Properties

Label 627.2.be.a.10.18
Level 627627
Weight 22
Character 627.10
Analytic conductor 5.0075.007
Analytic rank 00
Dimension 240240
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] = [627,2,Mod(10,627)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(627, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 17])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("627.10"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 627=31119 627 = 3 \cdot 11 \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 627.be (of order 1818, degree 66, 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: 5.006620206735.00662020673
Analytic rank: 00
Dimension: 240240
Relative dimension: 4040 over Q(ζ18)\Q(\zeta_{18})
Twist minimal: yes
Sato-Tate group: SU(2)[C18]\mathrm{SU}(2)[C_{18}]

Embedding invariants

Embedding label 10.18
Character χ\chi == 627.10
Dual form 627.2.be.a.439.18

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+(0.03770670.213846i)q2+(0.6427880.766044i)q3+(1.835080.667913i)q4+(2.084880.758835i)q5+(0.139578+0.166342i)q6+(3.25299+1.87811i)q7+(0.4291690.743343i)q8+(0.173648+0.984808i)q9+(0.0836593+0.474456i)q10+(0.641700+3.25395i)q11+(1.691220.976424i)q12+(2.75799+2.31423i)q13+(0.2789670.766455i)q14+(0.758835+2.08488i)q15+(2.849162.39073i)q16+(3.820490.673656i)q17+0.217144q18+(3.240432.91541i)q194.33275q20+(0.6522623.69916i)q21+(0.6716470.259921i)q22+(1.93230+0.703298i)q23+(0.293569+0.806575i)q24+(0.05932180.0497769i)q25+(0.3908920.677045i)q26+(0.8660250.500000i)q27+(7.22391+1.27377i)q28+(0.2286941.29699i)q29+(0.4172290.240887i)q30+(6.196623.57762i)q31+(1.933731.62259i)q32+(2.080202.58317i)q33+(0.2881170.791594i)q34+(5.356926.38413i)q35+(0.339109+1.92318i)q360.219776iq37+(0.7456330.583021i)q383.60030iq39+(0.330693+1.87545i)q40+(1.990861.67053i)q41+(0.766455+0.278967i)q42+(0.7229311.98624i)q43+(3.35093+5.54266i)q44+(1.109341.92144i)q45+(0.223258+0.386694i)q46+(0.2036561.15499i)q47+(3.662810.645852i)q48+(3.55463+6.15680i)q49+(0.00840774+0.0145626i)q50+(2.971812.49365i)q51+(6.60682+2.40469i)q52+(0.774672+2.12839i)q53+(0.1395780.166342i)q54+(1.131347.27105i)q553.22412iq56+(4.316240.608324i)q570.285978q58+(8.756981.54409i)q59+(2.78504+3.31908i)q60+(5.03183+13.8248i)q61+(0.531404+1.46002i)q62+(2.41446+2.87744i)q63+(3.445245.96734i)q64+(3.993966.91774i)q65+(0.6308370.347438i)q66+(10.94861.93053i)q67+(6.560953.78797i)q68+(1.78081+1.02815i)q69+(1.16323+1.38628i)q70+(2.271766.24160i)q71+(0.8065750.293569i)q72+(3.424544.08121i)q73+(0.0469982+0.00828705i)q74+0.0774392iq75+(3.999207.51433i)q76+(4.02385+11.7903i)q77+(0.769907+0.135755i)q78+(12.1389+10.1858i)q79+(7.75433+2.82234i)q80+(0.9396930.342020i)q81+(0.4323030.362746i)q82+(15.0510+8.68972i)q83+(3.667676.35260i)q84+(8.476461.49463i)q85+(0.4520070.0797011i)q86+(1.14055+0.658497i)q87+(2.143411.87350i)q88+(7.29087+8.68892i)q89+(0.4527200.164777i)q90+(4.62532+12.7080i)q91+(3.07617+2.58121i)q92+(1.24249+7.04654i)q930.254668q94+(8.96823+3.61933i)q95+2.52431iq96+(5.457060.962226i)q97+(1.182570.992294i)q98+(3.31595+0.0669082i)q99+O(q100)q+(-0.0377067 - 0.213846i) q^{2} +(-0.642788 - 0.766044i) q^{3} +(1.83508 - 0.667913i) q^{4} +(-2.08488 - 0.758835i) q^{5} +(-0.139578 + 0.166342i) q^{6} +(3.25299 + 1.87811i) q^{7} +(-0.429169 - 0.743343i) q^{8} +(-0.173648 + 0.984808i) q^{9} +(-0.0836593 + 0.474456i) q^{10} +(0.641700 + 3.25395i) q^{11} +(-1.69122 - 0.976424i) q^{12} +(2.75799 + 2.31423i) q^{13} +(0.278967 - 0.766455i) q^{14} +(0.758835 + 2.08488i) q^{15} +(2.84916 - 2.39073i) q^{16} +(3.82049 - 0.673656i) q^{17} +0.217144 q^{18} +(3.24043 - 2.91541i) q^{19} -4.33275 q^{20} +(-0.652262 - 3.69916i) q^{21} +(0.671647 - 0.259921i) q^{22} +(-1.93230 + 0.703298i) q^{23} +(-0.293569 + 0.806575i) q^{24} +(-0.0593218 - 0.0497769i) q^{25} +(0.390892 - 0.677045i) q^{26} +(0.866025 - 0.500000i) q^{27} +(7.22391 + 1.27377i) q^{28} +(0.228694 - 1.29699i) q^{29} +(0.417229 - 0.240887i) q^{30} +(-6.19662 - 3.57762i) q^{31} +(-1.93373 - 1.62259i) q^{32} +(2.08020 - 2.58317i) q^{33} +(-0.288117 - 0.791594i) q^{34} +(-5.35692 - 6.38413i) q^{35} +(0.339109 + 1.92318i) q^{36} -0.219776i q^{37} +(-0.745633 - 0.583021i) q^{38} -3.60030i q^{39} +(0.330693 + 1.87545i) q^{40} +(1.99086 - 1.67053i) q^{41} +(-0.766455 + 0.278967i) q^{42} +(0.722931 - 1.98624i) q^{43} +(3.35093 + 5.54266i) q^{44} +(1.10934 - 1.92144i) q^{45} +(0.223258 + 0.386694i) q^{46} +(0.203656 - 1.15499i) q^{47} +(-3.66281 - 0.645852i) q^{48} +(3.55463 + 6.15680i) q^{49} +(-0.00840774 + 0.0145626i) q^{50} +(-2.97181 - 2.49365i) q^{51} +(6.60682 + 2.40469i) q^{52} +(0.774672 + 2.12839i) q^{53} +(-0.139578 - 0.166342i) q^{54} +(1.13134 - 7.27105i) q^{55} -3.22412i q^{56} +(-4.31624 - 0.608324i) q^{57} -0.285978 q^{58} +(8.75698 - 1.54409i) q^{59} +(2.78504 + 3.31908i) q^{60} +(5.03183 + 13.8248i) q^{61} +(-0.531404 + 1.46002i) q^{62} +(-2.41446 + 2.87744i) q^{63} +(3.44524 - 5.96734i) q^{64} +(-3.99396 - 6.91774i) q^{65} +(-0.630837 - 0.347438i) q^{66} +(-10.9486 - 1.93053i) q^{67} +(6.56095 - 3.78797i) q^{68} +(1.78081 + 1.02815i) q^{69} +(-1.16323 + 1.38628i) q^{70} +(2.27176 - 6.24160i) q^{71} +(0.806575 - 0.293569i) q^{72} +(-3.42454 - 4.08121i) q^{73} +(-0.0469982 + 0.00828705i) q^{74} +0.0774392i q^{75} +(3.99920 - 7.51433i) q^{76} +(-4.02385 + 11.7903i) q^{77} +(-0.769907 + 0.135755i) q^{78} +(-12.1389 + 10.1858i) q^{79} +(-7.75433 + 2.82234i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(-0.432303 - 0.362746i) q^{82} +(15.0510 + 8.68972i) q^{83} +(-3.66767 - 6.35260i) q^{84} +(-8.47646 - 1.49463i) q^{85} +(-0.452007 - 0.0797011i) q^{86} +(-1.14055 + 0.658497i) q^{87} +(2.14341 - 1.87350i) q^{88} +(-7.29087 + 8.68892i) q^{89} +(-0.452720 - 0.164777i) q^{90} +(4.62532 + 12.7080i) q^{91} +(-3.07617 + 2.58121i) q^{92} +(1.24249 + 7.04654i) q^{93} -0.254668 q^{94} +(-8.96823 + 3.61933i) q^{95} +2.52431i q^{96} +(5.45706 - 0.962226i) q^{97} +(1.18257 - 0.992294i) q^{98} +(-3.31595 + 0.0669082i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 240q+6q1148q14+24q15216q20+24q2636q316q33132q34+180q38+12q4224q4412q45+72q47+48q48+132q49+108q5330q55+12q99+O(q100) 240 q + 6 q^{11} - 48 q^{14} + 24 q^{15} - 216 q^{20} + 24 q^{26} - 36 q^{31} - 6 q^{33} - 132 q^{34} + 180 q^{38} + 12 q^{42} - 24 q^{44} - 12 q^{45} + 72 q^{47} + 48 q^{48} + 132 q^{49} + 108 q^{53} - 30 q^{55}+ \cdots - 12 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/627Z)×\left(\mathbb{Z}/627\mathbb{Z}\right)^\times.

