Properties

Label 1000.2.d.c.501.6
Level 10001000
Weight 22
Character 1000.501
Analytic conductor 7.9857.985
Analytic rank 00
Dimension 4040
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1000,2,Mod(501,1000)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1000, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1000.501");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1000=2353 1000 = 2^{3} \cdot 5^{3}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1000.d (of order 22, degree 11, 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: 7.985040202137.98504020213
Analytic rank: 00
Dimension: 4040
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 501.6
Character χ\chi == 1000.501
Dual form 1000.2.d.c.501.5

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+(1.36535+0.368522i)q20.513027iq3+(1.728381.00633i)q4+(0.189062+0.700464i)q6+1.12889q7+(1.98900+2.01094i)q8+2.73680q93.99787iq11+(0.5162720.886708i)q12+1.12390iq13+(1.54133+0.416020i)q14+(1.974623.47863i)q16+2.93982q17+(3.73671+1.00857i)q183.24181iq190.579150iq21+(1.47330+5.45850i)q225.39053q23+(1.03167+1.02041i)q24+(0.4141831.53452i)q262.94314iq27+(1.951151.13603i)q28+7.35068iq29+7.19613q31+(1.41410+5.47725i)q322.05101q33+(4.01389+1.08339i)q34+(4.730252.75411i)q3610.6176iq37+(1.19468+4.42622i)q38+0.576592q39+2.08421q41+(0.213429+0.790745i)q42+6.26007iq43+(4.023156.90984i)q44+(7.359991.98653i)q46+2.24328q47+(1.784631.01303i)q485.72561q491.50821iq51+(1.13101+1.94253i)q52+1.64494iq53+(1.08461+4.01842i)q54+(2.24536+2.27012i)q561.66314q57+(2.7088910.0363i)q585.55039iq596.65010iq61+(9.82527+2.65193i)q62+3.08954q63+(0.08773827.99952i)q64+(2.800360.755843i)q666.79788iq67+(5.081132.95841i)q68+2.76549iq693.27833q71+(5.44351+5.50354i)q72+6.97819q73+(3.91280+14.4967i)q74+(3.262325.60310i)q764.51314iq77+(0.787253+0.212487i)q78+8.60333q79+6.70050q81+(2.84568+0.768075i)q8213.4761iq83+(0.5828131.00099i)q84+(2.306978.54721i)q86+3.77110q87+(8.03946+7.95176i)q8810.9910q89+1.26876iq91+(9.31691+5.42463i)q923.69181iq93+(3.06287+0.826697i)q94+(2.80998+0.725472i)q96+18.6691q97+(7.817492.11001i)q9810.9414iq99+O(q100)q+(-1.36535 + 0.368522i) q^{2} -0.513027i q^{3} +(1.72838 - 1.00633i) q^{4} +(0.189062 + 0.700464i) q^{6} +1.12889 q^{7} +(-1.98900 + 2.01094i) q^{8} +2.73680 q^{9} -3.99787i q^{11} +(-0.516272 - 0.886708i) q^{12} +1.12390i q^{13} +(-1.54133 + 0.416020i) q^{14} +(1.97462 - 3.47863i) q^{16} +2.93982 q^{17} +(-3.73671 + 1.00857i) q^{18} -3.24181i q^{19} -0.579150i q^{21} +(1.47330 + 5.45850i) q^{22} -5.39053 q^{23} +(1.03167 + 1.02041i) q^{24} +(-0.414183 - 1.53452i) q^{26} -2.94314i q^{27} +(1.95115 - 1.13603i) q^{28} +7.35068i q^{29} +7.19613 q^{31} +(-1.41410 + 5.47725i) q^{32} -2.05101 q^{33} +(-4.01389 + 1.08339i) q^{34} +(4.73025 - 2.75411i) q^{36} -10.6176i q^{37} +(1.19468 + 4.42622i) q^{38} +0.576592 q^{39} +2.08421 q^{41} +(0.213429 + 0.790745i) q^{42} +6.26007i q^{43} +(-4.02315 - 6.90984i) q^{44} +(7.35999 - 1.98653i) q^{46} +2.24328 q^{47} +(-1.78463 - 1.01303i) q^{48} -5.72561 q^{49} -1.50821i q^{51} +(1.13101 + 1.94253i) q^{52} +1.64494i q^{53} +(1.08461 + 4.01842i) q^{54} +(-2.24536 + 2.27012i) q^{56} -1.66314 q^{57} +(-2.70889 - 10.0363i) q^{58} -5.55039i q^{59} -6.65010i q^{61} +(-9.82527 + 2.65193i) q^{62} +3.08954 q^{63} +(-0.0877382 - 7.99952i) q^{64} +(2.80036 - 0.755843i) q^{66} -6.79788i q^{67} +(5.08113 - 2.95841i) q^{68} +2.76549i q^{69} -3.27833 q^{71} +(-5.44351 + 5.50354i) q^{72} +6.97819 q^{73} +(3.91280 + 14.4967i) q^{74} +(-3.26232 - 5.60310i) q^{76} -4.51314i q^{77} +(-0.787253 + 0.212487i) q^{78} +8.60333 q^{79} +6.70050 q^{81} +(-2.84568 + 0.768075i) q^{82} -13.4761i q^{83} +(-0.582813 - 1.00099i) q^{84} +(-2.30697 - 8.54721i) q^{86} +3.77110 q^{87} +(8.03946 + 7.95176i) q^{88} -10.9910 q^{89} +1.26876i q^{91} +(-9.31691 + 5.42463i) q^{92} -3.69181i q^{93} +(-3.06287 + 0.826697i) q^{94} +(2.80998 + 0.725472i) q^{96} +18.6691 q^{97} +(7.81749 - 2.11001i) q^{98} -10.9414i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 40q+6q42q624q9+12q14+18q166q24+20q26+48q316q3440q36+8q39+44q41+8q4430q46+12q492q54+50q56+72q64++12q96+O(q100) 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9} + 12 q^{14} + 18 q^{16} - 6 q^{24} + 20 q^{26} + 48 q^{31} - 6 q^{34} - 40 q^{36} + 8 q^{39} + 44 q^{41} + 8 q^{44} - 30 q^{46} + 12 q^{49} - 2 q^{54} + 50 q^{56} + 72 q^{64}+ \cdots + 12 q^{96}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1000Z)×\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times.

nn 377377 501501 751751
χ(n)\chi(n) 11 1-1 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 −1.36535 + 0.368522i −0.965451 + 0.260584i
33 0.513027i 0.296196i −0.988973 0.148098i 0.952685π-0.952685\pi
0.988973 0.148098i 0.0473152π-0.0473152\pi
44 1.72838 1.00633i 0.864192 0.503163i
55 0 0
66 0.189062 + 0.700464i 0.0771841 + 0.285963i
77 1.12889 0.426679 0.213340 0.976978i 0.431566π-0.431566\pi
0.213340 + 0.976978i 0.431566π0.431566\pi
88 −1.98900 + 2.01094i −0.703219 + 0.710974i
99 2.73680 0.912268
1010 0 0
1111 3.99787i 1.20540i −0.797967 0.602701i 0.794091π-0.794091\pi
0.797967 0.602701i 0.205909π-0.205909\pi
1212 −0.516272 0.886708i −0.149035 0.255970i
1313 1.12390i 0.311714i 0.987780 + 0.155857i 0.0498140π0.0498140\pi
−0.987780 + 0.155857i 0.950186π0.950186\pi
1414 −1.54133 + 0.416020i −0.411938 + 0.111186i
1515 0 0
1616 1.97462 3.47863i 0.493655 0.869658i
1717 2.93982 0.713010 0.356505 0.934293i 0.383968π-0.383968\pi
0.356505 + 0.934293i 0.383968π0.383968\pi
1818 −3.73671 + 1.00857i −0.880750 + 0.237723i
1919 3.24181i 0.743723i −0.928288 0.371862i 0.878720π-0.878720\pi
0.928288 0.371862i 0.121280π-0.121280\pi
2020 0 0
2121 0.579150i 0.126381i
2222 1.47330 + 5.45850i 0.314109 + 1.16376i
2323 −5.39053 −1.12400 −0.562002 0.827136i 0.689969π-0.689969\pi
−0.562002 + 0.827136i 0.689969π0.689969\pi
2424 1.03167 + 1.02041i 0.210588 + 0.208291i
2525 0 0
2626 −0.414183 1.53452i −0.0812279 0.300945i
2727 2.94314i 0.566407i
2828 1.95115 1.13603i 0.368733 0.214689i
2929 7.35068i 1.36499i 0.730891 + 0.682494i 0.239105π0.239105\pi
−0.730891 + 0.682494i 0.760895π0.760895\pi
3030 0 0
3131 7.19613 1.29246 0.646232 0.763141i 0.276344π-0.276344\pi
0.646232 + 0.763141i 0.276344π0.276344\pi
3232 −1.41410 + 5.47725i −0.249980 + 0.968251i
3333 −2.05101 −0.357036
3434 −4.01389 + 1.08339i −0.688377 + 0.185799i
3535 0 0
