Properties

Label 637.2.h.a.471.1
Level $637$
Weight $2$
Character 637.471
Analytic conductor $5.086$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [637,2,Mod(165,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.165");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 471.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 637.471
Dual form 637.2.h.a.165.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-1.50000 + 2.59808i) q^{3} -1.00000 q^{4} +(1.50000 - 2.59808i) q^{5} +(-1.50000 + 2.59808i) q^{6} -3.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(-1.50000 + 2.59808i) q^{3} -1.00000 q^{4} +(1.50000 - 2.59808i) q^{5} +(-1.50000 + 2.59808i) q^{6} -3.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +(1.50000 - 2.59808i) q^{10} +(1.50000 - 2.59808i) q^{11} +(1.50000 - 2.59808i) q^{12} +(1.00000 - 3.46410i) q^{13} +(4.50000 + 7.79423i) q^{15} -1.00000 q^{16} +2.00000 q^{17} +(-3.00000 - 5.19615i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(-1.50000 + 2.59808i) q^{20} +(1.50000 - 2.59808i) q^{22} +(4.50000 - 7.79423i) q^{24} +(-2.00000 - 3.46410i) q^{25} +(1.00000 - 3.46410i) q^{26} +9.00000 q^{27} +(-3.50000 - 6.06218i) q^{29} +(4.50000 + 7.79423i) q^{30} +(1.50000 + 2.59808i) q^{31} +5.00000 q^{32} +(4.50000 + 7.79423i) q^{33} +2.00000 q^{34} +(3.00000 + 5.19615i) q^{36} +2.00000 q^{37} +(-0.500000 - 0.866025i) q^{38} +(7.50000 + 7.79423i) q^{39} +(-4.50000 + 7.79423i) q^{40} +(1.50000 + 2.59808i) q^{41} +(3.50000 - 6.06218i) q^{43} +(-1.50000 + 2.59808i) q^{44} -18.0000 q^{45} +(0.500000 - 0.866025i) q^{47} +(1.50000 - 2.59808i) q^{48} +(-2.00000 - 3.46410i) q^{50} +(-3.00000 + 5.19615i) q^{51} +(-1.00000 + 3.46410i) q^{52} +(-1.50000 - 2.59808i) q^{53} +9.00000 q^{54} +(-4.50000 - 7.79423i) q^{55} +3.00000 q^{57} +(-3.50000 - 6.06218i) q^{58} +4.00000 q^{59} +(-4.50000 - 7.79423i) q^{60} +(-6.50000 - 11.2583i) q^{61} +(1.50000 + 2.59808i) q^{62} +7.00000 q^{64} +(-7.50000 - 7.79423i) q^{65} +(4.50000 + 7.79423i) q^{66} +(1.50000 - 2.59808i) q^{67} -2.00000 q^{68} +(-6.50000 + 11.2583i) q^{71} +(9.00000 + 15.5885i) q^{72} +(-6.50000 - 11.2583i) q^{73} +2.00000 q^{74} +12.0000 q^{75} +(0.500000 + 0.866025i) q^{76} +(7.50000 + 7.79423i) q^{78} +(1.50000 - 2.59808i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(1.50000 + 2.59808i) q^{82} +(3.00000 - 5.19615i) q^{85} +(3.50000 - 6.06218i) q^{86} +21.0000 q^{87} +(-4.50000 + 7.79423i) q^{88} -6.00000 q^{89} -18.0000 q^{90} -9.00000 q^{93} +(0.500000 - 0.866025i) q^{94} -3.00000 q^{95} +(-7.50000 + 12.9904i) q^{96} +(-2.50000 + 4.33013i) q^{97} -18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} - 3 q^{3} - 2 q^{4} + 3 q^{5} - 3 q^{6} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} - 3 q^{3} - 2 q^{4} + 3 q^{5} - 3 q^{6} - 6 q^{8} - 6 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} + 2 q^{13} + 9 q^{15} - 2 q^{16} + 4 q^{17} - 6 q^{18} - q^{19} - 3 q^{20} + 3 q^{22} + 9 q^{24} - 4 q^{25} + 2 q^{26} + 18 q^{27} - 7 q^{29} + 9 q^{30} + 3 q^{31} + 10 q^{32} + 9 q^{33} + 4 q^{34} + 6 q^{36} + 4 q^{37} - q^{38} + 15 q^{39} - 9 q^{40} + 3 q^{41} + 7 q^{43} - 3 q^{44} - 36 q^{45} + q^{47} + 3 q^{48} - 4 q^{50} - 6 q^{51} - 2 q^{52} - 3 q^{53} + 18 q^{54} - 9 q^{55} + 6 q^{57} - 7 q^{58} + 8 q^{59} - 9 q^{60} - 13 q^{61} + 3 q^{62} + 14 q^{64} - 15 q^{65} + 9 q^{66} + 3 q^{67} - 4 q^{68} - 13 q^{71} + 18 q^{72} - 13 q^{73} + 4 q^{74} + 24 q^{75} + q^{76} + 15 q^{78} + 3 q^{79} - 3 q^{80} - 9 q^{81} + 3 q^{82} + 6 q^{85} + 7 q^{86} + 42 q^{87} - 9 q^{88} - 12 q^{89} - 36 q^{90} - 18 q^{93} + q^{94} - 6 q^{95} - 15 q^{96} - 5 q^{97} - 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107 0.353553 0.935414i \(-0.384973\pi\)
0.353553 + 0.935414i \(0.384973\pi\)
\(3\) −1.50000 + 2.59808i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) −1.00000 −0.500000
\(5\) 1.50000 2.59808i 0.670820 1.16190i −0.306851 0.951757i \(-0.599275\pi\)
0.977672 0.210138i \(-0.0673912\pi\)
\(6\) −1.50000 + 2.59808i −0.612372 + 1.06066i
\(7\) 0 0
\(8\) −3.00000 −1.06066
\(9\) −3.00000 5.19615i −1.00000 1.73205i
\(10\) 1.50000 2.59808i 0.474342 0.821584i
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 1.50000 2.59808i 0.433013 0.750000i
\(13\) 1.00000 3.46410i 0.277350 0.960769i
\(14\) 0 0
\(15\) 4.50000 + 7.79423i 1.16190 + 2.01246i
\(16\) −1.00000 −0.250000
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) −3.00000 5.19615i −0.707107 1.22474i
\(19\) −0.500000 0.866025i −0.114708 0.198680i 0.802955 0.596040i \(-0.203260\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) −1.50000 + 2.59808i −0.335410 + 0.580948i
\(21\) 0 0
\(22\) 1.50000 2.59808i 0.319801 0.553912i
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 4.50000 7.79423i 0.918559 1.59099i
\(25\) −2.00000 3.46410i −0.400000 0.692820i
\(26\) 1.00000 3.46410i 0.196116 0.679366i
\(27\) 9.00000 1.73205
\(28\) 0 0
\(29\) −3.50000 6.06218i −0.649934 1.12572i −0.983138 0.182864i \(-0.941463\pi\)
0.333205 0.942855i \(-0.391870\pi\)
\(30\) 4.50000 + 7.79423i 0.821584 + 1.42302i
\(31\) 1.50000 + 2.59808i 0.269408 + 0.466628i 0.968709 0.248199i \(-0.0798387\pi\)
−0.699301 + 0.714827i \(0.746505\pi\)
\(32\) 5.00000 0.883883
\(33\) 4.50000 + 7.79423i 0.783349 + 1.35680i
\(34\) 2.00000 0.342997
\(35\) 0 0
\(36\) 3.00000 + 5.19615i 0.500000 + 0.866025i
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −0.500000 0.866025i −0.0811107 0.140488i
\(39\) 7.50000 + 7.79423i 1.20096 + 1.24808i
\(40\) −4.50000 + 7.79423i −0.711512 + 1.23238i
\(41\) 1.50000 + 2.59808i 0.234261 + 0.405751i 0.959058 0.283211i \(-0.0913998\pi\)
−0.724797 + 0.688963i \(0.758066\pi\)
\(42\) 0 0
\(43\) 3.50000 6.06218i 0.533745 0.924473i −0.465478 0.885059i \(-0.654118\pi\)
0.999223 0.0394140i \(-0.0125491\pi\)
\(44\) −1.50000 + 2.59808i −0.226134 + 0.391675i
\(45\) −18.0000 −2.68328
\(46\) 0 0
\(47\) 0.500000 0.866025i 0.0729325 0.126323i −0.827253 0.561830i \(-0.810098\pi\)
0.900185 + 0.435507i \(0.143431\pi\)
\(48\) 1.50000 2.59808i 0.216506 0.375000i
\(49\) 0 0
\(50\) −2.00000 3.46410i −0.282843 0.489898i
\(51\) −3.00000 + 5.19615i −0.420084 + 0.727607i
\(52\) −1.00000 + 3.46410i −0.138675 + 0.480384i
\(53\) −1.50000 2.59808i −0.206041 0.356873i 0.744423 0.667708i \(-0.232725\pi\)
−0.950464 + 0.310835i \(0.899391\pi\)
\(54\) 9.00000 1.22474
\(55\) −4.50000 7.79423i −0.606780 1.05097i
\(56\) 0 0
\(57\) 3.00000 0.397360
\(58\) −3.50000 6.06218i −0.459573 0.796003i
