Properties

Label 378.2.bf.a.101.7
Level 378378
Weight 22
Character 378.101
Analytic conductor 3.0183.018
Analytic rank 00
Dimension 144144
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [378,2,Mod(5,378)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(378, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([5, 15]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 378=2337 378 = 2 \cdot 3^{3} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 378.bf (of order 1818, degree 66, 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: 3.018345196403.01834519640
Analytic rank: 00
Dimension: 144144
Relative dimension: 2424 over Q(ζ18)\Q(\zeta_{18})
Twist minimal: yes
Sato-Tate group: SU(2)[C18]\mathrm{SU}(2)[C_{18}]

Embedding invariants

Embedding label 101.7
Character χ\chi == 378.101
Dual form 378.2.bf.a.131.7

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+(0.642788+0.766044i)q2+(0.3247161.70134i)q3+(0.1736480.984808i)q4+(2.51689+2.11192i)q5+(1.51203+0.844853i)q6+(2.589430.542996i)q7+(0.866025+0.500000i)q8+(2.78912+1.10491i)q93.28557iq10+(2.313202.75676i)q11+(1.61911+0.615218i)q12+(1.074882.95321i)q13+(1.24850+2.33265i)q14+(4.41037+3.59631i)q15+(0.939693+0.342020i)q165.93277q17+(0.9464042.84681i)q185.92479iq19+(2.51689+2.11192i)q20+(1.764654.22918i)q21+(0.624907+3.54402i)q22+(2.312076.35235i)q23+(0.5694581.63576i)q24+(1.006285.70690i)q25+(1.57137+2.72170i)q26+(2.78549+4.38646i)q27+(0.9843972.45580i)q28+(1.667554.58155i)q29+(5.58987+1.06688i)q30+(5.71905+1.00842i)q31+(0.3420200.939693i)q32+(5.441323.04037i)q33+(3.813514.54476i)q34+(5.37055+6.83534i)q35+(1.57245+2.55488i)q36+(0.378361+0.655341i)q37+(4.53865+3.80838i)q38+(5.373450.869783i)q39+(3.23565+0.570532i)q40+(0.362685+0.132007i)q41+(4.37404+1.36667i)q42+(0.5637443.19715i)q43+(3.116561.79935i)q44+(4.686438.67132i)q45+(3.38002+5.85436i)q46+(0.6942673.93738i)q47+(0.887026+1.48768i)q48+(6.410312.81210i)q49+(3.72492+4.43918i)q50+(1.92647+10.0937i)q51+(3.095000.545732i)q52+(7.08260+4.08914i)q53+(5.150700.685750i)q54+11.8238iq55+(2.51401+0.824467i)q56+(10.0801+1.92388i)q57+(4.58155+1.66755i)q58+(10.0710+3.66555i)q59+(2.775824.96786i)q60+(14.1733+2.49913i)q61+(2.903645.02925i)q62+(6.62227+4.37556i)q63+(0.500000+0.866025i)q64+(3.53159+9.70297i)q65+(5.826672.21398i)q66+(1.85767+1.55877i)q67+(1.03021+5.84263i)q68+(11.55831.87090i)q69+(1.784058.50775i)q70+(1.698730.980762i)q71+(2.967900.437683i)q72+(13.7210+7.92182i)q73+(0.2588140.711086i)q74+(10.0361+0.141098i)q75+(5.83478+1.02883i)q76+(4.492968.39450i)q77+(4.120283.55722i)q78+(0.103645+0.0869684i)q79+(1.642782.84538i)q80+(6.558376.16343i)q81+(0.334253+0.192981i)q82+(5.39571+1.96388i)q83+(3.85851+2.47223i)q84+(14.932112.5295i)q85+(2.08679+2.48694i)q86+(7.25329+4.32477i)q87+(3.381671.23083i)q8814.2427q89+(3.63024+9.16383i)q90+(1.179758.23080i)q91+(6.657331.17387i)q92+(3.57274+9.40260i)q93+(2.56994+3.06274i)q94+(12.5127+14.9120i)q95+(1.709800.276759i)q96+(1.555580.274290i)q97+(1.96627+6.71817i)q98+(3.40582+10.2448i)q99+O(q100)q+(-0.642788 + 0.766044i) q^{2} +(-0.324716 - 1.70134i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-2.51689 + 2.11192i) q^{5} +(1.51203 + 0.844853i) q^{6} +(2.58943 - 0.542996i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.78912 + 1.10491i) q^{9} -3.28557i q^{10} +(2.31320 - 2.75676i) q^{11} +(-1.61911 + 0.615218i) q^{12} +(1.07488 - 2.95321i) q^{13} +(-1.24850 + 2.33265i) q^{14} +(4.41037 + 3.59631i) q^{15} +(-0.939693 + 0.342020i) q^{16} -5.93277 q^{17} +(0.946404 - 2.84681i) q^{18} -5.92479i q^{19} +(2.51689 + 2.11192i) q^{20} +(-1.76465 - 4.22918i) q^{21} +(0.624907 + 3.54402i) q^{22} +(2.31207 - 6.35235i) q^{23} +(0.569458 - 1.63576i) q^{24} +(1.00628 - 5.70690i) q^{25} +(1.57137 + 2.72170i) q^{26} +(2.78549 + 4.38646i) q^{27} +(-0.984397 - 2.45580i) q^{28} +(-1.66755 - 4.58155i) q^{29} +(-5.58987 + 1.06688i) q^{30} +(-5.71905 + 1.00842i) q^{31} +(0.342020 - 0.939693i) q^{32} +(-5.44132 - 3.04037i) q^{33} +(3.81351 - 4.54476i) q^{34} +(-5.37055 + 6.83534i) q^{35} +(1.57245 + 2.55488i) q^{36} +(-0.378361 + 0.655341i) q^{37} +(4.53865 + 3.80838i) q^{38} +(-5.37345 - 0.869783i) q^{39} +(-3.23565 + 0.570532i) q^{40} +(0.362685 + 0.132007i) q^{41} +(4.37404 + 1.36667i) q^{42} +(0.563744 - 3.19715i) q^{43} +(-3.11656 - 1.79935i) q^{44} +(4.68643 - 8.67132i) q^{45} +(3.38002 + 5.85436i) q^{46} +(0.694267 - 3.93738i) q^{47} +(0.887026 + 1.48768i) q^{48} +(6.41031 - 2.81210i) q^{49} +(3.72492 + 4.43918i) q^{50} +(1.92647 + 10.0937i) q^{51} +(-3.09500 - 0.545732i) q^{52} +(7.08260 + 4.08914i) q^{53} +(-5.15070 - 0.685750i) q^{54} +11.8238i q^{55} +(2.51401 + 0.824467i) q^{56} +(-10.0801 + 1.92388i) q^{57} +(4.58155 + 1.66755i) q^{58} +(10.0710 + 3.66555i) q^{59} +(2.77582 - 4.96786i) q^{60} +(14.1733 + 2.49913i) q^{61} +(2.90364 - 5.02925i) q^{62} +(-6.62227 + 4.37556i) q^{63} +(0.500000 + 0.866025i) q^{64} +(3.53159 + 9.70297i) q^{65} +(5.82667 - 2.21398i) q^{66} +(-1.85767 + 1.55877i) q^{67} +(1.03021 + 5.84263i) q^{68} +(-11.5583 - 1.87090i) q^{69} +(-1.78405 - 8.50775i) q^{70} +(1.69873 - 0.980762i) q^{71} +(-2.96790 - 0.437683i) q^{72} +(-13.7210 + 7.92182i) q^{73} +(-0.258814 - 0.711086i) q^{74} +(-10.0361 + 0.141098i) q^{75} +(-5.83478 + 1.02883i) q^{76} +(4.49296 - 8.39450i) q^{77} +(4.12028 - 3.55722i) q^{78} +(0.103645 + 0.0869684i) q^{79} +(1.64278 - 2.84538i) q^{80} +(6.55837 - 6.16343i) q^{81} +(-0.334253 + 0.192981i) q^{82} +(-5.39571 + 1.96388i) q^{83} +(-3.85851 + 2.47223i) q^{84} +(14.9321 - 12.5295i) q^{85} +(2.08679 + 2.48694i) q^{86} +(-7.25329 + 4.32477i) q^{87} +(3.38167 - 1.23083i) q^{88} -14.2427 q^{89} +(3.63024 + 9.16383i) q^{90} +(1.17975 - 8.23080i) q^{91} +(-6.65733 - 1.17387i) q^{92} +(3.57274 + 9.40260i) q^{93} +(2.56994 + 3.06274i) q^{94} +(12.5127 + 14.9120i) q^{95} +(-1.70980 - 0.276759i) q^{96} +(-1.55558 - 0.274290i) q^{97} +(-1.96627 + 6.71817i) q^{98} +(-3.40582 + 10.2448i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 144q+18q612q9+12q11+6q14+12q15+6q216q236q2918q3054q35+6q366q39+24q4254q47+18q49+12q50+18q51+108q99+O(q100) 144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51}+ \cdots - 108 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/378Z)×\left(\mathbb{Z}/378\mathbb{Z}\right)^\times.

