Properties

Label 588.2.n.h.263.3
Level 588588
Weight 22
Character 588.263
Analytic conductor 4.6954.695
Analytic rank 00
Dimension 2424
Inner twists 88

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [588,2,Mod(263,588)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(588, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("588.263");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 588=22372 588 = 2^{2} \cdot 3 \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 588.n (of order 66, degree 22, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.695203638854.69520363885
Analytic rank: 00
Dimension: 2424
Relative dimension: 1212 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 263.3
Character χ\chi == 588.263
Dual form 588.2.n.h.275.3

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.342960.443234i)q2+(1.661430.489533i)q3+(1.60709+1.19049i)q4+(1.085700.626827i)q5+(2.01426+1.39383i)q6+(1.630592.31110i)q8+(2.52072+1.62665i)q9+(1.73588+0.360587i)q10+(2.52914+4.38059i)q11+(2.087282.76464i)q12+4.41798q13+(2.11066+0.509947i)q15+(1.16546+3.82645i)q16+(5.069202.92671i)q17+(2.664233.30180i)q18+(1.32654+0.765881i)q19+(2.49104+0.285146i)q20+(5.338164.76197i)q22+(0.1567850.271560i)q23+(1.57776+4.63796i)q24+(1.71417+2.96904i)q25+(5.933171.95820i)q26+(3.391703.93654i)q27+5.53862iq29+(3.06057+0.250679i)q30+(4.24264+2.44949i)q31+(0.1308435.65534i)q32+(6.346436.03996i)q33+(5.51053+6.17729i)q34+(2.11450+5.61506i)q36+(2.66908+4.62298i)q37+(2.120960.440578i)q38+(7.340172.16275i)q39+(3.218991.48705i)q40+1.97938iq413.18613iq43+(9.27960+4.02908i)q44+(3.75636+0.185997i)q45+(0.0901918+0.434187i)q46+(5.74813+9.95606i)q47+(0.06316196.92792i)q48+(3.618053.22752i)q50+(6.98942+7.34407i)q51+(7.10008+5.25957i)q52+(11.0767+6.39513i)q53+(2.81011+6.78994i)q54+6.34133iq55+(2.578890.623072i)q57+(2.454907.43815i)q58+(3.983516.89964i)q59+(3.999111.69320i)q60+(0.151445+0.262310i)q61+(4.612005.17005i)q62+(2.68236+7.53691i)q64+(4.796592.76931i)q65+(11.2001+5.29848i)q66+(9.13122+5.27191i)q67+(4.6624410.7383i)q68+(0.127550+0.527930i)q69+4.53490q71+(0.3508998.47802i)q72+(0.707107+1.22474i)q73+(1.535417.39151i)q74+(4.301434.09371i)q75+(3.043650.348402i)q76+(8.89896+6.15790i)q78+(6.00000+3.46410i)q79+(3.66386+3.42382i)q80+(3.70801+8.20065i)q81+(0.8773282.65823i)q82+6.78340q837.33816q85+(1.41220+4.27885i)q86+(2.711349.20204i)q87+(14.24801.29786i)q88+(4.15480+2.39878i)q89+(4.962211.91473i)q90+(0.07132220.623072i)q92+(5.849756.14657i)q93+(3.3066615.9184i)q94+(0.960150+1.66303i)q95+(2.98586+9.33191i)q9613.6844q97+(13.5009+6.92820i)q99+O(q100)q+(-1.34296 - 0.443234i) q^{2} +(-1.66143 - 0.489533i) q^{3} +(1.60709 + 1.19049i) q^{4} +(1.08570 - 0.626827i) q^{5} +(2.01426 + 1.39383i) q^{6} +(-1.63059 - 2.31110i) q^{8} +(2.52072 + 1.62665i) q^{9} +(-1.73588 + 0.360587i) q^{10} +(-2.52914 + 4.38059i) q^{11} +(-2.08728 - 2.76464i) q^{12} +4.41798 q^{13} +(-2.11066 + 0.509947i) q^{15} +(1.16546 + 3.82645i) q^{16} +(-5.06920 - 2.92671i) q^{17} +(-2.66423 - 3.30180i) q^{18} +(-1.32654 + 0.765881i) q^{19} +(2.49104 + 0.285146i) q^{20} +(5.33816 - 4.76197i) q^{22} +(-0.156785 - 0.271560i) q^{23} +(1.57776 + 4.63796i) q^{24} +(-1.71417 + 2.96904i) q^{25} +(-5.93317 - 1.95820i) q^{26} +(-3.39170 - 3.93654i) q^{27} +5.53862i q^{29} +(3.06057 + 0.250679i) q^{30} +(4.24264 + 2.44949i) q^{31} +(0.130843 - 5.65534i) q^{32} +(6.34643 - 6.03996i) q^{33} +(5.51053 + 6.17729i) q^{34} +(2.11450 + 5.61506i) q^{36} +(2.66908 + 4.62298i) q^{37} +(2.12096 - 0.440578i) q^{38} +(-7.34017 - 2.16275i) q^{39} +(-3.21899 - 1.48705i) q^{40} +1.97938i q^{41} -3.18613i q^{43} +(-9.27960 + 4.02908i) q^{44} +(3.75636 + 0.185997i) q^{45} +(0.0901918 + 0.434187i) q^{46} +(5.74813 + 9.95606i) q^{47} +(-0.0631619 - 6.92792i) q^{48} +(3.61805 - 3.22752i) q^{50} +(6.98942 + 7.34407i) q^{51} +(7.10008 + 5.25957i) q^{52} +(11.0767 + 6.39513i) q^{53} +(2.81011 + 6.78994i) q^{54} +6.34133i q^{55} +(2.57889 - 0.623072i) q^{57} +(2.45490 - 7.43815i) q^{58} +(3.98351 - 6.89964i) q^{59} +(-3.99911 - 1.69320i) q^{60} +(0.151445 + 0.262310i) q^{61} +(-4.61200 - 5.17005i) q^{62} +(-2.68236 + 7.53691i) q^{64} +(4.79659 - 2.76931i) q^{65} +(-11.2001 + 5.29848i) q^{66} +(9.13122 + 5.27191i) q^{67} +(-4.66244 - 10.7383i) q^{68} +(0.127550 + 0.527930i) q^{69} +4.53490 q^{71} +(-0.350899 - 8.47802i) q^{72} +(-0.707107 + 1.22474i) q^{73} +(-1.53541 - 7.39151i) q^{74} +(4.30143 - 4.09371i) q^{75} +(-3.04365 - 0.348402i) q^{76} +(8.89896 + 6.15790i) q^{78} +(-6.00000 + 3.46410i) q^{79} +(3.66386 + 3.42382i) q^{80} +(3.70801 + 8.20065i) q^{81} +(0.877328 - 2.65823i) q^{82} +6.78340 q^{83} -7.33816 q^{85} +(-1.41220 + 4.27885i) q^{86} +(2.71134 - 9.20204i) q^{87} +(14.2480 - 1.29786i) q^{88} +(-4.15480 + 2.39878i) q^{89} +(-4.96221 - 1.91473i) q^{90} +(0.0713222 - 0.623072i) q^{92} +(-5.84975 - 6.14657i) q^{93} +(-3.30666 - 15.9184i) q^{94} +(-0.960150 + 1.66303i) q^{95} +(-2.98586 + 9.33191i) q^{96} -13.6844 q^{97} +(-13.5009 + 6.92820i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q+12q4+60q16+24q18+12q25+36q30+12q3696q39+24q46+12q5124q57+48q58+12q6048q6448q6736q7224q78144q79+24q93+O(q100) 24 q + 12 q^{4} + 60 q^{16} + 24 q^{18} + 12 q^{25} + 36 q^{30} + 12 q^{36} - 96 q^{39} + 24 q^{46} + 12 q^{51} - 24 q^{57} + 48 q^{58} + 12 q^{60} - 48 q^{64} - 48 q^{67} - 36 q^{72} - 24 q^{78} - 144 q^{79}+ \cdots - 24 q^{93}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/588Z)×\left(\mathbb{Z}/588\mathbb{Z}\right)^\times.

