Properties

Label 161.2.g.a.68.2
Level 161161
Weight 22
Character 161.68
Analytic conductor 1.2861.286
Analytic rank 00
Dimension 2828
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [161,2,Mod(45,161)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(161, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("161.45");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 161=723 161 = 7 \cdot 23
Weight: k k == 2 2
Character orbit: [χ][\chi] == 161.g (of order 66, degree 22, 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: 1.285591472541.28559147254
Analytic rank: 00
Dimension: 2828
Relative dimension: 1414 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 68.2
Character χ\chi == 161.68
Dual form 161.2.g.a.45.2

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+(1.23299+2.13559i)q2+(0.8544020.493289i)q3+(2.040513.53426i)q4+(1.243462.15373i)q5+2.43287iq6+(2.57635+0.602017i)q7+5.13171q8+(1.01333+1.75514i)q9+(3.06632+5.31103i)q10+(3.894152.24829i)q11+(3.486832.01312i)q12+2.10932iq13+(4.46226+4.75976i)q142.45353iq15+(2.24632+3.89073i)q16+(2.008233.47836i)q17+(2.498854.32813i)q18+(2.91949+5.05671i)q1910.1491q20+(2.498210.756521i)q21+11.0884iq22+(0.7929814.72982i)q23+(4.384552.53142i)q24+(0.5923631.02600i)q25+(4.504652.60076i)q26+4.95920iq27+(3.1293710.3339i)q28+2.64981q29+(5.23975+3.02517i)q30+(4.85302+2.80189i)q31+(0.4076370.706048i)q32+(2.218113.84188i)q33+9.90448q34+(4.500164.80017i)q35+8.27083q36+(0.6741160.389201i)q37+(7.1993812.4697i)q38+(1.04051+1.80221i)q39+(6.3810611.0523i)q40+1.68118iq41+(1.46463+6.26793i)q428.94389iq43+(15.89219.17528i)q44+(2.52006+4.36488i)q45+(9.12323+7.52528i)q46+(6.986424.03361i)q47+4.43234iq48+(6.27515+3.10201i)q49+2.92150q50+(3.431671.98128i)q51+(7.454894.30408i)q52+(5.49706+3.17373i)q53+(10.59086.11462i)q5411.1826iq55+(13.2211+3.08938i)q56+5.76061iq57+(3.26717+5.65891i)q58+(10.5475+6.08961i)q59+(8.67142+5.00645i)q60+(2.935705.08478i)q6113.8188iq62+(3.66732+3.91181i)q636.97482q64+(4.54291+2.62285i)q65+(5.46980+9.47397i)q66+(13.6208+7.86395i)q67+(8.19562+14.1952i)q68+(1.655644.43234i)q69+(4.70259+15.5290i)q70+5.33546q71+(5.20013+9.00688i)q72+(3.157491.82298i)q73+(1.662350.959758i)q74+(1.012230.584413i)q75+23.8290q76+(11.38623.44803i)q775.13171q78+(4.37340+2.52498i)q79+(5.58639+9.67591i)q80+(0.5936741.02827i)q81+(3.590332.07288i)q820.851415q83+(7.771357.28563i)q849.98859q85+(19.1005+11.0277i)q86+(2.264001.30712i)q87+(19.983611.5376i)q88+(3.977586.88938i)q8912.4288q90+(1.26985+5.43435i)q91+(18.3345+6.84862i)q92+(2.76429+4.78788i)q93+(17.22839.94677i)q94+(7.26051+12.5756i)q95+(0.6965720.402166i)q962.72009q97+(14.3618+9.57643i)q98+9.11304iq99+O(q100)q+(-1.23299 + 2.13559i) q^{2} +(0.854402 - 0.493289i) q^{3} +(-2.04051 - 3.53426i) q^{4} +(1.24346 - 2.15373i) q^{5} +2.43287i q^{6} +(2.57635 + 0.602017i) q^{7} +5.13171 q^{8} +(-1.01333 + 1.75514i) q^{9} +(3.06632 + 5.31103i) q^{10} +(3.89415 - 2.24829i) q^{11} +(-3.48683 - 2.01312i) q^{12} +2.10932i q^{13} +(-4.46226 + 4.75976i) q^{14} -2.45353i q^{15} +(-2.24632 + 3.89073i) q^{16} +(-2.00823 - 3.47836i) q^{17} +(-2.49885 - 4.32813i) q^{18} +(-2.91949 + 5.05671i) q^{19} -10.1491 q^{20} +(2.49821 - 0.756521i) q^{21} +11.0884i q^{22} +(0.792981 - 4.72982i) q^{23} +(4.38455 - 2.53142i) q^{24} +(-0.592363 - 1.02600i) q^{25} +(-4.50465 - 2.60076i) q^{26} +4.95920i q^{27} +(-3.12937 - 10.3339i) q^{28} +2.64981 q^{29} +(5.23975 + 3.02517i) q^{30} +(-4.85302 + 2.80189i) q^{31} +(-0.407637 - 0.706048i) q^{32} +(2.21811 - 3.84188i) q^{33} +9.90448 q^{34} +(4.50016 - 4.80017i) q^{35} +8.27083 q^{36} +(-0.674116 - 0.389201i) q^{37} +(-7.19938 - 12.4697i) q^{38} +(1.04051 + 1.80221i) q^{39} +(6.38106 - 11.0523i) q^{40} +1.68118i q^{41} +(-1.46463 + 6.26793i) q^{42} -8.94389i q^{43} +(-15.8921 - 9.17528i) q^{44} +(2.52006 + 4.36488i) q^{45} +(9.12323 + 7.52528i) q^{46} +(-6.98642 - 4.03361i) q^{47} +4.43234i q^{48} +(6.27515 + 3.10201i) q^{49} +2.92150 q^{50} +(-3.43167 - 1.98128i) q^{51} +(7.45489 - 4.30408i) q^{52} +(-5.49706 + 3.17373i) q^{53} +(-10.5908 - 6.11462i) q^{54} -11.1826i q^{55} +(13.2211 + 3.08938i) q^{56} +5.76061i q^{57} +(-3.26717 + 5.65891i) q^{58} +(-10.5475 + 6.08961i) q^{59} +(-8.67142 + 5.00645i) q^{60} +(2.93570 - 5.08478i) q^{61} -13.8188i q^{62} +(-3.66732 + 3.91181i) q^{63} -6.97482 q^{64} +(4.54291 + 2.62285i) q^{65} +(5.46980 + 9.47397i) q^{66} +(-13.6208 + 7.86395i) q^{67} +(-8.19562 + 14.1952i) q^{68} +(-1.65564 - 4.43234i) q^{69} +(4.70259 + 15.5290i) q^{70} +5.33546 q^{71} +(-5.20013 + 9.00688i) q^{72} +(3.15749 - 1.82298i) q^{73} +(1.66235 - 0.959758i) q^{74} +(-1.01223 - 0.584413i) q^{75} +23.8290 q^{76} +(11.3862 - 3.44803i) q^{77} -5.13171 q^{78} +(4.37340 + 2.52498i) q^{79} +(5.58639 + 9.67591i) q^{80} +(-0.593674 - 1.02827i) q^{81} +(-3.59033 - 2.07288i) q^{82} -0.851415 q^{83} +(-7.77135 - 7.28563i) q^{84} -9.98859 q^{85} +(19.1005 + 11.0277i) q^{86} +(2.26400 - 1.30712i) q^{87} +(19.9836 - 11.5376i) q^{88} +(3.97758 - 6.88938i) q^{89} -12.4288 q^{90} +(-1.26985 + 5.43435i) q^{91} +(-18.3345 + 6.84862i) q^{92} +(-2.76429 + 4.78788i) q^{93} +(17.2283 - 9.94677i) q^{94} +(7.26051 + 12.5756i) q^{95} +(-0.696572 - 0.402166i) q^{96} -2.72009 q^{97} +(-14.3618 + 9.57643i) q^{98} +9.11304i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 28q4q26q312q4+12q8+4q9+6q12+22q1836q2422q2512q2644q296q3210q3516q39+18q4636q47+28q49+84q50+146q98+O(q100) 28 q - 4 q^{2} - 6 q^{3} - 12 q^{4} + 12 q^{8} + 4 q^{9} + 6 q^{12} + 22 q^{18} - 36 q^{24} - 22 q^{25} - 12 q^{26} - 44 q^{29} - 6 q^{32} - 10 q^{35} - 16 q^{39} + 18 q^{46} - 36 q^{47} + 28 q^{49} + 84 q^{50}+ \cdots - 146 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/161Z)×\left(\mathbb{Z}/161\mathbb{Z}\right)^\times.

