Properties

Label 1100.2.q.b.221.9
Level 11001100
Weight 22
Character 1100.221
Analytic conductor 8.7848.784
Analytic rank 00
Dimension 5252
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1100,2,Mod(221,1100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1100, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1100.221");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1100=225211 1100 = 2^{2} \cdot 5^{2} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1100.q (of order 55, degree 44, 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: 8.783544222348.78354422234
Analytic rank: 00
Dimension: 5252
Relative dimension: 1313 over Q(ζ5)\Q(\zeta_{5})
Twist minimal: yes
Sato-Tate group: SU(2)[C5]\mathrm{SU}(2)[C_{5}]

Embedding invariants

Embedding label 221.9
Character χ\chi == 1100.221
Dual form 1100.2.q.b.881.9

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+(0.921658+0.669624i)q3+(1.47725+1.67861i)q54.58549q7+(0.5259931.61884i)q9+(0.309017+0.951057i)q11+(0.545520+1.67894i)q13+(2.48556+0.557910i)q15+(5.645234.10150i)q17+(0.2251770.163601i)q19+(4.226263.07056i)q21+(0.4330731.33286i)q23+(0.6354924.95945i)q25+(1.655355.09466i)q27+(4.484013.25782i)q29+(1.75233+1.27315i)q31+(0.921658+0.669624i)q33+(6.773907.69727i)q35+(3.203989.86084i)q37+(0.621474+1.91270i)q39+(0.4798081.47670i)q4110.0846q43+(3.49443+1.50849i)q45+(8.192245.95201i)q47+14.0267q49+7.94943q51+(8.313926.04042i)q53+(1.139961.92366i)q55+0.317087q57+(1.65927+5.10671i)q59+(0.419275+1.29039i)q61+(2.41194+7.42318i)q63+(3.624161.56449i)q65+(7.204925.23468i)q67+(1.291660.938447i)q69+(11.8891+8.63790i)q71+(2.82642+8.69883i)q73+(2.735264.99646i)q75+(1.417004.36106i)q77+(2.033461.47739i)q79+(0.8059710.585572i)q81+(2.577411.87260i)q83+(1.45455+15.5351i)q85+(1.951216.00519i)q87+(3.18037+9.78818i)q89+(2.501487.69876i)q912.46758q93+(0.0580193+0.619664i)q95+(13.8642+10.0729i)q97+1.70215q99+O(q100)q+(0.921658 + 0.669624i) q^{3} +(-1.47725 + 1.67861i) q^{5} -4.58549 q^{7} +(-0.525993 - 1.61884i) q^{9} +(-0.309017 + 0.951057i) q^{11} +(0.545520 + 1.67894i) q^{13} +(-2.48556 + 0.557910i) q^{15} +(5.64523 - 4.10150i) q^{17} +(0.225177 - 0.163601i) q^{19} +(-4.22626 - 3.07056i) q^{21} +(0.433073 - 1.33286i) q^{23} +(-0.635492 - 4.95945i) q^{25} +(1.65535 - 5.09466i) q^{27} +(-4.48401 - 3.25782i) q^{29} +(-1.75233 + 1.27315i) q^{31} +(-0.921658 + 0.669624i) q^{33} +(6.77390 - 7.69727i) q^{35} +(-3.20398 - 9.86084i) q^{37} +(-0.621474 + 1.91270i) q^{39} +(-0.479808 - 1.47670i) q^{41} -10.0846 q^{43} +(3.49443 + 1.50849i) q^{45} +(-8.19224 - 5.95201i) q^{47} +14.0267 q^{49} +7.94943 q^{51} +(-8.31392 - 6.04042i) q^{53} +(-1.13996 - 1.92366i) q^{55} +0.317087 q^{57} +(1.65927 + 5.10671i) q^{59} +(-0.419275 + 1.29039i) q^{61} +(2.41194 + 7.42318i) q^{63} +(-3.62416 - 1.56449i) q^{65} +(7.20492 - 5.23468i) q^{67} +(1.29166 - 0.938447i) q^{69} +(11.8891 + 8.63790i) q^{71} +(-2.82642 + 8.69883i) q^{73} +(2.73526 - 4.99646i) q^{75} +(1.41700 - 4.36106i) q^{77} +(-2.03346 - 1.47739i) q^{79} +(0.805971 - 0.585572i) q^{81} +(2.57741 - 1.87260i) q^{83} +(-1.45455 + 15.5351i) q^{85} +(-1.95121 - 6.00519i) q^{87} +(-3.18037 + 9.78818i) q^{89} +(-2.50148 - 7.69876i) q^{91} -2.46758 q^{93} +(-0.0580193 + 0.619664i) q^{95} +(13.8642 + 10.0729i) q^{97} +1.70215 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 52q3q59q9+13q11+12q1315q15+8q1710q196q21+22q23+5q25+21q27+12q2912q31+30q35+15q3720q3968q43+56q99+O(q100) 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1100Z)×\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times.

nn 101101 177177 551551
χ(n)\chi(n) 11 e(35)e\left(\frac{3}{5}\right) 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 0.921658 + 0.669624i 0.532120 + 0.386608i 0.821150 0.570712i 0.193333π-0.193333\pi
−0.289030 + 0.957320i 0.593333π0.593333\pi
44 0 0
55 −1.47725 + 1.67861i −0.660644 + 0.750699i
66 0 0
77 −4.58549 −1.73315 −0.866577 0.499044i 0.833685π-0.833685\pi
−0.866577 + 0.499044i 0.833685π0.833685\pi
88 0 0
99 −0.525993 1.61884i −0.175331 0.539614i
1010 0 0
1111 −0.309017 + 0.951057i −0.0931721 + 0.286754i
1212 0 0
1313 0.545520 + 1.67894i 0.151300 + 0.465654i 0.997767 0.0667872i 0.0212748π-0.0212748\pi
−0.846467 + 0.532441i 0.821275π0.821275\pi
1414 0 0
1515 −2.48556 + 0.557910i −0.641768 + 0.144052i
1616 0 0
1717 5.64523 4.10150i 1.36917 0.994759i 0.371367 0.928486i 0.378889π-0.378889\pi
0.997802 0.0662726i 0.0211107π-0.0211107\pi
1818 0 0
1919 0.225177 0.163601i 0.0516592 0.0375326i −0.561656 0.827371i 0.689836π-0.689836\pi
0.613315 + 0.789838i 0.289836π0.289836\pi
2020 0 0
2121 −4.22626 3.07056i −0.922245 0.670050i
2222 0 0
2323 0.433073 1.33286i 0.0903020 0.277921i −0.895699 0.444661i 0.853324π-0.853324\pi
0.986001 + 0.166740i 0.0533241π0.0533241\pi
2424 0 0
2525 −0.635492 4.95945i −0.127098 0.991890i
2626 0 0
2727 1.65535 5.09466i 0.318573 0.980467i
2828 0 0
2929 −4.48401 3.25782i −0.832659 0.604962i 0.0876513 0.996151i 0.472064π-0.472064\pi
−0.920310 + 0.391189i 0.872064π0.872064\pi
3030 0 0
3131 −1.75233 + 1.27315i −0.314728 + 0.228664i −0.733923 0.679233i 0.762313π-0.762313\pi
0.419194 + 0.907897i 0.362313π0.362313\pi
3232 0 0
3333 −0.921658 + 0.669624i −0.160440 + 0.116567i
3434 0 0
3535 6.77390 7.69727i 1.14500 1.30108i
3636 0 0
3737 −3.20398 9.86084i −0.526731 1.62111i −0.760867 0.648908i 0.775226π-0.775226\pi
0.234135 0.972204i 0.424774π-0.424774\pi
3838 0 0
3939 −0.621474 + 1.91270i −0.0995155 + 0.306277i
4040 0 0
4141 −0.479808 1.47670i −0.0749334 0.230621i 0.906574 0.422048i 0.138689π-0.138689\pi
−0.981507 + 0.191427i 0.938689π0.938689\pi
4242 0 0