3636 4.73025 2.75411i 0.788374 0.459019i
3737 10.6176i 1.74552i −0.488152 0.872759i 0.662329π-0.662329\pi
0.488152 0.872759i 0.337671π-0.337671\pi
3838 1.19468 + 4.42622i 0.193803 + 0.718028i
3939 0.576592 0.0923287
4040 0 0
4141 2.08421 0.325498 0.162749 0.986667i 0.447964π-0.447964\pi
0.162749 + 0.986667i 0.447964π0.447964\pi
4242 0.213429 + 0.790745i 0.0329329 + 0.122015i
4343 6.26007i 0.954652i 0.878726 + 0.477326i 0.158394π0.158394\pi
−0.878726 + 0.477326i 0.841606π0.841606\pi
4444 −4.02315 6.90984i −0.606513 1.04170i
4545 0 0
4646 7.35999 1.98653i 1.08517 0.292898i
4747 2.24328 0.327216 0.163608 0.986525i 0.447687π-0.447687\pi
0.163608 + 0.986525i 0.447687π0.447687\pi
4848 −1.78463 1.01303i −0.257590 0.146219i
4949 −5.72561 −0.817945
5050 0 0
5151 1.50821i 0.211191i
5252 1.13101 + 1.94253i 0.156843 + 0.269381i
5353 1.64494i 0.225950i 0.993598 + 0.112975i 0.0360380π0.0360380\pi
−0.993598 + 0.112975i 0.963962π0.963962\pi
5454 1.08461 + 4.01842i 0.147597 + 0.546838i
5555 0 0
5656 −2.24536 + 2.27012i −0.300049 + 0.303358i
5757 −1.66314 −0.220288
5858 −2.70889 10.0363i −0.355694 1.31783i
5959 5.55039i 0.722599i −0.932450 0.361299i 0.882333π-0.882333\pi
0.932450 0.361299i 0.117667π-0.117667\pi
6060 0 0
6161 6.65010i 0.851458i −0.904851 0.425729i 0.860018π-0.860018\pi
0.904851 0.425729i 0.139982π-0.139982\pi
6262 −9.82527 + 2.65193i −1.24781 + 0.336796i
6363 3.08954 0.389246
6464 −0.0877382 7.99952i −0.0109673 0.999940i
6565 0 0
6666 2.80036 0.755843i 0.344700 0.0930379i
6767 6.79788i 0.830493i −0.909709 0.415247i 0.863695π-0.863695\pi
0.909709 0.415247i 0.136305π-0.136305\pi
6868 5.08113 2.95841i 0.616178 0.358760i
6969 2.76549i 0.332926i
7070 0 0
7171 −3.27833 −0.389066 −0.194533 0.980896i 0.562319π-0.562319\pi
−0.194533 + 0.980896i 0.562319π0.562319\pi
7272 −5.44351 + 5.50354i −0.641524 + 0.648598i
7373 6.97819 0.816736 0.408368 0.912817i 0.366098π-0.366098\pi
0.408368 + 0.912817i 0.366098π0.366098\pi
7474 3.91280 + 14.4967i 0.454854 + 1.68521i
7575 0 0
7676 −3.26232 5.60310i −0.374214 0.642719i
7777 4.51314i 0.514320i
7878 −0.787253 + 0.212487i −0.0891388 + 0.0240594i
7979 8.60333 0.967950 0.483975 0.875082i 0.339193π-0.339193\pi
0.483975 + 0.875082i 0.339193π0.339193\pi
8080 0 0
8181 6.70050 0.744500
8282 −2.84568 + 0.768075i −0.314253 + 0.0848197i
8383 13.4761i 1.47919i −0.673052 0.739596i 0.735017π-0.735017\pi
0.673052 0.739596i 0.264983π-0.264983\pi
8484 −0.582813 1.00099i −0.0635901 0.109217i
8585 0 0
8686 −2.30697 8.54721i −0.248767 0.921669i
8787 3.77110 0.404304
8888 8.03946 + 7.95176i 0.857009 + 0.847661i
8989 −10.9910 −1.16504 −0.582521 0.812816i 0.697934π-0.697934\pi
−0.582521 + 0.812816i 0.697934π0.697934\pi
9090 0 0
9191 1.26876i 0.133002i
9292 −9.31691 + 5.42463i −0.971355 + 0.565557i
9393 3.69181i 0.382823i
9494 −3.06287 + 0.826697i −0.315911 + 0.0852673i
9595 0 0
9696 2.80998 + 0.725472i 0.286792 + 0.0740432i
9797 18.6691 1.89556 0.947778 0.318931i 0.103324π-0.103324\pi
0.947778 + 0.318931i 0.103324π0.103324\pi
9898 7.81749 2.11001i 0.789686 0.213144i
9999 10.9414i 1.09965i
100100 0 0
101101 1.76372i 0.175497i −0.996143 0.0877485i 0.972033π-0.972033\pi
0.996143 0.0877485i 0.0279672π-0.0279672\pi
102102 0.555807 + 2.05923i 0.0550331 + 0.203895i
103103 3.89194 0.383484 0.191742 0.981445i 0.438586π-0.438586\pi
0.191742 + 0.981445i 0.438586π0.438586\pi
104104 −2.26010 2.23545i −0.221621 0.219203i
105105 0 0
106106 −0.606196 2.24592i −0.0588789 0.218143i
107107 16.0146i 1.54819i −0.633071 0.774094i 0.718206π-0.718206\pi
0.633071 0.774094i 0.281794π-0.281794\pi
108108 −2.96175 5.08687i −0.284995 0.489484i
109109 15.6094i 1.49511i 0.664199 + 0.747556i 0.268773π0.268773\pi
−0.664199 + 0.747556i 0.731227π0.731227\pi
110110 0 0
111111 −5.44710 −0.517016
112112 2.22912 3.92698i 0.210632 0.371065i
113113 2.97052 0.279443 0.139722 0.990191i 0.455379π-0.455379\pi
0.139722 + 0.990191i 0.455379π0.455379\pi
114114 2.27077 0.612903i 0.212677 0.0574036i
115115 0 0
116116 7.39718 + 12.7048i 0.686811 + 1.17961i
117117 3.07590i 0.284367i
118118 2.04544 + 7.57824i 0.188298 + 0.697634i
119119 3.31872 0.304227
120120 0 0
121121 −4.98293 −0.452994
122122 2.45071 + 9.07974i 0.221876 + 0.822041i
123123 1.06925i 0.0964114i
124124 12.4377 7.24165i 1.11694 0.650320i
125125 0 0
126126 −4.21832 + 1.13856i −0.375798 + 0.101431i
127127 12.2692 1.08871 0.544356 0.838855i 0.316774π-0.316774\pi
0.544356 + 0.838855i 0.316774π0.316774\pi
128128 3.06779 + 10.8898i 0.271157 + 0.962535i
129129 3.21158 0.282764
130130 0 0
131131 13.2639i 1.15887i 0.815019 + 0.579434i 0.196726π0.196726\pi
−0.815019 + 0.579434i 0.803274π0.803274\pi
132132 −3.54494 + 2.06399i −0.308547 + 0.179647i
133133 3.65964i 0.317331i
134134 2.50517 + 9.28151i 0.216413 + 0.801800i
135135 0 0
136136 −5.84730 + 5.91179i −0.501402 + 0.506932i
137137 −13.3863 −1.14367 −0.571836 0.820368i 0.693769π-0.693769\pi
−0.571836 + 0.820368i 0.693769π0.693769\pi
138138 −1.01914 3.77587i −0.0867552 0.321424i
139139 20.2594i 1.71838i −0.511657 0.859190i 0.670968π-0.670968\pi
0.511657 0.859190i 0.329032π-0.329032\pi
140140 0 0
141141 1.15086i 0.0969201i
142142 4.47608 1.20814i 0.375624 0.101385i
143143 4.49321 0.375741
144144 5.40414 9.52033i 0.450345 0.793361i
145145 0 0
146146 −9.52770 + 2.57162i −0.788518 + 0.212828i
147147 2.93739i 0.242272i
148148 −10.6847 18.3512i −0.878279 1.50846i
149149 14.8567i 1.21711i 0.793512 + 0.608555i 0.208251π0.208251\pi
−0.793512 + 0.608555i 0.791749π0.791749\pi
150150 0 0
151151 10.1436 0.825477 0.412739 0.910850i 0.364572π-0.364572\pi
0.412739 + 0.910850i 0.364572π0.364572\pi
152152 6.51909 + 6.44798i 0.528768 + 0.523000i
153153 8.04570 0.650456
154154 1.66319 + 6.16203i 0.134024 + 0.496551i
155155 0 0
156156 0.996573 0.580240i 0.0797897 0.0464564i
157157 7.49744i 0.598361i −0.954197 0.299180i 0.903287π-0.903287\pi
0.954197 0.299180i 0.0967132π-0.0967132\pi
158158 −11.7466 + 3.17051i −0.934508 + 0.252232i
159159 0.843898 0.0669255
160160 0 0
161161 −6.08530 −0.479589
162162 −9.14856 + 2.46928i −0.718778 + 0.194005i
163163 8.95189i 0.701166i 0.936532 + 0.350583i 0.114017π0.114017\pi
−0.936532 + 0.350583i 0.885983π0.885983\pi
164164 3.60231 2.09739i 0.281293 0.163779i
165165 0 0
166166 4.96623 + 18.3996i 0.385454 + 1.42809i
167167 −2.49946 −0.193414 −0.0967070 0.995313i 0.530831π-0.530831\pi
−0.0967070 + 0.995313i 0.530831π0.530831\pi
