Properties

Label 841.2.e.c.236.2
Level 841841
Weight 22
Character 841.236
Analytic conductor 6.7156.715
Analytic rank 00
Dimension 1212
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [841,2,Mod(63,841)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(841, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("841.63");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 841=292 841 = 29^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 841.e (of order 1414, degree 66, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 6.715418809996.71541880999
Analytic rank: 00
Dimension: 1212
Relative dimension: 22 over Q(ζ14)\Q(\zeta_{14})
Coefficient field: Q(ζ28)\Q(\zeta_{28})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x12x10+x8x6+x4x2+1 x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 29)
Sato-Tate group: SU(2)[C14]\mathrm{SU}(2)[C_{14}]

Embedding invariants

Embedding label 236.2
Root 0.9749280.222521i-0.974928 - 0.222521i of defining polynomial
Character χ\chi == 841.236
Dual form 841.2.e.c.196.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.75676+0.400969i)q2+(0.1930960.400969i)q3+(1.12349+0.541044i)q4+(0.07941680.347948i)q5+(0.1784480.781831i)q6+(3.647951.75676i)q7+(1.060860.846011i)q8+(1.746982.19064i)q9+(0.2790320.579417i)q10+(2.27658+1.81551i)q110.554958iq12+(3.233414.05456i)q13+(7.112971.62349i)q14+(0.154851+0.0353438i)q15+(3.079423.86147i)q16+1.10992iq17+(3.947403.14795i)q18+(0.8889921.84601i)q19+(0.2774790.347948i)q20+(1.408811.12349i)q21+(4.72737+2.27658i)q22+(0.920583+4.03334i)q23+(0.134375+0.588735i)q24+(4.39008+2.11415i)q25+(4.054568.41939i)q26+(2.517370.574572i)q27+5.04892q280.286208q30+(6.19752+1.41454i)q31+(2.684005.57338i)q32+(1.16756+0.562269i)q33+(0.445042+1.94986i)q34+(0.3215521.40881i)q35+(3.147951.51597i)q36+(2.27658+1.81551i)q37+(2.301942.88654i)q38+(1.00139+2.07942i)q39+(0.378618+0.301938i)q400.396125iq41+(2.024462.53859i)q42+(5.597001.27748i)q43+(3.53999+0.807979i)q44+(0.6234900.781831i)q45+7.45473iq46+(6.09980+4.86443i)q47+(0.953703+1.98039i)q48+(5.856907.34432i)q49+(6.86461+5.47434i)q50+(0.4450420.214321i)q51+(1.439006.30468i)q52+(0.9695014.24766i)q53+(4.192022.01877i)q54+(0.450904+0.936313i)q55+(5.356211.22252i)q560.911854q579.10992q59+(0.1930960.0440730i)q60+(2.62453+5.44989i)q61+(10.3204+4.97002i)q62+(2.5244611.0604i)q63+(0.2823231.23694i)q64+(1.66756+0.803056i)q65+(1.82567+1.45593i)q66+(0.233406+0.292682i)q67+(0.600514+1.24698i)q68+(1.439481.14795i)q692.60388iq70+(7.11141+8.91742i)q71+(3.70662+0.846011i)q72+(8.724331.99127i)q73+(3.27144+4.10225i)q742.16852iq75+(1.997551.59299i)q76+(5.11543+10.6223i)q77+(2.59299+3.25151i)q78+(0.4645540.370469i)q79+(1.58815+0.764811i)q80+(1.614767.07473i)q81+(0.1588340.695895i)q82+(8.49880+4.09281i)q83+(0.9749282.02446i)q84+(0.386193+0.0881460i)q85+10.3448q86+3.95108q88+(1.387590.316708i)q89+(0.7818311.62349i)q90+(18.91829.11052i)q91+(1.14795+5.02949i)q92+(0.6295312.75815i)q93+(12.6664+6.09980i)q94+(0.5717140.455927i)q95+(1.71648+2.15240i)q96+(6.83394+14.1908i)q97+(13.234010.5538i)q98+8.15883iq99+O(q100)q+(1.75676 + 0.400969i) q^{2} +(-0.193096 - 0.400969i) q^{3} +(1.12349 + 0.541044i) q^{4} +(0.0794168 - 0.347948i) q^{5} +(-0.178448 - 0.781831i) q^{6} +(3.64795 - 1.75676i) q^{7} +(-1.06086 - 0.846011i) q^{8} +(1.74698 - 2.19064i) q^{9} +(0.279032 - 0.579417i) q^{10} +(-2.27658 + 1.81551i) q^{11} -0.554958i q^{12} +(-3.23341 - 4.05456i) q^{13} +(7.11297 - 1.62349i) q^{14} +(-0.154851 + 0.0353438i) q^{15} +(-3.07942 - 3.86147i) q^{16} +1.10992i q^{17} +(3.94740 - 3.14795i) q^{18} +(0.888992 - 1.84601i) q^{19} +(0.277479 - 0.347948i) q^{20} +(-1.40881 - 1.12349i) q^{21} +(-4.72737 + 2.27658i) q^{22} +(0.920583 + 4.03334i) q^{23} +(-0.134375 + 0.588735i) q^{24} +(4.39008 + 2.11415i) q^{25} +(-4.05456 - 8.41939i) q^{26} +(-2.51737 - 0.574572i) q^{27} +5.04892 q^{28} -0.286208 q^{30} +(6.19752 + 1.41454i) q^{31} +(-2.68400 - 5.57338i) q^{32} +(1.16756 + 0.562269i) q^{33} +(-0.445042 + 1.94986i) q^{34} +(-0.321552 - 1.40881i) q^{35} +(3.14795 - 1.51597i) q^{36} +(2.27658 + 1.81551i) q^{37} +(2.30194 - 2.88654i) q^{38} +(-1.00139 + 2.07942i) q^{39} +(-0.378618 + 0.301938i) q^{40} -0.396125i q^{41} +(-2.02446 - 2.53859i) q^{42} +(5.59700 - 1.27748i) q^{43} +(-3.53999 + 0.807979i) q^{44} +(-0.623490 - 0.781831i) q^{45} +7.45473i q^{46} +(-6.09980 + 4.86443i) q^{47} +(-0.953703 + 1.98039i) q^{48} +(5.85690 - 7.34432i) q^{49} +(6.86461 + 5.47434i) q^{50} +(0.445042 - 0.214321i) q^{51} +(-1.43900 - 6.30468i) q^{52} +(0.969501 - 4.24766i) q^{53} +(-4.19202 - 2.01877i) q^{54} +(0.450904 + 0.936313i) q^{55} +(-5.35621 - 1.22252i) q^{56} -0.911854 q^{57} -9.10992 q^{59} +(-0.193096 - 0.0440730i) q^{60} +(2.62453 + 5.44989i) q^{61} +(10.3204 + 4.97002i) q^{62} +(2.52446 - 11.0604i) q^{63} +(-0.282323 - 1.23694i) q^{64} +(-1.66756 + 0.803056i) q^{65} +(1.82567 + 1.45593i) q^{66} +(-0.233406 + 0.292682i) q^{67} +(-0.600514 + 1.24698i) q^{68} +(1.43948 - 1.14795i) q^{69} -2.60388i q^{70} +(7.11141 + 8.91742i) q^{71} +(-3.70662 + 0.846011i) q^{72} +(8.72433 - 1.99127i) q^{73} +(3.27144 + 4.10225i) q^{74} -2.16852i q^{75} +(1.99755 - 1.59299i) q^{76} +(-5.11543 + 10.6223i) q^{77} +(-2.59299 + 3.25151i) q^{78} +(-0.464554 - 0.370469i) q^{79} +(-1.58815 + 0.764811i) q^{80} +(-1.61476 - 7.07473i) q^{81} +(0.158834 - 0.695895i) q^{82} +(8.49880 + 4.09281i) q^{83} +(-0.974928 - 2.02446i) q^{84} +(0.386193 + 0.0881460i) q^{85} +10.3448 q^{86} +3.95108 q^{88} +(-1.38759 - 0.316708i) q^{89} +(-0.781831 - 1.62349i) q^{90} +(-18.9182 - 9.11052i) q^{91} +(-1.14795 + 5.02949i) q^{92} +(-0.629531 - 2.75815i) q^{93} +(-12.6664 + 6.09980i) q^{94} +(-0.571714 - 0.455927i) q^{95} +(-1.71648 + 2.15240i) q^{96} +(-6.83394 + 14.1908i) q^{97} +(13.2340 - 10.5538i) q^{98} +8.15883i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q+4q416q5+6q6+16q7+2q932q1320q16+4q2012q22+28q23+14q24+50q25+24q2836q30+12q334q3412q35+10q36++18q96+O(q100) 12 q + 4 q^{4} - 16 q^{5} + 6 q^{6} + 16 q^{7} + 2 q^{9} - 32 q^{13} - 20 q^{16} + 4 q^{20} - 12 q^{22} + 28 q^{23} + 14 q^{24} + 50 q^{25} + 24 q^{28} - 36 q^{30} + 12 q^{33} - 4 q^{34} - 12 q^{35} + 10 q^{36}+ \cdots + 18 q^{96}+O(q^{100}) Copy content Toggle raw display

Character values

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

nn 22
χ(n)\chi(n) e(114)e\left(\frac{1}{14}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.75676 + 0.400969i 1.24222 + 0.283528i 0.792627 0.609707i 0.208713π-0.208713\pi
0.449590 + 0.893235i 0.351570π0.351570\pi
33 −0.193096 0.400969i −0.111484 0.231499i 0.837760 0.546038i 0.183865π-0.183865\pi
−0.949245 + 0.314538i 0.898150π0.898150\pi
44 1.12349 + 0.541044i 0.561745 + 0.270522i
55 0.0794168 0.347948i 0.0355163 0.155607i −0.954060 0.299615i 0.903142π-0.903142\pi
0.989577 + 0.144008i 0.0459990π0.0459990\pi
66 −0.178448 0.781831i −0.0728511 0.319181i
77 3.64795 1.75676i 1.37879 0.663993i 0.410053 0.912062i 0.365510π-0.365510\pi
0.968742 + 0.248069i 0.0797960π0.0797960\pi
88 −1.06086 0.846011i −0.375072 0.299110i
99 1.74698 2.19064i 0.582327 0.730214i
1010 0.279032 0.579417i 0.0882378 0.183228i
1111 −2.27658 + 1.81551i −0.686414 + 0.547397i −0.903411 0.428775i 0.858945π-0.858945\pi
0.216997 + 0.976172i 0.430374π0.430374\pi
1212 0.554958i 0.160203i
1313 −3.23341 4.05456i −0.896785 1.12453i −0.991639 0.129042i 0.958810π-0.958810\pi
0.0948536 0.995491i 0.469762π-0.469762\pi
1414 7.11297 1.62349i 1.90102 0.433896i
1515 −0.154851 + 0.0353438i −0.0399824 + 0.00912573i
1616 −3.07942 3.86147i −0.769854 0.965367i
1717 1.10992i 0.269194i 0.990900 + 0.134597i 0.0429740π0.0429740\pi
−0.990900 + 0.134597i 0.957026π0.957026\pi
1818 3.94740 3.14795i 0.930412 0.741979i
1919 0.888992 1.84601i 0.203949 0.423504i −0.773757 0.633482i 0.781625π-0.781625\pi
0.977706 + 0.209978i 0.0673393π0.0673393\pi
2020 0.277479 0.347948i 0.0620462 0.0778035i
2121 −1.40881 1.12349i −0.307428 0.245166i
2222 −4.72737 + 2.27658i −1.00788 + 0.485368i
2323 0.920583 + 4.03334i 0.191955 + 0.841009i 0.975557 + 0.219746i 0.0705230π0.0705230\pi
−0.783602 + 0.621263i 0.786620π0.786620\pi
2424 −0.134375 + 0.588735i −0.0274292 + 0.120175i
2525 4.39008 + 2.11415i 0.878017 + 0.422831i
2626 −4.05456 8.41939i −0.795165 1.65118i
2727 −2.51737 0.574572i −0.484467 0.110577i
