Properties

Label 891.2.n.f.784.2
Level 891891
Weight 22
Character 891.784
Analytic conductor 7.1157.115
Analytic rank 00
Dimension 3232
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [891,2,Mod(136,891)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(891, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("891.136");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 891=3411 891 = 3^{4} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 891.n (of order 1515, degree 88, not 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: 7.114670820107.11467082010
Analytic rank: 00
Dimension: 3232
Relative dimension: 44 over Q(ζ15)\Q(\zeta_{15})
Twist minimal: no (minimal twist has level 297)
Sato-Tate group: SU(2)[C15]\mathrm{SU}(2)[C_{15}]

Embedding invariants

Embedding label 784.2
Character χ\chi == 891.784
Dual form 891.2.n.f.433.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.03786590.360270i)q2+(1.827930.388540i)q4+(0.2807352.67101i)q5+(1.668901.85350i)q7+(0.4330811.33288i)q80.972914q10+(3.26867+0.561950i)q11+(3.48756+1.55276i)q13+(0.604567+0.671439i)q14+(2.950621.31370i)q16+(0.9097820.660995i)q17+(2.09612+6.45120i)q19+(0.5246294.99151i)q20+(0.07868241.19888i)q22+(3.374705.84515i)q23+(2.164750.460133i)q25+(0.4273531.31526i)q26+(3.770802.73965i)q28+(4.967995.51751i)q29+(6.124822.72695i)q31+(1.986493.44070i)q32+(0.203687+0.352796i)q34+(5.41925+3.93732i)q35+(0.0589927+0.181561i)q37+(2.244800.999449i)q38+(3.68173+0.782576i)q40+(0.4257790.472875i)q41+(2.36375+4.09413i)q43+(6.193260.242800i)q44+(1.97805+1.43713i)q46+(11.0461+2.34792i)q47+(0.08145780.775019i)q49+(0.0838015+0.797318i)q50+(6.97834+1.48329i)q52+(4.45732+3.23843i)q53+(2.418608.57290i)q55+(1.74774+3.02717i)q56+(1.79967+1.99874i)q58+(8.24507+1.75254i)q59+(1.572970.700331i)q61+(0.750514+2.30984i)q62+(4.061652.95096i)q64+(5.126528.87939i)q65+(2.253353.90292i)q67+(1.919840.854770i)q68+(1.62370+1.80330i)q70+(9.95124+7.23000i)q71+(0.658284+2.02599i)q73+(0.0676446+0.0143783i)q74+(6.33812+10.9779i)q76+(4.413526.99633i)q77+(1.21066+11.5186i)q79+(2.680578.24994i)q80+(0.1864850.135489i)q82+(0.747666+0.332882i)q83+(2.02093+2.24447i)q85+(1.56449+0.696558i)q86+(0.6665834.60013i)q881.42041q89+(2.942349.05560i)q91+(8.439819.37336i)q92+(0.4276154.06848i)q94+(17.81973.78769i)q95+(1.0527310.0160i)q970.282300q98+O(q100)q+(-0.0378659 - 0.360270i) q^{2} +(1.82793 - 0.388540i) q^{4} +(0.280735 - 2.67101i) q^{5} +(-1.66890 - 1.85350i) q^{7} +(-0.433081 - 1.33288i) q^{8} -0.972914 q^{10} +(3.26867 + 0.561950i) q^{11} +(3.48756 + 1.55276i) q^{13} +(-0.604567 + 0.671439i) q^{14} +(2.95062 - 1.31370i) q^{16} +(-0.909782 - 0.660995i) q^{17} +(2.09612 + 6.45120i) q^{19} +(-0.524629 - 4.99151i) q^{20} +(0.0786824 - 1.19888i) q^{22} +(-3.37470 - 5.84515i) q^{23} +(-2.16475 - 0.460133i) q^{25} +(0.427353 - 1.31526i) q^{26} +(-3.77080 - 2.73965i) q^{28} +(-4.96799 - 5.51751i) q^{29} +(-6.12482 - 2.72695i) q^{31} +(-1.98649 - 3.44070i) q^{32} +(-0.203687 + 0.352796i) q^{34} +(-5.41925 + 3.93732i) q^{35} +(-0.0589927 + 0.181561i) q^{37} +(2.24480 - 0.999449i) q^{38} +(-3.68173 + 0.782576i) q^{40} +(0.425779 - 0.472875i) q^{41} +(-2.36375 + 4.09413i) q^{43} +(6.19326 - 0.242800i) q^{44} +(-1.97805 + 1.43713i) q^{46} +(11.0461 + 2.34792i) q^{47} +(0.0814578 - 0.775019i) q^{49} +(-0.0838015 + 0.797318i) q^{50} +(6.97834 + 1.48329i) q^{52} +(-4.45732 + 3.23843i) q^{53} +(2.41860 - 8.57290i) q^{55} +(-1.74774 + 3.02717i) q^{56} +(-1.79967 + 1.99874i) q^{58} +(-8.24507 + 1.75254i) q^{59} +(1.57297 - 0.700331i) q^{61} +(-0.750514 + 2.30984i) q^{62} +(4.06165 - 2.95096i) q^{64} +(5.12652 - 8.87939i) q^{65} +(-2.25335 - 3.90292i) q^{67} +(-1.91984 - 0.854770i) q^{68} +(1.62370 + 1.80330i) q^{70} +(9.95124 + 7.23000i) q^{71} +(-0.658284 + 2.02599i) q^{73} +(0.0676446 + 0.0143783i) q^{74} +(6.33812 + 10.9779i) q^{76} +(-4.41352 - 6.99633i) q^{77} +(1.21066 + 11.5186i) q^{79} +(-2.68057 - 8.24994i) q^{80} +(-0.186485 - 0.135489i) q^{82} +(-0.747666 + 0.332882i) q^{83} +(-2.02093 + 2.24447i) q^{85} +(1.56449 + 0.696558i) q^{86} +(-0.666583 - 4.60013i) q^{88} -1.42041 q^{89} +(-2.94234 - 9.05560i) q^{91} +(-8.43981 - 9.37336i) q^{92} +(0.427615 - 4.06848i) q^{94} +(17.8197 - 3.78769i) q^{95} +(-1.05273 - 10.0160i) q^{97} -0.282300 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 32q2q2+4q4q5+2q7+12q1013q11+2q13+22q14+24q164q174q1915q2214q23+19q25+42q26+30q28q2914q31++52q98+O(q100) 32 q - 2 q^{2} + 4 q^{4} - q^{5} + 2 q^{7} + 12 q^{10} - 13 q^{11} + 2 q^{13} + 22 q^{14} + 24 q^{16} - 4 q^{17} - 4 q^{19} - 15 q^{22} - 14 q^{23} + 19 q^{25} + 42 q^{26} + 30 q^{28} - q^{29} - 14 q^{31}+ \cdots + 52 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/891Z)×\left(\mathbb{Z}/891\mathbb{Z}\right)^\times.

nn 244244 650650
χ(n)\chi(n) e(45)e\left(\frac{4}{5}\right) e(23)e\left(\frac{2}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.0378659 0.360270i −0.0267752 0.254749i −0.999719 0.0237069i 0.992453π-0.992453\pi
0.972944 0.231042i 0.0742135π-0.0742135\pi
33 0 0
44 1.82793 0.388540i 0.913967 0.194270i
55 0.280735 2.67101i 0.125548 1.19451i −0.732436 0.680836i 0.761616π-0.761616\pi
0.857984 0.513676i 0.171717π-0.171717\pi
66 0 0
77 −1.66890 1.85350i −0.630786 0.700559i 0.340022 0.940417i 0.389565π-0.389565\pi
−0.970808 + 0.239859i 0.922899π0.922899\pi
88 −0.433081 1.33288i −0.153117 0.471246i
99 0 0
1010 −0.972914 −0.307663
1111 3.26867 + 0.561950i 0.985541 + 0.169434i
1212 0 0
1313 3.48756 + 1.55276i 0.967274 + 0.430658i 0.828700 0.559694i 0.189081π-0.189081\pi
0.138575 + 0.990352i 0.455748π0.455748\pi
1414 −0.604567 + 0.671439i −0.161577 + 0.179450i
1515 0 0
1616 2.95062 1.31370i 0.737654 0.328425i
1717 −0.909782 0.660995i −0.220654 0.160315i 0.471967 0.881616i 0.343544π-0.343544\pi
−0.692621 + 0.721301i 0.743544π0.743544\pi
1818 0 0
1919 2.09612 + 6.45120i 0.480883 + 1.48001i 0.837856 + 0.545891i 0.183809π0.183809\pi
−0.356973 + 0.934115i 0.616191π0.616191\pi
2020 −0.524629 4.99151i −0.117311 1.11614i
2121 0 0
2222 0.0786824 1.19888i 0.0167751 0.255602i
2323 −3.37470 5.84515i −0.703674 1.21880i −0.967168 0.254138i 0.918208π-0.918208\pi
0.263494 0.964661i 0.415125π-0.415125\pi
2424 0 0
2525 −2.16475 0.460133i −0.432951 0.0920266i
2626 0.427353 1.31526i 0.0838108 0.257943i
2727 0 0
2828 −3.77080 2.73965i −0.712615 0.517745i
2929 −4.96799 5.51751i −0.922532 1.02458i −0.999620 0.0275515i 0.991229π-0.991229\pi
0.0770882 0.997024i 0.475438π-0.475438\pi
3030 0 0
3131 −6.12482 2.72695i −1.10005 0.489774i −0.225271 0.974296i 0.572327π-0.572327\pi
−0.874779 + 0.484522i 0.838994π0.838994\pi
3232 −1.98649 3.44070i −0.351165 0.608236i
3333 0 0
3434 −0.203687 + 0.352796i −0.0349320 + 0.0605040i
3535 −5.41925 + 3.93732i −0.916020 + 0.665528i
3636 0 0
