Properties

Label 390.2.bb.c.361.4
Level 390390
Weight 22
Character 390.361
Analytic conductor 3.1143.114
Analytic rank 00
Dimension 88
Inner twists 22

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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] = [390,2,Mod(121,390)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("390.121"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(390, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 2, names="a")
 
Level: N N == 390=23513 390 = 2 \cdot 3 \cdot 5 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 390.bb (of order 66, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [8,0,-4,4,0,0,0,0,-4,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 3.114165678833.11416567883
Analytic rank: 00
Dimension: 88
Relative dimension: 44 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: 8.0.17284886784.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x82x7+2x6+30x5+185x4+36x3+8x2+208x+2704 x^{8} - 2x^{7} + 2x^{6} + 30x^{5} + 185x^{4} + 36x^{3} + 8x^{2} + 208x + 2704 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 361.4
Root 1.700061.70006i-1.70006 - 1.70006i of defining polynomial
Character χ\chi == 390.361
Dual form 390.2.bb.c.121.4

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+(0.8660250.500000i)q2+(0.5000000.866025i)q3+(0.5000000.866025i)q41.00000iq5+(0.8660250.500000i)q6+(4.02239+2.32233i)q71.00000iq8+(0.500000+0.866025i)q9+(0.5000000.866025i)q10+(3.810622.20006i)q111.00000q12+(3.35432+1.32233i)q13+4.64466q14+(0.866025+0.500000i)q15+(0.5000000.866025i)q16+(2.000003.46410i)q17+1.00000iq18+(6.966994.02239i)q19+(0.8660250.500000i)q204.64466iq21+(2.200063.81062i)q22+(0.4882920.845746i)q23+(0.866025+0.500000i)q241.00000q25+(2.24376+2.82233i)q26+1.00000q27+(4.022392.32233i)q28+(2.15637+3.73494i)q29+(0.500000+0.866025i)q30+6.44069iq31+(0.8660250.500000i)q32+(3.810622.20006i)q334.00000iq34+(2.322334.02239i)q35+(0.500000+0.866025i)q36+(3.287451.89801i)q378.04479q38+(2.82233+2.24376i)q391.00000q40+(6.31274+3.64466i)q41+(2.322334.02239i)q42+(0.3582280.620469i)q434.40013iq44+(0.866025+0.500000i)q45+(0.8457460.488292i)q46+9.75342iq47+(0.500000+0.866025i)q48+(7.28643+12.6205i)q49+(0.866025+0.500000i)q504.00000q51+(0.531987+3.56609i)q52+13.5089q53+(0.8660250.500000i)q54+(2.200063.81062i)q55+(2.322334.02239i)q56+8.04479iq57+(3.73494+2.15637i)q58+(1.888421.09028i)q59+1.00000iq60+(3.73205+6.46410i)q61+(3.22034+5.57780i)q62+(4.02239+2.32233i)q631.00000q64+(1.32233+3.35432i)q654.40013q66+(1.58068+0.912609i)q67+(2.000003.46410i)q68+(0.488292+0.845746i)q694.64466iq70+(6.887643.97658i)q71+(0.866025+0.500000i)q724.36112iq73+(1.898013.28745i)q74+(0.500000+0.866025i)q75+(6.96699+4.02239i)q76+20.4371q77+(3.56609+0.531987i)q7814.9340q79+(0.866025+0.500000i)q80+(0.5000000.866025i)q81+(3.64466+6.31274i)q82+3.51093iq83+(4.022392.32233i)q84+(3.464102.00000i)q850.716456iq86+(2.156373.73494i)q87+(2.200063.81062i)q88+(7.077804.08637i)q89+1.00000q90+(16.56332.47090i)q910.976584q92+(5.577803.22034i)q93+(4.87671+8.44671i)q94+(4.02239+6.96699i)q95+1.00000iq96+(11.9730+6.91261i)q97+(12.6205+7.28643i)q98+4.40013iq99+O(q100)q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(4.02239 + 2.32233i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(3.81062 - 2.20006i) q^{11} -1.00000 q^{12} +(-3.35432 + 1.32233i) q^{13} +4.64466 q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +1.00000i q^{18} +(-6.96699 - 4.02239i) q^{19} +(-0.866025 - 0.500000i) q^{20} -4.64466i q^{21} +(2.20006 - 3.81062i) q^{22} +(-0.488292 - 0.845746i) q^{23} +(-0.866025 + 0.500000i) q^{24} -1.00000 q^{25} +(-2.24376 + 2.82233i) q^{26} +1.00000 q^{27} +(4.02239 - 2.32233i) q^{28} +(2.15637 + 3.73494i) q^{29} +(-0.500000 + 0.866025i) q^{30} +6.44069i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-3.81062 - 2.20006i) q^{33} -4.00000i q^{34} +(2.32233 - 4.02239i) q^{35} +(0.500000 + 0.866025i) q^{36} +(3.28745 - 1.89801i) q^{37} -8.04479 q^{38} +(2.82233 + 2.24376i) q^{39} -1.00000 q^{40} +(-6.31274 + 3.64466i) q^{41} +(-2.32233 - 4.02239i) q^{42} +(0.358228 - 0.620469i) q^{43} -4.40013i q^{44} +(0.866025 + 0.500000i) q^{45} +(-0.845746 - 0.488292i) q^{46} +9.75342i q^{47} +(-0.500000 + 0.866025i) q^{48} +(7.28643 + 12.6205i) q^{49} +(-0.866025 + 0.500000i) q^{50} -4.00000 q^{51} +(-0.531987 + 3.56609i) q^{52} +13.5089 q^{53} +(0.866025 - 0.500000i) q^{54} +(-2.20006 - 3.81062i) q^{55} +(2.32233 - 4.02239i) q^{56} +8.04479i q^{57} +(3.73494 + 2.15637i) q^{58} +(-1.88842 - 1.09028i) q^{59} +1.00000i q^{60} +(-3.73205 + 6.46410i) q^{61} +(3.22034 + 5.57780i) q^{62} +(-4.02239 + 2.32233i) q^{63} -1.00000 q^{64} +(1.32233 + 3.35432i) q^{65} -4.40013 q^{66} +(-1.58068 + 0.912609i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(-0.488292 + 0.845746i) q^{69} -4.64466i q^{70} +(-6.88764 - 3.97658i) q^{71} +(0.866025 + 0.500000i) q^{72} -4.36112i q^{73} +(1.89801 - 3.28745i) q^{74} +(0.500000 + 0.866025i) q^{75} +(-6.96699 + 4.02239i) q^{76} +20.4371 q^{77} +(3.56609 + 0.531987i) q^{78} -14.9340 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.64466 + 6.31274i) q^{82} +3.51093i q^{83} +(-4.02239 - 2.32233i) q^{84} +(-3.46410 - 2.00000i) q^{85} -0.716456i q^{86} +(2.15637 - 3.73494i) q^{87} +(-2.20006 - 3.81062i) q^{88} +(7.07780 - 4.08637i) q^{89} +1.00000 q^{90} +(-16.5633 - 2.47090i) q^{91} -0.976584 q^{92} +(5.57780 - 3.22034i) q^{93} +(4.87671 + 8.44671i) q^{94} +(-4.02239 + 6.96699i) q^{95} +1.00000i q^{96} +(11.9730 + 6.91261i) q^{97} +(12.6205 + 7.28643i) q^{98} +4.40013i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q4q3+4q44q94q10+6q118q1212q13+4q144q16+16q176q19+2q22+4q238q2512q26+8q278q294q30++48q98+O(q100) 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9} - 4 q^{10} + 6 q^{11} - 8 q^{12} - 12 q^{13} + 4 q^{14} - 4 q^{16} + 16 q^{17} - 6 q^{19} + 2 q^{22} + 4 q^{23} - 8 q^{25} - 12 q^{26} + 8 q^{27} - 8 q^{29} - 4 q^{30}+ \cdots + 48 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/390Z)×\left(\mathbb{Z}/390\mathbb{Z}\right)^\times.

