Properties

Label 357.2.bl.a.10.7
Level 357357
Weight 22
Character 357.10
Analytic conductor 2.8512.851
Analytic rank 00
Dimension 384384
Inner twists 44

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [357,2,Mod(10,357)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("357.10"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([0, 8, 9])) N = Newforms(chi, 2, names="a")
 
Level: N N == 357=3717 357 = 3 \cdot 7 \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 357.bl (of order 4848, degree 1616, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 2.850659352162.85065935216
Analytic rank: 00
Dimension: 384384
Relative dimension: 2424 over Q(ζ48)\Q(\zeta_{48})
Twist minimal: yes
Sato-Tate group: SU(2)[C48]\mathrm{SU}(2)[C_{48}]

Embedding invariants

Embedding label 10.7
Character χ\chi == 357.10
Dual form 357.2.bl.a.250.7

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(1.37138+0.180546i)q2+(0.442289+0.896873i)q3+(0.0837632+0.0224443i)q4+(0.803646+0.704779i)q5+(0.7684731.15010i)q6+(0.896773+2.48914i)q7+(2.666671.10457i)q8+(0.608761+0.793353i)q9+(0.9748601.11161i)q10+(0.668362+0.0438068i)q11+(0.05717720.0651981i)q12+(0.642496+0.642496i)q13+(1.679223.25164i)q14+(0.9875400.409053i)q15+(3.30739+1.90952i)q16+(4.10201+0.416535i)q17+(0.6916071.19790i)q18+(0.340606+2.58716i)q19+(0.05149770.0770718i)q20+(1.83581+1.90521i)q21+(0.9086700.180746i)q22+(6.913153.40919i)q23+(2.17009+1.90312i)q24+(0.503497+3.82444i)q25+(0.9971060.765106i)q26+(0.9807850.195090i)q27+(0.1309830.188371i)q28+(0.1475170.741618i)q29+(1.42815+0.382671i)q30+(1.02931+0.507601i)q31+(0.388902+0.298415i)q32+(0.3348980.580060i)q33+(5.550221.31183i)q34+(2.474981.36836i)q35+(0.03318560.0801171i)q36+(0.168023+2.56354i)q37+(0.9342013.48649i)q38+(0.292068+0.860405i)q39+(1.36458+2.76709i)q40+(0.4616722.32098i)q41+(2.173612.94421i)q42+(1.653213.99121i)q43+(0.05500100.0186703i)q44+(0.06990981.06662i)q45+(10.0961+3.42715i)q46+(1.90759+7.11923i)q47+(3.175422.12175i)q48+(5.39160+4.46438i)q495.33567iq50+(2.187853.49475i)q51+(0.06823790.0393972i)q52+(0.529528+0.690095i)q53+(1.38025+0.0904665i)q54+(0.5062520.506252i)q55+(5.14082+5.64715i)q56+(2.16971+1.44975i)q57+(0.336198+0.990407i)q58+(2.343510.308529i)q59+(0.0919005+0.0120989i)q60+(2.17512+6.40769i)q61+(1.319930.881951i)q62+(2.520690.803832i)q63+(5.880405.88040i)q64+(0.9691560.0635219i)q65+(0.564000+0.735019i)q66+(2.148391.24038i)q67+(0.3342490.126957i)q687.70806iq69+(3.64119+1.42969i)q70+(10.0562+6.71931i)q71+(0.747050+2.78803i)q72+(8.77152+2.97753i)q73+(0.2324123.54592i)q74+(3.65273+1.23993i)q75+(0.08659730.209064i)q76+(0.7084101.62436i)q77+(0.2451941.23267i)q78+(5.2836410.7142i)q79+(1.312183.86556i)q80+(0.2588190.965926i)q81+(0.214085+3.26630i)q82+(1.02258+2.46874i)q83+(0.1110120.200790i)q84+(3.003003.22576i)q85+(2.98778+5.17499i)q86+(0.5998920.460313i)q87+(1.73391+0.855070i)q88+(7.65661+2.05158i)q89+(0.288446+1.45012i)q90+(1.02309+2.17543i)q91+(0.655584+0.130404i)q92+(0.9105060.698656i)q93+(1.3306910.1076i)q94+(2.097101.83911i)q95+(0.4396480.216810i)q96+(16.93103.36778i)q97+(6.587917.09579i)q98+(0.3721190.556915i)q99+O(q100)q+(-1.37138 + 0.180546i) q^{2} +(0.442289 + 0.896873i) q^{3} +(-0.0837632 + 0.0224443i) q^{4} +(-0.803646 + 0.704779i) q^{5} +(-0.768473 - 1.15010i) q^{6} +(0.896773 + 2.48914i) q^{7} +(2.66667 - 1.10457i) q^{8} +(-0.608761 + 0.793353i) q^{9} +(0.974860 - 1.11161i) q^{10} +(-0.668362 + 0.0438068i) q^{11} +(-0.0571772 - 0.0651981i) q^{12} +(0.642496 + 0.642496i) q^{13} +(-1.67922 - 3.25164i) q^{14} +(-0.987540 - 0.409053i) q^{15} +(-3.30739 + 1.90952i) q^{16} +(-4.10201 + 0.416535i) q^{17} +(0.691607 - 1.19790i) q^{18} +(0.340606 + 2.58716i) q^{19} +(0.0514977 - 0.0770718i) q^{20} +(-1.83581 + 1.90521i) q^{21} +(0.908670 - 0.180746i) q^{22} +(-6.91315 - 3.40919i) q^{23} +(2.17009 + 1.90312i) q^{24} +(-0.503497 + 3.82444i) q^{25} +(-0.997106 - 0.765106i) q^{26} +(-0.980785 - 0.195090i) q^{27} +(-0.130983 - 0.188371i) q^{28} +(-0.147517 - 0.741618i) q^{29} +(1.42815 + 0.382671i) q^{30} +(-1.02931 + 0.507601i) q^{31} +(-0.388902 + 0.298415i) q^{32} +(-0.334898 - 0.580060i) q^{33} +(5.55022 - 1.31183i) q^{34} +(-2.47498 - 1.36836i) q^{35} +(0.0331856 - 0.0801171i) q^{36} +(-0.168023 + 2.56354i) q^{37} +(-0.934201 - 3.48649i) q^{38} +(-0.292068 + 0.860405i) q^{39} +(-1.36458 + 2.76709i) q^{40} +(0.461672 - 2.32098i) q^{41} +(2.17361 - 2.94421i) q^{42} +(-1.65321 - 3.99121i) q^{43} +(0.0550010 - 0.0186703i) q^{44} +(-0.0699098 - 1.06662i) q^{45} +(10.0961 + 3.42715i) q^{46} +(-1.90759 + 7.11923i) q^{47} +(-3.17542 - 2.12175i) q^{48} +(-5.39160 + 4.46438i) q^{49} -5.33567i q^{50} +(-2.18785 - 3.49475i) q^{51} +(-0.0682379 - 0.0393972i) q^{52} +(0.529528 + 0.690095i) q^{53} +(1.38025 + 0.0904665i) q^{54} +(0.506252 - 0.506252i) q^{55} +(5.14082 + 5.64715i) q^{56} +(-2.16971 + 1.44975i) q^{57} +(0.336198 + 0.990407i) q^{58} +(-2.34351 - 0.308529i) q^{59} +(0.0919005 + 0.0120989i) q^{60} +(2.17512 + 6.40769i) q^{61} +(1.31993 - 0.881951i) q^{62} +(-2.52069 - 0.803832i) q^{63} +(5.88040 - 5.88040i) q^{64} +(-0.969156 - 0.0635219i) q^{65} +(0.564000 + 0.735019i) q^{66} +(-2.14839 - 1.24038i) q^{67} +(0.334249 - 0.126957i) q^{68} -7.70806i q^{69} +(3.64119 + 1.42969i) q^{70} +(10.0562 + 6.71931i) q^{71} +(-0.747050 + 2.78803i) q^{72} +(8.77152 + 2.97753i) q^{73} +(-0.232412 - 3.54592i) q^{74} +(-3.65273 + 1.23993i) q^{75} +(-0.0865973 - 0.209064i) q^{76} +(-0.708410 - 1.62436i) q^{77} +(0.245194 - 1.23267i) q^{78} +(5.28364 - 10.7142i) q^{79} +(1.31218 - 3.86556i) q^{80} +(-0.258819 - 0.965926i) q^{81} +(-0.214085 + 3.26630i) q^{82} +(-1.02258 + 2.46874i) q^{83} +(0.111012 - 0.200790i) q^{84} +(3.00300 - 3.22576i) q^{85} +(2.98778 + 5.17499i) q^{86} +(0.599892 - 0.460313i) q^{87} +(-1.73391 + 0.855070i) q^{88} +(7.65661 + 2.05158i) q^{89} +(0.288446 + 1.45012i) q^{90} +(-1.02309 + 2.17543i) q^{91} +(0.655584 + 0.130404i) q^{92} +(-0.910506 - 0.698656i) q^{93} +(1.33069 - 10.1076i) q^{94} +(-2.09710 - 1.83911i) q^{95} +(-0.439648 - 0.216810i) q^{96} +(16.9310 - 3.36778i) q^{97} +(6.58791 - 7.09579i) q^{98} +(0.372119 - 0.556915i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 384q16q11+32q1464q2216q2548q2864q3064q3532q3748q4264q44+32q4664q49+80q5632q58288q61528q68+176q70++32q99+O(q100) 384 q - 16 q^{11} + 32 q^{14} - 64 q^{22} - 16 q^{25} - 48 q^{28} - 64 q^{30} - 64 q^{35} - 32 q^{37} - 48 q^{42} - 64 q^{44} + 32 q^{46} - 64 q^{49} + 80 q^{56} - 32 q^{58} - 288 q^{61} - 528 q^{68} + 176 q^{70}+ \cdots + 32 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/357Z)×\left(\mathbb{Z}/357\mathbb{Z}\right)^\times.

