Properties

Label 525.2.i.h.226.3
Level $525$
Weight $2$
Character 525.226
Analytic conductor $4.192$
Analytic rank $0$
Dimension $8$
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] = [525,2,Mod(151,525)]
 
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, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.151");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.i (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} + 8x^{6} + 21x^{4} - 4x^{3} + 28x^{2} + 12x + 9 \) 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 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.3
Root \(0.643668 + 1.11487i\) of defining polynomial
Character \(\chi\) \(=\) 525.226
Dual form 525.2.i.h.151.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.143668 - 0.248840i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.958719 + 1.66055i) q^{4} +0.287336 q^{6} +(2.39939 + 1.11487i) q^{7} +1.12562 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.143668 - 0.248840i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.958719 + 1.66055i) q^{4} +0.287336 q^{6} +(2.39939 + 1.11487i) q^{7} +1.12562 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.66520 + 2.88421i) q^{11} +(-0.958719 + 1.66055i) q^{12} -4.54754 q^{13} +(0.622139 - 0.436894i) q^{14} +(-1.75572 + 3.04100i) q^{16} +(-2.77377 - 4.80431i) q^{17} +(0.143668 + 0.248840i) q^{18} +(0.828617 - 1.43521i) q^{19} +(0.234193 + 2.63537i) q^{21} +0.956942 q^{22} +(3.81683 - 6.61094i) q^{23} +(0.562810 + 0.974816i) q^{24} +(-0.653336 + 1.13161i) q^{26} -1.00000 q^{27} +(0.449051 + 5.05315i) q^{28} -0.118657 q^{29} +(3.13010 + 5.42150i) q^{31} +(1.63010 + 2.82342i) q^{32} +(-1.66520 + 2.88421i) q^{33} -1.59401 q^{34} -1.91744 q^{36} +(-3.87786 + 6.71665i) q^{37} +(-0.238091 - 0.412386i) q^{38} +(-2.27377 - 3.93829i) q^{39} +0.0701896 q^{41} +(0.689431 + 0.320341i) q^{42} +2.92981 q^{43} +(-3.19291 + 5.53029i) q^{44} +(-1.09671 - 1.89956i) q^{46} +(3.19291 - 5.53029i) q^{47} -3.51145 q^{48} +(4.51415 + 5.35000i) q^{49} +(2.77377 - 4.80431i) q^{51} +(-4.35981 - 7.55142i) q^{52} +(-0.369898 - 0.640682i) q^{53} +(-0.143668 + 0.248840i) q^{54} +(2.70080 + 1.25492i) q^{56} +1.65723 q^{57} +(-0.0170472 + 0.0295266i) q^{58} +(0.815051 + 1.41171i) q^{59} +(3.65901 - 6.33759i) q^{61} +1.79878 q^{62} +(-2.16520 + 1.52050i) q^{63} -6.08612 q^{64} +(0.478471 + 0.828736i) q^{66} +(-1.51805 - 2.62934i) q^{67} +(5.31853 - 9.21197i) q^{68} +7.63366 q^{69} -3.77048 q^{71} +(-0.562810 + 0.974816i) q^{72} +(-1.17757 - 2.03961i) q^{73} +(1.11425 + 1.92993i) q^{74} +3.17764 q^{76} +(0.779956 + 8.77681i) q^{77} -1.30667 q^{78} +(5.97016 - 10.3406i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(0.0100840 - 0.0174660i) q^{82} +1.22411 q^{83} +(-4.15163 + 2.91547i) q^{84} +(0.420920 - 0.729054i) q^{86} +(-0.0593285 - 0.102760i) q^{87} +(1.87438 + 3.24652i) q^{88} +(6.50007 - 11.2585i) q^{89} +(-10.9113 - 5.06990i) q^{91} +14.6371 q^{92} +(-3.13010 + 5.42150i) q^{93} +(-0.917438 - 1.58905i) q^{94} +(-1.63010 + 2.82342i) q^{96} -3.04306 q^{97} +(1.97983 - 0.354679i) q^{98} -3.33039 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{6} + 2 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{6} + 2 q^{7} + 12 q^{8} - 4 q^{9} + 4 q^{12} + 4 q^{13} + 12 q^{14} - 2 q^{17} - 2 q^{18} + 12 q^{19} - 2 q^{21} + 28 q^{22} - 10 q^{23} + 6 q^{24} - 6 q^{26} - 8 q^{27} - 12 q^{28} - 12 q^{29} + 8 q^{31} - 4 q^{32} - 8 q^{34} + 8 q^{36} - 24 q^{37} - 8 q^{38} + 2 q^{39} + 8 q^{41} - 6 q^{42} + 16 q^{43} - 10 q^{44} - 16 q^{46} + 10 q^{47} + 20 q^{49} + 2 q^{51} - 34 q^{52} - 20 q^{53} + 2 q^{54} + 42 q^{56} + 24 q^{57} - 10 q^{58} - 2 q^{59} + 8 q^{61} - 20 q^{62} - 4 q^{63} - 8 q^{64} + 14 q^{66} - 6 q^{67} + 30 q^{68} - 20 q^{69} - 28 q^{71} - 6 q^{72} - 12 q^{73} - 20 q^{74} - 32 q^{76} - 6 q^{77} - 12 q^{78} + 8 q^{79} - 4 q^{81} + 18 q^{82} - 12 q^{83} - 6 q^{84} - 24 q^{86} - 6 q^{87} + 12 q^{88} - 8 q^{89} + 4 q^{91} + 92 q^{92} - 8 q^{93} + 16 q^{94} + 4 q^{96} - 4 q^{97} - 20 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.143668 0.248840i 0.101589 0.175957i −0.810751 0.585392i \(-0.800941\pi\)
0.912339 + 0.409435i \(0.134274\pi\)
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0.958719 + 1.66055i 0.479360 + 0.830275i
\(5\) 0 0
\(6\) 0.287336 0.117304
\(7\) 2.39939 + 1.11487i 0.906884 + 0.421380i
\(8\) 1.12562 0.397967
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 1.66520 + 2.88421i 0.502076 + 0.869621i 0.999997 + 0.00239862i \(0.000763504\pi\)
−0.497921 + 0.867222i \(0.665903\pi\)
\(12\) −0.958719 + 1.66055i −0.276758 + 0.479360i
\(13\) −4.54754 −1.26126 −0.630630 0.776083i \(-0.717204\pi\)
−0.630630 + 0.776083i \(0.717204\pi\)
\(14\) 0.622139 0.436894i 0.166274 0.116765i
\(15\) 0 0
\(16\) −1.75572 + 3.04100i −0.438931 + 0.760250i
\(17\) −2.77377 4.80431i −0.672738 1.16522i −0.977125 0.212668i \(-0.931785\pi\)
0.304386 0.952549i \(-0.401549\pi\)
\(18\) 0.143668 + 0.248840i 0.0338629 + 0.0586522i
\(19\) 0.828617 1.43521i 0.190098 0.329259i −0.755185 0.655512i \(-0.772453\pi\)
0.945282 + 0.326253i \(0.105786\pi\)
\(20\) 0 0
\(21\) 0.234193 + 2.63537i 0.0511052 + 0.575084i
\(22\) 0.956942 0.204021
\(23\) 3.81683 6.61094i 0.795864 1.37848i −0.126425 0.991976i \(-0.540350\pi\)
0.922289 0.386500i \(-0.126316\pi\)
\(24\) 0.562810 + 0.974816i 0.114883 + 0.198983i
\(25\) 0 0
\(26\) −0.653336 + 1.13161i −0.128130 + 0.221927i
\(27\) −1.00000 −0.192450
\(28\) 0.449051 + 5.05315i 0.0848627 + 0.954956i
\(29\) −0.118657 −0.0220341 −0.0110170 0.999939i \(-0.503507\pi\)
−0.0110170 + 0.999939i \(0.503507\pi\)
\(30\) 0 0
\(31\) 3.13010 + 5.42150i 0.562183 + 0.973729i 0.997306 + 0.0733583i \(0.0233717\pi\)
−0.435123 + 0.900371i \(0.643295\pi\)
\(32\) 1.63010 + 2.82342i 0.288164 + 0.499115i
\(33\) −1.66520 + 2.88421i −0.289874 + 0.502076i
\(34\) −1.59401 −0.273370
\(35\) 0 0
\(36\) −1.91744 −0.319573
\(37\) −3.87786 + 6.71665i −0.637516 + 1.10421i 0.348460 + 0.937324i \(0.386705\pi\)
−0.985976 + 0.166887i \(0.946628\pi\)
\(38\) −0.238091 0.412386i −0.0386235 0.0668979i
\(39\) −2.27377 3.93829i −0.364095 0.630630i
\(40\) 0 0
\(41\) 0.0701896 0.0109618 0.00548089 0.999985i \(-0.498255\pi\)
0.00548089 + 0.999985i \(0.498255\pi\)
\(42\) 0.689431 + 0.320341i 0.106381 + 0.0494297i
\(43\) 2.92981 0.446792 0.223396 0.974728i \(-0.428286\pi\)
0.223396 + 0.974728i \(0.428286\pi\)
\(44\) −3.19291 + 5.53029i −0.481350 + 0.833722i
\(45\) 0 0
\(46\) −1.09671 1.89956i −0.161701 0.280075i
\(47\) 3.19291 5.53029i 0.465734 0.806675i −0.533500 0.845800i \(-0.679124\pi\)
0.999234 + 0.0391247i \(0.0124570\pi\)
\(48\) −3.51145 −0.506833
\(49\) 4.51415 + 5.35000i 0.644879 + 0.764285i
\(50\) 0 0
\(51\) 2.77377 4.80431i 0.388406 0.672738i
\(52\) −4.35981 7.55142i −0.604597 1.04719i
\(53\) −0.369898 0.640682i −0.0508094 0.0880044i 0.839502 0.543356i \(-0.182847\pi\)