nn 197197 295295 493493
χ(n)\chi(n) 1-1 1-1 e(23)e\left(\frac{2}{3}\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 −1.34296 0.443234i −0.949617 0.313414i
33 −1.66143 0.489533i −0.959228 0.282632i
44 1.60709 + 1.19049i 0.803544 + 0.595246i
55 1.08570 0.626827i 0.485538 0.280326i −0.237183 0.971465i 0.576224π-0.576224\pi
0.722722 + 0.691139i 0.242891π0.242891\pi
66 2.01426 + 1.39383i 0.822319 + 0.569027i
77 0 0
88 −1.63059 2.31110i −0.576500 0.817097i
99 2.52072 + 1.62665i 0.840238 + 0.542217i
1010 −1.73588 + 0.360587i −0.548933 + 0.114028i
1111 −2.52914 + 4.38059i −0.762563 + 1.32080i 0.178962 + 0.983856i 0.442726π0.442726\pi
−0.941525 + 0.336942i 0.890607π0.890607\pi
1212 −2.08728 2.76464i −0.602547 0.798084i
1313 4.41798 1.22533 0.612664 0.790344i 0.290098π-0.290098\pi
0.612664 + 0.790344i 0.290098π0.290098\pi
1414 0 0
1515 −2.11066 + 0.509947i −0.544971 + 0.131668i
1616 1.16546 + 3.82645i 0.291365 + 0.956612i
1717 −5.06920 2.92671i −1.22946 0.709831i −0.262545 0.964920i 0.584562π-0.584562\pi
−0.966918 + 0.255089i 0.917895π0.917895\pi
1818 −2.66423 3.30180i −0.627966 0.778241i
1919 −1.32654 + 0.765881i −0.304330 + 0.175705i −0.644386 0.764700i 0.722887π-0.722887\pi
0.340056 + 0.940405i 0.389554π0.389554\pi
2020 2.49104 + 0.285146i 0.557014 + 0.0637607i
2121 0 0
2222 5.33816 4.76197i 1.13810 1.01525i
2323 −0.156785 0.271560i −0.0326920 0.0566242i 0.849217 0.528045i 0.177075π-0.177075\pi
−0.881908 + 0.471421i 0.843741π0.843741\pi
2424 1.57776 + 4.63796i 0.322058 + 0.946720i
2525 −1.71417 + 2.96904i −0.342835 + 0.593808i
2626 −5.93317 1.95820i −1.16359 0.384034i
2727 −3.39170 3.93654i −0.652733 0.757588i
2828 0 0
2929 5.53862i 1.02850i 0.857642 + 0.514248i 0.171929π0.171929\pi
−0.857642 + 0.514248i 0.828071π0.828071\pi
3030 3.06057 + 0.250679i 0.558780 + 0.0457675i
3131 4.24264 + 2.44949i 0.762001 + 0.439941i 0.830014 0.557743i 0.188333π-0.188333\pi
−0.0680129 + 0.997684i 0.521666π0.521666\pi
3232 0.130843 5.65534i 0.0231301 0.999732i
3333 6.34643 6.03996i 1.10477 1.05142i
3434 5.51053 + 6.17729i 0.945048 + 1.05940i
3535 0 0
3636 2.11450 + 5.61506i 0.352416 + 0.935843i
3737 2.66908 + 4.62298i 0.438794 + 0.760013i 0.997597 0.0692872i 0.0220725π-0.0220725\pi
−0.558803 + 0.829301i 0.688739π0.688739\pi
3838 2.12096 0.440578i 0.344065 0.0714713i
3939 −7.34017 2.16275i −1.17537 0.346317i
4040 −3.21899 1.48705i −0.508966 0.235124i
4141 1.97938i 0.309127i 0.987983 + 0.154564i 0.0493971π0.0493971\pi
−0.987983 + 0.154564i 0.950603π0.950603\pi
4242 0 0
4343 3.18613i 0.485881i −0.970041 0.242940i 0.921888π-0.921888\pi
0.970041 0.242940i 0.0781119π-0.0781119\pi
4444 −9.27960 + 4.02908i −1.39895 + 0.607407i
4545 3.75636 + 0.185997i 0.559965 + 0.0277268i
4646 0.0901918 + 0.434187i 0.0132981 + 0.0640174i
4747 5.74813 + 9.95606i 0.838451 + 1.45224i 0.891189 + 0.453632i 0.149872π0.149872\pi
−0.0527378 + 0.998608i 0.516795π0.516795\pi
4848 −0.0631619 6.92792i −0.00911663 0.999958i
4949 0 0
5050 3.61805 3.22752i 0.511669 0.456440i
5151 6.98942 + 7.34407i 0.978715 + 1.02838i
5252 7.10008 + 5.25957i 0.984604 + 0.729371i
5353 11.0767 + 6.39513i 1.52150 + 0.878439i 0.999678 + 0.0253856i 0.00808135π0.00808135\pi
0.521823 + 0.853054i 0.325252π0.325252\pi
5454 2.81011 + 6.78994i 0.382407 + 0.923994i
5555 6.34133i 0.855064i
5656 0 0
5757 2.57889 0.623072i 0.341582 0.0825279i
5858 2.45490 7.43815i 0.322345 0.976677i
5959 3.98351 6.89964i 0.518608 0.898256i −0.481158 0.876634i 0.659784π-0.659784\pi
0.999766 0.0216222i 0.00688310π-0.00688310\pi
6060 −3.99911 1.69320i −0.516283 0.218591i
6161 0.151445 + 0.262310i 0.0193905 + 0.0335853i 0.875558 0.483113i 0.160494π-0.160494\pi
−0.856167 + 0.516699i 0.827161π0.827161\pi
6262 −4.61200 5.17005i −0.585725 0.656597i
6363 0 0
6464 −2.68236 + 7.53691i −0.335295 + 0.942113i
6565 4.79659 2.76931i 0.594943 0.343491i
6666 −11.2001 + 5.29848i −1.37864 + 0.652198i
6767 9.13122 + 5.27191i 1.11556 + 0.644067i 0.940263 0.340450i 0.110579π-0.110579\pi
0.175293 + 0.984516i 0.443913π0.443913\pi
6868 −4.66244 10.7383i −0.565403 1.30221i
6969 0.127550 + 0.527930i 0.0153553 + 0.0635553i
7070 0 0
7171 4.53490 0.538194 0.269097 0.963113i 0.413275π-0.413275\pi
0.269097 + 0.963113i 0.413275π0.413275\pi
7272 −0.350899 8.47802i −0.0413539 0.999145i
7373 −0.707107 + 1.22474i −0.0827606 + 0.143346i −0.904435 0.426612i 0.859707π-0.859707\pi
0.821674 + 0.569958i 0.193040π0.193040\pi
7474 −1.53541 7.39151i −0.178487 0.859245i
7575 4.30143 4.09371i 0.496686 0.472701i
7676 −3.04365 0.348402i −0.349130 0.0399645i
7777 0 0
7878 8.89896 + 6.15790i 1.00761 + 0.697245i
7979 −6.00000 + 3.46410i −0.675053 + 0.389742i −0.797988 0.602673i 0.794102π-0.794102\pi
0.122936 + 0.992415i 0.460769π0.460769\pi
8080 3.66386 + 3.42382i 0.409632 + 0.382795i
8181 3.70801 + 8.20065i 0.412001 + 0.911183i
8282 0.877328 2.65823i 0.0968847 0.293552i
8383 6.78340 0.744575 0.372287 0.928118i 0.378574π-0.378574\pi
0.372287 + 0.928118i 0.378574π0.378574\pi
8484 0 0
8585 −7.33816 −0.795935
8686 −1.41220 + 4.27885i −0.152282 + 0.461400i
8787 2.71134 9.20204i 0.290686 0.986563i
8888 14.2480 1.29786i 1.51884 0.138353i
8989 −4.15480 + 2.39878i −0.440408 + 0.254270i −0.703771 0.710427i 0.748502π-0.748502\pi
0.263363 + 0.964697i 0.415168π0.415168\pi
9090 −4.96221 1.91473i −0.523063 0.201831i
9191 0 0
9292 0.0713222 0.623072i 0.00743586 0.0649597i
9393 −5.84975 6.14657i −0.606591 0.637370i
9494 −3.30666 15.9184i −0.341055 1.64185i
9595 −0.960150 + 1.66303i −0.0985093 + 0.170623i
9696 −2.98586 + 9.33191i −0.304743 + 0.952435i
9797 −13.6844 −1.38944 −0.694719 0.719281i 0.744471π-0.744471\pi
−0.694719 + 0.719281i 0.744471π0.744471\pi
9898 0 0
9999 −13.5009 + 6.92820i −1.35689 + 0.696311i
100100 −6.28944 + 2.73079i −0.628944 + 0.273079i
101101 −3.52631 2.03591i −0.350881 0.202581i 0.314192 0.949359i 0.398266π-0.398266\pi
−0.665073 + 0.746778i 0.731600π0.731600\pi
102102 −6.13138 12.9607i −0.607097 1.28330i
103103 −11.3239 + 6.53788i −1.11578 + 0.644197i −0.940321 0.340290i 0.889475π-0.889475\pi
−0.175461 + 0.984486i 0.556141π0.556141\pi
104104 −7.20391 10.2104i −0.706402 1.00121i
105105 0 0
106106 −12.0410 13.4980i −1.16953 1.31104i
107107 −1.95388 3.38422i −0.188889 0.327165i 0.755991 0.654582i 0.227155π-0.227155\pi
−0.944880 + 0.327417i 0.893822π0.893822\pi
108108 −0.764334 10.3642i −0.0735481 0.997292i
109109 4.12398 7.14295i 0.395006 0.684170i −0.598096 0.801424i 0.704076π-0.704076\pi
0.993102 + 0.117254i 0.0374092π0.0374092\pi
110110 2.81069 8.51615i 0.267989 0.811983i
111111 −2.17139 8.98737i −0.206100 0.853044i
112112 0 0
113113 6.72485i 0.632621i 0.948656 + 0.316311i 0.102444π0.102444\pi
−0.948656 + 0.316311i 0.897556π0.897556\pi
114114 −3.73951 0.306289i −0.350237 0.0286866i
115115 −0.340442 0.196554i −0.0317464 0.0183288i
116116 −6.59368 + 8.90105i −0.612208 + 0.826442i
117117 11.1365 + 7.18651i 1.02957 + 0.664393i
118118 −8.40785 + 7.50032i −0.774005 + 0.690460i
119119 0 0
120120 4.62016 + 4.04644i 0.421761 + 0.369388i
121121 −7.29306 12.6320i −0.663006 1.14836i
122122 −0.0871196 0.419397i −0.00788744 0.0379704i
123123 0.968971 3.28861i 0.0873692 0.296524i
124124 3.90220 + 8.98737i 0.350428 + 0.807090i
125125 10.5662i 0.945073i
126126 0 0
127127 8.50404i 0.754611i −0.926089 0.377306i 0.876851π-0.876851\pi
0.926089 0.377306i 0.123149π-0.123149\pi
128128 6.94291 8.93286i 0.613672 0.789561i
129129 −1.55972 + 5.29354i −0.137325 + 0.466070i
130130 −7.66908 + 1.59307i −0.672623 + 0.139721i
131131 4.20524 + 7.28368i 0.367413 + 0.636378i 0.989160 0.146840i 0.0469102π-0.0469102\pi
−0.621747 + 0.783218i 0.713577π0.713577\pi
132132 17.3898 2.15138i 1.51359 0.187253i
133133 0 0
134134 −9.92618 11.1272i −0.857491 0.961247i
135135 −6.14989 2.14788i −0.529298 0.184860i
136136 1.50188 + 16.4877i 0.128785 + 1.41381i
137137 −11.9136 6.87834i −1.01785 0.587657i −0.104370 0.994539i 0.533283π-0.533283\pi
−0.913481 + 0.406882i 0.866616π0.866616\pi