nn 2929 325325
χ(n)\chi(n) e(718)e\left(\frac{7}{18}\right) e(16)e\left(\frac{1}{6}\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 −0.642788 + 0.766044i −0.454519 + 0.541675i
33 −0.324716 1.70134i −0.187475 0.982269i
44 −0.173648 0.984808i −0.0868241 0.492404i
55 −2.51689 + 2.11192i −1.12559 + 0.944480i −0.998873 0.0474597i 0.984887π-0.984887\pi
−0.126714 + 0.991939i 0.540443π0.540443\pi
66 1.51203 + 0.844853i 0.617282 + 0.344910i
77 2.58943 0.542996i 0.978713 0.205233i
88 0.866025 + 0.500000i 0.306186 + 0.176777i
99 −2.78912 + 1.10491i −0.929706 + 0.368302i
1010 3.28557i 1.03899i
1111 2.31320 2.75676i 0.697455 0.831195i −0.294781 0.955565i 0.595247π-0.595247\pi
0.992236 + 0.124370i 0.0396910π0.0396910\pi
1212 −1.61911 + 0.615218i −0.467396 + 0.177598i
1313 1.07488 2.95321i 0.298118 0.819074i −0.696696 0.717367i 0.745347π-0.745347\pi
0.994814 0.101707i 0.0324305π-0.0324305\pi
1414 −1.24850 + 2.33265i −0.333674 + 0.623427i
1515 4.41037 + 3.59631i 1.13875 + 0.928563i
1616 −0.939693 + 0.342020i −0.234923 + 0.0855050i
1717 −5.93277 −1.43891 −0.719453 0.694541i 0.755608π-0.755608\pi
−0.719453 + 0.694541i 0.755608π0.755608\pi
1818 0.946404 2.84681i 0.223070 0.670999i
1919 5.92479i 1.35924i −0.733564 0.679620i 0.762145π-0.762145\pi
0.733564 0.679620i 0.237855π-0.237855\pi
2020 2.51689 + 2.11192i 0.562794 + 0.472240i
2121 −1.76465 4.22918i −0.385079 0.922884i
2222 0.624907 + 3.54402i 0.133231 + 0.755588i
2323 2.31207 6.35235i 0.482099 1.32456i −0.425591 0.904916i 0.639934π-0.639934\pi
0.907690 0.419641i 0.137844π-0.137844\pi
2424 0.569458 1.63576i 0.116240 0.333899i
2525 1.00628 5.70690i 0.201256 1.14138i
2626 1.57137 + 2.72170i 0.308171 + 0.533768i
2727 2.78549 + 4.38646i 0.536068 + 0.844175i
2828 −0.984397 2.45580i −0.186034 0.464103i
2929 −1.66755 4.58155i −0.309656 0.850772i −0.992723 0.120417i 0.961577π-0.961577\pi
0.683068 0.730355i 0.260645π-0.260645\pi
3030 −5.58987 + 1.06688i −1.02057 + 0.194784i
3131 −5.71905 + 1.00842i −1.02717 + 0.181118i −0.661751 0.749724i 0.730186π-0.730186\pi
−0.365421 + 0.930842i 0.619075π0.619075\pi
3232 0.342020 0.939693i 0.0604612 0.166116i
3333 −5.44132 3.04037i −0.947213 0.529261i
3434 3.81351 4.54476i 0.654011 0.779420i
3535 −5.37055 + 6.83534i −0.907788 + 1.15538i
3636 1.57245 + 2.55488i 0.262074 + 0.425813i
3737 −0.378361 + 0.655341i −0.0622022 + 0.107737i −0.895449 0.445163i 0.853146π-0.853146\pi
0.833247 + 0.552900i 0.186479π0.186479\pi
3838 4.53865 + 3.80838i 0.736267 + 0.617801i
3939 −5.37345 0.869783i −0.860441 0.139277i
4040 −3.23565 + 0.570532i −0.511601 + 0.0902091i
4141 0.362685 + 0.132007i 0.0566419 + 0.0206160i 0.370186 0.928958i 0.379294π-0.379294\pi
−0.313544 + 0.949574i 0.601516π0.601516\pi
4242 4.37404 + 1.36667i 0.674929 + 0.210881i
4343 0.563744 3.19715i 0.0859701 0.487561i −0.911173 0.412024i 0.864822π-0.864822\pi
0.997143 0.0755366i 0.0240670π-0.0240670\pi
4444 −3.11656 1.79935i −0.469839 0.271262i
4545 4.68643 8.67132i 0.698612 1.29264i
4646 3.38002 + 5.85436i 0.498356 + 0.863178i
4747 0.694267 3.93738i 0.101269 0.574326i −0.891376 0.453265i 0.850259π-0.850259\pi
0.992645 0.121061i 0.0386297π-0.0386297\pi
4848 0.887026 + 1.48768i 0.128031 + 0.214728i
4949 6.41031 2.81210i 0.915759 0.401729i
5050 3.72492 + 4.43918i 0.526783 + 0.627795i
5151 1.92647 + 10.0937i 0.269759 + 1.41339i
5252 −3.09500 0.545732i −0.429199 0.0756793i
5353 7.08260 + 4.08914i 0.972870 + 0.561687i 0.900110 0.435663i 0.143486π-0.143486\pi
0.0727599 + 0.997349i 0.476819π0.476819\pi
5454 −5.15070 0.685750i −0.700922 0.0933188i
5555 11.8238i 1.59431i
5656 2.51401 + 0.824467i 0.335949 + 0.110174i
5757 −10.0801 + 1.92388i −1.33514 + 0.254824i
5858 4.58155 + 1.66755i 0.601587 + 0.218960i
5959 10.0710 + 3.66555i 1.31113 + 0.477214i 0.900607 0.434634i 0.143122π-0.143122\pi
0.410528 + 0.911848i 0.365345π0.365345\pi
6060 2.77582 4.96786i 0.358357 0.641348i
6161 14.1733 + 2.49913i 1.81470 + 0.319981i 0.974855 0.222839i 0.0715326π-0.0715326\pi
0.839849 + 0.542821i 0.182644π0.182644\pi
6262 2.90364 5.02925i 0.368762 0.638715i
6363 −6.62227 + 4.37556i −0.834328 + 0.551269i
6464 0.500000 + 0.866025i 0.0625000 + 0.108253i
6565 3.53159 + 9.70297i 0.438040 + 1.20351i
6666 5.82667 2.21398i 0.717214 0.272522i
6767 −1.85767 + 1.55877i −0.226950 + 0.190434i −0.749171 0.662376i 0.769548π-0.769548\pi
0.522221 + 0.852810i 0.325104π0.325104\pi
6868 1.03021 + 5.84263i 0.124932 + 0.708523i
6969 −11.5583 1.87090i −1.39145 0.225230i
7070 −1.78405 8.50775i −0.213235 1.01687i
7171 1.69873 0.980762i 0.201602 0.116395i −0.395800 0.918337i 0.629533π-0.629533\pi
0.597403 + 0.801941i 0.296199π0.296199\pi
7272 −2.96790 0.437683i −0.349770 0.0515814i
7373 −13.7210 + 7.92182i −1.60592 + 0.927179i −0.615651 + 0.788019i 0.711107π0.711107\pi
−0.990270 + 0.139160i 0.955560π0.955560\pi
7474 −0.258814 0.711086i −0.0300865 0.0826621i
7575 −10.0361 + 0.141098i −1.15887 + 0.0162925i
7676 −5.83478 + 1.02883i −0.669295 + 0.118015i
7777 4.49296 8.39450i 0.512020 0.956642i
7878 4.12028 3.55722i 0.466530 0.402775i
7979 0.103645 + 0.0869684i 0.0116610 + 0.00978471i 0.648599 0.761130i 0.275355π-0.275355\pi
−0.636939 + 0.770915i 0.719799π0.719799\pi
8080 1.64278 2.84538i 0.183669 0.318123i
8181 6.55837 6.16343i 0.728707 0.684825i
8282 −0.334253 + 0.192981i −0.0369120 + 0.0213112i
8383 −5.39571 + 1.96388i −0.592256 + 0.215564i −0.620722 0.784031i 0.713160π-0.713160\pi
0.0284651 + 0.999595i 0.490938π0.490938\pi
8484 −3.85851 + 2.47223i −0.420997 + 0.269743i
8585 14.9321 12.5295i 1.61962 1.35902i
8686 2.08679 + 2.48694i 0.225024 + 0.268174i
8787 −7.25329 + 4.32477i −0.777635 + 0.463664i
8888 3.38167 1.23083i 0.360487 0.131207i
8989 −14.2427 −1.50972 −0.754859 0.655887i 0.772295π-0.772295\pi
−0.754859 + 0.655887i 0.772295π0.772295\pi
9090 3.63024 + 9.16383i 0.382661 + 0.965953i
9191 1.17975 8.23080i 0.123671 0.862822i
9292 −6.65733 1.17387i −0.694075 0.122384i
9393 3.57274 + 9.40260i 0.370476 + 0.975004i
9494 2.56994 + 3.06274i 0.265069 + 0.315897i
9595 12.5127 + 14.9120i 1.28377 + 1.52994i
9696 −1.70980 0.276759i −0.174505 0.0282466i
9797 −1.55558 0.274290i −0.157945 0.0278500i 0.0941165 0.995561i 0.469997π-0.469997\pi
−0.252061 + 0.967711i 0.581109π0.581109\pi
9898 −1.96627 + 6.71817i −0.198624 + 0.678637i
9999 −3.40582 + 10.2448i −0.342298 + 1.02964i
100100 −5.79494 −0.579494
101101 −2.96745 + 1.08006i −0.295272 + 0.107470i −0.485409 0.874287i 0.661329π-0.661329\pi
0.190136 + 0.981758i 0.439107π0.439107\pi
102102 −8.97050 5.01232i −0.888211 0.496293i
103103 −12.1541 14.4847i −1.19758 1.42722i −0.877328 0.479891i 0.840676π-0.840676\pi
−0.320254 0.947332i 0.603768π-0.603768\pi
104104 2.40748 2.02012i 0.236073 0.198089i
105105 13.3731 + 6.91758i 1.30508 + 0.675087i
106106 −7.68507 + 2.79714i −0.746440 + 0.271682i
107107 −9.39646 + 5.42505i −0.908390 + 0.524459i −0.879913 0.475135i 0.842399π-0.842399\pi
−0.0284774 + 0.999594i 0.509066π0.509066\pi
108108 3.83612 3.50488i 0.369131 0.337257i
109109 0.897149 1.55391i 0.0859313 0.148837i −0.819856 0.572569i 0.805947π-0.805947\pi
0.905788 + 0.423732i 0.139280π0.139280\pi
110110 −9.05752 7.60016i −0.863601 0.724647i
111111 1.23782 + 0.430921i 0.117488 + 0.0409012i
112112 −2.24755 + 1.39589i −0.212374 + 0.131899i
113113 11.0887 1.95523i 1.04313 0.183933i 0.374272 0.927319i 0.377893π-0.377893\pi
0.668862 + 0.743386i 0.266781π0.266781\pi
114114 5.00558 8.95844i 0.468816 0.839035i
115115 7.59645 + 20.8711i 0.708372 + 1.94624i
116116 −4.22238 + 2.43779i −0.392038 + 0.226343i
117117 0.265050 + 9.42450i 0.0245038 + 0.871296i
118118 −9.28150 + 5.35868i −0.854431 + 0.493306i
119119 −15.3625 + 3.22147i −1.40828 + 0.295312i
120120 2.02134 + 5.31968i 0.184522 + 0.485618i
121121 −0.338721 1.92098i −0.0307928 0.174635i
122122 −11.0249 + 9.25096i −0.998144 + 0.837542i
123123 0.106818 0.659916i 0.00963150 0.0595026i
124124 1.98621 + 5.45706i 0.178367 + 0.490058i
125125 1.30591 + 2.26191i 0.116804 + 0.202311i
126126 0.904842 7.88551i 0.0806097 0.702497i
127127 −0.518152 + 0.897465i −0.0459785 + 0.0796371i −0.888099 0.459653i 0.847974π-0.847974\pi
0.842120 + 0.539290i 0.181307π0.181307\pi
128128 −0.984808 0.173648i −0.0870455 0.0153485i
129129 −5.62250 + 0.0790464i −0.495033 + 0.00695965i
130130 −9.70297 3.53159i −0.851007 0.309741i
131131 2.83791 + 1.03291i 0.247949 + 0.0902462i 0.463005 0.886356i 0.346771π-0.346771\pi
−0.215056 + 0.976602i 0.568993π0.568993\pi
132132 −2.04931 + 5.88661i −0.178369 + 0.512364i
133133 −3.21714 15.3418i −0.278961 1.33031i
134134 2.42501i 0.209489i
135135 −16.2746 5.15749i −1.40070 0.443886i
