Properties

Label 735.2.s.l.521.4
Level $735$
Weight $2$
Character 735.521
Analytic conductor $5.869$
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] = [735,2,Mod(521,735)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(735, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("735.521");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.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: \(5.86900454856\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.856615824.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 \) 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: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 521.4
Root \(-2.33086i\) of defining polynomial
Character \(\chi\) \(=\) 735.521
Dual form 735.2.s.l.656.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.01859 - 1.16543i) q^{2} +(1.67602 + 0.437000i) q^{3} +(1.71646 - 2.97300i) q^{4} +(0.500000 + 0.866025i) q^{5} +(3.89248 - 1.07116i) q^{6} -3.33995i q^{8} +(2.61806 + 1.46484i) q^{9} +O(q^{10})\) \(q+(2.01859 - 1.16543i) q^{2} +(1.67602 + 0.437000i) q^{3} +(1.71646 - 2.97300i) q^{4} +(0.500000 + 0.866025i) q^{5} +(3.89248 - 1.07116i) q^{6} -3.33995i q^{8} +(2.61806 + 1.46484i) q^{9} +(2.01859 + 1.16543i) q^{10} +(-2.42019 - 1.39730i) q^{11} +(4.17602 - 4.23270i) q^{12} -3.20486i q^{13} +(0.459555 + 1.66997i) q^{15} +(-0.459555 - 0.795973i) q^{16} +(-0.440969 + 0.763780i) q^{17} +(6.99195 - 0.0942709i) q^{18} +(-1.90160 + 1.09789i) q^{19} +3.43292 q^{20} -6.51381 q^{22} +(-6.53240 + 3.77148i) q^{23} +(1.45956 - 5.59780i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-3.73505 - 6.46929i) q^{26} +(3.74778 + 3.59918i) q^{27} -8.15270i q^{29} +(2.87389 + 2.83540i) q^{30} +(7.62645 + 4.40313i) q^{31} +(3.92965 + 2.26878i) q^{32} +(-3.44566 - 3.39951i) q^{33} +2.05568i q^{34} +(8.84876 - 5.26916i) q^{36} +(-0.203727 - 0.352865i) q^{37} +(-2.55903 + 4.43237i) q^{38} +(1.40052 - 5.37140i) q^{39} +(2.89248 - 1.66997i) q^{40} -8.55098 q^{41} -0.118062 q^{43} +(-8.30832 + 4.79681i) q^{44} +(0.0404447 + 2.99973i) q^{45} +(-8.79081 + 15.2261i) q^{46} +(-1.31486 - 2.27740i) q^{47} +(-0.422382 - 1.53489i) q^{48} +2.33086i q^{50} +(-1.07284 + 1.08741i) q^{51} +(-9.52805 - 5.50102i) q^{52} +(-6.46794 - 3.73427i) q^{53} +(11.7598 + 2.89748i) q^{54} -2.79459i q^{55} +(-3.66689 + 1.00908i) q^{57} +(-9.50142 - 16.4569i) q^{58} +(2.04991 - 3.55054i) q^{59} +(5.75363 + 1.50019i) q^{60} +(-10.7004 + 6.17786i) q^{61} +20.5262 q^{62} +12.4147 q^{64} +(2.77549 - 1.60243i) q^{65} +(-10.9173 - 2.84653i) q^{66} +(0.802125 - 1.38932i) q^{67} +(1.51381 + 2.62200i) q^{68} +(-12.5965 + 3.46641i) q^{69} +6.25869i q^{71} +(4.89248 - 8.74419i) q^{72} +(-0.192022 - 0.110864i) q^{73} +(-0.822480 - 0.474859i) q^{74} +(-1.21646 + 1.23297i) q^{75} +7.53794i q^{76} +(-3.43292 - 12.4749i) q^{78} +(1.56849 + 2.71671i) q^{79} +(0.459555 - 0.795973i) q^{80} +(4.70850 + 7.67007i) q^{81} +(-17.2609 + 9.96559i) q^{82} -0.666893 q^{83} -0.881938 q^{85} +(-0.238319 + 0.137594i) q^{86} +(3.56273 - 13.6641i) q^{87} +(-4.66689 + 8.08330i) q^{88} +(-0.437271 - 0.757376i) q^{89} +(3.57762 + 6.00807i) q^{90} +25.8944i q^{92} +(10.8579 + 10.7125i) q^{93} +(-5.30832 - 3.06476i) q^{94} +(-1.90160 - 1.09789i) q^{95} +(5.59470 + 5.51978i) q^{96} +6.37221i q^{97} +(-4.28939 - 7.20339i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 3 q^{2} - 2 q^{3} + 3 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 3 q^{2} - 2 q^{3} + 3 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{9} + 3 q^{10} + 18 q^{12} - q^{15} + q^{16} - 12 q^{17} + 26 q^{18} - 9 q^{19} + 6 q^{20} - 40 q^{22} - 27 q^{23} + 7 q^{24} - 4 q^{25} - 6 q^{26} + 4 q^{27} + 10 q^{30} + 21 q^{31} - 21 q^{32} - 4 q^{33} + 9 q^{36} + 7 q^{37} - 12 q^{38} + 15 q^{39} - 3 q^{40} - 30 q^{41} + 16 q^{43} + 5 q^{45} - 7 q^{46} - 6 q^{47} - 25 q^{48} + 12 q^{51} - 30 q^{52} - 24 q^{53} - 7 q^{54} + 6 q^{57} - 13 q^{58} - 12 q^{59} + 9 q^{60} - 15 q^{61} + 24 q^{62} + 38 q^{64} + 3 q^{65} + 16 q^{66} + 4 q^{67} - 13 q^{69} + 13 q^{72} - 15 q^{73} - 54 q^{74} + q^{75} - 6 q^{78} - 29 q^{79} - q^{80} + 28 q^{81} - 27 q^{82} + 30 q^{83} - 24 q^{85} - 9 q^{86} + 29 q^{87} - 2 q^{88} - 3 q^{89} + 7 q^{90} + 45 q^{93} + 24 q^{94} - 9 q^{95} + 42 q^{96} - 34 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.01859 1.16543i 1.42736 0.824085i 0.430445 0.902617i \(-0.358357\pi\)
0.996912 + 0.0785324i \(0.0250234\pi\)
\(3\) 1.67602 + 0.437000i 0.967649 + 0.252302i
\(4\) 1.71646 2.97300i 0.858231 1.48650i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 3.89248 1.07116i 1.58910 0.437299i
\(7\) 0 0
\(8\) 3.33995i 1.18085i
\(9\) 2.61806 + 1.46484i 0.872687 + 0.488279i
\(10\) 2.01859 + 1.16543i 0.638333 + 0.368542i
\(11\) −2.42019 1.39730i −0.729714 0.421301i 0.0886035 0.996067i \(-0.471760\pi\)
−0.818318 + 0.574766i \(0.805093\pi\)
\(12\) 4.17602 4.23270i 1.20551 1.22188i
\(13\) 3.20486i 0.888869i −0.895811 0.444434i \(-0.853405\pi\)
0.895811 0.444434i \(-0.146595\pi\)
\(14\) 0 0
\(15\) 0.459555 + 1.66997i 0.118657 + 0.431185i
\(16\) −0.459555 0.795973i −0.114889 0.198993i
\(17\) −0.440969 + 0.763780i −0.106951 + 0.185244i −0.914533 0.404510i \(-0.867442\pi\)
0.807583 + 0.589754i \(0.200775\pi\)
\(18\) 6.99195 0.0942709i 1.64802 0.0222199i
\(19\) −1.90160 + 1.09789i −0.436257 + 0.251873i −0.702009 0.712168i \(-0.747713\pi\)
0.265751 + 0.964042i \(0.414380\pi\)
\(20\) 3.43292 0.767625
\(21\) 0 0
\(22\) −6.51381 −1.38875
\(23\) −6.53240 + 3.77148i −1.36210 + 0.786408i −0.989903 0.141746i \(-0.954728\pi\)
−0.372196 + 0.928154i \(0.621395\pi\)
\(24\) 1.45956 5.59780i 0.297930 1.14265i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −3.73505 6.46929i −0.732503 1.26873i
\(27\) 3.74778 + 3.59918i 0.721261 + 0.692663i
\(28\) 0 0
\(29\) 8.15270i 1.51392i −0.653462 0.756959i \(-0.726684\pi\)
0.653462 0.756959i \(-0.273316\pi\)
\(30\) 2.87389 + 2.83540i 0.524698 + 0.517672i
\(31\) 7.62645 + 4.40313i 1.36975 + 0.790826i 0.990896 0.134630i \(-0.0429847\pi\)
0.378855 + 0.925456i \(0.376318\pi\)
\(32\) 3.92965 + 2.26878i 0.694671 + 0.401068i
\(33\) −3.44566 3.39951i −0.599812 0.591779i
\(34\) 2.05568i 0.352545i
\(35\) 0 0
\(36\) 8.84876 5.26916i 1.47479 0.878193i
\(37\) −0.203727 0.352865i −0.0334925 0.0580107i 0.848793 0.528725i \(-0.177330\pi\)
−0.882286 + 0.470714i \(0.843996\pi\)
\(38\) −2.55903 + 4.43237i −0.415130 + 0.719026i
\(39\) 1.40052 5.37140i 0.224263 0.860113i
\(40\) 2.89248 1.66997i 0.457341 0.264046i
\(41\) −8.55098 −1.33544 −0.667720 0.744413i \(-0.732730\pi\)
−0.667720 + 0.744413i \(0.732730\pi\)
\(42\) 0 0
\(43\) −0.118062 −0.0180044 −0.00900218 0.999959i \(-0.502866\pi\)
−0.00900218 + 0.999959i \(0.502866\pi\)
\(44\) −8.30832 + 4.79681i −1.25253 + 0.723146i
\(45\) 0.0404447 + 2.99973i 0.00602913 + 0.447173i
\(46\) −8.79081 + 15.2261i −1.29613 + 2.24497i
\(47\) −1.31486 2.27740i −0.191792 0.332194i 0.754052 0.656815i \(-0.228097\pi\)
−0.945844 + 0.324621i \(0.894763\pi\)
\(48\) −0.422382 1.53489i −0.0609656 0.221542i
\(49\) 0 0
\(50\) 2.33086i 0.329634i
\(51\) −1.07284 + 1.08741i −0.150228 + 0.152267i