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) −4.50000 7.79423i −0.580948 1.00623i
\(61\) −6.50000 11.2583i −0.832240 1.44148i −0.896258 0.443533i \(-0.853725\pi\)
0.0640184 0.997949i \(-0.479608\pi\)
\(62\) 1.50000 + 2.59808i 0.190500 + 0.329956i
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) −7.50000 7.79423i −0.930261 0.966755i
\(66\) 4.50000 + 7.79423i 0.553912 + 0.959403i
\(67\) 1.50000 2.59808i 0.183254 0.317406i −0.759733 0.650236i \(-0.774670\pi\)
0.942987 + 0.332830i \(0.108004\pi\)
\(68\) −2.00000 −0.242536
\(69\) 0 0
\(70\) 0 0
\(71\) −6.50000 + 11.2583i −0.771408 + 1.33612i 0.165383 + 0.986229i \(0.447114\pi\)
−0.936791 + 0.349889i \(0.886219\pi\)
\(72\) 9.00000 + 15.5885i 1.06066 + 1.83712i
\(73\) −6.50000 11.2583i −0.760767 1.31769i −0.942455 0.334332i \(-0.891489\pi\)
0.181688 0.983356i \(-0.441844\pi\)
\(74\) 2.00000 0.232495
\(75\) 12.0000 1.38564
\(76\) 0.500000 + 0.866025i 0.0573539 + 0.0993399i
\(77\) 0 0
\(78\) 7.50000 + 7.79423i 0.849208 + 0.882523i
\(79\) 1.50000 2.59808i 0.168763 0.292306i −0.769222 0.638982i \(-0.779356\pi\)
0.937985 + 0.346675i \(0.112689\pi\)
\(80\) −1.50000 + 2.59808i −0.167705 + 0.290474i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 1.50000 + 2.59808i 0.165647 + 0.286910i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 3.00000 5.19615i 0.325396 0.563602i
\(86\) 3.50000 6.06218i 0.377415 0.653701i
\(87\) 21.0000 2.25144
\(88\) −4.50000 + 7.79423i −0.479702 + 0.830868i
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) −18.0000 −1.89737
\(91\) 0 0
\(92\) 0 0
\(93\) −9.00000 −0.933257
\(94\) 0.500000 0.866025i 0.0515711 0.0893237i
\(95\) −3.00000 −0.307794
\(96\) −7.50000 + 12.9904i −0.765466 + 1.32583i
\(97\) −2.50000 + 4.33013i −0.253837 + 0.439658i −0.964579 0.263795i \(-0.915026\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 0 0
\(99\) −18.0000 −1.80907
\(100\) 2.00000 + 3.46410i 0.200000 + 0.346410i
\(101\) −2.50000 + 4.33013i −0.248759 + 0.430864i −0.963182 0.268851i \(-0.913356\pi\)
0.714423 + 0.699715i \(0.246689\pi\)
\(102\) −3.00000 + 5.19615i −0.297044 + 0.514496i
\(103\) 2.50000 4.33013i 0.246332 0.426660i −0.716173 0.697923i \(-0.754108\pi\)
0.962505 + 0.271263i \(0.0874412\pi\)
\(104\) −3.00000 + 10.3923i −0.294174 + 1.01905i
\(105\) 0 0
\(106\) −1.50000 2.59808i −0.145693 0.252347i
\(107\) 8.00000 0.773389 0.386695 0.922208i \(-0.373617\pi\)
0.386695 + 0.922208i \(0.373617\pi\)
\(108\) −9.00000 −0.866025
\(109\) −3.50000 6.06218i −0.335239 0.580651i 0.648292 0.761392i \(-0.275484\pi\)
−0.983531 + 0.180741i \(0.942150\pi\)
\(110\) −4.50000 7.79423i −0.429058 0.743151i
\(111\) −3.00000 + 5.19615i −0.284747 + 0.493197i
\(112\) 0 0
\(113\) −7.50000 + 12.9904i −0.705541 + 1.22203i 0.260955 + 0.965351i \(0.415962\pi\)
−0.966496 + 0.256681i \(0.917371\pi\)
\(114\) 3.00000 0.280976
\(115\) 0 0
\(116\) 3.50000 + 6.06218i 0.324967 + 0.562859i
\(117\) −21.0000 + 5.19615i −1.94145 + 0.480384i
\(118\) 4.00000 0.368230
\(119\) 0 0
\(120\) −13.5000 23.3827i −1.23238 2.13454i
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) −6.50000 11.2583i −0.588482 1.01928i
\(123\) −9.00000 −0.811503
\(124\) −1.50000 2.59808i −0.134704 0.233314i
\(125\) 3.00000 0.268328
\(126\) 0 0
\(127\) −5.50000 9.52628i −0.488046 0.845321i 0.511859 0.859069i \(-0.328957\pi\)
−0.999905 + 0.0137486i \(0.995624\pi\)
\(128\) −3.00000 −0.265165
\(129\) 10.5000 + 18.1865i 0.924473 + 1.60123i
\(130\) −7.50000 7.79423i −0.657794 0.683599i
\(131\) 2.50000 4.33013i 0.218426 0.378325i −0.735901 0.677089i \(-0.763241\pi\)
0.954327 + 0.298764i \(0.0965744\pi\)
\(132\) −4.50000 7.79423i −0.391675 0.678401i
\(133\) 0 0
\(134\) 1.50000 2.59808i 0.129580 0.224440i
\(135\) 13.5000 23.3827i 1.16190 2.01246i
\(136\) −6.00000 −0.514496
\(137\) 10.0000 0.854358 0.427179 0.904167i \(-0.359507\pi\)
0.427179 + 0.904167i \(0.359507\pi\)
\(138\) 0 0
\(139\) −7.50000 + 12.9904i −0.636142 + 1.10183i 0.350130 + 0.936701i \(0.386137\pi\)
−0.986272 + 0.165129i \(0.947196\pi\)
\(140\) 0 0
\(141\) 1.50000 + 2.59808i 0.126323 + 0.218797i
\(142\) −6.50000 + 11.2583i −0.545468 + 0.944778i
\(143\) −7.50000 7.79423i −0.627182 0.651786i
\(144\) 3.00000 + 5.19615i 0.250000 + 0.433013i
\(145\) −21.0000 −1.74396
\(146\) −6.50000 11.2583i −0.537944 0.931746i
\(147\) 0 0
\(148\) −2.00000 −0.164399
\(149\) −7.50000 12.9904i −0.614424 1.06421i −0.990485 0.137619i \(-0.956055\pi\)
0.376061 0.926595i \(-0.377278\pi\)
\(150\) 12.0000 0.979796
\(151\) 10.5000 + 18.1865i 0.854478 + 1.48000i 0.877129 + 0.480256i \(0.159456\pi\)
−0.0226507 + 0.999743i \(0.507211\pi\)
\(152\) 1.50000 + 2.59808i 0.121666 + 0.210732i
\(153\) −6.00000 10.3923i −0.485071 0.840168i
\(154\) 0 0
\(155\) 9.00000 0.722897
\(156\) −7.50000 7.79423i −0.600481 0.624038i
\(157\) 9.50000 + 16.4545i 0.758183 + 1.31321i 0.943777 + 0.330584i \(0.107246\pi\)
−0.185594 + 0.982627i \(0.559421\pi\)
\(158\) 1.50000 2.59808i 0.119334 0.206692i
\(159\) 9.00000 0.713746
\(160\) 7.50000 12.9904i 0.592927 1.02698i
\(161\) 0 0
\(162\) −4.50000 + 7.79423i −0.353553 + 0.612372i
\(163\) 0.500000 + 0.866025i 0.0391630 + 0.0678323i 0.884943 0.465700i \(-0.154198\pi\)
−0.845780 + 0.533533i \(0.820864\pi\)
\(164\) −1.50000 2.59808i −0.117130 0.202876i
\(165\) 27.0000 2.10195
\(166\) 0 0
\(167\) −6.50000 11.2583i −0.502985 0.871196i −0.999994 0.00345033i \(-0.998902\pi\)
0.497009 0.867745i \(-0.334432\pi\)
\(168\) 0 0
\(169\) −11.0000 6.92820i −0.846154 0.532939i
\(170\) 3.00000 5.19615i 0.230089 0.398527i
\(171\) −3.00000 + 5.19615i −0.229416 + 0.397360i
\(172\) −3.50000 + 6.06218i −0.266872 + 0.462237i
\(173\) 9.50000 + 16.4545i 0.722272 + 1.25101i 0.960087 + 0.279701i \(0.0902353\pi\)
−0.237816 + 0.971310i \(0.576431\pi\)
\(174\) 21.0000 1.59201
\(175\) 0 0
\(176\) −1.50000 + 2.59808i −0.113067 + 0.195837i
\(177\) −6.00000 + 10.3923i −0.450988 + 0.781133i
\(178\) −6.00000 −0.449719
\(179\) −8.50000 + 14.7224i −0.635320 + 1.10041i 0.351127 + 0.936328i \(0.385798\pi\)
−0.986447 + 0.164079i \(0.947535\pi\)
\(180\) 18.0000 1.34164
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) 0 0
\(183\) 39.0000 2.88296
\(184\) 0 0
\(185\) 3.00000 5.19615i 0.220564 0.382029i
\(186\) −9.00000 −0.659912
\(187\) 3.00000 5.19615i 0.219382 0.379980i
\(188\) −0.500000 + 0.866025i −0.0364662 + 0.0631614i
\(189\) 0 0
\(190\) −3.00000 −0.217643
\(191\) 8.50000 + 14.7224i 0.615038 + 1.06528i 0.990378 + 0.138390i \(0.0441928\pi\)
−0.375339 + 0.926887i \(0.622474\pi\)
\(192\) −10.5000 + 18.1865i −0.757772 + 1.31250i
