Properties

Label 224.2.bd.a.109.15
Level 224224
Weight 22
Character 224.109
Analytic conductor 1.7891.789
Analytic rank 00
Dimension 240240
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [224,2,Mod(37,224)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(224, base_ring=CyclotomicField(24))
 
chi = DirichletCharacter(H, H._module([0, 3, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("224.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 224=257 224 = 2^{5} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 224.bd (of order 2424, degree 88, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 1.788649005281.78864900528
Analytic rank: 00
Dimension: 240240
Relative dimension: 3030 over Q(ζ24)\Q(\zeta_{24})
Twist minimal: yes
Sato-Tate group: SU(2)[C24]\mathrm{SU}(2)[C_{24}]

Embedding invariants

Embedding label 109.15
Character χ\chi == 224.109
Dual form 224.2.bd.a.37.15

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.07139991.41241i)q2+(0.118403+0.154306i)q3+(1.989800.201692i)q4+(2.39583+1.83839i)q5+(0.2263980.156217i)q6+(1.47323+2.19764i)q7+(0.426943+2.79602i)q8+(0.7666662.86124i)q9+(2.767623.25263i)q10+(5.43183+0.715114i)q11+(0.2044770.330920i)q12+(5.506522.28087i)q13+(3.209151.92389i)q14+0.587363iq15+(3.91864+0.802655i)q16+(3.702492.13763i)q17+(3.986501.28714i)q18+(0.183696+1.39531i)q19+(4.396454.14125i)q20+(0.164674+0.487536i)q21+(1.397877.62091i)q22+(0.326660+1.21911i)q23+(0.481995+0.265178i)q24+(1.06625+3.97929i)q25+(3.61470+7.61461i)q26+(1.071360.443773i)q27+(2.488194.67000i)q28+(0.4972181.20039i)q29+(0.829598+0.0419377i)q30+(0.251275+0.435222i)q31+(1.413475.47742i)q32+(0.532801+0.922838i)q33+(3.28357+5.07681i)q34+(0.510497+7.97352i)q35+(2.10260+5.53867i)q36+(5.39866+4.14254i)q37+(1.983860.159829i)q38+(0.3000371.11975i)q39+(6.16304+5.91390i)q40+(3.022063.02206i)q41+(0.676843+0.267397i)q42+(3.498818.44689i)q43+(10.66402.51849i)q44+(7.096865.44561i)q45+(1.69856+0.548423i)q46+(7.99998+4.61879i)q47+(0.340126+0.699708i)q48+(2.65920+6.47523i)q49+(5.696521.22186i)q50+(0.1085370.824421i)q51+(10.4969+5.64911i)q52+(7.097300.934377i)q53+(0.5502951.54489i)q54+(11.6991+11.6991i)q55+(6.77361+3.18091i)q56+(0.193554+0.193554i)q57+(1.659940.787983i)q58+(0.009683330.0735522i)q59+(0.1184661.16874i)q60+(9.086571.19627i)q61+(0.596771+0.385979i)q62+(7.417432.53040i)q63+(7.635442.38748i)q64+(8.9995615.5877i)q65+(1.341470.686643i)q66+(0.469449+0.611798i)q67+(6.93609+5.00024i)q68+(0.226794+0.0939414i)q69+(11.2254+1.29034i)q70+(7.84105+7.84105i)q71+(7.67275+3.36520i)q72+(6.92569+1.85573i)q73+(6.236437.32935i)q74+(0.487783+0.635691i)q75+(0.08409622.81344i)q76+(6.43076+12.9907i)q77+(1.60297+0.343825i)q78+(0.877666+0.506720i)q79+(7.91281+9.12700i)q80+(7.500614.33048i)q81+(4.48416+4.05261i)q82+(6.186022.56233i)q83+(0.4260010.936888i)q84+(4.9407511.9280i)q85+(12.1803+4.33865i)q86+(0.2441000.0654064i)q87+(4.31856+14.8822i)q88+(13.99373.74960i)q89+(7.1847210.4125i)q90+(3.0998215.4616i)q91+(0.8958752.35991i)q92+(0.0969094+0.0127584i)q93+(5.95243+11.6290i)q94+(2.12501+3.68062i)q95+(1.012560.430438i)q96+0.451869q97+(8.95582+4.21821i)q98+(6.2105114.9935i)q99+O(q100)q+(0.0713999 - 1.41241i) q^{2} +(0.118403 + 0.154306i) q^{3} +(-1.98980 - 0.201692i) q^{4} +(2.39583 + 1.83839i) q^{5} +(0.226398 - 0.156217i) q^{6} +(1.47323 + 2.19764i) q^{7} +(-0.426943 + 2.79602i) q^{8} +(0.766666 - 2.86124i) q^{9} +(2.76762 - 3.25263i) q^{10} +(5.43183 + 0.715114i) q^{11} +(-0.204477 - 0.330920i) q^{12} +(-5.50652 - 2.28087i) q^{13} +(3.20915 - 1.92389i) q^{14} +0.587363i q^{15} +(3.91864 + 0.802655i) q^{16} +(-3.70249 - 2.13763i) q^{17} +(-3.98650 - 1.28714i) q^{18} +(0.183696 + 1.39531i) q^{19} +(-4.39645 - 4.14125i) q^{20} +(-0.164674 + 0.487536i) q^{21} +(1.39787 - 7.62091i) q^{22} +(-0.326660 + 1.21911i) q^{23} +(-0.481995 + 0.265178i) q^{24} +(1.06625 + 3.97929i) q^{25} +(-3.61470 + 7.61461i) q^{26} +(1.07136 - 0.443773i) q^{27} +(-2.48819 - 4.67000i) q^{28} +(0.497218 - 1.20039i) q^{29} +(0.829598 + 0.0419377i) q^{30} +(-0.251275 + 0.435222i) q^{31} +(1.41347 - 5.47742i) q^{32} +(0.532801 + 0.922838i) q^{33} +(-3.28357 + 5.07681i) q^{34} +(-0.510497 + 7.97352i) q^{35} +(-2.10260 + 5.53867i) q^{36} +(5.39866 + 4.14254i) q^{37} +(1.98386 - 0.159829i) q^{38} +(-0.300037 - 1.11975i) q^{39} +(-6.16304 + 5.91390i) q^{40} +(-3.02206 - 3.02206i) q^{41} +(0.676843 + 0.267397i) q^{42} +(-3.49881 - 8.44689i) q^{43} +(-10.6640 - 2.51849i) q^{44} +(7.09686 - 5.44561i) q^{45} +(1.69856 + 0.548423i) q^{46} +(-7.99998 + 4.61879i) q^{47} +(0.340126 + 0.699708i) q^{48} +(-2.65920 + 6.47523i) q^{49} +(5.69652 - 1.22186i) q^{50} +(-0.108537 - 0.824421i) q^{51} +(10.4969 + 5.64911i) q^{52} +(-7.09730 - 0.934377i) q^{53} +(-0.550295 - 1.54489i) q^{54} +(11.6991 + 11.6991i) q^{55} +(-6.77361 + 3.18091i) q^{56} +(-0.193554 + 0.193554i) q^{57} +(-1.65994 - 0.787983i) q^{58} +(0.00968333 - 0.0735522i) q^{59} +(0.118466 - 1.16874i) q^{60} +(9.08657 - 1.19627i) q^{61} +(0.596771 + 0.385979i) q^{62} +(7.41743 - 2.53040i) q^{63} +(-7.63544 - 2.38748i) q^{64} +(-8.99956 - 15.5877i) q^{65} +(1.34147 - 0.686643i) q^{66} +(0.469449 + 0.611798i) q^{67} +(6.93609 + 5.00024i) q^{68} +(-0.226794 + 0.0939414i) q^{69} +(11.2254 + 1.29034i) q^{70} +(-7.84105 + 7.84105i) q^{71} +(7.67275 + 3.36520i) q^{72} +(-6.92569 + 1.85573i) q^{73} +(6.23643 - 7.32935i) q^{74} +(-0.487783 + 0.635691i) q^{75} +(-0.0840962 - 2.81344i) q^{76} +(6.43076 + 12.9907i) q^{77} +(-1.60297 + 0.343825i) q^{78} +(-0.877666 + 0.506720i) q^{79} +(7.91281 + 9.12700i) q^{80} +(-7.50061 - 4.33048i) q^{81} +(-4.48416 + 4.05261i) q^{82} +(-6.18602 - 2.56233i) q^{83} +(0.426001 - 0.936888i) q^{84} +(-4.94075 - 11.9280i) q^{85} +(-12.1803 + 4.33865i) q^{86} +(0.244100 - 0.0654064i) q^{87} +(-4.31856 + 14.8822i) q^{88} +(-13.9937 - 3.74960i) q^{89} +(-7.18472 - 10.4125i) q^{90} +(-3.09982 - 15.4616i) q^{91} +(0.895875 - 2.35991i) q^{92} +(-0.0969094 + 0.0127584i) q^{93} +(5.95243 + 11.6290i) q^{94} +(-2.12501 + 3.68062i) q^{95} +(1.01256 - 0.430438i) q^{96} +0.451869 q^{97} +(8.95582 + 4.21821i) q^{98} +(6.21051 - 14.9935i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 240q4q24q34q44q516q68q716q84q94q104q114q1216q13+24q1424q1624q184q1948q208q21++8q99+O(q100) 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21}+ \cdots + 8 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/224Z)×\left(\mathbb{Z}/224\mathbb{Z}\right)^\times.