\(52\) −9.52805 5.50102i −1.32130 0.762854i
\(53\) −6.46794 3.73427i −0.888440 0.512941i −0.0150081 0.999887i \(-0.504777\pi\)
−0.873432 + 0.486946i \(0.838111\pi\)
\(54\) 11.7598 + 2.89748i 1.60031 + 0.394297i
\(55\) 2.79459i 0.376823i
\(56\) 0 0
\(57\) −3.66689 + 1.00908i −0.485692 + 0.133656i
\(58\) −9.50142 16.4569i −1.24760 2.16090i
\(59\) 2.04991 3.55054i 0.266875 0.462241i −0.701178 0.712986i \(-0.747342\pi\)
0.968053 + 0.250745i \(0.0806755\pi\)
\(60\) 5.75363 + 1.50019i 0.742791 + 0.193673i
\(61\) −10.7004 + 6.17786i −1.37004 + 0.790994i −0.990933 0.134358i \(-0.957103\pi\)
−0.379109 + 0.925352i \(0.623769\pi\)
\(62\) 20.5262 2.60683
\(63\) 0 0
\(64\) 12.4147 1.55183
\(65\) 2.77549 1.60243i 0.344257 0.198757i
\(66\) −10.9173 2.84653i −1.34382 0.350384i
\(67\) 0.802125 1.38932i 0.0979952 0.169733i −0.812860 0.582460i \(-0.802090\pi\)
0.910855 + 0.412727i \(0.135424\pi\)
\(68\) 1.51381 + 2.62200i 0.183577 + 0.317964i
\(69\) −12.5965 + 3.46641i −1.51645 + 0.417307i
\(70\) 0 0
\(71\) 6.25869i 0.742770i 0.928479 + 0.371385i \(0.121117\pi\)
−0.928479 + 0.371385i \(0.878883\pi\)
\(72\) 4.89248 8.74419i 0.576584 1.03051i
\(73\) −0.192022 0.110864i −0.0224745 0.0129757i 0.488721 0.872440i \(-0.337464\pi\)
−0.511195 + 0.859465i \(0.670797\pi\)
\(74\) −0.822480 0.474859i −0.0956114 0.0552012i
\(75\) −1.21646 + 1.23297i −0.140465 + 0.142371i
\(76\) 7.53794i 0.864661i
\(77\) 0 0
\(78\) −3.43292 12.4749i −0.388702 1.41250i
\(79\) 1.56849 + 2.71671i 0.176469 + 0.305654i 0.940669 0.339326i \(-0.110199\pi\)
−0.764199 + 0.644980i \(0.776866\pi\)
\(80\) 0.459555 0.795973i 0.0513798 0.0889925i
\(81\) 4.70850 + 7.67007i 0.523167 + 0.852230i
\(82\) −17.2609 + 9.96559i −1.90615 + 1.10051i
\(83\) −0.666893 −0.0732010 −0.0366005 0.999330i \(-0.511653\pi\)
−0.0366005 + 0.999330i \(0.511653\pi\)
\(84\) 0 0
\(85\) −0.881938 −0.0956596
\(86\) −0.238319 + 0.137594i −0.0256986 + 0.0148371i
\(87\) 3.56273 13.6641i 0.381965 1.46494i
\(88\) −4.66689 + 8.08330i −0.497492 + 0.861682i
\(89\) −0.437271 0.757376i −0.0463506 0.0802816i 0.841919 0.539603i \(-0.181426\pi\)
−0.888270 + 0.459322i \(0.848092\pi\)
\(90\) 3.57762 + 6.00807i 0.377114 + 0.633307i
\(91\) 0 0
\(92\) 25.8944i 2.69968i
\(93\) 10.8579 + 10.7125i 1.12591 + 1.11083i
\(94\) −5.30832 3.06476i −0.547511 0.316106i
\(95\) −1.90160 1.09789i −0.195100 0.112641i
\(96\) 5.59470 + 5.51978i 0.571007 + 0.563360i
\(97\) 6.37221i 0.647000i 0.946228 + 0.323500i \(0.104860\pi\)
−0.946228 + 0.323500i \(0.895140\pi\)
\(98\) 0 0
\(99\) −4.28939 7.20339i −0.431100 0.723968i
\(100\) 1.71646 + 2.97300i 0.171646 + 0.297300i
\(101\) 5.31267 9.20181i 0.528630 0.915614i −0.470813 0.882233i \(-0.656039\pi\)
0.999443 0.0333808i \(-0.0106274\pi\)
\(102\) −0.898330 + 3.44535i −0.0889479 + 0.341140i
\(103\) 0.868777 0.501589i 0.0856031 0.0494230i −0.456587 0.889679i \(-0.650928\pi\)
0.542191 + 0.840256i \(0.317595\pi\)
\(104\) −10.7041 −1.04962
\(105\) 0 0
\(106\) −17.4081 −1.69083
\(107\) 11.0651 6.38846i 1.06971 0.617596i 0.141606 0.989923i \(-0.454774\pi\)
0.928101 + 0.372328i \(0.121440\pi\)
\(108\) 17.1333 4.96429i 1.64865 0.477689i
\(109\) −0.00912370 + 0.0158027i −0.000873892 + 0.00151363i −0.866462 0.499243i \(-0.833612\pi\)
0.865588 + 0.500757i \(0.166945\pi\)
\(110\) −3.25691 5.64113i −0.310534 0.537860i
\(111\) −0.187247 0.680436i −0.0177727 0.0645841i
\(112\) 0 0
\(113\) 7.23027i 0.680166i 0.940395 + 0.340083i \(0.110455\pi\)
−0.940395 + 0.340083i \(0.889545\pi\)
\(114\) −6.22592 + 6.31043i −0.583111 + 0.591026i
\(115\) −6.53240 3.77148i −0.609149 0.351692i
\(116\) −24.2380 13.9938i −2.25044 1.29929i
\(117\) 4.69460 8.39053i 0.434016 0.775705i
\(118\) 9.55611i 0.879711i
\(119\) 0 0
\(120\) 5.57762 1.53489i 0.509165 0.140116i
\(121\) −1.59513 2.76284i −0.145012 0.251167i
\(122\) −14.3997 + 24.9411i −1.30369 + 2.25806i
\(123\) −14.3316 3.73678i −1.29224 0.336934i
\(124\) 26.1810 15.1156i 2.35112 1.35742i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 6.99561 0.620760 0.310380 0.950613i \(-0.399544\pi\)
0.310380 + 0.950613i \(0.399544\pi\)
\(128\) 17.2008 9.93088i 1.52035 0.877774i
\(129\) −0.197875 0.0515933i −0.0174219 0.00454253i
\(130\) 3.73505 6.46929i 0.327585 0.567394i
\(131\) 4.94673 + 8.56799i 0.432198 + 0.748589i 0.997062 0.0765948i \(-0.0244048\pi\)
−0.564864 + 0.825184i \(0.691071\pi\)
\(132\) −16.0211 + 4.40880i −1.39446 + 0.383737i
\(133\) 0 0
\(134\) 3.73929i 0.323025i
\(135\) −1.24309 + 5.04527i −0.106989 + 0.434227i
\(136\) 2.55098 + 1.47281i 0.218745 + 0.126293i
\(137\) 10.9111 + 6.29951i 0.932195 + 0.538203i 0.887505 0.460798i \(-0.152437\pi\)
0.0446900 + 0.999001i \(0.485770\pi\)
\(138\) −21.3874 + 21.6777i −1.82061 + 1.84532i
\(139\) 0.988113i 0.0838106i −0.999122 0.0419053i \(-0.986657\pi\)
0.999122 0.0419053i \(-0.0133428\pi\)
\(140\) 0 0
\(141\) −1.20850 4.39156i −0.101774 0.369836i
\(142\) 7.29408 + 12.6337i 0.612106 + 1.06020i
\(143\) −4.47814 + 7.75637i −0.374481 + 0.648620i
\(144\) −0.0371731 2.75708i −0.00309776 0.229757i
\(145\) 7.06045 4.07635i 0.586338 0.338523i
\(146\) −0.516818 −0.0427722
\(147\) 0 0
\(148\) −1.39876 −0.114977
\(149\) −15.3604 + 8.86834i −1.25837 + 0.726523i −0.972758 0.231821i \(-0.925532\pi\)
−0.285616 + 0.958344i \(0.592198\pi\)
\(150\) −1.01859 + 3.90656i −0.0831672 + 0.318970i
\(151\) 11.2504 19.4862i 0.915542 1.58576i 0.109435 0.993994i \(-0.465096\pi\)
0.806106 0.591771i \(-0.201571\pi\)
\(152\) 3.66689 + 6.35124i 0.297424 + 0.515154i
\(153\) −2.27330 + 1.35368i −0.183785 + 0.109438i
\(154\) 0 0
\(155\) 8.80626i 0.707336i
\(156\) −13.5652 13.3836i −1.08609 1.07154i
\(157\) 10.2988 + 5.94600i 0.821931 + 0.474542i 0.851082 0.525033i \(-0.175947\pi\)
−0.0291509 + 0.999575i \(0.509280\pi\)
\(158\) 6.33228 + 3.65594i 0.503769 + 0.290851i
\(159\) −9.20850 9.08518i −0.730282 0.720502i
\(160\) 4.53757i 0.358726i
\(161\) 0 0
\(162\) 18.4435 + 9.99527i 1.44906 + 0.785302i
\(163\) −4.26159 7.38130i −0.333794 0.578148i 0.649459 0.760397i \(-0.274996\pi\)
−0.983252 + 0.182249i \(0.941662\pi\)
\(164\) −14.6774 + 25.4221i −1.14611 + 1.98513i
\(165\) 1.22124 4.68378i 0.0950731 0.364632i
\(166\) −1.34618 + 0.777218i −0.104484 + 0.0603238i
\(167\) 3.56923 0.276195 0.138098 0.990419i \(-0.455901\pi\)
0.138098 + 0.990419i \(0.455901\pi\)
\(168\) 0 0
\(169\) 2.72886 0.209912
\(170\) −1.78027 + 1.02784i −0.136540 + 0.0788316i
\(171\) −6.58674 + 0.0888076i −0.503701 + 0.00679128i
\(172\) −0.202650 + 0.350999i −0.0154519 + 0.0267634i
\(173\) −4.27114 7.39784i −0.324729 0.562447i 0.656728 0.754127i \(-0.271940\pi\)
−0.981457 + 0.191680i \(0.938606\pi\)
\(174\) −8.73285 31.7342i −0.662036 2.40576i
\(175\) 0 0
\(176\) 2.56854i 0.193611i
\(177\) 4.98727 5.05496i 0.374866 0.379954i
\(178\) −1.76534 1.01922i −0.132318 0.0763937i
\(179\) −1.06480 0.614760i −0.0795866 0.0459493i 0.459679 0.888085i \(-0.347965\pi\)
−0.539265 + 0.842136i \(0.681298\pi\)
\(180\) 8.98760 + 5.02867i 0.669897 + 0.374815i
\(181\) 15.3995i 1.14464i −0.820032 0.572318i \(-0.806044\pi\)
0.820032 0.572318i \(-0.193956\pi\)
\(182\) 0 0
\(183\) −20.6337 + 5.67814i −1.52529 + 0.419740i