168168 1.16463 + 1.15193i 0.0898535 + 0.0888734i
169169 11.7368 0.902834
170170 0 0
171171 8.87221i 0.678475i
172172 6.29967 + 10.8198i 0.480345 + 0.825002i
173173 0.589561i 0.0448235i −0.999749 0.0224118i 0.992866π-0.992866\pi
0.999749 0.0224118i 0.00713448π-0.00713448\pi
174174 −5.14889 + 1.38973i −0.390336 + 0.105355i
175175 0 0
176176 −13.9071 7.89426i −1.04829 0.595052i
177177 −2.84750 −0.214031
178178 15.0066 4.05042i 1.12479 0.303592i
179179 10.3029i 0.770077i −0.922901 0.385038i 0.874188π-0.874188\pi
0.922901 0.385038i 0.125812π-0.125812\pi
180180 0 0
181181 17.8021i 1.32322i 0.749848 + 0.661610i 0.230127π0.230127\pi
−0.749848 + 0.661610i 0.769873π0.769873\pi
182182 −0.467565 1.73231i −0.0346583 0.128407i
183183 −3.41168 −0.252199
184184 10.7218 10.8400i 0.790420 0.799137i
185185 0 0
186186 1.36051 + 5.04063i 0.0997577 + 0.369597i
187187 11.7530i 0.859464i
188188 3.87724 2.25747i 0.282777 0.164643i
189189 3.32247i 0.241674i
190190 0 0
191191 −18.9069 −1.36806 −0.684029 0.729455i 0.739774π-0.739774\pi
−0.684029 + 0.729455i 0.739774π0.739774\pi
192192 −4.10397 + 0.0450121i −0.296179 + 0.00324847i
193193 −10.2705 −0.739288 −0.369644 0.929173i 0.620520π-0.620520\pi
−0.369644 + 0.929173i 0.620520π0.620520\pi
194194 −25.4899 + 6.87995i −1.83007 + 0.493952i
195195 0 0
196196 −9.89606 + 5.76183i −0.706861 + 0.411559i
197197 0.207142i 0.0147583i 0.999973 + 0.00737913i 0.00234887π0.00234887\pi
−0.999973 + 0.00737913i 0.997651π0.997651\pi
198198 4.03213 + 14.9388i 0.286551 + 1.06166i
199199 −12.2911 −0.871295 −0.435647 0.900117i 0.643481π-0.643481\pi
−0.435647 + 0.900117i 0.643481π0.643481\pi
200200 0 0
201201 −3.48750 −0.245989
202202 0.649970 + 2.40811i 0.0457318 + 0.169434i
203203 8.29809i 0.582412i
204204 −1.51775 2.60676i −0.106263 0.182510i
205205 0 0
206206 −5.31387 + 1.43426i −0.370235 + 0.0999299i
207207 −14.7528 −1.02539
208208 3.90964 + 2.21928i 0.271085 + 0.153879i
209209 −12.9603 −0.896485
210210 0 0
211211 3.91559i 0.269560i −0.990876 0.134780i 0.956967π-0.956967\pi
0.990876 0.134780i 0.0430328π-0.0430328\pi
212212 1.65534 + 2.84309i 0.113689 + 0.195264i
213213 1.68187i 0.115240i
214214 5.90172 + 21.8656i 0.403433 + 1.49470i
215215 0 0
216216 5.91846 + 5.85390i 0.402700 + 0.398308i
217217 8.12363 0.551468
218218 −5.75241 21.3124i −0.389603 1.44346i
219219 3.58000i 0.241914i
220220 0 0
221221 3.30407i 0.222256i
222222 7.43722 2.00737i 0.499153 0.134726i
223223 −23.8519 −1.59724 −0.798621 0.601834i 0.794437π-0.794437\pi
−0.798621 + 0.601834i 0.794437π0.794437\pi
224224 −1.59636 + 6.18320i −0.106661 + 0.413133i
225225 0 0
226226 −4.05582 + 1.09470i −0.269789 + 0.0728185i
227227 24.7012i 1.63948i 0.572738 + 0.819738i 0.305881π0.305881\pi
−0.572738 + 0.819738i 0.694119π0.694119\pi
228228 −2.87454 + 1.67366i −0.190371 + 0.110841i
229229 22.0732i 1.45864i 0.684175 + 0.729318i 0.260163π0.260163\pi
−0.684175 + 0.729318i 0.739837π0.739837\pi
230230 0 0
231231 −2.31536 −0.152340
232232 −14.7818 14.6205i −0.970470 0.959884i
233233 −19.6085 −1.28460 −0.642299 0.766454i 0.722019π-0.722019\pi
−0.642299 + 0.766454i 0.722019π0.722019\pi
234234 −1.13354 4.19969i −0.0741016 0.274543i
235235 0 0
236236 −5.58550 9.59320i −0.363585 0.624464i
237237 4.41374i 0.286703i
238238 −4.53123 + 1.22302i −0.293716 + 0.0792767i
239239 −12.3845 −0.801088 −0.400544 0.916278i 0.631179π-0.631179\pi
−0.400544 + 0.916278i 0.631179π0.631179\pi
240240 0 0
241241 −20.4095 −1.31469 −0.657347 0.753588i 0.728321π-0.728321\pi
−0.657347 + 0.753588i 0.728321π0.728321\pi
242242 6.80346 1.83632i 0.437343 0.118043i
243243 12.2669i 0.786925i
244244 −6.69216 11.4939i −0.428422 0.735823i
245245 0 0
246246 0.394043 + 1.45991i 0.0251233 + 0.0930805i
247247 3.64348 0.231829
248248 −14.3131 + 14.4710i −0.908885 + 0.918908i
249249 −6.91359 −0.438131
250250 0 0
251251 22.2016i 1.40135i 0.713479 + 0.700676i 0.247118π0.247118\pi
−0.713479 + 0.700676i 0.752882π0.752882\pi
252252 5.33991 3.10908i 0.336383 0.195854i
253253 21.5506i 1.35488i
254254 −16.7517 + 4.52145i −1.05110 + 0.283701i
255255 0 0
256256 −8.20176 13.7379i −0.512610 0.858621i
257257 13.0592 0.814614 0.407307 0.913291i 0.366468π-0.366468\pi
0.407307 + 0.913291i 0.366468π0.366468\pi
258258 −4.38495 + 1.18354i −0.272995 + 0.0736839i
259259 11.9860i 0.744776i
260260 0 0
261261 20.1174i 1.24523i
262262 −4.88802 18.1099i −0.301983 1.11883i
263263 29.2389 1.80295 0.901473 0.432835i 0.142487π-0.142487\pi
0.901473 + 0.432835i 0.142487π0.142487\pi
264264 4.07947 4.12446i 0.251074 0.253843i
265265 0 0
266266 1.34866 + 4.99671i 0.0826915 + 0.306368i
267267 5.63867i 0.345081i
268268 −6.84088 11.7493i −0.417873 0.717705i
269269 21.4247i 1.30629i 0.757235 + 0.653143i 0.226550π0.226550\pi
−0.757235 + 0.653143i 0.773450π0.773450\pi
270270 0 0
271271 1.15797 0.0703415 0.0351708 0.999381i 0.488802π-0.488802\pi
0.0351708 + 0.999381i 0.488802π0.488802\pi
272272 5.80502 10.2265i 0.351981 0.620075i
273273 0.650908 0.0393947
274274 18.2771 4.93316i 1.10416 0.298023i
275275 0 0
276276 2.78298 + 4.77983i 0.167516 + 0.287712i
277277 16.8055i 1.00975i 0.863194 + 0.504873i 0.168461π0.168461\pi
−0.863194 + 0.504873i 0.831539π0.831539\pi
278278 7.46603 + 27.6612i 0.447783 + 1.65901i
279279 19.6944 1.17907
280280 0 0
281281 8.99127 0.536374 0.268187 0.963367i 0.413575π-0.413575\pi
0.268187 + 0.963367i 0.413575π0.413575\pi
282282 0.424118 + 1.57133i 0.0252559 + 0.0935716i
283283 15.4397i 0.917798i 0.888489 + 0.458899i 0.151756π0.151756\pi
−0.888489 + 0.458899i 0.848244π0.848244\pi
284284 −5.66621 + 3.29907i −0.336228 + 0.195764i
285285 0 0
286286 −6.13482 + 1.65585i −0.362760 + 0.0979122i
287287 2.35283 0.138883
288288 −3.87012 + 14.9902i −0.228049 + 0.883304i
289289 −8.35748 −0.491616
290290 0 0
291291 9.57773i 0.561457i
292292 12.0610 7.02233i 0.705816 0.410951i
293293 1.62062i 0.0946777i −0.998879 0.0473389i 0.984926π-0.984926\pi
0.998879 0.0473389i 0.0150741π-0.0150741\pi
294294 −1.08249 4.01058i −0.0631323 0.233902i
295295 0 0
296296 21.3513 + 21.1184i 1.24102 + 1.22748i
297297 −11.7663 −0.682748
298298 −5.47503 20.2847i −0.317160 1.17506i
299299 6.05843i 0.350368i
300300 0 0
301301 7.06691i 0.407330i
302302 −13.8496 + 3.73815i −0.796958 + 0.215106i
303303 −0.904838 −0.0519816
304304 −11.2771 6.40135i −0.646785 0.367142i
305305 0 0
306306 −10.9852 + 2.96502i −0.627984 + 0.169499i
