Properties

Label 841.2.e.m.267.9
Level 841841
Weight 22
Character 841.267
Analytic conductor 6.7156.715
Analytic rank 00
Dimension 9696
Inner twists 1212

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [841,2,Mod(63,841)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(841, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("841.63");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 841=292 841 = 29^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 841.e (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: 6.715418809996.71541880999
Analytic rank: 00
Dimension: 9696
Relative dimension: 1616 over Q(ζ14)\Q(\zeta_{14})
Twist minimal: yes
Sato-Tate group: SU(2)[C14]\mathrm{SU}(2)[C_{14}]

Embedding invariants

Embedding label 267.9
Character χ\chi == 841.267
Dual form 841.2.e.m.63.9

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+(0.0327942+0.0261525i)q2+(2.95182+0.673734i)q3+(0.4446501.94814i)q4+(1.086141.36198i)q5+(0.0791828+0.0992921i)q6+(0.456981+2.00217i)q7+(0.07276570.151099i)q8+(5.55642+2.67583i)q9+(0.07123840.0162597i)q10+(0.8034881.66846i)q116.05014iq12+(2.322601.11851i)q13+(0.0673480+0.0537083i)q14+(4.123713.28855i)q15+(3.59437+1.73096i)q165.23359iq17+(0.112239+0.233066i)q18+(0.369537+0.0843444i)q19+(3.136281.51035i)q20+(2.69785+5.60215i)q21+(0.01728470.0757291i)q22+(2.26357+2.83842i)q23+(0.3165920.396994i)q24+(0.437322+1.91603i)q25+(0.105420+0.0240614i)q26+(7.49723+5.97884i)q27+4.10370q28+0.221238q30+(1.849521.47494i)q31+(0.4901490.111873i)q32+(1.247655.46633i)q33+(0.1368720.171631i)q34+(2.23056+2.79704i)q35+(2.7422312.0145i)q36+(2.84946+5.91697i)q37+(0.01432450.00689831i)q38+(7.609491.73682i)q39+(0.1267600.263221i)q40+9.44586iq41+(0.234984+0.113163i)q42+(0.778328+0.620696i)q43+(2.89312+2.30719i)q44+(9.679494.66140i)q45+0.152282iq46+(4.411539.16063i)q47+(11.7761+2.68782i)q48+(2.50694+1.20728i)q49+(0.0357675+0.0742719i)q50+(3.5260515.4486i)q51+(3.211764.02742i)q52+(6.191277.76360i)q53+(0.0895040+0.392143i)q54+(3.145110.717851i)q55+(0.269274+0.214739i)q561.14763q576.24449q59+(8.240166.57131i)q60+(7.785081.77689i)q61+(0.02208010.0967392i)q62+(7.89664+9.90207i)q63+(4.96161+6.22166i)q64+(0.9992954.37820i)q65+(0.1020420.211893i)q66+(3.728411.79551i)q67+(10.1958+2.32712i)q68+(4.76930+9.90355i)q69+0.150061iq70+(2.05682+0.990512i)q71+(0.8086330.644863i)q72+(7.086535.65132i)q73+(0.248190+0.119522i)q74+5.95042iq75+(0.328629+0.682406i)q76+(3.707710.846262i)q77+(0.294969+0.142050i)q78+(4.45891+9.25903i)q79+(1.54647+6.77552i)q80+(6.56684+8.23455i)q81+(0.247033+0.309770i)q82+(3.47592+15.2290i)q83+(12.1134+2.76480i)q84+(7.128045.68442i)q850.0417574q860.310570q88+(7.51879+5.99604i)q89+(0.439339+0.100276i)q90+(1.17805+5.16138i)q91+(4.523155.67185i)q92+(4.465735.59985i)q93+(0.09490090.415788i)q94+(0.286494+0.594912i)q95+(1.371460.660460i)q96+(5.047951.15216i)q97+(0.0506399+0.105155i)q9811.4207iq99+O(q100)q+(0.0327942 + 0.0261525i) q^{2} +(2.95182 + 0.673734i) q^{3} +(-0.444650 - 1.94814i) q^{4} +(1.08614 - 1.36198i) q^{5} +(0.0791828 + 0.0992921i) q^{6} +(-0.456981 + 2.00217i) q^{7} +(0.0727657 - 0.151099i) q^{8} +(5.55642 + 2.67583i) q^{9} +(0.0712384 - 0.0162597i) q^{10} +(-0.803488 - 1.66846i) q^{11} -6.05014i q^{12} +(2.32260 - 1.11851i) q^{13} +(-0.0673480 + 0.0537083i) q^{14} +(4.12371 - 3.28855i) q^{15} +(-3.59437 + 1.73096i) q^{16} -5.23359i q^{17} +(0.112239 + 0.233066i) q^{18} +(-0.369537 + 0.0843444i) q^{19} +(-3.13628 - 1.51035i) q^{20} +(-2.69785 + 5.60215i) q^{21} +(0.0172847 - 0.0757291i) q^{22} +(2.26357 + 2.83842i) q^{23} +(0.316592 - 0.396994i) q^{24} +(0.437322 + 1.91603i) q^{25} +(0.105420 + 0.0240614i) q^{26} +(7.49723 + 5.97884i) q^{27} +4.10370 q^{28} +0.221238 q^{30} +(-1.84952 - 1.47494i) q^{31} +(-0.490149 - 0.111873i) q^{32} +(-1.24765 - 5.46633i) q^{33} +(0.136872 - 0.171631i) q^{34} +(2.23056 + 2.79704i) q^{35} +(2.74223 - 12.0145i) q^{36} +(-2.84946 + 5.91697i) q^{37} +(-0.0143245 - 0.00689831i) q^{38} +(7.60949 - 1.73682i) q^{39} +(-0.126760 - 0.263221i) q^{40} +9.44586i q^{41} +(-0.234984 + 0.113163i) q^{42} +(-0.778328 + 0.620696i) q^{43} +(-2.89312 + 2.30719i) q^{44} +(9.67949 - 4.66140i) q^{45} +0.152282i q^{46} +(-4.41153 - 9.16063i) q^{47} +(-11.7761 + 2.68782i) q^{48} +(2.50694 + 1.20728i) q^{49} +(-0.0357675 + 0.0742719i) q^{50} +(3.52605 - 15.4486i) q^{51} +(-3.21176 - 4.02742i) q^{52} +(6.19127 - 7.76360i) q^{53} +(0.0895040 + 0.392143i) q^{54} +(-3.14511 - 0.717851i) q^{55} +(0.269274 + 0.214739i) q^{56} -1.14763 q^{57} -6.24449 q^{59} +(-8.24016 - 6.57131i) q^{60} +(-7.78508 - 1.77689i) q^{61} +(-0.0220801 - 0.0967392i) q^{62} +(-7.89664 + 9.90207i) q^{63} +(4.96161 + 6.22166i) q^{64} +(0.999295 - 4.37820i) q^{65} +(0.102042 - 0.211893i) q^{66} +(-3.72841 - 1.79551i) q^{67} +(-10.1958 + 2.32712i) q^{68} +(4.76930 + 9.90355i) q^{69} +0.150061i q^{70} +(-2.05682 + 0.990512i) q^{71} +(0.808633 - 0.644863i) q^{72} +(7.08653 - 5.65132i) q^{73} +(-0.248190 + 0.119522i) q^{74} +5.95042i q^{75} +(0.328629 + 0.682406i) q^{76} +(3.70771 - 0.846262i) q^{77} +(0.294969 + 0.142050i) q^{78} +(-4.45891 + 9.25903i) q^{79} +(-1.54647 + 6.77552i) q^{80} +(6.56684 + 8.23455i) q^{81} +(-0.247033 + 0.309770i) q^{82} +(3.47592 + 15.2290i) q^{83} +(12.1134 + 2.76480i) q^{84} +(-7.12804 - 5.68442i) q^{85} -0.0417574 q^{86} -0.310570 q^{88} +(7.51879 + 5.99604i) q^{89} +(0.439339 + 0.100276i) q^{90} +(1.17805 + 5.16138i) q^{91} +(4.52315 - 5.67185i) q^{92} +(-4.46573 - 5.59985i) q^{93} +(0.0949009 - 0.415788i) q^{94} +(-0.286494 + 0.594912i) q^{95} +(-1.37146 - 0.660460i) q^{96} +(5.04795 - 1.15216i) q^{97} +(0.0506399 + 0.105155i) q^{98} -11.4207i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 96q+12q42q5+6q6+16q98q13+4q16+14q20+50q22+14q2350q24+26q25300q28312q30+24q3410q35+38q3628q38+4q96+O(q100) 96 q + 12 q^{4} - 2 q^{5} + 6 q^{6} + 16 q^{9} - 8 q^{13} + 4 q^{16} + 14 q^{20} + 50 q^{22} + 14 q^{23} - 50 q^{24} + 26 q^{25} - 300 q^{28} - 312 q^{30} + 24 q^{34} - 10 q^{35} + 38 q^{36} - 28 q^{38}+ \cdots - 4 q^{96}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/841Z)×\left(\mathbb{Z}/841\mathbb{Z}\right)^\times.

