Properties

Label 525.3.s.b.124.1
Level $525$
Weight $3$
Character 525.124
Analytic conductor $14.305$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,3,Mod(124,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.124");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 525.s (of order \(6\), 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: \(14.3052138789\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 124.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 525.124
Dual form 525.3.s.b.199.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(-1.50000 - 2.59808i) q^{4} +1.73205i q^{6} +(-4.33013 + 5.50000i) q^{7} +7.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(-1.50000 - 2.59808i) q^{4} +1.73205i q^{6} +(-4.33013 + 5.50000i) q^{7} +7.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-2.00000 - 3.46410i) q^{11} +(-2.59808 + 4.50000i) q^{12} +17.3205 q^{13} +(6.50000 - 2.59808i) q^{14} +(-2.50000 + 4.33013i) q^{16} +(4.33013 + 7.50000i) q^{17} +(2.59808 - 1.50000i) q^{18} +(-6.00000 - 3.46410i) q^{19} +(12.0000 + 1.73205i) q^{21} +4.00000i q^{22} +(26.8468 + 15.5000i) q^{23} +(10.5000 - 6.06218i) q^{24} +(-15.0000 - 8.66025i) q^{26} +5.19615 q^{27} +(20.7846 + 3.00000i) q^{28} -10.0000 q^{29} +(25.5000 - 14.7224i) q^{31} +(28.5788 - 16.5000i) q^{32} +(-3.46410 + 6.00000i) q^{33} -8.66025i q^{34} +9.00000 q^{36} +(-43.3013 - 25.0000i) q^{37} +(3.46410 + 6.00000i) q^{38} +(-15.0000 - 25.9808i) q^{39} -53.6936i q^{41} +(-9.52628 - 7.50000i) q^{42} +34.0000i q^{43} +(-6.00000 + 10.3923i) q^{44} +(-15.5000 - 26.8468i) q^{46} +(-21.6506 + 37.5000i) q^{47} +8.66025 q^{48} +(-11.5000 - 47.6314i) q^{49} +(7.50000 - 12.9904i) q^{51} +(-25.9808 - 45.0000i) q^{52} +(43.3013 - 25.0000i) q^{53} +(-4.50000 - 2.59808i) q^{54} +(-38.5000 - 30.3109i) q^{56} +12.0000i q^{57} +(8.66025 + 5.00000i) q^{58} +(48.0000 - 27.7128i) q^{59} +(21.0000 + 12.1244i) q^{61} -29.4449 q^{62} +(-7.79423 - 19.5000i) q^{63} -13.0000 q^{64} +(6.00000 - 3.46410i) q^{66} +(43.3013 - 25.0000i) q^{67} +(12.9904 - 22.5000i) q^{68} -53.6936i q^{69} +97.0000 q^{71} +(-18.1865 - 10.5000i) q^{72} +(-24.2487 - 42.0000i) q^{73} +(25.0000 + 43.3013i) q^{74} +20.7846i q^{76} +(27.7128 + 4.00000i) q^{77} +30.0000i q^{78} +(-3.50000 + 6.06218i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-26.8468 + 46.5000i) q^{82} +152.420 q^{83} +(-13.5000 - 33.7750i) q^{84} +(17.0000 - 29.4449i) q^{86} +(8.66025 + 15.0000i) q^{87} +(24.2487 - 14.0000i) q^{88} +(136.500 + 78.8083i) q^{89} +(-75.0000 + 95.2628i) q^{91} -93.0000i q^{92} +(-44.1673 - 25.5000i) q^{93} +(37.5000 - 21.6506i) q^{94} +(-49.5000 - 28.5788i) q^{96} -112.583 q^{97} +(-13.8564 + 47.0000i) q^{98} +12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 6 q^{4} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 6 q^{4} - 6 q^{9} - 8 q^{11} + 26 q^{14} - 10 q^{16} - 24 q^{19} + 48 q^{21} + 42 q^{24} - 60 q^{26} - 40 q^{29} + 102 q^{31} + 36 q^{36} - 60 q^{39} - 24 q^{44} - 62 q^{46} - 46 q^{49} + 30 q^{51} - 18 q^{54} - 154 q^{56} + 192 q^{59} + 84 q^{61} - 52 q^{64} + 24 q^{66} + 388 q^{71} + 100 q^{74} - 14 q^{79} - 18 q^{81} - 54 q^{84} + 68 q^{86} + 546 q^{89} - 300 q^{91} + 150 q^{94} - 198 q^{96} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.433013 0.250000i 0.267617 0.963525i \(-0.413764\pi\)
−0.700629 + 0.713525i \(0.747097\pi\)
\(3\) −0.866025 1.50000i −0.288675 0.500000i
\(4\) −1.50000 2.59808i −0.375000 0.649519i
\(5\) 0 0
\(6\) 1.73205i 0.288675i
\(7\) −4.33013 + 5.50000i −0.618590 + 0.785714i
\(8\) 7.00000i 0.875000i
\(9\) −1.50000 + 2.59808i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −2.00000 3.46410i −0.181818 0.314918i 0.760682 0.649125i \(-0.224865\pi\)
−0.942500 + 0.334207i \(0.891532\pi\)
\(12\) −2.59808 + 4.50000i −0.216506 + 0.375000i
\(13\) 17.3205 1.33235 0.666173 0.745797i \(-0.267931\pi\)
0.666173 + 0.745797i \(0.267931\pi\)
\(14\) 6.50000 2.59808i 0.464286 0.185577i
\(15\) 0 0
\(16\) −2.50000 + 4.33013i −0.156250 + 0.270633i
\(17\) 4.33013 + 7.50000i 0.254713 + 0.441176i 0.964818 0.262920i \(-0.0846856\pi\)
−0.710104 + 0.704097i \(0.751352\pi\)
\(18\) 2.59808 1.50000i 0.144338 0.0833333i
\(19\) −6.00000 3.46410i −0.315789 0.182321i 0.333725 0.942671i \(-0.391694\pi\)
−0.649514 + 0.760349i \(0.725028\pi\)
\(20\) 0 0
\(21\) 12.0000 + 1.73205i 0.571429 + 0.0824786i
\(22\) 4.00000i 0.181818i
\(23\) 26.8468 + 15.5000i 1.16725 + 0.673913i 0.953031 0.302872i \(-0.0979456\pi\)
0.214220 + 0.976785i \(0.431279\pi\)
\(24\) 10.5000 6.06218i 0.437500 0.252591i
\(25\) 0 0
\(26\) −15.0000 8.66025i −0.576923 0.333087i
\(27\) 5.19615 0.192450
\(28\) 20.7846 + 3.00000i 0.742307 + 0.107143i
\(29\) −10.0000 −0.344828 −0.172414 0.985025i \(-0.555157\pi\)
−0.172414 + 0.985025i \(0.555157\pi\)
\(30\) 0 0
\(31\) 25.5000 14.7224i 0.822581 0.474917i −0.0287249 0.999587i \(-0.509145\pi\)
0.851306 + 0.524670i \(0.175811\pi\)
\(32\) 28.5788 16.5000i 0.893089 0.515625i
\(33\) −3.46410 + 6.00000i −0.104973 + 0.181818i
\(34\) 8.66025i 0.254713i
\(35\) 0 0
\(36\) 9.00000 0.250000
\(37\) −43.3013 25.0000i −1.17030 0.675676i −0.216553 0.976271i \(-0.569481\pi\)
−0.953752 + 0.300595i \(0.902815\pi\)
\(38\) 3.46410 + 6.00000i 0.0911606 + 0.157895i
\(39\) −15.0000 25.9808i −0.384615 0.666173i
\(40\) 0 0
\(41\) 53.6936i 1.30960i −0.755802 0.654800i \(-0.772753\pi\)
0.755802 0.654800i \(-0.227247\pi\)
\(42\) −9.52628 7.50000i −0.226816 0.178571i
\(43\) 34.0000i 0.790698i 0.918531 + 0.395349i \(0.129376\pi\)
−0.918531 + 0.395349i \(0.870624\pi\)
\(44\) −6.00000 + 10.3923i −0.136364 + 0.236189i
\(45\) 0 0
\(46\) −15.5000 26.8468i −0.336957 0.583626i
\(47\) −21.6506 + 37.5000i −0.460652 + 0.797872i −0.998994 0.0448543i \(-0.985718\pi\)
0.538342 + 0.842727i \(0.319051\pi\)
\(48\) 8.66025 0.180422
\(49\) −11.5000 47.6314i −0.234694 0.972069i
\(50\) 0 0
\(51\) 7.50000 12.9904i 0.147059 0.254713i
\(52\) −25.9808 45.0000i −0.499630 0.865385i
\(53\) 43.3013 25.0000i 0.817005 0.471698i −0.0323775 0.999476i \(-0.510308\pi\)
0.849383 + 0.527778i \(0.176975\pi\)
\(54\) −4.50000 2.59808i −0.0833333 0.0481125i
\(55\) 0 0
\(56\) −38.5000 30.3109i −0.687500 0.541266i
\(57\) 12.0000i 0.210526i
\(58\) 8.66025 + 5.00000i 0.149315 + 0.0862069i
\(59\) 48.0000 27.7128i 0.813559 0.469709i −0.0346311 0.999400i \(-0.511026\pi\)
0.848190 + 0.529691i \(0.177692\pi\)
\(60\) 0 0
\(61\) 21.0000 + 12.1244i 0.344262 + 0.198760i 0.662155 0.749367i \(-0.269642\pi\)
−0.317893 + 0.948127i \(0.602975\pi\)