nn 5252 190190 239239
χ(n)\chi(n) e(16)e\left(\frac{1}{6}\right) e(316)e\left(\frac{3}{16}\right) 11

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 −1.37138 + 0.180546i −0.969713 + 0.127665i −0.598709 0.800966i 0.704320π-0.704320\pi
−0.371003 + 0.928632i 0.620986π0.620986\pi
33 0.442289 + 0.896873i 0.255355 + 0.517810i
44 −0.0837632 + 0.0224443i −0.0418816 + 0.0112221i
55 −0.803646 + 0.704779i −0.359401 + 0.315187i −0.819936 0.572455i 0.805991π-0.805991\pi
0.460535 + 0.887642i 0.347658π0.347658\pi
66 −0.768473 1.15010i −0.313728 0.469527i
77 0.896773 + 2.48914i 0.338948 + 0.940805i
88 2.66667 1.10457i 0.942809 0.390524i
99 −0.608761 + 0.793353i −0.202920 + 0.264451i
1010 0.974860 1.11161i 0.308278 0.351523i
1111 −0.668362 + 0.0438068i −0.201519 + 0.0132082i −0.165828 0.986155i 0.553030π-0.553030\pi
−0.0356905 + 0.999363i 0.511363π0.511363\pi
1212 −0.0571772 0.0651981i −0.0165056 0.0188211i
1313 0.642496 + 0.642496i 0.178196 + 0.178196i 0.790569 0.612373i 0.209785π-0.209785\pi
−0.612373 + 0.790569i 0.709785π0.709785\pi
1414 −1.67922 3.25164i −0.448790 0.869039i
1515 −0.987540 0.409053i −0.254982 0.105617i
1616 −3.30739 + 1.90952i −0.826847 + 0.477380i
1717 −4.10201 + 0.416535i −0.994884 + 0.101025i
1818 0.691607 1.19790i 0.163013 0.282347i
1919 0.340606 + 2.58716i 0.0781404 + 0.593535i 0.985057 + 0.172226i 0.0550960π0.0550960\pi
−0.906917 + 0.421309i 0.861571π0.861571\pi
2020 0.0514977 0.0770718i 0.0115152 0.0172338i
2121 −1.83581 + 1.90521i −0.400606 + 0.415750i
2222 0.908670 0.180746i 0.193729 0.0385351i
2323 −6.91315 3.40919i −1.44149 0.710864i −0.457521 0.889199i 0.651262π-0.651262\pi
−0.983970 + 0.178335i 0.942929π0.942929\pi
2424 2.17009 + 1.90312i 0.442969 + 0.388473i
2525 −0.503497 + 3.82444i −0.100699 + 0.764888i
2626 −0.997106 0.765106i −0.195549 0.150050i
2727 −0.980785 0.195090i −0.188752 0.0375451i
2828 −0.130983 0.188371i −0.0247536 0.0355987i
2929 −0.147517 0.741618i −0.0273932 0.137715i 0.964669 0.263466i 0.0848658π-0.0848658\pi
−0.992062 + 0.125751i 0.959866π0.959866\pi
3030 1.42815 + 0.382671i 0.260743 + 0.0698658i
3131 −1.02931 + 0.507601i −0.184870 + 0.0911677i −0.532368 0.846513i 0.678698π-0.678698\pi
0.347498 + 0.937681i 0.387031π0.387031\pi
3232 −0.388902 + 0.298415i −0.0687489 + 0.0527529i
3333 −0.334898 0.580060i −0.0582983 0.100976i
3434 5.55022 1.31183i 0.951854 0.224977i
3535 −2.47498 1.36836i −0.418348 0.231295i
3636 0.0331856 0.0801171i 0.00553093 0.0133528i
3737 −0.168023 + 2.56354i −0.0276229 + 0.421443i 0.961544 + 0.274650i 0.0885619π0.0885619\pi
−0.989167 + 0.146793i 0.953105π0.953105\pi
3838 −0.934201 3.48649i −0.151547 0.565583i
3939 −0.292068 + 0.860405i −0.0467684 + 0.137775i
4040 −1.36458 + 2.76709i −0.215759 + 0.437516i
4141 0.461672 2.32098i 0.0721011 0.362477i −0.927844 0.372969i 0.878340π-0.878340\pi
0.999945 + 0.0104922i 0.00333985π0.00333985\pi
4242 2.17361 2.94421i 0.335396 0.454302i
4343 −1.65321 3.99121i −0.252113 0.608654i 0.746261 0.665653i 0.231847π-0.231847\pi
−0.998374 + 0.0569988i 0.981847π0.981847\pi
4444 0.0550010 0.0186703i 0.00829171 0.00281466i
4545 −0.0699098 1.06662i −0.0104215 0.159002i
4646 10.0961 + 3.42715i 1.48858 + 0.505306i
4747 −1.90759 + 7.11923i −0.278251 + 1.03845i 0.675381 + 0.737469i 0.263979π0.263979\pi
−0.953631 + 0.300977i 0.902687π0.902687\pi
4848 −3.17542 2.12175i −0.458332 0.306248i
4949 −5.39160 + 4.46438i −0.770228 + 0.637768i
5050 5.33567i 0.754577i
5151 −2.18785 3.49475i −0.306361 0.489363i
5252 −0.0682379 0.0393972i −0.00946289 0.00546340i
5353 0.529528 + 0.690095i 0.0727363 + 0.0947918i 0.828304 0.560278i 0.189306π-0.189306\pi
−0.755568 + 0.655070i 0.772639π0.772639\pi
5454 1.38025 + 0.0904665i 0.187829 + 0.0123109i
5555 0.506252 0.506252i 0.0682631 0.0682631i
5656 5.14082 + 5.64715i 0.686970 + 0.754632i
5757 −2.16971 + 1.44975i −0.287385 + 0.192024i
5858 0.336198 + 0.990407i 0.0441450 + 0.130047i
5959 −2.34351 0.308529i −0.305099 0.0401671i −0.0235778 0.999722i 0.507506π-0.507506\pi
−0.281521 + 0.959555i 0.590839π0.590839\pi
6060 0.0919005 + 0.0120989i 0.0118643 + 0.00156196i
6161 2.17512 + 6.40769i 0.278495 + 0.820421i 0.992714 + 0.120498i 0.0384490π0.0384490\pi
−0.714218 + 0.699923i 0.753218π0.753218\pi
6262 1.31993 0.881951i 0.167632 0.112008i
6363 −2.52069 0.803832i −0.317576 0.101273i
6464 5.88040 5.88040i 0.735050 0.735050i
6565 −0.969156 0.0635219i −0.120209 0.00787892i
6666 0.564000 + 0.735019i 0.0694236 + 0.0904746i
6767 −2.14839 1.24038i −0.262468 0.151536i 0.362992 0.931792i 0.381755π-0.381755\pi
−0.625460 + 0.780256i 0.715089π0.715089\pi
6868 0.334249 0.126957i 0.0405336 0.0153958i
6969 7.70806i 0.927941i
7070 3.64119 + 1.42969i 0.435205 + 0.170881i
7171 10.0562 + 6.71931i 1.19345 + 0.797436i 0.983611 0.180301i 0.0577072π-0.0577072\pi
0.209835 + 0.977737i 0.432707π0.432707\pi
7272 −0.747050 + 2.78803i −0.0880407 + 0.328572i
7373 8.77152 + 2.97753i 1.02663 + 0.348494i 0.783428 0.621482i 0.213469π-0.213469\pi
0.243201 + 0.969976i 0.421803π0.421803\pi
7474 −0.232412 3.54592i −0.0270174 0.412205i
7575 −3.65273 + 1.23993i −0.421781 + 0.143175i
7676 −0.0865973 0.209064i −0.00993339 0.0239813i
7777 −0.708410 1.62436i −0.0807308 0.185113i
7878 0.245194 1.23267i 0.0277628 0.139573i
7979 5.28364 10.7142i 0.594456 1.20544i −0.366934 0.930247i 0.619593π-0.619593\pi
0.961390 0.275190i 0.0887407π-0.0887407\pi
8080 1.31218 3.86556i 0.146706 0.432182i
8181 −0.258819 0.965926i −0.0287577 0.107325i
8282 −0.214085 + 3.26630i −0.0236417 + 0.360703i
8383 −1.02258 + 2.46874i −0.112243 + 0.270979i −0.970012 0.243056i 0.921850π-0.921850\pi
0.857769 + 0.514035i 0.171850π0.171850\pi
8484 0.111012 0.200790i 0.0121124 0.0219080i
8585 3.00300 3.22576i 0.325721 0.349882i
8686 2.98778 + 5.17499i 0.322181 + 0.558034i
8787 0.599892 0.460313i 0.0643152 0.0493508i
8888 −1.73391 + 0.855070i −0.184835 + 0.0911508i
8989 7.65661 + 2.05158i 0.811599 + 0.217467i 0.640670 0.767816i 0.278657π-0.278657\pi
0.170929 + 0.985283i 0.445323π0.445323\pi
9090 0.288446 + 1.45012i 0.0304049 + 0.152856i
9191 −1.02309 + 2.17543i −0.107249 + 0.228047i
9292 0.655584 + 0.130404i 0.0683494 + 0.0135955i
9393 −0.910506 0.698656i −0.0944151 0.0724472i
9494 1.33069 10.1076i 0.137250 1.04252i
9595 −2.09710 1.83911i −0.215158 0.188689i
9696 −0.439648 0.216810i −0.0448713 0.0221281i
9797 16.9310 3.36778i 1.71908 0.341946i 0.765579 0.643341i 0.222452π-0.222452\pi
0.953499 + 0.301395i 0.0974524π0.0974524\pi
9898 6.58791 7.09579i 0.665479 0.716783i
9999 0.372119 0.556915i 0.0373993 0.0559721i
100100 −0.0436623 0.331648i −0.00436623 0.0331648i
101101 5.98470 10.3658i 0.595500 1.03144i −0.397976 0.917396i 0.630287π-0.630287\pi
0.993476 0.114040i 0.0363792π-0.0363792\pi
102102 3.63134 + 4.39763i 0.359556 + 0.435430i
103103 −6.10881 + 3.52693i −0.601919 + 0.347518i −0.769796 0.638290i 0.779642π-0.779642\pi
0.167877 + 0.985808i 0.446309π0.446309\pi
104104 2.42300 + 1.00364i 0.237595 + 0.0984150i
105105 0.132588 2.82495i 0.0129393 0.275687i
106106 −0.850779 0.850779i −0.0826349 0.0826349i
107107 10.2407 + 11.6773i 0.990005 + 1.12888i 0.991659 + 0.128885i 0.0411399π0.0411399\pi
−0.00165473 + 0.999999i 0.500527π0.500527\pi
108108 0.0865324 0.00567163i 0.00832659 0.000545753i
109109 4.22067 4.81275i 0.404267 0.460978i −0.513505 0.858087i 0.671653π-0.671653\pi
0.917772 + 0.397109i 0.129986π0.129986\pi
110110 −0.602863 + 0.785666i −0.0574807 + 0.0749104i
111111 −2.37348 + 0.983129i −0.225281 + 0.0933145i
112112 −7.71904 6.52013i −0.729380 0.616095i
113113 1.62212 + 2.42768i 0.152596 + 0.228377i 0.899890 0.436118i 0.143647π-0.143647\pi
−0.747293 + 0.664495i 0.768647π0.768647\pi
114114 2.71375 2.37989i 0.254166 0.222897i
115115 7.95844 2.13246i 0.742129 0.198853i
116116 0.0290016 + 0.0588094i 0.00269273 + 0.00546032i
117117 −0.900853 + 0.118599i −0.0832839 + 0.0109645i
118118 3.26955 0.300987
119119 −4.71538 9.83693i −0.432259 0.901750i
120120 −3.08527 −0.281645
121121 −10.4611 + 1.37723i −0.951010 + 0.125203i
122122 −4.13980 8.39467i −0.374799 0.760018i
123123 2.28582 0.612483i 0.206105 0.0552257i
124124 0.0748258 0.0656204i 0.00671955 0.00589289i
125125 −5.26001 7.87216i −0.470470 0.704108i
126126 3.60195 + 0.647262i 0.320887 + 0.0576626i
127127 −1.51729 + 0.628483i −0.134638 + 0.0557689i −0.448985 0.893539i 0.648214π-0.648214\pi
0.314347 + 0.949308i 0.398214π0.398214\pi
128128 −6.40575 + 8.34814i −0.566194 + 0.737879i
129129 2.84841 3.24799i 0.250789 0.285970i
130130 1.34055 0.0878643i 0.117574 0.00770621i
131131 6.23743 + 7.11243i 0.544967 + 0.621416i 0.957117 0.289700i 0.0935556π-0.0935556\pi
−0.412151 + 0.911116i 0.635222π0.635222\pi
132132 0.0410712 + 0.0410712i 0.00357479 + 0.00357479i
133133 −6.13435 + 3.16791i −0.531915 + 0.274693i
134134 3.17021 + 1.31314i 0.273864 + 0.113438i
135135 0.925700 0.534453i 0.0796715 0.0459984i
