Properties

Label 117.2.r.b.43.2
Level 117117
Weight 22
Character 117.43
Analytic conductor 0.9340.934
Analytic rank 00
Dimension 2222
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [117,2,Mod(43,117)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 1])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("117.43"); 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.r (of order 66, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 0.9342497036490.934249703649
Analytic rank: 00
Dimension: 2222
Relative dimension: 1111 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 43.2
Character χ\chi == 117.43
Dual form 117.2.r.b.49.2

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(2.00627+1.15832i)q2+(1.714540.245682i)q3+(1.683412.91575i)q4+(1.095050.632228i)q5+(3.15524+2.47889i)q64.17527iq7+3.16642iq8+(2.879280.842464i)q9+(1.46464+2.53684i)q10+(2.34999+1.35677i)q11+(2.169925.41274i)q12+(2.05335+2.96374i)q13+(4.83630+8.37672i)q14+(1.722181.35301i)q15+(0.3009070.521186i)q16+(1.05102+1.82043i)q17+(4.80077+5.02533i)q18+(2.74246+1.58336i)q194.25719iq20+(1.025797.15866i)q21+(3.143145.44409i)q22+0.452373q23+(0.777933+5.42894i)q24+(1.70057+2.94548i)q25+(7.552533.56763i)q26+(4.729662.15182i)q27+(12.17407.02869i)q28+(4.292097.43413i)q29+(1.88793+4.70934i)q30+(3.34195+1.92947i)q31+(4.277002.46932i)q32+(3.69582+2.90358i)q33+(4.217272.43484i)q34+(2.639734.57214i)q35+(2.390599.81346i)q36+(7.55106+4.35961i)q37+(3.668076.35328i)q38+(4.24868+4.57697i)q39+(2.00190+3.46739i)q40+2.51117iq41+(10.3500+13.1740i)q424.98614q43+9.13598iq44+(2.620332.74290i)q45+(0.907582+0.523993i)q46+(10.8108+6.24161i)q47+(0.6439620.819665i)q4810.4329q497.87923iq50+(2.24927+2.86297i)q51+(12.09810.997861i)q521.14568q53+(6.99646+9.79559i)q54+(1.71558+2.97147i)q55+13.2207q56+(4.31304+3.38850i)q57+(17.2222+9.94323i)q58+(5.476803.16203i)q59+(1.045927.29912i)q605.09646q61+(4.469897.74208i)q62+(3.5175212.0218i)q63+12.6447q64+(4.12228+1.94726i)q65+(4.0515210.1063i)q6614.1824iq67+7.07720q68+(0.7756110.111140i)q69+(10.5920+6.11529i)q70+(6.49685+3.75096i)q71+(2.66759+9.11700i)q72+7.95754iq7320.1993q74+(2.19205+5.46794i)q75+10.6617iq76+(5.66488+9.81187i)q77+(13.82564.26131i)q78+(1.82489+3.16081i)q79+(0.6590170.380484i)q80+(7.580514.85138i)q81+(2.908735.03807i)q82+(1.960051.13164i)q83+(22.59979.06000i)q84+(2.30185+1.32897i)q85+(10.00355.77554i)q86+(9.1853911.6916i)q87+(4.296107.44106i)q88+(1.31792+0.760899i)q89+(2.07993+8.53818i)q90+(12.37448.57329i)q91+(0.7615281.31901i)q92+(5.25585+4.12921i)q9328.9191q94+(2.00209+3.46772i)q95+(7.939743.18297i)q96+2.38580iq97+(20.931212.0846i)q98+(5.62326+5.88630i)q99+O(q100)q+(-2.00627 + 1.15832i) q^{2} +(1.71454 - 0.245682i) q^{3} +(1.68341 - 2.91575i) q^{4} +(1.09505 - 0.632228i) q^{5} +(-3.15524 + 2.47889i) q^{6} -4.17527i q^{7} +3.16642i q^{8} +(2.87928 - 0.842464i) q^{9} +(-1.46464 + 2.53684i) q^{10} +(-2.34999 + 1.35677i) q^{11} +(2.16992 - 5.41274i) q^{12} +(2.05335 + 2.96374i) q^{13} +(4.83630 + 8.37672i) q^{14} +(1.72218 - 1.35301i) q^{15} +(-0.300907 - 0.521186i) q^{16} +(1.05102 + 1.82043i) q^{17} +(-4.80077 + 5.02533i) q^{18} +(-2.74246 + 1.58336i) q^{19} -4.25719i q^{20} +(-1.02579 - 7.15866i) q^{21} +(3.14314 - 5.44409i) q^{22} +0.452373 q^{23} +(0.777933 + 5.42894i) q^{24} +(-1.70057 + 2.94548i) q^{25} +(-7.55253 - 3.56763i) q^{26} +(4.72966 - 2.15182i) q^{27} +(-12.1740 - 7.02869i) q^{28} +(-4.29209 - 7.43413i) q^{29} +(-1.88793 + 4.70934i) q^{30} +(-3.34195 + 1.92947i) q^{31} +(-4.27700 - 2.46932i) q^{32} +(-3.69582 + 2.90358i) q^{33} +(-4.21727 - 2.43484i) q^{34} +(-2.63973 - 4.57214i) q^{35} +(2.39059 - 9.81346i) q^{36} +(7.55106 + 4.35961i) q^{37} +(3.66807 - 6.35328i) q^{38} +(4.24868 + 4.57697i) q^{39} +(2.00190 + 3.46739i) q^{40} +2.51117i q^{41} +(10.3500 + 13.1740i) q^{42} -4.98614 q^{43} +9.13598i q^{44} +(2.62033 - 2.74290i) q^{45} +(-0.907582 + 0.523993i) q^{46} +(10.8108 + 6.24161i) q^{47} +(-0.643962 - 0.819665i) q^{48} -10.4329 q^{49} -7.87923i q^{50} +(2.24927 + 2.86297i) q^{51} +(12.0981 - 0.997861i) q^{52} -1.14568 q^{53} +(-6.99646 + 9.79559i) q^{54} +(-1.71558 + 2.97147i) q^{55} +13.2207 q^{56} +(-4.31304 + 3.38850i) q^{57} +(17.2222 + 9.94323i) q^{58} +(-5.47680 - 3.16203i) q^{59} +(-1.04592 - 7.29912i) q^{60} -5.09646 q^{61} +(4.46989 - 7.74208i) q^{62} +(-3.51752 - 12.0218i) q^{63} +12.6447 q^{64} +(4.12228 + 1.94726i) q^{65} +(4.05152 - 10.1063i) q^{66} -14.1824i q^{67} +7.07720 q^{68} +(0.775611 - 0.111140i) q^{69} +(10.5920 + 6.11529i) q^{70} +(-6.49685 + 3.75096i) q^{71} +(2.66759 + 9.11700i) q^{72} +7.95754i q^{73} -20.1993 q^{74} +(-2.19205 + 5.46794i) q^{75} +10.6617i q^{76} +(5.66488 + 9.81187i) q^{77} +(-13.8256 - 4.26131i) q^{78} +(-1.82489 + 3.16081i) q^{79} +(-0.659017 - 0.380484i) q^{80} +(7.58051 - 4.85138i) q^{81} +(-2.90873 - 5.03807i) q^{82} +(-1.96005 - 1.13164i) q^{83} +(-22.5997 - 9.06000i) q^{84} +(2.30185 + 1.32897i) q^{85} +(10.0035 - 5.77554i) q^{86} +(-9.18539 - 11.6916i) q^{87} +(-4.29610 - 7.44106i) q^{88} +(1.31792 + 0.760899i) q^{89} +(-2.07993 + 8.53818i) q^{90} +(12.3744 - 8.57329i) q^{91} +(0.761528 - 1.31901i) q^{92} +(-5.25585 + 4.12921i) q^{93} -28.9191 q^{94} +(-2.00209 + 3.46772i) q^{95} +(-7.93974 - 3.18297i) q^{96} +2.38580i q^{97} +(20.9312 - 12.0846i) q^{98} +(-5.62326 + 5.88630i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 22q+2q3+10q4+3q56q62q97q10+3q1111q12+3q139q1415q1512q16+9q1730q186q19+12q2113q2212q23+18q99+O(q100) 22 q + 2 q^{3} + 10 q^{4} + 3 q^{5} - 6 q^{6} - 2 q^{9} - 7 q^{10} + 3 q^{11} - 11 q^{12} + 3 q^{13} - 9 q^{14} - 15 q^{15} - 12 q^{16} + 9 q^{17} - 30 q^{18} - 6 q^{19} + 12 q^{21} - 13 q^{22} - 12 q^{23}+ \cdots - 18 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(16)e\left(\frac{1}{6}\right) e(23)e\left(\frac{2}{3}\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 −2.00627 + 1.15832i −1.41865 + 0.819055i −0.996180 0.0873234i 0.972169π-0.972169\pi
−0.422466 + 0.906379i 0.638835π0.638835\pi
33 1.71454 0.245682i 0.989889 0.141845i
44 1.68341 2.91575i 0.841704 1.45787i
55 1.09505 0.632228i 0.489722 0.282741i −0.234737 0.972059i 0.575423π-0.575423\pi
0.724459 + 0.689318i 0.242090π0.242090\pi
66 −3.15524 + 2.47889i −1.28812 + 1.01200i
77 4.17527i 1.57811i −0.614326 0.789053i 0.710572π-0.710572\pi
0.614326 0.789053i 0.289428π-0.289428\pi
88 3.16642i 1.11950i
99 2.87928 0.842464i 0.959760 0.280821i
1010 −1.46464 + 2.53684i −0.463161 + 0.802219i
1111 −2.34999 + 1.35677i −0.708550 + 0.409081i −0.810524 0.585706i 0.800817π-0.800817\pi
0.101974 + 0.994787i 0.467484π0.467484\pi
1212 2.16992 5.41274i 0.626401 1.56252i
1313 2.05335 + 2.96374i 0.569496 + 0.821994i
1414 4.83630 + 8.37672i 1.29256 + 2.23877i
1515 1.72218 1.35301i 0.444665 0.349347i
1616 −0.300907 0.521186i −0.0752267 0.130296i
1717 1.05102 + 1.82043i 0.254911 + 0.441518i 0.964871 0.262723i 0.0846206π-0.0846206\pi
−0.709961 + 0.704241i 0.751287π0.751287\pi
1818 −4.80077 + 5.02533i −1.13155 + 1.18448i
1919 −2.74246 + 1.58336i −0.629163 + 0.363247i −0.780428 0.625246i 0.784999π-0.784999\pi
0.151265 + 0.988493i 0.451665π0.451665\pi
2020 4.25719i 0.951937i
2121 −1.02579 7.15866i −0.223846 1.56215i
2222 3.14314 5.44409i 0.670121 1.16068i
2323 0.452373 0.0943263 0.0471632 0.998887i 0.484982π-0.484982\pi
0.0471632 + 0.998887i 0.484982π0.484982\pi
2424 0.777933 + 5.42894i 0.158795 + 1.10818i
2525 −1.70057 + 2.94548i −0.340115 + 0.589096i
2626 −7.55253 3.56763i −1.48117 0.699669i
2727 4.72966 2.15182i 0.910223 0.414119i
2828 −12.1740 7.02869i −2.30068 1.32830i
2929 −4.29209 7.43413i −0.797022 1.38048i −0.921547 0.388266i 0.873074π-0.873074\pi
0.124525 0.992216i 0.460259π-0.460259\pi
3030 −1.88793 + 4.70934i −0.344688 + 0.859805i
3131 −3.34195 + 1.92947i −0.600231 + 0.346544i −0.769133 0.639089i 0.779311π-0.779311\pi
0.168901 + 0.985633i 0.445978π0.445978\pi