−0.890311 + 0.455352i \(0.849513\pi\)
\(54\) −0.143668 + 0.248840i −0.0195507 + 0.0338629i
\(55\) 0 0
\(56\) 2.70080 + 1.25492i 0.360910 + 0.167695i
\(57\) 1.65723 0.219506
\(58\) −0.0170472 + 0.0295266i −0.00223841 + 0.00387704i
\(59\) 0.815051 + 1.41171i 0.106111 + 0.183789i 0.914191 0.405283i \(-0.132827\pi\)
−0.808081 + 0.589072i \(0.799494\pi\)
\(60\) 0 0
\(61\) 3.65901 6.33759i 0.468488 0.811446i −0.530863 0.847458i \(-0.678132\pi\)
0.999351 + 0.0360120i \(0.0114655\pi\)
\(62\) 1.79878 0.228445
\(63\) −2.16520 + 1.52050i −0.272789 + 0.191565i
\(64\) −6.08612 −0.760765
\(65\) 0 0
\(66\) 0.478471 + 0.828736i 0.0588957 + 0.102010i
\(67\) −1.51805 2.62934i −0.185459 0.321224i 0.758272 0.651938i \(-0.226044\pi\)
−0.943731 + 0.330714i \(0.892711\pi\)
\(68\) 5.31853 9.21197i 0.644967 1.11712i
\(69\) 7.63366 0.918984
\(70\) 0 0
\(71\) −3.77048 −0.447474 −0.223737 0.974650i \(-0.571826\pi\)
−0.223737 + 0.974650i \(0.571826\pi\)
\(72\) −0.562810 + 0.974816i −0.0663278 + 0.114883i
\(73\) −1.17757 2.03961i −0.137824 0.238718i 0.788849 0.614588i \(-0.210678\pi\)
−0.926673 + 0.375869i \(0.877344\pi\)
\(74\) 1.11425 + 1.92993i 0.129529 + 0.224350i
\(75\) 0 0
\(76\) 3.17764 0.364501
\(77\) 0.779956 + 8.77681i 0.0888843 + 1.00021i
\(78\) −1.30667 −0.147951
\(79\) 5.97016 10.3406i 0.671696 1.16341i −0.305727 0.952119i \(-0.598899\pi\)
0.977423 0.211292i \(-0.0677672\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0.0100840 0.0174660i 0.00111359 0.00192880i
\(83\) 1.22411 0.134363 0.0671817 0.997741i \(-0.478599\pi\)
0.0671817 + 0.997741i \(0.478599\pi\)
\(84\) −4.15163 + 2.91547i −0.452980 + 0.318103i
\(85\) 0 0
\(86\) 0.420920 0.729054i 0.0453889 0.0786160i
\(87\) −0.0593285 0.102760i −0.00636069 0.0110170i
\(88\) 1.87438 + 3.24652i 0.199810 + 0.346080i
\(89\) 6.50007 11.2585i 0.689006 1.19339i −0.283153 0.959075i \(-0.591381\pi\)
0.972160 0.234319i \(-0.0752862\pi\)
\(90\) 0 0
\(91\) −10.9113 5.06990i −1.14382 0.531470i
\(92\) 14.6371 1.52602
\(93\) −3.13010 + 5.42150i −0.324576 + 0.562183i
\(94\) −0.917438 1.58905i −0.0946265 0.163898i
\(95\) 0 0
\(96\) −1.63010 + 2.82342i −0.166372 + 0.288164i
\(97\) −3.04306 −0.308976 −0.154488 0.987995i \(-0.549373\pi\)
−0.154488 + 0.987995i \(0.549373\pi\)
\(98\) 1.97983 0.354679i 0.199993 0.0358280i
\(99\) −3.33039 −0.334717
\(100\) 0 0
\(101\) −8.01983 13.8907i −0.798002 1.38218i −0.920915 0.389763i \(-0.872557\pi\)
0.122913 0.992417i \(-0.460776\pi\)
\(102\) −0.797004 1.38045i −0.0789151 0.136685i
\(103\) −2.64596 + 4.58293i −0.260714 + 0.451570i −0.966432 0.256923i \(-0.917291\pi\)
0.705718 + 0.708493i \(0.250625\pi\)
\(104\) −5.11880 −0.501940
\(105\) 0 0
\(106\) −0.212570 −0.0206466
\(107\) −2.58086 + 4.47018i −0.249501 + 0.432148i −0.963387 0.268113i \(-0.913600\pi\)
0.713886 + 0.700261i \(0.246933\pi\)
\(108\) −0.958719 1.66055i −0.0922528 0.159787i
\(109\) −1.62043 2.80668i −0.155209 0.268831i 0.777926 0.628356i \(-0.216272\pi\)
−0.933135 + 0.359525i \(0.882939\pi\)
\(110\) 0 0
\(111\) −7.75572 −0.736141
\(112\) −7.60297 + 5.33915i −0.718413 + 0.504503i
\(113\) 12.6608 1.19103 0.595513 0.803345i \(-0.296949\pi\)
0.595513 + 0.803345i \(0.296949\pi\)
\(114\) 0.238091 0.412386i 0.0222993 0.0386235i
\(115\) 0 0
\(116\) −0.113759 0.197036i −0.0105622 0.0182943i
\(117\) 2.27377 3.93829i 0.210210 0.364095i
\(118\) 0.468387 0.0431185
\(119\) −1.29920 14.6198i −0.119097 1.34019i
\(120\) 0 0
\(121\) −0.0457629 + 0.0792637i −0.00416027 + 0.00720579i
\(122\) −1.05136 1.82102i −0.0951861 0.164867i
\(123\) 0.0350948 + 0.0607860i 0.00316439 + 0.00548089i
\(124\) −6.00178 + 10.3954i −0.538976 + 0.933533i
\(125\) 0 0
\(126\) 0.0672922 + 0.757235i 0.00599486 + 0.0674599i
\(127\) 16.5475 1.46836 0.734178 0.678957i \(-0.237568\pi\)
0.734178 + 0.678957i \(0.237568\pi\)
\(128\) −4.13458 + 7.16131i −0.365449 + 0.632976i
\(129\) 1.46491 + 2.53729i 0.128978 + 0.223396i
\(130\) 0 0
\(131\) 2.64893 4.58808i 0.231438 0.400862i −0.726794 0.686856i \(-0.758990\pi\)
0.958231 + 0.285994i \(0.0923237\pi\)
\(132\) −6.38582 −0.555815
\(133\) 3.58824 2.51982i 0.311140 0.218496i
\(134\) −0.872379 −0.0753621
\(135\) 0 0
\(136\) −3.12221 5.40783i −0.267727 0.463718i
\(137\) −7.43507 12.8779i −0.635221 1.10023i −0.986468 0.163952i \(-0.947576\pi\)
0.351247 0.936283i \(-0.385758\pi\)
\(138\) 1.09671 1.89956i 0.0933583 0.161701i
\(139\) −9.51685 −0.807209 −0.403605 0.914934i \(-0.632243\pi\)
−0.403605 + 0.914934i \(0.632243\pi\)
\(140\) 0 0
\(141\) 6.38582 0.537783
\(142\) −0.541697 + 0.938247i −0.0454582 + 0.0787359i
\(143\) −7.57255 13.1160i −0.633249 1.09682i
\(144\) −1.75572 3.04100i −0.146310 0.253417i
\(145\) 0 0
\(146\) −0.676716 −0.0560054
\(147\) −2.37616 + 6.58437i −0.195982 + 0.543069i
\(148\) −14.8711 −1.22240
\(149\) −5.68502 + 9.84675i −0.465735 + 0.806677i −0.999234 0.0391236i \(-0.987543\pi\)
0.533499 + 0.845801i \(0.320877\pi\)
\(150\) 0 0
\(151\) −4.47016 7.74255i −0.363777 0.630080i 0.624802 0.780783i \(-0.285180\pi\)
−0.988579 + 0.150703i \(0.951846\pi\)
\(152\) 0.932708 1.61550i 0.0756526 0.131034i
\(153\) 5.54754 0.448492
\(154\) 2.29608 + 1.06686i 0.185023 + 0.0859701i
\(155\) 0 0
\(156\) 4.35981 7.55142i 0.349064 0.604597i
\(157\) 1.67316 + 2.89800i 0.133533 + 0.231286i 0.925036 0.379879i \(-0.124035\pi\)
−0.791503 + 0.611165i \(0.790701\pi\)
\(158\) −1.71544 2.97123i −0.136473 0.236379i
\(159\) 0.369898 0.640682i 0.0293348 0.0508094i
\(160\) 0 0
\(161\) 16.5284 11.6070i 1.30262 0.914758i
\(162\) −0.287336 −0.0225752
\(163\) −7.87793 + 13.6450i −0.617047 + 1.06876i 0.372974 + 0.927842i \(0.378338\pi\)
−0.990022 + 0.140916i \(0.954995\pi\)
\(164\) 0.0672922 + 0.116553i 0.00525463 + 0.00910129i
\(165\) 0 0
\(166\) 0.175865 0.304608i 0.0136498 0.0236421i
\(167\) −22.5942 −1.74839 −0.874194 0.485577i \(-0.838610\pi\)
−0.874194 + 0.485577i \(0.838610\pi\)
\(168\) 0.263613 + 2.96642i 0.0203382 + 0.228864i
\(169\) 7.68012 0.590779
\(170\) 0 0
\(171\) 0.828617 + 1.43521i 0.0633659 + 0.109753i
\(172\) 2.80887 + 4.86510i 0.214174 + 0.370960i
\(173\) −4.26310 + 7.38391i −0.324118 + 0.561388i −0.981333 0.192314i \(-0.938401\pi\)
0.657216 + 0.753703i \(0.271734\pi\)
\(174\) −0.0340944 −0.00258469
\(175\) 0 0
\(176\) −11.6945 −0.881506
\(177\) −0.815051 + 1.41171i −0.0612630 + 0.106111i
\(178\) −1.86770 3.23496i −0.139990 0.242470i
\(179\) 5.89031 + 10.2023i 0.440262 + 0.762557i 0.997709 0.0676564i \(-0.0215522\pi\)
−0.557446 + 0.830213i \(0.688219\pi\)
\(180\) 0 0
\(181\) 9.08967 0.675630 0.337815 0.941213i \(-0.390312\pi\)
0.337815 + 0.941213i \(0.390312\pi\)
\(182\) −2.82920 + 1.98679i −0.209714 + 0.147271i
\(183\) 7.31802 0.540964
\(184\) 4.29630 7.44141i 0.316727 0.548588i
\(185\) 0 0
\(186\) 0.899391 + 1.55779i 0.0659465 + 0.114223i
\(187\) 9.23775 16.0002i 0.675531 1.17005i
\(188\) 12.2444 0.893016
