Properties

Label 234.2.t.a.103.12
Level 234234
Weight 22
Character 234.103
Analytic conductor 1.8681.868
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] = [234,2,Mod(25,234)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(234, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("234.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 234=23213 234 = 2 \cdot 3^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 234.t (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: 1.868499407301.86849940730
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 103.12
Character χ\chi == 234.103
Dual form 234.2.t.a.25.12

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.8660250.500000i)q2+(0.523143+1.65116i)q3+(0.5000000.866025i)q4+(0.4193780.242128i)q5+(1.27863+1.16837i)q6+(4.377222.52719i)q71.00000iq8+(2.45264+1.72758i)q90.484256q10+(2.78126+1.60576i)q11+(1.69152+0.372524i)q12+(0.722307+3.53246i)q13+(2.527194.37722i)q14+(0.1803970.819127i)q15+(0.5000000.866025i)q16+4.20245q17+(1.26026+2.72245i)q183.21153iq19+(0.419378+0.242128i)q20+(6.46270+5.90540i)q21+(1.60576+2.78126i)q22+(3.13608+5.43186i)q23+(1.651160.523143i)q24+(2.382754.12704i)q25+(1.14069+3.42035i)q26+(4.135593.14593i)q275.05438iq28+(2.296273.97725i)q29+(0.2533350.799583i)q30+(5.615043.24185i)q31+(0.8660250.500000i)q32+(4.106373.75226i)q33+(3.639432.10123i)q342.44761q35+(0.269808+2.98784i)q36+2.08429iq37+(1.605762.78126i)q38+(6.21052+0.655337i)q39+(0.242128+0.419378i)q40+(9.573015.52698i)q41+(8.54956+1.88288i)q42+(4.73367+8.19896i)q43+3.21153iq44+(1.446880.130656i)q45+6.27217iq46+(4.57369+2.64062i)q47+(1.168371.27863i)q48+(9.2733716.0619i)q49+(4.127042.38275i)q50+(2.19848+6.93891i)q51+(2.69805+2.39177i)q52+6.41990q53+(5.154490.656660i)q54+1.55520q55+(2.527194.37722i)q56+(5.302741.68009i)q57+(3.977252.29627i)q58+(3.13771+1.81156i)q59+(0.6191860.565792i)q60+(0.500864+0.867521i)q616.48369q62+(6.36984+13.7603i)q631.00000q64+(1.158231.30655i)q65+(5.432351.19637i)q66+(0.936987+0.540970i)q67+(2.101233.63943i)q68+(10.60952.33653i)q69+(2.11969+1.22381i)q704.63041iq71+(1.72758+2.45264i)q72+0.325525iq73+(1.04214+1.80504i)q74+(5.567886.09332i)q75+(2.781261.60576i)q76+(8.11614+14.0576i)q77+(5.05080+3.67280i)q78+(3.91818+6.78649i)q79+0.484256iq80+(3.030928.47428i)q8111.0540q82+(5.08022+2.93306i)q83+(8.345572.64416i)q84+(1.762421.01753i)q85+(8.19896+4.73367i)q86+(5.365805.87217i)q87+(1.60576+2.78126i)q88+8.42912iq89+(1.187710.836592i)q90+(5.76550+17.2878i)q91+(3.13608+5.43186i)q92+(2.4153310.9673i)q93+(2.64062+4.57369i)q94+(0.777601+1.34684i)q95+(0.3725241.69152i)q96+(11.30216.52525i)q9718.5467iq98+(4.047368.74323i)q99+O(q100)q+(0.866025 - 0.500000i) q^{2} +(0.523143 + 1.65116i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.419378 - 0.242128i) q^{5} +(1.27863 + 1.16837i) q^{6} +(4.37722 - 2.52719i) q^{7} -1.00000i q^{8} +(-2.45264 + 1.72758i) q^{9} -0.484256 q^{10} +(-2.78126 + 1.60576i) q^{11} +(1.69152 + 0.372524i) q^{12} +(-0.722307 + 3.53246i) q^{13} +(2.52719 - 4.37722i) q^{14} +(0.180397 - 0.819127i) q^{15} +(-0.500000 - 0.866025i) q^{16} +4.20245 q^{17} +(-1.26026 + 2.72245i) q^{18} -3.21153i q^{19} +(-0.419378 + 0.242128i) q^{20} +(6.46270 + 5.90540i) q^{21} +(-1.60576 + 2.78126i) q^{22} +(-3.13608 + 5.43186i) q^{23} +(1.65116 - 0.523143i) q^{24} +(-2.38275 - 4.12704i) q^{25} +(1.14069 + 3.42035i) q^{26} +(-4.13559 - 3.14593i) q^{27} -5.05438i q^{28} +(-2.29627 - 3.97725i) q^{29} +(-0.253335 - 0.799583i) q^{30} +(-5.61504 - 3.24185i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-4.10637 - 3.75226i) q^{33} +(3.63943 - 2.10123i) q^{34} -2.44761 q^{35} +(0.269808 + 2.98784i) q^{36} +2.08429i q^{37} +(-1.60576 - 2.78126i) q^{38} +(-6.21052 + 0.655337i) q^{39} +(-0.242128 + 0.419378i) q^{40} +(-9.57301 - 5.52698i) q^{41} +(8.54956 + 1.88288i) q^{42} +(4.73367 + 8.19896i) q^{43} +3.21153i q^{44} +(1.44688 - 0.130656i) q^{45} +6.27217i q^{46} +(-4.57369 + 2.64062i) q^{47} +(1.16837 - 1.27863i) q^{48} +(9.27337 - 16.0619i) q^{49} +(-4.12704 - 2.38275i) q^{50} +(2.19848 + 6.93891i) q^{51} +(2.69805 + 2.39177i) q^{52} +6.41990 q^{53} +(-5.15449 - 0.656660i) q^{54} +1.55520 q^{55} +(-2.52719 - 4.37722i) q^{56} +(5.30274 - 1.68009i) q^{57} +(-3.97725 - 2.29627i) q^{58} +(3.13771 + 1.81156i) q^{59} +(-0.619186 - 0.565792i) q^{60} +(0.500864 + 0.867521i) q^{61} -6.48369 q^{62} +(-6.36984 + 13.7603i) q^{63} -1.00000 q^{64} +(1.15823 - 1.30655i) q^{65} +(-5.43235 - 1.19637i) q^{66} +(0.936987 + 0.540970i) q^{67} +(2.10123 - 3.63943i) q^{68} +(-10.6095 - 2.33653i) q^{69} +(-2.11969 + 1.22381i) q^{70} -4.63041i q^{71} +(1.72758 + 2.45264i) q^{72} +0.325525i q^{73} +(1.04214 + 1.80504i) q^{74} +(5.56788 - 6.09332i) q^{75} +(-2.78126 - 1.60576i) q^{76} +(-8.11614 + 14.0576i) q^{77} +(-5.05080 + 3.67280i) q^{78} +(3.91818 + 6.78649i) q^{79} +0.484256i q^{80} +(3.03092 - 8.47428i) q^{81} -11.0540 q^{82} +(-5.08022 + 2.93306i) q^{83} +(8.34557 - 2.64416i) q^{84} +(-1.76242 - 1.01753i) q^{85} +(8.19896 + 4.73367i) q^{86} +(5.36580 - 5.87217i) q^{87} +(1.60576 + 2.78126i) q^{88} +8.42912i q^{89} +(1.18771 - 0.836592i) q^{90} +(5.76550 + 17.2878i) q^{91} +(3.13608 + 5.43186i) q^{92} +(2.41533 - 10.9673i) q^{93} +(-2.64062 + 4.57369i) q^{94} +(-0.777601 + 1.34684i) q^{95} +(0.372524 - 1.69152i) q^{96} +(11.3021 - 6.52525i) q^{97} -18.5467i q^{98} +(4.04736 - 8.74323i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 28q+14q416q9+2q13+8q1414q16+16q178q23+14q25+8q26+18q2716q298q3068q358q368q3910q424q43+10q49++8q92+O(q100) 28 q + 14 q^{4} - 16 q^{9} + 2 q^{13} + 8 q^{14} - 14 q^{16} + 16 q^{17} - 8 q^{23} + 14 q^{25} + 8 q^{26} + 18 q^{27} - 16 q^{29} - 8 q^{30} - 68 q^{35} - 8 q^{36} - 8 q^{39} - 10 q^{42} - 4 q^{43} + 10 q^{49}+ \cdots + 8 q^{92}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/234Z)×\left(\mathbb{Z}/234\mathbb{Z}\right)^\times.

