Properties

Label 42.6.e.b.25.1
Level 4242
Weight 66
Character 42.25
Analytic conductor 6.7366.736
Analytic rank 00
Dimension 22
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [42,6,Mod(25,42)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(42, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("42.25");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 42=237 42 = 2 \cdot 3 \cdot 7
Weight: k k == 6 6
Character orbit: [χ][\chi] == 42.e (of order 33, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 6.736120432156.73612043215
Analytic rank: 00
Dimension: 22
Coefficient field: Q(ζ6)\Q(\zeta_{6})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2x+1 x^{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)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 25.1
Root 0.5000000.866025i0.500000 - 0.866025i of defining polynomial
Character χ\chi == 42.25
Dual form 42.6.e.b.37.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(2.00000+3.46410i)q2+(4.500007.79423i)q3+(8.00000+13.8564i)q4+(43.000074.4782i)q5+36.0000q6+(24.5000127.306i)q764.0000q8+(40.500070.1481i)q9+(172.000297.913i)q10+(17.0000+29.4449i)q11+(72.0000+124.708i)q123.00000q13+(490.000169.741i)q14774.000q15+(128.000221.703i)q16+(952.0001648.91i)q17+(162.000280.592i)q18+(744.500+1289.51i)q19+1376.00q20+(882.000763.834i)q21136.000q22+(112.000+193.990i)q23+(288.000+498.831i)q24+(2135.50+3698.79i)q25+(6.0000010.3923i)q26729.000q27+(1568.00+1357.93i)q286508.00q29+(1548.002681.21i)q30+(865.500+1499.09i)q31+(512.000886.810i)q32+(153.000+265.004i)q33+7616.00q34+(10535.0+3649.43i)q35+1296.00q36+(3816.50+6610.37i)q37+(2978.00+5158.05i)q38+(13.5000+23.3827i)q39+(2752.00+4766.60i)q40+15414.0q41+(882.0004583.01i)q42+18491.0q43+(272.000471.118i)q44+(3483.00+6032.73i)q45+(448.000+775.959i)q46+(9231.0015988.6i)q472304.00q48+(15606.56237.98i)q4917084.0q50+(8568.0014840.2i)q51+(24.000041.5692i)q52+(9978.0017282.4i)q53+(1458.002525.33i)q54+2924.00q55+(1568.00+8147.57i)q56+13401.0q57+(13016.022544.4i)q58+(15914.027563.9i)q59+(6192.0010724.9i)q60+(28827.0+49929.8i)q616924.00q62+(9922.50+3437.25i)q63+4096.00q64+(129.000+223.435i)q65+(612.000+1060.02i)q66+(30281.552449.1i)q67+(15232.0+26382.6i)q68+2016.00q69+(33712.029195.4i)q7044834.0q71+(2592.00+4489.48i)q72+(10410.5+18031.5i)q73+(15266.0+26441.5i)q74+(19219.5+33289.2i)q7523824.0q76+(3332.00+2885.60i)q77108.000q78+(15265.5+26440.6i)q79+(11008.0+19066.4i)q80+(3280.50+5681.99i)q81+(30828.0+53395.7i)q82+110602.q83+(17640.06110.68i)q84163744.q85+(36982.0+64054.7i)q86+(29286.0+50724.8i)q87+(1088.001884.47i)q88+(29496.0+51088.6i)q8927864.0q90+(73.5000+381.917i)q913584.00q92+(7789.50+13491.8i)q93+(36924.063954.2i)q94+(64027.0110898.i)q95+(4608.007981.29i)q96119846.q97+(9604.0066538.5i)q98+2754.00q99+O(q100)q+(2.00000 + 3.46410i) q^{2} +(4.50000 - 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-43.0000 - 74.4782i) q^{5} +36.0000 q^{6} +(24.5000 - 127.306i) q^{7} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(172.000 - 297.913i) q^{10} +(-17.0000 + 29.4449i) q^{11} +(72.0000 + 124.708i) q^{12} -3.00000 q^{13} +(490.000 - 169.741i) q^{14} -774.000 q^{15} +(-128.000 - 221.703i) q^{16} +(952.000 - 1648.91i) q^{17} +(162.000 - 280.592i) q^{18} +(744.500 + 1289.51i) q^{19} +1376.00 q^{20} +(-882.000 - 763.834i) q^{21} -136.000 q^{22} +(112.000 + 193.990i) q^{23} +(-288.000 + 498.831i) q^{24} +(-2135.50 + 3698.79i) q^{25} +(-6.00000 - 10.3923i) q^{26} -729.000 q^{27} +(1568.00 + 1357.93i) q^{28} -6508.00 q^{29} +(-1548.00 - 2681.21i) q^{30} +(-865.500 + 1499.09i) q^{31} +(512.000 - 886.810i) q^{32} +(153.000 + 265.004i) q^{33} +7616.00 q^{34} +(-10535.0 + 3649.43i) q^{35} +1296.00 q^{36} +(3816.50 + 6610.37i) q^{37} +(-2978.00 + 5158.05i) q^{38} +(-13.5000 + 23.3827i) q^{39} +(2752.00 + 4766.60i) q^{40} +15414.0 q^{41} +(882.000 - 4583.01i) q^{42} +18491.0 q^{43} +(-272.000 - 471.118i) q^{44} +(-3483.00 + 6032.73i) q^{45} +(-448.000 + 775.959i) q^{46} +(-9231.00 - 15988.6i) q^{47} -2304.00 q^{48} +(-15606.5 - 6237.98i) q^{49} -17084.0 q^{50} +(-8568.00 - 14840.2i) q^{51} +(24.0000 - 41.5692i) q^{52} +(9978.00 - 17282.4i) q^{53} +(-1458.00 - 2525.33i) q^{54} +2924.00 q^{55} +(-1568.00 + 8147.57i) q^{56} +13401.0 q^{57} +(-13016.0 - 22544.4i) q^{58} +(15914.0 - 27563.9i) q^{59} +(6192.00 - 10724.9i) q^{60} +(28827.0 + 49929.8i) q^{61} -6924.00 q^{62} +(-9922.50 + 3437.25i) q^{63} +4096.00 q^{64} +(129.000 + 223.435i) q^{65} +(-612.000 + 1060.02i) q^{66} +(30281.5 - 52449.1i) q^{67} +(15232.0 + 26382.6i) q^{68} +2016.00 q^{69} +(-33712.0 - 29195.4i) q^{70} -44834.0 q^{71} +(2592.00 + 4489.48i) q^{72} +(-10410.5 + 18031.5i) q^{73} +(-15266.0 + 26441.5i) q^{74} +(19219.5 + 33289.2i) q^{75} -23824.0 q^{76} +(3332.00 + 2885.60i) q^{77} -108.000 q^{78} +(15265.5 + 26440.6i) q^{79} +(-11008.0 + 19066.4i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(30828.0 + 53395.7i) q^{82} +110602. q^{83} +(17640.0 - 6110.68i) q^{84} -163744. q^{85} +(36982.0 + 64054.7i) q^{86} +(-29286.0 + 50724.8i) q^{87} +(1088.00 - 1884.47i) q^{88} +(29496.0 + 51088.6i) q^{89} -27864.0 q^{90} +(-73.5000 + 381.917i) q^{91} -3584.00 q^{92} +(7789.50 + 13491.8i) q^{93} +(36924.0 - 63954.2i) q^{94} +(64027.0 - 110898. i) q^{95} +(-4608.00 - 7981.29i) q^{96} -119846. q^{97} +(-9604.00 - 66538.5i) q^{98} +2754.00 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+4q2+9q316q486q5+72q6+49q7128q881q9+344q1034q11+144q126q13+980q141548q15256q16+1904q17+324q18++5508q99+O(q100) 2 q + 4 q^{2} + 9 q^{3} - 16 q^{4} - 86 q^{5} + 72 q^{6} + 49 q^{7} - 128 q^{8} - 81 q^{9} + 344 q^{10} - 34 q^{11} + 144 q^{12} - 6 q^{13} + 980 q^{14} - 1548 q^{15} - 256 q^{16} + 1904 q^{17} + 324 q^{18}+ \cdots + 5508 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/42Z)×\left(\mathbb{Z}/42\mathbb{Z}\right)^\times.