2828 5.04892 0.954156
2929 0 0
3030 −0.286208 −0.0522542
3131 6.19752 + 1.41454i 1.11311 + 0.254059i 0.739253 0.673428i 0.235179π-0.235179\pi
0.373854 + 0.927488i 0.378036π0.378036\pi
3232 −2.68400 5.57338i −0.474468 0.985243i
3333 1.16756 + 0.562269i 0.203247 + 0.0978784i
3434 −0.445042 + 1.94986i −0.0763241 + 0.334398i
3535 −0.321552 1.40881i −0.0543522 0.238133i
3636 3.14795 1.51597i 0.524658 0.252662i
3737 2.27658 + 1.81551i 0.374267 + 0.298468i 0.792500 0.609872i 0.208779π-0.208779\pi
−0.418233 + 0.908340i 0.637350π0.637350\pi
3838 2.30194 2.88654i 0.373424 0.468258i
3939 −1.00139 + 2.07942i −0.160351 + 0.332973i
4040 −0.378618 + 0.301938i −0.0598648 + 0.0477405i
4141 0.396125i 0.0618643i −0.999521 0.0309321i 0.990152π-0.990152\pi
0.999521 0.0309321i 0.00984757π-0.00984757\pi
4242 −2.02446 2.53859i −0.312381 0.391713i
4343 5.59700 1.27748i 0.853535 0.194814i 0.226699 0.973965i 0.427207π-0.427207\pi
0.626836 + 0.779151i 0.284350π0.284350\pi
4444 −3.53999 + 0.807979i −0.533673 + 0.121807i
4545 −0.623490 0.781831i −0.0929444 0.116549i
4646 7.45473i 1.09914i
4747 −6.09980 + 4.86443i −0.889747 + 0.709550i −0.957586 0.288146i 0.906961π-0.906961\pi
0.0678390 + 0.997696i 0.478390π0.478390\pi
4848 −0.953703 + 1.98039i −0.137655 + 0.285844i
4949 5.85690 7.34432i 0.836699 1.04919i
5050 6.86461 + 5.47434i 0.970803 + 0.774189i
5151 0.445042 0.214321i 0.0623183 0.0300109i
5252 −1.43900 6.30468i −0.199554 0.874301i
5353 0.969501 4.24766i 0.133171 0.583461i −0.863671 0.504055i 0.831841π-0.831841\pi
0.996842 0.0794054i 0.0253022π-0.0253022\pi
5454 −4.19202 2.01877i −0.570462 0.274720i
5555 0.450904 + 0.936313i 0.0607999 + 0.126252i
5656 −5.35621 1.22252i −0.715754 0.163366i
5757 −0.911854 −0.120778
5858 0 0
5959 −9.10992 −1.18601 −0.593005 0.805199i 0.702059π-0.702059\pi
−0.593005 + 0.805199i 0.702059π0.702059\pi
6060 −0.193096 0.0440730i −0.0249286 0.00568980i
6161 2.62453 + 5.44989i 0.336036 + 0.697786i 0.998692 0.0511381i 0.0162849π-0.0162849\pi
−0.662655 + 0.748924i 0.730571π0.730571\pi
6262 10.3204 + 4.97002i 1.31069 + 0.631193i
6363 2.52446 11.0604i 0.318052 1.39348i
6464 −0.282323 1.23694i −0.0352904 0.154617i
6565 −1.66756 + 0.803056i −0.206836 + 0.0996068i
6666 1.82567 + 1.45593i 0.224725 + 0.179212i
6767 −0.233406 + 0.292682i −0.0285151 + 0.0357568i −0.795885 0.605448i 0.792994π-0.792994\pi
0.767369 + 0.641205i 0.221565π0.221565\pi
6868 −0.600514 + 1.24698i −0.0728230 + 0.151218i
6969 1.43948 1.14795i 0.173293 0.138197i
7070 2.60388i 0.311223i
7171 7.11141 + 8.91742i 0.843969 + 1.05830i 0.997535 + 0.0701652i 0.0223526π0.0223526\pi
−0.153567 + 0.988138i 0.549076π0.549076\pi
7272 −3.70662 + 0.846011i −0.436829 + 0.0997033i
7373 8.72433 1.99127i 1.02111 0.233061i 0.320984 0.947085i 0.395986π-0.395986\pi
0.700121 + 0.714024i 0.253129π0.253129\pi
7474 3.27144 + 4.10225i 0.380297 + 0.476877i
7575 2.16852i 0.250399i
7676 1.99755 1.59299i 0.229134 0.182729i
7777 −5.11543 + 10.6223i −0.582957 + 1.21052i
7878 −2.59299 + 3.25151i −0.293598 + 0.368161i
7979 −0.464554 0.370469i −0.0522664 0.0416811i 0.597008 0.802235i 0.296356π-0.296356\pi
−0.649275 + 0.760554i 0.724927π0.724927\pi
8080 −1.58815 + 0.764811i −0.177560 + 0.0855084i
8181 −1.61476 7.07473i −0.179418 0.786081i
8282 0.158834 0.695895i 0.0175402 0.0768488i
8383 8.49880 + 4.09281i 0.932865 + 0.449244i 0.837647 0.546212i 0.183931π-0.183931\pi
0.0952182 + 0.995456i 0.469645π0.469645\pi
8484 −0.974928 2.02446i −0.106373 0.220887i
8585 0.386193 + 0.0881460i 0.0418885 + 0.00956078i
8686 10.3448 1.11551
8787 0 0
8888 3.95108 0.421187
8989 −1.38759 0.316708i −0.147084 0.0335710i 0.148345 0.988936i 0.452605π-0.452605\pi
−0.295429 + 0.955365i 0.595463π0.595463\pi
9090 −0.781831 1.62349i −0.0824123 0.171131i
9191 −18.9182 9.11052i −1.98317 0.955042i
9292 −1.14795 + 5.02949i −0.119682 + 0.524361i
9393 −0.629531 2.75815i −0.0652793 0.286007i
9494 −12.6664 + 6.09980i −1.30644 + 0.629146i
9595 −0.571714 0.455927i −0.0586567 0.0467771i
9696 −1.71648 + 2.15240i −0.175188 + 0.219678i
9797 −6.83394 + 14.1908i −0.693882 + 1.44086i 0.194100 + 0.980982i 0.437821π0.437821\pi
−0.887982 + 0.459878i 0.847893π0.847893\pi
9898 13.2340 10.5538i 1.33684 1.06609i
9999 8.15883i 0.819994i
100100 3.78836 + 4.75046i 0.378836 + 0.475046i
101101 −17.0053 + 3.88135i −1.69209 + 0.386209i −0.956619 0.291343i 0.905898π-0.905898\pi
−0.735475 + 0.677552i 0.763041π0.763041\pi
102102 0.867767 0.198062i 0.0859218 0.0196111i
103103 −1.75451 2.20009i −0.172877 0.216781i 0.687843 0.725860i 0.258558π-0.258558\pi
−0.860720 + 0.509078i 0.829986π0.829986\pi
104104 7.03684i 0.690019i
105105 −0.502799 + 0.400969i −0.0490682 + 0.0391306i
106106 3.40636 7.07338i 0.330855 0.687027i
107107 −4.65130 + 5.83255i −0.449658 + 0.563854i −0.954060 0.299615i 0.903142π-0.903142\pi
0.504402 + 0.863469i 0.331713π0.331713\pi
108108 −2.51737 2.00753i −0.242234 0.193175i
109109 −1.48911 + 0.717120i −0.142631 + 0.0686876i −0.503838 0.863798i 0.668079π-0.668079\pi
0.361207 + 0.932486i 0.382365π0.382365\pi
110110 0.416698 + 1.82567i 0.0397306 + 0.174071i
111111 0.288364 1.26341i 0.0273703 0.119917i
112112 −18.0172 8.67664i −1.70247 0.819865i
113113 3.74906 + 7.78501i 0.352682 + 0.732352i 0.999542 0.0302566i 0.00963243π-0.00963243\pi
−0.646860 + 0.762609i 0.723918π0.723918\pi
114114 −1.60191 0.365625i −0.150032 0.0342439i
115115 1.47650 0.137684
116116 0 0
117117 −14.5308 −1.34337
118118 −16.0039 3.65279i −1.47328 0.336267i
119119 1.94986 + 4.04892i 0.178743 + 0.371164i
120120 0.194177 + 0.0935109i 0.0177259 + 0.00853634i
121121 −0.560999 + 2.45790i −0.0509999 + 0.223445i
122122 2.42543 + 10.6265i 0.219588 + 0.962077i
123123 −0.158834 + 0.0764902i −0.0143215 + 0.00689689i
124124 6.19752 + 4.94235i 0.556553 + 0.443836i
125125 2.19687 2.75478i 0.196494 0.246395i
126126 8.86973 18.4182i 0.790179 1.64082i
127127 −8.18749 + 6.52930i −0.726522 + 0.579382i −0.915365 0.402625i 0.868098π-0.868098\pi
0.188843 + 0.982007i 0.439526π0.439526\pi
128128 10.0858i 0.891463i
129129 −1.59299 1.99755i −0.140255 0.175874i
130130 −3.25151 + 0.742135i −0.285176 + 0.0650896i
131131 0.443330 0.101187i 0.0387339 0.00884076i −0.203110 0.979156i 0.565105π-0.565105\pi
0.241844 + 0.970315i 0.422248π0.422248\pi
132132 1.00753 + 1.26341i 0.0876945 + 0.109965i
133133 8.29590i 0.719345i
134134 −0.527395 + 0.420583i −0.0455600 + 0.0363329i
135135 −0.399842 + 0.830281i −0.0344130 + 0.0714592i
136136 0.939001 1.17747i 0.0805187 0.100967i
137137 −10.3517 8.25518i −0.884402 0.705287i 0.0719797 0.997406i 0.477068π-0.477068\pi
−0.956382 + 0.292119i 0.905640π0.905640\pi
138138 2.98911 1.43948i 0.254450 0.122537i
139139 0.622293 + 2.72645i 0.0527822 + 0.231254i 0.994438 0.105323i 0.0335878π-0.0335878\pi
−0.941656 + 0.336577i 0.890731π0.890731\pi
140140 0.400969 1.75676i 0.0338881 0.148473i
141141 3.12833 + 1.50653i 0.263453 + 0.126872i
142142 8.91742 + 18.5172i 0.748334 + 1.55393i
143143 14.7222 + 3.36025i 1.23113 + 0.280998i
144144 −13.8388 −1.15323
145145 0 0
146146 16.1250 1.33451
147147 −4.07579 0.930272i −0.336165 0.0767275i
148148 1.57544 + 3.27144i 0.129501 + 0.268911i
149149 2.44020 + 1.17514i 0.199909 + 0.0962710i 0.531160 0.847272i 0.321756π-0.321756\pi
−0.331251 + 0.943543i 0.607471π0.607471\pi
150150 0.869510 3.80957i 0.0709952 0.311050i
151151 −0.541917 2.37429i −0.0441006 0.193217i 0.948079 0.318034i 0.103023π-0.103023\pi
−0.992180 + 0.124817i 0.960166π0.960166\pi
152152 −2.50484 + 1.20627i −0.203170 + 0.0978414i
153153 2.43143 + 1.93900i 0.196570 + 0.156759i
154154 −13.2458 + 16.6097i −1.06738 + 1.33845i
155155 0.984374 2.04407i 0.0790668 0.164184i
156156 −2.25011 + 1.79440i −0.180153 + 0.143667i
157157 17.6775i 1.41082i −0.708799 0.705411i 0.750762π-0.750762\pi
0.708799 0.705411i 0.249238π-0.249238\pi
158158 −0.667563 0.837097i −0.0531084 0.0665959i
159159 −1.89039 + 0.431468i −0.149917 + 0.0342177i
160160 −2.15240 + 0.491271i −0.170162 + 0.0388384i
161161 10.4438 + 13.0962i 0.823090 + 1.03212i
162162 13.0761i 1.02735i
163163 −3.88269 + 3.09634i −0.304116 + 0.242524i −0.763642 0.645640i 0.776591π-0.776591\pi
0.459526 + 0.888164i 0.348019π0.348019\pi
164164 0.214321 0.445042i 0.0167356 0.0347519i
165165 0.288364 0.361597i 0.0224491 0.0281503i
166166 13.2893 + 10.5978i 1.03145 + 0.822551i
