Properties

Label 460.2.e.b.91.11
Level 460460
Weight 22
Character 460.91
Analytic conductor 3.6733.673
Analytic rank 00
Dimension 3232
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [460,2,Mod(91,460)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(460, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("460.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 460=22523 460 = 2^{2} \cdot 5 \cdot 23
Weight: k k == 2 2
Character orbit: [χ][\chi] == 460.e (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: 3.673118492983.67311849298
Analytic rank: 00
Dimension: 3232
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 91.11
Character χ\chi == 460.91
Dual form 460.2.e.b.91.10

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+(0.265302+1.38911i)q2+0.0612154iq3+(1.859230.737066i)q41.00000iq5+(0.08503460.0162406i)q60.810885q7+(1.517122.38712i)q8+2.99625q9+(1.38911+0.265302i)q102.10140q11+(0.04511980.113813i)q12+2.93504q13+(0.2151301.12641i)q14+0.0612154q15+(2.91347+2.74075i)q164.65004iq17+(0.794913+4.16211i)q18+6.20768q19+(0.737066+1.85923i)q200.0496387iq21+(0.5575072.91907i)q22+(4.03517+2.59180i)q23+(0.146129+0.0928711i)q241.00000q25+(0.778674+4.07709i)q26+0.367063iq27+(1.50762+0.597676i)q28+5.24402q29+(0.0162406+0.0850346i)q30+2.58292iq31+(4.58014+3.31999i)q320.128638iq33+(6.45940+1.23367i)q34+0.810885iq35+(5.570722.20844i)q362.99380iq37+(1.64691+8.62312i)q38+0.179670iq39+(2.387121.51712i)q40+8.21934q41+(0.0689533+0.0131693i)q4210.1620q43+(3.90699+1.54887i)q442.99625iq45+(4.67082+4.91766i)q46+1.89447iq47+(0.167776+0.178349i)q486.34247q49+(0.2653021.38911i)q50+0.284654q51+(5.456922.16332i)q528.12090iq53+(0.5098890.0973827i)q54+2.10140iq55+(1.23021+1.93568i)q56+0.380006iq57+(1.39125+7.28450i)q5813.1005iq59+(0.1138130.0451198i)q60+13.7022iq61+(3.587950.685255i)q622.42962q63+(3.396697.24310i)q642.93504iq65+(0.178692+0.0341280i)q66+1.42460q67+(3.42739+8.64549i)q68+(0.158658+0.247014i)q69+(1.126410.215130i)q702.26145iq71+(4.545687.15242i)q724.13040q73+(4.15870+0.794262i)q740.0612154iq75+(11.54154.57547i)q76+1.70400q77+(0.2495800.0476668i)q78+14.9553q79+(2.740752.91347i)q80+8.96629q81+(2.18061+11.4175i)q828.73564q83+(0.0365870+0.0922896i)q844.65004q85+(2.6960114.1162i)q86+0.321015iq87+(3.18808+5.01630i)q88+5.82961iq89+(4.16211+0.794913i)q902.37998q91+(5.591987.79293i)q920.158114q93+(2.631610.502606i)q946.20768iq95+(0.2032340.280375i)q96+2.73446iq97+(1.682678.81035i)q986.29633q99+O(q100)q+(-0.265302 + 1.38911i) q^{2} +0.0612154i q^{3} +(-1.85923 - 0.737066i) q^{4} -1.00000i q^{5} +(-0.0850346 - 0.0162406i) q^{6} -0.810885 q^{7} +(1.51712 - 2.38712i) q^{8} +2.99625 q^{9} +(1.38911 + 0.265302i) q^{10} -2.10140 q^{11} +(0.0451198 - 0.113813i) q^{12} +2.93504 q^{13} +(0.215130 - 1.12641i) q^{14} +0.0612154 q^{15} +(2.91347 + 2.74075i) q^{16} -4.65004i q^{17} +(-0.794913 + 4.16211i) q^{18} +6.20768 q^{19} +(-0.737066 + 1.85923i) q^{20} -0.0496387i q^{21} +(0.557507 - 2.91907i) q^{22} +(4.03517 + 2.59180i) q^{23} +(0.146129 + 0.0928711i) q^{24} -1.00000 q^{25} +(-0.778674 + 4.07709i) q^{26} +0.367063i q^{27} +(1.50762 + 0.597676i) q^{28} +5.24402 q^{29} +(-0.0162406 + 0.0850346i) q^{30} +2.58292i q^{31} +(-4.58014 + 3.31999i) q^{32} -0.128638i q^{33} +(6.45940 + 1.23367i) q^{34} +0.810885i q^{35} +(-5.57072 - 2.20844i) q^{36} -2.99380i q^{37} +(-1.64691 + 8.62312i) q^{38} +0.179670i q^{39} +(-2.38712 - 1.51712i) q^{40} +8.21934 q^{41} +(0.0689533 + 0.0131693i) q^{42} -10.1620 q^{43} +(3.90699 + 1.54887i) q^{44} -2.99625i q^{45} +(-4.67082 + 4.91766i) q^{46} +1.89447i q^{47} +(-0.167776 + 0.178349i) q^{48} -6.34247 q^{49} +(0.265302 - 1.38911i) q^{50} +0.284654 q^{51} +(-5.45692 - 2.16332i) q^{52} -8.12090i q^{53} +(-0.509889 - 0.0973827i) q^{54} +2.10140i q^{55} +(-1.23021 + 1.93568i) q^{56} +0.380006i q^{57} +(-1.39125 + 7.28450i) q^{58} -13.1005i q^{59} +(-0.113813 - 0.0451198i) q^{60} +13.7022i q^{61} +(-3.58795 - 0.685255i) q^{62} -2.42962 q^{63} +(-3.39669 - 7.24310i) q^{64} -2.93504i q^{65} +(0.178692 + 0.0341280i) q^{66} +1.42460 q^{67} +(-3.42739 + 8.64549i) q^{68} +(-0.158658 + 0.247014i) q^{69} +(-1.12641 - 0.215130i) q^{70} -2.26145i q^{71} +(4.54568 - 7.15242i) q^{72} -4.13040 q^{73} +(4.15870 + 0.794262i) q^{74} -0.0612154i q^{75} +(-11.5415 - 4.57547i) q^{76} +1.70400 q^{77} +(-0.249580 - 0.0476668i) q^{78} +14.9553 q^{79} +(2.74075 - 2.91347i) q^{80} +8.96629 q^{81} +(-2.18061 + 11.4175i) q^{82} -8.73564 q^{83} +(-0.0365870 + 0.0922896i) q^{84} -4.65004 q^{85} +(2.69601 - 14.1162i) q^{86} +0.321015i q^{87} +(-3.18808 + 5.01630i) q^{88} +5.82961i q^{89} +(4.16211 + 0.794913i) q^{90} -2.37998 q^{91} +(-5.59198 - 7.79293i) q^{92} -0.158114 q^{93} +(-2.63161 - 0.502606i) q^{94} -6.20768i q^{95} +(-0.203234 - 0.280375i) q^{96} +2.73446i q^{97} +(1.68267 - 8.81035i) q^{98} -6.29633 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 32q+4q24q416q62q852q9+24q124q13+20q1656q186q2432q25+68q26+8q2916q32+8q36+44q414q464q48++62q98+O(q100) 32 q + 4 q^{2} - 4 q^{4} - 16 q^{6} - 2 q^{8} - 52 q^{9} + 24 q^{12} - 4 q^{13} + 20 q^{16} - 56 q^{18} - 6 q^{24} - 32 q^{25} + 68 q^{26} + 8 q^{29} - 16 q^{32} + 8 q^{36} + 44 q^{41} - 4 q^{46} - 4 q^{48}+ \cdots + 62 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/460Z)×\left(\mathbb{Z}/460\mathbb{Z}\right)^\times.