307307 13.3243i 0.760458i 0.924892 + 0.380229i 0.124155π0.124155\pi
−0.924892 + 0.380229i 0.875845π0.875845\pi
308308 −4.54169 7.80044i −0.258787 0.444471i
309309 1.99667i 0.113587i
310310 0 0
311311 −3.20457 −0.181714 −0.0908572 0.995864i 0.528961π-0.528961\pi
−0.0908572 + 0.995864i 0.528961π0.528961\pi
312312 −1.14684 + 1.15949i −0.0649273 + 0.0656433i
313313 −24.2715 −1.37190 −0.685952 0.727647i 0.740614π-0.740614\pi
−0.685952 + 0.727647i 0.740614π0.740614\pi
314314 2.76297 + 10.2367i 0.155923 + 0.577688i
315315 0 0
316316 14.8698 8.65775i 0.836494 0.487036i
317317 3.79177i 0.212967i 0.994314 + 0.106483i 0.0339591π0.0339591\pi
−0.994314 + 0.106483i 0.966041π0.966041\pi
318318 −1.15222 + 0.310995i −0.0646133 + 0.0174397i
319319 29.3870 1.64536
320320 0 0
321321 −8.21591 −0.458567
322322 8.30859 2.24257i 0.463020 0.124973i
323323 9.53034i 0.530282i
324324 11.5810 6.74288i 0.643391 0.374605i
325325 0 0
326326 −3.29897 12.2225i −0.182713 0.676941i
327327 8.00806 0.442847
328328 −4.14549 + 4.19121i −0.228896 + 0.231421i
329329 2.53241 0.139616
330330 0 0
331331 2.26196i 0.124328i −0.998066 0.0621642i 0.980200π-0.980200\pi
0.998066 0.0621642i 0.0198002π-0.0198002\pi
332332 −13.5613 23.2918i −0.744274 1.27830i
333333 29.0582i 1.59238i
334334 3.41265 0.921106i 0.186732 0.0504007i
335335 0 0
336336 −2.01465 1.14360i −0.109908 0.0623885i
337337 −28.6654 −1.56150 −0.780751 0.624843i 0.785163π-0.785163\pi
−0.780751 + 0.624843i 0.785163π0.785163\pi
338338 −16.0249 + 4.32528i −0.871642 + 0.235264i
339339 1.52396i 0.0827701i
340340 0 0
341341 28.7692i 1.55794i
342342 3.26960 + 12.1137i 0.176800 + 0.655034i
343343 −14.3658 −0.775679
344344 −12.5886 12.4513i −0.678732 0.671329i
345345 0 0
346346 0.217266 + 0.804960i 0.0116803 + 0.0432749i
347347 3.03845i 0.163112i −0.996669 0.0815562i 0.974011π-0.974011\pi
0.996669 0.0815562i 0.0259890π-0.0259890\pi
348348 6.51791 3.79495i 0.349396 0.203431i
349349 26.1606i 1.40035i −0.713973 0.700173i 0.753106π-0.753106\pi
0.713973 0.700173i 0.246894π-0.246894\pi
350350 0 0
351351 3.30780 0.176557
352352 21.8973 + 5.65339i 1.16713 + 0.301327i
353353 29.4943 1.56983 0.784913 0.619606i 0.212708π-0.212708\pi
0.784913 + 0.619606i 0.212708π0.212708\pi
354354 3.88784 1.04937i 0.206637 0.0557731i
355355 0 0
356356 −18.9966 + 11.0605i −1.00682 + 0.586206i
357357 1.70259i 0.0901108i
358358 3.79685 + 14.0671i 0.200670 + 0.743472i
359359 8.91327 0.470424 0.235212 0.971944i 0.424422π-0.424422\pi
0.235212 + 0.971944i 0.424422π0.424422\pi
360360 0 0
361361 8.49064 0.446876
362362 −6.56046 24.3062i −0.344810 1.27750i
363363 2.55638i 0.134175i
364364 1.27678 + 2.19290i 0.0669217 + 0.114939i
365365 0 0
366366 4.65815 1.25728i 0.243485 0.0657190i
367367 −22.6852 −1.18416 −0.592079 0.805880i 0.701693π-0.701693\pi
−0.592079 + 0.805880i 0.701693π0.701693\pi
368368 −10.6442 + 18.7517i −0.554870 + 0.977499i
369369 5.70406 0.296942
370370 0 0
371371 1.85695i 0.0964081i
372372 −3.71516 6.38087i −0.192622 0.330833i
373373 6.46312i 0.334648i 0.985902 + 0.167324i 0.0535125π0.0535125\pi
−0.985902 + 0.167324i 0.946487π0.946487\pi
374374 4.33123 + 16.0470i 0.223963 + 0.829770i
375375 0 0
376376 −4.46189 + 4.51109i −0.230104 + 0.232642i
377377 −8.26145 −0.425486
378378 1.22440 + 4.53635i 0.0629764 + 0.233324i
379379 4.31785i 0.221793i 0.993832 + 0.110897i 0.0353722π0.0353722\pi
−0.993832 + 0.110897i 0.964628π0.964628\pi
380380 0 0
381381 6.29441i 0.322472i
382382 25.8147 6.96762i 1.32079 0.356494i
383383 11.1049 0.567432 0.283716 0.958908i 0.408433π-0.408433\pi
0.283716 + 0.958908i 0.408433π0.408433\pi
384384 5.58678 1.57386i 0.285099 0.0803157i
385385 0 0
386386 14.0229 3.78491i 0.713746 0.192647i
387387 17.1326i 0.870898i
388388 32.2673 18.7871i 1.63812 0.953773i
389389 15.5490i 0.788368i 0.919032 + 0.394184i 0.128973π0.128973\pi
−0.919032 + 0.394184i 0.871027π0.871027\pi
390390 0 0
391391 −15.8472 −0.801426
392392 11.3883 11.5139i 0.575194 0.581537i
393393 6.80472 0.343253
394394 −0.0763364 0.282822i −0.00384577 0.0142484i
395395 0 0
396396 −11.0106 18.9109i −0.553302 0.950308i
397397 26.9682i 1.35350i 0.736214 + 0.676748i 0.236611π0.236611\pi
−0.736214 + 0.676748i 0.763389π0.763389\pi
398398 16.7817 4.52955i 0.841193 0.227046i
399399 −1.87750 −0.0939924
400400 0 0
401401 36.1092 1.80321 0.901603 0.432565i 0.142391π-0.142391\pi
0.901603 + 0.432565i 0.142391π0.142391\pi
402402 4.76167 1.28522i 0.237490 0.0641009i
403403 8.08775i 0.402880i
404404 −1.77488 3.04839i −0.0883035 0.151663i
405405 0 0
406406 −3.05803 11.3298i −0.151767 0.562290i
407407 −42.4476 −2.10405
408408 3.03291 + 2.99982i 0.150151 + 0.148513i
409409 15.5149 0.767163 0.383581 0.923507i 0.374691π-0.374691\pi
0.383581 + 0.923507i 0.374691π0.374691\pi
410410 0 0
411411 6.86755i 0.338751i
412412 6.72676 3.91656i 0.331404 0.192955i
413413 6.26576i 0.308318i
414414 20.1428 5.43674i 0.989966 0.267201i
415415 0 0
416416 −6.15590 1.58931i −0.301818 0.0779225i
417417 −10.3936 −0.508978
418418 17.6955 4.77617i 0.865513 0.233610i
419419 26.9362i 1.31592i 0.753054 + 0.657959i 0.228580π0.228580\pi
−0.753054 + 0.657959i 0.771420π0.771420\pi
420420 0 0
421421 6.14641i 0.299557i −0.988720 0.149779i 0.952144π-0.952144\pi
0.988720 0.149779i 0.0478561π-0.0478561\pi
422422 1.44298 + 5.34616i 0.0702431 + 0.260247i
423423 6.13941 0.298508
424424 −3.30787 3.27179i −0.160644 0.158892i
425425 0 0
426426 −0.619807 2.29635i −0.0300297 0.111259i
427427 7.50721i 0.363299i
428428 −16.1159 27.6793i −0.778990 1.33793i
429429 2.30514i 0.111293i
430430 0 0
431431 36.8901 1.77693 0.888467 0.458940i 0.151771π-0.151771\pi
0.888467 + 0.458940i 0.151771π0.151771\pi
432432 −10.2381 5.81157i −0.492580 0.279609i
433433 −11.5824 −0.556617 −0.278308 0.960492i 0.589774π-0.589774\pi
−0.278308 + 0.960492i 0.589774π0.589774\pi
434434 −11.0916 + 2.99373i −0.532415 + 0.143704i
435435 0 0
436436 15.7082 + 26.9791i 0.752284 + 1.29206i
437437 17.4751i 0.835948i
438438 1.31931 + 4.88797i 0.0630390 + 0.233556i
439439 −4.15174 −0.198152 −0.0990760 0.995080i 0.531589π-0.531589\pi
−0.0990760 + 0.995080i 0.531589π0.531589\pi
440440 0 0
441441 −15.6699 −0.746185
442442 −1.21762 4.51122i −0.0579163 0.214577i
443443 15.7327i 0.747482i −0.927533 0.373741i 0.878075π-0.878075\pi
0.927533 0.373741i 0.121925π-0.121925\pi
444444 −9.41468 + 5.48155i −0.446801 + 0.260143i
445445 0 0
446446 32.5663 8.78995i 1.54206 0.416216i
