Properties

Label 42.6.f.a.17.12
Level 4242
Weight 66
Character 42.17
Analytic conductor 6.7366.736
Analytic rank 00
Dimension 2828
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [42,6,Mod(5,42)]
 
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([3, 5]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("42.5");
 
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.f (of order 66, 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: 2828
Relative dimension: 1414 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 17.12
Character χ\chi == 42.17
Dual form 42.6.f.a.5.12

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+(3.464102.00000i)q2+(9.95138+11.9988i)q3+(8.0000013.8564i)q4+(41.5931+72.0414i)q5+(58.4701+21.6621i)q6+(128.74615.2171i)q764.0000iq8+(44.9401+238.808i)q9+(288.166+166.372i)q10+(455.598+263.039i)q11+(245.87141.9003i)q12776.119iq13+(476.422+204.778i)q14+(450.498+1215.98i)q15+(128.000221.703i)q16+(236.487409.607i)q17+(321.939+917.136i)q18+(1715.14990.236i)q19+1330.98q20+(1098.611696.22i)q21+2104.32q22+(1495.70+863.545i)q23+(767.920636.888i)q24+(1897.48+3286.52i)q25+(1552.242688.56i)q26+(3312.62+1837.25i)q27+(1240.82+1662.22i)q286041.29iq29+(871.383+5113.26i)q30+(7504.864332.93i)q31+(886.810512.000i)q32+(1377.68+8084.21i)q331891.89iq34+(4258.679907.94i)q35+(2949.50+2533.17i)q36+(1507.67+2611.36i)q37+(3960.946860.55i)q38+(9312.467723.46i)q39+(4610.652661.96i)q401633.44q41+(7198.143678.65i)q421198.75q43+(7289.564208.63i)q44+(19073.3+6695.23i)q45+(3454.18+5982.81i)q46+(1937.57+3355.97i)q47+(1386.383742.09i)q48+(16343.9+3918.26i)q49+15179.8iq50+(7268.141238.61i)q51+(10754.26208.95i)q52+(3242.15+1871.86i)q53+(7800.75+12989.6i)q54+43762.5iq55+(973.892+8239.72i)q56+(28949.6+10725.3i)q57+(12082.620927.6i)q58+(3242.615616.36i)q59+(13245.1+15970.1i)q60+(38557.122260.9i)q6134663.5q62+(9419.8130061.7i)q634096.00q64+(55912.732281.2i)q65+(20940.8+25249.2i)q66+(12183.6+21102.5i)q67+(3783.796553.71i)q68+(25245.89353.12i)q69+(34568.425804.8i)q70+83508.1iq71+(15283.7+2876.17i)q72+(11102.7+6410.14i)q73+(10445.5+6030.69i)q74+(58316.7+9938.11i)q7531687.5iq76+(54653.540798.0i)q77+(16812.445379.8i)q78+(20166.234928.9i)q79+(10647.818442.6i)q80+(55009.821464.1i)q81+(5658.42+3266.89i)q8272802.8q83+(32292.4+1653.06i)q84+39344.9q85+(4152.59+2397.50i)q86+(72487.960119.1i)q87+(16834.529158.2i)q88+(29278.350711.6i)q89+(52681.3+61339.5i)q90+(11810.3+99922.0i)q91+27633.4iq92+(22693.9133168.i)q93+(13423.9+7750.29i)q94+(142676.+82374.0i)q95+(2681.6215735.7i)q961016.75iq97+(64453.419114.5i)q98+(83290.6+96979.4i)q99+O(q100)q+(3.46410 - 2.00000i) q^{2} +(9.95138 + 11.9988i) q^{3} +(8.00000 - 13.8564i) q^{4} +(41.5931 + 72.0414i) q^{5} +(58.4701 + 21.6621i) q^{6} +(-128.746 - 15.2171i) q^{7} -64.0000i q^{8} +(-44.9401 + 238.808i) q^{9} +(288.166 + 166.372i) q^{10} +(455.598 + 263.039i) q^{11} +(245.871 - 41.9003i) q^{12} -776.119i q^{13} +(-476.422 + 204.778i) q^{14} +(-450.498 + 1215.98i) q^{15} +(-128.000 - 221.703i) q^{16} +(236.487 - 409.607i) q^{17} +(321.939 + 917.136i) q^{18} +(1715.14 - 990.236i) q^{19} +1330.98 q^{20} +(-1098.61 - 1696.22i) q^{21} +2104.32 q^{22} +(-1495.70 + 863.545i) q^{23} +(767.920 - 636.888i) q^{24} +(-1897.48 + 3286.52i) q^{25} +(-1552.24 - 2688.56i) q^{26} +(-3312.62 + 1837.25i) q^{27} +(-1240.82 + 1662.22i) q^{28} -6041.29i q^{29} +(871.383 + 5113.26i) q^{30} +(-7504.86 - 4332.93i) q^{31} +(-886.810 - 512.000i) q^{32} +(1377.68 + 8084.21i) q^{33} -1891.89i q^{34} +(-4258.67 - 9907.94i) q^{35} +(2949.50 + 2533.17i) q^{36} +(1507.67 + 2611.36i) q^{37} +(3960.94 - 6860.55i) q^{38} +(9312.46 - 7723.46i) q^{39} +(4610.65 - 2661.96i) q^{40} -1633.44 q^{41} +(-7198.14 - 3678.65i) q^{42} -1198.75 q^{43} +(7289.56 - 4208.63i) q^{44} +(-19073.3 + 6695.23i) q^{45} +(-3454.18 + 5982.81i) q^{46} +(1937.57 + 3355.97i) q^{47} +(1386.38 - 3742.09i) q^{48} +(16343.9 + 3918.26i) q^{49} +15179.8i q^{50} +(7268.14 - 1238.61i) q^{51} +(-10754.2 - 6208.95i) q^{52} +(3242.15 + 1871.86i) q^{53} +(-7800.75 + 12989.6i) q^{54} +43762.5i q^{55} +(-973.892 + 8239.72i) q^{56} +(28949.6 + 10725.3i) q^{57} +(-12082.6 - 20927.6i) q^{58} +(3242.61 - 5616.36i) q^{59} +(13245.1 + 15970.1i) q^{60} +(38557.1 - 22260.9i) q^{61} -34663.5 q^{62} +(9419.81 - 30061.7i) q^{63} -4096.00 q^{64} +(55912.7 - 32281.2i) q^{65} +(20940.8 + 25249.2i) q^{66} +(-12183.6 + 21102.5i) q^{67} +(-3783.79 - 6553.71i) q^{68} +(-25245.8 - 9353.12i) q^{69} +(-34568.4 - 25804.8i) q^{70} +83508.1i q^{71} +(15283.7 + 2876.17i) q^{72} +(11102.7 + 6410.14i) q^{73} +(10445.5 + 6030.69i) q^{74} +(-58316.7 + 9938.11i) q^{75} -31687.5i q^{76} +(-54653.5 - 40798.0i) q^{77} +(16812.4 - 45379.8i) q^{78} +(-20166.2 - 34928.9i) q^{79} +(10647.8 - 18442.6i) q^{80} +(-55009.8 - 21464.1i) q^{81} +(-5658.42 + 3266.89i) q^{82} -72802.8 q^{83} +(-32292.4 + 1653.06i) q^{84} +39344.9 q^{85} +(-4152.59 + 2397.50i) q^{86} +(72487.9 - 60119.1i) q^{87} +(16834.5 - 29158.2i) q^{88} +(-29278.3 - 50711.6i) q^{89} +(-52681.3 + 61339.5i) q^{90} +(-11810.3 + 99922.0i) q^{91} +27633.4i q^{92} +(-22693.9 - 133168. i) q^{93} +(13423.9 + 7750.29i) q^{94} +(142676. + 82374.0i) q^{95} +(-2681.62 - 15735.7i) q^{96} -1016.75i q^{97} +(64453.4 - 19114.5i) q^{98} +(-83290.6 + 96979.4i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 28q+224q4154q730q9+744q10516q153584q16+1632q18+2652q19+7236q21+3312q221920q2413208q255024q28+2448q30+22458q31++153216q99+O(q100) 28 q + 224 q^{4} - 154 q^{7} - 30 q^{9} + 744 q^{10} - 516 q^{15} - 3584 q^{16} + 1632 q^{18} + 2652 q^{19} + 7236 q^{21} + 3312 q^{22} - 1920 q^{24} - 13208 q^{25} - 5024 q^{28} + 2448 q^{30} + 22458 q^{31}+ \cdots + 153216 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) 1-1 e(16)e\left(\frac{1}{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 3.46410 2.00000i 0.612372 0.353553i
33 9.95138 + 11.9988i 0.638381 + 0.769720i
44 8.00000 13.8564i 0.250000 0.433013i
55 41.5931 + 72.0414i 0.744040 + 1.28872i 0.950642 + 0.310291i 0.100426π0.100426\pi
−0.206601 + 0.978425i 0.566240π0.566240\pi
66 58.4701 + 21.6621i 0.663064 + 0.245654i
77 −128.746 15.2171i −0.993087 0.117378i
88 64.0000i 0.353553i
99 −44.9401 + 238.808i −0.184939 + 0.982750i
1010 288.166 + 166.372i 0.911260 + 0.526116i
1111 455.598 + 263.039i 1.13527 + 0.655449i 0.945255 0.326332i 0.105813π-0.105813\pi
0.190016 + 0.981781i 0.439146π0.439146\pi
1212 245.871 41.9003i 0.492894 0.0839971i
1313 776.119i 1.27371i −0.770984 0.636854i 0.780235π-0.780235\pi
0.770984 0.636854i 0.219765π-0.219765\pi
1414 −476.422 + 204.778i −0.649639 + 0.279230i
1515 −450.498 + 1215.98i −0.516969 + 1.39540i
1616 −128.000 221.703i −0.125000 0.216506i
1717 236.487 409.607i 0.198465 0.343752i −0.749566 0.661930i 0.769738π-0.769738\pi
0.948031 + 0.318178i 0.103071π0.103071\pi
1818 321.939 + 917.136i 0.234203 + 0.667195i
1919 1715.14 990.236i 1.08997 0.629295i 0.156403 0.987693i 0.450010π-0.450010\pi
0.933569 + 0.358398i 0.116677π0.116677\pi
2020 1330.98 0.744040
2121 −1098.61 1696.22i −0.543620 0.839331i
2222 2104.32 0.926945
2323 −1495.70 + 863.545i −0.589557 + 0.340381i −0.764922 0.644122i 0.777223π-0.777223\pi
0.175365 + 0.984503i 0.443889π0.443889\pi
2424 767.920 636.888i 0.272137 0.225702i
2525 −1897.48 + 3286.52i −0.607192 + 1.05169i
2626 −1552.24 2688.56i −0.450324 0.779984i
2727 −3312.62 + 1837.25i −0.874504 + 0.485018i
2828 −1240.82 + 1662.22i −0.299098 + 0.400675i
2929 6041.29i 1.33393i −0.745087 0.666967i 0.767592π-0.767592\pi
0.745087 0.666967i 0.232408π-0.232408\pi
3030 871.383 + 5113.26i 0.176769 + 1.03728i
3131 −7504.86 4332.93i −1.40262 0.809800i −0.407955 0.913002i 0.633758π-0.633758\pi
−0.994660 + 0.103202i 0.967091π0.967091\pi
3232 −886.810 512.000i −0.153093 0.0883883i
3333 1377.68 + 8084.21i 0.220223 + 1.29227i
3434 1891.89i 0.280672i
3535 −4258.67 9907.94i −0.587631 1.36714i
3636 2949.50 + 2533.17i 0.379309 + 0.325768i
3737 1507.67 + 2611.36i 0.181052 + 0.313591i 0.942239 0.334941i 0.108717π-0.108717\pi
−0.761187 + 0.648532i 0.775383π0.775383\pi
3838 3960.94 6860.55i 0.444979 0.770726i
3939 9312.46 7723.46i 0.980399 0.813112i