136136 −5.13793 2.96638i −0.440573 0.254365i
137137 10.3397 + 1.82318i 0.883384 + 0.155764i 0.596895 0.802319i 0.296401π-0.296401\pi
0.286489 + 0.958084i 0.407512π0.407512\pi
138138 8.86271 7.65156i 0.754444 0.651344i
139139 8.31587 + 9.91047i 0.705343 + 0.840595i 0.993120 0.117102i 0.0373605π-0.0373605\pi
−0.287777 + 0.957698i 0.592916π0.592916\pi
140140 7.66408 + 4.10201i 0.647733 + 0.346683i
141141 −6.92427 + 0.0973479i −0.583128 + 0.00819817i
142142 −0.340615 + 1.93172i −0.0285838 + 0.162107i
143143 −5.65489 9.79455i −0.472886 0.819062i
144144 2.24301 1.99221i 0.186918 0.166017i
145145 13.8729 + 8.00952i 1.15208 + 0.665155i
146146 2.75122 15.6029i 0.227692 1.29131i
147147 −6.86588 9.99298i −0.566288 0.824208i
148148 0.711086 + 0.258814i 0.0584509 + 0.0212744i
149149 1.42182 0.250705i 0.116480 0.0205386i −0.115104 0.993353i 0.536720π-0.536720\pi
0.231584 + 0.972815i 0.425609π0.425609\pi
150150 6.34302 7.77882i 0.517905 0.635138i
151151 3.10788 + 2.60782i 0.252916 + 0.212222i 0.760427 0.649424i 0.224990π-0.224990\pi
−0.507511 + 0.861645i 0.669434π0.669434\pi
152152 2.96240 5.13102i 0.240282 0.416181i
153153 16.5472 6.55515i 1.33776 0.529952i
154154 3.54255 + 8.83769i 0.285466 + 0.712161i
155155 12.2645 14.6163i 0.985109 1.17401i
156156 0.0765208 + 5.44285i 0.00612656 + 0.435777i
157157 −0.0993042 + 0.272836i −0.00792534 + 0.0217747i −0.943592 0.331110i 0.892577π-0.892577\pi
0.935667 + 0.352885i 0.114799π0.114799\pi
158158 −0.133243 + 0.0234944i −0.0106003 + 0.00186911i
159159 4.65719 13.3777i 0.369339 1.06092i
160160 1.12373 + 3.08742i 0.0888386 + 0.244082i
161161 2.53764 17.7044i 0.199994 1.39530i
162162 0.505822 + 8.98577i 0.0397411 + 0.705989i
163163 8.34897 + 14.4608i 0.653942 + 1.13266i 0.982158 + 0.188058i 0.0602193π0.0602193\pi
−0.328216 + 0.944603i 0.606447π0.606447\pi
164164 0.0670216 0.380098i 0.00523350 0.0296807i
165165 20.1162 3.83936i 1.56605 0.298894i
166166 1.96388 5.39571i 0.152427 0.418789i
167167 −3.48153 19.7448i −0.269409 1.52789i −0.756179 0.654365i 0.772936π-0.772936\pi
0.486770 0.873530i 0.338175π-0.338175\pi
168168 0.586359 4.54491i 0.0452386 0.350647i
169169 2.39249 + 2.00753i 0.184037 + 0.154426i
170170 19.4925i 1.49501i
171171 6.54634 + 16.5249i 0.500611 + 1.26369i
172172 −3.24647 −0.247541
173173 5.44727 1.98264i 0.414148 0.150738i −0.126538 0.991962i 0.540387π-0.540387\pi
0.540687 + 0.841224i 0.318164π0.318164\pi
174174 1.34936 8.33625i 0.102295 0.631970i
175175 −0.493131 15.3240i −0.0372772 1.15839i
176176 −1.23083 + 3.38167i −0.0927771 + 0.254903i
177177 2.96613 18.3245i 0.222948 1.37735i
178178 9.15500 10.9105i 0.686196 0.817777i
179179 5.38259i 0.402314i −0.979559 0.201157i 0.935530π-0.935530\pi
0.979559 0.201157i 0.0644701π-0.0644701\pi
180180 −9.35338 3.10947i −0.697159 0.231766i
181181 5.96343 + 3.44299i 0.443258 + 0.255915i 0.704979 0.709228i 0.250957π-0.250957\pi
−0.261721 + 0.965144i 0.584290π0.584290\pi
182182 5.54683 + 6.19439i 0.411158 + 0.459159i
183183 −0.350421 24.9251i −0.0259038 1.84252i
184184 5.17848 4.34526i 0.381763 0.320337i
185185 −0.431735 2.44849i −0.0317418 0.180016i
186186 −9.49932 3.30700i −0.696524 0.242481i
187187 −13.7237 + 16.3552i −1.00357 + 1.19601i
188188 −3.99812 −0.291593
189189 9.59467 + 9.84592i 0.697910 + 0.716186i
190190 −19.4663 −1.41223
191191 0.658273 0.784499i 0.0476310 0.0567644i −0.741703 0.670728i 0.765982π-0.765982\pi
0.789334 + 0.613964i 0.210426π0.210426\pi
192192 1.31105 1.13188i 0.0946166 0.0816866i
193193 0.332875 + 1.88783i 0.0239608 + 0.135889i 0.994442 0.105290i 0.0335771π-0.0335771\pi
−0.970481 + 0.241179i 0.922466π0.922466\pi
194194 1.21002 1.01533i 0.0868747 0.0728965i
195195 15.3613 9.15915i 1.10005 0.655901i
196196 −3.88252 5.82461i −0.277323 0.416043i
197197 −10.8249 6.24979i −0.771246 0.445279i 0.0620732 0.998072i 0.480229π-0.480229\pi
−0.833319 + 0.552793i 0.813562π0.813562\pi
198198 −5.65875 9.19424i −0.402150 0.653406i
199199 13.3247i 0.944560i 0.881449 + 0.472280i 0.156569π0.156569\pi
−0.881449 + 0.472280i 0.843431π0.843431\pi
200200 3.72492 4.43918i 0.263391 0.313898i
201201 3.25521 + 2.65437i 0.229605 + 0.187225i
202202 1.08006 2.96745i 0.0759930 0.208789i
203203 −6.80576 10.9581i −0.477671 0.769110i
204204 9.60578 3.64994i 0.672539 0.255547i
205205 −1.19163 + 0.433717i −0.0832268 + 0.0302921i
206206 18.9085 1.31742
207207 0.570121 + 20.2721i 0.0396261 + 1.40901i
208208 3.14274i 0.217910i
209209 −16.3332 13.7052i −1.12979 0.948009i
210210 −13.8953 + 5.79788i −0.958864 + 0.400092i
211211 1.90492 + 10.8034i 0.131140 + 0.743734i 0.977470 + 0.211074i 0.0676962π0.0676962\pi
−0.846330 + 0.532659i 0.821193π0.821193\pi
212212 2.79714 7.68507i 0.192108 0.527813i
213213 −2.22022 2.57165i −0.152127 0.176207i
214214 1.88410 10.6853i 0.128794 0.730429i
215215 5.33325 + 9.23745i 0.363724 + 0.629989i
216216 0.219078 + 5.19153i 0.0149064 + 0.353239i
217217 −14.2615 + 5.71667i −0.968135 + 0.388073i
218218 0.613686 + 1.68609i 0.0415641 + 0.114196i
219219 17.9331 + 20.7717i 1.21181 + 1.40362i
220220 11.6441 2.05317i 0.785047 0.138425i
221221 −6.37702 + 17.5207i −0.428965 + 1.17857i
222222 −1.12576 + 0.671232i −0.0755560 + 0.0450502i
223223 −0.181176 + 0.215917i −0.0121324 + 0.0144589i −0.772077 0.635530i 0.780782π-0.780782\pi
0.759944 + 0.649988i 0.225226π0.225226\pi
224224 0.375388 2.61899i 0.0250817 0.174988i
225225 3.49895 + 17.0291i 0.233263 + 1.13527i
226226 −5.62987 + 9.75121i −0.374493 + 0.648641i
227227 7.76814 + 6.51824i 0.515589 + 0.432631i 0.863091 0.505049i 0.168525π-0.168525\pi
−0.347502 + 0.937679i 0.612970π0.612970\pi
228228 3.64504 + 9.59287i 0.241398 + 0.635303i
229229 −15.6963 + 2.76769i −1.03724 + 0.182894i −0.666240 0.745738i 0.732097π-0.732097\pi
−0.371003 + 0.928632i 0.620986π0.620986\pi
230230 −20.8711 7.59645i −1.37620 0.500895i
231231 −15.7408 4.91822i −1.03567 0.323595i
232232 0.846636 4.80151i 0.0555844 0.315235i
233233 −23.2127 13.4019i −1.52072 0.877986i −0.999701 0.0244388i 0.992220π-0.992220\pi
−0.521015 0.853547i 0.674447π-0.674447\pi
234234 −7.38996 5.85491i −0.483097 0.382748i
235235 6.56805 + 11.3762i 0.428452 + 0.742101i
236236 1.86105 10.5545i 0.121144 0.687041i
237237 0.114308 0.204575i 0.00742508 0.0132886i
238238 7.40703 13.8391i 0.480126 0.897054i
239239 13.3347 + 15.8917i 0.862552 + 1.02795i 0.999302 + 0.0373443i 0.0118898π0.0118898\pi
−0.136750 + 0.990606i 0.543666π0.543666\pi
240240 −5.37440 1.87099i −0.346916 0.120772i
241241 23.6617 + 4.17219i 1.52418 + 0.268754i 0.872075 0.489372i 0.162774π-0.162774\pi
0.652107 + 0.758127i 0.273885π0.273885\pi
242242 1.68928 + 0.975308i 0.108591 + 0.0626952i
243243 −12.6157 9.15665i −0.809297 0.587399i
244244 14.3919i 0.921349i
245245 −10.1951 + 20.6158i −0.651341 + 1.31710i
246246 0.436863 + 0.506014i 0.0278534 + 0.0322622i
247247 −17.4972 6.36845i −1.11332 0.405215i
248248 −5.45706 1.98621i −0.346523 0.126124i
249249 5.09330 + 8.54224i 0.322775 + 0.541343i
250250 −2.57215 0.453539i −0.162677 0.0286843i
251251 14.9759 25.9391i 0.945273 1.63726i 0.190068 0.981771i 0.439129π-0.439129\pi
0.755204 0.655489i 0.227538π-0.227538\pi
252252 5.45903 + 5.76186i 0.343887 + 0.362963i
253253 −12.1636 21.0681i −0.764722 1.32454i
254254 −0.354437 0.973807i −0.0222393 0.0611021i
255255 −26.1657 21.3361i −1.63856 1.33612i
256256 0.766044 0.642788i 0.0478778 0.0401742i
257257 1.94308 + 11.0198i 0.121206 + 0.687394i 0.983489 + 0.180967i 0.0579228π0.0579228\pi
−0.862283 + 0.506427i 0.830966π0.830966\pi
258258 3.55352 4.35789i 0.221232 0.271311i
259259 −0.623893 + 1.90241i −0.0387668 + 0.118210i
260260 8.94231 5.16284i 0.554578 0.320186i
261261 9.71317 + 10.9360i 0.601230 + 0.676921i
262262 −2.61543 + 1.51002i −0.161582 + 0.0932894i
263263 −5.57444 15.3157i −0.343735 0.944404i −0.984301 0.176500i 0.943522π-0.943522\pi
0.640566 0.767903i 0.278700π-0.278700\pi
264264 −3.19214 5.35370i −0.196463 0.329497i
265265 −26.4621 + 4.66597i −1.62555 + 0.286629i
266266 13.8205 + 7.39707i 0.847387 + 0.453544i
267267 4.62482 + 24.2316i 0.283034 + 1.48295i
268268 1.85767 + 1.55877i 0.113475 + 0.0952169i
269269 8.00969 13.8732i 0.488359 0.845863i −0.511551 0.859253i 0.670929π-0.670929\pi
0.999910 + 0.0133899i 0.00426227π0.00426227\pi
270270 14.4120 9.15192i 0.877086 0.556968i
271271 3.22979 1.86472i 0.196196 0.113274i −0.398684 0.917088i 0.630533π-0.630533\pi
0.594880 + 0.803815i 0.297200π0.297200\pi
272272 5.57498 2.02913i 0.338033 0.123034i
273273 −14.3865 + 0.665519i −0.870709 + 0.0402791i
274274 −8.04289 + 6.74879i −0.485889 + 0.407709i
275275 −13.4048 15.9753i −0.808342 0.963345i