447447 7.62190 0.360504
448448 −0.0990465 9.03056i −0.00467951 0.426654i
449449 −20.6861 −0.976239 −0.488120 0.872777i 0.662317π-0.662317\pi
−0.488120 + 0.872777i 0.662317π0.662317\pi
450450 0 0
451451 8.33238i 0.392356i
452452 5.13420 2.98931i 0.241493 0.140605i
453453 5.20396i 0.244503i
454454 −9.10293 33.7259i −0.427222 1.58283i
455455 0 0
456456 3.30799 3.34447i 0.154911 0.156619i
457457 28.7187 1.34340 0.671702 0.740821i 0.265564π-0.265564\pi
0.671702 + 0.740821i 0.265564π0.265564\pi
458458 −8.13444 30.1377i −0.380098 1.40824i
459459 8.65228i 0.403854i
460460 0 0
461461 27.7063i 1.29041i −0.764008 0.645207i 0.776771π-0.776771\pi
0.764008 0.645207i 0.223229π-0.223229\pi
462462 3.16129 0.853262i 0.147077 0.0396973i
463463 26.9572 1.25281 0.626404 0.779499i 0.284526π-0.284526\pi
0.626404 + 0.779499i 0.284526π0.284526\pi
464464 25.5703 + 14.5148i 1.18707 + 0.673832i
465465 0 0
466466 26.7726 7.22617i 1.24022 0.334746i
467467 31.3052i 1.44863i 0.689468 + 0.724316i 0.257844π0.257844\pi
−0.689468 + 0.724316i 0.742156π0.742156\pi
468468 3.09536 + 5.31633i 0.143083 + 0.245748i
469469 7.67404i 0.354354i
470470 0 0
471471 −3.84639 −0.177232
472472 11.1615 + 11.0397i 0.513749 + 0.508145i
473473 25.0269 1.15074
474474 1.62656 + 6.02632i 0.0747103 + 0.276798i
475475 0 0
476476 5.73602 3.33971i 0.262910 0.153076i
477477 4.50187i 0.206127i
478478 16.9093 4.56397i 0.773411 0.208751i
479479 −32.6888 −1.49359 −0.746794 0.665056i 0.768408π-0.768408\pi
−0.746794 + 0.665056i 0.768408π0.768408\pi
480480 0 0
481481 11.9331 0.544103
482482 27.8662 7.52136i 1.26927 0.342589i
483483 3.12193i 0.142053i
484484 −8.61241 + 5.01445i −0.391473 + 0.227929i
485485 0 0
486486 4.52064 + 16.7487i 0.205060 + 0.759738i
487487 17.6043 0.797726 0.398863 0.917011i 0.369405π-0.369405\pi
0.398863 + 0.917011i 0.369405π0.369405\pi
488488 13.3729 + 13.2271i 0.605364 + 0.598761i
489489 4.59256 0.207683
490490 0 0
491491 1.31132i 0.0591790i −0.999562 0.0295895i 0.990580π-0.990580\pi
0.999562 0.0295895i 0.00942000π-0.00942000\pi
492492 −1.07602 1.84808i −0.0485106 0.0833179i
493493 21.6097i 0.973250i
494494 −4.97465 + 1.34270i −0.223820 + 0.0604111i
495495 0 0
496496 14.2096 25.0327i 0.638031 1.12400i
497497 −3.70087 −0.166007
498498 9.43950 2.54781i 0.422994 0.114170i
499499 21.2655i 0.951973i −0.879453 0.475987i 0.842091π-0.842091\pi
0.879453 0.475987i 0.157909π-0.157909\pi
500500 0 0
501501 1.28229i 0.0572885i
502502 −8.18177 30.3130i −0.365170 1.35294i
503503 −34.4786 −1.53733 −0.768663 0.639654i 0.779078π-0.779078\pi
−0.768663 + 0.639654i 0.779078π0.779078\pi
504504 −6.14511 + 6.21288i −0.273725 + 0.276743i
505505 0 0
506506 −7.94188 29.4242i −0.353059 1.30807i
507507 6.02132i 0.267416i
508508 21.2058 12.3468i 0.940855 0.547799i
509509 8.61795i 0.381984i 0.981592 + 0.190992i 0.0611704π0.0611704\pi
−0.981592 + 0.190992i 0.938830π0.938830\pi
510510 0 0
511511 7.87759 0.348484
512512 16.2610 + 15.7346i 0.718643 + 0.695379i
513513 −9.54110 −0.421250
514514 −17.8305 + 4.81262i −0.786470 + 0.212275i
515515 0 0
516516 5.55085 3.23190i 0.244363 0.142276i
517517 8.96833i 0.394426i
518518 4.41711 + 16.3652i 0.194077 + 0.719045i
519519 −0.302461 −0.0132766
520520 0 0
521521 −5.28810 −0.231676 −0.115838 0.993268i 0.536955π-0.536955\pi
−0.115838 + 0.993268i 0.536955π0.536955\pi
522522 −7.41369 27.4673i −0.324488 1.20221i
523523 18.0301i 0.788400i −0.919025 0.394200i 0.871022π-0.871022\pi
0.919025 0.394200i 0.128978π-0.128978\pi
524524 13.3478 + 22.9250i 0.583099 + 1.00148i
525525 0 0
526526 −39.9214 + 10.7752i −1.74066 + 0.469819i
527527 21.1553 0.921540
528528 −4.04997 + 7.13472i −0.176252 + 0.310499i
529529 6.05785 0.263385
530530 0 0
531531 15.1903i 0.659204i
532532 −3.68279 6.32527i −0.159669 0.274235i
533533 2.34244i 0.101463i
534534 −2.07797 7.69878i −0.0899227 0.333159i
535535 0 0
536536 13.6701 + 13.5210i 0.590459 + 0.584018i
537537 −5.28568 −0.228094
538538 −7.89546 29.2523i −0.340397 1.26115i
539539 22.8902i 0.985952i
540540 0 0
541541 2.53085i 0.108810i −0.998519 0.0544050i 0.982674π-0.982674\pi
0.998519 0.0544050i 0.0173262π-0.0173262\pi
542542 −1.58104 + 0.426736i −0.0679113 + 0.0183299i
543543 9.13296 0.391933
544544 −4.15720 + 16.1021i −0.178238 + 0.690373i
545545 0 0
546546 −0.888720 + 0.239874i −0.0380337 + 0.0102656i
547547 37.9439i 1.62236i 0.584794 + 0.811182i 0.301175π0.301175\pi
−0.584794 + 0.811182i 0.698825π0.698825\pi
548548 −23.1367 + 13.4710i −0.988352 + 0.575453i
549549 18.2000i 0.776757i
550550 0 0
551551 23.8295 1.01517
552552 −5.56123 5.50057i −0.236702 0.234120i
553553 9.71219 0.413004
554554 −6.19320 22.9455i −0.263124 0.974860i
555555 0 0
556556 −20.3875 35.0160i −0.864624 1.48501i
557557 37.0123i 1.56826i 0.620596 + 0.784130i 0.286891π0.286891\pi
−0.620596 + 0.784130i 0.713109π0.713109\pi
558558 −26.8898 + 7.25782i −1.13834 + 0.307248i
559559 −7.03571 −0.297579
560560 0 0
561561 −6.02960 −0.254570
562562 −12.2763 + 3.31348i −0.517843 + 0.139771i
563563 14.2506i 0.600590i 0.953846 + 0.300295i 0.0970852π0.0970852\pi
−0.953846 + 0.300295i 0.902915π0.902915\pi
564564 −1.15814 1.98913i −0.0487666 0.0837576i
565565 0 0
566566 −5.68988 21.0807i −0.239164 0.886089i
567567 7.56411 0.317663
568568 6.52061 6.59252i 0.273599 0.276616i
569569 25.9576 1.08820 0.544101 0.839020i 0.316871π-0.316871\pi
0.544101 + 0.839020i 0.316871π0.316871\pi
570570 0 0
571571 20.3690i 0.852416i −0.904625 0.426208i 0.859849π-0.859849\pi
0.904625 0.426208i 0.140151π-0.140151\pi
572572 7.76599 4.52163i 0.324712 0.189059i
573573 9.69977i 0.405214i
574574 −3.21245 + 0.867070i −0.134085 + 0.0361908i
575575 0 0
576576 −0.240122 21.8931i −0.0100051 0.912213i
577577 −44.6310 −1.85801 −0.929007 0.370063i 0.879336π-0.879336\pi
−0.929007 + 0.370063i 0.879336π0.879336\pi
578578 11.4109 3.07991i 0.474632 0.128107i
579579 5.26905i 0.218974i
580580 0 0
581581 15.2130i 0.631140i
582582 3.52960 + 13.0770i 0.146307 + 0.542059i
583583 6.57625 0.272360
584584 −13.8796 + 14.0327i −0.574344 + 0.580678i
585585 0 0
586586 0.597234 + 2.21272i 0.0246715 + 0.0914067i
587587 18.9398i 0.781729i −0.920448 0.390865i 0.872176π-0.872176\pi
0.920448 0.390865i 0.127824π-0.127824\pi
588588 2.95598 + 5.07694i 0.121902 + 0.209370i
589589 23.3285i 0.961236i
590590 0 0
591591 0.106270 0.00437134
592592 −36.9346 20.9656i −1.51800 0.861683i
593593 8.22399 0.337719 0.168859 0.985640i 0.445992π-0.445992\pi
