Properties

Label 845.2.l.d.654.3
Level 845845
Weight 22
Character 845.654
Analytic conductor 6.7476.747
Analytic rank 00
Dimension 1212
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(654,845)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(845, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("845.654");
 
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.l (of order 66, degree 22, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 6.747358970806.74735897080
Analytic rank: 00
Dimension: 1212
Relative dimension: 66 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: 12.0.89539436150784.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x122x11+2x108x9+4x8+16x78x6+20x5+20x424x3+8x28x+4 x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 Copy content Toggle raw display
Coefficient ring: Z[a1,,a4]\Z[a_1, \ldots, a_{4}]
Coefficient ring index: 24 2^{4}
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 654.3
Root 1.16746+0.312819i-1.16746 + 0.312819i of defining polynomial
Character χ\chi == 845.654
Dual form 845.2.l.d.699.3

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+(0.769594+1.33298i)q2+(2.745381.58504i)q3+(0.1845510.319652i)q4+(2.17009+0.539189i)q5+(4.225652.43968i)q6+(0.8546381.48028i)q72.51026q8+(3.52472+6.10500i)q9+(2.38881+2.47772i)q10+(2.199001.26959i)q11+1.17009iq12+2.63090q14+(5.103064.91996i)q15+(2.300983.98542i)q16+(0.7981480.460811i)q1710.8504q18+(0.4669510.269594i)q19+(0.2281390.793181i)q20+5.41855iq21+(3.384681.95415i)q22+(2.45078+1.41496i)q23+(6.89160+3.97887i)q24+(4.41855+2.34017i)q2512.8371iq27+(0.315449+0.546373i)q28+(2.56391+4.44083i)q29+(10.48553.01589i)q30+0.879362iq31+(1.03139+1.78642i)q32+(4.02472+6.97103i)q33+1.41855iq34+(1.056493.67314i)q35+(1.300982.25337i)q36+(3.02472+5.23898i)q37+0.829914iq38+(5.447481.35350i)q40+(1.092750.630898i)q41+(7.222804.17009i)q42+(5.57017+3.21594i)q43+0.937221iq44+(4.35721+15.1489i)q45+(3.77221+2.17789i)q465.70928q47+(12.6341+7.29432i)q48+(2.039193.53198i)q49+(6.51989+4.08884i)q502.92162q51+8.49693iq53+(17.1116+9.87936i)q54+(4.087473.94081i)q55+(2.14536+3.71588i)q561.70928q57+(3.946356.83527i)q58+(4.08990+2.36130i)q59+(0.630898+2.53919i)q60+(4.024726.97103i)q61+(1.172170.676752i)q62+(6.0247210.4351i)q63+6.02893q6412.3896q66+(3.93302+6.81218i)q67+(0.2945980.170086i)q68+(4.485547.76918i)q69+(5.70928+1.41855i)q70+(12.5412+7.24067i)q71+(8.8479715.3251i)q721.95055q73+(4.655628.06377i)q74+(8.4213113.4282i)q75+(0.1723530.0995079i)q76+4.34017iq770.496928q79+(7.142237.40804i)q80+(9.77319+16.9277i)q81+(1.681940.971071i)q828.63090q83+(1.732051.00000i)q84+(1.980520.569647i)q859.89988iq86+(14.07788.12783i)q87+(5.52007+3.18701i)q88+(11.11736.41855i)q89+(23.54645.85043i)q901.04453iq92+(1.393832.41418i)q93+(4.393837.61033i)q94+(1.158690.333268i)q956.53919iq96+(2.957745.12296i)q97+(3.13870+5.43638i)q9817.8999iq99+O(q100)q+(-0.769594 + 1.33298i) q^{2} +(-2.74538 - 1.58504i) q^{3} +(-0.184551 - 0.319652i) q^{4} +(2.17009 + 0.539189i) q^{5} +(4.22565 - 2.43968i) q^{6} +(-0.854638 - 1.48028i) q^{7} -2.51026 q^{8} +(3.52472 + 6.10500i) q^{9} +(-2.38881 + 2.47772i) q^{10} +(-2.19900 - 1.26959i) q^{11} +1.17009i q^{12} +2.63090 q^{14} +(-5.10306 - 4.91996i) q^{15} +(2.30098 - 3.98542i) q^{16} +(0.798148 - 0.460811i) q^{17} -10.8504 q^{18} +(0.466951 - 0.269594i) q^{19} +(-0.228139 - 0.793181i) q^{20} +5.41855i q^{21} +(3.38468 - 1.95415i) q^{22} +(2.45078 + 1.41496i) q^{23} +(6.89160 + 3.97887i) q^{24} +(4.41855 + 2.34017i) q^{25} -12.8371i q^{27} +(-0.315449 + 0.546373i) q^{28} +(-2.56391 + 4.44083i) q^{29} +(10.4855 - 3.01589i) q^{30} +0.879362i q^{31} +(1.03139 + 1.78642i) q^{32} +(4.02472 + 6.97103i) q^{33} +1.41855i q^{34} +(-1.05649 - 3.67314i) q^{35} +(1.30098 - 2.25337i) q^{36} +(-3.02472 + 5.23898i) q^{37} +0.829914i q^{38} +(-5.44748 - 1.35350i) q^{40} +(-1.09275 - 0.630898i) q^{41} +(-7.22280 - 4.17009i) q^{42} +(-5.57017 + 3.21594i) q^{43} +0.937221i q^{44} +(4.35721 + 15.1489i) q^{45} +(-3.77221 + 2.17789i) q^{46} -5.70928 q^{47} +(-12.6341 + 7.29432i) q^{48} +(2.03919 - 3.53198i) q^{49} +(-6.51989 + 4.08884i) q^{50} -2.92162 q^{51} +8.49693i q^{53} +(17.1116 + 9.87936i) q^{54} +(-4.08747 - 3.94081i) q^{55} +(2.14536 + 3.71588i) q^{56} -1.70928 q^{57} +(-3.94635 - 6.83527i) q^{58} +(-4.08990 + 2.36130i) q^{59} +(-0.630898 + 2.53919i) q^{60} +(-4.02472 - 6.97103i) q^{61} +(-1.17217 - 0.676752i) q^{62} +(6.02472 - 10.4351i) q^{63} +6.02893 q^{64} -12.3896 q^{66} +(-3.93302 + 6.81218i) q^{67} +(-0.294598 - 0.170086i) q^{68} +(-4.48554 - 7.76918i) q^{69} +(5.70928 + 1.41855i) q^{70} +(-12.5412 + 7.24067i) q^{71} +(-8.84797 - 15.3251i) q^{72} -1.95055 q^{73} +(-4.65562 - 8.06377i) q^{74} +(-8.42131 - 13.4282i) q^{75} +(-0.172353 - 0.0995079i) q^{76} +4.34017i q^{77} -0.496928 q^{79} +(7.14223 - 7.40804i) q^{80} +(-9.77319 + 16.9277i) q^{81} +(1.68194 - 0.971071i) q^{82} -8.63090 q^{83} +(1.73205 - 1.00000i) q^{84} +(1.98052 - 0.569647i) q^{85} -9.89988i q^{86} +(14.0778 - 8.12783i) q^{87} +(5.52007 + 3.18701i) q^{88} +(-11.1173 - 6.41855i) q^{89} +(-23.5464 - 5.85043i) q^{90} -1.04453i q^{92} +(1.39383 - 2.41418i) q^{93} +(4.39383 - 7.61033i) q^{94} +(1.15869 - 0.333268i) q^{95} -6.53919i q^{96} +(-2.95774 - 5.12296i) q^{97} +(3.13870 + 5.43638i) q^{98} -17.8999i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q6q210q4+4q5+4q7+36q8+6q9+2q10+16q144q1510q1620q18+14q204q25+4q28+12q29+8q3022q32+12q33++50q98+O(q100) 12 q - 6 q^{2} - 10 q^{4} + 4 q^{5} + 4 q^{7} + 36 q^{8} + 6 q^{9} + 2 q^{10} + 16 q^{14} - 4 q^{15} - 10 q^{16} - 20 q^{18} + 14 q^{20} - 4 q^{25} + 4 q^{28} + 12 q^{29} + 8 q^{30} - 22 q^{32} + 12 q^{33}+ \cdots + 50 q^{98}+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(16)e\left(\frac{1}{6}\right) 1-1

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 −0.769594 + 1.33298i −0.544185 + 0.942557i 0.454472 + 0.890761i 0.349828π0.349828\pi
−0.998658 + 0.0517959i 0.983505π0.983505\pi
33 −2.74538 1.58504i −1.58504 0.915125i −0.994107 0.108407i 0.965425π-0.965425\pi
−0.590937 0.806718i 0.701242π-0.701242\pi
44 −0.184551 0.319652i −0.0922756 0.159826i
55 2.17009 + 0.539189i 0.970492 + 0.241133i
66 4.22565 2.43968i 1.72511 0.995996i
77 −0.854638 1.48028i −0.323023 0.559492i 0.658088 0.752941i 0.271366π-0.271366\pi
−0.981110 + 0.193450i 0.938032π0.938032\pi
88 −2.51026 −0.887511
99 3.52472 + 6.10500i 1.17491 + 2.03500i
1010 −2.38881 + 2.47772i −0.755409 + 0.783523i
1111 −2.19900 1.26959i −0.663024 0.382797i 0.130404 0.991461i 0.458373π-0.458373\pi
−0.793428 + 0.608664i 0.791706π0.791706\pi
1212 1.17009i 0.337775i
1313 0 0
1414 2.63090 0.703137
1515 −5.10306 4.91996i −1.31761 1.27033i
1616 2.30098 3.98542i 0.575246 0.996355i
1717 0.798148 0.460811i 0.193579 0.111763i −0.400078 0.916481i 0.631017π-0.631017\pi
0.593657 + 0.804718i 0.297684π0.297684\pi
1818 −10.8504 −2.55747
1919 0.466951 0.269594i 0.107126 0.0618492i −0.445480 0.895292i 0.646967π-0.646967\pi
0.552606 + 0.833443i 0.313634π0.313634\pi
2020 −0.228139 0.793181i −0.0510135 0.177361i
2121 5.41855i 1.18242i
2222 3.38468 1.95415i 0.721616 0.416625i
2323 2.45078 + 1.41496i 0.511022 + 0.295039i 0.733254 0.679955i 0.238001π-0.238001\pi
−0.222231 + 0.974994i 0.571334π0.571334\pi
2424 6.89160 + 3.97887i 1.40674 + 0.812183i
2525 4.41855 + 2.34017i 0.883710 + 0.468035i
2626 0 0
2727 12.8371i 2.47050i
2828 −0.315449 + 0.546373i −0.0596142 + 0.103255i
2929 −2.56391 + 4.44083i −0.476107 + 0.824641i −0.999625 0.0273733i 0.991286π-0.991286\pi
0.523519 + 0.852014i 0.324619π0.324619\pi
3030 10.4855 3.01589i 1.91438 0.550624i
3131 0.879362i 0.157938i 0.996877 + 0.0789690i 0.0251628π0.0251628\pi
