Properties

Label 150.2.h.a.139.2
Level 150150
Weight 22
Character 150.139
Analytic conductor 1.1981.198
Analytic rank 00
Dimension 88
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [150,2,Mod(19,150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(150, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("150.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 150=2352 150 = 2 \cdot 3 \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 150.h (of order 1010, degree 44, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 1.197756030321.19775603032
Analytic rank: 00
Dimension: 88
Relative dimension: 22 over Q(ζ10)\Q(\zeta_{10})
Coefficient field: Q(ζ20)\Q(\zeta_{20})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x8x6+x4x2+1 x^{8} - x^{6} + x^{4} - x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C10]\mathrm{SU}(2)[C_{10}]

Embedding invariants

Embedding label 139.2
Root 0.587785+0.809017i0.587785 + 0.809017i of defining polynomial
Character χ\chi == 150.139
Dual form 150.2.h.a.109.2

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+(0.587785+0.809017i)q2+(0.9510570.309017i)q3+(0.309017+0.951057i)q4+(1.70582+1.44575i)q5+(0.3090170.951057i)q6+1.72654iq7+(0.951057+0.309017i)q8+(0.809017+0.587785i)q9+(0.166977+2.22982i)q10+(1.975991.43564i)q11+(0.5877850.809017i)q12+(1.74524+2.40211i)q13+(1.39680+1.01484i)q14+(1.175571.90211i)q15+(0.8090170.587785i)q16+(3.180881.03353i)q17+1.00000iq18+(0.6942652.13673i)q19+(1.90211+1.17557i)q20+(0.5335311.64204i)q21+(2.32292+0.754763i)q22+(5.359417.37660i)q23+1.00000q24+(0.819639+4.93236i)q252.96917q26+(0.5877850.809017i)q27+(1.642040.533531i)q28+(2.898258.91991i)q29+(0.8478592.06909i)q30+(1.892945.82588i)q311.00000iq32+(2.32292+0.754763i)q33+(2.70582+1.96589i)q34+(2.49614+2.94517i)q35+(0.809017+0.587785i)q36+(1.94043+2.67078i)q37+(1.320571.81761i)q38+(2.402111.74524i)q39+(2.069090.847859i)q40+(4.95730+3.60169i)q41+(1.642040.533531i)q42+7.06997iq43+(0.754763+2.32292i)q44+(0.530249+2.17229i)q45+(2.817618.67171i)q46+(4.74794+1.54270i)q47+(0.587785+0.809017i)q48+4.01905q49+(3.50859+3.56227i)q503.34458q51+(1.745242.40211i)q52+(6.515772.11710i)q53+(0.3090170.951057i)q54+(5.44627+0.407836i)q55+(0.5335311.64204i)q56+2.24669iq57+(8.919912.89825i)q58+(0.1477630.107356i)q59+(2.172290.530249i)q60+(4.16750+3.02786i)q61+(3.600594.95579i)q62+(1.01484+1.39680i)q63+(0.8090170.587785i)q64+(6.44990+1.57440i)q65+(1.975991.43564i)q66+(11.3084+3.67432i)q67+3.34458iq68+(2.81761+8.67171i)q69+(3.849890.288294i)q70+(3.51098+10.8057i)q71+(0.9510570.309017i)q72+(3.953095.44095i)q733.30127q74+(0.7446614.94424i)q75+2.24669q76+(2.47870+3.41164i)q77+(2.82385+0.917526i)q78+(3.5095310.8012i)q79+(0.5302492.17229i)q80+(0.309017+0.951057i)q81+6.12756iq82+(8.691922.82417i)q83+(1.39680+1.01484i)q84+(6.92023+2.83573i)q85+(5.71972+4.15562i)q86+(5.51281+7.58773i)q87+(1.43564+1.97599i)q88+(6.56674+4.77102i)q89+(1.44575+1.70582i)q90+(4.147353.01323i)q91+(8.671712.81761i)q92+6.12569iq93+(1.54270+4.74794i)q94+(1.904884.64860i)q95+(0.309017+0.951057i)q96+(9.40211+3.05493i)q97+(2.36234+3.25148i)q98+2.44246q99+O(q100)q+(0.587785 + 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.70582 + 1.44575i) q^{5} +(-0.309017 - 0.951057i) q^{6} +1.72654i q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-0.166977 + 2.22982i) q^{10} +(1.97599 - 1.43564i) q^{11} +(0.587785 - 0.809017i) q^{12} +(-1.74524 + 2.40211i) q^{13} +(-1.39680 + 1.01484i) q^{14} +(-1.17557 - 1.90211i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(3.18088 - 1.03353i) q^{17} +1.00000i q^{18} +(-0.694265 - 2.13673i) q^{19} +(-1.90211 + 1.17557i) q^{20} +(0.533531 - 1.64204i) q^{21} +(2.32292 + 0.754763i) q^{22} +(-5.35941 - 7.37660i) q^{23} +1.00000 q^{24} +(0.819639 + 4.93236i) q^{25} -2.96917 q^{26} +(-0.587785 - 0.809017i) q^{27} +(-1.64204 - 0.533531i) q^{28} +(2.89825 - 8.91991i) q^{29} +(0.847859 - 2.06909i) q^{30} +(-1.89294 - 5.82588i) q^{31} -1.00000i q^{32} +(-2.32292 + 0.754763i) q^{33} +(2.70582 + 1.96589i) q^{34} +(-2.49614 + 2.94517i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-1.94043 + 2.67078i) q^{37} +(1.32057 - 1.81761i) q^{38} +(2.40211 - 1.74524i) q^{39} +(-2.06909 - 0.847859i) q^{40} +(4.95730 + 3.60169i) q^{41} +(1.64204 - 0.533531i) q^{42} +7.06997i q^{43} +(0.754763 + 2.32292i) q^{44} +(0.530249 + 2.17229i) q^{45} +(2.81761 - 8.67171i) q^{46} +(4.74794 + 1.54270i) q^{47} +(0.587785 + 0.809017i) q^{48} +4.01905 q^{49} +(-3.50859 + 3.56227i) q^{50} -3.34458 q^{51} +(-1.74524 - 2.40211i) q^{52} +(-6.51577 - 2.11710i) q^{53} +(0.309017 - 0.951057i) q^{54} +(5.44627 + 0.407836i) q^{55} +(-0.533531 - 1.64204i) q^{56} +2.24669i q^{57} +(8.91991 - 2.89825i) q^{58} +(-0.147763 - 0.107356i) q^{59} +(2.17229 - 0.530249i) q^{60} +(-4.16750 + 3.02786i) q^{61} +(3.60059 - 4.95579i) q^{62} +(-1.01484 + 1.39680i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-6.44990 + 1.57440i) q^{65} +(-1.97599 - 1.43564i) q^{66} +(-11.3084 + 3.67432i) q^{67} +3.34458i q^{68} +(2.81761 + 8.67171i) q^{69} +(-3.84989 - 0.288294i) q^{70} +(-3.51098 + 10.8057i) q^{71} +(-0.951057 - 0.309017i) q^{72} +(-3.95309 - 5.44095i) q^{73} -3.30127 q^{74} +(0.744661 - 4.94424i) q^{75} +2.24669 q^{76} +(2.47870 + 3.41164i) q^{77} +(2.82385 + 0.917526i) q^{78} +(3.50953 - 10.8012i) q^{79} +(-0.530249 - 2.17229i) q^{80} +(0.309017 + 0.951057i) q^{81} +6.12756i q^{82} +(8.69192 - 2.82417i) q^{83} +(1.39680 + 1.01484i) q^{84} +(6.92023 + 2.83573i) q^{85} +(-5.71972 + 4.15562i) q^{86} +(-5.51281 + 7.58773i) q^{87} +(-1.43564 + 1.97599i) q^{88} +(-6.56674 + 4.77102i) q^{89} +(-1.44575 + 1.70582i) q^{90} +(-4.14735 - 3.01323i) q^{91} +(8.67171 - 2.81761i) q^{92} +6.12569i q^{93} +(1.54270 + 4.74794i) q^{94} +(1.90488 - 4.64860i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(9.40211 + 3.05493i) q^{97} +(2.36234 + 3.25148i) q^{98} +2.44246 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+2q4+2q6+2q9+10q1120q132q142q16+10q178q192q2110q23+8q2410q25+4q2610q2822q2910q30+24q31++20q99+O(q100) 8 q + 2 q^{4} + 2 q^{6} + 2 q^{9} + 10 q^{11} - 20 q^{13} - 2 q^{14} - 2 q^{16} + 10 q^{17} - 8 q^{19} - 2 q^{21} - 10 q^{23} + 8 q^{24} - 10 q^{25} + 4 q^{26} - 10 q^{28} - 22 q^{29} - 10 q^{30} + 24 q^{31}+ \cdots + 20 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/150Z)×\left(\mathbb{Z}/150\mathbb{Z}\right)^\times.

