Properties

Label 170.2.r.b.23.1
Level 170170
Weight 22
Character 170.23
Analytic conductor 1.3571.357
Analytic rank 00
Dimension 4040
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [170,2,Mod(23,170)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(170, base_ring=CyclotomicField(16))
 
chi = DirichletCharacter(H, H._module([12, 15]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("170.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 170=2517 170 = 2 \cdot 5 \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 170.r (of order 1616, degree 88, 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: 1.357456834361.35745683436
Analytic rank: 00
Dimension: 4040
Relative dimension: 55 over Q(ζ16)\Q(\zeta_{16})
Twist minimal: yes
Sato-Tate group: SU(2)[C16]\mathrm{SU}(2)[C_{16}]

Embedding invariants

Embedding label 23.1
Character χ\chi == 170.23
Dual form 170.2.r.b.37.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.9238800.382683i)q2+(2.479361.65666i)q3+(0.7071070.707107i)q4+(2.20283+0.384106i)q5+(2.924600.581740i)q6+(2.116000.420899i)q7+(0.3826830.923880i)q8+(2.25467+5.44325i)q9+(1.88816+1.19785i)q10+(0.5811412.92159i)q11+(2.92460+0.581740i)q125.10274q13+(2.11600+0.420899i)q14+(6.09794+2.69699i)q151.00000iq16+(2.911012.91993i)q17+(4.16608+4.16608i)q18+(2.473065.97048i)q19+(1.28603+1.82924i)q20+(4.54905+4.54905i)q21+(0.5811412.92159i)q22+(0.847753+1.26875i)q23+(2.47936+1.65666i)q24+(4.704931.69224i)q25+(4.71431+1.95273i)q26+(1.682238.45716i)q27+(1.79386+1.19862i)q28+(3.82051+5.71779i)q29+(6.66586+0.158117i)q30+(0.9425524.73853i)q31+(0.3826830.923880i)q32+(6.28093+6.28093i)q33+(1.572023.81166i)q34+(4.82287+0.114401i)q35+(5.44325+2.25467i)q36+(4.043826.05201i)q376.46241iq38+(12.6515+8.45347i)q39+(0.488119+2.18214i)q40+(2.01733+3.01915i)q41+(5.94362+2.46193i)q42+(1.735290.718779i)q43+(1.654952.47681i)q44+(7.0574311.1245i)q45+(1.26875+0.847753i)q46+4.65062iq47+(1.65666+2.47936i)q48+(2.166840.897536i)q49+(3.699193.36392i)q50+(12.0548+2.41701i)q51+(3.60818+3.60818i)q52+(1.11881+2.70105i)q53+(1.682238.45716i)q54+(0.157954+6.65899i)q55+(1.19862+1.79386i)q56+(16.0226+10.7060i)q57+(1.34158+6.74460i)q58+(3.66553+1.51831i)q59+(6.218962.40483i)q60+(3.45296+2.30720i)q61+(2.684164.01713i)q62+(2.4798212.4669i)q63+(0.7071070.707107i)q64+(11.24051.95999i)q65+(3.39921+8.20642i)q66+(2.255902.25590i)q67+(0.006304154.12310i)q684.55013iq69+(4.499531.73994i)q70+(5.635091.12089i)q71+5.89173q72+(9.628891.91531i)q73+(1.420007.13883i)q74+(14.46873.59877i)q75+(2.473065.97048i)q76+(2.45939+5.93749i)q77+(14.9235+2.96847i)q78+(15.14073.01167i)q79+(0.384106+2.20283i)q80+(5.68322+5.68322i)q81+(3.01915+2.01733i)q82+(9.030703.74064i)q83+6.43332q84+(5.29091+7.55025i)q851.87826q86+(18.94487.84720i)q87+(2.476811.65495i)q88+(5.41083+5.41083i)q89+(10.77747.57696i)q90+(10.7974+2.14774i)q91+(1.49660+0.297691i)q92+(5.51318+13.3100i)q93+(1.77972+4.29662i)q94+(3.15442+14.1019i)q95+(0.581740+2.92460i)q96+(2.63292+0.523720i)q972.34537q98+(17.21323.42392i)q99+O(q100)q+(0.923880 - 0.382683i) q^{2} +(-2.47936 - 1.65666i) q^{3} +(0.707107 - 0.707107i) q^{4} +(-2.20283 + 0.384106i) q^{5} +(-2.92460 - 0.581740i) q^{6} +(-2.11600 - 0.420899i) q^{7} +(0.382683 - 0.923880i) q^{8} +(2.25467 + 5.44325i) q^{9} +(-1.88816 + 1.19785i) q^{10} +(0.581141 - 2.92159i) q^{11} +(-2.92460 + 0.581740i) q^{12} -5.10274 q^{13} +(-2.11600 + 0.420899i) q^{14} +(6.09794 + 2.69699i) q^{15} -1.00000i q^{16} +(2.91101 - 2.91993i) q^{17} +(4.16608 + 4.16608i) q^{18} +(2.47306 - 5.97048i) q^{19} +(-1.28603 + 1.82924i) q^{20} +(4.54905 + 4.54905i) q^{21} +(-0.581141 - 2.92159i) q^{22} +(0.847753 + 1.26875i) q^{23} +(-2.47936 + 1.65666i) q^{24} +(4.70493 - 1.69224i) q^{25} +(-4.71431 + 1.95273i) q^{26} +(1.68223 - 8.45716i) q^{27} +(-1.79386 + 1.19862i) q^{28} +(-3.82051 + 5.71779i) q^{29} +(6.66586 + 0.158117i) q^{30} +(-0.942552 - 4.73853i) q^{31} +(-0.382683 - 0.923880i) q^{32} +(-6.28093 + 6.28093i) q^{33} +(1.57202 - 3.81166i) q^{34} +(4.82287 + 0.114401i) q^{35} +(5.44325 + 2.25467i) q^{36} +(4.04382 - 6.05201i) q^{37} -6.46241i q^{38} +(12.6515 + 8.45347i) q^{39} +(-0.488119 + 2.18214i) q^{40} +(2.01733 + 3.01915i) q^{41} +(5.94362 + 2.46193i) q^{42} +(-1.73529 - 0.718779i) q^{43} +(-1.65495 - 2.47681i) q^{44} +(-7.05743 - 11.1245i) q^{45} +(1.26875 + 0.847753i) q^{46} +4.65062i q^{47} +(-1.65666 + 2.47936i) q^{48} +(-2.16684 - 0.897536i) q^{49} +(3.69919 - 3.36392i) q^{50} +(-12.0548 + 2.41701i) q^{51} +(-3.60818 + 3.60818i) q^{52} +(1.11881 + 2.70105i) q^{53} +(-1.68223 - 8.45716i) q^{54} +(-0.157954 + 6.65899i) q^{55} +(-1.19862 + 1.79386i) q^{56} +(-16.0226 + 10.7060i) q^{57} +(-1.34158 + 6.74460i) q^{58} +(-3.66553 + 1.51831i) q^{59} +(6.21896 - 2.40483i) q^{60} +(-3.45296 + 2.30720i) q^{61} +(-2.68416 - 4.01713i) q^{62} +(-2.47982 - 12.4669i) q^{63} +(-0.707107 - 0.707107i) q^{64} +(11.2405 - 1.95999i) q^{65} +(-3.39921 + 8.20642i) q^{66} +(-2.25590 - 2.25590i) q^{67} +(-0.00630415 - 4.12310i) q^{68} -4.55013i q^{69} +(4.49953 - 1.73994i) q^{70} +(5.63509 - 1.12089i) q^{71} +5.89173 q^{72} +(9.62889 - 1.91531i) q^{73} +(1.42000 - 7.13883i) q^{74} +(-14.4687 - 3.59877i) q^{75} +(-2.47306 - 5.97048i) q^{76} +(-2.45939 + 5.93749i) q^{77} +(14.9235 + 2.96847i) q^{78} +(-15.1407 - 3.01167i) q^{79} +(0.384106 + 2.20283i) q^{80} +(-5.68322 + 5.68322i) q^{81} +(3.01915 + 2.01733i) q^{82} +(9.03070 - 3.74064i) q^{83} +6.43332 q^{84} +(-5.29091 + 7.55025i) q^{85} -1.87826 q^{86} +(18.9448 - 7.84720i) q^{87} +(-2.47681 - 1.65495i) q^{88} +(-5.41083 + 5.41083i) q^{89} +(-10.7774 - 7.57696i) q^{90} +(10.7974 + 2.14774i) q^{91} +(1.49660 + 0.297691i) q^{92} +(-5.51318 + 13.3100i) q^{93} +(1.77972 + 4.29662i) q^{94} +(-3.15442 + 14.1019i) q^{95} +(-0.581740 + 2.92460i) q^{96} +(-2.63292 + 0.523720i) q^{97} -2.34537 q^{98} +(17.2132 - 3.42392i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 40q16q1016q18+8q258q26+24q278q28+8q29+16q3016q3132q33+8q3432q3532q3956q4124q42+16q43+16q44++160q99+O(q100) 40 q - 16 q^{10} - 16 q^{18} + 8 q^{25} - 8 q^{26} + 24 q^{27} - 8 q^{28} + 8 q^{29} + 16 q^{30} - 16 q^{31} - 32 q^{33} + 8 q^{34} - 32 q^{35} - 32 q^{39} - 56 q^{41} - 24 q^{42} + 16 q^{43} + 16 q^{44}+ \cdots + 160 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/170Z)×\left(\mathbb{Z}/170\mathbb{Z}\right)^\times.