\(62\) −29.4449 −0.474917
\(63\) −7.79423 19.5000i −0.123718 0.309524i
\(64\) −13.0000 −0.203125
\(65\) 0 0
\(66\) 6.00000 3.46410i 0.0909091 0.0524864i
\(67\) 43.3013 25.0000i 0.646288 0.373134i −0.140745 0.990046i \(-0.544950\pi\)
0.787032 + 0.616912i \(0.211616\pi\)
\(68\) 12.9904 22.5000i 0.191035 0.330882i
\(69\) 53.6936i 0.778168i
\(70\) 0 0
\(71\) 97.0000 1.36620 0.683099 0.730326i \(-0.260632\pi\)
0.683099 + 0.730326i \(0.260632\pi\)
\(72\) −18.1865 10.5000i −0.252591 0.145833i
\(73\) −24.2487 42.0000i −0.332174 0.575342i 0.650764 0.759280i \(-0.274449\pi\)
−0.982938 + 0.183938i \(0.941115\pi\)
\(74\) 25.0000 + 43.3013i 0.337838 + 0.585152i
\(75\) 0 0
\(76\) 20.7846i 0.273482i
\(77\) 27.7128 + 4.00000i 0.359907 + 0.0519481i
\(78\) 30.0000i 0.384615i
\(79\) −3.50000 + 6.06218i −0.0443038 + 0.0767364i −0.887327 0.461141i \(-0.847440\pi\)
0.843023 + 0.537877i \(0.180774\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) −26.8468 + 46.5000i −0.327400 + 0.567073i
\(83\) 152.420 1.83639 0.918196 0.396127i \(-0.129646\pi\)
0.918196 + 0.396127i \(0.129646\pi\)
\(84\) −13.5000 33.7750i −0.160714 0.402083i
\(85\) 0 0
\(86\) 17.0000 29.4449i 0.197674 0.342382i
\(87\) 8.66025 + 15.0000i 0.0995431 + 0.172414i
\(88\) 24.2487 14.0000i 0.275554 0.159091i
\(89\) 136.500 + 78.8083i 1.53371 + 0.885487i 0.999186 + 0.0403318i \(0.0128415\pi\)
0.534522 + 0.845155i \(0.320492\pi\)
\(90\) 0 0
\(91\) −75.0000 + 95.2628i −0.824176 + 1.04684i
\(92\) 93.0000i 1.01087i
\(93\) −44.1673 25.5000i −0.474917 0.274194i
\(94\) 37.5000 21.6506i 0.398936 0.230326i
\(95\) 0 0
\(96\) −49.5000 28.5788i −0.515625 0.297696i
\(97\) −112.583 −1.16065 −0.580326 0.814384i \(-0.697075\pi\)
−0.580326 + 0.814384i \(0.697075\pi\)
\(98\) −13.8564 + 47.0000i −0.141392 + 0.479592i
\(99\) 12.0000 0.121212
\(100\) 0 0
\(101\) −18.0000 + 10.3923i −0.178218 + 0.102894i −0.586455 0.809982i \(-0.699477\pi\)
0.408237 + 0.912876i \(0.366144\pi\)
\(102\) −12.9904 + 7.50000i −0.127357 + 0.0735294i
\(103\) −49.3634 + 85.5000i −0.479257 + 0.830097i −0.999717 0.0237888i \(-0.992427\pi\)
0.520460 + 0.853886i \(0.325760\pi\)
\(104\) 121.244i 1.16580i
\(105\) 0 0
\(106\) −50.0000 −0.471698
\(107\) 152.420 + 88.0000i 1.42449 + 0.822430i 0.996678 0.0814379i \(-0.0259512\pi\)
0.427812 + 0.903868i \(0.359285\pi\)
\(108\) −7.79423 13.5000i −0.0721688 0.125000i
\(109\) −2.00000 3.46410i −0.0183486 0.0317807i 0.856705 0.515806i \(-0.172508\pi\)
−0.875054 + 0.484025i \(0.839174\pi\)
\(110\) 0 0
\(111\) 86.6025i 0.780203i
\(112\) −12.9904 32.5000i −0.115986 0.290179i
\(113\) 115.000i 1.01770i −0.860855 0.508850i \(-0.830071\pi\)
0.860855 0.508850i \(-0.169929\pi\)
\(114\) 6.00000 10.3923i 0.0526316 0.0911606i
\(115\) 0 0
\(116\) 15.0000 + 25.9808i 0.129310 + 0.223972i
\(117\) −25.9808 + 45.0000i −0.222058 + 0.384615i
\(118\) −55.4256 −0.469709
\(119\) −60.0000 8.66025i −0.504202 0.0727752i
\(120\) 0 0
\(121\) 52.5000 90.9327i 0.433884 0.751510i
\(122\) −12.1244 21.0000i −0.0993800 0.172131i
\(123\) −80.5404 + 46.5000i −0.654800 + 0.378049i
\(124\) −76.5000 44.1673i −0.616935 0.356188i
\(125\) 0 0
\(126\) −3.00000 + 20.7846i −0.0238095 + 0.164957i
\(127\) 62.0000i 0.488189i 0.969751 + 0.244094i \(0.0784907\pi\)
−0.969751 + 0.244094i \(0.921509\pi\)
\(128\) −103.057 59.5000i −0.805133 0.464844i
\(129\) 51.0000 29.4449i 0.395349 0.228255i
\(130\) 0 0
\(131\) −27.0000 15.5885i −0.206107 0.118996i 0.393394 0.919370i \(-0.371301\pi\)
−0.599501 + 0.800374i \(0.704634\pi\)
\(132\) 20.7846 0.157459
\(133\) 45.0333 18.0000i 0.338596 0.135338i
\(134\) −50.0000 −0.373134
\(135\) 0 0
\(136\) −52.5000 + 30.3109i −0.386029 + 0.222874i
\(137\) 193.124 111.500i 1.40966 0.813869i 0.414306 0.910137i \(-0.364024\pi\)
0.995355 + 0.0962688i \(0.0306909\pi\)
\(138\) −26.8468 + 46.5000i −0.194542 + 0.336957i
\(139\) 79.6743i 0.573197i −0.958051 0.286598i \(-0.907475\pi\)
0.958051 0.286598i \(-0.0925245\pi\)
\(140\) 0 0
\(141\) 75.0000 0.531915
\(142\) −84.0045 48.5000i −0.591581 0.341549i
\(143\) −34.6410 60.0000i −0.242245 0.419580i
\(144\) −7.50000 12.9904i −0.0520833 0.0902110i
\(145\) 0 0
\(146\) 48.4974i 0.332174i
\(147\) −61.4878 + 58.5000i −0.418284 + 0.397959i
\(148\) 150.000i 1.01351i
\(149\) −106.000 + 183.597i −0.711409 + 1.23220i 0.252919 + 0.967488i \(0.418609\pi\)
−0.964328 + 0.264710i \(0.914724\pi\)
\(150\) 0 0
\(151\) 119.000 + 206.114i 0.788079 + 1.36499i 0.927142 + 0.374710i \(0.122258\pi\)
−0.139063 + 0.990284i \(0.544409\pi\)
\(152\) 24.2487 42.0000i 0.159531 0.276316i
\(153\) −25.9808 −0.169809
\(154\) −22.0000 17.3205i −0.142857 0.112471i
\(155\) 0 0
\(156\) −45.0000 + 77.9423i −0.288462 + 0.499630i
\(157\) 126.440 + 219.000i 0.805348 + 1.39490i 0.916056 + 0.401051i \(0.131355\pi\)
−0.110707 + 0.993853i \(0.535312\pi\)
\(158\) 6.06218 3.50000i 0.0383682 0.0221519i
\(159\) −75.0000 43.3013i −0.471698 0.272335i
\(160\) 0 0
\(161\) −201.500 + 80.5404i −1.25155 + 0.500251i
\(162\) 9.00000i 0.0555556i
\(163\) −252.879 146.000i −1.55141 0.895706i −0.998028 0.0627765i \(-0.980004\pi\)
−0.553380 0.832929i \(-0.686662\pi\)
\(164\) −139.500 + 80.5404i −0.850610 + 0.491100i
\(165\) 0 0
\(166\) −132.000 76.2102i −0.795181 0.459098i
\(167\) 131.636 0.788239 0.394119 0.919059i \(-0.371050\pi\)
0.394119 + 0.919059i \(0.371050\pi\)
\(168\) −12.1244 + 84.0000i −0.0721688 + 0.500000i
\(169\) 131.000 0.775148
\(170\) 0 0
\(171\) 18.0000 10.3923i 0.105263 0.0607737i
\(172\) 88.3346 51.0000i 0.513573 0.296512i
\(173\) −74.4782 + 129.000i −0.430510 + 0.745665i −0.996917 0.0784606i \(-0.975000\pi\)
0.566407 + 0.824125i \(0.308333\pi\)
\(174\) 17.3205i 0.0995431i
\(175\) 0 0
\(176\) 20.0000 0.113636
\(177\) −83.1384 48.0000i −0.469709 0.271186i
\(178\) −78.8083 136.500i −0.442743 0.766854i
\(179\) 95.0000 + 164.545i 0.530726 + 0.919245i 0.999357 + 0.0358508i \(0.0114141\pi\)
−0.468631 + 0.883394i \(0.655253\pi\)
\(180\) 0 0
\(181\) 20.7846i 0.114832i −0.998350 0.0574160i \(-0.981714\pi\)
0.998350 0.0574160i \(-0.0182862\pi\)
\(182\) 112.583 45.0000i 0.618590 0.247253i
\(183\) 42.0000i 0.229508i
\(184\) −108.500 + 187.928i −0.589674 + 1.02135i
\(185\) 0 0
\(186\) 25.5000 + 44.1673i 0.137097 + 0.237459i
\(187\) 17.3205 30.0000i 0.0926230 0.160428i
\(188\) 129.904 0.690978
\(189\) −22.5000 + 28.5788i −0.119048 + 0.151211i
\(190\) 0 0
\(191\) 134.500 232.961i 0.704188 1.21969i −0.262795 0.964852i \(-0.584644\pi\)
0.966984 0.254839i \(-0.0820223\pi\)
\(192\) 11.2583 + 19.5000i 0.0586371 + 0.101562i