nn 343343 419419 496496
χ(n)\chi(n) 1-1 11 e(1718)e\left(\frac{17}{18}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.0377067 0.213846i −0.0266627 0.151212i 0.968570 0.248741i 0.0800170π-0.0800170\pi
−0.995233 + 0.0975299i 0.968906π0.968906\pi
33 −0.642788 0.766044i −0.371114 0.442276i
44 1.83508 0.667913i 0.917539 0.333957i
55 −2.08488 0.758835i −0.932387 0.339361i −0.169232 0.985576i 0.554129π-0.554129\pi
−0.763155 + 0.646215i 0.776351π0.776351\pi
66 −0.139578 + 0.166342i −0.0569824 + 0.0679090i
77 3.25299 + 1.87811i 1.22951 + 0.709861i 0.966928 0.255048i 0.0820913π-0.0820913\pi
0.262586 + 0.964909i 0.415425π0.415425\pi
88 −0.429169 0.743343i −0.151734 0.262812i
99 −0.173648 + 0.984808i −0.0578827 + 0.328269i
1010 −0.0836593 + 0.474456i −0.0264554 + 0.150036i
1111 0.641700 + 3.25395i 0.193480 + 0.981104i
1212 −1.69122 0.976424i −0.488212 0.281869i
1313 2.75799 + 2.31423i 0.764928 + 0.641851i 0.939405 0.342810i 0.111379π-0.111379\pi
−0.174477 + 0.984661i 0.555823π0.555823\pi
1414 0.278967 0.766455i 0.0745570 0.204844i
1515 0.758835 + 2.08488i 0.195930 + 0.538314i
1616 2.84916 2.39073i 0.712290 0.597682i
1717 3.82049 0.673656i 0.926605 0.163386i 0.310071 0.950713i 0.399647π-0.399647\pi
0.616534 + 0.787328i 0.288536π0.288536\pi
1818 0.217144 0.0511814
1919 3.24043 2.91541i 0.743406 0.668841i
2020 −4.33275 −0.968833
2121 −0.652262 3.69916i −0.142335 0.807224i
2222 0.671647 0.259921i 0.143196 0.0554153i
2323 −1.93230 + 0.703298i −0.402912 + 0.146648i −0.535524 0.844520i 0.679886π-0.679886\pi
0.132612 + 0.991168i 0.457664π0.457664\pi
2424 −0.293569 + 0.806575i −0.0599246 + 0.164641i
2525 −0.0593218 0.0497769i −0.0118644 0.00995539i
2626 0.390892 0.677045i 0.0766603 0.132779i
2727 0.866025 0.500000i 0.166667 0.0962250i
2828 7.22391 + 1.27377i 1.36519 + 0.240720i
2929 0.228694 1.29699i 0.0424673 0.240844i −0.956184 0.292767i 0.905424π-0.905424\pi
0.998651 + 0.0519229i 0.0165350π0.0165350\pi
3030 0.417229 0.240887i 0.0761753 0.0439798i
3131 −6.19662 3.57762i −1.11295 0.642560i −0.173355 0.984859i 0.555461π-0.555461\pi
−0.939591 + 0.342300i 0.888794π0.888794\pi
3232 −1.93373 1.62259i −0.341839 0.286837i
3333 2.08020 2.58317i 0.362116 0.449673i
3434 −0.288117 0.791594i −0.0494116 0.135757i
3535 −5.35692 6.38413i −0.905485 1.07911i
3636 0.339109 + 1.92318i 0.0565181 + 0.320530i
3737 0.219776i 0.0361310i −0.999837 0.0180655i 0.994249π-0.994249\pi
0.999837 0.0180655i 0.00575074π-0.00575074\pi
3838 −0.745633 0.583021i −0.120958 0.0945785i
3939 3.60030i 0.576509i
4040 0.330693 + 1.87545i 0.0522871 + 0.296535i
4141 1.99086 1.67053i 0.310919 0.260892i −0.473952 0.880550i 0.657173π-0.657173\pi
0.784872 + 0.619658i 0.212729π0.212729\pi
4242 −0.766455 + 0.278967i −0.118267 + 0.0430455i
4343 0.722931 1.98624i 0.110246 0.302898i −0.872285 0.488998i 0.837363π-0.837363\pi
0.982531 + 0.186100i 0.0595847π0.0595847\pi
4444 3.35093 + 5.54266i 0.505172 + 0.835587i
4545 1.10934 1.92144i 0.165371 0.286431i
4646 0.223258 + 0.386694i 0.0329176 + 0.0570149i
4747 0.203656 1.15499i 0.0297062 0.168472i −0.966345 0.257248i 0.917184π-0.917184\pi
0.996052 + 0.0887756i 0.0282954π0.0282954\pi
4848 −3.66281 0.645852i −0.528681 0.0932207i
4949 3.55463 + 6.15680i 0.507804 + 0.879542i
5050 −0.00840774 + 0.0145626i −0.00118903 + 0.00205947i
5151 −2.97181 2.49365i −0.416137 0.349181i
5252 6.60682 + 2.40469i 0.916201 + 0.333470i
5353 0.774672 + 2.12839i 0.106409 + 0.292357i 0.981458 0.191678i 0.0613929π-0.0613929\pi
−0.875048 + 0.484035i 0.839171π0.839171\pi
5454 −0.139578 0.166342i −0.0189941 0.0226363i
5555 1.13134 7.27105i 0.152550 0.980429i
5656 3.22412i 0.430841i
5757 −4.31624 0.608324i −0.571700 0.0805745i
5858 −0.285978 −0.0375507
5959 8.75698 1.54409i 1.14006 0.201024i 0.428429 0.903575i 0.359067π-0.359067\pi
0.711633 + 0.702552i 0.247956π0.247956\pi
6060 2.78504 + 3.31908i 0.359547 + 0.428492i
6161 5.03183 + 13.8248i 0.644260 + 1.77009i 0.637912 + 0.770109i 0.279798π0.279798\pi
0.00634771 + 0.999980i 0.497979π0.497979\pi
6262 −0.531404 + 1.46002i −0.0674884 + 0.185423i
6363 −2.41446 + 2.87744i −0.304193 + 0.362523i
6464 3.44524 5.96734i 0.430655 0.745917i
6565 −3.99396 6.91774i −0.495390 0.858041i
6666 −0.630837 0.347438i −0.0776507 0.0427666i
6767 −10.9486 1.93053i −1.33758 0.235852i −0.541327 0.840812i 0.682078π-0.682078\pi
−0.796256 + 0.604960i 0.793189π0.793189\pi
6868 6.56095 3.78797i 0.795632 0.459359i
6969 1.78081 + 1.02815i 0.214385 + 0.123775i
7070 −1.16323 + 1.38628i −0.139032 + 0.165692i
7171 2.27176 6.24160i 0.269608 0.740742i −0.728821 0.684705i 0.759931π-0.759931\pi
0.998429 0.0560372i 0.0178465π-0.0178465\pi
7272 0.806575 0.293569i 0.0950558 0.0345975i
7373 −3.42454 4.08121i −0.400812 0.477669i 0.527455 0.849583i 0.323146π-0.323146\pi
−0.928267 + 0.371914i 0.878702π0.878702\pi
7474 −0.0469982 + 0.00828705i −0.00546343 + 0.000963350i
7575 0.0774392i 0.00894190i
7676 3.99920 7.51433i 0.458739 0.861953i
7777 −4.02385 + 11.7903i −0.458561 + 1.34363i
7878 −0.769907 + 0.135755i −0.0871748 + 0.0153713i
7979 −12.1389 + 10.1858i −1.36574 + 1.14599i −0.391572 + 0.920148i 0.628068π0.628068\pi
−0.974164 + 0.225841i 0.927487π0.927487\pi
8080 −7.75433 + 2.82234i −0.866960 + 0.315548i
8181 −0.939693 0.342020i −0.104410 0.0380022i
8282 −0.432303 0.362746i −0.0477399 0.0400585i
8383 15.0510 + 8.68972i 1.65207 + 0.953820i 0.976221 + 0.216776i 0.0695540π0.0695540\pi
0.675844 + 0.737045i 0.263779π0.263779\pi
8484 −3.66767 6.35260i −0.400176 0.693125i
8585 −8.47646 1.49463i −0.919402 0.162115i
8686 −0.452007 0.0797011i −0.0487412 0.00859439i
8787 −1.14055 + 0.658497i −0.122280 + 0.0705983i
8888 2.14341 1.87350i 0.228488 0.199716i
8989 −7.29087 + 8.68892i −0.772831 + 0.921024i −0.998586 0.0531601i 0.983071π-0.983071\pi
0.225755 + 0.974184i 0.427515π0.427515\pi
9090 −0.452720 0.164777i −0.0477209 0.0173690i
9191 4.62532 + 12.7080i 0.484866 + 1.33216i
9292 −3.07617 + 2.58121i −0.320713 + 0.269110i
9393 1.24249 + 7.04654i 0.128841 + 0.730692i
9494 −0.254668 −0.0262670
9595 −8.96823 + 3.61933i −0.920121 + 0.371336i
9696 2.52431i 0.257636i
9797 5.45706 0.962226i 0.554080 0.0976993i 0.110405 0.993887i 0.464785π-0.464785\pi
0.443676 + 0.896187i 0.353674π0.353674\pi
9898 1.18257 0.992294i 0.119458 0.100237i
9999 −3.31595 + 0.0669082i −0.333265 + 0.00672453i
100100 −0.142107 0.0517227i −0.0142107 0.00517227i
101101 3.68920 4.39662i 0.367089 0.437480i −0.550606 0.834765i 0.685603π-0.685603\pi
0.917695 + 0.397285i 0.130048π0.130048\pi
102102 −0.421198 + 0.729537i −0.0417048 + 0.0722349i
103103 7.95007 4.58998i 0.783344 0.452264i −0.0542701 0.998526i 0.517283π-0.517283\pi
0.837614 + 0.546262i 0.183950π0.183950\pi
104104 0.536621 3.04333i 0.0526200 0.298423i
105105 −1.44716 + 8.20728i −0.141229 + 0.800948i
106106 0.425937 0.245915i 0.0413707 0.0238854i
107107 −1.05075 + 1.81995i −0.101580 + 0.175941i −0.912336 0.409443i 0.865723π-0.865723\pi
0.810756 + 0.585384i 0.199056π0.199056\pi
108108 1.25527 1.49597i 0.120788 0.143950i
109109 −7.64338 2.78196i −0.732103 0.266464i −0.0510481 0.998696i 0.516256π-0.516256\pi
−0.681055 + 0.732233i 0.738478π0.738478\pi
110110 −1.59754 + 0.0322347i −0.152320 + 0.00307346i
111111 −0.168358 + 0.141270i −0.0159799 + 0.0134087i
112112 13.7583 2.42597i 1.30004 0.229232i
113113 18.6552i 1.75494i −0.479634 0.877469i 0.659230π-0.659230\pi
0.479634 0.877469i 0.340770π-0.340770\pi
114114 0.0326640 + 0.945947i 0.00305926 + 0.0885960i
115115 4.56229 0.425436
116116 −0.446604 2.53282i −0.0414661 0.235166i
117117 −2.75799 + 2.31423i −0.254976 + 0.213950i
118118 −0.660394 1.81442i −0.0607942 0.167031i
119119 13.6932 + 4.98393i 1.25526 + 0.456876i
120120 1.22411 1.45884i 0.111746 0.133173i
121121 −10.1764 + 4.17613i −0.925131 + 0.379648i
122122 2.76665 1.59732i 0.250480 0.144615i
123123 −2.55939 0.451290i −0.230773 0.0406915i
124124 −13.7608 2.42640i −1.23576 0.217897i
125125 5.63262 + 9.75598i 0.503797 + 0.872601i
126126 0.706369 + 0.407822i 0.0629283 + 0.0363317i
127127 8.81473 + 7.39644i 0.782181 + 0.656328i 0.943797 0.330526i 0.107226π-0.107226\pi
−0.161616 + 0.986854i 0.551671π0.551671\pi
128128 −6.15014 2.23847i −0.543601 0.197855i
129129 −1.98624 + 0.722931i −0.174878 + 0.0636506i
130130 −1.32873 + 1.11494i −0.116537 + 0.0977864i
131131 −16.8043 + 2.96306i −1.46820 + 0.258883i −0.849852 0.527021i 0.823309π-0.823309\pi
−0.618348 + 0.785904i 0.712198π0.712198\pi
132132 2.09199 6.12971i 0.182084 0.533523i
133133 16.0166 3.39790i 1.38881 0.294635i
134134 2.41410i 0.208547i
135135 −2.18498 + 0.385271i −0.188053 + 0.0331588i
136136 −2.14040 2.55082i −0.183537 0.218731i
