Properties

Label 735.2.s.l.656.4
Level $735$
Weight $2$
Character 735.656
Analytic conductor $5.869$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 656.4
Root \(2.33086i\) of defining polynomial
Character \(\chi\) \(=\) 735.656
Dual form 735.2.s.l.521.4

$q$-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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

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 0.996912 0.0785324i \(-0.0250234\pi\)
0.430445 + 0.902617i \(0.358357\pi\)
\(3\) 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 −0.818318 0.574766i \(-0.805093\pi\)
0.0886035 + 0.996067i \(0.471760\pi\)
\(12\) 4.17602 + 4.23270i 1.20551 + 1.22188i
\(13\) 3.20486i 0.888869i 0.895811 + 0.444434i \(0.146595\pi\)
−0.895811 + 0.444434i \(0.853405\pi\)
\(14\) 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 0.807583 0.589754i \(-0.200775\pi\)
−0.914533 + 0.404510i \(0.867442\pi\)
\(18\) 6.99195 + 0.0942709i 1.64802 + 0.0222199i
\(19\) −1.90160 1.09789i −0.436257 0.251873i 0.265751 0.964042i \(-0.414380\pi\)
−0.702009 + 0.712168i \(0.747713\pi\)
\(20\) 3.43292 0.767625
\(21\) 0 0
\(22\) −6.51381 −1.38875
\(23\) −6.53240 3.77148i −1.36210 0.786408i −0.372196 0.928154i \(-0.621395\pi\)
−0.989903 + 0.141746i \(0.954728\pi\)
\(24\) 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 \(0.273316\pi\)
−0.653462 + 0.756959i \(0.726684\pi\)
\(30\) 2.87389 2.83540i 0.524698 0.517672i
\(31\) 7.62645 4.40313i 1.36975 0.790826i 0.378855 0.925456i \(-0.376318\pi\)
0.990896 + 0.134630i \(0.0429847\pi\)
\(32\) 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 −0.882286 0.470714i \(-0.843996\pi\)
0.848793 + 0.528725i \(0.177330\pi\)
\(38\) −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 −0.945844 0.324621i \(-0.894763\pi\)
0.754052 + 0.656815i \(0.228097\pi\)
\(48\) −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 −0.873432 0.486946i \(-0.838111\pi\)
−0.0150081 + 0.999887i \(0.504777\pi\)
\(54\) 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 0.968053 0.250745i \(-0.0806755\pi\)
−0.701178 + 0.712986i \(0.747342\pi\)
\(60\) 5.75363 1.50019i 0.742791 0.193673i
\(61\) −10.7004 6.17786i −1.37004 0.790994i −0.379109 0.925352i \(-0.623769\pi\)
−0.990933 + 0.134358i \(0.957103\pi\)
\(62\) 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 0.910855 0.412727i \(-0.135424\pi\)
−0.812860 + 0.582460i \(0.802090\pi\)
\(68\) 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 \(-0.878883\pi\)
0.928479 0.371385i \(-0.121117\pi\)
\(72\) 4.89248 + 8.74419i 0.576584 + 1.03051i
\(73\) −0.192022 + 0.110864i −0.0224745 + 0.0129757i −0.511195 0.859465i \(-0.670797\pi\)
0.488721 + 0.872440i \(0.337464\pi\)
\(74\) −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 −0.764199 0.644980i \(-0.776866\pi\)
0.940669 + 0.339326i \(0.110199\pi\)
\(80\) 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 −0.888270 0.459322i \(-0.848092\pi\)
0.841919 + 0.539603i \(0.181426\pi\)
\(90\) 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 \(-0.895140\pi\)
0.946228 0.323500i \(-0.104860\pi\)
\(98\) 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 0.999443 + 0.0333808i \(0.0106274\pi\)
−0.470813 + 0.882233i \(0.656039\pi\)
\(102\) −0.898330 3.44535i −0.0889479 0.341140i
\(103\) 0.868777 + 0.501589i 0.0856031 + 0.0494230i 0.542191 0.840256i \(-0.317595\pi\)
−0.456587 + 0.889679i \(0.650928\pi\)
\(104\) −10.7041 −1.04962
\(105\) 0 0
\(106\) −17.4081 −1.69083
\(107\) 11.0651 + 6.38846i 1.06971 + 0.617596i 0.928101 0.372328i \(-0.121440\pi\)
0.141606 + 0.989923i \(0.454774\pi\)
\(108\) 17.1333 + 4.96429i 1.64865 + 0.477689i