\(193\) −25.1147 + 14.5000i −0.130128 + 0.0751295i −0.563651 0.826013i \(-0.690604\pi\)
0.433523 + 0.901143i \(0.357270\pi\)
\(194\) 97.5000 + 56.2917i 0.502577 + 0.290163i
\(195\) 0 0
\(196\) −106.500 + 101.325i −0.543367 + 0.516964i
\(197\) 52.0000i 0.263959i 0.991252 + 0.131980i \(0.0421334\pi\)
−0.991252 + 0.131980i \(0.957867\pi\)
\(198\) −10.3923 6.00000i −0.0524864 0.0303030i
\(199\) −154.500 + 89.2006i −0.776382 + 0.448244i −0.835147 0.550028i \(-0.814617\pi\)
0.0587646 + 0.998272i \(0.481284\pi\)
\(200\) 0 0
\(201\) −75.0000 43.3013i −0.373134 0.215429i
\(202\) 20.7846 0.102894
\(203\) 43.3013 55.0000i 0.213307 0.270936i
\(204\) −45.0000 −0.220588
\(205\) 0 0
\(206\) 85.5000 49.3634i 0.415049 0.239628i
\(207\) −80.5404 + 46.5000i −0.389084 + 0.224638i
\(208\) −43.3013 + 75.0000i −0.208179 + 0.360577i
\(209\) 27.7128i 0.132597i
\(210\) 0 0
\(211\) 344.000 1.63033 0.815166 0.579228i \(-0.196646\pi\)
0.815166 + 0.579228i \(0.196646\pi\)
\(212\) −129.904 75.0000i −0.612754 0.353774i
\(213\) −84.0045 145.500i −0.394387 0.683099i
\(214\) −88.0000 152.420i −0.411215 0.712245i
\(215\) 0 0
\(216\) 36.3731i 0.168394i
\(217\) −29.4449 + 204.000i −0.135691 + 0.940092i
\(218\) 4.00000i 0.0183486i
\(219\) −42.0000 + 72.7461i −0.191781 + 0.332174i
\(220\) 0 0
\(221\) 75.0000 + 129.904i 0.339367 + 0.587800i
\(222\) 43.3013 75.0000i 0.195051 0.337838i
\(223\) −219.970 −0.986415 −0.493207 0.869912i \(-0.664176\pi\)
−0.493207 + 0.869912i \(0.664176\pi\)
\(224\) −33.0000 + 228.631i −0.147321 + 1.02067i
\(225\) 0 0
\(226\) −57.5000 + 99.5929i −0.254425 + 0.440677i
\(227\) −41.5692 72.0000i −0.183124 0.317181i 0.759819 0.650135i \(-0.225288\pi\)
−0.942943 + 0.332955i \(0.891954\pi\)
\(228\) 31.1769 18.0000i 0.136741 0.0789474i
\(229\) 108.000 + 62.3538i 0.471616 + 0.272287i 0.716916 0.697160i \(-0.245553\pi\)
−0.245300 + 0.969447i \(0.578887\pi\)
\(230\) 0 0
\(231\) −18.0000 45.0333i −0.0779221 0.194949i
\(232\) 70.0000i 0.301724i
\(233\) −168.009 97.0000i −0.721068 0.416309i 0.0940774 0.995565i \(-0.470010\pi\)
−0.815146 + 0.579256i \(0.803343\pi\)
\(234\) 45.0000 25.9808i 0.192308 0.111029i
\(235\) 0 0
\(236\) −144.000 83.1384i −0.610169 0.352282i
\(237\) 12.1244 0.0511576
\(238\) 47.6314 + 37.5000i 0.200132 + 0.157563i
\(239\) 155.000 0.648536 0.324268 0.945965i \(-0.394882\pi\)
0.324268 + 0.945965i \(0.394882\pi\)
\(240\) 0 0
\(241\) 234.000 135.100i 0.970954 0.560581i 0.0714273 0.997446i \(-0.477245\pi\)
0.899527 + 0.436865i \(0.143911\pi\)
\(242\) −90.9327 + 52.5000i −0.375755 + 0.216942i
\(243\) −7.79423 + 13.5000i −0.0320750 + 0.0555556i
\(244\) 72.7461i 0.298140i
\(245\) 0 0
\(246\) 93.0000 0.378049
\(247\) −103.923 60.0000i −0.420741 0.242915i
\(248\) 103.057 + 178.500i 0.415553 + 0.719758i
\(249\) −132.000 228.631i −0.530120 0.918196i
\(250\) 0 0
\(251\) 207.846i 0.828072i 0.910260 + 0.414036i \(0.135881\pi\)
−0.910260 + 0.414036i \(0.864119\pi\)
\(252\) −38.9711 + 49.5000i −0.154647 + 0.196429i
\(253\) 124.000i 0.490119i
\(254\) 31.0000 53.6936i 0.122047 0.211392i
\(255\) 0 0
\(256\) 85.5000 + 148.090i 0.333984 + 0.578478i
\(257\) −239.023 + 414.000i −0.930051 + 1.61089i −0.146820 + 0.989163i \(0.546904\pi\)
−0.783230 + 0.621732i \(0.786429\pi\)
\(258\) −58.8897 −0.228255
\(259\) 325.000 129.904i 1.25483 0.501559i
\(260\) 0 0
\(261\) 15.0000 25.9808i 0.0574713 0.0995431i
\(262\) 15.5885 + 27.0000i 0.0594979 + 0.103053i
\(263\) 51.0955 29.5000i 0.194279 0.112167i −0.399705 0.916644i \(-0.630887\pi\)
0.593984 + 0.804477i \(0.297554\pi\)
\(264\) −42.0000 24.2487i −0.159091 0.0918512i
\(265\) 0 0
\(266\) −48.0000 6.92820i −0.180451 0.0260459i
\(267\) 273.000i 1.02247i
\(268\) −129.904 75.0000i −0.484716 0.279851i
\(269\) 6.00000 3.46410i 0.0223048 0.0128777i −0.488806 0.872392i \(-0.662567\pi\)
0.511111 + 0.859515i \(0.329234\pi\)
\(270\) 0 0
\(271\) −223.500 129.038i −0.824723 0.476154i 0.0273193 0.999627i \(-0.491303\pi\)
−0.852043 + 0.523473i \(0.824636\pi\)
\(272\) −43.3013 −0.159196
\(273\) 207.846 + 30.0000i 0.761341 + 0.109890i
\(274\) −223.000 −0.813869
\(275\) 0 0
\(276\) −139.500 + 80.5404i −0.505435 + 0.291813i
\(277\) 188.794 109.000i 0.681565 0.393502i −0.118879 0.992909i \(-0.537930\pi\)
0.800444 + 0.599407i \(0.204597\pi\)
\(278\) −39.8372 + 69.0000i −0.143299 + 0.248201i
\(279\) 88.3346i 0.316611i
\(280\) 0 0
\(281\) −389.000 −1.38434 −0.692171 0.721734i \(-0.743346\pi\)
−0.692171 + 0.721734i \(0.743346\pi\)
\(282\) −64.9519 37.5000i −0.230326 0.132979i
\(283\) 107.387 + 186.000i 0.379460 + 0.657244i 0.990984 0.133982i \(-0.0427765\pi\)
−0.611524 + 0.791226i \(0.709443\pi\)
\(284\) −145.500 252.013i −0.512324 0.887371i
\(285\) 0 0
\(286\) 69.2820i 0.242245i
\(287\) 295.315 + 232.500i 1.02897 + 0.810105i
\(288\) 99.0000i 0.343750i
\(289\) 107.000 185.329i 0.370242 0.641278i
\(290\) 0 0
\(291\) 97.5000 + 168.875i 0.335052 + 0.580326i
\(292\) −72.7461 + 126.000i −0.249131 + 0.431507i
\(293\) 491.902 1.67885 0.839424 0.543477i \(-0.182893\pi\)
0.839424 + 0.543477i \(0.182893\pi\)
\(294\) 82.5000 19.9186i 0.280612 0.0677503i
\(295\) 0 0
\(296\) 175.000 303.109i 0.591216 1.02402i
\(297\) −10.3923 18.0000i −0.0349909 0.0606061i
\(298\) 183.597 106.000i 0.616099 0.355705i
\(299\) 465.000 + 268.468i 1.55518 + 0.897886i
\(300\) 0 0
\(301\) −187.000 147.224i −0.621262 0.489117i
\(302\) 238.000i 0.788079i
\(303\) 31.1769 + 18.0000i 0.102894 + 0.0594059i
\(304\) 30.0000 17.3205i 0.0986842 0.0569754i
\(305\) 0 0
\(306\) 22.5000 + 12.9904i 0.0735294 + 0.0424522i
\(307\) 145.492 0.473916 0.236958 0.971520i \(-0.423850\pi\)
0.236958 + 0.971520i \(0.423850\pi\)
\(308\) −31.1769 78.0000i −0.101224 0.253247i
\(309\) 171.000 0.553398
\(310\) 0 0
\(311\) −277.500 + 160.215i −0.892283 + 0.515160i −0.874689 0.484685i \(-0.838934\pi\)
−0.0175944 + 0.999845i \(0.505601\pi\)
\(312\) 181.865 105.000i 0.582902 0.336538i
\(313\) 25.1147 43.5000i 0.0802388 0.138978i −0.823114 0.567877i \(-0.807765\pi\)
0.903352 + 0.428899i \(0.141098\pi\)
\(314\) 252.879i 0.805348i
\(315\) 0 0
\(316\) 21.0000 0.0664557
\(317\) −117.779 68.0000i −0.371544 0.214511i 0.302589 0.953121i \(-0.402149\pi\)
−0.674133 + 0.738610i \(0.735482\pi\)
\(318\) 43.3013 + 75.0000i 0.136168 + 0.235849i
\(319\) 20.0000 + 34.6410i 0.0626959 + 0.108593i
\(320\) 0 0
\(321\) 304.841i 0.949660i
\(322\) 214.774 + 31.0000i 0.667001 + 0.0962733i
\(323\) 60.0000i 0.185759i
\(324\) −13.5000 + 23.3827i −0.0416667 + 0.0721688i
\(325\) 0 0