137137 −14.8447 + 5.40304i −1.26827 + 0.461613i −0.886536 0.462659i 0.846895π-0.846895\pi
−0.381734 + 0.924272i 0.624673π0.624673\pi
138138 0.152717 0.419587i 0.0130002 0.0357176i
139139 −4.24929 + 5.06411i −0.360420 + 0.429532i −0.915533 0.402243i 0.868231π-0.868231\pi
0.555113 + 0.831775i 0.312675π0.312675\pi
140140 −14.0944 8.13741i −1.19119 0.687737i
141141 −1.01568 + 0.586403i −0.0855356 + 0.0493840i
142142 −1.42040 0.250455i −0.119197 0.0210177i
143143 −5.76059 + 10.4594i −0.481724 + 0.874659i
144144 1.85966 + 3.22102i 0.154971 + 0.268418i
145145 −1.46100 + 2.53052i −0.121329 + 0.210148i
146146 −0.743620 + 0.886212i −0.0615424 + 0.0733434i
147147 2.43151 6.68052i 0.200547 0.551000i
148148 −0.146792 0.403307i −0.0120662 0.0331516i
149149 −2.60277 3.10186i −0.213227 0.254114i 0.648821 0.760941i 0.275263π-0.275263\pi
−0.862048 + 0.506827i 0.830818π0.830818\pi
150150 0.0165600 0.00291998i 0.00135212 0.000238415i
151151 −18.0109 −1.46570 −0.732852 0.680388i 0.761811π-0.761811\pi
−0.732852 + 0.680388i 0.761811π0.761811\pi
152152 −3.55784 1.15755i −0.288579 0.0938895i
153153 3.87943i 0.313633i
154154 2.67302 + 0.415911i 0.215398 + 0.0335150i
155155 10.2044 + 12.1611i 0.819637 + 0.976805i
156156 −2.40469 6.60682i −0.192529 0.528969i
157157 14.7559 + 5.37071i 1.17765 + 0.428629i 0.855371 0.518016i 0.173329π-0.173329\pi
0.322278 + 0.946645i 0.395551π0.395551\pi
158158 2.63590 + 2.21178i 0.209701 + 0.175960i
159159 1.13250 1.96154i 0.0898127 0.155560i
160160 2.80032 + 4.85030i 0.221385 + 0.383450i
161161 −7.60661 1.34125i −0.599485 0.105705i
162162 −0.0377067 + 0.213846i −0.00296252 + 0.0168013i
163163 2.60867 + 4.51834i 0.204326 + 0.353904i 0.949918 0.312500i 0.101166π-0.101166\pi
−0.745591 + 0.666403i 0.767833π0.767833\pi
164164 2.53761 4.39526i 0.198154 0.343212i
165165 −6.29716 + 3.80708i −0.490234 + 0.296381i
166166 1.29073 3.54626i 0.100180 0.275243i
167167 −19.6983 + 7.16958i −1.52430 + 0.554799i −0.962217 0.272284i 0.912221π-0.912221\pi
−0.562080 + 0.827083i 0.689999π0.689999\pi
168168 −2.46982 + 2.07242i −0.190551 + 0.159891i
169169 −0.00657467 0.0372868i −0.000505744 0.00286822i
170170 1.86901i 0.143347i
171171 2.30842 + 3.69746i 0.176530 + 0.282752i
172172 4.12775i 0.314738i
173173 −1.91724 10.8732i −0.145765 0.826677i −0.966749 0.255726i 0.917686π-0.917686\pi
0.820984 0.570951i 0.193425π-0.193425\pi
174174 0.183823 + 0.219072i 0.0139356 + 0.0166078i
175175 −0.0994866 0.273337i −0.00752048 0.0206623i
176176 9.60763 + 7.73690i 0.724202 + 0.583191i
177177 −6.81172 5.71571i −0.512000 0.429619i
178178 2.13300 + 1.23149i 0.159875 + 0.0923040i
179179 −1.95677 + 1.12974i −0.146256 + 0.0844407i −0.571342 0.820712i 0.693577π-0.693577\pi
0.425086 + 0.905153i 0.360244π0.360244\pi
180180 0.752375 4.26693i 0.0560787 0.318038i
181181 −23.8266 4.20127i −1.77102 0.312278i −0.809520 0.587093i 0.800272π-0.800272\pi
−0.961497 + 0.274815i 0.911383π0.911383\pi
182182 2.54314 1.46828i 0.188510 0.108836i
183183 7.35604 12.7410i 0.543774 0.941845i
184184 1.35207 + 1.13453i 0.0996763 + 0.0836383i
185185 −0.166774 + 0.458208i −0.0122615 + 0.0336881i
186186 1.46002 0.531404i 0.107054 0.0389644i
187187 4.64366 + 11.9994i 0.339578 + 0.877485i
188188 −0.397708 2.25552i −0.0290059 0.164500i
189189 3.75623 0.273225
190190 1.11214 + 1.78134i 0.0806832 + 0.129232i
191191 −26.1276 −1.89053 −0.945264 0.326307i 0.894196π-0.894196\pi
−0.945264 + 0.326307i 0.894196π0.894196\pi
192192 −6.78581 + 1.19652i −0.489723 + 0.0863514i
193193 7.65982 6.42735i 0.551366 0.462651i −0.324037 0.946044i 0.605040π-0.605040\pi
0.875403 + 0.483393i 0.160596π0.160596\pi
194194 −0.411536 1.13068i −0.0295465 0.0811784i
195195 −2.73203 + 7.50619i −0.195645 + 0.537530i
196196 10.6352 + 8.92401i 0.759659 + 0.637429i
197197 6.14747 + 3.54924i 0.437989 + 0.252873i 0.702744 0.711443i 0.251958π-0.251958\pi
−0.264755 + 0.964316i 0.585291π0.585291\pi
198198 0.139342 + 0.706578i 0.00990258 + 0.0502143i
199199 −0.947198 + 5.37183i −0.0671451 + 0.380799i 0.932654 + 0.360771i 0.117486π0.117486\pi
−0.999799 + 0.0200275i 0.993625π0.993625\pi
200200 −0.0115422 + 0.0654592i −0.000816159 + 0.00462867i
201201 5.55875 + 9.62803i 0.392084 + 0.679109i
202202 −1.07930 0.623137i −0.0759396 0.0438438i
203203 3.17983 3.78957i 0.223180 0.265976i
204204 −7.11905 2.59112i −0.498433 0.181415i
205205 −5.41835 + 1.97212i −0.378434 + 0.137739i
206206 −1.28132 1.52701i −0.0892736 0.106392i
207207 −0.357074 2.02507i −0.0248183 0.140752i
208208 13.3906 0.928473
209209 11.5660 + 8.67339i 0.800037 + 0.599951i
210210 1.80966 0.124878
211211 3.42742 + 19.4379i 0.235953 + 1.33816i 0.840596 + 0.541662i 0.182205π0.182205\pi
−0.604643 + 0.796497i 0.706684π0.706684\pi
212212 2.84317 + 3.38835i 0.195269 + 0.232713i
213213 −6.24160 + 2.27176i −0.427667 + 0.155658i
214214 0.428808 + 0.156073i 0.0293127 + 0.0106690i
215215 −3.01445 + 3.59248i −0.205584 + 0.245005i
216216 −0.743343 0.429169i −0.0505781 0.0292013i
217217 −13.4384 23.2759i −0.912256 1.58007i
218218 −0.306703 + 1.73940i −0.0207726 + 0.117807i
219219 −0.925135 + 5.24670i −0.0625148 + 0.354539i
220220 −2.78033 14.0986i −0.187450 0.950526i
221221 12.0959 + 6.98355i 0.813656 + 0.469764i
222222 0.0365581 + 0.0306759i 0.00245362 + 0.00205883i
223223 3.42391 9.40712i 0.229282 0.629947i −0.770692 0.637208i 0.780089π-0.780089\pi
0.999974 + 0.00726100i 0.00231127π0.00231127\pi
224224 −3.24299 8.91004i −0.216681 0.595327i
225225 0.0593218 0.0497769i 0.00395479 0.00331846i
226226 −3.98934 + 0.703428i −0.265367 + 0.0467914i
227227 −4.42566 −0.293741 −0.146871 0.989156i 0.546920π-0.546920\pi
−0.146871 + 0.989156i 0.546920π0.546920\pi
228228 −8.32694 + 1.76655i −0.551465 + 0.116993i
229229 −6.32793 −0.418162 −0.209081 0.977898i 0.567047π-0.567047\pi
−0.209081 + 0.977898i 0.567047π0.567047\pi
230230 −0.172029 0.975626i −0.0113433 0.0643309i
231231 11.6184 4.49619i 0.764432 0.295827i
232232 −1.06225 + 0.386629i −0.0697404 + 0.0253834i
233233 9.00576 24.7431i 0.589987 1.62098i −0.180539 0.983568i 0.557784π-0.557784\pi
0.770526 0.637408i 0.219993π-0.219993\pi
234234 0.598882 + 0.502521i 0.0391501 + 0.0328508i
235235 −1.30104 + 2.25347i −0.0848707 + 0.147000i
236236 15.0384 8.68243i 0.978918 0.565178i
237237 15.6055 + 2.75167i 1.01369 + 0.178740i
238238 0.549463 3.11616i 0.0356164 0.201991i
239239 6.42125 3.70731i 0.415356 0.239806i −0.277732 0.960658i 0.589583π-0.589583\pi
0.693088 + 0.720853i 0.256250π0.256250\pi
240240 7.14643 + 4.12599i 0.461300 + 0.266332i
241241 4.69931 + 3.94319i 0.302709 + 0.254003i 0.781471 0.623942i 0.214470π-0.214470\pi
−0.478762 + 0.877945i 0.658914π0.658914\pi
242242 1.27677 + 2.01872i 0.0820737 + 0.129768i
243243 0.342020 + 0.939693i 0.0219406 + 0.0602813i
244244 18.4676 + 22.0088i 1.18227 + 1.40897i
245245 −2.73899 15.5336i −0.174987 0.992403i
246246 0.564332i 0.0359805i
247247 15.6840 0.541576i 0.997948 0.0344596i
248248 6.14162i 0.389993i
249249 −3.01791 17.1154i −0.191252 1.08464i
250250 1.87388 1.57238i 0.118515 0.0994458i
251251 2.36384 0.860368i 0.149204 0.0543060i −0.266338 0.963880i 0.585814π-0.585814\pi
0.415543 + 0.909574i 0.363592π0.363592\pi
252252 −2.50884 + 6.89297i −0.158042 + 0.434216i
253253 −3.52846 5.83630i −0.221832 0.366925i
254254 1.24932 2.16389i 0.0783893 0.135774i
255255 4.30361 + 7.45408i 0.269503 + 0.466792i
256256 2.14626 12.1720i 0.134141 0.760752i
257257 3.88019 + 0.684182i 0.242040 + 0.0426781i 0.293352 0.956005i 0.405229π-0.405229\pi
−0.0513123 + 0.998683i 0.516340π0.516340\pi
258258 0.229490 + 0.397489i 0.0142874 + 0.0247466i
259259 0.412765 0.714930i 0.0256480 0.0444236i
260260 −11.9497 10.0270i −0.741088 0.621847i
261261 1.23757 + 0.450439i 0.0766036 + 0.0278814i
262262 1.26727 + 3.48180i 0.0782923 + 0.215106i
263263 12.0602 + 14.3728i 0.743663 + 0.886263i 0.996698 0.0811941i 0.0258734π-0.0258734\pi
−0.253035 + 0.967457i 0.581429π0.581429\pi
264264 −2.81294 0.437682i −0.173125 0.0269374i
265265 5.02530i 0.308702i
266266 −1.33056 3.29695i −0.0815817 0.202149i
267267 11.3426 0.694155
268268 −21.3809 + 3.77004i −1.30605 + 0.230292i
269269 −15.9613 19.0219i −0.973178 1.15979i −0.987136 0.159886i 0.948887π-0.948887\pi
0.0139575 0.999903i 0.495557π-0.495557\pi
270270 0.164777 + 0.452720i 0.0100280 + 0.0275517i
271271 8.65263 23.7729i 0.525610 1.44410i −0.338581 0.940937i 0.609947π-0.609947\pi
0.864191 0.503164i 0.167831π-0.167831\pi
272272 9.27466 11.0531i 0.562359 0.670193i
273273 6.76177 11.7117i 0.409241 0.708826i
274274 1.71516 + 2.97075i 0.103617 + 0.179469i
275275 0.123905 0.224972i 0.00747176 0.0135664i
276276 3.95465 + 0.697311i 0.238042 + 0.0419732i