\(184\) 12.5965 + 21.8179i 0.928630 + 1.60843i
\(185\) 0.203727 0.352865i 0.0149783 0.0259432i
\(186\) 34.4022 + 8.96994i 2.52249 + 0.657708i
\(187\) 2.13445 1.23233i 0.156087 0.0901167i
\(188\) −9.02762 −0.658407
\(189\) 0 0
\(190\) −5.11806 −0.371303
\(191\) 12.5795 7.26275i 0.910218 0.525514i 0.0297166 0.999558i \(-0.490540\pi\)
0.880501 + 0.474044i \(0.157206\pi\)
\(192\) 20.8072 + 5.42521i 1.50163 + 0.391531i
\(193\) 0.201572 0.349134i 0.0145095 0.0251312i −0.858679 0.512513i \(-0.828715\pi\)
0.873189 + 0.487382i \(0.162048\pi\)
\(194\) 7.42638 + 12.8629i 0.533183 + 0.923500i
\(195\) 5.35203 1.47281i 0.383267 0.105470i
\(196\) 0 0
\(197\) 11.6716i 0.831564i −0.909464 0.415782i \(-0.863508\pi\)
0.909464 0.415782i \(-0.136492\pi\)
\(198\) −17.0536 9.54168i −1.21194 0.678097i
\(199\) 16.0886 + 9.28875i 1.14049 + 0.658462i 0.946552 0.322552i \(-0.104541\pi\)
0.193938 + 0.981014i \(0.437874\pi\)
\(200\) 2.89248 + 1.66997i 0.204529 + 0.118085i
\(201\) 1.95151 1.97800i 0.137649 0.139517i
\(202\) 24.7662i 1.74254i
\(203\) 0 0
\(204\) 1.39136 + 5.05605i 0.0974147 + 0.353994i
\(205\) −4.27549 7.40537i −0.298613 0.517213i
\(206\) 1.16913 2.02500i 0.0814574 0.141088i
\(207\) −22.6268 + 0.305073i −1.57267 + 0.0212040i
\(208\) −2.55098 + 1.47281i −0.176879 + 0.102121i
\(209\) 6.13631 0.424457
\(210\) 0 0
\(211\) 6.98175 0.480644 0.240322 0.970693i \(-0.422747\pi\)
0.240322 + 0.970693i \(0.422747\pi\)
\(212\) −22.2039 + 12.8194i −1.52497 + 0.880443i
\(213\) −2.73505 + 10.4897i −0.187402 + 0.718741i
\(214\) 14.8906 25.7913i 1.01790 1.76306i
\(215\) −0.0590312 0.102245i −0.00402590 0.00697306i
\(216\) 12.0211 12.5174i 0.817931 0.851700i
\(217\) 0 0
\(218\) 0.0425322i 0.00288064i
\(219\) −0.273385 0.269724i −0.0184737 0.0182263i
\(220\) −8.30832 4.79681i −0.560147 0.323401i
\(221\) 2.44781 + 1.41324i 0.164658 + 0.0950651i
\(222\) −1.17098 1.15530i −0.0785908 0.0775383i
\(223\) 1.44594i 0.0968271i 0.998827 + 0.0484135i \(0.0154165\pi\)
−0.998827 + 0.0484135i \(0.984583\pi\)
\(224\) 0 0
\(225\) −2.57762 + 1.53489i −0.171841 + 0.102326i
\(226\) 8.42638 + 14.5949i 0.560514 + 0.970839i
\(227\) −0.533562 + 0.924157i −0.0354138 + 0.0613385i −0.883189 0.469017i \(-0.844608\pi\)
0.847775 + 0.530356i \(0.177942\pi\)
\(228\) −3.29408 + 12.6337i −0.218156 + 0.836688i
\(229\) 6.58058 3.79930i 0.434857 0.251065i −0.266557 0.963819i \(-0.585886\pi\)
0.701414 + 0.712755i \(0.252553\pi\)
\(230\) −17.5816 −1.15930
\(231\) 0 0
\(232\) −27.2296 −1.78771
\(233\) −15.5882 + 8.99983i −1.02121 + 0.589598i −0.914455 0.404687i \(-0.867381\pi\)
−0.106759 + 0.994285i \(0.534047\pi\)
\(234\) −0.302125 22.4082i −0.0197506 1.46487i
\(235\) 1.31486 2.27740i 0.0857720 0.148561i
\(236\) −7.03717 12.1887i −0.458081 0.793419i
\(237\) 1.44162 + 5.23868i 0.0936433 + 0.340289i
\(238\) 0 0
\(239\) 29.8816i 1.93288i 0.256892 + 0.966440i \(0.417302\pi\)
−0.256892 + 0.966440i \(0.582698\pi\)
\(240\) 1.11806 1.13324i 0.0721706 0.0731502i
\(241\) −4.53760 2.61978i −0.292292 0.168755i 0.346683 0.937982i \(-0.387308\pi\)
−0.638975 + 0.769227i \(0.720641\pi\)
\(242\) −6.43980 3.71802i −0.413966 0.239004i
\(243\) 4.53971 + 14.9128i 0.291222 + 0.956655i
\(244\) 42.4162i 2.71542i
\(245\) 0 0
\(246\) −33.2845 + 9.15948i −2.12214 + 0.583987i
\(247\) 3.51859 + 6.09437i 0.223882 + 0.387776i
\(248\) 14.7062 25.4719i 0.933846 1.61747i
\(249\) −1.11772 0.291432i −0.0708328 0.0184688i
\(250\) −2.01859 + 1.16543i −0.127667 + 0.0737084i
\(251\) −15.0765 −0.951620 −0.475810 0.879548i \(-0.657845\pi\)
−0.475810 + 0.879548i \(0.657845\pi\)
\(252\) 0 0
\(253\) 21.0795 1.32526
\(254\) 14.1212 8.15291i 0.886046 0.511559i
\(255\) −1.47814 0.385407i −0.0925648 0.0241351i
\(256\) 10.7329 18.5898i 0.670803 1.16187i
\(257\) 7.95478 + 13.7781i 0.496206 + 0.859453i 0.999990 0.00437591i \(-0.00139290\pi\)
−0.503785 + 0.863829i \(0.668060\pi\)
\(258\) −0.459555 + 0.126464i −0.0286107 + 0.00787329i
\(259\) 0 0
\(260\) 11.0020i 0.682318i
\(261\) 11.9424 21.3443i 0.739215 1.32118i
\(262\) 19.9708 + 11.5302i 1.23380 + 0.712336i
\(263\) −7.19124 4.15187i −0.443431 0.256015i 0.261621 0.965171i \(-0.415743\pi\)
−0.705052 + 0.709156i \(0.749076\pi\)
\(264\) −11.3542 + 11.5083i −0.698802 + 0.708287i
\(265\) 7.46853i 0.458788i
\(266\) 0 0
\(267\) −0.401900 1.46046i −0.0245959 0.0893788i
\(268\) −2.75363 4.76943i −0.168205 0.291340i
\(269\) 8.69353 15.0576i 0.530054 0.918080i −0.469332 0.883022i \(-0.655505\pi\)
0.999385 0.0350578i \(-0.0111615\pi\)
\(270\) 3.37062 + 11.6330i 0.205129 + 0.707965i
\(271\) 8.82614 5.09577i 0.536150 0.309546i −0.207367 0.978263i \(-0.566490\pi\)
0.743517 + 0.668717i \(0.233156\pi\)
\(272\) 0.810598 0.0491497
\(273\) 0 0
\(274\) 29.3666 1.77410
\(275\) 2.42019 1.39730i 0.145943 0.0842601i
\(276\) −11.3158 + 43.3995i −0.681134 + 2.61234i
\(277\) −4.78018 + 8.27951i −0.287213 + 0.497468i −0.973143 0.230199i \(-0.926062\pi\)
0.685930 + 0.727667i \(0.259395\pi\)
\(278\) −1.15158 1.99459i −0.0690670 0.119628i
\(279\) 13.5166 + 22.6992i 0.809220 + 1.35896i
\(280\) 0 0
\(281\) 11.9239i 0.711320i −0.934616 0.355660i \(-0.884256\pi\)
0.934616 0.355660i \(-0.115744\pi\)
\(282\) −7.55753 7.45632i −0.450044 0.444017i
\(283\) −17.2940 9.98469i −1.02802 0.593528i −0.111604 0.993753i \(-0.535599\pi\)
−0.916417 + 0.400225i \(0.868932\pi\)
\(284\) 18.6071 + 10.7428i 1.10413 + 0.637468i
\(285\) −2.70734 2.67108i −0.160369 0.158221i
\(286\) 20.8759i 1.23442i
\(287\) 0 0
\(288\) 6.96467 + 11.6961i 0.410397 + 0.689201i
\(289\) 8.11109 + 14.0488i 0.477123 + 0.826401i
\(290\) 9.50142 16.4569i 0.557942 0.966385i
\(291\) −2.78466 + 10.6799i −0.163239 + 0.626069i
\(292\) −0.659198 + 0.380588i −0.0385766 + 0.0222722i
\(293\) 3.01023 0.175859 0.0879297 0.996127i \(-0.471975\pi\)
0.0879297 + 0.996127i \(0.471975\pi\)
\(294\) 0 0
\(295\) 4.09982 0.238700
\(296\) −1.17855 + 0.680436i −0.0685018 + 0.0395495i
\(297\) −4.04121 13.9475i −0.234495 0.809314i
\(298\) −20.6709 + 35.8030i −1.19743 + 2.07401i
\(299\) 12.0871 + 20.9354i 0.699014 + 1.21073i
\(300\) 1.57762 + 5.73289i 0.0910838 + 0.330988i
\(301\) 0 0
\(302\) 52.4461i 3.01793i
\(303\) 12.9253 13.1007i 0.742539 0.752618i
\(304\) 1.74778 + 1.00908i 0.100242 + 0.0578748i
\(305\) −10.7004 6.17786i −0.612701 0.353743i
\(306\) −3.01123 + 5.38189i −0.172141 + 0.307662i
\(307\) 20.3794i 1.16311i −0.813507 0.581556i \(-0.802444\pi\)
0.813507 0.581556i \(-0.197556\pi\)
\(308\) 0 0
\(309\) 1.67528 0.461015i 0.0953033 0.0262263i
\(310\) 10.2631 + 17.7762i 0.582905 + 1.00962i
\(311\) 13.6359 23.6181i 0.773222 1.33926i −0.162567 0.986697i \(-0.551977\pi\)
0.935789 0.352562i \(-0.114689\pi\)
\(312\) −17.9402 4.67767i −1.01566 0.264821i
\(313\) −0.546210 + 0.315354i −0.0308736 + 0.0178249i −0.515357 0.856975i \(-0.672341\pi\)
0.484484 + 0.874800i \(0.339007\pi\)
\(314\) 27.7186 1.56425
\(315\) 0 0
\(316\) 10.7690 0.605806
\(317\) −22.0233 + 12.7151i −1.23695 + 0.714153i −0.968470 0.249132i \(-0.919855\pi\)
−0.268480 + 0.963285i \(0.586521\pi\)
\(318\) −29.1763 7.60735i −1.63613 0.426599i
\(319\) −11.3917 + 19.7311i −0.637815 + 1.10473i
\(320\) 6.20734 + 10.7514i 0.347001 + 0.601023i