276276 0.164596 + 11.7076i 0.00990751 + 0.704712i
277277 11.4251 4.15840i 0.686468 0.249854i 0.0248460 0.999691i 0.492090π-0.492090\pi
0.661622 + 0.749837i 0.269868π0.269868\pi
278278 −12.9372 −0.775922
279279 14.8369 9.13162i 0.888262 0.546696i
280280 −8.06870 + 3.23430i −0.482197 + 0.193286i
281281 30.0504 + 5.29870i 1.79266 + 0.316094i 0.968266 0.249923i 0.0804053π-0.0804053\pi
0.824394 + 0.566017i 0.191516π0.191516\pi
282282 4.37626 5.36687i 0.260602 0.319592i
283283 4.63819 + 5.52757i 0.275712 + 0.328580i 0.886076 0.463541i 0.153421π-0.153421\pi
−0.610364 + 0.792121i 0.708977π0.708977\pi
284284 −1.26084 1.50262i −0.0748173 0.0891638i
285285 21.3074 26.1305i 1.26214 1.54784i
286286 11.1380 + 1.96392i 0.658601 + 0.116129i
287287 1.01083 + 0.144886i 0.0596673 + 0.00855232i
288288 0.0843370 + 2.99881i 0.00496961 + 0.176707i
289289 18.1977 1.07045
290290 −15.0530 + 5.47883i −0.883941 + 0.321728i
291291 0.0384601 + 2.73563i 0.00225457 + 0.160366i
292292 10.1841 + 12.1369i 0.595979 + 0.710260i
293293 −15.4530 + 12.9666i −0.902775 + 0.757518i −0.970731 0.240170i 0.922797π-0.922797\pi
0.0679558 + 0.997688i 0.478352π0.478352\pi
294294 12.0684 + 1.16380i 0.703842 + 0.0678742i
295295 −33.0890 + 12.0434i −1.92652 + 0.701194i
296296 −0.655341 + 0.378361i −0.0380909 + 0.0219918i
297297 18.5358 + 2.46781i 1.07556 + 0.143197i
298298 −0.721877 + 1.25033i −0.0418172 + 0.0724296i
299299 −16.2746 13.6560i −0.941187 0.789749i
300300 1.88171 + 9.85917i 0.108641 + 0.569219i
301301 −0.276264 8.58491i −0.0159236 0.494826i
302302 −3.99542 + 0.704500i −0.229910 + 0.0405394i
303303 2.80114 + 4.69793i 0.160921 + 0.269889i
304304 2.02640 + 5.56748i 0.116222 + 0.319317i
305305 −40.9506 + 23.6428i −2.34482 + 1.35378i
306306 −5.61479 + 16.8894i −0.320976 + 0.965505i
307307 21.4952 12.4103i 1.22680 0.708292i 0.260439 0.965490i 0.416133π-0.416133\pi
0.966359 + 0.257199i 0.0827995π0.0827995\pi
308308 −9.04716 2.96701i −0.515510 0.169061i
309309 −20.6968 + 25.3817i −1.17740 + 1.44392i
310310 3.31324 + 18.7903i 0.188179 + 1.06722i
311311 4.36005 3.65851i 0.247236 0.207455i −0.510745 0.859732i 0.670630π-0.670630\pi
0.757981 + 0.652277i 0.226186π0.226186\pi
312312 −4.21865 3.43998i −0.238834 0.194750i
313313 −1.15994 3.18690i −0.0655634 0.180134i 0.902585 0.430513i 0.141667π-0.141667\pi
−0.968148 + 0.250378i 0.919445π0.919445\pi
314314 −0.145173 0.251447i −0.00819259 0.0141900i
315315 7.42669 24.9985i 0.418447 1.40851i
316316 0.0676494 0.117172i 0.00380558 0.00659145i
317317 12.5437 + 2.21179i 0.704523 + 0.124226i 0.514421 0.857538i 0.328007π-0.328007\pi
0.190102 + 0.981764i 0.439118π0.439118\pi
318318 7.25435 + 12.1666i 0.406804 + 0.682272i
319319 −16.4876 6.00100i −0.923128 0.335991i
320320 −3.08742 1.12373i −0.172592 0.0628184i
321321 12.2810 + 14.2250i 0.685461 + 0.793961i
322322 11.9312 + 13.3241i 0.664900 + 0.742524i
323323 35.1504i 1.95582i
324324 −7.20864 5.38846i −0.400480 0.299359i
325325 −15.7721 9.10600i −0.874876 0.505110i
326326 −16.4443 2.89957i −0.910764 0.160592i
327327 −2.93504 1.02178i −0.162308 0.0565044i
328328 0.248091 + 0.295664i 0.0136986 + 0.0163253i
329329 −0.340227 10.5726i −0.0187573 0.582884i
330330 −9.98934 + 17.8778i −0.549895 + 0.984142i
331331 −0.644422 + 3.65470i −0.0354207 + 0.200881i −0.997383 0.0723024i 0.976965π-0.976965\pi
0.961962 + 0.273183i 0.0880764π0.0880764\pi
332332 2.87100 + 4.97272i 0.157567 + 0.272913i
333333 0.331204 2.24588i 0.0181499 0.123073i
334334 17.3632 + 10.0247i 0.950074 + 0.548526i
335335 1.38355 7.84649i 0.0755913 0.428700i
336336 3.10470 + 3.37059i 0.169375 + 0.183881i
337337 −31.6420 11.5168i −1.72365 0.627358i −0.725506 0.688216i 0.758394π-0.758394\pi
−0.998146 + 0.0608583i 0.980616π0.980616\pi
338338 −3.07572 + 0.542332i −0.167297 + 0.0294990i
339339 −6.92719 18.2307i −0.376233 0.990156i
340340 −14.9321 12.5295i −0.809808 0.679509i
341341 −10.4493 + 18.0987i −0.565862 + 0.980102i
342342 −16.8667 5.60725i −0.912049 0.303205i
343343 15.0721 10.7625i 0.813817 0.581122i
344344 2.08679 2.48694i 0.112512 0.134087i
345345 33.0421 19.7013i 1.77893 1.06068i
346346 −1.98264 + 5.44727i −0.106588 + 0.292847i
347347 −30.7658 + 5.42484i −1.65159 + 0.291221i −0.920409 0.390957i 0.872144π-0.872144\pi
−0.731186 + 0.682178i 0.761033π0.761033\pi
348348 5.51859 + 6.39211i 0.295827 + 0.342653i
349349 −1.03957 2.85621i −0.0556471 0.152889i 0.908754 0.417331i 0.137034π-0.137034\pi
−0.964402 + 0.264442i 0.914812π0.914812\pi
350350 12.0559 + 9.47234i 0.644413 + 0.506318i
351351 15.9482 3.51123i 0.851253 0.187416i
352352 −1.79935 3.11656i −0.0959056 0.166113i
353353 −0.0854082 + 0.484374i −0.00454582 + 0.0257806i −0.986996 0.160743i 0.948611π-0.948611\pi
0.982450 + 0.186524i 0.0597221π0.0597221\pi
354354 12.1308 + 14.0509i 0.644744 + 0.746799i
355355 −2.20422 + 6.05605i −0.116988 + 0.321422i
356356 2.47321 + 14.0263i 0.131080 + 0.743391i
357357 10.4693 + 25.0908i 0.554092 + 1.32794i
358358 4.12331 + 3.45986i 0.217923 + 0.182860i
359359 22.3463i 1.17939i 0.807625 + 0.589697i 0.200753π0.200753\pi
−0.807625 + 0.589697i 0.799247π0.799247\pi
360360 8.39423 5.16637i 0.442415 0.272292i
361361 −16.1031 −0.847534
362362 −6.47070 + 2.35514i −0.340092 + 0.123784i
363363 −3.15826 + 1.20005i −0.165765 + 0.0629865i
364364 −8.31061 + 0.267437i −0.435595 + 0.0140175i
365365 17.8040 48.9160i 0.931902 2.56038i
366366 19.3190 + 15.7531i 1.00982 + 0.823428i
367367 6.98984 8.33016i 0.364866 0.434831i −0.552111 0.833771i 0.686177π-0.686177\pi
0.916977 + 0.398940i 0.130622π0.130622\pi
368368 6.76003i 0.352391i
369369 −1.15743 + 0.0325509i −0.0602533 + 0.00169453i
370370 2.15316 + 1.24313i 0.111938 + 0.0646273i
371371 20.5603 + 6.74273i 1.06744 + 0.350065i
372372 8.63936 5.15121i 0.447930 0.267078i
373373 7.76621 6.51662i 0.402119 0.337418i −0.419193 0.907897i 0.637687π-0.637687\pi
0.821312 + 0.570479i 0.193243π0.193243\pi
374374 −3.70743 21.0259i −0.191706 1.08722i
375375 3.42422 2.95628i 0.176826 0.152662i
376376 2.56994 3.06274i 0.132535 0.157949i
377377 −15.3227 −0.789159
378378 −13.7098 + 1.02111i −0.705154 + 0.0525201i
379379 9.75561 0.501112 0.250556 0.968102i 0.419387π-0.419387\pi
0.250556 + 0.968102i 0.419387π0.419387\pi
380380 12.5127 14.9120i 0.641887 0.764972i
381381 1.69515 + 0.590131i 0.0868449 + 0.0302333i
382382 0.177832 + 1.00853i 0.00909865 + 0.0516010i
383383 −5.78307 + 4.85257i −0.295501 + 0.247955i −0.778469 0.627683i 0.784003π-0.784003\pi
0.482968 + 0.875638i 0.339559π0.339559\pi
384384 0.0243484 + 1.73188i 0.00124252 + 0.0883796i
385385 6.42025 + 30.6168i 0.327206 + 1.56038i
386386 −1.66013 0.958474i −0.0844982 0.0487851i
387387 1.96020 + 9.54011i 0.0996426 + 0.484951i
388388 1.57957i 0.0801908i
389389 3.51334 4.18703i 0.178133 0.212291i −0.669588 0.742733i 0.733529π-0.733529\pi
0.847722 + 0.530442i 0.177974π0.177974\pi
390390 −2.85773 + 17.6548i −0.144707 + 0.893987i
391391 −13.7169 + 37.6870i −0.693696 + 1.90591i
392392 6.95754 + 0.769803i 0.351409 + 0.0388809i
393393 0.835824 5.16365i 0.0421617 0.260472i
394394 11.7458 4.27511i 0.591743 0.215377i
395395 −0.444533 −0.0223669
396396 10.6806 + 1.57509i 0.536719 + 0.0791511i
397397 31.1158i 1.56166i −0.624745 0.780829i 0.714797π-0.714797\pi
0.624745 0.780829i 0.285203π-0.285203\pi
398398 −10.2073 8.56493i −0.511645 0.429321i
399399 −25.0570 + 10.4552i −1.25442 + 0.523414i
400400 1.00628 + 5.70690i 0.0503140 + 0.285345i
401401 −4.67699 + 12.8499i −0.233558 + 0.641694i −1.00000 0.000619001i 0.999803π-0.999803\pi
0.766442 + 0.642313i 0.222025π0.222025\pi
402402 −4.12577 + 0.787441i −0.205775 + 0.0392740i
403403 −3.16921 + 17.9735i −0.157870 + 0.895324i
404404 1.57895 + 2.73482i 0.0785556 + 0.136062i
405405 −3.49001 + 29.3634i −0.173420 + 1.45908i
406406 12.7691 + 1.83024i 0.633719 + 0.0908331i
407407 0.931394 + 2.55898i 0.0461675 + 0.126844i
408408 −3.37846 + 9.70459i −0.167259 + 0.480449i
409409 −15.6493 + 2.75939i −0.773806 + 0.136443i −0.546589 0.837401i 0.684074π-0.684074\pi
−0.227217 + 0.973844i 0.572963π0.572963\pi
410410 0.433717 1.19163i 0.0214197 0.0588502i
411411 −0.255640 18.1834i −0.0126098 0.896923i
412412 −12.1541 + 14.4847i −0.598791 + 0.713611i
413413 28.0686 + 4.02317i 1.38116 + 0.197967i
414414 −15.8958 12.5939i −0.781235 0.618956i
415415 9.43286 16.3382i 0.463041 0.802010i
416416 −2.40748 2.02012i −0.118036 0.0990443i
417417 14.1608 17.3662i 0.693457 0.850428i
418418 20.9976 3.70244i 1.02703 0.181092i
419419 19.8533 + 7.22602i 0.969898 + 0.353014i 0.777905 0.628382i 0.216283π-0.216283\pi
0.191993 + 0.981396i 0.438505π0.438505\pi
