Properties

Label 58.2.d.b.25.2
Level 5858
Weight 22
Character 58.25
Analytic conductor 0.4630.463
Analytic rank 00
Dimension 1212
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [58,2,Mod(7,58)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(58, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("58.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 58=229 58 = 2 \cdot 29
Weight: k k == 2 2
Character orbit: [χ][\chi] == 58.d (of order 77, degree 66, 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: 0.4631323317230.463132331723
Analytic rank: 00
Dimension: 1212
Relative dimension: 22 over Q(ζ7)\Q(\zeta_{7})
Coefficient field: Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x123x11+13x109x95x8+35x7+197x6140x580x4++4096 x^{12} - 3 x^{11} + 13 x^{10} - 9 x^{9} - 5 x^{8} + 35 x^{7} + 197 x^{6} - 140 x^{5} - 80 x^{4} + \cdots + 4096 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C7]\mathrm{SU}(2)[C_{7}]

Embedding invariants

Embedding label 25.2
Root 1.569200.755686i-1.56920 - 0.755686i of defining polynomial
Character χ\chi == 58.25
Dual form 58.2.d.b.7.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.222521+0.974928i)q2+(1.569200.755686i)q3+(0.9009690.433884i)q4+(0.1100810.482295i)q5+(0.387560+1.69801i)q6+(2.82760+1.36170i)q7+(0.6234900.781831i)q8+(0.02085060.0261458i)q9+(0.445708+0.214642i)q10+(0.870839+1.09200i)q111.74168q12+(3.563534.46852i)q13+(0.6983593.05971i)q14+(0.1917250.840003i)q15+(0.623490+0.781831i)q16+5.31800q17+(0.0208506+0.0261458i)q18+(4.474712.15491i)q19+(0.308439+0.386771i)q20+(3.40804+4.27355i)q21+(1.25840+0.606013i)q22+(0.181045+0.793210i)q23+(0.3875601.69801i)q24+(4.28435+2.06324i)q25+(5.149442.47984i)q26+(1.14972+5.03725i)q27+3.13840q28+(5.385010.0414712i)q29+0.861605q30+(1.41596+6.20373i)q31+(0.900969+0.433884i)q32+(2.19173+1.05548i)q33+(1.18337+5.18466i)q34+(0.345477+1.51363i)q35+(0.0301299+0.0145098i)q36+(5.566306.97992i)q37+(3.096603.88301i)q38+(8.968674.31909i)q39+(0.3084390.386771i)q404.01226q41+(3.408044.27355i)q42+(0.310799+1.36170i)q43+(0.3107991.36170i)q44+(0.01031470.0129343i)q450.813609q46+(6.420798.05142i)q47+(1.56920+0.755686i)q48+(1.776652.22785i)q49+(2.96486+3.71782i)q50+(8.344994.01873i)q51+(1.27181+5.57215i)q52+(0.944288+4.13720i)q53+(4.655122.24179i)q54+(0.6225280.299794i)q55+(0.698359+3.05971i)q568.65014q57+(1.15784+5.25922i)q58+11.1598q59+(0.191725+0.840003i)q60+(4.38454+2.11149i)q61+(5.733112.76092i)q62+(0.0233543+0.102322i)q63+(0.2225210.974928i)q64+(2.54742+1.22677i)q65+(1.51672+1.90191i)q66+(4.450725.58102i)q67+(4.791352.30739i)q68+(0.883513+1.10789i)q691.55256q70+(3.76423+4.72019i)q71+(0.007441480.0326033i)q72+(2.7323811.9713i)q73+(5.56630+6.97992i)q74+8.28215q75+(3.09660+3.88301i)q76+(3.949351.90191i)q77+(6.206517.78272i)q78+(5.86220+7.35096i)q79+(0.4457080.214642i)q80+(2.02476+8.87107i)q81+(0.8928133.91167i)q82+(11.45085.51441i)q83+(4.924762.37164i)q84+(0.5854092.56484i)q851.39672q86+(8.418804.13445i)q87+1.39672q88+(0.398796+1.74724i)q89+(0.01490520.00717798i)q90+(16.1610+7.78272i)q91+(0.1810450.793210i)q92+(2.46615+10.8049i)q93+(9.278314.46820i)q94+(1.53188+1.92092i)q95+(1.08592+1.36170i)q96+(3.420351.64715i)q97+(1.77665+2.22785i)q98+0.0467086q99+O(q100)q+(-0.222521 + 0.974928i) q^{2} +(1.56920 - 0.755686i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.110081 - 0.482295i) q^{5} +(0.387560 + 1.69801i) q^{6} +(-2.82760 + 1.36170i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.0208506 - 0.0261458i) q^{9} +(0.445708 + 0.214642i) q^{10} +(0.870839 + 1.09200i) q^{11} -1.74168 q^{12} +(-3.56353 - 4.46852i) q^{13} +(-0.698359 - 3.05971i) q^{14} +(-0.191725 - 0.840003i) q^{15} +(0.623490 + 0.781831i) q^{16} +5.31800 q^{17} +(0.0208506 + 0.0261458i) q^{18} +(-4.47471 - 2.15491i) q^{19} +(-0.308439 + 0.386771i) q^{20} +(-3.40804 + 4.27355i) q^{21} +(-1.25840 + 0.606013i) q^{22} +(0.181045 + 0.793210i) q^{23} +(0.387560 - 1.69801i) q^{24} +(4.28435 + 2.06324i) q^{25} +(5.14944 - 2.47984i) q^{26} +(-1.14972 + 5.03725i) q^{27} +3.13840 q^{28} +(5.38501 - 0.0414712i) q^{29} +0.861605 q^{30} +(-1.41596 + 6.20373i) q^{31} +(-0.900969 + 0.433884i) q^{32} +(2.19173 + 1.05548i) q^{33} +(-1.18337 + 5.18466i) q^{34} +(0.345477 + 1.51363i) q^{35} +(-0.0301299 + 0.0145098i) q^{36} +(5.56630 - 6.97992i) q^{37} +(3.09660 - 3.88301i) q^{38} +(-8.96867 - 4.31909i) q^{39} +(-0.308439 - 0.386771i) q^{40} -4.01226 q^{41} +(-3.40804 - 4.27355i) q^{42} +(0.310799 + 1.36170i) q^{43} +(-0.310799 - 1.36170i) q^{44} +(-0.0103147 - 0.0129343i) q^{45} -0.813609 q^{46} +(-6.42079 - 8.05142i) q^{47} +(1.56920 + 0.755686i) q^{48} +(1.77665 - 2.22785i) q^{49} +(-2.96486 + 3.71782i) q^{50} +(8.34499 - 4.01873i) q^{51} +(1.27181 + 5.57215i) q^{52} +(-0.944288 + 4.13720i) q^{53} +(-4.65512 - 2.24179i) q^{54} +(0.622528 - 0.299794i) q^{55} +(-0.698359 + 3.05971i) q^{56} -8.65014 q^{57} +(-1.15784 + 5.25922i) q^{58} +11.1598 q^{59} +(-0.191725 + 0.840003i) q^{60} +(-4.38454 + 2.11149i) q^{61} +(-5.73311 - 2.76092i) q^{62} +(-0.0233543 + 0.102322i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-2.54742 + 1.22677i) q^{65} +(-1.51672 + 1.90191i) q^{66} +(4.45072 - 5.58102i) q^{67} +(-4.79135 - 2.30739i) q^{68} +(0.883513 + 1.10789i) q^{69} -1.55256 q^{70} +(3.76423 + 4.72019i) q^{71} +(-0.00744148 - 0.0326033i) q^{72} +(-2.73238 - 11.9713i) q^{73} +(5.56630 + 6.97992i) q^{74} +8.28215 q^{75} +(3.09660 + 3.88301i) q^{76} +(-3.94935 - 1.90191i) q^{77} +(6.20651 - 7.78272i) q^{78} +(-5.86220 + 7.35096i) q^{79} +(0.445708 - 0.214642i) q^{80} +(2.02476 + 8.87107i) q^{81} +(0.892813 - 3.91167i) q^{82} +(-11.4508 - 5.51441i) q^{83} +(4.92476 - 2.37164i) q^{84} +(0.585409 - 2.56484i) q^{85} -1.39672 q^{86} +(8.41880 - 4.13445i) q^{87} +1.39672 q^{88} +(-0.398796 + 1.74724i) q^{89} +(0.0149052 - 0.00717798i) q^{90} +(16.1610 + 7.78272i) q^{91} +(0.181045 - 0.793210i) q^{92} +(2.46615 + 10.8049i) q^{93} +(9.27831 - 4.46820i) q^{94} +(-1.53188 + 1.92092i) q^{95} +(-1.08592 + 1.36170i) q^{96} +(-3.42035 - 1.64715i) q^{97} +(1.77665 + 2.22785i) q^{98} +0.0467086 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q2q23q32q4+4q6+q72q811q97q102q11+4q12+q13+q149q152q1612q1711q186q19+7q2013q21+8q99+O(q100) 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + 4 q^{6} + q^{7} - 2 q^{8} - 11 q^{9} - 7 q^{10} - 2 q^{11} + 4 q^{12} + q^{13} + q^{14} - 9 q^{15} - 2 q^{16} - 12 q^{17} - 11 q^{18} - 6 q^{19} + 7 q^{20} - 13 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/58Z)×\left(\mathbb{Z}/58\mathbb{Z}\right)^\times.

