Properties

Label 357.2.k.b.64.7
Level 357357
Weight 22
Character 357.64
Analytic conductor 2.8512.851
Analytic rank 00
Dimension 2020
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [357,2,Mod(64,357)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(357, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("357.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 357=3717 357 = 3 \cdot 7 \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 357.k (of order 44, 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: 2.850659352162.85065935216
Analytic rank: 00
Dimension: 2020
Relative dimension: 1010 over Q(i)\Q(i)
Coefficient field: Q[x]/(x20+)\mathbb{Q}[x]/(x^{20} + \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x20+32x18+426x16+3072x14+13121x12+34148x10+53608x8+48276x6++4 x^{20} + 32 x^{18} + 426 x^{16} + 3072 x^{14} + 13121 x^{12} + 34148 x^{10} + 53608 x^{8} + 48276 x^{6} + \cdots + 4 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 24 2^{4}
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 64.7
Root 0.661473i0.661473i of defining polynomial
Character χ\chi == 357.64
Dual form 357.2.k.b.106.4

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+0.661473iq2+(0.7071070.707107i)q3+1.56245q4+(1.663721.66372i)q5+(0.4677320.467732i)q6+(0.707107+0.707107i)q7+2.35647iq8+1.00000iq9+(1.100501.10050i)q10+(3.712913.71291i)q11+(1.104821.10482i)q12+4.49854q13+(0.4677320.467732i)q14+2.35286iq15+1.56617q16+(0.6869634.06547i)q170.661473q183.58834iq19+(2.599492.59949i)q20+1.00000q21+(2.45599+2.45599i)q22+(0.4267920.426792i)q23+(1.666271.66627i)q24+0.535927iq25+2.97566iq26+(0.7071070.707107i)q27+(1.10482+1.10482i)q28+(4.070144.07014i)q291.55635q30+(0.1412370.141237i)q31+5.74891iq325.25085q33+(2.689200.454407i)q34+2.35286q35+1.56245iq36+(5.41429+5.41429i)q37+2.37359q38+(3.180953.18095i)q39+(3.920503.92050i)q40+(4.30993+4.30993i)q41+0.661473iq42+9.93667iq43+(5.801255.80125i)q44+(1.663721.66372i)q45+(0.282311+0.282311i)q46+6.16149q47+(1.107451.10745i)q481.00000iq490.354501q50+(2.38897+3.36048i)q51+7.02876q52+9.47974iq53+(0.467732+0.467732i)q5412.3545q55+(1.666271.66627i)q56+(2.53734+2.53734i)q57+(2.692282.69228i)q581.92313iq59+3.67623iq60+(7.45587+7.45587i)q61+(0.09342410.0934241i)q62+(0.7071070.707107i)q630.670404q64+(7.484317.48431i)q653.47329iq667.47259q67+(1.073356.35212i)q680.603575q69+1.55635iq70+(1.091941.09194i)q712.35647q72+(6.993296.99329i)q73+(3.58140+3.58140i)q74+(0.3789570.378957i)q755.60662iq76+5.25085iq77+(2.104112.10411i)q78+(7.404157.40415i)q79+(2.605672.60567i)q801.00000q81+(2.850902.85090i)q82+8.09294iq83+1.56245q84+(5.62090+7.90672i)q856.57283q86+5.75604iq87+(8.74934+8.74934i)q8812.3039q89+(1.10050+1.10050i)q90+(3.18095+3.18095i)q91+(0.6668430.666843i)q92+0.199739iq93+4.07566iq94+(5.97000+5.97000i)q95+(4.065094.06509i)q96+(5.83964+5.83964i)q97+0.661473q98+(3.71291+3.71291i)q99+O(q100)q+0.661473i q^{2} +(-0.707107 - 0.707107i) q^{3} +1.56245 q^{4} +(-1.66372 - 1.66372i) q^{5} +(0.467732 - 0.467732i) q^{6} +(-0.707107 + 0.707107i) q^{7} +2.35647i q^{8} +1.00000i q^{9} +(1.10050 - 1.10050i) q^{10} +(3.71291 - 3.71291i) q^{11} +(-1.10482 - 1.10482i) q^{12} +4.49854 q^{13} +(-0.467732 - 0.467732i) q^{14} +2.35286i q^{15} +1.56617 q^{16} +(-0.686963 - 4.06547i) q^{17} -0.661473 q^{18} -3.58834i q^{19} +(-2.59949 - 2.59949i) q^{20} +1.00000 q^{21} +(2.45599 + 2.45599i) q^{22} +(0.426792 - 0.426792i) q^{23} +(1.66627 - 1.66627i) q^{24} +0.535927i q^{25} +2.97566i q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.10482 + 1.10482i) q^{28} +(-4.07014 - 4.07014i) q^{29} -1.55635 q^{30} +(-0.141237 - 0.141237i) q^{31} +5.74891i q^{32} -5.25085 q^{33} +(2.68920 - 0.454407i) q^{34} +2.35286 q^{35} +1.56245i q^{36} +(5.41429 + 5.41429i) q^{37} +2.37359 q^{38} +(-3.18095 - 3.18095i) q^{39} +(3.92050 - 3.92050i) q^{40} +(-4.30993 + 4.30993i) q^{41} +0.661473i q^{42} +9.93667i q^{43} +(5.80125 - 5.80125i) q^{44} +(1.66372 - 1.66372i) q^{45} +(0.282311 + 0.282311i) q^{46} +6.16149 q^{47} +(-1.10745 - 1.10745i) q^{48} -1.00000i q^{49} -0.354501 q^{50} +(-2.38897 + 3.36048i) q^{51} +7.02876 q^{52} +9.47974i q^{53} +(0.467732 + 0.467732i) q^{54} -12.3545 q^{55} +(-1.66627 - 1.66627i) q^{56} +(-2.53734 + 2.53734i) q^{57} +(2.69228 - 2.69228i) q^{58} -1.92313i q^{59} +3.67623i q^{60} +(-7.45587 + 7.45587i) q^{61} +(0.0934241 - 0.0934241i) q^{62} +(-0.707107 - 0.707107i) q^{63} -0.670404 q^{64} +(-7.48431 - 7.48431i) q^{65} -3.47329i q^{66} -7.47259 q^{67} +(-1.07335 - 6.35212i) q^{68} -0.603575 q^{69} +1.55635i q^{70} +(-1.09194 - 1.09194i) q^{71} -2.35647 q^{72} +(-6.99329 - 6.99329i) q^{73} +(-3.58140 + 3.58140i) q^{74} +(0.378957 - 0.378957i) q^{75} -5.60662i q^{76} +5.25085i q^{77} +(2.10411 - 2.10411i) q^{78} +(7.40415 - 7.40415i) q^{79} +(-2.60567 - 2.60567i) q^{80} -1.00000 q^{81} +(-2.85090 - 2.85090i) q^{82} +8.09294i q^{83} +1.56245 q^{84} +(-5.62090 + 7.90672i) q^{85} -6.57283 q^{86} +5.75604i q^{87} +(8.74934 + 8.74934i) q^{88} -12.3039 q^{89} +(1.10050 + 1.10050i) q^{90} +(-3.18095 + 3.18095i) q^{91} +(0.666843 - 0.666843i) q^{92} +0.199739i q^{93} +4.07566i q^{94} +(-5.97000 + 5.97000i) q^{95} +(4.06509 - 4.06509i) q^{96} +(5.83964 + 5.83964i) q^{97} +0.661473 q^{98} +(3.71291 + 3.71291i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q24q4+8q54q6+16q10+4q1112q13+4q14+40q16+4q17+8q1852q20+20q2124q224q23+4q248q29+8q314q33++4q99+O(q100) 20 q - 24 q^{4} + 8 q^{5} - 4 q^{6} + 16 q^{10} + 4 q^{11} - 12 q^{13} + 4 q^{14} + 40 q^{16} + 4 q^{17} + 8 q^{18} - 52 q^{20} + 20 q^{21} - 24 q^{22} - 4 q^{23} + 4 q^{24} - 8 q^{29} + 8 q^{31} - 4 q^{33}+ \cdots + 4 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/357Z)×\left(\mathbb{Z}/357\mathbb{Z}\right)^\times.

