Properties

Label 845.2.f.f.408.20
Level 845845
Weight 22
Character 845.408
Analytic conductor 6.7476.747
Analytic rank 00
Dimension 7272
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [845,2,Mod(408,845)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(845, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("845.408");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 845=5132 845 = 5 \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 845.f (of order 44, degree 22, 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: 6.747358970806.74735897080
Analytic rank: 00
Dimension: 7272
Relative dimension: 3636 over Q(i)\Q(i)
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 408.20
Character χ\chi == 845.408
Dual form 845.2.f.f.437.17

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+0.689692iq2+(0.06218710.0621871i)q3+1.52433q4+(0.454257+2.18944i)q5+(0.04289000.0428900i)q60.806945q7+2.43070iq82.99227iq9+(1.510040.313297i)q10+(0.314448+0.314448i)q11+(0.09479340.0947934i)q120.556544iq14+(0.1644040.107906i)q15+1.37222q16+(3.71523+3.71523i)q17+2.06374q18+(4.78901+4.78901i)q19+(0.692436+3.33742i)q20+(0.0501816+0.0501816i)q21+(0.216872+0.216872i)q22+(3.80361+3.80361i)q23+(0.1511580.151158i)q24+(4.587301.98914i)q25+(0.372642+0.372642i)q271.23005q28+4.79138iq29+(0.0744220+0.113388i)q30+(0.106205+0.106205i)q31+5.80780iq320.0391092iq33+(2.56236+2.56236i)q34+(0.3665611.76676i)q354.56119iq365.97196q37+(3.30294+3.30294i)q38+(5.321871.10416i)q40+(6.135996.13599i)q41+(0.0346098+0.0346098i)q42+(6.828466.82846i)q43+(0.479320+0.479320i)q44+(6.55139+1.35926i)q45+(2.623322.62332i)q469.32662q47+(0.08533430.0853343i)q486.34884q49+(1.371893.16382i)q500.462079iq51+(5.61903+5.61903i)q53+(0.2570080.257008i)q54+(0.831304+0.545624i)q551.96144iq560.595630iq573.30457q58+(1.55637+1.55637i)q59+(0.2506050.164484i)q60+3.03084q61+(0.07324840.0732484i)q62+2.41459iq631.26116q64+0.0269733q66+11.6119iq67+(5.66322+5.66322i)q68+0.473071q69+(1.21852+0.252814i)q70+(1.009311.00931i)q71+7.27329q72+0.265877iq734.11881iq74+(0.161572+0.408970i)q75+(7.30001+7.30001i)q76+(0.2537420.253742i)q778.98397iq79+(0.623340+3.00439i)q808.93045q81+(4.23194+4.23194i)q82+2.59025q83+(0.0764931+0.0764931i)q84+(9.82194+6.44660i)q85+(4.70953+4.70953i)q86+(0.2979620.297962i)q87+(0.764327+0.764327i)q88+(6.102046.10204i)q89+(0.937469+4.51844i)q90+(5.79794+5.79794i)q92+0.0132091q936.43250iq94+(12.6607+8.30982i)q95+(0.3611710.361171i)q9614.4934iq974.37874iq98+(0.9409110.940911i)q99+O(q100)q+0.689692i q^{2} +(-0.0621871 - 0.0621871i) q^{3} +1.52433 q^{4} +(-0.454257 + 2.18944i) q^{5} +(0.0428900 - 0.0428900i) q^{6} -0.806945 q^{7} +2.43070i q^{8} -2.99227i q^{9} +(-1.51004 - 0.313297i) q^{10} +(0.314448 + 0.314448i) q^{11} +(-0.0947934 - 0.0947934i) q^{12} -0.556544i q^{14} +(0.164404 - 0.107906i) q^{15} +1.37222 q^{16} +(3.71523 + 3.71523i) q^{17} +2.06374 q^{18} +(4.78901 + 4.78901i) q^{19} +(-0.692436 + 3.33742i) q^{20} +(0.0501816 + 0.0501816i) q^{21} +(-0.216872 + 0.216872i) q^{22} +(-3.80361 + 3.80361i) q^{23} +(0.151158 - 0.151158i) q^{24} +(-4.58730 - 1.98914i) q^{25} +(-0.372642 + 0.372642i) q^{27} -1.23005 q^{28} +4.79138i q^{29} +(0.0744220 + 0.113388i) q^{30} +(-0.106205 + 0.106205i) q^{31} +5.80780i q^{32} -0.0391092i q^{33} +(-2.56236 + 2.56236i) q^{34} +(0.366561 - 1.76676i) q^{35} -4.56119i q^{36} -5.97196 q^{37} +(-3.30294 + 3.30294i) q^{38} +(-5.32187 - 1.10416i) q^{40} +(6.13599 - 6.13599i) q^{41} +(-0.0346098 + 0.0346098i) q^{42} +(6.82846 - 6.82846i) q^{43} +(0.479320 + 0.479320i) q^{44} +(6.55139 + 1.35926i) q^{45} +(-2.62332 - 2.62332i) q^{46} -9.32662 q^{47} +(-0.0853343 - 0.0853343i) q^{48} -6.34884 q^{49} +(1.37189 - 3.16382i) q^{50} -0.462079i q^{51} +(5.61903 + 5.61903i) q^{53} +(-0.257008 - 0.257008i) q^{54} +(-0.831304 + 0.545624i) q^{55} -1.96144i q^{56} -0.595630i q^{57} -3.30457 q^{58} +(-1.55637 + 1.55637i) q^{59} +(0.250605 - 0.164484i) q^{60} +3.03084 q^{61} +(-0.0732484 - 0.0732484i) q^{62} +2.41459i q^{63} -1.26116 q^{64} +0.0269733 q^{66} +11.6119i q^{67} +(5.66322 + 5.66322i) q^{68} +0.473071 q^{69} +(1.21852 + 0.252814i) q^{70} +(1.00931 - 1.00931i) q^{71} +7.27329 q^{72} +0.265877i q^{73} -4.11881i q^{74} +(0.161572 + 0.408970i) q^{75} +(7.30001 + 7.30001i) q^{76} +(-0.253742 - 0.253742i) q^{77} -8.98397i q^{79} +(-0.623340 + 3.00439i) q^{80} -8.93045 q^{81} +(4.23194 + 4.23194i) q^{82} +2.59025 q^{83} +(0.0764931 + 0.0764931i) q^{84} +(-9.82194 + 6.44660i) q^{85} +(4.70953 + 4.70953i) q^{86} +(0.297962 - 0.297962i) q^{87} +(-0.764327 + 0.764327i) q^{88} +(6.10204 - 6.10204i) q^{89} +(-0.937469 + 4.51844i) q^{90} +(-5.79794 + 5.79794i) q^{92} +0.0132091 q^{93} -6.43250i q^{94} +(-12.6607 + 8.30982i) q^{95} +(0.361171 - 0.361171i) q^{96} -14.4934i q^{97} -4.37874i q^{98} +(0.940911 - 0.940911i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 72q4q380q412q10+64q12+80q16+8q17+24q22+36q2348q2564q274q30+80q35+28q3824q4056q42+76q4376q48+92q95+O(q100) 72 q - 4 q^{3} - 80 q^{4} - 12 q^{10} + 64 q^{12} + 80 q^{16} + 8 q^{17} + 24 q^{22} + 36 q^{23} - 48 q^{25} - 64 q^{27} - 4 q^{30} + 80 q^{35} + 28 q^{38} - 24 q^{40} - 56 q^{42} + 76 q^{43} - 76 q^{48}+ \cdots - 92 q^{95}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/845Z)×\left(\mathbb{Z}/845\mathbb{Z}\right)^\times.

