Properties

Label 637.2.h.f.165.2
Level $637$
Weight $2$
Character 637.165
Analytic conductor $5.086$
Analytic rank $0$
Dimension $4$
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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 2x^{2} + x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 165.2
Root \(0.809017 - 1.40126i\) of defining polynomial
Character \(\chi\) \(=\) 637.165
Dual form 637.2.h.f.471.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.61803 q^{2} +(-1.30902 - 2.26728i) q^{3} +4.85410 q^{4} +(1.30902 + 2.26728i) q^{5} +(-3.42705 - 5.93583i) q^{6} +7.47214 q^{8} +(-1.92705 + 3.33775i) q^{9} +O(q^{10})\) \(q+2.61803 q^{2} +(-1.30902 - 2.26728i) q^{3} +4.85410 q^{4} +(1.30902 + 2.26728i) q^{5} +(-3.42705 - 5.93583i) q^{6} +7.47214 q^{8} +(-1.92705 + 3.33775i) q^{9} +(3.42705 + 5.93583i) q^{10} +(-0.927051 - 1.60570i) q^{11} +(-6.35410 - 11.0056i) q^{12} +(2.50000 - 2.59808i) q^{13} +(3.42705 - 5.93583i) q^{15} +9.85410 q^{16} +1.47214 q^{17} +(-5.04508 + 8.73834i) q^{18} +(-0.927051 + 1.60570i) q^{19} +(6.35410 + 11.0056i) q^{20} +(-2.42705 - 4.20378i) q^{22} -4.47214 q^{23} +(-9.78115 - 16.9415i) q^{24} +(-0.927051 + 1.60570i) q^{25} +(6.54508 - 6.80185i) q^{26} +2.23607 q^{27} +(-3.54508 + 6.14027i) q^{29} +(8.97214 - 15.5402i) q^{30} +(-2.35410 + 4.07742i) q^{31} +10.8541 q^{32} +(-2.42705 + 4.20378i) q^{33} +3.85410 q^{34} +(-9.35410 + 16.2018i) q^{36} +4.00000 q^{37} +(-2.42705 + 4.20378i) q^{38} +(-9.16312 - 2.26728i) q^{39} +(9.78115 + 16.9415i) q^{40} +(0.381966 - 0.661585i) q^{41} +(-6.28115 - 10.8793i) q^{43} +(-4.50000 - 7.79423i) q^{44} -10.0902 q^{45} -11.7082 q^{46} +(-1.11803 - 1.93649i) q^{47} +(-12.8992 - 22.3420i) q^{48} +(-2.42705 + 4.20378i) q^{50} +(-1.92705 - 3.33775i) q^{51} +(12.1353 - 12.6113i) q^{52} +(-1.88197 + 3.25966i) q^{53} +5.85410 q^{54} +(2.42705 - 4.20378i) q^{55} +4.85410 q^{57} +(-9.28115 + 16.0754i) q^{58} +2.23607 q^{59} +(16.6353 - 28.8131i) q^{60} +(-3.00000 + 5.19615i) q^{61} +(-6.16312 + 10.6748i) q^{62} +8.70820 q^{64} +(9.16312 + 2.26728i) q^{65} +(-6.35410 + 11.0056i) q^{66} +(6.35410 + 11.0056i) q^{67} +7.14590 q^{68} +(5.85410 + 10.1396i) q^{69} +(7.09017 + 12.2805i) q^{71} +(-14.3992 + 24.9401i) q^{72} +(-1.00000 + 1.73205i) q^{73} +10.4721 q^{74} +4.85410 q^{75} +(-4.50000 + 7.79423i) q^{76} +(-23.9894 - 5.93583i) q^{78} +(-2.00000 - 3.46410i) q^{79} +(12.8992 + 22.3420i) q^{80} +(2.85410 + 4.94345i) q^{81} +(1.00000 - 1.73205i) q^{82} -6.70820 q^{83} +(1.92705 + 3.33775i) q^{85} +(-16.4443 - 28.4823i) q^{86} +18.5623 q^{87} +(-6.92705 - 11.9980i) q^{88} -4.90983 q^{89} -26.4164 q^{90} -21.7082 q^{92} +12.3262 q^{93} +(-2.92705 - 5.06980i) q^{94} -4.85410 q^{95} +(-14.2082 - 24.6093i) q^{96} +(9.42705 + 16.3281i) q^{97} +7.14590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 6 q^{2} - 3 q^{3} + 6 q^{4} + 3 q^{5} - 7 q^{6} + 12 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 6 q^{2} - 3 q^{3} + 6 q^{4} + 3 q^{5} - 7 q^{6} + 12 q^{8} - q^{9} + 7 q^{10} + 3 q^{11} - 12 q^{12} + 10 q^{13} + 7 q^{15} + 26 q^{16} - 12 q^{17} - 9 q^{18} + 3 q^{19} + 12 q^{20} - 3 q^{22} - 19 q^{24} + 3 q^{25} + 15 q^{26} - 3 q^{29} + 18 q^{30} + 4 q^{31} + 30 q^{32} - 3 q^{33} + 2 q^{34} - 24 q^{36} + 16 q^{37} - 3 q^{38} - 21 q^{39} + 19 q^{40} + 6 q^{41} - 5 q^{43} - 18 q^{44} - 18 q^{45} - 20 q^{46} - 27 q^{48} - 3 q^{50} - q^{51} + 15 q^{52} - 12 q^{53} + 10 q^{54} + 3 q^{55} + 6 q^{57} - 17 q^{58} + 33 q^{60} - 12 q^{61} - 9 q^{62} + 8 q^{64} + 21 q^{65} - 12 q^{66} + 12 q^{67} + 42 q^{68} + 10 q^{69} + 6 q^{71} - 33 q^{72} - 4 q^{73} + 24 q^{74} + 6 q^{75} - 18 q^{76} - 49 q^{78} - 8 q^{79} + 27 q^{80} - 2 q^{81} + 4 q^{82} + q^{85} - 30 q^{86} + 34 q^{87} - 21 q^{88} - 42 q^{89} - 52 q^{90} - 60 q^{92} + 18 q^{93} - 5 q^{94} - 6 q^{95} - 30 q^{96} + 31 q^{97} + 42 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.61803 1.85123 0.925615 0.378467i \(-0.123549\pi\)
0.925615 + 0.378467i \(0.123549\pi\)
\(3\) −1.30902 2.26728i −0.755761 1.30902i −0.944995 0.327085i \(-0.893934\pi\)
0.189234 0.981932i \(-0.439400\pi\)
\(4\) 4.85410 2.42705
\(5\) 1.30902 + 2.26728i 0.585410 + 1.01396i 0.994824 + 0.101611i \(0.0323999\pi\)
−0.409414 + 0.912349i \(0.634267\pi\)
\(6\) −3.42705 5.93583i −1.39909 2.42329i
\(7\) 0 0
\(8\) 7.47214 2.64180
\(9\) −1.92705 + 3.33775i −0.642350 + 1.11258i
\(10\) 3.42705 + 5.93583i 1.08373 + 1.87707i
\(11\) −0.927051 1.60570i −0.279516 0.484137i 0.691748 0.722139i \(-0.256841\pi\)
−0.971265 + 0.238002i \(0.923507\pi\)
\(12\) −6.35410 11.0056i −1.83427 3.17705i
\(13\) 2.50000 2.59808i 0.693375 0.720577i
\(14\) 0 0
\(15\) 3.42705 5.93583i 0.884861 1.53262i
\(16\) 9.85410 2.46353
\(17\) 1.47214 0.357045 0.178523 0.983936i \(-0.442868\pi\)
0.178523 + 0.983936i \(0.442868\pi\)
\(18\) −5.04508 + 8.73834i −1.18914 + 2.05965i
\(19\) −0.927051 + 1.60570i −0.212680 + 0.368373i −0.952552 0.304375i \(-0.901553\pi\)
0.739872 + 0.672747i \(0.234886\pi\)
\(20\) 6.35410 + 11.0056i 1.42082 + 2.46093i
\(21\) 0 0
\(22\) −2.42705 4.20378i −0.517449 0.896248i
\(23\) −4.47214 −0.932505 −0.466252 0.884652i \(-0.654396\pi\)
−0.466252 + 0.884652i \(0.654396\pi\)
\(24\) −9.78115 16.9415i −1.99657 3.45816i
\(25\) −0.927051 + 1.60570i −0.185410 + 0.321140i
\(26\) 6.54508 6.80185i 1.28360 1.33395i
\(27\) 2.23607 0.430331
\(28\) 0 0
\(29\) −3.54508 + 6.14027i −0.658306 + 1.14022i 0.322748 + 0.946485i \(0.395393\pi\)
−0.981054 + 0.193734i \(0.937940\pi\)
\(30\) 8.97214 15.5402i 1.63808 2.83724i
\(31\) −2.35410 + 4.07742i −0.422809 + 0.732327i −0.996213 0.0869459i \(-0.972289\pi\)
0.573404 + 0.819273i \(0.305623\pi\)
\(32\) 10.8541 1.91875
\(33\) −2.42705 + 4.20378i −0.422495 + 0.731783i
\(34\) 3.85410 0.660973
\(35\) 0 0
\(36\) −9.35410 + 16.2018i −1.55902 + 2.70030i
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) −2.42705 + 4.20378i −0.393720 + 0.681942i
\(39\) −9.16312 2.26728i −1.46727 0.363056i
\(40\) 9.78115 + 16.9415i 1.54654 + 2.67868i
\(41\) 0.381966 0.661585i 0.0596531 0.103322i −0.834657 0.550771i \(-0.814334\pi\)
0.894310 + 0.447449i \(0.147667\pi\)
\(42\) 0 0
\(43\) −6.28115 10.8793i −0.957867 1.65907i −0.727667 0.685931i \(-0.759395\pi\)
−0.230200 0.973143i \(-0.573938\pi\)
\(44\) −4.50000 7.79423i −0.678401 1.17502i
\(45\) −10.0902 −1.50415
\(46\) −11.7082 −1.72628
\(47\) −1.11803 1.93649i −0.163082 0.282466i 0.772890 0.634539i \(-0.218810\pi\)
−0.935973 + 0.352073i \(0.885477\pi\)
\(48\) −12.8992 22.3420i −1.86184 3.22480i
\(49\) 0 0
\(50\) −2.42705 + 4.20378i −0.343237 + 0.594504i
\(51\) −1.92705 3.33775i −0.269841 0.467379i
\(52\) 12.1353 12.6113i 1.68286 1.74888i
\(53\) −1.88197 + 3.25966i −0.258508 + 0.447749i −0.965842 0.259130i \(-0.916564\pi\)
0.707334 + 0.706879i \(0.249897\pi\)