\(321\) 21.3371 5.87170i 1.19092 0.327726i
\(322\) 0 0
\(323\) 1.93654i 0.107752i
\(324\) 30.8851 0.832984i 1.71584 0.0462769i
\(325\) 2.77549 + 1.60243i 0.153957 + 0.0888869i
\(326\) −17.2048 9.93319i −0.952885 0.550149i
\(327\) −0.0221973 + 0.0224986i −0.00122751 + 0.00124417i
\(328\) 28.5598i 1.57695i
\(329\) 0 0
\(330\) −2.99346 10.8779i −0.164784 0.598808i
\(331\) −5.74666 9.95352i −0.315865 0.547095i 0.663756 0.747949i \(-0.268961\pi\)
−0.979621 + 0.200855i \(0.935628\pi\)
\(332\) −1.14470 + 1.98267i −0.0628233 + 0.108813i
\(333\) −0.0164793 1.22225i −0.000903061 0.0669788i
\(334\) 7.20480 4.15970i 0.394229 0.227608i
\(335\) 1.60425 0.0876496
\(336\) 0 0
\(337\) −16.2041 −0.882694 −0.441347 0.897336i \(-0.645499\pi\)
−0.441347 + 0.897336i \(0.645499\pi\)
\(338\) 5.50843 3.18030i 0.299619 0.172985i
\(339\) −3.15962 + 12.1180i −0.171607 + 0.658162i
\(340\) −1.51381 + 2.62200i −0.0820980 + 0.142198i
\(341\) −12.3050 21.3128i −0.666351 1.15415i
\(342\) −13.1924 + 7.85566i −0.713364 + 0.424786i
\(343\) 0 0
\(344\) 0.394322i 0.0212604i
\(345\) −9.30027 9.17572i −0.500710 0.494004i
\(346\) −17.2433 9.95545i −0.927008 0.535208i
\(347\) 15.5732 + 8.99121i 0.836015 + 0.482673i 0.855908 0.517129i \(-0.172999\pi\)
−0.0198929 + 0.999802i \(0.506333\pi\)
\(348\) −34.5079 34.0458i −1.84982 1.82505i
\(349\) 6.15422i 0.329428i −0.986341 0.164714i \(-0.947330\pi\)
0.986341 0.164714i \(-0.0526701\pi\)
\(350\) 0 0
\(351\) 11.5349 12.0111i 0.615687 0.641106i
\(352\) −6.34033 10.9818i −0.337941 0.585330i
\(353\) −14.7332 + 25.5186i −0.784169 + 1.35822i 0.145326 + 0.989384i \(0.453577\pi\)
−0.929494 + 0.368836i \(0.879756\pi\)
\(354\) 4.17602 16.0162i 0.221953 0.851251i
\(355\) −5.42019 + 3.12935i −0.287674 + 0.166088i
\(356\) −3.00223 −0.159118
\(357\) 0 0
\(358\) −2.86584 −0.151465
\(359\) 30.5228 17.6224i 1.61093 0.930073i 0.621779 0.783192i \(-0.286410\pi\)
0.989154 0.146881i \(-0.0469233\pi\)
\(360\) 10.0189 0.135083i 0.528044 0.00711950i
\(361\) −7.08928 + 12.2790i −0.373120 + 0.646262i
\(362\) −17.9471 31.0852i −0.943277 1.63380i
\(363\) −1.46610 5.32764i −0.0769502 0.279628i
\(364\) 0 0
\(365\) 0.221728i 0.0116058i
\(366\) −35.0335 + 35.5090i −1.83123 + 1.85608i
\(367\) −30.1613 17.4136i −1.57441 0.908984i −0.995619 0.0935065i \(-0.970192\pi\)
−0.578788 0.815478i \(-0.696474\pi\)
\(368\) 6.00400 + 3.46641i 0.312980 + 0.180699i
\(369\) −22.3870 12.5258i −1.16542 0.652067i
\(370\) 0.949718i 0.0493735i
\(371\) 0 0
\(372\) 50.4853 13.8929i 2.61754 0.720314i
\(373\) −10.1371 17.5579i −0.524878 0.909115i −0.999580 0.0289688i \(-0.990778\pi\)
0.474702 0.880146i \(-0.342556\pi\)
\(374\) 2.87239 4.97512i 0.148528 0.257257i
\(375\) −1.67602 0.437000i −0.0865491 0.0225666i
\(376\) −7.60641 + 4.39156i −0.392270 + 0.226477i
\(377\) −26.1283 −1.34568
\(378\) 0 0
\(379\) −9.07202 −0.465998 −0.232999 0.972477i \(-0.574854\pi\)
−0.232999 + 0.972477i \(0.574854\pi\)
\(380\) −6.52805 + 3.76897i −0.334882 + 0.193344i
\(381\) 11.7248 + 3.05708i 0.600678 + 0.156619i
\(382\) 16.9285 29.3210i 0.866137 1.50019i
\(383\) −13.8881 24.0549i −0.709648 1.22915i −0.964988 0.262295i \(-0.915521\pi\)
0.255339 0.966851i \(-0.417813\pi\)
\(384\) 33.1686 9.12758i 1.69263 0.465790i
\(385\) 0 0
\(386\) 0.939675i 0.0478282i
\(387\) −0.309095 0.172942i −0.0157122 0.00879115i
\(388\) 18.9446 + 10.9377i 0.961765 + 0.555275i
\(389\) 13.4945 + 7.79107i 0.684200 + 0.395023i 0.801436 0.598081i \(-0.204070\pi\)
−0.117236 + 0.993104i \(0.537403\pi\)
\(390\) 9.08708 9.21043i 0.460142 0.466388i
\(391\) 6.65242i 0.336427i
\(392\) 0 0
\(393\) 4.54660 + 16.5218i 0.229345 + 0.833416i
\(394\) −13.6024 23.5600i −0.685279 1.18694i
\(395\) −1.56849 + 2.71671i −0.0789195 + 0.136693i
\(396\) −28.7782 + 0.388011i −1.44616 + 0.0194983i
\(397\) 16.3596 9.44524i 0.821067 0.474043i −0.0297174 0.999558i \(-0.509461\pi\)
0.850784 + 0.525515i \(0.176127\pi\)
\(398\) 43.3016 2.17051
\(399\) 0 0
\(400\) 0.919111 0.0459555
\(401\) −18.0127 + 10.3996i −0.899511 + 0.519333i −0.877042 0.480415i \(-0.840486\pi\)
−0.0224695 + 0.999748i \(0.507153\pi\)
\(402\) 1.63407 6.26711i 0.0814999 0.312575i
\(403\) 14.1114 24.4417i 0.702941 1.21753i
\(404\) −18.2380 31.5891i −0.907373 1.57162i
\(405\) −4.28823 + 7.91272i −0.213084 + 0.393186i
\(406\) 0 0
\(407\) 1.13867i 0.0564416i
\(408\) 3.63187 + 3.58324i 0.179805 + 0.177397i
\(409\) −24.9664 14.4143i −1.23451 0.712744i −0.266542 0.963823i \(-0.585881\pi\)
−0.967966 + 0.251080i \(0.919214\pi\)
\(410\) −17.2609 9.96559i −0.852455 0.492165i
\(411\) 15.5342 + 15.3262i 0.766248 + 0.755986i
\(412\) 3.44383i 0.169665i
\(413\) 0 0
\(414\) −45.3187 + 26.9858i −2.22729 + 1.32628i
\(415\) −0.333446 0.577546i −0.0163682 0.0283506i
\(416\) 7.27114 12.5940i 0.356497 0.617471i
\(417\) 0.431805 1.65609i 0.0211456 0.0810992i
\(418\) 12.3867 7.15145i 0.605852 0.349789i
\(419\) −3.24500 −0.158528 −0.0792642 0.996854i \(-0.525257\pi\)
−0.0792642 + 0.996854i \(0.525257\pi\)
\(420\) 0 0
\(421\) 27.9322 1.36133 0.680665 0.732594i \(-0.261691\pi\)
0.680665 + 0.732594i \(0.261691\pi\)
\(422\) 14.0933 8.13675i 0.686050 0.396091i
\(423\) −0.106358 7.88844i −0.00517131 0.383549i
\(424\) −12.4722 + 21.6026i −0.605706 + 1.04911i
\(425\) −0.440969 0.763780i −0.0213901 0.0370488i
\(426\) 6.70407 + 24.3618i 0.324813 + 1.18033i
\(427\) 0 0
\(428\) 43.8622i 2.12016i
\(429\) −10.8950 + 11.0429i −0.526014 + 0.533154i
\(430\) −0.238319 0.137594i −0.0114928 0.00663536i
\(431\) 33.1792 + 19.1560i 1.59819 + 0.922714i 0.991836 + 0.127516i \(0.0407006\pi\)
0.606351 + 0.795197i \(0.292633\pi\)
\(432\) 1.14254 4.63716i 0.0549705 0.223105i
\(433\) 28.9533i 1.39140i 0.718330 + 0.695702i \(0.244907\pi\)
−0.718330 + 0.695702i \(0.755093\pi\)
\(434\) 0 0
\(435\) 13.6148 3.74662i 0.652779 0.179637i
\(436\) 0.0313210 + 0.0542495i 0.00150000 + 0.00259808i
\(437\) 8.28134 14.3437i 0.396150 0.686153i
\(438\) −0.866196 0.225850i −0.0413885 0.0107915i
\(439\) 13.2197 7.63242i 0.630943 0.364275i −0.150174 0.988660i \(-0.547983\pi\)
0.781117 + 0.624384i \(0.214650\pi\)
\(440\) −9.33379 −0.444971
\(441\) 0 0
\(442\) 6.58816 0.313367
\(443\) 1.97776 1.14186i 0.0939660 0.0542513i −0.452281 0.891876i \(-0.649389\pi\)
0.546247 + 0.837624i \(0.316056\pi\)
\(444\) −2.34434 0.611256i −0.111257 0.0290089i
\(445\) 0.437271 0.757376i 0.0207286 0.0359030i
\(446\) 1.68514 + 2.91875i 0.0797937 + 0.138207i
\(447\) −29.6198 + 8.15099i −1.40097 + 0.385528i
\(448\) 0 0
\(449\) 10.3113i 0.486619i −0.969949 0.243310i \(-0.921767\pi\)
0.969949 0.243310i \(-0.0782331\pi\)
\(450\) −3.41434 + 6.10234i −0.160953 + 0.287667i
\(451\) 20.6950 + 11.9483i 0.974489 + 0.562621i
\(452\) 21.4956 + 12.4105i 1.01107 + 0.583739i
\(453\) 27.3713 27.7428i 1.28601 1.30347i
\(454\) 2.48732i 0.116736i
\(455\) 0 0
\(456\) 3.37028 + 12.2472i 0.157828 + 0.573529i
\(457\) −16.3987 28.4033i −0.767097 1.32865i −0.939131 0.343560i \(-0.888367\pi\)
0.172033 0.985091i \(-0.444966\pi\)
\(458\) 8.85564 15.3384i 0.413797 0.716718i
\(459\) −4.40164 + 1.27535i −0.205451 + 0.0595284i
\(460\) −22.4252 + 12.9472i −1.04558 + 0.603666i
\(461\) 16.5678 0.771637 0.385819 0.922575i \(-0.373919\pi\)