nn 231231 277277 281281
χ(n)\chi(n) 1-1 11 1-1

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 −0.265302 + 1.38911i −0.187597 + 0.982246i
33 0.0612154i 0.0353427i 0.999844 + 0.0176714i 0.00562526π0.00562526\pi
−0.999844 + 0.0176714i 0.994375π0.994375\pi
44 −1.85923 0.737066i −0.929615 0.368533i
55 1.00000i 0.447214i
66 −0.0850346 0.0162406i −0.0347152 0.00663019i
77 −0.810885 −0.306486 −0.153243 0.988189i 0.548972π-0.548972\pi
−0.153243 + 0.988189i 0.548972π0.548972\pi
88 1.51712 2.38712i 0.536383 0.843975i
99 2.99625 0.998751
1010 1.38911 + 0.265302i 0.439274 + 0.0838960i
1111 −2.10140 −0.633596 −0.316798 0.948493i 0.602608π-0.602608\pi
−0.316798 + 0.948493i 0.602608π0.602608\pi
1212 0.0451198 0.113813i 0.0130250 0.0328551i
1313 2.93504 0.814035 0.407017 0.913420i 0.366569π-0.366569\pi
0.407017 + 0.913420i 0.366569π0.366569\pi
1414 0.215130 1.12641i 0.0574959 0.301044i
1515 0.0612154 0.0158057
1616 2.91347 + 2.74075i 0.728367 + 0.685187i
1717 4.65004i 1.12780i −0.825843 0.563900i 0.809300π-0.809300\pi
0.825843 0.563900i 0.190700π-0.190700\pi
1818 −0.794913 + 4.16211i −0.187363 + 0.981019i
1919 6.20768 1.42414 0.712070 0.702109i 0.247758π-0.247758\pi
0.712070 + 0.702109i 0.247758π0.247758\pi
2020 −0.737066 + 1.85923i −0.164813 + 0.415736i
2121 0.0496387i 0.0108320i
2222 0.557507 2.91907i 0.118861 0.622348i
2323 4.03517 + 2.59180i 0.841391 + 0.540427i
2424 0.146129 + 0.0928711i 0.0298284 + 0.0189572i
2525 −1.00000 −0.200000
2626 −0.778674 + 4.07709i −0.152711 + 0.799582i
2727 0.367063i 0.0706413i
2828 1.50762 + 0.597676i 0.284914 + 0.112950i
2929 5.24402 0.973790 0.486895 0.873461i 0.338129π-0.338129\pi
0.486895 + 0.873461i 0.338129π0.338129\pi
3030 −0.0162406 + 0.0850346i −0.00296511 + 0.0155251i
3131 2.58292i 0.463906i 0.972727 + 0.231953i 0.0745116π0.0745116\pi
−0.972727 + 0.231953i 0.925488π0.925488\pi
3232 −4.58014 + 3.31999i −0.809662 + 0.586896i
3333 0.128638i 0.0223930i
3434 6.45940 + 1.23367i 1.10778 + 0.211572i
3535 0.810885i 0.137065i
3636 −5.57072 2.20844i −0.928453 0.368073i
3737 2.99380i 0.492178i −0.969247 0.246089i 0.920855π-0.920855\pi
0.969247 0.246089i 0.0791455π-0.0791455\pi
3838 −1.64691 + 8.62312i −0.267164 + 1.39886i
3939 0.179670i 0.0287702i
4040 −2.38712 1.51712i −0.377437 0.239878i
4141 8.21934 1.28365 0.641823 0.766853i 0.278178π-0.278178\pi
0.641823 + 0.766853i 0.278178π0.278178\pi
4242 0.0689533 + 0.0131693i 0.0106397 + 0.00203206i
4343 −10.1620 −1.54970 −0.774849 0.632147i 0.782174π-0.782174\pi
−0.774849 + 0.632147i 0.782174π0.782174\pi
4444 3.90699 + 1.54887i 0.589001 + 0.233501i
4545 2.99625i 0.446655i
4646 −4.67082 + 4.91766i −0.688675 + 0.725070i
4747 1.89447i 0.276336i 0.990409 + 0.138168i 0.0441214π0.0441214\pi
−0.990409 + 0.138168i 0.955879π0.955879\pi
4848 −0.167776 + 0.178349i −0.0242164 + 0.0257425i
4949 −6.34247 −0.906066
5050 0.265302 1.38911i 0.0375194 0.196449i
5151 0.284654 0.0398595
5252 −5.45692 2.16332i −0.756738 0.299999i
5353 8.12090i 1.11549i −0.830012 0.557745i 0.811667π-0.811667\pi
0.830012 0.557745i 0.188333π-0.188333\pi
5454 −0.509889 0.0973827i −0.0693871 0.0132521i
5555 2.10140i 0.283353i
5656 −1.23021 + 1.93568i −0.164394 + 0.258666i
5757 0.380006i 0.0503330i
5858 −1.39125 + 7.28450i −0.182680 + 0.956501i
5959 13.1005i 1.70554i −0.522284 0.852772i 0.674920π-0.674920\pi
0.522284 0.852772i 0.325080π-0.325080\pi
6060 −0.113813 0.0451198i −0.0146933 0.00582494i
6161 13.7022i 1.75439i 0.480133 + 0.877196i 0.340588π0.340588\pi
−0.480133 + 0.877196i 0.659412π0.659412\pi
6262 −3.58795 0.685255i −0.455670 0.0870275i
6363 −2.42962 −0.306103
6464 −3.39669 7.24310i −0.424586 0.905387i
6565 2.93504i 0.364047i
6666 0.178692 + 0.0341280i 0.0219955 + 0.00420087i
6767 1.42460 0.174042 0.0870211 0.996206i 0.472265π-0.472265\pi
0.0870211 + 0.996206i 0.472265π0.472265\pi
6868 −3.42739 + 8.64549i −0.415632 + 1.04842i
6969 −0.158658 + 0.247014i −0.0191002 + 0.0297370i
7070 −1.12641 0.215130i −0.134631 0.0257129i
7171 2.26145i 0.268384i −0.990955 0.134192i 0.957156π-0.957156\pi
0.990955 0.134192i 0.0428439π-0.0428439\pi
7272 4.54568 7.15242i 0.535713 0.842920i
7373 −4.13040 −0.483426 −0.241713 0.970348i 0.577709π-0.577709\pi
−0.241713 + 0.970348i 0.577709π0.577709\pi
7474 4.15870 + 0.794262i 0.483440 + 0.0923311i
7575 0.0612154i 0.00706854i
7676 −11.5415 4.57547i −1.32390 0.524842i
7777 1.70400 0.194188
7878 −0.249580 0.0476668i −0.0282594 0.00539720i
7979 14.9553 1.68261 0.841304 0.540562i 0.181788π-0.181788\pi
0.841304 + 0.540562i 0.181788π0.181788\pi
8080 2.74075 2.91347i 0.306425 0.325736i
8181 8.96629 0.996254
8282 −2.18061 + 11.4175i −0.240808 + 1.26086i
8383 −8.73564 −0.958861 −0.479431 0.877580i 0.659157π-0.659157\pi
−0.479431 + 0.877580i 0.659157π0.659157\pi
8484 −0.0365870 + 0.0922896i −0.00399197 + 0.0100696i
8585 −4.65004 −0.504368
8686 2.69601 14.1162i 0.290719 1.52218i
8787 0.321015i 0.0344164i
8888 −3.18808 + 5.01630i −0.339850 + 0.534739i
8989 5.82961i 0.617938i 0.951072 + 0.308969i 0.0999839π0.0999839\pi
−0.951072 + 0.308969i 0.900016π0.900016\pi
9090 4.16211 + 0.794913i 0.438725 + 0.0837912i
9191 −2.37998 −0.249490
9292 −5.59198 7.79293i −0.583004 0.812469i
9393 −0.158114 −0.0163957
9494 −2.63161 0.502606i −0.271430 0.0518399i
9595 6.20768i 0.636895i
9696 −0.203234 0.280375i −0.0207425 0.0286157i
9797 2.73446i 0.277643i 0.990317 + 0.138821i 0.0443314π0.0443314\pi
−0.990317 + 0.138821i 0.955669π0.955669\pi
9898 1.68267 8.81035i 0.169975 0.889980i
9999 −6.29633 −0.632805
100100 1.85923 + 0.737066i 0.185923 + 0.0737066i
101101 −1.66981 −0.166152 −0.0830761 0.996543i 0.526474π-0.526474\pi
−0.0830761 + 0.996543i 0.526474π0.526474\pi
102102 −0.0755194 + 0.395414i −0.00747753 + 0.0391519i
103103 3.01723 0.297297 0.148648 0.988890i 0.452508π-0.452508\pi
0.148648 + 0.988890i 0.452508π0.452508\pi
104104 4.45281 7.00630i 0.436634 0.687024i
105105 −0.0496387 −0.00484424
106106 11.2808 + 2.15449i 1.09569 + 0.209263i
107107 −12.4870 −1.20716 −0.603580 0.797302i 0.706260π-0.706260\pi
−0.603580 + 0.797302i 0.706260π0.706260\pi
108108 0.270550 0.682454i 0.0260336 0.0656692i
109109 11.3533i 1.08745i −0.839263 0.543726i 0.817013π-0.817013\pi
0.839263 0.543726i 0.182987π-0.182987\pi
110110 −2.91907 0.557507i −0.278322 0.0531562i
111111 0.183267 0.0173949
112112 −2.36249 2.22243i −0.223234 0.210000i
113113 2.38506i 0.224367i −0.993687 0.112184i 0.964216π-0.964216\pi
0.993687 0.112184i 0.0357845π-0.0357845\pi
114114 −0.527868 0.100816i −0.0494394 0.00944232i
115115 2.59180 4.03517i 0.241686 0.376281i
116116 −9.74983 3.86519i −0.905249 0.358874i
117117 8.79413 0.813018
118118 18.1980 + 3.47560i 1.67526 + 0.319955i
119119 3.77065i 0.345655i
120120 0.0928711 0.146129i 0.00847793 0.0133396i
121121 −6.58411 −0.598556
122122 −19.0338 3.63523i −1.72324 0.329119i
123123 0.503150i 0.0453675i
124124 1.90378 4.80224i 0.170965 0.431254i
125125 1.00000i 0.0894427i
126126 0.644583 3.37500i 0.0574240 0.300668i
127127 6.12439i 0.543452i −0.962375 0.271726i 0.912406π-0.912406\pi
0.962375 0.271726i 0.0875945π-0.0875945\pi
128128 10.9626 2.79675i 0.968964 0.247200i
129129 0.622073i 0.0547705i
130130 4.07709 + 0.778674i 0.357584 + 0.0682942i
131131 15.4796i 1.35245i −0.736693 0.676227i 0.763614π-0.763614\pi
0.736693 0.676227i 0.236386π-0.236386\pi
132132 −0.0948148 + 0.239168i −0.00825257 + 0.0208169i
133133 −5.03372 −0.436479
134134 −0.377949 + 1.97892i −0.0326498 + 0.170952i