nn 127127 129129 197197
χ(n)\chi(n) 11 e(23)e\left(\frac{2}{3}\right) e(78)e\left(\frac{7}{8}\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 0.0713999 1.41241i 0.0504874 0.998725i
33 0.118403 + 0.154306i 0.0683603 + 0.0890888i 0.826282 0.563257i 0.190452π-0.190452\pi
−0.757922 + 0.652346i 0.773785π0.773785\pi
44 −1.98980 0.201692i −0.994902 0.100846i
55 2.39583 + 1.83839i 1.07145 + 0.822151i 0.984731 0.174082i 0.0556958π-0.0556958\pi
0.0867170 + 0.996233i 0.472362π0.472362\pi
66 0.226398 0.156217i 0.0924265 0.0637752i
77 1.47323 + 2.19764i 0.556828 + 0.830628i
88 −0.426943 + 2.79602i −0.150947 + 0.988542i
99 0.766666 2.86124i 0.255555 0.953746i
1010 2.76762 3.25263i 0.875197 1.02857i
1111 5.43183 + 0.715114i 1.63776 + 0.215615i 0.892464 0.451120i 0.148975π-0.148975\pi
0.745295 + 0.666735i 0.232309π0.232309\pi
1212 −0.204477 0.330920i −0.0590275 0.0955285i
1313 −5.50652 2.28087i −1.52723 0.632601i −0.548209 0.836342i 0.684690π-0.684690\pi
−0.979025 + 0.203741i 0.934690π0.934690\pi
1414 3.20915 1.92389i 0.857681 0.514181i
1515 0.587363i 0.151657i
1616 3.91864 + 0.802655i 0.979660 + 0.200664i
1717 −3.70249 2.13763i −0.897986 0.518453i −0.0214399 0.999770i 0.506825π-0.506825\pi
−0.876546 + 0.481318i 0.840158π0.840158\pi
1818 −3.98650 1.28714i −0.939627 0.303382i
1919 0.183696 + 1.39531i 0.0421427 + 0.320105i 0.999512 + 0.0312385i 0.00994513π0.00994513\pi
−0.957369 + 0.288867i 0.906722π0.906722\pi
2020 −4.39645 4.14125i −0.983075 0.926011i
2121 −0.164674 + 0.487536i −0.0359348 + 0.106389i
2222 1.39787 7.62091i 0.298026 1.62478i
2323 −0.326660 + 1.21911i −0.0681133 + 0.254202i −0.991584 0.129467i 0.958673π-0.958673\pi
0.923470 + 0.383670i 0.125340π0.125340\pi
2424 −0.481995 + 0.265178i −0.0983868 + 0.0541293i
2525 1.06625 + 3.97929i 0.213250 + 0.795859i
2626 −3.61470 + 7.61461i −0.708900 + 1.49335i
2727 1.07136 0.443773i 0.206184 0.0854042i
2828 −2.48819 4.67000i −0.470224 0.882547i
2929 0.497218 1.20039i 0.0923310 0.222907i −0.870967 0.491342i 0.836507π-0.836507\pi
0.963298 + 0.268435i 0.0865065π0.0865065\pi
3030 0.829598 + 0.0419377i 0.151463 + 0.00765674i
3131 −0.251275 + 0.435222i −0.0451304 + 0.0781682i −0.887708 0.460406i 0.847704π-0.847704\pi
0.842578 + 0.538575i 0.181037π0.181037\pi
3232 1.41347 5.47742i 0.249868 0.968280i
3333 0.532801 + 0.922838i 0.0927487 + 0.160646i
3434 −3.28357 + 5.07681i −0.563128 + 0.870666i
3535 −0.510497 + 7.97352i −0.0862897 + 1.34777i
3636 −2.10260 + 5.53867i −0.350434 + 0.923112i
3737 5.39866 + 4.14254i 0.887535 + 0.681029i 0.948386 0.317118i 0.102715π-0.102715\pi
−0.0608517 + 0.998147i 0.519382π0.519382\pi
3838 1.98386 0.159829i 0.321825 0.0259276i
3939 −0.300037 1.11975i −0.0480444 0.179304i
4040 −6.16304 + 5.91390i −0.974463 + 0.935070i
4141 −3.02206 3.02206i −0.471966 0.471966i 0.430584 0.902550i 0.358308π-0.358308\pi
−0.902550 + 0.430584i 0.858308π0.858308\pi
4242 0.676843 + 0.267397i 0.104439 + 0.0412603i
4343 −3.49881 8.44689i −0.533564 1.28814i −0.929148 0.369708i 0.879458π-0.879458\pi
0.395584 0.918430i 0.370542π-0.370542\pi
4444 −10.6640 2.51849i −1.60767 0.379677i
4545 7.09686 5.44561i 1.05794 0.811784i
4646 1.69856 + 0.548423i 0.250439 + 0.0808605i
4747 −7.99998 + 4.61879i −1.16692 + 0.673720i −0.952952 0.303121i 0.901971π-0.901971\pi
−0.213965 + 0.976841i 0.568638π0.568638\pi
4848 0.340126 + 0.699708i 0.0490929 + 0.100994i
4949 −2.65920 + 6.47523i −0.379886 + 0.925033i
5050 5.69652 1.22186i 0.805610 0.172797i
5151 −0.108537 0.824421i −0.0151982 0.115442i
5252 10.4969 + 5.64911i 1.45565 + 0.783391i
5353 −7.09730 0.934377i −0.974889 0.128347i −0.373783 0.927516i 0.621940π-0.621940\pi
−0.601106 + 0.799169i 0.705273π0.705273\pi
5454 −0.550295 1.54489i −0.0748856 0.210233i
5555 11.6991 + 11.6991i 1.57751 + 1.57751i
5656 −6.77361 + 3.18091i −0.905162 + 0.425066i
5757 −0.193554 + 0.193554i −0.0256369 + 0.0256369i
5858 −1.65994 0.787983i −0.217961 0.103467i
5959 0.00968333 0.0735522i 0.00126066 0.00957568i −0.990803 0.135313i 0.956796π-0.956796\pi
0.992064 + 0.125737i 0.0401295π0.0401295\pi
6060 0.118466 1.16874i 0.0152939 0.150883i
6161 9.08657 1.19627i 1.16342 0.153167i 0.476010 0.879440i 0.342083π-0.342083\pi
0.687406 + 0.726273i 0.258749π0.258749\pi
6262 0.596771 + 0.385979i 0.0757900 + 0.0490194i
6363 7.41743 2.53040i 0.934508 0.318800i
6464 −7.63544 2.38748i −0.954430 0.298435i
6565 −8.99956 15.5877i −1.11626 1.93342i
6666 1.34147 0.686643i 0.165123 0.0845199i
6767 0.469449 + 0.611798i 0.0573523 + 0.0747430i 0.821149 0.570714i 0.193334π-0.193334\pi
−0.763796 + 0.645457i 0.776667π0.776667\pi
6868 6.93609 + 5.00024i 0.841124 + 0.606368i
6969 −0.226794 + 0.0939414i −0.0273028 + 0.0113092i
7070 11.2254 + 1.29034i 1.34170 + 0.154225i
7171 −7.84105 + 7.84105i −0.930561 + 0.930561i −0.997741 0.0671798i 0.978600π-0.978600\pi
0.0671798 + 0.997741i 0.478600π0.478600\pi
7272 7.67275 + 3.36520i 0.904242 + 0.396592i
7373 −6.92569 + 1.85573i −0.810591 + 0.217197i −0.640229 0.768184i 0.721160π-0.721160\pi
−0.170362 + 0.985382i 0.554494π0.554494\pi
7474 6.23643 7.32935i 0.724970 0.852019i
7575 −0.487783 + 0.635691i −0.0563243 + 0.0734033i
7676 −0.0840962 2.81344i −0.00964650 0.322723i
7777 6.43076 + 12.9907i 0.732854 + 1.48043i
7878 −1.60297 + 0.343825i −0.181501 + 0.0389305i
7979 −0.877666 + 0.506720i −0.0987451 + 0.0570105i −0.548559 0.836112i 0.684824π-0.684824\pi
0.449814 + 0.893122i 0.351490π0.351490\pi
8080 7.91281 + 9.12700i 0.884679 + 1.02043i
8181 −7.50061 4.33048i −0.833402 0.481165i
8282 −4.48416 + 4.05261i −0.495193 + 0.447536i
8383 −6.18602 2.56233i −0.679004 0.281253i 0.0164063 0.999865i 0.494777π-0.494777\pi
−0.695411 + 0.718613i 0.744777π0.744777\pi
8484 0.426001 0.936888i 0.0464805 0.102223i
8585 −4.94075 11.9280i −0.535899 1.29378i
8686 −12.1803 + 4.33865i −1.31343 + 0.467849i
8787 0.244100 0.0654064i 0.0261703 0.00701231i
8888 −4.31856 + 14.8822i −0.460360 + 1.58645i
8989 −13.9937 3.74960i −1.48333 0.397456i −0.575849 0.817556i 0.695328π-0.695328\pi
−0.907478 + 0.420100i 0.861995π0.861995\pi
9090 −7.18472 10.4125i −0.757336 1.09757i
9191 −3.09982 15.4616i −0.324950 1.62081i
9292 0.895875 2.35991i 0.0934014 0.246038i
9393 −0.0969094 + 0.0127584i −0.0100490 + 0.00132298i
9494 5.95243 + 11.6290i 0.613946 + 1.19944i
9595 −2.12501 + 3.68062i −0.218021 + 0.377624i
9696 1.01256 0.430438i 0.103344 0.0439314i
9797 0.451869 0.0458804 0.0229402 0.999737i 0.492697π-0.492697\pi
0.0229402 + 0.999737i 0.492697π0.492697\pi
9898 8.95582 + 4.21821i 0.904674 + 0.426104i
9999 6.21051 14.9935i 0.624180 1.50690i
100100 −1.31903 8.13307i −0.131903 0.813307i
101101 0.453155 3.44206i 0.0450906 0.342497i −0.953998 0.299813i 0.903076π-0.903076\pi
0.999089 0.0426844i 0.0135910π-0.0135910\pi
102102 −1.17217 + 0.0944353i −0.116062 + 0.00935049i
103103 8.80466 + 2.35920i 0.867549 + 0.232459i 0.665028 0.746819i 0.268420π-0.268420\pi
0.202522 + 0.979278i 0.435086π0.435086\pi
104104 8.72834 14.4225i 0.855884 1.41424i
105105 −1.29081 + 0.865320i −0.125970 + 0.0844466i
106106 −1.82647 + 9.95758i −0.177402 + 0.967166i
107107 7.67351 10.0003i 0.741826 0.966766i −0.258174 0.966098i 0.583121π-0.583121\pi
1.00000 0.000667722i 0.000212542π-0.000212542\pi
108108 −2.22131 + 0.666937i −0.213746 + 0.0641760i
109109 11.0120 8.44984i 1.05476 0.809348i 0.0725963 0.997361i 0.476872π-0.476872\pi
0.982166 + 0.188014i 0.0602049π0.0602049\pi
110110 17.3592 15.6886i 1.65514 1.49585i
111111 1.32354i 0.125625i
112112 4.00911 + 9.79424i 0.378825 + 0.925468i
113113 0.0684958i 0.00644354i −0.999995 0.00322177i 0.998974π-0.998974\pi
0.999995 0.00322177i 0.00102552π-0.00102552\pi
114114 0.259559 + 0.287198i 0.0243099 + 0.0268986i
115115 −3.02382 + 2.32026i −0.281973 + 0.216365i
116116 −1.23147 + 2.28826i −0.114340 + 0.212459i
117117 −10.7478 + 14.0068i −0.993633 + 1.29493i
118118 −0.103194 0.0189284i −0.00949982 0.00174250i
119119 −0.756872 11.2859i −0.0693823 1.03458i
120120 −1.64228 0.250771i −0.149919 0.0228921i
121121 18.3682 + 4.92175i 1.66984 + 0.447432i
122122 −1.04084 12.9194i −0.0942335 1.16967i
123123 0.108501 0.824145i 0.00978318 0.0743107i
124124 0.587770 0.815326i 0.0527833 0.0732184i
125125 1.01736 2.45613i 0.0909957 0.219683i
126126 −3.04436 10.6571i −0.271213 0.949412i
127127 −6.18288 −0.548642 −0.274321 0.961638i 0.588453π-0.588453\pi
−0.274321 + 0.961638i 0.588453π0.588453\pi
128128 −3.91728 + 10.6139i −0.346242 + 0.938145i
129129 0.889137 1.54003i 0.0782841 0.135592i
130130 −22.6588 + 11.5981i −1.98731 + 1.01722i
131131 8.65291 1.13918i 0.756009 0.0995304i 0.257337 0.966322i 0.417155π-0.417155\pi
0.498671 + 0.866791i 0.333822π0.333822\pi
132132 −0.874040 1.94373i −0.0760755 0.169180i
133133 −2.79575 + 2.45930i −0.242422 + 0.213248i
134134 0.897628 0.619372i 0.0775432 0.0535056i
135135 3.38263 + 0.906374i 0.291131 + 0.0780082i