−0.996877 + 0.0789690i 0.974837π0.974837\pi
3232 1.03139 + 1.78642i 0.182326 + 0.315797i
3333 4.02472 + 6.97103i 0.700615 + 1.21350i
3434 1.41855i 0.243279i
3535 −1.05649 3.67314i −0.178579 0.620874i
3636 1.30098 2.25337i 0.216831 0.375562i
3737 −3.02472 + 5.23898i −0.497262 + 0.861282i −0.999995 0.00315916i 0.998994π-0.998994\pi
0.502733 + 0.864442i 0.332328π0.332328\pi
3838 0.829914i 0.134630i
3939 0 0
4040 −5.44748 1.35350i −0.861322 0.214008i
4141 −1.09275 0.630898i −0.170658 0.0985297i 0.412238 0.911076i 0.364747π-0.364747\pi
−0.582896 + 0.812547i 0.698081π0.698081\pi
4242 −7.22280 4.17009i −1.11450 0.643458i
4343 −5.57017 + 3.21594i −0.849443 + 0.490426i −0.860463 0.509513i 0.829826π-0.829826\pi
0.0110196 + 0.999939i 0.496492π0.496492\pi
4444 0.937221i 0.141291i
4545 4.35721 + 15.1489i 0.649534 + 2.25826i
4646 −3.77221 + 2.17789i −0.556182 + 0.321112i
4747 −5.70928 −0.832783 −0.416392 0.909185i 0.636705π-0.636705\pi
−0.416392 + 0.909185i 0.636705π0.636705\pi
4848 −12.6341 + 7.29432i −1.82358 + 1.05284i
4949 2.03919 3.53198i 0.291313 0.504568i
5050 −6.51989 + 4.08884i −0.922051 + 0.578249i
5151 −2.92162 −0.409109
5252 0 0
5353 8.49693i 1.16714i 0.812062 + 0.583571i 0.198345π0.198345\pi
−0.812062 + 0.583571i 0.801655π0.801655\pi
5454 17.1116 + 9.87936i 2.32859 + 1.34441i
5555 −4.08747 3.94081i −0.551155 0.531378i
5656 2.14536 + 3.71588i 0.286686 + 0.496555i
5757 −1.70928 −0.226399
5858 −3.94635 6.83527i −0.518181 0.897515i
5959 −4.08990 + 2.36130i −0.532459 + 0.307415i −0.742017 0.670381i 0.766131π-0.766131\pi
0.209558 + 0.977796i 0.432797π0.432797\pi
6060 −0.630898 + 2.53919i −0.0814485 + 0.327808i
6161 −4.02472 6.97103i −0.515313 0.892549i −0.999842 0.0177733i 0.994342π-0.994342\pi
0.484529 0.874775i 0.338991π-0.338991\pi
6262 −1.17217 0.676752i −0.148866 0.0859476i
6363 6.02472 10.4351i 0.759044 1.31470i
6464 6.02893 0.753616
6565 0 0
6666 −12.3896 −1.52506
6767 −3.93302 + 6.81218i −0.480494 + 0.832241i −0.999750 0.0223786i 0.992876π-0.992876\pi
0.519255 + 0.854619i 0.326209π0.326209\pi
6868 −0.294598 0.170086i −0.0357253 0.0206260i
6969 −4.48554 7.76918i −0.539995 0.935299i
7070 5.70928 + 1.41855i 0.682389 + 0.169549i
7171 −12.5412 + 7.24067i −1.48837 + 0.859309i −0.999912 0.0132804i 0.995773π-0.995773\pi
−0.488455 + 0.872589i 0.662439π0.662439\pi
7272 −8.84797 15.3251i −1.04274 1.80608i
7373 −1.95055 −0.228295 −0.114147 0.993464i 0.536414π-0.536414\pi
−0.114147 + 0.993464i 0.536414π0.536414\pi
7474 −4.65562 8.06377i −0.541205 0.937395i
7575 −8.42131 13.4282i −0.972409 1.55056i
7676 −0.172353 0.0995079i −0.0197702 0.0114143i
7777 4.34017i 0.494609i
7878 0 0
7979 −0.496928 −0.0559088 −0.0279544 0.999609i 0.508899π-0.508899\pi
−0.0279544 + 0.999609i 0.508899π0.508899\pi
8080 7.14223 7.40804i 0.798526 0.828245i
8181 −9.77319 + 16.9277i −1.08591 + 1.88085i
8282 1.68194 0.971071i 0.185740 0.107237i
8383 −8.63090 −0.947364 −0.473682 0.880696i 0.657075π-0.657075\pi
−0.473682 + 0.880696i 0.657075π0.657075\pi
8484 1.73205 1.00000i 0.188982 0.109109i
8585 1.98052 0.569647i 0.214817 0.0617869i
8686 9.89988i 1.06753i
8787 14.0778 8.12783i 1.50930 0.871394i
8888 5.52007 + 3.18701i 0.588441 + 0.339737i
8989 −11.1173 6.41855i −1.17843 0.680365i −0.222777 0.974870i 0.571512π-0.571512\pi
−0.955650 + 0.294504i 0.904845π0.904845\pi
9090 −23.5464 5.85043i −2.48201 0.616690i
9191 0 0
9292 1.04453i 0.108900i
9393 1.39383 2.41418i 0.144533 0.250339i
9494 4.39383 7.61033i 0.453189 0.784946i
9595 1.15869 0.333268i 0.118879 0.0341926i
9696 6.53919i 0.667403i
9797 −2.95774 5.12296i −0.300313 0.520157i 0.675894 0.736999i 0.263758π-0.263758\pi
−0.976207 + 0.216842i 0.930424π0.930424\pi
9898 3.13870 + 5.43638i 0.317056 + 0.549158i
9999 17.8999i 1.79901i
100100 −0.0674077 1.84428i −0.00674077 0.184428i
101101 −8.21953 + 14.2367i −0.817874 + 1.41660i 0.0893712 + 0.995998i 0.471514π0.471514\pi
−0.907246 + 0.420601i 0.861819π0.861819\pi
102102 2.24846 3.89445i 0.222631 0.385608i
103103 10.1906i 1.00411i 0.864836 + 0.502055i 0.167423π0.167423\pi
−0.864836 + 0.502055i 0.832577π0.832577\pi
104104 0 0
105105 −2.92162 + 11.7587i −0.285121 + 1.14753i
106106 −11.3262 6.53919i −1.10010 0.635142i
107107 8.44508 + 4.87577i 0.816416 + 0.471358i 0.849179 0.528105i 0.177097π-0.177097\pi
−0.0327627 + 0.999463i 0.510431π0.510431\pi
108108 −4.10341 + 2.36910i −0.394850 + 0.227967i
109109 16.8638i 1.61526i 0.589693 + 0.807628i 0.299249π0.299249\pi
−0.589693 + 0.807628i 0.700751π0.700751\pi
110110 8.39870 2.41568i 0.800785 0.230326i
111111 16.6080 9.58864i 1.57636 0.910113i
112112 −7.86603 −0.743270
113113 −10.1834 + 5.87936i −0.957969 + 0.553084i −0.895547 0.444966i 0.853216π-0.853216\pi
−0.0624219 + 0.998050i 0.519882π0.519882\pi
114114 1.31545 2.27842i 0.123203 0.213394i
115115 4.55547 + 4.39201i 0.424800 + 0.409557i
116116 1.89269 0.175732
117117 0 0
118118 7.26898i 0.669164i
119119 −1.36426 0.787653i −0.125061 0.0722040i
120120 12.8100 + 12.3504i 1.16939 + 1.12743i
121121 −2.27626 3.94260i −0.206933 0.358418i
122122 12.3896 1.12170
123123 2.00000 + 3.46410i 0.180334 + 0.312348i
124124 0.281090 0.162287i 0.0252426 0.0145738i
125125 8.32684 + 7.46081i 0.744775 + 0.667315i
126126 9.27319 + 16.0616i 0.826121 + 1.43088i
127127 15.5947 + 9.00359i 1.38380 + 0.798940i 0.992608 0.121367i 0.0387279π-0.0387279\pi
0.391197 + 0.920307i 0.372061π0.372061\pi
128128 −6.70261 + 11.6093i −0.592433 + 1.02612i
129129 20.3896 1.79521
130130 0 0
131131 14.2557 1.24552 0.622761 0.782412i 0.286011π-0.286011\pi
0.622761 + 0.782412i 0.286011π0.286011\pi
132132 1.48554 2.57302i 0.129299 0.223953i
133133 −0.798148 0.460811i −0.0692082 0.0399574i
134134 −6.05365 10.4852i −0.522956 0.905786i
135135 6.92162 27.8576i 0.595718 2.39760i
136136 −2.00356 + 1.15676i −0.171804 + 0.0991910i
137137 6.89269 + 11.9385i 0.588882 + 1.01997i 0.994379 + 0.105878i 0.0337653π0.0337653\pi
−0.405497 + 0.914097i 0.632901π0.632901\pi
138138 13.8082 1.17543
139139 −3.32684 5.76226i −0.282179 0.488748i 0.689742 0.724055i 0.257724π-0.257724\pi
−0.971921 + 0.235307i 0.924391π0.924391\pi
140140 −0.979150 + 1.01559i −0.0827532 + 0.0858331i
141141 15.6741 + 9.04945i 1.32000 + 0.762101i
142142 22.2895i 1.87049i
143143 0 0
144144 32.4413 2.70344
145145 −7.95836 + 8.25455i −0.660906 + 0.685503i
146146 1.50113 2.60004i 0.124235 0.215181i
147147 −11.1967 + 6.46441i −0.923486 + 0.533175i
148148 2.23287 0.183540
149149 7.86211 4.53919i 0.644089 0.371865i −0.142099 0.989852i 0.545385π-0.545385\pi
0.786188 + 0.617988i 0.212052π0.212052\pi
150150 24.3805 0.891099i 1.99066 0.0727579i
151151 3.27739i 0.266711i −0.991068 0.133355i 0.957425π-0.957425\pi
0.991068 0.133355i 0.0425751π-0.0425751\pi
152152 −1.17217 + 0.676752i −0.0950754 + 0.0548918i
153153 5.62651 + 3.24846i 0.454876 + 0.262623i
154154 −5.78535 3.34017i −0.466197 0.269159i
155155 −0.474142 + 1.90829i −0.0380840 + 0.153278i
156156 0 0
157157 12.8371i 1.02451i −0.858833 0.512256i 0.828810π-0.828810\pi
0.858833 0.512256i 0.171190π-0.171190\pi
158158 0.382433 0.662394i 0.0304248 0.0526972i
159159 13.4680 23.3273i 1.06808 1.84997i
160160 1.27499 + 4.43280i 0.100797 + 0.350443i
161161 4.83710i 0.381217i
162162 −15.0428 26.0549i −1.18187 2.04706i
163163 −6.02472 10.4351i −0.471893 0.817342i 0.527590 0.849499i 0.323096π-0.323096\pi
−0.999483 + 0.0321568i 0.989762π0.989762\pi
164164 0.465732i 0.0363675i
165165 4.97530 + 17.2978i 0.387327 + 1.34663i
166166 6.64229 11.5048i 0.515542 0.892945i
167167 4.36490 7.56022i 0.337766 0.585028i −0.646246 0.763129i 0.723662π-0.723662\pi
0.984012 + 0.178101i 0.0569955π0.0569955\pi
