Properties

Label 891.2.n.l.433.6
Level 891891
Weight 22
Character 891.433
Analytic conductor 7.1157.115
Analytic rank 00
Dimension 9696
Inner twists 88

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [891,2,Mod(136,891)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(891, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("891.136");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 891=3411 891 = 3^{4} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 891.n (of order 1515, degree 88, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 7.114670820107.11467082010
Analytic rank: 00
Dimension: 9696
Relative dimension: 1212 over Q(ζ15)\Q(\zeta_{15})
Twist minimal: yes
Sato-Tate group: SU(2)[C15]\mathrm{SU}(2)[C_{15}]

Embedding invariants

Embedding label 433.6
Character χ\chi == 891.433
Dual form 891.2.n.l.784.6

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+(0.0658016+0.626061i)q2+(1.56867+0.333432i)q4+(0.1428681.35930i)q5+(0.393445+0.436965i)q7+(0.701028+2.15754i)q8+0.860404q10+(0.9270903.18442i)q11+(3.471391.54556i)q13+(0.2476770.275073i)q14+(1.62551+0.723726i)q16+(0.156539+0.113732i)q17+(0.601281+1.85055i)q19+(0.2291202.17993i)q20+(1.93263+0.789954i)q22+(0.1606160.278195i)q23+(3.063460.651158i)q25+(0.739193+2.27500i)q26+(0.762884+0.554268i)q28+(2.791223.09996i)q29+(5.148372.29220i)q31+(2.82863+4.89933i)q32+(0.06090290.105487i)q34+(0.650176+0.472381i)q35+(3.17822+9.78156i)q37+(1.118990.498208i)q38+(3.03290+0.644662i)q40+(4.590785.09857i)q41+(3.405445.89840i)q43+(2.516094.68619i)q44+(0.163598+0.118861i)q46+(4.976661.05782i)q47+(0.695560+6.61781i)q49+(0.206084+1.96076i)q50+(5.960821.26701i)q52+(6.36368+4.62348i)q53+(4.461020.805240i)q55+(0.6669541.15520i)q56+(1.75710+1.95146i)q58+(7.047191.49793i)q59+(7.890613.51312i)q61+(1.09629+3.37402i)q62+(0.002108880.00153219i)q64+(2.596834.49784i)q65+(4.548707.87858i)q67+(0.283481+0.126214i)q68+(0.338522+0.375966i)q70+(2.31775+1.68394i)q71+(0.131206+0.403812i)q73+(6.33298+1.34612i)q74+(1.56025+2.70242i)q76+(1.02672+1.65800i)q77+(0.4291384.08298i)q79+(0.7515252.31296i)q80+(3.494102.53861i)q82+(6.79686+3.02616i)q83+(0.176961+0.196535i)q85+(3.916841.74389i)q86+(6.22060+4.23260i)q883.38915q89+(0.690444+2.12497i)q91+(0.3447130.382842i)q92+(0.334788+3.18530i)q94+(2.60135+0.552935i)q95+(0.675694+6.42880i)q974.18892q98+O(q100)q+(-0.0658016 + 0.626061i) q^{2} +(1.56867 + 0.333432i) q^{4} +(-0.142868 - 1.35930i) q^{5} +(-0.393445 + 0.436965i) q^{7} +(-0.701028 + 2.15754i) q^{8} +0.860404 q^{10} +(0.927090 - 3.18442i) q^{11} +(3.47139 - 1.54556i) q^{13} +(-0.247677 - 0.275073i) q^{14} +(1.62551 + 0.723726i) q^{16} +(-0.156539 + 0.113732i) q^{17} +(-0.601281 + 1.85055i) q^{19} +(0.229120 - 2.17993i) q^{20} +(1.93263 + 0.789954i) q^{22} +(0.160616 - 0.278195i) q^{23} +(3.06346 - 0.651158i) q^{25} +(0.739193 + 2.27500i) q^{26} +(-0.762884 + 0.554268i) q^{28} +(2.79122 - 3.09996i) q^{29} +(5.14837 - 2.29220i) q^{31} +(-2.82863 + 4.89933i) q^{32} +(-0.0609029 - 0.105487i) q^{34} +(0.650176 + 0.472381i) q^{35} +(3.17822 + 9.78156i) q^{37} +(-1.11899 - 0.498208i) q^{38} +(3.03290 + 0.644662i) q^{40} +(-4.59078 - 5.09857i) q^{41} +(-3.40544 - 5.89840i) q^{43} +(2.51609 - 4.68619i) q^{44} +(0.163598 + 0.118861i) q^{46} +(4.97666 - 1.05782i) q^{47} +(0.695560 + 6.61781i) q^{49} +(0.206084 + 1.96076i) q^{50} +(5.96082 - 1.26701i) q^{52} +(6.36368 + 4.62348i) q^{53} +(-4.46102 - 0.805240i) q^{55} +(-0.666954 - 1.15520i) q^{56} +(1.75710 + 1.95146i) q^{58} +(-7.04719 - 1.49793i) q^{59} +(-7.89061 - 3.51312i) q^{61} +(1.09629 + 3.37402i) q^{62} +(-0.00210888 - 0.00153219i) q^{64} +(-2.59683 - 4.49784i) q^{65} +(4.54870 - 7.87858i) q^{67} +(-0.283481 + 0.126214i) q^{68} +(-0.338522 + 0.375966i) q^{70} +(-2.31775 + 1.68394i) q^{71} +(0.131206 + 0.403812i) q^{73} +(-6.33298 + 1.34612i) q^{74} +(-1.56025 + 2.70242i) q^{76} +(1.02672 + 1.65800i) q^{77} +(0.429138 - 4.08298i) q^{79} +(0.751525 - 2.31296i) q^{80} +(3.49410 - 2.53861i) q^{82} +(6.79686 + 3.02616i) q^{83} +(0.176961 + 0.196535i) q^{85} +(3.91684 - 1.74389i) q^{86} +(6.22060 + 4.23260i) q^{88} -3.38915 q^{89} +(-0.690444 + 2.12497i) q^{91} +(0.344713 - 0.382842i) q^{92} +(0.334788 + 3.18530i) q^{94} +(2.60135 + 0.552935i) q^{95} +(-0.675694 + 6.42880i) q^{97} -4.18892 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 96q+8q4+14q7+64q10+14q13+4q1616q1916q22+20q2536q28+4q3184q3424q37+106q4084q4376q46+54q4952q52++66q97+O(q100) 96 q + 8 q^{4} + 14 q^{7} + 64 q^{10} + 14 q^{13} + 4 q^{16} - 16 q^{19} - 16 q^{22} + 20 q^{25} - 36 q^{28} + 4 q^{31} - 84 q^{34} - 24 q^{37} + 106 q^{40} - 84 q^{43} - 76 q^{46} + 54 q^{49} - 52 q^{52}+ \cdots + 66 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

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

nn 244244 650650
χ(n)\chi(n) e(15)e\left(\frac{1}{5}\right) e(13)e\left(\frac{1}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.0658016 + 0.626061i −0.0465288 + 0.442692i 0.946313 + 0.323253i 0.104776π0.104776\pi
−0.992842 + 0.119439i 0.961890π0.961890\pi
33 0 0
44 1.56867 + 0.333432i 0.784336 + 0.166716i
55 −0.142868 1.35930i −0.0638925 0.607896i −0.978883 0.204421i 0.934469π-0.934469\pi
0.914991 0.403475i 0.132198π-0.132198\pi
66 0 0
77 −0.393445 + 0.436965i −0.148708 + 0.165157i −0.812897 0.582408i 0.802111π-0.802111\pi
0.664188 + 0.747565i 0.268777π0.268777\pi
88 −0.701028 + 2.15754i −0.247851 + 0.762806i
99 0 0
1010 0.860404 0.272084
1111 0.927090 3.18442i 0.279528 0.960138i
1212 0 0
1313 3.47139 1.54556i 0.962791 0.428662i 0.135712 0.990748i 0.456668π-0.456668\pi
0.827079 + 0.562086i 0.190001π0.190001\pi
1414 −0.247677 0.275073i −0.0661945 0.0735165i
1515 0 0
1616 1.62551 + 0.723726i 0.406379 + 0.180931i
1717 −0.156539 + 0.113732i −0.0379663 + 0.0275842i −0.606607 0.795002i 0.707470π-0.707470\pi
0.568640 + 0.822586i 0.307470π0.307470\pi
1818 0 0
1919 −0.601281 + 1.85055i −0.137943 + 0.424546i −0.996036 0.0889487i 0.971649π-0.971649\pi
0.858093 + 0.513494i 0.171649π0.171649\pi
2020 0.229120 2.17993i 0.0512328 0.487447i
2121 0 0
2222 1.93263 + 0.789954i 0.412039 + 0.168419i
2323 0.160616 0.278195i 0.0334907 0.0580076i −0.848794 0.528723i 0.822671π-0.822671\pi
0.882285 + 0.470716i 0.156004π0.156004\pi
2424 0 0
2525 3.06346 0.651158i 0.612692 0.130232i
2626 0.739193 + 2.27500i 0.144968 + 0.446165i
2727 0 0
2828 −0.762884 + 0.554268i −0.144172 + 0.104747i
2929 2.79122 3.09996i 0.518316 0.575649i −0.425985 0.904730i 0.640072π-0.640072\pi
0.944301 + 0.329082i 0.106739π0.106739\pi
3030 0 0
3131 5.14837 2.29220i 0.924674 0.411692i 0.111535 0.993761i 0.464423π-0.464423\pi
0.813139 + 0.582069i 0.197757π0.197757\pi
3232 −2.82863 + 4.89933i −0.500036 + 0.866088i
3333 0 0
3434 −0.0609029 0.105487i −0.0104448 0.0180908i
3535 0.650176 + 0.472381i 0.109900 + 0.0798469i
3636 0 0