135135 0.367063 0.0315917
136136 −11.1002 7.05467i −0.951835 0.604933i
137137 17.6295i 1.50619i 0.657914 + 0.753093i 0.271439π0.271439\pi
−0.657914 + 0.753093i 0.728561π0.728561\pi
138138 −0.301037 0.285926i −0.0256259 0.0243396i
139139 2.39357i 0.203020i −0.994835 0.101510i 0.967633π-0.967633\pi
0.994835 0.101510i 0.0323674π-0.0323674\pi
140140 0.597676 1.50762i 0.0505128 0.127417i
141141 −0.115970 −0.00976647
142142 3.14139 + 0.599967i 0.263619 + 0.0503481i
143143 −6.16770 −0.515769
144144 8.72948 + 8.21198i 0.727457 + 0.684332i
145145 5.24402i 0.435492i
146146 1.09580 5.73756i 0.0906894 0.474843i
147147 0.388256i 0.0320228i
148148 −2.20663 + 5.56616i −0.181384 + 0.457536i
149149 0.398304i 0.0326303i −0.999867 0.0163152i 0.994806π-0.994806\pi
0.999867 0.0163152i 0.00519351π-0.00519351\pi
150150 0.0850346 + 0.0162406i 0.00694305 + 0.00132604i
151151 18.3711i 1.49502i 0.664249 + 0.747511i 0.268751π0.268751\pi
−0.664249 + 0.747511i 0.731249π0.731249\pi
152152 9.41780 14.8185i 0.763884 1.20194i
153153 13.9327i 1.12639i
154154 −0.452074 + 2.36703i −0.0364292 + 0.190741i
155155 2.58292 0.207465
156156 0.132429 0.334047i 0.0106028 0.0267452i
157157 18.5760i 1.48252i 0.671216 + 0.741261i 0.265772π0.265772\pi
−0.671216 + 0.741261i 0.734228π0.734228\pi
158158 −3.96769 + 20.7746i −0.315652 + 1.65274i
159159 0.497124 0.0394245
160160 3.31999 + 4.58014i 0.262468 + 0.362092i
161161 −3.27206 2.10165i −0.257874 0.165633i
162162 −2.37878 + 12.4551i −0.186894 + 0.978567i
163163 13.2878i 1.04078i 0.853928 + 0.520392i 0.174214π0.174214\pi
−0.853928 + 0.520392i 0.825786π0.825786\pi
164164 −15.2816 6.05820i −1.19330 0.473066i
165165 −0.128638 −0.0100145
166166 2.31759 12.1347i 0.179880 0.941838i
167167 4.05918i 0.314109i −0.987590 0.157054i 0.949800π-0.949800\pi
0.987590 0.157054i 0.0501998π-0.0501998\pi
168168 −0.118493 0.0753078i −0.00914197 0.00581012i
169169 −4.38552 −0.337348
170170 1.23367 6.45940i 0.0946179 0.495413i
171171 18.5998 1.42236
172172 18.8936 + 7.49010i 1.44062 + 0.571115i
173173 −18.4562 −1.40320 −0.701600 0.712571i 0.747531π-0.747531\pi
−0.701600 + 0.712571i 0.747531π0.747531\pi
174174 −0.445923 0.0851659i −0.0338053 0.00645641i
175175 0.810885 0.0612972
176176 −6.12236 5.75942i −0.461491 0.434132i
177177 0.801954 0.0602785
178178 −8.09795 1.54661i −0.606967 0.115923i
179179 8.67585i 0.648464i −0.945978 0.324232i 0.894894π-0.894894\pi
0.945978 0.324232i 0.105106π-0.105106\pi
180180 −2.20844 + 5.57072i −0.164607 + 0.415217i
181181 21.9722i 1.63318i 0.577218 + 0.816590i 0.304138π0.304138\pi
−0.577218 + 0.816590i 0.695862π0.695862\pi
182182 0.631415 3.30605i 0.0468036 0.245061i
183183 −0.838787 −0.0620049
184184 12.3088 5.70036i 0.907415 0.420236i
185185 −2.99380 −0.220109
186186 0.0419481 0.219638i 0.00307579 0.0161046i
187187 9.77160i 0.714570i
188188 1.39635 3.52225i 0.101839 0.256886i
189189 0.297646i 0.0216506i
190190 8.62312 + 1.64691i 0.625587 + 0.119480i
191191 −12.6841 −0.917792 −0.458896 0.888490i 0.651755π-0.651755\pi
−0.458896 + 0.888490i 0.651755π0.651755\pi
192192 0.443389 0.207930i 0.0319989 0.0150060i
193193 −15.3963 −1.10825 −0.554126 0.832433i 0.686947π-0.686947\pi
−0.554126 + 0.832433i 0.686947π0.686947\pi
194194 −3.79846 0.725460i −0.272713 0.0520850i
195195 0.179670 0.0128664
196196 11.7921 + 4.67482i 0.842293 + 0.333915i
197197 −9.62990 −0.686102 −0.343051 0.939317i 0.611460π-0.611460\pi
−0.343051 + 0.939317i 0.611460π0.611460\pi
198198 1.67043 8.74627i 0.118712 0.621570i
199199 2.04990 0.145313 0.0726567 0.997357i 0.476852π-0.476852\pi
0.0726567 + 0.997357i 0.476852π0.476852\pi
200200 −1.51712 + 2.38712i −0.107277 + 0.168795i
201201 0.0872072i 0.00615112i
202202 0.443004 2.31954i 0.0311697 0.163202i
203203 −4.25230 −0.298453
204204 −0.529237 0.209809i −0.0370540 0.0146896i
205205 8.21934i 0.574064i
206206 −0.800479 + 4.19125i −0.0557720 + 0.292019i
207207 12.0904 + 7.76568i 0.840340 + 0.539752i
208208 8.55115 + 8.04422i 0.592916 + 0.557766i
209209 −13.0448 −0.902330
210210 0.0131693 0.0689533i 0.000908765 0.00475823i
211211 4.14576i 0.285406i −0.989766 0.142703i 0.954421π-0.954421\pi
0.989766 0.142703i 0.0455793π-0.0455793\pi
212212 −5.98564 + 15.0986i −0.411095 + 1.03698i
213213 0.138435 0.00948543
214214 3.31282 17.3457i 0.226460 1.18573i
215215 10.1620i 0.693046i
216216 0.876223 + 0.556879i 0.0596195 + 0.0378908i
217217 2.09445i 0.142181i
218218 15.7710 + 3.01207i 1.06815 + 0.204003i
219219 0.252844i 0.0170856i
220220 1.54887 3.90699i 0.104425 0.263409i
221221 13.6481i 0.918068i
222222 −0.0486211 + 0.254577i −0.00326323 + 0.0170861i
223223 15.8065i 1.05848i 0.848472 + 0.529240i 0.177523π0.177523\pi
−0.848472 + 0.529240i 0.822477π0.822477\pi
224224 3.71397 2.69213i 0.248150 0.179875i
225225 −2.99625 −0.199750
226226 3.31310 + 0.632761i 0.220384 + 0.0420907i
227227 10.1465 0.673449 0.336725 0.941603i 0.390681π-0.390681\pi
0.336725 + 0.941603i 0.390681π0.390681\pi
228228 0.280089 0.706517i 0.0185494 0.0467903i
229229 12.6776i 0.837757i 0.908042 + 0.418878i 0.137577π0.137577\pi
−0.908042 + 0.418878i 0.862423π0.862423\pi
230230 4.91766 + 4.67082i 0.324261 + 0.307985i
231231 0.104311i 0.00686314i
232232 7.95581 12.5181i 0.522324 0.821854i
233233 13.5503 0.887710 0.443855 0.896099i 0.353611π-0.353611\pi
0.443855 + 0.896099i 0.353611π0.353611\pi
234234 −2.33310 + 12.2160i −0.152520 + 0.798583i
235235 1.89447 0.123581
236236 −9.65595 + 24.3569i −0.628549 + 1.58550i
237237 0.915497i 0.0594679i
238238 −5.23783 1.00036i −0.339518 0.0648438i
239239 10.8030i 0.698785i 0.936976 + 0.349392i 0.113612π0.113612\pi
−0.936976 + 0.349392i 0.886388π0.886388\pi
240240 0.178349 + 0.167776i 0.0115124 + 0.0108299i
241241 23.5923i 1.51971i 0.650090 + 0.759857i 0.274731π0.274731\pi
−0.650090 + 0.759857i 0.725269π0.725269\pi
242242 1.74678 9.14603i 0.112287 0.587929i
243243 1.65006i 0.105852i
244244 10.0995 25.4756i 0.646551 1.63091i
245245 6.34247i 0.405205i
246246 −0.698929 0.133487i −0.0445621 0.00851082i
247247 18.2198 1.15930
248248 6.16574 + 3.91860i 0.391525 + 0.248831i
249249 0.534756i 0.0338888i
250250 −1.38911 0.265302i −0.0878548 0.0167792i
251251 −3.93647 −0.248468 −0.124234 0.992253i 0.539647π-0.539647\pi
−0.124234 + 0.992253i 0.539647π0.539647\pi
252252 4.51722 + 1.79079i 0.284558 + 0.112809i
253253 −8.47951 5.44641i −0.533102 0.342413i
254254 8.50743 + 1.62482i 0.533804 + 0.101950i
255255 0.284654i 0.0178257i
256256 0.976582 + 15.9702i 0.0610364 + 0.998136i
257257 9.47781 0.591209 0.295605 0.955310i 0.404479π-0.404479\pi
0.295605 + 0.955310i 0.404479π0.404479\pi
258258 0.864126 + 0.165038i 0.0537981 + 0.0102748i
259259 2.42763i 0.150845i
260260 −2.16332 + 5.45692i −0.134163 + 0.338424i
261261 15.7124 0.972573
262262 21.5027 + 4.10676i 1.32844 + 0.253717i
263263 24.4123 1.50532 0.752662 0.658407i 0.228769π-0.228769\pi
0.752662 + 0.658407i 0.228769π0.228769\pi
264264 −0.307075 0.195160i −0.0188991 0.0120112i
265265 −8.12090 −0.498863
266266 1.33546 6.99236i 0.0818821 0.428729i
267267 −0.356862 −0.0218396
268268 −2.64865 1.05002i −0.161792 0.0641403i
269269 −2.11000 −0.128649 −0.0643245 0.997929i 0.520489π-0.520489\pi
−0.0643245 + 0.997929i 0.520489π0.520489\pi
270270 −0.0973827 + 0.509889i −0.00592652 + 0.0310309i
271271 25.7964i 1.56702i 0.621379 + 0.783510i 0.286573π0.286573\pi
−0.621379 + 0.783510i 0.713427π0.713427\pi
272272 12.7446 13.5477i 0.772755 0.821452i
273273 0.145692i 0.00881766i