168168 13.6020i 1.04941i
169169 0 0
170170 −0.764867 + 3.07838i −0.0586626 + 0.236101i
171171 3.29175 + 1.90049i 0.251726 + 0.145334i
172172 2.05596 + 1.18701i 0.156766 + 0.0905088i
173173 −0.748041 + 0.431882i −0.0568725 + 0.0328354i −0.528167 0.849141i 0.677120π-0.677120\pi
0.471294 + 0.881976i 0.343787π0.343787\pi
174174 25.0205i 1.89680i
175175 −0.312158 8.54067i −0.0235970 0.645614i
176176 −10.1197 + 5.84263i −0.762804 + 0.440405i
177177 14.9711 1.12529
178178 17.1116 9.87936i 1.28257 0.740489i
179179 −9.95774 + 17.2473i −0.744276 + 1.28912i 0.206256 + 0.978498i 0.433872π0.433872\pi
−0.950532 + 0.310626i 0.899461π0.899461\pi
180180 4.03824 4.18853i 0.300993 0.312195i
181181 −14.3896 −1.06957 −0.534786 0.844987i 0.679608π-0.679608\pi
−0.534786 + 0.844987i 0.679608π0.679608\pi
182182 0 0
183183 25.5174i 1.88630i
184184 −6.15209 3.55191i −0.453538 0.261850i
185185 −9.38871 + 9.73813i −0.690272 + 0.715962i
186186 2.14536 + 3.71588i 0.157306 + 0.272461i
187187 −2.34017 −0.171130
188188 1.05365 + 1.82498i 0.0768456 + 0.133100i
189189 −19.0025 + 10.9711i −1.38222 + 0.798028i
190190 −0.447480 + 1.80098i −0.0324636 + 0.130657i
191191 −0.738205 1.27861i −0.0534146 0.0925168i 0.838082 0.545545i 0.183677π-0.183677\pi
−0.891496 + 0.453028i 0.850344π0.850344\pi
192192 −16.5517 9.55611i −1.19451 0.689653i
193193 8.86603 15.3564i 0.638191 1.10538i −0.347639 0.937629i 0.613016π-0.613016\pi
0.985829 0.167750i 0.0536503π-0.0536503\pi
194194 9.10504 0.653704
195195 0 0
196196 −1.50534 −0.107524
197197 −1.00000 + 1.73205i −0.0712470 + 0.123404i −0.899448 0.437028i 0.856031π-0.856031\pi
0.828201 + 0.560431i 0.189365π0.189365\pi
198198 23.8601 + 13.7756i 1.69567 + 0.978993i
199199 2.69594 + 4.66951i 0.191110 + 0.331013i 0.945619 0.325278i 0.105458π-0.105458\pi
−0.754508 + 0.656291i 0.772124π0.772124\pi
200200 −11.0917 5.87444i −0.784302 0.415386i
201201 21.5952 12.4680i 1.52321 0.879425i
202202 −12.6514 21.9129i −0.890151 1.54179i
203203 8.76487 0.615173
204204 0.539189 + 0.933903i 0.0377508 + 0.0653863i
205205 −2.03118 1.95830i −0.141864 0.136774i
206206 −13.5838 7.84263i −0.946431 0.546422i
207207 19.9493i 1.38657i
208208 0 0
209209 −1.36910 −0.0947028
210210 −13.4256 12.9439i −0.926457 0.893214i
211211 11.3763 19.7043i 0.783176 1.35650i −0.146906 0.989150i 0.546932π-0.546932\pi
0.930083 0.367350i 0.119735π-0.119735\pi
212212 2.71606 1.56812i 0.186540 0.107699i
213213 45.9071 3.14550
214214 −12.9986 + 7.50473i −0.888564 + 0.513013i
215215 −13.8218 + 3.97549i −0.942636 + 0.271126i
216216 32.2245i 2.19260i
217217 1.30170 0.751536i 0.0883650 0.0510176i
218218 −22.4790 12.9783i −1.52247 0.878999i
219219 5.35500 + 3.09171i 0.361857 + 0.208918i
220220 −0.505339 + 2.03385i −0.0340699 + 0.137122i
221221 0 0
222222 29.5174i 1.98108i
223223 4.38050 7.58724i 0.293340 0.508079i −0.681258 0.732044i 0.738567π-0.738567\pi
0.974597 + 0.223965i 0.0719000π0.0719000\pi
224224 1.76293 3.05348i 0.117791 0.204019i
225225 1.28741 + 35.2237i 0.0858276 + 2.34825i
226226 18.0989i 1.20392i
227227 8.61336 + 14.9188i 0.571689 + 0.990194i 0.996393 + 0.0848618i 0.0270449π0.0270449\pi
−0.424704 + 0.905332i 0.639622π0.639622\pi
228228 0.315449 + 0.546373i 0.0208911 + 0.0361845i
229229 3.07838i 0.203425i 0.994814 + 0.101712i 0.0324322π0.0324322\pi
−0.994814 + 0.101712i 0.967568π0.967568\pi
230230 −9.36031 + 2.69227i −0.617201 + 0.177523i
231231 6.87936 11.9154i 0.452629 0.783976i
232232 6.43609 11.1476i 0.422550 0.731878i
233233 18.9360i 1.24054i −0.784389 0.620269i 0.787023π-0.787023\pi
0.784389 0.620269i 0.212977π-0.212977\pi
234234 0 0
235235 −12.3896 3.07838i −0.808210 0.200811i
236236 1.50959 + 0.871563i 0.0982660 + 0.0567339i
237237 1.36426 + 0.787653i 0.0886179 + 0.0511636i
238238 2.09985 1.21235i 0.136113 0.0785848i
239239 6.63809i 0.429382i −0.976682 0.214691i 0.931126π-0.931126\pi
0.976682 0.214691i 0.0688745π-0.0688745\pi
240240 −31.3502 + 9.01712i −2.02364 + 0.582053i
241241 8.20681 4.73820i 0.528647 0.305215i −0.211818 0.977309i 0.567938π-0.567938\pi
0.740465 + 0.672094i 0.234605π0.234605\pi
242242 7.00719 0.450439
243243 20.3104 11.7262i 1.30291 0.752236i
244244 −1.48554 + 2.57302i −0.0951017 + 0.164721i
245245 6.32962 6.56519i 0.404385 0.419435i
246246 −6.15676 −0.392540
247247 0 0
248248 2.20743i 0.140172i
249249 23.6951 + 13.6803i 1.50161 + 0.866957i
250250 −16.3534 + 5.35769i −1.03428 + 0.338850i
251251 14.7298 + 25.5128i 0.929736 + 1.61035i 0.783761 + 0.621062i 0.213299π0.213299\pi
0.145975 + 0.989288i 0.453368π0.453368\pi
252252 −4.44748 −0.280165
253253 −3.59284 6.22299i −0.225880 0.391236i
254254 −24.0032 + 13.8582i −1.50609 + 0.869543i
255255 −6.34017 1.57531i −0.397037 0.0986495i
256256 −4.28765 7.42643i −0.267978 0.464152i
257257 17.7238 + 10.2329i 1.10558 + 0.638309i 0.937682 0.347495i 0.112968π-0.112968\pi
0.167901 + 0.985804i 0.446301π0.446301\pi
258258 −15.6917 + 27.1789i −0.976925 + 1.69208i
259259 10.3402 0.642507
260260 0 0
261261 −36.1483 −2.23753
262262 −10.9711 + 19.0025i −0.677795 + 1.17398i
263263 −7.91844 4.57171i −0.488272 0.281904i 0.235585 0.971854i 0.424299π-0.424299\pi
−0.723857 + 0.689950i 0.757633π0.757633\pi
264264 −10.1031 17.4991i −0.621803 1.07699i
265265 −4.58145 + 18.4391i −0.281436 + 1.13270i
266266 1.22850 0.709275i 0.0753242 0.0434885i
267267 20.3474 + 35.2427i 1.24524 + 2.15682i
268268 2.90337 0.177352
269269 5.69594 + 9.86567i 0.347288 + 0.601520i 0.985767 0.168119i 0.0537693π-0.0537693\pi
−0.638479 + 0.769639i 0.720436π0.720436\pi
270270 31.8067 + 30.6654i 1.93570 + 1.86624i
271271 −18.3035 10.5675i −1.11186 0.641930i −0.172546 0.985001i 0.555200π-0.555200\pi
−0.939309 + 0.343071i 0.888533π0.888533\pi
272272 4.24128i 0.257165i
273273 0 0
274274 −21.2183 −1.28185
275275 −6.74533 10.7558i −0.406759 0.648600i
276276 −1.65562 + 2.86762i −0.0996567 + 0.172611i
277277 −11.3262 + 6.53919i −0.680526 + 0.392902i −0.800053 0.599929i 0.795195π-0.795195\pi
0.119527 + 0.992831i 0.461862π0.461862\pi
278278 10.2413 0.614231
279279 −5.36851 + 3.09951i −0.321404 + 0.185563i
280280 2.65206 + 9.22053i 0.158491 + 0.551032i
281281 0.680346i 0.0405860i 0.999794 + 0.0202930i 0.00645991π0.00645991\pi
−0.999794 + 0.0202930i 0.993540π0.993540\pi
282282 −24.1254 + 13.9288i −1.43665 + 0.829449i
283283 −16.7105 9.64782i −0.993337 0.573504i −0.0870671 0.996202i 0.527749π-0.527749\pi
−0.906270 + 0.422699i 0.861083π0.861083\pi
284284 4.62899 + 2.67255i 0.274680 + 0.158586i
285285 −3.70928 0.921622i −0.219719 0.0545922i
286286 0 0
287287 2.15676i 0.127309i
288288 −7.27073 + 12.5933i −0.428432 + 0.742066i
289289 −8.07531 + 13.9868i −0.475018 + 0.822755i
290290 −4.87841 16.9610i −0.286470 0.995982i
291291 18.7526i 1.09930i
292292 0.359977 + 0.623498i 0.0210660 + 0.0364875i
293293 4.73400 + 8.19953i 0.276563 + 0.479022i 0.970528 0.240987i 0.0774712π-0.0774712\pi
−0.693965 + 0.720009i 0.744138π0.744138\pi
294294 19.8999i 1.16058i
295295 −10.1486 + 2.91901i −0.590875 + 0.169951i
296296 7.59284 13.1512i 0.441325 0.764397i
297297 −16.2979 + 28.2288i −0.945701 + 1.63800i
298298 13.9733i 0.809454i
299299 0 0
300300 −2.73820 + 5.17009i −0.158090 + 0.298495i
301301 9.52096 + 5.49693i 0.548779 + 0.316838i
302302 4.36869 + 2.52226i 0.251390 + 0.145140i
303303 45.1314 26.0566i 2.59273 1.49691i
304304 2.48133i 0.142314i
305305 −4.97530 17.2978i −0.284885 0.990470i
306306 −8.66025 + 5.00000i −0.495074 + 0.285831i
307307 0.264063 0.0150709 0.00753543 0.999972i 0.497601π-0.497601\pi
0.00753543 + 0.999972i 0.497601π0.497601\pi
308308 1.38735 0.800984i 0.0790513 0.0456403i
309309 16.1526 27.9770i 0.918886 1.59156i
310310 −2.17881 2.10063i −0.123748 0.119308i