nn 145145 209209
χ(n)\chi(n) 1-1 e(13)e\left(\frac{1}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.866025 0.500000i 0.612372 0.353553i
33 0.523143 + 1.65116i 0.302036 + 0.953296i
44 0.500000 0.866025i 0.250000 0.433013i
55 −0.419378 0.242128i −0.187552 0.108283i 0.403284 0.915075i 0.367869π-0.367869\pi
−0.590836 + 0.806792i 0.701202π0.701202\pi
66 1.27863 + 1.16837i 0.522000 + 0.476986i
77 4.37722 2.52719i 1.65443 0.955188i 0.679216 0.733938i 0.262320π-0.262320\pi
0.975217 0.221249i 0.0710134π-0.0710134\pi
88 1.00000i 0.353553i
99 −2.45264 + 1.72758i −0.817548 + 0.575861i
1010 −0.484256 −0.153135
1111 −2.78126 + 1.60576i −0.838583 + 0.484156i −0.856782 0.515678i 0.827540π-0.827540\pi
0.0181994 + 0.999834i 0.494207π0.494207\pi
1212 1.69152 + 0.372524i 0.488299 + 0.107538i
1313 −0.722307 + 3.53246i −0.200332 + 0.979728i
1414 2.52719 4.37722i 0.675420 1.16986i
1515 0.180397 0.819127i 0.0465783 0.211498i
1616 −0.500000 0.866025i −0.125000 0.216506i
1717 4.20245 1.01924 0.509622 0.860398i 0.329785π-0.329785\pi
0.509622 + 0.860398i 0.329785π0.329785\pi
1818 −1.26026 + 2.72245i −0.297046 + 0.641688i
1919 3.21153i 0.736775i −0.929672 0.368388i 0.879910π-0.879910\pi
0.929672 0.368388i 0.120090π-0.120090\pi
2020 −0.419378 + 0.242128i −0.0937758 + 0.0541415i
2121 6.46270 + 5.90540i 1.41028 + 1.28866i
2222 −1.60576 + 2.78126i −0.342350 + 0.592968i
2323 −3.13608 + 5.43186i −0.653919 + 1.13262i 0.328245 + 0.944593i 0.393543π0.393543\pi
−0.982164 + 0.188028i 0.939791π0.939791\pi
2424 1.65116 0.523143i 0.337041 0.106786i
2525 −2.38275 4.12704i −0.476550 0.825408i
2626 1.14069 + 3.42035i 0.223708 + 0.670787i
2727 −4.13559 3.14593i −0.795895 0.605435i
2828 5.05438i 0.955188i
2929 −2.29627 3.97725i −0.426406 0.738557i 0.570144 0.821544i 0.306887π-0.306887\pi
−0.996551 + 0.0829873i 0.973554π0.973554\pi
3030 −0.253335 0.799583i −0.0462524 0.145983i
3131 −5.61504 3.24185i −1.00849 0.582253i −0.0977420 0.995212i 0.531162π-0.531162\pi
−0.910750 + 0.412959i 0.864495π0.864495\pi
3232 −0.866025 0.500000i −0.153093 0.0883883i
3333 −4.10637 3.75226i −0.714827 0.653185i
3434 3.63943 2.10123i 0.624157 0.360357i
3535 −2.44761 −0.413722
3636 0.269808 + 2.98784i 0.0449679 + 0.497974i
3737 2.08429i 0.342654i 0.985214 + 0.171327i 0.0548055π0.0548055\pi
−0.985214 + 0.171327i 0.945194π0.945194\pi
3838 −1.60576 2.78126i −0.260489 0.451181i
3939 −6.21052 + 0.655337i −0.994479 + 0.104938i
4040 −0.242128 + 0.419378i −0.0382838 + 0.0663095i
4141 −9.57301 5.52698i −1.49505 0.863169i −0.495070 0.868853i 0.664857π-0.664857\pi
−0.999984 + 0.00568392i 0.998191π0.998191\pi
4242 8.54956 + 1.88288i 1.31923 + 0.290534i
4343 4.73367 + 8.19896i 0.721879 + 1.25033i 0.960246 + 0.279155i 0.0900544π0.0900544\pi
−0.238367 + 0.971175i 0.576612π0.576612\pi
4444 3.21153i 0.484156i
4545 1.44688 0.130656i 0.215688 0.0194770i
4646 6.27217i 0.924780i
4747 −4.57369 + 2.64062i −0.667141 + 0.385174i −0.794992 0.606619i 0.792525π-0.792525\pi
0.127851 + 0.991793i 0.459192π0.459192\pi
4848 1.16837 1.27863i 0.168640 0.184555i
4949 9.27337 16.0619i 1.32477 2.29456i
5050 −4.12704 2.38275i −0.583652 0.336971i
5151 2.19848 + 6.93891i 0.307849 + 0.971642i
5252 2.69805 + 2.39177i 0.374152 + 0.331678i
5353 6.41990 0.881841 0.440921 0.897546i 0.354652π-0.354652\pi
0.440921 + 0.897546i 0.354652π0.354652\pi
5454 −5.15449 0.656660i −0.701438 0.0893601i
5555 1.55520 0.209703
5656 −2.52719 4.37722i −0.337710 0.584931i
5757 5.30274 1.68009i 0.702365 0.222533i
5858 −3.97725 2.29627i −0.522239 0.301515i
5959 3.13771 + 1.81156i 0.408495 + 0.235844i 0.690143 0.723673i 0.257548π-0.257548\pi
−0.281648 + 0.959518i 0.590881π0.590881\pi
6060 −0.619186 0.565792i −0.0799366 0.0730434i
6161 0.500864 + 0.867521i 0.0641290 + 0.111075i 0.896307 0.443433i 0.146240π-0.146240\pi
−0.832178 + 0.554508i 0.812906π0.812906\pi
6262 −6.48369 −0.823430
6363 −6.36984 + 13.7603i −0.802524 + 1.73363i
6464 −1.00000 −0.125000
6565 1.15823 1.30655i 0.143660 0.162057i
6666 −5.43235 1.19637i −0.668676 0.147263i
6767 0.936987 + 0.540970i 0.114471 + 0.0660900i 0.556142 0.831087i 0.312281π-0.312281\pi
−0.441671 + 0.897177i 0.645614π0.645614\pi
6868 2.10123 3.63943i 0.254811 0.441346i
6969 −10.6095 2.33653i −1.27723 0.281286i
7070 −2.11969 + 1.22381i −0.253352 + 0.146273i
7171 4.63041i 0.549529i −0.961512 0.274764i 0.911400π-0.911400\pi
0.961512 0.274764i 0.0885999π-0.0885999\pi
7272 1.72758 + 2.45264i 0.203597 + 0.289047i
7373 0.325525i 0.0380998i 0.999819 + 0.0190499i 0.00606414π0.00606414\pi
−0.999819 + 0.0190499i 0.993936π0.993936\pi
7474 1.04214 + 1.80504i 0.121147 + 0.209832i
7575 5.56788 6.09332i 0.642923 0.703596i
7676 −2.78126 1.60576i −0.319033 0.184194i
7777 −8.11614 + 14.0576i −0.924920 + 1.60201i
7878 −5.05080 + 3.67280i −0.571890 + 0.415862i
7979 3.91818 + 6.78649i 0.440830 + 0.763540i 0.997751 0.0670253i 0.0213508π-0.0213508\pi
−0.556921 + 0.830565i 0.688017π0.688017\pi
8080 0.484256i 0.0541415i
8181 3.03092 8.47428i 0.336769 0.941587i
8282 −11.0540 −1.22071
8383 −5.08022 + 2.93306i −0.557626 + 0.321946i −0.752192 0.658944i 0.771003π-0.771003\pi
0.194566 + 0.980889i 0.437670π0.437670\pi
8484 8.34557 2.64416i 0.910577 0.288501i
8585 −1.76242 1.01753i −0.191161 0.110367i
8686 8.19896 + 4.73367i 0.884117 + 0.510445i
8787 5.36580 5.87217i 0.575274 0.629563i
8888 1.60576 + 2.78126i 0.171175 + 0.296484i
8989 8.42912i 0.893485i 0.894662 + 0.446743i 0.147416π0.147416\pi
−0.894662 + 0.446743i 0.852584π0.852584\pi
9090 1.18771 0.836592i 0.125195 0.0881845i
9191 5.76550 + 17.2878i 0.604388 + 1.81225i
9292 3.13608 + 5.43186i 0.326959 + 0.566310i
9393 2.41533 10.9673i 0.250458 1.13725i
9494 −2.64062 + 4.57369i −0.272359 + 0.471740i
9595 −0.777601 + 1.34684i −0.0797802 + 0.138183i
9696 0.372524 1.69152i 0.0380206 0.172640i
9797 11.3021 6.52525i 1.14755 0.662539i 0.199262 0.979946i 0.436145π-0.436145\pi
0.948289 + 0.317407i 0.102812π0.102812\pi
9898 18.5467i 1.87350i
9999 4.04736 8.74323i 0.406775 0.878728i
100100 −4.76550 −0.476550
101101 3.42351 + 5.92969i 0.340652 + 0.590027i 0.984554 0.175081i 0.0560189π-0.0560189\pi
−0.643902 + 0.765108i 0.722686π0.722686\pi
102102 5.37340 + 4.91003i 0.532046 + 0.486166i
103103 −1.77760 + 3.07889i −0.175152 + 0.303373i −0.940214 0.340584i 0.889375π-0.889375\pi
0.765062 + 0.643957i 0.222708π0.222708\pi
104104 3.53246 + 0.722307i 0.346386 + 0.0708280i
105105 −1.28045 4.04139i −0.124959 0.394400i
106106 5.55980 3.20995i 0.540015 0.311778i
107107 1.41392 0.136689 0.0683445 0.997662i 0.478228π-0.478228\pi
0.0683445 + 0.997662i 0.478228π0.478228\pi
108108 −4.79225 + 2.00856i −0.461135 + 0.193274i
109109 4.97525i 0.476543i 0.971199 + 0.238271i 0.0765808π0.0765808\pi
−0.971199 + 0.238271i 0.923419π0.923419\pi
110110 1.34684 0.777601i 0.128417 0.0741413i
111111 −3.44148 + 1.09038i −0.326651 + 0.103494i
112112 −4.37722 2.52719i −0.413608 0.238797i
113113 6.54415 11.3348i 0.615622 1.06629i −0.374653 0.927165i 0.622238π-0.622238\pi
0.990275 0.139124i 0.0444286π-0.0444286\pi
114114 3.75226 4.10637i 0.351432 0.384597i
115115 2.63041 1.51867i 0.245287 0.141616i
116116 −4.59254 −0.426406
117117 −4.33105 9.91171i −0.400406 0.916338i
118118 3.62311 0.333534
119119 18.3951 10.6204i 1.68627 0.973570i
120120 −0.819127 0.180397i −0.0747757 0.0164679i
121121 −0.343044 + 0.594169i −0.0311858 + 0.0540154i
122122 0.867521 + 0.500864i 0.0785417 + 0.0453461i
123123 4.11787 18.6980i 0.371296 1.68594i
124124 −5.61504 + 3.24185i −0.504246 + 0.291126i
125125 4.72900i 0.422975i
126126 1.36371 + 15.1017i 0.121489 + 1.34536i
127127 −4.56300 −0.404901 −0.202450 0.979293i 0.564890π-0.564890\pi
−0.202450 + 0.979293i 0.564890π0.564890\pi
128128 −0.866025 + 0.500000i −0.0765466 + 0.0441942i
129129 −11.0614 + 12.1053i −0.973902 + 1.06581i
130130 0.349781 1.71061i 0.0306779 0.150031i
131131 −1.23473 + 2.13862i −0.107879 + 0.186852i −0.914911 0.403656i 0.867739π-0.867739\pi
0.807032 + 0.590508i 0.201073π0.201073\pi
132132 −5.30274 + 1.68009i −0.461544 + 0.146233i
133133 −8.11614 14.0576i −0.703758 1.21895i
134134 1.08194 0.0934654
135135 0.972658 + 2.32068i 0.0837131 + 0.199732i
136136 4.20245i 0.360357i
137137 16.9831 9.80519i 1.45096 0.837714i 0.452427 0.891802i 0.350558π-0.350558\pi