4040 4610.65 2661.96i 0.455630 0.263058i
4141 −1633.44 −0.151756 −0.0758778 0.997117i 0.524176π-0.524176\pi
−0.0758778 + 0.997117i 0.524176π0.524176\pi
4242 −7198.14 3678.65i −0.629646 0.321785i
4343 −1198.75 −0.0988682 −0.0494341 0.998777i 0.515742π-0.515742\pi
−0.0494341 + 0.998777i 0.515742π0.515742\pi
4444 7289.56 4208.63i 0.567636 0.327725i
4545 −19073.3 + 6695.23i −1.40409 + 0.492872i
4646 −3454.18 + 5982.81i −0.240686 + 0.416880i
4747 1937.57 + 3355.97i 0.127942 + 0.221602i 0.922879 0.385090i 0.125830π-0.125830\pi
−0.794937 + 0.606692i 0.792496π0.792496\pi
4848 1386.38 3742.09i 0.0868517 0.234429i
4949 16343.9 + 3918.26i 0.972445 + 0.233133i
5050 15179.8i 0.858700i
5151 7268.14 1238.61i 0.391289 0.0666820i
5252 −10754.2 6208.95i −0.551532 0.318427i
5353 3242.15 + 1871.86i 0.158542 + 0.0915342i 0.577172 0.816623i 0.304156π-0.304156\pi
−0.418630 + 0.908157i 0.637490π0.637490\pi
5454 −7800.75 + 12989.6i −0.364042 + 0.606196i
5555 43762.5i 1.95072i
5656 −973.892 + 8239.72i −0.0414993 + 0.351109i
5757 28949.6 + 10725.3i 1.18020 + 0.437243i
5858 −12082.6 20927.6i −0.471617 0.816865i
5959 3242.61 5616.36i 0.121273 0.210051i −0.798997 0.601335i 0.794636π-0.794636\pi
0.920270 + 0.391284i 0.127969π0.127969\pi
6060 13245.1 + 15970.1i 0.474981 + 0.572703i
6161 38557.1 22260.9i 1.32672 0.765983i 0.341930 0.939725i 0.388919π-0.388919\pi
0.984791 + 0.173742i 0.0555860π0.0555860\pi
6262 −34663.5 −1.14523
6363 9419.81 30061.7i 0.299013 0.954249i
6464 −4096.00 −0.125000
6565 55912.7 32281.2i 1.64145 0.947691i
6666 20940.8 + 25249.2i 0.591744 + 0.713489i
6767 −12183.6 + 21102.5i −0.331579 + 0.574312i −0.982822 0.184558i 0.940915π-0.940915\pi
0.651243 + 0.758870i 0.274248π0.274248\pi
6868 −3783.79 6553.71i −0.0992326 0.171876i
6969 −25245.8 9353.12i −0.638360 0.236501i
7070 −34568.4 25804.8i −0.843206 0.629441i
7171 83508.1i 1.96600i 0.183614 + 0.982999i 0.441221π0.441221\pi
−0.183614 + 0.982999i 0.558779π0.558779\pi
7272 15283.7 + 2876.17i 0.347455 + 0.0653857i
7373 11102.7 + 6410.14i 0.243849 + 0.140786i 0.616944 0.787007i 0.288370π-0.288370\pi
−0.373096 + 0.927793i 0.621704π0.621704\pi
7474 10445.5 + 6030.69i 0.221742 + 0.128023i
7575 −58316.7 + 9938.11i −1.19713 + 0.204010i
7676 31687.5i 0.629295i
7777 −54653.5 40798.0i −1.05049 0.784174i
7878 16812.4 45379.8i 0.312891 0.844551i
7979 −20166.2 34928.9i −0.363544 0.629677i 0.624997 0.780627i 0.285100π-0.285100\pi
−0.988541 + 0.150950i 0.951767π0.951767\pi
8080 10647.8 18442.6i 0.186010 0.322179i
8181 −55009.8 21464.1i −0.931595 0.363497i
8282 −5658.42 + 3266.89i −0.0929310 + 0.0536537i
8383 −72802.8 −1.15999 −0.579993 0.814621i 0.696945π-0.696945\pi
−0.579993 + 0.814621i 0.696945π0.696945\pi
8484 −32292.4 + 1653.06i −0.499346 + 0.0255617i
8585 39344.9 0.590664
8686 −4152.59 + 2397.50i −0.0605442 + 0.0349552i
8787 72487.9 60119.1i 1.02676 0.851559i
8888 16834.5 29158.2i 0.231736 0.401379i
8989 −29278.3 50711.6i −0.391806 0.678629i 0.600882 0.799338i 0.294816π-0.294816\pi
−0.992688 + 0.120710i 0.961483π0.961483\pi
9090 −52681.3 + 61339.5i −0.685568 + 0.798241i
9191 −11810.3 + 99922.0i −0.149505 + 1.26490i
9292 27633.4i 0.340381i
9393 −22693.9 133168.i −0.272083 1.59658i
9494 13423.9 + 7750.29i 0.156696 + 0.0904687i
9595 142676. + 82374.0i 1.62197 + 0.936442i
9696 −2681.62 15735.7i −0.0296975 0.174264i
9797 1016.75i 0.0109720i −0.999985 0.00548598i 0.998254π-0.998254\pi
0.999985 0.00548598i 0.00174625π-0.00174625\pi
9898 64453.4 19114.5i 0.677923 0.201047i
9999 −83290.6 + 96979.4i −0.854099 + 0.994470i
100100 30359.6 + 52584.4i 0.303596 + 0.525844i
101101 −38949.4 + 67462.3i −0.379924 + 0.658048i −0.991051 0.133485i 0.957383π-0.957383\pi
0.611127 + 0.791533i 0.290717π0.290717\pi
102102 22700.4 18826.9i 0.216039 0.179176i
103103 −27539.1 + 15899.7i −0.255774 + 0.147671i −0.622405 0.782695i 0.713844π-0.713844\pi
0.366631 + 0.930366i 0.380511π0.380511\pi
104104 −49671.6 −0.450324
105105 76503.3 149696.i 0.677184 1.32507i
106106 14974.9 0.129449
107107 −16416.1 + 9477.84i −0.138615 + 0.0800295i −0.567704 0.823233i 0.692168π-0.692168\pi
0.429089 + 0.903262i 0.358835π0.358835\pi
108108 −1043.31 + 60598.9i −0.00860706 + 0.499926i
109109 73590.8 127463.i 0.593277 1.02759i −0.400511 0.916292i 0.631167π-0.631167\pi
0.993788 0.111293i 0.0354993π-0.0354993\pi
110110 87525.0 + 151598.i 0.689685 + 1.19457i
111111 −16329.7 + 44076.9i −0.125797 + 0.339550i
112112 13105.8 + 30491.0i 0.0987229 + 0.229682i
113113 156121.i 1.15018i 0.818090 + 0.575091i 0.195033π0.195033\pi
−0.818090 + 0.575091i 0.804967π0.804967\pi
114114 121735. 20745.6i 0.877310 0.149508i
115115 −124422. 71835.1i −0.877309 0.506514i
116116 −83710.5 48330.3i −0.577610 0.333484i
117117 185344. + 34878.9i 1.25174 + 0.235558i
118118 25940.9i 0.171506i
119119 −36679.6 + 49136.5i −0.237442 + 0.318080i
120120 77822.5 + 28831.9i 0.493347 + 0.182776i
121121 57853.9 + 100206.i 0.359227 + 0.622200i
122122 89043.8 154228.i 0.541632 0.938134i
123123 −16255.0 19599.3i −0.0968779 0.116809i
124124 −120078. + 69327.0i −0.701308 + 0.404900i
125125 −55730.8 −0.319022
126126 −27492.2 122976.i −0.154270 0.690073i
127127 −93493.1 −0.514364 −0.257182 0.966363i 0.582794π-0.582794\pi
−0.257182 + 0.966363i 0.582794π0.582794\pi
128128 −14189.0 + 8192.00i −0.0765466 + 0.0441942i
129129 −11929.2 14383.5i −0.0631156 0.0761009i
130130 129125. 223651.i 0.670118 1.16068i
131131 41351.8 + 71623.4i 0.210531 + 0.364651i 0.951881 0.306468i 0.0991474π-0.0991474\pi
−0.741350 + 0.671119i 0.765814π0.765814\pi
132132 123039. + 45584.0i 0.614624 + 0.227707i
133133 −235885. + 101389.i −1.15630 + 0.497007i
134134 97468.4i 0.468924i
135135 −270140. 162229.i −1.27572 0.766114i
136136 −26214.8 15135.1i −0.121535 0.0701680i
137137 67342.4 + 38880.2i 0.306540 + 0.176981i 0.645377 0.763864i 0.276700π-0.276700\pi
−0.338837 + 0.940845i 0.610034π0.610034\pi
138138 −106160. + 18091.4i −0.474530 + 0.0808676i
139139 37846.0i 0.166143i 0.996544 + 0.0830717i 0.0264731π0.0264731\pi
−0.996544 + 0.0830717i 0.973527π0.973527\pi
140140 −171358. 20253.6i −0.738897 0.0873338i
141141 −20986.0 + 56645.0i −0.0888959 + 0.239946i
142142 167016. + 289281.i 0.695085 + 1.20392i
143143 204150. 353598.i 0.834851 1.44600i
144144 58696.7 20604.1i 0.235889 0.0828033i
145145 435223. 251276.i 1.71906 0.992501i
146146 51281.1 0.199102
147147 115630. + 235098.i 0.441344 + 0.897338i
148148 48245.5 0.181052
149149 −27044.6 + 15614.2i −0.0997963 + 0.0576174i −0.549068 0.835778i 0.685017π-0.685017\pi
0.449271 + 0.893395i 0.351684π0.351684\pi
150150 −182139. + 151060.i −0.660958 + 0.548178i
151151 −178073. + 308431.i −0.635559 + 1.10082i 0.350838 + 0.936436i 0.385897π0.385897\pi
−0.986397 + 0.164383i 0.947437π0.947437\pi
152152 −63375.1 109769.i −0.222490 0.385363i
153153 87189.8 + 74882.7i 0.301118 + 0.258615i
154154 −270921. 32021.5i −0.920538 0.108803i
155155 720881.i 2.41010i
156156 −32519.7 190825.i −0.106988 0.627803i
157157 274500. + 158483.i 0.888778 + 0.513136i 0.873543 0.486748i 0.161817π-0.161817\pi
0.0152354 + 0.999884i 0.495150π0.495150\pi
158158 −139716. 80664.9i −0.445249 0.257064i
159159 9803.94 + 57529.4i 0.0307544 + 0.180467i
160160 85182.7i 0.263058i
161161 205706. 88417.4i 0.625435 0.268827i
162162 −233488. + 35665.6i −0.698999 + 0.106773i
163163 −82192.0 142361.i −0.242304 0.419683i 0.719066 0.694942i 0.244570π-0.244570\pi
−0.961370 + 0.275259i 0.911236π0.911236\pi
164164 −13067.6 + 22633.7i −0.0379389 + 0.0657121i
165165 −525096. + 435497.i −1.50151 + 1.24530i
166166 −252196. + 145606.i −0.710344 + 0.410117i
167167 −628234. −1.74313 −0.871565 0.490279i 0.836895π-0.836895\pi
−0.871565 + 0.490279i 0.836895π0.836895\pi
168168 −108558. + 70311.1i −0.296748 + 0.192199i
169169 −231068. −0.622334
170170 136295. 78689.7i 0.361707 0.208831i
171171 159398. + 454091.i 0.416862 + 1.18755i
172172 −9589.98 + 16610.3i −0.0247171 + 0.0428112i
173173 −305092. 528435.i −0.775024 1.34238i −0.934781 0.355225i 0.884404π-0.884404\pi
0.159756 0.987156i 0.448929π-0.448929\pi
174174 130867. 353235.i 0.327686 0.884484i
175175 294303. 394252.i 0.726440 0.973147i
176176 134676.i 0.327725i
