Properties

Label 315.2.bh.b.169.1
Level $315$
Weight $2$
Character 315.169
Analytic conductor $2.515$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [315,2,Mod(169,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.169");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.bh (of order \(6\), 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: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 169.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 315.169
Dual form 315.2.bh.b.274.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.73205 - 1.00000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.133975 + 2.23205i) q^{5} +(3.00000 - 1.73205i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.73205 - 1.00000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.133975 + 2.23205i) q^{5} +(3.00000 - 1.73205i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(2.00000 - 4.00000i) q^{10} +(-1.50000 + 2.59808i) q^{11} -3.46410 q^{12} +(1.73205 - 1.00000i) q^{13} +(-1.00000 - 1.73205i) q^{14} +(-3.46410 - 1.73205i) q^{15} +(2.00000 - 3.46410i) q^{16} -2.00000i q^{17} +6.00000i q^{18} -6.00000 q^{19} +(-3.73205 + 2.46410i) q^{20} +(-1.50000 + 0.866025i) q^{21} +(5.19615 - 3.00000i) q^{22} +(-5.19615 + 3.00000i) q^{23} +(-4.96410 + 0.598076i) q^{25} -4.00000 q^{26} +5.19615 q^{27} +2.00000i q^{28} +(-2.50000 + 4.33013i) q^{29} +(4.26795 + 6.46410i) q^{30} +(2.00000 + 3.46410i) q^{31} +(-6.92820 + 4.00000i) q^{32} +(-2.59808 - 4.50000i) q^{33} +(-2.00000 + 3.46410i) q^{34} +(-1.00000 + 2.00000i) q^{35} +(3.00000 - 5.19615i) q^{36} +2.00000i q^{37} +(10.3923 + 6.00000i) q^{38} +3.46410i q^{39} +(-4.00000 - 6.92820i) q^{41} +3.46410 q^{42} +(1.73205 + 1.00000i) q^{43} -6.00000 q^{44} +(5.59808 - 3.69615i) q^{45} +12.0000 q^{46} +(-2.59808 - 1.50000i) q^{47} +(3.46410 + 6.00000i) q^{48} +(0.500000 + 0.866025i) q^{49} +(9.19615 + 3.92820i) q^{50} +(3.00000 + 1.73205i) q^{51} +(3.46410 + 2.00000i) q^{52} +(-9.00000 - 5.19615i) q^{54} +(-6.00000 - 3.00000i) q^{55} +(5.19615 - 9.00000i) q^{57} +(8.66025 - 5.00000i) q^{58} +(-7.00000 - 12.1244i) q^{59} +(-0.464102 - 7.73205i) q^{60} +(-5.00000 + 8.66025i) q^{61} -8.00000i q^{62} -3.00000i q^{63} +8.00000 q^{64} +(2.46410 + 3.73205i) q^{65} +10.3923i q^{66} +(-8.66025 + 5.00000i) q^{67} +(3.46410 - 2.00000i) q^{68} -10.3923i q^{69} +(3.73205 - 2.46410i) q^{70} +7.00000 q^{71} -9.00000i q^{73} +(2.00000 - 3.46410i) q^{74} +(3.40192 - 7.96410i) q^{75} +(-6.00000 - 10.3923i) q^{76} +(-2.59808 + 1.50000i) q^{77} +(3.46410 - 6.00000i) q^{78} +(0.500000 - 0.866025i) q^{79} +(8.00000 + 4.00000i) q^{80} +(-4.50000 + 7.79423i) q^{81} +16.0000i q^{82} +(14.7224 + 8.50000i) q^{83} +(-3.00000 - 1.73205i) q^{84} +(4.46410 - 0.267949i) q^{85} +(-2.00000 - 3.46410i) q^{86} +(-4.33013 - 7.50000i) q^{87} +12.0000 q^{89} +(-13.3923 + 0.803848i) q^{90} +2.00000 q^{91} +(-10.3923 - 6.00000i) q^{92} -6.92820 q^{93} +(3.00000 + 5.19615i) q^{94} +(-0.803848 - 13.3923i) q^{95} -13.8564i q^{96} +(-6.06218 - 3.50000i) q^{97} -2.00000i q^{98} +9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{4} + 4 q^{5} + 12 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{4} + 4 q^{5} + 12 q^{6} - 6 q^{9} + 8 q^{10} - 6 q^{11} - 4 q^{14} + 8 q^{16} - 24 q^{19} - 8 q^{20} - 6 q^{21} - 6 q^{25} - 16 q^{26} - 10 q^{29} + 24 q^{30} + 8 q^{31} - 8 q^{34} - 4 q^{35} + 12 q^{36} - 16 q^{41} - 24 q^{44} + 12 q^{45} + 48 q^{46} + 2 q^{49} + 16 q^{50} + 12 q^{51} - 36 q^{54} - 24 q^{55} - 28 q^{59} + 12 q^{60} - 20 q^{61} + 32 q^{64} - 4 q^{65} + 8 q^{70} + 28 q^{71} + 8 q^{74} + 24 q^{75} - 24 q^{76} + 2 q^{79} + 32 q^{80} - 18 q^{81} - 12 q^{84} + 4 q^{85} - 8 q^{86} + 48 q^{89} - 12 q^{90} + 8 q^{91} + 12 q^{94} - 24 q^{95} + 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.73205 1.00000i −1.22474 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(3\) −0.866025 + 1.50000i −0.500000 + 0.866025i
\(4\) 1.00000 + 1.73205i 0.500000 + 0.866025i
\(5\) 0.133975 + 2.23205i 0.0599153 + 0.998203i
\(6\) 3.00000 1.73205i 1.22474 0.707107i
\(7\) 0.866025 + 0.500000i 0.327327 + 0.188982i
\(8\) 0 0
\(9\) −1.50000 2.59808i −0.500000 0.866025i
\(10\) 2.00000 4.00000i 0.632456 1.26491i
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) −3.46410 −1.00000
\(13\) 1.73205 1.00000i 0.480384 0.277350i −0.240192 0.970725i \(-0.577210\pi\)
0.720577 + 0.693375i \(0.243877\pi\)
\(14\) −1.00000 1.73205i −0.267261 0.462910i
\(15\) −3.46410 1.73205i −0.894427 0.447214i
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) 2.00000i 0.485071i −0.970143 0.242536i \(-0.922021\pi\)
0.970143 0.242536i \(-0.0779791\pi\)
\(18\) 6.00000i 1.41421i
\(19\) −6.00000 −1.37649 −0.688247 0.725476i \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) −3.73205 + 2.46410i −0.834512 + 0.550990i
\(21\) −1.50000 + 0.866025i −0.327327 + 0.188982i
\(22\) 5.19615 3.00000i 1.10782 0.639602i
\(23\) −5.19615 + 3.00000i −1.08347 + 0.625543i −0.931831 0.362892i \(-0.881789\pi\)
−0.151642 + 0.988436i \(0.548456\pi\)
\(24\) 0 0
\(25\) −4.96410 + 0.598076i −0.992820 + 0.119615i
\(26\) −4.00000 −0.784465
\(27\) 5.19615 1.00000
\(28\) 2.00000i 0.377964i
\(29\) −2.50000 + 4.33013i −0.464238 + 0.804084i −0.999167 0.0408130i \(-0.987005\pi\)
0.534928 + 0.844897i \(0.320339\pi\)
\(30\) 4.26795 + 6.46410i 0.779217 + 1.18018i
\(31\) 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) −6.92820 + 4.00000i −1.22474 + 0.707107i
\(33\) −2.59808 4.50000i −0.452267 0.783349i
\(34\) −2.00000 + 3.46410i −0.342997 + 0.594089i
\(35\) −1.00000 + 2.00000i −0.169031 + 0.338062i
\(36\) 3.00000 5.19615i 0.500000 0.866025i
\(37\) 2.00000i 0.328798i 0.986394 + 0.164399i \(0.0525685\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(38\) 10.3923 + 6.00000i 1.68585 + 0.973329i
\(39\) 3.46410i 0.554700i
\(40\) 0 0
\(41\) −4.00000 6.92820i −0.624695 1.08200i −0.988600 0.150567i \(-0.951890\pi\)
0.363905 0.931436i \(-0.381443\pi\)
\(42\) 3.46410 0.534522
\(43\) 1.73205 + 1.00000i 0.264135 + 0.152499i 0.626219 0.779647i \(-0.284601\pi\)
−0.362084 + 0.932145i \(0.617935\pi\)
\(44\) −6.00000 −0.904534
\(45\) 5.59808 3.69615i 0.834512 0.550990i
\(46\) 12.0000 1.76930
\(47\) −2.59808 1.50000i −0.378968 0.218797i 0.298401 0.954441i \(-0.403547\pi\)
−0.677369 + 0.735643i \(0.736880\pi\)
\(48\) 3.46410 + 6.00000i 0.500000 + 0.866025i
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) 9.19615 + 3.92820i 1.30053 + 0.555532i
\(51\) 3.00000 + 1.73205i 0.420084 + 0.242536i
\(52\) 3.46410 + 2.00000i 0.480384 + 0.277350i
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) −9.00000 5.19615i −1.22474 0.707107i
\(55\) −6.00000 3.00000i −0.809040 0.404520i
\(56\) 0 0
\(57\) 5.19615 9.00000i 0.688247 1.19208i
\(58\) 8.66025 5.00000i 1.13715 0.656532i