3737 3.17822 + 9.78156i 0.522496 + 1.60808i 0.769214 + 0.638991i 0.220648π0.220648\pi
−0.246718 + 0.969087i 0.579352π0.579352\pi
3838 −1.11899 0.498208i −0.181525 0.0808199i
3939 0 0
4040 3.03290 + 0.644662i 0.479543 + 0.101930i
4141 −4.59078 5.09857i −0.716959 0.796263i 0.269020 0.963135i 0.413300π-0.413300\pi
−0.985979 + 0.166871i 0.946634π0.946634\pi
4242 0 0
4343 −3.40544 5.89840i −0.519325 0.899497i −0.999748 0.0224601i 0.992850π-0.992850\pi
0.480423 0.877037i 0.340483π-0.340483\pi
4444 2.51609 4.68619i 0.379314 0.706469i
4545 0 0
4646 0.163598 + 0.118861i 0.0241212 + 0.0175251i
4747 4.97666 1.05782i 0.725920 0.154299i 0.169892 0.985463i 0.445658π-0.445658\pi
0.556028 + 0.831163i 0.312325π0.312325\pi
4848 0 0
4949 0.695560 + 6.61781i 0.0993657 + 0.945401i
5050 0.206084 + 1.96076i 0.0291447 + 0.277293i
5151 0 0
5252 5.96082 1.26701i 0.826616 0.175703i
5353 6.36368 + 4.62348i 0.874119 + 0.635084i 0.931689 0.363257i 0.118335π-0.118335\pi
−0.0575702 + 0.998341i 0.518335π0.518335\pi
5454 0 0
5555 −4.46102 0.805240i −0.601524 0.108579i
5656 −0.666954 1.15520i −0.0891255 0.154370i
5757 0 0
5858 1.75710 + 1.95146i 0.230718 + 0.256239i
5959 −7.04719 1.49793i −0.917465 0.195013i −0.275103 0.961415i 0.588712π-0.588712\pi
−0.642362 + 0.766401i 0.722045π0.722045\pi
6060 0 0
6161 −7.89061 3.51312i −1.01029 0.449809i −0.166245 0.986084i 0.553164π-0.553164\pi
−0.844043 + 0.536275i 0.819831π0.819831\pi
6262 1.09629 + 3.37402i 0.139229 + 0.428501i
6363 0 0
6464 −0.00210888 0.00153219i −0.000263611 0.000191524i
6565 −2.59683 4.49784i −0.322097 0.557889i
6666 0 0
6767 4.54870 7.87858i 0.555712 0.962522i −0.442135 0.896948i 0.645779π-0.645779\pi
0.997848 0.0655738i 0.0208878π-0.0208878\pi
6868 −0.283481 + 0.126214i −0.0343771 + 0.0153057i
6969 0 0
7070 −0.338522 + 0.375966i −0.0404611 + 0.0449366i
7171 −2.31775 + 1.68394i −0.275066 + 0.199847i −0.716763 0.697317i 0.754377π-0.754377\pi
0.441696 + 0.897165i 0.354377π0.354377\pi
7272 0 0
7373 0.131206 + 0.403812i 0.0153565 + 0.0472626i 0.958441 0.285290i 0.0920900π-0.0920900\pi
−0.943085 + 0.332553i 0.892090π0.892090\pi
7474 −6.33298 + 1.34612i −0.736194 + 0.156483i
7575 0 0
7676 −1.56025 + 2.70242i −0.178972 + 0.309989i
7777 1.02672 + 1.65800i 0.117005 + 0.188946i
7878 0 0
7979 0.429138 4.08298i 0.0482818 0.459371i −0.943495 0.331388i 0.892483π-0.892483\pi
0.991776 0.127983i 0.0408502π-0.0408502\pi
8080 0.751525 2.31296i 0.0840230 0.258596i
8181 0 0
8282 3.49410 2.53861i 0.385859 0.280343i
8383 6.79686 + 3.02616i 0.746052 + 0.332164i 0.744310 0.667835i 0.232779π-0.232779\pi
0.00174242 + 0.999998i 0.499445π0.499445\pi
8484 0 0
8585 0.176961 + 0.196535i 0.0191941 + 0.0213172i
8686 3.91684 1.74389i 0.422364 0.188048i
8787 0 0
8888 6.22060 + 4.23260i 0.663118 + 0.451197i
8989 −3.38915 −0.359249 −0.179625 0.983735i 0.557488π-0.557488\pi
−0.179625 + 0.983735i 0.557488π0.557488\pi
9090 0 0
9191 −0.690444 + 2.12497i −0.0723782 + 0.222757i
9292 0.344713 0.382842i 0.0359388 0.0399141i
9393 0 0
9494 0.334788 + 3.18530i 0.0345308 + 0.328538i
9595 2.60135 + 0.552935i 0.266893 + 0.0567299i
9696 0 0
9797 −0.675694 + 6.42880i −0.0686063 + 0.652746i 0.905141 + 0.425112i 0.139765π0.139765\pi
−0.973747 + 0.227633i 0.926901π0.926901\pi
9898 −4.18892 −0.423145
9999 0 0
100100 5.02268 0.502268
101101 −1.93351 + 18.3961i −0.192391 + 1.83048i 0.292921 + 0.956137i 0.405373π0.405373\pi
−0.485312 + 0.874341i 0.661294π0.661294\pi
102102 0 0
103103 −3.16596 0.672945i −0.311951 0.0663072i 0.0492758 0.998785i 0.484309π-0.484309\pi
−0.361227 + 0.932478i 0.617642π0.617642\pi
104104 0.901075 + 8.57316i 0.0883577 + 0.840667i
105105 0 0
106106 −3.31332 + 3.67982i −0.321818 + 0.357416i
107107 −5.21311 + 16.0443i −0.503970 + 1.55106i 0.298524 + 0.954402i 0.403506π0.403506\pi
−0.802495 + 0.596659i 0.796494π0.796494\pi
108108 0 0
109109 8.90745 0.853179 0.426589 0.904445i 0.359715π-0.359715\pi
0.426589 + 0.904445i 0.359715π0.359715\pi
110110 0.797672 2.73988i 0.0760550 0.261238i
111111 0 0
112112 −0.955793 + 0.425547i −0.0903140 + 0.0402104i
113113 −1.93074 2.14430i −0.181629 0.201719i 0.645454 0.763799i 0.276668π-0.276668\pi
−0.827083 + 0.562080i 0.810001π0.810001\pi
114114 0 0
115115 −0.401097 0.178580i −0.0374024 0.0166526i
116116 5.41213 3.93215i 0.502504 0.365091i
117117 0 0
118118 1.40151 4.31340i 0.129019 0.397081i
119119 0.0118925 0.113150i 0.00109018 0.0103724i
120120 0 0
121121 −9.28101 5.90448i −0.843728 0.536771i
122122 2.71864 4.70883i 0.246134 0.426317i
123123 0 0
124124 8.84040 1.87908i 0.793891 0.168747i
125125 −3.43459 10.5706i −0.307199 0.945461i
126126 0 0
127127 1.03914 0.754980i 0.0922088 0.0669936i −0.540726 0.841199i 0.681850π-0.681850\pi
0.632934 + 0.774205i 0.281850π0.281850\pi
128128 −7.56980 + 8.40711i −0.669082 + 0.743091i
129129 0 0
130130 2.98680 1.32981i 0.261960 0.116632i
131131 −3.16899 + 5.48885i −0.276876 + 0.479563i −0.970607 0.240671i 0.922632π-0.922632\pi
0.693731 + 0.720234i 0.255966π0.255966\pi
132132 0 0
133133 −0.572055 0.990829i −0.0496035 0.0859157i
134134 4.63316 + 3.36619i 0.400244 + 0.290794i
135135 0 0
136136 −0.135644 0.417470i −0.0116314 0.0357977i
137137 15.1320 + 6.73719i 1.29281 + 0.575597i 0.933820 0.357744i 0.116454π-0.116454\pi
0.358992 + 0.933341i 0.383121π0.383121\pi
138138 0 0
139139 −17.0679 3.62789i −1.44768 0.307713i −0.583998 0.811755i 0.698513π-0.698513\pi
−0.863679 + 0.504041i 0.831846π0.831846\pi
140140 0.862407 + 0.957800i 0.0728867 + 0.0809489i
141141 0 0
142142 −0.901739 1.56186i −0.0756723 0.131068i
143143 −1.70342 12.4872i −0.142447 1.04423i
144144 0 0
145145 −4.61255 3.35121i −0.383051 0.278303i
146146 −0.261444 + 0.0555717i −0.0216373 + 0.00459915i
147147 0 0
148148 1.72411 + 16.4038i 0.141721 + 1.34838i
149149 −0.659140 6.27130i −0.0539989 0.513765i −0.987773 0.155901i 0.950172π-0.950172\pi
0.933774 0.357864i 0.116495π-0.116495\pi
150150 0 0
151151 −15.8769 + 3.37473i −1.29204 + 0.274632i −0.802135 0.597143i 0.796302π-0.796302\pi
−0.489907 + 0.871775i 0.662969π0.662969\pi
152152 −3.57113 2.59458i −0.289657 0.210448i
153153 0 0
154154 −1.10557 + 0.533690i −0.0890892 + 0.0430059i
155155 −3.85132 6.67068i −0.309346 0.535802i
156156 0 0
157157 −11.4048 12.6663i −0.910202 1.01088i −0.999889 0.0149120i 0.995253π-0.995253\pi
0.0896865 0.995970i 0.471413π-0.471413\pi
158158 2.52795 + 0.537333i 0.201113 + 0.0427479i
159159 0 0
160160 7.06378 + 3.14500i 0.558440 + 0.248634i
161161 0.0583679 + 0.179638i 0.00460003 + 0.0141574i
162162 0 0
163163 −15.0263 10.9173i −1.17695 0.855105i −0.185127 0.982715i 0.559270π-0.559270\pi
−0.991824 + 0.127609i 0.959270π0.959270\pi
164164 −5.50140 9.52870i −0.429587 0.744067i
165165 0 0
166166 −2.34180 + 4.05612i −0.181759 + 0.314816i
167167 8.64837 3.85050i 0.669231 0.297961i −0.0438545 0.999038i 0.513964π-0.513964\pi
0.713085 + 0.701077i 0.247297π0.247297\pi