nn 101101 127127
χ(n)\chi(n) 11 e(310)e\left(\frac{3}{10}\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 0.587785 + 0.809017i 0.415627 + 0.572061i
33 −0.951057 0.309017i −0.549093 0.178411i
44 −0.309017 + 0.951057i −0.154508 + 0.475528i
55 1.70582 + 1.44575i 0.762866 + 0.646557i
66 −0.309017 0.951057i −0.126156 0.388267i
77 1.72654i 0.652572i 0.945271 + 0.326286i 0.105797π0.105797\pi
−0.945271 + 0.326286i 0.894203π0.894203\pi
88 −0.951057 + 0.309017i −0.336249 + 0.109254i
99 0.809017 + 0.587785i 0.269672 + 0.195928i
1010 −0.166977 + 2.22982i −0.0528029 + 0.705133i
1111 1.97599 1.43564i 0.595785 0.432863i −0.248595 0.968607i 0.579969π-0.579969\pi
0.844380 + 0.535744i 0.179969π0.179969\pi
1212 0.587785 0.809017i 0.169679 0.233543i
1313 −1.74524 + 2.40211i −0.484042 + 0.666226i −0.979275 0.202534i 0.935082π-0.935082\pi
0.495234 + 0.868760i 0.335082π0.335082\pi
1414 −1.39680 + 1.01484i −0.373311 + 0.271226i
1515 −1.17557 1.90211i −0.303531 0.491123i
1616 −0.809017 0.587785i −0.202254 0.146946i
1717 3.18088 1.03353i 0.771477 0.250668i 0.103280 0.994652i 0.467066π-0.467066\pi
0.668197 + 0.743984i 0.267066π0.267066\pi
1818 1.00000i 0.235702i
1919 −0.694265 2.13673i −0.159275 0.490199i 0.839294 0.543678i 0.182969π-0.182969\pi
−0.998569 + 0.0534793i 0.982969π0.982969\pi
2020 −1.90211 + 1.17557i −0.425325 + 0.262866i
2121 0.533531 1.64204i 0.116426 0.358322i
2222 2.32292 + 0.754763i 0.495248 + 0.160916i
2323 −5.35941 7.37660i −1.11751 1.53813i −0.809854 0.586631i 0.800454π-0.800454\pi
−0.307660 0.951496i 0.599546π-0.599546\pi
2424 1.00000 0.204124
2525 0.819639 + 4.93236i 0.163928 + 0.986472i
2626 −2.96917 −0.582303
2727 −0.587785 0.809017i −0.113119 0.155695i
2828 −1.64204 0.533531i −0.310316 0.100828i
2929 2.89825 8.91991i 0.538192 1.65639i −0.198456 0.980110i 0.563593π-0.563593\pi
0.736648 0.676276i 0.236407π-0.236407\pi
3030 0.847859 2.06909i 0.154797 0.377763i
3131 −1.89294 5.82588i −0.339983 1.04636i −0.964215 0.265121i 0.914588π-0.914588\pi
0.624233 0.781239i 0.285412π-0.285412\pi
3232 1.00000i 0.176777i
3333 −2.32292 + 0.754763i −0.404369 + 0.131387i
3434 2.70582 + 1.96589i 0.464044 + 0.337148i
3535 −2.49614 + 2.94517i −0.421925 + 0.497825i
3636 −0.809017 + 0.587785i −0.134836 + 0.0979642i
3737 −1.94043 + 2.67078i −0.319006 + 0.439073i −0.938163 0.346193i 0.887474π-0.887474\pi
0.619158 + 0.785267i 0.287474π0.287474\pi
3838 1.32057 1.81761i 0.214225 0.294855i
3939 2.40211 1.74524i 0.384646 0.279462i
4040 −2.06909 0.847859i −0.327152 0.134058i
4141 4.95730 + 3.60169i 0.774200 + 0.562489i 0.903233 0.429151i 0.141187π-0.141187\pi
−0.129033 + 0.991640i 0.541187π0.541187\pi
4242 1.64204 0.533531i 0.253372 0.0823256i
4343 7.06997i 1.07816i 0.842255 + 0.539080i 0.181228π0.181228\pi
−0.842255 + 0.539080i 0.818772π0.818772\pi
4444 0.754763 + 2.32292i 0.113785 + 0.350193i
4545 0.530249 + 2.17229i 0.0790448 + 0.323826i
4646 2.81761 8.67171i 0.415434 1.27857i
4747 4.74794 + 1.54270i 0.692559 + 0.225026i 0.634085 0.773263i 0.281377π-0.281377\pi
0.0584733 + 0.998289i 0.481377π0.481377\pi
4848 0.587785 + 0.809017i 0.0848395 + 0.116772i
4949 4.01905 0.574150
5050 −3.50859 + 3.56227i −0.496190 + 0.503781i
5151 −3.34458 −0.468334
5252 −1.74524 2.40211i −0.242021 0.333113i
5353 −6.51577 2.11710i −0.895010 0.290806i −0.174834 0.984598i 0.555939π-0.555939\pi
−0.720176 + 0.693792i 0.755939π0.755939\pi
5454 0.309017 0.951057i 0.0420519 0.129422i
5555 5.44627 + 0.407836i 0.734374 + 0.0549926i
5656 −0.533531 1.64204i −0.0712961 0.219427i
5757 2.24669i 0.297581i
5858 8.91991 2.89825i 1.17124 0.380559i
5959 −0.147763 0.107356i −0.0192371 0.0139766i 0.578125 0.815948i 0.303785π-0.303785\pi
−0.597362 + 0.801972i 0.703785π0.703785\pi
6060 2.17229 0.530249i 0.280441 0.0684548i
6161 −4.16750 + 3.02786i −0.533593 + 0.387678i −0.821700 0.569920i 0.806974π-0.806974\pi
0.288107 + 0.957598i 0.406974π0.406974\pi
6262 3.60059 4.95579i 0.457276 0.629386i
6363 −1.01484 + 1.39680i −0.127857 + 0.175981i
6464 0.809017 0.587785i 0.101127 0.0734732i
6565 −6.44990 + 1.57440i −0.800012 + 0.195280i
6666 −1.97599 1.43564i −0.243228 0.176716i
6767 −11.3084 + 3.67432i −1.38154 + 0.448889i −0.903175 0.429272i 0.858770π-0.858770\pi
−0.478364 + 0.878162i 0.658770π0.658770\pi
6868 3.34458i 0.405589i
6969 2.81761 + 8.67171i 0.339200 + 1.04395i
7070 −3.84989 0.288294i −0.460150 0.0344577i
7171 −3.51098 + 10.8057i −0.416676 + 1.28240i 0.494066 + 0.869424i 0.335510π0.335510\pi
−0.910743 + 0.412974i 0.864490π0.864490\pi
7272 −0.951057 0.309017i −0.112083 0.0364180i
7373 −3.95309 5.44095i −0.462674 0.636816i 0.512387 0.858755i 0.328761π-0.328761\pi
−0.975061 + 0.221939i 0.928761π0.928761\pi
7474 −3.30127 −0.383764
7575 0.744661 4.94424i 0.0859860 0.570911i
7676 2.24669 0.257713
7777 2.47870 + 3.41164i 0.282474 + 0.388792i
7878 2.82385 + 0.917526i 0.319738 + 0.103889i
7979 3.50953 10.8012i 0.394852 1.21523i −0.534224 0.845343i 0.679396π-0.679396\pi
0.929076 0.369888i 0.120604π-0.120604\pi
8080 −0.530249 2.17229i −0.0592836 0.242869i
8181 0.309017 + 0.951057i 0.0343352 + 0.105673i
8282 6.12756i 0.676676i
8383 8.69192 2.82417i 0.954062 0.309993i 0.209697 0.977766i 0.432752π-0.432752\pi
0.744365 + 0.667773i 0.232752π0.232752\pi
8484 1.39680 + 1.01484i 0.152404 + 0.110728i
8585 6.92023 + 2.83573i 0.750604 + 0.307578i
8686 −5.71972 + 4.15562i −0.616774 + 0.448112i
8787 −5.51281 + 7.58773i −0.591035 + 0.813490i
8888 −1.43564 + 1.97599i −0.153040 + 0.210642i
8989 −6.56674 + 4.77102i −0.696073 + 0.505727i −0.878651 0.477465i 0.841556π-0.841556\pi
0.182578 + 0.983191i 0.441556π0.441556\pi
9090 −1.44575 + 1.70582i −0.152395 + 0.179809i
9191 −4.14735 3.01323i −0.434760 0.315872i
9292 8.67171 2.81761i 0.904088 0.293756i
9393 6.12569i 0.635205i
9494 1.54270 + 4.74794i 0.159117 + 0.489713i
9595 1.90488 4.64860i 0.195436 0.476937i
9696 −0.309017 + 0.951057i −0.0315389 + 0.0970668i
9797 9.40211 + 3.05493i 0.954640 + 0.310181i 0.744600 0.667511i 0.232640π-0.232640\pi
0.210040 + 0.977693i 0.432640π0.432640\pi
9898 2.36234 + 3.25148i 0.238632 + 0.328449i
9999 2.44246 0.245477
100100 −4.94424 0.744661i −0.494424 0.0744661i
101101 6.28885 0.625764 0.312882 0.949792i 0.398706π-0.398706\pi
0.312882 + 0.949792i 0.398706π0.398706\pi
102102 −1.96589 2.70582i −0.194652 0.267916i
103103 8.15958 + 2.65121i 0.803987 + 0.261231i 0.682049 0.731306i 0.261089π-0.261089\pi
0.121938 + 0.992538i 0.461089π0.461089\pi
104104 0.917526 2.82385i 0.0899708 0.276902i
105105 3.28408 2.02967i 0.320493 0.198076i
106106 −2.11710 6.51577i −0.205631 0.632867i
107107 9.09673i 0.879415i 0.898141 + 0.439707i 0.144918π0.144918\pi
−0.898141 + 0.439707i 0.855082π0.855082\pi
108108 0.951057 0.309017i 0.0915155 0.0297352i
109109 −11.0110 7.99994i −1.05466 0.766256i −0.0815673 0.996668i 0.525993π-0.525993\pi
−0.973093 + 0.230412i 0.925993π0.925993\pi
110110 2.87129 + 4.64584i 0.273767 + 0.442964i
111111 2.67078 1.94043i 0.253499 0.184178i
112112 1.01484 1.39680i 0.0958930 0.131985i
113113 4.85958 6.68863i 0.457150 0.629214i −0.516764 0.856128i 0.672864π-0.672864\pi
0.973915 + 0.226914i 0.0728636π0.0728636\pi
114114 −1.81761 + 1.32057i −0.170235 + 0.123683i
115115 1.52250 20.3315i 0.141974 1.89592i
116116 7.58773 + 5.51281i 0.704503 + 0.511851i
117117 −2.82385 + 0.917526i −0.261065 + 0.0848253i
118118 0.182645i 0.0168138i
119119 1.78444 + 5.49193i 0.163579 + 0.503444i
120120 1.70582 + 1.44575i 0.155719 + 0.131978i
121121 −1.55571 + 4.78797i −0.141428 + 0.435270i
122122 −4.89919 1.59184i −0.443552 0.144119i
123123 −3.60169 4.95730i −0.324753 0.446985i
124124 6.12569 0.550104
125125 −5.73279 + 9.59871i −0.512756 + 0.858534i
126126 −1.72654 −0.153813
127127 −10.4700 14.4107i −0.929064 1.27875i −0.960224 0.279232i 0.909920π-0.909920\pi
0.0311599 0.999514i 0.490080π-0.490080\pi
128128 0.951057 + 0.309017i 0.0840623 + 0.0273135i
129129 2.18474 6.72394i 0.192356 0.592010i
130130 −5.06488 4.29267i −0.444219 0.376492i
131131 3.19446 + 9.83155i 0.279102 + 0.858986i 0.988105 + 0.153781i 0.0491451π0.0491451\pi
−0.709003 + 0.705205i 0.750855π0.750855\pi
132132 2.44246i 0.212589i
133133 3.68915 1.19868i 0.319890 0.103939i
134134 −9.61949 6.98897i −0.830997 0.603755i
135135 0.166977 2.22982i 0.0143711 0.191913i
136136 −2.70582 + 1.96589i −0.232022 + 0.168574i
137137 9.45254 13.0103i 0.807585 1.11155i −0.184106 0.982906i 0.558939π-0.558939\pi