\(59\) −7.00000 12.1244i −0.911322 1.57846i −0.812198 0.583382i \(-0.801729\pi\)
−0.0991242 0.995075i \(-0.531604\pi\)
\(60\) −0.464102 7.73205i −0.0599153 0.998203i
\(61\) −5.00000 + 8.66025i −0.640184 + 1.10883i 0.345207 + 0.938527i \(0.387809\pi\)
−0.985391 + 0.170305i \(0.945525\pi\)
\(62\) 8.00000i 1.01600i
\(63\) 3.00000i 0.377964i
\(64\) 8.00000 1.00000
\(65\) 2.46410 + 3.73205i 0.305634 + 0.462904i
\(66\) 10.3923i 1.27920i
\(67\) −8.66025 + 5.00000i −1.05802 + 0.610847i −0.924883 0.380251i \(-0.875838\pi\)
−0.133135 + 0.991098i \(0.542504\pi\)
\(68\) 3.46410 2.00000i 0.420084 0.242536i
\(69\) 10.3923i 1.25109i
\(70\) 3.73205 2.46410i 0.446065 0.294516i
\(71\) 7.00000 0.830747 0.415374 0.909651i \(-0.363651\pi\)
0.415374 + 0.909651i \(0.363651\pi\)
\(72\) 0 0
\(73\) 9.00000i 1.05337i −0.850060 0.526685i \(-0.823435\pi\)
0.850060 0.526685i \(-0.176565\pi\)
\(74\) 2.00000 3.46410i 0.232495 0.402694i
\(75\) 3.40192 7.96410i 0.392820 0.919615i
\(76\) −6.00000 10.3923i −0.688247 1.19208i
\(77\) −2.59808 + 1.50000i −0.296078 + 0.170941i
\(78\) 3.46410 6.00000i 0.392232 0.679366i
\(79\) 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i \(-0.815418\pi\)
0.892781 + 0.450490i \(0.148751\pi\)
\(80\) 8.00000 + 4.00000i 0.894427 + 0.447214i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 16.0000i 1.76690i
\(83\) 14.7224 + 8.50000i 1.61600 + 0.932996i 0.987942 + 0.154828i \(0.0494822\pi\)
0.628055 + 0.778169i \(0.283851\pi\)
\(84\) −3.00000 1.73205i −0.327327 0.188982i
\(85\) 4.46410 0.267949i 0.484200 0.0290632i
\(86\) −2.00000 3.46410i −0.215666 0.373544i
\(87\) −4.33013 7.50000i −0.464238 0.804084i
\(88\) 0 0
\(89\) 12.0000 1.27200 0.635999 0.771690i \(-0.280588\pi\)
0.635999 + 0.771690i \(0.280588\pi\)
\(90\) −13.3923 + 0.803848i −1.41167 + 0.0847330i
\(91\) 2.00000 0.209657
\(92\) −10.3923 6.00000i −1.08347 0.625543i
\(93\) −6.92820 −0.718421
\(94\) 3.00000 + 5.19615i 0.309426 + 0.535942i
\(95\) −0.803848 13.3923i −0.0824730 1.37402i
\(96\) 13.8564i 1.41421i
\(97\) −6.06218 3.50000i −0.615521 0.355371i 0.159602 0.987181i \(-0.448979\pi\)
−0.775123 + 0.631810i \(0.782312\pi\)
\(98\) 2.00000i 0.202031i
\(99\) 9.00000 0.904534
\(100\) −6.00000 8.00000i −0.600000 0.800000i
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) −3.46410 6.00000i −0.342997 0.594089i
\(103\) −4.33013 + 2.50000i −0.426660 + 0.246332i −0.697923 0.716173i \(-0.745892\pi\)
0.271263 + 0.962505i \(0.412559\pi\)
\(104\) 0 0
\(105\) −2.13397 3.23205i −0.208255 0.315416i
\(106\) 0 0
\(107\) 16.0000i 1.54678i 0.633932 + 0.773389i \(0.281440\pi\)
−0.633932 + 0.773389i \(0.718560\pi\)
\(108\) 5.19615 + 9.00000i 0.500000 + 0.866025i
\(109\) 19.0000 1.81987 0.909935 0.414751i \(-0.136131\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) 7.39230 + 11.1962i 0.704829 + 1.06751i
\(111\) −3.00000 1.73205i −0.284747 0.164399i
\(112\) 3.46410 2.00000i 0.327327 0.188982i
\(113\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(114\) −18.0000 + 10.3923i −1.68585 + 0.973329i
\(115\) −7.39230 11.1962i −0.689336 1.04405i
\(116\) −10.0000 −0.928477
\(117\) −5.19615 3.00000i −0.480384 0.277350i
\(118\) 28.0000i 2.57761i
\(119\) 1.00000 1.73205i 0.0916698 0.158777i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 17.3205 10.0000i 1.56813 0.905357i
\(123\) 13.8564 1.24939
\(124\) −4.00000 + 6.92820i −0.359211 + 0.622171i
\(125\) −2.00000 11.0000i −0.178885 0.983870i
\(126\) −3.00000 + 5.19615i −0.267261 + 0.462910i
\(127\) 20.0000i 1.77471i 0.461084 + 0.887357i \(0.347461\pi\)
−0.461084 + 0.887357i \(0.652539\pi\)
\(128\) 0 0
\(129\) −3.00000 + 1.73205i −0.264135 + 0.152499i
\(130\) −0.535898 8.92820i −0.0470014 0.783055i
\(131\) 7.00000 + 12.1244i 0.611593 + 1.05931i 0.990972 + 0.134069i \(0.0428042\pi\)
−0.379379 + 0.925241i \(0.623862\pi\)
\(132\) 5.19615 9.00000i 0.452267 0.783349i
\(133\) −5.19615 3.00000i −0.450564 0.260133i
\(134\) 20.0000 1.72774
\(135\) 0.696152 + 11.5981i 0.0599153 + 0.998203i
\(136\) 0 0
\(137\) −15.5885 9.00000i −1.33181 0.768922i −0.346235 0.938148i \(-0.612540\pi\)
−0.985577 + 0.169226i \(0.945873\pi\)
\(138\) −10.3923 + 18.0000i −0.884652 + 1.53226i
\(139\) 10.0000 + 17.3205i 0.848189 + 1.46911i 0.882823 + 0.469706i \(0.155640\pi\)
−0.0346338 + 0.999400i \(0.511026\pi\)
\(140\) −4.46410 + 0.267949i −0.377285 + 0.0226458i
\(141\) 4.50000 2.59808i 0.378968 0.218797i
\(142\) −12.1244 7.00000i −1.01745 0.587427i
\(143\) 6.00000i 0.501745i
\(144\) −12.0000 −1.00000
\(145\) −10.0000 5.00000i −0.830455 0.415227i
\(146\) −9.00000 + 15.5885i −0.744845 + 1.29011i
\(147\) −1.73205 −0.142857
\(148\) −3.46410 + 2.00000i −0.284747 + 0.164399i
\(149\) −2.50000 4.33013i −0.204808 0.354738i 0.745264 0.666770i \(-0.232324\pi\)
−0.950072 + 0.312032i \(0.898990\pi\)
\(150\) −13.8564 + 10.3923i −1.13137 + 0.848528i
\(151\) −10.0000 + 17.3205i −0.813788 + 1.40952i 0.0964061 + 0.995342i \(0.469265\pi\)
−0.910195 + 0.414181i \(0.864068\pi\)
\(152\) 0 0
\(153\) −5.19615 + 3.00000i −0.420084 + 0.242536i
\(154\) 6.00000 0.483494
\(155\) −7.46410 + 4.92820i −0.599531 + 0.395843i
\(156\) −6.00000 + 3.46410i −0.480384 + 0.277350i
\(157\) 7.79423 4.50000i 0.622047 0.359139i −0.155618 0.987817i \(-0.549737\pi\)
0.777666 + 0.628678i \(0.216404\pi\)
\(158\) −1.73205 + 1.00000i −0.137795 + 0.0795557i
\(159\) 0 0
\(160\) −9.85641 14.9282i −0.779217 1.18018i
\(161\) −6.00000 −0.472866
\(162\) 15.5885 9.00000i 1.22474 0.707107i
\(163\) 4.00000i 0.313304i −0.987654 0.156652i \(-0.949930\pi\)
0.987654 0.156652i \(-0.0500701\pi\)
\(164\) 8.00000 13.8564i 0.624695 1.08200i
\(165\) 9.69615 6.40192i 0.754844 0.498389i
\(166\) −17.0000 29.4449i −1.31946 2.28536i
\(167\) −10.3923 + 6.00000i −0.804181 + 0.464294i −0.844931 0.534875i \(-0.820359\pi\)
0.0407502 + 0.999169i \(0.487025\pi\)
\(168\) 0 0
\(169\) −4.50000 + 7.79423i −0.346154 + 0.599556i
\(170\) −8.00000 4.00000i −0.613572 0.306786i
\(171\) 9.00000 + 15.5885i 0.688247 + 1.19208i
\(172\) 4.00000i 0.304997i
\(173\) 12.9904 + 7.50000i 0.987640 + 0.570214i 0.904568 0.426329i \(-0.140193\pi\)
0.0830722 + 0.996544i \(0.473527\pi\)
\(174\) 17.3205i 1.31306i
\(175\) −4.59808 1.96410i −0.347582 0.148472i
\(176\) 6.00000 + 10.3923i 0.452267 + 0.783349i
\(177\) 24.2487 1.82264
\(178\) −20.7846 12.0000i −1.55787 0.899438i
\(179\) 11.0000 0.822179 0.411089 0.911595i \(-0.365148\pi\)
0.411089 + 0.911595i \(0.365148\pi\)
\(180\) 12.0000 + 6.00000i 0.894427 + 0.447214i
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) −3.46410 2.00000i −0.256776 0.148250i
\(183\) −8.66025 15.0000i −0.640184 1.10883i
\(184\) 0 0
\(185\) −4.46410 + 0.267949i −0.328207 + 0.0197000i
\(186\) 12.0000 + 6.92820i 0.879883 + 0.508001i
\(187\) 5.19615 + 3.00000i 0.379980 + 0.219382i
\(188\) 6.00000i 0.437595i
\(189\) 4.50000 + 2.59808i 0.327327 + 0.188982i
\(190\) −12.0000 + 24.0000i −0.870572 + 1.74114i