nn 171171 677677
χ(n)\chi(n) e(34)e\left(\frac{3}{4}\right) e(34)e\left(\frac{3}{4}\right)

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.689692i 0.487686i 0.969815 + 0.243843i 0.0784081π0.0784081\pi
−0.969815 + 0.243843i 0.921592π0.921592\pi
33 −0.0621871 0.0621871i −0.0359038 0.0359038i 0.688927 0.724831i 0.258082π-0.258082\pi
−0.724831 + 0.688927i 0.758082π0.758082\pi
44 1.52433 0.762163
55 −0.454257 + 2.18944i −0.203150 + 0.979148i
66 0.0428900 0.0428900i 0.0175098 0.0175098i
77 −0.806945 −0.304997 −0.152498 0.988304i 0.548732π-0.548732\pi
−0.152498 + 0.988304i 0.548732π0.548732\pi
88 2.43070i 0.859382i
99 2.99227i 0.997422i
1010 −1.51004 0.313297i −0.477516 0.0990733i
1111 0.314448 + 0.314448i 0.0948095 + 0.0948095i 0.752921 0.658111i 0.228644π-0.228644\pi
−0.658111 + 0.752921i 0.728644π0.728644\pi
1212 −0.0947934 0.0947934i −0.0273645 0.0273645i
1313 0 0
1414 0.556544i 0.148743i
1515 0.164404 0.107906i 0.0424489 0.0278612i
1616 1.37222 0.343054
1717 3.71523 + 3.71523i 0.901075 + 0.901075i 0.995529 0.0944538i 0.0301105π-0.0301105\pi
−0.0944538 + 0.995529i 0.530110π0.530110\pi
1818 2.06374 0.486428
1919 4.78901 + 4.78901i 1.09867 + 1.09867i 0.994566 + 0.104109i 0.0331991π0.0331991\pi
0.104109 + 0.994566i 0.466801π0.466801\pi
2020 −0.692436 + 3.33742i −0.154833 + 0.746270i
2121 0.0501816 + 0.0501816i 0.0109505 + 0.0109505i
2222 −0.216872 + 0.216872i −0.0462372 + 0.0462372i
2323 −3.80361 + 3.80361i −0.793108 + 0.793108i −0.981998 0.188891i 0.939511π-0.939511\pi
0.188891 + 0.981998i 0.439511π0.439511\pi
2424 0.151158 0.151158i 0.0308550 0.0308550i
2525 −4.58730 1.98914i −0.917460 0.397828i
2626 0 0
2727 −0.372642 + 0.372642i −0.0717149 + 0.0717149i
2828 −1.23005 −0.232457
2929 4.79138i 0.889736i 0.895596 + 0.444868i 0.146749π0.146749\pi
−0.895596 + 0.444868i 0.853251π0.853251\pi
3030 0.0744220 + 0.113388i 0.0135875 + 0.0207017i
3131 −0.106205 + 0.106205i −0.0190749 + 0.0190749i −0.716580 0.697505i 0.754293π-0.754293\pi
0.697505 + 0.716580i 0.254293π0.254293\pi
3232 5.80780i 1.02668i
3333 0.0391092i 0.00680804i
3434 −2.56236 + 2.56236i −0.439442 + 0.439442i
3535 0.366561 1.76676i 0.0619600 0.298637i
3636 4.56119i 0.760198i
3737 −5.97196 −0.981784 −0.490892 0.871220i 0.663329π-0.663329\pi
−0.490892 + 0.871220i 0.663329π0.663329\pi
3838 −3.30294 + 3.30294i −0.535808 + 0.535808i
3939 0 0
4040 −5.32187 1.10416i −0.841461 0.174583i
4141 6.13599 6.13599i 0.958281 0.958281i −0.0408834 0.999164i 0.513017π-0.513017\pi
0.999164 + 0.0408834i 0.0130172π0.0130172\pi
4242 −0.0346098 + 0.0346098i −0.00534041 + 0.00534041i
4343 6.82846 6.82846i 1.04133 1.04133i 0.0422217 0.999108i 0.486556π-0.486556\pi
0.999108 0.0422217i 0.0134436π-0.0134436\pi
4444 0.479320 + 0.479320i 0.0722603 + 0.0722603i
4545 6.55139 + 1.35926i 0.976623 + 0.202626i
4646 −2.62332 2.62332i −0.386787 0.386787i
4747 −9.32662 −1.36043 −0.680214 0.733014i 0.738113π-0.738113\pi
−0.680214 + 0.733014i 0.738113π0.738113\pi
4848 −0.0853343 0.0853343i −0.0123169 0.0123169i
4949 −6.34884 −0.906977
5050 1.37189 3.16382i 0.194015 0.447432i
5151 0.462079i 0.0647040i
5252 0 0
5353 5.61903 + 5.61903i 0.771833 + 0.771833i 0.978427 0.206594i 0.0662378π-0.0662378\pi
−0.206594 + 0.978427i 0.566238π0.566238\pi
5454 −0.257008 0.257008i −0.0349744 0.0349744i
5555 −0.831304 + 0.545624i −0.112093 + 0.0735720i
5656 1.96144i 0.262108i
5757 0.595630i 0.0788931i
5858 −3.30457 −0.433912
5959 −1.55637 + 1.55637i −0.202622 + 0.202622i −0.801122 0.598500i 0.795763π-0.795763\pi
0.598500 + 0.801122i 0.295763π0.295763\pi
6060 0.250605 0.164484i 0.0323530 0.0212348i
6161 3.03084 0.388059 0.194029 0.980996i 0.437844π-0.437844\pi
0.194029 + 0.980996i 0.437844π0.437844\pi
6262 −0.0732484 0.0732484i −0.00930256 0.00930256i
6363 2.41459i 0.304210i
6464 −1.26116 −0.157645
6565 0 0
6666 0.0269733 0.00332018
6767 11.6119i 1.41862i 0.704899 + 0.709308i 0.250992π0.250992\pi
−0.704899 + 0.709308i 0.749008π0.749008\pi
6868 5.66322 + 5.66322i 0.686766 + 0.686766i
6969 0.473071 0.0569511
7070 1.21852 + 0.252814i 0.145641 + 0.0302170i
7171 1.00931 1.00931i 0.119783 0.119783i −0.644674 0.764457i 0.723007π-0.723007\pi
0.764457 + 0.644674i 0.223007π0.223007\pi
7272 7.27329 0.857166
7373 0.265877i 0.0311186i 0.999879 + 0.0155593i 0.00495288π0.00495288\pi
−0.999879 + 0.0155593i 0.995047π0.995047\pi
7474 4.11881i 0.478802i
7575 0.161572 + 0.408970i 0.0186568 + 0.0472238i
7676 7.30001 + 7.30001i 0.837369 + 0.837369i
7777 −0.253742 0.253742i −0.0289166 0.0289166i
7878 0 0
7979 8.98397i 1.01078i −0.862892 0.505388i 0.831350π-0.831350\pi
0.862892 0.505388i 0.168650π-0.168650\pi
8080 −0.623340 + 3.00439i −0.0696915 + 0.335901i
8181 −8.93045 −0.992272
8282 4.23194 + 4.23194i 0.467340 + 0.467340i
8383 2.59025 0.284317 0.142159 0.989844i 0.454596π-0.454596\pi
0.142159 + 0.989844i 0.454596π0.454596\pi
8484 0.0764931 + 0.0764931i 0.00834608 + 0.00834608i
8585 −9.82194 + 6.44660i −1.06534 + 0.699232i
8686 4.70953 + 4.70953i 0.507842 + 0.507842i
8787 0.297962 0.297962i 0.0319449 0.0319449i
8888 −0.764327 + 0.764327i −0.0814776 + 0.0814776i
8989 6.10204 6.10204i 0.646815 0.646815i −0.305407 0.952222i 0.598792π-0.598792\pi
0.952222 + 0.305407i 0.0987925π0.0987925\pi
9090 −0.937469 + 4.51844i −0.0988179 + 0.476285i
9191 0 0
9292 −5.79794 + 5.79794i −0.604477 + 0.604477i
9393 0.0132091 0.00136972
9494 6.43250i 0.663461i
9595 −12.6607 + 8.30982i −1.29896 + 0.852569i
9696 0.361171 0.361171i 0.0368618 0.0368618i
9797 14.4934i 1.47158i −0.677210 0.735789i 0.736811π-0.736811\pi
0.677210 0.735789i 0.263189π-0.263189\pi
9898 4.37874i 0.442320i
9999 0.940911 0.940911i 0.0945651 0.0945651i
100100 −6.99254 3.03209i −0.699254 0.303209i
101101 3.93288i 0.391336i −0.980670 0.195668i 0.937312π-0.937312\pi
0.980670 0.195668i 0.0626875π-0.0626875\pi
102102 0.318692 0.0315552
103103 12.2725 12.2725i 1.20924 1.20924i 0.237970 0.971272i 0.423518π-0.423518\pi
0.971272 0.237970i 0.0764820π-0.0764820\pi
104104 0 0
105105 −0.132665 + 0.0870743i −0.0129468 + 0.00849758i
106106 −3.87540 + 3.87540i −0.376412 + 0.376412i
107107 −3.47737 + 3.47737i −0.336170 + 0.336170i −0.854924 0.518754i 0.826396π-0.826396\pi
0.518754 + 0.854924i 0.326396π0.326396\pi
108108 −0.568027 + 0.568027i −0.0546585 + 0.0546585i
109109 −5.74206 5.74206i −0.549990 0.549990i 0.376448 0.926438i 0.377145π-0.377145\pi
−0.926438 + 0.376448i 0.877145π0.877145\pi
110110 −0.376313 0.573344i −0.0358800 0.0546662i
111111 0.371379 + 0.371379i 0.0352497 + 0.0352497i
112112 −1.10730 −0.104630
113113 3.36820 + 3.36820i 0.316853 + 0.316853i 0.847557 0.530704i 0.178072π-0.178072\pi
−0.530704 + 0.847557i 0.678072π0.678072\pi
114114 0.410801 0.0384751
115115 −6.59996 10.0556i −0.615450 0.937689i
116116 7.30362i 0.678124i
117117 0 0
118118 −1.07342 1.07342i −0.0988159 0.0988159i
119119 −2.99799 2.99799i −0.274825 0.274825i
120120 0.262287 + 0.399616i 0.0239434 + 0.0364798i
121121 10.8022i 0.982022i
122122 2.09034i 0.189251i
123123 −0.763159 −0.0688117
124124 −0.161890 + 0.161890i −0.0145382 + 0.0145382i
125125 6.43891 9.14004i 0.575914 0.817510i
126126 −1.66533 −0.148359
127127 10.3616 + 10.3616i 0.919445 + 0.919445i 0.996989 0.0775440i 0.0247078π-0.0247078\pi
−0.0775440 + 0.996989i 0.524708π0.524708\pi
128128 10.7458i 0.949803i
129129 −0.849284 −0.0747753
130130 0 0
131131 21.1674 1.84941 0.924704 0.380686i 0.124312π-0.124312\pi
0.924704 + 0.380686i 0.124312π0.124312\pi
132132 0.0596151i 0.00518883i
133133 −3.86447 3.86447i −0.335092 0.335092i
134134 −8.00861 −0.691838
135135 −0.646602 0.985152i −0.0556506 0.0847884i
136136 −9.03060 + 9.03060i −0.774368 + 0.774368i