420420 4.49027 14.3712i 0.219103 0.701242i
421421 5.50568 31.2242i 0.268330 1.52178i −0.491051 0.871131i 0.663387π-0.663387\pi
0.759382 0.650646i 0.225502π-0.225502\pi
422422 −9.50031 5.48501i −0.462468 0.267006i
423423 2.41404 + 11.7489i 0.117375 + 0.571252i
424424 4.08914 + 7.08260i 0.198586 + 0.343961i
425425 −5.97003 + 33.8577i −0.289589 + 1.64234i
426426 3.39713 0.0477600i 0.164591 0.00231398i
427427 38.0578 1.22471i 1.84175 0.0592677i
428428 6.97431 + 8.31166i 0.337116 + 0.401759i
429429 −14.8276 + 12.8013i −0.715885 + 0.618055i
430430 −10.5044 1.85222i −0.506569 0.0893218i
431431 14.1867 + 8.19067i 0.683347 + 0.394531i 0.801115 0.598511i 0.204241π-0.204241\pi
−0.117768 + 0.993041i 0.537574π0.537574\pi
432432 −4.11776 3.16923i −0.198116 0.152480i
433433 20.4469i 0.982615i 0.870986 + 0.491307i 0.163481π0.163481\pi
−0.870986 + 0.491307i 0.836519π0.836519\pi
434434 4.78791 14.5996i 0.229827 0.700801i
435435 9.12217 26.2033i 0.437374 1.25635i
436436 −1.68609 0.613686i −0.0807490 0.0293902i
437437 −37.6363 13.6985i −1.80039 0.655289i
438438 −27.4393 + 0.385767i −1.31110 + 0.0184327i
439439 38.4267 + 6.77566i 1.83400 + 0.323385i 0.980321 0.197408i 0.0632524π-0.0632524\pi
0.853683 + 0.520793i 0.174364π0.174364\pi
440440 −5.91188 + 10.2397i −0.281838 + 0.488157i
441441 −14.7720 + 14.9261i −0.703429 + 0.710766i
442442 −9.32258 16.1472i −0.443430 0.768043i
443443 −6.47072 17.7782i −0.307433 0.844666i −0.993155 0.116802i 0.962736π-0.962736\pi
0.685722 0.727864i 0.259487π-0.259487\pi
444444 0.209430 1.29384i 0.00993910 0.0614030i
445445 35.8472 30.0794i 1.69932 1.42590i
446446 −0.0489445 0.277578i −0.00231759 0.0131437i
447447 −0.888224 2.33759i −0.0420115 0.110564i
448448 1.76496 + 1.97102i 0.0833867 + 0.0931217i
449449 1.23187 0.711219i 0.0581354 0.0335645i −0.470651 0.882320i 0.655981π-0.655981\pi
0.528786 + 0.848755i 0.322647π0.322647\pi
450450 −15.2941 8.26572i −0.720971 0.389650i
451451 1.20287 0.694480i 0.0566411 0.0327018i
452452 −3.85106 10.5807i −0.181138 0.497674i
453453 3.42762 6.13437i 0.161043 0.288218i
454454 −9.98653 + 1.76089i −0.468691 + 0.0826428i
455455 14.4135 + 23.2075i 0.675715 + 1.08799i
456456 −9.69155 3.37392i −0.453848 0.157998i
457457 −25.5772 21.4618i −1.19645 1.00394i −0.999724 0.0234833i 0.992524π-0.992524\pi
−0.196727 0.980458i 0.563031π-0.563031\pi
458458 7.96924 13.8031i 0.372378 0.644978i
459459 −16.5257 26.0238i −0.771353 1.21469i
460460 19.2349 11.1053i 0.896831 0.517785i
461461 4.99360 1.81752i 0.232575 0.0846504i −0.223104 0.974795i 0.571619π-0.571619\pi
0.455679 + 0.890144i 0.349397π0.349397\pi
462462 13.8856 8.89682i 0.646016 0.413917i
463463 −17.6114 + 14.7777i −0.818471 + 0.686779i −0.952614 0.304183i 0.901617π-0.901617\pi
0.134142 + 0.990962i 0.457172π0.457172\pi
464464 3.13396 + 3.73491i 0.145491 + 0.173389i
465465 −28.8497 16.1200i −1.33787 0.747545i
466466 25.1873 9.16742i 1.16678 0.424673i
467467 36.5062 1.68930 0.844652 0.535316i 0.179807π-0.179807\pi
0.844652 + 0.535316i 0.179807π0.179807\pi
468468 9.23530 1.89757i 0.426902 0.0877152i
469469 −3.96390 + 5.04503i −0.183036 + 0.232958i
470470 −12.9365 2.28106i −0.596717 0.105217i
471471 0.496433 + 0.0803560i 0.0228744 + 0.00370261i
472472 6.88898 + 8.20997i 0.317091 + 0.377894i
473473 −7.50973 8.94975i −0.345298 0.411510i
474474 0.0832382 + 0.219063i 0.00382326 + 0.0100619i
475475 −33.8122 5.96200i −1.55141 0.273555i
476476 5.84020 + 14.5697i 0.267685 + 0.667801i
477477 −24.2723 3.57949i −1.11135 0.163894i
478478 −20.7452 −0.948862
479479 −13.3938 + 4.87496i −0.611980 + 0.222742i −0.629369 0.777106i 0.716687π-0.716687\pi
0.0173895 + 0.999849i 0.494464π0.494464\pi
480480 4.88786 2.91438i 0.223099 0.133023i
481481 1.52867 + 1.82179i 0.0697012 + 0.0830667i
482482 −18.4055 + 15.4441i −0.838348 + 0.703457i
483483 −30.9453 + 1.43153i −1.40806 + 0.0651369i
484484 −1.83298 + 0.667150i −0.0833173 + 0.0303250i
485485 4.49450 2.59490i 0.204085 0.117828i
486486 15.1236 3.77840i 0.686021 0.171392i
487487 −3.73664 + 6.47205i −0.169323 + 0.293276i −0.938182 0.346142i 0.887492π-0.887492\pi
0.768859 + 0.639419i 0.220825π0.220825\pi
488488 11.0249 + 9.25096i 0.499072 + 0.418771i
489489 21.8918 18.9001i 0.989980 0.854693i
490490 −9.23935 21.0615i −0.417391 0.951461i
491491 16.4226 2.89575i 0.741143 0.130683i 0.209686 0.977769i 0.432756π-0.432756\pi
0.531457 + 0.847085i 0.321645π0.321645\pi
492492 −0.668439 + 0.00939755i −0.0301356 + 0.000423674i
493493 9.89317 + 27.1812i 0.445566 + 1.22418i
494494 16.1255 9.31005i 0.725519 0.418879i
495495 −13.0641 32.9778i −0.587189 1.48224i
496496 5.02925 2.90364i 0.225820 0.130377i
497497 3.86620 3.46202i 0.173423 0.155293i
498498 −9.81765 1.58915i −0.439939 0.0712116i
499499 1.39403 + 7.90591i 0.0624051 + 0.353917i 0.999981 + 0.00613676i 0.00195340π0.00195340\pi
−0.937576 + 0.347780i 0.886935π0.886935\pi
500500 2.00078 1.67885i 0.0894774 0.0750804i
501501 −32.4620 + 12.3347i −1.45030 + 0.551074i
502502 10.2441 + 28.1456i 0.457219 + 1.25620i
503503 −0.766281 1.32724i −0.0341668 0.0591786i 0.848436 0.529297i 0.177544π-0.177544\pi
−0.882603 + 0.470119i 0.844211π0.844211\pi
504504 −7.92284 + 0.478209i −0.352911 + 0.0213011i
505505 5.18774 8.98542i 0.230851 0.399846i
506506 23.9577 + 4.22439i 1.06505 + 0.187797i
507507 2.63862 4.72231i 0.117185 0.209725i
508508 0.973807 + 0.354437i 0.0432057 + 0.0157256i
509509 10.3589 + 3.77032i 0.459149 + 0.167116i 0.561230 0.827660i 0.310328π-0.310328\pi
−0.102082 + 0.994776i 0.532550π0.532550\pi
510510 33.1634 6.32953i 1.46850 0.280276i
511511 −31.2281 + 27.9635i −1.38145 + 1.23703i
512512 1.00000i 0.0441942i
513513 25.9889 16.5035i 1.14744 0.728646i
514514 −9.69061 5.59488i −0.427435 0.246780i
515515 61.1812 + 10.7879i 2.69597 + 0.475371i
516516 1.05418 + 5.52335i 0.0464078 + 0.243152i
517517 −9.24845 11.0219i −0.406746 0.484741i
518518 −1.05630 1.70077i −0.0464111 0.0747277i
519519 −5.14197 8.62386i −0.225707 0.378546i
520520 −1.79304 + 10.1688i −0.0786299 + 0.445932i
521521 6.32917 + 10.9624i 0.277286 + 0.480273i 0.970709 0.240257i 0.0772317π-0.0772317\pi
−0.693423 + 0.720530i 0.743898π0.743898\pi
522522 −14.6210 + 0.411192i −0.639942 + 0.0179974i
523523 −4.54862 2.62615i −0.198897 0.114833i 0.397244 0.917713i 0.369967π-0.369967\pi
−0.596141 + 0.802880i 0.703300π0.703300\pi
524524 0.524424 2.97416i 0.0229096 0.129927i
525525 −25.9113 + 5.81495i −1.13086 + 0.253785i
526526 15.3157 + 5.57444i 0.667794 + 0.243057i
527527 33.9298 5.98274i 1.47800 0.260612i
528528 6.15304 + 0.995973i 0.267777 + 0.0433441i
529529 −17.3877 14.5900i −0.755986 0.634348i
530530 13.4351 23.2703i 0.583585 1.01080i
531531 −32.1393 + 0.903869i −1.39473 + 0.0392246i
532532 −14.5501 + 5.83235i −0.630827 + 0.252864i
533533 0.779688 0.929195i 0.0337720 0.0402479i
534534 −21.5353 12.0330i −0.931922 0.520717i
535535 12.1926 33.4988i 0.527131 1.44828i
536536 −2.38817 + 0.421099i −0.103153 + 0.0181887i
537537 −9.15762 + 1.74782i −0.395181 + 0.0754238i
538538 5.47895 + 15.0533i 0.236214 + 0.648993i
539539 7.07602 24.1766i 0.304786 1.04136i
540540 −2.25308 + 16.9230i −0.0969570 + 0.728249i
541541 −14.7793 25.5986i −0.635414 1.10057i −0.986427 0.164199i 0.947496π-0.947496\pi
0.351013 0.936370i 0.385837π-0.385837\pi
542542 −0.647611 + 3.67278i −0.0278173 + 0.157760i
543543 3.92127 11.2638i 0.168278 0.483377i
544544 −2.02913 + 5.57498i −0.0869980 + 0.239025i
545545 1.02371 + 5.80572i 0.0438507 + 0.248690i
546546 8.73763 11.4485i 0.373936 0.489949i
547547 −30.7531 25.8049i −1.31491 1.10334i −0.987359 0.158503i 0.949333π-0.949333\pi
−0.327548 0.944835i 0.606222π-0.606222\pi
548548 10.4993i 0.448506i
549549 −42.2923 + 8.68977i −1.80499 + 0.370870i
550550 20.8542 0.889227
551551 −27.1447 + 9.87987i −1.15640 + 0.420897i
552552 −9.07431 7.39939i −0.386228 0.314939i
553553 0.315605 + 0.168920i 0.0134209 + 0.00718321i
554554 −4.15840 + 11.4251i −0.176673 + 0.485406i
555555 −4.02552 + 1.52959i −0.170874 + 0.0649275i
556556 8.31587 9.91047i 0.352672 0.420298i
557557 18.5445i 0.785756i −0.919591 0.392878i 0.871479π-0.871479\pi
0.919591 0.392878i 0.128521π-0.128521\pi
558558 −2.54175 + 17.2354i −0.107601 + 0.729634i
559559 −8.83590 5.10141i −0.373719 0.215767i
560560 2.70884 8.25995i 0.114469 0.349047i
561561 32.2821 + 18.0378i 1.36295 + 0.761557i
562562 −23.3751 + 19.6140i −0.986019 + 0.827368i
563563 5.22122 + 29.6110i 0.220048 + 1.24796i 0.871928 + 0.489634i 0.162870π0.162870\pi
−0.651880 + 0.758322i 0.726019π0.726019\pi
564564 1.29826 + 6.80217i 0.0546664 + 0.286423i
565565 −23.7797 + 28.3395i −1.00042 + 1.19225i