nn 5252 190190 239239
χ(n)\chi(n) 11 e(14)e\left(\frac{1}{4}\right) 11

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 0.661473i 0.467732i 0.972269 + 0.233866i 0.0751377π0.0751377\pi
−0.972269 + 0.233866i 0.924862π0.924862\pi
33 −0.707107 0.707107i −0.408248 0.408248i
44 1.56245 0.781227
55 −1.66372 1.66372i −0.744038 0.744038i 0.229314 0.973352i 0.426352π-0.426352\pi
−0.973352 + 0.229314i 0.926352π0.926352\pi
66 0.467732 0.467732i 0.190951 0.190951i
77 −0.707107 + 0.707107i −0.267261 + 0.267261i
88 2.35647i 0.833136i
99 1.00000i 0.333333i
1010 1.10050 1.10050i 0.348010 0.348010i
1111 3.71291 3.71291i 1.11948 1.11948i 0.127668 0.991817i 0.459251π-0.459251\pi
0.991817 0.127668i 0.0407490π-0.0407490\pi
1212 −1.10482 1.10482i −0.318935 0.318935i
1313 4.49854 1.24767 0.623835 0.781556i 0.285574π-0.285574\pi
0.623835 + 0.781556i 0.285574π0.285574\pi
1414 −0.467732 0.467732i −0.125007 0.125007i
1515 2.35286i 0.607505i
1616 1.56617 0.391543
1717 −0.686963 4.06547i −0.166613 0.986022i
1818 −0.661473 −0.155911
1919 3.58834i 0.823222i −0.911360 0.411611i 0.864966π-0.864966\pi
0.911360 0.411611i 0.135034π-0.135034\pi
2020 −2.59949 2.59949i −0.581263 0.581263i
2121 1.00000 0.218218
2222 2.45599 + 2.45599i 0.523618 + 0.523618i
2323 0.426792 0.426792i 0.0889923 0.0889923i −0.661209 0.750202i 0.729956π-0.729956\pi
0.750202 + 0.661209i 0.229956π0.229956\pi
2424 1.66627 1.66627i 0.340127 0.340127i
2525 0.535927i 0.107185i
2626 2.97566i 0.583575i
2727 0.707107 0.707107i 0.136083 0.136083i
2828 −1.10482 + 1.10482i −0.208792 + 0.208792i
2929 −4.07014 4.07014i −0.755805 0.755805i 0.219751 0.975556i 0.429476π-0.429476\pi
−0.975556 + 0.219751i 0.929476π0.929476\pi
3030 −1.55635 −0.284149
3131 −0.141237 0.141237i −0.0253668 0.0253668i 0.694310 0.719676i 0.255710π-0.255710\pi
−0.719676 + 0.694310i 0.755710π0.755710\pi
3232 5.74891i 1.01627i
3333 −5.25085 −0.914055
3434 2.68920 0.454407i 0.461194 0.0779302i
3535 2.35286 0.397705
3636 1.56245i 0.260409i
3737 5.41429 + 5.41429i 0.890104 + 0.890104i 0.994532 0.104429i 0.0333014π-0.0333014\pi
−0.104429 + 0.994532i 0.533301π0.533301\pi
3838 2.37359 0.385047
3939 −3.18095 3.18095i −0.509359 0.509359i
4040 3.92050 3.92050i 0.619885 0.619885i
4141 −4.30993 + 4.30993i −0.673098 + 0.673098i −0.958429 0.285331i 0.907897π-0.907897\pi
0.285331 + 0.958429i 0.407897π0.407897\pi
4242 0.661473i 0.102067i
4343 9.93667i 1.51533i 0.652645 + 0.757664i 0.273659π0.273659\pi
−0.652645 + 0.757664i 0.726341π0.726341\pi
4444 5.80125 5.80125i 0.874572 0.874572i
4545 1.66372 1.66372i 0.248013 0.248013i
4646 0.282311 + 0.282311i 0.0416245 + 0.0416245i
4747 6.16149 0.898745 0.449373 0.893344i 0.351648π-0.351648\pi
0.449373 + 0.893344i 0.351648π0.351648\pi
4848 −1.10745 1.10745i −0.159847 0.159847i
4949 1.00000i 0.142857i
5050 −0.354501 −0.0501340
5151 −2.38897 + 3.36048i −0.334522 + 0.470561i
5252 7.02876 0.974714
5353 9.47974i 1.30214i 0.759017 + 0.651071i 0.225680π0.225680\pi
−0.759017 + 0.651071i 0.774320π0.774320\pi
5454 0.467732 + 0.467732i 0.0636502 + 0.0636502i
5555 −12.3545 −1.66588
5656 −1.66627 1.66627i −0.222665 0.222665i
5757 −2.53734 + 2.53734i −0.336079 + 0.336079i
5858 2.69228 2.69228i 0.353514 0.353514i
5959 1.92313i 0.250370i −0.992133 0.125185i 0.960048π-0.960048\pi
0.992133 0.125185i 0.0399525π-0.0399525\pi
6060 3.67623i 0.474599i
6161 −7.45587 + 7.45587i −0.954626 + 0.954626i −0.999014 0.0443882i 0.985866π-0.985866\pi
0.0443882 + 0.999014i 0.485866π0.485866\pi
6262 0.0934241 0.0934241i 0.0118649 0.0118649i
6363 −0.707107 0.707107i −0.0890871 0.0890871i
6464 −0.670404 −0.0838006
6565 −7.48431 7.48431i −0.928314 0.928314i
6666 3.47329i 0.427533i
6767 −7.47259 −0.912922 −0.456461 0.889743i 0.650883π-0.650883\pi
−0.456461 + 0.889743i 0.650883π0.650883\pi
6868 −1.07335 6.35212i −0.130163 0.770307i
6969 −0.603575 −0.0726619
7070 1.55635i 0.186019i
7171 −1.09194 1.09194i −0.129590 0.129590i 0.639337 0.768927i 0.279209π-0.279209\pi
−0.768927 + 0.639337i 0.779209π0.779209\pi
7272 −2.35647 −0.277712
7373 −6.99329 6.99329i −0.818503 0.818503i 0.167388 0.985891i 0.446467π-0.446467\pi
−0.985891 + 0.167388i 0.946467π0.946467\pi
7474 −3.58140 + 3.58140i −0.416330 + 0.416330i
7575 0.378957 0.378957i 0.0437582 0.0437582i
7676 5.60662i 0.643123i
7777 5.25085i 0.598390i
7878 2.10411 2.10411i 0.238243 0.238243i
7979 7.40415 7.40415i 0.833032 0.833032i −0.154898 0.987930i 0.549505π-0.549505\pi
0.987930 + 0.154898i 0.0495049π0.0495049\pi
8080 −2.60567 2.60567i −0.291323 0.291323i
8181 −1.00000 −0.111111
8282 −2.85090 2.85090i −0.314829 0.314829i
8383 8.09294i 0.888316i 0.895949 + 0.444158i 0.146497π0.146497\pi
−0.895949 + 0.444158i 0.853503π0.853503\pi
8484 1.56245 0.170478
8585 −5.62090 + 7.90672i −0.609672 + 0.857605i
8686 −6.57283 −0.708767
8787 5.75604i 0.617113i
8888 8.74934 + 8.74934i 0.932683 + 0.932683i
8989 −12.3039 −1.30421 −0.652105 0.758129i 0.726114π-0.726114\pi
−0.652105 + 0.758129i 0.726114π0.726114\pi
9090 1.10050 + 1.10050i 0.116003 + 0.116003i
9191 −3.18095 + 3.18095i −0.333454 + 0.333454i
9292 0.666843 0.666843i 0.0695232 0.0695232i
9393 0.199739i 0.0207119i
9494 4.07566i 0.420372i
9595 −5.97000 + 5.97000i −0.612509 + 0.612509i
9696 4.06509 4.06509i 0.414892 0.414892i
9797 5.83964 + 5.83964i 0.592925 + 0.592925i 0.938421 0.345495i 0.112289π-0.112289\pi
−0.345495 + 0.938421i 0.612289π0.612289\pi
9898 0.661473 0.0668188
9999 3.71291 + 3.71291i 0.373162 + 0.373162i
100100 0.837361i 0.0837361i
101101 12.3613 1.22999 0.614995 0.788531i 0.289158π-0.289158\pi
0.614995 + 0.788531i 0.289158π0.289158\pi
102102 −2.22287 1.58024i −0.220097 0.156467i
103103 3.48146 0.343039 0.171519 0.985181i 0.445132π-0.445132\pi
0.171519 + 0.985181i 0.445132π0.445132\pi
104104 10.6007i 1.03948i
105105 −1.66372 1.66372i −0.162362 0.162362i
106106 −6.27059 −0.609053
107107 −3.28575 3.28575i −0.317645 0.317645i 0.530217 0.847862i 0.322111π-0.322111\pi
−0.847862 + 0.530217i 0.822111π0.822111\pi
108108 1.10482 1.10482i 0.106312 0.106312i
109109 9.85208 9.85208i 0.943659 0.943659i −0.0548368 0.998495i 0.517464π-0.517464\pi
0.998495 + 0.0548368i 0.0174638π0.0174638\pi
110110 8.17215i 0.779184i
111111 7.65696i 0.726767i
112112 −1.10745 + 1.10745i −0.104644 + 0.104644i
113113 −6.98837 + 6.98837i −0.657411 + 0.657411i −0.954767 0.297356i 0.903895π-0.903895\pi
0.297356 + 0.954767i 0.403895π0.403895\pi
114114 −1.67838 1.67838i −0.157195 0.157195i
115115 −1.42012 −0.132427
116116 −6.35940 6.35940i −0.590456 0.590456i
117117 4.49854i 0.415890i
118118 1.27210 0.117106
119119 3.36048 + 2.38897i 0.308055 + 0.218996i
120120 −5.54442 −0.506134
121121 16.5714i 1.50649i
122122 −4.93185 4.93185i −0.446509 0.446509i
123123 6.09517 0.549583
124124 −0.220676 0.220676i −0.0198173 0.0198173i
125125 −7.42697 + 7.42697i −0.664288 + 0.664288i
126126 0.467732 0.467732i 0.0416689 0.0416689i
127127 14.8193i 1.31500i −0.753456 0.657499i 0.771614π-0.771614\pi
0.753456 0.657499i 0.228386π-0.228386\pi
128128 11.0544i 0.977077i
129129 7.02628 7.02628i 0.618630 0.618630i
130130 4.95066 4.95066i 0.434202 0.434202i
131131 6.46192 + 6.46192i 0.564580 + 0.564580i 0.930605 0.366025i 0.119281π-0.119281\pi
−0.366025 + 0.930605i 0.619281π0.619281\pi
132132 −8.20421 −0.714085
133133 2.53734 + 2.53734i 0.220015 + 0.220015i
134134 4.94291i 0.427003i
135135 −2.35286 −0.202502
136136 9.58015 1.61881i 0.821491 0.138811i