136136 7.55762 9.43959i 0.648061 0.809438i
137137 11.1426 2.98566i 0.951980 0.255082i 0.250778 0.968045i 0.419314π-0.419314\pi
0.701202 + 0.712962i 0.252647π0.252647\pi
138138 0.116491 + 0.327034i 0.00991634 + 0.0278390i
139139 6.81777 + 16.4595i 0.578275 + 1.39608i 0.894359 + 0.447349i 0.147632π0.147632\pi
−0.316084 + 0.948731i 0.602368π0.602368\pi
140140 2.62398 15.7628i 0.221767 1.33220i
141141 −1.65993 0.687567i −0.139792 0.0579036i
142142 10.5149 + 11.6346i 0.882393 + 0.976356i
143143 −28.2794 16.3271i −2.36484 1.36534i
144144 5.30087 10.5968i 0.441739 0.883066i
145145 3.39803 1.96185i 0.282191 0.162923i
146146 2.12656 + 9.91441i 0.175996 + 0.820523i
147147 −1.31403 + 0.356358i −0.108379 + 0.0293919i
148148 −9.90676 9.33171i −0.814331 0.767062i
149149 7.52295 9.80409i 0.616304 0.803183i −0.376051 0.926599i 0.622718π-0.622718\pi
0.992355 + 0.123416i 0.0393850π0.0393850\pi
150150 0.863029 + 0.734338i 0.0704660 + 0.0599584i
151151 −6.48936 + 1.73882i −0.528097 + 0.141503i −0.513009 0.858383i 0.671469π-0.671469\pi
−0.0150875 + 0.999886i 0.504803π0.504803\pi
152152 −3.97973 0.0821008i −0.322799 0.00665925i
153153 −8.95485 + 8.95485i −0.723957 + 0.723957i
154154 18.8074 8.15534i 1.51554 0.657176i
155155 −1.40212 + 0.580777i −0.112621 + 0.0466491i
156156 0.371170 + 2.28861i 0.0297174 + 0.183235i
157157 0.632229 + 0.823937i 0.0504574 + 0.0657573i 0.817900 0.575360i 0.195138π-0.195138\pi
−0.767443 + 0.641117i 0.778471π0.778471\pi
158158 0.653032 + 1.27580i 0.0519524 + 0.101497i
159159 −0.696164 1.20579i −0.0552094 0.0956255i
160160 13.4560 10.5245i 1.06379 0.832032i
161161 −3.16041 + 1.07815i −0.249075 + 0.0849701i
162162 −6.65196 + 10.2847i −0.522627 + 0.808046i
163163 2.67408 0.352050i 0.209450 0.0275747i −0.0250708 0.999686i 0.507981π-0.507981\pi
0.234521 + 0.972111i 0.424648π0.424648\pi
164164 5.40378 + 6.62283i 0.421964 + 0.517156i
165165 −0.420032 + 3.19046i −0.0326994 + 0.248377i
166166 −4.06075 + 8.55425i −0.315175 + 0.663939i
167167 4.37579 4.37579i 0.338609 0.338609i −0.517235 0.855843i 0.673039π-0.673039\pi
0.855843 + 0.517235i 0.173039π0.173039\pi
168168 −1.29285 0.668582i −0.0997458 0.0515822i
169169 15.9270 + 15.9270i 1.22515 + 1.22515i
170170 −17.2000 + 6.12670i −1.31918 + 0.469897i
171171 4.13313 + 0.544137i 0.316069 + 0.0416112i
172172 5.25829 + 17.5133i 0.400941 + 1.33538i
173173 0.198608 + 1.50858i 0.0150999 + 0.114695i 0.997335 0.0729600i 0.0232446π-0.0232446\pi
−0.982235 + 0.187655i 0.939911π0.939911\pi
174174 −0.0749520 0.349439i −0.00568209 0.0264909i
175175 −7.17421 + 8.20563i −0.542319 + 0.620287i
176176 20.7114 + 7.16216i 1.56118 + 0.539868i
177177 0.0124961 0.00721463i 0.000939265 0.000542285i
178178 −6.29511 + 19.4971i −0.471839 + 1.46137i
179179 −17.8811 + 13.7206i −1.33650 + 1.02553i −0.340127 + 0.940379i 0.610470π0.610470\pi
−0.996368 + 0.0851496i 0.972863π0.972863\pi
180180 −15.2197 + 9.40432i −1.13441 + 0.700957i
181181 6.77001 + 16.3442i 0.503211 + 1.21486i 0.947726 + 0.319087i 0.103376π0.103376\pi
−0.444515 + 0.895772i 0.646624π0.646624\pi
182182 −22.0594 + 3.27427i −1.63515 + 0.242705i
183183 1.26047 + 1.26047i 0.0931769 + 0.0931769i
184184 −3.26919 1.43384i −0.241008 0.105704i
185185 5.31870 + 19.8496i 0.391038 + 1.45937i
186186 0.0111007 + 0.137787i 0.000813944 + 0.0101030i
187187 −18.5827 14.2590i −1.35890 1.04272i
188188 16.8500 7.57696i 1.22891 0.552607i
189189 2.55361 + 1.70069i 0.185748 + 0.123707i
190190 5.04682 + 3.26418i 0.366135 + 0.236808i
191191 10.0442 + 17.3971i 0.726772 + 1.25881i 0.958240 + 0.285964i 0.0923139π0.0923139\pi
−0.231468 + 0.972843i 0.574353π0.574353\pi
192192 −0.535658 1.46088i −0.0386578 0.105430i
193193 8.76441 15.1804i 0.630876 1.09271i −0.356497 0.934296i 0.616029π-0.616029\pi
0.987373 0.158413i 0.0506376π-0.0506376\pi
194194 0.0322634 0.638225i 0.00231638 0.0458219i
195195 1.33970 3.23433i 0.0959380 0.231615i
196196 6.59729 12.3481i 0.471235 0.882008i
197197 −8.32147 + 3.44687i −0.592880 + 0.245579i −0.658889 0.752240i 0.728973π-0.728973\pi
0.0660089 + 0.997819i 0.478973π0.478973\pi
198198 −20.7335 9.84232i −1.47347 0.699463i
199199 −2.15738 8.05144i −0.152932 0.570751i −0.999274 0.0381102i 0.987866π-0.987866\pi
0.846341 0.532641i 0.178800π-0.178800\pi
200200 −11.5814 + 1.28232i −0.818929 + 0.0906735i
201201 −0.0388199 + 0.144878i −0.00273815 + 0.0102189i
202202 −4.82924 0.885804i −0.339784 0.0623249i
203203 3.37053 0.675744i 0.236565 0.0474279i
204204 0.0496885 + 1.66233i 0.00347889 + 0.116386i
205205 −1.68463 12.7960i −0.117660 0.893715i
206206 3.96081 12.2673i 0.275963 0.854707i
207207 3.23773 + 1.86930i 0.225038 + 0.129926i
208208 −19.7473 13.3578i −1.36923 0.926194i
209209 7.71043i 0.533342i
210210 1.13002 + 1.88494i 0.0779790 + 0.130073i
211211 −0.534006 0.221193i −0.0367625 0.0152275i 0.364226 0.931310i 0.381333π-0.381333\pi
−0.400989 + 0.916083i 0.631333π0.631333\pi
212212 13.9338 + 3.29070i 0.956976 + 0.226006i
213213 −2.13833 0.281517i −0.146516 0.0192892i
214214 −13.5766 11.5522i −0.928080 0.789689i
215215 7.14607 26.6695i 0.487358 1.81884i
216216 0.783387 + 3.18502i 0.0533027 + 0.216713i
217217 −1.32664 + 0.0889691i −0.0900585 + 0.00603961i
218218 −11.1484 16.1568i −0.755064 1.09428i
219219 −1.10638 0.848953i −0.0747620 0.0573669i
220220 −20.9193 25.6385i −1.41038 1.72855i
221221 15.5122 + 20.2158i 1.04346 + 1.35986i
222222 1.86938 + 0.0945006i 0.125465 + 0.00634246i
223223 −5.07246 −0.339677 −0.169839 0.985472i 0.554325π-0.554325\pi
−0.169839 + 0.985472i 0.554325π0.554325\pi
224224 14.1197 4.96320i 0.943414 0.331617i
225225 12.2032 0.813544
226226 −0.0967441 0.00489059i −0.00643532 0.000325317i
227227 6.69399 + 8.72378i 0.444296 + 0.579018i 0.960791 0.277272i 0.0894304π-0.0894304\pi
−0.516496 + 0.856290i 0.672764π0.672764\pi
228228 0.424174 0.346097i 0.0280916 0.0229208i
229229 12.5005 + 9.59199i 0.826058 + 0.633856i 0.932786 0.360432i 0.117371π-0.117371\pi
−0.106728 + 0.994288i 0.534037π0.534037\pi
230230 3.06126 + 4.43654i 0.201853 + 0.292537i
231231 −1.24312 + 2.53045i −0.0817916 + 0.166492i
232232 3.14403 + 1.90273i 0.206416 + 0.124920i
233233 −3.50730 + 13.0894i −0.229771 + 0.857516i 0.750666 + 0.660682i 0.229733π0.229733\pi
−0.980437 + 0.196834i 0.936934π0.936934\pi
234234 19.0159 + 16.1804i 1.24311 + 1.05774i
235235 −27.6577 3.64121i −1.80419 0.237526i
236236 −0.0341028 + 0.144401i −0.00221990 + 0.00939973i
237237 −0.182109 0.0754319i −0.0118292 0.00489983i
238238 −15.9944 + 0.263198i −1.03676 + 0.0170606i
239239 5.02121i 0.324795i −0.986725 0.162397i 0.948077π-0.948077\pi
0.986725 0.162397i 0.0519227π-0.0519227\pi
240240 −0.471450 + 2.30167i −0.0304320 + 0.148572i
241241 −20.7477 11.9787i −1.33648 0.771615i −0.350194 0.936677i 0.613884π-0.613884\pi
−0.986283 + 0.165062i 0.947218π0.947218\pi
242242 8.26302 25.5920i 0.531167 1.64512i
243243 −0.673966 5.11928i −0.0432349 0.328402i
244244 −18.3218 + 0.547655i −1.17293 + 0.0350600i
245245 −18.2750 + 10.6249i −1.16755 + 0.678802i
246246 −1.15628 0.212091i −0.0737220 0.0135225i
247247 2.17100 8.10227i 0.138137 0.515535i
248248 −1.10961 0.888386i −0.0704602 0.0564126i
249249 −0.337062 1.25793i −0.0213604 0.0797182i
250250 −3.39642 1.61230i −0.214809 0.101971i
251251 15.8433 6.56249i 1.00002 0.414221i 0.178214 0.983992i 0.442968π-0.442968\pi
0.821803 + 0.569771i 0.192968π0.192968\pi
252252 −15.2696 + 3.53897i −0.961894 + 0.222934i
253253 −2.64617 + 6.38841i −0.166363 + 0.401636i
254254 −0.441457 + 8.73276i −0.0276995 + 0.547942i
255255 1.25557 2.17471i 0.0786267 0.136185i
256256 14.7115 + 6.29063i 0.919468 + 0.393164i
257257 1.21717 + 2.10820i 0.0759249 + 0.131506i 0.901488 0.432804i 0.142476π-0.142476\pi
−0.825563 + 0.564310i 0.809142π0.809142\pi
258258 −2.11167 1.36578i −0.131467 0.0850300i
259259 −1.15033 + 17.9672i −0.0714782 + 1.11643i
260260 14.7634 + 32.8316i 0.915590 + 2.03613i
261261 −3.05340 2.34296i −0.189001 0.145025i
262262 −0.991169 12.3028i −0.0612346 0.760069i
263263 7.18443 + 26.8126i 0.443011 + 1.65334i 0.721136 + 0.692794i 0.243620π0.243620\pi
−0.278125 + 0.960545i 0.589713π0.589713\pi
264264 −2.80775 + 1.09572i −0.172805 + 0.0674370i
265265 −15.2862 15.2862i −0.939023 0.939023i
266266 3.27392 + 4.12434i 0.200737 + 0.252879i
267267 −1.07831 2.60328i −0.0659917 0.159318i
268268 −0.810717 1.31204i −0.0495224 0.0801457i
269269 −7.77004 + 5.96216i −0.473747 + 0.363519i −0.817868 0.575406i 0.804844π-0.804844\pi
0.344120 + 0.938926i 0.388177π0.388177\pi
270270 1.52169 4.71295i 0.0926072 0.286821i
271271 23.9839 13.8471i 1.45692 0.841152i 0.458059 0.888922i 0.348545π-0.348545\pi
0.998858 + 0.0477701i 0.0152115π0.0152115\pi
272272 −12.7930 11.3484i −0.775687 0.688101i
273273 2.01879 2.30903i 0.122183 0.139749i
274274 −3.42139 15.9512i −0.206694 0.963644i