\(54\) 5.85410 0.796642
\(55\) 2.42705 4.20378i 0.327263 0.566837i
\(56\) 0 0
\(57\) 4.85410 0.642942
\(58\) −9.28115 + 16.0754i −1.21868 + 2.11081i
\(59\) 2.23607 0.291111 0.145556 0.989350i \(-0.453503\pi\)
0.145556 + 0.989350i \(0.453503\pi\)
\(60\) 16.6353 28.8131i 2.14760 3.71976i
\(61\) −3.00000 + 5.19615i −0.384111 + 0.665299i −0.991645 0.128994i \(-0.958825\pi\)
0.607535 + 0.794293i \(0.292159\pi\)
\(62\) −6.16312 + 10.6748i −0.782717 + 1.35571i
\(63\) 0 0
\(64\) 8.70820 1.08853
\(65\) 9.16312 + 2.26728i 1.13655 + 0.281222i
\(66\) −6.35410 + 11.0056i −0.782136 + 1.35470i
\(67\) 6.35410 + 11.0056i 0.776277 + 1.34455i 0.934074 + 0.357080i \(0.116228\pi\)
−0.157797 + 0.987472i \(0.550439\pi\)
\(68\) 7.14590 0.866567
\(69\) 5.85410 + 10.1396i 0.704751 + 1.22066i
\(70\) 0 0
\(71\) 7.09017 + 12.2805i 0.841448 + 1.45743i 0.888670 + 0.458547i \(0.151630\pi\)
−0.0472218 + 0.998884i \(0.515037\pi\)
\(72\) −14.3992 + 24.9401i −1.69696 + 2.93922i
\(73\) −1.00000 + 1.73205i −0.117041 + 0.202721i −0.918594 0.395203i \(-0.870674\pi\)
0.801553 + 0.597924i \(0.204008\pi\)
\(74\) 10.4721 1.21736
\(75\) 4.85410 0.560503
\(76\) −4.50000 + 7.79423i −0.516185 + 0.894059i
\(77\) 0 0
\(78\) −23.9894 5.93583i −2.71626 0.672100i
\(79\) −2.00000 3.46410i −0.225018 0.389742i 0.731307 0.682048i \(-0.238911\pi\)
−0.956325 + 0.292306i \(0.905577\pi\)
\(80\) 12.8992 + 22.3420i 1.44217 + 2.49792i
\(81\) 2.85410 + 4.94345i 0.317122 + 0.549272i
\(82\) 1.00000 1.73205i 0.110432 0.191273i
\(83\) −6.70820 −0.736321 −0.368161 0.929762i \(-0.620012\pi\)
−0.368161 + 0.929762i \(0.620012\pi\)
\(84\) 0 0
\(85\) 1.92705 + 3.33775i 0.209018 + 0.362030i
\(86\) −16.4443 28.4823i −1.77323 3.07133i
\(87\) 18.5623 1.99009
\(88\) −6.92705 11.9980i −0.738426 1.27899i
\(89\) −4.90983 −0.520441 −0.260220 0.965549i \(-0.583795\pi\)
−0.260220 + 0.965549i \(0.583795\pi\)
\(90\) −26.4164 −2.78453
\(91\) 0 0
\(92\) −21.7082 −2.26324
\(93\) 12.3262 1.27817
\(94\) −2.92705 5.06980i −0.301902 0.522910i
\(95\) −4.85410 −0.498020
\(96\) −14.2082 24.6093i −1.45012 2.51168i
\(97\) 9.42705 + 16.3281i 0.957172 + 1.65787i 0.729318 + 0.684175i \(0.239838\pi\)
0.227854 + 0.973695i \(0.426829\pi\)
\(98\) 0 0
\(99\) 7.14590 0.718190
\(100\) −4.50000 + 7.79423i −0.450000 + 0.779423i
\(101\) −5.78115 10.0133i −0.575246 0.996356i −0.996015 0.0891877i \(-0.971573\pi\)
0.420769 0.907168i \(-0.361760\pi\)
\(102\) −5.04508 8.73834i −0.499538 0.865225i
\(103\) −4.35410 7.54153i −0.429022 0.743089i 0.567764 0.823191i \(-0.307809\pi\)
−0.996787 + 0.0801026i \(0.974475\pi\)
\(104\) 18.6803 19.4132i 1.83176 1.90362i
\(105\) 0 0
\(106\) −4.92705 + 8.53390i −0.478557 + 0.828886i
\(107\) −3.38197 −0.326947 −0.163473 0.986548i \(-0.552270\pi\)
−0.163473 + 0.986548i \(0.552270\pi\)
\(108\) 10.8541 1.04444
\(109\) 1.35410 2.34537i 0.129699 0.224646i −0.793861 0.608100i \(-0.791932\pi\)
0.923560 + 0.383454i \(0.125265\pi\)
\(110\) 6.35410 11.0056i 0.605840 1.04935i
\(111\) −5.23607 9.06914i −0.496986 0.860804i
\(112\) 0 0
\(113\) −0.736068 1.27491i −0.0692435 0.119933i 0.829325 0.558766i \(-0.188725\pi\)
−0.898568 + 0.438833i \(0.855392\pi\)
\(114\) 12.7082 1.19023
\(115\) −5.85410 10.1396i −0.545898 0.945523i
\(116\) −17.2082 + 29.8055i −1.59774 + 2.76737i
\(117\) 3.85410 + 13.3510i 0.356312 + 1.23430i
\(118\) 5.85410 0.538914
\(119\) 0 0
\(120\) 25.6074 44.3533i 2.33762 4.04888i
\(121\) 3.78115 6.54915i 0.343741 0.595377i
\(122\) −7.85410 + 13.6037i −0.711077 + 1.23162i
\(123\) −2.00000 −0.180334
\(124\) −11.4271 + 19.7922i −1.02618 + 1.77739i
\(125\) 8.23607 0.736656
\(126\) 0 0
\(127\) 10.4271 18.0602i 0.925251 1.60258i 0.134094 0.990969i \(-0.457187\pi\)
0.791157 0.611613i \(-0.209479\pi\)
\(128\) 1.09017 0.0963583
\(129\) −16.4443 + 28.4823i −1.44784 + 2.50773i
\(130\) 23.9894 + 5.93583i 2.10401 + 0.520606i
\(131\) −7.66312 13.2729i −0.669530 1.15966i −0.978036 0.208437i \(-0.933162\pi\)
0.308506 0.951222i \(-0.400171\pi\)
\(132\) −11.7812 + 20.4056i −1.02542 + 1.77608i
\(133\) 0 0
\(134\) 16.6353 + 28.8131i 1.43707 + 2.48907i
\(135\) 2.92705 + 5.06980i 0.251920 + 0.436339i
\(136\) 11.0000 0.943242
\(137\) −2.61803 −0.223674 −0.111837 0.993727i \(-0.535673\pi\)
−0.111837 + 0.993727i \(0.535673\pi\)
\(138\) 15.3262 + 26.5458i 1.30466 + 2.25973i
\(139\) 2.28115 + 3.95107i 0.193485 + 0.335126i 0.946403 0.322989i \(-0.104688\pi\)
−0.752918 + 0.658114i \(0.771354\pi\)
\(140\) 0 0
\(141\) −2.92705 + 5.06980i −0.246502 + 0.426954i
\(142\) 18.5623 + 32.1509i 1.55771 + 2.69804i
\(143\) −6.48936 1.60570i −0.542667 0.134275i
\(144\) −18.9894 + 32.8905i −1.58245 + 2.74088i
\(145\) −18.5623 −1.54152
\(146\) −2.61803 + 4.53457i −0.216670 + 0.375284i
\(147\) 0 0
\(148\) 19.4164 1.59602
\(149\) −0.927051 + 1.60570i −0.0759470 + 0.131544i −0.901498 0.432784i \(-0.857531\pi\)
0.825551 + 0.564328i \(0.190865\pi\)
\(150\) 12.7082 1.03762
\(151\) 0.645898 1.11873i 0.0525624 0.0910408i −0.838547 0.544829i \(-0.816594\pi\)
0.891109 + 0.453788i \(0.149928\pi\)
\(152\) −6.92705 + 11.9980i −0.561858 + 0.973167i
\(153\) −2.83688 + 4.91362i −0.229348 + 0.397243i
\(154\) 0 0
\(155\) −12.3262 −0.990067
\(156\) −44.4787 11.0056i −3.56115 0.881155i
\(157\) 7.42705 12.8640i 0.592743 1.02666i −0.401118 0.916026i \(-0.631378\pi\)
0.993861 0.110635i \(-0.0352884\pi\)
\(158\) −5.23607 9.06914i −0.416559 0.721502i
\(159\) 9.85410 0.781481
\(160\) 14.2082 + 24.6093i 1.12326 + 1.94554i
\(161\) 0 0
\(162\) 7.47214 + 12.9421i 0.587066 + 1.01683i
\(163\) 1.85410 3.21140i 0.145224 0.251536i −0.784232 0.620467i \(-0.786943\pi\)
0.929457 + 0.368931i \(0.120276\pi\)
\(164\) 1.85410 3.21140i 0.144781 0.250768i
\(165\) −12.7082 −0.989332
\(166\) −17.5623 −1.36310
\(167\) 7.11803 12.3288i 0.550810 0.954031i −0.447406 0.894331i \(-0.647652\pi\)
0.998216 0.0597001i \(-0.0190144\pi\)
\(168\) 0 0
\(169\) −0.500000 12.9904i −0.0384615 0.999260i
\(170\) 5.04508 + 8.73834i 0.386940 + 0.670200i
\(171\) −3.57295 6.18853i −0.273230 0.473249i
\(172\) −30.4894 52.8091i −2.32479 4.02666i
\(173\) −4.50000 + 7.79423i −0.342129 + 0.592584i −0.984828 0.173534i \(-0.944481\pi\)
0.642699 + 0.766119i \(0.277815\pi\)
\(174\) 48.5967 3.68411
\(175\) 0 0
\(176\) −9.13525 15.8227i −0.688596 1.19268i
\(177\) −2.92705 5.06980i −0.220011 0.381070i
\(178\) −12.8541 −0.963456
\(179\) 4.50000 + 7.79423i 0.336346 + 0.582568i 0.983742 0.179585i \(-0.0574756\pi\)
−0.647397 + 0.762153i \(0.724142\pi\)
\(180\) −48.9787 −3.65066
\(181\) −9.70820 −0.721605 −0.360803 0.932642i \(-0.617497\pi\)
−0.360803 + 0.932642i \(0.617497\pi\)
\(182\) 0 0
\(183\) 15.7082 1.16118
\(184\) −33.4164 −2.46349
\(185\) 5.23607 + 9.06914i 0.384963 + 0.666776i
\(186\) 32.2705 2.36619
\(187\) −1.36475 2.36381i −0.0998000 0.172859i