137137 −7.53516 −0.643772 −0.321886 0.946778i 0.604317π-0.604317\pi
−0.321886 + 0.946778i 0.604317π0.604317\pi
138138 0.399248i 0.0339863i
139139 −0.364800 0.364800i −0.0309419 0.0309419i 0.691467 0.722408i 0.256965π-0.256965\pi
−0.722408 + 0.691467i 0.756965π0.756965\pi
140140 3.67623 0.310698
141141 −4.35683 4.35683i −0.366911 0.366911i
142142 0.722289 0.722289i 0.0606132 0.0606132i
143143 16.7027 16.7027i 1.39675 1.39675i
144144 1.56617i 0.130514i
145145 13.5431i 1.12470i
146146 4.62587 4.62587i 0.382840 0.382840i
147147 −0.707107 + 0.707107i −0.0583212 + 0.0583212i
148148 8.45958 + 8.45958i 0.695373 + 0.695373i
149149 2.24948 0.184284 0.0921422 0.995746i 0.470629π-0.470629\pi
0.0921422 + 0.995746i 0.470629π0.470629\pi
150150 0.250670 + 0.250670i 0.0204671 + 0.0204671i
151151 10.1044i 0.822286i 0.911571 + 0.411143i 0.134870π0.134870\pi
−0.911571 + 0.411143i 0.865130π0.865130\pi
152152 8.45580 0.685856
153153 4.06547 0.686963i 0.328674 0.0555377i
154154 −3.47329 −0.279886
155155 0.469956i 0.0377478i
156156 −4.97008 4.97008i −0.397925 0.397925i
157157 −23.6643 −1.88862 −0.944310 0.329058i 0.893269π-0.893269\pi
−0.944310 + 0.329058i 0.893269π0.893269\pi
158158 4.89764 + 4.89764i 0.389636 + 0.389636i
159159 6.70319 6.70319i 0.531597 0.531597i
160160 9.56458 9.56458i 0.756146 0.756146i
161161 0.603575i 0.0475684i
162162 0.661473i 0.0519702i
163163 16.9353 16.9353i 1.32648 1.32648i 0.418054 0.908422i 0.362712π-0.362712\pi
0.908422 0.418054i 0.137288π-0.137288\pi
164164 −6.73407 + 6.73407i −0.525843 + 0.525843i
165165 8.73594 + 8.73594i 0.680092 + 0.680092i
166166 −5.35326 −0.415493
167167 17.8008 + 17.8008i 1.37747 + 1.37747i 0.848875 + 0.528593i 0.177280π0.177280\pi
0.528593 + 0.848875i 0.322720π0.322720\pi
168168 2.35647i 0.181805i
169169 7.23686 0.556681
170170 −5.23008 3.71807i −0.401129 0.285163i
171171 3.58834 0.274407
172172 15.5256i 1.18381i
173173 7.89482 + 7.89482i 0.600232 + 0.600232i 0.940374 0.340142i 0.110475π-0.110475\pi
−0.340142 + 0.940374i 0.610475π0.610475\pi
174174 −3.80746 −0.288643
175175 −0.378957 0.378957i −0.0286465 0.0286465i
176176 5.81505 5.81505i 0.438326 0.438326i
177177 −1.35986 + 1.35986i −0.102213 + 0.102213i
178178 8.13869i 0.610020i
179179 2.39571i 0.179064i −0.995984 0.0895320i 0.971463π-0.971463\pi
0.995984 0.0895320i 0.0285371π-0.0285371\pi
180180 2.59949 2.59949i 0.193754 0.193754i
181181 −13.8862 + 13.8862i −1.03216 + 1.03216i −0.0326907 + 0.999466i 0.510408π0.510408\pi
−0.999466 + 0.0326907i 0.989592π0.989592\pi
182182 −2.10411 2.10411i −0.155967 0.155967i
183183 10.5442 0.779449
184184 1.00572 + 1.00572i 0.0741427 + 0.0741427i
185185 18.0157i 1.32454i
186186 −0.132122 −0.00968763
187187 −17.6454 12.5441i −1.29036 0.917316i
188188 9.62704 0.702124
189189 1.00000i 0.0727393i
190190 −3.94899 3.94899i −0.286490 0.286490i
191191 5.22705 0.378216 0.189108 0.981956i 0.439440π-0.439440\pi
0.189108 + 0.981956i 0.439440π0.439440\pi
192192 0.474048 + 0.474048i 0.0342114 + 0.0342114i
193193 −15.3421 + 15.3421i −1.10435 + 1.10435i −0.110467 + 0.993880i 0.535235π0.535235\pi
−0.993880 + 0.110467i 0.964765π0.964765\pi
194194 −3.86276 + 3.86276i −0.277330 + 0.277330i
195195 10.5844i 0.757965i
196196 1.56245i 0.111604i
197197 4.73493 4.73493i 0.337350 0.337350i −0.518019 0.855369i 0.673330π-0.673330\pi
0.855369 + 0.518019i 0.173330π0.173330\pi
198198 −2.45599 + 2.45599i −0.174539 + 0.174539i
199199 −4.74936 4.74936i −0.336673 0.336673i 0.518441 0.855114i 0.326513π-0.326513\pi
−0.855114 + 0.518441i 0.826513π0.826513\pi
200200 −1.26289 −0.0893000
201201 5.28392 + 5.28392i 0.372699 + 0.372699i
202202 8.17663i 0.575306i
203203 5.75604 0.403995
204204 −3.73265 + 5.25060i −0.261338 + 0.367615i
205205 14.3410 1.00162
206206 2.30289i 0.160450i
207207 0.426792 + 0.426792i 0.0296641 + 0.0296641i
208208 7.04548 0.488516
209209 −13.3232 13.3232i −0.921584 0.921584i
210210 1.10050 1.10050i 0.0759421 0.0759421i
211211 −9.31494 + 9.31494i −0.641267 + 0.641267i −0.950867 0.309600i 0.899805π-0.899805\pi
0.309600 + 0.950867i 0.399805π0.399805\pi
212212 14.8117i 1.01727i
213213 1.54424i 0.105809i
214214 2.17343 2.17343i 0.148573 0.148573i
215215 16.5318 16.5318i 1.12746 1.12746i
216216 1.66627 + 1.66627i 0.113376 + 0.113376i
217217 0.199739 0.0135591
218218 6.51688 + 6.51688i 0.441379 + 0.441379i
219219 9.89000i 0.668305i
220220 −19.3033 −1.30143
221221 −3.09033 18.2887i −0.207878 1.23023i
222222 5.06487 0.339932
223223 12.0749i 0.808596i −0.914627 0.404298i 0.867516π-0.867516\pi
0.914627 0.404298i 0.132484π-0.132484\pi
224224 −4.06509 4.06509i −0.271610 0.271610i
225225 −0.535927 −0.0357285
226226 −4.62262 4.62262i −0.307492 0.307492i
227227 7.04430 7.04430i 0.467547 0.467547i −0.433572 0.901119i 0.642747π-0.642747\pi
0.901119 + 0.433572i 0.142747π0.142747\pi
228228 −3.96448 + 3.96448i −0.262554 + 0.262554i
229229 0.341524i 0.0225685i 0.999936 + 0.0112843i 0.00359197π0.00359197\pi
−0.999936 + 0.0112843i 0.996408π0.996408\pi
230230 0.939374i 0.0619405i
231231 3.71291 3.71291i 0.244292 0.244292i
232232 9.59114 9.59114i 0.629689 0.629689i
233233 11.2402 + 11.2402i 0.736371 + 0.736371i 0.971874 0.235502i 0.0756736π-0.0756736\pi
−0.235502 + 0.971874i 0.575674π0.575674\pi
234234 −2.97566 −0.194525
235235 −10.2510 10.2510i −0.668701 0.668701i
236236 3.00480i 0.195596i
237237 −10.4711 −0.680168
238238 −1.58024 + 2.22287i −0.102432 + 0.144087i
239239 −1.16131 −0.0751187 −0.0375594 0.999294i 0.511958π-0.511958\pi
−0.0375594 + 0.999294i 0.511958π0.511958\pi
240240 3.68497i 0.237864i
241241 6.45266 + 6.45266i 0.415652 + 0.415652i 0.883702 0.468050i 0.155043π-0.155043\pi
−0.468050 + 0.883702i 0.655043π0.655043\pi
242242 10.9615 0.704634
243243 0.707107 + 0.707107i 0.0453609 + 0.0453609i
244244 −11.6495 + 11.6495i −0.745780 + 0.745780i
245245 −1.66372 + 1.66372i −0.106291 + 0.106291i
246246 4.03178i 0.257057i
247247 16.1423i 1.02711i
248248 0.332819 0.332819i 0.0211340 0.0211340i
249249 5.72257 5.72257i 0.362653 0.362653i
250250 −4.91273 4.91273i −0.310709 0.310709i
251251 −2.02464 −0.127794 −0.0638970 0.997956i 0.520353π-0.520353\pi
−0.0638970 + 0.997956i 0.520353π0.520353\pi
252252 −1.10482 1.10482i −0.0695972 0.0695972i
253253 3.16928i 0.199251i
254254 9.80254 0.615066
255255 9.56547 1.61632i 0.599013 0.101218i
256256 −8.65297 −0.540811
257257 19.5756i 1.22109i 0.791982 + 0.610545i 0.209049π0.209049\pi
−0.791982 + 0.610545i 0.790951π0.790951\pi
258258 4.64769 + 4.64769i 0.289353 + 0.289353i
259259 −7.65696 −0.475780
260260 −11.6939 11.6939i −0.725224 0.725224i
261261 4.07014 4.07014i 0.251935 0.251935i
262262 −4.27438 + 4.27438i −0.264072 + 0.264072i
263263 23.4356i 1.44510i −0.691319 0.722550i 0.742970π-0.742970\pi
0.691319 0.722550i 0.257030π-0.257030\pi
264264 12.3734i 0.761533i
265265 15.7716 15.7716i 0.968843 0.968843i
266266 −1.67838 + 1.67838i −0.102908 + 0.102908i
267267 8.70017 + 8.70017i 0.532441 + 0.532441i
268268 −11.6756 −0.713200
269269 5.65950 + 5.65950i 0.345066 + 0.345066i 0.858268 0.513202i 0.171541π-0.171541\pi
−0.513202 + 0.858268i 0.671541π0.671541\pi
270270 1.55635i 0.0947164i
271271 24.5987 1.49427 0.747133 0.664675i 0.231430π-0.231430\pi
0.747133 + 0.664675i 0.231430π0.231430\pi
272272 −1.07590 6.36723i −0.0652361 0.386070i
273273 4.49854 0.272264
274274 4.98430i 0.301112i
275275 1.98985 + 1.98985i 0.119992 + 0.119992i