275275 2.94603 + 22.3773i 0.177652 + 1.34940i
276276 0.470224 0.141182i 0.0283041 0.00849817i
277277 1.11886 + 0.147300i 0.0672256 + 0.00885042i 0.164064 0.986450i 0.447540π-0.447540\pi
−0.0968384 + 0.995300i 0.530873π0.530873\pi
278278 23.7344 8.45427i 1.42350 0.507054i
279279 1.05263 + 1.05263i 0.0630192 + 0.0630192i
280280 −22.0762 4.83160i −1.31930 0.288743i
281281 6.68419 6.68419i 0.398746 0.398746i −0.479045 0.877790i 0.659017π-0.659017\pi
0.877790 + 0.479045i 0.159017π0.159017\pi
282282 −1.08965 + 2.29542i −0.0648875 + 0.136690i
283283 −2.81117 + 21.3530i −0.167107 + 1.26930i 0.678143 + 0.734930i 0.262785π0.262785\pi
−0.845250 + 0.534372i 0.820548π0.820548\pi
284284 17.1836 14.0207i 1.01966 0.831974i
285285 −0.819552 + 0.107896i −0.0485460 + 0.00639121i
286286 −25.0797 + 38.7763i −1.48300 + 2.29289i
287287 2.18920 11.0936i 0.129225 0.654832i
288288 −14.5885 8.24362i −0.859637 0.485760i
289289 0.638965 + 1.10672i 0.0375862 + 0.0651012i
290290 −2.52832 4.93949i −0.148468 0.290057i
291291 0.0535029 + 0.0697263i 0.00313639 + 0.00408743i
292292 14.1551 2.29569i 0.828362 0.134345i
293293 −11.8675 + 4.91570i −0.693309 + 0.287178i −0.701378 0.712789i 0.747432π-0.747432\pi
0.00806883 + 0.999967i 0.497432π0.497432\pi
294294 0.409503 + 1.88139i 0.0238827 + 0.109725i
295295 0.158417 0.158417i 0.00922339 0.00922339i
296296 −13.8875 + 13.3261i −0.807197 + 0.774565i
297297 6.13682 1.64435i 0.356094 0.0954151i
298298 −13.3103 11.3255i −0.771043 0.656068i
299299 4.57940 5.96799i 0.264834 0.345138i
300300 1.09881 1.16652i 0.0634396 0.0673490i
301301 13.4086 20.1333i 0.772860 1.16046i
302302 1.99259 + 9.28979i 0.114660 + 0.534567i
303303 0.584787 0.337627i 0.0335951 0.0193961i
304304 −0.400112 + 5.61515i −0.0229480 + 0.322051i
305305 23.9691 + 13.8386i 1.37247 + 0.792394i
306306 12.0085 + 13.2873i 0.686483 + 0.759584i
307307 18.8697 + 7.81608i 1.07695 + 0.446087i 0.849438 0.527688i 0.176941π-0.176941\pi
0.227512 + 0.973775i 0.426941π0.426941\pi
308308 −10.1758 27.1460i −0.579822 1.54679i
309309 0.678463 + 1.63795i 0.0385964 + 0.0931799i
310310 0.720184 + 2.02183i 0.0409037 + 0.114832i
311311 2.85627 0.765335i 0.161964 0.0433981i −0.176926 0.984224i 0.556615π-0.556615\pi
0.338890 + 0.940826i 0.389949π0.389949\pi
312312 3.25895 0.360838i 0.184502 0.0204284i
313313 26.9261 + 7.21483i 1.52195 + 0.407806i 0.920384 0.391015i 0.127876π-0.127876\pi
0.601569 + 0.798821i 0.294542π0.294542\pi
314314 1.20888 0.834137i 0.0682209 0.0470731i
315315 22.4228 + 7.57368i 1.26338 + 0.426729i
316316 1.84858 0.831256i 0.103991 0.0467618i
317317 −32.5474 + 4.28495i −1.82805 + 0.240667i −0.964590 0.263756i 0.915039π-0.915039\pi
−0.863457 + 0.504422i 0.831705π0.831705\pi
318318 −1.75278 + 0.897176i −0.0982910 + 0.0503111i
319319 3.55922 6.16475i 0.199278 0.345160i
320320 −13.9041 19.7569i −0.777263 1.10444i
321321 2.45168 0.136839
322322 1.29714 + 4.54077i 0.0722866 + 0.253047i
323323 2.30252 5.55878i 0.128116 0.309299i
324324 14.0513 + 10.1296i 0.780629 + 0.562757i
325325 3.20495 24.3440i 0.177779 1.35036i
326326 −0.306309 3.80204i −0.0169649 0.210575i
327327 2.60773 + 0.698739i 0.144208 + 0.0386403i
328328 9.73998 7.15948i 0.537800 0.395316i
329329 −21.9362 10.7765i −1.20938 0.594128i
330330 4.47624 + 0.821055i 0.246409 + 0.0451976i
331331 3.65442 4.76253i 0.200865 0.261772i −0.682050 0.731306i 0.738911π-0.738911\pi
0.882915 + 0.469534i 0.155578π0.155578\pi
332332 11.7922 + 6.34621i 0.647180 + 0.348294i
333333 15.9918 12.2709i 0.876343 0.672441i
334334 −5.86797 6.49284i −0.321081 0.355272i
335335 2.32879i 0.127236i
336336 −1.03662 + 1.77830i −0.0565523 + 0.0970143i
337337 8.26077i 0.449993i −0.974360 0.224996i 0.927763π-0.927763\pi
0.974360 0.224996i 0.0722370π-0.0722370\pi
338338 23.6326 21.3582i 1.28544 1.16173i
339339 0.0105693 0.00811014i 0.000574048 0.000440482i
340340 7.42533 + 24.7309i 0.402695 + 1.34122i
341341 −1.67612 + 2.18436i −0.0907670 + 0.118290i
342342 1.06365 5.79883i 0.0575156 0.313565i
343343 −18.1478 + 3.69554i −0.979890 + 0.199540i
344344 25.1114 6.17641i 1.35392 0.333010i
345345 −0.716062 0.191868i −0.0385515 0.0103298i
346346 2.14491 0.172804i 0.115311 0.00929000i
347347 3.23389 24.5639i 0.173605 1.31866i −0.653636 0.756809i 0.726757π-0.726757\pi
0.827240 0.561848i 0.189910π-0.189910\pi
348348 −0.498903 + 0.0809130i −0.0267440 + 0.00433739i
349349 7.17014 17.3102i 0.383809 0.926596i −0.607413 0.794386i 0.707793π-0.707793\pi
0.991222 0.132210i 0.0422073π-0.0422073\pi
350350 11.0775 + 10.7188i 0.592116 + 0.572944i
351351 −6.91168 −0.368918
352352 11.5947 28.7416i 0.618000 1.53193i
353353 −1.24335 + 2.15355i −0.0661769 + 0.114622i −0.897215 0.441593i 0.854413π-0.854413\pi
0.831039 + 0.556215i 0.187747π0.187747\pi
354354 −0.00929780 0.0181648i −0.000494172 0.000965446i
355355 −33.2007 + 4.37095i −1.76211 + 0.231986i
356356 27.0884 + 10.2834i 1.43568 + 0.545018i
357357 1.65188 1.45309i 0.0874266 0.0769054i
358358 18.1025 + 26.2351i 0.956745 + 1.38657i
359359 −16.1733 4.33362i −0.853594 0.228720i −0.194614 0.980880i 0.562345π-0.562345\pi
−0.658980 + 0.752160i 0.729012π0.729012\pi
360360 12.1961 + 22.1679i 0.642789 + 1.16835i
361361 16.4395 4.40494i 0.865234 0.231839i
362362 23.5682 8.39505i 1.23871 0.441234i
363363 1.41540 + 3.41709i 0.0742894 + 0.179350i
364364 3.04957 + 31.3907i 0.159841 + 1.64532i
365365 −20.0043 8.28607i −1.04707 0.433712i
366366 1.87030 1.69031i 0.0977623 0.0883538i
367367 −6.07154 3.50540i −0.316932 0.182981i 0.333092 0.942894i 0.391908π-0.391908\pi
−0.650024 + 0.759914i 0.725241π0.725241\pi
368368 −2.25859 + 4.51507i −0.117737 + 0.235364i
369369 −10.9637 + 6.32991i −0.570749 + 0.329522i
370370 28.4156 6.09492i 1.47726 0.316860i
371371 −8.40252 16.9738i −0.436237 0.881237i
372372 0.195404 0.00584081i 0.0101312 0.000302832i
373373 10.9932 14.3266i 0.569207 0.741805i −0.416710 0.909039i 0.636817π-0.636817\pi
0.985917 + 0.167234i 0.0534836π0.0534836\pi
374374 −21.4663 + 25.2282i −1.11000 + 1.30452i
375375 0.499456 0.133829i 0.0257918 0.00691089i
376376 −9.49869 24.3401i −0.489857 1.25524i
377377 −5.47588 + 5.47588i −0.282022 + 0.282022i
378378 2.58440 3.48532i 0.132927 0.179266i
379379 −3.29244 + 1.36377i −0.169121 + 0.0700523i −0.465638 0.884975i 0.654175π-0.654175\pi
0.296516 + 0.955028i 0.404175π0.404175\pi
380380 4.97070 6.89512i 0.254992 0.353712i
381381 −0.732074 0.954058i −0.0375053 0.0488779i
382382 25.2889 12.9444i 1.29389 0.662292i
383383 −10.0023 17.3246i −0.511096 0.885244i −0.999917 0.0128604i 0.995906π-0.995906\pi
0.488821 0.872384i 0.337427π-0.337427\pi
384384 −2.10161 + 0.652262i −0.107247 + 0.0332856i
385385 −8.47491 + 42.9458i −0.431922 + 2.18872i
386386 −20.8152 13.4628i −1.05946 0.685239i
387387 −26.8510 + 3.53500i −1.36491 + 0.179694i
388388 −0.899131 0.0911384i −0.0456465 0.00462685i
389389 −0.604023 + 4.58801i −0.0306252 + 0.232621i −0.999911 0.0133142i 0.995762π-0.995762\pi
0.969286 + 0.245936i 0.0790952π0.0790952\pi
390390 −4.47254 2.12314i −0.226476 0.107509i
391391 3.81547 3.81547i 0.192957 0.192957i
392392 −16.9695 10.1997i −0.857091 0.515164i
393393 1.20032 + 1.20032i 0.0605480 + 0.0605480i
394394 4.27424 + 11.9994i 0.215333 + 0.604523i
395395 −3.03429 0.399471i −0.152671 0.0200996i
396396 −15.3818 + 28.5815i −0.772963 + 1.43628i
397397 3.56041 + 27.0440i 0.178692 + 1.35730i 0.812117 + 0.583495i 0.198315π0.198315\pi
−0.633425 + 0.773804i 0.718352π0.718352\pi
398398 −11.5260 + 2.47223i −0.577745 + 0.123922i
399399 −0.710512 0.140212i −0.0355701 0.00701940i
400400 0.984246 + 16.4493i 0.0492123 + 0.822463i
401401 1.09372 0.631459i 0.0546177 0.0315336i −0.472442 0.881362i 0.656628π-0.656628\pi
0.527060 + 0.849828i 0.323294π0.323294\pi
402402 0.201855 + 0.0651739i 0.0100676 + 0.00325058i
403403 2.37634 1.82343i 0.118374 0.0908315i
404404 −1.59593 + 6.75762i −0.0794003 + 0.336204i
405405 −10.0091 24.1641i −0.497357 1.20072i
406406 −0.713772 4.80882i −0.0354239 0.238658i
407407 26.3622 + 26.3622i 1.30673 + 1.30673i
408408 2.35144 + 0.0485095i 0.116413 + 0.00240158i
409409 −2.26792 8.46400i −0.112142 0.418518i 0.886916 0.461931i 0.152843π-0.152843\pi
−0.999057 + 0.0434134i 0.986177π0.986177\pi
410410 −18.1936 + 1.46575i −0.898515 + 0.0723884i
411411 1.78003 + 1.36587i 0.0878026 + 0.0673733i
412412 −17.0437 6.47018i −0.839684 0.318763i
413413 0.175907 0.0870787i 0.00865580 0.00428486i
414414 2.87140 4.43953i 0.141121 0.218191i
415415 −10.1101 17.5112i −0.496286 0.859592i
416416 −20.2766 + 26.9376i −0.994142 + 1.32072i
417417 −1.73257 + 3.00089i −0.0848441 + 0.146954i
418418 10.8903 + 0.550524i 0.532662 + 0.0269270i
419419 0.789499 1.90602i 0.0385696 0.0931152i −0.903421 0.428755i 0.858952π-0.858952\pi
0.941990 + 0.335640i 0.108952π0.108952\pi
420420 2.74299 1.46147i 0.133844 0.0713125i