\(189\) −2.39939 1.11487i −0.174530 0.0810945i
\(190\) 0 0
\(191\) −10.2478 + 17.7498i −0.741507 + 1.28433i 0.210302 + 0.977637i \(0.432555\pi\)
−0.951809 + 0.306692i \(0.900778\pi\)
\(192\) −3.04306 5.27073i −0.219614 0.380382i
\(193\) −4.27148 7.39842i −0.307468 0.532550i 0.670340 0.742054i \(-0.266148\pi\)
−0.977808 + 0.209504i \(0.932815\pi\)
\(194\) −0.437190 + 0.757235i −0.0313884 + 0.0543663i
\(195\) 0 0
\(196\) −4.55613 + 12.6251i −0.325438 + 0.901794i
\(197\) 13.8086 0.983820 0.491910 0.870646i \(-0.336299\pi\)
0.491910 + 0.870646i \(0.336299\pi\)
\(198\) −0.478471 + 0.828736i −0.0340034 + 0.0588957i
\(199\) −1.89549 3.28309i −0.134368 0.232732i 0.790988 0.611832i \(-0.209567\pi\)
−0.925356 + 0.379100i \(0.876234\pi\)
\(200\) 0 0
\(201\) 1.51805 2.62934i 0.107075 0.185459i
\(202\) −4.60877 −0.324272
\(203\) −0.284705 0.132287i −0.0199824 0.00928471i
\(204\) 10.6371 0.744744
\(205\) 0 0
\(206\) 0.760278 + 1.31684i 0.0529711 + 0.0917486i
\(207\) 3.81683 + 6.61094i 0.265288 + 0.459492i
\(208\) 7.98422 13.8291i 0.553606 0.958874i
\(209\) 5.51924 0.381774
\(210\) 0 0
\(211\) −0.114416 −0.00787674 −0.00393837 0.999992i \(-0.501254\pi\)
−0.00393837 + 0.999992i \(0.501254\pi\)
\(212\) 0.709256 1.22847i 0.0487119 0.0843715i
\(213\) −1.88524 3.26533i −0.129175 0.223737i
\(214\) 0.741573 + 1.28444i 0.0506929 + 0.0878026i
\(215\) 0 0
\(216\) −1.12562 −0.0765888
\(217\) 1.46610 + 16.4979i 0.0995253 + 1.11995i
\(218\) −0.931218 −0.0630700
\(219\) 1.17757 2.03961i 0.0795728 0.137824i
\(220\) 0 0
\(221\) 12.6138 + 21.8478i 0.848498 + 1.46964i
\(222\) −1.11425 + 1.92993i −0.0747835 + 0.129529i
\(223\) 7.86673 0.526795 0.263398 0.964687i \(-0.415157\pi\)
0.263398 + 0.964687i \(0.415157\pi\)
\(224\) 0.763518 + 8.59183i 0.0510147 + 0.574066i
\(225\) 0 0
\(226\) 1.81895 3.15051i 0.120995 0.209569i
\(227\) −4.48933 7.77575i −0.297967 0.516095i 0.677703 0.735335i \(-0.262975\pi\)
−0.975671 + 0.219241i \(0.929642\pi\)
\(228\) 1.58882 + 2.75192i 0.105222 + 0.182250i
\(229\) 2.54306 4.40471i 0.168050 0.291071i −0.769684 0.638425i \(-0.779586\pi\)
0.937734 + 0.347354i \(0.112920\pi\)
\(230\) 0 0
\(231\) −7.21096 + 5.06387i −0.474446 + 0.333178i
\(232\) −0.133563 −0.00876883
\(233\) −10.9091 + 18.8952i −0.714681 + 1.23786i 0.248401 + 0.968657i \(0.420095\pi\)
−0.963082 + 0.269207i \(0.913239\pi\)
\(234\) −0.653336 1.13161i −0.0427099 0.0739757i
\(235\) 0 0
\(236\) −1.56281 + 2.70687i −0.101730 + 0.176202i
\(237\) 11.9403 0.775608
\(238\) −3.82465 1.77710i −0.247915 0.115193i
\(239\) 7.44905 0.481839 0.240920 0.970545i \(-0.422551\pi\)
0.240920 + 0.970545i \(0.422551\pi\)
\(240\) 0 0
\(241\) 12.0879 + 20.9368i 0.778650 + 1.34866i 0.932720 + 0.360601i \(0.117428\pi\)
−0.154070 + 0.988060i \(0.549238\pi\)
\(242\) 0.0131493 + 0.0227753i 0.000845271 + 0.00146405i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 14.0319 0.898297
\(245\) 0 0
\(246\) 0.0201680 0.00128586
\(247\) −3.76817 + 6.52666i −0.239763 + 0.415281i
\(248\) 3.52331 + 6.10255i 0.223730 + 0.387512i
\(249\) 0.612055 + 1.06011i 0.0387874 + 0.0671817i
\(250\) 0 0
\(251\) 6.00200 0.378843 0.189421 0.981896i \(-0.439339\pi\)
0.189421 + 0.981896i \(0.439339\pi\)
\(252\) −4.60068 2.13769i −0.289816 0.134662i
\(253\) 25.4231 1.59834
\(254\) 2.37735 4.11769i 0.149168 0.258367i
\(255\) 0 0
\(256\) −4.89810 8.48376i −0.306131 0.530235i
\(257\) −3.66697 + 6.35139i −0.228740 + 0.396189i −0.957435 0.288650i \(-0.906794\pi\)
0.728695 + 0.684838i \(0.240127\pi\)
\(258\) 0.841839 0.0524106
\(259\) −16.7927 + 11.7926i −1.04345 + 0.732755i
\(260\) 0 0
\(261\) 0.0593285 0.102760i 0.00367234 0.00636069i
\(262\) −0.761132 1.31832i −0.0470229 0.0814460i
\(263\) −4.74386 8.21661i −0.292519 0.506658i 0.681886 0.731459i \(-0.261160\pi\)
−0.974405 + 0.224801i \(0.927827\pi\)
\(264\) −1.87438 + 3.24652i −0.115360 + 0.199810i
\(265\) 0 0
\(266\) −0.111519 1.25492i −0.00683766 0.0769438i
\(267\) 13.0001 0.795596
\(268\) 2.91076 5.04159i 0.177803 0.307964i
\(269\) −8.02423 13.8984i −0.489246 0.847399i 0.510677 0.859772i \(-0.329395\pi\)
−0.999923 + 0.0123733i \(0.996061\pi\)
\(270\) 0 0
\(271\) −12.0845 + 20.9309i −0.734080 + 1.27146i 0.221045 + 0.975264i \(0.429053\pi\)
−0.955126 + 0.296201i \(0.904280\pi\)
\(272\) 19.4799 1.18114
\(273\) −1.06500 11.9844i −0.0644570 0.725331i
\(274\) −4.27272 −0.258125
\(275\) 0 0
\(276\) 7.31853 + 12.6761i 0.440524 + 0.763010i
\(277\) −11.6088 20.1071i −0.697508 1.20812i −0.969328 0.245771i \(-0.920959\pi\)
0.271820 0.962348i \(-0.412374\pi\)
\(278\) −1.36727 + 2.36818i −0.0820032 + 0.142034i
\(279\) −6.26020 −0.374789
\(280\) 0 0
\(281\) 12.4472 0.742538 0.371269 0.928525i \(-0.378923\pi\)
0.371269 + 0.928525i \(0.378923\pi\)
\(282\) 0.917438 1.58905i 0.0546326 0.0946265i
\(283\) 4.33388 + 7.50649i 0.257622 + 0.446215i 0.965604 0.260016i \(-0.0837277\pi\)
−0.707982 + 0.706230i \(0.750394\pi\)
\(284\) −3.61483 6.26107i −0.214501 0.371526i
\(285\) 0 0
\(286\) −4.35173 −0.257323
\(287\) 0.168412 + 0.0782520i 0.00994107 + 0.00461907i
\(288\) −3.26020 −0.192109
\(289\) −6.88760 + 11.9297i −0.405153 + 0.701746i
\(290\) 0 0
\(291\) −1.52153 2.63537i −0.0891936 0.154488i
\(292\) 2.25792 3.91083i 0.132135 0.228864i
\(293\) −27.0063 −1.57772 −0.788862 0.614571i \(-0.789329\pi\)
−0.788862 + 0.614571i \(0.789329\pi\)
\(294\) 1.29708 + 1.53725i 0.0756471 + 0.0896540i
\(295\) 0 0
\(296\) −4.36500 + 7.56040i −0.253710 + 0.439439i
\(297\) −1.66520 2.88421i −0.0966245 0.167359i
\(298\) 1.63351 + 2.82932i 0.0946267 + 0.163898i
\(299\) −17.3572 + 30.0635i −1.00379 + 1.73862i
\(300\) 0 0
\(301\) 7.02976 + 3.26634i 0.405189 + 0.188269i
\(302\) −2.56888 −0.147822
\(303\) 8.01983 13.8907i 0.460727 0.798002i
\(304\) 2.90964 + 5.03965i 0.166879 + 0.289044i
\(305\) 0 0
\(306\) 0.797004 1.38045i 0.0455617 0.0789151i
\(307\) 2.24681 0.128232 0.0641161 0.997942i \(-0.479577\pi\)
0.0641161 + 0.997942i \(0.479577\pi\)
\(308\) −13.8266 + 9.70965i −0.787842 + 0.553259i
\(309\) −5.29191 −0.301046
\(310\) 0 0
\(311\) −14.2994 24.7672i −0.810843 1.40442i −0.912275 0.409578i \(-0.865676\pi\)
0.101432 0.994842i \(-0.467657\pi\)
\(312\) −2.55940 4.43301i −0.144898 0.250970i
\(313\) 6.66427 11.5429i 0.376687 0.652441i −0.613891 0.789391i \(-0.710397\pi\)
0.990578 + 0.136950i \(0.0437300\pi\)
\(314\) 0.961518 0.0542616
\(315\) 0 0
\(316\) 22.8948 1.28794
\(317\) −14.5963 + 25.2815i −0.819808 + 1.41995i 0.0860147 + 0.996294i \(0.472587\pi\)
−0.905823 + 0.423656i \(0.860747\pi\)
\(318\) −0.106285 0.184091i −0.00596016 0.0103233i
\(319\) −0.197587 0.342231i −0.0110628 0.0191613i
\(320\) 0 0
\(321\) −5.16172 −0.288099
\(322\) −0.513685 5.78047i −0.0286266 0.322133i
\(323\) −9.19357 −0.511544
\(324\) 0.958719 1.66055i 0.0532622 0.0922528i
\(325\) 0 0
\(326\) 2.26361 + 3.92069i 0.125370 + 0.217147i
\(327\) 1.62043 2.80668i 0.0896102 0.155209i