276276 −0.943058 −0.0567654
277277 −18.9255 18.9255i −1.13712 1.13712i −0.988963 0.148162i 0.952664π-0.952664\pi
−0.148162 0.988963i 0.547336π-0.547336\pi
278278 0.241305 0.241305i 0.0144725 0.0144725i
279279 0.141237 0.141237i 0.00845562 0.00845562i
280280 5.54442i 0.331343i
281281 24.2978i 1.44948i 0.689020 + 0.724742i 0.258041π0.258041\pi
−0.689020 + 0.724742i 0.741959π0.741959\pi
282282 2.88192 2.88192i 0.171616 0.171616i
283283 −6.48189 + 6.48189i −0.385308 + 0.385308i −0.873010 0.487702i 0.837835π-0.837835\pi
0.487702 + 0.873010i 0.337835π0.337835\pi
284284 −1.70611 1.70611i −0.101239 0.101239i
285285 8.44285 0.500111
286286 11.0484 + 11.0484i 0.653303 + 0.653303i
287287 6.09517i 0.359786i
288288 −5.74891 −0.338758
289289 −16.0562 + 5.58566i −0.944480 + 0.328568i
290290 −8.95841 −0.526056
291291 8.25850i 0.484122i
292292 −10.9267 10.9267i −0.639436 0.639436i
293293 2.19698 0.128349 0.0641746 0.997939i 0.479559π-0.479559\pi
0.0641746 + 0.997939i 0.479559π0.479559\pi
294294 −0.467732 0.467732i −0.0272787 0.0272787i
295295 −3.19955 + 3.19955i −0.186285 + 0.186285i
296296 −12.7586 + 12.7586i −0.741578 + 0.741578i
297297 5.25085i 0.304685i
298298 1.48797i 0.0861956i
299299 1.91994 1.91994i 0.111033 0.111033i
300300 0.592104 0.592104i 0.0341851 0.0341851i
301301 −7.02628 7.02628i −0.404988 0.404988i
302302 −6.68379 −0.384609
303303 −8.74073 8.74073i −0.502142 0.502142i
304304 5.61996i 0.322327i
305305 24.8090 1.42056
306306 0.454407 + 2.68920i 0.0259767 + 0.153731i
307307 21.0887 1.20360 0.601798 0.798648i 0.294451π-0.294451\pi
0.601798 + 0.798648i 0.294451π0.294451\pi
308308 8.20421i 0.467478i
309309 −2.46176 2.46176i −0.140045 0.140045i
310310 −0.310863 −0.0176558
311311 −7.97525 7.97525i −0.452235 0.452235i 0.443861 0.896096i 0.353608π-0.353608\pi
−0.896096 + 0.443861i 0.853608π0.853608\pi
312312 7.49579 7.49579i 0.424366 0.424366i
313313 −14.0917 + 14.0917i −0.796511 + 0.796511i −0.982544 0.186033i 0.940437π-0.940437\pi
0.186033 + 0.982544i 0.440437π0.440437\pi
314314 15.6533i 0.883367i
315315 2.35286i 0.132568i
316316 11.5686 11.5686i 0.650787 0.650787i
317317 −21.5746 + 21.5746i −1.21175 + 1.21175i −0.241299 + 0.970451i 0.577574π0.577574\pi
−0.970451 + 0.241299i 0.922426π0.922426\pi
318318 4.43397 + 4.43397i 0.248645 + 0.248645i
319319 −30.2241 −1.69222
320320 1.11537 + 1.11537i 0.0623508 + 0.0623508i
321321 4.64675i 0.259356i
322322 −0.399248 −0.0222492
323323 −14.5883 + 2.46506i −0.811715 + 0.137160i
324324 −1.56245 −0.0868030
325325 2.41089i 0.133732i
326326 11.2022 + 11.2022i 0.620435 + 0.620435i
327327 −13.9330 −0.770494
328328 −10.1562 10.1562i −0.560783 0.560783i
329329 −4.35683 + 4.35683i −0.240200 + 0.240200i
330330 −5.77858 + 5.77858i −0.318101 + 0.318101i
331331 24.7998i 1.36312i 0.731763 + 0.681560i 0.238698π0.238698\pi
−0.731763 + 0.681560i 0.761302π0.761302\pi
332332 12.6448i 0.693976i
333333 −5.41429 + 5.41429i −0.296701 + 0.296701i
334334 −11.7748 + 11.7748i −0.644286 + 0.644286i
335335 12.4323 + 12.4323i 0.679249 + 0.679249i
336336 1.56617 0.0854416
337337 6.17698 + 6.17698i 0.336482 + 0.336482i 0.855041 0.518560i 0.173532π-0.173532\pi
−0.518560 + 0.855041i 0.673532π0.673532\pi
338338 4.78698i 0.260378i
339339 9.88305 0.536774
340340 −8.78239 + 12.3539i −0.476292 + 0.669984i
341341 −1.04880 −0.0567956
342342 2.37359i 0.128349i
343343 0.707107 + 0.707107i 0.0381802 + 0.0381802i
344344 −23.4154 −1.26247
345345 1.00418 + 1.00418i 0.0540632 + 0.0540632i
346346 −5.22221 + 5.22221i −0.280748 + 0.280748i
347347 −5.65098 + 5.65098i −0.303360 + 0.303360i −0.842327 0.538967i 0.818815π-0.818815\pi
0.538967 + 0.842327i 0.318815π0.318815\pi
348348 8.99355i 0.482105i
349349 20.2193i 1.08232i −0.840921 0.541158i 0.817986π-0.817986\pi
0.840921 0.541158i 0.182014π-0.182014\pi
350350 0.250670 0.250670i 0.0133989 0.0133989i
351351 3.18095 3.18095i 0.169786 0.169786i
352352 21.3452 + 21.3452i 1.13770 + 1.13770i
353353 0.363744 0.0193601 0.00968007 0.999953i 0.496919π-0.496919\pi
0.00968007 + 0.999953i 0.496919π0.496919\pi
354354 −0.899509 0.899509i −0.0478084 0.0478084i
355355 3.63337i 0.192839i
356356 −19.2243 −1.01888
357357 −0.686963 4.06547i −0.0363579 0.215168i
358358 1.58470 0.0837539
359359 26.3254i 1.38940i −0.719299 0.694701i 0.755537π-0.755537\pi
0.719299 0.694701i 0.244463π-0.244463\pi
360360 3.92050 + 3.92050i 0.206628 + 0.206628i
361361 6.12380 0.322305
362362 −9.18537 9.18537i −0.482772 0.482772i
363363 −11.7178 + 11.7178i −0.615022 + 0.615022i
364364 −4.97008 + 4.97008i −0.260503 + 0.260503i
365365 23.2697i 1.21799i
366366 6.97469i 0.364573i
367367 −6.99722 + 6.99722i −0.365252 + 0.365252i −0.865742 0.500490i 0.833153π-0.833153\pi
0.500490 + 0.865742i 0.333153π0.333153\pi
368368 0.668429 0.668429i 0.0348443 0.0348443i
369369 −4.30993 4.30993i −0.224366 0.224366i
370370 11.9169 0.619530
371371 −6.70319 6.70319i −0.348012 0.348012i
372372 0.312083i 0.0161807i
373373 12.9157 0.668751 0.334376 0.942440i 0.391475π-0.391475\pi
0.334376 + 0.942440i 0.391475π0.391475\pi
374374 8.29758 11.6719i 0.429058 0.603541i
375375 10.5033 0.542389
376376 14.5193i 0.748778i
377377 −18.3097 18.3097i −0.942996 0.942996i
378378 −0.661473 −0.0340225
379379 11.2530 + 11.2530i 0.578026 + 0.578026i 0.934359 0.356333i 0.115973π-0.115973\pi
−0.356333 + 0.934359i 0.615973π0.615973\pi
380380 −9.32784 + 9.32784i −0.478508 + 0.478508i
381381 −10.4788 + 10.4788i −0.536846 + 0.536846i
382382 3.45755i 0.176904i
383383 19.1824i 0.980176i 0.871673 + 0.490088i 0.163035π0.163035\pi
−0.871673 + 0.490088i 0.836965π0.836965\pi
384384 7.81662 7.81662i 0.398890 0.398890i
385385 8.73594 8.73594i 0.445225 0.445225i
386386 −10.1484 10.1484i −0.516538 0.516538i
387387 −9.93667 −0.505109
388388 9.12417 + 9.12417i 0.463209 + 0.463209i
389389 24.5986i 1.24720i −0.781745 0.623598i 0.785670π-0.785670\pi
0.781745 0.623598i 0.214330π-0.214330\pi
390390 −7.00130 −0.354524
391391 −2.02830 1.44192i −0.102576 0.0729211i
392392 2.35647 0.119019
393393 9.13853i 0.460978i
394394 3.13203 + 3.13203i 0.157789 + 0.157789i
395395 −24.6369 −1.23962
396396 5.80125 + 5.80125i 0.291524 + 0.291524i
397397 −15.7916 + 15.7916i −0.792560 + 0.792560i −0.981910 0.189350i 0.939362π-0.939362\pi
0.189350 + 0.981910i 0.439362π0.439362\pi
398398 3.14157 3.14157i 0.157473 0.157473i
399399 3.58834i 0.179642i
400400 0.839353i 0.0419676i
401401 −18.2732 + 18.2732i −0.912518 + 0.912518i −0.996470 0.0839522i 0.973246π-0.973246\pi
0.0839522 + 0.996470i 0.473246π0.473246\pi
402402 −3.49517 + 3.49517i −0.174323 + 0.174323i
403403 −0.635358 0.635358i −0.0316495 0.0316495i
404404 19.3139 0.960902
405405 1.66372 + 1.66372i 0.0826709 + 0.0826709i
406406 3.80746i 0.188961i
407407 40.2055 1.99291
408408 −7.91886 5.62952i −0.392042 0.278703i
409409 15.7611 0.779339 0.389669 0.920955i 0.372589π-0.372589\pi
0.389669 + 0.920955i 0.372589π0.372589\pi
410410 9.48620i 0.468490i
411411 5.32816 + 5.32816i 0.262819 + 0.262819i
412412 5.43962 0.267991
413413 1.35986 + 1.35986i 0.0669143 + 0.0669143i
414414 −0.282311 + 0.282311i −0.0138748 + 0.0138748i
415415 13.4644 13.4644i 0.660941 0.660941i
416416 25.8617i 1.26797i
417417 0.515904i 0.0252640i
418418 8.81293 8.81293i 0.431054 0.431054i
419419 9.48958 9.48958i 0.463597 0.463597i −0.436236 0.899832i 0.643689π-0.643689\pi
0.899832 + 0.436236i 0.143689π0.143689\pi