136136 −10.4786 + 5.64172i −0.898533 + 0.483773i
137137 −8.86326 + 15.3516i −0.757239 + 1.31158i 0.187014 + 0.982357i 0.440119π0.440119\pi
−0.944253 + 0.329219i 0.893214π0.893214\pi
138138 1.39166 + 10.5707i 0.118466 + 0.899836i
139139 −9.24593 + 13.8375i −0.784230 + 1.17368i 0.196917 + 0.980420i 0.436907π0.436907\pi
−0.981147 + 0.193263i 0.938093π0.938093\pi
140140 0.238024 + 0.0590690i 0.0201167 + 0.00499224i
141141 −7.22875 + 1.43789i −0.608770 + 0.121092i
142142 −15.0040 7.39914i −1.25911 0.620922i
143143 −0.457565 0.401274i −0.0382635 0.0335562i
144144 0.498485 3.78637i 0.0415404 0.315531i
145145 0.641228 + 0.492032i 0.0532511 + 0.0408610i
146146 −12.5667 2.49967i −1.04003 0.206874i
147147 −6.38862 2.86103i −0.526925 0.235974i
148148 −0.0434627 0.218502i −0.00357261 0.0179607i
149149 −2.44808 0.655960i −0.200554 0.0537383i 0.157143 0.987576i 0.449771π-0.449771\pi
−0.357698 + 0.933837i 0.616438π0.616438\pi
150150 4.78541 2.35991i 0.390727 0.192685i
151151 0.780968 0.599258i 0.0635543 0.0487669i −0.576496 0.817100i 0.695580π-0.695580\pi
0.640050 + 0.768333i 0.278914π0.278914\pi
152152 3.76598 + 6.52287i 0.305461 + 0.529075i
153153 2.16669 3.50791i 0.175166 0.283598i
154154 1.26477 + 2.09971i 0.101918 + 0.169200i
155155 0.469457 1.13337i 0.0377077 0.0910343i
156156 0.00515339 0.0786256i 0.000412602 0.00629509i
157157 3.41911 + 12.7603i 0.272875 + 1.01838i 0.957252 + 0.289255i 0.0934075π0.0934075\pi
−0.684377 + 0.729128i 0.739926π0.739926\pi
158158 −5.31148 + 15.6471i −0.422559 + 1.24482i
159159 −0.384723 + 0.780141i −0.0305105 + 0.0618692i
160160 0.102223 0.513910i 0.00808145 0.0406282i
161161 2.28641 20.2650i 0.180194 1.59711i
162162 0.529333 + 1.27792i 0.0415883 + 0.100403i
163163 −21.6654 + 7.35442i −1.69697 + 0.576042i −0.991197 0.132399i 0.957732π-0.957732\pi
−0.705770 + 0.708441i 0.749399π0.749399\pi
164164 0.0134217 + 0.204775i 0.00104806 + 0.0159902i
165165 0.677954 + 0.230134i 0.0527786 + 0.0179159i
166166 0.956633 3.57020i 0.0742491 0.277102i
167167 13.1552 + 8.79000i 1.01798 + 0.680191i 0.948299 0.317379i 0.102803π-0.102803\pi
0.0696784 + 0.997570i 0.477803π0.477803\pi
168168 −2.79105 + 7.10833i −0.215334 + 0.548419i
169169 12.1744i 0.936492i
170170 −3.53586 + 4.96592i −0.271188 + 0.380869i
171171 −2.25988 1.30474i −0.172817 0.0997761i
172172 0.228059 + 0.297212i 0.0173893 + 0.0226622i
173173 15.9298 + 1.04409i 1.21112 + 0.0793808i 0.657542 0.753418i 0.271596π-0.271596\pi
0.553576 + 0.832799i 0.313263π0.313263\pi
174174 −0.739573 + 0.739573i −0.0560669 + 0.0560669i
175175 −9.97107 + 2.17638i −0.753742 + 0.164519i
176176 2.12688 1.42114i 0.160320 0.107122i
177177 −0.759797 2.23829i −0.0571099 0.168240i
178178 −10.8705 1.43113i −0.814781 0.107268i
179179 −11.6927 1.53937i −0.873953 0.115058i −0.319812 0.947481i 0.603620π-0.603620\pi
−0.554141 + 0.832423i 0.686953π0.686953\pi
180180 0.0297953 + 0.0877742i 0.00222081 + 0.00654231i
181181 −1.46775 + 0.980720i −0.109097 + 0.0728963i −0.608922 0.793230i 0.708398π-0.708398\pi
0.499825 + 0.866127i 0.333398π0.333398\pi
182182 1.01028 3.16806i 0.0748867 0.234832i
183183 −4.78485 + 4.78485i −0.353706 + 0.353706i
184184 −22.2007 1.45511i −1.63666 0.107272i
185185 −1.67170 2.17860i −0.122906 0.160174i
186186 1.37479 + 0.793735i 0.100804 + 0.0581995i
187187 2.72338 0.458092i 0.199153 0.0334990i
188188 0.639144i 0.0466144i
189189 −0.393935 2.61626i −0.0286546 0.190305i
190190 3.20797 + 2.14350i 0.232731 + 0.155506i
191191 −1.43113 + 5.34105i −0.103553 + 0.386465i −0.998177 0.0603549i 0.980777π-0.980777\pi
0.894624 + 0.446820i 0.147443π0.147443\pi
192192 7.87480 + 2.67314i 0.568315 + 0.192917i
193193 −1.60673 24.5139i −0.115655 1.76455i −0.523994 0.851722i 0.675558π-0.675558\pi
0.408339 0.912830i 0.366108π-0.366108\pi
194194 −22.6108 + 7.67532i −1.62336 + 0.551056i
195195 −0.371676 0.897305i −0.0266163 0.0642573i
196196 0.351418 0.494961i 0.0251013 0.0353544i
197197 −4.89438 + 24.6057i −0.348710 + 1.75308i 0.265660 + 0.964067i 0.414410π0.414410\pi
−0.614371 + 0.789018i 0.710590π0.710590\pi
198198 −0.409768 + 0.830927i −0.0291209 + 0.0590514i
199199 6.05179 17.8280i 0.429000 1.26379i −0.490755 0.871298i 0.663279π-0.663279\pi
0.919754 0.392495i 0.128388π-0.128388\pi
200200 2.88170 + 10.7546i 0.203767 + 0.760469i
201201 0.162249 2.47544i 0.0114442 0.174604i
202202 −6.33580 + 15.2960i −0.445785 + 1.07622i
203203 1.71370 1.03225i 0.120278 0.0724500i
204204 0.261699 + 0.243627i 0.0183226 + 0.0170573i
205205 1.26476 + 2.19062i 0.0883345 + 0.153000i
206206 7.74074 5.93968i 0.539323 0.413837i
207207 6.91315 3.40919i 0.480497 0.236955i
208208 −3.35184 0.898123i −0.232408 0.0622737i
209209 −0.340983 1.71424i −0.0235863 0.118576i
210210 0.328203 + 3.89802i 0.0226482 + 0.268989i
211211 1.61226 + 0.320699i 0.110993 + 0.0220778i 0.250274 0.968175i 0.419479π-0.419479\pi
−0.139281 + 0.990253i 0.544479π0.544479\pi
212212 −0.0598437 0.0459197i −0.00411008 0.00315378i
213213 −1.57864 + 11.9910i −0.108167 + 0.821608i
214214 −16.1522 14.1651i −1.10414 0.968304i
215215 4.14152 + 2.04237i 0.282449 + 0.139289i
216216 −2.83092 + 0.563104i −0.192620 + 0.0383144i
217217 −2.18655 2.10690i −0.148432 0.143025i
218218 −4.91923 + 7.36214i −0.333172 + 0.498627i
219219 1.20908 + 9.18387i 0.0817020 + 0.620588i
220220 −0.0310429 + 0.0537678i −0.00209291 + 0.00362503i
221221 −2.90315 2.36790i −0.195287 0.159282i
222222 3.07745 1.77677i 0.206545 0.119249i
223223 18.2973 + 7.57899i 1.22528 + 0.507527i 0.899084 0.437776i 0.144234π-0.144234\pi
0.326194 + 0.945303i 0.394234π0.394234\pi
224224 −1.09155 0.700420i −0.0729325 0.0467988i
225225 −2.72762 2.72762i −0.181841 0.181841i
226226 −2.66285 3.03640i −0.177130 0.201979i
227227 −2.32372 + 0.152305i −0.154231 + 0.0101088i −0.142323 0.989820i 0.545457π-0.545457\pi
−0.0119078 + 0.999929i 0.503790π0.503790\pi
228228 0.149203 0.170133i 0.00988121 0.0112674i
229229 17.2042 22.4210i 1.13689 1.48162i 0.284527 0.958668i 0.408163π-0.408163\pi
0.852361 0.522954i 0.175170π-0.175170\pi
230230 −10.5290 + 4.36127i −0.694265 + 0.287574i
231231 1.14352 1.35379i 0.0752382 0.0890728i
232232 −1.21255 1.81471i −0.0796076 0.119141i
233233 7.03919 6.17320i 0.461152 0.404420i −0.396997 0.917820i 0.629948π-0.629948\pi
0.858149 + 0.513400i 0.171614π0.171614\pi
234234 1.21400 0.325290i 0.0793616 0.0212649i
235235 −3.48445 7.06577i −0.227301 0.460920i
236236 0.203225 0.0267551i 0.0132288 0.00174161i
237237 11.9461 0.775984
238238 8.24260 + 12.6388i 0.534289 + 0.819254i
239239 −25.3218 −1.63793 −0.818965 0.573844i 0.805452π-0.805452\pi
−0.818965 + 0.573844i 0.805452π0.805452\pi
240240 4.04727 0.532834i 0.261250 0.0343943i
241241 9.45982 + 19.1826i 0.609360 + 1.23566i 0.954808 + 0.297223i 0.0960604π0.0960604\pi
−0.345448 + 0.938438i 0.612273π0.612273\pi
242242 14.0975 3.77741i 0.906222 0.242821i
243243 0.751840 0.659346i 0.0482305 0.0422971i
244244 −0.326011 0.487910i −0.0208707 0.0312352i
245245 1.18654 7.38766i 0.0758051 0.471980i
246246 −3.02415 + 1.25264i −0.192812 + 0.0798656i
247247 −1.44340 + 1.88108i −0.0918414 + 0.119690i
248248 −2.18415 + 2.49055i −0.138694 + 0.158150i
249249 −2.66642 + 0.174767i −0.168978 + 0.0110754i
250250 8.63476 + 9.84606i 0.546110 + 0.622720i
251251 3.06183 + 3.06183i 0.193261 + 0.193261i 0.797104 0.603842i 0.206364π-0.206364\pi
−0.603842 + 0.797104i 0.706364π0.706364\pi
252252 0.229182 + 0.0107566i 0.0144371 + 0.000677603i
253253 4.76983 + 1.97573i 0.299877 + 0.124213i
254254 1.96732 1.13583i 0.123440 0.0712683i
255255 4.22129 + 1.26659i 0.264347 + 0.0793171i
256256 −1.03863 + 1.79896i −0.0649145 + 0.112435i
257257 −1.11213 8.44749i −0.0693730 0.526940i −0.990483 0.137637i 0.956049π-0.956049\pi
0.921110 0.389303i 0.127284π-0.127284\pi
258258 −3.31985 + 4.96850i −0.206685 + 0.309325i
259259 −6.53168 + 1.88068i −0.405859 + 0.116860i
260260 0.0826054 0.0164312i 0.00512297 0.00101902i
261261 0.678168 + 0.334435i 0.0419775 + 0.0207010i
262262 −9.83801 8.62770i −0.607794 0.533021i
263263 −0.950261 + 7.21795i −0.0585956 + 0.445078i 0.936849 + 0.349735i 0.113728π0.113728\pi
−0.995444 + 0.0953433i 0.969605π0.969605\pi
264264 −1.53378 1.17691i −0.0943975 0.0724338i
265265 −0.911917 0.181392i −0.0560186 0.0111428i
266266 7.84057 5.45194i 0.480736 0.334280i
267267 1.54642 + 7.77439i 0.0946396 + 0.475785i
268268 0.207796 + 0.0556787i 0.0126931 + 0.00340112i
269269 20.4877 10.1034i 1.24916 0.616016i 0.307167 0.951656i 0.400619π-0.400619\pi
0.941991 + 0.335639i 0.108952π0.108952\pi
270270 −1.17299 + 0.900070i −0.0713861 + 0.0547765i
271271 −8.92111 15.4518i −0.541919 0.938631i −0.998794 0.0491001i 0.984365π-0.984365\pi
0.456875 0.889531i 0.348969π-0.348969\pi
272272 12.7716 9.21052i 0.774390 0.558470i
273273 −2.40358 + 0.0445904i −0.145472 + 0.00269873i
274274 9.38323 22.6531i 0.566862 1.36853i
