Properties

Label 57.2.i.a.4.1
Level 5757
Weight 22
Character 57.4
Analytic conductor 0.4550.455
Analytic rank 00
Dimension 66
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [57,2,Mod(4,57)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(57, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("57.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 57=319 57 = 3 \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 57.i (of order 99, 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: 0.4551472915210.455147291521
Analytic rank: 00
Dimension: 66
Coefficient field: Q(ζ18)\Q(\zeta_{18})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x6x3+1 x^{6} - x^{3} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C9]\mathrm{SU}(2)[C_{9}]

Embedding invariants

Embedding label 4.1
Root 0.939693+0.342020i0.939693 + 0.342020i of defining polynomial
Character χ\chi == 57.4
Dual form 57.2.i.a.43.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.43969+0.524005i)q2+(0.1736480.984808i)q3+(0.266044+0.223238i)q4+(1.93969+1.62760i)q5+(0.2660441.50881i)q6+(0.266044+0.460802i)q7+(1.266042.19285i)q8+(0.939693+0.342020i)q9+(3.64543+1.32683i)q10+(2.55303+4.42198i)q11+(0.1736480.300767i)q12+(0.7057374.00243i)q13+(0.624485+0.524005i)q14+(1.93969+1.62760i)q15+(0.7942634.50449i)q16+(1.826350.664738i)q171.53209q18+(2.233963.74292i)q190.879385q20+(0.500000+0.181985i)q21+(1.35844+7.70410i)q22+(2.33022+1.95529i)q23+(1.93969+1.62760i)q24+(0.2451001.39003i)q25+(3.113345.39246i)q26+(0.500000+0.866025i)q27+(0.173648+0.0632028i)q28+(1.51367+0.550931i)q29+(1.93969+3.35965i)q30+(4.93969+8.55580i)q31+(0.3374961.91404i)q32+(3.911473.28212i)q33+(2.281061.91404i)q34+(0.2339561.32683i)q35+(0.3263520.118782i)q36+6.10607q37+(5.177524.21805i)q384.06418q39+(6.02481+2.19285i)q40+(1.471788.34689i)q41+(0.624485+0.524005i)q42+(0.135630+0.113807i)q43+(0.307934+1.74638i)q44+(1.266042.19285i)q45+(2.33022+4.03606i)q46+(7.10354+2.58548i)q47+(4.29813+1.56439i)q48+(3.35844+5.81699i)q49+(1.081251.87278i)q50+(0.337496+1.91404i)q51+(1.081250.907278i)q52+(7.585126.36467i)q53+(0.266044+1.50881i)q54+(12.14934.42198i)q55+1.34730q56+(4.073981.55007i)q572.46791q58+(3.58512+1.30488i)q59+(0.152704+0.866025i)q60+(10.67028.95340i)q61+(11.5949+9.72930i)q62+(0.09239630.524005i)q63+(3.08512+5.34359i)q64+(5.14543+8.91215i)q65+(7.351172.67561i)q66+(9.596273.49276i)q67+(0.3374960.584561i)q68+(1.520942.63435i)q69+(0.3584412.03282i)q70+(2.928552.45734i)q71+(1.93969+1.62760i)q72+(0.3224811.82888i)q73+(8.79086+3.19961i)q741.41147q75+(1.429890.497079i)q762.71688q77+(5.851172.12965i)q78+(1.82635+10.3578i)q79+(8.87211+7.44459i)q80+(0.7660440.642788i)q81+(2.2549012.7882i)q82+(5.737839.93821i)q83+(0.0923963+0.160035i)q84+(4.624491.68317i)q85+(0.254900+0.0927760i)q86+(0.805407+1.39501i)q87+(6.4645111.1969i)q88+(1.02869+5.83396i)q89+(2.971782.49362i)q90+(1.65657+1.39003i)q91+(0.183448+1.04039i)q92+(9.28359+3.37895i)q9311.5817q94+(1.75877+10.8961i)q951.94356q96+(6.39053+2.32596i)q97+(1.78699+10.1345i)q98+(3.911473.28212i)q99+O(q100)q+(1.43969 + 0.524005i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.266044 + 0.223238i) q^{4} +(-1.93969 + 1.62760i) q^{5} +(0.266044 - 1.50881i) q^{6} +(-0.266044 + 0.460802i) q^{7} +(-1.26604 - 2.19285i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-3.64543 + 1.32683i) q^{10} +(2.55303 + 4.42198i) q^{11} +(0.173648 - 0.300767i) q^{12} +(0.705737 - 4.00243i) q^{13} +(-0.624485 + 0.524005i) q^{14} +(1.93969 + 1.62760i) q^{15} +(-0.794263 - 4.50449i) q^{16} +(-1.82635 - 0.664738i) q^{17} -1.53209 q^{18} +(2.23396 - 3.74292i) q^{19} -0.879385 q^{20} +(0.500000 + 0.181985i) q^{21} +(1.35844 + 7.70410i) q^{22} +(2.33022 + 1.95529i) q^{23} +(-1.93969 + 1.62760i) q^{24} +(0.245100 - 1.39003i) q^{25} +(3.11334 - 5.39246i) q^{26} +(0.500000 + 0.866025i) q^{27} +(-0.173648 + 0.0632028i) q^{28} +(-1.51367 + 0.550931i) q^{29} +(1.93969 + 3.35965i) q^{30} +(-4.93969 + 8.55580i) q^{31} +(0.337496 - 1.91404i) q^{32} +(3.91147 - 3.28212i) q^{33} +(-2.28106 - 1.91404i) q^{34} +(-0.233956 - 1.32683i) q^{35} +(-0.326352 - 0.118782i) q^{36} +6.10607 q^{37} +(5.17752 - 4.21805i) q^{38} -4.06418 q^{39} +(6.02481 + 2.19285i) q^{40} +(-1.47178 - 8.34689i) q^{41} +(0.624485 + 0.524005i) q^{42} +(-0.135630 + 0.113807i) q^{43} +(-0.307934 + 1.74638i) q^{44} +(1.26604 - 2.19285i) q^{45} +(2.33022 + 4.03606i) q^{46} +(-7.10354 + 2.58548i) q^{47} +(-4.29813 + 1.56439i) q^{48} +(3.35844 + 5.81699i) q^{49} +(1.08125 - 1.87278i) q^{50} +(-0.337496 + 1.91404i) q^{51} +(1.08125 - 0.907278i) q^{52} +(-7.58512 - 6.36467i) q^{53} +(0.266044 + 1.50881i) q^{54} +(-12.1493 - 4.42198i) q^{55} +1.34730 q^{56} +(-4.07398 - 1.55007i) q^{57} -2.46791 q^{58} +(3.58512 + 1.30488i) q^{59} +(0.152704 + 0.866025i) q^{60} +(-10.6702 - 8.95340i) q^{61} +(-11.5949 + 9.72930i) q^{62} +(0.0923963 - 0.524005i) q^{63} +(-3.08512 + 5.34359i) q^{64} +(5.14543 + 8.91215i) q^{65} +(7.35117 - 2.67561i) q^{66} +(9.59627 - 3.49276i) q^{67} +(-0.337496 - 0.584561i) q^{68} +(1.52094 - 2.63435i) q^{69} +(0.358441 - 2.03282i) q^{70} +(2.92855 - 2.45734i) q^{71} +(1.93969 + 1.62760i) q^{72} +(-0.322481 - 1.82888i) q^{73} +(8.79086 + 3.19961i) q^{74} -1.41147 q^{75} +(1.42989 - 0.497079i) q^{76} -2.71688 q^{77} +(-5.85117 - 2.12965i) q^{78} +(1.82635 + 10.3578i) q^{79} +(8.87211 + 7.44459i) q^{80} +(0.766044 - 0.642788i) q^{81} +(2.25490 - 12.7882i) q^{82} +(5.73783 - 9.93821i) q^{83} +(0.0923963 + 0.160035i) q^{84} +(4.62449 - 1.68317i) q^{85} +(-0.254900 + 0.0927760i) q^{86} +(0.805407 + 1.39501i) q^{87} +(6.46451 - 11.1969i) q^{88} +(-1.02869 + 5.83396i) q^{89} +(2.97178 - 2.49362i) q^{90} +(1.65657 + 1.39003i) q^{91} +(0.183448 + 1.04039i) q^{92} +(9.28359 + 3.37895i) q^{93} -11.5817 q^{94} +(1.75877 + 10.8961i) q^{95} -1.94356 q^{96} +(6.39053 + 2.32596i) q^{97} +(1.78699 + 10.1345i) q^{98} +(-3.91147 - 3.28212i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q+3q23q46q53q6+3q73q86q10+3q116q13+9q14+6q1515q1612q17+18q19+6q20+3q219q236q24+12q26+3q99+O(q100) 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} - 6 q^{10} + 3 q^{11} - 6 q^{13} + 9 q^{14} + 6 q^{15} - 15 q^{16} - 12 q^{17} + 18 q^{19} + 6 q^{20} + 3 q^{21} - 9 q^{23} - 6 q^{24} + 12 q^{26}+ \cdots - 3 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/57Z)×\left(\mathbb{Z}/57\mathbb{Z}\right)^\times.