0.991691 0.128639i 0.0410610π-0.0410610\pi
138138 −5.35941 + 7.37660i −0.456224 + 0.627938i
139139 −13.3564 + 9.70399i −1.13287 + 0.823082i −0.986111 0.166090i 0.946886π-0.946886\pi
−0.146764 + 0.989172i 0.546886π0.546886\pi
140140 −2.02967 3.28408i −0.171539 0.277555i
141141 −4.03884 2.93439i −0.340132 0.247120i
142142 −10.8057 + 3.51098i −0.906792 + 0.294635i
143143 7.25210i 0.606451i
144144 −0.309017 0.951057i −0.0257514 0.0792547i
145145 17.8398 11.0256i 1.48152 0.915628i
146146 2.07826 6.39623i 0.171998 0.529355i
147147 −3.82234 1.24196i −0.315262 0.102435i
148148 −1.94043 2.67078i −0.159503 0.219537i
149149 −20.5325 −1.68209 −0.841045 0.540965i 0.818059π-0.818059\pi
−0.841045 + 0.540965i 0.818059π0.818059\pi
150150 4.43767 2.30371i 0.362334 0.188097i
151151 2.78808 0.226891 0.113445 0.993544i 0.463811π-0.463811\pi
0.113445 + 0.993544i 0.463811π0.463811\pi
152152 1.32057 + 1.81761i 0.107112 + 0.147428i
153153 3.18088 + 1.03353i 0.257159 + 0.0835560i
154154 −1.30313 + 4.01062i −0.105009 + 0.323185i
155155 5.19372 12.6746i 0.417170 1.01805i
156156 0.917526 + 2.82385i 0.0734608 + 0.226089i
157157 14.3416i 1.14458i −0.820051 0.572291i 0.806055π-0.806055\pi
0.820051 0.572291i 0.193945π-0.193945\pi
158158 10.8012 3.50953i 0.859298 0.279203i
159159 5.54264 + 4.02697i 0.439560 + 0.319359i
160160 1.44575 1.70582i 0.114296 0.134857i
161161 12.7360 9.25325i 1.00374 0.729259i
162162 −0.587785 + 0.809017i −0.0461808 + 0.0635624i
163163 −3.46979 + 4.77575i −0.271775 + 0.374066i −0.922988 0.384829i 0.874260π-0.874260\pi
0.651213 + 0.758895i 0.274260π0.274260\pi
164164 −4.95730 + 3.60169i −0.387100 + 0.281245i
165165 −5.05368 2.07086i −0.393428 0.161217i
166166 7.39378 + 5.37190i 0.573869 + 0.416940i
167167 −8.50651 + 2.76393i −0.658253 + 0.213879i −0.619050 0.785352i 0.712482π-0.712482\pi
−0.0392036 + 0.999231i 0.512482π0.512482\pi
168168 1.72654i 0.133206i
169169 1.29293 + 3.97922i 0.0994559 + 0.306094i
170170 1.77346 + 7.26538i 0.136018 + 0.557230i
171171 0.694265 2.13673i 0.0530918 0.163400i
172172 −6.72394 2.18474i −0.512695 0.166585i
173173 −15.2325 20.9658i −1.15811 1.59400i −0.717980 0.696064i 0.754933π-0.754933\pi
−0.440128 0.897935i 0.645067π-0.645067\pi
174174 −9.37895 −0.711016
175175 −8.51593 + 1.41514i −0.643744 + 0.106975i
176176 −2.44246 −0.184108
177177 0.107356 + 0.147763i 0.00806937 + 0.0111065i
178178 −7.71967 2.50827i −0.578613 0.188003i
179179 −0.0148362 + 0.0456612i −0.00110891 + 0.00341288i −0.951609 0.307310i 0.900571π-0.900571\pi
0.950501 + 0.310723i 0.100571π0.100571\pi
180180 −2.22982 0.166977i −0.166201 0.0124458i
181181 6.34558 + 19.5297i 0.471663 + 1.45163i 0.850406 + 0.526127i 0.176356π0.176356\pi
−0.378743 + 0.925502i 0.623644π0.623644\pi
182182 5.12641i 0.379995i
183183 4.89919 1.59184i 0.362158 0.117672i
184184 7.37660 + 5.35941i 0.543810 + 0.395101i
185185 −7.17130 + 1.75049i −0.527244 + 0.128699i
186186 −4.95579 + 3.60059i −0.363376 + 0.264008i
187187 4.80162 6.60886i 0.351129 0.483288i
188188 −2.93439 + 4.03884i −0.214012 + 0.294563i
189189 1.39680 1.01484i 0.101602 0.0738185i
190190 4.88046 1.19130i 0.354066 0.0864263i
191191 −1.95814 1.42267i −0.141686 0.102941i 0.514684 0.857380i 0.327909π-0.327909\pi
−0.656370 + 0.754439i 0.727909π0.727909\pi
192192 −0.951057 + 0.309017i −0.0686366 + 0.0223014i
193193 13.3764i 0.962857i 0.876485 + 0.481429i 0.159882π0.159882\pi
−0.876485 + 0.481429i 0.840118π0.840118\pi
194194 3.05493 + 9.40211i 0.219331 + 0.675032i
195195 6.62074 + 0.495785i 0.474121 + 0.0355039i
196196 −1.24196 + 3.82234i −0.0887111 + 0.273025i
197197 −17.9974 5.84770i −1.28226 0.416631i −0.412884 0.910783i 0.635479π-0.635479\pi
−0.869376 + 0.494152i 0.835479π0.835479\pi
198198 1.43564 + 1.97599i 0.102027 + 0.140428i
199199 22.6784 1.60763 0.803815 0.594879i 0.202800π-0.202800\pi
0.803815 + 0.594879i 0.202800π0.202800\pi
200200 −2.30371 4.43767i −0.162897 0.313791i
201201 11.8903 0.838680
202202 3.69649 + 5.08779i 0.260084 + 0.357975i
203203 15.4006 + 5.00396i 1.08091 + 0.351209i
204204 1.03353 3.18088i 0.0723616 0.222706i
205205 3.24913 + 13.3108i 0.226929 + 0.929668i
206206 2.65121 + 8.15958i 0.184718 + 0.568505i
207207 9.11798i 0.633743i
208208 2.82385 0.917526i 0.195799 0.0636189i
209209 −4.43945 3.22545i −0.307083 0.223109i
210210 3.57237 + 1.46386i 0.246517 + 0.101016i
211211 −2.07008 + 1.50400i −0.142510 + 0.103540i −0.656756 0.754103i 0.728072π-0.728072\pi
0.514246 + 0.857643i 0.328072π0.328072\pi
212212 4.02697 5.54264i 0.276573 0.380670i
213213 6.67828 9.19186i 0.457588 0.629816i
214214 −7.35941 + 5.34693i −0.503079 + 0.365508i
215215 −10.2214 + 12.0601i −0.697092 + 0.822491i
216216 0.809017 + 0.587785i 0.0550466 + 0.0399937i
217217 10.0586 3.26825i 0.682824 0.221863i
218218 13.6103i 0.921807i
219219 2.07826 + 6.39623i 0.140436 + 0.432217i
220220 −2.07086 + 5.05368i −0.139618 + 0.340719i
221221 −3.06873 + 9.44459i −0.206425 + 0.635312i
222222 3.13969 + 1.02015i 0.210722 + 0.0684678i
223223 10.9647 + 15.0916i 0.734251 + 1.01061i 0.998929 + 0.0462729i 0.0147344π0.0147344\pi
−0.264678 + 0.964337i 0.585266π0.585266\pi
224224 1.72654 0.115359
225225 −2.23607 + 4.47214i −0.149071 + 0.298142i
226226 8.26761 0.549953
227227 6.50181 + 8.94897i 0.431540 + 0.593964i 0.968306 0.249767i 0.0803541π-0.0803541\pi
−0.536766 + 0.843731i 0.680354π0.680354\pi
228228 −2.13673 0.694265i −0.141508 0.0459788i
229229 −8.35868 + 25.7254i −0.552357 + 1.69998i 0.150466 + 0.988615i 0.451923π0.451923\pi
−0.702823 + 0.711365i 0.748077π0.748077\pi
230230 17.3434 10.7188i 1.14359 0.706778i
231231 −1.30313 4.01062i −0.0857397 0.263880i
232232 9.37895i 0.615758i
233233 17.3828 5.64803i 1.13879 0.370015i 0.321879 0.946781i 0.395686π-0.395686\pi
0.816909 + 0.576766i 0.195686π0.195686\pi
234234 −2.40211 1.74524i −0.157031 0.114090i
235235 5.86878 + 9.49589i 0.382837 + 0.619443i
236236 0.147763 0.107356i 0.00961854 0.00698828i
237237 −6.67551 + 9.18806i −0.433621 + 0.596828i
238238 −3.39420 + 4.67171i −0.220013 + 0.302822i
239239 −2.07768 + 1.50953i −0.134394 + 0.0976431i −0.652951 0.757400i 0.726469π-0.726469\pi
0.518557 + 0.855043i 0.326469π0.326469\pi
240240 −0.166977 + 2.22982i −0.0107783 + 0.143935i
241241 −10.7918 7.84068i −0.695159 0.505063i 0.183193 0.983077i 0.441357π-0.441357\pi
−0.878352 + 0.478014i 0.841357π0.841357\pi
242242 −4.78797 + 1.55571i −0.307783 + 0.100005i
243243 1.00000i 0.0641500i
244244 −1.59184 4.89919i −0.101907 0.313638i
245245 6.85577 + 5.81053i 0.437999 + 0.371221i
246246 1.89352 5.82766i 0.120726 0.371558i
247247 6.34432 + 2.06140i 0.403680 + 0.131163i
248248 3.60059 + 4.95579i 0.228638 + 0.314693i
249249 −9.13922 −0.579175
250250 −11.1352 + 1.00406i −0.704250 + 0.0635021i
251251 −14.3409 −0.905191 −0.452595 0.891716i 0.649502π-0.649502\pi
−0.452595 + 0.891716i 0.649502π0.649502\pi
252252 −1.01484 1.39680i −0.0639287 0.0879903i
253253 −21.1803 6.88191i −1.33160 0.432662i
254254 5.50441 16.9408i 0.345378 1.06296i
255255 −5.70524 4.83541i −0.357276 0.302805i
256256 0.309017 + 0.951057i 0.0193136 + 0.0594410i
257257 16.0010i 0.998117i −0.866568 0.499059i 0.833679π-0.833679\pi
0.866568 0.499059i 0.166321π-0.166321\pi
258258 6.72394 2.18474i 0.418614 0.136016i
259259 −4.61121 3.35024i −0.286527 0.208174i
260260 0.495785 6.62074i 0.0307473 0.410601i
261261 7.58773 5.51281i 0.469669 0.341234i
262262 −6.07623 + 8.36321i −0.375391 + 0.516681i
263263 −11.6725 + 16.0658i −0.719754 + 0.990657i 0.279778 + 0.960065i 0.409739π0.409739\pi
−0.999532 + 0.0305919i 0.990261π0.990261\pi
264264 1.97599 1.43564i 0.121614 0.0883578i
265265 −8.05393 13.0315i −0.494749 0.800521i
266266 3.13818 + 2.28002i 0.192414 + 0.139797i
267267 7.71967 2.50827i 0.472436 0.153504i
268268 11.8903i 0.726318i
269269 0.822243 + 2.53060i 0.0501331 + 0.154294i 0.972989 0.230852i 0.0741513π-0.0741513\pi
−0.922856 + 0.385146i 0.874151π0.874151\pi
270270 1.90211 1.17557i 0.115759 0.0715429i
271271 −4.15958 + 12.8019i −0.252677 + 0.777659i 0.741602 + 0.670840i 0.234066π0.234066\pi
−0.994279 + 0.106818i 0.965934π0.965934\pi
272272 −3.18088 1.03353i −0.192869 0.0626670i
273273 3.01323 + 4.14735i 0.182369 + 0.251009i
274274 16.0816 0.971527
275275 8.70072 + 8.56961i 0.524673 + 0.516767i
276276 −9.11798 −0.548838
277277 −3.14317 4.32620i −0.188855 0.259936i 0.704082 0.710119i 0.251359π-0.251359\pi
−0.892936 + 0.450183i 0.851359π0.851359\pi