3737 −0.0589927 + 0.181561i −0.00969834 + 0.0298484i −0.955789 0.294055i 0.904995π-0.904995\pi
0.946090 + 0.323903i 0.104995π0.104995\pi
3838 2.24480 0.999449i 0.364154 0.162132i
3939 0 0
4040 −3.68173 + 0.782576i −0.582133 + 0.123736i
4141 0.425779 0.472875i 0.0664954 0.0738507i −0.708979 0.705229i 0.750844π-0.750844\pi
0.775475 + 0.631379i 0.217511π0.217511\pi
4242 0 0
4343 −2.36375 + 4.09413i −0.360468 + 0.624349i −0.988038 0.154212i 0.950716π-0.950716\pi
0.627570 + 0.778560i 0.284050π0.284050\pi
4444 6.19326 0.242800i 0.933669 0.0366035i
4545 0 0
4646 −1.97805 + 1.43713i −0.291647 + 0.211894i
4747 11.0461 + 2.34792i 1.61124 + 0.342480i 0.923536 0.383512i 0.125285π-0.125285\pi
0.687704 + 0.725991i 0.258619π0.258619\pi
4848 0 0
4949 0.0814578 0.775019i 0.0116368 0.110717i
5050 −0.0838015 + 0.797318i −0.0118513 + 0.112758i
5151 0 0
5252 6.97834 + 1.48329i 0.967721 + 0.205695i
5353 −4.45732 + 3.23843i −0.612259 + 0.444833i −0.850209 0.526445i 0.823525π-0.823525\pi
0.237950 + 0.971277i 0.423525π0.423525\pi
5454 0 0
5555 2.41860 8.57290i 0.326125 1.15597i
5656 −1.74774 + 3.02717i −0.233551 + 0.404523i
5757 0 0
5858 −1.79967 + 1.99874i −0.236309 + 0.262447i
5959 −8.24507 + 1.75254i −1.07342 + 0.228162i −0.710527 0.703670i 0.751543π-0.751543\pi
−0.362890 + 0.931832i 0.618210π0.618210\pi
6060 0 0
6161 1.57297 0.700331i 0.201398 0.0896682i −0.303559 0.952813i 0.598175π-0.598175\pi
0.504957 + 0.863144i 0.331508π0.331508\pi
6262 −0.750514 + 2.30984i −0.0953154 + 0.293351i
6363 0 0
6464 4.06165 2.95096i 0.507706 0.368870i
6565 5.12652 8.87939i 0.635866 1.10135i
6666 0 0
6767 −2.25335 3.90292i −0.275291 0.476817i 0.694918 0.719089i 0.255441π-0.255441\pi
−0.970208 + 0.242272i 0.922107π0.922107\pi
6868 −1.91984 0.854770i −0.232815 0.103656i
6969 0 0
7070 1.62370 + 1.80330i 0.194069 + 0.215536i
7171 9.95124 + 7.23000i 1.18099 + 0.858043i 0.992284 0.123990i 0.0395689π-0.0395689\pi
0.188711 + 0.982033i 0.439569π0.439569\pi
7272 0 0
7373 −0.658284 + 2.02599i −0.0770463 + 0.237124i −0.982161 0.188044i 0.939785π-0.939785\pi
0.905114 + 0.425168i 0.139785π0.139785\pi
7474 0.0676446 + 0.0143783i 0.00786353 + 0.00167144i
7575 0 0
7676 6.33812 + 10.9779i 0.727032 + 1.25926i
7777 −4.41352 6.99633i −0.502967 0.797306i
7878 0 0
7979 1.21066 + 11.5186i 0.136210 + 1.29595i 0.822561 + 0.568677i 0.192545π0.192545\pi
−0.686351 + 0.727270i 0.740789π0.740789\pi
8080 −2.68057 8.24994i −0.299696 0.922371i
8181 0 0
8282 −0.186485 0.135489i −0.0205938 0.0149623i
8383 −0.747666 + 0.332882i −0.0820670 + 0.0365386i −0.447360 0.894354i 0.647636π-0.647636\pi
0.365293 + 0.930893i 0.380969π0.380969\pi
8484 0 0
8585 −2.02093 + 2.24447i −0.219201 + 0.243447i
8686 1.56449 + 0.696558i 0.168704 + 0.0751118i
8787 0 0
8888 −0.666583 4.60013i −0.0710580 0.490376i
8989 −1.42041 −0.150564 −0.0752818 0.997162i 0.523986π-0.523986\pi
−0.0752818 + 0.997162i 0.523986π0.523986\pi
9090 0 0
9191 −2.94234 9.05560i −0.308441 0.949285i
9292 −8.43981 9.37336i −0.879911 0.977240i
9393 0 0
9494 0.427615 4.06848i 0.0441051 0.419632i
9595 17.8197 3.78769i 1.82826 0.388609i
9696 0 0
9797 −1.05273 10.0160i −0.106888 1.01697i −0.908146 0.418654i 0.862502π-0.862502\pi
0.801257 0.598320i 0.204165π-0.204165\pi
9898 −0.282300 −0.0285166
9999 0 0
100100 −4.13581 −0.413581
101101 2.00110 + 19.0392i 0.199117 + 1.89447i 0.402580 + 0.915385i 0.368113π0.368113\pi
−0.203464 + 0.979082i 0.565220π0.565220\pi
102102 0 0
103103 3.03862 0.645879i 0.299404 0.0636404i −0.0557601 0.998444i 0.517758π-0.517758\pi
0.355164 + 0.934804i 0.384425π0.384425\pi
104104 0.559258 5.32098i 0.0548397 0.521765i
105105 0 0
106106 1.33549 + 1.48321i 0.129714 + 0.144062i
107107 −3.05389 9.39890i −0.295231 0.908626i −0.983144 0.182833i 0.941473π-0.941473\pi
0.687913 0.725793i 0.258527π-0.258527\pi
108108 0 0
109109 18.0851 1.73224 0.866121 0.499834i 0.166606π-0.166606\pi
0.866121 + 0.499834i 0.166606π0.166606\pi
110110 −3.18014 0.546729i −0.303214 0.0521286i
111111 0 0
112112 −7.35924 3.27654i −0.695383 0.309604i
113113 −3.39913 + 3.77511i −0.319763 + 0.355133i −0.881501 0.472183i 0.843466π-0.843466\pi
0.561738 + 0.827315i 0.310133π0.310133\pi
114114 0 0
115115 −16.5599 + 7.37293i −1.54422 + 0.687529i
116116 −11.2249 8.15539i −1.04221 0.757209i
117117 0 0
118118 0.943595 + 2.90409i 0.0868650 + 0.267343i
119119 0.293180 + 2.78942i 0.0268758 + 0.255706i
120120 0 0
121121 10.3684 + 3.67366i 0.942584 + 0.333969i
122122 −0.311870 0.540174i −0.0282354 0.0489051i
123123 0 0
124124 −12.2553 2.60494i −1.10056 0.233931i
125125 2.31293 7.11847i 0.206875 0.636695i
126126 0 0
127127 −0.674959 0.490387i −0.0598930 0.0435148i 0.557436 0.830220i 0.311785π-0.311785\pi
−0.617329 + 0.786705i 0.711785π0.711785\pi
128128 −6.53383 7.25655i −0.577514 0.641395i
129129 0 0
130130 −3.39309 1.51070i −0.297594 0.132497i
131131 9.87633 + 17.1063i 0.862899 + 1.49459i 0.869118 + 0.494605i 0.164687π0.164687\pi
−0.00621860 + 0.999981i 0.501979π0.501979\pi
132132 0 0
133133 8.45910 14.6516i 0.733497 1.27045i
134134 −1.32078 + 0.959601i −0.114098 + 0.0828969i
135135 0 0
136136 −0.487022 + 1.49890i −0.0417618 + 0.128529i
137137 −3.62037 + 1.61189i −0.309309 + 0.137713i −0.555520 0.831503i 0.687481π-0.687481\pi
0.246211 + 0.969216i 0.420814π0.420814\pi
138138 0 0
139139 3.33035 0.707887i 0.282476 0.0600422i −0.0644947 0.997918i 0.520544π-0.520544\pi
0.346971 + 0.937876i 0.387210π0.387210\pi
140140 −8.37623 + 9.30275i −0.707921 + 0.786226i
141141 0 0
142142 2.22794 3.85890i 0.186964 0.323832i
143143 10.5271 + 7.03530i 0.880321 + 0.588321i
144144 0 0
145145 −16.1320 + 11.7206i −1.33969 + 0.973343i
146146 0.754828 + 0.160444i 0.0624700 + 0.0132784i
147147 0 0
148148 −0.0372912 + 0.354802i −0.00306532 + 0.0291646i
149149 −0.538739 + 5.12576i −0.0441352 + 0.419918i 0.950039 + 0.312132i 0.101043π0.101043\pi
−0.994174 + 0.107787i 0.965624π0.965624\pi
150150 0 0
151151 13.4449 + 2.85780i 1.09413 + 0.232564i 0.719418 0.694578i 0.244409π-0.244409\pi
0.374710 + 0.927142i 0.377742π0.377742\pi
152152 7.69091 5.58778i 0.623816 0.453229i
153153 0 0
154154 −2.35344 + 1.85498i −0.189646 + 0.149478i
155155 −9.00316 + 15.5939i −0.723151 + 1.25253i
156156 0 0
157157 11.1305 12.3617i 0.888311 0.986569i −0.111663 0.993746i 0.535618π-0.535618\pi
0.999974 + 0.00717663i 0.00228441π0.00228441\pi
158158 4.10397 0.872326i 0.326494 0.0693985i
159159 0 0
160160 −9.74784 + 4.34002i −0.770634 + 0.343109i
161161 −5.20197 + 16.0100i −0.409973 + 1.26177i
162162 0 0
163163 −18.4445 + 13.4007i −1.44469 + 1.04963i −0.457648 + 0.889134i 0.651308π0.651308\pi
−0.987037 + 0.160492i 0.948692π0.948692\pi
164164 0.594565 1.02982i 0.0464277 0.0804152i
165165 0 0
166166 0.148238 + 0.256756i 0.0115055 + 0.0199282i
167167 11.5103 + 5.12470i 0.890691 + 0.396561i 0.800478 0.599362i 0.204579π-0.204579\pi