167167 13.0320 6.27588i 1.00845 0.485642i 0.144649 0.989483i 0.453795π-0.453795\pi
0.863796 + 0.503841i 0.168080π0.168080\pi
168168 0.544073 + 2.38374i 0.0419761 + 0.183910i
169169 −3.09179 + 13.5460i −0.237830 + 1.04200i
170170 0.643104 + 0.309703i 0.0493238 + 0.0237531i
171171 −2.49090 5.17241i −0.190484 0.395544i
172172 6.97935 + 1.59299i 0.532170 + 0.121464i
173173 −10.5133 −0.799314 −0.399657 0.916665i 0.630871π-0.630871\pi
−0.399657 + 0.916665i 0.630871π0.630871\pi
174174 0 0
175175 19.7289 1.49136
176176 14.0211 + 3.20022i 1.05688 + 0.241226i
177177 1.75909 + 3.65279i 0.132221 + 0.274561i
178178 −2.31067 1.11276i −0.173192 0.0834048i
179179 −1.27748 + 5.59700i −0.0954833 + 0.418340i −0.999967 0.00816938i 0.997400π-0.997400\pi
0.904483 + 0.426509i 0.140257π0.140257\pi
180180 −0.277479 1.21572i −0.0206821 0.0906141i
181181 5.98307 2.88130i 0.444718 0.214165i −0.198103 0.980181i 0.563478π-0.563478\pi
0.642821 + 0.766016i 0.277764π0.277764\pi
182182 −29.5817 23.5906i −2.19274 1.74865i
183183 1.67845 2.10471i 0.124074 0.155584i
184184 2.43563 5.05765i 0.179557 0.372855i
185185 0.812502 0.647948i 0.0597363 0.0476381i
186186 5.09783i 0.373791i
187187 −2.01507 2.52681i −0.147356 0.184779i
188188 −9.48493 + 2.16487i −0.691760 + 0.157890i
189189 −10.1926 + 2.32640i −0.741403 + 0.169220i
190190 −0.821552 1.03019i −0.0596017 0.0747381i
191191 18.8116i 1.36116i −0.732673 0.680581i 0.761728π-0.761728\pi
0.732673 0.680581i 0.238272π-0.238272\pi
192192 −0.441459 + 0.352052i −0.0318595 + 0.0254071i
193193 4.72270 9.80678i 0.339947 0.705908i −0.658983 0.752158i 0.729013π-0.729013\pi
0.998930 + 0.0462505i 0.0147272π0.0147272\pi
194194 −17.6957 + 22.1897i −1.27048 + 1.59313i
195195 0.644001 + 0.513574i 0.0461179 + 0.0367778i
196196 10.5538 5.08242i 0.753840 0.363030i
197197 1.86927 + 8.18982i 0.133180 + 0.583501i 0.996841 + 0.0794266i 0.0253089π0.0253089\pi
−0.863661 + 0.504074i 0.831834π0.831834\pi
198198 −3.27144 + 14.3331i −0.232491 + 1.01861i
199199 5.96562 + 2.87289i 0.422891 + 0.203654i 0.633211 0.773979i 0.281736π-0.281736\pi
−0.210320 + 0.977633i 0.567451π0.567451\pi
200200 −2.86869 5.95689i −0.202847 0.421215i
201201 0.162426 + 0.0370727i 0.0114567 + 0.00261491i
202202 −31.4306 −2.21145
203203 0 0
204204 0.615957 0.0431256
205205 −0.137831 0.0314589i −0.00962651 0.00219719i
206206 −2.20009 4.56853i −0.153287 0.318305i
207207 10.4438 + 5.02949i 0.725897 + 0.349574i
208208 −5.69955 + 24.9714i −0.395193 + 1.73145i
209209 1.32759 + 5.81656i 0.0918315 + 0.402340i
210210 −1.04407 + 0.502799i −0.0720479 + 0.0346964i
211211 6.33301 + 5.05041i 0.435983 + 0.347685i 0.816755 0.576984i 0.195771π-0.195771\pi
−0.380773 + 0.924669i 0.624342π0.624342\pi
212212 3.38740 4.24766i 0.232647 0.291730i
213213 2.20242 4.57338i 0.150907 0.313363i
214214 −10.5099 + 8.38135i −0.718441 + 0.572938i
215215 2.04892i 0.139735i
216216 2.18449 + 2.73926i 0.148636 + 0.186383i
217217 25.0932 5.72737i 1.70344 0.388799i
218218 −2.90356 + 0.662718i −0.196654 + 0.0448850i
219219 −2.48307 3.11368i −0.167791 0.210403i
220220 1.29590i 0.0873694i
221221 4.50023 3.58881i 0.302718 0.241409i
222222 1.01317 2.10388i 0.0679997 0.141203i
223223 13.6664 17.1371i 0.915168 1.14758i −0.0734749 0.997297i 0.523409π-0.523409\pi
0.988642 0.150287i 0.0480197π-0.0480197\pi
224224 −19.5822 15.6163i −1.30839 1.04340i
225225 12.3007 5.92372i 0.820049 0.394915i
226226 3.46466 + 15.1797i 0.230466 + 1.00974i
227227 4.06734 17.8202i 0.269959 1.18277i −0.640102 0.768290i 0.721108π-0.721108\pi
0.910060 0.414476i 0.136035π-0.136035\pi
228228 −1.02446 0.493353i −0.0678464 0.0326731i
229229 6.95288 + 14.4378i 0.459459 + 0.954077i 0.994046 + 0.108963i 0.0347531π0.0347531\pi
−0.534587 + 0.845114i 0.679533π0.679533\pi
230230 2.59386 + 0.592031i 0.171034 + 0.0390374i
231231 5.24698 0.345226
232232 0 0
233233 1.95646 0.128172 0.0640860 0.997944i 0.479587π-0.479587\pi
0.0640860 + 0.997944i 0.479587π0.479587\pi
234234 −25.5271 5.82640i −1.66876 0.380883i
235235 1.20814 + 2.50873i 0.0788104 + 0.163651i
236236 −10.2349 4.92887i −0.666235 0.320842i
237237 −0.0588430 + 0.257808i −0.00382226 + 0.0167464i
238238 1.80194 + 7.89481i 0.116802 + 0.511744i
239239 8.07553 3.88897i 0.522363 0.251557i −0.154071 0.988060i 0.549239π-0.549239\pi
0.676434 + 0.736503i 0.263524π0.263524\pi
240240 0.613331 + 0.489115i 0.0395903 + 0.0315722i
241241 −12.4073 + 15.5583i −0.799225 + 1.00220i 0.200522 + 0.979689i 0.435736π0.435736\pi
−0.999747 + 0.0225070i 0.992835π0.992835\pi
242242 −1.97108 + 4.09299i −0.126706 + 0.263107i
243243 −8.58125 + 6.84332i −0.550488 + 0.438999i
244244 7.54288i 0.482883i
245245 −2.09030 2.62116i −0.133544 0.167459i
246246 −0.309703 + 0.0706876i −0.0197459 + 0.00450688i
247247 −10.3592 + 2.36443i −0.659143 + 0.150445i
248248 −5.37800 6.74380i −0.341503 0.428232i
249249 4.19806i 0.266041i
250250 4.96395 3.95862i 0.313948 0.250365i
251251 11.1963 23.2494i 0.706706 1.46749i −0.169487 0.985532i 0.554211π-0.554211\pi
0.876194 0.481959i 0.160074π-0.160074\pi
252252 8.82036 11.0604i 0.555630 0.696738i
253253 −9.41835 7.51089i −0.592127 0.472205i
254254 −17.0015 + 8.18749i −1.06677 + 0.513729i
255255 −0.0392287 0.171872i −0.00245659 0.0107630i
256256 −4.60872 + 20.1921i −0.288045 + 1.26201i
257257 −10.7676 5.18538i −0.671662 0.323455i 0.0667848 0.997767i 0.478726π-0.478726\pi
−0.738446 + 0.674312i 0.764440π0.764440\pi
258258 −1.99755 4.14795i −0.124362 0.258240i
259259 11.4943 + 2.62349i 0.714219 + 0.163016i
260260 −2.30798 −0.143135
261261 0 0
262262 0.819396 0.0506225
263263 0.324390 + 0.0740400i 0.0200028 + 0.00456550i 0.232511 0.972594i 0.425306π-0.425306\pi
−0.212508 + 0.977159i 0.568163π0.568163\pi
264264 −0.762940 1.58426i −0.0469557 0.0975045i
265265 −1.40097 0.674671i −0.0860608 0.0414447i
266266 3.32640 14.5739i 0.203954 0.893583i
267267 0.140948 + 0.617534i 0.00862589 + 0.0377925i
268268 −0.420583 + 0.202542i −0.0256912 + 0.0123722i
269269 0.831855 + 0.663382i 0.0507191 + 0.0404471i 0.648521 0.761197i 0.275388π-0.275388\pi
−0.597802 + 0.801644i 0.703959π0.703959\pi
270270 −1.03534 + 1.29828i −0.0630090 + 0.0790108i
271271 7.14364 14.8339i 0.433945 0.901097i −0.563252 0.826285i 0.690450π-0.690450\pi
0.997198 0.0748120i 0.0238357π-0.0238357\pi
272272 4.28590 3.41789i 0.259871 0.207240i
273273 9.34481i 0.565574i
274274 −14.8753 18.6531i −0.898651 1.12687i
275275 −13.8326 + 3.15721i −0.834140 + 0.190387i
276276 2.23833 0.510885i 0.134732 0.0307517i
277277 4.11141 + 5.15554i 0.247031 + 0.309767i 0.889852 0.456250i 0.150808π-0.150808\pi
−0.642821 + 0.766016i 0.722236π0.722236\pi
278278 5.03923i 0.302233i
279279 13.9257 11.1054i 0.833709 0.664861i
280280 −0.850747 + 1.76659i −0.0508418 + 0.105574i
281281 −19.0383 + 23.8733i −1.13573 + 1.42416i −0.245064 + 0.969507i 0.578809π0.578809\pi
−0.890668 + 0.454655i 0.849762π0.849762\pi
282282 4.89166 + 3.90097i 0.291294 + 0.232299i
283283 −3.20291 + 1.54244i −0.190393 + 0.0916885i −0.526652 0.850081i 0.676553π-0.676553\pi
0.336258 + 0.941770i 0.390838π0.390838\pi
284284 3.16487 + 13.8662i 0.187801 + 0.822809i
285285 −0.0724165 + 0.317278i −0.00428958 + 0.0187939i
286286 24.5160 + 11.8063i 1.44966 + 0.698121i
287287 −0.695895 1.44504i −0.0410774 0.0852981i
288288 −16.8982 3.85690i −0.995734 0.227270i
289289 15.7681 0.927534
290290 0 0
291291 7.00969 0.410915
292292 10.8791 + 2.48307i 0.636649 + 0.145311i
293293 −14.2661 29.6238i −0.833432 1.73064i −0.667647 0.744478i 0.732698π-0.732698\pi
−0.165786 0.986162i 0.553016π-0.553016\pi
294294 −6.78717 3.26853i −0.395836 0.190624i
295295 −0.723480 + 3.16977i −0.0421227 + 0.184551i
296296 −0.879199 3.85202i −0.0511024 0.223894i
297297 6.77413 3.26225i 0.393075 0.189295i
298298 3.81565 + 3.04288i 0.221034 + 0.176269i
299299 13.3768 16.7740i 0.773601 0.970065i
300300 1.17327 2.43631i 0.0677386 0.140661i
301301 18.1733 14.4928i 1.04749 0.835349i
302302 4.38835i 0.252521i
303303 4.83997 + 6.06913i 0.278049 + 0.348662i
304304 −9.86589 + 2.25182i −0.565847 + 0.129151i
305305 2.10471 0.480386i 0.120515 0.0275068i
306306 3.49396 + 4.38129i 0.199736 + 0.250461i
307307 14.6703i 0.837275i 0.908153 + 0.418638i 0.137492π0.137492\pi
−0.908153 + 0.418638i 0.862508π0.862508\pi
308308 −11.4943 + 9.16637i −0.654946 + 0.522302i
309309 −0.543377 + 1.12833i −0.0309116 + 0.0641887i