275275 0.168982 2.57817i 0.0101900 0.155469i
276276 0.173002 + 0.645652i 0.0104135 + 0.0388637i
277277 1.78796 5.26715i 0.107428 0.316472i −0.879902 0.475156i 0.842392π-0.842392\pi
0.987329 + 0.158684i 0.0507250π0.0507250\pi
278278 10.1814 20.6458i 0.610639 1.23825i
279279 0.223899 1.12562i 0.0134045 0.0673889i
280280 −8.11138 0.915170i −0.484748 0.0546918i
281281 −4.58180 11.0614i −0.273327 0.659870i 0.726294 0.687384i 0.241241π-0.241241\pi
−0.999621 + 0.0275139i 0.991241π0.991241\pi
282282 9.65376 3.27701i 0.574873 0.195143i
283283 0.898138 + 13.7029i 0.0533887 + 0.814555i 0.937654 + 0.347570i 0.112993π0.112993\pi
−0.884265 + 0.466985i 0.845340π0.845340\pi
284284 −0.993147 0.337128i −0.0589324 0.0200049i
285285 0.721922 2.69425i 0.0427630 0.159594i
286286 0.699945 + 0.467688i 0.0413886 + 0.0276550i
287287 6.19126 0.932229i 0.365458 0.0550277i
288288 0.490201i 0.0288853i
289289 16.6530 3.41726i 0.979588 0.201015i
290290 −0.968202 0.558992i −0.0568548 0.0328251i
291291 10.5088 + 13.6954i 0.616039 + 0.802838i
292292 −0.801560 0.0525370i −0.0469077 0.00307449i
293293 −5.11998 + 5.11998i −0.299112 + 0.299112i −0.840666 0.541554i 0.817836π-0.817836\pi
0.541554 + 0.840666i 0.317836π0.317836\pi
294294 9.27778 + 2.77013i 0.541091 + 0.161557i
295295 2.10080 1.40371i 0.122313 0.0817271i
296296 2.38354 + 7.02170i 0.138541 + 0.408128i
297297 0.664066 + 0.0874259i 0.0385330 + 0.00507297i
298298 3.47567 + 0.457581i 0.201340 + 0.0265070i
299299 −2.25128 6.63205i −0.130195 0.383541i
300300 0.278135 0.185844i 0.0160581 0.0107297i
301301 8.45211 7.69428i 0.487172 0.443491i
302302 −0.962811 + 0.962811i −0.0554035 + 0.0554035i
303303 11.9438 + 0.782836i 0.686152 + 0.0449728i
304304 −6.06676 7.90635i −0.347952 0.453460i
305305 −6.26403 3.61654i −0.358677 0.207082i
306306 −2.33801 + 5.20187i −0.133655 + 0.297371i
307307 25.7178i 1.46779i 0.679261 + 0.733897i 0.262301π0.262301\pi
−0.679261 + 0.733897i 0.737699π0.737699\pi
308308 0.0957963 + 0.120162i 0.00545850 + 0.00684686i
309309 −5.86506 3.91891i −0.333652 0.222939i
310310 −0.439179 + 1.63904i −0.0249437 + 0.0930911i
311311 3.37752 + 1.14651i 0.191521 + 0.0650127i 0.415552 0.909569i 0.363588π-0.363588\pi
−0.224031 + 0.974582i 0.571922π0.571922\pi
312312 0.171529 + 2.61702i 0.00971090 + 0.148160i
313313 21.9608 7.45468i 1.24130 0.421364i 0.377880 0.925855i 0.376653π-0.376653\pi
0.863417 + 0.504491i 0.168320π0.168320\pi
314314 −6.99272 16.8819i −0.394622 0.952702i
315315 2.59226 1.13053i 0.146057 0.0636980i
316316 −0.202103 + 1.01604i −0.0113692 + 0.0571567i
317317 13.3167 27.0037i 0.747943 1.51668i −0.104884 0.994484i 0.533447π-0.533447\pi
0.852827 0.522194i 0.174886π-0.174886\pi
318318 0.386750 1.13933i 0.0216879 0.0638904i
319319 0.131083 + 0.489207i 0.00733922 + 0.0273903i
320320 −0.581380 + 8.87014i −0.0325001 + 0.495856i
321321 −5.94368 + 14.3493i −0.331744 + 0.800901i
322322 0.523227 + 28.2039i 0.0291583 + 1.57174i
323323 −2.47481 10.4707i −0.137702 0.582605i
324324 0.0433590 + 0.0751001i 0.00240884 + 0.00417223i
325325 −2.78068 + 2.13369i −0.154244 + 0.118356i
326326 28.3837 13.9973i 1.57203 0.775239i
327327 6.18318 + 1.65678i 0.341931 + 0.0916201i
328328 −1.33256 6.69923i −0.0735783 0.369903i
329329 −19.4314 + 1.63607i −1.07129 + 0.0901997i
330330 −0.971282 0.193200i −0.0534673 0.0106353i
331331 13.1568 + 10.0956i 0.723164 + 0.554903i 0.903441 0.428713i 0.141033π-0.141033\pi
−0.180277 + 0.983616i 0.557699π0.557699\pi
332332 0.0302459 0.229741i 0.00165996 0.0126087i
333333 −1.93151 1.69389i −0.105846 0.0928244i
334334 −19.6277 9.67933i −1.07398 0.529629i
335335 2.60074 0.517319i 0.142094 0.0282642i
336336 2.43369 9.80677i 0.132769 0.535003i
337337 −4.10158 + 6.13845i −0.223427 + 0.334383i −0.926200 0.377031i 0.876945π-0.876945\pi
0.702773 + 0.711414i 0.251945π0.251945\pi
338338 2.19804 + 16.6957i 0.119557 + 0.908128i
339339 −1.45987 + 2.52857i −0.0792893 + 0.137333i
340340 −0.179141 + 0.337600i −0.00971530 + 0.0183089i
341341 0.665717 0.384352i 0.0360506 0.0208138i
342342 3.33472 + 1.38129i 0.180321 + 0.0746914i
343343 −15.9475 9.41689i −0.861083 0.508464i
344344 −8.81714 8.81714i −0.475388 0.475388i
345345 5.43247 + 6.19455i 0.292475 + 0.333503i
346346 −22.0343 + 1.44420i −1.18457 + 0.0776408i
347347 −20.4982 + 23.3737i −1.10040 + 1.25477i −0.135891 + 0.990724i 0.543390π0.543390\pi
−0.964511 + 0.264044i 0.914944π0.914944\pi
348348 −0.0399175 + 0.0520215i −0.00213980 + 0.00278864i
349349 10.9728 4.54509i 0.587362 0.243293i −0.0691535 0.997606i 0.522030π-0.522030\pi
0.656515 + 0.754313i 0.272030π0.272030\pi
350350 13.2812 4.78488i 0.709910 0.255763i
351351 −0.504806 0.755495i −0.0269445 0.0403253i
352352 0.246855 0.216486i 0.0131574 0.0115387i
353353 −13.5497 + 3.63062i −0.721176 + 0.193238i −0.600696 0.799477i 0.705110π-0.705110\pi
−0.120479 + 0.992716i 0.538443π0.538443\pi
354354 1.44609 + 2.93237i 0.0768586 + 0.155854i
355355 −12.8172 + 1.68742i −0.680268 + 0.0895589i
356356 −0.687389 −0.0364315
357357 6.73691 8.57986i 0.356555 0.454094i
358358 16.3131 0.862172
359359 9.48593 1.24885i 0.500648 0.0659116i 0.124027 0.992279i 0.460419π-0.460419\pi
0.376621 + 0.926367i 0.377086π0.377086\pi
360360 −1.36458 2.76709i −0.0719196 0.145839i
361361 11.7752 3.15516i 0.619748 0.166061i
362362 1.83578 1.60994i 0.0964865 0.0846164i
363363 −5.86203 8.77315i −0.307677 0.460471i
364364 0.0368710 0.205184i 0.00193257 0.0107545i
365365 −9.14770 + 3.78910i −0.478812 + 0.198331i
366366 5.69797 7.42574i 0.297838 0.388150i
367367 −0.818300 + 0.933092i −0.0427149 + 0.0487070i −0.772803 0.634646i 0.781146π-0.781146\pi
0.730088 + 0.683353i 0.239479π0.239479\pi
368368 29.3744 1.92530i 1.53125 0.100363i
369369 1.56031 + 1.77919i 0.0812265 + 0.0926211i
370370 2.68587 + 2.68587i 0.139632 + 0.139632i
371371 −1.24287 + 1.93693i −0.0645268 + 0.100560i
372372 0.0919478 + 0.0380860i 0.00476727 + 0.00197467i
373373 −18.2625 + 10.5439i −0.945598 + 0.545942i −0.891711 0.452606i 0.850495π-0.850495\pi
−0.0538876 + 0.998547i 0.517161π0.517161\pi
374374 −3.65209 + 1.11991i −0.188845 + 0.0579093i
375375 4.73388 8.19933i 0.244457 0.423412i
376376 2.77677 + 21.0917i 0.143201 + 1.08772i
377377 0.381707 0.571265i 0.0196589 0.0294217i
378378 1.01259 + 3.51676i 0.0520820 + 0.180883i
379379 −11.3061 + 2.24893i −0.580757 + 0.115520i −0.476722 0.879054i 0.658175π-0.658175\pi
−0.104035 + 0.994574i 0.533175π0.533175\pi
380380 0.216938 + 0.106982i 0.0111287 + 0.00548805i
381381 −1.23475 1.08285i −0.0632582 0.0554760i
382382 0.998321 7.58300i 0.0510785 0.387980i
383383 2.17868 + 1.67176i 0.111325 + 0.0854229i 0.662924 0.748687i 0.269315π-0.269315\pi
−0.551599 + 0.834110i 0.685982π0.685982\pi
384384 −10.3204 2.05286i −0.526661 0.104759i
385385 1.71412 + 0.806138i 0.0873599 + 0.0410846i
386386 6.62933 + 33.3279i 0.337424 + 1.69634i
387387 4.17285 + 1.11811i 0.212118 + 0.0568369i
388388 −1.34260 + 0.662099i −0.0681604 + 0.0336130i
389389 −19.9964 + 15.3438i −1.01386 + 0.777960i −0.975207 0.221293i 0.928972π-0.928972\pi
−0.0386499 + 0.999253i 0.512306π0.512306\pi
390390 0.671714 + 1.16344i 0.0340135 + 0.0589132i
391391 29.7778 + 11.1050i 1.50593 + 0.561602i
392392 −9.44637 + 17.8604i −0.477114 + 0.902086i
393393 −3.62020 + 8.73993i −0.182615 + 0.440871i
394394 2.26960 34.6275i 0.114341 1.74451i
395395 3.30493 + 12.3342i 0.166289 + 0.620600i
396396 −0.0186703 + 0.0550010i −0.000938218 + 0.00276390i
397397 0.786047 1.59395i 0.0394506 0.0799979i −0.876255 0.481848i 0.839966π-0.839966\pi
0.915706 + 0.401850i 0.131633π0.131633\pi
398398 −5.08054 + 25.5416i −0.254664 + 1.28028i
399399 −5.55436 4.10060i −0.278066 0.205287i
400400 −5.63759 13.6103i −0.281880 0.680517i
401401 29.4373 9.99261i 1.47003 0.499007i 0.532353 0.846522i 0.321308π-0.321308\pi
0.937674 + 0.347515i 0.112975π0.112975\pi
402402 0.224425 + 3.42406i 0.0111933 + 0.170777i
403403 −0.987460 0.335197i −0.0491889 0.0166974i
404404 −0.268645 + 1.00260i −0.0133656 + 0.0498810i
405405 0.888763 + 0.593852i 0.0441630 + 0.0295088i
406406 −2.16377 + 1.72501i −0.107386 + 0.0856109i
407407 1.72073i 0.0852936i
408408 −9.69447 6.90271i −0.479948 0.341735i
409409 28.2808 + 16.3279i 1.39840 + 0.807364i 0.994225 0.107319i 0.0342266π-0.0342266\pi
0.404171 + 0.914683i 0.367560π0.367560\pi
410410 −2.12997 2.77583i −0.105192 0.137089i
411411 −17.6886 1.15937i −0.872512 0.0571875i
412412 0.432535 0.432535i 0.0213095 0.0213095i
413413 −1.33363 6.11000i −0.0656235 0.300653i
414414 −8.86504 + 5.92343i −0.435693 + 0.291121i
415415 −0.918118 2.70469i −0.0450686 0.132768i
416416 −0.441599 0.0581375i −0.0216511 0.00285043i
417417 −16.4999 2.17225i −0.808002 0.106375i
418418 0.777116 + 2.28931i 0.0380100 + 0.111974i
419419 −3.44051 + 2.29887i −0.168080 + 0.112307i −0.636765 0.771058i 0.719728π-0.719728\pi
0.468685 + 0.883365i 0.344728π0.344728\pi