137137 15.2364 1.30173 0.650867 0.759192i 0.274406π-0.274406\pi
0.650867 + 0.759192i 0.274406π0.274406\pi
138138 0.326273i 0.0277742i
139139 11.8714i 1.00692i 0.864019 + 0.503459i 0.167939π0.167939\pi
−0.864019 + 0.503459i 0.832061π0.832061\pi
140140 0.558758 2.69311i 0.0472236 0.227610i
141141 0.579996 + 0.579996i 0.0488445 + 0.0488445i
142142 0.696114 + 0.696114i 0.0584166 + 0.0584166i
143143 0 0
144144 4.10604i 0.342170i
145145 −10.4904 2.17652i −0.871183 0.180750i
146146 −0.183373 −0.0151761
147147 0.394816 + 0.394816i 0.0325639 + 0.0325639i
148148 −9.10321 −0.748279
149149 −9.54060 9.54060i −0.781597 0.781597i 0.198504 0.980100i 0.436392π-0.436392\pi
−0.980100 + 0.198504i 0.936392π0.936392\pi
150150 −0.282063 + 0.111435i −0.0230304 + 0.00909864i
151151 3.86706 + 3.86706i 0.314697 + 0.314697i 0.846726 0.532029i 0.178570π-0.178570\pi
−0.532029 + 0.846726i 0.678570π0.678570\pi
152152 −11.6406 + 11.6406i −0.944181 + 0.944181i
153153 11.1170 11.1170i 0.898752 0.898752i
154154 0.175004 0.175004i 0.0141022 0.0141022i
155155 −0.184284 0.280773i −0.0148021 0.0225522i
156156 0 0
157157 −12.0199 + 12.0199i −0.959293 + 0.959293i −0.999203 0.0399100i 0.987293π-0.987293\pi
0.0399100 + 0.999203i 0.487293π0.487293\pi
158158 6.19617 0.492941
159159 0.698863i 0.0554234i
160160 −12.7158 2.63824i −1.00528 0.208571i
161161 3.06931 3.06931i 0.241895 0.241895i
162162 6.15926i 0.483917i
163163 20.9573i 1.64150i −0.571288 0.820750i 0.693556π-0.693556\pi
0.571288 0.820750i 0.306444π-0.306444\pi
164164 9.35324 9.35324i 0.730366 0.730366i
165165 0.0856272 + 0.0177656i 0.00666607 + 0.00138305i
166166 1.78648i 0.138657i
167167 −17.8277 −1.37955 −0.689773 0.724026i 0.742289π-0.742289\pi
−0.689773 + 0.724026i 0.742289π0.742289\pi
168168 −0.121976 + 0.121976i −0.00941068 + 0.00941068i
169169 0 0
170170 −4.44617 6.77411i −0.341006 0.519551i
171171 14.3300 14.3300i 1.09584 1.09584i
172172 10.4088 10.4088i 0.793663 0.793663i
173173 4.52475 4.52475i 0.344010 0.344010i −0.513862 0.857873i 0.671786π-0.671786\pi
0.857873 + 0.513862i 0.171786π0.171786\pi
174174 0.205502 + 0.205502i 0.0155791 + 0.0155791i
175175 3.70170 + 1.60513i 0.279822 + 0.121336i
176176 0.431490 + 0.431490i 0.0325248 + 0.0325248i
177177 0.193572 0.0145498
178178 4.20853 + 4.20853i 0.315442 + 0.315442i
179179 5.20422 0.388982 0.194491 0.980904i 0.437695π-0.437695\pi
0.194491 + 0.980904i 0.437695π0.437695\pi
180180 9.98645 + 2.07195i 0.744346 + 0.154434i
181181 10.7283i 0.797430i −0.917075 0.398715i 0.869456π-0.869456\pi
0.917075 0.398715i 0.130544π-0.130544\pi
182182 0 0
183183 −0.188479 0.188479i −0.0139328 0.0139328i
184184 −9.24543 9.24543i −0.681582 0.681582i
185185 2.71281 13.0753i 0.199449 0.961312i
186186 0.00911022i 0.000667993i
187187 2.33649i 0.170861i
188188 −14.2168 −1.03687
189189 0.300702 0.300702i 0.0218728 0.0218728i
190190 −5.73121 8.73198i −0.415786 0.633485i
191191 16.1353 1.16751 0.583753 0.811931i 0.301584π-0.301584\pi
0.583753 + 0.811931i 0.301584π0.301584\pi
192192 0.0784279 + 0.0784279i 0.00566005 + 0.00566005i
193193 7.60539i 0.547448i −0.961808 0.273724i 0.911744π-0.911744\pi
0.961808 0.273724i 0.0882555π-0.0882555\pi
194194 9.99596 0.717668
195195 0 0
196196 −9.67770 −0.691264
197197 4.90103i 0.349184i −0.984641 0.174592i 0.944139π-0.944139\pi
0.984641 0.174592i 0.0558606π-0.0558606\pi
198198 0.648938 + 0.648938i 0.0461180 + 0.0461180i
199199 −19.9759 −1.41605 −0.708027 0.706186i 0.750414π-0.750414\pi
−0.708027 + 0.706186i 0.750414π0.750414\pi
200200 4.83499 11.1503i 0.341886 0.788448i
201201 0.722109 0.722109i 0.0509336 0.0509336i
202202 2.71248 0.190849
203203 3.86638i 0.271367i
204204 0.704358i 0.0493150i
205205 10.6471 + 16.2217i 0.743623 + 1.13297i
206206 8.46422 + 8.46422i 0.589730 + 0.589730i
207207 11.3814 + 11.3814i 0.791063 + 0.791063i
208208 0 0
209209 3.01179i 0.208330i
210210 −0.0600544 0.0914980i −0.00414415 0.00631396i
211211 11.6968 0.805238 0.402619 0.915368i 0.368100π-0.368100\pi
0.402619 + 0.915368i 0.368100π0.368100\pi
212212 8.56523 + 8.56523i 0.588262 + 0.588262i
213213 −0.125532 −0.00860134
214214 −2.39831 2.39831i −0.163945 0.163945i
215215 11.8486 + 18.0524i 0.808070 + 1.23116i
216216 −0.905780 0.905780i −0.0616305 0.0616305i
217217 0.0857012 0.0857012i 0.00581778 0.00581778i
218218 3.96025 3.96025i 0.268222 0.268222i
219219 0.0165342 0.0165342i 0.00111727 0.00111727i
220220 −1.26718 + 0.831709i −0.0854331 + 0.0560738i
221221 0 0
222222 −0.256137 + 0.256137i −0.0171908 + 0.0171908i
223223 −2.83093 −0.189573 −0.0947864 0.995498i 0.530217π-0.530217\pi
−0.0947864 + 0.995498i 0.530217π0.530217\pi
224224 4.68658i 0.313135i
225225 −5.95203 + 13.7264i −0.396802 + 0.915095i
226226 −2.32302 + 2.32302i −0.154525 + 0.154525i
227227 15.4930i 1.02830i −0.857699 0.514152i 0.828107π-0.828107\pi
0.857699 0.514152i 0.171893π-0.171893\pi
228228 0.907934i 0.0601294i
229229 14.5346 14.5346i 0.960475 0.960475i −0.0387727 0.999248i 0.512345π-0.512345\pi
0.999248 + 0.0387727i 0.0123448π0.0123448\pi
230230 6.93526 4.55194i 0.457298 0.300146i
231231 0.0315590i 0.00207643i
232232 −11.6464 −0.764623
233233 −4.84530 + 4.84530i −0.317426 + 0.317426i −0.847778 0.530352i 0.822060π-0.822060\pi
0.530352 + 0.847778i 0.322060π0.322060\pi
234234 0 0
235235 4.23668 20.4201i 0.276371 1.33206i
236236 −2.37241 + 2.37241i −0.154431 + 0.154431i
237237 −0.558687 + 0.558687i −0.0362906 + 0.0362906i
238238 2.06769 2.06769i 0.134028 0.134028i
239239 10.0017 + 10.0017i 0.646957 + 0.646957i 0.952257 0.305299i 0.0987564π-0.0987564\pi
−0.305299 + 0.952257i 0.598756π0.598756\pi
240240 0.225598 0.148071i 0.0145623 0.00955792i
241241 −17.2524 17.2524i −1.11132 1.11132i −0.992972 0.118350i 0.962239π-0.962239\pi
−0.118350 0.992972i 0.537761π-0.537761\pi
242242 7.45022 0.478918
243243 1.67328 + 1.67328i 0.107341 + 0.107341i
244244 4.61998 0.295764
245245 2.88401 13.9004i 0.184252 0.888064i
246246 0.526345i 0.0335585i
247247 0 0
248248 −0.258151 0.258151i −0.0163926 0.0163926i
249249 −0.161080 0.161080i −0.0102081 0.0102081i
250250 6.30381 + 4.44087i 0.398688 + 0.280865i
251251 5.39488i 0.340522i −0.985399 0.170261i 0.945539π-0.945539\pi
0.985399 0.170261i 0.0544611π-0.0544611\pi
252252 3.68063i 0.231858i
253253 −2.39207 −0.150388
254254 −7.14632 + 7.14632i −0.448400 + 0.448400i
255255 1.01169 + 0.209903i 0.0633548 + 0.0131446i
256256 −9.93361 −0.620850
257257 −0.280852 0.280852i −0.0175191 0.0175191i 0.698293 0.715812i 0.253943π-0.253943\pi
−0.715812 + 0.698293i 0.753943π0.753943\pi
258258 0.585744i 0.0364669i
259259 4.81905 0.299441
260260 0 0
261261 14.3371 0.887442
262262 14.5990i 0.901930i
263263 −19.1244 19.1244i −1.17926 1.17926i −0.979933 0.199327i 0.936124π-0.936124\pi
−0.199327 0.979933i 0.563876π-0.563876\pi
264264 0.0950626 0.00585070
265265 −14.8550 + 9.75005i −0.912536 + 0.598941i
266266 2.66529 2.66529i 0.163420 0.163420i
267267 −0.758937 −0.0464462
268268 17.7003i 1.08122i
269269 6.80280i 0.414774i −0.978259 0.207387i 0.933504π-0.933504\pi
0.978259 0.207387i 0.0664960π-0.0664960\pi
270270 0.679452 0.445956i 0.0413501 0.0271400i
271271 −1.19369 1.19369i −0.0725115 0.0725115i 0.669921 0.742432i 0.266328π-0.266328\pi
−0.742432 + 0.669921i 0.766328π0.766328\pi
272272 5.09810 + 5.09810i 0.309118 + 0.309118i
273273 0 0
274274 10.5084i 0.634837i
275275 −0.816986 2.06795i −0.0492661 0.124702i
276276 0.721114 0.0434060
277277 7.48071 + 7.48071i 0.449472 + 0.449472i 0.895179 0.445707i 0.147048π-0.147048\pi
−0.445707 + 0.895179i 0.647048π0.647048\pi
278278 −8.18759 −0.491059
279279 0.317792 + 0.317792i 0.0190257 + 0.0190257i