0.998536 + 0.0540880i 0.0172251π0.0172251\pi
138138 −10.3563 + 3.28124i −0.881590 + 0.279317i
139139 0.193698 0.335495i 0.0164293 0.0284563i −0.857694 0.514161i 0.828104π-0.828104\pi
0.874123 + 0.485704i 0.161437π0.161437\pi
140140 −1.22381 + 2.11969i −0.103430 + 0.179147i
141141 −6.75277 6.17046i −0.568686 0.519646i
142142 −2.31521 4.01005i −0.194288 0.336516i
143143 −3.66337 10.9846i −0.306346 0.918575i
144144 2.72245 + 1.26026i 0.226871 + 0.105022i
145145 2.22396i 0.184690i
146146 0.162762 + 0.281913i 0.0134703 + 0.0233313i
147147 31.3721 + 6.90911i 2.58753 + 0.569853i
148148 1.80504 + 1.04214i 0.148374 + 0.0856636i
149149 8.19151 + 4.72937i 0.671075 + 0.387445i 0.796484 0.604660i 0.206691π-0.206691\pi
−0.125409 + 0.992105i 0.540024π0.540024\pi
150150 1.77526 8.06091i 0.144950 0.658171i
151151 1.15323 0.665819i 0.0938487 0.0541836i −0.452341 0.891845i 0.649411π-0.649411\pi
0.546190 + 0.837661i 0.316078π0.316078\pi
152152 −3.21153 −0.260489
153153 −10.3071 + 7.26008i −0.833281 + 0.586943i
154154 16.2323i 1.30803i
155155 1.56988 + 2.71912i 0.126096 + 0.218405i
156156 −2.53772 + 5.70613i −0.203180 + 0.456856i
157157 2.92122 5.05970i 0.233139 0.403808i −0.725592 0.688126i 0.758434π-0.758434\pi
0.958730 + 0.284318i 0.0917671π0.0917671\pi
158158 6.78649 + 3.91818i 0.539904 + 0.311714i
159159 3.35852 + 10.6003i 0.266348 + 0.840656i
160160 0.242128 + 0.419378i 0.0191419 + 0.0331547i
161161 31.7019i 2.49846i
162162 −1.61229 8.85441i −0.126673 0.695668i
163163 15.1340i 1.18538i 0.805430 + 0.592691i 0.201935π0.201935\pi
−0.805430 + 0.592691i 0.798065π0.798065\pi
164164 −9.57301 + 5.52698i −0.747527 + 0.431585i
165165 0.813592 + 2.56788i 0.0633381 + 0.199909i
166166 −2.93306 + 5.08022i −0.227650 + 0.394301i
167167 10.4155 + 6.01341i 0.805978 + 0.465331i 0.845557 0.533885i 0.179268π-0.179268\pi
−0.0395794 + 0.999216i 0.512602π0.512602\pi
168168 5.90540 6.46270i 0.455611 0.498608i
169169 −11.9565 5.10304i −0.919734 0.392542i
170170 −2.03506 −0.156082
171171 5.54818 + 7.87673i 0.424280 + 0.602349i
172172 9.46735 0.721879
173173 −4.42932 7.67180i −0.336755 0.583276i 0.647066 0.762434i 0.275996π-0.275996\pi
−0.983820 + 0.179158i 0.942663π0.942663\pi
174174 1.71083 7.76835i 0.129698 0.588917i
175175 −20.8596 12.0433i −1.57684 0.910389i
176176 2.78126 + 1.60576i 0.209646 + 0.121039i
177177 −1.34970 + 6.12855i −0.101449 + 0.460650i
178178 4.21456 + 7.29984i 0.315895 + 0.547146i
179179 10.3704 0.775121 0.387561 0.921844i 0.373318π-0.373318\pi
0.387561 + 0.921844i 0.373318π0.373318\pi
180180 0.610289 1.31836i 0.0454883 0.0982650i
181181 10.8407 0.805783 0.402892 0.915248i 0.368005π-0.368005\pi
0.402892 + 0.915248i 0.368005π0.368005\pi
182182 13.6369 + 12.0889i 1.01084 + 0.896088i
183183 −1.17039 + 1.28084i −0.0865178 + 0.0946826i
184184 5.43186 + 3.13608i 0.400442 + 0.231195i
185185 0.504664 0.874103i 0.0371036 0.0642653i
186186 −3.39190 10.7056i −0.248706 0.784973i
187187 −11.6881 + 6.74815i −0.854721 + 0.493474i
188188 5.28124i 0.385174i
189189 −26.0528 3.31901i −1.89506 0.241422i
190190 1.55520i 0.112826i
191191 −5.62900 9.74971i −0.407300 0.705464i 0.587286 0.809379i 0.300196π-0.300196\pi
−0.994586 + 0.103915i 0.966863π0.966863\pi
192192 −0.523143 1.65116i −0.0377546 0.119162i
193193 6.60401 + 3.81283i 0.475367 + 0.274453i 0.718484 0.695544i 0.244836π-0.244836\pi
−0.243117 + 0.969997i 0.578170π0.578170\pi
194194 6.52525 11.3021i 0.468486 0.811441i
195195 2.76323 + 1.22891i 0.197879 + 0.0880038i
196196 −9.27337 16.0619i −0.662383 1.14728i
197197 24.5170i 1.74677i −0.487035 0.873383i 0.661921π-0.661921\pi
0.487035 0.873383i 0.338079π-0.338079\pi
198198 −0.866495 9.59554i −0.0615791 0.681925i
199199 −13.5310 −0.959187 −0.479593 0.877491i 0.659216π-0.659216\pi
−0.479593 + 0.877491i 0.659216π0.659216\pi
200200 −4.12704 + 2.38275i −0.291826 + 0.168486i
201201 −0.403049 + 1.83012i −0.0284289 + 0.129087i
202202 5.92969 + 3.42351i 0.417212 + 0.240877i
203203 −20.1025 11.6062i −1.41092 0.814596i
204204 7.10852 + 1.56552i 0.497696 + 0.109608i
205205 2.67647 + 4.63579i 0.186933 + 0.323777i
206206 3.55520i 0.247703i
207207 −1.69228 18.7402i −0.117621 1.30254i
208208 3.42035 1.14069i 0.237159 0.0790929i
209209 5.15696 + 8.93211i 0.356714 + 0.617847i
210210 −3.12960 2.85972i −0.215963 0.197340i
211211 −11.9346 + 20.6713i −0.821610 + 1.42307i 0.0828724 + 0.996560i 0.473591π0.473591\pi
−0.904483 + 0.426511i 0.859743π0.859743\pi
212212 3.20995 5.55980i 0.220460 0.381849i
213213 7.64554 2.42237i 0.523864 0.165978i
214214 1.22449 0.706961i 0.0837045 0.0483268i
215215 4.58462i 0.312668i
216216 −3.14593 + 4.13559i −0.214053 + 0.281391i
217217 −32.7710 −2.22464
218218 2.48763 + 4.30869i 0.168483 + 0.291822i
219219 −0.537493 + 0.170296i −0.0363204 + 0.0115075i
220220 0.777601 1.34684i 0.0524258 0.0908042i
221221 −3.03546 + 14.8450i −0.204187 + 0.998583i
222222 −2.43522 + 2.66504i −0.163441 + 0.178866i
223223 −11.1456 + 6.43490i −0.746363 + 0.430913i −0.824378 0.566040i 0.808475π-0.808475\pi
0.0780155 + 0.996952i 0.475142π0.475142\pi
224224 −5.05438 −0.337710
225225 12.9738 + 6.00577i 0.864922 + 0.400385i
226226 13.0883i 0.870621i
227227 −15.6362 + 9.02759i −1.03781 + 0.599182i −0.919213 0.393760i 0.871174π-0.871174\pi
−0.118600 + 0.992942i 0.537841π0.537841\pi
228228 1.19637 5.43235i 0.0792317 0.359766i
229229 −18.3370 10.5869i −1.21174 0.699599i −0.248603 0.968606i 0.579971π-0.579971\pi
−0.963138 + 0.269006i 0.913305π0.913305\pi
230230 1.51867 2.63041i 0.100138 0.173444i
231231 −27.4571 6.04691i −1.80655 0.397858i
232232 −3.97725 + 2.29627i −0.261119 + 0.150757i
233233 29.0610 1.90385 0.951923 0.306337i 0.0991033π-0.0991033\pi
0.951923 + 0.306337i 0.0991033π0.0991033\pi
234234 −8.70666 6.41827i −0.569172 0.419575i
235235 2.55747 0.166831
236236 3.13771 1.81156i 0.204247 0.117922i
237237 −9.15580 + 10.0198i −0.594733 + 0.650859i
238238 10.6204 18.3951i 0.688418 1.19237i
239239 6.29516 + 3.63451i 0.407200 + 0.235097i 0.689586 0.724204i 0.257793π-0.257793\pi
−0.282386 + 0.959301i 0.591126π0.591126\pi
240240 −0.799583 + 0.253335i −0.0516129 + 0.0163527i
241241 15.5109 8.95521i 0.999144 0.576856i 0.0911491 0.995837i 0.470946π-0.470946\pi
0.907995 + 0.418981i 0.137613π0.137613\pi
242242 0.686087i 0.0441034i
243243 15.5780 + 0.571274i 0.999328 + 0.0366473i
244244 1.00173 0.0641290
245245 −7.77809 + 4.49068i −0.496924 + 0.286899i
246246 −5.78280 18.2518i −0.368698 1.16369i
247247 11.3446 + 2.31971i 0.721839 + 0.147600i
248248 −3.24185 + 5.61504i −0.205857 + 0.356556i
249249 −7.50063 6.85383i −0.475333 0.434344i
250250 2.36450 + 4.09543i 0.149544 + 0.259018i
251251 −3.84702 −0.242822 −0.121411 0.992602i 0.538742π-0.538742\pi
−0.121411 + 0.992602i 0.538742π0.538742\pi
252252 8.73185 + 12.3966i 0.550055 + 0.780912i
253253 20.1432i 1.26639i
254254 −3.95167 + 2.28150i −0.247950 + 0.143154i
255255 0.758110 3.44234i 0.0474747 0.215568i
256256 −0.500000 + 0.866025i −0.0312500 + 0.0541266i
257257 7.38375 12.7890i 0.460586 0.797758i −0.538404 0.842687i 0.680973π-0.680973\pi
0.998990 + 0.0449285i 0.0143060π0.0143060\pi
258258 −3.52682 + 16.0142i −0.219570 + 0.996999i
259259 5.26738 + 9.12337i 0.327299 + 0.566899i
260260 −0.552388 1.65633i −0.0342576 0.102721i
261261 12.5030 + 5.78779i 0.773913 + 0.358255i
262262 2.46946i 0.152564i
263263 −4.38124 7.58853i −0.270159 0.467929i 0.698743 0.715372i 0.253743π-0.253743\pi
−0.968902 + 0.247443i 0.920410π0.920410\pi
264264 −3.75226 + 4.10637i −0.230936 + 0.252729i
265265 −2.69237 1.55444i −0.165391 0.0954884i
266266 −14.0576 8.11614i −0.861924 0.497632i
267267 −13.9178 + 4.40963i −0.851756 + 0.269865i
268268 0.936987 0.540970i 0.0572356 0.0330450i
269269 −8.90736 −0.543091 −0.271546 0.962426i 0.587535π-0.587535\pi
−0.271546 + 0.962426i 0.587535π0.587535\pi
270270 2.00269 + 1.52344i 0.121880 + 0.0927133i
271271 3.58551i 0.217804i −0.994052 0.108902i 0.965266π-0.965266\pi
0.994052 0.108902i 0.0347335π-0.0347335\pi
272272 −2.10123 3.63943i −0.127406 0.220673i
273273 −25.5286 + 18.5637i −1.54506 + 1.12353i
274274 9.80519 16.9831i 0.592353 1.02599i
275275 13.2541 + 7.65226i 0.799253 + 0.461449i
276276 −7.32823 + 8.01980i −0.441108 + 0.482735i
277277 7.43966 + 12.8859i 0.447006 + 0.774237i 0.998190 0.0601468i 0.0191569π-0.0191569\pi
