Properties

Label 117.2.x.a.59.7
Level 117117
Weight 22
Character 117.59
Analytic conductor 0.9340.934
Analytic rank 00
Dimension 4848
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [117,2,Mod(2,117)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(117, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([2, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("117.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 117=3213 117 = 3^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 117.x (of order 1212, degree 44, 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: 0.9342497036490.934249703649
Analytic rank: 00
Dimension: 4848
Relative dimension: 1212 over Q(ζ12)\Q(\zeta_{12})
Twist minimal: yes
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 59.7
Character χ\chi == 117.59
Dual form 117.2.x.a.2.7

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+(0.06047080.0604708i)q2+(1.255731.19295i)q3+1.99269iq4+(0.466078+1.73943i)q5+(0.003796420.148074i)q6+(0.132635+0.495001i)q7+(0.241441+0.241441i)q8+(0.1537312.99606i)q9+(0.133369+0.0770004i)q10+(4.051194.05119i)q11+(2.37718+2.50228i)q12+(3.180761.69788i)q13+(0.0379537+0.0219126i)q14+(2.66032+1.62825i)q153.95617q16+(2.736834.74032i)q17+(0.1718780.190470i)q18+(1.92187+7.17250i)q19+(3.46613+0.928747i)q20+(0.757066+0.463362i)q210.489958q22+(2.21820+3.84203i)q23+(0.591213+0.0151579i)q24+(1.521750.878584i)q25+(0.08967070.295015i)q26+(3.381113.94564i)q27+(0.986381+0.264300i)q280.515564iq29+(0.2593330.0624104i)q30+(3.18763+0.854124i)q31+(0.722115+0.722115i)q32+(9.920100.254338i)q33+(0.4521490.121153i)q34+(0.799199+0.461418i)q35+(5.97021+0.306337i)q36+(0.8156023.04387i)q37+(0.317510+0.549944i)q38+(1.968695.92657i)q39+(0.307439+0.532499i)q40+(2.703480.724395i)q41+(0.07380030.0177606i)q42+(1.81412+1.04738i)q43+(8.072768.07276i)q44+(5.283071.12899i)q45+(0.366467+0.0981945i)q46+(1.08839+4.06193i)q47+(4.96790+4.71952i)q48+(5.834743.36869i)q49+(0.03889290.145150i)q50+(9.091702.68768i)q51+(3.38334+6.33825i)q52+8.79692iq53+(0.4430550.0341378i)q54+(5.158588.93492i)q55+(0.0874900+0.151537i)q56+(6.14310+11.2994i)q57+(0.03117660.0311766i)q58+(5.47412+5.47412i)q59+(3.24458+5.30119i)q60+(2.899975.02290i)q61+(0.141109+0.244409i)q62+(1.503440.321286i)q637.82501iq64+(4.43582+4.74134i)q65+(0.615257+0.584497i)q66+(1.38685+5.17581i)q67+(9.445975.45364i)q68+(7.36882+2.17836i)q69+(0.0204259+0.0762306i)q70+(2.49660+0.668962i)q71+(0.7604890.686255i)q72+(4.21361+4.21361i)q73+(0.2333850.134745i)q74+(0.8628062.91864i)q75+(14.29253.82968i)q76+(1.468012.54267i)q77+(0.2393360.477433i)q78+(2.430094.20904i)q79+(1.843886.88147i)q80+(8.952730.921173i)q81+(0.207286+0.119677i)q82+(3.281090.879166i)q83+(0.923334+1.50860i)q84+(6.969866.96986i)q85+(0.1730370.0463652i)q86+(0.6150440.647411i)q871.95625iq88+(10.85052.90739i)q89+(0.2512010.387743i)q90+(1.26233+1.34928i)q91+(7.65596+4.42017i)q92+(2.98389+4.87525i)q93+(0.179812+0.311444i)q9413.3718q95+(0.0453351+1.76823i)q96+(2.144130.574518i)q97+(0.1491240.556539i)q98+(12.7604+11.5148i)q99+O(q100)q+(0.0604708 - 0.0604708i) q^{2} +(1.25573 - 1.19295i) q^{3} +1.99269i q^{4} +(0.466078 + 1.73943i) q^{5} +(0.00379642 - 0.148074i) q^{6} +(0.132635 + 0.495001i) q^{7} +(0.241441 + 0.241441i) q^{8} +(0.153731 - 2.99606i) q^{9} +(0.133369 + 0.0770004i) q^{10} +(-4.05119 - 4.05119i) q^{11} +(2.37718 + 2.50228i) q^{12} +(3.18076 - 1.69788i) q^{13} +(0.0379537 + 0.0219126i) q^{14} +(2.66032 + 1.62825i) q^{15} -3.95617 q^{16} +(-2.73683 - 4.74032i) q^{17} +(-0.171878 - 0.190470i) q^{18} +(-1.92187 + 7.17250i) q^{19} +(-3.46613 + 0.928747i) q^{20} +(0.757066 + 0.463362i) q^{21} -0.489958 q^{22} +(2.21820 + 3.84203i) q^{23} +(0.591213 + 0.0151579i) q^{24} +(1.52175 - 0.878584i) q^{25} +(0.0896707 - 0.295015i) q^{26} +(-3.38111 - 3.94564i) q^{27} +(-0.986381 + 0.264300i) q^{28} -0.515564i q^{29} +(0.259333 - 0.0624104i) q^{30} +(-3.18763 + 0.854124i) q^{31} +(-0.722115 + 0.722115i) q^{32} +(-9.92010 - 0.254338i) q^{33} +(-0.452149 - 0.121153i) q^{34} +(-0.799199 + 0.461418i) q^{35} +(5.97021 + 0.306337i) q^{36} +(-0.815602 - 3.04387i) q^{37} +(0.317510 + 0.549944i) q^{38} +(1.96869 - 5.92657i) q^{39} +(-0.307439 + 0.532499i) q^{40} +(-2.70348 - 0.724395i) q^{41} +(0.0738003 - 0.0177606i) q^{42} +(1.81412 + 1.04738i) q^{43} +(8.07276 - 8.07276i) q^{44} +(5.28307 - 1.12899i) q^{45} +(0.366467 + 0.0981945i) q^{46} +(-1.08839 + 4.06193i) q^{47} +(-4.96790 + 4.71952i) q^{48} +(5.83474 - 3.36869i) q^{49} +(0.0388929 - 0.145150i) q^{50} +(-9.09170 - 2.68768i) q^{51} +(3.38334 + 6.33825i) q^{52} +8.79692i q^{53} +(-0.443055 - 0.0341378i) q^{54} +(5.15858 - 8.93492i) q^{55} +(-0.0874900 + 0.151537i) q^{56} +(6.14310 + 11.2994i) q^{57} +(-0.0311766 - 0.0311766i) q^{58} +(5.47412 + 5.47412i) q^{59} +(-3.24458 + 5.30119i) q^{60} +(2.89997 - 5.02290i) q^{61} +(-0.141109 + 0.244409i) q^{62} +(1.50344 - 0.321286i) q^{63} -7.82501i q^{64} +(4.43582 + 4.74134i) q^{65} +(-0.615257 + 0.584497i) q^{66} +(-1.38685 + 5.17581i) q^{67} +(9.44597 - 5.45364i) q^{68} +(7.36882 + 2.17836i) q^{69} +(-0.0204259 + 0.0762306i) q^{70} +(2.49660 + 0.668962i) q^{71} +(0.760489 - 0.686255i) q^{72} +(-4.21361 + 4.21361i) q^{73} +(-0.233385 - 0.134745i) q^{74} +(0.862806 - 2.91864i) q^{75} +(-14.2925 - 3.82968i) q^{76} +(1.46801 - 2.54267i) q^{77} +(-0.239336 - 0.477433i) q^{78} +(-2.43009 - 4.20904i) q^{79} +(-1.84388 - 6.88147i) q^{80} +(-8.95273 - 0.921173i) q^{81} +(-0.207286 + 0.119677i) q^{82} +(-3.28109 - 0.879166i) q^{83} +(-0.923334 + 1.50860i) q^{84} +(6.96986 - 6.96986i) q^{85} +(0.173037 - 0.0463652i) q^{86} +(-0.615044 - 0.647411i) q^{87} -1.95625i q^{88} +(10.8505 - 2.90739i) q^{89} +(0.251201 - 0.387743i) q^{90} +(1.26233 + 1.34928i) q^{91} +(-7.65596 + 4.42017i) q^{92} +(-2.98389 + 4.87525i) q^{93} +(0.179812 + 0.311444i) q^{94} -13.3718 q^{95} +(-0.0453351 + 1.76823i) q^{96} +(2.14413 - 0.574518i) q^{97} +(0.149124 - 0.556539i) q^{98} +(-12.7604 + 11.5148i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 48q6q22q36q58q64q7+30q82q912q106q11+18q122q1312q1426q1528q1614q184q1918q208q21+8q99+O(q100) 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9} - 12 q^{10} - 6 q^{11} + 18 q^{12} - 2 q^{13} - 12 q^{14} - 26 q^{15} - 28 q^{16} - 14 q^{18} - 4 q^{19} - 18 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/117Z)×\left(\mathbb{Z}/117\mathbb{Z}\right)^\times.