nn 131131 157157 301301
χ(n)\chi(n) 11 11 e(56)e\left(\frac{5}{6}\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 0.866025 0.500000i 0.612372 0.353553i
33 −0.500000 0.866025i −0.288675 0.500000i
44 0.500000 0.866025i 0.250000 0.433013i
55 1.00000i 0.447214i
66 −0.866025 0.500000i −0.353553 0.204124i
77 4.02239 + 2.32233i 1.52032 + 0.877758i 0.999713 + 0.0239629i 0.00762835π0.00762835\pi
0.520609 + 0.853795i 0.325705π0.325705\pi
88 1.00000i 0.353553i
99 −0.500000 + 0.866025i −0.166667 + 0.288675i
1010 −0.500000 0.866025i −0.158114 0.273861i
1111 3.81062 2.20006i 1.14895 0.663344i 0.200316 0.979731i 0.435803π-0.435803\pi
0.948630 + 0.316387i 0.102470π0.102470\pi
1212 −1.00000 −0.288675
1313 −3.35432 + 1.32233i −0.930320 + 0.366748i
1414 4.64466 1.24134
1515 −0.866025 + 0.500000i −0.223607 + 0.129099i
1616 −0.500000 0.866025i −0.125000 0.216506i
1717 2.00000 3.46410i 0.485071 0.840168i −0.514782 0.857321i 0.672127π-0.672127\pi
0.999853 + 0.0171533i 0.00546033π0.00546033\pi
1818 1.00000i 0.235702i
1919 −6.96699 4.02239i −1.59834 0.922800i −0.991808 0.127739i 0.959228π-0.959228\pi
−0.606529 0.795061i 0.707439π-0.707439\pi
2020 −0.866025 0.500000i −0.193649 0.111803i
2121 4.64466i 1.01355i
2222 2.20006 3.81062i 0.469055 0.812427i
2323 −0.488292 0.845746i −0.101816 0.176350i 0.810617 0.585577i 0.199132π-0.199132\pi
−0.912433 + 0.409226i 0.865799π0.865799\pi
2424 −0.866025 + 0.500000i −0.176777 + 0.102062i
2525 −1.00000 −0.200000
2626 −2.24376 + 2.82233i −0.440037 + 0.553504i
2727 1.00000 0.192450
2828 4.02239 2.32233i 0.760161 0.438879i
2929 2.15637 + 3.73494i 0.400427 + 0.693561i 0.993777 0.111384i 0.0355283π-0.0355283\pi
−0.593350 + 0.804945i 0.702195π0.702195\pi
3030 −0.500000 + 0.866025i −0.0912871 + 0.158114i
3131 6.44069i 1.15678i 0.815760 + 0.578391i 0.196319π0.196319\pi
−0.815760 + 0.578391i 0.803681π0.803681\pi
3232 −0.866025 0.500000i −0.153093 0.0883883i
3333 −3.81062 2.20006i −0.663344 0.382982i
3434 4.00000i 0.685994i
3535 2.32233 4.02239i 0.392545 0.679909i
3636 0.500000 + 0.866025i 0.0833333 + 0.144338i
3737 3.28745 1.89801i 0.540454 0.312031i −0.204809 0.978802i 0.565657π-0.565657\pi
0.745263 + 0.666771i 0.232324π0.232324\pi
3838 −8.04479 −1.30504
3939 2.82233 + 2.24376i 0.451934 + 0.359289i
4040 −1.00000 −0.158114
4141 −6.31274 + 3.64466i −0.985884 + 0.569200i −0.904041 0.427445i 0.859414π-0.859414\pi
−0.0818424 + 0.996645i 0.526080π0.526080\pi
4242 −2.32233 4.02239i −0.358343 0.620669i
4343 0.358228 0.620469i 0.0546293 0.0946207i −0.837418 0.546564i 0.815936π-0.815936\pi
0.892047 + 0.451943i 0.149269π0.149269\pi
4444 4.40013i 0.663344i
4545 0.866025 + 0.500000i 0.129099 + 0.0745356i
4646 −0.845746 0.488292i −0.124698 0.0719947i
4747 9.75342i 1.42268i 0.702847 + 0.711341i 0.251912π0.251912\pi
−0.702847 + 0.711341i 0.748088π0.748088\pi
4848 −0.500000 + 0.866025i −0.0721688 + 0.125000i
4949 7.28643 + 12.6205i 1.04092 + 1.80292i
5050 −0.866025 + 0.500000i −0.122474 + 0.0707107i
5151 −4.00000 −0.560112
5252 −0.531987 + 3.56609i −0.0737734 + 0.494528i
5353 13.5089 1.85559 0.927794 0.373092i 0.121703π-0.121703\pi
0.927794 + 0.373092i 0.121703π0.121703\pi
5454 0.866025 0.500000i 0.117851 0.0680414i
5555 −2.20006 3.81062i −0.296656 0.513824i
5656 2.32233 4.02239i 0.310334 0.537515i
5757 8.04479i 1.06556i
5858 3.73494 + 2.15637i 0.490421 + 0.283145i
5959 −1.88842 1.09028i −0.245851 0.141942i 0.372012 0.928228i 0.378668π-0.378668\pi
−0.617863 + 0.786286i 0.712001π0.712001\pi
6060 1.00000i 0.129099i
6161 −3.73205 + 6.46410i −0.477840 + 0.827643i −0.999677 0.0254017i 0.991914π-0.991914\pi
0.521837 + 0.853045i 0.325247π0.325247\pi
6262 3.22034 + 5.57780i 0.408984 + 0.708381i
6363 −4.02239 + 2.32233i −0.506774 + 0.292586i
6464 −1.00000 −0.125000
6565 1.32233 + 3.35432i 0.164015 + 0.416052i
6666 −4.40013 −0.541618
6767 −1.58068 + 0.912609i −0.193111 + 0.111493i −0.593438 0.804879i 0.702230π-0.702230\pi
0.400327 + 0.916372i 0.368897π0.368897\pi
6868 −2.00000 3.46410i −0.242536 0.420084i
6969 −0.488292 + 0.845746i −0.0587834 + 0.101816i
7070 4.64466i 0.555143i
7171 −6.88764 3.97658i −0.817413 0.471934i 0.0321105 0.999484i 0.489777π-0.489777\pi
−0.849524 + 0.527551i 0.823110π0.823110\pi
7272 0.866025 + 0.500000i 0.102062 + 0.0589256i
7373 4.36112i 0.510430i −0.966884 0.255215i 0.917854π-0.917854\pi
0.966884 0.255215i 0.0821463π-0.0821463\pi
7474 1.89801 3.28745i 0.220640 0.382159i
7575 0.500000 + 0.866025i 0.0577350 + 0.100000i
7676 −6.96699 + 4.02239i −0.799168 + 0.461400i
7777 20.4371 2.32902
7878 3.56609 + 0.531987i 0.403780 + 0.0602357i
7979 −14.9340 −1.68020 −0.840102 0.542429i 0.817505π-0.817505\pi
−0.840102 + 0.542429i 0.817505π0.817505\pi
8080 −0.866025 + 0.500000i −0.0968246 + 0.0559017i
8181 −0.500000 0.866025i −0.0555556 0.0962250i
8282 −3.64466 + 6.31274i −0.402485 + 0.697125i
8383 3.51093i 0.385375i 0.981260 + 0.192688i 0.0617204π0.0617204\pi
−0.981260 + 0.192688i 0.938280π0.938280\pi
8484 −4.02239 2.32233i −0.438879 0.253387i
8585 −3.46410 2.00000i −0.375735 0.216930i
8686 0.716456i 0.0772575i
8787 2.15637 3.73494i 0.231187 0.400427i
8888 −2.20006 3.81062i −0.234528 0.406214i
8989 7.07780 4.08637i 0.750245 0.433154i −0.0755374 0.997143i 0.524067π-0.524067\pi
0.825782 + 0.563989i 0.190734π0.190734\pi
9090 1.00000 0.105409
9191 −16.5633 2.47090i −1.73630 0.259021i
9292 −0.976584 −0.101816
9393 5.57780 3.22034i 0.578391 0.333934i
9494 4.87671 + 8.44671i 0.502994 + 0.871212i
9595 −4.02239 + 6.96699i −0.412689 + 0.714798i
9696 1.00000i 0.102062i
9797 11.9730 + 6.91261i 1.21567 + 0.701869i 0.963989 0.265941i 0.0856825π-0.0856825\pi
0.251683 + 0.967810i 0.419016π0.419016\pi
9898 12.6205 + 7.28643i 1.27486 + 0.736041i
9999 4.40013i 0.442229i
100100 −0.500000 + 0.866025i −0.0500000 + 0.0866025i
101101 −3.40013 5.88919i −0.338325 0.585997i 0.645793 0.763513i 0.276527π-0.276527\pi
−0.984118 + 0.177516i 0.943194π0.943194\pi
102102 −3.46410 + 2.00000i −0.342997 + 0.198030i
103103 −5.29137 −0.521374 −0.260687 0.965423i 0.583949π-0.583949\pi
−0.260687 + 0.965423i 0.583949π0.583949\pi
104104 1.32233 + 3.35432i 0.129665 + 0.328918i
105105 −4.64466 −0.453272
106106 11.6990 6.75444i 1.13631 0.656050i
107107 −8.46410 14.6603i −0.818256 1.41726i −0.906966 0.421203i 0.861608π-0.861608\pi
0.0887109 0.996057i 0.471725π-0.471725\pi
108108 0.500000 0.866025i 0.0481125 0.0833333i
109109 12.8003i 1.22604i 0.790067 + 0.613021i 0.210046π0.210046\pi
−0.790067 + 0.613021i 0.789954π0.789954\pi
110110 −3.81062 2.20006i −0.363329 0.209768i
111111 −3.28745 1.89801i −0.312031 0.180151i
112112 4.64466i 0.438879i
113113 −6.53308 + 11.3156i −0.614580 + 1.06448i 0.375878 + 0.926669i 0.377341π0.377341\pi
−0.990458 + 0.137815i 0.955992π0.955992\pi
114114 4.02239 + 6.96699i 0.376732 + 0.652518i
115115 −0.845746 + 0.488292i −0.0788662 + 0.0455334i
116116 4.31274 0.400427
117117 0.531987 3.56609i 0.0491823 0.329685i
118118 −2.18056 −0.200737
119119 16.0896 9.28932i 1.47493 0.851550i
120120 0.500000 + 0.866025i 0.0456435 + 0.0790569i
121121 4.18056 7.24094i 0.380051 0.658267i
122122 7.46410i 0.675768i
123123 6.31274 + 3.64466i 0.569200 + 0.328628i
124124 5.57780 + 3.22034i 0.500901 + 0.289195i
125125 1.00000i 0.0894427i
126126 −2.32233 + 4.02239i −0.206890 + 0.358343i
127127 6.10978 + 10.5825i 0.542156 + 0.939041i 0.998780 + 0.0493816i 0.0157250π0.0157250\pi
−0.456624 + 0.889660i 0.650942π0.650942\pi
128128 −0.866025 + 0.500000i −0.0765466 + 0.0441942i
129129 −0.716456 −0.0630805
130130 2.82233 + 2.24376i 0.247535 + 0.196791i
131131 −0.378757 −0.0330921 −0.0165461 0.999863i 0.505267π-0.505267\pi
−0.0165461 + 0.999863i 0.505267π0.505267\pi
132132 −3.81062 + 2.20006i −0.331672 + 0.191491i
133133 −18.6826 32.3593i −1.61999 2.80591i
134134 −0.912609 + 1.58068i −0.0788374 + 0.136550i
135135 1.00000i 0.0860663i
136136 −3.46410 2.00000i −0.297044 0.171499i
137137 −1.08457 0.626177i −0.0926612 0.0534979i 0.452953 0.891534i 0.350370π-0.350370\pi