4343 −10.0846 −1.53789 −0.768944 0.639316i 0.779218π-0.779218\pi
−0.768944 + 0.639316i 0.779218π0.779218\pi
4444 0 0
4545 3.49443 + 1.50849i 0.520919 + 0.224872i
4646 0 0
4747 −8.19224 5.95201i −1.19496 0.868190i −0.201181 0.979554i 0.564478π-0.564478\pi
−0.993780 + 0.111364i 0.964478π0.964478\pi
4848 0 0
4949 14.0267 2.00382
5050 0 0
5151 7.94943 1.11314
5252 0 0
5353 −8.31392 6.04042i −1.14201 0.829715i −0.154608 0.987976i 0.549411π-0.549411\pi
−0.987397 + 0.158260i 0.949411π0.949411\pi
5454 0 0
5555 −1.13996 1.92366i −0.153713 0.259387i
5656 0 0
5757 0.317087 0.0419992
5858 0 0
5959 1.65927 + 5.10671i 0.216019 + 0.664837i 0.999080 + 0.0428920i 0.0136571π0.0136571\pi
−0.783061 + 0.621945i 0.786343π0.786343\pi
6060 0 0
6161 −0.419275 + 1.29039i −0.0536826 + 0.165218i −0.974303 0.225240i 0.927683π-0.927683\pi
0.920621 + 0.390458i 0.127683π0.127683\pi
6262 0 0
6363 2.41194 + 7.42318i 0.303876 + 0.935233i
6464 0 0
6565 −3.62416 1.56449i −0.449521 0.194051i
6666 0 0
6767 7.20492 5.23468i 0.880221 0.639518i −0.0530889 0.998590i 0.516907π-0.516907\pi
0.933310 + 0.359072i 0.116907π0.116907\pi
6868 0 0
6969 1.29166 0.938447i 0.155498 0.112976i
7070 0 0
7171 11.8891 + 8.63790i 1.41097 + 1.02513i 0.993180 + 0.116587i 0.0371955π0.0371955\pi
0.417791 + 0.908543i 0.362805π0.362805\pi
7272 0 0
7373 −2.82642 + 8.69883i −0.330808 + 1.01812i 0.637943 + 0.770084i 0.279786π0.279786\pi
−0.968750 + 0.248038i 0.920214π0.920214\pi
7474 0 0
7575 2.73526 4.99646i 0.315841 0.576941i
7676 0 0
7777 1.41700 4.36106i 0.161482 0.496989i
7878 0 0
7979 −2.03346 1.47739i −0.228782 0.166220i 0.467489 0.883999i 0.345159π-0.345159\pi
−0.696271 + 0.717779i 0.745159π0.745159\pi
8080 0 0
8181 0.805971 0.585572i 0.0895523 0.0650636i
8282 0 0
8383 2.57741 1.87260i 0.282908 0.205545i −0.437277 0.899327i 0.644057π-0.644057\pi
0.720185 + 0.693782i 0.244057π0.244057\pi
8484 0 0
8585 −1.45455 + 15.5351i −0.157768 + 1.68502i
8686 0 0
8787 −1.95121 6.00519i −0.209191 0.643824i
8888 0 0
8989 −3.18037 + 9.78818i −0.337119 + 1.03754i 0.628550 + 0.777769i 0.283649π0.283649\pi
−0.965669 + 0.259776i 0.916351π0.916351\pi
9090 0 0
9191 −2.50148 7.69876i −0.262226 0.807049i
9292 0 0
9393 −2.46758 −0.255876
9494 0 0
9595 −0.0580193 + 0.619664i −0.00595265 + 0.0635762i
9696 0 0
9797 13.8642 + 10.0729i 1.40770 + 1.02275i 0.993652 + 0.112497i 0.0358850π0.0358850\pi
0.414047 + 0.910256i 0.364115π0.364115\pi
9898 0 0
9999 1.70215 0.171073
100100 0 0
101101 −10.6373 −1.05845 −0.529224 0.848482i 0.677517π-0.677517\pi
−0.529224 + 0.848482i 0.677517π0.677517\pi
102102 0 0
103103 2.75387 + 2.00080i 0.271346 + 0.197145i 0.715134 0.698987i 0.246366π-0.246366\pi
−0.443788 + 0.896132i 0.646366π0.646366\pi
104104 0 0
105105 11.3975 2.55829i 1.11228 0.249664i
106106 0 0
107107 −17.5843 −1.69994 −0.849968 0.526834i 0.823379π-0.823379\pi
−0.849968 + 0.526834i 0.823379π0.823379\pi
108108 0 0
109109 −4.60659 14.1776i −0.441231 1.35797i −0.886564 0.462605i 0.846915π-0.846915\pi
0.445333 0.895365i 0.353085π-0.353085\pi
110110 0 0
111111 3.65008 11.2338i 0.346450 1.06626i
112112 0 0
113113 1.52667 + 4.69861i 0.143617 + 0.442008i 0.996831 0.0795537i 0.0253495π-0.0253495\pi
−0.853213 + 0.521562i 0.825350π0.825350\pi
114114 0 0
115115 1.59761 + 2.69593i 0.148978 + 0.251396i
116116 0 0
117117 2.43099 1.76622i 0.224746 0.163287i
118118 0 0
119119 −25.8861 + 18.8074i −2.37298 + 1.72407i
120120 0 0
121121 −0.809017 0.587785i −0.0735470 0.0534350i
122122 0 0
123123 0.546613 1.68230i 0.0492864 0.151688i
124124 0 0
125125 9.26378 + 6.25958i 0.828578 + 0.559874i
126126 0 0
127127 −3.84281 + 11.8270i −0.340994 + 1.04947i 0.622699 + 0.782462i 0.286036π0.286036\pi
−0.963693 + 0.267011i 0.913964π0.913964\pi
128128 0 0
129129 −9.29456 6.75289i −0.818340 0.594559i
130130 0 0
131131 −0.0419436 + 0.0304738i −0.00366463 + 0.00266251i −0.589616 0.807684i 0.700721π-0.700721\pi
0.585951 + 0.810346i 0.300721π0.300721\pi
132132 0 0
133133 −1.03255 + 0.750190i −0.0895332 + 0.0650497i
134134 0 0
135135 6.10660 + 10.3048i 0.525573 + 0.886893i
136136 0 0
137137 −5.54272 17.0587i −0.473546 1.45743i −0.847908 0.530143i 0.822138π-0.822138\pi
0.374362 0.927283i 0.377862π-0.377862\pi
138138 0 0
139139 −4.53157 + 13.9467i −0.384362 + 1.18295i 0.552579 + 0.833460i 0.313644π0.313644\pi
−0.936942 + 0.349486i 0.886356π0.886356\pi
140140 0 0
141141 −3.56484 10.9714i −0.300213 0.923962i
142142 0 0
143143 −1.76534 −0.147625
144144 0 0
145145 12.0926 2.71432i 1.00424 0.225412i
146146 0 0
147147 12.9279 + 9.39264i 1.06627 + 0.774692i
148148 0 0
149149 6.79887 0.556985 0.278492 0.960438i 0.410165π-0.410165\pi
0.278492 + 0.960438i 0.410165π0.410165\pi
150150 0 0
151151 2.83345 0.230583 0.115291 0.993332i 0.463220π-0.463220\pi
0.115291 + 0.993332i 0.463220π0.463220\pi
152152 0 0
153153 −9.60902 6.98136i −0.776843 0.564410i
154154 0 0
155155 0.451508 4.82224i 0.0362660 0.387332i
156156 0 0
157157 −3.72445 −0.297244 −0.148622 0.988894i 0.547484π-0.547484\pi
−0.148622 + 0.988894i 0.547484π0.547484\pi
158158 0 0
159159 −3.61779 11.1344i −0.286909 0.883016i
160160 0 0
161161 −1.98585 + 6.11183i −0.156507 + 0.481680i
162162 0 0
163163 −7.65663 23.5647i −0.599713 1.84573i −0.529706 0.848181i 0.677698π-0.677698\pi
−0.0700069 0.997547i 0.522302π-0.522302\pi
164164 0 0
165165 0.237475 2.53631i 0.0184874 0.197451i
166166 0 0
167167 −13.3087 + 9.66933i −1.02986 + 0.748235i −0.968280 0.249867i 0.919613π-0.919613\pi
−0.0615774 + 0.998102i 0.519613π0.519613\pi
168168 0 0
169169 7.99598 5.80942i 0.615075 0.446878i
170170 0 0
171171 −0.383285 0.278473i −0.0293105 0.0212954i
172172 0 0