\(328\) 0.0790069 0.00436243
\(329\) 13.8266 9.70965i 0.762283 0.535310i
\(330\) 0 0
\(331\) 12.4457 21.5566i 0.684080 1.18486i −0.289646 0.957134i \(-0.593537\pi\)
0.973725 0.227727i \(-0.0731293\pi\)
\(332\) 1.17358 + 2.03270i 0.0644084 + 0.111559i
\(333\) −3.87786 6.71665i −0.212505 0.368070i
\(334\) −3.24605 + 5.62233i −0.177616 + 0.307640i
\(335\) 0 0
\(336\) −8.42533 3.91479i −0.459639 0.213569i
\(337\) 4.72659 0.257474 0.128737 0.991679i \(-0.458908\pi\)
0.128737 + 0.991679i \(0.458908\pi\)
\(338\) 1.10339 1.91112i 0.0600164 0.103951i
\(339\) 6.33039 + 10.9646i 0.343820 + 0.595513i
\(340\) 0 0
\(341\) −10.4245 + 18.0557i −0.564517 + 0.977772i
\(342\) 0.476183 0.0257490
\(343\) 4.86668 + 17.8694i 0.262776 + 0.964857i
\(344\) 3.29785 0.177808
\(345\) 0 0
\(346\) 1.22494 + 2.12166i 0.0658533 + 0.114061i
\(347\) 7.07915 + 12.2615i 0.380029 + 0.658229i 0.991066 0.133373i \(-0.0425807\pi\)
−0.611037 + 0.791602i \(0.709247\pi\)
\(348\) 0.113759 0.197036i 0.00609811 0.0105622i
\(349\) 5.04930 0.270283 0.135141 0.990826i \(-0.456851\pi\)
0.135141 + 0.990826i \(0.456851\pi\)
\(350\) 0 0
\(351\) 4.54754 0.242730
\(352\) −5.42888 + 9.40310i −0.289360 + 0.501187i
\(353\) 8.04924 + 13.9417i 0.428418 + 0.742042i 0.996733 0.0807694i \(-0.0257377\pi\)
−0.568315 + 0.822811i \(0.692404\pi\)
\(354\) 0.234193 + 0.405635i 0.0124472 + 0.0215592i
\(355\) 0 0
\(356\) 24.9270 1.32113
\(357\) 12.0115 8.43504i 0.635717 0.446430i
\(358\) 3.38499 0.178902
\(359\) −0.153241 + 0.265421i −0.00808776 + 0.0140084i −0.870041 0.492979i \(-0.835908\pi\)
0.861953 + 0.506988i \(0.169241\pi\)
\(360\) 0 0
\(361\) 8.12679 + 14.0760i 0.427726 + 0.740843i
\(362\) 1.30589 2.26188i 0.0686363 0.118882i
\(363\) −0.0915259 −0.00480386
\(364\) −2.04208 22.9794i −0.107034 1.20445i
\(365\) 0 0
\(366\) 1.05136 1.82102i 0.0549557 0.0951861i
\(367\) −11.8249 20.4813i −0.617253 1.06911i −0.989985 0.141174i \(-0.954912\pi\)
0.372732 0.927939i \(-0.378421\pi\)
\(368\) 13.4026 + 23.2140i 0.698658 + 1.21011i
\(369\) −0.0350948 + 0.0607860i −0.00182696 + 0.00316439i
\(370\) 0 0
\(371\) −0.173255 1.94963i −0.00899496 0.101220i
\(372\) −12.0036 −0.622355
\(373\) 9.41887 16.3140i 0.487691 0.844705i −0.512209 0.858861i \(-0.671173\pi\)
0.999900 + 0.0141557i \(0.00450604\pi\)
\(374\) −2.65434 4.59744i −0.137252 0.237728i
\(375\) 0 0
\(376\) 3.59401 6.22500i 0.185347 0.321030i
\(377\) 0.539598 0.0277907
\(378\) −0.622139 + 0.436894i −0.0319994 + 0.0224714i
\(379\) 14.2534 0.732147 0.366074 0.930586i \(-0.380702\pi\)
0.366074 + 0.930586i \(0.380702\pi\)
\(380\) 0 0
\(381\) 8.27377 + 14.3306i 0.423878 + 0.734178i
\(382\) 2.94457 + 5.10014i 0.150657 + 0.260946i
\(383\) −12.5282 + 21.6995i −0.640161 + 1.10879i 0.345235 + 0.938516i \(0.387799\pi\)
−0.985396 + 0.170276i \(0.945534\pi\)
\(384\) −8.26917 −0.421984
\(385\) 0 0
\(386\) −2.45470 −0.124941
\(387\) −1.46491 + 2.53729i −0.0744653 + 0.128978i
\(388\) −2.91744 5.05315i −0.148110 0.256535i
\(389\) 6.73590 + 11.6669i 0.341524 + 0.591536i 0.984716 0.174169i \(-0.0557238\pi\)
−0.643192 + 0.765705i \(0.722390\pi\)
\(390\) 0 0
\(391\) −42.3480 −2.14163
\(392\) 5.08122 + 6.02206i 0.256640 + 0.304160i
\(393\) 5.29785 0.267241
\(394\) 1.98385 3.43613i 0.0999449 0.173110i
\(395\) 0 0
\(396\) −3.19291 5.53029i −0.160450 0.277907i
\(397\) −9.22418 + 15.9768i −0.462948 + 0.801850i −0.999106 0.0422675i \(-0.986542\pi\)
0.536158 + 0.844118i \(0.319875\pi\)
\(398\) −1.08929 −0.0546010
\(399\) 3.97635 + 1.84759i 0.199067 + 0.0924953i
\(400\) 0 0
\(401\) −12.7093 + 22.0131i −0.634670 + 1.09928i 0.351915 + 0.936032i \(0.385531\pi\)
−0.986585 + 0.163249i \(0.947803\pi\)
\(402\) −0.436189 0.755502i −0.0217552 0.0376810i
\(403\) −14.2343 24.6545i −0.709059 1.22813i
\(404\) 15.3775 26.6346i 0.765060 1.32512i
\(405\) 0 0
\(406\) −0.0738212 + 0.0518406i −0.00366368 + 0.00257281i
\(407\) −25.8296 −1.28033
\(408\) 3.12221 5.40783i 0.154573 0.267727i
\(409\) 9.36556 + 16.2216i 0.463097 + 0.802108i 0.999113 0.0420997i \(-0.0134047\pi\)
−0.536016 + 0.844208i \(0.680071\pi\)
\(410\) 0 0
\(411\) 7.43507 12.8779i 0.366745 0.635221i
\(412\) −10.1469 −0.499903
\(413\) 0.381759 + 4.29592i 0.0187851 + 0.211388i
\(414\) 2.19342 0.107801
\(415\) 0 0
\(416\) −7.41296 12.8396i −0.363450 0.629514i
\(417\) −4.75843 8.24184i −0.233021 0.403605i
\(418\) 0.792938 1.37341i 0.0387839 0.0671756i
\(419\) 2.04745 0.100024 0.0500121 0.998749i \(-0.484074\pi\)
0.0500121 + 0.998749i \(0.484074\pi\)
\(420\) 0 0
\(421\) −16.0512 −0.782287 −0.391144 0.920330i \(-0.627920\pi\)
−0.391144 + 0.920330i \(0.627920\pi\)
\(422\) −0.0164380 + 0.0284714i −0.000800187 + 0.00138596i
\(423\) 3.19291 + 5.53029i 0.155245 + 0.268892i
\(424\) −0.416364 0.721164i −0.0202204 0.0350228i
\(425\) 0 0
\(426\) −1.08339 −0.0524906
\(427\) 15.8450 11.1271i 0.766791 0.538476i
\(428\) −9.89727 −0.478403
\(429\) 7.57255 13.1160i 0.365606 0.633249i
\(430\) 0 0
\(431\) −18.3063 31.7075i −0.881784 1.52729i −0.849356 0.527820i \(-0.823009\pi\)
−0.0324277 0.999474i \(-0.510324\pi\)
\(432\) 1.75572 3.04100i 0.0844722 0.146310i
\(433\) −18.0047 −0.865252 −0.432626 0.901574i \(-0.642413\pi\)
−0.432626 + 0.901574i \(0.642413\pi\)
\(434\) 4.31598 + 2.00540i 0.207174 + 0.0962622i
\(435\) 0 0
\(436\) 3.10708 5.38163i 0.148802 0.257733i
\(437\) −6.32538 10.9559i −0.302584 0.524090i
\(438\) −0.338358 0.586053i −0.0161674 0.0280027i
\(439\) 9.68731 16.7789i 0.462350 0.800814i −0.536727 0.843756i \(-0.680340\pi\)
0.999078 + 0.0429418i \(0.0136730\pi\)
\(440\) 0 0
\(441\) −6.89031 + 1.23437i −0.328110 + 0.0587796i
\(442\) 7.24881 0.344791
\(443\) 8.22121 14.2396i 0.390602 0.676542i −0.601927 0.798551i \(-0.705600\pi\)
0.992529 + 0.122009i \(0.0389337\pi\)
\(444\) −7.43556 12.8788i −0.352876 0.611199i
\(445\) 0 0
\(446\) 1.13020 1.95756i 0.0535164 0.0926931i
\(447\) −11.3700 −0.537785
\(448\) −14.6030 6.78520i −0.689926 0.320571i
\(449\) −32.7245 −1.54436 −0.772182 0.635401i \(-0.780835\pi\)
−0.772182 + 0.635401i \(0.780835\pi\)
\(450\) 0 0
\(451\) 0.116880 + 0.202441i 0.00550365 + 0.00953259i
\(452\) 12.1381 + 21.0239i 0.570930 + 0.988880i
\(453\) 4.47016 7.74255i 0.210027 0.363777i
\(454\) −2.57989 −0.121080
\(455\) 0 0
\(456\) 1.86542 0.0873561
\(457\) 18.7152 32.4156i 0.875459 1.51634i 0.0191857 0.999816i \(-0.493893\pi\)
0.856273 0.516523i \(-0.172774\pi\)
\(458\) −0.730712 1.26563i −0.0341439 0.0591390i
\(459\) 2.77377 + 4.80431i 0.129469 + 0.224246i
\(460\) 0 0
\(461\) 28.3604 1.32088 0.660438 0.750881i \(-0.270371\pi\)
0.660438 + 0.750881i \(0.270371\pi\)
\(462\) 0.224109 + 2.52189i 0.0104265 + 0.117329i
\(463\) −7.20833 −0.334999 −0.167500 0.985872i \(-0.553569\pi\)
−0.167500 + 0.985872i \(0.553569\pi\)
\(464\) 0.208329 0.360836i 0.00967143 0.0167514i
\(465\) 0 0
\(466\) 3.13458 + 5.42926i 0.145207 + 0.251506i