138138 0.0627011 0.765524i 0.00533747 0.0651657i
139139 13.1652i 1.11666i 0.829620 + 0.558328i 0.188557π0.188557\pi
−0.829620 + 0.558328i 0.811443π0.811443\pi
140140 0 0
141141 −4.67632 19.3552i −0.393817 1.63000i
142142 −6.09019 2.01002i −0.511078 0.168677i
143143 −11.1737 + 19.3534i −0.934389 + 1.61841i
144144 −3.28650 + 11.5412i −0.273875 + 0.961765i
145145 3.47176 + 6.01326i 0.288314 + 0.499374i
146146 1.49247 1.33137i 0.123517 0.110185i
147147 0 0
148148 −1.21417 + 10.6071i −0.0998046 + 0.871894i
149149 9.78354 5.64853i 0.801499 0.462745i −0.0424963 0.999097i 0.513531π-0.513531\pi
0.843995 + 0.536351i 0.180198π0.180198\pi
150150 −7.59112 + 3.59116i −0.619812 + 0.293217i
151151 −9.61268 5.54988i −0.782269 0.451643i 0.0549650 0.998488i 0.482495π-0.482495\pi
−0.837234 + 0.546845i 0.815829π0.815829\pi
152152 3.93307 + 1.81694i 0.319015 + 0.147373i
153153 −8.01729 15.6232i −0.648159 1.26306i
154154 0 0
155155 6.14163 0.493307
156156 −9.22157 12.2141i −0.738317 0.977914i
157157 7.39785 12.8135i 0.590413 1.02262i −0.403764 0.914863i 0.632298π-0.632298\pi
0.994177 0.107762i 0.0343684π-0.0343684\pi
158158 9.59317 1.99275i 0.763192 0.158535i
159159 −15.2726 16.0475i −1.21119 1.27265i
160160 −3.40287 6.22200i −0.269020 0.491892i
161161 0 0
162162 −1.34491 12.6567i −0.105666 0.994402i
163163 11.4887 6.63300i 0.899864 0.519537i 0.0227080 0.999742i 0.492771π-0.492771\pi
0.877156 + 0.480205i 0.159438π0.159438\pi
164164 −2.35643 + 3.18104i −0.184007 + 0.248397i
165165 3.10429 10.5357i 0.241668 0.820202i
166166 −9.10984 3.00663i −0.707060 0.233360i
167167 4.78624 0.370371 0.185185 0.982704i 0.440711π-0.440711\pi
0.185185 + 0.982704i 0.440711π0.440711\pi
168168 0 0
169169 6.51854 0.501426
170170 9.85486 + 3.25252i 0.755833 + 0.249457i
171171 −4.58966 0.227258i −0.350980 0.0173789i
172172 3.79306 5.12039i 0.289218 0.390426i
173173 −12.4811 + 7.20596i −0.948920 + 0.547859i −0.892745 0.450562i 0.851224π-0.851224\pi
−0.0561749 + 0.998421i 0.517890π0.517890\pi
174174 −7.71988 + 11.1562i −0.585242 + 0.845751i
175175 0 0
176176 −19.7097 4.57220i −1.48568 0.344643i
177177 −9.99593 + 9.51322i −0.751340 + 0.715058i
178178 6.64296 1.37991i 0.497911 0.103429i
179179 −0.347150 + 0.601281i −0.0259472 + 0.0449419i −0.878707 0.477361i 0.841594π-0.841594\pi
0.852760 + 0.522303i 0.174927π0.174927\pi
180180 5.81537 + 4.77083i 0.433452 + 0.355597i
181181 6.31042 0.469050 0.234525 0.972110i 0.424647π-0.424647\pi
0.234525 + 0.972110i 0.424647π0.424647\pi
182182 0 0
183183 −0.123206 0.509947i −0.00910763 0.0376964i
184184 −0.371950 + 0.805149i −0.0274205 + 0.0593564i
185185 5.79562 + 3.34610i 0.426103 + 0.246010i
186186 5.13162 + 10.8474i 0.376269 + 0.795371i
187187 25.6414 14.8041i 1.87509 1.08258i
188188 −2.61485 + 22.8434i −0.190707 + 1.66602i
189189 0 0
190190 2.02655 1.80781i 0.147022 0.131152i
191191 −1.95388 3.38422i −0.141378 0.244873i 0.786638 0.617415i 0.211820π-0.211820\pi
−0.928016 + 0.372541i 0.878487π0.878487\pi
192192 8.14612 11.2090i 0.587895 0.808937i
193193 −0.785825 + 1.36109i −0.0565649 + 0.0979733i −0.892921 0.450213i 0.851348π-0.851348\pi
0.836356 + 0.548186i 0.184681π0.184681\pi
194194 18.3776 + 6.06538i 1.31943 + 0.435469i
195195 −9.32487 + 2.25294i −0.667768 + 0.161336i
196196 0 0
197197 1.83285i 0.130585i 0.997866 + 0.0652924i 0.0207980π0.0207980\pi
−0.997866 + 0.0652924i 0.979202π0.979202\pi
198198 21.2020 3.32024i 1.50676 0.235959i
199199 3.17910 + 1.83546i 0.225361 + 0.130112i 0.608430 0.793608i 0.291800π-0.291800\pi
−0.383069 + 0.923720i 0.625133π0.625133\pi
200200 9.65686 0.879654i 0.682843 0.0622010i
201201 −12.5901 13.2290i −0.888039 0.933099i
202202 3.83331 + 4.29713i 0.269710 + 0.302345i
203203 0 0
204204 2.48956 + 20.1234i 0.174304 + 1.40892i
205205 1.24073 + 2.14901i 0.0866563 + 0.150093i
206206 18.1054 3.76096i 1.26146 0.262039i
207207 0.0465225 0.939560i 0.00323354 0.0653039i
208208 5.14898 + 16.9052i 0.357018 + 1.17216i
209209 7.74807i 0.535945i
210210 0 0
211211 14.8763i 1.02413i 0.858948 + 0.512063i 0.171119π0.171119\pi
−0.858948 + 0.512063i 0.828881π0.828881\pi
212212 10.1879 + 23.4642i 0.699706 + 1.61153i
213213 −7.53443 2.21998i −0.516251 0.152111i
214214 1.12398 + 5.41090i 0.0768339 + 0.369881i
215215 −1.99715 3.45917i −0.136205 0.235914i
216216 −3.56728 + 14.2574i −0.242722 + 0.970096i
217217 0 0
218218 −8.70434 + 7.76481i −0.589533 + 0.525899i
219219 1.77436 1.68868i 0.119900 0.114110i
220220 −7.54930 + 10.1911i −0.508973 + 0.687082i
221221 −22.3956 12.9301i −1.50649 0.869775i
222222 −1.06741 + 13.0321i −0.0716399 + 0.874659i
223223 19.4171i 1.30026i −0.759821 0.650132i 0.774713π-0.774713\pi
0.759821 0.650132i 0.225287π-0.225287\pi
224224 0 0
225225 −9.15054 + 4.69573i −0.610036 + 0.313049i
226226 2.98068 9.03122i 0.198272 0.600748i
227227 −5.34136 + 9.25151i −0.354519 + 0.614045i −0.987035 0.160502i 0.948689π-0.948689\pi
0.632517 + 0.774547i 0.282022π0.282022\pi
228228 4.88626 + 2.06881i 0.323600 + 0.137010i
229229 −3.75075 6.49650i −0.247857 0.429301i 0.715074 0.699049i 0.246393π-0.246393\pi
−0.962931 + 0.269748i 0.913060π0.913060\pi
230230 0.370081 + 0.414861i 0.0244024 + 0.0273551i
231231 0 0
232232 12.8003 9.03122i 0.840381 0.592928i
233233 −2.42423 + 1.39963i −0.158817 + 0.0916930i −0.577302 0.816531i 0.695895π-0.695895\pi
0.418485 + 0.908224i 0.362561π0.362561\pi
234234 −11.7705 14.5873i −0.769464 0.953599i
235235 12.4815 + 7.20617i 0.814201 + 0.470079i
236236 14.6158 6.34599i 0.951408 0.413089i
237237 11.6644 2.81817i 0.757683 0.183060i
238238 0 0
239239 20.5467 1.32905 0.664527 0.747265i 0.268633π-0.268633\pi
0.664527 + 0.747265i 0.268633π0.268633\pi
240240 −4.41118 7.48202i −0.284741 0.482963i
241241 −9.02728 + 15.6357i −0.581499 + 1.00718i 0.413804 + 0.910366i 0.364200π0.364200\pi
−0.995302 + 0.0968188i 0.969133π0.969133\pi
242242 4.19539 + 20.1968i 0.269690 + 1.29830i
243243 −2.14612 15.4400i −0.137674 0.990478i
244244 −0.0688928 + 0.601848i −0.00441041 + 0.0385294i
245245 0 0
246246 −2.75891 + 3.98699i −0.175902 + 0.254201i
247247 −5.86064 + 3.38364i −0.372904 + 0.215296i
248248 −1.25699 13.7993i −0.0798191 0.876255i
249249 −11.2702 3.32070i −0.714217 0.210441i
250250 4.68332 14.1900i 0.296199 0.897457i
251251 −10.4810 −0.661555 −0.330777 0.943709i 0.607311π-0.607311\pi
−0.330777 + 0.943709i 0.607311π0.607311\pi
252252 0 0
253253 1.58612 0.0997188
254254 −3.76928 + 11.4206i −0.236505 + 0.716591i
255255 12.1919 + 3.59227i 0.763483 + 0.224957i
256256 −13.2834 + 8.91915i −0.830213 + 0.557447i
257257 −7.24060 + 4.18036i −0.451656 + 0.260764i −0.708529 0.705681i 0.750641π-0.750641\pi
0.256873 + 0.966445i 0.417308π0.417308\pi
258258 4.44091 6.41770i 0.276479 0.399549i
259259 0 0
260260 11.0054 + 1.25977i 0.682524 + 0.0781277i
261261 −9.00941 + 13.9613i −0.557668 + 0.864182i
262262 −2.41909 11.6456i −0.149452 0.719468i
263263 14.6850 25.4352i 0.905517 1.56840i 0.0852962 0.996356i 0.472816π-0.472816\pi
0.820221 0.572046i 0.193850π-0.193850\pi
264264 −24.3074 4.81853i −1.49602 0.296560i
265265 16.0346 0.984996
266266 0 0
267267 8.07720 1.95149i 0.494317 0.119429i
268268 8.39850 + 19.3431i 0.513020 + 1.18157i
269269 17.6649 + 10.1988i 1.07705 + 0.621834i 0.930099 0.367310i 0.119721π-0.119721\pi
0.146950 + 0.989144i 0.453054π0.453054\pi
270270 7.30705 + 5.61036i 0.444693 + 0.341436i
271271 −17.8370 + 10.2982i −1.08352 + 0.625572i −0.931844 0.362858i 0.881801π-0.881801\pi
−0.151678 + 0.988430i 0.548468π0.548468\pi
272272 5.29093 22.8080i 0.320810 1.38294i
273273 0 0
274274 12.9508 + 14.5179i 0.782389 + 0.877057i
275275 −8.67076 15.0182i −0.522867 0.905632i
276276 −0.423511 + 1.00028i −0.0254924 + 0.0602096i
277277 1.97345 3.41811i 0.118573 0.205374i −0.800629 0.599160i 0.795501π-0.795501\pi
0.919202 + 0.393786i 0.128835π0.128835\pi
278278 5.83525 17.6803i 0.349975 1.06039i
279279 6.71002 + 13.0758i 0.401719 + 0.782825i
280280 0 0