168168 0 0
169169 0.963092 1.06962i 0.0740840 0.0822786i
170170 −0.134687 + 0.0978558i −0.0103300 + 0.00750520i
171171 0 0
172172 −3.37531 10.3881i −0.257365 0.792088i
173173 −17.5754 + 3.73576i −1.33623 + 0.284025i −0.819970 0.572406i 0.806010π-0.806010\pi
−0.516261 + 0.856431i 0.672677π0.672677\pi
174174 0 0
175175 −0.920769 + 1.59482i −0.0696036 + 0.120557i
176176 3.81164 4.50536i 0.287313 0.339604i
177177 0 0
178178 0.223012 2.12182i 0.0167154 0.159037i
179179 8.17595 25.1630i 0.611099 1.88077i 0.163474 0.986548i 0.447730π-0.447730\pi
0.447625 0.894221i 0.352270π-0.352270\pi
180180 0 0
181181 0.711098 0.516643i 0.0528555 0.0384018i −0.561044 0.827786i 0.689600π-0.689600\pi
0.613899 + 0.789384i 0.289600π0.289600\pi
182182 −1.28493 0.572087i −0.0952452 0.0424059i
183183 0 0
184184 0.487621 + 0.541558i 0.0359479 + 0.0399242i
185185 12.8420 5.71762i 0.944161 0.420368i
186186 0 0
187187 0.217045 + 0.603926i 0.0158719 + 0.0441635i
188188 8.15946 0.595090
189189 0 0
190190 −0.517344 + 1.59222i −0.0375321 + 0.115512i
191191 10.3859 11.5347i 0.751496 0.834621i −0.239163 0.970979i 0.576873π-0.576873\pi
0.990660 + 0.136358i 0.0435398π0.0435398\pi
192192 0 0
193193 −1.01127 9.62158i −0.0727927 0.692577i −0.968683 0.248301i 0.920128π-0.920128\pi
0.895890 0.444276i 0.146539π-0.146539\pi
194194 −3.98036 0.846051i −0.285773 0.0607429i
195195 0 0
196196 −1.11548 + 10.6131i −0.0796773 + 0.758079i
197197 −26.0364 −1.85502 −0.927508 0.373803i 0.878053π-0.878053\pi
−0.927508 + 0.373803i 0.878053π0.878053\pi
198198 0 0
199199 −20.4538 −1.44993 −0.724967 0.688784i 0.758145π-0.758145\pi
−0.724967 + 0.688784i 0.758145π0.758145\pi
200200 −0.742669 + 7.06602i −0.0525146 + 0.499643i
201201 0 0
202202 −11.3898 2.42098i −0.801386 0.170340i
203203 0.256384 + 2.43933i 0.0179946 + 0.171207i
204204 0 0
205205 −6.27461 + 6.96866i −0.438237 + 0.486712i
206206 0.629630 1.93780i 0.0438684 0.135013i
207207 0 0
208208 6.76136 0.468816
209209 5.33548 + 3.63035i 0.369063 + 0.251117i
210210 0 0
211211 −14.5408 + 6.47396i −1.00103 + 0.445686i −0.840772 0.541389i 0.817898π-0.817898\pi
−0.160255 + 0.987076i 0.551232π0.551232\pi
212212 8.44092 + 9.37459i 0.579725 + 0.643849i
213213 0 0
214214 −9.70168 4.31947i −0.663193 0.295273i
215215 −7.53115 + 5.47170i −0.513620 + 0.373167i
216216 0 0
217217 −1.02399 + 3.15151i −0.0695128 + 0.213939i
218218 −0.586125 + 5.57660i −0.0396974 + 0.377695i
219219 0 0
220220 −6.72939 2.75060i −0.453695 0.185446i
221221 −0.367628 + 0.636751i −0.0247294 + 0.0428325i
222222 0 0
223223 −2.44695 + 0.520115i −0.163860 + 0.0348294i −0.289111 0.957296i 0.593360π-0.593360\pi
0.125251 + 0.992125i 0.460026π0.460026\pi
224224 −1.02793 3.16363i −0.0686812 0.211379i
225225 0 0
226226 1.46951 1.06766i 0.0977504 0.0710198i
227227 −10.7822 + 11.9749i −0.715641 + 0.794800i −0.985783 0.168021i 0.946263π-0.946263\pi
0.270143 + 0.962820i 0.412929π0.412929\pi
228228 0 0
229229 3.01903 1.34416i 0.199503 0.0888245i −0.304553 0.952495i 0.598507π-0.598507\pi
0.504056 + 0.863671i 0.331840π0.331840\pi
230230 0.138195 0.239360i 0.00911228 0.0157829i
231231 0 0
232232 4.73158 + 8.19533i 0.310643 + 0.538050i
233233 3.48837 + 2.53445i 0.228531 + 0.166037i 0.696158 0.717888i 0.254891π-0.254891\pi
−0.467627 + 0.883926i 0.654891π0.654891\pi
234234 0 0
235235 −2.14890 6.61363i −0.140179 0.431426i
236236 −10.5553 4.69951i −0.687090 0.305912i
237237 0 0
238238 0.0700560 + 0.0148909i 0.00454105 + 0.000965231i
239239 10.0638 + 11.1770i 0.650974 + 0.722980i 0.974786 0.223141i 0.0716312π-0.0716312\pi
−0.323812 + 0.946121i 0.604965π0.604965\pi
240240 0 0
241241 −6.88547 11.9260i −0.443532 0.768220i 0.554417 0.832239i 0.312941π-0.312941\pi
−0.997949 + 0.0640192i 0.979608π0.979608\pi
242242 4.30727 5.42195i 0.276882 0.348536i
243243 0 0
244244 −11.2064 8.14192i −0.717416 0.521233i
245245 8.89620 1.89095i 0.568357 0.120808i
246246 0 0
247247 0.772863 + 7.35330i 0.0491761 + 0.467880i
248248 1.33637 + 12.7147i 0.0848596 + 0.807386i
249249 0 0
250250 6.84382 1.45470i 0.432841 0.0920033i
251251 22.3625 + 16.2473i 1.41151 + 1.02552i 0.993101 + 0.117264i 0.0374123π0.0374123\pi
0.418409 + 0.908259i 0.362588π0.362588\pi
252252 0 0
253253 −0.736983 0.769379i −0.0463337 0.0483705i
254254 0.404286 + 0.700244i 0.0253672 + 0.0439372i
255255 0 0
256256 −4.76875 5.29623i −0.298047 0.331014i
257257 −10.7426 2.28340i −0.670103 0.142435i −0.139718 0.990191i 0.544619π-0.544619\pi
−0.530385 + 0.847757i 0.677953π0.677953\pi
258258 0 0
259259 −5.52465 2.45973i −0.343285 0.152840i
260260 −2.57385 7.92151i −0.159624 0.491271i
261261 0 0
262262 −3.22783 2.34516i −0.199416 0.144884i
263263 −8.97517 15.5455i −0.553433 0.958574i −0.998024 0.0628399i 0.979984π-0.979984\pi
0.444591 0.895734i 0.353349π-0.353349\pi
264264 0 0
265265 5.37553 9.31068i 0.330216 0.571951i
266266 0.657961 0.292943i 0.0403422 0.0179615i
267267 0 0
268268 9.76239 10.8422i 0.596333 0.662295i
269269 −19.5359 + 14.1937i −1.19113 + 0.865404i −0.993383 0.114850i 0.963361π-0.963361\pi
−0.197743 + 0.980254i 0.563361π0.563361\pi
270270 0 0
271271 −4.49596 13.8371i −0.273110 0.840547i −0.989713 0.143065i 0.954304π-0.954304\pi
0.716603 0.697481i 0.245696π-0.245696\pi
272272 −0.336768 + 0.0715822i −0.0204195 + 0.00434031i
273273 0 0
274274 −5.21360 + 9.03022i −0.314965 + 0.545535i
275275 0.766543 10.3590i 0.0462243 0.624672i
276276 0 0
277277 −2.52035 + 23.9795i −0.151433 + 1.44079i 0.609925 + 0.792459i 0.291200π0.291200\pi
−0.761358 + 0.648332i 0.775467π0.775467\pi
278278 3.39437 10.4468i 0.203581 0.626558i
279279 0 0
280280 −1.47497 + 1.07163i −0.0881465 + 0.0640422i
281281 1.08521 + 0.483167i 0.0647382 + 0.0288233i 0.438850 0.898560i 0.355386π-0.355386\pi
−0.374112 + 0.927383i 0.622052π0.622052\pi
282282 0 0
283283 10.2726 + 11.4089i 0.610645 + 0.678190i 0.966593 0.256316i 0.0825088π-0.0825088\pi
−0.355948 + 0.934506i 0.615842π0.615842\pi
284284 −4.19727 + 1.86875i −0.249062 + 0.110890i
285285 0 0
286286 7.92985 0.244767i 0.468902 0.0144734i
287287 4.03412 0.238126
288288 0 0
289289 −5.24172 + 16.1324i −0.308336 + 0.948962i
290290 2.40158 2.66722i 0.141025 0.156625i
291291 0 0
292292 0.0711762 + 0.677197i 0.00416527 + 0.0396299i
293293 31.3963 + 6.67348i 1.83419 + 0.389869i 0.989398 0.145227i 0.0463912π-0.0463912\pi
0.844791 + 0.535096i 0.179725π0.179725\pi
294294 0 0
295295 −1.02931 + 9.79323i −0.0599287 + 0.570184i
296296 −23.3321 −1.35615
297297 0 0
298298 3.96959 0.229952
299299 0.127593 1.21396i 0.00737889 0.0702054i
300300 0 0
301301 3.91725 + 0.832636i 0.225786 + 0.0479924i
302302 −1.06806 10.1619i −0.0614602 0.584754i
303303 0 0
304304 −2.31668 + 2.57294i −0.132871 + 0.147568i
305305 −3.64807 + 11.2276i −0.208888 + 0.642890i
306306 0 0
307307 33.1199 1.89025 0.945126 0.326707i 0.105939π-0.105939\pi
0.945126 + 0.326707i 0.105939π0.105939\pi