310310 2.54892 3.19624i 0.144769 0.181534i
311311 14.4846 + 11.5511i 0.821346 + 0.655001i 0.941222 0.337788i 0.109679π-0.109679\pi
−0.119877 + 0.992789i 0.538250π0.538250\pi
312312 2.82155 1.35879i 0.159739 0.0769262i
313313 −5.11625 22.4158i −0.289188 1.26701i −0.885643 0.464367i 0.846282π-0.846282\pi
0.596455 0.802647i 0.296575π-0.296575\pi
314314 7.08815 31.0552i 0.400007 1.75255i
315315 −3.64795 1.75676i −0.205539 0.0989822i
316316 −0.321481 0.667563i −0.0180847 0.0375533i
317317 13.7061 + 3.12833i 0.769813 + 0.175705i 0.589351 0.807877i 0.299384π-0.299384\pi
0.180462 + 0.983582i 0.442241π0.442241\pi
318318 −3.49396 −0.195932
319319 0 0
320320 −0.452812 −0.0253129
321321 3.23682 + 0.738783i 0.180662 + 0.0412348i
322322 13.0962 + 27.1945i 0.729821 + 1.51549i
323323 2.04892 + 0.986707i 0.114005 + 0.0549018i
324324 2.01357 8.82204i 0.111865 0.490113i
325325 −5.62296 24.6358i −0.311906 1.36655i
326326 −8.06249 + 3.88269i −0.446540 + 0.215042i
327327 0.575086 + 0.458615i 0.0318023 + 0.0253615i
328328 −0.335126 + 0.420234i −0.0185042 + 0.0232036i
329329 −13.7061 + 28.4611i −0.755643 + 1.56911i
330330 0.651576 0.519614i 0.0358681 0.0286038i
331331 13.9565i 0.767116i −0.923517 0.383558i 0.874699π-0.874699\pi
0.923517 0.383558i 0.125301π-0.125301\pi
332332 7.33393 + 9.19646i 0.402502 + 0.504721i
333333 7.95427 1.81551i 0.435892 0.0994894i
334334 25.4105 5.79978i 1.39040 0.317350i
335335 0.0833017 + 0.104457i 0.00455126 + 0.00570709i
336336 8.89977i 0.485522i
337337 −10.9438 + 8.72737i −0.596145 + 0.475410i −0.874472 0.485077i 0.838792π-0.838792\pi
0.278327 + 0.960487i 0.410220π0.410220\pi
338338 −10.8631 + 22.5574i −0.590873 + 1.22696i
339339 2.39762 3.00652i 0.130221 0.163292i
340340 0.386193 + 0.307979i 0.0209442 + 0.0167025i
341341 −16.6773 + 8.03134i −0.903124 + 0.434922i
342342 −2.30194 10.0854i −0.124475 0.545359i
343343 2.15668 9.44902i 0.116450 0.510199i
344344 −7.01842 3.37989i −0.378408 0.182232i
345345 −0.285107 0.592031i −0.0153496 0.0318739i
346346 −18.4694 4.21552i −0.992921 0.226628i
347347 19.8538 1.06581 0.532905 0.846175i 0.321100π-0.321100\pi
0.532905 + 0.846175i 0.321100π0.321100\pi
348348 0 0
349349 −26.9202 −1.44101 −0.720503 0.693452i 0.756089π-0.756089\pi
−0.720503 + 0.693452i 0.756089π0.756089\pi
350350 34.6589 + 7.91066i 1.85259 + 0.422842i
351351 5.81003 + 12.0646i 0.310116 + 0.643963i
352352 16.2289 + 7.81541i 0.865001 + 0.416563i
353353 −0.893436 + 3.91440i −0.0475528 + 0.208342i −0.993123 0.117076i 0.962648π-0.962648\pi
0.945570 + 0.325418i 0.105505π0.105505\pi
354354 1.62565 + 7.12242i 0.0864021 + 0.378552i
355355 3.66756 1.76621i 0.194654 0.0937404i
356356 −1.38759 1.10656i −0.0735420 0.0586478i
357357 1.24698 1.56366i 0.0659972 0.0827578i
358358 −4.48845 + 9.32036i −0.237222 + 0.492596i
359359 0.583493 0.465320i 0.0307956 0.0245587i −0.607971 0.793959i 0.708016π-0.708016\pi
0.638767 + 0.769401i 0.279445π0.279445\pi
360360 1.35690i 0.0715147i
361361 9.22886 + 11.5726i 0.485729 + 0.609085i
362362 11.6661 2.66272i 0.613158 0.139949i
363363 1.09387 0.249668i 0.0574131 0.0131042i
364364 −16.3252 20.4712i −0.855673 1.07298i
365365 3.19375i 0.167169i
366366 3.79255 3.02446i 0.198240 0.158091i
367367 −14.7733 + 30.6770i −0.771158 + 1.60133i 0.0275585 + 0.999620i 0.491227π0.491227\pi
−0.798717 + 0.601707i 0.794488π0.794488\pi
368368 12.7397 15.9751i 0.664105 0.832761i
369369 −0.867767 0.692021i −0.0451742 0.0360252i
370370 1.68718 0.812502i 0.0877122 0.0422400i
371371 −3.92543 17.1984i −0.203798 0.892898i
372372 0.785012 3.43936i 0.0407010 0.178323i
373373 −25.2277 12.1490i −1.30624 0.629051i −0.354240 0.935154i 0.615261π-0.615261\pi
−0.951998 + 0.306103i 0.900975π0.900975\pi
374374 −2.52681 5.24698i −0.130658 0.271315i
375375 −1.52879 0.348936i −0.0789463 0.0180190i
376376 10.5864 0.545953
377377 0 0
378378 −18.8388 −0.968962
379379 −22.3073 5.09150i −1.14585 0.261533i −0.392881 0.919589i 0.628522π-0.628522\pi
−0.752969 + 0.658057i 0.771379π0.771379\pi
380380 −0.395639 0.821552i −0.0202958 0.0421447i
381381 4.19902 + 2.02214i 0.215122 + 0.103597i
382382 7.54288 33.0475i 0.385927 1.69086i
383383 2.63869 + 11.5608i 0.134831 + 0.590731i 0.996524 + 0.0833027i 0.0265468π0.0265468\pi
−0.861694 + 0.507429i 0.830596π0.830596\pi
384384 4.04407 1.94752i 0.206373 0.0993841i
385385 3.28975 + 2.62349i 0.167661 + 0.133705i
386386 12.2289 15.3345i 0.622432 0.780506i
387387 6.97935 14.4928i 0.354780 0.736709i
388388 −15.3557 + 12.2458i −0.779569 + 0.621685i
389389 10.3913i 0.526862i 0.964678 + 0.263431i 0.0848541π0.0848541\pi
−0.964678 + 0.263431i 0.915146π0.915146\pi
390390 0.925428 + 1.16045i 0.0468608 + 0.0587616i
391391 −4.47667 + 1.02177i −0.226395 + 0.0516731i
392392 −12.4267 + 2.83632i −0.627645 + 0.143256i
393393 −0.126178 0.158222i −0.00636485 0.00798127i
394394 15.1371i 0.762594i
395395 −0.165797 + 0.132219i −0.00834217 + 0.00665266i
396396 −4.41429 + 9.16637i −0.221826 + 0.460627i
397397 5.12349 6.42465i 0.257141 0.322444i −0.636458 0.771312i 0.719601π-0.719601\pi
0.893598 + 0.448867i 0.148172π0.148172\pi
398398 9.32821 + 7.43900i 0.467581 + 0.372883i
399399 −3.32640 + 1.60191i −0.166528 + 0.0801957i
400400 −5.35517 23.4625i −0.267758 1.17313i
401401 −5.53654 + 24.2572i −0.276482 + 1.21135i 0.625726 + 0.780043i 0.284803π0.284803\pi
−0.902208 + 0.431302i 0.858054π0.858054\pi
402402 0.270479 + 0.130256i 0.0134903 + 0.00649656i
403403 −14.3037 29.7020i −0.712520 1.47956i
404404 −21.2053 4.83997i −1.05500 0.240798i
405405 −2.58987 −0.128692
406406 0 0
407407 −8.47889 −0.420283
408408 −0.653447 0.149145i −0.0323504 0.00738377i
409409 −8.19843 17.0242i −0.405386 0.841794i −0.999305 0.0372686i 0.988134π-0.988134\pi
0.593919 0.804525i 0.297580π-0.297580\pi
410410 −0.229521 0.110532i −0.0113352 0.00545877i
411411 −1.31120 + 5.74474i −0.0646767 + 0.283367i
412412 −0.780831 3.42105i −0.0384688 0.168543i
413413 −33.2325 + 16.0039i −1.63526 + 0.787502i
414414 16.3307 + 13.0233i 0.802608 + 0.640058i
415415 2.09903 2.63210i 0.103037 0.129205i
416416 −13.9192 + 28.9034i −0.682443 + 1.41711i
417417 0.973057 0.775987i 0.0476508 0.0380003i
418418 10.7506i 0.525830i
419419 6.79135 + 8.51608i 0.331779 + 0.416038i 0.919540 0.392997i 0.128562π-0.128562\pi
−0.587761 + 0.809035i 0.699990π0.699990\pi
420420 −0.781831 + 0.178448i −0.0381495 + 0.00870737i
421421 19.4603 4.44169i 0.948438 0.216475i 0.279796 0.960059i 0.409733π-0.409733\pi
0.668642 + 0.743585i 0.266876π0.266876\pi
422422 9.10052 + 11.4117i 0.443007 + 0.555513i
423423 21.8605i 1.06290i
424424 −4.62207 + 3.68598i −0.224468 + 0.179007i
425425 −2.34653 + 4.87263i −0.113824 + 0.236357i
426426 5.70291 7.15122i 0.276307 0.346478i
427427 19.1483 + 15.2702i 0.926650 + 0.738979i
428428 −8.38135 + 4.03625i −0.405128 + 0.195099i
429429 −1.49545 6.55200i −0.0722011 0.316334i
430430 0.821552 3.59945i 0.0396188 0.173581i
431431 27.2005 + 13.0991i 1.31020 + 0.630960i 0.952973 0.303056i 0.0980070π-0.0980070\pi
0.357230 + 0.934016i 0.383721π0.383721\pi
432432 5.53333 + 11.4901i 0.266222 + 0.552816i
433433 −19.6851 4.49300i −0.946006 0.215920i −0.278426 0.960458i 0.589813π-0.589813\pi
−0.667580 + 0.744538i 0.732670π0.732670\pi
434434 46.3793 2.22628
435435 0 0
436436 −2.06100 −0.0987039
437437 8.26398 + 1.88620i 0.395320 + 0.0902291i
438438 −3.11368 6.46562i −0.148777 0.308939i
439439 −9.60872 4.62732i −0.458599 0.220850i 0.190297 0.981727i 0.439055π-0.439055\pi
−0.648896 + 0.760877i 0.724769π0.724769\pi
440440 0.313782 1.37477i 0.0149590 0.0655396i
441441 −5.85690 25.6607i −0.278900 1.22194i
442442 9.34481 4.50023i 0.444487 0.214054i
443443 15.9104 + 12.6881i 0.755927 + 0.602832i 0.923755 0.382985i 0.125104π-0.125104\pi
−0.167828 + 0.985816i 0.553675π0.553675\pi
444444 1.00753 1.26341i 0.0478154 0.0599586i
445445 −0.220395 + 0.457656i −0.0104477 + 0.0216950i
446446 30.8800 24.6259i 1.46221 1.16607i
447447 1.20536i 0.0570115i
448448 −3.20291 4.01632i −0.151323 0.189753i
449449 18.9363 4.32208i 0.893659 0.203972i 0.249056 0.968489i 0.419880π-0.419880\pi
0.644603 + 0.764517i 0.277023π0.277023\pi
450450 23.9847 5.47434i 1.13065 0.258063i
451451 0.719169 + 0.901809i 0.0338643 + 0.0424645i
452452 10.7748i 0.506804i
453453 −0.847376 + 0.675760i −0.0398132 + 0.0317500i
454454 14.2907 29.6749i 0.670694 1.39271i