280280 4.29446 + 0.890998i 0.256643 + 0.0532473i
281281 −0.943634 0.943634i −0.0562925 0.0562925i 0.678400 0.734693i 0.262674π-0.262674\pi
−0.734693 + 0.678400i 0.762674π0.762674\pi
282282 −0.400018 + 0.400018i −0.0238208 + 0.0238208i
283283 −3.00754 + 3.00754i −0.178779 + 0.178779i −0.790824 0.612044i 0.790347π-0.790347\pi
0.612044 + 0.790824i 0.290347π0.290347\pi
284284 1.53852 1.53852i 0.0912944 0.0912944i
285285 1.30410 + 0.270569i 0.0772480 + 0.0160271i
286286 0 0
287287 −4.95141 + 4.95141i −0.292272 + 0.292272i
288288 17.3785 1.02404
289289 10.6059i 0.623874i
290290 1.50113 7.23517i 0.0881491 0.424864i
291291 −0.901301 + 0.901301i −0.0528352 + 0.0528352i
292292 0.405284i 0.0237174i
293293 6.74295i 0.393927i −0.980411 0.196964i 0.936892π-0.936892\pi
0.980411 0.196964i 0.0631081π-0.0631081\pi
294294 −0.272301 + 0.272301i −0.0158809 + 0.0158809i
295295 −2.70059 4.11457i −0.157234 0.239560i
296296 14.5160i 0.843727i
297297 −0.234353 −0.0135985
298298 6.58008 6.58008i 0.381174 0.381174i
299299 0 0
300300 0.246289 + 0.623403i 0.0142195 + 0.0359922i
301301 −5.51019 + 5.51019i −0.317602 + 0.317602i
302302 −2.66708 + 2.66708i −0.153473 + 0.153473i
303303 −0.244575 + 0.244575i −0.0140504 + 0.0140504i
304304 6.57157 + 6.57157i 0.376905 + 0.376905i
305305 −1.37678 + 6.63583i −0.0788341 + 0.379967i
306306 7.66727 + 7.66727i 0.438309 + 0.438309i
307307 −9.60697 −0.548298 −0.274149 0.961687i 0.588396π-0.588396\pi
−0.274149 + 0.961687i 0.588396π0.588396\pi
308308 −0.386785 0.386785i −0.0220391 0.0220391i
309309 −1.52638 −0.0868327
310310 0.193647 0.127099i 0.0109984 0.00721876i
311311 5.22449i 0.296254i 0.988968 + 0.148127i 0.0473244π0.0473244\pi
−0.988968 + 0.148127i 0.952676π0.952676\pi
312312 0 0
313313 2.37979 + 2.37979i 0.134514 + 0.134514i 0.771158 0.636644i 0.219678π-0.219678\pi
−0.636644 + 0.771158i 0.719678π0.719678\pi
314314 −8.29003 8.29003i −0.467834 0.467834i
315315 −5.28661 1.09685i −0.297867 0.0618003i
316316 13.6945i 0.770375i
317317 14.8061i 0.831593i −0.909458 0.415796i 0.863503π-0.863503\pi
0.909458 0.415796i 0.136497π-0.136497\pi
318318 0.482000 0.0270292
319319 −1.50664 + 1.50664i −0.0843555 + 0.0843555i
320320 0.572891 2.76123i 0.0320256 0.154358i
321321 0.432495 0.0241395
322322 2.11687 + 2.11687i 0.117969 + 0.117969i
323323 35.5846i 1.97998i
324324 −13.6129 −0.756273
325325 0 0
326326 14.4541 0.800536
327327 0.714165i 0.0394934i
328328 14.9147 + 14.9147i 0.823529 + 0.823529i
329329 7.52607 0.414926
330330 −0.0122528 + 0.0590564i −0.000674495 + 0.00325095i
331331 −11.0229 + 11.0229i −0.605871 + 0.605871i −0.941864 0.335993i 0.890928π-0.890928\pi
0.335993 + 0.941864i 0.390928π0.390928\pi
332332 3.94839 0.216696
333333 17.8697i 0.979253i
334334 12.2956i 0.672784i
335335 −25.4235 5.27477i −1.38903 0.288192i
336336 0.0688601 + 0.0688601i 0.00375663 + 0.00375663i
337337 −18.1944 18.1944i −0.991112 0.991112i 0.00884867 0.999961i 0.497183π-0.497183\pi
−0.999961 + 0.00884867i 0.997183π0.997183\pi
338338 0 0
339339 0.418917i 0.0227525i
340340 −14.9718 + 9.82672i −0.811962 + 0.532929i
341341 −0.0667915 −0.00361696
342342 9.88328 + 9.88328i 0.534427 + 0.534427i
343343 10.7718 0.581622
344344 16.5979 + 16.5979i 0.894900 + 0.894900i
345345 −0.214896 + 1.03576i −0.0115696 + 0.0557635i
346346 3.12068 + 3.12068i 0.167769 + 0.167769i
347347 −16.9091 + 16.9091i −0.907730 + 0.907730i −0.996089 0.0883583i 0.971838π-0.971838\pi
0.0883583 + 0.996089i 0.471838π0.471838\pi
348348 0.454191 0.454191i 0.0243472 0.0243472i
349349 7.73307 7.73307i 0.413942 0.413942i −0.469167 0.883109i 0.655446π-0.655446\pi
0.883109 + 0.469167i 0.155446π0.155446\pi
350350 −1.10704 + 2.55303i −0.0591739 + 0.136465i
351351 0 0
352352 −1.82625 + 1.82625i −0.0973394 + 0.0973394i
353353 0.867256 0.0461594 0.0230797 0.999734i 0.492653π-0.492653\pi
0.0230797 + 0.999734i 0.492653π0.492653\pi
354354 0.133505i 0.00709572i
355355 1.75134 + 2.66832i 0.0929516 + 0.141620i
356356 9.30149 9.30149i 0.492978 0.492978i
357357 0.372872i 0.0197345i
358358 3.58931i 0.189701i
359359 −19.2831 + 19.2831i −1.01773 + 1.01773i −0.0178852 + 0.999840i 0.505693π0.505693\pi
−0.999840 + 0.0178852i 0.994307π0.994307\pi
360360 −3.30395 + 15.9244i −0.174133 + 0.839292i
361361 26.8693i 1.41417i
362362 7.39924 0.388895
363363 −0.671761 + 0.671761i −0.0352583 + 0.0352583i
364364 0 0
365365 −0.582123 0.120777i −0.0304697 0.00632174i
366366 0.129992 0.129992i 0.00679481 0.00679481i
367367 −11.7243 + 11.7243i −0.612003 + 0.612003i −0.943468 0.331465i 0.892457π-0.892457\pi
0.331465 + 0.943468i 0.392457π0.392457\pi
368368 −5.21938 + 5.21938i −0.272079 + 0.272079i
369369 −18.3605 18.3605i −0.955810 0.955810i
370370 9.01790 + 1.87100i 0.468818 + 0.0972687i
371371 −4.53425 4.53425i −0.235407 0.235407i
372372 0.0201350 0.00104395
373373 −5.18869 5.18869i −0.268660 0.268660i 0.559900 0.828560i 0.310840π-0.310840\pi
−0.828560 + 0.559900i 0.810840π0.810840\pi
374374 −1.61146 −0.0833265
375375 −0.968811 + 0.167976i −0.0500292 + 0.00867422i
376376 22.6702i 1.16913i
377377 0 0
378378 0.207391 + 0.207391i 0.0106671 + 0.0106671i
379379 23.7312 + 23.7312i 1.21899 + 1.21899i 0.967986 + 0.251004i 0.0807608π0.0807608\pi
0.251004 + 0.967986i 0.419239π0.419239\pi
380380 −19.2990 + 12.6669i −0.990019 + 0.649796i
381381 1.28872i 0.0660231i
382382 11.1284i 0.569376i
383383 29.3750 1.50099 0.750497 0.660874i 0.229814π-0.229814\pi
0.750497 + 0.660874i 0.229814π0.229814\pi
384384 0.668250 0.668250i 0.0341015 0.0341015i
385385 0.670817 0.440289i 0.0341880 0.0224392i
386386 5.24538 0.266983
387387 −20.4326 20.4326i −1.03865 1.03865i
388388 22.0926i 1.12158i
389389 −28.8837 −1.46446 −0.732231 0.681056i 0.761521π-0.761521\pi
−0.732231 + 0.681056i 0.761521π0.761521\pi
390390 0 0
391391 −28.2626 −1.42930
392392 15.4321i 0.779439i
393393 −1.31634 1.31634i −0.0664007 0.0664007i
394394 3.38020 0.170292
395395 19.6699 + 4.08103i 0.989698 + 0.205339i
396396 1.43425 1.43425i 0.0720740 0.0720740i
397397 5.89089 0.295655 0.147828 0.989013i 0.452772π-0.452772\pi
0.147828 + 0.989013i 0.452772π0.452772\pi
398398 13.7772i 0.690589i
399399 0.480641i 0.0240621i
400400 −6.29477 2.72953i −0.314739 0.136476i
401401 −2.56134 2.56134i −0.127907 0.127907i 0.640255 0.768162i 0.278829π-0.278829\pi
−0.768162 + 0.640255i 0.778829π0.778829\pi
402402 0.498032 + 0.498032i 0.0248396 + 0.0248396i
403403 0 0
404404 5.99499i 0.298262i
405405 4.05672 19.5527i 0.201580 0.971581i
406406 2.66661 0.132342
407407 −1.87787 1.87787i −0.0930825 0.0930825i
408408 1.12317 0.0556054
409409 8.48983 + 8.48983i 0.419795 + 0.419795i 0.885133 0.465338i 0.154067π-0.154067\pi
−0.465338 + 0.885133i 0.654067π0.654067\pi
410410 −11.1880 + 7.34320i −0.552535 + 0.362655i
411411 −0.947508 0.947508i −0.0467371 0.0467371i
412412 18.7072 18.7072i 0.921639 0.921639i
413413 1.25590 1.25590i 0.0617990 0.0617990i
414414 −7.84967 + 7.84967i −0.385790 + 0.385790i
415415 −1.17664 + 5.67120i −0.0577590 + 0.278388i
416416 0 0
417417 0.738247 0.738247i 0.0361521 0.0361521i
418418 −2.07720 −0.101599
419419 12.6173i 0.616393i 0.951323 + 0.308197i 0.0997255π0.0997255\pi
−0.951323 + 0.308197i 0.900275π0.900275\pi
420420 −0.202225 + 0.132730i −0.00986755 + 0.00647654i
421421 −2.72216 + 2.72216i −0.132670 + 0.132670i −0.770323 0.637653i 0.779905π-0.779905\pi
0.637653 + 0.770323i 0.279905π0.279905\pi
422422 8.06716i 0.392703i
423423 27.9077i 1.35692i
424424 −13.6582 + 13.6582i −0.663299 + 0.663299i
425425 −9.65277 24.4330i −0.468228 1.18517i
426426 0.0865787i 0.00419475i
427427 −2.44572 −0.118357
428428 −5.30063 + 5.30063i −0.256216 + 0.256216i