nn 7171 137137
χ(n)\chi(n) e(1516)e\left(\frac{15}{16}\right) e(34)e\left(\frac{3}{4}\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 0.923880 0.382683i 0.653281 0.270598i
33 −2.47936 1.65666i −1.43146 0.956470i −0.998483 0.0550648i 0.982463π-0.982463\pi
−0.432976 0.901405i 0.642537π-0.642537\pi
44 0.707107 0.707107i 0.353553 0.353553i
55 −2.20283 + 0.384106i −0.985136 + 0.171777i
66 −2.92460 0.581740i −1.19396 0.237494i
77 −2.11600 0.420899i −0.799774 0.159085i −0.221749 0.975104i 0.571176π-0.571176\pi
−0.578025 + 0.816019i 0.696176π0.696176\pi
88 0.382683 0.923880i 0.135299 0.326641i
99 2.25467 + 5.44325i 0.751556 + 1.81442i
1010 −1.88816 + 1.19785i −0.597088 + 0.378795i
1111 0.581141 2.92159i 0.175220 0.880893i −0.788715 0.614758i 0.789253π-0.789253\pi
0.963936 0.266134i 0.0857465π-0.0857465\pi
1212 −2.92460 + 0.581740i −0.844260 + 0.167934i
1313 −5.10274 −1.41524 −0.707622 0.706591i 0.750232π-0.750232\pi
−0.707622 + 0.706591i 0.750232π0.750232\pi
1414 −2.11600 + 0.420899i −0.565526 + 0.112490i
1515 6.09794 + 2.69699i 1.57448 + 0.696361i
1616 1.00000i 0.250000i
1717 2.91101 2.91993i 0.706025 0.708187i
1818 4.16608 + 4.16608i 0.981955 + 0.981955i
1919 2.47306 5.97048i 0.567358 1.36972i −0.336416 0.941713i 0.609215π-0.609215\pi
0.903774 0.428010i 0.140785π-0.140785\pi
2020 −1.28603 + 1.82924i −0.287566 + 0.409031i
2121 4.54905 + 4.54905i 0.992684 + 0.992684i
2222 −0.581141 2.92159i −0.123900 0.622885i
2323 0.847753 + 1.26875i 0.176769 + 0.264553i 0.909265 0.416218i 0.136645π-0.136645\pi
−0.732496 + 0.680771i 0.761645π0.761645\pi
2424 −2.47936 + 1.65666i −0.506097 + 0.338163i
2525 4.70493 1.69224i 0.940985 0.338448i
2626 −4.71431 + 1.95273i −0.924553 + 0.382962i
2727 1.68223 8.45716i 0.323746 1.62758i
2828 −1.79386 + 1.19862i −0.339008 + 0.226518i
2929 −3.82051 + 5.71779i −0.709450 + 1.06177i 0.285200 + 0.958468i 0.407940π0.407940\pi
−0.994650 + 0.103300i 0.967060π0.967060\pi
3030 6.66586 + 0.158117i 1.21701 + 0.0288681i
3131 −0.942552 4.73853i −0.169287 0.851065i −0.968308 0.249761i 0.919648π-0.919648\pi
0.799020 0.601304i 0.205352π-0.205352\pi
3232 −0.382683 0.923880i −0.0676495 0.163320i
3333 −6.28093 + 6.28093i −1.09337 + 1.09337i
3434 1.57202 3.81166i 0.269599 0.653694i
3535 4.82287 + 0.114401i 0.815213 + 0.0193372i
3636 5.44325 + 2.25467i 0.907208 + 0.375778i
3737 4.04382 6.05201i 0.664801 0.994945i −0.333830 0.942633i 0.608341π-0.608341\pi
0.998631 0.0523113i 0.0166588π-0.0166588\pi
3838 6.46241i 1.04834i
3939 12.6515 + 8.45347i 2.02586 + 1.35364i
4040 −0.488119 + 2.18214i −0.0771784 + 0.345027i
4141 2.01733 + 3.01915i 0.315054 + 0.471511i 0.954873 0.297014i 0.0959908π-0.0959908\pi
−0.639819 + 0.768525i 0.720991π0.720991\pi
4242 5.94362 + 2.46193i 0.917120 + 0.379884i
4343 −1.73529 0.718779i −0.264629 0.109613i 0.246424 0.969162i 0.420744π-0.420744\pi
−0.511053 + 0.859549i 0.670744π0.670744\pi
4444 −1.65495 2.47681i −0.249493 0.373392i
4545 −7.05743 11.1245i −1.05206 1.65835i
4646 1.26875 + 0.847753i 0.187067 + 0.124994i
4747 4.65062i 0.678363i 0.940721 + 0.339182i 0.110150π0.110150\pi
−0.940721 + 0.339182i 0.889850π0.889850\pi
4848 −1.65666 + 2.47936i −0.239118 + 0.357865i
4949 −2.16684 0.897536i −0.309549 0.128219i
5050 3.69919 3.36392i 0.523145 0.475731i
5151 −12.0548 + 2.41701i −1.68801 + 0.338449i
5252 −3.60818 + 3.60818i −0.500364 + 0.500364i
5353 1.11881 + 2.70105i 0.153680 + 0.371017i 0.981904 0.189381i 0.0606481π-0.0606481\pi
−0.828223 + 0.560398i 0.810648π0.810648\pi
5454 −1.68223 8.45716i −0.228923 1.15087i
5555 −0.157954 + 6.65899i −0.0212986 + 0.897898i
5656 −1.19862 + 1.79386i −0.160172 + 0.239715i
5757 −16.0226 + 10.7060i −2.12225 + 1.41804i
5858 −1.34158 + 6.74460i −0.176159 + 0.885609i
5959 −3.66553 + 1.51831i −0.477211 + 0.197667i −0.608306 0.793703i 0.708151π-0.708151\pi
0.131095 + 0.991370i 0.458151π0.458151\pi
6060 6.21896 2.40483i 0.802864 0.310462i
6161 −3.45296 + 2.30720i −0.442107 + 0.295406i −0.756630 0.653844i 0.773155π-0.773155\pi
0.314523 + 0.949250i 0.398155π0.398155\pi
6262 −2.68416 4.01713i −0.340889 0.510176i
6363 −2.47982 12.4669i −0.312428 1.57068i
6464 −0.707107 0.707107i −0.0883883 0.0883883i
6565 11.2405 1.95999i 1.39421 0.243107i
6666 −3.39921 + 8.20642i −0.418414 + 1.01014i
6767 −2.25590 2.25590i −0.275602 0.275602i 0.555749 0.831350i 0.312432π-0.312432\pi
−0.831350 + 0.555749i 0.812432π0.812432\pi
6868 −0.00630415 4.12310i −0.000764491 0.499999i
6969 4.55013i 0.547771i
7070 4.49953 1.73994i 0.537796 0.207962i
7171 5.63509 1.12089i 0.668762 0.133025i 0.150979 0.988537i 0.451757π-0.451757\pi
0.517783 + 0.855512i 0.326757π0.326757\pi
7272 5.89173 0.694347
7373 9.62889 1.91531i 1.12698 0.224170i 0.403810 0.914843i 0.367686π-0.367686\pi
0.723167 + 0.690674i 0.242686π0.242686\pi
7474 1.42000 7.13883i 0.165072 0.829873i
7575 −14.4687 3.59877i −1.67070 0.415550i
7676 −2.47306 5.97048i −0.283679 0.684861i
7777 −2.45939 + 5.93749i −0.280274 + 0.676640i
7878 14.9235 + 2.96847i 1.68975 + 0.336113i
7979 −15.1407 3.01167i −1.70346 0.338839i −0.754996 0.655729i 0.772361π-0.772361\pi
−0.948462 + 0.316890i 0.897361π0.897361\pi
8080 0.384106 + 2.20283i 0.0429443 + 0.246284i
8181 −5.68322 + 5.68322i −0.631469 + 0.631469i
8282 3.01915 + 2.01733i 0.333409 + 0.222777i
8383 9.03070 3.74064i 0.991249 0.410589i 0.172668 0.984980i 0.444761π-0.444761\pi
0.818581 + 0.574391i 0.194761π0.194761\pi
8484 6.43332 0.701933
8585 −5.29091 + 7.55025i −0.573880 + 0.818940i
8686 −1.87826 −0.202538
8787 18.9448 7.84720i 2.03110 0.841309i
8888 −2.47681 1.65495i −0.264028 0.176418i
8989 −5.41083 + 5.41083i −0.573547 + 0.573547i −0.933118 0.359571i 0.882923π-0.882923\pi
0.359571 + 0.933118i 0.382923π0.382923\pi
9090 −10.7774 7.57696i −1.13604 0.798681i
9191 10.7974 + 2.14774i 1.13188 + 0.225144i
9292 1.49660 + 0.297691i 0.156031 + 0.0310365i
9393 −5.51318 + 13.3100i −0.571690 + 1.38018i
9494 1.77972 + 4.29662i 0.183564 + 0.443162i
9595 −3.15442 + 14.1019i −0.323637 + 1.44682i
9696 −0.581740 + 2.92460i −0.0593736 + 0.298491i
9797 −2.63292 + 0.523720i −0.267332 + 0.0531757i −0.326936 0.945046i 0.606016π-0.606016\pi
0.0596039 + 0.998222i 0.481016π0.481016\pi
9898 −2.34537 −0.236919
9999 17.2132 3.42392i 1.72999 0.344117i
100100 2.13029 4.52348i 0.213029 0.452348i
101101 12.8077i 1.27441i −0.770693 0.637207i 0.780090π-0.780090\pi
0.770693 0.637207i 0.219910π-0.219910\pi
102102 −10.2122 + 6.84619i −1.01116 + 0.677873i
103103 −8.68917 8.68917i −0.856170 0.856170i 0.134715 0.990884i 0.456988π-0.456988\pi
−0.990884 + 0.134715i 0.956988π0.956988\pi
104104 −1.95273 + 4.71431i −0.191481 + 0.462276i
105105 −11.7681 8.27347i −1.14845 0.807408i
106106 2.06729 + 2.06729i 0.200793 + 0.200793i
107107 −0.486150 2.44404i −0.0469978 0.236274i 0.950145 0.311807i 0.100934π-0.100934\pi
−0.997143 + 0.0755328i 0.975934π0.975934\pi
108108 −4.79060 7.16964i −0.460976 0.689899i
109109 15.1896 10.1494i 1.45490 0.972132i 0.458380 0.888756i 0.348430π-0.348430\pi
0.996518 0.0833759i 0.0265702π-0.0265702\pi
110110 2.40235 + 6.21255i 0.229055 + 0.592343i
111111 −20.0522 + 8.30589i −1.90327 + 0.788360i
112112 −0.420899 + 2.11600i −0.0397712 + 0.199944i
113113 10.4494 6.98206i 0.982997 0.656817i 0.0433845 0.999058i 0.486186π-0.486186\pi
0.939612 + 0.342241i 0.111186π0.111186\pi
114114 −10.7060 + 16.0226i −1.00271 + 1.50066i
115115 −2.35479 2.46922i −0.219586 0.230256i
116116 1.34158 + 6.74460i 0.124563 + 0.626220i
117117 −11.5050 27.7755i −1.06364 2.56784i
118118 −2.80547 + 2.80547i −0.258265 + 0.258265i
119119 −7.38871 + 4.95334i −0.677322 + 0.454072i
120120 4.82528 4.60167i 0.440486 0.420073i
121121 1.96470 + 0.813807i 0.178610 + 0.0739825i
122122 −2.30720 + 3.45296i −0.208884 + 0.312617i
123123 10.8276i 0.976289i
124124 −4.01713 2.68416i −0.360749 0.241045i
125125 −9.71415 + 5.53491i −0.868860 + 0.495057i
126126 −7.06194 10.5689i −0.629128 0.941556i
127127 2.06022 + 0.853371i 0.182815 + 0.0757245i 0.472213 0.881484i 0.343455π-0.343455\pi
−0.289398 + 0.957209i 0.593455π0.593455\pi
128128 −0.923880 0.382683i −0.0816602 0.0338248i
129129 3.11163 + 4.65688i 0.273964 + 0.410016i
130130 9.63478 6.11233i 0.845026 0.536087i
131131 10.4931 + 7.01129i 0.916790 + 0.612579i 0.921909 0.387407i 0.126629π-0.126629\pi
−0.00511864 + 0.999987i 0.501629π0.501629\pi
132132 8.88257i 0.773128i
133133 −7.74596 + 11.5927i −0.671660 + 1.00521i
134134 −2.94747 1.22088i −0.254623 0.105468i
135135 −0.457232 + 19.2759i −0.0393523 + 1.65900i
136136 −1.58367 3.80684i −0.135798 0.326433i