173173 3.87771 11.9343i 0.294816 0.907352i −0.688467 0.725268i 0.741716π-0.741716\pi
0.983283 0.182084i 0.0582842π-0.0582842\pi
174174 0 0
175175 2.91404 + 22.7415i 0.220281 + 1.71910i
176176 0 0
177177 −1.89029 + 5.81773i −0.142083 + 0.437287i
178178 0 0
179179 −3.89837 2.83233i −0.291378 0.211698i 0.432487 0.901640i 0.357636π-0.357636\pi
−0.723865 + 0.689942i 0.757636π0.757636\pi
180180 0 0
181181 17.6958 12.8567i 1.31532 0.955633i 0.315338 0.948979i 0.397882π-0.397882\pi
0.999978 0.00665351i 0.00211790π-0.00211790\pi
182182 0 0
183183 −1.25051 + 0.908547i −0.0924401 + 0.0671617i
184184 0 0
185185 21.2856 + 9.18863i 1.56495 + 0.675562i
186186 0 0
187187 2.15628 + 6.63636i 0.157683 + 0.485299i
188188 0 0
189189 −7.59062 + 23.3615i −0.552136 + 1.69930i
190190 0 0
191191 −0.110617 0.340443i −0.00800394 0.0246336i 0.946975 0.321308i 0.104122π-0.104122\pi
−0.954979 + 0.296674i 0.904122π0.904122\pi
192192 0 0
193193 −8.83535 −0.635983 −0.317991 0.948094i 0.603008π-0.603008\pi
−0.317991 + 0.948094i 0.603008π0.603008\pi
194194 0 0
195195 −2.29262 3.86874i −0.164178 0.277047i
196196 0 0
197197 −18.0192 13.0917i −1.28381 0.932746i −0.284154 0.958779i 0.591713π-0.591713\pi
−0.999661 + 0.0260325i 0.991713π0.991713\pi
198198 0 0
199199 −2.73266 −0.193713 −0.0968564 0.995298i 0.530879π-0.530879\pi
−0.0968564 + 0.995298i 0.530879π0.530879\pi
200200 0 0
201201 10.1457 0.715625
202202 0 0
203203 20.5614 + 14.9387i 1.44313 + 1.04849i
204204 0 0
205205 3.18760 + 1.37603i 0.222632 + 0.0961062i
206206 0 0
207207 −2.38549 −0.165803
208208 0 0
209209 0.0860100 + 0.264711i 0.00594943 + 0.0183105i
210210 0 0
211211 4.73541 14.5741i 0.325999 1.00332i −0.644989 0.764192i 0.723138π-0.723138\pi
0.970988 0.239129i 0.0768620π-0.0768620\pi
212212 0 0
213213 5.17350 + 15.9224i 0.354482 + 1.09098i
214214 0 0
215215 14.8974 16.9282i 1.01600 1.15449i
216216 0 0
217217 8.03531 5.83800i 0.545473 0.396309i
218218 0 0
219219 −8.42994 + 6.12471i −0.569643 + 0.413870i
220220 0 0
221221 9.96574 + 7.24054i 0.670369 + 0.487051i
222222 0 0
223223 −4.53228 + 13.9489i −0.303504 + 0.934090i 0.676727 + 0.736234i 0.263398π0.263398\pi
−0.980231 + 0.197856i 0.936602π0.936602\pi
224224 0 0
225225 −7.69430 + 3.63740i −0.512953 + 0.242493i
226226 0 0
227227 0.260500 0.801738i 0.0172900 0.0532132i −0.942039 0.335503i 0.891094π-0.891094\pi
0.959329 + 0.282289i 0.0910939π0.0910939\pi
228228 0 0
229229 6.76463 + 4.91479i 0.447019 + 0.324778i 0.788418 0.615140i 0.210901π-0.210901\pi
−0.341399 + 0.939919i 0.610901π0.610901\pi
230230 0 0
231231 4.22626 3.07056i 0.278067 0.202028i
232232 0 0
233233 4.34638 3.15783i 0.284741 0.206876i −0.436242 0.899829i 0.643691π-0.643691\pi
0.720982 + 0.692953i 0.243691π0.243691\pi
234234 0 0
235235 22.0931 4.95903i 1.44119 0.323492i
236236 0 0
237237 −0.884854 2.72330i −0.0574775 0.176897i
238238 0 0
239239 −6.49070 + 19.9763i −0.419849 + 1.29216i 0.487993 + 0.872848i 0.337729π0.337729\pi
−0.907841 + 0.419314i 0.862271π0.862271\pi
240240 0 0
241241 −4.00121 12.3145i −0.257740 0.793244i −0.993277 0.115759i 0.963070π-0.963070\pi
0.735537 0.677485i 0.236930π-0.236930\pi
242242 0 0
243243 −14.9356 −0.958118
244244 0 0
245245 −20.7209 + 23.5455i −1.32381 + 1.50427i
246246 0 0
247247 0.397514 + 0.288811i 0.0252932 + 0.0183766i
248248 0 0
249249 3.62943 0.230006
250250 0 0
251251 −22.4497 −1.41701 −0.708507 0.705704i 0.750631π-0.750631\pi
−0.708507 + 0.705704i 0.750631π0.750631\pi
252252 0 0
253253 1.13380 + 0.823754i 0.0712814 + 0.0517890i
254254 0 0
255255 −11.7433 + 13.3440i −0.735391 + 0.835635i
256256 0 0
257257 −7.47518 −0.466289 −0.233144 0.972442i 0.574901π-0.574901\pi
−0.233144 + 0.972442i 0.574901π0.574901\pi
258258 0 0
259259 14.6918 + 45.2168i 0.912906 + 2.80964i
260260 0 0
261261 −2.91534 + 8.97248i −0.180455 + 0.555383i
262262 0 0
263263 9.89291 + 30.4472i 0.610023 + 1.87746i 0.457645 + 0.889135i 0.348693π0.348693\pi
0.152378 + 0.988322i 0.451307π0.451307\pi
264264 0 0
265265 22.4212 5.03269i 1.37733 0.309156i
266266 0 0
267267 −9.48561 + 6.89170i −0.580510 + 0.421765i
268268 0 0
269269 −11.7758 + 8.55564i −0.717985 + 0.521647i −0.885740 0.464182i 0.846348π-0.846348\pi
0.167755 + 0.985829i 0.446348π0.446348\pi
270270 0 0
271271 −4.98543 3.62213i −0.302843 0.220028i 0.425976 0.904734i 0.359931π-0.359931\pi
−0.728820 + 0.684706i 0.759931π0.759931\pi
272272 0 0
273273 2.84977 8.77068i 0.172476 0.530825i
274274 0 0
275275 4.91310 + 0.928165i 0.296271 + 0.0559705i
276276 0 0
277277 3.74157 11.5154i 0.224809 0.691891i −0.773502 0.633794i 0.781497π-0.781497\pi
0.998311 0.0580970i 0.0185033π-0.0185033\pi
278278 0 0
279279 2.98274 + 2.16708i 0.178572 + 0.129740i
280280 0 0
281281 −14.9792 + 10.8830i −0.893582 + 0.649226i −0.936810 0.349840i 0.886236π-0.886236\pi
0.0432272 + 0.999065i 0.486236π0.486236\pi
282282 0 0
283283 −8.00704 + 5.81746i −0.475969 + 0.345812i −0.799763 0.600316i 0.795042π-0.795042\pi
0.323794 + 0.946128i 0.395042π0.395042\pi
284284 0 0
285285 −0.468416 + 0.532267i −0.0277465 + 0.0315288i
286286 0 0
287287 2.20016 + 6.77139i 0.129871 + 0.399702i
288288 0 0
289289 9.79301 30.1398i 0.576059 1.77293i
290290 0 0
291291 6.03299 + 18.5676i 0.353660 + 1.08845i
292292 0 0
293293 −21.8732 −1.27784 −0.638922 0.769272i 0.720619π-0.720619\pi
−0.638922 + 0.769272i 0.720619π0.720619\pi
294294 0 0
295295 −11.0233 4.75859i −0.641804 0.277056i
296296 0 0
297297 4.33378 + 3.14867i 0.251471 + 0.182704i
298298 0 0
299299 2.47404 0.143078
300300 0 0
301301 46.2429 2.66540
302302 0 0
303303 −9.80393 7.12297i −0.563221 0.409204i
304304 0 0
305305 −1.54670 2.61003i −0.0885640 0.149450i
306306 0 0
307307 13.7714 0.785973 0.392987 0.919544i 0.371442π-0.371442\pi