566566 −7.21574 −0.303300
567567 13.6357 19.5209i 0.572647 0.819802i
568568 1.96152 0.0823038
569569 −4.79220 + 5.71112i −0.200900 + 0.239423i −0.857083 0.515179i 0.827725π-0.827725\pi
0.656183 + 0.754602i 0.272170π0.272170\pi
570570 6.32102 + 33.1188i 0.264758 + 1.38719i
571571 −4.05675 23.0070i −0.169770 0.962812i −0.944009 0.329919i 0.892979π-0.892979\pi
0.774239 0.632893i 0.218133π-0.218133\pi
572572 −8.66379 + 7.26978i −0.362251 + 0.303965i
573573 −1.54845 0.865207i −0.0646875 0.0361445i
574574 −0.760737 + 0.681209i −0.0317525 + 0.0284331i
575575 −33.9257 19.5870i −1.41480 0.816834i
576576 −2.35144 1.86299i −0.0979765 0.0776248i
577577 35.4895i 1.47745i 0.674009 + 0.738723i 0.264571π0.264571\pi
−0.674009 + 0.738723i 0.735429π0.735429\pi
578578 −11.6973 + 13.9403i −0.486542 + 0.579838i
579579 3.10375 1.17934i 0.128987 0.0490117i
580580 5.47883 15.0530i 0.227496 0.625041i
581581 −12.9055 + 8.01518i −0.535408 + 0.332526i
582582 −2.12034 1.72897i −0.0878909 0.0716681i
583583 27.6562 10.0660i 1.14540 0.416893i
584584 −15.8436 −0.655614
585585 −20.5709 23.1607i −0.850502 0.957576i
586586 20.1725i 0.833318i
587587 14.4979 + 12.1652i 0.598393 + 0.502111i 0.890929 0.454144i 0.150055π-0.150055\pi
−0.292536 + 0.956255i 0.594499π0.594499\pi
588588 −8.64892 + 8.49683i −0.356676 + 0.350403i
589589 5.97470 + 33.8842i 0.246183 + 1.39617i
590590 12.0434 33.0890i 0.495819 1.36225i
591591 −7.11798 + 20.4463i −0.292794 + 0.841050i
592592 0.131403 0.745226i 0.00540065 0.0306286i
593593 13.5580 + 23.4831i 0.556759 + 0.964335i 0.997764 + 0.0668307i 0.0212887π0.0212887\pi
−0.441005 + 0.897505i 0.645378π0.645378\pi
594594 −13.8050 + 12.6130i −0.566428 + 0.517517i
595595 31.8622 40.5524i 1.30622 1.66249i
596596 −0.493793 1.35669i −0.0202266 0.0555720i
597597 22.6698 4.32673i 0.927813 0.177081i
598598 20.9223 3.68916i 0.855575 0.150861i
599599 −6.10131 + 16.7632i −0.249293 + 0.684926i 0.750420 + 0.660961i 0.229851π0.229851\pi
−0.999713 + 0.0239649i 0.992371π0.992371\pi
600600 −8.76210 4.89588i −0.357711 0.199873i
601601 −0.667624 + 0.795644i −0.0272330 + 0.0324550i −0.779489 0.626416i 0.784521π-0.784521\pi
0.752256 + 0.658871i 0.228966π0.228966\pi
602602 6.75400 + 5.30664i 0.275273 + 0.216283i
603603 3.45896 6.40013i 0.140860 0.260634i
604604 2.02853 3.51351i 0.0825396 0.142963i
605605 4.90949 + 4.11955i 0.199599 + 0.167483i
606606 −5.39936 0.873977i −0.219334 0.0355029i
607607 31.9491 5.63348i 1.29677 0.228656i 0.517685 0.855571i 0.326794π-0.326794\pi
0.779088 + 0.626915i 0.215683π0.215683\pi
608608 −5.56748 2.02640i −0.225791 0.0821813i
609609 −16.4336 + 15.1372i −0.665922 + 0.613390i
610610 8.21107 46.5673i 0.332456 1.88545i
611611 −10.8817 6.28253i −0.440225 0.254164i
612612 −9.32895 15.1575i −0.377100 0.612706i
613613 17.7854 + 30.8051i 0.718344 + 1.24421i 0.961656 + 0.274260i 0.0884327π0.0884327\pi
−0.243312 + 0.969948i 0.578234π0.578234\pi
614614 −4.31004 + 24.4435i −0.173939 + 0.986458i
615615 1.12484 + 1.88653i 0.0453579 + 0.0760721i
616616 8.08826 5.02337i 0.325885 0.202398i
617617 −18.5665 22.1267i −0.747458 0.890786i 0.249528 0.968368i 0.419724π-0.419724\pi
−0.996986 + 0.0775820i 0.975280π0.975280\pi
618618 −6.13989 32.1697i −0.246982 1.29406i
619619 −6.77747 1.19505i −0.272409 0.0480331i 0.0357747 0.999360i 0.488610π-0.488610\pi
−0.308184 + 0.951327i 0.599721π0.599721\pi
620620 −16.5239 9.54009i −0.663617 0.383139i
621621 34.3046 7.55264i 1.37660 0.303077i
622622 5.69164i 0.228214i
623623 −36.8804 + 7.73371i −1.47758 + 0.309844i
624624 5.34688 1.02050i 0.214046 0.0408527i
625625 19.1635 + 6.97494i 0.766540 + 0.278998i
626626 3.18690 + 1.15994i 0.127374 + 0.0463603i
627627 −18.0136 + 32.2387i −0.719392 + 1.28749i
628628 0.285935 + 0.0504181i 0.0114100 + 0.00201190i
629629 2.24473 3.88798i 0.0895031 0.155024i
630630 14.3762 + 21.7579i 0.572761 + 0.866856i
631631 8.22286 + 14.2424i 0.327347 + 0.566982i 0.981985 0.188961i 0.0605121π-0.0605121\pi
−0.654638 + 0.755943i 0.727179π0.727179\pi
632632 0.0462749 + 0.127139i 0.00184072 + 0.00505733i
633633 17.7616 6.74895i 0.705961 0.268247i
634634 −9.75725 + 8.18730i −0.387510 + 0.325159i
635635 −0.591245 3.35312i −0.0234628 0.133064i
636636 −13.9832 2.26341i −0.554470 0.0897502i
637637 −1.41441 21.9537i −0.0560411 0.869837i
638638 15.1951 8.77287i 0.601578 0.347321i
639639 −3.65431 + 4.61240i −0.144562 + 0.182464i
640640 2.84538 1.64278i 0.112474 0.0649367i
641641 11.4189 + 31.3733i 0.451021 + 1.23917i 0.932006 + 0.362442i 0.118057π0.118057\pi
−0.480985 + 0.876729i 0.659721π0.659721\pi
642642 −18.7911 + 0.264183i −0.741624 + 0.0104265i
643643 17.2520 3.04199i 0.680352 0.119964i 0.177216 0.984172i 0.443291π-0.443291\pi
0.503135 + 0.864208i 0.332180π0.332180\pi
644644 −17.8761 + 0.575257i −0.704417 + 0.0226683i
645645 13.9843 12.0732i 0.550630 0.475382i
646646 −26.9268 22.5942i −1.05942 0.888958i
647647 12.0992 20.9565i 0.475670 0.823884i −0.523942 0.851754i 0.675539π-0.675539\pi
0.999612 + 0.0278698i 0.00887240π0.00887240\pi
648648 8.76143 2.05850i 0.344181 0.0808656i
649649 33.4013 19.2842i 1.31112 0.756973i
650650 17.1137 6.22887i 0.671254 0.244316i
651651 14.3569 + 22.4074i 0.562693 + 0.878216i
652652 12.7914 10.7332i 0.500949 0.420346i
653653 −1.69858 2.02429i −0.0664706 0.0792166i 0.731784 0.681536i 0.238688π-0.238688\pi
−0.798255 + 0.602320i 0.794243π0.794243\pi
654654 2.66934 1.59159i 0.104379 0.0622361i
655655 −9.32414 + 3.39371i −0.364324 + 0.132603i
656656 −0.385962 −0.0150693
657657 29.5166 37.2553i 1.15155 1.45347i
658658 8.31775 + 6.53528i 0.324260 + 0.254772i
659659 −18.3488 3.23539i −0.714769 0.126033i −0.195574 0.980689i 0.562657π-0.562657\pi
−0.519195 + 0.854656i 0.673768π0.673768\pi
660660 −7.27418 19.1439i −0.283147 0.745176i
661661 −27.1142 32.3135i −1.05462 1.25685i −0.965383 0.260838i 0.916001π-0.916001\pi
−0.0892379 0.996010i 0.528443π-0.528443\pi
662662 −2.38544 2.84285i −0.0927126 0.110491i
663663 31.8794 + 5.16022i 1.23809 + 0.200406i
664664 −5.65476 0.997088i −0.219447 0.0386945i
665665 40.4979 + 31.8194i 1.57044 + 1.23390i
666666 1.50755 + 1.69734i 0.0584163 + 0.0657705i
667667 −32.9591 −1.27618
668668 −18.8402 + 6.85728i −0.728950 + 0.265316i
669669 0.426179 + 0.238130i 0.0164771 + 0.00920665i
670670 5.12143 + 6.10349i 0.197858 + 0.235798i
671671 39.6751 33.2914i 1.53164 1.28520i
672672 −4.57768 + 0.211764i −0.176588 + 0.00816897i
673673 1.49663 0.544729i 0.0576908 0.0209977i −0.313014 0.949749i 0.601339π-0.601339\pi
0.370704 + 0.928751i 0.379116π0.379116\pi
674674 29.1615 16.8364i 1.12326 0.648513i
675675 27.8361 11.4825i 1.07141 0.441963i
676676 1.56158 2.70474i 0.0600609 0.104029i
677677 11.6428 + 9.76946i 0.447469 + 0.375471i 0.838495 0.544909i 0.183436π-0.183436\pi
−0.391027 + 0.920379i 0.627880π0.627880\pi
678678 18.4182 + 6.41194i 0.707348 + 0.246249i
679679 −4.17700 + 0.134417i −0.160299 + 0.00515844i
680680 19.1964 3.38484i 0.736147 0.129803i
681681 8.56731 15.3328i 0.328300 0.587555i
682682 −7.14775 19.6383i −0.273702 0.751989i
683683 23.8221 13.7537i 0.911528 0.526271i 0.0306055 0.999532i 0.490256π-0.490256\pi
0.880922 + 0.473261i 0.156923π0.156923\pi
684684 15.1371 9.31641i 0.578783 0.356222i
685685 −29.8744 + 17.2480i −1.14144 + 0.659012i
686686 −1.44359 + 18.4639i −0.0551165 + 0.704955i
687687 9.80563 + 25.8061i 0.374108 + 0.984564i
688688 0.563744 + 3.19715i 0.0214925 + 0.121890i
689689 19.6891 16.5211i 0.750093 0.629403i
690690 −6.14697 + 37.9755i −0.234011 + 1.44570i
691691 −4.91735 13.5103i −0.187065 0.513957i 0.810339 0.585961i 0.199283π-0.199283\pi
−0.997404 + 0.0720041i 0.977061π0.977061\pi
692692 −2.89843 5.02023i −0.110182 0.190841i
693693 −3.25625 + 28.3776i −0.123695 + 1.07797i
694694 15.6202 27.0550i 0.592935 1.02699i
695695 −41.8603 7.38109i −1.58785 0.279981i
696696 −8.44392 + 0.118713i −0.320066 + 0.00449979i
697697 −2.15173 0.783165i −0.0815025 0.0296645i
698698 2.85621 + 1.03957i 0.108109 + 0.0393484i
699699 −15.2636 + 43.8446i −0.577323 + 1.65835i
700700 −15.0056 + 3.14663i −0.567158 + 0.118931i
701701 33.8191i 1.27733i 0.769485 + 0.638664i 0.220513π0.220513\pi
−0.769485 + 0.638664i 0.779487π0.779487\pi
702702 −7.56156 + 14.4740i −0.285393 + 0.546287i
703703 3.88276 + 2.24171i 0.146441 + 0.0845477i
704704 3.54402 + 0.624907i 0.133570 + 0.0235521i
705705 17.2220 14.8685i 0.648619 0.559981i
706706 −0.316152 0.376776i −0.0118986 0.0141801i
707707 −7.09754 + 4.40807i −0.266931 + 0.165782i
708708 −18.5612 + 0.260950i −0.697571 + 0.00980712i
709709 4.20359 23.8398i 0.157869 0.895321i −0.798246 0.602331i 0.794239π-0.794239\pi
