Properties

Label 841.2.d.i.645.1
Level 841841
Weight 22
Character 841.645
Analytic conductor 6.7156.715
Analytic rank 00
Dimension 1212
Inner twists 66

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [841,2,Mod(190,841)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("841.190"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 841=292 841 = 29^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 841.d (of order 77, degree 66, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [12,1,-1,1,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 6.715418809996.71541880999
Analytic rank: 00
Dimension: 1212
Relative dimension: 22 over Q(ζ7)\Q(\zeta_{7})
Coefficient field: 12.0.4413675765625.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x12x11+2x103x9+5x88x7+13x6+8x5+5x4+3x3+2x2+x+1 x^{12} - x^{11} + 2x^{10} - 3x^{9} + 5x^{8} - 8x^{7} + 13x^{6} + 8x^{5} + 5x^{4} + 3x^{3} + 2x^{2} + x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C7]\mathrm{SU}(2)[C_{7}]

Embedding invariants

Embedding label 645.1
Root 0.1375260.602539i-0.137526 - 0.602539i of defining polynomial
Character χ\chi == 841.645
Dual form 841.2.d.i.605.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(0.1375260.602539i)q2+(0.556829+0.268155i)q3+(1.457800.702039i)q4+(0.8576183.75747i)q5+(0.08499540.372389i)q6+(2.01463+0.970194i)q7+(1.394171.74823i)q8+(1.632322.04686i)q9+(2.14608+1.03350i)q10+(0.861642+1.08046i)q11+1.00000q12+(0.147186+0.184565i)q13+(0.3075161.34732i)q14+(0.5300372.32225i)q15+(1.156011.44960i)q164.38197q17+(1.00883+1.26503i)q18+(4.373392.10612i)q19+(3.888124.87555i)q20+(0.861642+1.08046i)q21+(0.769519+0.370581i)q22+(0.2750511.20508i)q23+(0.3075161.34732i)q24+(8.87824+4.27553i)q25+(0.131450+0.0633028i)q26+(0.7726233.38508i)q27+3.61803q281.47214q30+(2.24527+9.83719i)q31+(5.061672.43757i)q32+(0.769519+0.370581i)q33+(0.602632+2.64030i)q34+(1.917698.40196i)q35+(3.816571.83796i)q36+(2.93552+3.68102i)q37+(1.870472.34549i)q38+(0.131450+0.0633028i)q39+(5.37326+6.73785i)q40+3.85410q41+(0.5325240.667764i)q42+(1.610187.05464i)q43+(0.497572+2.18001i)q44+(6.29112+7.88881i)q450.763932q46+(4.36443+5.47282i)q47+(1.032420.497187i)q48+(1.246981.56366i)q49+(3.79716+4.76149i)q50+(2.440011.17505i)q51+(0.0849954+0.372389i)q52+(0.445042+1.94986i)q53+(1.93339+0.931070i)q54+(4.79877+2.31097i)q55+(1.112604.87464i)q56+3.00000q57+6.09017q59+(0.8576183.75747i)q60+(0.556829+0.268155i)q61+(5.618502.70573i)q62+(1.302665.70733i)q63+(0.05253010.230149i)q64+(0.819729+0.394760i)q65+(0.329118+0.412701i)q66+(0.9526081.19453i)q67+(6.38802+3.07631i)q68+(0.4763040.597266i)q695.32624q70+(6.529278.18745i)q71+(1.30266+5.70733i)q72+(3.0503613.3645i)q73+(1.814252.27500i)q746.09017q75+(4.896956.14058i)q76+(2.78415+1.34077i)q77+(0.0562200+0.0704977i)q78+(3.797164.76149i)q79+(6.438233.10049i)q80+(1.27019+5.56509i)q81+(0.5300372.32225i)q82+(8.959484.31466i)q83+(2.01463+0.970194i)q84+(3.75805+16.4651i)q854.47214q86+3.09017q88+(1.047674.59016i)q89+(5.61850+2.70573i)q90+(0.475589+0.229032i)q91+(0.4450421.94986i)q92+(1.38766+6.07972i)q93+(3.89781+1.87708i)q94+(11.664414.6267i)q95+(2.164842.71463i)q96+(3.20953+1.54563i)q97+(0.770676+0.966397i)q98+3.61803q99+O(q100)q+(-0.137526 - 0.602539i) q^{2} +(0.556829 + 0.268155i) q^{3} +(1.45780 - 0.702039i) q^{4} +(-0.857618 - 3.75747i) q^{5} +(0.0849954 - 0.372389i) q^{6} +(2.01463 + 0.970194i) q^{7} +(-1.39417 - 1.74823i) q^{8} +(-1.63232 - 2.04686i) q^{9} +(-2.14608 + 1.03350i) q^{10} +(-0.861642 + 1.08046i) q^{11} +1.00000 q^{12} +(-0.147186 + 0.184565i) q^{13} +(0.307516 - 1.34732i) q^{14} +(0.530037 - 2.32225i) q^{15} +(1.15601 - 1.44960i) q^{16} -4.38197 q^{17} +(-1.00883 + 1.26503i) q^{18} +(4.37339 - 2.10612i) q^{19} +(-3.88812 - 4.87555i) q^{20} +(0.861642 + 1.08046i) q^{21} +(0.769519 + 0.370581i) q^{22} +(0.275051 - 1.20508i) q^{23} +(-0.307516 - 1.34732i) q^{24} +(-8.87824 + 4.27553i) q^{25} +(0.131450 + 0.0633028i) q^{26} +(-0.772623 - 3.38508i) q^{27} +3.61803 q^{28} -1.47214 q^{30} +(2.24527 + 9.83719i) q^{31} +(-5.06167 - 2.43757i) q^{32} +(-0.769519 + 0.370581i) q^{33} +(0.602632 + 2.64030i) q^{34} +(1.91769 - 8.40196i) q^{35} +(-3.81657 - 1.83796i) q^{36} +(2.93552 + 3.68102i) q^{37} +(-1.87047 - 2.34549i) q^{38} +(-0.131450 + 0.0633028i) q^{39} +(-5.37326 + 6.73785i) q^{40} +3.85410 q^{41} +(0.532524 - 0.667764i) q^{42} +(1.61018 - 7.05464i) q^{43} +(-0.497572 + 2.18001i) q^{44} +(-6.29112 + 7.88881i) q^{45} -0.763932 q^{46} +(-4.36443 + 5.47282i) q^{47} +(1.03242 - 0.497187i) q^{48} +(-1.24698 - 1.56366i) q^{49} +(3.79716 + 4.76149i) q^{50} +(-2.44001 - 1.17505i) q^{51} +(-0.0849954 + 0.372389i) q^{52} +(0.445042 + 1.94986i) q^{53} +(-1.93339 + 0.931070i) q^{54} +(4.79877 + 2.31097i) q^{55} +(-1.11260 - 4.87464i) q^{56} +3.00000 q^{57} +6.09017 q^{59} +(-0.857618 - 3.75747i) q^{60} +(0.556829 + 0.268155i) q^{61} +(5.61850 - 2.70573i) q^{62} +(-1.30266 - 5.70733i) q^{63} +(0.0525301 - 0.230149i) q^{64} +(0.819729 + 0.394760i) q^{65} +(0.329118 + 0.412701i) q^{66} +(-0.952608 - 1.19453i) q^{67} +(-6.38802 + 3.07631i) q^{68} +(0.476304 - 0.597266i) q^{69} -5.32624 q^{70} +(6.52927 - 8.18745i) q^{71} +(-1.30266 + 5.70733i) q^{72} +(3.05036 - 13.3645i) q^{73} +(1.81425 - 2.27500i) q^{74} -6.09017 q^{75} +(4.89695 - 6.14058i) q^{76} +(-2.78415 + 1.34077i) q^{77} +(0.0562200 + 0.0704977i) q^{78} +(-3.79716 - 4.76149i) q^{79} +(-6.43823 - 3.10049i) q^{80} +(-1.27019 + 5.56509i) q^{81} +(-0.530037 - 2.32225i) q^{82} +(8.95948 - 4.31466i) q^{83} +(2.01463 + 0.970194i) q^{84} +(3.75805 + 16.4651i) q^{85} -4.47214 q^{86} +3.09017 q^{88} +(-1.04767 - 4.59016i) q^{89} +(5.61850 + 2.70573i) q^{90} +(-0.475589 + 0.229032i) q^{91} +(-0.445042 - 1.94986i) q^{92} +(-1.38766 + 6.07972i) q^{93} +(3.89781 + 1.87708i) q^{94} +(-11.6644 - 14.6267i) q^{95} +(-2.16484 - 2.71463i) q^{96} +(-3.20953 + 1.54563i) q^{97} +(-0.770676 + 0.966397i) q^{98} +3.61803 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q+q2q3+q4q5+3q6+3q97q10+5q11+12q124q13+5q14+7q15+3q1666q17+q18+3q19+8q205q215q22++30q99+O(q100) 12 q + q^{2} - q^{3} + q^{4} - q^{5} + 3 q^{6} + 3 q^{9} - 7 q^{10} + 5 q^{11} + 12 q^{12} - 4 q^{13} + 5 q^{14} + 7 q^{15} + 3 q^{16} - 66 q^{17} + q^{18} + 3 q^{19} + 8 q^{20} - 5 q^{21} - 5 q^{22}+ \cdots + 30 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/841Z)×\left(\mathbb{Z}/841\mathbb{Z}\right)^\times.