311311 −13.0472 −0.739838 −0.369919 0.929064i 0.620615π-0.620615\pi
−0.369919 + 0.929064i 0.620615π0.620615\pi
312312 0 0
313313 33.7009i 1.90489i −0.304718 0.952443i 0.598562π-0.598562\pi
0.304718 0.952443i 0.401438π-0.401438\pi
314314 17.1116 + 9.87936i 0.965661 + 0.557525i
315315 18.7007 19.3967i 1.05366 1.09288i
316316 0.0917087 + 0.158844i 0.00515902 + 0.00893568i
317317 −13.9506 −0.783541 −0.391771 0.920063i 0.628137π-0.628137\pi
−0.391771 + 0.920063i 0.628137π0.628137\pi
318318 20.7298 + 35.9051i 1.16247 + 2.01346i
319319 11.2761 6.51026i 0.631340 0.364505i
320320 13.0833 + 3.25073i 0.731379 + 0.181721i
321321 −15.4566 26.7716i −0.862704 1.49425i
322322 6.44774 + 3.72261i 0.359319 + 0.207453i
323323 0.248464 0.430353i 0.0138249 0.0239455i
324324 7.21461 0.400812
325325 0 0
326326 18.5464 1.02719
327327 26.7298 46.2974i 1.47816 2.56025i
328328 2.74308 + 1.58372i 0.151461 + 0.0874461i
329329 4.87936 + 8.45130i 0.269008 + 0.465935i
330330 −26.8865 6.68035i −1.48006 0.367741i
331331 −15.9822 + 9.22733i −0.878462 + 0.507180i −0.870151 0.492785i 0.835979π-0.835979\pi
−0.00831086 + 0.999965i 0.502645π0.502645\pi
332332 1.59284 + 2.75888i 0.0874186 + 0.151413i
333333 −42.6453 −2.33695
334334 6.71840 + 11.6366i 0.367615 + 0.636727i
335335 −12.2080 + 12.6624i −0.666996 + 0.691820i
336336 21.5952 + 12.4680i 1.17812 + 0.680185i
337337 15.8576i 0.863820i −0.901917 0.431910i 0.857840π-0.857840\pi
0.901917 0.431910i 0.142160π-0.142160\pi
338338 0 0
339339 37.2762 2.02456
340340 −0.547595 0.527947i −0.0296975 0.0286319i
341341 1.11643 1.93372i 0.0604582 0.104717i
342342 −5.06662 + 2.92522i −0.273972 + 0.158178i
343343 −18.9360 −1.02245
344344 13.9826 8.07285i 0.753890 0.435259i
345345 −5.54495 19.2783i −0.298530 1.03791i
346346 1.32950i 0.0714741i
347347 −8.42199 + 4.86244i −0.452116 + 0.261029i −0.708723 0.705486i 0.750729π-0.750729\pi
0.256607 + 0.966516i 0.417395π0.417395\pi
348348 −5.19615 3.00000i −0.278543 0.160817i
349349 26.7683 + 15.4547i 1.43287 + 0.827269i 0.997339 0.0729030i 0.0232264π-0.0232264\pi
0.435534 + 0.900172i 0.356560π0.356560\pi
350350 11.6248 + 6.15676i 0.621369 + 0.329092i
351351 0 0
352352 5.23779i 0.279175i
353353 2.97528 5.15333i 0.158358 0.274284i −0.775919 0.630833i 0.782713π-0.782713\pi
0.934277 + 0.356549i 0.116047π0.116047\pi
354354 −11.5217 + 19.9561i −0.612369 + 1.06065i
355355 −31.1196 + 8.95079i −1.65166 + 0.475059i
356356 4.73820i 0.251124i
357357 2.49693 + 4.32481i 0.132151 + 0.228893i
358358 −15.3268 26.5469i −0.810049 1.40305i
359359 10.9783i 0.579410i 0.957116 + 0.289705i 0.0935573π0.0935573\pi
−0.957116 + 0.289705i 0.906443π0.906443\pi
360360 −10.9377 38.0276i −0.576469 2.00423i
361361 −9.35464 + 16.2027i −0.492349 + 0.852774i
362362 11.0742 19.1810i 0.582046 1.00813i
363363 14.4319i 0.757477i
364364 0 0
365365 −4.23287 1.05172i −0.221558 0.0550493i
366366 −34.0142 19.6381i −1.77795 1.02650i
367367 8.98417 + 5.18701i 0.468970 + 0.270760i 0.715808 0.698297i 0.246058π-0.246058\pi
−0.246839 + 0.969057i 0.579392π0.579392\pi
368368 11.2784 6.51159i 0.587927 0.339440i
369369 8.89496i 0.463053i
370370 −5.75520 20.0093i −0.299199 1.04024i
371371 12.5778 7.26180i 0.653007 0.377014i
372372 −1.02893 −0.0533475
373373 20.7740 11.9939i 1.07564 0.621018i 0.145920 0.989296i 0.453386π-0.453386\pi
0.929716 + 0.368278i 0.120053π0.120053\pi
374374 1.80098 3.11940i 0.0931267 0.161300i
375375 −11.0346 33.6811i −0.569824 1.73929i
376376 14.3318 0.739104
377377 0 0
378378 33.7731i 1.73710i
379379 25.7708 + 14.8788i 1.32375 + 0.764270i 0.984325 0.176362i 0.0564328π-0.0564328\pi
0.339429 + 0.940632i 0.389766π0.389766\pi
380380 −0.320367 0.308872i −0.0164345 0.0158448i
381381 −28.5422 49.4365i −1.46226 2.53271i
382382 2.27247 0.116270
383383 6.20814 + 10.7528i 0.317221 + 0.549443i 0.979907 0.199454i 0.0639169π-0.0639169\pi
−0.662686 + 0.748897i 0.730584π0.730584\pi
384384 36.8024 21.2479i 1.87806 1.08430i
385385 −2.34017 + 9.41855i −0.119266 + 0.480014i
386386 13.6465 + 23.6364i 0.694588 + 1.20306i
387387 −39.2666 22.6706i −1.99604 1.15241i
388388 −1.09171 + 1.89090i −0.0554231 + 0.0959956i
389389 −16.8371 −0.853675 −0.426837 0.904328i 0.640372π-0.640372\pi
−0.426837 + 0.904328i 0.640372π0.640372\pi
390390 0 0
391391 2.60811 0.131898
392392 −5.11889 + 8.86618i −0.258543 + 0.447810i
393393 −39.1371 22.5958i −1.97421 1.13981i
394394 −1.53919 2.66595i −0.0775432 0.134309i
395395 −1.07838 0.267938i −0.0542591 0.0134814i
396396 −5.72173 + 3.30344i −0.287528 + 0.166004i
397397 −1.94635 3.37117i −0.0976843 0.169194i 0.813041 0.582206i 0.197810π-0.197810\pi
−0.910726 + 0.413012i 0.864477π0.864477\pi
398398 −8.29914 −0.415998
399399 1.46081 + 2.53020i 0.0731320 + 0.126668i
400400 19.4936 12.2251i 0.974680 0.611254i
401401 −7.88520 4.55252i −0.393768 0.227342i 0.290024 0.957020i 0.406337π-0.406337\pi
−0.683791 + 0.729678i 0.739670π0.739670\pi
402402 38.3812i 1.91428i
403403 0 0
404404 6.06770 0.301879
405405 −30.3359 + 31.4649i −1.50740 + 1.56350i
406406 −6.74539 + 11.6834i −0.334768 + 0.579836i
407407 13.3027 7.68035i 0.659393 0.380701i
408408 7.33403 0.363089
409409 16.8170 9.70928i 0.831545 0.480093i −0.0228363 0.999739i 0.507270π-0.507270\pi
0.854381 + 0.519646i 0.173936π0.173936\pi
410410 4.17355 1.20042i 0.206117 0.0592846i
411411 43.7009i 2.15560i
412412 3.25745 1.88069i 0.160483 0.0926549i
413413 6.99076 + 4.03612i 0.343993 + 0.198604i
414414 −26.5920 15.3529i −1.30693 0.754554i
415415 −18.7298 4.65368i −0.919409 0.228440i
416416 0 0
417417 21.0928i 1.03292i
418418 1.05365 1.82498i 0.0515359 0.0892628i
419419 −8.38962 + 14.5313i −0.409860 + 0.709898i −0.994874 0.101125i 0.967756π-0.967756\pi
0.585014 + 0.811023i 0.301089π0.301089\pi
420420 4.29789 1.23618i 0.209716 0.0603196i
421421 19.0205i 0.927003i −0.886096 0.463502i 0.846593π-0.846593\pi
0.886096 0.463502i 0.153407π-0.153407\pi
422422 17.5103 + 30.3287i 0.852386 + 1.47638i
423423 −20.1236 34.8551i −0.978444 1.69471i
424424 21.3295i 1.03585i
425425 4.60504 0.168312i 0.223377 0.00816435i
426426 −35.3298 + 61.1931i −1.71174 + 2.96481i
427427 −6.87936 + 11.9154i −0.332916 + 0.576627i
428428 3.59932i 0.173979i
429429 0 0
430430 5.33791 21.4836i 0.257417 1.03603i
431431 −6.95416 4.01499i −0.334970 0.193395i 0.323075 0.946373i 0.395283π-0.395283\pi
−0.658046 + 0.752978i 0.728617π0.728617\pi
432432 −51.1613 29.5380i −2.46150 1.42115i
433433 −11.2992 + 6.52359i −0.543004 + 0.313504i −0.746296 0.665615i 0.768170π-0.768170\pi
0.203291 + 0.979118i 0.434836π0.434836\pi
434434 2.31351i 0.111052i
435435 34.9325 10.0475i 1.67488 0.481740i
436436 5.39054 3.11223i 0.258160 0.149049i
437437 1.52586 0.0729917
438438 −8.24235 + 4.75872i −0.393835 + 0.227381i
439439 3.85043 6.66914i 0.183771 0.318301i −0.759391 0.650635i 0.774503π-0.774503\pi
0.943162 + 0.332334i 0.107836π0.107836\pi
440440 10.2606 + 9.89245i 0.489156 + 0.471604i
441441 28.7503 1.36906
442442 0 0
443443 6.39084i 0.303638i 0.988408 + 0.151819i 0.0485131π0.0485131\pi
−0.988408 + 0.151819i 0.951487π0.951487\pi
444444 −6.13005 3.53919i −0.290920 0.167962i
445445 −20.6646 19.9231i −0.979596 0.944446i
446446 6.74241 + 11.6782i 0.319262 + 0.552979i
447447 −28.7792 −1.36121
448448 −5.15255 8.92448i −0.243435 0.421642i
449449 27.3806 15.8082i 1.29217 0.746034i 0.313130 0.949710i 0.398622π-0.398622\pi
0.979038 + 0.203676i 0.0652891π0.0652891\pi
450450 −47.9432 25.3919i −2.26006 1.19699i
451451 1.60197 + 2.77469i 0.0754337 + 0.130655i
452452 3.75870 + 2.17009i 0.176794 + 0.102072i
453453 −5.19481 + 8.99768i −0.244073 + 0.422748i
454454 −26.5152 −1.24442
455455 0 0
456456 4.29072 0.200932