3232 −4.27700 2.46932i −0.756073 0.436519i
3333 −3.69582 + 2.90358i −0.643359 + 0.505449i
3434 −4.21727 2.43484i −0.723256 0.417572i
3535 −2.63973 4.57214i −0.446195 0.772833i
3636 2.39059 9.81346i 0.398432 1.63558i
3737 7.55106 + 4.35961i 1.24139 + 0.716715i 0.969377 0.245579i 0.0789782π-0.0789782\pi
0.272010 + 0.962294i 0.412311π0.412311\pi
3838 3.66807 6.35328i 0.595039 1.03064i
3939 4.24868 + 4.57697i 0.680334 + 0.732903i
4040 2.00190 + 3.46739i 0.316528 + 0.548243i
4141 2.51117i 0.392178i 0.980586 + 0.196089i 0.0628242π0.0628242\pi
−0.980586 + 0.196089i 0.937176π0.937176\pi
4242 10.3500 + 13.1740i 1.59704 + 2.03279i
4343 −4.98614 −0.760379 −0.380189 0.924909i 0.624141π-0.624141\pi
−0.380189 + 0.924909i 0.624141π0.624141\pi
4444 9.13598i 1.37730i
4545 2.62033 2.74290i 0.390616 0.408888i
4646 −0.907582 + 0.523993i −0.133816 + 0.0772585i
4747 10.8108 + 6.24161i 1.57692 + 0.910432i 0.995287 + 0.0969780i 0.0309176π0.0309176\pi
0.581629 + 0.813454i 0.302416π0.302416\pi
4848 −0.643962 0.819665i −0.0929480 0.118309i
4949 −10.4329 −1.49042
5050 7.87923i 1.11429i
5151 2.24927 + 2.86297i 0.314960 + 0.400896i
5252 12.0981 0.997861i 1.67771 0.138378i
5353 −1.14568 −0.157371 −0.0786857 0.996899i 0.525072π-0.525072\pi
−0.0786857 + 0.996899i 0.525072π0.525072\pi
5454 −6.99646 + 9.79559i −0.952098 + 1.33301i
5555 −1.71558 + 2.97147i −0.231328 + 0.400672i
5656 13.2207 1.76668
5757 −4.31304 + 3.38850i −0.571277 + 0.448818i
5858 17.2222 + 9.94323i 2.26138 + 1.30561i
5959 −5.47680 3.16203i −0.713019 0.411662i 0.0991588 0.995072i 0.468385π-0.468385\pi
−0.812178 + 0.583410i 0.801718π0.801718\pi
6060 −1.04592 7.29912i −0.135027 0.942312i
6161 −5.09646 −0.652535 −0.326267 0.945278i 0.605791π-0.605791\pi
−0.326267 + 0.945278i 0.605791π0.605791\pi
6262 4.46989 7.74208i 0.567677 0.983245i
6363 −3.51752 12.0218i −0.443165 1.51460i
6464 12.6447 1.58059
6565 4.12228 + 1.94726i 0.511306 + 0.241528i
6666 4.05152 10.1063i 0.498708 1.24400i
6767 14.1824i 1.73266i −0.499476 0.866328i 0.666474π-0.666474\pi
0.499476 0.866328i 0.333526π-0.333526\pi
6868 7.07720 0.858237
6969 0.775611 0.111140i 0.0933726 0.0133797i
7070 10.5920 + 6.11529i 1.26599 + 0.730917i
7171 −6.49685 + 3.75096i −0.771034 + 0.445157i −0.833243 0.552906i 0.813519π-0.813519\pi
0.0622094 + 0.998063i 0.480185π0.480185\pi
7272 2.66759 + 9.11700i 0.314379 + 1.07445i
7373 7.95754i 0.931360i 0.884953 + 0.465680i 0.154190π0.154190\pi
−0.884953 + 0.465680i 0.845810π0.845810\pi
7474 −20.1993 −2.34812
7575 −2.19205 + 5.46794i −0.253116 + 0.631383i
7676 10.6617i 1.22299i
7777 5.66488 + 9.81187i 0.645573 + 1.11817i
7878 −13.8256 4.26131i −1.56544 0.482498i
7979 −1.82489 + 3.16081i −0.205317 + 0.355619i −0.950234 0.311538i 0.899156π-0.899156\pi
0.744917 + 0.667157i 0.232489π0.232489\pi
8080 −0.659017 0.380484i −0.0736804 0.0425394i
8181 7.58051 4.85138i 0.842279 0.539042i
8282 −2.90873 5.03807i −0.321216 0.556362i
8383 −1.96005 1.13164i −0.215144 0.124213i 0.388556 0.921425i 0.372974π-0.372974\pi
−0.603700 + 0.797212i 0.706307π0.706307\pi
8484 −22.5997 9.06000i −2.46583 0.988527i
8585 2.30185 + 1.32897i 0.249671 + 0.144147i
8686 10.0035 5.77554i 1.07871 0.622792i
8787 −9.18539 11.6916i −0.984778 1.25347i
8888 −4.29610 7.44106i −0.457966 0.793220i
8989 1.31792 + 0.760899i 0.139699 + 0.0806552i 0.568220 0.822876i 0.307632π-0.307632\pi
−0.428522 + 0.903532i 0.640965π0.640965\pi
9090 −2.07993 + 8.53818i −0.219244 + 0.900003i
9191 12.3744 8.57329i 1.29719 0.898725i
9292 0.761528 1.31901i 0.0793948 0.137516i
9393 −5.25585 + 4.12921i −0.545007 + 0.428179i
9494 −28.9191 −2.98278
9595 −2.00209 + 3.46772i −0.205410 + 0.355780i
9696 −7.93974 3.18297i −0.810346 0.324860i
9797 2.38580i 0.242242i 0.992638 + 0.121121i 0.0386489π0.0386489\pi
−0.992638 + 0.121121i 0.961351π0.961351\pi
9898 20.9312 12.0846i 2.11437 1.22073i
9999 −5.62326 + 5.88630i −0.565159 + 0.591596i
100100 5.72552 + 9.91689i 0.572552 + 0.991689i
101101 5.59898 + 9.69772i 0.557119 + 0.964959i 0.997735 + 0.0672632i 0.0214267π0.0214267\pi
−0.440616 + 0.897696i 0.645240π0.645240\pi
102102 −7.82887 3.13852i −0.775173 0.310760i
103103 −1.45757 2.52458i −0.143618 0.248754i 0.785238 0.619194i 0.212540π-0.212540\pi
−0.928857 + 0.370440i 0.879207π0.879207\pi
104104 −9.38444 + 6.50176i −0.920220 + 0.637550i
105105 −5.64921 7.19057i −0.551306 0.701728i
106106 2.29854 1.32706i 0.223254 0.128896i
107107 −1.33105 + 2.30545i −0.128678 + 0.222876i −0.923164 0.384405i 0.874407π-0.874407\pi
0.794487 + 0.607281i 0.207740π0.207740\pi
108108 1.68776 17.4129i 0.162405 1.67556i
109109 8.32143i 0.797049i −0.917158 0.398524i 0.869522π-0.869522\pi
0.917158 0.398524i 0.130478π-0.130478\pi
110110 7.94874i 0.757883i
111111 14.0177 + 5.61955i 1.33050 + 0.533384i
112112 −2.17609 + 1.25637i −0.205622 + 0.118716i
113113 −1.75803 + 3.04500i −0.165382 + 0.286449i −0.936791 0.349890i 0.886219π-0.886219\pi
0.771409 + 0.636340i 0.219552π0.219552\pi
114114 4.72815 11.7941i 0.442832 1.10462i
115115 0.495372 0.286003i 0.0461937 0.0266699i
116116 −28.9014 −2.68343
117117 8.40901 + 6.80357i 0.777413 + 0.628990i
118118 14.6506 1.34870
119119 7.60078 4.38831i 0.696762 0.402276i
120120 4.28421 + 5.45314i 0.391093 + 0.497801i
121121 −1.81835 + 3.14948i −0.165305 + 0.286316i
122122 10.2249 5.90333i 0.925715 0.534462i
123123 0.616949 + 4.30549i 0.0556284 + 0.388213i
124124 12.9924i 1.16675i
125125 10.6229i 0.950140i
126126 20.9821 + 20.0445i 1.86924 + 1.78571i
127127 7.86992 13.6311i 0.698342 1.20956i −0.270699 0.962664i 0.587255π-0.587255\pi
0.969041 0.246900i 0.0794119π-0.0794119\pi
128128 −16.8147 + 9.70794i −1.48622 + 0.858069i
129129 −8.54892 + 1.22501i −0.752690 + 0.107856i
130130 −10.5260 + 0.868186i −0.923188 + 0.0761450i
131131 −6.82094 11.8142i −0.595949 1.03221i −0.993412 0.114595i 0.963443π-0.963443\pi
0.397464 0.917618i 0.369890π-0.369890\pi
132132 2.24455 + 15.6640i 0.195363 + 1.36338i
133133 6.61095 + 11.4505i 0.573242 + 0.992885i
134134 16.4277 + 28.4537i 1.41914 + 2.45802i
135135 3.81877 5.34658i 0.328668 0.460161i
136136 −5.76423 + 3.32798i −0.494278 + 0.285372i
137137 11.4539i 0.978569i −0.872124 0.489285i 0.837258π-0.837258\pi
0.872124 0.489285i 0.162742π-0.162742\pi
138138 −1.42735 + 1.12138i −0.121504 + 0.0954584i
139139 −2.42317 + 4.19706i −0.205531 + 0.355990i −0.950302 0.311330i 0.899225π-0.899225\pi
0.744771 + 0.667320i 0.232559π0.232559\pi
140140 −17.7749 −1.50226
141141 20.0690 + 8.04546i 1.69011 + 0.677550i
142142 8.68961 15.0508i 0.729216 1.26304i
143143 −8.84647 4.17885i −0.739779 0.349453i
144144 −1.30548 1.24714i −0.108790 0.103928i
145145 −9.40013 5.42717i −0.780639 0.450702i
146146 −9.21738 15.9650i −0.762836 1.32127i
147147 −17.8876 + 2.56318i −1.47535 + 0.211408i
148148 25.4230 14.6780i 2.08976 1.20652i
149149 18.7955 + 10.8516i 1.53978 + 0.888994i 0.998851 + 0.0479284i 0.0152619π0.0152619\pi
0.540933 + 0.841066i 0.318071π0.318071\pi
150150 −1.93579 13.5092i −0.158056 1.10303i
151151 −2.34152 1.35188i −0.190550 0.110014i 0.401690 0.915776i 0.368423π-0.368423\pi
−0.592240 + 0.805762i 0.701756π0.701756\pi
152152 −5.01357 8.68376i −0.406654 0.704346i
153153 4.55983 + 4.35607i 0.368641 + 0.352167i
154154 −22.7305 13.1235i −1.83168 1.05752i
155155 −2.43974 + 4.22575i −0.195964 + 0.339420i
156156 20.4976 4.68317i 1.64112 0.374954i
157157 −7.83378 13.5685i −0.625204 1.08288i −0.988501 0.151212i 0.951682π-0.951682\pi
0.363298 0.931673i 0.381651π-0.381651\pi
158158 8.45524i 0.672663i
159159 −1.96431 + 0.281474i −0.155780 + 0.0223223i
160160 −6.24471 −0.493688
161161 1.88878i 0.148857i
162162 −9.58909 + 18.5138i −0.753390 + 1.45458i
163163 −5.73759 + 3.31260i −0.449403 + 0.259463i −0.707578 0.706635i 0.750212π-0.750212\pi
0.258175 + 0.966098i 0.416879π0.416879\pi
164164 7.32193 + 4.22732i 0.571746 + 0.330098i