0.392987 + 0.919544i 0.371442π0.371442\pi
308308 0 0
309309 1.19834 + 3.68811i 0.0681711 + 0.209809i
310310 0 0
311311 8.35233 25.7058i 0.473617 1.45764i −0.374196 0.927350i 0.622081π-0.622081\pi
0.847813 0.530295i 0.177919π-0.177919\pi
312312 0 0
313313 −7.32139 22.5329i −0.413829 1.27364i −0.913294 0.407301i 0.866470π-0.866470\pi
0.499464 0.866334i 0.333530π-0.333530\pi
314314 0 0
315315 −16.0237 6.91715i −0.902832 0.389737i
316316 0 0
317317 10.5954 7.69801i 0.595097 0.432363i −0.249038 0.968494i 0.580114π-0.580114\pi
0.844135 + 0.536130i 0.180114π0.180114\pi
318318 0 0
319319 4.48401 3.25782i 0.251056 0.182403i
320320 0 0
321321 −16.2067 11.7749i −0.904569 0.657208i
322322 0 0
323323 0.600167 1.84713i 0.0333942 0.102777i
324324 0 0
325325 7.97994 3.77243i 0.442647 0.209257i
326326 0 0
327327 5.24798 16.1516i 0.290214 0.893186i
328328 0 0
329329 37.5655 + 27.2929i 2.07105 + 1.50471i
330330 0 0
331331 1.33122 0.967189i 0.0731705 0.0531615i −0.550599 0.834770i 0.685601π-0.685601\pi
0.623769 + 0.781609i 0.285601π0.285601\pi
332332 0 0
333333 −14.2779 + 10.3735i −0.782422 + 0.568463i
334334 0 0
335335 −1.85642 + 19.8272i −0.101427 + 1.08328i
336336 0 0
337337 −6.94397 21.3714i −0.378262 1.16417i −0.941251 0.337707i 0.890349π-0.890349\pi
0.562989 0.826465i 0.309651π-0.309651\pi
338338 0 0
339339 −1.73923 + 5.35281i −0.0944622 + 0.290725i
340340 0 0
341341 −0.669332 2.05999i −0.0362464 0.111555i
342342 0 0
343343 −32.2211 −1.73977
344344 0 0
345345 −0.332810 + 3.55452i −0.0179179 + 0.191369i
346346 0 0
347347 5.08911 + 3.69745i 0.273198 + 0.198490i 0.715945 0.698157i 0.245996π-0.245996\pi
−0.442747 + 0.896646i 0.645996π0.645996\pi
348348 0 0
349349 29.5658 1.58262 0.791310 0.611415i 0.209399π-0.209399\pi
0.791310 + 0.611415i 0.209399π0.209399\pi
350350 0 0
351351 9.45665 0.504759
352352 0 0
353353 12.4799 + 9.06715i 0.664236 + 0.482596i 0.868091 0.496405i 0.165347π-0.165347\pi
−0.203855 + 0.979001i 0.565347π0.565347\pi
354354 0 0
355355 −32.0628 + 7.19683i −1.70171 + 0.381968i
356356 0 0
357357 −36.4520 −1.92925
358358 0 0
359359 4.02855 + 12.3986i 0.212619 + 0.654374i 0.999314 + 0.0370321i 0.0117904π0.0117904\pi
−0.786695 + 0.617342i 0.788210π0.788210\pi
360360 0 0
361361 −5.84738 + 17.9964i −0.307757 + 0.947179i
362362 0 0
363363 −0.352042 1.08347i −0.0184774 0.0568676i
364364 0 0
365365 −10.4267 17.5948i −0.545757 0.920953i
366366 0 0
367367 10.7106 7.78171i 0.559089 0.406202i −0.272036 0.962287i 0.587697π-0.587697\pi
0.831126 + 0.556085i 0.187697π0.187697\pi
368368 0 0
369369 −2.13816 + 1.55347i −0.111308 + 0.0808702i
370370 0 0
371371 38.1234 + 27.6983i 1.97927 + 1.43802i
372372 0 0
373373 −1.39598 + 4.29638i −0.0722811 + 0.222458i −0.980670 0.195667i 0.937313π-0.937313\pi
0.908389 + 0.418126i 0.137313π0.137313\pi
374374 0 0
375375 4.34648 + 11.9724i 0.224451 + 0.618254i
376376 0 0
377377 3.02357 9.30558i 0.155722 0.479262i
378378 0 0
379379 −6.97127 5.06492i −0.358090 0.260168i 0.394165 0.919040i 0.371034π-0.371034\pi
−0.752255 + 0.658872i 0.771034π0.771034\pi
380380 0 0
381381 −11.4614 + 8.32718i −0.587184 + 0.426614i
382382 0 0
383383 4.31988 3.13857i 0.220735 0.160374i −0.471922 0.881640i 0.656440π-0.656440\pi
0.692658 + 0.721267i 0.256440π0.256440\pi
384384 0 0
385385 5.22729 + 8.82095i 0.266408 + 0.449557i
386386 0 0
387387 5.30444 + 16.3254i 0.269640 + 0.829865i
388388 0 0
389389 4.92524 15.1583i 0.249720 0.768559i −0.745104 0.666948i 0.767600π-0.767600\pi
0.994824 0.101611i 0.0323996π-0.0323996\pi
390390 0 0
391391 −3.02193 9.30055i −0.152826 0.470349i
392392 0 0
393393 −0.0590637 −0.00297937
394394 0 0
395395 5.48389 1.23092i 0.275924 0.0619342i
396396 0 0
397397 −8.58441 6.23694i −0.430839 0.313023i 0.351145 0.936321i 0.385792π-0.385792\pi
−0.781984 + 0.623298i 0.785792π0.785792\pi
398398 0 0
399399 −1.45400 −0.0727911
400400 0 0
401401 2.39723 0.119712 0.0598561 0.998207i 0.480936π-0.480936\pi
0.0598561 + 0.998207i 0.480936π0.480936\pi
402402 0 0
403403 −3.09347 2.24753i −0.154097 0.111958i
404404 0 0
405405 −0.207667 + 2.21795i −0.0103191 + 0.110211i
406406 0 0
407407 10.3683 0.513938
408408 0 0
409409 3.81628 + 11.7453i 0.188703 + 0.580768i 0.999992 0.00387685i 0.00123404π-0.00123404\pi
−0.811290 + 0.584644i 0.801234π0.801234\pi
410410 0 0
411411 6.31444 19.4339i 0.311469 0.958602i
412412 0 0
413413 −7.60857 23.4168i −0.374393 1.15226i
414414 0 0
415415 −0.664098 + 7.09277i −0.0325993 + 0.348171i
416416 0 0
417417 −13.5156 + 9.81967i −0.661863 + 0.480871i
418418 0 0
419419 −11.9035 + 8.64837i −0.581522 + 0.422500i −0.839272 0.543711i 0.817019π-0.817019\pi
0.257751 + 0.966211i 0.417019π0.417019\pi
420420 0 0
421421 25.6588 + 18.6422i 1.25054 + 0.908567i 0.998253 0.0590866i 0.0188188π-0.0188188\pi
0.252282 + 0.967654i 0.418819π0.418819\pi
422422 0 0
423423 −5.32630 + 16.3927i −0.258973 + 0.797038i
424424 0 0
425425 −23.9287 25.3907i −1.16071 1.23163i
426426 0 0
427427 1.92258 5.91710i 0.0930402 0.286348i
428428 0 0
429429 −1.62704 1.18211i −0.0785543 0.0570730i
430430 0 0
431431 −4.27343 + 3.10483i −0.205844 + 0.149554i −0.685931 0.727666i 0.740605π-0.740605\pi
0.480087 + 0.877221i 0.340605π0.340605\pi
432432 0 0
433433 22.2601 16.1729i 1.06975 0.777221i 0.0938847 0.995583i 0.470072π-0.470072\pi
0.975868 + 0.218362i 0.0700715π0.0700715\pi
434434 0 0
435435 12.9628 + 5.59582i 0.621519 + 0.268299i
436436 0 0
437437 −0.120539 0.370981i −0.00576616 0.0177464i
438438 0 0
439439 10.8600 33.4237i 0.518320 1.59523i −0.258838 0.965921i 0.583340π-0.583340\pi
0.777159 0.629305i 0.216660π-0.216660\pi
440440 0 0
441441 −7.37797 22.7071i −0.351332 1.08129i