277277 −11.0076 + 6.35526i −0.661385 + 0.381851i −0.792804 0.609476i 0.791380π-0.791380\pi
0.131420 + 0.991327i 0.458046π0.458046\pi
278278 1.24316 + 0.717741i 0.0745600 + 0.0430472i
279279 4.59930 5.48123i 0.275353 0.328153i
280280 −2.44657 + 6.72190i −0.146211 + 0.401711i
281281 24.9859 9.09413i 1.49053 0.542510i 0.536945 0.843617i 0.319578π-0.319578\pi
0.953590 + 0.301107i 0.0973562π0.0973562\pi
282282 0.163698 + 0.195087i 0.00974805 + 0.0116173i
283283 3.65870 0.645127i 0.217487 0.0383488i −0.0638428 0.997960i 0.520336π-0.520336\pi
0.281330 + 0.959611i 0.409225π0.409225\pi
284284 12.9712i 0.769697i
285285 8.53723 + 4.54360i 0.505702 + 0.269140i
286286 2.45391 + 0.837485i 0.145103 + 0.0495215i
287287 9.61367 1.69515i 0.567477 0.100062i
288288 1.93373 1.62259i 0.113946 0.0956122i
289289 −1.83243 + 0.666951i −0.107790 + 0.0392324i
290290 0.596230 + 0.217010i 0.0350118 + 0.0127433i
291291 −4.24484 3.56184i −0.248837 0.208799i
292292 −9.01019 5.20204i −0.527281 0.304426i
293293 13.2780 + 22.9981i 0.775708 + 1.34357i 0.934396 + 0.356237i 0.115940π0.115940\pi
−0.158687 + 0.987329i 0.550726π0.550726\pi
294294 −1.52028 0.268067i −0.0886647 0.0156340i
295295 −19.4290 3.42585i −1.13120 0.199461i
296296 −0.163369 + 0.0943213i −0.00949565 + 0.00548232i
297297 2.18271 + 2.49716i 0.126653 + 0.144900i
298298 −0.565176 + 0.673551i −0.0327398 + 0.0390178i
299299 −6.95684 2.53208i −0.402324 0.146434i
300300 0.0517227 + 0.142107i 0.00298621 + 0.00820454i
301301 6.08207 5.10346i 0.350565 0.294159i
302302 0.679131 + 3.85155i 0.0390796 + 0.221632i
303303 −5.73938 −0.329719
304304 2.26255 16.0535i 0.129766 0.920729i
305305 32.6415i 1.86905i
306306 0.829598 0.146281i 0.0474250 0.00836230i
307307 2.55596 2.14471i 0.145876 0.122405i −0.566929 0.823767i 0.691869π-0.691869\pi
0.712805 + 0.701362i 0.247424π0.247424\pi
308308 0.490795 + 24.3236i 0.0279656 + 1.38597i
309309 −8.62634 3.13973i −0.490735 0.178613i
310310 2.21583 2.64072i 0.125851 0.149983i
311311 −13.1277 + 22.7379i −0.744405 + 1.28935i 0.206068 + 0.978538i 0.433933π0.433933\pi
−0.950472 + 0.310809i 0.899400π0.899400\pi
312312 −2.67626 + 1.54514i −0.151513 + 0.0874762i
313313 −2.03498 + 11.5409i −0.115024 + 0.652332i 0.871715 + 0.490014i 0.163008π0.163008\pi
−0.986738 + 0.162318i 0.948103π0.948103\pi
314314 0.592105 3.35799i 0.0334144 0.189503i
315315 7.21736 4.16694i 0.406652 0.234781i
316316 −15.4727 + 26.7994i −0.870405 + 1.50759i
317317 12.1253 14.4503i 0.681023 0.811612i −0.309216 0.950992i 0.600066π-0.600066\pi
0.990239 + 0.139380i 0.0445109π0.0445109\pi
318318 −0.462169 0.168216i −0.0259172 0.00943307i
319319 4.36709 0.0881177i 0.244510 0.00493365i
320320 −11.7111 + 9.82682i −0.654673 + 0.549336i
321321 2.06957 0.364921i 0.115512 0.0203679i
322322 1.67721i 0.0934675i
323323 10.4161 13.3212i 0.579565 0.741213i
324324 −1.95285 −0.108492
325325 −0.0484138 0.274568i −0.00268551 0.0152303i
326326 0.867863 0.728223i 0.0480665 0.0403326i
327327 2.78196 + 7.64338i 0.153843 + 0.422680i
328328 −2.09619 0.762951i −0.115743 0.0421269i
329329 2.83169 3.37468i 0.156116 0.186052i
330330 1.05157 + 1.20307i 0.0578872 + 0.0662267i
331331 −1.69795 + 0.980313i −0.0933279 + 0.0538829i −0.545938 0.837826i 0.683826π-0.683826\pi
0.452610 + 0.891709i 0.350493π0.350493\pi
332332 33.4238 + 5.89351i 1.83437 + 0.323449i
333333 0.216437 + 0.0381638i 0.0118607 + 0.00209136i
334334 2.27594 + 3.94204i 0.124534 + 0.215699i
335335 21.3616 + 12.3331i 1.16711 + 0.673829i
336336 −10.7021 8.98012i −0.583847 0.489906i
337337 −20.1329 7.32778i −1.09671 0.399170i −0.270608 0.962690i 0.587225π-0.587225\pi
−0.826102 + 0.563520i 0.809447π0.809447\pi
338338 −0.00772571 + 0.00281193i −0.000420223 + 0.000152949i
339339 −14.2907 + 11.9914i −0.776167 + 0.651281i
340340 −16.5533 + 2.91878i −0.897726 + 0.158293i
341341 7.66504 22.4593i 0.415085 1.21624i
342342 0.703641 0.633065i 0.0380486 0.0342322i
343343 0.410392i 0.0221591i
344344 −1.78672 + 0.315046i −0.0963333 + 0.0169862i
345345 −2.93259 3.49492i −0.157885 0.188160i
346346 −2.25290 + 0.819988i −0.121117 + 0.0440829i
347347 −10.7764 + 29.6079i −0.578508 + 1.58944i 0.212188 + 0.977229i 0.431941π0.431941\pi
−0.790696 + 0.612209i 0.790281π0.790281\pi
348348 −1.65318 + 1.97018i −0.0886197 + 0.105613i
349349 −15.8077 9.12656i −0.846165 0.488533i 0.0131903 0.999913i 0.495801π-0.495801\pi
−0.859355 + 0.511380i 0.829135π0.829135\pi
350350 −0.0547006 + 0.0315814i −0.00292387 + 0.00168810i
351351 3.54560 + 0.625185i 0.189250 + 0.0333699i
352352 4.03897 7.33349i 0.215278 0.390876i
353353 0.934288 + 1.61824i 0.0497272 + 0.0861300i 0.889818 0.456316i 0.150831π-0.150831\pi
−0.840090 + 0.542446i 0.817498π0.817498\pi
354354 −0.965432 + 1.67218i −0.0513121 + 0.0888752i
355355 −9.47269 + 11.2891i −0.502758 + 0.599164i
356356 −7.57586 + 20.8145i −0.401520 + 1.10317i
357357 −4.98393 13.6932i −0.263777 0.724722i
358358 0.315373 + 0.375847i 0.0166680 + 0.0198641i
359359 −20.3351 + 3.58563i −1.07325 + 0.189242i −0.682228 0.731140i 0.738989π-0.738989\pi
−0.391020 + 0.920382i 0.627878π0.627878\pi
360360 −1.90438 −0.100370
361361 2.00077 18.8944i 0.105304 0.994440i
362362 5.25363i 0.276124i
363363 9.74039 + 5.11124i 0.511238 + 0.268271i
364364 16.9756 + 20.2308i 0.889766 + 1.06038i
365365 4.04280 + 11.1075i 0.211610 + 0.581393i
366366 −3.00199 1.09263i −0.156916 0.0571129i
367367 2.03328 + 1.70613i 0.106137 + 0.0890591i 0.694312 0.719675i 0.255709π-0.255709\pi
−0.588175 + 0.808734i 0.700153π0.700153\pi
368368 −3.82402 + 6.62340i −0.199341 + 0.345269i
369369 1.29944 + 2.25069i 0.0676461 + 0.117166i
370370 0.104274 + 0.0183863i 0.00542096 + 0.000955861i
371371 −1.47737 + 8.37857i −0.0767011 + 0.434994i
372372 6.98655 + 12.1011i 0.362236 + 0.627411i
373373 1.25034 2.16565i 0.0647402 0.112133i −0.831839 0.555018i 0.812711π-0.812711\pi
0.896579 + 0.442884i 0.146045π0.146045\pi
374374 2.39093 1.44548i 0.123632 0.0747442i
375375 3.85294 10.5859i 0.198965 0.546651i
376376 −0.945955 + 0.344300i −0.0487839 + 0.0177559i
377377 3.63225 3.04782i 0.187071 0.156971i
378378 −0.141635 0.803253i −0.00728492 0.0413149i
379379 9.01018i 0.462822i 0.972856 + 0.231411i 0.0743342π0.0743342\pi
−0.972856 + 0.231411i 0.925666π0.925666\pi
380380 −14.0400 + 12.6318i −0.720236 + 0.647995i
381381 11.5068i 0.589512i
382382 0.985187 + 5.58727i 0.0504066 + 0.285870i
383383 −4.43215 5.28203i −0.226472 0.269899i 0.640828 0.767685i 0.278591π-0.278591\pi
−0.867300 + 0.497785i 0.834147π0.834147\pi
384384 2.23847 + 6.15014i 0.114231 + 0.313848i
385385 17.3361 21.5279i 0.883531 1.09716i
386386 −1.66329 1.39566i −0.0846591 0.0710374i
387387 1.83053 + 1.05686i 0.0930509 + 0.0537230i
388388 9.37144 5.41060i 0.475763 0.274682i
389389 −2.36957 + 13.4385i −0.120142 + 0.681358i 0.863934 + 0.503606i 0.167994π0.167994\pi
−0.984075 + 0.177752i 0.943118π0.943118\pi
390390 1.70818 + 0.301198i 0.0864971 + 0.0152518i
391391 −6.90854 + 3.98865i −0.349380 + 0.201715i
392392 3.05108 5.28462i 0.154103 0.266914i
393393 13.0714 + 10.9682i 0.659367 + 0.553275i
394394 0.527188 1.44844i 0.0265594 0.0729713i
395395 33.0375 12.0247i 1.66230 0.605027i
396396 −6.04033 + 2.33755i −0.303538 + 0.117466i
397397 −4.39085 24.9018i −0.220371 1.24978i −0.871340 0.490680i 0.836748π-0.836748\pi
0.650969 0.759104i 0.274363π-0.274363\pi
398398 1.18446 0.0593715
399399 −12.8982 10.0853i −0.645717 0.504895i
400400 −0.288021 −0.0144010
401401 −15.0902 + 2.66081i −0.753568 + 0.132874i −0.537220 0.843442i 0.680526π-0.680526\pi
−0.216348 + 0.976316i 0.569414π0.569414\pi
402402 1.84931 1.55175i 0.0922351 0.0773945i
403403 −8.81078 24.2074i −0.438896 1.20586i
404404 3.83341 10.5322i 0.190719 0.523997i
405405 1.69961 + 1.42614i 0.0844543 + 0.0708656i
406406 −0.930283 0.537099i −0.0461692 0.0266558i
407407 0.715142 0.141031i 0.0354483 0.00699063i
408408 −0.578225 + 3.27928i −0.0286264 + 0.162348i
409409 1.15771 6.56570i 0.0572451 0.324653i −0.942715 0.333599i 0.891737π-0.891737\pi
0.999960 + 0.00894652i 0.00284780π0.00284780\pi
410410 0.626037 + 1.08433i 0.0309178 + 0.0535511i
411411 13.6810 + 7.89871i 0.674833 + 0.389615i
412412 11.5233 13.7329i 0.567712 0.676573i
413413 31.3864 + 11.4237i 1.54442 + 0.562123i
414414 −0.419587 + 0.152717i −0.0206216 + 0.00750564i
415415 −24.7856 29.5383i −1.21668 1.44998i
416416 −1.57816 8.95018i −0.0773756 0.438819i
417417 6.61072 0.323728
418418 1.41865 2.80038i 0.0693884 0.136971i
419419 −3.54084 −0.172981 −0.0864906 0.996253i 0.527565π-0.527565\pi
−0.0864906 + 0.996253i 0.527565π0.527565\pi
420420 2.82609 + 16.0276i 0.137899 + 0.782065i