165165 −2.21138 + 5.51618i −0.172156 + 0.429434i
166166 5.24319 0.406950
167167 10.7941i 0.835270i −0.908615 0.417635i 0.862859π-0.862859\pi
0.908615 0.417635i 0.137141π-0.137141\pi
168168 22.6673 3.24808i 1.74882 0.250595i
169169 −4.56752 + 12.1712i −0.351348 + 0.936245i
170170 −6.15751 −0.472259
171171 −6.56238 + 6.86935i −0.501838 + 0.525313i
172172 −8.39370 + 14.5383i −0.640013 + 1.10854i
173173 4.87660 0.370761 0.185380 0.982667i 0.440648π-0.440648\pi
0.185380 + 0.982667i 0.440648π0.440648\pi
174174 31.9710 + 12.8169i 2.42371 + 0.971644i
175175 12.2982 + 7.10036i 0.929656 + 0.536737i
176176 1.41426 + 0.816522i 0.106604 + 0.0615477i
177177 −10.1670 4.07587i −0.764202 0.306361i
178178 −3.52546 −0.264244
179179 6.61646 11.4601i 0.494538 0.856564i −0.505442 0.862860i 0.668671π-0.668671\pi
0.999980 + 0.00629588i 0.00200406π0.00200406\pi
180180 −3.58653 12.2577i −0.267324 0.913631i
181181 −18.2227 −1.35448 −0.677242 0.735760i 0.736825π-0.736825\pi
−0.677242 + 0.735760i 0.736825π0.736825\pi
182182 −14.8958 + 31.5339i −1.10415 + 2.33745i
183183 −8.73807 + 1.25211i −0.645937 + 0.0925586i
184184 1.43240i 0.105598i
185185 11.0251 0.810579
186186 5.76171 14.3723i 0.422469 1.05383i
187187 −4.93980 2.85199i −0.361234 0.208558i
188188 36.3979 21.0143i 2.65459 1.53263i
189189 −8.98445 19.7476i −0.653523 1.43643i
190190 9.27623i 0.672969i
191191 15.3708 1.11219 0.556096 0.831118i 0.312299π-0.312299\pi
0.556096 + 0.831118i 0.312299π0.312299\pi
192192 21.6798 3.10658i 1.56461 0.224198i
193193 5.65364i 0.406958i −0.979079 0.203479i 0.934775π-0.934775\pi
0.979079 0.203479i 0.0652249π-0.0652249\pi
194194 −2.76352 4.78656i −0.198409 0.343655i
195195 7.54622 + 2.32589i 0.540396 + 0.166560i
196196 −17.5628 + 30.4197i −1.25449 + 2.17284i
197197 5.46126 + 3.15306i 0.389098 + 0.224646i 0.681769 0.731567i 0.261211π-0.261211\pi
−0.292671 + 0.956213i 0.594544π0.594544\pi
198198 4.46355 18.3230i 0.317211 1.30216i
199199 −0.849701 1.47173i −0.0602337 0.104328i 0.834336 0.551256i 0.185851π-0.185851\pi
−0.894570 + 0.446928i 0.852518π0.852518\pi
200200 −9.32662 5.38473i −0.659492 0.380758i
201201 −3.48437 24.3163i −0.245768 1.71514i
202202 −22.4661 12.9708i −1.58071 0.912623i
203203 −31.0395 + 17.9207i −2.17855 + 1.25778i
204204 12.1341 1.73874i 0.849559 0.121736i
205205 1.58763 + 2.74986i 0.110885 + 0.192058i
206206 5.84854 + 3.37665i 0.407487 + 0.235263i
207207 1.30251 0.381108i 0.0905306 0.0264888i
208208 0.926794 1.96199i 0.0642616 0.136039i
209209 4.29650 7.44176i 0.297195 0.514758i
210210 19.6628 + 7.88263i 1.35686 + 0.543953i
211211 4.56391 0.314193 0.157096 0.987583i 0.449787π-0.449787\pi
0.157096 + 0.987583i 0.449787π0.449787\pi
212212 −1.92865 + 3.34052i −0.132460 + 0.229428i
213213 −10.2175 + 8.02732i −0.700095 + 0.550023i
214214 6.16713i 0.421577i
215215 −5.46008 + 3.15238i −0.372374 + 0.214990i
216216 6.81357 + 14.9761i 0.463605 + 1.01899i
217217 8.05608 + 13.9535i 0.546882 + 0.947228i
218218 9.63888 + 16.6950i 0.652827 + 1.13073i
219219 1.95503 + 13.6435i 0.132109 + 0.921943i
220220 5.77603 + 10.0044i 0.389420 + 0.674495i
221221 −3.23715 + 6.85293i −0.217755 + 0.460978i
222222 −34.6324 + 4.96261i −2.32438 + 0.333068i
223223 19.2946 11.1398i 1.29206 0.745974i 0.313045 0.949738i 0.398651π-0.398651\pi
0.979020 + 0.203764i 0.0653177π0.0653177\pi
224224 −10.3101 + 17.8576i −0.688873 + 1.19316i
225225 −2.41497 + 9.91354i −0.160998 + 0.660903i
226226 8.14545i 0.541827i
227227 4.20189i 0.278889i −0.990230 0.139445i 0.955468π-0.955468\pi
0.990230 0.139445i 0.0445318π-0.0445318\pi
228228 2.61940 + 18.2800i 0.173474 + 1.21062i
229229 19.7986 11.4307i 1.30833 0.755365i 0.326513 0.945193i 0.394126π-0.394126\pi
0.981817 + 0.189827i 0.0607929π0.0607929\pi
230230 −0.662566 + 1.14760i −0.0436883 + 0.0756704i
231231 12.1233 + 15.4311i 0.797652 + 1.01529i
232232 23.5395 13.5906i 1.54545 0.892264i
233233 17.2872 1.13252 0.566260 0.824226i 0.308390π-0.308390\pi
0.566260 + 0.824226i 0.308390π0.308390\pi
234234 −24.7514 3.90947i −1.61805 0.255570i
235235 15.7845 1.02967
236236 −18.4394 + 10.6460i −1.20030 + 0.692994i
237237 −2.35229 + 5.86767i −0.152798 + 0.381146i
238238 −10.1661 + 17.6083i −0.658972 + 1.14137i
239239 −5.61354 + 3.24098i −0.363110 + 0.209642i −0.670444 0.741960i 0.733896π-0.733896\pi
0.307334 + 0.951602i 0.400563π0.400563\pi
240240 −1.22339 0.490445i −0.0789694 0.0316581i
241241 0.183966i 0.0118503i 0.999982 + 0.00592515i 0.00188605π0.00188605\pi
−0.999982 + 0.00592515i 0.998114π0.998114\pi
242242 8.42494i 0.541575i
243243 11.8052 10.1803i 0.757302 0.653065i
244244 −8.57941 + 14.8600i −0.549241 + 0.951313i
245245 −11.4246 + 6.59598i −0.729889 + 0.421402i
246246 −6.22490 7.92334i −0.396885 0.505174i
247247 −10.3239 4.87675i −0.656893 0.310300i
248248 −6.10952 10.5820i −0.387955 0.671957i
249249 −3.63861 1.45868i −0.230587 0.0924404i
250250 −12.3047 21.3124i −0.778218 1.34791i
251251 −11.8003 20.4387i −0.744827 1.29008i −0.950276 0.311410i 0.899199π-0.899199\pi
0.205449 0.978668i 0.434135π-0.434135\pi
252252 −40.9739 9.98137i −2.58111 0.628767i
253253 −1.06307 + 0.613766i −0.0668349 + 0.0385871i
254254 36.4635i 2.28792i
255255 4.27312 + 1.71305i 0.267593 + 0.107275i
256256 9.84511 17.0522i 0.615319 1.06576i
257257 −5.84983 −0.364902 −0.182451 0.983215i 0.558403π-0.558403\pi
−0.182451 + 0.983215i 0.558403π0.558403\pi
258258 15.7325 12.3601i 0.979461 0.769504i
259259 18.2026 31.5277i 1.13105 1.95904i
260260 12.6172 8.74150i 0.782487 0.542125i
261261 −18.6211 17.7890i −1.15262 1.10111i
262262 27.3693 + 15.8017i 1.69088 + 0.976230i
263263 4.84907 + 8.39884i 0.299007 + 0.517895i 0.975909 0.218178i 0.0700114π-0.0700114\pi
−0.676902 + 0.736073i 0.736678π0.736678\pi
264264 −9.19396 11.7025i −0.565849 0.720239i
265265 −1.25458 + 0.724332i −0.0770683 + 0.0444954i
266266 −26.5267 15.3152i −1.62646 0.939035i
267267 2.44656 + 0.980802i 0.149727 + 0.0600241i
268268 −41.3523 23.8748i −2.52599 1.45838i
269269 −10.4720 18.1380i −0.638487 1.10589i −0.985765 0.168130i 0.946227π-0.946227\pi
0.347278 0.937762i 0.387106π-0.387106\pi
270270 −1.46844 + 15.1500i −0.0893661 + 0.922002i
271271 4.98580 + 2.87855i 0.302866 + 0.174860i 0.643730 0.765253i 0.277386π-0.277386\pi
−0.340864 + 0.940113i 0.610720π0.610720\pi
272272 0.632520 1.09556i 0.0383522 0.0664279i
273273 19.1101 17.7394i 1.15660 1.07364i
274274 13.2672 + 22.9795i 0.801502 + 1.38824i
275275 9.22915i 0.556539i
276276 0.981613 2.44858i 0.0590861 0.147387i
277277 −15.9997 −0.961330 −0.480665 0.876904i 0.659605π-0.659605\pi
−0.480665 + 0.876904i 0.659605π0.659605\pi
278278 11.2272i 0.673364i
279279 −7.99689 + 8.37096i −0.478761 + 0.501156i
280280 14.4773 8.35848i 0.865184 0.499514i
281281 −16.2457 9.37948i −0.969139 0.559533i −0.0701653 0.997535i 0.522353π-0.522353\pi
−0.898974 + 0.438003i 0.855686π0.855686\pi
282282 −49.5829 + 7.10492i −2.95262 + 0.423092i
283283 −4.52331 −0.268883 −0.134442 0.990922i 0.542924π-0.542924\pi
−0.134442 + 0.990922i 0.542924π0.542924\pi
284284 25.2576i 1.49876i
285285 −2.58070 + 6.43741i −0.152867 + 0.381319i
286286 22.5888 1.86314i 1.33571 0.110170i
287287 10.4848 0.618899
288288 −14.3950 3.50666i −0.848233 0.206632i
289289 6.29070 10.8958i 0.370041 0.640930i
290290 25.1456 1.47660
291291 0.586150 + 4.09055i 0.0343607 + 0.239792i
292292 23.2022 + 13.3958i 1.35781 + 0.783929i
293293 0.274290 + 0.158362i 0.0160242 + 0.00925159i 0.507991 0.861363i 0.330388π-0.330388\pi
−0.491966 + 0.870614i 0.663722π0.663722\pi
294294 32.9184 25.8620i 1.91984 1.50830i
295295 −7.99651 −0.465575
296296 −13.8043 + 23.9098i −0.802361 + 1.38973i
297297 −8.19513 + 11.4738i −0.475530 + 0.665779i
298298 −50.2783 −2.91254
299299 0.928879 + 1.34072i 0.0537185 + 0.0775356i
300300 12.2530 + 15.5962i 0.707429 + 0.900448i
301301 20.8185i 1.19996i
302302 6.26361 0.360430
303303 11.9822 + 15.2515i 0.688361 + 0.876178i