\(109\) −0.00912370 0.0158027i −0.000873892 0.00151363i 0.865588 0.500757i \(-0.166945\pi\)
−0.866462 + 0.499243i \(0.833612\pi\)
\(110\) −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 \(-0.889545\pi\)
0.940395 0.340083i \(-0.110455\pi\)
\(114\) −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 −0.564864 0.825184i \(-0.691071\pi\)
0.997062 + 0.0765948i \(0.0244048\pi\)
\(132\) −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 0.0446900 0.999001i \(-0.485770\pi\)
0.887505 + 0.460798i \(0.152437\pi\)
\(138\) −21.3874 21.6777i −1.82061 1.84532i
\(139\) 0.988113i 0.0838106i 0.999122 + 0.0419053i \(0.0133428\pi\)
−0.999122 + 0.0419053i \(0.986657\pi\)
\(140\) 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 −0.285616 0.958344i \(-0.592198\pi\)
−0.972758 + 0.231821i \(0.925532\pi\)
\(150\) −1.01859 3.90656i −0.0831672 0.318970i
\(151\) 11.2504 + 19.4862i 0.915542 + 1.58576i 0.806106 + 0.591771i \(0.201571\pi\)
0.109435 + 0.993994i \(0.465096\pi\)
\(152\) 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 −0.0291509 0.999575i \(-0.509280\pi\)
0.851082 + 0.525033i \(0.175947\pi\)
\(158\) 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 −0.983252 0.182249i \(-0.941662\pi\)
0.649459 + 0.760397i \(0.274996\pi\)
\(164\) −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 −0.981457 0.191680i \(-0.938606\pi\)
0.656728 + 0.754127i \(0.271940\pi\)
\(174\) −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 −0.539265 0.842136i \(-0.681298\pi\)
0.459679 + 0.888085i \(0.347965\pi\)
\(180\) 8.98760 5.02867i 0.669897 0.374815i
\(181\) 15.3995i 1.14464i 0.820032 + 0.572318i \(0.193956\pi\)
−0.820032 + 0.572318i \(0.806044\pi\)
\(182\) 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 0.880501 0.474044i \(-0.157206\pi\)
0.0297166 + 0.999558i \(0.490540\pi\)
\(192\) 20.8072 5.42521i 1.50163 0.391531i
\(193\) 0.201572 + 0.349134i 0.0145095 + 0.0251312i 0.873189 0.487382i \(-0.162048\pi\)
−0.858679 + 0.512513i \(0.828715\pi\)
\(194\) 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 \(0.136492\pi\)
−0.909464 + 0.415782i \(0.863508\pi\)
\(198\) −17.0536 + 9.54168i −1.21194 + 0.678097i
\(199\) 16.0886 9.28875i 1.14049 0.658462i 0.193938 0.981014i \(-0.437874\pi\)
0.946552 + 0.322552i \(0.104541\pi\)
\(200\) 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 \(-0.984583\pi\)
0.998827 0.0484135i \(-0.0154165\pi\)
\(224\) 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 0.847775 0.530356i \(-0.177942\pi\)
−0.883189 + 0.469017i \(0.844608\pi\)
\(228\) −3.29408 12.6337i −0.218156 0.836688i
\(229\) 6.58058 + 3.79930i 0.434857 + 0.251065i 0.701414 0.712755i \(-0.252553\pi\)
−0.266557 + 0.963819i \(0.585886\pi\)
\(230\) −17.5816 −1.15930
\(231\) 0 0
\(232\) −27.2296 −1.78771
\(233\) −15.5882 8.99983i −1.02121 0.589598i −0.106759 0.994285i \(-0.534047\pi\)
−0.914455 + 0.404687i \(0.867381\pi\)
\(234\) −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 \(-0.582698\pi\)
0.256892 0.966440i \(-0.417302\pi\)
\(240\) 1.11806 + 1.13324i 0.0721706 + 0.0731502i
\(241\) −4.53760 + 2.61978i −0.292292 + 0.168755i −0.638975 0.769227i \(-0.720641\pi\)
0.346683 + 0.937982i \(0.387308\pi\)
\(242\) −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 −0.503785 0.863829i \(-0.668060\pi\)
0.999990 + 0.00437591i \(0.00139290\pi\)
\(258\) −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 −0.705052 0.709156i \(-0.749076\pi\)
0.261621 + 0.965171i \(0.415743\pi\)
\(264\) −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 0.999385 + 0.0350578i \(0.0111615\pi\)
−0.469332 + 0.883022i \(0.655505\pi\)
\(270\) 3.37062 11.6330i 0.205129 0.707965i