442442 0 0
443443 −19.1930 −0.911889 −0.455944 0.890008i 0.650698π-0.650698\pi
−0.455944 + 0.890008i 0.650698π0.650698\pi
444444 0 0
445445 −11.7324 19.7982i −0.556168 0.938523i
446446 0 0
447447 6.26623 + 4.55268i 0.296383 + 0.215335i
448448 0 0
449449 4.97256 0.234670 0.117335 0.993092i 0.462565π-0.462565\pi
0.117335 + 0.993092i 0.462565π0.462565\pi
450450 0 0
451451 1.55269 0.0731134
452452 0 0
453453 2.61147 + 1.89735i 0.122698 + 0.0891451i
454454 0 0
455455 16.6185 + 7.17394i 0.779090 + 0.336319i
456456 0 0
457457 32.8864 1.53836 0.769181 0.639031i 0.220664π-0.220664\pi
0.769181 + 0.639031i 0.220664π0.220664\pi
458458 0 0
459459 −11.5509 35.5499i −0.539148 1.65933i
460460 0 0
461461 2.33973 7.20094i 0.108972 0.335381i −0.881670 0.471866i 0.843581π-0.843581\pi
0.990642 + 0.136485i 0.0435805π0.0435805\pi
462462 0 0
463463 5.06969 + 15.6029i 0.235608 + 0.725128i 0.997040 + 0.0768831i 0.0244968π0.0244968\pi
−0.761432 + 0.648245i 0.775503π0.775503\pi
464464 0 0
465465 3.64522 4.14212i 0.169043 0.192086i
466466 0 0
467467 6.05684 4.40055i 0.280277 0.203633i −0.438761 0.898604i 0.644583π-0.644583\pi
0.719038 + 0.694971i 0.244583π0.244583\pi
468468 0 0
469469 −33.0381 + 24.0036i −1.52556 + 1.10838i
470470 0 0
471471 −3.43267 2.49398i −0.158169 0.114917i
472472 0 0
473473 3.11631 9.59103i 0.143288 0.440996i
474474 0 0
475475 −0.954468 1.01279i −0.0437940 0.0464699i
476476 0 0
477477 −5.40541 + 16.6361i −0.247497 + 0.761717i
478478 0 0
479479 13.7560 + 9.99436i 0.628530 + 0.456654i 0.855891 0.517157i 0.173010π-0.173010\pi
−0.227361 + 0.973811i 0.573010π0.573010\pi
480480 0 0
481481 14.8079 10.7586i 0.675183 0.490549i
482482 0 0
483483 −5.92291 + 4.30324i −0.269502 + 0.195804i
484484 0 0
485485 −37.3895 + 8.39247i −1.69777 + 0.381082i
486486 0 0
487487 0.709421 + 2.18337i 0.0321470 + 0.0989381i 0.965843 0.259130i 0.0834357π-0.0834357\pi
−0.933696 + 0.358068i 0.883436π0.883436\pi
488488 0 0
489489 8.72268 26.8456i 0.394453 1.21400i
490490 0 0
491491 −0.814069 2.50545i −0.0367384 0.113069i 0.931006 0.365005i 0.118933π-0.118933\pi
−0.967744 + 0.251936i 0.918933π0.918933\pi
492492 0 0
493493 −38.6752 −1.74184
494494 0 0
495495 −2.51449 + 2.85725i −0.113018 + 0.128424i
496496 0 0
497497 −54.5172 39.6090i −2.44543 1.77671i
498498 0 0
499499 −13.3532 −0.597773 −0.298887 0.954289i 0.596615π-0.596615\pi
−0.298887 + 0.954289i 0.596615π0.596615\pi
500500 0 0
501501 −18.7409 −0.837281
502502 0 0
503503 −5.51952 4.01016i −0.246103 0.178804i 0.457895 0.889006i 0.348604π-0.348604\pi
−0.703998 + 0.710202i 0.748604π0.748604\pi
504504 0 0
505505 15.7139 17.8559i 0.699258 0.794576i
506506 0 0
507507 11.2597 0.500060
508508 0 0
509509 3.74714 + 11.5325i 0.166089 + 0.511170i 0.999115 0.0420645i 0.0133935π-0.0133935\pi
−0.833026 + 0.553234i 0.813394π0.813394\pi
510510 0 0
511511 12.9605 39.8884i 0.573340 1.76456i
512512 0 0
513513 −0.460742 1.41802i −0.0203422 0.0626070i
514514 0 0
515515 −7.42671 + 1.66701i −0.327260 + 0.0734570i
516516 0 0
517517 8.19224 5.95201i 0.360294 0.261769i
518518 0 0
519519 11.5654 8.40279i 0.507667 0.368841i
520520 0 0
521521 13.6406 + 9.91051i 0.597607 + 0.434187i 0.845029 0.534721i 0.179583π-0.179583\pi
−0.247421 + 0.968908i 0.579583π0.579583\pi
522522 0 0
523523 6.52443 20.0801i 0.285294 0.878043i −0.701017 0.713145i 0.747270π-0.747270\pi
0.986311 0.164899i 0.0527297π-0.0527297\pi
524524 0 0
525525 −12.5425 + 22.9112i −0.547400 + 0.999928i
526526 0 0
527527 −4.67052 + 14.3744i −0.203451 + 0.626158i
528528 0 0
529529 17.0184 + 12.3646i 0.739931 + 0.537592i
530530 0 0
531531 7.39418 5.37219i 0.320880 0.233133i
532532 0 0
533533 2.21754 1.61114i 0.0960523 0.0697861i
534534 0 0
535535 25.9763 29.5172i 1.12305 1.27614i
536536 0 0
537537 −1.69637 5.22088i −0.0732037 0.225298i
538538 0 0
539539 −4.33450 + 13.3402i −0.186700 + 0.574604i
540540 0 0
541541 5.55390 + 17.0931i 0.238781 + 0.734891i 0.996597 + 0.0824238i 0.0262661π0.0262661\pi
−0.757817 + 0.652468i 0.773734π0.773734\pi
542542 0 0
543543 24.9186 1.06936
544544 0 0
545545 30.6038 + 13.2111i 1.31092 + 0.565903i
546546 0 0
547547 −20.8191 15.1259i −0.890159 0.646739i 0.0457603 0.998952i 0.485429π-0.485429\pi
−0.935920 + 0.352214i 0.885429π0.885429\pi
548548 0 0
549549 2.30948 0.0985662
550550 0 0
551551 −1.54268 −0.0657202
552552 0 0
553553 9.32440 + 6.77457i 0.396514 + 0.288084i
554554 0 0
555555 13.4651 + 22.7221i 0.571563 + 0.964501i
556556 0 0
557557 −8.80469 −0.373067 −0.186533 0.982449i 0.559725π-0.559725\pi
−0.186533 + 0.982449i 0.559725π0.559725\pi
558558 0 0
559559 −5.50136 16.9314i −0.232683 0.716123i
560560 0 0
561561 −2.45651 + 7.56035i −0.103714 + 0.319198i
562562 0 0
563563 −5.16793 15.9053i −0.217802 0.670326i −0.998943 0.0459712i 0.985362π-0.985362\pi
0.781140 0.624355i 0.214638π-0.214638\pi
564564 0 0
565565 −10.1424 4.37831i −0.426695 0.184197i
566566 0 0
567567 −3.69577 + 2.68514i −0.155208 + 0.112765i
568568 0 0
569569 1.65776 1.20443i 0.0694967 0.0504923i −0.552494 0.833517i 0.686324π-0.686324\pi
0.621991 + 0.783024i 0.286324π0.286324\pi
570570 0 0
571571 −31.0693 22.5731i −1.30021 0.944657i −0.300251 0.953860i 0.597070π-0.597070\pi
−0.999958 + 0.00920359i 0.997070π0.997070\pi
572572 0 0
573573 0.126018 0.387843i 0.00526448 0.0162024i
574574 0 0
575575 −6.88548 1.30078i −0.287144 0.0542463i
576576 0 0
577577 −2.90734 + 8.94789i −0.121034 + 0.372505i −0.993158 0.116781i 0.962743π-0.962743\pi
0.872123 + 0.489286i 0.162743π0.162743\pi
578578 0 0
579579 −8.14318 5.91636i −0.338419 0.245876i
580580 0 0
581581 −11.8187 + 8.58679i −0.490323 + 0.356240i
582582 0 0
583583 8.31392 6.04042i 0.344328 0.250169i