nn 2828 9292
χ(n)\chi(n) e(1112)e\left(\frac{11}{12}\right) e(56)e\left(\frac{5}{6}\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 0.0604708 0.0604708i 0.0427593 0.0427593i −0.685404 0.728163i 0.740374π-0.740374\pi
0.728163 + 0.685404i 0.240374π0.240374\pi
33 1.25573 1.19295i 0.724998 0.688751i
44 1.99269i 0.996343i
55 0.466078 + 1.73943i 0.208436 + 0.777895i 0.988375 + 0.152039i 0.0485838π0.0485838\pi
−0.779938 + 0.625857i 0.784750π0.784750\pi
66 0.00379642 0.148074i 0.00154988 0.0604510i
77 0.132635 + 0.495001i 0.0501313 + 0.187093i 0.986451 0.164056i 0.0524578π-0.0524578\pi
−0.936320 + 0.351149i 0.885791π0.885791\pi
88 0.241441 + 0.241441i 0.0853623 + 0.0853623i
99 0.153731 2.99606i 0.0512436 0.998686i
1010 0.133369 + 0.0770004i 0.0421749 + 0.0243497i
1111 −4.05119 4.05119i −1.22148 1.22148i −0.967106 0.254375i 0.918130π-0.918130\pi
−0.254375 0.967106i 0.581870π-0.581870\pi
1212 2.37718 + 2.50228i 0.686233 + 0.722347i
1313 3.18076 1.69788i 0.882183 0.470907i
1414 0.0379537 + 0.0219126i 0.0101435 + 0.00585638i
1515 2.66032 + 1.62825i 0.686892 + 0.420411i
1616 −3.95617 −0.989043
1717 −2.73683 4.74032i −0.663778 1.14970i −0.979615 0.200883i 0.935619π-0.935619\pi
0.315837 0.948813i 0.397715π-0.397715\pi
1818 −0.171878 0.190470i −0.0405120 0.0448943i
1919 −1.92187 + 7.17250i −0.440906 + 1.64548i 0.285618 + 0.958344i 0.407801π0.407801\pi
−0.726524 + 0.687141i 0.758865π0.758865\pi
2020 −3.46613 + 0.928747i −0.775050 + 0.207674i
2121 0.757066 + 0.463362i 0.165205 + 0.101114i
2222 −0.489958 −0.104459
2323 2.21820 + 3.84203i 0.462526 + 0.801118i 0.999086 0.0427438i 0.0136099π-0.0136099\pi
−0.536560 + 0.843862i 0.680277π0.680277\pi
2424 0.591213 + 0.0151579i 0.120681 + 0.00309409i
2525 1.52175 0.878584i 0.304350 0.175717i
2626 0.0896707 0.295015i 0.0175859 0.0578572i
2727 −3.38111 3.94564i −0.650695 0.759339i
2828 −0.986381 + 0.264300i −0.186409 + 0.0499480i
2929 0.515564i 0.0957379i −0.998854 0.0478690i 0.984757π-0.984757\pi
0.998854 0.0478690i 0.0152430π-0.0152430\pi
3030 0.259333 0.0624104i 0.0473476 0.0113945i
3131 −3.18763 + 0.854124i −0.572516 + 0.153405i −0.533450 0.845831i 0.679105π-0.679105\pi
−0.0390658 + 0.999237i 0.512438π0.512438\pi
3232 −0.722115 + 0.722115i −0.127653 + 0.127653i
3333 −9.92010 0.254338i −1.72687 0.0442745i
3434 −0.452149 0.121153i −0.0775430 0.0207776i
3535 −0.799199 + 0.461418i −0.135089 + 0.0779938i
3636 5.97021 + 0.306337i 0.995034 + 0.0510562i
3737 −0.815602 3.04387i −0.134084 0.500409i −1.00000 0.000219073i 0.999930π-0.999930\pi
0.865916 0.500190i 0.166736π-0.166736\pi
3838 0.317510 + 0.549944i 0.0515070 + 0.0892127i
3939 1.96869 5.92657i 0.315243 0.949011i
4040 −0.307439 + 0.532499i −0.0486103 + 0.0841955i
4141 −2.70348 0.724395i −0.422213 0.113132i 0.0414558 0.999140i 0.486800π-0.486800\pi
−0.463668 + 0.886009i 0.653467π0.653467\pi
4242 0.0738003 0.0177606i 0.0113876 0.00274052i
4343 1.81412 + 1.04738i 0.276650 + 0.159724i 0.631906 0.775045i 0.282273π-0.282273\pi
−0.355256 + 0.934769i 0.615606π0.615606\pi
4444 8.07276 8.07276i 1.21701 1.21701i
4545 5.28307 1.12899i 0.787554 0.168300i
4646 0.366467 + 0.0981945i 0.0540326 + 0.0144780i
4747 −1.08839 + 4.06193i −0.158758 + 0.592493i 0.839996 + 0.542592i 0.182557π0.182557\pi
−0.998754 + 0.0499006i 0.984110π0.984110\pi
4848 −4.96790 + 4.71952i −0.717054 + 0.681205i
4949 5.83474 3.36869i 0.833535 0.481242i
5050 0.0388929 0.145150i 0.00550029 0.0205274i
5151 −9.09170 2.68768i −1.27309 0.376350i
5252 3.38334 + 6.33825i 0.469185 + 0.878957i
5353 8.79692i 1.20835i 0.796852 + 0.604175i 0.206497π0.206497\pi
−0.796852 + 0.604175i 0.793503π0.793503\pi
5454 −0.443055 0.0341378i −0.0602921 0.00464557i
5555 5.15858 8.93492i 0.695583 1.20478i
5656 −0.0874900 + 0.151537i −0.0116913 + 0.0202500i
5757 6.14310 + 11.2994i 0.813674 + 1.49665i
5858 −0.0311766 0.0311766i −0.00409369 0.00409369i
5959 5.47412 + 5.47412i 0.712669 + 0.712669i 0.967093 0.254424i 0.0818858π-0.0818858\pi
−0.254424 + 0.967093i 0.581886π0.581886\pi
6060 −3.24458 + 5.30119i −0.418874 + 0.684380i
6161 2.89997 5.02290i 0.371303 0.643117i −0.618463 0.785814i 0.712244π-0.712244\pi
0.989766 + 0.142698i 0.0455776π0.0455776\pi
6262 −0.141109 + 0.244409i −0.0179209 + 0.0310399i
6363 1.50344 0.321286i 0.189416 0.0404782i
6464 7.82501i 0.978126i
6565 4.43582 + 4.74134i 0.550195 + 0.588091i
6666 −0.615257 + 0.584497i −0.0757329 + 0.0719466i
6767 −1.38685 + 5.17581i −0.169431 + 0.632326i 0.828002 + 0.560725i 0.189477π0.189477\pi
−0.997433 + 0.0716009i 0.977189π0.977189\pi
6868 9.44597 5.45364i 1.14549 0.661350i
6969 7.36882 + 2.17836i 0.887101 + 0.262244i
7070 −0.0204259 + 0.0762306i −0.00244136 + 0.00911129i
7171 2.49660 + 0.668962i 0.296292 + 0.0793912i 0.403903 0.914802i 0.367653π-0.367653\pi
−0.107611 + 0.994193i 0.534320π0.534320\pi
7272 0.760489 0.686255i 0.0896244 0.0808759i
7373 −4.21361 + 4.21361i −0.493166 + 0.493166i −0.909302 0.416136i 0.863384π-0.863384\pi
0.416136 + 0.909302i 0.363384π0.363384\pi
7474 −0.233385 0.134745i −0.0271305 0.0156638i
7575 0.862806 2.91864i 0.0996282 0.337016i
7676 −14.2925 3.82968i −1.63947 0.439294i
7777 1.46801 2.54267i 0.167296 0.289765i
7878 −0.239336 0.477433i −0.0270995 0.0540587i
7979 −2.43009 4.20904i −0.273407 0.473554i 0.696325 0.717726i 0.254817π-0.254817\pi
−0.969732 + 0.244172i 0.921484π0.921484\pi
8080 −1.84388 6.88147i −0.206153 0.769372i
8181 −8.95273 0.921173i −0.994748 0.102353i
8282 −0.207286 + 0.119677i −0.0228910 + 0.0132161i
8383 −3.28109 0.879166i −0.360147 0.0965010i 0.0742084 0.997243i 0.476357π-0.476357\pi
−0.434355 + 0.900742i 0.643024π0.643024\pi
8484 −0.923334 + 1.50860i −0.100744 + 0.164601i
8585 6.96986 6.96986i 0.755988 0.755988i
8686 0.173037 0.0463652i 0.0186591 0.00499969i
8787 −0.615044 0.647411i −0.0659396 0.0694098i
8888 1.95625i 0.208537i
8989 10.8505 2.90739i 1.15015 0.308183i 0.367128 0.930171i 0.380341π-0.380341\pi
0.783027 + 0.621988i 0.213675π0.213675\pi
9090 0.251201 0.387743i 0.0264789 0.0408717i
9191 1.26233 + 1.34928i 0.132328 + 0.141443i
9292 −7.65596 + 4.42017i −0.798189 + 0.460835i
9393 −2.98389 + 4.87525i −0.309415 + 0.505540i
9494 0.179812 + 0.311444i 0.0185462 + 0.0321230i
9595 −13.3718 −1.37192
9696 −0.0453351 + 1.76823i −0.00462699 + 0.180470i
9797 2.14413 0.574518i 0.217703 0.0583334i −0.148319 0.988940i 0.547386π-0.547386\pi
0.366022 + 0.930606i 0.380719π0.380719\pi
9898 0.149124 0.556539i 0.0150638 0.0562190i
9999 −12.7604 + 11.5148i −1.28247 + 1.15728i
100100 1.75074 + 3.03238i 0.175074 + 0.303238i
101101 11.8701 1.18112 0.590558 0.806995i 0.298908π-0.298908\pi
0.590558 + 0.806995i 0.298908π0.298908\pi
102102 −0.712309 + 0.387257i −0.0705291 + 0.0383441i
103103 −8.74348 5.04805i −0.861521 0.497399i 0.00300033 0.999995i 0.499045π-0.499045\pi
−0.864521 + 0.502596i 0.832378π0.832378\pi
104104 1.17790 + 0.358027i 0.115503 + 0.0351074i
105105 −0.453131 + 1.53282i −0.0442211 + 0.149588i
106106 0.531957 + 0.531957i 0.0516682 + 0.0516682i
107107 −2.46578 1.42362i −0.238376 0.137626i 0.376054 0.926598i 0.377281π-0.377281\pi
−0.614430 + 0.788971i 0.710614π0.710614\pi
108108 7.86243 6.73749i 0.756563 0.648315i
109109 −6.88447 6.88447i −0.659412 0.659412i 0.295829 0.955241i 0.404404π-0.404404\pi
−0.955241 + 0.295829i 0.904404π0.904404\pi
110110 −0.228359 0.852246i −0.0217731 0.0812585i
111111 −4.65537 2.84931i −0.441868 0.270445i
112112 −0.524727 1.95831i −0.0495821 0.185043i
113113 15.1786i 1.42788i 0.700208 + 0.713939i 0.253091π0.253091\pi
−0.700208 + 0.713939i 0.746909π0.746909\pi
114114 1.05477 + 0.311808i 0.0987878 + 0.0292035i
115115 −5.64907 + 5.64907i −0.526779 + 0.526779i
116116 1.02736 0.0953878
117117 −4.59797 9.79074i −0.425082 0.905155i
118118 0.662049 0.0609465
119119 1.98346 1.98346i 0.181824 0.181824i
120120 0.249185 + 1.03544i 0.0227474 + 0.0945220i
121121 21.8243i 1.98403i
122122 −0.128375 0.479103i −0.0116225 0.0433759i
123123 −4.25902 + 2.31547i −0.384023 + 0.208779i
124124 −1.70200 6.35196i −0.152844 0.570423i
125125 8.60423 + 8.60423i 0.769586 + 0.769586i
126126 0.0714860 0.110343i 0.00636848 0.00983012i
127127 7.16053 + 4.13413i 0.635394 + 0.366845i 0.782838 0.622225i 0.213771π-0.213771\pi
−0.147444 + 0.989070i 0.547105π0.547105\pi
128128 −1.91742 1.91742i −0.169477 0.169477i
129129 3.52752 0.848925i 0.310581 0.0747436i
130130 0.554951 + 0.0184755i 0.0486724 + 0.00162041i
131131 −8.77573 5.06667i −0.766739 0.442677i 0.0649708 0.997887i 0.479305π-0.479305\pi
−0.831710 + 0.555210i 0.812638π0.812638\pi
132132 0.506816 19.7676i 0.0441126 1.72055i
133133 −3.80530 −0.329961
134134 0.229121 + 0.396850i 0.0197931 + 0.0342826i
135135 5.28729 7.72017i 0.455058 0.664446i