nn 2929 3131
χ(n)\chi(n) 11 e(23)e\left(\frac{2}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 2.00000 + 3.46410i 0.353553 + 0.612372i
33 4.50000 7.79423i 0.288675 0.500000i
44 −8.00000 + 13.8564i −0.250000 + 0.433013i
55 −43.0000 74.4782i −0.769207 1.33231i −0.937993 0.346654i 0.887318π-0.887318\pi
0.168786 0.985653i 0.446015π-0.446015\pi
66 36.0000 0.408248
77 24.5000 127.306i 0.188982 0.981981i
88 −64.0000 −0.353553
99 −40.5000 70.1481i −0.166667 0.288675i
1010 172.000 297.913i 0.543912 0.942083i
1111 −17.0000 + 29.4449i −0.0423611 + 0.0733716i −0.886429 0.462865i 0.846821π-0.846821\pi
0.844067 + 0.536237i 0.180155π0.180155\pi
1212 72.0000 + 124.708i 0.144338 + 0.250000i
1313 −3.00000 −0.00492337 −0.00246169 0.999997i 0.500784π-0.500784\pi
−0.00246169 + 0.999997i 0.500784π0.500784\pi
1414 490.000 169.741i 0.668153 0.231455i
1515 −774.000 −0.888204
1616 −128.000 221.703i −0.125000 0.216506i
1717 952.000 1648.91i 0.798941 1.38381i −0.121366 0.992608i 0.538727π-0.538727\pi
0.920306 0.391198i 0.127939π-0.127939\pi
1818 162.000 280.592i 0.117851 0.204124i
1919 744.500 + 1289.51i 0.473130 + 0.819486i 0.999527 0.0307534i 0.00979067π-0.00979067\pi
−0.526397 + 0.850239i 0.676457π0.676457\pi
2020 1376.00 0.769207
2121 −882.000 763.834i −0.436436 0.377964i
2222 −136.000 −0.0599076
2323 112.000 + 193.990i 0.0441467 + 0.0764644i 0.887254 0.461280i 0.152610π-0.152610\pi
−0.843108 + 0.537745i 0.819276π0.819276\pi
2424 −288.000 + 498.831i −0.102062 + 0.176777i
2525 −2135.50 + 3698.79i −0.683360 + 1.18361i
2626 −6.00000 10.3923i −0.00174068 0.00301494i
2727 −729.000 −0.192450
2828 1568.00 + 1357.93i 0.377964 + 0.327327i
2929 −6508.00 −1.43699 −0.718493 0.695534i 0.755168π-0.755168\pi
−0.718493 + 0.695534i 0.755168π0.755168\pi
3030 −1548.00 2681.21i −0.314028 0.543912i
3131 −865.500 + 1499.09i −0.161757 + 0.280171i −0.935499 0.353330i 0.885049π-0.885049\pi
0.773742 + 0.633501i 0.218383π0.218383\pi
3232 512.000 886.810i 0.0883883 0.153093i
3333 153.000 + 265.004i 0.0244572 + 0.0423611i
3434 7616.00 1.12987
3535 −10535.0 + 3649.43i −1.45367 + 0.503564i
3636 1296.00 0.166667
3737 3816.50 + 6610.37i 0.458312 + 0.793819i 0.998872 0.0474862i 0.0151210π-0.0151210\pi
−0.540560 + 0.841305i 0.681788π0.681788\pi
3838 −2978.00 + 5158.05i −0.334554 + 0.579464i
3939 −13.5000 + 23.3827i −0.00142126 + 0.00246169i
4040 2752.00 + 4766.60i 0.271956 + 0.471041i
4141 15414.0 1.43204 0.716021 0.698079i 0.245961π-0.245961\pi
0.716021 + 0.698079i 0.245961π0.245961\pi
4242 882.000 4583.01i 0.0771517 0.400892i
4343 18491.0 1.52507 0.762534 0.646948i 0.223955π-0.223955\pi
0.762534 + 0.646948i 0.223955π0.223955\pi
4444 −272.000 471.118i −0.0211805 0.0366858i
4545 −3483.00 + 6032.73i −0.256402 + 0.444102i
4646 −448.000 + 775.959i −0.0312164 + 0.0540685i
4747 −9231.00 15988.6i −0.609543 1.05576i −0.991316 0.131503i 0.958020π-0.958020\pi
0.381773 0.924256i 0.375314π-0.375314\pi
4848 −2304.00 −0.144338
4949 −15606.5 6237.98i −0.928571 0.371154i
5050 −17084.0 −0.966417
5151 −8568.00 14840.2i −0.461269 0.798941i
5252 24.0000 41.5692i 0.00123084 0.00213188i
5353 9978.00 17282.4i 0.487926 0.845112i −0.511978 0.858999i 0.671087π-0.671087\pi
0.999904 + 0.0138864i 0.00442031π0.00442031\pi
5454 −1458.00 2525.33i −0.0680414 0.117851i
5555 2924.00 0.130338
5656 −1568.00 + 8147.57i −0.0668153 + 0.347183i
5757 13401.0 0.546324
5858 −13016.0 22544.4i −0.508051 0.879971i
5959 15914.0 27563.9i 0.595181 1.03088i −0.398340 0.917238i 0.630414π-0.630414\pi
0.993521 0.113646i 0.0362531π-0.0362531\pi
6060 6192.00 10724.9i 0.222051 0.384604i
6161 28827.0 + 49929.8i 0.991916 + 1.71805i 0.605854 + 0.795576i 0.292832π0.292832\pi
0.386062 + 0.922473i 0.373835π0.373835\pi
6262 −6924.00 −0.228759
6363 −9922.50 + 3437.25i −0.314970 + 0.109109i
6464 4096.00 0.125000
6565 129.000 + 223.435i 0.00378710 + 0.00655944i
6666 −612.000 + 1060.02i −0.0172938 + 0.0299538i
6767 30281.5 52449.1i 0.824120 1.42742i −0.0784702 0.996916i 0.525004π-0.525004\pi
0.902590 0.430501i 0.141663π-0.141663\pi
6868 15232.0 + 26382.6i 0.399470 + 0.691903i
6969 2016.00 0.0509762
7070 −33712.0 29195.4i −0.822317 0.712148i
7171 −44834.0 −1.05551 −0.527754 0.849397i 0.676966π-0.676966\pi
−0.527754 + 0.849397i 0.676966π0.676966\pi
7272 2592.00 + 4489.48i 0.0589256 + 0.102062i
7373 −10410.5 + 18031.5i −0.228646 + 0.396027i −0.957407 0.288741i 0.906763π-0.906763\pi
0.728761 + 0.684768i 0.240097π0.240097\pi
7474 −15266.0 + 26441.5i −0.324075 + 0.561315i
7575 19219.5 + 33289.2i 0.394538 + 0.683360i
7676 −23824.0 −0.473130
7777 3332.00 + 2885.60i 0.0640440 + 0.0554637i
7878 −108.000 −0.00200996
7979 15265.5 + 26440.6i 0.275197 + 0.476655i 0.970185 0.242367i 0.0779237π-0.0779237\pi
−0.694988 + 0.719021i 0.744590π0.744590\pi
8080 −11008.0 + 19066.4i −0.192302 + 0.333077i
8181 −3280.50 + 5681.99i −0.0555556 + 0.0962250i
8282 30828.0 + 53395.7i 0.506303 + 0.876943i
8383 110602. 1.76225 0.881125 0.472883i 0.156787π-0.156787\pi
0.881125 + 0.472883i 0.156787π0.156787\pi
8484 17640.0 6110.68i 0.272772 0.0944911i
8585 −163744. −2.45820
8686 36982.0 + 64054.7i 0.539193 + 0.933910i
8787 −29286.0 + 50724.8i −0.414822 + 0.718493i
8888 1088.00 1884.47i 0.0149769 0.0259408i
8989 29496.0 + 51088.6i 0.394719 + 0.683673i 0.993065 0.117564i 0.0375086π-0.0375086\pi
−0.598346 + 0.801238i 0.704175π0.704175\pi
9090 −27864.0 −0.362608
9191 −73.5000 + 381.917i −0.000930430 + 0.00483466i
9292 −3584.00 −0.0441467
9393 7789.50 + 13491.8i 0.0933904 + 0.161757i
9494 36924.0 63954.2i 0.431012 0.746534i
9595 64027.0 110898.i 0.727871 1.26071i
9696 −4608.00 7981.29i −0.0510310 0.0883883i
9797 −119846. −1.29328 −0.646642 0.762793i 0.723827π-0.723827\pi
−0.646642 + 0.762793i 0.723827π0.723827\pi
9898 −9604.00 66538.5i −0.101015 0.699854i
9999 2754.00 0.0282407
100100 −34168.0 59180.7i −0.341680 0.591807i
101101 −50005.0 + 86611.2i −0.487764 + 0.844833i −0.999901 0.0140714i 0.995521π-0.995521\pi
0.512137 + 0.858904i 0.328854π0.328854\pi
102102 34272.0 59360.8i 0.326166 0.564937i
103103 −60845.5 105387.i −0.565113 0.978805i −0.997039 0.0768956i 0.975499π-0.975499\pi
0.431926 0.901909i 0.357834π-0.357834\pi
104104 192.000 0.00174068
105105 −18963.0 + 98534.6i −0.167855 + 0.872199i
106106 79824.0 0.690031
107107 24324.0 + 42130.4i 0.205388 + 0.355743i 0.950256 0.311469i 0.100821π-0.100821\pi
−0.744868 + 0.667212i 0.767488π0.767488\pi
108108 5832.00 10101.3i 0.0481125 0.0833333i
109109 76037.5 131701.i 0.613002 1.06175i −0.377730 0.925916i 0.623295π-0.623295\pi
0.990732 0.135834i 0.0433714π-0.0433714\pi
110110 5848.00 + 10129.0i 0.0460814 + 0.0798153i
111111 68697.0 0.529213
112112 −31360.0 + 10863.4i −0.236228 + 0.0818317i
113113 −60886.0 −0.448561 −0.224280 0.974525i 0.572003π-0.572003\pi
−0.224280 + 0.974525i 0.572003π0.572003\pi
114114 26802.0 + 46422.4i 0.193155 + 0.334554i
115115 9632.00 16683.1i 0.0679160 0.117634i
116116 52064.0 90177.5i 0.359247 0.622233i
117117 121.500 + 210.444i 0.000820562 + 0.00142126i
118118 127312. 0.841714
119119 −186592. 161593.i −1.20789 1.04606i
120120 49536.0 0.314028
121121 79947.5 + 138473.i 0.496411 + 0.859809i
122122 −115308. + 199719.i −0.701390 + 1.21484i
123123 69363.0 120140.i 0.413395 0.716021i
124124 −13848.0 23985.4i −0.0808785 0.140086i
125125 98556.0 0.564167
126126 −31752.0 27498.0i −0.178174 0.154303i
127127 −151965. −0.836054 −0.418027 0.908435i 0.637278π-0.637278\pi
−0.418027 + 0.908435i 0.637278π0.637278\pi
128128 8192.00 + 14189.0i 0.0441942 + 0.0765466i
129129 83209.5 144123.i 0.440249 0.762534i
130130 −516.000 + 893.738i −0.00267788 + 0.00463823i
131131 −117751. 203951.i −0.599496 1.03836i −0.992895 0.118990i 0.962034π-0.962034\pi
0.393399 0.919368i 0.371299π-0.371299\pi
132132 −4896.00 −0.0244572
133133 182402. 63186.1i 0.894132 0.309736i
134134 242252. 1.16548
135135 31347.0 + 54294.6i 0.148034 + 0.256402i
136136 −60928.0 + 105530.i −0.282468 + 0.489249i
137137 −162754. + 281898.i −0.740850 + 1.28319i 0.211259 + 0.977430i 0.432244π0.432244\pi
−0.952109 + 0.305760i 0.901090π0.901090\pi
138138 4032.00 + 6983.63i 0.0180228 + 0.0312164i
139139 3211.00 0.0140962 0.00704812 0.999975i 0.497756π-0.497756\pi
0.00704812 + 0.999975i 0.497756π0.497756\pi