nn 3131
χ(n)\chi(n) e(47)e\left(\frac{4}{7}\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 −0.222521 + 0.974928i −0.157346 + 0.689378i
33 1.56920 0.755686i 0.905977 0.436295i 0.0779327 0.996959i 0.475168π-0.475168\pi
0.828044 + 0.560663i 0.189454π0.189454\pi
44 −0.900969 0.433884i −0.450484 0.216942i
55 0.110081 0.482295i 0.0492296 0.215689i −0.944330 0.329000i 0.893288π-0.893288\pi
0.993560 + 0.113311i 0.0361456π0.0361456\pi
66 0.387560 + 1.69801i 0.158221 + 0.693210i
77 −2.82760 + 1.36170i −1.06873 + 0.514674i −0.883697 0.468059i 0.844954π-0.844954\pi
−0.185033 + 0.982732i 0.559239π0.559239\pi
88 0.623490 0.781831i 0.220437 0.276419i
99 0.0208506 0.0261458i 0.00695019 0.00871526i
1010 0.445708 + 0.214642i 0.140945 + 0.0678756i
1111 0.870839 + 1.09200i 0.262568 + 0.329250i 0.895587 0.444887i 0.146756π-0.146756\pi
−0.633019 + 0.774136i 0.718185π0.718185\pi
1212 −1.74168 −0.502779
1313 −3.56353 4.46852i −0.988344 1.23934i −0.970897 0.239497i 0.923018π-0.923018\pi
−0.0174472 0.999848i 0.505554π-0.505554\pi
1414 −0.698359 3.05971i −0.186644 0.817742i
1515 −0.191725 0.840003i −0.0495032 0.216888i
1616 0.623490 + 0.781831i 0.155872 + 0.195458i
1717 5.31800 1.28980 0.644902 0.764265i 0.276898π-0.276898\pi
0.644902 + 0.764265i 0.276898π0.276898\pi
1818 0.0208506 + 0.0261458i 0.00491453 + 0.00616262i
1919 −4.47471 2.15491i −1.02657 0.494370i −0.156697 0.987647i 0.550085π-0.550085\pi
−0.869872 + 0.493277i 0.835799π0.835799\pi
2020 −0.308439 + 0.386771i −0.0689691 + 0.0864845i
2121 −3.40804 + 4.27355i −0.743695 + 0.932565i
2222 −1.25840 + 0.606013i −0.268292 + 0.129202i
2323 0.181045 + 0.793210i 0.0377505 + 0.165396i 0.990289 0.139021i 0.0443956π-0.0443956\pi
−0.952539 + 0.304417i 0.901538π0.901538\pi
2424 0.387560 1.69801i 0.0791103 0.346605i
2525 4.28435 + 2.06324i 0.856871 + 0.412647i
2626 5.14944 2.47984i 1.00989 0.486337i
2727 −1.14972 + 5.03725i −0.221263 + 0.969419i
2828 3.13840 0.593101
2929 5.38501 0.0414712i 0.999970 0.00770101i
3030 0.861605 0.157307
3131 −1.41596 + 6.20373i −0.254314 + 1.11422i 0.672912 + 0.739722i 0.265043π0.265043\pi
−0.927226 + 0.374501i 0.877814π0.877814\pi
3232 −0.900969 + 0.433884i −0.159270 + 0.0767005i
3333 2.19173 + 1.05548i 0.381530 + 0.183735i
3434 −1.18337 + 5.18466i −0.202946 + 0.889162i
3535 0.345477 + 1.51363i 0.0583962 + 0.255851i
3636 −0.0301299 + 0.0145098i −0.00502166 + 0.00241830i
3737 5.56630 6.97992i 0.915095 1.14749i −0.0735606 0.997291i 0.523436π-0.523436\pi
0.988655 0.150202i 0.0479923π-0.0479923\pi
3838 3.09660 3.88301i 0.502335 0.629908i
3939 −8.96867 4.31909i −1.43614 0.691607i
4040 −0.308439 0.386771i −0.0487685 0.0611538i
4141 −4.01226 −0.626610 −0.313305 0.949652i 0.601436π-0.601436\pi
−0.313305 + 0.949652i 0.601436π0.601436\pi
4242 −3.40804 4.27355i −0.525872 0.659423i
4343 0.310799 + 1.36170i 0.0473964 + 0.207657i 0.993082 0.117427i 0.0374646π-0.0374646\pi
−0.945685 + 0.325084i 0.894607π0.894607\pi
4444 −0.310799 1.36170i −0.0468547 0.205284i
4545 −0.0103147 0.0129343i −0.00153763 0.00192813i
4646 −0.813609 −0.119960
4747 −6.42079 8.05142i −0.936569 1.17442i −0.984467 0.175568i 0.943824π-0.943824\pi
0.0478986 0.998852i 0.484748π-0.484748\pi
4848 1.56920 + 0.755686i 0.226494 + 0.109074i
4949 1.77665 2.22785i 0.253807 0.318264i
5050 −2.96486 + 3.71782i −0.419295 + 0.525780i
5151 8.34499 4.01873i 1.16853 0.562735i
5252 1.27181 + 5.57215i 0.176368 + 0.772719i
5353 −0.944288 + 4.13720i −0.129708 + 0.568288i 0.867748 + 0.497004i 0.165567π0.165567\pi
−0.997456 + 0.0712835i 0.977291π0.977291\pi
5454 −4.65512 2.24179i −0.633481 0.305068i
5555 0.622528 0.299794i 0.0839416 0.0404241i
5656 −0.698359 + 3.05971i −0.0933221 + 0.408871i
5757 −8.65014 −1.14574
5858 −1.15784 + 5.25922i −0.152032 + 0.690569i
5959 11.1598 1.45288 0.726438 0.687232i 0.241174π-0.241174\pi
0.726438 + 0.687232i 0.241174π0.241174\pi
6060 −0.191725 + 0.840003i −0.0247516 + 0.108444i
6161 −4.38454 + 2.11149i −0.561383 + 0.270348i −0.692982 0.720955i 0.743703π-0.743703\pi
0.131598 + 0.991303i 0.457989π0.457989\pi
6262 −5.73311 2.76092i −0.728106 0.350637i
6363 −0.0233543 + 0.102322i −0.00294237 + 0.0128913i
6464 −0.222521 0.974928i −0.0278151 0.121866i
6565 −2.54742 + 1.22677i −0.315969 + 0.152163i
6666 −1.51672 + 1.90191i −0.186695 + 0.234109i
6767 4.45072 5.58102i 0.543742 0.681830i −0.431718 0.902009i 0.642092π-0.642092\pi
0.975460 + 0.220178i 0.0706639π0.0706639\pi
6868 −4.79135 2.30739i −0.581036 0.279812i
6969 0.883513 + 1.10789i 0.106362 + 0.133374i
7070 −1.55256 −0.185566
7171 3.76423 + 4.72019i 0.446732 + 0.560184i 0.953304 0.302014i 0.0976589π-0.0976589\pi
−0.506572 + 0.862198i 0.669087π0.669087\pi
7272 −0.00744148 0.0326033i −0.000876987 0.00384233i
7373 −2.73238 11.9713i −0.319801 1.40114i −0.837903 0.545819i 0.816219π-0.816219\pi
0.518103 0.855319i 0.326639π-0.326639\pi
7474 5.56630 + 6.97992i 0.647070 + 0.811400i
7575 8.28215 0.956341
7676 3.09660 + 3.88301i 0.355204 + 0.445412i
7777 −3.94935 1.90191i −0.450070 0.216743i
7878 6.20651 7.78272i 0.702749 0.881220i
7979 −5.86220 + 7.35096i −0.659549 + 0.827048i −0.993294 0.115615i 0.963116π-0.963116\pi
0.333745 + 0.942663i 0.391687π0.391687\pi
8080 0.445708 0.214642i 0.0498316 0.0239977i
8181 2.02476 + 8.87107i 0.224974 + 0.985675i
8282 0.892813 3.91167i 0.0985947 0.431971i
8383 −11.4508 5.51441i −1.25689 0.605285i −0.317538 0.948246i 0.602856π-0.602856\pi
−0.939350 + 0.342960i 0.888570π0.888570\pi
8484 4.92476 2.37164i 0.537336 0.258767i
8585 0.585409 2.56484i 0.0634965 0.278196i
8686 −1.39672 −0.150612
8787 8.41880 4.13445i 0.902590 0.443259i
8888 1.39672 0.148891
8989 −0.398796 + 1.74724i −0.0422722 + 0.185207i −0.991656 0.128911i 0.958852π-0.958852\pi
0.949384 + 0.314118i 0.101709π0.101709\pi
9090 0.0149052 0.00717798i 0.00157115 0.000756626i
9191 16.1610 + 7.78272i 1.69413 + 0.815851i
9292 0.181045 0.793210i 0.0188753 0.0826979i
9393 2.46615 + 10.8049i 0.255728 + 1.12042i
9494 9.27831 4.46820i 0.956985 0.460860i
9595 −1.53188 + 1.92092i −0.157168 + 0.197082i
9696 −1.08592 + 1.36170i −0.110831 + 0.138978i
9797 −3.42035 1.64715i −0.347283 0.167243i 0.252108 0.967699i 0.418876π-0.418876\pi
−0.599391 + 0.800456i 0.704591π0.704591\pi
9898 1.77665 + 2.22785i 0.179469 + 0.225047i
9999 0.0467086 0.00469439
100100 −2.96486 3.71782i −0.296486 0.371782i
101101 0.271881 + 1.19119i 0.0270532 + 0.118528i 0.986652 0.162846i 0.0520672π-0.0520672\pi
−0.959598 + 0.281373i 0.909210π0.909210\pi
102102 2.06104 + 9.03001i 0.204074 + 0.894104i
103103 1.12736 + 1.41366i 0.111082 + 0.139292i 0.834264 0.551365i 0.185893π-0.185893\pi
−0.723182 + 0.690657i 0.757321π0.757321\pi
104104 −5.71545 −0.560446
105105 1.68595 + 2.11412i 0.164532 + 0.206317i
106106 −3.82334 1.84123i −0.371356 0.178836i
107107 2.58788 3.24509i 0.250179 0.313715i −0.640845 0.767670i 0.721416π-0.721416\pi
0.891025 + 0.453955i 0.149987π0.149987\pi
108108 3.22144 4.03956i 0.309983 0.388707i
109109 −13.0682 + 6.29330i −1.25170 + 0.602789i −0.937968 0.346721i 0.887295π-0.887295\pi
−0.313736 + 0.949510i 0.601581π0.601581\pi
110110 0.153752 + 0.673630i 0.0146596 + 0.0642281i
111111 3.46000 15.1593i 0.328409 1.43885i
112112 −2.82760 1.36170i −0.267183 0.128668i
113113 −15.0312 + 7.23864i −1.41402 + 0.680954i −0.975951 0.217989i 0.930050π-0.930050\pi
−0.438065 + 0.898943i 0.644336π0.644336\pi
114114 1.92484 8.43327i 0.180278 0.789848i
115115 0.402491 0.0375325
116116 −4.86972 2.29910i −0.452142 0.213466i
117117 −0.191135 −0.0176704
118118 −2.48328 + 10.8800i −0.228604 + 1.00158i
119119 −15.0371 + 7.24151i −1.37845 + 0.663828i
120120 −0.776279 0.373836i −0.0708643 0.0341264i
121121 2.01363 8.82230i 0.183057 0.802027i
122122 −1.08289 4.74446i −0.0980405 0.429544i
123123 −6.29603 + 3.03201i −0.567694 + 0.273387i
124124 3.96744 4.97501i 0.356286 0.446769i
125125 3.00891 3.77305i 0.269125 0.337472i
126126 −0.0945597 0.0455375i −0.00842405 0.00405681i
127127 −7.91387 9.92368i −0.702243 0.880584i 0.294946 0.955514i 0.404698π-0.404698\pi
−0.997189 + 0.0749295i 0.976127π0.976127\pi
128128 1.00000 0.0883883
129129 1.51672 + 1.90191i 0.133540 + 0.167454i
130130 −0.629161 2.75653i −0.0551811 0.241764i
131131 3.29243 + 14.4251i 0.287661 + 1.26033i 0.887725 + 0.460374i 0.152285π0.152285\pi
−0.600064 + 0.799952i 0.704858π0.704858\pi
132132 −1.51672 1.90191i −0.132014 0.165540i
133133 15.5870 1.35157
134134 4.45072 + 5.58102i 0.384483 + 0.482127i
135135 2.30288 + 1.10901i 0.198200 + 0.0954482i
136136 3.31572 4.15778i 0.284320 0.356526i