0.0902121 + 0.995923i 0.471245π0.471245\pi
168168 0 0
169169 1.05329 + 1.16980i 0.0810222 + 0.0899843i
170170 0.885140 + 0.643092i 0.0678871 + 0.0493229i
171171 0 0
172172 −2.73004 + 8.40221i −0.208164 + 0.640662i
173173 7.02306 + 1.49280i 0.533954 + 0.113495i 0.466994 0.884260i 0.345337π-0.345337\pi
0.0669594 + 0.997756i 0.478670π0.478670\pi
174174 0 0
175175 2.75991 + 4.78030i 0.208629 + 0.361357i
176176 10.3828 2.63595i 0.782635 0.198692i
177177 0 0
178178 0.0537852 + 0.511732i 0.00403137 + 0.0383559i
179179 2.78001 + 8.55598i 0.207788 + 0.639504i 0.999587 + 0.0287236i 0.00914427π0.00914427\pi
−0.791800 + 0.610781i 0.790856π0.790856\pi
180180 0 0
181181 −1.51882 1.10349i −0.112893 0.0820215i 0.529906 0.848056i 0.322227π-0.322227\pi
−0.642799 + 0.766035i 0.722227π0.722227\pi
182182 −3.15104 + 1.40294i −0.233571 + 0.103992i
183183 0 0
184184 −6.32940 + 7.02951i −0.466610 + 0.518222i
185185 0.468390 + 0.208541i 0.0344367 + 0.0153322i
186186 0 0
187187 −2.60233 2.67183i −0.190301 0.195383i
188188 21.1038 1.53915
189189 0 0
190190 −2.03935 6.27646i −0.147950 0.455343i
191191 4.28583 + 4.75989i 0.310111 + 0.344414i 0.877973 0.478711i 0.158896π-0.158896\pi
−0.567861 + 0.823124i 0.692229π0.692229\pi
192192 0 0
193193 −0.294602 + 2.80295i −0.0212059 + 0.201761i −0.999995 0.00310888i 0.999010π-0.999010\pi
0.978789 + 0.204870i 0.0656771π0.0656771\pi
194194 −3.56861 + 0.758531i −0.256211 + 0.0544594i
195195 0 0
196196 −0.152226 1.44833i −0.0108733 0.103452i
197197 −25.7193 −1.83243 −0.916213 0.400692i 0.868770π-0.868770\pi
−0.916213 + 0.400692i 0.868770π0.868770\pi
198198 0 0
199199 13.3474 0.946174 0.473087 0.881016i 0.343140π-0.343140\pi
0.473087 + 0.881016i 0.343140π0.343140\pi
200200 0.324209 + 3.08464i 0.0229250 + 0.218117i
201201 0 0
202202 6.78346 1.44187i 0.477282 0.101449i
203203 −1.93564 + 18.4164i −0.135855 + 1.29258i
204204 0 0
205205 −1.14352 1.27001i −0.0798672 0.0887015i
206206 −0.347751 1.07027i −0.0242289 0.0745690i
207207 0 0
208208 12.3303 0.854953
209209 3.22628 + 22.2648i 0.223167 + 1.54009i
210210 0 0
211211 −14.3717 6.39869i −0.989388 0.440504i −0.152753 0.988264i 0.548814π-0.548814\pi
−0.836635 + 0.547761i 0.815480π0.815480\pi
212212 −6.88943 + 7.65148i −0.473168 + 0.525506i
213213 0 0
214214 −3.27050 + 1.45612i −0.223567 + 0.0995384i
215215 10.2719 + 7.46296i 0.700536 + 0.508969i
216216 0 0
217217 5.16732 + 15.9034i 0.350781 + 1.07959i
218218 −0.684809 6.51553i −0.0463811 0.441287i
219219 0 0
220220 1.09014 16.6104i 0.0734972 1.11987i
221221 −2.14655 3.71793i −0.144392 0.250095i
222222 0 0
223223 18.4700 + 3.92592i 1.23684 + 0.262899i 0.779506 0.626394i 0.215470π-0.215470\pi
0.457337 + 0.889293i 0.348803π0.348803\pi
224224 −3.06210 + 9.42417i −0.204595 + 0.629679i
225225 0 0
226226 1.48877 + 1.08165i 0.0990314 + 0.0719505i
227227 0.722287 + 0.802181i 0.0479399 + 0.0532426i 0.766638 0.642080i 0.221928π-0.221928\pi
−0.718698 + 0.695322i 0.755262π0.755262\pi
228228 0 0
229229 −11.2023 4.98760i −0.740272 0.329590i 0.00172076 0.999999i 0.499452π-0.499452\pi
−0.741992 + 0.670408i 0.766119π0.766119\pi
230230 3.28330 + 5.68684i 0.216494 + 0.374979i
231231 0 0
232232 −5.20267 + 9.01128i −0.341572 + 0.591620i
233233 12.1863 8.85388i 0.798353 0.580037i −0.112078 0.993699i 0.535751π-0.535751\pi
0.910430 + 0.413662i 0.135751π0.135751\pi
234234 0 0
235235 9.37235 28.8451i 0.611385 1.88165i
236236 −14.3905 + 6.40707i −0.936743 + 0.417065i
237237 0 0
238238 0.993842 0.211248i 0.0644212 0.0136931i
239239 −9.63117 + 10.6965i −0.622988 + 0.691899i −0.969205 0.246256i 0.920800π-0.920800\pi
0.346216 + 0.938155i 0.387466π0.387466\pi
240240 0 0
241241 6.01413 10.4168i 0.387404 0.671004i −0.604695 0.796457i 0.706705π-0.706705\pi
0.992100 + 0.125453i 0.0400384π0.0400384\pi
242242 0.930898 3.87453i 0.0598404 0.249064i
243243 0 0
244244 2.60318 1.89132i 0.166651 0.121079i
245245 −2.04722 0.435150i −0.130792 0.0278007i
246246 0 0
247247 −2.70682 + 25.7537i −0.172231 + 1.63867i
248248 −0.982164 + 9.34467i −0.0623675 + 0.593387i
249249 0 0
250250 −2.65215 0.563732i −0.167737 0.0356535i
251251 −11.5075 + 8.36069i −0.726347 + 0.527722i −0.888406 0.459059i 0.848187π-0.848187\pi
0.162058 + 0.986781i 0.448187π0.448187\pi
252252 0 0
253253 −7.74611 21.0023i −0.486994 1.32040i
254254 −0.151113 + 0.261736i −0.00948170 + 0.0164228i
255255 0 0
256256 4.35180 4.83317i 0.271988 0.302073i
257257 10.6299 2.25945i 0.663073 0.140941i 0.135932 0.990718i 0.456597π-0.456597\pi
0.527141 + 0.849778i 0.323264π0.323264\pi
258258 0 0
259259 0.434977 0.193664i 0.0270281 0.0120337i
260260 5.92095 18.2228i 0.367202 1.13013i
261261 0 0
262262 5.78891 4.20589i 0.357640 0.259841i
263263 1.29031 2.23489i 0.0795640 0.137809i −0.823498 0.567319i 0.807981π-0.807981\pi
0.903062 + 0.429510i 0.141314π0.141314\pi
264264 0 0
265265 7.39856 + 12.8147i 0.454490 + 0.787200i
266266 −5.59883 2.49276i −0.343286 0.152841i
267267 0 0
268268 −5.63542 6.25876i −0.344238 0.382315i
269269 4.58187 + 3.32892i 0.279361 + 0.202968i 0.718639 0.695383i 0.244765π-0.244765\pi
−0.439277 + 0.898351i 0.644765π0.644765\pi
270270 0 0
271271 0.742616 2.28554i 0.0451107 0.138836i −0.925964 0.377611i 0.876746π-0.876746\pi
0.971075 + 0.238775i 0.0767457π0.0767457\pi
272272 −3.55277 0.755164i −0.215418 0.0457885i
273273 0 0
274274 0.717804 + 1.24327i 0.0433641 + 0.0751088i
275275 −6.81730 2.72051i −0.411099 0.164053i
276276 0 0
277277 −0.272826 2.59577i −0.0163925 0.155965i 0.983264 0.182189i 0.0583183π-0.0583183\pi
−0.999656 + 0.0262243i 0.991652π0.991652\pi
278278 −0.381136 1.17302i −0.0228590 0.0703529i
279279 0 0
280280 7.59496 + 5.51806i 0.453886 + 0.329767i
281281 −8.09216 + 3.60286i −0.482738 + 0.214929i −0.633652 0.773618i 0.718445π-0.718445\pi
0.150914 + 0.988547i 0.451778π0.451778\pi
282282 0 0
283283 −9.04049 + 10.0405i −0.537401 + 0.596845i −0.949295 0.314387i 0.898201π-0.898201\pi
0.411893 + 0.911232i 0.364868π0.364868\pi
284284 20.9994 + 9.34952i 1.24608 + 0.554792i
285285 0 0
286286 2.13598 4.05899i 0.126303 0.240013i
287287 −1.58706 −0.0936811
288288 0 0
289289 −4.86250 14.9652i −0.286029 0.880308i
290290 4.83343 + 5.36806i 0.283829 + 0.315224i
291291 0 0
292292 −0.416123 + 3.95914i −0.0243517 + 0.231691i
293293 17.3312 3.68386i 1.01250 0.215213i 0.328351 0.944556i 0.393507π-0.393507\pi
0.684149 + 0.729342i 0.260174π0.260174\pi
294294 0 0
295295 2.36639 + 22.5147i 0.137776 + 1.31086i
296296 0.267548 0.0155509
297297 0 0
298298 1.86705 0.108156
299299 −2.69334 25.6254i −0.155760 1.48196i
300300 0 0
301301 11.5333 2.45149i 0.664771 0.141301i
302302 0.520475 4.95199i 0.0299500 0.284955i
303303 0 0
304304 14.6598 + 16.2813i 0.840797 + 0.933799i
305305 −1.42901 4.39803i −0.0818246 0.251830i
306306 0 0
307307 11.3039 0.645145 0.322573 0.946545i 0.395452π-0.395452\pi