140140 33712.0 175173.i 0.145367 0.755347i
141141 −166158. −0.703839
142142 −89668.0 155310.i −0.373179 0.646364i
143143 51.0000 88.3346i 0.000208560 0.000361236i
144144 −10368.0 + 17957.9i −0.0416667 + 0.0721688i
145145 279844. + 484704.i 1.10534 + 1.91451i
146146 −83284.0 −0.323355
147147 −118850. + 93569.7i −0.453632 + 0.357143i
148148 −122128. −0.458312
149149 75942.0 + 131535.i 0.280231 + 0.485375i 0.971442 0.237279i 0.0762556π-0.0762556\pi
−0.691210 + 0.722654i 0.742922π0.742922\pi
150150 −76878.0 + 133157.i −0.278981 + 0.483208i
151151 −38324.0 + 66379.1i −0.136782 + 0.236913i −0.926277 0.376844i 0.877009π-0.877009\pi
0.789495 + 0.613757i 0.210343π0.210343\pi
152152 −47648.0 82528.8i −0.167277 0.289732i
153153 −154224. −0.532627
154154 −3332.00 + 17313.6i −0.0113215 + 0.0588281i
155155 148866. 0.497698
156156 −216.000 374.123i −0.000710628 0.00123084i
157157 194855. 337499.i 0.630903 1.09276i −0.356465 0.934309i 0.616018π-0.616018\pi
0.987368 0.158447i 0.0506487π-0.0506487\pi
158158 −61062.0 + 105762.i −0.194593 + 0.337046i
159159 −89802.0 155542.i −0.281704 0.487926i
160160 −88064.0 −0.271956
161161 27440.0 9505.49i 0.0834295 0.0289008i
162162 −26244.0 −0.0785674
163163 56186.0 + 97317.0i 0.165638 + 0.286893i 0.936882 0.349647i 0.113698π-0.113698\pi
−0.771244 + 0.636540i 0.780365π0.780365\pi
164164 −123312. + 213583.i −0.358010 + 0.620092i
165165 13158.0 22790.3i 0.0376253 0.0651689i
166166 221204. + 383137.i 0.623050 + 1.07915i
167167 52550.0 0.145808 0.0729040 0.997339i 0.476773π-0.476773\pi
0.0729040 + 0.997339i 0.476773π0.476773\pi
168168 56448.0 + 48885.4i 0.154303 + 0.133631i
169169 −371284. −0.999976
170170 −327488. 567226.i −0.869107 1.50534i
171171 60304.5 104450.i 0.157710 0.273162i
172172 −147928. + 256219.i −0.381267 + 0.660374i
173173 67628.0 + 117135.i 0.171795 + 0.297558i 0.939048 0.343787i 0.111710π-0.111710\pi
−0.767252 + 0.641345i 0.778377π0.778377\pi
174174 −234288. −0.586647
175175 418558. + 362482.i 1.03314 + 0.894728i
176176 8704.00 0.0211805
177177 −143226. 248075.i −0.343628 0.595181i
178178 −117984. + 204354.i −0.279109 + 0.483430i
179179 −125319. + 217059.i −0.292337 + 0.506343i −0.974362 0.224986i 0.927766π-0.927766\pi
0.682025 + 0.731329i 0.261100π0.261100\pi
180180 −55728.0 96523.7i −0.128201 0.222051i
181181 199233. 0.452027 0.226014 0.974124i 0.427431π-0.427431\pi
0.226014 + 0.974124i 0.427431π0.427431\pi
182182 −1470.00 + 509.223i −0.00328957 + 0.00113954i
183183 518886. 1.14537
184184 −7168.00 12415.3i −0.0156082 0.0270342i
185185 328219. 568492.i 0.705074 1.22122i
186186 −31158.0 + 53967.2i −0.0660370 + 0.114379i
187187 32368.0 + 56063.0i 0.0676880 + 0.117239i
188188 295392. 0.609543
189189 −17860.5 + 92805.9i −0.0363696 + 0.188982i
190190 512216. 1.02936
191191 119385. + 206781.i 0.236792 + 0.410135i 0.959792 0.280713i 0.0905708π-0.0905708\pi
−0.723000 + 0.690848i 0.757237π0.757237\pi
192192 18432.0 31925.2i 0.0360844 0.0625000i
193193 −42845.5 + 74210.6i −0.0827965 + 0.143408i −0.904450 0.426579i 0.859718π-0.859718\pi
0.821654 + 0.569987i 0.193052π0.193052\pi
194194 −239692. 415159.i −0.457245 0.791972i
195195 2322.00 0.00437296
196196 211288. 166346.i 0.392857 0.309295i
197197 −71408.0 −0.131094 −0.0655468 0.997849i 0.520879π-0.520879\pi
−0.0655468 + 0.997849i 0.520879π0.520879\pi
198198 5508.00 + 9540.14i 0.00998461 + 0.0172938i
199199 355676. 616049.i 0.636681 1.10276i −0.349475 0.936946i 0.613640π-0.613640\pi
0.986156 0.165818i 0.0530265π-0.0530265\pi
200200 136672. 236723.i 0.241604 0.418471i
201201 −272534. 472042.i −0.475806 0.824120i
202202 −400040. −0.689803
203203 −159446. + 828506.i −0.271565 + 1.41109i
204204 274176. 0.461269
205205 −662802. 1.14801e6i −1.10154 1.90792i
206206 243382. 421550.i 0.399595 0.692119i
207207 9072.00 15713.2i 0.0147156 0.0254881i
208208 384.000 + 665.108i 0.000615422 + 0.00106594i
209209 −50626.0 −0.0801693
210210 −379260. + 131380.i −0.593456 + 0.205579i
211211 −260260. −0.402440 −0.201220 0.979546i 0.564491π-0.564491\pi
−0.201220 + 0.979546i 0.564491π0.564491\pi
212212 159648. + 276518.i 0.243963 + 0.422556i
213213 −201753. + 349446.i −0.304699 + 0.527754i
214214 −97296.0 + 168522.i −0.145231 + 0.251548i
215215 −795113. 1.37718e6i −1.17309 2.03186i
216216 46656.0 0.0680414
217217 169638. + 146911.i 0.244553 + 0.211790i
218218 608300. 0.866915
219219 93694.5 + 162284.i 0.132009 + 0.228646i
220220 −23392.0 + 40516.1i −0.0325845 + 0.0564380i
221221 −2856.00 + 4946.74i −0.00393349 + 0.00681300i
222222 137394. + 237973.i 0.187105 + 0.324075i
223223 105656. 0.142276 0.0711381 0.997466i 0.477337π-0.477337\pi
0.0711381 + 0.997466i 0.477337π0.477337\pi
224224 −100352. 86907.4i −0.133631 0.115728i
225225 345951. 0.455573
226226 −121772. 210915.i −0.158590 0.274686i
227227 −327375. + 567030.i −0.421678 + 0.730368i −0.996104 0.0881890i 0.971892π-0.971892\pi
0.574426 + 0.818557i 0.305225π0.305225\pi
228228 −107208. + 185690.i −0.136581 + 0.236565i
229229 −278856. 482994.i −0.351392 0.608629i 0.635101 0.772429i 0.280958π-0.280958\pi
−0.986494 + 0.163800i 0.947625π0.947625\pi
230230 77056.0 0.0960477
231231 37485.0 12985.2i 0.0462197 0.0160110i
232232 416512. 0.508051
233233 623797. + 1.08045e6i 0.752755 + 1.30381i 0.946483 + 0.322754i 0.104609π0.104609\pi
−0.193728 + 0.981055i 0.562058π0.562058\pi
234234 −486.000 + 841.777i −0.000580225 + 0.00100498i
235235 −793866. + 1.37502e6i −0.937729 + 1.62420i
236236 254624. + 441022.i 0.297591 + 0.515442i
237237 274779. 0.317770
238238 186592. 969560.i 0.213526 1.10951i
239239 −496926. −0.562726 −0.281363 0.959601i 0.590786π-0.590786\pi
−0.281363 + 0.959601i 0.590786π0.590786\pi
240240 99072.0 + 171598.i 0.111026 + 0.192302i
241241 138809. 240424.i 0.153948 0.266646i −0.778727 0.627363i 0.784134π-0.784134\pi
0.932676 + 0.360716i 0.117468π0.117468\pi
242242 −319790. + 553893.i −0.351016 + 0.607977i
243243 29524.5 + 51137.9i 0.0320750 + 0.0555556i
244244 −922464. −0.991916
245245 206486. + 1.43058e6i 0.219774 + 1.52264i
246246 554904. 0.584629
247247 −2233.50 3868.54i −0.00232940 0.00403463i
248248 55392.0 95941.8i 0.0571897 0.0990555i
249249 497709. 862057.i 0.508718 0.881125i
250250 197112. + 341408.i 0.199463 + 0.345481i
251251 −308328. −0.308908 −0.154454 0.988000i 0.549362π-0.549362\pi
−0.154454 + 0.988000i 0.549362π0.549362\pi
252252 31752.0 164988.i 0.0314970 0.163663i
253253 −7616.00 −0.00748041
254254 −303930. 526422.i −0.295590 0.511976i
255255 −736848. + 1.27626e6i −0.709623 + 1.22910i
256256 −32768.0 + 56755.8i −0.0312500 + 0.0541266i
257257 −204381. 353998.i −0.193022 0.334325i 0.753228 0.657759i 0.228496π-0.228496\pi
−0.946250 + 0.323435i 0.895162π0.895162\pi
258258 665676. 0.622606
259259 935042. 323908.i 0.866128 0.300035i
260260 −4128.00 −0.00378710
261261 263574. + 456524.i 0.239498 + 0.414822i
262262 471004. 815803.i 0.423908 0.734230i
263263 −544062. + 942343.i −0.485019 + 0.840078i −0.999852 0.0172127i 0.994521π-0.994521\pi
0.514833 + 0.857291i 0.327854π0.327854\pi
264264 −9792.00 16960.2i −0.00864692 0.0149769i
265265 −1.71622e6 −1.50126
266266 583688. + 505489.i 0.505797 + 0.438033i
267267 530928. 0.455782
268268 484504. + 839186.i 0.412060 + 0.713709i
269269 334145. 578756.i 0.281549 0.487657i −0.690217 0.723602i 0.742485π-0.742485\pi
0.971766 + 0.235945i 0.0758184π0.0758184\pi
270270 −125388. + 217178.i −0.104676 + 0.181304i
271271 415332. + 719376.i 0.343536 + 0.595022i 0.985087 0.172059i 0.0550419π-0.0550419\pi
−0.641551 + 0.767081i 0.721709π0.721709\pi
272272 −487424. −0.399470
273273 2646.00 + 2291.50i 0.00214874 + 0.00186086i
274274 −1.30203e6 −1.04772
275275 −72607.0 125759.i −0.0578958 0.100278i
276276 −16128.0 + 27934.5i −0.0127441 + 0.0220734i
277277 −462537. + 801137.i −0.362198 + 0.627346i −0.988322 0.152377i 0.951307π-0.951307\pi
0.626124 + 0.779724i 0.284640π0.284640\pi
278278 6422.00 + 11123.2i 0.00498377 + 0.00863215i
279279 140211. 0.107838
280280 674240. 233564.i 0.513948 0.178037i
281281 1.33635e6 1.00961 0.504805 0.863233i 0.331564π-0.331564\pi
0.504805 + 0.863233i 0.331564π0.331564\pi
282282 −332316. 575588.i −0.248845 0.431012i
283283 496478. 859926.i 0.368497 0.638256i −0.620833 0.783942i 0.713206π-0.713206\pi