421421 −10.6880 12.7375i −0.520903 0.620789i 0.439891 0.898051i 0.355017π-0.355017\pi
−0.960794 + 0.277263i 0.910573π0.910573\pi
422422 4.02747 1.46588i 0.196054 0.0713578i
423423 1.10208 + 0.401123i 0.0535848 + 0.0195033i
424424 1.24966 1.48929i 0.0606890 0.0723263i
425425 −0.260171 0.150210i −0.0126202 0.00728625i
426426 0.721155 + 1.24908i 0.0349401 + 0.0605180i
427427 −9.59614 + 54.4224i −0.464390 + 2.63368i
428428 −0.712635 + 4.04155i −0.0344465 + 0.195356i
429429 11.7152 2.31031i 0.565615 0.111543i
430430 0.881902 + 0.509166i 0.0425291 + 0.0245542i
431431 9.42865 + 7.91158i 0.454162 + 0.381087i 0.840978 0.541070i 0.181981π-0.181981\pi
−0.386816 + 0.922157i 0.626425π0.626425\pi
432432 1.27208 3.49501i 0.0612030 0.168154i
433433 1.59774 + 4.38977i 0.0767827 + 0.210959i 0.972145 0.234379i 0.0753057π-0.0753057\pi
−0.895363 + 0.445338i 0.853084π0.853084\pi
434434 −4.47074 + 3.75139i −0.214602 + 0.180073i
435435 2.87760 0.507399i 0.137970 0.0243279i
436436 −15.8843 −0.760720
437437 −4.21107 + 7.91242i −0.201443 + 0.378503i
438438 1.15687 0.0552772
439439 2.32305 + 13.1747i 0.110873 + 0.628793i 0.988711 + 0.149835i 0.0478742π0.0478742\pi
−0.877838 + 0.478958i 0.841015π0.841015\pi
440440 −5.89043 + 2.27954i −0.280815 + 0.108673i
441441 −6.68052 + 2.43151i −0.318120 + 0.115786i
442442 1.03730 2.84997i 0.0493396 0.135559i
443443 5.72196 + 4.80129i 0.271858 + 0.228116i 0.768516 0.639830i 0.220995π-0.220995\pi
−0.496658 + 0.867946i 0.665440π0.665440\pi
444444 −0.214595 + 0.371689i −0.0101842 + 0.0176396i
445445 21.7941 12.5828i 1.03314 0.596482i
446446 −2.14078 0.377476i −0.101369 0.0178740i
447447 −0.703134 + 3.98767i −0.0332571 + 0.188610i
448448 22.4147 12.9411i 1.05899 0.611411i
449449 −21.4566 12.3880i −1.01260 0.584625i −0.100648 0.994922i 0.532092π-0.532092\pi
−0.911952 + 0.410297i 0.865425π0.865425\pi
450450 −0.0128814 0.0108088i −0.000607235 0.000509531i
451451 6.71335 + 5.40618i 0.316119 + 0.254567i
452452 −12.4601 34.2338i −0.586073 1.61022i
453453 11.5772 + 13.7971i 0.543943 + 0.648246i
454454 0.166877 + 0.946407i 0.00783193 + 0.0444171i
455455 30.0045i 1.40663i
456456 1.40021 + 3.46952i 0.0655706 + 0.162475i
457457 29.7206i 1.39027i −0.718880 0.695134i 0.755345π-0.755345\pi
0.718880 0.695134i 0.244655π-0.244655\pi
458458 0.238606 + 1.35320i 0.0111493 + 0.0632309i
459459 2.97181 2.49365i 0.138712 0.116394i
460460 8.37216 3.04722i 0.390354 0.142077i
461461 5.83587 16.0339i 0.271803 0.746774i −0.726423 0.687248i 0.758819π-0.758819\pi
0.998227 0.0595263i 0.0189590π-0.0189590\pi
462462 −1.39958 2.31500i −0.0651143 0.107703i
463463 −4.90409 + 8.49413i −0.227912 + 0.394756i −0.957189 0.289463i 0.906523π-0.906523\pi
0.729277 + 0.684219i 0.239857π0.239857\pi
464464 −2.44916 4.24206i −0.113699 0.196933i
465465 2.75670 15.6340i 0.127839 0.725011i
466466 −5.63078 0.992859i −0.260841 0.0459933i
467467 10.0747 + 17.4500i 0.466204 + 0.807488i 0.999255 0.0385946i 0.0122881π-0.0122881\pi
−0.533051 + 0.846083i 0.678955π0.678955\pi
468468 −3.51542 + 6.08888i −0.162500 + 0.281459i
469469 −31.9899 26.8427i −1.47716 1.23948i
470470 0.530953 + 0.193251i 0.0244910 + 0.00891401i
471471 −5.37071 14.7559i −0.247469 0.679916i
472472 −4.90602 5.84677i −0.225818 0.269119i
473473 6.92703 + 1.07782i 0.318505 + 0.0495581i
474474 3.44092i 0.158047i
475475 −0.337348 + 0.0116488i −0.0154786 + 0.000534484i
476476 28.4569 1.30432
477477 −2.23058 + 0.393311i −0.102131 + 0.0180085i
478478 −1.03492 1.23336i −0.0473359 0.0564128i
479479 −4.97949 13.6810i −0.227519 0.625103i 0.772431 0.635098i 0.219040π-0.219040\pi
−0.999950 + 0.00999556i 0.996818π0.996818\pi
480480 1.91553 5.26288i 0.0874316 0.240216i
481481 0.508612 0.606141i 0.0231907 0.0276376i
482482 0.666038 1.15361i 0.0303372 0.0525456i
483483 3.86198 + 6.68914i 0.175726 + 0.304367i
484484 −15.8853 + 14.4605i −0.722057 + 0.657295i
485485 −12.1075 2.13488i −0.549773 0.0969397i
486486 0.188053 0.108572i 0.00853024 0.00492494i
487487 7.46275 + 4.30862i 0.338169 + 0.195242i 0.659462 0.751738i 0.270784π-0.270784\pi
−0.321293 + 0.946980i 0.604117π0.604117\pi
488488 8.11709 9.67358i 0.367444 0.437902i
489489 1.78443 4.90269i 0.0806948 0.221707i
490490 −3.21851 + 1.17144i −0.145397 + 0.0529203i
491491 11.4392 + 13.6328i 0.516245 + 0.615237i 0.959689 0.281065i 0.0906877π-0.0906877\pi
−0.443443 + 0.896302i 0.646243π0.646243\pi
492492 −4.99811 + 0.881302i −0.225332 + 0.0397321i
493493 5.10918i 0.230106i
494494 −0.707205 3.33353i −0.0318187 0.149983i
495495 6.96413 + 2.37676i 0.313015 + 0.106828i
496496 −26.2083 + 4.62123i −1.17679 + 0.207499i
497497 19.1124 16.0372i 0.857310 0.719369i
498498 −3.54626 + 1.29073i −0.158912 + 0.0578391i
499499 14.1992 + 5.16810i 0.635645 + 0.231356i 0.639687 0.768636i 0.279064π-0.279064\pi
−0.00404128 + 0.999992i 0.501286π0.501286\pi
500500 16.8524 + 14.1409i 0.753664 + 0.632399i
501501 18.1540 + 10.4812i 0.811061 + 0.468266i
502502 −0.273119 0.473056i −0.0121899 0.0211135i
503503 14.5307 + 2.56215i 0.647890 + 0.114240i 0.487930 0.872883i 0.337752π-0.337752\pi
0.159960 + 0.987123i 0.448863π0.448863\pi
504504 3.17514 + 0.559862i 0.141432 + 0.0249382i
505505 −11.0279 + 6.36693i −0.490733 + 0.283325i
506506 −1.11502 + 0.974612i −0.0495687 + 0.0433268i
507507 −0.0243372 + 0.0290040i −0.00108085 + 0.00128811i
508508 21.1159 + 7.68556i 0.936866 + 0.340992i
509509 8.30762 + 22.8250i 0.368229 + 1.01170i 0.976035 + 0.217615i 0.0698277π0.0698277\pi
−0.607806 + 0.794086i 0.707950π0.707950\pi
510510 1.43175 1.20138i 0.0633988 0.0531979i
511511 −3.47502 19.7078i −0.153726 0.871822i
512512 −15.7735 −0.697099
513513 1.34859 4.14503i 0.0595417 0.183008i
514514 0.855559i 0.0377371i
515515 −20.0580 + 3.53677i −0.883861 + 0.155849i
516516 −3.16204 + 2.65327i −0.139201 + 0.116804i
517517 3.88896 0.0784703i 0.171036 0.00345112i
518518 −0.168449 0.0613103i −0.00740121 0.00269382i
519519 −7.09700 + 8.45788i −0.311524 + 0.371260i
520520 −3.42817 + 5.93777i −0.150335 + 0.260388i
521521 23.1613 13.3722i 1.01471 0.585845i 0.102145 0.994770i 0.467429π-0.467429\pi
0.912568 + 0.408925i 0.134096π0.134096\pi
522522 0.0496595 0.281633i 0.00217354 0.0123268i
523523 −5.31941 + 30.1679i −0.232601 + 1.31915i 0.615005 + 0.788523i 0.289154π0.289154\pi
−0.847607 + 0.530625i 0.821957π0.821957\pi
524524 −28.8582 + 16.6613i −1.26067 + 0.727851i
525525 −0.145440 + 0.251909i −0.00634751 + 0.0109942i
526526 2.61880 3.12097i 0.114185 0.136081i
527527 −26.0842 9.49388i −1.13625 0.413560i
528528 −0.248853 12.3331i −0.0108299 0.536727i
529529 −14.3799 + 12.0662i −0.625212 + 0.524615i
530530 −1.07464 + 0.189488i −0.0466793 + 0.00823081i
531531 8.89207i 0.385883i
532532 27.1221 16.9331i 1.17589 0.734142i
533533 9.35673 0.405285
534534 −0.427692 2.42556i −0.0185080 0.104964i
535535 3.57172 2.99703i 0.154419 0.129573i
536536 3.26375 + 8.96709i 0.140973 + 0.387319i
537537 2.12322 + 0.772787i 0.0916235 + 0.0333482i
538538 −3.46591 + 4.13051i −0.149426 + 0.178079i
539539 −17.7529 + 15.5174i −0.764673 + 0.668382i
540540 −3.75228 + 2.16638i −0.161472 + 0.0932260i
541541 −0.623720 0.109979i −0.0268158 0.00472835i 0.160224 0.987081i 0.448778π-0.448778\pi
−0.187040 + 0.982352i 0.559889π0.559889\pi
542542 −5.40999 0.953927i −0.232379 0.0409747i
543543 12.0971 + 20.9528i 0.519135 + 0.899169i
544544 −8.48087 4.89643i −0.363614 0.209933i
545545 13.8245 + 11.6001i 0.592176 + 0.496895i
546546 −2.75947 1.00436i −0.118094 0.0429828i
547547 1.32644 0.482786i 0.0567147 0.0206424i −0.313507 0.949586i 0.601504π-0.601504\pi
0.370222 + 0.928943i 0.379282π0.379282\pi
548548 −23.6325 + 19.8300i −1.00953 + 0.847095i
549549 −14.4886 + 2.55473i −0.618357 + 0.109033i
550550 −0.0527814 0.0180136i −0.00225061 0.000768101i
551551 −3.04018 4.86953i −0.129516 0.207449i
552552 1.76501i 0.0751237i
553553 −58.6178 + 10.3359i −2.49268 + 0.439527i
554554 1.77411 + 2.11430i 0.0753746 + 0.0898279i
555555 0.458208 0.166774i 0.0194498 0.00707916i
556556 −4.41539 + 12.1312i −0.187254 + 0.514477i
557557 7.31641 8.71936i 0.310006 0.369451i −0.588435 0.808544i 0.700256π-0.700256\pi
0.898442 + 0.439093i 0.144700π0.144700\pi
558558 −1.34556 0.776860i −0.0569622 0.0328871i
559559 6.59044 3.80499i 0.278746 0.160934i
560560 −30.5254 5.38246i −1.28993 0.227450i
561561 6.20720 11.2703i 0.262068 0.475834i
562562 −2.88688 5.00022i −0.121776 0.210921i
563563 −3.32120 + 5.75249i −0.139972 + 0.242438i −0.927486 0.373858i 0.878035π-0.878035\pi
0.787514 + 0.616297i 0.211368π0.211368\pi
564564 −1.47218 + 1.75448i −0.0619901 + 0.0738769i
565565 −14.1562 + 38.8940i −0.595558 + 1.63628i
566566 −0.275915 0.758070i −0.0115976 0.0318641i