177177 99657.8 16983.3i 0.239099 0.0407464i
178178 −202846. 117113.i −0.479863 0.277049i
179179 663103. + 382843.i 1.54685 + 0.893075i 0.998380 + 0.0569050i 0.0181232π0.0181232\pi
0.548471 + 0.836170i 0.315210π0.315210\pi
180180 −59814.4 + 317849.i −0.137602 + 0.731206i
181181 490433.i 1.11271i −0.830944 0.556356i 0.812199π-0.812199\pi
0.830944 0.556356i 0.187801π-0.187801\pi
182182 158932. + 369760.i 0.355658 + 0.827450i
183183 650800. + 241110.i 1.43655 + 0.532215i
184184 55266.9 + 95725.0i 0.120343 + 0.208440i
185185 −125418. + 217230.i −0.269420 + 0.466648i
186186 −344949. 415918.i −0.731094 0.881507i
187187 215485. 124411.i 0.450624 0.260168i
188188 62002.3 0.127942
189189 454443. 186129.i 0.925389 0.379018i
190190 658992. 1.32433
191191 −295276. + 170477.i −0.585658 + 0.338130i −0.763379 0.645951i 0.776461π-0.776461\pi
0.177721 + 0.984081i 0.443128π0.443128\pi
192192 −40760.8 49146.9i −0.0797977 0.0962150i
193193 −108547. + 188009.i −0.209761 + 0.363316i −0.951639 0.307218i 0.900602π-0.900602\pi
0.741878 + 0.670534i 0.233935π0.233935\pi
194194 −2033.50 3522.12i −0.00387918 0.00671893i
195195 943743. + 349640.i 1.77733 + 0.658468i
196196 185044. 195121.i 0.344061 0.362798i
197197 7576.18i 0.0139086i −0.999976 0.00695432i 0.997786π-0.997786\pi
0.999976 0.00695432i 0.00221365π-0.00221365\pi
198198 −94568.2 + 502528.i −0.171428 + 0.910955i
199199 −634693. 366440.i −1.13614 0.655950i −0.190667 0.981655i 0.561065π-0.561065\pi
−0.945472 + 0.325705i 0.894398π0.894398\pi
200200 210338. + 121438.i 0.371828 + 0.214675i
201201 −374447. + 63811.9i −0.653733 + 0.111407i
202202 311595.i 0.537294i
203203 −91930.7 + 777789.i −0.156574 + 1.32471i
204204 40982.4 110619.i 0.0689481 0.186104i
205205 −67940.1 117676.i −0.112912 0.195570i
206206 −63598.9 + 110156.i −0.104419 + 0.180860i
207207 −139005. 395994.i −0.225477 0.642337i
208208 −172068. + 99343.3i −0.275766 + 0.159214i
209209 1.04188e6 1.64988
210210 −34377.9 671570.i −0.0537936 1.05086i
211211 −438196. −0.677583 −0.338791 0.940862i 0.610018π-0.610018\pi
−0.338791 + 0.940862i 0.610018π0.610018\pi
212212 51874.5 29949.7i 0.0792709 0.0457671i
213213 −1.00199e6 + 831021.i −1.51327 + 1.25506i
214214 −37911.4 + 65664.4i −0.0565894 + 0.0980157i
215215 −49859.7 86359.5i −0.0735620 0.127413i
216216 117584. + 212008.i 0.171480 + 0.309184i
217217 900284. + 672048.i 1.29787 + 0.968838i
218218 588726.i 0.839020i
219219 33573.4 + 197008.i 0.0473026 + 0.277571i
220220 606391. + 350100.i 0.844688 + 0.487681i
221221 −317904. 183542.i −0.437840 0.252787i
222222 31586.0 + 185346.i 0.0430142 + 0.252407i
223223 650877.i 0.876470i 0.898860 + 0.438235i 0.144396π0.144396\pi
−0.898860 + 0.438235i 0.855604π0.855604\pi
224224 106382. + 79412.4i 0.141660 + 0.105747i
225225 −699576. 600830.i −0.921253 0.791216i
226226 312243. + 540820.i 0.406651 + 0.704339i
227227 233294. 404077.i 0.300496 0.520475i −0.675752 0.737129i 0.736181π-0.736181\pi
0.976248 + 0.216654i 0.0695143π0.0695143\pi
228228 380211. 315335.i 0.484381 0.401730i
229229 268050. 154759.i 0.337775 0.195015i −0.321513 0.946905i 0.604191π-0.604191\pi
0.659288 + 0.751891i 0.270858π0.270858\pi
230230 −574680. −0.716320
231231 −54352.3 1.06177e6i −0.0670175 1.30918i
232232 −386642. −0.471617
233233 −1.09359e6 + 631387.i −1.31967 + 0.761914i −0.983676 0.179949i 0.942407π-0.942407\pi
−0.335998 + 0.941863i 0.609073π0.609073\pi
234234 711807. 249863.i 0.849812 0.298307i
235235 −161179. + 279171.i −0.190388 + 0.329762i
236236 −51881.7 89861.8i −0.0606365 0.105026i
237237 218422. 589561.i 0.252595 0.681801i
238238 −28789.1 + 243573.i −0.0329447 + 0.278732i
239239 110206.i 0.124799i −0.998051 0.0623997i 0.980125π-0.980125\pi
0.998051 0.0623997i 0.0198753π-0.0198753\pi
240240 327249. 55768.5i 0.366733 0.0624972i
241241 −918936. 530548.i −1.01916 0.588412i −0.105300 0.994441i 0.533580π-0.533580\pi
−0.913861 + 0.406028i 0.866914π0.866914\pi
242242 400824. + 231416.i 0.439962 + 0.254012i
243243 −289880. 873646.i −0.314922 0.949118i
244244 712350.i 0.765983i
245245 397516. + 1.34041e6i 0.423096 + 1.42667i
246246 −95507.7 35383.9i −0.100624 0.0372793i
247247 −768541. 1.33115e6i −0.801539 1.38831i
248248 −277308. + 480311.i −0.286308 + 0.495899i
249249 −724488. 873543.i −0.740514 0.892865i
250250 −193057. + 111462.i −0.195360 + 0.112791i
251251 982577. 0.984424 0.492212 0.870475i 0.336188π-0.336188\pi
0.492212 + 0.870475i 0.336188π0.336188\pi
252252 −341188. 371018.i −0.338449 0.368039i
253253 −908585. −0.892410
254254 −323870. + 186986.i −0.314982 + 0.181855i
255255 391536. + 472089.i 0.377069 + 0.454646i
256256 −32768.0 + 56755.8i −0.0312500 + 0.0541266i
257257 −107232. 185731.i −0.101272 0.175409i 0.810937 0.585134i 0.198958π-0.198958\pi
−0.912209 + 0.409725i 0.865625π0.865625\pi
258258 −70090.9 25967.4i −0.0655560 0.0242873i
259259 −154369. 359144.i −0.142992 0.332674i
260260 1.03300e6i 0.947691i
261261 1.44271e6 + 271496.i 1.31092 + 0.246696i
262262 286494. + 165407.i 0.257847 + 0.148868i
263263 −815650. 470916.i −0.727134 0.419811i 0.0902388 0.995920i 0.471237π-0.471237\pi
−0.817373 + 0.576109i 0.804570π0.804570\pi
264264 517389. 88171.5i 0.456886 0.0778607i
265265 311426.i 0.272421i
266266 −614352. + 822992.i −0.532369 + 0.713168i
267267 317116. 855954.i 0.272232 0.734805i
268268 194937. + 337641.i 0.165790 + 0.287156i
269269 928208. 1.60770e6i 0.782104 1.35464i −0.148610 0.988896i 0.547480π-0.547480\pi
0.930714 0.365748i 0.119187π-0.119187\pi
270270 −1.26025e6 21697.3i −1.05208 0.0181133i
271271 295454. 170581.i 0.244381 0.141093i −0.372808 0.927909i 0.621605π-0.621605\pi
0.617189 + 0.786815i 0.288272π0.288272\pi
272272 −121081. −0.0992326
273273 −1.31647e6 + 852653.i −1.06906 + 0.692414i
274274 311041. 0.250289
275275 −1.72897e6 + 998222.i −1.37866 + 0.795967i
276276 −331567. + 274991.i −0.261998 + 0.217293i
277277 −297325. + 514983.i −0.232827 + 0.403268i −0.958639 0.284625i 0.908131π-0.908131\pi
0.725812 + 0.687893i 0.241464π0.241464\pi
278278 75692.1 + 131102.i 0.0587406 + 0.101742i
279279 1.37201e6 1.59750e6i 1.05523 1.22866i
280280 −634108. + 272555.i −0.483357 + 0.207759i
281281 1.03881e6i 0.784819i 0.919791 + 0.392409i 0.128358π0.128358\pi
−0.919791 + 0.392409i 0.871642π0.871642\pi
282282 40592.5 + 238196.i 0.0303964 + 0.178366i
283283 2.18141e6 + 1.25944e6i 1.61909 + 0.934782i 0.987156 + 0.159761i 0.0510722π0.0510722\pi
0.631935 + 0.775022i 0.282261π0.282261\pi
284284 1.15712e6 + 668065.i 0.851302 + 0.491499i
285285 431437. + 2.53167e6i 0.314634 + 1.84627i
286286 1.63320e6i 1.18066i
287287 210299. + 24856.2i 0.150707 + 0.0178127i
288288 162123. 188768.i 0.115177 0.134106i
289289 598077. + 1.03590e6i 0.421223 + 0.729580i
290290 1.00510e6 1.74089e6i 0.701804 1.21556i
291291 12199.7 10118.1i 0.00844535 0.00700430i
292292 177643. 102562.i 0.121924 0.0703931i
293293 −2.51299e6 −1.71010 −0.855049 0.518547i 0.826473π-0.826473\pi
−0.855049 + 0.518547i 0.826473π0.826473\pi
294294 870750. + 583145.i 0.587524 + 0.393467i
295295 539481. 0.360928
296296 167127. 96491.0i 0.110871 0.0640114i
297297 −1.99249e6 34304.0i −1.31070 0.0225660i
298298 −62456.8 + 108178.i −0.0407417 + 0.0705666i
299299 670214. + 1.16084e6i 0.433546 + 0.750924i
300300 −328827. + 887565.i −0.210943 + 0.569373i
301301 154334. + 18241.4i 0.0981848 + 0.0116049i
302302 1.42458e6i 0.898815i
303303 −1.19706e6 + 203999.i −0.749049 + 0.127650i
304304 −439075. 253500.i −0.272493 0.157324i
305305 3.20742e6 + 1.85180e6i 1.97427 + 1.13984i
306306 451800. + 85021.9i 0.275831 + 0.0519072i
307307 791101.i 0.479055i 0.970890 + 0.239528i 0.0769926π0.0769926\pi
−0.970890 + 0.239528i 0.923007π0.923007\pi
308308 −1.00254e6 + 430917.i −0.602179 + 0.258831i
309309 −464829. 172211.i −0.276947 0.102604i
310310 −1.44176e6 2.49721e6i −0.852098 1.47588i
311311 83650.7 144887.i 0.0490420 0.0849433i −0.840462 0.541870i 0.817717π-0.817717\pi
0.889504 + 0.456927i 0.151050π0.151050\pi
312312 −494301. 595998.i −0.287478 0.346624i
313313 1.09825e6 634075.i 0.633637 0.365830i −0.148523 0.988909i 0.547452π-0.547452\pi
0.782159 + 0.623079i 0.214118π0.214118\pi
314314 1.26786e6 0.725684