0.989331 + 0.145686i 0.0465390π0.0465390\pi
284284 358672. 621238.i 0.263877 0.457048i
285285 −576243. 998082.i −0.420236 0.727871i
286286 408.000 0.000294948
287287 377643. 1.96229e6i 0.270630 1.40624i
288288 −82944.0 −0.0589256
289289 −1.10268e6 1.90990e6i −0.776613 1.34513i
290290 −1.11938e6 + 1.93882e6i −0.781594 + 1.35376i
291291 −539307. + 934107.i −0.373339 + 0.646642i
292292 −166568. 288504.i −0.114323 0.198014i
293293 563544. 0.383494 0.191747 0.981444i 0.438585π-0.438585\pi
0.191747 + 0.981444i 0.438585π0.438585\pi
294294 −561834. 224567.i −0.379088 0.151523i
295295 −2.73721e6 −1.83127
296296 −244256. 423064.i −0.162038 0.280657i
297297 12393.0 21465.3i 0.00815240 0.0141204i
298298 −303768. + 526142.i −0.198153 + 0.343212i
299299 −336.000 581.969i −0.000217351 0.000376463i
300300 −615024. −0.394538
301301 453029. 2.35401e6i 0.288211 1.49759i
302302 −306592. −0.193439
303303 450045. + 779501.i 0.281611 + 0.487764i
304304 190592. 330115.i 0.118283 0.204871i
305305 2.47912e6 4.29397e6i 1.52598 2.64307i
306306 −308448. 534248.i −0.188312 0.326166i
307307 2.82703e6 1.71193 0.855963 0.517037i 0.172965π-0.172965\pi
0.855963 + 0.517037i 0.172965π0.172965\pi
308308 −66640.0 + 23084.8i −0.0400275 + 0.0138659i
309309 −1.09522e6 −0.652536
310310 297732. + 515687.i 0.175963 + 0.304777i
311311 563657. 976283.i 0.330456 0.572367i −0.652145 0.758094i 0.726131π-0.726131\pi
0.982601 + 0.185727i 0.0594641π0.0594641\pi
312312 864.000 1496.49i 0.000502490 0.000870338i
313313 1.18006e6 + 2.04393e6i 0.680840 + 1.17925i 0.974725 + 0.223408i 0.0717183π0.0717183\pi
−0.293885 + 0.955841i 0.594948π0.594948\pi
314314 1.55884e6 0.892231
315315 682668. + 591208.i 0.387644 + 0.335710i
316316 −488496. −0.275197
317317 1.11210e6 + 1.92621e6i 0.621578 + 1.07660i 0.989192 + 0.146626i 0.0468415π0.0468415\pi
−0.367614 + 0.929979i 0.619825π0.619825\pi
318318 359208. 622167.i 0.199195 0.345016i
319319 110636. 191627.i 0.0608723 0.105434i
320320 −176128. 305063.i −0.0961509 0.166538i
321321 437832. 0.237162
322322 87808.0 + 76044.0i 0.0471948 + 0.0408719i
323323 2.83506e6 1.51201
324324 −52488.0 90911.9i −0.0277778 0.0481125i
325325 6406.50 11096.4i 0.00336444 0.00582738i
326326 −224744. + 389268.i −0.117124 + 0.202864i
327327 −684338. 1.18531e6i −0.353917 0.613002i
328328 −986496. −0.506303
329329 −2.26160e6 + 783439.i −1.15193 + 0.399039i
330330 105264. 0.0532102
331331 1.85152e6 + 3.20693e6i 0.928877 + 1.60886i 0.785204 + 0.619237i 0.212558π0.212558\pi
0.143673 + 0.989625i 0.454109π0.454109\pi
332332 −884816. + 1.53255e6i −0.440563 + 0.763077i
333333 309136. 535440.i 0.152771 0.264606i
334334 105100. + 182039.i 0.0515509 + 0.0892888i
335335 −5.20842e6 −2.53568
336336 −56448.0 + 293312.i −0.0272772 + 0.141737i
337337 1.21432e6 0.582452 0.291226 0.956654i 0.405937π-0.405937\pi
0.291226 + 0.956654i 0.405937π0.405937\pi
338338 −742568. 1.28617e6i −0.353545 0.612358i
339339 −273987. + 474559.i −0.129488 + 0.224280i
340340 1.30995e6 2.26890e6i 0.614551 1.06443i
341341 −29427.0 50969.1i −0.0137044 0.0237367i
342342 482436. 0.223036
343343 −1.17649e6 + 1.83397e6i −0.539949 + 0.841698i
344344 −1.18342e6 −0.539193
345345 −86688.0 150148.i −0.0392113 0.0679160i
346346 −270512. + 468541.i −0.121478 + 0.210405i
347347 488952. 846890.i 0.217993 0.377575i −0.736201 0.676763i 0.763382π-0.763382\pi
0.954194 + 0.299188i 0.0967157π0.0967157\pi
348348 −468576. 811597.i −0.207411 0.359247i
349349 511282. 0.224697 0.112348 0.993669i 0.464163π-0.464163\pi
0.112348 + 0.993669i 0.464163π0.464163\pi
350350 −418558. + 2.17489e6i −0.182636 + 0.949003i
351351 2187.00 0.000947504
352352 17408.0 + 30151.5i 0.00748845 + 0.0129704i
353353 −1.51376e6 + 2.62191e6i −0.646577 + 1.11990i 0.337357 + 0.941377i 0.390467π0.390467\pi
−0.983935 + 0.178528i 0.942866π0.942866\pi
354354 572904. 992299.i 0.242982 0.420857i
355355 1.92786e6 + 3.33915e6i 0.811905 + 1.40626i
356356 −943872. −0.394719
357357 −2.09916e6 + 727170.i −0.871716 + 0.301971i
358358 −1.00255e6 −0.413427
359359 −2.29728e6 3.97900e6i −0.940757 1.62944i −0.764032 0.645179i 0.776783π-0.776783\pi
−0.176725 0.984260i 0.556550π-0.556550\pi
360360 222912. 386095.i 0.0906520 0.157014i
361361 129489. 224282.i 0.0522956 0.0905786i
362362 398466. + 690163.i 0.159816 + 0.276809i
363363 1.43906e6 0.573206
364364 −4704.00 4073.78i −0.00186086 0.00161155i
365365 1.79061e6 0.703506
366366 1.03777e6 + 1.79747e6i 0.404948 + 0.701390i
367367 556365. 963653.i 0.215623 0.373470i −0.737842 0.674973i 0.764155π-0.764155\pi
0.953465 + 0.301503i 0.0974885π0.0974885\pi
368368 28672.0 49661.4i 0.0110367 0.0191161i
369369 −624267. 1.08126e6i −0.238674 0.413395i
370370 2.62575e6 0.997125
371371 −1.95569e6 1.69368e6i −0.737675 0.638845i
372372 −249264. −0.0933904
373373 1.22947e6 + 2.12951e6i 0.457559 + 0.792516i 0.998831 0.0483315i 0.0153904π-0.0153904\pi
−0.541272 + 0.840848i 0.682057π0.682057\pi
374374 −129472. + 224252.i −0.0478627 + 0.0829006i
375375 443502. 768168.i 0.162861 0.282084i
376376 590784. + 1.02327e6i 0.215506 + 0.373267i
377377 19524.0 0.00707482
378378 −357210. + 123741.i −0.128586 + 0.0445435i
379379 −4.10130e6 −1.46664 −0.733320 0.679884i 0.762030π-0.762030\pi
−0.733320 + 0.679884i 0.762030π0.762030\pi
380380 1.02443e6 + 1.77437e6i 0.363935 + 0.630354i
381381 −683842. + 1.18445e6i −0.241348 + 0.418027i
382382 −477540. + 827124.i −0.167437 + 0.290009i
383383 1.29707e6 + 2.24658e6i 0.451820 + 0.782575i 0.998499 0.0547673i 0.0174417π-0.0174417\pi
−0.546679 + 0.837342i 0.684108π0.684108\pi
384384 147456. 0.0510310
385385 71638.0 372242.i 0.0246315 0.127989i
386386 −342764. −0.117092
387387 −748886. 1.29711e6i −0.254178 0.440249i
388388 958768. 1.66063e6i 0.323321 0.560009i
389389 −1.11703e6 + 1.93476e6i −0.374276 + 0.648265i −0.990218 0.139526i 0.955442π-0.955442\pi
0.615942 + 0.787791i 0.288775π0.288775\pi
390390 4644.00 + 8043.64i 0.00154608 + 0.00267788i
391391 426496. 0.141082
392392 998816. + 399231.i 0.328300 + 0.131223i
393393 −2.11952e6 −0.692238
394394 −142816. 247365.i −0.0463486 0.0802781i
395395 1.31283e6 2.27389e6i 0.423367 0.733293i
396396 −22032.0 + 38160.5i −0.00706018 + 0.0122286i
397397 1.03200e6 + 1.78747e6i 0.328627 + 0.569198i 0.982240 0.187631i 0.0600809π-0.0600809\pi
−0.653613 + 0.756829i 0.726748π0.726748\pi
398398 2.84541e6 0.900403
399399 328324. 1.70602e6i 0.103245 0.536479i
400400 1.09338e6 0.341680
401401 −576414. 998378.i −0.179008 0.310052i 0.762533 0.646950i 0.223956π-0.223956\pi
−0.941541 + 0.336898i 0.890622π0.890622\pi
402402 1.09013e6 1.88817e6i 0.336446 0.582741i
403403 2596.50 4497.27i 0.000796390 0.00137939i
404404 −800080. 1.38578e6i −0.243882 0.422416i
405405 564246. 0.170935
406406 −3.18892e6 + 1.10467e6i −0.960127 + 0.332598i
407407 −259522. −0.0776583
408408 548352. + 949774.i 0.163083 + 0.282468i
409409 −2.96706e6 + 5.13910e6i −0.877038 + 1.51907i −0.0224623 + 0.999748i 0.507151π0.507151\pi
−0.854576 + 0.519327i 0.826183π0.826183\pi
410410 2.65121e6 4.59203e6i 0.778904 1.34910i
411411 1.46479e6 + 2.53708e6i 0.427730 + 0.740850i
412412 1.94706e6 0.565113
413413 −3.11914e6 2.70126e6i −0.899830 0.779275i
414414 72576.0 0.0208110
415415 −4.75589e6 8.23744e6i −1.35554 2.34786i
416416 −1536.00 + 2660.43i −0.000435169 + 0.000753735i
417417 14449.5 25027.3i 0.00406923 0.00704812i
418418 −101252. 175374.i −0.0283441 0.0490934i
419419 771666. 0.214731 0.107365 0.994220i 0.465759π-0.465759\pi
0.107365 + 0.994220i 0.465759π0.465759\pi
420420 −1.21363e6 1.05104e6i −0.335710 0.290733i
421421 −2.87542e6 −0.790671 −0.395336 0.918537i 0.629372π-0.629372\pi
−0.395336 + 0.918537i 0.629372π0.629372\pi
422422 −520520. 901567.i −0.142284 0.246443i
423423 −747711. + 1.29507e6i −0.203181 + 0.351920i
424424 −638592. + 1.10607e6i −0.172508 + 0.298792i
425425 4.06599e6 + 7.04250e6i 1.09193 + 1.89128i
426426 −1.61402e6 −0.430909
427427 7.06261e6 2.44656e6i 1.87454 0.649361i
428428 −778368. −0.205388
429429 −459.000 795.011i −0.000120412 0.000208560i
430430 3.18045e6 5.50870e6i 0.829503 1.43674i
431431 68931.0 119392.i 0.0178740 0.0309587i −0.856950 0.515399i 0.827644π-0.827644\pi
0.874824 + 0.484441i 0.160977π0.160977\pi