137137 −2.33320 + 2.33320i −0.199339 + 0.199339i −0.799717 0.600378i 0.795017π-0.795017\pi
0.600378 + 0.799717i 0.295017π0.295017\pi
138138 −1.74126 4.20377i −0.148226 0.357849i
139139 2.59433 + 13.0426i 0.220049 + 1.10626i 0.919955 + 0.392024i 0.128225π0.128225\pi
−0.699906 + 0.714235i 0.746775π0.746775\pi
140140 3.49117 3.32939i 0.295058 0.281385i
141141 7.70448 11.5306i 0.648834 0.971049i
142142 4.77720 3.19202i 0.400894 0.267869i
143143 −2.96541 + 14.9081i −0.247980 + 1.24668i
144144 5.44325 2.25467i 0.453604 0.187889i
145145 6.21969 14.0628i 0.516517 1.16785i
146146 8.16298 5.45433i 0.675573 0.451403i
147147 3.88548 + 5.81503i 0.320469 + 0.479615i
148148 −1.42000 7.13883i −0.116723 0.586809i
149149 −5.78244 5.78244i −0.473716 0.473716i 0.429399 0.903115i 0.358725π-0.358725\pi
−0.903115 + 0.429399i 0.858725π0.858725\pi
150150 −14.7445 + 2.21209i −1.20388 + 0.180616i
151151 3.31607 8.00571i 0.269858 0.651495i −0.729618 0.683855i 0.760302π-0.760302\pi
0.999476 + 0.0323595i 0.0103021π0.0103021\pi
152152 −4.56961 4.56961i −0.370644 0.370644i
153153 22.4573 + 9.26191i 1.81556 + 0.748781i
154154 6.42670i 0.517878i
155155 3.89638 + 10.0761i 0.312965 + 0.809335i
156156 14.9235 2.96847i 1.19483 0.237667i
157157 6.12399 0.488747 0.244374 0.969681i 0.421418π-0.421418\pi
0.244374 + 0.969681i 0.421418π0.421418\pi
158158 −15.1407 + 3.01167i −1.20453 + 0.239595i
159159 1.70077 8.55035i 0.134880 0.678087i
160160 1.19785 + 1.88816i 0.0946987 + 0.149272i
161161 −1.25983 3.04150i −0.0992887 0.239704i
162162 −3.07574 + 7.42549i −0.241653 + 0.583401i
163163 −12.9467 2.57526i −1.01407 0.201710i −0.340034 0.940413i 0.610439π-0.610439\pi
−0.674031 + 0.738703i 0.735439π0.735439\pi
164164 3.56132 + 0.708391i 0.278093 + 0.0553161i
165165 11.4233 16.2484i 0.889301 1.26493i
166166 6.91180 6.91180i 0.536460 0.536460i
167167 14.6882 + 9.81435i 1.13661 + 0.759457i 0.973846 0.227209i 0.0729599π-0.0729599\pi
0.162761 + 0.986665i 0.447960π0.447960\pi
168168 5.94362 2.46193i 0.458560 0.189942i
169169 13.0379 1.00292
170170 −1.99881 + 9.00026i −0.153302 + 0.690289i
171171 38.0747 2.91165
172172 −1.73529 + 0.718779i −0.132314 + 0.0548064i
173173 8.19533 + 5.47594i 0.623079 + 0.416328i 0.826638 0.562734i 0.190251π-0.190251\pi
−0.203558 + 0.979063i 0.565251π0.565251\pi
174174 14.4997 14.4997i 1.09922 1.09922i
175175 −10.6679 + 1.60049i −0.806417 + 0.120985i
176176 −2.92159 0.581141i −0.220223 0.0438051i
177177 11.6035 + 2.30807i 0.872170 + 0.173485i
178178 −2.92832 + 7.06959i −0.219487 + 0.529888i
179179 0.836227 + 2.01883i 0.0625026 + 0.150895i 0.952045 0.305958i 0.0989767π-0.0989767\pi
−0.889542 + 0.456853i 0.848977π0.848977\pi
180180 −12.8566 2.87587i −0.958273 0.214354i
181181 2.38233 11.9768i 0.177077 0.890225i −0.785426 0.618955i 0.787556π-0.787556\pi
0.962503 0.271270i 0.0874437π-0.0874437\pi
182182 10.7974 2.14774i 0.800357 0.159201i
183183 12.3834 0.915405
184184 1.49660 0.297691i 0.110330 0.0219461i
185185 −6.58325 + 14.8848i −0.484010 + 1.09435i
186186 14.4066i 1.05635i
187187 −6.83913 10.2017i −0.500127 0.746021i
188188 3.28849 + 3.28849i 0.239838 + 0.239838i
189189 −7.11923 + 17.1873i −0.517848 + 1.25019i
190190 2.48225 + 14.2356i 0.180081 + 1.03276i
191191 −3.12333 3.12333i −0.225996 0.225996i 0.585021 0.811018i 0.301086π-0.301086\pi
−0.811018 + 0.585021i 0.801086π0.801086\pi
192192 0.581740 + 2.92460i 0.0419835 + 0.211065i
193193 13.1386 + 19.6632i 0.945734 + 1.41539i 0.909340 + 0.416054i 0.136587π0.136587\pi
0.0363943 + 0.999338i 0.488413π0.488413\pi
194194 −2.23208 + 1.49143i −0.160254 + 0.107078i
195195 −31.1162 13.7621i −2.22828 0.985521i
196196 −2.16684 + 0.897536i −0.154775 + 0.0641097i
197197 −0.300658 + 1.51151i −0.0214210 + 0.107691i −0.990017 0.140951i 0.954984π-0.954984\pi
0.968596 + 0.248641i 0.0799840π0.0799840\pi
198198 14.5927 9.75051i 1.03706 0.692938i
199199 −2.72577 + 4.07940i −0.193224 + 0.289181i −0.915413 0.402515i 0.868136π-0.868136\pi
0.722189 + 0.691696i 0.243136π0.243136\pi
200200 0.237071 4.99438i 0.0167635 0.353156i
201201 1.85594 + 9.33042i 0.130908 + 0.658117i
202202 −4.90129 11.8328i −0.344854 0.832551i
203203 10.4908 10.4908i 0.736311 0.736311i
204204 −6.81493 + 10.2331i −0.477140 + 0.716460i
205205 −5.60350 5.87580i −0.391366 0.410384i
206206 −11.3530 4.70255i −0.790998 0.327642i
207207 −4.99473 + 7.47515i −0.347158 + 0.519559i
208208 5.10274i 0.353811i
209209 −16.0061 10.6949i −1.10717 0.739785i
210210 −14.0384 3.14023i −0.968743 0.216696i
211211 −14.8005 22.1505i −1.01891 1.52490i −0.841131 0.540832i 0.818110π-0.818110\pi
−0.177777 0.984071i 0.556890π-0.556890\pi
212212 2.70105 + 1.11881i 0.185509 + 0.0768402i
213213 −15.8283 6.55631i −1.08454 0.449231i
214214 −1.38444 2.07196i −0.0946381 0.141636i
215215 4.09863 + 0.916815i 0.279524 + 0.0625263i
216216 −7.16964 4.79060i −0.487832 0.325959i
217217 10.4235i 0.707591i
218218 10.1494 15.1896i 0.687401 1.02877i
219219 −27.0465 11.2030i −1.82763 0.757030i
220220 4.59693 + 4.82031i 0.309925 + 0.324985i
221221 −14.8541 + 14.8996i −0.999198 + 1.00226i
222222 −15.3473 + 15.3473i −1.03004 + 1.03004i
223223 −3.78056 9.12708i −0.253165 0.611195i 0.745291 0.666739i 0.232310π-0.232310\pi
−0.998456 + 0.0555446i 0.982310π0.982310\pi
224224 0.420899 + 2.11600i 0.0281225 + 0.141381i
225225 19.8193 + 21.7946i 1.32129 + 1.45298i
226226 6.98206 10.4494i 0.464440 0.695084i
227227 −6.88241 + 4.59868i −0.456801 + 0.305225i −0.762599 0.646872i 0.776077π-0.776077\pi
0.305797 + 0.952097i 0.401077π0.401077\pi
228228 −3.75944 + 18.9000i −0.248975 + 1.25168i
229229 21.1923 8.77812i 1.40042 0.580074i 0.450562 0.892745i 0.351224π-0.351224\pi
0.949862 + 0.312671i 0.101224π0.101224\pi
230230 −3.12047 1.38012i −0.205758 0.0910025i
231231 15.9341 10.6468i 1.04839 0.700509i
232232 3.82051 + 5.71779i 0.250829 + 0.375392i
233233 −5.40843 27.1900i −0.354318 1.78128i −0.587894 0.808938i 0.700043π-0.700043\pi
0.233576 0.972339i 0.424957π-0.424957\pi
234234 −21.2584 21.2584i −1.38971 1.38971i
235235 −1.78633 10.2445i −0.116527 0.668280i
236236 −1.51831 + 3.66553i −0.0988336 + 0.238605i
237237 32.5499 + 32.5499i 2.11434 + 2.11434i
238238 −4.93072 + 7.40383i −0.319611 + 0.479919i
239239 21.8340i 1.41232i −0.708051 0.706161i 0.750425π-0.750425\pi
0.708051 0.706161i 0.249575π-0.249575\pi
240240 2.69699 6.09794i 0.174090 0.393620i
241241 −10.9377 + 2.17563i −0.704556 + 0.140145i −0.534350 0.845264i 0.679443π-0.679443\pi
−0.170206 + 0.985408i 0.554443π0.554443\pi
242242 2.12658 0.136702
243243 −1.86561 + 0.371092i −0.119679 + 0.0238056i
244244 −0.810180 + 4.07305i −0.0518664 + 0.260750i
245245 5.11794 + 1.14482i 0.326973 + 0.0731400i
246246 −4.14353 10.0034i −0.264182 0.637791i
247247 −12.6193 + 30.4658i −0.802950 + 1.93849i
248248 −4.73853 0.942552i −0.300897 0.0598521i
249249 −28.5873 5.68637i −1.81165 0.360359i
250250 −6.85659 + 8.83103i −0.433649 + 0.558524i
251251 −5.63823 + 5.63823i −0.355882 + 0.355882i −0.862292 0.506411i 0.830972π-0.830972\pi
0.506411 + 0.862292i 0.330972π0.330972\pi
252252 −10.5689 7.06194i −0.665781 0.444861i
253253 4.19944 1.73947i 0.264017 0.109359i
254254 2.22997 0.139921
255255 25.6262 9.95457i 1.60478 0.623379i
256256 −1.00000 −0.0625000
257257 −11.0133 + 4.56187i −0.686992 + 0.284561i −0.698746 0.715370i 0.746258π-0.746258\pi
0.0117544 + 0.999931i 0.496258π0.496258\pi
258258 4.65688 + 3.11163i 0.289925 + 0.193722i
259259 −11.1040 + 11.1040i −0.689971 + 0.689971i
260260 6.56229 9.33413i 0.406976 0.578878i
261261 −39.7373 7.90425i −2.45968 0.489261i
262262 12.3775 + 2.46204i 0.764685 + 0.152105i
263263 −5.39184 + 13.0171i −0.332475 + 0.802666i 0.665919 + 0.746024i 0.268039π0.268039\pi
−0.998395 + 0.0566422i 0.981961π0.981961\pi
264264 3.39921 + 8.20642i 0.209207 + 0.505070i
265265 −3.50204 5.52021i −0.215129 0.339104i
266266 −2.72002 + 13.6745i −0.166775 + 0.838436i
267267 22.3793 4.45151i 1.36959 0.272428i
268268 −3.19032 −0.194880
269269 −4.26081 + 0.847528i −0.259786 + 0.0516747i −0.323265 0.946308i 0.604781π-0.604781\pi
0.0634787 + 0.997983i 0.479781π0.479781\pi
270270 6.95412 + 17.9835i 0.423214 + 1.09444i
271271 3.27703i 0.199065i 0.995034 + 0.0995326i 0.0317347π0.0317347\pi
−0.995034 + 0.0995326i 0.968265π0.968265\pi
272272 −2.91993 2.91101i −0.177047 0.176506i
273273 −23.2126 23.2126i −1.40489 1.40489i
274274 −1.26272 + 3.04848i −0.0762837 + 0.184165i
275275 −2.20981 14.7293i −0.133257 0.888210i
276276 −3.21743 3.21743i −0.193666 0.193666i