420420 −2.59949 2.59949i −0.126842 0.126842i
421421 −10.2759 −0.500818 −0.250409 0.968140i 0.580565π-0.580565\pi
−0.250409 + 0.968140i 0.580565π0.580565\pi
422422 −6.16158 6.16158i −0.299941 0.299941i
423423 6.16149i 0.299582i
424424 −22.3387 −1.08486
425425 2.17880 0.368162i 0.105687 0.0178585i
426426 −1.02147 −0.0494904
427427 10.5442i 0.510269i
428428 −5.13383 5.13383i −0.248153 0.248153i
429429 −23.6211 −1.14044
430430 10.9353 + 10.9353i 0.527349 + 0.527349i
431431 20.3715 20.3715i 0.981261 0.981261i −0.0185668 0.999828i 0.505910π-0.505910\pi
0.999828 + 0.0185668i 0.00591032π0.00591032\pi
432432 1.10745 1.10745i 0.0532822 0.0532822i
433433 25.4783i 1.22441i −0.790699 0.612205i 0.790283π-0.790283\pi
0.790699 0.612205i 0.209717π-0.209717\pi
434434 0.132122i 0.00634204i
435435 9.57644 9.57644i 0.459155 0.459155i
436436 15.3934 15.3934i 0.737212 0.737212i
437437 −1.53148 1.53148i −0.0732604 0.0732604i
438438 −6.54197 −0.312587
439439 −23.9545 23.9545i −1.14329 1.14329i −0.987845 0.155441i 0.950320π-0.950320\pi
−0.155441 0.987845i 0.549680π-0.549680\pi
440440 29.1129i 1.38790i
441441 1.00000 0.0476190
442442 12.0975 2.04417i 0.575418 0.0972312i
443443 −10.6561 −0.506289 −0.253144 0.967429i 0.581465π-0.581465\pi
−0.253144 + 0.967429i 0.581465π0.581465\pi
444444 11.9637i 0.567770i
445445 20.4702 + 20.4702i 0.970382 + 0.970382i
446446 7.98722 0.378206
447447 −1.59062 1.59062i −0.0752338 0.0752338i
448448 0.474048 0.474048i 0.0223966 0.0223966i
449449 29.1315 29.1315i 1.37480 1.37480i 0.521622 0.853176i 0.325327π-0.325327\pi
0.853176 0.521622i 0.174673π-0.174673\pi
450450 0.354501i 0.0167113i
451451 32.0048i 1.50705i
452452 −10.9190 + 10.9190i −0.513587 + 0.513587i
453453 7.14490 7.14490i 0.335697 0.335697i
454454 4.65961 + 4.65961i 0.218686 + 0.218686i
455455 10.5844 0.496205
456456 −5.97916 5.97916i −0.280000 0.280000i
457457 42.1677i 1.97252i −0.165202 0.986260i 0.552828π-0.552828\pi
0.165202 0.986260i 0.447172π-0.447172\pi
458458 −0.225909 −0.0105560
459459 −3.36048 2.38897i −0.156854 0.111507i
460460 −2.21888 −0.103456
461461 8.08845i 0.376717i −0.982100 0.188358i 0.939683π-0.939683\pi
0.982100 0.188358i 0.0603167π-0.0603167\pi
462462 2.45599 + 2.45599i 0.114263 + 0.114263i
463463 31.1333 1.44688 0.723442 0.690385i 0.242559π-0.242559\pi
0.723442 + 0.690385i 0.242559π0.242559\pi
464464 −6.37453 6.37453i −0.295930 0.295930i
465465 0.332309 0.332309i 0.0154105 0.0154105i
466466 −7.43510 + 7.43510i −0.344424 + 0.344424i
467467 7.39951i 0.342408i 0.985236 + 0.171204i 0.0547658π0.0547658\pi
−0.985236 + 0.171204i 0.945234π0.945234\pi
468468 7.02876i 0.324905i
469469 5.28392 5.28392i 0.243989 0.243989i
470470 6.78075 6.78075i 0.312773 0.312773i
471471 16.7332 + 16.7332i 0.771026 + 0.771026i
472472 4.53179 0.208593
473473 36.8939 + 36.8939i 1.69639 + 1.69639i
474474 6.92631i 0.318136i
475475 1.92309 0.0882374
476476 5.25060 + 3.73265i 0.240661 + 0.171086i
477477 −9.47974 −0.434047
478478 0.768173i 0.0351354i
479479 19.1726 + 19.1726i 0.876019 + 0.876019i 0.993120 0.117101i 0.0373601π-0.0373601\pi
−0.117101 + 0.993120i 0.537360π0.537360\pi
480480 −13.5264 −0.617391
481481 24.3564 + 24.3564i 1.11056 + 1.11056i
482482 −4.26825 + 4.26825i −0.194414 + 0.194414i
483483 0.426792 0.426792i 0.0194197 0.0194197i
484484 25.8921i 1.17691i
485485 19.4310i 0.882318i
486486 −0.467732 + 0.467732i −0.0212167 + 0.0212167i
487487 22.2738 22.2738i 1.00932 1.00932i 0.00936691 0.999956i 0.497018π-0.497018\pi
0.999956 0.00936691i 0.00298162π-0.00298162\pi
488488 −17.5695 17.5695i −0.795334 0.795334i
489489 −23.9501 −1.08306
490490 −1.10050 1.10050i −0.0497157 0.0497157i
491491 3.17369i 0.143227i 0.997432 + 0.0716133i 0.0228148π0.0228148\pi
−0.997432 + 0.0716133i 0.977185π0.977185\pi
492492 9.52342 0.429349
493493 −13.7510 + 19.3431i −0.619314 + 0.871168i
494494 10.6777 0.480412
495495 12.3545i 0.555293i
496496 −0.221201 0.221201i −0.00993220 0.00993220i
497497 1.54424 0.0692686
498498 3.78532 + 3.78532i 0.169624 + 0.169624i
499499 −7.08666 + 7.08666i −0.317242 + 0.317242i −0.847707 0.530465i 0.822017π-0.822017\pi
0.530465 + 0.847707i 0.322017π0.322017\pi
500500 −11.6043 + 11.6043i −0.518960 + 0.518960i
501501 25.1742i 1.12470i
502502 1.33924i 0.0597734i
503503 −23.0866 + 23.0866i −1.02938 + 1.02938i −0.0298242 + 0.999555i 0.509495π0.509495\pi
−0.999555 + 0.0298242i 0.990505π0.990505\pi
504504 1.66627 1.66627i 0.0742217 0.0742217i
505505 −20.5657 20.5657i −0.915160 0.915160i
506506 2.09639 0.0931960
507507 −5.11723 5.11723i −0.227264 0.227264i
508508 23.1544i 1.02731i
509509 −6.78115 −0.300569 −0.150285 0.988643i 0.548019π-0.548019\pi
−0.150285 + 0.988643i 0.548019π0.548019\pi
510510 1.06915 + 6.32730i 0.0473430 + 0.280177i
511511 9.89000 0.437508
512512 16.3850i 0.724123i
513513 −2.53734 2.53734i −0.112026 0.112026i
514514 −12.9487 −0.571142
515515 −5.79217 5.79217i −0.255234 0.255234i
516516 10.9782 10.9782i 0.483290 0.483290i
517517 22.8771 22.8771i 1.00613 1.00613i
518518 5.06487i 0.222538i
519519 11.1650i 0.490088i
520520 17.6365 17.6365i 0.773412 0.773412i
521521 9.60414 9.60414i 0.420765 0.420765i −0.464702 0.885467i 0.653839π-0.653839\pi
0.885467 + 0.464702i 0.153839π0.153839\pi
522522 2.69228 + 2.69228i 0.117838 + 0.117838i
523523 −43.7951 −1.91502 −0.957512 0.288392i 0.906879π-0.906879\pi
−0.957512 + 0.288392i 0.906879π0.906879\pi
524524 10.0965 + 10.0965i 0.441065 + 0.441065i
525525 0.535927i 0.0233898i
526526 15.5020 0.675919
527527 −0.477169 + 0.671218i −0.0207858 + 0.0292387i
528528 −8.22373 −0.357892
529529 22.6357i 0.984161i
530530 10.4325 + 10.4325i 0.453159 + 0.453159i
531531 1.92313 0.0834568
532532 3.96448 + 3.96448i 0.171882 + 0.171882i
533533 −19.3884 + 19.3884i −0.839805 + 0.839805i
534534 −5.75492 + 5.75492i −0.249040 + 0.249040i
535535 10.9331i 0.472681i
536536 17.6089i 0.760589i
537537 −1.69403 + 1.69403i −0.0731026 + 0.0731026i
538538 −3.74360 + 3.74360i −0.161398 + 0.161398i
539539 −3.71291 3.71291i −0.159926 0.159926i
540540 −3.67623 −0.158200
541541 −1.33085 1.33085i −0.0572177 0.0572177i 0.677919 0.735137i 0.262882π-0.262882\pi
−0.735137 + 0.677919i 0.762882π0.762882\pi
542542 16.2714i 0.698915i
543543 19.6381 0.842752
544544 23.3720 3.94929i 1.00207 0.169324i
545545 −32.7822 −1.40424
546546 2.97566i 0.127347i
547547 −12.7406 12.7406i −0.544751 0.544751i 0.380167 0.924918i 0.375866π-0.375866\pi
−0.924918 + 0.380167i 0.875866π0.875866\pi
548548 −11.7733 −0.502932
549549 −7.45587 7.45587i −0.318209 0.318209i
550550 −1.31623 + 1.31623i −0.0561242 + 0.0561242i
551551 −14.6050 + 14.6050i −0.622196 + 0.622196i
552552 1.42230i 0.0605373i
553553 10.4711i 0.445275i
554554 12.5187 12.5187i 0.531869 0.531869i
555555 −12.7390 + 12.7390i −0.540742 + 0.540742i
556556 −0.569983 0.569983i −0.0241726 0.0241726i
557557 −19.5144 −0.826851 −0.413426 0.910538i 0.635668π-0.635668\pi
−0.413426 + 0.910538i 0.635668π0.635668\pi
558558 0.0934241 + 0.0934241i 0.00395496 + 0.00395496i
559559 44.7005i 1.89063i
560560 3.68497 0.155719
561561 3.60714 + 21.3472i 0.152294 + 0.901279i
562562 −16.0723 −0.677970
563563 32.4814i 1.36893i 0.729046 + 0.684465i 0.239964π0.239964\pi
−0.729046 + 0.684465i 0.760036π0.760036\pi
564564 −6.80735 6.80735i −0.286641 0.286641i
565565 23.2534 0.978278
566566 −4.28759 4.28759i −0.180221 0.180221i
567567 0.707107 0.707107i 0.0296957 0.0296957i