nn 2424 120120
χ(n)\chi(n) e(56)e\left(\frac{5}{6}\right) 1-1

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 −1.23299 + 2.13559i −0.871852 + 1.51009i −0.0117739 + 0.999931i 0.503748π0.503748\pi
−0.860078 + 0.510162i 0.829586π0.829586\pi
33 0.854402 0.493289i 0.493289 0.284801i −0.232649 0.972561i 0.574739π-0.574739\pi
0.725938 + 0.687760i 0.241406π0.241406\pi
44 −2.04051 3.53426i −1.02025 1.76713i
55 1.24346 2.15373i 0.556090 0.963176i −0.441728 0.897149i 0.645634π-0.645634\pi
0.997818 0.0660272i 0.0210324π-0.0210324\pi
66 2.43287i 0.993217i
77 2.57635 + 0.602017i 0.973768 + 0.227541i
88 5.13171 1.81433
99 −1.01333 + 1.75514i −0.337777 + 0.585047i
1010 3.06632 + 5.31103i 0.969657 + 1.67950i
1111 3.89415 2.24829i 1.17413 0.677884i 0.219480 0.975617i 0.429564π-0.429564\pi
0.954649 + 0.297733i 0.0962305π0.0962305\pi
1212 −3.48683 2.01312i −1.00656 0.581138i
1313 2.10932i 0.585021i 0.956262 + 0.292510i 0.0944906π0.0944906\pi
−0.956262 + 0.292510i 0.905509π0.905509\pi
1414 −4.46226 + 4.75976i −1.19259 + 1.27210i
1515 2.45353i 0.633500i
1616 −2.24632 + 3.89073i −0.561579 + 0.972684i
1717 −2.00823 3.47836i −0.487068 0.843626i 0.512822 0.858495i 0.328600π-0.328600\pi
−0.999889 + 0.0148691i 0.995267π0.995267\pi
1818 −2.49885 4.32813i −0.588983 1.02015i
1919 −2.91949 + 5.05671i −0.669777 + 1.16009i 0.308189 + 0.951325i 0.400277π0.400277\pi
−0.977966 + 0.208763i 0.933056π0.933056\pi
2020 −10.1491 −2.26941
2121 2.49821 0.756521i 0.545153 0.165086i
2222 11.0884i 2.36406i
2323 0.792981 4.72982i 0.165348 0.986235i
2424 4.38455 2.53142i 0.894992 0.516724i
2525 −0.592363 1.02600i −0.118473 0.205201i
2626 −4.50465 2.60076i −0.883435 0.510052i
2727 4.95920i 0.954398i
2828 −3.12937 10.3339i −0.591396 1.95292i
2929 2.64981 0.492057 0.246028 0.969263i 0.420874π-0.420874\pi
0.246028 + 0.969263i 0.420874π0.420874\pi
3030 5.23975 + 3.02517i 0.956643 + 0.552318i
3131 −4.85302 + 2.80189i −0.871628 + 0.503234i −0.867889 0.496759i 0.834523π-0.834523\pi
−0.00373884 + 0.999993i 0.501190π0.501190\pi
3232 −0.407637 0.706048i −0.0720607 0.124813i
3333 2.21811 3.84188i 0.386124 0.668786i
3434 9.90448 1.69860
3535 4.50016 4.80017i 0.760665 0.811378i
3636 8.27083 1.37847
3737 −0.674116 0.389201i −0.110824 0.0639842i 0.443563 0.896243i 0.353714π-0.353714\pi
−0.554387 + 0.832259i 0.687047π0.687047\pi
3838 −7.19938 12.4697i −1.16789 2.02285i
3939 1.04051 + 1.80221i 0.166614 + 0.288584i
4040 6.38106 11.0523i 1.00893 1.74752i
4141 1.68118i 0.262557i 0.991346 + 0.131278i 0.0419082π0.0419082\pi
−0.991346 + 0.131278i 0.958092π0.958092\pi
4242 −1.46463 + 6.26793i −0.225998 + 0.967163i
4343 8.94389i 1.36393i −0.731384 0.681965i 0.761125π-0.761125\pi
0.731384 0.681965i 0.238875π-0.238875\pi
4444 −15.8921 9.17528i −2.39582 1.38323i
4545 2.52006 + 4.36488i 0.375669 + 0.650678i
4646 9.12323 + 7.52528i 1.34515 + 1.10954i
4747 −6.98642 4.03361i −1.01907 0.588363i −0.105239 0.994447i 0.533561π-0.533561\pi
−0.913836 + 0.406084i 0.866894π0.866894\pi
4848 4.43234i 0.639753i
4949 6.27515 + 3.10201i 0.896450 + 0.443145i
5050 2.92150 0.413162
5151 −3.43167 1.98128i −0.480531 0.277434i
5252 7.45489 4.30408i 1.03381 0.596869i
5353 −5.49706 + 3.17373i −0.755079 + 0.435945i −0.827526 0.561427i 0.810253π-0.810253\pi
0.0724468 + 0.997372i 0.476919π0.476919\pi
5454 −10.5908 6.11462i −1.44123 0.832094i
5555 11.1826i 1.50786i
5656 13.2211 + 3.08938i 1.76674 + 0.412836i
5757 5.76061i 0.763012i
5858 −3.26717 + 5.65891i −0.429001 + 0.743051i
5959 −10.5475 + 6.08961i −1.37317 + 0.792799i −0.991326 0.131428i 0.958044π-0.958044\pi
−0.381843 + 0.924227i 0.624711π0.624711\pi
6060 −8.67142 + 5.00645i −1.11948 + 0.646330i
6161 2.93570 5.08478i 0.375878 0.651039i −0.614580 0.788854i 0.710675π-0.710675\pi
0.990458 + 0.137815i 0.0440080π0.0440080\pi
6262 13.8188i 1.75498i
6363 −3.66732 + 3.91181i −0.462039 + 0.492842i
6464 −6.97482 −0.871853
6565 4.54291 + 2.62285i 0.563478 + 0.325324i
6666 5.46980 + 9.47397i 0.673286 + 1.16617i
6767 −13.6208 + 7.86395i −1.66404 + 0.960734i −0.693284 + 0.720664i 0.743837π0.743837\pi
−0.970756 + 0.240070i 0.922830π0.922830\pi
6868 −8.19562 + 14.1952i −0.993864 + 1.72142i
6969 −1.65564 4.43234i −0.199316 0.533591i
7070 4.70259 + 15.5290i 0.562067 + 1.85608i
7171 5.33546 0.633203 0.316601 0.948559i 0.397458π-0.397458\pi
0.316601 + 0.948559i 0.397458π0.397458\pi
7272 −5.20013 + 9.00688i −0.612841 + 1.06147i
7373 3.15749 1.82298i 0.369556 0.213364i −0.303708 0.952765i 0.598225π-0.598225\pi
0.673265 + 0.739402i 0.264891π0.264891\pi
7474 1.66235 0.959758i 0.193244 0.111570i
7575 −1.01223 0.584413i −0.116883 0.0674822i
7676 23.8290 2.73337
7777 11.3862 3.44803i 1.29758 0.392939i
7878 −5.13171 −0.581052
7979 4.37340 + 2.52498i 0.492046 + 0.284083i 0.725423 0.688304i 0.241644π-0.241644\pi
−0.233377 + 0.972386i 0.574978π0.574978\pi
8080 5.58639 + 9.67591i 0.624577 + 1.08180i
8181 −0.593674 1.02827i −0.0659638 0.114253i
8282 −3.59033 2.07288i −0.396485 0.228911i
8383 −0.851415 −0.0934550 −0.0467275 0.998908i 0.514879π-0.514879\pi
−0.0467275 + 0.998908i 0.514879π0.514879\pi
8484 −7.77135 7.28563i −0.847924 0.794927i
8585 −9.98859 −1.08341
8686 19.1005 + 11.0277i 2.05966 + 1.18915i
8787 2.26400 1.30712i 0.242726 0.140138i
8888 19.9836 11.5376i 2.13026 1.22991i
8989 3.97758 6.88938i 0.421623 0.730273i −0.574475 0.818522i 0.694794π-0.694794\pi
0.996098 + 0.0882493i 0.0281272π0.0281272\pi
9090 −12.4288 −1.31011
9191 −1.26985 + 5.43435i −0.133116 + 0.569675i
9292 −18.3345 + 6.84862i −1.91150 + 0.714018i
9393 −2.76429 + 4.78788i −0.286643 + 0.496480i
9494 17.2283 9.94677i 1.77696 1.02593i
9595 7.26051 + 12.5756i 0.744913 + 1.29023i
9696 −0.696572 0.402166i −0.0710936 0.0410459i
9797 −2.72009 −0.276184 −0.138092 0.990419i 0.544097π-0.544097\pi
−0.138092 + 0.990419i 0.544097π0.544097\pi
9898 −14.3618 + 9.57643i −1.45076 + 0.967366i
9999 9.11304i 0.915895i
100100 −2.41744 + 4.18713i −0.241744 + 0.418713i
101101 −12.3302 + 7.11884i −1.22690 + 0.708351i −0.966380 0.257118i 0.917227π-0.917227\pi
−0.260519 + 0.965469i 0.583894π0.583894\pi
102102 8.46241 4.88577i 0.837903 0.483764i
103103 −4.71247 + 8.16223i −0.464333 + 0.804249i −0.999171 0.0407059i 0.987039π-0.987039\pi
0.534838 + 0.844955i 0.320373π0.320373\pi
104104 10.8244i 1.06142i
105105 1.47707 6.32116i 0.144147 0.616882i
106106 15.6527i 1.52032i
107107 −15.3817 8.88064i −1.48701 0.858524i −0.487117 0.873337i 0.661952π-0.661952\pi
−0.999890 + 0.0148126i 0.995285π0.995285\pi
108108 17.5271 10.1193i 1.68655 0.973727i
109109 5.63239 3.25186i 0.539485 0.311472i −0.205385 0.978681i 0.565845π-0.565845\pi
0.744870 + 0.667209i 0.232511π0.232511\pi
110110 23.8814 + 13.7880i 2.27701 + 1.31463i
111111 −0.767955 −0.0728910
112112 −8.12958 + 8.67157i −0.768174 + 0.819386i
113113 3.54545i 0.333528i 0.985997 + 0.166764i 0.0533318π0.0533318\pi
−0.985997 + 0.166764i 0.946668π0.946668\pi
114114 −12.3023 7.10275i −1.15222 0.665234i
115115 −9.20071 7.58918i −0.857970 0.707695i
116116 −5.40694 9.36510i −0.502022 0.869528i
117117 −3.70216 2.13744i −0.342265 0.197607i
118118 30.0336i 2.76482i
119119 −3.07987 10.1705i −0.282332 0.932324i
120120 12.5908i 1.14938i
121121 4.60959 7.98404i 0.419053 0.725822i
122122 7.23935 + 12.5389i 0.655420 + 1.13522i
123123 0.829310 + 1.43641i 0.0747764 + 0.129516i
124124 19.8052 + 11.4345i 1.77856 + 1.02685i
125125 9.48825 0.848655
126126 −3.83229 12.6551i −0.341408 1.12741i
127127 0.227609 0.0201970 0.0100985 0.999949i 0.496785π-0.496785\pi
0.0100985 + 0.999949i 0.496785π0.496785\pi
128128 9.41513 16.3075i 0.832188 1.44139i
129129 −4.41193 7.64168i −0.388449 0.672813i
130130 −11.2027 + 6.46787i −0.982539 + 0.567269i
131131 8.89889 + 5.13777i 0.777499 + 0.448889i 0.835543 0.549425i 0.185153π-0.185153\pi
−0.0580441 + 0.998314i 0.518486π0.518486\pi
132132 −18.1043 −1.57578
133133 −10.5659 + 11.2703i −0.916175 + 0.977255i
134134 38.7845i 3.35047i
135135 10.6808 + 6.16654i 0.919254 + 0.530731i
