Properties

Label 725.2.p.a.399.4
Level 725725
Weight 22
Character 725.399
Analytic conductor 5.7895.789
Analytic rank 00
Dimension 2424
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [725,2,Mod(149,725)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(725, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([7, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("725.149");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 725=5229 725 = 5^{2} \cdot 29
Weight: k k == 2 2
Character orbit: [χ][\chi] == 725.p (of order 1414, degree 66, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 5.789154146545.78915414654
Analytic rank: 00
Dimension: 2424
Relative dimension: 44 over Q(ζ14)\Q(\zeta_{14})
Twist minimal: no (minimal twist has level 29)
Sato-Tate group: SU(2)[C14]\mathrm{SU}(2)[C_{14}]

Embedding invariants

Embedding label 399.4
Character χ\chi == 725.399
Dual form 725.2.p.a.149.4

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+(0.504621+2.21089i)q2+(2.559261.23248i)q3+(2.83146+1.36356i)q4+(1.433416.28018i)q6+(0.6777091.40728i)q7+(1.615652.02596i)q8+(3.16036+3.96297i)q9+(3.10613+2.47705i)q11+8.92699q12+(0.3166310.252504i)q13+(3.45332+0.788198i)q14+(0.254963+0.319714i)q165.16843q17+(7.16690+8.98701i)q18+(1.49728+3.10914i)q19+(3.46887+2.76633i)q21+(3.90908+8.11728i)q22+(0.2244140.0512209i)q23+(1.63793+7.17623i)q24+(0.3984810.827455i)q26+(1.307685.72931i)q27+4.90874iq28+(5.007511.98113i)q29+(4.21005+0.960917i)q31+(5.504882.65101i)q32+(4.8964910.1677i)q33+(2.6081011.4268i)q34+(14.35226.91164i)q36+(3.34857+4.19898i)q37+(6.11841+4.87927i)q38+(0.499135+1.03647i)q391.46294iq41+(7.866536.27335i)q42+(1.44264+6.32061i)q43+(12.17252.77829i)q440.522001iq46+(5.96928+7.48524i)q47+(1.046560.503996i)q48+(2.84329+3.56537i)q49+(13.2274+6.36997i)q51+(1.24083+0.283211i)q52+(1.74395+0.398044i)q53+(12.00705.78226i)q54+(3.94604+0.900657i)q569.80247iq57+(1.8531712.0708i)q58+1.05216q59+(1.383822.87352i)q61+(4.248978.82307i)q62+(7.718801.76177i)q63+(2.9012312.7111i)q64+(20.008715.9564i)q66+(8.50052+6.77893i)q67+(14.63427.04745i)q68+(0.511205+0.407672i)q69+(8.38773+10.5179i)q71+(2.9227912.8056i)q72+(1.56113+6.83974i)q73+(7.59372+9.52223i)q74+(8.478986.76176i)q76+(5.590952.69246i)q77+(2.03964+1.62656i)q78+(3.74078+2.98318i)q79+(0.330785+1.44926i)q81+(3.234400.738232i)q82+(3.654807.58927i)q83+(6.0499012.5628i)q8414.7022q86+(10.3738+11.2419i)q8710.2950iq88+(1.10427+0.252043i)q89+(0.569927+0.274462i)q91+(0.7052600.160971i)q92+(11.9589+2.72955i)q93+(19.56139.42022i)q94+(10.8211+13.5693i)q96+(15.50857.46850i)q97+(6.44786+8.08536i)q98+20.1379iq99+O(q100)q+(0.504621 + 2.21089i) q^{2} +(-2.55926 - 1.23248i) q^{3} +(-2.83146 + 1.36356i) q^{4} +(1.43341 - 6.28018i) q^{6} +(0.677709 - 1.40728i) q^{7} +(-1.61565 - 2.02596i) q^{8} +(3.16036 + 3.96297i) q^{9} +(3.10613 + 2.47705i) q^{11} +8.92699 q^{12} +(-0.316631 - 0.252504i) q^{13} +(3.45332 + 0.788198i) q^{14} +(-0.254963 + 0.319714i) q^{16} -5.16843 q^{17} +(-7.16690 + 8.98701i) q^{18} +(1.49728 + 3.10914i) q^{19} +(-3.46887 + 2.76633i) q^{21} +(-3.90908 + 8.11728i) q^{22} +(-0.224414 - 0.0512209i) q^{23} +(1.63793 + 7.17623i) q^{24} +(0.398481 - 0.827455i) q^{26} +(-1.30768 - 5.72931i) q^{27} +4.90874i q^{28} +(-5.00751 - 1.98113i) q^{29} +(-4.21005 + 0.960917i) q^{31} +(-5.50488 - 2.65101i) q^{32} +(-4.89649 - 10.1677i) q^{33} +(-2.60810 - 11.4268i) q^{34} +(-14.3522 - 6.91164i) q^{36} +(3.34857 + 4.19898i) q^{37} +(-6.11841 + 4.87927i) q^{38} +(0.499135 + 1.03647i) q^{39} -1.46294i q^{41} +(-7.86653 - 6.27335i) q^{42} +(-1.44264 + 6.32061i) q^{43} +(-12.1725 - 2.77829i) q^{44} -0.522001i q^{46} +(-5.96928 + 7.48524i) q^{47} +(1.04656 - 0.503996i) q^{48} +(2.84329 + 3.56537i) q^{49} +(13.2274 + 6.36997i) q^{51} +(1.24083 + 0.283211i) q^{52} +(-1.74395 + 0.398044i) q^{53} +(12.0070 - 5.78226i) q^{54} +(-3.94604 + 0.900657i) q^{56} -9.80247i q^{57} +(1.85317 - 12.0708i) q^{58} +1.05216 q^{59} +(1.38382 - 2.87352i) q^{61} +(-4.24897 - 8.82307i) q^{62} +(7.71880 - 1.76177i) q^{63} +(2.90123 - 12.7111i) q^{64} +(20.0087 - 15.9564i) q^{66} +(-8.50052 + 6.77893i) q^{67} +(14.6342 - 7.04745i) q^{68} +(0.511205 + 0.407672i) q^{69} +(-8.38773 + 10.5179i) q^{71} +(2.92279 - 12.8056i) q^{72} +(-1.56113 + 6.83974i) q^{73} +(-7.59372 + 9.52223i) q^{74} +(-8.47898 - 6.76176i) q^{76} +(5.59095 - 2.69246i) q^{77} +(-2.03964 + 1.62656i) q^{78} +(-3.74078 + 2.98318i) q^{79} +(-0.330785 + 1.44926i) q^{81} +(3.23440 - 0.738232i) q^{82} +(-3.65480 - 7.58927i) q^{83} +(6.04990 - 12.5628i) q^{84} -14.7022 q^{86} +(10.3738 + 11.2419i) q^{87} -10.2950i q^{88} +(-1.10427 + 0.252043i) q^{89} +(-0.569927 + 0.274462i) q^{91} +(0.705260 - 0.160971i) q^{92} +(11.9589 + 2.72955i) q^{93} +(-19.5613 - 9.42022i) q^{94} +(10.8211 + 13.5693i) q^{96} +(15.5085 - 7.46850i) q^{97} +(-6.44786 + 8.08536i) q^{98} +20.1379i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q+2q46q6+6q9+14q11+14q14+18q16+14q1914q21+50q2442q26+30q2942q31+26q3480q3642q3984q4426q49++60q96+O(q100) 24 q + 2 q^{4} - 6 q^{6} + 6 q^{9} + 14 q^{11} + 14 q^{14} + 18 q^{16} + 14 q^{19} - 14 q^{21} + 50 q^{24} - 42 q^{26} + 30 q^{29} - 42 q^{31} + 26 q^{34} - 80 q^{36} - 42 q^{39} - 84 q^{44} - 26 q^{49}+ \cdots + 60 q^{96}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/725Z)×\left(\mathbb{Z}/725\mathbb{Z}\right)^\times.