136136 0.483726 1.80529i 0.0414792 0.154802i
137137 −8.98344 + 2.40710i −0.767507 + 0.205653i −0.621270 0.783597i 0.713383π-0.713383\pi
−0.146237 + 0.989250i 0.546716π0.546716\pi
138138 0.577326 0.313871i 0.0491452 0.0267185i
139139 13.5884 1.15255 0.576277 0.817255i 0.304505π-0.304505\pi
0.576277 + 0.817255i 0.304505π0.304505\pi
140140 −0.919461 1.59255i −0.0777086 0.134595i
141141 3.47896 + 6.39909i 0.292981 + 0.538901i
142142 0.191424 0.110519i 0.0160640 0.00927454i
143143 −19.7643 6.00741i −1.65277 0.502365i
144144 −0.608186 + 11.8529i −0.0506821 + 0.987744i
145145 0.896786 0.240293i 0.0744740 0.0199553i
146146 0.509602i 0.0421749i
147147 3.30819 11.1907i 0.272855 0.922997i
148148 6.06547 1.62524i 0.498579 0.133594i
149149 −1.45878 + 1.45878i −0.119508 + 0.119508i −0.764331 0.644824i 0.776931π-0.776931\pi
0.644824 + 0.764331i 0.276931π0.276931\pi
150150 −0.124318 0.228667i −0.0101505 0.0186706i
151151 1.98170 + 0.530995i 0.161269 + 0.0432118i 0.338550 0.940948i 0.390064π-0.390064\pi
−0.177281 + 0.984160i 0.556730π0.556730\pi
152152 −2.19575 + 1.26772i −0.178099 + 0.102826i
153153 −14.6230 + 7.47096i −1.18220 + 0.603991i
154154 −0.0649856 0.242530i −0.00523669 0.0195436i
155155 −2.97137 5.14657i −0.238666 0.413382i
156156 11.8098 + 3.92298i 0.945541 + 0.314090i
157157 0.367627 0.636748i 0.0293398 0.0508180i −0.850983 0.525194i 0.823993π-0.823993\pi
0.880322 + 0.474376i 0.157326π0.157326\pi
158158 −0.401474 0.107575i −0.0319395 0.00855817i
159159 10.4943 + 11.0466i 0.832252 + 0.876051i
160160 −1.59263 0.919504i −0.125908 0.0726932i
161161 −1.60760 + 1.60760i −0.126696 + 0.126696i
162162 −0.597083 + 0.485675i −0.0469113 + 0.0381582i
163163 7.01940 + 1.88084i 0.549801 + 0.147319i 0.523017 0.852322i 0.324806π-0.324806\pi
0.0267847 + 0.999641i 0.491473π0.491473\pi
164164 1.44349 5.38719i 0.112718 0.420669i
165165 −4.18114 17.3738i −0.325501 1.35255i
166166 −0.251574 + 0.145246i −0.0195259 + 0.0112733i
167167 6.17150 23.0324i 0.477565 1.78230i −0.133866 0.990999i 0.542739π-0.542739\pi
0.611431 0.791298i 0.290594π-0.290594\pi
168168 0.0709124 + 0.294662i 0.00547101 + 0.0227336i
169169 7.23441 10.8011i 0.556493 0.830852i
170170 0.842947i 0.0646511i
171171 21.1938 + 6.86066i 1.62073 + 0.524648i
172172 −2.08710 + 3.61497i −0.159140 + 0.275639i
173173 4.11922 7.13471i 0.313179 0.542442i −0.665870 0.746068i 0.731939π-0.731939\pi
0.979049 + 0.203626i 0.0652727π0.0652727\pi
174174 −0.0763417 0.00195730i −0.00578745 0.000148382i
175175 0.636738 + 0.636738i 0.0481328 + 0.0481328i
176176 16.0272 + 16.0272i 1.20810 + 1.20810i
177177 13.4044 + 0.343670i 1.00754 + 0.0258318i
178178 0.480329 0.831953i 0.0360021 0.0623576i
179179 −7.94103 + 13.7543i −0.593541 + 1.02804i 0.400210 + 0.916423i 0.368937π0.368937\pi
−0.993751 + 0.111619i 0.964396π0.964396\pi
180180 2.24973 + 10.5275i 0.167685 + 0.784674i
181181 21.7854i 1.61929i 0.586918 + 0.809646i 0.300341π0.300341\pi
−0.586918 + 0.809646i 0.699659π0.699659\pi
182182 0.157926 + 0.00525771i 0.0117063 + 0.000389727i
183183 −2.35049 9.76695i −0.173753 0.721994i
184184 −0.392060 + 1.46319i −0.0289030 + 0.107868i
185185 4.91445 2.83736i 0.361317 0.208607i
186186 0.114372 + 0.475249i 0.00838616 + 0.0348469i
187187 −8.11655 + 30.2914i −0.593541 + 2.21512i
188188 −8.09415 2.16882i −0.590326 0.158177i
189189 1.50464 2.19698i 0.109447 0.159807i
190190 −0.808603 + 0.808603i −0.0586622 + 0.0586622i
191191 −7.31301 4.22217i −0.529151 0.305505i 0.211520 0.977374i 0.432159π-0.432159\pi
−0.740671 + 0.671868i 0.765492π0.765492\pi
192192 −9.33486 9.82613i −0.673686 0.709140i
193193 −4.11483 1.10257i −0.296192 0.0793644i 0.107663 0.994187i 0.465663π-0.465663\pi
−0.403855 + 0.914823i 0.632330π0.632330\pi
194194 0.0949157 0.164399i 0.00681455 0.0118032i
195195 11.2264 + 0.662146i 0.803939 + 0.0474173i
196196 6.71275 + 11.6268i 0.479482 + 0.830487i
197197 2.32810 + 8.68859i 0.165870 + 0.619036i 0.997928 + 0.0643467i 0.0204964π0.0204964\pi
−0.832057 + 0.554690i 0.812837π0.812837\pi
198198 −0.0753217 + 1.46794i −0.00535288 + 0.104322i
199199 −6.29646 + 3.63526i −0.446344 + 0.257697i −0.706285 0.707928i 0.749630π-0.749630\pi
0.259941 + 0.965625i 0.416297π0.416297\pi
200200 0.579540 + 0.155287i 0.0409797 + 0.0109805i
201201 4.43297 + 8.15388i 0.312678 + 0.575131i
202202 0.717793 0.717793i 0.0505037 0.0505037i
203203 0.255205 0.0683819i 0.0179119 0.00479947i
204204 5.35570 18.1169i 0.374974 1.26844i
205205 5.04013i 0.352018i
206206 −0.833986 + 0.223466i −0.0581065 + 0.0155696i
207207 11.8519 6.05521i 0.823767 0.420866i
208208 −12.5836 + 6.71711i −0.872517 + 0.465748i
209209 36.8430 21.2713i 2.54849 1.47137i
210210 0.0652899 + 0.120092i 0.00450543 + 0.00828716i
211211 −9.51719 16.4843i −0.655191 1.13482i −0.981846 0.189680i 0.939255π-0.939255\pi
0.326655 0.945143i 0.394078π-0.394078\pi
212212 −17.5295 −1.20393
213213 3.93311 2.13829i 0.269492 0.146513i
214214 −0.235195 + 0.0630203i −0.0160776 + 0.00430798i
215215 −0.976323 + 3.64369i −0.0665847 + 0.248497i
216216 0.136302 1.76898i 0.00927415 0.120364i
217217 −0.845584 1.46460i −0.0574020 0.0994232i
218218 −0.832619 −0.0563921
219219 −0.264535 + 10.3178i −0.0178756 + 0.697213i
220220 17.8045 + 10.2794i 1.20038 + 0.693039i
221221 −16.7537 10.4310i −1.12697 0.701665i
222222 −0.453814 + 0.109214i −0.0304580 + 0.00732994i
223223 −1.43067 1.43067i −0.0958051 0.0958051i 0.657580 0.753385i 0.271580π-0.271580\pi
−0.753385 + 0.657580i 0.771580π0.771580\pi
224224 −0.453225 0.261670i −0.0302824 0.0174836i
225225 −2.39835 4.69432i −0.159890 0.312955i
226226 0.917860 + 0.917860i 0.0610551 + 0.0610551i
227227 1.61467 + 6.02603i 0.107169 + 0.399962i 0.998582 0.0532304i 0.0169518π-0.0169518\pi
−0.891413 + 0.453192i 0.850285π0.850285\pi
228228 −22.5162 + 12.2413i −1.49117 + 0.810698i
229229 −5.67722 21.1877i −0.375161 1.40012i −0.853109 0.521733i 0.825286π-0.825286\pi
0.477947 0.878389i 0.341381π-0.341381\pi
230230 0.683208i 0.0450494i
231231 −1.18986 4.94419i −0.0782867 0.325304i
232232 0.124478 0.124478i 0.00817241 0.00817241i
233233 −15.5136 −1.01633 −0.508164 0.861260i 0.669676π-0.669676\pi
−0.508164 + 0.861260i 0.669676π0.669676\pi
234234 −0.870098 0.314012i −0.0568801 0.0205276i
235235 −7.57270 −0.493988
236236 −10.9082 + 10.9082i −0.710063 + 0.710063i
237237 −8.07273 2.38645i −0.524380 0.155017i
238238 0.239883i 0.0155493i
239239 −5.56653 20.7746i −0.360069 1.34380i −0.873984 0.485954i 0.838472π-0.838472\pi
0.513915 0.857841i 0.328195π-0.328195\pi
240240 −10.5247 6.44162i −0.679366 0.415805i
241241 −5.30489 19.7981i −0.341718 1.27531i −0.896400 0.443246i 0.853827π-0.853827\pi
0.554682 0.832062i 0.312840π-0.312840\pi
242242 1.31974 + 1.31974i 0.0848358 + 0.0848358i
243243 −12.3412 + 9.52343i −0.791686 + 0.610929i
244244 10.0091 + 5.77874i 0.640765 + 0.369946i
245245 8.57903 + 8.57903i 0.548094 + 0.548094i
246246 −0.117528 + 0.397565i −0.00749329 + 0.0253478i
247247 6.06506 + 26.0771i 0.385911 + 1.65924i
248248 −0.975847 0.563405i −0.0619663 0.0357763i
249249 −5.16898 + 2.81019i −0.327571 + 0.178088i
250250 1.04061 0.0658139
251251 2.74538 + 4.75513i 0.173287 + 0.300141i 0.939567 0.342365i 0.111228π-0.111228\pi
−0.766280 + 0.642506i 0.777895π0.777895\pi
252252 0.640221 + 2.99589i 0.0403302 + 0.188723i
253253 6.57846 24.5511i 0.413584 1.54352i
254254 0.682998 0.183009i 0.0428551 0.0114830i
255255 0.437575 17.0670i 0.0274020 1.06878i
256256 15.4181 0.963633
257257 −5.50207 9.52986i −0.343209 0.594456i 0.641817 0.766858i 0.278181π-0.278181\pi
−0.985027 + 0.172401i 0.944847π0.944847\pi
258258 0.161977 0.264648i 0.0100843 0.0164762i
259259 1.39854 0.807447i 0.0869010 0.0501723i
260260 −9.44801 + 8.83919i −0.585941 + 0.548183i
261261 −1.54466 0.0792582i −0.0956121 0.00490596i
262262 −0.837062 + 0.224290i −0.0517139 + 0.0138567i
263263 23.5579i 1.45264i 0.687355 + 0.726322i 0.258772π0.258772\pi
−0.687355 + 0.726322i 0.741228π0.741228\pi
264264 −2.33371 2.45653i −0.143630 0.151189i
265265 −15.3016 + 4.10005i −0.939969 + 0.251864i
266266 −0.230110 + 0.230110i −0.0141089 + 0.0141089i
267267 10.1570 16.5951i 0.621598 1.01560i
268268 −10.3138 2.76357i −0.630013 0.168812i
269269 −8.45703 + 4.88267i −0.515634 + 0.297701i −0.735147 0.677908i 0.762887π-0.762887\pi
0.219512 + 0.975610i 0.429553π0.429553\pi
270270 −0.147118 0.786572i −0.00895330 0.0478693i
271271 −3.75576 14.0167i −0.228146 0.851453i −0.981120 0.193402i 0.938048π-0.938048\pi
0.752973 0.658051i 0.228619π-0.228619\pi
272272 10.8274 + 18.7535i 0.656505 + 1.13710i
273273 3.19478 + 0.188432i 0.193357 + 0.0114044i
274274 −0.397676 + 0.688796i −0.0240245 + 0.0416117i
275275 −9.72423 2.60560i −0.586393 0.157124i