432432 93312.0 + 161621.i 0.0240563 + 0.0416667i
433433 1.56526e6 0.401204 0.200602 0.979673i 0.435710π-0.435710\pi
0.200602 + 0.979673i 0.435710π0.435710\pi
434434 −169638. + 881465.i −0.0432314 + 0.224637i
435435 5.03719e6 1.27634
436436 1.21660e6 + 2.10721e6i 0.306501 + 0.530875i
437437 −166768. + 288851.i −0.0417743 + 0.0723552i
438438 −374778. + 649135.i −0.0933445 + 0.161677i
439439 −2.44079e6 4.22757e6i −0.604462 1.04696i −0.992136 0.125162i 0.960055π-0.960055\pi
0.387675 0.921796i 0.373278π-0.373278\pi
440440 −187136. −0.0460814
441441 194481. + 1.34740e6i 0.0476190 + 0.329914i
442442 −22848.0 −0.00556279
443443 650758. + 1.12715e6i 0.157547 + 0.272879i 0.933984 0.357316i 0.116308π-0.116308\pi
−0.776437 + 0.630195i 0.782975π0.782975\pi
444444 −549576. + 951894.i −0.132303 + 0.229156i
445445 2.53666e6 4.39362e6i 0.607242 1.05177i
446446 211312. + 366003.i 0.0503022 + 0.0871260i
447447 1.36696e6 0.323583
448448 100352. 521444.i 0.0236228 0.122748i
449449 −3.13141e6 −0.733034 −0.366517 0.930411i 0.619450π-0.619450\pi
−0.366517 + 0.930411i 0.619450π0.619450\pi
450450 691902. + 1.19841e6i 0.161069 + 0.278981i
451451 −262038. + 453863.i −0.0606629 + 0.105071i
452452 487088. 843661.i 0.112140 0.194233i
453453 344916. + 597412.i 0.0789710 + 0.136782i
454454 −2.61900e6 −0.596343
455455 31605.0 10948.3i 0.00715694 0.00247924i
456456 −857664. −0.193155
457457 −3.24634e6 5.62283e6i −0.727116 1.25940i −0.958097 0.286444i 0.907527π-0.907527\pi
0.230981 0.972958i 0.425807π-0.425807\pi
458458 1.11543e6 1.93197e6i 0.248472 0.430366i
459459 −694008. + 1.20206e6i −0.153756 + 0.266314i
460460 154112. + 266930.i 0.0339580 + 0.0588170i
461461 5.34717e6 1.17185 0.585925 0.810365i 0.300731π-0.300731\pi
0.585925 + 0.810365i 0.300731π0.300731\pi
462462 119952. + 103881.i 0.0261458 + 0.0226430i
463463 3.37285e6 0.731215 0.365607 0.930769i 0.380861π-0.380861\pi
0.365607 + 0.930769i 0.380861π0.380861\pi
464464 833024. + 1.44284e6i 0.179623 + 0.311117i
465465 669897. 1.16030e6i 0.143673 0.248849i
466466 −2.49519e6 + 4.32179e6i −0.532278 + 0.921932i
467467 −1.11726e6 1.93515e6i −0.237062 0.410604i 0.722808 0.691049i 0.242851π-0.242851\pi
−0.959870 + 0.280445i 0.909518π0.909518\pi
468468 −3888.00 −0.000820562
469469 −5.93517e6 5.14001e6i −1.24595 1.07903i
470470 −6.35093e6 −1.32615
471471 −1.75369e6 3.03749e6i −0.364252 0.630903i
472472 −1.01850e6 + 1.76409e6i −0.210428 + 0.364473i
473473 −314347. + 544465.i −0.0646036 + 0.111897i
474474 549558. + 951862.i 0.112349 + 0.194593i
475475 −6.35952e6 −1.29327
476476 3.73184e6 1.29275e6i 0.754928 0.261515i
477477 −1.61644e6 −0.325284
478478 −993852. 1.72140e6i −0.198954 0.344598i
479479 1.26068e6 2.18357e6i 0.251054 0.434838i −0.712762 0.701406i 0.752556π-0.752556\pi
0.963816 + 0.266568i 0.0858896π0.0858896\pi
480480 −396288. + 686391.i −0.0785069 + 0.135978i
481481 −11449.5 19831.1i −0.00225644 0.00390827i
482482 1.11047e6 0.217716
483483 49392.0 256648.i 0.00963360 0.0500577i
484484 −2.55832e6 −0.496411
485485 5.15338e6 + 8.92591e6i 0.994804 + 1.72305i
486486 −118098. + 204552.i −0.0226805 + 0.0392837i
487487 −958358. + 1.65993e6i −0.183107 + 0.317151i −0.942937 0.332971i 0.891949π-0.891949\pi
0.759830 + 0.650122i 0.225282π0.225282\pi
488488 −1.84493e6 3.19551e6i −0.350695 0.607422i
489489 1.01135e6 0.191262
490490 −4.54269e6 + 3.57644e6i −0.854718 + 0.672916i
491491 5.82875e6 1.09112 0.545559 0.838073i 0.316317π-0.316317\pi
0.545559 + 0.838073i 0.316317π0.316317\pi
492492 1.10981e6 + 1.92224e6i 0.206697 + 0.358010i
493493 −6.19562e6 + 1.07311e7i −1.14807 + 1.98851i
494494 8934.00 15474.1i 0.00164713 0.00285292i
495495 −118422. 205113.i −0.0217230 0.0376253i
496496 443136. 0.0808785
497497 −1.09843e6 + 5.70763e6i −0.199472 + 1.03649i
498498 3.98167e6 0.719436
499499 5.00243e6 + 8.66446e6i 0.899352 + 1.55772i 0.828324 + 0.560249i 0.189295π0.189295\pi
0.0710277 + 0.997474i 0.477372π0.477372\pi
500500 −788448. + 1.36563e6i −0.141042 + 0.244292i
501501 236475. 409587.i 0.0420912 0.0729040i
502502 −616656. 1.06808e6i −0.109215 0.189167i
503503 1.13666e6 0.200313 0.100157 0.994972i 0.468066π-0.468066\pi
0.100157 + 0.994972i 0.468066π0.468066\pi
504504 635040. 219984.i 0.111359 0.0385758i
505505 8.60086e6 1.50077
506506 −15232.0 26382.6i −0.00264473 0.00458080i
507507 −1.67078e6 + 2.89387e6i −0.288668 + 0.499988i
508508 1.21572e6 2.10569e6i 0.209013 0.362022i
509509 −2.00968e6 3.48088e6i −0.343822 0.595517i 0.641317 0.767276i 0.278388π-0.278388\pi
−0.985139 + 0.171759i 0.945055π0.945055\pi
510510 −5.89478e6 −1.00356
511511 2.04046e6 + 1.76709e6i 0.345681 + 0.299368i
512512 −262144. −0.0441942
513513 −542740. 940054.i −0.0910540 0.157710i
514514 817524. 1.41599e6i 0.136487 0.236403i
515515 −5.23271e6 + 9.06332e6i −0.869378 + 1.50581i
516516 1.33135e6 + 2.30597e6i 0.220125 + 0.381267i
517517 627708. 0.103284
518518 2.99214e6 + 2.59127e6i 0.489956 + 0.424314i
519519 1.21730e6 0.198372
520520 −8256.00 14299.8i −0.00133894 0.00231911i
521521 2.76014e6 4.78070e6i 0.445488 0.771609i −0.552598 0.833448i 0.686363π-0.686363\pi
0.998086 + 0.0618395i 0.0196967π0.0196967\pi
522522 −1.05430e6 + 1.82609e6i −0.169350 + 0.293324i
523523 −4.47236e6 7.74636e6i −0.714961 1.23835i −0.962974 0.269593i 0.913111π-0.913111\pi
0.248013 0.968757i 0.420222π-0.420222\pi
524524 3.76803e6 0.599496
525525 4.70878e6 1.63117e6i 0.745607 0.258286i
526526 −4.35250e6 −0.685921
527527 1.64791e6 + 2.85427e6i 0.258468 + 0.447680i
528528 39168.0 67841.0i 0.00611430 0.0105903i
529529 3.19308e6 5.53058e6i 0.496102 0.859274i
530530 −3.43243e6 5.94515e6i −0.530777 0.919333i
531531 −2.57807e6 −0.396788
532532 −583688. + 3.03293e6i −0.0894132 + 0.464605i
533533 −46242.0 −0.00705048
534534 1.06186e6 + 1.83919e6i 0.161143 + 0.279109i
535535 2.09186e6 3.62321e6i 0.315972 0.547280i
536536 −1.93802e6 + 3.35674e6i −0.291370 + 0.504668i
537537 1.12787e6 + 1.95353e6i 0.168781 + 0.292337i
538538 2.67316e6 0.398171
539539 448987. 353486.i 0.0665674 0.0524083i
540540 −1.00310e6 −0.148034
541541 −424528. 735305.i −0.0623611 0.108013i 0.833159 0.553033i 0.186530π-0.186530\pi
−0.895520 + 0.445021i 0.853196π0.853196\pi
542542 −1.66133e6 + 2.87750e6i −0.242917 + 0.420744i
543543 896548. 1.55287e6i 0.130489 0.226014i
544544 −974848. 1.68849e6i −0.141234 0.244625i
545545 −1.30784e7 −1.88610
546546 −2646.00 + 13749.0i −0.000379847 + 0.00197374i
547547 8.61340e6 1.23085 0.615426 0.788194i 0.288984π-0.288984\pi
0.615426 + 0.788194i 0.288984π0.288984\pi
548548 −2.60406e6 4.51037e6i −0.370425 0.641595i
549549 2.33499e6 4.04432e6i 0.330639 0.572683i
550550 290428. 503036.i 0.0409385 0.0709075i
551551 −4.84521e6 8.39214e6i −0.679882 1.17759i
552552 −129024. −0.0180228
553553 3.74005e6 1.29559e6i 0.520073 0.180159i
554554 −3.70029e6 −0.512226
555555 −2.95397e6 5.11643e6i −0.407074 0.705074i
556556 −25688.0 + 44492.9i −0.00352406 + 0.00610385i
557557 −3.89940e6 + 6.75395e6i −0.532549 + 0.922401i 0.466729 + 0.884400i 0.345432π0.345432\pi
−0.999278 + 0.0380009i 0.987901π0.987901\pi
558558 280422. + 485705.i 0.0381265 + 0.0660370i
559559 −55473.0 −0.00750848
560560 2.15757e6 + 1.86851e6i 0.290733 + 0.251782i
561561 582624. 0.0781594
562562 2.67270e6 + 4.62925e6i 0.356951 + 0.618258i
563563 −536357. + 928998.i −0.0713153 + 0.123522i −0.899478 0.436966i 0.856053π-0.856053\pi
0.828163 + 0.560488i 0.189386π0.189386\pi
564564 1.32926e6 2.30235e6i 0.175960 0.304771i
565565 2.61810e6 + 4.53468e6i 0.345036 + 0.597620i
566566 3.97183e6 0.521134
567567 642978. + 556835.i 0.0839921 + 0.0727393i
568568 2.86938e6 0.373179
569569 507621. + 879225.i 0.0657293 + 0.113846i 0.897017 0.441996i 0.145729π-0.145729\pi
−0.831288 + 0.555842i 0.812396π0.812396\pi
570570 2.30497e6 3.99233e6i 0.297152 0.514682i
571571 3.39047e6 5.87246e6i 0.435180 0.753754i −0.562130 0.827049i 0.690018π-0.690018\pi
0.997310 + 0.0732945i 0.0233513π0.0233513\pi
572572 816.000 + 1413.35i 0.000104280 + 0.000180618i
573573 2.14893e6 0.273423
574574 7.55286e6 2.61639e6i 0.956823 0.331453i
575575 −956704. −0.120672
576576 −165888. 287326.i −0.0208333 0.0360844i
577577 1.65268e6 2.86253e6i 0.206657 0.357941i −0.744002 0.668177i 0.767075π-0.767075\pi