−0.545615 + 0.838036i 0.683704π0.683704\pi
138138 0.976584i 0.0831323i
139139 −1.67767 + 2.90581i −0.142298 + 0.246468i −0.928362 0.371678i 0.878783π-0.878783\pi
0.786064 + 0.618146i 0.212116π0.212116\pi
140140 −2.32233 4.02239i −0.196273 0.339954i
141141 8.44671 4.87671i 0.711341 0.410693i
142142 −7.95317 −0.667415
143143 −9.87282 + 12.4186i −0.825607 + 1.03850i
144144 1.00000 0.0833333
145145 3.73494 2.15637i 0.310170 0.179077i
146146 −2.18056 3.77684i −0.180464 0.312573i
147147 7.28643 12.6205i 0.600975 1.04092i
148148 3.79603i 0.312031i
149149 −4.00077 2.30985i −0.327756 0.189230i 0.327088 0.944994i 0.393933π-0.393933\pi
−0.654844 + 0.755764i 0.727266π0.727266\pi
150150 0.866025 + 0.500000i 0.0707107 + 0.0408248i
151151 11.2425i 0.914901i 0.889235 + 0.457450i 0.151237π0.151237\pi
−0.889235 + 0.457450i 0.848763π0.848763\pi
152152 −4.02239 + 6.96699i −0.326259 + 0.565097i
153153 2.00000 + 3.46410i 0.161690 + 0.280056i
154154 17.6990 10.2185i 1.42623 0.823434i
155155 6.44069 0.517328
156156 3.35432 1.32233i 0.268560 0.105871i
157157 −1.50311 −0.119961 −0.0599807 0.998200i 0.519104π-0.519104\pi
−0.0599807 + 0.998200i 0.519104π0.519104\pi
158158 −12.9332 + 7.46699i −1.02891 + 0.594042i
159159 −6.75444 11.6990i −0.535662 0.927794i
160160 −0.500000 + 0.866025i −0.0395285 + 0.0684653i
161161 4.53590i 0.357479i
162162 −0.866025 0.500000i −0.0680414 0.0392837i
163163 −0.152706 0.0881650i −0.0119609 0.00690561i 0.494008 0.869458i 0.335531π-0.335531\pi
−0.505969 + 0.862552i 0.668865π0.668865\pi
164164 7.28932i 0.569200i
165165 −2.20006 + 3.81062i −0.171275 + 0.296656i
166166 1.75547 + 3.04056i 0.136251 + 0.235993i
167167 7.51851 4.34081i 0.581800 0.335902i −0.180049 0.983658i 0.557626π-0.557626\pi
0.761848 + 0.647756i 0.224292π0.224292\pi
168168 −4.64466 −0.358343
169169 9.50289 8.87103i 0.730991 0.682387i
170170 −4.00000 −0.306786
171171 6.96699 4.02239i 0.532779 0.307600i
172172 −0.358228 0.620469i −0.0273146 0.0473103i
173173 0.890216 1.54190i 0.0676818 0.117228i −0.830199 0.557468i 0.811773π-0.811773\pi
0.897880 + 0.440239i 0.145106π0.145106\pi
174174 4.31274i 0.326948i
175175 −4.02239 2.32233i −0.304064 0.175552i
176176 −3.81062 2.20006i −0.287236 0.165836i
177177 2.18056i 0.163901i
178178 4.08637 7.07780i 0.306286 0.530503i
179179 −8.70786 15.0825i −0.650856 1.12732i −0.982916 0.184057i 0.941077π-0.941077\pi
0.332059 0.943258i 0.392257π-0.392257\pi
180180 0.866025 0.500000i 0.0645497 0.0372678i
181181 −10.3611 −0.770136 −0.385068 0.922888i 0.625822π-0.625822\pi
−0.385068 + 0.922888i 0.625822π0.625822\pi
182182 −15.5797 + 6.14177i −1.15484 + 0.455258i
183183 7.46410 0.551762
184184 −0.845746 + 0.488292i −0.0623492 + 0.0359973i
185185 −1.89801 3.28745i −0.139545 0.241698i
186186 3.22034 5.57780i 0.236127 0.408984i
187187 17.6005i 1.28708i
188188 8.44671 + 4.87671i 0.616040 + 0.355671i
189189 4.02239 + 2.32233i 0.292586 + 0.168925i
190190 8.04479i 0.583630i
191191 0.448507 0.776837i 0.0324528 0.0562100i −0.849343 0.527842i 0.823001π-0.823001\pi
0.881796 + 0.471632i 0.156335π0.156335\pi
192192 0.500000 + 0.866025i 0.0360844 + 0.0625000i
193193 17.5494 10.1322i 1.26324 0.729330i 0.289537 0.957167i 0.406499π-0.406499\pi
0.973699 + 0.227837i 0.0731652π0.0731652\pi
194194 13.8252 0.992593
195195 2.24376 2.82233i 0.160679 0.202111i
196196 14.5729 1.04092
197197 7.95060 4.59028i 0.566457 0.327044i −0.189276 0.981924i 0.560614π-0.560614\pi
0.755733 + 0.654880i 0.227281π0.227281\pi
198198 2.20006 + 3.81062i 0.156352 + 0.270809i
199199 −8.10876 + 14.0448i −0.574815 + 0.995609i 0.421247 + 0.906946i 0.361593π0.361593\pi
−0.996062 + 0.0886625i 0.971741π0.971741\pi
200200 1.00000i 0.0707107i
201201 1.58068 + 0.912609i 0.111493 + 0.0643705i
202202 −5.88919 3.40013i −0.414362 0.239232i
203203 20.0312i 1.40591i
204204 −2.00000 + 3.46410i −0.140028 + 0.242536i
205205 3.64466 + 6.31274i 0.254554 + 0.440901i
206206 −4.58246 + 2.64568i −0.319275 + 0.184333i
207207 0.976584 0.0678773
208208 2.82233 + 2.24376i 0.195693 + 0.155577i
209209 −35.3981 −2.44854
210210 −4.02239 + 2.32233i −0.277572 + 0.160256i
211211 0.809848 + 1.40270i 0.0557522 + 0.0965657i 0.892555 0.450939i 0.148911π-0.148911\pi
−0.836802 + 0.547505i 0.815578π0.815578\pi
212212 6.75444 11.6990i 0.463897 0.803493i
213213 7.95317i 0.544942i
214214 −14.6603 8.46410i −1.00215 0.578594i
215215 −0.620469 0.358228i −0.0423157 0.0244310i
216216 1.00000i 0.0680414i
217217 −14.9574 + 25.9070i −1.01537 + 1.75868i
218218 6.40013 + 11.0853i 0.433471 + 0.750794i
219219 −3.77684 + 2.18056i −0.255215 + 0.147348i
220220 −4.40013 −0.296656
221221 −2.12795 + 14.2644i −0.143141 + 0.959524i
222222 −3.79603 −0.254773
223223 1.93705 1.11836i 0.129714 0.0748906i −0.433739 0.901039i 0.642806π-0.642806\pi
0.563453 + 0.826148i 0.309473π0.309473\pi
224224 −2.32233 4.02239i −0.155167 0.268757i
225225 0.500000 0.866025i 0.0333333 0.0577350i
226226 13.0662i 0.869148i
227227 −13.2679 7.66025i −0.880625 0.508429i −0.00976038 0.999952i 0.503107π-0.503107\pi
−0.870864 + 0.491523i 0.836440π0.836440\pi
228228 6.96699 + 4.02239i 0.461400 + 0.266389i
229229 10.1279i 0.669274i −0.942347 0.334637i 0.891386π-0.891386\pi
0.942347 0.334637i 0.108614π-0.108614\pi
230230 −0.488292 + 0.845746i −0.0321970 + 0.0557669i
231231 −10.2185 17.6990i −0.672331 1.16451i
232232 3.73494 2.15637i 0.245211 0.141572i
233233 20.7519 1.35950 0.679750 0.733444i 0.262088π-0.262088\pi
0.679750 + 0.733444i 0.262088π0.262088\pi
234234 −1.32233 3.35432i −0.0864434 0.219279i
235235 9.75342 0.636243
236236 −1.88842 + 1.09028i −0.122926 + 0.0709711i
237237 7.46699 + 12.9332i 0.485033 + 0.840102i
238238 9.28932 16.0896i 0.602137 1.04293i
239239 24.3539i 1.57532i −0.616107 0.787662i 0.711291π-0.711291\pi
0.616107 0.787662i 0.288709π-0.288709\pi
240240 0.866025 + 0.500000i 0.0559017 + 0.0322749i
241241 −17.2066 9.93423i −1.10837 0.639920i −0.169966 0.985450i 0.554366π-0.554366\pi
−0.938408 + 0.345530i 0.887699π0.887699\pi
242242 8.36112i 0.537473i
243243 −0.500000 + 0.866025i −0.0320750 + 0.0555556i
244244 3.73205 + 6.46410i 0.238920 + 0.413822i
245245 12.6205 7.28643i 0.806292 0.465513i
246246 7.28932 0.464750
247247 28.6884 + 4.27973i 1.82540 + 0.272312i
248248 6.44069 0.408984
249249 3.04056 1.75547i 0.192688 0.111248i
250250 0.500000 + 0.866025i 0.0316228 + 0.0547723i
251251 6.78566 11.7531i 0.428307 0.741849i −0.568416 0.822741i 0.692444π-0.692444\pi
0.996723 + 0.0808920i 0.0257769π0.0257769\pi
252252 4.64466i 0.292586i
253253 −3.72139 2.14855i −0.233962 0.135078i
254254 10.5825 + 6.10978i 0.664002 + 0.383362i
255255 4.00000i 0.250490i
256256 −0.500000 + 0.866025i −0.0312500 + 0.0541266i
257257 0.331150 + 0.573569i 0.0206566 + 0.0357783i 0.876169 0.482004i 0.160091π-0.160091\pi
−0.855512 + 0.517782i 0.826758π0.826758\pi
258258 −0.620469 + 0.358228i −0.0386287 + 0.0223023i
259259 17.6312 1.09555
260260 3.56609 + 0.531987i 0.221159 + 0.0329925i
261261 −4.31274 −0.266952
262262 −0.328013 + 0.189378i −0.0202647 + 0.0116998i
263263 −15.3749 26.6301i −0.948058 1.64208i −0.749510 0.661993i 0.769711π-0.769711\pi
−0.198548 0.980091i 0.563623π-0.563623\pi
264264 −2.20006 + 3.81062i −0.135405 + 0.234528i
265265 13.5089i 0.829844i
266266 −32.3593 18.6826i −1.98408 1.14551i
267267 −7.07780 4.08637i −0.433154 0.250082i
268268 1.82522i 0.111493i
269269 1.87205 3.24249i 0.114141 0.197698i −0.803295 0.595581i 0.796922π-0.796922\pi
0.917436 + 0.397883i 0.130255π0.130255\pi
270270 −0.500000 0.866025i −0.0304290 0.0527046i
271271 24.0419 13.8806i 1.46044 0.843186i 0.461410 0.887187i 0.347344π-0.347344\pi
0.999031 + 0.0440009i 0.0140104π0.0140104\pi
272272 −4.00000 −0.242536
273273 6.14177 + 15.5797i 0.371717 + 0.942924i
274274 −1.25235 −0.0756575
275275 −3.81062 + 2.20006i −0.229789 + 0.132669i
276276 0.488292 + 0.845746i 0.0293917 + 0.0509079i
277277 5.99609 10.3855i 0.360270 0.624006i −0.627735 0.778427i 0.716018π-0.716018\pi