304304 1.65045 + 0.952887i 0.0946597 + 0.0546518i
305305 −5.58089 + 3.22213i −0.319561 + 0.184498i
306306 −14.1940 3.45770i −0.811415 0.197663i
307307 11.2849i 0.644066i 0.946728 + 0.322033i 0.104366π0.104366\pi
−0.946728 + 0.322033i 0.895634π0.895634\pi
308308 38.1452 2.17353
309309 −3.11930 3.97039i −0.177451 0.225867i
310310 11.3040i 0.642023i
311311 15.9070 + 27.5517i 0.902004 + 1.56232i 0.824890 + 0.565294i 0.191237π0.191237\pi
0.0771139 + 0.997022i 0.475429π0.475429\pi
312312 −14.4926 + 13.4531i −0.820482 + 0.761632i
313313 −0.0740804 + 0.128311i −0.00418727 + 0.00725257i −0.868111 0.496369i 0.834666π-0.834666\pi
0.863924 + 0.503622i 0.168000π0.168000\pi
314314 31.4333 + 18.1480i 1.77389 + 1.02415i
315315 −11.4524 10.9406i −0.645268 0.616433i
316316 6.14408 + 10.6419i 0.345631 + 0.598651i
317317 −17.0960 9.87036i −0.960205 0.554375i −0.0639691 0.997952i 0.520376π-0.520376\pi
−0.896236 + 0.443577i 0.853709π0.853709\pi
318318 3.61490 2.84001i 0.202714 0.159260i
319319 20.1728 + 11.6468i 1.12946 + 0.652094i
320320 13.8466 7.99433i 0.774048 0.446897i
321321 −1.71573 + 4.27980i −0.0957627 + 0.238875i
322322 2.18781 + 3.78940i 0.121922 + 0.211175i
323323 −5.76477 3.32829i −0.320761 0.185191i
324324 −1.38430 30.2697i −0.0769057 1.68165i
325325 −12.2215 + 1.00804i −0.677928 + 0.0559158i
326326 7.67410 13.2919i 0.425029 0.736172i
327327 −2.04443 14.2674i −0.113057 0.788990i
328328 −7.95140 −0.439043
329329 26.0604 45.1380i 1.43676 2.48854i
330330 −1.95287 13.6284i −0.107502 0.750220i
331331 17.0277i 0.935926i 0.883748 + 0.467963i 0.155012π0.155012\pi
−0.883748 + 0.467963i 0.844988π0.844988\pi
332332 −6.59914 + 3.81001i −0.362175 + 0.209102i
333333 25.4144 + 6.19104i 1.39270 + 0.339267i
334334 12.5030 + 21.6558i 0.684132 + 1.18495i
335335 −8.96652 15.5305i −0.489893 0.848520i
336336 −3.42233 + 2.68872i −0.186703 + 0.146682i
337337 6.54226 + 11.3315i 0.356379 + 0.617267i 0.987353 0.158537i 0.0506777π-0.0506777\pi
−0.630974 + 0.775804i 0.717344π0.717344\pi
338338 −4.93445 29.7093i −0.268398 1.61597i
339339 −2.26611 + 5.65269i −0.123078 + 0.307012i
340340 7.74990 4.47441i 0.420298 0.242659i
341341 5.23570 9.06850i 0.283529 0.491087i
342342 5.20899 21.3831i 0.281670 1.15627i
343343 14.3333i 0.773927i
344344 15.7882i 0.851242i
345345 0.779068 0.612067i 0.0419436 0.0329526i
346346 −9.78377 + 5.64866i −0.525978 + 0.303674i
347347 −7.49603 + 12.9835i −0.402408 + 0.696991i −0.994016 0.109235i 0.965160π-0.965160\pi
0.591608 + 0.806226i 0.298493π0.298493\pi
348348 −49.5525 + 7.10056i −2.65629 + 0.380630i
349349 1.80559 1.04246i 0.0966511 0.0558015i −0.450895 0.892577i 0.648895π-0.648895\pi
0.547546 + 0.836775i 0.315562π0.315562\pi
350350 −32.8980 −1.75847
351351 16.0891 + 9.59903i 0.858772 + 0.512359i
352352 13.4012 0.714287
353353 −3.58076 + 2.06735i −0.190584 + 0.110034i −0.592256 0.805750i 0.701763π-0.701763\pi
0.401672 + 0.915784i 0.368429π0.368429\pi
354354 25.1190 3.59939i 1.33506 0.191305i
355355 −4.74292 + 8.21498i −0.251728 + 0.436006i
356356 4.43718 2.56181i 0.235170 0.135776i
357357 11.9537 9.39130i 0.632656 0.497040i
358358 30.6559i 1.62022i
359359 20.5783i 1.08608i 0.839706 + 0.543042i 0.182727π0.182727\pi
−0.839706 + 0.543042i 0.817273π0.817273\pi
360360 8.68518 + 8.29706i 0.457749 + 0.437294i
361361 −4.48595 + 7.76990i −0.236103 + 0.408942i
362362 36.5597 21.1077i 1.92153 1.10940i
363363 −2.34386 + 5.84664i −0.123021 + 0.306869i
364364 −4.16634 50.5131i −0.218376 2.64760i
365365 5.03099 + 8.71392i 0.263334 + 0.456108i
366366 16.0806 12.6335i 0.840545 0.660366i
367367 7.33819 + 12.7101i 0.383050 + 0.663463i 0.991497 0.130132i 0.0415402π-0.0415402\pi
−0.608446 + 0.793595i 0.708207π0.708207\pi
368368 −0.136122 0.235770i −0.00709586 0.0122904i
369369 2.11557 + 7.23035i 0.110132 + 0.376397i
370370 −22.1192 + 12.7706i −1.14993 + 0.663910i
371371 4.78353i 0.248349i
372372 3.19199 + 22.2759i 0.165497 + 1.15495i
373373 14.8959 25.8004i 0.771279 1.33589i −0.165583 0.986196i 0.552951π-0.552951\pi
0.936862 0.349699i 0.113716π-0.113716\pi
374374 13.2141 0.683284
375375 2.60986 + 18.2133i 0.134772 + 0.940533i
376376 −19.7635 + 34.2315i −1.01923 + 1.76535i
377377 13.2197 27.9855i 0.680847 1.44133i
378378 40.8993 + 29.2121i 2.10363 + 1.50251i
379379 −11.5590 6.67356i −0.593743 0.342798i 0.172833 0.984951i 0.444708π-0.444708\pi
−0.766576 + 0.642153i 0.778041π0.778041\pi
380380 6.74066 + 11.6752i 0.345789 + 0.598924i
381381 10.1443 25.3045i 0.519711 1.29639i
382382 −30.8379 + 17.8043i −1.57781 + 0.910946i
383383 −2.55425 1.47470i −0.130516 0.0753536i 0.433320 0.901240i 0.357342π-0.357342\pi
−0.563837 + 0.825886i 0.690675π0.690675\pi
384384 −26.4443 + 20.7757i −1.34948 + 1.06021i
385385 12.4067 + 7.16300i 0.632303 + 0.365060i
386386 6.54872 + 11.3427i 0.333321 + 0.577329i
387387 −14.3565 + 4.20064i −0.729781 + 0.213530i
388388 6.95640 + 4.01628i 0.353158 + 0.203896i
389389 8.31532 14.4026i 0.421603 0.730238i −0.574493 0.818509i 0.694801π-0.694801\pi
0.996096 + 0.0882711i 0.0281342π0.0281342\pi
390390 −17.8339 + 4.07458i −0.903053 + 0.206324i
391391 0.475455 + 0.823512i 0.0240448 + 0.0416468i
392392 33.0349i 1.66852i
393393 −14.5973 18.5801i −0.736337 0.937244i
394394 −14.6090 −0.735990
395395 4.61500i 0.232206i
396396 7.69673 + 26.3051i 0.386775 + 1.32188i
397397 5.23157 3.02045i 0.262565 0.151592i −0.362939 0.931813i 0.618227π-0.618227\pi
0.625504 + 0.780221i 0.284893π0.284893\pi
398398 3.40946 + 1.96845i 0.170901 + 0.0986695i
399399 14.1479 + 18.0081i 0.708282 + 0.901534i
400400 2.04686 0.102343
401401 14.3432i 0.716266i −0.933671 0.358133i 0.883413π-0.883413\pi
0.933671 0.358133i 0.116587π-0.116587\pi
402402 35.1566 + 44.7489i 1.75345 + 2.23187i
403403 −12.5806 5.94278i −0.626686 0.296031i
404404 37.7015 1.87572
405405 5.23387 10.1051i 0.260073 0.502128i
406406 41.5157 71.9073i 2.06039 3.56870i
407407 −23.6599 −1.17278
408408 −9.06536 + 7.12211i −0.448802 + 0.352597i
409409 −5.33628 3.08090i −0.263862 0.152341i 0.362233 0.932088i 0.382014π-0.382014\pi
−0.626095 + 0.779747i 0.715348π0.715348\pi
410410 −6.37043 3.67797i −0.314613 0.181642i
411411 −2.81401 19.6381i −0.138805 0.968675i
412412 −9.81471 −0.483536
413413 −13.2024 + 22.8672i −0.649645 + 1.12522i
414414 −2.17174 + 2.27333i −0.106735 + 0.111728i
415415 −2.86181 −0.140481
416416 −1.46372 17.7463i −0.0717649 0.870083i
417417 −3.12348 + 7.79134i −0.152957 + 0.381544i
418418 19.9069i 0.973678i
419419 −13.8846 −0.678306 −0.339153 0.940731i 0.610140π-0.610140\pi
−0.339153 + 0.940731i 0.610140π0.610140\pi
420420 −30.4758 + 4.36699i −1.48707 + 0.213087i
421421 4.55207 + 2.62814i 0.221854 + 0.128088i 0.606808 0.794848i 0.292449π-0.292449\pi
−0.384954 + 0.922936i 0.625783π0.625783\pi
422422 −9.15643 + 5.28647i −0.445728 + 0.257341i
423423 36.3856 + 8.86365i 1.76913 + 0.430966i
424424 3.62770i 0.176177i
425425 −7.14937 −0.346796
426426 11.2009 27.9401i 0.542687 1.35370i
427427 21.2791i 1.02977i
428428 4.48141 + 7.76202i 0.216617 + 0.375191i
429429 −16.1943 4.99138i −0.781867 0.240986i
430430 7.30292 12.6490i 0.352178 0.609990i
431431 −29.8506 17.2343i −1.43785 0.830145i −0.440152 0.897923i 0.645076π-0.645076\pi
−0.997700 + 0.0677785i 0.978409π0.978409\pi
432432 −2.54469 1.81753i −0.122431 0.0874460i
433433 7.36538 + 12.7572i 0.353957 + 0.613072i 0.986939 0.161095i 0.0515024π-0.0515024\pi
−0.632982 + 0.774167i 0.718169π0.718169\pi
434434 −32.3253 18.6630i −1.55166 0.895854i
435435 −17.4502 6.99564i −0.836675 0.335415i
436436 −24.2632 14.0084i −1.16200 0.670879i
437437 −1.24061 + 0.716269i −0.0593466 + 0.0342638i
438438 −19.7259 25.1080i −0.942538 1.19971i
439439 1.27254 + 2.20410i 0.0607349 + 0.105196i 0.894794 0.446479i 0.147322π-0.147322\pi
−0.834059 + 0.551675i 0.813989π0.813989\pi
440440 −9.40890 5.43223i −0.448552 0.258971i