274274 −24.4892 4.67714i −1.47944 0.282556i
275275 2.10140 0.126719
276276 0.477047 0.342315i 0.0287149 0.0206049i
277277 −6.05641 −0.363894 −0.181947 0.983308i 0.558240π-0.558240\pi
−0.181947 + 0.983308i 0.558240π0.558240\pi
278278 3.32492 + 0.635020i 0.199416 + 0.0380860i
279279 7.73908i 0.463327i
280280 1.93568 + 1.23021i 0.115679 + 0.0735192i
281281 27.0312i 1.61255i 0.591543 + 0.806274i 0.298519π0.298519\pi
−0.591543 + 0.806274i 0.701481π0.701481\pi
282282 0.0307672 0.161095i 0.00183216 0.00959308i
283283 −21.0525 −1.25144 −0.625720 0.780048i 0.715195π-0.715195\pi
−0.625720 + 0.780048i 0.715195π0.715195\pi
284284 −1.66684 + 4.20455i −0.0989085 + 0.249494i
285285 0.380006 0.0225096
286286 1.63631 8.56759i 0.0967568 0.506612i
287287 −6.66494 −0.393419
288288 −13.7233 + 9.94752i −0.808651 + 0.586163i
289289 −4.62287 −0.271934
290290 7.28450 + 1.39125i 0.427760 + 0.0816970i
291291 −0.167391 −0.00981265
292292 7.67935 + 3.04437i 0.449400 + 0.178159i
293293 19.4086i 1.13386i −0.823766 0.566931i 0.808131π-0.808131\pi
0.823766 0.566931i 0.191869π-0.191869\pi
294294 0.539329 + 0.103005i 0.0314543 + 0.00600739i
295295 −13.1005 −0.762742
296296 −7.14656 4.54196i −0.415385 0.263996i
297297 0.771347i 0.0447581i
298298 0.553286 + 0.105671i 0.0320510 + 0.00612136i
299299 11.8434 + 7.60704i 0.684921 + 0.439926i
300300 −0.0451198 + 0.113813i −0.00260499 + 0.00657102i
301301 8.24025 0.474960
302302 −25.5195 4.87391i −1.46848 0.280462i
303303 0.102218i 0.00587227i
304304 18.0859 + 17.0137i 1.03730 + 0.975803i
305305 13.7022 0.784588
306306 19.3540 + 3.69638i 1.10639 + 0.211308i
307307 24.0934i 1.37508i −0.726144 0.687542i 0.758690π-0.758690\pi
0.726144 0.687542i 0.241310π-0.241310\pi
308308 −3.16812 1.25596i −0.180520 0.0715648i
309309 0.184701i 0.0105073i
310310 −0.685255 + 3.58795i −0.0389199 + 0.203782i
311311 15.5862i 0.883811i −0.897062 0.441906i 0.854303π-0.854303\pi
0.897062 0.441906i 0.145697π-0.145697\pi
312312 0.428893 + 0.272581i 0.0242813 + 0.0154318i
313313 26.8531i 1.51783i −0.651191 0.758914i 0.725730π-0.725730\pi
0.651191 0.758914i 0.274270π-0.274270\pi
314314 −25.8040 4.92825i −1.45620 0.278117i
315315 2.42962i 0.136893i
316316 −27.8054 11.0231i −1.56418 0.620097i
317317 9.87979 0.554905 0.277452 0.960739i 0.410510π-0.410510\pi
0.277452 + 0.960739i 0.410510π0.410510\pi
318318 −0.131888 + 0.690557i −0.00739592 + 0.0387245i
319319 −11.0198 −0.616990
320320 −7.24310 + 3.39669i −0.404902 + 0.189881i
321321 0.764394i 0.0426643i
322322 3.78750 3.98766i 0.211069 0.222224i
323323 28.8660i 1.60615i
324324 −16.6704 6.60875i −0.926133 0.367153i
325325 −2.93504 −0.162807
326326 −18.4582 3.52530i −1.02231 0.195248i
327327 0.694999 0.0384335
328328 12.4697 19.6206i 0.688526 1.08336i
329329 1.53619i 0.0846931i
330330 0.0341280 0.178692i 0.00187868 0.00983667i
331331 16.4661i 0.905061i −0.891749 0.452531i 0.850521π-0.850521\pi
0.891749 0.452531i 0.149479π-0.149479\pi
332332 16.2416 + 6.43875i 0.891371 + 0.353372i
333333 8.97018i 0.491563i
334334 5.63863 + 1.07691i 0.308532 + 0.0589259i
335335 1.42460i 0.0778340i
336336 0.136047 0.144621i 0.00742198 0.00788970i
337337 6.50726i 0.354473i −0.984168 0.177237i 0.943284π-0.943284\pi
0.984168 0.177237i 0.0567158π-0.0567158\pi
338338 1.16349 6.09195i 0.0632855 0.331359i
339339 0.146002 0.00792975
340340 8.64549 + 3.42739i 0.468868 + 0.185876i
341341 5.42775i 0.293929i
342342 −4.93457 + 25.8371i −0.266831 + 1.39711i
343343 10.8192 0.584182
344344 −15.4170 + 24.2580i −0.831231 + 1.30791i
345345 0.247014 + 0.158658i 0.0132988 + 0.00854185i
346346 4.89648 25.6376i 0.263236 1.37829i
347347 3.84426i 0.206371i −0.994662 0.103185i 0.967097π-0.967097\pi
0.994662 0.103185i 0.0329035π-0.0329035\pi
348348 0.236609 0.596840i 0.0126836 0.0319940i
349349 7.73983 0.414304 0.207152 0.978309i 0.433581π-0.433581\pi
0.207152 + 0.978309i 0.433581π0.433581\pi
350350 −0.215130 + 1.12641i −0.0114992 + 0.0602089i
351351 1.07735i 0.0575044i
352352 9.62472 6.97663i 0.512999 0.371855i
353353 −21.2558 −1.13133 −0.565667 0.824634i 0.691381π-0.691381\pi
−0.565667 + 0.824634i 0.691381π0.691381\pi
354354 −0.212760 + 1.11400i −0.0113081 + 0.0592084i
355355 −2.26145 −0.120025
356356 4.29681 10.8386i 0.227730 0.574444i
357357 −0.230822 −0.0122164
358358 12.0517 + 2.30172i 0.636951 + 0.121650i
359359 −20.5153 −1.08275 −0.541377 0.840780i 0.682097π-0.682097\pi
−0.541377 + 0.840780i 0.682097π0.682097\pi
360360 −7.15242 4.54568i −0.376965 0.239578i
361361 19.5353 1.02817
362362 −30.5217 5.82927i −1.60418 0.306380i
363363 0.403049i 0.0211546i
364364 4.42493 + 1.75420i 0.231930 + 0.0919453i
365365 4.13040i 0.216195i
366366 0.222532 1.16516i 0.0116319 0.0609041i
367367 11.4965 0.600113 0.300057 0.953921i 0.402994π-0.402994\pi
0.300057 + 0.953921i 0.402994π0.402994\pi
368368 4.65286 + 18.6105i 0.242547 + 0.970140i
369369 24.6272 1.28204
370370 0.794262 4.15870i 0.0412917 0.216201i
371371 6.58511i 0.341882i
372372 0.293971 + 0.116541i 0.0152417 + 0.00604236i
373373 16.8099i 0.870386i 0.900337 + 0.435193i 0.143320π0.143320\pi
−0.900337 + 0.435193i 0.856680π0.856680\pi
374374 −13.5738 2.59243i −0.701884 0.134051i
375375 −0.0612154 −0.00316115
376376 4.52232 + 2.87413i 0.233221 + 0.148222i
377377 15.3914 0.792698
378378 0.413462 + 0.0789662i 0.0212662 + 0.00406158i
379379 4.04643 0.207851 0.103926 0.994585i 0.466860π-0.466860\pi
0.103926 + 0.994585i 0.466860π0.466860\pi
380380 −4.57547 + 11.5415i −0.234717 + 0.592067i
381381 0.374907 0.0192071
382382 3.36513 17.6196i 0.172175 0.901498i
383383 −11.0961 −0.566986 −0.283493 0.958974i 0.591493π-0.591493\pi
−0.283493 + 0.958974i 0.591493π0.591493\pi
384384 0.171204 + 0.671079i 0.00873672 + 0.0342458i
385385 1.70400i 0.0868437i
386386 4.08468 21.3871i 0.207905 1.08858i
387387 −30.4481 −1.54776
388388 2.01548 5.08399i 0.102321 0.258101i
389389 18.0429i 0.914809i −0.889259 0.457405i 0.848779π-0.848779\pi
0.889259 0.457405i 0.151221π-0.151221\pi
390390 −0.0476668 + 0.249580i −0.00241370 + 0.0126380i
391391 12.0520 18.7637i 0.609494 0.948921i
392392 −9.62228 + 15.1402i −0.485999 + 0.764697i
393393 0.947587 0.0477994
394394 2.55483 13.3769i 0.128711 0.673921i
395395 14.9553i 0.752485i
396396 11.7063 + 4.64081i 0.588265 + 0.233210i
397397 −26.5667 −1.33334 −0.666672 0.745351i 0.732282π-0.732282\pi
−0.666672 + 0.745351i 0.732282π0.732282\pi
398398 −0.543843 + 2.84753i −0.0272604 + 0.142734i
399399 0.308141i 0.0154263i
400400 −2.91347 2.74075i −0.145673 0.137037i
401401 0.934463i 0.0466649i −0.999728 0.0233324i 0.992572π-0.992572\pi
0.999728 0.0233324i 0.00742762π-0.00742762\pi
402402 −0.121140 0.0231363i −0.00604192 0.00115393i
403403 7.58098i 0.377636i
404404 3.10456 + 1.23076i 0.154458 + 0.0612326i
405405 8.96629i 0.445538i
406406 1.12814 5.90689i 0.0559889 0.293154i
407407 6.29118i 0.311842i
408408 0.431854 0.679503i 0.0213800 0.0336404i
409409 −15.7550 −0.779037 −0.389518 0.921019i 0.627359π-0.627359\pi
−0.389518 + 0.921019i 0.627359π0.627359\pi
410410 11.4175 + 2.18061i 0.563872 + 0.107693i
411411 −1.07919 −0.0532327
412412 −5.60973 2.22390i −0.276371 0.109564i
413413 10.6230i 0.522725i
414414 −13.9950 + 14.7346i −0.687815 + 0.724164i
415415 8.73564i 0.428816i
416416 −13.4429 + 9.74430i −0.659093 + 0.477754i
417417 0.146523 0.00717528
418418 3.46082 18.1206i 0.169274 0.886310i
419419 −24.9291 −1.21787 −0.608933 0.793222i 0.708402π-0.708402\pi
−0.608933 + 0.793222i 0.708402π0.708402\pi