0.956116 0.292990i 0.0946503π-0.0946503\pi
710710 −3.22236 5.58129i −0.120933 0.209462i
711711 −0.385170 0.128047i −0.0144450 0.00480215i
712712 −12.3345 7.12133i −0.462255 0.266883i
713713 −6.81697 + 38.6610i −0.255298 + 1.44786i
714714 −25.9502 8.10811i −0.971160 0.303438i
715715 34.9180 + 12.7091i 1.30586 + 0.475295i
716716 −5.30082 + 0.934677i −0.198101 + 0.0349305i
717717 22.7072 27.8472i 0.848017 1.03997i
718718 −17.1183 14.3639i −0.638849 0.536058i
719719 1.89246 3.27783i 0.0705767 0.122242i −0.828577 0.559874i 0.810849π-0.810849\pi
0.899154 + 0.437632i 0.144183π0.144183\pi
720720 −1.43804 + 9.75123i −0.0535924 + 0.363407i
721721 −39.3374 30.9076i −1.46500 1.15106i
722722 10.3509 12.3357i 0.385221 0.459088i
723723 −0.585011 41.6113i −0.0217568 1.54754i
724724 2.35514 6.47070i 0.0875282 0.240482i
725725 −27.8245 + 4.90620i −1.03337 + 0.182212i
726726 1.11079 3.19074i 0.0412254 0.118420i
727727 −10.8547 29.8232i −0.402580 1.10608i −0.961007 0.276526i 0.910817π-0.910817\pi
0.558426 0.829554i 0.311405π-0.311405\pi
728728 5.13709 6.53820i 0.190393 0.242322i
729729 −11.4821 + 24.4369i −0.425261 + 0.905071i
730730 26.0277 + 45.0812i 0.963327 + 1.66853i
731731 −3.34456 + 18.9679i −0.123703 + 0.701555i
732732 −24.4856 + 4.67330i −0.905013 + 0.172730i
733733 −15.6683 + 43.0484i −0.578724 + 1.59003i 0.211611 + 0.977354i 0.432129π0.432129\pi
−0.790334 + 0.612676i 0.790093π0.790093\pi
734734 1.88829 + 10.7090i 0.0696982 + 0.395278i
735735 38.3850 + 10.6510i 1.41585 + 0.392870i
736736 −5.17848 4.34526i −0.190881 0.160169i
737737 8.72688i 0.321459i
738738 0.719045 0.907564i 0.0264684 0.0334079i
739739 5.63850 0.207415 0.103708 0.994608i 0.466929π-0.466929\pi
0.103708 + 0.994608i 0.466929π0.466929\pi
740740 −2.33632 + 0.850351i −0.0858848 + 0.0312595i
741741 −5.15328 + 31.8366i −0.189311 + 1.16955i
742742 −18.3811 + 11.4160i −0.674792 + 0.419093i
743743 −6.33835 + 17.4145i −0.232532 + 0.638875i −0.999998 0.00221452i 0.999295π-0.999295\pi
0.767466 + 0.641090i 0.221517π0.221517\pi
744744 −1.60722 + 9.92926i −0.0589235 + 0.364024i
745745 −3.04910 + 3.63377i −0.111710 + 0.133131i
746746 10.1381i 0.371181i
747747 12.8794 11.4392i 0.471232 0.418540i
748748 18.4898 + 10.6751i 0.676055 + 0.390321i
749749 −21.3857 + 19.1500i −0.781417 + 0.699727i
750750 0.0635938 + 4.52337i 0.00232212 + 0.165170i
751751 4.86527 4.08245i 0.177536 0.148971i −0.549689 0.835369i 0.685254π-0.685254\pi
0.727226 + 0.686399i 0.240809π0.240809\pi
752752 0.694267 + 3.93738i 0.0253173 + 0.143582i
753753 −48.9941 17.0563i −1.78545 0.621567i
754754 9.84924 11.7379i 0.358688 0.427468i
755755 −13.3297 −0.485118
756756 8.03025 11.1586i 0.292057 0.405836i
757757 22.7132 0.825525 0.412763 0.910839i 0.364564π-0.364564\pi
0.412763 + 0.910839i 0.364564π0.364564\pi
758758 −6.27079 + 7.47323i −0.227765 + 0.271440i
759759 −31.8942 + 27.5356i −1.15769 + 0.999481i
760760 3.38029 + 19.1706i 0.122616 + 0.695389i
761761 30.1453 25.2949i 1.09277 0.916941i 0.0958501 0.995396i 0.469443π-0.469443\pi
0.996918 + 0.0784548i 0.0249986π0.0249986\pi
762762 −1.54169 + 0.919228i −0.0558494 + 0.0333001i
763763 1.47934 4.51088i 0.0535557 0.163305i
764764 −0.886889 0.512046i −0.0320865 0.0185252i
765765 −27.8035 + 51.4449i −1.00524 + 1.86000i
766766 7.54926i 0.272766i
767767 21.6503 25.8018i 0.781747 0.931650i
768768 −1.34235 1.09458i −0.0484378 0.0394972i
769769 2.42858 6.67247i 0.0875768 0.240615i −0.888171 0.459513i 0.848024π-0.848024\pi
0.975748 + 0.218898i 0.0702461π0.0702461\pi
770770 −27.5807 14.7619i −0.993939 0.531982i
771771 18.1174 6.88414i 0.652483 0.247926i
772772 1.80134 0.655635i 0.0648317 0.0235968i
773773 −1.65044 −0.0593622 −0.0296811 0.999559i 0.509449π-0.509449\pi
−0.0296811 + 0.999559i 0.509449π0.509449\pi
774774 −8.56814 4.63067i −0.307976 0.166446i
775775 33.6528i 1.20885i
776776 −1.21002 1.01533i −0.0434373 0.0364483i
777777 3.43923 + 0.443711i 0.123382 + 0.0159180i
778778 0.949123 + 5.38275i 0.0340277 + 0.192981i
779779 0.782112 2.14884i 0.0280221 0.0769900i
780780 −11.6875 13.5374i −0.418478 0.484718i
781781 1.22577 6.95169i 0.0438615 0.248751i
782782 −20.0528 34.7325i −0.717088 1.24203i
783783 15.4518 20.0765i 0.552204 0.717476i
784784 −5.06193 + 4.83497i −0.180783 + 0.172677i
785785 −0.326270 0.896421i −0.0116451 0.0319946i
786786 3.41833 + 3.95941i 0.121928 + 0.141228i
787787 23.4455 4.13407i 0.835741 0.147364i 0.260630 0.965439i 0.416070π-0.416070\pi
0.575111 + 0.818075i 0.304959π0.304959\pi
788788 −4.27511 + 11.7458i −0.152294 + 0.418425i
789789 −24.2470 + 14.4573i −0.863217 + 0.514692i
790790 0.285740 0.340532i 0.0101662 0.0121156i
791791 27.6517 11.0840i 0.983180 0.394103i
792792 −8.07193 + 7.16935i −0.286823 + 0.254752i
793793 22.6151 39.1705i 0.803085 1.39098i
794794 23.8361 + 20.0009i 0.845911 + 0.709804i
795795 16.5311 + 43.5059i 0.586297 + 1.54299i
796796 13.1222 2.31380i 0.465105 0.0820106i
797797 19.0250 + 6.92454i 0.673901 + 0.245280i 0.656226 0.754564i 0.272152π-0.272152\pi
0.0176742 + 0.999844i 0.494374π0.494374\pi
798798 8.09721 25.9153i 0.286638 0.917391i
799799 −4.11892 + 23.3596i −0.145717 + 0.826402i
800800 −5.01857 2.89747i −0.177433 0.102441i
801801 39.7244 15.7368i 1.40359 0.556032i
802802 −6.83730 11.8425i −0.241433 0.418175i
803803 −9.90080 + 56.1502i −0.349392 + 1.98150i
804804 2.04878 3.66668i 0.0722549 0.129314i
805805 31.0034 + 49.9193i 1.09273 + 1.75943i
806806 −11.7314 13.9809i −0.413220 0.492456i
807807 −26.2039 9.12235i −0.922420 0.321122i
808808 −3.10992 0.548363i −0.109407 0.0192913i
809809 −33.5775 19.3860i −1.18052 0.681575i −0.224388 0.974500i 0.572038π-0.572038\pi
−0.956136 + 0.292925i 0.905372π0.905372\pi
810810 −20.2503 21.5479i −0.711524 0.757118i
811811 21.7970i 0.765396i 0.923873 + 0.382698i 0.125005π0.125005\pi
−0.923873 + 0.382698i 0.874995π0.874995\pi
812812 −9.60985 + 8.60523i −0.337239 + 0.301984i
813813 −4.22129 4.88947i −0.148047 0.171481i
814814 −2.55898 0.931394i −0.0896923 0.0326453i
815815 −51.5536 18.7640i −1.80584 0.657273i
816816 −5.26252 8.82604i −0.184225 0.308973i
817817 −18.9424 3.34006i −0.662712 0.116854i
818818 7.94533 13.7617i 0.277802 0.481167i
819819 5.80380 + 24.2602i 0.202801 + 0.847719i
820820 0.634051 + 1.09821i 0.0221420 + 0.0383511i
821821 −1.15335 3.16880i −0.0402522 0.110592i 0.917938 0.396723i 0.129853π-0.129853\pi
−0.958190 + 0.286131i 0.907631π0.907631\pi
822822 14.0936 + 11.4923i 0.491572 + 0.400839i
823823 −29.0512 + 24.3769i −1.01266 + 0.849725i −0.988688 0.149988i 0.952077π-0.952077\pi
−0.0239749 + 0.999713i 0.507632π0.507632\pi
824824 −3.28342 18.6212i −0.114383 0.648700i
825825 −22.8266 + 27.9936i −0.794720 + 0.974613i
826826 −21.1241 + 18.9157i −0.735000 + 0.658163i
827827 32.4938 18.7603i 1.12992 0.652360i 0.186006 0.982549i 0.440446π-0.440446\pi
0.943915 + 0.330188i 0.107112π0.107112\pi
828828 19.8651 4.08167i 0.690360 0.141848i
829829 5.12381 2.95824i 0.177957 0.102744i −0.408375 0.912814i 0.633904π-0.633904\pi
0.586333 + 0.810070i 0.300571π0.300571\pi
830830 6.45245 + 17.7280i 0.223968 + 0.615347i
831831 −10.7848 18.0877i −0.374120 0.627455i
832832 3.09500 0.545732i 0.107300 0.0189198i
833833 −38.0309 + 16.6835i −1.31769 + 0.578051i
834834 4.20092 + 22.0106i 0.145466 + 0.762164i
835835 50.4620 + 42.3426i 1.74631 + 1.46533i
836836 −10.6608 + 18.4650i −0.368710 + 0.638625i
837837 −20.3538 22.2774i −0.703530 0.770021i
838838 −18.2969 + 10.5637i −0.632057 + 0.364918i
839839 3.44126 1.25252i 0.118806 0.0432417i −0.281933 0.959434i 0.590976π-0.590976\pi
0.400739 + 0.916192i 0.368753π0.368753\pi
840840 8.12268 + 12.6774i 0.280259 + 0.437411i
841841 4.00542 3.36095i 0.138118 0.115895i
842842 20.3802 + 24.2881i 0.702347 + 0.837025i
843843 −0.742968 52.8466i −0.0255892 1.82013i
844844 10.3084 3.75197i 0.354831 0.129148i
845845 −10.2614 −0.353002
846846 −10.5519 5.70280i −0.362782 0.196066i
847847 −1.92018 4.79033i −0.0659782 0.164598i
848848 −8.05403 1.42014i −0.276577 0.0487679i
849849 7.89819 9.68603i 0.271065 0.332424i
850850 −22.0991 26.3366i −0.757991 0.903339i
851851 3.28816 + 3.91867i 0.112717 + 0.134330i
852852 −2.14704 + 2.63305i −0.0735565 + 0.0902067i
853853 15.8877 + 2.80143i 0.543984 + 0.0959191i 0.438886 0.898543i 0.355373π-0.355373\pi
0.105098 + 0.994462i 0.466484π0.466484\pi
854854 −23.5249 + 29.9412i −0.805005 + 1.02457i
855855 −51.3758 27.7661i −1.75701 0.949581i
856856 −10.8501 −0.370849
857857 10.2777 3.74077i 0.351079 0.127782i −0.160460 0.987042i 0.551298π-0.551298\pi
0.511539 + 0.859260i 0.329076π0.329076\pi
858858 −0.275375 19.5872i −0.00940115 0.668695i