0.385819 + 0.922575i \(0.373919\pi\)
\(462\) 0 0
\(463\) −36.5866 −1.70032 −0.850162 0.526522i \(-0.823496\pi\)
−0.850162 + 0.526522i \(0.823496\pi\)
\(464\) −6.48933 + 3.74662i −0.301260 + 0.173932i
\(465\) −3.84834 + 14.7594i −0.178462 + 0.684453i
\(466\) −20.9774 + 36.3339i −0.971758 + 1.68313i
\(467\) 20.5550 + 35.6023i 0.951171 + 1.64748i 0.742896 + 0.669406i \(0.233451\pi\)
0.208275 + 0.978070i \(0.433215\pi\)
\(468\) −16.8869 28.3591i −0.780598 1.31090i
\(469\) 0 0
\(470\) 6.12952i 0.282733i
\(471\) 14.6625 + 14.4661i 0.675613 + 0.666565i
\(472\) −11.8586 6.84658i −0.545837 0.315139i
\(473\) 0.285733 + 0.164968i 0.0131380 + 0.00758524i
\(474\) 9.01536 + 8.89463i 0.414089 + 0.408544i
\(475\) 2.19578i 0.100749i
\(476\) 0 0
\(477\) −11.4634 19.2510i −0.524872 0.881444i
\(478\) 34.8250 + 60.3186i 1.59286 + 2.75891i
\(479\) −8.25944 + 14.3058i −0.377383 + 0.653647i −0.990681 0.136205i \(-0.956509\pi\)
0.613297 + 0.789852i \(0.289843\pi\)
\(480\) −1.98292 + 7.60504i −0.0905074 + 0.347121i
\(481\) −1.13088 + 0.652916i −0.0515639 + 0.0297704i
\(482\) −12.2127 −0.556274
\(483\) 0 0
\(484\) −10.9519 −0.497813
\(485\) −5.51850 + 3.18611i −0.250582 + 0.144674i
\(486\) 26.5436 + 24.8120i 1.20404 + 1.12550i
\(487\) 1.01601 1.75977i 0.0460396 0.0797430i −0.842087 0.539341i \(-0.818673\pi\)
0.888127 + 0.459598i \(0.152007\pi\)
\(488\) 20.6337 + 35.7386i 0.934044 + 1.61781i
\(489\) −3.91688 14.2335i −0.177127 0.643661i
\(490\) 0 0
\(491\) 5.97889i 0.269824i −0.990858 0.134912i \(-0.956925\pi\)
0.990858 0.134912i \(-0.0430751\pi\)
\(492\) −35.7091 + 36.1938i −1.60989 + 1.63174i
\(493\) 6.22687 + 3.59509i 0.280444 + 0.161915i
\(494\) 14.2051 + 8.20134i 0.639120 + 0.368996i
\(495\) 4.09362 7.31642i 0.183995 0.328848i
\(496\) 8.09393i 0.363428i
\(497\) 0 0
\(498\) −2.59587 + 0.714349i −0.116323 + 0.0320108i
\(499\) −4.24155 7.34658i −0.189878 0.328878i 0.755331 0.655343i \(-0.227476\pi\)
−0.945209 + 0.326465i \(0.894143\pi\)
\(500\) −1.71646 + 2.97300i −0.0767625 + 0.132957i
\(501\) 5.98209 + 1.55975i 0.267260 + 0.0696846i
\(502\) −30.4332 + 17.5706i −1.35830 + 0.784216i
\(503\) 17.0296 0.759312 0.379656 0.925128i \(-0.376042\pi\)
0.379656 + 0.925128i \(0.376042\pi\)
\(504\) 0 0
\(505\) 10.6253 0.472821
\(506\) 42.5508 24.5667i 1.89161 1.09212i
\(507\) 4.57361 + 1.19251i 0.203121 + 0.0529612i
\(508\) 12.0077 20.7979i 0.532755 0.922759i
\(509\) 6.43409 + 11.1442i 0.285186 + 0.493956i 0.972654 0.232258i \(-0.0746113\pi\)
−0.687468 + 0.726214i \(0.741278\pi\)
\(510\) −3.43292 + 0.944697i −0.152012 + 0.0418319i
\(511\) 0 0
\(512\) 10.3101i 0.455646i
\(513\) −11.0783 2.72956i −0.489119 0.120513i
\(514\) 32.1148 + 18.5415i 1.41652 + 0.817831i
\(515\) 0.868777 + 0.501589i 0.0382829 + 0.0221026i
\(516\) −0.493031 + 0.499723i −0.0217045 + 0.0219991i
\(517\) 7.34899i 0.323208i
\(518\) 0 0
\(519\) −3.92565 14.2654i −0.172317 0.626181i
\(520\) −5.35203 9.26999i −0.234702 0.406516i
\(521\) −8.32724 + 14.4232i −0.364823 + 0.631892i −0.988748 0.149592i \(-0.952204\pi\)
0.623925 + 0.781485i \(0.285537\pi\)
\(522\) −0.768563 57.0033i −0.0336391 2.49497i
\(523\) −31.4934 + 18.1827i −1.37711 + 0.795075i −0.991811 0.127716i \(-0.959235\pi\)
−0.385300 + 0.922791i \(0.625902\pi\)
\(524\) 33.9635 1.48370
\(525\) 0 0
\(526\) −19.3549 −0.843912
\(527\) −6.72605 + 3.88329i −0.292991 + 0.169159i
\(528\) −1.12245 + 4.30491i −0.0488484 + 0.187347i
\(529\) 16.9482 29.3551i 0.736876 1.27631i
\(530\) −8.70407 15.0759i −0.378080 0.654855i
\(531\) 10.5678 6.29276i 0.458602 0.273083i
\(532\) 0 0
\(533\) 27.4047i 1.18703i
\(534\) −2.51334 2.47968i −0.108763 0.107306i
\(535\) 11.0651 + 6.38846i 0.478388 + 0.276197i
\(536\) −4.64026 2.67906i −0.200429 0.115718i
\(537\) −1.51597 1.49566i −0.0654188 0.0645427i
\(538\) 40.5268i 1.74724i
\(539\) 0 0
\(540\) 12.8658 + 12.3557i 0.553658 + 0.531706i
\(541\) −1.89575 3.28353i −0.0815046 0.141170i 0.822392 0.568922i \(-0.192639\pi\)
−0.903896 + 0.427751i \(0.859306\pi\)
\(542\) 11.8775 20.5725i 0.510184 0.883665i
\(543\) 6.72958 25.8098i 0.288794 1.10761i
\(544\) −3.46571 + 2.00093i −0.148591 + 0.0857890i
\(545\) −0.0182474 −0.000781633
\(546\) 0 0
\(547\) −10.9382 −0.467684 −0.233842 0.972275i \(-0.575130\pi\)
−0.233842 + 0.972275i \(0.575130\pi\)
\(548\) 37.4568 21.6257i 1.60008 0.923805i
\(549\) −37.0638 + 0.499723i −1.58184 + 0.0213277i
\(550\) 3.25691 5.64113i 0.138875 0.240538i
\(551\) 8.95077 + 15.5032i 0.381316 + 0.660458i
\(552\) 11.5776 + 42.0718i 0.492776 + 1.79069i
\(553\) 0 0
\(554\) 22.2839i 0.946752i
\(555\) 0.495651 0.502379i 0.0210392 0.0213248i
\(556\) −2.93766 1.69606i −0.124584 0.0719288i
\(557\) −8.42853 4.86622i −0.357128 0.206188i 0.310692 0.950511i \(-0.399439\pi\)
−0.667820 + 0.744322i \(0.732773\pi\)
\(558\) 53.7389 + 30.0675i 2.27495 + 1.27286i
\(559\) 0.378374i 0.0160035i
\(560\) 0 0
\(561\) 4.11591 1.13265i 0.173774 0.0478203i
\(562\) −13.8965 24.0694i −0.586187 1.01531i
\(563\) 0.235135 0.407265i 0.00990975 0.0171642i −0.861028 0.508558i \(-0.830179\pi\)
0.870938 + 0.491393i \(0.163512\pi\)
\(564\) −15.1304 3.94507i −0.637107 0.166117i
\(565\) −6.26159 + 3.61513i −0.263427 + 0.152090i
\(566\) −46.5459 −1.95647
\(567\) 0 0
\(568\) 20.9037 0.877100
\(569\) 5.38387 3.10838i 0.225703 0.130310i −0.382885 0.923796i \(-0.625069\pi\)
0.608588 + 0.793486i \(0.291736\pi\)
\(570\) −8.57796 2.23659i −0.359291 0.0936805i
\(571\) −5.31121 + 9.19928i −0.222267 + 0.384978i −0.955496 0.295004i \(-0.904679\pi\)
0.733229 + 0.679982i \(0.238012\pi\)
\(572\) 15.3731 + 26.6270i 0.642782 + 1.11333i
\(573\) 24.2572 6.67528i 1.01336 0.278864i
\(574\) 0 0
\(575\) 7.54296i 0.314563i
\(576\) 32.5024 + 18.1855i 1.35427 + 0.757728i
\(577\) 2.56914 + 1.48330i 0.106955 + 0.0617504i 0.552523 0.833497i \(-0.313665\pi\)
−0.445568 + 0.895248i \(0.646998\pi\)
\(578\) 32.7459 + 18.9058i 1.36205 + 0.786380i
\(579\) 0.490410 0.497067i 0.0203807 0.0206574i
\(580\) 27.9876i 1.16212i
\(581\) 0 0
\(582\) 6.82566 + 24.8037i 0.282933 + 1.02815i
\(583\) 10.4358 + 18.0753i 0.432205 + 0.748601i
\(584\) −0.370280 + 0.641344i −0.0153223 + 0.0265390i
\(585\) 9.61371 0.129620i 0.397478 0.00535911i
\(586\) 6.07641 3.50821i 0.251014 0.144923i
\(587\) 18.8819 0.779341 0.389670 0.920954i \(-0.372589\pi\)
0.389670 + 0.920954i \(0.372589\pi\)
\(588\) 0 0
\(589\) −19.3366 −0.796751
\(590\) 8.27583 4.77805i 0.340711 0.196709i
\(591\) 5.10047 19.5617i 0.209805 0.804661i
\(592\) −0.187247 + 0.324322i −0.00769582 + 0.0133296i
\(593\) 15.1472 + 26.2357i 0.622020 + 1.07737i 0.989109 + 0.147185i \(0.0470213\pi\)
−0.367088 + 0.930186i \(0.619645\pi\)
\(594\) −24.4123 23.4444i −1.00165 0.961936i
\(595\) 0 0
\(596\) 60.8887i 2.49410i
\(597\) 22.9056 + 22.5988i 0.937462 + 0.924907i
\(598\) 48.7976 + 28.1733i 1.99548 + 1.15209i
\(599\) −6.29024 3.63167i −0.257012 0.148386i 0.365959 0.930631i \(-0.380741\pi\)
−0.622971 + 0.782245i \(0.714075\pi\)
\(600\) 4.11806 + 4.06291i 0.168119 + 0.165868i
\(601\) 45.3302i 1.84906i −0.381110 0.924530i \(-0.624458\pi\)
0.381110 0.924530i \(-0.375542\pi\)
\(602\) 0 0
\(603\) 4.13515 2.46235i 0.168396 0.100275i