\(467\) −6.03950 + 10.4607i −0.279475 + 0.484065i −0.971254 0.238044i \(-0.923494\pi\)
0.691779 + 0.722109i \(0.256827\pi\)
\(468\) 8.71963 0.403065
\(469\) −0.711033 8.00122i −0.0328325 0.369462i
\(470\) 0 0
\(471\) −1.67316 + 2.89800i −0.0770952 + 0.133533i
\(472\) 0.917438 + 1.58905i 0.0422285 + 0.0731419i
\(473\) 4.87871 + 8.45018i 0.224323 + 0.388540i
\(474\) 1.71544 2.97123i 0.0787929 0.136473i
\(475\) 0 0
\(476\) 23.0313 16.1737i 1.05564 0.741319i
\(477\) 0.739795 0.0338729
\(478\) 1.07019 1.85362i 0.0489493 0.0847827i
\(479\) −10.0708 17.4432i −0.460149 0.797001i 0.538819 0.842421i \(-0.318871\pi\)
−0.998968 + 0.0454204i \(0.985537\pi\)
\(480\) 0 0
\(481\) 17.6347 30.5443i 0.804075 1.39270i
\(482\) 6.94657 0.316408
\(483\) 18.3161 + 8.51050i 0.833413 + 0.387241i
\(484\) −0.175495 −0.00797705
\(485\) 0 0
\(486\) −0.143668 0.248840i −0.00651691 0.0112876i
\(487\) 19.9698 + 34.5887i 0.904919 + 1.56737i 0.821026 + 0.570891i \(0.193402\pi\)
0.0838930 + 0.996475i \(0.473265\pi\)
\(488\) 4.11866 7.13372i 0.186443 0.322928i
\(489\) −15.7559 −0.712505
\(490\) 0 0
\(491\) −31.5989 −1.42604 −0.713019 0.701145i \(-0.752673\pi\)
−0.713019 + 0.701145i \(0.752673\pi\)
\(492\) −0.0672922 + 0.116553i −0.00303376 + 0.00525463i
\(493\) 0.329127 + 0.570066i 0.0148232 + 0.0256745i
\(494\) 1.08273 + 1.87534i 0.0487143 + 0.0843757i
\(495\) 0 0
\(496\) −21.9824 −0.987037
\(497\) −9.04686 4.20358i −0.405807 0.188556i
\(498\) 0.351730 0.0157614
\(499\) −19.8929 + 34.4556i −0.890530 + 1.54244i −0.0512890 + 0.998684i \(0.516333\pi\)
−0.839241 + 0.543759i \(0.817000\pi\)
\(500\) 0 0
\(501\) −11.2971 19.5671i −0.504716 0.874194i
\(502\) 0.862295 1.49354i 0.0384861 0.0666599i
\(503\) −12.8734 −0.573995 −0.286997 0.957931i \(-0.592657\pi\)
−0.286997 + 0.957931i \(0.592657\pi\)
\(504\) −2.43719 + 1.71151i −0.108561 + 0.0762365i
\(505\) 0 0
\(506\) 3.65248 6.32628i 0.162373 0.281238i
\(507\) 3.84006 + 6.65118i 0.170543 + 0.295389i
\(508\) 15.8644 + 27.4780i 0.703871 + 1.21914i
\(509\) −16.6981 + 28.9219i −0.740128 + 1.28194i 0.212308 + 0.977203i \(0.431902\pi\)
−0.952437 + 0.304737i \(0.901431\pi\)
\(510\) 0 0
\(511\) −0.551558 6.20665i −0.0243995 0.274566i
\(512\) −19.3531 −0.855296
\(513\) −0.828617 + 1.43521i −0.0365843 + 0.0633659i
\(514\) 1.05365 + 1.82498i 0.0464746 + 0.0804965i
\(515\) 0 0
\(516\) −2.80887 + 4.86510i −0.123653 + 0.214174i
\(517\) 21.2673 0.935335
\(518\) 0.521899 + 5.87290i 0.0229309 + 0.258041i
\(519\) −8.52620 −0.374259
\(520\) 0 0
\(521\) −6.77589 11.7362i −0.296857 0.514172i 0.678558 0.734547i \(-0.262605\pi\)
−0.975415 + 0.220375i \(0.929272\pi\)
\(522\) −0.0170472 0.0295266i −0.000746136 0.00129235i
\(523\) −10.1066 + 17.5052i −0.441933 + 0.765450i −0.997833 0.0657991i \(-0.979040\pi\)
0.555900 + 0.831249i \(0.312374\pi\)
\(524\) 10.1583 0.443768
\(525\) 0 0
\(526\) −2.72616 −0.118866
\(527\) 17.3644 30.0760i 0.756404 1.31013i
\(528\) −5.84725 10.1277i −0.254469 0.440753i
\(529\) −17.6364 30.5471i −0.766798 1.32813i
\(530\) 0 0
\(531\) −1.63010 −0.0707404
\(532\) 7.62441 + 3.54264i 0.330560 + 0.153593i
\(533\) −0.319190 −0.0138257
\(534\) 1.86770 3.23496i 0.0808235 0.139990i
\(535\) 0 0
\(536\) −1.70875 2.95963i −0.0738066 0.127837i
\(537\) −5.89031 + 10.2023i −0.254186 + 0.440262i
\(538\) −4.61130 −0.198807
\(539\) −7.91354 + 21.9285i −0.340860 + 0.944529i
\(540\) 0 0
\(541\) 16.4854 28.5535i 0.708762 1.22761i −0.256554 0.966530i \(-0.582587\pi\)
0.965317 0.261082i \(-0.0840794\pi\)
\(542\) 3.47231 + 6.01421i 0.149148 + 0.258332i
\(543\) 4.54484 + 7.87189i 0.195038 + 0.337815i
\(544\) 9.04306 15.6630i 0.387718 0.671547i
\(545\) 0 0
\(546\) −3.13521 1.45676i −0.134175 0.0623437i
\(547\) −24.6221 −1.05277 −0.526383 0.850248i \(-0.676452\pi\)
−0.526383 + 0.850248i \(0.676452\pi\)
\(548\) 14.2563 24.6926i 0.608998 1.05482i
\(549\) 3.65901 + 6.33759i 0.156163 + 0.270482i
\(550\) 0 0
\(551\) −0.0983213 + 0.170297i −0.00418863 + 0.00725491i
\(552\) 8.59260 0.365725
\(553\) 25.8532 18.1553i 1.09939 0.772041i
\(554\) −6.67127 −0.283435
\(555\) 0 0
\(556\) −9.12399 15.8032i −0.386943 0.670206i
\(557\) −11.9971 20.7796i −0.508334 0.880460i −0.999953 0.00964963i \(-0.996928\pi\)
0.491620 0.870810i \(-0.336405\pi\)
\(558\) −0.899391 + 1.55779i −0.0380742 + 0.0659465i
\(559\) −13.3234 −0.563521
\(560\) 0 0
\(561\) 18.4755 0.780036
\(562\) 1.78826 3.09736i 0.0754333 0.130654i
\(563\) −0.113248 0.196151i −0.00477284 0.00826680i 0.863629 0.504128i \(-0.168186\pi\)
−0.868402 + 0.495861i \(0.834853\pi\)
\(564\) 6.12221 + 10.6040i 0.257792 + 0.446508i
\(565\) 0 0
\(566\) 2.49056 0.104686
\(567\) −0.234193 2.63537i −0.00983520 0.110675i
\(568\) −4.24413 −0.178080
\(569\) 6.40275 11.0899i 0.268417 0.464912i −0.700036 0.714108i \(-0.746833\pi\)
0.968453 + 0.249195i \(0.0801660\pi\)
\(570\) 0 0
\(571\) 0.780149 + 1.35126i 0.0326482 + 0.0565484i 0.881888 0.471459i \(-0.156273\pi\)
−0.849240 + 0.528008i \(0.822939\pi\)
\(572\) 14.5199 25.1492i 0.607107 1.05154i
\(573\) −20.4957 −0.856219
\(574\) 0.0436677 0.0306655i 0.00182265 0.00127995i
\(575\) 0 0
\(576\) 3.04306 5.27073i 0.126794 0.219614i
\(577\) 21.8249 + 37.8018i 0.908581 + 1.57371i 0.816037 + 0.578000i \(0.196167\pi\)
0.0925443 + 0.995709i \(0.470500\pi\)
\(578\) 1.97905 + 3.42782i 0.0823178 + 0.142579i
\(579\) 4.27148 7.39842i 0.177517 0.307468i
\(580\) 0 0
\(581\) 2.93712 + 1.36472i 0.121852 + 0.0566180i
\(582\) −0.874380 −0.0362442
\(583\) 1.23191 2.13372i 0.0510203 0.0883697i
\(584\) −1.32550 2.29583i −0.0548494 0.0950020i
\(585\) 0 0
\(586\) −3.87994 + 6.72025i −0.160279 + 0.277611i
\(587\) −13.6961 −0.565297 −0.282648 0.959224i \(-0.591213\pi\)
−0.282648 + 0.959224i \(0.591213\pi\)
\(588\) −13.2117 + 2.36683i −0.544843 + 0.0976064i
\(589\) 10.3746 0.427479
\(590\) 0 0
\(591\) 6.90429 + 11.9586i 0.284004 + 0.491910i
\(592\) −13.6169 23.5852i −0.559651 0.969344i
\(593\) 4.57745 7.92838i 0.187973 0.325579i −0.756601 0.653877i \(-0.773141\pi\)
0.944574 + 0.328297i \(0.106475\pi\)
\(594\) −0.956942 −0.0392638
\(595\) 0 0
\(596\) −21.8014 −0.893018
\(597\) 1.89549 3.28309i 0.0775773 0.134368i
\(598\) 4.98734 + 8.63833i 0.203948 + 0.353247i
\(599\) −20.1368 34.8780i −0.822767 1.42507i −0.903614 0.428348i \(-0.859096\pi\)
0.0808467 0.996727i \(-0.474238\pi\)
\(600\) 0 0
\(601\) −8.82450 −0.359959 −0.179980 0.983670i \(-0.557603\pi\)
−0.179980 + 0.983670i \(0.557603\pi\)
\(602\) 1.82275 1.28002i 0.0742897 0.0521696i
\(603\) 3.03610 0.123639
\(604\) 8.57126 14.8459i 0.348760 0.604070i
\(605\) 0 0
\(606\) −2.30438 3.99131i −0.0936092 0.162136i
\(607\) −14.0532 + 24.3409i −0.570402 + 0.987966i 0.426122 + 0.904666i \(0.359879\pi\)
−0.996524 + 0.0833003i \(0.973454\pi\)
\(608\) 5.40292 0.219117
\(609\) −0.0277887 0.312705i −0.00112606 0.0126714i
\(610\) 0 0
\(611\) −14.5199 + 25.1492i −0.587412 + 1.01743i
\(612\) 5.31853 + 9.21197i 0.214989 + 0.372372i
