.346641 + 0.219235i
\(750\) −25.0000 + 25.0000i −0.912871 + 0.912871i
\(751\) 37.0000 1.35015 0.675075 0.737749i \(-0.264111\pi\)
0.675075 + 0.737749i \(0.264111\pi\)
\(752\) −18.9737 18.9737i −0.691898 0.691898i
\(753\) 20.0000 + 20.0000i 0.728841 + 0.728841i
\(754\) −9.48683 −0.345490
\(755\) −14.2302 + 14.2302i −0.517892 + 0.517892i
\(756\) 0 0
\(757\) −16.0000 + 16.0000i −0.581530 + 0.581530i −0.935324 0.353794i \(-0.884892\pi\)
0.353794 + 0.935324i \(0.384892\pi\)
\(758\) 8.00000 + 8.00000i 0.290573 + 0.290573i
\(759\) −6.32456 −0.229567
\(760\) 20.0000 0.725476
\(761\) 25.2982i 0.917060i 0.888679 + 0.458530i \(0.151624\pi\)
−0.888679 + 0.458530i \(0.848376\pi\)
\(762\) 28.4605 + 28.4605i 1.03102 + 1.03102i
\(763\) 18.0680 4.06797i 0.654104 0.147270i
\(764\) 0 0
\(765\) 10.0000i 0.361551i
\(766\) 31.6228i 1.14258i
\(767\) −15.0000 + 15.0000i −0.541619 + 0.541619i
\(768\) 0 0
\(769\) −22.1359 −0.798243 −0.399121 0.916898i \(-0.630685\pi\)
−0.399121 + 0.916898i \(0.630685\pi\)
\(770\) 8.16228 1.83772i 0.294148 0.0662269i
\(771\) 40.0000 1.44056
\(772\) 0 0
\(773\) −36.3662 + 36.3662i −1.30800 + 1.30800i −0.385145 + 0.922856i \(0.625849\pi\)
−0.922856 + 0.385145i \(0.874151\pi\)
\(774\) 12.0000i 0.431331i
\(775\) 15.8114 0.567962
\(776\) 6.32456i 0.227038i
\(777\) 48.9737 11.0263i 1.75692 0.395568i
\(778\) 23.0000 + 23.0000i 0.824590 + 0.824590i
\(779\) 30.0000i 1.07486i
\(780\) 0 0
\(781\) 6.00000 0.214697
\(782\) −6.32456 6.32456i −0.226166 0.226166i
\(783\) 4.74342 4.74342i 0.169516 0.169516i
\(784\) −25.2982 + 12.0000i −0.903508 + 0.428571i
\(785\) −20.0000 −0.713831
\(786\) 0 0
\(787\) 17.3925 + 17.3925i 0.619977 + 0.619977i 0.945525 0.325549i \(-0.105549\pi\)
−0.325549 + 0.945525i \(0.605549\pi\)
\(788\) 0 0
\(789\) 22.1359 0.788060
\(790\) −41.1096 −1.46261
\(791\) 24.0000 37.9473i 0.853342 1.34925i
\(792\) 4.00000 4.00000i 0.142134 0.142134i
\(793\) −10.0000 10.0000i −0.355110 0.355110i
\(794\) 47.4342 1.68338
\(795\) −5.00000 + 5.00000i −0.177332 + 0.177332i
\(796\) 0 0
\(797\) 1.58114 + 1.58114i 0.0560068 + 0.0560068i 0.734555 0.678549i \(-0.237391\pi\)
−0.678549 + 0.734555i \(0.737391\pi\)
\(798\) 25.8114 5.81139i 0.913713 0.205721i
\(799\) 15.0000i 0.530662i
\(800\) 0 0
\(801\) 12.6491i 0.446934i
\(802\) 1.00000 1.00000i 0.0353112 0.0353112i
\(803\) 0 0
\(804\) 0 0
\(805\) 3.67544 + 16.3246i 0.129542 + 0.575365i
\(806\) 10.0000 0.352235
\(807\) −30.0000 + 30.0000i −1.05605 + 1.05605i
\(808\) −6.32456 + 6.32456i −0.222497 + 0.222497i
\(809\) 3.00000i 0.105474i −0.998608 0.0527372i \(-0.983205\pi\)