\(604\) −38.6216 66.8946i −1.57149 2.72190i
\(605\) 1.59513 2.76284i 0.0648511 0.112325i
\(606\) 10.8228 41.5085i 0.439647 1.68617i
\(607\) −22.5370 + 13.0117i −0.914748 + 0.528130i −0.881956 0.471332i \(-0.843773\pi\)
−0.0327925 + 0.999462i \(0.510440\pi\)
\(608\) −9.96351 −0.404073
\(609\) 0 0
\(610\) −28.7995 −1.16606
\(611\) −7.29877 + 4.21394i −0.295276 + 0.170478i
\(612\) 0.122451 + 9.08204i 0.00494980 + 0.367120i
\(613\) −12.8525 + 22.2611i −0.519106 + 0.899118i 0.480648 + 0.876914i \(0.340402\pi\)
−0.999753 + 0.0222040i \(0.992932\pi\)
\(614\) −23.7507 41.1375i −0.958502 1.66017i
\(615\) −3.92965 14.2799i −0.158459 0.575822i
\(616\) 0 0
\(617\) 8.88258i 0.357599i −0.983886 0.178800i \(-0.942779\pi\)
0.983886 0.178800i \(-0.0572213\pi\)
\(618\) 2.84441 2.88302i 0.114419 0.115972i
\(619\) 26.4112 + 15.2485i 1.06156 + 0.612890i 0.925863 0.377861i \(-0.123340\pi\)
0.135694 + 0.990751i \(0.456673\pi\)
\(620\) 26.1810 + 15.1156i 1.05145 + 0.607057i
\(621\) −38.0563 9.37661i −1.52715 0.376271i
\(622\) 63.5669i 2.54880i
\(623\) 0 0
\(624\) −4.91911 + 1.35368i −0.196922 + 0.0541904i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −0.735048 + 1.27314i −0.0293784 + 0.0508849i
\(627\) 10.2846 + 2.68157i 0.410726 + 0.107091i
\(628\) 35.3549 20.4121i 1.41081 0.814533i
\(629\) 0.359349 0.0143282
\(630\) 0 0
\(631\) 44.3335 1.76489 0.882445 0.470416i \(-0.155896\pi\)
0.882445 + 0.470416i \(0.155896\pi\)
\(632\) 9.07367 5.23868i 0.360931 0.208384i
\(633\) 11.7015 + 3.05102i 0.465094 + 0.121267i
\(634\) −29.6372 + 51.3332i −1.17705 + 2.03870i
\(635\) 3.49781 + 6.05838i 0.138806 + 0.240419i
\(636\) −42.8163 + 11.7825i −1.69778 + 0.467206i
\(637\) 0 0
\(638\) 53.1052i 2.10245i
\(639\) −9.16797 + 16.3857i −0.362679 + 0.648206i
\(640\) 17.2008 + 9.93088i 0.679921 + 0.392553i
\(641\) −6.03197 3.48256i −0.238249 0.137553i 0.376123 0.926570i \(-0.377257\pi\)
−0.614371 + 0.789017i \(0.710590\pi\)
\(642\) 36.2277 36.7195i 1.42979 1.44920i
\(643\) 25.8907i 1.02103i 0.859869 + 0.510514i \(0.170545\pi\)
−0.859869 + 0.510514i \(0.829455\pi\)
\(644\) 0 0
\(645\) −0.0542562 0.197161i −0.00213634 0.00776321i
\(646\) −2.25691 3.90908i −0.0887968 0.153801i
\(647\) 5.01859 8.69245i 0.197301 0.341735i −0.750351 0.661039i \(-0.770116\pi\)
0.947652 + 0.319304i \(0.103449\pi\)
\(648\) 25.6176 15.7261i 1.00636 0.617781i
\(649\) −9.92232 + 5.72866i −0.389485 + 0.224869i
\(650\) 7.47010 0.293001
\(651\) 0 0
\(652\) −29.2594 −1.14589
\(653\) −34.2946 + 19.8000i −1.34205 + 0.774833i −0.987108 0.160055i \(-0.948833\pi\)
−0.354942 + 0.934888i \(0.615500\pi\)
\(654\) −0.0185866 + 0.0712847i −0.000726792 + 0.00278745i
\(655\) −4.94673 + 8.56799i −0.193285 + 0.334779i
\(656\) 3.92965 + 6.80635i 0.153427 + 0.265744i
\(657\) −0.340329 0.571531i −0.0132775 0.0222975i
\(658\) 0 0
\(659\) 17.9364i 0.698705i −0.936991 0.349352i \(-0.886402\pi\)
0.936991 0.349352i \(-0.113598\pi\)
\(660\) −11.8287 11.6703i −0.460430 0.454264i
\(661\) 3.31012 + 1.91110i 0.128749 + 0.0743332i 0.562991 0.826463i \(-0.309650\pi\)
−0.434242 + 0.900796i \(0.642984\pi\)
\(662\) −23.2003 13.3947i −0.901705 0.520599i
\(663\) 3.48498 + 3.43831i 0.135346 + 0.133533i
\(664\) 2.22739i 0.0864393i
\(665\) 0 0
\(666\) −1.45771 2.44801i −0.0564852 0.0948585i
\(667\) 30.7478 + 53.2567i 1.19056 + 2.06211i
\(668\) 6.12645 10.6113i 0.237039 0.410564i
\(669\) −0.631874 + 2.42341i −0.0244297 + 0.0936946i
\(670\) 3.23832 1.86964i 0.125107 0.0722307i
\(671\) 34.5292 1.33299
\(672\) 0 0
\(673\) 1.08304 0.0417483 0.0208741 0.999782i \(-0.493355\pi\)
0.0208741 + 0.999782i \(0.493355\pi\)
\(674\) −32.7094 + 18.8848i −1.25992 + 0.727415i
\(675\) −4.99088 + 1.44608i −0.192099 + 0.0556597i
\(676\) 4.68398 8.11288i 0.180153 0.312034i
\(677\) −15.5014 26.8492i −0.595766 1.03190i −0.993438 0.114370i \(-0.963515\pi\)
0.397672 0.917528i \(-0.369818\pi\)
\(678\) 7.74478 + 28.1436i 0.297436 + 1.08085i
\(679\) 0 0
\(680\) 2.94562i 0.112960i
\(681\) −1.29812 + 1.31574i −0.0497439 + 0.0504191i
\(682\) −49.6772 28.6812i −1.90224 1.09826i
\(683\) 16.5419 + 9.55050i 0.632960 + 0.365440i 0.781898 0.623407i \(-0.214252\pi\)
−0.148937 + 0.988847i \(0.547585\pi\)
\(684\) −11.0419 + 19.7348i −0.422196 + 0.754579i
\(685\) 12.5990i 0.481383i
\(686\) 0 0
\(687\) 12.6894 3.49198i 0.484133 0.133227i
\(688\) 0.0542562 + 0.0939745i 0.00206850 + 0.00358275i
\(689\) −11.9678 + 20.7289i −0.455937 + 0.789707i
\(690\) −29.4671 7.68316i −1.12179 0.292493i
\(691\) 14.5775 8.41632i 0.554554 0.320172i −0.196403 0.980523i \(-0.562926\pi\)
0.750957 + 0.660351i \(0.229593\pi\)
\(692\) −29.3250 −1.11477
\(693\) 0 0
\(694\) 41.9145 1.59105
\(695\) 0.855731 0.494056i 0.0324597 0.0187406i
\(696\) −45.6372 11.8993i −1.72987 0.451043i
\(697\) 3.77072 6.53107i 0.142826 0.247382i
\(698\) −7.17232 12.4228i −0.271476 0.470211i
\(699\) −30.0589 + 8.27184i −1.13693 + 0.312870i
\(700\) 0 0
\(701\) 21.8878i 0.826691i −0.910574 0.413345i \(-0.864360\pi\)
0.910574 0.413345i \(-0.135640\pi\)
\(702\) 9.28603 37.6886i 0.350479 1.42247i
\(703\) 0.774814 + 0.447339i 0.0292227 + 0.0168717i
\(704\) −30.0458 17.3470i −1.13240 0.653789i
\(705\) 3.19895 3.24237i 0.120479 0.122115i
\(706\) 68.6821i 2.58489i
\(707\) 0 0
\(708\) −6.46794 23.5038i −0.243080 0.883326i
\(709\) 5.41030 + 9.37091i 0.203188 + 0.351932i 0.949554 0.313604i \(-0.101536\pi\)
−0.746366 + 0.665536i \(0.768203\pi\)
\(710\) −7.29408 + 12.6337i −0.273742 + 0.474135i
\(711\) 0.126874 + 9.41011i 0.00475816 + 0.352907i
\(712\) −2.52959 + 1.46046i −0.0948005 + 0.0547331i
\(713\) −66.4253 −2.48765
\(714\) 0 0
\(715\) −8.95628 −0.334946
\(716\) −3.65536 + 2.11042i −0.136607 + 0.0788703i
\(717\) −13.0583 + 50.0821i −0.487669 + 1.87035i
\(718\) 41.0753 71.1445i 1.53292 2.65509i
\(719\) 11.1296 + 19.2770i 0.415064 + 0.718912i 0.995435 0.0954404i \(-0.0304259\pi\)
−0.580371 + 0.814352i \(0.697093\pi\)
\(720\) 2.36912 1.41073i 0.0882917 0.0525749i
\(721\) 0 0
\(722\) 33.0483i 1.22993i
\(723\) −6.46025 6.37373i −0.240259 0.237042i
\(724\) −45.7827 26.4327i −1.70150 0.982362i
\(725\) 7.06045 + 4.07635i 0.262218 + 0.151392i
\(726\) −9.16844 9.04566i −0.340273 0.335716i
\(727\) 43.7899i 1.62408i 0.583604 + 0.812038i \(0.301642\pi\)
−0.583604 + 0.812038i \(0.698358\pi\)
\(728\) 0 0
\(729\) 1.09174 + 26.9779i 0.0404349 + 0.999182i
\(730\) −0.258409 0.447578i −0.00956415 0.0165656i
\(731\) 0.0520618 0.0901738i 0.00192558 0.00333520i
\(732\) −18.5359 + 71.0903i −0.685106 + 2.62757i
\(733\) −22.6647 + 13.0854i −0.837138 + 0.483322i −0.856290 0.516495i \(-0.827237\pi\)
0.0191524 + 0.999817i \(0.493903\pi\)
\(734\) −81.1776 −2.99632
\(735\) 0 0
\(736\) −34.2267 −1.26161
\(737\) −3.88259 + 2.24161i −0.143017 + 0.0825709i
\(738\) −59.7881 + 0.806109i −2.20083 + 0.0296733i
\(739\) −20.1777 + 34.9489i −0.742250 + 1.28561i 0.209219 + 0.977869i \(0.432908\pi\)
−0.951469 + 0.307746i \(0.900425\pi\)
\(740\) −0.699378 1.21136i −0.0257096 0.0445304i
\(741\) 3.23397 + 11.7519i 0.118803 + 0.431716i
\(742\) 0 0
\(743\) 8.82565i 0.323782i −0.986809 0.161891i \(-0.948241\pi\)
0.986809 0.161891i \(-0.0517593\pi\)
\(744\) 35.7791 36.2647i 1.31173 1.32953i