−0.551183 + 0.834384i 0.685824π0.685824\pi
278278 0.387396i 0.0232345i
279279 19.3723 1.74935i 1.15979 0.104731i
280280 2.44761i 0.146273i
281281 14.2995 8.25582i 0.853037 0.492501i −0.00863764 0.999963i 0.502749π-0.502749\pi
0.861674 + 0.507462i 0.169416π0.169416\pi
282282 −8.93330 1.96739i −0.531970 0.117156i
283283 0.267833 0.463900i 0.0159210 0.0275760i −0.857955 0.513725i 0.828265π-0.828265\pi
0.873876 + 0.486149i 0.161599π0.161599\pi
284284 −4.01005 2.31521i −0.237953 0.137382i
285285 −2.63065 0.579350i −0.155826 0.0343177i
286286 −8.66485 7.68122i −0.512363 0.454200i
287287 −55.8709 −3.29795
288288 2.98784 0.269808i 0.176060 0.0158986i
289289 0.660618 0.0388599
290290 1.11198 + 1.92601i 0.0652978 + 0.113099i
291291 16.6868 + 15.2479i 0.978199 + 0.893846i
292292 0.281913 + 0.162762i 0.0164977 + 0.00952495i
293293 −16.9651 9.79482i −0.991113 0.572220i −0.0855065 0.996338i 0.527251π-0.527251\pi
−0.905607 + 0.424118i 0.860584π0.860584\pi
294294 30.6236 9.70258i 1.78600 0.565866i
295295 −0.877257 1.51945i −0.0510758 0.0884660i
296296 2.08429 0.121147
297297 16.5538 + 2.10888i 0.960549 + 0.122370i
298298 9.45874 0.547930
299299 −16.9226 15.0016i −0.978659 0.867562i
300300 −2.49303 7.86859i −0.143935 0.454293i
301301 41.4407 + 23.9258i 2.38860 + 1.37906i
302302 0.665819 1.15323i 0.0383136 0.0663611i
303303 −7.99988 + 8.75483i −0.459581 + 0.502952i
304304 −2.78126 + 1.60576i −0.159516 + 0.0920969i
305305 0.485092i 0.0277763i
306306 −5.29619 + 11.4410i −0.302763 + 0.654037i
307307 1.26064i 0.0719485i 0.999353 + 0.0359743i 0.0114534π0.0114534\pi
−0.999353 + 0.0359743i 0.988547π0.988547\pi
308308 8.11614 + 14.0576i 0.462460 + 0.801004i
309309 −6.01368 1.32440i −0.342106 0.0753424i
310310 2.71912 + 1.56988i 0.154436 + 0.0891634i
311311 8.79222 15.2286i 0.498561 0.863533i −0.501438 0.865194i 0.667195π-0.667195\pi
0.999999 + 0.00166095i 0.000528697π0.000528697\pi
312312 0.655337 + 6.21052i 0.0371011 + 0.351601i
313313 −0.102706 0.177891i −0.00580526 0.0100550i 0.863108 0.505019i 0.168515π-0.168515\pi
−0.868913 + 0.494964i 0.835181π0.835181\pi
314314 5.84243i 0.329708i
315315 6.00312 4.22845i 0.338238 0.238246i
316316 7.83637 0.440830
317317 −15.6583 + 9.04030i −0.879455 + 0.507754i −0.870479 0.492206i 0.836191π-0.836191\pi
−0.00897641 + 0.999960i 0.502857π0.502857\pi
318318 8.20870 + 7.50084i 0.460321 + 0.420626i
319319 12.7731 + 7.37453i 0.715154 + 0.412894i
320320 0.419378 + 0.242128i 0.0234439 + 0.0135354i
321321 0.739682 + 2.33461i 0.0412850 + 0.130305i
322322 15.8509 + 27.4546i 0.883339 + 1.52999i
323323 13.4963i 0.750954i
324324 −5.82348 6.86200i −0.323527 0.381222i
325325 16.2997 5.43597i 0.904144 0.301533i
326326 7.56698 + 13.1064i 0.419096 + 0.725896i
327327 −8.21492 + 2.60277i −0.454286 + 0.143933i
328328 −5.52698 + 9.57301i −0.305176 + 0.528581i
329329 −13.3467 + 23.1171i −0.735827 + 1.27449i
330330 1.98853 + 1.81706i 0.109465 + 0.100026i
331331 3.63300 2.09751i 0.199688 0.115290i −0.396822 0.917896i 0.629887π-0.629887\pi
0.596510 + 0.802606i 0.296554π0.296554\pi
332332 5.86613i 0.321946i
333333 −3.60077 5.11201i −0.197321 0.280136i
334334 12.0268 0.658078
335335 −0.261968 0.453742i −0.0143128 0.0247906i
336336 1.88288 8.54956i 0.102719 0.466417i
337337 −6.88041 + 11.9172i −0.374800 + 0.649172i −0.990297 0.138967i 0.955622π-0.955622\pi
0.615497 + 0.788139i 0.288955π0.288955\pi
338338 −12.9062 + 1.55891i −0.702004 + 0.0847935i
339339 22.1391 + 4.87571i 1.20243 + 0.264812i
340340 −1.76242 + 1.01753i −0.0955805 + 0.0551834i
341341 20.8226 1.12761
342342 8.74323 + 4.04736i 0.472780 + 0.218856i
343343 58.3615i 3.15123i
344344 8.19896 4.73367i 0.442059 0.255223i
345345 3.88364 + 3.54874i 0.209088 + 0.191058i
346346 −7.67180 4.42932i −0.412439 0.238122i
347347 11.9351 20.6722i 0.640710 1.10974i −0.344565 0.938763i 0.611974π-0.611974\pi
0.985275 0.170979i 0.0546931π-0.0546931\pi
348348 −2.40255 7.58300i −0.128790 0.406491i
349349 −16.7557 + 9.67391i −0.896913 + 0.517833i −0.876197 0.481953i 0.839928π-0.839928\pi
−0.0207153 + 0.999785i 0.506594π0.506594\pi
350350 −24.0866 −1.28748
351351 14.1000 12.3365i 0.752604 0.658473i
352352 3.21153 0.171175
353353 −24.0606 + 13.8914i −1.28062 + 0.739365i −0.976961 0.213417i 0.931541π-0.931541\pi
−0.303656 + 0.952782i 0.598207π0.598207\pi
354354 1.89540 + 5.98233i 0.100740 + 0.317957i
355355 −1.12115 + 1.94189i −0.0595046 + 0.103065i
356356 7.29984 + 4.21456i 0.386891 + 0.223371i
357357 27.1592 + 24.8172i 1.43742 + 1.31346i
358358 8.98104 5.18521i 0.474663 0.274047i
359359 23.8304i 1.25772i 0.777517 + 0.628861i 0.216479π0.216479\pi
−0.777517 + 0.628861i 0.783521π0.783521\pi
360360 −0.130656 1.44688i −0.00688617 0.0762573i
361361 8.68609 0.457162
362362 9.38833 5.42035i 0.493440 0.284887i
363363 −1.16053 0.255584i −0.0609119 0.0134147i
364364 17.8544 + 3.65081i 0.935824 + 0.191355i
365365 0.0788187 0.136518i 0.00412556 0.00714568i
366366 −0.373168 + 1.69444i −0.0195058 + 0.0885697i
367367 5.04643 + 8.74067i 0.263421 + 0.456259i 0.967149 0.254211i 0.0818157π-0.0818157\pi
−0.703728 + 0.710470i 0.748482π0.748482\pi
368368 6.27217 0.326959
369369 33.0275 2.98244i 1.71934 0.155260i
370370 1.00933i 0.0524724i
371371 28.1013 16.2243i 1.45895 0.842324i
372372 −8.29027 7.57538i −0.429830 0.392765i
373373 4.27370 7.40227i 0.221284 0.383275i −0.733914 0.679242i 0.762309π-0.762309\pi
0.955198 + 0.295967i 0.0956419π0.0956419\pi
374374 −6.74815 + 11.6881i −0.348938 + 0.604379i
375375 −7.80832 + 2.47394i −0.403220 + 0.127754i
376376 2.64062 + 4.57369i 0.136180 + 0.235870i
377377 15.7081 5.23868i 0.809008 0.269806i
378378 −24.2218 + 10.1520i −1.24584 + 0.522164i
379379 30.7125i 1.57760i −0.614653 0.788798i 0.710704π-0.710704\pi
0.614653 0.788798i 0.289296π-0.289296\pi
380380 0.777601 + 1.34684i 0.0398901 + 0.0690916i
381381 −2.38710 7.53423i −0.122295 0.385990i
382382 −9.74971 5.62900i −0.498839 0.288005i
383383 −2.49892 1.44275i −0.127689 0.0737212i 0.434795 0.900529i 0.356821π-0.356821\pi
−0.562484 + 0.826808i 0.690154π0.690154\pi
384384 −1.27863 1.16837i −0.0652500 0.0596233i
385385 6.80746 3.93029i 0.346940 0.200306i
386386 7.62566 0.388136
387387 −25.7744 11.9313i −1.31019 0.606504i
388388 13.0505i 0.662539i
389389 5.94776 + 10.3018i 0.301564 + 0.522323i 0.976490 0.215561i 0.0691581π-0.0691581\pi
−0.674927 + 0.737885i 0.735825π0.735825\pi
390390 3.00748 0.317351i 0.152290 0.0160697i
391391 −13.1792 + 22.8271i −0.666503 + 1.15442i
392392 −16.0619 9.27337i −0.811250 0.468376i
393393 −4.17714 0.919935i −0.210709 0.0464046i
394394 −12.2585 21.2324i −0.617575 1.06967i
395395 3.79481i 0.190937i
396396 −5.54818 7.87673i −0.278806 0.395821i
397397 23.8021i 1.19459i 0.802020 + 0.597297i 0.203759π0.203759\pi
−0.802020 + 0.597297i 0.796241π0.796241\pi
398398 −11.7182 + 6.76550i −0.587379 + 0.339124i
399399 18.9654 20.7551i 0.949455 1.03906i
400400 −2.38275 + 4.12704i −0.119137 + 0.206352i
401401 −7.79168 4.49853i −0.389098 0.224646i 0.292671 0.956213i 0.405456π-0.405456\pi
−0.681769 + 0.731567i 0.738789π0.738789\pi
402402 0.566009 + 1.78645i 0.0282300 + 0.0891002i
403403 15.5075 17.4933i 0.772483 0.871404i
404404 6.84702 0.340652
405405 −3.32296 + 2.82006i −0.165119 + 0.140130i
406406 −23.2124 −1.15201
407407 −3.34687 5.79695i −0.165898 0.287344i
408408 6.93891 2.19848i 0.343527 0.108841i
409409 −27.8344 16.0702i −1.37632 0.794620i −0.384608 0.923080i 0.625663π-0.625663\pi
−0.991715 + 0.128460i 0.958997π0.958997\pi
410410 4.63579 + 2.67647i 0.228945 + 0.132182i
411411 25.0745 + 22.9122i 1.23683 + 1.13018i
412412 1.77760 + 3.07889i 0.0875761 + 0.151686i
413413 18.3126 0.901103
414414 −10.8357 15.3834i −0.532545 0.756052i
415415 2.84071 0.139445
416416 2.39177 2.69805i 0.117266 0.132283i
417417 0.655287 + 0.144314i 0.0320895 + 0.00706711i
418418 8.93211 + 5.15696i 0.436884 + 0.252235i
419419 −1.68689 + 2.92177i −0.0824098 + 0.142738i −0.904285 0.426930i 0.859595π-0.859595\pi
0.821875 + 0.569668i 0.192928π0.192928\pi
420420 −4.14017 0.911795i −0.202020 0.0444910i
421421 −2.26626 + 1.30842i −0.110451 + 0.0637687i −0.554208 0.832378i 0.686979π-0.686979\pi
0.443757 + 0.896147i 0.353645π0.353645\pi
422422 23.8692i 1.16193i
423423 6.65574 14.3779i 0.323613 0.699078i