420420 0.0522980 + 0.239603i 0.00255188 + 0.0116914i
421421 1.98656 1.98656i 0.0968190 0.0968190i −0.657038 0.753857i 0.728191π-0.728191\pi
0.753857 + 0.657038i 0.228191π0.228191\pi
422422 −2.26892 0.148713i −0.110449 0.00723924i
423423 −4.48680 5.84731i −0.218155 0.284306i
424424 2.17433 + 1.25535i 0.105595 + 0.0609653i
425425 0.472338 15.8976i 0.0229117 0.771148i
426426 16.7292i 0.810533i
427427 −13.9990 + 11.1604i −0.677460 + 0.540090i
428428 −1.11988 0.748281i −0.0541315 0.0361695i
429429 0.157516 0.587857i 0.00760493 0.0283820i
430430 −6.04834 2.05314i −0.291677 0.0990110i
431431 −1.56960 23.9474i −0.0756048 1.15351i −0.852098 0.523382i 0.824670π-0.824670\pi
0.776494 0.630125i 0.216996π-0.216996\pi
432432 3.61637 1.22759i 0.173993 0.0590625i
433433 −3.76218 9.08270i −0.180799 0.436487i 0.807333 0.590096i 0.200910π-0.200910\pi
−0.988132 + 0.153610i 0.950910π0.950910\pi
434434 3.37898 + 2.49458i 0.162196 + 0.119744i
435435 −0.157682 + 0.792720i −0.00756026 + 0.0380080i
436436 −0.245518 + 0.497862i −0.0117582 + 0.0238433i
437437 6.46545 19.0466i 0.309284 0.911123i
438438 −3.31621 12.3763i −0.158455 0.591362i
439439 1.69942 25.9282i 0.0811091 1.23749i −0.742312 0.670055i 0.766271π-0.766271\pi
0.823421 0.567431i 0.192063π-0.192063\pi
440440 0.790815 1.90920i 0.0377006 0.0910174i
441441 −0.259633 6.99518i −0.0123635 0.333104i
442442 4.40883 + 2.72315i 0.209707 + 0.129527i
443443 −0.614548 1.06443i −0.0291980 0.0505725i 0.851057 0.525073i 0.175962π-0.175962\pi
−0.880255 + 0.474501i 0.842629π0.842629\pi
444444 0.176745 0.135621i 0.00838795 0.00643630i
445445 −7.59911 + 3.74747i −0.360232 + 0.177647i
446446 −26.4609 7.09018i −1.25296 0.335730i
447447 −0.494444 2.48574i −0.0233864 0.117571i
448448 19.9105 + 9.36373i 0.940682 + 0.442395i
449449 21.4211 + 4.26092i 1.01092 + 0.201085i 0.672648 0.739962i 0.265157π-0.265157\pi
0.338275 + 0.941047i 0.390157π0.390157\pi
450450 4.23307 + 3.24815i 0.199549 + 0.153119i
451451 −0.206889 + 1.57148i −0.00974204 + 0.0739981i
452452 −0.190362 0.166943i −0.00895386 0.00785233i
453453 0.882871 + 0.435384i 0.0414809 + 0.0204561i
454454 3.15921 0.628405i 0.148269 0.0294925i
455455 −0.710998 2.46933i −0.0333321 0.115764i
456456 −4.18453 + 6.26260i −0.195959 + 0.293273i
457457 −2.45266 18.6298i −0.114730 0.871465i −0.947927 0.318488i 0.896825π-0.896825\pi
0.833197 0.552977i 0.186508π-0.186508\pi
458458 −19.5455 + 33.8539i −0.913304 + 1.58189i
459459 4.10445 + 0.391731i 0.191580 + 0.0182845i
460460 −0.618763 + 0.357243i −0.0288500 + 0.0166566i
461461 −26.1091 10.8148i −1.21602 0.503693i −0.319880 0.947458i 0.603642π-0.603642\pi
−0.896143 + 0.443765i 0.853642π0.853642\pi
462462 −1.32378 + 2.06302i −0.0615880 + 0.0959803i
463463 −24.0509 24.0509i −1.11774 1.11774i −0.992073 0.125665i 0.959893π-0.959893\pi
−0.125665 0.992073i 0.540107π-0.540107\pi
464464 1.90403 + 2.17113i 0.0883925 + 0.100792i
465465 1.22412 0.0802332i 0.0567673 0.00372073i
466466 −8.53886 + 9.73670i −0.395555 + 0.451044i
467467 1.16845 1.52275i 0.0540693 0.0704645i −0.765536 0.643393i 0.777526π-0.777526\pi
0.819605 + 0.572929i 0.194193π0.194193\pi
468468 0.0727965 0.0301533i 0.00336502 0.00139384i
469469 1.16084 6.45998i 0.0536028 0.298294i
470470 6.05420 + 9.06076i 0.279260 + 0.417942i
471471 −9.93213 + 8.71025i −0.457649 + 0.401347i
472472 −6.59015 + 1.76583i −0.303336 + 0.0812788i
473473 1.27979 + 2.59515i 0.0588447 + 0.119325i
474474 −16.3827 + 2.15682i −0.752482 + 0.0990661i
475475 −10.0659 −0.461857
476476 0.615759 + 0.718140i 0.0282233 + 0.0329159i
477477 −0.869845 −0.0398275
478478 34.7258 4.57174i 1.58832 0.209106i
479479 −9.49271 19.2493i −0.433733 0.879523i −0.998525 0.0542901i 0.982710π-0.982710\pi
0.564792 0.825233i 0.308956π-0.308956\pi
480480 0.506124 0.135616i 0.0231013 0.00618998i
481481 −1.75502 + 1.53911i −0.0800219 + 0.0701773i
482482 −16.4363 24.5987i −0.748655 1.12044i
483483 19.1864 6.91237i 0.873011 0.314524i
484484 0.845345 0.350153i 0.0384248 0.0159161i
485485 −11.2330 + 14.6391i −0.510062 + 0.664726i
486486 −0.912017 + 1.03996i −0.0413699 + 0.0471733i
487487 13.3196 0.873013i 0.603569 0.0395600i 0.239444 0.970910i 0.423035π-0.423035\pi
0.364125 + 0.931350i 0.381368π0.381368\pi
488488 12.8780 + 14.6846i 0.582962 + 0.664741i
489489 −16.1783 16.1783i −0.731610 0.731610i
490490 −0.293383 + 10.3455i −0.0132537 + 0.467363i
491491 14.9273 + 6.18310i 0.673661 + 0.279040i 0.693174 0.720770i 0.256212π-0.256212\pi
−0.0195131 + 0.999810i 0.506212π0.506212\pi
492492 −0.177721 + 0.102607i −0.00801227 + 0.00462589i
493493 0.914026 + 2.98068i 0.0411657 + 0.134243i
494494 1.63983 2.84027i 0.0737795 0.127790i
495495 0.0934501 + 0.709824i 0.00420027 + 0.0319042i
496496 2.43506 3.64433i 0.109337 0.163635i
497497 −7.70719 + 31.0569i −0.345715 + 1.39309i
498498 3.62513 0.721082i 0.162446 0.0323125i
499499 9.21824 + 4.54593i 0.412665 + 0.203504i 0.636758 0.771064i 0.280275π-0.280275\pi
−0.224093 + 0.974568i 0.571942π0.571942\pi
500500 0.617281 + 0.541341i 0.0276056 + 0.0242095i
501501 −2.06513 + 15.6862i −0.0922632 + 0.700809i
502502 −4.75174 3.64614i −0.212081 0.162735i
503503 14.0311 + 2.79096i 0.625615 + 0.124443i 0.497710 0.867344i 0.334175π-0.334175\pi
0.127906 + 0.991786i 0.459175π0.459175\pi
504504 −7.60971 + 0.640718i −0.338964 + 0.0285399i
505505 2.49602 + 12.5483i 0.111071 + 0.558393i
506506 −6.89796 1.84830i −0.306652 0.0821671i
507507 10.9189 5.38460i 0.484925 0.239138i
508508 0.112987 0.0866983i 0.00501301 0.00384662i
509509 −15.2057 26.3370i −0.673979 1.16737i −0.976766 0.214308i 0.931250π-0.931250\pi
0.302787 0.953058i 0.402083π-0.402083\pi
510510 −6.01767 0.974847i −0.266467 0.0431669i
511511 0.454583 + 24.5037i 0.0201095 + 1.08398i
512512 9.15322 22.0978i 0.404519 0.976595i
513513 0.170668 2.60390i 0.00753520 0.114965i
514514 3.05032 + 11.3839i 0.134544 + 0.502124i
515515 2.42362 7.13976i 0.106798 0.314615i
516516 −0.165693 + 0.335993i −0.00729424 + 0.0147913i
517517 0.963091 4.84179i 0.0423567 0.212942i
518518 8.61787 3.75839i 0.378647 0.165134i
519519 6.10914 + 14.7488i 0.268161 + 0.647399i
520520 −2.65458 + 0.901108i −0.116411 + 0.0395162i
521521 2.61560 + 39.9063i 0.114591 + 1.74833i 0.538502 + 0.842624i 0.318990π0.318990\pi
−0.423911 + 0.905704i 0.639343π0.639343\pi
522522 −0.990407 0.336198i −0.0433490 0.0147150i
523523 −7.53174 + 28.1088i −0.329340 + 1.22911i 0.580537 + 0.814234i 0.302843π0.302843\pi
−0.909877 + 0.414879i 0.863824π0.863824\pi
524524 −0.682101 0.455765i −0.0297977 0.0199102i
525525 −6.36203 7.98019i −0.277662 0.348284i
526526 10.0701i 0.439078i
527527 4.01082 2.51093i 0.174714 0.109378i
528528 2.21528 + 1.27899i 0.0964075 + 0.0556609i
529529 22.1675 + 28.8893i 0.963805 + 1.25606i
530530 1.28334 + 0.0841142i 0.0557445 + 0.00365369i
531531 1.67141 1.67141i 0.0725331 0.0725331i
532532 0.442731 0.403036i 0.0191948 0.0174738i
533533 1.78784 1.19460i 0.0774401 0.0517438i
534534 −3.52437 10.3825i −0.152514 0.449293i
535535 −16.4598 2.16697i −0.711618 0.0936863i
536536 −7.09913 0.934618i −0.306636 0.0403694i
537537 −3.79093 11.1677i −0.163591 0.481922i
538538 −26.2723 + 17.5546i −1.13268 + 0.756832i
539539 3.40797 3.22001i 0.146792 0.138696i
540540 −0.0655442 + 0.0655442i −0.00282057 + 0.00282057i
541541 −9.01957 0.591174i −0.387782 0.0254165i −0.129734 0.991549i 0.541412π-0.541412\pi
−0.258047 + 0.966132i 0.583079π0.583079\pi
542542 15.0240 + 19.5797i 0.645336 + 0.841018i
543543 −1.52875 0.882625i −0.0656050 0.0378771i
544544 1.47098 1.38609i 0.0630678 0.0594283i
545545 6.84239i 0.293096i
546546 3.28818 0.495107i 0.140721 0.0211886i
547547 14.4328 + 9.64369i 0.617102 + 0.412334i 0.824452 0.565933i 0.191484π-0.191484\pi
−0.207350 + 0.978267i 0.566484π0.566484\pi
548548 0.397859 1.48483i 0.0169957 0.0634288i
549549 −6.40769 2.17512i −0.273474 0.0928318i
550550 0.233738 + 3.56616i 0.00996663 + 0.152061i
551551 1.86844 0.634250i 0.0795982 0.0270200i
552552 −8.51408 20.5548i −0.362383 0.874871i
553553 31.4072 + 3.54353i 1.33557 + 0.150686i
554554 −1.50101 + 7.54607i −0.0637717 + 0.320602i
555555 1.21455 2.46287i 0.0515549 0.104543i
556556 0.463896 1.36659i 0.0196736 0.0579565i
557557 0.205440 + 0.766712i 0.00870476 + 0.0324866i 0.970142 0.242539i 0.0779803π-0.0779803\pi
−0.961437 + 0.275026i 0.911314π0.911314\pi
558558 −0.103826 + 1.58407i −0.00439529 + 0.0670591i
559559 1.50215 3.62652i 0.0635343 0.153385i
560560 10.7986 0.200332i 0.456325 0.00846556i
561561 1.61537 + 2.23992i 0.0682010 + 0.0945694i
562562 8.28048 + 14.3422i 0.349291 + 0.604990i
563563 −23.0419 + 17.6807i −0.971102 + 0.745153i −0.966984 0.254839i 0.917978π-0.917978\pi
−0.00411829 + 0.999992i 0.501311π0.501311\pi
564564 0.573231 0.282686i 0.0241374 0.0119032i
565565 −3.01459 0.807756i −0.126825 0.0339826i
566566 −3.70569 18.6298i −0.155762 0.783068i