\(191\) 1.50000 2.59808i 0.108536 0.187990i −0.806641 0.591041i \(-0.798717\pi\)
0.915177 + 0.403051i \(0.132050\pi\)
\(192\) −6.92820 + 12.0000i −0.500000 + 0.866025i
\(193\) 12.1244 7.00000i 0.872730 0.503871i 0.00447566 0.999990i \(-0.498575\pi\)
0.868255 + 0.496119i \(0.165242\pi\)
\(194\) 7.00000 + 12.1244i 0.502571 + 0.870478i
\(195\) −7.73205 + 0.464102i −0.553704 + 0.0332350i
\(196\) −1.00000 + 1.73205i −0.0714286 + 0.123718i
\(197\) 8.00000i 0.569976i 0.958531 + 0.284988i \(0.0919897\pi\)
−0.958531 + 0.284988i \(0.908010\pi\)
\(198\) −15.5885 9.00000i −1.10782 0.639602i
\(199\) −8.00000 −0.567105 −0.283552 0.958957i \(-0.591513\pi\)
−0.283552 + 0.958957i \(0.591513\pi\)
\(200\) 0 0
\(201\) 17.3205i 1.22169i
\(202\) 0 0
\(203\) −4.33013 + 2.50000i −0.303915 + 0.175466i
\(204\) 6.92820i 0.485071i
\(205\) 14.9282 9.85641i 1.04263 0.688401i
\(206\) 10.0000 0.696733
\(207\) 15.5885 + 9.00000i 1.08347 + 0.625543i
\(208\) 8.00000i 0.554700i
\(209\) 9.00000 15.5885i 0.622543 1.07828i
\(210\) 0.464102 + 7.73205i 0.0320261 + 0.533562i
\(211\) −8.50000 14.7224i −0.585164 1.01353i −0.994855 0.101310i \(-0.967697\pi\)
0.409691 0.912224i \(-0.365637\pi\)
\(212\) 0 0
\(213\) −6.06218 + 10.5000i −0.415374 + 0.719448i
\(214\) 16.0000 27.7128i 1.09374 1.89441i
\(215\) −2.00000 + 4.00000i −0.136399 + 0.272798i
\(216\) 0 0
\(217\) 4.00000i 0.271538i
\(218\) −32.9090 19.0000i −2.22888 1.28684i
\(219\) 13.5000 + 7.79423i 0.912245 + 0.526685i
\(220\) −0.803848 13.3923i −0.0541954 0.902909i
\(221\) −2.00000 3.46410i −0.134535 0.233021i
\(222\) 3.46410 + 6.00000i 0.232495 + 0.402694i
\(223\) 20.7846 + 12.0000i 1.39184 + 0.803579i 0.993519 0.113666i \(-0.0362595\pi\)
0.398321 + 0.917246i \(0.369593\pi\)
\(224\) −8.00000 −0.534522
\(225\) 9.00000 + 12.0000i 0.600000 + 0.800000i
\(226\) 0 0
\(227\) −17.3205 10.0000i −1.14960 0.663723i −0.200812 0.979630i \(-0.564358\pi\)
−0.948790 + 0.315906i \(0.897691\pi\)
\(228\) 20.7846 1.37649
\(229\) −5.00000 8.66025i −0.330409 0.572286i 0.652183 0.758062i \(-0.273853\pi\)
−0.982592 + 0.185776i \(0.940520\pi\)
\(230\) 1.60770 + 26.7846i 0.106008 + 1.76612i
\(231\) 5.19615i 0.341882i
\(232\) 0 0
\(233\) 16.0000i 1.04819i −0.851658 0.524097i \(-0.824403\pi\)
0.851658 0.524097i \(-0.175597\pi\)
\(234\) 6.00000 + 10.3923i 0.392232 + 0.679366i
\(235\) 3.00000 6.00000i 0.195698 0.391397i
\(236\) 14.0000 24.2487i 0.911322 1.57846i
\(237\) 0.866025 + 1.50000i 0.0562544 + 0.0974355i
\(238\) −3.46410 + 2.00000i −0.224544 + 0.129641i
\(239\) −4.50000 7.79423i −0.291081 0.504167i 0.682985 0.730433i \(-0.260682\pi\)
−0.974066 + 0.226266i \(0.927348\pi\)
\(240\) −12.9282 + 8.53590i −0.834512 + 0.550990i
\(241\) −2.00000 + 3.46410i −0.128831 + 0.223142i −0.923224 0.384262i \(-0.874456\pi\)
0.794393 + 0.607404i \(0.207789\pi\)
\(242\) 4.00000i 0.257130i
\(243\) −7.79423 13.5000i −0.500000 0.866025i
\(244\) −20.0000 −1.28037
\(245\) −1.86603 + 1.23205i −0.119216 + 0.0787128i
\(246\) −24.0000 13.8564i −1.53018 0.883452i
\(247\) −10.3923 + 6.00000i −0.661247 + 0.381771i
\(248\) 0 0
\(249\) −25.5000 + 14.7224i −1.61600 + 0.932996i
\(250\) −7.53590 + 21.0526i −0.476612 + 1.33148i
\(251\) 18.0000 1.13615 0.568075 0.822977i \(-0.307688\pi\)
0.568075 + 0.822977i \(0.307688\pi\)
\(252\) 5.19615 3.00000i 0.327327 0.188982i
\(253\) 18.0000i 1.13165i
\(254\) 20.0000 34.6410i 1.25491 2.17357i
\(255\) −3.46410 + 6.92820i −0.216930 + 0.433861i
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) 6.06218 3.50000i 0.378148 0.218324i −0.298864 0.954296i \(-0.596608\pi\)
0.677012 + 0.735972i \(0.263274\pi\)
\(258\) 6.92820 0.431331
\(259\) −1.00000 + 1.73205i −0.0621370 + 0.107624i
\(260\) −4.00000 + 8.00000i −0.248069 + 0.496139i
\(261\) 15.0000 0.928477
\(262\) 28.0000i 1.72985i
\(263\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 6.00000 + 10.3923i 0.367884 + 0.637193i
\(267\) −10.3923 + 18.0000i −0.635999 + 1.10158i
\(268\) −17.3205 10.0000i −1.05802 0.610847i
\(269\) −16.0000 −0.975537 −0.487769 0.872973i \(-0.662189\pi\)
−0.487769 + 0.872973i \(0.662189\pi\)
\(270\) 10.3923 20.7846i 0.632456 1.26491i
\(271\) −14.0000 −0.850439 −0.425220 0.905090i \(-0.639803\pi\)
−0.425220 + 0.905090i \(0.639803\pi\)
\(272\) −6.92820 4.00000i −0.420084 0.242536i
\(273\) −1.73205 + 3.00000i −0.104828 + 0.181568i
\(274\) 18.0000 + 31.1769i 1.08742 + 1.88347i
\(275\) 5.89230 13.7942i 0.355319 0.831823i
\(276\) 18.0000 10.3923i 1.08347 0.625543i
\(277\) 24.2487 + 14.0000i 1.45696 + 0.841178i 0.998861 0.0477206i \(-0.0151957\pi\)
0.458103 + 0.888899i \(0.348529\pi\)
\(278\) 40.0000i 2.39904i
\(279\) 6.00000 10.3923i 0.359211 0.622171i
\(280\) 0 0
\(281\) −3.50000 + 6.06218i −0.208792 + 0.361639i −0.951334 0.308160i \(-0.900287\pi\)
0.742542 + 0.669800i \(0.233620\pi\)
\(282\) −10.3923 −0.618853
\(283\) 6.06218 3.50000i 0.360359 0.208053i −0.308879 0.951101i \(-0.599954\pi\)
0.669238 + 0.743048i \(0.266621\pi\)
\(284\) 7.00000 + 12.1244i 0.415374 + 0.719448i
\(285\) 20.7846 + 10.3923i 1.23117 + 0.615587i
\(286\) 6.00000 10.3923i 0.354787 0.614510i
\(287\) 8.00000i 0.472225i
\(288\) 20.7846 + 12.0000i 1.22474 + 0.707107i
\(289\) 13.0000 0.764706
\(290\) 12.3205 + 18.6603i 0.723485 + 1.09577i
\(291\) 10.5000 6.06218i 0.615521 0.355371i
\(292\) 15.5885 9.00000i 0.912245 0.526685i
\(293\) −23.3827 + 13.5000i −1.36603 + 0.788678i −0.990419 0.138098i \(-0.955901\pi\)
−0.375613 + 0.926777i \(0.622568\pi\)
\(294\) 3.00000 + 1.73205i 0.174964 + 0.101015i
\(295\) 26.1244 17.2487i 1.52102 1.00426i
\(296\) 0 0
\(297\) −7.79423 + 13.5000i −0.452267 + 0.783349i
\(298\) 10.0000i 0.579284i
\(299\) −6.00000 + 10.3923i −0.346989 + 0.601003i
\(300\) 17.1962 2.07180i 0.992820 0.119615i
\(301\) 1.00000 + 1.73205i 0.0576390 + 0.0998337i
\(302\) 34.6410 20.0000i 1.99337 1.15087i
\(303\) 0 0
\(304\) −12.0000 + 20.7846i −0.688247 + 1.19208i
\(305\) −20.0000 10.0000i −1.14520 0.572598i
\(306\) 12.0000 0.685994
\(307\) 4.00000i 0.228292i 0.993464 + 0.114146i \(0.0364132\pi\)
−0.993464 + 0.114146i \(0.963587\pi\)
\(308\) −5.19615 3.00000i −0.296078 0.170941i
\(309\) 8.66025i 0.492665i
\(310\) 17.8564 1.07180i 1.01418 0.0608740i
\(311\) 3.00000 + 5.19615i 0.170114 + 0.294647i 0.938460 0.345389i \(-0.112253\pi\)
−0.768345 + 0.640036i \(0.778920\pi\)
\(312\) 0 0
\(313\) 7.79423 + 4.50000i 0.440556 + 0.254355i 0.703833 0.710365i \(-0.251470\pi\)
−0.263278 + 0.964720i \(0.584803\pi\)
\(314\) −18.0000 −1.01580
\(315\) 6.69615 0.401924i 0.377285 0.0226458i
\(316\) 2.00000 0.112509
\(317\) 25.9808 + 15.0000i 1.45922 + 0.842484i 0.998973 0.0453045i \(-0.0144258\pi\)
0.460252 + 0.887788i \(0.347759\pi\)
\(318\) 0 0
\(319\) −7.50000 12.9904i −0.419919 0.727322i
\(320\) 1.07180 + 17.8564i 0.0599153 + 0.998203i
\(321\) −24.0000 13.8564i −1.33955 0.773389i