315315 2.55748e6 571743.i 1.45223 0.324657i
316316 −645319. −0.363544
317317 2.59960e6 1.50088e6i 1.45297 0.838875i 0.454326 0.890836i 0.349880π-0.349880\pi
0.998649 + 0.0519603i 0.0165469π0.0165469\pi
318318 149021. + 179680.i 0.0826378 + 0.0996395i
319319 1.58910e6 2.75240e6i 0.874326 1.51438i
320320 −170365. 295082.i −0.0930051 0.161089i
321321 −277085. 102655.i −0.150090 0.0556056i
322322 535751. 717699.i 0.287954 0.385747i
323323 936710.i 0.499573i
324324 −737494. + 590525.i −0.390298 + 0.312518i
325325 2.55073e6 + 1.47267e6i 1.33954 + 0.773386i
326326 −569443. 328768.i −0.296761 0.171335i
327327 2.26173e6 385435.i 1.16969 0.199334i
328328 104540.i 0.0536537i
329329 −198386. 461551.i −0.101046 0.235088i
330330 −947990. + 2.55880e6i −0.479202 + 1.29345i
331331 300997. + 521341.i 0.151005 + 0.261549i 0.931597 0.363492i 0.118416π-0.118416\pi
−0.780592 + 0.625041i 0.785082π0.785082\pi
332332 −582422. + 1.00879e6i −0.289997 + 0.502289i
333333 −691370. + 242689.i −0.341665 + 0.119933i
334334 −2.17627e6 + 1.25647e6i −1.06745 + 0.616290i
335335 −2.02701e6 −0.986833
336336 −235434. + 460681.i −0.113768 + 0.222614i
337337 −515158. −0.247096 −0.123548 0.992339i 0.539427π-0.539427\pi
−0.123548 + 0.992339i 0.539427π0.539427\pi
338338 −800443. + 462136.i −0.381100 + 0.220028i
339339 −1.87326e6 + 1.55362e6i −0.885318 + 0.734254i
340340 314759. 545178.i 0.147666 0.255765i
341341 −2.27946e6 3.94815e6i −1.06157 1.83869i
342342 1.46035e6 + 1.25422e6i 0.675137 + 0.579840i
343343 −2.04458e6 753165.i −0.938358 0.345665i
344344 76719.9i 0.0349552i
345345 −376239. 2.20777e6i −0.170183 0.998632i
346346 −2.11374e6 1.22037e6i −0.949207 0.548025i
347347 −1.93407e6 1.11664e6i −0.862281 0.497838i 0.00249446 0.999997i 0.499206π-0.499206\pi
−0.864775 + 0.502159i 0.832539π0.832539\pi
348348 −253132. 1.48537e6i −0.112047 0.657488i
349349 2.51946e6i 1.10725i 0.832767 + 0.553623i 0.186755π0.186755\pi
−0.832767 + 0.553623i 0.813245π0.813245\pi
350350 230992. 1.95433e6i 0.100792 0.852764i
351351 1.42592e6 + 2.57099e6i 0.617772 + 1.11386i
352352 −269352. 466532.i −0.115868 0.200690i
353353 888524. 1.53897e6i 0.379518 0.657345i −0.611474 0.791264i 0.709423π-0.709423\pi
0.990992 + 0.133920i 0.0427565π0.0427565\pi
354354 311258. 258147.i 0.132012 0.109486i
355355 −6.01604e6 + 3.47336e6i −2.53361 + 1.46278i
356356 −936907. −0.391806
357357 −954589. + 48865.7i −0.396411 + 0.0202924i
358358 3.06274e6 1.26300
359359 3.92647e6 2.26695e6i 1.60793 0.928337i 0.618093 0.786105i 0.287905π-0.287905\pi
0.989833 0.142232i 0.0454280π-0.0454280\pi
360360 428495. + 1.22069e6i 0.174257 + 0.496420i
361361 723084. 1.25242e6i 0.292025 0.505803i
362362 −980865. 1.69891e6i −0.393403 0.681394i
363363 −626620. + 1.69136e6i −0.249596 + 0.673706i
364364 1.29008e6 + 963024.i 0.510343 + 0.380964i
365365 1.06647e6i 0.419003i
366366 2.73666e6 466371.i 1.06787 0.181982i
367367 −1.18287e6 682930.i −0.458428 0.264674i 0.252955 0.967478i 0.418598π-0.418598\pi
−0.711383 + 0.702804i 0.751931π0.751931\pi
368368 382900. + 221067.i 0.147389 + 0.0850953i
369369 73407.2 390080.i 0.0280655 0.149138i
370370 1.00334e6i 0.381017i
371371 −388929. 290330.i −0.146702 0.109511i
372372 −2.02678e6 750885.i −0.759361 0.281330i
373373 1.44131e6 + 2.49642e6i 0.536395 + 0.929063i 0.999094 + 0.0425480i 0.0135475π0.0135475\pi
−0.462700 + 0.886515i 0.653119π0.653119\pi
374374 497642. 861942.i 0.183966 0.318639i
375375 −554598. 668700.i −0.203657 0.245557i
376376 214782. 124005.i 0.0783482 0.0452343i
377377 −4.68876e6 −1.69904
378378 1.20198e6 1.55366e6i 0.432680 0.559275i
379379 1.79197e6 0.640815 0.320408 0.947280i 0.396180π-0.396180\pi
0.320408 + 0.947280i 0.396180π0.396180\pi
380380 2.28281e6 1.31798e6i 0.810983 0.468221i
381381 −930386. 1.12180e6i −0.328360 0.395916i
382382 −681910. + 1.18110e6i −0.239094 + 0.414123i
383383 814355. + 1.41050e6i 0.283672 + 0.491335i 0.972286 0.233793i 0.0751139π-0.0751139\pi
−0.688614 + 0.725128i 0.741781π0.741781\pi
384384 −239493. 88728.1i −0.0828830 0.0307067i
385385 665937. 5.63423e6i 0.228971 1.93724i
386386 868375.i 0.296646i
387387 53871.9 286271.i 0.0182846 0.0971628i
388388 −14088.5 8133.99i −0.00475100 0.00274299i
389389 4.13271e6 + 2.38602e6i 1.38472 + 0.799466i 0.992714 0.120498i 0.0384490π-0.0384490\pi
0.392003 + 0.919964i 0.371782π0.371782\pi
390390 3.96850e6 676297.i 1.32119 0.225152i
391391 816867.i 0.270215i
392392 250769. 1.04601e6i 0.0824249 0.343811i
393393 −447884. + 1.20892e6i −0.146280 + 0.394836i
394394 −15152.4 26244.7i −0.00491745 0.00851727i
395395 1.67755e6 2.90561e6i 0.540983 0.937010i
396396 677462. + 1.92994e6i 0.217094 + 0.618453i
397397 87165.5 50325.0i 0.0277567 0.0160254i −0.486057 0.873927i 0.661565π-0.661565\pi
0.513814 + 0.857902i 0.328232π0.328232\pi
398398 −2.93152e6 −0.927653
399399 −3.56393e6 1.82136e6i −1.12072 0.572750i
400400 971508. 0.303596
401401 −4.80374e6 + 2.77344e6i −1.49183 + 0.861307i −0.999956 0.00936110i 0.997020π-0.997020\pi
−0.491871 + 0.870668i 0.663687π0.663687\pi
402402 −1.16950e6 + 969945.i −0.360940 + 0.299352i
403403 −3.36287e6 + 5.82467e6i −1.03145 + 1.78652i
404404 623190. + 1.07940e6i 0.189962 + 0.329024i
405405 −741721. 4.85574e6i −0.224700 1.47102i
406406 1.23712e6 + 2.87820e6i 0.372475 + 0.866575i
407407 1.58631e6i 0.474681i
408408 −79270.9 465161.i −0.0235756 0.138342i
409409 629717. + 363567.i 0.186139 + 0.107467i 0.590174 0.807276i 0.299059π-0.299059\pi
−0.404035 + 0.914744i 0.632393π0.632393\pi
410410 −470703. 271760.i −0.138289 0.0798411i
411411 203637. + 1.19494e6i 0.0594636 + 0.348932i
412412 508791.i 0.147671i
413413 −502936. + 673739.i −0.145090 + 0.194364i
414414 −1.27351e6 1.09376e6i −0.365177 0.313631i
415415 −3.02810e6 5.24482e6i −0.863077 1.49489i
416416 −397373. + 688270.i −0.112581 + 0.194996i
417417 −454105. + 376620.i −0.127884 + 0.106063i
418418 3.60919e6 2.08377e6i 1.01034 0.583322i
419419 1.32060e6 0.367482 0.183741 0.982975i 0.441179π-0.441179\pi
0.183741 + 0.982975i 0.441179π0.441179\pi
420420 −1.46223e6 2.25763e6i −0.404475 0.624496i
421421 5.02517e6 1.38180 0.690901 0.722950i 0.257214π-0.257214\pi
0.690901 + 0.722950i 0.257214π0.257214\pi
422422 −1.51796e6 + 876392.i −0.414933 + 0.239562i
423423 −888509. + 311890.i −0.241441 + 0.0847522i
424424 119799. 207498.i 0.0323622 0.0560530i
425425 897455. + 1.55444e6i 0.241013 + 0.417447i
426426 −1.80896e6 + 4.88273e6i −0.482954 + 1.30358i
427427 −5.30280e6 + 2.27927e6i −1.40746 + 0.604960i
428428 303291.i 0.0800295i
429429 6.27431e6 1.06924e6i 1.64597 0.280500i
430430 −345438. 199439.i −0.0900946 0.0520162i
431431 1.60910e6 + 929013.i 0.417243 + 0.240895i 0.693897 0.720074i 0.255892π-0.255892\pi
−0.276654 + 0.960970i 0.589226π0.589226\pi
432432 831337. + 499248.i 0.214323 + 0.128708i
433433 5.52697e6i 1.41667i −0.705878 0.708333i 0.749447π-0.749447\pi
0.705878 0.708333i 0.250553π-0.250553\pi
434434 4.46277e6 + 527476.i 1.13731 + 0.134425i
435435 7.34606e6 + 2.72159e6i 1.86137 + 0.689603i
436436 −1.17745e6 2.03941e6i −0.296638 0.513793i
437437 −1.71023e6 + 2.96220e6i −0.428400 + 0.742011i
438438 510318. + 615309.i 0.127103 + 0.153253i
439439 4.94162e6 2.85305e6i 1.22379 0.706558i 0.258069 0.966126i 0.416914π-0.416914\pi
0.965725 + 0.259569i 0.0835805π0.0835805\pi
440440 2.80080e6 0.689685
441441 −1.67021e6 + 3.72697e6i −0.408954 + 0.912555i
442442 −1.46833e6 −0.357494
443443 4.44494e6 2.56629e6i 1.07611 0.621293i 0.146266 0.989245i 0.453274π-0.453274\pi
0.929845 + 0.367952i 0.119941π0.119941\pi
444444 480109. + 578886.i 0.115580 + 0.139359i
445445 2.43556e6 4.21851e6i 0.583040 1.00985i
446446 1.30175e6 + 2.25471e6i 0.309879 + 0.536726i
447447 −456482. 169118.i −0.108057 0.0400334i
448448 527342. + 62329.1i 0.124136 + 0.0146722i
449449 1.56362e6i 0.366030i −0.983110 0.183015i 0.941414π-0.941414\pi
0.983110 0.183015i 0.0585856π-0.0585856\pi
450450 −3.62506e6 682182.i −0.843887 0.158807i
451451 −744193. 429660.i −0.172284 0.0994681i
452452 2.16328e6 + 1.24897e6i 0.498043 + 0.287545i
453453 −5.47286e6 + 932664.i −1.25305 + 0.213540i
454454 1.86635e6i 0.424966i
455455 −7.68974e6 + 3.30524e6i −1.74134 + 0.748470i