\(613\) 1.05670 + 1.83025i 0.0426796 + 0.0739232i 0.886576 0.462583i \(-0.153077\pi\)
−0.843896 + 0.536506i \(0.819744\pi\)
\(614\) 0.322795 0.559097i 0.0130269 0.0225633i
\(615\) 0 0
\(616\) 0.877935 + 9.87935i 0.0353730 + 0.398050i
\(617\) 18.0390 0.726221 0.363111 0.931746i \(-0.381715\pi\)
0.363111 + 0.931746i \(0.381715\pi\)
\(618\) −0.760278 + 1.31684i −0.0305829 + 0.0529711i
\(619\) 7.31895 + 12.6768i 0.294173 + 0.509523i 0.974792 0.223114i \(-0.0716223\pi\)
−0.680619 + 0.732638i \(0.738289\pi\)
\(620\) 0 0
\(621\) −3.81683 + 6.61094i −0.153164 + 0.265288i
\(622\) −8.21744 −0.329489
\(623\) 28.1479 19.7667i 1.12772 0.791937i
\(624\) 15.9684 0.639249
\(625\) 0 0
\(626\) −1.91488 3.31668i −0.0765341 0.132561i
\(627\) 2.75962 + 4.77980i 0.110209 + 0.190887i
\(628\) −3.20818 + 5.55673i −0.128020 + 0.221738i
\(629\) 43.0252 1.71553
\(630\) 0 0
\(631\) 12.1251 0.482692 0.241346 0.970439i \(-0.422411\pi\)
0.241346 + 0.970439i \(0.422411\pi\)
\(632\) 6.72014 11.6396i 0.267313 0.462999i
\(633\) −0.0572082 0.0990874i −0.00227382 0.00393837i
\(634\) 4.19403 + 7.26428i 0.166566 + 0.288501i
\(635\) 0 0
\(636\) 1.41851 0.0562477
\(637\) −20.5283 24.3293i −0.813360 0.963963i
\(638\) −0.113548 −0.00449540
\(639\) 1.88524 3.26533i 0.0745790 0.129175i
\(640\) 0 0
\(641\) 6.52024 + 11.2934i 0.257534 + 0.446062i 0.965581 0.260104i \(-0.0837567\pi\)
−0.708047 + 0.706166i \(0.750423\pi\)
\(642\) −0.741573 + 1.28444i −0.0292675 + 0.0506929i
\(643\) 27.0185 1.06550 0.532752 0.846271i \(-0.321158\pi\)
0.532752 + 0.846271i \(0.321158\pi\)
\(644\) 35.1200 + 16.3184i 1.38392 + 0.643033i
\(645\) 0 0
\(646\) −1.32082 + 2.28773i −0.0519670 + 0.0900095i
\(647\) 17.4895 + 30.2927i 0.687582 + 1.19093i 0.972618 + 0.232411i \(0.0746613\pi\)
−0.285035 + 0.958517i \(0.592005\pi\)
\(648\) −0.562810 0.974816i −0.0221093 0.0382944i
\(649\) −2.71444 + 4.70155i −0.106551 + 0.184552i
\(650\) 0 0
\(651\) −13.5546 + 9.51864i −0.531246 + 0.373065i
\(652\) −30.2109 −1.18315
\(653\) −16.1755 + 28.0168i −0.632997 + 1.09638i 0.353939 + 0.935269i \(0.384842\pi\)
−0.986936 + 0.161114i \(0.948491\pi\)
\(654\) −0.465609 0.806458i −0.0182067 0.0315350i
\(655\) 0 0
\(656\) −0.123234 + 0.213447i −0.00481146 + 0.00833370i
\(657\) 2.35514 0.0918827
\(658\) −0.429716 4.83557i −0.0167521 0.188510i
\(659\) 8.54282 0.332781 0.166390 0.986060i \(-0.446789\pi\)
0.166390 + 0.986060i \(0.446789\pi\)
\(660\) 0 0
\(661\) 15.1715 + 26.2779i 0.590104 + 1.02209i 0.994218 + 0.107382i \(0.0342467\pi\)
−0.404114 + 0.914709i \(0.632420\pi\)
\(662\) −3.57611 6.19400i −0.138989 0.240737i
\(663\) −12.6138 + 21.8478i −0.489881 + 0.848498i
\(664\) 1.37788 0.0534722
\(665\) 0 0
\(666\) −2.22850 −0.0863525
\(667\) −0.452894 + 0.784435i −0.0175361 + 0.0303734i
\(668\) −21.6614 37.5187i −0.838107 1.45164i
\(669\) 3.93337 + 6.81279i 0.152073 + 0.263398i
\(670\) 0 0
\(671\) 24.3719 0.940867
\(672\) −7.05899 + 4.95714i −0.272306 + 0.191226i
\(673\) −40.5075 −1.56145 −0.780725 0.624875i \(-0.785150\pi\)
−0.780725 + 0.624875i \(0.785150\pi\)
\(674\) 0.679059 1.17617i 0.0261564 0.0453042i
\(675\) 0 0
\(676\) 7.36308 + 12.7532i 0.283195 + 0.490509i
\(677\) −11.7105 + 20.2833i −0.450073 + 0.779549i −0.998390 0.0567215i \(-0.981935\pi\)
0.548317 + 0.836270i \(0.315269\pi\)
\(678\) 3.63790 0.139713
\(679\) −7.30149 3.39260i −0.280205 0.130196i
\(680\) 0 0
\(681\) 4.48933 7.77575i 0.172032 0.297967i
\(682\) 2.99533 + 5.18806i 0.114697 + 0.198661i
\(683\) −25.5124 44.1887i −0.976204 1.69083i −0.675904 0.736989i \(-0.736247\pi\)
−0.300299 0.953845i \(-0.597087\pi\)
\(684\) −1.58882 + 2.75192i −0.0607501 + 0.105222i
\(685\) 0 0
\(686\) 5.14581 + 1.35623i 0.196468 + 0.0517812i
\(687\) 5.08612 0.194047
\(688\) −5.14393 + 8.90956i −0.196111 + 0.339674i
\(689\) 1.68212 + 2.91353i 0.0640838 + 0.110996i
\(690\) 0 0
\(691\) −12.3057 + 21.3142i −0.468133 + 0.810829i −0.999337 0.0364144i \(-0.988406\pi\)
0.531204 + 0.847244i \(0.321740\pi\)
\(692\) −16.3485 −0.621476
\(693\) −7.99092 3.71294i −0.303550 0.141043i
\(694\) 4.06819 0.154426
\(695\) 0 0
\(696\) −0.0667814 0.115669i −0.00253134 0.00438441i
\(697\) −0.194690 0.337213i −0.00737441 0.0127728i
\(698\) 0.725422 1.25647i 0.0274576 0.0475580i
\(699\) −21.8183 −0.825243
\(700\) 0 0
\(701\) 25.7244 0.971595 0.485798 0.874071i \(-0.338529\pi\)
0.485798 + 0.874071i \(0.338529\pi\)
\(702\) 0.653336 1.13161i 0.0246586 0.0427099i
\(703\) 6.42652 + 11.1311i 0.242381 + 0.419816i
\(704\) −10.1346 17.5536i −0.381962 0.661577i
\(705\) 0 0
\(706\) 4.62567 0.174089
\(707\) −3.75638 42.2703i −0.141273 1.58974i
\(708\) −3.12562 −0.117468
\(709\) −5.85482 + 10.1408i −0.219882 + 0.380848i −0.954772 0.297339i \(-0.903901\pi\)
0.734889 + 0.678187i \(0.237234\pi\)
\(710\) 0 0
\(711\) 5.97016 + 10.3406i 0.223899 + 0.387804i
\(712\) 7.31661 12.6727i 0.274202 0.474931i
\(713\) 47.7883 1.78968
\(714\) −0.373306 4.20079i −0.0139706 0.157211i
\(715\) 0 0
\(716\) −11.2943 + 19.5623i −0.422088 + 0.731077i
\(717\) 3.72453 + 6.45107i 0.139095 + 0.240920i
\(718\) 0.0440317 + 0.0762651i 0.00164325 + 0.00284619i
\(719\) 6.16037 10.6701i 0.229743 0.397927i −0.727989 0.685589i \(-0.759545\pi\)
0.957732 + 0.287662i \(0.0928781\pi\)
\(720\) 0 0
\(721\) −11.4580 + 8.04635i −0.426719 + 0.299662i
\(722\) 4.67023 0.173808
\(723\) −12.0879 + 20.9368i −0.449554 + 0.778650i
\(724\) 8.71444 + 15.0939i 0.323870 + 0.560959i
\(725\) 0 0
\(726\) −0.0131493 + 0.0227753i −0.000488017 + 0.000845271i
\(727\) −17.6540 −0.654751 −0.327376 0.944894i \(-0.606164\pi\)
−0.327376 + 0.944894i \(0.606164\pi\)
\(728\) −12.2820 5.70678i −0.455202 0.211507i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −8.12662 14.0757i −0.300574 0.520609i
\(732\) 7.01593 + 12.1519i 0.259316 + 0.449149i
\(733\) −5.01795 + 8.69135i −0.185342 + 0.321022i −0.943692 0.330826i \(-0.892673\pi\)
0.758349 + 0.651848i \(0.226006\pi\)
\(734\) −6.79541 −0.250823
\(735\) 0 0
\(736\) 24.8873 0.917357
\(737\) 5.05570 8.75672i 0.186229 0.322558i
\(738\) 0.0100840 + 0.0174660i 0.000371197 + 0.000642932i
\(739\) 15.5360 + 26.9092i 0.571502 + 0.989870i 0.996412 + 0.0846345i \(0.0269723\pi\)
−0.424910 + 0.905235i \(0.639694\pi\)
\(740\) 0 0
\(741\) −7.53634 −0.276854
\(742\) −0.510038 0.236987i −0.0187241 0.00870005i
\(743\) −4.04189 −0.148283 −0.0741413 0.997248i \(-0.523622\pi\)
−0.0741413 + 0.997248i \(0.523622\pi\)
\(744\) −3.52331 + 6.10255i −0.129171 + 0.223730i
\(745\) 0 0
\(746\) −2.70638 4.68759i −0.0990876 0.171625i
\(747\) −0.612055 + 1.06011i −0.0223939 + 0.0387874i
\(748\) 35.4256 1.29529
\(749\) −11.1761 + 7.84839i −0.408367 + 0.286774i
\(750\) 0 0
\(751\) −7.34725 + 12.7258i −0.268105 + 0.464371i −0.968372 0.249509i \(-0.919731\pi\)
0.700268 + 0.713881i \(0.253064\pi\)
\(752\) 11.2117 + 19.4193i 0.408850 + 0.708149i
\(753\) 3.00100 + 5.19789i 0.109363 + 0.189421i