\(322\) 10.3923 + 6.00000i 0.579141 + 0.334367i
\(323\) 12.0000i 0.667698i
\(324\) −18.0000 −1.00000
\(325\) −8.00000 + 6.00000i −0.443760 + 0.332820i
\(326\) −4.00000 + 6.92820i −0.221540 + 0.383718i
\(327\) −16.4545 + 28.5000i −0.909935 + 1.57605i
\(328\) 0 0
\(329\) −1.50000 2.59808i −0.0826977 0.143237i
\(330\) −23.1962 + 1.39230i −1.27691 + 0.0766439i
\(331\) −13.5000 + 23.3827i −0.742027 + 1.28523i 0.209544 + 0.977799i \(0.432802\pi\)
−0.951571 + 0.307429i \(0.900531\pi\)
\(332\) 34.0000i 1.86599i
\(333\) 5.19615 3.00000i 0.284747 0.164399i
\(334\) 24.0000 1.31322
\(335\) −12.3205 18.6603i −0.673141 1.01952i
\(336\) 6.92820i 0.377964i
\(337\) −15.5885 + 9.00000i −0.849157 + 0.490261i −0.860366 0.509676i \(-0.829765\pi\)
0.0112091 + 0.999937i \(0.496432\pi\)
\(338\) 15.5885 9.00000i 0.847900 0.489535i
\(339\) 0 0
\(340\) 4.92820 + 7.46410i 0.267269 + 0.404798i
\(341\) −12.0000 −0.649836
\(342\) 36.0000i 1.94666i
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 23.1962 1.39230i 1.24884 0.0749592i
\(346\) −15.0000 25.9808i −0.806405 1.39673i
\(347\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(348\) 8.66025 15.0000i 0.464238 0.804084i
\(349\) 5.00000 8.66025i 0.267644 0.463573i −0.700609 0.713545i \(-0.747088\pi\)
0.968253 + 0.249973i \(0.0804216\pi\)
\(350\) 6.00000 + 8.00000i 0.320713 + 0.427618i
\(351\) 9.00000 5.19615i 0.480384 0.277350i
\(352\) 24.0000i 1.27920i
\(353\) 9.52628 + 5.50000i 0.507033 + 0.292735i 0.731613 0.681720i \(-0.238768\pi\)
−0.224580 + 0.974456i \(0.572101\pi\)
\(354\) −42.0000 24.2487i −2.23227 1.28880i
\(355\) 0.937822 + 15.6244i 0.0497744 + 0.829255i
\(356\) 12.0000 + 20.7846i 0.635999 + 1.10158i
\(357\) 1.73205 + 3.00000i 0.0916698 + 0.158777i
\(358\) −19.0526 11.0000i −1.00696 0.581368i
\(359\) −4.00000 −0.211112 −0.105556 0.994413i \(-0.533662\pi\)
−0.105556 + 0.994413i \(0.533662\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) 0 0
\(363\) −3.46410 −0.181818
\(364\) 2.00000 + 3.46410i 0.104828 + 0.181568i
\(365\) 20.0885 1.20577i 1.05148 0.0631130i
\(366\) 34.6410i 1.81071i
\(367\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(368\) 24.0000i 1.25109i
\(369\) −12.0000 + 20.7846i −0.624695 + 1.08200i
\(370\) 8.00000 + 4.00000i 0.415900 + 0.207950i
\(371\) 0 0
\(372\) −6.92820 12.0000i −0.359211 0.622171i
\(373\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(374\) −6.00000 10.3923i −0.310253 0.537373i
\(375\) 18.2321 + 6.52628i 0.941499 + 0.337016i
\(376\) 0 0
\(377\) 10.0000i 0.515026i
\(378\) −5.19615 9.00000i −0.267261 0.462910i
\(379\) −23.0000 −1.18143 −0.590715 0.806880i \(-0.701154\pi\)
−0.590715 + 0.806880i \(0.701154\pi\)
\(380\) 22.3923 14.7846i 1.14870 0.758434i
\(381\) −30.0000 17.3205i −1.53695 0.887357i
\(382\) −5.19615 + 3.00000i −0.265858 + 0.153493i
\(383\) 4.33013 2.50000i 0.221259 0.127744i −0.385274 0.922802i \(-0.625893\pi\)
0.606533 + 0.795058i \(0.292560\pi\)
\(384\) 0 0
\(385\) −3.69615 5.59808i −0.188373 0.285304i
\(386\) −28.0000 −1.42516
\(387\) 6.00000i 0.304997i
\(388\) 14.0000i 0.710742i
\(389\) −9.50000 + 16.4545i −0.481669 + 0.834275i −0.999779 0.0210389i \(-0.993303\pi\)
0.518110 + 0.855314i \(0.326636\pi\)
\(390\) 13.8564 + 6.92820i 0.701646 + 0.350823i
\(391\) 6.00000 + 10.3923i 0.303433 + 0.525561i
\(392\) 0 0
\(393\) −24.2487 −1.22319
\(394\) 8.00000 13.8564i 0.403034 0.698076i
\(395\) 2.00000 + 1.00000i 0.100631 + 0.0503155i
\(396\) 9.00000 + 15.5885i 0.452267 + 0.783349i
\(397\) 17.0000i 0.853206i −0.904439 0.426603i \(-0.859710\pi\)
0.904439 0.426603i \(-0.140290\pi\)
\(398\) 13.8564 + 8.00000i 0.694559 + 0.401004i
\(399\) 9.00000 5.19615i 0.450564 0.260133i
\(400\) −7.85641 + 18.3923i −0.392820 + 0.919615i
\(401\) 7.50000 + 12.9904i 0.374532 + 0.648709i 0.990257 0.139253i \(-0.0444700\pi\)
−0.615725 + 0.787961i \(0.711137\pi\)
\(402\) −17.3205 + 30.0000i −0.863868 + 1.49626i
\(403\) 6.92820 + 4.00000i 0.345118 + 0.199254i
\(404\) 0 0
\(405\) −18.0000 9.00000i −0.894427 0.447214i
\(406\) 10.0000 0.496292
\(407\) −5.19615 3.00000i −0.257564 0.148704i
\(408\) 0 0
\(409\) 4.00000 + 6.92820i 0.197787 + 0.342578i 0.947811 0.318834i \(-0.103291\pi\)
−0.750023 + 0.661411i \(0.769958\pi\)
\(410\) −35.7128 + 2.14359i −1.76373 + 0.105865i
\(411\) 27.0000 15.5885i 1.33181 0.768922i
\(412\) −8.66025 5.00000i −0.426660 0.246332i
\(413\) 14.0000i 0.688895i
\(414\) −18.0000 31.1769i −0.884652 1.53226i
\(415\) −17.0000 + 34.0000i −0.834497 + 1.66899i
\(416\) −8.00000 + 13.8564i −0.392232 + 0.679366i
\(417\) −34.6410 −1.69638
\(418\) −31.1769 + 18.0000i −1.52491 + 0.880409i
\(419\) −15.0000 25.9808i −0.732798 1.26924i −0.955683 0.294398i \(-0.904881\pi\)
0.222885 0.974845i \(-0.428453\pi\)
\(420\) 3.46410 6.92820i 0.169031 0.338062i
\(421\) 7.50000 12.9904i 0.365528 0.633112i −0.623333 0.781956i \(-0.714222\pi\)
0.988861 + 0.148844i \(0.0475552\pi\)
\(422\) 34.0000i 1.65509i
\(423\) 9.00000i 0.437595i
\(424\) 0 0
\(425\) 1.19615 + 9.92820i 0.0580219 + 0.481589i
\(426\) 21.0000 12.1244i 1.01745 0.587427i
\(427\) −8.66025 + 5.00000i −0.419099 + 0.241967i
\(428\) −27.7128 + 16.0000i −1.33955 + 0.773389i
\(429\) −9.00000 5.19615i −0.434524 0.250873i
\(430\) 7.46410 4.92820i 0.359951 0.237659i
\(431\) 16.0000 0.770693 0.385346 0.922772i \(-0.374082\pi\)
0.385346 + 0.922772i \(0.374082\pi\)
\(432\) 10.3923 18.0000i 0.500000 0.866025i
\(433\) 2.00000i 0.0961139i −0.998845 0.0480569i \(-0.984697\pi\)
0.998845 0.0480569i \(-0.0153029\pi\)
\(434\) 4.00000 6.92820i 0.192006 0.332564i
\(435\) 16.1603 10.6699i 0.774825 0.511581i
\(436\) 19.0000 + 32.9090i 0.909935 + 1.57605i
\(437\) 31.1769 18.0000i 1.49139 0.861057i
\(438\) −15.5885 27.0000i −0.744845 1.29011i
\(439\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(440\) 0 0
\(441\) 1.50000 2.59808i 0.0714286 0.123718i
\(442\) 8.00000i 0.380521i
\(443\) −3.46410 2.00000i −0.164584 0.0950229i 0.415445 0.909618i \(-0.363626\pi\)
−0.580030 + 0.814595i \(0.696959\pi\)
\(444\) 6.92820i 0.328798i
\(445\) 1.60770 + 26.7846i 0.0762121 + 1.26971i
\(446\) −24.0000 41.5692i −1.13643 1.96836i
\(447\) 8.66025 0.409616
\(448\) 6.92820 + 4.00000i 0.327327 + 0.188982i
\(449\) −31.0000 −1.46298 −0.731490 0.681852i \(-0.761175\pi\)
−0.731490 + 0.681852i \(0.761175\pi\)
\(450\) −3.58846 29.7846i −0.169161 1.40406i
\(451\) 24.0000 1.13012
\(452\) 0 0
\(453\) −17.3205 30.0000i −0.813788 1.40952i
\(454\) 20.0000 + 34.6410i 0.938647 + 1.62578i
\(455\) 0.267949 + 4.46410i 0.0125617 + 0.209280i
\(456\) 0 0
\(457\) −24.2487 14.0000i −1.13431 0.654892i −0.189292 0.981921i \(-0.560619\pi\)
−0.945015 + 0.327028i \(0.893953\pi\)
\(458\) 20.0000i 0.934539i
\(459\) 10.3923i 0.485071i
\(460\) 12.0000 24.0000i 0.559503 1.11901i
\(461\) 6.00000 10.3923i 0.279448 0.484018i −0.691800 0.722089i \(-0.743182\pi\)
0.971248 + 0.238071i \(0.0765153\pi\)