\(271\) 8.82614 + 5.09577i 0.536150 + 0.309546i 0.743517 0.668717i \(-0.233156\pi\)
−0.207367 + 0.978263i \(0.566490\pi\)
\(272\) 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 0.685930 0.727667i \(-0.259395\pi\)
−0.973143 + 0.230199i \(0.926062\pi\)
\(278\) −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 \(0.115744\pi\)
−0.934616 + 0.355660i \(0.884256\pi\)
\(282\) −7.55753 + 7.45632i −0.450044 + 0.444017i
\(283\) −17.2940 + 9.98469i −1.02802 + 0.593528i −0.916417 0.400225i \(-0.868932\pi\)
−0.111604 + 0.993753i \(0.535599\pi\)
\(284\) 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 \(0.197556\pi\)
−0.813507 + 0.581556i \(0.802444\pi\)
\(308\) 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 0.935789 + 0.352562i \(0.114689\pi\)
−0.162567 + 0.986697i \(0.551977\pi\)
\(312\) −17.9402 + 4.67767i −1.01566 + 0.264821i
\(313\) −0.546210 0.315354i −0.0308736 0.0178249i 0.484484 0.874800i \(-0.339007\pi\)
−0.515357 + 0.856975i \(0.672341\pi\)
\(314\) 27.7186 1.56425
\(315\) 0 0
\(316\) 10.7690 0.605806
\(317\) −22.0233 12.7151i −1.23695 0.714153i −0.268480 0.963285i \(-0.586521\pi\)
−0.968470 + 0.249132i \(0.919855\pi\)
\(318\) −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 −0.979621 0.200855i \(-0.935628\pi\)
0.663756 + 0.747949i \(0.268961\pi\)
\(332\) −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 −0.0198929 0.999802i \(-0.506333\pi\)
0.855908 + 0.517129i \(0.172999\pi\)
\(348\) −34.5079 + 34.0458i −1.84982 + 1.82505i
\(349\) 6.15422i 0.329428i 0.986341 + 0.164714i \(0.0526701\pi\)
−0.986341 + 0.164714i \(0.947330\pi\)
\(350\) 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 −0.929494 0.368836i \(-0.879756\pi\)
0.145326 0.989384i \(-0.453577\pi\)
\(354\) 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 0.989154 + 0.146881i \(0.0469233\pi\)
0.621779 + 0.783192i \(0.286410\pi\)
\(360\) 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 −0.578788 + 0.815478i \(0.696474\pi\)
−0.995619 + 0.0935065i \(0.970192\pi\)
\(368\) 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 0.474702 + 0.880146i \(0.342556\pi\)
−0.999580 + 0.0289688i \(0.990778\pi\)
\(374\) 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 0.255339 + 0.966851i \(0.417813\pi\)
−0.964988 + 0.262295i \(0.915521\pi\)
\(384\) 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 −0.117236 0.993104i \(-0.537403\pi\)
0.801436 + 0.598081i \(0.204070\pi\)
\(390\) 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 0.850784 0.525515i \(-0.176127\pi\)
−0.0297174 + 0.999558i \(0.509461\pi\)
\(398\) 43.3016 2.17051
\(399\) 0 0
\(400\) 0.919111 0.0459555
\(401\) −18.0127 10.3996i −0.899511 0.519333i −0.0224695 0.999748i \(-0.507153\pi\)
−0.877042 + 0.480415i \(0.840486\pi\)
\(402\) 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 −0.967966 0.251080i \(-0.919214\pi\)
−0.266542 + 0.963823i \(0.585881\pi\)
\(410\) −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 0.606351 0.795197i \(-0.292633\pi\)
0.991836 0.127516i \(-0.0407006\pi\)
\(432\) 1.14254 + 4.63716i 0.0549705 + 0.223105i
\(433\) 28.9533i 1.39140i −0.718330 0.695702i \(-0.755093\pi\)
0.718330 0.695702i \(-0.244907\pi\)
\(434\) 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 0.781117 0.624384i \(-0.214650\pi\)
−0.150174 + 0.988660i \(0.547983\pi\)
\(440\) −9.33379 −0.444971
\(441\) 0 0
\(442\) 6.58816 0.313367
\(443\) 1.97776 + 1.14186i 0.0939660 + 0.0542513i 0.546247 0.837624i \(-0.316056\pi\)
−0.452281 + 0.891876i \(0.649389\pi\)
\(444\) −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 \(0.0782331\pi\)
−0.969949 + 0.243310i \(0.921767\pi\)
\(450\) −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 0.172033 + 0.985091i \(0.444966\pi\)