456456 686420. 1.85277e6i 0.154589 0.417263i
457457 3.15021e6 + 5.45633e6i 0.705585 + 1.22211i 0.966480 + 0.256742i 0.0826492π0.0826492\pi
−0.260895 + 0.965367i 0.584018π0.584018\pi
458458 619036. 1.07220e6i 0.137896 0.238843i
459459 −30841.2 + 1.79135e6i −0.00683281 + 0.396871i
460460 −1.99075e6 + 1.14936e6i −0.438654 + 0.253257i
461461 −162855. −0.0356901 −0.0178450 0.999841i 0.505681π-0.505681\pi
−0.0178450 + 0.999841i 0.505681π0.505681\pi
462462 −2.31182e6 3.56938e6i −0.503906 0.778014i
463463 −8.40996e6 −1.82323 −0.911615 0.411044i 0.865164π-0.865164\pi
−0.911615 + 0.411044i 0.865164π0.865164\pi
464464 −1.33937e6 + 773285.i −0.288805 + 0.166742i
465465 8.64967e6 7.17376e6i 1.85510 1.53856i
466466 −2.52555e6 + 4.37438e6i −0.538754 + 0.933150i
467467 3.23078e6 + 5.59588e6i 0.685513 + 1.18734i 0.973275 + 0.229641i 0.0737553π0.0737553\pi
−0.287762 + 0.957702i 0.592911π0.592911\pi
468468 1.96605e6 2.28917e6i 0.414934 0.483129i
469469 1.88970e6 2.53146e6i 0.396698 0.531422i
470470 1.28943e6i 0.269249i
471471 830060. + 4.87078e6i 0.172408 + 1.01169i
472472 −359447. 207527.i −0.0742643 0.0428765i
473473 −546147. 315318.i −0.112242 0.0648031i
474474 −422486. 2.47914e6i −0.0863707 0.506822i
475475 7.51579e6i 1.52841i
476476 387418. + 901340.i 0.0783722 + 0.182335i
477477 −592718. + 690132.i −0.119276 + 0.138879i
478478 −220413. 381766.i −0.0441232 0.0764237i
479479 −2.65810e6 + 4.60397e6i −0.529338 + 0.916841i 0.470076 + 0.882626i 0.344226π0.344226\pi
−0.999414 + 0.0342149i 0.989107π0.989107\pi
480480 1.02209e6 847685.i 0.202481 0.167931i
481481 2.02673e6 1.17013e6i 0.399423 0.230607i
482482 −4.24438e6 −0.832141
483483 3.10796e6 + 1.58834e6i 0.606188 + 0.309796i
484484 1.85133e6 0.359227
485485 73248.0 42289.8i 0.0141397 0.00816359i
486486 −2.75147e6 2.44664e6i −0.528413 0.469872i
487487 3.81386e6 6.60581e6i 0.728690 1.26213i −0.228747 0.973486i 0.573463π-0.573463\pi
0.957437 0.288642i 0.0932038π-0.0932038\pi
488488 −1.42470e6 2.46765e6i −0.270816 0.469067i
489489 890228. 2.40289e6i 0.168356 0.454424i
490490 4.05785e6 + 3.84828e6i 0.763495 + 0.724063i
491491 2.32379e6i 0.435003i −0.976060 0.217502i 0.930209π-0.930209\pi
0.976060 0.217502i 0.0697908π-0.0697908\pi
492492 −401616. + 68441.9i −0.0747994 + 0.0127470i
493493 −2.47455e6 1.42868e6i −0.458542 0.264739i
494494 −5.32461e6 3.07416e6i −0.981681 0.566774i
495495 −1.04509e7 1.96669e6i −1.91707 0.360764i
496496 2.21846e6i 0.404900i
497497 1.27075e6 1.07513e7i 0.230764 1.95241i
498498 −4.25679e6 1.57706e6i −0.769146 0.284955i
499499 2.49887e6 + 4.32818e6i 0.449255 + 0.778133i 0.998338 0.0576355i 0.0183561π-0.0183561\pi
−0.549083 + 0.835768i 0.685023π0.685023\pi
500500 −445846. + 772228.i −0.0797554 + 0.138140i
501501 −6.25179e6 7.53802e6i −1.11278 1.34172i
502502 3.40375e6 1.96515e6i 0.602834 0.348046i
503503 3.01055e6 0.530549 0.265275 0.964173i 0.414537π-0.414537\pi
0.265275 + 0.964173i 0.414537π0.414537\pi
504504 −1.92395e6 602868.i −0.337378 0.105717i
505505 −6.48010e6 −1.13072
506506 −3.14743e6 + 1.81717e6i −0.546487 + 0.315515i
507507 −2.29945e6 2.77253e6i −0.397286 0.479023i
508508 −747945. + 1.29548e6i −0.128591 + 0.222726i
509509 449651. + 778819.i 0.0769274 + 0.133242i 0.901923 0.431897i 0.142156π-0.142156\pi
−0.824995 + 0.565139i 0.808822π0.808822\pi
510510 2.30050e6 + 852294.i 0.391648 + 0.145099i
511511 −1.33188e6 994228.i −0.225638 0.168435i
512512 262144.i 0.0441942i
513513 −3.86229e6 + 6.43140e6i −0.647965 + 1.07898i
514514 −742923. 428927.i −0.124033 0.0716103i
515515 −2.29088e6 1.32264e6i −0.380613 0.219747i
516516 −294737. + 50227.9i −0.0487316 + 0.00830465i
517517 2.03863e6i 0.335438i
518518 −1.25304e6 935374.i −0.205182 0.153165i
519519 3.30447e6 8.91937e6i 0.538497 1.45350i
520520 −2.06600e6 3.57841e6i −0.335059 0.580340i
521521 359362. 622433.i 0.0580013 0.100461i −0.835567 0.549389i 0.814861π-0.814861\pi
0.893568 + 0.448928i 0.148194π0.148194\pi
522522 5.54068e6 1.94493e6i 0.889994 0.312412i
523523 5.01382e6 2.89473e6i 0.801520 0.462758i −0.0424821 0.999097i 0.513527π-0.513527\pi
0.844003 + 0.536339i 0.180193π0.180193\pi
524524 1.32326e6 0.210531
525525 7.65925e6 392079.i 1.21280 0.0620834i
526526 −3.76733e6 −0.593702
527527 −3.54960e6 + 2.04936e6i −0.556740 + 0.321434i
528528 1.61595e6 1.34021e6i 0.252256 0.209213i
529529 −1.72675e6 + 2.99082e6i −0.268282 + 0.464677i
530530 622852. + 1.07881e6i 0.0963152 + 0.166823i
531531 1.19551e6 + 1.02676e6i 0.184000 + 0.158028i
532532 −482191. + 4.07963e6i −0.0738653 + 0.624945i
533533 1.26775e6i 0.193292i
534534 −613386. 3.59934e6i −0.0930852 0.546223i
535535 −1.36559e6 788426.i −0.206270 0.119090i
536536 1.35056e6 + 779748.i 0.203050 + 0.117231i
537537 2.00515e6 + 1.17662e7i 0.300063 + 1.76076i
538538 7.42566e6i 1.10606i
539539 6.41558e6 + 6.08424e6i 0.951182 + 0.902057i
540540 −4.40903e6 + 2.44534e6i −0.650666 + 0.360873i
541541 −3.26861e6 5.66140e6i −0.480143 0.831632i 0.519598 0.854411i 0.326082π-0.326082\pi
−0.999741 + 0.0227794i 0.992748π0.992748\pi
542542 682323. 1.18182e6i 0.0997681 0.172803i
543543 5.88458e6 4.88048e6i 0.856477 0.710335i
544544 −419437. + 242162.i −0.0607673 + 0.0350840i
545545 1.22435e7 1.76569
546546 −2.85507e6 + 5.58661e6i −0.409860 + 0.801986i
547547 3.31420e6 0.473598 0.236799 0.971559i 0.423902π-0.423902\pi
0.236799 + 0.971559i 0.423902π0.423902\pi
548548 1.07748e6 622083.i 0.153270 0.0884905i
549549 3.58334e6 + 1.02082e7i 0.507408 + 1.44550i
550550 −3.99289e6 + 6.91588e6i −0.562834 + 0.974857i
551551 −5.98230e6 1.03616e7i −0.839439 1.45395i
552552 −598599. + 1.61573e6i −0.0836158 + 0.225694i
553553 2.06480e6 + 4.80382e6i 0.287121 + 0.667996i
554554 2.37860e6i 0.329267i
555555 −3.85456e6 + 656880.i −0.531181 + 0.0905218i
556556 524410. + 302768.i 0.0719422 + 0.0415359i
557557 −6.74821e6 3.89608e6i −0.921618 0.532096i −0.0374668 0.999298i 0.511929π-0.511929\pi
−0.884151 + 0.467202i 0.845262π0.845262\pi
558558 1.55778e6 8.27792e6i 0.211798 1.12548i
559559 930371.i 0.125929i
560560 −1.65151e6 + 2.21238e6i −0.222541 + 0.298118i
561561 3.63715e6 + 1.34750e6i 0.487926 + 0.180768i
562562 2.07762e6 + 3.59854e6i 0.277475 + 0.480601i
563563 −3.38663e6 + 5.86582e6i −0.450295 + 0.779933i −0.998404 0.0564733i 0.982014π-0.982014\pi
0.548109 + 0.836407i 0.315348π0.315348\pi
564564 617009. + 743950.i 0.0816758 + 0.0984796i
565565 −1.12472e7 + 6.49358e6i −1.48226 + 0.855781i
566566 1.00755e7 1.32198
567567 6.75565e6 + 3.60050e6i 0.882489 + 0.470333i
568568 5.34452e6 0.695085
569569 −230925. + 133325.i −0.0299013 + 0.0172635i −0.514876 0.857265i 0.672162π-0.672162\pi
0.484975 + 0.874528i 0.338829π0.338829\pi
570570 6.55788e6 + 7.90708e6i 0.845427 + 1.01936i
571571 6.04858e6 1.04764e7i 0.776359 1.34469i −0.157668 0.987492i 0.550398π-0.550398\pi
0.934027 0.357202i 0.116269π-0.116269\pi
572572 −3.26640e6 5.65757e6i −0.417426 0.723002i
573573 −4.98392e6 1.84645e6i −0.634138 0.234937i
574574 778209. 334493.i 0.0985863 0.0423748i
575575 6.55422e6i 0.826707i
576576 184075. 978159.i 0.0231173 0.122844i
577577 1.21462e7 + 7.01259e6i 1.51880 + 0.876877i 0.999755 + 0.0221276i 0.00704399π0.00704399\pi
0.519041 + 0.854750i 0.326289π0.326289\pi
578578 4.14360e6 + 2.39231e6i 0.515891 + 0.297850i
579579 −3.33606e6 + 568519.i −0.413559 + 0.0704771i
580580 8.04083e6i 0.992501i
581581 9.37304e6 + 1.10785e6i 1.15197 + 0.136157i
582582 22025.0 59449.4i 0.00269530 0.00727512i
583583 984745. + 1.70563e6i 0.119992 + 0.207832i
584584 410249. 710572.i 0.0497755 0.0862136i
585585 5.19630e6 + 1.48031e7i 0.627776 + 1.78840i
586586 −8.70524e6 + 5.02597e6i −1.04722 + 0.604611i
587587 −689161. −0.0825516 −0.0412758 0.999148i 0.513142π-0.513142\pi
−0.0412758 + 0.999148i 0.513142π0.513142\pi
588588 4.18266e6 + 278571.i 0.498895 + 0.0332272i
589589 −1.71625e7 −2.03841
590590 1.86882e6 1.07896e6i 0.221023 0.127607i
591591 90904.7 75393.4i 0.0107058 0.00887902i
592592 385964. 668509.i 0.0452629 0.0783977i
593593 5.54269e6 + 9.60022e6i 0.647267 + 1.12110i 0.983773 + 0.179418i 0.0574216π0.0574216\pi
−0.336505 + 0.941682i 0.609245π0.609245\pi
594594 −6.97079e6 + 3.86614e6i −0.810617 + 0.449585i