420420 0.0922896 + 0.0365870i 0.00450327 + 0.00178526i
421421 16.2869i 0.793775i −0.917867 0.396888i 0.870090π-0.870090\pi
0.917867 0.396888i 0.129910π-0.129910\pi
422422 5.75889 + 1.09988i 0.280338 + 0.0535413i
423423 5.67630i 0.275991i
424424 −19.3856 12.3204i −0.941446 0.598330i
425425 4.65004i 0.225560i
426426 −0.0367272 + 0.192301i −0.00177944 + 0.00931703i
427427 11.1109i 0.537696i
428428 23.2161 + 9.20372i 1.12219 + 0.444879i
429429 0.377558i 0.0182287i
430430 −14.1162 2.69601i −0.680741 0.130013i
431431 24.5994 1.18491 0.592456 0.805603i 0.298158π-0.298158\pi
0.592456 + 0.805603i 0.298158π0.298158\pi
432432 −1.00603 + 1.06943i −0.0484025 + 0.0514528i
433433 2.41636i 0.116123i 0.998313 + 0.0580615i 0.0184920π0.0184920\pi
−0.998313 + 0.0580615i 0.981508π0.981508\pi
434434 2.90942 + 0.555663i 0.139656 + 0.0266727i
435435 0.321015 0.0153915
436436 −8.36816 + 21.1085i −0.400762 + 1.01091i
437437 25.0490 + 16.0891i 1.19826 + 0.769644i
438438 0.351227 + 0.0670800i 0.0167823 + 0.00320521i
439439 20.2396i 0.965984i 0.875625 + 0.482992i 0.160450π0.160450\pi
−0.875625 + 0.482992i 0.839550π0.839550\pi
440440 5.01630 + 3.18808i 0.239143 + 0.151986i
441441 −19.0036 −0.904935
442442 18.9586 + 3.62087i 0.901769 + 0.172227i
443443 16.4810i 0.783035i −0.920171 0.391517i 0.871950π-0.871950\pi
0.920171 0.391517i 0.128050π-0.128050\pi
444444 −0.340735 0.135080i −0.0161705 0.00641059i
445445 5.82961 0.276350
446446 −21.9569 4.19350i −1.03969 0.198568i
447447 0.0243823 0.00115324
448448 2.75433 + 5.87332i 0.130130 + 0.277488i
449449 28.5354 1.34667 0.673335 0.739337i 0.264861π-0.264861\pi
0.673335 + 0.739337i 0.264861π0.264861\pi
450450 0.794913 4.16211i 0.0374726 0.196204i
451451 −17.2721 −0.813313
452452 −1.75794 + 4.43437i −0.0826868 + 0.208575i
453453 −1.12460 −0.0528382
454454 −2.69190 + 14.0946i −0.126337 + 0.661493i
455455 2.37998i 0.111575i
456456 0.907119 + 0.576514i 0.0424797 + 0.0269978i
457457 4.16624i 0.194888i 0.995241 + 0.0974442i 0.0310667π0.0310667\pi
−0.995241 + 0.0974442i 0.968933π0.968933\pi
458458 −17.6105 3.36339i −0.822883 0.157161i
459459 1.70686 0.0796693
460460 −7.79293 + 5.59198i −0.363347 + 0.260727i
461461 −15.8725 −0.739255 −0.369628 0.929180i 0.620515π-0.620515\pi
−0.369628 + 0.929180i 0.620515π0.620515\pi
462462 −0.144899 0.0276739i −0.00674130 0.00128751i
463463 39.4302i 1.83248i −0.400632 0.916239i 0.631209π-0.631209\pi
0.400632 0.916239i 0.368791π-0.368791\pi
464464 15.2783 + 14.3725i 0.709276 + 0.667228i
465465 0.158114i 0.00733238i
466466 −3.59493 + 18.8228i −0.166532 + 0.871949i
467467 −11.3406 −0.524780 −0.262390 0.964962i 0.584511π-0.584511\pi
−0.262390 + 0.964962i 0.584511π0.584511\pi
468468 −16.3503 6.48186i −0.755793 0.299624i
469469 −1.15518 −0.0533415
470470 −0.502606 + 2.63161i −0.0231835 + 0.121387i
471471 −1.13713 −0.0523964
472472 −31.2725 19.8751i −1.43944 0.914825i
473473 21.3545 0.981883
474474 −1.27172 0.242884i −0.0584122 0.0111560i
475475 −6.20768 −0.284828
476476 2.77922 7.01050i 0.127385 0.321326i
477477 24.3323i 1.11410i
478478 −15.0064 2.86605i −0.686379 0.131090i
479479 −23.3114 −1.06512 −0.532562 0.846391i 0.678771π-0.678771\pi
−0.532562 + 0.846391i 0.678771π0.678771\pi
480480 −0.280375 + 0.203234i −0.0127973 + 0.00927633i
481481 8.78693i 0.400650i
482482 −32.7722 6.25910i −1.49273 0.285094i
483483 0.128653 0.200300i 0.00585393 0.00911398i
484484 12.2414 + 4.85292i 0.556426 + 0.220587i
485485 2.73446 0.124166
486486 −2.29211 0.437766i −0.103972 0.0198575i
487487 31.8314i 1.44242i 0.692718 + 0.721209i 0.256413π0.256413\pi
−0.692718 + 0.721209i 0.743587π0.743587\pi
488488 32.7089 + 20.7879i 1.48066 + 0.941026i
489489 −0.813420 −0.0367841
490490 −8.81035 1.68267i −0.398011 0.0760153i
491491 27.6085i 1.24595i 0.782241 + 0.622976i 0.214077π0.214077\pi
−0.782241 + 0.622976i 0.785923π0.785923\pi
492492 0.370855 0.935472i 0.0167194 0.0421743i
493493 24.3849i 1.09824i
494494 −4.83376 + 25.3092i −0.217481 + 1.13872i
495495 6.29633i 0.282999i
496496 −7.07914 + 7.52525i −0.317863 + 0.337894i
497497 1.83377i 0.0822560i
498498 0.742832 + 0.141872i 0.0332871 + 0.00635743i
499499 36.7032i 1.64306i −0.570165 0.821530i 0.693121π-0.693121\pi
0.570165 0.821530i 0.306879π-0.306879\pi
500500 0.737066 1.85923i 0.0329626 0.0831473i
501501 0.248484 0.0111015
502502 1.04436 5.46818i 0.0466119 0.244057i
503503 43.1029 1.92186 0.960932 0.276783i 0.0892683π-0.0892683\pi
0.960932 + 0.276783i 0.0892683π0.0892683\pi
504504 −3.68602 + 5.79979i −0.164188 + 0.258343i
505505 1.66981i 0.0743056i
506506 9.81527 10.3340i 0.436342 0.459402i
507507 0.268461i 0.0119228i
508508 −4.51408 + 11.3867i −0.200280 + 0.505201i
509509 6.26173 0.277546 0.138773 0.990324i 0.455684π-0.455684\pi
0.138773 + 0.990324i 0.455684π0.455684\pi
510510 0.395414 + 0.0755194i 0.0175092 + 0.00334405i
511511 3.34928 0.148163
512512 −22.4433 2.88035i −0.991865 0.127295i
513513 2.27861i 0.100603i
514514 −2.51448 + 13.1657i −0.110909 + 0.580713i
515515 3.01723i 0.132955i
516516 −0.458509 + 1.15658i −0.0201847 + 0.0509155i
517517 3.98103i 0.175086i
518518 −3.37223 0.644056i −0.148167 0.0282982i
519519 1.12980i 0.0495929i
520520 −7.00630 4.45281i −0.307247 0.195269i
521521 28.1514i 1.23334i −0.787223 0.616668i 0.788482π-0.788482\pi
0.787223 0.616668i 0.211518π-0.211518\pi
522522 −4.16854 + 21.8262i −0.182452 + 0.955306i
523523 27.1711 1.18811 0.594054 0.804425i 0.297526π-0.297526\pi
0.594054 + 0.804425i 0.297526π0.297526\pi
524524 −11.4095 + 28.7800i −0.498424 + 1.25726i
525525 0.0496387i 0.00216641i
526526 −6.47663 + 33.9112i −0.282395 + 1.47860i
527527 12.0107 0.523194
528528 0.352565 0.374783i 0.0153434 0.0163103i
529529 9.56516 + 20.9167i 0.415877 + 0.909421i
530530 2.15449 11.2808i 0.0935852 0.490006i
531531 39.2525i 1.70341i
532532 9.35883 + 3.71018i 0.405757 + 0.160857i
533533 24.1241 1.04493
534534 0.0946763 0.495719i 0.00409704 0.0214519i
535535 12.4870i 0.539859i
536536 2.16129 3.40068i 0.0933533 0.146887i
537537 0.531096 0.0229185
538538 0.559788 2.93101i 0.0241342 0.126365i
539539 13.3281 0.574080
540540 −0.682454 0.270550i −0.0293681 0.0116426i
541541 22.7074 0.976269 0.488134 0.872769i 0.337678π-0.337678\pi
0.488134 + 0.872769i 0.337678π0.337678\pi
542542 −35.8339 6.84385i −1.53920 0.293969i
543543 −1.34504 −0.0577210
544544 15.4381 + 21.2978i 0.661902 + 0.913137i
545545 −11.3533 −0.486324
546546 0.202381 + 0.0386523i 0.00866111 + 0.00165417i
547547 35.1637i 1.50349i −0.659454 0.751745i 0.729213π-0.729213\pi
0.659454 0.751745i 0.270787π-0.270787\pi
548548 12.9941 32.7772i 0.555079 1.40017i
549549 41.0553i 1.75220i
550550 −0.557507 + 2.91907i −0.0237722 + 0.124470i
551551 32.5532 1.38681
552552 0.348950 + 0.753486i 0.0148523 + 0.0320705i
553553 −12.1271 −0.515696
554554 1.60678 8.41299i 0.0682655 0.357434i
555555 0.183267i 0.00777923i
556556 −1.76422 + 4.45020i −0.0748196 + 0.188730i
557557 16.2425i 0.688219i 0.938930 + 0.344109i 0.111819π0.111819\pi
−0.938930 + 0.344109i 0.888181π0.888181\pi
558558 −10.7504 2.05320i −0.455101 0.0869188i
559559 −29.8260 −1.26151
560560 −2.22243 + 2.36249i −0.0939150 + 0.0998333i
561561 −0.598172 −0.0252549
562562 −37.5492 7.17145i −1.58392 0.302509i
563563 −30.7320 −1.29520 −0.647599 0.761981i 0.724227π-0.724227\pi
−0.647599 + 0.761981i 0.724227π0.724227\pi
564564 0.215616 + 0.0854779i 0.00907906 + 0.00359927i
565565 −2.38506 −0.100340
566566 5.58528 29.2441i 0.234767 1.22922i