429429 0 0
430430 −12.4506 + 8.17190i −0.600420 + 0.394084i
431431 −9.87188 + 9.87188i −0.475512 + 0.475512i −0.903693 0.428181i 0.859155π-0.859155\pi
0.428181 + 0.903693i 0.359155π0.359155\pi
432432 −0.511346 + 0.511346i −0.0246021 + 0.0246021i
433433 24.1128 24.1128i 1.15879 1.15879i 0.174050 0.984737i 0.444315π-0.444315\pi
0.984737 0.174050i 0.0556853π-0.0556853\pi
434434 0.0591074 + 0.0591074i 0.00283725 + 0.00283725i
435435 0.517019 + 0.787721i 0.0247891 + 0.0377683i
436436 −8.75277 8.75277i −0.419182 0.419182i
437437 −36.4311 −1.74273
438438 0.0114035 + 0.0114035i 0.000544879 + 0.000544879i
439439 −29.0839 −1.38810 −0.694049 0.719927i 0.744175π-0.744175\pi
−0.694049 + 0.719927i 0.744175π0.744175\pi
440440 −1.32625 2.02065i −0.0632264 0.0963307i
441441 18.9974i 0.904639i
442442 0 0
443443 7.18973 + 7.18973i 0.341594 + 0.341594i 0.856966 0.515372i 0.172346π-0.172346\pi
−0.515372 + 0.856966i 0.672346π0.672346\pi
444444 0.566103 + 0.566103i 0.0268660 + 0.0268660i
445445 10.5882 + 16.1320i 0.501927 + 0.764728i
446446 1.95247i 0.0924520i
447447 1.18661i 0.0561245i
448448 1.01769 0.0480812
449449 −11.2814 + 11.2814i −0.532401 + 0.532401i −0.921286 0.388885i 0.872860π-0.872860\pi
0.388885 + 0.921286i 0.372860π0.372860\pi
450450 −9.46700 4.10507i −0.446279 0.193515i
451451 3.85889 0.181708
452452 5.13423 + 5.13423i 0.241494 + 0.241494i
453453 0.480963i 0.0225976i
454454 10.6854 0.501490
455455 0 0
456456 1.44780 0.0677993
457457 19.2290i 0.899495i 0.893156 + 0.449748i 0.148486π0.148486\pi
−0.893156 + 0.449748i 0.851514π0.851514\pi
458458 10.0244 + 10.0244i 0.468410 + 0.468410i
459459 −2.76890 −0.129241
460460 −10.0605 15.3280i −0.469073 0.714672i
461461 −3.13390 + 3.13390i −0.145960 + 0.145960i −0.776311 0.630350i 0.782911π-0.782911\pi
0.630350 + 0.776311i 0.282911π0.282911\pi
462462 −0.0217660 −0.00101264
463463 12.2584i 0.569696i −0.958573 0.284848i 0.908057π-0.908057\pi
0.958573 0.284848i 0.0919431π-0.0919431\pi
464464 6.57481i 0.305228i
465465 −0.00600033 + 0.0289206i −0.000278259 + 0.00134116i
466466 −3.34177 3.34177i −0.154804 0.154804i
467467 10.5138 + 10.5138i 0.486522 + 0.486522i 0.907207 0.420685i 0.138210π-0.138210\pi
−0.420685 + 0.907207i 0.638210π0.638210\pi
468468 0 0
469469 9.37014i 0.432673i
470470 14.0836 + 2.92201i 0.649627 + 0.134782i
471471 1.49497 0.0688845
472472 −3.78306 3.78306i −0.174130 0.174130i
473473 4.29438 0.197456
474474 −0.385322 0.385322i −0.0176984 0.0176984i
475475 −12.4426 31.4947i −0.570907 1.44507i
476476 −4.56991 4.56991i −0.209461 0.209461i
477477 16.8136 16.8136i 0.769843 0.769843i
478478 −6.89810 + 6.89810i −0.315512 + 0.315512i
479479 8.32128 8.32128i 0.380209 0.380209i −0.490968 0.871177i 0.663357π-0.663357\pi
0.871177 + 0.490968i 0.163357π0.163357\pi
480480 0.626697 + 0.954826i 0.0286047 + 0.0435816i
481481 0 0
482482 11.8988 11.8988i 0.541976 0.541976i
483483 −0.381743 −0.0173699
484484 16.4661i 0.748461i
485485 31.7324 + 6.58372i 1.44089 + 0.298951i
486486 −1.15405 + 1.15405i −0.0523488 + 0.0523488i
487487 26.4997i 1.20082i 0.799694 + 0.600408i 0.204995π0.204995\pi
−0.799694 + 0.600408i 0.795005π0.795005\pi
488488 7.36705i 0.333491i
489489 −1.30327 + 1.30327i −0.0589360 + 0.0589360i
490490 9.58700 + 1.98907i 0.433096 + 0.0898572i
491491 14.2507i 0.643123i −0.946889 0.321562i 0.895792π-0.895792\pi
0.946889 0.321562i 0.104208π-0.104208\pi
492492 −1.16330 −0.0524457
493493 −17.8011 + 17.8011i −0.801719 + 0.801719i
494494 0 0
495495 1.63265 + 2.48748i 0.0733823 + 0.111804i
496496 −0.145736 + 0.145736i −0.00654373 + 0.00654373i
497497 −0.814460 + 0.814460i −0.0365335 + 0.0365335i
498498 0.111096 0.111096i 0.00497832 0.00497832i
499499 20.1666 + 20.1666i 0.902783 + 0.902783i 0.995676 0.0928929i 0.0296114π-0.0296114\pi
−0.0928929 + 0.995676i 0.529611π0.529611\pi
500500 9.81500 13.9324i 0.438940 0.623076i
501501 1.10865 + 1.10865i 0.0495308 + 0.0495308i
502502 3.72081 0.166068
503503 −6.41738 6.41738i −0.286137 0.286137i 0.549414 0.835551i 0.314851π-0.314851\pi
−0.835551 + 0.549414i 0.814851π0.814851\pi
504504 −5.86915 −0.261433
505505 8.61081 + 1.78654i 0.383176 + 0.0794999i
506506 1.64979i 0.0733422i
507507 0 0
508508 15.7945 + 15.7945i 0.700767 + 0.700767i
509509 9.67201 + 9.67201i 0.428704 + 0.428704i 0.888187 0.459483i 0.151965π-0.151965\pi
−0.459483 + 0.888187i 0.651965π0.651965\pi
510510 −0.144768 + 0.697757i −0.00641044 + 0.0308972i
511511 0.214548i 0.00949107i
512512 14.6405i 0.647023i
513513 −3.56917 −0.157583
514514 0.193701 0.193701i 0.00854380 0.00854380i
515515 21.2950 + 32.4447i 0.938369 + 1.42968i
516516 −1.29459 −0.0569909
517517 −2.93273 2.93273i −0.128981 0.128981i
518518 3.32366i 0.146033i
519519 −0.562762 −0.0247025
520520 0 0
521521 −29.1893 −1.27881 −0.639403 0.768872i 0.720819π-0.720819\pi
−0.639403 + 0.768872i 0.720819π0.720819\pi
522522 9.88816i 0.432793i
523523 10.0289 + 10.0289i 0.438533 + 0.438533i 0.891518 0.452985i 0.149641π-0.149641\pi
−0.452985 + 0.891518i 0.649641π0.649641\pi
524524 32.2661 1.40955
525525 −0.130380 0.330016i −0.00569025 0.0144031i
526526 13.1899 13.1899i 0.575108 0.575108i
527527 −0.789148 −0.0343758
528528 0.0536663i 0.00233553i
529529 5.93490i 0.258039i
530530 −6.72453 10.2454i −0.292095 0.445031i
531531 4.65707 + 4.65707i 0.202100 + 0.202100i
532532 −5.89071 5.89071i −0.255395 0.255395i
533533 0 0
534534 0.523432i 0.0226511i
535535 −6.03387 9.19310i −0.260867 0.397452i
536536 −28.2249 −1.21913
537537 −0.323635 0.323635i −0.0139659 0.0139659i
538538 4.69184 0.202279
539539 −1.99638 1.99638i −0.0859901 0.0859901i
540540 −0.985632 1.50169i −0.0424148 0.0646226i
541541 10.8210 + 10.8210i 0.465233 + 0.465233i 0.900366 0.435133i 0.143299π-0.143299\pi
−0.435133 + 0.900366i 0.643299π0.643299\pi
542542 0.823278 0.823278i 0.0353628 0.0353628i
543543 −0.667164 + 0.667164i −0.0286307 + 0.0286307i
544544 −21.5773 + 21.5773i −0.925120 + 0.925120i
545545 15.1803 9.96353i 0.650251 0.426791i
546546 0 0
547547 0.334432 0.334432i 0.0142993 0.0142993i −0.699921 0.714220i 0.746781π-0.746781\pi
0.714220 + 0.699921i 0.246781π0.246781\pi
548548 23.2252 0.992133
549549 9.06906i 0.387058i
550550 1.42624 0.563469i 0.0608153 0.0240264i
551551 −22.9460 + 22.9460i −0.977531 + 0.977531i
552552 1.14989i 0.0489427i
553553 7.24957i 0.308283i
554554 −5.15938 + 5.15938i −0.219201 + 0.219201i
555555 −0.981814 + 0.644411i −0.0416757 + 0.0273537i
556556 18.0958i 0.767435i
557557 34.3584 1.45581 0.727906 0.685677i 0.240494π-0.240494\pi
0.727906 + 0.685677i 0.240494π0.240494\pi
558558 −0.219179 + 0.219179i −0.00927857 + 0.00927857i
559559 0 0
560560 0.503001 2.42438i 0.0212557 0.102449i
561561 0.145300 0.145300i 0.00613455 0.00613455i
562562 0.650816 0.650816i 0.0274530 0.0274530i
563563 −19.0692 + 19.0692i −0.803671 + 0.803671i −0.983667 0.179996i 0.942391π-0.942391\pi
0.179996 + 0.983667i 0.442391π0.442391\pi
564564 0.884102 + 0.884102i 0.0372274 + 0.0372274i
565565 −8.90450 + 5.84444i −0.374615 + 0.245878i
566566 −2.07427 2.07427i −0.0871882 0.0871882i
567567 7.20638 0.302640
568568 2.45333 + 2.45333i 0.102940 + 0.102940i
569569 36.5069 1.53045 0.765224 0.643765i 0.222628π-0.222628\pi
0.765224 + 0.643765i 0.222628π0.222628\pi
570570 −0.186609 + 0.899425i −0.00781620 + 0.0376728i
571571 31.2687i 1.30855i −0.756255 0.654277i 0.772973π-0.772973\pi
0.756255 0.654277i 0.227027π-0.227027\pi
572572 0 0
573573 −1.00341 1.00341i −0.0419178 0.0419178i
574574 −3.41495 3.41495i −0.142537 0.142537i
575575 25.0142 9.88240i 1.04316 0.412125i
576576 3.77373i 0.157239i
577577 28.3409i 1.17985i −0.807460 0.589923i 0.799158π-0.799158\pi