421421 8.35055 3.45891i 0.406981 0.168577i −0.169795 0.985479i 0.554311π-0.554311\pi
0.576776 + 0.816902i 0.304311π0.304311\pi
422422 −0.350543 + 0.738442i −0.0170641 + 0.0359468i
423423 7.08214 + 26.4309i 0.344346 + 1.28512i
424424 5.64268 19.4453i 0.274033 0.944345i
425425 4.55850 17.0126i 0.221120 0.825230i
426426 −0.550293 + 3.00010i −0.0266618 + 0.145355i
427427 16.0156 + 18.2066i 0.775047 + 0.881079i
428428 −17.2858 + 18.3510i −0.835538 + 0.887028i
429429 −0.829000 6.29688i −0.0400245 0.304016i
430430 −37.1580 11.9974i −1.79192 0.578565i
431431 2.36261 + 1.36406i 0.113803 + 0.0657043i 0.555821 0.831302i 0.312404π-0.312404\pi
−0.442018 + 0.897006i 0.645737π0.645737\pi
432432 4.55449 0.879053i 0.219128 0.0422935i
433433 23.1713i 1.11354i −0.830666 0.556771i 0.812040π-0.812040\pi
0.830666 0.556771i 0.187960π-0.187960\pi
434434 0.0309385 + 1.88012i 0.00148509 + 0.0902486i
435435 0.705065 + 0.292047i 0.0338053 + 0.0140026i
436436 −23.6161 + 14.5925i −1.13101 + 0.698853i
437437 −1.76104 0.231845i −0.0842420 0.0110907i
438438 −1.27806 + 1.50204i −0.0610683 + 0.0717704i
439439 −4.54888 + 16.9766i −0.217106 + 0.810251i 0.768308 + 0.640080i 0.221099π0.221099\pi
−0.985415 + 0.170171i 0.945568π0.945568\pi
440440 −37.7057 + 27.7160i −1.79755 + 1.32131i
441441 16.4885 + 12.5729i 0.785165 + 0.598712i
442442 29.6606 20.4661i 1.41081 0.973474i
443443 5.38327 + 4.13073i 0.255767 + 0.196257i 0.728684 0.684850i 0.240132π-0.240132\pi
−0.472917 + 0.881107i 0.656799π0.656799\pi
444444 0.266947 2.63358i 0.0126687 0.124984i
445445 −26.6333 34.7092i −1.26254 1.64537i
446446 −0.362173 + 7.16440i −0.0171494 + 0.339244i
447447 2.40358 0.113685
448448 −6.00192 20.2972i −0.283564 0.958953i
449449 18.3637 0.866635 0.433318 0.901241i 0.357343π-0.357343\pi
0.433318 + 0.901241i 0.357343π0.357343\pi
450450 0.871304 17.2359i 0.0410737 0.812506i
451451 −14.2542 18.5764i −0.671204 0.874730i
452452 −0.0138150 + 0.136293i −0.000649805 + 0.00641069i
453453 −1.03667 0.795468i −0.0487072 0.0373743i
454454 12.7995 8.83178i 0.600710 0.414496i
455455 20.9977 42.7420i 0.984386 2.00377i
456456 −0.458545 0.623819i −0.0214733 0.0292130i
457457 −6.02250 + 22.4763i −0.281720 + 1.05140i 0.669482 + 0.742828i 0.266516π0.266516\pi
−0.951203 + 0.308567i 0.900151π0.900151\pi
458458 14.4404 16.9710i 0.674753 0.793002i
459459 −4.91534 0.647117i −0.229428 0.0302048i
460460 6.48479 4.00698i 0.302355 0.186826i
461461 −25.1245 10.4069i −1.17016 0.484698i −0.288917 0.957354i 0.593295π-0.593295\pi
−0.881247 + 0.472657i 0.843295π0.843295\pi
462462 3.48528 + 1.93648i 0.162150 + 0.0900930i
463463 11.5497i 0.536761i 0.963313 + 0.268381i 0.0864885π0.0864885\pi
−0.963313 + 0.268381i 0.913512π0.913512\pi
464464 2.91192 4.30480i 0.135182 0.199845i
465465 −0.255633 0.147590i −0.0118547 0.00684432i
466466 18.2372 + 5.88833i 0.844822 + 0.272772i
467467 1.34169 + 10.1912i 0.0620861 + 0.471590i 0.994040 + 0.109014i 0.0347694π0.0347694\pi
−0.931954 + 0.362576i 0.881897π0.881897\pi
468468 24.2110 25.7030i 1.11916 1.18812i
469469 −0.652903 + 1.93299i −0.0301483 + 0.0892574i
470470 −7.11764 + 38.8041i −0.328312 + 1.78990i
471471 −0.0522806 + 0.195114i −0.00240896 + 0.00899037i
472472 0.201519 + 0.0584774i 0.00927566 + 0.00269164i
473473 −12.9645 48.3841i −0.596108 2.22470i
474474 −0.119543 + 0.251826i −0.00549081 + 0.0115668i
475475 −5.35647 + 2.21872i −0.245772 + 0.101802i
476476 −0.770258 + 22.6095i −0.0353047 + 1.03630i
477477 −8.11473 + 19.5907i −0.371548 + 0.896997i
478478 −7.09200 0.358514i −0.324381 0.0163980i
479479 −8.77291 + 15.1951i −0.400844 + 0.694283i −0.993828 0.110932i 0.964617π-0.964617\pi
0.592984 + 0.805215i 0.297950π0.297950\pi
480480 3.21723 + 0.830219i 0.146846 + 0.0378941i
481481 −20.2792 35.1246i −0.924653 1.60155i
482482 −18.4002 + 28.4490i −0.838106 + 1.29582i
483483 −0.540569 0.360015i −0.0245967 0.0163812i
484484 −35.5565 13.4980i −1.61620 0.613547i
485485 1.08260 + 0.830710i 0.0491584 + 0.0377206i
486486 −7.27865 + 0.586400i −0.330166 + 0.0265997i
487487 −3.33054 12.4297i −0.150921 0.563245i −0.999420 0.0340483i 0.989160π-0.989160\pi
0.848499 0.529197i 0.177507π-0.177507\pi
488488 −0.534660 + 25.9170i −0.0242029 + 1.17321i
489489 0.370944 + 0.370944i 0.0167747 + 0.0167747i
490490 13.7019 + 26.5704i 0.618990 + 1.20033i
491491 15.2024 + 36.7019i 0.686076 + 1.65633i 0.752542 + 0.658544i 0.228828π0.228828\pi
−0.0664663 + 0.997789i 0.521172π0.521172\pi
492492 −0.382119 + 1.61800i −0.0172272 + 0.0729452i
493493 −4.40694 + 3.38156i −0.198479 + 0.152298i
494494 −11.2887 3.64484i −0.507903 0.163989i
495495 42.4432 24.5046i 1.90768 1.10140i
496496 −1.33399 + 1.50379i −0.0598980 + 0.0675222i
497497 −28.7834 5.68011i −1.29111 0.254788i
498498 −1.80078 + 0.386253i −0.0806950 + 0.0173084i
499499 3.23014 + 24.5353i 0.144601 + 1.09835i 0.897751 + 0.440504i 0.145200π0.145200\pi
−0.753150 + 0.657849i 0.771467π0.771467\pi
500500 −2.51973 + 4.68203i −0.112686 + 0.209387i
501501 1.19332 + 0.157104i 0.0533136 + 0.00701887i
502502 −8.13772 22.8457i −0.363204 1.01965i
503503 −13.6066 13.6066i −0.606689 0.606689i 0.335390 0.942079i 0.391132π-0.391132\pi
−0.942079 + 0.335390i 0.891132π0.891132\pi
504504 3.90822 + 21.8196i 0.174086 + 0.971922i
505505 7.41351 7.41351i 0.329897 0.329897i
506506 8.83412 + 4.19361i 0.392725 + 0.186428i
507507 −0.571825 + 4.34344i −0.0253956 + 0.192899i
508508 12.3027 + 1.24704i 0.545845 + 0.0553283i
509509 −24.1716 + 3.18225i −1.07139 + 0.141051i −0.645527 0.763738i 0.723362π-0.723362\pi
−0.425861 + 0.904789i 0.640029π0.640029\pi
510510 −2.98193 1.92865i −0.132042 0.0854021i
511511 −14.2813 12.4862i −0.631769 0.552358i
512512 9.93535 20.3295i 0.439085 0.898446i
513513 0.816005 + 1.41336i 0.0360275 + 0.0624014i
514514 3.06455 1.56862i 0.135171 0.0691887i
515515 16.7574 + 21.8386i 0.738418 + 0.962324i
516516 −2.07982 + 2.88503i −0.0915589 + 0.127006i
517517 −46.7575 + 19.3676i −2.05639 + 0.851786i
518518 25.2949 + 2.90760i 1.11139 + 0.127752i
519519 −0.209268 + 0.209268i −0.00918583 + 0.00918583i
520520 47.4258 18.5079i 2.07976 0.811624i
521521 19.7383 5.28886i 0.864750 0.231709i 0.200934 0.979605i 0.435602π-0.435602\pi
0.663816 + 0.747896i 0.268936π0.268936\pi
522522 −3.52723 + 4.14537i −0.154383 + 0.181438i
523523 −21.5776 + 28.1205i −0.943525 + 1.22963i 0.0296506 + 0.999560i 0.490561π0.490561\pi
−0.973175 + 0.230065i 0.926106π0.926106\pi
524524 −17.4474 + 0.521518i −0.762192 + 0.0227826i
525525 −2.11563 0.135451i −0.0923338 0.00591158i
526526 38.3834 8.23294i 1.67360 0.358973i
527527 1.86069 1.07427i 0.0810530 0.0467960i
528528 1.34713 + 4.04393i 0.0586265 + 0.175989i
529529 18.5391 + 10.7035i 0.806046 + 0.465371i
530530 −22.6818 + 20.4989i −0.985234 + 0.890417i
531531 −0.203026 0.0840963i −0.00881059 0.00364947i
532532 6.05901 4.32964i 0.262692 0.187714i
533533 9.74808 + 23.5340i 0.422236 + 1.01937i
534534 −3.75389 + 1.33715i −0.162447 + 0.0578640i
535535 36.7688 9.85218i 1.58966 0.425947i
536536 −1.91103 + 1.05138i −0.0825438 + 0.0454129i
537537 −4.23437 1.13459i −0.182726 0.0489614i
538538 7.86623 + 11.4002i 0.339137 + 0.491496i
539539 −19.0749 + 33.2707i −0.821613 + 1.43307i
540540 −6.54797 2.48576i −0.281780 0.106970i
541541 9.81306 1.29191i 0.421896 0.0555437i 0.0834107 0.996515i 0.473419π-0.473419\pi
0.338486 + 0.940972i 0.390085π0.390085\pi
542542 −17.8453 34.8638i −0.766523 1.49753i
543543 −1.72043 + 2.97987i −0.0738307 + 0.127878i
544544 −16.9421 + 17.2586i −0.726385 + 0.739957i
545545 41.9171 1.79553
546546 −3.11715 3.01622i −0.133402 0.129082i
547547 −2.30920 + 5.57491i −0.0987344 + 0.238366i −0.965527 0.260303i 0.916178π-0.916178\pi
0.866793 + 0.498669i 0.166178π0.166178\pi
548548 −22.7739 + 3.69350i −0.972851 + 0.157779i
549549 3.54356 26.9160i 0.151235 1.14875i
550550 31.8163 2.56327i 1.35665 0.109298i
551551 1.76625 + 0.473265i 0.0752447 + 0.0201618i
552552 −0.165833 0.674229i −0.00705834 0.0286971i
553553 −2.40659 1.18227i −0.102339 0.0502754i
554554 0.287935 1.56977i 0.0122332 0.0666930i
555555 −2.43317 + 3.17098i −0.103283 + 0.134600i
556556 −10.2463 34.1264i −0.434538 1.44728i
557557 −26.1993 + 20.1034i −1.11010 + 0.851810i −0.990016 0.140953i 0.954983π-0.954983\pi
−0.120085 + 0.992764i 0.538317π0.538317\pi
558558 1.56190 1.41159i 0.0661205 0.0597572i
559559 54.4933i 2.30482i
560560 −8.40044 + 30.8356i −0.354983 + 1.30304i
561561 4.55574i 0.192343i
562562 −8.96357 9.91807i −0.378105 0.418369i
563563 33.6425 25.8148i 1.41786 1.08797i 0.435668 0.900108i 0.356512π-0.356512\pi
0.982196 0.187858i 0.0601543π-0.0601543\pi
564564 3.16427 + 1.70292i 0.133240 + 0.0717059i
565565 0.125922 0.164104i 0.00529757 0.00690392i
566566 29.9584 + 5.49512i 1.25925 + 0.230977i
567567 −1.53329 22.8634i −0.0643922 0.960172i
568568 −18.5760 25.2714i −0.779433 1.06036i