424424 6.41990i 0.311778i
425425 −10.0134 17.3437i −0.485721 0.841293i
426426 5.41005 5.92060i 0.262118 0.286854i
427427 4.38478 + 2.53155i 0.212194 + 0.122510i
428428 0.706961 1.22449i 0.0341722 0.0591880i
429429 16.2208 11.7953i 0.783147 0.569482i
430430 −2.29231 3.97040i −0.110545 0.191470i
431431 1.25113i 0.0602647i 0.999546 + 0.0301324i 0.00959288π0.00959288\pi
−0.999546 + 0.0301324i 0.990407π0.990407\pi
432432 −0.656660 + 5.15449i −0.0315936 + 0.247996i
433433 −4.77117 −0.229288 −0.114644 0.993407i 0.536573π-0.536573\pi
−0.114644 + 0.993407i 0.536573π0.536573\pi
434434 −28.3806 + 16.3855i −1.36231 + 0.786530i
435435 −3.67211 + 1.16345i −0.176064 + 0.0557831i
436436 4.30869 + 2.48763i 0.206349 + 0.119136i
437437 17.4446 + 10.0716i 0.834486 + 0.481791i
438438 −0.380335 + 0.416227i −0.0181731 + 0.0198881i
439439 −16.8509 29.1867i −0.804252 1.39300i −0.916795 0.399358i 0.869233π-0.869233\pi
0.112543 0.993647i 0.464100π-0.464100\pi
440440 1.55520i 0.0741413i
441441 5.00405 + 55.4147i 0.238288 + 2.63880i
442442 4.79371 + 14.3739i 0.228014 + 0.683696i
443443 2.68876 + 4.65706i 0.127747 + 0.221264i 0.922803 0.385272i 0.125892π-0.125892\pi
−0.795057 + 0.606535i 0.792559π0.792559\pi
444444 −0.776447 + 3.52560i −0.0368485 + 0.167318i
445445 2.04093 3.53499i 0.0967492 0.167575i
446446 −6.43490 + 11.1456i −0.304701 + 0.527758i
447447 −3.52361 + 15.9996i −0.166661 + 0.756756i
448448 −4.37722 + 2.52719i −0.206804 + 0.119398i
449449 16.7813i 0.791958i −0.918260 0.395979i 0.870405π-0.870405\pi
0.918260 0.395979i 0.129595π-0.129595\pi
450450 14.2386 1.28577i 0.671212 0.0606116i
451451 35.5001 1.67163
452452 −6.54415 11.3348i −0.307811 0.533145i
453453 1.70268 + 1.55585i 0.0799988 + 0.0731002i
454454 −9.02759 + 15.6362i −0.423686 + 0.733845i
455455 1.76793 8.64609i 0.0828817 0.405335i
456456 −1.68009 5.30274i −0.0786773 0.248324i
457457 −20.5067 + 11.8396i −0.959263 + 0.553831i −0.895946 0.444162i 0.853501π-0.853501\pi
−0.0633172 + 0.997993i 0.520168π0.520168\pi
458458 −21.1737 −0.989383
459459 −17.3796 13.2206i −0.811212 0.617086i
460460 3.03733i 0.141616i
461461 −29.8451 + 17.2311i −1.39003 + 0.802533i −0.993318 0.115412i 0.963181π-0.963181\pi
−0.396709 + 0.917944i 0.629848π0.629848\pi
462462 −26.8020 + 8.49179i −1.24694 + 0.395074i
463463 19.4659 + 11.2386i 0.904657 + 0.522304i 0.878708 0.477359i 0.158406π-0.158406\pi
0.0259487 + 0.999663i 0.491739π0.491739\pi
464464 −2.29627 + 3.97725i −0.106602 + 0.184639i
465465 −3.66842 + 4.01461i −0.170119 + 0.186173i
466466 25.1675 14.5305i 1.16586 0.673111i
467467 −4.43632 −0.205288 −0.102644 0.994718i 0.532730π-0.532730\pi
−0.102644 + 0.994718i 0.532730π0.532730\pi
468468 −10.7493 1.20506i −0.496887 0.0557037i
469469 5.46853 0.252513
470470 2.21484 1.27874i 0.102163 0.0589837i
471471 9.88257 + 2.17645i 0.455365 + 0.100285i
472472 1.81156 3.13771i 0.0833836 0.144425i
473473 −26.3312 15.2023i −1.21071 0.699004i
474474 −2.91924 + 13.2553i −0.134085 + 0.608838i
475475 −13.2541 + 7.65226i −0.608140 + 0.351110i
476476 21.2408i 0.973570i
477477 −15.7457 + 11.0909i −0.720948 + 0.507818i
478478 7.26902 0.332477
479479 10.2334 5.90827i 0.467577 0.269956i −0.247648 0.968850i 0.579658π-0.579658\pi
0.715225 + 0.698894i 0.246324π0.246324\pi
480480 −0.565792 + 0.619186i −0.0258247 + 0.0282618i
481481 −7.36265 1.50549i −0.335708 0.0686446i
482482 8.95521 15.5109i 0.407899 0.706501i
483483 −52.3448 + 16.5846i −2.38177 + 0.754626i
484484 0.343044 + 0.594169i 0.0155929 + 0.0270077i
485485 −6.31979 −0.286967
486486 13.7766 7.29425i 0.624918 0.330874i
487487 25.8373i 1.17080i 0.810745 + 0.585400i 0.199062π0.199062\pi
−0.810745 + 0.585400i 0.800938π0.800938\pi
488488 0.867521 0.500864i 0.0392708 0.0226730i
489489 −24.9885 + 7.91721i −1.13002 + 0.358029i
490490 −4.49068 + 7.77809i −0.202868 + 0.351378i
491491 −5.59995 + 9.69940i −0.252722 + 0.437728i −0.964274 0.264906i 0.914659π-0.914659\pi
0.711552 + 0.702633i 0.247993π0.247993\pi
492492 −14.1340 12.9152i −0.637208 0.582260i
493493 −9.64996 16.7142i −0.434612 0.752771i
494494 10.9846 3.66337i 0.494219 0.164823i
495495 −3.81436 + 2.68674i −0.171443 + 0.120760i
496496 6.48369i 0.291126i
497497 −11.7019 20.2683i −0.524903 0.909159i
498498 −9.92265 2.18527i −0.444644 0.0979245i
499499 −13.3884 7.72982i −0.599349 0.346034i 0.169436 0.985541i 0.445805π-0.445805\pi
−0.768786 + 0.639507i 0.779139π0.779139\pi
500500 4.09543 + 2.36450i 0.183153 + 0.105744i
501501 −4.48028 + 20.3435i −0.200164 + 0.908883i
502502 −3.33162 + 1.92351i −0.148697 + 0.0858505i
503503 −6.00330 −0.267674 −0.133837 0.991003i 0.542730π-0.542730\pi
−0.133837 + 0.991003i 0.542730π0.542730\pi
504504 13.7603 + 6.36984i 0.612932 + 0.283735i
505505 3.31571i 0.147547i
506506 −10.0716 17.4446i −0.447738 0.775505i
507507 2.17095 22.4118i 0.0964153 0.995341i
508508 −2.28150 + 3.95167i −0.101225 + 0.175327i
509509 18.6801 + 10.7849i 0.827979 + 0.478034i 0.853160 0.521649i 0.174683π-0.174683\pi
−0.0251810 + 0.999683i 0.508016π0.508016\pi
510510 −1.06463 3.36021i −0.0471425 0.148793i
511511 0.822663 + 1.42489i 0.0363925 + 0.0630336i
512512 1.00000i 0.0441942i
513513 −10.1032 + 13.2816i −0.446069 + 0.586396i
514514 14.7675i 0.651367i
515515 1.49097 0.860814i 0.0657001 0.0379320i
516516 4.95277 + 15.6321i 0.218034 + 0.688164i
517517 8.48043 14.6885i 0.372969 0.646001i
518518 9.12337 + 5.26738i 0.400858 + 0.231435i
519519 10.3502 11.3269i 0.454323 0.497198i
520520 −1.30655 1.15823i −0.0572958 0.0507916i
521521 24.0543 1.05384 0.526918 0.849916i 0.323347π-0.323347\pi
0.526918 + 0.849916i 0.323347π0.323347\pi
522522 13.7218 1.23910i 0.600586 0.0542340i
523523 −10.8449 −0.474215 −0.237107 0.971483i 0.576199π-0.576199\pi
−0.237107 + 0.971483i 0.576199π0.576199\pi
524524 1.23473 + 2.13862i 0.0539395 + 0.0934260i
525525 8.97285 40.7429i 0.391607 1.77817i
526526 −7.58853 4.38124i −0.330876 0.191031i
527527 −23.5970 13.6237i −1.02790 0.593458i
528528 −1.19637 + 5.43235i −0.0520654 + 0.236413i
529529 −8.17003 14.1509i −0.355219 0.615257i
530530 −3.10888 −0.135041
531531 −10.8253 + 0.977543i −0.469777 + 0.0424218i
532532 −16.2323 −0.703758
533533 26.4385 29.8241i 1.14518 1.29183i
534534 −9.84836 + 10.7778i −0.426180 + 0.466399i
535535 −0.592967 0.342350i −0.0256362 0.0148011i
536536 0.540970 0.936987i 0.0233663 0.0404717i
537537 5.42520 + 17.1232i 0.234115 + 0.738920i
538538 −7.71400 + 4.45368i −0.332574 + 0.192012i
539539 59.5633i 2.56558i
540540 2.49609 + 0.317991i 0.107415 + 0.0136842i
541541 12.2998i 0.528808i −0.964412 0.264404i 0.914825π-0.914825\pi
0.964412 0.264404i 0.0851753π-0.0851753\pi
542542 −1.79275 3.10514i −0.0770054 0.133377i
543543 5.67123 + 17.8997i 0.243376 + 0.768150i
544544 −3.63943 2.10123i −0.156039 0.0900894i
545545 1.20465 2.08651i 0.0516014 0.0893763i
546546 −12.8266 + 28.8410i −0.548928 + 1.23428i
547547 10.3452 + 17.9183i 0.442327 + 0.766133i 0.997862 0.0653602i 0.0208196π-0.0208196\pi
−0.555534 + 0.831493i 0.687486π0.687486\pi
548548 19.6104i 0.837714i
549549 −2.72715 1.26244i −0.116392 0.0538795i
550550 15.3045 0.652587
551551 −12.7731 + 7.37453i −0.544151 + 0.314165i
552552 −2.33653 + 10.6095i −0.0994495 + 0.451569i
553553 34.3015 + 19.8040i 1.45865 + 0.842151i
554554 12.8859 + 7.43966i 0.547468 + 0.316081i
555555 1.70729 + 0.375999i 0.0724706 + 0.0159603i
556556 −0.193698 0.335495i −0.00821463 0.0142282i
557557 14.2838i 0.605226i −0.953114 0.302613i 0.902141π-0.902141\pi
0.953114 0.302613i 0.0978589π-0.0978589\pi
558558 15.9022 11.2011i 0.673193 0.474181i
559559 −32.3817 + 10.7993i −1.36960 + 0.456764i
560560 1.22381 + 2.11969i 0.0517152 + 0.0895734i
561561 −17.2568 15.7687i −0.728584 0.665756i
562562 8.25582 14.2995i 0.348251 0.603188i
563563 17.9673 31.1203i 0.757231 1.31156i −0.187026 0.982355i 0.559885π-0.559885\pi
0.944257 0.329208i 0.106782π-0.106782\pi
564564 −8.72016 + 2.76284i −0.367185 + 0.116337i
565565 −5.48895 + 3.16905i −0.230922 + 0.133323i
566566 0.535666i 0.0225157i
567567 −8.14910 44.7535i −0.342230 1.87947i
568568 −4.63041 −0.194288
569569 18.5315 + 32.0976i 0.776882 + 1.34560i 0.933730 + 0.357977i 0.116533π0.116533\pi
−0.156848 + 0.987623i 0.550133π0.550133\pi
570570 −2.56788 + 0.813592i −0.107557 + 0.0340776i