nn 2020 4040
χ(n)\chi(n) 11 e(19)e\left(\frac{1}{9}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.43969 + 0.524005i 1.01802 + 0.370528i 0.796506 0.604630i 0.206679π-0.206679\pi
0.221510 + 0.975158i 0.428901π0.428901\pi
33 −0.173648 0.984808i −0.100256 0.568579i
44 0.266044 + 0.223238i 0.133022 + 0.111619i
55 −1.93969 + 1.62760i −0.867457 + 0.727883i −0.963561 0.267489i 0.913806π-0.913806\pi
0.0961041 + 0.995371i 0.469362π0.469362\pi
66 0.266044 1.50881i 0.108612 0.615970i
77 −0.266044 + 0.460802i −0.100555 + 0.174167i −0.911914 0.410382i 0.865395π-0.865395\pi
0.811358 + 0.584549i 0.198729π0.198729\pi
88 −1.26604 2.19285i −0.447614 0.775291i
99 −0.939693 + 0.342020i −0.313231 + 0.114007i
1010 −3.64543 + 1.32683i −1.15279 + 0.419580i
1111 2.55303 + 4.42198i 0.769769 + 1.33328i 0.937688 + 0.347478i 0.112962π0.112962\pi
−0.167920 + 0.985801i 0.553705π0.553705\pi
1212 0.173648 0.300767i 0.0501279 0.0868241i
1313 0.705737 4.00243i 0.195736 1.11008i −0.715630 0.698479i 0.753860π-0.753860\pi
0.911366 0.411596i 0.135029π-0.135029\pi
1414 −0.624485 + 0.524005i −0.166901 + 0.140046i
1515 1.93969 + 1.62760i 0.500826 + 0.420243i
1616 −0.794263 4.50449i −0.198566 1.12612i
1717 −1.82635 0.664738i −0.442955 0.161223i 0.110907 0.993831i 0.464624π-0.464624\pi
−0.553862 + 0.832608i 0.686847π0.686847\pi
1818 −1.53209 −0.361117
1919 2.23396 3.74292i 0.512505 0.858685i
2020 −0.879385 −0.196637
2121 0.500000 + 0.181985i 0.109109 + 0.0397124i
2222 1.35844 + 7.70410i 0.289621 + 1.64252i
2323 2.33022 + 1.95529i 0.485885 + 0.407706i 0.852549 0.522648i 0.175056π-0.175056\pi
−0.366664 + 0.930353i 0.619500π0.619500\pi
2424 −1.93969 + 1.62760i −0.395938 + 0.332232i
2525 0.245100 1.39003i 0.0490200 0.278006i
2626 3.11334 5.39246i 0.610576 1.05755i
2727 0.500000 + 0.866025i 0.0962250 + 0.166667i
2828 −0.173648 + 0.0632028i −0.0328164 + 0.0119442i
2929 −1.51367 + 0.550931i −0.281082 + 0.102305i −0.478714 0.877971i 0.658897π-0.658897\pi
0.197633 + 0.980276i 0.436675π0.436675\pi
3030 1.93969 + 3.35965i 0.354138 + 0.613385i
3131 −4.93969 + 8.55580i −0.887195 + 1.53667i −0.0440180 + 0.999031i 0.514016π0.514016\pi
−0.843177 + 0.537636i 0.819317π0.819317\pi
3232 0.337496 1.91404i 0.0596615 0.338357i
3333 3.91147 3.28212i 0.680900 0.571343i
3434 −2.28106 1.91404i −0.391198 0.328254i
3535 −0.233956 1.32683i −0.0395457 0.224275i
3636 −0.326352 0.118782i −0.0543920 0.0197971i
3737 6.10607 1.00383 0.501916 0.864917i 0.332629π-0.332629\pi
0.501916 + 0.864917i 0.332629π0.332629\pi
3838 5.17752 4.21805i 0.839904 0.684258i
3939 −4.06418 −0.650789
4040 6.02481 + 2.19285i 0.952607 + 0.346721i
4141 −1.47178 8.34689i −0.229854 1.30356i −0.853186 0.521607i 0.825333π-0.825333\pi
0.623332 0.781957i 0.285779π-0.285779\pi
4242 0.624485 + 0.524005i 0.0963602 + 0.0808558i
4343 −0.135630 + 0.113807i −0.0206833 + 0.0173554i −0.653071 0.757297i 0.726520π-0.726520\pi
0.632387 + 0.774652i 0.282075π0.282075\pi
4444 −0.307934 + 1.74638i −0.0464227 + 0.263276i
4545 1.26604 2.19285i 0.188731 0.326891i
4646 2.33022 + 4.03606i 0.343573 + 0.595085i
4747 −7.10354 + 2.58548i −1.03616 + 0.377131i −0.803422 0.595409i 0.796990π-0.796990\pi
−0.232735 + 0.972540i 0.574768π0.574768\pi
4848 −4.29813 + 1.56439i −0.620382 + 0.225801i
4949 3.35844 + 5.81699i 0.479777 + 0.830999i
5050 1.08125 1.87278i 0.152912 0.264852i
5151 −0.337496 + 1.91404i −0.0472589 + 0.268019i
5252 1.08125 0.907278i 0.149943 0.125817i
5353 −7.58512 6.36467i −1.04190 0.874255i −0.0496783 0.998765i 0.515820π-0.515820\pi
−0.992218 + 0.124510i 0.960264π0.960264\pi
5454 0.266044 + 1.50881i 0.0362041 + 0.205323i
5555 −12.1493 4.42198i −1.63821 0.596260i
5656 1.34730 0.180040
5757 −4.07398 1.55007i −0.539612 0.205311i
5858 −2.46791 −0.324053
5959 3.58512 + 1.30488i 0.466743 + 0.169881i 0.564676 0.825312i 0.309001π-0.309001\pi
−0.0979333 + 0.995193i 0.531223π0.531223\pi
6060 0.152704 + 0.866025i 0.0197140 + 0.111803i
6161 −10.6702 8.95340i −1.36618 1.14637i −0.974018 0.226471i 0.927281π-0.927281\pi
−0.392167 0.919894i 0.628274π-0.628274\pi
6262 −11.5949 + 9.72930i −1.47256 + 1.23562i
6363 0.0923963 0.524005i 0.0116408 0.0660185i
6464 −3.08512 + 5.34359i −0.385640 + 0.667949i
6565 5.14543 + 8.91215i 0.638212 + 1.10542i
6666 7.35117 2.67561i 0.904866 0.329344i
6767 9.59627 3.49276i 1.17237 0.426708i 0.318869 0.947799i 0.396697π-0.396697\pi
0.853501 + 0.521091i 0.174475π0.174475\pi
6868 −0.337496 0.584561i −0.0409274 0.0708884i
6969 1.52094 2.63435i 0.183100 0.317139i
7070 0.358441 2.03282i 0.0428419 0.242968i
7171 2.92855 2.45734i 0.347555 0.291633i −0.452253 0.891890i 0.649379π-0.649379\pi
0.799807 + 0.600257i 0.204935π0.204935\pi
7272 1.93969 + 1.62760i 0.228595 + 0.191814i
7373 −0.322481 1.82888i −0.0377436 0.214055i 0.960103 0.279647i 0.0902174π-0.0902174\pi
−0.997847 + 0.0655924i 0.979106π0.979106\pi
7474 8.79086 + 3.19961i 1.02192 + 0.371947i
7575 −1.41147 −0.162983
7676 1.42989 0.497079i 0.164020 0.0570189i
7777 −2.71688 −0.309617
7878 −5.85117 2.12965i −0.662514 0.241135i
7979 1.82635 + 10.3578i 0.205481 + 1.16534i 0.896682 + 0.442676i 0.145971π0.145971\pi
−0.691201 + 0.722663i 0.742918π0.742918\pi
8080 8.87211 + 7.44459i 0.991932 + 0.832330i
8181 0.766044 0.642788i 0.0851160 0.0714208i
8282 2.25490 12.7882i 0.249012 1.41222i
8383 5.73783 9.93821i 0.629808 1.09086i −0.357782 0.933805i 0.616467π-0.616467\pi
0.987590 0.157055i 0.0501999π-0.0501999\pi
8484 0.0923963 + 0.160035i 0.0100813 + 0.0174613i
8585 4.62449 1.68317i 0.501596 0.182566i
8686 −0.254900 + 0.0927760i −0.0274866 + 0.0100043i
8787 0.805407 + 1.39501i 0.0863487 + 0.149560i
8888 6.46451 11.1969i 0.689119 1.19359i
8989 −1.02869 + 5.83396i −0.109040 + 0.618399i 0.880489 + 0.474067i 0.157214π0.157214\pi
−0.989529 + 0.144332i 0.953897π0.953897\pi
9090 2.97178 2.49362i 0.313253 0.262851i
9191 1.65657 + 1.39003i 0.173656 + 0.145715i
9292 0.183448 + 1.04039i 0.0191258 + 0.108468i
9393 9.28359 + 3.37895i 0.962663 + 0.350381i
9494 −11.5817 −1.19456
9595 1.75877 + 10.8961i 0.180446 + 1.11792i
9696 −1.94356 −0.198364
9797 6.39053 + 2.32596i 0.648860 + 0.236166i 0.645419 0.763828i 0.276683π-0.276683\pi
0.00344055 + 0.999994i 0.498905π0.498905\pi
9898 1.78699 + 10.1345i 0.180513 + 1.02374i
9999 −3.91147 3.28212i −0.393118 0.329865i
100100 0.375515 0.315094i 0.0375515 0.0315094i
101101 −1.52094 + 8.62571i −0.151340 + 0.858290i 0.810717 + 0.585439i 0.199078π0.199078\pi
−0.962056 + 0.272851i 0.912033π0.912033\pi
102102 −1.48886 + 2.57877i −0.147419 + 0.255337i
103103 1.92262 + 3.33007i 0.189441 + 0.328122i 0.945064 0.326885i 0.105999π-0.105999\pi
−0.755623 + 0.655007i 0.772666π0.772666\pi
104104 −9.67024 + 3.51968i −0.948245 + 0.345133i
105105 −1.26604 + 0.460802i −0.123553 + 0.0449697i
106106 −7.58512 13.1378i −0.736732 1.27606i
107107 2.83750 4.91469i 0.274311 0.475121i −0.695650 0.718381i 0.744884π-0.744884\pi
0.969961 + 0.243260i 0.0782169π0.0782169\pi
108108 −0.0603074 + 0.342020i −0.00580308 + 0.0329109i
109109 −1.59833 + 1.34115i −0.153092 + 0.128459i −0.716116 0.697981i 0.754082π-0.754082\pi
0.563025 + 0.826440i 0.309638π0.309638\pi
110110 −15.1741 12.7326i −1.44680 1.21401i
111111 −1.06031 6.01330i −0.100640 0.570757i
112112 2.28699 + 0.832396i 0.216100 + 0.0786540i
113113 7.27631 0.684498 0.342249 0.939609i 0.388811π-0.388811\pi
0.342249 + 0.939609i 0.388811π0.388811\pi
114114 −5.05303 4.36640i −0.473260 0.408951i
115115 −7.70233 −0.718246
116116 −0.525692 0.191336i −0.0488093 0.0177651i
117117 0.705737 + 4.00243i 0.0652454 + 0.370025i
118118 4.47771 + 3.75725i 0.412207 + 0.345883i
119119 0.792204 0.664738i 0.0726212 0.0609364i
120120 1.11334 6.31407i 0.101634 0.576393i
121121 −7.53596 + 13.0527i −0.685087 + 1.18661i
122122 −10.6702 18.4814i −0.966039 1.67323i
123123 −7.96451 + 2.89884i −0.718135 + 0.261380i
124124 −3.22416 + 1.17350i −0.289538 + 0.105383i
125125 −4.54323 7.86911i −0.406359 0.703835i
126126 0.407604 0.705990i 0.0363122 0.0628946i
127127 0.317734 1.80196i 0.0281943 0.159898i −0.967460 0.253024i 0.918575π-0.918575\pi
0.995654 + 0.0931261i 0.0296860π0.0296860\pi
128128 −10.2194 + 8.57510i −0.903277 + 0.757939i
129129 0.135630 + 0.113807i 0.0119415 + 0.0100201i
130130 2.73783 + 15.5270i 0.240123 + 1.36181i
131131 8.25624 + 3.00503i 0.721351 + 0.262550i 0.676499 0.736443i 0.263496π-0.263496\pi
0.0448520 + 0.998994i 0.485718π0.485718\pi
132132 1.77332 0.154348
133133 1.13041 + 2.02520i 0.0980194 + 0.175607i
134134 15.6459 1.35160
135135 −2.37939 0.866025i −0.204785 0.0745356i
136136 0.854570 + 4.84651i 0.0732788 + 0.415585i