0.322573 + 0.946545i 0.395452π0.395452\pi
308308 −10.7860 11.0740i −0.614588 0.631001i
309309 0 0
310310 5.95893 + 2.65309i 0.338444 + 0.150685i
311311 4.41971 4.90859i 0.250619 0.278340i −0.604688 0.796463i 0.706702π-0.706702\pi
0.855307 + 0.518122i 0.173369π0.173369\pi
312312 0 0
313313 28.5934 12.7306i 1.61619 0.719576i 0.618395 0.785868i 0.287783π-0.287783\pi
0.997800 + 0.0662913i 0.0211167π0.0211167\pi
314314 −4.87500 3.54190i −0.275112 0.199881i
315315 0 0
316316 6.68845 + 20.5849i 0.376254 + 1.15799i
317317 1.34281 + 12.7759i 0.0754195 + 0.717569i 0.965259 + 0.261295i 0.0841495π0.0841495\pi
−0.889839 + 0.456274i 0.849184π0.849184\pi
318318 0 0
319319 −13.1382 20.8267i −0.735595 1.16607i
320320 −6.74181 11.6772i −0.376879 0.652773i
321321 0 0
322322 5.96490 + 1.26788i 0.332411 + 0.0706561i
323323 2.35720 7.25471i 0.131158 0.403663i
324324 0 0
325325 −6.83523 4.96608i −0.379150 0.275469i
326326 5.52629 + 6.13756i 0.306073 + 0.339928i
327327 0 0
328328 −0.814684 0.362721i −0.0449834 0.0200279i
329329 −14.0830 24.3924i −0.776420 1.34480i
330330 0 0
331331 −9.58347 + 16.5991i −0.526755 + 0.912367i 0.472759 + 0.881192i 0.343258π0.343258\pi
−0.999514 + 0.0311751i 0.990075π0.990075\pi
332332 −1.23735 + 0.898985i −0.0679082 + 0.0493382i
333333 0 0
334334 1.41043 4.34085i 0.0771751 0.237521i
335335 −11.0573 + 4.92304i −0.604127 + 0.268975i
336336 0 0
337337 −31.9855 + 6.79873i −1.74236 + 0.370350i −0.965719 0.259591i 0.916412π-0.916412\pi
−0.776643 + 0.629941i 0.783079π0.783079\pi
338338 0.381558 0.423763i 0.0207540 0.0230497i
339339 0 0
340340 −2.82207 + 4.88796i −0.153048 + 0.265087i
341341 −18.4876 12.3553i −1.00116 0.669079i
342342 0 0
343343 −15.6970 + 11.4046i −0.847560 + 0.615788i
344344 6.48069 + 1.37751i 0.349416 + 0.0742706i
345345 0 0
346346 0.271875 2.58672i 0.0146161 0.139063i
347347 1.14779 10.9205i 0.0616165 0.586242i −0.919536 0.393006i 0.871435π-0.871435\pi
0.981152 0.193236i 0.0618982π-0.0618982\pi
348348 0 0
349349 −23.1824 4.92757i −1.24093 0.263767i −0.459733 0.888057i 0.652055π-0.652055\pi
−0.781192 + 0.624290i 0.785388π0.785388\pi
350350 1.61769 1.17532i 0.0864691 0.0628235i
351351 0 0
352352 −4.55968 12.3628i −0.243032 0.658942i
353353 14.7938 25.6236i 0.787394 1.36381i −0.140165 0.990128i 0.544763π-0.544763\pi
0.927559 0.373678i 0.121903π-0.121903\pi
354354 0 0
355355 22.1051 24.5502i 1.17322 1.30299i
356356 −2.59642 + 0.551887i −0.137610 + 0.0292499i
357357 0 0
358358 2.97719 1.32553i 0.157350 0.0700565i
359359 −8.83869 + 27.2027i −0.466488 + 1.43570i 0.390614 + 0.920555i 0.372263π0.372263\pi
−0.857102 + 0.515148i 0.827737π0.827737\pi
360360 0 0
361361 −21.8529 + 15.8771i −1.15015 + 0.835635i
362362 −0.340041 + 0.588968i −0.0178722 + 0.0309555i
363363 0 0
364364 −8.89687 15.4098i −0.466323 0.807695i
365365 5.22664 + 2.32705i 0.273575 + 0.121803i
366366 0 0
367367 −2.39541 2.66037i −0.125039 0.138870i 0.677374 0.735639i 0.263118π-0.263118\pi
−0.802414 + 0.596768i 0.796451π0.796451\pi
368368 −17.6362 12.8135i −0.919352 0.667948i
369369 0 0
370370 0.0573948 0.176643i 0.00298382 0.00918324i
371371 13.4413 + 2.85703i 0.697836 + 0.148330i
372372 0 0
373373 18.4968 + 32.0373i 0.957726 + 1.65883i 0.728004 + 0.685573i 0.240448π0.240448\pi
0.229722 + 0.973256i 0.426218π0.426218\pi
374374 −0.864039 + 1.03871i −0.0446784 + 0.0537105i
375375 0 0
376376 −1.65434 15.7400i −0.0853162 0.811730i
377377 −8.75877 26.9567i −0.451100 1.38834i
378378 0 0
379379 19.4747 + 14.1492i 1.00035 + 0.726796i 0.962163 0.272474i 0.0878420π-0.0878420\pi
0.0381863 + 0.999271i 0.487842π0.487842\pi
380380 31.1015 13.8473i 1.59548 0.710352i
381381 0 0
382382 1.55256 1.72429i 0.0794357 0.0882223i
383383 −31.9916 14.2436i −1.63469 0.727812i −0.635667 0.771963i 0.719275π-0.719275\pi
−0.999025 + 0.0441515i 0.985942π0.985942\pi
384384 0 0
385385 −19.9263 + 9.82444i −1.01554 + 0.500700i
386386 1.02097 0.0519662
387387 0 0
388388 −5.81594 17.8996i −0.295260 0.908716i
389389 2.74982 + 3.05399i 0.139422 + 0.154843i 0.808812 0.588068i 0.200111π-0.200111\pi
−0.669390 + 0.742911i 0.733444π0.733444\pi
390390 0 0
391391 −0.793377 + 7.54848i −0.0401228 + 0.381743i
392392 −1.06829 + 0.227072i −0.0539568 + 0.0114689i
393393 0 0
394394 0.973884 + 9.26589i 0.0490636 + 0.466809i
395395 31.1063 1.56513
396396 0 0
397397 −23.0629 −1.15749 −0.578747 0.815507i 0.696458π-0.696458\pi
−0.578747 + 0.815507i 0.696458π0.696458\pi
398398 −0.505412 4.80867i −0.0253340 0.241037i
399399 0 0
400400 −6.99184 + 1.48616i −0.349592 + 0.0743081i
401401 0.392024 3.72986i 0.0195768 0.186260i −0.980363 0.197199i 0.936815π-0.936815\pi
0.999940 + 0.0109389i 0.00348203π0.00348203\pi
402402 0 0
403403 −17.1264 19.0208i −0.853125 0.947492i
404404 11.0553 + 34.0248i 0.550024 + 1.69280i
405405 0 0
406406 6.70815 0.332920
407407 −0.294856 + 0.560312i −0.0146155 + 0.0277736i
408408 0 0
409409 −25.0719 11.1627i −1.23972 0.551960i −0.321081 0.947052i 0.604046π-0.604046\pi
−0.918642 + 0.395091i 0.870713π0.870713\pi
410410 −0.414246 + 0.460067i −0.0204582 + 0.0227211i
411411 0 0
412412 5.30345 2.36125i 0.261282 0.116330i
413413 17.0086 + 12.3574i 0.836937 + 0.608070i
414414 0 0
415415 0.679237 + 2.09048i 0.0333424 + 0.102617i
416416 −1.58541 15.0842i −0.0777313 0.739564i
417417 0 0
418418 7.89915 2.00540i 0.386360 0.0980876i
419419 10.7023 + 18.5369i 0.522840 + 0.905586i 0.999647 + 0.0265777i 0.00846093π0.00846093\pi
−0.476806 + 0.879008i 0.658206π0.658206\pi
420420 0 0
421421 −10.6840 2.27096i −0.520708 0.110680i −0.0599425 0.998202i 0.519092π-0.519092\pi
−0.460765 + 0.887522i 0.652425π0.652425\pi
422422 −1.76106 + 5.41997i −0.0857269 + 0.263840i
423423 0 0
424424 6.24683 + 4.53859i 0.303373 + 0.220413i
425425 1.66531 + 1.84951i 0.0807793 + 0.0897145i
426426 0 0
427427 −3.92320 1.74672i −0.189857 0.0845297i
428428 −9.23416 15.9940i −0.446350 0.773101i
429429 0 0
430430 2.29972 3.98324i 0.110902 0.192089i
431431 9.56381 6.94852i 0.460673 0.334698i −0.333122 0.942884i 0.608102π-0.608102\pi
0.793795 + 0.608185i 0.208102π0.208102\pi
432432 0 0
433433 −7.50566 + 23.1000i −0.360699 + 1.11012i 0.591932 + 0.805988i 0.298365π0.298365\pi
−0.952631 + 0.304129i 0.901635π0.901635\pi
434434 5.53384 2.46382i 0.265633 0.118267i
435435 0 0
436436 33.0585 7.02679i 1.58321 0.336522i
437437 30.6345 34.0230i 1.46545 1.62754i
438438 0 0
439439 9.28957 16.0900i 0.443367 0.767934i −0.554570 0.832137i 0.687117π-0.687117\pi
0.997937 + 0.0642030i 0.0204505π0.0204505\pi
440440 −12.4741 + 0.489035i −0.594681 + 0.0233139i
441441 0 0
442442 −1.25818 + 0.914119i −0.0598453 + 0.0434802i
443443 −19.3148 4.10548i −0.917672 0.195057i −0.275218 0.961382i 0.588750π-0.588750\pi
−0.642454 + 0.766325i 0.722083π0.722083\pi
444444 0 0
445445 −0.398759 + 3.79394i −0.0189030 + 0.179850i