\(193\) −3.50000 + 6.06218i −0.251936 + 0.436365i −0.964059 0.265689i \(-0.914400\pi\)
0.712123 + 0.702055i \(0.247734\pi\)
\(194\) −2.50000 + 4.33013i −0.179490 + 0.310885i
\(195\) 31.5000 7.79423i 2.25576 0.558156i
\(196\) 0 0
\(197\) 0.500000 + 0.866025i 0.0356235 + 0.0617018i 0.883287 0.468832i \(-0.155325\pi\)
−0.847664 + 0.530534i \(0.821992\pi\)
\(198\) −18.0000 −1.27920
\(199\) 20.0000 1.41776 0.708881 0.705328i \(-0.249200\pi\)
0.708881 + 0.705328i \(0.249200\pi\)
\(200\) 6.00000 + 10.3923i 0.424264 + 0.734847i
\(201\) 4.50000 + 7.79423i 0.317406 + 0.549762i
\(202\) −2.50000 + 4.33013i −0.175899 + 0.304667i
\(203\) 0 0
\(204\) 3.00000 5.19615i 0.210042 0.363803i
\(205\) 9.00000 0.628587
\(206\) 2.50000 4.33013i 0.174183 0.301694i
\(207\) 0 0
\(208\) −1.00000 + 3.46410i −0.0693375 + 0.240192i
\(209\) −3.00000 −0.207514
\(210\) 0 0
\(211\) −3.50000 6.06218i −0.240950 0.417338i 0.720035 0.693938i \(-0.244126\pi\)
−0.960985 + 0.276600i \(0.910792\pi\)
\(212\) 1.50000 + 2.59808i 0.103020 + 0.178437i
\(213\) −19.5000 33.7750i −1.33612 2.31422i
\(214\) 8.00000 0.546869
\(215\) −10.5000 18.1865i −0.716094 1.24031i
\(216\) −27.0000 −1.83712
\(217\) 0 0
\(218\) −3.50000 6.06218i −0.237050 0.410582i
\(219\) 39.0000 2.63538
\(220\) 4.50000 + 7.79423i 0.303390 + 0.525487i
\(221\) 2.00000 6.92820i 0.134535 0.466041i
\(222\) −3.00000 + 5.19615i −0.201347 + 0.348743i
\(223\) −4.50000 7.79423i −0.301342 0.521940i 0.675098 0.737728i \(-0.264101\pi\)
−0.976440 + 0.215788i \(0.930768\pi\)
\(224\) 0 0
\(225\) −12.0000 + 20.7846i −0.800000 + 1.38564i
\(226\) −7.50000 + 12.9904i −0.498893 + 0.864107i
\(227\) 4.00000 0.265489 0.132745 0.991150i \(-0.457621\pi\)
0.132745 + 0.991150i \(0.457621\pi\)
\(228\) −3.00000 −0.198680
\(229\) −6.50000 + 11.2583i −0.429532 + 0.743971i −0.996832 0.0795401i \(-0.974655\pi\)
0.567300 + 0.823511i \(0.307988\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 10.5000 + 18.1865i 0.689359 + 1.19400i
\(233\) 10.5000 18.1865i 0.687878 1.19144i −0.284645 0.958633i \(-0.591876\pi\)
0.972523 0.232806i \(-0.0747909\pi\)
\(234\) −21.0000 + 5.19615i −1.37281 + 0.339683i
\(235\) −1.50000 2.59808i −0.0978492 0.169480i
\(236\) −4.00000 −0.260378
\(237\) 4.50000 + 7.79423i 0.292306 + 0.506290i
\(238\) 0 0
\(239\) −4.00000 −0.258738 −0.129369 0.991596i \(-0.541295\pi\)
−0.129369 + 0.991596i \(0.541295\pi\)
\(240\) −4.50000 7.79423i −0.290474 0.503115i
\(241\) 26.0000 1.67481 0.837404 0.546585i \(-0.184072\pi\)
0.837404 + 0.546585i \(0.184072\pi\)
\(242\) 1.00000 + 1.73205i 0.0642824 + 0.111340i
\(243\) 0 0
\(244\) 6.50000 + 11.2583i 0.416120 + 0.720741i
\(245\) 0 0
\(246\) −9.00000 −0.573819
\(247\) −3.50000 + 0.866025i −0.222700 + 0.0551039i
\(248\) −4.50000 7.79423i −0.285750 0.494934i
\(249\) 0 0
\(250\) 3.00000 0.189737
\(251\) −11.5000 + 19.9186i −0.725874 + 1.25725i 0.232740 + 0.972539i \(0.425231\pi\)
−0.958613 + 0.284711i \(0.908102\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −5.50000 9.52628i −0.345101 0.597732i
\(255\) 9.00000 + 15.5885i 0.563602 + 0.976187i
\(256\) −17.0000 −1.06250
\(257\) 2.00000 0.124757 0.0623783 0.998053i \(-0.480131\pi\)
0.0623783 + 0.998053i \(0.480131\pi\)
\(258\) 10.5000 + 18.1865i 0.653701 + 1.13224i
\(259\) 0 0
\(260\) 7.50000 + 7.79423i 0.465130 + 0.483378i
\(261\) −21.0000 + 36.3731i −1.29987 + 2.25144i
\(262\) 2.50000 4.33013i 0.154451 0.267516i
\(263\) 13.5000 23.3827i 0.832446 1.44184i −0.0636476 0.997972i \(-0.520273\pi\)
0.896093 0.443866i \(-0.146393\pi\)
\(264\) −13.5000 23.3827i −0.830868 1.43910i
\(265\) −9.00000 −0.552866
\(266\) 0 0
\(267\) 9.00000 15.5885i 0.550791 0.953998i
\(268\) −1.50000 + 2.59808i −0.0916271 + 0.158703i
\(269\) −18.0000 −1.09748 −0.548740 0.835993i \(-0.684892\pi\)
−0.548740 + 0.835993i \(0.684892\pi\)
\(270\) 13.5000 23.3827i 0.821584 1.42302i
\(271\) 16.0000 0.971931 0.485965 0.873978i \(-0.338468\pi\)
0.485965 + 0.873978i \(0.338468\pi\)
\(272\) −2.00000 −0.121268
\(273\) 0 0
\(274\) 10.0000 0.604122
\(275\) −12.0000 −0.723627
\(276\) 0 0
\(277\) 22.0000 1.32185 0.660926 0.750451i \(-0.270164\pi\)
0.660926 + 0.750451i \(0.270164\pi\)
\(278\) −7.50000 + 12.9904i −0.449820 + 0.779111i
\(279\) 9.00000 15.5885i 0.538816 0.933257i
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 1.50000 + 2.59808i 0.0893237 + 0.154713i
\(283\) 0.500000 0.866025i 0.0297219 0.0514799i −0.850782 0.525519i \(-0.823871\pi\)
0.880504 + 0.474039i \(0.157204\pi\)
\(284\) 6.50000 11.2583i 0.385704 0.668059i
\(285\) 4.50000 7.79423i 0.266557 0.461690i
\(286\) −7.50000 7.79423i −0.443484 0.460882i
\(287\) 0 0
\(288\) −15.0000 25.9808i −0.883883 1.53093i
\(289\) −13.0000 −0.764706
\(290\) −21.0000 −1.23316
\(291\) −7.50000 12.9904i −0.439658 0.761510i
\(292\) 6.50000 + 11.2583i 0.380384 + 0.658844i
\(293\) 5.50000 9.52628i 0.321313 0.556531i −0.659446 0.751752i \(-0.729209\pi\)
0.980759 + 0.195221i \(0.0625424\pi\)
\(294\) 0 0
\(295\) 6.00000 10.3923i 0.349334 0.605063i
\(296\) −6.00000 −0.348743
\(297\) 13.5000 23.3827i 0.783349 1.35680i
\(298\) −7.50000 12.9904i −0.434463 0.752513i
\(299\) 0 0
\(300\) −12.0000 −0.692820
\(301\) 0 0
\(302\) 10.5000 + 18.1865i 0.604207 + 1.04652i
\(303\) −7.50000 12.9904i −0.430864 0.746278i
\(304\) 0.500000 + 0.866025i 0.0286770 + 0.0496700i
\(305\) −39.0000 −2.23313
\(306\) −6.00000 10.3923i −0.342997 0.594089i
\(307\) −12.0000 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 0 0
\(309\) 7.50000 + 12.9904i 0.426660 + 0.738997i
\(310\) 9.00000 0.511166
\(311\) −4.50000 7.79423i −0.255172 0.441970i 0.709771 0.704433i \(-0.248799\pi\)
−0.964942 + 0.262463i \(0.915465\pi\)
\(312\) −22.5000 23.3827i −1.27381 1.32378i
\(313\) 9.50000 16.4545i 0.536972 0.930062i −0.462093 0.886831i \(-0.652902\pi\)
0.999065 0.0432311i \(-0.0137652\pi\)
\(314\) 9.50000 + 16.4545i 0.536116 + 0.928580i
\(315\) 0 0
\(316\) −1.50000 + 2.59808i −0.0843816 + 0.146153i
\(317\) 4.50000 7.79423i 0.252745 0.437767i −0.711535 0.702650i \(-0.752000\pi\)
0.964281 + 0.264883i \(0.0853332\pi\)
\(318\) 9.00000 0.504695
\(319\) −21.0000 −1.17577
\(320\) 10.5000 18.1865i 0.586968 1.01666i
\(321\) −12.0000 + 20.7846i −0.669775 + 1.16008i
\(322\) 0 0
\(323\) −1.00000 1.73205i −0.0556415 0.0963739i
\(324\) 4.50000 7.79423i 0.250000 0.433013i
\(325\) −14.0000 + 3.46410i −0.776580 + 0.192154i
\(326\) 0.500000 + 0.866025i 0.0276924 + 0.0479647i
\(327\) 21.0000 1.16130
\(328\) −4.50000 7.79423i −0.248471 0.430364i
\(329\) 0 0
\(330\) 27.0000 1.48630