\(745\) −15.3604 8.86834i −0.562762 0.324911i
\(746\) −40.9251 23.6281i −1.49838 0.865087i
\(747\) −1.74597 0.976890i −0.0638816 0.0357425i
\(748\) 8.46097i 0.309364i
\(749\) 0 0
\(750\) −3.89248 + 1.07116i −0.142133 + 0.0391133i
\(751\) −18.9165 32.7644i −0.690274 1.19559i −0.971748 0.236020i \(-0.924157\pi\)
0.281475 0.959569i \(-0.409176\pi\)
\(752\) −1.20850 + 2.09319i −0.0440695 + 0.0763307i
\(753\) −25.2685 6.58843i −0.920834 0.240096i
\(754\) −52.7422 + 30.4507i −1.92076 + 1.10895i
\(755\) 22.5007 0.818885
\(756\) 0 0
\(757\) −34.7636 −1.26351 −0.631753 0.775170i \(-0.717664\pi\)
−0.631753 + 0.775170i \(0.717664\pi\)
\(758\) −18.3127 + 10.5728i −0.665146 + 0.384022i
\(759\) 35.3296 + 9.21174i 1.28238 + 0.334365i
\(760\) −3.66689 + 6.35124i −0.133012 + 0.230384i
\(761\) −0.915074 1.58495i −0.0331714 0.0574545i 0.848963 0.528452i \(-0.177227\pi\)
−0.882135 + 0.470998i \(0.843894\pi\)
\(762\) 27.2303 7.49342i 0.986448 0.271458i
\(763\) 0 0
\(764\) 49.8649i 1.80405i
\(765\) −2.30897 1.29190i −0.0834809 0.0467086i
\(766\) −56.0686 32.3712i −2.02584 1.16962i
\(767\) −11.3790 6.56967i −0.410872 0.237217i
\(768\) 26.1122 26.4666i 0.942243 0.955032i
\(769\) 23.5601i 0.849598i 0.905288 + 0.424799i \(0.139655\pi\)
−0.905288 + 0.424799i \(0.860345\pi\)
\(770\) 0 0
\(771\) 7.31132 + 26.5685i 0.263311 + 0.956842i
\(772\) −0.691982 1.19855i −0.0249050 0.0431367i
\(773\) −24.0437 + 41.6448i −0.864790 + 1.49786i 0.00246461 + 0.999997i \(0.499215\pi\)
−0.867255 + 0.497864i \(0.834118\pi\)
\(774\) −0.825487 + 0.0111299i −0.0296715 + 0.000400054i
\(775\) −7.62645 + 4.40313i −0.273950 + 0.158165i
\(776\) 21.2828 0.764010
\(777\) 0 0
\(778\) 36.3198 1.30213
\(779\) 16.2606 9.38804i 0.582595 0.336361i
\(780\) 4.80789 18.4396i 0.172150 0.660244i
\(781\) 8.74525 15.1472i 0.312930 0.542010i
\(782\) −7.75294 13.4285i −0.277245 0.480202i
\(783\) 29.3431 30.5546i 1.04864 1.09193i
\(784\) 0 0
\(785\) 11.8920i 0.424443i
\(786\) 28.4327 + 28.0520i 1.01416 + 1.00058i
\(787\) 26.1234 + 15.0823i 0.931197 + 0.537627i 0.887190 0.461404i \(-0.152654\pi\)
0.0440072 + 0.999031i \(0.485988\pi\)
\(788\) −34.6995 20.0338i −1.23612 0.713673i
\(789\) −10.2383 10.1012i −0.364492 0.359611i
\(790\) 7.31189i 0.260145i
\(791\) 0 0
\(792\) −24.0589 + 14.3263i −0.854897 + 0.509064i
\(793\) 19.7992 + 34.2932i 0.703090 + 1.21779i
\(794\) 22.0156 38.1321i 0.781303 1.35326i
\(795\) 3.26375 12.5174i 0.115753 0.443946i
\(796\) 55.2309 31.8876i 1.95761 1.13022i
\(797\) 3.60475 0.127687 0.0638435 0.997960i \(-0.479664\pi\)
0.0638435 + 0.997960i \(0.479664\pi\)
\(798\) 0 0
\(799\) 2.31925 0.0820491
\(800\) −3.92965 + 2.26878i −0.138934 + 0.0802137i
\(801\) −0.0353705 2.62339i −0.00124976 0.0926928i
\(802\) −24.2401 + 41.9851i −0.855948 + 1.48255i
\(803\) 0.309820 + 0.536624i 0.0109333 + 0.0189371i
\(804\) −2.53089 9.19699i −0.0892578 0.324353i
\(805\) 0 0
\(806\) 65.7836i 2.31713i
\(807\) 21.1507 21.4378i 0.744539 0.754645i
\(808\) −30.7335 17.7440i −1.08120 0.624232i
\(809\) 18.7612 + 10.8318i 0.659607 + 0.380824i 0.792127 0.610356i \(-0.208974\pi\)
−0.132520 + 0.991180i \(0.542307\pi\)
\(810\) 0.565574 + 20.9701i 0.0198723 + 0.736816i
\(811\) 27.6526i 0.971015i 0.874232 + 0.485508i \(0.161365\pi\)
−0.874232 + 0.485508i \(0.838635\pi\)
\(812\) 0 0
\(813\) 17.0196 4.68358i 0.596904 0.164260i
\(814\) 1.32704 + 2.29850i 0.0465126 + 0.0805623i
\(815\) 4.26159 7.38130i 0.149277 0.258556i
\(816\) 1.35858 + 0.354231i 0.0475597 + 0.0124006i
\(817\) 0.224508 0.129620i 0.00785453 0.00453481i
\(818\) −67.1957 −2.34944
\(819\) 0 0
\(820\) −29.3549 −1.02512
\(821\) −12.2722 + 7.08534i −0.428302 + 0.247280i −0.698623 0.715490i \(-0.746203\pi\)
0.270321 + 0.962770i \(0.412870\pi\)
\(822\) 49.2189 + 12.8332i 1.71670 + 0.447609i
\(823\) −11.6538 + 20.1850i −0.406227 + 0.703605i −0.994463 0.105084i \(-0.966489\pi\)
0.588237 + 0.808689i \(0.299822\pi\)
\(824\) −1.67528 2.90167i −0.0583611 0.101084i
\(825\) 4.66689 1.28427i 0.162480 0.0447125i
\(826\) 0 0
\(827\) 32.0877i 1.11580i 0.829908 + 0.557900i \(0.188393\pi\)
−0.829908 + 0.557900i \(0.811607\pi\)
\(828\) −37.9311 + 67.7932i −1.31820 + 2.35598i
\(829\) −25.9947 15.0080i −0.902833 0.521251i −0.0247149 0.999695i \(-0.507868\pi\)
−0.878118 + 0.478444i \(0.841201\pi\)
\(830\) −1.34618 0.777218i −0.0467266 0.0269776i
\(831\) −11.6298 + 11.7877i −0.403434 + 0.408910i
\(832\) 39.7873i 1.37938i
\(833\) 0 0
\(834\) −1.05843 3.84621i −0.0366503 0.133183i
\(835\) 1.78462 + 3.09105i 0.0617592 + 0.106970i
\(836\) 10.5327 18.2432i 0.364282 0.630956i
\(837\) 12.7346 + 43.9510i 0.440172 + 1.51917i
\(838\) −6.55031 + 3.78182i −0.226277 + 0.130641i
\(839\) 28.6277 0.988337 0.494168 0.869366i \(-0.335473\pi\)
0.494168 + 0.869366i \(0.335473\pi\)
\(840\) 0 0
\(841\) −37.4666 −1.29195
\(842\) 56.3835 32.5530i 1.94310 1.12185i
\(843\) 5.21074 19.9846i 0.179467 0.688307i
\(844\) 11.9839 20.7567i 0.412503 0.714476i
\(845\) 1.36443 + 2.36326i 0.0469378 + 0.0812986i
\(846\) −9.40813 15.7995i −0.323458 0.543200i
\(847\) 0 0
\(848\) 6.86441i 0.235725i
\(849\) −24.6217 24.2920i −0.845015 0.833698i
\(850\) −1.78027 1.02784i −0.0610627 0.0352545i
\(851\) 2.66165 + 1.53670i 0.0912401 + 0.0526775i
\(852\) 26.4912 + 26.1364i 0.907573 + 0.895419i
\(853\) 17.3563i 0.594269i 0.954836 + 0.297135i \(0.0960310\pi\)
−0.954836 + 0.297135i \(0.903969\pi\)
\(854\) 0 0
\(855\) −3.37028 5.65988i −0.115261 0.193564i
\(856\) −21.3371 36.9569i −0.729287 1.26316i
\(857\) −23.2842 + 40.3294i −0.795372 + 1.37763i 0.127230 + 0.991873i \(0.459391\pi\)
−0.922602 + 0.385752i \(0.873942\pi\)
\(858\) −9.12275 + 34.9883i −0.311446 + 1.19448i
\(859\) −31.5359 + 18.2072i −1.07599 + 0.621223i −0.929812 0.368035i \(-0.880031\pi\)
−0.146178 + 0.989258i \(0.546697\pi\)
\(860\) −0.405299 −0.0138206
\(861\) 0 0
\(862\) 89.3002 3.04158
\(863\) 2.05942 1.18901i 0.0701034 0.0404742i −0.464539 0.885553i \(-0.653780\pi\)
0.534642 + 0.845079i \(0.320446\pi\)
\(864\) 6.56170 + 22.6464i 0.223234 + 0.770448i
\(865\) 4.27114 7.39784i 0.145223 0.251534i
\(866\) 33.7430 + 58.4447i 1.14664 + 1.98603i
\(867\) 7.45499 + 27.0906i 0.253185 + 0.920045i
\(868\) 0 0
\(869\) 8.76660i 0.297387i
\(870\) 23.1162 23.4300i 0.783713 0.794351i
\(871\) −4.45259 2.57070i −0.150870 0.0871049i
\(872\) 0.0527802 + 0.0304727i 0.00178736 + 0.00103193i
\(873\) −9.33426 + 16.6829i −0.315917 + 0.564629i
\(874\) 38.6054i 1.30585i
\(875\) 0 0
\(876\) −1.27114 + 0.349803i −0.0429480 + 0.0118187i
\(877\) 11.0465 + 19.1332i 0.373015 + 0.646082i 0.990028 0.140872i \(-0.0449905\pi\)
−0.617012 + 0.786953i \(0.711657\pi\)
\(878\) 17.7901 30.8134i 0.600387 1.03990i
\(879\) 5.04519 + 1.31547i 0.170170 + 0.0443697i
\(880\) −2.22442 + 1.28427i −0.0749852 + 0.0432927i
\(881\) −33.5633 −1.13078 −0.565388 0.824825i \(-0.691273\pi\)
−0.565388 + 0.824825i \(0.691273\pi\)
\(882\) 0 0
\(883\) −3.74124 −0.125903 −0.0629514 0.998017i \(-0.520051\pi\)
−0.0629514 + 0.998017i \(0.520051\pi\)
\(884\) 8.40314 4.85156i 0.282628 0.163176i
\(885\) 6.87136 + 1.79162i 0.230978 + 0.0602246i
\(886\) 2.66151 4.60988i 0.0894153 0.154872i