−0.939131 + 0.343560i \(0.888367\pi\)
\(458\) 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 0.208275 0.978070i \(-0.433215\pi\)
0.742896 0.669406i \(-0.233451\pi\)
\(468\) −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 0.613297 0.789852i \(-0.289843\pi\)
−0.990681 + 0.136205i \(0.956509\pi\)
\(480\) −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 0.888127 0.459598i \(-0.152007\pi\)
−0.842087 + 0.539341i \(0.818673\pi\)
\(488\) 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 \(0.0430751\pi\)
−0.990858 + 0.134912i \(0.956925\pi\)
\(492\) −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 −0.945209 0.326465i \(-0.894143\pi\)
0.755331 + 0.655343i \(0.227476\pi\)
\(500\) −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 −0.687468 0.726214i \(-0.741278\pi\)
0.972654 + 0.232258i \(0.0746113\pi\)
\(510\) −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 0.623925 0.781485i \(-0.285537\pi\)
−0.988748 + 0.149592i \(0.952204\pi\)
\(522\) −0.768563 + 57.0033i −0.0336391 + 2.49497i
\(523\) −31.4934 18.1827i −1.37711 0.795075i −0.385300 0.922791i \(-0.625902\pi\)
−0.991811 + 0.127716i \(0.959235\pi\)
\(524\) 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 −0.903896 0.427751i \(-0.859306\pi\)
0.822392 + 0.568922i \(0.192639\pi\)
\(542\) 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 −0.667820 0.744322i \(-0.732773\pi\)
0.310692 + 0.950511i \(0.399439\pi\)
\(558\) 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 0.870938 0.491393i \(-0.163512\pi\)
−0.861028 + 0.508558i \(0.830179\pi\)
\(564\) −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 0.608588 0.793486i \(-0.291736\pi\)
−0.382885 + 0.923796i \(0.625069\pi\)
\(570\) −8.57796 + 2.23659i −0.359291 + 0.0936805i
\(571\) −5.31121 9.19928i −0.222267 0.384978i 0.733229 0.679982i \(-0.238012\pi\)
−0.955496 + 0.295004i \(0.904679\pi\)
\(572\) 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 −0.445568 0.895248i \(-0.646998\pi\)
0.552523 + 0.833497i \(0.313665\pi\)
\(578\) 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 −0.367088 0.930186i \(-0.619645\pi\)
0.989109 0.147185i \(-0.0470213\pi\)
\(594\) −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 −0.622971 0.782245i \(-0.714075\pi\)
0.365959 + 0.930631i \(0.380741\pi\)
\(600\) 4.11806 4.06291i 0.168119 0.165868i
\(601\) 45.3302i 1.84906i 0.381110 + 0.924530i \(0.375542\pi\)
−0.381110 + 0.924530i \(0.624458\pi\)
\(602\) 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 −0.0327925 0.999462i \(-0.510440\pi\)
−0.881956 + 0.471332i \(0.843773\pi\)
\(608\) −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 −0.999753 0.0222040i \(-0.992932\pi\)
0.480648 0.876914i \(-0.340402\pi\)
\(614\) −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 \(0.0572213\pi\)
−0.983886 + 0.178800i \(0.942779\pi\)
\(618\) 2.84441 + 2.88302i 0.114419 + 0.115972i
\(619\) 26.4112 15.2485i 1.06156 0.612890i 0.135694 0.990751i \(-0.456673\pi\)
0.925863 + 0.377861i \(0.123340\pi\)
\(620\) 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 −0.614371 0.789017i \(-0.710590\pi\)
0.376123 + 0.926570i \(0.377257\pi\)
\(642\) 36.2277 + 36.7195i 1.42979 + 1.44920i
\(643\) 25.8907i 1.02103i −0.859869 0.510514i \(-0.829455\pi\)
0.859869 0.510514i \(-0.170545\pi\)
\(644\) 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 0.947652 0.319304i \(-0.103449\pi\)
−0.750351 + 0.661039i \(0.770116\pi\)
\(648\) 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 −0.354942 0.934888i \(-0.615500\pi\)
−0.987108 + 0.160055i \(0.948833\pi\)
\(654\) −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 \(0.113598\pi\)