584584 0 0
585585 −0.626372 + 6.68984i −0.0258973 + 0.276591i
586586 0 0
587587 −10.7447 33.0687i −0.443480 1.36489i −0.884142 0.467217i 0.845257π-0.845257\pi
0.440663 0.897673i 0.354743π-0.354743\pi
588588 0 0
589589 −0.186298 + 0.573366i −0.00767627 + 0.0236251i
590590 0 0
591591 −7.84102 24.1322i −0.322536 0.992665i
592592 0 0
593593 −40.7019 −1.67143 −0.835713 0.549166i 0.814945π-0.814945\pi
−0.835713 + 0.549166i 0.814945π0.814945\pi
594594 0 0
595595 6.66984 71.2360i 0.273437 2.92039i
596596 0 0
597597 −2.51858 1.82985i −0.103078 0.0748909i
598598 0 0
599599 −6.80611 −0.278090 −0.139045 0.990286i 0.544403π-0.544403\pi
−0.139045 + 0.990286i 0.544403π0.544403\pi
600600 0 0
601601 −12.3566 −0.504036 −0.252018 0.967722i 0.581094π-0.581094\pi
−0.252018 + 0.967722i 0.581094π0.581094\pi
602602 0 0
603603 −12.2639 8.91021i −0.499423 0.362852i
604604 0 0
605605 2.18178 0.489724i 0.0887020 0.0199101i
606606 0 0
607607 −7.11226 −0.288678 −0.144339 0.989528i 0.546106π-0.546106\pi
−0.144339 + 0.989528i 0.546106π0.546106\pi
608608 0 0
609609 8.94724 + 27.5368i 0.362561 + 1.11585i
610610 0 0
611611 5.52403 17.0012i 0.223478 0.687795i
612612 0 0
613613 8.05789 + 24.7996i 0.325455 + 1.00165i 0.971235 + 0.238124i 0.0765325π0.0765325\pi
−0.645779 + 0.763524i 0.723467π0.723467\pi
614614 0 0
615615 2.01645 + 3.40272i 0.0813113 + 0.137211i
616616 0 0
617617 −18.3156 + 13.3071i −0.737359 + 0.535723i −0.891883 0.452266i 0.850616π-0.850616\pi
0.154524 + 0.987989i 0.450616π0.450616\pi
618618 0 0
619619 −0.445488 + 0.323666i −0.0179057 + 0.0130092i −0.596702 0.802463i 0.703523π-0.703523\pi
0.578796 + 0.815472i 0.303523π0.303523\pi
620620 0 0
621621 −6.07359 4.41272i −0.243725 0.177076i
622622 0 0
623623 14.5836 44.8836i 0.584278 1.79822i
624624 0 0
625625 −24.1923 + 6.30338i −0.967692 + 0.252135i
626626 0 0
627627 −0.0979853 + 0.301568i −0.00391316 + 0.0120435i
628628 0 0
629629 −58.5314 42.5256i −2.33380 1.69560i
630630 0 0
631631 2.23979 1.62730i 0.0891646 0.0647819i −0.542310 0.840179i 0.682450π-0.682450\pi
0.631474 + 0.775397i 0.282450π0.282450\pi
632632 0 0
633633 14.1236 10.2614i 0.561362 0.407853i
634634 0 0
635635 −14.1761 23.9219i −0.562562 0.949312i
636636 0 0
637637 7.65187 + 23.5500i 0.303178 + 0.933087i
638638 0 0
639639 7.72983 23.7900i 0.305787 0.941117i
640640 0 0
641641 −0.307565 0.946588i −0.0121481 0.0373880i 0.944799 0.327651i 0.106257π-0.106257\pi
−0.956947 + 0.290263i 0.906257π0.906257\pi
642642 0 0
643643 15.0690 0.594264 0.297132 0.954836i 0.403970π-0.403970\pi
0.297132 + 0.954836i 0.403970π0.403970\pi
644644 0 0
645645 25.0658 5.62630i 0.986967 0.221535i
646646 0 0
647647 32.4314 + 23.5628i 1.27501 + 0.926348i 0.999390 0.0349197i 0.0111175π-0.0111175\pi
0.275618 + 0.961267i 0.411118π0.411118\pi
648648 0 0
649649 −5.36951 −0.210772
650650 0 0
651651 11.3151 0.443473
652652 0 0
653653 6.17534 + 4.48664i 0.241660 + 0.175576i 0.702022 0.712155i 0.252281π-0.252281\pi
−0.460363 + 0.887731i 0.652281π0.652281\pi
654654 0 0
655655 0.0108072 0.115425i 0.000422273 0.00451001i
656656 0 0
657657 15.5687 0.607393
658658 0 0
659659 9.38662 + 28.8891i 0.365651 + 1.12536i 0.949572 + 0.313548i 0.101518π0.101518\pi
−0.583922 + 0.811810i 0.698482π0.698482\pi
660660 0 0
661661 0.602895 1.85552i 0.0234499 0.0721714i −0.938647 0.344880i 0.887920π-0.887920\pi
0.962097 + 0.272709i 0.0879196π0.0879196\pi
662662 0 0
663663 4.33657 + 13.3466i 0.168419 + 0.518339i
664664 0 0
665665 0.266047 2.84146i 0.0103169 0.110187i
666666 0 0
667667 −6.28413 + 4.56569i −0.243322 + 0.176784i
668668 0 0
669669 −13.5178 + 9.82123i −0.522627 + 0.379711i
670670 0 0
671671 −1.09768 0.797508i −0.0423753 0.0307874i
672672 0 0
673673 −5.86346 + 18.0459i −0.226020 + 0.695617i 0.772167 + 0.635420i 0.219173π0.219173\pi
−0.998186 + 0.0601973i 0.980827π0.980827\pi
674674 0 0
675675 −26.3187 4.97203i −1.01301 0.191374i
676676 0 0
677677 8.84693 27.2280i 0.340015 1.04646i −0.624184 0.781278i 0.714568π-0.714568\pi
0.964199 0.265181i 0.0854317π-0.0854317\pi
678678 0 0
679679 −63.5743 46.1894i −2.43976 1.77259i
680680 0 0
681681 0.776955 0.564491i 0.0297730 0.0216313i
682682 0 0
683683 −3.99716 + 2.90411i −0.152947 + 0.111123i −0.661627 0.749833i 0.730134π-0.730134\pi
0.508680 + 0.860956i 0.330134π0.330134\pi
684684 0 0
685685 36.8230 + 15.8958i 1.40693 + 0.607349i
686686 0 0
687687 2.94361 + 9.05951i 0.112306 + 0.345642i
688688 0 0
689689 5.60608 17.2537i 0.213575 0.657315i
690690 0 0
691691 12.1626 + 37.4325i 0.462685 + 1.42400i 0.861870 + 0.507129i 0.169293π0.169293\pi
−0.399185 + 0.916871i 0.630707π0.630707\pi
692692 0 0
693693 −7.80520 −0.296495
694694 0 0
695695 −16.7169 28.2095i −0.634110 1.07005i
696696 0 0
697697 −8.76529 6.36836i −0.332009 0.241219i
698698 0 0
699699 6.12043 0.231496
700700 0 0
701701 2.25152 0.0850387 0.0425194 0.999096i 0.486462π-0.486462\pi
0.0425194 + 0.999096i 0.486462π0.486462\pi
702702 0 0
703703 −2.33470 1.69626i −0.0880550 0.0639757i
704704 0 0
705705 23.6830 + 10.2235i 0.891952 + 0.385040i
706706 0 0
707707 48.7772 1.83445
708708 0 0
709709 7.33541 + 22.5761i 0.275487 + 0.847863i 0.989090 + 0.147312i 0.0470622π0.0470622\pi
−0.713603 + 0.700551i 0.752938π0.752938\pi
710710 0 0
711711 −1.32208 + 4.06894i −0.0495818 + 0.152597i
712712 0 0
713713 0.938038 + 2.88698i 0.0351298 + 0.108118i
714714 0 0
715715 2.60784 2.96333i 0.0975277 0.110822i
716716 0 0
717717 −19.3588 + 14.0650i −0.722969 + 0.525268i
718718 0 0
719719 24.5662 17.8484i 0.916163 0.665631i −0.0264030 0.999651i 0.508405π-0.508405\pi
0.942566 + 0.334020i 0.108405π0.108405\pi
720720 0 0
721721 −12.6278 9.17466i −0.470285 0.341682i