567567 −2.41446 2.87744i −0.101398 0.120841i
568568 −5.61462 + 0.990009i −0.235584 + 0.0415399i
569569 −32.2213 −1.35079 −0.675393 0.737458i 0.736026π-0.736026\pi
−0.675393 + 0.737458i 0.736026π0.736026\pi
570570 0.649717 1.99697i 0.0272136 0.0836440i
571571 28.9368i 1.21097i 0.795857 + 0.605484i 0.207020π0.207020\pi
−0.795857 + 0.605484i 0.792980π0.792980\pi
572572 −3.58514 + 23.0414i −0.149902 + 0.963409i
573573 16.7945 + 20.0149i 0.701601 + 0.836135i
574574 −0.725000 1.99192i −0.0302609 0.0831412i
575575 0.149635 + 0.0544628i 0.00624023 + 0.00227126i
576576 5.27842 + 4.42912i 0.219934 + 0.184547i
577577 −18.3138 + 31.7205i −0.762415 + 1.32054i 0.179188 + 0.983815i 0.442653π0.442653\pi
−0.941603 + 0.336726i 0.890680π0.890680\pi
578578 0.211719 + 0.366709i 0.00880637 + 0.0152531i
579579 −9.84727 1.73634i −0.409239 0.0721598i
580580 −0.990873 + 5.61952i −0.0411438 + 0.233338i
581581 32.6406 + 56.5351i 1.35416 + 2.34547i
582582 −0.601625 + 1.04204i −0.0249381 + 0.0431941i
583583 −6.42859 + 3.88654i −0.266245 + 0.160964i
584584 −1.56403 + 4.29714i −0.0647201 + 0.177817i
585585 7.50619 2.73203i 0.310343 0.112956i
586586 4.41738 3.70662i 0.182480 0.153119i
587587 −2.23997 12.7035i −0.0924535 0.524330i −0.995498 0.0947827i 0.969784π-0.969784\pi
0.903045 0.429547i 0.141327π-0.141327\pi
588588 13.8833i 0.572538i
589589 −30.5099 + 6.47266i −1.25714 + 0.266701i
590590 4.28398i 0.176369i
591591 −1.23264 6.99064i −0.0507040 0.287557i
592592 −0.525426 0.626178i −0.0215949 0.0257358i
593593 −10.3049 28.3124i −0.423170 1.16265i −0.949883 0.312607i 0.898798π-0.898798\pi
0.526712 0.850044i 0.323425π-0.323425\pi
594594 0.451703 0.560922i 0.0185336 0.0230149i
595595 −24.7668 20.7818i −1.01534 0.851970i
596596 −6.84805 3.95372i −0.280507 0.161951i
597597 4.72391 2.72735i 0.193337 0.111623i
598598 −0.279155 + 1.58317i −0.0114155 + 0.0647404i
599599 7.02375 + 1.23848i 0.286983 + 0.0506028i 0.315286 0.948997i 0.397899π-0.397899\pi
−0.0283036 + 0.999599i 0.509011π0.509011\pi
600600 0.0575639 0.0332345i 0.00235004 0.00135679i
601601 −0.433823 + 0.751403i −0.0176960 + 0.0306504i −0.874738 0.484597i 0.838966π-0.838966\pi
0.857042 + 0.515247i 0.172300π0.172300\pi
602602 −1.32069 1.10819i −0.0538272 0.0451664i
603603 3.80241 10.4470i 0.154846 0.425436i
604604 −33.0514 + 12.0297i −1.34484 + 0.489482i
605605 24.3857 0.984494i 0.991418 0.0400254i
606606 0.216413 + 1.22734i 0.00879119 + 0.0498573i
607607 −33.9163 −1.37662 −0.688311 0.725416i 0.741647π-0.741647\pi
−0.688311 + 0.725416i 0.741647π0.741647\pi
608608 −10.9966 + 0.379719i −0.445973 + 0.0153997i
609609 −4.94693 −0.200460
610610 −6.98023 + 1.23080i −0.282621 + 0.0498338i
611611 3.23458 2.71414i 0.130857 0.109802i
612612 2.59112 + 7.11905i 0.104740 + 0.287771i
613613 −4.52557 + 12.4339i −0.182786 + 0.502201i −0.996915 0.0784829i 0.974992π-0.974992\pi
0.814129 + 0.580683i 0.197215π0.197215\pi
614614 −0.555012 0.465711i −0.0223985 0.0187946i
615615 4.99358 + 2.88304i 0.201361 + 0.116256i
616616 10.4911 2.06892i 0.422700 0.0833591i
617617 0.175574 0.995730i 0.00706835 0.0400866i −0.981070 0.193655i 0.937966π-0.937966\pi
0.988138 + 0.153569i 0.0490767π0.0490767\pi
618618 −0.346146 + 1.96309i −0.0139240 + 0.0789671i
619619 −9.63592 16.6899i −0.387300 0.670824i 0.604785 0.796389i 0.293259π-0.293259\pi
−0.992085 + 0.125565i 0.959926π0.959926\pi
620620 26.8484 + 15.5010i 1.07826 + 0.622533i
621621 −1.32177 + 1.57522i −0.0530407 + 0.0632115i
622622 5.35740 + 1.94993i 0.214812 + 0.0781852i
623623 −40.0359 + 14.5719i −1.60401 + 0.583810i
624624 −8.60733 10.2578i −0.344569 0.410641i
625625 −4.27293 24.2330i −0.170917 0.969319i
626626 2.54471 0.101707
627627 −0.790275 14.4352i −0.0315605 0.576487i
628628 30.6654 1.22368
629629 −0.148054 0.839654i −0.00590328 0.0334792i
630630 −1.16323 1.38628i −0.0463440 0.0552306i
631631 −2.31048 + 0.840948i −0.0919790 + 0.0334776i −0.387600 0.921828i 0.626696π-0.626696\pi
0.295621 + 0.955305i 0.404474π0.404474\pi
632632 12.7812 + 4.65197i 0.508408 + 0.185045i
633633 12.6872 15.1200i 0.504270 0.600965i
634634 −3.54735 2.04806i −0.140883 0.0813389i
635635 −12.7650 22.1096i −0.506564 0.877394i
636636 0.768077 4.35598i 0.0304563 0.172726i
637637 −4.44460 + 25.2066i −0.176101 + 0.998721i
638638 −0.183512 0.930559i −0.00726532 0.0368412i
639639 5.75229 + 3.32109i 0.227557 + 0.131380i
640640 11.1237 + 9.33388i 0.439702 + 0.368954i
641641 5.22558 14.3572i 0.206398 0.567074i −0.792697 0.609616i 0.791324π-0.791324\pi
0.999095 + 0.0425425i 0.0135458π0.0135458\pi
642642 −0.156073 0.428808i −0.00615972 0.0169237i
643643 24.0824 20.2075i 0.949717 0.796907i −0.0295327 0.999564i 0.509402π-0.509402\pi
0.979250 + 0.202656i 0.0649575π0.0649575\pi
644644 −14.8546 + 2.61926i −0.585352 + 0.103213i
645645 4.68966 0.184655
646646 −3.24144 1.72513i −0.127533 0.0678742i
647647 8.77766 0.345085 0.172543 0.985002i 0.444802π-0.444802\pi
0.172543 + 0.985002i 0.444802π0.444802\pi
648648 0.149049 + 0.845299i 0.00585520 + 0.0332065i
649649 10.6438 + 27.5040i 0.417804 + 1.07963i
650650 −0.0568897 + 0.0207062i −0.00223140 + 0.000812162i
651651 −9.19238 + 25.2559i −0.360278 + 0.989855i
652652 7.80496 + 6.54914i 0.305666 + 0.256484i
653653 −9.46954 + 16.4017i −0.370572 + 0.641849i −0.989654 0.143477i 0.954172π-0.954172\pi
0.619082 + 0.785326i 0.287505π0.287505\pi
654654 1.52960 0.883117i 0.0598122 0.0345326i
655655 37.2835 + 6.57408i 1.45679 + 0.256871i
656656 1.67849 9.51919i 0.0655340 0.371662i
657657 4.61387 2.66382i 0.180004 0.103925i
658658 −0.828433 0.478296i −0.0322957 0.0186459i
659659 −26.1563 21.9478i −1.01891 0.854964i −0.0294167 0.999567i 0.509365π-0.509365\pi
−0.989490 + 0.144603i 0.953809π0.953809\pi
660660 −9.01298 + 11.1923i −0.350830 + 0.435658i
661661 6.39151 + 17.5605i 0.248601 + 0.683026i 0.999738 + 0.0228797i 0.00728347π0.00728347\pi
−0.751137 + 0.660146i 0.770494π0.770494\pi
662662 0.273660 + 0.326135i 0.0106361 + 0.0126756i
663663 −2.42536 13.7549i −0.0941932 0.534196i
664664 14.9174i 0.578909i
665665 −35.9711 5.06970i −1.39490 0.196595i
666666 0.0477232i 0.00184924i
667667 0.470264 + 2.66700i 0.0182087 + 0.103267i
668668 −31.3592 + 26.3135i −1.21332 + 1.01810i
669669 −9.40712 + 3.42391i −0.363700 + 0.132376i
670670 1.83190 5.03312i 0.0707726 0.194446i
671671 −41.7565 + 25.2447i −1.61199 + 0.974563i
672672 −4.74094 + 8.21154i −0.182886 + 0.316767i
673673 −6.84011 11.8474i −0.263667 0.456684i 0.703547 0.710649i 0.251599π-0.251599\pi
−0.967213 + 0.253965i 0.918265π0.918265\pi
674674 −0.807867 + 4.58164i −0.0311179 + 0.176478i
675675 −0.0762627 0.0134472i −0.00293535 0.000517582i
676676 −0.0369694 0.0640329i −0.00142190 0.00246280i
677677 −14.2616 + 24.7018i −0.548118 + 0.949368i 0.450285 + 0.892885i 0.351322π0.351322\pi
−0.998404 + 0.0564837i 0.982011π0.982011\pi
678678 3.10316 + 2.60386i 0.119176 + 0.100001i
679679 19.5589 + 7.11886i 0.750602 + 0.273197i
680680 2.52682 + 6.94237i 0.0968990 + 0.266228i
681681 2.84476 + 3.39025i 0.109011 + 0.129915i
682682 −5.09184 0.792269i −0.194977 0.0303375i
683683 41.9580i 1.60548i −0.596331 0.802739i 0.703375π-0.703375\pi
0.596331 0.802739i 0.296625π-0.296625\pi
684684 6.70572 + 5.24329i 0.256399 + 0.200482i
685685 35.0495 1.33917
686686 0.0877605 0.0154745i 0.00335071 0.000590821i
687687 4.06752 + 4.84748i 0.155185 + 0.184943i
688688 −2.68881 7.38744i −0.102510 0.281644i
689689 −2.78905 + 7.66285i −0.106254 + 0.291931i
690690 −0.636795 + 0.758903i −0.0242424 + 0.0288909i
691691 21.0823 36.5157i 0.802010 1.38912i −0.116281 0.993216i 0.537097π-0.537097\pi
0.918291 0.395906i 0.129569π-0.129569\pi
692692 −10.7807 18.6727i −0.409820 0.709829i
693693 −10.9124 6.01008i −0.414528 0.228304i
694694 6.73787 + 1.18807i 0.255766 + 0.0450984i
695695 12.7021 7.33355i 0.481817 0.278177i
696696 0.978979 + 0.565214i 0.0371081 + 0.0214244i
697697 6.48069 7.72338i 0.245474 0.292544i
698698 −1.35562 + 3.72453i −0.0513109 + 0.140976i
699699 −24.7431 + 9.00576i −0.935871 + 0.340629i
700700 −0.365131 0.435146i −0.0138007 0.0164470i
701701 31.9852 5.63986i 1.20807 0.213015i 0.466884 0.884319i 0.345377π-0.345377\pi
0.741182 + 0.671304i 0.234266π0.234266\pi
702702 0.781784i 0.0295066i
703703 −0.640738 0.712170i −0.0241659 0.0268600i
704704 21.6283 + 7.38142i 0.815146 + 0.278198i
705705 2.56255 0.451847i 0.0965114 0.0170176i
706706 0.310823 0.260812i 0.0116980 0.00981578i
707707 20.2583 7.37341i 0.761891 0.277306i
708708 −16.3176 5.93913i −0.613254 0.223206i
709709 1.07665 + 0.903420i 0.0404346 + 0.0339286i 0.662781 0.748813i 0.269376π-0.269376\pi
−0.622346 + 0.782742i 0.713820π0.713820\pi