276276 −4.34079 + 14.6837i −0.261285 + 0.883857i
277277 14.0333 + 8.10215i 0.843181 + 0.486811i 0.858344 0.513074i 0.171493π-0.171493\pi
−0.0151630 + 0.999885i 0.504827π0.504827\pi
278278 0.821702 0.821702i 0.0492824 0.0492824i
279279 2.06897 + 9.68165i 0.123866 + 0.579625i
280280 −0.304365 0.0815543i −0.0181893 0.00487380i
281281 6.62158 24.7121i 0.395010 1.47420i −0.426753 0.904368i 0.640343π-0.640343\pi
0.821763 0.569829i 0.192991π-0.192991\pi
282282 0.597334 + 0.176583i 0.0355707 + 0.0105154i
283283 −4.62683 + 2.67130i −0.275036 + 0.158792i −0.631174 0.775641i 0.717427π-0.717427\pi
0.356138 + 0.934433i 0.384093π0.384093\pi
284284 −1.33303 + 4.97494i −0.0791009 + 0.295209i
285285 −16.7914 + 15.9519i −0.994636 + 0.944908i
286286 −1.55844 + 0.831890i −0.0921523 + 0.0491907i
287287 1.43430i 0.0846643i
288288 2.05249 + 2.27451i 0.120944 + 0.134027i
289289 −6.48043 + 11.2244i −0.381202 + 0.660261i
290290 0.0396987 0.0687601i 0.00233119 0.00403773i
291291 2.00708 3.27928i 0.117657 0.192235i
292292 −8.39641 8.39641i −0.491363 0.491363i
293293 11.1976 + 11.1976i 0.654171 + 0.654171i 0.953995 0.299824i 0.0969278π-0.0969278\pi
−0.299824 + 0.953995i 0.596928π0.596928\pi
294294 −0.476665 0.876763i −0.0277996 0.0511339i
295295 −6.97046 + 12.0732i −0.405836 + 0.702928i
296296 0.537995 0.931835i 0.0312703 0.0541618i
297297 −2.28704 + 29.6821i −0.132707 + 1.72233i
298298 0.176427i 0.0102202i
299299 13.5788 + 8.45432i 0.785285 + 0.488926i
300300 5.81594 + 1.71930i 0.335784 + 0.0992639i
301301 −0.277839 + 1.03691i −0.0160144 + 0.0597665i
302302 0.151945 0.0877254i 0.00874345 0.00504803i
303303 14.9056 14.1604i 0.856306 0.813495i
304304 7.60323 28.3757i 0.436075 1.62746i
305305 10.0886 + 2.70323i 0.577670 + 0.154786i
306306 −0.432491 + 1.33604i −0.0247239 + 0.0763764i
307307 21.2032 21.2032i 1.21013 1.21013i 0.239150 0.970983i 0.423131π-0.423131\pi
0.970983 0.239150i 0.0768687π-0.0768687\pi
308308 5.06675 + 2.92529i 0.288705 + 0.166684i
309309 −17.0016 + 4.09155i −0.967185 + 0.232760i
310310 −0.490899 0.131536i −0.0278812 0.00747074i
311311 9.06279 15.6972i 0.513903 0.890107i −0.485966 0.873977i 0.661532π-0.661532\pi
0.999870 0.0161295i 0.00513439π-0.00513439\pi
312312 1.90624 0.955596i 0.107920 0.0540999i
313313 −8.03021 13.9087i −0.453894 0.786168i 0.544730 0.838612i 0.316632π-0.316632\pi
−0.998624 + 0.0524437i 0.983299π0.983299\pi
314314 −0.0162740 0.0607354i −0.000918394 0.00342749i
315315 1.25957 + 2.46538i 0.0709689 + 0.138909i
316316 8.38730 4.84241i 0.471822 0.272407i
317317 −17.2705 4.62761i −0.970006 0.259912i −0.261175 0.965291i 0.584110π-0.584110\pi
−0.708830 + 0.705379i 0.750777π0.750777\pi
318318 1.30260 + 0.0333968i 0.0730459 + 0.00187280i
319319 −2.08865 + 2.08865i −0.116942 + 0.116942i
320320 13.6110 3.64706i 0.760880 0.203877i
321321 −4.79467 + 1.15387i −0.267612 + 0.0644028i
322322 0.194425i 0.0108349i
323323 39.2598 10.5196i 2.18447 0.585328i
324324 1.83561 17.8400i 0.101978 0.991111i
325325 3.34859 5.37831i 0.185746 0.298335i
326326 0.538205 0.310733i 0.0298084 0.0172099i
327327 −16.8579 0.432213i −0.932243 0.0239015i
328328 −0.477832 0.827630i −0.0263839 0.0456982i
329329 −2.15502 −0.118810
330330 −1.30345 0.797773i −0.0717523 0.0439159i
331331 1.60047 0.428846i 0.0879700 0.0235715i −0.214566 0.976710i 0.568834π-0.568834\pi
0.302536 + 0.953138i 0.402167π0.402167\pi
332332 1.75190 6.53819i 0.0961481 0.358830i
333333 −9.24499 + 1.97565i −0.506622 + 0.108265i
334334 −1.01959 1.76598i −0.0557895 0.0966302i
335335 −9.64932 −0.527199
336336 −2.99509 1.83314i −0.163395 0.100006i
337337 −17.1704 9.91335i −0.935333 0.540015i −0.0468388 0.998902i 0.514915π-0.514915\pi
−0.888494 + 0.458888i 0.848248π0.848248\pi
338338 −0.215680 1.09062i −0.0117314 0.0593220i
339339 18.1073 + 19.0602i 0.983453 + 1.03521i
340340 13.8888 + 13.8888i 0.753223 + 0.753223i
341341 16.3739 + 9.45350i 0.886699 + 0.511936i
342342 1.69648 0.866736i 0.0917349 0.0468677i
343343 4.97796 + 4.97796i 0.268784 + 0.268784i
344344 0.185122 + 0.690884i 0.00998110 + 0.0372500i
345345 −0.354654 + 13.8328i −0.0190939 + 0.744733i
346346 −0.182349 0.680535i −0.00980313 0.0365858i
347347 16.1885i 0.869044i 0.900661 + 0.434522i 0.143083π0.143083\pi
−0.900661 + 0.434522i 0.856917π0.856917\pi
348348 1.29009 1.22559i 0.0691560 0.0656985i
349349 −16.0469 + 16.0469i −0.858970 + 0.858970i −0.991217 0.132247i 0.957781π-0.957781\pi
0.132247 + 0.991217i 0.457781π0.457781\pi
350350 0.0770081 0.00411626
351351 −17.4537 6.80941i −0.931610 0.363459i
352352 5.85086 0.311852
353353 8.18677 8.18677i 0.435738 0.435738i −0.454837 0.890575i 0.650302π-0.650302\pi
0.890575 + 0.454837i 0.150302π0.150302\pi
354354 0.831356 0.789792i 0.0441861 0.0419770i
355355 4.65444i 0.247032i
356356 5.79352 + 21.6217i 0.307056 + 1.14595i
357357 0.124524 4.85688i 0.00659050 0.257053i
358358 0.351531 + 1.31193i 0.0185790 + 0.0693378i
359359 7.58368 + 7.58368i 0.400251 + 0.400251i 0.878322 0.478070i 0.158664π-0.158664\pi
−0.478070 + 0.878322i 0.658664π0.658664\pi
360360 1.54814 + 1.00297i 0.0815939 + 0.0528609i
361361 −31.2967 18.0692i −1.64720 0.951009i
362362 1.31738 + 1.31738i 0.0692399 + 0.0692399i
363363 26.0354 + 27.4055i 1.36650 + 1.43842i
364364 −2.68869 + 2.51543i −0.140926 + 0.131844i
365365 −9.29314 5.36540i −0.486425 0.280838i
366366 −0.732752 0.448480i −0.0383015 0.0234424i
367367 23.3494 1.21883 0.609415 0.792851i 0.291404π-0.291404\pi
0.609415 + 0.792851i 0.291404π0.291404\pi
368368 −8.77557 15.1997i −0.457458 0.792341i
369369 −2.58594 + 7.98842i −0.134619 + 0.415861i
370370 0.125603 0.468758i 0.00652981 0.0243696i
371371 −4.35448 + 1.16678i −0.226073 + 0.0605762i
372372 −9.71484 5.94596i −0.503691 0.308283i
373373 −2.45355 −0.127040 −0.0635199 0.997981i 0.520233π-0.520233\pi
−0.0635199 + 0.997981i 0.520233π0.520233\pi
374374 1.34093 + 2.32256i 0.0693378 + 0.120097i
375375 21.0690 + 0.540182i 1.08800 + 0.0278949i
376376 −1.24350 + 0.717934i −0.0641285 + 0.0370246i
377377 −0.875367 1.63988i −0.0450837 0.0844583i
378378 −0.0418664 0.223840i −0.00215337 0.0115131i
379379 −12.8719 + 3.44903i −0.661187 + 0.177165i −0.573782 0.819008i 0.694524π-0.694524\pi
−0.0874055 + 0.996173i 0.527858π0.527858\pi
380380 26.6458i 1.36690i
381381 13.9235 3.35080i 0.713324 0.171667i
382382 −0.697542 + 0.186906i −0.0356893 + 0.00956293i
383383 26.4716 26.4716i 1.35264 1.35264i 0.469938 0.882700i 0.344276π-0.344276\pi
0.882700 0.469938i 0.155724π-0.155724\pi
384384 −4.69515 0.120377i −0.239598 0.00614297i
385385 5.10700 + 1.36842i 0.260277 + 0.0697410i
386386 −0.315500 + 0.182154i −0.0160585 + 0.00927141i
387387 3.41690 5.27419i 0.173691 0.268102i
388388 1.14483 + 4.27258i 0.0581201 + 0.216907i
389389 11.9117 + 20.6316i 0.603945 + 1.04606i 0.992217 + 0.124519i 0.0397387π0.0397387\pi
−0.388272 + 0.921545i 0.626928π0.626928\pi
390390 0.718910 0.638829i 0.0364034 0.0323484i
391391 12.1416 21.0299i 0.614029 1.06353i
392392 2.22209 + 0.595407i 0.112232 + 0.0300726i
393393 −17.0643 + 4.10664i −0.860779 + 0.207153i
394394 0.666189 + 0.384624i 0.0335621 + 0.0193771i
395395 6.18870 6.18870i 0.311387 0.311387i
396396 −22.9454 25.4275i −1.15305 1.27778i
397397 21.9602 + 5.88421i 1.10215 + 0.295320i 0.763639 0.645643i 0.223411π-0.223411\pi
0.338510 + 0.940963i 0.390077π0.390077\pi
398398 −0.160925 + 0.600579i −0.00806643 + 0.0301043i
399399 −4.77844 + 4.53954i −0.239221 + 0.227261i
400400 −6.02032 + 3.47583i −0.301016 + 0.173792i
401401 −7.36155 + 27.4737i −0.367618 + 1.37197i 0.496218 + 0.868198i 0.334722π0.334722\pi
−0.863836 + 0.503772i 0.831945π0.831945\pi
402402 0.761138 + 0.225007i 0.0379621 + 0.0112223i
403403 −8.68889 + 8.12898i −0.432824 + 0.404933i
404404 23.6533i 1.17680i
405405 −2.57036 16.0020i −0.127722 0.795144i
406406 0.0112973 0.0195676i 0.000560677 0.000971122i
407407 −9.02714 + 15.6355i −0.447459 + 0.775021i
408408 −1.54619 2.84402i −0.0765480 0.140800i
409409 2.31831 + 2.31831i 0.114633 + 0.114633i 0.762096 0.647463i 0.224170π-0.224170\pi
−0.647463 + 0.762096i 0.724170π0.724170\pi
410410 −0.304781 0.304781i −0.0150520 0.0150520i
411411 −8.40924 + 13.7395i −0.414797 + 0.677719i
412412 10.0592 17.4230i 0.495581 0.858371i
413413 −1.98363 + 3.43575i −0.0976082 + 0.169062i
414414 0.350534 1.08286i 0.0172278 0.0532197i
415415 6.11698i 0.300271i
416416 −1.07081 + 3.52294i −0.0525006 + 0.172726i
417417 17.0634 16.2103i 0.835599 0.793823i
418418 0.941634 3.51423i 0.0460568 0.171886i
419419 −7.99132 + 4.61379i −0.390402 + 0.225399i −0.682334 0.731040i 0.739035π-0.739035\pi
0.291932 + 0.956439i 0.405702π0.405702\pi
420420 −3.05444 0.902949i −0.149041 0.0440594i