136136 −10.3057 17.8499i −0.883704 1.53062i
137137 9.01269 5.20348i 0.770006 0.444563i −0.0628708 0.998022i 0.520026π-0.520026\pi
0.832877 + 0.553459i 0.186692π0.186692\pi
138138 11.5071 + 1.92922i 0.979545 + 0.164226i
139139 6.21923i 0.527508i −0.964590 0.263754i 0.915039π-0.915039\pi
0.964590 0.263754i 0.0849607π-0.0849607\pi
140140 −26.1477 6.10994i −2.20988 0.516384i
141141 −7.95895 −0.670265
142142 −6.57855 + 11.3944i −0.552059 + 0.956195i
143143 4.74236 + 8.21401i 0.396576 + 0.686890i
144144 −4.55253 7.88521i −0.379377 0.657100i
145145 3.29491 5.70696i 0.273628 0.473937i
146146 8.99082i 0.744086i
147147 6.89169 0.445099i 0.568417 0.0367111i
148148 3.17667i 0.261120i
149149 15.3369 + 8.85477i 1.25645 + 0.725411i 0.972382 0.233393i 0.0749830π-0.0749830\pi
0.284067 + 0.958805i 0.408316π0.408316\pi
150150 2.49614 1.44114i 0.203809 0.117669i
151151 1.79196 + 3.10377i 0.145828 + 0.252581i 0.929681 0.368364i 0.120082π-0.120082\pi
−0.783854 + 0.620946i 0.786749π0.786749\pi
152152 −14.9820 + 25.9496i −1.21520 + 2.10479i
153153 8.14002 0.658081
154154 −6.67542 + 28.5676i −0.537920 + 2.30205i
155155 13.9361i 1.11937i
156156 4.24632 7.35484i 0.339977 0.588858i
157157 4.35719 + 7.54688i 0.347742 + 0.602306i 0.985848 0.167642i 0.0536153π-0.0536153\pi
−0.638106 + 0.769948i 0.720282π0.720282\pi
158158 −10.7847 + 6.22653i −0.857983 + 0.495356i
159159 −3.13113 + 5.42328i −0.248315 + 0.430094i
160160 −2.02751 −0.160289
161161 4.89043 11.7083i 0.385420 0.922741i
162162 2.92797 0.230043
163163 −3.03003 + 5.24816i −0.237330 + 0.411068i −0.959947 0.280181i 0.909606π-0.909606\pi
0.722617 + 0.691248i 0.242939π0.242939\pi
164164 5.94174 3.43047i 0.463972 0.267874i
165165 −5.51625 9.55442i −0.429439 0.743811i
166166 1.04978 1.81828i 0.0814789 0.141126i
167167 4.39200i 0.339863i 0.985456 + 0.169931i 0.0543546π0.0543546\pi
−0.985456 + 0.169931i 0.945645π0.945645\pi
168168 12.8201 3.88225i 0.989091 0.299522i
169169 8.55076 0.657751
170170 12.3158 21.3316i 0.944577 1.63606i
171171 −5.91682 10.2482i −0.452471 0.783702i
172172 −31.6100 + 18.2501i −2.41024 + 1.39155i
173173 7.29534 + 4.21197i 0.554655 + 0.320230i 0.750997 0.660305i 0.229573π-0.229573\pi
−0.196343 + 0.980535i 0.562906π0.562906\pi
174174 6.44664i 0.488719i
175175 −0.908463 2.99995i −0.0686733 0.226775i
176176 20.2015i 1.52274i
177177 −6.00788 + 10.4059i −0.451580 + 0.782159i
178178 9.80861 + 16.9890i 0.735186 + 1.27338i
179179 −3.81304 6.60438i −0.285000 0.493634i 0.687609 0.726081i 0.258660π-0.258660\pi
−0.972609 + 0.232447i 0.925327π0.925327\pi
180180 10.2844 17.8131i 0.766555 1.32771i
181181 −13.6135 −1.01189 −0.505943 0.862567i 0.668855π-0.668855\pi
−0.505943 + 0.862567i 0.668855π0.668855\pi
182182 −10.0399 9.41235i −0.744204 0.697690i
183183 5.79259i 0.428201i
184184 4.06935 24.2721i 0.299997 1.78936i
185185 −1.67647 + 0.967908i −0.123256 + 0.0711620i
186186 −6.81665 11.8068i −0.499821 0.865715i
187187 −15.6407 9.03016i −1.14376 0.660351i
188188 32.9224i 2.40112i
189189 −2.98552 + 12.7766i −0.217165 + 0.929363i
190190 −35.8084 −2.59782
191191 −8.68258 5.01289i −0.628249 0.362720i 0.151824 0.988407i 0.451485π-0.451485\pi
−0.780074 + 0.625687i 0.784819π0.784819\pi
192192 −5.95931 + 3.44061i −0.430076 + 0.248304i
193193 6.77881 + 11.7412i 0.487950 + 0.845154i 0.999904 0.0138591i 0.00441163π-0.00441163\pi
−0.511954 + 0.859013i 0.671078π0.671078\pi
194194 3.35383 5.80901i 0.240791 0.417063i
195195 5.17529 0.370610
196196 −1.84116 28.5077i −0.131512 2.03626i
197197 24.0652 1.71458 0.857288 0.514837i 0.172148π-0.172148\pi
0.857288 + 0.514837i 0.172148π0.172148\pi
198198 −19.4617 11.2362i −1.38309 0.798525i
199199 12.0641 + 20.8956i 0.855198 + 1.48125i 0.876461 + 0.481473i 0.159898π0.159898\pi
−0.0212629 + 0.999774i 0.506769π0.506769\pi
200200 −3.03984 5.26515i −0.214949 0.372302i
201201 −7.75840 + 13.4379i −0.547235 + 0.947840i
202202 35.1097i 2.47031i
203203 6.82682 + 1.59523i 0.479149 + 0.111963i
204204 16.1712i 1.13221i
205205 3.62081 + 2.09048i 0.252889 + 0.146005i
206206 −11.6208 20.1278i −0.809660 1.40237i
207207 7.49795 + 6.18467i 0.521143 + 0.429864i
208208 −8.20681 4.73820i −0.569040 0.328535i
209209 26.2554i 1.81612i
210210 11.6782 + 10.9483i 0.805874 + 0.755505i
211211 22.0361 1.51703 0.758515 0.651656i 0.225925π-0.225925\pi
0.758515 + 0.651656i 0.225925π0.225925\pi
212212 22.4336 + 12.9520i 1.54074 + 0.889549i
213213 4.55863 2.63193i 0.312352 0.180337i
214214 37.9309 21.8994i 2.59290 1.49701i
215215 −19.2627 11.1213i −1.31371 0.758469i
216216 25.4492i 1.73160i
217217 −14.1899 + 4.29705i −0.963270 + 0.291703i
218218 16.0380i 1.08623i
219219 1.79851 3.11511i 0.121532 0.210500i
220220 −39.5221 + 22.8181i −2.66458 + 1.53840i
221221 7.33698 4.23601i 0.493539 0.284945i
222222 0.946877 1.64004i 0.0635502 0.110072i
223223 16.7338i 1.12058i −0.828297 0.560290i 0.810690π-0.810690\pi
0.828297 0.560290i 0.189310π-0.189310\pi
224224 −0.625162 2.06443i −0.0417704 0.137936i
225225 2.40104 0.160069
226226 −7.57164 4.37149i −0.503658 0.290787i
227227 −14.6339 25.3467i −0.971289 1.68232i −0.691675 0.722208i 0.743127π-0.743127\pi
−0.279613 0.960113i 0.590206π-0.590206\pi
228228 20.3595 11.7546i 1.34834 0.778465i
229229 2.53147 4.38464i 0.167284 0.289745i −0.770180 0.637827i 0.779834π-0.779834\pi
0.937464 + 0.348082i 0.113167π0.113167\pi
230230 27.5517 10.2916i 1.81671 0.678609i
231231 8.02751 8.56269i 0.528171 0.563384i
232232 13.5980 0.892755
233233 1.05963 1.83533i 0.0694186 0.120237i −0.829227 0.558912i 0.811219π-0.811219\pi
0.898646 + 0.438676i 0.144552π0.144552\pi
234234 9.12941 5.27087i 0.596808 0.344567i
235235 −17.3746 + 10.0312i −1.13339 + 0.654366i
236236 43.0445 + 24.8518i 2.80196 + 1.61771i
237237 4.98219 0.323628
238238 25.5174 + 5.96267i 1.65405 + 0.386502i
239239 −11.1996 −0.724444 −0.362222 0.932092i 0.617982π-0.617982\pi
−0.362222 + 0.932092i 0.617982π0.617982\pi
240240 9.54605 + 5.51141i 0.616195 + 0.355760i
241241 −3.32975 5.76730i −0.214488 0.371504i 0.738626 0.674115i 0.235475π-0.235475\pi
−0.953114 + 0.302611i 0.902142π0.902142\pi
242242 11.3671 + 19.6884i 0.730705 + 1.26562i
243243 −13.8988 8.02450i −0.891611 0.514772i
244244 −23.9612 −1.53396
245245 14.4838 9.65775i 0.925334 0.617011i
246246 −4.09011 −0.260776
247247 −10.6662 6.15814i −0.678675 0.391833i
248248 −24.9043 + 14.3785i −1.58142 + 0.913036i
249249 −0.727451 + 0.419994i −0.0461003 + 0.0266160i
250250 −11.6989 + 20.2630i −0.739901 + 1.28155i
251251 2.15008 0.135712 0.0678559 0.997695i 0.478384π-0.478384\pi
0.0678559 + 0.997695i 0.478384π0.478384\pi
252252 21.3086 + 4.97918i 1.34231 + 0.313659i
253253 −7.54600 20.2015i −0.474413 1.27005i
254254 −0.280638 + 0.486080i −0.0176088 + 0.0304994i
255255 −8.53427 + 4.92726i −0.534437 + 0.308557i
256256 16.2426 + 28.1330i 1.01516 + 1.75831i
257257 −24.6604 14.2377i −1.53827 0.888122i −0.998940 0.0460288i 0.985343π-0.985343\pi
−0.539332 0.842093i 0.681323π-0.681323\pi
258258 21.7594 1.35468
259259 −1.50245 1.40855i −0.0933578 0.0875228i
260260 21.4077i 1.32765i
261261 −2.68513 + 4.65078i −0.166205 + 0.287876i
262262 −21.9444 + 12.6696i −1.35573 + 0.782731i
263263 10.8838 6.28378i 0.671126 0.387475i −0.125377 0.992109i 0.540014π-0.540014\pi
0.796503 + 0.604635i 0.206681π0.206681\pi
264264 11.3827 19.7154i 0.700558 1.21340i
265265 15.7856i 0.969700i
266266 −11.0411 36.4604i −0.676976 2.23553i
267267 7.84840i 0.480314i
268268 55.5865 + 32.0929i 3.39548 + 1.96038i
269269 13.5285 7.81069i 0.824848 0.476226i −0.0272372 0.999629i 0.508671π-0.508671\pi
0.852086 + 0.523403i 0.175338π0.175338\pi
270270 −26.3385 + 15.2065i −1.60291 + 0.925439i
271271 13.4285 + 7.75294i 0.815722 + 0.470957i 0.848939 0.528491i 0.177242π-0.177242\pi
−0.0332170 + 0.999448i 0.510575π0.510575\pi
272272 18.0445 1.09411
273273 1.59575 + 5.26952i 0.0965789 + 0.318926i
274274 25.6632i 1.55037i
275275 −4.61350 2.66360i −0.278204 0.160621i