567567 −7.27063 −0.305338
568568 −5.39835 3.43089i −0.226510 0.143957i
569569 27.0381i 1.13350i −0.823891 0.566748i 0.808201π-0.808201\pi
0.823891 0.566748i 0.191799π-0.191799\pi
570570 −0.100816 + 0.527868i −0.00422273 + 0.0221100i
571571 −35.8888 −1.50190 −0.750949 0.660360i 0.770404π-0.770404\pi
−0.750949 + 0.660360i 0.770404π0.770404\pi
572572 11.4672 + 4.54601i 0.479467 + 0.190078i
573573 0.776464i 0.0324373i
574574 1.76823 9.25831i 0.0738043 0.386434i
575575 −4.03517 2.59180i −0.168278 0.108085i
576576 −10.1773 21.7022i −0.424056 0.904257i
577577 13.0988 0.545309 0.272654 0.962112i 0.412098π-0.412098\pi
0.272654 + 0.962112i 0.412098π0.412098\pi
578578 1.22646 6.42166i 0.0510140 0.267106i
579579 0.942492i 0.0391686i
580580 −3.86519 + 9.74983i −0.160493 + 0.404840i
581581 7.08360 0.293877
582582 0.0444093 0.232524i 0.00184082 0.00963843i
583583 17.0653i 0.706771i
584584 −6.26631 + 9.85975i −0.259302 + 0.407999i
585585 8.79413i 0.363593i
586586 26.9606 + 5.14914i 1.11373 + 0.212709i
587587 22.9195i 0.945990i 0.881065 + 0.472995i 0.156827π0.156827\pi
−0.881065 + 0.472995i 0.843173π0.843173\pi
588588 −0.286171 + 0.721858i −0.0118015 + 0.0297689i
589589 16.0339i 0.660667i
590590 3.47560 18.1980i 0.143088 0.749201i
591591 0.589498i 0.0242487i
592592 8.20526 8.72234i 0.337234 0.358486i
593593 −17.0185 −0.698866 −0.349433 0.936961i 0.613626π-0.613626\pi
−0.349433 + 0.936961i 0.613626π0.613626\pi
594594 1.07148 + 0.204640i 0.0439634 + 0.00839648i
595595 3.77065 0.154582
596596 −0.293576 + 0.740538i −0.0120254 + 0.0303336i
597597 0.125485i 0.00513577i
598598 −13.7091 + 14.4336i −0.560605 + 0.590232i
599599 47.0562i 1.92266i 0.275391 + 0.961332i 0.411193π0.411193\pi
−0.275391 + 0.961332i 0.588807π0.588807\pi
600600 −0.146129 0.0928711i −0.00596567 0.00379145i
601601 −17.1272 −0.698633 −0.349316 0.937005i 0.613586π-0.613586\pi
−0.349316 + 0.937005i 0.613586π0.613586\pi
602602 −2.18616 + 11.4466i −0.0891012 + 0.466528i
603603 4.26845 0.173825
604604 13.5407 34.1562i 0.550965 1.38979i
605605 6.58411i 0.267682i
606606 0.141992 + 0.0271187i 0.00576802 + 0.00110162i
607607 4.02268i 0.163276i 0.996662 + 0.0816379i 0.0260151π0.0260151\pi
−0.996662 + 0.0816379i 0.973985π0.973985\pi
608608 −28.4321 + 20.6094i −1.15307 + 0.835822i
609609 0.260306i 0.0105481i
610610 −3.63523 + 19.0338i −0.147186 + 0.770658i
611611 5.56034i 0.224947i
612612 −10.2693 + 25.9041i −0.415113 + 1.04711i
613613 11.6582i 0.470870i 0.971890 + 0.235435i 0.0756515π0.0756515\pi
−0.971890 + 0.235435i 0.924348π0.924348\pi
614614 33.4683 + 6.39204i 1.35067 + 0.257962i
615615 0.503150 0.0202890
616616 2.58517 4.06764i 0.104159 0.163890i
617617 20.3418i 0.818928i −0.912326 0.409464i 0.865716π-0.865716\pi
0.912326 0.409464i 0.134284π-0.134284\pi
618618 −0.256569 0.0490016i −0.0103207 0.00197113i
619619 27.1446 1.09103 0.545516 0.838100i 0.316334π-0.316334\pi
0.545516 + 0.838100i 0.316334π0.316334\pi
620620 −4.80224 1.90378i −0.192863 0.0764578i
621621 −0.951353 + 1.48116i −0.0381765 + 0.0594369i
622622 21.6508 + 4.13505i 0.868120 + 0.165800i
623623 4.72715i 0.189389i
624624 −0.492430 + 0.523462i −0.0197130 + 0.0209553i
625625 1.00000 0.0400000
626626 37.3018 + 7.12420i 1.49088 + 0.284740i
627627 0.798544i 0.0318908i
628628 13.6917 34.5370i 0.546359 1.37818i
629629 −13.9213 −0.555078
630630 −3.37500 0.644583i −0.134463 0.0256808i
631631 −1.23029 −0.0489770 −0.0244885 0.999700i 0.507796π-0.507796\pi
−0.0244885 + 0.999700i 0.507796π0.507796\pi
632632 22.6891 35.7002i 0.902523 1.42008i
633633 0.253784 0.0100870
634634 −2.62113 + 13.7241i −0.104098 + 0.545053i
635635 −6.12439 −0.243039
636636 −0.924267 0.366413i −0.0366496 0.0145292i
637637 −18.6154 −0.737569
638638 2.92358 15.3077i 0.115745 0.606036i
639639 6.77587i 0.268049i
640640 −2.79675 10.9626i −0.110551 0.433334i
641641 24.7595i 0.977943i −0.872300 0.488971i 0.837372π-0.837372\pi
0.872300 0.488971i 0.162628π-0.162628\pi
642642 1.06182 + 0.202796i 0.0419069 + 0.00800371i
643643 24.5967 0.969999 0.485000 0.874514i 0.338820π-0.338820\pi
0.485000 + 0.874514i 0.338820π0.338820\pi
644644 4.53445 + 6.31917i 0.178682 + 0.249010i
645645 −0.622073 −0.0244941
646646 40.0979 + 7.65821i 1.57763 + 0.301308i
647647 15.0168i 0.590372i 0.955440 + 0.295186i 0.0953817π0.0953817\pi
−0.955440 + 0.295186i 0.904618π0.904618\pi
648648 13.6029 21.4036i 0.534374 0.840813i
649649 27.5295i 1.08063i
650650 0.778674 4.07709i 0.0305421 0.159916i
651651 0.128213 0.00502505
652652 9.79402 24.7051i 0.383563 0.967528i
653653 37.5839 1.47077 0.735385 0.677650i 0.237001π-0.237001\pi
0.735385 + 0.677650i 0.237001π0.237001\pi
654654 −0.184385 + 0.965427i −0.00721002 + 0.0377512i
655655 −15.4796 −0.604836
656656 23.9468 + 22.5272i 0.934965 + 0.879538i
657657 −12.3757 −0.482822
658658 2.13394 + 0.407556i 0.0831895 + 0.0158882i
659659 −11.1544 −0.434512 −0.217256 0.976115i 0.569711π-0.569711\pi
−0.217256 + 0.976115i 0.569711π0.569711\pi
660660 0.239168 + 0.0948148i 0.00930959 + 0.00369066i
661661 10.2362i 0.398141i 0.979985 + 0.199070i 0.0637922π0.0637922\pi
−0.979985 + 0.199070i 0.936208π0.936208\pi
662662 22.8732 + 4.36851i 0.888993 + 0.169787i
663663 0.835472 0.0324470
664664 −13.2530 + 20.8530i −0.514317 + 0.809255i
665665 5.03372i 0.195199i
666666 12.4605 + 2.37981i 0.482836 + 0.0922158i
667667 21.1605 + 13.5914i 0.819338 + 0.526263i
668668 −2.99188 + 7.54694i −0.115759 + 0.292000i
669669 −0.967600 −0.0374096
670670 1.97892 + 0.377949i 0.0764522 + 0.0146014i
671671 28.7939i 1.11158i
672672 0.164800 + 0.227352i 0.00635728 + 0.00877029i
673673 30.8981 1.19103 0.595517 0.803343i 0.296947π-0.296947\pi
0.595517 + 0.803343i 0.296947π0.296947\pi
674674 9.03927 + 1.72639i 0.348180 + 0.0664981i
675675 0.367063i 0.0141283i
676676 8.15369 + 3.23242i 0.313603 + 0.124324i
677677 9.44975i 0.363184i −0.983374 0.181592i 0.941875π-0.941875\pi
0.983374 0.181592i 0.0581249π-0.0581249\pi
678678 −0.0387347 + 0.202812i −0.00148760 + 0.00778897i
679679 2.21734i 0.0850936i
680680 −7.05467 + 11.1002i −0.270534 + 0.425674i
681681 0.621124i 0.0238015i
682682 7.53972 + 1.44000i 0.288711 + 0.0551403i
683683 44.7124i 1.71087i 0.517908 + 0.855436i 0.326711π0.326711\pi
−0.517908 + 0.855436i 0.673289π0.673289\pi
684684 −34.5813 13.7093i −1.32225 0.524187i
685685 17.6295 0.673587
686686 −2.87036 + 15.0290i −0.109591 + 0.573811i
687687 −0.776061 −0.0296086
688688 −29.6068 27.8516i −1.12875 1.06183i
689689 23.8352i 0.908048i
690690 −0.285926 + 0.301037i −0.0108850 + 0.0114603i
691691 8.99904i 0.342339i −0.985242 0.171170i 0.945245π-0.945245\pi
0.985242 0.171170i 0.0547546π-0.0547546\pi
692692 34.3143 + 13.6035i 1.30444 + 0.517126i
693693 5.10560 0.193946
694694 5.34008 + 1.01989i 0.202707 + 0.0387146i
695695 −2.39357 −0.0907933
696696 0.766300 + 0.487018i 0.0290465 + 0.0184604i
697697 38.2203i 1.44770i
698698 −2.05340 + 10.7514i −0.0777222 + 0.406948i
699699 0.829487i 0.0313741i
700700 −1.50762 0.597676i −0.0569827 0.0225900i
701701 21.2257i 0.801685i −0.916147 0.400842i 0.868717π-0.868717\pi
0.916147 0.400842i 0.131283π-0.131283\pi
702702 −1.49655 0.285822i −0.0564835 0.0107877i
703703 18.5846i 0.700930i
704704 7.13781 + 15.2207i 0.269016 + 0.573650i
705705 0.115970i 0.00436770i
706706 5.63922 29.5266i 0.212235 1.11125i
707707 1.35402 0.0509233
708708 −1.49102 0.591093i −0.0560358 0.0222146i
709709 22.2321i 0.834944i −0.908690 0.417472i 0.862916π-0.862916\pi
0.908690 0.417472i 0.137084π-0.137084\pi