\(331\) 14.5000 + 25.1147i 0.796992 + 1.38043i 0.921567 + 0.388221i \(0.126910\pi\)
−0.124574 + 0.992210i \(0.539757\pi\)
\(332\) 0 0
\(333\) −6.00000 10.3923i −0.328798 0.569495i
\(334\) −6.50000 11.2583i −0.355664 0.616028i
\(335\) −4.50000 7.79423i −0.245861 0.425844i
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) −11.0000 6.92820i −0.598321 0.376845i
\(339\) −22.5000 38.9711i −1.22203 2.11662i
\(340\) −3.00000 + 5.19615i −0.162698 + 0.281801i
\(341\) 9.00000 0.487377
\(342\) −3.00000 + 5.19615i −0.162221 + 0.280976i
\(343\) 0 0
\(344\) −10.5000 + 18.1865i −0.566122 + 0.980552i
\(345\) 0 0
\(346\) 9.50000 + 16.4545i 0.510723 + 0.884598i
\(347\) −8.00000 −0.429463 −0.214731 0.976673i \(-0.568888\pi\)
−0.214731 + 0.976673i \(0.568888\pi\)
\(348\) −21.0000 −1.12572
\(349\) 11.5000 + 19.9186i 0.615581 + 1.06622i 0.990282 + 0.139072i \(0.0444119\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 0 0
\(351\) 9.00000 31.1769i 0.480384 1.66410i
\(352\) 7.50000 12.9904i 0.399751 0.692390i
\(353\) −12.5000 + 21.6506i −0.665308 + 1.15235i 0.313894 + 0.949458i \(0.398366\pi\)
−0.979202 + 0.202889i \(0.934967\pi\)
\(354\) −6.00000 + 10.3923i −0.318896 + 0.552345i
\(355\) 19.5000 + 33.7750i 1.03495 + 1.79259i
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) −8.50000 + 14.7224i −0.449239 + 0.778105i
\(359\) −8.50000 + 14.7224i −0.448613 + 0.777020i −0.998296 0.0583530i \(-0.981415\pi\)
0.549683 + 0.835373i \(0.314748\pi\)
\(360\) 54.0000 2.84605
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) 22.0000 1.15629
\(363\) −6.00000 −0.314918
\(364\) 0 0
\(365\) −39.0000 −2.04135
\(366\) 39.0000 2.03856
\(367\) −15.5000 + 26.8468i −0.809093 + 1.40139i 0.104399 + 0.994535i \(0.466708\pi\)
−0.913493 + 0.406855i \(0.866625\pi\)
\(368\) 0 0
\(369\) 9.00000 15.5885i 0.468521 0.811503i
\(370\) 3.00000 5.19615i 0.155963 0.270135i
\(371\) 0 0
\(372\) 9.00000 0.466628
\(373\) 4.50000 + 7.79423i 0.233001 + 0.403570i 0.958690 0.284453i \(-0.0918121\pi\)
−0.725689 + 0.688023i \(0.758479\pi\)
\(374\) 3.00000 5.19615i 0.155126 0.268687i
\(375\) −4.50000 + 7.79423i −0.232379 + 0.402492i
\(376\) −1.50000 + 2.59808i −0.0773566 + 0.133986i
\(377\) −24.5000 + 6.06218i −1.26181 + 0.312218i
\(378\) 0 0
\(379\) 16.5000 + 28.5788i 0.847548 + 1.46800i 0.883390 + 0.468639i \(0.155255\pi\)
−0.0358418 + 0.999357i \(0.511411\pi\)
\(380\) 3.00000 0.153897
\(381\) 33.0000 1.69064
\(382\) 8.50000 + 14.7224i 0.434898 + 0.753265i
\(383\) −10.5000 18.1865i −0.536525 0.929288i −0.999088 0.0427020i \(-0.986403\pi\)
0.462563 0.886586i \(-0.346930\pi\)
\(384\) 4.50000 7.79423i 0.229640 0.397748i
\(385\) 0 0
\(386\) −3.50000 + 6.06218i −0.178145 + 0.308557i
\(387\) −42.0000 −2.13498
\(388\) 2.50000 4.33013i 0.126918 0.219829i
\(389\) 16.5000 + 28.5788i 0.836583 + 1.44900i 0.892735 + 0.450582i \(0.148784\pi\)
−0.0561516 + 0.998422i \(0.517883\pi\)
\(390\) 31.5000 7.79423i 1.59506 0.394676i
\(391\) 0 0
\(392\) 0 0
\(393\) 7.50000 + 12.9904i 0.378325 + 0.655278i
\(394\) 0.500000 + 0.866025i 0.0251896 + 0.0436297i
\(395\) −4.50000 7.79423i −0.226420 0.392170i
\(396\) 18.0000 0.904534
\(397\) −0.500000 0.866025i −0.0250943 0.0434646i 0.853206 0.521575i \(-0.174655\pi\)
−0.878300 + 0.478110i \(0.841322\pi\)
\(398\) 20.0000 1.00251
\(399\) 0 0
\(400\) 2.00000 + 3.46410i 0.100000 + 0.173205i
\(401\) −2.00000 −0.0998752 −0.0499376 0.998752i \(-0.515902\pi\)
−0.0499376 + 0.998752i \(0.515902\pi\)
\(402\) 4.50000 + 7.79423i 0.224440 + 0.388741i
\(403\) 10.5000 2.59808i 0.523042 0.129419i
\(404\) 2.50000 4.33013i 0.124380 0.215432i
\(405\) 13.5000 + 23.3827i 0.670820 + 1.16190i
\(406\) 0 0
\(407\) 3.00000 5.19615i 0.148704 0.257564i
\(408\) 9.00000 15.5885i 0.445566 0.771744i
\(409\) −14.0000 −0.692255 −0.346128 0.938187i \(-0.612504\pi\)
−0.346128 + 0.938187i \(0.612504\pi\)
\(410\) 9.00000 0.444478
\(411\) −15.0000 + 25.9808i −0.739895 + 1.28154i
\(412\) −2.50000 + 4.33013i −0.123166 + 0.213330i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 5.00000 17.3205i 0.245145 0.849208i
\(417\) −22.5000 38.9711i −1.10183 1.90843i
\(418\) −3.00000 −0.146735
\(419\) −12.5000 21.6506i −0.610665 1.05770i −0.991129 0.132907i \(-0.957569\pi\)
0.380464 0.924796i \(-0.375764\pi\)
\(420\) 0 0
\(421\) 18.0000 0.877266 0.438633 0.898666i \(-0.355463\pi\)
0.438633 + 0.898666i \(0.355463\pi\)
\(422\) −3.50000 6.06218i −0.170377 0.295102i
\(423\) −6.00000 −0.291730
\(424\) 4.50000 + 7.79423i 0.218539 + 0.378521i
\(425\) −4.00000 6.92820i −0.194029 0.336067i
\(426\) −19.5000 33.7750i −0.944778 1.63640i
\(427\) 0 0
\(428\) −8.00000 −0.386695
\(429\) 31.5000 7.79423i 1.52083 0.376309i
\(430\) −10.5000 18.1865i −0.506355 0.877033i
\(431\) −4.50000 + 7.79423i −0.216757 + 0.375435i −0.953815 0.300395i \(-0.902881\pi\)
0.737057 + 0.675830i \(0.236215\pi\)
\(432\) −9.00000 −0.433013
\(433\) 13.5000 23.3827i 0.648769 1.12370i −0.334649 0.942343i \(-0.608618\pi\)
0.983417 0.181357i \(-0.0580490\pi\)
\(434\) 0 0
\(435\) 31.5000 54.5596i 1.51031 2.61593i
\(436\) 3.50000 + 6.06218i 0.167620 + 0.290326i
\(437\) 0 0
\(438\) 39.0000 1.86349
\(439\) 16.0000 0.763638 0.381819 0.924237i \(-0.375298\pi\)
0.381819 + 0.924237i \(0.375298\pi\)
\(440\) 13.5000 + 23.3827i 0.643587 + 1.11473i
\(441\) 0 0
\(442\) 2.00000 6.92820i 0.0951303 0.329541i
\(443\) 5.50000 9.52628i 0.261313 0.452607i −0.705278 0.708931i \(-0.749178\pi\)
0.966591 + 0.256323i \(0.0825112\pi\)
\(444\) 3.00000 5.19615i 0.142374 0.246598i
\(445\) −9.00000 + 15.5885i −0.426641 + 0.738964i
\(446\) −4.50000 7.79423i −0.213081 0.369067i
\(447\) 45.0000 2.12843
\(448\) 0 0
\(449\) −7.50000 + 12.9904i −0.353947 + 0.613054i −0.986937 0.161106i \(-0.948494\pi\)
0.632990 + 0.774160i \(0.281827\pi\)
\(450\) −12.0000 + 20.7846i −0.565685 + 0.979796i
\(451\) 9.00000 0.423793
\(452\) 7.50000 12.9904i 0.352770 0.611016i
\(453\) −63.0000 −2.96000
\(454\) 4.00000 0.187729
\(455\) 0 0
\(456\) −9.00000 −0.421464
\(457\) −18.0000 −0.842004 −0.421002 0.907060i \(-0.638322\pi\)
−0.421002 + 0.907060i \(0.638322\pi\)
\(458\) −6.50000 + 11.2583i −0.303725 + 0.526067i
\(459\) 18.0000 0.840168
\(460\) 0 0
\(461\) 17.5000 30.3109i 0.815056 1.41172i −0.0942312 0.995550i \(-0.530039\pi\)
0.909288 0.416169i \(-0.136627\pi\)
\(462\) 0 0
\(463\) −8.00000 −0.371792 −0.185896 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) 3.50000 + 6.06218i 0.162483 + 0.281430i
\(465\) −13.5000 + 23.3827i −0.626048 + 1.08435i
\(466\) 10.5000 18.1865i 0.486403 0.842475i