457457 −17.8215 + 30.8677i −0.833655 + 1.44393i 0.0614663 + 0.998109i 0.480422π0.480422\pi
−0.895121 + 0.445823i 0.852911π0.852911\pi
458458 −4.10341 2.36910i −0.191740 0.110701i
459459 −5.91548 10.2459i −0.276111 0.478238i
460460 0.563198 2.26672i 0.0262592 0.105686i
461461 −12.9726 + 7.48974i −0.604195 + 0.348832i −0.770690 0.637210i 0.780088π-0.780088\pi
0.166495 + 0.986042i 0.446755π0.446755\pi
462462 10.5886 + 18.3401i 0.492628 + 0.853257i
463463 9.09663 0.422756 0.211378 0.977404i 0.432205π-0.432205\pi
0.211378 + 0.977404i 0.432205π0.432205\pi
464464 11.7990 + 20.4365i 0.547757 + 0.948743i
465465 4.32642 4.48744i 0.200633 0.208100i
466466 25.2412 + 14.5730i 1.16928 + 0.675083i
467467 1.87709i 0.0868616i −0.999056 0.0434308i 0.986171π-0.986171\pi
0.999056 0.0434308i 0.0138288π-0.0138288\pi
468468 0 0
469469 13.4452 0.620842
470470 13.6384 14.1460i 0.629092 0.652505i
471471 −20.3474 + 35.2427i −0.937557 + 1.62390i
472472 10.2667 5.92748i 0.472563 0.272835i
473473 16.3318 0.750935
474474 −2.09985 + 1.21235i −0.0964491 + 0.0556849i
475475 2.69415 0.0984700i 0.123616 0.00451811i
476476 0.581449i 0.0266507i
477477 −51.8738 + 29.9493i −2.37514 + 1.37129i
478478 8.84841 + 5.10863i 0.404717 + 0.233663i
479479 13.6339 + 7.87156i 0.622951 + 0.359661i 0.778017 0.628243i 0.216226π-0.216226\pi
−0.155066 + 0.987904i 0.549559π0.549559\pi
480480 3.52586 14.1906i 0.160933 0.647710i
481481 0 0
482482 14.5860i 0.664373i
483483 −7.66701 + 13.2797i −0.348861 + 0.604245i
484484 −0.840173 + 1.45522i −0.0381897 + 0.0661465i
485485 −3.65631 12.7120i −0.166024 0.577224i
486486 36.0977i 1.63742i
487487 2.47220 + 4.28198i 0.112026 + 0.194035i 0.916587 0.399835i 0.130933π-0.130933\pi
−0.804561 + 0.593870i 0.797599π0.797599\pi
488488 10.1031 + 17.4991i 0.457346 + 0.792146i
489489 38.1978i 1.72736i
490490 3.88001 + 13.4898i 0.175281 + 0.609406i
491491 19.7431 34.1961i 0.890995 1.54325i 0.0523101 0.998631i 0.483342π-0.483342\pi
0.838685 0.544617i 0.183325π-0.183325\pi
492492 0.738205 1.27861i 0.0332808 0.0576441i
493493 4.72592i 0.212845i
494494 0 0
495495 9.65142 38.8443i 0.433799 1.74592i
496496 3.50463 + 2.02340i 0.157362 + 0.0908532i
497497 21.4364 + 12.3763i 0.961552 + 0.555152i
498498 −36.4712 + 21.0566i −1.63431 + 0.943570i
499499 1.67089i 0.0747993i −0.999300 0.0373997i 0.988093π-0.988093\pi
0.999300 0.0373997i 0.0119075π-0.0119075\pi
500500 0.848135 4.03859i 0.0379297 0.180611i
501501 −23.9666 + 13.8371i −1.07075 + 0.618196i
502502 −45.3439 −2.02380
503503 −7.86833 + 4.54278i −0.350832 + 0.202553i −0.665051 0.746798i 0.731590π-0.731590\pi
0.314220 + 0.949350i 0.398257π0.398257\pi
504504 −15.1236 + 26.1949i −0.673660 + 1.16681i
505505 −25.5133 + 26.4629i −1.13533 + 1.17758i
506506 11.0601 0.491683
507507 0 0
508508 6.64650i 0.294891i
509509 −16.9257 9.77205i −0.750218 0.433139i 0.0755545 0.997142i 0.475927π-0.475927\pi
−0.825773 + 0.564003i 0.809261π0.809261\pi
510510 6.97921 7.23896i 0.309045 0.320546i
511511 1.66701 + 2.88735i 0.0737444 + 0.127729i
512512 −13.6114 −0.601546
513513 −3.46081 5.99430i −0.152799 0.264655i
514514 −27.2803 + 15.7503i −1.20328 + 0.694717i
515515 −5.49466 + 22.1145i −0.242124 + 0.974481i
516516 −3.76293 6.51758i −0.165654 0.286921i
517517 12.5547 + 7.24846i 0.552155 + 0.318787i
518518 −7.95774 + 13.7832i −0.349643 + 0.605599i
519519 2.73820 0.120194
520520 0 0
521521 6.50534 0.285004 0.142502 0.989795i 0.454485π-0.454485\pi
0.142502 + 0.989795i 0.454485π0.454485\pi
522522 27.8196 48.1849i 1.21763 2.10900i
523523 31.6490 + 18.2726i 1.38392 + 0.799004i 0.992621 0.121261i 0.0386939π-0.0386939\pi
0.391295 + 0.920265i 0.372027π0.372027\pi
524524 −2.63090 4.55685i −0.114931 0.199067i
525525 −12.6803 + 23.9421i −0.553416 + 1.04492i
526526 12.1880 7.03673i 0.531421 0.306816i
527527 0.405220 + 0.701861i 0.0176516 + 0.0305736i
528528 37.0433 1.61210
529529 −7.49579 12.9831i −0.325904 0.564482i
530530 −21.0530 20.2976i −0.914484 0.881670i
531531 −28.8315 16.6459i −1.25118 0.722370i
532532 0.340173i 0.0147484i
533533 0 0
534534 −62.6369 −2.71056
535535 15.6976 + 15.1343i 0.678666 + 0.654314i
536536 9.87289 17.1003i 0.426444 0.738622i
537537 54.6755 31.5669i 2.35942 1.36221i
538538 −17.5343 −0.755956
539539 −8.96836 + 5.17789i −0.386295 + 0.223027i
540540 −10.1821 + 2.92865i −0.438169 + 0.126029i
541541 20.3402i 0.874492i −0.899342 0.437246i 0.855954π-0.855954\pi
0.899342 0.437246i 0.144046π-0.144046\pi
542542 28.1725 16.2654i 1.21011 0.698658i
543543 39.5049 + 22.8082i 1.69532 + 0.978792i
544544 1.64640 + 0.950552i 0.0705890 + 0.0407546i
545545 −9.09275 + 36.5958i −0.389491 + 1.56759i
546546 0 0
547547 11.5948i 0.495757i −0.968791 0.247879i 0.920267π-0.920267\pi
0.968791 0.247879i 0.0797334π-0.0797334\pi
548548 2.54411 4.40653i 0.108679 0.188237i
549549 28.3721 49.1419i 1.21089 2.09732i
550550 19.5284 0.713756i 0.832694 0.0304347i
551551 2.76487i 0.117787i
552552 11.2599 + 19.5026i 0.479251 + 0.830088i
553553 0.424694 + 0.735591i 0.0180598 + 0.0312805i
554554 20.1301i 0.855246i
555555 41.2109 11.8533i 1.74931 0.503145i
556556 −1.22795 + 2.12686i −0.0520765 + 0.0901991i
557557 −5.36490 + 9.29227i −0.227318 + 0.393726i −0.957012 0.290047i 0.906329π-0.906329\pi
0.729694 + 0.683773i 0.239662π0.239662\pi
558558 9.54146i 0.403922i
559559 0 0
560560 −17.0700 4.24128i −0.721338 0.179227i
561561 6.42465 + 3.70928i 0.271249 + 0.156606i
562562 −0.906885 0.523590i −0.0382546 0.0220863i
563563 8.87543 5.12423i 0.374055 0.215961i −0.301174 0.953569i 0.597378π-0.597378\pi
0.675228 + 0.737609i 0.264045π0.264045\pi
564564 6.68035i 0.281293i
565565 −25.2688 + 7.26797i −1.06307 + 0.305766i
566566 25.7206 14.8498i 1.08112 0.624185i
567567 33.4101 1.40309
568568 31.4817 18.1759i 1.32094 0.762646i
569569 4.42276 7.66044i 0.185412 0.321142i −0.758304 0.651902i 0.773972π-0.773972\pi
0.943715 + 0.330759i 0.107305π0.107305\pi
570570 4.08314 4.23510i 0.171024 0.177389i
571571 −9.29299 −0.388900 −0.194450 0.980912i 0.562292π-0.562292\pi
−0.194450 + 0.980912i 0.562292π0.562292\pi
572572 0 0
573573 4.68035i 0.195524i
574574 −2.87490 1.65983i −0.119996 0.0692798i
575575 7.51764 + 11.9873i 0.313507 + 0.499905i
576576 21.2503 + 36.8066i 0.885430 + 1.53361i
577577 19.5259 0.812872 0.406436 0.913679i 0.366771π-0.366771\pi
0.406436 + 0.913679i 0.366771π0.366771\pi
578578 −12.4294 21.5284i −0.516996 0.895463i
579579 −48.6812 + 28.1061i −2.02312 + 1.16805i
580580 4.10731 + 1.02052i 0.170547 + 0.0423747i
581581 7.37629 + 12.7761i 0.306020 + 0.530042i
582582 −24.9968 14.4319i −1.03615 0.598221i
583583 10.7877 18.6848i 0.446779 0.773844i
584584 4.89639 0.202614
585585 0 0
586586 −14.5730 −0.602007
587587 11.2514 19.4881i 0.464397 0.804359i −0.534777 0.844993i 0.679604π-0.679604\pi
0.999174 + 0.0406341i 0.0129378π0.0129378\pi
588588 4.13272 + 2.38603i 0.170431 + 0.0983981i
589589 0.237071 + 0.410619i 0.00976834 + 0.0169193i
590590 3.91935 15.7743i 0.161357 0.649419i
591591 5.49075 3.17009i 0.225859 0.130400i
592592 13.9197 + 24.1096i 0.572096 + 0.990898i
593593 −4.43907 −0.182291 −0.0911454 0.995838i 0.529053π-0.529053\pi
−0.0911454 + 0.995838i 0.529053π0.529053\pi
594594 −25.0856 43.4495i −1.02927 1.78275i
595595 −2.53586 2.44487i −0.103960 0.100230i
596596 −2.90192 1.67543i −0.118867 0.0686281i
597597 17.0928i 0.699560i
598598 0 0
599599 −33.3607 −1.36308 −0.681540 0.731780i 0.738690π-0.738690\pi
−0.681540 + 0.731780i 0.738690π0.738690\pi
600600 21.1397 + 33.7084i 0.863023 + 1.37614i
601601 −6.65983 + 11.5352i −0.271660 + 0.470529i −0.969287 0.245932i 0.920906π-0.920906\pi
0.697627 + 0.716461i 0.254239π0.254239\pi