568568 2.57312 2.57312i 0.107966 0.107966i
569569 32.6889i 1.37039i −0.728361 0.685194i 0.759717π-0.759717\pi
0.728361 0.685194i 0.240283π-0.240283\pi
570570 5.58471i 0.233918i
571571 13.8918 13.8918i 0.581353 0.581353i −0.353922 0.935275i 0.615152π-0.615152\pi
0.935275 + 0.353922i 0.115152π0.115152\pi
572572 26.0972 26.0972i 1.09118 1.09118i
573573 −3.69608 3.69608i −0.154406 0.154406i
574574 4.03178 0.168283
575575 0.228729 + 0.228729i 0.00953867 + 0.00953867i
576576 0.670404i 0.0279335i
577577 −22.6080 −0.941182 −0.470591 0.882351i 0.655959π-0.655959\pi
−0.470591 + 0.882351i 0.655959π0.655959\pi
578578 −3.69476 10.6207i −0.153682 0.441763i
579579 21.6970 0.901696
580580 21.1605i 0.878643i
581581 −5.72257 5.72257i −0.237412 0.237412i
582582 5.46277 0.226439
583583 35.1974 + 35.1974i 1.45773 + 1.45773i
584584 16.4794 16.4794i 0.681924 0.681924i
585585 7.48431 7.48431i 0.309438 0.309438i
586586 1.45324i 0.0600330i
587587 1.89079i 0.0780414i 0.999238 + 0.0390207i 0.0124238π0.0124238\pi
−0.999238 + 0.0390207i 0.987576π0.987576\pi
588588 −1.10482 + 1.10482i −0.0455621 + 0.0455621i
589589 −0.506805 + 0.506805i −0.0208825 + 0.0208825i
590590 −2.11642 2.11642i −0.0871314 0.0871314i
591591 −6.69620 −0.275445
592592 8.47970 + 8.47970i 0.348514 + 0.348514i
593593 33.0067i 1.35542i −0.735329 0.677711i 0.762972π-0.762972\pi
0.735329 0.677711i 0.237028π-0.237028\pi
594594 3.47329 0.142511
595595 −1.61632 9.56547i −0.0662629 0.392146i
596596 3.51470 0.143968
597597 6.71661i 0.274892i
598598 1.26999 + 1.26999i 0.0519337 + 0.0519337i
599599 −12.9658 −0.529767 −0.264884 0.964280i 0.585334π-0.585334\pi
−0.264884 + 0.964280i 0.585334π0.585334\pi
600600 0.893000 + 0.893000i 0.0364566 + 0.0364566i
601601 24.5515 24.5515i 1.00148 1.00148i 0.00147859 0.999999i 0.499529π-0.499529\pi
0.999999 0.00147859i 0.000470649π-0.000470649\pi
602602 4.64769 4.64769i 0.189426 0.189426i
603603 7.47259i 0.304307i
604604 15.7877i 0.642392i
605605 −27.5702 + 27.5702i −1.12089 + 1.12089i
606606 5.78175 5.78175i 0.234868 0.234868i
607607 14.3918 + 14.3918i 0.584143 + 0.584143i 0.936039 0.351896i 0.114463π-0.114463\pi
−0.351896 + 0.936039i 0.614463π0.614463\pi
608608 20.6291 0.836619
609609 −4.07014 4.07014i −0.164930 0.164930i
610610 16.4104i 0.664439i
611611 27.7177 1.12134
612612 6.35212 1.07335i 0.256769 0.0433875i
613613 34.0233 1.37419 0.687095 0.726568i 0.258886π-0.258886\pi
0.687095 + 0.726568i 0.258886π0.258886\pi
614614 13.9496i 0.562960i
615615 −10.1406 10.1406i −0.408910 0.408910i
616616 −12.3734 −0.498540
617617 −20.8759 20.8759i −0.840433 0.840433i 0.148482 0.988915i 0.452561π-0.452561\pi
−0.988915 + 0.148482i 0.952561π0.952561\pi
618618 1.62839 1.62839i 0.0655034 0.0655034i
619619 4.38648 4.38648i 0.176308 0.176308i −0.613436 0.789744i 0.710213π-0.710213\pi
0.789744 + 0.613436i 0.210213π0.210213\pi
620620 0.734285i 0.0294896i
621621 0.603575i 0.0242206i
622622 5.27541 5.27541i 0.211525 0.211525i
623623 8.70017 8.70017i 0.348565 0.348565i
624624 −4.98191 4.98191i −0.199436 0.199436i
625625 27.3924 1.09570
626626 −9.32128 9.32128i −0.372553 0.372553i
627627 18.8418i 0.752471i
628628 −36.9744 −1.47544
629629 18.2922 25.7311i 0.729359 1.02597i
630630 −1.55635 −0.0620064
631631 5.22637i 0.208059i −0.994574 0.104029i 0.966826π-0.966826\pi
0.994574 0.104029i 0.0331736π-0.0331736\pi
632632 17.4476 + 17.4476i 0.694030 + 0.694030i
633633 13.1733 0.523592
634634 −14.2710 14.2710i −0.566774 0.566774i
635635 −24.6551 + 24.6551i −0.978408 + 0.978408i
636636 10.4734 10.4734i 0.415298 0.415298i
637637 4.49854i 0.178239i
638638 19.9924i 0.791507i
639639 1.09194 1.09194i 0.0431965 0.0431965i
640640 18.3914 18.3914i 0.726983 0.726983i
641641 −16.2540 16.2540i −0.641994 0.641994i 0.309051 0.951045i 0.399989π-0.399989\pi
−0.951045 + 0.309051i 0.899989π0.899989\pi
642642 −3.07370 −0.121309
643643 −2.55336 2.55336i −0.100695 0.100695i 0.654965 0.755659i 0.272683π-0.272683\pi
−0.755659 + 0.654965i 0.772683π0.772683\pi
644644 0.943058i 0.0371617i
645645 −23.3795 −0.920568
646646 −1.63057 9.64977i −0.0641539 0.379665i
647647 7.56712 0.297494 0.148747 0.988875i 0.452476π-0.452476\pi
0.148747 + 0.988875i 0.452476π0.452476\pi
648648 2.35647i 0.0925707i
649649 −7.14041 7.14041i −0.280286 0.280286i
650650 −1.59474 −0.0625507
651651 −0.141237 0.141237i −0.00553550 0.00553550i
652652 26.4606 26.4606i 1.03628 1.03628i
653653 −11.7538 + 11.7538i −0.459964 + 0.459964i −0.898643 0.438680i 0.855446π-0.855446\pi
0.438680 + 0.898643i 0.355446π0.355446\pi
654654 9.21627i 0.360384i
655655 21.5016i 0.840139i
656656 −6.75009 + 6.75009i −0.263547 + 0.263547i
657657 6.99329 6.99329i 0.272834 0.272834i
658658 −2.88192 2.88192i −0.112349 0.112349i
659659 −20.8412 −0.811859 −0.405929 0.913904i 0.633052π-0.633052\pi
−0.405929 + 0.913904i 0.633052π0.633052\pi
660660 13.6495 + 13.6495i 0.531306 + 0.531306i
661661 8.01914i 0.311908i 0.987764 + 0.155954i 0.0498452π0.0498452\pi
−0.987764 + 0.155954i 0.950155π0.950155\pi
662662 −16.4044 −0.637574
663663 −10.7469 + 15.1173i −0.417374 + 0.587106i
664664 −19.0707 −0.740088
665665 8.44285i 0.327400i
666666 −3.58140 3.58140i −0.138777 0.138777i
667667 −3.47420 −0.134522
668668 27.8130 + 27.8130i 1.07612 + 1.07612i
669669 −8.53825 + 8.53825i −0.330108 + 0.330108i
670670 −8.22362 + 8.22362i −0.317706 + 0.317706i
671671 55.3659i 2.13738i
672672 5.74891i 0.221769i
673673 −2.05382 + 2.05382i −0.0791688 + 0.0791688i −0.745582 0.666414i 0.767829π-0.767829\pi
0.666414 + 0.745582i 0.267829π0.267829\pi
674674 −4.08590 + 4.08590i −0.157383 + 0.157383i
675675 0.378957 + 0.378957i 0.0145861 + 0.0145861i
676676 11.3073 0.434894
677677 −10.6917 10.6917i −0.410917 0.410917i 0.471141 0.882058i 0.343842π-0.343842\pi
−0.882058 + 0.471141i 0.843842π0.843842\pi
678678 6.53737i 0.251066i
679679 −8.25850 −0.316932
680680 −18.6319 13.2454i −0.714502 0.507940i
681681 −9.96214 −0.381750
682682 0.693751i 0.0265651i
683683 −14.5366 14.5366i −0.556228 0.556228i 0.372003 0.928231i 0.378671π-0.378671\pi
−0.928231 + 0.372003i 0.878671π0.878671\pi
684684 5.60662 0.214374
685685 12.5364 + 12.5364i 0.478991 + 0.478991i
686686 −0.467732 + 0.467732i −0.0178581 + 0.0178581i
687687 0.241494 0.241494i 0.00921357 0.00921357i
688688 15.5625i 0.593315i
689689 42.6450i 1.62464i
690690 −0.664237 + 0.664237i −0.0252871 + 0.0252871i
691691 −10.5531 + 10.5531i −0.401458 + 0.401458i −0.878747 0.477288i 0.841620π-0.841620\pi
0.477288 + 0.878747i 0.341620π0.341620\pi
692692 12.3353 + 12.3353i 0.468918 + 0.468918i
693693 −5.25085 −0.199463
694694 −3.73797 3.73797i −0.141891 0.141891i
695695 1.21385i 0.0460439i
696696 −13.5639 −0.514139
697697 20.4827 + 14.5612i 0.775837 + 0.551543i
698698 13.3745 0.506234
699699 15.8961i 0.601245i
700700 −0.592104 0.592104i −0.0223794 0.0223794i
701701 42.2529 1.59587 0.797936 0.602743i 0.205925π-0.205925\pi
0.797936 + 0.602743i 0.205925π0.205925\pi
702702 2.10411 + 2.10411i 0.0794145 + 0.0794145i
703703 19.4283 19.4283i 0.732753 0.732753i
704704 −2.48915 + 2.48915i −0.0938134 + 0.0938134i
705705 14.4971i 0.545992i
706706 0.240607i 0.00905535i
707707 −8.74073 + 8.74073i −0.328729 + 0.328729i
708708 −2.12472 + 2.12472i −0.0798518 + 0.0798518i
709709 29.5551 + 29.5551i 1.10997 + 1.10997i 0.993154 + 0.116813i 0.0372678π0.0372678\pi
0.116813 + 0.993154i 0.462732π0.462732\pi
710710 −2.40337 −0.0901970