−0.936991 + 0.349352i \(0.886402\pi\)
\(660\) −11.8287 + 11.6703i −0.460430 + 0.454264i
\(661\) 3.31012 1.91110i 0.128749 0.0743332i −0.434242 0.900796i \(-0.642984\pi\)
0.562991 + 0.826463i \(0.309650\pi\)
\(662\) −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 0.397672 + 0.917528i \(0.369818\pi\)
−0.993438 + 0.114370i \(0.963515\pi\)
\(678\) 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 −0.148937 0.988847i \(-0.547585\pi\)
0.781898 + 0.623407i \(0.214252\pi\)
\(684\) −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 0.750957 0.660351i \(-0.229593\pi\)
−0.196403 + 0.980523i \(0.562926\pi\)
\(692\) −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 \(0.135640\pi\)
−0.910574 + 0.413345i \(0.864360\pi\)
\(702\) 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 −0.746366 0.665536i \(-0.768203\pi\)
0.949554 + 0.313604i \(0.101536\pi\)
\(710\) −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 −0.580371 0.814352i \(-0.697093\pi\)
0.995435 + 0.0954404i \(0.0304259\pi\)
\(720\) 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 \(-0.698358\pi\)
0.583604 0.812038i \(-0.301642\pi\)
\(728\) 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 0.0191524 0.999817i \(-0.493903\pi\)
−0.856290 + 0.516495i \(0.827237\pi\)
\(734\) −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 −0.951469 0.307746i \(-0.900425\pi\)
0.209219 0.977869i \(-0.432908\pi\)
\(740\) −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 \(0.0517593\pi\)
−0.986809 + 0.161891i \(0.948241\pi\)
\(744\) 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 0.281475 + 0.959569i \(0.409176\pi\)
−0.971748 + 0.236020i \(0.924157\pi\)
\(752\) −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 −0.882135 0.470998i \(-0.843894\pi\)
0.848963 + 0.528452i \(0.177227\pi\)
\(762\) 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 \(-0.860345\pi\)
0.905288 0.424799i \(-0.139655\pi\)
\(770\) 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 −0.867255 0.497864i \(-0.834118\pi\)
0.00246461 0.999997i \(-0.499215\pi\)
\(774\) −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 0.0440072 0.999031i \(-0.485988\pi\)
0.887190 + 0.461404i \(0.152654\pi\)
\(788\) −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 −0.132520 0.991180i \(-0.542307\pi\)
0.792127 + 0.610356i \(0.208974\pi\)
\(810\) 0.565574 20.9701i 0.0198723 0.736816i
\(811\) 27.6526i 0.971015i −0.874232 0.485508i \(-0.838635\pi\)
0.874232 0.485508i \(-0.161365\pi\)
\(812\) 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 0.270321 0.962770i \(-0.412870\pi\)
−0.698623 + 0.715490i \(0.746203\pi\)
\(822\) 49.2189 12.8332i 1.71670 0.447609i
\(823\) −11.6538 20.1850i −0.406227 0.703605i 0.588237 0.808689i \(-0.299822\pi\)
−0.994463 + 0.105084i \(0.966489\pi\)
\(824\) −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 \(-0.811607\pi\)
0.829908 0.557900i \(-0.188393\pi\)
\(828\) −37.9311 67.7932i −1.31820 2.35598i
\(829\) −25.9947 + 15.0080i −0.902833 + 0.521251i −0.878118 0.478444i \(-0.841201\pi\)
−0.0247149 + 0.999695i \(0.507868\pi\)
\(830\) −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 \(-0.903969\pi\)
0.954836 0.297135i \(-0.0960310\pi\)
\(854\) 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 −0.922602 0.385752i \(-0.873942\pi\)
0.127230 0.991873i \(-0.459391\pi\)
\(858\) −9.12275 34.9883i −0.311446 1.19448i
\(859\) −31.5359 18.2072i −1.07599 0.621223i −0.146178 0.989258i \(-0.546697\pi\)
−0.929812 + 0.368035i \(0.880031\pi\)
\(860\) −0.405299 −0.0138206
\(861\) 0 0
\(862\) 89.3002 3.04158
\(863\) 2.05942 + 1.18901i 0.0701034 + 0.0404742i 0.534642 0.845079i \(-0.320446\pi\)