571571 23.1732 40.1372i 0.969769 1.67969i 0.273551 0.961857i 0.411802π-0.411802\pi
0.696217 0.717831i 0.254865π-0.254865\pi
572572 −11.3446 2.31971i −0.474341 0.0969919i
573573 13.1535 14.3949i 0.549497 0.601354i
574574 −48.3856 + 27.9354i −2.01958 + 1.16600i
575575 29.8900 1.24650
576576 2.45264 1.72758i 0.102193 0.0719826i
577577 31.4447i 1.30906i −0.756036 0.654530i 0.772866π-0.772866\pi
0.756036 0.654530i 0.227134π-0.227134\pi
578578 0.572112 0.330309i 0.0237967 0.0137390i
579579 −2.84074 + 12.8989i −0.118057 + 0.536061i
580580 1.92601 + 1.11198i 0.0799731 + 0.0461725i
581581 −14.8248 + 25.6773i −0.615037 + 1.06527i
582582 22.0751 + 4.86163i 0.915044 + 0.201521i
583583 −17.8555 + 10.3088i −0.739497 + 0.426949i
584584 0.325525 0.0134703
585585 −0.583555 + 5.20542i −0.0241270 + 0.215218i
586586 −19.5896 −0.809241
587587 27.0638 15.6253i 1.11704 0.644924i 0.176397 0.984319i 0.443556π-0.443556\pi
0.940644 + 0.339395i 0.110222π0.110222\pi
588588 21.6695 23.7145i 0.893635 0.977968i
589589 −10.4113 + 18.0329i −0.428989 + 0.743031i
590590 −1.51945 0.877257i −0.0625549 0.0361161i
591591 40.4815 12.8259i 1.66519 0.527587i
592592 1.80504 1.04214i 0.0741868 0.0428318i
593593 26.3978i 1.08403i 0.840370 + 0.542013i 0.182338π0.182338\pi
−0.840370 + 0.542013i 0.817662π0.817662\pi
594594 15.3905 6.45055i 0.631478 0.264669i
595595 −10.2860 −0.421684
596596 8.19151 4.72937i 0.335537 0.193723i
597597 −7.07864 22.3418i −0.289709 0.914389i
598598 −22.1562 4.53043i −0.906033 0.185263i
599599 3.40524 5.89806i 0.139135 0.240988i −0.788035 0.615631i 0.788901π-0.788901\pi
0.927169 + 0.374643i 0.122235π0.122235\pi
600600 −6.09332 5.56788i −0.248759 0.227308i
601601 −4.82516 8.35742i −0.196822 0.340906i 0.750674 0.660673i 0.229729π-0.229729\pi
−0.947496 + 0.319766i 0.896396π0.896396\pi
602602 47.8516 1.95028
603603 −3.23267 + 0.291916i −0.131644 + 0.0118877i
604604 1.33164i 0.0541836i
605605 0.287730 0.166121i 0.0116979 0.00675377i
606606 −2.55068 + 11.5818i −0.103614 + 0.470480i
607607 −13.7896 + 23.8842i −0.559702 + 0.969432i 0.437819 + 0.899063i 0.355751π0.355751\pi
−0.997521 + 0.0703688i 0.977582π0.977582\pi
608608 −1.60576 + 2.78126i −0.0651223 + 0.112795i
609609 8.64718 39.2642i 0.350402 1.59106i
610610 −0.242546 0.420102i −0.00982041 0.0170094i
611611 −6.02428 18.0637i −0.243716 0.730779i
612612 1.13385 + 12.5563i 0.0458333 + 0.507557i
613613 16.0314i 0.647502i 0.946142 + 0.323751i 0.104944π0.104944\pi
−0.946142 + 0.323751i 0.895056π0.895056\pi
614614 0.630320 + 1.09175i 0.0254377 + 0.0440593i
615615 −6.25424 + 6.84446i −0.252195 + 0.275995i
616616 14.0576 + 8.11614i 0.566395 + 0.327009i
617617 11.4362 + 6.60269i 0.460404 + 0.265814i 0.712214 0.701962i 0.247693π-0.247693\pi
−0.251810 + 0.967777i 0.581026π0.581026\pi
618618 −5.87020 + 1.85988i −0.236134 + 0.0748152i
619619 1.53649 0.887091i 0.0617566 0.0356552i −0.468804 0.883302i 0.655315π-0.655315\pi
0.530560 + 0.847647i 0.321982π0.321982\pi
620620 3.13977 0.126096
621621 30.0578 12.5980i 1.20618 0.505542i
622622 17.5844i 0.705072i
623623 21.3020 + 36.8961i 0.853446 + 1.47821i
624624 3.67280 + 5.05080i 0.147030 + 0.202194i
625625 −10.7687 + 18.6520i −0.430749 + 0.746079i
626626 −0.177891 0.102706i −0.00710997 0.00410494i
627627 −12.0505 + 13.1877i −0.481251 + 0.526667i
628628 −2.92122 5.05970i −0.116569 0.201904i
629629 8.75911i 0.349249i
630630 3.08463 6.66351i 0.122895 0.265480i
631631 30.2211i 1.20308i 0.798841 + 0.601542i 0.205447π0.205447\pi
−0.798841 + 0.601542i 0.794553π0.794553\pi
632632 6.78649 3.91818i 0.269952 0.155857i
633633 −40.3751 8.89184i −1.60476 0.353419i
634634 −9.04030 + 15.6583i −0.359036 + 0.621869i
635635 1.91362 + 1.10483i 0.0759397 + 0.0438438i
636636 10.8594 + 2.39157i 0.430602 + 0.0948319i
637637 50.0399 + 44.3594i 1.98265 + 1.75759i
638638 14.7491 0.583921
639639 7.99942 + 11.3568i 0.316452 + 0.449266i
640640 0.484256 0.0191419
641641 0.301673 + 0.522512i 0.0119154 + 0.0206380i 0.871922 0.489646i 0.162874π-0.162874\pi
−0.860006 + 0.510284i 0.829540π0.829540\pi
642642 1.80789 + 1.65199i 0.0713516 + 0.0651988i
643643 27.0250 + 15.6029i 1.06576 + 0.615317i 0.927020 0.375012i 0.122361π-0.122361\pi
0.138740 + 0.990329i 0.455695π0.455695\pi
644644 27.4546 + 15.8509i 1.08186 + 0.624615i
645645 7.56993 2.39841i 0.298066 0.0944373i
646646 −6.74815 11.6881i −0.265502 0.459864i
647647 −48.8937 −1.92221 −0.961105 0.276182i 0.910931π-0.910931\pi
−0.961105 + 0.276182i 0.910931π0.910931\pi
648648 −8.47428 3.03092i −0.332901 0.119066i
649649 −11.6357 −0.456742
650650 11.3980 12.8575i 0.447064 0.504314i
651651 −17.1439 54.1102i −0.671923 2.12074i
652652 13.1064 + 7.56698i 0.513286 + 0.296346i
653653 −19.1944 + 33.2457i −0.751135 + 1.30100i 0.196138 + 0.980576i 0.437160π0.437160\pi
−0.947273 + 0.320427i 0.896173π0.896173\pi
654654 −5.81295 + 6.36152i −0.227304 + 0.248755i
655655 1.03564 0.597926i 0.0404658 0.0233629i
656656 11.0540i 0.431585i
657657 −0.562371 0.798397i −0.0219402 0.0311484i
658658 26.6934i 1.04062i
659659 20.9568 + 36.2983i 0.816362 + 1.41398i 0.908346 + 0.418220i 0.137346π0.137346\pi
−0.0919840 + 0.995760i 0.529321π0.529321\pi
660660 2.63065 + 0.579350i 0.102398 + 0.0225512i
661661 10.5208 + 6.07418i 0.409211 + 0.236258i 0.690451 0.723379i 0.257412π-0.257412\pi
−0.281240 + 0.959638i 0.590746π0.590746\pi
662662 2.09751 3.63300i 0.0815221 0.141200i
663663 −26.0994 + 2.75402i −1.01362 + 0.106957i
664664 2.93306 + 5.08022i 0.113825 + 0.197151i
665665 7.86058i 0.304820i
666666 −5.67437 2.62674i −0.219877 0.101784i
667667 28.8051 1.11534
668668 10.4155 6.01341i 0.402989 0.232666i
669669 −16.4558 15.0367i −0.636216 0.581353i
670670 −0.453742 0.261968i −0.0175296 0.0101207i
671671 −2.78607 1.60854i −0.107555 0.0620969i
672672 −2.64416 8.34557i −0.102001 0.321938i
673673 −18.3252 31.7403i −0.706386 1.22350i −0.966189 0.257835i 0.916991π-0.916991\pi
0.259803 0.965662i 0.416342π-0.416342\pi
674674 13.7608i 0.530047i
675675 −3.12931 + 24.5637i −0.120447 + 0.945458i
676676 −10.3976 + 7.80315i −0.399909 + 0.300121i
677677 −19.2964 33.4223i −0.741620 1.28452i −0.951757 0.306851i 0.900725π-0.900725\pi
0.210138 0.977672i 0.432609π-0.432609\pi
678678 21.6109 6.84705i 0.829960 0.262959i
679679 32.9811 57.1249i 1.26570 2.19225i
680680 −1.01753 + 1.76242i −0.0390206 + 0.0675856i
681681 −23.0860 21.0952i −0.884656 0.808369i
682682 18.0329 10.4113i 0.690514 0.398669i
683683 31.4038i 1.20163i −0.799387 0.600816i 0.794842π-0.794842\pi
0.799387 0.600816i 0.205158π-0.205158\pi
684684 9.59554 0.866495i 0.366895 0.0331313i
685685 −9.49644 −0.362840
686686 −29.1808 50.5426i −1.11413 1.92972i
687687 7.88772 35.8157i 0.300935 1.36645i
688688 4.73367 8.19896i 0.180470 0.312583i
689689 −4.63714 + 22.6780i −0.176661 + 0.863965i
690690 5.13770 + 1.13148i 0.195589 + 0.0430747i
691691 −16.6786 + 9.62941i −0.634485 + 0.366320i −0.782487 0.622667i 0.786049π-0.786049\pi
0.148002 + 0.988987i 0.452716π0.452716\pi
692692 −8.85863 −0.336755
693693 −4.37959 48.4995i −0.166367 1.84234i
694694 23.8702i 0.906100i
695695 −0.162465 + 0.0937995i −0.00616266 + 0.00355802i
696696 −5.87217 5.36580i −0.222584 0.203390i
697697 −40.2301 23.2269i −1.52383 0.879781i
698698 −9.67391 + 16.7557i −0.366163 + 0.634213i
699699 15.2030 + 47.9842i 0.575031 + 1.81493i
700700 −20.8596 + 12.0433i −0.788420 + 0.455194i
701701 −26.7781 −1.01139 −0.505697 0.862711i 0.668765π-0.668765\pi
−0.505697 + 0.862711i 0.668765π0.668765\pi
702702 6.04275 17.7337i 0.228069 0.669316i
703703 6.69374 0.252459
704704 2.78126 1.60576i 0.104823 0.0605195i
705705 1.33792 + 4.22279i 0.0503891 + 0.159039i
706706 −13.8914 + 24.0606i −0.522810 + 0.905533i
707707 29.9709 + 17.3037i 1.12717 + 0.650773i
708708 4.63263 + 4.23315i 0.174105 + 0.159091i
709709 −40.2439 + 23.2348i −1.51139 + 0.872602i −0.511479 + 0.859296i 0.670902π0.670902\pi
−0.999911 + 0.0133058i 0.995764π0.995764\pi
710710 2.24230i 0.0841522i
711711 −21.3341 9.87587i −0.800092 0.370374i
712712 8.42912 0.315895
713713 35.2185 20.3334i 1.31894 0.761492i
714714 35.9291 + 7.91271i 1.34461 + 0.296126i
715715 −1.12333 + 5.49369i −0.0420103 + 0.205452i
716716 5.18521 8.98104i 0.193780 0.335637i
717717 −2.70789 + 12.2957i −0.101128 + 0.459190i