421421 −0.574114 + 2.14262i −0.0279806 + 0.104425i −0.978504 0.206228i 0.933881π-0.933881\pi
0.950523 + 0.310653i 0.100548π0.100548\pi
422422 −1.57233 0.421304i −0.0765398 0.0205088i
423423 12.0024 + 3.88532i 0.583579 + 0.188911i
424424 −2.12394 + 2.12394i −0.103148 + 0.103148i
425425 −8.32954 4.80906i −0.404042 0.233274i
426426 0.108534 0.367142i 0.00525850 0.0177881i
427427 2.87098 + 0.769276i 0.138936 + 0.0372279i
428428 2.83682 4.91352i 0.137123 0.237504i
429429 −31.9852 + 16.0341i −1.54426 + 0.774136i
430430 0.161298 + 0.279376i 0.00777847 + 0.0134727i
431431 −7.72277 28.8218i −0.371993 1.38830i −0.857690 0.514168i 0.828101π-0.828101\pi
0.485697 0.874127i 0.338566π-0.338566\pi
432432 13.3763 + 15.6096i 0.643565 + 0.751019i
433433 −11.3084 + 6.52890i −0.543446 + 0.313759i −0.746474 0.665414i 0.768255π-0.768255\pi
0.203028 + 0.979173i 0.434922π0.434922\pi
434434 −0.139698 0.0374321i −0.00670574 0.00179680i
435435 0.839466 1.37157i 0.0402493 0.0657616i
436436 13.7186 13.7186i 0.657001 0.657001i
437437 −31.8200 + 8.52615i −1.52216 + 0.407861i
438438 0.607930 + 0.639923i 0.0290480 + 0.0305767i
439439 14.3104i 0.683000i −0.939882 0.341500i 0.889065π-0.889065\pi
0.939882 0.341500i 0.110935π-0.110935\pi
440440 3.40275 0.911764i 0.162220 0.0434667i
441441 −9.19582 17.9991i −0.437896 0.857100i
442442 −1.64388 + 0.382337i −0.0781914 + 0.0181859i
443443 −14.2467 + 8.22531i −0.676879 + 0.390796i −0.798678 0.601758i 0.794467π-0.794467\pi
0.121799 + 0.992555i 0.461134π0.461134\pi
444444 5.67778 9.27669i 0.269456 0.440252i
445445 10.1144 + 17.5186i 0.479468 + 0.830463i
446446 −0.173028 −0.00819312
447447 −0.0915837 + 3.57209i −0.00433176 + 0.168954i
448448 3.87339 1.03787i 0.183000 0.0490348i
449449 6.52875 24.3656i 0.308111 1.14989i −0.622123 0.782919i 0.713730π-0.713730\pi
0.930234 0.366966i 0.119604π-0.119604\pi
450450 −0.428900 0.138840i −0.0202185 0.00654496i
451451 8.01765 + 13.8870i 0.377537 + 0.653913i
452452 −30.2461 −1.42266
453453 3.12194 1.69729i 0.146682 0.0797455i
454454 0.462040 + 0.266759i 0.0216846 + 0.0125196i
455455 −1.75862 + 2.82460i −0.0824456 + 0.132419i
456456 −1.24495 + 4.21135i −0.0583003 + 0.197214i
457457 −3.18313 3.18313i −0.148901 0.148901i 0.628726 0.777627i 0.283577π-0.283577\pi
−0.777627 + 0.628726i 0.783577π0.783577\pi
458458 −1.62454 0.937931i −0.0759099 0.0438266i
459459 −9.45011 + 26.8261i −0.441093 + 1.25213i
460460 −11.2568 11.2568i −0.524852 0.524852i
461461 −1.15832 4.32292i −0.0539485 0.201339i 0.933691 0.358079i 0.116568π-0.116568\pi
−0.987640 + 0.156740i 0.949901π0.949901\pi
462462 −0.370931 0.227028i −0.0172573 0.0105623i
463463 4.33486 + 16.1779i 0.201458 + 0.751851i 0.990500 + 0.137512i 0.0439107π0.0439107\pi
−0.789042 + 0.614339i 0.789423π0.789423\pi
464464 2.03966i 0.0946889i
465465 −9.87086 2.91801i −0.457750 0.135319i
466466 −0.938118 + 0.938118i −0.0434575 + 0.0434575i
467467 −34.2212 −1.58357 −0.791785 0.610800i 0.790848π-0.790848\pi
−0.791785 + 0.610800i 0.790848π0.790848\pi
468468 19.5099 9.16231i 0.901845 0.423528i
469469 −2.74598 −0.126797
470470 −0.457927 + 0.457927i −0.0211226 + 0.0211226i
471471 −0.297969 1.23815i −0.0137297 0.0570508i
472472 2.64335i 0.121670i
473473 −3.10620 11.5925i −0.142823 0.533023i
474474 −0.632475 + 0.343854i −0.0290505 + 0.0157937i
475475 3.37704 + 12.6033i 0.154949 + 0.578279i
476476 3.95242 + 3.95242i 0.181159 + 0.181159i
477477 26.3561 + 1.35236i 1.20676 + 0.0619202i
478478 −1.59287 0.919643i −0.0728561 0.0420635i
479479 −23.3970 23.3970i −1.06904 1.06904i −0.997433 0.0716026i 0.977189π-0.977189\pi
−0.0716026 0.997433i 0.522811π-0.522811\pi
480480 −3.09684 + 0.745277i −0.141351 + 0.0340171i
481481 −7.76235 8.29700i −0.353933 0.378311i
482482 −1.51800 0.876417i −0.0691430 0.0399197i
483483 −0.100926 + 3.93650i −0.00459231 + 0.179117i
484484 −43.4891 −1.97678
485485 1.99866 + 3.46179i 0.0907546 + 0.157192i
486486 −0.170390 + 1.32217i −0.00772905 + 0.0599749i
487487 −9.41355 + 35.1319i −0.426569 + 1.59198i 0.333904 + 0.942607i 0.391634π0.391634\pi
−0.760473 + 0.649369i 0.775033π0.775033\pi
488488 1.91291 0.512562i 0.0865932 0.0232026i
489489 11.0582 6.01197i 0.500071 0.271871i
490490 1.03756 0.0468723
491491 14.3100 + 24.7857i 0.645802 + 1.11856i 0.984116 + 0.177529i 0.0568103π0.0568103\pi
−0.338313 + 0.941034i 0.609856π0.609856\pi
492492 −4.61402 8.48689i −0.208016 0.382618i
493493 −2.44394 + 1.41101i −0.110070 + 0.0635487i
494494 1.94366 + 1.21014i 0.0874495 + 0.0544469i
495495 −25.9765 16.8290i −1.16756 0.756406i
496496 12.6108 3.37906i 0.566243 0.151724i
497497 1.32455i 0.0594141i
498498 −0.142638 + 0.482507i −0.00639176 + 0.0216216i
499499 −16.2614 + 4.35722i −0.727959 + 0.195056i −0.603720 0.797196i 0.706316π-0.706316\pi
−0.124239 + 0.992252i 0.539649π0.539649\pi
500500 −17.1455 + 17.1455i −0.766771 + 0.766771i
501501 −19.7267 36.2848i −0.881326 1.62109i
502502 0.453562 + 0.121532i 0.0202435 + 0.00542422i
503503 23.3028 13.4539i 1.03902 0.599878i 0.119464 0.992839i 0.461882π-0.461882\pi
0.919555 + 0.392960i 0.128549π0.128549\pi
504504 0.440564 + 0.285421i 0.0196243 + 0.0127137i
505505 5.53238 + 20.6471i 0.246187 + 0.918784i
506506 −1.08682 1.88243i −0.0483152 0.0836843i
507507 −3.80069 22.1936i −0.168795 0.985651i
508508 −8.23803 + 14.2687i −0.365504 + 0.633071i
509509 36.1565 + 9.68811i 1.60261 + 0.429418i 0.945829 0.324664i 0.105251π-0.105251\pi
0.656780 + 0.754082i 0.271918π0.271918\pi
510510 −1.00560 1.05852i −0.0445285 0.0468719i
511511 −2.64462 1.52687i −0.116991 0.0675447i
512512 4.76718 4.76718i 0.210682 0.210682i
513513 34.7982 16.6680i 1.53638 0.735911i
514514 −0.908993 0.243564i −0.0400940 0.0107431i
515515 4.70557 17.5614i 0.207352 0.773849i
516516 1.69164 + 7.02925i 0.0744703 + 0.309446i
517517 20.8649 12.0464i 0.917638 0.529799i
518518 0.0357439 0.133398i 0.00157049 0.00586117i
519519 −3.33872 13.8733i −0.146553 0.608971i
520520 −0.0737669 + 2.21574i −0.00323489 + 0.0971668i
521521 3.14358i 0.137723i 0.997626 + 0.0688615i 0.0219366π0.0219366\pi
−0.997626 + 0.0688615i 0.978063π0.978063\pi
522522 −0.0981998 + 0.0886142i −0.00429809 + 0.00387854i
523523 0.246164 0.426368i 0.0107640 0.0186438i −0.860593 0.509293i 0.829907π-0.829907\pi
0.871357 + 0.490649i 0.163240π0.163240\pi
524524 10.0963 17.4873i 0.441058 0.763936i
525525 1.55917 + 0.0399750i 0.0680477 + 0.00174465i
526526 1.42457 + 1.42457i 0.0621141 + 0.0621141i
527527 12.7728 + 12.7728i 0.556393 + 0.556393i
528528 39.2456 + 1.00620i 1.70795 + 0.0437894i
529529 1.65921 2.87384i 0.0721397 0.124950i
530530 −0.677367 + 1.17323i −0.0294229 + 0.0509620i
531531 17.2423 15.5592i 0.748253 0.675213i
532532 7.58277i 0.328755i
533533 −9.82904 + 2.28606i −0.425743 + 0.0990203i
534534 −0.389316 1.61772i −0.0168474 0.0700056i
535535 1.32703 4.95256i 0.0573727 0.214118i
536536 −1.58450 + 0.914810i −0.0684398 + 0.0395138i
537537 6.43637 + 26.7450i 0.277750 + 1.15413i
538538 −0.216145 + 0.806662i −0.00931865 + 0.0347777i
539539 −37.2849 9.99046i −1.60597 0.430319i
540540 15.3839 + 10.5359i 0.662016 + 0.453394i
541541 −9.46307 + 9.46307i −0.406849 + 0.406849i −0.880638 0.473789i 0.842886π-0.842886\pi
0.473789 + 0.880638i 0.342886π0.342886\pi
542542 −1.07471 0.620487i −0.0461629 0.0266522i
543543 25.9889 + 27.3566i 1.11529 + 1.17398i
544544 5.39936 + 1.44675i 0.231496 + 0.0620291i
545545 8.76632 15.1837i 0.375508 0.650399i
546546 0.204585 0.181796i 0.00875545 0.00778016i
547547 9.38285 + 16.2516i 0.401182 + 0.694867i 0.993869 0.110566i 0.0352663π-0.0352663\pi
−0.592687 + 0.805433i 0.701933π0.701933\pi
548548 −4.79660 17.9012i −0.204901 0.764700i
549549 −14.6031 9.46066i −0.623245 0.403771i
550550 −0.745595 + 0.430469i −0.0317923 + 0.0183553i
551551 3.69789 + 0.990846i 0.157535 + 0.0422115i
552552 1.25319 + 2.30508i 0.0533393 + 0.0981108i
553553 1.76116 1.76116i 0.0748923 0.0748923i
554554 1.33855 0.358664i 0.0568696 0.0152382i
555555 2.78640 9.42567i 0.118276 0.400097i
556556 27.0774i 1.14834i
557557 −36.4402 + 9.76411i −1.54402 + 0.413719i −0.927562 0.373669i 0.878099π-0.878099\pi
−0.616457 + 0.787388i 0.711433π0.711433\pi
558558 0.710569 + 0.460345i 0.0300808 + 0.0194880i
559559 7.54860 + 0.251309i 0.319272 + 0.0106292i
560560 3.16177 1.82545i 0.133609 0.0771393i
561561 25.9439 + 47.7205i 1.09535 + 2.01476i
562562 −1.09395 1.89477i −0.0461453 0.0799261i
563563 −2.74973 −0.115887 −0.0579437 0.998320i 0.518454π-0.518454\pi
−0.0579437 + 0.998320i 0.518454π0.518454\pi
564564 −12.7514 + 6.93247i −0.536930 + 0.291910i
565565 −26.4020 + 7.07439i −1.11074 + 0.297622i
566566 −0.118252 + 0.441324i −0.00497052 + 0.0185502i
567567 −0.731465 4.55379i −0.0307186 0.191241i
568568 0.441267 + 0.764297i 0.0185152 + 0.0320692i