441441 −30.0393 + 8.78935i −1.43044 + 0.418540i
442442 −1.44328 17.4985i −0.0686500 0.832317i
443443 −15.7844 + 27.3394i −0.749941 + 1.29894i 0.197909 + 0.980220i 0.436585π0.436585\pi
−0.947850 + 0.318716i 0.896748π0.896748\pi
444444 39.9826 31.4120i 1.89749 1.49075i
445445 1.92425 0.0912181
446446 −25.8068 + 44.6987i −1.22199 + 2.11655i
447447 34.8915 + 13.9877i 1.65031 + 0.661595i
448448 52.7950i 2.49433i
449449 −22.0161 + 12.7110i −1.03900 + 0.599869i −0.919551 0.392971i 0.871447π-0.871447\pi
−0.119453 + 0.992840i 0.538114π0.538114\pi
450450 −6.63797 22.6865i −0.312917 1.06945i
451451 −3.40707 5.90122i −0.160433 0.277878i
452452 5.91897 + 10.2520i 0.278405 + 0.482211i
453453 −4.34675 1.74257i −0.204228 0.0818732i
454454 4.86713 + 8.43012i 0.228426 + 0.395645i
455455 8.13036 17.2117i 0.381157 0.806895i
456456 −10.7294 13.6569i −0.502451 0.639543i
457457 19.6897 11.3678i 0.921044 0.531765i 0.0370761 0.999312i 0.488196π-0.488196\pi
0.883968 + 0.467547i 0.154862π0.154862\pi
458458 −26.4809 + 45.8663i −1.23737 + 2.14319i
459459 8.88822 + 6.34837i 0.414866 + 0.296317i
460460 1.92584i 0.0897927i
461461 20.4265i 0.951359i −0.879619 0.475679i 0.842202π-0.842202\pi
0.879619 0.475679i 0.157798π-0.157798\pi
462462 −42.1966 16.9162i −1.96316 0.787014i
463463 −4.68063 + 2.70237i −0.217528 + 0.125590i −0.604805 0.796374i 0.706749π-0.706749\pi
0.387277 + 0.921963i 0.373416π0.373416\pi
464464 −2.58304 + 4.47396i −0.119915 + 0.207698i
465465 −3.14483 + 7.84460i −0.145838 + 0.363785i
466466 −34.6827 + 20.0241i −1.60665 + 0.927597i
467467 10.0719 0.466072 0.233036 0.972468i 0.425134π-0.425134\pi
0.233036 + 0.972468i 0.425134π0.425134\pi
468468 33.9933 13.0654i 1.57134 0.603947i
469469 −59.2154 −2.73431
470470 −31.6679 + 18.2835i −1.46073 + 0.843354i
471471 −16.7649 21.3391i −0.772484 0.983254i
472472 10.0123 17.3418i 0.460854 0.798223i
473473 11.7174 6.76504i 0.538766 0.311057i
474474 −2.07730 14.4968i −0.0954137 0.665861i
475475 10.7705i 0.494183i
476476 29.5493i 1.35439i
477477 −3.29874 + 0.965195i −0.151039 + 0.0441932i
478478 7.50818 13.0046i 0.343416 0.594814i
479479 19.3968 11.1988i 0.886264 0.511685i 0.0135454 0.999908i 0.495688π-0.495688\pi
0.872719 + 0.488223i 0.162355π0.162355\pi
480480 −10.7068 + 1.53421i −0.488696 + 0.0700270i
481481 2.58421 + 31.3312i 0.117830 + 1.42858i
482482 −0.213092 0.369085i −0.00970605 0.0168114i
483483 −0.464040 3.23839i −0.0211146 0.147352i
484484 6.12206 + 10.6037i 0.278275 + 0.481987i
485485 1.50837 + 2.61258i 0.0684917 + 0.118631i
486486 −11.8923 + 34.0985i −0.539448 + 1.54674i
487487 −1.75362 + 1.01245i −0.0794641 + 0.0458786i −0.539206 0.842174i 0.681275π-0.681275\pi
0.459741 + 0.888053i 0.347942π0.347942\pi
488488 16.1375i 0.730511i
489489 −9.02347 + 7.08920i −0.408055 + 0.320585i
490490 15.2805 26.4666i 0.690303 1.19564i
491491 3.05618 0.137924 0.0689618 0.997619i 0.478031π-0.478031\pi
0.0689618 + 0.997619i 0.478031π0.478031\pi
492492 13.5923 + 5.44903i 0.612788 + 0.245661i
493493 9.02218 15.6269i 0.406339 0.703799i
494494 26.3613 2.17429i 1.18605 0.0978261i
495495 −2.43627 + 10.0010i −0.109502 + 0.449511i
496496 2.01123 + 1.16118i 0.0903068 + 0.0521387i
497497 15.6613 + 27.1261i 0.702504 + 1.21677i
498498 8.98965 1.28816i 0.402836 0.0577238i
499499 −17.6833 + 10.2094i −0.791613 + 0.457038i −0.840530 0.541765i 0.817756π-0.817756\pi
0.0489173 + 0.998803i 0.484423π0.484423\pi
500500 30.9737 + 17.8827i 1.38518 + 0.799737i
501501 −2.65191 18.5068i −0.118479 0.826824i
502502 47.3490 + 27.3370i 2.11329 + 1.22011i
503503 1.22893 + 2.12856i 0.0547951 + 0.0949080i 0.892122 0.451795i 0.149216π-0.149216\pi
−0.837327 + 0.546703i 0.815883π0.815883\pi
504504 38.0660 11.1379i 1.69559 0.496122i
505505 12.2623 + 7.07967i 0.545667 + 0.315041i
506506 1.42187 2.46276i 0.0632100 0.109483i
507507 −4.84094 + 21.9901i −0.214994 + 0.976615i
508508 −26.4966 45.8934i −1.17559 2.03619i
509509 39.4938i 1.75053i 0.483643 + 0.875265i 0.339313π0.339313\pi
−0.483643 + 0.875265i 0.660687π0.660687\pi
510510 −10.5573 + 1.51279i −0.467484 + 0.0669875i
511511 33.2249 1.46978
512512 6.78333i 0.299784i
513513 −9.56377 + 13.3900i −0.422251 + 0.591184i
514514 11.7363 6.77597i 0.517667 0.298875i
515515 −3.19222 1.84303i −0.140666 0.0812136i
516516 −10.8195 + 26.9887i −0.476302 + 1.18811i
517517 −33.8737 −1.48976
518518 84.3375i 3.70558i
519519 8.36111 1.19809i 0.367012 0.0525905i
520520 −6.16585 + 13.0529i −0.270391 + 0.572406i
521521 33.5976 1.47194 0.735970 0.677015i 0.236727π-0.236727\pi
0.735970 + 0.677015i 0.236727π0.236727\pi
522522 57.9643 + 14.1203i 2.53703 + 0.618028i
523523 3.09661 5.36349i 0.135405 0.234529i −0.790347 0.612660i 0.790100π-0.790100\pi
0.925752 + 0.378131i 0.123433π0.123433\pi
524524 −45.9297 −2.00645
525525 22.8301 + 9.15239i 0.996389 + 0.399443i
526526 −19.4571 11.2335i −0.848369 0.489806i
527527 −7.02493 4.05584i −0.306011 0.176675i
528528 2.62540 + 1.05250i 0.114256 + 0.0458042i
529529 −22.7954 −0.991103
530530 1.67802 2.90641i 0.0728884 0.126246i
531531 −18.4332 4.49037i −0.799931 0.194866i
532532 44.5157 1.93000
533533 −7.44245 + 5.15630i −0.322368 + 0.223344i
534534 −6.04453 + 0.866143i −0.261572 + 0.0374817i
535535 3.36612i 0.145530i
536536 44.9074 1.93970
537537 8.52864 21.2742i 0.368038 0.918051i
538538 42.0192 + 24.2598i 1.81157 + 1.04591i
539539 24.5173 14.1551i 1.05603 0.609701i
540540 −9.16073 20.1351i −0.394215 0.866475i
541541 13.3436i 0.573685i −0.957978 0.286843i 0.907394π-0.907394\pi
0.957978 0.286843i 0.0926057π-0.0926057\pi
542542 −13.3371 −0.572879
543543 −31.2435 + 4.47700i −1.34079 + 0.192127i
544544 10.3813i 0.445093i
545545 −5.26105 9.11240i −0.225358 0.390332i
546546 −17.7921 + 57.7256i −0.761433 + 2.47043i
547547 −2.28845 + 3.96371i −0.0978471 + 0.169476i −0.910793 0.412863i 0.864529π-0.864529\pi
0.812946 + 0.582339i 0.197862π0.197862\pi
548548 −33.3966 19.2815i −1.42663 0.823665i
549549 −14.6741 + 4.29358i −0.626277 + 0.183246i
550550 10.6903 + 18.5161i 0.455836 + 0.789531i
551551 23.5418 + 13.5918i 1.00291 + 0.579032i
552552 0.351916 + 2.45591i 0.0149785 + 0.104530i
553553 13.1972 + 7.61943i 0.561204 + 0.324011i
554554 32.0997 18.5328i 1.36379 0.787382i
555555 18.9029 2.70867i 0.802384 0.114976i
556556 8.15837 + 14.1307i 0.345992 + 0.599276i
557557 −31.3528 18.1016i −1.32846 0.766988i −0.343400 0.939189i 0.611579π-0.611579\pi
−0.985062 + 0.172201i 0.944912π0.944912\pi
558558 6.34765 26.0573i 0.268718 1.10310i
559559 −10.2383 14.7776i −0.433033 0.625026i
560560 −1.58862 + 2.75158i −0.0671316 + 0.116275i
561561 −9.17015 3.67623i −0.387164 0.155211i
562562 43.4577 1.83315
563563 −20.3321 + 35.2161i −0.856894 + 1.48418i 0.0179832 + 0.999838i 0.494275π0.494275\pi
−0.874877 + 0.484345i 0.839058π0.839058\pi
564564 57.2428 44.9722i 2.41035 1.89367i
565565 4.44591i 0.187041i
566566 9.07498 5.23944i 0.381450 0.220230i
567567 −20.2558 31.6507i −0.850665 1.32920i
568568 −11.8771 20.5717i −0.498352 0.863171i
569569 8.50764 + 14.7357i 0.356659 + 0.617751i 0.987400 0.158242i 0.0505825π-0.0505825\pi
−0.630742 + 0.775993i 0.717249π0.717249\pi
570570 −2.27901 15.9045i −0.0954571 0.666164i
571571 −11.0113 19.0721i −0.460809 0.798144i 0.538193 0.842822i 0.319107π-0.319107\pi
−0.999001 + 0.0446778i 0.985774π0.985774\pi
572572 −27.0767 + 18.7594i −1.13213 + 0.784368i
573573 26.3538 3.77633i 1.10095 0.157759i
574574 −21.0353 + 12.1448i −0.877998 + 0.506912i
575575 −0.769294 + 1.33246i −0.0320818 + 0.0555673i
576576 36.4076 10.6527i 1.51698 0.443862i
577577 8.16526i 0.339924i −0.985451 0.169962i 0.945635π-0.945635\pi
0.985451 0.169962i 0.0543645π-0.0543645\pi
578578 29.1466i 1.21234i
579579 −1.38900 9.69338i −0.0577249 0.402843i
580580 −31.6485 + 18.2723i −1.31413 + 0.758715i
581581 −4.72490 + 8.18376i −0.196022 + 0.339520i
582582 −5.91414 7.52779i −0.245149 0.312037i
583583 2.69234 1.55443i 0.111505 0.0643777i