nn 22
χ(n)\chi(n) e(314)e\left(\frac{3}{14}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.0327942 + 0.0261525i 0.0231890 + 0.0184926i 0.635016 0.772499i 0.280994π-0.280994\pi
−0.611827 + 0.790992i 0.709565π0.709565\pi
33 2.95182 + 0.673734i 1.70423 + 0.388980i 0.960233 0.279198i 0.0900687π-0.0900687\pi
0.744001 + 0.668179i 0.232926π0.232926\pi
44 −0.444650 1.94814i −0.222325 0.974070i
55 1.08614 1.36198i 0.485738 0.609096i −0.477208 0.878790i 0.658351π-0.658351\pi
0.962946 + 0.269695i 0.0869227π0.0869227\pi
66 0.0791828 + 0.0992921i 0.0323262 + 0.0405358i
77 −0.456981 + 2.00217i −0.172723 + 0.756748i 0.812147 + 0.583453i 0.198299π0.198299\pi
−0.984870 + 0.173295i 0.944559π0.944559\pi
88 0.0727657 0.151099i 0.0257265 0.0534217i
99 5.55642 + 2.67583i 1.85214 + 0.891944i
1010 0.0712384 0.0162597i 0.0225276 0.00514177i
1111 −0.803488 1.66846i −0.242261 0.503060i 0.744016 0.668162i 0.232919π-0.232919\pi
−0.986276 + 0.165102i 0.947205π0.947205\pi
1212 6.05014i 1.74652i
1313 2.32260 1.11851i 0.644175 0.310218i −0.0831241 0.996539i 0.526490π-0.526490\pi
0.727299 + 0.686321i 0.240775π0.240775\pi
1414 −0.0673480 + 0.0537083i −0.0179995 + 0.0143541i
1515 4.12371 3.28855i 1.06474 0.849099i
1616 −3.59437 + 1.73096i −0.898592 + 0.432739i
1717 5.23359i 1.26933i −0.772787 0.634666i 0.781138π-0.781138\pi
0.772787 0.634666i 0.218862π-0.218862\pi
1818 0.112239 + 0.233066i 0.0264549 + 0.0549342i
1919 −0.369537 + 0.0843444i −0.0847776 + 0.0193499i −0.264699 0.964331i 0.585273π-0.585273\pi
0.179922 + 0.983681i 0.442416π0.442416\pi
2020 −3.13628 1.51035i −0.701294 0.337725i
2121 −2.69785 + 5.60215i −0.588720 + 1.22249i
2222 0.0172847 0.0757291i 0.00368510 0.0161455i
2323 2.26357 + 2.83842i 0.471986 + 0.591852i 0.959656 0.281176i 0.0907245π-0.0907245\pi
−0.487670 + 0.873028i 0.662153π0.662153\pi
2424 0.316592 0.396994i 0.0646241 0.0810360i
2525 0.437322 + 1.91603i 0.0874644 + 0.383207i
2626 0.105420 + 0.0240614i 0.0206745 + 0.00471883i
2727 7.49723 + 5.97884i 1.44284 + 1.15063i
2828 4.10370 0.775526
2929 0 0
3030 0.221238 0.0403923
3131 −1.84952 1.47494i −0.332184 0.264908i 0.443166 0.896439i 0.353855π-0.353855\pi
−0.775350 + 0.631532i 0.782427π0.782427\pi
3232 −0.490149 0.111873i −0.0866470 0.0197766i
3333 −1.24765 5.46633i −0.217189 0.951566i
3434 0.136872 0.171631i 0.0234733 0.0294346i
3535 2.23056 + 2.79704i 0.377034 + 0.472785i
3636 2.74223 12.0145i 0.457038 2.00242i
3737 −2.84946 + 5.91697i −0.468449 + 0.972744i 0.524186 + 0.851604i 0.324369π0.324369\pi
−0.992635 + 0.121141i 0.961345π0.961345\pi
3838 −0.0143245 0.00689831i −0.00232374 0.00111905i
3939 7.60949 1.73682i 1.21849 0.278113i
4040 −0.126760 0.263221i −0.0200426 0.0416189i
4141 9.44586i 1.47520i 0.675240 + 0.737598i 0.264040π0.264040\pi
−0.675240 + 0.737598i 0.735960π0.735960\pi
4242 −0.234984 + 0.113163i −0.0362589 + 0.0174614i
4343 −0.778328 + 0.620696i −0.118694 + 0.0946553i −0.681038 0.732248i 0.738471π-0.738471\pi
0.562344 + 0.826903i 0.309900π0.309900\pi
4444 −2.89312 + 2.30719i −0.436155 + 0.347822i
4545 9.67949 4.66140i 1.44293 0.694880i
4646 0.152282i 0.0224527i
4747 −4.41153 9.16063i −0.643487 1.33621i −0.926208 0.377013i 0.876951π-0.876951\pi
0.282721 0.959202i 0.408763π-0.408763\pi
4848 −11.7761 + 2.68782i −1.69974 + 0.387954i
4949 2.50694 + 1.20728i 0.358135 + 0.172469i
5050 −0.0357675 + 0.0742719i −0.00505828 + 0.0105036i
5151 3.52605 15.4486i 0.493745 2.16324i
5252 −3.21176 4.02742i −0.445391 0.558502i
5353 6.19127 7.76360i 0.850436 1.06641i −0.146579 0.989199i 0.546826π-0.546826\pi
0.997015 0.0772140i 0.0246025π-0.0246025\pi
5454 0.0895040 + 0.392143i 0.0121800 + 0.0533639i
5555 −3.14511 0.717851i −0.424087 0.0967950i
5656 0.269274 + 0.214739i 0.0359832 + 0.0286956i
5757 −1.14763 −0.152008
5858 0 0
5959 −6.24449 −0.812963 −0.406482 0.913659i 0.633244π-0.633244\pi
−0.406482 + 0.913659i 0.633244π0.633244\pi
6060 −8.24016 6.57131i −1.06380 0.848352i
6161 −7.78508 1.77689i −0.996777 0.227508i −0.307141 0.951664i 0.599372π-0.599372\pi
−0.689636 + 0.724156i 0.742229π0.742229\pi
6262 −0.0220801 0.0967392i −0.00280417 0.0122859i
6363 −7.89664 + 9.90207i −0.994883 + 1.24754i
6464 4.96161 + 6.22166i 0.620201 + 0.777708i
6565 0.999295 4.37820i 0.123947 0.543049i
6666 0.102042 0.211893i 0.0125606 0.0260823i
6767 −3.72841 1.79551i −0.455498 0.219356i 0.192044 0.981386i 0.438489π-0.438489\pi
−0.647542 + 0.762030i 0.724203π0.724203\pi
6868 −10.1958 + 2.32712i −1.23642 + 0.282204i
6969 4.76930 + 9.90355i 0.574156 + 1.19225i
7070 0.150061i 0.0179358i
7171 −2.05682 + 0.990512i −0.244100 + 0.117552i −0.551934 0.833888i 0.686110π-0.686110\pi
0.307834 + 0.951440i 0.400396π0.400396\pi
7272 0.808633 0.644863i 0.0952983 0.0759979i
7373 7.08653 5.65132i 0.829416 0.661437i −0.113842 0.993499i 0.536316π-0.536316\pi
0.943258 + 0.332062i 0.107744π0.107744\pi
7474 −0.248190 + 0.119522i −0.0288515 + 0.0138941i
7575 5.95042i 0.687096i
7676 0.328629 + 0.682406i 0.0376964 + 0.0782774i
7777 3.70771 0.846262i 0.422533 0.0964405i
7878 0.294969 + 0.142050i 0.0333987 + 0.0160840i
7979 −4.45891 + 9.25903i −0.501667 + 1.04172i 0.484318 + 0.874892i 0.339068π0.339068\pi
−0.985986 + 0.166831i 0.946647π0.946647\pi
8080 −1.54647 + 6.77552i −0.172900 + 0.757526i
8181 6.56684 + 8.23455i 0.729648 + 0.914950i
8282 −0.247033 + 0.309770i −0.0272802 + 0.0342083i
8383 3.47592 + 15.2290i 0.381532 + 1.67160i 0.692685 + 0.721240i 0.256428π0.256428\pi
−0.311153 + 0.950360i 0.600715π0.600715\pi
8484 12.1134 + 2.76480i 1.32168 + 0.301664i
8585 −7.12804 5.68442i −0.773145 0.616562i
8686 −0.0417574 −0.00450282
8787 0 0
8888 −0.310570 −0.0331069
8989 7.51879 + 5.99604i 0.796990 + 0.635578i 0.934918 0.354864i 0.115473π-0.115473\pi
−0.137928 + 0.990442i 0.544044π0.544044\pi
9090 0.439339 + 0.100276i 0.0463103 + 0.0105700i
9191 1.17805 + 5.16138i 0.123493 + 0.541059i
9292 4.52315 5.67185i 0.471571 0.591331i
9393 −4.46573 5.59985i −0.463075 0.580677i
9494 0.0949009 0.415788i 0.00978828 0.0428853i
9595 −0.286494 + 0.594912i −0.0293937 + 0.0610367i
9696 −1.37146 0.660460i −0.139974 0.0674079i
9797 5.04795 1.15216i 0.512542 0.116984i 0.0415754 0.999135i 0.486762π-0.486762\pi
0.470967 + 0.882151i 0.343905π0.343905\pi
9898 0.0506399 + 0.105155i 0.00511540 + 0.0106222i
9999 11.4207i 1.14782i
100100 3.53825 1.70393i 0.353825 0.170393i
101101 −6.61542 + 5.27562i −0.658259 + 0.524944i −0.894681 0.446706i 0.852597π-0.852597\pi
0.236421 + 0.971651i 0.424025π0.424025\pi
102102 0.519654 0.414410i 0.0514534 0.0410327i
103103 −3.16609 + 1.52471i −0.311964 + 0.150234i −0.583314 0.812247i 0.698244π-0.698244\pi
0.271350 + 0.962481i 0.412530π0.412530\pi
104104 0.432333i 0.0423938i
105105 4.69976 + 9.75915i 0.458650 + 0.952396i
106106 0.406076 0.0926841i 0.0394415 0.00900228i
107107 4.00371 + 1.92808i 0.387053 + 0.186395i 0.617283 0.786741i 0.288234π-0.288234\pi
−0.230230 + 0.973136i 0.573948π0.573948\pi
108108 8.31397 17.2641i 0.800012 1.66124i
109109 −2.61746 + 11.4679i −0.250708 + 1.09842i 0.680159 + 0.733064i 0.261911π0.261911\pi
−0.930867 + 0.365358i 0.880947π0.880947\pi
110110 −0.0843679 0.105794i −0.00804416 0.0100871i
111111 −12.3976 + 15.5461i −1.17673 + 1.47557i
112112 −1.82310 7.98753i −0.172267 0.754751i
113113 −11.1334 2.54113i −1.04734 0.239049i −0.335977 0.941870i 0.609066π-0.609066\pi
−0.711367 + 0.702821i 0.751923π0.751923\pi
114114 −0.0376357 0.0300135i −0.00352491 0.00281102i
115115 6.32443 0.589756
116116 0 0
117117 15.8983 1.46980
118118 −0.204783 0.163309i −0.0188518 0.0150338i
119119 10.4785 + 2.39165i 0.960564 + 0.219242i
120120 −0.196833 0.862383i −0.0179683 0.0787245i
121121 4.72022 5.91897i 0.429111 0.538088i
122122 −0.208835 0.261871i −0.0189071 0.0237087i
123123 −6.36400 + 27.8825i −0.573822 + 2.51408i
124124 −2.05101 + 4.25896i −0.184186 + 0.382466i
125125 10.9322 + 5.26467i 0.977805 + 0.470886i
126126 −0.517928 + 0.118214i −0.0461407 + 0.0105313i
127127 −5.22667 10.8533i −0.463792 0.963074i −0.993386 0.114823i 0.963370π-0.963370\pi
0.529594 0.848251i 0.322344π-0.322344\pi
128128 1.33930i 0.118379i
129129 −2.71567 + 1.30780i −0.239101 + 0.115145i
130130 0.147272 0.117446i 0.0129166 0.0103007i
131131 −11.4103 + 9.09941i −0.996922 + 0.795019i −0.978800 0.204817i 0.934340π-0.934340\pi
−0.0181218 + 0.999836i 0.505769π0.505769\pi
132132 −10.0944 + 4.86121i −0.878606 + 0.423114i
133133 0.778418i 0.0674974i
134134 −0.0753133 0.156390i −0.00650608 0.0135100i
135135 16.2861 3.71720i 1.40169 0.319925i
136136 −0.790793 0.380826i −0.0678099 0.0326555i
137137 1.24195 2.57894i 0.106107 0.220334i −0.841155 0.540795i 0.818124π-0.818124\pi