137137 −0.941003 + 1.17998i −0.0803953 + 0.100813i −0.820403 0.571786i 0.806251π-0.806251\pi
0.740007 + 0.672599i 0.234822π0.234822\pi
138138 −1.27671 + 0.614833i −0.108681 + 0.0523380i
139139 −1.94848 8.53684i −0.165268 0.724086i −0.987846 0.155434i 0.950322π-0.950322\pi
0.822578 0.568652i 0.192535π-0.192535\pi
140140 0.345477 1.51363i 0.0291981 0.127925i
141141 −16.1598 7.78216i −1.36090 0.655377i
142142 −5.43947 + 2.61951i −0.456470 + 0.219824i
143143 1.77636 7.78272i 0.148546 0.650824i
144144 0.0334417 0.00278681
145145 0.572784 2.60173i 0.0475671 0.216062i
146146 12.2792 1.01623
147147 1.10436 4.83852i 0.0910861 0.399074i
148148 −8.04354 + 3.87357i −0.661175 + 0.318405i
149149 4.27124 + 2.05692i 0.349914 + 0.168510i 0.600581 0.799564i 0.294936π-0.294936\pi
−0.250668 + 0.968073i 0.580650π0.580650\pi
150150 −1.84295 + 8.07450i −0.150476 + 0.659280i
151151 1.44508 + 6.33133i 0.117599 + 0.515236i 0.999075 + 0.0430064i 0.0136936π0.0136936\pi
−0.881475 + 0.472230i 0.843449π0.843449\pi
152152 −4.47471 + 2.15491i −0.362947 + 0.174786i
153153 0.110883 0.139043i 0.00896438 0.0112410i
154154 2.73304 3.42712i 0.220234 0.276165i
155155 2.83616 + 1.36582i 0.227806 + 0.109706i
156156 6.20651 + 7.78272i 0.496919 + 0.623117i
157157 6.56139 0.523656 0.261828 0.965115i 0.415675π-0.415675\pi
0.261828 + 0.965115i 0.415675π0.415675\pi
158158 −5.86220 7.35096i −0.466371 0.584811i
159159 1.64465 + 7.20566i 0.130429 + 0.571446i
160160 0.110081 + 0.482295i 0.00870264 + 0.0381288i
161161 −1.59204 1.99635i −0.125470 0.157334i
162162 −9.09921 −0.714901
163163 3.52776 + 4.42367i 0.276315 + 0.346488i 0.900553 0.434746i 0.143162π-0.143162\pi
−0.624238 + 0.781234i 0.714590π0.714590\pi
164164 3.61493 + 1.74086i 0.282278 + 0.135938i
165165 0.750319 0.940870i 0.0584123 0.0732467i
166166 7.92419 9.93663i 0.615037 0.771232i
167167 10.8919 5.24527i 0.842842 0.405891i 0.0379260 0.999281i 0.487925π-0.487925\pi
0.804915 + 0.593389i 0.202211π0.202211\pi
168168 1.21632 + 5.32903i 0.0938408 + 0.411143i
169169 −4.37618 + 19.1733i −0.336630 + 1.47487i
170170 2.37027 + 1.14146i 0.181792 + 0.0875462i
171171 −0.149642 + 0.0720639i −0.0114434 + 0.00551086i
172172 0.310799 1.36170i 0.0236982 0.103829i
173173 11.6405 0.885008 0.442504 0.896767i 0.354090π-0.354090\pi
0.442504 + 0.896767i 0.354090π0.354090\pi
174174 2.15743 + 9.12772i 0.163554 + 0.691971i
175175 −14.9239 −1.12814
176176 −0.310799 + 1.36170i −0.0234273 + 0.102642i
177177 17.5119 8.43327i 1.31627 0.633883i
178178 −1.61469 0.777594i −0.121026 0.0582831i
179179 4.08440 17.8949i 0.305282 1.33753i −0.556752 0.830678i 0.687953π-0.687953\pi
0.862034 0.506850i 0.169190π-0.169190\pi
180180 0.00368129 + 0.0161288i 0.000274387 + 0.00120217i
181181 8.91422 4.29286i 0.662589 0.319086i −0.0721917 0.997391i 0.522999π-0.522999\pi
0.734781 + 0.678305i 0.237285π0.237285\pi
182182 −11.1838 + 14.0240i −0.828995 + 1.03953i
183183 −5.28460 + 6.62667i −0.390649 + 0.489858i
184184 0.733037 + 0.353012i 0.0540402 + 0.0260244i
185185 −2.75364 3.45296i −0.202452 0.253866i
186186 −11.0828 −0.812629
187187 4.63112 + 5.80724i 0.338661 + 0.424667i
188188 2.29155 + 10.0400i 0.167129 + 0.732239i
189189 −3.60827 15.8089i −0.262463 1.14993i
190190 −1.53188 1.92092i −0.111134 0.139358i
191191 0.424259 0.0306983 0.0153492 0.999882i 0.495114π-0.495114\pi
0.0153492 + 0.999882i 0.495114π0.495114\pi
192192 −1.08592 1.36170i −0.0783694 0.0982721i
193193 9.30230 + 4.47975i 0.669594 + 0.322460i 0.737612 0.675225i 0.235953π-0.235953\pi
−0.0680181 + 0.997684i 0.521668π0.521668\pi
194194 2.36695 2.96806i 0.169937 0.213095i
195195 −3.07035 + 3.85010i −0.219872 + 0.275711i
196196 −2.56733 + 1.23636i −0.183381 + 0.0883116i
197197 5.97308 + 26.1698i 0.425564 + 1.86452i 0.498050 + 0.867148i 0.334050π0.334050\pi
−0.0724862 + 0.997369i 0.523093π0.523093\pi
198198 −0.0103936 + 0.0455375i −0.000738644 + 0.00323621i
199199 6.12924 + 2.95169i 0.434490 + 0.209239i 0.638327 0.769765i 0.279627π-0.279627\pi
−0.203837 + 0.979005i 0.565341π0.565341\pi
200200 4.28435 2.06324i 0.302950 0.145893i
201201 2.76655 12.1211i 0.195138 0.854954i
202202 −1.22182 −0.0859671
203203 −15.1701 + 7.45002i −1.06474 + 0.522889i
204204 −9.26224 −0.648486
205205 −0.441673 + 1.93510i −0.0308478 + 0.135153i
206206 −1.62908 + 0.784523i −0.113503 + 0.0546603i
207207 0.0245140 + 0.0118053i 0.00170384 + 0.000820526i
208208 1.27181 5.57215i 0.0881840 0.386359i
209209 −1.54360 6.76296i −0.106773 0.467803i
210210 −2.43627 + 1.17325i −0.168119 + 0.0809617i
211211 3.64156 4.56638i 0.250696 0.314362i −0.640521 0.767941i 0.721281π-0.721281\pi
0.891216 + 0.453579i 0.149853π0.149853\pi
212212 2.64584 3.31777i 0.181717 0.227866i
213213 9.47380 + 4.56234i 0.649134 + 0.312607i
214214 2.58788 + 3.24509i 0.176904 + 0.221830i
215215 0.690954 0.0471226
216216 3.22144 + 4.03956i 0.219191 + 0.274857i
217217 −4.44385 19.4698i −0.301668 1.32169i
218218 −3.22757 14.1409i −0.218599 0.957744i
219219 −13.3342 16.7206i −0.901042 1.12987i
220220 −0.690954 −0.0465841
221221 −18.9508 23.7636i −1.27477 1.59851i
222222 14.0093 + 6.74650i 0.940240 + 0.452796i
223223 −13.6769 + 17.1503i −0.915874 + 1.14847i 0.0726432 + 0.997358i 0.476857π0.476857\pi
−0.988517 + 0.151111i 0.951715π0.951715\pi
224224 1.95676 2.45370i 0.130741 0.163944i
225225 0.143276 0.0689982i 0.00955174 0.00459988i
226226 −3.71240 16.2651i −0.246945 1.08194i
227227 0.479626 2.10138i 0.0318339 0.139474i −0.956514 0.291688i 0.905783π-0.905783\pi
0.988348 + 0.152214i 0.0486403π0.0486403\pi
228228 7.79351 + 3.75316i 0.516138 + 0.248559i
229229 −8.37172 + 4.03161i −0.553219 + 0.266416i −0.689539 0.724249i 0.742187π-0.742187\pi
0.136320 + 0.990665i 0.456472π0.456472\pi
230230 −0.0895627 + 0.392400i −0.00590559 + 0.0258741i
231231 −7.63456 −0.502317
232232 3.32507 4.23602i 0.218302 0.278109i
233233 −11.7848 −0.772045 −0.386022 0.922489i 0.626151π-0.626151\pi
−0.386022 + 0.922489i 0.626151π0.626151\pi
234234 0.0425314 0.186342i 0.00278037 0.0121816i
235235 −4.58996 + 2.21041i −0.299416 + 0.144191i
236236 −10.0546 4.84204i −0.654498 0.315190i
237237 −3.64393 + 15.9651i −0.236699 + 1.03704i
238238 −3.71387 16.2715i −0.240734 1.05473i
239239 12.9462 6.23455i 0.837419 0.403280i 0.0345265 0.999404i 0.489008π-0.489008\pi
0.802892 + 0.596124i 0.203293π0.203293\pi
240240 0.537202 0.673630i 0.0346762 0.0434826i
241241 −5.73880 + 7.19623i −0.369669 + 0.463550i −0.931521 0.363688i 0.881517π-0.881517\pi
0.561852 + 0.827238i 0.310089π0.310089\pi
242242 8.15303 + 3.92629i 0.524097 + 0.252392i
243243 0.216675 + 0.271702i 0.0138997 + 0.0174297i
244244 4.86648 0.311544
245245 −0.878905 1.10211i −0.0561512 0.0704114i
246246 −1.55499 6.81287i −0.0991427 0.434372i
247247 6.31651 + 27.6744i 0.401910 + 1.76088i
248248 3.96744 + 4.97501i 0.251933 + 0.315913i
249249 −22.1357 −1.40279
250250 3.00891 + 3.77305i 0.190300 + 0.238629i
251251 −5.33012 2.56685i −0.336434 0.162018i 0.258037 0.966135i 0.416924π-0.416924\pi
−0.594471 + 0.804117i 0.702639π0.702639\pi
252252 0.0654373 0.0820558i 0.00412216 0.00516903i
253253 −0.708523 + 0.888459i −0.0445444 + 0.0558569i
254254 11.4359 5.50723i 0.717551 0.345554i
255255 −1.01959 4.46713i −0.0638494 0.279743i
256256 −0.222521 + 0.974928i −0.0139076 + 0.0609330i
257257 24.0750 + 11.5939i 1.50176 + 0.723209i 0.990665 0.136316i 0.0435263π-0.0435263\pi
0.511094 + 0.859525i 0.329241π0.329241\pi
258258 −2.19173 + 1.05548i −0.136451 + 0.0657113i
259259 −6.23471 + 27.3160i −0.387406 + 1.69734i
260260 2.82742 0.175349
261261 0.111196 0.141660i 0.00688287 0.00876853i
262262 −14.7961 −0.914104
263263 5.19684 22.7688i 0.320451 1.40399i −0.516302 0.856407i 0.672692π-0.672692\pi
0.836753 0.547581i 0.184451π-0.184451\pi
264264 2.19173 1.05548i 0.134891 0.0649603i
265265 1.89140 + 0.910851i 0.116188 + 0.0559531i
266266 −3.46844 + 15.1962i −0.212664 + 0.931740i
267267 0.694573 + 3.04312i 0.0425072 + 0.186236i
268268 −6.43147 + 3.09723i −0.392865 + 0.189194i
269269 9.73222 12.2038i 0.593384 0.744080i −0.390946 0.920413i 0.627852π-0.627852\pi
0.984331 + 0.176333i 0.0564236π0.0564236\pi
270270 −1.59364 + 1.99836i −0.0969859 + 0.121616i
271271 −0.197924 0.0953153i −0.0120230 0.00578999i 0.427863 0.903844i 0.359267π-0.359267\pi
−0.439886 + 0.898054i 0.644981π0.644981\pi
272272 3.31572 + 4.15778i 0.201045 + 0.252102i
273273 31.2411 1.89080
274274 −0.941003 1.17998i −0.0568481 0.0712853i
275275 1.47793 + 6.47525i 0.0891227 + 0.390472i
276276 −0.315322 1.38152i −0.0189802 0.0831575i