718718 11.9152 + 20.6378i 0.444672 + 0.770195i
719719 −4.81378 −0.179524 −0.0897619 0.995963i 0.528611π-0.528611\pi
−0.0897619 + 0.995963i 0.528611π0.528611\pi
720720 −0.836592 1.18771i −0.0311779 0.0442632i
721721 17.9693i 0.669213i
722722 7.52237 4.34304i 0.279954 0.161631i
723723 22.9009 + 20.9261i 0.851693 + 0.778249i
724724 5.42035 9.38833i 0.201446 0.348914i
725725 −10.9429 + 18.9536i −0.406407 + 0.703918i
726726 −1.13284 + 0.358921i −0.0420436 + 0.0133208i
727727 −6.35915 11.0144i −0.235848 0.408501i 0.723671 0.690145i 0.242453π-0.242453\pi
−0.959519 + 0.281645i 0.909120π0.909120\pi
728728 17.2878 5.76550i 0.640727 0.213684i
729729 7.20624 + 26.0206i 0.266898 + 0.963725i
730730 0.157637i 0.00583442i
731731 19.8930 + 34.4558i 0.735771 + 1.27439i
732732 0.524046 + 1.65401i 0.0193693 + 0.0611340i
733733 3.68483 + 2.12744i 0.136102 + 0.0785787i 0.566505 0.824058i 0.308295π-0.308295\pi
−0.430403 + 0.902637i 0.641628π0.641628\pi
734734 8.74067 + 5.04643i 0.322624 + 0.186267i
735735 −11.4839 10.4936i −0.423589 0.387062i
736736 5.43186 3.13608i 0.200221 0.115598i
737737 −3.47468 −0.127991
738738 27.1114 19.0966i 0.997986 0.702956i
739739 9.71484i 0.357366i −0.983907 0.178683i 0.942816π-0.942816\pi
0.983907 0.178683i 0.0571837π-0.0571837\pi
740740 −0.504664 0.874103i −0.0185518 0.0321327i
741741 2.10463 + 19.9453i 0.0773156 + 0.732707i
742742 16.2243 28.1013i 0.595613 1.03163i
743743 −10.6739 6.16261i −0.391589 0.226084i 0.291259 0.956644i 0.405926π-0.405926\pi
−0.682848 + 0.730560i 0.739259π0.739259\pi
744744 −10.9673 2.41533i −0.402080 0.0885504i
745745 −2.29023 3.96679i −0.0839074 0.145332i
746746 8.54741i 0.312943i
747747 7.39285 15.9702i 0.270490 0.584321i
748748 13.4963i 0.493474i
749749 6.18904 3.57325i 0.226143 0.130564i
750750 −5.52524 + 6.04666i −0.201753 + 0.220793i
751751 1.43490 2.48532i 0.0523603 0.0906908i −0.838657 0.544660i 0.816659π-0.816659\pi
0.891018 + 0.453969i 0.149992π0.149992\pi
752752 4.57369 + 2.64062i 0.166785 + 0.0962935i
753753 −2.01254 6.35204i −0.0733410 0.231481i
754754 10.9843 12.3909i 0.400024 0.451249i
755755 −0.644854 −0.0234686
756756 −15.9007 + 20.9028i −0.578304 + 0.760229i
757757 33.1438 1.20463 0.602316 0.798258i 0.294245π-0.294245\pi
0.602316 + 0.798258i 0.294245π0.294245\pi
758758 −15.3563 26.5978i −0.557764 0.966076i
759759 33.2597 10.5378i 1.20725 0.382497i
760760 1.34684 + 0.777601i 0.0488552 + 0.0282065i
761761 37.0264 + 21.3772i 1.34221 + 0.774923i 0.987131 0.159915i 0.0511220π-0.0511220\pi
0.355075 + 0.934838i 0.384455π0.384455\pi
762762 −5.83440 5.33128i −0.211358 0.193132i
763763 12.5734 + 21.7778i 0.455188 + 0.788408i
764764 −11.2580 −0.407300
765765 6.08045 0.549076i 0.219839 0.0198519i
766766 −2.88551 −0.104258
767767 −8.66563 + 9.77532i −0.312898 + 0.352966i
768768 −1.69152 0.372524i −0.0610373 0.0134423i
769769 41.6797 + 24.0638i 1.50301 + 0.867762i 0.999994 + 0.00348401i 0.00110900π0.00110900\pi
0.503014 + 0.864278i 0.332224π0.332224\pi
770770 3.93029 6.80746i 0.141638 0.245324i
771771 24.9795 + 5.50125i 0.899614 + 0.198123i
772772 6.60401 3.81283i 0.237684 0.137227i
773773 21.3661i 0.768484i −0.923232 0.384242i 0.874463π-0.874463\pi
0.923232 0.384242i 0.125537π-0.125537\pi
774774 −28.2869 + 2.55436i −1.01675 + 0.0918147i
775775 30.8980i 1.10989i
776776 −6.52525 11.3021i −0.234243 0.405721i
777777 −12.3085 + 13.4701i −0.441566 + 0.483237i
778778 10.3018 + 5.94776i 0.369338 + 0.213238i
779779 −17.7501 + 30.7440i −0.635962 + 1.10152i
780780 2.44588 1.77857i 0.0875765 0.0636832i
781781 7.43535 + 12.8784i 0.266058 + 0.460826i
782782 26.3585i 0.942578i
783783 −3.01573 + 23.6722i −0.107774 + 0.845975i
784784 −18.5467 −0.662383
785785 −2.45019 + 1.41462i −0.0874510 + 0.0504898i
786786 −4.07747 + 1.29188i −0.145439 + 0.0460799i
787787 −29.5928 17.0854i −1.05487 0.609029i −0.130860 0.991401i 0.541774π-0.541774\pi
−0.924008 + 0.382372i 0.875107π0.875107\pi
788788 −21.2324 12.2585i −0.756372 0.436691i
789789 10.2379 11.2040i 0.364477 0.398873i
790790 −1.89740 3.28640i −0.0675066 0.116925i
791791 66.1533i 2.35214i
792792 −8.74323 4.04736i −0.310677 0.143817i
793793 −3.42626 + 1.14266i −0.121670 + 0.0405772i
794794 11.9011 + 20.6132i 0.422353 + 0.731537i
795795 1.15813 5.25871i 0.0410747 0.186507i
796796 −6.76550 + 11.7182i −0.239797 + 0.415340i
797797 −6.26917 + 10.8585i −0.222066 + 0.384629i −0.955435 0.295201i 0.904613π-0.904613\pi
0.733369 + 0.679830i 0.237947π0.237947\pi
798798 6.04691 27.4571i 0.214058 0.971973i
799799 −19.2207 + 11.0971i −0.679980 + 0.392587i
800800 4.76550i 0.168486i
801801 −14.5620 20.6736i −0.514523 0.730467i
802802 −8.99705 −0.317697
803803 −0.522716 0.905371i −0.0184463 0.0319498i
804804 1.38340 + 1.26411i 0.0487889 + 0.0445817i
805805 7.67592 13.2951i 0.270540 0.468590i
806806 4.68322 22.9034i 0.164959 0.806737i
807807 −4.65982 14.7075i −0.164033 0.517727i
808808 5.92969 3.42351i 0.208606 0.120439i
809809 −23.7653 −0.835543 −0.417772 0.908552i 0.637189π-0.637189\pi
−0.417772 + 0.908552i 0.637189π0.637189\pi
810810 −1.46774 + 4.10372i −0.0515712 + 0.144190i
811811 12.1844i 0.427853i −0.976850 0.213926i 0.931375π-0.931375\pi
0.976850 0.213926i 0.0686253π-0.0686253\pi
812812 −20.1025 + 11.6062i −0.705461 + 0.407298i
813813 5.92024 1.87573i 0.207632 0.0657848i
814814 −5.79695 3.34687i −0.203183 0.117308i
815815 3.66435 6.34685i 0.128357 0.222320i
816816 4.91003 5.37340i 0.171886 0.188107i
817817 26.3312 15.2023i 0.921212 0.531862i
818818 −32.1404 −1.12376
819819 −44.0067 32.4403i −1.53772 1.13356i
820820 5.35295 0.186933
821821 −14.8532 + 8.57549i −0.518379 + 0.299287i −0.736271 0.676686i 0.763415π-0.763415\pi
0.217892 + 0.975973i 0.430082π0.430082\pi
822822 33.1713 + 7.30534i 1.15698 + 0.254803i
823823 −19.0983 + 33.0792i −0.665725 + 1.15307i 0.313363 + 0.949633i 0.398544π0.398544\pi
−0.979088 + 0.203436i 0.934789π0.934789\pi
824824 3.07889 + 1.77760i 0.107258 + 0.0619257i
825825 −5.70131 + 25.8878i −0.198494 + 0.901299i
826826 15.8592 9.15629i 0.551810 0.318588i
827827 16.3182i 0.567441i −0.958907 0.283721i 0.908431π-0.908431\pi
0.958907 0.283721i 0.0915688π-0.0915688\pi
828828 −17.0757 7.90457i −0.593420 0.274703i
829829 13.6052 0.472529 0.236265 0.971689i 0.424077π-0.424077\pi
0.236265 + 0.971689i 0.424077π0.424077\pi
830830 2.46012 1.42035i 0.0853922 0.0493012i
831831 −17.3846 + 19.0252i −0.603065 + 0.659977i
832832 0.722307 3.53246i 0.0250415 0.122466i
833833 38.9709 67.4996i 1.35026 2.33872i
834834 0.639652 0.202663i 0.0221493 0.00701766i
835835 −2.91203 5.04378i −0.100775 0.174547i
836836 10.3139 0.356714
837837 13.0229 + 31.0715i 0.450137 + 1.07399i
838838 3.37377i 0.116545i
839839 −43.9792 + 25.3914i −1.51833 + 0.876609i −0.518563 + 0.855039i 0.673533π0.673533\pi
−0.999767 + 0.0215696i 0.993134π0.993134\pi
840840 −4.04139 + 1.28045i −0.139441 + 0.0441797i
841841 3.95431 6.84907i 0.136356 0.236175i
842842 −1.30842 + 2.26626i −0.0450913 + 0.0781004i
843843 21.1123 + 19.2918i 0.727148 + 0.664443i
844844 11.9346 + 20.6713i 0.410805 + 0.711535i
845845 3.77872 + 5.03512i 0.129992 + 0.173213i
846846 −1.42492 15.7795i −0.0489897 0.542511i
847847 3.46774i 0.119153i
848848 −3.20995 5.55980i −0.110230 0.190924i
849849 0.906087 + 0.199548i 0.0310968 + 0.00684848i
850850 −17.3437 10.0134i −0.594884 0.343456i
851851 −11.3215 6.53649i −0.388097 0.224068i
852852 1.72494 7.83242i 0.0590955 0.268334i
853853 31.1360 17.9764i 1.06608 0.615499i 0.138969 0.990297i 0.455621π-0.455621\pi
0.927106 + 0.374798i 0.122288π0.122288\pi
854854 5.06311 0.173256
855855 −0.419605 4.64670i −0.0143502 0.158914i
856856 1.41392i 0.0483268i
857857 2.28591 + 3.95932i 0.0780853 + 0.135248i 0.902424 0.430849i 0.141786π-0.141786\pi
−0.824339 + 0.566097i 0.808453π0.808453\pi
858858 8.14996 18.3254i 0.278235 0.625619i
859859 −5.82450 + 10.0883i −0.198729 + 0.344209i −0.948117 0.317923i 0.897015π-0.897015\pi
0.749387 + 0.662132i 0.230348π0.230348\pi
860860 −3.97040 2.29231i −0.135389 0.0781671i
861861 −29.2284 92.2517i −0.996103 3.14393i
862862 0.625564 + 1.08351i 0.0213068 + 0.0369044i
863863 26.2523i 0.893640i 0.894624 + 0.446820i 0.147444π0.147444\pi
−0.894624 + 0.446820i 0.852556π0.852556\pi
864864 2.00856 + 4.79225i 0.0683327 + 0.163036i
865865 4.28985i 0.145859i