nn 176176 552552
χ(n)\chi(n) e(1314)e\left(\frac{13}{14}\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 0.504621 + 2.21089i 0.356821 + 1.56334i 0.761060 + 0.648682i 0.224679π0.224679\pi
−0.404239 + 0.914654i 0.632463π0.632463\pi
33 −2.55926 1.23248i −1.47759 0.711571i −0.490457 0.871465i 0.663170π-0.663170\pi
−0.987134 + 0.159895i 0.948885π0.948885\pi
44 −2.83146 + 1.36356i −1.41573 + 0.681779i
55 0 0
66 1.43341 6.28018i 0.585188 2.56387i
77 0.677709 1.40728i 0.256150 0.531901i −0.732747 0.680501i 0.761762π-0.761762\pi
0.988897 + 0.148600i 0.0474766π0.0474766\pi
88 −1.61565 2.02596i −0.571220 0.716287i
99 3.16036 + 3.96297i 1.05345 + 1.32099i
1010 0 0
1111 3.10613 + 2.47705i 0.936533 + 0.746860i 0.967555 0.252659i 0.0813051π-0.0813051\pi
−0.0310229 + 0.999519i 0.509876π0.509876\pi
1212 8.92699 2.57700
1313 −0.316631 0.252504i −0.0878175 0.0700321i 0.578597 0.815614i 0.303600π-0.303600\pi
−0.666415 + 0.745581i 0.732172π0.732172\pi
1414 3.45332 + 0.788198i 0.922939 + 0.210655i
1515 0 0
1616 −0.254963 + 0.319714i −0.0637408 + 0.0799285i
1717 −5.16843 −1.25353 −0.626764 0.779209i 0.715621π-0.715621\pi
−0.626764 + 0.779209i 0.715621π0.715621\pi
1818 −7.16690 + 8.98701i −1.68926 + 2.11826i
1919 1.49728 + 3.10914i 0.343500 + 0.713286i 0.999126 0.0418005i 0.0133094π-0.0133094\pi
−0.655626 + 0.755086i 0.727595π0.727595\pi
2020 0 0
2121 −3.46887 + 2.76633i −0.756970 + 0.603663i
2222 −3.90908 + 8.11728i −0.833418 + 1.73061i
2323 −0.224414 0.0512209i −0.0467935 0.0106803i 0.199060 0.979987i 0.436211π-0.436211\pi
−0.245854 + 0.969307i 0.579068π0.579068\pi
2424 1.63793 + 7.17623i 0.334341 + 1.46484i
2525 0 0
2626 0.398481 0.827455i 0.0781486 0.162277i
2727 −1.30768 5.72931i −0.251663 1.10261i
2828 4.90874i 0.927664i
2929 −5.00751 1.98113i −0.929870 0.367887i
3030 0 0
3131 −4.21005 + 0.960917i −0.756148 + 0.172586i −0.583182 0.812342i 0.698192π-0.698192\pi
−0.172967 + 0.984928i 0.555335π0.555335\pi
3232 −5.50488 2.65101i −0.973135 0.468637i
3333 −4.89649 10.1677i −0.852369 1.76996i
3434 −2.60810 11.4268i −0.447285 1.95968i
3535 0 0
3636 −14.3522 6.91164i −2.39203 1.15194i
3737 3.34857 + 4.19898i 0.550502 + 0.690308i 0.976770 0.214289i 0.0687434π-0.0687434\pi
−0.426268 + 0.904597i 0.640172π0.640172\pi
3838 −6.11841 + 4.87927i −0.992536 + 0.791521i
3939 0.499135 + 1.03647i 0.0799256 + 0.165967i
4040 0 0
4141 1.46294i 0.228473i −0.993454 0.114237i 0.963558π-0.963558\pi
0.993454 0.114237i 0.0364422π-0.0364422\pi
4242 −7.86653 6.27335i −1.21383 0.967998i
4343 −1.44264 + 6.32061i −0.220000 + 0.963884i 0.737476 + 0.675373i 0.236017π0.236017\pi
−0.957477 + 0.288511i 0.906840π0.906840\pi
4444 −12.1725 2.77829i −1.83507 0.418842i
4545 0 0
4646 0.522001i 0.0769648i
4747 −5.96928 + 7.48524i −0.870709 + 1.09184i 0.124319 + 0.992242i 0.460325π0.460325\pi
−0.995028 + 0.0995928i 0.968246π0.968246\pi
4848 1.04656 0.503996i 0.151058 0.0727455i
4949 2.84329 + 3.56537i 0.406184 + 0.509339i
5050 0 0
5151 13.2274 + 6.36997i 1.85220 + 0.891974i
5252 1.24083 + 0.283211i 0.172072 + 0.0392743i
5353 −1.74395 + 0.398044i −0.239549 + 0.0546756i −0.340610 0.940205i 0.610634π-0.610634\pi
0.101061 + 0.994880i 0.467776π0.467776\pi
5454 12.0070 5.78226i 1.63394 0.786866i
5555 0 0
5656 −3.94604 + 0.900657i −0.527311 + 0.120355i
5757 9.80247i 1.29837i
5858 1.85317 12.0708i 0.243333 1.58497i
5959 1.05216 0.136980 0.0684900 0.997652i 0.478182π-0.478182\pi
0.0684900 + 0.997652i 0.478182π0.478182\pi
6060 0 0
6161 1.38382 2.87352i 0.177179 0.367917i −0.793399 0.608702i 0.791691π-0.791691\pi
0.970578 + 0.240785i 0.0774049π0.0774049\pi
6262 −4.24897 8.82307i −0.539619 1.12053i
6363 7.71880 1.76177i 0.972478 0.221962i
6464 2.90123 12.7111i 0.362653 1.58889i
6565 0 0
6666 20.0087 15.9564i 2.46290 1.96410i
6767 −8.50052 + 6.77893i −1.03850 + 0.828179i −0.985373 0.170409i 0.945491π-0.945491\pi
−0.0531298 + 0.998588i 0.516920π0.516920\pi
6868 14.6342 7.04745i 1.77465 0.854628i
6969 0.511205 + 0.407672i 0.0615418 + 0.0490780i
7070 0 0
7171 −8.38773 + 10.5179i −0.995440 + 1.24824i −0.0268346 + 0.999640i 0.508543π0.508543\pi
−0.968606 + 0.248603i 0.920029π0.920029\pi
7272 2.92279 12.8056i 0.344454 1.50915i
7373 −1.56113 + 6.83974i −0.182716 + 0.800531i 0.797615 + 0.603167i 0.206095π0.206095\pi
−0.980330 + 0.197363i 0.936762π0.936762\pi
7474 −7.59372 + 9.52223i −0.882752 + 1.10694i
7575 0 0
7676 −8.47898 6.76176i −0.972605 0.775627i
7777 5.59095 2.69246i 0.637148 0.306834i
7878 −2.03964 + 1.62656i −0.230943 + 0.184171i
7979 −3.74078 + 2.98318i −0.420871 + 0.335634i −0.810916 0.585162i 0.801031π-0.801031\pi
0.390045 + 0.920796i 0.372459π0.372459\pi
8080 0 0
8181 −0.330785 + 1.44926i −0.0367539 + 0.161029i
8282 3.23440 0.738232i 0.357180 0.0815241i
8383 −3.65480 7.58927i −0.401166 0.833030i −0.999495 0.0317796i 0.989883π-0.989883\pi
0.598329 0.801251i 0.295832π-0.295832\pi
8484 6.04990 12.5628i 0.660099 1.37071i
8585 0 0
8686 −14.7022 −1.58537
8787 10.3738 + 11.2419i 1.11219 + 1.20526i
8888 10.2950i 1.09745i
8989 −1.10427 + 0.252043i −0.117053 + 0.0267165i −0.280646 0.959811i 0.590549π-0.590549\pi
0.163593 + 0.986528i 0.447692π0.447692\pi
9090 0 0
9191 −0.569927 + 0.274462i −0.0597446 + 0.0287715i
9292 0.705260 0.160971i 0.0735284 0.0167824i
9393 11.9589 + 2.72955i 1.24009 + 0.283041i
9494 −19.5613 9.42022i −2.01759 0.971621i
9595 0 0
9696 10.8211 + 13.5693i 1.10443 + 1.38491i
9797 15.5085 7.46850i 1.57465 0.758311i 0.576383 0.817180i 0.304464π-0.304464\pi
0.998266 + 0.0588689i 0.0187494π0.0187494\pi
9898 −6.44786 + 8.08536i −0.651332 + 0.816745i
9999 20.1379i 2.02393i
100100 0 0
101101 −6.08315 1.38844i −0.605296 0.138155i −0.0911203 0.995840i 0.529045π-0.529045\pi
−0.514175 + 0.857685i 0.671902π0.671902\pi
102102 −7.40848 + 32.4587i −0.733549 + 3.21389i
103103 10.3284 + 8.23659i 1.01768 + 0.811576i 0.982208 0.187795i 0.0601340π-0.0601340\pi
0.0354755 + 0.999371i 0.488705π0.488705\pi
104104 1.04944i 0.102906i
105105 0 0
106106 −1.76006 3.65481i −0.170953 0.354987i
107107 7.24619 5.77864i 0.700516 0.558642i −0.207164 0.978306i 0.566423π-0.566423\pi
0.907680 + 0.419664i 0.137852π0.137852\pi
108108 11.5149 + 14.4392i 1.10802 + 1.38941i
109109 5.18545 + 2.49718i 0.496676 + 0.239187i 0.665414 0.746474i 0.268255π-0.268255\pi
−0.168738 + 0.985661i 0.553969π0.553969\pi
110110 0 0
111111 −3.39474 14.8733i −0.322215 1.41171i
112112 0.277135 + 0.575477i 0.0261868 + 0.0543775i
113113 7.26385 + 3.49809i 0.683326 + 0.329072i 0.743139 0.669137i 0.233336π-0.233336\pi
−0.0598131 + 0.998210i 0.519050π0.519050\pi
114114 21.6722 4.94654i 2.02979 0.463286i
115115 0 0
116116 16.8799 1.21853i 1.56726 0.113138i
117117 2.05280i 0.189782i
118118 0.530944 + 2.32622i 0.0488774 + 0.214146i
119119 −3.50269 + 7.27341i −0.321091 + 0.666753i
120120 0 0
121121 1.06450 + 4.66388i 0.0967727 + 0.423989i
122122 7.05135 + 1.60942i 0.638399 + 0.145710i
123123 −1.80304 + 3.74405i −0.162575 + 0.337590i
124124 10.6103 8.46144i 0.952834 0.759860i
125125 0 0
126126 7.79014 + 16.1764i 0.694001 + 1.44111i
127127 −10.9570 + 13.7396i −0.972277 + 1.21920i 0.00340252 + 0.999994i 0.498917π0.498917\pi
−0.975679 + 0.219202i 0.929654π0.929654\pi
128128 17.3469 1.53327
129129 11.4821 14.3981i 1.01094 1.26768i
130130 0 0
131131 −3.26398 0.744983i −0.285176 0.0650895i 0.0775403 0.996989i 0.475293π-0.475293\pi
−0.362716 + 0.931900i 0.618150π0.618150\pi
132132 27.7284 + 22.1126i 2.41345 + 1.92466i
133133 5.39014 0.467385
134134 −19.2770 15.3729i −1.66528 1.32802i
135135 0 0
136136 8.35039 + 10.4711i 0.716040 + 0.897885i
137137 3.44204 + 4.31618i 0.294073 + 0.368756i 0.906816 0.421526i 0.138505π-0.138505\pi
−0.612743 + 0.790282i 0.709934π0.709934\pi
138138 −0.643354 + 1.33594i −0.0547659 + 0.113723i