584584 −25.1969 −1.04266
585585 13.5097 + 2.13385i 0.558558 + 0.0882237i
586586 −0.733734 −0.0303103
587587 9.24313 5.33652i 0.381505 0.220262i −0.296968 0.954887i 0.595975π-0.595975\pi
0.678473 + 0.734626i 0.262642π0.262642\pi
588588 −22.6386 + 56.4707i −0.933598 + 2.32881i
589589 6.11010 10.5830i 0.251762 0.436065i
590590 16.0431 9.26251i 0.660486 0.381332i
591591 10.1382 + 4.06430i 0.417029 + 0.167183i
592592 5.24734i 0.215664i
593593 9.84678i 0.404359i 0.979348 + 0.202179i 0.0648024π0.0648024\pi
−0.979348 + 0.202179i 0.935198π0.935198\pi
594594 3.15128 32.5122i 0.129299 1.33399i
595595 5.54883 9.61085i 0.227480 0.394007i
596596 63.2808 36.5352i 2.59208 1.49654i
597597 −1.81842 2.31457i −0.0744230 0.0947291i
598598 −3.41656 1.61390i −0.139713 0.0659972i
599599 6.98478 + 12.0980i 0.285391 + 0.494311i 0.972704 0.232050i 0.0745434π-0.0745434\pi
−0.687313 + 0.726361i 0.741210π0.741210\pi
600600 −17.3138 6.94093i −0.706832 0.283362i
601601 20.3592 + 35.2632i 0.830471 + 1.43842i 0.897665 + 0.440678i 0.145262π0.145262\pi
−0.0671948 + 0.997740i 0.521405π0.521405\pi
602602 −24.1144 41.7674i −0.982831 1.70231i
603603 −11.9482 40.8351i −0.486566 1.66293i
604604 −7.88345 + 4.55151i −0.320773 + 0.185198i
605605 4.59846i 0.186954i
606606 −41.7057 16.7194i −1.69418 0.679180i
607607 22.1684 38.3969i 0.899789 1.55848i 0.0720264 0.997403i 0.477053π-0.477053\pi
0.827763 0.561078i 0.189613π-0.189613\pi
608608 15.6393 0.634257
609609 −48.8156 + 38.3515i −1.97811 + 1.55408i
610610 7.46450 12.9289i 0.302229 0.523476i
611611 3.69979 + 44.8566i 0.149678 + 1.81470i
612612 20.3773 5.96229i 0.823702 0.241011i
613613 7.43045 + 4.28997i 0.300113 + 0.173270i 0.642494 0.766291i 0.277900π-0.277900\pi
−0.342381 + 0.939561i 0.611233π0.611233\pi
614614 −13.0716 22.6406i −0.527526 0.913702i
615615 3.39764 + 4.32468i 0.137006 + 0.174388i
616616 −31.0685 + 17.9374i −1.25178 + 0.722718i
617617 −37.3259 21.5501i −1.50268 0.867575i −0.999995 0.00310830i 0.999011π-0.999011\pi
−0.502689 0.864467i 0.667656π-0.667656\pi
618618 10.8571 + 4.35252i 0.436738 + 0.175084i
619619 −40.7267 23.5136i −1.63694 0.945090i −0.981877 0.189520i 0.939307π-0.939307\pi
−0.655067 0.755570i 0.727360π-0.727360\pi
620620 8.21414 + 14.2273i 0.329888 + 0.571382i
621621 2.13957 0.973427i 0.0858580 0.0390623i
622622 −63.8274 36.8508i −2.55925 1.47758i
623623 3.17696 5.50266i 0.127282 0.220459i
624624 1.10700 3.59160i 0.0443154 0.143779i
625625 −1.78678 3.09479i −0.0714711 0.123792i
626626 0.343235i 0.0137184i
627627 5.53821 13.8148i 0.221175 0.551708i
628628 −52.7498 −2.10495
629629 18.3282i 0.730793i
630630 35.6492 + 8.68427i 1.42030 + 0.345990i
631631 24.6130 14.2103i 0.979828 0.565704i 0.0776098 0.996984i 0.475271π-0.475271\pi
0.902218 + 0.431280i 0.141938π0.141938\pi
632632 −10.0084 5.77837i −0.398114 0.229851i
633633 7.82500 1.12127i 0.311016 0.0445666i
634634 45.7321 1.81625
635635 19.9023i 0.789800i
636636 −2.48603 + 6.20128i −0.0985777 + 0.245897i
637637 −21.4224 30.9204i −0.848786 1.22511i
638638 −53.9627 −2.13640
639639 −15.5462 + 16.2734i −0.614998 + 0.643766i
640640 −12.2753 + 21.2614i −0.485223 + 0.840431i
641641 16.7063 0.659860 0.329930 0.944005i 0.392975π-0.392975\pi
0.329930 + 0.944005i 0.392975π0.392975\pi
642642 −1.51516 10.5738i −0.0597984 0.417314i
643643 17.2202 + 9.94208i 0.679098 + 0.392077i 0.799515 0.600646i 0.205090π-0.205090\pi
−0.120417 + 0.992723i 0.538423π0.538423\pi
644644 −5.50721 3.17959i −0.217014 0.125293i
645645 −8.58702 + 6.74631i −0.338114 + 0.265636i
646646 15.4209 0.606728
647647 4.08938 7.08301i 0.160770 0.278462i −0.774375 0.632727i 0.781936π-0.781936\pi
0.935145 + 0.354265i 0.115269π0.115269\pi
648648 15.3615 + 24.0031i 0.603456 + 0.942929i
649649 17.1606 0.673613
650650 23.3520 16.1788i 0.915941 0.634585i
651651 17.2406 + 21.9446i 0.675712 + 0.860078i
652652 22.3058i 0.873563i
653653 −21.7572 −0.851426 −0.425713 0.904858i 0.639977π-0.639977\pi
−0.425713 + 0.904858i 0.639977π0.639977\pi
654654 20.6279 + 26.2562i 0.806615 + 1.02670i
655655 −14.9386 8.62479i −0.583698 0.336998i
656656 1.30878 0.755627i 0.0510994 0.0295023i
657657 6.70394 + 22.9120i 0.261546 + 0.893882i
658658 120.745i 4.70714i
659659 37.4141 1.45745 0.728723 0.684809i 0.240114π-0.240114\pi
0.728723 + 0.684809i 0.240114π0.240114\pi
660660 12.3611 + 15.7338i 0.481156 + 0.612438i
661661 8.41108i 0.327153i −0.986531 0.163576i 0.947697π-0.947697\pi
0.986531 0.163576i 0.0523030π-0.0523030\pi
662662 −19.7235 34.1621i −0.766575 1.32775i
663663 −3.86658 + 12.5449i −0.150166 + 0.487204i
664664 3.58324 6.20635i 0.139057 0.240853i
665665 14.4787 + 8.35927i 0.561459 + 0.324158i
666666 −58.1594 + 17.0172i −2.25363 + 0.659401i
667667 −1.94163 3.36300i −0.0751801 0.130216i
668668 −31.4728 18.1708i −1.21772 0.703050i
669669 30.3445 23.8399i 1.17319 0.921704i
670670 35.9785 + 20.7722i 1.38997 + 0.802499i
671671 11.9766 6.91472i 0.462353 0.266940i
672672 −13.2898 + 33.1506i −0.512664 + 1.27881i
673673 −16.4682 28.5238i −0.634803 1.09951i −0.986557 0.163418i 0.947748π-0.947748\pi
0.351754 0.936092i 0.385585π-0.385585\pi
674674 −26.2510 15.1560i −1.01115 0.583789i
675675 −1.70498 + 17.5905i −0.0656245 + 0.677057i
676676 27.7991 + 33.8068i 1.06920 + 1.30026i
677677 −0.651673 + 1.12873i −0.0250458 + 0.0433806i −0.878277 0.478153i 0.841306π-0.841306\pi
0.853231 + 0.521533i 0.174640π0.174640\pi
678678 −2.00119 13.9657i −0.0768554 0.536349i
679679 9.96138 0.382283
680680 −4.20809 + 7.28862i −0.161373 + 0.279506i
681681 −1.03233 7.20430i −0.0395590 0.276070i
682682 24.2585i 0.928904i
683683 −0.152548 + 0.0880738i −0.00583710 + 0.00337005i −0.502916 0.864335i 0.667739π-0.667739\pi
0.497079 + 0.867706i 0.334406π0.334406\pi
684684 8.98214 + 30.6982i 0.343441 + 1.17377i
685685 −7.24145 12.5426i −0.276682 0.479227i
686686 −16.6026 28.7565i −0.633889 1.09793i
687687 31.1372 24.4626i 1.18796 0.933307i
688688 1.50036 + 2.59870i 0.0572008 + 0.0990746i
689689 −2.35248 3.39550i −0.0896224 0.129358i
690690 −0.854050 + 2.13038i −0.0325131 + 0.0811022i
691691 2.44577 1.41206i 0.0930414 0.0537175i −0.452757 0.891634i 0.649560π-0.649560\pi
0.545799 + 0.837916i 0.316226π0.316226\pi
692692 8.20930 14.2189i 0.312071 0.540523i
693693 24.5769 + 23.4787i 0.933600 + 0.891880i
694694 34.7312i 1.31838i
695695 6.12799i 0.232448i
696696 37.0205 29.0848i 1.40326 1.10246i
697697 −4.57139 + 2.63929i −0.173154 + 0.0999704i
698698 −2.41500 + 4.18290i −0.0914091 + 0.158325i
699699 29.6395 4.24716i 1.12107 0.160642i
700700 41.4057 23.9056i 1.56499 0.903547i
701701 30.2245 1.14156 0.570782 0.821102i 0.306640π-0.306640\pi
0.570782 + 0.821102i 0.306640π0.306640\pi
702702 −43.3978 0.621939i −1.63794 0.0234736i
703703 −27.6113 −1.04138
704704 −29.7149 + 17.1559i −1.11992 + 0.646589i
705705 27.0631 3.87797i 1.01926 0.146053i
706706 4.78931 8.29532i 0.180248 0.312199i
707707 40.4906 23.3773i 1.52281 0.879193i
708708 −28.9995 + 22.7832i −1.08987 + 0.856244i
709709 10.2338i 0.384340i 0.981362 + 0.192170i 0.0615525π0.0615525\pi
−0.981362 + 0.192170i 0.938447π0.938447\pi
710710 21.9753i 0.824718i
711711 −2.59151 + 10.6383i −0.0971894 + 0.398966i
712712 −2.40932 + 4.17307i −0.0902932 + 0.156392i
713713 −1.51181 + 0.872842i −0.0566176 + 0.0326882i
714714 −13.1042 + 32.6877i −0.490412 + 1.22330i
715715 −12.3293 + 1.01693i −0.461091 + 0.0380310i
716716 −22.2764 38.5839i −0.832508 1.44195i
717717 −8.82838 + 6.93593i −0.329702 + 0.259027i
718718 −23.8363 41.2857i −0.889562 1.54077i
719719 −15.5196 26.8808i −0.578785 1.00248i −0.995619 0.0935023i 0.970194π-0.970194\pi
0.416834 0.908983i 0.363140π-0.363140\pi
720720 −2.21804 0.540321i −0.0826614 0.0201366i
721721 −10.5408 + 6.08574i −0.392560 + 0.226645i
722722 20.7847i 0.773525i
723723 0.0451972 + 0.315417i 0.00168090 + 0.0117305i
724724 −30.6763 + 53.1328i −1.14007 + 1.97467i