0.168859 + 0.985640i 0.445992π0.445992\pi
594594 16.0651 4.33612i 0.659160 0.177913i
595595 0 0
596596 14.9507 + 25.6781i 0.612404 + 1.05182i
597597 6.30568i 0.258074i
598598 2.23266 + 8.27191i 0.0913005 + 0.338263i
599599 −37.2899 −1.52362 −0.761812 0.647798i 0.775690π-0.775690\pi
−0.761812 + 0.647798i 0.775690π0.775690\pi
600600 0 0
601601 23.7882 0.970341 0.485170 0.874420i 0.338758π-0.338758\pi
0.485170 + 0.874420i 0.338758π0.338758\pi
602602 −2.60431 9.64884i −0.106144 0.393257i
603603 18.6045i 0.757632i
604604 17.5321 10.2078i 0.713370 0.415349i
605605 0 0
606606 1.23542 0.333452i 0.0501857 0.0135456i
607607 −32.6940 −1.32701 −0.663505 0.748172i 0.730932π-0.730932\pi
−0.663505 + 0.748172i 0.730932π0.730932\pi
608608 17.7562 + 4.58425i 0.720111 + 0.185916i
609609 4.25715 0.172508
610610 0 0
611611 2.52123i 0.101998i
612612 13.9061 8.09659i 0.562119 0.327285i
613613 5.70642i 0.230480i −0.993338 0.115240i 0.963236π-0.963236\pi
0.993338 0.115240i 0.0367637π-0.0367637\pi
614614 −4.91029 18.1924i −0.198163 0.734185i
615615 0 0
616616 9.07564 + 8.97665i 0.365668 + 0.361679i
617617 18.9653 0.763514 0.381757 0.924263i 0.375319π-0.375319\pi
0.381757 + 0.924263i 0.375319π0.375319\pi
618618 0.735816 + 2.72616i 0.0295989 + 0.109662i
619619 32.0663i 1.28885i 0.764666 + 0.644427i 0.222904π0.222904\pi
−0.764666 + 0.644427i 0.777096π0.777096\pi
620620 0 0
621621 15.8651i 0.636643i
622622 4.37537 1.18095i 0.175436 0.0473519i
623623 −12.4076 −0.497099
624624 1.13855 2.00575i 0.0455785 0.0802944i
625625 0 0
626626 33.1391 8.94456i 1.32451 0.357497i
627627 6.64901i 0.265536i
628628 −7.54486 12.9585i −0.301073 0.517098i
629629 31.2137i 1.24457i
630630 0 0
631631 −11.4737 −0.456762 −0.228381 0.973572i 0.573343π-0.573343\pi
−0.228381 + 0.973572i 0.573343π0.573343\pi
632632 −17.1120 + 17.3008i −0.680680 + 0.688187i
633633 −2.00880 −0.0798427
634634 −1.39735 5.17711i −0.0554958 0.205609i
635635 0 0
636636 1.45858 0.849236i 0.0578365 0.0336744i
637637 6.43503i 0.254965i
638638 −40.1237 + 10.8298i −1.58851 + 0.428754i
639639 −8.97215 −0.354933
640640 0 0
641641 −0.258289 −0.0102018 −0.00510089 0.999987i 0.501624π-0.501624\pi
−0.00510089 + 0.999987i 0.501624π0.501624\pi
642642 11.2176 3.02774i 0.442724 0.119495i
643643 31.8119i 1.25454i 0.778802 + 0.627269i 0.215827π0.215827\pi
−0.778802 + 0.627269i 0.784173π0.784173\pi
644644 −10.5177 + 6.12380i −0.414457 + 0.241311i
645645 0 0
646646 3.51214 + 13.0123i 0.138183 + 0.511962i
647647 −24.3294 −0.956486 −0.478243 0.878228i 0.658726π-0.658726\pi
−0.478243 + 0.878228i 0.658726π0.658726\pi
648648 −13.3273 + 13.4743i −0.523546 + 0.529320i
649649 −22.1897 −0.871022
650650 0 0
651651 4.16764i 0.163343i
652652 9.00851 + 15.4723i 0.352801 + 0.605942i
653653 39.3785i 1.54100i −0.637440 0.770500i 0.720007π-0.720007\pi
0.637440 0.770500i 0.279993π-0.279993\pi
654654 −10.9338 + 2.95114i −0.427547 + 0.115399i
655655 0 0
656656 4.11551 7.25019i 0.160684 0.283072i
657657 19.0979 0.745082
658658 −3.45763 + 0.933248i −0.134793 + 0.0363818i
659659 33.7063i 1.31301i 0.754321 + 0.656506i 0.227966π0.227966\pi
−0.754321 + 0.656506i 0.772034π0.772034\pi
660660 0 0
661661 32.9163i 1.28029i 0.768252 + 0.640147i 0.221127π0.221127\pi
−0.768252 + 0.640147i 0.778873π0.778873\pi
662662 0.833580 + 3.08837i 0.0323980 + 0.120033i
663663 1.69508 0.0658313
664664 27.0995 + 26.8039i 1.05167 + 1.04019i
665665 0 0
666666 10.7086 + 39.6747i 0.414949 + 1.53736i
667667 39.6241i 1.53425i
668668 −4.32003 + 2.51527i −0.167147 + 0.0973187i
669669 12.2367i 0.473097i
670670 0 0
671671 −26.5862 −1.02635
672672 3.17215 + 0.818977i 0.122368 + 0.0315927i
673673 2.87683 0.110894 0.0554468 0.998462i 0.482342π-0.482342\pi
0.0554468 + 0.998462i 0.482342π0.482342\pi
674674 39.1384 10.5638i 1.50755 0.406903i
675675 0 0
676676 20.2858 11.8111i 0.780222 0.454272i
677677 28.6415i 1.10078i −0.834907 0.550391i 0.814479π-0.814479\pi
0.834907 0.550391i 0.185521π-0.185521\pi
678678 0.561612 + 2.08074i 0.0215686 + 0.0799105i
679679 21.0753 0.808794
680680 0 0
681681 12.6724 0.485607
682682 10.6021 + 39.2801i 0.405974 + 1.50411i
683683 18.3147i 0.700792i −0.936602 0.350396i 0.886047π-0.886047\pi
0.936602 0.350396i 0.113953π-0.113953\pi
684684 −8.92833 15.3346i −0.341383 0.586332i
685685 0 0
686686 19.6144 5.29410i 0.748881 0.202130i
687687 11.3241 0.432043
688688 21.7765 + 12.3612i 0.830220 + 0.471268i
689689 −1.84875 −0.0704318
690690 0 0
691691 14.4710i 0.550502i −0.961372 0.275251i 0.911239π-0.911239\pi
0.961372 0.275251i 0.0887610π-0.0887610\pi
692692 −0.593291 1.01899i −0.0225535 0.0387361i
693693 12.3516i 0.469198i
694694 1.11973 + 4.14856i 0.0425045 + 0.157477i
695695 0 0
696696 −7.50073 + 7.58344i −0.284314 + 0.287450i
697697 6.12718 0.232084
698698 9.64076 + 35.7185i 0.364908 + 1.35197i
699699 10.0597i 0.380493i
700700 0 0
701701 18.5603i 0.701013i 0.936560 + 0.350506i 0.113991π0.113991\pi
−0.936560 + 0.350506i 0.886009π0.886009\pi
702702 −4.51631 + 1.21900i −0.170457 + 0.0460080i
703703 −34.4202 −1.29818
704704 −31.9810 + 0.350765i −1.20533 + 0.0132200i
705705 0 0
706706 −40.2702 + 10.8693i −1.51559 + 0.409072i
707707 1.99104i 0.0748809i
708708 −4.92157 + 2.86551i −0.184964 + 0.107692i
709709 43.3934i 1.62967i −0.579690 0.814837i 0.696826π-0.696826\pi
0.579690 0.814837i 0.303174π-0.303174\pi
710710 0 0
711711 23.5456 0.883029
712712 21.8611 22.1022i 0.819279 0.828314i
713713 −38.7910 −1.45273
714714 0.627443 + 2.32464i 0.0234815 + 0.0869976i
715715 0 0
716716 −10.3681 17.8074i −0.387474 0.665494i
717717 6.35359i 0.237279i
718718 −12.1698 + 3.28473i −0.454172 + 0.122585i
719719 14.8496 0.553797 0.276899 0.960899i 0.410693π-0.410693\pi
0.276899 + 0.960899i 0.410693π0.410693\pi
720720 0 0
721721 4.39356 0.163625
722722 −11.5927 + 3.12899i −0.431437 + 0.116449i
723723 10.4706i 0.389408i
724724 17.9147 + 30.7689i 0.665795 + 1.14352i
725725 0 0
726726 −0.942081 3.49036i −0.0349639 0.129539i
727727 6.22824 0.230993 0.115496 0.993308i 0.463154π-0.463154\pi
0.115496 + 0.993308i 0.463154π0.463154\pi
728728 −2.55140 2.52357i −0.0945610 0.0935296i
729729 13.8082 0.511416
730730 0 0
731731 18.4035i 0.680676i
732732 −5.89669 + 3.43326i −0.217948 + 0.126897i
733733 43.2406i 1.59713i 0.601910 + 0.798564i 0.294407π0.294407\pi
−0.601910 + 0.798564i 0.705593π0.705593\pi
734734 30.9733 8.35999i 1.14325 0.308573i
735735 0 0