139139 −0.132958 + 0.582528i −0.0112774 + 0.0494094i −0.980254 0.197745i 0.936638π-0.936638\pi
0.968976 + 0.247154i 0.0794954π0.0794954\pi
140140 0 0
141141 24.5024 11.7997i 2.06347 0.993715i
142142 −27.4865 13.2368i −2.30662 1.11081i
143143 −0.358028 1.56862i −0.0299398 0.131175i
144144 −2.07279 −0.172733
145145 0 0
146146 −15.9097 −1.31669
147147 −2.88249 12.6290i −0.237744 1.04162i
148148 −15.2069 7.32325i −1.25000 0.601968i
149149 −4.60312 + 2.21675i −0.377102 + 0.181603i −0.612827 0.790217i 0.709968π-0.709968\pi
0.235725 + 0.971820i 0.424254π0.424254\pi
150150 0 0
151151 −1.73572 + 7.60469i −0.141251 + 0.618861i 0.853894 + 0.520446i 0.174234π0.174234\pi
−0.995145 + 0.0984149i 0.968623π0.968623\pi
152152 3.87992 8.05673i 0.314703 0.653487i
153153 −16.3341 20.4823i −1.32053 1.65590i
154154 8.77405 + 11.0023i 0.707033 + 0.886591i
155155 0 0
156156 −2.82656 2.25411i −0.226306 0.180473i
157157 18.8577 1.50501 0.752504 0.658588i 0.228846π-0.228846\pi
0.752504 + 0.658588i 0.228846π0.228846\pi
158158 −8.48315 6.76509i −0.674884 0.538202i
159159 4.95380 + 1.13067i 0.392862 + 0.0896681i
160160 0 0
161161 −0.224169 + 0.281099i −0.0176670 + 0.0221537i
162162 −3.37109 −0.264858
163163 1.41033 1.76850i 0.110466 0.138520i −0.723525 0.690298i 0.757479π-0.757479\pi
0.833991 + 0.551779i 0.186051π0.186051\pi
164164 1.99481 + 4.14226i 0.155768 + 0.323456i
165165 0 0
166166 14.9347 11.9101i 1.15916 0.924400i
167167 5.09159 10.5728i 0.393999 0.818147i −0.605748 0.795656i 0.707126π-0.707126\pi
0.999747 0.0224905i 0.00715956π-0.00715956\pi
168168 11.2090 + 2.55838i 0.864792 + 0.197383i
169169 −2.85628 12.5142i −0.219714 0.962628i
170170 0 0
171171 −7.58947 + 15.7597i −0.580381 + 1.20517i
172172 −4.53375 19.8636i −0.345695 1.51459i
173173 19.2889i 1.46651i −0.679954 0.733254i 0.738000π-0.738000\pi
0.679954 0.733254i 0.262000π-0.262000\pi
174174 −19.6197 + 28.6083i −1.48737 + 2.16879i
175175 0 0
176176 −1.58390 + 0.361514i −0.119391 + 0.0272501i
177177 −2.69276 1.29677i −0.202401 0.0974710i
178178 −1.11448 2.31424i −0.0835337 0.173460i
179179 −0.202580 0.887562i −0.0151416 0.0663395i 0.966793 0.255562i 0.0822604π-0.0822604\pi
−0.981934 + 0.189222i 0.939403π0.939403\pi
180180 0 0
181181 −4.74107 2.28318i −0.352401 0.169707i 0.249305 0.968425i 0.419798π-0.419798\pi
−0.601706 + 0.798718i 0.705512π0.705512\pi
182182 −0.894404 1.12155i −0.0662976 0.0831346i
183183 −7.08310 + 5.64858i −0.523598 + 0.417555i
184184 0.258803 + 0.537409i 0.0190792 + 0.0396183i
185185 0 0
186186 27.8173i 2.03966i
187187 −16.0538 12.8025i −1.17397 0.936210i
188188 6.69520 29.3336i 0.488298 2.13937i
189189 −8.94895 2.04254i −0.650940 0.148573i
190190 0 0
191191 10.3088i 0.745920i 0.927847 + 0.372960i 0.121657π0.121657\pi
−0.927847 + 0.372960i 0.878343π0.878343\pi
192192 −23.0911 + 28.9554i −1.66646 + 2.08967i
193193 2.44160 1.17581i 0.175750 0.0846368i −0.343940 0.938992i 0.611762π-0.611762\pi
0.519690 + 0.854355i 0.326047π0.326047\pi
194194 24.3379 + 30.5188i 1.74736 + 2.19112i
195195 0 0
196196 −12.9122 6.21820i −0.922302 0.444157i
197197 −14.4081 3.28855i −1.02653 0.234300i −0.324080 0.946030i 0.605055π-0.605055\pi
−0.702453 + 0.711730i 0.747912π0.747912\pi
198198 −44.5226 + 10.1620i −3.16409 + 0.722182i
199199 13.5173 6.50959i 0.958216 0.461453i 0.111657 0.993747i 0.464384π-0.464384\pi
0.846560 + 0.532294i 0.178670π0.178670\pi
200200 0 0
201201 30.1099 6.87240i 2.12379 0.484741i
202202 14.1498i 0.995577i
203203 −6.18163 + 5.70432i −0.433866 + 0.400365i
204204 −46.1385 −3.23034
205205 0 0
206206 −12.9983 + 26.9912i −0.905634 + 1.88057i
207207 −0.506241 1.05122i −0.0351862 0.0730649i
208208 0.161458 0.0368518i 0.0111951 0.00255521i
209209 −3.05076 + 13.3662i −0.211025 + 0.924562i
210210 0 0
211211 9.36088 7.46505i 0.644430 0.513916i −0.245863 0.969305i 0.579071π-0.579071\pi
0.890293 + 0.455389i 0.150500π0.150500\pi
212212 4.39515 3.50501i 0.301860 0.240725i
213213 34.4294 16.5803i 2.35907 1.13607i
214214 16.4325 + 13.1045i 1.12330 + 0.895805i
215215 0 0
216216 −9.49462 + 11.9059i −0.646027 + 0.810093i
217217 −1.50091 + 6.57594i −0.101889 + 0.446404i
218218 −2.90430 + 12.7246i −0.196704 + 0.861818i
219219 12.4251 15.5806i 0.839613 1.05284i
220220 0 0
221221 1.63648 + 1.30505i 0.110082 + 0.0877872i
222222 31.1703 15.0108i 2.09201 1.00746i
223223 −10.4541 + 8.33685i −0.700057 + 0.558277i −0.907542 0.419962i 0.862044π-0.862044\pi
0.207485 + 0.978238i 0.433472π0.433472\pi
224224 −7.46142 + 5.95028i −0.498537 + 0.397570i
225225 0 0
226226 −4.06839 + 17.8248i −0.270625 + 1.18569i
227227 2.06910 0.472258i 0.137331 0.0313448i −0.153303 0.988179i 0.548991π-0.548991\pi
0.290634 + 0.956834i 0.406134π0.406134\pi
228228 13.3662 + 27.7553i 0.885200 + 1.83814i
229229 11.8839 24.6772i 0.785312 1.63072i 0.00933352 0.999956i 0.497029π-0.497029\pi
0.775978 0.630760i 0.217257π-0.217257\pi
230230 0 0
231231 −17.6271 −1.15978
232232 4.07669 + 13.3459i 0.267648 + 0.876198i
233233 17.4774i 1.14498i 0.819910 + 0.572492i 0.194023π0.194023\pi
−0.819910 + 0.572492i 0.805977π0.805977\pi
234234 4.53852 1.03589i 0.296692 0.0677181i
235235 0 0
236236 −2.97915 + 1.43468i −0.193926 + 0.0933900i
237237 13.2503 3.02431i 0.860703 0.196450i
238238 −17.8482 4.07375i −1.15693 0.264062i
239239 15.5439 + 7.48555i 1.00545 + 0.484200i 0.862785 0.505571i 0.168718π-0.168718\pi
0.142667 + 0.989771i 0.454432π0.454432\pi
240240 0 0
241241 −13.7085 17.1899i −0.883040 1.10730i −0.993547 0.113422i 0.963819π-0.963819\pi
0.110507 0.993875i 0.464753π-0.464753\pi
242242 −9.77415 + 4.70698i −0.628306 + 0.302576i
243243 −8.35934 + 10.4823i −0.536252 + 0.672439i
244244 10.0232i 0.641667i
245245 0 0
246246 −9.18755 2.09700i −0.585777 0.133700i
247247 0.310986 1.36252i 0.0197876 0.0866950i
248248 8.74877 + 6.97691i 0.555548 + 0.443034i
249249 23.9274i 1.51634i
250250 0 0
251251 −4.23936 8.80311i −0.267586 0.555648i 0.723271 0.690564i 0.242638π-0.242638\pi
−0.990857 + 0.134917i 0.956923π0.956923\pi
252252 −19.4532 + 15.5134i −1.22544 + 0.977252i
253253 −0.570180 0.714983i −0.0358469 0.0449506i
254254 −35.9060 17.2914i −2.25294 1.08496i
255255 0 0
256256 2.95119 + 12.9300i 0.184449 + 0.808124i
257257 −6.68278 13.8769i −0.416861 0.865620i −0.998633 0.0522684i 0.983355π-0.983355\pi
0.581772 0.813352i 0.302359π-0.302359\pi
258258 37.6267 + 18.1201i 2.34254 + 1.12811i
259259 8.17849 1.86669i 0.508187 0.115990i
260260 0 0
261261 −7.97437 26.1057i −0.493601 1.61590i
262262 7.59225i 0.469050i
263263 6.89666 + 30.2162i 0.425266 + 1.86321i 0.500026 + 0.866010i 0.333324π0.333324\pi
−0.0747599 + 0.997202i 0.523819π0.523819\pi
264264 −12.6883 + 26.3475i −0.780911 + 1.62158i
265265 0 0
266266 2.71998 + 11.9170i 0.166773 + 0.730679i
267267 3.13676 + 0.715945i 0.191967 + 0.0438151i
268268 14.8254 30.7852i 0.905603 1.88050i
269269 −10.8322 + 8.63841i −0.660453 + 0.526693i −0.895371 0.445322i 0.853089π-0.853089\pi
0.234918 + 0.972015i 0.424518π0.424518\pi
270270 0 0
271271 11.6447 + 24.1804i 0.707362 + 1.46885i 0.875565 + 0.483100i 0.160489π0.160489\pi
−0.168203 + 0.985752i 0.553796π0.553796\pi
272272 1.31776 1.65242i 0.0799009 0.100193i
273273 1.79686 0.108751
274274 −7.80567 + 9.78800i −0.471558 + 0.591315i
275275 0 0
276276 −2.00334 0.457249i −0.120587 0.0275232i
277277 17.6352 + 14.0636i 1.05960 + 0.845002i 0.988311 0.152454i 0.0487175π-0.0487175\pi
0.0712885 + 0.997456i 0.477289π0.477289\pi
278278 −1.35500 −0.0812675
279279 −17.1134 13.6475i −1.02455 0.817053i
280280 0 0
281281 −2.05756 2.58010i −0.122744 0.153916i 0.716663 0.697420i 0.245669π-0.245669\pi
−0.839406 + 0.543504i 0.817097π0.817097\pi
282282 38.4523 + 48.2176i 2.28980 + 2.87132i
283283 7.66611 15.9189i 0.455703 0.946277i −0.538885 0.842380i 0.681154π-0.681154\pi