277277 2.33928 + 2.93336i 0.140554 + 0.176249i 0.847126 0.531392i 0.178331π-0.178331\pi
−0.706572 + 0.707641i 0.749759π0.749759\pi
278278 8.75639 0.525173
279279 0.132678 + 0.166373i 0.00794322 + 0.00996048i
280280 1.39881 + 0.673630i 0.0835947 + 0.0402571i
281281 −15.2450 + 19.1167i −0.909442 + 1.14040i 0.0801905 + 0.996780i 0.474447π0.474447\pi
−0.989632 + 0.143624i 0.954124π0.954124\pi
282282 11.1830 14.0230i 0.665935 0.835056i
283283 −6.84512 + 3.29644i −0.406900 + 0.195953i −0.626127 0.779721i 0.715361π-0.715361\pi
0.219227 + 0.975674i 0.429647π0.429647\pi
284284 −1.34344 5.88599i −0.0797184 0.349269i
285285 −0.952214 + 4.17192i −0.0564043 + 0.247123i
286286 7.19232 + 3.46364i 0.425291 + 0.204809i
287287 11.3451 5.46349i 0.669678 0.322500i
288288 −0.00744148 + 0.0326033i −0.000438494 + 0.00192117i
289289 11.2811 0.663593
290290 2.40904 + 1.13736i 0.141464 + 0.0667882i
291291 −6.61193 −0.387598
292292 −2.73238 + 11.9713i −0.159900 + 0.700569i
293293 23.1750 11.1605i 1.35390 0.652003i 0.390631 0.920547i 0.372257π-0.372257\pi
0.963267 + 0.268545i 0.0865427π0.0865427\pi
294294 4.47147 + 2.15334i 0.260781 + 0.125586i
295295 1.22847 5.38230i 0.0715245 0.313369i
296296 −1.98659 8.70382i −0.115468 0.505899i
297297 −6.50188 + 3.13114i −0.377277 + 0.181687i
298298 −2.95579 + 3.70644i −0.171224 + 0.214709i
299299 2.89932 3.63563i 0.167672 0.210254i
300300 −7.46196 3.59349i −0.430817 0.207470i
301301 −2.73304 3.42712i −0.157530 0.197536i
302302 −6.49415 −0.373696
303303 1.32680 + 1.66375i 0.0762226 + 0.0955801i
304304 −1.10516 4.84204i −0.0633855 0.277710i
305305 0.535705 + 2.34708i 0.0306744 + 0.134393i
306306 0.110883 + 0.139043i 0.00633877 + 0.00794857i
307307 1.81399 0.103530 0.0517649 0.998659i 0.483515π-0.483515\pi
0.0517649 + 0.998659i 0.483515π0.483515\pi
308308 2.73304 + 3.42712i 0.155729 + 0.195278i
309309 2.83733 + 1.36639i 0.161410 + 0.0777310i
310310 −1.96268 + 2.46113i −0.111473 + 0.139783i
311311 12.1020 15.1754i 0.686239 0.860517i −0.309673 0.950843i 0.600220π-0.600220\pi
0.995912 + 0.0903265i 0.0287910π0.0287910\pi
312312 −8.96867 + 4.31909i −0.507751 + 0.244520i
313313 −7.54006 33.0352i −0.426189 1.86726i −0.493847 0.869549i 0.664410π-0.664410\pi
0.0676576 0.997709i 0.478447π-0.478447\pi
314314 −1.46005 + 6.39688i −0.0823952 + 0.360997i
315315 0.0467785 + 0.0225273i 0.00263567 + 0.00126927i
316316 8.47112 4.07948i 0.476538 0.229489i
317317 −1.22333 + 5.35977i −0.0687092 + 0.301035i −0.997593 0.0693356i 0.977912π-0.977912\pi
0.928884 + 0.370370i 0.120769π0.120769\pi
318318 −7.39097 −0.414465
319319 4.73476 + 5.84430i 0.265096 + 0.327218i
320320 −0.494698 −0.0276545
321321 1.60862 7.04781i 0.0897843 0.393371i
322322 2.30056 1.10789i 0.128205 0.0617403i
323323 −23.7965 11.4598i −1.32407 0.637640i
324324 2.02476 8.87107i 0.112487 0.492837i
325325 −6.04779 26.4971i −0.335471 1.46980i
326326 −5.09776 + 2.45495i −0.282339 + 0.135967i
327327 −15.7508 + 19.7509i −0.871021 + 1.09223i
328328 −2.50161 + 3.13691i −0.138128 + 0.173207i
329329 29.1190 + 14.0230i 1.60538 + 0.773112i
330330 0.750319 + 0.940870i 0.0413037 + 0.0517932i
331331 −13.6463 −0.750067 −0.375034 0.927011i 0.622369π-0.622369\pi
−0.375034 + 0.927011i 0.622369π0.622369\pi
332332 7.92419 + 9.93663i 0.434897 + 0.545343i
333333 −0.0664350 0.291071i −0.00364062 0.0159506i
334334 2.69008 + 11.7860i 0.147195 + 0.644902i
335335 −2.20176 2.76092i −0.120295 0.150845i
336336 −5.46607 −0.298199
337337 14.0705 + 17.6438i 0.766469 + 0.961122i 0.999937 0.0112429i 0.00357882π-0.00357882\pi
−0.233468 + 0.972365i 0.575007π0.575007\pi
338338 −17.7188 8.53293i −0.963776 0.464130i
339339 −18.1168 + 22.7177i −0.983968 + 1.23386i
340340 −1.64028 + 2.05684i −0.0889566 + 0.111548i
341341 −8.00754 + 3.85623i −0.433632 + 0.208826i
342342 −0.0369586 0.161926i −0.00199849 0.00875596i
343343 2.89852 12.6993i 0.156505 0.685695i
344344 1.25840 + 0.606013i 0.0678483 + 0.0326740i
345345 0.631588 0.304157i 0.0340036 0.0163752i
346346 −2.59025 + 11.3486i −0.139253 + 0.610105i
347347 −2.97305 −0.159602 −0.0798008 0.996811i 0.525428π-0.525428\pi
−0.0798008 + 0.996811i 0.525428π0.525428\pi
348348 −9.37894 + 0.0722295i −0.502764 + 0.00387191i
349349 −5.73913 −0.307208 −0.153604 0.988132i 0.549088π-0.549088\pi
−0.153604 + 0.988132i 0.549088π0.549088\pi
350350 3.32089 14.5498i 0.177509 0.777717i
351351 26.6061 12.8128i 1.42013 0.683898i
352352 −1.25840 0.606013i −0.0670729 0.0323006i
353353 1.44019 6.30988i 0.0766536 0.335841i −0.922031 0.387116i 0.873471π-0.873471\pi
0.998685 + 0.0512748i 0.0163284π0.0163284\pi
354354 4.32507 + 18.9494i 0.229875 + 1.00715i
355355 2.69090 1.29587i 0.142818 0.0687775i
356356 1.11740 1.40118i 0.0592221 0.0742622i
357357 −18.1239 + 22.7267i −0.959221 + 1.20283i
358358 16.5374 + 7.96398i 0.874028 + 0.420910i
359359 6.69717 + 8.39798i 0.353463 + 0.443229i 0.926496 0.376303i 0.122805π-0.122805\pi
−0.573034 + 0.819532i 0.694234π0.694234\pi
360360 −0.0165436 −0.000871922
361361 3.53313 + 4.43041i 0.185954 + 0.233179i
362362 2.20163 + 9.64598i 0.115715 + 0.506981i
363363 −3.50710 15.3656i −0.184075 0.806485i
364364 −11.1838 14.0240i −0.586188 0.735056i
365365 −6.07449 −0.317954
366366 −5.28460 6.62667i −0.276230 0.346382i
367367 −17.0637 8.21747i −0.890720 0.428948i −0.0681919 0.997672i 0.521723π-0.521723\pi
−0.822529 + 0.568724i 0.807437π0.807437\pi
368368 −0.507277 + 0.636105i −0.0264436 + 0.0331593i
369369 −0.0836580 + 0.104904i −0.00435506 + 0.00546107i
370370 3.97913 1.91625i 0.206865 0.0996209i
371371 −2.96355 12.9842i −0.153860 0.674104i
372372 2.46615 10.8049i 0.127864 0.560208i
373373 −2.19298 1.05608i −0.113548 0.0546819i 0.376247 0.926519i 0.377214π-0.377214\pi
−0.489796 + 0.871837i 0.662929π0.662929\pi
374374 −6.69216 + 3.22277i −0.346043 + 0.166646i
375375 1.87033 8.19446i 0.0965835 0.423160i
376376 −10.2982 −0.531087
377377 −19.3749 23.9152i −0.997859 1.23170i
378378 16.2154 0.834031
379379 3.81433 16.7117i 0.195929 0.858422i −0.777400 0.629007i 0.783462π-0.783462\pi
0.973329 0.229415i 0.0736812π-0.0736812\pi
380380 2.21363 1.06603i 0.113557 0.0546862i
381381 −19.9176 9.59182i −1.02041 0.491404i
382382 −0.0944066 + 0.413622i −0.00483026 + 0.0211628i
383383 5.29096 + 23.1812i 0.270355 + 1.18450i 0.909595 + 0.415497i 0.136392π0.136392\pi
−0.639239 + 0.769008i 0.720751π0.720751\pi
384384 1.56920 0.755686i 0.0800778 0.0385634i
385385 −1.35203 + 1.69539i −0.0689057 + 0.0864051i
386386 −6.43739 + 8.07223i −0.327655 + 0.410866i
387387 0.0420830 + 0.0202661i 0.00213920 + 0.00103018i
388388 2.36695 + 2.96806i 0.120164 + 0.150681i
389389 −11.5272 −0.584453 −0.292227 0.956349i 0.594396π-0.594396\pi
−0.292227 + 0.956349i 0.594396π0.594396\pi
390390 −3.07035 3.85010i −0.155473 0.194957i
391391 0.962797 + 4.21829i 0.0486907 + 0.213328i
392392 −0.634079 2.77808i −0.0320258 0.140314i
393393 16.0673 + 20.1478i 0.810489 + 1.01632i
394394 −26.8428 −1.35232
395395 2.90002 + 3.63651i 0.145916 + 0.182973i
396396 −0.0420830 0.0202661i −0.00211475 0.00101841i
397397 18.0708 22.6601i 0.906948 1.13728i −0.0830990 0.996541i 0.526482π-0.526482\pi
0.990047 0.140736i 0.0449468π-0.0449468\pi
398398 −4.24156 + 5.31875i −0.212610 + 0.266605i
399399 24.4591 11.7789i 1.22449 0.589682i
400400 1.05815 + 4.63605i 0.0529074 + 0.231802i
401401 −2.29856 + 10.0707i −0.114785 + 0.502905i 0.884550 + 0.466445i 0.154465π0.154465\pi
−0.999335 + 0.0364602i 0.988392π0.988392\pi
402402 11.2016 + 5.39438i 0.558683 + 0.269047i
403403 32.7673 15.7799i 1.63226 0.786054i
404404 0.271881 1.19119i 0.0135266 0.0592638i
405405 4.50136 0.223674
406406 −3.88755 16.4476i −0.192936 0.816280i
407407 12.4694 0.618086
408408 2.06104 9.03001i 0.102037 0.447052i
409409 −8.97519 + 4.32222i −0.443794 + 0.213720i −0.642416 0.766356i 0.722068π-0.722068\pi
0.198622 + 0.980076i 0.436354π0.436354\pi
410410 −1.78830 0.861198i −0.0883177 0.0425316i
411411 −0.584925 + 2.56273i −0.0288522 + 0.126410i
412412 −0.402349 1.76281i −0.0198223 0.0868473i
413413 −31.5553 + 15.1962i −1.55273 + 0.747757i
414414 −0.0169642 + 0.0212725i −0.000833746 + 0.00104548i
415415 −3.92009 + 4.91563i −0.192429 + 0.241299i
416416 5.14944 + 2.47984i 0.252472 + 0.121584i
417417 −9.50872 11.9236i −0.465644 0.583899i
418418 6.93688 0.339294
419419 17.6773 + 22.1667i 0.863595 + 1.08291i 0.995788 + 0.0916894i 0.0292267π0.0292267\pi
−0.132193 + 0.991224i 0.542202π0.542202\pi
420420 −0.601709 2.63626i −0.0293604 0.128636i
421421 2.11840 + 9.28130i 0.103244 + 0.452343i 0.999953 + 0.00972116i 0.00309439π0.00309439\pi