455455 −4.67241 + 5.85901i −0.219046 + 0.274675i
456456 0.967353 + 0.771438i 0.0453005 + 0.0361259i
457457 −11.1908 + 5.38922i −0.523485 + 0.252097i −0.676913 0.736063i 0.736683π-0.736683\pi
0.153429 + 0.988160i 0.450969π0.450969\pi
458458 6.42543 + 28.1516i 0.300241 + 1.31544i
459459 0.637727 2.79407i 0.0297666 0.130416i
460460 1.65883 + 0.798852i 0.0773435 + 0.0372467i
461461 −9.52214 19.7729i −0.443490 0.920917i −0.996163 0.0875187i 0.972106π-0.972106\pi
0.552673 0.833399i 0.313608π-0.313608\pi
462462 9.21768 + 2.10388i 0.428845 + 0.0978811i
463463 33.0073 1.53398 0.766990 0.641660i 0.221754π-0.221754\pi
0.766990 + 0.641660i 0.221754π0.221754\pi
464464 0 0
465465 −1.00969 −0.0468232
466466 3.43703 + 0.784479i 0.159217 + 0.0363403i
467467 11.3258 + 23.5182i 0.524094 + 1.08829i 0.980135 + 0.198333i 0.0635527π0.0635527\pi
−0.456041 + 0.889959i 0.650733π0.650733\pi
468468 −16.3252 7.86180i −0.754633 0.363412i
469469 −0.337282 + 1.47773i −0.0155742 + 0.0682351i
470470 1.11649 + 4.89166i 0.0514998 + 0.225635i
471471 −7.08815 + 3.41347i −0.326605 + 0.157284i
472472 9.66438 + 7.70709i 0.444839 + 0.354747i
473473 −10.4227 + 13.0697i −0.479238 + 0.600946i
474474 −0.206746 + 0.429312i −0.00949616 + 0.0197190i
475475 7.80550 6.22468i 0.358141 0.285608i
476476 5.60388i 0.256853i
477477 −7.61141 9.54440i −0.348502 0.437008i
478478 15.7461 3.59395i 0.720211 0.164383i
479479 −32.2369 + 7.35786i −1.47294 + 0.336189i −0.882278 0.470730i 0.843991π-0.843991\pi
−0.590663 + 0.806919i 0.701134π0.701134\pi
480480 0.612605 + 0.768182i 0.0279614 + 0.0350625i
481481 15.1008i 0.688538i
482482 −28.0350 + 22.3572i −1.27696 + 1.01834i
483483 3.23449 6.71648i 0.147174 0.305610i
484484 −1.96011 + 2.45790i −0.0890958 + 0.111723i
485485 4.39494 + 3.50484i 0.199564 + 0.159147i
486486 −17.8192 + 8.58125i −0.808293 + 0.389254i
487487 2.26002 + 9.90180i 0.102411 + 0.448693i 0.999970 + 0.00779746i 0.00248203π0.00248203\pi
−0.897558 + 0.440896i 0.854661π0.854661\pi
488488 1.82640 8.00197i 0.0826771 0.362232i
489489 1.99127 + 0.958945i 0.0900484 + 0.0433650i
490490 −2.62116 5.44289i −0.118412 0.245885i
491491 −19.1884 4.37963i −0.865960 0.197650i −0.233608 0.972331i 0.575053π-0.575053\pi
−0.632352 + 0.774681i 0.717910π0.717910\pi
492492 −0.219833 −0.00991082
493493 0 0
494494 −19.1468 −0.861453
495495 2.83885 + 0.647948i 0.127597 + 0.0291231i
496496 −13.6225 28.2875i −0.611669 1.27014i
497497 41.6078 + 20.0373i 1.86637 + 0.898794i
498498 1.68329 7.37499i 0.0754301 0.330481i
499499 6.19710 + 27.1513i 0.277420 + 1.21546i 0.901042 + 0.433732i 0.142803π0.142803\pi
−0.623622 + 0.781726i 0.714339π0.714339\pi
500500 3.95862 1.90637i 0.177035 0.0852554i
501501 −5.03286 4.01357i −0.224852 0.179313i
502502 28.9916 36.3543i 1.29396 1.62257i
503503 0.0977147 0.202907i 0.00435688 0.00904716i −0.898779 0.438402i 0.855545π-0.855545\pi
0.903136 + 0.429355i 0.141259π0.141259\pi
504504 −12.0353 + 9.59783i −0.536095 + 0.427522i
505505 6.22521i 0.277018i
506506 −13.5341 16.9713i −0.601666 0.754466i
507507 6.02855 1.37598i 0.267737 0.0611093i
508508 −12.7312 + 2.90581i −0.564856 + 0.128925i
509509 −15.7763 19.7828i −0.699271 0.876859i 0.297697 0.954660i 0.403781π-0.403781\pi
−0.996969 + 0.0778016i 0.975210π0.975210\pi
510510 0.317667i 0.0140665i
511511 28.3277 22.5906i 1.25314 0.999349i
512512 −7.44074 + 15.4508i −0.328837 + 0.682837i
513513 −3.29859 + 4.13630i −0.145636 + 0.182622i
514514 −16.8368 13.4269i −0.742640 0.592236i
515515 −0.904854 + 0.435755i −0.0398726 + 0.0192016i
516516 −0.708947 3.10610i −0.0312097 0.136738i
517517 5.05525 22.1485i 0.222330 0.974091i
518518 19.1407 + 9.21768i 0.840995 + 0.405002i
519519 2.03009 + 4.21552i 0.0891110 + 0.185041i
520520 2.44845 + 0.558843i 0.107372 + 0.0245069i
521521 −23.5797 −1.03305 −0.516523 0.856273i 0.672774π-0.672774\pi
−0.516523 + 0.856273i 0.672774π0.672774\pi
522522 0 0
523523 3.96508 0.173381 0.0866905 0.996235i 0.472371π-0.472371\pi
0.0866905 + 0.996235i 0.472371π0.472371\pi
524524 0.552823 + 0.126178i 0.0241502 + 0.00551212i
525525 −3.80957 7.91066i −0.166263 0.345249i
526526 0.540188 + 0.260141i 0.0235533 + 0.0113427i
527527 −1.57002 + 6.87872i −0.0683913 + 0.299642i
528528 −1.42423 6.23996i −0.0619817 0.271560i
529529 5.30194 2.55328i 0.230519 0.111012i
530530 −2.19064 1.74698i −0.0951555 0.0758839i
531531 −15.9148 + 19.9566i −0.690645 + 0.866042i
532532 4.48845 9.32036i 0.194599 0.404089i
533533 −1.60611 + 1.28083i −0.0695684 + 0.0554790i
534534 1.14138i 0.0493921i
535535 1.66003 + 2.08161i 0.0717694 + 0.0899959i
536536 0.495224 0.113032i 0.0213904 0.00488222i
537537 2.49090 0.568532i 0.107490 0.0245340i
538538 1.19537 + 1.49895i 0.0515362 + 0.0646244i
539539 27.3532i 1.17818i
540540 −0.898438 + 0.716480i −0.0386626 + 0.0308324i
541541 −10.6996 + 22.2180i −0.460012 + 0.955225i 0.533951 + 0.845515i 0.320707π0.320707\pi
−0.993964 + 0.109710i 0.965008π0.965008\pi
542542 18.4976 23.1953i 0.794540 0.996322i
543543 −2.31062 1.84266i −0.0991582 0.0790760i
544544 6.18598 2.97901i 0.265222 0.127724i
545545 0.131260 + 0.575086i 0.00562254 + 0.0246340i
546546 −3.74698 + 16.4166i −0.160356 + 0.702565i
547547 −22.3811 10.7782i −0.956947 0.460842i −0.110831 0.993839i 0.535351π-0.535351\pi
−0.846117 + 0.532998i 0.821065π0.821065\pi
548548 −7.16357 14.8753i −0.306013 0.635442i
549549 16.5238 + 3.77144i 0.705216 + 0.160961i
550550 −25.5666 −1.09016
551551 0 0
552552 −2.49827 −0.106333
553553 −2.34549 0.535344i −0.0997406 0.0227651i
554554 5.15554 + 10.7056i 0.219038 + 0.454837i
555555 −0.416698 0.200671i −0.0176879 0.00851802i
556556 −0.775987 + 3.39982i −0.0329092 + 0.144185i
557557 1.72790 + 7.57041i 0.0732134 + 0.320769i 0.998252 0.0591048i 0.0188246π-0.0188246\pi
−0.925038 + 0.379874i 0.875967π0.875967\pi
558558 28.9170 13.9257i 1.22415 0.589521i
559559 −23.2770 18.5628i −0.984512 0.785122i
560560 −4.44989 + 5.57998i −0.188042 + 0.235797i
561561 −0.624071 + 1.29590i −0.0263483 + 0.0547128i
562562 −43.0182 + 34.3059i −1.81461 + 1.44711i
563563 20.8009i 0.876652i −0.898816 0.438326i 0.855571π-0.855571\pi
0.898816 0.438326i 0.144429π-0.144429\pi
564564 2.69955 + 3.38513i 0.113672 + 0.142540i
565565 3.00652 0.686218i 0.126485 0.0288694i
566566 −6.24521 + 1.42543i −0.262506 + 0.0599152i
567567 −18.3192 22.9715i −0.769332 0.964712i
568568 15.4765i 0.649380i
569569 2.19635 1.75153i 0.0920757 0.0734279i −0.576370 0.817189i 0.695531π-0.695531\pi
0.668446 + 0.743761i 0.266960π0.266960\pi
570570 −0.254437 + 0.528344i −0.0106572 + 0.0221299i
571571 1.80343 2.26143i 0.0754712 0.0946379i −0.742663 0.669666i 0.766437π-0.766437\pi
0.818134 + 0.575028i 0.195009π0.195009\pi
572572 14.7222 + 11.7406i 0.615567 + 0.490898i
573573 −7.54288 + 3.63246i −0.315108 + 0.151748i
574574 −0.643104 2.81762i −0.0268426 0.117605i
575575 −4.48566 + 19.6529i −0.187065 + 0.819585i
576576 −3.20291 1.54244i −0.133454 0.0642683i
577577 3.11917 + 6.47703i 0.129853 + 0.269642i 0.955751 0.294177i 0.0950456π-0.0950456\pi
−0.825898 + 0.563820i 0.809331π0.809331\pi
578578 27.7007 + 6.32251i 1.15220 + 0.262982i
579579 −4.84415 −0.201316
580580 0 0
581581 38.1933 1.58452
582582 12.3143 + 2.81067i 0.510446 + 0.116506i
583583 5.50453 + 11.4303i 0.227974 + 0.473393i
584584 −10.9400 5.26841i −0.452699 0.218008i
585585 −1.15399 + 5.05596i −0.0477116 + 0.209038i
586586 −13.1838 57.7621i −0.544619 2.38613i
587587 27.9632 13.4664i 1.15417 0.555817i 0.243883 0.969805i 0.421579π-0.421579\pi
0.910282 + 0.413988i 0.135864π0.135864\pi
588588 −4.07579 3.25033i −0.168083 0.134041i
589589 8.12080 10.1832i 0.334612 0.419590i
590590 −2.54196 + 5.27844i −0.104651 + 0.217310i
591591 2.92291 2.33095i 0.120233 0.0958823i
592592 14.3817i 0.591082i
593593 −22.7371 28.5114i −0.933699 1.17082i −0.985072 0.172142i 0.944931π-0.944931\pi
0.0513733 0.998680i 0.483640π-0.483640\pi
594594 13.2086 3.01477i 0.541954 0.123698i
595595 1.56366 0.356896i 0.0641039 0.0146313i
596596 2.10574 + 2.64051i 0.0862543 + 0.108159i
597597 2.94677i 0.120603i
598598 30.2257 24.1042i 1.23602 0.985693i
599599 13.0461 27.0906i 0.533051 1.10689i −0.444419 0.895819i 0.646590π-0.646590\pi
0.977470 0.211073i 0.0676958π-0.0676958\pi
600600 −1.83459 + 2.30051i −0.0748970 + 0.0939178i
601601 −25.9458 20.6911i −1.05835 0.844008i −0.0702081 0.997532i 0.522366π-0.522366\pi