278278 −15.7014 5.10169i −0.941706 0.305979i
279279 1.89294 5.82588i 0.113328 0.348786i
280280 1.46386 3.57237i 0.0874826 0.213490i
281281 −5.16582 15.8988i −0.308167 0.948441i −0.978476 0.206359i 0.933838π-0.933838\pi
0.670309 0.742082i 0.266162π-0.266162\pi
282282 4.99228i 0.297286i
283283 13.4698 4.37660i 0.800696 0.260162i 0.120044 0.992769i 0.461697π-0.461697\pi
0.680652 + 0.732607i 0.261697π0.261697\pi
284284 −9.19186 6.67828i −0.545436 0.396283i
285285 −3.24814 + 3.83245i −0.192403 + 0.227015i
286286 −5.86707 + 4.26268i −0.346927 + 0.252057i
287287 −6.21847 + 8.55899i −0.367065 + 0.505221i
288288 0.587785 0.809017i 0.0346356 0.0476718i
289289 −4.70347 + 3.41727i −0.276675 + 0.201016i
290290 19.4059 + 7.95202i 1.13955 + 0.466959i
291291 −7.99792 5.81083i −0.468846 0.340637i
292292 6.39623 2.07826i 0.374311 0.121621i
293293 12.4643i 0.728175i 0.931365 + 0.364088i 0.118619π0.118619\pi
−0.931365 + 0.364088i 0.881381π0.881381\pi
294294 −1.24196 3.82234i −0.0724323 0.222924i
295295 −0.0968473 0.396757i −0.00563867 0.0231001i
296296 1.02015 3.13969i 0.0592948 0.182491i
297297 −2.32292 0.754763i −0.134790 0.0437958i
298298 −12.0687 16.6112i −0.699122 0.962259i
299299 27.0729 1.56566
300300 4.47214 + 2.23607i 0.258199 + 0.129099i
301301 −12.2066 −0.703577
302302 1.63879 + 2.25560i 0.0943019 + 0.129795i
303303 −5.98105 1.94336i −0.343602 0.111643i
304304 −0.694265 + 2.13673i −0.0398188 + 0.122550i
305305 −11.4865 0.860153i −0.657716 0.0492522i
306306 1.03353 + 3.18088i 0.0590830 + 0.181839i
307307 23.9974i 1.36960i 0.728730 + 0.684801i 0.240111π0.240111\pi
−0.728730 + 0.684801i 0.759889π0.759889\pi
308308 −4.01062 + 1.30313i −0.228526 + 0.0742527i
309309 −6.94095 5.04290i −0.394857 0.286880i
310310 13.3068 3.24814i 0.755774 0.184482i
311311 11.2931 8.20494i 0.640375 0.465260i −0.219604 0.975589i 0.570477π-0.570477\pi
0.859979 + 0.510329i 0.170477π0.170477\pi
312312 −1.74524 + 2.40211i −0.0988046 + 0.135993i
313313 5.65884 7.78872i 0.319856 0.440245i −0.618567 0.785732i 0.712286π-0.712286\pi
0.938423 + 0.345488i 0.112286π0.112286\pi
314314 11.6026 8.42976i 0.654771 0.475719i
315315 −3.75055 + 0.915497i −0.211319 + 0.0515824i
316316 9.18806 + 6.67551i 0.516869 + 0.375527i
317317 −0.529086 + 0.171911i −0.0297164 + 0.00965546i −0.323838 0.946113i 0.604973π-0.604973\pi
0.294121 + 0.955768i 0.404973π0.404973\pi
318318 6.85108i 0.384190i
319319 −7.07888 21.7866i −0.396341 1.21981i
320320 2.22982 + 0.166977i 0.124651 + 0.00933432i
321321 2.81105 8.65151i 0.156897 0.482880i
322322 14.9721 + 4.86472i 0.834361 + 0.271100i
323323 −4.41675 6.07914i −0.245755 0.338252i
324324 −1.00000 −0.0555556
325325 −13.2786 6.63928i −0.736562 0.368281i
326326 −5.90315 −0.326945
327327 7.99994 + 11.0110i 0.442398 + 0.608908i
328328 −5.82766 1.89352i −0.321778 0.104552i
329329 −2.66354 + 8.19753i −0.146846 + 0.451944i
330330 −1.29511 5.30573i −0.0712936 0.292071i
331331 −3.57383 10.9991i −0.196435 0.604565i −0.999957 0.00928983i 0.997043π-0.997043\pi
0.803522 0.595276i 0.202957π-0.202957\pi
332332 9.13922i 0.501580i
333333 −3.13969 + 1.02015i −0.172054 + 0.0559037i
334334 −7.23607 5.25731i −0.395940 0.287667i
335335 −24.6022 10.0813i −1.34416 0.550802i
336336 −1.39680 + 1.01484i −0.0762018 + 0.0553639i
337337 17.5611 24.1708i 0.956613 1.31667i 0.00808669 0.999967i 0.497426π-0.497426\pi
0.948526 0.316698i 0.102574π-0.102574\pi
338338 −2.45929 + 3.38493i −0.133768 + 0.184116i
339339 −6.68863 + 4.85958i −0.363277 + 0.263936i
340340 −4.83541 + 5.70524i −0.262237 + 0.309410i
341341 −12.1043 8.79432i −0.655487 0.476239i
342342 2.13673 0.694265i 0.115541 0.0375416i
343343 19.0249i 1.02725i
344344 −2.18474 6.72394i −0.117793 0.362530i
345345 −7.73076 + 18.8659i −0.416210 + 1.01571i
346346 8.00822 24.6468i 0.430524 1.32502i
347347 −4.03884 1.31230i −0.216816 0.0704479i 0.198595 0.980082i 0.436362π-0.436362\pi
−0.415411 + 0.909634i 0.636362π0.636362\pi
348348 −5.51281 7.58773i −0.295518 0.406745i
349349 19.3711 1.03691 0.518456 0.855104i 0.326507π-0.326507\pi
0.518456 + 0.855104i 0.326507π0.326507\pi
350350 −6.15041 6.05774i −0.328753 0.323800i
351351 2.96917 0.158483
352352 −1.43564 1.97599i −0.0765201 0.105321i
353353 0.231368 + 0.0751761i 0.0123145 + 0.00400122i 0.315168 0.949036i 0.397939π-0.397939\pi
−0.302853 + 0.953037i 0.597939π0.597939\pi
354354 −0.0564404 + 0.173706i −0.00299977 + 0.00923235i
355355 −21.6114 + 13.3566i −1.14701 + 0.708892i
356356 −2.50827 7.71967i −0.132938 0.409142i
357357 5.77455i 0.305622i
358358 −0.0456612 + 0.0148362i −0.00241327 + 0.000784119i
359359 17.0243 + 12.3689i 0.898508 + 0.652805i 0.938082 0.346412i 0.112600π-0.112600\pi
−0.0395740 + 0.999217i 0.512600π0.512600\pi
360360 −1.17557 1.90211i −0.0619580 0.100250i
361361 11.2877 8.20101i 0.594090 0.431632i
362362 −12.0700 + 16.6129i −0.634385 + 0.873156i
363363 2.95913 4.07289i 0.155314 0.213771i
364364 4.14735 3.01323i 0.217380 0.157936i
365365 1.12299 14.9964i 0.0587799 0.784950i
366366 4.16750 + 3.02786i 0.217839 + 0.158269i
367367 7.45000 2.42065i 0.388887 0.126357i −0.108046 0.994146i 0.534459π-0.534459\pi
0.496933 + 0.867789i 0.334459π0.334459\pi
368368 9.11798i 0.475307i
369369 1.89352 + 5.82766i 0.0985727 + 0.303376i
370370 −5.63136 4.77279i −0.292761 0.248126i
371371 3.65527 11.2498i 0.189772 0.584058i
372372 −5.82588 1.89294i −0.302058 0.0981446i
373373 −9.12569 12.5604i −0.472511 0.650355i 0.504534 0.863392i 0.331664π-0.331664\pi
−0.977044 + 0.213037i 0.931664π0.931664\pi
374374 8.16901 0.422409
375375 8.41837 7.35738i 0.434723 0.379934i
376376 −4.99228 −0.257457
377377 16.3685 + 22.5293i 0.843020 + 1.16032i
378378 1.64204 + 0.533531i 0.0844574 + 0.0274419i
379379 3.35706 10.3320i 0.172441 0.530718i −0.827067 0.562104i 0.809992π-0.809992\pi
0.999507 + 0.0313859i 0.00999209π0.00999209\pi
380380 3.83245 + 3.24814i 0.196600 + 0.166626i
381381 5.50441 + 16.9408i 0.282000 + 0.867906i
382382 2.42040i 0.123838i
383383 −9.12648 + 2.96537i −0.466341 + 0.151523i −0.532756 0.846269i 0.678844π-0.678844\pi
0.0664152 + 0.997792i 0.478844π0.478844\pi
384384 −0.809017 0.587785i −0.0412850 0.0299953i
385385 −0.704147 + 9.40321i −0.0358866 + 0.479232i
386386 −10.8218 + 7.86247i −0.550814 + 0.400189i
387387 −4.15562 + 5.71972i −0.211242 + 0.290750i
388388 −5.81083 + 7.99792i −0.295000 + 0.406033i
389389 28.1716 20.4679i 1.42836 1.03776i 0.438037 0.898957i 0.355674π-0.355674\pi
0.990320 0.138805i 0.0443261π-0.0443261\pi
390390 3.49047 + 5.64771i 0.176747 + 0.285983i
391391 −24.6716 17.9250i −1.24770 0.906504i
392392 −3.82234 + 1.24196i −0.193058 + 0.0627282i
393393 10.3375i 0.521458i
394394 −5.84770 17.9974i −0.294603 0.906695i
395395 21.6024 13.3510i 1.08694 0.671763i
396396 −0.754763 + 2.32292i −0.0379283 + 0.116731i
397397 15.2224 + 4.94607i 0.763992 + 0.248236i 0.664991 0.746851i 0.268435π-0.268435\pi
0.0990008 + 0.995087i 0.468435π0.468435\pi
398398 13.3300 + 18.3472i 0.668175 + 0.919663i
399399 −3.87901 −0.194193
400400 2.23607 4.47214i 0.111803 0.223607i
401401 11.5284 0.575701 0.287850 0.957675i 0.407059π-0.407059\pi
0.287850 + 0.957675i 0.407059π0.407059\pi
402402 6.98897 + 9.61949i 0.348578 + 0.479776i
403403 17.2981 + 5.62048i 0.861678 + 0.279976i
404404 −1.94336 + 5.98105i −0.0966858 + 0.297568i
405405 −0.847859 + 2.06909i −0.0421304 + 0.102814i
406406 5.00396 + 15.4006i 0.248342 + 0.764319i
407407 8.06322i 0.399679i
408408 3.18088 1.03353i 0.157477 0.0511674i
409409 −11.8041 8.57616i −0.583674 0.424064i 0.256373 0.966578i 0.417473π-0.417473\pi
−0.840047 + 0.542514i 0.817473π0.817473\pi
410410 −8.85889 + 10.4525i −0.437510 + 0.516213i
411411 −13.0103 + 9.45254i −0.641751 + 0.466260i
412412 −5.04290 + 6.94095i −0.248446 + 0.341956i
413413 0.185355 0.255119i 0.00912071 0.0125536i
414414 7.37660 5.35941i 0.362540 0.263401i
415415 18.9099 + 7.74877i 0.928249 + 0.380372i
416416 2.40211 + 1.74524i 0.117773 + 0.0855673i
417417 15.7014 5.10169i 0.768900 0.249831i
418418 5.48746i 0.268400i
419419 4.35926 + 13.4164i 0.212964 + 0.655434i 0.999292 + 0.0376256i 0.0119794π0.0119794\pi
−0.786328 + 0.617809i 0.788021π0.788021\pi
420420 0.915497 + 3.75055i 0.0446717 + 0.183008i
421421 −3.98266 + 12.2574i −0.194103 + 0.597388i 0.805883 + 0.592075i 0.201691π0.201691\pi
−0.999986 + 0.00531260i 0.998309π0.998309\pi
422422 −2.43352 0.790700i −0.118462 0.0384907i
423423 2.93439 + 4.03884i 0.142675 + 0.196375i