446446 0.715007 6.80284i 0.0338566 0.322124i
447447 0 0
448448 −12.2481 2.60342i −0.578669 0.123000i
449449 −1.68475 + 1.22404i −0.0795083 + 0.0577662i −0.626829 0.779157i 0.715648π-0.715648\pi
0.547321 + 0.836923i 0.315648π0.315648\pi
450450 0 0
451451 1.65746 1.30641i 0.0780468 0.0615163i
452452 −4.74660 + 8.22135i −0.223261 + 0.386700i
453453 0 0
454454 0.261651 0.290593i 0.0122799 0.0136382i
455455 −25.0136 + 5.31681i −1.17266 + 0.249256i
456456 0 0
457457 −7.57135 + 3.37098i −0.354173 + 0.157688i −0.576108 0.817373i 0.695429π-0.695429\pi
0.221935 + 0.975061i 0.428763π0.428763\pi
458458 −1.37270 + 4.22472i −0.0641418 + 0.197408i
459459 0 0
460460 −27.4057 + 19.9114i −1.27780 + 0.928374i
461461 3.27711 5.67613i 0.152630 0.264364i −0.779563 0.626324i 0.784559π-0.784559\pi
0.932194 + 0.361960i 0.117892π0.117892\pi
462462 0 0
463463 −0.136703 0.236776i −0.00635310 0.0110039i 0.862831 0.505492i 0.168689π-0.168689\pi
−0.869184 + 0.494488i 0.835356π0.835356\pi
464464 −21.9070 9.75362i −1.01701 0.452800i
465465 0 0
466466 −3.65123 4.05510i −0.169140 0.187849i
467467 −6.19971 4.50435i −0.286888 0.208437i 0.435028 0.900417i 0.356738π-0.356738\pi
−0.721916 + 0.691980i 0.756738π0.756738\pi
468468 0 0
469469 −3.47345 + 10.6902i −0.160389 + 0.493627i
470470 −10.7469 2.28433i −0.495718 0.105368i
471471 0 0
472472 5.90672 + 10.2307i 0.271879 + 0.470908i
473473 −10.0270 + 12.0541i −0.461042 + 0.554246i
474474 0 0
475475 −1.56918 14.9298i −0.0719989 0.685024i
476476 1.61971 + 4.98497i 0.0742395 + 0.228486i
477477 0 0
478478 4.21831 + 3.06478i 0.192941 + 0.140180i
479479 21.2009 9.43926i 0.968695 0.431291i 0.139482 0.990225i 0.455456π-0.455456\pi
0.829212 + 0.558934i 0.188789π0.188789\pi
480480 0 0
481481 −0.487661 + 0.541602i −0.0222354 + 0.0246949i
482482 −3.98058 1.77227i −0.181310 0.0807246i
483483 0 0
484484 20.3802 + 2.68667i 0.926371 + 0.122121i
485485 −27.0485 −1.22821
486486 0 0
487487 −7.44592 22.9162i −0.337407 1.03843i −0.965524 0.260313i 0.916174π-0.916174\pi
0.628117 0.778119i 0.283826π-0.283826\pi
488488 −1.61468 1.79329i −0.0730932 0.0811783i
489489 0 0
490490 −0.0792515 + 0.754028i −0.00358022 + 0.0340635i
491491 −34.3994 + 7.31181i −1.55242 + 0.329977i −0.902725 0.430217i 0.858437π-0.858437\pi
−0.649696 + 0.760194i 0.725104π0.725104\pi
492492 0 0
493493 0.872738 + 8.30354i 0.0393061 + 0.373973i
494494 9.38077 0.422061
495495 0 0
496496 −21.6544 −0.972311
497497 −3.20682 30.5108i −0.143845 1.36860i
498498 0 0
499499 22.2539 4.73022i 0.996222 0.211754i 0.319177 0.947695i 0.396593π-0.396593\pi
0.677045 + 0.735941i 0.263260π0.263260\pi
500500 1.46208 13.9108i 0.0653862 0.622108i
501501 0 0
502502 3.44784 + 3.82922i 0.153885 + 0.170906i
503503 1.55585 + 4.78840i 0.0693718 + 0.213504i 0.979732 0.200312i 0.0641956π-0.0641956\pi
−0.910360 + 0.413816i 0.864196π0.864196\pi
504504 0 0
505505 51.4156 2.28796
506506 −7.27318 + 3.58596i −0.323332 + 0.159415i
507507 0 0
508508 −1.42432 0.634146i −0.0631938 0.0281357i
509509 −6.22700 + 6.91578i −0.276007 + 0.306537i −0.865171 0.501476i 0.832790π-0.832790\pi
0.589164 + 0.808013i 0.299457π0.299457\pi
510510 0 0
511511 4.85379 2.16105i 0.214719 0.0955990i
512512 −17.7056 12.8639i −0.782483 0.568507i
513513 0 0
514514 −1.21652 3.74406i −0.0536584 0.165144i
515515 −0.872104 8.29752i −0.0384295 0.365632i
516516 0 0
517517 34.7867 + 13.8819i 1.52992 + 0.610527i
518518 −0.0862420 0.149376i −0.00378926 0.00656319i
519519 0 0
520520 −14.0554 2.98757i −0.616370 0.131014i
521521 −3.41257 + 10.5028i −0.149507 + 0.460136i −0.997563 0.0697708i 0.977773π-0.977773\pi
0.848056 + 0.529907i 0.177773π0.177773\pi
522522 0 0
523523 15.7075 + 11.4122i 0.686841 + 0.499019i 0.875620 0.483001i 0.160453π-0.160453\pi
−0.188779 + 0.982020i 0.560453π0.560453\pi
524524 24.6998 + 27.4319i 1.07901 + 1.19837i
525525 0 0
526526 −0.854020 0.380234i −0.0372370 0.0165790i
527527 3.76975 + 6.52940i 0.164213 + 0.284425i
528528 0 0
529529 −11.2772 + 19.5327i −0.490314 + 0.849249i
530530 4.33659 3.15071i 0.188369 0.136858i
531531 0 0
532532 9.76996 30.0688i 0.423581 1.30365i
533533 2.21919 0.988046i 0.0961237 0.0427970i
534534 0 0
535535 −25.9619 + 5.51838i −1.12243 + 0.238580i
536536 −4.22626 + 4.69374i −0.182547 + 0.202738i
537537 0 0
538538 1.02581 1.77676i 0.0442259 0.0766016i
539539 0.701781 2.48751i 0.0302278 0.107145i
540540 0 0
541541 17.0772 12.4073i 0.734205 0.533431i −0.156686 0.987649i 0.550081π-0.550081\pi
0.890891 + 0.454217i 0.150081π0.150081\pi
542542 −0.851529 0.180998i −0.0365763 0.00777453i
543543 0 0
544544 −0.467015 + 4.44335i −0.0200231 + 0.190507i
545545 5.07713 48.3056i 0.217480 2.06919i
546546 0 0
547547 13.7372 + 2.91993i 0.587360 + 0.124847i 0.491999 0.870596i 0.336266π-0.336266\pi
0.0953606 + 0.995443i 0.469600π0.469600\pi
548548 −5.99151 + 4.35309i −0.255945 + 0.185955i
549549 0 0
550550 −0.721973 + 2.55908i −0.0307850 + 0.109120i
551551 25.1810 43.6148i 1.07275 1.85805i
552552 0 0
553553 19.3294 21.4674i 0.821968 0.912888i
554554 −0.924846 + 0.196582i −0.0392929 + 0.00835197i
555555 0 0
556556 5.81261 2.58794i 0.246510 0.109753i
557557 12.8094 39.4233i 0.542752 1.67042i −0.183524 0.983015i 0.558751π-0.558751\pi
0.726276 0.687403i 0.241249π-0.241249\pi
558558 0 0
559559 −14.6009 + 10.6082i −0.617552 + 0.448678i
560560 −10.8177 + 18.7368i −0.457131 + 0.791773i
561561 0 0
562562 1.60442 + 2.77893i 0.0676783 + 0.117222i
563563 6.80544 + 3.02998i 0.286815 + 0.127698i 0.545101 0.838370i 0.316491π-0.316491\pi
−0.258286 + 0.966068i 0.583158π0.583158\pi
564564 0 0
565565 9.12911 + 10.1389i 0.384065 + 0.426547i
566566 3.95961 + 2.87682i 0.166435 + 0.120922i
567567 0 0
568568 5.32707 16.3950i 0.223519 0.687920i
569569 −23.8888 5.07772i −1.00147 0.212869i −0.322133 0.946694i 0.604400π-0.604400\pi
−0.679338 + 0.733825i 0.737733π0.737733\pi
570570 0 0
571571 6.40805 + 11.0991i 0.268169 + 0.464482i 0.968389 0.249445i 0.0802482π-0.0802482\pi
−0.700220 + 0.713927i 0.746915π0.746915\pi
572572 21.9763 + 8.76987i 0.918877 + 0.366687i
573573 0 0
574574 0.0600953 + 0.571769i 0.00250833 + 0.0238652i
575575 4.61585 + 14.2061i 0.192494 + 0.592437i
576576 0 0
577577 11.7428 + 8.53166i 0.488860 + 0.355178i 0.804746 0.593620i 0.202302π-0.202302\pi
−0.315886 + 0.948797i 0.602302π0.602302\pi
578578 −5.20740 + 2.31848i −0.216599 + 0.0964362i
579579 0 0
580580 −24.9344 + 27.6924i −1.03534 + 1.14987i
581581 1.86478 + 0.830253i 0.0773641 + 0.0344447i
582582 0 0
583583 −16.3893 + 8.08057i −0.678777 + 0.334663i
584584 2.98550 0.123541
585585 0 0
586586 −1.98344 6.10441i −0.0819353 0.252171i
587587 14.9988 + 16.6579i 0.619069 + 0.687545i 0.968385 0.249459i 0.0802529π-0.0802529\pi
−0.349317 + 0.937005i 0.613586π0.613586\pi
588588 0 0
589589 4.75370 45.2284i 0.195873 1.86361i
590590 8.02175 1.70508i 0.330250 0.0701969i