nn 22
χ(n)\chi(n) e(37)e\left(\frac{3}{7}\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 −0.137526 0.602539i −0.0972452 0.426059i 0.902746 0.430173i 0.141548π-0.141548\pi
−0.999992 + 0.00411419i 0.998690π0.998690\pi
33 0.556829 + 0.268155i 0.321486 + 0.154819i 0.587665 0.809104i 0.300047π-0.300047\pi
−0.266180 + 0.963923i 0.585761π0.585761\pi
44 1.45780 0.702039i 0.728899 0.351019i
55 −0.857618 3.75747i −0.383539 1.68039i −0.686294 0.727324i 0.740764π-0.740764\pi
0.302756 0.953068i 0.402093π-0.402093\pi
66 0.0849954 0.372389i 0.0346992 0.152027i
77 2.01463 + 0.970194i 0.761458 + 0.366699i 0.773969 0.633223i 0.218268π-0.218268\pi
−0.0125117 + 0.999922i 0.503983π0.503983\pi
88 −1.39417 1.74823i −0.492912 0.618092i
99 −1.63232 2.04686i −0.544106 0.682287i
1010 −2.14608 + 1.03350i −0.678649 + 0.326820i
1111 −0.861642 + 1.08046i −0.259795 + 0.325772i −0.894573 0.446922i 0.852520π-0.852520\pi
0.634778 + 0.772694i 0.281092π0.281092\pi
1212 1.00000 0.288675
1313 −0.147186 + 0.184565i −0.0408220 + 0.0511892i −0.801823 0.597561i 0.796137π-0.796137\pi
0.761001 + 0.648750i 0.224708π0.224708\pi
1414 0.307516 1.34732i 0.0821872 0.360086i
1515 0.530037 2.32225i 0.136855 0.599601i
1616 1.15601 1.44960i 0.289003 0.362399i
1717 −4.38197 −1.06278 −0.531391 0.847126i 0.678331π-0.678331\pi
−0.531391 + 0.847126i 0.678331π0.678331\pi
1818 −1.00883 + 1.26503i −0.237783 + 0.298170i
1919 4.37339 2.10612i 1.00333 0.483176i 0.141260 0.989973i 0.454885π-0.454885\pi
0.862066 + 0.506796i 0.169170π0.169170\pi
2020 −3.88812 4.87555i −0.869411 1.09021i
2121 0.861642 + 1.08046i 0.188026 + 0.235777i
2222 0.769519 + 0.370581i 0.164062 + 0.0790081i
2323 0.275051 1.20508i 0.0573521 0.251276i −0.938123 0.346303i 0.887437π-0.887437\pi
0.995475 + 0.0950275i 0.0302939π0.0302939\pi
2424 −0.307516 1.34732i −0.0627715 0.275020i
2525 −8.87824 + 4.27553i −1.77565 + 0.855107i
2626 0.131450 + 0.0633028i 0.0257794 + 0.0124147i
2727 −0.772623 3.38508i −0.148691 0.651459i
2828 3.61803 0.683744
2929 0 0
3030 −1.47214 −0.268774
3131 2.24527 + 9.83719i 0.403263 + 1.76681i 0.614038 + 0.789277i 0.289544π0.289544\pi
−0.210775 + 0.977535i 0.567599π0.567599\pi
3232 −5.06167 2.43757i −0.894786 0.430906i
3333 −0.769519 + 0.370581i −0.133956 + 0.0645099i
3434 0.602632 + 2.64030i 0.103351 + 0.452808i
3535 1.91769 8.40196i 0.324149 1.42019i
3636 −3.81657 1.83796i −0.636094 0.306327i
3737 2.93552 + 3.68102i 0.482596 + 0.605156i 0.962205 0.272326i 0.0877929π-0.0877929\pi
−0.479609 + 0.877482i 0.659221π0.659221\pi
3838 −1.87047 2.34549i −0.303430 0.380489i
3939 −0.131450 + 0.0633028i −0.0210488 + 0.0101366i
4040 −5.37326 + 6.73785i −0.849586 + 1.06535i
4141 3.85410 0.601910 0.300955 0.953638i 0.402695π-0.402695\pi
0.300955 + 0.953638i 0.402695π0.402695\pi
4242 0.532524 0.667764i 0.0821702 0.103038i
4343 1.61018 7.05464i 0.245550 1.07582i −0.690328 0.723497i 0.742534π-0.742534\pi
0.935877 0.352326i 0.114609π-0.114609\pi
4444 −0.497572 + 2.18001i −0.0750118 + 0.328648i
4545 −6.29112 + 7.88881i −0.937825 + 1.17599i
4646 −0.763932 −0.112636
4747 −4.36443 + 5.47282i −0.636617 + 0.798293i −0.990575 0.136968i 0.956264π-0.956264\pi
0.353958 + 0.935261i 0.384836π0.384836\pi
4848 1.03242 0.497187i 0.149017 0.0717627i
4949 −1.24698 1.56366i −0.178140 0.223380i
5050 3.79716 + 4.76149i 0.536999 + 0.673376i
5151 −2.44001 1.17505i −0.341669 0.164539i
5252 −0.0849954 + 0.372389i −0.0117867 + 0.0516411i
5353 0.445042 + 1.94986i 0.0611312 + 0.267833i 0.996252 0.0864950i 0.0275667π-0.0275667\pi
−0.935121 + 0.354328i 0.884710π0.884710\pi
5454 −1.93339 + 0.931070i −0.263101 + 0.126703i
5555 4.79877 + 2.31097i 0.647067 + 0.311611i
5656 −1.11260 4.87464i −0.148678 0.651401i
5757 3.00000 0.397360
5858 0 0
5959 6.09017 0.792873 0.396436 0.918062i 0.370247π-0.370247\pi
0.396436 + 0.918062i 0.370247π0.370247\pi
6060 −0.857618 3.75747i −0.110718 0.485087i
6161 0.556829 + 0.268155i 0.0712947 + 0.0343337i 0.469191 0.883097i 0.344545π-0.344545\pi
−0.397897 + 0.917430i 0.630260π0.630260\pi
6262 5.61850 2.70573i 0.713551 0.343628i
6363 −1.30266 5.70733i −0.164120 0.719056i
6464 0.0525301 0.230149i 0.00656626 0.0287687i
6565 0.819729 + 0.394760i 0.101675 + 0.0489640i
6666 0.329118 + 0.412701i 0.0405116 + 0.0507999i
6767 −0.952608 1.19453i −0.116380 0.145935i 0.720229 0.693736i 0.244037π-0.244037\pi
−0.836609 + 0.547801i 0.815465π0.815465\pi
6868 −6.38802 + 3.07631i −0.774662 + 0.373057i
6969 0.476304 0.597266i 0.0573402 0.0719024i
7070 −5.32624 −0.636607
7171 6.52927 8.18745i 0.774882 0.971671i −0.225115 0.974332i 0.572276π-0.572276\pi
0.999996 + 0.00266125i 0.000847104π0.000847104\pi
7272 −1.30266 + 5.70733i −0.153520 + 0.672615i
7373 3.05036 13.3645i 0.357018 1.56420i −0.403561 0.914953i 0.632228π-0.632228\pi
0.760579 0.649245i 0.224915π-0.224915\pi
7474 1.81425 2.27500i 0.210902 0.264463i
7575 −6.09017 −0.703232
7676 4.89695 6.14058i 0.561719 0.704373i
7777 −2.78415 + 1.34077i −0.317283 + 0.152795i
7878 0.0562200 + 0.0704977i 0.00636567 + 0.00798229i
7979 −3.79716 4.76149i −0.427214 0.535709i 0.520910 0.853612i 0.325593π-0.325593\pi
−0.948123 + 0.317903i 0.897021π0.897021\pi
8080 −6.43823 3.10049i −0.719816 0.346645i
8181 −1.27019 + 5.56509i −0.141133 + 0.618343i
8282 −0.530037 2.32225i −0.0585328 0.256449i
8383 8.95948 4.31466i 0.983431 0.473595i 0.128147 0.991755i 0.459097π-0.459097\pi
0.855284 + 0.518160i 0.173383π0.173383\pi
8484 2.01463 + 0.970194i 0.219814 + 0.105857i
8585 3.75805 + 16.4651i 0.407618 + 1.78589i
8686 −4.47214 −0.482243
8787 0 0
8888 3.09017 0.329413
8989 −1.04767 4.59016i −0.111053 0.486556i −0.999614 0.0277963i 0.991151π-0.991151\pi
0.888560 0.458760i 0.151706π-0.151706\pi
9090 5.61850 + 2.70573i 0.592242 + 0.285209i
9191 −0.475589 + 0.229032i −0.0498553 + 0.0240090i
9292 −0.445042 1.94986i −0.0463988 0.203287i
9393 −1.38766 + 6.07972i −0.143893 + 0.630437i
9494 3.89781 + 1.87708i 0.402028 + 0.193606i
9595 −11.6644 14.6267i −1.19674 1.50066i
9696 −2.16484 2.71463i −0.220948 0.277060i
9797 −3.20953 + 1.54563i −0.325878 + 0.156935i −0.589668 0.807645i 0.700742π-0.700742\pi
0.263790 + 0.964580i 0.415027π0.415027\pi
9898 −0.770676 + 0.966397i −0.0778500 + 0.0976208i
9999 3.61803 0.363626
100100 −9.94109 + 12.4657i −0.994109 + 1.24657i
101101 0.137526 0.602539i 0.0136843 0.0599548i −0.967625 0.252393i 0.918782π-0.918782\pi
0.981309 + 0.192438i 0.0616395π0.0616395\pi
102102 −0.372447 + 1.63180i −0.0368778 + 0.161572i
103103 5.72385 7.17748i 0.563988 0.707218i −0.415302 0.909684i 0.636324π-0.636324\pi
0.979289 + 0.202466i 0.0648955π0.0648955\pi
104104 0.527864 0.0517613
105105 3.32086 4.16422i 0.324082 0.406386i
106106 1.11366 0.536310i 0.108168 0.0520910i
107107 4.21724 + 5.28826i 0.407696 + 0.511235i 0.942712 0.333607i 0.108266π-0.108266\pi
−0.535016 + 0.844842i 0.679694π0.679694\pi
108108 −3.50279 4.39236i −0.337056 0.422655i
109109 12.9577 + 6.24010i 1.24112 + 0.597693i 0.935118 0.354337i 0.115293π-0.115293\pi
0.306005 + 0.952030i 0.401008π0.401008\pi
110110 0.732494 3.20926i 0.0698405 0.305991i
111111 0.647498 + 2.83687i 0.0614578 + 0.269264i
112112 3.73533 1.79884i 0.352955 0.169974i
113113 −7.15754 3.44689i −0.673325 0.324256i 0.0657920 0.997833i 0.479043π-0.479043\pi
−0.739117 + 0.673577i 0.764757π0.764757\pi
114114 −0.412577 1.80762i −0.0386413 0.169299i
115115 −4.76393 −0.444239
116116 0 0
117117 0.618034 0.0571373
118118 −0.837554 3.66956i −0.0771031 0.337811i
119119 −8.82803 4.25136i −0.809264 0.389721i
120120 −4.79877 + 2.31097i −0.438066 + 0.210962i
121121 2.02275 + 8.86226i 0.183887 + 0.805660i
122122 0.0849954 0.372389i 0.00769512 0.0337145i
123123 2.14608 + 1.03350i 0.193505 + 0.0931872i
124124 10.1792 + 12.7644i 0.914123 + 1.14627i
125125 11.6644 + 14.6267i 1.04329 + 1.30825i
126126 −3.25974 + 1.56981i −0.290400 + 0.139849i
127127 9.94109 12.4657i 0.882129 1.10615i −0.111534 0.993761i 0.535577π-0.535577\pi
0.993664 0.112394i 0.0358520π-0.0358520\pi
128128 −11.3820 −1.00603
129129 2.78833 3.49646i 0.245499 0.307846i
130130 0.125125 0.548208i 0.0109742 0.0480810i
131131 −3.18789 + 13.9670i −0.278527 + 1.22031i 0.621129 + 0.783708i 0.286674π0.286674\pi
−0.899656 + 0.436599i 0.856183π0.856183\pi
132132 −0.861642 + 1.08046i −0.0749963 + 0.0940424i
133133 10.8541 0.941170
134134 −0.588744 + 0.738262i −0.0508597 + 0.0637761i
135135 −12.0567 + 5.80622i −1.03768 + 0.499720i
136136 6.10919 + 7.66068i 0.523858 + 0.656898i
137137 4.45539 + 5.58689i 0.380650 + 0.477320i 0.934840 0.355070i 0.115543π-0.115543\pi