722722 0 0
723723 4.55830 14.0290i 0.169525 0.521745i
724724 0 0
725725 −13.3075 + 24.3085i −0.494226 + 0.902796i
726726 0 0
727727 1.43839 4.42691i 0.0533470 0.164185i −0.920833 0.389956i 0.872490π-0.872490\pi
0.974180 + 0.225771i 0.0724901π0.0724901\pi
728728 0 0
729729 −16.1834 11.7579i −0.599386 0.435479i
730730 0 0
731731 −56.9299 + 41.3620i −2.10563 + 1.52983i
732732 0 0
733733 30.9322 22.4735i 1.14251 0.830079i 0.155039 0.987908i 0.450450π-0.450450\pi
0.987466 + 0.157830i 0.0504497π0.0504497\pi
734734 0 0
735735 −34.8642 + 7.82566i −1.28599 + 0.288654i
736736 0 0
737737 2.75203 + 8.46989i 0.101372 + 0.311992i
738738 0 0
739739 −5.73319 + 17.6450i −0.210899 + 0.649080i 0.788520 + 0.615008i 0.210847π0.210847\pi
−0.999419 + 0.0340716i 0.989153π0.989153\pi
740740 0 0
741741 0.172977 + 0.532370i 0.00635449 + 0.0195571i
742742 0 0
743743 28.1558 1.03294 0.516469 0.856306i 0.327246π-0.327246\pi
0.516469 + 0.856306i 0.327246π0.327246\pi
744744 0 0
745745 −10.0436 + 11.4127i −0.367969 + 0.418128i
746746 0 0
747747 −4.38714 3.18745i −0.160517 0.116623i
748748 0 0
749749 80.6326 2.94625
750750 0 0
751751 −1.68076 −0.0613319 −0.0306660 0.999530i 0.509763π-0.509763\pi
−0.0306660 + 0.999530i 0.509763π0.509763\pi
752752 0 0
753753 −20.6910 15.0329i −0.754020 0.547828i
754754 0 0
755755 −4.18570 + 4.75627i −0.152333 + 0.173098i
756756 0 0
757757 11.4300 0.415430 0.207715 0.978189i 0.433397π-0.433397\pi
0.207715 + 0.978189i 0.433397π0.433397\pi
758758 0 0
759759 0.493371 + 1.51844i 0.0179082 + 0.0551159i
760760 0 0
761761 −6.66007 + 20.4976i −0.241427 + 0.743037i 0.754776 + 0.655982i 0.227745π0.227745\pi
−0.996204 + 0.0870547i 0.972255π0.972255\pi
762762 0 0
763763 21.1235 + 65.0114i 0.764722 + 2.35357i
764764 0 0
765765 25.9139 5.81665i 0.936919 0.210302i
766766 0 0
767767 −7.66868 + 5.57162i −0.276900 + 0.201180i
768768 0 0
769769 10.7228 7.79053i 0.386672 0.280934i −0.377418 0.926043i 0.623188π-0.623188\pi
0.764091 + 0.645109i 0.223188π0.223188\pi
770770 0 0
771771 −6.88956 5.00556i −0.248121 0.180271i
772772 0 0
773773 2.52496 7.77103i 0.0908165 0.279505i −0.895324 0.445415i 0.853056π-0.853056\pi
0.986141 + 0.165910i 0.0530562π0.0530562\pi
774774 0 0
775775 7.42769 + 7.88154i 0.266811 + 0.283113i
776776 0 0
777777 −16.7374 + 51.5125i −0.600451 + 1.84800i
778778 0 0
779779 −0.349631 0.254021i −0.0125268 0.00910126i
780780 0 0
781781 −11.8891 + 8.63790i −0.425424 + 0.309089i
782782 0 0
783783 −24.0201 + 17.4516i −0.858409 + 0.623670i
784784 0 0
785785 5.50193 6.25192i 0.196372 0.223141i
786786 0 0
787787 14.5311 + 44.7220i 0.517976 + 1.59417i 0.777800 + 0.628511i 0.216335π0.216335\pi
−0.259824 + 0.965656i 0.583665π0.583665\pi
788788 0 0
789789 −11.2703 + 34.6865i −0.401234 + 1.23487i
790790 0 0
791791 −7.00054 21.5455i −0.248911 0.766068i
792792 0 0
793793 −2.39522 −0.0850566
794794 0 0
795795 24.0347 + 10.3754i 0.852424 + 0.367977i
796796 0 0
797797 34.8436 + 25.3154i 1.23422 + 0.896716i 0.997199 0.0747878i 0.0238279π-0.0238279\pi
0.237024 + 0.971504i 0.423828π0.423828\pi
798798 0 0
799799 −70.6592 −2.49974
800800 0 0
801801 17.5184 0.618981
802802 0 0
803803 −7.39967 5.37617i −0.261129 0.189721i
804804 0 0
805805 −7.32581 12.3622i −0.258201 0.435709i
806806 0 0
807807 −16.5824 −0.583727
808808 0 0
809809 7.56461 + 23.2815i 0.265958 + 0.818534i 0.991471 + 0.130326i 0.0416023π0.0416023\pi
−0.725514 + 0.688208i 0.758398π0.758398\pi
810810 0 0
811811 −9.79588 + 30.1486i −0.343980 + 1.05866i 0.618148 + 0.786062i 0.287883π0.287883\pi
−0.962128 + 0.272599i 0.912117π0.912117\pi
812812 0 0
813813 −2.16940 6.67672i −0.0760841 0.234163i
814814 0 0
815815 50.8667 + 21.9583i 1.78178 + 0.769165i
816816 0 0
817817 −2.27082 + 1.64985i −0.0794460 + 0.0577209i
818818 0 0
819819 −11.1473 + 8.09899i −0.389518 + 0.283002i
820820 0 0
821821 −8.15139 5.92233i −0.284485 0.206691i 0.436386 0.899760i 0.356258π-0.356258\pi
−0.720871 + 0.693069i 0.756258π0.756258\pi
822822 0 0
823823 2.79584 8.60472i 0.0974569 0.299942i −0.890429 0.455122i 0.849596π-0.849596\pi
0.987886 + 0.155180i 0.0495958π0.0495958\pi
824824 0 0
825825 3.90667 + 4.14538i 0.136013 + 0.144324i
826826 0 0
827827 11.1649 34.3619i 0.388240 1.19488i −0.545862 0.837875i 0.683798π-0.683798\pi
0.934102 0.357006i 0.116202π-0.116202\pi
828828 0 0
829829 16.9324 + 12.3021i 0.588085 + 0.427269i 0.841630 0.540055i 0.181596π-0.181596\pi
−0.253545 + 0.967324i 0.581596π0.581596\pi
830830 0 0
831831 11.1594 8.10778i 0.387115 0.281256i
832832 0 0
833833 79.1841 57.5306i 2.74357 1.99332i
834834 0 0
835835 3.42913 36.6241i 0.118670 1.26743i
836836 0 0
837837 3.58550 + 11.0350i 0.123933 + 0.381427i
838838 0 0
839839 16.3818 50.4181i 0.565564 1.74063i −0.100706 0.994916i 0.532110π-0.532110\pi
0.666270 0.745710i 0.267890π-0.267890\pi
840840 0 0
841841 0.531419 + 1.63554i 0.0183248 + 0.0563979i
842842 0 0
843843 −21.0932 −0.726488
844844 0 0
845845 −2.06025 + 22.0041i −0.0708747 + 0.756964i
846846 0 0
847847 3.70974 + 2.69528i 0.127468 + 0.0926111i
848848 0 0
849849 −11.2753 −0.386966
850850 0 0
851851 −14.5307 −0.498106
852852 0 0
853853 24.2281 + 17.6027i 0.829553 + 0.602705i 0.919433 0.393247i 0.128648π-0.128648\pi
−0.0898799 + 0.995953i 0.528648π0.528648\pi
854854 0 0
855855 1.03365 0.232015i 0.0353502 0.00793475i
856856 0 0
857857 −45.4353 −1.55204 −0.776020 0.630708i 0.782764π-0.782764\pi
−0.776020 + 0.630708i 0.782764π0.782764\pi
858858 0 0
859859 −6.39177 19.6719i −0.218084 0.671195i −0.998920 0.0464586i 0.985206π-0.985206\pi
0.780836 0.624736i 0.214794π-0.214794\pi
860860 0 0
861861 −2.50649 + 7.71418i −0.0854209 + 0.262899i