0.988005 + 0.154421i 0.0493512π0.0493512\pi
278278 3.35534i 0.201240i
279279 −5.57780 3.22034i −0.333934 0.192797i
280280 −4.02239 2.32233i −0.240384 0.138786i
281281 3.63888i 0.217078i 0.994092 + 0.108539i 0.0346172π0.0346172\pi
−0.994092 + 0.108539i 0.965383π0.965383\pi
282282 4.87671 8.44671i 0.290404 0.502994i
283283 2.42220 + 4.19538i 0.143985 + 0.249389i 0.928994 0.370095i 0.120675π-0.120675\pi
−0.785009 + 0.619485i 0.787342π0.787342\pi
284284 −6.88764 + 3.97658i −0.408707 + 0.235967i
285285 8.04479 0.476532
286286 −2.34081 + 15.6912i −0.138415 + 0.927843i
287287 −33.8564 −1.99848
288288 0.866025 0.500000i 0.0510310 0.0294628i
289289 0.500000 + 0.866025i 0.0294118 + 0.0509427i
290290 2.15637 3.73494i 0.126626 0.219323i
291291 13.8252i 0.810449i
292292 −3.77684 2.18056i −0.221023 0.127608i
293293 3.20500 + 1.85041i 0.187238 + 0.108102i 0.590689 0.806899i 0.298856π-0.298856\pi
−0.403451 + 0.915001i 0.632189π0.632189\pi
294294 14.5729i 0.849907i
295295 −1.09028 + 1.88842i −0.0634785 + 0.109948i
296296 −1.89801 3.28745i −0.110320 0.191079i
297297 3.81062 2.20006i 0.221115 0.127661i
298298 −4.61970 −0.267612
299299 2.75624 + 2.19122i 0.159398 + 0.126721i
300300 1.00000 0.0577350
301301 2.88187 1.66385i 0.166108 0.0959026i
302302 5.62124 + 9.73628i 0.323466 + 0.560260i
303303 −3.40013 + 5.88919i −0.195332 + 0.338325i
304304 8.04479i 0.461400i
305305 6.46410 + 3.73205i 0.370133 + 0.213697i
306306 3.46410 + 2.00000i 0.198030 + 0.114332i
307307 7.11454i 0.406048i −0.979174 0.203024i 0.934923π-0.934923\pi
0.979174 0.203024i 0.0650770π-0.0650770\pi
308308 10.2185 17.6990i 0.582256 1.00850i
309309 2.64568 + 4.58246i 0.150508 + 0.260687i
310310 5.57780 3.22034i 0.316798 0.182903i
311311 −19.9148 −1.12926 −0.564632 0.825343i 0.690982π-0.690982\pi
−0.564632 + 0.825343i 0.690982π0.690982\pi
312312 2.24376 2.82233i 0.127028 0.159783i
313313 6.13950 0.347025 0.173513 0.984832i 0.444488π-0.444488\pi
0.173513 + 0.984832i 0.444488π0.444488\pi
314314 −1.30173 + 0.751556i −0.0734611 + 0.0424128i
315315 2.32233 + 4.02239i 0.130848 + 0.226636i
316316 −7.46699 + 12.9332i −0.420051 + 0.727550i
317317 7.85286i 0.441061i 0.975380 + 0.220530i 0.0707788π0.0707788\pi
−0.975380 + 0.220530i 0.929221π0.929221\pi
318318 −11.6990 6.75444i −0.656050 0.378770i
319319 16.4342 + 9.48829i 0.920139 + 0.531242i
320320 1.00000i 0.0559017i
321321 −8.46410 + 14.6603i −0.472420 + 0.818256i
322322 −2.26795 3.92820i −0.126388 0.218910i
323323 −27.8680 + 16.0896i −1.55061 + 0.895248i
324324 −1.00000 −0.0555556
325325 3.35432 1.32233i 0.186064 0.0733497i
326326 −0.176330 −0.00976601
327327 11.0853 6.40013i 0.613021 0.353928i
328328 3.64466 + 6.31274i 0.201243 + 0.348563i
329329 −22.6507 + 39.2321i −1.24877 + 2.16294i
330330 4.40013i 0.242219i
331331 27.7093 + 15.9980i 1.52304 + 0.879327i 0.999629 + 0.0272463i 0.00867385π0.00867385\pi
0.523410 + 0.852081i 0.324659π0.324659\pi
332332 3.04056 + 1.75547i 0.166872 + 0.0963438i
333333 3.79603i 0.208021i
334334 4.34081 7.51851i 0.237519 0.411394i
335335 0.912609 + 1.58068i 0.0498611 + 0.0863620i
336336 −4.02239 + 2.32233i −0.219440 + 0.126693i
337337 −35.6432 −1.94161 −0.970806 0.239867i 0.922896π-0.922896\pi
−0.970806 + 0.239867i 0.922896π0.922896\pi
338338 3.79423 12.4340i 0.206379 0.676319i
339339 13.0662 0.709656
340340 −3.46410 + 2.00000i −0.187867 + 0.108465i
341341 14.1699 + 24.5430i 0.767344 + 1.32908i
342342 4.02239 6.96699i 0.217506 0.376732i
343343 35.1734i 1.89918i
344344 −0.620469 0.358228i −0.0334535 0.0193144i
345345 0.845746 + 0.488292i 0.0455334 + 0.0262887i
346346 1.78043i 0.0957166i
347347 3.44851 5.97299i 0.185126 0.320647i −0.758493 0.651681i 0.774064π-0.774064\pi
0.943619 + 0.331034i 0.107397π0.107397\pi
348348 −2.15637 3.73494i −0.115593 0.200214i
349349 16.7321 9.66025i 0.895646 0.517102i 0.0198610 0.999803i 0.493678π-0.493678\pi
0.875785 + 0.482701i 0.160344π0.160344\pi
350350 −4.64466 −0.248267
351351 −3.35432 + 1.32233i −0.179040 + 0.0705807i
352352 −4.40013 −0.234528
353353 −23.7441 + 13.7086i −1.26377 + 0.729637i −0.973802 0.227400i 0.926978π-0.926978\pi
−0.289967 + 0.957037i 0.593644π0.593644\pi
354354 1.09028 + 1.88842i 0.0579477 + 0.100368i
355355 −3.97658 + 6.88764i −0.211055 + 0.365558i
356356 8.17274i 0.433154i
357357 −16.0896 9.28932i −0.851550 0.491643i
358358 −15.0825 8.70786i −0.797133 0.460225i
359359 14.3611i 0.757951i 0.925407 + 0.378975i 0.123723π0.123723\pi
−0.925407 + 0.378975i 0.876277π0.876277\pi
360360 0.500000 0.866025i 0.0263523 0.0456435i
361361 22.8593 + 39.5935i 1.20312 + 2.08387i
362362 −8.97299 + 5.18056i −0.471610 + 0.272284i
363363 −8.36112 −0.438845
364364 −10.4215 + 13.1088i −0.546235 + 0.687086i
365365 −4.36112 −0.228271
366366 6.46410 3.73205i 0.337884 0.195077i
367367 6.88764 + 11.9298i 0.359532 + 0.622728i 0.987883 0.155202i 0.0496030π-0.0496030\pi
−0.628351 + 0.777930i 0.716270π0.716270\pi
368368 −0.488292 + 0.845746i −0.0254540 + 0.0440876i
369369 7.28932i 0.379467i
370370 −3.28745 1.89801i −0.170907 0.0986730i
371371 54.3381 + 31.3721i 2.82109 + 1.62876i
372372 6.44069i 0.333934i
373373 16.7313 28.9795i 0.866316 1.50050i 0.000581860 1.00000i 0.499815π-0.499815\pi
0.865734 0.500504i 0.166852π-0.166852\pi
374374 −8.80025 15.2425i −0.455050 0.788170i
375375 0.866025 0.500000i 0.0447214 0.0258199i
376376 9.75342 0.502994
377377 −12.1720 9.67674i −0.626888 0.498377i
378378 4.64466 0.238896
379379 −28.9052 + 16.6884i −1.48476 + 0.857227i −0.999850 0.0173371i 0.994481π-0.994481\pi
−0.484910 + 0.874564i 0.661148π0.661148\pi
380380 4.02239 + 6.96699i 0.206344 + 0.357399i
381381 6.10978 10.5825i 0.313014 0.542156i
382382 0.897014i 0.0458952i
383383 6.34829 + 3.66519i 0.324383 + 0.187282i 0.653344 0.757061i 0.273365π-0.273365\pi
−0.328962 + 0.944343i 0.606699π0.606699\pi
384384 0.866025 + 0.500000i 0.0441942 + 0.0255155i
385385 20.4371i 1.04157i
386386 10.1322 17.5494i 0.515714 0.893243i
387387 0.358228 + 0.620469i 0.0182098 + 0.0315402i
388388 11.9730 6.91261i 0.607836 0.350935i
389389 −32.6198 −1.65389 −0.826946 0.562282i 0.809924π-0.809924\pi
−0.826946 + 0.562282i 0.809924π0.809924\pi
390390 0.531987 3.56609i 0.0269382 0.180576i
391391 −3.90633 −0.197552
392392 12.6205 7.28643i 0.637430 0.368020i
393393 0.189378 + 0.328013i 0.00955288 + 0.0165461i
394394 4.59028 7.95060i 0.231255 0.400545i
395395 14.9340i 0.751410i
396396 3.81062 + 2.20006i 0.191491 + 0.110557i
397397 12.5299 + 7.23416i 0.628860 + 0.363072i 0.780310 0.625392i 0.215061π-0.215061\pi
−0.151451 + 0.988465i 0.548394π0.548394\pi
398398 16.2175i 0.812911i
399399 −18.6826 + 32.3593i −0.935302 + 1.61999i
400400 0.500000 + 0.866025i 0.0250000 + 0.0433013i
401401 −6.31096 + 3.64364i −0.315154 + 0.181955i −0.649231 0.760592i 0.724909π-0.724909\pi
0.334076 + 0.942546i 0.391576π0.391576\pi
402402 1.82522 0.0910336
403403 −8.51671 21.6041i −0.424248 1.07618i
404404 −6.80025 −0.338325
405405 −0.866025 + 0.500000i −0.0430331 + 0.0248452i
406406 10.0156 + 17.3475i 0.497066 + 0.860943i
407407 8.35150 14.4652i 0.413968 0.717014i
408408 4.00000i 0.198030i
409409 −21.2840 12.2883i −1.05242 0.607617i −0.129097 0.991632i 0.541208π-0.541208\pi
−0.923327 + 0.384015i 0.874541π0.874541\pi
410410 6.31274 + 3.64466i 0.311764 + 0.179997i
411411 1.25235i 0.0617741i
412412 −2.64568 + 4.58246i −0.130343 + 0.225761i
413413 −5.06397 8.77106i −0.249182 0.431596i
414414 0.845746 0.488292i 0.0415662 0.0239982i
415415 3.51093 0.172345
416416 3.56609 + 0.531987i 0.174842 + 0.0260828i
417417 3.35534 0.164312
418418 −30.6556 + 17.6990i −1.49942 + 0.865688i
419419 −7.77684 13.4699i −0.379923 0.658047i 0.611127 0.791532i 0.290716π-0.290716\pi
−0.991051 + 0.133486i 0.957383π0.957383\pi
420420 −2.32233 + 4.02239i −0.113318 + 0.196273i
421421 22.3143i 1.08753i −0.839237 0.543766i 0.816998π-0.816998\pi
0.839237 0.543766i 0.183002π-0.183002\pi
422422 1.40270 + 0.809848i 0.0682822 + 0.0394228i
423423 −8.44671 4.87671i −0.410693 0.237114i