569569 15.7889 0.661906 0.330953 0.943647i 0.392630π-0.392630\pi
0.330953 + 0.943647i 0.392630π0.392630\pi
570570 −0.0507649 + 1.98001i −0.00212631 + 0.0829336i
571571 24.3390 + 14.0521i 1.01855 + 0.588062i 0.913685 0.406424i 0.133224π-0.133224\pi
0.104869 + 0.994486i 0.466558π0.466558\pi
572572 11.9709 39.3840i 0.500528 1.64673i
573573 −14.2200 + 3.42215i −0.594050 + 0.142963i
574574 −0.0867336 0.0867336i −0.00362019 0.00362019i
575575 6.75109 + 3.89774i 0.281540 + 0.162547i
576576 −23.4442 1.20295i −0.976841 0.0501227i
577577 18.1311 + 18.1311i 0.754805 + 0.754805i 0.975372 0.220566i 0.0707906π-0.0707906\pi
−0.220566 + 0.975372i 0.570791π0.570791\pi
578578 0.286874 + 1.07063i 0.0119324 + 0.0445322i
579579 −6.48244 + 3.52427i −0.269401 + 0.146464i
580580 0.478829 + 1.78701i 0.0198823 + 0.0742017i
581581 1.74075i 0.0722185i
582582 −0.0769312 0.319671i −0.00318890 0.0132508i
583583 35.6380 35.6380i 1.47598 1.47598i
584584 −2.03468 −0.0841956
585585 14.8873 12.5611i 0.615513 0.519337i
586586 1.35426 0.0559439
587587 −19.1347 + 19.1347i −0.789775 + 0.789775i −0.981457 0.191682i 0.938606π-0.938606\pi
0.191682 + 0.981457i 0.438606π0.438606\pi
588588 22.2997 + 6.59219i 0.919622 + 0.271857i
589589 24.5048i 1.00970i
590590 0.308566 + 1.15158i 0.0127035 + 0.0474100i
591591 13.2885 + 8.13324i 0.546618 + 0.334557i
592592 3.22666 + 12.0421i 0.132615 + 0.494926i
593593 14.1213 + 14.1213i 0.579890 + 0.579890i 0.934873 0.354982i 0.115513π-0.115513\pi
−0.354982 + 0.934873i 0.615513π0.615513\pi
594594 1.65660 + 1.93320i 0.0679712 + 0.0793202i
595595 4.37454 + 2.52564i 0.179339 + 0.103541i
596596 −2.90689 2.90689i −0.119071 0.119071i
597597 −3.56998 + 12.0763i −0.146109 + 0.494250i
598598 1.33236 0.309884i 0.0544844 0.0126721i
599599 26.7528 + 15.4457i 1.09309 + 0.631096i 0.934397 0.356232i 0.115939π-0.115939\pi
0.158693 + 0.987328i 0.449272π0.449272\pi
600600 0.912998 0.496364i 0.0372730 0.0202640i
601601 13.5608 0.553158 0.276579 0.960991i 0.410799π-0.410799\pi
0.276579 + 0.960991i 0.410799π0.410799\pi
602602 0.0459016 + 0.0795040i 0.00187081 + 0.00324034i
603603 15.2938 + 4.95078i 0.622813 + 0.201611i
604604 −1.05811 + 3.94891i −0.0430538 + 0.160679i
605605 −37.9618 + 10.1718i −1.54337 + 0.413544i
606606 0.0450637 1.75765i 0.00183059 0.0713996i
607607 −34.4682 −1.39902 −0.699510 0.714623i 0.746598π-0.746598\pi
−0.699510 + 0.714623i 0.746598π0.746598\pi
608608 −3.79156 6.56718i −0.153768 0.266334i
609609 0.238893 0.390317i 0.00968042 0.0158164i
610610 0.773531 0.446598i 0.0313194 0.0180822i
611611 3.43476 + 14.7679i 0.138956 + 0.597447i
612612 −14.8873 29.1391i −0.601782 1.17788i
613613 4.38796 1.17575i 0.177228 0.0474881i −0.169114 0.985597i 0.554090π-0.554090\pi
0.346342 + 0.938108i 0.387424π0.387424\pi
614614 2.56435i 0.103489i
615615 −6.01263 6.32906i −0.242453 0.255212i
616616 0.968345 0.259467i 0.0390157 0.0104542i
617617 4.53555 4.53555i 0.182594 0.182594i −0.609891 0.792485i 0.708787π-0.708787\pi
0.792485 + 0.609891i 0.208787π0.208787\pi
618618 −0.780679 + 1.27552i −0.0314035 + 0.0513089i
619619 −14.7951 3.96432i −0.594663 0.159340i −0.0510797 0.998695i 0.516266π-0.516266\pi
−0.543584 + 0.839355i 0.682933π0.682933\pi
620620 10.2555 5.92101i 0.411871 0.237794i
621621 7.65931 21.7425i 0.307357 0.872498i
622622 −0.401189 1.49726i −0.0160862 0.0600346i
623623 2.87832 + 4.98540i 0.115318 + 0.199736i
624624 −7.78848 + 23.4465i −0.311789 + 0.938613i
625625 −6.56326 + 11.3679i −0.262530 + 0.454716i
626626 −1.32667 0.355479i −0.0530242 0.0142078i
627627 20.8893 70.6631i 0.834240 2.82201i
628628 1.26884 + 0.732564i 0.0506322 + 0.0292325i
629629 −12.1967 + 12.1967i −0.486316 + 0.486316i
630630 0.225251 + 0.0729162i 0.00897422 + 0.00290505i
631631 −22.3199 5.98060i −0.888542 0.238084i −0.214453 0.976734i 0.568797π-0.568797\pi
−0.674089 + 0.738650i 0.735464π0.735464\pi
632632 0.429512 1.60296i 0.0170851 0.0637623i
633633 −31.6160 9.34628i −1.25662 0.371481i
634634 −1.32419 + 0.764524i −0.0525905 + 0.0303631i
635635 −3.85366 + 14.3820i −0.152928 + 0.570734i
636636 −22.0124 + 20.9119i −0.872847 + 0.829209i
637637 12.8393 20.6217i 0.508710 0.817061i
638638 0.252605i 0.0100007i
639639 2.38806 7.37713i 0.0944700 0.291835i
640640 2.44154 4.22887i 0.0965103 0.167161i
641641 12.0181 20.8159i 0.474685 0.822178i −0.524895 0.851167i 0.675895π-0.675895\pi
0.999580 + 0.0289891i 0.00922880π0.00922880\pi
642642 −0.220162 + 0.359713i −0.00868910 + 0.0141967i
643643 10.9466 + 10.9466i 0.431690 + 0.431690i 0.889203 0.457513i 0.151260π-0.151260\pi
−0.457513 + 0.889203i 0.651260π0.651260\pi
644644 −3.20344 3.20344i −0.126233 0.126233i
645645 3.12074 + 5.74020i 0.122879 + 0.226020i
646646 1.73794 3.01020i 0.0683784 0.118435i
647647 16.2559 28.1560i 0.639084 1.10693i −0.346550 0.938032i 0.612647π-0.612647\pi
0.985634 0.168895i 0.0540199π-0.0540199\pi
648648 −1.93915 2.38397i −0.0761770 0.0936511i
649649 44.3534i 1.74102i
650650 −0.122739 0.527723i −0.00481422 0.0206990i
651651 −2.80902 0.830399i −0.110094 0.0325459i
652652 −3.74793 + 13.9875i −0.146780 + 0.547791i
653653 −28.4531 + 16.4274i −1.11346 + 0.642854i −0.939722 0.341939i 0.888917π-0.888917\pi
−0.173734 + 0.984793i 0.555583π0.555583\pi
654654 −1.04555 + 0.993274i −0.0408841 + 0.0388401i
655655 4.72293 17.6262i 0.184540 0.688713i
656656 10.6954 + 2.86583i 0.417587 + 0.111892i
657657 11.9765 + 13.2720i 0.467247 + 0.517790i
658658 −0.130316 + 0.130316i −0.00508023 + 0.00508023i
659659 −12.1233 6.99940i −0.472257 0.272658i 0.244927 0.969542i 0.421236π-0.421236\pi
−0.717184 + 0.696884i 0.754569π0.754569\pi
660660 34.6206 8.33169i 1.34760 0.324311i
661661 13.5253 + 3.62408i 0.526072 + 0.140961i 0.512074 0.858941i 0.328877π-0.328877\pi
0.0139982 + 0.999902i 0.495544π0.495544\pi
662662 0.0708494 0.122715i 0.00275364 0.00476944i
663663 −33.4818 + 6.88777i −1.30033 + 0.267499i
664664 −0.579924 1.00446i −0.0225054 0.0389805i
665665 −1.77357 6.61904i −0.0687760 0.256675i
666666 −0.439583 + 0.678522i −0.0170335 + 0.0262922i
667667 1.98081 1.14362i 0.0766974 0.0442813i
668668 45.8963 + 12.2979i 1.77578 + 0.475819i
669669 −3.50327 0.0898192i −0.135444 0.00347261i
670670 −0.583502 + 0.583502i −0.0225427 + 0.0225427i
671671 −32.0971 + 8.60039i −1.23909 + 0.332014i
672672 −0.881290 + 0.212089i −0.0339965 + 0.00818150i
673673 5.82726i 0.224624i 0.993673 + 0.112312i 0.0358257π0.0358257\pi
−0.993673 + 0.112312i 0.964174π0.964174\pi
674674 −1.63778 + 0.438842i −0.0630849 + 0.0169035i
675675 −8.61179 3.03370i −0.331468 0.116767i
676676 21.5232 + 14.4159i 0.827814 + 0.554458i
677677 −7.74373 + 4.47084i −0.297616 + 0.171828i −0.641371 0.767231i 0.721634π-0.721634\pi
0.343756 + 0.939059i 0.388301π0.388301\pi
678678 2.24755 + 0.0576241i 0.0863166 + 0.00221304i
679679 0.568774 + 0.985145i 0.0218275 + 0.0378064i
680680 3.36562 0.129066
681681 9.21636 + 5.64086i 0.353172 + 0.216158i
682682 1.56181 0.418485i 0.0598047 0.0160246i
683683 6.18232 23.0727i 0.236560 0.882854i −0.740879 0.671638i 0.765591π-0.765591\pi
0.977439 0.211216i 0.0677423π-0.0677423\pi
684684 −13.6711 + 42.2326i −0.522729 + 1.61480i
685685 −8.37396 14.5041i −0.319953 0.554174i
686686 0.602042 0.0229861
687687 −32.4050 19.8334i −1.23633 0.756692i
688688 −7.17697 4.14362i −0.273619 0.157974i
689689 14.9361 + 27.9808i 0.569021 + 1.06599i
690690 0.815035 + 0.857927i 0.0310278 + 0.0326607i
691691 −25.8128 25.8128i −0.981966 0.981966i 0.0178746 0.999840i 0.494310π-0.494310\pi
−0.999840 + 0.0178746i 0.994310π0.994310\pi
692692 14.2172 + 8.20832i 0.540458 + 0.312034i
693693 −7.39232 4.78914i −0.280811 0.181924i
694694 0.978931 + 0.978931i 0.0371597 + 0.0371597i
695695 6.33325 + 23.6360i 0.240234 + 0.896566i
696696 0.00781488 0.304809i 0.000296222 0.0115537i
697697 3.96509 + 14.7979i 0.150188 + 0.560511i
698698 1.94074i 0.0734579i
699699 −19.4809 + 18.5069i −0.736835 + 0.699997i
700700 −1.26882 + 1.26882i −0.0479568 + 0.0479568i
701701 19.6744 0.743092 0.371546 0.928415i 0.378828π-0.378828\pi
0.371546 + 0.928415i 0.378828π0.378828\pi
702702 −1.46721 + 0.643670i −0.0553763 + 0.0242938i
703703 23.3996 0.882534
704704 −31.7006 + 31.7006i −1.19476 + 1.19476i
705705 −9.50928 + 9.03386i −0.358140 + 0.340235i
706706 0.990121i 0.0372637i
707707 1.57439 + 5.87569i 0.0592109 + 0.220978i
708708 −0.684827 + 26.7107i −0.0257374 + 1.00385i
709709 9.38929 + 35.0413i 0.352622 + 1.31600i 0.883450 + 0.468525i 0.155214π0.155214\pi
−0.530828 + 0.847480i 0.678119π0.678119\pi
710710 0.281458 + 0.281458i 0.0105629 + 0.0105629i
711711 −12.9841 + 6.63363i −0.486942 + 0.248781i
712712 3.32173 + 1.91780i 0.124487 + 0.0718726i
713713 −10.3524 10.3524i −0.387699 0.387699i