308308 1.05776 + 2.94320i 0.0602713 + 0.167704i
309309 0 0
310310 4.42968 1.97222i 0.251589 0.112015i
311311 −22.7387 25.2539i −1.28939 1.43201i −0.843687 0.536835i 0.819620π-0.819620\pi
−0.445705 0.895180i 0.647047π-0.647047\pi
312312 0 0
313313 4.30580 + 1.91706i 0.243378 + 0.108359i 0.524801 0.851225i 0.324140π-0.324140\pi
−0.281423 + 0.959584i 0.590806π0.590806\pi
314314 8.68034 6.30664i 0.489860 0.355904i
315315 0 0
316316 2.03457 6.26176i 0.114454 0.352252i
317317 −1.82058 + 17.3217i −0.102254 + 0.972883i 0.816311 + 0.577613i 0.196016π0.196016\pi
−0.918565 + 0.395270i 0.870651π0.870651\pi
318318 0 0
319319 −7.28386 11.7623i −0.407818 0.658565i
320320 −0.00178142 + 0.00308550i −9.95842e−5 + 0.000172485i
321321 0 0
322322 −0.116305 + 0.0247214i −0.00648142 + 0.00137767i
323323 −0.116344 0.358069i −0.00647353 0.0199235i
324324 0 0
325325 9.62806 6.99519i 0.534068 0.388023i
326326 7.82362 8.68901i 0.433310 0.481240i
327327 0 0
328328 14.2187 6.33055i 0.785094 0.349546i
329329 −1.49581 + 2.59082i −0.0824667 + 0.142837i
330330 0 0
331331 −6.48845 11.2383i −0.356637 0.617714i 0.630759 0.775978i 0.282743π-0.282743\pi
−0.987397 + 0.158264i 0.949410π0.949410\pi
332332 9.65303 + 7.01334i 0.529779 + 0.384907i
333333 0 0
334334 1.84157 + 5.66778i 0.100766 + 0.310127i
335335 −11.3592 5.05744i −0.620620 0.276318i
336336 0 0
337337 10.1176 + 2.15056i 0.551139 + 0.117148i 0.475060 0.879954i 0.342426π-0.342426\pi
0.0760793 + 0.997102i 0.475760π0.475760\pi
338338 0.606275 + 0.673337i 0.0329770 + 0.0366247i
339339 0 0
340340 0.212062 + 0.367303i 0.0115007 + 0.0199198i
341341 −2.52632 18.5196i −0.136808 1.00289i
342342 0 0
343343 −6.49530 4.71911i −0.350713 0.254808i
344344 15.1134 3.21244i 0.814857 0.173203i
345345 0 0
346346 −1.18233 11.2491i −0.0635622 0.604754i
347347 −0.642191 6.11004i −0.0344746 0.328004i −0.998144 0.0609047i 0.980601π-0.980601\pi
0.963669 0.267099i 0.0860652π-0.0860652\pi
348348 0 0
349349 −19.9329 + 4.23686i −1.06698 + 0.226794i −0.707756 0.706457i 0.750292π-0.750292\pi
−0.359225 + 0.933251i 0.616959π0.616959\pi
350350 −0.937866 0.681399i −0.0501310 0.0364223i
351351 0 0
352352 12.9791 + 13.5497i 0.691790 + 0.722200i
353353 5.99407 + 10.3820i 0.319032 + 0.552580i 0.980286 0.197582i 0.0633089π-0.0633089\pi
−0.661254 + 0.750162i 0.729976π0.729976\pi
354354 0 0
355355 2.62011 + 2.90993i 0.139061 + 0.154443i
356356 −5.31647 1.13005i −0.281772 0.0598926i
357357 0 0
358358 15.2156 + 6.77441i 0.804167 + 0.358038i
359359 5.52583 + 17.0067i 0.291642 + 0.897582i 0.984329 + 0.176343i 0.0564269π0.0564269\pi
−0.692687 + 0.721239i 0.743573π0.743573\pi
360360 0 0
361361 12.3083 + 8.94252i 0.647806 + 0.470659i
362362 0.276659 + 0.479187i 0.0145409 + 0.0251855i
363363 0 0
364364 −1.79161 + 3.10317i −0.0939061 + 0.162650i
365365 0.530155 0.236040i 0.0277496 0.0123549i
366366 0 0
367367 18.4810 20.5252i 0.964699 1.07141i −0.0327103 0.999465i 0.510414π-0.510414\pi
0.997409 0.0719415i 0.0229195π-0.0229195\pi
368368 0.462420 0.335968i 0.0241053 0.0175135i
369369 0 0
370370 2.73455 + 8.41609i 0.142163 + 0.437532i
371371 −4.52406 + 0.961618i −0.234877 + 0.0499247i
372372 0 0
373373 −6.19435 + 10.7289i −0.320731 + 0.555523i −0.980639 0.195824i 0.937262π-0.937262\pi
0.659908 + 0.751347i 0.270595π0.270595\pi
374374 −0.392376 + 0.0961443i −0.0202893 + 0.00497150i
375375 0 0
376376 −1.20648 + 11.4789i −0.0622196 + 0.591980i
377377 4.89822 15.0752i 0.252271 0.776411i
378378 0 0
379379 −13.6170 + 9.89335i −0.699459 + 0.508187i −0.879756 0.475425i 0.842294π-0.842294\pi
0.180297 + 0.983612i 0.442294π0.442294\pi
380380 3.89631 + 1.73475i 0.199876 + 0.0889907i
381381 0 0
382382 6.53801 + 7.26120i 0.334514 + 0.371515i
383383 −11.3727 + 5.06346i −0.581119 + 0.258731i −0.676175 0.736741i 0.736364π-0.736364\pi
0.0950561 + 0.995472i 0.469697π0.469697\pi
384384 0 0
385385 2.10703 1.63249i 0.107384 0.0831995i
386386 6.09024 0.309985
387387 0 0
388388 −3.20351 + 9.85939i −0.162634 + 0.500534i
389389 0.822220 0.913167i 0.0416882 0.0462994i −0.721940 0.691956i 0.756749π-0.756749\pi
0.763628 + 0.645656i 0.223416π0.223416\pi
390390 0 0
391391 0.00649708 + 0.0618156i 0.000328572 + 0.00312615i
392392 −14.7658 3.13857i −0.745786 0.158522i
393393 0 0
394394 1.71324 16.3004i 0.0863117 0.821201i
395395 −5.61129 −0.282335
396396 0 0
397397 20.5917 1.03347 0.516734 0.856146i 0.327148π-0.327148\pi
0.516734 + 0.856146i 0.327148π0.327148\pi
398398 1.34590 12.8053i 0.0674637 0.641874i
399399 0 0
400400 5.45096 + 1.15864i 0.272548 + 0.0579318i
401401 −0.704387 6.70180i −0.0351754 0.334672i −0.997931 0.0642977i 0.979519π-0.979519\pi
0.962755 0.270374i 0.0871474π-0.0871474\pi
402402 0 0
403403 14.3293 15.9143i 0.713791 0.792745i
404404 −9.16687 + 28.2127i −0.456069 + 1.40364i
405405 0 0
406406 −1.54404 −0.0766294
407407 34.0950 1.05239i 1.69003 0.0521653i
408408 0 0
409409 26.6486 11.8647i 1.31769 0.586672i 0.377084 0.926179i 0.376927π-0.376927\pi
0.940604 + 0.339507i 0.110260π0.110260\pi
410410 −3.94992 4.38683i −0.195073 0.216650i
411411 0 0
412412 −4.74197 2.11126i −0.233620 0.104014i
413413 3.42722 2.49002i 0.168642 0.122526i
414414 0 0
415415 3.14239 9.67129i 0.154254 0.474745i
416416 −2.24706 + 21.3793i −0.110171 + 1.04821i
417417 0 0
418418 −2.62391 + 3.10145i −0.128339 + 0.151697i
419419 −18.9851 + 32.8832i −0.927483 + 1.60645i −0.139965 + 0.990156i 0.544699π0.544699\pi
−0.787518 + 0.616292i 0.788634π0.788634\pi
420420 0 0
421421 7.93108 1.68580i 0.386537 0.0821610i −0.0105442 0.999944i 0.503356π-0.503356\pi
0.397081 + 0.917783i 0.370023π0.370023\pi
422422 −3.09629 9.52940i −0.150725 0.463884i
423423 0 0
424424 −14.4365 + 10.4887i −0.701098 + 0.509377i
425425 −0.405494 + 0.450346i −0.0196693 + 0.0218450i
426426 0 0
427427 4.63963 2.06570i 0.224527 0.0999661i
428428 −13.5273 + 23.4301i −0.653869 + 1.13253i
429429 0 0
430430 −2.93006 5.07500i −0.141300 0.244738i
431431 24.6339 + 17.8976i 1.18657 + 0.862095i 0.992898 0.118971i 0.0379595π-0.0379595\pi
0.193674 + 0.981066i 0.437959π0.437959\pi
432432 0 0
433433 7.44285 + 22.9067i 0.357681 + 1.10083i 0.954439 + 0.298407i 0.0964551π0.0964551\pi
−0.596758 + 0.802421i 0.703545π0.703545\pi
434434 −1.90566 0.848454i −0.0914745 0.0407271i
435435 0 0
436436 13.9729 + 2.97003i 0.669179 + 0.142238i
437437 0.418239 + 0.464501i 0.0200071 + 0.0222201i
438438 0 0
439439 −17.1588 29.7199i −0.818943 1.41845i −0.906461 0.422289i 0.861227π-0.861227\pi
0.0875179 0.996163i 0.472106π-0.472106\pi
440440 4.86464 9.06035i 0.231913 0.431935i
441441 0 0
442442 −0.374454 0.272057i −0.0178110 0.0129404i
443443 8.35358 1.77561i 0.396890 0.0843617i −0.00514270 0.999987i 0.501637π-0.501637\pi
0.402033 + 0.915625i 0.368304π0.368304\pi
444444 0 0
445445 0.484201 + 4.60687i 0.0229533 + 0.218386i
446446 −0.164610 1.56616i −0.00779452 0.0741599i