569569 −0.667826 0.178943i −0.0279967 0.00750170i 0.244794 0.969575i 0.421280π-0.421280\pi
−0.272790 + 0.962074i 0.587946π0.587946\pi
570570 0.0938775 + 1.16525i 0.00393210 + 0.0488068i
571571 −0.400155 + 3.03948i −0.0167460 + 0.127198i −0.997776 0.0666583i 0.978766π-0.978766\pi
0.981030 + 0.193856i 0.0620996π0.0620996\pi
572572 52.9774 + 38.1915i 2.21510 + 1.59687i
573573 −1.49521 + 3.60975i −0.0624633 + 0.150800i
574574 −15.5123 3.88413i −0.647473 0.162120i
575575 −5.19951 −0.216834
576576 −12.6850 + 20.0164i −0.528541 + 0.834016i
577577 −23.0936 + 39.9993i −0.961399 + 1.66519i −0.242406 + 0.970175i 0.577936π0.577936\pi
−0.718993 + 0.695017i 0.755397π0.755397\pi
578578 1.60876 0.823461i 0.0669158 0.0342515i
579579 3.38017 0.445008i 0.140475 0.0184939i
580580 −7.15710 + 3.21835i −0.297183 + 0.133635i
581581 −3.48234 17.3695i −0.144472 0.720609i
582582 0.102302 0.0705895i 0.00424056 0.00292603i
583583 −37.8832 10.1508i −1.56896 0.420402i
584584 −2.23179 20.1566i −0.0923519 0.834088i
585585 −51.4997 + 13.7993i −2.12925 + 0.570531i
586586 6.09564 + 17.1128i 0.251809 + 0.706924i
587587 −0.997077 2.40716i −0.0411538 0.0993540i 0.901966 0.431807i 0.142124π-0.142124\pi
−0.943120 + 0.332453i 0.892124π0.892124\pi
588588 2.68653 0.444054i 0.110791 0.0183125i
589589 −0.653426 0.270658i −0.0269239 0.0111523i
590590 −0.212439 0.235061i −0.00874596 0.00967729i
591591 −1.51716 0.875935i −0.0624078 0.0360312i
592592 17.8304 + 20.5664i 0.732824 + 0.845273i
593593 19.2249 11.0995i 0.789473 0.455802i −0.0503042 0.998734i 0.516019π-0.516019\pi
0.839777 + 0.542932i 0.182686π0.182686\pi
594594 −1.88434 8.78511i −0.0773152 0.360457i
595595 18.9346 28.4306i 0.776243 1.16554i
596596 −16.9466 + 17.9909i −0.694160 + 0.736936i
597597 0.986948 1.28622i 0.0403931 0.0526413i
598598 −8.10228 6.89411i −0.331327 0.281921i
599599 −19.3702 + 5.19023i −0.791446 + 0.212067i −0.631825 0.775111i 0.717694π-0.717694\pi
−0.159621 + 0.987178i 0.551027π0.551027\pi
600600 −1.56915 1.63525i −0.0640602 0.0667590i
601601 17.5555 17.5555i 0.716102 0.716102i −0.251703 0.967805i 0.580991π-0.580991\pi
0.967805 + 0.251703i 0.0809905π0.0809905\pi
602602 −27.4791 20.3760i −1.11996 0.830463i
603603 2.11041 0.874160i 0.0859425 0.0355985i
604604 13.2633 2.15106i 0.539675 0.0875253i
605605 34.9591 + 45.5596i 1.42129 + 1.85226i
606606 −0.435114 0.850065i −0.0176753 0.0345315i
607607 15.1703 + 26.2757i 0.615742 + 1.06650i 0.990254 + 0.139274i 0.0444768π0.0444768\pi
−0.374512 + 0.927222i 0.622190π0.622190\pi
608608 7.90232 + 0.966044i 0.320482 + 0.0391782i
609609 0.503355 + 0.440084i 0.0203970 + 0.0178331i
610610 21.2571 32.8661i 0.860676 1.33071i
611611 54.5869 7.18651i 2.20835 0.290735i
612612 19.6245 16.0123i 0.793274 0.647258i
613613 −0.908361 + 6.89968i −0.0366883 + 0.278676i 0.963261 + 0.268569i 0.0865506π0.0865506\pi
−0.999949 + 0.0101071i 0.996783π0.996783\pi
614614 12.3868 26.0937i 0.499891 1.05305i
615615 1.77505 1.77505i 0.0715768 0.0715768i
616616 −39.0678 + 12.4342i −1.57409 + 0.500990i
617617 3.00134 + 3.00134i 0.120829 + 0.120829i 0.764936 0.644106i 0.222771π-0.222771\pi
−0.644106 + 0.764936i 0.722771π0.722771\pi
618618 2.36190 0.841318i 0.0950097 0.0338428i
619619 0.367838 + 0.0484268i 0.0147847 + 0.00194644i 0.137915 0.990444i 0.455960π-0.455960\pi
−0.123130 + 0.992391i 0.539293π0.539293\pi
620620 2.90708 0.872836i 0.116751 0.0350539i
621621 0.191038 + 1.45108i 0.00766608 + 0.0582297i
622622 −0.877029 4.08887i −0.0351657 0.163949i
623623 −12.3756 36.2770i −0.495819 1.45341i
624624 −0.276962 4.62874i −0.0110874 0.185298i
625625 24.7914 14.3133i 0.991657 0.572534i
626626 12.1128 37.5156i 0.484126 1.49942i
627627 −1.18977 + 0.912942i −0.0475148 + 0.0364594i
628628 −1.09183 1.76699i −0.0435688 0.0705105i
629629 −11.1333 26.8781i −0.443912 1.07170i
630630 12.2981 31.1294i 0.489969 1.24022i
631631 −34.5848 34.5848i −1.37680 1.37680i −0.849971 0.526830i 0.823381π-0.823381\pi
−0.526830 0.849971i 0.676619π-0.676619\pi
632632 −1.04209 2.67031i −0.0414520 0.106219i
633633 −0.0290967 0.108591i −0.00115649 0.00431609i
634634 3.72822 + 46.2763i 0.148067 + 1.83787i
635635 −14.8131 11.3665i −0.587841 0.451067i
636636 1.14203 + 2.53970i 0.0452845 + 0.100706i
637637 29.4121 29.5907i 1.16535 1.17243i
638638 −8.45302 5.46724i −0.334658 0.216450i
639639 16.4236 + 28.4466i 0.649709 + 1.12533i
640640 −28.8976 + 18.2277i −1.14228 + 0.720511i
641641 3.23073 5.59579i 0.127606 0.221021i −0.795142 0.606423i 0.792604π-0.792604\pi
0.922749 + 0.385402i 0.125937π0.125937\pi
642642 0.175050 3.46278i 0.00690866 0.136665i
643643 2.82466 6.81934i 0.111394 0.268929i −0.858345 0.513073i 0.828507π-0.828507\pi
0.969739 + 0.244144i 0.0785070π0.0785070\pi
644644 6.50605 1.50788i 0.256374 0.0594187i
645645 4.96139 2.05508i 0.195355 0.0809185i
646646 −7.68688 3.64900i −0.302436 0.143568i
647647 −0.271500 1.01325i −0.0106738 0.0398351i 0.960384 0.278682i 0.0898974π-0.0898974\pi
−0.971057 + 0.238846i 0.923231π0.923231\pi
648648 15.3104 19.1230i 0.601451 0.751222i
649649 0.105196 0.392598i 0.00412932 0.0154108i
650650 −34.1549 6.26487i −1.33967 0.245728i
651651 −0.170808 0.194176i −0.00669449 0.00761034i
652652 −5.39191 + 0.161169i −0.211163 + 0.00631187i
653653 1.71660 + 13.0389i 0.0671757 + 0.510250i 0.991645 + 0.128994i 0.0411749π0.0411749\pi
−0.924470 + 0.381256i 0.875492π0.875492\pi
654654 1.17310 3.63329i 0.0458717 0.142073i
655655 22.8252 + 13.1781i 0.891853 + 0.514912i
656656 −9.41669 14.2680i −0.367660 0.557073i
657657 21.2388i 0.828603i
658658 −16.7871 + 30.2135i −0.654429 + 1.17784i
659659 −9.08982 3.76512i −0.354089 0.146668i 0.198547 0.980091i 0.436378π-0.436378\pi
−0.552636 + 0.833423i 0.686378π0.686378\pi
660660 1.47927 6.26367i 0.0575805 0.243813i
661661 26.6893 + 3.51371i 1.03809 + 0.136668i 0.630256 0.776387i 0.282950π-0.282950\pi
0.407837 + 0.913055i 0.366283π0.366283\pi
662662 −6.46572 5.50158i −0.251297 0.213825i
663663 −1.28274 + 4.78725i −0.0498175 + 0.185921i
664664 9.80542 16.2023i 0.380524 0.628770i
665665 −11.2193 + 0.752401i −0.435065 + 0.0291769i
666666 −16.1897 23.4631i −0.627340 0.909175i
667667 1.30099 + 0.998284i 0.0503745 + 0.0386537i
668668 −9.58952 + 7.82440i −0.371030 + 0.302735i
669669 −0.600597 0.782713i −0.0232204 0.0302614i
670670 3.28921 + 0.166276i 0.127073 + 0.00642379i
671671 50.2122 1.93842
672672 2.43768 + 1.59110i 0.0940354 + 0.0613782i
673673 −28.1530 −1.08522 −0.542609 0.839985i 0.682563π-0.682563\pi
−0.542609 + 0.839985i 0.682563π0.682563\pi
674674 −11.6676 0.589818i −0.449419 0.0227189i
675675 2.90824 + 3.79010i 0.111938 + 0.145881i
676676 −28.4792 34.9039i −1.09535 1.34246i
677677 20.6879 + 15.8744i 0.795102 + 0.610103i 0.924366 0.381507i 0.124595π-0.124595\pi
−0.129264 + 0.991610i 0.541261π0.541261\pi
678678 −0.0107002 0.0155073i −0.000410938 0.000595554i
679679 0.665706 + 0.993044i 0.0255475 + 0.0381095i
680680 35.4604 8.72183i 1.35984 0.334467i
681681 −0.553543 + 2.06585i −0.0212118 + 0.0791636i
682682 2.96554 + 2.52333i 0.113556 + 0.0966233i
683683 3.51722 + 0.463050i 0.134583 + 0.0177181i 0.197516 0.980300i 0.436712π-0.436712\pi
−0.0629339 + 0.998018i 0.520046π0.520046\pi
684684 −8.11438 1.91635i −0.310261 0.0732734i
685685 32.1847 + 13.3313i 1.22971 + 0.509364i
686686 3.92386 + 25.8960i 0.149814 + 0.988714i
687687 3.06463i 0.116923i
688688 −6.93067 35.9087i −0.264229 1.36900i
689689 36.9502 + 21.3332i 1.40769 + 0.812731i
690690 −0.322123 + 0.997673i −0.0122630 + 0.0379808i
691691 −0.159432 1.21101i −0.00606507 0.0460688i 0.988145 0.153525i 0.0490627π-0.0490627\pi
−0.994210 + 0.107457i 0.965729π0.965729\pi
692692 −0.0909233 3.04184i −0.00345639 0.115633i
693693 42.0997 8.44040i 1.59924 0.320624i
694694 −34.4634 6.32144i −1.30821 0.239959i
695695 −13.9248 + 51.9680i −0.528197 + 1.97126i
696696 0.0786606 + 0.710433i 0.00298162 + 0.0269289i
697697 4.72909 + 17.6492i 0.179127 + 0.668511i
698698 −23.9372 11.3631i −0.906037 0.430101i
699699 −2.43506 + 1.00863i −0.0921023 + 0.0381500i
700700 15.9303 14.8806i 0.602108 0.562434i
701701 9.67092 23.3477i 0.365266 0.881830i −0.629246 0.777206i 0.716636π-0.716636\pi
0.994512 0.104623i 0.0333637π-0.0333637\pi
702702 −0.493493 + 9.76212i −0.0186257 + 0.368447i
703703 −4.78840 + 8.29375i −0.180598 + 0.312805i
704704 −39.7671 18.4286i −1.49878 0.694555i
705705 −2.71291 4.69890i −0.102174 0.176971i
706706 2.95292 + 1.90988i 0.111134 + 0.0718794i
707707 8.23199 4.07506i 0.309596 0.153259i
708708 −0.0263199 + 0.0118353i −0.000989164 + 0.000444799i
709709 −1.27025 0.974694i −0.0477051 0.0366054i 0.584634 0.811297i 0.301238π-0.301238\pi
−0.632339 + 0.774692i 0.717905π0.717905\pi
710710 3.80305 + 47.2051i 0.142726 + 1.77157i
711711 0.776971 + 2.89969i 0.0291387 + 0.108747i
712712 16.4584 37.5257i 0.616806 1.40634i
713713 −0.448503 0.448503i −0.0167966 0.0167966i