0.950659 + 0.310236i 0.100408π0.100408\pi
578578 4.41072e6 7.63959e6i 0.549148 0.951153i
579579 385610. + 667895.i 0.0478026 + 0.0827965i
580580 −8.95501e6 −1.10534
581581 2.70975e6 1.40803e7i 0.333034 1.73050i
582582 −4.31446e6 −0.527981
583583 339252. + 587602.i 0.0413381 + 0.0715998i
584584 666272. 1.15402e6i 0.0808387 0.140017i
585585 10449.0 18098.2i 0.00126237 0.00218648i
586586 1.12709e6 + 1.95217e6i 0.135586 + 0.234841i
587587 −1.19833e7 −1.43543 −0.717715 0.696337i 0.754812π-0.754812\pi
−0.717715 + 0.696337i 0.754812π0.754812\pi
588588 −345744. 2.39538e6i −0.0412393 0.285714i
589589 −2.57746e6 −0.306128
590590 −5.47442e6 9.48197e6i −0.647452 1.12142i
591591 −321336. + 556570.i −0.0378434 + 0.0655468i
592592 977024. 1.69226e6i 0.114578 0.198455i
593593 2.65510e6 + 4.59877e6i 0.310059 + 0.537038i 0.978375 0.206840i 0.0663179π-0.0663179\pi
−0.668316 + 0.743877i 0.732985π0.732985\pi
594594 99144.0 0.0115292
595595 −4.01173e6 + 2.08456e7i −0.464557 + 2.41391i
596596 −2.43014e6 −0.280231
597597 −3.20108e6 5.54444e6i −0.367588 0.636681i
598598 1344.00 2327.88i 0.000153690 0.000266199i
599599 −1.21118e6 + 2.09782e6i −0.137924 + 0.238892i −0.926711 0.375775i 0.877376π-0.877376\pi
0.788786 + 0.614667i 0.210710π0.210710\pi
600600 −1.23005e6 2.13051e6i −0.139490 0.241604i
601601 −7.10659e6 −0.802556 −0.401278 0.915956i 0.631434π-0.631434\pi
−0.401278 + 0.915956i 0.631434π0.631434\pi
602602 9.06059e6 3.13868e6i 1.01898 0.352985i
603603 −4.90560e6 −0.549413
604604 −613184. 1.06207e6i −0.0683909 0.118457i
605605 6.87548e6 1.19087e7i 0.763686 1.32274i
606606 −1.80018e6 + 3.11800e6i −0.199129 + 0.344901i
607607 −8.95970e6 1.55187e7i −0.987011 1.70955i −0.632636 0.774449i 0.718027π-0.718027\pi
−0.354374 0.935104i 0.615306π-0.615306\pi
608608 1.52474e6 0.167277
609609 5.74006e6 + 4.97103e6i 0.627152 + 0.543130i
610610 1.98330e7 2.15806
611611 27693.0 + 47965.7i 0.00300101 + 0.00519790i
612612 1.23379e6 2.13699e6i 0.133157 0.230634i
613613 −6.98950e6 + 1.21062e7i −0.751269 + 1.30124i 0.195940 + 0.980616i 0.437224π0.437224\pi
−0.947208 + 0.320619i 0.896109π0.896109\pi
614614 5.65407e6 + 9.79313e6i 0.605257 + 1.04834i
615615 −1.19304e7 −1.27195
616616 −213248. 184678.i −0.0226430 0.0196094i
617617 −5.25594e6 −0.555824 −0.277912 0.960606i 0.589642π-0.589642\pi
−0.277912 + 0.960606i 0.589642π0.589642\pi
618618 −2.19044e6 3.79395e6i −0.230706 0.399595i
619619 −721506. + 1.24969e6i −0.0756857 + 0.131091i −0.901384 0.433020i 0.857448π-0.857448\pi
0.825699 + 0.564112i 0.190781π0.190781\pi
620620 −1.19093e6 + 2.06275e6i −0.124425 + 0.215510i
621621 −81648.0 141418.i −0.00849604 0.0147156i
622622 4.50926e6 0.467336
623623 7.22652e6 2.50334e6i 0.745949 0.258404i
624624 6912.00 0.000710628
625625 2.43553e6 + 4.21846e6i 0.249398 + 0.431970i
626626 −4.72026e6 + 8.17573e6i −0.481426 + 0.833855i
627627 −227817. + 394591.i −0.0231429 + 0.0400846i
628628 3.11768e6 + 5.39998e6i 0.315451 + 0.546378i
629629 1.45332e7 1.46466
630630 −682668. + 3.54725e6i −0.0685264 + 0.356074i
631631 1.51723e7 1.51697 0.758487 0.651688i 0.225939π-0.225939\pi
0.758487 + 0.651688i 0.225939π0.225939\pi
632632 −976992. 1.69220e6i −0.0972967 0.168523i
633633 −1.17117e6 + 2.02853e6i −0.116174 + 0.201220i
634634 −4.44840e6 + 7.70485e6i −0.439522 + 0.761275i
635635 6.53450e6 + 1.13181e7i 0.643099 + 1.11388i
636636 2.87366e6 0.281704
637637 46819.5 + 18713.9i 0.00457170 + 0.00182733i
638638 885088. 0.0860864
639639 1.81578e6 + 3.14502e6i 0.175918 + 0.304699i
640640 704512. 1.22025e6i 0.0679890 0.117760i
641641 72424.0 125442.i 0.00696205 0.0120586i −0.862523 0.506017i 0.831117π-0.831117\pi
0.869485 + 0.493959i 0.164451π0.164451\pi
642642 875664. + 1.51669e6i 0.0838494 + 0.145231i
643643 −27469.0 −0.00262009 −0.00131004 0.999999i 0.500417π-0.500417\pi
−0.00131004 + 0.999999i 0.500417π0.500417\pi
644644 −87808.0 + 456264.i −0.00834295 + 0.0433512i
645645 −1.43120e7 −1.35457
646646 5.67011e6 + 9.82092e6i 0.534577 + 0.925915i
647647 −4.27892e6 + 7.41130e6i −0.401858 + 0.696039i −0.993950 0.109831i 0.964969π-0.964969\pi
0.592092 + 0.805870i 0.298302π0.298302\pi
648648 209952. 363648.i 0.0196419 0.0340207i
649649 541076. + 937171.i 0.0504251 + 0.0873388i
650650 51252.0 0.00475803
651651 1.90843e6 661099.i 0.176491 0.0611384i
652652 −1.79795e6 −0.165638
653653 −6.25152e6 1.08279e7i −0.573723 0.993718i −0.996179 0.0873343i 0.972165π-0.972165\pi
0.422456 0.906384i 0.361168π-0.361168\pi
654654 2.73735e6 4.74123e6i 0.250257 0.433458i
655655 −1.01266e7 + 1.75398e7i −0.922274 + 1.59742i
656656 −1.97299e6 3.41732e6i −0.179005 0.310046i
657657 1.68650e6 0.152431
658658 −7.23710e6 6.26752e6i −0.651629 0.564327i
659659 1.80471e7 1.61880 0.809400 0.587258i 0.199793π-0.199793\pi
0.809400 + 0.587258i 0.199793π0.199793\pi
660660 210528. + 364645.i 0.0188127 + 0.0325845i
661661 −1.67072e6 + 2.89377e6i −0.148731 + 0.257609i −0.930759 0.365634i 0.880852π-0.880852\pi
0.782028 + 0.623243i 0.214185π0.214185\pi
662662 −7.40608e6 + 1.28277e7i −0.656815 + 1.13764i
663663 25704.0 + 44520.6i 0.00227100 + 0.00393349i
664664 −7.07853e6 −0.623050
665665 −1.25493e7 1.08680e7i −1.10044 0.953006i
666666 2.47309e6 0.216050
667667 −728896. 1.26248e6i −0.0634382 0.109878i
668668 −420400. + 728154.i −0.0364520 + 0.0631367i
669669 475452. 823507.i 0.0410716 0.0711381i
670670 −1.04168e7 1.80425e7i −0.896497 1.55278i
671671 −1.96024e6 −0.168075
672672 −1.12896e6 + 391083.i −0.0964396 + 0.0334077i
673673 −8.47066e6 −0.720907 −0.360454 0.932777i 0.617378π-0.617378\pi
−0.360454 + 0.932777i 0.617378π0.617378\pi
674674 2.42865e6 + 4.20655e6i 0.205928 + 0.356678i
675675 1.55678e6 2.69642e6i 0.131513 0.227787i
676676 2.97027e6 5.14466e6i 0.249994 0.433002i
677677 −7.32764e6 1.26918e7i −0.614458 1.06427i −0.990479 0.137662i 0.956041π-0.956041\pi
0.376021 0.926611i 0.377292π-0.377292\pi
678678 −2.19190e6 −0.183124
679679 −2.93623e6 + 1.52571e7i −0.244408 + 1.26998i
680680 1.04796e7 0.869107
681681 2.94638e6 + 5.10327e6i 0.243456 + 0.421678i
682682 117708. 203876.i 0.00969047 0.0167844i
683683 −9.88081e6 + 1.71141e7i −0.810477 + 1.40379i 0.102054 + 0.994779i 0.467459π0.467459\pi
−0.912531 + 0.409008i 0.865875π0.865875\pi
684684 964872. + 1.67121e6i 0.0788550 + 0.136581i
685685 2.79937e7 2.27947
686686 −8.70603e6 407548.i −0.706333 0.0330650i
687687 −5.01942e6 −0.405753
688688 −2.36685e6 4.09950e6i −0.190634 0.330187i
689689 −29934.0 + 51847.2i −0.00240224 + 0.00416080i
690690 346752. 600592.i 0.0277266 0.0480238i
691691 −6.79162e6 1.17634e7i −0.541101 0.937214i −0.998841 0.0481282i 0.984674π-0.984674\pi
0.457740 0.889086i 0.348659π-0.348659\pi
692692 −2.16410e6 −0.171795
693693 67473.0 350600.i 0.00533700 0.0277318i
694694 3.91162e6 0.308289
695695 −138073. 239149.i −0.0108429 0.0187805i
696696 1.87430e6 3.24639e6i 0.146662 0.254026i
697697 1.46741e7 2.54163e7i 1.14412 1.98167i
698698 1.02256e6 + 1.77113e6i 0.0794423 + 0.137598i
699699 1.12283e7 0.869206
700700 −8.37116e6 + 2.89985e6i −0.645715 + 0.223682i
701701 −1.29915e7 −0.998538 −0.499269 0.866447i 0.666398π-0.666398\pi
−0.499269 + 0.866447i 0.666398π0.666398\pi
702702 4374.00 + 7575.99i 0.000334993 + 0.000580225i
703703 −5.68277e6 + 9.84284e6i −0.433682 + 0.751160i
704704 −69632.0 + 120606.i −0.00529514 + 0.00917145i
705705 7.14479e6 + 1.23751e7i 0.541398 + 0.937729i
706706 −1.21101e7 −0.914399
707707 9.80098e6 + 8.48790e6i 0.737430 + 0.638633i
708708 4.58323e6 0.343628
709709 −954367. 1.65301e6i −0.0713017 0.123498i 0.828170 0.560476i 0.189382π-0.189382\pi
−0.899472 + 0.436978i 0.856049π0.856049\pi
710710 −7.71145e6 + 1.33566e7i −0.574103 + 0.994376i
711711 1.23651e6 2.14169e6i 0.0917323 0.158885i
712712 −1.88774e6 3.26967e6i −0.139554 0.241715i
713713 −387744. −0.0285641
714714 −6.71731e6 5.81736e6i −0.493117 0.427052i
715715 −8772.00 −0.000641702
716716 −2.00510e6 3.47294e6i −0.146169 0.253172i
717717 −2.23617e6 + 3.87315e6i −0.162445 + 0.281363i
718718 9.18911e6 1.59160e7i 0.665216 1.15219i
719719 5.55999e6 + 9.63018e6i 0.401099 + 0.694724i 0.993859 0.110655i 0.0352950π-0.0352950\pi
−0.592760 + 0.805379i 0.701962π0.701962\pi
720720 1.78330e6 0.128201
721721 −1.49071e7 + 5.16399e6i −1.06796 + 0.369953i