\(188\) −5.42705 9.39993i −0.395808 0.685560i
\(189\) 0 0
\(190\) −12.7082 −0.921950
\(191\) −10.6910 + 18.5173i −0.773572 + 1.33987i 0.162021 + 0.986787i \(0.448199\pi\)
−0.935593 + 0.353079i \(0.885135\pi\)
\(192\) −11.3992 19.7440i −0.822665 1.42490i
\(193\) 3.00000 + 5.19615i 0.215945 + 0.374027i 0.953564 0.301189i \(-0.0973836\pi\)
−0.737620 + 0.675216i \(0.764050\pi\)
\(194\) 24.6803 + 42.7476i 1.77195 + 3.06910i
\(195\) −6.85410 23.7433i −0.490832 1.70029i
\(196\) 0 0
\(197\) 8.39919 14.5478i 0.598417 1.03649i −0.394638 0.918837i \(-0.629130\pi\)
0.993055 0.117652i \(-0.0375368\pi\)
\(198\) 18.7082 1.32953
\(199\) 24.4164 1.73083 0.865417 0.501053i \(-0.167054\pi\)
0.865417 + 0.501053i \(0.167054\pi\)
\(200\) −6.92705 + 11.9980i −0.489816 + 0.848387i
\(201\) 16.6353 28.8131i 1.17336 2.03232i
\(202\) −15.1353 26.2150i −1.06491 1.84448i
\(203\) 0 0
\(204\) −9.35410 16.2018i −0.654918 1.13435i
\(205\) 2.00000 0.139686
\(206\) −11.3992 19.7440i −0.794219 1.37563i
\(207\) 8.61803 14.9269i 0.598995 1.03749i
\(208\) 24.6353 25.6017i 1.70815 1.77516i
\(209\) 3.43769 0.237790
\(210\) 0 0
\(211\) −2.35410 + 4.07742i −0.162063 + 0.280701i −0.935608 0.353039i \(-0.885148\pi\)
0.773545 + 0.633741i \(0.218481\pi\)
\(212\) −9.13525 + 15.8227i −0.627412 + 1.08671i
\(213\) 18.5623 32.1509i 1.27187 2.20294i
\(214\) −8.85410 −0.605254
\(215\) 16.4443 28.4823i 1.12149 1.94248i
\(216\) 16.7082 1.13685
\(217\) 0 0
\(218\) 3.54508 6.14027i 0.240103 0.415871i
\(219\) 5.23607 0.353821
\(220\) 11.7812 20.4056i 0.794285 1.37574i
\(221\) 3.68034 3.82472i 0.247566 0.257279i
\(222\) −13.7082 23.7433i −0.920034 1.59355i
\(223\) 10.1353 17.5548i 0.678707 1.17555i −0.296664 0.954982i \(-0.595874\pi\)
0.975371 0.220573i \(-0.0707926\pi\)
\(224\) 0 0
\(225\) −3.57295 6.18853i −0.238197 0.412569i
\(226\) −1.92705 3.33775i −0.128186 0.222024i
\(227\) −1.47214 −0.0977091 −0.0488545 0.998806i \(-0.515557\pi\)
−0.0488545 + 0.998806i \(0.515557\pi\)
\(228\) 23.5623 1.56045
\(229\) −6.56231 11.3662i −0.433649 0.751103i 0.563535 0.826092i \(-0.309441\pi\)
−0.997184 + 0.0749895i \(0.976108\pi\)
\(230\) −15.3262 26.5458i −1.01058 1.75038i
\(231\) 0 0
\(232\) −26.4894 + 45.8809i −1.73911 + 3.01223i
\(233\) −1.30902 2.26728i −0.0857566 0.148535i 0.819957 0.572425i \(-0.193997\pi\)
−0.905713 + 0.423891i \(0.860664\pi\)
\(234\) 10.0902 + 34.9534i 0.659615 + 2.28497i
\(235\) 2.92705 5.06980i 0.190940 0.330717i
\(236\) 10.8541 0.706542
\(237\) −5.23607 + 9.06914i −0.340119 + 0.589104i
\(238\) 0 0
\(239\) −24.7082 −1.59824 −0.799120 0.601171i \(-0.794701\pi\)
−0.799120 + 0.601171i \(0.794701\pi\)
\(240\) 33.7705 58.4922i 2.17988 3.77566i
\(241\) −24.5623 −1.58220 −0.791099 0.611689i \(-0.790491\pi\)
−0.791099 + 0.611689i \(0.790491\pi\)
\(242\) 9.89919 17.1459i 0.636344 1.10218i
\(243\) 10.8262 18.7516i 0.694503 1.20292i
\(244\) −14.5623 + 25.2227i −0.932256 + 1.61471i
\(245\) 0 0
\(246\) −5.23607 −0.333840
\(247\) 1.85410 + 6.42280i 0.117974 + 0.408673i
\(248\) −17.5902 + 30.4671i −1.11698 + 1.93466i
\(249\) 8.78115 + 15.2094i 0.556483 + 0.963857i
\(250\) 21.5623 1.36372
\(251\) 0.381966 + 0.661585i 0.0241095 + 0.0417588i 0.877828 0.478975i \(-0.158992\pi\)
−0.853719 + 0.520734i \(0.825658\pi\)
\(252\) 0 0
\(253\) 4.14590 + 7.18091i 0.260650 + 0.451460i
\(254\) 27.2984 47.2822i 1.71285 2.96675i
\(255\) 5.04508 8.73834i 0.315935 0.547216i
\(256\) −14.5623 −0.910144
\(257\) −16.7426 −1.04438 −0.522189 0.852830i \(-0.674884\pi\)
−0.522189 + 0.852830i \(0.674884\pi\)
\(258\) −43.0517 + 74.5677i −2.68028 + 4.64238i
\(259\) 0 0
\(260\) 44.4787 + 11.0056i 2.75845 + 0.682540i
\(261\) −13.6631 23.6652i −0.845726 1.46484i
\(262\) −20.0623 34.7489i −1.23945 2.14680i
\(263\) −4.50000 7.79423i −0.277482 0.480613i 0.693276 0.720672i \(-0.256167\pi\)
−0.970758 + 0.240059i \(0.922833\pi\)
\(264\) −18.1353 + 31.4112i −1.11615 + 1.93322i
\(265\) −9.85410 −0.605333
\(266\) 0 0
\(267\) 6.42705 + 11.1320i 0.393329 + 0.681266i
\(268\) 30.8435 + 53.4224i 1.88406 + 3.26329i
\(269\) 28.7426 1.75247 0.876235 0.481884i \(-0.160047\pi\)
0.876235 + 0.481884i \(0.160047\pi\)
\(270\) 7.66312 + 13.2729i 0.466363 + 0.807764i
\(271\) 8.41641 0.511260 0.255630 0.966775i \(-0.417717\pi\)
0.255630 + 0.966775i \(0.417717\pi\)
\(272\) 14.5066 0.879590
\(273\) 0 0
\(274\) −6.85410 −0.414071
\(275\) 3.43769 0.207301
\(276\) 28.4164 + 49.2187i 1.71047 + 2.96262i
\(277\) −5.00000 −0.300421 −0.150210 0.988654i \(-0.547995\pi\)
−0.150210 + 0.988654i \(0.547995\pi\)
\(278\) 5.97214 + 10.3440i 0.358185 + 0.620394i
\(279\) −9.07295 15.7148i −0.543183 0.940821i
\(280\) 0 0
\(281\) 20.1803 1.20386 0.601929 0.798550i \(-0.294399\pi\)
0.601929 + 0.798550i \(0.294399\pi\)
\(282\) −7.66312 + 13.2729i −0.456332 + 0.790390i
\(283\) 6.70820 + 11.6190i 0.398761 + 0.690675i 0.993573 0.113190i \(-0.0361069\pi\)
−0.594812 + 0.803865i \(0.702774\pi\)
\(284\) 34.4164 + 59.6110i 2.04224 + 3.53726i
\(285\) 6.35410 + 11.0056i 0.376385 + 0.651917i
\(286\) −16.9894 4.20378i −1.00460 0.248574i
\(287\) 0 0
\(288\) −20.9164 + 36.2283i −1.23251 + 2.13477i
\(289\) −14.8328 −0.872519
\(290\) −48.5967 −2.85370
\(291\) 24.6803 42.7476i 1.44679 2.50591i
\(292\) −4.85410 + 8.40755i −0.284065 + 0.492015i
\(293\) −3.38197 5.85774i −0.197577 0.342213i 0.750166 0.661250i \(-0.229974\pi\)
−0.947742 + 0.319037i \(0.896640\pi\)
\(294\) 0 0
\(295\) 2.92705 + 5.06980i 0.170419 + 0.295175i
\(296\) 29.8885 1.73724
\(297\) −2.07295 3.59045i −0.120285 0.208339i
\(298\) −2.42705 + 4.20378i −0.140595 + 0.243518i
\(299\) −11.1803 + 11.6190i −0.646576 + 0.671941i
\(300\) 23.5623 1.36037
\(301\) 0 0
\(302\) 1.69098 2.92887i 0.0973051 0.168537i
\(303\) −15.1353 + 26.2150i −0.869498 + 1.50601i
\(304\) −9.13525 + 15.8227i −0.523943 + 0.907496i
\(305\) −15.7082 −0.899449
\(306\) −7.42705 + 12.8640i −0.424576 + 0.735388i
\(307\) 4.85410 0.277038 0.138519 0.990360i \(-0.455766\pi\)
0.138519 + 0.990360i \(0.455766\pi\)
\(308\) 0 0
\(309\) −11.3992 + 19.7440i −0.648477 + 1.12320i
\(310\) −32.2705 −1.83284
\(311\) 1.66312 2.88061i 0.0943068 0.163344i −0.815012 0.579444i \(-0.803270\pi\)
0.909319 + 0.416099i \(0.136603\pi\)
\(312\) −68.4681 16.9415i −3.87624 0.959121i
\(313\) 12.5623 + 21.7586i 0.710064 + 1.22987i 0.964833 + 0.262864i \(0.0846671\pi\)
−0.254769 + 0.967002i \(0.582000\pi\)
\(314\) 19.4443 33.6785i 1.09730 1.90059i
\(315\) 0 0
\(316\) −9.70820 16.8151i −0.546129 0.945923i
\(317\) −13.1180 22.7211i −0.736782 1.27614i −0.953937 0.300007i \(-0.903011\pi\)
0.217155 0.976137i \(-0.430322\pi\)
\(318\) 25.7984 1.44670
\(319\) 13.1459 0.736029
\(320\) 11.3992 + 19.7440i 0.637234 + 1.10372i
\(321\) 4.42705 + 7.66788i 0.247094 + 0.427979i
\(322\) 0 0
\(323\) −1.36475 + 2.36381i −0.0759364 + 0.131526i