277277 3.34480 + 16.8154i 0.200970 + 1.01034i 0.941164 + 0.337950i 0.109733π0.109733\pi
−0.740195 + 0.672393i 0.765267π0.765267\pi
278278 7.38804 + 11.0570i 0.443105 + 0.663154i
279279 23.6678 15.8143i 1.41696 0.946780i
280280 1.95132 4.41197i 0.116614 0.263666i
281281 26.4043 10.9370i 1.57515 0.652447i 0.587511 0.809216i 0.300108π-0.300108\pi
0.987635 + 0.156769i 0.0501079π0.0501079\pi
282282 2.70545 13.6012i 0.161107 0.809942i
283283 −2.50708 + 1.67518i −0.149030 + 0.0995789i −0.627850 0.778334i 0.716065π-0.716065\pi
0.478820 + 0.877913i 0.341065π0.341065\pi
284284 3.19202 4.77720i 0.189412 0.283475i
285285 31.1829 29.7378i 1.84712 1.76152i
286286 2.96541 + 14.9081i 0.175348 + 0.881535i
287287 −2.99792 7.23761i −0.176961 0.427223i
288288 4.16608 4.16608i 0.245489 0.245489i
289289 −0.0519853 16.9999i −0.00305796 0.999995i
290290 0.364643 15.3725i 0.0214126 0.902705i
291291 7.39558 + 3.06335i 0.433536 + 0.179577i
292292 5.45433 8.16298i 0.319190 0.477702i
293293 7.90877i 0.462035i 0.972950 + 0.231018i 0.0742055π0.0742055\pi
−0.972950 + 0.231018i 0.925794π0.925794\pi
294294 5.81503 + 3.88548i 0.339139 + 0.226606i
295295 7.49134 4.75253i 0.436163 0.276703i
296296 −4.04382 6.05201i −0.235043 0.351766i
297297 −23.7308 9.82960i −1.37700 0.570371i
298298 −7.55512 3.12943i −0.437656 0.181283i
299299 −4.32586 6.47411i −0.250171 0.374407i
300300 −12.7756 + 7.68617i −0.737600 + 0.443761i
301301 3.36934 + 2.25132i 0.194205 + 0.129764i
302302 8.66532i 0.498633i
303303 −21.2179 + 31.7549i −1.21894 + 1.82427i
304304 −5.97048 2.47306i −0.342431 0.141839i
305305 6.72009 6.40867i 0.384791 0.366959i
306306 24.2922 0.0371424i 1.38869 0.00212329i
307307 −10.8126 + 10.8126i −0.617106 + 0.617106i −0.944788 0.327682i 0.893733π-0.893733\pi
0.327682 + 0.944788i 0.393733π0.393733\pi
308308 2.45939 + 5.93749i 0.140137 + 0.338320i
309309 7.14862 + 35.9386i 0.406671 + 2.04447i
310310 7.45575 + 7.81806i 0.423458 + 0.444036i
311311 0.359069 0.537385i 0.0203609 0.0304723i −0.821150 0.570713i 0.806667π-0.806667\pi
0.841510 + 0.540241i 0.181667π0.181667\pi
312312 12.6515 8.45347i 0.716251 0.478584i
313313 0.645545 3.24537i 0.0364883 0.183439i −0.958243 0.285955i 0.907689π-0.907689\pi
0.994731 + 0.102516i 0.0326892π0.0326892\pi
314314 5.65783 2.34355i 0.319290 0.132254i
315315 10.2512 + 26.5100i 0.577592 + 1.49367i
316316 −12.8356 + 8.57650i −0.722061 + 0.482466i
317317 −7.87772 11.7898i −0.442457 0.662183i 0.541477 0.840715i 0.317865π-0.317865\pi
−0.983934 + 0.178532i 0.942865π0.942865\pi
318318 −1.70077 8.55035i −0.0953745 0.479480i
319319 14.4848 + 14.4848i 0.810993 + 0.810993i
320320 1.82924 + 1.28603i 0.102258 + 0.0718914i
321321 −2.84359 + 6.86503i −0.158714 + 0.383169i
322322 −2.32787 2.32787i −0.129727 0.129727i
323323 −10.2343 24.6013i −0.569451 1.36885i
324324 8.03729i 0.446516i
325325 −24.0080 + 8.63505i −1.33172 + 0.478987i
326326 −12.9467 + 2.57526i −0.717053 + 0.142631i
327327 −54.4744 −3.01244
328328 3.56132 0.708391i 0.196641 0.0391144i
329329 1.95744 9.84074i 0.107917 0.542537i
330330 4.33575 19.3830i 0.238675 1.06700i
331331 10.8628 + 26.2251i 0.597073 + 1.44146i 0.876550 + 0.481310i 0.159839π0.159839\pi
−0.279477 + 0.960152i 0.590161π0.590161\pi
332332 3.74064 9.03070i 0.205294 0.495624i
333333 42.0601 + 8.36627i 2.30488 + 0.458469i
334334 17.3259 + 3.44634i 0.948032 + 0.188575i
335335 5.83586 + 4.10285i 0.318847 + 0.224163i
336336 4.54905 4.54905i 0.248171 0.248171i
337337 −2.20255 1.47169i −0.119980 0.0801683i 0.494132 0.869387i 0.335486π-0.335486\pi
−0.614112 + 0.789219i 0.710486π0.710486\pi
338338 12.0455 4.98940i 0.655187 0.271387i
339339 −37.4747 −2.03535
340340 1.59759 + 9.08007i 0.0866417 + 0.492436i
341341 −14.3918 −0.779360
342342 35.1765 14.5706i 1.90213 0.787886i
343343 16.7643 + 11.2015i 0.905187 + 0.604827i
344344 −1.32813 + 1.32813i −0.0716080 + 0.0716080i
345345 1.74773 + 10.0232i 0.0940947 + 0.539629i
346346 9.66705 + 1.92290i 0.519704 + 0.103376i
347347 −21.2587 4.22862i −1.14123 0.227004i −0.411940 0.911211i 0.635149π-0.635149\pi
−0.729288 + 0.684207i 0.760149π0.760149\pi
348348 7.84720 18.9448i 0.420654 1.01555i
349349 2.37113 + 5.72441i 0.126923 + 0.306420i 0.974549 0.224174i 0.0719686π-0.0719686\pi
−0.847626 + 0.530595i 0.821969π0.821969\pi
350350 −9.24337 + 5.56108i −0.494079 + 0.297252i
351351 −8.58400 + 43.1547i −0.458180 + 2.30343i
352352 −2.92159 + 0.581141i −0.155721 + 0.0309749i
353353 18.7851 0.999831 0.499915 0.866074i 0.333364π-0.333364\pi
0.499915 + 0.866074i 0.333364π0.333364\pi
354354 11.6035 2.30807i 0.616718 0.122673i
355355 −11.9826 + 4.63360i −0.635971 + 0.245926i
356356 7.65207i 0.405559i
357357 26.5252 0.0405567i 1.40386 0.00214649i
358358 1.54515 + 1.54515i 0.0816635 + 0.0816635i
359359 −0.798627 + 1.92806i −0.0421499 + 0.101759i −0.943552 0.331223i 0.892539π-0.892539\pi
0.901402 + 0.432982i 0.142539π0.142539\pi
360360 −12.9785 + 2.26305i −0.684026 + 0.119273i
361361 −16.0956 16.0956i −0.847139 0.847139i
362362 −2.38233 11.9768i −0.125212 0.629484i
363363 −3.52301 5.27256i −0.184910 0.276738i
364364 9.15360 6.11624i 0.479779 0.320578i
365365 −20.4751 + 7.91760i −1.07172 + 0.414426i
366366 11.4407 4.73891i 0.598017 0.247707i
367367 −0.264915 + 1.33182i −0.0138285 + 0.0695204i −0.987083 0.160208i 0.948784π-0.948784\pi
0.973255 + 0.229728i 0.0737837π0.0737837\pi
368368 1.26875 0.847753i 0.0661383 0.0441922i
369369 −11.8856 + 17.7880i −0.618737 + 0.926006i
370370 −0.385957 + 16.2711i −0.0200650 + 0.845893i
371371 −1.23054 6.18633i −0.0638863 0.321178i
372372 5.51318 + 13.3100i 0.285845 + 0.690091i
373373 −6.12982 + 6.12982i −0.317390 + 0.317390i −0.847764 0.530374i 0.822052π-0.822052\pi
0.530374 + 0.847764i 0.322052π0.322052\pi
374374 −10.2226 6.80790i −0.528596 0.352028i
375375 33.2543 + 2.36998i 1.71725 + 0.122385i
376376 4.29662 + 1.77972i 0.221581 + 0.0917819i
377377 19.4950 29.1764i 1.00405 1.50266i
378378 18.6034i 0.956857i
379379 9.90108 + 6.61569i 0.508584 + 0.339825i 0.783242 0.621717i 0.213565π-0.213565\pi
−0.274658 + 0.961542i 0.588565π0.588565\pi
380380 7.74102 + 12.2020i 0.397106 + 0.625952i
381381 −3.69429 5.52889i −0.189264 0.283254i
382382 −4.08083 1.69034i −0.208793 0.0864851i
383383 −13.9138 5.76328i −0.710962 0.294490i −0.00225919 0.999997i 0.500719π-0.500719\pi
−0.708702 + 0.705507i 0.750719π0.750719\pi
384384 1.65666 + 2.47936i 0.0845408 + 0.126524i
385385 3.13700 14.0240i 0.159876 0.714727i
386386 19.6632 + 13.1386i 1.00083 + 0.668735i
387387 11.0662i 0.562527i
388388 −1.49143 + 2.23208i −0.0757158 + 0.113317i
389389 24.1120 + 9.98753i 1.22253 + 0.506388i 0.898213 0.439561i 0.144866π-0.144866\pi
0.324315 + 0.945949i 0.394866π0.394866\pi
390390 −34.0141 0.806830i −1.72237 0.0408554i
391391 6.17249 + 1.21798i 0.312156 + 0.0615957i
392392 −1.65843 + 1.65843i −0.0837634 + 0.0837634i
393393 −14.4010 34.7670i −0.726433 1.75376i
394394 0.300658 + 1.51151i 0.0151469 + 0.0761487i
395395 34.5091 + 0.818573i 1.73634 + 0.0411869i
396396 9.75051 14.5927i 0.489981 0.733309i
397397 21.0338 14.0544i 1.05566 0.705368i 0.0985598 0.995131i 0.468576π-0.468576\pi
0.957098 + 0.289763i 0.0935764π0.0935764\pi
398398 −0.957161 + 4.81198i −0.0479782 + 0.241203i
399399 38.4101 15.9100i 1.92291 0.796495i
400400 −1.69224 4.70493i −0.0846120 0.235246i
401401 −8.53692 + 5.70419i −0.426314 + 0.284854i −0.750160 0.661256i 0.770024π-0.770024\pi
0.323847 + 0.946110i 0.395024π0.395024\pi
402402 5.28526 + 7.90995i 0.263605 + 0.394512i
403403 4.80959 + 24.1795i 0.239583 + 1.20446i
404404 −9.05641 9.05641i −0.450573 0.450573i
405405 10.3362 14.7021i 0.513611 0.730555i
406406 5.67759 13.7069i 0.281774 0.680263i
407407 −15.3315 15.3315i −0.759953 0.759953i
408408 −2.38014 + 12.0621i −0.117834 + 0.597163i
409409 18.8720i 0.933158i 0.884480 + 0.466579i 0.154514π0.154514\pi
−0.884480 + 0.466579i 0.845486π0.845486\pi
410410 −7.42553 3.28416i −0.366721 0.162193i
411411 9.65016 1.91954i 0.476007 0.0946838i
412412 −12.2883 −0.605403
413413 8.39532 1.66993i 0.413107 0.0821720i
414414 −1.75392 + 8.81754i −0.0862003 + 0.433358i
415415 −18.4563 + 11.7087i −0.905985 + 0.574760i
416416 1.95273 + 4.71431i 0.0957406 + 0.231138i
417417 15.1748 36.6352i 0.743113 1.79403i
418418 −18.8805 3.75557i −0.923476 0.183691i
419419 2.17804 + 0.433238i 0.106404 + 0.0211651i 0.248005 0.968759i 0.420225π-0.420225\pi
−0.141601 + 0.989924i 0.545225π0.545225\pi
420420 −14.1715 + 2.47108i −0.691500 + 0.120576i