0.994588 0.103898i 0.0331315π-0.0331315\pi
284284 9.40775 41.2180i 0.558247 2.44584i
285285 0 0
286286 3.28738 1.58312i 0.194387 0.0936118i
287287 −2.05877 0.991449i −0.121525 0.0585234i
288288 −6.89155 30.1938i −0.406088 1.77919i
289289 9.71265 0.571332
290290 0 0
291291 −48.8951 −2.86628
292292 −4.90611 21.4951i −0.287109 1.25790i
293293 −12.1939 5.87226i −0.712374 0.343061i 0.0423508 0.999103i 0.486515π-0.486515\pi
−0.754725 + 0.656042i 0.772230π0.772230\pi
294294 26.4668 12.7457i 1.54357 0.743346i
295295 0 0
296296 3.09685 13.5682i 0.180001 0.788635i
297297 10.1300 21.0351i 0.587802 1.22058i
298298 −7.22382 9.05838i −0.418464 0.524738i
299299 0.0581227 + 0.0728835i 0.00336132 + 0.00421496i
300300 0 0
301301 7.91716 + 6.31373i 0.456338 + 0.363917i
302302 −17.6890 −1.01789
303303 13.8572 + 11.0507i 0.796073 + 0.634847i
304304 −1.37579 0.314014i −0.0789068 0.0180100i
305305 0 0
306306 37.0416 46.4487i 2.11753 2.65530i
307307 −6.51865 −0.372039 −0.186020 0.982546i 0.559559π-0.559559\pi
−0.186020 + 0.982546i 0.559559π0.559559\pi
308308 −12.1592 + 15.2472i −0.692835 + 0.868788i
309309 −16.2816 33.8091i −0.926227 1.92333i
310310 0 0
311311 19.1908 15.3042i 1.08821 0.867820i 0.0963761 0.995345i 0.469275π-0.469275\pi
0.991835 + 0.127525i 0.0407034π0.0407034\pi
312312 1.29341 2.68580i 0.0732251 0.152053i
313313 −1.92496 0.439360i −0.108805 0.0248341i 0.167772 0.985826i 0.446343π-0.446343\pi
−0.276577 + 0.960992i 0.589200π0.589200\pi
314314 9.51599 + 41.6923i 0.537019 + 2.35283i
315315 0 0
316316 6.52413 13.5475i 0.367011 0.762107i
317317 6.60459 + 28.9366i 0.370951 + 1.62524i 0.724114 + 0.689680i 0.242249π0.242249\pi
−0.353163 + 0.935562i 0.614894π0.614894\pi
318318 11.5229i 0.646170i
319319 −10.6466 18.5575i −0.596094 1.03902i
320320 0 0
321321 −25.6669 + 5.85831i −1.43259 + 0.326979i
322322 −0.734600 0.353765i −0.0409377 0.0197145i
323323 −7.73860 16.0694i −0.430587 0.894123i
324324 −1.03955 4.55457i −0.0577529 0.253032i
325325 0 0
326326 4.62165 + 2.22567i 0.255969 + 0.123268i
327327 −10.1932 12.7819i −0.563686 0.706840i
328328 −2.96387 + 2.36361i −0.163652 + 0.130508i
329329 6.48838 + 13.4733i 0.357716 + 0.742805i
330330 0 0
331331 28.3740i 1.55958i −0.626044 0.779788i 0.715327π-0.715327\pi
0.626044 0.779788i 0.284673π-0.284673\pi
332332 20.6968 + 16.5051i 1.13588 + 0.905838i
333333 −6.05772 + 26.5406i −0.331961 + 1.45442i
334334 25.9446 + 5.92168i 1.41963 + 0.324020i
335335 0 0
336336 1.81436i 0.0989814i
337337 −2.50472 + 3.14082i −0.136441 + 0.171091i −0.845358 0.534201i 0.820613π-0.820613\pi
0.708917 + 0.705292i 0.249184π0.249184\pi
338338 26.2261 12.6298i 1.42651 0.686972i
339339 −14.2788 17.9051i −0.775518 0.972469i
340340 0 0
341341 −15.4572 7.44380i −0.837055 0.403104i
342342 −38.6728 8.82681i −2.09118 0.477299i
343343 17.6040 4.01799i 0.950525 0.216951i
344344 15.1361 7.28918i 0.816086 0.393006i
345345 0 0
346346 42.6457 9.73360i 2.29265 0.523281i
347347 3.55272i 0.190720i −0.995443 0.0953601i 0.969600π-0.969600\pi
0.995443 0.0953601i 0.0304003π-0.0304003\pi
348348 −44.7020 17.6856i −2.39628 0.948045i
349349 −3.34203 −0.178895 −0.0894473 0.995992i 0.528510π-0.528510\pi
−0.0894473 + 0.995992i 0.528510π0.528510\pi
350350 0 0
351351 −1.03263 + 2.14427i −0.0551175 + 0.114453i
352352 −10.5322 21.8703i −0.561366 1.16569i
353353 −12.2016 + 2.78493i −0.649424 + 0.148227i −0.534528 0.845151i 0.679511π-0.679511\pi
−0.114896 + 0.993378i 0.536653π0.536653\pi
354354 1.50818 6.60778i 0.0801590 0.351200i
355355 0 0
356356 2.78302 2.21939i 0.147500 0.117627i
357357 17.9286 14.2976i 0.948883 0.756709i
358358 1.86008 0.895765i 0.0983080 0.0473426i
359359 14.3825 + 11.4697i 0.759080 + 0.605346i 0.924635 0.380855i 0.124370π-0.124370\pi
−0.165555 + 0.986201i 0.552942π0.552942\pi
360360 0 0
361361 4.42141 5.54428i 0.232706 0.291804i
362362 2.65541 11.6341i 0.139566 0.611476i
363363 3.02378 13.2481i 0.158708 0.695343i
364364 1.23948 1.55426i 0.0649663 0.0814652i
365365 0 0
366366 −16.0627 12.8096i −0.839609 0.669566i
367367 8.85669 4.26516i 0.462316 0.222639i −0.188202 0.982130i 0.560266π-0.560266\pi
0.650518 + 0.759491i 0.274552π0.274552\pi
368368 0.0735933 0.0586887i 0.00383631 0.00305936i
369369 5.79760 4.62343i 0.301811 0.240686i
370370 0 0
371371 −0.621729 + 2.72397i −0.0322786 + 0.141422i
372372 −37.5831 + 8.57810i −1.94859 + 0.444754i
373373 −9.62338 19.9832i −0.498280 1.03469i −0.986771 0.162120i 0.948167π-0.948167\pi
0.488491 0.872569i 0.337547π-0.337547\pi
374374 20.2038 41.9536i 1.04471 2.16937i
375375 0 0
376376 24.8091 1.27943
377377 1.08528 + 1.89170i 0.0558950 + 0.0974277i
378378 20.8159i 1.07065i
379379 8.48209 1.93598i 0.435696 0.0994447i 0.000953214 1.00000i 0.499697π-0.499697\pi
0.434742 + 0.900555i 0.356839π0.356839\pi
380380 0 0
381381 44.9757 21.6591i 2.30417 1.10963i
382382 −22.7917 + 5.20205i −1.16612 + 0.266160i
383383 4.95869 + 1.13179i 0.253377 + 0.0578317i 0.347323 0.937746i 0.387091π-0.387091\pi
−0.0939456 + 0.995577i 0.529948π0.529948\pi
384384 −44.3954 21.3797i −2.26554 1.09103i
385385 0 0
386386 3.83167 + 4.80477i 0.195027 + 0.244556i
387387 −29.6076 + 14.2583i −1.50504 + 0.724790i
388388 −33.7279 + 42.2934i −1.71227 + 2.14712i
389389 29.8408i 1.51299i −0.654000 0.756494i 0.726910π-0.726910\pi
0.654000 0.756494i 0.273090π-0.273090\pi
390390 0 0
391391 1.15987 + 0.264732i 0.0586569 + 0.0133881i
392392 2.62955 11.5208i 0.132812 0.581888i
393393 7.43522 + 5.92939i 0.375057 + 0.299098i
394394 33.5142i 1.68842i
395395 0 0
396396 −27.4591 57.0195i −1.37987 2.86534i
397397 −2.28497 + 1.82220i −0.114679 + 0.0914537i −0.679150 0.733999i 0.737652π-0.737652\pi
0.564471 + 0.825453i 0.309080π0.309080\pi
398398 21.2131 + 26.6004i 1.06332 + 1.33336i
399399 −13.7948 6.64322i −0.690604 0.332577i
400400 0 0
401401 4.54850 + 19.9283i 0.227141 + 0.995171i 0.951958 + 0.306229i 0.0990674π0.0990674\pi
−0.724817 + 0.688942i 0.758075π0.758075\pi
402402 30.3882 + 63.1018i 1.51563 + 3.14723i
403403 1.57567 + 0.758802i 0.0784896 + 0.0377986i
404404 19.1174 4.36341i 0.951125 0.217088i
405405 0 0
406406 −15.7310 10.7884i −0.780717 0.535419i
407407 21.3372i 1.05764i
408408 −8.46551 37.0898i −0.419105 1.83622i
409409 −14.5837 + 30.2833i −0.721116 + 1.49741i 0.140625 + 0.990063i 0.455089π0.455089\pi
−0.861741 + 0.507349i 0.830626π0.830626\pi
410410 0 0
411411 −3.48949 15.2885i −0.172124 0.754124i
412412 −40.4754 9.23824i −1.99408 0.455135i
413413 0.713061 1.48069i 0.0350874 0.0728598i
414414 2.06867 1.64971i 0.101670 0.0810789i
415415 0 0
416416 1.07362 + 2.22940i 0.0526387 + 0.109305i
417417 1.05823 1.32698i 0.0518216 0.0649823i
418418 −31.0907 −1.52070
419419 −4.69488 + 5.88719i −0.229360 + 0.287608i −0.883173 0.469048i 0.844597π-0.844597\pi
0.653813 + 0.756656i 0.273168π0.273168\pi
420420 0 0
421421 19.8646 + 4.53398i 0.968144 + 0.220972i 0.677226 0.735775i 0.263182π-0.263182\pi
0.290918 + 0.956748i 0.406039π0.406039\pi
422422 21.2281 + 16.9289i 1.03337 + 0.824084i
423423 −48.5289 −2.35956
424424 3.62403 + 2.89007i 0.175999 + 0.140354i
425425 0 0
426426 54.0312 + 67.7529i 2.61782 + 3.28264i
427427 −3.10602 3.89482i −0.150311 0.188484i
428428 −12.6378 + 26.2426i −0.610869 + 1.26848i
429429 −1.01700 + 4.45578i −0.0491013 + 0.215127i
430430 0 0
431431 −10.6631 + 5.13509i −0.513625 + 0.247349i −0.672697 0.739918i 0.734864π-0.734864\pi
0.159072 + 0.987267i 0.449150π0.449150\pi
432432 2.16515 + 1.04268i 0.104171 + 0.0501660i
433433 −3.80447 16.6685i −0.182831 0.801037i −0.980274 0.197642i 0.936672π-0.936672\pi
0.797443 0.603394i 0.206186π-0.206186\pi
434434 −15.2961 −0.734235
435435 0 0
436436 −18.0874 −0.866230
437437 −0.176758 0.774425i −0.00845546 0.0370458i