\(467\) −3.50000 + 6.06218i −0.161961 + 0.280524i −0.935572 0.353137i \(-0.885115\pi\)
0.773611 + 0.633661i \(0.218448\pi\)
\(468\) 21.0000 5.19615i 0.970725 0.240192i
\(469\) 0 0
\(470\) −1.50000 2.59808i −0.0691898 0.119840i
\(471\) −57.0000 −2.62642
\(472\) −12.0000 −0.552345
\(473\) −10.5000 18.1865i −0.482791 0.836218i
\(474\) 4.50000 + 7.79423i 0.206692 + 0.358001i
\(475\) −2.00000 + 3.46410i −0.0917663 + 0.158944i
\(476\) 0 0
\(477\) −9.00000 + 15.5885i −0.412082 + 0.713746i
\(478\) −4.00000 −0.182956
\(479\) −17.5000 + 30.3109i −0.799595 + 1.38494i 0.120284 + 0.992739i \(0.461619\pi\)
−0.919880 + 0.392200i \(0.871714\pi\)
\(480\) 22.5000 + 38.9711i 1.02698 + 1.77878i
\(481\) 2.00000 6.92820i 0.0911922 0.315899i
\(482\) 26.0000 1.18427
\(483\) 0 0
\(484\) −1.00000 1.73205i −0.0454545 0.0787296i
\(485\) 7.50000 + 12.9904i 0.340557 + 0.589863i
\(486\) 0 0
\(487\) 16.0000 0.725029 0.362515 0.931978i \(-0.381918\pi\)
0.362515 + 0.931978i \(0.381918\pi\)
\(488\) 19.5000 + 33.7750i 0.882724 + 1.52892i
\(489\) −3.00000 −0.135665
\(490\) 0 0
\(491\) −7.50000 12.9904i −0.338470 0.586248i 0.645675 0.763612i \(-0.276576\pi\)
−0.984145 + 0.177365i \(0.943243\pi\)
\(492\) 9.00000 0.405751
\(493\) −7.00000 12.1244i −0.315264 0.546054i
\(494\) −3.50000 + 0.866025i −0.157472 + 0.0389643i
\(495\) −27.0000 + 46.7654i −1.21356 + 2.10195i
\(496\) −1.50000 2.59808i −0.0673520 0.116657i
\(497\) 0 0
\(498\) 0 0
\(499\) 15.5000 26.8468i 0.693875 1.20183i −0.276683 0.960961i \(-0.589235\pi\)
0.970558 0.240866i \(-0.0774314\pi\)
\(500\) −3.00000 −0.134164
\(501\) 39.0000 1.74239
\(502\) −11.5000 + 19.9186i −0.513270 + 0.889010i
\(503\) −15.5000 + 26.8468i −0.691111 + 1.19704i 0.280363 + 0.959894i \(0.409545\pi\)
−0.971474 + 0.237145i \(0.923788\pi\)
\(504\) 0 0
\(505\) 7.50000 + 12.9904i 0.333746 + 0.578064i
\(506\) 0 0
\(507\) 34.5000 18.1865i 1.53220 0.807692i
\(508\) 5.50000 + 9.52628i 0.244023 + 0.422660i
\(509\) 34.0000 1.50702 0.753512 0.657434i \(-0.228358\pi\)
0.753512 + 0.657434i \(0.228358\pi\)
\(510\) 9.00000 + 15.5885i 0.398527 + 0.690268i
\(511\) 0 0
\(512\) −11.0000 −0.486136
\(513\) −4.50000 7.79423i −0.198680 0.344124i
\(514\) 2.00000 0.0882162
\(515\) −7.50000 12.9904i −0.330489 0.572425i
\(516\) −10.5000 18.1865i −0.462237 0.800617i
\(517\) −1.50000 2.59808i −0.0659699 0.114263i
\(518\) 0 0
\(519\) −57.0000 −2.50202
\(520\) 22.5000 + 23.3827i 0.986690 + 1.02540i
\(521\) −8.50000 14.7224i −0.372392 0.645001i 0.617541 0.786539i \(-0.288129\pi\)
−0.989933 + 0.141537i \(0.954796\pi\)
\(522\) −21.0000 + 36.3731i −0.919145 + 1.59201i
\(523\) −4.00000 −0.174908 −0.0874539 0.996169i \(-0.527873\pi\)
−0.0874539 + 0.996169i \(0.527873\pi\)
\(524\) −2.50000 + 4.33013i −0.109213 + 0.189162i
\(525\) 0 0
\(526\) 13.5000 23.3827i 0.588628 1.01953i
\(527\) 3.00000 + 5.19615i 0.130682 + 0.226348i
\(528\) −4.50000 7.79423i −0.195837 0.339200i
\(529\) −23.0000 −1.00000
\(530\) −9.00000 −0.390935
\(531\) −12.0000 20.7846i −0.520756 0.901975i
\(532\) 0 0
\(533\) 10.5000 2.59808i 0.454805 0.112535i
\(534\) 9.00000 15.5885i 0.389468 0.674579i
\(535\) 12.0000 20.7846i 0.518805 0.898597i
\(536\) −4.50000 + 7.79423i −0.194370 + 0.336659i
\(537\) −25.5000 44.1673i −1.10041 1.90596i
\(538\) −18.0000 −0.776035
\(539\) 0 0
\(540\) −13.5000 + 23.3827i −0.580948 + 1.00623i
\(541\) 18.5000 32.0429i 0.795377 1.37763i −0.127222 0.991874i \(-0.540606\pi\)
0.922599 0.385759i \(-0.126061\pi\)
\(542\) 16.0000 0.687259
\(543\) −33.0000 + 57.1577i −1.41617 + 2.45287i
\(544\) 10.0000 0.428746
\(545\) −21.0000 −0.899541
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) −10.0000 −0.427179
\(549\) −39.0000 + 67.5500i −1.66448 + 2.88296i
\(550\) −12.0000 −0.511682
\(551\) −3.50000 + 6.06218i −0.149105 + 0.258257i
\(552\) 0 0
\(553\) 0 0
\(554\) 22.0000 0.934690
\(555\) 9.00000 + 15.5885i 0.382029 + 0.661693i
\(556\) 7.50000 12.9904i 0.318071 0.550915i
\(557\) −1.50000 + 2.59808i −0.0635570 + 0.110084i −0.896053 0.443947i \(-0.853578\pi\)
0.832496 + 0.554031i \(0.186911\pi\)
\(558\) 9.00000 15.5885i 0.381000 0.659912i
\(559\) −17.5000 18.1865i −0.740171 0.769208i
\(560\) 0 0
\(561\) 9.00000 + 15.5885i 0.379980 + 0.658145i
\(562\) −18.0000 −0.759284
\(563\) −4.00000 −0.168580 −0.0842900 0.996441i \(-0.526862\pi\)
−0.0842900 + 0.996441i \(0.526862\pi\)
\(564\) −1.50000 2.59808i −0.0631614 0.109399i
\(565\) 22.5000 + 38.9711i 0.946582 + 1.63953i
\(566\) 0.500000 0.866025i 0.0210166 0.0364018i
\(567\) 0 0
\(568\) 19.5000 33.7750i 0.818202 1.41717i
\(569\) 10.0000 0.419222 0.209611 0.977785i \(-0.432780\pi\)
0.209611 + 0.977785i \(0.432780\pi\)
\(570\) 4.50000 7.79423i 0.188484 0.326464i
\(571\) −21.5000 37.2391i −0.899747 1.55841i −0.827817 0.560998i \(-0.810418\pi\)
−0.0719297 0.997410i \(-0.522916\pi\)
\(572\) 7.50000 + 7.79423i 0.313591 + 0.325893i
\(573\) −51.0000 −2.13056
\(574\) 0 0
\(575\) 0 0
\(576\) −21.0000 36.3731i −0.875000 1.51554i
\(577\) −0.500000 0.866025i −0.0208153 0.0360531i 0.855430 0.517918i \(-0.173293\pi\)
−0.876245 + 0.481865i \(0.839960\pi\)
\(578\) −13.0000 −0.540729
\(579\) −10.5000 18.1865i −0.436365 0.755807i
\(580\) 21.0000 0.871978
\(581\) 0 0
\(582\) −7.50000 12.9904i −0.310885 0.538469i
\(583\) −9.00000 −0.372742
\(584\) 19.5000 + 33.7750i 0.806916 + 1.39762i
\(585\) −18.0000 + 62.3538i −0.744208 + 2.57801i
\(586\) 5.50000 9.52628i 0.227203 0.393527i
\(587\) −16.5000 28.5788i −0.681028 1.17957i −0.974668 0.223659i \(-0.928200\pi\)
0.293640 0.955916i \(-0.405133\pi\)
\(588\) 0 0
\(589\) 1.50000 2.59808i 0.0618064 0.107052i
\(590\) 6.00000 10.3923i 0.247016 0.427844i
\(591\) −3.00000 −0.123404
\(592\) −2.00000 −0.0821995
\(593\) 13.5000 23.3827i 0.554379 0.960212i −0.443573 0.896238i \(-0.646289\pi\)
0.997952 0.0639736i \(-0.0203773\pi\)
\(594\) 13.5000 23.3827i 0.553912 0.959403i
\(595\) 0 0
\(596\) 7.50000 + 12.9904i 0.307212 + 0.532107i
\(597\) −30.0000 + 51.9615i −1.22782 + 2.12664i
\(598\) 0 0
\(599\) 12.5000 + 21.6506i 0.510736 + 0.884621i 0.999923 + 0.0124417i \(0.00396043\pi\)
−0.489186 + 0.872179i \(0.662706\pi\)
\(600\) −36.0000 −1.46969
\(601\) 17.5000 + 30.3109i 0.713840 + 1.23641i 0.963405 + 0.268049i \(0.0863789\pi\)
−0.249565 + 0.968358i \(0.580288\pi\)
\(602\) 0 0
\(603\) −18.0000 −0.733017
\(604\) −10.5000 18.1865i −0.427239 0.740000i
\(605\) 6.00000 0.243935
\(606\) −7.50000 12.9904i −0.304667 0.527698i
\(607\) 5.50000 + 9.52628i 0.223238 + 0.386660i 0.955789 0.294052i \(-0.0950039\pi\)