137137 −9.67546 8.11867i −0.826630 0.693625i 0.127884 0.991789i 0.459181π-0.459181\pi
−0.954515 + 0.298164i 0.903626π0.903626\pi
138138 3.57011 2.99568i 0.303908 0.255009i
139139 −0.703211 + 3.98811i −0.0596456 + 0.338267i −0.999998 0.00193468i 0.999384π-0.999384\pi
0.940353 + 0.340201i 0.110495π0.110495\pi
140140 0.233956 0.405223i 0.0197729 0.0342476i
141141 3.77972 + 6.54666i 0.318309 + 0.551328i
142142 5.50387 2.00324i 0.461875 0.168109i
143143 19.5005 7.09759i 1.63071 0.593530i
144144 2.28699 + 3.96118i 0.190582 + 0.330098i
145145 2.03936 3.53228i 0.169360 0.293340i
146146 0.494070 2.80201i 0.0408895 0.231896i
147147 5.14543 4.31753i 0.424388 0.356104i
148148 1.62449 + 1.36310i 0.133532 + 0.112047i
149149 1.05391 + 5.97702i 0.0863397 + 0.489657i 0.997059 + 0.0766320i 0.0244167π0.0244167\pi
−0.910720 + 0.413025i 0.864472π0.864472\pi
150150 −2.03209 0.739620i −0.165919 0.0603897i
151151 −0.162504 −0.0132244 −0.00661219 0.999978i 0.502105π-0.502105\pi
−0.00661219 + 0.999978i 0.502105π0.502105\pi
152152 −11.0360 0.160035i −0.895134 0.0129806i
153153 1.94356 0.157128
154154 −3.91147 1.42366i −0.315196 0.114722i
155155 −4.34389 24.6354i −0.348910 1.97877i
156156 −1.08125 0.907278i −0.0865694 0.0726404i
157157 5.10220 4.28125i 0.407200 0.341681i −0.416069 0.909333i 0.636593π-0.636593\pi
0.823269 + 0.567652i 0.192148π0.192148\pi
158158 −2.79813 + 15.8690i −0.222608 + 1.26247i
159159 −4.95084 + 8.57510i −0.392627 + 0.680050i
160160 2.46064 + 4.26195i 0.194530 + 0.336937i
161161 −1.52094 + 0.553579i −0.119867 + 0.0436281i
162162 1.43969 0.524005i 0.113113 0.0411697i
163163 0.224155 + 0.388249i 0.0175572 + 0.0304100i 0.874671 0.484718i 0.161078π-0.161078\pi
−0.857113 + 0.515128i 0.827744π0.827744\pi
164164 1.47178 2.54920i 0.114927 0.199059i
165165 −2.24510 + 12.7326i −0.174781 + 0.991231i
166166 13.4684 11.3013i 1.04535 0.877152i
167167 2.59627 + 2.17853i 0.200905 + 0.168579i 0.737690 0.675140i 0.235917π-0.235917\pi
−0.536785 + 0.843719i 0.680361π0.680361\pi
168168 −0.233956 1.32683i −0.0180501 0.102367i
169169 −3.30541 1.20307i −0.254262 0.0925438i
170170 7.53983 0.578279
171171 −0.819078 + 4.28125i −0.0626364 + 0.327395i
172172 −0.0614894 −0.00468852
173173 1.51842 + 0.552659i 0.115443 + 0.0420179i 0.399096 0.916909i 0.369324π-0.369324\pi
−0.283653 + 0.958927i 0.591546π0.591546\pi
174174 0.428548 + 2.43042i 0.0324882 + 0.184250i
175175 0.575322 + 0.482753i 0.0434903 + 0.0364927i
176176 17.8910 15.0123i 1.34858 1.13160i
177177 0.662504 3.75725i 0.0497968 0.282412i
178178 −4.53802 + 7.86008i −0.340139 + 0.589138i
179179 −1.05690 1.83061i −0.0789967 0.136826i 0.823821 0.566851i 0.191838π-0.191838\pi
−0.902817 + 0.430024i 0.858505π0.858505\pi
180180 0.826352 0.300767i 0.0615926 0.0224179i
181181 −8.22416 + 2.99335i −0.611297 + 0.222494i −0.629071 0.777348i 0.716564π-0.716564\pi
0.0177739 + 0.999842i 0.494342π0.494342\pi
182182 1.65657 + 2.86927i 0.122793 + 0.212684i
183183 −6.96451 + 12.0629i −0.514831 + 0.891714i
184184 1.33750 7.58532i 0.0986015 0.559197i
185185 −11.8439 + 9.93821i −0.870780 + 0.730671i
186186 11.5949 + 9.72930i 0.850181 + 0.713387i
187187 −1.72328 9.77320i −0.126019 0.714687i
188188 −2.46703 0.897927i −0.179927 0.0654880i
189189 −0.532089 −0.0387038
190190 −3.17752 + 16.6086i −0.230521 + 1.20492i
191191 −19.0719 −1.38000 −0.689998 0.723811i 0.742389π-0.742389\pi
−0.689998 + 0.723811i 0.742389π0.742389\pi
192192 5.79813 + 2.11035i 0.418444 + 0.152301i
193193 −4.13903 23.4736i −0.297934 1.68967i −0.655032 0.755601i 0.727345π-0.727345\pi
0.357098 0.934067i 0.383766π-0.383766\pi
194194 7.98158 + 6.69734i 0.573044 + 0.480841i
195195 7.88326 6.61484i 0.564532 0.473698i
196196 −0.405078 + 2.29731i −0.0289341 + 0.164093i
197197 2.19459 3.80115i 0.156358 0.270820i −0.777195 0.629260i 0.783358π-0.783358\pi
0.933553 + 0.358440i 0.116691π0.116691\pi
198198 −3.91147 6.77487i −0.277976 0.481469i
199199 18.8293 6.85332i 1.33478 0.485819i 0.426613 0.904434i 0.359707π-0.359707\pi
0.908164 + 0.418615i 0.137484π0.137484\pi
200200 −3.35844 + 1.22237i −0.237478 + 0.0864348i
201201 −5.10607 8.84397i −0.360154 0.623805i
202202 −6.70961 + 11.6214i −0.472086 + 0.817678i
203203 0.148833 0.844075i 0.0104460 0.0592425i
204204 −0.517074 + 0.433877i −0.0362024 + 0.0303774i
205205 16.4402 + 13.7949i 1.14823 + 0.963480i
206206 1.02300 + 5.80174i 0.0712761 + 0.404227i
207207 −2.85844 1.04039i −0.198675 0.0723119i
208208 −18.5895 −1.28895
209209 22.2545 + 0.322718i 1.53938 + 0.0223228i
210210 −2.06418 −0.142442
211211 −25.5526 9.30039i −1.75912 0.640266i −0.759172 0.650891i 0.774396π-0.774396\pi
−0.999944 + 0.0106250i 0.996618π0.996618\pi
212212 −0.597144 3.38657i −0.0410120 0.232591i
213213 −2.92855 2.45734i −0.200661 0.168374i
214214 6.66044 5.58878i 0.455299 0.382041i
215215 0.0778483 0.441500i 0.00530921 0.0301100i
216216 1.26604 2.19285i 0.0861434 0.149205i
217217 −2.62836 4.55245i −0.178424 0.309040i
218218 −3.00387 + 1.09332i −0.203448 + 0.0740489i
219219 −1.74510 + 0.635164i −0.117923 + 0.0429204i
220220 −2.24510 3.88863i −0.151365 0.262171i
221221 −3.94949 + 6.84072i −0.265672 + 0.460157i
222222 1.62449 9.21291i 0.109028 0.618330i
223223 −9.20233 + 7.72167i −0.616234 + 0.517082i −0.896617 0.442807i 0.853983π-0.853983\pi
0.280383 + 0.959888i 0.409538π0.409538\pi
224224 0.792204 + 0.664738i 0.0529313 + 0.0444147i
225225 0.245100 + 1.39003i 0.0163400 + 0.0926687i
226226 10.4757 + 3.81283i 0.696830 + 0.253625i
227227 4.34049 0.288088 0.144044 0.989571i 0.453989π-0.453989\pi
0.144044 + 0.989571i 0.453989π0.453989\pi
228228 −0.737826 1.32185i −0.0488637 0.0875418i
229229 3.29591 0.217800 0.108900 0.994053i 0.465267π-0.465267\pi
0.108900 + 0.994053i 0.465267π0.465267\pi
230230 −11.0890 4.03606i −0.731187 0.266130i
231231 0.471782 + 2.67561i 0.0310409 + 0.176042i
232232 3.12449 + 2.62175i 0.205132 + 0.172127i
233233 −11.8209 + 9.91890i −0.774412 + 0.649809i −0.941835 0.336076i 0.890900π-0.890900\pi
0.167423 + 0.985885i 0.446456π0.446456\pi
234234 −1.08125 + 6.13208i −0.0706836 + 0.400867i
235235 9.57057 16.5767i 0.624315 1.08135i
236236 0.662504 + 1.14749i 0.0431253 + 0.0746953i
237237 9.88326 3.59721i 0.641986 0.233664i
238238 1.48886 0.541899i 0.0965082 0.0351261i
239239 −7.91147 13.7031i −0.511751 0.886378i −0.999907 0.0136221i 0.995664π-0.995664\pi
0.488156 0.872756i 0.337670π-0.337670\pi
240240 5.79086 10.0301i 0.373798 0.647438i
241241 −4.10607 + 23.2867i −0.264495 + 1.50003i 0.505974 + 0.862549i 0.331133π0.331133\pi
−0.770469 + 0.637477i 0.779978π0.779978\pi
242242 −17.6891 + 14.8429i −1.13710 + 0.954140i
243243 −0.766044 0.642788i −0.0491418 0.0412348i
244244 −0.840022 4.76400i −0.0537769 0.304984i
245245 −15.9820 5.81699i −1.02106 0.371634i
246246 −12.9855 −0.827922
247247 −13.4042 11.5828i −0.852889 0.736994i
248248 25.0155 1.58848
249249 −10.7836 3.92490i −0.683382 0.248731i
250250 −2.41740 13.7098i −0.152890 0.867083i
251251 14.8701 + 12.4775i 0.938589 + 0.787570i 0.977339 0.211679i 0.0678931π-0.0678931\pi
−0.0387499 + 0.999249i 0.512338π0.512338\pi
252252 0.141559 0.118782i 0.00891740 0.00748258i
253253 −2.69712 + 15.2961i −0.169566 + 0.961659i
254254 1.40167 2.42777i 0.0879488 0.152332i
255255 −2.46064 4.26195i −0.154091 0.266894i
256256 −7.60994 + 2.76979i −0.475621 + 0.173112i
257257 −11.5544 + 4.20545i −0.720742 + 0.262329i −0.676241 0.736681i 0.736392π-0.736392\pi
−0.0445014 + 0.999009i 0.514170π0.514170\pi
258258 0.135630 + 0.234917i 0.00844392 + 0.0146253i
259259 −1.62449 + 2.81369i −0.100941 + 0.174834i
260260 −0.620615 + 3.51968i −0.0384889 + 0.218281i
261261 1.23396 1.03541i 0.0763799 0.0640904i
262262 10.3118 + 8.65263i 0.637065 + 0.534561i
263263 1.10101 + 6.24416i 0.0678915 + 0.385032i 0.999753 + 0.0222179i 0.00707275π0.00707275\pi
−0.931862 + 0.362814i 0.881816π0.881816\pi
264264 −12.1493 4.42198i −0.747738 0.272154i
265265 25.0719 1.54016
266266 0.566237 + 3.50800i 0.0347182 + 0.215089i
267267 5.92396 0.362541
268268 3.33275 + 1.21302i 0.203580 + 0.0740971i
269269 −0.403733 2.28969i −0.0246161 0.139605i 0.970023 0.243014i 0.0781360π-0.0781360\pi
−0.994639 + 0.103409i 0.967025π0.967025\pi
270270 −2.97178 2.49362i −0.180857 0.151757i
271271 11.4474 9.60554i 0.695382 0.583495i −0.225074 0.974342i 0.572262π-0.572262\pi
0.920456 + 0.390847i 0.127818π0.127818\pi
272272 −1.54370 + 8.75476i −0.0936006 + 0.530835i
273273 1.08125 1.87278i 0.0654403 0.113346i
274274 −9.67546 16.7584i −0.584516 1.01241i
275275 6.77244 2.46497i 0.408394 0.148643i
276276 0.992726 0.361323i 0.0597551 0.0217491i