276276 −12.2867 + 14.8957i −0.739571 + 0.896615i
277277 −0.909988 1.57615i −0.0546759 0.0947014i 0.837392 0.546603i 0.184079π-0.184079\pi
−0.892068 + 0.451901i 0.850746π0.850746\pi
278278 13.2817 + 7.66822i 0.796586 + 0.459909i
279279 11.3570i 0.679924i
280280 23.0935 24.6331i 1.38010 1.47211i
281281 16.5334i 0.986301i 0.869944 + 0.493150i 0.164155π0.164155\pi
−0.869944 + 0.493150i 0.835845π0.835845\pi
282282 9.81327 16.9971i 0.584372 1.01216i
283283 −14.6412 25.3592i −0.870327 1.50745i −0.861659 0.507487i 0.830574π-0.830574\pi
−0.00866737 0.999962i 0.502759π-0.502759\pi
284284 −10.8870 18.8569i −0.646027 1.11895i
285285 12.4068 + 7.16307i 0.734915 + 0.424303i
286286 −23.3890 −1.38302
287287 −1.01210 + 4.33132i −0.0597425 + 0.255670i
288288 1.65229 0.0973619
289289 0.434012 0.751731i 0.0255301 0.0442195i
290290 8.12516 + 14.0732i 0.477126 + 0.826407i
291291 −2.32405 + 1.34179i −0.136238 + 0.0786573i
292292 −12.8858 7.43960i −0.754082 0.435370i
293293 −19.5508 −1.14217 −0.571085 0.820891i 0.693477π-0.693477\pi
−0.571085 + 0.820891i 0.693477π0.693477\pi
294294 −7.54681 + 15.2667i −0.440139 + 0.890369i
295295 30.2886i 1.76347i
296296 −3.45937 1.99727i −0.201072 0.116089i
297297 11.1497 + 19.3118i 0.646971 + 1.12059i
298298 −37.8204 + 21.8356i −2.19088 + 1.26490i
299299 9.97671 + 1.67265i 0.576968 + 0.0967320i
300300 4.76999i 0.275395i
301301 5.38438 23.0426i 0.310350 1.32815i
302302 −8.83785 −0.508561
303303 −7.02329 + 12.1647i −0.403478 + 0.698844i
304304 −13.1162 22.7179i −0.752266 1.30296i
305305 −7.30082 12.6454i −0.418044 0.724073i
306306 −10.0365 + 17.3838i −0.573750 + 0.993764i
307307 0.893505i 0.0509950i −0.999675 0.0254975i 0.991883π-0.991883\pi
0.999675 0.0254975i 0.00811699π-0.00811699\pi
308308 −35.4198 33.2060i −2.01823 1.89209i
309309 9.29844i 0.528970i
310310 −29.7619 17.1830i −1.69036 0.975930i
311311 −23.5660 + 13.6058i −1.33630 + 0.771516i −0.986257 0.165216i 0.947168π-0.947168\pi
−0.350047 + 0.936732i 0.613834π0.613834\pi
312312 5.33958 + 9.24842i 0.302294 + 0.523589i
313313 8.97878 15.5517i 0.507511 0.879034i −0.492452 0.870340i 0.663899π-0.663899\pi
0.999962 0.00869421i 0.00276749π-0.00276749\pi
314314 −21.4894 −1.21272
315315 3.86483 + 12.7626i 0.217759 + 0.719090i
316316 20.6090i 1.15935i
317317 5.65331 9.79182i 0.317522 0.549964i −0.662449 0.749107i 0.730483π-0.730483\pi
0.979970 + 0.199144i 0.0638161π0.0638161\pi
318318 −7.72129 13.3737i −0.432988 0.749958i
319319 10.3187 5.95752i 0.577738 0.333557i
320320 −8.67288 + 15.0219i −0.484829 + 0.839748i
321321 −17.5229 −0.978033
322322 18.9743 + 24.8801i 1.05740 + 1.38651i
323323 23.4521 1.30491
324324 −2.42279 + 4.19640i −0.134600 + 0.233133i
325325 2.16417 1.24948i 0.120047 0.0693089i
326326 −7.47196 12.9418i −0.413833 0.716781i
327327 3.20822 5.55679i 0.177415 0.307291i
328328 8.62736i 0.476366i
329329 −15.5712 14.5979i −0.858466 0.804810i
330330 27.2058 1.49763
331331 17.8442 30.9071i 0.980808 1.69881i 0.321551 0.946892i 0.395796π-0.395796\pi
0.659258 0.751917i 0.270871π-0.270871\pi
332332 1.73732 + 3.00912i 0.0953477 + 0.165147i
333333 1.36621 0.788779i 0.0748676 0.0432248i
334334 −9.37952 5.41527i −0.513225 0.296310i
335335 39.1139i 2.13702i
336336 −2.66834 + 11.4192i −0.145570 + 0.622971i
337337 17.0125i 0.926730i −0.886167 0.463365i 0.846642π-0.846642\pi
0.886167 0.463365i 0.153358π-0.153358\pi
338338 −10.5430 + 18.2610i −0.573462 + 0.993265i
339339 1.74893 + 3.02924i 0.0949891 + 0.164526i
340340 20.3818 + 35.3023i 1.10536 + 1.91453i
341341 −12.5989 + 21.8219i −0.682269 + 1.18172i
342342 29.1814 1.57795
343343 14.2995 + 11.7696i 0.772101 + 0.635500i
344344 45.8975i 2.47463i
345345 −11.6048 1.94561i −0.624780 0.104748i
346346 −17.9901 + 10.3866i −0.967154 + 0.558387i
347347 −0.944481 1.63589i −0.0507024 0.0878191i 0.839560 0.543266i 0.182813π-0.182813\pi
−0.890263 + 0.455447i 0.849479π0.849479\pi
348348 −9.23941 5.33437i −0.495284 0.285953i
349349 29.0312i 1.55401i 0.629497 + 0.777003i 0.283261π0.283261\pi
−0.629497 + 0.777003i 0.716739π0.716739\pi
350350 7.52680 + 1.75879i 0.402325 + 0.0940114i
351351 −10.4605 −0.558343
352352 −3.17480 1.83297i −0.169217 0.0976976i
353353 15.8172 9.13208i 0.841866 0.486052i −0.0160319 0.999871i 0.505103π-0.505103\pi
0.857898 + 0.513820i 0.171770π0.171770\pi
354354 −14.8152 25.6608i −0.787422 1.36385i
355355 6.63441 11.4911i 0.352118 0.609886i
356356 −32.4651 −1.72065
357357 −7.64843 7.17039i −0.404798 0.379497i
358358 18.8057 0.993911
359359 4.45099 + 2.56978i 0.234914 + 0.135628i 0.612837 0.790209i 0.290028π-0.290028\pi
−0.377923 + 0.925837i 0.623362π0.623362\pi
360360 12.9323 + 22.3993i 0.681589 + 1.18055i
361361 −7.54685 13.0715i −0.397203 0.687975i
362362 16.7853 29.0730i 0.882215 1.52804i
363363 9.09544i 0.477387i
364364 21.7975 6.60085i 1.14250 0.345979i
365365 9.06717i 0.474597i
366366 12.3706 + 7.14218i 0.646623 + 0.373328i
367367 4.82808 + 8.36248i 0.252024 + 0.436518i 0.964083 0.265602i 0.0855706π-0.0855706\pi
−0.712059 + 0.702119i 0.752237π0.752237\pi
368368 16.6212 + 13.7099i 0.866439 + 0.714680i
369369 −2.95072 1.70360i −0.153608 0.0886857i
370370 4.77367i 0.248171i
371371 −16.0730 + 4.86731i −0.834468 + 0.252698i
372372 22.5622 1.16979
373373 −5.35579 3.09216i −0.277312 0.160106i 0.354894 0.934907i 0.384517π-0.384517\pi
−0.632206 + 0.774800i 0.717850π0.717850\pi
374374 38.5695 22.2681i 1.99438 1.15146i
375375 8.10678 4.68045i 0.418632 0.241697i
376376 −35.8523 20.6993i −1.84894 1.06749i
377377 5.58929i 0.287863i
378378 −23.6046 22.1293i −1.21409 1.13821i
379379 13.0402i 0.669830i −0.942248 0.334915i 0.891292π-0.891292\pi
0.942248 0.334915i 0.108708π-0.108708\pi
380380 29.6302 51.3211i 1.52000 2.63272i
381381 0.194469 0.112277i 0.00996297 0.00575212i
382382 21.4110 12.3616i 1.09548 0.632477i
383383 12.2159 21.1585i 0.624201 1.08115i −0.364494 0.931206i 0.618758π-0.618758\pi
0.988695 0.149942i 0.0479087π-0.0479087\pi
384384 18.5775i 0.948031i
385385 6.73210 28.8102i 0.343100 1.46831i
386386 −33.4327 −1.70168
387387 15.6978 + 9.06313i 0.797964 + 0.460705i
388388 5.55036 + 9.61351i 0.281777 + 0.488052i
389389 −13.7847 + 7.95860i −0.698912 + 0.403517i −0.806942 0.590630i 0.798879π-0.798879\pi
0.108030 + 0.994148i 0.465546π0.465546\pi
390390 −6.38106 + 11.0523i −0.323117 + 0.559656i
391391 −18.0445 + 6.74030i −0.912549 + 0.340872i
392392 32.2023 + 15.9186i 1.62646 + 0.804013i
393393 10.1376 0.511376
394394 −29.6721 + 51.3935i −1.49486 + 2.58917i
395395 10.8763 6.27941i 0.547244 0.315951i
396396 32.2078 18.5952i 1.61850 0.934444i
397397 13.7111 + 7.91614i 0.688143 + 0.397299i 0.802916 0.596092i 0.203281π-0.203281\pi
−0.114773 + 0.993392i 0.536614π0.536614\pi
398398 −59.4992 −2.98243
399399 −3.46799 + 14.8414i −0.173617 + 0.742997i
400400 5.32254 0.266127
401401 0.612134 + 0.353416i 0.0305685 + 0.0176487i 0.515206 0.857066i 0.327715π-0.327715\pi
−0.484638 + 0.874715i 0.661049π0.661049\pi
402402 −19.1320 33.1376i −0.954217 1.65275i
403403 −5.91009 10.2366i −0.294402 0.509920i
404404 50.3196 + 29.0520i 2.50349 + 1.44539i
405405 −2.95283 −0.146727
406406 −11.8241 + 12.6124i −0.586822 + 0.625944i
407407 −3.50014 −0.173496
408408 −17.6104 10.1674i −0.871843 0.503359i
409409 19.8589 11.4655i 0.981960 0.566935i 0.0790984 0.996867i 0.474796π-0.474796\pi
0.902861 + 0.429932i 0.141463π0.141463\pi
410410 −8.92882 + 5.15506i −0.440963 + 0.254590i
411411 5.13364 8.89173i 0.253224 0.438596i
412412 38.4633 1.89495
413413 −30.8401 + 9.33917i −1.51754 + 0.459551i
414414 −22.4528 + 8.38696i −1.10349 + 0.412197i
415415 −1.05870 + 1.83372i −0.0519694 + 0.0900136i
416416 1.48928 0.859838i 0.0730181 0.0421570i
417417 −3.06788 5.31372i −0.150235 0.260214i
418418 −56.0709 32.3725i −2.74252 1.58339i
419419 −8.27756 −0.404385 −0.202193 0.979346i 0.564807π-0.564807\pi
−0.202193 + 0.979346i 0.564807π0.564807\pi
420420 −25.3546 + 7.67802i −1.23718 + 0.374649i