591591 0 0
592592 0.0644515 + 0.613215i 0.00264894 + 0.0252030i
593593 −18.2533 −0.749572 −0.374786 0.927111i 0.622284π-0.622284\pi
−0.374786 + 0.927111i 0.622284π0.622284\pi
594594 0 0
595595 7.53288 0.308818
596596 1.00678 + 9.57887i 0.0412393 + 0.392366i
597597 0 0
598598 −9.13007 + 1.94066i −0.373356 + 0.0793593i
599599 −2.76195 + 26.2782i −0.112850 + 1.07370i 0.780753 + 0.624840i 0.214836π0.214836\pi
−0.893603 + 0.448859i 0.851831π0.851831\pi
600600 0 0
601601 9.25098 + 10.2743i 0.377355 + 0.419096i 0.901667 0.432431i 0.142344π-0.142344\pi
−0.524312 + 0.851526i 0.675677π0.675677\pi
602602 −1.31992 4.06228i −0.0537958 0.165566i
603603 0 0
604604 25.6867 1.04518
605605 12.7232 26.6629i 0.517270 1.08400i
606606 0 0
607607 −13.3213 5.93104i −0.540696 0.240733i 0.118170 0.992993i 0.462297π-0.462297\pi
−0.658866 + 0.752260i 0.728964π0.728964\pi
608608 18.0327 20.0274i 0.731324 0.812218i
609609 0 0
610610 −1.53036 + 0.681362i −0.0619626 + 0.0275875i
611611 34.8782 + 25.3405i 1.41102 + 1.02517i
612612 0 0
613613 −9.31252 28.6610i −0.376129 1.15761i −0.942714 0.333603i 0.891736π-0.891736\pi
0.566585 0.824004i 0.308264π-0.308264\pi
614614 −0.428030 4.07244i −0.0172739 0.164350i
615615 0 0
616616 −7.41390 + 8.91269i −0.298715 + 0.359102i
617617 −9.84784 17.0570i −0.396459 0.686687i 0.596827 0.802370i 0.296428π-0.296428\pi
−0.993286 + 0.115683i 0.963094π0.963094\pi
618618 0 0
619619 −1.26485 0.268852i −0.0508387 0.0108061i 0.182422 0.983220i 0.441606π-0.441606\pi
−0.233261 + 0.972414i 0.574940π0.574940\pi
620620 −10.3983 + 32.0028i −0.417607 + 1.28526i
621621 0 0
622622 −1.93577 1.40642i −0.0776173 0.0563923i
623623 2.37053 + 2.63274i 0.0949733 + 0.105479i
624624 0 0
625625 −28.4731 12.6770i −1.13892 0.507082i
626626 −5.66916 9.81928i −0.226585 0.392457i
627627 0 0
628628 15.5428 26.9210i 0.620227 1.07426i
629629 0.173681 0.126187i 0.00692513 0.00503140i
630630 0 0
631631 13.6277 41.9417i 0.542509 1.66967i −0.184330 0.982864i 0.559012π-0.559012\pi
0.726839 0.686808i 0.240988π-0.240988\pi
632632 14.8287 6.60216i 0.589854 0.262620i
633633 0 0
634634 4.55194 0.967544i 0.180781 0.0384261i
635635 −1.49931 + 1.66516i −0.0594984 + 0.0660797i
636636 0 0
637637 1.48751 2.57644i 0.0589372 0.102082i
638638 −7.00573 + 5.52190i −0.277360 + 0.218614i
639639 0 0
640640 −21.2166 + 15.4148i −0.838660 + 0.609322i
641641 −26.4042 5.61239i −1.04290 0.221676i −0.345548 0.938401i 0.612307π-0.612307\pi
−0.697356 + 0.716725i 0.745640π0.745640\pi
642642 0 0
643643 1.06164 10.1009i 0.0418671 0.398339i −0.953441 0.301580i 0.902486π-0.902486\pi
0.995308 0.0967587i 0.0308475π-0.0308475\pi
644644 −3.28834 + 31.2864i −0.129579 + 1.23286i
645645 0 0
646646 −2.70291 0.574521i −0.106344 0.0226042i
647647 27.2093 19.7687i 1.06971 0.777189i 0.0938493 0.995586i 0.470083π-0.470083\pi
0.975860 + 0.218397i 0.0700828π0.0700828\pi
648648 0 0
649649 −27.9353 + 1.09517i −1.09656 + 0.0429893i
650650 −1.53031 + 2.65057i −0.0600236 + 0.103964i
651651 0 0
652652 −28.5086 + 31.6621i −1.11648 + 1.23998i
653653 11.0802 2.35516i 0.433600 0.0921645i 0.0140596 0.999901i 0.495525π-0.495525\pi
0.419540 + 0.907737i 0.362191π0.362191\pi
654654 0 0
655655 48.4638 21.5775i 1.89364 0.843102i
656656 0.635094 1.95462i 0.0247963 0.0763150i
657657 0 0
658658 −8.25459 + 5.99731i −0.321797 + 0.233800i
659659 −16.1903 + 28.0424i −0.630684 + 1.09238i 0.356729 + 0.934208i 0.383892π0.383892\pi
−0.987412 + 0.158168i 0.949441π0.949441\pi
660660 0 0
661661 −1.57119 2.72139i −0.0611123 0.105850i 0.833851 0.551990i 0.186131π-0.186131\pi
−0.894963 + 0.446141i 0.852798π0.852798\pi
662662 6.34302 + 2.82410i 0.246529 + 0.109762i
663663 0 0
664664 0.767493 + 0.852388i 0.0297845 + 0.0330791i
665665 −36.7598 26.7076i −1.42548 1.03567i
666666 0 0
667667 −15.4852 + 47.6586i −0.599590 + 1.84535i
668668 23.0312 + 4.89542i 0.891102 + 0.189410i
669669 0 0
670670 2.19232 + 3.79721i 0.0846966 + 0.146699i
671671 5.53507 1.40522i 0.213679 0.0542480i
672672 0 0
673673 4.04197 + 38.4567i 0.155806 + 1.48240i 0.741000 + 0.671505i 0.234352π0.234352\pi
−0.585194 + 0.810894i 0.698982π0.698982\pi
674674 3.66053 + 11.2660i 0.140998 + 0.433949i
675675 0 0
676676 2.37986 + 1.72907i 0.0915329 + 0.0665025i
677677 −41.7683 + 18.5964i −1.60528 + 0.714719i −0.996882 0.0789093i 0.974856π-0.974856\pi
−0.608403 + 0.793628i 0.708190π0.708190\pi
678678 0 0
679679 −16.8079 + 18.6670i −0.645027 + 0.716375i
680680 3.86685 + 1.72163i 0.148287 + 0.0660216i
681681 0 0
682682 −3.75120 + 7.12837i −0.143641 + 0.272959i
683683 −11.3550 −0.434485 −0.217243 0.976118i 0.569706π-0.569706\pi
−0.217243 + 0.976118i 0.569706π0.569706\pi
684684 0 0
685685 3.28902 + 10.1226i 0.125667 + 0.386763i
686686 4.70310 + 5.22332i 0.179565 + 0.199427i
687687 0 0
688688 −1.59606 + 15.1855i −0.0608491 + 0.578940i
689689 −20.5736 + 4.37306i −0.783793 + 0.166600i
690690 0 0
691691 −0.911473 8.67209i −0.0346741 0.329902i −0.998084 0.0618702i 0.980294π-0.980294\pi
0.963410 0.268032i 0.0863731π-0.0863731\pi
692692 13.4177 0.510065
693693 0 0
694694 −3.97778 −0.150994
695695 −0.955831 9.09412i −0.0362567 0.344960i
696696 0 0
697697 −0.699934 + 0.148775i −0.0265119 + 0.00563527i
698698 −0.897432 + 8.53850i −0.0339683 + 0.323187i
699699 0 0
700700 6.90226 + 7.66574i 0.260881 + 0.289738i
701701 −12.5650 38.6712i −0.474575 1.46059i −0.846530 0.532342i 0.821312π-0.821312\pi
0.371954 0.928251i 0.378688π-0.378688\pi
702702 0 0
703703 −1.29494 −0.0488396
704704 14.9345 7.36328i 0.562865 0.277514i
705705 0 0
706706 −9.79158 4.35949i −0.368511 0.164072i
707707 31.9495 35.4835i 1.20159 1.33450i
708708 0 0
709709 −15.2948 + 6.80970i −0.574410 + 0.255744i −0.673318 0.739353i 0.735132π-0.735132\pi
0.0989083 + 0.995097i 0.468465π0.468465\pi
710710 −9.68171 7.03417i −0.363348 0.263988i
711711 0 0
712712 0.615154 + 1.89325i 0.0230539 + 0.0709525i
713713 4.73002 + 45.0032i 0.177141 + 1.68538i
714714 0 0
715715 21.7467 26.1430i 0.813280 0.977691i
716716 8.40601 + 14.5596i 0.314147 + 0.544119i
717717 0 0
718718 10.1350 + 2.15426i 0.378234 + 0.0803961i
719719 5.99373 18.4468i 0.223528 0.687949i −0.774909 0.632072i 0.782205π-0.782205\pi
0.998438 0.0558770i 0.0177955π-0.0177955\pi
720720 0 0
721721 −6.26830 4.55419i −0.233444 0.169607i
722722 6.54750 + 7.27174i 0.243673 + 0.270626i
723723 0 0
724724 −3.20505 1.42698i −0.119115 0.0530333i
725725 8.21569 + 14.2300i 0.305123 + 0.528488i
726726 0 0
727727 −2.89216 + 5.00937i −0.107264 + 0.185787i −0.914661 0.404222i 0.867542π-0.867542\pi
0.807397 + 0.590009i 0.200876π0.200876\pi
728728 −10.7958 + 7.84361i −0.400119 + 0.290704i
729729 0 0
730730 0.640454 1.97111i 0.0237043 0.0729542i
731731 4.85669 2.16234i 0.179631 0.0799770i
732732 0 0
733733 −22.2159 + 4.72214i −0.820563 + 0.174416i −0.599020 0.800734i 0.704443π-0.704443\pi