\(326\) 146.000 + 252.879i 0.447853 + 0.775704i
\(327\) −3.46410 + 6.00000i −0.0105936 + 0.0183486i
\(328\) 375.855 1.14590
\(329\) −112.500 281.458i −0.341945 0.855496i
\(330\) 0 0
\(331\) 221.000 382.783i 0.667674 1.15644i −0.310879 0.950449i \(-0.600623\pi\)
0.978553 0.205995i \(-0.0660432\pi\)
\(332\) −228.631 396.000i −0.688647 1.19277i
\(333\) 129.904 75.0000i 0.390102 0.225225i
\(334\) −114.000 65.8179i −0.341317 0.197060i
\(335\) 0 0
\(336\) −37.5000 + 47.6314i −0.111607 + 0.141760i
\(337\) 331.000i 0.982196i −0.871104 0.491098i \(-0.836596\pi\)
0.871104 0.491098i \(-0.163404\pi\)
\(338\) −113.449 65.5000i −0.335649 0.193787i
\(339\) −172.500 + 99.5929i −0.508850 + 0.293784i
\(340\) 0 0
\(341\) −102.000 58.8897i −0.299120 0.172697i
\(342\) −20.7846 −0.0607737
\(343\) 311.769 + 143.000i 0.908948 + 0.416910i
\(344\) −238.000 −0.691860
\(345\) 0 0
\(346\) 129.000 74.4782i 0.372832 0.215255i
\(347\) −105.655 + 61.0000i −0.304482 + 0.175793i −0.644454 0.764643i \(-0.722915\pi\)
0.339973 + 0.940435i \(0.389582\pi\)
\(348\) 25.9808 45.0000i 0.0746574 0.129310i
\(349\) 367.195i 1.05213i −0.850443 0.526067i \(-0.823666\pi\)
0.850443 0.526067i \(-0.176334\pi\)
\(350\) 0 0
\(351\) 90.0000 0.256410
\(352\) −114.315 66.0000i −0.324760 0.187500i
\(353\) 59.7558 + 103.500i 0.169280 + 0.293201i 0.938167 0.346183i \(-0.112523\pi\)
−0.768887 + 0.639385i \(0.779189\pi\)
\(354\) 48.0000 + 83.1384i 0.135593 + 0.234854i
\(355\) 0 0
\(356\) 472.850i 1.32823i
\(357\) 38.9711 + 97.5000i 0.109163 + 0.273109i
\(358\) 190.000i 0.530726i
\(359\) 119.000 206.114i 0.331476 0.574134i −0.651325 0.758799i \(-0.725787\pi\)
0.982802 + 0.184665i \(0.0591200\pi\)
\(360\) 0 0
\(361\) −156.500 271.066i −0.433518 0.750875i
\(362\) −10.3923 + 18.0000i −0.0287080 + 0.0497238i
\(363\) −181.865 −0.501006
\(364\) 360.000 + 51.9615i 0.989011 + 0.142751i
\(365\) 0 0
\(366\) −21.0000 + 36.3731i −0.0573770 + 0.0993800i
\(367\) −114.315 198.000i −0.311486 0.539510i 0.667198 0.744880i \(-0.267493\pi\)
−0.978684 + 0.205371i \(0.934160\pi\)
\(368\) −134.234 + 77.5000i −0.364766 + 0.210598i
\(369\) 139.500 + 80.5404i 0.378049 + 0.218267i
\(370\) 0 0
\(371\) −50.0000 + 346.410i −0.134771 + 0.933720i
\(372\) 153.000i 0.411290i
\(373\) 178.401 + 103.000i 0.478287 + 0.276139i 0.719703 0.694283i \(-0.244278\pi\)
−0.241415 + 0.970422i \(0.577612\pi\)
\(374\) −30.0000 + 17.3205i −0.0802139 + 0.0463115i
\(375\) 0 0
\(376\) −262.500 151.554i −0.698138 0.403070i
\(377\) −173.205 −0.459430
\(378\) 33.7750 13.5000i 0.0893518 0.0357143i
\(379\) 430.000 1.13456 0.567282 0.823523i \(-0.307995\pi\)
0.567282 + 0.823523i \(0.307995\pi\)
\(380\) 0 0
\(381\) 93.0000 53.6936i 0.244094 0.140928i
\(382\) −232.961 + 134.500i −0.609845 + 0.352094i
\(383\) −283.190 + 490.500i −0.739400 + 1.28068i 0.213365 + 0.976972i \(0.431558\pi\)
−0.952766 + 0.303706i \(0.901776\pi\)
\(384\) 206.114i 0.536755i
\(385\) 0 0
\(386\) 29.0000 0.0751295
\(387\) −88.3346 51.0000i −0.228255 0.131783i
\(388\) 168.875 + 292.500i 0.435245 + 0.753866i
\(389\) −280.000 484.974i −0.719794 1.24672i −0.961081 0.276267i \(-0.910903\pi\)
0.241287 0.970454i \(-0.422431\pi\)
\(390\) 0 0
\(391\) 268.468i 0.686619i
\(392\) 333.420 80.5000i 0.850561 0.205357i
\(393\) 54.0000i 0.137405i
\(394\) 26.0000 45.0333i 0.0659898 0.114298i
\(395\) 0 0
\(396\) −18.0000 31.1769i −0.0454545 0.0787296i
\(397\) −315.233 + 546.000i −0.794038 + 1.37531i 0.129410 + 0.991591i \(0.458692\pi\)
−0.923448 + 0.383724i \(0.874642\pi\)
\(398\) 178.401 0.448244
\(399\) −66.0000 51.9615i −0.165414 0.130229i
\(400\) 0 0
\(401\) 277.000 479.778i 0.690773 1.19645i −0.280812 0.959763i \(-0.590604\pi\)
0.971585 0.236691i \(-0.0760630\pi\)
\(402\) 43.3013 + 75.0000i 0.107715 + 0.186567i
\(403\) 441.673 255.000i 1.09596 0.632754i
\(404\) 54.0000 + 31.1769i 0.133663 + 0.0771706i
\(405\) 0 0
\(406\) −65.0000 + 25.9808i −0.160099 + 0.0639920i
\(407\) 200.000i 0.491400i
\(408\) 90.9327 + 52.5000i 0.222874 + 0.128676i
\(409\) −601.500 + 347.276i −1.47066 + 0.849086i −0.999457 0.0329389i \(-0.989513\pi\)
−0.471203 + 0.882025i \(0.656180\pi\)
\(410\) 0 0
\(411\) −334.500 193.124i −0.813869 0.469887i
\(412\) 296.181 0.718885
\(413\) −55.4256 + 384.000i −0.134202 + 0.929782i
\(414\) 93.0000 0.224638
\(415\) 0 0
\(416\) 495.000 285.788i 1.18990 0.686991i
\(417\) −119.512 + 69.0000i −0.286598 + 0.165468i
\(418\) 13.8564 24.0000i 0.0331493 0.0574163i
\(419\) 647.787i 1.54603i −0.634387 0.773016i \(-0.718747\pi\)
0.634387 0.773016i \(-0.281253\pi\)
\(420\) 0 0
\(421\) 638.000 1.51544 0.757720 0.652580i \(-0.226313\pi\)
0.757720 + 0.652580i \(0.226313\pi\)
\(422\) −297.913 172.000i −0.705954 0.407583i
\(423\) −64.9519 112.500i −0.153551 0.265957i
\(424\) 175.000 + 303.109i 0.412736 + 0.714879i
\(425\) 0 0
\(426\) 168.009i 0.394387i
\(427\) −157.617 + 63.0000i −0.369126 + 0.147541i
\(428\) 528.000i 1.23364i
\(429\) −60.0000 + 103.923i −0.139860 + 0.242245i
\(430\) 0 0
\(431\) 287.500 + 497.965i 0.667053 + 1.15537i 0.978724 + 0.205180i \(0.0657780\pi\)
−0.311671 + 0.950190i \(0.600889\pi\)
\(432\) −12.9904 + 22.5000i −0.0300703 + 0.0520833i
\(433\) −368.927 −0.852025 −0.426012 0.904717i \(-0.640082\pi\)
−0.426012 + 0.904717i \(0.640082\pi\)
\(434\) 127.500 161.947i 0.293779 0.373149i
\(435\) 0 0
\(436\) −6.00000 + 10.3923i −0.0137615 + 0.0238356i
\(437\) −107.387 186.000i −0.245737 0.425629i
\(438\) 72.7461 42.0000i 0.166087 0.0958904i
\(439\) −115.500 66.6840i −0.263098 0.151900i 0.362649 0.931926i \(-0.381872\pi\)
−0.625747 + 0.780026i \(0.715206\pi\)
\(440\) 0 0
\(441\) 141.000 + 41.5692i 0.319728 + 0.0942613i
\(442\) 150.000i 0.339367i
\(443\) 232.095 + 134.000i 0.523916 + 0.302483i 0.738535 0.674215i \(-0.235518\pi\)
−0.214619 + 0.976698i \(0.568851\pi\)
\(444\) 225.000 129.904i 0.506757 0.292576i
\(445\) 0 0
\(446\) 190.500 + 109.985i 0.427130 + 0.246604i
\(447\) 367.195 0.821465
\(448\) 56.2917 71.5000i 0.125651 0.159598i
\(449\) −685.000 −1.52561 −0.762806 0.646627i \(-0.776179\pi\)
−0.762806 + 0.646627i \(0.776179\pi\)
\(450\) 0 0
\(451\) −186.000 + 107.387i −0.412417 + 0.238109i
\(452\) −298.779 + 172.500i −0.661015 + 0.381637i
\(453\) 206.114 357.000i 0.454998 0.788079i
\(454\) 83.1384i 0.183124i
\(455\) 0 0
\(456\) −84.0000 −0.184211
\(457\) −282.324 163.000i −0.617777 0.356674i 0.158226 0.987403i \(-0.449423\pi\)
−0.776003 + 0.630729i \(0.782756\pi\)
\(458\) −62.3538 108.000i −0.136144 0.235808i
\(459\) 22.5000 + 38.9711i 0.0490196 + 0.0849045i
\(460\) 0 0