424424 13.5089i 0.656050i
425425 −2.00000 + 3.46410i −0.0970143 + 0.168034i
426426 3.97658 + 6.88764i 0.192666 + 0.333707i
427427 −30.0236 + 17.3341i −1.45294 + 0.838856i
428428 −16.9282 −0.818256
429429 15.6912 + 2.34081i 0.757580 + 0.113015i
430430 −0.716456 −0.0345506
431431 21.0135 12.1322i 1.01219 0.584386i 0.100356 0.994952i 0.468002π-0.468002\pi
0.911831 + 0.410565i 0.134669π0.134669\pi
432432 −0.500000 0.866025i −0.0240563 0.0416667i
433433 −11.5494 + 20.0042i −0.555031 + 0.961342i 0.442870 + 0.896586i 0.353960π0.353960\pi
−0.997901 + 0.0647561i 0.979373π0.979373\pi
434434 29.9148i 1.43596i
435435 −3.73494 2.15637i −0.179077 0.103390i
436436 11.0853 + 6.40013i 0.530892 + 0.306510i
437437 7.85641i 0.375823i
438438 −2.18056 + 3.77684i −0.104191 + 0.180464i
439439 −19.9980 34.6375i −0.954450 1.65316i −0.735621 0.677393i 0.763110π-0.763110\pi
−0.218829 0.975763i 0.570224π-0.570224\pi
440440 −3.81062 + 2.20006i −0.181664 + 0.104884i
441441 −14.5729 −0.693946
442442 5.28932 + 13.4173i 0.251587 + 0.638194i
443443 −15.6036 −0.741350 −0.370675 0.928763i 0.620874π-0.620874\pi
−0.370675 + 0.928763i 0.620874π0.620874\pi
444444 −3.28745 + 1.89801i −0.156016 + 0.0900757i
445445 −4.08637 7.07780i −0.193712 0.335520i
446446 1.11836 1.93705i 0.0529557 0.0917219i
447447 4.61970i 0.218504i
448448 −4.02239 2.32233i −0.190040 0.109720i
449449 23.3863 + 13.5021i 1.10367 + 0.637203i 0.937182 0.348841i 0.113425π-0.113425\pi
0.166486 + 0.986044i 0.446758π0.446758\pi
450450 1.00000i 0.0471405i
451451 −16.0370 + 27.7768i −0.755151 + 1.30796i
452452 6.53308 + 11.3156i 0.307290 + 0.532242i
453453 9.73628 5.62124i 0.457450 0.264109i
454454 −15.3205 −0.719027
455455 −2.47090 + 16.5633i −0.115838 + 0.776498i
456456 8.04479 0.376732
457457 15.4039 8.89342i 0.720562 0.416017i −0.0943975 0.995535i 0.530092π-0.530092\pi
0.814959 + 0.579518i 0.196759π0.196759\pi
458458 −5.06397 8.77106i −0.236624 0.409845i
459459 2.00000 3.46410i 0.0933520 0.161690i
460460 0.976584i 0.0455334i
461461 21.6205 + 12.4826i 1.00697 + 0.581372i 0.910302 0.413945i 0.135849π-0.135849\pi
0.0966638 + 0.995317i 0.469183π0.469183\pi
462462 −17.6990 10.2185i −0.823434 0.475410i
463463 15.6389i 0.726801i 0.931633 + 0.363400i 0.118384π0.118384\pi
−0.931633 + 0.363400i 0.881616π0.881616\pi
464464 2.15637 3.73494i 0.100107 0.173390i
465465 −3.22034 5.57780i −0.149340 0.258664i
466466 17.9716 10.3759i 0.832521 0.480656i
467467 −2.43914 −0.112870 −0.0564349 0.998406i 0.517973π-0.517973\pi
−0.0564349 + 0.998406i 0.517973π0.517973\pi
468468 −2.82233 2.24376i −0.130462 0.103718i
469469 −8.47751 −0.391455
470470 8.44671 4.87671i 0.389618 0.224946i
471471 0.751556 + 1.30173i 0.0346299 + 0.0599807i
472472 −1.09028 + 1.88842i −0.0501842 + 0.0869215i
473473 3.15250i 0.144952i
474474 12.9332 + 7.46699i 0.594042 + 0.342970i
475475 6.96699 + 4.02239i 0.319667 + 0.184560i
476476 18.5786i 0.851550i
477477 −6.75444 + 11.6990i −0.309265 + 0.535662i
478478 −12.1770 21.0911i −0.556961 0.964685i
479479 12.2857 7.09317i 0.561349 0.324095i −0.192338 0.981329i 0.561607π-0.561607\pi
0.753687 + 0.657234i 0.228274π0.228274\pi
480480 1.00000 0.0456435
481481 −8.51737 + 10.7136i −0.388358 + 0.488500i
482482 −19.8685 −0.904983
483483 −3.92820 + 2.26795i −0.178739 + 0.103195i
484484 −4.18056 7.24094i −0.190025 0.329134i
485485 6.91261 11.9730i 0.313885 0.543665i
486486 1.00000i 0.0453609i
487487 4.99115 + 2.88164i 0.226171 + 0.130580i 0.608804 0.793320i 0.291649π-0.291649\pi
−0.382633 + 0.923900i 0.624983π0.624983\pi
488488 6.46410 + 3.73205i 0.292616 + 0.168942i
489489 0.176330i 0.00797392i
490490 7.28643 12.6205i 0.329167 0.570135i
491491 −0.537671 0.931273i −0.0242647 0.0420278i 0.853638 0.520867i 0.174391π-0.174391\pi
−0.877903 + 0.478839i 0.841058π0.841058\pi
492492 6.31274 3.64466i 0.284600 0.164314i
493493 17.2509 0.776943
494494 26.9848 10.6379i 1.21410 0.478620i
495495 4.40013 0.197771
496496 5.57780 3.22034i 0.250450 0.144598i
497497 −18.4699 31.9908i −0.828487 1.43498i
498498 1.75547 3.04056i 0.0786644 0.136251i
499499 14.7534i 0.660454i 0.943902 + 0.330227i 0.107125π0.107125\pi
−0.943902 + 0.330227i 0.892875π0.892875\pi
500500 0.866025 + 0.500000i 0.0387298 + 0.0223607i
501501 −7.51851 4.34081i −0.335902 0.193933i
502502 13.5713i 0.605717i
503503 13.3309 23.0898i 0.594395 1.02952i −0.399236 0.916848i 0.630725π-0.630725\pi
0.993632 0.112675i 0.0359419π-0.0359419\pi
504504 2.32233 + 4.02239i 0.103445 + 0.179172i
505505 −5.88919 + 3.40013i −0.262066 + 0.151304i
506506 −4.29709 −0.191029
507507 −12.4340 3.79423i −0.552212 0.168508i
508508 12.2196 0.542156
509509 12.2807 7.09028i 0.544333 0.314271i −0.202500 0.979282i 0.564907π-0.564907\pi
0.746833 + 0.665011i 0.231573π0.231573\pi
510510 2.00000 + 3.46410i 0.0885615 + 0.153393i
511511 10.1279 17.5421i 0.448034 0.776018i
512512 1.00000i 0.0441942i
513513 −6.96699 4.02239i −0.307600 0.177593i
514514 0.573569 + 0.331150i 0.0252990 + 0.0146064i
515515 5.29137i 0.233165i
516516 −0.358228 + 0.620469i −0.0157701 + 0.0273146i
517517 21.4581 + 37.1666i 0.943728 + 1.63459i
518518 15.2691 8.81562i 0.670886 0.387336i
519519 −1.78043 −0.0781523
520520 3.35432 1.32233i 0.147097 0.0579880i
521521 23.7476 1.04040 0.520202 0.854043i 0.325857π-0.325857\pi
0.520202 + 0.854043i 0.325857π0.325857\pi
522522 −3.73494 + 2.15637i −0.163474 + 0.0943817i
523523 −6.92532 11.9950i −0.302823 0.524505i 0.673951 0.738776i 0.264596π-0.264596\pi
−0.976774 + 0.214271i 0.931262π0.931262\pi
524524 −0.189378 + 0.328013i −0.00827303 + 0.0143293i
525525 4.64466i 0.202710i
526526 −26.6301 15.3749i −1.16113 0.670378i
527527 22.3112 + 12.8814i 0.971891 + 0.561121i
528528 4.40013i 0.191491i
529529 11.0231 19.0926i 0.479267 0.830115i
530530 −6.75444 11.6990i −0.293394 0.508174i
531531 1.88842 1.09028i 0.0819504 0.0473141i
532532 −37.3653 −1.61999
533533 16.3555 20.5729i 0.708434 0.891110i
534534 −8.17274 −0.353669
535535 −14.6603 + 8.46410i −0.633818 + 0.365935i
536536 0.912609 + 1.58068i 0.0394187 + 0.0682752i
537537 −8.70786 + 15.0825i −0.375772 + 0.650856i
538538 3.74410i 0.161420i
539539 55.5317 + 32.0612i 2.39192 + 1.38097i
540540 −0.866025 0.500000i −0.0372678 0.0215166i
541541 14.8898i 0.640164i 0.947390 + 0.320082i 0.103710π0.103710\pi
−0.947390 + 0.320082i 0.896290π0.896290\pi
542542 13.8806 24.0419i 0.596223 1.03269i
543543 5.18056 + 8.97299i 0.222319 + 0.385068i
544544 −3.46410 + 2.00000i −0.148522 + 0.0857493i
545545 12.8003 0.548303
546546 13.1088 + 10.4215i 0.561003 + 0.445999i
547547 −22.2019 −0.949284 −0.474642 0.880179i 0.657422π-0.657422\pi
−0.474642 + 0.880179i 0.657422π0.657422\pi
548548 −1.08457 + 0.626177i −0.0463306 + 0.0267490i
549549 −3.73205 6.46410i −0.159280 0.275881i
550550 −2.20006 + 3.81062i −0.0938110 + 0.162485i
551551 34.6950i 1.47806i
552552 0.845746 + 0.488292i 0.0359973 + 0.0207831i
553553 −60.0703 34.6816i −2.55445 1.47481i
554554 11.9922i 0.509499i
555555 −1.89801 + 3.28745i −0.0805662 + 0.139545i
556556 1.67767 + 2.90581i 0.0711491 + 0.123234i
557557 1.64518 0.949847i 0.0697087 0.0402463i −0.464741 0.885447i 0.653852π-0.653852\pi
0.534449 + 0.845201i 0.320519π0.320519\pi
558558 −6.44069 −0.272656
559559 −0.381146 + 2.55495i −0.0161207 + 0.108063i
560560 −4.64466 −0.196273
561561 −15.2425 + 8.80025i −0.643538 + 0.371547i
562562 1.81944 + 3.15137i 0.0767485 + 0.132932i
563563 −0.860000 + 1.48956i −0.0362447 + 0.0627777i −0.883579 0.468283i 0.844873π-0.844873\pi
0.847334 + 0.531060i 0.178206π0.178206\pi
564564 9.75342i 0.410693i
565565 11.3156 + 6.53308i 0.476052 + 0.274849i
566566 4.19538 + 2.42220i 0.176345 + 0.101813i
567567 4.64466i 0.195057i
568568 −3.97658 + 6.88764i −0.166854 + 0.288999i
569569 −0.300960 0.521278i −0.0126169 0.0218531i 0.859648 0.510887i 0.170683π-0.170683\pi
−0.872265 + 0.489034i 0.837350π0.837350\pi
570570 6.96699 4.02239i 0.291815 0.168480i
571571 11.9808 0.501381 0.250691 0.968067i 0.419342π-0.419342\pi