714714 −0.286169 0.301230i −0.0107096 0.0112732i
715715 1.23775 37.1785i 0.0462893 1.39040i
716716 −27.4080 15.8240i −1.02428 0.591370i
717717 −31.7731 19.4467i −1.18659 0.726251i
718718 0.917183 0.0342290
719719 1.23089 + 2.13196i 0.0459043 + 0.0795086i 0.888065 0.459719i 0.152050π-0.152050\pi
−0.842160 + 0.539227i 0.818716π0.818716\pi
720720 −20.9008 + 4.46649i −0.778925 + 0.166456i
721721 1.33910 4.99758i 0.0498706 0.186120i
722722 −2.98520 + 0.799881i −0.111098 + 0.0297685i
723723 −30.2797 18.5327i −1.12611 0.689237i
724724 −43.4114 −1.61337
725725 −0.452967 0.784561i −0.0168228 0.0291379i
726726 3.23162 + 0.0828543i 0.119937 + 0.00307501i
727727 −34.1223 + 19.7005i −1.26552 + 0.730651i −0.974138 0.225955i 0.927450π-0.927450\pi
−0.291387 + 0.956605i 0.594117π0.594117\pi
728728 −0.0209924 + 0.630550i −0.000778029 + 0.0233697i
729729 −4.13620 + 26.6813i −0.153193 + 0.988196i
730730 −0.886414 + 0.237514i −0.0328077 + 0.00879079i
731731 11.4660i 0.424086i
732732 19.4625 4.68379i 0.719354 0.173118i
733733 26.0719 6.98594i 0.962988 0.258032i 0.257123 0.966379i 0.417225π-0.417225\pi
0.705864 + 0.708347i 0.250559π0.250559\pi
734734 1.41196 1.41196i 0.0521164 0.0521164i
735735 21.0074 + 0.538600i 0.774868 + 0.0198666i
736736 −4.37618 1.17259i −0.161308 0.0432224i
737737 26.5866 15.3498i 0.979331 0.565417i
738738 0.326693 + 0.639440i 0.0120257 + 0.0235381i
739739 −1.77661 6.63041i −0.0653537 0.243903i 0.925520 0.378700i 0.123629π-0.123629\pi
−0.990873 + 0.134796i 0.956962π0.956962\pi
740740 5.65397 + 9.79296i 0.207844 + 0.359996i
741741 38.7248 + 25.5105i 1.42259 + 0.937152i
742742 −0.192763 + 0.333875i −0.00707655 + 0.0122569i
743743 46.8324 + 12.5487i 1.71811 + 0.460367i 0.977390 0.211444i 0.0678166π-0.0678166\pi
0.740723 + 0.671811i 0.234483π0.234483\pi
744744 −1.89752 + 0.456652i −0.0695664 + 0.0167417i
745745 −3.21735 1.85754i −0.117874 0.0680549i
746746 −0.148368 + 0.148368i −0.00543214 + 0.00543214i
747747 −3.13844 + 9.69519i −0.114829 + 0.354728i
748748 −60.3612 16.1737i −2.20702 0.591370i
749749 0.377643 1.40938i 0.0137988 0.0514978i
750750 1.30673 1.24140i 0.0477150 0.0453294i
751751 −3.31754 + 1.91539i −0.121059 + 0.0698934i −0.559307 0.828961i 0.688933π-0.688933\pi
0.438248 + 0.898854i 0.355599π0.355599\pi
752752 4.30586 16.0697i 0.157019 0.586001i
753753 9.12010 + 2.69607i 0.332355 + 0.0982503i
754754 −0.152099 0.0462310i −0.00553913 0.00168363i
755755 3.69451i 0.134457i
756756 4.37790 + 2.99828i 0.159223 + 0.109046i
757757 11.7765 20.3975i 0.428024 0.741360i −0.568673 0.822563i 0.692543π-0.692543\pi
0.996698 + 0.0812038i 0.0258765π0.0258765\pi
758758 −0.569812 + 0.986943i −0.0206965 + 0.0358474i
759759 −21.0275 38.6775i −0.763252 1.40390i
760760 −3.22850 3.22850i −0.117110 0.117110i
761761 −20.4670 20.4670i −0.741929 0.741929i 0.231020 0.972949i 0.425794π-0.425794\pi
−0.972949 + 0.231020i 0.925794π0.925794\pi
762762 0.639342 1.04459i 0.0231609 0.0378416i
763763 2.49469 4.32094i 0.0903140 0.156428i
764764 8.41346 14.5725i 0.304388 0.527216i
765765 −19.8106 21.9536i −0.716255 0.793734i
766766 3.20152i 0.115676i
767767 26.7062 + 8.11743i 0.964306 + 0.293103i
768768 19.3611 18.3931i 0.698632 0.663703i
769769 −1.58276 + 5.90694i −0.0570757 + 0.213010i −0.988574 0.150736i 0.951836π-0.951836\pi
0.931498 + 0.363746i 0.118502π0.118502\pi
770770 0.391574 0.226075i 0.0141114 0.00814719i
771771 −18.2778 5.40326i −0.658259 0.194594i
772772 2.19707 8.19957i 0.0790742 0.295109i
773773 −0.445447 0.119357i −0.0160216 0.00429298i 0.250799 0.968039i 0.419307π-0.419307\pi
−0.266821 + 0.963746i 0.585973π0.585973\pi
774774 −0.112312 0.525558i −0.00403696 0.0188908i
775775 −4.10037 + 4.10037i −0.147290 + 0.147290i
776776 0.656393 + 0.378969i 0.0235631 + 0.0136042i
777777 0.792947 2.68233i 0.0284468 0.0962280i
778778 1.96792 + 0.527302i 0.0705533 + 0.0189047i
779779 10.3915 17.9985i 0.372312 0.644864i
780780 −1.31945 + 22.3707i −0.0472439 + 0.800999i
781781 −7.40412 12.8243i −0.264940 0.458890i
782782 −0.537482 2.00591i −0.0192203 0.0717312i
783783 −2.03423 + 1.74318i −0.0726976 + 0.0622962i
784784 −23.0833 + 13.3271i −0.824402 + 0.475969i
785785 1.27892 + 0.342685i 0.0456466 + 0.0122310i
786786 −0.783559 + 1.28022i −0.0279486 + 0.0456640i
787787 −22.4505 + 22.4505i −0.800274 + 0.800274i −0.983138 0.182864i 0.941463π-0.941463\pi
0.182864 + 0.983138i 0.441463π0.441463\pi
788788 −17.3136 + 4.63917i −0.616773 + 0.165264i
789789 28.1035 + 29.5825i 1.00051 + 1.05316i
790790 0.748472i 0.0266294i
791791 −7.51340 + 2.01321i −0.267146 + 0.0715815i
792792 −5.86104 0.300736i −0.208263 0.0106862i
793793 0.695820 20.9004i 0.0247093 0.742196i
794794 1.68377 0.972126i 0.0597548 0.0344995i
795795 −14.3236 + 23.4026i −0.508004 + 0.830006i
796796 −7.24394 12.5469i −0.256754 0.444712i
797797 37.3254 1.32213 0.661067 0.750327i 0.270104π-0.270104\pi
0.661067 + 0.750327i 0.270104π0.270104\pi
798798 −0.0144465 + 0.563466i −0.000511401 + 0.0199465i
799799 22.2336 5.95747i 0.786567 0.210760i
800800 −0.464442 + 1.73332i −0.0164205 + 0.0612821i
801801 −7.04266 32.9558i −0.248840 1.16444i
802802 1.21620 + 2.10652i 0.0429454 + 0.0743837i
803803 34.1403 1.20479
804804 −16.2481 + 8.83353i −0.573028 + 0.311534i
805805 −3.54556 2.04703i −0.124965 0.0721483i
806806 −0.0338578 + 1.01699i −0.00119259 + 0.0358220i
807807 −4.79498 + 16.2202i −0.168791 + 0.570976i
808808 2.86592 + 2.86592i 0.100823 + 0.100823i
809809 −36.4293 21.0325i −1.28079 0.739462i −0.303793 0.952738i 0.598253π-0.598253\pi
−0.976992 + 0.213276i 0.931587π0.931587\pi
810810 −1.12308 0.812220i −0.0394611 0.0285385i
811811 −11.9459 11.9459i −0.419478 0.419478i 0.465546 0.885024i 0.345858π-0.345858\pi
−0.885024 + 0.465546i 0.845858π0.845858\pi
812812 0.136264 + 0.508543i 0.00478192 + 0.0178464i
813813 −21.4375 13.1208i −0.751845 0.460166i
814814 0.399611 + 1.49137i 0.0140064 + 0.0522724i
815815 13.0863i 0.458394i
816816 35.9683 + 10.6329i 1.25914 + 0.372226i
817817 −10.9988 + 10.9988i −0.384801 + 0.384801i
818818 0.280380 0.00980326
819819 4.23658 3.57459i 0.148038 0.124906i
820820 10.0434 0.350731
821821 12.0935 12.0935i 0.422066 0.422066i −0.463848 0.885915i 0.653532π-0.653532\pi
0.885915 + 0.463848i 0.153532π0.153532\pi
822822 0.322325 + 1.33935i 0.0112424 + 0.0467153i
823823 47.9181i 1.67032i −0.550008 0.835160i 0.685375π-0.685375\pi
0.550008 0.835160i 0.314625π-0.314625\pi
824824 −0.892229 3.32984i −0.0310823 0.116001i
825825 −15.3194 + 8.32860i −0.533353 + 0.289965i
826826 0.0878109 + 0.327715i 0.00305533 + 0.0114027i
827827 17.3519 + 17.3519i 0.603386 + 0.603386i 0.941209 0.337824i 0.109691π-0.109691\pi
−0.337824 + 0.941209i 0.609691π0.609691\pi
828828 12.0661 + 23.6172i 0.419327 + 0.820755i
829829 18.5597 + 10.7155i 0.644606 + 0.372164i 0.786387 0.617735i 0.211949π-0.211949\pi
−0.141780 + 0.989898i 0.545283π0.545283\pi
830830 −0.369899 0.369899i −0.0128394 0.0128394i
831831 27.2876 6.56696i 0.946596 0.227805i
832832 −13.2859 24.8894i −0.460607 0.862886i
833833 −31.9374 18.4390i −1.10656 0.638875i
834834 0.0515873 2.01209i 0.00178632 0.0696730i
835835 42.9395 1.48598
836836 42.3871 + 73.4166i 1.46599 + 2.53917i
837837 14.1478 + 9.68938i 0.489020 + 0.334914i
838838 −0.204242 + 0.762242i −0.00705543 + 0.0263312i
839839 −38.1327 + 10.2176i −1.31649 + 0.352752i −0.847661 0.530539i 0.821990π-0.821990\pi
−0.468826 + 0.883291i 0.655323π0.655323\pi
840840 −0.479491 + 0.260682i −0.0165440 + 0.00899439i
841841 28.7342 0.990834
842842 0.0948491 + 0.164283i 0.00326872 + 0.00566158i
843843 −21.1654 38.9310i −0.728974 1.34085i
844844 32.8480 18.9648i 1.13067 0.652795i
845845 22.1595 + 7.54957i 0.762309 + 0.259713i
846846 0.960747 0.490849i 0.0330312 0.0168758i
847847 −10.8031 + 2.89467i −0.371198 + 0.0994621i
848848 34.8021i 1.19511i
849849 −2.62333 + 8.87402i −0.0900324 + 0.304556i
850850 −0.794502 + 0.212886i −0.0272512 + 0.00730194i
851851 9.88546 9.88546i 0.338869 0.338869i
852852 4.26094 + 7.83745i 0.145977 + 0.268506i
853853 27.1772 + 7.28211i 0.930530 + 0.249335i 0.692081 0.721820i 0.256694π-0.256694\pi
0.238449 + 0.971155i 0.423361π0.423361\pi
854854 0.220129 0.127092i 0.00753267 0.00434899i
855855 −2.05565 + 40.0626i −0.0703019 + 1.37011i
856856 −0.251620 0.939060i −0.00860021 0.0320964i
857857 19.3381 + 33.4945i 0.660576 + 1.14415i 0.980465 + 0.196696i 0.0630211π0.0630211\pi
−0.319889 + 0.947455i 0.603646π0.603646\pi
858858 −0.964575 + 2.90377i −0.0329301 + 0.0991332i
859859 8.08690 14.0069i 0.275921 0.477910i −0.694446 0.719545i 0.744350π-0.744350\pi
0.970367 + 0.241635i 0.0776837π0.0776837\pi
860860 −7.26073 1.94551i −0.247589 0.0663412i
861861 −1.71106 1.80110i −0.0583127 0.0613815i