602602 −14.6546 + 8.46081i −0.597275 + 0.344837i
603603 −55.4512 −2.25815
604604 −1.04763 + 0.604847i −0.0426273 + 0.0246109i
605605 −2.81388 9.78311i −0.114400 0.397740i
606606 80.2122i 3.25840i
607607 12.2269 7.05919i 0.496273 0.286523i −0.230900 0.972977i 0.574167π-0.574167\pi
0.727173 + 0.686454i 0.240834π0.240834\pi
608608 0.963217 + 0.556114i 0.0390636 + 0.0225534i
609609 −24.0628 13.8927i −0.975076 0.562960i
610610 26.8865 + 6.68035i 1.08860 + 0.270479i
611611 0 0
612612 2.39803i 0.0969347i
613613 13.4052 23.2185i 0.541432 0.937787i −0.457390 0.889266i 0.651216π-0.651216\pi
0.998822 0.0485213i 0.0154509π-0.0154509\pi
614614 −0.203221 + 0.351989i −0.00820134 + 0.0142051i
615615 2.47237 + 8.59578i 0.0996955 + 0.346615i
616616 10.8950i 0.438970i
617617 7.44748 + 12.8994i 0.299824 + 0.519311i 0.976096 0.217342i 0.0697386π-0.0697386\pi
−0.676271 + 0.736653i 0.736405π0.736405\pi
618618 24.8618 + 43.0619i 1.00009 + 1.73221i
619619 45.3184i 1.82150i 0.412956 + 0.910751i 0.364496π0.364496\pi
−0.412956 + 0.910751i 0.635504π0.635504\pi
620620 0.697493 0.200617i 0.0280120 0.00805697i
621621 18.1639 31.4609i 0.728894 1.26248i
622622 10.0410 17.3916i 0.402609 0.697339i
623623 21.9421i 0.879093i
624624 0 0
625625 14.0472 + 20.6803i 0.561887 + 0.827214i
626626 44.9225 + 25.9360i 1.79546 + 1.03661i
627627 3.75870 + 2.17009i 0.150108 + 0.0866649i
628628 −4.10341 + 2.36910i −0.163744 + 0.0945375i
629629 5.57531i 0.222302i
630630 11.4634 + 39.8551i 0.456711 + 1.58787i
631631 −32.8116 + 18.9438i −1.30621 + 0.754141i −0.981461 0.191660i 0.938613π-0.938613\pi
−0.324749 + 0.945800i 0.605280π0.605280\pi
632632 1.24742 0.0496197
633633 −62.4644 + 36.0638i −2.48274 + 1.43341i
634634 10.7363 18.5958i 0.426392 0.738532i
635635 28.9872 + 27.9471i 1.15032 + 1.10905i
636636 −9.94214 −0.394232
637637 0 0
638638 20.0410i 0.793432i
639639 −88.4085 51.0427i −3.49739 2.01922i
640640 −20.8048 + 21.5791i −0.822383 + 0.852990i
641641 −4.23513 7.33547i −0.167278 0.289733i 0.770184 0.637822i 0.220164π-0.220164\pi
−0.937462 + 0.348088i 0.886831π0.886831\pi
642642 47.5813 1.87788
643643 −17.0875 29.5964i −0.673865 1.16717i −0.976799 0.214157i 0.931299π-0.931299\pi
0.302934 0.953012i 0.402034π-0.402034\pi
644644 −1.54619 + 0.892693i −0.0609284 + 0.0351770i
645645 44.2472 + 10.9939i 1.74223 + 0.432883i
646646 0.382433 + 0.662394i 0.0150466 + 0.0260615i
647647 −11.9717 6.91189i −0.470658 0.271734i 0.245857 0.969306i 0.420931π-0.420931\pi
−0.716515 + 0.697572i 0.754264π0.754264\pi
648648 24.5332 42.4928i 0.963757 1.66928i
649649 11.9916 0.470711
650650 0 0
651651 −4.76487 −0.186750
652652 −2.22374 + 3.85163i −0.0870884 + 0.150842i
653653 −37.1336 21.4391i −1.45315 0.838976i −0.454490 0.890752i 0.650178π-0.650178\pi
−0.998659 + 0.0517764i 0.983512π0.983512\pi
654654 41.1422 + 71.2604i 1.60879 + 2.78650i
655655 30.9360 + 7.68649i 1.20877 + 0.300336i
656656 −5.02879 + 2.90337i −0.196341 + 0.113358i
657657 −6.87516 11.9081i −0.268225 0.464580i
658658 −15.0205 −0.585561
659659 −11.6248 20.1347i −0.452836 0.784335i 0.545725 0.837964i 0.316254π-0.316254\pi
−0.998561 + 0.0536293i 0.982921π0.982921\pi
660660 4.61109 4.78270i 0.179486 0.186166i
661661 23.4399 + 13.5330i 0.911707 + 0.526374i 0.880980 0.473153i 0.156884π-0.156884\pi
0.0307272 + 0.999528i 0.490218π0.490218\pi
662662 28.4052i 1.10400i
663663 0 0
664664 21.6658 0.840796
665665 −1.48359 1.43035i −0.0575310 0.0554667i
666666 32.8196 56.8452i 1.27173 2.20270i
667667 −12.5672 + 7.25565i −0.486602 + 0.280940i
668668 −3.22219 −0.124670
669669 −24.0522 + 13.8865i −0.929912 + 0.536885i
670670 −7.48343 26.0179i −0.289110 1.00516i
671671 20.4391i 0.789042i
672672 −9.67980 + 5.58864i −0.373407 + 0.215586i
673673 −14.0046 8.08557i −0.539838 0.311676i 0.205175 0.978725i 0.434224π-0.434224\pi
−0.745013 + 0.667050i 0.767557π0.767557\pi
674674 21.1378 + 12.2039i 0.814199 + 0.470078i
675675 30.0410 56.7214i 1.15628 2.18321i
676676 0 0
677677 43.1194i 1.65721i 0.559831 + 0.828607i 0.310866π0.310866\pi
−0.559831 + 0.828607i 0.689134π0.689134\pi
678678 −28.6875 + 49.6883i −1.10174 + 1.90827i
679679 −5.05559 + 8.75654i −0.194016 + 0.336045i
680680 −4.97161 + 1.42996i −0.190652 + 0.0548366i
681681 54.6102i 2.09267i
682682 1.71840 + 2.97636i 0.0658010 + 0.113971i
683683 −8.85464 15.3367i −0.338813 0.586842i 0.645396 0.763848i 0.276692π-0.276692\pi
−0.984210 + 0.177006i 0.943359π0.943359\pi
684684 1.40295i 0.0536432i
685685 8.52064 + 29.6240i 0.325557 + 1.13188i
686686 14.5730 25.2412i 0.556401 0.963715i
687687 4.87936 8.45130i 0.186159 0.322437i
688688 29.5993i 1.12846i
689689 0 0
690690 29.9649 + 7.44521i 1.14075 + 0.283434i
691691 21.5462 + 12.4397i 0.819655 + 0.473228i 0.850297 0.526303i 0.176422π-0.176422\pi
−0.0306428 + 0.999530i 0.509755π0.509755\pi
692692 0.276104 + 0.159409i 0.0104959 + 0.00605980i
693693 −26.4968 + 15.2979i −1.00653 + 0.581120i
694694 14.9684i 0.568193i
695695 −4.11259 14.2984i −0.155999 0.542369i
696696 −35.3390 + 20.4030i −1.33952 + 0.773372i
697697 −1.16290 −0.0440479
698698 −41.2014 + 23.7877i −1.55950 + 0.900376i
699699 −30.0144 + 51.9864i −1.13525 + 1.96631i
700700 −2.67243 + 1.67597i −0.101009 + 0.0633458i
701701 −33.0661 −1.24889 −0.624445 0.781069i 0.714675π-0.714675\pi
−0.624445 + 0.781069i 0.714675π0.714675\pi
702702 0 0
703703 3.26180i 0.123021i
704704 −13.2576 7.65430i −0.499666 0.288482i
705705 29.1348 + 28.0894i 1.09728 + 1.05791i
706706 4.57951 + 7.93195i 0.172352 + 0.298523i
707707 28.0989 1.05677
708708 −2.76293 4.78553i −0.103837 0.179851i
709709 1.89090 1.09171i 0.0710141 0.0410000i −0.464073 0.885797i 0.653612π-0.653612\pi
0.535087 + 0.844797i 0.320279π0.320279\pi
710710 12.0183 48.3701i 0.451037 1.81530i
711711 −1.75154 3.03375i −0.0656877 0.113774i
712712 27.9072 + 16.1122i 1.04587 + 0.603831i
713713 −1.24426 + 2.15512i −0.0465979 + 0.0807099i
714714 −7.68649 −0.287660
715715 0 0
716716 7.35085 0.274714
717717 −10.5217 + 18.2240i −0.392938 + 0.680589i
718718 −14.6338 8.44881i −0.546127 0.315307i
719719 −2.60424 4.51067i −0.0971216 0.168220i 0.813370 0.581746i 0.197630π-0.197630\pi
−0.910492 + 0.413526i 0.864297π0.864297\pi
720720 70.4005 + 17.4920i 2.62367 + 0.651889i
721721 15.0849 8.70928i 0.561791 0.324350i
722722 −14.3986 24.9390i −0.535859 0.928134i
723723 −30.0410 −1.11724
724724 2.65562 + 4.59967i 0.0986954 + 0.170945i
725725 −21.7211 + 13.6220i −0.806701 + 0.505909i
726726 −19.2374 11.1067i −0.713965 0.412208i
727727 3.52464i 0.130721i 0.997862 + 0.0653607i 0.0208198π0.0208198\pi
−0.997862 + 0.0653607i 0.979180π0.979180\pi
728728 0 0
729729 −15.7070 −0.581741
730730 4.65950 4.83292i 0.172456 0.178874i
731731 −2.96388 + 5.13360i −0.109623 + 0.189873i
732732 8.15670 4.70928i 0.301480 0.174060i
733733 −21.8310 −0.806345 −0.403172 0.915124i 0.632093π-0.632093\pi
−0.403172 + 0.915124i 0.632093π0.632093\pi
734734 −13.8283 + 7.98379i −0.510413 + 0.294687i
735735 −27.7833 + 7.99119i −1.02480 + 0.294760i
736736 5.83749i 0.215173i
737737 17.2974 9.98667i 0.637159 0.367864i
738738 11.8568 + 6.84551i 0.436454 + 0.251987i
739739 −43.6073 25.1767i −1.60412 0.926139i −0.990651 0.136419i 0.956441π-0.956441\pi
−0.613468 0.789720i 0.710226π-0.710226\pi
740740 4.84551 + 1.20394i 0.178125 + 0.0442576i
741741 0 0
742742 22.3545i 0.820661i
743743 −15.3938 + 26.6629i −0.564745 + 0.978167i 0.432329 + 0.901716i 0.357692π0.357692\pi
−0.997073 + 0.0764505i 0.975641π0.975641\pi
744744 −3.49887 + 6.06021i −0.128275 + 0.222178i
745745 19.5089 5.61127i 0.714752 0.205581i
746746 36.9216i 1.35180i
747747 −30.4215 52.6916i −1.11307 1.92789i
748748 0.431882 + 0.748041i 0.0157912 + 0.0273511i