\(461\) 38.1051i 0.0826575i 0.999146 + 0.0413288i \(0.0131591\pi\)
−0.999146 + 0.0413288i \(0.986841\pi\)
\(462\) −6.92820 + 48.0000i −0.0149961 + 0.103896i
\(463\) 115.000i 0.248380i 0.992258 + 0.124190i \(0.0396333\pi\)
−0.992258 + 0.124190i \(0.960367\pi\)
\(464\) 25.0000 43.3013i 0.0538793 0.0933217i
\(465\) 0 0
\(466\) 97.0000 + 168.009i 0.208155 + 0.360534i
\(467\) 174.937 303.000i 0.374598 0.648822i −0.615669 0.788005i \(-0.711114\pi\)
0.990267 + 0.139183i \(0.0444475\pi\)
\(468\) 155.885 0.333087
\(469\) −50.0000 + 346.410i −0.106610 + 0.738614i
\(470\) 0 0
\(471\) 219.000 379.319i 0.464968 0.805348i
\(472\) 193.990 + 336.000i 0.410995 + 0.711864i
\(473\) 117.779 68.0000i 0.249005 0.143763i
\(474\) −10.5000 6.06218i −0.0221519 0.0127894i
\(475\) 0 0
\(476\) 67.5000 + 168.875i 0.141807 + 0.354779i
\(477\) 150.000i 0.314465i
\(478\) −134.234 77.5000i −0.280824 0.162134i
\(479\) 265.500 153.286i 0.554280 0.320014i −0.196567 0.980490i \(-0.562979\pi\)
0.750846 + 0.660477i \(0.229646\pi\)
\(480\) 0 0
\(481\) −750.000 433.013i −1.55925 0.900234i
\(482\) −270.200 −0.560581
\(483\) 295.315 + 232.500i 0.611418 + 0.481366i
\(484\) −315.000 −0.650826
\(485\) 0 0
\(486\) 13.5000 7.79423i 0.0277778 0.0160375i
\(487\) 347.276 200.500i 0.713093 0.411704i −0.0991123 0.995076i \(-0.531600\pi\)
0.812205 + 0.583372i \(0.198267\pi\)
\(488\) −84.8705 + 147.000i −0.173915 + 0.301230i
\(489\) 505.759i 1.03427i
\(490\) 0 0
\(491\) −218.000 −0.443992 −0.221996 0.975048i \(-0.571257\pi\)
−0.221996 + 0.975048i \(0.571257\pi\)
\(492\) 241.621 + 139.500i 0.491100 + 0.283537i
\(493\) −43.3013 75.0000i −0.0878322 0.152130i
\(494\) 60.0000 + 103.923i 0.121457 + 0.210371i
\(495\) 0 0
\(496\) 147.224i 0.296823i
\(497\) −420.022 + 533.500i −0.845115 + 1.07344i
\(498\) 264.000i 0.530120i
\(499\) −437.000 + 756.906i −0.875752 + 1.51685i −0.0197915 + 0.999804i \(0.506300\pi\)
−0.855960 + 0.517042i \(0.827033\pi\)
\(500\) 0 0
\(501\) −114.000 197.454i −0.227545 0.394119i
\(502\) 103.923 180.000i 0.207018 0.358566i
\(503\) −498.831 −0.991711 −0.495855 0.868405i \(-0.665145\pi\)
−0.495855 + 0.868405i \(0.665145\pi\)
\(504\) 136.500 54.5596i 0.270833 0.108253i
\(505\) 0 0
\(506\) −62.0000 + 107.387i −0.122530 + 0.212228i
\(507\) −113.449 196.500i −0.223766 0.387574i
\(508\) 161.081 93.0000i 0.317088 0.183071i
\(509\) −558.000 322.161i −1.09627 0.632930i −0.161029 0.986950i \(-0.551481\pi\)
−0.935238 + 0.354019i \(0.884815\pi\)
\(510\) 0 0
\(511\) 336.000 + 48.4974i 0.657534 + 0.0949069i
\(512\) 305.000i 0.595703i
\(513\) −31.1769 18.0000i −0.0607737 0.0350877i
\(514\) 414.000 239.023i 0.805447 0.465025i
\(515\) 0 0
\(516\) −153.000 88.3346i −0.296512 0.171191i
\(517\) 173.205 0.335019
\(518\) −346.410 50.0000i −0.668745 0.0965251i
\(519\) 258.000 0.497110
\(520\) 0 0
\(521\) −1.50000 + 0.866025i −0.00287908 + 0.00166224i −0.501439 0.865193i \(-0.667196\pi\)
0.498560 + 0.866855i \(0.333862\pi\)
\(522\) −25.9808 + 15.0000i −0.0497716 + 0.0287356i
\(523\) −479.778 + 831.000i −0.917358 + 1.58891i −0.113945 + 0.993487i \(0.536349\pi\)
−0.803412 + 0.595423i \(0.796984\pi\)
\(524\) 93.5307i 0.178494i
\(525\) 0 0
\(526\) −59.0000 −0.112167
\(527\) 220.836 + 127.500i 0.419045 + 0.241935i
\(528\) −17.3205 30.0000i −0.0328040 0.0568182i
\(529\) 216.000 + 374.123i 0.408318 + 0.707227i
\(530\) 0 0
\(531\) 166.277i 0.313139i
\(532\) −114.315 90.0000i −0.214878 0.169173i
\(533\) 930.000i 1.74484i
\(534\) −136.500 + 236.425i −0.255618 + 0.442743i
\(535\) 0 0
\(536\) 175.000 + 303.109i 0.326493 + 0.565502i
\(537\) 164.545 285.000i 0.306415 0.530726i
\(538\) −6.92820 −0.0128777
\(539\) −142.000 + 135.100i −0.263451 + 0.250649i
\(540\) 0 0
\(541\) 146.000 252.879i 0.269871 0.467430i −0.698958 0.715163i \(-0.746352\pi\)
0.968828 + 0.247733i \(0.0796857\pi\)
\(542\) 129.038 + 223.500i 0.238077 + 0.412362i
\(543\) −31.1769 + 18.0000i −0.0574160 + 0.0331492i
\(544\) 247.500 + 142.894i 0.454963 + 0.262673i
\(545\) 0 0
\(546\) −165.000 129.904i −0.302198 0.237919i
\(547\) 316.000i 0.577697i −0.957375 0.288848i \(-0.906728\pi\)
0.957375 0.288848i \(-0.0932723\pi\)
\(548\) −579.371 334.500i −1.05725 0.610401i
\(549\) −63.0000 + 36.3731i −0.114754 + 0.0662533i
\(550\) 0 0
\(551\) 60.0000 + 34.6410i 0.108893 + 0.0628694i
\(552\) 375.855 0.680897
\(553\) −18.1865 45.5000i −0.0328870 0.0822785i
\(554\) −218.000 −0.393502
\(555\) 0 0
\(556\) −207.000 + 119.512i −0.372302 + 0.214949i
\(557\) 424.352 245.000i 0.761854 0.439856i −0.0681073 0.997678i \(-0.521696\pi\)
0.829961 + 0.557822i \(0.188363\pi\)
\(558\) 44.1673 76.5000i 0.0791529 0.137097i
\(559\) 588.897i 1.05348i
\(560\) 0 0
\(561\) −60.0000 −0.106952
\(562\) 336.884 + 194.500i 0.599438 + 0.346085i
\(563\) 17.3205 + 30.0000i 0.0307647 + 0.0532860i 0.880998 0.473120i \(-0.156872\pi\)
−0.850233 + 0.526406i \(0.823539\pi\)
\(564\) −112.500 194.856i −0.199468 0.345489i
\(565\) 0 0
\(566\) 214.774i 0.379460i
\(567\) 62.3538 + 9.00000i 0.109971 + 0.0158730i
\(568\) 679.000i 1.19542i
\(569\) 252.500 437.343i 0.443761 0.768617i −0.554204 0.832381i \(-0.686977\pi\)
0.997965 + 0.0637643i \(0.0203106\pi\)
\(570\) 0 0
\(571\) 62.0000 + 107.387i 0.108581 + 0.188069i 0.915196 0.403009i \(-0.132036\pi\)
−0.806614 + 0.591078i \(0.798703\pi\)
\(572\) −103.923 + 180.000i −0.181684 + 0.314685i
\(573\) −465.922 −0.813127
\(574\) −139.500 349.008i −0.243031 0.608028i
\(575\) 0 0
\(576\) 19.5000 33.7750i 0.0338542 0.0586371i
\(577\) −79.6743 138.000i −0.138084 0.239168i 0.788687 0.614794i \(-0.210761\pi\)
−0.926771 + 0.375626i \(0.877428\pi\)
\(578\) −185.329 + 107.000i −0.320639 + 0.185121i
\(579\) 43.5000 + 25.1147i 0.0751295 + 0.0433761i
\(580\) 0 0
\(581\) −660.000 + 838.313i −1.13597 + 1.44288i
\(582\) 195.000i 0.335052i
\(583\) −173.205 100.000i −0.297093 0.171527i
\(584\) 294.000 169.741i 0.503425 0.290652i
\(585\) 0 0
\(586\) −426.000 245.951i −0.726962 0.419712i
\(587\) −329.090 −0.560630 −0.280315 0.959908i \(-0.590439\pi\)
−0.280315 + 0.959908i \(0.590439\pi\)
\(588\) 244.219 + 72.0000i 0.415339 + 0.122449i
\(589\) −204.000 −0.346350
\(590\) 0 0
\(591\) 78.0000 45.0333i 0.131980 0.0761985i
\(592\) 216.506 125.000i 0.365720 0.211149i
\(593\) −317.831 + 550.500i −0.535972 + 0.928331i 0.463144 + 0.886283i \(0.346721\pi\)
−0.999116 + 0.0420473i \(0.986612\pi\)
\(594\) 20.7846i 0.0349909i
\(595\) 0 0
\(596\) 636.000 1.06711
\(597\) 267.602 + 154.500i 0.448244 + 0.258794i
\(598\) −268.468 465.000i −0.448943 0.777592i