438438 40.7171 + 19.6083i 1.94554 + 0.936921i
439439 −16.8940 + 8.13573i −0.806308 + 0.388297i −0.791176 0.611588i 0.790531π-0.790531\pi
−0.0151314 + 0.999886i 0.504817π0.504817\pi
440440 0 0
441441 −5.14363 + 22.5357i −0.244935 + 1.07313i
442442 −2.05952 + 4.27664i −0.0979614 + 0.203419i
443443 −2.12225 2.66122i −0.100831 0.126438i 0.728856 0.684667i 0.240052π-0.240052\pi
−0.829687 + 0.558229i 0.811481π0.811481\pi
444444 29.8927 + 37.4843i 1.41864 + 1.77892i
445445 0 0
446446 −23.7072 18.9059i −1.12257 0.895219i
447447 14.5127 0.686427
448448 −15.9219 12.6973i −0.752237 0.599889i
449449 −0.135791 0.0309934i −0.00640836 0.00146267i 0.219316 0.975654i 0.429618π-0.429618\pi
−0.225724 + 0.974191i 0.572475π0.572475\pi
450450 0 0
451451 3.62379 4.54408i 0.170637 0.213973i
452452 −25.3371 −1.19176
453453 13.8148 17.3232i 0.649075 0.813914i
454454 2.08822 + 4.33623i 0.0980050 + 0.203509i
455455 0 0
456456 −19.8595 + 15.8374i −0.930005 + 0.741654i
457457 13.9188 28.9026i 0.651093 1.35201i −0.270073 0.962840i 0.587048π-0.587048\pi
0.921166 0.389169i 0.127238π-0.127238\pi
458458 60.5555 + 13.8214i 2.82957 + 0.645831i
459459 6.75864 + 29.6115i 0.315466 + 1.38215i
460460 0 0
461461 −0.314786 + 0.653661i −0.0146611 + 0.0304440i −0.908171 0.418600i 0.862521π-0.862521\pi
0.893510 + 0.449044i 0.148235π0.148235\pi
462462 −8.89502 38.9716i −0.413834 1.81312i
463463 9.14813i 0.425150i 0.977145 + 0.212575i 0.0681849π0.0681849\pi
−0.977145 + 0.212575i 0.931815π0.931815\pi
464464 1.91013 1.09585i 0.0886753 0.0508737i
465465 0 0
466466 −38.6407 + 8.81948i −1.78999 + 0.408554i
467467 27.6274 + 13.3047i 1.27844 + 0.615667i 0.944990 0.327099i 0.106071π-0.106071\pi
0.333455 + 0.942766i 0.391785π0.391785\pi
468468 2.79911 + 5.81242i 0.129389 + 0.268679i
469469 3.77897 + 16.5567i 0.174496 + 0.764519i
470470 0 0
471471 −48.2618 23.2417i −2.22379 1.07092i
472472 −1.69993 2.13165i −0.0782457 0.0981170i
473473 −20.1375 + 16.0591i −0.925924 + 0.738399i
474474 13.3728 + 27.7689i 0.614234 + 1.27547i
475475 0 0
476476 25.3705i 1.16285i
477477 −7.08894 5.65324i −0.324580 0.258844i
478478 −8.70595 + 38.1433i −0.398201 + 1.74463i
479479 5.16447 + 1.17876i 0.235971 + 0.0538588i 0.338871 0.940833i 0.389955π-0.389955\pi
−0.102900 + 0.994692i 0.532812π0.532812\pi
480480 0 0
481481 2.17506i 0.0991740i
482482 31.0873 38.9823i 1.41599 1.77559i
483483 0.920156 0.443124i 0.0418686 0.0201628i
484484 −9.37355 11.7541i −0.426070 0.534275i
485485 0 0
486486 −27.3935 13.1920i −1.24259 0.598401i
487487 −3.39429 0.774725i −0.153810 0.0351062i 0.144922 0.989443i 0.453707π-0.453707\pi
−0.298733 + 0.954337i 0.596564π0.596564\pi
488488 −8.05742 + 1.83905i −0.364742 + 0.0832500i
489489 −5.78905 + 2.78786i −0.261790 + 0.126071i
490490 0 0
491491 5.70489 1.30210i 0.257458 0.0587631i −0.0918437 0.995773i 0.529276π-0.529276\pi
0.349302 + 0.937010i 0.386419π0.386419\pi
492492 13.0597i 0.588776i
493493 25.8809 + 10.2393i 1.16562 + 0.461157i
494494 3.16931 0.142594
495495 0 0
496496 0.766191 1.59101i 0.0344030 0.0714385i
497497 9.11713 + 18.9319i 0.408959 + 0.849213i
498498 −52.9008 + 12.0743i −2.37054 + 0.541061i
499499 5.27783 23.1237i 0.236268 1.03516i −0.708060 0.706152i 0.750429π-0.750429\pi
0.944328 0.329005i 0.106713π-0.106713\pi
500500 0 0
501501 −26.0614 + 20.7833i −1.16434 + 0.928529i
502502 17.3234 13.8150i 0.773183 0.616593i
503503 −17.4212 + 8.38962i −0.776774 + 0.374075i −0.779887 0.625920i 0.784723π-0.784723\pi
0.00311266 + 0.999995i 0.499009π0.499009\pi
504504 −16.0402 12.7916i −0.714487 0.569784i
505505 0 0
506506 1.29302 1.62140i 0.0574819 0.0720801i
507507 −8.11345 + 35.5473i −0.360331 + 1.57871i
508508 12.2895 53.8437i 0.545257 2.38893i
509509 −24.2136 + 30.3629i −1.07325 + 1.34581i −0.138555 + 0.990355i 0.544246π0.544246\pi
−0.934693 + 0.355456i 0.884326π0.884326\pi
510510 0 0
511511 8.56742 + 6.83229i 0.379000 + 0.302243i
512512 4.16055 2.00362i 0.183872 0.0885482i
513513 15.8553 12.6441i 0.700027 0.558253i
514514 27.3081 21.7775i 1.20451 0.960565i
515515 0 0
516516 −12.8784 + 56.4240i −0.566941 + 2.48393i
517517 −37.0827 + 8.46389i −1.63090 + 0.372241i
518518 8.25408 + 17.1398i 0.362663 + 0.753078i
519519 −23.7731 + 49.3654i −1.04352 + 2.16690i
520520 0 0
521521 33.3472 1.46097 0.730484 0.682930i 0.239294π-0.239294\pi
0.730484 + 0.682930i 0.239294π0.239294\pi
522522 53.6928 30.8039i 2.35007 1.34825i
523523 31.8103i 1.39097i 0.718542 + 0.695484i 0.244810π0.244810\pi
−0.718542 + 0.695484i 0.755190π0.755190\pi
524524 10.2577 2.34124i 0.448108 0.102278i
525525 0 0
526526 −63.3246 + 30.4955i −2.76108 + 1.32967i
527527 21.7594 4.96643i 0.947853 0.216341i
528528 4.49917 + 1.02691i 0.195801 + 0.0446903i
529529 −20.6745 9.95634i −0.898893 0.432884i
530530 0 0
531531 3.32522 + 4.16969i 0.144302 + 0.180949i
532532 −15.2620 + 7.34977i −0.661689 + 0.318653i
533533 −0.369399 + 0.463212i −0.0160005 + 0.0200640i
534534 7.29632i 0.315742i
535535 0 0
536536 27.4678 + 6.26934i 1.18643 + 0.270794i
537537 −0.575443 + 2.52118i −0.0248322 + 0.108797i
538538 −24.5648 19.5897i −1.05906 0.844574i
539539 18.1175i 0.780375i
540540 0 0
541541 16.8087 + 34.9037i 0.722664 + 1.50063i 0.860105 + 0.510117i 0.170398π0.170398\pi
−0.137441 + 0.990510i 0.543888π0.543888\pi
542542 −47.5840 + 37.9470i −2.04391 + 1.62996i
543543 9.31969 + 11.6865i 0.399946 + 0.501517i
544544 28.4516 + 13.7016i 1.21985 + 0.587450i
545545 0 0
546546 0.906735 + 3.97267i 0.0388047 + 0.170014i
547547 2.59920 + 5.39730i 0.111134 + 0.230772i 0.949117 0.314925i 0.101979π-0.101979\pi
−0.837983 + 0.545697i 0.816265π0.816265\pi
548548 −15.6313 7.52765i −0.667737 0.321565i
549549 15.7610 3.59735i 0.672665 0.153531i
550550 0 0
551551 −1.33803 18.5353i −0.0570022 0.789632i
552552 1.69434i 0.0721159i
553553 1.66299 + 7.28605i 0.0707176 + 0.309834i
554554 −22.1940 + 46.0864i −0.942934 + 1.95802i
555555 0 0
556556 −0.417845 1.83070i −0.0177206 0.0776389i
557557 −1.83032 0.417760i −0.0775533 0.0177010i 0.183568 0.983007i 0.441235π-0.441235\pi
−0.261122 + 0.965306i 0.584092π0.584092\pi
558558 21.5373 44.7226i 0.911746 1.89326i
559559 2.05277 1.63703i 0.0868227 0.0692388i
560560 0 0
561561 25.3071 + 52.5508i 1.06847 + 2.21870i
562562 4.66602 5.85101i 0.196824 0.246810i
563563 −26.4739 −1.11574 −0.557872 0.829927i 0.688382π-0.688382\pi
−0.557872 + 0.829927i 0.688382π0.688382\pi
564564 −53.2877 + 66.8207i −2.24382 + 2.81366i
565565 0 0
566566 39.0633 + 8.91595i 1.64195 + 0.374765i
567567 1.81534 + 1.44769i 0.0762372 + 0.0607971i
568568 34.8605 1.46271
569569 9.99580 + 7.97139i 0.419046 + 0.334178i 0.810207 0.586144i 0.199355π-0.199355\pi
−0.391161 + 0.920322i 0.627926π0.627926\pi
570570 0 0
571571 −23.7265 29.7521i −0.992924 1.24509i −0.969431 0.245363i 0.921093π-0.921093\pi
−0.0234924 0.999724i 0.507479π-0.507479\pi
572572 3.15264 + 3.95329i 0.131819 + 0.165295i
573573 12.7054 26.3830i 0.530775 1.10216i
574574 1.15309 5.05201i 0.0481290 0.210867i
575575 0 0
576576 59.5426 28.6742i 2.48094 1.19476i
577577 −0.0921290 0.0443670i −0.00383538 0.00184702i 0.431965 0.901890i 0.357820π-0.357820\pi
−0.435800 + 0.900043i 0.643535π0.643535\pi
578578 4.90121 + 21.4736i 0.203863 + 0.893184i
579579 −7.69786 −0.319912
580580 0 0
581581 −13.1571 −0.545848
582582 −24.6735 108.102i −1.02275 4.48096i
583583 −6.40289 3.08347i −0.265181 0.127704i
584584 16.3793 7.88785i 0.677780 0.326402i
585585 0 0
586586 6.82964 29.9226i 0.282130 1.23609i
587587 0.319039 0.662492i 0.0131682 0.0273440i −0.894281 0.447506i 0.852312π-0.852312\pi
0.907449 + 0.420162i 0.138027π0.138027\pi
588588 25.3820 + 31.8280i 1.04674 + 1.31257i
589589 −9.29127 11.6509i −0.382840 0.480066i
590590 0 0
591591 32.8210 + 26.1739i 1.35008 + 1.07665i
592592 −2.19624 −0.0902647