567567 2.17222 1.51045i 0.0912246 0.0634330i
568568 34.2384 + 6.81044i 1.43661 + 0.285760i
569569 11.0102 + 8.44844i 0.461572 + 0.354177i 0.813221 0.581955i 0.197712π-0.197712\pi
−0.351649 + 0.936132i 0.614379π0.614379\pi
570570 −0.503595 + 3.82518i −0.0210933 + 0.160219i
571571 −23.1160 20.2722i −0.967376 0.848366i 0.0210949 0.999777i 0.493285π-0.493285\pi
−0.988471 + 0.151412i 0.951618π0.951618\pi
572572 0.0473335 + 0.0233423i 0.00197911 + 0.000975990i
573573 −5.42321 + 1.07874i −0.226558 + 0.0450652i
574574 −8.32226 + 2.39625i −0.347364 + 0.100017i
575575 16.5190 24.7224i 0.688889 1.03099i
576576 1.08547 + 8.24499i 0.0452281 + 0.343541i
577577 −12.1044 + 20.9655i −0.503914 + 0.872805i 0.496076 + 0.868279i 0.334774π0.334774\pi
−0.999990 + 0.00452570i 0.998559π0.998559\pi
578578 −22.2206 + 7.69300i −0.924256 + 0.319986i
579579 21.2753 12.2833i 0.884169 0.510475i
580580 −0.0647546 0.0268223i −0.00268879 0.00111373i
581581 −7.06205 0.331456i −0.292983 0.0137511i
582582 −16.8843 16.8843i −0.699875 0.699875i
583583 −0.384147 0.438036i −0.0159098 0.0181416i
584584 26.6796 1.74867i 1.10401 0.0723606i
585585 0.640380 0.730214i 0.0264765 0.0301906i
586586 6.09705 7.94583i 0.251867 0.328239i
587587 −30.9736 + 12.8297i −1.27842 + 0.529538i −0.915513 0.402288i 0.868215π-0.868215\pi
−0.362905 + 0.931826i 0.618215π0.618215\pi
588588 0.599346 + 0.0962613i 0.0247166 + 0.00396975i
589589 −1.66383 2.49010i −0.0685571 0.102603i
590590 −2.62756 + 2.30431i −0.108175 + 0.0948669i
591591 −24.2329 + 6.49319i −0.996809 + 0.267094i
592592 −4.33942 8.79947i −0.178349 0.361656i
593593 −6.01179 + 0.791467i −0.246875 + 0.0325017i −0.252948 0.967480i 0.581400π-0.581400\pi
0.00607328 + 0.999982i 0.498067π0.498067\pi
594594 −0.926472 −0.0380136
595595 10.7224 + 4.58211i 0.439574 + 0.187848i
596596 0.219781 0.00900259
597597 18.6661 2.45743i 0.763951 0.100576i
598598 4.28475 + 8.68861i 0.175216 + 0.355304i
599599 37.5279 10.0556i 1.53335 0.410859i 0.609238 0.792988i 0.291476π-0.291476\pi
0.924109 + 0.382129i 0.124809π0.124809\pi
600600 −8.37101 + 7.34118i −0.341745 + 0.299702i
601601 6.03449 + 9.03125i 0.246152 + 0.368393i 0.933886 0.357570i 0.116395π-0.116395\pi
−0.687734 + 0.725962i 0.741395π0.741395\pi
602602 −10.2019 + 12.0778i −0.415798 + 0.492254i
603603 2.29192 0.949342i 0.0933340 0.0386602i
604604 −0.0519665 + 0.0677240i −0.00211449 + 0.00275565i
605605 7.43638 8.47957i 0.302332 0.344743i
606606 −16.5208 + 1.08283i −0.671111 + 0.0439870i
607607 −18.4153 20.9986i −0.747453 0.852306i 0.245674 0.969353i 0.420991π-0.420991\pi
−0.993126 + 0.117046i 0.962657π0.962657\pi
608608 −0.904511 0.904511i −0.0366827 0.0366827i
609609 1.68375 + 1.08042i 0.0682290 + 0.0437807i
610610 9.24332 + 3.82871i 0.374251 + 0.155020i
611611 −5.79969 + 3.34845i −0.234630 + 0.135464i
612612 −0.102756 + 0.342464i −0.00415367 + 0.0138433i
613613 14.8281 25.6830i 0.598901 1.03733i −0.394083 0.919075i 0.628938π-0.628938\pi
0.992984 0.118252i 0.0377290π-0.0377290\pi
614614 −4.64324 35.2689i −0.187386 1.42334i
615615 −1.40532 + 2.10322i −0.0566681 + 0.0848098i
616616 −3.68331 3.54914i −0.148405 0.142999i
617617 −33.8513 + 6.73345i −1.36280 + 0.271078i −0.821720 0.569891i 0.806985π-0.806985\pi
−0.541083 + 0.840969i 0.681985π0.681985\pi
618618 8.75078 + 4.31541i 0.352008 + 0.173591i
619619 −27.0991 23.7653i −1.08921 0.955208i −0.0900360 0.995939i 0.528698π-0.528698\pi
−0.999170 + 0.0407304i 0.987032π0.987032\pi
620620 −0.0138855 + 0.105471i −0.000557657 + 0.00423583i
621621 6.11521 + 4.69237i 0.245395 + 0.188298i
622622 −4.83886 0.962509i −0.194021 0.0385931i
623623 1.75957 + 20.8981i 0.0704957 + 0.837266i
624624 −0.676980 3.40341i −0.0271009 0.136245i
625625 −8.85469 2.37261i −0.354187 0.0949043i
626626 −28.7707 + 14.1881i −1.14991 + 0.567072i
627627 1.38664 1.06401i 0.0553771 0.0424924i
628628 −0.572792 0.992105i −0.0228569 0.0395893i
629629 −0.378571 10.5857i −0.0150946 0.422078i
630630 −3.35087 + 2.01841i −0.133502 + 0.0804152i
631631 −16.7963 + 40.5499i −0.668651 + 1.61427i 0.115219 + 0.993340i 0.463243π0.463243\pi
−0.783870 + 0.620925i 0.786757π0.786757\pi
632632 2.25517 34.4072i 0.0897058 1.36865i
633633 0.425459 + 1.58783i 0.0169105 + 0.0631107i
634634 −13.3869 + 39.4366i −0.531663 + 1.56623i
635635 0.776425 1.57443i 0.0308115 0.0624795i
636636 0.0147159 0.0739819i 0.000583524 0.00293357i
637637 −6.33242 0.595734i −0.250900 0.0236038i
638638 −0.268089 0.647223i −0.0106137 0.0256238i
639639 −11.4526 + 3.88763i −0.453058 + 0.153792i
640640 −0.735633 11.2236i −0.0290784 0.443651i
641641 −20.0057 6.79102i −0.790177 0.268229i −0.102964 0.994685i 0.532833π-0.532833\pi
−0.687213 + 0.726456i 0.741166π0.741166\pi
642642 5.56034 20.7515i 0.219449 0.818996i
643643 20.7482 + 13.8635i 0.818228 + 0.546722i 0.892779 0.450495i 0.148752π-0.148752\pi
−0.0745512 + 0.997217i 0.523752π0.523752\pi
644644 0.263317 + 1.74878i 0.0103762 + 0.0689116i
645645 4.61773i 0.181823i
646646 5.28435 + 13.9125i 0.207910 + 0.547379i
647647 5.75925 + 3.32510i 0.226419 + 0.130723i 0.608919 0.793232i 0.291603π-0.291603\pi
−0.382500 + 0.923956i 0.624937π0.624937\pi
648648 −1.75712 2.28992i −0.0690260 0.0899565i
649649 1.57983 + 0.103548i 0.0620137 + 0.00406460i
650650 3.42814 3.42814i 0.134463 0.134463i
651651 0.922533 2.89291i 0.0361569 0.113382i
652652 1.64970 1.10229i 0.0646073 0.0431692i
653653 −6.25812 18.4358i −0.244899 0.721450i −0.997980 0.0635224i 0.979767π-0.979767\pi
0.753081 0.657928i 0.228567π-0.228567\pi
654654 −8.77862 1.15573i −0.343271 0.0451925i
655655 −10.0254 1.31987i −0.391724 0.0515714i
656656 2.90504 + 8.55796i 0.113423 + 0.334132i
657657 −7.70200 + 5.14631i −0.300484 + 0.200777i
658658 26.3525 5.75194i 1.02733 0.224234i
659659 −23.1046 + 23.1046i −0.900027 + 0.900027i −0.995438 0.0954108i 0.969584π-0.969584\pi
0.0954108 + 0.995438i 0.469584π0.469584\pi
660660 −0.0619528 0.00406060i −0.00241151 0.000158059i
661661 −21.0291 27.4056i −0.817936 1.06595i −0.996628 0.0820496i 0.973853π-0.973853\pi
0.178693 0.983905i 0.442813π-0.442813\pi
662662 −19.8657 11.4695i −0.772103 0.445774i
663663 0.839678 3.65105i 0.0326104 0.141795i
664664 7.71282i 0.299315i
665665 2.69717 6.86924i 0.104592 0.266378i
666666 2.95465 + 1.97424i 0.114491 + 0.0765001i
667667 −1.50851 + 5.62983i −0.0584096 + 0.217988i
668668 −1.29920 0.441021i −0.0502677 0.0170636i
669669 1.29530 + 19.7625i 0.0500792 + 0.764061i
670670 −3.47320 + 1.17899i −0.134182 + 0.0455485i
671671 −1.73447 4.18737i −0.0669583 0.161652i
672672 0.145406 1.28877i 0.00560916 0.0497155i
673673 −0.971552 + 4.88432i −0.0374506 + 0.188277i −0.994982 0.100051i 0.968099π-0.968099\pi
0.957532 + 0.288328i 0.0930993π0.0930993\pi
674674 4.51656 9.15867i 0.173971 0.352779i
675675 1.23993 3.65273i 0.0477251 0.140594i
676676 0.273246 + 1.01977i 0.0105095 + 0.0392218i
677677 −1.13075 + 17.2519i −0.0434582 + 0.663045i 0.919449 + 0.393210i 0.128636π0.128636\pi
−0.962907 + 0.269834i 0.913031π0.913031\pi
678678 1.54552 3.73121i 0.0593552 0.143296i
679679 23.5661 + 39.1233i 0.904383 + 1.50142i
680680 4.44493 11.9190i 0.170455 0.457074i
681681 −1.16435 2.01672i −0.0446181 0.0772808i
682682 −0.843558 + 0.647285i −0.0323015 + 0.0247858i
683683 37.3015 18.3951i 1.42730 0.703868i 0.445767 0.895149i 0.352931π-0.352931\pi
0.981535 + 0.191281i 0.0612642π0.0612642\pi
684684 0.218579 + 0.0585680i 0.00835757 + 0.00223941i
685685 −3.69657 18.5839i −0.141239 0.710054i
686686 23.5703 + 10.0349i 0.899916 + 0.383134i
687687 27.7180 + 5.51346i 1.05751 + 0.210352i
688688 13.0891 + 10.0436i 0.499018 + 0.382910i
689689 −0.103163 + 0.783602i −0.00393021 + 0.0298529i
690690 −8.56839 7.51427i −0.326193 0.286064i
691691 −30.6671 15.1233i −1.16663 0.575318i −0.247352 0.968926i 0.579560π-0.579560\pi
−0.919279 + 0.393607i 0.871227π0.871227\pi
692692 −1.35776 + 0.270076i −0.0516144 + 0.0102667i
693693 1.71994 + 0.426828i 0.0653353 + 0.0162139i
694694 23.8908 35.7552i 0.906883 1.35725i
695695 −2.32193 17.6368i −0.0880758 0.669002i
696696 1.09126 1.89012i 0.0413642 0.0716450i
697697 −0.927014 + 9.71300i −0.0351132 + 0.367906i
698698 −14.2273 + 8.21415i −0.538512 + 0.310910i
699699 8.64993 + 3.58292i 0.327170 + 0.135518i
700700 0.786362 0.406094i 0.0297217 0.0153489i
701701 −1.57170 1.57170i −0.0593623 0.0593623i 0.676802 0.736165i 0.263365π-0.263365\pi
−0.736165 + 0.676802i 0.763365π0.763365\pi
702702 0.828682 + 0.944931i 0.0312766 + 0.0356641i
703703 −6.68952 + 0.438454i −0.252300 + 0.0165366i
704704 −3.67263 + 4.18784i −0.138418 + 0.157835i
705705 4.79596 6.25022i 0.180626 0.235397i
706706 17.9263 7.42530i 0.674663 0.279455i
707707 31.1688 + 5.60096i 1.17222 + 0.210646i
708708 0.113880 + 0.170433i 0.00427987 + 0.00640528i
709709 20.2610 17.7684i 0.760917 0.667306i −0.188235 0.982124i 0.560277π-0.560277\pi
0.949152 + 0.314818i 0.101943π0.101943\pi