421421 2.27003i 0.110635i −0.998469 0.0553173i 0.982383π-0.982383\pi
0.998469 0.0553173i 0.0176170π-0.0176170\pi
422422 −27.1702 + 47.0602i −1.32263 + 2.29085i
423423 14.1591 8.17477i 0.688440 0.397471i
424424 −28.2093 + 16.2867i −1.36997 + 0.790951i
425425 −2.37920 + 4.12090i −0.115408 + 0.199893i
426426 12.9805i 0.628908i
427427 10.6245 11.3328i 0.514156 0.548434i
428428 72.4840i 3.50365i
429429 8.10377 + 4.67871i 0.391253 + 0.225890i
430430 47.5013 27.4249i 2.29072 1.32255i
431431 −0.522666 + 0.301761i −0.0251759 + 0.0145353i −0.512535 0.858666i 0.671294π-0.671294\pi
0.487359 + 0.873202i 0.337960π0.337960\pi
432432 −19.2949 11.1399i −0.928327 0.535970i
433433 27.0009 1.29758 0.648790 0.760968i 0.275275π-0.275275\pi
0.648790 + 0.760968i 0.275275π0.275275\pi
434434 8.31913 35.6020i 0.399331 1.70895i
435435 6.50139i 0.311718i
436436 −22.9858 13.2709i −1.10082 0.635560i
437437 21.6022 + 17.8185i 1.03337 + 0.852376i
438438 4.43508 + 7.68178i 0.211916 + 0.367050i
439439 −6.76947 3.90836i −0.323089 0.186536i 0.329679 0.944093i 0.393059π-0.393059\pi
−0.652769 + 0.757557i 0.726393π0.726393\pi
440440 57.3858i 2.73576i
441441 −11.8033 + 7.87041i −0.562061 + 0.374781i
442442 20.8917i 0.993718i
443443 −3.09922 + 5.36801i −0.147248 + 0.255042i −0.930210 0.367029i 0.880375π-0.880375\pi
0.782961 + 0.622071i 0.213708π0.213708\pi
444444 1.56702 + 2.71415i 0.0743673 + 0.128808i
445445 −9.89190 17.1333i −0.468921 0.812195i
446446 35.7366 + 20.6325i 1.69218 + 0.976979i
447447 17.4719 0.826391
448448 −17.9696 4.19896i −0.848983 0.198382i
449449 −12.0380 −0.568109 −0.284055 0.958808i 0.591680π-0.591680\pi
−0.284055 + 0.958808i 0.591680π0.591680\pi
450450 −2.96045 + 5.12764i −0.139557 + 0.241719i
451451 3.77978 + 6.54678i 0.177983 + 0.308276i
452452 12.5306 7.23452i 0.589388 0.340283i
453453 3.06211 + 1.76791i 0.143871 + 0.0830637i
454454 72.1737 3.38728
455455 10.1251 + 9.49228i 0.474673 + 0.445005i
456456 29.5618i 1.38436i
457457 −15.5450 8.97490i −0.727164 0.419828i 0.0902199 0.995922i 0.471243π-0.471243\pi
−0.817384 + 0.576094i 0.804576π0.804576\pi
458458 6.24253 + 10.8124i 0.291694 + 0.505230i
459459 17.2499 9.95922i 0.805155 0.464856i
460460 −8.04805 + 48.0035i −0.375242 + 2.23817i
461461 12.3887i 0.577001i 0.957480 + 0.288501i 0.0931567π0.0931567\pi
−0.957480 + 0.288501i 0.906843π0.906843\pi
462462 8.38862 + 27.7012i 0.390274 + 1.28877i
463463 12.7244 0.591354 0.295677 0.955288i 0.404455π-0.404455\pi
0.295677 + 0.955288i 0.404455π0.404455\pi
464464 −5.95230 + 10.3097i −0.276329 + 0.478615i
465465 6.87453 + 11.9070i 0.318799 + 0.552176i
466466 2.61301 + 4.52587i 0.121046 + 0.209657i
467467 −2.05265 + 3.55529i −0.0949853 + 0.164519i −0.909602 0.415480i 0.863614π-0.863614\pi
0.814617 + 0.579999i 0.196947π0.196947\pi
468468 17.4458i 0.806435i
469469 −39.8260 + 12.0603i −1.83900 + 0.556895i
470470 49.4735i 2.28204i
471471 7.44559 + 4.29871i 0.343075 + 0.198074i
472472 −54.1268 + 31.2501i −2.49139 + 1.43840i
473473 −20.1084 34.8288i −0.924587 1.60143i
474474 −6.14297 + 10.6399i −0.282156 + 0.488708i
475475 6.91759 0.317401
476476 −29.6605 + 31.6380i −1.35949 + 1.45012i
477477 12.8642i 0.589009i
478478 13.8090 23.9178i 0.631608 1.09398i
479479 10.0244 + 17.3627i 0.458025 + 0.793323i 0.998857 0.0478079i 0.0152235π-0.0152235\pi
−0.540831 + 0.841131i 0.681890π0.681890\pi
480480 −1.73231 + 1.00015i −0.0790689 + 0.0456504i
481481 0.820950 1.42193i 0.0374321 0.0648343i
482482 16.4221 0.748008
483483 −1.59718 12.4160i −0.0726740 0.564946i
484484 −37.6236 −1.71016
485485 −3.38231 + 5.85834i −0.153583 + 0.266013i
486486 34.2742 19.7882i 1.55471 0.897611i
487487 13.5230 + 23.4226i 0.612787 + 1.06138i 0.990768 + 0.135565i 0.0432851π0.0432851\pi
−0.377981 + 0.925813i 0.623382π0.623382\pi
488488 15.0652 26.0936i 0.681968 1.18120i
489489 5.97872i 0.270367i
490490 2.76677 + 42.8393i 0.124990 + 1.93528i
491491 10.5974 0.478256 0.239128 0.970988i 0.423138π-0.423138\pi
0.239128 + 0.970988i 0.423138π0.423138\pi
492492 3.38442 5.86199i 0.152582 0.264279i
493493 −5.32142 9.21697i −0.239665 0.415112i
494494 26.3026 15.1858i 1.18341 0.683242i
495495 19.6270 + 11.3317i 0.882168 + 0.509320i
496496 25.1757i 1.13042i
497497 13.7460 + 3.21204i 0.616593 + 0.144080i
498498 2.07139i 0.0928210i
499499 −13.8512 + 23.9911i −0.620067 + 1.07399i 0.369406 + 0.929268i 0.379561π0.379561\pi
−0.989473 + 0.144719i 0.953772π0.953772\pi
500500 −19.3608 33.5339i −0.865842 1.49968i
501501 2.16653 + 3.75253i 0.0967932 + 0.167651i
502502 −2.65102 + 4.59169i −0.118321 + 0.204937i
503503 14.7700 0.658561 0.329280 0.944232i 0.393194π-0.393194\pi
0.329280 + 0.944232i 0.393194π0.393194\pi
504504 −18.8196 + 20.0743i −0.838293 + 0.894181i
505505 35.4078i 1.57563i
506506 52.4462 + 8.79290i 2.33152 + 0.390892i
507507 7.30579 4.21800i 0.324462 0.187328i
508508 −0.464437 0.804428i −0.0206061 0.0356907i
509509 10.9718 + 6.33457i 0.486316 + 0.280775i 0.723045 0.690801i 0.242742π-0.242742\pi
−0.236729 + 0.971576i 0.576075π0.576075\pi
510510 24.3010i 1.07607i
511511 9.23227 2.79577i 0.408411 0.123677i
512512 −42.4471 −1.87591
513513 −25.0772 14.4783i −1.10719 0.639234i
514514 60.8118 35.1097i 2.68229 1.54862i
515515 11.7195 + 20.2987i 0.516422 + 0.894470i
516516 −18.0051 + 31.1858i −0.792631 + 1.37288i
517517 −36.2749 −1.59537
518518 4.86059 1.47191i 0.213562 0.0646720i
519519 8.31088 0.364807
520520 23.3129 + 13.4597i 1.02234 + 0.590247i
521521 −3.89689 6.74961i −0.170726 0.295706i 0.767948 0.640512i 0.221278π-0.221278\pi
−0.938674 + 0.344806i 0.887945π0.887945\pi
522522 −6.62145 11.4687i −0.289813 0.501971i
523523 −1.88214 + 3.25996i −0.0823002 + 0.142548i −0.904238 0.427030i 0.859560π-0.859560\pi
0.821937 + 0.569578i 0.192893π0.192893\pi
524524 41.9346i 1.83192i
525525 −2.25604 2.11503i −0.0984616 0.0923076i
526526 30.9912i 1.35128i
527527 19.4920 + 11.2537i 0.849083 + 0.490218i
528528 9.96516 + 17.2602i 0.433678 + 0.751152i
529529 −21.7424 7.50131i −0.945320 0.326144i
530530 −33.7116 19.4634i −1.46434 0.845435i
531531 24.6832i 1.07116i
532532 61.3917 + 14.3454i 2.66167 + 0.621954i
533533 −3.54616 −0.153601
534534 16.7610 + 9.67696i 0.725319 + 0.418763i
535535 −38.2530 + 22.0854i −1.65382 + 0.954834i
536536 −69.8978 + 40.3555i −3.01913 + 1.74309i
537537 −6.51574 3.76186i −0.281175 0.162336i
538538 38.5219i 1.66080i
539539 31.4106 2.02865i 1.35295 0.0873800i
540540 50.3315i 2.16592i
541541 6.61885 11.4642i 0.284567 0.492884i −0.687937 0.725770i 0.741484π-0.741484\pi
0.972504 + 0.232886i 0.0748170π0.0748170\pi
542542 −33.1142 + 19.1185i −1.42238 + 0.821210i
543543 −11.6314 + 6.71541i −0.499152 + 0.288186i
544544 −1.63726 + 2.83582i −0.0701969 + 0.121585i
545545 16.1742i 0.692826i
546546 −13.2211 3.08938i −0.565810 0.132213i
547547 −40.0668 −1.71313 −0.856567 0.516036i 0.827407π-0.827407\pi
−0.856567 + 0.516036i 0.827407π0.827407\pi
548548 −36.7809 21.2355i −1.57120 0.907134i
549549 5.94967 + 10.3051i 0.253926 + 0.439812i
550550 11.3767 6.56837i 0.485106 0.280076i
551551 −7.73608 + 13.3993i −0.329568 + 0.570829i
552552 −8.49629 22.7455i −0.361626 0.968112i
553553 9.74732 + 9.13810i 0.414498 + 0.388592i
554554 4.48801 0.190677
555555 −0.954918 + 1.65397i −0.0405340 + 0.0702069i
556556 −21.9804 + 12.6904i −0.932175 + 0.538192i
557557 −9.00856 + 5.20109i −0.381705 + 0.220377i −0.678560 0.734545i 0.737396π-0.737396\pi
0.296855 + 0.954923i 0.404062π0.404062\pi
558558 24.2539 + 14.0030i 1.02675 + 0.592794i
559559 18.8655 0.797928
560560 8.56743 + 28.2916i 0.362040 + 1.19554i
561561 −17.8179 −0.752274
562562 −35.3086 20.3855i −1.48941 0.859909i
563563 0.976420 + 1.69121i 0.0411512 + 0.0712760i 0.885867 0.463938i 0.153564π-0.153564\pi
−0.844716 + 0.535214i 0.820231π0.820231\pi
564564 16.2403 + 28.1290i 0.683839 + 1.18444i
565565 7.63594 + 4.40861i 0.321246 + 0.185472i
566566 72.2093 3.03518
567567 −0.910474 3.00660i −0.0382363 0.126265i
568568 27.3801 1.14884