281281 1.18623i 0.0707648i 0.999374 + 0.0353824i 0.0112649π0.0112649\pi
−0.999374 + 0.0353824i 0.988735π0.988735\pi
282282 −2.29878 + 28.0660i −0.136890 + 1.67131i
283283 −23.9744 13.8416i −1.42513 0.822800i −0.428401 0.903589i 0.640923π-0.640923\pi
−0.996731 + 0.0807885i 0.974256π0.974256\pi
284284 7.28798 + 5.39876i 0.432462 + 0.320357i
285285 2.40933 2.29298i 0.142716 0.135825i
286286 23.5839 21.0383i 1.39454 1.24402i
287287 0 0
288288 9.52909 14.0427i 0.561507 0.827472i
289289 8.63122 + 14.9497i 0.507719 + 0.879395i
290290 −1.99715 9.61438i −0.117277 0.564576i
291291 22.7357 + 6.69895i 1.33279 + 0.392700i
292292 −2.59443 + 1.12647i −0.151828 + 0.0659215i
293293 0.197795i 0.0115553i 0.999983 + 0.00577765i 0.00183909π0.00183909\pi
−0.999983 + 0.00577765i 0.998161π0.998161\pi
294294 0 0
295295 9.98789i 0.581517i
296296 6.33199 13.7067i 0.368040 0.796685i
297297 25.8225 4.90159i 1.49837 0.284419i
298298 −15.6425 + 3.24936i −0.906147 + 0.188230i
299299 −0.692674 1.19975i −0.0400584 0.0693831i
300300 11.7863 1.45814i 0.680482 0.0841857i
301301 0 0
302302 10.4496 + 11.7139i 0.601304 + 0.674061i
303303 4.86207 + 5.10878i 0.279319 + 0.293492i
304304 −4.47664 4.18335i −0.256753 0.239931i
305305 0.328846 + 0.189859i 0.0188297 + 0.0108713i
306306 3.84216 + 24.5349i 0.219642 + 1.40257i
307307 16.6218i 0.948657i −0.880348 0.474328i 0.842691π-0.842691\pi
0.880348 0.474328i 0.157309π-0.157309\pi
308308 0 0
309309 22.0145 5.31881i 1.25236 0.302576i
310310 −8.24797 2.72218i −0.468453 0.154609i
311311 5.37805 9.31506i 0.304961 0.528209i −0.672291 0.740287i 0.734690π-0.734690\pi
0.977253 + 0.212078i 0.0680231π0.0680231\pi
312312 6.97049 + 20.4904i 0.394626 + 1.16004i
313313 −2.47200 4.28163i −0.139726 0.242012i 0.787667 0.616101i 0.211289π-0.211289\pi
−0.927393 + 0.374089i 0.877955π0.877955\pi
314314 −15.6144 + 13.9290i −0.881170 + 0.786058i
315315 0 0
316316 −13.7665 1.57583i −0.774427 0.0886476i
317317 −18.9960 + 10.9673i −1.06692 + 0.615987i −0.927338 0.374224i 0.877909π-0.877909\pi
−0.139582 + 0.990211i 0.544576π0.544576\pi
318318 13.3977 + 28.3205i 0.751303 + 1.58813i
319319 −24.2624 14.0079i −1.35844 0.784293i
320320 1.81211 + 9.86417i 0.101300 + 0.551424i
321321 1.58955 + 6.57914i 0.0887202 + 0.367212i
322322 0 0
323323 8.96603 0.498883
324324 −3.80371 + 17.5935i −0.211317 + 0.977418i
325325 −7.57319 + 13.1171i −0.420085 + 0.727609i
326326 −18.3688 + 3.81568i −1.01736 + 0.211331i
327327 −10.3484 + 9.84870i −0.572269 + 0.544634i
328328 4.57454 3.22756i 0.252587 0.178212i
329329 0 0
330330 −8.83871 + 12.7731i −0.486555 + 0.703135i
331331 −3.24073 + 1.87104i −0.178127 + 0.102841i −0.586412 0.810013i 0.699460π-0.699460\pi
0.408286 + 0.912854i 0.366127π0.366127\pi
332332 10.9015 + 8.07558i 0.598298 + 0.443205i
333333 −0.791990 + 15.9949i −0.0434008 + 0.876514i
334334 −6.42774 2.12142i −0.351710 0.116079i
335335 13.2183 0.722194
336336 0 0
337337 22.9774 1.25166 0.625829 0.779960i 0.284761π-0.284761\pi
0.625829 + 0.779960i 0.284761π0.284761\pi
338338 −8.75415 2.88924i −0.476163 0.157154i
339339 3.29204 11.1729i 0.178799 0.606828i
340340 −11.7931 8.73601i −0.639569 0.473777i
341341 −21.4604 + 12.3902i −1.16215 + 0.670966i
342342 6.06301 + 2.33949i 0.327850 + 0.126505i
343343 0 0
344344 −7.36347 + 5.19527i −0.397011 + 0.280110i
345345 0.469402 + 0.493220i 0.0252718 + 0.0265541i
346346 19.9556 4.14528i 1.07282 0.222852i
347347 1.06505 1.84472i 0.0571750 0.0990299i −0.836021 0.548697i 0.815124π-0.815124\pi
0.893196 + 0.449667i 0.148457π0.148457\pi
348348 15.3123 11.5607i 0.820826 0.619717i
349349 −3.55710 −0.190407 −0.0952036 0.995458i 0.530350π-0.530350\pi
−0.0952036 + 0.995458i 0.530350π0.530350\pi
350350 0 0
351351 −14.9845 17.3916i −0.799811 0.928293i
352352 24.4428 + 14.8763i 1.30281 + 0.792909i
353353 −16.3912 9.46348i −0.872417 0.503690i −0.00426642 0.999991i 0.501358π-0.501358\pi
−0.868151 + 0.496301i 0.834691π0.834691\pi
354354 17.6407 8.34535i 0.937594 0.443550i
355355 4.92353 2.84260i 0.261314 0.150869i
356356 −9.53285 1.09121i −0.505240 0.0578342i
357357 0 0
358358 0.732717 0.653628i 0.0387253 0.0345453i
359359 0.613000 + 1.06175i 0.0323529 + 0.0560369i 0.881748 0.471720i 0.156367π-0.156367\pi
−0.849396 + 0.527757i 0.823033π0.823033\pi
360360 −5.69523 8.98461i −0.300165 0.473530i
361361 −8.32685 + 14.4225i −0.438255 + 0.759081i
362362 −8.47465 2.79699i −0.445418 0.147007i
363363 5.93317 + 24.5573i 0.311411 + 1.28893i
364364 0 0
365365 1.77294i 0.0927997i
366366 −0.0605653 + 0.739448i −0.00316580 + 0.0386516i
367367 17.4966 + 10.1017i 0.913314 + 0.527302i 0.881496 0.472192i 0.156537π-0.156537\pi
0.0318180 + 0.999494i 0.489870π0.489870\pi
368368 0.856383 0.916423i 0.0446420 0.0477718i
369369 −3.21976 + 4.98945i −0.167614 + 0.259740i
370370 −6.30019 7.06250i −0.327531 0.367162i
371371 0 0
372372 −2.08363 16.8422i −0.108031 0.873226i
373373 4.09019 + 7.08442i 0.211782 + 0.366817i 0.952272 0.305250i 0.0987400π-0.0987400\pi
−0.740490 + 0.672067i 0.765407π0.765407\pi
374374 −40.9971 + 8.51615i −2.11991 + 0.440360i
375375 5.17252 17.5551i 0.267108 0.906541i
376376 13.6366 29.5187i 0.703253 1.52231i
377377 24.4695i 1.26024i
378378 0 0
379379 31.2020i 1.60274i 0.598170 + 0.801369i 0.295895π0.295895\pi
−0.598170 + 0.801369i 0.704105π0.704105\pi
380380 −3.52287 + 1.52958i −0.180719 + 0.0784659i
381381 −4.16301 + 14.1289i −0.213277 + 0.723845i
382382 1.12398 + 5.41090i 0.0575080 + 0.276846i
383383 −12.2089 21.1465i −0.623848 1.08054i −0.988763 0.149495i 0.952235π-0.952235\pi
0.364915 0.931041i 0.381098π-0.381098\pi
384384 −15.9081 + 11.4426i −0.811807 + 0.583926i
385385 0 0
386386 1.65861 1.47958i 0.0844212 0.0753089i
387387 5.18273 8.03133i 0.263453 0.408255i
388388 −21.9920 16.2911i −1.11647 0.827057i
389389 7.86740 + 4.54225i 0.398893 + 0.230301i 0.686006 0.727596i 0.259362π-0.259362\pi
−0.287113 + 0.957897i 0.592696π0.592696\pi
390390 13.5215 + 1.10750i 0.684688 + 0.0560802i
391391 1.83546i 0.0928230i
392392 0 0
393393 −3.42111 14.1599i −0.172572 0.714275i
394394 0.812379 2.46144i 0.0409271 0.124006i
395395 −4.34279 + 7.52193i −0.218509 + 0.378469i
396396 −29.9451 4.93851i −1.50480 0.248170i
397397 −11.6405 20.1619i −0.584220 1.01190i −0.994972 0.100151i 0.968067π-0.968067\pi
0.410753 0.911747i 0.365266π-0.365266\pi
398398 −3.45588 3.87403i −0.173227 0.194188i
399399 0 0
400400 −13.3587 3.09890i −0.667934 0.154945i
401401 6.57424 3.79564i 0.328302 0.189545i −0.326785 0.945099i 0.605965π-0.605965\pi
0.655087 + 0.755553i 0.272632π0.272632\pi
402402 11.0445 + 23.3463i 0.550851 + 1.16441i
403403 18.7439 + 10.8218i 0.933700 + 0.539072i
404404 −3.24335 7.46993i −0.161362 0.371643i
405405 9.16617 + 6.57914i 0.455470 + 0.326920i
406406 0 0
407407 −27.0019 −1.33843
408408 5.57599 28.1284i 0.276053 1.39256i
409409 3.19509 5.53406i 0.157987 0.273642i −0.776156 0.630541i 0.782833π-0.782833\pi
0.934143 + 0.356900i 0.116166π0.116166\pi
410410 −0.713738 3.43596i −0.0352490 0.169690i
411411 16.4265 + 17.2600i 0.810261 + 0.851374i
412412 −25.9819 2.97411i −1.28003 0.146524i
413413 0 0
414414 −0.478923 + 1.24117i −0.0235378 + 0.0610003i
415415 7.36471 4.25202i 0.361520 0.208723i
416416 0.578064 24.9852i 0.0283419 1.22500i
417417 6.44479 21.8731i 0.315603 1.07113i
418418 −3.43421 + 10.4054i −0.167972 + 0.508942i
419419 29.1307 1.42313 0.711565 0.702620i 0.247987π-0.247987\pi
0.711565 + 0.702620i 0.247987π0.247987\pi
420420 0 0
421421 −32.0821 −1.56358 −0.781792 0.623539i 0.785694π-0.785694\pi
−0.781792 + 0.623539i 0.785694π0.785694\pi
422422 6.59368 19.9783i 0.320975 0.972528i
423423 −1.70563 + 34.4466i −0.0829306 + 1.67485i
424424 −3.28176 36.0272i −0.159376 1.74963i
425425 17.3790 10.0338i 0.843006 0.486710i
426426 9.13447 + 6.32086i 0.442567 + 0.306247i
427427 0 0
428428 0.888828 7.76481i 0.0429631 0.375326i
429429 28.0384 26.6844i 1.35371 1.28834i
430430 1.14888 + 5.53074i 0.0554038 + 0.266716i