749749 16.6681i 0.609038i
750750 53.3883 + 11.2119i 1.94947 + 0.409402i
751751 −5.31124 + 9.19934i −0.193810 + 0.335689i −0.946510 0.322675i 0.895418π-0.895418\pi
0.752700 + 0.658364i 0.228751π0.228751\pi
752752 −13.1370 + 22.7539i −0.479055 + 0.829748i
753753 93.3894i 3.40330i
754754 0 0
755755 1.76713 7.11223i 0.0643126 0.258840i
756756 7.01385 + 4.04945i 0.255091 + 0.147277i
757757 6.91575 + 3.99281i 0.251357 + 0.145121i 0.620386 0.784297i 0.286976π-0.286976\pi
−0.369028 + 0.929418i 0.620309π0.620309\pi
758758 −39.6661 + 22.9012i −1.44074 + 0.831809i
759759 22.7792i 0.826834i
760760 −2.90860 + 0.836590i −0.105506 + 0.0303463i
761761 42.3798 24.4680i 1.53627 0.886964i 0.537215 0.843446i 0.319477π-0.319477\pi
0.999053 0.0435187i 0.0138568π-0.0138568\pi
762762 87.8636 3.18296
763763 24.9630 14.4124i 0.903722 0.521764i
764764 −0.272473 + 0.471937i −0.00985773 + 0.0170741i
765765 10.4585 + 10.0832i 0.378127 + 0.364559i
766766 −19.1110 −0.690509
767767 0 0
768768 27.1845i 0.980935i
769769 −6.92428 3.99773i −0.249696 0.144162i 0.369929 0.929060i 0.379382π-0.379382\pi
−0.619625 + 0.784898i 0.712715π0.712715\pi
770770 −10.7537 10.3679i −0.387537 0.373632i
771771 −32.4391 56.1861i −1.16826 2.02349i
772772 −6.54495 −0.235558
773773 −13.3070 23.0485i −0.478621 0.828996i 0.521079 0.853509i 0.325530π-0.325530\pi
−0.999700 + 0.0245130i 0.992196π0.992196\pi
774774 60.4388 34.8943i 2.17243 1.25425i
775775 −2.05786 + 3.88550i −0.0739205 + 0.139571i
776776 7.42469 + 12.8599i 0.266531 + 0.461645i
777777 −28.3877 16.3896i −1.01840 0.587974i
778778 12.9577 22.4435i 0.464557 0.804637i
779779 −0.680346 −0.0243759
780780 0 0
781781 36.7708 1.31576
782782 −2.00719 + 3.47655i −0.0717769 + 0.124321i
783783 57.0074 + 32.9132i 2.03728 + 1.17622i
784784 −9.38428 16.2541i −0.335153 0.580502i
785785 6.92162 27.8576i 0.247043 0.994281i
786786 60.2394 34.7792i 2.14867 1.24053i
787787 −4.62896 8.01759i −0.165005 0.285796i 0.771652 0.636045i 0.219431π-0.219431\pi
−0.936657 + 0.350248i 0.886097π0.886097\pi
788788 0.738205 0.0262975
789789 14.4927 + 25.1021i 0.515955 + 0.893660i
790790 1.18707 1.23125i 0.0422340 0.0438059i
791791 17.4062 + 10.0494i 0.618892 + 0.357317i
792792 44.9333i 1.59664i
793793 0 0
794794 5.99159 0.212634
795795 41.8045 43.3604i 1.48265 1.53783i
796796 0.995079 1.72353i 0.0352697 0.0610888i
797797 −13.8063 + 7.97107i −0.489044 + 0.282350i −0.724178 0.689613i 0.757781π-0.757781\pi
0.235134 + 0.971963i 0.424447π0.424447\pi
798798 −4.49693 −0.159190
799799 −4.55685 + 2.63090i −0.161210 + 0.0930745i
800800 0.376717 + 10.3070i 0.0133190 + 0.364408i
801801 90.4945i 3.19747i
802802 12.1368 7.00719i 0.428566 0.247432i
803803 4.28927 + 2.47641i 0.151365 + 0.0873906i
804804 −7.97084 4.60197i −0.281110 0.162299i
805805 2.60811 10.4969i 0.0919238 0.369968i
806806 0 0
807807 36.1133i 1.27125i
808808 20.6332 35.7377i 0.725872 1.25725i
809809 8.96194 15.5225i 0.315085 0.545744i −0.664370 0.747403i 0.731300π-0.731300\pi
0.979456 + 0.201660i 0.0646336π0.0646336\pi
810810 −18.5956 64.6522i −0.653384 2.27165i
811811 7.43415i 0.261048i 0.991445 + 0.130524i 0.0416660π0.0416660\pi
−0.991445 + 0.130524i 0.958334π0.958334\pi
812812 −1.61757 2.80171i −0.0567655 0.0983207i
813813 33.4999 + 58.0235i 1.17489 + 2.03497i
814814 23.6430i 0.828687i
815815 −7.44767 25.8936i −0.260880 0.907013i
816816 −6.72261 + 11.6439i −0.235338 + 0.407618i
817817 −1.73400 + 3.00338i −0.0606650 + 0.105075i
818818 29.8888i 1.04504i
819819 0 0
820820 −0.251117 + 1.01068i −0.00876940 + 0.0352944i
821821 −17.7363 10.2401i −0.619001 0.357380i 0.157479 0.987522i 0.449663π-0.449663\pi
−0.776480 + 0.630142i 0.782997π0.782997\pi
822822 58.2522 + 33.6319i 2.03178 + 1.17305i
823823 −3.24893 + 1.87577i −0.113250 + 0.0653852i −0.555555 0.831480i 0.687494π-0.687494\pi
0.442305 + 0.896865i 0.354161π0.354161\pi
824824 25.5811i 0.891159i
825825 1.47004 + 40.2204i 0.0511802 + 1.40029i
826826 −10.7601 + 6.21235i −0.374392 + 0.216155i
827827 −48.1483 −1.67428 −0.837141 0.546987i 0.815775π-0.815775\pi
−0.837141 + 0.546987i 0.815775π0.815775\pi
828828 6.37684 3.68167i 0.221611 0.127947i
829829 −18.2804 + 31.6625i −0.634904 + 1.09969i 0.351632 + 0.936138i 0.385627π0.385627\pi
−0.986536 + 0.163547i 0.947706π0.947706\pi
830830 20.6176 21.3849i 0.715647 0.742282i
831831 41.4596 1.43822
832832 0 0
833833 3.75872i 0.130232i
834834 −28.1161 16.2329i −0.973583 0.562098i
835835 13.5486 14.0528i 0.468868 0.486318i
836836 0.252669 + 0.437636i 0.00873876 + 0.0151360i
837837 11.2885 0.390186
838838 −12.9132 22.3663i −0.446079 0.772632i
839839 39.1698 22.6147i 1.35229 0.780746i 0.363721 0.931508i 0.381506π-0.381506\pi
0.988570 + 0.150762i 0.0481728π0.0481728\pi
840840 7.33403 29.5174i 0.253048 1.01845i
841841 1.35270 + 2.34294i 0.0466448 + 0.0807912i
842842 25.3539 + 14.6381i 0.873753 + 0.504462i
843843 1.07838 1.86781i 0.0371413 0.0643306i
844844 −8.39803 −0.289072
845845 0 0
846846 61.9481 2.12982
847847 −3.89076 + 6.73899i −0.133688 + 0.231554i
848848 33.8638 + 19.5513i 1.16289 + 0.671394i
849849 30.5844 + 52.9738i 1.04965 + 1.81806i
850850 −3.31965 + 6.26794i −0.113863 + 0.214989i
851851 −14.8258 + 8.55971i −0.508224 + 0.293423i
852852 −8.47220 14.6743i −0.290253 0.502733i
853853 37.2534 1.27553 0.637766 0.770230i 0.279859π-0.279859\pi
0.637766 + 0.770230i 0.279859π0.279859\pi
854854 −10.5886 18.3401i −0.362336 0.627584i
855855 6.11866 + 5.89911i 0.209254 + 0.201745i
856856 −21.1993 12.2394i −0.724578 0.418336i
857857 10.8371i 0.370188i −0.982721 0.185094i 0.940741π-0.940741\pi
0.982721 0.185094i 0.0592590π-0.0592590\pi
858858 0 0
859859 −14.6081 −0.498422 −0.249211 0.968449i 0.580171π-0.580171\pi
−0.249211 + 0.968449i 0.580171π0.580171\pi
860860 3.82160 + 3.68447i 0.130315 + 0.125639i
861861 3.41855 5.92110i 0.116504 0.201791i
862862 10.7038 6.17982i 0.364572 0.210486i
863863 −10.3440 −0.352116 −0.176058 0.984380i 0.556335π-0.556335\pi
−0.176058 + 0.984380i 0.556335π0.556335\pi
864864 22.9324 13.2401i 0.780178 0.450436i
865865 −1.85618 + 0.533885i −0.0631120 + 0.0181526i
866866 20.0821i 0.682417i
867867 44.3395 25.5994i 1.50585 0.869402i
868868 −0.480460 0.277394i −0.0163079 0.00941535i
869869 1.09275 + 0.630898i 0.0370689 + 0.0214017i
870870 −13.4908 + 54.2967i −0.457380 + 1.84083i
871871 0 0
872872 42.3324i 1.43356i
873873 20.8504 36.1140i 0.705680 1.22227i
874874 −1.17429 + 2.03393i −0.0397210 + 0.0687988i
875875 3.92763 18.7023i 0.132778 0.632254i
876876 2.28231i 0.0771122i
877877 19.0338 + 32.9676i 0.642727 + 1.11324i 0.984821 + 0.173571i 0.0555306π0.0555306\pi
−0.342094 + 0.939666i 0.611136π0.611136\pi
878878 5.92654 + 10.2651i 0.200011 + 0.346429i
879879 30.0144i 1.01236i
880880 −25.1110 + 7.22257i −0.846491 + 0.243473i
881881 6.02472 10.4351i 0.202978 0.351568i −0.746509 0.665376i 0.768271π-0.768271\pi
0.949487 + 0.313807i 0.101605π0.101605\pi
882882 −22.1261 + 38.3235i −0.745024 + 1.29042i
883883 0.320699i 0.0107924i −0.999985 0.00539619i 0.998282π-0.998282\pi
0.999985 0.00539619i 0.00171767π-0.00171767\pi
884884 0 0
885885 32.4885 + 8.07223i 1.09209 + 0.271345i
886886 −8.51885 4.91836i −0.286196 0.165235i
887887 −3.13626 1.81072i −0.105305 0.0607981i 0.446422 0.894822i 0.352698π-0.352698\pi
−0.551728 + 0.834024i 0.686031π0.686031\pi
888888 −41.6904 + 24.0700i −1.39904 + 0.807735i
889889 30.7792i 1.03230i
890890 42.4604 12.2127i 1.42328 0.409371i
891891 42.9825 24.8160i 1.43997 0.831366i
892892 −3.23370 −0.108272
893893 −2.66595 + 1.53919i −0.0892127 + 0.0515070i
894894 22.1483 38.3621i 0.740751 1.28302i
895895 −30.9087 + 32.0591i −1.03316 + 1.07162i
896896 22.9132 0.765477
897897 0 0