595595 −5.06548e6 598713.i −0.586581 0.0693309i
596596 499654.i 0.0576174i
597597 −1.91925e6 1.12621e7i −0.220392 1.29326i
598598 4.64338e6 + 2.68086e6i 0.530983 + 0.306563i
599599 −1.11153e7 6.41740e6i −1.26576 0.730789i −0.291580 0.956546i 0.594181π-0.594181\pi
−0.974184 + 0.225757i 0.927514π0.927514\pi
600600 636039. + 3.73227e6i 0.0721283 + 0.423248i
601601 1.35097e7i 1.52566i −0.646597 0.762832i 0.723808π-0.723808\pi
0.646597 0.762832i 0.276192π-0.276192\pi
602602 571110. 245477.i 0.0642286 0.0276070i
603603 −4.49193e6 3.85788e6i −0.503083 0.432072i
604604 2.84917e6 + 4.93490e6i 0.317779 + 0.550410i
605605 −4.81265e6 + 8.33576e6i −0.534559 + 0.925884i
606606 −3.73875e6 + 3.10080e6i −0.413566 + 0.342998i
607607 8.39395e6 4.84625e6i 0.924686 0.533868i 0.0395592 0.999217i 0.487405π-0.487405\pi
0.885127 + 0.465349i 0.154071π0.154071\pi
608608 −2.02800e6 −0.222490
609609 −1.02473e7 + 6.63702e6i −1.11961 + 0.725154i
610610 1.48144e7 1.61198
611611 2.60464e6 1.50379e6i 0.282257 0.162961i
612612 1.73512e6 609075.i 0.187263 0.0657343i
613613 −3.85451e6 + 6.67621e6i −0.414303 + 0.717594i −0.995355 0.0962726i 0.969308π-0.969308\pi
0.581052 + 0.813866i 0.302641π0.302641\pi
614614 1.58220e6 + 2.74045e6i 0.169372 + 0.293360i
615615 735864. 1.98623e6i 0.0784530 0.211759i
616616 −2.61107e6 + 3.49783e6i −0.277247 + 0.371404i
617617 9.52706e6i 1.00750i −0.863849 0.503751i 0.831953π-0.831953\pi
0.863849 0.503751i 0.168047π-0.168047\pi
618618 −1.95464e6 + 333102.i −0.205871 + 0.0350837i
619619 −7.10455e6 4.10181e6i −0.745263 0.430278i 0.0787166 0.996897i 0.474918π-0.474918\pi
−0.823980 + 0.566619i 0.808251π0.808251\pi
620620 −9.98882e6 5.76705e6i −1.04360 0.602524i
621621 3.36815e6 5.60857e6i 0.350479 0.583610i
622622 669205.i 0.0693559i
623623 2.99778e6 + 6.97443e6i 0.309442 + 0.719927i
624624 −2.90430e6 1.07599e6i −0.298594 0.110624i
625625 3.61160e6 + 6.25547e6i 0.369827 + 0.640560i
626626 2.53630e6 4.39300e6i 0.258681 0.448049i
627627 1.03682e7 + 1.25013e7i 1.05326 + 1.26995i
628628 4.39200e6 2.53572e6i 0.444389 0.256568i
629629 1.42618e6 0.143730
630630 7.71590e6 7.09554e6i 0.774524 0.712253i
631631 8.59744e6 0.859599 0.429799 0.902924i 0.358584π-0.358584\pi
0.429799 + 0.902924i 0.358584π0.358584\pi
632632 −2.23545e6 + 1.29064e6i −0.222624 + 0.128532i
633633 −4.36065e6 5.25780e6i −0.432556 0.521549i
634634 6.00351e6 1.03984e7i 0.593174 1.02741i
635635 −3.88867e6 6.73538e6i −0.382708 0.662869i
636636 875582. + 324388.i 0.0858329 + 0.0317996i
637637 3.04104e6 1.26848e7i 0.296943 1.23861i
638638 1.27128e7i 1.23648i
639639 −1.99424e7 3.75287e6i −1.93208 0.363589i
640640 −1.18033e6 681462.i −0.113907 0.0657645i
641641 −1.42405e7 8.22176e6i −1.36893 0.790350i −0.378136 0.925750i 0.623435π-0.623435\pi
−0.990791 + 0.135400i 0.956768π0.956768\pi
642642 −1.16516e6 + 198562.i −0.111570 + 0.0190134i
643643 5.31877e6i 0.507322i 0.967293 + 0.253661i 0.0816348π0.0816348\pi
−0.967293 + 0.253661i 0.918365π0.918365\pi
644644 420500. 3.55768e6i 0.0399532 0.338028i
645645 540034. 1.45765e6i 0.0511118 0.137960i
646646 −1.87342e6 3.24486e6i −0.176626 0.305925i
647647 1.32944e6 2.30266e6i 0.124856 0.216257i −0.796821 0.604216i 0.793486π-0.793486\pi
0.921677 + 0.387959i 0.126820π0.126820\pi
648648 −1.37371e6 + 3.52063e6i −0.128516 + 0.329369i
649649 2.95465e6 1.70587e6i 0.275356 0.158977i
650650 1.17813e7 1.09373
651651 895322. + 1.74901e7i 0.0827994 + 1.61748i
652652 −2.63014e6 −0.242304
653653 1.02822e6 593641.i 0.0943630 0.0544805i −0.452076 0.891979i 0.649316π-0.649316\pi
0.546439 + 0.837499i 0.315983π0.315983\pi
654654 7.06398e6 5.85864e6i 0.645811 0.535615i
655655 −3.43990e6 + 5.95808e6i −0.313287 + 0.542629i
656656 209081. + 362139.i 0.0189695 + 0.0328561i
657657 −2.02975e6 + 2.36334e6i −0.183455 + 0.213606i
658658 −1.61033e6 1.20209e6i −0.144994 0.108236i
659659 373152.i 0.0334713i 0.999860 + 0.0167356i 0.00532737π0.00532737\pi
−0.999860 + 0.0167356i 0.994673π0.994673\pi
660660 1.83366e6 + 1.07599e7i 0.163855 + 0.961500i
661661 −5.30523e6 3.06297e6i −0.472281 0.272671i 0.244913 0.969545i 0.421241π-0.421241\pi
−0.717194 + 0.696874i 0.754574π0.754574\pi
662662 2.08537e6 + 1.20399e6i 0.184943 + 0.106777i
663663 −961308. 5.64094e6i −0.0849334 0.498388i
664664 4.65938e6i 0.410117i
665665 −1.71154e7 1.27764e7i −1.50084 1.12035i
666666 −1.90960e6 + 2.22344e6i −0.166823 + 0.194241i
667667 5.21692e6 + 9.03597e6i 0.454046 + 0.786431i
668668 −5.02587e6 + 8.70506e6i −0.435783 + 0.754798i
669669 −7.80972e6 + 6.47713e6i −0.674637 + 0.559522i
670670 −7.02176e6 + 4.05402e6i −0.604309 + 0.348898i
671671 2.34220e7 2.00825
672672 105796. + 2.06671e6i 0.00903741 + 0.176546i
673673 −2.06386e7 −1.75647 −0.878237 0.478226i 0.841280π-0.841280\pi
−0.878237 + 0.478226i 0.841280π0.841280\pi
674674 −1.78456e6 + 1.03032e6i −0.151315 + 0.0873616i
675675 247457. 1.43731e7i 0.0209046 1.21420i
676676 −1.84854e6 + 3.20177e6i −0.155583 + 0.269478i
677677 −3.56149e6 6.16868e6i −0.298648 0.517274i 0.677179 0.735819i 0.263202π-0.263202\pi
−0.975827 + 0.218545i 0.929869π0.929869\pi
678678 −3.38192e6 + 9.12843e6i −0.282546 + 0.762644i
679679 −15471.9 + 130902.i −0.00128786 + 0.0108961i
680680 2.51807e6i 0.208831i
681681 7.17002e6 1.22189e6i 0.592452 0.100963i
682682 −1.57926e7 9.11786e6i −1.30015 0.750640i
683683 639959. + 369480.i 0.0524929 + 0.0303068i 0.526017 0.850474i 0.323685π-0.323685\pi
−0.473524 + 0.880781i 0.657018π0.657018\pi
684684 7.56725e6 + 1.42404e6i 0.618440 + 0.116381i
685685 6.46859e6i 0.526724i
686686 −8.58896e6 + 1.48012e6i −0.696836 + 0.120084i
687687 4.52438e6 + 1.67620e6i 0.365736 + 0.135499i
688688 153440. + 265765.i 0.0123585 + 0.0214056i
689689 1.45279e6 2.51630e6i 0.116588 0.201936i
690690 −5.71886e6 6.89545e6i −0.457285 0.551366i
691691 7.52113e6 4.34233e6i 0.599223 0.345961i −0.169513 0.985528i 0.554219π-0.554219\pi
0.768736 + 0.639567i 0.220886π0.220886\pi
692692 −9.76294e6 −0.775024
693693 1.21990e7 1.12182e7i 0.964923 0.887343i
694694 −8.93309e6 −0.704050
695695 −2.72648e6 + 1.57413e6i −0.214112 + 0.123617i
696696 −3.84762e6 4.63923e6i −0.301071 0.363013i
697697 −386288. + 669070.i −0.0301182 + 0.0521663i
698698 5.03892e6 + 8.72767e6i 0.391471 + 0.678047i
699699 −1.84586e7 6.83860e6i −1.42892 0.529388i
700700 −3.10849e6 7.23200e6i −0.239775 0.557844i
701701 2.53605e7i 1.94923i 0.223887 + 0.974615i 0.428125π0.428125\pi
−0.223887 + 0.974615i 0.571875π0.571875\pi
702702 1.00815e7 + 6.05431e6i 0.772117 + 0.463684i
703703 5.17173e6 + 2.98590e6i 0.394682 + 0.227870i
704704 −1.86613e6 1.07741e6i −0.141909 0.0819312i
705705 −4.95366e6 + 844184.i −0.375365 + 0.0639682i
706706 7.10819e6i 0.536720i
707707 6.04114e6 8.09278e6i 0.454538 0.608904i
708708 561935. 1.51676e6i 0.0421311 0.113720i
709709 9.54640e6 + 1.65348e7i 0.713221 + 1.23533i 0.963642 + 0.267197i 0.0860975π0.0860975\pi
−0.250421 + 0.968137i 0.580569π0.580569\pi
710710 −1.38935e7 + 2.40642e7i −1.03434 + 1.79153i
711711 9.24759e6 3.24615e6i 0.686048 0.240821i
712712 −3.24554e6 + 1.87381e6i −0.239931 + 0.138524i
713713 1.49667e7 1.10256
714714 −3.20906e6 + 2.07845e6i −0.235577 + 0.152579i
715715 3.39649e7 2.48465
716716 1.06096e7 6.12548e6i 0.773425 0.446537i
717717 1.32234e6 1.09671e6i 0.0960606 0.0796695i
718718 9.06780e6 1.57059e7i 0.656433 1.13698i
719719 7.75609e6 + 1.34339e7i 0.559526 + 0.969128i 0.997536 + 0.0701578i 0.0223503π0.0223503\pi
−0.438009 + 0.898970i 0.644316π0.644316\pi
720720 3.92573e6 + 3.37160e6i 0.282221 + 0.242385i
721721 3.78749e6 1.62795e6i 0.271340 0.116628i
722722 5.78467e6i 0.412986i
723723 −2.77877e6 1.63058e7i −0.197700 1.16010i
724724 −6.79563e6 3.92346e6i −0.481819 0.278178i
725725 1.98548e7 + 1.14632e7i 1.40288 + 0.809955i
726726 1.21205e6 + 7.11229e6i 0.0853451 + 0.500804i
727727 2.14536e7i 1.50544i 0.658338 + 0.752722i 0.271260π0.271260\pi
−0.658338 + 0.752722i 0.728740π0.728740\pi
728728 6.39501e6 + 755856.i 0.447211 + 0.0528580i
729729 7.59796e6 1.21722e7i 0.529515 0.848301i
730730 2.13294e6 + 3.69436e6i 0.148140 + 0.256586i
731731 −283488. + 491015.i −0.0196219 + 0.0339861i
732732 8.54732e6 7.08887e6i 0.589593 0.488989i