725725 29.1961 1.08432
726726 −2.06986 14.4449i −0.0768197 0.536099i
727727 −12.3666 + 21.4195i −0.458650 + 0.794406i −0.998890 0.0471055i 0.985000π-0.985000\pi
0.540240 + 0.841511i 0.318334π0.318334\pi
728728 27.1466 + 39.1826i 1.00612 + 1.45220i
729729 17.7393 20.3548i 0.657011 0.753881i
730730 −20.1870 11.6550i −0.747155 0.431370i
731731 −5.24055 9.07689i −0.193829 0.335721i
732732 −11.0589 + 27.5858i −0.408749 + 1.01960i
733733 32.6554 18.8536i 1.20616 0.696375i 0.244239 0.969715i 0.421462π-0.421462\pi
0.961917 + 0.273341i 0.0881286π0.0881286\pi
734734 −29.4448 16.9999i −1.08683 0.627479i
735735 −17.9674 + 14.1159i −0.662736 + 0.520672i
736736 −1.93480 1.11706i −0.0713176 0.0411752i
737737 19.2422 + 33.3285i 0.708797 + 1.22767i
738738 −12.6194 12.0555i −0.464528 0.443770i
739739 23.9351 + 13.8189i 0.880468 + 0.508338i 0.870813 0.491615i 0.163593π-0.163593\pi
0.00965499 + 0.999953i 0.496927π0.496927\pi
740740 18.5597 32.1463i 0.682268 1.18172i
741741 −18.8988 5.82497i −0.694266 0.213986i
742742 −5.54086 9.59705i −0.203411 0.352319i
743743 9.72719i 0.356856i −0.983953 0.178428i 0.942899π-0.942899\pi
0.983953 0.178428i 0.0571011π-0.0571011\pi
744744 −13.0748 16.6422i −0.479346 0.610134i
745745 27.4427 1.00542
746746 69.0167i 2.52688i
747747 −6.59691 1.60703i −0.241368 0.0587981i
748748 −16.6314 + 9.60213i −0.608104 + 0.351089i
749749 9.62588 + 5.55751i 0.351722 + 0.203067i
750750 −26.3329 33.5178i −0.961543 1.22390i
751751 −27.2580 −0.994658 −0.497329 0.867562i 0.665686π-0.665686\pi
−0.497329 + 0.867562i 0.665686π0.665686\pi
752752 7.51257i 0.273955i
753753 −25.2534 32.1438i −0.920287 1.17138i
754754 5.89397 + 71.4590i 0.214646 + 2.60238i
755755 −3.41878 −0.124422
756756 −72.7035 7.04688i −2.64420 0.256292i
757757 −16.3688 + 28.3517i −0.594936 + 1.03046i 0.398620 + 0.917116i 0.369489π0.369489\pi
−0.993556 + 0.113343i 0.963844π0.963844\pi
758758 30.9205 1.12308
759759 −1.67189 + 1.31350i −0.0606857 + 0.0476772i
760760 −10.9802 6.33945i −0.398295 0.229956i
761761 40.3005 + 23.2675i 1.46089 + 0.843447i 0.999053 0.0435166i 0.0138562π-0.0138562\pi
0.461840 + 0.886963i 0.347189π0.347189\pi
762762 8.95844 + 62.5181i 0.324530 + 2.26479i
763763 −34.7443 −1.25783
764764 25.8753 44.8173i 0.936136 1.62143i
765765 7.74728 + 1.88726i 0.280104 + 0.0682342i
766766 6.83269 0.246875
767767 −1.87433 22.7246i −0.0676783 0.820537i
768768 12.6904 31.6555i 0.457924 1.14227i
769769 16.5704i 0.597544i 0.954325 + 0.298772i 0.0965770π0.0965770\pi
−0.954325 + 0.298772i 0.903423π0.903423\pi
770770 −33.1882 −1.19602
771771 −10.0298 + 1.43720i −0.361213 + 0.0517595i
772772 −16.4846 9.51738i −0.593293 0.342538i
773773 2.28752 1.32070i 0.0822764 0.0475023i −0.458297 0.888799i 0.651541π-0.651541\pi
0.540574 + 0.841297i 0.318207π0.318207\pi
774774 23.9373 25.0570i 0.860407 0.900655i
775775 13.1249i 0.471459i
776776 −7.55445 −0.271189
777777 23.4632 58.5276i 0.841736 2.09966i
778778 38.5272i 1.38127i
779779 −3.97608 6.88677i −0.142458 0.246744i
780780 19.4851 18.0875i 0.697677 0.647635i
781781 10.1784 17.6294i 0.364211 0.630831i
782782 −1.90778 1.10146i −0.0682220 0.0393880i
783783 −36.2971 25.9250i −1.29715 0.926485i
784784 3.13933 + 5.43748i 0.112119 + 0.194196i
785785 −17.1568 9.90548i −0.612352 0.353542i
786786 50.8079 + 20.3684i 1.81226 + 0.726517i
787787 6.17903 + 3.56746i 0.220259 + 0.127166i 0.606070 0.795411i 0.292745π-0.292745\pi
−0.385811 + 0.922578i 0.626078π0.626078\pi
788788 18.3870 10.6158i 0.655011 0.378171i
789789 10.3774 + 13.2088i 0.369444 + 0.470246i
790790 −5.34564 9.25892i −0.190189 0.329418i
791791 12.7137 + 7.34026i 0.452047 + 0.260990i
792792 −18.6385 17.8056i −0.662290 0.632694i
793793 −10.4648 15.1046i −0.371616 0.536379i
794794 −6.99729 + 12.1197i −0.248324 + 0.430111i
795795 −1.97307 + 1.55012i −0.0699776 + 0.0549772i
796796 −5.72157 −0.202796
797797 14.4085 24.9563i 0.510376 0.883998i −0.489551 0.871974i 0.662839π-0.662839\pi
0.999928 0.0120233i 0.00382723π-0.00382723\pi
798798 −49.2437 19.7413i −1.74321 0.698836i
799799 26.2403i 0.928316i
800800 14.5467 8.39854i 0.514303 0.296933i
801801 4.43568 + 1.08055i 0.156727 + 0.0381792i
802802 16.6140 + 28.7763i 0.586662 + 1.01613i
803803 −10.7966 18.7002i −0.381002 0.659915i
804804 −76.7657 30.7746i −2.70732 1.08534i
805805 −1.19414 2.06831i −0.0420880 0.0728985i
806806 32.1238 2.64958i 1.13151 0.0933276i
807807 −22.4108 28.5255i −0.788897 1.00414i
808808 −30.7070 + 17.7287i −1.08027 + 0.623694i
809809 −3.89514 + 6.74657i −0.136946 + 0.237197i −0.926339 0.376691i 0.877062π-0.877062\pi
0.789393 + 0.613888i 0.210395π0.210395\pi
810810 1.20441 + 26.3361i 0.0423186 + 0.925356i
811811 43.2768i 1.51965i 0.650125 + 0.759827i 0.274717π0.274717\pi
−0.650125 + 0.759827i 0.725283π0.725283\pi
812812 120.671i 4.23473i
813813 9.25555 + 3.71046i 0.324606 + 0.130132i
814814 47.4682 27.4058i 1.66376 0.960571i
815815 −4.18864 + 7.25494i −0.146722 + 0.254129i
816816 0.815321 2.03377i 0.0285419 0.0711963i
817817 13.6743 7.89484i 0.478402 0.276205i
818818 14.2747 0.499103
819819 28.4068 35.1099i 0.992613 1.22684i
820820 10.6905 0.373329
821821 −39.6462 + 22.8898i −1.38366 + 0.798858i −0.992591 0.121503i 0.961229π-0.961229\pi
−0.391071 + 0.920360i 0.627895π0.627895\pi
822822 28.3928 + 36.1397i 0.990313 + 1.26052i
823823 −9.61698 + 16.6571i −0.335227 + 0.580630i −0.983528 0.180754i 0.942146π-0.942146\pi
0.648302 + 0.761384i 0.275480π0.275480\pi
824824 7.99387 4.61526i 0.278480 0.160780i
825825 −2.26744 15.8237i −0.0789421 0.550911i
826826 61.1702i 2.12838i
827827 34.1215i 1.18652i 0.805010 + 0.593261i 0.202160π0.202160\pi
−0.805010 + 0.593261i 0.797840π0.797840\pi
828828 1.08144 4.43935i 0.0375826 0.154278i
829829 21.0159 36.4006i 0.729913 1.26425i −0.227007 0.973893i 0.572894π-0.572894\pi
0.956920 0.290353i 0.0937727π-0.0937727\pi
830830 5.74156 3.31489i 0.199293 0.115062i
831831 −27.4321 + 3.93085i −0.951610 + 0.136360i
832832 25.9640 + 37.4756i 0.900138 + 1.29923i
833833 −10.9652 18.9923i −0.379923 0.658046i
834834 −2.75833 19.2495i −0.0955132 0.666556i
835835 −6.82432 11.8201i −0.236165 0.409050i
836836 −14.4655 25.0550i −0.500301 0.866547i
837837 −11.6544 + 16.3170i −0.402834 + 0.563999i
838838 27.8562 16.0828i 0.962276 0.555570i
839839 24.0777i 0.831254i 0.909535 + 0.415627i 0.136438π0.136438\pi
−0.909535 + 0.415627i 0.863562π0.863562\pi
840840 22.7684 17.8877i 0.785583 0.617186i
841841 −22.3442 + 38.7012i −0.770488 + 1.33452i
842842 −12.1769 −0.419643
843843 −30.1583 12.0902i −1.03871 0.416408i
844844 7.68292 13.3072i 0.264457 0.458053i
845845 2.69330 + 16.2158i 0.0926522 + 0.557840i
846846 −83.2662 + 24.3633i −2.86275 + 0.837627i
847847 13.1499 + 7.59212i 0.451837 + 0.260868i
848848 0.344743 + 0.597113i 0.0118385 + 0.0205049i
849849 −7.75539 + 1.11130i −0.266164 + 0.0381397i
850850 14.3436 8.28126i 0.491980 0.284045i
851851 3.41590 + 1.97217i 0.117095 + 0.0676051i
852852 6.20534 + 43.3050i 0.212591 + 1.48361i
853853 27.8602 + 16.0851i 0.953914 + 0.550742i 0.894295 0.447479i 0.147678π-0.147678\pi
0.0596193 + 0.998221i 0.481011π0.481011\pi
854854 −24.6480 42.6916i −0.843437 1.46088i
855855 −2.84315 + 11.6712i −0.0972336 + 0.399147i
856856 −7.30001 4.21466i −0.249509 0.144054i
857857 7.08968 12.2797i 0.242179 0.419466i −0.719156 0.694849i 0.755471π-0.755471\pi
0.961335 + 0.275383i 0.0888046π0.0888046\pi
858858 38.2717 8.74410i 1.30657 0.298519i
859859 4.77386 + 8.26856i 0.162882 + 0.282120i 0.935901 0.352263i 0.114588π-0.114588\pi
−0.773019 + 0.634383i 0.781254π0.781254\pi
860860 21.2269i 0.723833i
861861 17.9766 2.57593i 0.612641 0.0877875i
862862 79.8511 2.71974
863863 27.1037i 0.922622i −0.887238 0.461311i 0.847379π-0.847379\pi
0.887238 0.461311i 0.152621π-0.152621\pi
864864 −25.5423 2.47571i −0.868966 0.0842255i
865865 5.34013 3.08313i 0.181570 0.104829i