736736 7.62276 29.5253i 0.280979 1.08832i
737737 −27.1770 −1.00108
738738 −7.78806 + 2.10207i −0.286683 + 0.0773783i
739739 10.0469i 0.369582i 0.982778 + 0.184791i 0.0591608π0.0591608\pi
−0.982778 + 0.184791i 0.940839π0.940839\pi
740740 0 0
741741 1.86921i 0.0686670i
742742 −0.684327 2.53540i −0.0251224 0.0930773i
743743 5.85860 0.214931 0.107466 0.994209i 0.465726π-0.465726\pi
0.107466 + 0.994209i 0.465726π0.465726\pi
744744 7.42400 + 7.34302i 0.272177 + 0.269208i
745745 0 0
746746 −2.38180 8.82445i −0.0872039 0.323086i
747747 36.8814i 1.34942i
748748 −11.8273 20.3137i −0.432450 0.742742i
749749 18.0786i 0.660579i
750750 0 0
751751 −16.0419 −0.585377 −0.292688 0.956208i 0.594550π-0.594550\pi
−0.292688 + 0.956208i 0.594550π0.594550\pi
752752 4.42962 7.80354i 0.161532 0.284566i
753753 11.3900 0.415075
754754 11.2798 3.04452i 0.410786 0.110875i
755755 0 0
756756 −3.34348 5.74250i −0.121601 0.208853i
757757 15.5665i 0.565773i 0.959153 + 0.282886i 0.0912919π0.0912919\pi
−0.959153 + 0.282886i 0.908708π0.908708\pi
758758 −1.59122 5.89540i −0.0577958 0.214130i
759759 11.0561 0.401309
760760 0 0
761761 −26.9097 −0.975477 −0.487739 0.872990i 0.662178π-0.662178\pi
−0.487739 + 0.872990i 0.662178π0.662178\pi
762762 2.31963 + 8.59410i 0.0840312 + 0.311331i
763763 17.6213i 0.637933i
764764 −32.6784 + 19.0265i −1.18226 + 0.688356i
765765 0 0
766766 −15.1621 + 4.09238i −0.547828 + 0.147864i
767767 6.23810 0.225245
768768 −7.04794 + 4.20773i −0.254321 + 0.151833i
769769 17.0952 0.616470 0.308235 0.951310i 0.400262π-0.400262\pi
0.308235 + 0.951310i 0.400262π0.400262\pi
770770 0 0
771771 6.69975i 0.241286i
772772 −17.7514 + 10.3355i −0.638886 + 0.371982i
773773 6.32624i 0.227539i 0.993507 + 0.113770i 0.0362926π0.0362926\pi
−0.993507 + 0.113770i 0.963707π0.963707\pi
774774 −6.31373 23.3920i −0.226942 0.840809i
775775 0 0
776776 −37.1328 + 37.5423i −1.33299 + 1.34769i
777777 −6.14916 −0.220600
778778 −5.73016 21.2300i −0.205436 0.761131i
779779 6.75661i 0.242081i
780780 0 0
781781 13.1063i 0.468981i
782782 21.6370 5.84003i 0.773738 0.208839i
783783 21.6341 0.773138
784784 −11.3059 + 19.9173i −0.403782 + 0.711332i
785785 0 0
786786 −9.29085 + 2.50769i −0.331394 + 0.0894462i
787787 53.5766i 1.90980i 0.296929 + 0.954899i 0.404037π0.404037\pi
−0.296929 + 0.954899i 0.595963π0.595963\pi
788788 0.208452 + 0.358021i 0.00742581 + 0.0127540i
789789 15.0003i 0.534026i
790790 0 0
791791 3.35339 0.119233
792792 22.0024 + 21.7624i 0.781822 + 0.773294i
793793 7.47406 0.265412
794794 −9.93838 36.8212i −0.352700 1.30673i
795795 0 0
796796 −21.2438 + 12.3689i −0.752966 + 0.438403i
797797 41.6834i 1.47650i −0.674527 0.738251i 0.735652π-0.735652\pi
0.674527 0.738251i 0.264348π-0.264348\pi
798798 2.56345 0.691898i 0.0907450 0.0244929i
799799 6.59483 0.233308
800800 0 0
801801 −30.0802 −1.06283
802802 −49.3018 + 13.3070i −1.74091 + 0.469887i
803803 27.8979i 0.984495i
804804 −6.02773 + 3.50956i −0.212582 + 0.123772i
805805 0 0
806806 −2.98051 11.0426i −0.104984 0.388961i
807807 10.9914 0.386917
808808 3.54674 + 3.50805i 0.124774 + 0.123413i
809809 −26.9010 −0.945788 −0.472894 0.881119i 0.656791π-0.656791\pi
−0.472894 + 0.881119i 0.656791π0.656791\pi
810810 0 0
811811 5.88980i 0.206819i −0.994639 0.103409i 0.967025π-0.967025\pi
0.994639 0.103409i 0.0329752π-0.0329752\pi
812812 8.35058 + 14.3423i 0.293048 + 0.503315i
813813 0.594069i 0.0208349i
814814 57.9560 15.6429i 2.03136 0.548282i
815815 0 0
816816 −5.24649 2.97813i −0.183664 0.104255i
817817 20.2940 0.709997
818818 −21.1833 + 5.71758i −0.740658 + 0.199911i
819819 3.47234i 0.121334i
820820 0 0
821821 48.2445i 1.68374i −0.539677 0.841872i 0.681454π-0.681454\pi
0.539677 0.841872i 0.318546π-0.318546\pi
822822 −2.53084 9.37664i −0.0882733 0.327048i
823823 −51.9289 −1.81013 −0.905063 0.425277i 0.860177π-0.860177\pi
−0.905063 + 0.425277i 0.860177π0.860177\pi
824824 −7.74107 + 7.82644i −0.269673 + 0.272647i
825825 0 0
826826 2.30907 + 8.55498i 0.0803428 + 0.297666i
827827 28.2849i 0.983562i −0.870719 0.491781i 0.836346π-0.836346\pi
0.870719 0.491781i 0.163654π-0.163654\pi
828828 −25.4985 + 14.8461i −0.886136 + 0.515939i
829829 14.2294i 0.494209i −0.968989 0.247104i 0.920521π-0.920521\pi
0.968989 0.247104i 0.0794790π-0.0794790\pi
830830 0 0
831831 8.62168 0.299083
832832 8.99068 0.0986092i 0.311696 0.00341866i
833833 −16.8323 −0.583203
834834 14.1910 3.83027i 0.491393 0.132632i
835835 0 0
836836 −22.4004 + 13.0423i −0.774735 + 0.451078i
837837 21.1792i 0.732060i
838838 −9.92656 36.7774i −0.342907 1.27045i
839839 5.04346 0.174120 0.0870598 0.996203i 0.472253π-0.472253\pi
0.0870598 + 0.996203i 0.472253π0.472253\pi
840840 0 0
841841 −25.0325 −0.863191
842842 2.26508 + 8.39202i 0.0780600 + 0.289208i
843843 4.61277i 0.158872i
844844 −3.94035 6.76763i −0.135633 0.232952i
845845 0 0
846846 −8.38247 + 2.26251i −0.288195 + 0.0777866i
847847 −5.62517 −0.193283
848848 5.72214 + 3.24813i 0.196499 + 0.111541i
849849 7.92101 0.271848
850850 0 0
851851 57.2343i 1.96197i
852852 1.69251 + 2.90692i 0.0579845 + 0.0995895i
853853 46.2026i 1.58195i 0.611850 + 0.790974i 0.290426π0.290426\pi
−0.611850 + 0.790974i 0.709574π0.709574\pi
854854 2.76657 + 10.2500i 0.0946701 + 0.350748i
855855 0 0
856856 32.2043 + 31.8530i 1.10072 + 1.08871i
857857 41.5405 1.41900 0.709499 0.704707i 0.248921π-0.248921\pi
0.709499 + 0.704707i 0.248921π0.248921\pi
858858 0.849494 + 3.14733i 0.0290012 + 0.107448i
859859 37.9644i 1.29533i 0.761925 + 0.647665i 0.224254π0.224254\pi
−0.761925 + 0.647665i 0.775746π0.775746\pi
860860 0 0
861861 1.20707i 0.0411368i
862862 −50.3681 + 13.5948i −1.71554 + 0.463041i
863863 −2.89022 −0.0983843 −0.0491922 0.998789i 0.515665π-0.515665\pi
−0.0491922 + 0.998789i 0.515665π0.515665\pi
864864 16.1203 + 4.16189i 0.548424 + 0.141590i
865865 0 0
866866 15.8141 4.26838i 0.537386 0.145046i
867867 4.28761i 0.145615i
868868 14.0407 8.17501i 0.476574 0.277478i
869869 34.3949i 1.16677i
870870 0 0
871871 7.64015 0.258877
872872 −31.3896 31.0472i −1.06299 1.05139i
873873 51.0935 1.72925
874874 −6.43996 23.8597i −0.217835 0.807067i
875875 0 0
876876 −3.60265 6.18762i −0.121722 0.209060i
877877 43.0916i 1.45510i −0.686055 0.727550i 0.740659π-0.740659\pi
0.686055 0.727550i 0.259341π-0.259341\pi
878878 5.66860 1.53001i 0.191306 0.0516353i
879879 −0.831423 −0.0280432
880880 0 0
881881 −2.06410 −0.0695414 −0.0347707 0.999395i 0.511070π-0.511070\pi