−0.554189 + 0.832391i 0.686972π0.686972\pi
138138 −0.425380 0.204852i −0.0362107 0.0174382i
139139 −0.287452 + 1.25941i −0.0243813 + 0.106822i −0.985654 0.168776i 0.946019π-0.946019\pi
0.961273 + 0.275598i 0.0888757π0.0888757\pi
140140 −3.10289 13.5947i −0.262242 1.14896i
141141 −3.89781 + 1.87708i −0.328254 + 0.158079i
142142 −5.83119 2.80815i −0.489343 0.235655i
143143 −0.0725948 0.318058i −0.00607068 0.0265974i
144144 −4.85410 −0.404508
145145 0 0
146146 −8.47214 −0.701159
147147 −0.275051 1.20508i −0.0226858 0.0993931i
148148 6.86361 + 3.30534i 0.564185 + 0.271697i
149149 −8.66555 + 4.17311i −0.709909 + 0.341874i −0.753747 0.657164i 0.771756π-0.771756\pi
0.0438379 + 0.999039i 0.486041π0.486041\pi
150150 0.837554 + 3.66956i 0.0683860 + 0.299619i
151151 −0.594968 + 2.60673i −0.0484178 + 0.212132i −0.993350 0.115134i 0.963270π-0.963270\pi
0.944932 + 0.327266i 0.106127π0.106127\pi
152152 −9.77921 4.70942i −0.793199 0.381984i
153153 7.15276 + 8.96928i 0.578266 + 0.725123i
154154 1.19076 + 1.49317i 0.0959541 + 0.120323i
155155 35.0374 16.8731i 2.81427 1.35528i
156156 −0.147186 + 0.184565i −0.0117843 + 0.0147771i
157157 14.5623 1.16220 0.581099 0.813833i 0.302623π-0.302623\pi
0.581099 + 0.813833i 0.302623π0.302623\pi
158158 −2.34677 + 2.94276i −0.186699 + 0.234113i
159159 −0.275051 + 1.20508i −0.0218130 + 0.0955688i
160160 −4.81813 + 21.1096i −0.380907 + 1.66886i
161161 1.72328 2.16093i 0.135814 0.170305i
162162 3.52786 0.277175
163163 −3.76241 + 4.71792i −0.294695 + 0.369536i −0.907032 0.421061i 0.861658π-0.861658\pi
0.612338 + 0.790596i 0.290229π0.290229\pi
164164 5.61850 2.70573i 0.438731 0.211282i
165165 2.05240 + 2.57363i 0.159779 + 0.200357i
166166 −3.83190 4.80506i −0.297413 0.372945i
167167 −9.48528 4.56787i −0.733993 0.353472i 0.0292604 0.999572i 0.490685π-0.490685\pi
−0.763253 + 0.646100i 0.776399π0.776399\pi
168168 0.687628 3.01269i 0.0530516 0.232434i
169169 2.88037 + 12.6197i 0.221567 + 0.970749i
170170 9.40404 4.52875i 0.721257 0.347339i
171171 −11.4497 5.51388i −0.875580 0.421657i
172172 −2.60532 11.4147i −0.198654 0.870359i
173173 4.09017 0.310970 0.155485 0.987838i 0.450306π-0.450306\pi
0.155485 + 0.987838i 0.450306π0.450306\pi
174174 0 0
175175 −22.0344 −1.66565
176176 0.570167 + 2.49806i 0.0429779 + 0.188299i
177177 3.39119 + 1.63311i 0.254897 + 0.122752i
178178 −2.62167 + 1.26253i −0.196502 + 0.0946305i
179179 3.56033 + 15.5988i 0.266112 + 1.16591i 0.914495 + 0.404598i 0.132589π0.132589\pi
−0.648383 + 0.761315i 0.724554π0.724554\pi
180180 −3.63293 + 15.9169i −0.270783 + 1.18638i
181181 −5.35560 2.57912i −0.398079 0.191705i 0.224124 0.974561i 0.428048π-0.428048\pi
−0.622203 + 0.782856i 0.713762π0.713762\pi
182182 0.203406 + 0.255063i 0.0150775 + 0.0189065i
183183 0.238152 + 0.298633i 0.0176047 + 0.0220756i
184184 −2.49022 + 1.19923i −0.183581 + 0.0884081i
185185 11.3138 14.1870i 0.831806 1.04305i
186186 3.85410 0.282596
187187 3.77568 4.73456i 0.276105 0.346225i
188188 −2.52033 + 11.0423i −0.183814 + 0.805340i
189189 1.72764 7.56927i 0.125667 0.550584i
190190 −7.20898 + 9.03977i −0.522994 + 0.655814i
191191 17.0344 1.23257 0.616284 0.787524i 0.288637π-0.288637\pi
0.616284 + 0.787524i 0.288637π0.288637\pi
192192 0.0909659 0.114068i 0.00656490 0.00823213i
193193 −11.2370 + 5.41146i −0.808857 + 0.389525i −0.792143 0.610335i 0.791035π-0.791035\pi
−0.0167141 + 0.999860i 0.505321π0.505321\pi
194194 1.37269 + 1.72130i 0.0985535 + 0.123582i
195195 0.350592 + 0.439628i 0.0251064 + 0.0314824i
196196 −2.91560 1.40408i −0.208257 0.100291i
197197 1.40006 6.13405i 0.0997499 0.437033i −0.900249 0.435376i 0.856615π-0.856615\pi
0.999999 0.00165687i 0.000527397π-0.000527397\pi
198198 −0.497572 2.18001i −0.0353609 0.154926i
199199 5.27436 2.54000i 0.373890 0.180056i −0.237496 0.971389i 0.576327π-0.576327\pi
0.611386 + 0.791333i 0.290612π0.290612\pi
200200 19.8523 + 9.56039i 1.40377 + 0.676021i
201201 −0.210120 0.920597i −0.0148207 0.0649339i
202202 −0.381966 −0.0268750
203203 0 0
204204 −4.38197 −0.306799
205205 −3.30535 14.4817i −0.230856 1.01144i
206206 −5.11188 2.46175i −0.356162 0.171518i
207207 −2.91560 + 1.40408i −0.202648 + 0.0975901i
208208 0.0973961 + 0.426720i 0.00675320 + 0.0295877i
209209 −1.49272 + 6.54002i −0.103253 + 0.452382i
210210 −2.96581 1.42826i −0.204660 0.0985591i
211211 −7.26520 9.11027i −0.500157 0.627177i 0.466108 0.884728i 0.345656π-0.345656\pi
−0.966265 + 0.257551i 0.917084π0.917084\pi
212212 2.01766 + 2.53006i 0.138573 + 0.173765i
213213 5.83119 2.80815i 0.399547 0.192412i
214214 2.60640 3.26832i 0.178170 0.223418i
215215 −27.8885 −1.90198
216216 −4.84073 + 6.07009i −0.329370 + 0.413017i
217217 −5.02059 + 21.9966i −0.340820 + 1.49323i
218218 1.97789 8.66569i 0.133959 0.586915i
219219 5.28229 6.62378i 0.356944 0.447594i
220220 8.61803 0.581028
221221 0.644964 0.808759i 0.0433850 0.0544030i
222222 1.62028 0.780285i 0.108746 0.0523693i
223223 1.66706 + 2.09043i 0.111635 + 0.139986i 0.834510 0.550993i 0.185751π-0.185751\pi
−0.722875 + 0.690979i 0.757180π0.757180\pi
224224 −7.83247 9.82161i −0.523329 0.656234i
225225 23.2435 + 11.1935i 1.54957 + 0.746233i
226226 −1.09254 + 4.78673i −0.0726747 + 0.318409i
227227 4.64814 + 20.3648i 0.308508 + 1.35166i 0.856919 + 0.515452i 0.172376π0.172376\pi
−0.548411 + 0.836209i 0.684767π0.684767\pi
228228 4.37339 2.10612i 0.289635 0.139481i
229229 −2.06484 0.994373i −0.136448 0.0657100i 0.364414 0.931237i 0.381269π-0.381269\pi
−0.500862 + 0.865527i 0.666984π0.666984\pi
230230 0.655162 + 2.87045i 0.0432001 + 0.189272i
231231 −1.90983 −0.125658
232232 0 0
233233 15.2361 0.998148 0.499074 0.866559i 0.333674π-0.333674\pi
0.499074 + 0.866559i 0.333674π0.333674\pi
234234 −0.0849954 0.372389i −0.00555633 0.0243439i
235235 24.3070 + 11.7056i 1.58561 + 0.763591i
236236 8.87824 4.27553i 0.577924 0.278314i
237237 −0.837554 3.66956i −0.0544050 0.238364i
238238 −1.34753 + 5.90390i −0.0873472 + 0.382693i
239239 24.9953 + 12.0371i 1.61681 + 0.778614i 0.999964 0.00847060i 0.00269631π-0.00269631\pi
0.616845 + 0.787085i 0.288411π0.288411\pi
240240 −2.75359 3.45289i −0.177743 0.222883i
241241 −2.90077 3.63745i −0.186855 0.234309i 0.679577 0.733605i 0.262164π-0.262164\pi
−0.866432 + 0.499296i 0.833592π0.833592\pi
242242 5.06167 2.43757i 0.325377 0.156693i
243243 −8.69411 + 10.9021i −0.557728 + 0.699368i
244244 1.00000 0.0640184
245245 −4.80599 + 6.02652i −0.307043 + 0.385020i
246246 0.327581 1.43523i 0.0208858 0.0915067i
247247 −0.254986 + 1.11717i −0.0162244 + 0.0710837i
248248 14.0674 17.6399i 0.893279 1.12014i
249249 6.14590 0.389480
250250 7.20898 9.03977i 0.455936 0.571726i
251251 17.7063 8.52689i 1.11761 0.538213i 0.218457 0.975847i 0.429898π-0.429898\pi
0.899153 + 0.437634i 0.144183π0.144183\pi
252252 −5.90578 7.40561i −0.372029 0.466510i
253253 1.06505 + 1.33553i 0.0669590 + 0.0839639i
254254 −8.87824 4.27553i −0.557070 0.268271i
255255 −2.32261 + 10.1760i −0.145447 + 0.637246i
256256 1.46025 + 6.39778i 0.0912657 + 0.399861i
257257 20.8848 10.0576i 1.30276 0.627374i 0.351619 0.936143i 0.385631π-0.385631\pi
0.951137 + 0.308769i 0.0999170π0.0999170\pi
258258 −2.49022 1.19923i −0.155034 0.0746605i
259259 2.34267 + 10.2639i 0.145566 + 0.637768i
260260 1.47214 0.0912980
261261 0 0
262262 8.85410 0.547008
263263 3.71793 + 16.2893i 0.229257 + 1.00444i 0.950248 + 0.311496i 0.100830π0.100830\pi
−0.720990 + 0.692945i 0.756313π0.756313\pi
264264 1.72070 + 0.828644i 0.105902 + 0.0509995i
265265 6.94485 3.34446i 0.426619 0.205449i
266266 −1.49272 6.54002i −0.0915243 0.400994i
267267 0.647498 2.83687i 0.0396262 0.173614i
268268 −2.22732 1.07262i −0.136055 0.0655207i
269269 −3.74094 4.69099i −0.228089 0.286015i 0.654597 0.755978i 0.272838π-0.272838\pi
−0.882686 + 0.469964i 0.844267π0.844267\pi
270270 5.15658 + 6.46614i 0.313819 + 0.393517i
271271 −9.17217 + 4.41708i −0.557170 + 0.268319i −0.691206 0.722658i 0.742920π-0.742920\pi
0.134037 + 0.990976i 0.457206π0.457206\pi
272272 −5.06561 + 6.35208i −0.307148 + 0.385151i
273273 −0.326238 −0.0197448
274274 2.75359 3.45289i 0.166350 0.208597i
275275 3.03030 13.2766i 0.182734 0.800609i
276276 0.275051 1.20508i 0.0165561 0.0725371i
277277 −13.3314 + 16.7171i −0.801008 + 1.00443i 0.198695 + 0.980061i 0.436330π0.436330\pi
−0.999703 + 0.0243714i 0.992242π0.992242\pi
278278 0.798374 0.0478833
279279 16.4704 20.6532i 0.986055 1.23647i
280280 −17.3621 + 8.36116i −1.03759 + 0.499675i