862862 −2.20988 1.27587i −0.0752687 0.0434564i
863863 −24.7751 + 24.7751i −0.843353 + 0.843353i −0.989293 0.145941i 0.953379π-0.953379\pi
0.145941 + 0.989293i 0.453379π0.453379\pi
864864 5.29076 + 0.407659i 0.179995 + 0.0138688i
865865 14.3302 + 3.83976i 0.487241 + 0.130556i
866866 −0.289019 + 1.07864i −0.00982128 + 0.0366535i
867867 5.25252 + 21.8257i 0.178385 + 0.741241i
868868 2.91848 1.68498i 0.0990596 0.0571921i
869869 −7.20687 + 26.8964i −0.244476 + 0.912398i
870870 −0.0321766 0.133703i −0.00109089 0.00453296i
871871 4.37666 + 18.8177i 0.148298 + 0.637613i
872872 3.32439i 0.112578i
873873 −1.39167 6.51226i −0.0471009 0.220407i
874874 −1.40860 + 2.43977i −0.0476466 + 0.0825264i
875875 −3.11788 + 5.40032i −0.105404 + 0.182564i
876876 −20.5602 0.527135i −0.694664 0.0178102i
877877 14.1609 + 14.1609i 0.478178 + 0.478178i 0.904549 0.426370i 0.140208π-0.140208\pi
−0.426370 + 0.904549i 0.640208π0.640208\pi
878878 −0.865364 0.865364i −0.0292046 0.0292046i
879879 27.4194 + 0.702997i 0.924834 + 0.0237115i
880880 −20.4082 + 35.3481i −0.687961 + 1.19158i
881881 7.53795 13.0561i 0.253960 0.439872i −0.710653 0.703543i 0.751600π-0.751600\pi
0.964613 + 0.263672i 0.0849335π0.0849335\pi
882882 −1.64450 0.532342i −0.0553732 0.0179249i
883883 39.2575i 1.32112i 0.750773 + 0.660560i 0.229681π0.229681\pi
−0.750773 + 0.660560i 0.770319π0.770319\pi
884884 20.7857 33.3848i 0.699099 1.12285i
885885 5.64970 + 23.4761i 0.189913 + 0.789141i
886886 −0.364116 + 1.35890i −0.0122327 + 0.0456531i
887887 13.5741 7.83699i 0.455773 0.263140i −0.254492 0.967075i 0.581908π-0.581908\pi
0.710265 + 0.703934i 0.248575π0.248575\pi
888888 −0.436056 1.81194i −0.0146331 0.0608046i
889889 −1.09666 + 4.09280i −0.0367809 + 0.137268i
890890 1.67099 + 0.447741i 0.0560118 + 0.0150083i
891891 32.5374 + 40.0011i 1.09004 + 1.34009i
892892 2.85089 2.85089i 0.0954547 0.0954547i
893893 −27.0424 15.6130i −0.904941 0.522468i
894894 0.210469 + 0.221546i 0.00703915 + 0.00740960i
895895 −27.6257 7.40228i −0.923425 0.247431i
896896 0.694806 1.20344i 0.0232118 0.0402041i
897897 27.1370 5.58254i 0.906078 0.186396i
898898 −1.07861 1.86821i −0.0359937 0.0623430i
899899 0.440356 + 1.64343i 0.0146867 + 0.0548115i
900900 9.35432 4.77916i 0.311811 0.159305i
901901 41.7002 24.0756i 1.38924 0.802076i
902902 1.32459 + 0.354923i 0.0441041 + 0.0118177i
903903 0.888092 + 1.63353i 0.0295538 + 0.0543605i
904904 −3.66473 + 3.66473i −0.121887 + 0.121887i
905905 −37.8940 + 10.1537i −1.25964 + 0.337519i
906906 0.0861500 0.291423i 0.00286214 0.00968187i
907907 6.13756i 0.203794i −0.994795 0.101897i 0.967509π-0.967509\pi
0.994795 0.101897i 0.0324912π-0.0324912\pi
908908 −12.0080 + 3.21753i −0.398499 + 0.106778i
909909 1.82480 35.5634i 0.0605246 1.17956i
910910 0.0644605 + 0.277152i 0.00213685 + 0.00918748i
911911 7.64862 4.41593i 0.253410 0.146306i −0.367915 0.929860i 0.619928π-0.619928\pi
0.621325 + 0.783553i 0.286595π0.286595\pi
912912 −24.3032 44.7025i −0.804758 1.48025i
913913 9.73067 + 16.8540i 0.322038 + 0.557786i
914914 −0.384973 −0.0127338
915915 15.8934 8.64066i 0.525419 0.285651i
916916 42.2204 11.3129i 1.39500 0.373790i
917917 1.34404 5.01601i 0.0443840 0.165643i
918918 1.05074 + 2.19365i 0.0346796 + 0.0724013i
919919 −5.30900 9.19546i −0.175128 0.303330i 0.765078 0.643938i 0.222701π-0.222701\pi
−0.940205 + 0.340608i 0.889367π0.889367\pi
920920 −2.72784 −0.0899341
921921 1.33116 51.9200i 0.0438632 1.71082i
922922 −0.331456 0.191366i −0.0109159 0.00630230i
923923 9.07690 2.11113i 0.298770 0.0694885i
924924 9.85222 2.37101i 0.324114 0.0780005i
925925 −3.91544 3.91544i −0.128739 0.128739i
926926 1.24042 + 0.716159i 0.0407629 + 0.0235345i
927927 −16.4684 + 25.4199i −0.540893 + 0.834901i
928928 0.372297 + 0.372297i 0.0122212 + 0.0122212i
929929 8.01779 + 29.9228i 0.263055 + 0.981735i 0.963430 + 0.267960i 0.0863494π0.0863494\pi
−0.700375 + 0.713775i 0.746984π0.746984\pi
930930 −0.773354 + 0.420444i −0.0253593 + 0.0137869i
931931 12.9483 + 48.3239i 0.424365 + 1.58375i
932932 30.9137i 1.01261i
933933 −7.34557 30.5230i −0.240483 0.999277i
934934 −2.06939 + 2.06939i −0.0677124 + 0.0677124i
935935 −56.4725 −1.84685
936936 1.25375 3.47403i 0.0409801 0.113552i
937937 −47.1338 −1.53979 −0.769897 0.638168i 0.779692π-0.779692\pi
−0.769897 + 0.638168i 0.779692π0.779692\pi
938938 −0.166051 + 0.166051i −0.00542177 + 0.00542177i
939939 −26.6763 7.88600i −0.870547 0.257350i
940940 15.0900i 0.492182i
941941 −0.0981573 0.366328i −0.00319984 0.0119420i 0.964307 0.264785i 0.0853010π-0.0853010\pi
−0.967507 + 0.252843i 0.918634π0.918634\pi
942942 −0.0928902 0.0568533i −0.00302652 0.00185238i
943943 −3.21370 11.9937i −0.104653 0.390568i
944944 −21.6565 21.6565i −0.704861 0.704861i
945945 4.52277 + 1.59325i 0.147126 + 0.0518284i
946946 −0.888842 0.513173i −0.0288988 0.0166847i
947947 22.1926 + 22.1926i 0.721163 + 0.721163i 0.968842 0.247679i 0.0796680π-0.0796680\pi
−0.247679 + 0.968842i 0.579668π0.579668\pi
948948 4.75545 16.0864i 0.154450 0.522463i
949949 −6.24826 + 20.5567i −0.202827 + 0.667298i
950950 0.966344 + 0.557919i 0.0313523 + 0.0181013i
951951 −27.2076 + 14.7918i −0.882267 + 0.479657i
952952 0.957779 0.0310418
953953 13.5922 + 23.5423i 0.440294 + 0.762611i 0.997711 0.0676211i 0.0215409π-0.0215409\pi
−0.557417 + 0.830233i 0.688208π0.688208\pi
954954 1.67555 1.51200i 0.0542480 0.0489527i
955955 3.93572 14.6883i 0.127357 0.475302i
956956 41.3972 11.0923i 1.33888 0.358752i
957957 −0.131128 + 5.11445i −0.00423875 + 0.165327i
958958 −2.82967 −0.0914225
959959 −2.38304 4.12754i −0.0769523 0.133285i
960960 12.7410 20.8170i 0.411216 0.671867i
961961 −17.4153 + 10.0547i −0.561784 + 0.324346i
962962 −0.971123 0.0323308i −0.0313103 0.00104239i
963963 −4.64431 + 7.16876i −0.149661 + 0.231010i
964964 39.4514 10.5710i 1.27064 0.340468i
965965 7.67133i 0.246949i
966966 0.231940 + 0.244146i 0.00746255 + 0.00785528i
967967 33.7881 9.05350i 1.08655 0.291141i 0.329275 0.944234i 0.393196π-0.393196\pi
0.757278 + 0.653093i 0.226529π0.226529\pi
968968 −5.26929 + 5.26929i −0.169361 + 0.169361i
969969 36.7504 60.0449i 1.18059 1.92892i
970970 0.330198 + 0.0884762i 0.0106020 + 0.00284080i
971971 2.18627 1.26224i 0.0701606 0.0405072i −0.464509 0.885568i 0.653769π-0.653769\pi
0.534670 + 0.845061i 0.320436π0.320436\pi
972972 −18.9772 24.5921i −0.608695 0.788791i
973973 1.80230 + 6.72627i 0.0577791 + 0.215634i
974974 1.55521 + 2.69370i 0.0498321 + 0.0863117i
975975 −2.21113 10.7484i −0.0708130 0.344225i
976976 −11.4728 + 19.8715i −0.367235 + 0.636070i
977977 0.347770 + 0.0931847i 0.0111262 + 0.00298124i 0.264378 0.964419i 0.414833π-0.414833\pi
−0.253252 + 0.967400i 0.581500π0.581500\pi
978978 0.305152 1.03225i 0.00975770 0.0330077i
979979 −55.7360 32.1792i −1.78133 1.02845i
980980 −17.0953 + 17.0953i −0.546090 + 0.546090i
981981 −21.6846 + 19.5679i −0.692336 + 0.624755i
982982 2.36415 + 0.633472i 0.0754431 + 0.0202149i
983983 −5.27343 + 19.6807i −0.168196 + 0.627717i 0.829415 + 0.558634i 0.188674π0.188674\pi
−0.997611 + 0.0690837i 0.977992π0.977992\pi
984984 −1.58735 0.469251i −0.0506030 0.0149592i
985985 −14.0281 + 8.09912i −0.446972 + 0.258059i
986986 −0.0624622 + 0.233112i −0.00198920 + 0.00742380i
987987 −2.70612 + 2.57083i −0.0861369 + 0.0818304i
988988 −51.9634 + 12.0858i −1.65318 + 0.384500i
989989 9.29319i 0.295506i
990990 −2.58848 + 0.553159i −0.0822674 + 0.0175806i
991991 −10.5948 + 18.3508i −0.336556 + 0.582931i −0.983782 0.179366i 0.942595π-0.942595\pi
0.647227 + 0.762298i 0.275929π0.275929\pi
992992 1.68506 2.91862i 0.0535008 0.0926661i
993993 1.49818 2.44781i 0.0475432 0.0776788i
994994 0.0800965 + 0.0800965i 0.00254051 + 0.00254051i
995995 −9.25791 9.25791i −0.293495 0.293495i
996996 −5.59982 10.3002i −0.177437 0.326373i
997997 −1.82391 + 3.15911i −0.0577638 + 0.100050i −0.893461 0.449140i 0.851730π-0.851730\pi
0.835697 + 0.549190i 0.185064π0.185064\pi
998998 −0.719854 + 1.24682i −0.0227866 + 0.0394675i
999999 −9.25238 + 13.5097i −0.292732 + 0.427429i
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 117.2.x.a.59.7 yes 48
3.2 odd 2 351.2.ba.a.98.6 48
9.2 odd 6 117.2.bc.a.20.7 yes 48
9.7 even 3 351.2.bf.a.332.6 48
13.2 odd 12 117.2.bc.a.41.7 yes 48
39.2 even 12 351.2.bf.a.314.6 48
117.2 even 12 inner 117.2.x.a.2.7 48
117.106 odd 12 351.2.ba.a.197.6 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
117.2.x.a.2.7 48 117.2 even 12 inner
117.2.x.a.59.7 yes 48 1.1 even 1 trivial
117.2.bc.a.20.7 yes 48 9.2 odd 6
117.2.bc.a.41.7 yes 48 13.2 odd 12
351.2.ba.a.98.6 48 3.2 odd 2
351.2.ba.a.197.6 48 117.106 odd 12
351.2.bf.a.314.6 48 39.2 even 12
351.2.bf.a.332.6 48 9.7 even 3