−0.0347707 + 0.999395i 0.511070π0.511070\pi
882882 21.3949 5.77469i 0.720405 0.194444i
883883 51.4835i 1.73256i 0.499562 + 0.866278i 0.333494π0.333494\pi
−0.499562 + 0.866278i 0.666506π0.666506\pi
884884 3.32497 + 5.71070i 0.111831 + 0.192071i
885885 0 0
886886 5.79783 + 21.4807i 0.194782 + 0.721657i
887887 55.5749 1.86602 0.933012 0.359845i 0.117171π-0.117171\pi
0.933012 + 0.359845i 0.117171π0.117171\pi
888888 10.8343 10.9538i 0.363575 0.367585i
889889 13.8505 0.464531
890890 0 0
891891 26.7877i 0.897422i
892892 −41.2252 + 24.0028i −1.38032 + 0.803672i
893893 7.27229i 0.243358i
894894 −10.4066 + 2.80884i −0.348049 + 0.0939415i
895895 0 0
896896 3.46319 + 12.2934i 0.115697 + 0.410694i
897897 −3.10814 −0.103778
898898 28.2439 7.62329i 0.942511 0.254393i
899899 52.8965i 1.76420i
900900 0 0
901901 4.83582i 0.161105i
902902 3.07066 + 11.3766i 0.102242 + 0.378801i
903903 3.62552 0.120650
904904 −5.90838 + 5.97354i −0.196510 + 0.198677i
905905 0 0
906906 1.91777 + 7.10525i 0.0637137 + 0.236056i
907907 15.8669i 0.526852i −0.964680 0.263426i 0.915147π-0.915147\pi
0.964680 0.263426i 0.0848526π-0.0848526\pi
908908 24.8574 + 42.6931i 0.824923 + 1.41682i
909909 4.82696i 0.160100i
910910 0 0
911911 −30.4293 −1.00817 −0.504084 0.863655i 0.668170π-0.668170\pi
−0.504084 + 0.863655i 0.668170π0.668170\pi
912912 −3.28406 + 5.78545i −0.108746 + 0.191575i
913913 −53.8755 −1.78302
914914 −39.2112 + 10.5835i −1.29699 + 0.350070i
915915 0 0
916916 22.2128 + 38.1509i 0.733931 + 1.26054i
917917 14.9734i 0.494465i
918918 3.18855 + 11.8134i 0.105238 + 0.389901i
919919 −15.1819 −0.500803 −0.250402 0.968142i 0.580563π-0.580563\pi
−0.250402 + 0.968142i 0.580563π0.580563\pi
920920 0 0
921921 6.83572 0.225245
922922 10.2104 + 37.8290i 0.336261 + 1.24583i
923923 3.68452i 0.121278i
924924 −4.00183 + 2.33001i −0.131651 + 0.0766517i
925925 0 0
926926 −36.8061 + 9.93432i −1.20952 + 0.326462i
927927 10.6515 0.349840
928928 −40.2616 10.3946i −1.32165 0.341220i
929929 −8.00028 −0.262481 −0.131240 0.991351i 0.541896π-0.541896\pi
−0.131240 + 0.991351i 0.541896π0.541896\pi
930930 0 0
931931 18.5614i 0.608325i
932932 −33.8911 + 19.7326i −1.11014 + 0.646362i
933933 1.64403i 0.0538231i
934934 −11.5367 42.7427i −0.377491 1.39858i
935935 0 0
936936 −6.18544 6.11797i −0.202178 0.199972i
937937 10.0303 0.327676 0.163838 0.986487i 0.447613π-0.447613\pi
0.163838 + 0.986487i 0.447613π0.447613\pi
938938 2.82805 + 10.4778i 0.0923391 + 0.342112i
939939 12.4519i 0.406353i
940940 0 0
941941 4.23635i 0.138101i −0.997613 0.0690506i 0.978003π-0.978003\pi
0.997613 0.0690506i 0.0219970π-0.0219970\pi
942942 5.25168 1.41748i 0.171109 0.0461839i
943943 −11.2350 −0.365861
944944 −19.3078 10.9599i −0.628414 0.356714i
945945 0 0
946946 −34.1706 + 9.22296i −1.11098 + 0.299864i
947947 3.33715i 0.108443i 0.998529 + 0.0542213i 0.0172677π0.0172677\pi
−0.998529 + 0.0542213i 0.982732π0.982732\pi
948948 −4.44166 7.62863i −0.144258 0.247767i
949949 7.84281i 0.254588i
950950 0 0
951951 1.94528 0.0630800
952952 −6.60095 + 6.67374i −0.213938 + 0.216297i
953953 −10.9309 −0.354086 −0.177043 0.984203i 0.556653π-0.556653\pi
−0.177043 + 0.984203i 0.556653π0.556653\pi
954954 −1.65904 6.14665i −0.0537134 0.199005i
955955 0 0
956956 −21.4052 + 12.4629i −0.692294 + 0.403078i
957957 15.0763i 0.487349i
958958 44.6317 12.0465i 1.44199 0.389205i
959959 −15.1117 −0.487981
960960 0 0
961961 20.7844 0.670463
962962 −16.2929 + 4.39761i −0.525305 + 0.141785i
963963 43.8287i 1.41236i
964964 −35.2755 + 20.5386i −1.13615 + 0.661505i
965965 0 0
966966 −1.15050 4.26253i −0.0370167 0.137145i
967967 −40.7599 −1.31075 −0.655375 0.755304i 0.727489π-0.727489\pi
−0.655375 + 0.755304i 0.727489π0.727489\pi
968968 9.91106 10.0204i 0.318553 0.322067i
969969 −4.88932 −0.157068
970970 0 0
971971 56.9328i 1.82706i 0.406772 + 0.913530i 0.366654π0.366654\pi
−0.406772 + 0.913530i 0.633346π0.633346\pi
972972 −12.3445 21.2020i −0.395951 0.680054i
973973 22.8706i 0.733197i
974974 −24.0361 + 6.48756i −0.770165 + 0.207875i
975975 0 0
976976 −23.1332 13.1314i −0.740477 0.420326i
977977 17.1254 0.547892 0.273946 0.961745i 0.411671π-0.411671\pi
0.273946 + 0.961745i 0.411671π0.411671\pi
978978 −6.27047 + 1.69246i −0.200508 + 0.0541189i
979979 43.9405i 1.40434i
980980 0 0
981981 42.7199i 1.36394i
982982 0.483250 + 1.79041i 0.0154211 + 0.0571344i
983983 51.3738 1.63857 0.819284 0.573388i 0.194371π-0.194371\pi
0.819284 + 0.573388i 0.194371π0.194371\pi
984984 2.15020 + 2.12675i 0.0685460 + 0.0677983i
985985 0 0
986986 −7.96363 29.5048i −0.253614 0.939625i
987987 1.29919i 0.0413538i
988988 6.29734 3.66653i 0.200345 0.116648i
989989 33.7451i 1.07303i
990990 0 0
991991 −23.9933 −0.762171 −0.381085 0.924540i 0.624450π-0.624450\pi
−0.381085 + 0.924540i 0.624450π0.624450\pi
992992 −10.1761 + 39.4151i −0.323090 + 1.25143i
993993 −1.16045 −0.0368256
994994 5.05299 1.36385i 0.160271 0.0432587i
995995 0 0
996996 −11.9493 + 6.95732i −0.378629 + 0.220451i
997997 7.90228i 0.250268i −0.992140 0.125134i 0.960064π-0.960064\pi
0.992140 0.125134i 0.0399361π-0.0399361\pi
998998 7.83679 + 29.0349i 0.248069 + 0.919084i
999999 −31.2489 −0.988673
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 1000.2.d.c.501.6 yes 40
4.3 odd 2 4000.2.d.c.2001.20 40
5.2 odd 4 1000.2.f.c.749.9 20
5.3 odd 4 1000.2.f.d.749.12 20
5.4 even 2 inner 1000.2.d.c.501.35 yes 40
8.3 odd 2 4000.2.d.c.2001.19 40
8.5 even 2 inner 1000.2.d.c.501.5 40
20.3 even 4 4000.2.f.d.3249.8 20
20.7 even 4 4000.2.f.c.3249.13 20
20.19 odd 2 4000.2.d.c.2001.21 40
40.3 even 4 4000.2.f.c.3249.14 20
40.13 odd 4 1000.2.f.c.749.10 20
40.19 odd 2 4000.2.d.c.2001.22 40
40.27 even 4 4000.2.f.d.3249.7 20
40.29 even 2 inner 1000.2.d.c.501.36 yes 40
40.37 odd 4 1000.2.f.d.749.11 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1000.2.d.c.501.5 40 8.5 even 2 inner
1000.2.d.c.501.6 yes 40 1.1 even 1 trivial
1000.2.d.c.501.35 yes 40 5.4 even 2 inner
1000.2.d.c.501.36 yes 40 40.29 even 2 inner
1000.2.f.c.749.9 20 5.2 odd 4
1000.2.f.c.749.10 20 40.13 odd 4
1000.2.f.d.749.11 20 40.37 odd 4
1000.2.f.d.749.12 20 5.3 odd 4
4000.2.d.c.2001.19 40 8.3 odd 2
4000.2.d.c.2001.20 40 4.3 odd 2
4000.2.d.c.2001.21 40 20.19 odd 2
4000.2.d.c.2001.22 40 40.19 odd 2
4000.2.f.c.3249.13 20 20.7 even 4
4000.2.f.c.3249.14 20 40.3 even 4
4000.2.f.d.3249.7 20 40.27 even 4
4000.2.f.d.3249.8 20 20.3 even 4