0.998608 0.0527372i \(-0.0167946\pi\)
\(810\) 34.7851i 1.22222i
\(811\) 37.9473i 1.33251i −0.745724 0.666256i \(-0.767896\pi\)
0.745724 0.666256i \(-0.232104\pi\)
\(812\) 0 0
\(813\) −20.0000 20.0000i −0.701431 0.701431i
\(814\) 12.0000i 0.420600i
\(815\) −18.9737 −0.664619
\(816\) 20.0000 0.700140
\(817\) −9.48683 9.48683i −0.331902 0.331902i
\(818\) −3.16228 + 3.16228i −0.110566 + 0.110566i
\(819\) 6.32456 10.0000i 0.220998 0.349428i
\(820\) 0 0
\(821\) −23.0000 −0.802706 −0.401353 0.915924i \(-0.631460\pi\)
−0.401353 + 0.915924i \(0.631460\pi\)
\(822\) 6.32456 + 6.32456i 0.220594 + 0.220594i
\(823\) −3.00000 3.00000i −0.104573 0.104573i 0.652884 0.757458i \(-0.273559\pi\)
−0.757458 + 0.652884i \(0.773559\pi\)
\(824\) −44.2719 −1.54228
\(825\) 7.90569 + 7.90569i 0.275241 + 0.275241i
\(826\) 30.0000 + 18.9737i 1.04383 + 0.660178i
\(827\) −26.0000 + 26.0000i −0.904109 + 0.904109i −0.995789 0.0916799i \(-0.970776\pi\)
0.0916799 + 0.995789i \(0.470776\pi\)
\(828\) 0 0
\(829\) 28.4605 0.988474 0.494237 0.869327i \(-0.335448\pi\)
0.494237 + 0.869327i \(0.335448\pi\)
\(830\) 10.0000 + 10.0000i 0.347105 + 0.347105i
\(831\) 56.9210i 1.97457i
\(832\) −12.6491 12.6491i −0.438529 0.438529i
\(833\) −14.7434 5.25658i −0.510829 0.182130i
\(834\) 60.0000i 2.07763i
\(835\) −35.0000 −1.21122
\(836\) 0 0
\(837\) −5.00000 + 5.00000i −0.172825 + 0.172825i
\(838\) 15.8114 15.8114i 0.546195 0.546195i
\(839\) 50.5964 1.74678 0.873392 0.487019i \(-0.161916\pi\)
0.873392 + 0.487019i \(0.161916\pi\)
\(840\) −31.6228 20.0000i −1.09109 0.690066i
\(841\) 20.0000 0.689655
\(842\) −19.0000 + 19.0000i −0.654783 + 0.654783i
\(843\) 14.2302 14.2302i 0.490116 0.490116i
\(844\) 0 0
\(845\) −12.6491 12.6491i −0.435143 0.435143i
\(846\) 18.9737i 0.652328i
\(847\) 5.81139 + 25.8114i 0.199682 + 0.886890i
\(848\) 4.00000 + 4.00000i 0.137361 + 0.137361i
\(849\) 15.0000i 0.514799i
\(850\) 15.8114i 0.542326i
\(851\) −24.0000 −0.822709
\(852\) 0 0
\(853\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(854\) −12.6491 + 20.0000i −0.432844 + 0.684386i
\(855\) 10.0000 + 10.0000i 0.341993 + 0.341993i
\(856\) 12.0000 0.410152
\(857\) −31.6228 31.6228i −1.08021 1.08021i −0.996489 0.0837245i \(-0.973318\pi\)
−0.0837245 0.996489i \(-0.526682\pi\)
\(858\) 5.00000 + 5.00000i 0.170697 + 0.170697i
\(859\) 12.6491 0.431582 0.215791 0.976440i \(-0.430767\pi\)
0.215791 + 0.976440i \(0.430767\pi\)
\(860\) 0 0
\(861\) −30.0000 + 47.4342i −1.02240 + 1.61655i
\(862\) 23.0000 23.0000i 0.783383 0.783383i