−0.988145 + 0.153524i 0.950938π0.950938\pi
602602 37.7373 18.1733i 1.53806 0.740690i
603603 0.233406 + 1.02262i 0.00950503 + 0.0416443i
604604 0.675760 2.96070i 0.0274963 0.120469i
605605 0.810667 + 0.390397i 0.0329583 + 0.0158719i
606606 6.06913 + 12.6027i 0.246542 + 0.511949i
607607 −14.7411 3.36456i −0.598323 0.136563i −0.0873757 0.996175i 0.527848π-0.527848\pi
−0.510947 + 0.859612i 0.670705π0.670705\pi
608608 −12.6746 −0.514021
609609 0 0
610610 3.89008 0.157505
611611 39.4463 + 9.00335i 1.59583 + 0.364237i
612612 1.68260 + 3.49396i 0.0680152 + 0.141235i
613613 3.38351 + 1.62941i 0.136659 + 0.0658114i 0.500964 0.865468i 0.332979π-0.332979\pi
−0.364305 + 0.931280i 0.618693π0.618693\pi
614614 −5.88231 + 25.7721i −0.237391 + 1.04008i
615615 0.0140005 + 0.0613404i 0.000564557 + 0.00247348i
616616 14.4133 6.94110i 0.580730 0.279665i
617617 −23.3425 18.6151i −0.939735 0.749414i 0.0284638 0.999595i 0.490938π-0.490938\pi
−0.968199 + 0.250181i 0.919510π0.919510\pi
618618 −1.40701 + 1.76433i −0.0565982 + 0.0709719i
619619 20.0098 41.5507i 0.804260 1.67006i 0.0638010 0.997963i 0.479678π-0.479678\pi
0.740459 0.672101i 0.234608π-0.234608\pi
620620 2.21187 1.76391i 0.0888307 0.0708402i
621621 10.6823i 0.428667i
622622 20.8143 + 26.1003i 0.834578 + 1.04653i
623623 −5.61823 + 1.28232i −0.225089 + 0.0513752i
624624 11.1133 2.53654i 0.444888 0.101543i
625625 14.4061 + 18.0647i 0.576244 + 0.722588i
626626 41.4306i 1.65590i
627627 2.07591 1.65548i 0.0829038 0.0661136i
628628 9.56433 19.8605i 0.381658 0.792522i
629629 −2.01507 + 2.52681i −0.0803459 + 0.100751i
630630 −5.70416 4.54892i −0.227259 0.181233i
631631 11.3792 5.47993i 0.452999 0.218153i −0.193450 0.981110i 0.561968π-0.561968\pi
0.646449 + 0.762957i 0.276253π0.276253\pi
632632 0.179407 + 0.786035i 0.00713644 + 0.0312668i
633633 0.802175 3.51456i 0.0318836 0.139691i
634634 22.8240 + 10.9915i 0.906457 + 0.436527i
635635 1.62163 + 3.36735i 0.0643525 + 0.133629i
636636 −2.35727 0.538032i −0.0934720 0.0213344i
637637 −48.7157 −1.93019
638638 0 0
639639 31.9584 1.26425
640640 3.50932 + 0.800978i 0.138718 + 0.0316614i
641641 −16.9223 35.1395i −0.668391 1.38793i −0.908790 0.417253i 0.862993π-0.862993\pi
0.240400 0.970674i 0.422722π-0.422722\pi
642642 5.39008 + 2.59573i 0.212730 + 0.102445i
643643 9.18933 40.2611i 0.362392 1.58774i −0.384713 0.923036i 0.625699π-0.625699\pi
0.747105 0.664706i 0.231443π-0.231443\pi
644644 4.64795 + 20.3640i 0.183155 + 0.802454i
645645 −0.821552 + 0.395639i −0.0323486 + 0.0155783i
646646 3.20382 + 2.55496i 0.126052 + 0.100523i
647647 11.1670 14.0030i 0.439021 0.550515i −0.512264 0.858828i 0.671193π-0.671193\pi
0.951285 + 0.308313i 0.0997644π0.0997644\pi
648648 −4.27225 + 8.87143i −0.167830 + 0.348503i
649649 20.7394 16.5392i 0.814094 0.649219i
650650 45.5338i 1.78598i
651651 −7.14191 8.95567i −0.279913 0.351000i
652652 −6.03742 + 1.37800i −0.236444 + 0.0539667i
653653 12.9867 2.96412i 0.508208 0.115995i 0.0392741 0.999228i 0.487495π-0.487495\pi
0.468934 + 0.883233i 0.344638π0.344638\pi
654654 0.826396 + 1.03627i 0.0323147 + 0.0405213i
655655 0.162291i 0.00634125i
656656 −1.52962 + 1.21983i −0.0597217 + 0.0476265i
657657 10.8791 22.5906i 0.424432 0.881343i
658658 −35.4904 + 44.5035i −1.38356 + 1.73493i
659659 14.6716 + 11.7002i 0.571525 + 0.455776i 0.866113 0.499849i 0.166611π-0.166611\pi
−0.294588 + 0.955624i 0.595182π0.595182\pi
660660 0.519614 0.250233i 0.0202260 0.00974031i
661661 5.50269 + 24.1089i 0.214030 + 0.937726i 0.961797 + 0.273764i 0.0882689π0.0882689\pi
−0.747767 + 0.663961i 0.768874π0.768874\pi
662662 5.59611 24.5181i 0.217499 0.952925i
663663 −2.30798 1.11146i −0.0896345 0.0431657i
664664 −5.55351 11.5320i −0.215518 0.447528i
665665 −2.88654 0.658834i −0.111935 0.0255485i
666666 14.7017 0.569680
667667 0 0
668668 18.0368 0.697866
669669 −9.51036 2.17068i −0.367692 0.0839233i
670670 0.104457 + 0.216907i 0.00403553 + 0.00837985i
671671 −15.8693 7.64224i −0.612626 0.295025i
672672 −2.48039 + 10.8673i −0.0956830 + 0.419214i
673673 5.66152 + 24.8047i 0.218236 + 0.956153i 0.958781 + 0.284146i 0.0917102π0.0917102\pi
−0.740545 + 0.672006i 0.765433π0.765433\pi
674674 −22.7250 + 10.9438i −0.875333 + 0.421538i
675675 −9.83672 7.84452i −0.378615 0.301936i
676676 −10.8026 + 13.5460i −0.415485 + 0.521001i
677677 −0.267510 + 0.555491i −0.0102813 + 0.0213492i −0.906046 0.423179i 0.860914π-0.860914\pi
0.895765 + 0.444528i 0.146629π0.146629\pi
678678 5.41755 4.32036i 0.208060 0.165922i
679679 63.7730i 2.44738i
680680 −0.335126 0.420234i −0.0128515 0.0161152i
681681 −7.93072 + 1.81013i −0.303906 + 0.0693645i
682682 −32.5182 + 7.42208i −1.24519 + 0.284206i
683683 11.2364 + 14.0900i 0.429949 + 0.539138i 0.948863 0.315688i 0.102235π-0.102235\pi
−0.518915 + 0.854826i 0.673664π0.673664\pi
684684 7.15883i 0.273725i
685685 −3.69447 + 2.94624i −0.141158 + 0.112570i
686686 7.57753 15.7349i 0.289311 0.600761i
687687 4.44653 5.57578i 0.169646 0.212729i
688688 −22.1684 17.6787i −0.845164 0.673996i
689689 −20.3572 + 9.80351i −0.775547 + 0.373484i
690690 −0.263479 1.15437i −0.0100305 0.0439463i
691691 −2.74728 + 12.0366i −0.104511 + 0.457894i 0.895409 + 0.445245i 0.146883π0.146883\pi
−0.999920 + 0.0126487i 0.995974π0.995974\pi
692692 −11.8116 5.68818i −0.449011 0.216232i
693693 14.3331 + 29.7630i 0.544470 + 1.13060i
694694 34.8784 + 7.96077i 1.32397 + 0.302187i
695695 0.998081 0.0378594
696696 0 0
697697 0.439665 0.0166535
698698 −47.2923 10.7942i −1.79004 0.408565i
699699 −0.377785 0.784479i −0.0142892 0.0296717i
700700 22.1652 + 10.6742i 0.837765 + 0.403446i
701701 −7.58738 + 33.2425i −0.286571 + 1.25555i 0.602625 + 0.798025i 0.294122π0.294122\pi
−0.889196 + 0.457526i 0.848736π0.848736\pi
702702 5.36927 + 23.5243i 0.202650 + 0.887868i
703703 5.37531 2.58861i 0.202734 0.0976315i
704704 2.88841 + 2.30343i 0.108861 + 0.0868138i
705705 0.772635 0.968853i 0.0290991 0.0364891i
706706 −3.13910 + 6.51842i −0.118142 + 0.245324i
707707 −55.2159 + 44.0332i −2.07661 + 1.65604i
708708 5.05562i 0.190002i
709709 −26.2461 32.9115i −0.985692 1.23602i −0.971725 0.236116i 0.924125π-0.924125\pi
−0.0139674 0.999902i 0.504446π-0.504446\pi
710710 7.15122 1.63222i 0.268380 0.0612561i
711711 −1.62313 + 0.370469i −0.0608722 + 0.0138937i
712712 1.20410 + 1.50990i 0.0451257 + 0.0565858i
713713 26.2989i 0.984901i
714714 2.81762 2.24698i 0.105447 0.0840911i
715715 2.33838 4.85570i 0.0874505 0.181593i
716716 −4.46346 + 5.59700i −0.166807 + 0.209170i
717717 −3.11871 2.48709i −0.116470 0.0928821i
718718 1.21164 0.583493i 0.0452178 0.0217758i
719719 11.6277 + 50.9442i 0.433639 + 1.89990i 0.436098 + 0.899899i 0.356360π0.356360\pi
−0.00245885 + 0.999997i 0.500783π0.500783\pi
720720 −1.09903 + 4.81517i −0.0409585 + 0.179451i
721721 −10.2654 4.94355i −0.382303 0.184108i
722722 11.5726 + 24.0308i 0.430688 + 0.894334i
723723 8.63419 + 1.97070i 0.321109 + 0.0732910i
724724 8.28083 0.307755
725725 0 0
726726 2.02177 0.0750349
727727 −29.2331 6.67228i −1.08420 0.247461i −0.357149 0.934047i 0.616251π-0.616251\pi
−0.727048 + 0.686586i 0.759108π0.759108\pi
728728 12.3620 + 25.6700i 0.458167 + 0.951394i
729729 −15.2131 7.32626i −0.563449 0.271343i
730730 1.28059 5.61065i 0.0473969 0.207660i
731731 1.41789 + 6.21220i 0.0524427 + 0.229767i
732732 3.02446 1.45650i 0.111787 0.0538339i
733733 −2.35681 1.87949i −0.0870508 0.0694207i 0.578997 0.815329i 0.303444π-0.303444\pi
−0.666048 + 0.745909i 0.732016π0.732016\pi
734734 −38.2536 + 47.9685i −1.41197 + 1.77055i
735735 −0.647372 + 1.34428i −0.0238787 + 0.0495846i
736736 20.0085 15.9562i 0.737522 0.588154i
737737 1.09006i 0.0401531i
738738 −1.24698 1.56366i −0.0459020 0.0575592i
739739 −20.3150 + 4.63677i −0.747300 + 0.170566i −0.579179 0.815200i 0.696627π-0.696627\pi
−0.168120 + 0.985766i 0.553770π0.553770\pi
740740 1.26341 0.288364i 0.0464437 0.0106005i
741741 2.94839 + 3.69717i 0.108312 + 0.135819i
742742 31.7875i 1.16695i
743743 −24.0536 + 19.1821i −0.882441 + 0.703723i −0.955937 0.293573i 0.905156π-0.905156\pi
0.0734962 + 0.997295i 0.476584π0.476584\pi
744744 −1.66558 + 3.45862i −0.0610632 + 0.126799i
745745 0.602679 0.755736i 0.0220805 0.0276880i
746746 −39.4476 31.4584i −1.44428 1.15177i
747747 23.8131 11.4678i 0.871276 0.419585i
748748 −0.896789 3.92909i −0.0327898 0.143662i