\(462\) −5.19615 + 9.00000i −0.241747 + 0.418718i
\(463\) 5.19615 3.00000i 0.241486 0.139422i −0.374374 0.927278i \(-0.622142\pi\)
0.615859 + 0.787856i \(0.288809\pi\)
\(464\) 10.0000 + 17.3205i 0.464238 + 0.804084i
\(465\) −0.928203 15.4641i −0.0430444 0.717131i
\(466\) −16.0000 + 27.7128i −0.741186 + 1.28377i
\(467\) 3.00000i 0.138823i −0.997588 0.0694117i \(-0.977888\pi\)
0.997588 0.0694117i \(-0.0221122\pi\)
\(468\) 12.0000i 0.554700i
\(469\) −10.0000 −0.461757
\(470\) −11.1962 + 7.39230i −0.516440 + 0.340982i
\(471\) 15.5885i 0.718278i
\(472\) 0 0
\(473\) −5.19615 + 3.00000i −0.238919 + 0.137940i
\(474\) 3.46410i 0.159111i
\(475\) 29.7846 3.58846i 1.36661 0.164650i
\(476\) 4.00000 0.183340
\(477\) 0 0
\(478\) 18.0000i 0.823301i
\(479\) 18.0000 31.1769i 0.822441 1.42451i −0.0814184 0.996680i \(-0.525945\pi\)
0.903859 0.427830i \(-0.140722\pi\)
\(480\) 30.9282 1.85641i 1.41167 0.0847330i
\(481\) 2.00000 + 3.46410i 0.0911922 + 0.157949i
\(482\) 6.92820 4.00000i 0.315571 0.182195i
\(483\) 5.19615 9.00000i 0.236433 0.409514i
\(484\) −2.00000 + 3.46410i −0.0909091 + 0.157459i
\(485\) 7.00000 14.0000i 0.317854 0.635707i
\(486\) 31.1769i 1.41421i
\(487\) 12.0000i 0.543772i −0.962329 0.271886i \(-0.912353\pi\)
0.962329 0.271886i \(-0.0876473\pi\)
\(488\) 0 0
\(489\) 6.00000 + 3.46410i 0.271329 + 0.156652i
\(490\) 4.46410 0.267949i 0.201668 0.0121047i
\(491\) −14.0000 24.2487i −0.631811 1.09433i −0.987181 0.159603i \(-0.948978\pi\)
0.355370 0.934726i \(-0.384355\pi\)
\(492\) 13.8564 + 24.0000i 0.624695 + 1.08200i
\(493\) 8.66025 + 5.00000i 0.390038 + 0.225189i
\(494\) 24.0000 1.07981
\(495\) 1.20577 + 20.0885i 0.0541954 + 0.902909i
\(496\) 16.0000 0.718421
\(497\) 6.06218 + 3.50000i 0.271926 + 0.156996i
\(498\) 58.8897 2.63891
\(499\) 2.00000 + 3.46410i 0.0895323 + 0.155074i 0.907314 0.420455i \(-0.138129\pi\)
−0.817781 + 0.575529i \(0.804796\pi\)
\(500\) 17.0526 14.4641i 0.762614 0.646854i
\(501\) 20.7846i 0.928588i
\(502\) −31.1769 18.0000i −1.39149 0.803379i
\(503\) 27.0000i 1.20387i −0.798545 0.601935i \(-0.794397\pi\)
0.798545 0.601935i \(-0.205603\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −18.0000 + 31.1769i −0.800198 + 1.38598i
\(507\) −7.79423 13.5000i −0.346154 0.599556i
\(508\) −34.6410 + 20.0000i −1.53695 + 0.887357i
\(509\) 9.00000 + 15.5885i 0.398918 + 0.690946i 0.993593 0.113020i \(-0.0360525\pi\)
−0.594675 + 0.803966i \(0.702719\pi\)
\(510\) 12.9282 8.53590i 0.572470 0.377976i
\(511\) 4.50000 7.79423i 0.199068 0.344796i
\(512\) 32.0000i 1.41421i
\(513\) −31.1769 −1.37649
\(514\) −14.0000 −0.617514
\(515\) −6.16025 9.33013i −0.271453 0.411135i
\(516\) −6.00000 3.46410i −0.264135 0.152499i
\(517\) 7.79423 4.50000i 0.342790 0.197910i
\(518\) 3.46410 2.00000i 0.152204 0.0878750i
\(519\) −22.5000 + 12.9904i −0.987640 + 0.570214i
\(520\) 0 0
\(521\) 2.00000 0.0876216 0.0438108 0.999040i \(-0.486050\pi\)
0.0438108 + 0.999040i \(0.486050\pi\)
\(522\) −25.9808 15.0000i −1.13715 0.656532i
\(523\) 23.0000i 1.00572i −0.864368 0.502860i \(-0.832281\pi\)
0.864368 0.502860i \(-0.167719\pi\)
\(524\) −14.0000 + 24.2487i −0.611593 + 1.05931i
\(525\) 6.92820 5.19615i 0.302372 0.226779i
\(526\) 0 0
\(527\) 6.92820 4.00000i 0.301797 0.174243i
\(528\) −20.7846 −0.904534
\(529\) 6.50000 11.2583i 0.282609 0.489493i
\(530\) 0 0
\(531\) −21.0000 + 36.3731i −0.911322 + 1.57846i
\(532\) 12.0000i 0.520266i
\(533\) −13.8564 8.00000i −0.600188 0.346518i
\(534\) 36.0000 20.7846i 1.55787 0.899438i
\(535\) −35.7128 + 2.14359i −1.54400 + 0.0926756i
\(536\) 0 0
\(537\) −9.52628 + 16.5000i −0.411089 + 0.712028i
\(538\) 27.7128 + 16.0000i 1.19478 + 0.689809i
\(539\) −3.00000 −0.129219
\(540\) −19.3923 + 12.8038i −0.834512 + 0.550990i
\(541\) −30.0000 −1.28980 −0.644900 0.764267i \(-0.723101\pi\)
−0.644900 + 0.764267i \(0.723101\pi\)
\(542\) 24.2487 + 14.0000i 1.04157 + 0.601351i
\(543\) 0 0
\(544\) 8.00000 + 13.8564i 0.342997 + 0.594089i
\(545\) 2.54552 + 42.4090i 0.109038 + 1.81660i
\(546\) 6.00000 3.46410i 0.256776 0.148250i
\(547\) 19.0526 + 11.0000i 0.814629 + 0.470326i 0.848561 0.529098i \(-0.177470\pi\)
−0.0339321 + 0.999424i \(0.510803\pi\)
\(548\) 36.0000i 1.53784i
\(549\) 30.0000 1.28037
\(550\) −24.0000 + 18.0000i −1.02336 + 0.767523i
\(551\) 15.0000 25.9808i 0.639021 1.10682i
\(552\) 0 0
\(553\) 0.866025 0.500000i 0.0368271 0.0212622i
\(554\) −28.0000 48.4974i −1.18961 2.06046i
\(555\) 3.46410 6.92820i 0.147043 0.294086i
\(556\) −20.0000 + 34.6410i −0.848189 + 1.46911i
\(557\) 2.00000i 0.0847427i 0.999102 + 0.0423714i \(0.0134913\pi\)
−0.999102 + 0.0423714i \(0.986509\pi\)
\(558\) −20.7846 + 12.0000i −0.879883 + 0.508001i
\(559\) 4.00000 0.169182
\(560\) 4.92820 + 7.46410i 0.208255 + 0.315416i
\(561\) −9.00000 + 5.19615i −0.379980 + 0.219382i
\(562\) 12.1244 7.00000i 0.511435 0.295277i
\(563\) −7.79423 + 4.50000i −0.328488 + 0.189652i −0.655169 0.755482i \(-0.727403\pi\)
0.326682 + 0.945134i \(0.394069\pi\)
\(564\) 9.00000 + 5.19615i 0.378968 + 0.218797i
\(565\) 0 0
\(566\) −14.0000 −0.588464
\(567\) −7.79423 + 4.50000i −0.327327 + 0.188982i
\(568\) 0 0
\(569\) −19.5000 + 33.7750i −0.817483 + 1.41592i 0.0900490 + 0.995937i \(0.471298\pi\)
−0.907532 + 0.419984i \(0.862036\pi\)
\(570\) −25.6077 38.7846i −1.07259 1.62451i
\(571\) 22.5000 + 38.9711i 0.941596 + 1.63089i 0.762428 + 0.647073i \(0.224007\pi\)
0.179168 + 0.983819i \(0.442660\pi\)
\(572\) −10.3923 + 6.00000i −0.434524 + 0.250873i
\(573\) 2.59808 + 4.50000i 0.108536 + 0.187990i
\(574\) −8.00000 + 13.8564i −0.333914 + 0.578355i
\(575\) 24.0000 18.0000i 1.00087 0.750652i
\(576\) −12.0000 20.7846i −0.500000 0.866025i
\(577\) 7.00000i 0.291414i −0.989328 0.145707i \(-0.953454\pi\)
0.989328 0.145707i \(-0.0465456\pi\)
\(578\) −22.5167 13.0000i −0.936570 0.540729i
\(579\) 24.2487i 1.00774i
\(580\) −1.33975 22.3205i −0.0556299 0.926809i
\(581\) 8.50000 + 14.7224i 0.352639 + 0.610789i
\(582\) −24.2487 −1.00514
\(583\) 0 0
\(584\) 0 0
\(585\) 6.00000 12.0000i 0.248069 0.496139i
\(586\) 54.0000 2.23072
\(587\) 20.7846 + 12.0000i 0.857873 + 0.495293i 0.863299 0.504692i \(-0.168394\pi\)
−0.00542667 + 0.999985i \(0.501727\pi\)
\(588\) −1.73205 3.00000i −0.0714286 0.123718i
\(589\) −12.0000 20.7846i −0.494451 0.856415i
\(590\) −62.4974 + 3.75129i −2.57298 + 0.154438i
\(591\) −12.0000 6.92820i −0.493614 0.284988i
\(592\) 6.92820 + 4.00000i 0.284747 + 0.164399i
\(593\) 43.0000i 1.76580i 0.469563 + 0.882899i \(0.344412\pi\)
−0.469563 + 0.882899i \(0.655588\pi\)
\(594\) 27.0000 15.5885i 1.10782 0.639602i
\(595\) 4.00000 + 2.00000i 0.163984 + 0.0819920i
\(596\) 5.00000 8.66025i 0.204808 0.354738i
\(597\) 6.92820 12.0000i 0.283552 0.491127i
\(598\) 20.7846 12.0000i 0.849946 0.490716i
\(599\) 20.0000 + 34.6410i 0.817178 + 1.41539i 0.907754 + 0.419504i \(0.137796\pi\)
−0.0905757 + 0.995890i \(0.528871\pi\)