447447 0 0
448448 0.00149924 0.000318674i 7.08327e−5 1.50559e-5i
449449 29.8272 + 21.6707i 1.40763 + 1.02271i 0.993661 + 0.112416i 0.0358589π0.0358589\pi
0.413972 + 0.910290i 0.364141π0.364141\pi
450450 0 0
451451 −20.4920 + 9.89211i −0.964933 + 0.465801i
452452 −2.31372 4.00748i −0.108828 0.188496i
453453 0 0
454454 −6.78751 7.53829i −0.318554 0.353790i
455455 2.98711 + 0.634930i 0.140038 + 0.0297660i
456456 0 0
457457 21.6365 + 9.63318i 1.01211 + 0.450621i 0.844685 0.535264i 0.179788π-0.179788\pi
0.167426 + 0.985885i 0.446454π0.446454\pi
458458 0.642868 + 1.97854i 0.0300392 + 0.0924513i
459459 0 0
460460 −0.569645 0.413871i −0.0265598 0.0192969i
461461 −14.3431 24.8430i −0.668024 1.15705i −0.978456 0.206456i 0.933807π-0.933807\pi
0.310432 0.950596i 0.399526π-0.399526\pi
462462 0 0
463463 −5.43156 + 9.40774i −0.252426 + 0.437215i −0.964193 0.265201i 0.914562π-0.914562\pi
0.711767 + 0.702416i 0.247895π0.247895\pi
464464 6.78069 3.01896i 0.314786 0.140152i
465465 0 0
466466 −1.81626 + 2.01716i −0.0841367 + 0.0934433i
467467 −23.8560 + 17.3324i −1.10392 + 0.802046i −0.981696 0.190456i 0.939003π-0.939003\pi
−0.122226 + 0.992502i 0.539003π0.539003\pi
468468 0 0
469469 1.65300 + 5.08741i 0.0763285 + 0.234915i
470470 4.28194 0.910154i 0.197511 0.0419823i
471471 0 0
472472 8.17211 14.1545i 0.376152 0.651514i
473473 −21.9401 + 5.37600i −1.00881 + 0.247189i
474474 0 0
475475 −0.636997 + 6.06062i −0.0292274 + 0.278080i
476476 0.0563831 0.173529i 0.00258431 0.00795370i
477477 0 0
478478 −7.65970 + 5.56510i −0.350346 + 0.254542i
479479 −19.5106 8.68669i −0.891463 0.396905i −0.0906944 0.995879i 0.528909π-0.528909\pi
−0.800769 + 0.598974i 0.795575π0.795575\pi
480480 0 0
481481 26.1509 + 29.0435i 1.19238 + 1.32427i
482482 7.91947 3.52597i 0.360722 0.160604i
483483 0 0
484484 −12.5901 12.3568i −0.572278 0.561672i
485485 8.83519 0.401185
486486 0 0
487487 −0.703448 + 2.16499i −0.0318763 + 0.0981051i −0.965729 0.259553i 0.916425π-0.916425\pi
0.933853 + 0.357658i 0.116425π0.116425\pi
488488 13.1112 14.5615i 0.593518 0.659169i
489489 0 0
490490 0.598463 + 5.69399i 0.0270358 + 0.257228i
491491 −9.31751 1.98050i −0.420493 0.0893786i −0.00719464 0.999974i 0.502290π-0.502290\pi
−0.413299 + 0.910595i 0.635623π0.635623\pi
492492 0 0
493493 −0.0843690 + 0.802718i −0.00379979 + 0.0361526i
494494 −4.65447 −0.209415
495495 0 0
496496 10.0277 0.450256
497497 0.176083 1.67531i 0.00789838 0.0751481i
498498 0 0
499499 12.4452 + 2.64531i 0.557124 + 0.118420i 0.477864 0.878434i 0.341411π-0.341411\pi
0.0792598 + 0.996854i 0.474744π0.474744\pi
500500 −1.86318 17.7270i −0.0833239 0.792774i
501501 0 0
502502 −11.6433 + 12.9312i −0.519666 + 0.577148i
503503 1.78686 5.49939i 0.0796722 0.245206i −0.903285 0.429041i 0.858851π-0.858851\pi
0.982957 + 0.183836i 0.0588514π0.0588514\pi
504504 0 0
505505 25.2820 1.12503
506506 0.530173 0.410770i 0.0235691 0.0182609i
507507 0 0
508508 1.88181 0.837834i 0.0834916 0.0371729i
509509 6.18794 + 6.87240i 0.274275 + 0.304614i 0.864508 0.502620i 0.167630π-0.167630\pi
−0.590232 + 0.807234i 0.700964π0.700964\pi
510510 0 0
511511 −0.228074 0.101545i −0.0100894 0.00449209i
512512 −14.6751 + 10.6621i −0.648553 + 0.471201i
513513 0 0
514514 2.13643 6.57525i 0.0942338 0.290022i
515515 −0.462419 + 4.39962i −0.0203766 + 0.193870i
516516 0 0
517517 1.24527 16.8285i 0.0547667 0.740114i
518518 1.90347 3.29691i 0.0836338 0.144858i
519519 0 0
520520 11.5247 2.44966i 0.505393 0.107425i
521521 −7.83400 24.1106i −0.343214 1.05630i −0.962533 0.271164i 0.912591π-0.912591\pi
0.619320 0.785139i 0.287409π-0.287409\pi
522522 0 0
523523 −16.9781 + 12.3353i −0.742398 + 0.539384i −0.893461 0.449140i 0.851730π-0.851730\pi
0.151063 + 0.988524i 0.451730π0.451730\pi
524524 −6.80127 + 7.55357i −0.297115 + 0.329979i
525525 0 0
526526 10.3230 4.59609i 0.450103 0.200399i
527527 −0.545224 + 0.944356i −0.0237503 + 0.0411368i
528528 0 0
529529 11.4484 + 19.8292i 0.497757 + 0.862140i
530530 5.47534 + 3.97806i 0.237833 + 0.172796i
531531 0 0
532532 −0.566994 1.74503i −0.0245823 0.0756565i
533533 −23.8165 10.6038i −1.03161 0.459302i
534534 0 0
535535 22.5538 + 4.79395i 0.975085 + 0.207261i
536536 13.8096 + 15.3371i 0.596484 + 0.662463i
537537 0 0
538538 −7.60061 13.1646i −0.327686 0.567568i
539539 21.7187 + 3.92035i 0.935491 + 0.168862i
540540 0 0
541541 9.02363 + 6.55605i 0.387956 + 0.281867i 0.764617 0.644484i 0.222928π-0.222928\pi
−0.376661 + 0.926351i 0.622928π0.622928\pi
542542 8.95874 1.90424i 0.384811 0.0817940i
543543 0 0
544544 −0.114421 1.08865i −0.00490577 0.0466753i
545545 −1.27259 12.1079i −0.0545117 0.518644i
546546 0 0
547547 −5.96315 + 1.26751i −0.254966 + 0.0541947i −0.333621 0.942707i 0.608271π-0.608271\pi
0.0786553 + 0.996902i 0.474937π0.474937\pi
548548 21.4907 + 15.6139i 0.918038 + 0.666994i
549549 0 0
550550 6.43493 + 1.16154i 0.274386 + 0.0495283i
551551 4.05833 + 7.02924i 0.172891 + 0.299456i
552552 0 0
553553 1.61527 + 1.79394i 0.0686885 + 0.0762863i
554554 −14.8468 3.15579i −0.630780 0.134077i
555555 0 0
556556 −25.5643 11.3819i −1.08417 0.482702i
557557 3.05982 + 9.41715i 0.129649 + 0.399018i 0.994719 0.102632i 0.0327265π-0.0327265\pi
−0.865071 + 0.501650i 0.832727π0.832727\pi
558558 0 0
559559 −20.9380 15.2123i −0.885581 0.643412i
560560 0.714997 + 1.23841i 0.0302141 + 0.0523324i
561561 0 0
562562 −0.373900 + 0.647614i −0.0157720 + 0.0273180i
563563 −0.503872 + 0.224338i −0.0212357 + 0.00945473i −0.417327 0.908756i 0.637033π-0.637033\pi
0.396091 + 0.918211i 0.370366π0.370366\pi
564564 0 0
565565 −2.63891 + 2.93080i −0.111020 + 0.123300i
566566 −7.81863 + 5.68057i −0.328642 + 0.238772i
567567 0 0
568568 −2.00837 6.18113i −0.0842694 0.259355i
569569 18.8280 4.00202i 0.789313 0.167774i 0.204419 0.978884i 0.434470π-0.434470\pi
0.584894 + 0.811110i 0.301136π0.301136\pi
570570 0 0
571571 −13.7061 + 23.7396i −0.573582 + 0.993473i 0.422612 + 0.906311i 0.361113π0.361113\pi
−0.996194 + 0.0871624i 0.972220π0.972220\pi
572572 1.49152 20.1563i 0.0623637 0.842779i
573573 0 0
574574 −0.265451 + 2.52560i −0.0110797 + 0.105417i
575575 0.310891 0.956825i 0.0129651 0.0399024i
576576 0 0
577577 24.2732 17.6355i 1.01050 0.734175i 0.0461898 0.998933i 0.485292π-0.485292\pi
0.964315 + 0.264758i 0.0852921π0.0852921\pi
578578 −9.75492 4.34317i −0.405751 0.180652i
579579 0 0
580580 −6.11818 6.79492i −0.254043 0.282144i
581581 −3.99651 + 1.77936i −0.165803 + 0.0738204i
582582 0 0
583583 20.6228 15.9782i 0.854109 0.661750i
584584 −0.963220 −0.0398583
585585 0 0
586586 −6.24393 + 19.2169i −0.257935 + 0.793841i
587587 3.90905 4.34143i 0.161344 0.179190i −0.657052 0.753845i 0.728197π-0.728197\pi
0.818396 + 0.574655i 0.194864π0.194864\pi
588588 0 0
589589 1.14622 + 10.9056i 0.0472293 + 0.449357i
590590 −6.06343 1.28882i −0.249627 0.0530599i
591591 0 0
592592 −1.91292 + 18.2002i −0.0786205 + 0.748025i