424424 6.85108 0.332718
425425 7.70492 + 14.8421i 0.373744 + 0.719949i
426426 11.3618 0.550479
427427 −5.22774 7.19536i −0.252988 0.348208i
428428 −8.65151 2.81105i −0.418186 0.135877i
429429 2.24102 6.89716i 0.108198 0.332998i
430430 −15.7648 1.18053i −0.760246 0.0569300i
431431 −7.15141 22.0098i −0.344471 1.06017i −0.961866 0.273520i 0.911812π-0.911812\pi
0.617395 0.786653i 0.288188π-0.288188\pi
432432 1.00000i 0.0481125i
433433 −22.3599 + 7.26516i −1.07455 + 0.349142i −0.792257 0.610188i 0.791094π-0.791094\pi
−0.282290 + 0.959329i 0.591094π0.591094\pi
434434 8.55638 + 6.21658i 0.410720 + 0.298405i
435435 −20.3738 + 4.97318i −0.976848 + 0.238446i
436436 11.0110 7.99994i 0.527330 0.383128i
437437 −12.0409 + 16.5729i −0.575996 + 0.792791i
438438 −3.95309 + 5.44095i −0.188886 + 0.259979i
439439 1.61188 1.17110i 0.0769309 0.0558936i −0.548655 0.836049i 0.684860π-0.684860\pi
0.625586 + 0.780155i 0.284860π0.284860\pi
440440 −5.30573 + 1.29511i −0.252941 + 0.0617421i
441441 3.25148 + 2.36234i 0.154832 + 0.112492i
442442 −9.44459 + 3.06873i −0.449233 + 0.145965i
443443 13.0327i 0.619202i 0.950867 + 0.309601i 0.100195π0.100195\pi
−0.950867 + 0.309601i 0.899805π0.899805\pi
444444 1.02015 + 3.13969i 0.0484140 + 0.149003i
445445 −18.0993 1.35535i −0.857991 0.0642496i
446446 −5.76449 + 17.7413i −0.272956 + 0.840073i
447447 19.5276 + 6.34490i 0.923623 + 0.300103i
448448 1.01484 + 1.39680i 0.0479465 + 0.0659927i
449449 −12.0846 −0.570310 −0.285155 0.958481i 0.592045π-0.592045\pi
−0.285155 + 0.958481i 0.592045π0.592045\pi
450450 −4.93236 + 0.819639i −0.232514 + 0.0386381i
451451 14.9663 0.704737
452452 4.85958 + 6.68863i 0.228575 + 0.314607i
453453 −2.65162 0.861564i −0.124584 0.0404798i
454454 −3.41820 + 10.5201i −0.160424 + 0.493735i
455455 −2.71827 11.1360i −0.127434 0.522065i
456456 −0.694265 2.13673i −0.0325119 0.100061i
457457 5.62762i 0.263249i 0.991300 + 0.131624i 0.0420193π0.0420193\pi
−0.991300 + 0.131624i 0.957981π0.957981\pi
458458 −25.7254 + 8.35868i −1.20207 + 0.390575i
459459 −2.70582 1.96589i −0.126297 0.0917600i
460460 18.8659 + 7.73076i 0.879628 + 0.360448i
461461 3.74321 2.71960i 0.174339 0.126664i −0.497194 0.867639i 0.665636π-0.665636\pi
0.671533 + 0.740975i 0.265636π0.265636\pi
462462 2.47870 3.41164i 0.115320 0.158724i
463463 3.38513 4.65923i 0.157320 0.216533i −0.723080 0.690764i 0.757274π-0.757274\pi
0.880400 + 0.474232i 0.157274π0.157274\pi
464464 −7.58773 + 5.51281i −0.352251 + 0.255926i
465465 −8.85620 + 10.4493i −0.410696 + 0.484576i
466466 14.7867 + 10.7432i 0.684982 + 0.497669i
467467 23.3787 7.59619i 1.08184 0.351510i 0.286749 0.958006i 0.407425π-0.407425\pi
0.795087 + 0.606496i 0.207425π0.207425\pi
468468 2.96917i 0.137250i
469469 −6.34386 19.5244i −0.292932 0.901553i
470470 −4.23275 + 10.3295i −0.195242 + 0.476464i
471471 −4.43179 + 13.6396i −0.204206 + 0.628481i
472472 0.173706 + 0.0564404i 0.00799545 + 0.00259788i
473473 10.1500 + 13.9702i 0.466695 + 0.642351i
474474 −11.3571 −0.521647
475475 9.97007 5.17571i 0.457458 0.237478i
476476 −5.77455 −0.264676
477477 −4.02697 5.54264i −0.184382 0.253780i
478478 −2.44246 0.793604i −0.111716 0.0362986i
479479 1.80512 5.55560i 0.0824782 0.253842i −0.901310 0.433174i 0.857394π-0.857394\pi
0.983789 + 0.179332i 0.0573936π0.0573936\pi
480480 −1.90211 + 1.17557i −0.0868192 + 0.0536572i
481481 −3.02900 9.32229i −0.138110 0.425060i
482482 13.3394i 0.607592i
483483 −14.9721 + 4.86472i −0.681253 + 0.221353i
484484 −4.07289 2.95913i −0.185131 0.134506i
485485 11.6217 + 18.8042i 0.527712 + 0.853856i
486486 0.809017 0.587785i 0.0366978 0.0266625i
487487 −2.99990 + 4.12901i −0.135939 + 0.187103i −0.871559 0.490290i 0.836891π-0.836891\pi
0.735621 + 0.677394i 0.236891π0.236891\pi
488488 3.02786 4.16750i 0.137065 0.188654i
489489 4.77575 3.46979i 0.215967 0.156909i
490490 −0.671091 + 8.96178i −0.0303168 + 0.404852i
491491 −31.6198 22.9731i −1.42698 1.03676i −0.990569 0.137015i 0.956249π-0.956249\pi
−0.436412 0.899747i 0.643751π-0.643751\pi
492492 5.82766 1.89352i 0.262731 0.0853665i
493493 31.3686i 1.41277i
494494 2.06140 + 6.34432i 0.0927465 + 0.285445i
495495 4.16640 + 3.53118i 0.187266 + 0.158715i
496496 −1.89294 + 5.82588i −0.0849957 + 0.261590i
497497 −18.6565 6.06185i −0.836857 0.271911i
498498 −5.37190 7.39378i −0.240721 0.331323i
499499 12.0527 0.539553 0.269777 0.962923i 0.413050π-0.413050\pi
0.269777 + 0.962923i 0.413050π0.413050\pi
500500 −7.35738 8.41837i −0.329032 0.376481i
501501 8.94427 0.399601
502502 −8.42938 11.6020i −0.376222 0.517825i
503503 9.39747 + 3.05342i 0.419012 + 0.136145i 0.510932 0.859621i 0.329300π-0.329300\pi
−0.0919197 + 0.995766i 0.529300π0.529300\pi
504504 0.533531 1.64204i 0.0237654 0.0731423i
505505 10.7276 + 9.09208i 0.477374 + 0.404592i
506506 −6.88191 21.1803i −0.305938 0.941581i
507507 4.18400i 0.185818i
508508 16.9408 5.50441i 0.751628 0.244219i
509509 16.1886 + 11.7617i 0.717546 + 0.521328i 0.885599 0.464450i 0.153748π-0.153748\pi
−0.168053 + 0.985778i 0.553748π0.553748\pi
510510 0.558469 7.45782i 0.0247294 0.330238i
511511 9.39404 6.82517i 0.415568 0.301928i
512512 −0.587785 + 0.809017i −0.0259767 + 0.0357538i
513513 −1.32057 + 1.81761i −0.0583046 + 0.0802494i
514514 12.9451 9.40518i 0.570984 0.414844i
515515 10.0858 + 16.3192i 0.444433 + 0.719108i
516516 5.71972 + 4.15562i 0.251797 + 0.182941i
517517 11.5967 3.76799i 0.510021 0.165716i
518518 5.69977i 0.250434i
519519 8.00822 + 24.6468i 0.351522 + 1.08187i
520520 5.64771 3.49047i 0.247668 0.153067i
521521 3.33077 10.2511i 0.145924 0.449107i −0.851205 0.524834i 0.824128π-0.824128\pi
0.997129 + 0.0757262i 0.0241275π0.0241275\pi
522522 8.91991 + 2.89825i 0.390414 + 0.126853i
523523 −15.5498 21.4025i −0.679945 0.935865i 0.319988 0.947422i 0.396321π-0.396321\pi
−0.999933 + 0.0115570i 0.996321π0.996321\pi
524524 −10.3375 −0.451596
525525 8.53644 + 1.28569i 0.372561 + 0.0561121i
526526 −19.8584 −0.865866
527527 −12.0425 16.5750i −0.524578 0.722019i
528528 2.32292 + 0.754763i 0.101092 + 0.0328468i
529529 −18.5835 + 57.1942i −0.807979 + 2.48670i
530530 5.80875 14.1755i 0.252316 0.615745i
531531 −0.0564404 0.173706i −0.00244930 0.00753818i
532532 3.87901i 0.168176i
533533 −17.3033 + 5.62219i −0.749490 + 0.243524i
534534 6.56674 + 4.77102i 0.284171 + 0.206462i
535535 −13.1516 + 15.5174i −0.568592 + 0.670875i
536536 9.61949 6.98897i 0.415499 0.301877i
537537 0.0282202 0.0388418i 0.00121779 0.00167615i
538538 −1.56400 + 2.15266i −0.0674288 + 0.0928078i
539539 7.94162 5.76993i 0.342070 0.248528i
540540 2.06909 + 0.847859i 0.0890395 + 0.0364860i
541541 22.7282 + 16.5130i 0.977161 + 0.709949i 0.957072 0.289849i 0.0936051π-0.0936051\pi
0.0200887 + 0.999798i 0.493605π0.493605\pi
542542 −12.8019 + 4.15958i −0.549888 + 0.178669i
543543 20.5347i 0.881229i
544544 −1.03353 3.18088i −0.0443123 0.136379i
545545 −7.21685 29.5655i −0.309136 1.26645i
546546 −1.58415 + 4.87550i −0.0677952 + 0.208652i
547547 −7.01640 2.27977i −0.300000 0.0974758i 0.155150 0.987891i 0.450414π-0.450414\pi
−0.455149 + 0.890415i 0.650414π0.650414\pi
548548 9.45254 + 13.0103i 0.403793 + 0.555773i
549549 −5.15131 −0.219853
550550 −1.81881 + 12.0761i −0.0775542 + 0.514927i
551551 −21.0716 −0.897680
552552 −5.35941 7.37660i −0.228112 0.313969i
553553 18.6487 + 6.05934i 0.793025 + 0.257670i
554554 1.65246 5.08576i 0.0702064 0.216073i
555555 7.36124 + 0.551237i 0.312467 + 0.0233987i
556556 −5.10169 15.7014i −0.216360 0.665887i
557557 17.2189i 0.729587i −0.931088 0.364794i 0.881140π-0.881140\pi
0.931088 0.364794i 0.118860π-0.118860\pi
558558 5.82588 1.89294i 0.246629 0.0801347i
559559 −16.9829 12.3388i −0.718298 0.521874i
560560 3.75055 0.915497i 0.158490 0.0386868i
561561 −6.60886 + 4.80162i −0.279026 + 0.202725i
562562 9.82598 13.5243i 0.414484 0.570488i
563563 0.117265 0.161402i 0.00494214 0.00680228i −0.806539 0.591181i 0.798662π-0.798662\pi
0.811481 + 0.584379i 0.198662π0.198662\pi
564564 4.03884 2.93439i 0.170066 0.123560i
565565 17.9596 4.38389i 0.755567 0.184432i
566566 11.4581 + 8.32479i 0.481619 + 0.349917i
567567 −1.64204 + 0.533531i −0.0689592 + 0.0224062i
568568 11.3618i 0.476729i
569569 5.82382 + 17.9239i 0.244147 + 0.751408i 0.995776 + 0.0918209i 0.0292687π0.0292687\pi
−0.751628 + 0.659587i 0.770731π0.770731\pi
570570 −5.00972 0.375147i −0.209834 0.0157132i
571571 5.61672 17.2865i 0.235053 0.723417i −0.762062 0.647504i 0.775813π-0.775813\pi