733733 179972. 103907.i 0.0123721 0.00714306i −0.493801 0.869575i 0.664393π-0.664393\pi
0.506173 + 0.862432i 0.331060π0.331060\pi
734734 −5.46344e6 −0.374305
735735 −1.21274e7 + 1.81086e7i −0.828036 + 1.23642i
736736 1.76854e6 0.120343
737737 −1.11016e7 + 6.40951e6i −0.752864 + 0.434666i
738738 −525870. 1.49809e6i −0.0355416 0.101251i
739739 5.29314e6 9.16799e6i 0.356535 0.617537i −0.630844 0.775909i 0.717291π-0.717291\pi
0.987379 + 0.158372i 0.0506247π0.0506247\pi
740740 2.00668e6 + 3.47567e6i 0.134710 + 0.233324i
741741 8.32412e6 2.24683e7i 0.556920 1.50323i
742742 −1.92795e6 227874.i −0.128554 0.0151944i
743743 8.74779e6i 0.581335i 0.956824 + 0.290667i 0.0938773π0.0938773\pi
−0.956824 + 0.290667i 0.906123π0.906123\pi
744744 −8.52273e6 + 1.45241e6i −0.564477 + 0.0961960i
745745 −2.24974e6 1.29889e6i −0.148505 0.0857394i
746746 9.98567e6 + 5.76523e6i 0.656947 + 0.379288i
747747 3.27177e6 1.73859e7i 0.214526 1.13998i
748748 3.98114e6i 0.260168i
749749 2.25773e6 970426.i 0.147051 0.0632059i
750750 −3.25858e6 1.20725e6i −0.211532 0.0783688i
751751 −7.94497e6 1.37611e7i −0.514035 0.890334i −0.999867 0.0162823i 0.994817π-0.994817\pi
0.485833 0.874052i 0.338516π-0.338516\pi
752752 496019. 859129.i 0.0319855 0.0554005i
753753 9.77800e6 + 1.17897e7i 0.628438 + 0.757731i
754754 −1.62423e7 + 9.37752e6i −1.04045 + 0.600703i
755755 −2.96264e7 −1.89152
756756 1.05646e6 7.78597e6i 0.0672277 0.495460i
757757 −1.26269e7 −0.800860 −0.400430 0.916327i 0.631139π-0.631139\pi
−0.400430 + 0.916327i 0.631139π0.631139\pi
758758 6.20757e6 3.58394e6i 0.392418 0.226562i
759759 −9.04168e6 1.09019e7i −0.569698 0.686906i
760760 5.27194e6 9.13126e6i 0.331082 0.573452i
761761 7.44430e6 + 1.28939e7i 0.465974 + 0.807091i 0.999245 0.0388535i 0.0123706π-0.0123706\pi
−0.533271 + 0.845945i 0.679037π0.679037\pi
762762 −5.46655e6 2.02526e6i −0.341056 0.126355i
763763 −1.14141e7 + 1.52905e7i −0.709791 + 0.950845i
764764 5.45528e6i 0.338130i
765765 −1.76816e6 + 9.39588e6i −0.109237 + 0.580475i
766766 5.64202e6 + 3.25742e6i 0.347426 + 0.200587i
767767 −4.35897e6 2.51665e6i −0.267544 0.154467i
768768 −1.00709e6 + 171624.i −0.0616117 + 0.0104996i
769769 6.82644e6i 0.416273i 0.978100 + 0.208137i 0.0667399π0.0667399\pi
−0.978100 + 0.208137i 0.933260π0.933260\pi
770770 −8.96159e6 2.08494e7i −0.544701 1.26726i
771771 1.16143e6 3.13493e6i 0.0703653 0.189929i
772772 1.73675e6 + 3.00814e6i 0.104880 + 0.181658i
773773 −3.58514e6 + 6.20964e6i −0.215803 + 0.373781i −0.953521 0.301328i 0.902570π-0.902570\pi
0.737718 + 0.675109i 0.235903π0.235903\pi
774774 −385924. 1.09942e6i −0.0231553 0.0659644i
775775 2.84806e7 1.64433e7i 1.70331 0.983409i
776776 −65071.9 −0.00387918
777777 2.77310e6 5.42621e6i 0.164783 0.322437i
778778 1.90882e7 1.13062
779779 −2.80158e6 + 1.61750e6i −0.165409 + 0.0954991i
780780 1.23947e7 1.02798e7i 0.729457 0.604988i
781781 −2.19659e7 + 3.80461e7i −1.28861 + 2.23194i
782782 1.63373e6 + 2.82971e6i 0.0955355 + 0.165472i
783783 1.10993e7 + 2.00125e7i 0.646982 + 1.16653i
784784 −1.22333e6 4.12502e6i −0.0710809 0.239682i
785785 2.63672e7i 1.52718i
786786 866327. + 5.08360e6i 0.0500179 + 0.293504i
787787 1.03687e7 + 5.98637e6i 0.596743 + 0.344530i 0.767759 0.640738i 0.221372π-0.221372\pi
−0.171016 + 0.985268i 0.554705π0.554705\pi
788788 −104979. 60609.5i −0.00602262 0.00347716i
789789 −2.46644e6 1.44730e7i −0.141052 0.827689i
790790 1.34204e7i 0.765065i
791791 2.37571e6 2.01000e7i 0.135006 1.14223i
792792 6.20668e6 + 5.33060e6i 0.351598 + 0.301969i
793793 −1.72772e7 2.99249e7i −0.975639 1.68986i
794794 201300. 348662.i 0.0113316 0.0196270i
795795 −3.73672e6 + 3.09912e6i −0.209688 + 0.173908i
796796 −1.01551e7 + 5.86305e6i −0.568069 + 0.327975i
797797 −2.26127e7 −1.26097 −0.630487 0.776200i 0.717145π-0.717145\pi
−0.630487 + 0.776200i 0.717145π0.717145\pi
798798 −1.59885e7 + 818457.i −0.888794 + 0.0454976i
799799 1.83284e6 0.101568
800800 3.36540e6 1.94302e6i 0.185914 0.107337i
801801 1.34261e7 4.71293e6i 0.739382 0.259543i
802802 −1.10938e7 + 1.92150e7i −0.609036 + 1.05488i
803803 3.37224e6 + 5.84089e6i 0.184557 + 0.319661i
804804 −2.11138e6 + 5.69899e6i −0.115193 + 0.310926i
805805 1.49257e7 + 1.11418e7i 0.811791 + 0.605990i
806806 2.69030e7i 1.45869i
807807 2.85274e7 4.86153e6i 1.54198 0.262778i
808808 4.31758e6 + 2.49276e6i 0.232655 + 0.134323i
809809 −2.77615e6 1.60281e6i −0.149132 0.0861015i 0.423577 0.905860i 0.360774π-0.360774\pi
−0.572709 + 0.819759i 0.694108π0.694108\pi
810810 −1.22809e7 1.53373e7i −0.657684 0.821368i
811811 1.69321e7i 0.903979i −0.892023 0.451989i 0.850715π-0.850715\pi
0.892023 0.451989i 0.149285π-0.149285\pi
812812 1.00419e7 + 7.49614e6i 0.534474 + 0.398977i
813813 4.98693e6 + 1.84757e6i 0.264611 + 0.0980335i
814814 3.17262e6 + 5.49513e6i 0.167825 + 0.290681i
815815 6.83725e6 1.18425e7i 0.360568 0.624522i
816816 −1.20492e6 1.45282e6i −0.0633482 0.0763813i
817817 −2.05602e6 + 1.18704e6i −0.107764 + 0.0622173i
818818 2.90854e6 0.151982
819819 −2.33314e7 7.31089e6i −1.21544 0.380856i
820820 −2.17408e6 −0.112912
821821 1.95734e7 1.13007e7i 1.01346 0.585123i 0.101259 0.994860i 0.467713π-0.467713\pi
0.912204 + 0.409737i 0.134380π0.134380\pi
822822 3.09529e6 + 3.73211e6i 0.159780 + 0.192653i
823823 −8.63253e6 + 1.49520e7i −0.444261 + 0.769483i −0.998000 0.0632072i 0.979867π-0.979867\pi
0.553739 + 0.832690i 0.313200π0.313200\pi
824824 1.01758e6 + 1.76250e6i 0.0522097 + 0.0904299i
825825 −2.91831e7 1.08118e7i −1.49278 0.553049i
826826 −394744. + 3.33977e6i −0.0201310 + 0.170320i
827827 1.66638e7i 0.847246i −0.905839 0.423623i 0.860758π-0.860758\pi
0.905839 0.423623i 0.139242π-0.139242\pi
828828 −6.59909e6 1.24185e6i −0.334509 0.0629497i
829829 7.96656e6 + 4.59949e6i 0.402610 + 0.232447i 0.687609 0.726081i 0.258660π-0.258660\pi
−0.285000 + 0.958528i 0.591993π0.591993\pi
830830 −2.09793e7 1.21124e7i −1.05705 0.610287i
831831 −9.13795e6 + 1.55725e6i −0.459035 + 0.0782270i
832832 3.17898e6i 0.159214i
833833 5.47006e6 5.76795e6i 0.273136 0.288011i
834834 −819826. + 2.21286e6i −0.0408138 + 0.110164i
835835 −2.61302e7 4.52588e7i −1.29696 2.24640i
836836 8.33507e6 1.44368e7i 0.412471 0.714421i
837837 3.28214e7 + 565075.i 1.61936 + 0.0278800i
838838 4.57470e6 2.64120e6i 0.225036 0.129925i
839839 −1.21622e7 −0.596495 −0.298248 0.954489i 0.596402π-0.596402\pi
−0.298248 + 0.954489i 0.596402π0.596402\pi
840840 −9.58057e6 4.89621e6i −0.468482 0.239421i
841841 −1.59860e7 −0.779381
842842 1.74077e7 1.00503e7i 0.846177 0.488541i
843843 −1.24644e7 + 1.03376e7i −0.604091 + 0.501014i
844844 −3.50557e6 + 6.07182e6i −0.169396 + 0.293402i
845845 −9.61084e6 1.66465e7i −0.463041 0.802011i
846846 −2.45410e6 + 2.85744e6i −0.117887 + 0.137262i
847847 −5.92360e6 1.37814e7i −0.283712 0.660064i
848848 958392.i 0.0457671i
849849 6.59635e6 + 3.87073e7i 0.314076 + 1.84299i
850850 6.21775e6 + 3.58982e6i 0.295179 + 0.170422i
851851 −4.51006e6 2.60389e6i −0.213481 0.123253i
852852 3.49902e6 + 2.05322e7i 0.165138 + 0.969028i
853853 2.68757e6i 0.126470i 0.997999 + 0.0632349i 0.0201417π0.0201417\pi
−0.997999 + 0.0632349i 0.979858π0.979858\pi
854854 −1.38109e7 + 1.85012e7i −0.648004 + 0.868073i
855855 −2.60835e7 + 3.03703e7i −1.22025 + 1.42080i
856856 606582. + 1.05063e6i 0.0282947 + 0.0490078i
857857 16391.7 28391.2i 0.000762380 0.00132048i −0.865644 0.500660i 0.833091π-0.833091\pi
0.866406 + 0.499340i 0.166424π0.166424\pi
858858 1.95964e7 1.62526e7i 0.908777 0.753710i
859859 −2.24671e7 + 1.29714e7i −1.03888 + 0.599796i −0.919515 0.393055i 0.871418π-0.871418\pi
−0.119362 + 0.992851i 0.538085π0.538085\pi
860860 −1.59551e6 −0.0735620
861861 1.79452e6 + 2.77068e6i 0.0824974 + 0.127373i
862862 7.43210e6 0.340678
863863 1.00839e7 5.82196e6i 0.460896 0.266098i −0.251525 0.967851i 0.580932π-0.580932\pi
0.712421 + 0.701752i 0.247599π0.247599\pi
864864 3.87833e6 + 66772.0i 0.176751 + 0.00304306i
865865 2.53794e7 4.39585e7i 1.15330 1.99757i
866866 −1.10539e7 1.91460e7i −0.500867 0.867528i
867867 −6.47781e6 + 1.74848e7i −0.292672 + 0.789974i
868868 1.65144e7 7.09831e6i 0.743986 0.319783i
869869 2.12181e7i 0.953139i
870870 3.08907e7 5.26427e6i 1.38366 0.235798i