−0.464539 + 0.885553i \(0.653780\pi\)
\(864\) 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 −0.617012 0.786953i \(-0.711657\pi\)
0.990028 + 0.140872i \(0.0449905\pi\)
\(878\) 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 −0.999075 0.0429963i \(-0.986310\pi\)
0.536773 + 0.843726i \(0.319643\pi\)
\(888\) −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 −0.984758 0.173928i \(-0.944354\pi\)
0.341754 0.939790i \(-0.388979\pi\)
\(908\) 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 \(-0.873310\pi\)
0.921835 0.387583i \(-0.126690\pi\)
\(912\) 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 −0.785867 0.618395i \(-0.787783\pi\)
0.928480 + 0.371383i \(0.121116\pi\)
\(920\) −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 −0.744428 0.667703i \(-0.767278\pi\)
0.950462 + 0.310842i \(0.100611\pi\)
\(930\) 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 \(-0.940432\pi\)
0.982541 0.186048i \(-0.0595681\pi\)
\(938\) 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 −0.973123 0.230285i \(-0.926034\pi\)
0.287129 0.957892i \(-0.407299\pi\)
\(942\) 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 0.280172 0.959950i \(-0.409608\pi\)
−0.691255 + 0.722611i \(0.742942\pi\)
\(948\) 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 \(0.154948\pi\)
−0.883842 + 0.467785i \(0.845052\pi\)
\(954\) −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 −0.905391 0.424579i \(-0.860422\pi\)
0.820392 + 0.571802i \(0.193755\pi\)
\(972\) 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 −0.833523 0.552485i \(-0.813680\pi\)
0.0617045 + 0.998094i \(0.480346\pi\)
\(978\) −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 0.860705 0.509104i \(-0.170023\pi\)
−0.871250 + 0.490840i \(0.836690\pi\)
\(984\) −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 0.916380 + 0.400309i \(0.131097\pi\)
−0.111513 + 0.993763i \(0.535570\pi\)
\(992\) 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 −0.580359 0.814361i \(-0.697088\pi\)
0.415078 + 0.909786i \(0.363754\pi\)
\(998\) −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.656.4 8
3.2 odd 2 735.2.s.k.656.1 8
7.2 even 3 735.2.b.d.146.1 8
7.3 odd 6 735.2.s.k.521.1 8
7.4 even 3 105.2.s.c.101.1 yes 8
7.5 odd 6 735.2.b.c.146.1 8
7.6 odd 2 105.2.s.d.26.4 yes 8
21.2 odd 6 735.2.b.c.146.8 8
21.5 even 6 735.2.b.d.146.8 8
21.11 odd 6 105.2.s.d.101.4 yes 8
21.17 even 6 inner 735.2.s.l.521.4 8
21.20 even 2 105.2.s.c.26.1 8
35.4 even 6 525.2.t.g.101.4 8
35.13 even 4 525.2.q.e.299.8 16
35.18 odd 12 525.2.q.f.374.8 16
35.27 even 4 525.2.q.e.299.1 16
35.32 odd 12 525.2.q.f.374.1 16
35.34 odd 2 525.2.t.f.26.1 8
105.32 even 12 525.2.q.e.374.8 16
105.53 even 12 525.2.q.e.374.1 16
105.62 odd 4 525.2.q.f.299.8 16
105.74 odd 6 525.2.t.f.101.1 8
105.83 odd 4 525.2.q.f.299.1 16
105.104 even 2 525.2.t.g.26.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.s.c.26.1 8 21.20 even 2
105.2.s.c.101.1 yes 8 7.4 even 3
105.2.s.d.26.4 yes 8 7.6 odd 2
105.2.s.d.101.4 yes 8 21.11 odd 6
525.2.q.e.299.1 16 35.27 even 4
525.2.q.e.299.8 16 35.13 even 4
525.2.q.e.374.1 16 105.53 even 12
525.2.q.e.374.8 16 105.32 even 12
525.2.q.f.299.1 16 105.83 odd 4
525.2.q.f.299.8 16 105.62 odd 4
525.2.q.f.374.1 16 35.32 odd 12
525.2.q.f.374.8 16 35.18 odd 12
525.2.t.f.26.1 8 35.34 odd 2
525.2.t.f.101.1 8 105.74 odd 6
525.2.t.g.26.4 8 105.104 even 2
525.2.t.g.101.4 8 35.4 even 6
735.2.b.c.146.1 8 7.5 odd 6
735.2.b.c.146.8 8 21.2 odd 6
735.2.b.d.146.1 8 7.2 even 3
735.2.b.d.146.8 8 21.5 even 6
735.2.s.k.521.1 8 7.3 odd 6
735.2.s.k.656.1 8 3.2 odd 2
735.2.s.l.521.4 8 21.17 even 6 inner
735.2.s.l.656.4 8 1.1 even 1 trivial