277277 11.9829 + 20.7550i 0.719984 + 1.24705i 0.961005 + 0.276529i 0.0891843π0.0891843\pi
−0.241021 + 0.970520i 0.577482π0.577482\pi
278278 −3.10220 + 5.37316i −0.186057 + 0.322261i
279279 1.71554 9.72930i 0.102707 0.582478i
280280 −2.61334 + 2.19285i −0.156177 + 0.131048i
281281 19.5804 + 16.4299i 1.16807 + 0.980125i 0.999984 0.00564805i 0.00179784π-0.00179784\pi
0.168083 + 0.985773i 0.446242π0.446242\pi
282282 2.01114 + 11.4058i 0.119762 + 0.679204i
283283 7.05778 + 2.56882i 0.419542 + 0.152701i 0.543160 0.839629i 0.317228π-0.317228\pi
−0.123619 + 0.992330i 0.539450π0.539450\pi
284284 1.32770 0.0787843
285285 10.4251 3.62414i 0.617532 0.214675i
286286 31.7939 1.88001
287287 4.23783 + 1.54244i 0.250151 + 0.0910475i
288288 0.337496 + 1.91404i 0.0198872 + 0.112786i
289289 −10.1291 8.49930i −0.595828 0.499959i
290290 4.78699 4.01676i 0.281102 0.235872i
291291 1.18092 6.69734i 0.0692269 0.392605i
292292 0.322481 0.558554i 0.0188718 0.0326869i
293293 −7.38326 12.7882i −0.431334 0.747093i 0.565654 0.824643i 0.308624π-0.308624\pi
−0.996989 + 0.0775495i 0.975290π0.975290\pi
294294 9.67024 3.51968i 0.563980 0.205272i
295295 −9.07785 + 3.30407i −0.528533 + 0.192370i
296296 −7.73055 13.3897i −0.449329 0.778261i
297297 −2.55303 + 4.42198i −0.148142 + 0.256590i
298298 −1.61468 + 9.15733i −0.0935362 + 0.530470i
299299 9.47044 7.94664i 0.547690 0.459566i
300300 −0.375515 0.315094i −0.0216804 0.0181920i
301301 −0.0163589 0.0927760i −0.000942912 0.00534752i
302302 −0.233956 0.0851529i −0.0134626 0.00490000i
303303 8.75877 0.503178
304304 −18.6343 7.08997i −1.06875 0.406637i
305305 35.2695 2.01953
306306 2.79813 + 1.01844i 0.159959 + 0.0582202i
307307 0.957234 + 5.42874i 0.0546322 + 0.309835i 0.999863 0.0165689i 0.00527428π-0.00527428\pi
−0.945231 + 0.326404i 0.894163π0.894163\pi
308308 −0.722811 0.606511i −0.0411860 0.0345591i
309309 2.94562 2.47167i 0.167571 0.140608i
310310 6.65523 37.7437i 0.377992 2.14370i
311311 −8.69981 + 15.0685i −0.493321 + 0.854457i −0.999970 0.00769537i 0.997550π-0.997550\pi
0.506650 + 0.862152i 0.330884π0.330884\pi
312312 5.14543 + 8.91215i 0.291303 + 0.504551i
313313 −14.9820 + 5.45302i −0.846835 + 0.308223i −0.728749 0.684780i 0.759898π-0.759898\pi
−0.118086 + 0.993003i 0.537676π0.537676\pi
314314 9.58899 3.49011i 0.541138 0.196958i
315315 0.673648 + 1.16679i 0.0379558 + 0.0657413i
316316 −1.82635 + 3.16333i −0.102740 + 0.177951i
317317 0.342711 1.94361i 0.0192486 0.109164i −0.973670 0.227963i 0.926793π-0.926793\pi
0.992918 + 0.118799i 0.0379045π0.0379045\pi
318318 −11.6211 + 9.75125i −0.651678 + 0.546823i
319319 −6.30066 5.28688i −0.352769 0.296009i
320320 −2.71301 15.3863i −0.151662 0.860118i
321321 −5.33275 1.94096i −0.297645 0.108334i
322322 −2.47977 −0.138192
323323 −6.56805 + 5.35089i −0.365456 + 0.297732i
324324 0.347296 0.0192942
325325 −5.39053 1.96199i −0.299013 0.108832i
326326 0.119271 + 0.676417i 0.00660579 + 0.0374633i
327327 1.59833 + 1.34115i 0.0883876 + 0.0741660i
328328 −16.4402 + 13.7949i −0.907756 + 0.761698i
329329 0.698463 3.96118i 0.0385075 0.218387i
330330 −9.90420 + 17.1546i −0.545208 + 0.944328i
331331 0.418748 + 0.725293i 0.0230165 + 0.0398657i 0.877304 0.479935i 0.159340π-0.159340\pi
−0.854288 + 0.519800i 0.826006π0.826006\pi
332332 3.74510 1.36310i 0.205539 0.0748101i
333333 −5.73783 + 2.08840i −0.314431 + 0.114443i
334334 2.59627 + 4.49687i 0.142061 + 0.246058i
335335 −12.9290 + 22.3937i −0.706388 + 1.22350i
336336 0.422618 2.39679i 0.0230557 0.130756i
337337 −2.54916 + 2.13900i −0.138862 + 0.116519i −0.709573 0.704632i 0.751112π-0.751112\pi
0.570711 + 0.821151i 0.306668π0.306668\pi
338338 −4.12836 3.46410i −0.224553 0.188422i
339339 −1.26352 7.16577i −0.0686249 0.389191i
340340 1.60607 + 0.584561i 0.0871012 + 0.0317022i
341341 −50.4448 −2.73174
342342 −3.42262 + 5.73448i −0.185074 + 0.310085i
343343 −7.29860 −0.394087
344344 0.421274 + 0.153331i 0.0227136 + 0.00826707i
345345 1.33750 + 7.58532i 0.0720084 + 0.408380i
346346 1.89646 + 1.59132i 0.101954 + 0.0855498i
347347 3.07011 2.57613i 0.164812 0.138294i −0.556652 0.830746i 0.687914π-0.687914\pi
0.721464 + 0.692452i 0.243470π0.243470\pi
348348 −0.0971440 + 0.550931i −0.00520747 + 0.0295330i
349349 13.9513 24.1644i 0.746796 1.29349i −0.202555 0.979271i 0.564924π-0.564924\pi
0.949351 0.314218i 0.101742π-0.101742\pi
350350 0.575322 + 0.996487i 0.0307523 + 0.0532645i
351351 3.81908 1.39003i 0.203847 0.0741943i
352352 9.32547 3.39420i 0.497049 0.180911i
353353 −6.47178 11.2095i −0.344458 0.596619i 0.640797 0.767710i 0.278604π-0.278604\pi
−0.985255 + 0.171091i 0.945271π0.945271\pi
354354 2.92262 5.06212i 0.155335 0.269049i
355355 −1.68092 + 9.53298i −0.0892141 + 0.505958i
356356 −1.57604 + 1.32245i −0.0835298 + 0.0700898i
357357 −0.792204 0.664738i −0.0419279 0.0351816i
358358 −0.562367 3.18934i −0.0297220 0.168562i
359359 −10.7562 3.91495i −0.567693 0.206623i 0.0421972 0.999109i 0.486564π-0.486564\pi
−0.609890 + 0.792486i 0.708786π0.708786\pi
360360 −6.41147 −0.337914
361361 −9.01889 16.7230i −0.474678 0.880159i
362362 −13.4088 −0.704750
363363 14.1630 + 5.15490i 0.743363 + 0.270562i
364364 0.130415 + 0.739620i 0.00683560 + 0.0387666i
365365 3.60220 + 3.02260i 0.188548 + 0.158210i
366366 −16.3478 + 13.7174i −0.854511 + 0.717020i
367367 −4.96657 + 28.1668i −0.259253 + 1.47030i 0.525663 + 0.850693i 0.323817π0.323817\pi
−0.784916 + 0.619602i 0.787294π0.787294\pi
368368 6.95677 12.0495i 0.362647 0.628122i
369369 4.23783 + 7.34013i 0.220612 + 0.382112i
370370 −22.2592 + 8.10170i −1.15720 + 0.421187i
371371 4.95084 1.80196i 0.257035 0.0935530i
372372 1.71554 + 2.97140i 0.0889465 + 0.154060i
373373 6.28312 10.8827i 0.325328 0.563484i −0.656251 0.754543i 0.727859π-0.727859\pi
0.981579 + 0.191059i 0.0611921π0.0611921\pi
374374 2.64022 14.9734i 0.136522 0.774256i
375375 −6.96064 + 5.84067i −0.359446 + 0.301611i
376376 14.6630 + 12.3037i 0.756185 + 0.634515i
377377 1.13681 + 6.44718i 0.0585488 + 0.332047i
378378 −0.766044 0.278817i −0.0394011 0.0143408i
379379 −2.19934 −0.112973 −0.0564863 0.998403i 0.517990π-0.517990\pi
−0.0564863 + 0.998403i 0.517990π0.517990\pi
380380 −1.96451 + 3.29147i −0.100777 + 0.168849i
381381 −1.82976 −0.0937412
382382 −27.4577 9.99379i −1.40486 0.511327i
383383 −1.02940 5.83802i −0.0525999 0.298309i 0.947147 0.320799i 0.103952π-0.103952\pi
−0.999747 + 0.0224905i 0.992840π0.992840\pi
384384 10.2194 + 8.57510i 0.521507 + 0.437596i
385385 5.26991 4.42198i 0.268580 0.225365i
386386 6.34137 35.9637i 0.322767 1.83050i
387387 0.0885259 0.153331i 0.00450002 0.00779427i
388388 1.18092 + 2.04542i 0.0599522 + 0.103840i
389389 31.1215 11.3273i 1.57793 0.574318i 0.603174 0.797610i 0.293903π-0.293903\pi
0.974752 + 0.223292i 0.0716804π0.0716804\pi
390390 14.8157 5.39246i 0.750221 0.273058i
391391 −2.95605 5.12003i −0.149494 0.258931i
392392 8.50387 14.7291i 0.429510 0.743934i
393393 1.52569 8.65263i 0.0769610 0.436467i
394394 5.15136 4.32250i 0.259522 0.217765i
395395 −20.4008 17.1183i −1.02648 0.861315i
396396 −0.307934 1.74638i −0.0154742 0.0877588i
397397 24.4786 + 8.90950i 1.22855 + 0.447155i 0.873100 0.487541i 0.162106π-0.162106\pi
0.355448 + 0.934696i 0.384328π0.384328\pi
398398 30.6996 1.53883
399399 1.79813 1.46491i 0.0900193 0.0733374i
400400 −6.45605 −0.322803
401401 15.0052 + 5.46145i 0.749325 + 0.272732i 0.688322 0.725406i 0.258348π-0.258348\pi
0.0610031 + 0.998138i 0.480570π0.480570\pi
402402 −2.71688 15.4082i −0.135506 0.768491i
403403 30.7579 + 25.8089i 1.53216 + 1.28563i
404404 −2.33022 + 1.95529i −0.115933 + 0.0972792i
405405 −0.439693 + 2.49362i −0.0218485 + 0.123909i
406406 0.656574 1.13722i 0.0325852 0.0564393i
407407 15.5890 + 27.0009i 0.772718 + 1.33839i
408408 4.62449 1.68317i 0.228946 0.0833296i
409409 2.77079 1.00849i 0.137007 0.0498664i −0.272607 0.962126i 0.587886π-0.587886\pi
0.409614 + 0.912259i 0.365664π0.365664\pi
410410 16.4402 + 28.4752i 0.811922 + 1.40629i
411411 −6.31521 + 10.9383i −0.311506 + 0.539545i
412412 −0.231896 + 1.31515i −0.0114247 + 0.0647927i
413413 −1.55509 + 1.30488i −0.0765211 + 0.0642088i
414414 −3.57011 2.99568i −0.175461 0.147229i
415415 5.04576 + 28.6159i 0.247687 + 1.40470i
416416 −7.42262 2.70161i −0.363924 0.132457i
417417 4.04963 0.198311
418418 31.8705 + 12.1261i 1.55884 + 0.593106i
419419 −33.4962 −1.63640 −0.818198 0.574937i 0.805027π-0.805027\pi
−0.818198 + 0.574937i 0.805027π0.805027\pi
420420 −0.439693 0.160035i −0.0214548 0.00780891i
421421 3.12877 + 17.7441i 0.152487 + 0.864795i 0.961048 + 0.276383i 0.0891357π0.0891357\pi