0.997114 0.0759132i 0.0241872π-0.0241872\pi
572572 −6.89716 2.24102i −0.288385 0.0937019i
573573 1.42267 + 1.95814i 0.0594330 + 0.0818025i
574574 −10.5795 −0.441579
575575 31.9913 32.4807i 1.33413 1.35454i
576576 1.00000 0.0416667
577577 −0.223184 0.307187i −0.00929129 0.0127884i 0.804346 0.594161i 0.202516π-0.202516\pi
−0.813637 + 0.581373i 0.802516π0.802516\pi
578578 −5.52926 1.79657i −0.229987 0.0747273i
579579 4.13355 12.7218i 0.171784 0.528698i
580580 4.97318 + 20.3738i 0.206500 + 0.845975i
581581 4.87606 + 15.0070i 0.202293 + 0.622594i
582582 9.88597i 0.409787i
583583 −15.9145 + 5.17094i −0.659112 + 0.214159i
584584 5.44095 + 3.95309i 0.225148 + 0.163580i
585585 −6.14349 2.51744i −0.254002 0.104083i
586586 −10.0839 + 7.32636i −0.416561 + 0.302649i
587587 9.12959 12.5658i 0.376819 0.518646i −0.577920 0.816094i 0.696135π-0.696135\pi
0.954738 + 0.297447i 0.0961353π0.0961353\pi
588588 2.36234 3.25148i 0.0974212 0.134089i
589589 −11.1341 + 8.08941i −0.458774 + 0.333319i
590590 0.264058 0.311559i 0.0108711 0.0128267i
591591 15.3095 + 11.1230i 0.629748 + 0.457539i
592592 3.13969 1.02015i 0.129040 0.0419278i
593593 4.62686i 0.190002i −0.995477 0.0950012i 0.969715π-0.969715\pi
0.995477 0.0950012i 0.0302855π-0.0302855\pi
594594 −0.754763 2.32292i −0.0309683 0.0953106i
595595 −4.89601 + 11.9481i −0.200717 + 0.489823i
596596 6.34490 19.5276i 0.259897 0.799881i
597597 −21.5685 7.00802i −0.882738 0.286819i
598598 15.9130 + 21.9024i 0.650732 + 0.895656i
599599 −28.6517 −1.17067 −0.585337 0.810790i 0.699038π-0.699038\pi
−0.585337 + 0.810790i 0.699038π0.699038\pi
600600 0.819639 + 4.93236i 0.0334616 + 0.201363i
601601 7.54545 0.307785 0.153893 0.988088i 0.450819π-0.450819\pi
0.153893 + 0.988088i 0.450819π0.450819\pi
602602 −7.17486 9.87535i −0.292425 0.402489i
603603 −11.3084 3.67432i −0.460513 0.149630i
604604 −0.861564 + 2.65162i −0.0350565 + 0.107893i
605605 −9.57594 + 5.91826i −0.389318 + 0.240611i
606606 −1.94336 5.98105i −0.0789436 0.242964i
607607 0.971865i 0.0394468i 0.999805 + 0.0197234i 0.00627856π0.00627856\pi
−0.999805 + 0.0197234i 0.993721π0.993721\pi
608608 −2.13673 + 0.694265i −0.0866558 + 0.0281562i
609609 −13.1005 9.51810i −0.530861 0.385693i
610610 −6.05573 9.79837i −0.245189 0.396725i
611611 −11.9920 + 8.71272i −0.485146 + 0.352479i
612612 −1.96589 + 2.70582i −0.0794665 + 0.109376i
613613 24.1418 33.2284i 0.975080 1.34208i 0.0356409 0.999365i 0.488653π-0.488653\pi
0.939439 0.342717i 0.111347π-0.111347\pi
614614 −19.4143 + 14.1053i −0.783497 + 0.569244i
615615 1.02316 13.6634i 0.0412580 0.550961i
616616 −3.41164 2.47870i −0.137459 0.0998697i
617617 −7.80690 + 2.53661i −0.314294 + 0.102120i −0.461916 0.886924i 0.652838π-0.652838\pi
0.147622 + 0.989044i 0.452838π0.452838\pi
618618 8.57949i 0.345118i
619619 −14.0919 43.3705i −0.566402 1.74321i −0.663748 0.747956i 0.731035π-0.731035\pi
0.0973461 0.995251i 0.468965π-0.468965\pi
620620 10.4493 + 8.85620i 0.419655 + 0.355673i
621621 −2.81761 + 8.67171i −0.113067 + 0.347984i
622622 13.2759 + 4.31359i 0.532314 + 0.172959i
623623 −8.23736 11.3378i −0.330023 0.454238i
624624 −2.96917 −0.118862
625625 −23.6564 + 8.08551i −0.946255 + 0.323420i
626626 9.62739 0.384788
627627 3.22545 + 4.43945i 0.128812 + 0.177294i
628628 13.6396 + 4.43179i 0.544281 + 0.176847i
629629 −3.41196 + 10.5009i −0.136044 + 0.418700i
630630 −2.94517 2.49614i −0.117338 0.0994487i
631631 10.5472 + 32.4610i 0.419878 + 1.29225i 0.907814 + 0.419372i 0.137750π0.137750\pi
−0.487936 + 0.872879i 0.662250π0.662250\pi
632632 11.3571i 0.451760i
633633 2.43352 0.790700i 0.0967239 0.0314275i
634634 −0.450068 0.326993i −0.0178745 0.0129866i
635635 2.97431 39.7191i 0.118032 1.57620i
636636 −5.54264 + 4.02697i −0.219780 + 0.159680i
637637 −7.01420 + 9.65421i −0.277913 + 0.382514i
638638 13.4648 18.5328i 0.533078 0.733719i
639639 −9.19186 + 6.67828i −0.363624 + 0.264189i
640640 1.17557 + 1.90211i 0.0464685 + 0.0751876i
641641 27.8267 + 20.2173i 1.09909 + 0.798535i 0.980911 0.194458i 0.0622946π-0.0622946\pi
0.118178 + 0.992992i 0.462295π0.462295\pi
642642 8.65151 2.81105i 0.341448 0.110943i
643643 2.71413i 0.107035i 0.998567 + 0.0535173i 0.0170432π0.0170432\pi
−0.998567 + 0.0535173i 0.982957π0.982957\pi
644644 4.86472 + 14.9721i 0.191697 + 0.589983i
645645 13.4479 8.31124i 0.529510 0.327255i
646646 2.32202 7.14645i 0.0913588 0.281173i
647647 −27.2042 8.83917i −1.06951 0.347504i −0.279211 0.960230i 0.590073π-0.590073\pi
−0.790295 + 0.612726i 0.790073π0.790073\pi
648648 −0.587785 0.809017i −0.0230904 0.0317812i
649649 −0.446104 −0.0175111
650650 −2.43365 14.6450i −0.0954556 0.574426i
651651 −10.5763 −0.414517
652652 −3.46979 4.77575i −0.135887 0.187033i
653653 32.6040 + 10.5937i 1.27589 + 0.414562i 0.867132 0.498079i 0.165961π-0.165961\pi
0.408760 + 0.912642i 0.365961π0.365961\pi
654654 −4.20582 + 12.9442i −0.164461 + 0.506158i
655655 −8.76474 + 21.3892i −0.342467 + 0.835746i
656656 −1.89352 5.82766i −0.0739295 0.227532i
657657 6.72539i 0.262382i
658658 −8.19753 + 2.66354i −0.319573 + 0.103836i
659659 14.9714 + 10.8774i 0.583203 + 0.423722i 0.839878 0.542776i 0.182627π-0.182627\pi
−0.256674 + 0.966498i 0.582627π0.582627\pi
660660 3.53118 4.16640i 0.137451 0.162177i
661661 −10.7699 + 7.82476i −0.418899 + 0.304348i −0.777195 0.629260i 0.783358π-0.783358\pi
0.358296 + 0.933608i 0.383358π0.383358\pi
662662 6.79782 9.35640i 0.264205 0.363647i
663663 5.83708 8.03405i 0.226693 0.312017i
664664 −7.39378 + 5.37190i −0.286935 + 0.208470i
665665 8.02601 + 3.28885i 0.311235 + 0.127536i
666666 −2.67078 1.94043i −0.103491 0.0751903i
667667 −81.3315 + 26.4262i −3.14917 + 1.02323i
668668 8.94427i 0.346064i
669669 −5.76449 17.7413i −0.222868 0.685917i
670670 −6.30484 25.8292i −0.243577 0.997871i
671671 −3.88802 + 11.9661i −0.150095 + 0.461946i
672672 −1.64204 0.533531i −0.0633430 0.0205814i
673673 21.1357 + 29.0908i 0.814722 + 1.12137i 0.990578 + 0.136952i 0.0437307π0.0437307\pi
−0.175856 + 0.984416i 0.556269π0.556269\pi
674674 29.8767 1.15081
675675 3.50859 3.56227i 0.135046 0.137112i
676676 −4.18400 −0.160923
677677 3.59723 + 4.95116i 0.138253 + 0.190289i 0.872529 0.488562i 0.162478π-0.162478\pi
−0.734276 + 0.678851i 0.762478π0.762478\pi
678678 −7.86296 2.55483i −0.301975 0.0981177i
679679 −5.27447 + 16.2331i −0.202416 + 0.622971i
680680 −7.45782 0.558469i −0.285994 0.0214163i
681681 −3.41820 10.5201i −0.130986 0.403133i
682682 14.9618i 0.572916i
683683 −7.03739 + 2.28659i −0.269278 + 0.0874938i −0.440544 0.897731i 0.645214π-0.645214\pi
0.171266 + 0.985225i 0.445214π0.445214\pi
684684 1.81761 + 1.32057i 0.0694981 + 0.0504933i
685685 34.9339 8.52726i 1.33476 0.325810i
686686 −15.3914 + 11.1825i −0.587648 + 0.426951i
687687 15.8992 21.8833i 0.606590 0.834900i
688688 4.15562 5.71972i 0.158432 0.218062i
689689 16.4571 11.9568i 0.626965 0.455517i
690690 −19.8069 + 4.83480i −0.754035 + 0.184058i
691691 26.4101 + 19.1880i 1.00469 + 0.729947i 0.963088 0.269187i 0.0867549π-0.0867549\pi
0.0415986 + 0.999134i 0.486755π0.486755\pi
692692 24.6468 8.00822i 0.936929 0.304427i
693693 4.21702i 0.160191i
694694 −1.31230 4.03884i −0.0498142 0.153312i
695695 −36.8131 2.75670i −1.39640 0.104568i
696696 2.89825 8.91991i 0.109858 0.338108i
697697 19.4910 + 6.33302i 0.738276 + 0.239880i
698698 11.3861 + 15.6716i 0.430969 + 0.593177i
699699 −18.2774 −0.691315
700700 1.28569 8.53644i 0.0485945 0.322647i
701701 15.4733 0.584418 0.292209 0.956354i 0.405610π-0.405610\pi
0.292209 + 0.956354i 0.405610π0.405610\pi
702702 1.74524 + 2.40211i 0.0658697 + 0.0906619i
703703 7.05391 + 2.29195i 0.266043 + 0.0864427i
704704 0.754763 2.32292i 0.0284462 0.0875484i
705705 −2.64715 10.8447i −0.0996975 0.408434i
706706 0.0751761 + 0.231368i 0.00282929 + 0.00870766i
707707 10.8580i 0.408356i
708708 −0.173706 + 0.0564404i −0.00652826 + 0.00212116i
709709 5.10700 + 3.71045i 0.191797 + 0.139349i 0.679540 0.733639i 0.262179π-0.262179\pi
−0.487742 + 0.872988i 0.662179π0.662179\pi
710710 −23.5085 9.63317i −0.882259 0.361526i
711711 9.18806 6.67551i 0.344579 0.250351i
712712 4.77102 6.56674i 0.178801 0.246099i
713713 −32.8301 + 45.1868i −1.22950 + 1.69226i
714714 4.67171 3.39420i 0.174834 0.127025i
715715 −10.4847 + 12.3708i −0.392105 + 0.462641i
716716 −0.0388418 0.0282202i −0.00145159 0.00105464i
717717 2.44246 0.793604i 0.0912155 0.0296377i
718718 21.0432i 0.785325i