−0.732551 + 0.680712i \(0.761671\pi\)
\(608\) −2.50000 4.33013i −0.101388 0.175610i
\(609\) 0 0
\(610\) −39.0000 −1.57906
\(611\) −2.50000 2.59808i −0.101139 0.105107i
\(612\) 6.00000 + 10.3923i 0.242536 + 0.420084i
\(613\) 12.5000 21.6506i 0.504870 0.874461i −0.495114 0.868828i \(-0.664874\pi\)
0.999984 0.00563283i \(-0.00179300\pi\)
\(614\) −12.0000 −0.484281
\(615\) −13.5000 + 23.3827i −0.544373 + 0.942881i
\(616\) 0 0
\(617\) 16.5000 28.5788i 0.664265 1.15054i −0.315219 0.949019i \(-0.602078\pi\)
0.979484 0.201522i \(-0.0645887\pi\)
\(618\) 7.50000 + 12.9904i 0.301694 + 0.522550i
\(619\) 5.50000 + 9.52628i 0.221064 + 0.382893i 0.955131 0.296183i \(-0.0957138\pi\)
−0.734068 + 0.679076i \(0.762380\pi\)
\(620\) −9.00000 −0.361449
\(621\) 0 0
\(622\) −4.50000 7.79423i −0.180434 0.312520i
\(623\) 0 0
\(624\) −7.50000 7.79423i −0.300240 0.312019i
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) 9.50000 16.4545i 0.379696 0.657653i
\(627\) 4.50000 7.79423i 0.179713 0.311272i
\(628\) −9.50000 16.4545i −0.379091 0.656605i
\(629\) 4.00000 0.159490
\(630\) 0 0
\(631\) −12.5000 + 21.6506i −0.497617 + 0.861898i −0.999996 0.00274930i \(-0.999125\pi\)
0.502379 + 0.864647i \(0.332458\pi\)
\(632\) −4.50000 + 7.79423i −0.179000 + 0.310038i
\(633\) 21.0000 0.834675
\(634\) 4.50000 7.79423i 0.178718 0.309548i
\(635\) −33.0000 −1.30957
\(636\) −9.00000 −0.356873
\(637\) 0 0
\(638\) −21.0000 −0.831398
\(639\) 78.0000 3.08563
\(640\) −4.50000 + 7.79423i −0.177878 + 0.308094i
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) −12.0000 + 20.7846i −0.473602 + 0.820303i
\(643\) −9.50000 + 16.4545i −0.374643 + 0.648901i −0.990274 0.139134i \(-0.955568\pi\)
0.615630 + 0.788035i \(0.288902\pi\)
\(644\) 0 0
\(645\) 63.0000 2.48062
\(646\) −1.00000 1.73205i −0.0393445 0.0681466i
\(647\) 4.50000 7.79423i 0.176913 0.306423i −0.763908 0.645325i \(-0.776722\pi\)
0.940822 + 0.338902i \(0.110055\pi\)
\(648\) 13.5000 23.3827i 0.530330 0.918559i
\(649\) 6.00000 10.3923i 0.235521 0.407934i
\(650\) −14.0000 + 3.46410i −0.549125 + 0.135873i
\(651\) 0 0
\(652\) −0.500000 0.866025i −0.0195815 0.0339162i
\(653\) 18.0000 0.704394 0.352197 0.935926i \(-0.385435\pi\)
0.352197 + 0.935926i \(0.385435\pi\)
\(654\) 21.0000 0.821165
\(655\) −7.50000 12.9904i −0.293049 0.507576i
\(656\) −1.50000 2.59808i −0.0585652 0.101438i
\(657\) −39.0000 + 67.5500i −1.52153 + 2.63538i
\(658\) 0 0
\(659\) −14.5000 + 25.1147i −0.564840 + 0.978331i 0.432225 + 0.901766i \(0.357729\pi\)
−0.997065 + 0.0765653i \(0.975605\pi\)
\(660\) −27.0000 −1.05097
\(661\) −4.50000 + 7.79423i −0.175030 + 0.303160i −0.940172 0.340701i \(-0.889335\pi\)
0.765142 + 0.643862i \(0.222669\pi\)
\(662\) 14.5000 + 25.1147i 0.563559 + 0.976112i
\(663\) 15.0000 + 15.5885i 0.582552 + 0.605406i
\(664\) 0 0
\(665\) 0 0
\(666\) −6.00000 10.3923i −0.232495 0.402694i
\(667\) 0 0
\(668\) 6.50000 + 11.2583i 0.251493 + 0.435598i
\(669\) 27.0000 1.04388
\(670\) −4.50000 7.79423i −0.173850 0.301117i
\(671\) −39.0000 −1.50558
\(672\) 0 0
\(673\) 20.5000 + 35.5070i 0.790217 + 1.36870i 0.925832 + 0.377934i \(0.123365\pi\)
−0.135615 + 0.990762i \(0.543301\pi\)
\(674\) 14.0000 0.539260
\(675\) −18.0000 31.1769i −0.692820 1.20000i
\(676\) 11.0000 + 6.92820i 0.423077 + 0.266469i
\(677\) 3.50000 6.06218i 0.134516 0.232988i −0.790897 0.611950i \(-0.790385\pi\)
0.925412 + 0.378962i \(0.123719\pi\)
\(678\) −22.5000 38.9711i −0.864107 1.49668i
\(679\) 0 0
\(680\) −9.00000 + 15.5885i −0.345134 + 0.597790i
\(681\) −6.00000 + 10.3923i −0.229920 + 0.398234i
\(682\) 9.00000 0.344628
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 3.00000 5.19615i 0.114708 0.198680i
\(685\) 15.0000 25.9808i 0.573121 0.992674i
\(686\) 0 0
\(687\) −19.5000 33.7750i −0.743971 1.28860i
\(688\) −3.50000 + 6.06218i −0.133436 + 0.231118i
\(689\) −10.5000 + 2.59808i −0.400018 + 0.0989788i
\(690\) 0 0
\(691\) 4.00000 0.152167 0.0760836 0.997101i \(-0.475758\pi\)
0.0760836 + 0.997101i \(0.475758\pi\)
\(692\) −9.50000 16.4545i −0.361136 0.625506i
\(693\) 0 0
\(694\) −8.00000 −0.303676
\(695\) 22.5000 + 38.9711i 0.853474 + 1.47826i
\(696\) −63.0000 −2.38801
\(697\) 3.00000 + 5.19615i 0.113633 + 0.196818i
\(698\) 11.5000 + 19.9186i 0.435281 + 0.753930i
\(699\) 31.5000 + 54.5596i 1.19144 + 2.06363i
\(700\) 0 0
\(701\) 42.0000 1.58632 0.793159 0.609015i \(-0.208435\pi\)
0.793159 + 0.609015i \(0.208435\pi\)
\(702\) 9.00000 31.1769i 0.339683 1.17670i
\(703\) −1.00000 1.73205i −0.0377157 0.0653255i
\(704\) 10.5000 18.1865i 0.395734 0.685431i
\(705\) 9.00000 0.338960
\(706\) −12.5000 + 21.6506i −0.470444 + 0.814832i
\(707\) 0 0
\(708\) 6.00000 10.3923i 0.225494 0.390567i
\(709\) −5.50000 9.52628i −0.206557 0.357767i 0.744071 0.668101i \(-0.232892\pi\)
−0.950628 + 0.310334i \(0.899559\pi\)
\(710\) 19.5000 + 33.7750i 0.731822 + 1.26755i
\(711\) −18.0000 −0.675053
\(712\) 18.0000 0.674579
\(713\) 0 0
\(714\) 0 0
\(715\) −31.5000 + 7.79423i −1.17803 + 0.291488i
\(716\) 8.50000 14.7224i 0.317660 0.550203i
\(717\) 6.00000 10.3923i 0.224074 0.388108i
\(718\) −8.50000 + 14.7224i −0.317217 + 0.549436i
\(719\) −4.50000 7.79423i −0.167822 0.290676i 0.769832 0.638247i \(-0.220340\pi\)
−0.937654 + 0.347571i \(0.887007\pi\)
\(720\) 18.0000 0.670820
\(721\) 0 0
\(722\) 9.00000 15.5885i 0.334945 0.580142i
\(723\) −39.0000 + 67.5500i −1.45043 + 2.51221i
\(724\) −22.0000 −0.817624
\(725\) −14.0000 + 24.2487i −0.519947 + 0.900575i
\(726\) −6.00000 −0.222681
\(727\) 8.00000 0.296704 0.148352 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) −39.0000 −1.44345
\(731\) 7.00000 12.1244i 0.258904 0.448435i
\(732\) −39.0000 −1.44148
\(733\) −4.50000 + 7.79423i −0.166211 + 0.287886i −0.937085 0.349102i \(-0.886487\pi\)
0.770873 + 0.636988i \(0.219820\pi\)
\(734\) −15.5000 + 26.8468i −0.572115 + 0.990933i
\(735\) 0 0
\(736\) 0 0
\(737\) −4.50000 7.79423i −0.165760 0.287104i
\(738\) 9.00000 15.5885i 0.331295 0.573819i
\(739\) −0.500000 + 0.866025i −0.0183928 + 0.0318573i −0.875075 0.483987i \(-0.839188\pi\)
0.856683 + 0.515844i \(0.172522\pi\)
\(740\) −3.00000 + 5.19615i −0.110282 + 0.191014i
\(741\) 3.00000 10.3923i 0.110208 0.381771i
\(742\) 0 0
\(743\) −25.5000 44.1673i −0.935504 1.62034i −0.773732 0.633513i \(-0.781612\pi\)
−0.161772 0.986828i \(-0.551721\pi\)
\(744\) 27.0000 0.989868
\(745\) −45.0000 −1.64867
\(746\) 4.50000 + 7.79423i 0.164757 + 0.285367i
\(747\) 0 0
\(748\) −3.00000 + 5.19615i −0.109691 + 0.189990i
\(749\) 0 0
\(750\) −4.50000 + 7.79423i −0.164317 + 0.284605i