\(599\) −23.5000 40.7032i −0.0392321 0.0679519i 0.845743 0.533591i \(-0.179158\pi\)
−0.884975 + 0.465639i \(0.845824\pi\)
\(600\) 0 0
\(601\) 1157.01i 1.92514i 0.271031 + 0.962571i \(0.412635\pi\)
−0.271031 + 0.962571i \(0.587365\pi\)
\(602\) 88.3346 + 221.000i 0.146735 + 0.367110i
\(603\) 150.000i 0.248756i
\(604\) 357.000 618.342i 0.591060 1.02375i
\(605\) 0 0
\(606\) −18.0000 31.1769i −0.0297030 0.0514471i
\(607\) 226.033 391.500i 0.372377 0.644975i −0.617554 0.786528i \(-0.711876\pi\)
0.989931 + 0.141553i \(0.0452096\pi\)
\(608\) −228.631 −0.376037
\(609\) −120.000 17.3205i −0.197044 0.0284409i
\(610\) 0 0
\(611\) −375.000 + 649.519i −0.613748 + 1.06304i
\(612\) 38.9711 + 67.5000i 0.0636783 + 0.110294i
\(613\) 788.083 455.000i 1.28562 0.742251i 0.307748 0.951468i \(-0.400425\pi\)
0.977869 + 0.209217i \(0.0670914\pi\)
\(614\) −126.000 72.7461i −0.205212 0.118479i
\(615\) 0 0
\(616\) −28.0000 + 193.990i −0.0454545 + 0.314918i
\(617\) 313.000i 0.507293i 0.967297 + 0.253647i \(0.0816301\pi\)
−0.967297 + 0.253647i \(0.918370\pi\)
\(618\) −148.090 85.5000i −0.239628 0.138350i
\(619\) −657.000 + 379.319i −1.06139 + 0.612793i −0.925816 0.377974i \(-0.876621\pi\)
−0.135573 + 0.990767i \(0.543288\pi\)
\(620\) 0 0
\(621\) 139.500 + 80.5404i 0.224638 + 0.129695i
\(622\) 320.429 0.515160
\(623\) −1024.51 + 409.500i −1.64448 + 0.657303i
\(624\) 150.000 0.240385
\(625\) 0 0
\(626\) −43.5000 + 25.1147i −0.0694888 + 0.0401194i
\(627\) 41.5692 24.0000i 0.0662986 0.0382775i
\(628\) 379.319 657.000i 0.604011 1.04618i
\(629\) 433.013i 0.688414i
\(630\) 0 0
\(631\) −793.000 −1.25674 −0.628368 0.777916i \(-0.716277\pi\)
−0.628368 + 0.777916i \(0.716277\pi\)
\(632\) −42.4352 24.5000i −0.0671444 0.0387658i
\(633\) −297.913 516.000i −0.470636 0.815166i
\(634\) 68.0000 + 117.779i 0.107256 + 0.185772i
\(635\) 0 0
\(636\) 259.808i 0.408503i
\(637\) −199.186 825.000i −0.312694 1.29513i
\(638\) 40.0000i 0.0626959i
\(639\) −145.500 + 252.013i −0.227700 + 0.394387i
\(640\) 0 0
\(641\) 68.5000 + 118.645i 0.106864 + 0.185094i 0.914498 0.404590i \(-0.132586\pi\)
−0.807634 + 0.589684i \(0.799252\pi\)
\(642\) −152.420 + 264.000i −0.237415 + 0.411215i
\(643\) −1073.87 −1.67010 −0.835048 0.550177i \(-0.814560\pi\)
−0.835048 + 0.550177i \(0.814560\pi\)
\(644\) 511.500 + 402.702i 0.794255 + 0.625313i
\(645\) 0 0
\(646\) −30.0000 + 51.9615i −0.0464396 + 0.0804358i
\(647\) −169.741 294.000i −0.262351 0.454405i 0.704515 0.709689i \(-0.251164\pi\)
−0.966866 + 0.255284i \(0.917831\pi\)
\(648\) 54.5596 31.5000i 0.0841969 0.0486111i
\(649\) −192.000 110.851i −0.295840 0.170803i
\(650\) 0 0
\(651\) 331.500 132.502i 0.509217 0.203536i
\(652\) 876.000i 1.34356i
\(653\) 860.829 + 497.000i 1.31827 + 0.761103i 0.983450 0.181180i \(-0.0579917\pi\)
0.334818 + 0.942283i \(0.391325\pi\)
\(654\) 6.00000 3.46410i 0.00917431 0.00529679i
\(655\) 0 0
\(656\) 232.500 + 134.234i 0.354421 + 0.204625i
\(657\) 145.492 0.221449
\(658\) −43.3013 + 300.000i −0.0658074 + 0.455927i
\(659\) −226.000 −0.342944 −0.171472 0.985189i \(-0.554852\pi\)
−0.171472 + 0.985189i \(0.554852\pi\)
\(660\) 0 0
\(661\) −447.000 + 258.076i −0.676248 + 0.390432i −0.798440 0.602074i \(-0.794341\pi\)
0.122192 + 0.992507i \(0.461008\pi\)
\(662\) −382.783 + 221.000i −0.578222 + 0.333837i
\(663\) 129.904 225.000i 0.195933 0.339367i
\(664\) 1066.94i 1.60684i
\(665\) 0 0
\(666\) −150.000 −0.225225
\(667\) −268.468 155.000i −0.402501 0.232384i
\(668\) −197.454 342.000i −0.295590 0.511976i
\(669\) 190.500 + 329.956i 0.284753 + 0.493207i
\(670\) 0 0
\(671\) 96.9948i 0.144553i
\(672\) 371.525 148.500i 0.552864 0.220982i
\(673\) 755.000i 1.12184i −0.827869 0.560921i \(-0.810447\pi\)
0.827869 0.560921i \(-0.189553\pi\)
\(674\) −165.500 + 286.654i −0.245549 + 0.425303i
\(675\) 0 0
\(676\) −196.500 340.348i −0.290680 0.503473i
\(677\) 12.1244 21.0000i 0.0179089 0.0310192i −0.856932 0.515429i \(-0.827632\pi\)
0.874841 + 0.484410i \(0.160966\pi\)
\(678\) 199.186 0.293784
\(679\) 487.500 619.208i 0.717968 0.911941i
\(680\) 0 0
\(681\) −72.0000 + 124.708i −0.105727 + 0.183124i
\(682\) 58.8897 + 102.000i 0.0863486 + 0.149560i
\(683\) −928.379 + 536.000i −1.35927 + 0.784773i −0.989525 0.144361i \(-0.953887\pi\)
−0.369742 + 0.929135i \(0.620554\pi\)
\(684\) −54.0000 31.1769i −0.0789474 0.0455803i
\(685\) 0 0
\(686\) −198.500 279.726i −0.289359 0.407764i
\(687\) 216.000i 0.314410i
\(688\) −147.224 85.0000i −0.213989 0.123547i
\(689\) 750.000 433.013i 1.08853 0.628465i
\(690\) 0 0
\(691\) 1110.00 + 640.859i 1.60637 + 0.927437i 0.990174 + 0.139842i \(0.0446595\pi\)
0.616194 + 0.787595i \(0.288674\pi\)
\(692\) 446.869 0.645765
\(693\) −51.9615 + 66.0000i −0.0749806 + 0.0952381i
\(694\) 122.000 0.175793
\(695\) 0 0
\(696\) −105.000 + 60.6218i −0.150862 + 0.0871003i
\(697\) 402.702 232.500i 0.577764 0.333572i
\(698\) −183.597 + 318.000i −0.263034 + 0.455587i
\(699\) 336.018i 0.480712i
\(700\) 0 0
\(701\) −1070.00 −1.52639 −0.763195 0.646168i \(-0.776371\pi\)
−0.763195 + 0.646168i \(0.776371\pi\)
\(702\) −77.9423 45.0000i −0.111029 0.0641026i
\(703\) 173.205 + 300.000i 0.246380 + 0.426743i
\(704\) 26.0000 + 45.0333i 0.0369318 + 0.0639678i
\(705\) 0 0
\(706\) 119.512i 0.169280i
\(707\) 20.7846 144.000i 0.0293983 0.203678i
\(708\) 288.000i 0.406780i
\(709\) −167.000 + 289.252i −0.235543 + 0.407972i −0.959430 0.281946i \(-0.909020\pi\)
0.723887 + 0.689918i \(0.242354\pi\)
\(710\) 0 0
\(711\) −10.5000 18.1865i −0.0147679 0.0255788i
\(712\) −551.658 + 955.500i −0.774801 + 1.34199i
\(713\) 912.791 1.28021
\(714\) 15.0000 103.923i 0.0210084 0.145550i
\(715\) 0 0
\(716\) 285.000 493.634i 0.398045 0.689434i
\(717\) −134.234 232.500i −0.187216 0.324268i
\(718\) −206.114 + 119.000i −0.287067 + 0.165738i
\(719\) 1054.50 + 608.816i 1.46662 + 0.846754i 0.999303 0.0373359i \(-0.0118872\pi\)
0.467318 + 0.884090i \(0.345220\pi\)
\(720\) 0 0
\(721\) −256.500 641.725i −0.355756 0.890048i
\(722\) 313.000i 0.433518i
\(723\) −405.300 234.000i −0.560581 0.323651i
\(724\) −54.0000 + 31.1769i −0.0745856 + 0.0430620i
\(725\) 0 0
\(726\) 157.500 + 90.9327i 0.216942 + 0.125252i
\(727\) −455.529 −0.626588 −0.313294 0.949656i \(-0.601433\pi\)
−0.313294 + 0.949656i \(0.601433\pi\)
\(728\) −666.840 525.000i −0.915988 0.721154i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) −255.000 + 147.224i −0.348837 + 0.201401i
\(732\) −109.119 + 63.0000i −0.149070 + 0.0860656i
\(733\) 644.323 1116.00i 0.879022 1.52251i 0.0266057 0.999646i \(-0.491530\pi\)