0.947262 + 0.320461i 0.103838π0.103838\pi
138138 −0.102597 + 0.449509i −0.00873367 + 0.0382647i
139139 −13.8841 17.4101i −1.17763 1.47670i −0.845910 0.533326i 0.820942π-0.820942\pi
−0.331722 0.943377i 0.607630π-0.607630\pi
140140 4.45720 5.58915i 0.376702 0.472370i
141141 −6.85021 30.0127i −0.576892 2.52753i
142142 −0.0933562 0.0213079i −0.00783428 0.00178812i
143143 −3.73237 2.97647i −0.312117 0.248905i
144144 −24.6036 −2.05030
145145 0 0
146146 0.380194 0.0314650
147147 6.58666 + 5.25269i 0.543259 + 0.433235i
148148 12.7941 + 2.92017i 1.05167 + 0.240037i
149149 0.942652 + 4.13003i 0.0772250 + 0.338345i 0.998751 0.0499728i 0.0159134π-0.0159134\pi
−0.921526 + 0.388318i 0.873056π0.873056\pi
150150 −0.155619 + 0.195140i −0.0127062 + 0.0159331i
151151 −4.85985 6.09406i −0.395489 0.495927i 0.543723 0.839265i 0.317014π-0.317014\pi
−0.939212 + 0.343337i 0.888443π0.888443\pi
152152 −0.0141452 + 0.0619742i −0.00114733 + 0.00502677i
153153 14.0042 29.0800i 1.13217 2.35098i
154154 0.143723 + 0.0692136i 0.0115816 + 0.00557739i
155155 −4.01768 + 0.917010i −0.322708 + 0.0736560i
156156 −6.76712 14.0521i −0.541803 1.12507i
157157 6.32741i 0.504982i 0.967599 + 0.252491i 0.0812498π0.0812498\pi
−0.967599 + 0.252491i 0.918750π0.918750\pi
158158 −0.388374 + 0.187031i −0.0308973 + 0.0148794i
159159 23.5061 18.7455i 1.86416 1.48661i
160160 −0.684741 + 0.546063i −0.0541335 + 0.0431700i
161161 −6.71740 + 3.23493i −0.529405 + 0.254948i
162162 0.441785i 0.0347099i
163163 0.763393 + 1.58520i 0.0597936 + 0.124163i 0.928724 0.370771i 0.120907π-0.120907\pi
−0.868931 + 0.494934i 0.835192π0.835192\pi
164164 18.4019 4.20011i 1.43694 0.327973i
165165 −8.80016 4.23793i −0.685092 0.329923i
166166 −0.284287 + 0.590327i −0.0220649 + 0.0458183i
167167 −3.09755 + 13.5713i −0.239696 + 1.05018i 0.701594 + 0.712577i 0.252472π0.252472\pi
−0.941290 + 0.337600i 0.890385π0.890385\pi
168168 0.650171 + 0.815288i 0.0501618 + 0.0629009i
169169 −3.96193 + 4.96811i −0.304764 + 0.382162i
170170 −0.0850966 0.372832i −0.00652661 0.0285949i
171171 −2.27899 0.520165i −0.174279 0.0397780i
172172 1.55529 + 1.24030i 0.118590 + 0.0945720i
173173 8.38553 0.637540 0.318770 0.947832i 0.396730π-0.396730\pi
0.318770 + 0.947832i 0.396730π0.396730\pi
174174 0 0
175175 −4.03606 −0.305098
176176 5.77606 + 4.60626i 0.435387 + 0.347210i
177177 −18.4326 4.20712i −1.38548 0.316227i
178178 0.0897614 + 0.393271i 0.00672790 + 0.0294769i
179179 12.2675 15.3829i 0.916914 1.14977i −0.0714156 0.997447i 0.522752π-0.522752\pi
0.988330 0.152328i 0.0486769π-0.0486769\pi
180180 −13.3850 16.7843i −0.997662 1.25103i
181181 −2.68216 + 11.7513i −0.199364 + 0.873469i 0.771953 + 0.635679i 0.219280π0.219280\pi
−0.971317 + 0.237789i 0.923577π0.923577\pi
182182 −0.0963498 + 0.200072i −0.00714192 + 0.0148303i
183183 −21.7830 10.4901i −1.61025 0.775453i
184184 0.593594 0.135484i 0.0437603 0.00998801i
185185 4.96387 + 10.3076i 0.364951 + 0.757829i
186186 0.300433i 0.0220288i
187187 −8.73204 + 4.20513i −0.638550 + 0.307509i
188188 −15.8846 + 12.6675i −1.15850 + 0.923876i
189189 −15.3967 + 12.2785i −1.11995 + 0.893128i
190190 −0.0249538 + 0.0120171i −0.00181034 + 0.000871813i
191191 11.6202i 0.840810i −0.907337 0.420405i 0.861888π-0.861888\pi
0.907337 0.420405i 0.138112π-0.138112\pi
192192 10.4540 + 21.7080i 0.754455 + 1.56664i
193193 −18.5748 + 4.23958i −1.33704 + 0.305172i −0.830489 0.557035i 0.811939π-0.811939\pi
−0.506556 + 0.862207i 0.669082π0.669082\pi
194194 0.195676 + 0.0942324i 0.0140487 + 0.00676549i
195195 5.89948 12.2504i 0.422470 0.877269i
196196 1.23724 5.42070i 0.0883742 0.387193i
197197 10.4165 + 13.0618i 0.742142 + 0.930616i 0.999361 0.0357368i 0.0113778π-0.0113778\pi
−0.257220 + 0.966353i 0.582806π0.582806\pi
198198 0.298679 0.374532i 0.0212262 0.0266168i
199199 1.98233 + 8.68517i 0.140524 + 0.615676i 0.995313 + 0.0967009i 0.0308290π0.0308290\pi
−0.854790 + 0.518975i 0.826314π0.826314\pi
200200 0.321334 + 0.0733423i 0.0227217 + 0.00518608i
201201 −9.79591 7.81197i −0.690950 0.551014i
202202 −0.354918 −0.0249720
203203 0 0
204204 −31.6639 −2.21692
205205 12.8651 + 10.2596i 0.898536 + 0.716558i
206206 −0.143704 0.0327996i −0.0100124 0.00228526i
207207 4.98219 + 21.8284i 0.346286 + 1.51718i
208208 −6.41221 + 8.04065i −0.444607 + 0.557519i
209209 0.437644 + 0.548788i 0.0302725 + 0.0379605i
210210 −0.101101 + 0.442954i −0.00697666 + 0.0305668i
211211 0.110300 0.229041i 0.00759339 0.0157678i −0.897138 0.441751i 0.854357π-0.854357\pi
0.904731 + 0.425983i 0.140072π0.140072\pi
212212 −17.8775 8.60937i −1.22783 0.591294i
213213 −6.73870 + 1.53807i −0.461728 + 0.105386i
214214 0.0808742 + 0.167937i 0.00552844 + 0.0114799i
215215 1.73423i 0.118274i
216216 1.44894 0.697773i 0.0985879 0.0474774i
217217 3.79828 3.02902i 0.257844 0.205624i
218218 −0.385751 + 0.307626i −0.0261264 + 0.0208351i
219219 24.7257 11.9072i 1.67080 0.804617i
220220 6.44631i 0.434610i
221221 −5.85381 12.1556i −0.393770 0.817671i
222222 −0.813137 + 0.185593i −0.0545742 + 0.0124562i
223223 −8.24994 3.97296i −0.552457 0.266049i 0.136760 0.990604i 0.456331π-0.456331\pi
−0.689217 + 0.724555i 0.742045π0.742045\pi
224224 0.447978 0.930236i 0.0299318 0.0621540i
225225 −2.69704 + 11.8165i −0.179802 + 0.787766i
226226 −0.298655 0.374501i −0.0198662 0.0249114i
227227 −3.00177 + 3.76410i −0.199234 + 0.249832i −0.871405 0.490564i 0.836791π-0.836791\pi
0.672171 + 0.740396i 0.265362π0.265362\pi
228228 0.510295 + 2.23575i 0.0337951 + 0.148066i
229229 6.69386 + 1.52783i 0.442343 + 0.100962i 0.437891 0.899028i 0.355726π-0.355726\pi
0.00445223 + 0.999990i 0.498583π0.498583\pi
230230 0.207405 + 0.165400i 0.0136759 + 0.0109061i
231231 11.5147 0.757609
232232 0 0
233233 17.2302 1.12879 0.564393 0.825507i 0.309110π-0.309110\pi
0.564393 + 0.825507i 0.309110π0.309110\pi
234234 0.521372 + 0.415781i 0.0340832 + 0.0271804i
235235 −17.2681 3.94134i −1.12645 0.257105i
236236 2.77661 + 12.1651i 0.180742 + 0.791883i
237237 −19.4000 + 24.3269i −1.26017 + 1.58020i
238238 0.281087 + 0.352472i 0.0182202 + 0.0228474i
239239 4.74062 20.7700i 0.306645 1.34350i −0.553244 0.833019i 0.686610π-0.686610\pi
0.859889 0.510481i 0.170533π-0.170533\pi
240240 −9.12979 + 18.9582i −0.589325 + 1.22375i
241241 −8.10252 3.90197i −0.521929 0.251348i 0.154320 0.988021i 0.450681π-0.450681\pi
−0.676249 + 0.736673i 0.736396π0.736396\pi
242242 0.309592 0.0706623i 0.0199013 0.00454235i
243243 1.35428 + 2.81220i 0.0868773 + 0.180402i
244244 15.9565i 1.02151i
245245 4.36719 2.10313i 0.279010 0.134364i
246246 −0.937900 + 0.747950i −0.0597983 + 0.0476876i
247247 −0.763948 + 0.609229i −0.0486089 + 0.0387643i
248248 −0.357445 + 0.172136i −0.0226978 + 0.0109307i
249249 47.2951i 2.99721i
250250 0.220829 + 0.458555i 0.0139664 + 0.0290016i
251251 6.33959 1.44697i 0.400151 0.0913319i −0.0177090 0.999843i 0.505637π-0.505637\pi
0.417860 + 0.908511i 0.362780π0.362780\pi
252252 22.8019 + 10.9808i 1.43638 + 0.691725i
253253 2.91705 6.05731i 0.183393 0.380820i
254254 0.112436 0.492616i 0.00705488 0.0309095i
255255 −17.2109 21.5818i −1.07779 1.35150i
256256 9.88819 12.3994i 0.618012 0.774963i
257257 1.28785 + 5.64245i 0.0803341 + 0.351966i 0.999080 0.0428824i 0.0136541π-0.0136541\pi
−0.918746 + 0.394849i 0.870797π0.870797\pi
258258 −0.123260 0.0281334i −0.00767386 0.00175151i
259259 −10.5446 8.40905i −0.655210 0.522513i
260260 −8.97368 −0.556524
261261 0 0
262262 −0.612164 −0.0378196
263263 −23.6479 18.8585i −1.45819 1.16287i −0.954205 0.299155i 0.903295π-0.903295\pi
−0.503985 0.863712i 0.668133π-0.668133\pi
264264 −0.916746 0.209241i −0.0564218 0.0128779i
265265 −3.84927 16.8648i −0.236459 1.03599i
266266 0.0203576 0.0255276i 0.00124820 0.00156520i
267267 18.1544 + 22.7649i 1.11103 + 1.39319i
268268 −1.84006 + 8.06184i −0.112400 + 0.492455i
269269 5.17894 10.7542i 0.315766 0.655695i −0.681320 0.731986i 0.738594π-0.738594\pi
0.997086 + 0.0762914i 0.0243079π0.0243079\pi
270270 0.631304 + 0.304020i 0.0384200 + 0.0185021i
271271 −17.1169 + 3.90683i −1.03978 + 0.237323i −0.708132 0.706080i 0.750462π-0.750462\pi
−0.331648 + 0.943403i 0.607605π0.607605\pi
272272 9.05911 + 18.8114i 0.549289 + 1.14061i
273273 16.0292i 0.970128i
274274 0.108175 0.0520941i 0.00653506 0.00314712i
275275 2.84544 2.26916i 0.171587 0.136836i
276276 17.1728 13.6949i 1.03368 0.824335i
277277 −0.968331 + 0.466324i −0.0581814 + 0.0280187i −0.462748 0.886490i 0.653137π-0.653137\pi
0.404567 + 0.914508i 0.367422π0.367422\pi
278278 0.934053i 0.0560208i
279279 −6.33001 13.1444i −0.378968 0.786935i
280280 0.584939 0.133509i 0.0349568 0.00797866i