\(324\) 13.8541 + 23.9960i 0.769672 + 1.33311i
\(325\) 1.85410 + 6.42280i 0.102847 + 0.356273i
\(326\) 4.85410 8.40755i 0.268844 0.465651i
\(327\) −7.09017 −0.392087
\(328\) 2.85410 4.94345i 0.157591 0.272956i
\(329\) 0 0
\(330\) −33.2705 −1.83148
\(331\) 5.07295 8.78661i 0.278834 0.482956i −0.692261 0.721647i \(-0.743385\pi\)
0.971095 + 0.238692i \(0.0767186\pi\)
\(332\) −32.5623 −1.78709
\(333\) −7.70820 + 13.3510i −0.422407 + 0.731630i
\(334\) 18.6353 32.2772i 1.01968 1.76613i
\(335\) −16.6353 + 28.8131i −0.908881 + 1.57423i
\(336\) 0 0
\(337\) −11.5623 −0.629839 −0.314919 0.949118i \(-0.601978\pi\)
−0.314919 + 0.949118i \(0.601978\pi\)
\(338\) −1.30902 34.0093i −0.0712011 1.84986i
\(339\) −1.92705 + 3.33775i −0.104663 + 0.181282i
\(340\) 9.35410 + 16.2018i 0.507297 + 0.878665i
\(341\) 8.72949 0.472728
\(342\) −9.35410 16.2018i −0.505812 0.876092i
\(343\) 0 0
\(344\) −46.9336 81.2914i −2.53049 4.38294i
\(345\) −15.3262 + 26.5458i −0.825137 + 1.42918i
\(346\) −11.7812 + 20.4056i −0.633359 + 1.09701i
\(347\) 30.7639 1.65149 0.825747 0.564040i \(-0.190754\pi\)
0.825747 + 0.564040i \(0.190754\pi\)
\(348\) 90.1033 4.83005
\(349\) 10.3541 17.9338i 0.554242 0.959976i −0.443720 0.896166i \(-0.646341\pi\)
0.997962 0.0638103i \(-0.0203253\pi\)
\(350\) 0 0
\(351\) 5.59017 5.80948i 0.298381 0.310087i
\(352\) −10.0623 17.4284i −0.536323 0.928938i
\(353\) 11.0729 + 19.1789i 0.589354 + 1.02079i 0.994317 + 0.106458i \(0.0339508\pi\)
−0.404964 + 0.914333i \(0.632716\pi\)
\(354\) −7.66312 13.2729i −0.407290 0.705447i
\(355\) −18.5623 + 32.1509i −0.985185 + 1.70639i
\(356\) −23.8328 −1.26314
\(357\) 0 0
\(358\) 11.7812 + 20.4056i 0.622653 + 1.07847i
\(359\) 11.0451 + 19.1306i 0.582937 + 1.00968i 0.995129 + 0.0985799i \(0.0314300\pi\)
−0.412192 + 0.911097i \(0.635237\pi\)
\(360\) −75.3951 −3.97367
\(361\) 7.78115 + 13.4774i 0.409534 + 0.709334i
\(362\) −25.4164 −1.33586
\(363\) −19.7984 −1.03915
\(364\) 0 0
\(365\) −5.23607 −0.274068
\(366\) 41.1246 2.14962
\(367\) −0.708204 1.22665i −0.0369679 0.0640304i 0.846949 0.531673i \(-0.178437\pi\)
−0.883917 + 0.467643i \(0.845103\pi\)
\(368\) −44.0689 −2.29725
\(369\) 1.47214 + 2.54981i 0.0766363 + 0.132738i
\(370\) 13.7082 + 23.7433i 0.712656 + 1.23436i
\(371\) 0 0
\(372\) 59.8328 3.10219
\(373\) 10.2812 17.8075i 0.532338 0.922036i −0.466949 0.884284i \(-0.654647\pi\)
0.999287 0.0377522i \(-0.0120198\pi\)
\(374\) −3.57295 6.18853i −0.184753 0.320001i
\(375\) −10.7812 18.6735i −0.556736 0.964296i
\(376\) −8.35410 14.4697i −0.430830 0.746219i
\(377\) 7.09017 + 24.5611i 0.365162 + 1.26496i
\(378\) 0 0
\(379\) 3.07295 5.32250i 0.157847 0.273399i −0.776245 0.630431i \(-0.782878\pi\)
0.934092 + 0.357032i \(0.116211\pi\)
\(380\) −23.5623 −1.20872
\(381\) −54.5967 −2.79708
\(382\) −27.9894 + 48.4790i −1.43206 + 2.48040i
\(383\) −10.9894 + 19.0341i −0.561530 + 0.972598i 0.435833 + 0.900027i \(0.356454\pi\)
−0.997363 + 0.0725709i \(0.976880\pi\)
\(384\) −1.42705 2.47172i −0.0728239 0.126135i
\(385\) 0 0
\(386\) 7.85410 + 13.6037i 0.399763 + 0.692410i
\(387\) 48.4164 2.46114
\(388\) 45.7599 + 79.2584i 2.32311 + 4.02374i
\(389\) 5.94427 10.2958i 0.301387 0.522017i −0.675064 0.737759i \(-0.735884\pi\)
0.976450 + 0.215743i \(0.0692172\pi\)
\(390\) −17.9443 62.1608i −0.908644 3.14763i
\(391\) −6.58359 −0.332947
\(392\) 0 0
\(393\) −20.0623 + 34.7489i −1.01201 + 1.75285i
\(394\) 21.9894 38.0867i 1.10781 1.91878i
\(395\) 5.23607 9.06914i 0.263455 0.456318i
\(396\) 34.6869 1.74308
\(397\) 0.708204 1.22665i 0.0355437 0.0615636i −0.847706 0.530466i \(-0.822017\pi\)
0.883250 + 0.468902i \(0.155350\pi\)
\(398\) 63.9230 3.20417
\(399\) 0 0
\(400\) −9.13525 + 15.8227i −0.456763 + 0.791136i
\(401\) 35.4508 1.77033 0.885165 0.465276i \(-0.154045\pi\)
0.885165 + 0.465276i \(0.154045\pi\)
\(402\) 43.5517 75.4337i 2.17216 3.76229i
\(403\) 4.70820 + 16.3097i 0.234532 + 0.812444i
\(404\) −28.0623 48.6053i −1.39615 2.41821i
\(405\) −7.47214 + 12.9421i −0.371293 + 0.643099i
\(406\) 0 0
\(407\) −3.70820 6.42280i −0.183809 0.318366i
\(408\) −14.3992 24.9401i −0.712866 1.23472i
\(409\) −14.4377 −0.713898 −0.356949 0.934124i \(-0.616183\pi\)
−0.356949 + 0.934124i \(0.616183\pi\)
\(410\) 5.23607 0.258591
\(411\) 3.42705 + 5.93583i 0.169044 + 0.292793i
\(412\) −21.1353 36.6073i −1.04126 1.80351i
\(413\) 0 0
\(414\) 22.5623 39.0791i 1.10888 1.92063i
\(415\) −8.78115 15.2094i −0.431050 0.746600i
\(416\) 27.1353 28.1998i 1.33042 1.38261i
\(417\) 5.97214 10.3440i 0.292457 0.506550i
\(418\) 9.00000 0.440204
\(419\) −5.97214 + 10.3440i −0.291758 + 0.505340i −0.974226 0.225576i \(-0.927574\pi\)
0.682468 + 0.730916i \(0.260907\pi\)
\(420\) 0 0
\(421\) 1.41641 0.0690315 0.0345157 0.999404i \(-0.489011\pi\)
0.0345157 + 0.999404i \(0.489011\pi\)
\(422\) −6.16312 + 10.6748i −0.300016 + 0.519643i
\(423\) 8.61803 0.419023
\(424\) −14.0623 + 24.3566i −0.682926 + 1.18286i
\(425\) −1.36475 + 2.36381i −0.0661999 + 0.114662i
\(426\) 48.5967 84.1720i 2.35452 4.07815i
\(427\) 0 0
\(428\) −16.4164 −0.793517
\(429\) 4.85410 + 16.8151i 0.234358 + 0.811841i
\(430\) 43.0517 74.5677i 2.07614 3.59597i
\(431\) −3.89919 6.75359i −0.187817 0.325309i 0.756705 0.653756i \(-0.226808\pi\)
−0.944522 + 0.328448i \(0.893475\pi\)
\(432\) 22.0344 1.06013
\(433\) 0.500000 + 0.866025i 0.0240285 + 0.0416185i 0.877790 0.479046i \(-0.159017\pi\)
−0.853761 + 0.520665i \(0.825684\pi\)
\(434\) 0 0
\(435\) 24.2984 + 42.0860i 1.16502 + 2.01787i
\(436\) 6.57295 11.3847i 0.314787 0.545227i
\(437\) 4.14590 7.18091i 0.198325 0.343509i
\(438\) 13.7082 0.655003
\(439\) −14.8541 −0.708948 −0.354474 0.935066i \(-0.615340\pi\)
−0.354474 + 0.935066i \(0.615340\pi\)
\(440\) 18.1353 31.4112i 0.864564 1.49747i
\(441\) 0 0
\(442\) 9.63525 10.0133i 0.458302 0.476282i
\(443\) 2.61803 + 4.53457i 0.124387 + 0.215444i 0.921493 0.388395i \(-0.126970\pi\)
−0.797106 + 0.603839i \(0.793637\pi\)
\(444\) −25.4164 44.0225i −1.20621 2.08922i
\(445\) −6.42705 11.1320i −0.304671 0.527706i
\(446\) 26.5344 45.9590i 1.25644 2.17622i
\(447\) 4.85410 0.229591
\(448\) 0 0
\(449\) −9.76393 16.9116i −0.460788 0.798109i 0.538212 0.842809i \(-0.319100\pi\)
−0.999000 + 0.0447005i \(0.985767\pi\)
\(450\) −9.35410 16.2018i −0.440957 0.763759i
\(451\) −1.41641 −0.0666960
\(452\) −3.57295 6.18853i −0.168057 0.291084i
\(453\) −3.38197 −0.158899
\(454\) −3.85410 −0.180882
\(455\) 0 0
\(456\) 36.2705 1.69852
\(457\) 15.4164 0.721149 0.360575 0.932730i \(-0.382581\pi\)
0.360575 + 0.932730i \(0.382581\pi\)
\(458\) −17.1803 29.7572i −0.802785 1.39046i
\(459\) 3.29180 0.153648
\(460\) −28.4164 49.2187i −1.32492 2.29483i
\(461\) −6.10739 10.5783i −0.284450 0.492681i 0.688026 0.725686i \(-0.258477\pi\)
−0.972476 + 0.233005i \(0.925144\pi\)
\(462\) 0 0