−0.808561 + 0.588412i 0.799753π0.799753\pi
422422 −31.9145 26.7794i −1.55357 1.30360i
423423 5.79086 4.85911i 0.281561 0.236258i
424424 −4.35369 + 24.6910i −0.211434 + 1.19910i
425425 −1.37164 + 2.37576i −0.0665345 + 0.115241i
426426 −2.92855 5.07239i −0.141889 0.245758i
427427 6.96451 2.53487i 0.337036 0.122671i
428428 1.85204 0.674089i 0.0895219 0.0325833i
429429 −10.3760 17.9717i −0.500957 0.867683i
430430 0.343426 0.594831i 0.0165615 0.0286853i
431431 3.70233 20.9970i 0.178335 1.01139i −0.755888 0.654701i 0.772795π-0.772795\pi
0.934223 0.356688i 0.116094π-0.116094\pi
432432 3.50387 2.94010i 0.168580 0.141455i
433433 −16.8931 14.1750i −0.811828 0.681205i 0.139215 0.990262i 0.455542π-0.455542\pi
−0.951043 + 0.309057i 0.899987π0.899987\pi
434434 −1.39852 7.93139i −0.0671310 0.380719i
435435 −3.83275 1.39501i −0.183766 0.0668854i
436436 −0.724622 −0.0347031
437437 12.5241 4.35381i 0.599109 0.208271i
438438 −2.84524 −0.135951
439439 3.18257 + 1.15836i 0.151896 + 0.0552856i 0.416849 0.908976i 0.363134π-0.363134\pi
−0.264953 + 0.964261i 0.585357π0.585357\pi
440440 5.68479 + 32.2401i 0.271012 + 1.53698i
441441 −5.14543 4.31753i −0.245020 0.205597i
442442 −9.27063 + 7.77898i −0.440959 + 0.370008i
443443 −5.23799 + 29.7061i −0.248864 + 1.41138i 0.562480 + 0.826811i 0.309847π0.309847\pi
−0.811344 + 0.584569i 0.801264π0.801264\pi
444444 1.06031 1.83651i 0.0503200 0.0871567i
445445 −7.50000 12.9904i −0.355534 0.615803i
446446 −17.2947 + 6.29477i −0.818929 + 0.298066i
447447 5.70321 2.07580i 0.269753 0.0981819i
448448 −1.64156 2.84326i −0.0775564 0.134332i
449449 15.4559 26.7704i 0.729409 1.26337i −0.227725 0.973725i 0.573129π-0.573129\pi
0.957134 0.289647i 0.0935380π-0.0935380\pi
450450 −0.375515 + 2.12965i −0.0177019 + 0.100393i
451451 33.1523 27.8181i 1.56108 1.30990i
452452 1.93582 + 1.62435i 0.0910534 + 0.0764029i
453453 0.0282185 + 0.160035i 0.00132582 + 0.00751910i
454454 6.24897 + 2.27444i 0.293279 + 0.106745i
455455 −5.47565 −0.256703
456456 1.75877 + 10.8961i 0.0823620 + 0.510256i
457457 −39.0479 −1.82658 −0.913291 0.407307i 0.866468π-0.866468\pi
−0.913291 + 0.407307i 0.866468π0.866468\pi
458458 4.74510 + 1.72708i 0.221724 + 0.0807009i
459459 −0.337496 1.91404i −0.0157530 0.0893395i
460460 −2.04916 1.71945i −0.0955427 0.0801699i
461461 −1.15476 + 0.968961i −0.0537827 + 0.0451290i −0.669283 0.743008i 0.733399π-0.733399\pi
0.615500 + 0.788137i 0.288954π0.288954\pi
462462 −0.722811 + 4.09927i −0.0336282 + 0.190715i
463463 1.64156 2.84326i 0.0762897 0.132138i −0.825357 0.564612i 0.809026π-0.809026\pi
0.901646 + 0.432474i 0.142359π0.142359\pi
464464 3.68392 + 6.38073i 0.171021 + 0.296218i
465465 −23.5069 + 8.55580i −1.09010 + 0.396766i
466466 −22.2160 + 8.08596i −1.02914 + 0.374575i
467467 11.4436 + 19.8208i 0.529545 + 0.917199i 0.999406 + 0.0344584i 0.0109706π0.0109706\pi
−0.469861 + 0.882740i 0.655696π0.655696\pi
468468 −0.705737 + 1.22237i −0.0326227 + 0.0565042i
469469 −0.943563 + 5.35121i −0.0435697 + 0.247096i
470470 22.4650 18.8504i 1.03623 0.869502i
471471 −5.10220 4.28125i −0.235097 0.197270i
472472 −1.67752 9.51368i −0.0772141 0.437903i
473473 −0.849518 0.309199i −0.0390609 0.0142170i
474474 16.1138 0.740132
475475 −4.65523 4.02266i −0.213597 0.184572i
476476 0.359156 0.0164619
477477 9.30453 + 3.38657i 0.426025 + 0.155060i
478478 −4.20961 23.8739i −0.192543 1.09197i
479479 −7.39827 6.20789i −0.338036 0.283646i 0.457929 0.888989i 0.348591π-0.348591\pi
−0.795965 + 0.605343i 0.793036π0.793036\pi
480480 3.76991 3.16333i 0.172072 0.144386i
481481 4.30928 24.4391i 0.196486 1.11433i
482482 −18.1138 + 31.3740i −0.825061 + 1.42905i
483483 0.809278 + 1.40171i 0.0368234 + 0.0637800i
484484 −4.91875 + 1.79028i −0.223579 + 0.0813763i
485485 −16.1814 + 5.88954i −0.734759 + 0.267430i
486486 −0.766044 1.32683i −0.0347485 0.0601861i
487487 11.2554 19.4949i 0.510029 0.883397i −0.489903 0.871777i 0.662968π-0.662968\pi
0.999932 0.0116199i 0.00369881π-0.00369881\pi
488488 −6.12449 + 34.7337i −0.277242 + 1.57232i
489489 0.343426 0.288169i 0.0155303 0.0130314i
490490 −19.9611 16.7494i −0.901751 0.756659i
491491 1.26264 + 7.16079i 0.0569822 + 0.323162i 0.999953 0.00971390i 0.00309208π-0.00309208\pi
−0.942971 + 0.332876i 0.891981π0.891981\pi
492492 −2.76604 1.00676i −0.124703 0.0453881i
493493 3.13072 0.141001
494494 −13.2285 23.6995i −0.595178 1.06629i
495495 12.9290 0.581116
496496 42.4629 + 15.4552i 1.90664 + 0.693961i
497497 0.353226 + 2.00324i 0.0158444 + 0.0898578i
498498 −13.4684 11.3013i −0.603532 0.506424i
499499 −9.81386 + 8.23481i −0.439329 + 0.368641i −0.835458 0.549554i 0.814798π-0.814798\pi
0.396129 + 0.918195i 0.370353π0.370353\pi
500500 0.547981 3.10775i 0.0245065 0.138983i
501501 1.69459 2.93512i 0.0757088 0.131132i
502502 14.8701 + 25.7557i 0.663683 + 1.14953i
503503 −7.86571 + 2.86289i −0.350715 + 0.127650i −0.511370 0.859361i 0.670862π-0.670862\pi
0.160655 + 0.987011i 0.448639π0.448639\pi
504504 −1.26604 + 0.460802i −0.0563941 + 0.0205258i
505505 −11.0890 19.2067i −0.493454 0.854687i
506506 −11.8983 + 20.6084i −0.528943 + 0.916156i
507507 −0.610815 + 3.46410i −0.0271272 + 0.153846i
508508 0.486796 0.408471i 0.0215981 0.0181230i
509509 10.4816 + 8.79509i 0.464588 + 0.389836i 0.844816 0.535057i 0.179710π-0.179710\pi
−0.380228 + 0.924893i 0.624154π0.624154\pi
510510 −1.30928 7.42528i −0.0579758 0.328797i
511511 0.928548 + 0.337964i 0.0410766 + 0.0149506i
512512 14.2736 0.630811
513513 4.35844 + 0.0632028i 0.192430 + 0.00279047i
514514 −18.8384 −0.830928
515515 −9.14930 3.33007i −0.403166 0.146741i
516516 0.0106775 + 0.0605553i 0.000470052 + 0.00266580i
517517 −29.5685 24.8109i −1.30042 1.09118i
518518 −3.81315 + 3.19961i −0.167540 + 0.140583i
519519 0.280592 1.59132i 0.0123166 0.0698511i
520520 13.0287 22.5663i 0.571346 0.989600i
521521 8.48205 + 14.6913i 0.371605 + 0.643639i 0.989813 0.142376i 0.0454741π-0.0454741\pi
−0.618207 + 0.786015i 0.712141π0.712141\pi
522522 2.31908 0.844075i 0.101503 0.0369442i
523523 3.67112 1.33618i 0.160527 0.0584270i −0.260507 0.965472i 0.583890π-0.583890\pi
0.421034 + 0.907045i 0.361667π0.361667\pi
524524 1.52569 + 2.64258i 0.0666502 + 0.115441i
525525 0.375515 0.650411i 0.0163888 0.0283863i
526526 −1.68685 + 9.56661i −0.0735502 + 0.417124i
527527 14.7090 12.3423i 0.640733 0.537639i
528528 −17.8910 15.0123i −0.778606 0.653328i
529529 −2.38713 13.5381i −0.103788 0.588611i
530530 36.0959 + 13.1378i 1.56790 + 0.570670i
531531 −3.81521 −0.165566
532532 −0.151359 + 0.791143i −0.00656227 + 0.0343004i
533533 −34.4466 −1.49205
534534 8.52869 + 3.10419i 0.369072 + 0.134331i
535535 2.49525 + 14.1513i 0.107879 + 0.611813i
536536 −19.8084 16.6212i −0.855593 0.717927i
537537 −1.61927 + 1.35873i −0.0698767 + 0.0586335i
538538 0.618555 3.50800i 0.0266678 0.151241i
539539 −17.1484 + 29.7019i −0.738635 + 1.27935i
540540 −0.439693 0.761570i −0.0189214 0.0327728i
541541 −12.4017 + 4.51384i −0.533190 + 0.194065i −0.594562 0.804050i 0.702675π-0.702675\pi
0.0613724 + 0.998115i 0.480452π0.480452\pi
542542 21.5141 7.83051i 0.924111 0.336349i
543543 4.37598 + 7.57942i 0.187791 + 0.325264i
544544 −1.88872 + 3.27136i −0.0809781 + 0.140258i
545545 0.917404 5.20286i 0.0392973 0.222866i
546546 2.53802 2.12965i 0.108617 0.0911406i
547547 −24.1878 20.2960i −1.03420 0.867793i −0.0428509 0.999081i 0.513644π-0.513644\pi
−0.991344 + 0.131289i 0.958088π0.958088\pi
548548 −0.761707 4.31986i −0.0325385 0.184535i
549549 13.0890 + 4.76400i 0.558625 + 0.203323i
550550 11.0419 0.470828
551551 −1.31938 + 6.89630i −0.0562076 + 0.293792i
552552 −7.70233 −0.327833
553553 −5.25877 1.91404i −0.223626 0.0813931i
554554 6.37598 + 36.1600i 0.270890 + 1.53629i
555555 11.8439 + 9.93821i 0.502745 + 0.421853i
556556 −1.07738 + 0.904030i −0.0456912 + 0.0383394i
557557 6.18748 35.0909i 0.262172 1.48685i −0.514797 0.857312i 0.672133π-0.672133\pi
0.776969 0.629539i 0.216756π-0.216756\pi
558558 7.56805 13.1082i 0.320381 0.554916i
559559 0.359785 + 0.623166i 0.0152173 + 0.0263571i
560560 −5.79086 + 2.10770i −0.244708 + 0.0890666i
561561 −9.32547 + 3.39420i −0.393722 + 0.143303i
562562 19.5804 + 33.9142i 0.825948 + 1.43058i
563563 10.9957 19.0451i 0.463414 0.802657i −0.535714 0.844399i 0.679958π-0.679958\pi
0.999128 + 0.0417423i 0.0132909π0.0132909\pi
564564 −0.455889 + 2.58548i −0.0191964 + 0.108868i
565565 −14.1138 + 11.8429i −0.593772 + 0.498234i
566566 8.81496 + 7.39663i 0.370520 + 0.310904i
567567 0.0923963 + 0.524005i 0.00388028 + 0.0220062i
568568 −9.09627 3.31077i −0.381671 0.138917i