\(600\) 0 0
\(601\) 4.00000 6.92820i 0.163163 0.282607i −0.772838 0.634603i \(-0.781164\pi\)
0.936002 + 0.351996i \(0.114497\pi\)
\(602\) 4.00000i 0.163028i
\(603\) 25.9808 + 15.0000i 1.05802 + 0.610847i
\(604\) −40.0000 −1.62758
\(605\) −3.73205 + 2.46410i −0.151729 + 0.100180i
\(606\) 0 0
\(607\) 33.7750 19.5000i 1.37088 0.791481i 0.379845 0.925050i \(-0.375977\pi\)
0.991039 + 0.133570i \(0.0426439\pi\)
\(608\) 41.5692 24.0000i 1.68585 0.973329i
\(609\) 8.66025i 0.350931i
\(610\) 24.6410 + 37.3205i 0.997686 + 1.51106i
\(611\) −6.00000 −0.242734
\(612\) −10.3923 6.00000i −0.420084 0.242536i
\(613\) 8.00000i 0.323117i 0.986863 + 0.161558i \(0.0516520\pi\)
−0.986863 + 0.161558i \(0.948348\pi\)
\(614\) 4.00000 6.92820i 0.161427 0.279600i
\(615\) 1.85641 + 30.9282i 0.0748575 + 1.24715i
\(616\) 0 0
\(617\) −6.92820 + 4.00000i −0.278919 + 0.161034i −0.632934 0.774206i \(-0.718150\pi\)
0.354015 + 0.935240i \(0.384816\pi\)
\(618\) −8.66025 + 15.0000i −0.348367 + 0.603388i
\(619\) −10.0000 + 17.3205i −0.401934 + 0.696170i −0.993959 0.109749i \(-0.964995\pi\)
0.592025 + 0.805919i \(0.298329\pi\)
\(620\) −16.0000 8.00000i −0.642575 0.321288i
\(621\) −27.0000 + 15.5885i −1.08347 + 0.625543i
\(622\) 12.0000i 0.481156i
\(623\) 10.3923 + 6.00000i 0.416359 + 0.240385i
\(624\) 12.0000 + 6.92820i 0.480384 + 0.277350i
\(625\) 24.2846 5.93782i 0.971384 0.237513i
\(626\) −9.00000 15.5885i −0.359712 0.623040i
\(627\) 15.5885 + 27.0000i 0.622543 + 1.07828i
\(628\) 15.5885 + 9.00000i 0.622047 + 0.359139i
\(629\) 4.00000 0.159490
\(630\) −12.0000 6.00000i −0.478091 0.239046i
\(631\) −5.00000 −0.199047 −0.0995234 0.995035i \(-0.531732\pi\)
−0.0995234 + 0.995035i \(0.531732\pi\)
\(632\) 0 0
\(633\) 29.4449 1.17033
\(634\) −30.0000 51.9615i −1.19145 2.06366i
\(635\) −44.6410 + 2.67949i −1.77152 + 0.106332i
\(636\) 0 0
\(637\) 1.73205 + 1.00000i 0.0686264 + 0.0396214i
\(638\) 30.0000i 1.18771i
\(639\) −10.5000 18.1865i −0.415374 0.719448i
\(640\) 0 0
\(641\) −17.0000 + 29.4449i −0.671460 + 1.16300i 0.306031 + 0.952022i \(0.400999\pi\)
−0.977490 + 0.210981i \(0.932334\pi\)
\(642\) 27.7128 + 48.0000i 1.09374 + 1.89441i
\(643\) 4.33013 2.50000i 0.170764 0.0985904i −0.412182 0.911101i \(-0.635233\pi\)
0.582946 + 0.812511i \(0.301900\pi\)
\(644\) −6.00000 10.3923i −0.236433 0.409514i
\(645\) −4.26795 6.46410i −0.168050 0.254524i
\(646\) 12.0000 20.7846i 0.472134 0.817760i
\(647\) 32.0000i 1.25805i −0.777385 0.629025i \(-0.783454\pi\)
0.777385 0.629025i \(-0.216546\pi\)
\(648\) 0 0
\(649\) 42.0000 1.64864
\(650\) 19.8564 2.39230i 0.778832 0.0938339i
\(651\) −6.00000 3.46410i −0.235159 0.135769i
\(652\) 6.92820 4.00000i 0.271329 0.156652i
\(653\) 8.66025 5.00000i 0.338902 0.195665i −0.320884 0.947118i \(-0.603980\pi\)
0.659786 + 0.751453i \(0.270647\pi\)
\(654\) 57.0000 32.9090i 2.22888 1.28684i
\(655\) −26.1244 + 17.2487i −1.02076 + 0.673963i
\(656\) −32.0000 −1.24939
\(657\) −23.3827 + 13.5000i −0.912245 + 0.526685i
\(658\) 6.00000i 0.233904i
\(659\) −18.0000 + 31.1769i −0.701180 + 1.21448i 0.266872 + 0.963732i \(0.414010\pi\)
−0.968052 + 0.250748i \(0.919323\pi\)
\(660\) 20.7846 + 10.3923i 0.809040 + 0.404520i
\(661\) −12.0000 20.7846i −0.466746 0.808428i 0.532533 0.846410i \(-0.321240\pi\)
−0.999278 + 0.0379819i \(0.987907\pi\)
\(662\) 46.7654 27.0000i 1.81759 1.04938i
\(663\) 6.92820 0.269069
\(664\) 0 0
\(665\) 6.00000 12.0000i 0.232670 0.465340i
\(666\) −12.0000 −0.464991
\(667\) 30.0000i 1.16160i
\(668\) −20.7846 12.0000i −0.804181 0.464294i
\(669\) −36.0000 + 20.7846i −1.39184 + 0.803579i
\(670\) 2.67949 + 44.6410i 0.103518 + 1.72463i
\(671\) −15.0000 25.9808i −0.579069 1.00298i
\(672\) 6.92820 12.0000i 0.267261 0.462910i
\(673\) −10.3923 6.00000i −0.400594 0.231283i 0.286146 0.958186i \(-0.407626\pi\)
−0.686740 + 0.726903i \(0.740959\pi\)
\(674\) 36.0000 1.38667
\(675\) −25.7942 + 3.10770i −0.992820 + 0.119615i
\(676\) −18.0000 −0.692308
\(677\) 19.0526 + 11.0000i 0.732249 + 0.422764i 0.819244 0.573444i \(-0.194393\pi\)
−0.0869952 + 0.996209i \(0.527726\pi\)
\(678\) 0 0
\(679\) −3.50000 6.06218i −0.134318 0.232645i
\(680\) 0 0
\(681\) 30.0000 17.3205i 1.14960 0.663723i
\(682\) 20.7846 + 12.0000i 0.795884 + 0.459504i
\(683\) 4.00000i 0.153056i −0.997067 0.0765279i \(-0.975617\pi\)
0.997067 0.0765279i \(-0.0243834\pi\)
\(684\) −18.0000 + 31.1769i −0.688247 + 1.19208i
\(685\) 18.0000 36.0000i 0.687745 1.37549i
\(686\) 1.00000 1.73205i 0.0381802 0.0661300i
\(687\) 17.3205 0.660819
\(688\) 6.92820 4.00000i 0.264135 0.152499i
\(689\) 0 0
\(690\) −41.5692 20.7846i −1.58251 0.791257i
\(691\) 25.0000 43.3013i 0.951045 1.64726i 0.207875 0.978155i \(-0.433345\pi\)
0.743170 0.669102i \(-0.233321\pi\)
\(692\) 30.0000i 1.14043i
\(693\) 7.79423 + 4.50000i 0.296078 + 0.170941i
\(694\) 0 0
\(695\) −37.3205 + 24.6410i −1.41565 + 0.934687i
\(696\) 0 0
\(697\) −13.8564 + 8.00000i −0.524849 + 0.303022i
\(698\) −17.3205 + 10.0000i −0.655591 + 0.378506i
\(699\) 24.0000 + 13.8564i 0.907763 + 0.524097i
\(700\) −1.19615 9.92820i −0.0452103 0.375251i
\(701\) 26.0000 0.982006 0.491003 0.871158i \(-0.336630\pi\)
0.491003 + 0.871158i \(0.336630\pi\)
\(702\) −20.7846 −0.784465
\(703\) 12.0000i 0.452589i
\(704\) −12.0000 + 20.7846i −0.452267 + 0.783349i
\(705\) 6.40192 + 9.69615i 0.241110 + 0.365178i
\(706\) −11.0000 19.0526i −0.413990 0.717053i
\(707\) 0 0
\(708\) 24.2487 + 42.0000i 0.911322 + 1.57846i
\(709\) 17.5000 30.3109i 0.657226 1.13835i −0.324104 0.946021i \(-0.605063\pi\)
0.981331 0.192328i \(-0.0616038\pi\)
\(710\) 14.0000 28.0000i 0.525411 1.05082i
\(711\) −3.00000 −0.112509
\(712\) 0 0
\(713\) −20.7846 12.0000i −0.778390 0.449404i
\(714\) 6.92820i 0.259281i
\(715\) −13.3923 + 0.803848i −0.500844 + 0.0300622i
\(716\) 11.0000 + 19.0526i 0.411089 + 0.712028i
\(717\) 15.5885 0.582162
\(718\) 6.92820 + 4.00000i 0.258558 + 0.149279i
\(719\) 18.0000 0.671287 0.335643 0.941989i \(-0.391046\pi\)
0.335643 + 0.941989i \(0.391046\pi\)
\(720\) −1.60770 26.7846i −0.0599153 0.998203i
\(721\) −5.00000 −0.186210
\(722\) −29.4449 17.0000i −1.09582 0.632674i
\(723\) −3.46410 6.00000i −0.128831 0.223142i
\(724\) 0 0
\(725\) 9.82051 22.9904i 0.364725 0.853841i
\(726\) 6.00000 + 3.46410i 0.222681 + 0.128565i
\(727\) −40.7032 23.5000i −1.50960 0.871567i −0.999937 0.0111912i \(-0.996438\pi\)
−0.509661 0.860376i \(-0.670229\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) −36.0000 18.0000i −1.33242 0.666210i
\(731\) 2.00000 3.46410i 0.0739727 0.128124i
\(732\) 17.3205 30.0000i 0.640184 1.10883i
\(733\) 9.52628 5.50000i 0.351861 0.203147i −0.313644 0.949541i \(-0.601550\pi\)
0.665505 + 0.746394i \(0.268216\pi\)
\(734\) 0 0
\(735\) −0.232051 3.86603i −0.00855932 0.142600i
\(736\) 24.0000 41.5692i 0.884652 1.53226i
\(737\) 30.0000i 1.10506i
\(738\) 41.5692 24.0000i 1.53018 0.883452i