710710 17.2726 4.62819i 0.648231 0.173693i
711711 5.28364 + 10.7142i 0.198152 + 0.401812i
712712 22.6837 2.98637i 0.850109 0.111919i
713713 8.84629 0.331296
714714 −7.68981 + 12.9826i −0.287784 + 0.485861i
715715 0.650530 0.0243284
716716 1.01397 0.133491i 0.0378938 0.00498881i
717717 −11.1995 22.7104i −0.418254 0.848136i
718718 −12.7833 + 3.42529i −0.477070 + 0.127831i
719719 −7.38589 + 6.47725i −0.275447 + 0.241561i −0.785913 0.618337i 0.787806π-0.787806\pi
0.510465 + 0.859898i 0.329473π0.329473\pi
720720 2.26795 + 3.39422i 0.0845214 + 0.126495i
721721 −14.2572 12.0428i −0.530966 0.448498i
722722 −15.5786 + 6.45288i −0.579777 + 0.240151i
723723 −13.0204 + 16.9685i −0.484234 + 0.631065i
724724 0.100932 0.115091i 0.00375111 0.00427732i
725725 2.91055 0.190767i 0.108095 0.00708492i
726726 9.62303 + 10.9730i 0.357144 + 0.407245i
727727 −3.92134 3.92134i −0.145434 0.145434i 0.630641 0.776075i 0.282792π-0.282792\pi
−0.776075 + 0.630641i 0.782792π0.782792\pi
728728 −0.325315 + 6.93122i −0.0120570 + 0.256888i
729729 0.923880 + 0.382683i 0.0342178 + 0.0141735i
730730 11.8609 6.84788i 0.438990 0.253451i
731731 8.44398 + 15.6834i 0.312312 + 0.580071i
732732 0.293402 0.508187i 0.0108445 0.0187831i
733733 1.88581 + 14.3242i 0.0696541 + 0.529075i 0.990328 + 0.138744i 0.0443064π0.0443064\pi
−0.920674 + 0.390332i 0.872360π0.872360\pi
734734 0.953735 1.42736i 0.0352030 0.0526850i
735735 7.15058 2.20331i 0.263753 0.0812702i
736736 3.70589 0.737148i 0.136601 0.0271716i
737737 1.49024 + 0.734906i 0.0548938 + 0.0270706i
738738 −2.46101 2.15824i −0.0905909 0.0794461i
739739 −6.37062 + 48.3897i −0.234347 + 1.78004i 0.319662 + 0.947532i 0.396431π0.396431\pi
−0.554009 + 0.832511i 0.686903π0.686903\pi
740740 0.188924 + 0.144966i 0.00694498 + 0.00532907i
741741 −2.32549 0.462568i −0.0854289 0.0169929i
742742 1.35475 2.88066i 0.0497344 0.105752i
743743 −0.204346 1.02732i −0.00749675 0.0376887i 0.976856 0.213899i 0.0686162π-0.0686162\pi
−0.984353 + 0.176210i 0.943616π0.943616\pi
744744 −3.19973 0.857365i −0.117308 0.0314325i
745745 2.42969 1.19819i 0.0890170 0.0438984i
746746 23.1412 17.7569i 0.847261 0.650126i
747747 −1.33607 2.31414i −0.0488843 0.0846701i
748748 −0.217838 + 0.0994957i −0.00796494 + 0.00363792i
749749 −19.8827 + 35.9623i −0.726499 + 1.31403i
750750 −5.01160 + 12.0991i −0.182998 + 0.441796i
751751 1.32649 20.2383i 0.0484043 0.738507i −0.902822 0.430014i 0.858509π-0.858509\pi
0.951227 0.308493i 0.0998247π-0.0998247\pi
752752 −7.28518 27.1886i −0.265663 0.991468i
753753 −1.39186 + 4.10029i −0.0507222 + 0.149423i
754754 −0.420327 + 0.852338i −0.0153074 + 0.0310403i
755755 −0.205278 + 1.03200i −0.00747082 + 0.0375583i
756756 0.0917174 + 0.210305i 0.00333573 + 0.00764871i
757757 18.4908 + 44.6409i 0.672061 + 1.62250i 0.778102 + 0.628138i 0.216183π0.216183\pi
−0.106041 + 0.994362i 0.533817π0.533817\pi
758758 15.0990 5.12541i 0.548420 0.186163i
759759 0.337665 + 5.15177i 0.0122565 + 0.186997i
760760 −7.62369 2.58790i −0.276540 0.0938728i
761761 −1.23440 + 4.60684i −0.0447469 + 0.166998i −0.984684 0.174351i 0.944217π-0.944217\pi
0.939937 + 0.341349i 0.110884π0.110884\pi
762762 1.88882 + 1.26207i 0.0684246 + 0.0457199i
763763 15.7646 + 6.18988i 0.570716 + 0.224089i
764764 0.479504i 0.0173479i
765765 0.731054 + 4.34616i 0.0264313 + 0.157136i
766766 −3.28963 1.89927i −0.118859 0.0686233i
767767 −1.30747 1.70392i −0.0472099 0.0615252i
768768 −2.07282 0.135860i −0.0747964 0.00490241i
769769 32.4954 32.4954i 1.17181 1.17181i 0.190036 0.981777i 0.439140π-0.439140\pi
0.981777 0.190036i 0.0608603π-0.0608603\pi
770770 −2.49626 0.796044i −0.0899590 0.0286874i
771771 7.08444 4.73367i 0.255140 0.170479i
772772 0.684783 + 2.01731i 0.0246459 + 0.0726044i
773773 −45.6418 6.00886i −1.64162 0.216124i −0.747601 0.664148i 0.768794π-0.768794\pi
−0.894021 + 0.448025i 0.852128π0.852128\pi
774774 −5.92444 0.779968i −0.212950 0.0280354i
775775 −1.42303 4.19212i −0.0511168 0.150585i
776776 41.4293 27.6822i 1.48722 0.993731i
777777 −4.57562 5.02628i −0.164149 0.180317i
778778 24.6524 24.6524i 0.883832 0.883832i
779779 6.16200 + 0.403879i 0.220777 + 0.0144705i
780780 0.0512721 + 0.0668192i 0.00183584 + 0.00239251i
781781 −7.01551 4.05041i −0.251035 0.144935i
782782 −42.8417 9.85286i −1.53202 0.352337i
783783 0.756147i 0.0270225i
784784 9.30728 25.0608i 0.332403 0.895029i
785785 −11.7409 7.84505i −0.419052 0.280002i
786786 3.38671 12.6394i 0.120800 0.450832i
787787 19.2711 + 6.54167i 0.686942 + 0.233185i 0.643020 0.765850i 0.277681π-0.277681\pi
0.0439221 + 0.999035i 0.486015π0.486015\pi
788788 −0.142289 2.17090i −0.00506882 0.0773353i
789789 −6.89387 + 2.34015i −0.245428 + 0.0833117i
790790 −6.75921 16.3182i −0.240482 0.580574i
791791 −4.58814 + 6.21476i −0.163136 + 0.220971i
792792 0.377165 1.89614i 0.0134020 0.0673763i
793793 −2.71941 + 5.51442i −0.0965690 + 0.195823i
794794 −0.790190 + 2.32782i −0.0280428 + 0.0826114i
795795 −0.240646 0.898101i −0.00853482 0.0318524i
796796 −0.106781 + 1.62916i −0.00378474 + 0.0577440i
797797 9.48224 22.8922i 0.335878 0.810882i −0.662224 0.749306i 0.730387π-0.730387\pi
0.998102 0.0615760i 0.0196127π-0.0196127\pi
798798 8.35749 + 4.62067i 0.295852 + 0.163570i
799799 4.85955 29.9977i 0.171919 1.06124i
800800 −0.945460 1.63758i −0.0334271 0.0578974i
801801 −6.28868 + 4.82547i −0.222199 + 0.170500i
802802 −38.5656 + 19.0184i −1.36180 + 0.671565i
803803 −5.99299 1.60582i −0.211488 0.0566680i
804804 0.0419690 + 0.210992i 0.00148013 + 0.00744113i
805805 12.4449 + 17.8973i 0.438625 + 0.630798i
806806 1.41470 + 0.281402i 0.0498307 + 0.00991195i
807807 18.1230 + 13.9062i 0.637958 + 0.489523i
808808 4.50945 34.2526i 0.158642 1.20500i
809809 8.88900 + 7.79544i 0.312521 + 0.274073i 0.801208 0.598386i 0.204191π-0.204191\pi
−0.488688 + 0.872459i 0.662524π0.662524\pi
810810 −1.32605 0.653935i −0.0465926 0.0229769i
811811 −51.1197 + 10.1683i −1.79506 + 0.357059i −0.976189 0.216923i 0.930398π-0.930398\pi
−0.818868 + 0.573982i 0.805398π0.805398\pi
812812 −0.120377 + 0.124928i −0.00422440 + 0.00438410i
813813 9.91261 14.8353i 0.347650 0.520295i
814814 0.310671 + 2.35978i 0.0108890 + 0.0827103i
815815 12.2281 21.1797i 0.428331 0.741891i
816816 13.9094 + 7.38076i 0.486926 + 0.258378i
817817 9.76281 5.63656i 0.341558 0.197198i
818818 −41.7317 17.2858i −1.45911 0.604385i
819819 −1.10307 2.13599i −0.0385444 0.0746375i
820820 −0.155107 0.155107i −0.00541658 0.00541658i
821821 −4.34417 4.95358i −0.151613 0.172881i 0.671048 0.741414i 0.265845π-0.265845\pi
−0.822661 + 0.568533i 0.807511π0.807511\pi
822822 24.4671 1.60366i 0.853387 0.0559339i
823823 28.2428 32.2048i 0.984483 1.12259i −0.00797025 0.999968i 0.502537π-0.502537\pi
0.992454 0.122620i 0.0391296π-0.0391296\pi
824824 −12.3944 + 16.1527i −0.431781 + 0.562707i
825825 2.38703 0.988739i 0.0831056 0.0344235i
826826 2.93204 + 8.13836i 0.102019 + 0.283170i
827827 −14.9072 22.3102i −0.518373 0.775800i 0.476256 0.879307i 0.341994π-0.341994\pi
−0.994629 + 0.103507i 0.966994π0.966994\pi
828828 −0.502551 + 0.440725i −0.0174648 + 0.0153163i
829829 24.0856 6.45373i 0.836529 0.224147i 0.184969 0.982744i 0.440782π-0.440782\pi
0.651560 + 0.758597i 0.274115π0.274115\pi
830830 1.74741 + 3.54339i 0.0606534 + 0.122993i
831831 5.51476 0.726031i 0.191305 0.0251857i
832832 7.55626 0.261966
833833 20.2568 20.5587i 0.701857 0.712317i
834834 23.0198 0.797110
835835 −16.7671 + 2.20743i −0.580249 + 0.0763913i
836836 0.0670367 + 0.135937i 0.00231851 + 0.00470148i
837837 1.10856 0.297038i 0.0383175 0.0102671i
838838 4.30320 3.77380i 0.148651 0.130364i
839839 4.18723 + 6.26663i 0.144559 + 0.216348i 0.896682 0.442674i 0.145970π-0.145970\pi
−0.752123 + 0.659022i 0.770970π0.770970\pi
840840 −2.76678 7.67965i −0.0954631 0.264973i
841841 26.2643 10.8790i 0.905664 0.375139i
842842 −2.36567 + 3.08299i −0.0815262 + 0.106247i
843843 7.89422 9.00164i 0.271891 0.310033i
844844 −0.142246 + 0.00932330i −0.00489631 + 0.000320921i
845845 8.58026 + 9.78391i 0.295170 + 0.336577i
846846 7.20881 + 7.20881i 0.247844 + 0.247844i
847847 −12.8093 24.8041i −0.440134 0.852277i
848848 −3.06911 1.27127i −0.105394 0.0436554i
849849 −11.8926 + 6.86617i −0.408151 + 0.235646i
850850 2.22249 + 21.8870i 0.0762308 + 0.750717i
851851 9.90115 17.1493i 0.339407 0.587870i
852852 −0.136897 1.03983i −0.00469001 0.0356241i
853853 −13.6442 + 20.4199i −0.467167 + 0.699165i −0.987993 0.154498i 0.950624π-0.950624\pi
0.520826 + 0.853663i 0.325624π0.325624\pi
854854 17.1830 17.8326i 0.587991 0.610220i
855855 2.73570 0.544164i 0.0935589 0.0186100i
856856 40.2068 + 19.8278i 1.37424 + 0.677701i
857857 −2.69901 2.36697i −0.0921965 0.0808542i 0.612007 0.790852i 0.290362π-0.290362\pi
−0.704204 + 0.709998i 0.748696π0.748696\pi
858858 −0.109879 + 0.834614i −0.00375121 + 0.0284933i