431431 −9.12282 + 15.8012i −0.439431 + 0.761116i −0.997646 0.0685802i 0.978153π-0.978153\pi
0.558215 + 0.829696i 0.311486π0.311486\pi
432432 11.1101 17.5660i 0.534534 0.845147i
433433 4.84842 0.233000 0.116500 0.993191i 0.462832π-0.462832\pi
0.116500 + 0.993191i 0.462832π0.462832\pi
434434 0 0
435435 −2.82440 11.6902i −0.135420 0.560501i
436436 15.1312 6.56978i 0.724654 0.314635i
437437 0.415965 + 0.240157i 0.0198983 + 0.0114883i
438438 −3.13138 + 1.48137i −0.149623 + 0.0707827i
439439 17.5388 10.1260i 0.837081 0.483289i −0.0191902 0.999816i 0.506109π-0.506109\pi
0.856271 + 0.516527i 0.172775π0.172775\pi
440440 14.6554 10.3401i 0.698670 0.492945i
441441 0 0
442442 24.3454 + 27.2912i 1.15799 + 1.29811i
443443 11.2335 + 19.4570i 0.533719 + 0.924428i 0.999224 + 0.0393830i 0.0125392π0.0125392\pi
−0.465505 + 0.885045i 0.654127π0.654127\pi
444444 7.20977 17.0285i 0.342161 0.808138i
445445 −3.00724 + 5.20869i −0.142557 + 0.246915i
446446 −8.60631 + 26.0764i −0.407521 + 1.23475i
447447 −19.0198 + 4.59528i −0.899607 + 0.217349i
448448 0 0
449449 29.5660i 1.39531i −0.716435 0.697654i 0.754227π-0.754227\pi
0.716435 0.697654i 0.245773π-0.245773\pi
450450 14.3701 2.25036i 0.677414 0.106083i
451451 −8.67086 5.00612i −0.408295 0.235729i
452452 −8.00588 + 10.8074i −0.376565 + 0.508339i
453453 13.2540 + 13.9265i 0.622726 + 0.654323i
454454 11.2738 10.0569i 0.529107 0.471996i
455455 0 0
456456 −5.64509 4.94409i −0.264355 0.231528i
457457 −9.09743 15.7572i −0.425560 0.737091i 0.570913 0.821011i 0.306589π-0.306589\pi
−0.996473 + 0.0839196i 0.973256π0.973256\pi
458458 2.15765 + 10.3870i 0.100820 + 0.485353i
459459 5.67210 + 29.8817i 0.264751 + 1.39476i
460460 −0.313124 0.721174i −0.0145995 0.0336249i
461461 24.9782i 1.16335i −0.813422 0.581675i 0.802398π-0.802398\pi
0.813422 0.581675i 0.197602π-0.197602\pi
462462 0 0
463463 6.37226i 0.296144i 0.988977 + 0.148072i 0.0473068π0.0473068\pi
−0.988977 + 0.148072i 0.952693π0.952693\pi
464464 −21.1932 + 6.45504i −0.983872 + 0.299668i
465465 −10.2039 3.00653i −0.473195 0.139424i
466466 3.87602 0.805149i 0.179553 0.0372978i
467467 13.6785 + 23.6918i 0.632964 + 1.09633i 0.986943 + 0.161072i 0.0514951π0.0514951\pi
−0.353979 + 0.935253i 0.615172π0.615172\pi
468468 9.34180 + 24.8072i 0.431825 + 1.14671i
469469 0 0
470470 −13.5681 15.2098i −0.625849 0.701576i
471471 −18.5636 + 17.6672i −0.855367 + 0.814061i
472472 −22.4412 + 2.04420i −1.03294 + 0.0940918i
473473 13.9571 + 8.05816i 0.641750 + 0.370515i
474474 −16.9139 1.38535i −0.776882 0.0636314i
475475 5.25141i 0.240951i
476476 0 0
477477 17.5185 + 34.1382i 0.802119 + 1.56308i
478478 −27.5934 9.10698i −1.26209 0.416543i
479479 9.91668 17.1762i 0.453105 0.784800i −0.545472 0.838129i 0.683650π-0.683650\pi
0.998577 + 0.0533285i 0.0169830π0.0169830\pi
480480 2.60776 + 12.0032i 0.119027 + 0.547871i
481481 11.7919 + 20.4242i 0.537666 + 0.931265i
482482 19.0536 16.9970i 0.867866 0.774190i
483483 0 0
484484 3.31764 28.9830i 0.150802 1.31741i
485485 −14.8571 + 8.57774i −0.674625 + 0.389495i
486486 −3.96138 + 21.6866i −0.179692 + 0.983723i
487487 −35.3792 20.4262i −1.60318 0.925599i −0.990845 0.135003i 0.956896π-0.956896\pi
−0.612339 0.790595i 0.709771π-0.709771\pi
488488 0.359280 0.777723i 0.0162638 0.0352059i
489489 −22.3348 + 5.39619i −1.01001 + 0.244024i
490490 0 0
491491 −20.3003 −0.916137 −0.458069 0.888917i 0.651459π-0.651459\pi
−0.458069 + 0.888917i 0.651459π0.651459\pi
492492 5.47228 4.13152i 0.246709 0.186263i
493493 16.2099 28.0764i 0.730058 1.26450i
494494 9.37036 1.94647i 0.421593 0.0875757i
495495 −10.3151 + 15.9847i −0.463631 + 0.718458i
496496 −4.42821 + 19.0890i −0.198833 + 0.857123i
497497 0 0
498498 13.6635 + 9.45488i 0.612278 + 0.423683i
499499 29.6416 17.1136i 1.32694 0.766110i 0.342116 0.939658i 0.388856π-0.388856\pi
0.984825 + 0.173548i 0.0555231π0.0555231\pi
500500 −12.5790 + 16.9809i −0.562551 + 0.759408i
501501 −7.95202 2.34302i −0.355270 0.104679i
502502 14.0756 + 4.64553i 0.628223 + 0.207340i
503503 −31.1279 −1.38792 −0.693962 0.720011i 0.744137π-0.744137\pi
−0.693962 + 0.720011i 0.744137π0.744137\pi
504504 0 0
505505 −5.10467 −0.227155
506506 −2.13010 0.703024i −0.0946946 0.0312532i
507507 −10.8301 3.19104i −0.480982 0.141719i
508508 10.1240 13.6667i 0.449179 0.606363i
509509 34.2107 19.7516i 1.51636 0.875474i 0.516549 0.856257i 0.327216π-0.327216\pi
0.999815 0.0192162i 0.00611708π-0.00611708\pi
510510 −14.7810 10.2281i −0.654512 0.452909i
511511 0 0
512512 21.7924 6.09041i 0.963095 0.269161i
513513 7.51416 + 2.62436i 0.331758 + 0.115868i
514514 11.5767 2.40478i 0.510627 0.106070i
515515 −8.19625 + 14.1963i −0.361170 + 0.625564i
516516 −8.80852 + 6.65036i −0.387773 + 0.292766i
517517 −58.1512 −2.55749
518518 0 0
519519 24.2641 5.86232i 1.06507 0.257327i
520520 −14.2214 6.56978i −0.623650 0.288104i
521521 −20.8808 12.0555i −0.914803 0.528162i −0.0328296 0.999461i 0.510452π-0.510452\pi
−0.881973 + 0.471299i 0.843785π0.843785\pi
522522 18.2874 14.7562i 0.800417 0.645861i
523523 8.02520 4.63335i 0.350917 0.202602i −0.314172 0.949366i 0.601727π-0.601727\pi
0.665089 + 0.746764i 0.268394π0.268394\pi
524524 −1.91298 + 16.7118i −0.0835689 + 0.730059i
525525 0 0
526526 −30.9952 + 27.6496i −1.35145 + 1.20558i
527527 −14.3379 24.8339i −0.624568 1.08178i
528528 30.5081 + 17.2450i 1.32770 + 0.750490i
529529 11.4508 19.8334i 0.497862 0.862323i
530530 −21.5338 7.10707i −0.935369 0.308711i
531531 21.2646 10.9122i 0.922805 0.473551i
532532 0 0
533533 8.74486i 0.378782i
534534 −11.7123 0.959312i −0.506842 0.0415135i
535535 −4.24264 2.44949i −0.183425 0.105901i
536536 −2.70536 29.6995i −0.116854 1.28282i
537537 0.871113 0.829047i 0.0375913 0.0357760i
538538 −19.2028 21.5263i −0.827892 0.928066i
539539 0 0
540540 −7.32637 10.7732i −0.315277 0.463606i
541541 −12.9508 22.4315i −0.556800 0.964406i −0.997761 0.0668796i 0.978696π-0.978696\pi
0.440961 0.897526i 0.354638π-0.354638\pi
542542 28.5189 5.92412i 1.22499 0.254463i
543543 −10.4843 3.08916i −0.449926 0.132568i
544544 −17.2148 + 28.2851i −0.738078 + 1.21272i
545545 10.3401i 0.442921i
546546 0 0
547547 32.9387i 1.40836i −0.710022 0.704179i 0.751315π-0.751315\pi
0.710022 0.704179i 0.248685π-0.248685\pi
548548 −10.9577 25.2372i −0.468088 1.07808i
549549 −0.0449378 + 0.907556i −0.00191790 + 0.0387335i
550550 4.98792 + 24.0120i 0.212686 + 1.02388i
551551 −4.24192 7.34722i −0.180712 0.313002i
552552 1.01212 1.15562i 0.0430785 0.0491864i
553553 0 0
554554 −4.16528 + 3.71569i −0.176966 + 0.157864i
555555 −7.99101 8.39647i −0.339199 0.356410i
556556 −15.6730 + 21.1576i −0.664685 + 0.897282i
557557 25.8991 + 14.9528i 1.09738 + 0.633572i 0.935531 0.353244i 0.114921π-0.114921\pi
0.161847 + 0.986816i 0.448255π0.448255\pi
558558 −3.21568 20.5343i −0.136130 0.869288i
559559 14.0763i 0.595363i
560560 0 0
561561 −49.8486 + 12.0437i −2.10461 + 0.508484i
562562 0.525779 1.59307i 0.0221787 0.0671994i
563563 15.5531 26.9388i 0.655487 1.13534i −0.326284 0.945272i 0.605797π-0.605797\pi
0.981771 0.190065i 0.0608699π-0.0608699\pi
564564 15.5270 36.6726i 0.653803 1.54420i
565565 4.21532 + 7.30115i 0.177340 + 0.307162i
566566 26.0616 + 29.2151i 1.09545 + 1.22800i
567567 0 0
568568 −7.39456 10.4806i −0.310269 0.439756i
569569 15.3022 8.83472i 0.641501 0.370371i −0.143691 0.989623i 0.545897π-0.545897\pi
0.785193 + 0.619252i 0.212564π0.212564\pi
570570 −4.25197 + 2.01149i −0.178095 + 0.0842521i
571571 −6.51130 3.75930i −0.272490 0.157322i 0.357529 0.933902i 0.383619π-0.383619\pi
−0.630018 + 0.776580i 0.716953π0.716953\pi
572572 −40.9971 + 17.8004i −1.71417 + 0.744272i
573573 1.58955 + 6.57914i 0.0664045 + 0.274847i
574574 0 0
575575 1.07503 0.0448318
576576 −19.0214 + 14.6351i −0.792557 + 0.609797i
577577 2.13156 3.69196i 0.0887378 0.153698i −0.818240 0.574877i 0.805050π-0.805050\pi
0.906978 + 0.421178i 0.138383π0.138383\pi
578578 −4.96517 23.9025i −0.206524 0.994214i
579579 1.97189 1.87667i 0.0819491 0.0779917i