281281 26.9268 + 12.9673i 1.60632 + 0.773563i 0.999769 0.0214813i 0.00683824π-0.00683824\pi
0.606551 + 0.795044i 0.292553π0.292553\pi
282282 0.560261 1.16339i 0.0333631 0.0692791i
283283 5.95247 26.0795i 0.353837 1.55026i −0.414398 0.910096i 0.636008π-0.636008\pi
0.768236 0.640167i 0.221135π-0.221135\pi
284284 2.84422 + 3.56654i 0.168774 + 0.211635i
285285 −1.24649 + 1.56305i −0.0738358 + 0.0925872i
286286 −0.0445581 0.195222i −0.00263478 0.0115437i
287287 −18.9122 4.31658i −1.11635 0.254800i
288288 −2.42412 1.93317i −0.142843 0.113913i
289289 −10.3905 −0.611204
290290 0 0
291291 15.6769 0.918996
292292 −14.1606 11.2927i −0.828686 0.660855i
293293 −5.66470 1.29293i −0.330935 0.0755338i 0.0538251 0.998550i 0.482859π-0.482859\pi
−0.384760 + 0.923017i 0.625716π0.625716\pi
294294 0.0786335 + 0.344516i 0.00458600 + 0.0200926i
295295 −6.78240 + 8.50486i −0.394887 + 0.495172i
296296 0.686708 + 0.861105i 0.0399141 + 0.0500507i
297297 3.95152 17.3128i 0.229291 1.00459i
298298 −0.0770971 + 0.160094i −0.00446611 + 0.00927398i
299299 8.43217 + 4.06072i 0.487645 + 0.234837i
300300 11.5923 2.64586i 0.669280 0.152759i
301301 −0.887055 1.84199i −0.0511290 0.106171i
302302 0.326947i 0.0188137i
303303 −23.0819 + 11.1157i −1.32602 + 0.638578i
304304 1.18226 0.942817i 0.0678070 0.0540743i
305305 −10.8758 + 8.67316i −0.622746 + 0.496623i
306306 1.21977 0.587412i 0.0697298 0.0335801i
307307 5.15345i 0.294123i −0.989127 0.147061i 0.953018π-0.953018\pi
0.989127 0.147061i 0.0469815π-0.0469815\pi
308308 −3.29727 6.84686i −0.187880 0.390136i
309309 −10.3730 + 2.36756i −0.590098 + 0.134686i
310310 −0.155739 0.0749999i −0.00884538 0.00425971i
311311 4.60974 9.57223i 0.261395 0.542792i −0.728424 0.685127i 0.759747π-0.759747\pi
0.989819 + 0.142335i 0.0454611π0.0454611\pi
312312 0.291277 1.27617i 0.0164903 0.0722489i
313313 10.4187 + 13.0647i 0.588902 + 0.738460i 0.983603 0.180350i 0.0577230π-0.0577230\pi
−0.394700 + 0.918810i 0.629152π0.629152\pi
314314 −0.165478 + 0.207502i −0.00933844 + 0.0117100i
315315 4.90954 + 21.5101i 0.276621 + 1.21196i
316316 20.0206 + 4.56956i 1.12624 + 0.257058i
317317 −1.16590 0.929772i −0.0654833 0.0522212i 0.590201 0.807256i 0.299048π-0.299048\pi
−0.655684 + 0.755035i 0.727620π0.727620\pi
318318 1.26111 0.0707193
319319 0 0
320320 13.8628 0.774954
321321 10.5192 + 8.38879i 0.587125 + 0.468216i
322322 −0.304893 0.0695899i −0.0169910 0.00387810i
323323 0.441424 + 1.93400i 0.0245615 + 0.107611i
324324 13.1221 16.4546i 0.729006 0.914145i
325325 3.15882 + 3.96104i 0.175220 + 0.219719i
326326 −0.0164222 + 0.0719501i −0.000909539 + 0.00398495i
327327 −15.4526 + 32.0876i −0.854529 + 1.77445i
328328 1.42726 + 0.687335i 0.0788075 + 0.0379517i
329329 20.3571 4.64637i 1.12232 0.256163i
330330 −0.177762 0.369126i −0.00978546 0.0203197i
331331 29.8803i 1.64237i −0.570663 0.821184i 0.693314π-0.693314\pi
0.570663 0.821184i 0.306686π-0.306686\pi
332332 28.1227 13.5432i 1.54343 0.743278i
333333 −31.6656 + 25.2525i −1.73527 + 1.38383i
334334 −0.456505 + 0.364050i −0.0249788 + 0.0199200i
335335 −6.49503 + 3.12784i −0.354861 + 0.170892i
336336 24.8061i 1.35328i
337337 0.408434 + 0.848122i 0.0222488 + 0.0462002i 0.911797 0.410641i 0.134695π-0.134695\pi
−0.889548 + 0.456841i 0.848981π0.848981\pi
338338 −0.259857 + 0.0593107i −0.0141344 + 0.00322608i
339339 −31.1518 15.0019i −1.69193 0.814792i
340340 −7.90457 + 16.4140i −0.428685 + 0.890174i
341341 −0.974816 + 4.27095i −0.0527893 + 0.231285i
342342 −0.0611342 0.0766598i −0.00330576 0.00414529i
343343 −12.5258 + 15.7069i −0.676332 + 0.848093i
344344 0.0371513 + 0.162770i 0.00200306 + 0.00877599i
345345 18.6686 + 4.26098i 1.00508 + 0.229403i
346346 0.274997 + 0.219303i 0.0147839 + 0.0117898i
347347 8.65358 0.464548 0.232274 0.972650i 0.425383π-0.425383\pi
0.232274 + 0.972650i 0.425383π0.425383\pi
348348 0 0
349349 −34.5616 −1.85004 −0.925021 0.379916i 0.875953π-0.875953\pi
−0.925021 + 0.379916i 0.875953π0.875953\pi
350350 −0.132360 0.105553i −0.00707492 0.00564206i
351351 24.1005 + 5.50077i 1.28639 + 0.293610i
352352 0.207173 + 0.907684i 0.0110423 + 0.0483797i
353353 8.99264 11.2764i 0.478630 0.600183i −0.482631 0.875824i 0.660319π-0.660319\pi
0.961261 + 0.275641i 0.0888901π0.0888901\pi
354354 −0.494456 0.620028i −0.0262801 0.0329541i
355355 −0.884942 + 3.87718i −0.0469678 + 0.205780i
356356 8.33789 17.3138i 0.441907 0.917630i
357357 29.3194 + 14.1195i 1.55175 + 0.747281i
358358 0.804605 0.183646i 0.0425247 0.00970598i
359359 9.67167 + 20.0834i 0.510451 + 1.05996i 0.983830 + 0.179104i 0.0573199π0.0573199\pi
−0.473379 + 0.880859i 0.656966π0.656966\pi
360360 1.80175i 0.0949608i
361361 −16.9890 + 8.18145i −0.894156 + 0.430603i
362362 −0.395286 + 0.315230i −0.0207758 + 0.0165681i
363363 17.9211 14.2916i 0.940611 0.750113i
364364 9.53127 4.59002i 0.499574 0.240582i
365365 15.7898i 0.826478i
366366 −0.440013 0.913696i −0.0229998 0.0477597i
367367 4.95309 1.13051i 0.258549 0.0590121i −0.0912815 0.995825i 0.529096π-0.529096\pi
0.349831 + 0.936813i 0.386239π0.386239\pi
368368 −13.0493 6.28420i −0.680240 0.327586i
369369 −25.2755 + 52.4852i −1.31579 + 2.73227i
370370 −0.106783 + 0.467847i −0.00555138 + 0.0243222i
371371 12.7147 + 15.9438i 0.660116 + 0.827759i
372372 −8.92361 + 11.1898i −0.462667 + 0.580167i
373373 −5.67645 24.8702i −0.293916 1.28773i −0.879026 0.476774i 0.841806π-0.841806\pi
0.585110 0.810954i 0.301051π-0.301051\pi
374374 −0.396335 0.0904609i −0.0204940 0.00467762i
375375 28.7229 + 22.9057i 1.48324 + 1.18285i
376376 −1.70517 −0.0879376
377377 0 0
378378 −0.826036 −0.0424867
379379 6.50423 + 5.18695i 0.334100 + 0.266436i 0.776141 0.630559i 0.217174π-0.217174\pi
−0.442042 + 0.896994i 0.645746π0.645746\pi
380380 1.28636 + 0.293604i 0.0659889 + 0.0150615i
381381 −8.11596 35.5584i −0.415793 1.82171i
382382 0.303898 0.381076i 0.0155488 0.0194976i
383383 −15.7882 19.7978i −0.806741 1.01162i −0.999538 0.0303822i 0.990328π-0.990328\pi
0.192798 0.981239i 0.438244π-0.438244\pi
384384 −0.902333 + 3.95338i −0.0460470 + 0.201745i
385385 2.87451 5.96899i 0.146499 0.304208i
386386 −0.720022 0.346745i −0.0366482 0.0176488i
387387 −5.98560 + 1.36617i −0.304265 + 0.0694465i
388388 −4.48915 9.32181i −0.227902 0.473243i
389389 27.3249i 1.38543i −0.721212 0.692714i 0.756415π-0.756415\pi
0.721212 0.692714i 0.243585π-0.243585\pi
390390 0.513848 0.247456i 0.0260197 0.0125304i
391391 14.8551 11.8466i 0.751257 0.599107i
392392 0.364839 0.290949i 0.0184272 0.0146952i
393393 −39.8117 + 19.1723i −2.00824 + 0.967115i
394394 0.700769i 0.0353042i
395395 7.76759 + 16.1296i 0.390830 + 0.811567i
396396 −22.2491 + 5.07820i −1.11806 + 0.255189i
397397 −10.1136 4.87046i −0.507588 0.244441i 0.162520 0.986705i 0.448038π-0.448038\pi
−0.670108 + 0.742264i 0.733752π0.733752\pi
398398 −0.162130 + 0.336667i −0.00812685 + 0.0168756i
399399 0.524447 2.29775i 0.0262552 0.115031i
400400 −4.88846 6.12994i −0.244423 0.306497i
401401 20.7632 26.0362i 1.03686 1.30019i 0.0841055 0.996457i 0.473197π-0.473197\pi
0.952758 0.303729i 0.0982319π-0.0982319\pi
402402 −0.116946 0.512375i −0.00583275 0.0255550i
403403 −5.94544 1.35701i −0.296163 0.0675974i
404404 13.2192 + 10.5420i 0.657680 + 0.524482i
405405 18.3478 0.911710
406406 0 0
407407 12.1617 0.602835
408408 −2.07770 1.65691i −0.102862 0.0820294i
409409 15.6788 + 3.57858i 0.775266 + 0.176949i 0.591809 0.806078i 0.298414π-0.298414\pi
0.183457 + 0.983028i 0.441271π0.441271\pi
410410 0.153587 + 0.672908i 0.00758512 + 0.0332326i
411411 5.40353 6.77582i 0.266537 0.334226i
412412 4.37815 + 5.49002i 0.215696 + 0.270474i
413413 2.85362 12.5025i 0.140417 0.615208i
414414 −0.407480 + 0.846142i −0.0200266 + 0.0415856i
415415 24.5169 + 11.8067i 1.20349 + 0.579570i
416416 −1.26355 + 0.288398i −0.0619508 + 0.0141399i
417417 −29.2535 60.7456i −1.43255 2.97472i
418418 0.0294426i 0.00144008i
419419 25.2958 12.1818i 1.23578 0.595120i 0.302116 0.953271i 0.402307π-0.402307\pi
0.933664 + 0.358151i 0.116593π0.116593\pi
420420 16.9225 13.4952i 0.825731 0.658499i
421421 23.8443 19.0152i 1.16210 0.926745i 0.163888 0.986479i 0.447597π-0.447597\pi
0.998214 + 0.0597337i 0.0190252π0.0190252\pi
422422 0.00960722 0.00462659i 0.000467672 0.000225219i
423423 62.7048i 3.04881i
424424 −0.722565 1.50042i −0.0350908 0.0728669i
425425 10.0277 2.28876i 0.486416 0.111021i
426426 −0.261215 0.125794i −0.0126559 0.00609476i
427427 7.11527 14.7750i 0.344332 0.715013i
428428 1.97593 8.65710i 0.0955101 0.418457i
429429 −9.01194 11.3006i −0.435101 0.545599i
430430 −0.0453545 + 0.0568728i −0.00218719 + 0.00274265i