−0.896708 + 0.442622i 0.854048π0.854048\pi
422422 3.64156 + 4.56638i 0.177268 + 0.222288i
423423 −0.344388 −0.0167447
424424 2.64584 + 3.31777i 0.128493 + 0.161125i
425425 22.7842 + 10.9723i 1.10519 + 0.532234i
426426 −6.55608 + 8.22106i −0.317643 + 0.398312i
427427 9.52251 11.9409i 0.460827 0.577859i
428428 −3.73959 + 1.80089i −0.180760 + 0.0870493i
429429 −3.09384 13.5550i −0.149372 0.654441i
430430 −0.153752 + 0.673630i −0.00741456 + 0.0324853i
431431 17.0958 + 8.23291i 0.823477 + 0.396566i 0.797665 0.603101i 0.206069π-0.206069\pi
0.0258122 + 0.999667i 0.491783π0.491783\pi
432432 −4.65512 + 2.24179i −0.223969 + 0.107858i
433433 −6.30063 + 27.6049i −0.302789 + 1.32661i 0.563108 + 0.826383i 0.309605π0.309605\pi
−0.865897 + 0.500222i 0.833252π0.833252\pi
434434 19.9705 0.958613
435435 −1.06728 4.51547i −0.0511720 0.216500i
436436 14.5046 0.694644
437437 0.899171 3.93953i 0.0430132 0.188453i
438438 19.2685 9.27921i 0.920683 0.443378i
439439 17.9255 + 8.63248i 0.855539 + 0.412006i 0.809631 0.586940i 0.199667π-0.199667\pi
0.0459084 + 0.998946i 0.485382π0.485382\pi
440440 0.153752 0.673630i 0.00732982 0.0321140i
441441 −0.0212047 0.0929038i −0.00100975 0.00442399i
442442 27.3847 13.1878i 1.30256 0.627279i
443443 −22.1713 + 27.8019i −1.05339 + 1.32091i −0.108292 + 0.994119i 0.534538π0.534538\pi
−0.945097 + 0.326790i 0.894033π0.894033\pi
444444 −9.69471 + 12.1568i −0.460091 + 0.576935i
445445 0.798784 + 0.384674i 0.0378660 + 0.0182353i
446446 −13.6769 17.1503i −0.647620 0.812090i
447447 8.25681 0.390534
448448 1.95676 + 2.45370i 0.0924481 + 0.115926i
449449 −2.41460 10.5790i −0.113952 0.499256i −0.999404 0.0345250i 0.989008π-0.989008\pi
0.885452 0.464731i 0.153849π-0.153849\pi
450450 0.0353863 + 0.155037i 0.00166813 + 0.00730853i
451451 −3.49404 4.38138i −0.164528 0.206311i
452452 16.6834 0.784720
453453 7.05212 + 8.84307i 0.331337 + 0.415484i
454454 1.94197 + 0.935202i 0.0911411 + 0.0438912i
455455 5.53258 6.93764i 0.259371 0.325242i
456456 −5.39328 + 6.76296i −0.252563 + 0.316704i
457457 −29.1336 + 14.0300i −1.36281 + 0.656296i −0.965262 0.261285i 0.915854π-0.915854\pi
−0.397550 + 0.917580i 0.630140π0.630140\pi
458458 −2.06764 9.05894i −0.0966146 0.423296i
459459 −6.11420 + 26.7881i −0.285386 + 1.25036i
460460 −0.362632 0.174634i −0.0169078 0.00814237i
461461 −22.8888 + 11.0227i −1.06604 + 0.513377i −0.882828 0.469696i 0.844363π-0.844363\pi
−0.183211 + 0.983074i 0.558649π0.558649\pi
462462 1.69885 7.44314i 0.0790376 0.346286i
463463 3.22072 0.149680 0.0748398 0.997196i 0.476155π-0.476155\pi
0.0748398 + 0.997196i 0.476155π0.476155\pi
464464 3.38992 + 4.18431i 0.157373 + 0.194252i
465465 5.48263 0.254251
466466 2.62235 11.4893i 0.121478 0.532231i
467467 −20.5930 + 9.91706i −0.952929 + 0.458907i −0.844712 0.535221i 0.820228π-0.820228\pi
−0.108217 + 0.994127i 0.534514π0.534514\pi
468468 0.172206 + 0.0829302i 0.00796024 + 0.00383345i
469469 −4.98516 + 21.8414i −0.230193 + 1.00854i
470470 −1.13363 4.96675i −0.0522903 0.229099i
471471 10.2961 4.95835i 0.474420 0.228469i
472472 6.95799 8.72505i 0.320268 0.401603i
473473 −1.21632 + 1.52521i −0.0559263 + 0.0701293i
474474 −14.7540 7.10513i −0.677672 0.326350i
475475 −14.7252 18.4648i −0.675637 0.847222i
476476 16.6900 0.764984
477477 0.0884813 + 0.110952i 0.00405128 + 0.00508015i
478478 3.19744 + 14.0089i 0.146248 + 0.640753i
479479 −0.477409 2.09166i −0.0218134 0.0955706i 0.962849 0.270039i 0.0870365π-0.0870365\pi
−0.984663 + 0.174468i 0.944179π0.944179\pi
480480 0.537202 + 0.673630i 0.0245198 + 0.0307469i
481481 −51.0256 −2.32657
482482 −5.73880 7.19623i −0.261395 0.327779i
483483 −4.00683 1.92959i −0.182317 0.0877993i
484484 −5.64207 + 7.07493i −0.256458 + 0.321588i
485485 −1.17093 + 1.46830i −0.0531691 + 0.0666719i
486486 −0.313105 + 0.150783i −0.0142027 + 0.00683968i
487487 −4.84560 21.2300i −0.219575 0.962021i −0.957793 0.287459i 0.907190π-0.907190\pi
0.738218 0.674562i 0.235668π-0.235668\pi
488488 −1.08289 + 4.74446i −0.0490203 + 0.214772i
489489 8.87865 + 4.27573i 0.401507 + 0.193355i
490490 1.27005 0.611626i 0.0573752 0.0276304i
491491 8.64786 37.8888i 0.390273 1.70990i −0.273423 0.961894i 0.588156π-0.588156\pi
0.663696 0.748002i 0.268987π-0.268987\pi
492492 6.98807 0.315047
493493 28.6374 0.220544i 1.28977 0.00993279i
494494 −28.3861 −1.27715
495495 0.00514172 0.0225273i 0.000231103 0.00101253i
496496 −5.73311 + 2.76092i −0.257424 + 0.123969i
497497 −17.0712 8.22106i −0.765748 0.368765i
498498 4.92566 21.5807i 0.220724 0.967056i
499499 −8.74490 38.3139i −0.391476 1.71517i −0.659457 0.751742i 0.729214π-0.729214\pi
0.267981 0.963424i 0.413643π-0.413643\pi
500500 −4.34800 + 2.09389i −0.194449 + 0.0936415i
501501 13.1278 16.4617i 0.586506 0.735456i
502502 3.68856 4.62530i 0.164628 0.206437i
503503 −25.2735 12.1711i −1.12689 0.542680i −0.224874 0.974388i 0.572197π-0.572197\pi
−0.902014 + 0.431707i 0.857911π0.857911\pi
504504 0.0654373 + 0.0820558i 0.00291481 + 0.00365506i
505505 0.604433 0.0268969
506506 −0.708523 0.888459i −0.0314977 0.0394968i
507507 7.62190 + 33.3937i 0.338501 + 1.48307i
508508 2.82443 + 12.3746i 0.125314 + 0.549035i
509509 1.06278 + 1.33268i 0.0471069 + 0.0590701i 0.804827 0.593510i 0.202258π-0.202258\pi
−0.757720 + 0.652580i 0.773687π0.773687\pi
510510 4.58201 0.202895
511511 24.0274 + 30.1294i 1.06291 + 1.33285i
512512 −0.900969 0.433884i −0.0398176 0.0191751i
513513 15.9995 20.0627i 0.706394 0.885790i
514514 −16.6604 + 20.8915i −0.734860 + 0.921486i
515515 0.805903 0.388102i 0.0355123 0.0171018i
516516 −0.541311 2.37164i −0.0238299 0.104406i
517517 3.20065 14.0230i 0.140765 0.616730i
518518 −25.2438 12.1568i −1.10915 0.534138i
519519 18.2662 8.79653i 0.801797 0.386125i
520520 −0.629161 + 2.75653i −0.0275905 + 0.120882i
521521 −21.0834 −0.923678 −0.461839 0.886964i 0.652810π-0.652810\pi
−0.461839 + 0.886964i 0.652810π0.652810\pi
522522 0.113365 + 0.139930i 0.00496184 + 0.00612459i
523523 −8.93606 −0.390747 −0.195373 0.980729i 0.562592π-0.562592\pi
−0.195373 + 0.980729i 0.562592π0.562592\pi
524524 3.29243 14.4251i 0.143831 0.630163i
525525 −23.4186 + 11.2778i −1.02207 + 0.492203i
526526 21.0416 + 10.1331i 0.917457 + 0.441824i
527527 −7.53008 + 32.9914i −0.328015 + 1.43713i
528528 0.541311 + 2.37164i 0.0235576 + 0.103212i
529529 20.1259 9.69211i 0.875038 0.421396i
530530 −1.30889 + 1.64130i −0.0568546 + 0.0712934i
531531 0.232687 0.291781i 0.0100978 0.0126622i
532532 −14.0434 6.76296i −0.608860 0.293211i
533533 14.2978 + 17.9289i 0.619307 + 0.776586i
534534 −3.12138 −0.135076
535535 −1.28022 1.60534i −0.0553486 0.0694050i
536536 −1.58844 6.95942i −0.0686103 0.300601i
537537 −7.11370 31.1672i −0.306979 1.34496i
538538 9.73222 + 12.2038i 0.419586 + 0.526144i
539539 3.97998 0.171430
540540 −1.59364 1.99836i −0.0685794 0.0859958i
541541 10.7827 + 5.19269i 0.463586 + 0.223251i 0.651072 0.759016i 0.274320π-0.274320\pi
−0.187486 + 0.982267i 0.560034π0.560034\pi
542542 0.136968 0.171752i 0.00588327 0.00737739i
543543 10.7441 13.4727i 0.461074 0.578169i
544544 −4.79135 + 2.30739i −0.205427 + 0.0989286i
545545 1.59668 + 6.99549i 0.0683940 + 0.299654i
546546 −6.95179 + 30.4578i −0.297509 + 1.30347i
547547 21.7331 + 10.4661i 0.929239 + 0.447498i 0.836361 0.548180i 0.184679π-0.184679\pi
0.0928783 + 0.995677i 0.470393π0.470393\pi
548548 1.35979 0.654840i 0.0580873 0.0279734i
549549 −0.0362138 + 0.158663i −0.00154557 + 0.00677157i
550550 −6.64177 −0.283206
551551 −24.1857 11.4186i −1.03035 0.486450i
552552 1.41705 0.0603134
553553 6.56613 28.7681i 0.279220 1.22334i
554554 −3.38036 + 1.62789i −0.143618 + 0.0691626i
555555 −6.93036 3.33748i −0.294177 0.141668i
556556 −1.94848 + 8.53684i −0.0826339 + 0.362043i
557557 4.05033 + 17.7456i 0.171618 + 0.751907i 0.985333 + 0.170643i 0.0545844π0.0545844\pi
−0.813715 + 0.581264i 0.802558π0.802558\pi
558558 −0.191725 + 0.0923300i −0.00811637 + 0.00390864i
559559 4.97724 6.24126i 0.210515 0.263977i
560560 −0.968004 + 1.21384i −0.0409057 + 0.0512941i
561561 11.6556 + 5.61303i 0.492099 + 0.236982i
562562 −15.2450 19.1167i −0.643072 0.806387i
563563 −31.5149 −1.32820 −0.664098 0.747646i 0.731184π-0.731184\pi
−0.664098 + 0.747646i 0.731184π0.731184\pi
564564 11.1830 + 14.0230i 0.470887 + 0.590474i
565565 1.83652 + 8.04631i 0.0772629 + 0.338511i
566566 −1.69060 7.40702i −0.0710614 0.311340i
567567 −17.8049 22.3267i −0.747737 0.937633i
568568 6.03736 0.253322
569569 −17.7477 22.2549i −0.744023 0.932975i 0.255404 0.966834i 0.417792π-0.417792\pi