593593 −34.9913 27.9046i −1.43692 1.14590i −0.964356 0.264607i 0.914758π-0.914758\pi
−0.472562 0.881297i 0.656671π-0.656671\pi
594594 51.6182 + 11.7815i 2.11792 + 0.483402i
595595 0 0
596596 10.0109 12.5532i 0.410061 0.514201i
597597 −42.6173 −1.74421
598598 −0.131808 + 0.165281i −0.00539001 + 0.00675886i
599599 −1.76159 3.65797i −0.0719764 0.149461i 0.861876 0.507119i 0.169290π-0.169290\pi
−0.933853 + 0.357658i 0.883575π0.883575\pi
600600 0 0
601601 −34.7392 + 27.7036i −1.41704 + 1.13005i −0.444921 + 0.895570i 0.646768π0.646768\pi
−0.972120 + 0.234483i 0.924660π0.924660\pi
602602 −9.96379 + 20.6900i −0.406094 + 0.843262i
603603 −53.7294 12.2634i −2.18803 0.499404i
604604 −5.45481 23.8991i −0.221953 0.972441i
605605 0 0
606606 −17.4393 + 36.2131i −0.708423 + 1.47106i
607607 2.15884 + 9.45849i 0.0876246 + 0.383908i 0.999656 0.0262110i 0.00834417π-0.00834417\pi
−0.912032 + 0.410119i 0.865487π0.865487\pi
608608 21.0848i 0.855100i
609609 22.8509 6.98013i 0.925964 0.282849i
610610 0 0
611611 3.78012 0.862787i 0.152927 0.0349046i
612612 74.1781 + 35.7223i 2.99847 + 1.44399i
613613 −0.774505 1.60828i −0.0312820 0.0649576i 0.884742 0.466081i 0.154334π-0.154334\pi
−0.916024 + 0.401123i 0.868620π0.868620\pi
614614 −3.28945 14.4120i −0.132751 0.581622i
615615 0 0
616616 −14.4879 6.97699i −0.583733 0.281111i
617617 5.43065 + 6.80982i 0.218630 + 0.274153i 0.879036 0.476756i 0.158187π-0.158187\pi
−0.660406 + 0.750909i 0.729616π0.729616\pi
618618 66.5321 53.0576i 2.67631 2.13429i
619619 6.16293 + 12.7975i 0.247709 + 0.514373i 0.987336 0.158644i 0.0507122π-0.0507122\pi
−0.739627 + 0.673017i 0.764998π0.764998\pi
620620 0 0
621621 1.35272i 0.0542826i
622622 43.5199 + 34.7060i 1.74499 + 1.39158i
623623 −0.393681 + 1.72483i −0.0157725 + 0.0691038i
624624 −0.458633 0.104680i −0.0183600 0.00419056i
625625 0 0
626626 4.47759i 0.178961i
627627 24.2813 30.4477i 0.969700 1.21597i
628628 −53.3947 + 25.7135i −2.13068 + 1.02608i
629629 −17.3069 21.7021i −0.690070 0.865320i
630630 0 0
631631 14.9293 + 7.18958i 0.594327 + 0.286213i 0.706768 0.707446i 0.250153π-0.250153\pi
−0.112441 + 0.993658i 0.535867π0.535867\pi
632632 12.0876 + 2.75892i 0.480820 + 0.109744i
633633 −33.1575 + 7.56798i −1.31789 + 0.300800i
634634 −60.6429 + 29.2041i −2.40844 + 1.15984i
635635 0 0
636636 −15.5682 + 3.55334i −0.617319 + 0.140899i
637637 1.84685i 0.0731748i
638638 35.6561 32.9029i 1.41164 1.30264i
639639 −68.1903 −2.69757
640640 0 0
641641 3.16628 6.57486i 0.125061 0.259691i −0.829033 0.559200i 0.811108π-0.811108\pi
0.954094 + 0.299509i 0.0968227π0.0968227\pi
642642 −25.9042 53.7906i −1.02236 2.12294i
643643 33.0214 7.53691i 1.30224 0.297227i 0.485499 0.874237i 0.338638π-0.338638\pi
0.816737 + 0.577010i 0.195781π0.195781\pi
644644 0.251430 1.10159i 0.00990774 0.0434086i
645645 0 0
646646 31.6225 25.2181i 1.24417 0.992194i
647647 −26.1482 + 20.8525i −1.02799 + 0.819795i −0.983807 0.179228i 0.942640π-0.942640\pi
−0.0441829 + 0.999023i 0.514068π0.514068\pi
648648 3.47059 1.67135i 0.136338 0.0656568i
649649 3.26815 + 2.60627i 0.128286 + 0.102305i
650650 0 0
651651 11.9459 14.9797i 0.468198 0.587101i
652652 −1.58184 + 6.93051i −0.0619497 + 0.271420i
653653 5.28615 23.1601i 0.206863 0.906326i −0.759776 0.650184i 0.774692π-0.774692\pi
0.966639 0.256141i 0.0824512π-0.0824512\pi
654654 23.1156 28.9861i 0.903893 1.13345i
655655 0 0
656656 0.467723 + 0.372997i 0.0182615 + 0.0145631i
657657 −32.0394 + 15.4294i −1.24998 + 0.601956i
658658 −26.5137 + 21.1440i −1.03361 + 0.824278i
659659 3.85540 3.07458i 0.150185 0.119769i −0.545515 0.838101i 0.683666π-0.683666\pi
0.695700 + 0.718333i 0.255094π0.255094\pi
660660 0 0
661661 5.22326 22.8846i 0.203161 0.890107i −0.765836 0.643036i 0.777675π-0.777675\pi
0.968997 0.247071i 0.0794682π-0.0794682\pi
662662 62.7318 14.3181i 2.43814 0.556489i
663663 −2.57975 5.35690i −0.100189 0.208045i
664664 −9.47070 + 19.6661i −0.367535 + 0.763193i
665665 0 0
666666 −61.7352 −2.39219
667667 1.02228 + 0.701082i 0.0395827 + 0.0271460i
668668 36.8790i 1.42689i
669669 37.0297 8.45179i 1.43165 0.326765i
670670 0 0
671671 11.4162 5.49774i 0.440717 0.212238i
672672 26.4293 6.03232i 1.01953 0.232702i
673673 29.1789 + 6.65990i 1.12477 + 0.256720i 0.744150 0.668013i 0.232855π-0.232855\pi
0.380616 + 0.924733i 0.375712π0.375712\pi
674674 −8.20794 3.95274i −0.316158 0.152254i
675675 0 0
676676 25.1512 + 31.5386i 0.967353 + 1.21302i
677677 −19.8360 + 9.55250i −0.762358 + 0.367132i −0.774318 0.632796i 0.781907π-0.781907\pi
0.0119603 + 0.999928i 0.496193π0.496193\pi
678678 32.3807 40.6041i 1.24357 1.55939i
679679 26.8862i 1.03180i
680680 0 0
681681 −5.87741 1.34148i −0.225223 0.0514056i
682682 8.65739 37.9305i 0.331508 1.45243i
683683 −3.60979 2.87871i −0.138125 0.110151i 0.551990 0.833851i 0.313869π-0.313869\pi
−0.690115 + 0.723700i 0.742440π0.742440\pi
684684 54.9715i 2.10189i
685685 0 0
686686 17.7667 + 36.8929i 0.678335 + 1.40858i
687687 −60.8282 + 48.5088i −2.32074 + 1.85073i
688688 −1.65297 2.07275i −0.0630188 0.0790230i
689689 0.652694 + 0.314321i 0.0248657 + 0.0119747i
690690 0 0
691691 7.95421 + 34.8497i 0.302592 + 1.32574i 0.866199 + 0.499700i 0.166556π0.166556\pi
−0.563606 + 0.826044i 0.690586π0.690586\pi
692692 26.3015 + 54.6157i 0.999834 + 2.07618i
693693 28.3396 + 13.6476i 1.07653 + 0.518430i
694694 7.85468 1.79278i 0.298160 0.0680530i
695695 0 0
696696 6.01513 39.1800i 0.228003 1.48511i
697697 7.56111i 0.286398i
698698 −1.68646 7.38886i −0.0638334 0.279672i
699699 21.5405 44.7293i 0.814737 1.69182i
700700 0 0
701701 −0.811010 3.55327i −0.0306314 0.134205i 0.957300 0.289096i 0.0933546π-0.0933546\pi
−0.987932 + 0.154891i 0.950497π0.950497\pi
702702 −5.26183 1.20098i −0.198595 0.0453280i
703703 −8.04145 + 16.6982i −0.303289 + 0.629786i
704704 40.4976 32.2958i 1.52631 1.21719i
705705 0 0
706706 −12.3143 25.5710i −0.463457 0.962377i
707707 −6.07652 + 7.61972i −0.228531 + 0.286569i
708708 9.39266 0.352998
709709 −13.0877 + 16.4114i −0.491518 + 0.616344i −0.964293 0.264839i 0.914681π-0.914681\pi
0.472774 + 0.881184i 0.343253π0.343253\pi
710710 0 0
711711 −23.6445 5.39670i −0.886737 0.202392i
712712 2.29475 + 1.83000i 0.0859994 + 0.0685822i
713713 0.994013 0.0372261
714714 40.6576 + 32.4233i 1.52157 + 1.21341i
715715 0 0
716716 1.78384 + 2.23686i 0.0666651 + 0.0835954i
717717 −30.5552 38.3150i −1.14110 1.43090i
718718 −18.1005 + 37.5860i −0.675503 + 1.40270i
719719 5.39677 23.6448i 0.201266 0.881803i −0.768902 0.639367i 0.779197π-0.779197\pi
0.970167 0.242436i 0.0779463π-0.0779463\pi
720720 0 0
721721 18.5908 8.95286i 0.692357 0.333422i
722722 14.4889 + 6.97750i 0.539222 + 0.259676i
723723 13.8975 + 60.8888i 0.516852 + 2.26448i
724724 16.5374 0.614607
725725 0 0
726726 30.8159 1.14368
727727 6.88385 + 30.1601i 0.255308 + 1.11858i 0.926203 + 0.377025i 0.123053π0.123053\pi
−0.670895 + 0.741552i 0.734090π0.734090\pi
728728 1.47686 + 0.711216i 0.0547359 + 0.0263594i
729729 38.3309 18.4592i 1.41966 0.683673i
730730 0 0
731731 7.45617 32.6676i 0.275776 1.20826i
732732 12.3533 25.6519i 0.456591 0.948122i
733733 11.5408 + 14.4717i 0.426268 + 0.534523i 0.947866 0.318668i 0.103235π-0.103235\pi
−0.521598 + 0.853191i 0.674664π0.674664\pi
734734 13.8991 + 17.4289i 0.513024 + 0.643312i
735735 0 0
736736 1.09958 + 0.876889i 0.0405312 + 0.0323225i
737737 −43.1955 −1.59113
738738 13.1475 + 10.4848i 0.483966 + 0.385950i
739739 33.1954 + 7.57663i 1.22111 + 0.278711i 0.784037 0.620714i 0.213157π-0.213157\pi
0.437075 + 0.899425i 0.356014π0.356014\pi
740740 0 0
741741 −2.47517 + 3.10376i −0.0909276 + 0.114020i
742742 −6.33614 −0.232607
743743 21.7142 27.2288i 0.796618 0.998927i −0.203187 0.979140i 0.565130π-0.565130\pi
0.999804 0.0197868i 0.00629873π-0.00629873\pi