569569 11.3311 + 6.54204i 0.475026 + 0.274256i 0.718341 0.695691i 0.244902π-0.244902\pi
−0.243315 + 0.969947i 0.578235π0.578235\pi
570570 −30.5948 + 17.6639i −1.28148 + 0.739860i
571571 −15.3278 + 8.84950i −0.641448 + 0.370340i −0.785172 0.619278i 0.787426π-0.787426\pi
0.143724 + 0.989618i 0.454092π0.454092\pi
572572 19.3536 33.5215i 0.809216 1.40160i
573573 −9.89122 −0.413212
574574 −8.00203 7.50189i −0.333998 0.313123i
575575 −5.32254 + 1.98817i −0.221965 + 0.0829124i
576576 7.06781 12.2418i 0.294492 0.510075i
577577 −5.88411 + 3.39719i −0.244959 + 0.141427i −0.617454 0.786607i 0.711836π-0.711836\pi
0.372495 + 0.928034i 0.378502π0.378502\pi
578578 1.07026 + 1.85375i 0.0445170 + 0.0771057i
579579 11.5837 + 6.68783i 0.481401 + 0.277937i
580580 −26.8932 −1.11668
581581 −2.19354 0.512567i −0.0910035 0.0212648i
582582 6.61764i 0.274310i
583583 −14.2709 + 24.7179i −0.591041 + 1.02371i
584584 16.2033 9.35501i 0.670499 0.387113i
585585 −9.20694 + 5.31563i −0.380660 + 0.219774i
586586 24.1058 41.7525i 0.995803 1.72478i
587587 28.6736i 1.18349i −0.806126 0.591744i 0.798440π-0.798440\pi
0.806126 0.591744i 0.201560π-0.201560\pi
588588 −15.6356 23.4488i −0.644803 0.967012i
589589 32.7204i 1.34822i
590590 −64.6842 37.3454i −2.66301 1.53749i
591591 20.5614 11.8711i 0.845782 0.488312i
592592 3.02856 1.74854i 0.124473 0.0718644i
593593 −13.4997 7.79404i −0.554365 0.320063i 0.196515 0.980501i 0.437037π-0.437037\pi
−0.750881 + 0.660438i 0.770371π0.770371\pi
594594 −54.9897 −2.25625
595595 −25.7341 6.01330i −1.05499 0.246521i
596596 72.2729i 2.96041i
597597 20.6151 + 11.9021i 0.843720 + 0.487122i
598598 −15.8732 + 19.2438i −0.649105 + 0.786939i
599599 −0.559872 0.969726i −0.0228757 0.0396219i 0.854361 0.519680i 0.173949π-0.173949\pi
−0.877237 + 0.480058i 0.840616π0.840616\pi
600600 −5.19449 2.99904i −0.212064 0.122435i
601601 3.71483i 0.151531i 0.997126 + 0.0757656i 0.0241401π0.0241401\pi
−0.997126 + 0.0757656i 0.975860π0.975860\pi
602602 42.5707 + 39.9100i 1.73505 + 1.62661i
603603 31.8751i 1.29806i
604604 7.31302 12.6665i 0.297562 0.515393i
605605 −11.4636 19.8556i −0.466063 0.807245i
606606 −17.3192 29.9978i −0.703546 1.21858i
607607 8.88138 + 5.12767i 0.360484 + 0.208126i 0.669293 0.742999i 0.266597π-0.266597\pi
−0.308809 + 0.951124i 0.599930π0.599930\pi
608608 4.76037 0.193059
609609 6.61976 2.00463i 0.268246 0.0812318i
610610 36.0072 1.45789
611611 8.50819 14.7366i 0.344204 0.596179i
612612 −16.6097 28.7689i −0.671409 1.16292i
613613 34.1659 19.7257i 1.37995 0.796714i 0.387796 0.921745i 0.373237π-0.373237\pi
0.992153 + 0.125032i 0.0399033π0.0399033\pi
614614 1.90816 + 1.10168i 0.0770072 + 0.0444601i
615615 4.12484 0.166330
616616 58.4307 17.6943i 2.35424 0.712924i
617617 32.7292i 1.31763i 0.752305 + 0.658815i 0.228942π0.228942\pi
−0.752305 + 0.658815i 0.771058π0.771058\pi
618618 −19.8577 11.4648i −0.798793 0.461184i
619619 13.3844 + 23.1825i 0.537965 + 0.931784i 0.999013 + 0.0444084i 0.0141403π0.0141403\pi
−0.461048 + 0.887375i 0.652526π0.652526\pi
620620 49.2538 28.4367i 1.97808 1.14205i
621621 23.4561 + 3.93255i 0.941261 + 0.157808i
622622 67.1032i 2.69059i
623623 14.3952 15.3549i 0.576730 0.615180i
624624 −9.34922 −0.374268
625625 14.7600 25.5651i 0.590401 1.02260i
626626 22.1414 + 38.3500i 0.884948 + 1.53278i
627627 12.9515 + 22.4327i 0.517234 + 0.895875i
628628 17.7818 30.7989i 0.709569 1.22901i
629629 3.12642i 0.124659i
630630 −32.0210 7.48236i −1.27575 0.298104i
631631 3.62895i 0.144466i 0.997388 + 0.0722331i 0.0230125π0.0230125\pi
−0.997388 + 0.0722331i 0.976987π0.976987\pi
632632 22.4430 + 12.9575i 0.892736 + 0.515421i
633633 18.8277 10.8702i 0.748334 0.432051i
634634 13.9409 + 24.1463i 0.553664 + 0.958974i
635635 0.283021 0.490207i 0.0112314 0.0194533i
636636 25.5564 1.01338
637637 −6.54314 + 13.2363i −0.259249 + 0.524442i
638638 29.3822i 1.16325i
639639 −5.40659 + 9.36449i −0.213881 + 0.370453i
640640 −23.4146 40.5553i −0.925543 1.60309i
641641 −16.2330 + 9.37215i −0.641166 + 0.370177i −0.785064 0.619415i 0.787370π-0.787370\pi
0.143897 + 0.989593i 0.454036π0.454036\pi
642642 21.6055 37.4218i 0.852700 1.47692i
643643 −21.3880 −0.843460 −0.421730 0.906722i 0.638577π-0.638577\pi
−0.421730 + 0.906722i 0.638577π0.638577\pi
644644 −51.3590 + 6.60676i −2.02383 + 0.260343i
645645 −21.9441 −0.864050
646646 −28.9160 + 50.0840i −1.13769 + 1.97053i
647647 9.62615 5.55766i 0.378443 0.218494i −0.298698 0.954348i 0.596552π-0.596552\pi
0.677141 + 0.735854i 0.263219π0.263219\pi
648648 −3.04657 5.27681i −0.119680 0.207293i
649649 −27.3824 + 47.4277i −1.07485 + 1.86170i
650650 6.16238i 0.241708i
651651 −10.0042 + 10.6711i −0.392094 + 0.418234i
652652 24.7312 0.968547
653653 −1.47495 + 2.55469i −0.0577194 + 0.0999729i −0.893441 0.449180i 0.851716π-0.851716\pi
0.835722 + 0.549153i 0.185050π0.185050\pi
654654 7.91137 + 13.7029i 0.309359 + 0.535825i
655655 22.1307 12.7772i 0.864719 0.499246i
656656 −6.54104 3.77647i −0.255385 0.147446i
657657 7.38913i 0.288277i
658658 50.3743 15.2546i 1.96379 0.594687i
659659 13.6891i 0.533252i 0.963800 + 0.266626i 0.0859089π0.0859089\pi
−0.963800 + 0.266626i 0.914091π0.914091\pi
660660 −22.5119 + 38.9917i −0.876273 + 1.51775i
661661 −10.1060 17.5041i −0.393078 0.680830i 0.599776 0.800168i 0.295256π-0.295256\pi
−0.992854 + 0.119337i 0.961923π0.961923\pi
662662 44.0034 + 76.2161i 1.71024 + 2.96222i
663663 4.17915 7.23851i 0.162305 0.281120i
664664 −4.36922 −0.169559
665665 11.1349 + 36.7700i 0.431793 + 1.42588i
666666 3.89021i 0.150743i
667667 2.10125 12.5331i 0.0813605 0.485283i
668668 15.5225 8.96190i 0.600582 0.346746i
669669 −8.25461 14.2974i −0.319142 0.552770i
670670 −83.5313 48.2268i −3.22710 1.86316i
671671 26.4012i 1.01921i
672672 −1.55250 1.45547i −0.0598891 0.0561459i
673673 35.7251 1.37710 0.688551 0.725188i 0.258247π-0.258247\pi
0.688551 + 0.725188i 0.258247π0.258247\pi
674674 36.3318 + 20.9762i 1.39945 + 0.807972i
675675 5.08815 2.93765i 0.195843 0.113070i
676676 −17.4479 30.2206i −0.671072 1.16233i
677677 −16.1105 + 27.9042i −0.619177 + 1.07245i 0.370460 + 0.928849i 0.379200π0.379200\pi
−0.989636 + 0.143597i 0.954133π0.954133\pi
678678 −8.62564 −0.331266
679679 −7.00791 1.63754i −0.268939 0.0628431i
680680 −51.2586 −1.96568
681681 −25.0065 14.4375i −0.958253 0.553247i
682682 −31.0685 53.8123i −1.18968 2.06058i
683683 −2.81568 4.87691i −0.107739 0.186610i 0.807115 0.590394i 0.201028π-0.201028\pi
−0.914854 + 0.403785i 0.867694π0.867694\pi
684684 −24.1466 + 41.8232i −0.923269 + 1.59915i
685685 25.8812i 0.988869i
686686 −42.7662 + 16.0262i −1.63282 + 0.611883i
687687 4.99499i 0.190571i
688688 34.7983 + 20.0908i 1.32667 + 0.765955i
689689 −6.69442 11.5951i −0.255037 0.441737i
690690 18.4635 22.3842i 0.702895 0.852150i
691691 −8.76063 5.05795i −0.333270 0.192414i 0.324022 0.946050i 0.394965π-0.394965\pi
−0.657292 + 0.753636i 0.728298π0.728298\pi
692692 34.3782i 1.30686i
693693 −5.48620 + 23.4784i −0.208404 + 0.891869i
694694 4.65812 0.176820
695695 −13.3945 7.73333i −0.508083 0.293342i
696696 11.6182 6.70777i 0.440387 0.254257i
697697 5.84776 3.37621i 0.221500 0.127883i
698698 −61.9989 35.7951i −2.34669 1.35486i
699699 2.09081i 0.0790819i
700700 −8.74889 + 9.33217i −0.330677 + 0.352723i
701701 33.1633i 1.25256i 0.779598 + 0.626280i 0.215423π0.215423\pi
−0.779598 + 0.626280i 0.784577π0.784577\pi
702702 12.8977 22.3395i 0.486792 0.843149i
703703 3.93615 2.27254i 0.148455 0.0857104i
704704 −27.1610 + 15.6814i −1.02367 + 0.591015i
705705 −9.89660 + 17.1414i −0.372728 + 0.645583i
706706 45.0389i 1.69506i
707707 −36.0525 + 10.9176i −1.35589 + 0.410599i
708708 49.0364 1.84290
709709 −25.8075 14.9000i −0.969221 0.559580i −0.0702227 0.997531i 0.522371π-0.522371\pi
−0.898999 + 0.437951i 0.855704π0.855704\pi
710710 16.3603 + 28.3368i 0.613989 + 1.06346i
711711 −8.86340 + 5.11729i −0.332404 + 0.191913i
712712 20.4118 35.3543i 0.764965 1.32496i
713713 9.40408 + 25.1757i 0.352186 + 0.942839i