711711 7.40415 + 7.40415i 0.277677 + 0.277677i
712712 28.9937i 1.08658i
713713 −0.120557 −0.00451491
714714 2.68920 0.454407i 0.100641 0.0170058i
715715 −55.5771 −2.07847
716716 3.74319i 0.139890i
717717 0.821168 + 0.821168i 0.0306671 + 0.0306671i
718718 17.4135 0.649867
719719 −18.4733 18.4733i −0.688936 0.688936i 0.273060 0.961997i 0.411964π-0.411964\pi
−0.961997 + 0.273060i 0.911964π0.911964\pi
720720 2.60567 2.60567i 0.0971076 0.0971076i
721721 −2.46176 + 2.46176i −0.0916809 + 0.0916809i
722722 4.05073i 0.150752i
723723 9.12543i 0.339379i
724724 −21.6966 + 21.6966i −0.806348 + 0.806348i
725725 2.18130 2.18130i 0.0810113 0.0810113i
726726 −7.75097 7.75097i −0.287666 0.287666i
727727 −18.5323 −0.687325 −0.343663 0.939093i 0.611668π-0.611668\pi
−0.343663 + 0.939093i 0.611668π0.611668\pi
728728 −7.49579 7.49579i −0.277813 0.277813i
729729 1.00000i 0.0370370i
730730 −15.3923 −0.569695
731731 40.3973 6.82612i 1.49415 0.252473i
732732 16.4748 0.608927
733733 42.9060i 1.58477i 0.610021 + 0.792385i 0.291161π0.291161\pi
−0.610021 + 0.792385i 0.708839π0.708839\pi
734734 −4.62847 4.62847i −0.170840 0.170840i
735735 2.35286 0.0867864
736736 2.45359 + 2.45359i 0.0904405 + 0.0904405i
737737 −27.7451 + 27.7451i −1.02200 + 1.02200i
738738 2.85090 2.85090i 0.104943 0.104943i
739739 19.1622i 0.704893i 0.935832 + 0.352446i 0.114650π0.114650\pi
−0.935832 + 0.352446i 0.885350π0.885350\pi
740740 28.1487i 1.03477i
741741 −11.4143 + 11.4143i −0.419316 + 0.419316i
742742 4.43397 4.43397i 0.162776 0.162776i
743743 −20.2472 20.2472i −0.742797 0.742797i 0.230319 0.973115i 0.426023π-0.426023\pi
−0.973115 + 0.230319i 0.926023π0.926023\pi
744744 −0.470677 −0.0172559
745745 −3.74250 3.74250i −0.137115 0.137115i
746746 8.54340i 0.312796i
747747 −8.09294 −0.296105
748748 −27.5701 19.5996i −1.00806 0.716632i
749749 4.64675 0.169789
750750 6.94766i 0.253693i
751751 −6.54293 6.54293i −0.238755 0.238755i 0.577580 0.816334i 0.303997π-0.303997\pi
−0.816334 + 0.577580i 0.803997π0.803997\pi
752752 9.64994 0.351897
753753 1.43164 + 1.43164i 0.0521717 + 0.0521717i
754754 12.1113 12.1113i 0.441069 0.441069i
755755 16.8109 16.8109i 0.611812 0.611812i
756756 1.56245i 0.0568259i
757757 30.7343i 1.11706i 0.829485 + 0.558529i 0.188634π0.188634\pi
−0.829485 + 0.558529i 0.811366π0.811366\pi
758758 −7.44352 + 7.44352i −0.270361 + 0.270361i
759759 −2.24102 + 2.24102i −0.0813439 + 0.0813439i
760760 −14.0681 14.0681i −0.510303 0.510303i
761761 2.54666 0.0923164 0.0461582 0.998934i 0.485302π-0.485302\pi
0.0461582 + 0.998934i 0.485302π0.485302\pi
762762 −6.93144 6.93144i −0.251100 0.251100i
763763 13.9330i 0.504407i
764764 8.16703 0.295473
765765 −7.90672 5.62090i −0.285868 0.203224i
766766 −12.6886 −0.458459
767767 8.65128i 0.312380i
768768 6.11857 + 6.11857i 0.220785 + 0.220785i
769769 8.31448 0.299828 0.149914 0.988699i 0.452100π-0.452100\pi
0.149914 + 0.988699i 0.452100π0.452100\pi
770770 5.77858 + 5.77858i 0.208246 + 0.208246i
771771 13.8420 13.8420i 0.498508 0.498508i
772772 −23.9713 + 23.9713i −0.862746 + 0.862746i
773773 37.8279i 1.36058i −0.732945 0.680288i 0.761855π-0.761855\pi
0.732945 0.680288i 0.238145π-0.238145\pi
774774 6.57283i 0.236256i
775775 0.0756925 0.0756925i 0.00271895 0.00271895i
776776 −13.7609 + 13.7609i −0.493988 + 0.493988i
777777 5.41429 + 5.41429i 0.194237 + 0.194237i
778778 16.2713 0.583353
779779 15.4655 + 15.4655i 0.554110 + 0.554110i
780780 16.5377i 0.592143i
781781 −8.10856 −0.290147
782782 0.953792 1.34167i 0.0341075 0.0479779i
783783 −5.75604 −0.205704
784784 1.56617i 0.0559347i
785785 39.3708 + 39.3708i 1.40520 + 1.40520i
786786 6.04489 0.215614
787787 −31.9408 31.9408i −1.13857 1.13857i −0.988707 0.149859i 0.952118π-0.952118\pi
−0.149859 0.988707i 0.547882π-0.547882\pi
788788 7.39811 7.39811i 0.263547 0.263547i
789789 −16.5715 + 16.5715i −0.589959 + 0.589959i
790790 16.2966i 0.579808i
791791 9.88305i 0.351401i
792792 −8.74934 + 8.74934i −0.310894 + 0.310894i
793793 −33.5405 + 33.5405i −1.19106 + 1.19106i
794794 −10.4457 10.4457i −0.370705 0.370705i
795795 −22.3044 −0.791057
796796 −7.42066 7.42066i −0.263018 0.263018i
797797 6.59399i 0.233571i 0.993157 + 0.116786i 0.0372590π0.0372590\pi
−0.993157 + 0.116786i 0.962741π0.962741\pi
798798 2.37359 0.0840242
799799 −4.23272 25.0494i −0.149743 0.886183i
800800 −3.08099 −0.108930
801801 12.3039i 0.434737i
802802 −12.0872 12.0872i −0.426813 0.426813i
803803 −51.9309 −1.83260
804804 8.25588 + 8.25588i 0.291163 + 0.291163i
805805 1.00418 1.00418i 0.0353927 0.0353927i
806806 0.420272 0.420272i 0.0148035 0.0148035i
807807 8.00374i 0.281745i
808808 29.1289i 1.02475i
809809 −28.8037 + 28.8037i −1.01268 + 1.01268i −0.0127642 + 0.999919i 0.504063π0.504063\pi
−0.999919 + 0.0127642i 0.995937π0.995937\pi
810810 −1.10050 + 1.10050i −0.0386678 + 0.0386678i
811811 12.4244 + 12.4244i 0.436279 + 0.436279i 0.890758 0.454479i 0.150175π-0.150175\pi
−0.454479 + 0.890758i 0.650175π0.650175\pi
812812 8.99355 0.315612
813813 −17.3939 17.3939i −0.610031 0.610031i
814814 26.5949i 0.932149i
815815 −56.3512 −1.97390
816816 −3.74153 + 5.26309i −0.130980 + 0.184245i
817817 35.6562 1.24745
818818 10.4256i 0.364521i
819819 −3.18095 3.18095i −0.111151 0.111151i
820820 22.4072 0.782494
821821 −2.39839 2.39839i −0.0837045 0.0837045i 0.664015 0.747719i 0.268851π-0.268851\pi
−0.747719 + 0.664015i 0.768851π0.768851\pi
822822 −3.52443 + 3.52443i −0.122929 + 0.122929i
823823 −17.9237 + 17.9237i −0.624781 + 0.624781i −0.946750 0.321969i 0.895655π-0.895655\pi
0.321969 + 0.946750i 0.395655π0.395655\pi
824824 8.20394i 0.285798i
825825 2.81407i 0.0979733i
826826 −0.899509 + 0.899509i −0.0312979 + 0.0312979i
827827 5.93889 5.93889i 0.206516 0.206516i −0.596269 0.802785i 0.703351π-0.703351\pi
0.802785 + 0.596269i 0.203351π0.203351\pi
828828 0.666843 + 0.666843i 0.0231744 + 0.0231744i
829829 0.720245 0.0250151 0.0125076 0.999922i 0.496019π-0.496019\pi
0.0125076 + 0.999922i 0.496019π0.496019\pi
830830 8.90632 + 8.90632i 0.309143 + 0.309143i
831831 26.7647i 0.928458i
832832 −3.01584 −0.104555
833833 −4.06547 + 0.686963i −0.140860 + 0.0238019i
834834 −0.341257 −0.0118168
835835 59.2311i 2.04978i
836836 −20.8169 20.8169i −0.719967 0.719967i
837837 −0.199739 −0.00690398
838838 6.27710 + 6.27710i 0.216839 + 0.216839i
839839 −31.6356 + 31.6356i −1.09218 + 1.09218i −0.0968861 + 0.995295i 0.530888π0.530888\pi
−0.995295 + 0.0968861i 0.969112π0.969112\pi
840840 3.92050 3.92050i 0.135270 0.135270i
841841 4.13202i 0.142484i
842842 6.79724i 0.234248i
843843 17.1811 17.1811i 0.591749 0.591749i
844844 −14.5542 + 14.5542i −0.500975 + 0.500975i
845845 −12.0401 12.0401i −0.414192 0.414192i
846846 −4.07566 −0.140124
847847 11.7178 + 11.7178i 0.402627 + 0.402627i
848848 14.8469i 0.509844i
849849 9.16677 0.314603
850850 0.243529 + 1.44121i 0.00835298 + 0.0494332i
851851 4.62155 0.158425
852852 2.41280i 0.0826612i
853853 4.85222 + 4.85222i 0.166137 + 0.166137i 0.785279 0.619142i 0.212519π-0.212519\pi
−0.619142 + 0.785279i 0.712519π0.712519\pi
854854 6.97469 0.238669
855855 −5.97000 5.97000i −0.204170 0.204170i
856856 7.74276 7.74276i 0.264642 0.264642i
857857 14.6055 14.6055i 0.498916 0.498916i −0.412185 0.911100i 0.635234π-0.635234\pi
0.911100 + 0.412185i 0.135234π0.135234\pi
858858 15.6247i 0.533420i
859859 5.76996i 0.196868i 0.995144 + 0.0984342i 0.0313834π0.0313834\pi