898898 48.6635i 1.62392i
899899 −3.90509 2.25461i −0.130242 0.0751954i
900900 11.0217 6.91210i 0.367391 0.230403i
901901 3.91548 + 6.78181i 0.130444 + 0.225935i
902902 −4.93146 −0.164200
903903 −17.4257 30.1823i −0.579892 1.00440i
904904 25.5629 14.7587i 0.850208 0.490868i
905905 −31.2267 7.75872i −1.03801 0.257909i
906906 −7.99579 13.8491i −0.265642 0.460106i
907907 9.46855 + 5.46667i 0.314398 + 0.181518i 0.648893 0.760880i 0.275232π-0.275232\pi
−0.334495 + 0.942398i 0.608566π0.608566\pi
908908 3.17921 5.50656i 0.105506 0.182742i
909909 −115.886 −3.84371
910910 0 0
911911 −37.5897 −1.24540 −0.622701 0.782460i 0.713965π-0.713965\pi
−0.622701 + 0.782460i 0.713965π0.713965\pi
912912 −3.93302 + 6.81218i −0.130235 + 0.225574i
913913 18.9794 + 10.9577i 0.628125 + 0.362648i
914914 −27.4307 47.5113i −0.907326 1.57153i
915915 −13.7587 + 55.3751i −0.454849 + 1.83064i
916916 0.984010 0.568118i 0.0325126 0.0187712i
917917 −12.1834 21.1023i −0.402332 0.696859i
918918 18.2101 0.601022
919919 16.8371 + 29.1627i 0.555405 + 0.961989i 0.997872 + 0.0652045i 0.0207700π0.0207700\pi
−0.442467 + 0.896785i 0.645897π0.645897\pi
920920 −11.4354 11.0251i −0.377014 0.363486i
921921 −0.724951 0.418551i −0.0238880 0.0137917i
922922 23.0563i 0.759317i
923923 0 0
924924 −5.07838 −0.167066
925925 −25.6250 + 16.0703i −0.842545 + 0.528388i
926926 −7.00072 + 12.1256i −0.230058 + 0.398472i
927927 −62.2137 + 35.9191i −2.04336 + 1.17974i
928928 −10.5776 −0.347226
929929 37.4157 21.6020i 1.22757 0.708738i 0.261049 0.965326i 0.415932π-0.415932\pi
0.966521 + 0.256588i 0.0825984π0.0825984\pi
930930 2.65206 + 9.22053i 0.0869646 + 0.302353i
931931 2.19902i 0.0720698i
932932 −6.05293 + 3.49466i −0.198270 + 0.114471i
933933 35.8194 + 20.6803i 1.17267 + 0.677044i
934934 2.50212 + 1.44460i 0.0818720 + 0.0472688i
935935 −5.07838 1.26180i −0.166081 0.0412651i
936936 0 0
937937 27.5630i 0.900445i −0.892916 0.450222i 0.851345π-0.851345\pi
0.892916 0.450222i 0.148655π-0.148655\pi
938938 −10.3474 + 17.9222i −0.337853 + 0.585179i
939939 −53.4173 + 92.5215i −1.74321 + 3.01933i
940940 1.30251 + 4.52849i 0.0424832 + 0.147703i
941941 58.1666i 1.89618i 0.318007 + 0.948088i 0.396987π0.396987\pi
−0.318007 + 0.948088i 0.603013π0.603013\pi
942942 −31.3184 54.2451i −1.02041 1.76740i
943943 −1.78539 3.09238i −0.0581402 0.100702i
944944 21.7333i 0.707358i
945945 −47.1524 + 13.5623i −1.53387 + 0.441180i
946946 −12.5688 + 21.7699i −0.408648 + 0.707799i
947947 24.2576 42.0154i 0.788266 1.36532i −0.138763 0.990326i 0.544313π-0.544313\pi
0.927029 0.374991i 0.122354π-0.122354\pi
948948 0.581449i 0.0188846i
949949 0 0
950950 −1.94214 + 3.66701i −0.0630114 + 0.118974i
951951 38.2995 + 22.1122i 1.24195 + 0.717038i
952952 3.42463 + 1.97721i 0.110993 + 0.0640819i
953953 19.9488 11.5174i 0.646205 0.373087i −0.140796 0.990039i 0.544966π-0.544966\pi
0.787001 + 0.616952i 0.211633π0.211633\pi
954954 92.1953i 2.98493i
955955 −0.912557 3.17272i −0.0295296 0.102667i
956956 −2.12188 + 1.22507i −0.0686264 + 0.0396215i
957957 −41.2762 −1.33427
958958 −20.9852 + 12.1158i −0.678002 + 0.391444i
959959 11.7815 20.4062i 0.380445 0.658950i
960960 −30.7660 29.6621i −0.992969 0.957339i
961961 30.2267 0.975056
962962 0 0
963963 68.7429i 2.21521i
964964 −3.02915 1.74888i −0.0975625 0.0563277i
965965 27.5201 28.5443i 0.885902 0.918873i
966966 −11.8010 20.4399i −0.379690 0.657643i
967967 54.9998 1.76868 0.884338 0.466848i 0.154611π-0.154611\pi
0.884338 + 0.466848i 0.154611π0.154611\pi
968968 5.71400 + 9.89694i 0.183655 + 0.318100i
969969 −1.36426 + 0.787653i −0.0438262 + 0.0253031i
970970 19.7587 + 4.90934i 0.634414 + 0.157629i
971971 −4.85270 8.40512i −0.155731 0.269733i 0.777594 0.628766i 0.216440π-0.216440\pi
−0.933325 + 0.359033i 0.883106π0.883106\pi
972972 −7.49661 4.32817i −0.240454 0.138826i
973973 −5.68649 + 9.84929i −0.182300 + 0.315754i
974974 −7.61038 −0.243852
975975 0 0
976976 −37.0433 −1.18573
977977 −16.1031 + 27.8914i −0.515184 + 0.892325i 0.484661 + 0.874702i 0.338943π0.338943\pi
−0.999845 + 0.0176225i 0.994390π0.994390\pi
978978 −50.9168 29.3968i −1.62814 0.940006i
979979 16.2979 + 28.2288i 0.520884 + 0.902197i
980980 −3.26672 0.811662i −0.104351 0.0259276i
981981 −102.953 + 59.4401i −3.28705 + 1.89778i
982982 30.3884 + 52.6343i 0.969733 + 1.67963i
983983 44.0782 1.40588 0.702938 0.711251i 0.251871π-0.251871\pi
0.702938 + 0.711251i 0.251871π0.251871\pi
984984 −5.02052 8.69579i −0.160048 0.277212i
985985 −3.10399 + 3.21951i −0.0989013 + 0.102582i
986986 −6.29954 3.63704i −0.200618 0.115827i
987987 30.9360i 0.984704i
988988 0 0
989989 −18.2017 −0.578779
990990 44.3509 + 42.7595i 1.40956 + 1.35898i
991991 −6.03385 + 10.4509i −0.191672 + 0.331985i −0.945804 0.324737i 0.894724π-0.894724\pi
0.754133 + 0.656722i 0.228058π0.228058\pi
992992 −1.57091 + 0.906965i −0.0498764 + 0.0287962i
993993 58.5029 1.85653
994994 −32.9946 + 19.0494i −1.04653 + 0.604212i
995995 3.33268 + 11.5869i 0.105653 + 0.367328i
996996 10.0989i 0.319996i
997997 −39.6282 + 22.8794i −1.25504 + 0.724597i −0.972106 0.234543i 0.924641π-0.924641\pi
−0.282933 + 0.959140i 0.591307π0.591307\pi
998998 2.22726 + 1.28591i 0.0705026 + 0.0407047i
999999 67.2533 + 38.8287i 2.12780 + 1.22849i
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.l.d.654.3 12
5.4 even 2 845.2.l.e.654.4 12
13.2 odd 12 845.2.n.f.484.2 12
13.3 even 3 inner 845.2.l.d.699.4 12
13.4 even 6 845.2.d.a.844.4 6
13.5 odd 4 845.2.n.f.529.5 12
13.6 odd 12 65.2.b.a.14.2 6
13.7 odd 12 845.2.b.c.339.5 6
13.8 odd 4 845.2.n.g.529.2 12
13.9 even 3 845.2.d.b.844.4 6
13.10 even 6 845.2.l.e.699.4 12
13.11 odd 12 845.2.n.g.484.5 12
13.12 even 2 845.2.l.e.654.3 12
39.32 even 12 585.2.c.b.469.5 6
52.19 even 12 1040.2.d.c.209.1 6
65.4 even 6 845.2.d.b.844.3 6
65.7 even 12 4225.2.a.ba.1.2 3
65.9 even 6 845.2.d.a.844.3 6
65.19 odd 12 65.2.b.a.14.5 yes 6
65.24 odd 12 845.2.n.g.484.2 12
65.29 even 6 845.2.l.e.699.3 12
65.32 even 12 325.2.a.k.1.2 3
65.33 even 12 4225.2.a.bh.1.2 3
65.34 odd 4 845.2.n.g.529.5 12
65.44 odd 4 845.2.n.f.529.2 12
65.49 even 6 inner 845.2.l.d.699.3 12
65.54 odd 12 845.2.n.f.484.5 12
65.58 even 12 325.2.a.j.1.2 3
65.59 odd 12 845.2.b.c.339.2 6
65.64 even 2 inner 845.2.l.d.654.4 12
195.32 odd 12 2925.2.a.bf.1.2 3
195.149 even 12 585.2.c.b.469.2 6
195.188 odd 12 2925.2.a.bj.1.2 3
260.19 even 12 1040.2.d.c.209.6 6
260.123 odd 12 5200.2.a.cj.1.3 3
260.227 odd 12 5200.2.a.cb.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.b.a.14.2 6 13.6 odd 12
65.2.b.a.14.5 yes 6 65.19 odd 12
325.2.a.j.1.2 3 65.58 even 12
325.2.a.k.1.2 3 65.32 even 12
585.2.c.b.469.2 6 195.149 even 12
585.2.c.b.469.5 6 39.32 even 12
845.2.b.c.339.2 6 65.59 odd 12
845.2.b.c.339.5 6 13.7 odd 12
845.2.d.a.844.3 6 65.9 even 6
845.2.d.a.844.4 6 13.4 even 6
845.2.d.b.844.3 6 65.4 even 6
845.2.d.b.844.4 6 13.9 even 3
845.2.l.d.654.3 12 1.1 even 1 trivial
845.2.l.d.654.4 12 65.64 even 2 inner
845.2.l.d.699.3 12 65.49 even 6 inner
845.2.l.d.699.4 12 13.3 even 3 inner
845.2.l.e.654.3 12 13.12 even 2
845.2.l.e.654.4 12 5.4 even 2
845.2.l.e.699.3 12 65.29 even 6
845.2.l.e.699.4 12 13.10 even 6
845.2.n.f.484.2 12 13.2 odd 12
845.2.n.f.484.5 12 65.54 odd 12
845.2.n.f.529.2 12 65.44 odd 4
845.2.n.f.529.5 12 13.5 odd 4
845.2.n.g.484.2 12 65.24 odd 12
845.2.n.g.484.5 12 13.11 odd 12
845.2.n.g.529.2 12 13.8 odd 4
845.2.n.g.529.5 12 65.34 odd 4
1040.2.d.c.209.1 6 52.19 even 12
1040.2.d.c.209.6 6 260.19 even 12
2925.2.a.bf.1.2 3 195.32 odd 12
2925.2.a.bj.1.2 3 195.188 odd 12
4225.2.a.ba.1.2 3 65.7 even 12
4225.2.a.bh.1.2 3 65.33 even 12
5200.2.a.cb.1.1 3 260.227 odd 12
5200.2.a.cj.1.3 3 260.123 odd 12