0.852416 0.522864i \(-0.175137\pi\)
\(734\) 228.631i 0.311486i
\(735\) 0 0
\(736\) 1023.00 1.38995
\(737\) −173.205 100.000i −0.235014 0.135685i
\(738\) −80.5404 139.500i −0.109133 0.189024i
\(739\) 337.000 + 583.701i 0.456022 + 0.789853i 0.998746 0.0500580i \(-0.0159406\pi\)
−0.542725 + 0.839911i \(0.682607\pi\)
\(740\) 0 0
\(741\) 207.846i 0.280494i
\(742\) 216.506 275.000i 0.291788 0.370620i
\(743\) 1123.00i 1.51144i −0.654895 0.755720i \(-0.727287\pi\)
0.654895 0.755720i \(-0.272713\pi\)
\(744\) 178.500 309.171i 0.239919 0.415553i
\(745\) 0 0
\(746\) −103.000 178.401i −0.138070 0.239144i
\(747\) −228.631 + 396.000i −0.306065 + 0.530120i
\(748\) −103.923 −0.138935
\(749\) −1144.00 + 457.261i −1.52737 + 0.610496i
\(750\) 0 0
\(751\) 317.000 549.060i 0.422104 0.731105i −0.574041 0.818826i \(-0.694625\pi\)
0.996145 + 0.0877211i \(0.0279584\pi\)
\(752\) −108.253 187.500i −0.143954 0.249335i
\(753\) 311.769 180.000i 0.414036 0.239044i
\(754\) 150.000 + 86.6025i 0.198939 + 0.114857i
\(755\) 0 0
\(756\) 108.000 + 15.5885i 0.142857 + 0.0206197i
\(757\) 100.000i 0.132100i −0.997816 0.0660502i \(-0.978960\pi\)
0.997816 0.0660502i \(-0.0210397\pi\)
\(758\) −372.391 215.000i −0.491281 0.283641i
\(759\) −186.000 + 107.387i −0.245059 + 0.141485i
\(760\) 0 0
\(761\) 193.500 + 111.717i 0.254271 + 0.146803i 0.621718 0.783241i \(-0.286435\pi\)
−0.367448 + 0.930044i \(0.619768\pi\)
\(762\) −107.387 −0.140928
\(763\) 27.7128 + 4.00000i 0.0363209 + 0.00524246i
\(764\) −807.000 −1.05628
\(765\) 0 0
\(766\) 490.500 283.190i 0.640339 0.369700i
\(767\) 831.384 480.000i 1.08394 0.625815i
\(768\) 148.090 256.500i 0.192826 0.333984i
\(769\) 921.451i 1.19825i −0.800657 0.599123i \(-0.795516\pi\)
0.800657 0.599123i \(-0.204484\pi\)
\(770\) 0 0
\(771\) 828.000 1.07393
\(772\) 75.3442 + 43.5000i 0.0975961 + 0.0563472i
\(773\) 403.568 + 699.000i 0.522080 + 0.904269i 0.999670 + 0.0256863i \(0.00817710\pi\)
−0.477590 + 0.878583i \(0.658490\pi\)
\(774\) 51.0000 + 88.3346i 0.0658915 + 0.114127i
\(775\) 0 0
\(776\) 788.083i 1.01557i
\(777\) −476.314 375.000i −0.613017 0.482625i
\(778\) 560.000i 0.719794i
\(779\) −186.000 + 322.161i −0.238768 + 0.413558i
\(780\) 0 0
\(781\) −194.000 336.018i −0.248399 0.430241i
\(782\) 134.234 232.500i 0.171655 0.297315i
\(783\) −51.9615 −0.0663621
\(784\) 235.000 + 69.2820i 0.299745 + 0.0883699i
\(785\) 0 0
\(786\) 27.0000 46.7654i 0.0343511 0.0594979i
\(787\) −60.6218 105.000i −0.0770289 0.133418i 0.824938 0.565223i \(-0.191210\pi\)
−0.901967 + 0.431805i \(0.857877\pi\)
\(788\) 135.100 78.0000i 0.171447 0.0989848i
\(789\) −88.5000 51.0955i −0.112167 0.0647598i
\(790\) 0 0
\(791\) 632.500 + 497.965i 0.799621 + 0.629538i
\(792\) 84.0000i 0.106061i
\(793\) 363.731 + 210.000i 0.458677 + 0.264817i
\(794\) 546.000 315.233i 0.687657 0.397019i
\(795\) 0 0
\(796\) 463.500 + 267.602i 0.582286 + 0.336183i
\(797\) −585.433 −0.734546 −0.367273 0.930113i \(-0.619709\pi\)
−0.367273 + 0.930113i \(0.619709\pi\)
\(798\) 31.1769 + 78.0000i 0.0390688 + 0.0977444i
\(799\) −375.000 −0.469337
\(800\) 0 0
\(801\) −409.500 + 236.425i −0.511236 + 0.295162i
\(802\) −479.778 + 277.000i −0.598227 + 0.345387i
\(803\) −96.9948 + 168.000i −0.120791 + 0.209215i
\(804\) 259.808i 0.323144i
\(805\) 0 0
\(806\) −510.000 −0.632754
\(807\) −10.3923 6.00000i −0.0128777 0.00743494i
\(808\) −72.7461 126.000i −0.0900323 0.155941i
\(809\) −265.000 458.993i −0.327565 0.567359i 0.654463 0.756094i \(-0.272895\pi\)
−0.982028 + 0.188735i \(0.939561\pi\)
\(810\) 0 0
\(811\) 176.669i 0.217841i 0.994050 + 0.108921i \(0.0347394\pi\)
−0.994050 + 0.108921i \(0.965261\pi\)
\(812\) −207.846 30.0000i −0.255968 0.0369458i
\(813\) 447.000i 0.549815i
\(814\) 100.000 173.205i 0.122850 0.212783i
\(815\) 0 0
\(816\) 37.5000 + 64.9519i 0.0459559 + 0.0795979i
\(817\) 117.779 204.000i 0.144161 0.249694i
\(818\) 694.552 0.849086
\(819\) −135.000 337.750i −0.164835 0.412393i
\(820\) 0 0
\(821\) −356.000 + 616.610i −0.433618 + 0.751048i −0.997182 0.0750247i \(-0.976096\pi\)
0.563564 + 0.826072i \(0.309430\pi\)
\(822\) 193.124 + 334.500i 0.234944 + 0.406934i
\(823\) −968.216 + 559.000i −1.17645 + 0.679222i −0.955190 0.295993i \(-0.904349\pi\)
−0.221258 + 0.975215i \(0.571016\pi\)
\(824\) −598.500 345.544i −0.726335 0.419350i
\(825\) 0 0
\(826\) 240.000 304.841i 0.290557 0.369057i
\(827\) 196.000i 0.237001i 0.992954 + 0.118501i \(0.0378088\pi\)
−0.992954 + 0.118501i \(0.962191\pi\)
\(828\) 241.621 + 139.500i 0.291813 + 0.168478i
\(829\) 354.000 204.382i 0.427021 0.246540i −0.271056 0.962564i \(-0.587373\pi\)
0.698077 + 0.716023i \(0.254040\pi\)
\(830\) 0 0
\(831\) −327.000 188.794i −0.393502 0.227188i
\(832\) −225.167 −0.270633
\(833\) 307.439 292.500i 0.369074 0.351140i
\(834\) 138.000 0.165468
\(835\) 0 0
\(836\) 72.0000 41.5692i 0.0861244 0.0497239i
\(837\) 132.502 76.5000i 0.158306 0.0913978i
\(838\) −323.894 + 561.000i −0.386508 + 0.669451i
\(839\) 282.324i 0.336501i −0.985744 0.168250i \(-0.946188\pi\)
0.985744 0.168250i \(-0.0538117\pi\)
\(840\) 0 0
\(841\) −741.000 −0.881094
\(842\) −552.524 319.000i −0.656205 0.378860i
\(843\) 336.884 + 583.500i 0.399625 + 0.692171i
\(844\) −516.000 893.738i −0.611374 1.05893i
\(845\) 0 0
\(846\) 129.904i 0.153551i
\(847\) 272.798 + 682.500i 0.322076 + 0.805785i
\(848\) 250.000i 0.294811i
\(849\) 186.000 322.161i 0.219081 0.379460i
\(850\) 0 0
\(851\) −775.000 1342.34i −0.910693 1.57737i
\(852\) −252.013 + 436.500i −0.295790 + 0.512324i
\(853\) −38.1051 −0.0446719 −0.0223359 0.999751i \(-0.507110\pi\)
−0.0223359 + 0.999751i \(0.507110\pi\)
\(854\) 168.000 + 24.2487i 0.196721 + 0.0283943i
\(855\) 0 0
\(856\) −616.000 + 1066.94i −0.719626 + 1.24643i
\(857\) 436.477 + 756.000i 0.509308 + 0.882147i 0.999942 + 0.0107813i \(0.00343186\pi\)
−0.490634 + 0.871366i \(0.663235\pi\)
\(858\) 103.923 60.0000i 0.121122 0.0699301i
\(859\) −477.000 275.396i −0.555297 0.320601i 0.195959 0.980612i \(-0.437218\pi\)
−0.751256 + 0.660011i \(0.770551\pi\)
\(860\) 0 0
\(861\) 93.0000 644.323i 0.108014 0.748343i
\(862\) 575.000i 0.667053i
\(863\) 1201.18 + 693.500i 1.39186 + 0.803592i 0.993521 0.113645i \(-0.0362527\pi\)
0.398341 + 0.917237i \(0.369586\pi\)
\(864\) 148.500 85.7365i 0.171875 0.0992321i
\(865\) 0 0
\(866\) 319.500 + 184.463i 0.368938 + 0.213006i
\(867\) −370.659 −0.427519
\(868\) 574.175 229.500i 0.661492 0.264401i
\(869\) 28.0000 0.0322209
\(870\) 0 0
\(871\) 750.000 433.013i 0.861079 0.497144i
\(872\) 24.2487 14.0000i 0.0278082 0.0160550i