421421 −19.5353 + 19.5353i −0.952094 + 0.952094i −0.998904 0.0468096i 0.985095π-0.985095\pi
0.0468096 + 0.998904i 0.485095π0.485095\pi
422422 −22.1505 14.8005i −1.07827 0.720476i
423423 −25.3145 + 10.4856i −1.23083 + 0.509828i
424424 2.92359 0.141982
425425 8.75489 18.6642i 0.424674 0.905346i
426426 −17.1325 −0.830071
427427 8.27758 3.42869i 0.400580 0.165926i
428428 −2.07196 1.38444i −0.100152 0.0669193i
429429 32.0499 32.0499i 1.54738 1.54738i
430430 4.13749 0.721451i 0.199527 0.0347914i
431431 26.3843 + 5.24817i 1.27089 + 0.252796i 0.784051 0.620697i 0.213150π-0.213150\pi
0.486838 + 0.873492i 0.338150π0.338150\pi
432432 −8.45716 1.68223i −0.406895 0.0809365i
433433 2.65966 6.42099i 0.127815 0.308573i −0.846998 0.531596i 0.821592π-0.821592\pi
0.974813 + 0.223023i 0.0715925π0.0715925\pi
434434 3.98889 + 9.63002i 0.191473 + 0.462256i
435435 −38.7181 + 24.5629i −1.85639 + 1.17770i
436436 3.56398 17.9173i 0.170684 0.858085i
437437 9.67161 1.92380i 0.462656 0.0920279i
438438 −29.2749 −1.39881
439439 11.9718 2.38134i 0.571382 0.113655i 0.0990609 0.995081i 0.468416π-0.468416\pi
0.472321 + 0.881426i 0.343416π0.343416\pi
440440 6.09166 + 2.69422i 0.290408 + 0.128442i
441441 13.8183i 0.658015i
442442 −8.02159 + 19.4499i −0.381548 + 0.925137i
443443 18.3210 + 18.3210i 0.870456 + 0.870456i 0.992522 0.122066i 0.0389519π-0.0389519\pi
−0.122066 + 0.992522i 0.538952π0.538952\pi
444444 −8.30589 + 20.0522i −0.394180 + 0.951635i
445445 9.84081 13.9975i 0.466499 0.663544i
446446 −6.98556 6.98556i −0.330776 0.330776i
447447 4.75724 + 23.9163i 0.225010 + 1.13120i
448448 1.19862 + 1.79386i 0.0566294 + 0.0847520i
449449 −31.2145 + 20.8568i −1.47310 + 0.984295i −0.478773 + 0.877939i 0.658918π0.658918\pi
−0.994328 + 0.106356i 0.966082π0.966082\pi
450450 26.6511 + 12.5511i 1.25635 + 0.591664i
451451 9.99306 4.13926i 0.470555 0.194910i
452452 2.45178 12.3259i 0.115322 0.579762i
453453 −21.4844 + 14.3554i −1.00943 + 0.674478i
454454 −4.59868 + 6.88241i −0.215827 + 0.323007i
455455 −24.6098 0.583756i −1.15373 0.0273669i
456456 3.75944 + 18.9000i 0.176052 + 0.885072i
457457 −6.88648 16.6254i −0.322136 0.777705i −0.999130 0.0417158i 0.986718π-0.986718\pi
0.676994 0.735989i 0.263282π-0.263282\pi
458458 16.2199 16.2199i 0.757904 0.757904i
459459 −19.7973 29.5309i −0.924060 1.37839i
460460 −3.41109 0.0809127i −0.159043 0.00377257i
461461 22.1601 + 9.17900i 1.03210 + 0.427508i 0.833469 0.552566i 0.186351π-0.186351\pi
0.198628 + 0.980075i 0.436351π0.436351\pi
462462 10.6468 15.9341i 0.495335 0.741321i
463463 35.3808i 1.64428i −0.569283 0.822142i 0.692779π-0.692779\pi
0.569283 0.822142i 0.307221π-0.307221\pi
464464 5.71779 + 3.82051i 0.265442 + 0.177363i
465465 7.03216 31.4373i 0.326109 1.45787i
466466 −15.4019 23.0506i −0.713479 1.06780i
467467 20.7488 + 8.59445i 0.960142 + 0.397704i 0.807033 0.590506i 0.201072π-0.201072\pi
0.153108 + 0.988209i 0.451072π0.451072\pi
468468 −27.7755 11.5050i −1.28392 0.531818i
469469 3.82398 + 5.72299i 0.176575 + 0.264263i
470470 −5.57077 8.78112i −0.256960 0.405043i
471471 −15.1836 10.1453i −0.699622 0.467472i
472472 3.96754i 0.182621i
473473 −3.10842 + 4.65208i −0.142925 + 0.213903i
474474 42.5285 + 17.6159i 1.95340 + 0.809123i
475475 1.53205 32.2757i 0.0702953 1.48091i
476476 −1.72207 + 8.72715i −0.0789310 + 0.400008i
477477 −12.1799 + 12.1799i −0.557681 + 0.557681i
478478 −8.35550 20.1720i −0.382172 0.922644i
479479 −3.75915 18.8985i −0.171760 0.863496i −0.966524 0.256577i 0.917405π-0.917405\pi
0.794764 0.606919i 0.207595π-0.207595\pi
480480 0.158117 6.66586i 0.00721703 0.304253i
481481 −20.6346 + 30.8818i −0.940856 + 1.40809i
482482 −9.27249 + 6.19568i −0.422350 + 0.282206i
483483 −1.91515 + 9.62809i −0.0871421 + 0.438093i
484484 1.96470 0.813807i 0.0893048 0.0369912i
485485 5.59871 2.16499i 0.254224 0.0983070i
486486 −1.58158 + 1.05678i −0.0717422 + 0.0479366i
487487 17.2975 + 25.8876i 0.783826 + 1.17308i 0.981246 + 0.192760i 0.0617437π0.0617437\pi
−0.197420 + 0.980319i 0.563256π0.563256\pi
488488 0.810180 + 4.07305i 0.0366751 + 0.184378i
489489 27.8333 + 27.8333i 1.25866 + 1.25866i
490490 5.16646 0.900872i 0.233397 0.0406972i
491491 −12.1296 + 29.2835i −0.547403 + 1.32155i 0.372001 + 0.928232i 0.378672π0.378672\pi
−0.919404 + 0.393315i 0.871328π0.871328\pi
492492 −7.65624 7.65624i −0.345170 0.345170i
493493 5.57400 + 27.8002i 0.251041 + 1.25206i
494494 32.9759i 1.48366i
495495 −36.6027 + 14.1540i −1.64517 + 0.636176i
496496 −4.73853 + 0.942552i −0.212766 + 0.0423218i
497497 −12.3957 −0.556021
498498 −28.5873 + 5.68637i −1.28103 + 0.254812i
499499 −5.07928 + 25.5353i −0.227380 + 1.14312i 0.683343 + 0.730098i 0.260525π0.260525\pi
−0.910723 + 0.413018i 0.864475π0.864475\pi
500500 −2.95517 + 10.7827i −0.132159 + 0.482218i
501501 −20.1584 48.6666i −0.900609 2.17426i
502502 −3.05139 + 7.36670i −0.136190 + 0.328792i
503503 19.6945 + 3.91748i 0.878134 + 0.174672i 0.613517 0.789682i 0.289754π-0.289754\pi
0.264617 + 0.964353i 0.414754π0.414754\pi
504504 −12.4669 2.47982i −0.555321 0.110460i
505505 4.91951 + 28.2132i 0.218915 + 1.25547i
506506 3.21411 3.21411i 0.142885 0.142885i
507507 −32.3257 21.5993i −1.43563 0.959260i
508508 2.06022 0.853371i 0.0914075 0.0378622i
509509 −2.28523 −0.101291 −0.0506455 0.998717i 0.516128π-0.516128\pi
−0.0506455 + 0.998717i 0.516128π0.516128\pi
510510 19.8661 19.0036i 0.879686 0.841492i
511511 −21.1809 −0.936988
512512 −0.923880 + 0.382683i −0.0408301 + 0.0169124i
513513 −46.3331 30.9588i −2.04566 1.36686i
514514 −8.42923 + 8.42923i −0.371797 + 0.371797i
515515 22.4783 + 15.8032i 0.990514 + 0.696373i
516516 5.49317 + 1.09266i 0.241823 + 0.0481016i
517517 13.5872 + 2.70267i 0.597565 + 0.118863i
518518 −6.00946 + 14.5081i −0.264040 + 0.637450i
519519 −11.2474 27.1537i −0.493707 1.19191i
520520 2.49074 11.1349i 0.109226 0.488297i
521521 4.26245 21.4288i 0.186741 0.938812i −0.767790 0.640701i 0.778644π-0.778644\pi
0.954531 0.298110i 0.0963563π-0.0963563\pi
522522 −39.7373 + 7.90425i −1.73926 + 0.345960i
523523 38.7971 1.69648 0.848239 0.529614i 0.177663π-0.177663\pi
0.848239 + 0.529614i 0.177663π0.177663\pi
524524 12.3775 2.46204i 0.540714 0.107555i
525525 29.1010 + 13.7049i 1.27007 + 0.598129i
526526 14.0896i 0.614334i
527527 −16.5800 11.0417i −0.722234 0.480986i
528528 6.28093 + 6.28093i 0.273342 + 0.273342i
529529 7.91067 19.0981i 0.343942 0.830350i
530530 −5.34795 3.75984i −0.232300 0.163317i
531531 −16.5291 16.5291i −0.717301 0.717301i
532532 2.72002 + 13.6745i 0.117928 + 0.592863i
533533 −10.2939 15.4059i −0.445878 0.667304i
534534 18.9722 12.6768i 0.821008 0.548580i
535535 2.00967 + 5.19707i 0.0868858 + 0.224689i
536536 −2.94747 + 1.22088i −0.127311 + 0.0527341i
537537 1.27120 6.39075i 0.0548563 0.275781i
538538 −3.61214 + 2.41356i −0.155731 + 0.104056i
539539 −3.88147 + 5.80904i −0.167187 + 0.250213i
540540 13.3068 + 13.9534i 0.572632 + 0.600459i
541541 2.10863 + 10.6008i 0.0906572 + 0.455765i 0.999273 + 0.0381310i 0.0121404π0.0121404\pi
−0.908616 + 0.417634i 0.862860π0.862860\pi
542542 1.25406 + 3.02758i 0.0538666 + 0.130046i
543543 −25.7480 + 25.7480i −1.10495 + 1.10495i
544544 −3.81166 1.57202i −0.163424 0.0673997i
545545 −29.5617 + 28.1917i −1.26628 + 1.20760i
546546 −30.3287 12.5626i −1.29795 0.537628i
547547 13.3892 20.0384i 0.572482 0.856780i −0.426376 0.904546i 0.640210π-0.640210\pi
0.998859 + 0.0477657i 0.0152101π0.0152101\pi
548548 3.29965i 0.140954i
549549 −20.3439 13.5934i −0.868258 0.580151i
550550 −7.67826 12.7624i −0.327402 0.544192i
551551 24.6897 + 36.9507i 1.05182 + 1.57415i
552552 −4.20377 1.74126i −0.178924 0.0741129i
553553 30.7701 + 12.7454i 1.30848 + 0.541989i
554554 9.52519 + 14.2554i 0.404686 + 0.605656i
555555 40.9812 25.9986i 1.73956 1.10358i
556556 11.0570 + 7.38804i 0.468921 + 0.313323i
557557 33.9956i 1.44044i 0.693746 + 0.720220i 0.255959π0.255959\pi
−0.693746 + 0.720220i 0.744041π0.744041\pi
558558 15.8143 23.6678i 0.669475 1.00194i
559559 8.85471 + 3.66774i 0.374514 + 0.155129i
560560 0.114401 4.82287i 0.00483431 0.203803i
561561 0.0559971 + 36.6237i 0.00236420 + 1.54626i
562562 20.2089 20.2089i 0.852463 0.852463i
563563 −2.94572 7.11160i −0.124147 0.299718i 0.849571 0.527475i 0.176861π-0.176861\pi
−0.973718 + 0.227756i 0.926861π0.926861\pi
564564 −2.70545 13.6012i −0.113920 0.572715i
565565 −20.3364 + 19.3940i −0.855559 + 0.815911i
566566 −1.67518 + 2.50708i −0.0704129 + 0.105380i
567567 14.4178 9.63365i 0.605490 0.404575i
568568 1.12089 5.63509i 0.0470315 0.236443i