580580 −1.57932 + 13.7969i −0.0655776 + 0.572887i
581581 0 0
582582 −27.5639 19.0736i −1.14256 0.790628i
583583 −56.0289 + 32.3483i −2.32048 + 1.33973i
584584 3.98351 0.362862i 0.164839 0.0150154i
585585 16.5955 + 0.821731i 0.686141 + 0.0339744i
586586 0.0876693 0.265631i 0.00362159 0.0109731i
587587 −43.2909 −1.78681 −0.893404 0.449253i 0.851690π-0.851690\pi
−0.893404 + 0.449253i 0.851690π0.851690\pi
588588 0 0
589589 −7.50407 −0.309200
590590 −4.42697 + 13.4133i −0.182255 + 0.552218i
591591 0.897238 3.04515i 0.0369074 0.125261i
592592 −14.5789 + 15.6010i −0.599189 + 0.641197i
593593 −4.99583 + 2.88434i −0.205154 + 0.118446i −0.599057 0.800706i 0.704458π-0.704458\pi
0.393903 + 0.919152i 0.371125π0.371125\pi
594594 −36.8511 4.86274i −1.51202 0.199521i
595595 0 0
596596 22.4475 + 2.56954i 0.919486 + 0.105252i
597597 −4.38335 4.60576i −0.179399 0.188501i
598598 0.398466 + 1.91823i 0.0162945 + 0.0784422i
599599 −17.8985 + 31.0011i −0.731312 + 1.26667i 0.225010 + 0.974356i 0.427758π0.427758\pi
−0.956323 + 0.292313i 0.905575π0.905575\pi
600600 −16.4748 3.26586i −0.672582 0.133328i
601601 42.3193 1.72624 0.863121 0.504998i 0.168507π-0.168507\pi
0.863121 + 0.504998i 0.168507π0.168507\pi
602602 0 0
603603 14.4416 + 28.1423i 0.588109 + 1.14604i
604604 −8.84133 20.3630i −0.359749 0.828557i
605605 −15.8361 9.14298i −0.643829 0.371715i
606606 −4.26519 9.01592i −0.173262 0.366247i
607607 −41.0224 + 23.6843i −1.66505 + 0.961316i −0.694801 + 0.719202i 0.744508π0.744508\pi
−0.970248 + 0.242115i 0.922159π0.922159\pi
608608 4.15775 + 7.60227i 0.168619 + 0.308313i
609609 0 0
610610 −0.357475 0.400729i −0.0144737 0.0162250i
611611 25.3951 + 43.9857i 1.02738 + 1.77947i
612612 5.71483 34.6524i 0.231008 1.40074i
613613 −1.39456 + 2.41545i −0.0563257 + 0.0975590i −0.892813 0.450427i 0.851272π-0.851272\pi
0.836488 + 0.547986i 0.184605π0.184605\pi
614614 −7.36735 + 22.3224i −0.297322 + 0.900860i
615615 −1.00938 4.17781i −0.0407021 0.168465i
616616 0 0
617617 21.6549i 0.871795i 0.899996 + 0.435898i 0.143569π0.143569\pi
−0.899996 + 0.435898i 0.856431π0.856431\pi
618618 −31.9221 2.61461i −1.28409 0.105175i
619619 4.88830 + 2.82226i 0.196477 + 0.113436i 0.595011 0.803717i 0.297148π-0.297148\pi
−0.398534 + 0.917154i 0.630481π0.630481\pi
620620 9.87013 + 7.31156i 0.396394 + 0.293639i
621621 −0.537240 + 1.53824i −0.0215587 + 0.0617275i
622622 −11.3513 + 10.1260i −0.455144 + 0.406017i
623623 0 0
624624 −0.279048 30.6074i −0.0111709 1.22528i
625625 −1.94767 3.37346i −0.0779067 0.134938i
626626 1.42203 + 6.84573i 0.0568359 + 0.273610i
627627 −3.79293 + 12.8729i −0.151475 + 0.514094i
628628 27.1433 11.7853i 1.08314 0.470283i
629629 31.2464i 1.24588i
630630 0 0
631631 6.37226i 0.253676i 0.991923 + 0.126838i 0.0404828π0.0404828\pi
−0.991923 + 0.126838i 0.959517π0.959517\pi
632632 17.7894 + 8.21807i 0.707625 + 0.326897i
633633 7.28244 24.7160i 0.289451 0.982372i
634634 30.3719 6.30904i 1.20622 0.250564i
635635 −5.33056 9.23281i −0.211537 0.366393i
636636 −5.43993 43.9716i −0.215707 1.74359i
637637 0 0
638638 26.3747 + 29.5660i 1.04419 + 1.17053i
639639 11.4312 + 7.37670i 0.452211 + 0.291818i
640640 1.93854 14.0504i 0.0766274 0.555390i
641641 14.2860 + 8.24802i 0.564263 + 0.325777i 0.754855 0.655892i 0.227707π-0.227707\pi
−0.190592 + 0.981669i 0.561041π0.561041\pi
642642 0.781390 9.54007i 0.0308390 0.376516i
643643 2.36672i 0.0933343i 0.998910 + 0.0466671i 0.0148600π0.0148600\pi
−0.998910 + 0.0466671i 0.985140π0.985140\pi
644644 0 0
645645 1.62476 + 6.72485i 0.0639748 + 0.264791i
646646 −12.0410 3.97405i −0.473748 0.156357i
647647 5.67476 9.82897i 0.223098 0.386417i −0.732649 0.680606i 0.761716π-0.761716\pi
0.955747 + 0.294190i 0.0950497π0.0950497\pi
648648 12.9063 21.9415i 0.507006 0.861942i
649649 20.1497 + 34.9002i 0.790944 + 1.36995i
650650 15.9845 14.2591i 0.626962 0.559289i
651651 0 0
652652 26.3599 + 3.01738i 1.03233 + 0.118170i
653653 38.5978 22.2844i 1.51045 0.872057i 0.510522 0.859865i 0.329452π-0.329452\pi
0.999926 0.0121923i 0.00388102π-0.00388102\pi
654654 18.2628 8.63965i 0.714132 0.337837i
655655 9.13122 + 5.27191i 0.356786 + 0.205991i
656656 −7.57399 + 2.30689i −0.295715 + 0.0900689i
657657 −3.77465 + 1.93702i −0.147263 + 0.0755702i
658658 0 0
659659 0.590533 0.0230039 0.0115019 0.999934i 0.496339π-0.496339\pi
0.0115019 + 0.999934i 0.496339π0.496339\pi
660660 17.5315 13.2361i 0.682413 0.515216i
661661 −21.5502 + 37.3261i −0.838206 + 1.45182i 0.0531863 + 0.998585i 0.483062π0.483062\pi
−0.891393 + 0.453232i 0.850271π0.850271\pi
662662 5.18148 1.07633i 0.201384 0.0418326i
663663 30.8791 + 32.4459i 1.19925 + 1.26010i
664664 −11.0609 15.6771i −0.429248 0.608390i
665665 0 0
666666 8.15308 21.1295i 0.315926 0.818750i
667667 1.50407 0.868374i 0.0582377 0.0336236i
668668 7.69191 + 5.69798i 0.297609 + 0.220461i
669669 −9.50530 + 32.2602i −0.367496 + 1.24725i
670670 −17.7517 5.85880i −0.685807 0.226345i
671671 −1.53210 −0.0591459
672672 0 0
673673 15.2706 0.588637 0.294319 0.955707i 0.404907π-0.404907\pi
0.294319 + 0.955707i 0.404907π0.404907\pi
674674 −30.8577 10.1844i −1.18860 0.392287i
675675 17.5017 3.32216i 0.673641 0.127870i
676676 10.4759 + 7.76027i 0.402918 + 0.298472i
677677 35.8437 20.6944i 1.37759 0.795349i 0.385717 0.922617i 0.373954π-0.373954\pi
0.991868 + 0.127268i 0.0406207π0.0406207\pi
678678 −9.37328 + 13.5456i −0.359979 + 0.520216i
679679 0 0
680680 11.9655 + 16.9592i 0.458857 + 0.650356i
681681 13.4032 12.7560i 0.513613 0.488811i
682682 34.3123 7.12755i 1.31388 0.272928i
683683 2.26745 3.92734i 0.0867615 0.150275i −0.819379 0.573252i 0.805682π-0.805682\pi
0.906140 + 0.422977i 0.139015π0.139015\pi
684684 −7.10544 5.82918i −0.271683 0.222884i
685685 −17.2461 −0.658941
686686 0 0
687687 3.05138 + 12.6296i 0.116417 + 0.481850i
688688 12.1916 3.71331i 0.464799 0.141569i
689689 48.9366 + 28.2536i 1.86434 + 1.07638i
690690 −0.411777 0.870430i −0.0156761 0.0331367i
691691 23.6340 13.6451i 0.899079 0.519084i 0.0221779 0.999754i 0.492940π-0.492940\pi
0.876901 + 0.480670i 0.159607π0.159607\pi
692692 −28.6369 3.27802i −1.08861 0.124612i
693693 0 0
694694 −2.24797 + 2.00532i −0.0853316 + 0.0761211i
695695 8.25229 + 14.2934i 0.313027 + 0.542179i
696696 −25.6879 + 8.73859i −0.973698 + 0.331235i
697697 5.79306 10.0339i 0.219428 0.380060i
698698 4.77705 + 1.57663i 0.180814 + 0.0596762i
699699 4.71287 1.13865i 0.178257 0.0430678i
700700 0 0
701701 9.20431i 0.347642i −0.984777 0.173821i 0.944389π-0.944389\pi
0.984777 0.173821i 0.0556114π-0.0556114\pi
702702 12.4150 + 29.9978i 0.468574 + 1.13219i
703703 −7.08130 4.08839i −0.267076 0.154197i
704704 −26.2321 30.8122i −0.988659 1.16128i
705705 −17.2094 18.0827i −0.648145 0.681032i
706706 17.8182 + 19.9742i 0.670598 + 0.751740i
707707 0 0
708708 −27.3897 + 3.38852i −1.02937 + 0.127348i
709709 14.8003 + 25.6349i 0.555837 + 0.962738i 0.997838 + 0.0657232i 0.0209354π0.0209354\pi
−0.442001 + 0.897015i 0.645731π0.645731\pi
710710 −7.87204 + 1.63523i −0.295432 + 0.0613689i
711711 −20.7592 1.02790i −0.778530 0.0385491i
712712 12.3186 + 5.69074i 0.461659 + 0.213270i
713713 1.53617i 0.0575302i
714714 0 0
715715 28.0159i 1.04773i
716716 −1.27372 + 0.553033i −0.0476012 + 0.0206678i
717717 −34.1369 10.0583i −1.27487 0.375633i
718718 −0.352633 1.69759i −0.0131601 0.0633534i
719719 1.35786 + 2.35188i 0.0506395 + 0.0877102i 0.890234 0.455503i 0.150541π-0.150541\pi
−0.839595 + 0.543214i 0.817207π0.817207\pi
720720 3.66618 + 14.5903i 0.136631 + 0.543748i
721721 0 0
722722 17.5752 15.6782i 0.654081 0.583480i
723723 22.6524 21.5585i 0.842453 0.801770i
724724 10.1414 + 7.51250i 0.376902 + 0.279200i
725725 −16.4444 9.49416i −0.610729 0.352604i
726726 2.91662 35.6093i 0.108246 1.32159i
727727 18.9752i 0.703753i 0.936046 + 0.351876i 0.114456π0.114456\pi
−0.936046 + 0.351876i 0.885544π0.885544\pi
728728 0 0
729729 −3.99276 + 26.7031i −0.147880 + 0.989005i