0.807460 0.589923i 0.200842π-0.200842\pi
578578 −7.31477 −0.304254
579579 −0.472958 + 0.472958i −0.0196554 + 0.0196554i
580580 −15.9908 3.31772i −0.663983 0.137761i
581581 −2.09019 −0.0867158
582582 −0.621620 0.621620i −0.0257670 0.0257670i
583583 3.53378i 0.146354i
584584 −0.646268 −0.0267427
585585 0 0
586586 4.65056 0.192113
587587 21.1182i 0.871643i −0.900033 0.435822i 0.856458π-0.856458\pi
0.900033 0.435822i 0.143542π-0.143542\pi
588588 0.601828 + 0.601828i 0.0248190 + 0.0248190i
589589 −1.01723 −0.0419142
590590 2.83779 1.86257i 0.116830 0.0766809i
591591 −0.304781 + 0.304781i −0.0125370 + 0.0125370i
592592 −8.19483 −0.336805
593593 12.8500i 0.527685i −0.964566 0.263843i 0.915010π-0.915010\pi
0.964566 0.263843i 0.0849899π-0.0849899\pi
594594 0.161631i 0.00663180i
595595 7.92577 5.20206i 0.324925 0.213264i
596596 −14.5430 14.5430i −0.595704 0.595704i
597597 1.24224 + 1.24224i 0.0508416 + 0.0508416i
598598 0 0
599599 3.15330i 0.128840i −0.997923 0.0644201i 0.979480π-0.979480\pi
0.997923 0.0644201i 0.0205198π-0.0205198\pi
600600 −0.994082 + 0.392734i −0.0405832 + 0.0160333i
601601 23.7424 0.968472 0.484236 0.874938i 0.339098π-0.339098\pi
0.484236 + 0.874938i 0.339098π0.339098\pi
602602 −3.80033 3.80033i −0.154890 0.154890i
603603 34.7458 1.41496
604604 5.89466 + 5.89466i 0.239850 + 0.239850i
605605 23.6509 + 4.90700i 0.961545 + 0.199498i
606606 −0.168681 0.168681i −0.00685220 0.00685220i
607607 −3.00186 + 3.00186i −0.121842 + 0.121842i −0.765399 0.643557i 0.777458π-0.777458\pi
0.643557 + 0.765399i 0.277458π0.277458\pi
608608 −27.8136 + 27.8136i −1.12799 + 1.12799i
609609 −0.240439 + 0.240439i −0.00974308 + 0.00974308i
610610 −4.57668 0.949553i −0.185304 0.0384463i
611611 0 0
612612 16.9458 16.9458i 0.684995 0.684995i
613613 −43.6898 −1.76461 −0.882306 0.470676i 0.844010π-0.844010\pi
−0.882306 + 0.470676i 0.844010π0.844010\pi
614614 6.62585i 0.267397i
615615 0.346670 1.67089i 0.0139791 0.0673769i
616616 0.616770 0.616770i 0.0248504 0.0248504i
617617 14.4409i 0.581367i 0.956819 + 0.290684i 0.0938827π0.0938827\pi
−0.956819 + 0.290684i 0.906117π0.906117\pi
618618 1.05273i 0.0423471i
619619 3.86804 3.86804i 0.155470 0.155470i −0.625086 0.780556i 0.714936π-0.714936\pi
0.780556 + 0.625086i 0.214936π0.214936\pi
620620 −0.280909 0.427989i −0.0112816 0.0171884i
621621 2.83477i 0.113755i
622622 −3.60329 −0.144479
623623 −4.92401 + 4.92401i −0.197276 + 0.197276i
624624 0 0
625625 17.0867 + 18.2495i 0.683466 + 0.729982i
626626 −1.64132 + 1.64132i −0.0656004 + 0.0656004i
627627 0.187294 0.187294i 0.00747982 0.00747982i
628628 −18.3223 + 18.3223i −0.731137 + 0.731137i
629629 −22.1872 22.1872i −0.884662 0.884662i
630630 0.756486 3.64613i 0.0301391 0.145265i
631631 19.3475 + 19.3475i 0.770211 + 0.770211i 0.978143 0.207932i 0.0666734π-0.0666734\pi
−0.207932 + 0.978143i 0.566673π0.566673\pi
632632 21.8373 0.868642
633633 −0.727388 0.727388i −0.0289111 0.0289111i
634634 10.2116 0.405556
635635 −27.3930 + 17.9793i −1.08706 + 0.713487i
636636 1.06529i 0.0422417i
637637 0 0
638638 −1.03911 1.03911i −0.0411390 0.0411390i
639639 −3.02013 3.02013i −0.119475 0.119475i
640640 −23.5273 4.88135i −0.929998 0.192952i
641641 35.8310i 1.41524i 0.706593 + 0.707620i 0.250231π0.250231\pi
−0.706593 + 0.707620i 0.749769π0.749769\pi
642642 0.298288i 0.0117725i
643643 −5.93411 −0.234019 −0.117009 0.993131i 0.537331π-0.537331\pi
−0.117009 + 0.993131i 0.537331π0.537331\pi
644644 4.67862 4.67862i 0.184363 0.184363i
645645 0.385793 1.85946i 0.0151906 0.0732161i
646646 −24.5424 −0.965607
647647 4.39835 + 4.39835i 0.172917 + 0.172917i 0.788260 0.615343i 0.210982π-0.210982\pi
−0.615343 + 0.788260i 0.710982π0.710982\pi
648648 21.7072i 0.852740i
649649 −0.978793 −0.0384210
650650 0 0
651651 −0.0106590 −0.000417760
652652 31.9457i 1.25109i
653653 −21.8121 21.8121i −0.853575 0.853575i 0.136997 0.990571i 0.456255π-0.456255\pi
−0.990571 + 0.136997i 0.956255π0.956255\pi
654654 −0.492553 −0.0192604
655655 −9.61546 + 46.3449i −0.375707 + 1.81084i
656656 8.41991 8.41991i 0.328742 0.328742i
657657 0.795576 0.0310384
658658 5.19067i 0.202353i
659659 26.7893i 1.04356i 0.853079 + 0.521782i 0.174733π0.174733\pi
−0.853079 + 0.521782i 0.825267π0.825267\pi
660660 0.130524 + 0.0270806i 0.00508063 + 0.00105411i
661661 −9.23307 9.23307i −0.359125 0.359125i 0.504365 0.863490i 0.331726π-0.331726\pi
−0.863490 + 0.504365i 0.831726π0.831726\pi
662662 −7.60238 7.60238i −0.295475 0.295475i
663663 0 0
664664 6.29612i 0.244337i
665665 10.2165 6.70557i 0.396179 0.260031i
666666 −12.3246 −0.477568
667667 −18.2245 18.2245i −0.705657 0.705657i
668668 −27.1751 −1.05144
669669 0.176047 + 0.176047i 0.00680638 + 0.00680638i
670670 3.63797 17.5344i 0.140547 0.677412i
671671 0.953039 + 0.953039i 0.0367917 + 0.0367917i
672672 −0.291445 + 0.291445i −0.0112427 + 0.0112427i
673673 23.0361 23.0361i 0.887977 0.887977i −0.106351 0.994329i 0.533917π-0.533917\pi
0.994329 + 0.106351i 0.0339168π0.0339168\pi
674674 12.5485 12.5485i 0.483351 0.483351i
675675 2.45066 0.968184i 0.0943258 0.0372654i
676676 0 0
677677 7.47403 7.47403i 0.287250 0.287250i −0.548742 0.835992i 0.684893π-0.684893\pi
0.835992 + 0.548742i 0.184893π0.184893\pi
678678 0.288924 0.0110960
679679 11.6954i 0.448827i
680680 −15.6698 23.8742i −0.600908 0.915533i
681681 −0.963464 + 0.963464i −0.0369200 + 0.0369200i
682682 0.0460656i 0.00176394i
683683 1.28980i 0.0493526i −0.999695 0.0246763i 0.992144π-0.992144\pi
0.999695 0.0246763i 0.00785551π-0.00785551\pi
684684 21.8436 21.8436i 0.835210 0.835210i
685685 −6.92124 + 33.3592i −0.264447 + 1.27459i
686686 7.42921i 0.283649i
687687 −1.80773 −0.0689693
688688 9.37013 9.37013i 0.357233 0.357233i
689689 0 0
690690 −0.714356 0.148212i −0.0271951 0.00564233i
691691 −13.2988 + 13.2988i −0.505911 + 0.505911i −0.913269 0.407358i 0.866450π-0.866450\pi
0.407358 + 0.913269i 0.366450π0.366450\pi
692692 6.89719 6.89719i 0.262192 0.262192i
693693 −0.759263 + 0.759263i −0.0288420 + 0.0288420i
694694 −11.6621 11.6621i −0.442687 0.442687i
695695 −25.9917 5.39266i −0.985921 0.204555i
696696 0.724256 + 0.724256i 0.0274528 + 0.0274528i
697697 45.5932 1.72697
698698 5.33344 + 5.33344i 0.201874 + 0.201874i
699699 0.602631 0.0227936
700700 5.64260 + 2.44673i 0.213270 + 0.0924778i
701701 21.8278i 0.824425i 0.911088 + 0.412212i 0.135244π0.135244\pi
−0.911088 + 0.412212i 0.864756π0.864756\pi
702702 0 0
703703 −28.5998 28.5998i −1.07866 1.07866i
704704 −0.396569 0.396569i −0.0149462 0.0149462i
705705 −1.53333 + 1.00640i −0.0577487 + 0.0379032i
706706 0.598139i 0.0225113i
707707 3.17362i 0.119356i
708708 0.295067 0.0110893
709709 18.2874 18.2874i 0.686798 0.686798i −0.274725 0.961523i 0.588587π-0.588587\pi
0.961523 + 0.274725i 0.0885867π0.0885867\pi
710710 −1.84032 + 1.20789i −0.0690658 + 0.0453312i
711711 −26.8824 −1.00817
712712 14.8322 + 14.8322i 0.555861 + 0.555861i
713713 0.807921i 0.0302569i
714714 −0.257167 −0.00962423
715715 0 0
716716 7.93292 0.296467
717717 1.24396i 0.0464564i
718718 −13.2994 13.2994i −0.496330 0.496330i
719719 −17.7717 −0.662771 −0.331385 0.943495i 0.607516π-0.607516\pi
−0.331385 + 0.943495i 0.607516π0.607516\pi
720720 8.98993 + 1.86520i 0.335035 + 0.0695118i
721721 −9.90321 + 9.90321i −0.368815 + 0.368815i
722722 −18.5315 −0.689672
723723 2.14575i 0.0798013i
724724 16.3535i 0.607772i
725725 9.53071 21.9795i 0.353962 0.816298i
726726 −0.463308 0.463308i −0.0171950 0.0171950i
727727 14.6033 + 14.6033i 0.541607 + 0.541607i 0.924000 0.382393i 0.124900π-0.124900\pi
−0.382393 + 0.924000i 0.624900π0.624900\pi
728728 0 0
729729 26.5832i 0.984564i