710710 2.77131 + 1.60002i 0.104005 + 0.0600475i
711711 −7.92312 13.7232i −0.297140 0.514662i
712712 9.58787 + 1.69060i 0.359321 + 0.0633579i
713713 14.4898 + 2.55495i 0.542649 + 0.0956836i
714714 −2.74031 + 1.58212i −0.102553 + 0.0592092i
715715 19.9471 17.4353i 0.745979 0.652043i
716716 −2.83625 + 3.38011i −0.105996 + 0.126321i
717717 −6.96746 2.53595i −0.260205 0.0947067i
718718 1.53354 + 4.21337i 0.0572313 + 0.157242i
719719 −39.9898 + 33.5554i −1.49137 + 1.25141i −0.598471 + 0.801144i 0.704225π0.704225\pi
−0.892897 + 0.450262i 0.851331π0.851331\pi
720720 −1.43294 8.12662i −0.0534026 0.302861i
721721 34.4820 1.28418
722722 −4.11592 + 0.284589i −0.153179 + 0.0105913i
723723 6.13451i 0.228145i
724724 −46.5297 + 8.20444i −1.72926 + 0.304916i
725725 −0.0781265 + 0.0655559i −0.00290155 + 0.00243469i
726726 0.725738 2.27567i 0.0269347 0.0844579i
727727 35.6104 + 12.9611i 1.32072 + 0.480701i 0.903688 0.428192i 0.140849π-0.140849\pi
0.417029 + 0.908893i 0.363072π0.363072\pi
728728 7.46134 8.89208i 0.276536 0.329562i
729729 0.500000 0.866025i 0.0185185 0.0320750i
730730 2.22285 1.28336i 0.0822713 0.0474993i
731731 1.42391 8.07541i 0.0526653 0.298680i
732732 4.98899 28.2940i 0.184399 1.04578i
733733 29.7611 17.1826i 1.09925 0.634652i 0.163226 0.986589i 0.447810π-0.447810\pi
0.936024 + 0.351936i 0.114477π0.114477\pi
734734 0.288179 0.499141i 0.0106369 0.0184236i
735735 −10.1388 + 12.0830i −0.373976 + 0.445687i
736736 4.87771 + 1.77534i 0.179795 + 0.0654399i
737737 −0.743852 36.8650i −0.0274001 1.35794i
738738 0.432303 0.362746i 0.0159133 0.0133528i
739739 −12.5576 + 2.21425i −0.461940 + 0.0814524i −0.399775 0.916613i 0.630912π-0.630912\pi
−0.0621651 + 0.998066i 0.519801π0.519801\pi
740740 0.952237i 0.0350049i
741741 −10.4963 11.6665i −0.385593 0.428580i
742742 1.84743 0.0678211
743743 1.35313 + 7.67400i 0.0496416 + 0.281532i 0.999516 0.0310992i 0.00990079π-0.00990079\pi
−0.949875 + 0.312631i 0.898790π0.898790\pi
744744 4.70476 3.94776i 0.172485 0.144732i
745745 3.07266 + 8.44207i 0.112574 + 0.309294i
746746 −0.510262 0.185720i −0.0186820 0.00679969i
747747 −11.1713 + 13.3134i −0.408736 + 0.487113i
748748 16.5360 + 18.9183i 0.604618 + 0.691722i
749749 −6.83614 + 3.94685i −0.249787 + 0.144215i
750750 −2.40902 0.424775i −0.0879650 0.0155106i
751751 −10.7316 1.89226i −0.391600 0.0690496i −0.0256185 0.999672i 0.508156π-0.508156\pi
−0.365981 + 0.930622i 0.619267π0.619267\pi
752752 −2.18102 3.77763i −0.0795334 0.137756i
753753 −2.17853 1.25777i −0.0793900 0.0458359i
754754 −0.788724 0.661818i −0.0287236 0.0241020i
755755 37.5506 + 13.6673i 1.36660 + 0.497403i
756756 6.89297 2.50884i 0.250695 0.0912455i
757757 2.93854 2.46573i 0.106803 0.0896186i −0.587822 0.808990i 0.700015π-0.700015\pi
0.694625 + 0.719372i 0.255570π0.255570\pi
758758 1.92679 0.339744i 0.0699840 0.0123401i
759759 −2.20281 + 6.45445i −0.0799571 + 0.234282i
760760 6.53930 + 5.11316i 0.237205 + 0.185474i
761761 38.9898i 1.41338i −0.707523 0.706690i 0.750187π-0.750187\pi
0.707523 0.706690i 0.249813π-0.249813\pi
762762 −2.46068 + 0.433885i −0.0891411 + 0.0157180i
763763 −19.6390 23.4048i −0.710979 0.847312i
764764 −47.9462 + 17.4510i −1.73463 + 0.631354i
765765 2.94385 8.08815i 0.106435 0.292428i
766766 −0.962417 + 1.14696i −0.0347735 + 0.0414415i
767767 27.7250 + 16.0070i 1.00109 + 0.577981i
768768 −10.7039 + 6.17990i −0.386244 + 0.222998i
769769 9.83110 + 1.73349i 0.354519 + 0.0625112i 0.348071 0.937468i 0.386837π-0.386837\pi
0.00644716 + 0.999979i 0.497948π0.497948\pi
770770 −5.25733 2.89551i −0.189461 0.104347i
771771 −1.97002 3.41218i −0.0709487 0.122887i
772772 9.76345 16.9108i 0.351394 0.608632i
773773 −2.64944 + 3.15748i −0.0952937 + 0.113567i −0.811584 0.584236i 0.801394π-0.801394\pi
0.716290 + 0.697803i 0.245839π0.245839\pi
774774 0.156981 0.431300i 0.00564255 0.0155028i
775775 0.189512 + 0.520680i 0.00680747 + 0.0187034i
776776 −3.05727 3.64351i −0.109749 0.130794i
777777 −0.812989 + 0.143352i −0.0291658 + 0.00514272i
778778 2.96311 0.106232
779779 1.58096 11.2174i 0.0566438 0.401905i
780780 15.5992i 0.558541i
781781 21.7677 + 3.38696i 0.778909 + 0.121195i
782782 1.11345 + 1.32696i 0.0398170 + 0.0474520i
783783 −0.450439 1.23757i −0.0160974 0.0442271i
784784 24.8469 + 9.04354i 0.887390 + 0.322984i
785785 −26.6888 22.3946i −0.952565 0.799297i
786786 1.85263 3.20885i 0.0660811 0.114456i
787787 −18.7340 32.4482i −0.667794 1.15665i −0.978520 0.206154i 0.933905π-0.933905\pi
0.310725 0.950500i 0.399428π-0.399428\pi
788788 13.6517 + 2.40716i 0.486320 + 0.0857514i
789789 3.25804 18.4773i 0.115989 0.657808i
790790 −3.81716 6.61152i −0.135809 0.235227i
791791 35.0367 60.6853i 1.24576 2.15772i
792792 1.47284 + 2.43617i 0.0523351 + 0.0865657i
793793 −18.1161 + 49.7735i −0.643321 + 1.76751i
794794 −5.15957 + 1.87793i −0.183106 + 0.0666452i
795795 −3.84960 + 3.23020i −0.136531 + 0.114563i
796796 1.84973 + 10.4904i 0.0655621 + 0.371821i
797797 17.2739i 0.611873i 0.952052 + 0.305937i 0.0989695π0.0989695\pi
−0.952052 + 0.305937i 0.901030π0.901030\pi
798798 −1.67034 + 3.13850i −0.0591294 + 0.111102i
799799 4.54981i 0.160961i
800800 0.0339448 + 0.192510i 0.00120013 + 0.00680627i
801801 −7.29087 8.68892i −0.257610 0.307008i
802802 1.13800 + 3.12664i 0.0401843 + 0.110405i
803803 11.0825 13.7622i 0.391094 0.485658i
804804 16.6314 + 13.9554i 0.586545 + 0.492170i
805805 14.8411 + 8.56851i 0.523080 + 0.302000i
806806 −4.84442 + 2.79693i −0.170637 + 0.0985176i
807807 −4.31192 + 24.4541i −0.151787 + 0.860826i
808808 −4.85149 0.855449i −0.170675 0.0300946i
809809 35.3102 20.3863i 1.24144 0.716745i 0.272052 0.962283i 0.412298π-0.412298\pi
0.969387 + 0.245537i 0.0789644π0.0789644\pi
810810 0.240887 0.417229i 0.00846392 0.0146599i
811811 38.8293 + 32.5817i 1.36348 + 1.14410i 0.974890 + 0.222688i 0.0714832π0.0714832\pi
0.388593 + 0.921410i 0.372961π0.372961\pi
812812 3.30412 9.07800i 0.115952 0.318575i
813813 −23.7729 + 8.65263i −0.833752 + 0.303461i
814814 −0.0571244 0.147612i −0.00200221 0.00517380i
815815 −2.01008 11.3998i −0.0704102 0.399316i
816816 −14.4288 −0.505109
817817 −3.44809 8.54391i −0.120633 0.298913i
818818 −1.44770 −0.0506176
819819 −13.3181 + 2.34834i −0.465372 + 0.0820576i
820820 −8.62589 + 7.23798i −0.301229 + 0.252761i
821821 14.8021 + 40.6685i 0.516597 + 1.41934i 0.874246 + 0.485483i 0.161356π0.161356\pi
−0.357649 + 0.933856i 0.616421π0.616421\pi
822822 1.17324 3.22345i 0.0409214 0.112431i
823823 −29.1376 24.4494i −1.01567 0.852252i −0.0265964 0.999646i 0.508467π-0.508467\pi
−0.989078 + 0.147394i 0.952911π0.952911\pi
824824 −6.82386 3.93976i −0.237720 0.137248i
825825 −0.251984 + 0.0496927i −0.00877294 + 0.00173008i
826826 1.25943 7.14258i 0.0438212 0.248522i
827827 7.49007 42.4783i 0.260455 1.47712i −0.521216 0.853425i 0.674521π-0.674521\pi
0.781671 0.623691i 0.214368π-0.214368\pi
828828 −2.00783 3.47766i −0.0697768 0.120857i
829829 −21.7386 12.5508i −0.755012 0.435907i 0.0724898 0.997369i 0.476906π-0.476906\pi
−0.827502 + 0.561463i 0.810239π0.810239\pi
830830 −5.38205 + 6.41407i −0.186814 + 0.222636i
831831 11.9440 + 4.34726i 0.414332 + 0.150805i
832832 23.3117 8.48477i 0.808188 0.294156i
833833 17.7280 + 21.1274i 0.614238 + 0.732021i
834834 −0.249269 1.41367i −0.00863147 0.0489515i
835835 46.5090 1.60951
836836 27.0176 + 8.19126i 0.934422 + 0.283301i
837837 −7.15524 −0.247321
838838 0.133513 + 0.757192i 0.00461214 + 0.0261568i
839839 4.27855 + 5.09898i 0.147712 + 0.176036i 0.834827 0.550512i 0.185568π-0.185568\pi
−0.687115 + 0.726549i 0.741123π0.741123\pi
840840 6.72190 2.44657i 0.231928 0.0844148i
841841 25.6212 + 9.32536i 0.883490 + 0.321564i
842842 −2.32085 + 2.76588i −0.0799818 + 0.0953185i
843843 −23.0271 13.2947i −0.793097 0.457895i
844844 19.2724 + 33.3808i 0.663384 + 1.14901i
845845 −0.0145871 + 0.0827277i −0.000501812 + 0.00284592i
846846 0.0442227 0.250799i 0.00152041 0.00862265i
847847 −40.9471 5.52762i −1.40696 0.189931i
848848 7.29558 + 4.21210i 0.250531 + 0.144644i
849849 −2.84596 2.38804i −0.0976731 0.0819575i
850850 −0.0223115 + 0.0613003i −0.000765278 + 0.00210258i
851851 0.154568 + 0.424673i 0.00529853 + 0.0145576i
852852 −9.93648 + 8.33770i −0.340418 + 0.285645i
853853 33.5728 5.91979i 1.14951 0.202690i 0.433749 0.901034i 0.357190π-0.357190\pi
0.715762 + 0.698344i 0.246079π0.246079\pi
854854 11.9998 0.410626
855855 −2.00703 9.46047i −0.0686390 0.323541i
856856 1.80379 0.0616524
857857 −5.51703 31.2886i −0.188458 1.06880i −0.921431 0.388541i 0.872979π-0.872979\pi
0.732973 0.680257i 0.238132π-0.238132\pi
858858 −0.935792 2.41813i −0.0319474 0.0825536i