866866 −29.5538 17.0629i −1.00428 0.579822i
867867 8.10873 20.2268i 0.275387 0.686938i
868868 54.2467 1.84125
869869 9.90384i 0.335965i
870870 43.1130 6.17783i 1.46167 0.209448i
871871 42.0330 29.1214i 1.42423 0.986741i
872872 26.3491 0.892294
873873 2.00995 + 6.86940i 0.0680266 + 0.232494i
874874 1.65934 2.87405i 0.0561279 0.0972163i
875875 44.3535 1.49942
876876 43.0721 + 17.2672i 1.45527 + 0.583405i
877877 −34.3355 19.8236i −1.15943 0.669395i −0.208260 0.978074i 0.566780π-0.566780\pi
−0.951166 + 0.308678i 0.900113π0.900113\pi
878878 −5.10610 2.94801i −0.172322 0.0994904i
879879 0.509188 + 0.204129i 0.0171745 + 0.00688509i
880880 2.06491 0.0696083
881881 −4.91250 + 8.50870i −0.165506 + 0.286665i −0.936835 0.349772i 0.886259π-0.886259\pi
0.771329 + 0.636437i 0.219592π0.219592\pi
882882 50.0860 52.4288i 1.68648 1.76537i
883883 −31.5744 −1.06256 −0.531282 0.847195i 0.678290π-0.678290\pi
−0.531282 + 0.847195i 0.678290π0.678290\pi
884884 14.5320 + 20.9750i 0.488763 + 0.705466i
885885 −13.7103 + 1.96460i −0.460867 + 0.0660394i
886886 73.1337i 2.45697i
887887 15.1391 0.508322 0.254161 0.967162i 0.418201π-0.418201\pi
0.254161 + 0.967162i 0.418201π0.418201\pi
888888 −17.7938 + 44.3858i −0.597122 + 1.48949i
889889 −56.9135 32.8591i −1.90882 1.10206i
890890 −3.86056 + 2.22889i −0.129406 + 0.0747127i
891891 −11.2319 + 21.6857i −0.376284 + 0.726499i
892892 75.0111i 2.51156i
893893 −39.5308 −1.32285
894894 −86.2040 + 12.3525i −2.88309 + 0.413129i
895895 16.7325i 0.559305i
896896 40.5333 + 70.2058i 1.35412 + 2.34541i
897897 1.92199 + 2.07050i 0.0641734 + 0.0691320i
898898 29.4468 51.0033i 0.982652 1.70200i
899899 28.6879 + 16.5630i 0.956795 + 0.552406i
900900 24.8400 + 23.7300i 0.828000 + 0.790999i
901901 −1.20414 2.08563i −0.0401156 0.0694823i
902902 13.6710 + 7.89296i 0.455195 + 0.262807i
903903 5.11473 + 35.6941i 0.170208 + 1.18782i
904904 −9.64174 5.56666i −0.320679 0.185144i
905905 −19.9548 + 11.5209i −0.663321 + 0.382968i
906906 10.7392 1.53886i 0.356786 0.0511252i
907907 27.7852 + 48.1254i 0.922593 + 1.59798i 0.795388 + 0.606101i 0.207267π0.207267\pi
0.127205 + 0.991876i 0.459399π0.459399\pi
908908 −12.2517 7.07350i −0.406586 0.234742i
909909 24.2910 + 23.2055i 0.805682 + 0.769678i
910910 3.62492 + 43.9488i 0.120165 + 1.45689i
911911 −17.3371 + 30.0288i −0.574405 + 0.994899i 0.421701 + 0.906735i 0.361433π0.361433\pi
−0.996106 + 0.0881637i 0.971900π0.971900\pi
912912 3.06386 + 1.22827i 0.101455 + 0.0406722i
913913 6.14148 0.203253
914914 −26.3352 + 45.6139i −0.871090 + 1.50877i
915915 −8.77702 + 6.89558i −0.290159 + 0.227961i
916916 76.9704i 2.54317i
917917 −49.3276 + 28.4793i −1.62894 + 0.940469i
918918 −25.1856 2.44114i −0.831248 0.0805697i
919919 6.58230 + 11.4009i 0.217130 + 0.376080i 0.953929 0.300031i 0.0969971π-0.0969971\pi
−0.736799 + 0.676111i 0.763664π0.763664\pi
920920 0.905605 + 1.56855i 0.0298569 + 0.0517137i
921921 2.77251 + 19.3485i 0.0913574 + 0.637554i
922922 23.6604 + 40.9811i 0.779215 + 1.34964i
923923 −24.4572 11.5530i −0.805017 0.380270i
924924 65.4014 9.37161i 2.15155 0.308303i
925925 −25.6823 + 14.8277i −0.844428 + 0.487531i
926926 6.26040 10.8433i 0.205730 0.356334i
927927 −6.32361 6.04102i −0.207695 0.198413i
928928 42.3943i 1.39166i
929929 18.2960i 0.600271i 0.953897 + 0.300135i 0.0970319π0.0970319\pi
−0.953897 + 0.300135i 0.902968π0.902968\pi
930930 −2.77719 19.3811i −0.0910676 0.635531i
931931 28.6118 16.5190i 0.937714 0.541389i
932932 29.1014 50.4051i 0.953247 1.65107i
933933 34.0421 + 43.3304i 1.11449 + 1.41857i
934934 −20.2069 + 11.6665i −0.661191 + 0.381739i
935935 −7.21244 −0.235872
936936 −21.5429 + 26.6264i −0.704153 + 0.870312i
937937 50.7326 1.65736 0.828681 0.559722i 0.189092π-0.189092\pi
0.828681 + 0.559722i 0.189092π0.189092\pi
938938 118.802 68.5903i 3.87902 2.23955i
939939 −0.0954899 + 0.238194i −0.00311619 + 0.00777318i
940940 26.5717 46.0236i 0.866675 1.50112i
941941 −24.2843 + 14.0206i −0.791646 + 0.457057i −0.840542 0.541747i 0.817763π-0.817763\pi
0.0488955 + 0.998804i 0.484430π0.484430\pi
942942 58.3523 + 23.3929i 1.90122 + 0.762182i
943943 1.13598i 0.0369927i
944944 3.80591i 0.123872i
945945 −22.3234 15.9444i −0.726182 0.518672i
946946 −15.6721 + 27.1450i −0.509545 + 0.882558i
947947 −38.3313 + 22.1306i −1.24560 + 0.719148i −0.970229 0.242189i 0.922134π-0.922134\pi
−0.275372 + 0.961338i 0.588801π0.588801\pi
948948 13.1488 + 16.7364i 0.427052 + 0.543572i
949949 −23.5841 + 16.3396i −0.765572 + 0.530406i
950950 12.4756 + 21.6085i 0.404764 + 0.701071i
951951 −31.7367 12.7229i −1.02913 0.412569i
952952 13.8952 + 24.0672i 0.450347 + 0.780023i
953953 5.98910 + 10.3734i 0.194006 + 0.336028i 0.946574 0.322486i 0.104519π-0.104519\pi
−0.752568 + 0.658514i 0.771185π0.771185\pi
954954 5.50015 5.75743i 0.178074 0.186404i
955955 16.8318 9.71785i 0.544665 0.314462i
956956 21.8236i 0.705824i
957957 37.4484 + 15.0127i 1.21054 + 0.485292i
958958 −25.9435 + 44.9355i −0.838196 + 1.45180i
959959 −47.8230 −1.54428
960960 21.7764 17.1085i 0.702832 0.552173i
961961 −8.05427 + 13.9504i −0.259815 + 0.450013i
962962 −41.4761 59.8654i −1.33724 1.93014i
963963 −1.89021 + 7.75940i −0.0609113 + 0.250043i
964964 0.536399 + 0.309690i 0.0172762 + 0.00997444i
965965 −3.57439 6.19103i −0.115064 0.199296i
966966 4.68208 + 5.95957i 0.150643 + 0.191746i
967967 −7.75706 + 4.47854i −0.249450 + 0.144020i −0.619513 0.784987i 0.712670π-0.712670\pi
0.370062 + 0.929007i 0.379336π0.379336\pi
968968 −9.97257 5.75766i −0.320530 0.185058i
969969 −10.7016 4.29018i −0.343786 0.137821i
970970 −6.05240 3.49436i −0.194331 0.112197i
971971 −8.19718 14.1979i −0.263060 0.455633i 0.703994 0.710206i 0.251398π-0.251398\pi
−0.967054 + 0.254573i 0.918065π0.918065\pi
972972 −9.81017 51.5584i −0.314661 1.65374i
973973 17.5239 + 10.1174i 0.561789 + 0.324349i
974974 2.34549 4.06250i 0.0751542 0.130171i
975975 −20.7066 + 4.73093i −0.663142 + 0.151511i
976976 1.53356 + 2.65620i 0.0490880 + 0.0850229i
977977 37.3172i 1.19388i −0.802285 0.596941i 0.796383π-0.796383\pi
0.802285 0.596941i 0.203617π-0.203617\pi
978978 9.89194 24.6749i 0.316309 0.789016i
979979 −4.12946 −0.131978
980980 44.4149i 1.41878i
981981 −7.01050 23.9597i −0.223828 0.764976i
982982 −6.13152 + 3.54003i −0.195665 + 0.112967i
983983 −44.4140 25.6424i −1.41659 0.817866i −0.420589 0.907251i 0.638176π-0.638176\pi
−0.995997 + 0.0893852i 0.971510π0.971510\pi
984984 −13.6330 + 1.95352i −0.434603 + 0.0622759i
985985 7.97381 0.254067
986986 41.8023i 1.33126i
987987 33.5920 83.7934i 1.06924 2.66717i
988988 −31.5987 + 21.8923i −1.00529 + 0.696486i
989989 −2.25559 −0.0717237
990990 −6.69653 22.8867i −0.212830 0.727386i
991991 −28.1237 + 48.7116i −0.893378 + 1.54738i −0.0575787 + 0.998341i 0.518338π0.518338\pi
−0.835799 + 0.549035i 0.814995π0.814995\pi
992992 19.0580 0.605092
993993 4.18340 + 29.1946i 0.132756 + 0.926463i
994994 −62.8414 36.2815i −1.99321 1.15078i
995995 −1.86093 1.07441i −0.0589955 0.0340611i
996996 −10.3784 + 8.15370i −0.328853 + 0.258360i
997997 −5.35303 −0.169532 −0.0847661 0.996401i 0.527014π-0.527014\pi
−0.0847661 + 0.996401i 0.527014π0.527014\pi
998998 23.6516 40.9658i 0.748679 1.29675i
999999 45.0950 + 4.37089i 1.42674 + 0.138289i
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.r.b.43.2 yes 22
3.2 odd 2 351.2.r.b.316.10 22
9.4 even 3 117.2.l.b.4.2 22
9.5 odd 6 351.2.l.b.199.10 22
13.10 even 6 117.2.l.b.88.10 yes 22
39.23 odd 6 351.2.l.b.127.2 22
117.23 odd 6 351.2.r.b.10.10 22
117.49 even 6 inner 117.2.r.b.49.2 yes 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
117.2.l.b.4.2 22 9.4 even 3
117.2.l.b.88.10 yes 22 13.10 even 6
117.2.r.b.43.2 yes 22 1.1 even 1 trivial
117.2.r.b.49.2 yes 22 117.49 even 6 inner
351.2.l.b.127.2 22 39.23 odd 6
351.2.l.b.199.10 22 9.5 odd 6
351.2.r.b.10.10 22 117.23 odd 6
351.2.r.b.316.10 22 3.2 odd 2