281281 14.4180 + 18.0795i 0.860103 + 1.07854i 0.996135 + 0.0878311i 0.0279936π0.0279936\pi
−0.136032 + 0.990704i 0.543435π0.543435\pi
282282 1.66706 + 2.09043i 0.0992722 + 0.124483i
283283 4.71753 + 2.27184i 0.280428 + 0.135047i 0.568811 0.822468i 0.307403π-0.307403\pi
−0.288383 + 0.957515i 0.593118π0.593118\pi
284284 3.77046 16.5194i 0.223735 0.980249i
285285 −2.57286 11.2724i −0.152403 0.667720i
286286 −0.181659 + 0.0874823i −0.0107417 + 0.00517294i
287287 7.76458 + 3.73922i 0.458329 + 0.220719i
288288 3.27288 + 14.3394i 0.192856 + 0.844960i
289289 2.20163 0.129507
290290 0 0
291291 −2.20163 −0.129062
292292 −4.93559 21.6242i −0.288834 1.26546i
293293 −7.68334 3.70010i −0.448866 0.216162i 0.195774 0.980649i 0.437278π-0.437278\pi
−0.644639 + 0.764487i 0.722992π0.722992\pi
294294 −0.688279 + 0.331458i −0.0401412 + 0.0193310i
295295 −5.22304 22.8836i −0.304097 1.33234i
296296 2.34267 10.2639i 0.136165 0.596578i
297297 4.32319 + 2.08194i 0.250857 + 0.120806i
298298 3.70619 + 4.64742i 0.214694 + 0.269218i
299299 0.181932 + 0.228135i 0.0105214 + 0.0131934i
300300 −8.87824 + 4.27553i −0.512585 + 0.246848i
301301 10.0883 12.6503i 0.581479 0.729151i
302302 1.65248 0.0950893
303303 0.238152 0.298633i 0.0136815 0.0171560i
304304 2.00269 8.77435i 0.114862 0.503244i
305305 0.530037 2.32225i 0.0303498 0.132971i
306306 4.42065 5.54332i 0.252712 0.316890i
307307 −19.1803 −1.09468 −0.547340 0.836910i 0.684360π-0.684360\pi
−0.547340 + 0.836910i 0.684360π0.684360\pi
308308 −3.11745 + 3.90916i −0.177633 + 0.222745i
309309 5.11188 2.46175i 0.290805 0.140044i
310310 −14.9852 18.7909i −0.851104 1.06725i
311311 1.30320 + 1.63416i 0.0738977 + 0.0926647i 0.817406 0.576062i 0.195411π-0.195411\pi
−0.743509 + 0.668726i 0.766840π0.766840\pi
312312 0.293930 + 0.141549i 0.0166405 + 0.00801365i
313313 2.87271 12.5862i 0.162375 0.711411i −0.826534 0.562887i 0.809691π-0.809691\pi
0.988909 0.148524i 0.0474523π-0.0474523\pi
314314 −2.00269 8.77435i −0.113018 0.495165i
315315 −20.3279 + 9.78942i −1.14535 + 0.551571i
316316 −8.87824 4.27553i −0.499440 0.240518i
317317 −6.16566 27.0135i −0.346298 1.51723i −0.785512 0.618847i 0.787600π-0.787600\pi
0.439214 0.898383i 0.355257π-0.355257\pi
318318 0.763932 0.0428392
319319 0 0
320320 −0.909830 −0.0508610
321321 0.930213 + 4.07553i 0.0519194 + 0.227474i
322322 −1.53904 0.741162i −0.0857673 0.0413033i
323323 −19.1641 + 9.22893i −1.06632 + 0.513511i
324324 2.05522 + 9.00450i 0.114179 + 0.500250i
325325 0.517637 2.26791i 0.0287133 0.125801i
326326 3.36015 + 1.61817i 0.186102 + 0.0896219i
327327 5.54192 + 6.94934i 0.306469 + 0.384300i
328328 −5.37326 6.73785i −0.296688 0.372036i
329329 −14.1024 + 6.79135i −0.777490 + 0.374420i
330330 1.26845 1.59059i 0.0698261 0.0875591i
331331 21.1803 1.16418 0.582088 0.813126i 0.302236π-0.302236\pi
0.582088 + 0.813126i 0.302236π0.302236\pi
332332 10.0321 12.5798i 0.550581 0.690406i
333333 2.74285 12.0172i 0.150307 0.658538i
334334 −1.44785 + 6.34344i −0.0792228 + 0.347098i
335335 −3.67145 + 4.60385i −0.200593 + 0.251535i
336336 2.56231 0.139785
337337 −21.2416 + 26.6361i −1.15710 + 1.45096i −0.287111 + 0.957897i 0.592695π0.592695\pi
−0.869992 + 0.493065i 0.835876π0.835876\pi
338338 7.20775 3.47107i 0.392050 0.188801i
339339 −3.06123 3.83866i −0.166263 0.208487i
340340 17.0376 + 21.3645i 0.923995 + 1.15865i
341341 −12.5634 6.05019i −0.680344 0.327636i
342342 −1.74770 + 7.65718i −0.0945049 + 0.414053i
343343 −4.47815 19.6200i −0.241797 1.05938i
344344 −14.5780 + 7.02039i −0.785992 + 0.378514i
345345 −2.65270 1.27747i −0.142816 0.0687768i
346346 −0.562503 2.46449i −0.0302403 0.132492i
347347 −32.1246 −1.72454 −0.862270 0.506449i 0.830958π-0.830958\pi
−0.862270 + 0.506449i 0.830958π0.830958\pi
348348 0 0
349349 4.52786 0.242371 0.121186 0.992630i 0.461330π-0.461330\pi
0.121186 + 0.992630i 0.461330π0.461330\pi
350350 3.03030 + 13.2766i 0.161976 + 0.709664i
351351 0.738488 + 0.355637i 0.0394176 + 0.0189825i
352352 6.99506 3.36864i 0.372838 0.179549i
353353 4.25563 + 18.6451i 0.226504 + 0.992379i 0.952466 + 0.304645i 0.0985377π0.0985377\pi
−0.725962 + 0.687735i 0.758605π0.758605\pi
354354 0.517637 2.26791i 0.0275121 0.120538i
355355 −36.3637 17.5118i −1.92999 0.929432i
356356 −4.74977 5.95602i −0.251737 0.315668i
357357 −3.77568 4.73456i −0.199830 0.250579i
358358 8.90927 4.29048i 0.470870 0.226759i
359359 −14.8166 + 18.5794i −0.781989 + 0.980583i 0.218001 + 0.975949i 0.430047π0.430047\pi
−0.999989 + 0.00463409i 0.998525π0.998525\pi
360360 22.5623 1.18914
361361 2.84455 3.56695i 0.149713 0.187734i
362362 −0.817489 + 3.58165i −0.0429663 + 0.188248i
363363 −1.25013 + 5.47718i −0.0656148 + 0.287477i
364364 −0.532524 + 0.667764i −0.0279118 + 0.0350003i
365365 −52.8328 −2.76540
366366 0.147186 0.184565i 0.00769353 0.00964739i
367367 −24.5699 + 11.8322i −1.28254 + 0.617637i −0.946041 0.324047i 0.894956π-0.894956\pi
−0.336496 + 0.941685i 0.609242π0.609242\pi
368368 −1.42891 1.79180i −0.0744872 0.0934039i
369369 −6.29112 7.88881i −0.327503 0.410675i
370370 −10.1042 4.86591i −0.525291 0.252967i
371371 −0.995144 + 4.36001i −0.0516653 + 0.226360i
372372 2.24527 + 9.83719i 0.116412 + 0.510034i
373373 −18.5762 + 8.94583i −0.961840 + 0.463198i −0.847822 0.530281i 0.822086π-0.822086\pi
−0.114018 + 0.993479i 0.536372π0.536372\pi
374374 −3.37201 1.62387i −0.174362 0.0839685i
375375 2.57286 + 11.2724i 0.132862 + 0.582105i
376376 15.6525 0.807215
377377 0 0
378378 −4.79837 −0.246802
379379 5.40543 + 23.6828i 0.277658 + 1.21650i 0.900745 + 0.434348i 0.143021π0.143021\pi
−0.623087 + 0.782153i 0.714122π0.714122\pi
380380 −27.2728 13.1339i −1.39906 0.673754i
381381 8.87824 4.27553i 0.454846 0.219042i
382382 −2.34267 10.2639i −0.119861 0.525147i
383383 6.42064 28.1307i 0.328079 1.43741i −0.494707 0.869060i 0.664725π-0.664725\pi
0.822787 0.568350i 0.192418π-0.192418\pi
384384 −6.33781 3.05213i −0.323425 0.155753i
385385 7.42566 + 9.31148i 0.378447 + 0.474557i
386386 4.80599 + 6.02652i 0.244618 + 0.306742i
387387 −17.0682 + 8.21961i −0.867625 + 0.417826i
388388 −3.59375 + 4.50642i −0.182445 + 0.228779i
389389 −19.1246 −0.969656 −0.484828 0.874609i 0.661118π-0.661118\pi
−0.484828 + 0.874609i 0.661118π0.661118\pi
390390 0.216678 0.271705i 0.0109719 0.0137583i
391391 −1.20526 + 5.28061i −0.0609528 + 0.267052i
392392 −0.995144 + 4.36001i −0.0502624 + 0.220214i
393393 −5.52044 + 6.92242i −0.278469 + 0.349190i
394394 −3.88854 −0.195902
395395 −14.6346 + 18.3513i −0.736349 + 0.923352i
396396 5.27436 2.54000i 0.265047 0.127640i
397397 −8.76360 10.9892i −0.439833 0.551533i 0.511666 0.859184i 0.329028π-0.329028\pi
−0.951499 + 0.307651i 0.900457π0.900457\pi
398398 −2.25581 2.82869i −0.113073 0.141790i
399399 6.04388 + 2.91058i 0.302573 + 0.145711i
400400 −4.06557 + 17.8124i −0.203279 + 0.890622i
401401 −5.57835 24.4404i −0.278570 1.22049i −0.899603 0.436709i 0.856144π-0.856144\pi
0.621033 0.783784i 0.286713π-0.286713\pi
402402 −0.525798 + 0.253211i −0.0262244 + 0.0126290i
403403 −2.14608 1.03350i −0.106904 0.0514821i
404404 −0.222521 0.974928i −0.0110708 0.0485045i
405405 22.0000 1.09319
406406 0 0
407407 −6.50658 −0.322519
408408 1.34753 + 5.90390i 0.0667125 + 0.292287i
409409 −24.7013 11.8955i −1.22140 0.588196i −0.291700 0.956510i 0.594221π-0.594221\pi
−0.929702 + 0.368313i 0.879935π0.879935\pi
410410 −8.27120 + 3.98320i −0.408485 + 0.196716i
411411 0.982743 + 4.30568i 0.0484751 + 0.212383i
412412 3.30535 14.4817i 0.162843 0.713461i
413413 12.2694 + 5.90864i 0.603739 + 0.290745i
414414 1.24698 + 1.56366i 0.0612857 + 0.0768498i
415415 −23.8960 29.9647i −1.17301 1.47091i
416416 1.19490 0.575433i 0.0585847 0.0282129i
417417 −0.497778 + 0.624194i −0.0243763 + 0.0305669i
418418 4.14590 0.202783
419419 −10.9499 + 13.7308i −0.534939 + 0.670792i −0.973706 0.227809i 0.926844π-0.926844\pi
0.438767 + 0.898601i 0.355415π0.355415\pi
420420 1.91769 8.40196i 0.0935738 0.409974i
421421 6.90581 30.2563i 0.336569 1.47460i −0.469579 0.882890i 0.655594π-0.655594\pi
0.806148 0.591714i 0.201548π-0.201548\pi
422422 −4.49014 + 5.63046i −0.218577 + 0.274086i
423423 18.3262 0.891052
424424 2.78833 3.49646i 0.135413 0.169803i
425425 38.9041 18.7352i 1.88713 0.908793i
426426 −2.49396 3.12733i −0.120833 0.151519i
427427 0.861642 + 1.08046i 0.0416978 + 0.0522873i
428428 9.86045 + 4.74854i 0.476623 + 0.229529i
429429 0.0448660 0.196571i 0.00216615 0.00949053i
430430 3.83539 + 16.8039i 0.184959 + 0.810357i
431431 −13.1512 + 6.33329i −0.633472 + 0.305064i −0.722924 0.690927i 0.757203π-0.757203\pi