\(863\) −13.0000 13.0000i −0.442525 0.442525i 0.450335 0.892860i \(-0.351305\pi\)
−0.892860 + 0.450335i \(0.851305\pi\)
\(864\) 0 0
\(865\) 35.0000i 1.19004i
\(866\) 18.9737i 0.644751i
\(867\) −18.9737 18.9737i −0.644379 0.644379i
\(868\) 0 0
\(869\) 13.0000i 0.440995i
\(870\) −15.0000 + 15.0000i −0.508548 + 0.508548i
\(871\) 3.16228i 0.107150i
\(872\) 14.0000 14.0000i 0.474100 0.474100i
\(873\) −3.16228 + 3.16228i −0.107027 + 0.107027i
\(874\) −12.6491 −0.427863
\(875\) 15.8114 25.0000i 0.534522 0.845154i
\(876\) 0 0
\(877\) 17.0000 17.0000i 0.574049 0.574049i −0.359208 0.933257i \(-0.616953\pi\)
0.933257 + 0.359208i \(0.116953\pi\)
\(878\) 12.6491 12.6491i 0.426887 0.426887i
\(879\) 25.0000i 0.843229i
\(880\) 6.32456 6.32456i 0.213201 0.213201i
\(881\) 37.9473i 1.27848i 0.769008 + 0.639239i \(0.220751\pi\)
−0.769008 + 0.639239i \(0.779249\pi\)
\(882\) −18.6491 6.64911i −0.627948 0.223887i
\(883\) −18.0000 18.0000i −0.605748 0.605748i 0.336084 0.941832i \(-0.390897\pi\)
−0.941832 + 0.336084i \(0.890897\pi\)
\(884\) 0 0
\(885\) 47.4342i 1.59448i
\(886\) −2.00000 −0.0671913
\(887\) 3.16228 + 3.16228i 0.106179 + 0.106179i 0.758200 0.652022i \(-0.226079\pi\)
−0.652022 + 0.758200i \(0.726079\pi\)
\(888\) 37.9473 37.9473i 1.27343 1.27343i
\(889\) −28.4605 18.0000i −0.954534 0.603701i
\(890\) 20.0000i 0.670402i
\(891\) −11.0000 −0.368514
\(892\) 0 0
\(893\) −15.0000 15.0000i −0.501956 0.501956i
\(894\) −37.9473 −1.26915
\(895\) −9.48683 9.48683i −0.317110 0.317110i
\(896\) −16.0000 + 25.2982i −0.534522 + 0.845154i
\(897\) −10.0000 + 10.0000i −0.333890 + 0.333890i
\(898\) −17.0000 17.0000i −0.567297 0.567297i
\(899\) 9.48683 0.316404
\(900\) 0 0
\(901\) 3.16228i 0.105351i
\(902\) −9.48683 9.48683i −0.315877 0.315877i
\(903\) 5.51317 + 24.4868i 0.183467 + 0.814871i
\(904\) 48.0000i 1.59646i
\(905\) 35.0000 + 35.0000i 1.16344 + 1.16344i
\(906\) 28.4605i 0.945537i
\(907\) 22.0000 22.0000i 0.730498 0.730498i −0.240220 0.970718i \(-0.577220\pi\)
0.970718 + 0.240220i \(0.0772197\pi\)
\(908\) 0 0
\(909\) −6.32456 −0.209772
\(910\) 10.0000 15.8114i 0.331497 0.524142i
\(911\) 54.0000 1.78910 0.894550 0.446968i \(-0.147496\pi\)
0.894550 + 0.446968i \(0.147496\pi\)
\(912\) 20.0000 20.0000i 0.662266 0.662266i
\(913\) 3.16228 3.16228i 0.104656 0.104656i
\(914\) 2.00000i 0.0661541i
\(915\) −31.6228 −1.04542
\(916\) 0 0
\(917\) 0 0
\(918\) −5.00000 5.00000i −0.165025 0.165025i
\(919\) 27.0000i 0.890648i 0.895370 + 0.445324i \(0.146911\pi\)
−0.895370 + 0.445324i \(0.853089\pi\)
\(920\) 12.6491 + 12.6491i 0.417029 + 0.417029i