0.250691 + 0.968067i 0.419342π0.419342\pi
572572 5.81842 + 14.7594i 0.243280 + 0.617122i
573573 −0.897014 −0.0374733
574574 −29.3205 + 16.9282i −1.22381 + 0.706570i
575575 0.488292 + 0.845746i 0.0203632 + 0.0352701i
576576 0.500000 0.866025i 0.0208333 0.0360844i
577577 43.0293i 1.79133i −0.444725 0.895667i 0.646699π-0.646699\pi
0.444725 0.895667i 0.353301π-0.353301\pi
578578 0.866025 + 0.500000i 0.0360219 + 0.0207973i
579579 −17.5494 10.1322i −0.729330 0.421079i
580580 4.31274i 0.179077i
581581 −8.15355 + 14.1224i −0.338266 + 0.585894i
582582 −6.91261 11.9730i −0.286537 0.496296i
583583 51.4773 29.7204i 2.13197 1.23089i
584584 −4.36112 −0.180464
585585 −3.56609 0.531987i −0.147440 0.0219950i
586586 3.70081 0.152879
587587 −15.5147 + 8.95740i −0.640359 + 0.369711i −0.784753 0.619809i 0.787210π-0.787210\pi
0.144394 + 0.989520i 0.453877π0.453877\pi
588588 −7.28643 12.6205i −0.300487 0.520459i
589589 25.9070 44.8722i 1.06748 1.84893i
590590 2.18056i 0.0897722i
591591 −7.95060 4.59028i −0.327044 0.188819i
592592 −3.28745 1.89801i −0.135114 0.0780078i
593593 0.669624i 0.0274981i 0.999905 + 0.0137491i 0.00437660π0.00437660\pi
−0.999905 + 0.0137491i 0.995623π0.995623\pi
594594 2.20006 3.81062i 0.0902697 0.156352i
595595 −9.28932 16.0896i −0.380825 0.659608i
596596 −4.00077 + 2.30985i −0.163878 + 0.0946151i
597597 16.2175 0.663739
598598 3.48258 + 0.519530i 0.142413 + 0.0212452i
599599 1.29241 0.0528066 0.0264033 0.999651i 0.491595π-0.491595\pi
0.0264033 + 0.999651i 0.491595π0.491595\pi
600600 0.866025 0.500000i 0.0353553 0.0204124i
601601 5.73671 + 9.93627i 0.234005 + 0.405309i 0.958983 0.283463i 0.0914834π-0.0914834\pi
−0.724978 + 0.688772i 0.758150π0.758150\pi
602602 1.66385 2.88187i 0.0678134 0.117456i
603603 1.82522i 0.0743286i
604604 9.73628 + 5.62124i 0.396164 + 0.228725i
605605 −7.24094 4.18056i −0.294386 0.169964i
606606 6.80025i 0.276241i
607607 12.0672 20.9010i 0.489792 0.848344i −0.510139 0.860092i 0.670406π-0.670406\pi
0.999931 + 0.0117477i 0.00373949π0.00373949\pi
608608 4.02239 + 6.96699i 0.163130 + 0.282549i
609609 17.3475 10.0156i 0.702957 0.405852i
610610 7.46410 0.302213
611611 −12.8972 32.7161i −0.521766 1.32355i
612612 4.00000 0.161690
613613 25.0716 14.4751i 1.01263 0.584644i 0.100671 0.994920i 0.467901π-0.467901\pi
0.911961 + 0.410276i 0.134568π0.134568\pi
614614 −3.55727 6.16137i −0.143560 0.248653i
615615 3.64466 6.31274i 0.146967 0.254554i
616616 20.4371i 0.823434i
617617 −0.728597 0.420655i −0.0293322 0.0169349i 0.485262 0.874369i 0.338724π-0.338724\pi
−0.514594 + 0.857434i 0.672057π0.672057\pi
618618 4.58246 + 2.64568i 0.184333 + 0.106425i
619619 6.25076i 0.251239i −0.992078 0.125620i 0.959908π-0.959908\pi
0.992078 0.125620i 0.0400919π-0.0400919\pi
620620 3.22034 5.57780i 0.129332 0.224010i
621621 −0.488292 0.845746i −0.0195945 0.0339386i
622622 −17.2467 + 9.95740i −0.691530 + 0.399255i
623623 37.9596 1.52082
624624 0.531987 3.56609i 0.0212965 0.142758i
625625 1.00000 0.0400000
626626 5.31696 3.06975i 0.212509 0.122692i
627627 17.6990 + 30.6556i 0.706832 + 1.22427i
628628 −0.751556 + 1.30173i −0.0299904 + 0.0519448i
629629 15.1841i 0.605430i
630630 4.02239 + 2.32233i 0.160256 + 0.0925238i
631631 2.61970 + 1.51248i 0.104288 + 0.0602110i 0.551237 0.834349i 0.314156π-0.314156\pi
−0.446949 + 0.894560i 0.647489π0.647489\pi
632632 14.9340i 0.594042i
633633 0.809848 1.40270i 0.0321886 0.0557522i
634634 3.92643 + 6.80078i 0.155938 + 0.270093i
635635 10.5825 6.10978i 0.419952 0.242459i
636636 −13.5089 −0.535662
637637 −41.1294 32.6980i −1.62961 1.29554i
638638 18.9766 0.751290
639639 6.88764 3.97658i 0.272471 0.157311i
640640 0.500000 + 0.866025i 0.0197642 + 0.0342327i
641641 0.386305 0.669099i 0.0152581 0.0264278i −0.858296 0.513156i 0.828476π-0.828476\pi
0.873554 + 0.486728i 0.161810π0.161810\pi
642642 16.9282i 0.668103i
643643 16.7788 + 9.68726i 0.661693 + 0.382028i 0.792922 0.609324i 0.208559π-0.208559\pi
−0.131229 + 0.991352i 0.541892π0.541892\pi
644644 −3.92820 2.26795i −0.154793 0.0893697i
645645 0.716456i 0.0282104i
646646 −16.0896 + 27.8680i −0.633036 + 1.09645i
647647 −13.5953 23.5477i −0.534485 0.925755i −0.999188 0.0402882i 0.987172π-0.987172\pi
0.464703 0.885466i 0.346161π-0.346161\pi
648648 −0.866025 + 0.500000i −0.0340207 + 0.0196419i
649649 −9.59473 −0.376626
650650 2.24376 2.82233i 0.0880075 0.110701i
651651 29.9148 1.17245
652652 −0.152706 + 0.0881650i −0.00598044 + 0.00345281i
653653 −7.89799 13.6797i −0.309072 0.535329i 0.669088 0.743184i 0.266685π-0.266685\pi
−0.978160 + 0.207855i 0.933352π0.933352\pi
654654 6.40013 11.0853i 0.250265 0.433471i
655655 0.378757i 0.0147993i
656656 6.31274 + 3.64466i 0.246471 + 0.142300i
657657 3.77684 + 2.18056i 0.147348 + 0.0850717i
658658 45.3013i 1.76603i
659659 −15.2381 + 26.3932i −0.593593 + 1.02813i 0.400151 + 0.916449i 0.368958π0.368958\pi
−0.993744 + 0.111684i 0.964376π0.964376\pi
660660 2.20006 + 3.81062i 0.0856374 + 0.148328i
661661 −24.1514 + 13.9438i −0.939379 + 0.542351i −0.889766 0.456418i 0.849132π-0.849132\pi
−0.0496136 + 0.998768i 0.515799π0.515799\pi
662662 31.9959 1.24356
663663 13.4173 5.28932i 0.521084 0.205420i
664664 3.51093 0.136251
665665 −32.3593 + 18.6826i −1.25484 + 0.724482i
666666 1.89801 + 3.28745i 0.0735465 + 0.127386i
667667 2.10587 3.64748i 0.0815397 0.141231i
668668 8.68162i 0.335902i
669669 −1.93705 1.11836i −0.0748906 0.0432381i
670670 1.58068 + 0.912609i 0.0610672 + 0.0352572i
671671 32.8430i 1.26789i
672672 −2.32233 + 4.02239i −0.0895858 + 0.155167i
673673 −0.489066 0.847086i −0.0188521 0.0326528i 0.856445 0.516238i 0.172668π-0.172668\pi
−0.875298 + 0.483585i 0.839334π0.839334\pi
674674 −30.8680 + 17.8216i −1.18899 + 0.686463i
675675 −1.00000 −0.0384900
676676 −2.93109 12.6653i −0.112734 0.487125i
677677 −19.1926 −0.737630 −0.368815 0.929503i 0.620236π-0.620236\pi
−0.368815 + 0.929503i 0.620236π0.620236\pi
678678 11.3156 6.53308i 0.434574 0.250901i
679679 32.1067 + 55.6105i 1.23214 + 2.13413i
680680 −2.00000 + 3.46410i −0.0766965 + 0.132842i
681681 15.3205i 0.587083i
682682 24.5430 + 14.1699i 0.939801 + 0.542594i
683683 −1.30851 0.755467i −0.0500687 0.0289071i 0.474757 0.880117i 0.342536π-0.342536\pi
−0.524825 + 0.851210i 0.675869π0.675869\pi
684684 8.04479i 0.307600i
685685 −0.626177 + 1.08457i −0.0239250 + 0.0414393i
686686 17.5867 + 30.4610i 0.671463 + 1.16301i
687687 −8.77106 + 5.06397i −0.334637 + 0.193203i
688688 −0.716456 −0.0273146
689689 −45.3131 + 17.8632i −1.72629 + 0.680534i
690690 0.976584 0.0371779
691691 28.6798 16.5583i 1.09103 0.629907i 0.157180 0.987570i 0.449760π-0.449760\pi
0.933851 + 0.357663i 0.116426π0.116426\pi
692692 −0.890216 1.54190i −0.0338409 0.0586142i
693693 −10.2185 + 17.6990i −0.388170 + 0.672331i
694694 6.89701i 0.261807i
695695 2.90581 + 1.67767i 0.110224 + 0.0636377i
696696 −3.73494 2.15637i −0.141572 0.0817369i
697697 29.1573i 1.10441i
698698 9.66025 16.7321i 0.365646 0.633317i
699699 −10.3759 17.9716i −0.392454 0.679750i
700700 −4.02239 + 2.32233i −0.152032 + 0.0877758i
701701 27.8695 1.05262 0.526308 0.850294i 0.323576π-0.323576\pi
0.526308 + 0.850294i 0.323576π0.323576\pi
702702 −2.24376 + 2.82233i −0.0846852 + 0.106522i
703703 −30.5382 −1.15177
704704 −3.81062 + 2.20006i −0.143618 + 0.0829180i
705705 −4.87671 8.44671i −0.183668 0.318122i
706706 −13.7086 + 23.7441i −0.515931 + 0.893619i
707707 31.5849i 1.18787i
708708 1.88842 + 1.09028i 0.0709711 + 0.0409752i
709709 −9.57491 5.52808i −0.359593 0.207611i 0.309309 0.950962i 0.399902π-0.399902\pi
−0.668902 + 0.743350i 0.733236π0.733236\pi
710710 7.95317i 0.298477i
711711 7.46699 12.9332i 0.280034 0.485033i
712712 −4.08637 7.07780i −0.153143 0.265252i
713713 5.44719 3.14493i 0.203999 0.117779i
714714 −18.5786 −0.695288
715715 12.4186 + 9.87282i 0.464430 + 0.369223i
716716 −17.4157 −0.650856
717717 −21.0911 + 12.1770i −0.787662 + 0.454757i
718718 7.18056 + 12.4371i 0.267976 + 0.464148i