\(887\) −13.7685 23.8478i −0.462302 0.800730i 0.536773 0.843726i \(-0.319643\pi\)
−0.999075 + 0.0429963i \(0.986310\pi\)
\(888\) −2.27262 + 0.625396i −0.0762641 + 0.0209869i
\(889\) 0 0
\(890\) 2.03844i 0.0683286i
\(891\) −0.678096 25.1422i −0.0227171 0.842295i
\(892\) 4.29877 + 2.48189i 0.143933 + 0.0831000i
\(893\) 5.00068 + 2.88714i 0.167341 + 0.0966146i
\(894\) −50.2907 + 50.9733i −1.68197 + 1.70480i
\(895\) 1.22952i 0.0410983i
\(896\) 0 0
\(897\) 11.1094 + 40.3702i 0.370931 + 1.34792i
\(898\) −12.0171 20.8142i −0.401015 0.694579i
\(899\) 35.8974 62.1762i 1.19725 2.07369i
\(900\) 0.138843 + 10.2978i 0.00462811 + 0.343261i
\(901\) 5.70432 3.29339i 0.190038 0.109719i
\(902\) 55.6995 1.85459
\(903\) 0 0
\(904\) 24.1487 0.803174
\(905\) 13.3364 7.69975i 0.443316 0.255949i
\(906\) 22.9189 87.9005i 0.761431 2.92030i
\(907\) −19.3650 + 33.5412i −0.643005 + 1.11372i 0.341754 + 0.939790i \(0.388979\pi\)
−0.984758 + 0.173928i \(0.944354\pi\)
\(908\) 1.83168 + 3.17256i 0.0607864 + 0.105285i
\(909\) 27.3880 16.3087i 0.908404 0.540926i
\(910\) 0 0
\(911\) 23.3967i 0.775167i 0.921835 + 0.387583i \(0.126690\pi\)
−0.921835 + 0.387583i \(0.873310\pi\)
\(912\) 2.48834 + 2.45502i 0.0823973 + 0.0812938i
\(913\) 1.61401 + 0.931847i 0.0534158 + 0.0308396i
\(914\) −66.2043 38.2231i −2.18984 1.26431i
\(915\) −15.2343 15.0303i −0.503629 0.496885i
\(916\) 26.0854i 0.861886i
\(917\) 0 0
\(918\) −7.39876 + 7.70422i −0.244195 + 0.254277i
\(919\) 4.32329 + 7.48816i 0.142612 + 0.247012i 0.928480 0.371383i \(-0.121116\pi\)
−0.785867 + 0.618395i \(0.787783\pi\)
\(920\) −12.5965 + 21.8179i −0.415296 + 0.719313i
\(921\) 8.90578 34.1561i 0.293455 1.12548i
\(922\) 33.4434 19.3086i 1.10140 0.635894i
\(923\) 20.0583 0.660225
\(924\) 0 0
\(925\) 0.407453 0.0133970
\(926\) −73.8532 + 42.6392i −2.42697 + 1.40121i
\(927\) 3.00926 0.0405732i 0.0988370 0.00133260i
\(928\) 18.4967 32.0373i 0.607185 1.05168i
\(929\) 6.27980 + 10.8769i 0.206034 + 0.356861i 0.950462 0.310842i \(-0.100611\pi\)
−0.744428 + 0.667703i \(0.767278\pi\)
\(930\) 9.43292 + 34.2782i 0.309318 + 1.12403i
\(931\) 0 0
\(932\) 61.7914i 2.02405i
\(933\) 33.1751 33.6254i 1.08610 1.10085i
\(934\) 82.9840 + 47.9108i 2.71532 + 1.56769i
\(935\) 2.13445 + 1.23233i 0.0698041 + 0.0403014i
\(936\) −28.0239 15.6797i −0.915990 0.512508i
\(937\) 11.3901i 0.372097i 0.982541 + 0.186048i \(0.0595681\pi\)
−0.982541 + 0.186048i \(0.940432\pi\)
\(938\) 0 0
\(939\) −1.05327 + 0.289846i −0.0343720 + 0.00945875i
\(940\) −4.51381 7.81815i −0.147224 0.255000i
\(941\) −21.0434 + 36.4482i −0.685994 + 1.18818i 0.287129 + 0.957892i \(0.407299\pi\)
−0.973123 + 0.230285i \(0.926034\pi\)
\(942\) 46.4568 + 12.1130i 1.51365 + 0.394664i
\(943\) 55.8584 32.2499i 1.81900 1.05020i
\(944\) −3.76818 −0.122644
\(945\) 0 0
\(946\) 0.769036 0.0250035
\(947\) −12.6504 + 7.30370i −0.411082 + 0.237338i −0.691255 0.722611i \(-0.742942\pi\)
0.280172 + 0.959950i \(0.409608\pi\)
\(948\) 18.0491 + 4.70607i 0.586207 + 0.152846i
\(949\) −0.355304 + 0.615405i −0.0115337 + 0.0199769i
\(950\) −2.55903 4.43237i −0.0830259 0.143805i
\(951\) −42.4679 + 11.6866i −1.37711 + 0.378965i
\(952\) 0 0
\(953\) 28.8817i 0.935570i −0.883842 0.467785i \(-0.845052\pi\)
0.883842 0.467785i \(-0.154948\pi\)
\(954\) −45.5756 25.5001i −1.47556 0.825596i
\(955\) 12.5795 + 7.26275i 0.407062 + 0.235017i
\(956\) 88.8379 + 51.2906i 2.87322 + 1.65886i
\(957\) −27.7152 + 28.0914i −0.895906 + 0.908066i
\(958\) 38.5032i 1.24398i
\(959\) 0 0
\(960\) 5.70523 + 20.7322i 0.184136 + 0.669128i
\(961\) 23.2751 + 40.3137i 0.750811 + 1.30044i
\(962\) −1.52186 + 2.63594i −0.0490667 + 0.0849860i
\(963\) 38.3273 0.516758i 1.23508 0.0166523i
\(964\) −15.5772 + 8.99352i −0.501709 + 0.289662i
\(965\) 0.403145 0.0129777
\(966\) 0 0
\(967\) 0.409782 0.0131777 0.00658885 0.999978i \(-0.497903\pi\)
0.00658885 + 0.999978i \(0.497903\pi\)
\(968\) −9.22774 + 5.32764i −0.296591 + 0.171237i
\(969\) 0.846268 3.24567i 0.0271860 0.104266i
\(970\) −7.42638 + 12.8629i −0.238447 + 0.413002i
\(971\) −2.64865 4.58759i −0.0849991 0.147223i 0.820392 0.571802i \(-0.193755\pi\)
−0.905391 + 0.424579i \(0.860422\pi\)
\(972\) 52.1279 + 12.1007i 1.67200 + 0.388129i
\(973\) 0 0
\(974\) 4.73634i 0.151762i
\(975\) 3.95151 + 3.89859i 0.126550 + 0.124855i
\(976\) 9.83482 + 5.67814i 0.314805 + 0.181753i
\(977\) −24.1247 13.9284i −0.771818 0.445610i 0.0617045 0.998094i \(-0.480346\pi\)
−0.833523 + 0.552485i \(0.813680\pi\)
\(978\) −24.4947 24.1667i −0.783255 0.772765i
\(979\) 2.44399i 0.0781102i
\(980\) 0 0
\(981\) −0.0470348 + 0.0280077i −0.00150171 + 0.000894219i
\(982\) −6.96799 12.0689i −0.222357 0.385134i
\(983\) −0.330614 + 0.572640i −0.0105449 + 0.0182644i −0.871250 0.490840i \(-0.836690\pi\)
0.860705 + 0.509104i \(0.170023\pi\)
\(984\) −12.4806 + 47.8667i −0.397868 + 1.52594i
\(985\) 10.1079 5.83578i 0.322063 0.185943i
\(986\) 16.7593 0.533725
\(987\) 0 0
\(988\) 24.1581 0.768571
\(989\) 0.771231 0.445270i 0.0245237 0.0141588i
\(990\) −0.263449 19.5397i −0.00837295 0.621011i
\(991\) 25.3374 43.8856i 0.804868 1.39407i −0.111513 0.993763i \(-0.535570\pi\)
0.916380 0.400309i \(-0.131097\pi\)
\(992\) 19.9795 + 34.6055i 0.634350 + 1.09873i
\(993\) −5.28182 19.1935i −0.167614 0.609089i
\(994\) 0 0
\(995\) 18.5775i 0.588946i
\(996\) −2.78496 + 2.82276i −0.0882447 + 0.0894425i
\(997\) −5.21879 3.01307i −0.165281 0.0954249i 0.415078 0.909786i \(-0.363754\pi\)
−0.580359 + 0.814361i \(0.697088\pi\)
\(998\) −17.1239 9.88647i −0.542047 0.312951i
\(999\) 0.506503 2.05571i 0.0160250 0.0650398i
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 735.2.s.l.521.4 8
3.2 odd 2 735.2.s.k.521.1 8
7.2 even 3 105.2.s.c.26.1 8
7.3 odd 6 735.2.b.c.146.8 8
7.4 even 3 735.2.b.d.146.8 8
7.5 odd 6 735.2.s.k.656.1 8
7.6 odd 2 105.2.s.d.101.4 yes 8
21.2 odd 6 105.2.s.d.26.4 yes 8
21.5 even 6 inner 735.2.s.l.656.4 8
21.11 odd 6 735.2.b.c.146.1 8
21.17 even 6 735.2.b.d.146.1 8
21.20 even 2 105.2.s.c.101.1 yes 8
35.2 odd 12 525.2.q.f.299.8 16
35.9 even 6 525.2.t.g.26.4 8
35.13 even 4 525.2.q.e.374.1 16
35.23 odd 12 525.2.q.f.299.1 16
35.27 even 4 525.2.q.e.374.8 16
35.34 odd 2 525.2.t.f.101.1 8
105.2 even 12 525.2.q.e.299.1 16
105.23 even 12 525.2.q.e.299.8 16
105.44 odd 6 525.2.t.f.26.1 8
105.62 odd 4 525.2.q.f.374.1 16
105.83 odd 4 525.2.q.f.374.8 16
105.104 even 2 525.2.t.g.101.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.s.c.26.1 8 7.2 even 3
105.2.s.c.101.1 yes 8 21.20 even 2
105.2.s.d.26.4 yes 8 21.2 odd 6
105.2.s.d.101.4 yes 8 7.6 odd 2
525.2.q.e.299.1 16 105.2 even 12
525.2.q.e.299.8 16 105.23 even 12
525.2.q.e.374.1 16 35.13 even 4
525.2.q.e.374.8 16 35.27 even 4
525.2.q.f.299.1 16 35.23 odd 12
525.2.q.f.299.8 16 35.2 odd 12
525.2.q.f.374.1 16 105.62 odd 4
525.2.q.f.374.8 16 105.83 odd 4
525.2.t.f.26.1 8 105.44 odd 6
525.2.t.f.101.1 8 35.34 odd 2
525.2.t.g.26.4 8 35.9 even 6
525.2.t.g.101.4 8 105.104 even 2
735.2.b.c.146.1 8 21.11 odd 6
735.2.b.c.146.8 8 7.3 odd 6
735.2.b.d.146.1 8 21.17 even 6
735.2.b.d.146.8 8 7.4 even 3
735.2.s.k.521.1 8 3.2 odd 2
735.2.s.k.656.1 8 7.5 odd 6
735.2.s.l.521.4 8 1.1 even 1 trivial
735.2.s.l.656.4 8 21.5 even 6 inner