719719 −9.20729 28.3371i −0.343374 1.05680i −0.962448 0.271464i 0.912492π-0.912492\pi
0.619074 0.785332i 0.287508π-0.287508\pi
720720 0.847859 2.06909i 0.0315978 0.0771105i
721721 −4.57742 + 14.0879i −0.170472 + 0.524660i
722722 13.2695 + 4.31152i 0.493840 + 0.160458i
723723 7.84068 + 10.7918i 0.291598 + 0.401350i
724724 −20.5347 −0.763167
725725 46.3717 + 6.98414i 1.72220 + 0.259384i
726726 5.03437 0.186843
727727 −5.69196 7.83431i −0.211103 0.290559i 0.690314 0.723510i 0.257472π-0.257472\pi
−0.901417 + 0.432951i 0.857472π0.857472\pi
728728 4.87550 + 1.58415i 0.180698 + 0.0587124i
729729 −0.309017 + 0.951057i −0.0114451 + 0.0352243i
730730 12.7925 7.90617i 0.473470 0.292620i
731731 7.30703 + 22.4887i 0.270260 + 0.831776i
732732 5.15131i 0.190398i
733733 −33.0184 + 10.7283i −1.21956 + 0.396260i −0.846923 0.531716i 0.821548π-0.821548\pi
−0.372640 + 0.927976i 0.621548π0.621548\pi
734734 6.33734 + 4.60435i 0.233916 + 0.169950i
735735 −4.72468 7.64469i −0.174272 0.281979i
736736 −7.37660 + 5.35941i −0.271905 + 0.197551i
737737 −17.0703 + 23.4952i −0.628792 + 0.865458i
738738 −3.60169 + 4.95730i −0.132580 + 0.182481i
739739 −18.3619 + 13.3407i −0.675454 + 0.490746i −0.871846 0.489780i 0.837077π-0.837077\pi
0.196393 + 0.980525i 0.437077π0.437077\pi
740740 0.551237 7.36124i 0.0202639 0.270605i
741741 −5.39680 3.92101i −0.198256 0.144042i
742742 11.2498 3.65527i 0.412991 0.134189i
743743 9.53920i 0.349959i −0.984572 0.174980i 0.944014π-0.944014\pi
0.984572 0.174980i 0.0559860π-0.0559860\pi
744744 −1.89294 5.82588i −0.0693987 0.213587i
745745 −35.0248 29.6848i −1.28321 1.08757i
746746 4.79766 14.7657i 0.175655 0.540610i
747747 8.69192 + 2.82417i 0.318021 + 0.103331i
748748 4.80162 + 6.60886i 0.175565 + 0.241644i
749749 −15.7059 −0.573881
750750 10.9004 + 2.48604i 0.398028 + 0.0907773i
751751 22.5289 0.822090 0.411045 0.911615i 0.365164π-0.365164\pi
0.411045 + 0.911615i 0.365164π0.365164\pi
752752 −2.93439 4.03884i −0.107006 0.147281i
753753 13.6390 + 4.43159i 0.497034 + 0.161496i
754754 −8.60542 + 26.4848i −0.313391 + 0.964519i
755755 4.75596 + 4.03085i 0.173087 + 0.146698i
756756 0.533531 + 1.64204i 0.0194043 + 0.0597204i
757757 38.3200i 1.39276i 0.717672 + 0.696382i 0.245208π0.245208\pi
−0.717672 + 0.696382i 0.754792π0.754792\pi
758758 10.3320 3.35706i 0.375274 0.121934i
759759 18.0171 + 13.0902i 0.653978 + 0.475143i
760760 −0.375147 + 5.00972i −0.0136080 + 0.181722i
761761 −16.5112 + 11.9961i −0.598530 + 0.434857i −0.845357 0.534202i 0.820612π-0.820612\pi
0.246827 + 0.969060i 0.420612π0.420612\pi
762762 −10.4700 + 14.4107i −0.379289 + 0.522046i
763763 13.8122 19.0109i 0.500037 0.688242i
764764 1.95814 1.42267i 0.0708431 0.0514705i
765765 3.93179 + 6.36176i 0.142154 + 0.230010i
766766 −7.76345 5.64047i −0.280505 0.203799i
767767 0.515763 0.167581i 0.0186231 0.00605101i
768768 1.00000i 0.0360844i
769769 9.28293 + 28.5699i 0.334751 + 1.03026i 0.966845 + 0.255365i 0.0821958π0.0821958\pi
−0.632094 + 0.774892i 0.717804π0.717804\pi
770770 −8.02124 + 4.95740i −0.289066 + 0.178652i
771771 −4.94459 + 15.2179i −0.178075 + 0.548059i
772772 −12.7218 4.13355i −0.457866 0.148770i
773773 12.7825 + 17.5936i 0.459753 + 0.632796i 0.974458 0.224572i 0.0720982π-0.0720982\pi
−0.514704 + 0.857368i 0.672098π0.672098\pi
774774 −7.06997 −0.254125
775775 27.1838 14.1118i 0.976472 0.506911i
776776 −9.88597 −0.354886
777777 3.35024 + 4.61121i 0.120189 + 0.165426i
778778 33.1177 + 10.7606i 1.18733 + 0.385786i
779779 4.25415 13.0929i 0.152421 0.469103i
780780 −2.51744 + 6.14349i −0.0901388 + 0.219972i
781781 8.57543 + 26.3925i 0.306853 + 0.944397i
782782 30.4958i 1.09053i
783783 −8.91991 + 2.89825i −0.318772 + 0.103575i
784784 −3.25148 2.36234i −0.116124 0.0843692i
785785 20.7342 24.4641i 0.740037 0.873161i
786786 8.36321 6.07623i 0.298306 0.216732i
787787 7.75679 10.6763i 0.276500 0.380569i −0.648071 0.761580i 0.724424π-0.724424\pi
0.924571 + 0.381011i 0.124424π0.124424\pi
788788 11.1230 15.3095i 0.396240 0.545378i
789789 16.0658 11.6725i 0.571956 0.415550i
790790 23.4988 + 9.62919i 0.836049 + 0.342591i
791791 11.5482 + 8.39027i 0.410607 + 0.298323i
792792 −2.32292 + 0.754763i −0.0825414 + 0.0268193i
793793 15.2951i 0.543146i
794794 4.94607 + 15.2224i 0.175529 + 0.540224i
795795 3.63278 + 14.8825i 0.128841 + 0.527829i
796796 −7.00802 + 21.5685i −0.248393 + 0.764474i
797797 −15.8571 5.15230i −0.561689 0.182504i 0.0143921 0.999896i 0.495419π-0.495419\pi
−0.576081 + 0.817393i 0.695419π0.695419\pi
798798 −2.28002 3.13818i −0.0807119 0.111090i
799799 16.6971 0.590700
800800 4.93236 0.819639i 0.174385 0.0289786i
801801 −8.11694 −0.286798
802802 6.77622 + 9.32667i 0.239277 + 0.329336i
803803 −15.6225 5.07607i −0.551308 0.179131i
804804 −3.67432 + 11.3084i −0.129583 + 0.398816i
805805 35.1032 + 2.62866i 1.23722 + 0.0926479i
806806 5.62048 + 17.2981i 0.197973 + 0.609298i
807807 2.66084i 0.0936658i
808808 −5.98105 + 1.94336i −0.210413 + 0.0683672i
809809 −22.2409 16.1590i −0.781949 0.568119i 0.123614 0.992330i 0.460551π-0.460551\pi
−0.905563 + 0.424211i 0.860551π0.860551\pi
810810 −2.17229 + 0.530249i −0.0763264 + 0.0186310i
811811 20.9090 15.1913i 0.734213 0.533437i −0.156680 0.987649i 0.550079π-0.550079\pi
0.890894 + 0.454212i 0.150079π0.150079\pi
812812 −9.51810 + 13.1005i −0.334020 + 0.459739i
813813 7.91199 10.8899i 0.277486 0.381926i
814814 −6.52328 + 4.73944i −0.228641 + 0.166117i
815815 −12.8233 + 3.13014i −0.449182 + 0.109644i
816816 2.70582 + 1.96589i 0.0947226 + 0.0688200i
817817 15.1066 4.90843i 0.528513 0.171724i
818818 14.5906i 0.510150i
819819 −1.58415 4.87550i −0.0553546 0.170364i
820820 −13.6634 1.02316i −0.477146 0.0357305i
821821 −10.0931 + 31.0634i −0.352252 + 1.08412i 0.605333 + 0.795972i 0.293040π0.293040\pi
−0.957586 + 0.288149i 0.906960π0.906960\pi
822822 −15.2945 4.96950i −0.533458 0.173331i
823823 28.8122 + 39.6567i 1.00433 + 1.38234i 0.922630 + 0.385687i 0.126036π0.126036\pi
0.0817020 + 0.996657i 0.473964π0.473964\pi
824824 −8.57949 −0.298881
825825 −5.62672 10.8389i −0.195897 0.377360i
826826 0.315344 0.0109722
827827 −5.56611 7.66109i −0.193553 0.266402i 0.701200 0.712965i 0.252648π-0.252648\pi
−0.894752 + 0.446563i 0.852648π0.852648\pi
828828 8.67171 + 2.81761i 0.301363 + 0.0979187i
829829 17.1806 52.8765i 0.596707 1.83648i 0.0506676 0.998716i 0.483865π-0.483865\pi
0.546039 0.837760i 0.316135π-0.316135\pi
830830 4.84606 + 19.8530i 0.168209 + 0.689108i
831831 1.65246 + 5.08576i 0.0573233 + 0.176423i
832832 2.96917i 0.102938i
833833 12.7841 4.15381i 0.442944 0.143921i
834834 13.3564 + 9.70399i 0.462494 + 0.336022i
835835 −18.5065 7.58348i −0.640444 0.262437i
836836 4.43945 3.22545i 0.153541 0.111554i
837837 −3.60059 + 4.95579i −0.124455 + 0.171297i
838838 −8.29180 + 11.4127i −0.286435 + 0.394244i
839839 −4.96116 + 3.60449i −0.171278 + 0.124441i −0.670122 0.742251i 0.733758π-0.733758\pi
0.498844 + 0.866692i 0.333758π0.333758\pi
840840 −2.49614 + 2.94517i −0.0861251 + 0.101618i
841841 −47.7034 34.6586i −1.64495 1.19512i
842842 −12.2574 + 3.98266i −0.422417 + 0.137252i
843843 16.7170i 0.575763i
844844 −0.790700 2.43352i −0.0272170 0.0837654i
845845 −3.54744 + 8.65707i −0.122036 + 0.297812i
846846 −1.54270 + 4.74794i −0.0530391 + 0.163238i
847847 −8.26664 2.68599i −0.284045 0.0922918i
848848 4.02697 + 5.54264i 0.138287 + 0.190335i
849849 −14.1630 −0.486072
850850 −7.47870 + 14.9574i −0.256517 + 0.513035i
851851 30.1009 1.03184
852852 6.67828 + 9.19186i 0.228794 + 0.314908i
853853 −28.9856 9.41798i −0.992447 0.322465i −0.232603 0.972572i 0.574724π-0.574724\pi
−0.759843 + 0.650106i 0.774724π0.774724\pi
854854 2.74838 8.45865i 0.0940477 0.289449i
855855 4.27346 2.64114i 0.146149 0.0903251i
856856 −2.81105 8.65151i −0.0960796 0.295702i
857857 7.53137i 0.257267i −0.991692 0.128633i 0.958941π-0.958941\pi
0.991692 0.128633i 0.0410590π-0.0410590\pi
858858 6.89716 2.24102i 0.235465 0.0765073i
859859 39.9169 + 29.0013i 1.36195 + 0.989512i 0.998318 + 0.0579677i 0.0184621π0.0184621\pi
0.363628 + 0.931544i 0.381538π0.381538\pi
860860 −8.31124 13.4479i −0.283411 0.458569i
861861 8.55899 6.21847i 0.291690 0.211925i
862862 13.6028 18.7226i 0.463313 0.637695i
863863 18.5076 25.4736i 0.630008 0.867131i −0.368026 0.929816i 0.619966π-0.619966\pi
0.998033 + 0.0626845i 0.0199662π0.0199662\pi
864864 −0.809017 + 0.587785i −0.0275233 + 0.0199969i
865865 4.32724 57.7862i 0.147131 1.96479i