\(739\) −1.00000 −0.0367856 −0.0183928 0.999831i \(-0.505855\pi\)
−0.0183928 + 0.999831i \(0.505855\pi\)
\(740\) −4.92820 7.46410i −0.181164 0.274386i
\(741\) 20.7846i 0.763542i
\(742\) 0 0
\(743\) −8.66025 + 5.00000i −0.317714 + 0.183432i −0.650373 0.759615i \(-0.725387\pi\)
0.332659 + 0.943047i \(0.392054\pi\)
\(744\) 0 0
\(745\) 9.33013 6.16025i 0.341829 0.225694i
\(746\) 0 0
\(747\) 51.0000i 1.86599i
\(748\) 12.0000i 0.438763i
\(749\) −8.00000 + 13.8564i −0.292314 + 0.506302i
\(750\) −25.0526 29.5359i −0.914790 1.07850i
\(751\) −7.50000 12.9904i −0.273679 0.474026i 0.696122 0.717923i \(-0.254907\pi\)
−0.969801 + 0.243898i \(0.921574\pi\)
\(752\) −10.3923 + 6.00000i −0.378968 + 0.218797i
\(753\) −15.5885 + 27.0000i −0.568075 + 0.983935i
\(754\) 10.0000 17.3205i 0.364179 0.630776i
\(755\) −40.0000 20.0000i −1.45575 0.727875i
\(756\) 10.3923i 0.377964i
\(757\) 10.0000i 0.363456i −0.983349 0.181728i \(-0.941831\pi\)
0.983349 0.181728i \(-0.0581691\pi\)
\(758\) 39.8372 + 23.0000i 1.44695 + 0.835398i
\(759\) 27.0000 + 15.5885i 0.980038 + 0.565825i
\(760\) 0 0
\(761\) −7.00000 12.1244i −0.253750 0.439508i 0.710805 0.703389i \(-0.248331\pi\)
−0.964555 + 0.263881i \(0.914997\pi\)
\(762\) 34.6410 + 60.0000i 1.25491 + 2.17357i
\(763\) 16.4545 + 9.50000i 0.595692 + 0.343923i
\(764\) 6.00000 0.217072
\(765\) −7.39230 11.1962i −0.267269 0.404798i
\(766\) −10.0000 −0.361315
\(767\) −24.2487 14.0000i −0.875570 0.505511i
\(768\) 27.7128 1.00000
\(769\) 9.00000 + 15.5885i 0.324548 + 0.562134i 0.981421 0.191867i \(-0.0614544\pi\)
−0.656873 + 0.754002i \(0.728121\pi\)
\(770\) 0.803848 + 13.3923i 0.0289687 + 0.482625i
\(771\) 12.1244i 0.436648i
\(772\) 24.2487 + 14.0000i 0.872730 + 0.503871i
\(773\) 27.0000i 0.971123i 0.874203 + 0.485561i \(0.161385\pi\)
−0.874203 + 0.485561i \(0.838615\pi\)
\(774\) −6.00000 + 10.3923i −0.215666 + 0.373544i
\(775\) −12.0000 16.0000i −0.431053 0.574737i
\(776\) 0 0
\(777\) −1.73205 3.00000i −0.0621370 0.107624i
\(778\) 32.9090 19.0000i 1.17984 0.681183i
\(779\) 24.0000 + 41.5692i 0.859889 + 1.48937i
\(780\) −8.53590 12.9282i −0.305634 0.462904i
\(781\) −10.5000 + 18.1865i −0.375720 + 0.650765i
\(782\) 24.0000i 0.858238i
\(783\) −12.9904 + 22.5000i −0.464238 + 0.804084i
\(784\) 4.00000 0.142857
\(785\) 11.0885 + 16.7942i 0.395764 + 0.599412i
\(786\) 42.0000 + 24.2487i 1.49809 + 0.864923i
\(787\) −34.6410 + 20.0000i −1.23482 + 0.712923i −0.968031 0.250832i \(-0.919296\pi\)
−0.266788 + 0.963755i \(0.585962\pi\)
\(788\) −13.8564 + 8.00000i −0.493614 + 0.284988i
\(789\) 0 0
\(790\) −2.46410 3.73205i −0.0876688 0.132780i
\(791\) 0 0
\(792\) 0 0
\(793\) 20.0000i 0.710221i
\(794\) −17.0000 + 29.4449i −0.603307 + 1.04496i
\(795\) 0 0
\(796\) −8.00000 13.8564i −0.283552 0.491127i
\(797\) −19.0526 + 11.0000i −0.674876 + 0.389640i −0.797922 0.602761i \(-0.794067\pi\)
0.123045 + 0.992401i \(0.460734\pi\)
\(798\) −20.7846 −0.735767
\(799\) −3.00000 + 5.19615i −0.106132 + 0.183827i
\(800\) 32.0000 24.0000i 1.13137 0.848528i
\(801\) −18.0000 31.1769i −0.635999 1.10158i
\(802\) 30.0000i 1.05934i
\(803\) 23.3827 + 13.5000i 0.825157 + 0.476405i
\(804\) 30.0000 17.3205i 1.05802 0.610847i
\(805\) −0.803848 13.3923i −0.0283319 0.472017i
\(806\) −8.00000 13.8564i −0.281788 0.488071i
\(807\) 13.8564 24.0000i 0.487769 0.844840i
\(808\) 0 0
\(809\) 30.0000 1.05474 0.527372 0.849635i \(-0.323177\pi\)
0.527372 + 0.849635i \(0.323177\pi\)
\(810\) 22.1769 + 33.5885i 0.779217 + 1.18018i
\(811\) −20.0000 −0.702295 −0.351147 0.936320i \(-0.614208\pi\)
−0.351147 + 0.936320i \(0.614208\pi\)
\(812\) −8.66025 5.00000i −0.303915 0.175466i
\(813\) 12.1244 21.0000i 0.425220 0.736502i
\(814\) 6.00000 + 10.3923i 0.210300 + 0.364250i
\(815\) 8.92820 0.535898i 0.312741 0.0187717i
\(816\) 12.0000 6.92820i 0.420084 0.242536i
\(817\) −10.3923 6.00000i −0.363581 0.209913i
\(818\) 16.0000i 0.559427i
\(819\) −3.00000 5.19615i −0.104828 0.181568i
\(820\) 32.0000 + 16.0000i 1.11749 + 0.558744i
\(821\) 25.0000 43.3013i 0.872506 1.51122i 0.0131101 0.999914i \(-0.495827\pi\)
0.859396 0.511311i \(-0.170840\pi\)
\(822\) −62.3538 −2.17484
\(823\) 3.46410 2.00000i 0.120751 0.0697156i −0.438408 0.898776i \(-0.644457\pi\)
0.559159 + 0.829060i \(0.311124\pi\)
\(824\) 0 0
\(825\) 15.5885 + 20.7846i 0.542720 + 0.723627i
\(826\) −14.0000 + 24.2487i −0.487122 + 0.843721i
\(827\) 30.0000i 1.04320i 0.853189 + 0.521601i \(0.174665\pi\)
−0.853189 + 0.521601i \(0.825335\pi\)
\(828\) 36.0000i 1.25109i
\(829\) 24.0000 0.833554 0.416777 0.909009i \(-0.363160\pi\)
0.416777 + 0.909009i \(0.363160\pi\)
\(830\) 63.4449 41.8897i 2.20220 1.45401i
\(831\) −42.0000 + 24.2487i −1.45696 + 0.841178i
\(832\) 13.8564 8.00000i 0.480384 0.277350i
\(833\) 1.73205 1.00000i 0.0600120 0.0346479i
\(834\) 60.0000 + 34.6410i 2.07763 + 1.19952i
\(835\) −14.7846 22.3923i −0.511643 0.774918i
\(836\) 36.0000 1.24509
\(837\) 10.3923 + 18.0000i 0.359211 + 0.622171i
\(838\) 60.0000i 2.07267i
\(839\) 24.0000 41.5692i 0.828572 1.43513i −0.0705865 0.997506i \(-0.522487\pi\)
0.899158 0.437623i \(-0.144180\pi\)
\(840\) 0 0
\(841\) 2.00000 + 3.46410i 0.0689655 + 0.119452i
\(842\) −25.9808 + 15.0000i −0.895356 + 0.516934i
\(843\) −6.06218 10.5000i −0.208792 0.361639i
\(844\) 17.0000 29.4449i 0.585164 1.01353i
\(845\) −18.0000 9.00000i −0.619219 0.309609i
\(846\) 9.00000 15.5885i 0.309426 0.535942i
\(847\) 2.00000i 0.0687208i
\(848\) 0 0
\(849\) 12.1244i 0.416107i
\(850\) 7.85641 18.3923i 0.269473 0.630851i
\(851\) −6.00000 10.3923i −0.205677 0.356244i
\(852\) −24.2487 −0.830747
\(853\) −36.3731 21.0000i −1.24539 0.719026i −0.275204 0.961386i \(-0.588745\pi\)
−0.970186 + 0.242360i \(0.922079\pi\)
\(854\) 20.0000 0.684386
\(855\) −33.5885 + 22.1769i −1.14870 + 0.758434i
\(856\) 0 0
\(857\) −18.1865 10.5000i −0.621240 0.358673i 0.156112 0.987739i \(-0.450104\pi\)
−0.777352 + 0.629066i \(0.783437\pi\)
\(858\) 10.3923 + 18.0000i 0.354787 + 0.614510i
\(859\) −19.0000 32.9090i −0.648272 1.12284i −0.983535 0.180715i \(-0.942159\pi\)
0.335264 0.942124i \(-0.391175\pi\)
\(860\) −8.92820 + 0.535898i −0.304449 + 0.0182740i
\(861\) 12.0000 + 6.92820i 0.408959 + 0.236113i
\(862\) −27.7128 16.0000i −0.943902 0.544962i
\(863\) 6.00000i 0.204242i 0.994772 + 0.102121i \(0.0325630\pi\)
−0.994772 + 0.102121i \(0.967437\pi\)
\(864\) −36.0000 + 20.7846i −1.22474 + 0.707107i
\(865\) −15.0000 + 30.0000i −0.510015 + 1.02003i
\(866\) −2.00000 + 3.46410i −0.0679628 + 0.117715i
\(867\) −11.2583 + 19.5000i −0.382353 + 0.662255i
\(868\) −6.92820 + 4.00000i −0.235159 + 0.135769i
\(869\) 1.50000 + 2.59808i 0.0508840 + 0.0881337i
\(870\) −38.6603 + 2.32051i −1.31071 + 0.0786726i
\(871\) −10.0000 + 17.3205i −0.338837 + 0.586883i
\(872\) 0 0
\(873\) 21.0000i 0.710742i
\(874\) −72.0000 −2.43544
\(875\) 3.76795 10.5263i 0.127380 0.355853i