593593 −35.2941 −1.44936 −0.724678 0.689088i 0.758011π-0.758011\pi
−0.724678 + 0.689088i 0.758011π0.758011\pi
594594 0 0
595595 −0.155503 −0.00637500
596596 1.05707 10.0574i 0.0432995 0.411967i
597597 0 0
598598 0.751620 + 0.159762i 0.0307360 + 0.00653315i
599599 2.38691 + 22.7099i 0.0975263 + 0.927901i 0.928436 + 0.371493i 0.121154π0.121154\pi
−0.830909 + 0.556408i 0.812179π0.812179\pi
600600 0 0
601601 7.68359 8.53349i 0.313420 0.348088i −0.565767 0.824565i 0.691420π-0.691420\pi
0.879187 + 0.476477i 0.158086π0.158086\pi
602602 −0.779042 + 2.39765i −0.0317514 + 0.0977207i
603603 0 0
604604 −26.0309 −1.05918
605605 −6.69999 + 13.4592i −0.272393 + 0.547195i
606606 0 0
607607 11.8036 5.25531i 0.479095 0.213307i −0.152957 0.988233i 0.548880π-0.548880\pi
0.632052 + 0.774926i 0.282213π0.282213\pi
608608 −7.36567 8.18040i −0.298717 0.331759i
609609 0 0
610610 −6.78911 3.02271i −0.274883 0.122386i
611611 15.6410 11.3639i 0.632767 0.459732i
612612 0 0
613613 7.44676 22.9188i 0.300772 0.925680i −0.680450 0.732795i 0.738216π-0.738216\pi
0.981221 0.192885i 0.0617845π-0.0617845\pi
614614 −2.17934 + 20.7351i −0.0879511 + 0.836799i
615615 0 0
616616 −4.29696 + 1.05289i −0.173129 + 0.0424220i
617617 11.3955 19.7377i 0.458767 0.794608i −0.540129 0.841582i 0.681625π-0.681625\pi
0.998896 + 0.0469742i 0.0149578π0.0149578\pi
618618 0 0
619619 19.8734 4.22422i 0.798779 0.169786i 0.209599 0.977787i 0.432784π-0.432784\pi
0.589180 + 0.808002i 0.299451π0.299451\pi
620620 −3.81725 11.7483i −0.153304 0.471822i
621621 0 0
622622 17.3067 12.5740i 0.693935 0.504173i
623623 1.33344 1.48094i 0.0534233 0.0593326i
624624 0 0
625625 0.427795 0.190466i 0.0171118 0.00761866i
626626 −1.48353 + 2.56954i −0.0592937 + 0.102700i
627627 0 0
628628 −13.6671 23.6720i −0.545375 0.944617i
629629 −1.61000 1.16973i −0.0641947 0.0466402i
630630 0 0
631631 4.74547 + 14.6051i 0.188914 + 0.581418i 0.999994 0.00351764i 0.00111970π-0.00111970\pi
−0.811080 + 0.584936i 0.801120π0.801120\pi
632632 8.50836 + 3.78816i 0.338444 + 0.150685i
633633 0 0
634634 −10.7246 2.27959i −0.425930 0.0905342i
635635 −1.17470 1.30464i −0.0466166 0.0517730i
636636 0 0
637637 12.6428 + 21.8980i 0.500926 + 0.867629i
638638 7.84323 3.78616i 0.310517 0.149895i
639639 0 0
640640 12.5093 + 9.08850i 0.494472 + 0.359255i
641641 13.2372 2.81365i 0.522837 0.111132i 0.0610695 0.998134i 0.480549π-0.480549\pi
0.461767 + 0.887001i 0.347216π0.347216\pi
642642 0 0
643643 −1.32215 12.5794i −0.0521405 0.496083i −0.989164 0.146816i 0.953097π-0.953097\pi
0.937023 0.349267i 0.113569π-0.113569\pi
644644 0.0316631 + 0.301255i 0.00124770 + 0.0118711i
645645 0 0
646646 0.231829 0.0492767i 0.00912117 0.00193877i
647647 −1.31179 0.953069i −0.0515717 0.0374690i 0.561701 0.827340i 0.310147π-0.310147\pi
−0.613272 + 0.789871i 0.710147π0.710147\pi
648648 0 0
649649 −11.3034 + 21.0525i −0.443697 + 0.826381i
650650 3.74587 + 6.48804i 0.146925 + 0.254482i
651651 0 0
652652 −19.9312 22.1358i −0.780566 0.866907i
653653 32.3315 + 6.87228i 1.26523 + 0.268933i 0.791190 0.611570i 0.209462π-0.209462\pi
0.474040 + 0.880503i 0.342795π0.342795\pi
654654 0 0
655655 7.91373 + 3.52342i 0.309215 + 0.137671i
656656 −3.77240 11.6103i −0.147288 0.453305i
657657 0 0
658658 −1.52358 1.10695i −0.0593955 0.0431534i
659659 −23.9506 41.4836i −0.932983 1.61597i −0.778192 0.628026i 0.783863π-0.783863\pi
−0.154790 0.987947i 0.549470π-0.549470\pi
660660 0 0
661661 9.25259 16.0260i 0.359884 0.623337i −0.628057 0.778167i 0.716150π-0.716150\pi
0.987941 + 0.154830i 0.0494830π0.0494830\pi
662662 7.46282 3.32266i 0.290051 0.129139i
663663 0 0
664664 −11.2938 + 12.5431i −0.438286 + 0.486766i
665665 −1.26510 + 0.919151i −0.0490586 + 0.0356431i
666666 0 0
667667 −0.414080 1.27441i −0.0160332 0.0493452i
668668 14.8503 3.15654i 0.574577 0.122130i
669669 0 0
670670 3.91372 6.77876i 0.151200 0.261887i
671671 −18.5025 + 21.8700i −0.714283 + 0.844282i
672672 0 0
673673 −4.09073 + 38.9207i −0.157686 + 1.50028i 0.574121 + 0.818771i 0.305344π0.305344\pi
−0.731807 + 0.681512i 0.761323π0.761323\pi
674674 −2.01213 + 6.19270i −0.0775044 + 0.238534i
675675 0 0
676676 1.86742 1.35676i 0.0718239 0.0521831i
677677 11.4043 + 5.07750i 0.438301 + 0.195144i 0.614010 0.789298i 0.289555π-0.289555\pi
−0.175709 + 0.984442i 0.556222π0.556222\pi
678678 0 0
679679 −2.54331 2.82463i −0.0976033 0.108399i
680680 −0.548086 + 0.244024i −0.0210181 + 0.00935788i
681681 0 0
682682 11.7606 0.363010i 0.450338 0.0139004i
683683 −17.3888 −0.665363 −0.332681 0.943039i 0.607953π-0.607953\pi
−0.332681 + 0.943039i 0.607953π0.607953\pi
684684 0 0
685685 6.99597 21.5314i 0.267302 0.822672i
686686 3.38185 3.75593i 0.129120 0.143402i
687687 0 0
688688 −1.26677 12.0525i −0.0482952 0.459499i
689689 29.2367 + 6.21445i 1.11383 + 0.236752i
690690 0 0
691691 −0.382036 + 3.63483i −0.0145333 + 0.138275i −0.999382 0.0351379i 0.988813π-0.988813\pi
0.984849 + 0.173413i 0.0554796π0.0554796\pi
692692 −28.8156 −1.09541
693693 0 0
694694 3.86751 0.146809
695695 −2.49293 + 23.7186i −0.0945621 + 0.899699i
696696 0 0
697697 1.29851 + 0.276007i 0.0491846 + 0.0104545i
698698 −1.34092 12.7580i −0.0507545 0.482896i
699699 0 0
700700 −1.97615 + 2.19474i −0.0746914 + 0.0829532i
701701 −1.72623 + 5.31280i −0.0651989 + 0.200662i −0.978349 0.206962i 0.933642π-0.933642\pi
0.913150 + 0.407624i 0.133642π0.133642\pi
702702 0 0
703703 −20.0123 −0.754777
704704 −0.00683427 + 0.00529508i −0.000257576 + 0.000199566i
705705 0 0
706706 −6.89420 + 3.06950i −0.259467 + 0.115522i
707707 −7.27771 8.08272i −0.273706 0.303982i
708708 0 0
709709 12.6591 + 5.63618i 0.475421 + 0.211671i 0.630436 0.776241i 0.282876π-0.282876\pi
−0.155015 + 0.987912i 0.549543π0.549543\pi
710710 −1.99420 + 1.44887i −0.0748410 + 0.0543752i
711711 0 0
712712 2.37589 7.31224i 0.0890403 0.274038i
713713 0.189231 1.80041i 0.00708676 0.0674260i
714714 0 0
715715 −16.7305 + 4.09948i −0.625685 + 0.153312i
716716 21.2155 36.7464i 0.792861 1.37328i
717717 0 0
718718 −11.0109 + 2.34043i −0.410922 + 0.0873442i
719719 −8.24222 25.3669i −0.307383 0.946027i −0.978777 0.204927i 0.934304π-0.934304\pi
0.671394 0.741100i 0.265696π-0.265696\pi
720720 0 0
721721 1.53968 1.11865i 0.0573408 0.0416605i
722722 −6.40847 + 7.11733i −0.238499 + 0.264879i
723723 0 0
724724 1.28775 0.573342i 0.0478587 0.0213081i
725725 6.53222 11.3141i 0.242600 0.420196i
726726 0 0
727727 11.3198 + 19.6065i 0.419830 + 0.727166i 0.995922 0.0902184i 0.0287565π-0.0287565\pi
−0.576092 + 0.817385i 0.695423π0.695423\pi
728728 −4.10069 2.97933i −0.151982 0.110421i
729729 0 0
730730 0.112890 + 0.347441i 0.00417826 + 0.0128594i
731731 1.20392 + 0.536021i 0.0445287 + 0.0198255i
732732 0 0
733733 −21.5549 4.58163i −0.796148 0.169226i −0.208159 0.978095i 0.566747π-0.566747\pi
−0.587989 + 0.808869i 0.700080π0.700080\pi