714714 −1.93441 2.43688i −0.0723934 0.0911979i
715715 −37.7371 91.1054i −1.41129 3.40715i
716716 38.3472 23.6949i 1.43310 0.885521i
717717 0.774804 0.594528i 0.0289356 0.0222031i
718718 −7.27563 + 22.5339i −0.271524 + 0.840958i
719719 −6.32208 + 3.65005i −0.235774 + 0.136124i −0.613233 0.789902i 0.710131π-0.710131\pi
0.377459 + 0.926026i 0.376798π0.376798\pi
720720 32.1810 15.6431i 1.19931 0.582983i
721721 7.78661 + 22.8251i 0.289988 + 0.850050i
722722 −5.04780 23.5338i −0.187860 0.875836i
723723 −0.608211 4.61982i −0.0226196 0.171813i
724724 −10.1745 33.8873i −0.378132 1.25941i
725725 5.30686 + 0.698662i 0.197092 + 0.0259476i
726726 4.92739 1.75515i 0.182872 0.0651397i
727727 −15.9338 15.9338i −0.590952 0.590952i 0.346937 0.937888i 0.387222π-0.387222\pi
−0.937888 + 0.346937i 0.887222π0.887222\pi
728728 44.5543 2.06595i 1.65129 0.0765692i
729729 −17.6625 + 17.6625i −0.654168 + 0.654168i
730730 −13.1316 + 27.6627i −0.486023 + 1.02384i
731731 −5.10202 + 38.7537i −0.188705 + 1.43336i
732732 −2.25387 2.76232i −0.0833054 0.102098i
733733 8.04946 1.05973i 0.297314 0.0391421i 0.0196063 0.999808i 0.493759π-0.493759\pi
0.277707 + 0.960666i 0.410425π0.410425\pi
734734 −5.38457 + 8.32521i −0.198748 + 0.307289i
735735 −3.80331 1.56192i −0.140287 0.0576122i
736736 6.21586 + 3.51243i 0.229120 + 0.129470i
737737 2.11246 + 3.65889i 0.0778135 + 0.134777i
738738 8.15763 + 15.9372i 0.300286 + 0.586658i
739739 −24.1438 31.4648i −0.888143 1.15745i −0.986738 0.162323i 0.948101π-0.948101\pi
0.0985941 0.995128i 0.468565π-0.468565\pi
740740 −6.57965 40.5696i −0.241873 1.49137i
741741 1.50728 0.624338i 0.0553715 0.0229356i
742742 −24.5739 + 10.6559i −0.902138 + 0.391189i
743743 −33.9729 + 33.9729i −1.24634 + 1.24634i −0.289020 + 0.957323i 0.593329π0.593329\pi
−0.957323 + 0.289020i 0.906671π0.906671\pi
744744 0.00570221 0.276408i 0.000209053 0.0101336i
745745 36.0474 9.65887i 1.32067 0.353874i
746746 −19.4502 16.5498i −0.712121 0.605933i
747747 −12.0741 + 15.7352i −0.441767 + 0.575722i
748748 34.0999 + 32.1205i 1.24682 + 1.17444i
749749 33.2818 + 2.13084i 1.21609 + 0.0778591i
750750 −0.153360 0.714992i −0.00559992 0.0261078i
751751 9.05161 5.22595i 0.330298 0.190698i −0.325675 0.945482i 0.605592π-0.605592\pi
0.655973 + 0.754784i 0.272258π0.272258\pi
752752 −35.0564 + 11.6782i −1.27837 + 0.425859i
753753 2.88853 + 1.66769i 0.105264 + 0.0607741i
754754 7.34321 + 8.12516i 0.267424 + 0.295901i
755755 −18.7440 7.76403i −0.682165 0.282562i
756756 −4.73818 3.89908i −0.172326 0.141808i
757757 2.64470 + 6.38487i 0.0961232 + 0.232062i 0.964626 0.263622i 0.0849173π-0.0849173\pi
−0.868503 + 0.495684i 0.834917π0.834917\pi
758758 1.69113 + 4.74765i 0.0614245 + 0.172442i
759759 −1.29909 + 0.348090i −0.0471539 + 0.0126349i
760760 −9.38383 7.51298i −0.340387 0.272524i
761761 −43.3060 11.6038i −1.56984 0.420637i −0.634078 0.773269i 0.718620π-0.718620\pi
−0.935762 + 0.352632i 0.885287π0.885287\pi
762762 −1.39979 + 0.965870i −0.0507091 + 0.0349898i
763763 34.7929 + 11.7519i 1.25959 + 0.425448i
764764 −16.4771 36.6426i −0.596122 1.32568i
765765 −37.9168 + 4.99184i −1.37088 + 0.180480i
766766 −25.1836 + 12.8904i −0.909919 + 0.465751i
767767 −0.221085 + 0.382930i −0.00798291 + 0.0138268i
768768 0.771207 + 3.01491i 0.0278285 + 0.108791i
769769 −24.3333 −0.877480 −0.438740 0.898614i 0.644575π-0.644575\pi
−0.438740 + 0.898614i 0.644575π0.644575\pi
770770 60.0519 + 15.0364i 2.16412 + 0.541873i
771771 −0.181191 + 0.437435i −0.00652545 + 0.0157538i
772772 −20.5012 + 28.4383i −0.737855 + 1.02352i
773773 1.78908 13.5894i 0.0643486 0.488776i −0.928678 0.370887i 0.879054π-0.879054\pi
0.993027 0.117890i 0.0376129π-0.0376129\pi
774774 3.07571 + 38.1770i 0.110554 + 1.37224i
775775 −1.99980 0.535844i −0.0718349 0.0192481i
776776 −0.192923 + 1.26343i −0.00692552 + 0.0453547i
777777 −2.90866 + 1.94987i −0.104347 + 0.0699513i
778778 6.43703 + 1.18071i 0.230779 + 0.0423306i
779779 3.66156 4.77184i 0.131189 0.170969i
780780 −3.31808 + 6.16547i −0.118806 + 0.220759i
781781 −48.1985 + 36.9840i −1.72468 + 1.32339i
782782 −5.11659 5.66144i −0.182969 0.202453i
783783 1.50671i 0.0538453i
784784 −15.6178 + 23.2397i −0.557780 + 0.829989i
785785 3.13629i 0.111939i
786786 1.78104 1.60964i 0.0635277 0.0574139i
787787 43.4167 33.3148i 1.54764 1.18754i 0.639561 0.768740i 0.279116π-0.279116\pi
0.908076 0.418804i 0.137551π-0.137551\pi
788788 17.2533 5.18022i 0.614624 0.184538i
789789 −3.28670 + 4.28331i −0.117010 + 0.152490i
790790 −0.780865 + 4.25713i −0.0277819 + 0.151462i
791791 0.150529 0.100910i 0.00535219 0.00358794i
792792 39.2706 + 23.7661i 1.39542 + 0.844491i
793793 −52.7639 14.1381i −1.87370 0.502057i
794794 38.4514 3.09782i 1.36459 0.109937i
795795 0.548819 4.16869i 0.0194646 0.147848i
796796 2.66885 + 16.4559i 0.0945948 + 0.583264i
797797 13.4980 32.5870i 0.478122 1.15429i −0.482366 0.875970i 0.660223π-0.660223\pi
0.960489 0.278320i 0.0897774π-0.0897774\pi
798798 −0.248768 + 0.993523i −0.00880628 + 0.0351703i
799799 39.4932 1.39717
800800 23.3034 0.215684i 0.823898 0.00762558i
801801 −21.4570 + 37.1645i −0.758144 + 1.31314i
802802 −0.813787 1.58987i −0.0287358 0.0561401i
803803 −38.9462 + 5.12737i −1.37438 + 0.180941i
804804 0.106465 0.280449i 0.00375472 0.00989068i
805805 −9.55386 3.22699i −0.336729 0.113736i
806806 −2.40576 3.48656i −0.0847393 0.122809i
807807 −1.84000 0.493026i −0.0647710 0.0173553i
808808 9.43058 + 2.73659i 0.331767 + 0.0962731i
809809 23.5700 6.31557i 0.828678 0.222043i 0.180541 0.983567i 0.442215π-0.442215\pi
0.648137 + 0.761524i 0.275549π0.275549\pi
810810 −34.8443 + 12.4116i −1.22430 + 0.436101i
811811 −16.1023 38.8745i −0.565429 1.36507i −0.905371 0.424621i 0.860407π-0.860407\pi
0.339942 0.940446i 0.389593π-0.389593\pi
812812 −6.84299 + 0.664789i −0.240142 + 0.0233295i
813813 4.97647 + 2.06132i 0.174532 + 0.0722937i
814814 39.1165 35.3520i 1.37103 1.23909i
815815 7.05385 + 4.07254i 0.247086 + 0.142655i
816816 0.236408 3.31773i 0.00827593 0.116144i
817817 11.1433 6.43357i 0.389854 0.225082i
818818 −12.1166 + 2.59891i −0.423646 + 0.0908687i
819819 −46.6157 2.98453i −1.62889 0.104288i
820820 0.771228 + 25.8014i 0.0269324 + 0.901024i
821821 0.799478 1.04190i 0.0279020 0.0363625i −0.779194 0.626783i 0.784371π-0.784371\pi
0.807096 + 0.590420i 0.201038π0.201038\pi
822822 2.05626 2.41661i 0.0717203 0.0842891i
823823 8.10536 2.17183i 0.282535 0.0757051i −0.114768 0.993392i 0.536613π-0.536613\pi
0.397304 + 0.917687i 0.369946π0.369946\pi
824824 −10.3555 + 23.6108i −0.360750 + 0.822520i
825825 −3.10415 + 3.10415i −0.108072 + 0.108072i
826826 −0.110431 0.254670i −0.00384239 0.00886109i
827827 −9.70756 + 4.02100i −0.337565 + 0.139824i −0.545026 0.838419i 0.683480π-0.683480\pi
0.207461 + 0.978243i 0.433480π0.433480\pi
828828 −6.06542 4.37257i −0.210788 0.151957i
829829 −9.33231 12.1621i −0.324125 0.422407i 0.602661 0.797997i 0.294107π-0.294107\pi
−0.926786 + 0.375589i 0.877440π0.877440\pi
830830 −25.4549 + 13.0293i −0.883552 + 0.452254i
831831 0.109747 + 0.190088i 0.00380709 + 0.00659407i
832832 36.5991 + 30.5622i 1.26885 + 1.05955i
833833 23.6874 18.2901i 0.820718 0.633714i
834834 4.11479 + 2.66136i 0.142483 + 0.0921553i
835835 18.5280 2.43926i 0.641189 0.0844141i
836836 1.55513 15.3422i 0.0537854 0.530623i
837837 −0.0760675 + 0.577790i −0.00262928 + 0.0199714i
838838 −2.63571 1.25119i −0.0910491 0.0432215i
839839 13.7601 13.7601i 0.475050 0.475050i −0.428494 0.903545i 0.640956π-0.640956\pi
0.903545 + 0.428494i 0.140956π0.140956\pi
840840 −1.86835 3.97857i −0.0644641 0.137274i
841841 19.3124 + 19.3124i 0.665944 + 0.665944i
842842 −4.28917 12.0414i −0.147815 0.414973i
843843 1.82285 + 0.239982i 0.0627821 + 0.00826542i
844844 1.01795 + 0.547835i 0.0350395 + 0.0188572i
845845 8.87841 + 67.4382i 0.305427 + 2.31995i
846846 37.8370 8.11572i 1.30086 0.279024i
847847 16.2444 + 47.6175i 0.558163 + 1.63616i
848848 −27.0618 9.35817i −0.929306 0.321361i
849849 −3.62775 + 2.09448i −0.124504 + 0.0718825i
850850 −23.7032 7.65316i −0.813014 0.262501i
851851 −6.81375 + 5.22837i −0.233572 + 0.179226i
852852 4.19808 + 0.991447i 0.143824 + 0.0339664i
853853 18.5187 + 44.7080i 0.634067 + 1.53077i 0.834467 + 0.551058i 0.185776π0.185776\pi
−0.200400 + 0.979714i 0.564224π0.564224\pi
854854 26.8587 21.3206i 0.919085 0.729575i
855855 8.90196 + 8.90196i 0.304441 + 0.304441i
856856 24.6849 + 25.7248i 0.843712 + 0.879257i
857857 −6.34114 23.6655i −0.216609 0.808397i −0.985594 0.169129i 0.945904π-0.945904\pi
0.768985 0.639267i 0.220762π-0.220762\pi
858858 −8.95296 + 0.721291i −0.305649 + 0.0246245i
859859 4.83863 + 3.71281i 0.165092 + 0.126680i 0.688003 0.725708i 0.258487π-0.258487\pi
−0.522911 + 0.852387i 0.675154π0.675154\pi
860860 −19.5983 + 51.6257i −0.668296 + 1.76042i