866866 −4.13195 + 2.38558i −0.140409 + 0.0810655i
867867 0.345597 + 1.09078i 0.0117371 + 0.0370450i
868868 −16.3855 + 28.3806i −0.556161 + 0.963299i
869869 −21.7950 12.5834i −0.739345 0.426861i
870870 −2.59842 + 2.84363i −0.0880946 + 0.0964082i
871871 −2.58775 + 2.91912i −0.0876825 + 0.0989107i
872872 4.97525 0.168483
873873 −16.4470 + 35.5294i −0.556648 + 1.20249i
874874 20.1432 0.681355
875875 11.9511 + 20.6999i 0.404020 + 0.699783i
876876 −0.121266 + 0.550630i −0.00409719 + 0.0186041i
877877 −40.5146 23.3911i −1.36808 0.789862i −0.377398 0.926051i 0.623181π-0.623181\pi
−0.990683 + 0.136189i 0.956515π0.956515\pi
878878 −29.1867 16.8509i −0.985003 0.568692i
879879 7.29762 33.1362i 0.246142 1.11766i
880880 −0.777601 1.34684i −0.0262129 0.0454021i
881881 52.3698 1.76438 0.882192 0.470889i 0.156067π-0.156067\pi
0.882192 + 0.470889i 0.156067π0.156067\pi
882882 32.0410 + 45.4885i 1.07888 + 1.53168i
883883 −28.7233 −0.966617 −0.483309 0.875450i 0.660565π-0.660565\pi
−0.483309 + 0.875450i 0.660565π0.660565\pi
884884 11.3384 + 10.0513i 0.381352 + 0.338061i
885885 2.04993 2.24338i 0.0689075 0.0754104i
886886 4.65706 + 2.68876i 0.156457 + 0.0903305i
887887 −6.01188 + 10.4129i −0.201859 + 0.349631i −0.949128 0.314892i 0.898032π-0.898032\pi
0.747268 + 0.664523i 0.231365π0.231365\pi
888888 1.09038 + 3.44148i 0.0365907 + 0.115489i
889889 −19.9732 + 11.5316i −0.669881 + 0.386756i
890890 4.08185i 0.136824i
891891 5.17790 + 28.4362i 0.173466 + 0.952648i
892892 12.8698i 0.430913i
893893 8.48043 + 14.6885i 0.283787 + 0.491533i
894894 4.94827 + 15.6179i 0.165495 + 0.522340i
895895 −4.34912 2.51097i −0.145375 0.0839324i
896896 −2.52719 + 4.37722i −0.0844274 + 0.146233i
897897 15.9170 35.7898i 0.531453 1.19499i
898898 −8.39064 14.5330i −0.279999 0.484973i
899899 29.7766i 0.993105i
900900 11.6881 8.23278i 0.389602 0.274426i
901901 26.9793 0.898812
902902 30.7440 17.7501i 1.02366 0.591012i
903903 −17.8259 + 80.9417i −0.593207 + 2.69357i
904904 −11.3348 6.54415i −0.376990 0.217655i
905905 −4.54635 2.62484i −0.151126 0.0872526i
906906 2.25249 + 0.496067i 0.0748339 + 0.0164807i
907907 −13.8974 24.0710i −0.461456 0.799265i 0.537578 0.843214i 0.319339π-0.319339\pi
−0.999034 + 0.0439492i 0.986006π0.986006\pi
908908 18.0552i 0.599182i
909909 −18.6407 8.62903i −0.618272 0.286207i
910910 −2.79198 8.37170i −0.0925531 0.277519i
911911 10.3296 + 17.8914i 0.342235 + 0.592769i 0.984847 0.173423i 0.0554827π-0.0554827\pi
−0.642612 + 0.766191i 0.722149π0.722149\pi
912912 −4.10637 3.75226i −0.135975 0.124250i
913913 9.41962 16.3153i 0.311744 0.539956i
914914 −11.8396 + 20.5067i −0.391618 + 0.678302i
915915 0.800964 0.253772i 0.0264791 0.00838946i
916916 −18.3370 + 10.5869i −0.605871 + 0.349800i
917917 12.4816i 0.412179i
918918 −21.6615 2.75958i −0.714937 0.0910798i
919919 56.3658 1.85933 0.929667 0.368400i 0.120094π-0.120094\pi
0.929667 + 0.368400i 0.120094π0.120094\pi
920920 −1.51867 2.63041i −0.0500690 0.0867220i
921921 −2.08152 + 0.659495i −0.0685883 + 0.0217311i
922922 −17.2311 + 29.8451i −0.567476 + 0.982898i
923923 16.3567 + 3.34458i 0.538389 + 0.110088i
924924 −18.9654 + 20.7551i −0.623914 + 0.682794i
925925 8.60193 4.96633i 0.282830 0.163292i
926926 22.4773 0.738649
927927 −0.959221 10.6224i −0.0315049 0.348885i
928928 4.59254i 0.150757i
929929 −1.75111 + 1.01100i −0.0574520 + 0.0331699i −0.528451 0.848964i 0.677227π-0.677227\pi
0.470999 + 0.882134i 0.343894π0.343894\pi
930930 −1.16964 + 5.31097i −0.0383540 + 0.174153i
931931 −51.5834 29.7817i −1.69058 0.976055i
932932 14.5305 25.1675i 0.475962 0.824390i
933933 29.7443 + 6.55063i 0.973786 + 0.214458i
934934 −3.84196 + 2.21816i −0.125713 + 0.0725804i
935935 6.53566 0.213739
936936 −9.91171 + 4.33105i −0.323974 + 0.141565i
937937 −15.3243 −0.500622 −0.250311 0.968166i 0.580533π-0.580533\pi
−0.250311 + 0.968166i 0.580533π0.580533\pi
938938 4.73589 2.73427i 0.154632 0.0892770i
939939 0.239997 0.262646i 0.00783200 0.00857112i
940940 1.27874 2.21484i 0.0417078 0.0722400i
941941 −35.8714 20.7104i −1.16938 0.675139i −0.215842 0.976428i 0.569250π-0.569250\pi
−0.953533 + 0.301289i 0.902583π0.902583\pi
942942 9.64678 3.05643i 0.314309 0.0995837i
943943 60.0435 34.6661i 1.95529 1.12888i
944944 3.62311i 0.117922i
945945 10.1223 + 7.70002i 0.329279 + 0.250482i
946946 −30.4047 −0.988541
947947 −49.2660 + 28.4437i −1.60093 + 0.924297i −0.609628 + 0.792687i 0.708681π0.708681\pi
−0.991302 + 0.131610i 0.957985π0.957985\pi
948948 4.09954 + 12.9391i 0.133147 + 0.420242i
949949 −1.14990 0.235129i −0.0373274 0.00763261i
950950 −7.65226 + 13.2541i −0.248272 + 0.430020i
951951 −23.1185 21.1249i −0.749667 0.685021i
952952 −10.6204 18.3951i −0.344209 0.596187i
953953 −40.5931 −1.31494 −0.657470 0.753481i 0.728373π-0.728373\pi
−0.657470 + 0.753481i 0.728373π0.728373\pi
954954 −8.09075 + 17.4779i −0.261948 + 0.565867i
955955 5.45175i 0.176415i
956956 6.29516 3.63451i 0.203600 0.117548i
957957 −5.49438 + 24.9483i −0.177608 + 0.806463i
958958 5.90827 10.2334i 0.190888 0.330627i
959959 49.5591 85.8389i 1.60035 2.77188i
960960 −0.180397 + 0.819127i −0.00582229 + 0.0264372i
961961 5.51914 + 9.55944i 0.178037 + 0.308369i
962962 −7.12899 + 2.37753i −0.229848 + 0.0766547i
963963 −3.46785 + 2.44266i −0.111750 + 0.0787138i
964964 17.9104i 0.576856i
965965 −1.84638 3.19803i −0.0594372 0.102948i
966966 −37.0396 + 40.5351i −1.19173 + 1.30420i
967967 43.2958 + 24.9968i 1.39230 + 0.803844i 0.993569 0.113225i 0.0361182π-0.0361182\pi
0.398729 + 0.917069i 0.369452π0.369452\pi
968968 0.594169 + 0.343044i 0.0190973 + 0.0110258i
969969 22.2845 7.06049i 0.715882 0.226816i
970970 −5.47310 + 3.15989i −0.175730 + 0.101458i
971971 −31.1467 −0.999546 −0.499773 0.866156i 0.666583π-0.666583\pi
−0.499773 + 0.866156i 0.666583π0.666583\pi
972972 8.28373 13.2053i 0.265701 0.423560i
973973 1.95805i 0.0627721i
974974 12.9186 + 22.3758i 0.413940 + 0.716965i
975975 17.5027 + 24.0696i 0.560535 + 0.770843i
976976 0.500864 0.867521i 0.0160323 0.0277687i
977977 −5.97565 3.45004i −0.191178 0.110377i 0.401356 0.915922i 0.368539π-0.368539\pi
−0.592534 + 0.805546i 0.701872π0.701872\pi
978978 −17.6821 + 19.3508i −0.565411 + 0.618770i
979979 −13.5352 23.4436i −0.432586 0.749262i
980980 8.98136i 0.286899i
981981 −8.59515 12.2025i −0.274422 0.389596i
982982 11.1999i 0.357403i
983983 −45.4067 + 26.2156i −1.44825 + 0.836147i −0.998377 0.0569461i 0.981864π-0.981864\pi
−0.449872 + 0.893093i 0.648530π0.648530\pi
984984 −18.6980 4.11787i −0.596069 0.131273i
985985 −5.93626 + 10.2819i −0.189145 + 0.327608i
986986 −16.7142 9.64996i −0.532289 0.307317i
987987 −45.1523 9.94393i −1.43721 0.316519i
988988 7.68122 8.66485i 0.244372 0.275666i
989989 −59.3808 −1.88820
990990 −1.95996 + 4.23396i −0.0622916 + 0.134564i
991991 −26.0277 −0.826799 −0.413399 0.910550i 0.635659π-0.635659\pi
−0.413399 + 0.910550i 0.635659π0.635659\pi
992992 3.24185 + 5.61504i 0.102929 + 0.178278i
993993 5.36390 + 4.90135i 0.170218 + 0.155540i
994994 −20.2683 11.7019i −0.642872 0.371163i
995995 5.67460 + 3.27623i 0.179897 + 0.103864i
996996 −9.68590 + 3.06882i −0.306910 + 0.0972393i
997997 −13.6237 23.5970i −0.431468 0.747324i 0.565532 0.824726i 0.308671π-0.308671\pi
−0.997000 + 0.0774021i 0.975337π0.975337\pi
998998 −15.4596 −0.489367
999999 6.55702 8.61975i 0.207455 0.272717i
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 234.2.t.a.103.12 yes 28
3.2 odd 2 702.2.t.a.415.4 28
9.2 odd 6 702.2.t.a.181.11 28
9.4 even 3 2106.2.b.c.649.11 14
9.5 odd 6 2106.2.b.d.649.4 14
9.7 even 3 inner 234.2.t.a.25.5 28
13.12 even 2 inner 234.2.t.a.103.5 yes 28
39.38 odd 2 702.2.t.a.415.11 28
117.25 even 6 inner 234.2.t.a.25.12 yes 28
117.38 odd 6 702.2.t.a.181.4 28
117.77 odd 6 2106.2.b.d.649.11 14
117.103 even 6 2106.2.b.c.649.4 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
234.2.t.a.25.5 28 9.7 even 3 inner
234.2.t.a.25.12 yes 28 117.25 even 6 inner
234.2.t.a.103.5 yes 28 13.12 even 2 inner
234.2.t.a.103.12 yes 28 1.1 even 1 trivial
702.2.t.a.181.4 28 117.38 odd 6
702.2.t.a.181.11 28 9.2 odd 6
702.2.t.a.415.4 28 3.2 odd 2
702.2.t.a.415.11 28 39.38 odd 2
2106.2.b.c.649.4 14 117.103 even 6
2106.2.b.c.649.11 14 9.4 even 3
2106.2.b.d.649.4 14 9.5 odd 6
2106.2.b.d.649.11 14 117.77 odd 6