734734 11.6339 + 12.9208i 0.429417 + 0.476915i
735735 0 0
736736 0.908646 + 1.57382i 0.0334932 + 0.0580118i
737737 −20.8716 21.7891i −0.768816 0.802612i
738738 0 0
739739 −39.3226 28.5696i −1.44651 1.05095i −0.986632 0.162965i 0.947894π-0.947894\pi
−0.459875 0.887984i 0.652106π-0.652106\pi
740740 22.0513 4.68715i 0.810622 0.172303i
741741 0 0
742742 −0.304341 2.89561i −0.0111727 0.106301i
743743 0.575345 + 5.47405i 0.0211074 + 0.200823i 0.999994 0.00358270i 0.00114041π-0.00114041\pi
−0.978886 + 0.204406i 0.934474π0.934474\pi
744744 0 0
745745 −8.43039 + 1.79194i −0.308866 + 0.0656514i
746746 −6.30937 4.58402i −0.231002 0.167833i
747747 0 0
748748 0.139105 + 1.01973i 0.00508618 + 0.0372851i
749749 −4.95973 8.59050i −0.181224 0.313890i
750750 0 0
751751 −2.48961 2.76499i −0.0908470 0.100896i 0.696007 0.718035i 0.254958π-0.254958\pi
−0.786854 + 0.617139i 0.788292π0.788292\pi
752752 8.85521 + 1.88223i 0.322916 + 0.0686379i
753753 0 0
754754 9.11567 + 4.05856i 0.331973 + 0.147804i
755755 6.85556 + 21.0993i 0.249499 + 0.767880i
756756 0 0
757757 24.6209 + 17.8881i 0.894862 + 0.650155i 0.937141 0.348951i 0.113462π-0.113462\pi
−0.0422792 + 0.999106i 0.513462π0.513462\pi
758758 −5.29781 9.17608i −0.192425 0.333290i
759759 0 0
760760 −3.01660 + 5.22491i −0.109424 + 0.189527i
761761 20.5182 9.13531i 0.743786 0.331155i 0.000383921 1.00000i 0.499878π-0.499878\pi
0.743402 + 0.668845i 0.233211π0.233211\pi
762762 0 0
763763 −3.50459 + 3.89224i −0.126875 + 0.140909i
764764 20.1381 14.6312i 0.728571 0.529338i
765765 0 0
766766 −2.42169 7.45320i −0.0874992 0.269295i
767767 −26.7787 + 5.69198i −0.966922 + 0.205526i
768768 0 0
769769 −19.4798 + 33.7399i −0.702458 + 1.21669i 0.265143 + 0.964209i 0.414581π0.414581\pi
−0.967601 + 0.252484i 0.918752π0.918752\pi
770770 0.883393 + 1.42655i 0.0318353 + 0.0514092i
771771 0 0
772772 1.62179 15.4303i 0.0583695 0.555349i
773773 16.4951 50.7667i 0.593287 1.82595i 0.0302135 0.999543i 0.490381π-0.490381\pi
0.563074 0.826407i 0.309619π-0.309619\pi
774774 0 0
775775 14.2792 10.3745i 0.512925 0.372662i
776776 −13.3967 5.96461i −0.480914 0.214117i
777777 0 0
778778 0.517595 + 0.574847i 0.0185567 + 0.0206093i
779779 12.1955 5.42979i 0.436950 0.194543i
780780 0 0
781781 3.21361 + 8.94184i 0.114992 + 0.319964i
782782 −0.0391279 −0.00139921
783783 0 0
784784 −3.65884 + 11.2607i −0.130673 + 0.402169i
785785 −15.5879 + 17.3121i −0.556357 + 0.617897i
786786 0 0
787787 −3.01381 28.6745i −0.107431 1.02213i −0.906877 0.421396i 0.861540π-0.861540\pi
0.799446 0.600738i 0.205126π-0.205126\pi
788788 −40.8426 8.68136i −1.45496 0.309261i
789789 0 0
790790 0.369232 3.51301i 0.0131367 0.124987i
791791 1.69662 0.0603250
792792 0 0
793793 −32.8211 −1.16551
794794 −1.35497 + 12.8917i −0.0480860 + 0.457508i
795795 0 0
796796 −32.0854 6.81996i −1.13724 0.241727i
797797 3.46749 + 32.9910i 0.122825 + 1.16860i 0.866190 + 0.499715i 0.166562π0.166562\pi
−0.743365 + 0.668886i 0.766772π0.766772\pi
798798 0 0
799799 −0.658734 + 0.731598i −0.0233043 + 0.0258821i
800800 −5.47516 + 16.8508i −0.193576 + 0.595766i
801801 0 0
802802 4.24208 0.149793
803803 1.40754 0.0434460i 0.0496711 0.00153317i
804804 0 0
805805 0.235842 0.105004i 0.00831235 0.00370090i
806806 9.02040 + 10.0182i 0.317730 + 0.352875i
807807 0 0
808808 −38.3349 17.0678i −1.34862 0.600443i
809809 19.8771 14.4416i 0.698842 0.507739i −0.180713 0.983536i 0.557840π-0.557840\pi
0.879555 + 0.475797i 0.157840π0.157840\pi
810810 0 0
811811 11.5446 35.5307i 0.405387 1.24765i −0.515185 0.857079i 0.672277π-0.672277\pi
0.920572 0.390573i 0.127723π-0.127723\pi
812812 −0.411167 + 3.91200i −0.0144291 + 0.137284i
813813 0 0
814814 −1.58465 + 21.4148i −0.0555418 + 0.750589i
815815 −12.6930 + 21.9850i −0.444617 + 0.770099i
816816 0 0
817817 12.9629 2.75535i 0.453515 0.0963976i
818818 5.67451 + 17.4644i 0.198405 + 0.610627i
819819 0 0
820820 −12.1664 + 8.83939i −0.424868 + 0.308685i
821821 −8.16415 + 9.06720i −0.284931 + 0.316448i −0.868571 0.495565i 0.834961π-0.834961\pi
0.583640 + 0.812012i 0.301628π0.301628\pi
822822 0 0
823823 −45.2009 + 20.1248i −1.57561 + 0.701505i −0.993733 0.111776i 0.964346π-0.964346\pi
−0.581872 + 0.813280i 0.697680π0.697680\pi
824824 3.67133 6.35893i 0.127897 0.221524i
825825 0 0
826826 1.33339 + 2.30950i 0.0463945 + 0.0803576i
827827 2.45628 + 1.78459i 0.0854134 + 0.0620564i 0.629672 0.776861i 0.283189π-0.283189\pi
−0.544259 + 0.838917i 0.683189π0.683189\pi
828828 0 0
829829 −14.8814 45.8003i −0.516853 1.59071i −0.779885 0.625923i 0.784722π-0.784722\pi
0.263032 0.964787i 0.415278π-0.415278\pi
830830 5.84804 + 2.60372i 0.202989 + 0.0903763i
831831 0 0
832832 −0.00968886 0.00205943i −0.000335901 7.13979e-5i
833833 −0.861542 0.956839i −0.0298507 0.0331525i
834834 0 0
835835 −6.46955 11.2056i −0.223888 0.387786i
836836 7.15915 + 7.47386i 0.247605 + 0.258489i
837837 0 0
838838 −19.3376 14.0496i −0.668007 0.485335i
839839 −38.0873 + 8.09571i −1.31492 + 0.279495i −0.811401 0.584490i 0.801295π-0.801295\pi
−0.503519 + 0.863984i 0.667961π0.667961\pi
840840 0 0
841841 1.21246 + 11.5358i 0.0418090 + 0.397786i
842842 0.533537 + 5.07627i 0.0183869 + 0.174940i
843843 0 0
844844 −24.9683 + 5.30718i −0.859445 + 0.182681i
845845 −1.59153 1.15631i −0.0547503 0.0397784i
846846 0 0
847847 6.23162 1.73239i 0.214121 0.0595255i
848848 6.99812 + 12.1211i 0.240316 + 0.416240i
849849 0 0
850850 −0.255262 0.283497i −0.00875542 0.00972388i
851851 3.23165 + 0.686909i 0.110780 + 0.0235469i
852852 0 0
853853 −33.8107 15.0535i −1.15765 0.515421i −0.264153 0.964481i 0.585092π-0.585092\pi
−0.893502 + 0.449060i 0.851759π0.851759\pi
854854 0.987956 + 3.04062i 0.0338072 + 0.104048i
855855 0 0
856856 −30.9617 22.4950i −1.05825 0.768864i
857857 14.2713 + 24.7186i 0.487499 + 0.844372i 0.999897 0.0143758i 0.00457610π-0.00457610\pi
−0.512398 + 0.858748i 0.671243π0.671243\pi
858858 0 0
859859 −19.1707 + 33.2046i −0.654094 + 1.13292i 0.328025 + 0.944669i 0.393617π0.393617\pi
−0.982120 + 0.188256i 0.939717π0.939717\pi
860860 −13.6383 + 6.07218i −0.465064 + 0.207060i
861861 0 0
862862 −12.8259 + 14.2446i −0.436852 + 0.485174i
863863 22.6247 16.4378i 0.770153 0.559549i −0.131855 0.991269i 0.542093π-0.542093\pi
0.902008 + 0.431720i 0.142093π0.142093\pi
864864 0 0
865865 7.58897 + 23.3565i 0.258033 + 0.794143i
866866 −14.8308 + 3.15238i −0.503970 + 0.107122i
867867 0 0
868868 −2.65712 + 4.60226i −0.0901884 + 0.156211i
869869 −12.6040 5.15184i −0.427563 0.174764i
870870 0 0
871871 3.61348 34.3799i 0.122438 1.16492i
872872 −6.24437 + 19.2182i −0.211461 + 0.650810i
873873 0 0
874874 −0.318327 + 0.231278i −0.0107676 + 0.00782309i
875875 5.97029 + 2.65814i 0.201833 + 0.0898617i
876876 0 0
877877 −14.0783 15.6355i −0.475390 0.527974i 0.456981 0.889476i 0.348931π-0.348931\pi
−0.932371 + 0.361502i 0.882264π0.882264\pi