\(463\) 6.70820 0.311757 0.155878 0.987776i \(-0.450179\pi\)
0.155878 + 0.987776i \(0.450179\pi\)
\(464\) −34.9336 + 60.5068i −1.62175 + 2.80896i
\(465\) 16.1353 + 27.9471i 0.748255 + 1.29601i
\(466\) −3.42705 5.93583i −0.158755 0.274972i
\(467\) 1.17376 + 2.03302i 0.0543152 + 0.0940767i 0.891905 0.452224i \(-0.149369\pi\)
−0.837589 + 0.546300i \(0.816036\pi\)
\(468\) 18.7082 + 64.8071i 0.864787 + 2.99571i
\(469\) 0 0
\(470\) 7.66312 13.2729i 0.353473 0.612234i
\(471\) −38.8885 −1.79189
\(472\) 16.7082 0.769057
\(473\) −11.6459 + 20.1713i −0.535479 + 0.927477i
\(474\) −13.7082 + 23.7433i −0.629639 + 1.09057i
\(475\) −1.71885 2.97713i −0.0788661 0.136600i
\(476\) 0 0
\(477\) −7.25329 12.5631i −0.332105 0.575223i
\(478\) −64.6869 −2.95871
\(479\) 12.4894 + 21.6322i 0.570653 + 0.988400i 0.996499 + 0.0836047i \(0.0266433\pi\)
−0.425846 + 0.904796i \(0.640023\pi\)
\(480\) 37.1976 64.4281i 1.69783 2.94073i
\(481\) 10.0000 10.3923i 0.455961 0.473848i
\(482\) −64.3050 −2.92901
\(483\) 0 0
\(484\) 18.3541 31.7902i 0.834277 1.44501i
\(485\) −24.6803 + 42.7476i −1.12068 + 1.94107i
\(486\) 28.3435 49.0923i 1.28569 2.22687i
\(487\) 29.9787 1.35847 0.679233 0.733923i \(-0.262313\pi\)
0.679233 + 0.733923i \(0.262313\pi\)
\(488\) −22.4164 + 38.8264i −1.01474 + 1.75759i
\(489\) −9.70820 −0.439020
\(490\) 0 0
\(491\) −6.19098 + 10.7231i −0.279395 + 0.483927i −0.971235 0.238125i \(-0.923467\pi\)
0.691839 + 0.722051i \(0.256801\pi\)
\(492\) −9.70820 −0.437680
\(493\) −5.21885 + 9.03931i −0.235045 + 0.407110i
\(494\) 4.85410 + 16.8151i 0.218396 + 0.756547i
\(495\) 9.35410 + 16.2018i 0.420436 + 0.728216i
\(496\) −23.1976 + 40.1794i −1.04160 + 1.80411i
\(497\) 0 0
\(498\) 22.9894 + 39.8187i 1.03018 + 1.78432i
\(499\) −7.42705 12.8640i −0.332480 0.575873i 0.650517 0.759492i \(-0.274552\pi\)
−0.982998 + 0.183619i \(0.941219\pi\)
\(500\) 39.9787 1.78790
\(501\) −37.2705 −1.66512
\(502\) 1.00000 + 1.73205i 0.0446322 + 0.0773052i
\(503\) 13.3090 + 23.0519i 0.593420 + 1.02783i 0.993768 + 0.111470i \(0.0355559\pi\)
−0.400348 + 0.916363i \(0.631111\pi\)
\(504\) 0 0
\(505\) 15.1353 26.2150i 0.673510 1.16655i
\(506\) 10.8541 + 18.7999i 0.482524 + 0.835756i
\(507\) −28.7984 + 18.1383i −1.27898 + 0.805549i
\(508\) 50.6140 87.6660i 2.24563 3.88955i
\(509\) 18.5967 0.824286 0.412143 0.911119i \(-0.364780\pi\)
0.412143 + 0.911119i \(0.364780\pi\)
\(510\) 13.2082 22.8773i 0.584869 1.01302i
\(511\) 0 0
\(512\) −40.3050 −1.78124
\(513\) −2.07295 + 3.59045i −0.0915229 + 0.158522i
\(514\) −43.8328 −1.93338
\(515\) 11.3992 19.7440i 0.502308 0.870023i
\(516\) −79.8222 + 138.256i −3.51398 + 6.08638i
\(517\) −2.07295 + 3.59045i −0.0911682 + 0.157908i
\(518\) 0 0
\(519\) 23.5623 1.03427
\(520\) 68.4681 + 16.9415i 3.00252 + 0.742932i
\(521\) 9.32624 16.1535i 0.408590 0.707698i −0.586142 0.810208i \(-0.699354\pi\)
0.994732 + 0.102510i \(0.0326873\pi\)
\(522\) −35.7705 61.9563i −1.56563 2.71176i
\(523\) −1.12461 −0.0491758 −0.0245879 0.999698i \(-0.507827\pi\)
−0.0245879 + 0.999698i \(0.507827\pi\)
\(524\) −37.1976 64.4281i −1.62498 2.81455i
\(525\) 0 0
\(526\) −11.7812 20.4056i −0.513683 0.889724i
\(527\) −3.46556 + 6.00252i −0.150962 + 0.261474i
\(528\) −23.9164 + 41.4244i −1.04083 + 1.80277i
\(529\) −3.00000 −0.130435
\(530\) −25.7984 −1.12061
\(531\) −4.30902 + 7.46344i −0.186995 + 0.323886i
\(532\) 0 0
\(533\) −0.763932 2.64634i −0.0330896 0.114626i
\(534\) 16.8262 + 29.1439i 0.728143 + 1.26118i
\(535\) −4.42705 7.66788i −0.191398 0.331511i
\(536\) 47.4787 + 82.2355i 2.05077 + 3.55203i
\(537\) 11.7812 20.4056i 0.508394 0.880565i
\(538\) 75.2492 3.24422
\(539\) 0 0
\(540\) 14.2082 + 24.6093i 0.611424 + 1.05902i
\(541\) −17.6353 30.5452i −0.758199 1.31324i −0.943768 0.330608i \(-0.892746\pi\)
0.185569 0.982631i \(-0.440587\pi\)
\(542\) 22.0344 0.946460
\(543\) 12.7082 + 22.0113i 0.545361 + 0.944593i
\(544\) 15.9787 0.685082
\(545\) 7.09017 0.303710
\(546\) 0 0
\(547\) −3.00000 −0.128271 −0.0641354 0.997941i \(-0.520429\pi\)
−0.0641354 + 0.997941i \(0.520429\pi\)
\(548\) −12.7082 −0.542868
\(549\) −11.5623 20.0265i −0.493467 0.854710i
\(550\) 9.00000 0.383761
\(551\) −6.57295 11.3847i −0.280017 0.485004i
\(552\) 43.7426 + 75.7645i 1.86181 + 3.22475i
\(553\) 0 0
\(554\) −13.0902 −0.556148
\(555\) 13.7082 23.7433i 0.581881 1.00785i
\(556\) 11.0729 + 19.1789i 0.469598 + 0.813367i
\(557\) 13.9894 + 24.2303i 0.592748 + 1.02667i 0.993860 + 0.110641i \(0.0352904\pi\)
−0.401112 + 0.916029i \(0.631376\pi\)
\(558\) −23.7533 41.1419i −1.00556 1.74168i
\(559\) −43.9681 10.8793i −1.85965 0.460144i
\(560\) 0 0
\(561\) −3.57295 + 6.18853i −0.150850 + 0.261280i
\(562\) 52.8328 2.22862
\(563\) 21.0557 0.887393 0.443697 0.896177i \(-0.353667\pi\)
0.443697 + 0.896177i \(0.353667\pi\)
\(564\) −14.2082 + 24.6093i −0.598273 + 1.03624i
\(565\) 1.92705 3.33775i 0.0810716 0.140420i
\(566\) 17.5623 + 30.4188i 0.738199 + 1.27860i
\(567\) 0 0
\(568\) 52.9787 + 91.7618i 2.22294 + 3.85024i
\(569\) 14.9443 0.626496 0.313248 0.949671i \(-0.398583\pi\)
0.313248 + 0.949671i \(0.398583\pi\)
\(570\) 16.6353 + 28.8131i 0.696774 + 1.20685i
\(571\) −12.3435 + 21.3795i −0.516558 + 0.894704i 0.483257 + 0.875478i \(0.339453\pi\)
−0.999815 + 0.0192259i \(0.993880\pi\)
\(572\) −31.5000 7.79423i −1.31708 0.325893i
\(573\) 55.9787 2.33854
\(574\) 0 0
\(575\) 4.14590 7.18091i 0.172896 0.299464i
\(576\) −16.7812 + 29.0658i −0.699215 + 1.21108i
\(577\) −21.9164 + 37.9603i −0.912392 + 1.58031i −0.101717 + 0.994813i \(0.532433\pi\)
−0.810675 + 0.585496i \(0.800900\pi\)
\(578\) −38.8328 −1.61523
\(579\) 7.85410 13.6037i 0.326405 0.565351i
\(580\) −90.1033 −3.74134
\(581\) 0 0
\(582\) 64.6140 111.915i 2.67834 4.63901i
\(583\) 6.97871 0.289029
\(584\) −7.47214 + 12.9421i −0.309199 + 0.535549i
\(585\) −25.2254 + 26.2150i −1.04294 + 1.08386i
\(586\) −8.85410 15.3358i −0.365760 0.633514i
\(587\) −9.95492 + 17.2424i −0.410883 + 0.711671i −0.994987 0.100009i \(-0.968113\pi\)
0.584103 + 0.811679i \(0.301446\pi\)
\(588\) 0 0
\(589\) −4.36475 7.55996i −0.179846 0.311503i
\(590\) 7.66312 + 13.2729i 0.315486 + 0.546437i
\(591\) −43.9787 −1.80904
\(592\) 39.4164 1.62000
\(593\) 21.8992 + 37.9305i 0.899292 + 1.55762i 0.828401 + 0.560135i \(0.189251\pi\)
0.0708905 + 0.997484i \(0.477416\pi\)
\(594\) −5.42705 9.39993i −0.222675 0.385684i
\(595\) 0 0
\(596\) −4.50000 + 7.79423i −0.184327 + 0.319264i
\(597\) −31.9615 55.3589i −1.30810 2.26569i
\(598\) −29.2705 + 30.4188i −1.19696 + 1.24392i
\(599\) −14.7533 + 25.5534i −0.602803 + 1.04409i 0.389592 + 0.920988i \(0.372616\pi\)
−0.992395 + 0.123098i \(0.960717\pi\)
\(600\) 36.2705 1.48074
\(601\) 20.1976 34.9832i 0.823876 1.42699i −0.0788998 0.996883i \(-0.525141\pi\)
0.902776 0.430112i \(-0.141526\pi\)
\(602\) 0 0
\(603\) −48.9787 −1.99457