722722 1.03591e6 0.0739571
723723 −1.24928e6 2.16382e6i −0.0888821 0.153948i
724724 −1.59386e6 + 2.76065e6i −0.113007 + 0.195734i
725725 1.38978e7 2.40718e7i 0.981979 1.70084i
726726 2.87811e6 + 4.98503e6i 0.202659 + 0.351016i
727727 8.37406e6 0.587624 0.293812 0.955863i 0.405076π-0.405076\pi
0.293812 + 0.955863i 0.405076π0.405076\pi
728728 4704.00 24442.7i 0.000328957 0.00170931i
729729 531441. 0.0370370
730730 3.58121e6 + 6.20284e6i 0.248727 + 0.430808i
731731 1.76034e7 3.04900e7i 1.21844 2.11040i
732732 −4.15109e6 + 7.18990e6i −0.286341 + 0.495958i
733733 −2.32224e6 4.02224e6i −0.159642 0.276508i 0.775098 0.631841i 0.217701π-0.217701\pi
−0.934740 + 0.355334i 0.884367π0.884367\pi
734734 4.45092e6 0.304937
735735 1.20794e7 + 4.82820e6i 0.824761 + 0.329660i
736736 229376. 0.0156082
737737 1.02957e6 + 1.78327e6i 0.0698212 + 0.120934i
738738 2.49707e6 4.32505e6i 0.168768 0.292314i
739739 5.53116e6 9.58026e6i 0.372568 0.645307i −0.617392 0.786656i 0.711811π-0.711811\pi
0.989960 + 0.141349i 0.0451440π0.0451440\pi
740740 5.25150e6 + 9.09587e6i 0.352537 + 0.610612i
741741 −40203.0 −0.00268976
742742 1.95569e6 1.01621e7i 0.130404 0.677597i
743743 1.97245e6 0.131079 0.0655395 0.997850i 0.479123π-0.479123\pi
0.0655395 + 0.997850i 0.479123π0.479123\pi
744744 −498528. 863476.i −0.0330185 0.0571897i
745745 6.53101e6 1.13120e7i 0.431112 0.746707i
746746 −4.91790e6 + 8.51805e6i −0.323543 + 0.560393i
747747 −4.47938e6 7.75852e6i −0.293708 0.508718i
748748 −1.03578e6 −0.0676880
749749 5.95938e6 2.06439e6i 0.388147 0.134458i
750750 3.54802e6 0.230320
751751 −7.51232e6 1.30117e7i −0.486042 0.841850i 0.513829 0.857893i 0.328227π-0.328227\pi
−0.999871 + 0.0160425i 0.994893π0.994893\pi
752752 −2.36314e6 + 4.09307e6i −0.152386 + 0.263940i
753753 −1.38748e6 + 2.40318e6i −0.0891740 + 0.154454i
754754 39048.0 + 67633.1i 0.00250133 + 0.00433243i
755755 6.59173e6 0.420854
756756 −1.14307e6 989929.i −0.0727393 0.0629941i
757757 −4.72426e6 −0.299636 −0.149818 0.988714i 0.547869π-0.547869\pi
−0.149818 + 0.988714i 0.547869π0.547869\pi
758758 −8.20260e6 1.42073e7i −0.518535 0.898130i
759759 −34272.0 + 59360.8i −0.00215941 + 0.00374021i
760760 −4.09773e6 + 7.09747e6i −0.257341 + 0.445728i
761761 4.28918e6 + 7.42907e6i 0.268480 + 0.465021i 0.968470 0.249132i 0.0801453π-0.0801453\pi
−0.699989 + 0.714153i 0.746812π0.746812\pi
762762 −5.47074e6 −0.341318
763763 −1.49034e7 1.29067e7i −0.926771 0.802607i
764764 −3.82032e6 −0.236792
765765 6.63163e6 + 1.14863e7i 0.409701 + 0.709623i
766766 −5.18826e6 + 8.98634e6i −0.319485 + 0.553364i
767767 −47742.0 + 82691.6i −0.00293030 + 0.00507543i
768768 294912. + 510803.i 0.0180422 + 0.0312500i
769769 1.76168e7 1.07426 0.537131 0.843499i 0.319508π-0.319508\pi
0.537131 + 0.843499i 0.319508π0.319508\pi
770770 1.43276e6 496323.i 0.0870857 0.0301674i
771771 −3.67886e6 −0.222883
772772 −685528. 1.18737e6i −0.0413982 0.0717039i
773773 627101. 1.08617e6i 0.0377475 0.0653807i −0.846534 0.532334i 0.821315π-0.821315\pi
0.884282 + 0.466953i 0.154648π0.154648\pi
774774 2.99554e6 5.18843e6i 0.179731 0.311303i
775775 −3.69655e6 6.40261e6i −0.221076 0.382916i
776776 7.67014e6 0.457245
777777 1.68308e6 8.74552e6i 0.100012 0.519677i
778778 −8.93626e6 −0.529306
779779 1.14757e7 + 1.98765e7i 0.677542 + 1.17354i
780780 −18576.0 + 32174.6i −0.00109324 + 0.00189355i
781781 762178. 1.32013e6i 0.0447125 0.0774443i
782782 852992. + 1.47743e6i 0.0498802 + 0.0863950i
783783 4.74433e6 0.276548
784784 614656. + 4.25846e6i 0.0357143 + 0.247436i
785785 −3.35151e7 −1.94118
786786 −4.23904e6 7.34223e6i −0.244743 0.423908i
787787 −3.54560e6 + 6.14117e6i −0.204058 + 0.353439i −0.949832 0.312760i 0.898746π-0.898746\pi
0.745774 + 0.666199i 0.232080π0.232080\pi
788788 571264. 989458.i 0.0327734 0.0567652i
789789 4.89656e6 + 8.48109e6i 0.280026 + 0.485019i
790790 1.05027e7 0.598731
791791 −1.49171e6 + 7.75114e6i −0.0847700 + 0.440478i
792792 −176256. −0.00998461
793793 −86481.0 149789.i −0.00488357 0.00845860i
794794 −4.12799e6 + 7.14990e6i −0.232374 + 0.402484i
795795 −7.72297e6 + 1.33766e7i −0.433378 + 0.750632i
796796 5.69082e6 + 9.85678e6i 0.318340 + 0.551382i
797797 −2.71630e6 −0.151472 −0.0757358 0.997128i 0.524131π-0.524131\pi
−0.0757358 + 0.997128i 0.524131π0.524131\pi
798798 6.56649e6 2.27470e6i 0.365028 0.126449i
799799 −3.51516e7 −1.94795
800800 2.18675e6 + 3.78757e6i 0.120802 + 0.209235i
801801 2.38918e6 4.13817e6i 0.131573 0.227891i
802802 2.30566e6 3.99351e6i 0.126578 0.219240i
803803 −353957. 613072.i −0.0193714 0.0335523i
804804 8.72107e6 0.475806
805805 −1.88787e6 1.63495e6i −0.102679 0.0889229i
806806 20772.0 0.00112627
807807 −3.00730e6 5.20881e6i −0.162552 0.281549i
808808 3.20032e6 5.54312e6i 0.172451 0.298693i
809809 1.09370e7 1.89434e7i 0.587524 1.01762i −0.407032 0.913414i 0.633436π-0.633436\pi
0.994556 0.104207i 0.0332304π-0.0332304\pi
810810 1.12849e6 + 1.95461e6i 0.0604346 + 0.104676i
811811 −1.72352e7 −0.920164 −0.460082 0.887876i 0.652180π-0.652180\pi
−0.460082 + 0.887876i 0.652180π0.652180\pi
812812 −1.02045e7 8.83739e6i −0.543130 0.470364i
813813 7.47598e6 0.396681
814814 −519044. 899011.i −0.0274564 0.0475558i
815815 4.83200e6 8.36926e6i 0.254819 0.441360i
816816 −2.19341e6 + 3.79909e6i −0.115317 + 0.199735i
817817 1.37665e7 + 2.38444e7i 0.721556 + 1.24977i
818818 −2.37365e7 −1.24032
819819 29767.5 10311.8i 0.00155072 0.000537184i
820820 2.12097e7 1.10154
821821 1.13096e7 + 1.95887e7i 0.585582 + 1.01426i 0.994803 + 0.101823i 0.0324674π0.0324674\pi
−0.409220 + 0.912436i 0.634199π0.634199\pi
822822 −5.85914e6 + 1.01483e7i −0.302451 + 0.523860i
823823 −813164. + 1.40844e6i −0.0418484 + 0.0724835i −0.886191 0.463320i 0.846658π-0.846658\pi
0.844343 + 0.535804i 0.179991π0.179991\pi
824824 3.89411e6 + 6.74480e6i 0.199798 + 0.346060i
825825 −1.30693e6 −0.0668523
826826 3.11914e6 1.62075e7i 0.159069 0.826546i
827827 −2.28304e7 −1.16078 −0.580391 0.814338i 0.697100π-0.697100\pi
−0.580391 + 0.814338i 0.697100π0.697100\pi
828828 145152. + 251411.i 0.00735779 + 0.0127441i
829829 −1.29297e7 + 2.23948e7i −0.653432 + 1.13178i 0.328852 + 0.944382i 0.393338π0.393338\pi
−0.982284 + 0.187397i 0.939995π0.939995\pi
830830 1.90235e7 3.29497e7i 0.958509 1.66019i
831831 4.16283e6 + 7.21023e6i 0.209115 + 0.362198i
832832 −12288.0 −0.000615422
833833 −2.51433e7 + 1.97952e7i −1.25548 + 0.988433i
834834 115596. 0.00575477
835835 −2.25965e6 3.91383e6i −0.112157 0.194261i
836836 405008. 701494.i 0.0200423 0.0347143i
837837 630950. 1.09284e6i 0.0311301 0.0539190i
838838 1.54333e6 + 2.67313e6i 0.0759188 + 0.131495i
839839 −1.23061e7 −0.603554 −0.301777 0.953379i 0.597580π-0.597580\pi
−0.301777 + 0.953379i 0.597580π0.597580\pi
840840 1.21363e6 6.30622e6i 0.0593456 0.308369i
841841 2.18429e7 1.06493
842842 −5.75084e6 9.96074e6i −0.279544 0.484185i
843843 6.01357e6 1.04158e7i 0.291449 0.504805i
844844 2.08208e6 3.60627e6i 0.100610 0.174262i
845845 1.59652e7 + 2.76526e7i 0.769189 + 1.33227i
846846 −5.98169e6 −0.287341
847847 1.95871e7 6.78518e6i 0.938129 0.324977i
848848 −5.10874e6 −0.243963
849849 −4.46831e6 7.73933e6i −0.212752 0.368497i
850850 −1.62640e7 + 2.81700e7i −0.772110 + 1.33733i
851851 −854896. + 1.48072e6i −0.0404659 + 0.0700890i
852852 −3.22805e6 5.59114e6i −0.152349 0.263877i
853853 −1.91416e7 −0.900753 −0.450377 0.892839i 0.648710π-0.648710\pi
−0.450377 + 0.892839i 0.648710π0.648710\pi
854854 2.26004e7 + 1.95725e7i 1.06040 + 0.918336i
855855 −1.03724e7 −0.485247
856856 −1.55674e6 2.69635e6i −0.0726157 0.125774i
857857 2.37754e6 4.11801e6i 0.110580 0.191529i −0.805424 0.592698i 0.798063π-0.798063\pi
0.916004 + 0.401169i 0.131396π0.131396\pi
858858 1836.00 3180.05i 8.51441e−5 0.000147474i
859859 4.59938e6 + 7.96636e6i 0.212675 + 0.368364i 0.952551 0.304380i 0.0984491π-0.0984491\pi
−0.739876 + 0.672743i 0.765116π0.765116\pi
860860 2.54436e7 1.17309
861861 −1.35951e7 1.17737e7i −0.624994 0.541261i
862862 551448. 0.0252776
863863 8.67659e6 + 1.50283e7i 0.396572 + 0.686883i 0.993300 0.115560i 0.0368663π-0.0368663\pi
−0.596728 + 0.802443i 0.703533π0.703533\pi
864864 −373248. + 646484.i −0.0170103 + 0.0294628i
865865 5.81601e6 1.00736e7i 0.264292 0.457768i