859859 46.0997 16.7789i 1.57290 0.572489i 0.599256 0.800558i 0.295463π-0.295463\pi
0.973645 + 0.228068i 0.0732410π0.0732410\pi
860860 −3.13228 + 8.60588i −0.106810 + 0.293458i
861861 −7.47811 6.27488i −0.254853 0.213847i
862862 1.33633 2.31459i 0.0455156 0.0788354i
863863 41.9223 24.2038i 1.42705 0.823908i 0.430163 0.902751i 0.358456π-0.358456\pi
0.996887 + 0.0788435i 0.0251227π0.0251227\pi
864864 −2.48596 0.438341i −0.0845739 0.0149127i
865865 −4.25376 + 24.1243i −0.144632 + 0.820250i
866866 0.878486 0.507194i 0.0298522 0.0172352i
867867 1.68878 + 0.975017i 0.0573539 + 0.0331133i
868868 −40.2067 33.7375i −1.36471 1.14512i
869869 −40.9336 32.9633i −1.38858 1.11820i
870870 −0.217010 0.596230i −0.00735733 0.0202141i
871871 −25.7284 30.6619i −0.871773 1.03894i
872872 1.21235 + 6.87559i 0.0410554 + 0.232837i
873873 5.54124i 0.187543i
874874 1.85082 + 0.602166i 0.0626050 + 0.0203686i
875875 42.3148i 1.43050i
876876 1.80665 + 10.2460i 0.0610410 + 0.346181i
877877 10.7478 9.01846i 0.362927 0.304532i −0.443029 0.896507i 0.646096π-0.646096\pi
0.805956 + 0.591975i 0.201652π0.201652\pi
878878 2.72975 0.993548i 0.0921246 0.0335306i
879879 9.08268 24.9545i 0.306351 0.841693i
880880 −14.1597 23.4211i −0.477325 0.789526i
881881 25.4224 44.0329i 0.856503 1.48351i −0.0187397 0.999824i 0.505965π-0.505965\pi
0.875243 0.483683i 0.160701π-0.160701\pi
882882 0.771868 + 1.33691i 0.0259901 + 0.0450162i
883883 8.06045 45.7131i 0.271256 1.53837i −0.479354 0.877621i 0.659129π-0.659129\pi
0.750610 0.660745i 0.229760π-0.229760\pi
884884 26.8612 + 4.73636i 0.903441 + 0.159301i
885885 9.86435 + 17.0856i 0.331587 + 0.574325i
886886 0.810978 1.40466i 0.0272453 0.0471903i
887887 20.2376 + 16.9814i 0.679512 + 0.570179i 0.915864 0.401489i 0.131507π-0.131507\pi
−0.236351 + 0.971668i 0.575952π0.575952\pi
888888 0.177266 + 0.0645196i 0.00594866 + 0.00216514i
889889 14.7829 + 40.6156i 0.495802 + 1.36220i
890890 −3.51256 4.18611i −0.117741 0.140319i
891891 0.509917 3.27719i 0.0170829 0.109790i
892892 19.5497i 0.654571i
893893 −2.70733 4.33640i −0.0905974 0.145112i
894894 0.879258 0.0294068
895895 4.93691 0.870511i 0.165023 0.0290980i
896896 −15.8022 18.8324i −0.527916 0.629146i
897897 2.53208 + 6.95684i 0.0845438 + 0.232282i
898898 −1.84006 + 5.05551i −0.0614034 + 0.168705i
899899 −6.05725 + 7.21875i −0.202021 + 0.240759i
900900 0.0756135 0.130966i 0.00252045 0.00436555i
901901 4.39343 + 7.60965i 0.146366 + 0.253514i
902902 0.902948 1.63947i 0.0300649 0.0545884i
903903 −7.81896 1.37869i −0.260199 0.0458800i
904904 −13.8673 + 8.00626i −0.461218 + 0.266284i
905905 46.4875 + 26.8396i 1.54530 + 0.892178i
906906 2.51392 2.99597i 0.0835193 0.0995345i
907907 −9.39753 + 25.8195i −0.312040 + 0.857323i 0.680205 + 0.733022i 0.261891π0.261891\pi
−0.992245 + 0.124300i 0.960331π0.960331\pi
908908 −8.12143 + 2.95596i −0.269519 + 0.0980969i
909909 3.68920 + 4.39662i 0.122363 + 0.145827i
910910 −6.41632 + 1.13137i −0.212699 + 0.0375046i
911911 58.5420i 1.93958i 0.243935 + 0.969791i 0.421561π0.421561\pi
−0.243935 + 0.969791i 0.578439π0.578439\pi
912912 −13.7520 + 8.58575i −0.455374 + 0.284303i
913913 −18.6177 + 54.5516i −0.616156 + 1.80539i
914914 −6.35561 + 1.12067i −0.210225 + 0.0370683i
915915 −25.0048 + 20.9815i −0.826634 + 0.693628i
916916 −11.6122 + 4.22651i −0.383679 + 0.139648i
917917 −60.2292 21.9217i −1.98894 0.723917i
918918 −0.645313 0.541482i −0.0212985 0.0178716i
919919 −0.677193 0.390978i −0.0223385 0.0128972i 0.488789 0.872402i 0.337439π-0.337439\pi
−0.511128 + 0.859505i 0.670772π0.670772\pi
920920 −1.95800 3.39135i −0.0645533 0.111810i
921921 −3.28588 0.579389i −0.108273 0.0190915i
922922 −3.64883 0.643388i −0.120168 0.0211888i
923923 20.7100 11.9569i 0.681676 0.393566i
924924 18.3175 16.0109i 0.602602 0.526720i
925925 −0.0109398 + 0.0130375i −0.000359698 + 0.000428672i
926926 2.00135 + 0.728432i 0.0657684 + 0.0239377i
927927 3.13973 + 8.62634i 0.103122 + 0.283326i
928928 −2.54671 + 2.13695i −0.0835999 + 0.0701487i
929929 −4.48938 25.4605i −0.147292 0.835332i −0.965499 0.260409i 0.916143π-0.916143\pi
0.818207 0.574924i 0.194968π-0.194968\pi
930930 −3.44722 −0.113039
931931 29.4681 + 9.58747i 0.965778 + 0.314217i
932932 51.4206i 1.68434i
933933 25.8566 4.55921i 0.846506 0.149262i
934934 3.35171 2.81242i 0.109671 0.0920252i
935935 −0.575894 28.5411i −0.0188338 0.933395i
936936 2.90391 + 1.05694i 0.0949172 + 0.0345470i
937937 10.8583 12.9405i 0.354727 0.422747i −0.558942 0.829207i 0.688793π-0.688793\pi
0.913669 + 0.406460i 0.133237π0.133237\pi
938938 −4.53396 + 7.85305i −0.148039 + 0.256411i
939939 10.1489 5.85948i 0.331198 0.191217i
940940 −0.882389 + 5.00428i −0.0287804 + 0.163222i
941941 −6.95344 + 39.4349i −0.226676 + 1.28554i 0.632780 + 0.774331i 0.281914π0.281914\pi
−0.859456 + 0.511210i 0.829197π0.829197\pi
942942 −2.95297 + 1.70490i −0.0962130 + 0.0555486i
943943 −2.67204 + 4.62812i −0.0870137 + 0.150712i
944944 21.2585 25.3349i 0.691906 0.824582i
945945 −7.83129 2.85036i −0.254752 0.0927221i
946946 −0.0307096 1.52196i −0.000998454 0.0494831i
947947 −38.8908 + 32.6332i −1.26378 + 1.06044i −0.268511 + 0.963277i 0.586532π0.586532\pi
−0.995269 + 0.0971607i 0.969024π0.969024\pi
948948 30.4752 5.37360i 0.989788 0.174526i
949949 19.1811i 0.622644i
950950 0.0152114 + 0.0717012i 0.000493521 + 0.00232629i
951951 −18.8636 −0.611694
952952 −2.17195 12.3177i −0.0703932 0.399219i
953953 −16.4119 + 13.7712i −0.531634 + 0.446094i −0.868665 0.495399i 0.835022π-0.835022\pi
0.337031 + 0.941494i 0.390577π0.390577\pi
954954 0.168216 + 0.462169i 0.00544619 + 0.0149633i
955955 54.4730 + 19.8265i 1.76270 + 0.641572i
956956 9.30732 11.0920i 0.301020 0.358742i
957957 −2.87461 3.28874i −0.0929230 0.106310i
958958 −2.73787 + 1.58071i −0.0884566 + 0.0510704i
959959 −58.4373 10.3041i −1.88704 0.332736i
960960 15.0556 + 2.65470i 0.485916 + 0.0856801i
961961 10.0987 + 17.4915i 0.325766 + 0.564243i
962962 −0.148799 0.0859089i −0.00479746 0.00276981i
963963 −1.60984 1.35081i −0.0518763 0.0435294i
964964 11.2573 + 4.09732i 0.362573 + 0.131966i
965965 −20.8471 + 7.58773i −0.671092 + 0.244258i
966966 1.28482 1.07809i 0.0413384 0.0346871i
967967 −12.9619 + 2.28553i −0.416826 + 0.0734977i −0.378128 0.925753i 0.623432π-0.623432\pi
−0.0386979 + 0.999251i 0.512321π0.512321\pi
968968 7.47172 + 5.77232i 0.240150 + 0.185530i
969969 −16.9000 + 0.583564i −0.542905 + 0.0187468i
970970 2.66963i 0.0857167i
971971 −4.78251 + 0.843285i −0.153478 + 0.0270623i −0.249859 0.968282i 0.580384π-0.580384\pi
0.0963812 + 0.995344i 0.469273π0.469273\pi
972972 1.25527 + 1.49597i 0.0402627 + 0.0479832i
973973 −23.3339 + 8.49283i −0.748049 + 0.272268i
974974 0.639983 1.75834i 0.0205064 0.0563408i
975975 −0.179212 + 0.213576i −0.00573937 + 0.00683991i
976976 47.3879 + 27.3594i 1.51685 + 0.875754i
977977 14.4169 8.32362i 0.461238 0.266296i −0.251327 0.967902i 0.580867π-0.580867\pi
0.712565 + 0.701606i 0.247533π0.247533\pi
978978 −1.11570 0.196729i −0.0356762 0.00629068i
979979 −32.9519 18.1485i −1.05315 0.580028i
980980 −15.4013 26.6759i −0.491977 0.852130i
981981 4.06696 7.04418i 0.129848 0.224903i
982982 2.48397 2.96028i 0.0792665 0.0944662i
983983 2.03229 5.58368i 0.0648201 0.178092i −0.903054 0.429527i 0.858680π-0.858680\pi
0.967874 + 0.251435i 0.0809025π0.0809025\pi
984984 0.762951 + 2.09619i 0.0243220 + 0.0668241i
985985 −10.1235 12.0647i −0.322560 0.384412i
986986 −1.09258 + 0.192651i −0.0347947 + 0.00613525i
987987 −4.40533 −0.140223
988988 28.4196 11.4694i 0.904148 0.364889i
989989 4.34644i 0.138209i
990990 0.245665 1.57887i 0.00780775 0.0501797i
991991 23.5068 + 28.0143i 0.746719 + 0.889905i 0.996931 0.0782860i 0.0249447π-0.0249447\pi
−0.250212 + 0.968191i 0.580500π0.580500\pi
992992 6.17757 + 16.9727i 0.196138 + 0.538885i
993993 1.84239 + 0.670574i 0.0584664 + 0.0212800i
994994 −4.15016 3.48240i −0.131635 0.110455i
995995 6.05113 10.4809i 0.191834 0.332265i
996996 −16.9697 29.3924i −0.537706 0.931333i
997997 −15.6075 2.75202i −0.494294 0.0871573i −0.0790558 0.996870i 0.525191π-0.525191\pi
−0.415238 + 0.909713i 0.636302π0.636302\pi
998998 0.569768 3.23132i 0.0180357 0.102286i
999999 −0.109888 0.190332i −0.00347671 0.00602184i
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 627.2.be.a.10.18 240
11.10 odd 2 inner 627.2.be.a.10.23 yes 240
19.2 odd 18 inner 627.2.be.a.439.23 yes 240
209.21 even 18 inner 627.2.be.a.439.18 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
627.2.be.a.10.18 240 1.1 even 1 trivial
627.2.be.a.10.23 yes 240 11.10 odd 2 inner
627.2.be.a.439.18 yes 240 209.21 even 18 inner
627.2.be.a.439.23 yes 240 19.2 odd 18 inner