431431 2.16416 + 9.48182i 0.104244 + 0.456723i 0.999928 + 0.0120313i 0.00382976π0.00382976\pi
−0.895683 + 0.444692i 0.853313π0.853313\pi
432432 −37.2969 8.51277i −1.79445 0.409571i
433433 18.1617 + 14.4835i 0.872796 + 0.696032i 0.953722 0.300688i 0.0972164π-0.0972164\pi
−0.0809262 + 0.996720i 0.525788π0.525788\pi
434434 0.203778 0.00978166
435435 0 0
436436 23.5049 1.12568
437437 −1.07588 0.857983i −0.0514661 0.0410429i
438438 1.12226 + 0.256149i 0.0536238 + 0.0122393i
439439 −3.03245 13.2860i −0.144731 0.634107i −0.994299 0.106628i 0.965995π-0.965995\pi
0.849568 0.527479i 0.176863π-0.176863\pi
440440 −0.337323 + 0.422990i −0.0160812 + 0.0201652i
441441 10.6992 + 13.4163i 0.509484 + 0.638872i
442442 0.125927 0.551724i 0.00598976 0.0262428i
443443 3.98012 8.26480i 0.189101 0.392673i −0.784766 0.619793i 0.787217π-0.787217\pi
0.973867 + 0.227120i 0.0729310π0.0729310\pi
444444 35.7985 + 17.2396i 1.69892 + 0.818157i
445445 16.3330 3.72789i 0.774256 0.176719i
446446 −0.166647 0.346047i −0.00789098 0.0163858i
447447 12.8262i 0.606658i
448448 −14.7242 + 7.09078i −0.695651 + 0.335008i
449449 13.8731 11.0635i 0.654714 0.522117i −0.238848 0.971057i 0.576770π-0.576770\pi
0.893562 + 0.448940i 0.148198π0.148198\pi
450450 −0.397478 + 0.316978i −0.0187373 + 0.0149425i
451451 15.7601 7.58964i 0.742112 0.357382i
452452 22.8194i 1.07333i
453453 −10.2396 21.2628i −0.481100 0.999014i
454454 −0.196881 + 0.0449368i −0.00924009 + 0.00210899i
455455 8.30922 + 4.00151i 0.389542 + 0.187594i
456456 −0.0835082 + 0.173407i −0.00391063 + 0.00812051i
457457 0.561526 2.46020i 0.0262671 0.115084i −0.960095 0.279675i 0.909773π-0.909773\pi
0.986362 + 0.164591i 0.0526305π0.0526305\pi
458458 0.179563 + 0.225165i 0.00839045 + 0.0105213i
459459 31.2908 39.2374i 1.46053 1.83145i
460460 −2.81216 12.3209i −0.131118 0.574464i
461461 −9.76174 2.22805i −0.454649 0.103771i −0.0109374 0.999940i 0.503482π-0.503482\pi
−0.443712 + 0.896169i 0.646339π0.646339\pi
462462 0.377614 + 0.301137i 0.0175682 + 0.0140102i
463463 −27.8485 −1.29423 −0.647115 0.762393i 0.724024π-0.724024\pi
−0.647115 + 0.762393i 0.724024π0.724024\pi
464464 0 0
465465 −12.4773 −0.578621
466466 0.565050 + 0.450612i 0.0261754 + 0.0208742i
467467 19.8182 + 4.52337i 0.917076 + 0.209317i 0.654911 0.755706i 0.272706π-0.272706\pi
0.262165 + 0.965023i 0.415563π0.415563\pi
468468 −7.06919 30.9721i −0.326773 1.43169i
469469 5.29872 6.64439i 0.244672 0.306809i
470470 −0.463219 0.580858i −0.0213667 0.0267930i
471471 −4.26299 + 18.6774i −0.196428 + 0.860608i
472472 −0.454384 + 0.943539i −0.0209147 + 0.0434299i
473473 1.66098 + 0.799888i 0.0763722 + 0.0367789i
474474 −1.27242 + 0.290421i −0.0584441 + 0.0133395i
475475 −0.323213 0.671159i −0.0148300 0.0307949i
476476 21.4771i 0.984400i
477477 55.1754 26.5711i 2.52631 1.21661i
478478 0.698653 0.557157i 0.0319557 0.0254838i
479479 −16.7710 + 13.3745i −0.766288 + 0.611094i −0.926633 0.375967i 0.877311π-0.877311\pi
0.160345 + 0.987061i 0.448739π0.448739\pi
480480 −2.38913 + 1.15055i −0.109049 + 0.0525150i
481481 16.9299i 0.771939i
482482 −0.163670 0.339863i −0.00745495 0.0154804i
483483 −22.0080 + 5.02319i −1.00140 + 0.228563i
484484 −13.6298 6.56378i −0.619538 0.298354i
485485 3.91357 8.12662i 0.177706 0.369011i
486486 −0.0291334 + 0.127642i −0.00132152 + 0.00578994i
487487 10.2229 + 12.8192i 0.463245 + 0.580891i 0.957503 0.288424i 0.0931314π-0.0931314\pi
−0.494257 + 0.869316i 0.664560π0.664560\pi
488488 −0.834974 + 1.04702i −0.0377975 + 0.0473966i
489489 1.18540 + 5.19356i 0.0536054 + 0.234861i
490490 0.198221 + 0.0452426i 0.00895470 + 0.00204385i
491491 22.8879 + 18.2525i 1.03292 + 0.823723i 0.984550 0.175106i 0.0560269π-0.0560269\pi
0.0483669 + 0.998830i 0.484598π0.484598\pi
492492 57.1488 2.57647
493493 0 0
494494 −0.0409860 −0.00184405
495495 −15.5547 12.4045i −0.699132 0.557539i
496496 9.20091 + 2.10005i 0.413133 + 0.0942950i
497497 −1.04324 4.57074i −0.0467958 0.205026i
498498 −1.23689 + 1.55101i −0.0554262 + 0.0695023i
499499 2.91420 + 3.65430i 0.130458 + 0.163589i 0.842770 0.538274i 0.180923π-0.180923\pi
−0.712312 + 0.701863i 0.752352π0.752352\pi
500500 5.39531 23.6384i 0.241286 1.05714i
501501 −18.2868 + 37.9730i −0.816996 + 1.69651i
502502 0.245744 + 0.118344i 0.0109681 + 0.00528195i
503503 10.8288 2.47160i 0.482831 0.110203i 0.0258248 0.999666i 0.491779π-0.491779\pi
0.457006 + 0.889463i 0.348922π0.348922\pi
504504 0.921593 + 1.91371i 0.0410510 + 0.0852433i
505505 14.7401i 0.655928i
506506 0.254076 0.122357i 0.0112951 0.00543942i
507507 −15.0421 + 11.9957i −0.668043 + 0.532747i
508508 −18.8197 + 15.0082i −0.834989 + 0.665882i
509509 29.9589 14.4274i 1.32790 0.639484i 0.370660 0.928769i 0.379132π-0.379132\pi
0.957243 + 0.289284i 0.0934174π0.0934174\pi
510510 1.15787i 0.0512712i
511511 8.07647 + 16.7710i 0.357282 + 0.741904i
512512 3.26000 0.744073i 0.144073 0.0328837i
513513 −3.27478 1.57705i −0.144585 0.0696286i
514514 −0.105330 + 0.218720i −0.00464592 + 0.00964734i
515515 −1.36220 + 5.96820i −0.0600258 + 0.262990i
516516 3.75530 + 4.70899i 0.165318 + 0.207302i
517517 −11.7395 + 14.7209i −0.516304 + 0.647425i
518518 −0.125885 0.551536i −0.00553105 0.0242331i
519519 24.7526 + 5.64962i 1.08652 + 0.247991i
520520 −0.588829 0.469575i −0.0258219 0.0205922i
521521 11.6310 0.509565 0.254783 0.966998i 0.417996π-0.417996\pi
0.254783 + 0.966998i 0.417996π0.417996\pi
522522 0 0
523523 −0.747202 −0.0326728 −0.0163364 0.999867i 0.505200π-0.505200\pi
−0.0163364 + 0.999867i 0.505200π0.505200\pi
524524 22.8005 + 18.1828i 0.996045 + 0.794319i
525525 −11.9137 2.71923i −0.519958 0.118677i
526526 −0.282315 1.23690i −0.0123095 0.0539315i
527527 −7.71925 + 9.67963i −0.336256 + 0.421651i
528528 13.9465 + 17.4884i 0.606944 + 0.761084i
529529 2.18507 9.57343i 0.0950031 0.416236i
530530 0.314822 0.653735i 0.0136750 0.0283964i
531531 −34.6970 16.7092i −1.50572 0.725117i
532532 −1.51647 + 0.346124i −0.0657472 + 0.0150064i
533533 10.5653 + 21.9390i 0.457633 + 0.950284i
534534 1.22134i 0.0528525i
535535 6.97460 3.35879i 0.301538 0.145213i
536536 −0.542601 + 0.432710i −0.0234368 + 0.0186902i
537537 46.5754 37.1426i 2.00988 1.60282i
538538 0.451089 0.217233i 0.0194478 0.00936557i
539539 5.15277i 0.221946i
540540 −14.4832 30.0748i −0.623260 1.29421i
541541 −18.7646 + 4.28290i −0.806753 + 0.184136i −0.605957 0.795497i 0.707210π-0.707210\pi
−0.200795 + 0.979633i 0.564353π0.564353\pi
542542 −0.663510 0.319530i −0.0285002 0.0137250i
543543 −15.8345 + 32.8807i −0.679524 + 1.41105i
544544 −0.585499 + 2.56524i −0.0251031 + 0.109984i
545545 12.7761 + 16.0207i 0.547266 + 0.686250i
546546 −0.419203 + 0.525664i −0.0179402 + 0.0224963i
547547 5.62909 + 24.6627i 0.240683 + 1.05450i 0.940398 + 0.340077i 0.110453π0.110453\pi
−0.699715 + 0.714422i 0.746690π0.746690\pi
548548 −5.57637 1.27277i −0.238211 0.0543700i
549549 −38.5025 30.7047i −1.64325 1.31045i
550550 0.152658 0.00650938
551551 0 0
552552 1.84346 0.0784630
553553 −16.5005 13.1587i −0.701672 0.559565i
554554 −0.0439512 0.0100316i −0.00186731 0.000426201i
555555 7.70789 + 33.7705i 0.327182 + 1.43348i
556556 −27.7437 + 34.7895i −1.17660 + 1.47540i
557557 −22.5353 28.2584i −0.954851 1.19735i −0.980269 0.197668i 0.936663π-0.936663\pi
0.0254181 0.999677i 0.491908π-0.491908\pi
558558 0.136171 0.596606i 0.00576460 0.0252564i
559559 −1.11350 + 2.31220i −0.0470959 + 0.0977956i
560560 −12.8590 6.19257i −0.543392 0.261684i
561561 −28.6085 + 6.52971i −1.20785 + 0.275685i
562562 0.543918 + 1.12946i 0.0229438 + 0.0476432i
563563 8.84332i 0.372701i 0.982483 + 0.186351i 0.0596661π0.0596661\pi
−0.982483 + 0.186351i 0.940334π0.940334\pi
564564 −55.4230 + 26.6903i −2.33373 + 1.12387i
565565 −15.5534 + 12.4034i −0.654338 + 0.521817i
566566 0.877250 0.699584i 0.0368736 0.0294057i
567567 −19.4879 + 9.38486i −0.818413 + 0.394127i
568568 0.382860i 0.0160644i
569569 7.15474 + 14.8570i 0.299942 + 0.622837i 0.995408 0.0957226i 0.0305162π-0.0305162\pi
−0.695466 + 0.718559i 0.744802π0.744802\pi
570570 −0.0817555 + 0.0186602i −0.00342436 + 0.000781588i
571571 20.3900 + 9.81931i 0.853295 + 0.410925i 0.808800 0.588084i 0.200118π-0.200118\pi
0.0444957 + 0.999010i 0.485832π0.485832\pi
572572 −4.13898 + 8.59467i −0.173059 + 0.359361i
573573 7.82894 34.3008i 0.327058 1.43294i
574574 −0.507321 0.636160i −0.0211752 0.0265528i
575575 −4.44860 + 5.57837i −0.185520 + 0.232634i
576576 10.9207 + 47.8466i 0.455028 + 1.99361i
577577 40.1086 + 9.15453i 1.66974 + 0.381108i 0.949784 0.312907i 0.101303π-0.101303\pi
0.719960 + 0.694015i 0.244160π0.244160\pi
578578 −0.340747 0.271737i −0.0141732 0.0113028i
579579 −57.6859 −2.39734