749749 −6.72132 + 29.4480i −0.245592 + 1.07601i
750750 −2.54580 1.22599i −0.0929595 0.0447670i
751751 −1.93912 4.02661i −0.0707593 0.146933i 0.862589 0.505905i 0.168842π-0.168842\pi
−0.933348 + 0.358972i 0.883127π0.883127\pi
752752 37.5677 + 8.57457i 1.36995 + 0.312682i
753753 −11.4843 −0.418510
754754 0 0
755755 −0.869167 −0.0316322
756756 −12.7100 2.90097i −0.462257 0.105507i
757757 3.66883 + 7.61841i 0.133346 + 0.276896i 0.956941 0.290283i 0.0937493π-0.0937493\pi
−0.823595 + 0.567178i 0.808035π0.808035\pi
758758 −37.1470 17.8891i −1.34924 0.649760i
759759 −1.19298 + 5.22679i −0.0433025 + 0.189720i
760760 0.220792 + 0.967353i 0.00800897 + 0.0350896i
761761 −22.2494 + 10.7148i −0.806541 + 0.388410i −0.791265 0.611474i 0.790577π-0.790577\pi
−0.0152763 + 0.999883i 0.504863π0.504863\pi
762762 6.56585 + 5.23609i 0.237856 + 0.189684i
763763 −4.17241 + 5.23203i −0.151051 + 0.189412i
764764 10.1779 21.1347i 0.368224 0.764626i
765765 0.867767 0.692021i 0.0313742 0.0250201i
766766 21.3676i 0.772045i
767767 29.4561 + 36.9367i 1.06360 + 1.33371i
768768 8.98634 2.05107i 0.324267 0.0740117i
769769 −29.3873 + 6.70746i −1.05973 + 0.241877i −0.716653 0.697429i 0.754327π-0.754327\pi
−0.343079 + 0.939307i 0.611470π0.611470\pi
770770 4.72737 + 5.92793i 0.170362 + 0.213628i
771771 5.31873i 0.191549i
772772 10.6118 8.46263i 0.381927 0.304577i
773773 2.46314 5.11476i 0.0885929 0.183965i −0.851965 0.523599i 0.824589π-0.824589\pi
0.940558 + 0.339634i 0.110303π0.110303\pi
774774 18.0722 22.6618i 0.649591 0.814561i
775775 24.2171 + 19.3125i 0.869902 + 0.693724i
776776 19.2555 9.27295i 0.691231 0.332879i
777777 −1.16756 5.11543i −0.0418861 0.183515i
778778 −4.16660 + 18.2551i −0.149380 + 0.654476i
779779 −0.731250 0.352152i −0.0261998 0.0126171i
780780 0.445662 + 0.925428i 0.0159573 + 0.0331356i
781781 −32.3794 7.39038i −1.15862 0.264449i
782782 −8.27413 −0.295882
783783 0 0
784784 −46.3957 −1.65699
785785 −6.15086 1.40389i −0.219534 0.0501071i
786786 −0.158222 0.328552i −0.00564361 0.0117191i
787787 −3.25182 1.56600i −0.115915 0.0558217i 0.375028 0.927014i 0.377633π-0.377633\pi
−0.490943 + 0.871192i 0.663348π0.663348\pi
788788 −2.33095 + 10.2125i −0.0830365 + 0.363807i
789789 −0.0329509 0.144367i −0.00117308 0.00513961i
790790 −0.344282 + 0.165797i −0.0122490 + 0.00589881i
791791 27.3528 + 21.8131i 0.972553 + 0.775585i
792792 6.90246 8.65541i 0.245268 0.307557i
793793 13.6107 28.2630i 0.483332 1.00365i
794794 11.5768 9.23221i 0.410846 0.327639i
795795 0.692021i 0.0245435i
796796 5.14795 + 6.45532i 0.182464 + 0.228803i
797797 −30.0114 + 6.84990i −1.06306 + 0.242636i −0.718069 0.695972i 0.754974π-0.754974\pi
−0.344987 + 0.938607i 0.612117π0.612117\pi
798798 −6.48599 + 1.48039i −0.229602 + 0.0524051i
799799 −5.39911 6.77027i −0.191007 0.239515i
800800 30.1420i 1.06568i
801801 −3.11788 + 2.48643i −0.110165 + 0.0878536i
802802 −19.4527 + 40.3940i −0.686900 + 1.42636i
803803 −16.2464 + 20.3724i −0.573325 + 0.718926i
804804 0.162426 + 0.129531i 0.00572833 + 0.00456819i
805805 5.38620 2.59386i 0.189839 0.0914214i
806806 −13.2186 57.9146i −0.465607 2.03996i
807807 0.105367 0.461645i 0.00370911 0.0162507i
808808 21.3240 + 10.2691i 0.750176 + 0.361266i
809809 2.27238 + 4.71864i 0.0798925 + 0.165898i 0.937089 0.349092i 0.113510π-0.113510\pi
−0.857196 + 0.514990i 0.827796π0.827796\pi
810810 −4.54979 1.03846i −0.159863 0.0364877i
811811 −41.8646 −1.47006 −0.735032 0.678032i 0.762833π-0.762833\pi
−0.735032 + 0.678032i 0.762833π0.762833\pi
812812 0 0
813813 −7.32736 −0.256982
814814 −14.8954 3.39977i −0.522083 0.119162i
815815 0.769015 + 1.59688i 0.0269374 + 0.0559361i
816816 −2.19806 1.05853i −0.0769476 0.0370560i
817817 2.61745 11.4678i 0.0915729 0.401207i
818818 −7.57649 33.1948i −0.264906 1.16063i
819819 −53.0076 + 25.5271i −1.85224 + 0.891989i
820820 −0.137831 0.109916i −0.00481325 0.00383844i
821821 −9.60537 + 12.0447i −0.335230 + 0.420365i −0.920665 0.390355i 0.872352π-0.872352\pi
0.585435 + 0.810719i 0.300924π0.300924\pi
822822 −4.60692 + 9.56638i −0.160685 + 0.333666i
823823 27.8768 22.2310i 0.971724 0.774924i −0.00261763 0.999997i 0.500833π-0.500833\pi
0.974342 + 0.225072i 0.0722618π0.0722618\pi
824824 3.81833i 0.133018i
825825 3.93698 + 4.93681i 0.137068 + 0.171878i
826826 −64.7986 + 14.7899i −2.25463 + 0.514605i
827827 50.7487 11.5831i 1.76471 0.402783i 0.787711 0.616045i 0.211266π-0.211266\pi
0.976995 + 0.213262i 0.0684089π0.0684089\pi
828828 9.01238 + 11.3012i 0.313202 + 0.392743i
829829 13.4168i 0.465986i −0.972478 0.232993i 0.925148π-0.925148\pi
0.972478 0.232993i 0.0748519π-0.0748519\pi
830830 4.74288 3.78232i 0.164628 0.131286i
831831 1.27331 2.64406i 0.0441708 0.0917216i
832832 −4.10238 + 5.14423i −0.142225 + 0.178344i
833833 8.15157 + 6.50066i 0.282435 + 0.225235i
834834 2.02057 0.973057i 0.0699667 0.0336942i
835835 −1.14872 5.03286i −0.0397530 0.174169i
836836 −1.65548 + 7.25314i −0.0572560 + 0.250855i
837837 −14.7887 7.12184i −0.511171 0.246167i
838838 8.51608 + 17.6838i 0.294183 + 0.610878i
839839 −30.2728 6.90957i −1.04513 0.238545i −0.334711 0.942321i 0.608639π-0.608639\pi
−0.710422 + 0.703776i 0.751496π0.751496\pi
840840 0.872625 0.0301084
841841 0 0
842842 35.9681 1.23954
843843 13.2487 + 3.02393i 0.456309 + 0.104150i
844844 4.38258 + 9.10052i 0.150855 + 0.313253i
845845 4.46777 + 2.15157i 0.153696 + 0.0740161i
846846 −8.76540 + 38.4037i −0.301361 + 1.32035i
847847 2.27144 + 9.95182i 0.0780475 + 0.341949i
848848 −19.3877 + 9.33662i −0.665776 + 0.320621i
849849 1.23694 + 0.986426i 0.0424517 + 0.0338541i
850850 −6.07606 + 7.61914i −0.208407 + 0.261334i
851851 −5.22679 + 10.8535i −0.179172 + 0.372055i
852852 4.94880 3.94653i 0.169543 0.135206i
853853 21.3357i 0.730521i −0.930905 0.365261i 0.880980π-0.880980\pi
0.930905 0.365261i 0.119020π-0.119020\pi
854854 27.5160 + 34.5040i 0.941579 + 1.18070i
855855 −1.99755 + 0.455927i −0.0683147 + 0.0155924i
856856 9.86879 2.25249i 0.337308 0.0769885i
857857 −6.13019 7.68702i −0.209403 0.262584i 0.666027 0.745928i 0.267994π-0.267994\pi
−0.875431 + 0.483344i 0.839422π0.839422\pi
858858 12.1099i 0.413426i
859859 −40.4862 + 32.2866i −1.38137 + 1.10161i −0.398528 + 0.917156i 0.630479π0.630479\pi
−0.982842 + 0.184450i 0.940950π0.940950\pi
860860 1.10855 2.30194i 0.0378014 0.0784954i
861861 −0.445042 + 0.558065i −0.0151670 + 0.0190188i
862862 42.5324 + 33.9185i 1.44866 + 1.15527i
863863 −14.6630 + 7.06134i −0.499135 + 0.240371i −0.666473 0.745529i 0.732197π-0.732197\pi
0.167339 + 0.985899i 0.446483π0.446483\pi
864864 3.55429 + 15.5724i 0.120920 + 0.529783i
865865 −0.834936 + 3.65809i −0.0283887 + 0.124379i
866866 −32.7805 15.7862i −1.11393 0.536438i
867867 −3.04476 6.32251i −0.103406 0.214724i
868868 31.2907 + 7.14191i 1.06208 + 0.242412i
869869 1.73019 0.0586925
870870 0 0
871871 1.94139 0.0657816
872872 2.18644 + 0.499041i 0.0740422 + 0.0168996i
873873 19.1483 + 39.7618i 0.648071 + 1.34573i
874874 13.7615 + 6.62720i 0.465490 + 0.224168i
875875 3.17456 13.9087i 0.107320 0.470199i
876876 −1.10507 4.84164i −0.0373369 0.163584i
877877 −13.3400 + 6.42419i −0.450459 + 0.216930i −0.645337 0.763898i 0.723283π-0.723283\pi
0.194878 + 0.980827i 0.437569π0.437569\pi
878878 −15.0248 11.9819i −0.507062 0.404369i
879879 −9.12349 + 11.4405i −0.307728 + 0.385878i
880880 2.22702 4.62445i 0.0750727 0.155890i
881881 14.5716 11.6204i 0.490928 0.391502i −0.346499 0.938050i 0.612630π-0.612630\pi
0.837428 + 0.546548i 0.184058π0.184058\pi
882882 47.4282i 1.59699i
883883 20.1972 + 25.3264i 0.679689 + 0.852303i 0.995325 0.0965775i 0.0307896π-0.0307896\pi
−0.315637 + 0.948880i 0.602218π0.602218\pi
884884 6.99766 1.59717i 0.235357 0.0537187i
885885 1.41068 0.321979i 0.0474196 0.0108232i
886886 22.8632 + 28.6696i 0.768105 + 0.963174i
887887 6.16288i 0.206929i −0.994633 0.103465i 0.967007π-0.967007\pi
0.994633 0.103465i 0.0329929π-0.0329929\pi
888888 −1.37477 + 1.09634i −0.0461343 + 0.0367909i
889889 −18.3971 + 38.2020i −0.617019 + 1.28125i
890890 −0.570688 + 0.715620i −0.0191295 + 0.0239876i
891891 16.5204 + 13.1746i 0.553454 + 0.441364i
892892 24.6259 11.8592i 0.824537 0.397076i
893893 3.55711 + 15.5847i 0.119034 + 0.521523i
894894 0.483311 2.11752i 0.0161643 0.0708206i
895895 1.84601 + 0.888992i 0.0617053 + 0.0297157i