\(754\) 0.0775229 0.134274i 0.00282322 0.00488996i
\(755\) 0 0
\(756\) −0.449051 5.05315i −0.0163318 0.183781i
\(757\) −29.6087 −1.07615 −0.538073 0.842898i \(-0.680847\pi\)
−0.538073 + 0.842898i \(0.680847\pi\)
\(758\) 2.04775 3.54681i 0.0743778 0.128826i
\(759\) 12.7115 + 22.0170i 0.461400 + 0.799168i
\(760\) 0 0
\(761\) 7.12611 12.3428i 0.258321 0.447426i −0.707471 0.706742i \(-0.750164\pi\)
0.965792 + 0.259317i \(0.0834974\pi\)
\(762\) 4.75470 0.172245
\(763\) −0.758990 8.54088i −0.0274773 0.309200i
\(764\) −39.2992 −1.42179
\(765\) 0 0
\(766\) 3.59980 + 6.23504i 0.130066 + 0.225281i
\(767\) −3.70648 6.41981i −0.133833 0.231806i
\(768\) 4.89810 8.48376i 0.176745 0.306131i
\(769\) −20.6367 −0.744178 −0.372089 0.928197i \(-0.621358\pi\)
−0.372089 + 0.928197i \(0.621358\pi\)
\(770\) 0 0
\(771\) −7.33395 −0.264126
\(772\) 8.19030 14.1860i 0.294775 0.510566i
\(773\) 21.2800 + 36.8580i 0.765387 + 1.32569i 0.940042 + 0.341059i \(0.110786\pi\)
−0.174655 + 0.984630i \(0.555881\pi\)
\(774\) 0.420920 + 0.729054i 0.0151296 + 0.0262053i
\(775\) 0 0
\(776\) −3.42533 −0.122962
\(777\) −18.6090 8.64659i −0.667594 0.310195i
\(778\) 3.87093 0.138780
\(779\) 0.0581603 0.100737i 0.00208381 0.00360926i
\(780\) 0 0
\(781\) −6.27860 10.8748i −0.224666 0.389133i
\(782\) −6.08405 + 10.5379i −0.217565 + 0.376834i
\(783\) 0.118657 0.00424046
\(784\) −24.1949 + 4.33442i −0.864105 + 0.154801i
\(785\) 0 0
\(786\) 0.761132 1.31832i 0.0271487 0.0470229i
\(787\) 12.5996 + 21.8231i 0.449126 + 0.777909i 0.998329 0.0577798i \(-0.0184021\pi\)
−0.549203 + 0.835689i \(0.685069\pi\)
\(788\) 13.2385 + 22.9298i 0.471604 + 0.816842i
\(789\) 4.74386 8.21661i 0.168886 0.292519i
\(790\) 0 0
\(791\) 30.3782 + 14.1151i 1.08012 + 0.501874i
\(792\) −3.74876 −0.133206
\(793\) −16.6395 + 28.8205i −0.590886 + 1.02344i
\(794\) 2.65044 + 4.59069i 0.0940605 + 0.162918i
\(795\) 0 0
\(796\) 3.63449 6.29512i 0.128821 0.223125i
\(797\) 51.7211 1.83205 0.916027 0.401116i \(-0.131377\pi\)
0.916027 + 0.401116i \(0.131377\pi\)
\(798\) 1.03103 0.724036i 0.0364980 0.0256306i
\(799\) −35.4256 −1.25327
\(800\) 0 0
\(801\) 6.50007 + 11.2585i 0.229669 + 0.397798i
\(802\) 3.65182 + 6.32515i 0.128950 + 0.223349i
\(803\) 3.92177 6.79271i 0.138396 0.239709i
\(804\) 5.82152 0.205309
\(805\) 0 0
\(806\) −8.18003 −0.288129
\(807\) 8.02423 13.8984i 0.282466 0.489246i
\(808\) −9.02728 15.6357i −0.317579 0.550062i
\(809\) 25.8890 + 44.8410i 0.910207 + 1.57653i 0.813770 + 0.581187i \(0.197411\pi\)
0.0964371 + 0.995339i \(0.469255\pi\)
\(810\) 0 0
\(811\) 12.0263 0.422299 0.211149 0.977454i \(-0.432279\pi\)
0.211149 + 0.977454i \(0.432279\pi\)
\(812\) −0.0532831 0.599592i −0.00186987 0.0210416i
\(813\) −24.1690 −0.847643
\(814\) −3.71089 + 6.42744i −0.130067 + 0.225282i
\(815\) 0 0
\(816\) 9.73994 + 16.8701i 0.340966 + 0.590571i
\(817\) 2.42769 4.20488i 0.0849341 0.147110i
\(818\) 5.38212 0.188182
\(819\) 9.84632 6.91454i 0.344058 0.241613i
\(820\) 0 0
\(821\) −4.03967 + 6.99692i −0.140985 + 0.244194i −0.927868 0.372909i \(-0.878360\pi\)
0.786882 + 0.617103i \(0.211694\pi\)
\(822\) −2.13636 3.70029i −0.0745142 0.129062i
\(823\) 2.55762 + 4.42994i 0.0891532 + 0.154418i 0.907153 0.420800i \(-0.138251\pi\)
−0.818000 + 0.575218i \(0.804917\pi\)
\(824\) −2.97834 + 5.15864i −0.103755 + 0.179710i
\(825\) 0 0
\(826\) 1.12384 + 0.522188i 0.0391035 + 0.0181693i
\(827\) 0.705254 0.0245241 0.0122620 0.999925i \(-0.496097\pi\)
0.0122620 + 0.999925i \(0.496097\pi\)
\(828\) −7.31853 + 12.6761i −0.254337 + 0.440524i
\(829\) −12.4790 21.6143i −0.433415 0.750696i 0.563750 0.825945i \(-0.309358\pi\)
−0.997165 + 0.0752491i \(0.976025\pi\)
\(830\) 0 0
\(831\) 11.6088 20.1071i 0.402706 0.697508i
\(832\) 27.6769 0.959523
\(833\) 13.1818 36.5270i 0.456723 1.26559i
\(834\) −2.73453 −0.0946891
\(835\) 0 0
\(836\) 5.29140 + 9.16498i 0.183007 + 0.316977i
\(837\) −3.13010 5.42150i −0.108192 0.187394i
\(838\) 0.294152 0.509487i 0.0101613 0.0175999i
\(839\) −11.6389 −0.401819 −0.200909 0.979610i \(-0.564390\pi\)
−0.200909 + 0.979610i \(0.564390\pi\)
\(840\) 0 0
\(841\) −28.9859 −0.999514
\(842\) −2.30604 + 3.99418i −0.0794714 + 0.137649i
\(843\) 6.22360 + 10.7796i 0.214352 + 0.371269i
\(844\) −0.109693 0.189994i −0.00377579 0.00653986i
\(845\) 0 0
\(846\) 1.83488 0.0630843
\(847\) −0.198172 + 0.139165i −0.00680926 + 0.00478177i
\(848\) 2.59775 0.0892071
\(849\) −4.33388 + 7.50649i −0.148738 + 0.257622i
\(850\) 0 0
\(851\) 29.6023 + 51.2726i 1.01475 + 1.75760i
\(852\) 3.61483 6.26107i 0.123842 0.214501i
\(853\) −32.5996 −1.11619 −0.558094 0.829778i \(-0.688467\pi\)
−0.558094 + 0.829778i \(0.688467\pi\)
\(854\) −0.492445 5.54146i −0.0168511 0.189625i
\(855\) 0 0
\(856\) −2.90507 + 5.03172i −0.0992931 + 0.171981i
\(857\) 15.8456 + 27.4455i 0.541277 + 0.937519i 0.998831 + 0.0483371i \(0.0153922\pi\)
−0.457554 + 0.889182i \(0.651274\pi\)
\(858\) −2.17587 3.76871i −0.0742828 0.128662i
\(859\) 21.8456 37.8377i 0.745363 1.29101i −0.204662 0.978833i \(-0.565610\pi\)
0.950025 0.312174i \(-0.101057\pi\)
\(860\) 0 0
\(861\) 0.0164380 + 0.184975i 0.000560204 + 0.00630394i
\(862\) −10.5201 −0.358317
\(863\) 19.3992 33.6005i 0.660358 1.14377i −0.320164 0.947362i \(-0.603738\pi\)
0.980522 0.196411i \(-0.0629287\pi\)
\(864\) −1.63010 2.82342i −0.0554572 0.0960547i
\(865\) 0 0
\(866\) −2.58670 + 4.48030i −0.0878997 + 0.152247i
\(867\) −13.7752 −0.467830
\(868\) −25.9901 + 18.2514i −0.882160 + 0.619493i
\(869\) 39.7660 1.34897
\(870\) 0 0
\(871\) 6.90338 + 11.9570i 0.233912 + 0.405148i
\(872\) −1.82399 3.15925i −0.0617682 0.106986i
\(873\) 1.52153 2.63537i 0.0514960 0.0891936i
\(874\) −3.63501 −0.122956
\(875\) 0 0
\(876\) 4.51583 0.152576
\(877\) −2.15036 + 3.72454i −0.0726127 + 0.125769i −0.900046 0.435796i \(-0.856467\pi\)
0.827433 + 0.561565i \(0.189800\pi\)
\(878\) −2.78351 4.82118i −0.0939390 0.162707i
\(879\) −13.5031 23.3881i −0.455450 0.788862i
\(880\) 0 0
\(881\) −1.29308 −0.0435650 −0.0217825 0.999763i \(-0.506934\pi\)
−0.0217825 + 0.999763i \(0.506934\pi\)
\(882\) −0.682755 + 1.89192i −0.0229896 + 0.0637044i
\(883\) 1.49533 0.0503218 0.0251609 0.999683i \(-0.491990\pi\)
0.0251609 + 0.999683i \(0.491990\pi\)
\(884\) −24.1862 + 41.8918i −0.813471 + 1.40897i
\(885\) 0 0
\(886\) −2.36225 4.09153i −0.0793613 0.137458i
\(887\) −5.04584 + 8.73964i −0.169423 + 0.293449i −0.938217 0.346047i \(-0.887524\pi\)
0.768794 + 0.639496i \(0.220857\pi\)
\(888\) −8.73000 −0.292960
\(889\) 39.7040 + 18.4483i 1.33163 + 0.618736i
\(890\) 0 0
\(891\) 1.66520 2.88421i 0.0557862 0.0966245i
\(892\) 7.54198 + 13.0631i 0.252524 + 0.437385i
\(893\) −5.29140 9.16498i −0.177070 0.306694i
\(894\) −1.63351 + 2.82932i −0.0546328 + 0.0946267i
\(895\) 0 0
\(896\) −17.9044 + 12.5733i −0.598143 + 0.420044i
\(897\) −34.7144 −1.15908
\(898\) −4.70146 + 8.14317i −0.156890 + 0.271741i
\(899\) −0.371409 0.643299i −0.0123872 0.0214552i