0.0894526 + 0.995991i 0.471488π0.471488\pi
432432 −5.80016 2.79321i −0.279060 0.134388i
433433 −2.31020 10.1217i −0.111021 0.486416i −0.999616 0.0277224i 0.991175π-0.991175\pi
0.888594 0.458694i 0.151683π-0.151683\pi
434434 13.9443 0.669346
435435 0 0
436436 23.2705 1.11446
437437 −1.33513 5.84957i −0.0638677 0.279823i
438438 −4.71753 2.27184i −0.225413 0.108553i
439439 18.8701 9.08738i 0.900622 0.433717i 0.0745088 0.997220i 0.476261π-0.476261\pi
0.826114 + 0.563503i 0.190547π0.190547\pi
440440 −2.65019 11.6112i −0.126343 0.553543i
441441 −1.16513 + 5.10479i −0.0554826 + 0.243085i
442442 −0.576008 0.277391i −0.0273979 0.0131941i
443443 −1.19076 1.49317i −0.0565747 0.0709424i 0.752739 0.658319i 0.228732π-0.228732\pi
−0.809314 + 0.587377i 0.800161π0.800161\pi
444444 2.93552 + 3.68102i 0.139313 + 0.174694i
445445 −16.3489 + 7.87321i −0.775012 + 0.373226i
446446 1.03030 1.29196i 0.0487862 0.0611760i
447447 −5.94427 −0.281154
448448 0.329118 0.412701i 0.0155494 0.0194983i
449449 5.81327 25.4696i 0.274345 1.20199i −0.630481 0.776205i 0.717142π-0.717142\pi
0.904826 0.425781i 0.140001π-0.140001\pi
450450 3.54793 15.5445i 0.167251 0.732775i
451451 −3.32086 + 4.16422i −0.156373 + 0.196085i
452452 −12.8541 −0.604606
453453 −1.03030 + 1.29196i −0.0484078 + 0.0607015i
454454 11.6314 5.60137i 0.545887 0.262885i
455455 1.26845 + 1.59059i 0.0594660 + 0.0745680i
456456 −4.18250 5.24469i −0.195863 0.245605i
457457 −16.8555 8.11719i −0.788467 0.379706i −0.00409151 0.999992i 0.501302π-0.501302\pi
−0.784376 + 0.620286i 0.787017π0.787017\pi
458458 −0.315180 + 1.38090i −0.0147274 + 0.0645250i
459459 3.38561 + 14.8333i 0.158027 + 0.692360i
460460 −6.94485 + 3.34446i −0.323805 + 0.155936i
461461 35.1186 + 16.9122i 1.63564 + 0.787681i 0.999875 + 0.0157954i 0.00502805π0.00502805\pi
0.635761 + 0.771886i 0.280686π0.280686\pi
462462 0.262650 + 1.15075i 0.0122196 + 0.0535376i
463463 10.7082 0.497652 0.248826 0.968548i 0.419955π-0.419955\pi
0.248826 + 0.968548i 0.419955π0.419955\pi
464464 0 0
465465 24.0344 1.11457
466466 −2.09535 9.18032i −0.0970651 0.425270i
467467 16.1672 + 7.78573i 0.748130 + 0.360281i 0.768786 0.639506i 0.220861π-0.220861\pi
−0.0206558 + 0.999787i 0.506575π0.506575\pi
468468 0.900969 0.433884i 0.0416473 0.0200563i
469469 −0.760222 3.33075i −0.0351038 0.153800i
470470 3.71026 16.2557i 0.171142 0.749820i
471471 8.10872 + 3.90495i 0.373630 + 0.179931i
472472 −8.49071 10.6470i −0.390816 0.490068i
473473 6.23490 + 7.81831i 0.286681 + 0.359486i
474474 −2.09587 + 1.00932i −0.0962664 + 0.0463595i
475475 −29.8233 + 37.3972i −1.36839 + 1.71590i
476476 −15.8541 −0.726672
477477 3.26463 4.09372i 0.149477 0.187439i
478478 3.81532 16.7160i 0.174509 0.764573i
479479 2.48786 10.9000i 0.113673 0.498035i −0.885753 0.464157i 0.846357π-0.846357\pi
0.999426 0.0338776i 0.0107856π-0.0107856\pi
480480 −8.34352 + 10.4624i −0.380828 + 0.477543i
481481 −1.11146 −0.0506780
482482 −1.79278 + 2.24807i −0.0816587 + 0.102397i
483483 1.53904 0.741162i 0.0700287 0.0337240i
484484 9.17042 + 11.4993i 0.416837 + 0.522697i
485485 8.56020 + 10.7341i 0.388699 + 0.487413i
486486 7.76458 + 3.73922i 0.352209 + 0.169615i
487487 −9.47100 + 41.4952i −0.429172 + 1.88033i 0.0434408 + 0.999056i 0.486168π0.486168\pi
−0.472613 + 0.881270i 0.656689π0.656689\pi
488488 −0.307516 1.34732i −0.0139206 0.0609902i
489489 −3.36015 + 1.61817i −0.151951 + 0.0731760i
490490 4.29215 + 2.06699i 0.193900 + 0.0933772i
491491 3.36554 + 14.7454i 0.151885 + 0.665451i 0.992337 + 0.123564i 0.0394326π0.0394326\pi
−0.840452 + 0.541886i 0.817710π0.817710\pi
492492 3.85410 0.173756
493493 0 0
494494 0.708204 0.0318636
495495 −3.10289 13.5947i −0.139465 0.611035i
496496 16.8555 + 8.11719i 0.756835 + 0.364472i
497497 21.0975 10.1600i 0.946350 0.455738i
498498 −0.845218 3.70314i −0.0378751 0.165942i
499499 −5.49336 + 24.0680i −0.245916 + 1.07743i 0.689612 + 0.724179i 0.257781π0.257781\pi
−0.935529 + 0.353251i 0.885076π0.885076\pi
500500 27.2728 + 13.1339i 1.21968 + 0.587365i
501501 −4.05678 5.08705i −0.181244 0.227273i
502502 −7.57284 9.49605i −0.337993 0.423829i
503503 −12.8573 + 6.19174i −0.573278 + 0.276076i −0.697979 0.716118i 0.745917π-0.745917\pi
0.124701 + 0.992194i 0.460203π0.460203\pi
504504 −8.16159 + 10.2343i −0.363546 + 0.455872i
505505 −2.38197 −0.105996
506506 0.658236 0.825401i 0.0292621 0.0366936i
507507 −1.78017 + 7.79942i −0.0790600 + 0.346385i
508508 5.74068 25.1516i 0.254701 1.11592i
509509 19.6788 24.6764i 0.872246 1.09376i −0.122609 0.992455i 0.539126π-0.539126\pi
0.994855 0.101307i 0.0323025π-0.0323025\pi
510510 6.45085 0.285648
511511 19.1115 23.9651i 0.845443 1.06015i
512512 −16.8555 + 8.11719i −0.744915 + 0.358732i
513513 −10.5084 13.1771i −0.463955 0.581782i
514514 −8.93226 11.2007i −0.393985 0.494042i
515515 −31.8780 15.3517i −1.40471 0.676475i
516516 1.61018 7.05464i 0.0708841 0.310563i
517517 −2.15261 9.43122i −0.0946719 0.414785i
518518 5.86222 2.82310i 0.257571 0.124040i
519519 2.27753 + 1.09680i 0.0999723 + 0.0481441i
520520 −0.452706 1.98343i −0.0198525 0.0869793i
521521 4.09017 0.179194 0.0895968 0.995978i 0.471442π-0.471442\pi
0.0895968 + 0.995978i 0.471442π0.471442\pi
522522 0 0
523523 −20.3820 −0.891241 −0.445621 0.895222i 0.647017π-0.647017\pi
−0.445621 + 0.895222i 0.647017π0.647017\pi
524524 5.15811 + 22.5992i 0.225333 + 0.987249i
525525 −12.2694 5.90864i −0.535482 0.257874i
526526 9.30362 4.48039i 0.405657 0.195354i
527527 −9.83871 43.1062i −0.428581 1.87774i
528528 −0.352382 + 1.54389i −0.0153355 + 0.0671891i
529529 19.3457 + 9.31641i 0.841119 + 0.405061i
530530 −2.97026 3.72459i −0.129020 0.161786i
531531 −9.94109 12.4657i −0.431407 0.540967i
532532 15.8231 7.62000i 0.686018 0.330369i
533533 −0.567270 + 0.711334i −0.0245712 + 0.0308113i
534534 −1.79837 −0.0778232
535535 16.2537 20.3815i 0.702708 0.881168i
536536 −0.760222 + 3.33075i −0.0328366 + 0.143867i
537537 −2.20041 + 9.64062i −0.0949546 + 0.416023i
538538 −2.31203 + 2.89919i −0.0996786 + 0.124993i
539539 2.76393 0.119051
540540 −13.5001 + 16.9286i −0.580952 + 0.728490i
541541 13.1512 6.33329i 0.565415 0.272289i −0.129263 0.991610i 0.541261π-0.541261\pi
0.694678 + 0.719321i 0.255547π0.255547\pi
542542 3.92287 + 4.91912i 0.168502 + 0.211294i
543543 −2.29055 2.87226i −0.0982970 0.123261i
544544 22.1801 + 10.6814i 0.950963 + 0.457960i
545545 12.3342 54.0398i 0.528341 2.31481i
546546 0.0448660 + 0.196571i 0.00192009 + 0.00841246i
547547 −6.65092 + 3.20292i −0.284373 + 0.136947i −0.570633 0.821205i 0.693302π-0.693302\pi
0.286260 + 0.958152i 0.407588π0.407588\pi
548548 10.4173 + 5.01670i 0.445004 + 0.214303i
549549 −0.360046 1.57747i −0.0153664 0.0673246i
550550 −8.41641 −0.358877
551551 0 0
552552 −1.70820 −0.0727060
553553 −3.03030 13.2766i −0.128861 0.564579i
554554 11.9061 + 5.73368i 0.505842 + 0.243601i
555555 10.1042 4.86591i 0.428898 0.206546i
556556 0.465107 + 2.03777i 0.0197249 + 0.0864205i
557557 1.22533 5.36852i 0.0519188 0.227471i −0.942312 0.334737i 0.891352π-0.891352\pi
0.994230 + 0.107266i 0.0342096π0.0342096\pi
558558 −14.7094 7.08369i −0.622700 0.299876i
559559 1.06505 + 1.33553i 0.0450467 + 0.0564868i
560560 −9.96257 12.4927i −0.420995 0.527911i
561561 3.37201 1.62387i 0.142366 0.0685600i
562562 8.91079 11.1738i 0.375879 0.471337i
563563 28.3951 1.19671 0.598356 0.801230i 0.295821π-0.295821\pi
0.598356 + 0.801230i 0.295821π0.295821\pi
564564 −4.36443 + 5.47282i −0.183776 + 0.230447i
565565 −6.81315 + 29.8504i −0.286632 + 1.25581i
566566 0.720093 3.15493i 0.0302678 0.132612i
567567 −7.95818 + 9.97924i −0.334212 + 0.419089i
568568 −23.4164 −0.982531
569569 −1.21223 + 1.52009i −0.0508195 + 0.0637256i −0.806592 0.591109i 0.798690π-0.798690\pi
0.755772 + 0.654835i 0.227262π0.227262\pi
570570 −6.43823 + 3.10049i −0.269668 + 0.129865i
571571 −21.5145 26.9783i −0.900354 1.12901i −0.991098 0.133134i 0.957496π-0.957496\pi
0.0907443 0.995874i 0.471075π-0.471075\pi
572572 −0.329118 0.412701i −0.0137611 0.0172559i
573573 9.48528 + 4.56787i 0.396253 + 0.190825i
574574 1.18520 5.19270i 0.0494693 0.216739i
575575 2.71038 + 11.8750i 0.113031 + 0.495220i
576576 −0.556829 + 0.268155i −0.0232012 + 0.0111731i
577577 2.49022 + 1.19923i 0.103669 + 0.0499244i 0.485000 0.874514i 0.338820π-0.338820\pi
−0.381331 + 0.924439i 0.624534π0.624534\pi
578578 −0.302780 1.32656i −0.0125940 0.0551778i
579579 −7.70820 −0.320342
580580 0 0
581581 22.2361 0.922508