730730 0.785825 2.38098i 0.0290847 0.0881241i
731731 −9.32487 + 16.1512i −0.344893 + 0.597372i
732732 0.409085 0.966205i 0.0151202 0.0357120i
733733 −7.65295 13.2553i −0.282668 0.489596i 0.689373 0.724407i 0.257886π-0.257886\pi
−0.972041 + 0.234811i 0.924553π0.924553\pi
734734 −19.0198 21.3212i −0.702035 0.786980i
735735 0 0
736736 −1.55628 + 0.851142i −0.0573652 + 0.0313735i
737737 −46.1882 + 26.6668i −1.70136 + 0.982283i
738738 6.53551 5.27353i 0.240575 0.194121i
739739 23.2697 + 13.4348i 0.855989 + 0.494205i 0.862667 0.505772i 0.168792π-0.168792\pi
−0.00667810 + 0.999978i 0.502126π0.502126\pi
740740 5.33056 + 12.2771i 0.195955 + 0.451316i
741741 11.3935 2.75272i 0.418550 0.101124i
742742 0 0
743743 −23.4748 −0.861208 −0.430604 0.902541i 0.641699π-0.641699\pi
−0.430604 + 0.902541i 0.641699π0.641699\pi
744744 −4.66679 + 23.5419i −0.171093 + 0.863088i
745745 7.08130 12.2652i 0.259439 0.449361i
746746 −2.35291 11.3270i −0.0861462 0.414711i
747747 17.0990 + 11.0342i 0.625620 + 0.403721i
748748 58.8321 + 6.73444i 2.15112 + 0.246235i
749749 0 0
750750 −14.7275 + 21.2832i −0.537772 + 0.777151i
751751 31.1457 17.9820i 1.13652 0.656172i 0.190955 0.981599i 0.438841π-0.438841\pi
0.945567 + 0.325427i 0.105508π0.105508\pi
752752 −31.3971 + 33.5983i −1.14493 + 1.22520i
753753 17.4135 + 5.13079i 0.634582 + 0.186977i
754754 10.8457 32.8616i 0.394978 1.19675i
755755 −13.9153 −0.506429
756756 0 0
757757 23.4202 0.851222 0.425611 0.904906i 0.360059π-0.360059\pi
0.425611 + 0.904906i 0.360059π0.360059\pi
758758 13.8298 41.9030i 0.502320 1.52199i
759759 −2.63524 0.776460i −0.0956531 0.0281837i
760760 5.40903 0.492715i 0.196206 0.0178727i
761761 34.9126 20.1568i 1.26558 0.730684i 0.291433 0.956591i 0.405868π-0.405868\pi
0.974149 + 0.225908i 0.0725347π0.0725347\pi
762762 11.8532 17.1294i 0.429394 0.620531i
763763 0 0
764764 0.888828 7.76481i 0.0321567 0.280921i
765765 −18.4974 11.9366i −0.668775 0.431570i
766766 7.02328 + 33.8103i 0.253761 + 1.22162i
767767 17.5991 30.4825i 0.635465 1.10066i
768768 26.4357 8.31590i 0.953916 0.300074i
769769 20.6279 0.743861 0.371930 0.928261i 0.378696π-0.378696\pi
0.371930 + 0.928261i 0.378696π0.378696\pi
770770 0 0
771771 14.0762 3.40088i 0.506942 0.122480i
772772 −2.88325 + 1.25187i −0.103771 + 0.0450558i
773773 −20.1789 11.6503i −0.725784 0.419032i 0.0910936 0.995842i 0.470964π-0.470964\pi
−0.816878 + 0.576811i 0.804297π0.804297\pi
774774 −10.5200 + 8.48860i −0.378132 + 0.305117i
775775 −14.5453 + 8.39771i −0.522481 + 0.301655i
776776 22.3136 + 31.6260i 0.801012 + 1.13531i
777777 0 0
778778 −8.55233 9.58716i −0.306616 0.343716i
779779 −1.51597 2.62573i −0.0543152 0.0940767i
780780 −17.6680 7.48052i −0.632615 0.267845i
781781 −11.4694 + 19.8655i −0.410407 + 0.710845i
782782 0.813537 2.46495i 0.0290920 0.0881463i
783783 21.8030 18.7853i 0.779177 0.671333i
784784 0 0
785785 18.5487i 0.662032i
786786 −1.68175 + 20.5326i −0.0599859 + 0.732374i
787787 2.76123 + 1.59420i 0.0984271 + 0.0568269i 0.548406 0.836212i 0.315235π-0.315235\pi
−0.449978 + 0.893039i 0.648568π0.648568\pi
788788 −2.18199 + 2.94554i −0.0777301 + 0.104931i
789789 −36.8495 + 35.0701i −1.31188 + 1.24853i
790790 9.16617 8.17678i 0.326118 0.290917i
791791 0 0
792792 38.0262 + 19.9049i 1.35120 + 0.707291i
793793 0.669079 + 1.15888i 0.0237597 + 0.0411530i
794794 6.69628 + 32.2361i 0.237642 + 1.14402i
795795 −26.6404 7.84945i −0.944836 0.278391i
796796 2.92400 + 6.73444i 0.103639 + 0.238696i
797797 55.9985i 1.98357i 0.127925 + 0.991784i 0.459168π0.459168\pi
−0.127925 + 0.991784i 0.540832π0.540832\pi
798798 0 0
799799 67.2924i 2.38063i
800800 16.5666 + 10.0827i 0.585719 + 0.356478i
801801 −14.3750 0.711784i −0.507917 0.0251496i
802802 −10.5113 + 2.18347i −0.371167 + 0.0771010i
803803 −3.57674 6.19509i −0.126220 0.218620i
804804 −4.48448 36.2485i −0.158155 1.27839i
805805 0 0
806806 −20.3757 22.8412i −0.717705 0.804546i
807807 −24.3564 25.5922i −0.857385 0.900890i
808808 1.04476 + 11.4694i 0.0367545 + 0.403491i
809809 18.4879 + 10.6740i 0.649999 + 0.375277i 0.788456 0.615091i 0.210881π-0.210881\pi
−0.138457 + 0.990368i 0.544214π0.544214\pi
810810 −9.39371 12.8983i −0.330061 0.453199i
811811 52.7856i 1.85355i 0.375614 + 0.926776i 0.377432π0.377432\pi
−0.375614 + 0.926776i 0.622568π0.622568\pi
812812 0 0
813813 34.6763 8.37797i 1.21615 0.293828i
814814 36.2624 + 11.9681i 1.27100 + 0.419483i
815815 8.31549 14.4029i 0.291279 0.504510i
816816 −19.9558 + 35.3039i −0.698593 + 1.23588i
817817 2.44020 + 4.22654i 0.0853717 + 0.147868i
818818 −6.74377 + 6.01585i −0.235790 + 0.210339i
819819 0 0
820820 −0.564413 + 4.93072i −0.0197101 + 0.172188i
821821 −5.03883 + 2.90917i −0.175857 + 0.101531i −0.585344 0.810785i 0.699041π-0.699041\pi
0.409488 + 0.912316i 0.365707π0.365707\pi
822822 −14.4100 30.4603i −0.502605 1.06243i
823823 8.78912 + 5.07440i 0.306369 + 0.176882i 0.645301 0.763929i 0.276732π-0.276732\pi
−0.338931 + 0.940811i 0.610065π0.610065\pi
824824 33.5744 + 15.5102i 1.16962 + 0.540322i
825825 7.05398 + 29.1964i 0.245588 + 1.01649i
826826 0 0
827827 −53.0241 −1.84383 −0.921915 0.387393i 0.873376π-0.873376\pi
−0.921915 + 0.387393i 0.873376π0.873376\pi
828828 1.19330 1.45457i 0.0414702 0.0505498i
829829 16.3511 28.3210i 0.567898 0.983628i −0.428876 0.903364i 0.641090π-0.641090\pi
0.996774 0.0802647i 0.0255766π-0.0255766\pi
830830 −11.7752 + 2.44600i −0.408722 + 0.0849021i
831831 −4.95202 + 4.71289i −0.171784 + 0.163488i
832832 −11.8506 + 33.2979i −0.410845 + 1.15440i
833833 0 0
834834 −18.3500 + 26.5181i −0.635408 + 0.918247i
835835 5.19641 3.00015i 0.179829 0.103824i
836836 9.22401 12.4518i 0.319019 0.430655i
837837 −4.74723 25.0093i −0.164088 0.864447i
838838 −39.1214 12.9117i −1.35143 0.446028i
839839 37.5962 1.29796 0.648982 0.760803i 0.275195π-0.275195\pi
0.648982 + 0.760803i 0.275195π0.275195\pi
840840 0 0
841841 −1.67632 −0.0578040
842842 43.0849 + 14.2199i 1.48481 + 0.490049i
843843 0.580701 1.97085i 0.0200004 0.0678796i
844844 −17.7101 + 23.9075i −0.609607 + 0.822931i
845845 7.07716 4.08600i 0.243462 0.140563i
846846 17.5585 45.5044i 0.603673 1.56447i
847847 0 0
848848 −11.5612 + 49.8377i −0.397013 + 1.71143i
849849 33.0560 + 34.7332i 1.13448 + 1.19204i
850850 −27.7866 + 5.77200i −0.953074 + 0.197978i
851851 0.836944 1.44963i 0.0286901 0.0496927i
852852 −9.46562 12.5374i −0.324287 0.429523i
853853 −5.68417 −0.194622 −0.0973112 0.995254i 0.531024π-0.531024\pi
−0.0973112 + 0.995254i 0.531024π0.531024\pi
854854 0 0
855855 −5.12543 + 2.63019i −0.175286 + 0.0899507i
856856 −4.63529 + 10.0339i −0.158431 + 0.342951i
857857 27.4440 + 15.8448i 0.937471 + 0.541249i 0.889166 0.457584i 0.151285π-0.151285\pi
0.0483040 + 0.998833i 0.484618π0.484618\pi
858858 −49.4819 + 23.4086i −1.68929 + 0.799156i
859859 −5.22874 + 3.01882i −0.178402 + 0.103001i −0.586542 0.809919i 0.699511π-0.699511\pi
0.408139 + 0.912920i 0.366178π0.366178\pi
860860 0.908514 7.93679i 0.0309801 0.270642i
861861 0 0
862862 19.2552 17.1768i 0.655835 0.585045i
863863 20.0569 + 34.7395i 0.682744 + 1.18255i 0.974140 + 0.225944i 0.0725468π0.0725468\pi
−0.291396 + 0.956602i 0.594120π0.594120\pi
864864 −22.7063 + 18.6661i −0.772483 + 0.635035i
865865 −9.03379 + 15.6470i −0.307158 + 0.532013i
866866 −6.51124 2.14898i −0.221261 0.0730254i
867867 −7.02181 29.0632i −0.238473 0.987038i
868868 0 0
869869 35.0447i 1.18881i
870870 −1.38842 + 16.9513i −0.0470717 + 0.574703i
871871 40.3415 + 23.2912i 1.36692 + 0.789192i
872872 −23.2326 + 2.11628i −0.786755 + 0.0716664i
873873 −34.4944 22.2597i −1.16746 0.753377i
874874 −0.452179 0.506892i −0.0152952 0.0171459i
875875 0 0
876876 4.86191 0.601491i 0.164269 0.0203225i
877877 21.9436 + 38.0074i 0.740983 + 1.28342i 0.952048 + 0.305948i 0.0989733π0.0989733\pi
−0.211066 + 0.977472i 0.567693π0.567693\pi
878878 −28.0421 + 5.82507i −0.946375 + 0.196587i
879879 0.0968270 0.328623i 0.00326590 0.0110842i
880880 −24.2648 + 7.39057i −0.817965 + 0.249136i