871871 1.63781e7 + 9.45589e6i 0.731506 + 0.422335i
872872 −8.15763e6 4.70981e6i −0.363306 0.209755i
873873 242808. + 45692.8i 0.0107827 + 0.00202914i
874874 1.36818e7i 0.605850i
875875 7.17509e6 + 848059.i 0.316816 + 0.0374460i
876876 2.99841e6 + 1.11086e6i 0.132017 + 0.0489101i
877877 −1.21388e7 2.10250e7i −0.532936 0.923073i −0.999260 0.0384589i 0.987755π-0.987755\pi
0.466324 0.884614i 0.345578π-0.345578\pi
878878 1.14122e7 1.97665e7i 0.499612 0.865353i
879879 −2.50077e7 3.01527e7i −1.09169 1.31630i
880880 9.70226e6 5.60160e6i 0.422344 0.243840i
881881 −3.00774e7 −1.30557 −0.652787 0.757542i 0.726400π-0.726400\pi
−0.652787 + 0.757542i 0.726400π0.726400\pi
882882 1.66816e6 + 1.62510e7i 0.0722048 + 0.703411i
883883 1.55262e6 0.0670139 0.0335069 0.999438i 0.489332π-0.489332\pi
0.0335069 + 0.999438i 0.489332π0.489332\pi
884884 −5.08646e6 + 2.93667e6i −0.218920 + 0.126393i
885885 5.36858e6 + 6.47310e6i 0.230410 + 0.277814i
886886 1.02652e7 1.77798e7i 0.439320 0.760925i
887887 658464. + 1.14049e6i 0.0281011 + 0.0486725i 0.879734 0.475466i 0.157721π-0.157721\pi
−0.851633 + 0.524139i 0.824387π0.824387\pi
888888 2.82092e6 + 1.04510e6i 0.120049 + 0.0444760i
889889 1.20368e7 + 1.42269e6i 0.510808 + 0.0603749i
890890 1.94844e7i 0.824542i
891891 −1.94164e7 2.42487e7i −0.819360 1.02328i
892892 9.01882e6 + 5.20702e6i 0.379523 + 0.219118i
893893 6.64641e6 + 3.83731e6i 0.278906 + 0.161027i
894894 −1.91954e6 + 327120.i −0.0803253 + 0.0136887i
895895 6.36945e7i 2.65793i
896896 1.95143e6 838770.i 0.0812048 0.0349038i
897897 −7.25913e6 + 1.95937e7i −0.301234 + 0.813085i
898898 −3.12725e6 5.41655e6i −0.129411 0.224146i
899899 −2.61765e7 + 4.53390e7i −1.08022 + 1.87100i
900900 −1.39220e7 + 4.88698e6i −0.572920 + 0.201110i
901901 1.53345e6 885339.i 0.0629301 0.0363327i
902902 −3.43728e6 −0.140669
903903 1.31696e6 + 2.03334e6i 0.0537468 + 0.0829832i
904904 9.99177e6 0.406651
905905 3.53314e7 2.03986e7i 1.43397 0.827903i
906906 −1.70932e7 + 1.41766e7i −0.691837 + 0.573787i
907907 8.12564e6 1.40740e7i 0.327974 0.568068i −0.654136 0.756377i 0.726967π-0.726967\pi
0.982110 + 0.188310i 0.0603008π0.0603008\pi
908908 −3.73271e6 6.46524e6i −0.150248 0.260238i
909909 −1.43602e7 1.23332e7i −0.576434 0.495069i
910910 −2.00276e7 + 2.68292e7i −0.801724 + 1.07400i
911911 2.24793e7i 0.897402i 0.893682 + 0.448701i 0.148113π0.148113\pi
−0.893682 + 0.448701i 0.851887π0.851887\pi
912912 −1.32772e6 7.79104e6i −0.0528590 0.310176i
913913 −3.31688e7 1.91500e7i −1.31690 0.760312i
914914 2.18253e7 + 1.26009e7i 0.864162 + 0.498924i
915915 9.69890e6 + 5.69131e7i 0.382975 + 2.24729i
916916 4.95229e6i 0.195015i
917917 −4.23397e6 9.85046e6i −0.166274 0.386841i
918918 3.47587e6 + 6.26712e6i 0.136131 + 0.245449i
919919 5.60967e6 + 9.71623e6i 0.219103 + 0.379498i 0.954534 0.298102i 0.0963536π-0.0963536\pi
−0.735431 + 0.677600i 0.763020π0.763020\pi
920920 −4.59744e6 + 7.96301e6i −0.179080 + 0.310175i
921921 −9.49222e6 + 7.87254e6i −0.368739 + 0.305820i
922922 −564145. + 325709.i −0.0218556 + 0.0126184i
923923 6.48123e7 2.50411
924924 −1.51471e7 7.74104e6i −0.583648 0.298277i
925925 −1.14431e7 −0.439733
926926 −2.91330e7 + 1.68199e7i −1.11650 + 0.644609i
927927 −2.55937e6 7.29110e6i −0.0978215 0.278672i
928928 −3.09314e6 + 5.35747e6i −0.117904 + 0.204216i
929929 585570. + 1.01424e6i 0.0222607 + 0.0385567i 0.876941 0.480598i 0.159580π-0.159580\pi
−0.854680 + 0.519154i 0.826247π0.826247\pi
930930 1.56158e7 4.21500e7i 0.592049 1.59805i
931931 3.19120e7 9.46393e6i 1.20665 0.357847i
932932 2.02044e7i 0.761914i
933933 2.57091e6 438124.i 0.0966901 0.0164776i
934934 2.23835e7 + 1.29231e7i 0.839578 + 0.484731i
935935 1.79254e7 + 1.03492e7i 0.670564 + 0.387151i
936936 2.23225e6 1.18620e7i 0.0832824 0.442556i
937937 2.95716e7i 1.10034i −0.835053 0.550169i 0.814563π-0.814563\pi
0.835053 0.550169i 0.185437π-0.185437\pi
938938 1.48318e6 1.25486e7i 0.0550412 0.465682i
939939 1.85372e7 + 6.86771e6i 0.686089 + 0.254184i
940940 2.57887e6 + 4.46673e6i 0.0951940 + 0.164881i
941941 2.26652e7 3.92573e7i 0.834421 1.44526i −0.0600797 0.998194i 0.519135π-0.519135\pi
0.894501 0.447066i 0.147531π-0.147531\pi
942942 1.26170e7 + 1.52128e7i 0.463263 + 0.558574i
943943 2.44315e6 1.41055e6i 0.0894686 0.0516547i
944944 −1.66022e6 −0.0606365
945945 3.23107e7 + 2.49970e7i 1.17697 + 0.910559i
946946 −2.52254e6 −0.0916454
947947 −3.82062e7 + 2.20584e7i −1.38439 + 0.799279i −0.992676 0.120806i 0.961452π-0.961452\pi
−0.391717 + 0.920086i 0.628119π0.628119\pi
948948 −6.42182e6 7.74303e6i −0.232080 0.279827i
949949 4.97503e6 8.61701e6i 0.179321 0.310593i
950950 1.50316e7 + 2.60355e7i 0.540376 + 0.935958i
951951 4.38783e7 + 1.62561e7i 1.57325 + 0.582862i
952952 3.14473e6 + 2.34750e6i 0.112458 + 0.0839484i
953953 5.71596e6i 0.203872i 0.994791 + 0.101936i 0.0325036π0.0325036\pi
−0.994791 + 0.101936i 0.967496π0.967496\pi
954954 −672972. + 3.57612e6i −0.0239401 + 0.127216i
955955 −2.45629e7 1.41814e7i −0.871506 0.503164i
956956 −1.52707e6 881652.i −0.0540397 0.0311998i
957957 4.88390e7 8.32296e6i 1.72380 0.293763i
958958 2.12648e7i 0.748597i
959959 −8.07840e6 6.03041e6i −0.283648 0.211739i
960960 1.84524e6 4.98064e6i 0.0646212 0.174424i
961961 2.32341e7 + 4.02426e7i 0.811553 + 1.40565i
962962 4.68053e6 8.10692e6i 0.163064 0.282435i
963963 −1.52564e6 4.34624e6i −0.0530137 0.151025i
964964 −1.47030e7 + 8.48876e6i −0.509580 + 0.294206i
965965 −1.80592e7 −0.624282
966966 1.39430e7 713744.i 0.480742 0.0246093i
967967 −1.87898e7 −0.646182 −0.323091 0.946368i 0.604722π-0.604722\pi
−0.323091 + 0.946368i 0.604722π0.604722\pi
968968 6.41318e6 3.70265e6i 0.219981 0.127006i
969969 1.12394e7 9.32155e6i 0.384531 0.318918i
970970 169159. 292992.i 0.00577253 0.00999831i
971971 −3.13939e6 5.43759e6i −0.106856 0.185080i 0.807639 0.589677i 0.200745π-0.200745\pi
−0.914495 + 0.404598i 0.867412π0.867412\pi
972972 −1.44246e7 2.97248e6i −0.489710 0.100914i
973973 575906. 4.87251e6i 0.0195016 0.164995i
974974 3.05109e7i 1.03052i
975975 7.71316e6 + 4.52607e7i 0.259849 + 1.52479i
976976 −9.87062e6 5.69880e6i −0.331680 0.191496i
977977 −2.64868e7 1.52922e7i −0.887754 0.512545i −0.0145471 0.999894i 0.504631π-0.504631\pi
−0.873207 + 0.487349i 0.837964π0.837964\pi
978978 −1.72194e6 1.01043e7i −0.0575665 0.337800i
979979 3.08054e7i 1.02724i
980980 2.17534e7 + 5.21513e6i 0.723538 + 0.173460i
981981 2.71320e7 + 2.33023e7i 0.900140 + 0.773083i
982982 −4.64758e6 8.04984e6i −0.153797 0.266384i
983983 −93556.9 + 162045.i −0.00308811 + 0.00534876i −0.867565 0.497323i 0.834316π-0.834316\pi
0.864477 + 0.502672i 0.167650π0.167650\pi
984984 −1.25436e6 + 1.04032e6i −0.0412984 + 0.0342515i
985985 545799. 315117.i 0.0179243 0.0103486i
986986 −1.14295e7 −0.374398
987987 3.56382e6 6.97345e6i 0.116446 0.227853i
988988 −2.45933e7 −0.801539
989989 1.79297e6 1.03517e6i 0.0582885 0.0336529i
990990 −4.01362e7 + 1.40889e7i −1.30151 + 0.456866i
991991 −2.73564e7 + 4.73826e7i −0.884860 + 1.53262i −0.0389850 + 0.999240i 0.512412π0.512412\pi
−0.845875 + 0.533382i 0.820921π0.820921\pi
992992 4.43692e6 + 7.68498e6i 0.143154 + 0.247950i
993993 −3.26012e6 + 8.79965e6i −0.104920 + 0.283199i
994994 −1.71006e7 3.97851e7i −0.548966 1.27719i
995995 6.09656e7i 1.95221i
996996 −1.79001e7 + 3.05046e6i −0.571750 + 0.0974355i
997997 1.17404e7 + 6.77833e6i 0.374063 + 0.215966i 0.675232 0.737605i 0.264043π-0.264043\pi
−0.301169 + 0.953571i 0.597377π0.597377\pi
998998 1.73127e7 + 9.99550e6i 0.550223 + 0.317671i
999999 −9.79206e6 5.88049e6i −0.310428 0.186423i
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.f.a.17.12 yes 28
3.2 odd 2 inner 42.6.f.a.17.7 yes 28
7.3 odd 6 294.6.d.a.293.6 28
7.4 even 3 294.6.d.a.293.24 28
7.5 odd 6 inner 42.6.f.a.5.7 28
21.5 even 6 inner 42.6.f.a.5.12 yes 28
21.11 odd 6 294.6.d.a.293.5 28
21.17 even 6 294.6.d.a.293.23 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.6.f.a.5.7 28 7.5 odd 6 inner
42.6.f.a.5.12 yes 28 21.5 even 6 inner
42.6.f.a.17.7 yes 28 3.2 odd 2 inner
42.6.f.a.17.12 yes 28 1.1 even 1 trivial
294.6.d.a.293.5 28 21.11 odd 6
294.6.d.a.293.6 28 7.3 odd 6
294.6.d.a.293.23 28 21.17 even 6
294.6.d.a.293.24 28 7.4 even 3