744744 −13.7915 28.6384i −0.505622 1.04994i
745745 0 0
746746 39.3244 31.3602i 1.43977 1.14818i
747747 18.5255 38.4687i 0.677814 1.40750i
748748 62.9125 + 14.3594i 2.30031 + 0.525030i
749749 −3.22135 14.1136i −0.117705 0.515701i
750750 0 0
751751 −21.0818 + 43.7769i −0.769287 + 1.59744i 0.0322376 + 0.999480i 0.489737π0.489737\pi
−0.801525 + 0.597961i 0.795978π0.795978\pi
752752 −0.871188 3.81692i −0.0317690 0.139189i
753753 27.7544i 1.01143i
754754 −3.63469 + 3.35404i −0.132368 + 0.122147i
755755 0 0
756756 28.1237 6.41904i 1.02285 0.233458i
757757 −27.1118 13.0563i −0.985394 0.474541i −0.129437 0.991588i 0.541317π-0.541317\pi
−0.855957 + 0.517047i 0.827031π0.827031\pi
758758 8.56048 + 17.7760i 0.310931 + 0.645654i
759759 0.578041 + 2.53256i 0.0209816 + 0.0919262i
760760 0 0
761761 8.85531 + 4.26449i 0.321005 + 0.154588i 0.587446 0.809263i 0.300133π-0.300133\pi
−0.266441 + 0.963851i 0.585848π0.585848\pi
762762 70.5816 + 88.5066i 2.55690 + 3.20625i
763763 7.02845 5.60500i 0.254447 0.202915i
764764 −14.0567 29.1890i −0.508552 1.05602i
765765 0 0
766766 11.5342i 0.416749i
767767 −0.333147 0.265676i −0.0120292 0.00959300i
768768 8.38305 36.7285i 0.302497 1.32533i
769769 29.2236 + 6.67010i 1.05383 + 0.240530i 0.714137 0.700006i 0.246819π-0.246819\pi
0.339694 + 0.940536i 0.389677π0.389677\pi
770770 0 0
771771 43.7511i 1.57566i
772772 −5.30999 + 6.65852i −0.191111 + 0.239645i
773773 15.2398 7.33911i 0.548138 0.263969i −0.139253 0.990257i 0.544470π-0.544470\pi
0.687391 + 0.726287i 0.258756π0.258756\pi
774774 −46.4642 58.2642i −1.67012 2.09426i
775775 0 0
776776 −40.1872 19.3532i −1.44264 0.694738i
777777 −23.2316 5.30245i −0.833427 0.190224i
778778 65.9747 15.0583i 2.36531 0.539866i
779779 4.54849 2.19044i 0.162967 0.0784806i
780780 0 0
781781 −52.1067 + 11.8930i −1.86452 + 0.425565i
782782 2.69792i 0.0964776i
783783 −4.80232 + 31.2802i −0.171621 + 1.11786i
784784 −1.86483 −0.0666012
785785 0 0
786786 −9.35726 + 19.4306i −0.333763 + 0.693065i
787787 8.67579 + 18.0155i 0.309259 + 0.642182i 0.996440 0.0843036i 0.0268665π-0.0268665\pi
−0.687181 + 0.726486i 0.741152π0.741152\pi
788788 45.2800 10.3349i 1.61303 0.368164i
789789 19.5904 85.8312i 0.697437 3.05567i
790790 0 0
791791 9.84556 7.85157i 0.350068 0.279170i
792792 40.7986 32.5358i 1.44972 1.15611i
793793 −1.16374 + 0.560425i −0.0413255 + 0.0199013i
794794 −5.18173 4.13230i −0.183893 0.146650i
795795 0 0
796796 −29.3975 + 36.8632i −1.04197 + 1.30658i
797797 8.96777 39.2904i 0.317655 1.39174i −0.523999 0.851719i 0.675560π-0.675560\pi
0.841654 0.540017i 0.181582π-0.181582\pi
798798 7.72629 33.8511i 0.273508 1.19832i
799799 30.8518 38.6869i 1.09146 1.36865i
800800 0 0
801801 −4.48874 3.57965i −0.158602 0.126481i
802802 −41.7640 + 20.1125i −1.47474 + 0.710196i
803803 −21.7914 + 17.3781i −0.769003 + 0.613260i
804804 −75.8840 + 60.5155i −2.67622 + 2.13422i
805805 0 0
806806 −0.882512 + 3.86654i −0.0310851 + 0.136193i
807807 38.3692 8.75751i 1.35066 0.308279i
808808 7.01532 + 14.5675i 0.246798 + 0.512482i
809809 −21.7442 + 45.1522i −0.764484 + 1.58747i 0.0440579 + 0.999029i 0.485971π0.485971\pi
−0.808542 + 0.588439i 0.799743π0.799743\pi
810810 0 0
811811 24.7764 0.870017 0.435009 0.900426i 0.356745π-0.356745\pi
0.435009 + 0.900426i 0.356745π0.356745\pi
812812 9.72486 24.5805i 0.341276 0.862608i
813813 76.2357i 2.67370i
814814 −47.1741 + 10.7672i −1.65345 + 0.377390i
815815 0 0
816816 −5.40906 + 2.60487i −0.189355 + 0.0911885i
817817 −21.8117 + 4.97838i −0.763095 + 0.174171i
818818 −74.3122 16.9613i −2.59827 0.593037i
819819 −2.88886 1.39120i −0.100945 0.0486126i
820820 0 0
821821 22.1885 + 27.8235i 0.774384 + 0.971047i 0.999995 0.00317052i 0.00100921π-0.00100921\pi
−0.225611 + 0.974218i 0.572438π0.572438\pi
822822 32.0402 15.4298i 1.11753 0.538175i
823823 −9.60419 + 12.0433i −0.334781 + 0.419802i −0.920519 0.390699i 0.872233π-0.872233\pi
0.585738 + 0.810501i 0.300805π0.300805\pi
824824 34.2324i 1.19254i
825825 0 0
826826 3.63346 + 0.829313i 0.126424 + 0.0288555i
827827 9.21841 40.3885i 0.320556 1.40445i −0.516012 0.856581i 0.672584π-0.672584\pi
0.836567 0.547864i 0.184559π-0.184559\pi
828828 2.86680 + 2.28620i 0.0996282 + 0.0794508i
829829 4.64043i 0.161169i −0.996748 0.0805844i 0.974321π-0.974321\pi
0.996748 0.0805844i 0.0256787π-0.0256787\pi
830830 0 0
831831 −27.8001 57.7276i −0.964376 2.00255i
832832 −4.12823 + 3.29215i −0.143120 + 0.114135i
833833 −14.6953 18.4274i −0.509163 0.638470i
834834 3.46780 + 1.67000i 0.120080 + 0.0578275i
835835 0 0
836836 −9.58754 42.0058i −0.331592 1.45280i
837837 11.0108 + 22.8641i 0.380588 + 0.790300i
838838 −15.3851 7.40906i −0.531468 0.255942i
839839 −34.5374 + 7.88295i −1.19237 + 0.272150i −0.772248 0.635321i 0.780868π-0.780868\pi
−0.420117 + 0.907470i 0.638011π0.638011\pi
840840 0 0
841841 21.1502 + 19.8411i 0.729318 + 0.684175i
842842 46.2065i 1.59238i
843843 2.08593 + 9.13904i 0.0718431 + 0.314765i
844844 −16.3259 + 33.9011i −0.561960 + 1.16692i
845845 0 0
846846 −24.4887 107.292i −0.841939 3.68878i
847847 7.28479 + 1.66271i 0.250308 + 0.0571313i
848848 0.317382 0.659050i 0.0108989 0.0226319i
849849 −39.2392 + 31.2922i −1.34669 + 1.07395i
850850 0 0
851851 −0.536390 1.11383i −0.0183872 0.0381814i
852852 −74.8772 + 93.8930i −2.56525 + 3.21672i
853853 25.5045 0.873256 0.436628 0.899642i 0.356173π-0.356173\pi
0.436628 + 0.899642i 0.356173π0.356173\pi
854854 7.04367 8.83248i 0.241029 0.302241i
855855 0 0
856856 −23.4147 5.34424i −0.800296 0.182662i
857857 27.9793 + 22.3127i 0.955754 + 0.762189i 0.971341 0.237690i 0.0763902π-0.0763902\pi
−0.0155868 + 0.999879i 0.504962π0.504962\pi
858858 −10.3644 −0.353836
859859 −23.1233 18.4402i −0.788956 0.629171i 0.143830 0.989602i 0.454058π-0.454058\pi
−0.932786 + 0.360431i 0.882630π0.882630\pi
860860 0 0
861861 4.04699 + 5.07476i 0.137921 + 0.172947i
862862 −16.7340 20.9837i −0.569961 0.714709i
863863 17.4446 36.2241i 0.593822 1.23308i −0.360068 0.932926i 0.617246π-0.617246\pi
0.953890 0.300158i 0.0970393π-0.0970393\pi
864864 −7.98986 + 35.0058i −0.271820 + 1.19092i
865865 0 0
866866 34.9324 16.8225i 1.18705 0.571654i
867867 −24.8572 11.9706i −0.844196 0.406543i
868868 −4.71689 20.6661i −0.160102 0.701452i
869869 −19.0088 −0.644831
870870 0 0
871871 4.40323 0.149198
872872 −3.31869 14.5401i −0.112385 0.492390i
873873 78.6099 + 37.8565i 2.66054 + 1.28125i
874874 1.62297 0.781583i 0.0548979 0.0264374i
875875 0 0
876876 −13.9362 + 61.0583i −0.470859 + 2.06297i
877877 22.6064 46.9427i 0.763364 1.58514i −0.0467750 0.998905i 0.514894π-0.514894\pi
0.810139 0.586237i 0.199391π-0.199391\pi
878878 −26.5123 33.2454i −0.894747 1.12198i
879879 23.9699 + 30.0573i 0.808485 + 1.01381i
880880 0 0
881881 35.3863 + 28.2196i 1.19219 + 0.950743i 0.999534 0.0305225i 0.00971713π-0.00971713\pi
0.192660 + 0.981266i 0.438289π0.438289\pi
882882 −52.4196 −1.76506
883883 26.5025 + 21.1350i 0.891880 + 0.711251i 0.958063 0.286557i 0.0925107π-0.0925107\pi
−0.0661830 + 0.997808i 0.521082π0.521082\pi
884884 −6.41314 1.46376i −0.215697 0.0492315i
885885 0 0
886886 4.81273 6.03497i 0.161687 0.202749i
887887 −30.4108 −1.02110 −0.510548 0.859850i 0.670557π-0.670557\pi
−0.510548 + 0.859850i 0.670557π0.670557\pi
888888 −24.6481 + 30.9078i −0.827137 + 1.03720i
889889 11.9098 + 24.7310i 0.399443 + 0.829452i
890890 0 0
891891 −4.61737 + 3.68223i −0.154688 + 0.123359i
892892 18.2325 37.8601i 0.610469 1.26765i
893893 −32.2104 7.35181i −1.07788 0.246019i
894894 7.32341 + 32.0860i 0.244932 + 1.07312i
895895 0 0
896896 11.7562 24.4120i 0.392746 0.815546i
897897 −0.0589240 0.258163i −0.00196742 0.00861981i
898898 0.315858i 0.0105403i
899899 22.9856 + 3.52888i 0.766612 + 0.117695i
900900 0 0