719719 5.85641 10.1436i 0.218407 0.378292i −0.735914 0.677075i 0.763247π-0.763247\pi
0.954321 + 0.298783i 0.0965806π0.0965806\pi
720720 1.00000i 0.0372678i
721721 −21.2840 12.2883i −0.792656 0.457640i
722722 39.5935 + 22.8593i 1.47352 + 0.850735i
723723 19.8685i 0.738916i
724724 −5.18056 + 8.97299i −0.192534 + 0.333479i
725725 −2.15637 3.73494i −0.0800855 0.138712i
726726 −7.24094 + 4.18056i −0.268736 + 0.155155i
727727 −19.4152 −0.720071 −0.360035 0.932939i 0.617235π-0.617235\pi
−0.360035 + 0.932939i 0.617235π0.617235\pi
728728 −2.47090 + 16.5633i −0.0915777 + 0.613876i
729729 1.00000 0.0370370
730730 −3.77684 + 2.18056i −0.139787 + 0.0807061i
731731 −1.43291 2.48188i −0.0529982 0.0917956i
732732 3.73205 6.46410i 0.137941 0.238920i
733733 11.9340i 0.440792i 0.975411 + 0.220396i 0.0707349π0.0707349\pi
−0.975411 + 0.220396i 0.929265π0.929265\pi
734734 11.9298 + 6.88764i 0.440335 + 0.254228i
735735 −12.6205 7.28643i −0.465513 0.268764i
736736 0.976584i 0.0359973i
737737 −4.01559 + 6.95521i −0.147916 + 0.256199i
738738 −3.64466 6.31274i −0.134162 0.232375i
739739 17.2017 9.93141i 0.632775 0.365333i −0.149051 0.988830i 0.547622π-0.547622\pi
0.781826 + 0.623497i 0.214289π0.214289\pi
740740 −3.79603 −0.139545
741741 −10.6379 26.9848i −0.390792 0.991310i
742742 62.7442 2.30341
743743 14.2787 8.24383i 0.523836 0.302437i −0.214667 0.976687i 0.568867π-0.568867\pi
0.738503 + 0.674251i 0.235533π0.235533\pi
744744 −3.22034 5.57780i −0.118063 0.204492i
745745 −2.30985 + 4.00077i −0.0846263 + 0.146577i
746746 33.4627i 1.22516i
747747 −3.04056 1.75547i −0.111248 0.0642292i
748748 −15.2425 8.80025i −0.557320 0.321769i
749749 78.6257i 2.87292i
750750 0.500000 0.866025i 0.0182574 0.0316228i
751751 −23.3312 40.4109i −0.851368 1.47461i −0.879974 0.475022i 0.842440π-0.842440\pi
0.0286056 0.999591i 0.490893π-0.490893\pi
752752 8.44671 4.87671i 0.308020 0.177835i
753753 −13.5713 −0.494566
754754 −15.3796 2.29432i −0.560092 0.0835542i
755755 11.2425 0.409156
756756 4.02239 2.32233i 0.146293 0.0844623i
757757 −1.31799 2.28282i −0.0479030 0.0829705i 0.841080 0.540911i 0.181921π-0.181921\pi
−0.888983 + 0.457941i 0.848587π0.848587\pi
758758 −16.6884 + 28.9052i −0.606151 + 1.04988i
759759 4.29709i 0.155975i
760760 6.96699 + 4.02239i 0.252719 + 0.145908i
761761 0.0693410 + 0.0400340i 0.00251361 + 0.00145123i 0.501256 0.865299i 0.332871π-0.332871\pi
−0.498743 + 0.866750i 0.666205π0.666205\pi
762762 12.2196i 0.442668i
763763 −29.7264 + 51.4877i −1.07617 + 1.86398i
764764 −0.448507 0.776837i −0.0162264 0.0281050i
765765 3.46410 2.00000i 0.125245 0.0723102i
766766 7.33038 0.264857
767767 7.77606 + 1.16003i 0.280777 + 0.0418862i
768768 1.00000 0.0360844
769769 4.92177 2.84159i 0.177484 0.102470i −0.408626 0.912702i 0.633992π-0.633992\pi
0.586110 + 0.810232i 0.300659π0.300659\pi
770770 −10.2185 17.6990i −0.368251 0.637829i
771771 0.331150 0.573569i 0.0119261 0.0206566i
772772 20.2644i 0.729330i
773773 −6.57184 3.79425i −0.236373 0.136470i 0.377136 0.926158i 0.376909π-0.376909\pi
−0.613508 + 0.789688i 0.710242π0.710242\pi
774774 0.620469 + 0.358228i 0.0223023 + 0.0128762i
775775 6.44069i 0.231356i
776776 6.91261 11.9730i 0.248148 0.429805i
777777 −8.81562 15.2691i −0.316259 0.547776i
778778 −28.2496 + 16.3099i −1.01280 + 0.584739i
779779 58.6410 2.10103
780780 −1.32233 3.35432i −0.0473470 0.120104i
781781 −34.9949 −1.25222
782782 −3.38298 + 1.95317i −0.120975 + 0.0698451i
783783 2.15637 + 3.73494i 0.0770623 + 0.133476i
784784 7.28643 12.6205i 0.260230 0.450731i
785785 1.50311i 0.0536484i
786786 0.328013 + 0.189378i 0.0116998 + 0.00675490i
787787 −4.10169 2.36811i −0.146210 0.0844142i 0.425111 0.905141i 0.360235π-0.360235\pi
−0.571320 + 0.820727i 0.693569π0.693569\pi
788788 9.18056i 0.327044i
789789 −15.3749 + 26.6301i −0.547361 + 0.948058i
790790 7.46699 + 12.9332i 0.265664 + 0.460143i
791791 −52.5572 + 30.3439i −1.86872 + 1.07891i
792792 4.40013 0.156352
793793 3.97081 26.6176i 0.141008 0.945220i
794794 14.4683 0.513462
795795 −11.6990 + 6.75444i −0.414922 + 0.239555i
796796 8.10876 + 14.0448i 0.287407 + 0.497804i
797797 −20.5318 + 35.5621i −0.727274 + 1.25968i 0.230757 + 0.973011i 0.425880π0.425880\pi
−0.958031 + 0.286664i 0.907454π0.907454\pi
798798 37.3653i 1.32272i
799799 33.7868 + 19.5068i 1.19529 + 0.690102i
800800 0.866025 + 0.500000i 0.0306186 + 0.0176777i
801801 8.17274i 0.288769i
802802 −3.64364 + 6.31096i −0.128661 + 0.222848i
803803 −9.59473 16.6186i −0.338591 0.586456i
804804 1.58068 0.912609i 0.0557465 0.0321852i
805805 −4.53590 −0.159869
806806 −18.1777 14.4513i −0.640284 0.509027i
807807 −3.74410 −0.131799
808808 −5.88919 + 3.40013i −0.207181 + 0.119616i
809809 13.8003 + 23.9027i 0.485191 + 0.840376i 0.999855 0.0170163i 0.00541671π-0.00541671\pi
−0.514664 + 0.857392i 0.672083π0.672083\pi
810810 −0.500000 + 0.866025i −0.0175682 + 0.0304290i
811811 10.6930i 0.375482i 0.982219 + 0.187741i 0.0601165π0.0601165\pi
−0.982219 + 0.187741i 0.939883π0.939883\pi
812812 17.3475 + 10.0156i 0.608779 + 0.351478i
813813 −24.0419 13.8806i −0.843186 0.486814i
814814 16.7030i 0.585440i
815815 −0.0881650 + 0.152706i −0.00308828 + 0.00534907i
816816 2.00000 + 3.46410i 0.0700140 + 0.121268i
817817 −4.99154 + 2.88187i −0.174632 + 0.100824i
818818 −24.5766 −0.859300
819819 10.4215 13.1088i 0.364157 0.458057i
820820 7.28932 0.254554
821821 15.2105 8.78177i 0.530849 0.306486i −0.210513 0.977591i 0.567513π-0.567513\pi
0.741362 + 0.671105i 0.234180π0.234180\pi
822822 0.626177 + 1.08457i 0.0218404 + 0.0378288i
823823 −19.3565 + 33.5264i −0.674725 + 1.16866i 0.301824 + 0.953364i 0.402404π0.402404\pi
−0.976549 + 0.215295i 0.930929π0.930929\pi
824824 5.29137i 0.184333i
825825 3.81062 + 2.20006i 0.132669 + 0.0765964i
826826 −8.77106 5.06397i −0.305184 0.176198i
827827 28.4703i 0.990010i 0.868890 + 0.495005i 0.164834π0.164834\pi
−0.868890 + 0.495005i 0.835166π0.835166\pi
828828 0.488292 0.845746i 0.0169693 0.0293917i
829829 4.14354 + 7.17683i 0.143911 + 0.249262i 0.928966 0.370165i 0.120699π-0.120699\pi
−0.785055 + 0.619426i 0.787365π0.787365\pi
830830 3.04056 1.75547i 0.105539 0.0609332i
831831 −11.9922 −0.416004
832832 3.35432 1.32233i 0.116290 0.0458435i
833833 58.2915 2.01968
834834 2.90581 1.67767i 0.100620 0.0580930i
835835 −4.34081 7.51851i −0.150220 0.260189i
836836 −17.6990 + 30.6556i −0.612134 + 1.06025i
837837 6.44069i 0.222623i
838838 −13.4699 7.77684i −0.465309 0.268646i
839839 −36.8606 21.2815i −1.27257 0.734719i −0.297099 0.954847i 0.596019π-0.596019\pi
−0.975471 + 0.220128i 0.929353π0.929353\pi
840840 4.64466i 0.160256i
841841 5.20016 9.00693i 0.179316 0.310584i
842842 −11.1571 19.3247i −0.384500 0.665974i
843843 3.15137 1.81944i 0.108539 0.0626649i
844844 1.61970 0.0557522
845845 −8.87103 9.50289i −0.305173 0.326909i
846846 −9.75342 −0.335330
847847 33.6317 19.4173i 1.15560 0.667185i
848848 −6.75444 11.6990i −0.231949 0.401747i
849849 2.42220 4.19538i 0.0831298 0.143985i
850850 4.00000i 0.137199i
851851 −3.21047 1.85357i −0.110054 0.0635395i
852852 6.88764 + 3.97658i 0.235967 + 0.136236i
853853 28.1380i 0.963425i 0.876329 + 0.481713i 0.159985π0.159985\pi
−0.876329 + 0.481713i 0.840015π0.840015\pi
854854 −17.3341 + 30.0236i −0.593161 + 1.02738i
855855 −4.02239 6.96699i −0.137563 0.238266i
856856 −14.6603 + 8.46410i −0.501077 + 0.289297i
857857 −10.3355 −0.353053 −0.176526 0.984296i 0.556486π-0.556486\pi
−0.176526 + 0.984296i 0.556486π0.556486\pi
858858 14.7594 5.81842i 0.503878 0.198638i
859859 0.380304 0.0129758 0.00648791 0.999979i 0.497935π-0.497935\pi
0.00648791 + 0.999979i 0.497935π0.497935\pi
860860 −0.620469 + 0.358228i −0.0211578 + 0.0122155i
861861 16.9282 + 29.3205i 0.576912 + 0.999240i
862862 12.1322 21.0135i 0.413224 0.715724i
863863 47.1484i 1.60495i 0.596685 + 0.802475i 0.296484π0.296484\pi
−0.596685 + 0.802475i 0.703516π0.703516\pi
864864 −0.866025 0.500000i −0.0294628 0.0170103i
865865 −1.54190 0.890216i −0.0524261 0.0302682i
866866 23.0989i 0.784932i