\(604\) 3.13525 5.43042i 0.127572 0.220961i
\(605\) 19.7984 0.804918
\(606\) −39.6246 + 68.6318i −1.60964 + 2.78798i
\(607\) −11.5000 + 19.9186i −0.466771 + 0.808470i −0.999279 0.0379540i \(-0.987916\pi\)
0.532509 + 0.846424i \(0.321249\pi\)
\(608\) −10.0623 + 17.4284i −0.408080 + 0.706816i
\(609\) 0 0
\(610\) −41.1246 −1.66509
\(611\) −7.82624 1.93649i −0.316616 0.0783421i
\(612\) −13.7705 + 23.8512i −0.556640 + 0.964129i
\(613\) −17.2812 29.9318i −0.697979 1.20894i −0.969166 0.246409i \(-0.920749\pi\)
0.271187 0.962527i \(-0.412584\pi\)
\(614\) 12.7082 0.512861
\(615\) −2.61803 4.53457i −0.105569 0.182851i
\(616\) 0 0
\(617\) −0.0278640 0.0482619i −0.00112176 0.00194295i 0.865464 0.500971i \(-0.167024\pi\)
−0.866586 + 0.499028i \(0.833690\pi\)
\(618\) −29.8435 + 51.6904i −1.20048 + 2.07929i
\(619\) 4.70820 8.15485i 0.189239 0.327771i −0.755758 0.654851i \(-0.772731\pi\)
0.944997 + 0.327080i \(0.106065\pi\)
\(620\) −59.8328 −2.40294
\(621\) −10.0000 −0.401286
\(622\) 4.35410 7.54153i 0.174584 0.302388i
\(623\) 0 0
\(624\) −90.2943 22.3420i −3.61467 0.894398i
\(625\) 15.4164 + 26.7020i 0.616656 + 1.06808i
\(626\) 32.8885 + 56.9646i 1.31449 + 2.27676i
\(627\) −4.50000 7.79423i −0.179713 0.311272i
\(628\) 36.0517 62.4433i 1.43862 2.49176i
\(629\) 5.88854 0.234792
\(630\) 0 0
\(631\) −17.1976 29.7870i −0.684624 1.18580i −0.973555 0.228454i \(-0.926633\pi\)
0.288931 0.957350i \(-0.406700\pi\)
\(632\) −14.9443 25.8842i −0.594451 1.02962i
\(633\) 12.3262 0.489924
\(634\) −34.3435 59.4846i −1.36395 2.36244i
\(635\) 54.5967 2.16661
\(636\) 47.8328 1.89669
\(637\) 0 0
\(638\) 34.4164 1.36256
\(639\) −54.6525 −2.16202
\(640\) 1.42705 + 2.47172i 0.0564091 + 0.0977035i
\(641\) −47.5066 −1.87640 −0.938199 0.346098i \(-0.887507\pi\)
−0.938199 + 0.346098i \(0.887507\pi\)
\(642\) 11.5902 + 20.0748i 0.457428 + 0.792288i
\(643\) −3.50000 6.06218i −0.138027 0.239069i 0.788723 0.614749i \(-0.210743\pi\)
−0.926750 + 0.375680i \(0.877409\pi\)
\(644\) 0 0
\(645\) −86.1033 −3.39032
\(646\) −3.57295 + 6.18853i −0.140576 + 0.243484i
\(647\) 12.3820 + 21.4462i 0.486785 + 0.843137i 0.999885 0.0151924i \(-0.00483607\pi\)
−0.513099 + 0.858329i \(0.671503\pi\)
\(648\) 21.3262 + 36.9381i 0.837774 + 1.45107i
\(649\) −2.07295 3.59045i −0.0813704 0.140938i
\(650\) 4.85410 + 16.8151i 0.190394 + 0.659543i
\(651\) 0 0
\(652\) 9.00000 15.5885i 0.352467 0.610491i
\(653\) −0.381966 −0.0149475 −0.00747374 0.999972i \(-0.502379\pi\)
−0.00747374 + 0.999972i \(0.502379\pi\)
\(654\) −18.5623 −0.725844
\(655\) 20.0623 34.7489i 0.783899 1.35775i
\(656\) 3.76393 6.51932i 0.146957 0.254537i
\(657\) −3.85410 6.67550i −0.150363 0.260436i
\(658\) 0 0
\(659\) 11.9443 + 20.6881i 0.465283 + 0.805893i 0.999214 0.0396343i \(-0.0126193\pi\)
−0.533931 + 0.845528i \(0.679286\pi\)
\(660\) −61.6869 −2.40116
\(661\) −24.2705 42.0378i −0.944013 1.63508i −0.757715 0.652586i \(-0.773684\pi\)
−0.186299 0.982493i \(-0.559649\pi\)
\(662\) 13.2812 23.0036i 0.516187 0.894062i
\(663\) −13.4894 3.33775i −0.523883 0.129627i
\(664\) −50.1246 −1.94521
\(665\) 0 0
\(666\) −20.1803 + 34.9534i −0.781972 + 1.35442i
\(667\) 15.8541 27.4601i 0.613873 1.06326i
\(668\) 34.5517 59.8452i 1.33684 2.31548i
\(669\) −53.0689 −2.05176
\(670\) −43.5517 + 75.4337i −1.68255 + 2.91426i
\(671\) 11.1246 0.429461
\(672\) 0 0
\(673\) 19.6246 33.9908i 0.756473 1.31025i −0.188165 0.982137i \(-0.560254\pi\)
0.944639 0.328113i \(-0.106413\pi\)
\(674\) −30.2705 −1.16598
\(675\) −2.07295 + 3.59045i −0.0797878 + 0.138197i
\(676\) −2.42705 63.0566i −0.0933481 2.42526i
\(677\) 21.8713 + 37.8822i 0.840583 + 1.45593i 0.889402 + 0.457125i \(0.151121\pi\)
−0.0488191 + 0.998808i \(0.515546\pi\)
\(678\) −5.04508 + 8.73834i −0.193755 + 0.335594i
\(679\) 0 0
\(680\) 14.3992 + 24.9401i 0.552184 + 0.956410i
\(681\) 1.92705 + 3.33775i 0.0738448 + 0.127903i
\(682\) 22.8541 0.875129
\(683\) 1.47214 0.0563297 0.0281649 0.999603i \(-0.491034\pi\)
0.0281649 + 0.999603i \(0.491034\pi\)
\(684\) −17.3435 30.0398i −0.663144 1.14860i
\(685\) −3.42705 5.93583i −0.130941 0.226796i
\(686\) 0 0
\(687\) −17.1803 + 29.7572i −0.655471 + 1.13531i
\(688\) −61.8951 107.205i −2.35973 4.08717i
\(689\) 3.76393 + 13.0386i 0.143394 + 0.496733i
\(690\) −40.1246 + 69.4979i −1.52752 + 2.64574i
\(691\) 5.85410 0.222701 0.111350 0.993781i \(-0.464482\pi\)
0.111350 + 0.993781i \(0.464482\pi\)
\(692\) −21.8435 + 37.8340i −0.830364 + 1.43823i
\(693\) 0 0
\(694\) 80.5410 3.05730
\(695\) −5.97214 + 10.3440i −0.226536 + 0.392372i
\(696\) 138.700 5.25741
\(697\) 0.562306 0.973942i 0.0212989 0.0368907i
\(698\) 27.1074 46.9514i 1.02603 1.77714i
\(699\) −3.42705 + 5.93583i −0.129623 + 0.224514i
\(700\) 0 0
\(701\) 11.2361 0.424380 0.212190 0.977228i \(-0.431940\pi\)
0.212190 + 0.977228i \(0.431940\pi\)
\(702\) 14.6353 15.2094i 0.552372 0.574042i
\(703\) −3.70820 + 6.42280i −0.139858 + 0.242240i
\(704\) −8.07295 13.9828i −0.304261 0.526995i
\(705\) −15.3262 −0.577220
\(706\) 28.9894 + 50.2110i 1.09103 + 1.88972i
\(707\) 0 0
\(708\) −14.2082 24.6093i −0.533977 0.924875i
\(709\) −11.7812 + 20.4056i −0.442450 + 0.766347i −0.997871 0.0652231i \(-0.979224\pi\)
0.555420 + 0.831570i \(0.312557\pi\)
\(710\) −48.5967 + 84.1720i −1.82380 + 3.15892i
\(711\) 15.4164 0.578160
\(712\) −36.6869 −1.37490
\(713\) 10.5279 18.2348i 0.394272 0.682898i
\(714\) 0 0
\(715\) −4.85410 16.8151i −0.181533 0.628849i
\(716\) 21.8435 + 37.8340i 0.816328 + 1.41392i
\(717\) 32.3435 + 56.0205i 1.20789 + 2.09212i
\(718\) 28.9164 + 50.0847i 1.07915 + 1.86914i
\(719\) 4.06231 7.03612i 0.151498 0.262403i −0.780280 0.625430i \(-0.784923\pi\)
0.931779 + 0.363027i \(0.118257\pi\)
\(720\) −99.4296 −3.70552
\(721\) 0 0
\(722\) 20.3713 + 35.2842i 0.758142 + 1.31314i
\(723\) 32.1525 + 55.6897i 1.19576 + 2.07112i
\(724\) −47.1246 −1.75137
\(725\) −6.57295 11.3847i −0.244113 0.422816i
\(726\) −51.8328 −1.92370
\(727\) 30.7082 1.13890 0.569452 0.822025i \(-0.307155\pi\)
0.569452 + 0.822025i \(0.307155\pi\)
\(728\) 0 0
\(729\) −39.5623 −1.46527
\(730\) −13.7082 −0.507363
\(731\) −9.24671 16.0158i −0.342002 0.592365i
\(732\) 76.2492 2.81825
\(733\) −16.1353 27.9471i −0.595969 1.03225i −0.993409 0.114621i \(-0.963435\pi\)
0.397440 0.917628i \(-0.369899\pi\)
\(734\) −1.85410 3.21140i −0.0684362 0.118535i
\(735\) 0 0
\(736\) −48.5410 −1.78925
\(737\) 11.7812 20.4056i 0.433964 0.751648i
\(738\) 3.85410 + 6.67550i 0.141871 + 0.245729i
\(739\) 3.43769 + 5.95426i 0.126458 + 0.219031i 0.922302 0.386470i \(-0.126306\pi\)
−0.795844 + 0.605502i \(0.792973\pi\)
\(740\) 25.4164 + 44.0225i 0.934326 + 1.61830i
\(741\) 12.1353 12.6113i 0.445800 0.463289i
\(742\) 0 0
\(743\) −19.6631 + 34.0575i −0.721370 + 1.24945i 0.239081 + 0.971000i \(0.423154\pi\)
−0.960451 + 0.278450i \(0.910179\pi\)