569569 28.7588 1.20563 0.602815 0.797881i 0.294046π-0.294046\pi
0.602815 + 0.797881i 0.294046π0.294046\pi
570570 16.9081 + 0.245188i 0.708201 + 0.0102698i
571571 7.30365 0.305648 0.152824 0.988253i 0.451163π-0.451163\pi
0.152824 + 0.988253i 0.451163π0.451163\pi
572572 6.77244 + 2.46497i 0.283170 + 0.103065i
573573 3.31180 + 18.7822i 0.138353 + 0.784637i
574574 5.29292 + 4.44129i 0.220922 + 0.185376i
575575 3.28905 2.75984i 0.137163 0.115093i
576576 1.07145 6.07650i 0.0446438 0.253188i
577577 −15.7545 + 27.2876i −0.655868 + 1.13600i 0.325807 + 0.945436i 0.394364π0.394364\pi
−0.981675 + 0.190561i 0.938969π0.938969\pi
578578 −10.1291 17.5441i −0.421314 0.729737i
579579 −22.3983 + 8.15230i −0.930840 + 0.338798i
580580 1.33110 0.484481i 0.0552709 0.0201170i
581581 3.05303 + 5.28801i 0.126661 + 0.219384i
582582 5.20961 9.02330i 0.215945 0.374028i
583583 8.77941 49.7905i 0.363606 2.06211i
584584 −3.60220 + 3.02260i −0.149060 + 0.125076i
585585 −7.88326 6.61484i −0.325933 0.273490i
586586 −3.92855 22.2799i −0.162287 0.920374i
587587 −25.6434 9.33342i −1.05842 0.385232i −0.246583 0.969122i 0.579308π-0.579308\pi
−0.811833 + 0.583890i 0.801530π0.801530\pi
588588 2.33275 0.0962009
589589 20.9886 + 37.6021i 0.864820 + 1.54937i
590590 −14.8007 −0.609334
591591 −4.12449 1.50119i −0.169659 0.0617507i
592592 −4.84982 27.5047i −0.199326 1.13044i
593593 26.6366 + 22.3507i 1.09383 + 0.917834i 0.996995 0.0774657i 0.0246828π-0.0246828\pi
0.0968375 + 0.995300i 0.469127π0.469127\pi
594594 −5.99273 + 5.02849i −0.245885 + 0.206322i
595595 −0.454707 + 2.57877i −0.0186412 + 0.105719i
596596 −1.05391 + 1.82543i −0.0431699 + 0.0747724i
597597 −10.0189 17.3532i −0.410046 0.710220i
598598 17.7986 6.47816i 0.727839 0.264912i
599599 −14.9402 + 5.43777i −0.610438 + 0.222181i −0.628695 0.777652i 0.716411π-0.716411\pi
0.0182567 + 0.999833i 0.494188π0.494188\pi
600600 1.78699 + 3.09516i 0.0729535 + 0.126359i
601601 12.3464 21.3846i 0.503621 0.872297i −0.496370 0.868111i 0.665334π-0.665334\pi
0.999991 0.00418616i 0.00133250π-0.00133250\pi
602602 0.0250633 0.142141i 0.00102150 0.00579324i
603603 −7.82295 + 6.56423i −0.318575 + 0.267316i
604604 −0.0432332 0.0362770i −0.00175914 0.00147609i
605605 −6.62701 37.5836i −0.269426 1.52799i
606606 12.6099 + 4.58964i 0.512244 + 0.186441i
607607 4.01455 0.162945 0.0814727 0.996676i 0.474038π-0.474038\pi
0.0814727 + 0.996676i 0.474038π0.474038\pi
608608 −6.41013 5.53909i −0.259965 0.224640i
609609 −0.857097 −0.0347313
610610 50.7772 + 18.4814i 2.05591 + 0.748290i
611611 5.33497 + 30.2561i 0.215830 + 1.22403i
612612 0.517074 + 0.433877i 0.0209015 + 0.0175384i
613613 −30.8082 + 25.8511i −1.24433 + 1.04412i −0.247157 + 0.968976i 0.579496π0.579496\pi
−0.997173 + 0.0751409i 0.976059π0.976059\pi
614614 −1.46657 + 8.31731i −0.0591858 + 0.335659i
615615 10.7306 18.5859i 0.432698 0.749454i
616616 3.43969 + 5.95772i 0.138589 + 0.240043i
617617 20.8427 7.58613i 0.839096 0.305406i 0.113509 0.993537i 0.463791π-0.463791\pi
0.725586 + 0.688131i 0.241569π0.241569\pi
618618 5.53596 2.01492i 0.222689 0.0810521i
619619 11.6177 + 20.1224i 0.466954 + 0.808788i 0.999287 0.0377469i 0.0120181π-0.0120181\pi
−0.532333 + 0.846535i 0.678685π0.678685\pi
620620 4.34389 7.52384i 0.174455 0.302165i
621621 −0.528218 + 2.99568i −0.0211967 + 0.120212i
622622 −20.4210 + 17.1353i −0.818809 + 0.687062i
623623 −2.41463 2.02611i −0.0967401 0.0811746i
624624 3.22803 + 18.3070i 0.129224 + 0.732868i
625625 28.2520 + 10.2829i 1.13008 + 0.411315i
626626 −24.4270 −0.976298
627627 −3.54664 21.9724i −0.141639 0.877494i
628628 2.31315 0.0923047
629629 −11.1518 4.05893i −0.444652 0.161840i
630630 0.358441 + 2.03282i 0.0142806 + 0.0809894i
631631 21.4893 + 18.0317i 0.855476 + 0.717830i 0.960989 0.276588i 0.0892037π-0.0892037\pi
−0.105512 + 0.994418i 0.533648π0.533648\pi
632632 20.4008 17.1183i 0.811500 0.680929i
633633 −4.72193 + 26.7794i −0.187680 + 1.06439i
634634 1.51186 2.61862i 0.0600436 0.103999i
635635 2.31655 + 4.01239i 0.0919295 + 0.159227i
636636 −3.23143 + 1.17614i −0.128135 + 0.0466371i
637637 25.6523 9.33667i 1.01638 0.369932i
638638 −6.30066 10.9131i −0.249446 0.432052i
639639 −1.91147 + 3.31077i −0.0756167 + 0.130972i
640640 5.86571 33.2661i 0.231863 1.31496i
641641 33.3068 27.9477i 1.31554 1.10387i 0.328309 0.944570i 0.393521π-0.393521\pi
0.987230 0.159299i 0.0509233π-0.0509233\pi
642642 −6.66044 5.58878i −0.262867 0.220571i
643643 6.83322 + 38.7531i 0.269476 + 1.52827i 0.755980 + 0.654595i 0.227161π0.227161\pi
−0.486504 + 0.873678i 0.661728π0.661728\pi
644644 −0.528218 0.192256i −0.0208147 0.00757594i
645645 −0.448311 −0.0176522
646646 −12.2599 + 4.26195i −0.482358 + 0.167684i
647647 18.8862 0.742493 0.371246 0.928534i 0.378931π-0.378931\pi
0.371246 + 0.928534i 0.378931π0.378931\pi
648648 −2.37939 0.866025i −0.0934711 0.0340207i
649649 3.38279 + 19.1847i 0.132786 + 0.753067i
650650 −6.73261 5.64933i −0.264075 0.221585i
651651 −4.02687 + 3.37895i −0.157826 + 0.132431i
652652 −0.0270364 + 0.153331i −0.00105883 + 0.00600492i
653653 23.3714 40.4804i 0.914593 1.58412i 0.107098 0.994248i 0.465844π-0.465844\pi
0.807495 0.589874i 0.200823π-0.200823\pi
654654 1.59833 + 2.76838i 0.0624995 + 0.108252i
655655 −20.9055 + 7.60900i −0.816847 + 0.297308i
656656 −36.4295 + 13.2592i −1.42233 + 0.517687i
657657 0.928548 + 1.60829i 0.0362261 + 0.0627455i
658658 3.08125 5.33688i 0.120120 0.208053i
659659 0.362778 2.05742i 0.0141318 0.0801455i −0.976926 0.213577i 0.931489π-0.931489\pi
0.991058 + 0.133432i 0.0425996π0.0425996\pi
660660 −3.43969 + 2.88624i −0.133890 + 0.112347i
661661 −9.53596 8.00162i −0.370906 0.311227i 0.438214 0.898871i 0.355611π-0.355611\pi
−0.809120 + 0.587644i 0.800056π0.800056\pi
662662 0.222811 + 1.26363i 0.00865980 + 0.0491122i
663663 7.42262 + 2.70161i 0.288271 + 0.104922i
664664 −29.0574 −1.12764
665665 −5.48886 2.08840i −0.212849 0.0809846i
666666 −9.35504 −0.362500
667667 −4.60442 1.67587i −0.178284 0.0648900i
668668 0.204393 + 1.15917i 0.00790820 + 0.0448496i
669669 9.20233 + 7.72167i 0.355783 + 0.298537i
670670 −30.3482 + 25.4652i −1.17245 + 0.983806i
671671 12.3503 70.0420i 0.476778 2.70394i
672672 0.517074 0.895599i 0.0199466 0.0345485i
673673 5.41060 + 9.37143i 0.208563 + 0.361242i 0.951262 0.308383i 0.0997880π-0.0997880\pi
−0.742699 + 0.669625i 0.766455π0.766455\pi
674674 −4.79086 + 1.74373i −0.184537 + 0.0671660i
675675 1.32635 0.482753i 0.0510513 0.0185812i
676676 −0.610815 1.05796i −0.0234929 0.0406908i
677677 −2.18092 + 3.77747i −0.0838196 + 0.145180i −0.904888 0.425651i 0.860045π-0.860045\pi
0.821068 + 0.570830i 0.193379π0.193379\pi
678678 1.93582 10.9786i 0.0743448 0.421630i
679679 −2.77197 + 2.32596i −0.106379 + 0.0892623i
680680 −9.54576 8.00984i −0.366063 0.307163i
681681 −0.753718 4.27455i −0.0288825 0.163801i
682682 −72.6250 26.4333i −2.78096 1.01218i
683683 −44.6441 −1.70826 −0.854130 0.520059i 0.825910π-0.825910\pi
−0.854130 + 0.520059i 0.825910π0.825910\pi
684684 −1.17365 + 0.956154i −0.0448756 + 0.0365595i
685685 31.9813 1.22194
686686 −10.5077 3.82450i −0.401187 0.146020i
687687 −0.572329 3.24584i −0.0218357 0.123837i
688688 0.620366 + 0.520549i 0.0236512 + 0.0198458i
689689 −30.8273 + 25.8672i −1.17443 + 0.985460i
690690 −2.04916 + 11.6214i −0.0780103 + 0.442418i
691691 −12.1604 + 21.0625i −0.462605 + 0.801256i −0.999090 0.0426544i 0.986419π-0.986419\pi
0.536485 + 0.843910i 0.319752π0.319752\pi
692692 0.280592 + 0.486000i 0.0106665 + 0.0184750i
693693 2.55303 0.929228i 0.0969817 0.0352985i
694694 5.76991 2.10008i 0.219023 0.0797178i
695695 −5.12701 8.88024i −0.194479 0.336847i
696696 2.03936 3.53228i 0.0773018 0.133891i
697697 −2.86050 + 16.2227i −0.108349 + 0.614479i
698698 32.7478 27.4787i 1.23952 1.04008i
699699 11.8209 + 9.91890i 0.447107 + 0.375167i
700700 0.0452926 + 0.256867i 0.00171190 + 0.00970867i
701701 22.1386 + 8.05780i 0.836164 + 0.304339i 0.724386 0.689394i 0.242123π-0.242123\pi
0.111778 + 0.993733i 0.464345π0.464345\pi
702702 6.22668 0.235011
703703 13.6407 22.8545i 0.514468 0.861974i
704704 −31.5057 −1.18742
705705 −17.9868 6.54666i −0.677422 0.246561i
706706 −3.44356 19.5294i −0.129600 0.734999i
707707 −3.57011 2.99568i −0.134268 0.112664i
708708 1.01501 0.851698i 0.0381466 0.0320088i
709709 −1.06851 + 6.05985i −0.0401289 + 0.227582i −0.998276 0.0586939i 0.981306π-0.981306\pi
0.958147 + 0.286276i 0.0924175π0.0924175\pi
710710 −7.41534 + 12.8438i −0.278293 + 0.482017i
711711 −5.25877 9.10846i −0.197219 0.341594i
712712 14.0954 5.13030i 0.528247 0.192266i
713713 −28.2396 + 10.2784i −1.05758 + 0.384929i