569569 −18.4941 + 7.66052i −0.775314 + 0.321146i −0.735023 0.678042i 0.762829π-0.762829\pi
−0.0402912 + 0.999188i 0.512829π0.512829\pi
570570 17.4291 39.4074i 0.730023 1.65059i
571571 8.82341 5.89561i 0.369248 0.246724i −0.357077 0.934075i 0.616227π-0.616227\pi
0.726325 + 0.687351i 0.241227π0.241227\pi
572572 8.44477 + 12.6385i 0.353093 + 0.528442i
573573 2.56958 + 12.9181i 0.107346 + 0.539663i
574574 −5.53943 5.53943i −0.231211 0.231211i
575575 6.13565 + 4.53478i 0.255874 + 0.189114i
576576 2.25467 5.44325i 0.0939445 0.226802i
577577 −26.0481 26.0481i −1.08440 1.08440i −0.996094 0.0883015i 0.971856π-0.971856\pi
−0.0883015 0.996094i 0.528144π-0.528144\pi
578578 −6.55362 15.6860i −0.272594 0.652451i
579579 70.5183i 2.93064i
580580 −5.54592 14.3419i −0.230282 0.595515i
581581 −20.6834 + 4.11419i −0.858093 + 0.170685i
582582 8.00491 0.331814
583583 8.54154 1.69902i 0.353755 0.0703662i
584584 1.91531 9.62889i 0.0792559 0.398446i
585585 36.0122 + 56.7655i 1.48892 + 2.34696i
586586 3.02656 + 7.30675i 0.125026 + 0.301839i
587587 6.90430 16.6684i 0.284971 0.687980i −0.714967 0.699159i 0.753558π-0.753558\pi
0.999938 + 0.0111781i 0.00355817π0.00355817\pi
588588 6.85929 + 1.36440i 0.282872 + 0.0562668i
589589 −30.6223 6.09115i −1.26177 0.250982i
590590 5.10238 7.25758i 0.210062 0.298790i
591591 3.24949 3.24949i 0.133666 0.133666i
592592 −6.05201 4.04382i −0.248736 0.166200i
593593 19.0530 7.89203i 0.782414 0.324087i 0.0445250 0.999008i 0.485823π-0.485823\pi
0.737889 + 0.674922i 0.235823π0.235823\pi
594594 −25.6860 −1.05391
595595 14.3735 13.7494i 0.589255 0.563671i
596596 −8.17761 −0.334968
597597 13.5163 5.59864i 0.553185 0.229137i
598598 −6.47411 4.32586i −0.264746 0.176898i
599599 8.03343 8.03343i 0.328237 0.328237i −0.523679 0.851916i 0.675441π-0.675441\pi
0.851916 + 0.523679i 0.175441π0.175441\pi
600600 −8.86174 + 11.9901i −0.361779 + 0.489494i
601601 16.8364 + 3.34896i 0.686770 + 0.136607i 0.526127 0.850406i 0.323644π-0.323644\pi
0.160642 + 0.987013i 0.448644π0.448644\pi
602602 3.97440 + 0.790558i 0.161985 + 0.0322207i
603603 7.19311 17.3657i 0.292926 0.707186i
604604 −3.31607 8.00571i −0.134929 0.325748i
605605 −4.64050 1.03803i −0.188663 0.0422017i
606606 −7.45075 + 37.4574i −0.302666 + 1.52160i
607607 −15.0490 + 2.99343i −0.610821 + 0.121500i −0.490801 0.871272i 0.663296π-0.663296\pi
−0.120020 + 0.992772i 0.538296π0.538296\pi
608608 −6.46241 −0.262085
609609 −43.3902 + 8.63085i −1.75826 + 0.349740i
610610 3.75606 8.49250i 0.152078 0.343851i
611611 23.7309i 0.960050i
612612 22.4288 9.33054i 0.906632 0.377165i
613613 −5.02517 5.02517i −0.202965 0.202965i 0.598304 0.801269i 0.295841π-0.295841\pi
−0.801269 + 0.598304i 0.795841π0.795841\pi
614614 −5.85173 + 14.1273i −0.236156 + 0.570132i
615615 4.15893 + 23.8513i 0.167704 + 0.961777i
616616 4.54436 + 4.54436i 0.183098 + 0.183098i
617617 −1.51726 7.62776i −0.0610824 0.307082i 0.938151 0.346226i 0.112537π-0.112537\pi
−0.999234 + 0.0391439i 0.987537π0.987537\pi
618618 20.3576 + 30.4672i 0.818901 + 1.22557i
619619 23.2443 15.5314i 0.934268 0.624258i 0.00753243 0.999972i 0.497602π-0.497602\pi
0.926736 + 0.375714i 0.122602π0.122602\pi
620620 9.88006 + 4.36975i 0.396793 + 0.175493i
621621 12.1562 5.03525i 0.487810 0.202058i
622622 0.126088 0.633889i 0.00505568 0.0254166i
623623 13.7267 9.17192i 0.549950 0.367465i
624624 8.45347 12.6515i 0.338410 0.506466i
625625 19.2726 15.9237i 0.770906 0.636949i
626626 −0.645545 3.24537i −0.0258011 0.129711i
627627 21.9671 + 53.0332i 0.877281 + 2.11794i
628628 4.33031 4.33031i 0.172798 0.172798i
629629 −5.89982 29.4252i −0.235241 1.17326i
630630 19.6159 + 20.5691i 0.781514 + 0.819491i
631631 16.9058 + 7.00260i 0.673008 + 0.278769i 0.692901 0.721033i 0.256332π-0.256332\pi
−0.0198927 + 0.999802i 0.506332π0.506332\pi
632632 −8.57650 + 12.8356i −0.341155 + 0.510574i
633633 79.4383i 3.15739i
634634 −11.7898 7.87772i −0.468234 0.312864i
635635 −4.86610 1.08849i −0.193105 0.0431954i
636636 −4.84339 7.24864i −0.192053 0.287427i
637637 11.0568 + 4.57989i 0.438088 + 0.181462i
638638 18.9253 + 7.83912i 0.749260 + 0.310354i
639639 18.8065 + 28.1460i 0.743975 + 1.11344i
640640 2.18214 + 0.488119i 0.0862567 + 0.0192946i
641641 −29.4328 19.6664i −1.16253 0.776776i −0.184007 0.982925i 0.558907π-0.558907\pi
−0.978521 + 0.206149i 0.933907π0.933907\pi
642642 7.43066i 0.293265i
643643 5.81925 8.70912i 0.229489 0.343454i −0.698798 0.715319i 0.746281π-0.746281\pi
0.928287 + 0.371865i 0.121281π0.121281\pi
644644 −3.04150 1.25983i −0.119852 0.0496443i
645645 −8.64313 9.06313i −0.340323 0.356860i
646646 −18.8698 18.8122i −0.742421 0.740154i
647647 1.76443 1.76443i 0.0693668 0.0693668i −0.671572 0.740939i 0.734381π-0.734381\pi
0.740939 + 0.671572i 0.234381π0.234381\pi
648648 3.07574 + 7.42549i 0.120826 + 0.291701i
649649 2.30570 + 11.5915i 0.0905065 + 0.455007i
650650 −18.8760 + 17.1652i −0.740378 + 0.673275i
651651 17.2681 25.8435i 0.676789 1.01289i
652652 −10.9757 + 7.33373i −0.429842 + 0.287211i
653653 2.34838 11.8061i 0.0918991 0.462008i −0.907243 0.420606i 0.861818π-0.861818\pi
0.999143 0.0414020i 0.0131824π-0.0131824\pi
654654 −50.3278 + 20.8465i −1.96797 + 0.815161i
655655 −25.8077 11.4142i −1.00839 0.445990i
656656 3.01915 2.01733i 0.117878 0.0787634i
657657 32.1354 + 48.0941i 1.25372 + 1.87633i
658658 −1.95744 9.84074i −0.0763091 0.383632i
659659 −21.1376 21.1376i −0.823403 0.823403i 0.163192 0.986594i 0.447821π-0.447821\pi
−0.986594 + 0.163192i 0.947821π0.947821\pi
660660 −3.41185 19.5668i −0.132806 0.761637i
661661 −7.99380 + 19.2988i −0.310923 + 0.750634i 0.688748 + 0.725000i 0.258160π0.258160\pi
−0.999671 + 0.0256340i 0.991840π0.991840\pi
662662 20.0718 + 20.0718i 0.780114 + 0.780114i
663663 61.5123 12.3334i 2.38894 0.478988i
664664 9.77476i 0.379334i
665665 12.6102 28.5119i 0.489004 1.10565i
666666 42.0601 8.36627i 1.62980 0.324186i
667667 −10.4933 −0.406303
668668 17.3259 3.44634i 0.670360 0.133343i
669669 −5.74706 + 28.8924i −0.222194 + 1.11704i
670670 6.96173 + 1.55726i 0.268955 + 0.0601621i
671671 4.73403 + 11.4290i 0.182755 + 0.441210i
672672 2.46193 5.94362i 0.0949709 0.229280i
673673 −35.6232 7.08590i −1.37317 0.273141i −0.547272 0.836955i 0.684334π-0.684334\pi
−0.825902 + 0.563813i 0.809334π0.809334\pi
674674 −2.59808 0.516790i −0.100074 0.0199060i
675675 −6.39676 42.6371i −0.246211 1.64110i
676676 9.21920 9.21920i 0.354585 0.354585i
677677 5.06304 + 3.38302i 0.194588 + 0.130020i 0.649048 0.760748i 0.275168π-0.275168\pi
−0.454459 + 0.890767i 0.650168π0.650168\pi
678678 −34.6221 + 14.3409i −1.32965 + 0.550761i
679679 5.79170 0.222265
680680 4.95078 + 7.77752i 0.189854 + 0.298254i
681681 24.6824 0.945831
682682 −13.2963 + 5.50750i −0.509141 + 0.210893i
683683 −20.5178 13.7095i −0.785091 0.524581i 0.0972115 0.995264i 0.469008π-0.469008\pi
−0.882303 + 0.470683i 0.844008π0.844008\pi
684684 26.9229 26.9229i 1.02942 1.02942i
685685 4.24346 6.03585i 0.162134 0.230618i
686686 19.7748 + 3.93346i 0.755007 + 0.150180i
687687 −67.0855 13.3441i −2.55947 0.509111i
688688 −0.718779 + 1.73529i −0.0274032 + 0.0661572i
689689 −5.70900 13.7827i −0.217495 0.525080i
690690 5.45039 + 8.59137i 0.207493 + 0.327068i
691691 −5.00947 + 25.1843i −0.190569 + 0.958057i 0.760561 + 0.649267i 0.224924π0.224924\pi
−0.951130 + 0.308790i 0.900076π0.900076\pi
692692 9.66705 1.92290i 0.367486 0.0730975i
693693 −37.8644 −1.43835
694694 −21.2587 + 4.22862i −0.806970 + 0.160516i
695695 −10.7246 27.7341i −0.406808 1.05202i
696696 20.5057i 0.777268i
697697 14.6882 + 2.89832i 0.556354 + 0.109782i
698698 4.38127 + 4.38127i 0.165834 + 0.165834i
699699 −31.6350 + 76.3737i −1.19655 + 2.88872i
700700 −6.41163 + 8.67506i −0.242337 + 0.327886i
701701 −11.3764 11.3764i −0.429679 0.429679i 0.458840 0.888519i 0.348265π-0.348265\pi
−0.888519 + 0.458840i 0.848265π0.848265\pi
702702 8.58400 + 43.1547i 0.323982 + 1.62877i
703703 −26.1328 39.1106i −0.985619 1.47508i
704704 −2.47681 + 1.65495i −0.0933481 + 0.0623732i
705705 −12.5427 + 28.3592i −0.472386 + 1.06807i
706706 17.3552 7.18875i 0.653171 0.270552i
707707 −5.39075 + 27.1011i −0.202740 + 1.01924i
708708 9.83695 6.57284i 0.369695 0.247022i
709709 −3.94521 + 5.90443i −0.148165 + 0.221745i −0.898127 0.439736i 0.855072π-0.855072\pi
0.749962 + 0.661481i 0.230072π0.230072\pi
710710 −9.29729 + 8.86643i −0.348921 + 0.332751i
711711 −17.7439 89.2047i −0.665449 3.34544i
712712 2.92832 + 7.06959i 0.109743 + 0.264944i
713713 5.21297 5.21297i 0.195227 0.195227i
714714 24.4906 10.1882i 0.916538 0.381285i