−0.221544 + 0.975150i 0.571109π0.571109\pi
734734 −0.867748 + 0.963731i −0.0320291 + 0.0355720i
735735 0 0
736736 −13.4076 + 23.2227i −0.494212 + 0.856000i
737737 −5.17222 14.0236i −0.190521 0.516567i
738738 0 0
739739 9.31755 6.76960i 0.342752 0.249024i −0.403070 0.915169i 0.632057π-0.632057\pi
0.745822 + 0.666145i 0.232057π0.232057\pi
740740 0.937212 + 0.199211i 0.0344526 + 0.00732313i
741741 0 0
742742 0.520336 4.95066i 0.0191021 0.181745i
743743 −4.49533 + 42.7703i −0.164918 + 1.56909i 0.528740 + 0.848784i 0.322665π0.322665\pi
−0.693658 + 0.720305i 0.744002π0.744002\pi
744744 0 0
745745 13.5397 + 2.87796i 0.496057 + 0.105440i
746746 10.8417 7.87694i 0.396942 0.288395i
747747 0 0
748748 −5.79500 3.87282i −0.211886 0.141604i
749749 −12.3243 + 21.3462i −0.450319 + 0.779975i
750750 0 0
751751 2.40813 2.67449i 0.0878738 0.0975937i −0.697604 0.716483i 0.745751π-0.745751\pi
0.785478 + 0.618890i 0.212417π0.212417\pi
752752 35.6773 7.58344i 1.30102 0.276540i
753753 0 0
754754 −9.38003 + 4.17626i −0.341600 + 0.152090i
755755 11.4076 35.1091i 0.415167 1.27775i
756756 0 0
757757 12.2911 8.93000i 0.446727 0.324566i −0.341575 0.939855i 0.610960π-0.610960\pi
0.788302 + 0.615288i 0.210960π0.210960\pi
758758 4.36010 7.55192i 0.158366 0.274298i
759759 0 0
760760 −12.7659 22.1112i −0.463068 0.802058i
761761 −14.9046 6.63596i −0.540292 0.240553i 0.118400 0.992966i 0.462223π-0.462223\pi
−0.658692 + 0.752413i 0.728890π0.728890\pi
762762 0 0
763763 −30.1823 33.5209i −1.09267 1.21354i
764764 9.68362 + 7.03556i 0.350341 + 0.254538i
765765 0 0
766766 −3.92013 + 12.0649i −0.141640 + 0.435923i
767767 −31.4764 6.69052i −1.13655 0.241581i
768768 0 0
769769 −3.33336 5.77355i −0.120204 0.208200i 0.799644 0.600474i 0.205022π-0.205022\pi
−0.919848 + 0.392275i 0.871688π0.871688\pi
770770 4.29397 + 6.80683i 0.154744 + 0.245301i
771771 0 0
772772 0.550544 + 5.23808i 0.0198145 + 0.188523i
773773 15.7232 + 48.3910i 0.565524 + 1.74050i 0.666389 + 0.745604i 0.267839π0.267839\pi
−0.100865 + 0.994900i 0.532161π0.532161\pi
774774 0 0
775775 12.0040 + 8.72140i 0.431196 + 0.313282i
776776 −12.8943 + 5.74092i −0.462879 + 0.206087i
777777 0 0
778778 0.996135 1.10632i 0.0357132 0.0396635i
779779 3.94309 + 1.75558i 0.141276 + 0.0629001i
780780 0 0
781781 28.4644 + 29.2246i 1.01854 + 1.04574i
782782 2.74953 0.0983229
783783 0 0
784784 −0.777792 2.39380i −0.0277783 0.0854928i
785785 −29.8935 33.2001i −1.06694 1.18496i
786786 0 0
787787 3.17288 30.1879i 0.113101 1.07608i −0.779862 0.625952i 0.784711π-0.784711\pi
0.892963 0.450131i 0.148623π-0.148623\pi
788788 −47.0132 + 9.99297i −1.67478 + 0.355985i
789789 0 0
790790 −1.17787 11.2066i −0.0419066 0.398714i
791791 12.6700 0.450493
792792 0 0
793793 6.57326 0.233423
794794 0.873297 + 8.30886i 0.0309921 + 0.294870i
795795 0 0
796796 24.3982 5.18600i 0.864772 0.183813i
797797 −0.415201 + 3.95037i −0.0147072 + 0.139929i −0.999411 0.0343048i 0.989078π-0.989078\pi
0.984704 + 0.174234i 0.0557450π0.0557450\pi
798798 0 0
799799 −8.49758 9.43752i −0.300623 0.333875i
800800 2.71709 + 8.36233i 0.0960635 + 0.295653i
801801 0 0
802802 −1.35860 −0.0479738
803803 −3.29022 + 6.25237i −0.116109 + 0.220641i
804804 0 0
805805 41.3026 + 18.3891i 1.45572 + 0.648130i
806806 −6.20410 + 6.89035i −0.218530 + 0.242702i
807807 0 0
808808 24.5104 10.9127i 0.862272 0.383908i
809809 4.26011 + 3.09515i 0.149778 + 0.108820i 0.660150 0.751133i 0.270493π-0.270493\pi
−0.510373 + 0.859953i 0.670493π0.670493\pi
810810 0 0
811811 11.6366 + 35.8137i 0.408615 + 1.25759i 0.917838 + 0.396954i 0.129933π0.129933\pi
−0.509223 + 0.860635i 0.670067π0.670067\pi
812812 3.61727 + 34.4160i 0.126941 + 1.20776i
813813 0 0
814814 0.213028 + 0.0850109i 0.00746663 + 0.00297963i
815815 30.6155 + 53.0275i 1.07241 + 1.85747i
816816 0 0
817817 −31.3667 6.66720i −1.09738 0.233256i
818818 −3.07222 + 9.45531i −0.107418 + 0.330597i
819819 0 0
820820 −2.58374 1.87719i −0.0902280 0.0655545i
821821 −1.40616 1.56170i −0.0490753 0.0545037i 0.718107 0.695932i 0.245009π-0.245009\pi
−0.767183 + 0.641429i 0.778342π0.778342\pi
822822 0 0
823823 −6.07498 2.70475i −0.211760 0.0942818i 0.298115 0.954530i 0.403642π-0.403642\pi
−0.509876 + 0.860248i 0.670309π0.670309\pi
824824 −2.17685 3.77042i −0.0758342 0.131349i
825825 0 0
826826 3.80797 6.59559i 0.132496 0.229490i
827827 −17.8702 + 12.9834i −0.621407 + 0.451479i −0.853413 0.521236i 0.825471π-0.825471\pi
0.232006 + 0.972714i 0.425471π0.425471\pi
828828 0 0
829829 1.19544 3.67920i 0.0415195 0.127784i −0.928148 0.372211i 0.878600π-0.878600\pi
0.969668 + 0.244427i 0.0785998π0.0785998\pi
830830 0.727415 0.323866i 0.0252489 0.0112416i
831831 0 0
832832 18.7474 3.98488i 0.649948 0.138151i
833833 −0.586393 + 0.651255i −0.0203173 + 0.0225647i
834834 0 0
835835 16.9195 29.3054i 0.585522 1.01415i
836836 14.5482 + 39.4450i 0.503159 + 1.36423i
837837 0 0
838838 6.27302 4.55762i 0.216698 0.157440i
839839 −22.9258 4.87302i −0.791486 0.168235i −0.205607 0.978635i 0.565917π-0.565917\pi
−0.585878 + 0.810399i 0.699250π0.699250\pi
840840 0 0
841841 −2.73068 + 25.9807i −0.0941614 + 0.895886i
842842 −0.413598 + 3.93512i −0.0142535 + 0.135613i
843843 0 0
844844 −28.7567 6.11242i −0.989845 0.210398i
845845 3.42023 2.48494i 0.117660 0.0854847i
846846 0 0
847847 −10.4947 25.3489i −0.360604 0.870998i
848848 −8.89751 + 15.4109i −0.305542 + 0.529214i
849849 0 0
850850 0.603265 0.669993i 0.0206918 0.0229806i
851851 1.26033 0.267892i 0.0432037 0.00918323i
852852 0 0
853853 −19.1776 + 8.53842i −0.656629 + 0.292350i −0.707877 0.706336i 0.750347π-0.750347\pi
0.0512479 + 0.998686i 0.483680π0.483680\pi
854854 −0.480735 + 1.47955i −0.0164504 + 0.0506291i
855855 0 0
856856 −11.2051 + 8.14097i −0.382982 + 0.278252i
857857 14.1590 24.5241i 0.483662 0.837728i −0.516162 0.856491i 0.672640π-0.672640\pi
0.999824 + 0.0187634i 0.00597292π0.00597292\pi
858858 0 0
859859 27.8536 + 48.2438i 0.950351 + 1.64606i 0.744665 + 0.667439i 0.232609π0.232609\pi
0.205687 + 0.978618i 0.434057π0.434057\pi
860860 21.6760 + 9.65077i 0.739145 + 0.329088i
861861 0 0
862862 −2.86548 3.18244i −0.0975986 0.108394i
863863 24.8932 + 18.0860i 0.847375 + 0.615654i 0.924421 0.381374i 0.124549π-0.124549\pi
−0.0770462 + 0.997028i 0.524549π0.524549\pi
864864 0 0
865865 5.95890 18.3396i 0.202609 0.623565i
866866 8.60645 + 1.82936i 0.292459 + 0.0621641i
867867 0 0
868868 15.6246 + 27.0626i 0.530334 + 0.918566i
869869 −2.51565 + 38.3309i −0.0853377 + 1.30029i
870870 0 0
871871 −1.79839 17.1106i −0.0609362 0.579769i
872872 −7.83232 24.1054i −0.265236 0.816312i
873873 0 0
874874 −13.4175 9.74835i −0.453852 0.329743i
875875 −17.0542 + 7.59300i −0.576536 + 0.256690i
876876 0 0
877877 20.7384 23.0323i 0.700286 0.777747i −0.283136 0.959080i 0.591375π-0.591375\pi
0.983422 + 0.181333i 0.0580413π0.0580413\pi