710710 0.599967 3.14139i 0.0225164 0.117894i
711711 44.8100 1.68051
712712 13.9160 + 8.84422i 0.521524 + 0.331451i
713713 −6.69441 + 10.4225i −0.250708 + 0.390326i
714714 0.0612376 0.320636i 0.00229176 0.0119995i
715715 6.16770i 0.230659i
716716 −6.39468 + 16.1304i −0.238980 + 0.602821i
717717 −0.661307 −0.0246970
718718 5.44275 28.4979i 0.203122 1.06353i
719719 3.06420i 0.114275i −0.998366 0.0571377i 0.981803π-0.981803\pi
0.998366 0.0571377i 0.0181974π-0.0181974\pi
720720 8.21198 8.72948i 0.306042 0.325329i
721721 −2.44663 −0.0911172
722722 −5.18276 + 27.1366i −0.192882 + 1.00992i
723723 −1.44421 −0.0537108
724724 16.1950 40.8513i 0.601881 1.51823i
725725 −5.24402 −0.194758
726726 0.559877 + 0.106930i 0.0207790 + 0.00396854i
727727 −32.1935 −1.19399 −0.596995 0.802245i 0.703639π-0.703639\pi
−0.596995 + 0.802245i 0.703639π0.703639\pi
728728 −3.61072 + 5.68131i −0.133822 + 0.210563i
729729 26.7979 0.992513
730730 −5.73756 1.09580i −0.212356 0.0405575i
731731 47.2539i 1.74775i
732732 1.55950 + 0.618242i 0.0576407 + 0.0228509i
733733 32.2471i 1.19107i 0.803328 + 0.595536i 0.203060π0.203060\pi
−0.803328 + 0.595536i 0.796940π0.796940\pi
734734 −3.05005 + 15.9699i −0.112579 + 0.589459i
735735 −0.388256 −0.0143211
736736 −27.0864 + 1.52590i −0.998417 + 0.0562456i
737737 −2.99365 −0.110273
738738 −6.53366 + 34.2098i −0.240507 + 1.25928i
739739 9.69792i 0.356744i 0.983963 + 0.178372i 0.0570830π0.0570830\pi
−0.983963 + 0.178372i 0.942917π0.942917\pi
740740 5.56616 + 2.20663i 0.204616 + 0.0811173i
741741 1.11533i 0.0409728i
742742 −9.14742 1.74705i −0.335812 0.0641361i
743743 11.0808 0.406514 0.203257 0.979125i 0.434847π-0.434847\pi
0.203257 + 0.979125i 0.434847π0.434847\pi
744744 −0.239879 + 0.377438i −0.00879438 + 0.0138376i
745745 −0.398304 −0.0145927
746746 −23.3508 4.45972i −0.854933 0.163282i
747747 −26.1742 −0.957664
748748 7.20232 18.1676i 0.263343 0.664275i
749749 10.1255 0.369978
750750 0.0162406 0.0850346i 0.000593022 0.00310503i
751751 −12.5716 −0.458743 −0.229372 0.973339i 0.573667π-0.573667\pi
−0.229372 + 0.973339i 0.573667π0.573667\pi
752752 −5.19226 + 5.51946i −0.189342 + 0.201274i
753753 0.240973i 0.00878153i
754754 −4.08338 + 21.3803i −0.148708 + 0.778625i
755755 18.3711 0.668594
756756 −0.219385 + 0.553392i −0.00797894 + 0.0201267i
757757 53.8727i 1.95804i −0.203772 0.979018i 0.565320π-0.565320\pi
0.203772 0.979018i 0.434680π-0.434680\pi
758758 −1.07353 + 5.62092i −0.0389923 + 0.204161i
759759 0.333404 0.519076i 0.0121018 0.0188413i
760760 −14.8185 9.41780i −0.537523 0.341620i
761761 −19.8277 −0.718754 −0.359377 0.933192i 0.617011π-0.617011\pi
−0.359377 + 0.933192i 0.617011π0.617011\pi
762762 −0.0994638 + 0.520786i −0.00360319 + 0.0188661i
763763 9.20626i 0.333289i
764764 23.5827 + 9.34905i 0.853193 + 0.338237i
765765 −13.9327 −0.503738
766766 2.94383 15.4137i 0.106365 0.556919i
767767 38.4506i 1.38837i
768768 −0.977620 + 0.0597819i −0.0352768 + 0.00215719i
769769 24.6347i 0.888350i 0.895940 + 0.444175i 0.146503π0.146503\pi
−0.895940 + 0.444175i 0.853497π0.853497\pi
770770 2.36703 + 0.452074i 0.0853018 + 0.0162916i
771771 0.580188i 0.0208949i
772772 28.6253 + 11.3481i 1.03025 + 0.408427i
773773 14.1357i 0.508428i 0.967148 + 0.254214i 0.0818167π0.0818167\pi
−0.967148 + 0.254214i 0.918183π0.918183\pi
774774 8.07794 42.2956i 0.290356 1.52028i
775775 2.58292i 0.0927812i
776776 6.52749 + 4.14851i 0.234323 + 0.148923i
777777 −0.148608 −0.00533129
778778 25.0634 + 4.78681i 0.898568 + 0.171616i
779779 51.0231 1.82809
780780 −0.334047 0.132429i −0.0119608 0.00474170i
781781 4.75221i 0.170047i
782782 22.8673 + 21.7195i 0.817734 + 0.776688i
783783 1.92488i 0.0687898i
784784 −18.4786 17.3831i −0.659949 0.620825i
785785 18.5760 0.663004
786786 −0.251397 + 1.31630i −0.00896703 + 0.0469508i
787787 −11.4575 −0.408417 −0.204209 0.978927i 0.565462π-0.565462\pi
−0.204209 + 0.978927i 0.565462π0.565462\pi
788788 17.9042 + 7.09787i 0.637810 + 0.252851i
789789 1.49441i 0.0532023i
790790 20.7746 + 3.96769i 0.739126 + 0.141164i
791791 1.93401i 0.0687654i
792792 −9.55229 + 15.0301i −0.339426 + 0.534071i
793793 40.2166i 1.42813i
794794 7.04821 36.9040i 0.250132 1.30967i
795795 0.497124i 0.0176312i
796796 −3.81123 1.51091i −0.135086 0.0535528i
797797 13.6750i 0.484393i 0.970227 + 0.242197i 0.0778679π0.0778679\pi
−0.970227 + 0.242197i 0.922132π0.922132\pi
798798 0.428040 + 0.0817505i 0.0151525 + 0.00289394i
799799 8.80934 0.311652
800800 4.58014 3.31999i 0.161932 0.117379i
801801 17.4670i 0.617166i
802802 1.29807 + 0.247915i 0.0458364 + 0.00875420i
803803 8.67962 0.306297
804804 0.0642775 0.162138i 0.00226689 0.00571818i
805805 −2.10165 + 3.27206i −0.0740735 + 0.115325i
806806 −10.5308 2.01125i −0.370931 0.0708434i
807807 0.129164i 0.00454680i
808808 −2.53330 + 3.98604i −0.0891213 + 0.140228i
809809 −22.1172 −0.777598 −0.388799 0.921323i 0.627110π-0.627110\pi
−0.388799 + 0.921323i 0.627110π0.627110\pi
810810 12.4551 + 2.37878i 0.437628 + 0.0835817i
811811 52.1933i 1.83276i 0.400314 + 0.916378i 0.368901π0.368901\pi
−0.400314 + 0.916378i 0.631099π0.631099\pi
812812 7.90600 + 3.13422i 0.277446 + 0.109990i
813813 −1.57914 −0.0553828
814814 −8.73911 1.66906i −0.306306 0.0585007i
815815 13.2878 0.465453
816816 0.829330 + 0.780165i 0.0290324 + 0.0273112i
817817 −63.0827 −2.20699
818818 4.17985 21.8854i 0.146145 0.765206i
819819 −7.13103 −0.249178
820820 −6.05820 + 15.2816i −0.211561 + 0.533658i
821821 −30.4424 −1.06245 −0.531223 0.847232i 0.678267π-0.678267\pi
−0.531223 + 0.847232i 0.678267π0.678267\pi
822822 0.286313 1.49911i 0.00998630 0.0522876i
823823 13.7812i 0.480383i −0.970726 0.240191i 0.922790π-0.922790\pi
0.970726 0.240191i 0.0772102π-0.0772102\pi
824824 4.57751 7.20250i 0.159465 0.250911i
825825 0.128638i 0.00447860i
826826 −14.7565 2.81831i −0.513444 0.0980617i
827827 16.4113 0.570677 0.285339 0.958427i 0.407894π-0.407894\pi
0.285339 + 0.958427i 0.407894π0.407894\pi
828828 −16.7550 23.3496i −0.582276 0.811455i
829829 14.8055 0.514215 0.257108 0.966383i 0.417231π-0.417231\pi
0.257108 + 0.966383i 0.417231π0.417231\pi
830830 −12.1347 2.31759i −0.421203 0.0804446i
831831 0.370745i 0.0128610i
832832 −9.96943 21.2588i −0.345628 0.737017i
833833 29.4927i 1.02186i
834834 −0.0388730 + 0.203536i −0.00134606 + 0.00704789i
835835 −4.05918 −0.140474
836836 24.2533 + 9.61490i 0.838819 + 0.332538i
837837 −0.948094 −0.0327709
838838 6.61375 34.6291i 0.228468 1.19624i
839839 −52.1192 −1.79936 −0.899678 0.436554i 0.856199π-0.856199\pi
−0.899678 + 0.436554i 0.856199π0.856199\pi
840840 −0.0753078 + 0.118493i −0.00259837 + 0.00408841i
841841 −1.50027 −0.0517336
842842 22.6242 + 4.32095i 0.779683 + 0.148910i
843843 −1.65473 −0.0569918
844844 −3.05570 + 7.70791i −0.105181 + 0.265317i
845845 4.38552i 0.150867i
846846 −7.88498 1.50594i −0.271091 0.0517751i
847847 5.33896 0.183449
848848 22.2573 23.6600i 0.764320 0.812486i
849849 1.28874i 0.0442293i
850850 −6.45940 1.23367i −0.221556 0.0423144i
851851 7.75932 12.0805i 0.265986 0.414114i
852852 −0.257383 0.102036i −0.00881780 0.00349570i
853853 −55.0356 −1.88438 −0.942192 0.335074i 0.891239π-0.891239\pi
−0.942192 + 0.335074i 0.891239π0.891239\pi
854854 15.4343 + 2.94776i 0.528150 + 0.100870i
855855 18.5998i 0.636099i
856856 −18.9442 + 29.8079i −0.647501 + 1.01881i
857857 −12.5217 −0.427735 −0.213867 0.976863i 0.568606π-0.568606\pi
−0.213867 + 0.976863i 0.568606π0.568606\pi