862862 0 0
863863 9.67666 + 29.7817i 0.329397 + 1.01378i 0.969416 + 0.245422i 0.0789265π0.0789265\pi
−0.640019 + 0.768359i 0.721074π0.721074\pi
864864 0 0
865865 14.3048 + 24.1391i 0.486379 + 0.820755i
866866 0 0
867867 29.2081 21.2209i 0.991960 0.720701i
868868 0 0
869869 2.03346 1.47739i 0.0689803 0.0501171i
870870 0 0
871871 12.7191 + 9.24099i 0.430972 + 0.313119i
872872 0 0
873873 9.01401 27.7423i 0.305078 0.938934i
874874 0 0
875875 −42.4790 28.7033i −1.43605 0.970347i
876876 0 0
877877 3.55277 10.9343i 0.119968 0.369225i −0.872982 0.487752i 0.837817π-0.837817\pi
0.992951 + 0.118527i 0.0378171π0.0378171\pi
878878 0 0
879879 −20.1596 14.6468i −0.679966 0.494024i
880880 0 0
881881 14.9835 10.8862i 0.504809 0.366765i −0.306042 0.952018i 0.599005π-0.599005\pi
0.810851 + 0.585253i 0.199005π0.199005\pi
882882 0 0
883883 14.4200 10.4767i 0.485271 0.352570i −0.318092 0.948060i 0.603042π-0.603042\pi
0.803363 + 0.595490i 0.203042π0.203042\pi
884884 0 0
885885 −6.97329 11.7673i −0.234405 0.395553i
886886 0 0
887887 −4.86199 14.9637i −0.163250 0.502431i 0.835653 0.549257i 0.185089π-0.185089\pi
−0.998903 + 0.0468263i 0.985089π0.985089\pi
888888 0 0
889889 17.6212 54.2324i 0.590996 1.81890i
890890 0 0
891891 0.307854 + 0.947476i 0.0103135 + 0.0317416i
892892 0 0
893893 −2.81846 −0.0943161
894894 0 0
895895 10.5132 2.35981i 0.351419 0.0788798i
896896 0 0
897897 2.28022 + 1.65668i 0.0761344 + 0.0553149i
898898 0 0
899899 12.0052 0.400394
900900 0 0
901901 −71.7087 −2.38896
902902 0 0
903903 42.6201 + 30.9653i 1.41831 + 1.03046i
904904 0 0
905905 −4.55950 + 48.6969i −0.151563 + 1.61874i
906906 0 0
907907 41.9377 1.39252 0.696260 0.717790i 0.254846π-0.254846\pi
0.696260 + 0.717790i 0.254846π0.254846\pi
908908 0 0
909909 5.59514 + 17.2201i 0.185579 + 0.571153i
910910 0 0
911911 −1.31596 + 4.05011i −0.0435997 + 0.134186i −0.970487 0.241154i 0.922474π-0.922474\pi
0.926887 + 0.375340i 0.122474π0.122474\pi
912912 0 0
913913 0.984484 + 3.02993i 0.0325817 + 0.100276i
914914 0 0
915915 0.322206 3.44127i 0.0106518 0.113765i
916916 0 0
917917 0.192332 0.139738i 0.00635137 0.00461454i
918918 0 0
919919 18.0413 13.1078i 0.595129 0.432386i −0.249018 0.968499i 0.580108π-0.580108\pi
0.844146 + 0.536113i 0.180108π0.180108\pi
920920 0 0
921921 12.6925 + 9.22164i 0.418232 + 0.303863i
922922 0 0
923923 −8.01679 + 24.6731i −0.263876 + 0.812126i
924924 0 0
925925 −46.8683 + 22.1565i −1.54102 + 0.728500i
926926 0 0
927927 1.79046 5.51048i 0.0588065 0.180988i
928928 0 0
929929 −8.98659 6.52914i −0.294841 0.214214i 0.430524 0.902579i 0.358329π-0.358329\pi
−0.725365 + 0.688365i 0.758329π0.758329\pi
930930 0 0
931931 3.15850 2.29478i 0.103516 0.0752085i
932932 0 0
933933 24.9112 18.0991i 0.815557 0.592537i
934934 0 0
935935 −14.3253 6.18396i −0.468486 0.202237i
936936 0 0
937937 −1.55456 4.78445i −0.0507854 0.156301i 0.922447 0.386123i 0.126186π-0.126186\pi
−0.973233 + 0.229821i 0.926186π0.926186\pi
938938 0 0
939939 8.34076 25.6702i 0.272190 0.837716i
940940 0 0
941941 0.681989 + 2.09894i 0.0222322 + 0.0684236i 0.961557 0.274605i 0.0885471π-0.0885471\pi
−0.939325 + 0.343029i 0.888547π0.888547\pi
942942 0 0
943943 −2.17603 −0.0708612
944944 0 0
945945 −28.0018 47.2524i −0.910898 1.53712i
946946 0 0
947947 −5.33110 3.87327i −0.173238 0.125864i 0.497788 0.867299i 0.334146π-0.334146\pi
−0.671025 + 0.741434i 0.734146π0.734146\pi
948948 0 0
949949 −16.1467 −0.524143
950950 0 0
951951 14.9201 0.483818
952952 0 0
953953 28.2142 + 20.4988i 0.913948 + 0.664022i 0.942010 0.335584i 0.108934π-0.108934\pi
−0.0280620 + 0.999606i 0.508934π0.508934\pi
954954 0 0
955955 0.734880 + 0.317235i 0.0237802 + 0.0102655i
956956 0 0
957957 6.31424 0.204110
958958 0 0
959959 25.4161 + 78.2227i 0.820729 + 2.52594i
960960 0 0
961961 −8.12975 + 25.0208i −0.262250 + 0.807123i
962962 0 0
963963 9.24921 + 28.4661i 0.298052 + 0.917309i
964964 0 0
965965 13.0520 14.8312i 0.420158 0.477432i
966966 0 0
967967 −10.4451 + 7.58878i −0.335891 + 0.244039i −0.742926 0.669374i 0.766563π-0.766563\pi
0.407035 + 0.913412i 0.366563π0.366563\pi
968968 0 0
969969 1.79003 1.30053i 0.0575040 0.0417791i
970970 0 0
971971 −35.8313 26.0330i −1.14988 0.835437i −0.161416 0.986887i 0.551606π-0.551606\pi
−0.988465 + 0.151449i 0.951606π0.951606\pi
972972 0 0
973973 20.7795 63.9526i 0.666159 2.05023i
974974 0 0
975975 9.88089 + 1.86666i 0.316442 + 0.0597811i
976976 0 0
977977 −12.8772 + 39.6321i −0.411980 + 1.26794i 0.502945 + 0.864318i 0.332250π0.332250\pi
−0.914925 + 0.403624i 0.867750π0.867750\pi
978978 0 0
979979 −8.32632 6.04943i −0.266110 0.193341i
980980 0 0
981981 −20.5283 + 14.9147i −0.655418 + 0.476189i
982982 0 0
983983 −12.4536 + 9.04806i −0.397208 + 0.288588i −0.768403 0.639967i 0.778948π-0.778948\pi
0.371195 + 0.928555i 0.378948π0.378948\pi
984984 0 0
985985 48.5947 10.9076i 1.54836 0.347545i
986986 0 0
987987 16.3465 + 50.3095i 0.520316 + 1.60137i
988988 0 0
989989 −4.36737 + 13.4414i −0.138874 + 0.427411i
990990 0 0
991991 −6.62847 20.4003i −0.210560 0.648038i −0.999439 0.0334889i 0.989338π-0.989338\pi
0.788879 0.614549i 0.210662π-0.210662\pi
992992 0 0
993993 1.87458 0.0594881
994994 0 0
995995 4.03680 4.58708i 0.127975 0.145420i
996996 0 0
997997 2.25047 + 1.63506i 0.0712730 + 0.0517829i 0.622851 0.782340i 0.285974π-0.285974\pi
−0.551578 + 0.834123i 0.685974π0.685974\pi
998998 0 0
999999 −55.5413 −1.75725
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 1100.2.q.b.221.9 52
25.6 even 5 inner 1100.2.q.b.881.9 yes 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1100.2.q.b.221.9 52 1.1 even 1 trivial
1100.2.q.b.881.9 yes 52 25.6 even 5 inner