−0.999427 + 0.0338594i 0.989220π0.989220\pi
570570 −3.85544 1.85668i −0.161486 0.0777678i
571571 −2.65790 + 3.33290i −0.111230 + 0.139478i −0.834330 0.551266i 0.814145π-0.814145\pi
0.723100 + 0.690743i 0.242717π0.242717\pi
572572 −4.97724 + 6.24126i −0.208109 + 0.260960i
573573 0.665747 0.320607i 0.0278120 0.0133935i
574574 2.80200 + 12.2764i 0.116953 + 0.512405i
575575 −0.860919 + 3.77193i −0.0359028 + 0.157300i
576576 −0.0301299 0.0145098i −0.00125541 0.000604576i
577577 −20.3474 + 9.79878i −0.847072 + 0.407929i −0.806490 0.591248i 0.798636π-0.798636\pi
−0.0405823 + 0.999176i 0.512921π0.512921\pi
578578 −2.51028 + 10.9982i −0.104414 + 0.457467i
579579 17.9824 0.747324
580580 −1.64491 + 2.09555i −0.0683011 + 0.0870131i
581581 39.8872 1.65480
582582 1.47129 6.44615i 0.0609870 0.267202i
583583 −5.34013 + 2.57167i −0.221166 + 0.106508i
584584 −11.0632 5.32774i −0.457797 0.220463i
585585 −0.0210402 + 0.0921833i −0.000869906 + 0.00381131i
586586 5.72375 + 25.0774i 0.236446 + 1.03594i
587587 30.1868 14.5372i 1.24594 0.600015i 0.309523 0.950892i 0.399831π-0.399831\pi
0.936422 + 0.350877i 0.114116π0.114116\pi
588588 −3.09435 + 3.88019i −0.127609 + 0.160016i
589589 19.7045 24.7087i 0.811910 1.01810i
590590 4.97399 + 2.39535i 0.204776 + 0.0986149i
591591 29.1490 + 36.5517i 1.19903 + 1.50354i
592592 8.92766 0.366925
593593 8.32767 + 10.4426i 0.341977 + 0.428825i 0.922844 0.385173i 0.125858π-0.125858\pi
−0.580868 + 0.813998i 0.697287π0.697287\pi
594594 −1.60583 7.03561i −0.0658881 0.288675i
595595 1.83724 + 8.04949i 0.0753197 + 0.329997i
596596 −2.95579 3.70644i −0.121074 0.151822i
597597 11.8485 0.484928
598598 2.89932 + 3.63563i 0.118562 + 0.148672i
599599 −0.824990 0.397294i −0.0337082 0.0162330i 0.416954 0.908928i 0.363098π-0.363098\pi
−0.450662 + 0.892695i 0.648812π0.648812\pi
600600 5.16384 6.47525i 0.210813 0.264351i
601601 3.60037 4.51472i 0.146862 0.184159i −0.702959 0.711230i 0.748138π-0.748138\pi
0.849821 + 0.527071i 0.176710π0.176710\pi
602602 3.94935 1.90191i 0.160964 0.0775160i
603603 −0.0531202 0.232735i −0.00216322 0.00947770i
604604 1.44508 6.33133i 0.0587996 0.257618i
605605 −4.03329 1.94233i −0.163977 0.0789669i
606606 −1.91728 + 0.923313i −0.0778842 + 0.0375070i
607607 3.33385 14.6065i 0.135317 0.592861i −0.861111 0.508416i 0.830231π-0.830231\pi
0.996428 0.0844449i 0.0269117π-0.0269117\pi
608608 4.96656 0.201421
609609 −18.1751 + 23.1544i −0.736492 + 0.938264i
610610 −2.40744 −0.0974743
611611 −13.0973 + 57.3829i −0.529859 + 2.32146i
612612 −0.160231 + 0.0771631i −0.00647695 + 0.00311914i
613613 21.5458 + 10.3759i 0.870228 + 0.419080i 0.815046 0.579396i 0.196712π-0.196712\pi
0.0551825 + 0.998476i 0.482426π0.482426\pi
614614 −0.403651 + 1.76851i −0.0162900 + 0.0713712i
615615 0.769252 + 3.37031i 0.0310192 + 0.135904i
616616 −3.94935 + 1.90191i −0.159124 + 0.0766300i
617617 −9.16964 + 11.4984i −0.369156 + 0.462907i −0.931364 0.364089i 0.881380π-0.881380\pi
0.562208 + 0.826996i 0.309952π0.309952\pi
618618 −1.96349 + 2.46214i −0.0789833 + 0.0990419i
619619 −20.6449 9.94208i −0.829790 0.399606i −0.0297537 0.999557i 0.509472π-0.509472\pi
−0.800036 + 0.599951i 0.795187π0.795187\pi
620620 −1.96268 2.46113i −0.0788233 0.0988413i
621621 −4.20375 −0.168691
622622 12.1020 + 15.1754i 0.485244 + 0.608477i
623623 −1.25158 5.48352i −0.0501434 0.219693i
624624 −2.21508 9.70490i −0.0886741 0.388507i
625625 13.3358 + 16.7226i 0.533433 + 0.668904i
626626 33.8847 1.35431
627627 −7.53288 9.44594i −0.300834 0.377234i
628628 −5.91161 2.84688i −0.235899 0.113603i
629629 29.6016 37.1192i 1.18029 1.48004i
630630 −0.0323717 + 0.0405929i −0.00128972 + 0.00161726i
631631 −11.8128 + 5.68872i −0.470258 + 0.226465i −0.653977 0.756514i 0.726901π-0.726901\pi
0.183719 + 0.982979i 0.441186π0.441186\pi
632632 2.09219 + 9.16650i 0.0832230 + 0.364624i
633633 2.26359 9.91742i 0.0899695 0.394182i
634634 −4.95317 2.38532i −0.196716 0.0947333i
635635 −5.65731 + 2.72442i −0.224503 + 0.108115i
636636 1.64465 7.20566i 0.0652144 0.285723i
637637 −16.2863 −0.645287
638638 −6.75135 + 3.31557i −0.267289 + 0.131265i
639639 0.201900 0.00798702
640640 0.110081 0.482295i 0.00435132 0.0190644i
641641 38.8282 18.6987i 1.53362 0.738553i 0.539017 0.842295i 0.318796π-0.318796\pi
0.994604 + 0.103742i 0.0330816π0.0330816\pi
642642 6.51316 + 3.13657i 0.257054 + 0.123791i
643643 1.92324 8.42626i 0.0758451 0.332299i −0.922743 0.385415i 0.874058π-0.874058\pi
0.998588 + 0.0531161i 0.0169153π0.0169153\pi
644644 0.568191 + 2.48941i 0.0223899 + 0.0980964i
645645 1.08424 0.522144i 0.0426920 0.0205594i
646646 16.4677 20.6498i 0.647913 0.812457i
647647 −2.98700 + 3.74558i −0.117431 + 0.147254i −0.837073 0.547092i 0.815735π-0.815735\pi
0.719641 + 0.694346i 0.244306π0.244306\pi
648648 8.19810 + 3.94800i 0.322052 + 0.155092i
649649 9.71835 + 12.1864i 0.381479 + 0.478359i
650650 27.1785 1.06603
651651 −21.6863 27.1938i −0.849953 1.06581i
652652 −1.25904 5.51622i −0.0493079 0.216032i
653653 −1.22812 5.38073i −0.0480599 0.210564i 0.945197 0.326502i 0.105870π-0.105870\pi
−0.993257 + 0.115938i 0.963013π0.963013\pi
654654 −15.7508 19.7509i −0.615905 0.772320i
655655 7.31958 0.286000
656656 −2.50161 3.13691i −0.0976713 0.122476i
657657 −0.369971 0.178169i −0.0144340 0.00695103i
658658 −20.1510 + 25.2685i −0.785567 + 0.985070i
659659 −1.14932 + 1.44120i −0.0447712 + 0.0561413i −0.803713 0.595017i 0.797145π-0.797145\pi
0.758942 + 0.651158i 0.225717π0.225717\pi
660660 −1.08424 + 0.522144i −0.0422041 + 0.0203244i
661661 5.80735 + 25.4436i 0.225880 + 0.989643i 0.952961 + 0.303092i 0.0980190π0.0980190\pi
−0.727082 + 0.686551i 0.759124π0.759124\pi
662662 3.03658 13.3041i 0.118020 0.517080i
663663 −47.6954 22.9689i −1.85233 0.892037i
664664 −11.4508 + 5.51441i −0.444377 + 0.214001i
665665 1.71583 7.51754i 0.0665371 0.291518i
666666 0.298556 0.0115688
667667 1.00782 + 4.26393i 0.0390231 + 0.165100i
668668 −12.0891 −0.467742
669669 −8.50153 + 37.2477i −0.328688 + 1.44008i
670670 3.18164 1.53220i 0.122917 0.0591939i
671671 −6.12397 2.94915i −0.236413 0.113851i
672672 1.21632 5.32903i 0.0469204 0.205572i
673673 −4.88021 21.3816i −0.188118 0.824200i −0.977608 0.210436i 0.932512π-0.932512\pi
0.789489 0.613764i 0.210345π-0.210345\pi
674674 −20.3325 + 9.79160i −0.783177 + 0.377158i
675675 −15.3188 + 19.2092i −0.589622 + 0.739363i
676676 12.2618 15.3758i 0.471608 0.591377i
677677 −9.15884 4.41066i −0.352003 0.169516i 0.249523 0.968369i 0.419726π-0.419726\pi
−0.601526 + 0.798853i 0.705440π0.705440\pi
678678 −18.1168 22.7177i −0.695771 0.872469i
679679 11.9143 0.457228
680680 −1.64028 2.05684i −0.0629018 0.0788764i
681681 −0.835355 3.65993i −0.0320109 0.140249i
682682 −1.97770 8.66486i −0.0757300 0.331795i
683683 12.7734 + 16.0173i 0.488760 + 0.612886i 0.963653 0.267158i 0.0860845π-0.0860845\pi
−0.474893 + 0.880044i 0.657513π0.657513\pi
684684 0.166090 0.00635062
685685 0.465513 + 0.583735i 0.0177863 + 0.0223033i
686686 11.7359 + 5.65170i 0.448078 + 0.215783i
687687 −10.0903 + 12.6528i −0.384967 + 0.482733i
688688 −0.870839 + 1.09200i −0.0332004 + 0.0416320i
689689 21.8521 10.5234i 0.832500 0.400911i
690690 0.155989 + 0.683434i 0.00593841 + 0.0260179i
691691 6.86393 30.0728i 0.261116 1.14402i −0.658927 0.752207i 0.728989π-0.728989\pi
0.920043 0.391817i 0.128154π-0.128154\pi
692692 −10.4877 5.05061i −0.398682 0.191995i
693693 −0.132073 + 0.0636031i −0.00501704 + 0.00241608i
694694 0.661565 2.89851i 0.0251127 0.110026i
695695 −4.33177 −0.164313
696696 2.01659 9.15987i 0.0764388 0.347204i
697697 −21.3372 −0.808204
698698 1.27708 5.59523i 0.0483380 0.211783i
699699 −18.4926 + 8.90557i −0.699455 + 0.336840i
700700 13.4460 + 6.47525i 0.508211 + 0.244741i
701701 4.60087 20.1577i 0.173773 0.761347i −0.810650 0.585530i 0.800886π-0.800886\pi
0.984423 0.175817i 0.0562566π-0.0562566\pi
702702 6.57116 + 28.7901i 0.248013 + 1.08661i
703703 −39.9487 + 19.2383i −1.50669 + 0.725586i
704704 0.870839 1.09200i 0.0328210 0.0411562i
705705 −5.53219 + 6.93714i −0.208354 + 0.261268i
706706 5.83121 + 2.80816i 0.219460 + 0.105687i
707707 −2.39081 2.99798i −0.0899156 0.112751i
708708 −19.4367 −0.730476
709709 −28.0695 35.1981i −1.05417 1.32189i −0.944712 0.327901i 0.893659π-0.893659\pi
−0.109461 0.993991i 0.534913π-0.534913\pi
710710 0.664596 + 2.91179i 0.0249419 + 0.109277i
711711 0.0699666 + 0.306544i 0.00262395 + 0.0114963i
712712 1.11740 + 1.40118i 0.0418763 + 0.0525113i
713713 −5.17722 −0.193888
714714 −18.1239 22.7267i −0.678272 0.850526i