866866 3.13051e6 + 5.42220e6i 0.141847 + 0.245686i
867867 −1.98482e7 −0.896756
868868 −3.39276e6 + 1.17529e6i −0.152846 + 0.0529474i
869869 −1.03805e6 −0.0466305
870870 1.00744e7 + 1.74493e7i 0.451253 + 0.781594i
871871 −90844.5 + 157347.i −0.00405745 + 0.00702771i
872872 −4.86640e6 + 8.42885e6i −0.216729 + 0.375385i
873873 4.85376e6 + 8.40696e6i 0.215547 + 0.373339i
874874 −1.33414e6 −0.0590778
875875 2.41462e6 1.25467e7i 0.106618 0.554001i
876876 −2.99822e6 −0.132009
877877 1.77811e7 + 3.07978e7i 0.780655 + 1.35213i 0.931560 + 0.363587i 0.118448π0.118448\pi
−0.150905 + 0.988548i 0.548219π0.548219\pi
878878 9.76315e6 1.69103e7i 0.427419 0.740311i
879879 2.53595e6 4.39239e6i 0.110705 0.191747i
880880 −374272. 648258.i −0.0162922 0.0282190i
881881 −2.63056e7 −1.14185 −0.570923 0.821003i 0.693415π-0.693415\pi
−0.570923 + 0.821003i 0.693415π0.693415\pi
882882 −4.27858e6 + 3.36851e6i −0.185195 + 0.145803i
883883 1.20394e7 0.519642 0.259821 0.965657i 0.416336π-0.416336\pi
0.259821 + 0.965657i 0.416336π0.416336\pi
884884 −45696.0 79147.8i −0.00196674 0.00340650i
885885 −1.23174e7 + 2.13344e7i −0.528643 + 0.915636i
886886 −2.60303e6 + 4.50858e6i −0.111403 + 0.192955i
887887 66795.0 + 115692.i 0.00285059 + 0.00493737i 0.867447 0.497529i 0.165759π-0.165759\pi
−0.864597 + 0.502467i 0.832426π0.832426\pi
888888 −4.39661e6 −0.187105
889889 −3.72314e6 + 1.93460e7i −0.157999 + 0.820989i
890890 2.02932e7 0.858769
891891 −111537. 193188.i −0.00470679 0.00815240i
892892 −845248. + 1.46401e6i −0.0355690 + 0.0616074i
893893 1.37450e7 2.38070e7i 0.576786 0.999023i
894894 2.73391e6 + 4.73527e6i 0.114404 + 0.198153i
895895 2.15549e7 0.899472
896896 2.00704e6 695259.i 0.0835191 0.0289319i
897897 −6048.00 −0.000250975
898898 −6.26282e6 1.08475e7i −0.259167 0.448890i
899899 5.63267e6 9.75608e6i 0.232442 0.402602i
900900 −2.76761e6 + 4.79364e6i −0.113893 + 0.197269i
901901 −1.89981e7 3.29057e7i −0.779648 1.35039i
902902 −2.09630e6 −0.0857902
903903 −1.63091e7 1.41241e7i −0.665594 0.576422i
904904 3.89670e6 0.158590
905905 −8.56702e6 1.48385e7i −0.347703 0.602239i
906906 −1.37966e6 + 2.38965e6i −0.0558410 + 0.0967194i
907907 6.37379e6 1.10397e7i 0.257264 0.445595i −0.708244 0.705968i 0.750512π-0.750512\pi
0.965508 + 0.260373i 0.0838456π0.0838456\pi
908908 −5.23800e6 9.07248e6i −0.210839 0.365184i
909909 8.10081e6 0.325176
910910 101136. + 87586.3i 0.00404858 + 0.00350617i
911911 2.43253e7 0.971095 0.485548 0.874210i 0.338620π-0.338620\pi
0.485548 + 0.874210i 0.338620π0.338620\pi
912912 −1.71533e6 2.97104e6i −0.0682905 0.118283i
913913 −1.88023e6 + 3.25666e6i −0.0746509 + 0.129299i
914914 1.29854e7 2.24913e7i 0.514149 0.890532i
915915 −2.23121e7 3.86457e7i −0.881024 1.52598i
916916 8.92341e6 0.351392
917917 −2.88490e7 + 9.99359e6i −1.13294 + 0.392462i
918918 −5.55206e6 −0.217444
919919 1.92402e7 + 3.33251e7i 0.751487 + 1.30161i 0.947102 + 0.320933i 0.103996π0.103996\pi
−0.195615 + 0.980681i 0.562670π0.562670\pi
920920 −616448. + 1.06772e6i −0.0240119 + 0.0415899i
921921 1.27216e7 2.20345e7i 0.494190 0.855963i
922922 1.06943e7 + 1.85231e7i 0.414311 + 0.717608i
923923 134502. 0.00519666
924924 −119952. + 623289.i −0.00462197 + 0.0240165i
925925 −3.26005e7 −1.25277
926926 6.74571e6 + 1.16839e7i 0.258523 + 0.447776i
927927 −4.92849e6 + 8.53639e6i −0.188371 + 0.326268i
928928 −3.33210e6 + 5.77136e6i −0.127013 + 0.219993i
929929 −1.98339e7 3.43533e7i −0.753996 1.30596i −0.945872 0.324540i 0.894791π-0.894791\pi
0.191876 0.981419i 0.438543π-0.438543\pi
930930 5.35918e6 0.203185
931931 −3.57509e6 2.47689e7i −0.135180 0.936555i
932932 −1.99615e7 −0.752755
933933 −5.07291e6 8.78654e6i −0.190789 0.330456i
934934 4.46904e6 7.74061e6i 0.167628 0.290341i
935935 2.78365e6 4.82142e6i 0.104132 0.180362i
936936 −7776.00 13468.4i −0.000290113 0.000502490i
937937 1.48428e7 0.552288 0.276144 0.961116i 0.410943π-0.410943\pi
0.276144 + 0.961116i 0.410943π0.410943\pi
938938 5.93517e6 3.08401e7i 0.220255 1.14448i
939939 2.12412e7 0.786166
940940 −1.27019e7 2.20003e7i −0.468865 0.812098i
941941 −2.33532e7 + 4.04488e7i −0.859748 + 1.48913i 0.0124203 + 0.999923i 0.496046π0.496046\pi
−0.872169 + 0.489205i 0.837287π0.837287\pi
942942 7.01478e6 1.21500e7i 0.257565 0.446116i
943943 1.72637e6 + 2.99016e6i 0.0632199 + 0.109500i
944944 −8.14797e6 −0.297591
945945 7.68001e6 2.66044e6i 0.279758 0.0969110i
946946 −2.51478e6 −0.0913632
947947 −2.01190e7 3.48471e7i −0.729006 1.26267i −0.957304 0.289083i 0.906649π-0.906649\pi
0.228298 0.973591i 0.426684π-0.426684\pi
948948 −2.19823e6 + 3.80745e6i −0.0794425 + 0.137598i
949949 31231.5 54094.5i 0.00112571 0.00194979i
950950 −1.27190e7 2.20300e7i −0.457241 0.791965i
951951 2.00178e7 0.717737
952952 1.19419e7 + 1.03420e7i 0.427052 + 0.369838i
953953 2.45579e7 0.875908 0.437954 0.898997i 0.355703π-0.355703\pi
0.437954 + 0.898997i 0.355703π0.355703\pi
954954 −3.23287e6 5.59950e6i −0.115005 0.199195i
955955 1.02671e7 1.77832e7i 0.364284 0.630958i
956956 3.97541e6 6.88561e6i 0.140681 0.243667i
957957 −995724. 1.72464e6i −0.0351446 0.0608723i
958958 1.00855e7 0.355044
959959 3.18998e7 + 2.76260e7i 1.12006 + 0.970000i
960960 −3.17030e6 −0.111026
961961 1.28164e7 + 2.21986e7i 0.447669 + 0.775386i
962962 45798.0 79324.5i 0.00159554 0.00276356i
963963 1.97024e6 3.41256e6i 0.0684627 0.118581i
964964 2.22094e6 + 3.84679e6i 0.0769742 + 0.133323i
965965 7.36943e6 0.254751
966966 987840. 342198.i 0.0340599 0.0117987i
967967 5.34313e7 1.83751 0.918754 0.394830i 0.129197π-0.129197\pi
0.918754 + 0.394830i 0.129197π0.129197\pi
968968 −5.11664e6 8.86228e6i −0.175508 0.303988i
969969 1.27578e7 2.20971e7i 0.436480 0.756006i
970970 −2.06135e7 + 3.57037e7i −0.703433 + 1.21838i
971971 1.40743e6 + 2.43773e6i 0.0479046 + 0.0829733i 0.888983 0.457939i 0.151412π-0.151412\pi
−0.841079 + 0.540913i 0.818079π0.818079\pi
972972 −944784. −0.0320750
973973 78669.5 408779.i 0.00266394 0.0138422i
974974 −7.66687e6 −0.258953
975975 −57658.5 99867.5i −0.00194246 0.00336444i
976976 7.37971e6 1.27820e7i 0.247979 0.429512i
977977 −1.27356e7 + 2.20588e7i −0.426859 + 0.739341i −0.996592 0.0824885i 0.973713π-0.973713\pi
0.569733 + 0.821830i 0.307047π0.307047\pi
978978 2.02270e6 + 3.50341e6i 0.0676213 + 0.117124i
979979 −2.00573e6 −0.0668829
980980 −2.14745e7 8.58346e6i −0.714264 0.285494i
981981 −1.23181e7 −0.408668
982982 1.16575e7 + 2.01914e7i 0.385768 + 0.668170i
983983 1.45067e6 2.51264e6i 0.0478835 0.0829367i −0.841090 0.540895i 0.818086π-0.818086\pi
0.888974 + 0.457958i 0.151419π0.151419\pi
984984 −4.43923e6 + 7.68898e6i −0.146157 + 0.253152i
985985 3.07054e6 + 5.31834e6i 0.100838 + 0.174657i
986986 −4.95649e7 −1.62361
987987 −4.07087e6 + 2.11529e7i −0.133013 + 0.691156i
988988 71472.0 0.00232940
989989 2.07099e6 + 3.58706e6i 0.0673268 + 0.116613i
990990 473688. 820452.i 0.0153605 0.0266051i
991991 −1.36892e6 + 2.37103e6i −0.0442785 + 0.0766927i −0.887315 0.461163i 0.847432π-0.847432\pi
0.843037 + 0.537856i 0.180766π0.180766\pi
992992 886272. + 1.53507e6i 0.0285949 + 0.0495277i
993993 3.33274e7 1.07258
994994 −2.19687e7 + 7.61017e6i −0.705241 + 0.244303i
995995 −6.11763e7 −1.95896
996996 7.96334e6 + 1.37929e7i 0.254359 + 0.440563i
997997 1.37040e7 2.37359e7i 0.436624 0.756256i −0.560802 0.827950i 0.689507π-0.689507\pi
0.997427 + 0.0716942i 0.0228406π0.0228406\pi
998998 −2.00097e7 + 3.46579e7i −0.635938 + 1.10148i
999999 −2.78223e6 4.81896e6i −0.0882021 0.152771i
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 42.6.e.b.25.1 2
3.2 odd 2 126.6.g.b.109.1 2
4.3 odd 2 336.6.q.a.193.1 2
7.2 even 3 inner 42.6.e.b.37.1 yes 2
7.3 odd 6 294.6.a.e.1.1 1
7.4 even 3 294.6.a.d.1.1 1
7.5 odd 6 294.6.e.m.79.1 2
7.6 odd 2 294.6.e.m.67.1 2
21.2 odd 6 126.6.g.b.37.1 2
21.11 odd 6 882.6.a.m.1.1 1
21.17 even 6 882.6.a.y.1.1 1
28.23 odd 6 336.6.q.a.289.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.6.e.b.25.1 2 1.1 even 1 trivial
42.6.e.b.37.1 yes 2 7.2 even 3 inner
126.6.g.b.37.1 2 21.2 odd 6
126.6.g.b.109.1 2 3.2 odd 2
294.6.a.d.1.1 1 7.4 even 3
294.6.a.e.1.1 1 7.3 odd 6
294.6.e.m.67.1 2 7.6 odd 2
294.6.e.m.79.1 2 7.5 odd 6
336.6.q.a.193.1 2 4.3 odd 2
336.6.q.a.289.1 2 28.23 odd 6
882.6.a.m.1.1 1 21.11 odd 6
882.6.a.y.1.1 1 21.17 even 6