867867 0.500000 0.866025i 0.0169809 0.0294118i
868868 14.9574 + 25.9070i 0.507687 + 0.879340i
869869 −56.9077 + 32.8557i −1.93046 + 1.11455i
870870 −4.31274 −0.146215
871871 4.09535 5.15137i 0.138766 0.174547i
872872 12.8003 0.433471
873873 −11.9730 + 6.91261i −0.405224 + 0.233956i
874874 3.92820 + 6.80385i 0.132873 + 0.230144i
875875 −2.32233 + 4.02239i −0.0785091 + 0.135982i
876876 4.36112i 0.147348i
877877 34.6767 + 20.0206i 1.17095 + 0.676047i 0.953903 0.300114i 0.0970247π-0.0970247\pi
0.217045 + 0.976162i 0.430358π0.430358\pi
878878 −34.6375 19.9980i −1.16896 0.674898i
879879 3.70081i 0.124825i
880880 −2.20006 + 3.81062i −0.0741641 + 0.128456i
881881 −7.72246 13.3757i −0.260176 0.450638i 0.706112 0.708100i 0.250447π-0.250447\pi
−0.966289 + 0.257461i 0.917114π0.917114\pi
882882 −12.6205 + 7.28643i −0.424953 + 0.245347i
883883 −6.02142 −0.202637 −0.101318 0.994854i 0.532306π-0.532306\pi
−0.101318 + 0.994854i 0.532306π0.532306\pi
884884 11.2893 + 8.97504i 0.379701 + 0.301863i
885885 2.18056 0.0732987
886886 −13.5131 + 7.80180i −0.453982 + 0.262107i
887887 24.5690 + 42.5548i 0.824947 + 1.42885i 0.901960 + 0.431820i 0.142128π0.142128\pi
−0.0770129 + 0.997030i 0.524538π0.524538\pi
888888 −1.89801 + 3.28745i −0.0636931 + 0.110320i
889889 56.7557i 1.90353i
890890 −7.07780 4.08637i −0.237248 0.136975i
891891 −3.81062 2.20006i −0.127661 0.0737049i
892892 2.23671i 0.0748906i
893893 39.2321 67.9520i 1.31285 2.27393i
894894 2.30985 + 4.00077i 0.0772529 + 0.133806i
895895 −15.0825 + 8.70786i −0.504151 + 0.291072i
896896 −4.64466 −0.155167
897897 0.519530 3.48258i 0.0173466 0.116280i
898898 27.0042 0.901141
899899 −24.0556 + 13.8885i −0.802298 + 0.463207i
900900 −0.500000 0.866025i −0.0166667 0.0288675i
901901 27.0178 46.7962i 0.900093 1.55901i
902902 32.0739i 1.06795i
903903 −2.88187 1.66385i −0.0959026 0.0553694i
904904 11.3156 + 6.53308i 0.376352 + 0.217287i
905905 10.3611i 0.344415i
906906 5.62124 9.73628i 0.186753 0.323466i
907907 8.18345 + 14.1741i 0.271727 + 0.470645i 0.969304 0.245865i 0.0790719π-0.0790719\pi
−0.697577 + 0.716510i 0.745739π0.745739\pi
908908 −13.2679 + 7.66025i −0.440312 + 0.254214i
909909 6.80025 0.225550
910910 6.14177 + 15.5797i 0.203598 + 0.516461i
911911 −10.4819 −0.347280 −0.173640 0.984809i 0.555553π-0.555553\pi
−0.173640 + 0.984809i 0.555553π0.555553\pi
912912 6.96699 4.02239i 0.230700 0.133195i
913913 7.72428 + 13.3788i 0.255636 + 0.442775i
914914 8.89342 15.4039i 0.294168 0.509514i
915915 7.46410i 0.246756i
916916 −8.77106 5.06397i −0.289804 0.167318i
917917 −1.52351 0.879598i −0.0503107 0.0290469i
918918 4.00000i 0.132020i
919919 −1.60565 + 2.78107i −0.0529655 + 0.0917389i −0.891293 0.453429i 0.850201π-0.850201\pi
0.838327 + 0.545168i 0.183534π0.183534\pi
920920 0.488292 + 0.845746i 0.0160985 + 0.0278834i
921921 −6.16137 + 3.55727i −0.203024 + 0.117216i
922922 24.9652 0.822184
923923 28.3617 + 4.23098i 0.933537 + 0.139265i
924924 −20.4371 −0.672331
925925 −3.28745 + 1.89801i −0.108091 + 0.0624063i
926926 7.81944 + 13.5437i 0.256963 + 0.445073i
927927 2.64568 4.58246i 0.0868956 0.150508i
928928 4.31274i 0.141572i
929929 40.2518 + 23.2394i 1.32062 + 0.762460i 0.983827 0.179120i 0.0573249π-0.0573249\pi
0.336792 + 0.941579i 0.390658π0.390658\pi
930930 −5.57780 3.22034i −0.182903 0.105599i
931931 117.236i 3.84224i
932932 10.3759 17.9716i 0.339875 0.588681i
933933 9.95740 + 17.2467i 0.325990 + 0.564632i
934934 −2.11236 + 1.21957i −0.0691184 + 0.0399055i
935935 −17.6005 −0.575598
936936 −3.56609 0.531987i −0.116561 0.0173886i
937937 −27.7627 −0.906969 −0.453485 0.891264i 0.649819π-0.649819\pi
−0.453485 + 0.891264i 0.649819π0.649819\pi
938938 −7.34174 + 4.23876i −0.239716 + 0.138400i
939939 −3.06975 5.31696i −0.100178 0.173513i
940940 4.87671 8.44671i 0.159061 0.275501i
941941 20.7962i 0.677935i −0.940798 0.338968i 0.889922π-0.889922\pi
0.940798 0.338968i 0.110078π-0.110078\pi
942942 1.30173 + 0.751556i 0.0424128 + 0.0244870i
943943 6.16491 + 3.55931i 0.200757 + 0.115907i
944944 2.18056i 0.0709711i
945945 2.32233 4.02239i 0.0755454 0.130848i
946946 −1.57625 2.73014i −0.0512483 0.0887646i
947947 7.84554 4.52962i 0.254946 0.147193i −0.367081 0.930189i 0.619643π-0.619643\pi
0.622027 + 0.782996i 0.286309π0.286309\pi
948948 14.9340 0.485033
949949 5.76683 + 14.6286i 0.187199 + 0.474863i
950950 8.04479 0.261007
951951 6.80078 3.92643i 0.220530 0.127323i
952952 −9.28932 16.0896i −0.301069 0.521466i
953953 −7.63811 + 13.2296i −0.247423 + 0.428549i −0.962810 0.270180i 0.912917π-0.912917\pi
0.715387 + 0.698728i 0.246250π0.246250\pi
954954 13.5089i 0.437366i
955955 −0.776837 0.448507i −0.0251379 0.0145134i
956956 −21.0911 12.1770i −0.682136 0.393831i
957957 18.9766i 0.613426i
958958 7.09317 12.2857i 0.229170 0.396934i
959959 −2.90838 5.03746i −0.0939165 0.162668i
960960 0.866025 0.500000i 0.0279508 0.0161374i
961961 −10.4824 −0.338143
962962 −2.01944 + 13.5370i −0.0651093 + 0.436449i
963963 16.9282 0.545504
964964 −17.2066 + 9.93423i −0.554187 + 0.319960i
965965 −10.1322 17.5494i −0.326166 0.564937i
966966 −2.26795 + 3.92820i −0.0729701 + 0.126388i
967967 46.3036i 1.48902i 0.667610 + 0.744511i 0.267317π0.267317\pi
−0.667610 + 0.744511i 0.732683π0.732683\pi
968968 −7.24094 4.18056i −0.232733 0.134368i
969969 27.8680 + 16.0896i 0.895248 + 0.516872i
970970 13.8252i 0.443901i
971971 −5.98258 + 10.3621i −0.191990 + 0.332537i −0.945910 0.324430i 0.894828π-0.894828\pi
0.753919 + 0.656967i 0.228161π0.228161\pi
972972 0.500000 + 0.866025i 0.0160375 + 0.0277778i
973973 −13.4965 + 7.79221i −0.432678 + 0.249807i
974974 5.76329 0.184668
975975 −2.82233 2.24376i −0.0903869 0.0718578i
976976 7.46410 0.238920
977977 1.52780 0.882077i 0.0488787 0.0282201i −0.475362 0.879791i 0.657683π-0.657683\pi
0.524240 + 0.851570i 0.324349π0.324349\pi
978978 0.0881650 + 0.152706i 0.00281921 + 0.00488301i
979979 17.9805 31.1432i 0.574660 0.995341i
980980 14.5729i 0.465513i
981981 −11.0853 6.40013i −0.353928 0.204340i
982982 −0.931273 0.537671i −0.0297181 0.0171578i
983983 54.2821i 1.73133i 0.500623 + 0.865666i 0.333104π0.333104\pi
−0.500623 + 0.865666i 0.666896π0.666896\pi
984984 3.64466 6.31274i 0.116188 0.201243i
985985 −4.59028 7.95060i −0.146258 0.253327i
986986 14.9398 8.62547i 0.475779 0.274691i
987987 45.3013 1.44196
988988 18.0506 22.7050i 0.574265 0.722344i
989989 −0.699680 −0.0222485
990990 3.81062 2.20006i 0.121110 0.0699226i
991991 8.73917 + 15.1367i 0.277609 + 0.480833i 0.970790 0.239931i 0.0771248π-0.0771248\pi
−0.693181 + 0.720763i 0.743791π0.743791\pi
992992 3.22034 5.57780i 0.102246 0.177095i
993993 31.9959i 1.01536i
994994 −31.9908 18.4699i −1.01469 0.585829i
995995 14.0448 + 8.10876i 0.445250 + 0.257065i
996996 3.51093i 0.111248i
997997 10.6457 18.4389i 0.337152 0.583965i −0.646744 0.762707i 0.723870π-0.723870\pi
0.983896 + 0.178743i 0.0572030π0.0572030\pi
998998 7.37671 + 12.7768i 0.233506 + 0.404444i
999999 3.28745 1.89801i 0.104010 0.0600505i
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 390.2.bb.c.361.4 yes 8
3.2 odd 2 1170.2.bs.f.361.2 8
5.2 odd 4 1950.2.y.k.49.1 8
5.3 odd 4 1950.2.y.j.49.4 8
5.4 even 2 1950.2.bc.g.751.1 8
13.2 odd 12 5070.2.a.ca.1.4 4
13.3 even 3 5070.2.b.ba.1351.5 8
13.4 even 6 inner 390.2.bb.c.121.4 8
13.10 even 6 5070.2.b.ba.1351.4 8
13.11 odd 12 5070.2.a.bz.1.1 4
39.17 odd 6 1170.2.bs.f.901.2 8
65.4 even 6 1950.2.bc.g.901.1 8
65.17 odd 12 1950.2.y.j.199.4 8
65.43 odd 12 1950.2.y.k.199.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
390.2.bb.c.121.4 8 13.4 even 6 inner
390.2.bb.c.361.4 yes 8 1.1 even 1 trivial
1170.2.bs.f.361.2 8 3.2 odd 2
1170.2.bs.f.901.2 8 39.17 odd 6
1950.2.y.j.49.4 8 5.3 odd 4
1950.2.y.j.199.4 8 65.17 odd 12
1950.2.y.k.49.1 8 5.2 odd 4
1950.2.y.k.199.1 8 65.43 odd 12
1950.2.bc.g.751.1 8 5.4 even 2
1950.2.bc.g.901.1 8 65.4 even 6
5070.2.a.bz.1.1 4 13.11 odd 12
5070.2.a.ca.1.4 4 13.2 odd 12
5070.2.b.ba.1351.4 8 13.10 even 6
5070.2.b.ba.1351.5 8 13.3 even 3