714714 −0.792204 1.37214i −0.0296475 0.0513509i
715715 −26.2729 + 45.5060i −0.982551 + 1.70183i
716716 0.127478 0.722965i 0.00476408 0.0270185i
717717 −12.1211 + 10.1708i −0.452670 + 0.379835i
718718 −13.4342 11.2727i −0.501361 0.420692i
719719 5.65657 + 32.0800i 0.210955 + 1.19638i 0.887790 + 0.460249i 0.152240π0.152240\pi
−0.676835 + 0.736134i 0.736649π0.736649\pi
720720 −10.8833 3.96118i −0.405595 0.147625i
721721 −2.04601 −0.0761973
722722 −4.22147 28.8020i −0.157107 1.07190i
723723 23.6459 0.879400
724724 −2.85622 1.03958i −0.106151 0.0386356i
725725 0.394811 + 2.23908i 0.0146629 + 0.0831574i
726726 17.6891 + 14.8429i 0.656505 + 0.550873i
727727 24.6896 20.7170i 0.915686 0.768352i −0.0575058 0.998345i 0.518315π-0.518315\pi
0.973192 + 0.229993i 0.0738703π0.0738703\pi
728728 0.950837 5.39246i 0.0352404 0.199858i
729729 −0.500000 + 0.866025i −0.0185185 + 0.0320750i
730730 3.60220 + 6.23919i 0.133323 + 0.230923i
731731 0.323359 0.117693i 0.0119599 0.00435303i
732732 −4.54576 + 1.65452i −0.168016 + 0.0611529i
733733 −4.89053 8.47065i −0.180636 0.312870i 0.761461 0.648210i 0.224482π-0.224482\pi
−0.942097 + 0.335340i 0.891149π0.891149\pi
734734 −21.9099 + 37.9490i −0.808708 + 1.40072i
735735 −2.95336 + 16.7494i −0.108936 + 0.617809i
736736 4.52893 3.80023i 0.166939 0.140078i
737737 39.9445 + 33.5174i 1.47137 + 1.23463i
738738 2.25490 + 12.7882i 0.0830040 + 0.470739i
739739 −26.0993 9.49935i −0.960077 0.349439i −0.186013 0.982547i 0.559557π-0.559557\pi
−0.774064 + 0.633108i 0.781779π0.781779\pi
740740 −5.36959 −0.197390
741741 −9.07919 + 15.2119i −0.333532 + 0.558823i
742742 8.07192 0.296329
743743 30.3542 + 11.0480i 1.11359 + 0.405312i 0.832308 0.554314i 0.187019π-0.187019\pi
0.281278 + 0.959626i 0.409242π0.409242\pi
744744 −4.34389 24.6354i −0.159255 0.903179i
745745 −11.7724 9.87825i −0.431309 0.361911i
746746 14.7483 12.3753i 0.539975 0.453093i
747747 −1.99273 + 11.3013i −0.0729100 + 0.413493i
748748 1.72328 2.98481i 0.0630093 0.109135i
749749 1.50980 + 2.61505i 0.0551669 + 0.0955519i
750750 −13.0817 + 4.76136i −0.477677 + 0.173860i
751751 −3.27497 + 1.19199i −0.119505 + 0.0434964i −0.401081 0.916043i 0.631365π-0.631365\pi
0.281575 + 0.959539i 0.409143π0.409143\pi
752752 17.2883 + 29.9443i 0.630441 + 1.09196i
753753 9.70574 16.8108i 0.353697 0.612621i
754754 −1.74170 + 9.87765i −0.0634288 + 0.359723i
755755 0.315207 0.264490i 0.0114716 0.00962579i
756756 −0.141559 0.118782i −0.00514846 0.00432007i
757757 −6.41353 36.3730i −0.233104 1.32200i −0.846570 0.532277i 0.821337π-0.821337\pi
0.613467 0.789721i 0.289775π-0.289775\pi
758758 −3.16637 1.15247i −0.115008 0.0418594i
759759 15.5321 0.563779
760760 21.6668 17.6517i 0.785939 0.640293i
761761 31.3429 1.13618 0.568089 0.822967i 0.307683π-0.307683\pi
0.568089 + 0.822967i 0.307683π0.307683\pi
762762 −2.63429 0.958801i −0.0954301 0.0347337i
763763 −0.192782 1.09332i −0.00697917 0.0395808i
764764 −5.07398 4.25757i −0.183570 0.154034i
765765 −3.76991 + 3.16333i −0.136302 + 0.114371i
766766 1.57713 8.94437i 0.0569841 0.323173i
767767 7.75284 13.4283i 0.279939 0.484868i
768768 4.04916 + 7.01336i 0.146112 + 0.253073i
769769 29.8282 10.8566i 1.07563 0.391498i 0.257351 0.966318i 0.417150π-0.417150\pi
0.818280 + 0.574820i 0.194928π0.194928\pi
770770 9.90420 3.60483i 0.356923 0.129909i
771771 6.14796 + 10.6486i 0.221413 + 0.383499i
772772 4.13903 7.16902i 0.148967 0.258019i
773773 1.90269 10.7907i 0.0684351 0.388115i −0.931281 0.364301i 0.881308π-0.881308\pi
0.999716 0.0238140i 0.00758095π-0.00758095\pi
774774 0.207796 0.174362i 0.00746909 0.00626731i
775775 10.6821 + 8.96335i 0.383713 + 0.321973i
776776 −2.99020 16.9583i −0.107342 0.608766i
777777 3.05303 + 1.11121i 0.109527 + 0.0398646i
778778 50.7410 1.81915
779779 −34.5296 13.1378i −1.23715 0.470711i
780780 3.57398 0.127969
781781 18.3430 + 6.67631i 0.656365 + 0.238897i
782782 −1.57288 8.92026i −0.0562462 0.318988i
783783 −1.23396 1.03541i −0.0440980 0.0370026i
784784 23.5351 19.7483i 0.840539 0.705296i
785785 −2.92855 + 16.6086i −0.104524 + 0.592787i
786786 6.73055 11.6577i 0.240071 0.415815i
787787 −23.1771 40.1439i −0.826175 1.43098i −0.901018 0.433781i 0.857179π-0.857179\pi
0.0748436 0.997195i 0.476154π-0.476154\pi
788788 1.43242 0.521358i 0.0510278 0.0185726i
789789 5.95811 2.16858i 0.212114 0.0772033i
790790 −20.4008 35.3352i −0.725828 1.25717i
791791 −1.93582 + 3.35294i −0.0688299 + 0.119217i
792792 −2.24510 + 12.7326i −0.0797762 + 0.452433i
793793 −43.3658 + 36.3882i −1.53996 + 1.29218i
794794 30.5731 + 25.6539i 1.08500 + 0.910422i
795795 −4.35369 24.6910i −0.154410 0.875700i
796796 6.53936 + 2.38013i 0.231782 + 0.0843616i
797797 −3.47296 −0.123019 −0.0615093 0.998107i 0.519591π-0.519591\pi
−0.0615093 + 0.998107i 0.519591π0.519591\pi
798798 3.35638 1.16679i 0.118815 0.0413040i
799799 14.6922 0.519774
800800 −2.57785 0.938260i −0.0911407 0.0331725i
801801 −1.02869 5.83396i −0.0363468 0.206133i
802802 18.7411 + 15.7256i 0.661770 + 0.555291i
803803 7.26399 6.09521i 0.256340 0.215095i
804804 0.615867 3.49276i 0.0217200 0.123180i
805805 2.04916 3.54925i 0.0722235 0.125095i
806806 30.7579 + 53.2742i 1.08340 + 1.87650i
807807 −2.18479 + 0.795199i −0.0769083 + 0.0279923i
808808 20.8405 7.58532i 0.733166 0.266851i
809809 25.9748 + 44.9896i 0.913224 + 1.58175i 0.809480 + 0.587147i 0.199749π0.199749\pi
0.103744 + 0.994604i 0.466918π0.466918\pi
810810 −1.93969 + 3.35965i −0.0681539 + 0.118046i
811811 2.91329 16.5221i 0.102299 0.580168i −0.889965 0.456028i 0.849272π-0.849272\pi
0.992265 0.124140i 0.0396172π-0.0396172\pi
812812 0.228026 0.191336i 0.00800214 0.00671459i
813813 −11.4474 9.60554i −0.401479 0.336881i
814814 8.29473 + 47.0418i 0.290730 + 1.64881i
815815 −1.06670 0.388249i −0.0373650 0.0135998i
816816 8.88981 0.311206
817817 0.122979 + 0.761889i 0.00430249 + 0.0266551i
818818 4.51754 0.157952
819819 −2.03209 0.739620i −0.0710069 0.0258444i
820820 1.29426 + 7.34013i 0.0451976 + 0.256328i
821821 −28.5330 23.9420i −0.995809 0.835583i −0.00941101 0.999956i 0.502996π-0.502996\pi
−0.986398 + 0.164372i 0.947440π0.947440\pi
822822 −14.8237 + 12.4385i −0.517035 + 0.433844i
823823 −0.763985 + 4.33277i −0.0266308 + 0.151031i −0.995224 0.0976214i 0.968877π-0.968877\pi
0.968593 + 0.248652i 0.0799877π0.0799877\pi
824824 4.86824 8.43204i 0.169593 0.293744i
825825 −3.60354 6.24152i −0.125459 0.217302i
826826 −2.92262 + 1.06375i −0.101691 + 0.0370125i
827827 13.0265 4.74125i 0.452975 0.164869i −0.105450 0.994425i 0.533628π-0.533628\pi
0.558424 + 0.829555i 0.311406π0.311406\pi
828828 −0.528218 0.914901i −0.0183569 0.0317950i
829829 −8.18850 + 14.1829i −0.284398 + 0.492592i −0.972463 0.233057i 0.925127π-0.925127\pi
0.688065 + 0.725649i 0.258461π0.258461\pi
830830 −7.73055 + 43.8421i −0.268331 + 1.52178i
831831 18.3589 15.4050i 0.636863 0.534392i
832832 19.2101 + 16.1192i 0.665989 + 0.558832i
833833 −2.26692 12.8564i −0.0785442 0.445446i
834834 5.83022 + 2.12203i 0.201884 + 0.0734798i
835835 −8.58172 −0.296983
836836 5.84864 + 5.05390i 0.202279 + 0.174793i
837837 −9.87939 −0.341482
838838 −48.2242 17.5522i −1.66588 0.606330i
839839 −6.64883 37.7074i −0.229543 1.30180i −0.853807 0.520590i 0.825712π-0.825712\pi
0.624263 0.781214i 0.285399π-0.285399\pi
840840 2.61334 + 2.19285i 0.0901688 + 0.0756606i
841841 −20.2276 + 16.9730i −0.697504 + 0.585275i
842842 −4.79355 + 27.1856i −0.165197 + 0.936876i
843843 12.7802 22.1359i 0.440173 0.762402i
844844 −4.72193 8.17863i −0.162536 0.281520i
845845 8.36959 3.04628i 0.287922 0.104795i
846846 10.8833 3.96118i 0.374174 0.136188i
847847 −4.00980 6.94518i −0.137778 0.238639i
848848 −22.6450 + 39.2223i −0.777633 + 1.34690i
849849 1.30423 7.39663i 0.0447609 0.253852i
850850 −3.21966 + 2.70161i −0.110433 + 0.0926645i
851851 14.2285 + 11.9391i 0.487746 + 0.409268i
852852 −0.230552 1.30753i −0.00789858 0.0447951i
853853 −20.7579 7.55526i −0.710737 0.258687i −0.0387487 0.999249i 0.512337π-0.512337\pi
−0.671988 + 0.740562i 0.734559π0.734559\pi
854854 11.3550 0.388561
855855 −5.37939 9.63744i −0.183971 0.329593i
856856 −14.3696 −0.491142
857857 −42.2934 15.3936i −1.44472 0.525834i −0.503606 0.863933i 0.667994π-0.667994\pi
−0.941110 + 0.338100i 0.890216π0.890216\pi
858858 −5.52094 31.3108i −0.188482 1.06893i
859859 −12.2358 10.2670i −0.417479 0.350306i 0.409724 0.912209i 0.365625π-0.365625\pi
−0.827203 + 0.561903i 0.810069π0.810069\pi
860860 0.119271 0.100080i 0.00406709 0.00341270i
861861 0.783119 4.44129i 0.0266886 0.151359i
862862 16.3327 28.2892i 0.556296 0.963532i