878878 −6.14850 2.73749i −0.207502 0.0923857i
879879 0 0
880880 −4.12584 28.4727i −0.139082 0.959814i
881881 −29.9198 −1.00802 −0.504012 0.863697i 0.668143π-0.668143\pi
−0.504012 + 0.863697i 0.668143π0.668143\pi
882882 0 0
883883 4.39514 + 13.5269i 0.147908 + 0.455215i 0.997374 0.0724296i 0.0230753π-0.0230753\pi
−0.849465 + 0.527645i 0.823075π0.823075\pi
884884 −5.36831 5.96212i −0.180556 0.200528i
885885 0 0
886886 −0.747709 + 7.11398i −0.0251198 + 0.238999i
887887 −2.57329 + 0.546971i −0.0864028 + 0.0183655i −0.250910 0.968010i 0.580730π-0.580730\pi
0.164507 + 0.986376i 0.447397π0.447397\pi
888888 0 0
889889 0.217508 + 2.06945i 0.00729497 + 0.0694070i
890890 1.38194 0.0463228
891891 0 0
892892 35.2874 1.18151
893893 8.00706 + 76.1821i 0.267946 + 2.54934i
894894 0 0
895895 23.6336 5.02347i 0.789983 0.167916i
896896 −2.54572 + 24.2210i −0.0850467 + 0.809165i
897897 0 0
898898 0.504780 + 0.560615i 0.0168447 + 0.0187080i
899899 15.3821 + 47.3412i 0.513021 + 1.57892i
900900 0 0
901901 6.19577 0.206411
902902 −0.533420 0.547665i −0.0177609 0.0182352i
903903 0 0
904904 6.50388 + 2.89572i 0.216316 + 0.0963101i
905905 −3.37381 + 3.74700i −0.112149 + 0.124554i
906906 0 0
907907 −9.28389 + 4.13345i −0.308266 + 0.137249i −0.555039 0.831824i 0.687297π-0.687297\pi
0.246772 + 0.969073i 0.420630π0.420630\pi
908908 1.63197 + 1.18570i 0.0541589 + 0.0393488i
909909 0 0
910910 2.86265 + 8.81033i 0.0948959 + 0.292060i
911911 −0.615910 5.85999i −0.0204060 0.194150i 0.979570 0.201104i 0.0644530π-0.0644530\pi
−0.999976 + 0.00695428i 0.997786π0.997786\pi
912912 0 0
913913 −2.63094 + 0.667932i −0.0870713 + 0.0221053i
914914 1.50116 + 2.60008i 0.0496539 + 0.0860031i
915915 0 0
916916 −22.4150 4.76446i −0.740613 0.157422i
917917 15.2240 46.8546i 0.502740 1.54727i
918918 0 0
919919 −26.1285 18.9835i −0.861899 0.626206i 0.0665018 0.997786i 0.478816π-0.478816\pi
−0.928401 + 0.371580i 0.878816π0.878816\pi
920920 16.9990 + 18.8793i 0.560441 + 0.622433i
921921 0 0
922922 −2.16903 0.965713i −0.0714331 0.0318041i
923923 23.4791 + 40.6669i 0.772823 + 1.33857i
924924 0 0
925925 0.211247 0.365890i 0.00694575 0.0120304i
926926 −0.0801267 + 0.0582155i −0.00263313 + 0.00191308i
927927 0 0
928928 −9.11525 + 28.0539i −0.299223 + 0.920913i
929929 44.6570 19.8826i 1.46515 0.652327i 0.489568 0.871965i 0.337154π-0.337154\pi
0.975581 + 0.219639i 0.0704878π0.0704878\pi
930930 0 0
931931 5.17055 1.09903i 0.169458 0.0360194i
932932 18.8357 20.9192i 0.616985 0.685231i
933933 0 0
934934 −1.38802 + 2.40413i −0.0454175 + 0.0786655i
935935 −7.86705 + 6.20078i −0.257280 + 0.202787i
936936 0 0
937937 −36.4628 + 26.4917i −1.19119 + 0.865447i −0.993389 0.114796i 0.963379π-0.963379\pi
−0.197797 + 0.980243i 0.563379π0.563379\pi
938938 3.98287 + 0.846586i 0.130045 + 0.0276420i
939939 0 0
940940 5.92457 56.3686i 0.193238 1.83854i
941941 1.71991 16.3639i 0.0560675 0.533447i −0.930054 0.367423i 0.880240π-0.880240\pi
0.986122 0.166024i 0.0530930π-0.0530930\pi
942942 0 0
943943 −4.20090 0.892929i −0.136800 0.0290778i
944944 −22.0257 + 16.0026i −0.716877 + 0.520841i
945945 0 0
946946 4.72239 + 3.15599i 0.153538 + 0.102610i
947947 3.50636 6.07320i 0.113942 0.197352i −0.803415 0.595420i 0.796986π-0.796986\pi
0.917356 + 0.398067i 0.130319π0.130319\pi
948948 0 0
949949 −5.44168 + 6.04359i −0.176644 + 0.196183i
950950 −5.31932 + 1.13066i −0.172581 + 0.0366833i
951951 0 0
952952 3.59101 1.59882i 0.116385 0.0518180i
953953 3.34588 10.2976i 0.108384 0.333571i −0.882126 0.471014i 0.843888π-0.843888\pi
0.990510 + 0.137443i 0.0438883π0.0438883\pi
954954 0 0
955955 13.9169 10.1112i 0.450341 0.327192i
956956 −13.4491 + 23.2946i −0.434976 + 0.753401i
957957 0 0
958958 −4.20347 7.28062i −0.135808 0.235226i
959959 9.02969 + 4.02028i 0.291584 + 0.129821i
960960 0 0
961961 9.33416 + 10.3666i 0.301102 + 0.334407i
962962 0.213588 + 0.155181i 0.00688637 + 0.00500324i
963963 0 0
964964 6.94611 21.3779i 0.223719 0.688537i
965965 7.40401 + 1.57377i 0.238344 + 0.0506615i
966966 0 0
967967 −2.94103 5.09401i −0.0945771 0.163812i 0.814855 0.579665i 0.196817π-0.196817\pi
−0.909432 + 0.415853i 0.863483π0.863483\pi
968968 0.406202 15.4109i 0.0130558 0.495325i
969969 0 0
970970 1.02421 + 9.74475i 0.0328855 + 0.312885i
971971 5.64280 + 17.3667i 0.181086 + 0.557325i 0.999859 0.0167920i 0.00534530π-0.00534530\pi
−0.818773 + 0.574117i 0.805345π0.805345\pi
972972 0 0
973973 −6.87009 4.99141i −0.220245 0.160017i
974974 −7.97406 + 3.55028i −0.255505 + 0.113758i
975975 0 0
976976 3.72120 4.13282i 0.119113 0.132288i
977977 −1.53328 0.682658i −0.0490538 0.0218402i 0.382063 0.924136i 0.375214π-0.375214\pi
−0.431117 + 0.902296i 0.641880π0.641880\pi
978978 0 0
979979 −4.64287 0.798201i −0.148387 0.0255106i
980980 −3.91125 −0.124940
981981 0 0
982982 3.93678 + 12.1162i 0.125628 + 0.386643i
983983 7.50703 + 8.33740i 0.239437 + 0.265922i 0.850872 0.525373i 0.176074π-0.176074\pi
−0.611435 + 0.791295i 0.709407π0.709407\pi
984984 0 0
985985 −7.22030 + 68.6966i −0.230058 + 2.18886i
986986 2.95847 0.628842i 0.0942168 0.0200264i
987987 0 0
988988 5.05843 + 48.1278i 0.160930 + 1.53115i
989989 31.9077 1.01461
990990 0 0
991991 −7.78978 −0.247451 −0.123725 0.992317i 0.539484π-0.539484\pi
−0.123725 + 0.992317i 0.539484π0.539484\pi
992992 2.78429 + 26.4908i 0.0884013 + 0.841082i
993993 0 0
994994 −10.8707 + 2.31064i −0.344797 + 0.0732890i
995995 3.74709 35.6511i 0.118791 1.13022i
996996 0 0
997997 −28.9889 32.1954i −0.918088 1.01964i −0.999736 0.0229789i 0.992685π-0.992685\pi
0.0816479 0.996661i 0.473982π-0.473982\pi
998998 −2.54682 7.83830i −0.0806181 0.248117i
999999 0 0
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 891.2.n.f.784.2 32
3.2 odd 2 891.2.n.i.784.3 32
9.2 odd 6 297.2.f.a.190.3 yes 16
9.4 even 3 inner 891.2.n.f.190.3 32
9.5 odd 6 891.2.n.i.190.2 32
9.7 even 3 297.2.f.d.190.2 yes 16
11.4 even 5 inner 891.2.n.f.136.3 32
33.26 odd 10 891.2.n.i.136.2 32
99.2 even 30 3267.2.a.bf.1.6 8
99.4 even 15 inner 891.2.n.f.433.2 32
99.20 odd 30 3267.2.a.bm.1.3 8
99.59 odd 30 891.2.n.i.433.3 32
99.70 even 15 297.2.f.d.136.2 yes 16
99.79 odd 30 3267.2.a.bl.1.3 8
99.92 odd 30 297.2.f.a.136.3 16
99.97 even 15 3267.2.a.be.1.6 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
297.2.f.a.136.3 16 99.92 odd 30
297.2.f.a.190.3 yes 16 9.2 odd 6
297.2.f.d.136.2 yes 16 99.70 even 15
297.2.f.d.190.2 yes 16 9.7 even 3
891.2.n.f.136.3 32 11.4 even 5 inner
891.2.n.f.190.3 32 9.4 even 3 inner
891.2.n.f.433.2 32 99.4 even 15 inner
891.2.n.f.784.2 32 1.1 even 1 trivial
891.2.n.i.136.2 32 33.26 odd 10
891.2.n.i.190.2 32 9.5 odd 6
891.2.n.i.433.3 32 99.59 odd 30
891.2.n.i.784.3 32 3.2 odd 2
3267.2.a.be.1.6 8 99.97 even 15
3267.2.a.bf.1.6 8 99.2 even 30
3267.2.a.bl.1.3 8 99.79 odd 30
3267.2.a.bm.1.3 8 99.20 odd 30