715715 −3.55803 1.71346i −0.133063 0.0640796i
716716 −11.4442 + 14.3506i −0.427691 + 0.536307i
717717 15.6038 19.5665i 0.582733 0.730724i
718718 −9.67769 + 4.66053i −0.361168 + 0.173929i
719719 2.24249 + 9.82501i 0.0836309 + 0.366411i 0.999375 0.0353512i 0.0112550π-0.0112550\pi
−0.915744 + 0.401762i 0.868398π0.868398\pi
720720 0.00368129 0.0161288i 0.000137194 0.000601084i
721721 −5.11269 2.46214i −0.190407 0.0916950i
722722 −5.10552 + 2.45869i −0.190008 + 0.0915029i
723723 −3.56722 + 15.6290i −0.132666 + 0.581250i
724724 −9.89404 −0.367709
725725 23.1568 + 10.9329i 0.860023 + 0.406036i
726726 15.7608 0.584937
727727 −4.98758 + 21.8520i −0.184979 + 0.810447i 0.794234 + 0.607612i 0.207872π0.207872\pi
−0.979213 + 0.202835i 0.934985π0.934985\pi
728728 16.1610 7.78272i 0.598966 0.288447i
729729 −24.0490 11.5814i −0.890703 0.428940i
730730 1.35170 5.92219i 0.0500287 0.219190i
731731 1.65283 + 7.24151i 0.0611320 + 0.267837i
732732 7.63646 3.67753i 0.282252 0.135925i
733733 2.46035 3.08518i 0.0908749 0.113954i −0.734315 0.678809i 0.762497π-0.762497\pi
0.825190 + 0.564855i 0.191068π0.191068\pi
734734 11.8085 14.8074i 0.435859 0.546550i
735735 −2.21203 1.06526i −0.0815918 0.0392925i
736736 −0.507277 0.636105i −0.0186985 0.0234472i
737737 9.97032 0.367261
738738 −0.0836580 0.104904i −0.00307949 0.00386156i
739739 −1.38003 6.04632i −0.0507653 0.222417i 0.943182 0.332277i 0.107817π-0.107817\pi
−0.993947 + 0.109860i 0.964960π0.964960\pi
740740 0.982763 + 4.30577i 0.0361271 + 0.158283i
741741 30.8250 + 38.6533i 1.13239 + 1.41997i
742742 13.3181 0.488922
743743 30.3589 + 38.0689i 1.11376 + 1.39661i 0.908490 + 0.417907i 0.137236π0.137236\pi
0.205271 + 0.978705i 0.434192π0.434192\pi
744744 9.98524 + 4.80864i 0.366077 + 0.176293i
745745 1.46222 1.83357i 0.0535718 0.0671769i
746746 1.51759 1.90300i 0.0555629 0.0696737i
747747 −0.382934 + 0.184411i −0.0140108 + 0.00674726i
748748 −1.65283 7.24151i −0.0604333 0.264776i
749749 −2.89863 + 12.6997i −0.105914 + 0.464038i
750750 7.57282 + 3.64688i 0.276520 + 0.133165i
751751 −23.7677 + 11.4459i −0.867296 + 0.417668i −0.813968 0.580909i 0.802697π-0.802697\pi
−0.0533277 + 0.998577i 0.516983π0.516983\pi
752752 2.29155 10.0400i 0.0835644 0.366119i
753753 −10.3037 −0.375489
754754 27.6269 13.5675i 1.00611 0.494100i
755755 3.21264 0.116920
756756 −3.60827 + 15.8089i −0.131232 + 0.574963i
757757 −34.4086 + 16.5703i −1.25060 + 0.602259i −0.937673 0.347518i 0.887025π-0.887025\pi
−0.312930 + 0.949776i 0.601310π0.601310\pi
758758 15.4439 + 7.43740i 0.560949 + 0.270139i
759759 −0.440416 + 1.92959i −0.0159861 + 0.0700396i
760760 0.546722 + 2.39535i 0.0198317 + 0.0868884i
761761 −5.62055 + 2.70672i −0.203745 + 0.0981183i −0.532974 0.846132i 0.678926π-0.678926\pi
0.329229 + 0.944250i 0.393211π0.393211\pi
762762 13.7834 17.2839i 0.499320 0.626128i
763763 28.3820 35.5898i 1.02750 1.28844i
764764 −0.382244 0.184079i −0.0138291 0.00665975i
765765 −0.0548537 0.0687844i −0.00198324 0.00248691i
766766 −23.7774 −0.859111
767767 −39.7681 49.8676i −1.43594 1.80061i
768768 0.387560 + 1.69801i 0.0139849 + 0.0612717i
769769 6.26532 + 27.4502i 0.225933 + 0.989879i 0.952919 + 0.303226i 0.0980637π0.0980637\pi
−0.726985 + 0.686653i 0.759079π0.759079\pi
770770 −1.35203 1.69539i −0.0487237 0.0610976i
771771 46.5398 1.67609
772772 −6.43739 8.07223i −0.231687 0.290526i
773773 −31.5991 15.2173i −1.13654 0.547329i −0.231576 0.972817i 0.574388π-0.574388\pi
−0.904964 + 0.425488i 0.860103π0.860103\pi
774774 −0.0291223 + 0.0365183i −0.00104678 + 0.00131262i
775775 −18.8663 + 23.6575i −0.677696 + 0.849804i
776776 −3.42035 + 1.64715i −0.122783 + 0.0591293i
777777 10.8589 + 47.5757i 0.389559 + 1.70677i
778778 2.56505 11.2382i 0.0919614 0.402909i
779779 17.9537 + 8.64606i 0.643259 + 0.309777i
780780 4.43679 2.13664i 0.158862 0.0765041i
781781 −1.87640 + 8.22106i −0.0671430 + 0.294173i
782782 −4.32677 −0.154725
783783 −5.98234 + 27.1733i −0.213791 + 0.971094i
784784 2.84952 0.101769
785785 0.722283 3.16453i 0.0257794 0.112947i
786786 −23.2179 + 11.1812i −0.828157 + 0.398819i
787787 24.5984 + 11.8459i 0.876837 + 0.422262i 0.817468 0.575974i 0.195377π-0.195377\pi
0.0593688 + 0.998236i 0.481091π0.481091\pi
788788 5.97308 26.1698i 0.212782 0.932259i
789789 −9.05122 39.6560i −0.322232 1.41179i
790790 −4.19065 + 2.01811i −0.149097 + 0.0718011i
791791 32.6453 40.9359i 1.16073 1.45551i
792792 0.0291223 0.0365183i 0.00103482 0.00129762i
793793 25.0597 + 12.0681i 0.889894 + 0.428551i
794794 18.0708 + 22.6601i 0.641309 + 0.804176i
795795 3.65630 0.129676
796796 −4.24156 5.31875i −0.150338 0.188518i
797797 −9.11491 39.9350i −0.322867 1.41457i −0.832426 0.554136i 0.813049π-0.813049\pi
0.509560 0.860435i 0.329808π-0.329808\pi
798798 6.04090 + 26.4669i 0.213846 + 0.936919i
799799 −34.1457 42.8174i −1.20799 1.51477i
800800 −4.75527 −0.168124
801801 0.0373678 + 0.0468577i 0.00132033 + 0.00165564i
802802 −9.30669 4.48187i −0.328631 0.158260i
803803 10.6932 13.4088i 0.377355 0.473188i
804804 −7.75171 + 9.72034i −0.273382 + 0.342810i
805805 −1.13808 + 0.548071i −0.0401121 + 0.0193170i
806806 8.09286 + 35.4572i 0.285059 + 1.24892i
807807 6.04953 26.5047i 0.212953 0.933010i
808808 1.10082 + 0.530129i 0.0387268 + 0.0186499i
809809 38.8637 18.7158i 1.36638 0.658012i 0.400327 0.916372i 0.368896π-0.368896\pi
0.966049 + 0.258360i 0.0831821π0.0831821\pi
810810 −1.00165 + 4.38850i −0.0351943 + 0.154196i
811811 38.0001 1.33436 0.667182 0.744894i 0.267500π-0.267500\pi
0.667182 + 0.744894i 0.267500π0.267500\pi
812812 16.9003 0.130153i 0.593083 0.00456748i
813813 −0.382611 −0.0134187
814814 −2.77471 + 12.1568i −0.0972534 + 0.426095i
815815 2.52185 1.21446i 0.0883366 0.0425407i
816816 8.34499 + 4.01873i 0.292133 + 0.140684i
817817 1.54360 6.76296i 0.0540037 0.236606i
818818 −2.21669 9.71194i −0.0775047 0.339570i
819819 0.540451 0.260268i 0.0188849 0.00909449i
820820 1.23754 1.55183i 0.0432168 0.0541921i
821821 −7.61753 + 9.55208i −0.265854 + 0.333370i −0.896783 0.442470i 0.854102π-0.854102\pi
0.630930 + 0.775840i 0.282674π0.282674\pi
822822 −2.36831 1.14052i −0.0826045 0.0397802i
823823 22.8365 + 28.6361i 0.796030 + 0.998190i 0.999816 + 0.0191747i 0.00610387π0.00610387\pi
−0.203786 + 0.979015i 0.565325π0.565325\pi
824824 1.80814 0.0629896
825825 7.21242 + 9.04409i 0.251104 + 0.314875i
826826 −7.79351 34.1456i −0.271171 1.18808i
827827 5.74425 + 25.1672i 0.199747 + 0.875149i 0.971087 + 0.238726i 0.0767297π0.0767297\pi
−0.771340 + 0.636423i 0.780413π0.780413\pi
828828 −0.0169642 0.0212725i −0.000589547 0.000739269i
829829 −15.7732 −0.547825 −0.273913 0.961755i 0.588318π-0.588318\pi
−0.273913 + 0.961755i 0.588318π0.588318\pi
830830 −3.92009 4.91563i −0.136068 0.170624i
831831 5.88750 + 2.83527i 0.204235 + 0.0983544i
832832 −3.56353 + 4.46852i −0.123543 + 0.154918i
833833 9.44821 11.8477i 0.327361 0.410498i
834834 13.7405 6.61707i 0.475795 0.229131i
835835 −1.33078 5.83052i −0.0460535 0.201773i
836836 −1.54360 + 6.76296i −0.0533865 + 0.233902i
837837 −29.6218 14.2651i −1.02388 0.493074i
838838 −25.5445 + 12.3016i −0.882420 + 0.424951i
839839 −0.479893 + 2.10255i −0.0165677 + 0.0725880i −0.982536 0.186073i 0.940424π-0.940424\pi
0.965968 + 0.258661i 0.0832812π0.0832812\pi
840840 2.70406 0.0932988
841841 28.9966 0.446646i 0.999881 0.0154016i
842842 −9.51999 −0.328080
843843 −9.47627 + 41.5183i −0.326380 + 1.42996i
844844 −5.26221 + 2.53415i −0.181133 + 0.0872289i
845845 8.76546 + 4.22123i 0.301541 + 0.145215i
846846 0.0766335 0.335753i 0.00263471 0.0115434i
847847 6.31957 + 27.6879i 0.217143 + 0.951366i
848848 −3.82334 + 1.84123i −0.131294 + 0.0632279i
849849 −8.25027 + 10.3455i −0.283149 + 0.355057i
850850 −15.7671 + 19.7714i −0.540808 + 0.678152i
851851 6.54430 + 3.15157i 0.224336 + 0.108034i
852852 −6.55608 8.22106i −0.224607 0.281649i
853853 −21.6578 −0.741548 −0.370774 0.928723i 0.620908π-0.620908\pi
−0.370774 + 0.928723i 0.620908π0.620908\pi
854854 9.52251 + 11.9409i 0.325854 + 0.408608i
855855 0.0182833 + 0.0801045i 0.000625277 + 0.00273952i
856856 −0.923602 4.04656i −0.0315681 0.138309i
857857 −7.86892 9.86732i −0.268797 0.337061i 0.629053 0.777363i 0.283443π-0.283443\pi
−0.897850 + 0.440302i 0.854872π0.854872\pi
858858 13.9036 0.474661
859859 −12.1127 15.1888i −0.413280 0.518236i 0.531004 0.847369i 0.321815π-0.321815\pi
−0.944284 + 0.329133i 0.893244π0.893244\pi
860860 −0.622528 0.299794i −0.0212280 0.0102229i
861861 13.6740 17.1466i 0.466007 0.584355i
862862 −11.8307 + 14.8352i −0.402954 + 0.505289i