582582 0.302780 + 1.32656i 0.0125506 + 0.0549879i
583583 −2.49022 1.19923i −0.103134 0.0496668i
584584 −27.6169 + 13.2996i −1.14280 + 0.550342i
585585 −0.530037 2.32225i −0.0219143 0.0960130i
586586 −1.17280 + 5.13837i −0.0484479 + 0.212264i
587587 −42.0014 20.2268i −1.73358 0.834850i −0.985162 0.171626i 0.945098π-0.945098\pi
−0.748421 0.663224i 0.769188π-0.769188\pi
588588 −1.24698 1.56366i −0.0514246 0.0644844i
589589 30.5377 + 38.2931i 1.25829 + 1.57784i
590590 −13.0700 + 6.29417i −0.538082 + 0.259127i
591591 2.42447 3.04019i 0.0997293 0.125057i
592592 8.72949 0.358780
593593 −9.00176 + 11.2878i −0.369658 + 0.463536i −0.931518 0.363696i 0.881515π-0.881515\pi
0.561860 + 0.827232i 0.310086π0.310086\pi
594594 0.659899 2.89121i 0.0270760 0.118628i
595595 −8.40327 + 36.8171i −0.344500 + 1.50935i
596596 −9.70294 + 12.1671i −0.397448 + 0.498384i
597597 3.61803 0.148076
598598 0.112440 0.140995i 0.00459802 0.00576573i
599599 −11.7747 + 5.67038i −0.481099 + 0.231685i −0.658683 0.752420i 0.728886π-0.728886\pi
0.177584 + 0.984106i 0.443172π0.443172\pi
600600 8.49071 + 10.6470i 0.346632 + 0.434662i
601601 18.1804 + 22.7975i 0.741593 + 0.929928i 0.999342 0.0362840i 0.0115521π-0.0115521\pi
−0.257749 + 0.966212i 0.582981π0.582981\pi
602602 −9.00969 4.33884i −0.367207 0.176838i
603603 −0.890084 + 3.89971i −0.0362470 + 0.158809i
604604 0.962679 + 4.21777i 0.0391708 + 0.171619i
605605 31.5649 15.2009i 1.28330 0.618003i
606606 −0.212690 0.102426i −0.00863994 0.00416077i
607607 −2.44299 10.7035i −0.0991581 0.434440i −1.00000 0.000292533i 0.999907π-0.999907\pi
0.900842 0.434147i 0.142950π-0.142950\pi
608608 −27.2705 −1.10597
609609 0 0
610610 −1.47214 −0.0596050
611611 −0.367710 1.61104i −0.0148760 0.0651759i
612612 16.7241 + 8.05388i 0.676030 + 0.325559i
613613 −24.8136 + 11.9496i −1.00221 + 0.482640i −0.861689 0.507438i 0.830593π-0.830593\pi
−0.140523 + 0.990077i 0.544879π0.544879\pi
614614 2.63779 + 11.5569i 0.106452 + 0.466398i
615615 2.04282 8.95017i 0.0823744 0.360906i
616616 6.22554 + 2.99806i 0.250834 + 0.120795i
617617 −8.84130 11.0866i −0.355937 0.446331i 0.571336 0.820716i 0.306425π-0.306425\pi
−0.927273 + 0.374385i 0.877854π0.877854\pi
618618 −2.18632 2.74155i −0.0879465 0.110281i
619619 −6.35699 + 3.06137i −0.255509 + 0.123047i −0.557254 0.830342i 0.688145π-0.688145\pi
0.301745 + 0.953389i 0.402431π0.402431\pi
620620 39.2318 49.1952i 1.57559 1.97573i
621621 −4.29180 −0.172224
622622 0.805422 1.00997i 0.0322945 0.0404960i
623623 2.34267 10.2639i 0.0938571 0.411215i
624624 −0.0601941 + 0.263728i −0.00240969 + 0.0105576i
625625 14.2360 17.8514i 0.569441 0.714057i
626626 −7.97871 −0.318894
627627 −2.58493 + 3.24139i −0.103232 + 0.129449i
628628 21.2289 10.2233i 0.847125 0.407954i
629629 −12.8633 16.1301i −0.512895 0.643150i
630630 8.69411 + 10.9021i 0.346382 + 0.434349i
631631 25.4206 + 12.2419i 1.01198 + 0.487344i 0.864987 0.501794i 0.167326π-0.167326\pi
0.146992 + 0.989138i 0.453041π0.453041\pi
632632 −3.03030 + 13.2766i −0.120539 + 0.528115i
633633 −1.60251 7.02107i −0.0636942 0.279062i
634634 −15.4287 + 7.43009i −0.612754 + 0.295087i
635635 −55.3653 26.6625i −2.19711 1.05807i
636636 0.445042 + 1.94986i 0.0176471 + 0.0773168i
637637 0.472136 0.0187067
638638 0 0
639639 −27.4164 −1.08458
640640 9.76138 + 42.7674i 0.385853 + 1.69053i
641641 −9.96087 4.79690i −0.393431 0.189466i 0.226700 0.973965i 0.427206π-0.427206\pi
−0.620131 + 0.784498i 0.712921π0.712921\pi
642642 2.32774 1.12098i 0.0918684 0.0442415i
643643 8.32593 + 36.4783i 0.328343 + 1.43856i 0.822288 + 0.569071i 0.192697π0.192697\pi
−0.493946 + 0.869493i 0.664446π0.664446\pi
644644 0.995144 4.36001i 0.0392142 0.171808i
645645 −15.5292 7.47845i −0.611460 0.294464i
646646 8.19633 + 10.2779i 0.322480 + 0.404378i
647647 −19.0338 23.8676i −0.748296 0.938334i 0.251266 0.967918i 0.419153π-0.419153\pi
−0.999562 + 0.0295841i 0.990582π0.990582\pi
648648 11.4999 5.53806i 0.451759 0.217556i
649649 −5.24754 + 6.58021i −0.205984 + 0.258296i
650650 −1.43769 −0.0563910
651651 −8.69411 + 10.9021i −0.340749 + 0.427286i
652652 −2.17268 + 9.51913i −0.0850887 + 0.372798i
653653 −10.6839 + 46.8094i −0.418095 + 1.83179i 0.125047 + 0.992151i 0.460092π0.460092\pi
−0.543141 + 0.839641i 0.682765π0.682765\pi
654654 3.42509 4.29493i 0.133932 0.167945i
655655 55.2148 2.15742
656656 4.45539 5.58689i 0.173954 0.218131i
657657 −32.3345 + 15.5715i −1.26149 + 0.607500i
658658 6.03149 + 7.56325i 0.235132 + 0.294846i
659659 −4.39917 5.51639i −0.171368 0.214888i 0.688730 0.725018i 0.258169π-0.258169\pi
−0.860097 + 0.510130i 0.829597π0.829597\pi
660660 4.79877 + 2.31097i 0.186792 + 0.0899543i
661661 8.33360 36.5119i 0.324139 1.42015i −0.505972 0.862550i 0.668866π-0.668866\pi
0.830111 0.557598i 0.188277π-0.188277\pi
662662 −2.91284 12.7620i −0.113211 0.496008i
663663 0.576008 0.277391i 0.0223703 0.0107730i
664664 −20.0340 9.64787i −0.777470 0.374410i
665665 −9.30868 40.7840i −0.360975 1.58153i
666666 −7.61803 −0.295193
667667 0 0
668668 −17.0344 −0.659082
669669 0.367710 + 1.61104i 0.0142165 + 0.0622866i
670670 3.27891 + 1.57904i 0.126676 + 0.0610037i
671671 −0.769519 + 0.370581i −0.0297070 + 0.0143061i
672672 −1.72764 7.56927i −0.0666451 0.291991i
673673 1.44019 6.30987i 0.0555151 0.243227i −0.939556 0.342397i 0.888761π-0.888761\pi
0.995071 + 0.0991692i 0.0316185π0.0316185\pi
674674 18.9706 + 9.13574i 0.730718 + 0.351895i
675675 21.3326 + 26.7502i 0.821091 + 1.02962i
676676 13.0585 + 16.3749i 0.502252 + 0.629804i
677677 36.7891 17.7167i 1.41392 0.680908i 0.437987 0.898981i 0.355691π-0.355691\pi
0.975932 + 0.218073i 0.0699772π0.0699772\pi
678678 −1.89194 + 2.37242i −0.0726597 + 0.0911123i
679679 −7.96556 −0.305690
680680 23.5454 29.5250i 0.902926 1.13223i
681681 −2.87271 + 12.5862i −0.110082 + 0.482302i
682682 −1.91769 + 8.40196i −0.0734323 + 0.321728i
683683 13.0023 16.3044i 0.497520 0.623870i −0.468148 0.883650i 0.655079π-0.655079\pi
0.965668 + 0.259780i 0.0836500π0.0836500\pi
684684 −20.5623 −0.786219
685685 17.1715 21.5324i 0.656091 0.822712i
686686 −11.2060 + 5.39651i −0.427846 + 0.206040i
687687 −0.883116 1.10739i −0.0336930 0.0422496i
688688 −8.36499 10.4894i −0.318912 0.399903i
689689 −0.425380 0.204852i −0.0162057 0.00780424i
690690 −0.404912 + 1.77404i −0.0154148 + 0.0675365i
691691 −2.63305 11.5361i −0.100166 0.438856i −0.999997 0.00261618i 0.999167π-0.999167\pi
0.899831 0.436239i 0.143690π-0.143690\pi
692692 5.96264 2.87146i 0.226666 0.109156i
693693 7.28899 + 3.51019i 0.276886 + 0.133341i
694694 4.41795 + 19.3563i 0.167703 + 0.734756i
695695 4.97871 0.188853
696696 0 0
697697 −16.8885 −0.639699
698698 −0.622697 2.72821i −0.0235694 0.103264i
699699 8.48389 + 4.08563i 0.320890 + 0.154533i
700700 −32.1218 + 15.4690i −1.21409 + 0.584674i
701701 4.68534 + 20.5278i 0.176963 + 0.775325i 0.983022 + 0.183490i 0.0587393π0.0587393\pi
−0.806059 + 0.591835i 0.798404π0.798404\pi
702702 0.112724 0.493877i 0.00425450 0.0186402i
703703 20.5908 + 9.91602i 0.776598 + 0.373990i
704704 0.203406 + 0.255063i 0.00766615 + 0.00961305i
705705 10.3959 + 13.0361i 0.391533 + 0.490967i
706706 10.6491 5.12836i 0.400786 0.193008i
707707 0.861642 1.08046i 0.0324054 0.0406351i
708708 6.09017 0.228883
709709 −25.8789 + 32.4511i −0.971904 + 1.21873i 0.00388053 + 0.999992i 0.498765π0.498765\pi
−0.975784 + 0.218736i 0.929807π0.929807\pi
710710 −5.55062 + 24.3189i −0.208311 + 0.912671i
711711 −3.54793 + 15.5445i −0.133058 + 0.582965i
712712 −6.56402 + 8.23102i −0.245997 + 0.308470i
713713 12.4721 0.467085
714714 −2.33350 + 2.92612i −0.0873291 + 0.109507i
715715 −1.13284 + 0.545546i −0.0423657 + 0.0204022i
716716 16.1412 + 20.2405i 0.603227 + 0.756422i
717717 10.6903 + 13.4052i 0.399236 + 0.500626i
718718 13.2325 + 6.37241i 0.493831 + 0.237816i
719719 −1.89289 + 8.29330i −0.0705929 + 0.309288i −0.997881 0.0650598i 0.979276π-0.979276\pi
0.927288 + 0.374348i 0.122133π0.122133\pi
720720 4.16297 + 18.2392i 0.155145 + 0.679733i
721721 18.4950 8.90671i 0.688789 0.331703i
722722 −2.54043 1.22340i −0.0945449 0.0455304i
723723 −0.639834 2.80330i −0.0237957 0.104256i
724724 −9.61803 −0.357451
725725 0 0
726726 3.47214 0.128863
727727 −6.24299 27.3523i −0.231540 1.01444i −0.948363 0.317187i 0.897262π-0.897262\pi
0.716824 0.697255i 0.245595π-0.245595\pi
728728 1.06345 + 0.512130i 0.0394141 + 0.0189808i
729729 7.66416 3.69087i 0.283858 0.136699i
730730 7.26586 + 31.8338i 0.268922 + 1.17822i
731731 −7.05574 + 30.9132i −0.260966 + 1.14337i