878878 19.7355 8.78682i 0.666041 0.296541i
879879 0 0
880880 −6.66868 4.53748i −0.224801 0.152959i
881881 −17.0076 −0.573000 −0.286500 0.958080i 0.592492π-0.592492\pi
−0.286500 + 0.958080i 0.592492π0.592492\pi
882882 0 0
883883 2.08724 6.42388i 0.0702414 0.216181i −0.909773 0.415105i 0.863745π-0.863745\pi
0.980015 + 0.198924i 0.0637448π0.0637448\pi
884884 −0.789001 + 0.876275i −0.0265370 + 0.0294723i
885885 0 0
886886 0.561959 + 5.34669i 0.0188794 + 0.179625i
887887 33.1095 + 7.03764i 1.11171 + 0.236301i 0.726932 0.686709i 0.240946π-0.240946\pi
0.384775 + 0.923010i 0.374279π0.374279\pi
888888 0 0
889889 −0.0789449 + 0.751111i −0.00264773 + 0.0251915i
890890 −2.91604 −0.0977459
891891 0 0
892892 −4.01188 −0.134328
893893 −1.03482 + 9.84561i −0.0346288 + 0.329471i
894894 0 0
895895 −35.3721 7.51856i −1.18236 0.251318i
896896 −0.695314 6.61547i −0.0232288 0.221007i
897897 0 0
898898 −15.5299 + 17.2477i −0.518239 + 0.575563i
899899 7.26448 22.3578i 0.242284 0.745674i
900900 0 0
901901 −1.52201 −0.0507054
902902 −4.84465 13.4802i −0.161309 0.448841i
903903 0 0
904904 5.97993 2.66244i 0.198889 0.0885513i
905905 −0.803865 0.892783i −0.0267214 0.0296771i
906906 0 0
907907 25.7133 + 11.4483i 0.853795 + 0.380134i 0.786493 0.617599i 0.211894π-0.211894\pi
0.0673015 + 0.997733i 0.478561π0.478561\pi
908908 −20.9066 + 15.1895i −0.693809 + 0.504082i
909909 0 0
910910 −0.594061 + 1.82833i −0.0196929 + 0.0606086i
911911 0.855313 8.13776i 0.0283378 0.269616i −0.971174 0.238372i 0.923386π-0.923386\pi
0.999512 0.0312443i 0.00994700π-0.00994700\pi
912912 0 0
913913 15.9378 18.8385i 0.527465 0.623463i
914914 −7.45467 + 12.9119i −0.246579 + 0.427087i
915915 0 0
916916 5.18405 1.10190i 0.171286 0.0364080i
917917 −1.15161 3.54430i −0.0380296 0.117043i
918918 0 0
919919 −9.43023 + 6.85146i −0.311075 + 0.226009i −0.732357 0.680920i 0.761580π-0.761580\pi
0.421283 + 0.906929i 0.361580π0.361580\pi
920920 0.666473 0.740193i 0.0219730 0.0244035i
921921 0 0
922922 16.4970 7.34494i 0.543300 0.241893i
923923 −5.44317 + 9.42785i −0.179164 + 0.310322i
924924 0 0
925925 16.1057 + 27.8959i 0.529552 + 0.917211i
926926 −5.53241 4.01953i −0.181806 0.132090i
927927 0 0
928928 7.29242 + 22.4438i 0.239385 + 0.736753i
929929 −29.0262 12.9233i −0.952318 0.423999i −0.129041 0.991639i 0.541190π-0.541190\pi
−0.823277 + 0.567640i 0.807857π0.807857\pi
930930 0 0
931931 −12.6648 2.69199i −0.415073 0.0882265i
932932 4.62705 + 5.13886i 0.151564 + 0.168329i
933933 0 0
934934 −9.28136 16.0758i −0.303695 0.526016i
935935 0.789907 0.381311i 0.0258327 0.0124702i
936936 0 0
937937 34.9908 + 25.4223i 1.14310 + 0.830510i 0.987548 0.157318i 0.0502847π-0.0502847\pi
0.155551 + 0.987828i 0.450285π0.450285\pi
938938 −3.29380 + 0.700119i −0.107546 + 0.0228597i
939939 0 0
940940 −1.16573 11.0911i −0.0380218 0.361753i
941941 −1.27546 12.1352i −0.0415790 0.395597i −0.995443 0.0953585i 0.969600π-0.969600\pi
0.953864 0.300239i 0.0970664π-0.0970664\pi
942942 0 0
943943 −2.15575 + 0.458219i −0.0702008 + 0.0149216i
944944 −10.3712 7.53513i −0.337554 0.245248i
945945 0 0
946946 −1.92201 14.0896i −0.0624898 0.458092i
947947 15.5930 + 27.0079i 0.506706 + 0.877640i 0.999970 + 0.00776032i 0.00247021π0.00247021\pi
−0.493264 + 0.869879i 0.664196π0.664196\pi
948948 0 0
949949 1.07958 + 1.19900i 0.0350448 + 0.0389212i
950950 −3.75240 0.797597i −0.121744 0.0258775i
951951 0 0
952952 0.235788 + 0.104980i 0.00764193 + 0.00340241i
953953 5.66371 + 17.4311i 0.183466 + 0.564649i 0.999919 0.0127629i 0.00406266π-0.00406266\pi
−0.816453 + 0.577412i 0.804063π0.804063\pi
954954 0 0
955955 −17.1629 12.4696i −0.555378 0.403506i
956956 12.0601 + 20.8887i 0.390050 + 0.675587i
957957 0 0
958958 6.72223 11.6432i 0.217185 0.376176i
959959 −8.89751 + 3.96143i −0.287316 + 0.127921i
960960 0 0
961961 0.508465 0.564708i 0.0164021 0.0182164i
962962 −19.9037 + 14.4609i −0.641723 + 0.466239i
963963 0 0
964964 −6.82455 21.0038i −0.219804 0.676487i
965965 −12.9341 + 2.74923i −0.416364 + 0.0885009i
966966 0 0
967967 −10.4254 + 18.0573i −0.335258 + 0.580683i −0.983534 0.180722i 0.942157π-0.942157\pi
0.648277 + 0.761405i 0.275490π0.275490\pi
968968 19.2454 15.8850i 0.618571 0.510562i
969969 0 0
970970 −0.581370 + 5.53137i −0.0186667 + 0.177601i
971971 8.79427 27.0660i 0.282222 0.868589i −0.704996 0.709211i 0.749051π-0.749051\pi
0.987218 0.159378i 0.0509488π-0.0509488\pi
972972 0 0
973973 8.30053 6.03069i 0.266103 0.193335i
974974 −1.30913 0.582861i −0.0419472 0.0186761i
975975 0 0
976976 −10.2838 11.4213i −0.329175 0.365586i
977977 20.3347 9.05359i 0.650564 0.289650i −0.0547974 0.998497i 0.517451π-0.517451\pi
0.705362 + 0.708848i 0.250785π0.250785\pi
978978 0 0
979979 −3.14205 + 10.7925i −0.100420 + 0.344929i
980980 14.5857 0.465924
981981 0 0
982982 1.85302 5.70301i 0.0591322 0.181990i
983983 15.4525 17.1618i 0.492859 0.547375i −0.444482 0.895788i 0.646612π-0.646612\pi
0.937341 + 0.348412i 0.113279π0.113279\pi
984984 0 0
985985 3.71977 + 35.3912i 0.118522 + 1.12766i
986986 −0.496998 0.105640i −0.0158277 0.00336427i
987987 0 0
988988 −1.23945 + 11.7926i −0.0394323 + 0.375173i
989989 −2.18787 −0.0695703
990990 0 0
991991 −6.16408 −0.195809 −0.0979043 0.995196i 0.531214π-0.531214\pi
−0.0979043 + 0.995196i 0.531214π0.531214\pi
992992 −3.33258 + 31.7074i −0.105810 + 1.00671i
993993 0 0
994994 1.03726 + 0.220477i 0.0329000 + 0.00699310i
995995 2.92220 + 27.8028i 0.0926399 + 0.881409i
996996 0 0
997997 16.9821 18.8606i 0.537830 0.597320i −0.411575 0.911376i 0.635021π-0.635021\pi
0.949405 + 0.314056i 0.101688π0.101688\pi
998998 −2.47504 + 7.61739i −0.0783461 + 0.241124i
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 891.2.n.l.433.6 96
3.2 odd 2 inner 891.2.n.l.433.7 96
9.2 odd 6 inner 891.2.n.l.136.6 96
9.4 even 3 891.2.f.g.730.6 yes 48
9.5 odd 6 891.2.f.g.730.7 yes 48
9.7 even 3 inner 891.2.n.l.136.7 96
11.3 even 5 inner 891.2.n.l.190.7 96
33.14 odd 10 inner 891.2.n.l.190.6 96
99.5 odd 30 9801.2.a.cr.1.10 24
99.14 odd 30 891.2.f.g.487.7 yes 48
99.25 even 15 inner 891.2.n.l.784.6 96
99.47 odd 30 inner 891.2.n.l.784.7 96
99.49 even 15 9801.2.a.cr.1.15 24
99.50 even 30 9801.2.a.cq.1.15 24
99.58 even 15 891.2.f.g.487.6 48
99.94 odd 30 9801.2.a.cq.1.10 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
891.2.f.g.487.6 48 99.58 even 15
891.2.f.g.487.7 yes 48 99.14 odd 30
891.2.f.g.730.6 yes 48 9.4 even 3
891.2.f.g.730.7 yes 48 9.5 odd 6
891.2.n.l.136.6 96 9.2 odd 6 inner
891.2.n.l.136.7 96 9.7 even 3 inner
891.2.n.l.190.6 96 33.14 odd 10 inner
891.2.n.l.190.7 96 11.3 even 5 inner
891.2.n.l.433.6 96 1.1 even 1 trivial
891.2.n.l.433.7 96 3.2 odd 2 inner
891.2.n.l.784.6 96 99.25 even 15 inner
891.2.n.l.784.7 96 99.47 odd 30 inner
9801.2.a.cq.1.10 24 99.94 odd 30
9801.2.a.cq.1.15 24 99.50 even 30
9801.2.a.cr.1.10 24 99.5 odd 30
9801.2.a.cr.1.15 24 99.49 even 15