863863 41.3801 19.9276i 1.40860 0.678344i 0.433711 0.901052i 0.357204π-0.357204\pi
0.974885 + 0.222708i 0.0714896π0.0714896\pi
864864 −1.14972 5.03725i −0.0391142 0.171371i
865865 1.28139 5.61414i 0.0435686 0.190886i
866866 −25.5107 12.2853i −0.866890 0.417472i
867867 17.7022 8.52495i 0.601200 0.289523i
868868 −4.44385 + 19.4698i −0.150834 + 0.660847i
869869 −13.1323 −0.445482
870870 4.63975 0.0357318i 0.157302 0.00121142i
871871 −40.7992 −1.38243
872872 −3.22757 + 14.1409i −0.109299 + 0.478872i
873873 −0.114382 + 0.0550836i −0.00387125 + 0.00186430i
874874 3.64067 + 1.75325i 0.123147 + 0.0593047i
875875 −3.37022 + 14.7659i −0.113934 + 0.499179i
876876 4.75892 + 20.8502i 0.160789 + 0.704463i
877877 −7.29358 + 3.51240i −0.246287 + 0.118605i −0.552955 0.833211i 0.686500π-0.686500\pi
0.306669 + 0.951816i 0.400786π0.400786\pi
878878 −12.4049 + 15.5552i −0.418644 + 0.524962i
879879 27.9323 35.0260i 0.942134 1.18140i
880880 0.622528 + 0.299794i 0.0209854 + 0.0101060i
881881 1.87163 + 2.34695i 0.0630569 + 0.0790709i 0.812360 0.583157i 0.198183π-0.198183\pi
−0.749303 + 0.662228i 0.769611π0.769611\pi
882882 0.0952930 0.00320868
883883 −24.0764 30.1908i −0.810235 1.01600i −0.999420 0.0340614i 0.989156π-0.989156\pi
0.189184 0.981942i 0.439416π-0.439416\pi
884884 6.76347 + 29.6327i 0.227480 + 0.996655i
885885 −2.13961 9.37422i −0.0719221 0.315111i
886886 −22.1713 27.8019i −0.744859 0.934023i
887887 −29.4281 −0.988100 −0.494050 0.869433i 0.664484π-0.664484\pi
−0.494050 + 0.869433i 0.664484π0.664484\pi
888888 −9.69471 12.1568i −0.325333 0.407955i
889889 35.8903 + 17.2839i 1.20372 + 0.579682i
890890 −0.552776 + 0.693159i −0.0185291 + 0.0232347i
891891 −7.92394 + 9.93631i −0.265462 + 0.332879i
892892 19.7637 9.51770i 0.661738 0.318676i
893893 11.3811 + 49.8640i 0.380855 + 1.66864i
894894 −1.83731 + 8.04979i −0.0614489 + 0.269225i
895895 −8.18101 3.93977i −0.273461 0.131692i
896896 −2.82760 + 1.36170i −0.0944634 + 0.0454912i
897897 1.80221 7.89599i 0.0601740 0.263640i
898898 10.8511 0.362106
899899 −7.36769 + 33.4659i −0.245726 + 1.11615i
900900 −0.159025 −0.00530082
901901 −5.02172 + 22.0016i −0.167298 + 0.732979i
902902 5.04903 2.43148i 0.168114 0.0809596i
903903 −6.87850 3.31251i −0.228902 0.110233i
904904 −3.71240 + 16.2651i −0.123473 + 0.540969i
905905 −1.08914 4.77185i −0.0362043 0.158622i
906906 −10.1906 + 4.90754i −0.338560 + 0.163042i
907907 2.90939 3.64825i 0.0966046 0.121138i −0.731179 0.682185i 0.761030π-0.761030\pi
0.827784 + 0.561047i 0.189601π0.189601\pi
908908 −1.34388 + 1.68518i −0.0445983 + 0.0559245i
909909 0.0368134 + 0.0177284i 0.00122102 + 0.000588014i
910910 5.53258 + 6.93764i 0.183403 + 0.229981i
911911 −37.9571 −1.25758 −0.628788 0.777577i 0.716449π-0.716449\pi
−0.628788 + 0.777577i 0.716449π0.716449\pi
912912 −5.39328 6.76296i −0.178589 0.223944i
913913 −3.95007 17.3064i −0.130728 0.572758i
914914 −7.19540 31.5251i −0.238003 1.04276i
915915 2.61428 + 3.27820i 0.0864255 + 0.108374i
916916 9.29190 0.307013
917917 −28.9523 36.3050i −0.956089 1.19890i
918918 −24.7559 11.9218i −0.817066 0.393478i
919919 15.8113 19.8268i 0.521568 0.654026i −0.449373 0.893344i 0.648353π-0.648353\pi
0.970941 + 0.239318i 0.0769240π0.0769240\pi
920920 0.250949 0.314680i 0.00827355 0.0103747i
921921 2.84651 1.37081i 0.0937956 0.0451696i
922922 −5.65307 24.7677i −0.186174 0.815682i
923923 7.67836 33.6411i 0.252736 1.10731i
924924 6.87850 + 3.31251i 0.226286 + 0.108974i
925925 38.2492 18.4199i 1.25763 0.605641i
926926 −0.716678 + 3.13997i −0.0235515 + 0.103186i
927927 0.0604674 0.00198601
928928 −4.83373 + 2.37383i −0.158675 + 0.0779248i
929929 36.8642 1.20947 0.604737 0.796425i 0.293278π-0.293278\pi
0.604737 + 0.796425i 0.293278π0.293278\pi
930930 −1.22000 + 5.34517i −0.0400054 + 0.175275i
931931 −12.7508 + 6.14046i −0.417891 + 0.201246i
932932 10.6177 + 5.11321i 0.347794 + 0.167489i
933933 7.52255 32.9584i 0.246277 1.07901i
934934 −5.08605 22.2834i −0.166421 0.729136i
935935 3.31060 1.59430i 0.108268 0.0521392i
936936 −0.119170 + 0.149435i −0.00389521 + 0.00488444i
937937 −1.45551 + 1.82515i −0.0475493 + 0.0596249i −0.805038 0.593224i 0.797855π-0.797855\pi
0.757488 + 0.652849i 0.226426π0.226426\pi
938938 −20.1845 9.72034i −0.659047 0.317380i
939939 −36.7960 46.1408i −1.20079 1.50575i
940940 5.09448 0.166164
941941 5.47972 + 6.87136i 0.178634 + 0.224000i 0.863085 0.505059i 0.168529π-0.168529\pi
−0.684451 + 0.729059i 0.739958π0.739958\pi
942942 2.54293 + 11.1413i 0.0828532 + 0.363003i
943943 −0.726401 3.18257i −0.0236549 0.103639i
944944 6.95799 + 8.72505i 0.226463 + 0.283976i
945945 −8.02174 −0.260947
946946 −1.21632 1.52521i −0.0395458 0.0495889i
947947 11.4402 + 5.50930i 0.371756 + 0.179028i 0.610428 0.792072i 0.290998π-0.290998\pi
−0.238672 + 0.971100i 0.576712π0.576712\pi
948948 10.2101 12.8030i 0.331607 0.415822i
949949 −43.7572 + 54.8698i −1.42042 + 1.78115i
950950 21.2785 10.2472i 0.690365 0.332462i
951951 2.13065 + 9.33500i 0.0690911 + 0.302708i
952952 −3.71387 + 16.2715i −0.120367 + 0.527363i
953953 −49.0633 23.6277i −1.58932 0.765375i −0.590195 0.807261i 0.700949π-0.700949\pi
−0.999122 + 0.0418854i 0.986664π0.986664\pi
954954 −0.127859 + 0.0615737i −0.00413959 + 0.00199352i
955955 0.0467028 0.204618i 0.00151127 0.00662129i
956956 −14.3692 −0.464732
957957 11.8462 + 5.59287i 0.382934 + 0.180792i
958958 2.14546 0.0693165
959959 1.05400 4.61787i 0.0340354 0.149119i
960960 −0.776279 + 0.373836i −0.0250543 + 0.0120655i
961961 −8.55134 4.11811i −0.275850 0.132842i
962962 11.3543 49.7463i 0.366076 1.60388i
963963 −0.0308868 0.135324i −0.000995314 0.00436076i
964964 8.29280 3.99360i 0.267093 0.128625i
965965 3.18457 3.99332i 0.102515 0.128549i
966966 2.77281 3.47700i 0.0892138 0.111871i
967967 −44.6567 21.5055i −1.43606 0.691572i −0.455949 0.890006i 0.650700π-0.650700\pi
−0.980114 + 0.198434i 0.936414π0.936414\pi
968968 −5.64207 7.07493i −0.181343 0.227397i
969969 −46.0014 −1.47778
970970 −1.17093 1.46830i −0.0375962 0.0471442i
971971 6.13766 + 26.8909i 0.196967 + 0.862969i 0.972729 + 0.231944i 0.0745085π0.0745085\pi
−0.775762 + 0.631025i 0.782634π0.782634\pi
972972 −0.0773306 0.338807i −0.00248038 0.0108672i
973973 17.1341 + 21.4855i 0.549295 + 0.688794i
974974 21.7759 0.697746
975975 −29.5137 37.0090i −0.945194 1.18524i
976976 −4.38454 2.11149i −0.140346 0.0675870i
977977 −27.7654 + 34.8167i −0.888294 + 1.11389i 0.104556 + 0.994519i 0.466658π0.466658\pi
−0.992850 + 0.119367i 0.961914π0.961914\pi
978978 −6.14422 + 7.70461i −0.196470 + 0.246366i
979979 −2.25527 + 1.08608i −0.0720786 + 0.0347112i
980980 0.313678 + 1.37431i 0.0100201 + 0.0439008i
981981 −0.107936 + 0.472897i −0.00344612 + 0.0150984i
982982 35.0145 + 16.8621i 1.11736 + 0.538091i
983983 1.07817 0.519217i 0.0343882 0.0165605i −0.416611 0.909085i 0.636782π-0.636782\pi
0.450999 + 0.892525i 0.351068π0.351068\pi
984984 −1.55499 + 6.81287i −0.0495713 + 0.217186i
985985 13.2791 0.423106
986986 −6.15741 + 27.9685i −0.196092 + 0.890699i
987987 56.2904 1.79174
988988 6.31651 27.6744i 0.200955 0.880441i
989989 −1.02384 + 0.493058i −0.0325564 + 0.0156783i
990990 0.0208184 + 0.0100256i 0.000661652 + 0.000318635i
991991 −7.79435 + 34.1493i −0.247596 + 1.08479i 0.686321 + 0.727298i 0.259224π0.259224\pi
−0.933917 + 0.357490i 0.883633π0.883633\pi
992992 −1.41596 6.20373i −0.0449568 0.196969i
993993 −21.4137 + 10.3123i −0.679544 + 0.327251i
994994 11.8136 14.8138i 0.374706 0.469866i
995995 2.09829 2.63118i 0.0665204 0.0834139i
996996 19.9436 + 9.60433i 0.631937 + 0.304325i
997997 19.4359 + 24.3719i 0.615543 + 0.771866i 0.987710 0.156300i 0.0499566π-0.0499566\pi
−0.372167 + 0.928166i 0.621385π0.621385\pi
998998 39.2992 1.24400
999999 28.7599 + 36.0638i 0.909924 + 1.14101i
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 58.2.d.b.25.2 yes 12
3.2 odd 2 522.2.k.h.199.1 12
4.3 odd 2 464.2.u.h.257.1 12
29.6 even 14 1682.2.a.q.1.5 6
29.7 even 7 inner 58.2.d.b.7.2 12
29.14 odd 28 1682.2.b.i.1681.5 12
29.15 odd 28 1682.2.b.i.1681.8 12
29.23 even 7 1682.2.a.t.1.2 6
87.65 odd 14 522.2.k.h.181.1 12
116.7 odd 14 464.2.u.h.65.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
58.2.d.b.7.2 12 29.7 even 7 inner
58.2.d.b.25.2 yes 12 1.1 even 1 trivial
464.2.u.h.65.1 12 116.7 odd 14
464.2.u.h.257.1 12 4.3 odd 2
522.2.k.h.181.1 12 87.65 odd 14
522.2.k.h.199.1 12 3.2 odd 2
1682.2.a.q.1.5 6 29.6 even 14
1682.2.a.t.1.2 6 29.23 even 7
1682.2.b.i.1681.5 12 29.14 odd 28
1682.2.b.i.1681.8 12 29.15 odd 28