859859 13.5558 + 10.4017i 0.462517 + 0.354902i 0.813583 0.581449i 0.197514π-0.197514\pi
−0.351066 + 0.936351i 0.614181π0.614181\pi
860860 −0.392747 0.0781222i −0.0133926 0.00266394i
861861 3.57441 + 5.14045i 0.121816 + 0.175186i
862862 6.47612 + 32.5577i 0.220578 + 1.10892i
863863 15.0528 + 4.03338i 0.512402 + 0.137298i 0.505750 0.862680i 0.331216π-0.331216\pi
0.00665221 + 0.999978i 0.497883π0.497883\pi
864864 0.439648 0.216810i 0.0149571 0.00737603i
865865 −13.5377 + 10.3879i −0.460297 + 0.353198i
866866 6.79922 + 11.7766i 0.231047 + 0.400185i
867867 10.4303 + 13.4242i 0.354231 + 0.455910i
868868 0.230440 + 0.127405i 0.00782164 + 0.00432441i
869869 −3.06203 + 7.39239i −0.103872 + 0.250770i
870870 0.0731196 1.11559i 0.00247899 0.0378220i
871871 −0.583398 2.17727i −0.0197677 0.0737740i
872872 5.93910 17.4960i 0.201123 0.592490i
873873 −7.63508 + 15.4824i −0.258408 + 0.524000i
874874 −5.42781 + 27.2875i −0.183599 + 0.923012i
875875 14.8779 20.1524i 0.502963 0.681276i
876876 −0.307402 0.742133i −0.0103861 0.0250744i
877877 −33.4488 + 11.3544i −1.12949 + 0.383409i −0.822760 0.568388i 0.807567π-0.807567\pi
−0.306727 + 0.951798i 0.599234π0.599234\pi
878878 2.35067 + 35.8643i 0.0793312 + 1.21036i
879879 −6.85648 2.32746i −0.231263 0.0785033i
880880 −0.707674 + 2.64107i −0.0238557 + 0.0890306i
881881 36.7006 + 24.5226i 1.23648 + 0.826187i 0.989738 0.142895i 0.0456413π-0.0456413\pi
0.246738 + 0.969082i 0.420641π0.420641\pi
882882 1.61901 + 9.54618i 0.0545148 + 0.321437i
883883 2.09914i 0.0706416i −0.999376 0.0353208i 0.988755π-0.988755\pi
0.999376 0.0353208i 0.0112453π-0.0112453\pi
884884 0.296323 + 0.133184i 0.00996642 + 0.00447947i
885885 2.18811 + 1.26330i 0.0735524 + 0.0424655i
886886 1.03496 + 1.34878i 0.0347701 + 0.0453132i
887887 17.7395 + 1.16271i 0.595633 + 0.0390398i 0.360239 0.932860i 0.382695π-0.382695\pi
0.235394 + 0.971900i 0.424362π0.424362\pi
888888 −5.24335 + 5.24335i −0.175955 + 0.175955i
889889 −2.92505 3.21314i −0.0981029 0.107765i
890890 9.74469 6.51119i 0.326643 0.218256i
891891 0.215299 + 0.634250i 0.00721278 + 0.0212482i
892892 −1.70275 0.224171i −0.0570122 0.00750579i
893893 −19.0683 2.51039i −0.638097 0.0840071i
894894 1.12686 + 3.31962i 0.0376878 + 0.111025i
895895 10.4817 7.00365i 0.350365 0.234106i
896896 −26.5242 8.45841i −0.886110 0.282576i
897897 4.95239 4.95239i 0.165356 0.165356i
898898 −30.1457 1.97586i −1.00598 0.0659352i
899899 0.528287 + 0.688477i 0.0176194 + 0.0229620i
900900 0.289694 + 0.167255i 0.00965647 + 0.00557516i
901901 −2.45958 2.61021i −0.0819405 0.0869587i
902902 2.19245i 0.0730007i
903903 10.6391 + 4.17737i 0.354046 + 0.139014i
904904 7.00720 + 4.68206i 0.233056 + 0.155723i
905905 0.488362 1.82259i 0.0162337 0.0605850i
906906 −1.28936 0.437678i −0.0428361 0.0145409i
907907 −1.83693 28.0262i −0.0609943 0.930594i −0.913232 0.407439i 0.866422π-0.866422\pi
0.852238 0.523154i 0.175245π-0.175245\pi
908908 0.191224 0.0649118i 0.00634599 0.00215417i
909909 4.58049 + 11.0583i 0.151925 + 0.366780i
910910 1.42088 + 3.25802i 0.0471016 + 0.108002i
911911 −3.12922 + 15.7317i −0.103676 + 0.521213i 0.893690 + 0.448684i 0.148107π0.148107\pi
−0.997366 + 0.0725294i 0.976893π0.976893\pi
912912 4.40773 8.93800i 0.145955 0.295967i
913913 0.575309 1.69481i 0.0190400 0.0560899i
914914 6.72706 + 25.1057i 0.222511 + 0.830423i
915915 0.473066 7.21759i 0.0156391 0.238606i
916916 −0.937859 + 2.26419i −0.0309877 + 0.0748110i
917917 −12.1102 + 21.9040i −0.399915 + 0.723335i
918918 −5.69950 + 0.203829i −0.188111 + 0.00672735i
919919 −25.8715 44.8108i −0.853423 1.47817i −0.878101 0.478476i 0.841189π-0.841189\pi
0.0246783 0.999695i 0.492144π-0.492144\pi
920920 18.8671 14.4772i 0.622029 0.477299i
921921 −23.0656 + 11.3747i −0.760038 + 0.374809i
922922 37.7581 + 10.1173i 1.24350 + 0.333194i
923923 2.14391 + 10.7782i 0.0705677 + 0.354768i
924924 −0.0654003 + 0.139063i −0.00215151 + 0.00457485i
925925 −9.71950 1.93333i −0.319575 0.0635675i
926926 37.3252 + 28.6406i 1.22658 + 0.941189i
927927 0.920712 6.99350i 0.0302402 0.229697i
928928 0.278680 + 0.244396i 0.00914811 + 0.00802268i
929929 21.0535 + 10.3824i 0.690743 + 0.340637i 0.753552 0.657389i 0.228339π-0.228339\pi
−0.0628086 + 0.998026i 0.520006π0.520006\pi
930930 −1.66425 + 0.331040i −0.0545730 + 0.0108552i
931931 −13.3865 12.4283i −0.438724 0.407322i
932932 −0.451072 + 0.675077i −0.0147754 + 0.0221129i
933933 0.465562 + 3.53629i 0.0152418 + 0.115773i
934934 −1.32746 + 2.29923i −0.0434359 + 0.0752331i
935935 −1.86578 + 2.28752i −0.0610176 + 0.0748101i
936936 −2.27127 + 1.31132i −0.0742388 + 0.0428618i
937937 −29.3412 12.1535i −0.958534 0.397038i −0.152102 0.988365i 0.548604π-0.548604\pi
−0.806432 + 0.591327i 0.798604π0.798604\pi
938938 −0.425636 + 9.06868i −0.0138975 + 0.296103i
939939 16.3989 + 16.3989i 0.535158 + 0.535158i
940940 0.450455 + 0.513646i 0.0146922 + 0.0167533i
941941 56.7275 3.71811i 1.84926 0.121207i 0.900039 0.435809i 0.143538π-0.143538\pi
0.949224 + 0.314602i 0.101871π0.101871\pi
942942 12.0481 13.7383i 0.392550 0.447617i
943943 −11.1043 + 14.4714i −0.361605 + 0.471252i
944944 8.34005 3.45456i 0.271445 0.112436i
945945 2.16047 + 1.82491i 0.0702800 + 0.0593643i
946946 −2.22362 3.32788i −0.0722961 0.108199i
947947 −1.30702 + 1.14622i −0.0424723 + 0.0372472i −0.680319 0.732916i 0.738159π-0.738159\pi
0.637847 + 0.770163i 0.279825π0.279825\pi
948948 −1.00065 + 0.268122i −0.0324995 + 0.00870821i
949949 3.72261 + 7.54871i 0.120841 + 0.245042i
950950 13.8042 1.81736i 0.447868 0.0589630i
951951 30.1087 0.976342
952952 −23.4399 21.0233i −0.759692 0.681370i
953953 −0.879744 −0.0284977 −0.0142489 0.999898i 0.504536π-0.504536\pi
−0.0142489 + 0.999898i 0.504536π0.504536\pi
954954 1.19289 0.157047i 0.0386212 0.00508458i
955955 −2.61414 5.30094i −0.0845914 0.171534i
956956 2.12103 0.568329i 0.0685992 0.0183811i
957957 −0.380780 + 0.333935i −0.0123089 + 0.0107946i
958958 16.4935 + 24.6843i 0.532881 + 0.797512i
959959 −46.1606 8.29495i −1.49060 0.267858i
960960 −8.21252 + 3.40174i −0.265058 + 0.109791i
961961 −18.0698 + 23.5490i −0.582896 + 0.759645i
962962 2.12892 2.42756i 0.0686390 0.0782678i
963963 −15.4983 + 1.01581i −0.499427 + 0.0327342i
964964 −1.22293 1.39448i −0.0393878 0.0449131i
965965 18.5681 + 18.5681i 0.597730 + 0.597730i
966966 −25.0639 + 12.9435i −0.806416 + 0.416451i
967967 −42.5643 17.6307i −1.36878 0.566966i −0.427320 0.904101i 0.640542π-0.640542\pi
−0.941456 + 0.337135i 0.890542π0.890542\pi
968968 −26.3750 + 15.2276i −0.847725 + 0.489434i
969969 8.29629 6.85066i 0.266515 0.220075i
970970 12.7616 22.1038i 0.409752 0.709711i
971971 −3.60845 27.4089i −0.115801 0.879594i −0.946462 0.322816i 0.895371π-0.895371\pi
0.830661 0.556778i 0.187963π-0.187963\pi
972972 −0.0481780 + 0.0721035i −0.00154531 + 0.00231272i
973973 −42.7350 10.6053i −1.37002 0.339990i
974974 −18.1086 + 3.60203i −0.580238 + 0.115416i
975975 −3.14351 1.55021i −0.100673 0.0496464i
976976 −19.4296 17.0393i −0.621926 0.545414i
977977 −3.38410 + 25.7048i −0.108267 + 0.822370i 0.848025 + 0.529956i 0.177792π0.177792\pi
−0.956292 + 0.292414i 0.905542π0.905542\pi
978978 25.1076 + 19.2657i 0.802853 + 0.616050i
979979 −5.20726 1.03579i −0.166425 0.0331039i
980980 0.0664227 + 0.645446i 0.00212179 + 0.0206180i
981981 1.24883 + 6.27830i 0.0398721 + 0.200451i
982982 −21.5874 5.78432i −0.688881 0.184585i
983983 −15.4218 + 7.60518i −0.491879 + 0.242568i −0.671274 0.741209i 0.734253π-0.734253\pi
0.179395 + 0.983777i 0.442586π0.442586\pi
984984 5.41898 4.15813i 0.172751 0.132556i
985985 −13.4082 23.2237i −0.427222 0.739970i
986986 −1.79163 3.92262i −0.0570570 0.124922i
987987 −10.0616 16.7039i −0.320266 0.531690i
988988 0.0786845 0.189961i 0.00250329 0.00604347i
989989 −2.17787 + 33.2279i −0.0692524 + 1.05659i
990990 −0.256311 0.956567i −0.00814611 0.0304017i
991991 14.8402 43.7178i 0.471414 1.38874i −0.408130 0.912924i 0.633819π-0.633819\pi
0.879544 0.475817i 0.157848π-0.157848\pi
992992 0.248826 0.504569i 0.00790024 0.0160201i
993993 −3.23534 + 16.2652i −0.102670 + 0.516159i
994994 4.96231 43.9823i 0.157395 1.39503i
995995 7.70129 + 18.5926i 0.244147 + 0.589424i
996996 0.219426 0.0744850i 0.00695277 0.00236015i
997997 2.38289 + 36.3559i 0.0754669 + 1.15140i 0.852774 + 0.522280i 0.174919π0.174919\pi
−0.777307 + 0.629121i 0.783415π0.783415\pi
998998 −13.4625 4.56989i −0.426147 0.144657i
999999 0.664917 2.48150i 0.0210370 0.0785113i
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 357.2.bl.a.10.7 384
7.5 odd 6 inner 357.2.bl.a.61.18 yes 384
17.12 odd 16 inner 357.2.bl.a.199.18 yes 384
119.12 even 48 inner 357.2.bl.a.250.7 yes 384
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
357.2.bl.a.10.7 384 1.1 even 1 trivial
357.2.bl.a.61.18 yes 384 7.5 odd 6 inner
357.2.bl.a.199.18 yes 384 17.12 odd 16 inner
357.2.bl.a.250.7 yes 384 119.12 even 48 inner