866866 −19.0204 13.8192i −0.646341 0.469594i
867867 5.52926 1.79657i 0.187784 0.0610146i
868868 10.5763i 0.358982i
869869 −8.57189 26.3816i −0.290781 0.894933i
870870 −15.9988 13.5596i −0.542410 0.459713i
871871 10.9097 33.5766i 0.369661 1.13770i
872872 12.9442 + 4.20582i 0.438345 + 0.142427i
873873 5.81083 + 7.99792i 0.196667 + 0.270688i
874874 −20.4853 −0.692924
875875 −16.5726 9.89790i −0.560255 0.334610i
876876 −6.72539 −0.227230
877877 −4.63120 6.37431i −0.156385 0.215245i 0.723634 0.690184i 0.242470π-0.242470\pi
−0.880019 + 0.474939i 0.842470π0.842470\pi
878878 1.89488 + 0.615684i 0.0639491 + 0.0207783i
879879 3.85170 11.8543i 0.129914 0.399836i
880880 −4.16640 3.53118i −0.140449 0.119036i
881881 −10.2217 31.4592i −0.344378 1.05989i −0.961916 0.273346i 0.911870π-0.911870\pi
0.617537 0.786542i 0.288130π-0.288130\pi
882882 4.01905i 0.135328i
883883 −7.43225 + 2.41489i −0.250115 + 0.0812674i −0.431391 0.902165i 0.641977π-0.641977\pi
0.181276 + 0.983432i 0.441977π0.441977\pi
884884 −8.03405 5.83708i −0.270214 0.196322i
885885 −0.0304976 + 0.407266i −0.00102517 + 0.0136901i
886886 −10.5437 + 7.66042i −0.354221 + 0.257357i
887887 5.94363 8.18071i 0.199568 0.274681i −0.697490 0.716594i 0.745700π-0.745700\pi
0.897058 + 0.441913i 0.145700π0.145700\pi
888888 −1.94043 + 2.67078i −0.0651167 + 0.0896255i
889889 24.8808 18.0769i 0.834474 0.606281i
890890 −9.54203 15.4393i −0.319850 0.517528i
891891 1.97599 + 1.43564i 0.0661983 + 0.0480959i
892892 −17.7413 + 5.76449i −0.594022 + 0.193009i
893893 11.2161i 0.375333i
894894 6.34490 + 19.5276i 0.212205 + 0.653100i
895895 −0.0913225 + 0.0564404i −0.00305257 + 0.00188659i
896896 −0.533531 + 1.64204i −0.0178240 + 0.0548567i
897897 −25.7478 8.36598i −0.859695 0.279332i
898898 −7.10318 9.77668i −0.237036 0.326252i
899899 −57.4526 −1.91615
900900 −3.56227 3.50859i −0.118742 0.116953i
901901 −22.9140 −0.763375
902902 8.79699 + 12.1080i 0.292908 + 0.403153i
903903 11.6092 + 3.77205i 0.386329 + 0.125526i
904904 −2.55483 + 7.86296i −0.0849724 + 0.261518i
905905 −17.4105 + 42.4882i −0.578746 + 1.41235i
906906 −0.861564 2.65162i −0.0286235 0.0880942i
907907 10.2207i 0.339373i −0.985498 0.169686i 0.945725π-0.945725\pi
0.985498 0.169686i 0.0542755π-0.0542755\pi
908908 −10.5201 + 3.41820i −0.349123 + 0.113437i
909909 5.08779 + 3.69649i 0.168751 + 0.122605i
910910 7.41148 8.74472i 0.245688 0.289885i
911911 −34.3471 + 24.9546i −1.13797 + 0.826784i −0.986835 0.161729i 0.948293π-0.948293\pi
−0.151135 + 0.988513i 0.548293π0.548293\pi
912912 1.32057 1.81761i 0.0437285 0.0601871i
913913 13.1207 18.0590i 0.434231 0.597667i
914914 −4.55284 + 3.30783i −0.150594 + 0.109413i
915915 10.6585 + 4.36758i 0.352360 + 0.144388i
916916 −21.8833 15.8992i −0.723045 0.525323i
917917 −16.9746 + 5.51538i −0.560550 + 0.182134i
918918 3.34458i 0.110387i
919919 −16.0903 49.5209i −0.530770 1.63354i −0.752615 0.658461i 0.771208π-0.771208\pi
0.221844 0.975082i 0.428792π-0.428792\pi
920920 4.83480 + 19.8069i 0.159399 + 0.653013i
921921 7.41560 22.8229i 0.244352 0.752039i
922922 4.40041 + 1.42978i 0.144920 + 0.0470872i
923923 −19.8290 27.2922i −0.652679 0.898335i
924924 4.21702 0.138730
925925 −14.7637 7.38185i −0.485428 0.242714i
926926 5.75912 0.189256
927927 5.04290 + 6.94095i 0.165631 + 0.227971i
928928 −8.91991 2.89825i −0.292810 0.0951399i
929929 −8.13402 + 25.0339i −0.266869 + 0.821337i 0.724388 + 0.689392i 0.242122π0.242122\pi
−0.991257 + 0.131945i 0.957878π0.957878\pi
930930 −13.6592 1.02285i −0.447904 0.0335407i
931931 −2.79029 8.58762i −0.0914480 0.281448i
932932 18.2774i 0.598696i
933933 −13.2759 + 4.31359i −0.434633 + 0.141221i
934934 19.8871 + 14.4488i 0.650726 + 0.472780i
935935 17.7454 4.33161i 0.580338 0.141659i
936936 2.40211 1.74524i 0.0785155 0.0570449i
937937 −5.91758 + 8.14485i −0.193319 + 0.266081i −0.894662 0.446743i 0.852584π-0.852584\pi
0.701343 + 0.712823i 0.252584π0.252584\pi
938938 12.0667 16.6085i 0.393993 0.542285i
939939 −7.78872 + 5.65884i −0.254175 + 0.184669i
940940 −10.8447 + 2.64715i −0.353714 + 0.0863406i
941941 −8.08466 5.87385i −0.263552 0.191482i 0.448159 0.893954i 0.352080π-0.352080\pi
−0.711712 + 0.702472i 0.752080π0.752080\pi
942942 −13.6396 + 4.43179i −0.444403 + 0.144395i
943943 55.8709i 1.81941i
944944 0.0564404 + 0.173706i 0.00183698 + 0.00565364i
945945 3.84989 + 0.288294i 0.125237 + 0.00937820i
946946 −5.33615 + 16.4230i −0.173493 + 0.533957i
947947 52.7319 + 17.1336i 1.71356 + 0.556768i 0.990919 0.134460i 0.0429300π-0.0429300\pi
0.722637 + 0.691228i 0.242930π0.242930\pi
948948 −6.67551 9.18806i −0.216811 0.298414i
949949 19.9689 0.648217
950950 10.0475 + 5.02375i 0.325984 + 0.162992i
951951 0.556314 0.0180397
952952 −3.39420 4.67171i −0.110007 0.151411i
953953 −11.5125 3.74063i −0.372925 0.121171i 0.116557 0.993184i 0.462814π-0.462814\pi
−0.489482 + 0.872013i 0.662814π0.662814\pi
954954 2.11710 6.51577i 0.0685437 0.210956i
955955 −1.28341 5.25780i −0.0415302 0.170138i
956956 −0.793604 2.44246i −0.0256670 0.0789949i
957957 22.9077i 0.740502i
958958 5.55560 1.80512i 0.179493 0.0583209i
959959 22.4629 + 16.3202i 0.725363 + 0.527007i
960960 −2.06909 0.847859i −0.0667796 0.0273645i
961961 −5.27814 + 3.83479i −0.170262 + 0.123703i
962962 5.76149 7.93001i 0.185758 0.255674i
963963 −5.34693 + 7.35941i −0.172302 + 0.237154i
964964 10.7918 7.84068i 0.347580 0.252531i
965965 −19.3389 + 22.8178i −0.622542 + 0.734531i
966966 −12.7360 9.25325i −0.409774 0.297719i
967967 −2.77287 + 0.900961i −0.0891695 + 0.0289729i −0.353262 0.935524i 0.614928π-0.614928\pi
0.264092 + 0.964497i 0.414928π0.414928\pi
968968 5.03437i 0.161811i
969969 2.32202 + 7.14645i 0.0745941 + 0.229577i
970970 −8.38190 + 20.4550i −0.269127 + 0.656769i
971971 3.50206 10.7782i 0.112387 0.345890i −0.879006 0.476810i 0.841793π-0.841793\pi
0.991393 + 0.130920i 0.0417930π0.0417930\pi
972972 0.951057 + 0.309017i 0.0305052 + 0.00991172i
973973 −16.7544 23.0604i −0.537120 0.739282i
974974 −5.10374 −0.163534
975975 10.5770 + 10.4176i 0.338735 + 0.333631i
976976 5.15131 0.164889
977977 −2.82318 3.88577i −0.0903214 0.124317i 0.761465 0.648206i 0.224481π-0.224481\pi
−0.851786 + 0.523889i 0.824481π0.824481\pi
978978 5.61423 + 1.82417i 0.179523 + 0.0583307i
979979 −6.12636 + 18.8550i −0.195799 + 0.602609i
980980 −7.64469 + 4.72468i −0.244201 + 0.150924i
981981 −4.20582 12.9442i −0.134281 0.413276i
982982 39.0842i 1.24723i
983983 −7.38058 + 2.39810i −0.235404 + 0.0764874i −0.424343 0.905501i 0.639495π-0.639495\pi
0.188939 + 0.981989i 0.439495π0.439495\pi
984984 4.95730 + 3.60169i 0.158033 + 0.114818i
985985 −22.2460 35.9947i −0.708816 1.14689i
986986 25.3777 18.4380i 0.808192 0.587186i
987987 5.06635 6.97323i 0.161264 0.221960i
988988 −3.92101 + 5.39680i −0.124744 + 0.171695i
989989 52.1523 37.8909i 1.65835 1.20486i
990990 −0.407836 + 5.44627i −0.0129619 + 0.173094i
991991 36.2536 + 26.3398i 1.15163 + 0.836711i 0.988697 0.149925i 0.0479033π-0.0479033\pi
0.162937 + 0.986636i 0.447903π0.447903\pi
992992 −5.82588 + 1.89294i −0.184972 + 0.0601010i
993993 11.5651i 0.367009i
994994 −6.06185 18.6565i −0.192270 0.591747i
995995 38.6853 + 32.7872i 1.22641 + 1.03942i
996996 2.82417 8.69192i 0.0894874 0.275414i
997997 3.79651 + 1.23356i 0.120237 + 0.0390673i 0.368517 0.929621i 0.379866π-0.379866\pi
−0.248281 + 0.968688i 0.579866π0.579866\pi
998998 7.08441 + 9.75085i 0.224253 + 0.308658i
999999 3.30127 0.104447
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 150.2.h.a.139.2 yes 8
3.2 odd 2 450.2.l.a.289.1 8
5.2 odd 4 750.2.g.c.301.1 8
5.3 odd 4 750.2.g.e.301.2 8
5.4 even 2 750.2.h.c.199.1 8
25.3 odd 20 3750.2.a.m.1.3 4
25.4 even 10 3750.2.c.e.1249.6 8
25.9 even 10 inner 150.2.h.a.109.2 8
25.12 odd 20 750.2.g.c.451.1 8
25.13 odd 20 750.2.g.e.451.2 8
25.16 even 5 750.2.h.c.49.1 8
25.21 even 5 3750.2.c.e.1249.3 8
25.22 odd 20 3750.2.a.o.1.2 4
75.59 odd 10 450.2.l.a.109.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.2.h.a.109.2 8 25.9 even 10 inner
150.2.h.a.139.2 yes 8 1.1 even 1 trivial
450.2.l.a.109.1 8 75.59 odd 10
450.2.l.a.289.1 8 3.2 odd 2
750.2.g.c.301.1 8 5.2 odd 4
750.2.g.c.451.1 8 25.12 odd 20
750.2.g.e.301.2 8 5.3 odd 4
750.2.g.e.451.2 8 25.13 odd 20
750.2.h.c.49.1 8 25.16 even 5
750.2.h.c.199.1 8 5.4 even 2
3750.2.a.m.1.3 4 25.3 odd 20
3750.2.a.o.1.2 4 25.22 odd 20
3750.2.c.e.1249.3 8 25.21 even 5
3750.2.c.e.1249.6 8 25.4 even 10