859859 −21.5981 25.7397i −0.736919 0.878226i 0.259238 0.965813i 0.416529π-0.416529\pi
−0.996157 + 0.0875877i 0.972084π0.972084\pi
860860 8.17101 6.85629i 0.278629 0.233798i
861861 −0.0817328 1.76681i −0.00278545 0.0602127i
862862 −15.3934 + 5.60275i −0.524302 + 0.190830i
863863 −35.0893 + 20.2588i −1.19445 + 0.689617i −0.959313 0.282344i 0.908888π-0.908888\pi
−0.235139 + 0.971962i 0.575555π0.575555\pi
864864 5.07462 1.11725i 0.172642 0.0380096i
865865 −9.52299 + 16.4943i −0.323791 + 0.560823i
866866 −15.6632 13.1430i −0.532258 0.446618i
867867 −5.90909 30.9605i −0.200683 1.05147i
868868 8.10630 + 13.0522i 0.275146 + 0.443019i
869869 0.479502 0.0845492i 0.0162660 0.00286814i
870870 14.2093 + 23.8312i 0.481741 + 0.807952i
871871 2.60660 + 7.16157i 0.0883213 + 0.242661i
872872 1.55391 0.897149i 0.0526219 0.0303813i
873873 4.64176 0.953738i 0.157100 0.0322792i
874874 34.6858 20.0259i 1.17327 0.677386i
875875 4.60978 + 5.14795i 0.155839 + 0.174032i
876876 17.3421 21.2677i 0.585936 0.718568i
877877 6.62852 + 37.5922i 0.223829 + 1.26940i 0.864911 + 0.501926i 0.167375π0.167375\pi
−0.641082 + 0.767473i 0.721514π0.721514\pi
878878 −29.8906 + 25.0812i −1.00876 + 0.846450i
879879 27.0785 + 22.0804i 0.913335 + 0.744752i
880880 −4.04396 11.1107i −0.136322 0.374541i
881881 8.28919 + 14.3573i 0.279270 + 0.483709i 0.971203 0.238252i 0.0765743π-0.0765743\pi
−0.691934 + 0.721961i 0.743241π0.743241\pi
882882 −1.93877 20.9103i −0.0652819 0.704087i
883883 11.1658 19.3397i 0.375758 0.650832i −0.614682 0.788775i 0.710716π-0.710716\pi
0.990440 + 0.137943i 0.0440490π0.0440490\pi
884884 18.3619 + 3.23770i 0.617577 + 0.108896i
885885 31.2345 + 52.3849i 1.04994 + 1.76090i
886886 17.7782 + 6.47072i 0.597269 + 0.217388i
887887 −12.9256 4.70453i −0.433999 0.157963i 0.115776 0.993275i 0.463064π-0.463064\pi
−0.549775 + 0.835313i 0.685287π0.685287\pi
888888 0.856521 + 0.992098i 0.0287430 + 0.0332926i
889889 −0.854398 + 2.60528i −0.0286556 + 0.0873782i
890890 46.7952i 1.56858i
891891 −1.82030 32.3371i −0.0609823 1.08333i
892892 0.244098 + 0.140930i 0.00817300 + 0.00471868i
893893 −23.3282 4.11338i −0.780647 0.137649i
894894 2.36164 + 0.822157i 0.0789851 + 0.0274971i
895895 11.3676 + 13.5474i 0.379977 + 0.452839i
896896 −2.64438 + 0.0850968i −0.0883426 + 0.00284288i
897897 −17.9489 + 32.1230i −0.599298 + 1.07256i
898898 −0.247004 + 1.40083i −0.00824262 + 0.0467462i
899899 14.1569 + 24.5205i 0.472160 + 0.817805i
900900 16.1628 6.40286i 0.538759 0.213429i
901901 −42.0194 24.2599i −1.39987 0.808215i
902902 −0.241190 + 1.36786i −0.00803076 + 0.0455447i
903903 −14.5161 + 3.25768i −0.483067 + 0.108409i
904904 10.5807 + 3.85106i 0.351908 + 0.128084i
905905 −22.2806 + 3.92867i −0.740632 + 0.130593i
906906 2.49597 + 6.56880i 0.0829231 + 0.218234i
907907 27.6469 + 23.1985i 0.918001 + 0.770295i 0.973624 0.228157i 0.0732700π-0.0732700\pi
−0.0556230 + 0.998452i 0.517714π0.517714\pi
908908 5.07029 8.78200i 0.168264 0.291441i
909909 7.08321 6.29118i 0.234935 0.208665i
910910 −27.0428 3.87614i −0.896461 0.128493i
911911 28.8281 34.3560i 0.955117 1.13826i −0.0351922 0.999381i 0.511204π-0.511204\pi
0.990309 0.138883i 0.0443512π-0.0443512\pi
912912 8.81418 5.25544i 0.291867 0.174025i
913913 −7.06740 + 19.4175i −0.233897 + 0.642627i
914914 32.8814 5.79788i 1.08762 0.191777i
915915 53.5218 + 61.9937i 1.76938 + 2.04945i
916916 5.45128 + 14.9773i 0.180115 + 0.494863i
917917 7.90944 + 1.13369i 0.261193 + 0.0374377i
918918 30.5579 + 4.06840i 1.00856 + 0.134277i
919919 −19.3065 33.4398i −0.636862 1.10308i −0.986117 0.166050i 0.946899π-0.946899\pi
0.349255 0.937028i 0.386435π-0.386435\pi
920920 −3.85682 + 21.8731i −0.127155 + 0.721135i
921921 −28.0940 32.5409i −0.925727 1.07226i
922922 −1.81752 + 4.99360i −0.0598568 + 0.164455i
923923 −1.07047 6.07091i −0.0352348 0.199827i
924924 −2.11013 + 16.3557i −0.0694181 + 0.538064i
925925 3.35923 + 2.81873i 0.110451 + 0.0926791i
926926 22.9901i 0.755500i
927927 49.9036 + 26.9705i 1.63905 + 0.885826i
928928 −4.87558 −0.160049
929929 20.9045 7.60862i 0.685855 0.249631i 0.0244956 0.999700i 0.492202π-0.492202\pi
0.661359 + 0.750069i 0.269980π0.269980\pi
930930 30.8929 11.7385i 1.01302 0.384920i
931931 −16.6611 37.9797i −0.546046 1.24474i
932932 −9.16742 + 25.1873i −0.300289 + 0.825037i
933933 −7.64016 6.22995i −0.250128 0.203959i
934934 −23.4657 + 27.9653i −0.767822 + 0.915054i
935935 70.1476i 2.29407i
936936 −4.48271 + 8.29438i −0.146522 + 0.271110i
937937 −36.0663 20.8229i −1.17824 0.680255i −0.222630 0.974903i 0.571464π-0.571464\pi
−0.955606 + 0.294648i 0.904798π0.904798\pi
938938 −1.31677 6.27940i −0.0429941 0.205030i
939939 −5.04535 + 3.00828i −0.164649 + 0.0981716i
940940 10.0628 8.44372i 0.328213 0.275404i
941941 −5.83857 33.1122i −0.190332 1.07943i −0.918911 0.394464i 0.870930π-0.870930\pi
0.728579 0.684961i 0.240181π-0.240181\pi
942942 −0.380657 + 0.328638i −0.0124025 + 0.0107076i
943943 1.67711 1.99870i 0.0546141 0.0650865i
944944 −10.7174 −0.348820
945945 −44.9425 4.51791i −1.46198 0.146968i
946946 11.6831 0.379849
947947 −0.519822 + 0.619500i −0.0168919 + 0.0201310i −0.774424 0.632667i 0.781960π-0.781960\pi
0.757532 + 0.652798i 0.226405π0.226405\pi
948948 −0.221317 0.0770470i −0.00718803 0.00250237i
949949 8.64637 + 49.0360i 0.280673 + 1.59178i
950950 26.3012 22.0693i 0.853324 0.716024i
951951 −0.310130 22.0593i −0.0100567 0.715321i
952952 −14.9150 4.89137i −0.483399 0.158530i
953953 26.1971 + 15.1249i 0.848606 + 0.489943i 0.860180 0.509990i 0.170351π-0.170351\pi
−0.0115741 + 0.999933i 0.503684π0.503684\pi
954954 18.3440 16.2928i 0.593909 0.527500i
955955 3.36472i 0.108880i
956956 13.3347 15.8917i 0.431276 0.513975i
957957 −4.85595 + 29.9996i −0.156970 + 0.969751i
958958 4.87496 13.3938i 0.157503 0.432735i
959959 27.7640 0.893453i 0.896548 0.0288511i
960960 −0.909311 + 5.61765i −0.0293479 + 0.181309i
961961 2.56016 0.931822i 0.0825858 0.0300588i
962962 −2.37818 −0.0766757
963963 20.2137 25.5133i 0.651377 0.822155i
964964 24.0267i 0.773847i
965965 −4.82475 4.04844i −0.155314 0.130324i
966966 18.7946 24.6256i 0.604707 0.792316i
967967 −5.06837 28.7441i −0.162988 0.924349i −0.951115 0.308837i 0.900060π-0.900060\pi
0.788127 0.615512i 0.211051π-0.211051\pi
968968 0.667150 1.83298i 0.0214430 0.0589142i
969969 59.8028 11.4139i 1.92114 0.366667i
970970 −0.901199 + 5.11095i −0.0289357 + 0.164103i
971971 −23.8211 41.2593i −0.764454 1.32407i −0.940535 0.339697i 0.889675π-0.889675\pi
0.176081 0.984376i 0.443658π-0.443658\pi
972972 −6.82685 + 14.0141i −0.218971 + 0.449502i
973973 26.9147 + 21.1470i 0.862847 + 0.677942i
974974 −2.55601 7.02258i −0.0818999 0.225018i
975975 −10.3710 + 29.7905i −0.332137 + 0.954060i
976976 −14.1733 + 2.49913i −0.453676 + 0.0799953i
977977 −6.77212 + 18.6062i −0.216659 + 0.595266i −0.999641 0.0267779i 0.991475π-0.991475\pi
0.782982 + 0.622044i 0.213698π0.213698\pi
978978 0.406568 + 28.9188i 0.0130006 + 0.924722i
979979 −32.9461 + 39.2636i −1.05296 + 1.25487i
980980 22.0730 + 6.46032i 0.705095 + 0.206367i
981981 −0.785333 + 5.32530i −0.0250738 + 0.170024i
982982 −8.33799 + 14.4418i −0.266076 + 0.460857i
983983 20.7795 + 17.4360i 0.662762 + 0.556124i 0.910913 0.412598i 0.135378π-0.135378\pi
−0.248151 + 0.968721i 0.579823π0.579823\pi
984984 0.422466 0.518095i 0.0134677 0.0165163i
985985 40.4442 7.13141i 1.28866 0.227226i
986986 −27.1812 9.89317i −0.865627 0.315063i
987987 −17.8771 + 4.01193i −0.569033 + 0.127701i
988988 −3.23335 + 18.3372i −0.102866 + 0.583384i
989989 −19.0060 10.9731i −0.604356 0.348925i
990990 33.6600 + 11.1900i 1.06978 + 0.355643i
991991 12.7338 + 22.0557i 0.404504 + 0.700621i 0.994264 0.106958i 0.0341109π-0.0341109\pi
−0.589760 + 0.807579i 0.700778π0.700778\pi
992992 −1.00842 + 5.71905i −0.0320175 + 0.181580i
993993 6.42714 0.0903589i 0.203959 0.00286745i
994994 0.166919 + 5.18702i 0.00529436 + 0.164522i
995995 −28.1406 33.5367i −0.892118 1.06318i
996996 7.52802 6.49927i 0.238535 0.205937i
997997 26.6548 + 4.69997i 0.844167 + 0.148849i 0.578974 0.815346i 0.303453π-0.303453\pi
0.265193 + 0.964195i 0.414564π0.414564\pi
998998 −6.95234 4.01394i −0.220072 0.127059i
999999 −3.92855 + 0.165781i −0.124294 + 0.00524508i
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 378.2.bf.a.101.7 yes 144
7.5 odd 6 378.2.ba.a.47.14 144
27.23 odd 18 378.2.ba.a.185.14 yes 144
189.131 even 18 inner 378.2.bf.a.131.7 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.ba.a.47.14 144 7.5 odd 6
378.2.ba.a.185.14 yes 144 27.23 odd 18
378.2.bf.a.101.7 yes 144 1.1 even 1 trivial
378.2.bf.a.131.7 yes 144 189.131 even 18 inner