715715 0.805999 33.9791i 0.0301427 1.27075i
716716 2.01883 + 0.836227i 0.0754473 + 0.0312513i
717717 −36.1714 + 54.1343i −1.35084 + 2.02168i
718718 2.08691i 0.0778829i
719719 29.9430 + 20.0073i 1.11669 + 0.746146i 0.970016 0.243040i 0.0781446π-0.0781446\pi
0.146670 + 0.989186i 0.453145π0.453145\pi
720720 −11.1245 + 7.05743i −0.414587 + 0.263015i
721721 14.7291 + 22.0436i 0.548539 + 0.820946i
722722 −21.0300 8.71090i −0.782655 0.324186i
723723 30.7226 + 12.7257i 1.14259 + 0.473275i
724724 −6.78429 10.1534i −0.252136 0.377348i
725725 −8.29933 + 33.3670i −0.308229 + 1.23922i
726726 −5.27256 3.52301i −0.195683 0.130751i
727727 32.6875i 1.21231i −0.795345 0.606156i 0.792711π-0.792711\pi
0.795345 0.606156i 0.207289π-0.207289\pi
728728 6.11624 9.15360i 0.226683 0.339255i
729729 27.5167 + 11.3978i 1.01914 + 0.422141i
730730 −15.8866 + 15.1504i −0.587990 + 0.560742i
731731 −7.15023 + 2.97454i −0.264461 + 0.110017i
732732 8.75636 8.75636i 0.323645 0.323645i
733733 8.14076 + 19.6535i 0.300686 + 0.725920i 0.999939 + 0.0110459i 0.00351609π0.00351609\pi
−0.699253 + 0.714874i 0.746484π0.746484\pi
734734 0.264915 + 1.33182i 0.00977821 + 0.0491584i
735735 −10.7926 11.3171i −0.398092 0.417437i
736736 0.847753 1.26875i 0.0312486 0.0467668i
737737 −7.90180 + 5.27981i −0.291066 + 0.194484i
738738 −4.17365 + 20.9824i −0.153634 + 0.772371i
739739 −29.6823 + 12.2948i −1.09188 + 0.452271i −0.854662 0.519185i 0.826236π-0.826236\pi
−0.237218 + 0.971456i 0.576236π0.576236\pi
740740 5.87009 + 15.1802i 0.215789 + 0.558036i
741741 81.7592 54.6298i 3.00350 2.00687i
742742 −3.50428 5.24452i −0.128646 0.192532i
743743 −2.43650 12.2491i −0.0893863 0.449375i −0.999395 0.0347858i 0.988925π-0.988925\pi
0.910008 0.414590i 0.136075π-0.136075\pi
744744 10.1870 + 10.1870i 0.373475 + 0.373475i
745745 14.9588 + 10.5167i 0.548048 + 0.385301i
746746 −3.31743 + 8.00899i −0.121460 + 0.293230i
747747 40.7225 + 40.7225i 1.48996 + 1.48996i
748748 −12.0497 2.37768i −0.440580 0.0869367i
749749 5.37621i 0.196443i
750750 31.6299 10.5363i 1.15496 0.384731i
751751 1.41399 0.281260i 0.0515972 0.0102633i −0.169224 0.985578i 0.554126π-0.554126\pi
0.220821 + 0.975314i 0.429126π0.429126\pi
752752 4.65062 0.169591
753753 23.3198 4.63859i 0.849820 0.169040i
754754 6.84575 34.4159i 0.249307 1.25335i
755755 −4.22971 + 18.9089i −0.153935 + 0.688167i
756756 7.11923 + 17.1873i 0.258924 + 0.625097i
757757 10.3778 25.0542i 0.377187 0.910610i −0.615304 0.788290i 0.710967π-0.710967\pi
0.992491 0.122320i 0.0390334π-0.0390334\pi
758758 11.6791 + 2.32312i 0.424205 + 0.0843796i
759759 −13.2936 2.64426i −0.482528 0.0959807i
760760 11.8213 + 8.31086i 0.428803 + 0.301467i
761761 −23.9731 + 23.9731i −0.869023 + 0.869023i −0.992364 0.123342i 0.960639π-0.960639\pi
0.123342 + 0.992364i 0.460639π0.460639\pi
762762 −5.52889 3.69429i −0.200291 0.133830i
763763 −36.4131 + 15.0828i −1.31824 + 0.546034i
764764 −4.41706 −0.159804
765765 −53.0271 11.7764i −1.91720 0.425778i
766766 −15.0602 −0.544146
767767 18.7042 7.74754i 0.675370 0.279747i
768768 2.47936 + 1.65666i 0.0894662 + 0.0597794i
769769 15.9323 15.9323i 0.574535 0.574535i −0.358858 0.933392i 0.616834π-0.616834\pi
0.933392 + 0.358858i 0.116834π0.116834\pi
770770 −2.46853 14.1569i −0.0889597 0.510180i
771771 34.8634 + 6.93476i 1.25558 + 0.249749i
772772 23.1944 + 4.61365i 0.834784 + 0.166049i
773773 −13.5036 + 32.6005i −0.485690 + 1.17256i 0.471178 + 0.882038i 0.343829π0.343829\pi
−0.956868 + 0.290522i 0.906171π0.906171\pi
774774 −4.23485 10.2238i −0.152219 0.367488i
775775 −12.4534 20.6994i −0.447338 0.743544i
776776 −0.523720 + 2.63292i −0.0188005 + 0.0945163i
777777 45.9264 9.13534i 1.64760 0.327728i
778778 26.0987 0.935683
779779 23.0147 4.57791i 0.824588 0.164021i
780780 −31.7337 + 12.2712i −1.13625 + 0.439380i
781781 17.1148i 0.612417i
782782 6.16874 1.23685i 0.220594 0.0442295i
783783 41.9293 + 41.9293i 1.49843 + 1.49843i
784784 −0.897536 + 2.16684i −0.0320549 + 0.0773873i
785785 −13.4901 + 2.35226i −0.481483 + 0.0839557i
786786 −26.6095 26.6095i −0.949131 0.949131i
787787 −7.92509 39.8421i −0.282499 1.42022i −0.817774 0.575540i 0.804792π-0.804792\pi
0.535275 0.844678i 0.320208π-0.320208\pi
788788 0.856201 + 1.28139i 0.0305009 + 0.0456478i
789789 34.9331 23.3415i 1.24365 0.830981i
790790 32.1955 12.4498i 1.14547 0.442944i
791791 −25.0497 + 10.3759i −0.890665 + 0.368926i
792792 3.42392 17.2132i 0.121664 0.611645i
793793 17.6196 11.7730i 0.625689 0.418072i
794794 14.0544 21.0338i 0.498771 0.746463i
795795 −0.462270 + 19.4883i −0.0163950 + 0.691177i
796796 0.957161 + 4.81198i 0.0339257 + 0.170556i
797797 −12.3988 29.9332i −0.439186 1.06029i −0.976230 0.216736i 0.930459π-0.930459\pi
0.537044 0.843554i 0.319541π-0.319541\pi
798798 29.3978 29.3978i 1.04067 1.04067i
799799 13.5795 + 13.5380i 0.480408 + 0.478941i
800800 −3.36392 3.69919i −0.118933 0.130786i
801801 −41.6521 17.2529i −1.47170 0.609600i
802802 −5.70419 + 8.53692i −0.201422 + 0.301449i
803803 29.2447i 1.03202i
804804 7.90995 + 5.28526i 0.278962 + 0.186397i
805805 3.94345 + 6.21601i 0.138989 + 0.219085i
806806 13.6966 + 20.4984i 0.482441 + 0.722024i
807807 11.9681 + 4.95737i 0.421299 + 0.174508i
808808 −11.8328 4.90129i −0.416275 0.172427i
809809 2.83469 + 4.24242i 0.0996626 + 0.149156i 0.877950 0.478753i 0.158911π-0.158911\pi
−0.778287 + 0.627909i 0.783911π0.783911\pi
810810 3.92316 17.5385i 0.137846 0.616240i
811811 −17.3551 11.5963i −0.609421 0.407202i 0.212208 0.977224i 0.431934π-0.431934\pi
−0.821629 + 0.570022i 0.806934π0.806934\pi
812812 14.8363i 0.520651i
813813 5.42890 8.12493i 0.190400 0.284954i
814814 −20.0315 8.29733i −0.702105 0.290821i
815815 29.5086 + 0.699958i 1.03364 + 0.0245185i
816816 2.41701 + 12.0548i 0.0846123 + 0.422001i
817817 −8.58292 + 8.58292i −0.300278 + 0.300278i
818818 7.22198 + 17.4354i 0.252511 + 0.609615i
819819 12.6539 + 63.6154i 0.442163 + 2.22290i
820820 −8.11709 0.192541i −0.283461 0.00672383i
821821 −12.5463 + 18.7769i −0.437870 + 0.655318i −0.983121 0.182954i 0.941434π-0.941434\pi
0.545252 + 0.838272i 0.316434π0.316434\pi
822822 8.18101 5.46638i 0.285346 0.190662i
823823 5.50950 27.6981i 0.192049 0.965496i −0.757728 0.652570i 0.773691π-0.773691\pi
0.949777 0.312926i 0.101309π-0.101309\pi
824824 −11.3530 + 4.70255i −0.395499 + 0.163821i
825825 −18.9225 + 40.1801i −0.658795 + 1.39889i
826826 7.11721 4.75557i 0.247639 0.165467i
827827 13.1935 + 19.7455i 0.458783 + 0.686617i 0.986677 0.162693i 0.0520181π-0.0520181\pi
−0.527894 + 0.849310i 0.677018π0.677018\pi
828828 1.75392 + 8.81754i 0.0609528 + 0.306431i
829829 −29.1861 29.1861i −1.01367 1.01367i −0.999905 0.0137698i 0.995617π-0.995617\pi
−0.0137698 0.999905i 0.504383π-0.504383\pi
830830 −12.5707 + 17.8804i −0.436334 + 0.620637i
831831 19.5644 47.2327i 0.678683 1.63848i
832832 3.60818 + 3.60818i 0.125091 + 0.125091i
833833 −8.92846 + 3.71429i −0.309353 + 0.128693i
834834 39.6537i 1.37309i
835835 −36.1254 15.9775i −1.25017 0.552925i
836836 −18.8805 + 3.75557i −0.652996 + 0.129889i
837837 −41.6601 −1.43998
838838 2.17804 0.433238i 0.0752390 0.0149660i
839839 −2.28546 + 11.4898i −0.0789027 + 0.396671i 0.921071 + 0.389395i 0.127316π0.127316\pi
−0.999974 + 0.00727558i 0.997684π0.997684\pi
840840 −12.1471 + 7.70619i −0.419116 + 0.265889i
841841 −6.99907 16.8972i −0.241347 0.582664i
842842 −10.5724 + 25.5242i −0.364351 + 0.879620i
843843 −83.5845 16.6260i −2.87880 0.572630i
844844 −26.1283 5.19724i −0.899373 0.178896i
845845 −28.7203 + 5.00794i −0.988009 + 0.172278i
846846 −19.3749 + 19.3749i −0.666122 + 0.666122i
847847 −3.81479 2.54896i −0.131078 0.0875834i
848848 2.70105 1.11881i 0.0927544 0.0384201i
849849 8.99114 0.308575
850850 0.945983 20.5938i 0.0324470 0.706362i
851851 11.1067 0.380732
852852 −15.8283 + 6.55631i −0.542270 + 0.224616i
853853 −7.11121 4.75156i −0.243483 0.162690i 0.427841 0.903854i 0.359274π-0.359274\pi
−0.671324 + 0.741164i 0.734274π0.734274\pi
854854 6.33539 6.33539i 0.216792 0.216792i
855855 −83.8722 + 14.6247i −2.86837 + 0.500155i
856856 −2.44404 0.486150i −0.0835355 0.0166162i
857857 −38.0331 7.56525i −1.29919 0.258424i −0.503427 0.864038i 0.667928π-0.667928\pi
−0.795759 + 0.605614i 0.792928π0.792928\pi
858858 17.3453 41.8752i 0.592158 1.42960i
859859 3.49731 + 8.44324i 0.119327 + 0.288080i 0.972245 0.233964i 0.0751698π-0.0751698\pi
−0.852919 + 0.522044i 0.825170π0.825170\pi
860860 3.54645 2.24988i 0.120933 0.0767203i
861861 −4.55731 + 22.9112i −0.155313 + 0.780810i