−0.995144 + 0.0984342i 0.968617π0.968617\pi
860860 25.8302 25.8302i 0.880803 0.880803i
861861 −4.30993 + 4.30993i −0.146882 + 0.146882i
862862 13.4752 + 13.4752i 0.458967 + 0.458967i
863863 45.6981 1.55558 0.777790 0.628524i 0.216341π-0.216341\pi
0.777790 + 0.628524i 0.216341π0.216341\pi
864864 4.06509 + 4.06509i 0.138297 + 0.138297i
865865 26.2696i 0.893191i
866866 16.8532 0.572696
867867 15.3031 + 7.40376i 0.519720 + 0.251445i
868868 0.312083 0.0105928
869869 54.9819i 1.86513i
870870 6.33455 + 6.33455i 0.214761 + 0.214761i
871871 −33.6158 −1.13903
872872 23.2161 + 23.2161i 0.786196 + 0.786196i
873873 −5.83964 + 5.83964i −0.197642 + 0.197642i
874874 1.01303 1.01303i 0.0342662 0.0342662i
875875 10.5033i 0.355077i
876876 15.4527i 0.522098i
877877 4.16940 4.16940i 0.140791 0.140791i −0.633199 0.773989i 0.718258π-0.718258\pi
0.773989 + 0.633199i 0.218258π0.218258\pi
878878 15.8452 15.8452i 0.534751 0.534751i
879879 −1.55350 1.55350i −0.0523983 0.0523983i
880880 −19.3492 −0.652263
881881 −20.0194 20.0194i −0.674471 0.674471i 0.284273 0.958744i 0.408248π-0.408248\pi
−0.958744 + 0.284273i 0.908248π0.908248\pi
882882 0.661473i 0.0222729i
883883 −39.7453 −1.33754 −0.668768 0.743471i 0.733178π-0.733178\pi
−0.668768 + 0.743471i 0.733178π0.733178\pi
884884 −4.82850 28.5752i −0.162400 0.961090i
885885 4.52485 0.152101
886886 7.04875i 0.236807i
887887 9.02914 + 9.02914i 0.303169 + 0.303169i 0.842252 0.539083i 0.181229π-0.181229\pi
−0.539083 + 0.842252i 0.681229π0.681229\pi
888888 18.0434 0.605496
889889 10.4788 + 10.4788i 0.351448 + 0.351448i
890890 −13.5405 + 13.5405i −0.453878 + 0.453878i
891891 −3.71291 + 3.71291i −0.124387 + 0.124387i
892892 18.8665i 0.631697i
893893 22.1095i 0.739867i
894894 1.05215 1.05215i 0.0351892 0.0351892i
895895 −3.98580 + 3.98580i −0.133230 + 0.133230i
896896 −7.81662 7.81662i −0.261135 0.261135i
897897 −2.71521 −0.0906581
898898 19.2697 + 19.2697i 0.643037 + 0.643037i
899899 1.14970i 0.0383448i
900900 −0.837361 −0.0279120
901901 38.5396 6.51223i 1.28394 0.216954i
902902 −21.1703 −0.704893
903903 9.93667i 0.330672i
904904 −16.4679 16.4679i −0.547713 0.547713i
905905 46.2056 1.53593
906906 4.72616 + 4.72616i 0.157016 + 0.157016i
907907 8.76923 8.76923i 0.291177 0.291177i −0.546368 0.837545i 0.683990π-0.683990\pi
0.837545 + 0.546368i 0.183990π0.183990\pi
908908 11.0064 11.0064i 0.365260 0.365260i
909909 12.3613i 0.409997i
910910 7.00130i 0.232091i
911911 −4.06611 + 4.06611i −0.134716 + 0.134716i −0.771249 0.636533i 0.780368π-0.780368\pi
0.636533 + 0.771249i 0.280368π0.280368\pi
912912 −3.97391 + 3.97391i −0.131589 + 0.131589i
913913 30.0484 + 30.0484i 0.994455 + 0.994455i
914914 27.8927 0.922610
915915 −17.5426 17.5426i −0.579940 0.579940i
916916 0.533616i 0.0176312i
917917 −9.13853 −0.301781
918918 1.58024 2.22287i 0.0521556 0.0733655i
919919 −42.2895 −1.39500 −0.697500 0.716585i 0.745704π-0.745704\pi
−0.697500 + 0.716585i 0.745704π0.745704\pi
920920 3.34648i 0.110330i
921921 −14.9120 14.9120i −0.491366 0.491366i
922922 5.35029 0.176202
923923 −4.91214 4.91214i −0.161685 0.161685i
924924 5.80125 5.80125i 0.190847 0.190847i
925925 −2.90166 + 2.90166i −0.0954061 + 0.0954061i
926926 20.5938i 0.676754i
927927 3.48146i 0.114346i
928928 23.3988 23.3988i 0.768105 0.768105i
929929 8.33116 8.33116i 0.273337 0.273337i −0.557105 0.830442i 0.688088π-0.688088\pi
0.830442 + 0.557105i 0.188088π0.188088\pi
930930 0.219813 + 0.219813i 0.00720797 + 0.00720797i
931931 −3.58834 −0.117603
932932 17.5623 + 17.5623i 0.575273 + 0.575273i
933933 11.2787i 0.369248i
934934 −4.89457 −0.160155
935935 8.48708 + 50.2268i 0.277557 + 1.64259i
936936 −10.6007 −0.346493
937937 39.3993i 1.28712i −0.765396 0.643560i 0.777457π-0.777457\pi
0.765396 0.643560i 0.222543π-0.222543\pi
938938 3.49517 + 3.49517i 0.114121 + 0.114121i
939939 19.9287 0.650348
940940 −16.0167 16.0167i −0.522407 0.522407i
941941 −1.20597 + 1.20597i −0.0393135 + 0.0393135i −0.726490 0.687177i 0.758850π-0.758850\pi
0.687177 + 0.726490i 0.258850π0.258850\pi
942942 −11.0686 + 11.0686i −0.360633 + 0.360633i
943943 3.67889i 0.119801i
944944 3.01195i 0.0980307i
945945 1.66372 1.66372i 0.0541208 0.0541208i
946946 −24.4043 + 24.4043i −0.793453 + 0.793453i
947947 −27.1014 27.1014i −0.880678 0.880678i 0.112926 0.993603i 0.463978π-0.463978\pi
−0.993603 + 0.112926i 0.963978π0.963978\pi
948948 −16.3605 −0.531366
949949 −31.4596 31.4596i −1.02122 1.02122i
950950 1.27207i 0.0412714i
951951 30.5111 0.989390
952952 −5.62952 + 7.91886i −0.182454 + 0.256652i
953953 −43.5262 −1.40995 −0.704975 0.709232i 0.749042π-0.749042\pi
−0.704975 + 0.709232i 0.749042π0.749042\pi
954954 6.27059i 0.203018i
955955 −8.69635 8.69635i −0.281407 0.281407i
956956 −1.81449 −0.0586848
957957 21.3717 + 21.3717i 0.690848 + 0.690848i
958958 −12.6822 + 12.6822i −0.409742 + 0.409742i
959959 5.32816 5.32816i 0.172055 0.172055i
960960 1.57736i 0.0509092i
961961 30.9601i 0.998713i
962962 −16.1111 + 16.1111i −0.519442 + 0.519442i
963963 3.28575 3.28575i 0.105882 0.105882i
964964 10.0820 + 10.0820i 0.324719 + 0.324719i
965965 51.0498 1.64335
966966 0.282311 + 0.282311i 0.00908322 + 0.00908322i
967967 9.46568i 0.304396i −0.988350 0.152198i 0.951365π-0.951365\pi
0.988350 0.152198i 0.0486351π-0.0486351\pi
968968 39.0499 1.25511
969969 12.0586 + 8.57243i 0.387377 + 0.275386i
970970 12.8531 0.412688
971971 1.89708i 0.0608801i 0.999537 + 0.0304400i 0.00969086π0.00969086\pi
−0.999537 + 0.0304400i 0.990309π0.990309\pi
972972 1.10482 + 1.10482i 0.0354372 + 0.0354372i
973973 0.515904 0.0165391
974974 14.7335 + 14.7335i 0.472092 + 0.472092i
975975 1.70476 1.70476i 0.0545959 0.0545959i
976976 −11.6772 + 11.6772i −0.373777 + 0.373777i
977977 13.9325i 0.445739i 0.974848 + 0.222869i 0.0715423π0.0715423\pi
−0.974848 + 0.222869i 0.928458π0.928458\pi
978978 15.8424i 0.506583i
979979 −45.6832 + 45.6832i −1.46004 + 1.46004i
980980 −2.59949 + 2.59949i −0.0830375 + 0.0830375i
981981 9.85208 + 9.85208i 0.314553 + 0.314553i
982982 −2.09931 −0.0669917
983983 −18.0017 18.0017i −0.574164 0.574164i 0.359125 0.933289i 0.383075π-0.383075\pi
−0.933289 + 0.359125i 0.883075π0.883075\pi
984984 14.3630i 0.457877i
985985 −15.7552 −0.502002
986986 −12.7949 9.09591i −0.407473 0.289673i
987987 6.16149 0.196122
988988 25.2216i 0.802406i
989989 4.24089 + 4.24089i 0.134852 + 0.134852i
990990 8.17215 0.259728
991991 21.4207 + 21.4207i 0.680452 + 0.680452i 0.960102 0.279650i 0.0902184π-0.0902184\pi
−0.279650 + 0.960102i 0.590218π0.590218\pi
992992 0.811957 0.811957i 0.0257796 0.0257796i
993993 17.5361 17.5361i 0.556491 0.556491i
994994 1.02147i 0.0323991i
995995 15.8032i 0.500995i
996996 8.94126 8.94126i 0.283315 0.283315i
997997 21.0161 21.0161i 0.665587 0.665587i −0.291104 0.956691i 0.594023π-0.594023\pi
0.956691 + 0.291104i 0.0940227π0.0940227\pi
998998 −4.68763 4.68763i −0.148384 0.148384i
999999 7.65696 0.242256
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 357.2.k.b.64.7 20
3.2 odd 2 1071.2.n.b.64.4 20
17.2 even 8 6069.2.a.bd.1.4 10
17.4 even 4 inner 357.2.k.b.106.4 yes 20
17.15 even 8 6069.2.a.be.1.4 10
51.38 odd 4 1071.2.n.b.820.7 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
357.2.k.b.64.7 20 1.1 even 1 trivial
357.2.k.b.106.4 yes 20 17.4 even 4 inner
1071.2.n.b.64.4 20 3.2 odd 2
1071.2.n.b.820.7 20 51.38 odd 4
6069.2.a.bd.1.4 10 17.2 even 8
6069.2.a.be.1.4 10 17.15 even 8