881881 1.27293i 0.0428860i 0.999770 + 0.0214430i 0.00682603π0.00682603\pi
−0.999770 + 0.0214430i 0.993174π0.993174\pi
882882 0 0
883883 19.5118i 0.656625i −0.944569 0.328312i 0.893520π-0.893520\pi
0.944569 0.328312i 0.106480π-0.106480\pi
884884 −20.5985 47.4417i −0.692804 1.59564i
885885 −4.88940 + 16.5942i −0.164355 + 0.557808i
886886 −6.46214 31.1090i −0.217100 1.04513i
887887 −13.4459 23.2890i −0.451470 0.781969i 0.547007 0.837128i 0.315767π-0.315767\pi
−0.998478 + 0.0551585i 0.982434π0.982434\pi
888888 −17.2301 + 19.6730i −0.578203 + 0.660183i
889889 0 0
890890 6.34727 5.66215i 0.212761 0.189796i
891891 −45.3018 4.49728i −1.51767 0.150665i
892892 23.1159 31.2050i 0.773977 1.04482i
893893 −15.2503 8.80477i −0.510332 0.294640i
894894 27.5797 + 2.25894i 0.922402 + 0.0755504i
895895 0.870412i 0.0290947i
896896 0 0
897897 0.563515 + 2.33238i 0.0188152 + 0.0778760i
898898 −13.1047 + 39.7060i −0.437308 + 1.32501i
899899 −13.5668 + 23.4984i −0.452478 + 0.783715i
900900 −20.2959 3.34718i −0.676532 0.111573i
901901 −37.4334 64.8365i −1.24709 2.16002i
902902 9.42574 + 10.5662i 0.313843 + 0.351817i
903903 0 0
904904 15.5418 10.9655i 0.516913 0.364706i
905905 6.85120 3.95554i 0.227742 0.131487i
906906 −11.6269 24.5773i −0.386277 0.816527i
907907 16.1538 + 9.32642i 0.536379 + 0.309679i 0.743610 0.668613i 0.233112π-0.233112\pi
−0.207231 + 0.978292i 0.566445π0.566445\pi
908908 −19.5979 + 8.50914i −0.650379 + 0.282386i
909909 −5.57709 10.8680i −0.184980 0.360470i
910910 0 0
911911 8.12909 0.269329 0.134664 0.990891i 0.457004π-0.457004\pi
0.134664 + 0.990891i 0.457004π0.457004\pi
912912 5.38974 + 9.14181i 0.178472 + 0.302716i
913913 −17.1561 + 29.7153i −0.567785 + 0.983433i
914914 5.23336 + 25.1936i 0.173104 + 0.833330i
915915 −0.453413 0.476419i −0.0149894 0.0157499i
916916 1.70623 14.9057i 0.0563755 0.492497i
917917 0 0
918918 5.62715 42.6440i 0.185724 1.40746i
919919 −15.2109 + 8.78201i −0.501761 + 0.289692i −0.729440 0.684044i 0.760219π-0.760219\pi
0.227680 + 0.973736i 0.426886π0.426886\pi
920920 0.100865 + 1.10730i 0.00332542 + 0.0365065i
921921 −8.13692 + 27.6160i −0.268121 + 0.909979i
922922 −11.0712 + 33.5447i −0.364610 + 1.10474i
923923 20.0351 0.659463
924924 0 0
925925 −18.3011 −0.601736
926926 2.82440 8.55770i 0.0928156 0.281223i
927927 −39.1793 1.93997i −1.28682 0.0637170i
928928 31.3228 + 0.724692i 1.02822 + 0.0237892i
929929 −33.7624 + 19.4927i −1.10771 + 0.639535i −0.938235 0.345999i 0.887540π-0.887540\pi
−0.169473 + 0.985535i 0.554207π0.554207\pi
930930 12.3708 + 8.56036i 0.405656 + 0.280705i
931931 0 0
932932 −5.56221 0.636699i −0.182196 0.0208558i
933933 −13.4953 + 12.8436i −0.441816 + 0.420481i
934934 −7.86863 37.8799i −0.257470 1.23947i
935935 18.5592 32.1455i 0.606951 1.05127i
936936 −1.55027 37.4557i −0.0506720 1.22428i
937937 23.7865 0.777072 0.388536 0.921434i 0.372981π-0.372981\pi
0.388536 + 0.921434i 0.372981π0.372981\pi
938938 0 0
939939 2.01106 + 8.32376i 0.0656285 + 0.271636i
940940 11.4799 + 26.4400i 0.374433 + 0.862378i
941941 26.5129 + 15.3073i 0.864297 + 0.499002i 0.865449 0.500997i 0.167033π-0.167033\pi
−0.00115159 + 0.999999i 0.500367π0.500367\pi
942942 32.7609 15.4983i 1.06741 0.504963i
943943 0.537520 0.310337i 0.0175041 0.0101060i
944944 31.0437 + 7.20143i 1.01039 + 0.234387i
945945 0 0
946946 −15.1722 17.0081i −0.493292 0.552980i
947947 −7.73005 13.3888i −0.251193 0.435079i 0.712662 0.701508i 0.247490π-0.247490\pi
−0.963855 + 0.266429i 0.914156π0.914156\pi
948948 22.1007 + 9.35730i 0.717797 + 0.303911i
949949 −3.12398 + 5.41090i −0.101409 + 0.175645i
950950 −2.32760 + 7.05244i −0.0755175 + 0.228811i
951951 36.9294 8.92233i 1.19752 0.289326i
952952 0 0
953953 13.4497i 0.435679i −0.975985 0.217839i 0.930099π-0.930099\pi
0.975985 0.217839i 0.0699009π-0.0699009\pi
954954 −8.39549 53.6111i −0.271814 1.73572i
955955 −4.24264 2.44949i −0.137289 0.0792636i
956956 33.0203 + 24.4606i 1.06795 + 0.791113i
957957 33.4531 + 35.1505i 1.08138 + 1.13625i
958958 −20.9308 + 18.6715i −0.676243 + 0.603250i
959959 0 0
960960 1.81813 17.2757i 0.0586799 0.557572i
961961 −3.50000 6.06218i −0.112903 0.195554i
962962 −6.78340 32.6555i −0.218705 1.05286i
963963 0.579770 11.7089i 0.0186828 0.377315i
964964 −33.1218 + 14.3811i −1.06678 + 0.463183i
965965 1.97031i 0.0634264i
966966 0 0
967967 41.1554i 1.32347i 0.749738 + 0.661734i 0.230179π0.230179\pi
−0.749738 + 0.661734i 0.769821π0.769821\pi
968968 −17.3017 + 37.4525i −0.556098 + 1.20377i
969969 −14.8965 4.38917i −0.478543 0.141000i
970970 23.7544 4.93441i 0.762709 0.158434i
971971 −14.4445 25.0186i −0.463546 0.802886i 0.535588 0.844479i 0.320090π-0.320090\pi
−0.999135 + 0.0415934i 0.986757π0.986757\pi
972972 14.9322 27.3684i 0.478951 0.877842i
973973 0 0
974974 38.4593 + 43.1128i 1.23232 + 1.38142i
975975 19.0036 18.0859i 0.608603 0.579213i
976976 −0.827212 + 0.885206i −0.0264784 + 0.0283348i
977977 −40.6932 23.4942i −1.30189 0.751646i −0.321161 0.947024i 0.604073π-0.604073\pi
−0.980728 + 0.195378i 0.937407π0.937407\pi
978978 32.3865 + 2.65265i 1.03561 + 0.0848225i
979979 24.2673i 0.775587i
980980 0 0
981981 22.0145 11.2971i 0.702868 0.360687i
982982 27.2624 + 8.99776i 0.869979 + 0.287130i
983983 −13.6677 + 23.6731i −0.435931 + 0.755054i −0.997371 0.0724632i 0.976914π-0.976914\pi
0.561440 + 0.827517i 0.310247π0.310247\pi
984984 −9.18029 + 3.12298i −0.292657 + 0.0995568i
985985 1.14888 + 1.98991i 0.0366063 + 0.0634039i
986986 −34.2137 + 30.5207i −1.08959 + 0.971978i
987987 0 0
988988 −13.4468 1.53923i −0.427799 0.0489696i
989989 −0.865226 + 0.499538i −0.0275126 + 0.0158844i
990990 20.9378 16.8948i 0.665446 0.536951i
991991 18.0000 + 10.3923i 0.571789 + 0.330122i 0.757863 0.652413i 0.226243π-0.226243\pi
−0.186075 + 0.982536i 0.559577π0.559577\pi
992992 14.4078 23.6731i 0.457449 0.751621i
993993 6.30019 1.52216i 0.199930 0.0483042i
994994 0 0
995995 4.60206 0.145895
996996 −14.1589 18.7537i −0.448641 0.594233i
997997 6.02119 10.4290i 0.190693 0.330290i −0.754787 0.655970i 0.772260π-0.772260\pi
0.945480 + 0.325680i 0.105593π0.105593\pi
998998 −47.3929 + 9.84472i −1.50020 + 0.311629i
999999 9.14586 26.1867i 0.289362 0.828511i
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 588.2.n.h.263.3 24
3.2 odd 2 inner 588.2.n.h.263.9 24
4.3 odd 2 588.2.n.d.263.6 24
7.2 even 3 588.2.n.d.275.8 24
7.3 odd 6 588.2.e.f.491.17 yes 24
7.4 even 3 588.2.e.f.491.18 yes 24
7.5 odd 6 588.2.n.d.275.7 24
7.6 odd 2 inner 588.2.n.h.263.4 24
12.11 even 2 588.2.n.d.263.8 24
21.2 odd 6 588.2.n.d.275.6 24
21.5 even 6 588.2.n.d.275.5 24
21.11 odd 6 588.2.e.f.491.7 yes 24
21.17 even 6 588.2.e.f.491.8 yes 24
21.20 even 2 inner 588.2.n.h.263.10 24
28.3 even 6 588.2.e.f.491.6 yes 24
28.11 odd 6 588.2.e.f.491.5 24
28.19 even 6 inner 588.2.n.h.275.10 24
28.23 odd 6 inner 588.2.n.h.275.9 24
28.27 even 2 588.2.n.d.263.5 24
84.11 even 6 588.2.e.f.491.20 yes 24
84.23 even 6 inner 588.2.n.h.275.3 24
84.47 odd 6 inner 588.2.n.h.275.4 24
84.59 odd 6 588.2.e.f.491.19 yes 24
84.83 odd 2 588.2.n.d.263.7 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
588.2.e.f.491.5 24 28.11 odd 6
588.2.e.f.491.6 yes 24 28.3 even 6
588.2.e.f.491.7 yes 24 21.11 odd 6
588.2.e.f.491.8 yes 24 21.17 even 6
588.2.e.f.491.17 yes 24 7.3 odd 6
588.2.e.f.491.18 yes 24 7.4 even 3
588.2.e.f.491.19 yes 24 84.59 odd 6
588.2.e.f.491.20 yes 24 84.11 even 6
588.2.n.d.263.5 24 28.27 even 2
588.2.n.d.263.6 24 4.3 odd 2
588.2.n.d.263.7 24 84.83 odd 2
588.2.n.d.263.8 24 12.11 even 2
588.2.n.d.275.5 24 21.5 even 6
588.2.n.d.275.6 24 21.2 odd 6
588.2.n.d.275.7 24 7.5 odd 6
588.2.n.d.275.8 24 7.2 even 3
588.2.n.h.263.3 24 1.1 even 1 trivial
588.2.n.h.263.4 24 7.6 odd 2 inner
588.2.n.h.263.9 24 3.2 odd 2 inner
588.2.n.h.263.10 24 21.20 even 2 inner
588.2.n.h.275.3 24 84.23 even 6 inner
588.2.n.h.275.4 24 84.47 odd 6 inner
588.2.n.h.275.9 24 28.23 odd 6 inner
588.2.n.h.275.10 24 28.19 even 6 inner