714714 24.7434 7.49295i 0.926000 0.280416i
715715 23.5877 0.882128
716716 −15.5611 + 26.9525i −0.581544 + 1.00726i
717717 −9.56899 + 5.52466i −0.357360 + 0.206322i
718718 −10.9760 + 6.33701i −0.409621 + 0.236495i
719719 −40.1866 23.2017i −1.49871 0.865279i −0.498708 0.866770i 0.666192π-0.666192\pi
−0.999999 + 0.00149132i 0.999525π0.999525\pi
720720 −22.6435 −0.843872
721721 −17.0548 + 18.1918i −0.635153 + 0.677497i
722722 37.2206 1.38521
723723 −5.68989 3.28506i −0.211609 0.122173i
724724 27.7785 + 48.1138i 1.03238 + 1.78813i
725725 −1.56965 2.71871i −0.0582952 0.100970i
726726 19.4242 + 11.2145i 0.720898 + 0.416211i
727727 −2.32964 −0.0864016 −0.0432008 0.999066i 0.513756π-0.513756\pi
−0.0432008 + 0.999066i 0.513756π0.513756\pi
728728 −6.51650 + 27.8875i −0.241517 + 1.03358i
729729 −12.2716 −0.454502
730730 19.3638 + 11.1797i 0.716686 + 0.413779i
731731 −31.1101 + 17.9614i −1.15065 + 0.664327i
732732 −20.4725 + 11.8198i −0.756687 + 0.436873i
733733 −16.1650 + 27.9986i −0.597067 + 1.03415i 0.396184 + 0.918171i 0.370334π0.370334\pi
−0.993252 + 0.115980i 0.962999π0.962999\pi
734734 −23.8118 −0.878909
735735 7.61089 15.3963i 0.280732 0.567901i
736736 −3.66273 + 1.36817i −0.135010 + 0.0504313i
737737 −35.3608 + 61.2467i −1.30253 + 2.25605i
738738 7.27638 4.20102i 0.267847 0.154642i
739739 −10.2719 17.7914i −0.377858 0.654469i 0.612893 0.790166i 0.290006π-0.290006\pi
−0.990750 + 0.135697i 0.956672π0.956672\pi
740740 6.84168 + 3.95004i 0.251505 + 0.145207i
741741 −12.1510 −0.446378
742742 9.42316 40.3267i 0.345935 1.48044i
743743 7.41754i 0.272123i 0.990700 + 0.136062i 0.0434445π0.0434445\pi
−0.990700 + 0.136062i 0.956556π0.956556\pi
744744 −14.1855 + 24.5700i −0.520067 + 0.900782i
745745 38.1415 22.0210i 1.39740 0.806788i
746746 13.2072 7.62519i 0.483550 0.279178i
747747 0.862766 1.49435i 0.0315669 0.0546756i
748748 73.7044i 2.69490i
749749 −34.2824 32.1397i −1.25265 1.17436i
750750 23.0837i 0.842898i
751751 27.3532 + 15.7924i 0.998132 + 0.576272i 0.907695 0.419631i 0.137840π-0.137840\pi
0.0904367 + 0.995902i 0.471174π0.471174\pi
752752 31.3874 18.1215i 1.14458 0.660825i
753753 1.83703 1.06061i 0.0669452 0.0386508i
754754 −11.9365 6.89151i −0.434700 0.250974i
755755 8.91290 0.324374
756756 51.2479 15.5192i 1.86387 0.564427i
757757 31.9227i 1.16025i −0.814528 0.580125i 0.803004π-0.803004\pi
0.814528 0.580125i 0.196996π-0.196996\pi
758758 27.8485 + 16.0784i 1.01150 + 0.583993i
759759 −16.4125 13.5378i −0.595735 0.491391i
760760 37.2589 + 64.5343i 1.35152 + 2.34090i
761761 −3.76130 2.17159i −0.136347 0.0787199i 0.430275 0.902698i 0.358417π-0.358417\pi
−0.566622 + 0.823978i 0.691750π0.691750\pi
762762 0.553743i 0.0200600i
763763 16.4687 4.98714i 0.596206 0.180546i
764764 40.9153i 1.48026i
765765 10.1217 17.5314i 0.365953 0.633848i
766766 30.1239 + 52.1762i 1.08842 + 1.88520i
767767 −12.8449 22.2481i −0.463804 0.803332i
768768 27.7554 + 16.0246i 1.00154 + 0.578238i
769769 30.9232 1.11512 0.557559 0.830137i 0.311738π-0.311738\pi
0.557559 + 0.830137i 0.311738π0.311738\pi
770770 53.2263 + 49.8996i 1.91814 + 1.79826i
771771 −28.0932 −1.01175
772772 27.6644 47.9162i 0.995664 1.72454i
773773 4.83709 + 8.37808i 0.173978 + 0.301339i 0.939807 0.341705i 0.111005π-0.111005\pi
−0.765829 + 0.643044i 0.777671π0.777671\pi
774774 −38.7103 + 22.3494i −1.39141 + 0.803333i
775775 5.74949 + 3.31947i 0.206528 + 0.119239i
776776 −13.9587 −0.501089
777777 −1.97852 0.462322i −0.0709790 0.0165857i
778778 39.2514i 1.40723i
779779 −8.50125 4.90820i −0.304589 0.175855i
780780 −10.5602 18.2908i −0.378116 0.654916i
781781 20.7771 11.9956i 0.743462 0.429238i
782782 7.85406 46.8464i 0.280861 1.67522i
783783 13.1409i 0.469618i
784784 −26.1651 + 17.4468i −0.934467 + 0.623102i
785785 21.6719 0.773503
786786 −12.4996 + 21.6499i −0.445844 + 0.772225i
787787 −10.9244 18.9216i −0.389413 0.674484i 0.602957 0.797773i 0.293989π-0.293989\pi
−0.992371 + 0.123290i 0.960656π0.960656\pi
788788 −49.1052 85.0527i −1.74930 3.02988i
789789 6.19945 10.7378i 0.220706 0.382274i
790790 30.9697i 1.10185i
791791 −2.13442 + 9.13432i −0.0758913 + 0.324779i
792792 46.7655i 1.66174i
793793 10.7254 + 6.19233i 0.380871 + 0.219896i
794794 −33.8113 + 19.5210i −1.19992 + 0.692773i
795795 7.78685 + 13.4872i 0.276171 + 0.478343i
796796 49.2335 85.2750i 1.74504 3.02249i
797797 −21.0566 −0.745864 −0.372932 0.927859i 0.621648π-0.621648\pi
−0.372932 + 0.927859i 0.621648π0.621648\pi
798798 −27.4191 25.7054i −0.970626 0.909961i
799799 32.4017i 1.14629i
800800 −0.482938 + 0.836473i −0.0170744 + 0.0295738i
801801 8.06122 + 13.9624i 0.284829 + 0.493339i
802802 −1.50950 + 0.871512i −0.0533024 + 0.0307742i
803803 8.19716 14.1979i 0.289271 0.501033i
804804 63.3243 2.23327
805805 −19.1354 25.0914i −0.674435 0.884355i
806806 29.1482 1.02670
807807 7.70586 13.3469i 0.271259 0.469835i
808808 −63.2750 + 36.5318i −2.22601 + 1.28519i
809809 10.7424 + 18.6065i 0.377684 + 0.654168i 0.990725 0.135883i 0.0433871π-0.0433871\pi
−0.613041 + 0.790051i 0.710054π0.710054\pi
810810 3.64080 6.30604i 0.127925 0.221572i
811811 20.3429i 0.714337i 0.934040 + 0.357169i 0.116258π0.116258\pi
−0.934040 + 0.357169i 0.883742π0.883742\pi
812812 −8.29222 27.3828i −0.291000 0.960949i
813813 15.2978 0.536516
814814 4.31562 7.47488i 0.151263 0.261994i
815815 7.53541 + 13.0517i 0.263954 + 0.457181i
816816 15.4173 8.90116i 0.539712 0.311603i
817817 45.2266 + 26.1116i 1.58228 + 0.913530i
818818 56.5474i 1.97713i
819819 −8.25127 7.73556i −0.288323 0.270302i
820820 17.0625i 0.595849i
821821 14.0687 24.3678i 0.491003 0.850441i −0.508944 0.860800i 0.669964π-0.669964\pi
0.999946 + 0.0103584i 0.00329722π0.00329722\pi
822822 12.6594 + 21.9267i 0.441548 + 0.764783i
823823 16.7763 + 29.0574i 0.584786 + 1.01288i 0.994902 + 0.100846i 0.0321548π0.0321548\pi
−0.410116 + 0.912033i 0.634512π0.634512\pi
824824 −24.1830 + 41.8862i −0.842456 + 1.45918i
825825 −5.25571 −0.182980
826826 18.0807 77.3770i 0.629109 2.69229i
827827 27.0254i 0.939764i −0.882729 0.469882i 0.844297π-0.844297\pi
0.882729 0.469882i 0.155703π-0.155703\pi
828828 6.55861 39.1195i 0.227928 1.35950i
829829 14.0246 8.09710i 0.487094 0.281224i −0.236274 0.971686i 0.575926π-0.575926\pi
0.723368 + 0.690463i 0.242593π0.242593\pi
830830 −2.61072 4.52189i −0.0906193 0.156957i
831831 −1.55499 0.897775i −0.0539421 0.0311435i
832832 14.7121i 0.510052i
833833 −1.81204 28.0568i −0.0627835 0.972110i
834834 15.1306 0.523930
835835 9.45917 + 5.46125i 0.327348 + 0.188994i
836836 92.7934 53.5743i 3.20933 1.85291i
837837 −13.8951 24.0671i −0.480286 0.831880i
838838 10.2061 17.6775i 0.352564 0.610659i
839839 43.1817 1.49080 0.745399 0.666618i 0.232259π-0.232259\pi
0.745399 + 0.666618i 0.232259π0.232259\pi
840840 7.57990 32.4384i 0.261531 1.11923i
841841 −21.9785 −0.757880
842842 4.84787 + 2.79892i 0.167069 + 0.0964571i
843843 8.15576 + 14.1262i 0.280899 + 0.486532i
844844 −44.9648 77.8814i −1.54775 2.68079i
845845 10.6325 18.4160i 0.365769 0.633530i
846846 40.3175i 1.38614i
847847 16.6824 17.7946i 0.573215 0.611430i
848848 28.5168i 0.979271i
849849 −25.0189 14.4447i −0.858646 0.495739i
850850 −5.86705 10.1620i −0.201238 0.348555i
851851 −2.37541 + 2.87982i −0.0814280 + 0.0987188i
852852 −18.6038 10.7409i −0.637356 0.367978i
853853 18.9128i 0.647562i 0.946132 + 0.323781i 0.104954π0.104954\pi
−0.946132 + 0.323781i 0.895046π0.895046\pi
854854 11.1024 + 36.6628i 0.379918 + 1.25458i
855855 −29.4292 −1.00646
856856 −78.9346 45.5729i −2.69793 1.55765i
857857 −0.228365 + 0.131846i −0.00780079 + 0.00450379i −0.503895 0.863765i 0.668100π-0.668100\pi
0.496095 + 0.868269i 0.334767π0.334767\pi
858858 −19.9836 + 11.5376i −0.682231 + 0.393886i
859859 35.3191 + 20.3915i 1.20507 + 0.695748i 0.961678 0.274180i 0.0884063π-0.0884063\pi
0.243393 + 0.969928i 0.421740π0.421740\pi
860860 90.7726i 3.09532i
861861 1.27185 + 4.19995i 0.0433446 + 0.143134i
862862 1.48827i 0.0506907i