730730 0.0832987 0.401485i 0.00308302 0.0148596i
731731 50.7386 1.87663
732732 −0.287303 0.287303i −0.0106190 0.0106190i
733733 5.44505 0.201118 0.100559 0.994931i 0.467937π-0.467937\pi
0.100559 + 0.994931i 0.467937π0.467937\pi
734734 −8.08614 8.08614i −0.298465 0.298465i
735735 −1.04377 + 0.685078i −0.0385002 + 0.0252695i
736736 −22.0906 22.0906i −0.814271 0.814271i
737737 −3.65132 + 3.65132i −0.134498 + 0.134498i
738738 12.6631 12.6631i 0.466135 0.466135i
739739 −21.6891 + 21.6891i −0.797846 + 0.797846i −0.982756 0.184910i 0.940801π-0.940801\pi
0.184910 + 0.982756i 0.440801π0.440801\pi
740740 4.13520 19.9309i 0.152013 0.732676i
741741 0 0
742742 3.12723 3.12723i 0.114804 0.114804i
743743 0.675576 0.0247845 0.0123922 0.999923i 0.496055π-0.496055\pi
0.0123922 + 0.999923i 0.496055π0.496055\pi
744744 0.0321074i 0.00117711i
745745 25.2225 16.5547i 0.924080 0.606517i
746746 3.57860 3.57860i 0.131022 0.131022i
747747 7.75072i 0.283584i
748748 3.56157i 0.130224i
749749 2.80604 2.80604i 0.102531 0.102531i
750750 −0.115851 0.668181i −0.00423029 0.0243985i
751751 5.64380i 0.205945i 0.994684 + 0.102973i 0.0328354π0.0328354\pi
−0.994684 + 0.102973i 0.967165π0.967165\pi
752752 −12.7982 −0.466701
753753 −0.335492 + 0.335492i −0.0122260 + 0.0122260i
754754 0 0
755755 −10.2233 + 6.71006i −0.372065 + 0.244204i
756756 0.458367 0.458367i 0.0166706 0.0166706i
757757 21.3676 21.3676i 0.776619 0.776619i −0.202635 0.979254i 0.564951π-0.564951\pi
0.979254 + 0.202635i 0.0649506π0.0649506\pi
758758 −16.3672 + 16.3672i −0.594484 + 0.594484i
759759 0.148756 + 0.148756i 0.00539950 + 0.00539950i
760760 −20.1987 30.7743i −0.732682 1.11630i
761761 13.3384 + 13.3384i 0.483516 + 0.483516i 0.906253 0.422736i 0.138930π-0.138930\pi
−0.422736 + 0.906253i 0.638930π0.638930\pi
762762 0.888819 0.0321985
763763 4.63353 + 4.63353i 0.167745 + 0.167745i
764764 24.5954 0.889829
765765 19.2900 + 29.3899i 0.697430 + 1.06259i
766766 20.2597i 0.732013i
767767 0 0
768768 0.617743 + 0.617743i 0.0222909 + 0.0222909i
769769 8.21751 + 8.21751i 0.296331 + 0.296331i 0.839575 0.543244i 0.182804π-0.182804\pi
−0.543244 + 0.839575i 0.682804π0.682804\pi
770770 0.303664 + 0.462657i 0.0109433 + 0.0166730i
771771 0.0349307i 0.00125800i
772772 11.5931i 0.417244i
773773 −8.29320 −0.298286 −0.149143 0.988816i 0.547651π-0.547651\pi
−0.149143 + 0.988816i 0.547651π0.547651\pi
774774 14.0922 14.0922i 0.506533 0.506533i
775775 0.698448 0.275937i 0.0250890 0.00991194i
776776 35.2290 1.26465
777777 −0.299683 0.299683i −0.0107511 0.0107511i
778778 19.9209i 0.714198i
779779 58.7707 2.10568
780780 0 0
781781 0.634752 0.0227132
782782 19.4925i 0.697049i
783783 −1.78547 1.78547i −0.0638074 0.0638074i
784784 −8.71199 −0.311142
785785 −20.8568 31.7770i −0.744409 1.13417i
786786 0.907871 0.907871i 0.0323827 0.0323827i
787787 −48.6606 −1.73456 −0.867282 0.497817i 0.834135π-0.834135\pi
−0.867282 + 0.497817i 0.834135π0.834135\pi
788788 7.47076i 0.266135i
789789 2.37858i 0.0846797i
790790 −2.81465 + 13.5661i −0.100141 + 0.482662i
791791 −2.71795 2.71795i −0.0966392 0.0966392i
792792 2.28707 + 2.28707i 0.0812675 + 0.0812675i
793793 0 0
794794 4.06290i 0.144187i
795795 1.53012 + 0.317463i 0.0542677 + 0.0112593i
796796 −30.4498 −1.07926
797797 −36.6678 36.6678i −1.29884 1.29884i −0.929159 0.369679i 0.879468π-0.879468\pi
−0.369679 0.929159i 0.620532π-0.620532\pi
798798 −0.331494 −0.0117348
799799 −34.6505 34.6505i −1.22585 1.22585i
800800 11.5525 26.6421i 0.408443 0.941942i
801801 −18.2589 18.2589i −0.645147 0.645147i
802802 1.76653 1.76653i 0.0623785 0.0623785i
803803 −0.0836045 + 0.0836045i −0.00295034 + 0.00295034i
804804 1.10073 1.10073i 0.0388197 0.0388197i
805805 5.32581 + 8.11432i 0.187710 + 0.285992i
806806 0 0
807807 −0.423047 + 0.423047i −0.0148920 + 0.0148920i
808808 9.55965 0.336307
809809 11.3889i 0.400413i 0.979754 + 0.200206i 0.0641613π0.0641613\pi
−0.979754 + 0.200206i 0.935839π0.935839\pi
810810 13.4853 + 2.79789i 0.473826 + 0.0983077i
811811 23.0388 23.0388i 0.809003 0.809003i −0.175480 0.984483i 0.556148π-0.556148\pi
0.984483 + 0.175480i 0.0561477π0.0561477\pi
812812 5.89362i 0.206825i
813813 0.148464i 0.00520687i
814814 1.29515 1.29515i 0.0453950 0.0453950i
815815 45.8847 + 9.51999i 1.60727 + 0.333471i
816816 0.634073i 0.0221970i
817817 65.4031 2.28817
818818 −5.85536 + 5.85536i −0.204728 + 0.204728i
819819 0 0
820820 16.2296 + 24.7271i 0.566762 + 0.863509i
821821 7.31750 7.31750i 0.255383 0.255383i −0.567790 0.823173i 0.692202π-0.692202\pi
0.823173 + 0.567790i 0.192202π0.192202\pi
822822 0.653489 0.653489i 0.0227930 0.0227930i
823823 −7.13667 + 7.13667i −0.248769 + 0.248769i −0.820465 0.571697i 0.806285π-0.806285\pi
0.571697 + 0.820465i 0.306285π0.306285\pi
824824 29.8307 + 29.8307i 1.03920 + 1.03920i
825825 −0.0777936 + 0.179406i −0.00270842 + 0.00624610i
826826 0.866187 + 0.866187i 0.0301385 + 0.0301385i
827827 8.88196 0.308856 0.154428 0.988004i 0.450647π-0.450647\pi
0.154428 + 0.988004i 0.450647π0.450647\pi
828828 17.3490 + 17.3490i 0.602918 + 0.602918i
829829 10.4462 0.362812 0.181406 0.983408i 0.441935π-0.441935\pi
0.181406 + 0.983408i 0.441935π0.441935\pi
830830 −3.91138 0.811519i −0.135766 0.0281682i
831831 0.930407i 0.0322755i
832832 0 0
833833 −23.5874 23.5874i −0.817255 0.817255i
834834 0.509163 + 0.509163i 0.0176309 + 0.0176309i
835835 8.09834 39.0326i 0.280255 1.35078i
836836 4.59094i 0.158781i
837837 0.0791525i 0.00273591i
838838 −8.70202 −0.300606
839839 18.5309 18.5309i 0.639759 0.639759i −0.310737 0.950496i 0.600576π-0.600576\pi
0.950496 + 0.310737i 0.100576π0.100576\pi
840840 −0.211651 0.322469i −0.00730267 0.0111262i
841841 6.04271 0.208369
842842 −1.87745 1.87745i −0.0647012 0.0647012i
843843 0.117364i 0.00404222i
844844 17.8297 0.613723
845845 0 0
846846 −19.2477 −0.661751
847847 8.71682i 0.299513i
848848 7.71053 + 7.71053i 0.264781 + 0.264781i
849849 0.374060 0.0128377
850850 16.8512 6.65744i 0.577992 0.228348i
851851 22.7150 22.7150i 0.778661 0.778661i
852852 −0.191352 −0.00655562
853853 30.8130i 1.05502i −0.849550 0.527509i 0.823126π-0.823126\pi
0.849550 0.527509i 0.176874π-0.176874\pi
854854 1.68679i 0.0577208i
855855 24.8652 + 37.8842i 0.850371 + 1.29561i
856856 −8.45243 8.45243i −0.288898 0.288898i
857857 −7.54399 7.54399i −0.257698 0.257698i 0.566419 0.824117i 0.308328π-0.308328\pi
−0.824117 + 0.566419i 0.808328π0.808328\pi
858858 0 0
859859 9.75562i 0.332857i −0.986053 0.166429i 0.946776π-0.946776\pi
0.986053 0.166429i 0.0532235π-0.0532235\pi
860860 18.0612 + 27.5177i 0.615880 + 0.938346i
861861 0.615828 0.0209873
862862 −6.80856 6.80856i −0.231900 0.231900i
863863 −35.0410 −1.19281 −0.596405 0.802683i 0.703405π-0.703405\pi
−0.596405 + 0.802683i 0.703405π0.703405\pi
864864 −2.16423 2.16423i −0.0736286 0.0736286i
865865 7.85127 + 11.9621i 0.266951 + 0.406723i
866866 16.6304 + 16.6304i 0.565124 + 0.565124i
867867 0.659548 0.659548i 0.0223994 0.0223994i
868868 0.130637 0.130637i 0.00443409 0.00443409i
869869 2.82499 2.82499i 0.0958311 0.0958311i
870870 −0.543285 + 0.356584i −0.0184191 + 0.0120893i
871871 0 0
872872 13.9572 13.9572i 0.472651 0.472651i
873873 −43.3680 −1.46778
874874 25.1262i 0.849907i
875875 −5.19585 + 7.37551i −0.175652 + 0.249338i
876876 0.0252034 0.0252034i 0.000851545 0.000851545i
877877 37.9152i 1.28030i −0.768248 0.640152i 0.778871π-0.778871\pi
0.768248 0.640152i 0.221129π-0.221129\pi
878878 20.0589i 0.676956i
879879 −0.419325 + 0.419325i −0.0141435 + 0.0141435i
880880 −1.14073 + 0.748715i −0.0384540 + 0.0252392i
881881 18.6214i 0.627370i −0.949527 0.313685i 0.898436π-0.898436\pi
0.949527 0.313685i 0.101564π-0.101564\pi