\(744\) 92.1033 3.37667
\(745\) −4.85410 −0.177841
\(746\) 26.9164 46.6206i 0.985480 1.70690i
\(747\) 12.9271 22.3903i 0.472976 0.819219i
\(748\) −6.62461 11.4742i −0.242220 0.419537i
\(749\) 0 0
\(750\) −28.2254 48.8879i −1.03065 1.78513i
\(751\) 22.7082 0.828634 0.414317 0.910133i \(-0.364020\pi\)
0.414317 + 0.910133i \(0.364020\pi\)
\(752\) −11.0172 19.0824i −0.401757 0.695863i
\(753\) 1.00000 1.73205i 0.0364420 0.0631194i
\(754\) 18.5623 + 64.3017i 0.675999 + 2.34173i
\(755\) 3.38197 0.123082
\(756\) 0 0
\(757\) −14.0000 + 24.2487i −0.508839 + 0.881334i 0.491109 + 0.871098i \(0.336592\pi\)
−0.999948 + 0.0102362i \(0.996742\pi\)
\(758\) 8.04508 13.9345i 0.292211 0.506124i
\(759\) 10.8541 18.7999i 0.393979 0.682392i
\(760\) −36.2705 −1.31567
\(761\) −14.4271 + 24.9884i −0.522980 + 0.905828i 0.476662 + 0.879087i \(0.341846\pi\)
−0.999642 + 0.0267417i \(0.991487\pi\)
\(762\) −142.936 −5.17803
\(763\) 0 0
\(764\) −51.8951 + 89.8850i −1.87750 + 3.25192i
\(765\) −14.8541 −0.537051
\(766\) −28.7705 + 49.8320i −1.03952 + 1.80050i
\(767\) 5.59017 5.80948i 0.201849 0.209768i
\(768\) 19.0623 + 33.0169i 0.687852 + 1.19139i
\(769\) −9.20820 + 15.9491i −0.332056 + 0.575138i −0.982915 0.184061i \(-0.941076\pi\)
0.650859 + 0.759199i \(0.274409\pi\)
\(770\) 0 0
\(771\) 21.9164 + 37.9603i 0.789300 + 1.36711i
\(772\) 14.5623 + 25.2227i 0.524109 + 0.907783i
\(773\) −25.3607 −0.912160 −0.456080 0.889939i \(-0.650747\pi\)
−0.456080 + 0.889939i \(0.650747\pi\)
\(774\) 126.756 4.55614
\(775\) −4.36475 7.55996i −0.156786 0.271562i
\(776\) 70.4402 + 122.006i 2.52866 + 4.37976i
\(777\) 0 0
\(778\) 15.5623 26.9547i 0.557936 0.966373i
\(779\) 0.708204 + 1.22665i 0.0253740 + 0.0439491i
\(780\) −33.2705 115.252i −1.19128 4.12670i
\(781\) 13.1459 22.7694i 0.470397 0.814752i
\(782\) −17.2361 −0.616361
\(783\) −7.92705 + 13.7301i −0.283290 + 0.490672i
\(784\) 0 0
\(785\) 38.8885 1.38799
\(786\) −52.5238 + 90.9739i −1.87346 + 3.24493i
\(787\) −2.58359 −0.0920951 −0.0460476 0.998939i \(-0.514663\pi\)
−0.0460476 + 0.998939i \(0.514663\pi\)
\(788\) 40.7705 70.6166i 1.45239 2.51561i
\(789\) −11.7812 + 20.4056i −0.419420 + 0.726457i
\(790\) 13.7082 23.7433i 0.487716 0.844749i
\(791\) 0 0
\(792\) 53.3951 1.89731
\(793\) 6.00000 + 20.7846i 0.213066 + 0.738083i
\(794\) 1.85410 3.21140i 0.0657996 0.113968i
\(795\) 12.8992 + 22.3420i 0.457487 + 0.792391i
\(796\) 118.520 4.20082
\(797\) −4.09017 7.08438i −0.144881 0.250942i 0.784447 0.620195i \(-0.212947\pi\)
−0.929329 + 0.369254i \(0.879613\pi\)
\(798\) 0 0
\(799\) −1.64590 2.85078i −0.0582277 0.100853i
\(800\) −10.0623 + 17.4284i −0.355756 + 0.616188i
\(801\) 9.46149 16.3878i 0.334305 0.579034i
\(802\) 92.8115 3.27729
\(803\) 3.70820 0.130860
\(804\) 80.7492 139.862i 2.84781 4.93254i
\(805\) 0 0
\(806\) 12.3262 + 42.6993i 0.434173 + 1.50402i
\(807\) −37.6246 65.1677i −1.32445 2.29401i
\(808\) −43.1976 74.8204i −1.51968 2.63217i
\(809\) 2.20820 + 3.82472i 0.0776363 + 0.134470i 0.902230 0.431256i \(-0.141929\pi\)
−0.824593 + 0.565726i \(0.808596\pi\)
\(810\) −19.5623 + 33.8829i −0.687349 + 1.19052i
\(811\) −39.2705 −1.37897 −0.689487 0.724298i \(-0.742164\pi\)
−0.689487 + 0.724298i \(0.742164\pi\)
\(812\) 0 0
\(813\) −11.0172 19.0824i −0.386391 0.669249i
\(814\) −9.70820 16.8151i −0.340272 0.589369i
\(815\) 9.70820 0.340064
\(816\) −18.9894 32.8905i −0.664760 1.15140i
\(817\) 23.2918 0.814877
\(818\) −37.7984 −1.32159
\(819\) 0 0
\(820\) 9.70820 0.339025
\(821\) −7.36068 −0.256889 −0.128445 0.991717i \(-0.540998\pi\)
−0.128445 + 0.991717i \(0.540998\pi\)
\(822\) 8.97214 + 15.5402i 0.312939 + 0.542027i
\(823\) −38.4164 −1.33911 −0.669556 0.742762i \(-0.733516\pi\)
−0.669556 + 0.742762i \(0.733516\pi\)
\(824\) −32.5344 56.3513i −1.13339 1.96309i
\(825\) −4.50000 7.79423i −0.156670 0.271360i
\(826\) 0 0
\(827\) 15.9787 0.555634 0.277817 0.960634i \(-0.410389\pi\)
0.277817 + 0.960634i \(0.410389\pi\)
\(828\) 41.8328 72.4566i 1.45379 2.51804i
\(829\) 3.78115 + 6.54915i 0.131325 + 0.227461i 0.924188 0.381939i \(-0.124744\pi\)
−0.792863 + 0.609400i \(0.791410\pi\)
\(830\) −22.9894 39.8187i −0.797972 1.38213i
\(831\) 6.54508 + 11.3364i 0.227046 + 0.393256i
\(832\) 21.7705 22.6246i 0.754757 0.784366i
\(833\) 0 0
\(834\) 15.6353 27.0811i 0.541405 0.937740i
\(835\) 37.2705 1.28980
\(836\) 16.6869 0.577129
\(837\) −5.26393 + 9.11740i −0.181948 + 0.315143i
\(838\) −15.6353 + 27.0811i −0.540111 + 0.935500i
\(839\) 6.87132 + 11.9015i 0.237224 + 0.410885i 0.959917 0.280285i \(-0.0904290\pi\)
−0.722692 + 0.691170i \(0.757096\pi\)
\(840\) 0 0
\(841\) −10.6353 18.4208i −0.366733 0.635200i
\(842\) 3.70820 0.127793
\(843\) −26.4164 45.7546i −0.909829 1.57587i
\(844\) −11.4271 + 19.7922i −0.393335 + 0.681277i
\(845\) 28.7984 18.1383i 0.990694 0.623976i
\(846\) 22.5623 0.775708
\(847\) 0 0
\(848\) −18.5451 + 32.1210i −0.636841 + 1.10304i
\(849\) 17.5623 30.4188i 0.602737 1.04397i
\(850\) −3.57295 + 6.18853i −0.122551 + 0.212265i
\(851\) −17.8885 −0.613211
\(852\) 90.1033 156.064i 3.08689 5.34665i
\(853\) −14.1246 −0.483617 −0.241809 0.970324i \(-0.577741\pi\)
−0.241809 + 0.970324i \(0.577741\pi\)
\(854\) 0 0
\(855\) 9.35410 16.2018i 0.319904 0.554089i
\(856\) −25.2705 −0.863728
\(857\) −13.2254 + 22.9071i −0.451772 + 0.782492i −0.998496 0.0548208i \(-0.982541\pi\)
0.546724 + 0.837313i \(0.315875\pi\)
\(858\) 12.7082 + 44.0225i 0.433851 + 1.50290i
\(859\) −22.1246 38.3210i −0.754882 1.30749i −0.945433 0.325817i \(-0.894361\pi\)
0.190551 0.981677i \(-0.438973\pi\)
\(860\) 79.8222 138.256i 2.72191 4.71449i
\(861\) 0 0
\(862\) −10.2082 17.6811i −0.347693 0.602222i
\(863\) −5.94427 10.2958i −0.202345 0.350472i 0.746938 0.664893i \(-0.231523\pi\)
−0.949284 + 0.314421i \(0.898190\pi\)
\(864\) 24.2705 0.825700
\(865\) −23.5623 −0.801142
\(866\) 1.30902 + 2.26728i 0.0444822 + 0.0770454i
\(867\) 19.4164 + 33.6302i 0.659416 + 1.14214i
\(868\) 0 0
\(869\) −3.70820 + 6.42280i −0.125792 + 0.217878i
\(870\) 63.6140 + 110.183i 2.15672 + 3.73554i
\(871\) 44.4787 + 11.0056i 1.50710 + 0.372911i
\(872\) 10.1180 17.5249i 0.342640 0.593470i
\(873\) −72.6656 −2.45936
\(874\) 10.8541 18.7999i 0.367145 0.635915i
\(875\) 0 0
\(876\) 25.4164 0.858741
\(877\) −0.354102 + 0.613323i −0.0119572 + 0.0207104i −0.871942 0.489609i \(-0.837140\pi\)
0.859985 + 0.510319i \(0.170473\pi\)
\(878\) −38.8885 −1.31242
\(879\) −8.85410 + 15.3358i −0.298641 + 0.517262i
\(880\) 23.9164 41.4244i 0.806222 1.39642i
\(881\) −18.2984 + 31.6937i −0.616488 + 1.06779i 0.373634 + 0.927576i \(0.378112\pi\)
−0.990122 + 0.140212i \(0.955222\pi\)
\(882\) 0 0
\(883\) 29.0000 0.975928 0.487964 0.872864i \(-0.337740\pi\)
0.487964 + 0.872864i \(0.337740\pi\)
\(884\) 17.8647 18.5656i 0.600856 0.624428i
\(885\) 7.66312 13.2729i 0.257593 0.446164i