896896 17.7182 + 36.7923i 0.591925 + 1.22914i
897897 −9.30886 2.12469i −0.310814 0.0709412i
898898 34.9995 1.16795
899899 0 0
900900 17.0248 0.567492
901901 4.71455 + 1.07606i 0.157064 + 0.0358489i
902902 0.901809 + 1.87263i 0.0300269 + 0.0623516i
903903 −9.32036 4.48845i −0.310162 0.149366i
904904 2.60896 11.4306i 0.0867726 0.380176i
905905 −0.527384 2.31062i −0.0175308 0.0768076i
906906 −1.75959 + 0.847376i −0.0584586 + 0.0281522i
907907 −34.3882 27.4237i −1.14184 0.910589i −0.144956 0.989438i 0.546304π-0.546304\pi
−0.996887 + 0.0788492i 0.974875π0.974875\pi
908908 14.2111 17.8202i 0.471612 0.591383i
909909 −21.2053 + 44.0332i −0.703335 + 1.46049i
910910 −10.5576 + 8.41939i −0.349980 + 0.279100i
911911 25.6233i 0.848936i 0.905443 + 0.424468i 0.139539π0.139539\pi
−0.905443 + 0.424468i 0.860461π0.860461\pi
912912 2.80798 + 3.52109i 0.0929815 + 0.116595i
913913 −26.7787 + 6.11207i −0.886247 + 0.202280i
914914 −21.8205 + 4.98039i −0.721758 + 0.164737i
915915 −0.599031 0.751161i −0.0198034 0.0248326i
916916 19.9825i 0.660242i
917917 1.43948 1.14795i 0.0475359 0.0379086i
918918 2.24067 4.65279i 0.0739530 0.153565i
919919 −3.89158 + 4.87988i −0.128371 + 0.160972i −0.841863 0.539691i 0.818541π-0.818541\pi
0.713492 + 0.700663i 0.247113π0.247113\pi
920920 −1.56637 1.24914i −0.0516416 0.0411828i
921921 5.88231 2.83277i 0.193829 0.0933430i
922922 −8.79978 38.5544i −0.289805 1.26972i
923923 13.1622 57.6673i 0.433239 1.89814i
924924 5.89493 + 2.83885i 0.193929 + 0.0933912i
925925 6.15610 + 12.7833i 0.202411 + 0.420312i
926926 57.9859 + 13.2349i 1.90553 + 0.434926i
927927 −7.88471 −0.258968
928928 0 0
929929 −24.5133 −0.804256 −0.402128 0.915583i 0.631729π-0.631729\pi
−0.402128 + 0.915583i 0.631729π0.631729\pi
930930 −1.77378 0.404854i −0.0581645 0.0132757i
931931 −8.35095 17.3409i −0.273691 0.568326i
932932 2.19806 + 1.05853i 0.0719999 + 0.0346733i
933933 1.83470 8.03834i 0.0600653 0.263163i
934934 10.4666 + 45.8571i 0.342477 + 1.50049i
935935 −1.03923 + 0.500466i −0.0339864 + 0.0163670i
936936 15.4152 + 12.2932i 0.503861 + 0.401816i
937937 2.54975 3.19728i 0.0832965 0.104451i −0.738437 0.674323i 0.764436π-0.764436\pi
0.821734 + 0.569872i 0.193007π0.193007\pi
938938 −1.18505 + 2.46077i −0.0386931 + 0.0803470i
939939 −8.00009 + 6.37986i −0.261073 + 0.208199i
940940 3.47219i 0.113250i
941941 −3.84266 4.81854i −0.125267 0.157080i 0.715243 0.698876i 0.246316π-0.246316\pi
−0.840510 + 0.541796i 0.817745π0.817745\pi
942942 −13.8209 + 3.15452i −0.450308 + 0.102780i
943943 1.59770 0.364666i 0.0520284 0.0118751i
944944 28.0532 + 35.1776i 0.913055 + 1.14493i
945945 3.73125i 0.121378i
946946 −23.5508 + 18.7811i −0.765702 + 0.610627i
947947 −21.5650 + 44.7802i −0.700769 + 1.45516i 0.181001 + 0.983483i 0.442066π0.442066\pi
−0.881770 + 0.471679i 0.843648π0.843648\pi
948948 −0.205595 + 0.257808i −0.00667742 + 0.00837321i
949949 −36.2830 28.9347i −1.17780 0.939262i
950950 16.2083 7.80550i 0.525866 0.253244i
951951 −1.39224 6.09980i −0.0451465 0.197800i
952952 1.35690 5.94495i 0.0439772 0.192677i
953953 −15.9342 7.67349i −0.516158 0.248569i 0.157623 0.987499i 0.449617π-0.449617\pi
−0.673781 + 0.738931i 0.735331π0.735331\pi
954954 −9.54440 19.8192i −0.309011 0.641669i
955955 −6.54546 1.49396i −0.211806 0.0483434i
956956 11.1769 0.361486
957957 0 0
958958 −59.5827 −1.92503
959959 −52.2647 11.9291i −1.68772 0.385210i
960960 0.0874363 + 0.181563i 0.00282199 + 0.00585993i
961961 8.47823 + 4.08290i 0.273491 + 0.131706i
962962 6.05496 26.5285i 0.195220 0.855313i
963963 4.65130 + 20.3787i 0.149886 + 0.656694i
964964 −22.3572 + 10.7667i −0.720077 + 0.346771i
965965 −3.03719 2.42208i −0.0977705 0.0779694i
966966 8.37531 10.5023i 0.269471 0.337906i
967967 5.59421 11.6165i 0.179898 0.373561i −0.791447 0.611238i 0.790672π-0.790672\pi
0.971344 + 0.237677i 0.0763860π0.0763860\pi
968968 2.67455 2.13288i 0.0859633 0.0685535i
969969 1.01208i 0.0325127i
970970 6.31551 + 7.91940i 0.202779 + 0.254277i
971971 4.71616 1.07643i 0.151349 0.0345444i −0.146175 0.989259i 0.546696π-0.546696\pi
0.297524 + 0.954714i 0.403839π0.403839\pi
972972 −13.3435 + 3.04556i −0.427993 + 0.0976865i
973973 7.05980 + 8.85271i 0.226327 + 0.283805i
974974 18.3013i 0.586411i
975975 −8.79241 + 7.01171i −0.281582 + 0.224555i
976976 12.9625 26.9170i 0.414921 0.861592i
977977 10.2515 12.8549i 0.327973 0.411265i −0.590318 0.807171i 0.700998π-0.700998\pi
0.918291 + 0.395905i 0.129569π0.129569\pi
978978 3.11368 + 2.48307i 0.0995644 + 0.0794000i
979979 3.73394 1.79817i 0.119337 0.0574698i
980980 −0.930272 4.07579i −0.0297164 0.130196i
981981 −1.03050 + 4.51491i −0.0329013 + 0.144150i
982982 −31.9533 15.3879i −1.01967 0.491048i
983983 11.4976 + 23.8751i 0.366717 + 0.761497i 0.999922 0.0124878i 0.00397510π-0.00397510\pi
−0.633205 + 0.773984i 0.718261π0.718261\pi
984984 0.233212 + 0.0532292i 0.00743454 + 0.00169689i
985985 2.99808 0.0955268
986986 0 0
987987 14.0586 0.447490
988988 −12.9178 2.94839i −0.410969 0.0938009i
989989 10.3050 + 21.3986i 0.327680 + 0.680435i
990990 4.72737 + 2.27658i 0.150246 + 0.0723544i
991991 8.99127 39.3933i 0.285617 1.25137i −0.604856 0.796335i 0.706769π-0.706769\pi
0.890473 0.455036i 0.150373π-0.150373\pi
992992 −8.75033 38.3377i −0.277823 1.21722i
993993 −5.59611 + 2.69494i −0.177587 + 0.0855214i
994994 65.0606 + 51.8841i 2.06360 + 1.64566i
995995 1.47339 1.84757i 0.0467095 0.0585718i
996996 2.27134 4.71648i 0.0719701 0.149447i
997997 18.3381 14.6242i 0.580774 0.463152i −0.288502 0.957479i 0.593157π-0.593157\pi
0.869276 + 0.494328i 0.164586π0.164586\pi
998998 50.1831i 1.58852i
999999 −4.68784 5.87837i −0.148317 0.185983i
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 841.2.e.c.236.2 12
29.2 odd 28 841.2.d.e.190.1 6
29.3 odd 28 841.2.d.b.645.1 6
29.4 even 14 841.2.e.d.267.2 12
29.5 even 14 841.2.e.b.651.2 12
29.6 even 14 841.2.b.c.840.6 6
29.7 even 7 inner 841.2.e.c.196.1 12
29.8 odd 28 841.2.d.d.778.1 6
29.9 even 14 841.2.e.d.63.1 12
29.10 odd 28 841.2.d.d.574.1 6
29.11 odd 28 841.2.d.e.571.1 6
29.12 odd 4 841.2.d.c.605.1 6
29.13 even 14 841.2.e.b.270.1 12
29.14 odd 28 841.2.a.e.1.1 3
29.15 odd 28 841.2.a.f.1.3 3
29.16 even 7 841.2.e.b.270.2 12
29.17 odd 4 841.2.d.b.605.1 6
29.18 odd 28 841.2.d.a.571.1 6
29.19 odd 28 29.2.d.a.23.1 6
29.20 even 7 841.2.e.d.63.2 12
29.21 odd 28 29.2.d.a.24.1 yes 6
29.22 even 14 inner 841.2.e.c.196.2 12
29.23 even 7 841.2.b.c.840.1 6
29.24 even 7 841.2.e.b.651.1 12
29.25 even 7 841.2.e.d.267.1 12
29.26 odd 28 841.2.d.c.645.1 6
29.27 odd 28 841.2.d.a.190.1 6
29.28 even 2 inner 841.2.e.c.236.1 12
87.14 even 28 7569.2.a.r.1.3 3
87.44 even 28 7569.2.a.p.1.1 3
87.50 even 28 261.2.k.a.82.1 6
87.77 even 28 261.2.k.a.226.1 6
116.19 even 28 464.2.u.f.81.1 6
116.79 even 28 464.2.u.f.401.1 6
145.19 odd 28 725.2.l.b.226.1 6
145.48 even 28 725.2.r.b.574.2 12
145.77 even 28 725.2.r.b.574.1 12
145.79 odd 28 725.2.l.b.401.1 6
145.108 even 28 725.2.r.b.24.1 12
145.137 even 28 725.2.r.b.24.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.2.d.a.23.1 6 29.19 odd 28
29.2.d.a.24.1 yes 6 29.21 odd 28
261.2.k.a.82.1 6 87.50 even 28
261.2.k.a.226.1 6 87.77 even 28
464.2.u.f.81.1 6 116.19 even 28
464.2.u.f.401.1 6 116.79 even 28
725.2.l.b.226.1 6 145.19 odd 28
725.2.l.b.401.1 6 145.79 odd 28
725.2.r.b.24.1 12 145.108 even 28
725.2.r.b.24.2 12 145.137 even 28
725.2.r.b.574.1 12 145.77 even 28
725.2.r.b.574.2 12 145.48 even 28
841.2.a.e.1.1 3 29.14 odd 28
841.2.a.f.1.3 3 29.15 odd 28
841.2.b.c.840.1 6 29.23 even 7
841.2.b.c.840.6 6 29.6 even 14
841.2.d.a.190.1 6 29.27 odd 28
841.2.d.a.571.1 6 29.18 odd 28
841.2.d.b.605.1 6 29.17 odd 4
841.2.d.b.645.1 6 29.3 odd 28
841.2.d.c.605.1 6 29.12 odd 4
841.2.d.c.645.1 6 29.26 odd 28
841.2.d.d.574.1 6 29.10 odd 28
841.2.d.d.778.1 6 29.8 odd 28
841.2.d.e.190.1 6 29.2 odd 28
841.2.d.e.571.1 6 29.11 odd 28
841.2.e.b.270.1 12 29.13 even 14
841.2.e.b.270.2 12 29.16 even 7
841.2.e.b.651.1 12 29.24 even 7
841.2.e.b.651.2 12 29.5 even 14
841.2.e.c.196.1 12 29.7 even 7 inner
841.2.e.c.196.2 12 29.22 even 14 inner
841.2.e.c.236.1 12 29.28 even 2 inner
841.2.e.c.236.2 12 1.1 even 1 trivial
841.2.e.d.63.1 12 29.9 even 14
841.2.e.d.63.2 12 29.20 even 7
841.2.e.d.267.1 12 29.25 even 7
841.2.e.d.267.2 12 29.4 even 14
7569.2.a.p.1.1 3 87.44 even 28
7569.2.a.r.1.3 3 87.14 even 28