863863 −6.30497 + 10.9205i −0.214624 + 0.371739i −0.953156 0.302479i 0.902186π-0.902186\pi
0.738532 + 0.674218i 0.235519π0.235519\pi
864864 3.50143 2.02155i 0.119121 0.0687746i
865865 18.1429 10.4748i 0.616876 0.356154i
866866 −33.2917 + 57.6629i −1.13130 + 1.95947i
867867 0.856375i 0.0290840i
868868 44.1414 + 41.3825i 1.49826 + 1.40461i
869869 22.7075 0.770301
870870 13.8843 + 8.01611i 0.470722 + 0.271772i
871871 −16.5876 28.7306i −0.562049 0.973498i
872872 28.9038 16.6876i 0.978806 0.565114i
873873 2.75635 4.77415i 0.0932885 0.161580i
874874 −64.6883 + 24.1635i −2.18812 + 0.817343i
875875 24.4450 + 5.71209i 0.826393 + 0.193104i
876876 −14.6795 −0.495974
877877 8.44781 14.6320i 0.285262 0.494089i −0.687411 0.726269i 0.741253π-0.741253\pi
0.972673 + 0.232180i 0.0745860π0.0745860\pi
878878 16.6933 9.63789i 0.563372 0.325263i
879879 −16.7042 + 9.64420i −0.563420 + 0.325291i
880880 43.5084 + 25.1196i 1.46667 + 0.846782i
881881 −12.0628 −0.406406 −0.203203 0.979137i 0.565135π-0.565135\pi
−0.203203 + 0.979137i 0.565135π0.565135\pi
882882 −2.25473 34.9111i −0.0759206 1.17552i
883883 −49.2906 −1.65876 −0.829381 0.558684i 0.811307π-0.811307\pi
−0.829381 + 0.558684i 0.811307π0.811307\pi
884884 −29.9423 17.2872i −1.00707 0.581431i
885885 14.9411 + 25.8787i 0.502238 + 0.869902i
886886 −7.64259 13.2374i −0.256758 0.444718i
887887 −5.19931 3.00182i −0.174576 0.100791i 0.410166 0.912011i 0.365471π-0.365471\pi
−0.584742 + 0.811220i 0.698804π0.698804\pi
888888 −3.94092 −0.132249
889889 0.586400 + 0.137024i 0.0196672 + 0.00459565i
890890 48.7863 1.63532
891891 −4.62371 2.66950i −0.154900 0.0894316i
892892 −59.1416 + 34.1454i −1.98021 + 1.14327i
893893 40.7936 23.5522i 1.36511 0.788144i
894894 −21.5425 + 37.3128i −0.720491 + 1.24793i
895895 −18.9654 −0.633943
896896 34.0740 36.3457i 1.13833 1.21422i
897897 9.34922 3.49229i 0.312161 0.116604i
898898 14.8427 25.7083i 0.495307 0.857897i
899899 −12.8596 + 7.42447i −0.428890 + 0.247620i
900900 −4.89934 8.48590i −0.163311 0.282863i
901901 22.0787 + 12.7472i 0.735550 + 0.424670i
902902 −18.6417 −0.620700
903903 −6.76624 22.3437i −0.225166 0.743552i
904904 18.1942i 0.605132i
905905 −16.9278 + 29.3198i −0.562700 + 0.974625i
906906 −7.55108 + 4.35962i −0.250868 + 0.144839i
907907 −16.8846 + 9.74834i −0.560645 + 0.323688i −0.753404 0.657558i 0.771590π-0.771590\pi
0.192760 + 0.981246i 0.438256π0.438256\pi
908908 −59.7213 + 103.440i −1.98192 + 3.43279i
909909 28.8550i 0.957058i
910910 −32.7558 + 9.91928i −1.08584 + 0.328821i
911911 39.2121i 1.29916i −0.760295 0.649578i 0.774946π-0.774946\pi
0.760295 0.649578i 0.225054π-0.225054\pi
912912 −22.4130 12.9402i −0.742169 0.428492i
913913 −3.31554 + 1.91423i −0.109728 + 0.0633516i
914914 38.3335 22.1318i 1.26796 0.732056i
915915 −12.4757 7.20283i −0.412433 0.238118i
916916 −20.6619 −0.682689
917917 19.8336 + 18.5940i 0.654963 + 0.614027i
918918 49.1183i 1.62114i
919919 35.0711 + 20.2483i 1.15689 + 0.667929i 0.950556 0.310553i 0.100514π-0.100514\pi
0.206331 + 0.978482i 0.433848π0.433848\pi
920920 −47.2154 38.9455i −1.55665 1.28400i
921921 −0.440756 0.763412i −0.0145234 0.0251553i
922922 −26.4573 15.2751i −0.871325 0.503060i
923923 11.2542i 0.370437i
924924 −46.6429 10.8991i −1.53444 0.358554i
925925 0.922193i 0.0303215i
926926 −15.6890 + 27.1742i −0.515573 + 0.892999i
927927 −9.55058 16.5421i −0.313682 0.543314i
928928 −1.08016 1.87089i −0.0354580 0.0614150i
929929 19.1452 + 11.0535i 0.628134 + 0.362653i 0.780029 0.625743i 0.215204π-0.215204\pi
−0.151895 + 0.988397i 0.548538π0.548538\pi
930930 −33.9048 −1.11178
931931 −34.0062 + 22.6753i −1.11451 + 0.743153i
932932 −8.64872 −0.283298
933933 −13.4232 + 23.2497i −0.439457 + 0.761161i
934934 −5.06178 8.76725i −0.165626 0.286873i
935935 −38.8970 + 22.4572i −1.27207 + 0.734429i
936936 −18.9984 10.9687i −0.620983 0.358524i
937937 18.7417 0.612266 0.306133 0.951989i 0.400965π-0.400965\pi
0.306133 + 0.951989i 0.400965π0.400965\pi
938938 23.3489 99.9225i 0.762370 3.26258i
939939 17.7165i 0.578157i
940940 70.9060 + 40.9376i 2.31270 + 1.33524i
941941 −11.2642 19.5102i −0.367203 0.636014i 0.621924 0.783078i 0.286351π-0.286351\pi
−0.989127 + 0.147063i 0.953018π0.953018\pi
942942 −18.3606 + 10.6005i −0.598221 + 0.345383i
943943 7.95169 + 1.33315i 0.258943 + 0.0434132i
944944 54.7167i 1.78088i
945945 23.8050 + 22.3172i 0.774377 + 0.725978i
946946 99.1736 3.22441
947947 10.6083 18.3742i 0.344724 0.597080i −0.640579 0.767892i 0.721306π-0.721306\pi
0.985304 + 0.170812i 0.0546390π0.0546390\pi
948948 −10.1662 17.6084i −0.330182 0.571893i
949949 3.84525 + 6.66017i 0.124822 + 0.216198i
950950 −8.52929 + 14.7732i −0.276727 + 0.479305i
951951 11.1549i 0.361722i
952952 −15.8050 52.1919i −0.512244 1.69155i
953953 37.6405i 1.21930i 0.792673 + 0.609648i 0.208689π0.208689\pi
−0.792673 + 0.609648i 0.791311π0.791311\pi
954954 27.4726 + 15.8613i 0.889459 + 0.513529i
955955 −21.5928 + 12.4666i −0.698727 + 0.403410i
956956 22.8529 + 39.5824i 0.739116 + 1.28019i
957957 5.87756 10.1802i 0.189995 0.329080i
958958 −49.4396 −1.59732
959959 26.3524 7.98018i 0.850964 0.257694i
960960 17.1130i 0.552319i
961961 0.201184 0.348460i 0.00648979 0.0112407i
962962 2.02444 + 3.50643i 0.0652705 + 0.113052i
963963 31.1736 17.9981i 1.00455 0.579980i
964964 −13.5887 + 23.5364i −0.437664 + 0.758056i
965965 33.7166 1.08538
966966 28.4848 + 11.8978i 0.916482 + 0.382805i
967967 −22.5027 −0.723636 −0.361818 0.932249i 0.617844π-0.617844\pi
−0.361818 + 0.932249i 0.617844π0.617844\pi
968968 23.6551 40.9718i 0.760303 1.31688i
969969 20.0375 11.5686i 0.643697 0.371638i
970970 −8.34069 14.4465i −0.267803 0.463849i
971971 23.5861 40.8523i 0.756913 1.31101i −0.187505 0.982264i 0.560040π-0.560040\pi
0.944418 0.328748i 0.106627π-0.106627\pi
972972 65.4962i 2.10079i
973973 3.74408 16.0229i 0.120030 0.513671i
974974 −66.6948 −2.13704
975975 1.23271 2.13512i 0.0394784 0.0683787i
976976 13.1890 + 22.8440i 0.422170 + 0.731220i
977977 −2.11262 + 1.21972i −0.0675885 + 0.0390223i −0.533413 0.845855i 0.679091π-0.679091\pi
0.465825 + 0.884877i 0.345758π0.345758\pi
978978 −12.7681 7.37167i −0.408279 0.235720i
979979 35.7710i 1.14325i
980980 −63.6872 31.4827i −2.03441 1.00568i
981981 13.1808i 0.420832i
982982 −13.0665 + 22.6318i −0.416968 + 0.722210i
983983 12.4449 + 21.5553i 0.396932 + 0.687506i 0.993346 0.115171i 0.0367416π-0.0367416\pi
−0.596414 + 0.802677i 0.703408π0.703408\pi
984984 4.25578 + 7.37123i 0.135669 + 0.234986i
985985 29.9240 51.8299i 0.953459 1.65144i
986986 26.2449 0.835809
987987 −20.5050 4.79142i −0.652683 0.152513i
988988 50.2629i 1.59908i
989989 −42.3030 7.09234i −1.34516 0.225523i
990990 −48.3996 + 27.9435i −1.53824 + 0.888104i
991991 12.1383 + 21.0241i 0.385585 + 0.667853i 0.991850 0.127410i 0.0406663π-0.0406663\pi
−0.606265 + 0.795263i 0.707333π0.707333\pi
992992 3.95654 + 2.28431i 0.125620 + 0.0725269i
993993 35.2095i 1.11734i
994994 −23.8082 + 25.3955i −0.755152 + 0.805496i
995995 60.0045 1.90227
996996 2.96874 + 1.71400i 0.0940680 + 0.0543102i
997997 2.87855 1.66193i 0.0911647 0.0526340i −0.453725 0.891142i 0.649905π-0.649905\pi
0.544889 + 0.838508i 0.316572π0.316572\pi
998998 −34.1568 59.1612i −1.08121 1.87272i
999999 1.93012 3.34307i 0.0610664 0.105770i
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 161.2.g.a.68.2 yes 28
7.2 even 3 1127.2.c.c.1126.27 28
7.3 odd 6 inner 161.2.g.a.45.1 28
7.5 odd 6 1127.2.c.c.1126.28 28
23.22 odd 2 inner 161.2.g.a.68.1 yes 28
161.45 even 6 inner 161.2.g.a.45.2 yes 28
161.68 even 6 1127.2.c.c.1126.26 28
161.114 odd 6 1127.2.c.c.1126.25 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
161.2.g.a.45.1 28 7.3 odd 6 inner
161.2.g.a.45.2 yes 28 161.45 even 6 inner
161.2.g.a.68.1 yes 28 23.22 odd 2 inner
161.2.g.a.68.2 yes 28 1.1 even 1 trivial
1127.2.c.c.1126.25 28 161.114 odd 6
1127.2.c.c.1126.26 28 161.68 even 6
1127.2.c.c.1126.27 28 7.2 even 3
1127.2.c.c.1126.28 28 7.5 odd 6