732732 0.556829 + 0.268155i 0.0205810 + 0.00991129i
733733 9.23991 + 11.5865i 0.341284 + 0.427956i 0.922622 0.385706i 0.126042π-0.126042\pi
−0.581338 + 0.813662i 0.697471π0.697471\pi
734734 10.5084 + 13.1771i 0.387871 + 0.486374i
735735 −4.29215 + 2.06699i −0.158319 + 0.0762422i
736736 −4.32968 + 5.42925i −0.159594 + 0.200125i
737737 2.11146 0.0777765
738738 −3.88812 + 4.87555i −0.143124 + 0.179472i
739739 11.1414 48.8136i 0.409842 1.79564i −0.175089 0.984553i 0.556021π-0.556021\pi
0.584931 0.811083i 0.301122π-0.301122\pi
740740 6.53337 28.6245i 0.240171 1.05226i
741741 −0.441558 + 0.553696i −0.0162210 + 0.0203405i
742742 2.76393 0.101467
743743 21.9693 27.5487i 0.805977 1.01066i −0.193586 0.981083i 0.562012π-0.562012\pi
0.999562 0.0295793i 0.00941674π-0.00941674\pi
744744 12.5634 6.05019i 0.460595 0.221811i
745745 23.1121 + 28.9816i 0.846761 + 1.06180i
746746 7.94491 + 9.96260i 0.290884 + 0.364757i
747747 −23.4562 11.2959i −0.858218 0.413296i
748748 2.18034 9.55271i 0.0797212 0.349282i
749749 3.36554 + 14.7454i 0.122974 + 0.538785i
750750 6.43823 3.10049i 0.235091 0.113214i
751751 16.6930 + 8.03894i 0.609137 + 0.293345i 0.712910 0.701256i 0.247377π-0.247377\pi
−0.103772 + 0.994601i 0.533091π0.533091\pi
752752 2.88804 + 12.6533i 0.105316 + 0.461419i
753753 12.1459 0.442621
754754 0 0
755755 10.3050 0.375036
756756 −2.79538 12.2473i −0.101667 0.445432i
757757 0.0191782 + 0.00923575i 0.000697045 + 0.000335679i 0.434232 0.900801i 0.357020π-0.357020\pi
−0.433535 + 0.901137i 0.642734π0.642734\pi
758758 13.5264 6.51396i 0.491300 0.236598i
759759 0.234922 + 1.02926i 0.00852711 + 0.0373597i
760760 −9.30868 + 40.7840i −0.337661 + 1.47939i
761761 −22.7059 10.9346i −0.823088 0.396378i −0.0255694 0.999673i 0.508140π-0.508140\pi
−0.797518 + 0.603295i 0.793854π0.793854\pi
762762 −3.79716 4.76149i −0.137557 0.172490i
763763 20.0508 + 25.1430i 0.725889 + 0.910236i
764764 24.8328 11.9588i 0.898418 0.432656i
765765 27.5675 34.5685i 0.996704 1.24983i
766766 −17.8328 −0.644326
767767 −0.896388 + 1.12403i −0.0323667 + 0.0405865i
768768 −0.902484 + 3.95404i −0.0325656 + 0.142679i
769769 4.30816 18.8753i 0.155356 0.680660i −0.835919 0.548852i 0.815065π-0.815065\pi
0.991275 0.131807i 0.0420780π-0.0420780\pi
770770 4.58931 5.75481i 0.165387 0.207389i
771771 14.3262 0.515947
772772 −12.5822 + 15.7776i −0.452845 + 0.567849i
773773 12.6136 6.07437i 0.453678 0.218480i −0.193068 0.981185i 0.561844π-0.561844\pi
0.646746 + 0.762705i 0.276129π0.276129\pi
774774 7.29995 + 9.15384i 0.262391 + 0.329028i
775775 −61.9933 77.7372i −2.22687 2.79240i
776776 7.17672 + 3.45613i 0.257629 + 0.124068i
777777 −1.44785 + 6.34344i −0.0519413 + 0.227570i
778778 2.63012 + 11.5233i 0.0942944 + 0.413131i
779779 16.8555 8.11719i 0.603911 0.290828i
780780 0.819729 + 0.394760i 0.0293510 + 0.0141347i
781781 3.22035 + 14.1093i 0.115233 + 0.504870i
782782 3.34752 0.119707
783783 0 0
784784 −3.70820 −0.132436
785785 −12.4889 54.7175i −0.445748 1.95295i
786786 4.93022 + 2.37427i 0.175855 + 0.0846874i
787787 −17.4434 + 8.40028i −0.621789 + 0.299438i −0.718128 0.695911i 0.755001π-0.755001\pi
0.0963393 + 0.995349i 0.469287π0.469287\pi
788788 −2.26534 9.92510i −0.0806994 0.353567i
789789 −2.29780 + 10.0673i −0.0818040 + 0.358407i
790790 13.0700 + 6.29417i 0.465009 + 0.223936i
791791 −11.0756 13.8884i −0.393804 0.493815i
792792 −5.04414 6.32515i −0.179236 0.224754i
793793 −0.131450 + 0.0633028i −0.00466791 + 0.00224795i
794794 −5.41620 + 6.79171i −0.192214 + 0.241029i
795795 4.76393 0.168959
796796 5.90578 7.40561i 0.209325 0.262485i
797797 −9.60853 + 42.0977i −0.340352 + 1.49118i 0.457982 + 0.888962i 0.348573π0.348573\pi
−0.798333 + 0.602216i 0.794285π0.794285\pi
798798 0.922549 4.04195i 0.0326579 0.143084i
799799 19.1248 23.9817i 0.676586 0.848412i
800800 55.3607 1.95730
801801 −7.68528 + 9.63704i −0.271546 + 0.340508i
802802 −13.9591 + 6.72234i −0.492913 + 0.237374i
803803 11.8116 + 14.8112i 0.416821 + 0.522677i
804804 −0.952608 1.19453i −0.0335959 0.0421279i
805805 −9.59755 4.62194i −0.338269 0.162902i
806806 −0.327581 + 1.43523i −0.0115386 + 0.0505537i
807807 −0.825153 3.61523i −0.0290468 0.127262i
808808 −1.24511 + 0.599613i −0.0438028 + 0.0210943i
809809 38.8037 + 18.6869i 1.36427 + 0.656996i 0.965584 0.260093i 0.0837532π-0.0837532\pi
0.398683 + 0.917089i 0.369467π0.369467\pi
810810 −3.02556 13.2558i −0.106307 0.465763i
811811 5.65248 0.198485 0.0992426 0.995063i 0.468358π-0.468358\pi
0.0992426 + 0.995063i 0.468358π0.468358\pi
812812 0 0
813813 −6.29180 −0.220663
814814 0.894820 + 3.92046i 0.0313634 + 0.137412i
815815 20.9542 + 10.0910i 0.733992 + 0.353472i
816816 −4.52402 + 2.17865i −0.158372 + 0.0762682i
817817 −7.81596 34.2440i −0.273446 1.19804i
818818 −3.77046 + 16.5194i −0.131831 + 0.577589i
819819 1.24511 + 0.599613i 0.0435076 + 0.0209522i
820820 −14.9852 18.7909i −0.523307 0.656206i
821821 5.35178 + 6.71092i 0.186778 + 0.234213i 0.866401 0.499350i 0.166428π-0.166428\pi
−0.679622 + 0.733562i 0.737856π0.737856\pi
822822 2.45919 1.18428i 0.0857739 0.0413066i
823823 −3.41182 + 4.27829i −0.118929 + 0.149132i −0.837732 0.546082i 0.816119π-0.816119\pi
0.718803 + 0.695214i 0.244690π0.244690\pi
824824 −20.5279 −0.715122
825825 5.24754 6.58021i 0.182696 0.229094i
826826 1.87283 8.20539i 0.0651640 0.285502i
827827 −6.00040 + 26.2895i −0.208654 + 0.914175i 0.756809 + 0.653636i 0.226757π0.226757\pi
−0.965463 + 0.260539i 0.916100π0.916100\pi
828828 −3.26463 + 4.09372i −0.113454 + 0.142267i
829829 32.7984 1.13913 0.569567 0.821945i 0.307111π-0.307111\pi
0.569567 + 0.821945i 0.307111π0.307111\pi
830830 −14.7686 + 18.5192i −0.512624 + 0.642810i
831831 −11.9061 + 5.73368i −0.413018 + 0.198899i
832832 0.0347459 + 0.0435700i 0.00120460 + 0.00151052i
833833 5.46422 + 6.85192i 0.189324 + 0.237405i
834834 0.444558 + 0.214088i 0.0153938 + 0.00741326i
835835 −9.02889 + 39.5581i −0.312458 + 1.36897i
836836 2.41526 + 10.5820i 0.0835337 + 0.365985i
837837 31.5649 15.2009i 1.09104 0.525419i
838838 9.77921 + 4.70942i 0.337817 + 0.162684i
839839 10.7288 + 47.0059i 0.370399 + 1.62283i 0.725657 + 0.688057i 0.241536π0.241536\pi
−0.355258 + 0.934768i 0.615607π0.615607\pi
840840 −11.9098 −0.410928
841841 0 0
842842 −19.1803 −0.660998
843843 3.18022 + 13.9335i 0.109533 + 0.479894i
844844 −16.9870 8.18049i −0.584715 0.281584i
845845 44.9480 21.6458i 1.54626 0.744639i
846846 −2.52033 11.0423i −0.0866506 0.379641i
847847 −4.52301 + 19.8166i −0.155413 + 0.680907i
848848 3.34098 + 1.60893i 0.114730 + 0.0552509i
849849 2.01766 + 2.53006i 0.0692458 + 0.0868314i
850850 −16.6390 20.8647i −0.570714 0.715652i
851851 5.24333 2.52506i 0.179739 0.0865578i
852852 6.52927 8.18745i 0.223689 0.280497i
853853 −45.0000 −1.54077 −0.770385 0.637579i 0.779936π-0.779936\pi
−0.770385 + 0.637579i 0.779936π0.779936\pi
854854 0.532524 0.667764i 0.0182226 0.0228504i
855855 −10.8988 + 47.7507i −0.372731 + 1.63304i
856856 3.36554 14.7454i 0.115032 0.503988i
857857 −28.2604 + 35.4375i −0.965358 + 1.21052i 0.0122147 + 0.999925i 0.496112π0.496112\pi
−0.977573 + 0.210596i 0.932460π0.932460\pi
858858 −0.124612 −0.00425418
859859 20.3932 25.5723i 0.695808 0.872516i −0.300894 0.953657i 0.597285π-0.597285\pi
0.996703 + 0.0811417i 0.0258566π0.0258566\pi
860860 −40.6559 + 19.5788i −1.38635 + 0.667633i
861861 3.32086 + 4.16422i 0.113174 + 0.141916i
862862 5.62468 + 7.05313i 0.191577 + 0.240230i
863863 −15.9856 7.69825i −0.544155 0.262051i 0.141550 0.989931i 0.454792π-0.454792\pi
−0.685705 + 0.727880i 0.740506π0.740506\pi
864864 −4.34062 + 19.0175i −0.147671 + 0.646989i
865865 −3.50780 15.3687i −0.119269 0.522551i
866866 −5.78098 + 2.78398i −0.196446 + 0.0946033i
867867 1.22593 + 0.590377i 0.0416348 + 0.0200502i
868868 8.12348 + 35.5913i 0.275729 + 1.20805i
869869 8.41641 0.285507
870870 0 0
871871 0.360680 0.0122212
872872 −7.15606 31.3528i −0.242335 1.06174i
873873 8.40265 + 4.04650i 0.284387 + 0.136953i
874874 −3.34098 + 1.60893i −0.113010 + 0.0544228i
875875 9.30868 + 40.7840i 0.314691 + 1.37875i
876876 3.05036 13.3645i 0.103062 0.451545i
877877 −3.94801 1.90126i −0.133315 0.0642011i 0.366037 0.930600i 0.380714π-0.380714\pi
−0.499352 + 0.866399i 0.666429π0.666429\pi
878878 −8.07062 10.1202i −0.272370 0.341542i
879879 −3.28611 4.12065i −0.110838 0.138986i
880880 8.89742 4.28477i 0.299932 0.144440i
881881 2.66262 3.33882i 0.0897059 0.112488i −0.734953 0.678118i 0.762796π-0.762796\pi
0.824659 + 0.565631i 0.191367π0.191367\pi
882882 3.23607 0.108964