580580 0 0
581581 −32.0794 −1.33088
582582 0.514112 + 0.409991i 0.0213106 + 0.0169947i
583583 −17.9279 4.09192i −0.742497 0.169470i
584584 −0.338255 1.48199i −0.0139971 0.0613253i
585585 17.2678 21.6532i 0.713936 0.895248i
586586 −0.151956 0.190547i −0.00627724 0.00787141i
587587 5.82733 25.5312i 0.240520 1.05379i −0.700026 0.714118i 0.746828π-0.746828\pi
0.940545 0.339668i 0.110315π-0.110315\pi
588588 7.30422 15.1674i 0.301221 0.625491i
589589 0.807869 + 0.389049i 0.0332877 + 0.0160305i
590590 −0.444847 + 0.101533i −0.0183141 + 0.00418007i
591591 21.9473 + 45.5741i 0.902792 + 1.87467i
592592 26.2001i 1.07682i
593593 −28.3677 + 13.6611i −1.16492 + 0.560996i −0.913483 0.406877i 0.866618π-0.866618\pi
−0.251438 + 0.967873i 0.580903π0.580903\pi
594594 0.582359 0.464416i 0.0238945 0.0190552i
595595 14.6385 11.6738i 0.600122 0.478581i
596596 7.62672 3.67284i 0.312403 0.150445i
597597 26.9726i 1.10392i
598598 0.170328 + 0.353690i 0.00696524 + 0.0144635i
599599 −13.8236 + 3.15514i −0.564816 + 0.128916i −0.495389 0.868671i 0.664974π-0.664974\pi
−0.0694275 + 0.997587i 0.522117π0.522117\pi
600600 0.899106 + 0.432987i 0.0367058 + 0.0176766i
601601 6.08447 12.6345i 0.248191 0.515373i −0.739237 0.673445i 0.764814π-0.764814\pi
0.987428 + 0.158072i 0.0505280π0.0505280\pi
602602 0.0190824 0.0836053i 0.000777740 0.00340750i
603603 −15.9121 19.9532i −0.647993 0.812557i
604604 −9.71115 + 12.1774i −0.395141 + 0.495491i
605605 −2.93468 12.8577i −0.119312 0.522739i
606606 −1.04766 0.239121i −0.0425581 0.00971361i
607607 14.3075 + 11.4099i 0.580725 + 0.463113i 0.869259 0.494357i 0.164596π-0.164596\pi
−0.288534 + 0.957470i 0.593168π0.593168\pi
608608 0.190564 0.00772840
609609 0 0
610610 −0.583488 −0.0236247
611611 −20.4925 16.3422i −0.829036 0.661134i
612612 −62.8789 14.3517i −2.54173 0.580133i
613613 6.64203 + 29.1006i 0.268269 + 1.17536i 0.912026 + 0.410133i 0.134518π0.134518\pi
−0.643757 + 0.765230i 0.722625π0.722625\pi
614614 0.134776 0.169003i 0.00543911 0.00682042i
615615 31.0632 + 38.9520i 1.25259 + 1.57070i
616616 0.141925 0.621812i 0.00571831 0.0250535i
617617 1.99315 4.13882i 0.0802412 0.166623i −0.856988 0.515336i 0.827667π-0.827667\pi
0.937229 + 0.348714i 0.113381π0.113381\pi
618618 −0.402091 0.193637i −0.0161745 0.00778922i
619619 6.12797 1.39867i 0.246304 0.0562173i −0.0975864 0.995227i 0.531112π-0.531112\pi
0.343891 + 0.939010i 0.388255π0.388255\pi
620620 3.57293 + 7.41926i 0.143492 + 0.297965i
621621 34.8138i 1.39703i
622622 0.401511 0.193357i 0.0160991 0.00775293i
623623 −15.4410 + 12.3138i −0.618631 + 0.493342i
624624 −24.3449 + 19.4144i −0.974578 + 0.777200i
625625 10.1909 4.90767i 0.407635 0.196307i
626626 0.700923i 0.0280145i
627627 0.922109 + 1.91478i 0.0368255 + 0.0764689i
628628 12.3267 2.81348i 0.491888 0.112270i
629629 30.9670 + 14.9129i 1.23474 + 0.594617i
630630 −0.401539 + 0.833804i −0.0159977 + 0.0332196i
631631 2.15554 9.44402i 0.0858105 0.375961i −0.913728 0.406326i 0.866810π-0.866810\pi
0.999539 + 0.0303651i 0.00966700π0.00966700\pi
632632 1.07458 + 1.34748i 0.0427444 + 0.0535998i
633633 0.479900 0.601775i 0.0190743 0.0239184i
634634 −0.0139188 0.0609823i −0.000552787 0.00242192i
635635 −20.4589 4.66960i −0.811885 0.185308i
636636 −46.9709 37.4580i −1.86252 1.48531i
637637 7.17299 0.284204
638638 0 0
639639 −14.0790 −0.556956
640640 1.82410 + 1.45467i 0.0721039 + 0.0575010i
641641 −4.67849 1.06783i −0.184789 0.0421769i 0.129125 0.991628i 0.458783π-0.458783\pi
−0.313914 + 0.949451i 0.601640π0.601640\pi
642642 0.125581 + 0.550207i 0.00495630 + 0.0217150i
643643 −7.65128 + 9.59440i −0.301737 + 0.378366i −0.909466 0.415778i 0.863509π-0.863509\pi
0.607729 + 0.794144i 0.292081π0.292081\pi
644644 9.28899 + 11.6480i 0.366038 + 0.458997i
645645 −1.16841 + 5.11914i −0.0460061 + 0.201566i
646646 −0.0361029 + 0.0749685i −0.00142045 + 0.00294960i
647647 −9.57683 4.61196i −0.376504 0.181315i 0.236055 0.971740i 0.424146π-0.424146\pi
−0.612559 + 0.790425i 0.709860π0.709860\pi
648648 1.72208 0.393053i 0.0676495 0.0154406i
649649 5.01737 + 10.4187i 0.196949 + 0.408969i
650650 0.212510i 0.00833534i
651651 13.2526 6.38211i 0.519410 0.250135i
652652 2.74875 2.19206i 0.107650 0.0858476i
653653 −21.9246 + 17.4843i −0.857974 + 0.684212i −0.950239 0.311523i 0.899161π-0.899161\pi
0.0922642 + 0.995735i 0.470590π0.470590\pi
654654 −1.34593 + 0.648164i −0.0526299 + 0.0253452i
655655 25.4238i 0.993391i
656656 −16.3504 33.9519i −0.638375 1.32560i
657657 54.4977 12.4387i 2.12616 0.485282i
658658 0.789109 + 0.380015i 0.0307627 + 0.0148145i
659659 8.79977 18.2729i 0.342790 0.711812i −0.656298 0.754502i 0.727879π-0.727879\pi
0.999088 + 0.0426903i 0.0135929π0.0135929\pi
660660 −4.34310 + 19.0284i −0.169055 + 0.740678i
661661 −19.5336 24.4943i −0.759768 0.952719i 0.240069 0.970756i 0.422830π-0.422830\pi
−0.999837 + 0.0180369i 0.994258π0.994258\pi
662662 0.781444 0.979900i 0.0303717 0.0380849i
663663 −9.08978 39.8249i −0.353018 1.54667i
664664 2.55402 + 0.582939i 0.0991153 + 0.0226224i
665665 −1.06019 0.845473i −0.0411124 0.0327860i
666666 −1.69887 −0.0658297
667667 0 0
668668 27.8161 1.07624
669669 −21.6756 17.2857i −0.838028 0.668305i
670670 −0.294800 0.0672863i −0.0113891 0.00259950i
671671 3.29054 + 14.4168i 0.127030 + 0.556555i
672672 1.94908 2.44407i 0.0751875 0.0942821i
673673 −25.3813 31.8271i −0.978376 1.22685i −0.973929 0.226855i 0.927156π-0.927156\pi
−0.00444768 0.999990i 0.501416π-0.501416\pi
674674 −0.00878626 + 0.0384951i −0.000338434 + 0.00148278i
675675 −8.17695 + 16.9796i −0.314731 + 0.653546i
676676 11.4402 + 5.50933i 0.440009 + 0.211897i
677677 8.07381 1.84280i 0.310302 0.0708244i −0.0645342 0.997915i 0.520556π-0.520556\pi
0.374836 + 0.927091i 0.377699π0.377699\pi
678678 −0.629261 1.30667i −0.0241666 0.0501825i
679679 10.6334i 0.408071i
680680 −1.37759 + 0.663412i −0.0528282 + 0.0254407i
681681 −11.3967 + 9.08854i −0.436721 + 0.348274i
682682 −0.143664 + 0.114569i −0.00550120 + 0.00438706i
683683 −3.03215 + 1.46021i −0.116022 + 0.0558733i −0.490994 0.871163i 0.663366π-0.663366\pi
0.374972 + 0.927036i 0.377652π0.377652\pi
684684 4.67109i 0.178604i
685685 −2.16352 4.49260i −0.0826640 0.171654i
686686 −0.821550 + 0.187513i −0.0313669 + 0.00715930i
687687 18.7297 + 9.01976i 0.714584 + 0.344125i
688688 1.72320 3.57826i 0.0656964 0.136420i
689689 5.69622 24.9568i 0.217009 0.950777i
690690 0.500786 + 0.627966i 0.0190646 + 0.0239062i
691691 0.657864 0.824935i 0.0250263 0.0313820i −0.769161 0.639055i 0.779326π-0.779326\pi
0.794187 + 0.607673i 0.207897π0.207897\pi
692692 −3.72863 16.3362i −0.141741 0.621009i
693693 22.8661 + 5.21903i 0.868610 + 0.198255i
694694 0.283787 + 0.226313i 0.0107724 + 0.00859072i
695695 −38.7922 −1.47147
696696 0 0
697697 49.4358 1.87251
698698 −1.13342 0.903874i −0.0429007 0.0342121i
699699 50.8603 + 11.6085i 1.92371 + 0.439075i
700700 1.79464 + 7.86282i 0.0678309 + 0.297187i
701701 −8.76970 + 10.9969i −0.331227 + 0.415345i −0.919359 0.393419i 0.871292π-0.871292\pi
0.588132 + 0.808765i 0.299863π0.299863\pi
702702 0.646497 + 0.810682i 0.0244005 + 0.0305972i
703703 0.553919 2.42688i 0.0208914 0.0915314i
704704 6.39400 13.2773i 0.240983 0.500406i
705705 −48.3170 23.2682i −1.81972 0.876333i
706706 0.589813 0.134621i 0.0221979 0.00506653i
707707 −7.53955 15.6560i −0.283554 0.588806i
708708 37.7800i 1.41986i
709709 3.67395 1.76928i 0.137978 0.0664467i −0.363621 0.931547i 0.618460π-0.618460\pi
0.501599 + 0.865100i 0.332745π0.332745\pi
710710 −0.130419 + 0.104006i −0.00489454 + 0.00390327i
711711 −49.5512 + 39.5158i −1.85832 + 1.48196i
712712 1.45311 0.699780i 0.0544575 0.0262253i
713713 8.58835i 0.321636i
714714 0.592246 + 1.22981i 0.0221643 + 0.0460245i
715715 −8.10777 + 1.85055i −0.303213 + 0.0692065i
716716 −35.4229 17.0587i −1.32381 0.637515i
717717 27.9869 58.1154i 1.04519 2.17036i
718718 −0.208057 + 0.911559i −0.00776463 + 0.0340191i
719719 5.19082 + 6.50908i 0.193585 + 0.242748i 0.869145 0.494557i 0.164670π-0.164670\pi
−0.675560 + 0.737305i 0.736098π0.736098\pi
720720 −26.7230 + 33.5095i −0.995906 + 1.24883i
721721 −1.60588 7.03580i −0.0598059 0.262027i
722722 −0.771106 0.176000i −0.0286976 0.00655003i
723723 −21.2883 16.9769i −0.791720 0.631376i
724724 24.0858 0.895144
725725 0 0
726726 0.961467 0.0356834
727727 28.8392 + 22.9985i 1.06959 + 0.852968i 0.989603 0.143828i 0.0459411π-0.0459411\pi
0.0799858 + 0.996796i 0.474513π0.474513\pi
728728 0.865603 + 0.197568i 0.0320814 + 0.00732237i
729729 −4.92810 21.5914i −0.182522 0.799682i
730730 0.412944 0.517816i 0.0152838 0.0191652i
731731 3.24847 + 4.07345i 0.120149 + 0.150662i