\(876\) 31.1769i 1.05337i
\(877\) −29.4449 + 17.0000i −0.994282 + 0.574049i −0.906552 0.422095i \(-0.861295\pi\)
−0.0877308 + 0.996144i \(0.527962\pi\)
\(878\) 0 0
\(879\) 46.7654i 1.57736i
\(880\) −22.3923 + 14.7846i −0.754844 + 0.498389i
\(881\) 50.0000 1.68454 0.842271 0.539054i \(-0.181218\pi\)
0.842271 + 0.539054i \(0.181218\pi\)
\(882\) −5.19615 + 3.00000i −0.174964 + 0.101015i
\(883\) 42.0000i 1.41341i −0.707507 0.706706i \(-0.750180\pi\)
0.707507 0.706706i \(-0.249820\pi\)
\(884\) 4.00000 6.92820i 0.134535 0.233021i
\(885\) 3.24871 + 54.1244i 0.109204 + 1.81937i
\(886\) 4.00000 + 6.92820i 0.134383 + 0.232758i
\(887\) −13.8564 + 8.00000i −0.465253 + 0.268614i −0.714250 0.699890i \(-0.753232\pi\)
0.248998 + 0.968504i \(0.419899\pi\)
\(888\) 0 0
\(889\) −10.0000 + 17.3205i −0.335389 + 0.580911i
\(890\) 24.0000 48.0000i 0.804482 1.60896i
\(891\) −13.5000 23.3827i −0.452267 0.783349i
\(892\) 48.0000i 1.60716i
\(893\) 15.5885 + 9.00000i 0.521648 + 0.301174i
\(894\) −15.0000 8.66025i −0.501675 0.289642i
\(895\) 1.47372 + 24.5526i 0.0492610 + 0.820702i
\(896\) 0 0
\(897\) −10.3923 18.0000i −0.346989 0.601003i
\(898\) 53.6936 + 31.0000i 1.79178 + 1.03448i
\(899\) −20.0000 −0.667037
\(900\) −11.7846 + 27.5885i −0.392820 + 0.919615i
\(901\) 0 0
\(902\) −41.5692 24.0000i −1.38410 0.799113i
\(903\) −3.46410 −0.115278
\(904\) 0 0
\(905\) 0 0
\(906\) 69.2820i 2.30174i
\(907\) 12.1244 + 7.00000i 0.402583 + 0.232431i 0.687598 0.726092i \(-0.258665\pi\)
−0.285015 + 0.958523i \(0.591999\pi\)
\(908\) 40.0000i 1.32745i
\(909\) 0 0
\(910\) 4.00000 8.00000i 0.132599 0.265197i
\(911\) 13.5000 23.3827i 0.447275 0.774703i −0.550933 0.834550i \(-0.685728\pi\)
0.998208 + 0.0598468i \(0.0190612\pi\)
\(912\) −20.7846 36.0000i −0.688247 1.19208i
\(913\) −44.1673 + 25.5000i −1.46172 + 0.843927i
\(914\) 28.0000 + 48.4974i 0.926158 + 1.60415i
\(915\) 32.3205 21.3397i 1.06848 0.705470i
\(916\) 10.0000 17.3205i 0.330409 0.572286i
\(917\) 14.0000i 0.462321i
\(918\) −10.3923 + 18.0000i −0.342997 + 0.594089i
\(919\) −55.0000 −1.81428 −0.907141 0.420826i \(-0.861740\pi\)
−0.907141 + 0.420826i \(0.861740\pi\)
\(920\) 0 0
\(921\) −6.00000 3.46410i −0.197707 0.114146i
\(922\) −20.7846 + 12.0000i −0.684505 + 0.395199i
\(923\) 12.1244 7.00000i 0.399078 0.230408i
\(924\) 9.00000 5.19615i 0.296078 0.170941i
\(925\) −1.19615 9.92820i −0.0393292 0.326437i
\(926\) −12.0000 −0.394344
\(927\) 12.9904 + 7.50000i 0.426660 + 0.246332i
\(928\) 40.0000i 1.31306i
\(929\) −7.00000 + 12.1244i −0.229663 + 0.397787i −0.957708 0.287742i \(-0.907096\pi\)
0.728046 + 0.685529i \(0.240429\pi\)
\(930\) −13.8564 + 27.7128i −0.454369 + 0.908739i
\(931\) −3.00000 5.19615i −0.0983210 0.170297i
\(932\) 27.7128 16.0000i 0.907763 0.524097i
\(933\) −10.3923 −0.340229
\(934\) −3.00000 + 5.19615i −0.0981630 + 0.170023i
\(935\) −6.00000 + 12.0000i −0.196221 + 0.392442i
\(936\) 0 0
\(937\) 26.0000i 0.849383i 0.905338 + 0.424691i \(0.139617\pi\)
−0.905338 + 0.424691i \(0.860383\pi\)
\(938\) 17.3205 + 10.0000i 0.565535 + 0.326512i
\(939\) −13.5000 + 7.79423i −0.440556 + 0.254355i
\(940\) 13.3923 0.803848i 0.436809 0.0262186i
\(941\) 15.0000 + 25.9808i 0.488986 + 0.846949i 0.999920 0.0126715i \(-0.00403357\pi\)
−0.510934 + 0.859620i \(0.670700\pi\)
\(942\) 15.5885 27.0000i 0.507899 0.879708i
\(943\) 41.5692 + 24.0000i 1.35368 + 0.781548i
\(944\) −56.0000 −1.82264
\(945\) −5.19615 + 10.3923i −0.169031 + 0.338062i
\(946\) 12.0000 0.390154
\(947\) −31.1769 18.0000i −1.01311 0.584921i −0.101012 0.994885i \(-0.532208\pi\)
−0.912102 + 0.409964i \(0.865541\pi\)
\(948\) −1.73205 + 3.00000i −0.0562544 + 0.0974355i
\(949\) −9.00000 15.5885i −0.292152 0.506023i
\(950\) −55.1769 23.5692i −1.79018 0.764686i
\(951\) −45.0000 + 25.9808i −1.45922 + 0.842484i
\(952\) 0 0
\(953\) 24.0000i 0.777436i 0.921357 + 0.388718i \(0.127082\pi\)
−0.921357 + 0.388718i \(0.872918\pi\)
\(954\) 0 0
\(955\) 6.00000 + 3.00000i 0.194155 + 0.0970777i
\(956\) 9.00000 15.5885i 0.291081 0.504167i
\(957\) 25.9808 0.839839
\(958\) −62.3538 + 36.0000i −2.01456 + 1.16311i
\(959\) −9.00000 15.5885i −0.290625 0.503378i
\(960\) −27.7128 13.8564i −0.894427 0.447214i
\(961\) 7.50000 12.9904i 0.241935 0.419045i
\(962\) 8.00000i 0.257930i
\(963\) 41.5692 24.0000i 1.33955 0.773389i
\(964\) −8.00000 −0.257663
\(965\) 17.2487 + 26.1244i 0.555256 + 0.840973i
\(966\) −18.0000 + 10.3923i −0.579141 + 0.334367i
\(967\) −1.73205 + 1.00000i −0.0556990 + 0.0321578i −0.527591 0.849499i \(-0.676905\pi\)
0.471892 + 0.881656i \(0.343571\pi\)
\(968\) 0 0
\(969\) −18.0000 10.3923i −0.578243 0.333849i
\(970\) −26.1244 + 17.2487i −0.838803 + 0.553823i
\(971\) 10.0000 0.320915 0.160458 0.987043i \(-0.448703\pi\)
0.160458 + 0.987043i \(0.448703\pi\)
\(972\) 15.5885 27.0000i 0.500000 0.866025i
\(973\) 20.0000i 0.641171i
\(974\) −12.0000 + 20.7846i −0.384505 + 0.665982i
\(975\) −2.07180 17.1962i −0.0663506 0.550718i
\(976\) 20.0000 + 34.6410i 0.640184 + 1.10883i
\(977\) 36.3731 21.0000i 1.16368 0.671850i 0.211495 0.977379i \(-0.432167\pi\)
0.952183 + 0.305530i \(0.0988335\pi\)
\(978\) −6.92820 12.0000i −0.221540 0.383718i
\(979\) −18.0000 + 31.1769i −0.575282 + 0.996419i
\(980\) −4.00000 2.00000i −0.127775 0.0638877i
\(981\) −28.5000 49.3634i −0.909935 1.57605i
\(982\) 56.0000i 1.78703i
\(983\) −2.59808 1.50000i −0.0828658 0.0478426i 0.457995 0.888955i \(-0.348568\pi\)
−0.540860 + 0.841112i \(0.681901\pi\)
\(984\) 0 0
\(985\) −17.8564 + 1.07180i −0.568952 + 0.0341503i
\(986\) −10.0000 17.3205i −0.318465 0.551597i
\(987\) 5.19615 0.165395
\(988\) −20.7846 12.0000i −0.661247 0.381771i
\(989\) −12.0000 −0.381578
\(990\) 18.0000 36.0000i 0.572078 1.14416i
\(991\) −35.0000 −1.11181 −0.555906 0.831245i \(-0.687628\pi\)
−0.555906 + 0.831245i \(0.687628\pi\)
\(992\) −27.7128 16.0000i −0.879883 0.508001i
\(993\) −23.3827 40.5000i −0.742027 1.28523i
\(994\) −7.00000 12.1244i −0.222027 0.384561i
\(995\) −1.07180 17.8564i −0.0339782 0.566086i
\(996\) −51.0000 29.4449i −1.61600 0.932996i
\(997\) 21.6506 + 12.5000i 0.685682 + 0.395879i 0.801993 0.597334i \(-0.203773\pi\)
−0.116310 + 0.993213i \(0.537107\pi\)
\(998\) 8.00000i 0.253236i
\(999\) 10.3923i 0.328798i
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 315.2.bh.b.169.1 4
3.2 odd 2 945.2.bh.b.694.2 4
5.4 even 2 inner 315.2.bh.b.169.2 yes 4
9.4 even 3 inner 315.2.bh.b.274.2 yes 4
9.5 odd 6 945.2.bh.b.64.1 4
15.14 odd 2 945.2.bh.b.694.1 4
45.4 even 6 inner 315.2.bh.b.274.1 yes 4
45.14 odd 6 945.2.bh.b.64.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.bh.b.169.1 4 1.1 even 1 trivial
315.2.bh.b.169.2 yes 4 5.4 even 2 inner
315.2.bh.b.274.1 yes 4 45.4 even 6 inner
315.2.bh.b.274.2 yes 4 9.4 even 3 inner
945.2.bh.b.64.1 4 9.5 odd 6
945.2.bh.b.64.2 4 45.14 odd 6
945.2.bh.b.694.1 4 15.14 odd 2
945.2.bh.b.694.2 4 3.2 odd 2