861861 1.97102 0.975708i 0.0671721 0.0332520i
862862 2.09530 3.23959i 0.0713661 0.110341i
863863 −24.9061 43.1386i −0.847814 1.46846i −0.883155 0.469081i 0.844585π-0.844585\pi
0.0353411 0.999375i 0.488748π-0.488748\pi
864864 −0.916394 6.49557i −0.0311764 0.220984i
865865 −2.29752 + 3.97942i −0.0781181 + 0.135304i
866866 −32.7274 1.65443i −1.11212 0.0562198i
867867 −0.0951183 + 0.229636i −0.00323039 + 0.00779884i
868868 2.65771 + 0.0905425i 0.0902085 + 0.00307321i
869869 −5.12969 + 2.12479i −0.174013 + 0.0720785i
870870 0.462832 0.974989i 0.0156915 0.0330552i
871871 −1.18960 4.43963i −0.0403079 0.150431i
872872 18.9244 + 34.3975i 0.640861 + 1.16485i
873873 0.346433 1.29290i 0.0117250 0.0437582i
874874 −0.453199 + 2.47076i −0.0153297 + 0.0835746i
875875 6.89649 1.38265i 0.233144 0.0467420i
876876 2.03025 + 1.91240i 0.0685957 + 0.0646139i
877877 −4.30096 32.6691i −0.145233 1.10316i −0.896464 0.443116i 0.853873π-0.853873\pi
0.751231 0.660039i 0.229460π-0.229460\pi
878878 23.6532 + 7.63701i 0.798256 + 0.257737i
879879 −2.16368 1.24920i −0.0729792 0.0421345i
880880 36.4542 + 55.2349i 1.22887 + 1.86197i
881881 6.14703i 0.207099i 0.994624 + 0.103549i 0.0330200π0.0330200\pi
−0.994624 + 0.103549i 0.966980π0.966980\pi
882882 18.9354 22.3908i 0.637589 0.753936i
883883 36.8658 + 15.2703i 1.24063 + 0.513887i 0.903913 0.427717i 0.140682π-0.140682\pi
0.336721 + 0.941604i 0.390682π0.390682\pi
884884 −26.7888 43.3543i −0.901005 1.45816i
885885 0.0432018 + 0.00568763i 0.00145221 + 0.000191188i
886886 6.21865 7.30846i 0.208920 0.245532i
887887 −7.05302 + 26.3222i −0.236817 + 0.883814i 0.740504 + 0.672052i 0.234587π0.234587\pi
−0.977321 + 0.211762i 0.932080π0.932080\pi
888888 −3.70064 0.565076i −0.124185 0.0189627i
889889 −9.10879 13.5877i −0.305499 0.455717i
890890 −50.9252 + 35.1389i −1.70702 + 1.17786i
891891 −37.6453 28.8862i −1.26116 0.967725i
892892 10.0932 + 1.02307i 0.337946 + 0.0342551i
893893 −7.91419 10.3140i −0.264838 0.345144i
894894 0.171615 3.39484i 0.00573967 0.113540i
895895 −68.0639 −2.27513
896896 −29.0965 + 7.02795i −0.972047 + 0.234787i
897897 1.46312 0.0488520
898898 1.31116 25.9370i 0.0437541 0.865530i
899899 0.397497 + 0.518029i 0.0132573 + 0.0172772i
900900 −24.2819 2.46128i −0.809396 0.0820426i
901901 24.2803 + 18.6310i 0.808895 + 0.620687i
902902 −27.2553 + 18.8064i −0.907502 + 0.626185i
903903 4.69432 0.314816i 0.156217 0.0104764i
904904 0.191516 + 0.0292438i 0.00636971 + 0.000972635i
905905 −13.8272 + 51.6039i −0.459633 + 1.71537i
906906 −1.19755 + 1.40741i −0.0397858 + 0.0467581i
907907 19.5273 + 2.57082i 0.648394 + 0.0853627i 0.447548 0.894260i 0.352297π-0.352297\pi
0.200847 + 0.979623i 0.435631π0.435631\pi
908908 −11.5602 18.7087i −0.383639 0.620871i
909909 −9.50112 3.93549i −0.315132 0.130532i
910910 −58.8700 32.7091i −1.95152 1.08430i
911911 15.2338i 0.504719i −0.967634 0.252360i 0.918793π-0.918793\pi
0.967634 0.252360i 0.0812066π-0.0812066\pi
912912 −0.913828 + 0.603113i −0.0302599 + 0.0199711i
913913 −31.7691 18.3419i −1.05140 0.607028i
914914 31.3157 + 10.1110i 1.03583 + 0.334443i
915915 0.702645 + 5.33712i 0.0232287 + 0.176440i
916916 −22.9390 21.6074i −0.757925 0.713930i
917917 15.2512 + 17.3377i 0.503639 + 0.572541i
918918 −1.26495 + 6.89627i −0.0417496 + 0.227611i
919919 −13.9437 + 52.0387i −0.459961 + 1.71660i 0.213118 + 0.977026i 0.431638π0.431638\pi
−0.673079 + 0.739571i 0.735029π0.735029\pi
920920 −5.19649 9.44528i −0.171323 0.311402i
921921 1.02816 + 3.83716i 0.0338792 + 0.126439i
922922 −16.4927 + 34.7430i −0.543158 + 1.14420i
923923 61.0613 25.2924i 2.00986 0.832510i
924924 2.98395 4.78438i 0.0981646 0.157394i
925925 −10.7281 + 25.8998i −0.352737 + 0.851581i
926926 16.3129 + 0.824649i 0.536077 + 0.0270997i
927927 13.5005 23.3835i 0.443414 0.768015i
928928 −5.87224 4.42018i −0.192766 0.145100i
929929 −11.2640 19.5098i −0.369559 0.640095i 0.619938 0.784651i 0.287158π-0.287158\pi
−0.989497 + 0.144556i 0.953824π0.953824\pi
930930 −0.226710 + 0.350521i −0.00743411 + 0.0114940i
931931 −9.52342 2.52093i −0.312117 0.0826201i
932932 9.61887 25.3380i 0.315077 0.829973i
933933 0.456288 + 0.350122i 0.0149382 + 0.0114625i
934934 14.4899 1.16737i 0.474124 0.0381975i
935935 −18.3074 68.3242i −0.598716 2.23444i
936936 −34.5745 36.0311i −1.13010 1.17771i
937937 −10.5179 10.5179i −0.343606 0.343606i 0.514115 0.857721i 0.328120π-0.328120\pi
−0.857721 + 0.514115i 0.828120π0.828120\pi
938938 2.68356 + 1.06018i 0.0876215 + 0.0346162i
939939 2.07485 + 5.00913i 0.0677102 + 0.163467i
940940 54.2991 + 12.8236i 1.77104 + 0.418261i
941941 23.6476 18.1455i 0.770890 0.591525i −0.146640 0.989190i 0.546846π-0.546846\pi
0.917531 + 0.397665i 0.130179π0.130179\pi
942942 0.271848 + 0.0877728i 0.00885729 + 0.00285979i
943943 4.67141 2.69704i 0.152122 0.0878278i
944944 0.0969825 0.280452i 0.00315651 0.00912794i
945945 2.99151 + 8.76909i 0.0973138 + 0.285258i
946946 −69.2639 + 14.8565i −2.25196 + 0.483028i
947947 −6.68210 50.7556i −0.217139 1.64934i −0.658920 0.752213i 0.728987π-0.728987\pi
0.441781 0.897123i 0.354347π-0.354347\pi
948948 0.347147 + 0.186825i 0.0112748 + 0.00606778i
949949 42.3691 + 5.57800i 1.37536 + 0.181070i
950950 2.75129 + 7.72395i 0.0892637 + 0.250598i
951951 −4.51493 4.51493i −0.146406 0.146406i
952952 31.8789 + 2.70223i 1.03320 + 0.0875799i
953953 −6.86940 + 6.86940i −0.222522 + 0.222522i −0.809560 0.587038i 0.800294π-0.800294\pi
0.587038 + 0.809560i 0.300294π0.300294\pi
954954 27.0907 + 12.8601i 0.877094 + 0.416361i
955955 −7.91831 + 60.1455i −0.256230 + 1.94626i
956956 −1.01274 + 9.99122i −0.0327543 + 0.323139i
957957 1.37268 0.180717i 0.0443726 0.00584176i
958958 20.8354 + 13.4759i 0.673160 + 0.435386i
959959 22.9770 + 20.0889i 0.741967 + 0.648704i
960960 1.40232 4.48478i 0.0452597 0.144746i
961961 15.3737 + 26.6281i 0.495926 + 0.858970i
962962 −51.0583 + 26.1347i −1.64619 + 0.842616i
963963 −22.7302 29.6226i −0.732471 0.954575i
964964 38.8678 + 28.0199i 1.25185 + 0.902460i
965965 48.9055 20.2573i 1.57432 0.652106i
966966 −0.547085 + 0.737800i −0.0176022 + 0.0237383i
967967 10.0451 10.0451i 0.323029 0.323029i −0.526899 0.849928i 0.676645π-0.676645\pi
0.849928 + 0.526899i 0.176645π0.176645\pi
968968 −21.6035 + 49.2566i −0.694363 + 1.58317i
969969 1.13038 0.302885i 0.0363131 0.00973007i
970970 1.25060 1.46977i 0.0401544 0.0471913i
971971 3.80805 4.96274i 0.122206 0.159262i −0.728244 0.685318i 0.759663π-0.759663\pi
0.850450 + 0.526056i 0.176330π0.176330\pi
972972 0.308543 + 10.3223i 0.00989652 + 0.331088i
973973 −26.1280 + 39.2316i −0.837624 + 1.25771i
974974 −17.7937 + 3.81660i −0.570146 + 0.122292i
975975 4.13592 2.38787i 0.132455 0.0764731i
976976 36.5672 + 2.60563i 1.17049 + 0.0834041i
977977 −42.1874 24.3569i −1.34969 0.779246i −0.361488 0.932377i 0.617731π-0.617731\pi
−0.988206 + 0.153131i 0.951064π0.951064\pi
978978 0.550411 0.497440i 0.0176002 0.0159064i
979979 −73.3299 30.3743i −2.34363 0.970765i
980980 38.5066 17.4556i 1.23005 0.557599i
981981 −15.7344 37.9863i −0.502362 1.21281i
982982 52.9236 18.8515i 1.68886 0.601577i
983983 −49.5761 + 13.2839i −1.58123 + 0.423690i −0.939307 0.343078i 0.888530π-0.888530\pi
−0.641925 + 0.766768i 0.721864π0.721864\pi
984984 2.25800 + 0.655233i 0.0719824 + 0.0208881i
985985 −26.2735 7.03997i −0.837144 0.224312i
986986 4.46150 + 6.46585i 0.142083 + 0.205915i
987987 −0.934439 4.66087i −0.0297435 0.148357i
988988 −5.95402 + 15.6841i −0.189423 + 0.498976i
989989 11.4406 1.50619i 0.363791 0.0478940i
990990 −31.5801 61.6968i −1.00368 1.96085i
991991 −26.5712 + 46.0226i −0.844062 + 1.46196i 0.0423722 + 0.999102i 0.486508π0.486508\pi
−0.886434 + 0.462856i 0.846825π0.846825\pi
992992 2.02872 + 1.99151i 0.0644120 + 0.0632306i
993993 1.16758 0.0370522
994994 −10.0778 + 40.2484i −0.319648 + 1.27660i
995995 9.63294 23.2560i 0.305385 0.737264i
996996 0.416972 + 2.57102i 0.0132123 + 0.0814659i
997997 4.40157 33.4332i 0.139399 1.05884i −0.768559 0.639779i 0.779026π-0.779026\pi
0.907958 0.419062i 0.137641π-0.137641\pi
998998 34.8846 2.81046i 1.10425 0.0889635i
999999 7.62228 + 2.04238i 0.241158 + 0.0646182i
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 224.2.bd.a.109.15 yes 240
4.3 odd 2 896.2.bh.a.529.15 240
7.2 even 3 inner 224.2.bd.a.205.5 yes 240
28.23 odd 6 896.2.bh.a.401.16 240
32.5 even 8 inner 224.2.bd.a.165.5 yes 240
32.27 odd 8 896.2.bh.a.753.16 240
224.37 even 24 inner 224.2.bd.a.37.15 240
224.219 odd 24 896.2.bh.a.625.15 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
224.2.bd.a.37.15 240 224.37 even 24 inner
224.2.bd.a.109.15 yes 240 1.1 even 1 trivial
224.2.bd.a.165.5 yes 240 32.5 even 8 inner
224.2.bd.a.205.5 yes 240 7.2 even 3 inner
896.2.bh.a.401.16 240 28.23 odd 6
896.2.bh.a.529.15 240 4.3 odd 2
896.2.bh.a.625.15 240 224.219 odd 24
896.2.bh.a.753.16 240 32.27 odd 8