732732 −10.7504 + 47.1008i −0.397348 + 1.74090i
733733 −4.39963 + 9.13593i −0.162504 + 0.337443i −0.966282 0.257486i 0.917106π-0.917106\pi
0.803778 + 0.594930i 0.202820π0.202820\pi
734734 0.191998 + 0.0924615i 0.00708679 + 0.00341282i
735735 14.3081 3.26573i 0.527763 0.120458i
736736 −0.791941 1.64448i −0.0291913 0.0606165i
737737 7.66338i 0.282284i
738738 −2.20151 + 1.06019i −0.0810387 + 0.0390262i
739739 9.53463 7.60362i 0.350737 0.279704i −0.432234 0.901761i 0.642275π-0.642275\pi
0.782971 + 0.622058i 0.213703π0.213703\pi
740740 17.8734 14.2536i 0.657041 0.523972i
741741 −2.66550 + 1.28364i −0.0979195 + 0.0471555i
742742 0.855386i 0.0314022i
743743 14.2079 + 29.5030i 0.521237 + 1.08236i 0.980944 + 0.194289i 0.0622400π0.0622400\pi
−0.459707 + 0.888070i 0.652046π0.652046\pi
744744 −1.17109 + 0.267293i −0.0429341 + 0.00979943i
745745 6.64887 + 3.20192i 0.243596 + 0.117309i
746746 0.464263 0.964051i 0.0169979 0.0352964i
747747 −21.4366 + 93.9197i −0.784323 + 3.43634i
748748 12.0749 + 15.1414i 0.441501 + 0.553625i
749749 −5.68996 + 7.13499i −0.207907 + 0.260707i
750750 0.342902 + 1.50235i 0.0125210 + 0.0548581i
751751 −46.6110 10.6387i −1.70086 0.388210i −0.741624 0.670816i 0.765944π-0.765944\pi
−0.959236 + 0.282605i 0.908801π0.908801\pi
752752 31.7133 + 25.2905i 1.15646 + 0.922250i
753753 19.6882 0.717478
754754 0 0
755755 −13.5785 −0.494171
756756 30.7664 + 24.5353i 1.11896 + 0.892342i
757757 −14.4846 3.30601i −0.526450 0.120159i −0.0489682 0.998800i 0.515593π-0.515593\pi
−0.477482 + 0.878641i 0.658450π0.658450\pi
758758 0.0776493 + 0.340204i 0.00282035 + 0.0123568i
759759 12.6916 15.9148i 0.460676 0.577670i
760760 0.0690439 + 0.0865783i 0.00250448 + 0.00314052i
761761 −4.08433 + 17.8946i −0.148057 + 0.648680i 0.845367 + 0.534186i 0.179382π0.179382\pi
−0.993424 + 0.114494i 0.963475π0.963475\pi
762762 0.663784 1.37836i 0.0240464 0.0499328i
763763 −21.7644 10.4812i −0.787925 0.379445i
764764 −22.6378 + 5.16694i −0.819008 + 0.186933i
765765 −24.3958 50.6585i −0.882033 1.83156i
766766 1.06216i 0.0383772i
767767 −14.5035 + 6.98451i −0.523690 + 0.252196i
768768 37.5421 29.9388i 1.35468 1.08032i
769769 10.2099 8.14215i 0.368180 0.293614i −0.421870 0.906656i 0.638626π-0.638626\pi
0.790050 + 0.613043i 0.210055π0.210055\pi
770770 0.250372 0.120573i 0.00902277 0.00434513i
771771 17.5232i 0.631082i
772772 16.5186 + 34.3012i 0.594517 + 1.23453i
773773 29.5266 6.73926i 1.06200 0.242394i 0.344380 0.938830i 0.388089π-0.388089\pi
0.717619 + 0.696436i 0.245232π0.245232\pi
774774 −0.232022 0.111736i −0.00833985 0.00401626i
775775 2.01720 4.18877i 0.0724601 0.150465i
776776 0.193227 0.846581i 0.00693643 0.0303905i
777777 −25.4603 31.9262i −0.913384 1.14535i
778778 0.714615 0.896099i 0.0256202 0.0321267i
779779 −0.796706 3.49060i −0.0285449 0.125064i
780780 −26.4887 6.04587i −0.948447 0.216477i
781781 3.30526 + 2.63586i 0.118272 + 0.0943184i
782782 0.796981 0.0285000
783783 0 0
784784 −11.1006 −0.396451
785785 8.61780 + 6.87246i 0.307582 + 0.245289i
786786 −1.80700 0.412436i −0.0644535 0.0147111i
787787 −0.659533 2.88960i −0.0235098 0.103003i 0.961812 0.273712i 0.0882515π-0.0882515\pi
−0.985322 + 0.170709i 0.945394π0.945394\pi
788788 20.8146 26.1007i 0.741489 0.929798i
789789 −57.0986 71.5994i −2.03276 2.54901i
790790 −0.167097 + 0.732099i −0.00594504 + 0.0260469i
791791 10.1755 21.1297i 0.361800 0.751285i
792792 −1.72566 0.831032i −0.0613185 0.0295294i
793793 −20.0691 + 4.58065i −0.712676 + 0.162664i
794794 −0.204293 0.424219i −0.00725010 0.0150550i
795795 52.3751i 1.85755i
796796 16.0385 7.72373i 0.568469 0.273760i
797797 18.7344 14.9402i 0.663607 0.529209i −0.232753 0.972536i 0.574773π-0.574773\pi
0.896360 + 0.443327i 0.146202π0.146202\pi
798798 0.0772908 0.0616373i 0.00273606 0.00218194i
799799 −47.9430 + 23.0881i −1.69610 + 0.816799i
800800 0.988067i 0.0349334i
801801 25.7332 + 53.4355i 0.909237 + 1.88805i
802802 1.36182 0.310828i 0.0480877 0.0109757i
803803 −15.1229 7.28283i −0.533677 0.257005i
804804 −10.8631 + 22.5574i −0.383111 + 0.795538i
805805 −2.89015 + 12.6626i −0.101864 + 0.446296i
806806 −0.159487 0.199990i −0.00561768 0.00704435i
807807 22.5328 28.2552i 0.793191 0.994630i
808808 0.315768 + 1.38347i 0.0111087 + 0.0486703i
809809 47.5397 + 10.8506i 1.67141 + 0.381487i 0.950299 0.311337i 0.100777π-0.100777\pi
0.721106 + 0.692825i 0.243634π0.243634\pi
810810 0.601702 + 0.479841i 0.0211417 + 0.0168599i
811811 −23.3346 −0.819389 −0.409695 0.912223i 0.634365π-0.634365\pi
−0.409695 + 0.912223i 0.634365π0.634365\pi
812812 0 0
813813 −53.1583 −1.86434
814814 0.398835 + 0.318060i 0.0139792 + 0.0111480i
815815 2.98817 + 0.682030i 0.104671 + 0.0238905i
816816 14.0670 + 61.6314i 0.492443 + 2.15753i
817817 0.235269 0.295018i 0.00823102 0.0103214i
818818 0.420585 + 0.527396i 0.0147054 + 0.0184400i
819819 −7.26523 + 31.8310i −0.253868 + 1.11227i
820820 14.2666 29.6249i 0.498211 1.03455i
821821 33.0050 + 15.8944i 1.15188 + 0.554718i 0.909599 0.415487i 0.136389π-0.136389\pi
0.242284 + 0.970205i 0.422103π0.422103\pi
822822 0.354409 0.0808916i 0.0123614 0.00282142i
823823 −11.6578 24.2077i −0.406366 0.843828i −0.999257 0.0385451i 0.987728π-0.987728\pi
0.592891 0.805283i 0.297987π-0.297987\pi
824824 0.589341i 0.0205307i
825825 9.92805 4.78110i 0.345650 0.166456i
826826 0.420554 0.335381i 0.0146329 0.0116694i
827827 −1.99392 + 1.59010i −0.0693355 + 0.0552932i −0.657544 0.753416i 0.728405π-0.728405\pi
0.588209 + 0.808709i 0.299833π0.299833\pi
828828 40.3094 19.4120i 1.40085 0.674614i
829829 29.2663i 1.01646i −0.861221 0.508230i 0.830300π-0.830300\pi
0.861221 0.508230i 0.169700π-0.169700\pi
830830 0.495238 + 1.02837i 0.0171900 + 0.0356953i
831831 −3.17252 + 0.724106i −0.110053 + 0.0251190i
832832 18.4828 + 8.90086i 0.640777 + 0.308582i
833833 6.31841 13.1203i 0.218920 0.454592i
834834 0.629303 2.75716i 0.0217910 0.0954726i
835835 15.1194 + 18.9591i 0.523229 + 0.656108i
836836 0.874518 1.09661i 0.0302458 0.0379271i
837837 −5.04782 22.1160i −0.174478 0.764439i
838838 1.14814 + 0.262056i 0.0396619 + 0.00905256i
839839 −36.2667 28.9217i −1.25206 0.998488i −0.999522 0.0309019i 0.990162π-0.990162\pi
−0.252542 0.967586i 0.581267π-0.581267\pi
840840 1.81658 0.0626781
841841 0 0
842842 1.27925 0.0440860
843843 70.7467 + 56.4186i 2.43665 + 1.94316i
844844 −0.495249 0.113037i −0.0170472 0.00389091i
845845 2.46324 + 10.7921i 0.0847379 + 0.371261i
846846 1.63989 2.05635i 0.0563805 0.0706989i
847847 9.69371 + 12.1555i 0.333080 + 0.417669i
848848 −8.81523 + 38.6221i −0.302716 + 1.32629i
849849 35.1412 72.9715i 1.20604 2.50438i
850850 0.388709 + 0.187192i 0.0133326 + 0.00642064i
851851 −23.2448 + 5.30548i −0.796822 + 0.181869i
852852 5.99273 + 12.4440i 0.205308 + 0.426326i
853853 51.5353i 1.76453i −0.470749 0.882267i 0.656016π-0.656016\pi
0.470749 0.882267i 0.343984π-0.343984\pi
854854 0.619744 0.298453i 0.0212072 0.0102128i
855855 −3.18377 + 2.53897i −0.108882 + 0.0868309i
856856 0.582665 0.464659i 0.0199151 0.0158817i
857857 −15.5150 + 7.47163i −0.529982 + 0.255226i −0.679684 0.733505i 0.737883π-0.737883\pi
0.149701 + 0.988731i 0.452169π0.452169\pi
858858 0.606280i 0.0206981i
859859 −6.13784 12.7454i −0.209420 0.434866i 0.769628 0.638492i 0.220442π-0.220442\pi
−0.979049 + 0.203626i 0.934727π0.934727\pi
860860 3.37853 0.771127i 0.115207 0.0262952i
861861 −52.9172 25.4836i −1.80341 0.868477i
862862 −0.177001 + 0.367547i −0.00602869 + 0.0125187i
863863 −4.14122 + 18.1439i −0.140969 + 0.617624i 0.854242 + 0.519875i 0.174021π0.174021\pi
−0.995211 + 0.0977493i 0.968836π0.968836\pi
864864 −3.00589 3.76926i −0.102262 0.128233i
865865 9.10788 11.4209i 0.309677 0.388323i
866866 0.216820 + 0.949949i 0.00736783 + 0.0322806i
867867 −30.6708 7.00040i −1.04163 0.237746i
868868 −7.58987 6.05272i −0.257617 0.205443i
869869 19.0310 0.645583
870870 0 0
871871 −10.6679 −0.361469
872872 1.54233 + 1.22996i 0.0522298 + 0.0416518i
873873 31.1315 + 7.10557i 1.05364 + 0.240487i
874874 −0.0128441 0.0562738i −0.000434459 0.00190349i
875875 −15.5366 + 19.4822i −0.525231 + 0.658619i
876876 −34.1913 42.8745i −1.15522 1.44859i
877877 −1.89286 + 8.29317i −0.0639174 + 0.280041i −0.996779 0.0801937i 0.974446π-0.974446\pi
0.932862 + 0.360234i 0.117303π0.117303\pi
878878 0.248016 0.515010i 0.00837013 0.0173808i
879879 −15.8501 7.63299i −0.534610 0.257454i
880880 12.5473 2.86383i 0.422968 0.0965396i
881881 −13.5226 28.0800i −0.455588 0.946038i −0.994604 0.103743i 0.966918π-0.966918\pi
0.539016 0.842295i 0.318796π-0.318796\pi
882882 0.719788i 0.0242365i