\(900\) 0 0
\(901\) −2.05202 + 3.55421i −0.0683628 + 0.118408i
\(902\) 0.0671674 0.00223643
\(903\) 0.686142 + 7.72112i 0.0228334 + 0.256943i
\(904\) 14.2512 0.473989
\(905\) 0 0
\(906\) −1.28444 2.22471i −0.0426726 0.0739111i
\(907\) −2.13349 3.69531i −0.0708414 0.122701i 0.828429 0.560094i \(-0.189235\pi\)
−0.899270 + 0.437393i \(0.855902\pi\)
\(908\) 8.60802 14.9095i 0.285667 0.494790i
\(909\) 16.0397 0.532002
\(910\) 0 0
\(911\) −28.5451 −0.945742 −0.472871 0.881132i \(-0.656782\pi\)
−0.472871 + 0.881132i \(0.656782\pi\)
\(912\) −2.90964 + 5.03965i −0.0963479 + 0.166879i
\(913\) 2.03838 + 3.53058i 0.0674606 + 0.116845i
\(914\) −5.37754 9.31417i −0.177873 0.308085i
\(915\) 0 0
\(916\) 9.75231 0.322226
\(917\) 11.4709 8.05539i 0.378802 0.266012i
\(918\) 1.59401 0.0526101
\(919\) 23.2822 40.3259i 0.768008 1.33023i −0.170634 0.985335i \(-0.554581\pi\)
0.938642 0.344894i \(-0.112085\pi\)
\(920\) 0 0
\(921\) 1.12341 + 1.94580i 0.0370175 + 0.0641161i
\(922\) 4.07448 7.05720i 0.134186 0.232417i
\(923\) 17.1464 0.564381
\(924\) −15.3221 7.11934i −0.504060 0.234209i
\(925\) 0 0
\(926\) −1.03561 + 1.79372i −0.0340321 + 0.0589453i
\(927\) −2.64596 4.58293i −0.0869046 0.150523i
\(928\) −0.193423 0.335019i −0.00634943 0.0109975i
\(929\) −3.69774 + 6.40467i −0.121319 + 0.210130i −0.920288 0.391242i \(-0.872046\pi\)
0.798969 + 0.601372i \(0.205379\pi\)
\(930\) 0 0
\(931\) 11.4188 2.04564i 0.374238 0.0670432i
\(932\) −41.8352 −1.37036
\(933\) 14.2994 24.7672i 0.468140 0.810843i
\(934\) 1.73537 + 3.00574i 0.0567829 + 0.0983509i
\(935\) 0 0
\(936\) 2.55940 4.43301i 0.0836567 0.144898i
\(937\) 44.1988 1.44391 0.721956 0.691939i \(-0.243243\pi\)
0.721956 + 0.691939i \(0.243243\pi\)
\(938\) −2.09318 0.972585i −0.0683447 0.0317560i
\(939\) 13.3285 0.434960
\(940\) 0 0
\(941\) −18.0180 31.2080i −0.587369 1.01735i −0.994576 0.104017i \(-0.966830\pi\)
0.407206 0.913336i \(-0.366503\pi\)
\(942\) 0.480759 + 0.832699i 0.0156640 + 0.0271308i
\(943\) 0.267902 0.464020i 0.00872408 0.0151106i
\(944\) −5.72401 −0.186301
\(945\) 0 0
\(946\) 2.80366 0.0911548
\(947\) 17.1170 29.6476i 0.556229 0.963417i −0.441577 0.897223i \(-0.645581\pi\)
0.997807 0.0661943i \(-0.0210857\pi\)
\(948\) 11.4474 + 19.8275i 0.371795 + 0.643968i
\(949\) 5.35504 + 9.27521i 0.173832 + 0.301086i
\(950\) 0 0
\(951\) −29.1925 −0.946633
\(952\) −1.46240 16.4563i −0.0473967 0.533353i
\(953\) 30.9689 1.00318 0.501591 0.865105i \(-0.332748\pi\)
0.501591 + 0.865105i \(0.332748\pi\)
\(954\) 0.106285 0.184091i 0.00344110 0.00596016i
\(955\) 0 0
\(956\) 7.14155 + 12.3695i 0.230974 + 0.400059i
\(957\) 0.197587 0.342231i 0.00638709 0.0110628i
\(958\) −5.78743 −0.186983
\(959\) −3.48249 39.1883i −0.112455 1.26545i
\(960\) 0 0
\(961\) −4.09508 + 7.09289i −0.132099 + 0.228803i
\(962\) −5.06709 8.77646i −0.163370 0.282964i
\(963\) −2.58086 4.47018i −0.0831670 0.144049i
\(964\) −23.1778 + 40.1451i −0.746506 + 1.29299i
\(965\) 0 0
\(966\) 4.74919 3.33510i 0.152803 0.107305i
\(967\) 21.0270 0.676184 0.338092 0.941113i \(-0.390218\pi\)
0.338092 + 0.941113i \(0.390218\pi\)
\(968\) −0.0515117 + 0.0892209i −0.00165565 + 0.00286767i
\(969\) −4.59678 7.96187i −0.147670 0.255772i
\(970\) 0 0
\(971\) −22.3468 + 38.7058i −0.717144 + 1.24213i 0.244983 + 0.969527i \(0.421218\pi\)
−0.962127 + 0.272602i \(0.912116\pi\)
\(972\) 1.91744 0.0615019
\(973\) −22.8346 10.6100i −0.732045 0.340141i
\(974\) 11.4761 0.367718
\(975\) 0 0
\(976\) 12.8484 + 22.2541i 0.411268 + 0.712337i
\(977\) 7.21858 + 12.5029i 0.230943 + 0.400005i 0.958086 0.286481i \(-0.0924856\pi\)
−0.727143 + 0.686486i \(0.759152\pi\)
\(978\) −2.26361 + 3.92069i −0.0723824 + 0.125370i
\(979\) 43.2956 1.38373
\(980\) 0 0
\(981\) 3.24087 0.103473
\(982\) −4.53974 + 7.86307i −0.144869 + 0.250921i
\(983\) 8.39401 + 14.5389i 0.267727 + 0.463717i 0.968275 0.249889i \(-0.0803940\pi\)
−0.700547 + 0.713606i \(0.747061\pi\)
\(984\) 0.0395034 + 0.0684220i 0.00125932 + 0.00218121i
\(985\) 0 0
\(986\) 0.189140 0.00602345
\(987\) 15.3221 + 7.11934i 0.487707 + 0.226611i
\(988\) −14.4505 −0.459730
\(989\) 11.1826 19.3688i 0.355585 0.615892i
\(990\) 0 0
\(991\) −20.0539 34.7344i −0.637033 1.10337i −0.986081 0.166268i \(-0.946828\pi\)
0.349048 0.937105i \(-0.386505\pi\)
\(992\) −10.2048 + 17.6752i −0.324002 + 0.561188i
\(993\) 24.8915 0.789907
\(994\) −2.34576 + 1.64730i −0.0744031 + 0.0522492i
\(995\) 0 0
\(996\) −1.17358 + 2.03270i −0.0371862 + 0.0644084i
\(997\) −25.6602 44.4447i −0.812666 1.40758i −0.910992 0.412424i \(-0.864682\pi\)
0.0983259 0.995154i \(-0.468651\pi\)
\(998\) 5.71595 + 9.90032i 0.180935 + 0.313389i
\(999\) 3.87786 6.71665i 0.122690 0.212505i
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 525.2.i.h.226.3 8
5.2 odd 4 105.2.q.a.79.5 yes 16
5.3 odd 4 105.2.q.a.79.4 yes 16
5.4 even 2 525.2.i.k.226.2 8
7.2 even 3 3675.2.a.bz.1.2 4
7.4 even 3 inner 525.2.i.h.151.3 8
7.5 odd 6 3675.2.a.cb.1.2 4
15.2 even 4 315.2.bf.b.289.4 16
15.8 even 4 315.2.bf.b.289.5 16
20.3 even 4 1680.2.di.d.289.7 16
20.7 even 4 1680.2.di.d.289.3 16
35.2 odd 12 735.2.d.d.589.4 8
35.3 even 12 735.2.q.g.214.5 16
35.4 even 6 525.2.i.k.151.2 8
35.9 even 6 3675.2.a.bp.1.3 4
35.12 even 12 735.2.d.e.589.4 8
35.13 even 4 735.2.q.g.79.4 16
35.17 even 12 735.2.q.g.214.4 16
35.18 odd 12 105.2.q.a.4.5 yes 16
35.19 odd 6 3675.2.a.bn.1.3 4
35.23 odd 12 735.2.d.d.589.5 8
35.27 even 4 735.2.q.g.79.5 16
35.32 odd 12 105.2.q.a.4.4 16
35.33 even 12 735.2.d.e.589.5 8
105.2 even 12 2205.2.d.s.1324.5 8
105.23 even 12 2205.2.d.s.1324.4 8
105.32 even 12 315.2.bf.b.109.5 16
105.47 odd 12 2205.2.d.o.1324.5 8
105.53 even 12 315.2.bf.b.109.4 16
105.68 odd 12 2205.2.d.o.1324.4 8
140.67 even 12 1680.2.di.d.529.7 16
140.123 even 12 1680.2.di.d.529.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.q.a.4.4 16 35.32 odd 12
105.2.q.a.4.5 yes 16 35.18 odd 12
105.2.q.a.79.4 yes 16 5.3 odd 4
105.2.q.a.79.5 yes 16 5.2 odd 4
315.2.bf.b.109.4 16 105.53 even 12
315.2.bf.b.109.5 16 105.32 even 12
315.2.bf.b.289.4 16 15.2 even 4
315.2.bf.b.289.5 16 15.8 even 4
525.2.i.h.151.3 8 7.4 even 3 inner
525.2.i.h.226.3 8 1.1 even 1 trivial
525.2.i.k.151.2 8 35.4 even 6
525.2.i.k.226.2 8 5.4 even 2
735.2.d.d.589.4 8 35.2 odd 12
735.2.d.d.589.5 8 35.23 odd 12
735.2.d.e.589.4 8 35.12 even 12
735.2.d.e.589.5 8 35.33 even 12
735.2.q.g.79.4 16 35.13 even 4
735.2.q.g.79.5 16 35.27 even 4
735.2.q.g.214.4 16 35.17 even 12
735.2.q.g.214.5 16 35.3 even 12
1680.2.di.d.289.3 16 20.7 even 4
1680.2.di.d.289.7 16 20.3 even 4
1680.2.di.d.529.3 16 140.123 even 12
1680.2.di.d.529.7 16 140.67 even 12
2205.2.d.o.1324.4 8 105.68 odd 12
2205.2.d.o.1324.5 8 105.47 odd 12
2205.2.d.s.1324.4 8 105.23 even 12
2205.2.d.s.1324.5 8 105.2 even 12
3675.2.a.bn.1.3 4 35.19 odd 6
3675.2.a.bp.1.3 4 35.9 even 6
3675.2.a.bz.1.2 4 7.2 even 3
3675.2.a.cb.1.2 4 7.5 odd 6