862862 26.3843 5.24817i 0.898654 0.178753i
863863 −40.0088 −1.36191 −0.680957 0.732323i 0.738436π-0.738436\pi
−0.680957 + 0.732323i 0.738436π0.738436\pi
864864 −8.45716 + 1.68223i −0.287719 + 0.0572308i
865865 −20.1563 8.91471i −0.685334 0.303109i
866866 6.95003i 0.236172i
867867 −28.0341 + 42.2350i −0.952088 + 1.43438i
868868 7.37050 + 7.37050i 0.250171 + 0.250171i
869869 −17.5977 + 42.4846i −0.596962 + 1.44119i
870870 −26.3710 + 37.5099i −0.894062 + 1.27170i
871871 11.5112 + 11.5112i 0.390044 + 0.390044i
872872 −3.56398 17.9173i −0.120692 0.606758i
873873 −8.78710 13.1508i −0.297398 0.445088i
874874 8.19919 5.47853i 0.277342 0.185314i
875875 22.8848 7.62320i 0.773648 0.257711i
876876 −27.0465 + 11.2030i −0.913816 + 0.378515i
877877 0.434606 2.18491i 0.0146756 0.0737792i −0.972753 0.231842i 0.925525π-0.925525\pi
0.987429 + 0.158063i 0.0505248π0.0505248\pi
878878 10.1492 6.78147i 0.342519 0.228864i
879879 13.1021 19.6087i 0.441923 0.661385i
880880 6.65899 + 0.157954i 0.224474 + 0.00532464i
881881 −6.84061 34.3901i −0.230466 1.15863i −0.906645 0.421894i 0.861365π-0.861365\pi
0.676179 0.736737i 0.263635π-0.263635\pi
882882 −5.28804 12.7665i −0.178058 0.429869i
883883 −8.59552 + 8.59552i −0.289262 + 0.289262i −0.836788 0.547526i 0.815570π-0.815570\pi
0.547526 + 0.836788i 0.315570π0.315570\pi
884884 0.0321684 + 21.0391i 0.00108194 + 0.707621i
885885 −26.4470 0.627336i −0.889007 0.0210877i
886886 23.9375 + 9.91525i 0.804197 + 0.333109i
887887 −3.09981 + 4.63920i −0.104082 + 0.155769i −0.879855 0.475243i 0.842360π-0.842360\pi
0.775773 + 0.631012i 0.217360π0.217360\pi
888888 21.7043i 0.728350i
889889 −4.00025 2.67288i −0.134164 0.0896456i
890890 3.73512 16.6979i 0.125202 0.559714i
891891 13.3013 + 19.9068i 0.445610 + 0.666903i
892892 −9.12708 3.78056i −0.305597 0.126583i
893893 27.7665 + 11.5013i 0.929170 + 0.384875i
894894 13.5475 + 20.2752i 0.453095 + 0.678105i
895895 −2.61751 4.12594i −0.0874938 0.137915i
896896 1.79386 + 1.19862i 0.0599287 + 0.0400431i
897897 23.2181i 0.775230i
898898 −20.8568 + 31.2145i −0.696002 + 1.04164i
899899 30.6950 + 12.7143i 1.02373 + 0.424045i
900900 29.4255 + 1.39676i 0.980851 + 0.0465587i
901901 11.1437 + 4.59594i 0.371252 + 0.153113i
902902 7.64836 7.64836i 0.254662 0.254662i
903903 −4.62414 11.1637i −0.153882 0.371503i
904904 −2.45178 12.3259i −0.0815448 0.409954i
905905 −0.647517 + 27.2978i −0.0215242 + 0.907411i
906906 −14.3554 + 21.4844i −0.476928 + 0.713773i
907907 0.544935 0.364114i 0.0180943 0.0120902i −0.546490 0.837465i 0.684036π-0.684036\pi
0.564584 + 0.825375i 0.309036π0.309036\pi
908908 −1.61484 + 8.11835i −0.0535904 + 0.269417i
909909 69.7155 28.8771i 2.31232 0.957793i
910910 −22.9599 + 8.87845i −0.761113 + 0.294318i
911911 −0.784565 + 0.524230i −0.0259938 + 0.0173685i −0.568499 0.822684i 0.692476π-0.692476\pi
0.542505 + 0.840052i 0.317476π0.317476\pi
912912 10.7060 + 16.0226i 0.354510 + 0.530562i
913913 −5.68051 28.5579i −0.187998 0.945127i
914914 −12.7246 12.7246i −0.420891 0.420891i
915915 −27.2785 + 4.75652i −0.901798 + 0.157246i
916916 8.77812 21.1923i 0.290037 0.700212i
917917 −19.2525 19.2525i −0.635773 0.635773i
918918 −29.5913 19.7069i −0.976660 0.650425i
919919 7.40165i 0.244158i 0.992520 + 0.122079i 0.0389561π0.0389561\pi
−0.992520 + 0.122079i 0.961044π0.961044\pi
920920 −3.18240 + 1.23061i −0.104921 + 0.0405722i
921921 44.7210 8.89556i 1.47361 0.293119i
922922 23.9859 0.789933
923923 −28.7544 + 5.71960i −0.946462 + 0.188263i
924924 3.73867 18.7955i 0.122993 0.618328i
925925 8.78444 35.3174i 0.288831 1.16123i
926926 −13.5396 32.6876i −0.444940 1.07418i
927927 27.7061 66.8885i 0.909989 2.19691i
928928 6.74460 + 1.34158i 0.221402 + 0.0440397i
929929 45.9163 + 9.13333i 1.50647 + 0.299655i 0.878181 0.478328i 0.158757π-0.158757\pi
0.628285 + 0.777983i 0.283757π0.283757\pi
930930 −5.53367 31.7354i −0.181456 1.04064i
931931 −10.7174 + 10.7174i −0.351250 + 0.351250i
932932 −23.0506 15.4019i −0.755047 0.504506i
933933 −1.78052 + 0.737517i −0.0582917 + 0.0241452i
934934 22.4584 0.734861
935935 18.9840 + 19.8456i 0.620842 + 0.649022i
936936 −30.0639 −0.982671
937937 −20.4567 + 8.47343i −0.668291 + 0.276815i −0.690923 0.722929i 0.742795π-0.742795\pi
0.0226319 + 0.999744i 0.492795π0.492795\pi
938938 5.72299 + 3.82398i 0.186862 + 0.124857i
939939 −6.97700 + 6.97700i −0.227686 + 0.227686i
940940 −8.50711 5.98085i −0.277471 0.195074i
941941 16.4307 + 3.26827i 0.535626 + 0.106543i 0.455489 0.890241i 0.349464π-0.349464\pi
0.0801364 + 0.996784i 0.474464π0.474464\pi
942942 −17.9102 3.56257i −0.583547 0.116075i
943943 −2.12035 + 5.11898i −0.0690481 + 0.166697i
944944 1.51831 + 3.66553i 0.0494168 + 0.119303i
945945 9.08070 40.5953i 0.295395 1.32057i
946946 −1.09153 + 5.48751i −0.0354888 + 0.178414i
947947 41.4186 8.23868i 1.34592 0.267721i 0.531041 0.847346i 0.321801π-0.321801\pi
0.814883 + 0.579625i 0.196801π0.196801\pi
948948 46.0325 1.49507
949949 −49.1337 + 9.77330i −1.59495 + 0.317255i
950950 −10.9359 30.4051i −0.354809 0.986473i
951951 42.2819i 1.37109i
952952 1.74875 + 8.72184i 0.0566773 + 0.282676i
953953 24.8733 + 24.8733i 0.805725 + 0.805725i 0.983984 0.178259i 0.0570464π-0.0570464\pi
−0.178259 + 0.983984i 0.557046π0.557046\pi
954954 −6.59173 + 15.9138i −0.213415 + 0.515230i
955955 8.07986 + 5.68048i 0.261458 + 0.183816i
956956 −15.4390 15.4390i −0.499332 0.499332i
957957 −11.9167 59.9094i −0.385213 1.93659i
958958 −10.7052 16.0214i −0.345868 0.517628i
959959 5.91911 3.95502i 0.191138 0.127714i
960960 −2.40483 6.21896i −0.0776156 0.200716i
961961 7.07502 2.93057i 0.228226 0.0945345i
962962 −7.24590 + 36.4276i −0.233617 + 1.17447i
963963 12.2074 8.15673i 0.393378 0.262847i
964964 −6.19568 + 9.27249i −0.199549 + 0.298647i
965965 −36.4948 38.2682i −1.17481 1.23190i
966966 1.91515 + 9.62809i 0.0616188 + 0.309779i
967967 17.9448 + 43.3226i 0.577066 + 1.39316i 0.895435 + 0.445193i 0.146865π0.146865\pi
−0.318369 + 0.947967i 0.603135π0.603135\pi
968968 1.50372 1.50372i 0.0483314 0.0483314i
969969 −15.3814 + 77.9502i −0.494122 + 2.50412i
970970 4.34403 4.14272i 0.139478 0.133015i
971971 4.40078 + 1.82286i 0.141228 + 0.0584985i 0.452178 0.891928i 0.350647π-0.350647\pi
−0.310950 + 0.950426i 0.600647π0.600647\pi
972972 −1.05678 + 1.58158i −0.0338963 + 0.0507294i
973973 28.6901i 0.919764i
974974 25.8876 + 17.2975i 0.829492 + 0.554249i
975975 73.8298 + 18.3636i 2.36444 + 0.588105i
976976 2.30720 + 3.45296i 0.0738516 + 0.110527i
977977 −2.57938 1.06842i −0.0825218 0.0341816i 0.341041 0.940049i 0.389221π-0.389221\pi
−0.423562 + 0.905867i 0.639221π0.639221\pi
978978 36.3659 + 15.0633i 1.16285 + 0.481670i
979979 12.6638 + 18.9527i 0.404736 + 0.605730i
980980 4.42844 2.80942i 0.141461 0.0897435i
981981 89.4929 + 59.7973i 2.85729 + 1.90918i
982982 31.6963i 1.01147i
983983 7.38005 11.0450i 0.235387 0.352281i −0.694905 0.719102i 0.744554π-0.744554\pi
0.930292 + 0.366820i 0.119554π0.119554\pi
984984 −10.0034 4.14353i −0.318896 0.132091i
985985 0.0817189 3.44508i 0.00260378 0.109769i
986986 15.7884 + 23.5510i 0.502805 + 0.750015i
987987 −21.1559 + 21.1559i −0.673400 + 0.673400i
988988 12.6193 + 30.4658i 0.401475 + 0.969246i
989989 −0.559142 2.81100i −0.0177797 0.0893845i
990990 −28.3999 + 27.0838i −0.902610 + 0.860781i
991991 7.46029 11.1651i 0.236984 0.354671i −0.693847 0.720123i 0.744085π-0.744085\pi
0.930830 + 0.365451i 0.119085π0.119085\pi
992992 −4.01713 + 2.68416i −0.127544 + 0.0852222i
993993 16.5132 83.0174i 0.524030 2.63448i
994994 −11.4521 + 4.74361i −0.363238 + 0.150458i
995995 4.43748 10.0332i 0.140678 0.318074i
996996 −24.2352 + 16.1934i −0.767920 + 0.513108i
997997 −3.11894 4.66783i −0.0987780 0.147832i 0.778789 0.627286i 0.215834π-0.215834\pi
−0.877567 + 0.479455i 0.840834π0.840834\pi
998998 5.07928 + 25.5353i 0.160782 + 0.808305i
999999 −44.3802 44.3802i −1.40413 1.40413i
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 170.2.r.b.23.1 yes 40
5.2 odd 4 170.2.o.b.57.1 yes 40
5.3 odd 4 850.2.s.d.57.5 40
5.4 even 2 850.2.v.d.193.5 40
17.3 odd 16 170.2.o.b.3.1 40
85.3 even 16 850.2.v.d.207.5 40
85.37 even 16 inner 170.2.r.b.37.1 yes 40
85.54 odd 16 850.2.s.d.343.5 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
170.2.o.b.3.1 40 17.3 odd 16
170.2.o.b.57.1 yes 40 5.2 odd 4
170.2.r.b.23.1 yes 40 1.1 even 1 trivial
170.2.r.b.37.1 yes 40 85.37 even 16 inner
850.2.s.d.57.5 40 5.3 odd 4
850.2.s.d.343.5 40 85.54 odd 16
850.2.v.d.193.5 40 5.4 even 2
850.2.v.d.207.5 40 85.3 even 16