\(886\) 6.85410 + 11.8717i 0.230268 + 0.398836i
\(887\) −54.6525 −1.83505 −0.917525 0.397677i \(-0.869816\pi\)
−0.917525 + 0.397677i \(0.869816\pi\)
\(888\) −39.1246 67.7658i −1.31294 2.27407i
\(889\) 0 0
\(890\) −16.8262 29.1439i −0.564017 0.976906i
\(891\) 5.29180 9.16566i 0.177282 0.307061i
\(892\) 49.1976 85.2127i 1.64726 2.85313i
\(893\) 4.14590 0.138737
\(894\) 12.7082 0.425026
\(895\) −11.7812 + 20.4056i −0.393801 + 0.682082i
\(896\) 0 0
\(897\) 40.9787 + 10.1396i 1.36824 + 0.338551i
\(898\) −25.5623 44.2752i −0.853025 1.47748i
\(899\) −16.6910 28.9096i −0.556675 0.964190i
\(900\) −17.3435 30.0398i −0.578115 1.00133i
\(901\) −2.77051 + 4.79866i −0.0922991 + 0.159867i
\(902\) −3.70820 −0.123470
\(903\) 0 0
\(904\) −5.50000 9.52628i −0.182927 0.316839i
\(905\) −12.7082 22.0113i −0.422435 0.731679i
\(906\) −8.85410 −0.294158
\(907\) 12.0000 + 20.7846i 0.398453 + 0.690142i 0.993535 0.113523i \(-0.0362137\pi\)
−0.595082 + 0.803665i \(0.702880\pi\)
\(908\) −7.14590 −0.237145
\(909\) 44.5623 1.47804
\(910\) 0 0
\(911\) −22.6869 −0.751651 −0.375826 0.926690i \(-0.622641\pi\)
−0.375826 + 0.926690i \(0.622641\pi\)
\(912\) 47.8328 1.58390
\(913\) 6.21885 + 10.7714i 0.205814 + 0.356480i
\(914\) 40.3607 1.33501
\(915\) 20.5623 + 35.6150i 0.679769 + 1.17739i
\(916\) −31.8541 55.1729i −1.05249 1.82296i
\(917\) 0 0
\(918\) 8.61803 0.284438
\(919\) 15.0000 25.9808i 0.494804 0.857026i −0.505178 0.863015i \(-0.668573\pi\)
0.999982 + 0.00598907i \(0.00190639\pi\)
\(920\) −43.7426 75.7645i −1.44215 2.49788i
\(921\) −6.35410 11.0056i −0.209375 0.362648i
\(922\) −15.9894 27.6944i −0.526581 0.912066i
\(923\) 49.6312 + 12.2805i 1.63363 + 0.404219i
\(924\) 0 0
\(925\) −3.70820 + 6.42280i −0.121925 + 0.211180i
\(926\) 17.5623 0.577133
\(927\) 33.5623 1.10233
\(928\) −38.4787 + 66.6471i −1.26313 + 2.18780i
\(929\) 5.53444 9.58593i 0.181579 0.314504i −0.760839 0.648940i \(-0.775212\pi\)
0.942418 + 0.334436i \(0.108546\pi\)
\(930\) 42.2426 + 73.1664i 1.38519 + 2.39922i
\(931\) 0 0
\(932\) −6.35410 11.0056i −0.208136 0.360501i
\(933\) −8.70820 −0.285094
\(934\) 3.07295 + 5.32250i 0.100550 + 0.174158i
\(935\) 3.57295 6.18853i 0.116848 0.202387i
\(936\) 28.7984 + 99.7605i 0.941304 + 3.26077i
\(937\) 15.8754 0.518626 0.259313 0.965793i \(-0.416504\pi\)
0.259313 + 0.965793i \(0.416504\pi\)
\(938\) 0 0
\(939\) 32.8885 56.9646i 1.07328 1.85897i
\(940\) 14.2082 24.6093i 0.463421 0.802668i
\(941\) 10.1738 17.6215i 0.331655 0.574444i −0.651181 0.758922i \(-0.725726\pi\)
0.982837 + 0.184479i \(0.0590596\pi\)
\(942\) −101.812 −3.31720
\(943\) −1.70820 + 2.95870i −0.0556268 + 0.0963484i
\(944\) 22.0344 0.717160
\(945\) 0 0
\(946\) −30.4894 + 52.8091i −0.991294 + 1.71697i
\(947\) −36.8673 −1.19802 −0.599012 0.800740i \(-0.704440\pi\)
−0.599012 + 0.800740i \(0.704440\pi\)
\(948\) −25.4164 + 44.0225i −0.825487 + 1.42978i
\(949\) 2.00000 + 6.92820i 0.0649227 + 0.224899i
\(950\) −4.50000 7.79423i −0.145999 0.252878i
\(951\) −34.3435 + 59.4846i −1.11366 + 1.92892i
\(952\) 0 0
\(953\) −13.3885 23.1896i −0.433697 0.751186i 0.563491 0.826122i \(-0.309458\pi\)
−0.997188 + 0.0749362i \(0.976125\pi\)
\(954\) −18.9894 32.8905i −0.614803 1.06487i
\(955\) −55.9787 −1.81143
\(956\) −119.936 −3.87901
\(957\) −17.2082 29.8055i −0.556262 0.963474i
\(958\) 32.6976 + 56.6338i 1.05641 + 1.82976i
\(959\) 0 0
\(960\) 29.8435 51.6904i 0.963193 1.66830i
\(961\) 4.41641 + 7.64944i 0.142465 + 0.246756i
\(962\) 26.1803 27.2074i 0.844088 0.877202i
\(963\) 6.51722 11.2882i 0.210015 0.363756i
\(964\) −119.228 −3.84007
\(965\) −7.85410 + 13.6037i −0.252832 + 0.437919i
\(966\) 0 0
\(967\) −39.0000 −1.25416 −0.627078 0.778957i \(-0.715749\pi\)
−0.627078 + 0.778957i \(0.715749\pi\)
\(968\) 28.2533 48.9361i 0.908095 1.57287i
\(969\) 7.14590 0.229559
\(970\) −64.6140 + 111.915i −2.07463 + 3.59336i
\(971\) 15.7918 27.3522i 0.506783 0.877774i −0.493186 0.869924i \(-0.664168\pi\)
0.999969 0.00784995i \(-0.00249874\pi\)
\(972\) 52.5517 91.0221i 1.68560 2.91954i
\(973\) 0 0
\(974\) 78.4853 2.51483
\(975\) 12.1353 12.6113i 0.388639 0.403886i
\(976\) −29.5623 + 51.2034i −0.946266 + 1.63898i
\(977\) 11.2639 + 19.5097i 0.360365 + 0.624171i 0.988021 0.154320i \(-0.0493188\pi\)
−0.627656 + 0.778491i \(0.715985\pi\)
\(978\) −25.4164 −0.812727
\(979\) 4.55166 + 7.88371i 0.145472 + 0.251965i
\(980\) 0 0
\(981\) 5.21885 + 9.03931i 0.166625 + 0.288603i
\(982\) −16.2082 + 28.0734i −0.517225 + 0.895859i
\(983\) 9.19098 15.9192i 0.293147 0.507745i −0.681405 0.731906i \(-0.738631\pi\)
0.974552 + 0.224161i \(0.0719642\pi\)
\(984\) −14.9443 −0.476406
\(985\) 43.9787 1.40128
\(986\) −13.6631 + 23.6652i −0.435122 + 0.753654i
\(987\) 0 0
\(988\) 9.00000 + 31.1769i 0.286328 + 0.991870i
\(989\) 28.0902 + 48.6536i 0.893215 + 1.54709i
\(990\) 24.4894 + 42.4168i 0.778323 + 1.34809i
\(991\) 8.07295 + 13.9828i 0.256446 + 0.444177i 0.965287 0.261191i \(-0.0841152\pi\)
−0.708842 + 0.705368i \(0.750782\pi\)
\(992\) −25.5517 + 44.2568i −0.811266 + 1.40515i
\(993\) −26.5623 −0.842929
\(994\) 0 0
\(995\) 31.9615 + 55.3589i 1.01325 + 1.75500i
\(996\) 42.6246 + 73.8280i 1.35061 + 2.33933i
\(997\) −49.0000 −1.55185 −0.775923 0.630828i \(-0.782715\pi\)
−0.775923 + 0.630828i \(0.782715\pi\)
\(998\) −19.4443 33.6785i −0.615498 1.06607i
\(999\) 8.94427 0.282984
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.f.165.2 4
7.2 even 3 637.2.g.c.373.1 4
7.3 odd 6 91.2.f.a.22.1 4
7.4 even 3 637.2.f.c.295.1 4
7.5 odd 6 637.2.g.b.373.1 4
7.6 odd 2 637.2.h.g.165.2 4
13.3 even 3 637.2.g.c.263.1 4
21.17 even 6 819.2.o.c.568.2 4
28.3 even 6 1456.2.s.h.113.1 4
91.3 odd 6 91.2.f.a.29.1 yes 4
91.4 even 6 8281.2.a.n.1.1 2
91.16 even 3 inner 637.2.h.f.471.2 4
91.17 odd 6 1183.2.a.c.1.1 2
91.45 even 12 1183.2.c.c.337.1 4
91.55 odd 6 637.2.g.b.263.1 4
91.59 even 12 1183.2.c.c.337.4 4
91.68 odd 6 637.2.h.g.471.2 4
91.74 even 3 8281.2.a.bb.1.2 2
91.81 even 3 637.2.f.c.393.1 4
91.87 odd 6 1183.2.a.g.1.2 2
273.185 even 6 819.2.o.c.757.2 4
364.3 even 6 1456.2.s.h.1121.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.f.a.22.1 4 7.3 odd 6
91.2.f.a.29.1 yes 4 91.3 odd 6
637.2.f.c.295.1 4 7.4 even 3
637.2.f.c.393.1 4 91.81 even 3
637.2.g.b.263.1 4 91.55 odd 6
637.2.g.b.373.1 4 7.5 odd 6
637.2.g.c.263.1 4 13.3 even 3
637.2.g.c.373.1 4 7.2 even 3
637.2.h.f.165.2 4 1.1 even 1 trivial
637.2.h.f.471.2 4 91.16 even 3 inner
637.2.h.g.165.2 4 7.6 odd 2
637.2.h.g.471.2 4 91.68 odd 6
819.2.o.c.568.2 4 21.17 even 6
819.2.o.c.757.2 4 273.185 even 6
1183.2.a.c.1.1 2 91.17 odd 6
1183.2.a.g.1.2 2 91.87 odd 6
1183.2.c.c.337.1 4 91.45 even 12
1183.2.c.c.337.4 4 91.59 even 12
1456.2.s.h.113.1 4 28.3 even 6
1456.2.s.h.1121.1 4 364.3 even 6
8281.2.a.n.1.1 2 91.4 even 6
8281.2.a.bb.1.2 2 91.74 even 3