\(751\) 28.0000 1.02173 0.510867 0.859660i \(-0.329324\pi\)
0.510867 + 0.859660i \(0.329324\pi\)
\(752\) −0.500000 + 0.866025i −0.0182331 + 0.0315807i
\(753\) −34.5000 59.7558i −1.25725 2.17762i
\(754\) −24.5000 + 6.06218i −0.892237 + 0.220771i
\(755\) 63.0000 2.29280
\(756\) 0 0
\(757\) −1.50000 2.59808i −0.0545184 0.0944287i 0.837478 0.546471i \(-0.184029\pi\)
−0.891997 + 0.452042i \(0.850696\pi\)
\(758\) 16.5000 + 28.5788i 0.599307 + 1.03803i
\(759\) 0 0
\(760\) 9.00000 0.326464
\(761\) −4.50000 7.79423i −0.163125 0.282541i 0.772863 0.634573i \(-0.218824\pi\)
−0.935988 + 0.352032i \(0.885491\pi\)
\(762\) 33.0000 1.19546
\(763\) 0 0
\(764\) −8.50000 14.7224i −0.307519 0.532639i
\(765\) −36.0000 −1.30158
\(766\) −10.5000 18.1865i −0.379380 0.657106i
\(767\) 4.00000 13.8564i 0.144432 0.500326i
\(768\) 25.5000 44.1673i 0.920152 1.59375i
\(769\) 9.50000 + 16.4545i 0.342579 + 0.593364i 0.984911 0.173063i \(-0.0553663\pi\)
−0.642332 + 0.766426i \(0.722033\pi\)
\(770\) 0 0
\(771\) −3.00000 + 5.19615i −0.108042 + 0.187135i
\(772\) 3.50000 6.06218i 0.125968 0.218183i
\(773\) 6.00000 0.215805 0.107903 0.994161i \(-0.465587\pi\)
0.107903 + 0.994161i \(0.465587\pi\)
\(774\) −42.0000 −1.50966
\(775\) 6.00000 10.3923i 0.215526 0.373303i
\(776\) 7.50000 12.9904i 0.269234 0.466328i
\(777\) 0 0
\(778\) 16.5000 + 28.5788i 0.591554 + 1.02460i
\(779\) 1.50000 2.59808i 0.0537431 0.0930857i
\(780\) −31.5000 + 7.79423i −1.12788 + 0.279078i
\(781\) 19.5000 + 33.7750i 0.697765 + 1.20856i
\(782\) 0 0
\(783\) −31.5000 54.5596i −1.12572 1.94980i
\(784\) 0 0
\(785\) 57.0000 2.03442
\(786\) 7.50000 + 12.9904i 0.267516 + 0.463352i
\(787\) 20.0000 0.712923 0.356462 0.934310i \(-0.383983\pi\)
0.356462 + 0.934310i \(0.383983\pi\)
\(788\) −0.500000 0.866025i −0.0178118 0.0308509i
\(789\) 40.5000 + 70.1481i 1.44184 + 2.49734i
\(790\) −4.50000 7.79423i −0.160103 0.277306i
\(791\) 0 0
\(792\) 54.0000 1.91881
\(793\) −45.5000 + 11.2583i −1.61575 + 0.399795i
\(794\) −0.500000 0.866025i −0.0177443 0.0307341i
\(795\) 13.5000 23.3827i 0.478796 0.829298i
\(796\) −20.0000 −0.708881
\(797\) 1.50000 2.59808i 0.0531327 0.0920286i −0.838236 0.545308i \(-0.816413\pi\)
0.891368 + 0.453279i \(0.149746\pi\)
\(798\) 0 0
\(799\) 1.00000 1.73205i 0.0353775 0.0612756i
\(800\) −10.0000 17.3205i −0.353553 0.612372i
\(801\) 18.0000 + 31.1769i 0.635999 + 1.10158i
\(802\) −2.00000 −0.0706225
\(803\) −39.0000 −1.37628
\(804\) −4.50000 7.79423i −0.158703 0.274881i
\(805\) 0 0
\(806\) 10.5000 2.59808i 0.369847 0.0915133i
\(807\) 27.0000 46.7654i 0.950445 1.64622i
\(808\) 7.50000 12.9904i 0.263849 0.457000i
\(809\) −5.50000 + 9.52628i −0.193370 + 0.334926i −0.946365 0.323100i \(-0.895275\pi\)
0.752995 + 0.658026i \(0.228608\pi\)
\(810\) 13.5000 + 23.3827i 0.474342 + 0.821584i
\(811\) 4.00000 0.140459 0.0702295 0.997531i \(-0.477627\pi\)
0.0702295 + 0.997531i \(0.477627\pi\)
\(812\) 0 0
\(813\) −24.0000 + 41.5692i −0.841717 + 1.45790i
\(814\) 3.00000 5.19615i 0.105150 0.182125i
\(815\) 3.00000 0.105085
\(816\) 3.00000 5.19615i 0.105021 0.181902i
\(817\) −7.00000 −0.244899
\(818\) −14.0000 −0.489499
\(819\) 0 0
\(820\) −9.00000 −0.314294
\(821\) −54.0000 −1.88461 −0.942306 0.334751i \(-0.891348\pi\)
−0.942306 + 0.334751i \(0.891348\pi\)
\(822\) −15.0000 + 25.9808i −0.523185 + 0.906183i
\(823\) 40.0000 1.39431 0.697156 0.716919i \(-0.254448\pi\)
0.697156 + 0.716919i \(0.254448\pi\)
\(824\) −7.50000 + 12.9904i −0.261275 + 0.452541i
\(825\) 18.0000 31.1769i 0.626680 1.08544i
\(826\) 0 0
\(827\) 4.00000 0.139094 0.0695468 0.997579i \(-0.477845\pi\)
0.0695468 + 0.997579i \(0.477845\pi\)
\(828\) 0 0
\(829\) 5.50000 9.52628i 0.191023 0.330861i −0.754567 0.656223i \(-0.772153\pi\)
0.945589 + 0.325362i \(0.105486\pi\)
\(830\) 0 0
\(831\) −33.0000 + 57.1577i −1.14476 + 1.98278i
\(832\) 7.00000 24.2487i 0.242681 0.840673i
\(833\) 0 0
\(834\) −22.5000 38.9711i −0.779111 1.34946i
\(835\) −39.0000 −1.34965
\(836\) 3.00000 0.103757
\(837\) 13.5000 + 23.3827i 0.466628 + 0.808224i
\(838\) −12.5000 21.6506i −0.431805 0.747909i
\(839\) 18.5000 32.0429i 0.638691 1.10625i −0.347029 0.937854i \(-0.612810\pi\)
0.985720 0.168391i \(-0.0538571\pi\)
\(840\) 0 0
\(841\) −10.0000 + 17.3205i −0.344828 + 0.597259i
\(842\) 18.0000 0.620321
\(843\) 27.0000 46.7654i 0.929929 1.61068i
\(844\) 3.50000 + 6.06218i 0.120475 + 0.208669i
\(845\) −34.5000 + 18.1865i −1.18684 + 0.625636i
\(846\) −6.00000 −0.206284
\(847\) 0 0
\(848\) 1.50000 + 2.59808i 0.0515102 + 0.0892183i
\(849\) 1.50000 + 2.59808i 0.0514799 + 0.0891657i
\(850\) −4.00000 6.92820i −0.137199 0.237635i
\(851\) 0 0
\(852\) 19.5000 + 33.7750i 0.668059 + 1.15711i
\(853\) 6.00000 0.205436 0.102718 0.994711i \(-0.467246\pi\)
0.102718 + 0.994711i \(0.467246\pi\)
\(854\) 0 0
\(855\) 9.00000 + 15.5885i 0.307794 + 0.533114i
\(856\) −24.0000 −0.820303
\(857\) −16.5000 28.5788i −0.563629 0.976235i −0.997176 0.0751033i \(-0.976071\pi\)
0.433546 0.901131i \(-0.357262\pi\)
\(858\) 31.5000 7.79423i 1.07539 0.266091i
\(859\) 12.5000 21.6506i 0.426494 0.738710i −0.570064 0.821600i \(-0.693082\pi\)
0.996559 + 0.0828900i \(0.0264150\pi\)
\(860\) 10.5000 + 18.1865i 0.358047 + 0.620156i
\(861\) 0 0
\(862\) −4.50000 + 7.79423i −0.153271 + 0.265472i
\(863\) −18.5000 + 32.0429i −0.629747 + 1.09075i 0.357855 + 0.933777i \(0.383508\pi\)
−0.987602 + 0.156977i \(0.949825\pi\)
\(864\) 45.0000 1.53093
\(865\) 57.0000 1.93806
\(866\) 13.5000 23.3827i 0.458749 0.794576i
\(867\) 19.5000 33.7750i 0.662255 1.14706i
\(868\) 0 0
\(869\) −4.50000 7.79423i −0.152652 0.264401i
\(870\) 31.5000 54.5596i 1.06795 1.84974i
\(871\) −7.50000 7.79423i −0.254128 0.264097i
\(872\) 10.5000 + 18.1865i 0.355575 + 0.615874i
\(873\) 30.0000 1.01535
\(874\) 0 0
\(875\) 0 0
\(876\) −39.0000 −1.31769
\(877\) 22.5000 + 38.9711i 0.759771 + 1.31596i 0.942967 + 0.332886i \(0.108022\pi\)
−0.183196 + 0.983076i \(0.558644\pi\)
\(878\) 16.0000 0.539974
\(879\) 16.5000 + 28.5788i 0.556531 + 0.963940i
\(880\) 4.50000 + 7.79423i 0.151695 + 0.262743i
\(881\) 7.50000 + 12.9904i 0.252681 + 0.437657i 0.964263 0.264946i \(-0.0853542\pi\)
−0.711582 + 0.702603i \(0.752021\pi\)
\(882\) 0 0
\(883\) 20.0000 0.673054 0.336527 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) −2.00000 + 6.92820i −0.0672673 + 0.233021i
\(885\) 18.0000 + 31.1769i 0.605063 + 1.04800i
\(886\) 5.50000 9.52628i 0.184776 0.320042i
\(887\) −24.0000 −0.805841 −0.402921 0.915235i \(-0.632005\pi\)
−0.402921 + 0.915235i \(0.632005\pi\)