858858 0.524469 + 0.100167i 0.0179051 + 0.00341965i
859859 19.8656i 0.677806i −0.940821 0.338903i 0.889944π-0.889944\pi
0.940821 0.338903i 0.110056π-0.110056\pi
860860 7.49010 18.8936i 0.255410 0.644265i
861861 0.407997i 0.0139045i
862862 −6.52628 + 34.1712i −0.222286 + 1.16388i
863863 14.6491i 0.498663i −0.968418 0.249331i 0.919789π-0.919789\pi
0.968418 0.249331i 0.0802108π-0.0802108\pi
864864 −1.21864 1.68120i −0.0414591 0.0571956i
865865 18.4562i 0.627530i
866866 −3.35658 0.641067i −0.114061 0.0217843i
867867 0.282991i 0.00961088i
868868 −1.54375 + 3.89407i −0.0523983 + 0.132173i
869869 −31.4272 −1.06609
870870 −0.0851659 + 0.445923i −0.00288740 + 0.0151182i
871871 4.18125 0.141676
872872 −27.1018 17.2244i −0.917783 0.583291i
873873 8.19314i 0.277296i
874874 −28.9950 + 30.5273i −0.980769 + 1.03260i
875875 0.810885i 0.0274129i
876876 −0.186363 + 0.470094i −0.00629661 + 0.0158830i
877877 −34.0401 −1.14945 −0.574726 0.818346i 0.694891π-0.694891\pi
−0.574726 + 0.818346i 0.694891π0.694891\pi
878878 −28.1150 5.36962i −0.948834 0.181216i
879879 1.18810 0.0400737
880880 −5.75942 + 6.12236i −0.194150 + 0.206385i
881881 3.90153i 0.131446i −0.997838 0.0657230i 0.979065π-0.979065\pi
0.997838 0.0657230i 0.0209354π-0.0209354\pi
882882 5.04171 26.3980i 0.169763 0.888869i
883883 34.1418i 1.14896i −0.818518 0.574481i 0.805204π-0.805204\pi
0.818518 0.574481i 0.194796π-0.194796\pi
884884 −10.0595 + 25.3749i −0.338339 + 0.853450i
885885 0.801954i 0.0269574i
886886 22.8938 + 4.37244i 0.769133 + 0.146895i
887887 21.0867i 0.708023i 0.935241 + 0.354012i 0.115183π0.115183\pi
−0.935241 + 0.354012i 0.884817π0.884817\pi
888888 0.278038 0.437479i 0.00933033 0.0146809i
889889 4.96618i 0.166560i
890890 −1.54661 + 8.09795i −0.0518425 + 0.271444i
891891 −18.8418 −0.631223
892892 11.6504 29.3879i 0.390085 0.983979i
893893 11.7602i 0.393541i
894894 −0.00646869 + 0.0338696i −0.000216345 + 0.00113277i
895895 −8.67585 −0.290002
896896 −8.88940 + 2.26784i −0.296974 + 0.0757633i
897897 −0.465668 + 0.724998i −0.0155482 + 0.0242070i
898898 −7.57052 + 39.6388i −0.252632 + 1.32276i
899899 13.5449i 0.451747i
900900 5.57072 + 2.20844i 0.185691 + 0.0736145i
901901 −37.7625 −1.25805
902902 4.58234 23.9928i 0.152575 0.798874i
903903 0.504430i 0.0167864i
904904 −5.69342 3.61842i −0.189360 0.120347i
905905 21.9722 0.730380
906906 0.298358 1.56218i 0.00991229 0.0519001i
907907 40.0954 1.33135 0.665673 0.746243i 0.268145π-0.268145\pi
0.665673 + 0.746243i 0.268145π0.268145\pi
908908 −18.8647 7.47867i −0.626048 0.248188i
909909 −5.00317 −0.165945
910910 −3.30605 0.631415i −0.109594 0.0209312i
911911 −43.9481 −1.45607 −0.728033 0.685542i 0.759565π-0.759565\pi
−0.728033 + 0.685542i 0.759565π0.759565\pi
912912 −1.04150 + 1.10713i −0.0344875 + 0.0366609i
913913 18.3571 0.607531
914914 −5.78734 1.10531i −0.191428 0.0365605i
915915 0.838787i 0.0277295i
916916 9.34420 23.5705i 0.308741 0.778791i
917917 12.5521i 0.414508i
918918 −0.452833 + 2.37101i −0.0149457 + 0.0782548i
919919 29.9313 0.987342 0.493671 0.869649i 0.335655π-0.335655\pi
0.493671 + 0.869649i 0.335655π0.335655\pi
920920 −5.70036 12.3088i −0.187935 0.405808i
921921 1.47489 0.0485992
922922 4.21101 22.0486i 0.138682 0.726131i
923923 6.63744i 0.218474i
924924 0.0768839 0.193938i 0.00252929 0.00638008i
925925 2.99380i 0.0984355i
926926 54.7728 + 10.4609i 1.79994 + 0.343768i
927927 9.04039 0.296925
928928 −24.0183 + 17.4101i −0.788441 + 0.571514i
929929 −29.9571 −0.982862 −0.491431 0.870917i 0.663526π-0.663526\pi
−0.491431 + 0.870917i 0.663526π0.663526\pi
930930 −0.219638 0.0419481i −0.00720220 0.00137553i
931931 −39.3720 −1.29037
932932 −25.1931 9.98747i −0.825228 0.327150i
933933 0.954114 0.0312363
934934 3.00869 15.7533i 0.0984472 0.515463i
935935 9.77160 0.319566
936936 13.3418 20.9927i 0.436089 0.686166i
937937 38.2177i 1.24852i 0.781218 + 0.624259i 0.214599π0.214599\pi
−0.781218 + 0.624259i 0.785401π0.785401\pi
938938 0.306473 1.60467i 0.0100067 0.0523944i
939939 1.64382 0.0536442
940940 −3.52225 1.39635i −0.114883 0.0455438i
941941 1.41138i 0.0460096i 0.999735 + 0.0230048i 0.00732330π0.00732330\pi
−0.999735 + 0.0230048i 0.992677π0.992677\pi
942942 0.301684 1.57960i 0.00982941 0.0514661i
943943 33.1664 + 21.3029i 1.08005 + 0.693717i
944944 35.9053 38.1680i 1.16862 1.24226i
945945 −0.297646 −0.00968242
946946 −5.66541 + 29.6637i −0.184198 + 0.964450i
947947 40.9764i 1.33155i 0.746150 + 0.665777i 0.231900π0.231900\pi
−0.746150 + 0.665777i 0.768100π0.768100\pi
948948 0.674782 1.70212i 0.0219159 0.0552823i
949949 −12.1229 −0.393526
950950 1.64691 8.62312i 0.0534329 0.279771i
951951 0.604795i 0.0196118i
952952 9.00099 + 5.72053i 0.291724 + 0.185403i
953953 33.8456i 1.09637i 0.836358 + 0.548184i 0.184681π0.184681\pi
−0.836358 + 0.548184i 0.815319π0.815319\pi
954954 33.8001 + 6.45541i 1.09432 + 0.209001i
955955 12.6841i 0.410449i
956956 7.96249 20.0852i 0.257525 0.649601i
957957 0.674581i 0.0218061i
958958 6.18456 32.3819i 0.199814 1.04621i
959959 14.2955i 0.461625i
960960 −0.207930 0.443389i −0.00671090 0.0143103i
961961 24.3285 0.784791
962962 12.2060 + 2.33119i 0.393536 + 0.0751607i
963963 −37.4141 −1.20565
964964 17.3891 43.8635i 0.560065 1.41275i
965965 15.3963i 0.495625i
966966 0.244106 + 0.231853i 0.00785399 + 0.00745976i
967967 13.1812i 0.423879i 0.977283 + 0.211940i 0.0679780π0.0679780\pi
−0.977283 + 0.211940i 0.932022π0.932022\pi
968968 −9.98889 + 15.7171i −0.321055 + 0.505166i
969969 1.76704 0.0567655
970970 −0.725460 + 3.79846i −0.0232931 + 0.121961i
971971 −43.9189 −1.40942 −0.704712 0.709494i 0.748924π-0.748924\pi
−0.704712 + 0.709494i 0.748924π0.748924\pi
972972 1.21621 3.06785i 0.0390098 0.0984012i
973973 1.94091i 0.0622228i
974974 −44.2171 8.44494i −1.41681 0.270593i
975975 0.179670i 0.00575404i
976976 −37.5544 + 39.9210i −1.20209 + 1.27784i
977977 40.2462i 1.28759i 0.765198 + 0.643795i 0.222641π0.222641\pi
−0.765198 + 0.643795i 0.777359π0.777359\pi
978978 0.215802 1.12993i 0.00690060 0.0361311i
979979 12.2504i 0.391523i
980980 4.67482 11.7921i 0.149332 0.376685i
981981 34.0175i 1.08609i
982982 −38.3511 7.32459i −1.22383 0.233737i
983983 −0.484037 −0.0154384 −0.00771919 0.999970i 0.502457π-0.502457\pi
−0.00771919 + 0.999970i 0.502457π0.502457\pi
984984 1.20108 + 0.763340i 0.0382890 + 0.0243344i
985985 9.62990i 0.306834i
986986 33.8732 + 6.46937i 1.07874 + 0.206027i
987987 0.0940387 0.00299329
988988 −33.8748 13.4292i −1.07770 0.427240i
989989 −41.0056 26.3380i −1.30390 0.837499i
990990 −8.74627 1.67043i −0.277975 0.0530898i
991991 16.2271i 0.515471i −0.966215 0.257736i 0.917024π-0.917024\pi
0.966215 0.257736i 0.0829764π-0.0829764\pi
992992 −8.57526 11.8301i −0.272265 0.375607i
993993 1.00798 0.0319873
994994 −2.54731 0.486505i −0.0807956 0.0154310i
995995 2.04990i 0.0649862i
996996 −0.394150 + 0.994233i −0.0124891 + 0.0315035i
997997 36.2944 1.14946 0.574728 0.818345i 0.305108π-0.305108\pi
0.574728 + 0.818345i 0.305108π0.305108\pi
998998 50.9846 + 9.73744i 1.61389 + 0.308233i
999999 1.09891 0.0347681
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 460.2.e.b.91.11 yes 32
4.3 odd 2 inner 460.2.e.b.91.9 32
23.22 odd 2 inner 460.2.e.b.91.12 yes 32
92.91 even 2 inner 460.2.e.b.91.10 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.e.b.91.9 32 4.3 odd 2 inner
460.2.e.b.91.10 yes 32 92.91 even 2 inner
460.2.e.b.91.11 yes 32 1.1 even 1 trivial
460.2.e.b.91.12 yes 32 23.22 odd 2 inner