901901 9.01346 2.05726i 0.300282 0.0685374i
902902 11.8751 + 5.71875i 0.395398 + 0.190414i
903903 −12.4806 25.9162i −0.415328 0.862437i
904904 −4.64886 20.3680i −0.154619 0.677430i
905905 0 0
906906 45.2709 + 21.8013i 1.50402 + 0.724300i
907907 9.90255 + 12.4174i 0.328809 + 0.412313i 0.918566 0.395267i 0.129348π-0.129348\pi
−0.589757 + 0.807580i 0.700777π0.700777\pi
908908 −5.21460 + 4.15851i −0.173053 + 0.138005i
909909 −13.7226 28.4953i −0.455150 0.945129i
910910 0 0
911911 24.9672i 0.827199i −0.910459 0.413600i 0.864271π-0.864271\pi
0.910459 0.413600i 0.135729π-0.135729\pi
912912 3.13399 + 2.49927i 0.103777 + 0.0827591i
913913 7.44675 32.6264i 0.246452 1.07977i
914914 70.9243 + 16.1880i 2.34597 + 0.535452i
915915 0 0
916916 86.0768i 2.84406i
917917 −3.26043 + 4.08845i −0.107669 + 0.135012i
918918 −62.0573 + 29.8852i −2.04819 + 0.986359i
919919 −8.39456 10.5264i −0.276911 0.347236i 0.623855 0.781540i 0.285566π-0.285566\pi
−0.900766 + 0.434305i 0.856994π0.856994\pi
920920 0 0
921921 16.6830 + 8.03409i 0.549722 + 0.264732i
922922 −1.60402 0.366107i −0.0528256 0.0120571i
923923 5.31162 1.21234i 0.174834 0.0399048i
924924 49.9104 24.0356i 1.64193 0.790712i
925925 0 0
926926 −20.2255 + 4.61634i −0.664651 + 0.151702i
927927 66.9616i 2.19931i
928928 22.3137 + 24.1809i 0.732484 + 0.793776i
929929 −7.53667 −0.247270 −0.123635 0.992328i 0.539455π-0.539455\pi
−0.123635 + 0.992328i 0.539455π0.539455\pi
930930 0 0
931931 −6.82803 + 14.1785i −0.223780 + 0.464683i
932932 −23.8315 49.4865i −0.780625 1.62099i
933933 −67.9764 + 15.5152i −2.22545 + 0.507944i
934934 −15.4738 + 67.7950i −0.506317 + 2.21832i
935935 0 0
936936 −4.15891 + 3.31662i −0.135938 + 0.108407i
937937 28.5083 22.7346i 0.931326 0.742708i −0.0351723 0.999381i 0.511198π-0.511198\pi
0.966498 + 0.256674i 0.0826266π0.0826266\pi
938938 −34.6982 + 16.7098i −1.13294 + 0.545593i
939939 4.38499 + 3.49691i 0.143099 + 0.114117i
940940 0 0
941941 21.9323 27.5023i 0.714973 0.896548i −0.283068 0.959100i 0.591352π-0.591352\pi
0.998042 + 0.0625515i 0.0199238π0.0199238\pi
942942 27.0308 118.430i 0.880712 3.85865i
943943 −0.0749333 + 0.328304i −0.00244016 + 0.0106911i
944944 −0.268263 + 0.336391i −0.00873122 + 0.0109486i
945945 0 0
946946 −45.6668 36.4180i −1.48476 1.18405i
947947 −9.36711 + 4.51096i −0.304390 + 0.146587i −0.579843 0.814728i 0.696886π-0.696886\pi
0.275453 + 0.961314i 0.411172π0.411172\pi
948948 −33.3940 + 26.6308i −1.08459 + 0.864928i
949949 2.22136 1.77148i 0.0721085 0.0575046i
950950 0 0
951951 18.7608 82.1964i 0.608361 2.66540i
952952 20.3948 4.65498i 0.660999 0.150869i
953953 −23.3495 48.4858i −0.756366 1.57061i −0.819818 0.572625i 0.805925π-0.805925\pi
0.0634519 0.997985i 0.479789π-0.479789\pi
954954 8.92146 18.5256i 0.288843 0.599789i
955955 0 0
956956 −54.2189 −1.75356
957957 4.37571 + 60.6152i 0.141446 + 1.95941i
958958 12.0129i 0.388119i
959959 8.40676 1.91879i 0.271468 0.0619609i
960960 0 0
961961 −11.1288 + 5.35937i −0.358995 + 0.172883i
962962 4.80881 1.09758i 0.155042 0.0353874i
963963 45.8012 + 10.4538i 1.47592 + 0.336870i
964964 62.2543 + 29.9801i 2.00508 + 0.965594i
965965 0 0
966966 1.44403 + 1.81075i 0.0464609 + 0.0582601i
967967 10.7168 5.16092i 0.344628 0.165964i −0.253561 0.967319i 0.581602π-0.581602\pi
0.598188 + 0.801356i 0.295887π0.295887\pi
968968 7.72899 9.69185i 0.248419 0.311508i
969969 50.6634i 1.62754i
970970 0 0
971971 −48.8341 11.1461i −1.56716 0.357694i −0.651183 0.758921i 0.725727π-0.725727\pi
−0.915979 + 0.401226i 0.868584π0.868584\pi
972972 9.37591 41.0785i 0.300732 1.31759i
973973 0.729672 + 0.581894i 0.0233922 + 0.0186547i
974974 7.89535i 0.252983i
975975 0 0
976976 0.565883 + 1.17507i 0.0181135 + 0.0376130i
977977 10.7983 8.61138i 0.345469 0.275502i −0.435348 0.900262i 0.643375π-0.643375\pi
0.780817 + 0.624760i 0.214803π0.214803\pi
978978 −9.08493 11.3921i −0.290504 0.364281i
979979 −4.05433 1.95246i −0.129577 0.0624010i
980980 0 0
981981 6.49165 + 28.4418i 0.207262 + 0.908076i
982982 5.75762 + 11.9558i 0.183733 + 0.381525i
983983 10.5011 + 5.05705i 0.334932 + 0.161295i 0.593789 0.804621i 0.297631π-0.297631\pi
−0.258857 + 0.965916i 0.583346π0.583346\pi
984984 10.4984 2.39619i 0.334677 0.0763879i
985985 0 0
986986 −9.57799 + 62.3869i −0.305025 + 1.98680i
987987 42.4784i 1.35210i
988988 0.977329 + 4.28196i 0.0310930 + 0.136227i
989989 0.647495 1.34454i 0.0205891 0.0427538i
990990 0 0
991991 1.54324 + 6.76136i 0.0490225 + 0.214782i 0.993506 0.113776i 0.0362946π-0.0362946\pi
−0.944484 + 0.328558i 0.893437π0.893437\pi
992992 25.7233 + 5.87117i 0.816715 + 0.186410i
993993 −34.9703 + 72.6165i −1.10975 + 2.30442i
994994 −37.2557 + 29.7104i −1.18168 + 0.942358i
995995 0 0
996996 −32.6264 67.7493i −1.03381 2.14672i
997997 −14.9450 + 18.7405i −0.473314 + 0.593516i −0.959979 0.280072i 0.909642π-0.909642\pi
0.486665 + 0.873588i 0.338213π0.338213\pi
998998 53.7872 1.70260
999999 19.6784 24.6759i 0.622597 0.780712i
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 725.2.p.a.399.4 24
5.2 odd 4 29.2.e.a.22.1 yes 12
5.3 odd 4 725.2.q.a.51.2 12
5.4 even 2 inner 725.2.p.a.399.1 24
15.2 even 4 261.2.o.a.109.2 12
20.7 even 4 464.2.y.d.225.2 12
29.4 even 14 inner 725.2.p.a.149.1 24
145.2 even 28 841.2.a.k.1.2 12
145.4 even 14 inner 725.2.p.a.149.4 24
145.7 odd 28 841.2.e.e.63.2 12
145.12 even 4 841.2.d.m.645.1 24
145.17 even 4 841.2.d.m.645.4 24
145.22 odd 28 841.2.e.f.63.1 12
145.27 even 28 841.2.a.k.1.11 12
145.32 even 28 841.2.d.k.778.1 24
145.33 odd 28 725.2.q.a.526.2 12
145.37 even 28 841.2.d.l.190.1 24
145.42 odd 28 841.2.e.e.267.2 12
145.47 even 28 841.2.d.k.574.4 24
145.52 odd 28 841.2.e.h.270.2 12
145.57 odd 4 841.2.e.i.196.2 12
145.62 odd 28 29.2.e.a.4.1 12
145.67 odd 28 841.2.e.h.651.2 12
145.72 even 28 841.2.d.l.571.4 24
145.77 even 28 841.2.d.m.605.4 24
145.82 odd 28 841.2.b.e.840.2 12
145.92 odd 28 841.2.b.e.840.11 12
145.97 even 28 841.2.d.m.605.1 24
145.102 even 28 841.2.d.l.571.1 24
145.107 odd 28 841.2.e.a.651.1 12
145.112 odd 28 841.2.e.i.236.2 12
145.122 odd 28 841.2.e.a.270.1 12
145.127 even 28 841.2.d.k.574.1 24
145.132 odd 28 841.2.e.f.267.1 12
145.137 even 28 841.2.d.l.190.4 24
145.142 even 28 841.2.d.k.778.4 24
435.2 odd 28 7569.2.a.bp.1.11 12
435.62 even 28 261.2.o.a.91.2 12
435.317 odd 28 7569.2.a.bp.1.2 12
580.207 even 28 464.2.y.d.33.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.2.e.a.4.1 12 145.62 odd 28
29.2.e.a.22.1 yes 12 5.2 odd 4
261.2.o.a.91.2 12 435.62 even 28
261.2.o.a.109.2 12 15.2 even 4
464.2.y.d.33.2 12 580.207 even 28
464.2.y.d.225.2 12 20.7 even 4
725.2.p.a.149.1 24 29.4 even 14 inner
725.2.p.a.149.4 24 145.4 even 14 inner
725.2.p.a.399.1 24 5.4 even 2 inner
725.2.p.a.399.4 24 1.1 even 1 trivial
725.2.q.a.51.2 12 5.3 odd 4
725.2.q.a.526.2 12 145.33 odd 28
841.2.a.k.1.2 12 145.2 even 28
841.2.a.k.1.11 12 145.27 even 28
841.2.b.e.840.2 12 145.82 odd 28
841.2.b.e.840.11 12 145.92 odd 28
841.2.d.k.574.1 24 145.127 even 28
841.2.d.k.574.4 24 145.47 even 28
841.2.d.k.778.1 24 145.32 even 28
841.2.d.k.778.4 24 145.142 even 28
841.2.d.l.190.1 24 145.37 even 28
841.2.d.l.190.4 24 145.137 even 28
841.2.d.l.571.1 24 145.102 even 28
841.2.d.l.571.4 24 145.72 even 28
841.2.d.m.605.1 24 145.97 even 28
841.2.d.m.605.4 24 145.77 even 28
841.2.d.m.645.1 24 145.12 even 4
841.2.d.m.645.4 24 145.17 even 4
841.2.e.a.270.1 12 145.122 odd 28
841.2.e.a.651.1 12 145.107 odd 28
841.2.e.e.63.2 12 145.7 odd 28
841.2.e.e.267.2 12 145.42 odd 28
841.2.e.f.63.1 12 145.22 odd 28
841.2.e.f.267.1 12 145.132 odd 28
841.2.e.h.270.2 12 145.52 odd 28
841.2.e.h.651.2 12 145.67 odd 28
841.2.e.i.196.2 12 145.57 odd 4
841.2.e.i.236.2 12 145.112 odd 28
7569.2.a.bp.1.2 12 435.317 odd 28
7569.2.a.bp.1.11 12 435.2 odd 28