\(888\) 9.00000 15.5885i 0.302020 0.523114i
\(889\) 0 0
\(890\) −9.00000 + 15.5885i −0.301681 + 0.522526i
\(891\) 13.5000 + 23.3827i 0.452267 + 0.783349i
\(892\) 4.50000 + 7.79423i 0.150671 + 0.260970i
\(893\) −1.00000 −0.0334637
\(894\) 45.0000 1.50503
\(895\) 25.5000 + 44.1673i 0.852371 + 1.47635i
\(896\) 0 0
\(897\) 0 0
\(898\) −7.50000 + 12.9904i −0.250278 + 0.433495i
\(899\) 10.5000 18.1865i 0.350195 0.606555i
\(900\) 12.0000 20.7846i 0.400000 0.692820i
\(901\) −3.00000 5.19615i −0.0999445 0.173109i
\(902\) 9.00000 0.299667
\(903\) 0 0
\(904\) 22.5000 38.9711i 0.748339 1.29616i
\(905\) 33.0000 57.1577i 1.09696 1.89999i
\(906\) −63.0000 −2.09303
\(907\) 23.5000 40.7032i 0.780305 1.35153i −0.151460 0.988463i \(-0.548397\pi\)
0.931764 0.363064i \(-0.118269\pi\)
\(908\) −4.00000 −0.132745
\(909\) 30.0000 0.995037
\(910\) 0 0
\(911\) 48.0000 1.59031 0.795155 0.606406i \(-0.207389\pi\)
0.795155 + 0.606406i \(0.207389\pi\)
\(912\) −3.00000 −0.0993399
\(913\) 0 0
\(914\) −18.0000 −0.595387
\(915\) 58.5000 101.325i 1.93395 3.34970i
\(916\) 6.50000 11.2583i 0.214766 0.371986i
\(917\) 0 0
\(918\) 18.0000 0.594089
\(919\) 12.5000 + 21.6506i 0.412337 + 0.714189i 0.995145 0.0984214i \(-0.0313793\pi\)
−0.582808 + 0.812610i \(0.698046\pi\)
\(920\) 0 0
\(921\) 18.0000 31.1769i 0.593120 1.02731i
\(922\) 17.5000 30.3109i 0.576332 0.998236i
\(923\) 32.5000 + 33.7750i 1.06975 + 1.11172i
\(924\) 0 0
\(925\) −4.00000 6.92820i −0.131519 0.227798i
\(926\) −8.00000 −0.262896
\(927\) −30.0000 −0.985329
\(928\) −17.5000 30.3109i −0.574466 0.995004i
\(929\) −6.50000 11.2583i −0.213258 0.369374i 0.739474 0.673185i \(-0.235074\pi\)
−0.952732 + 0.303811i \(0.901741\pi\)
\(930\) −13.5000 + 23.3827i −0.442682 + 0.766748i
\(931\) 0 0
\(932\) −10.5000 + 18.1865i −0.343939 + 0.595720i
\(933\) 27.0000 0.883940
\(934\) −3.50000 + 6.06218i −0.114523 + 0.198361i
\(935\) −9.00000 15.5885i −0.294331 0.509797i
\(936\) 63.0000 15.5885i 2.05922 0.509525i
\(937\) −22.0000 −0.718709 −0.359354 0.933201i \(-0.617003\pi\)
−0.359354 + 0.933201i \(0.617003\pi\)
\(938\) 0 0
\(939\) 28.5000 + 49.3634i 0.930062 + 1.61092i
\(940\) 1.50000 + 2.59808i 0.0489246 + 0.0847399i
\(941\) −8.50000 14.7224i −0.277092 0.479938i 0.693569 0.720390i \(-0.256037\pi\)
−0.970661 + 0.240453i \(0.922704\pi\)
\(942\) −57.0000 −1.85716
\(943\) 0 0
\(944\) −4.00000 −0.130189
\(945\) 0 0
\(946\) −10.5000 18.1865i −0.341384 0.591295i
\(947\) −12.0000 −0.389948 −0.194974 0.980808i \(-0.562462\pi\)
−0.194974 + 0.980808i \(0.562462\pi\)
\(948\) −4.50000 7.79423i −0.146153 0.253145i
\(949\) −45.5000 + 11.2583i −1.47699 + 0.365461i
\(950\) −2.00000 + 3.46410i −0.0648886 + 0.112390i
\(951\) 13.5000 + 23.3827i 0.437767 + 0.758236i
\(952\) 0 0
\(953\) 16.5000 28.5788i 0.534487 0.925759i −0.464701 0.885468i \(-0.653838\pi\)
0.999188 0.0402915i \(-0.0128286\pi\)
\(954\) −9.00000 + 15.5885i −0.291386 + 0.504695i
\(955\) 51.0000 1.65032
\(956\) 4.00000 0.129369
\(957\) 31.5000 54.5596i 1.01825 1.76366i
\(958\) −17.5000 + 30.3109i −0.565399 + 0.979300i
\(959\) 0 0
\(960\) 31.5000 + 54.5596i 1.01666 + 1.76090i
\(961\) 11.0000 19.0526i 0.354839 0.614599i
\(962\) 2.00000 6.92820i 0.0644826 0.223374i
\(963\) −24.0000 41.5692i −0.773389 1.33955i
\(964\) −26.0000 −0.837404
\(965\) 10.5000 + 18.1865i 0.338007 + 0.585445i
\(966\) 0 0
\(967\) −8.00000 −0.257263 −0.128631 0.991692i \(-0.541058\pi\)
−0.128631 + 0.991692i \(0.541058\pi\)
\(968\) −3.00000 5.19615i −0.0964237 0.167011i
\(969\) 6.00000 0.192748
\(970\) 7.50000 + 12.9904i 0.240810 + 0.417096i
\(971\) −0.500000 0.866025i −0.0160458 0.0277921i 0.857891 0.513832i \(-0.171774\pi\)
−0.873937 + 0.486040i \(0.838441\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 16.0000 0.512673
\(975\) 12.0000 41.5692i 0.384308 1.33128i
\(976\) 6.50000 + 11.2583i 0.208060 + 0.360370i
\(977\) 2.50000 4.33013i 0.0799821 0.138533i −0.823260 0.567665i \(-0.807847\pi\)
0.903242 + 0.429132i \(0.141180\pi\)
\(978\) −3.00000 −0.0959294
\(979\) −9.00000 + 15.5885i −0.287641 + 0.498209i
\(980\) 0 0
\(981\) −21.0000 + 36.3731i −0.670478 + 1.16130i
\(982\) −7.50000 12.9904i −0.239335 0.414540i
\(983\) 23.5000 + 40.7032i 0.749534 + 1.29823i 0.948046 + 0.318132i \(0.103056\pi\)
−0.198513 + 0.980098i \(0.563611\pi\)
\(984\) 27.0000 0.860729
\(985\) 3.00000 0.0955879
\(986\) −7.00000 12.1244i −0.222925 0.386118i
\(987\) 0 0
\(988\) 3.50000 0.866025i 0.111350 0.0275519i
\(989\) 0 0
\(990\) −27.0000 + 46.7654i −0.858116 + 1.48630i
\(991\) −6.50000 + 11.2583i −0.206479 + 0.357633i −0.950603 0.310409i \(-0.899534\pi\)
0.744124 + 0.668042i \(0.232867\pi\)
\(992\) 7.50000 + 12.9904i 0.238125 + 0.412445i
\(993\) −87.0000 −2.76086
\(994\) 0 0
\(995\) 30.0000 51.9615i 0.951064 1.64729i
\(996\) 0 0
\(997\) −2.00000 −0.0633406 −0.0316703 0.999498i \(-0.510083\pi\)
−0.0316703 + 0.999498i \(0.510083\pi\)
\(998\) 15.5000 26.8468i 0.490644 0.849820i
\(999\) 18.0000 0.569495
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 637.2.h.a.471.1 2
7.2 even 3 637.2.f.a.393.1 2
7.3 odd 6 91.2.g.a.81.1 yes 2
7.4 even 3 637.2.g.a.263.1 2
7.5 odd 6 637.2.f.b.393.1 2
7.6 odd 2 91.2.h.a.16.1 yes 2
13.9 even 3 637.2.g.a.373.1 2
21.17 even 6 819.2.n.c.172.1 2
21.20 even 2 819.2.s.a.289.1 2
91.3 odd 6 1183.2.e.a.508.1 2
91.9 even 3 637.2.f.a.295.1 2
91.10 odd 6 1183.2.e.c.508.1 2
91.16 even 3 8281.2.a.j.1.1 1
91.23 even 6 8281.2.a.g.1.1 1
91.48 odd 6 91.2.g.a.9.1 2
91.55 odd 6 1183.2.e.a.170.1 2
91.61 odd 6 637.2.f.b.295.1 2
91.62 odd 6 1183.2.e.c.170.1 2
91.68 odd 6 8281.2.a.i.1.1 1
91.74 even 3 inner 637.2.h.a.165.1 2
91.75 odd 6 8281.2.a.c.1.1 1
91.87 odd 6 91.2.h.a.74.1 yes 2
273.230 even 6 819.2.n.c.100.1 2
273.269 even 6 819.2.s.a.802.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.g.a.9.1 2 91.48 odd 6
91.2.g.a.81.1 yes 2 7.3 odd 6
91.2.h.a.16.1 yes 2 7.6 odd 2
91.2.h.a.74.1 yes 2 91.87 odd 6
637.2.f.a.295.1 2 91.9 even 3
637.2.f.a.393.1 2 7.2 even 3
637.2.f.b.295.1 2 91.61 odd 6
637.2.f.b.393.1 2 7.5 odd 6
637.2.g.a.263.1 2 7.4 even 3
637.2.g.a.373.1 2 13.9 even 3
637.2.h.a.165.1 2 91.74 even 3 inner
637.2.h.a.471.1 2 1.1 even 1 trivial
819.2.n.c.100.1 2 273.230 even 6
819.2.n.c.172.1 2 21.17 even 6
819.2.s.a.289.1 2 21.20 even 2
819.2.s.a.802.1 2 273.269 even 6
1183.2.e.a.170.1 2 91.55 odd 6
1183.2.e.a.508.1 2 91.3 odd 6
1183.2.e.c.170.1 2 91.62 odd 6
1183.2.e.c.508.1 2 91.10 odd 6
8281.2.a.c.1.1 1 91.75 odd 6
8281.2.a.g.1.1 1 91.23 even 6
8281.2.a.i.1.1 1 91.68 odd 6
8281.2.a.j.1.1 1 91.16 even 3