\(873\) 168.875 292.500i 0.193442 0.335052i
\(874\) 214.774i 0.245737i
\(875\) 0 0
\(876\) 252.000 0.287671
\(877\) 658.179 + 380.000i 0.750490 + 0.433295i 0.825871 0.563859i \(-0.190684\pi\)
−0.0753812 + 0.997155i \(0.524017\pi\)
\(878\) 66.6840 + 115.500i 0.0759498 + 0.131549i
\(879\) −426.000 737.854i −0.484642 0.839424i
\(880\) 0 0
\(881\) 524.811i 0.595700i −0.954613 0.297850i \(-0.903731\pi\)
0.954613 0.297850i \(-0.0962695\pi\)
\(882\) −101.325 106.500i −0.114881 0.120748i
\(883\) 1324.00i 1.49943i 0.661759 + 0.749717i \(0.269810\pi\)
−0.661759 + 0.749717i \(0.730190\pi\)
\(884\) 225.000 389.711i 0.254525 0.440850i
\(885\) 0 0
\(886\) −134.000 232.095i −0.151242 0.261958i
\(887\) 758.638 1314.00i 0.855286 1.48140i −0.0210944 0.999777i \(-0.506715\pi\)
0.876380 0.481620i \(-0.159952\pi\)
\(888\) −606.218 −0.682678
\(889\) −341.000 268.468i −0.383577 0.301989i
\(890\) 0 0
\(891\) −18.0000 + 31.1769i −0.0202020 + 0.0349909i
\(892\) 329.956 + 571.500i 0.369905 + 0.640695i
\(893\) 259.808 150.000i 0.290938 0.167973i
\(894\) −318.000 183.597i −0.355705 0.205366i
\(895\) 0 0
\(896\) 773.500 309.171i 0.863281 0.345057i
\(897\) 930.000i 1.03679i
\(898\) 593.227 + 342.500i 0.660610 + 0.381403i
\(899\) −255.000 + 147.224i −0.283648 + 0.163765i
\(900\) 0 0
\(901\) 375.000 + 216.506i 0.416204 + 0.240296i
\(902\) 214.774 0.238109
\(903\) −58.8897 + 408.000i −0.0652156 + 0.451827i
\(904\) 805.000 0.890487
\(905\) 0 0
\(906\) −357.000 + 206.114i −0.394040 + 0.227499i
\(907\) 32.9090 19.0000i 0.0362833 0.0209482i −0.481749 0.876309i \(-0.659998\pi\)
0.518032 + 0.855361i \(0.326665\pi\)
\(908\) −124.708 + 216.000i −0.137343 + 0.237885i
\(909\) 62.3538i 0.0685961i
\(910\) 0 0
\(911\) −611.000 −0.670692 −0.335346 0.942095i \(-0.608853\pi\)
−0.335346 + 0.942095i \(0.608853\pi\)
\(912\) −51.9615 30.0000i −0.0569754 0.0328947i
\(913\) −304.841 528.000i −0.333889 0.578313i
\(914\) 163.000 + 282.324i 0.178337 + 0.308889i
\(915\) 0 0
\(916\) 374.123i 0.408431i
\(917\) 202.650 81.0000i 0.220992 0.0883315i
\(918\) 45.0000i 0.0490196i
\(919\) 155.500 269.334i 0.169206 0.293073i −0.768935 0.639327i \(-0.779213\pi\)
0.938141 + 0.346254i \(0.112546\pi\)
\(920\) 0 0
\(921\) −126.000 218.238i −0.136808 0.236958i
\(922\) 19.0526 33.0000i 0.0206644 0.0357918i
\(923\) 1680.09 1.82025
\(924\) −90.0000 + 114.315i −0.0974026 + 0.123718i
\(925\) 0 0
\(926\) 57.5000 99.5929i 0.0620950 0.107552i
\(927\) −148.090 256.500i −0.159752 0.276699i
\(928\) −285.788 + 165.000i −0.307962 + 0.177802i
\(929\) 948.000 + 547.328i 1.02045 + 0.589158i 0.914235 0.405185i \(-0.132793\pi\)
0.106217 + 0.994343i \(0.466126\pi\)
\(930\) 0 0
\(931\) −96.0000 + 325.626i −0.103115 + 0.349759i
\(932\) 582.000i 0.624464i
\(933\) 480.644 + 277.500i 0.515160 + 0.297428i
\(934\) −303.000 + 174.937i −0.324411 + 0.187299i
\(935\) 0 0
\(936\) −315.000 181.865i −0.336538 0.194301i
\(937\) −519.615 −0.554552 −0.277276 0.960790i \(-0.589432\pi\)
−0.277276 + 0.960790i \(0.589432\pi\)
\(938\) 216.506 275.000i 0.230817 0.293177i
\(939\) −87.0000 −0.0926518
\(940\) 0 0
\(941\) 1437.00 829.652i 1.52710 0.881671i 0.527617 0.849482i \(-0.323086\pi\)
0.999482 0.0321886i \(-0.0102477\pi\)
\(942\) −379.319 + 219.000i −0.402674 + 0.232484i
\(943\) 832.250 1441.50i 0.882556 1.52863i
\(944\) 277.128i 0.293568i
\(945\) 0 0
\(946\) −136.000 −0.143763
\(947\) −762.102 440.000i −0.804754 0.464625i 0.0403766 0.999185i \(-0.487144\pi\)
−0.845131 + 0.534559i \(0.820478\pi\)
\(948\) −18.1865 31.5000i −0.0191841 0.0332278i
\(949\) −420.000 727.461i −0.442571 0.766556i
\(950\) 0 0
\(951\) 235.559i 0.247696i
\(952\) 60.6218 420.000i 0.0636783 0.441176i
\(953\) 910.000i 0.954879i −0.878665 0.477440i \(-0.841565\pi\)
0.878665 0.477440i \(-0.158435\pi\)
\(954\) 75.0000 129.904i 0.0786164 0.136168i
\(955\) 0 0
\(956\) −232.500 402.702i −0.243201 0.421236i
\(957\) 34.6410 60.0000i 0.0361975 0.0626959i
\(958\) −306.573 −0.320014
\(959\) −223.000 + 1544.99i −0.232534 + 1.61104i
\(960\) 0 0
\(961\) −47.0000 + 81.4064i −0.0489074 + 0.0847101i
\(962\) 433.013 + 750.000i 0.450117 + 0.779626i
\(963\) −457.261 + 264.000i −0.474830 + 0.274143i
\(964\) −702.000 405.300i −0.728216 0.420436i
\(965\) 0 0
\(966\) −139.500 349.008i −0.144410 0.361292i
\(967\) 473.000i 0.489142i 0.969631 + 0.244571i \(0.0786471\pi\)
−0.969631 + 0.244571i \(0.921353\pi\)
\(968\) 636.529 + 367.500i 0.657571 + 0.379649i
\(969\) −90.0000 + 51.9615i −0.0928793 + 0.0536239i
\(970\) 0 0
\(971\) 777.000 + 448.601i 0.800206 + 0.461999i 0.843543 0.537061i \(-0.180466\pi\)
−0.0433372 + 0.999061i \(0.513799\pi\)
\(972\) 46.7654 0.0481125
\(973\) 438.209 + 345.000i 0.450369 + 0.354573i
\(974\) −401.000 −0.411704
\(975\) 0 0
\(976\) −105.000 + 60.6218i −0.107582 + 0.0621125i
\(977\) −196.588 + 113.500i −0.201216 + 0.116172i −0.597222 0.802076i \(-0.703729\pi\)
0.396007 + 0.918248i \(0.370396\pi\)
\(978\) 252.879 438.000i 0.258568 0.447853i
\(979\) 630.466i 0.643990i
\(980\) 0 0
\(981\) 12.0000 0.0122324
\(982\) 188.794 + 109.000i 0.192254 + 0.110998i
\(983\) 758.638 + 1314.00i 0.771758 + 1.33672i 0.936599 + 0.350404i \(0.113956\pi\)
−0.164840 + 0.986320i \(0.552711\pi\)
\(984\) −325.500 563.783i −0.330793 0.572950i
\(985\) 0 0
\(986\) 86.6025i 0.0878322i
\(987\) −324.760 + 412.500i −0.329037 + 0.417933i
\(988\) 360.000i 0.364372i
\(989\) −527.000 + 912.791i −0.532861 + 0.922943i
\(990\) 0 0
\(991\) −902.500 1563.18i −0.910696 1.57737i −0.813083 0.582148i \(-0.802213\pi\)
−0.0976133 0.995224i \(-0.531121\pi\)
\(992\) 485.840 841.500i 0.489758 0.848286i
\(993\) −765.566 −0.770963
\(994\) 630.500 252.013i 0.634306 0.253535i
\(995\) 0 0
\(996\) −396.000 + 685.892i −0.397590 + 0.688647i
\(997\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(998\) 756.906 437.000i 0.758423 0.437876i
\(999\) −225.000 129.904i −0.225225 0.130034i
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 525.3.s.b.124.1 4
5.2 odd 4 525.3.o.e.376.1 yes 2
5.3 odd 4 525.3.o.d.376.1 2
5.4 even 2 inner 525.3.s.b.124.2 4
7.3 odd 6 inner 525.3.s.b.199.2 4
35.3 even 12 525.3.o.d.451.1 yes 2
35.17 even 12 525.3.o.e.451.1 yes 2
35.24 odd 6 inner 525.3.s.b.199.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.3.o.d.376.1 2 5.3 odd 4
525.3.o.d.451.1 yes 2 35.3 even 12
525.3.o.e.376.1 yes 2 5.2 odd 4
525.3.o.e.451.1 yes 2 35.17 even 12
525.3.s.b.124.1 4 1.1 even 1 trivial
525.3.s.b.124.2 4 5.4 even 2 inner
525.3.s.b.199.1 4 35.24 odd 6 inner
525.3.s.b.199.2 4 7.3 odd 6 inner