863863 −20.6288 35.7302i −0.702213 1.21627i −0.967688 0.252151i 0.918862π-0.918862\pi
0.265475 0.964118i 0.414471π-0.414471\pi
864864 1.82635 0.664738i 0.0621338 0.0226148i
865865 −3.84477 + 1.39938i −0.130726 + 0.0475804i
866866 −16.8931 29.2596i −0.574049 0.994283i
867867 −6.61128 + 11.4511i −0.224531 + 0.388899i
868868 0.317018 1.79790i 0.0107603 0.0610247i
869869 −41.1391 + 34.5198i −1.39555 + 1.17100i
870870 −4.78699 4.01676i −0.162294 0.136181i
871871 −7.20708 40.8734i −0.244203 1.38494i
872872 4.96451 + 1.80693i 0.168119 + 0.0611905i
873873 −6.80066 −0.230167
874874 20.3123 + 0.294553i 0.687073 + 0.00996340i
875875 4.83481 0.163446
876876 −0.606067 0.220590i −0.0204771 0.00745306i
877877 8.01650 + 45.4638i 0.270698 + 1.53520i 0.752304 + 0.658817i 0.228943π0.228943\pi
−0.481606 + 0.876388i 0.659946π0.659946\pi
878878 3.97494 + 3.33537i 0.134148 + 0.112563i
879879 −11.3118 + 9.49173i −0.381538 + 0.320148i
880880 −10.2690 + 58.2386i −0.346169 + 1.96322i
881881 −9.47906 + 16.4182i −0.319357 + 0.553143i −0.980354 0.197245i 0.936800π-0.936800\pi
0.660997 + 0.750389i 0.270134π0.270134\pi
882882 −5.14543 8.91215i −0.173256 0.300088i
883883 −32.9359 + 11.9877i −1.10838 + 0.403418i −0.830399 0.557169i 0.811888π-0.811888\pi
−0.277981 + 0.960586i 0.589665π0.589665\pi
884884 −2.57785 + 0.938260i −0.0867024 + 0.0315571i
885885 4.83022 + 8.36619i 0.162366 + 0.281226i
886886 −23.1072 + 40.0229i −0.776303 + 1.34460i
887887 −3.09745 + 17.5665i −0.104002 + 0.589825i 0.887612 + 0.460592i 0.152363π0.152363\pi
−0.991614 + 0.129234i 0.958748π0.958748\pi
888888 −11.8439 + 9.93821i −0.397455 + 0.333504i
889889 0.745815 + 0.625813i 0.0250138 + 0.0209891i
890890 −3.99067 22.6322i −0.133767 0.758633i
891891 4.79813 + 1.74638i 0.160744 + 0.0585059i
892892 −4.17200 −0.139689
893893 −6.19176 + 32.3638i −0.207199 + 1.08301i
894894 9.29860 0.310992
895895 5.02956 + 1.83061i 0.168120 + 0.0611906i
896896 −1.23261 6.99049i −0.0411787 0.233536i
897897 −9.47044 7.94664i −0.316209 0.265331i
898898 36.2796 30.4422i 1.21066 1.01587i
899899 2.76341 15.6721i 0.0921650 0.522693i
900900 −0.245100 + 0.424525i −0.00817000 + 0.0141508i
901901 9.62226 + 16.6662i 0.320564 + 0.555233i
902902 62.3059 22.6775i 2.07456 0.755078i
903903 −0.0885259 + 0.0322208i −0.00294596 + 0.00107224i
904904 −9.21213 15.9559i −0.306391 0.530685i
905905 11.0804 19.1918i 0.368324 0.637956i
906906 −0.0432332 + 0.245188i −0.00143633 + 0.00814582i
907907 −10.9172 + 9.16058i −0.362498 + 0.304172i −0.805786 0.592207i 0.798257π-0.798257\pi
0.443287 + 0.896380i 0.353812π0.353812\pi
908908 1.15476 + 0.968961i 0.0383222 + 0.0321561i
909909 −1.52094 8.62571i −0.0504465 0.286097i
910910 −7.88326 2.86927i −0.261327 0.0951154i
911911 −16.4466 −0.544899 −0.272449 0.962170i 0.587834π-0.587834\pi
−0.272449 + 0.962170i 0.587834π0.587834\pi
912912 −3.74644 + 19.5823i −0.124057 + 0.648436i
913913 58.5954 1.93923
914914 −56.2169 20.4613i −1.85949 0.676799i
915915 −6.12449 34.7337i −0.202469 1.14826i
916916 0.876859 + 0.735772i 0.0289722 + 0.0243106i
917917 −3.58125 + 3.00503i −0.118263 + 0.0992347i
918918 0.517074 2.93247i 0.0170660 0.0967860i
919919 16.9500 29.3582i 0.559128 0.968437i −0.438442 0.898760i 0.644470π-0.644470\pi
0.997570 0.0696779i 0.0221971π-0.0221971\pi
920920 9.75150 + 16.8901i 0.321497 + 0.556850i
921921 5.18004 1.88538i 0.170688 0.0621255i
922922 −2.17024 + 0.789904i −0.0714732 + 0.0260141i
923923 −7.76857 13.4556i −0.255706 0.442895i
924924 −0.471782 + 0.817150i −0.0155205 + 0.0268822i
925925 1.49660 8.48762i 0.0492078 0.279071i
926926 3.85323 3.23324i 0.126625 0.106251i
927927 −2.94562 2.47167i −0.0967469 0.0811803i
928928 0.543644 + 3.08316i 0.0178460 + 0.101210i
929929 −20.2358 7.36522i −0.663914 0.241645i −0.0119887 0.999928i 0.503816π-0.503816\pi
−0.651925 + 0.758283i 0.726038π0.726038\pi
930930 −38.3259 −1.25676
931931 29.2751 + 0.424525i 0.959454 + 0.0139133i
932932 −5.35916 −0.175545
933933 16.3503 + 5.95102i 0.535284 + 0.194828i
934934 6.08899 + 34.5324i 0.199238 + 1.12993i
935935 19.2494 + 16.1522i 0.629524 + 0.528233i
936936 7.88326 6.61484i 0.257672 0.216213i
937937 1.31386 7.45129i 0.0429220 0.243423i −0.955797 0.294028i 0.905004π-0.905004\pi
0.998719 + 0.0506054i 0.0161151π0.0161151\pi
938938 −4.16250 + 7.20967i −0.135911 + 0.235404i
939939 7.97178 + 13.8075i 0.260149 + 0.450592i
940940 6.24675 2.27363i 0.203746 0.0741577i
941941 −17.9740 + 6.54200i −0.585936 + 0.213263i −0.617941 0.786225i 0.712033π-0.712033\pi
0.0320052 + 0.999488i 0.489811π0.489811\pi
942942 −5.10220 8.83726i −0.166239 0.287934i
943943 12.8910 22.3279i 0.419789 0.727095i
944944 3.03028 17.1856i 0.0986271 0.559342i
945945 1.03209 0.866025i 0.0335739 0.0281718i
946946 −1.06102 0.890304i −0.0344968 0.0289463i
947947 10.4549 + 59.2925i 0.339738 + 1.92675i 0.374214 + 0.927342i 0.377912π0.377912\pi
−0.0344768 + 0.999405i 0.510976π0.510976\pi
948948 3.43242 + 1.24930i 0.111480 + 0.0405753i
949949 −7.54757 −0.245005
950950 −4.59421 8.23075i −0.149056 0.267041i
951951 −1.97359 −0.0639981
952952 −2.46064 0.895599i −0.0797497 0.0290265i
953953 −3.42918 19.4478i −0.111082 0.629977i −0.988616 0.150462i 0.951924π-0.951924\pi
0.877534 0.479515i 0.159187π-0.159187\pi
954954 11.6211 + 9.75125i 0.376246 + 0.315708i
955955 36.9937 31.0414i 1.19709 1.00448i
956956 0.954241 5.41177i 0.0308623 0.175029i
957957 −4.11246 + 7.12300i −0.132937 + 0.230254i
958958 −7.39827 12.8142i −0.239027 0.414007i
959959 6.31521 2.29855i 0.203929 0.0742240i
960960 −14.6814 + 5.34359i −0.473840 + 0.172464i
961961 −33.3011 57.6792i −1.07423 1.86062i
962962 19.0103 32.9267i 0.612916 1.06160i
963963 −0.985452 + 5.58878i −0.0317557 + 0.180096i
964964 −6.29086 + 5.27866i −0.202615 + 0.170014i
965965 46.2340 + 38.7949i 1.48833 + 1.24885i
966966 0.430608 + 2.44210i 0.0138546 + 0.0785732i
967967 4.85679 + 1.76773i 0.156184 + 0.0568463i 0.418929 0.908019i 0.362406π-0.362406\pi
−0.262745 + 0.964865i 0.584628π0.584628\pi
968968 38.1634 1.22662
969969 6.41013 + 5.53909i 0.205923 + 0.177941i
970970 −26.3824 −0.847087
971971 8.22967 + 2.99536i 0.264103 + 0.0961256i 0.470678 0.882305i 0.344009π-0.344009\pi
−0.206575 + 0.978431i 0.566232π0.566232\pi
972972 −0.0603074 0.342020i −0.00193436 0.0109703i
973973 −1.65064 1.38505i −0.0529172 0.0444028i
974974 26.4197 22.1687i 0.846541 0.710332i
975975 −0.996130 + 5.64933i −0.0319017 + 0.180923i
976976 −31.8555 + 55.1754i −1.01967 + 1.76612i
977977 −20.3640 35.2714i −0.651501 1.12843i −0.982759 0.184892i 0.940806π-0.940806\pi
0.331258 0.943540i 0.392527π-0.392527\pi
978978 0.645430 0.234917i 0.0206386 0.00751182i
979979 −28.4240 + 10.3455i −0.908434 + 0.330643i
980980 −2.95336 5.11538i −0.0943417 0.163405i
981981 1.04323 1.80693i 0.0333079 0.0576909i
982982 −1.93448 + 10.9710i −0.0617317 + 0.350098i
983983 3.02616 2.53925i 0.0965195 0.0809895i −0.593251 0.805018i 0.702156π-0.702156\pi
0.689771 + 0.724028i 0.257711π0.257711\pi
984984 16.4402 + 13.7949i 0.524093 + 0.439766i
985985 1.92989 + 10.9450i 0.0614915 + 0.348736i
986986 4.50727 + 1.64051i 0.143541 + 0.0522446i
987987 −4.02229 −0.128031
988988 −0.980400 6.07386i −0.0311907 0.193235i
989989 −0.538572 −0.0171256
990990 18.6138 + 6.77487i 0.591586 + 0.215320i
991991 −3.22328 18.2801i −0.102391 0.580687i −0.992230 0.124414i 0.960295π-0.960295\pi
0.889840 0.456273i 0.150816π-0.150816\pi
992992 14.7090 + 12.3423i 0.467011 + 0.391868i
993993 0.641559 0.538332i 0.0203593 0.0170835i
994994 −0.541174 + 3.06915i −0.0171650 + 0.0973475i
995995 −25.3687 + 43.9399i −0.804242 + 1.39299i
996996 −1.99273 3.45150i −0.0631419 0.109365i
997997 −2.57398 + 0.936851i −0.0815187 + 0.0296704i −0.382458 0.923973i 0.624922π-0.624922\pi
0.300939 + 0.953643i 0.402700π0.402700\pi
998998 −18.4440 + 6.71308i −0.583836 + 0.212499i
999999 3.05303 + 5.28801i 0.0965937 + 0.167305i
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 57.2.i.a.4.1 6
3.2 odd 2 171.2.u.a.118.1 6
4.3 odd 2 912.2.bo.b.289.1 6
19.5 even 9 inner 57.2.i.a.43.1 yes 6
19.9 even 9 1083.2.a.m.1.1 3
19.10 odd 18 1083.2.a.n.1.3 3
57.5 odd 18 171.2.u.a.100.1 6
57.29 even 18 3249.2.a.x.1.1 3
57.47 odd 18 3249.2.a.w.1.3 3
76.43 odd 18 912.2.bo.b.385.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
57.2.i.a.4.1 6 1.1 even 1 trivial
57.2.i.a.43.1 yes 6 19.5 even 9 inner
171.2.u.a.100.1 6 57.5 odd 18
171.2.u.a.118.1 6 3.2 odd 2
912.2.bo.b.289.1 6 4.3 odd 2
912.2.bo.b.385.1 6 76.43 odd 18
1083.2.a.m.1.1 3 19.9 even 9
1083.2.a.n.1.3 3 19.10 odd 18
3249.2.a.w.1.3 3 57.47 odd 18
3249.2.a.x.1.1 3 57.29 even 18