882882 −13.1024 −0.441179
883883 13.2901 13.2901i 0.447248 0.447248i −0.447191 0.894439i 0.647575π-0.647575\pi
0.894439 + 0.447191i 0.147575π0.147575\pi
884884 0 0
885885 −0.0879316 + 0.423815i −0.00295579 + 0.0142464i
886886 −4.95870 + 4.95870i −0.166591 + 0.166591i
887887 −27.6979 + 27.6979i −0.930004 + 0.930004i −0.997706 0.0677017i 0.978433π-0.978433\pi
0.0677017 + 0.997706i 0.478433π0.478433\pi
888888 −0.902711 + 0.902711i −0.0302930 + 0.0302930i
889889 −8.36126 8.36126i −0.280428 0.280428i
890890 −11.1261 + 7.30257i −0.372947 + 0.244783i
891891 −2.80816 2.80816i −0.0940768 0.0940768i
892892 −4.31525 −0.144485
893893 −44.6653 44.6653i −1.49467 1.49467i
894894 −0.818392 −0.0273711
895895 −2.36405 + 11.3943i −0.0790216 + 0.380870i
896896 8.67127i 0.289687i
897897 0 0
898898 −7.78067 7.78067i −0.259644 0.259644i
899899 −0.508866 0.508866i −0.0169716 0.0169716i
900900 −9.07283 + 20.9235i −0.302428 + 0.697451i
901901 41.7520i 1.39096i
902902 2.66145i 0.0886165i
903903 0.685326 0.0228062
904904 −8.18707 + 8.18707i −0.272298 + 0.272298i
905905 23.4890 + 4.87342i 0.780802 + 0.161998i
906906 0.331716 0.0110205
907907 −26.8910 26.8910i −0.892900 0.892900i 0.101895 0.994795i 0.467510π-0.467510\pi
−0.994795 + 0.101895i 0.967510π0.967510\pi
908908 23.6163i 0.783735i
909909 −11.7682 −0.390327
910910 0 0
911911 −30.2074 −1.00081 −0.500407 0.865790i 0.666816π-0.666816\pi
−0.500407 + 0.865790i 0.666816π0.666816\pi
912912 0.817334i 0.0270646i
913913 0.814499 + 0.814499i 0.0269560 + 0.0269560i
914914 −13.2621 −0.438671
915915 0.498281 0.327046i 0.0164727 0.0108118i
916916 22.1555 22.1555i 0.732038 0.732038i
917917 −17.0810 −0.564063
918918 1.90969i 0.0630291i
919919 39.1747i 1.29225i 0.763230 + 0.646127i 0.223612π0.223612\pi
−0.763230 + 0.646127i 0.776388π0.776388\pi
920920 24.4421 16.0425i 0.805833 0.528906i
921921 0.597430 + 0.597430i 0.0196860 + 0.0196860i
922922 −2.16143 2.16143i −0.0711828 0.0711828i
923923 0 0
924924 0.0481061i 0.00158258i
925925 27.3952 + 11.8791i 0.900748 + 0.390581i
926926 8.45451 0.277833
927927 −36.7225 36.7225i −1.20612 1.20612i
928928 −27.8274 −0.913478
929929 −24.2932 24.2932i −0.797034 0.797034i 0.185593 0.982627i 0.440579π-0.440579\pi
−0.982627 + 0.185593i 0.940579π0.940579\pi
930930 −0.0199463 0.00413838i −0.000654064 0.000135703i
931931 −30.4047 30.4047i −0.996473 0.996473i
932932 −7.38582 + 7.38582i −0.241930 + 0.241930i
933933 0.324896 0.324896i 0.0106366 0.0106366i
934934 −7.25130 + 7.25130i −0.237270 + 0.237270i
935935 −5.11561 1.06137i −0.167298 0.0347104i
936936 0 0
937937 12.4007 12.4007i 0.405113 0.405113i −0.474917 0.880030i 0.657522π-0.657522\pi
0.880030 + 0.474917i 0.157522π0.157522\pi
938938 6.46251 0.211008
939939 0.295985i 0.00965910i
940940 6.45809 31.1269i 0.210640 1.01525i
941941 0.542863 0.542863i 0.0176968 0.0176968i −0.698203 0.715900i 0.746017π-0.746017\pi
0.715900 + 0.698203i 0.246017π0.246017\pi
942942 1.03107i 0.0335940i
943943 46.6778i 1.52004i
944944 −2.13568 + 2.13568i −0.0695104 + 0.0695104i
945945 0.521772 + 0.794964i 0.0169733 + 0.0258602i
946946 2.96180i 0.0962965i
947947 27.7644 0.902222 0.451111 0.892468i 0.351028π-0.351028\pi
0.451111 + 0.892468i 0.351028π0.351028\pi
948948 −0.851621 + 0.851621i −0.0276594 + 0.0276594i
949949 0 0
950950 21.7216 8.58158i 0.704742 0.278423i
951951 −0.920748 + 0.920748i −0.0298573 + 0.0298573i
952952 7.28720 7.28720i 0.236180 0.236180i
953953 −6.15610 + 6.15610i −0.199416 + 0.199416i −0.799750 0.600334i 0.795034π-0.795034\pi
0.600334 + 0.799750i 0.295034π0.295034\pi
954954 11.5962 + 11.5962i 0.375442 + 0.375442i
955955 −7.32955 + 35.3272i −0.237179 + 1.14316i
956956 15.2459 + 15.2459i 0.493087 + 0.493087i
957957 0.187387 0.00605736
958958 5.73912 + 5.73912i 0.185423 + 0.185423i
959959 −12.2949 −0.397024
960960 −0.207340 + 0.136087i −0.00669186 + 0.00439218i
961961 30.9774i 0.999272i
962962 0 0
963963 10.4052 + 10.4052i 0.335303 + 0.335303i
964964 −26.2982 26.2982i −0.847008 0.847008i
965965 16.6516 + 3.45480i 0.536033 + 0.111214i
966966 0.263285i 0.00847105i
967967 0.785304i 0.0252537i 0.999920 + 0.0126268i 0.00401935π0.00401935\pi
−0.999920 + 0.0126268i 0.995981π0.995981\pi
968968 26.2570 0.843932
969969 2.21290 2.21290i 0.0710886 0.0710886i
970970 −4.54074 + 21.8856i −0.145794 + 0.702703i
971971 −47.2589 −1.51661 −0.758305 0.651900i 0.773972π-0.773972\pi
−0.758305 + 0.651900i 0.773972π0.773972\pi
972972 2.55063 + 2.55063i 0.0818115 + 0.0818115i
973973 9.57955i 0.307106i
974974 −18.2766 −0.585621
975975 0 0
976976 4.15897 0.133125
977977 4.40336i 0.140876i 0.997516 + 0.0704380i 0.0224397π0.0224397\pi
−0.997516 + 0.0704380i 0.977560π0.977560\pi
978978 −0.898856 0.898856i −0.0287423 0.0287423i
979979 3.83754 0.122648
980980 4.39616 21.1887i 0.140430 0.676849i
981981 −17.1818 + 17.1818i −0.548572 + 0.548572i
982982 9.82856 0.313642
983983 33.3973i 1.06521i −0.846364 0.532604i 0.821213π-0.821213\pi
0.846364 0.532604i 0.178787π-0.178787\pi
984984 1.85501i 0.0591355i
985985 10.7305 + 2.22633i 0.341902 + 0.0709366i
986986 −12.2772 12.2772i −0.390987 0.390987i
987987 −0.468025 0.468025i −0.0148974 0.0148974i
988988 0 0
989989 51.9456i 1.65177i
990990 −1.71560 + 1.12603i −0.0545252 + 0.0357875i
991991 −46.0539 −1.46295 −0.731475 0.681868i 0.761168π-0.761168\pi
−0.731475 + 0.681868i 0.761168π0.761168\pi
992992 −0.616815 0.616815i −0.0195839 0.0195839i
993993 1.37096 0.0435061
994994 −0.561726 0.561726i −0.0178169 0.0178169i
995995 9.07419 43.7360i 0.287671 1.38653i
996996 −0.245539 0.245539i −0.00778020 0.00778020i
997997 9.23126 9.23126i 0.292357 0.292357i −0.545654 0.838011i 0.683719π-0.683719\pi
0.838011 + 0.545654i 0.183719π0.183719\pi
998998 −13.9088 + 13.9088i −0.440275 + 0.440275i
999999 2.22540 2.22540i 0.0704086 0.0704086i
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 845.2.f.f.408.20 yes 72
5.2 odd 4 845.2.k.f.577.17 yes 72
13.2 odd 12 845.2.o.i.488.17 144
13.3 even 3 845.2.t.i.188.17 144
13.4 even 6 845.2.t.i.418.17 144
13.5 odd 4 845.2.k.f.268.20 yes 72
13.6 odd 12 845.2.o.i.258.17 144
13.7 odd 12 845.2.o.i.258.20 144
13.8 odd 4 845.2.k.f.268.17 yes 72
13.9 even 3 845.2.t.i.418.20 144
13.10 even 6 845.2.t.i.188.20 144
13.11 odd 12 845.2.o.i.488.20 144
13.12 even 2 inner 845.2.f.f.408.17 72
65.2 even 12 845.2.t.i.657.17 144
65.7 even 12 845.2.t.i.427.17 144
65.12 odd 4 845.2.k.f.577.20 yes 72
65.17 odd 12 845.2.o.i.587.17 144
65.22 odd 12 845.2.o.i.587.20 144
65.32 even 12 845.2.t.i.427.20 144
65.37 even 12 845.2.t.i.657.20 144
65.42 odd 12 845.2.o.i.357.20 144
65.47 even 4 inner 845.2.f.f.437.17 yes 72
65.57 even 4 inner 845.2.f.f.437.20 yes 72
65.62 odd 12 845.2.o.i.357.17 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
845.2.f.f.408.17 72 13.12 even 2 inner
845.2.f.f.408.20 yes 72 1.1 even 1 trivial
845.2.f.f.437.17 yes 72 65.47 even 4 inner
845.2.f.f.437.20 yes 72 65.57 even 4 inner
845.2.k.f.268.17 yes 72 13.8 odd 4
845.2.k.f.268.20 yes 72 13.5 odd 4
845.2.k.f.577.17 yes 72 5.2 odd 4
845.2.k.f.577.20 yes 72 65.12 odd 4
845.2.o.i.258.17 144 13.6 odd 12
845.2.o.i.258.20 144 13.7 odd 12
845.2.o.i.357.17 144 65.62 odd 12
845.2.o.i.357.20 144 65.42 odd 12
845.2.o.i.488.17 144 13.2 odd 12
845.2.o.i.488.20 144 13.11 odd 12
845.2.o.i.587.17 144 65.17 odd 12
845.2.o.i.587.20 144 65.22 odd 12
845.2.t.i.188.17 144 13.3 even 3
845.2.t.i.188.20 144 13.10 even 6
845.2.t.i.418.17 144 13.4 even 6
845.2.t.i.418.20 144 13.9 even 3
845.2.t.i.427.17 144 65.7 even 12
845.2.t.i.427.20 144 65.32 even 12
845.2.t.i.657.17 144 65.2 even 12
845.2.t.i.657.20 144 65.37 even 12