883883 18.3332 8.82880i 0.616961 0.297113i −0.0991789 0.995070i 0.531622π-0.531622\pi
0.716140 + 0.697957i 0.245907π0.245907\pi
884884 −21.0778 + 16.8090i −0.708925 + 0.565348i
885885 −25.7505 + 20.5353i −0.865592 + 0.690287i
886886 0.346670 0.166948i 0.0116466 0.00560871i
887887 11.2240i 0.376866i −0.982086 0.188433i 0.939659π-0.939659\pi
0.982086 0.188433i 0.0603408π-0.0603408\pi
888888 1.44688 + 3.00448i 0.0485542 + 0.100824i
889889 24.1186 5.50491i 0.808911 0.184629i
890890 0.633120 + 0.304895i 0.0212222 + 0.0102201i
891891 8.46265 17.5729i 0.283509 0.588713i
892892 −4.07155 + 17.8386i −0.136325 + 0.597281i
893893 2.40287 + 3.01310i 0.0804089 + 0.100830i
894894 −0.335437 + 0.420625i −0.0112187 + 0.0140678i
895895 −7.62701 33.4161i −0.254943 1.11698i
896896 −2.68150 0.612036i −0.0895828 0.0204467i
897897 22.1544 + 17.6675i 0.739714 + 0.589902i
898898 0.744296 0.0248375
899899 0 0
900900 24.2194 0.807314
901901 −40.6315 32.4026i −1.35363 1.07949i
902902 0.715327 + 0.163269i 0.0238178 + 0.00543625i
903903 −1.37742 6.03486i −0.0458376 0.200828i
904904 −1.19409 + 1.49735i −0.0397149 + 0.0498010i
905905 13.0918 + 16.4167i 0.435188 + 0.545708i
906906 0.220275 0.965089i 0.00731816 0.0320629i
907907 −17.7000 + 36.7544i −0.587718 + 1.22041i 0.369011 + 0.929425i 0.379697π0.379697\pi
−0.956728 + 0.290983i 0.906018π0.906018\pi
908908 8.66772 + 4.17416i 0.287648 + 0.138524i
909909 −50.8747 + 11.6118i −1.68741 + 0.385140i
910910 0.167845 + 0.348533i 0.00556400 + 0.0115538i
911911 30.2991i 1.00385i 0.864910 + 0.501926i 0.167375π0.167375\pi
−0.864910 + 0.501926i 0.832625π0.832625\pi
912912 4.12501 1.98650i 0.136593 0.0657796i
913913 22.6161 18.0358i 0.748485 0.596897i
914914 0.0827553 0.0659952i 0.00273730 0.00218293i
915915 −37.9468 + 18.2742i −1.25448 + 0.604127i
916916 13.7199i 0.453320i
917917 −13.0042 27.0036i −0.429438 0.891736i
918918 2.05231 0.468427i 0.0677365 0.0154604i
919919 −23.9089 11.5139i −0.788680 0.379808i −0.00422290 0.999991i 0.501344π-0.501344\pi
−0.784457 + 0.620183i 0.787058π0.787058\pi
920920 0.460201 0.955618i 0.0151724 0.0315058i
921921 3.47205 15.2121i 0.114408 0.501254i
922922 −0.261859 0.328361i −0.00862388 0.0108140i
923923 −3.66928 + 4.60114i −0.120776 + 0.151448i
924924 −5.12000 22.4322i −0.168436 0.737964i
925925 −12.5832 2.87204i −0.413735 0.0944322i
926926 −0.913270 0.728308i −0.0300119 0.0239337i
927927 −21.6720 −0.711801
928928 0 0
929929 4.73988 0.155510 0.0777551 0.996972i 0.475225π-0.475225\pi
0.0777551 + 0.996972i 0.475225π0.475225\pi
930930 −0.409183 0.326313i −0.0134176 0.0107002i
931931 −1.02824 0.234688i −0.0336991 0.00769159i
932932 −7.66140 33.5668i −0.250957 1.09952i
933933 20.0563 25.1498i 0.656613 0.823367i
934934 0.531624 + 0.666636i 0.0173953 + 0.0218130i
935935 −3.75694 + 16.4602i −0.122865 + 0.538307i
936936 1.15685 2.40222i 0.0378128 0.0785192i
937937 −16.8106 8.09556i −0.549179 0.264471i 0.138653 0.990341i 0.455723π-0.455723\pi
−0.687831 + 0.725871i 0.741437π0.741437\pi
938938 0.347535 0.0793226i 0.0113474 0.00258997i
939939 21.9521 + 45.5841i 0.716381 + 1.48758i
940940 35.3933i 1.15440i
941941 −20.3307 + 9.79076i −0.662762 + 0.319170i −0.734851 0.678229i 0.762748π-0.762748\pi
0.0720885 + 0.997398i 0.477034π0.477034\pi
942942 −0.628261 + 0.501022i −0.0204699 + 0.0163242i
943943 −26.8114 + 21.3813i −0.873098 + 0.696272i
944944 22.4450 10.8089i 0.730522 0.351801i
945945 34.3062i 1.11598i
946946 0.0335516 + 0.0696706i 0.00109086 + 0.00226519i
947947 −26.9443 + 6.14987i −0.875573 + 0.199844i −0.636611 0.771185i 0.719664π-0.719664\pi
−0.238962 + 0.971029i 0.576807π0.576807\pi
948948 56.0184 + 26.9770i 1.81939 + 0.876174i
949949 10.1382 21.0521i 0.329099 0.683381i
950950 0.00695298 0.0304630i 0.000225584 0.000988350i
951951 −2.81510 3.53003i −0.0912859 0.114469i
952952 1.12385 1.40927i 0.0364243 0.0456746i
953953 8.31233 + 36.4187i 0.269263 + 1.17972i 0.910873 + 0.412687i 0.135410π0.135410\pi
−0.641610 + 0.767031i 0.721733π0.721733\pi
954954 2.50433 + 0.571598i 0.0810808 + 0.0185062i
955955 −15.8265 12.6212i −0.512134 0.408413i
956956 −42.5708 −1.37684
957957 0 0
958958 −0.899769 −0.0290702
959959 4.59591 + 3.66512i 0.148410 + 0.118353i
960960 40.9205 + 9.33983i 1.32070 + 0.301442i
961961 −5.65288 24.7669i −0.182351 0.798932i
962962 −0.442760 + 0.555204i −0.0142752 + 0.0179005i
963963 17.0870 + 21.4265i 0.550622 + 0.690458i
964964 −3.99879 + 17.5199i −0.128792 + 0.564277i
965965 −14.4007 + 29.9033i −0.463574 + 0.962621i
966966 −0.853106 0.410834i −0.0274482 0.0132184i
967967 38.9506 8.89021i 1.25257 0.285890i 0.455747 0.890109i 0.349372π-0.349372\pi
0.796818 + 0.604219i 0.206515π0.206515\pi
968968 −0.550883 1.14392i −0.0177061 0.0367670i
969969 6.00624i 0.192948i
970970 0.340874 0.164156i 0.0109448 0.00527074i
971971 11.5571 9.21647i 0.370885 0.295771i −0.420255 0.907406i 0.638059π-0.638059\pi
0.791140 + 0.611635i 0.209488π0.209488\pi
972972 4.87637 3.88878i 0.156410 0.124733i
973973 41.2026 19.8421i 1.32090 0.636110i
974974 0.687749i 0.0220369i
975975 6.65559 + 13.8205i 0.213150 + 0.442610i
976976 31.0582 7.08882i 0.994147 0.226908i
977977 8.85513 + 4.26441i 0.283301 + 0.136430i 0.570138 0.821549i 0.306890π-0.306890\pi
−0.286837 + 0.957979i 0.592604π0.592604\pi
978978 −0.0969505 + 0.201320i −0.00310013 + 0.00643750i
979979 3.96289 17.3625i 0.126654 0.554909i
980980 −6.03906 7.57274i −0.192911 0.241902i
981981 −45.2298 + 56.7164i −1.44408 + 1.81081i
982982 0.273242 + 1.19715i 0.00871951 + 0.0382027i
983983 46.1811 + 10.5405i 1.47295 + 0.336191i 0.882280 0.470724i 0.156007π-0.156007\pi
0.590667 + 0.806915i 0.298865π0.298865\pi
984984 3.74995 + 2.99048i 0.119544 + 0.0953332i
985985 29.1037 0.927320
986986 0 0
987987 63.2209 2.01234
988988 1.52655 + 1.21739i 0.0485661 + 0.0387302i
989989 −3.52360 0.804238i −0.112044 0.0255733i
990990 −0.185697 0.813590i −0.00590182 0.0258576i
991991 30.5393 38.2950i 0.970112 1.21648i −0.00617090 0.999981i 0.501964π-0.501964\pi
0.976283 0.216501i 0.0694643π-0.0694643\pi
992992 0.741534 + 0.929854i 0.0235437 + 0.0295229i
993993 20.1313 88.2012i 0.638849 2.79898i
994994 0.0853241 0.177177i 0.00270632 0.00561972i
995995 13.9821 + 6.73344i 0.443263 + 0.213464i
996996 92.1376 21.0298i 2.91949 0.666355i
997997 −0.504144 1.04687i −0.0159664 0.0331546i 0.892833 0.450388i 0.148714π-0.148714\pi
−0.908800 + 0.417233i 0.863000π0.863000\pi
998998 0.196054i 0.00620597i
999999 −56.7397 + 27.3244i −1.79516 + 0.864506i
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 841.2.e.m.267.9 96
29.2 odd 28 841.2.d.q.778.5 48
29.3 odd 28 841.2.d.q.605.4 48
29.4 even 14 inner 841.2.e.m.270.9 96
29.5 even 14 inner 841.2.e.m.63.9 96
29.6 even 14 inner 841.2.e.m.651.8 96
29.7 even 7 inner 841.2.e.m.236.8 96
29.8 odd 28 841.2.d.p.645.5 48
29.9 even 14 inner 841.2.e.m.196.8 96
29.10 odd 28 841.2.d.p.571.5 48
29.11 odd 28 841.2.a.i.1.5 8
29.12 odd 4 841.2.d.p.574.4 48
29.13 even 14 841.2.b.f.840.8 16
29.14 odd 28 841.2.d.q.190.4 48
29.15 odd 28 841.2.d.p.190.5 48
29.16 even 7 841.2.b.f.840.9 16
29.17 odd 4 841.2.d.q.574.5 48
29.18 odd 28 841.2.a.j.1.4 yes 8
29.19 odd 28 841.2.d.q.571.4 48
29.20 even 7 inner 841.2.e.m.196.9 96
29.21 odd 28 841.2.d.q.645.4 48
29.22 even 14 inner 841.2.e.m.236.9 96
29.23 even 7 inner 841.2.e.m.651.9 96
29.24 even 7 inner 841.2.e.m.63.8 96
29.25 even 7 inner 841.2.e.m.270.8 96
29.26 odd 28 841.2.d.p.605.5 48
29.27 odd 28 841.2.d.p.778.4 48
29.28 even 2 inner 841.2.e.m.267.8 96
87.11 even 28 7569.2.a.bi.1.4 8
87.47 even 28 7569.2.a.bd.1.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
841.2.a.i.1.5 8 29.11 odd 28
841.2.a.j.1.4 yes 8 29.18 odd 28
841.2.b.f.840.8 16 29.13 even 14
841.2.b.f.840.9 16 29.16 even 7
841.2.d.p.190.5 48 29.15 odd 28
841.2.d.p.571.5 48 29.10 odd 28
841.2.d.p.574.4 48 29.12 odd 4
841.2.d.p.605.5 48 29.26 odd 28
841.2.d.p.645.5 48 29.8 odd 28
841.2.d.p.778.4 48 29.27 odd 28
841.2.d.q.190.4 48 29.14 odd 28
841.2.d.q.571.4 48 29.19 odd 28
841.2.d.q.574.5 48 29.17 odd 4
841.2.d.q.605.4 48 29.3 odd 28
841.2.d.q.645.4 48 29.21 odd 28
841.2.d.q.778.5 48 29.2 odd 28
841.2.e.m.63.8 96 29.24 even 7 inner
841.2.e.m.63.9 96 29.5 even 14 inner
841.2.e.m.196.8 96 29.9 even 14 inner
841.2.e.m.196.9 96 29.20 even 7 inner
841.2.e.m.236.8 96 29.7 even 7 inner
841.2.e.m.236.9 96 29.22 even 14 inner
841.2.e.m.267.8 96 29.28 even 2 inner
841.2.e.m.267.9 96 1.1 even 1 trivial
841.2.e.m.270.8 96 29.25 even 7 inner
841.2.e.m.270.9 96 29.4 even 14 inner
841.2.e.m.651.8 96 29.6 even 14 inner
841.2.e.m.651.9 96 29.23 even 7 inner
7569.2.a.bd.1.5 8 87.47 even 28
7569.2.a.bi.1.4 8 87.11 even 28