\(921\) −15.0000 −0.494267
\(922\) 6.32456 + 6.32456i 0.208288 + 0.208288i
\(923\) 9.48683 9.48683i 0.312263 0.312263i
\(924\) 0 0
\(925\) 30.0000 + 30.0000i 0.986394 + 0.986394i
\(926\) 8.00000 0.262896
\(927\) −22.1359 22.1359i −0.727040 0.727040i
\(928\) 0 0
\(929\) 3.16228 0.103751 0.0518755 0.998654i \(-0.483480\pi\)
0.0518755 + 0.998654i \(0.483480\pi\)
\(930\) 15.8114 15.8114i 0.518476 0.518476i
\(931\) −20.0000 + 9.48683i −0.655474 + 0.310918i
\(932\) 0 0
\(933\) −35.0000 35.0000i −1.14585 1.14585i
\(934\) 22.1359 0.724310
\(935\) 5.00000 0.163517
\(936\) 12.6491i 0.413449i
\(937\) −14.2302 14.2302i −0.464882 0.464882i 0.435370 0.900252i \(-0.356618\pi\)
−0.900252 + 0.435370i \(0.856618\pi\)
\(938\) −5.16228 + 1.16228i −0.168554 + 0.0379497i
\(939\) 45.0000i 1.46852i
\(940\) 0 0
\(941\) 37.9473i 1.23705i −0.785766 0.618524i \(-0.787731\pi\)
0.785766 0.618524i \(-0.212269\pi\)
\(942\) −20.0000 + 20.0000i −0.651635 + 0.651635i
\(943\) 18.9737 18.9737i 0.617868 0.617868i
\(944\) 37.9473 1.23508
\(945\) 2.90569 + 12.9057i 0.0945222 + 0.419822i
\(946\) −6.00000 −0.195077
\(947\) 7.00000 7.00000i 0.227469 0.227469i −0.584165 0.811635i \(-0.698578\pi\)
0.811635 + 0.584165i \(0.198578\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 15.8114 + 15.8114i 0.512989 + 0.512989i
\(951\) 60.0833i 1.94833i
\(952\) −16.3246 + 3.67544i −0.529082 + 0.119122i
\(953\) −3.00000 3.00000i −0.0971795 0.0971795i 0.656846 0.754025i \(-0.271890\pi\)
−0.754025 + 0.656846i \(0.771890\pi\)
\(954\) 4.00000i 0.129505i
\(955\) 4.74342 4.74342i 0.153493 0.153493i
\(956\) 0 0
\(957\) 4.74342 + 4.74342i 0.153333 + 0.153333i
\(958\) 6.32456 6.32456i 0.204337 0.204337i
\(959\) −6.32456 4.00000i −0.204231 0.129167i
\(960\) −40.0000 −1.29099
\(961\) 21.0000 0.677419
\(962\) 18.9737 + 18.9737i 0.611736 + 0.611736i
\(963\) 6.00000 + 6.00000i 0.193347 + 0.193347i
\(964\) 0 0
\(965\) 25.2982 0.814379
\(966\) 20.0000 + 12.6491i 0.643489 + 0.406978i
\(967\) −33.0000 + 33.0000i −1.06121 + 1.06121i −0.0632081 + 0.998000i \(0.520133\pi\)
−0.998000 + 0.0632081i \(0.979867\pi\)
\(968\) 20.0000 + 20.0000i 0.642824 + 0.642824i
\(969\) 15.8114 0.507935
\(970\) −5.00000 + 5.00000i −0.160540 + 0.160540i
\(971\) 34.7851i 1.11631i −0.829738 0.558153i \(-0.811510\pi\)
0.829738 0.558153i \(-0.188490\pi\)
\(972\) 0 0
\(973\) 11.0263 + 48.9737i 0.353488 + 1.57002i
\(974\) 8.00000i 0.256337i
\(975\) 25.0000 0.800641
\(976\) 25.2982i 0.809776i
\(977\) −1.00000 + 1.00000i −0.0319928 + 0.0319928i −0.722922 0.690929i \(-0.757202\pi\)