883883 −12.8981 + 16.1737i −0.434055 + 0.544288i −0.949966 0.312355i 0.898882π-0.898882\pi
0.515911 + 0.856642i 0.327454π0.327454\pi
884884 0.372447 1.63180i 0.0125268 0.0548833i
885885 3.22802 14.1429i 0.108509 0.475407i
886886 −0.735930 + 0.922827i −0.0247240 + 0.0310030i
887887 −38.0689 −1.27823 −0.639114 0.769112i 0.720699π-0.720699\pi
−0.639114 + 0.769112i 0.720699π0.720699\pi
888888 4.05678 5.08705i 0.136137 0.170710i
889889 32.1218 15.4690i 1.07733 0.518815i
890890 6.99230 + 8.76807i 0.234382 + 0.293906i
891891 −4.91843 6.16751i −0.164773 0.206619i
892892 3.89781 + 1.87708i 0.130508 + 0.0628494i
893893 −7.56098 + 33.1268i −0.253018 + 1.10855i
894894 0.817489 + 3.58165i 0.0273409 + 0.119788i
895895 55.5588 26.7557i 1.85713 0.894345i
896896 −22.9304 11.0427i −0.766052 0.368911i
897897 0.0401294 + 0.175818i 0.00133988 + 0.00587041i
898898 −16.1459 −0.538796
899899 0 0
900900 41.7426 1.39142
901901 −1.95016 8.54420i −0.0649692 0.284649i
902902 2.96581 + 1.42826i 0.0987505 + 0.0475557i
903903 9.00969 4.33884i 0.299824 0.144387i
904904 3.95285 + 17.3186i 0.131470 + 0.576007i
905905 −5.09792 + 22.3354i −0.169460 + 0.742455i
906906 0.920147 + 0.443119i 0.0305698 + 0.0147217i
907907 6.08771 + 7.63375i 0.202139 + 0.253474i 0.872560 0.488506i 0.162458π-0.162458\pi
−0.670421 + 0.741981i 0.733887π0.733887\pi
908908 21.0729 + 26.4246i 0.699330 + 0.876932i
909909 −1.45780 + 0.702039i −0.0483521 + 0.0232852i
910910 0.783948 0.983039i 0.0259876 0.0325874i
911911 −10.9443 −0.362600 −0.181300 0.983428i 0.558030π-0.558030\pi
−0.181300 + 0.983428i 0.558030π0.558030\pi
912912 3.46804 4.34879i 0.114838 0.144003i
913913 −3.05803 + 13.3981i −0.101206 + 0.443412i
914914 −2.57286 + 11.2724i −0.0851025 + 0.372858i
915915 0.917862 1.15096i 0.0303436 0.0380496i
916916 −3.70820 −0.122523
917917 −19.9731 + 25.0455i −0.659571 + 0.827076i
918918 8.47204 4.07992i 0.279619 0.134657i
919919 19.5183 + 24.4752i 0.643850 + 0.807362i 0.991479 0.130270i 0.0415844π-0.0415844\pi
−0.347629 + 0.937632i 0.613013π0.613013\pi
920920 6.64171 + 8.32844i 0.218971 + 0.274581i
921921 −10.6802 5.14330i −0.351924 0.169478i
922922 5.36057 23.4862i 0.176541 0.773476i
923923 0.550102 + 2.41015i 0.0181068 + 0.0793312i
924924 −2.78415 + 1.34077i −0.0915917 + 0.0441082i
925925 −41.8006 20.1301i −1.37439 0.661873i
926926 −1.47265 6.45211i −0.0483943 0.212029i
927927 −24.0344 −0.789395
928928 0 0
929929 −3.65248 −0.119834 −0.0599169 0.998203i 0.519084π-0.519084\pi
−0.0599169 + 0.998203i 0.519084π0.519084\pi
930930 −3.30535 14.4817i −0.108387 0.474873i
931931 −8.74679 4.21223i −0.286664 0.138050i
932932 22.2111 10.6963i 0.727549 0.350369i
933933 0.287452 + 1.25941i 0.00941075 + 0.0412312i
934934 2.46779 10.8121i 0.0807487 0.353783i
935935 −21.0281 10.1266i −0.687691 0.331175i
936936 −0.861642 1.08046i −0.0281636 0.0353161i
937937 4.14775 + 5.20112i 0.135501 + 0.169913i 0.844952 0.534841i 0.179629π-0.179629\pi
−0.709451 + 0.704754i 0.751057π0.751057\pi
938938 −1.90236 + 0.916127i −0.0621141 + 0.0299126i
939939 4.97465 6.23801i 0.162341 0.203570i
940940 43.6525 1.42379
941941 −21.7527 + 27.2770i −0.709116 + 0.889204i −0.997668 0.0682609i 0.978255π-0.978255\pi
0.288551 + 0.957464i 0.406826π0.406826\pi
942942 1.23773 5.42285i 0.0403274 0.176686i
943943 1.06007 4.64449i 0.0345208 0.151245i
944944 7.04032 8.82828i 0.229143 0.287336i
945945 −29.9230 −0.973395
946946 3.85338 4.83198i 0.125284 0.157101i
947947 −38.7727 + 18.6719i −1.25994 + 0.606757i −0.940160 0.340734i 0.889324π-0.889324\pi
−0.319783 + 0.947491i 0.603610π0.603610\pi
948948 −3.79716 4.76149i −0.123326 0.154646i
949949 2.01766 + 2.53006i 0.0654959 + 0.0821292i
950950 26.6347 + 12.8266i 0.864144 + 0.416150i
951951 3.81058 16.6953i 0.123567 0.541381i
952952 4.87540 + 21.3605i 0.158012 + 0.692298i
953953 −38.4094 + 18.4970i −1.24420 + 0.599176i −0.935951 0.352129i 0.885458π-0.885458\pi
−0.308250 + 0.951305i 0.599743π0.599743\pi
954954 −2.91560 1.40408i −0.0943959 0.0454587i
955955 −14.6091 64.0064i −0.472738 2.07120i
956956 44.8885 1.45180
957957 0 0
958958 −6.90983 −0.223246
959959 3.55560 + 15.5781i 0.114816 + 0.503043i
960960 −0.506620 0.243975i −0.0163511 0.00787427i
961961 −63.7990 + 30.7240i −2.05803 + 0.991096i
962962 0.152854 + 0.669695i 0.00492820 + 0.0215918i
963963 3.94045 17.2642i 0.126979 0.556332i
964964 −6.78237 3.26622i −0.218445 0.105198i
965965 29.9705 + 37.5818i 0.964783 + 1.20980i
966966 −0.658236 0.825401i −0.0211784 0.0265569i
967967 −3.20953 + 1.54563i −0.103211 + 0.0497040i −0.484777 0.874638i 0.661099π-0.661099\pi
0.381566 + 0.924342i 0.375385π0.375385\pi
968968 12.6732 15.8917i 0.407332 0.510778i
969969 −13.1459 −0.422307
970970 5.29049 6.63407i 0.169867 0.213007i
971971 4.34062 19.0175i 0.139297 0.610301i −0.856293 0.516491i 0.827238π-0.827238\pi
0.995590 0.0938103i 0.0299047π-0.0299047\pi
972972 −5.02059 + 21.9966i −0.161035 + 0.705542i
973973 −1.80098 + 2.25835i −0.0577367 + 0.0723995i
974974 26.3050 0.842865
975975 0.896388 1.12403i 0.0287074 0.0359979i
976976 1.03242 0.497187i 0.0330469 0.0159146i
977977 −28.1910 35.3503i −0.901909 1.13096i −0.990856 0.134921i 0.956922π-0.956922\pi
0.0889478 0.996036i 0.471650π-0.471650\pi
978978 1.43711 + 1.80208i 0.0459538 + 0.0576243i
979979 5.86222 + 2.82310i 0.187357 + 0.0902266i
980980 −2.77531 + 12.1594i −0.0886541 + 0.388419i
981981 −8.37846 36.7084i −0.267504 1.17201i
982982 8.42183 4.05574i 0.268751 0.129424i
983983 9.86045 + 4.74854i 0.314499 + 0.151455i 0.584474 0.811413i 0.301301π-0.301301\pi
−0.269974 + 0.962868i 0.587015π0.587015\pi
984984 −1.18520 5.19270i −0.0377828 0.165537i
985985 −24.2492 −0.772645
986986 0 0
987987 −9.67376 −0.307919
988988 0.412577 + 1.80762i 0.0131258 + 0.0575079i
989989 −8.05851 3.88077i −0.256246 0.123401i
990990 −7.76458 + 3.73922i −0.246775 + 0.118840i
991991 −1.63498 7.16331i −0.0519368 0.227550i 0.942298 0.334775i 0.108660π-0.108660\pi
−0.994235 + 0.107226i 0.965803π0.965803\pi
992992 12.6140 55.2657i 0.400496 1.75469i
993993 11.7938 + 5.67961i 0.374266 + 0.180237i
994994 −9.02323 11.3148i −0.286199 0.358883i
995995 −14.0674 17.6399i −0.445966 0.559223i
996996 8.95948 4.31466i 0.283892 0.136715i
997997 10.5431 13.2206i 0.333904 0.418702i −0.586330 0.810073i 0.699428π-0.699428\pi
0.920233 + 0.391371i 0.127999π0.127999\pi
998998 15.2574 0.482963
999999 10.1925 12.7810i 0.322477 0.404373i
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 841.2.d.i.645.1 12
29.2 odd 28 841.2.b.b.840.2 4
29.3 odd 28 841.2.e.j.63.3 24
29.4 even 14 841.2.d.g.605.2 12
29.5 even 14 841.2.a.c.1.1 yes 2
29.6 even 14 841.2.d.g.571.2 12
29.7 even 7 inner 841.2.d.i.778.2 12
29.8 odd 28 841.2.e.j.651.3 24
29.9 even 14 841.2.d.g.190.2 12
29.10 odd 28 841.2.e.j.236.2 24
29.11 odd 28 841.2.e.j.267.2 24
29.12 odd 4 841.2.e.j.196.3 24
29.13 even 14 841.2.d.g.574.1 12
29.14 odd 28 841.2.e.j.270.3 24
29.15 odd 28 841.2.e.j.270.2 24
29.16 even 7 inner 841.2.d.i.574.2 12
29.17 odd 4 841.2.e.j.196.2 24
29.18 odd 28 841.2.e.j.267.3 24
29.19 odd 28 841.2.e.j.236.3 24
29.20 even 7 inner 841.2.d.i.190.1 12
29.21 odd 28 841.2.e.j.651.2 24
29.22 even 14 841.2.d.g.778.1 12
29.23 even 7 inner 841.2.d.i.571.1 12
29.24 even 7 841.2.a.a.1.2 2
29.25 even 7 inner 841.2.d.i.605.1 12
29.26 odd 28 841.2.e.j.63.2 24
29.27 odd 28 841.2.b.b.840.3 4
29.28 even 2 841.2.d.g.645.2 12
87.5 odd 14 7569.2.a.d.1.2 2
87.53 odd 14 7569.2.a.l.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
841.2.a.a.1.2 2 29.24 even 7
841.2.a.c.1.1 yes 2 29.5 even 14
841.2.b.b.840.2 4 29.2 odd 28
841.2.b.b.840.3 4 29.27 odd 28
841.2.d.g.190.2 12 29.9 even 14
841.2.d.g.571.2 12 29.6 even 14
841.2.d.g.574.1 12 29.13 even 14
841.2.d.g.605.2 12 29.4 even 14
841.2.d.g.645.2 12 29.28 even 2
841.2.d.g.778.1 12 29.22 even 14
841.2.d.i.190.1 12 29.20 even 7 inner
841.2.d.i.571.1 12 29.23 even 7 inner
841.2.d.i.574.2 12 29.16 even 7 inner
841.2.d.i.605.1 12 29.25 even 7 inner
841.2.d.i.645.1 12 1.1 even 1 trivial
841.2.d.i.778.2 12 29.7 even 7 inner
841.2.e.j.63.2 24 29.26 odd 28
841.2.e.j.63.3 24 29.3 odd 28
841.2.e.j.196.2 24 29.17 odd 4
841.2.e.j.196.3 24 29.12 odd 4
841.2.e.j.236.2 24 29.10 odd 28
841.2.e.j.236.3 24 29.19 odd 28
841.2.e.j.267.2 24 29.11 odd 28
841.2.e.j.267.3 24 29.18 odd 28
841.2.e.j.270.2 24 29.15 odd 28
841.2.e.j.270.3 24 29.14 odd 28
841.2.e.j.651.2 24 29.21 odd 28
841.2.e.j.651.3 24 29.8 odd 28
7569.2.a.d.1.2 2 87.5 odd 14
7569.2.a.l.1.1 2 87.53 odd 14