0.690929 + 0.722922i \(0.257202\pi\)
\(978\) −18.9737 + 18.9737i −0.606711 + 0.606711i
\(979\) 6.32456 0.202134
\(980\) 0 0
\(981\) 14.0000 0.446986
\(982\) 41.0000 41.0000i 1.30836 1.30836i
\(983\) −20.5548 + 20.5548i −0.655596 + 0.655596i −0.954335 0.298739i \(-0.903434\pi\)
0.298739 + 0.954335i \(0.403434\pi\)
\(984\) 60.0000i 1.91273i
\(985\) 3.16228i 0.100759i
\(986\) 9.48683i 0.302122i
\(987\) 8.71708 + 38.7171i 0.277468 + 1.23238i
\(988\) 0 0
\(989\) 12.0000i 0.381578i
\(990\) 6.32456 0.201008
\(991\) 4.00000 0.127064 0.0635321 0.997980i \(-0.479763\pi\)
0.0635321 + 0.997980i \(0.479763\pi\)
\(992\) 0 0
\(993\) −9.48683 + 9.48683i −0.301056 + 0.301056i
\(994\) −18.9737 12.0000i −0.601808 0.380617i
\(995\) 15.0000 15.0000i 0.475532 0.475532i
\(996\) 0 0
\(997\) 14.2302 + 14.2302i 0.450677 + 0.450677i 0.895579 0.444902i \(-0.146762\pi\)
−0.444902 + 0.895579i \(0.646762\pi\)
\(998\) 19.0000 + 19.0000i 0.601434 + 0.601434i
\(999\) −18.9737 −0.600300
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 35.2.f.a.13.2 yes 4
3.2 odd 2 315.2.p.c.118.2 4
4.3 odd 2 560.2.bj.a.433.1 4
5.2 odd 4 inner 35.2.f.a.27.1 yes 4
5.3 odd 4 175.2.f.c.132.2 4
5.4 even 2 175.2.f.c.118.1 4
7.2 even 3 245.2.l.c.178.2 8
7.3 odd 6 245.2.l.c.68.2 8
7.4 even 3 245.2.l.c.68.1 8
7.5 odd 6 245.2.l.c.178.1 8
7.6 odd 2 inner 35.2.f.a.13.1 4
15.2 even 4 315.2.p.c.307.1 4
20.7 even 4 560.2.bj.a.97.2 4
21.20 even 2 315.2.p.c.118.1 4
28.27 even 2 560.2.bj.a.433.2 4
35.2 odd 12 245.2.l.c.227.2 8
35.12 even 12 245.2.l.c.227.1 8
35.13 even 4 175.2.f.c.132.1 4
35.17 even 12 245.2.l.c.117.2 8
35.27 even 4 inner 35.2.f.a.27.2 yes 4
35.32 odd 12 245.2.l.c.117.1 8
35.34 odd 2 175.2.f.c.118.2 4
105.62 odd 4 315.2.p.c.307.2 4
140.27 odd 4 560.2.bj.a.97.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.2.f.a.13.1 4 7.6 odd 2 inner
35.2.f.a.13.2 yes 4 1.1 even 1 trivial
35.2.f.a.27.1 yes 4 5.2 odd 4 inner
35.2.f.a.27.2 yes 4 35.27 even 4 inner
175.2.f.c.118.1 4 5.4 even 2
175.2.f.c.118.2 4 35.34 odd 2
175.2.f.c.132.1 4 35.13 even 4
175.2.f.c.132.2 4 5.3 odd 4
245.2.l.c.68.1 8 7.4 even 3
245.2.l.c.68.2 8 7.3 odd 6
245.2.l.c.117.1 8 35.32 odd 12
245.2.l.c.117.2 8 35.17 even 12
245.2.l.c.178.1 8 7.5 odd 6
245.2.l.c.178.2 8 7.2 even 3
245.2.l.c.227.1 8 35.12 even 12
245.2.l.c.227.2 8 35.2 odd 12
315.2.p.c.118.1 4 21.20 even 2
315.2.p.c.118.2 4 3.2 odd 2
315.2.p.c.307.1 4 15.2 even 4
315.2.p.c.307.2 4 105.62 odd 4
560.2.bj.a.97.1 4 140.27 odd 4
560.2.bj.a.97.2 4 20.7 even 4
560.2.bj.a.433.1 4 4.3 odd 2
560.2.bj.a.433.2 4 28.27 even 2