Properties

Label 195.6.bb.a.166.16
Level 195195
Weight 66
Character 195.166
Analytic conductor 31.27531.275
Analytic rank 00
Dimension 4444
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [195,6,Mod(121,195)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(195, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("195.121");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 195=3513 195 = 3 \cdot 5 \cdot 13
Weight: k k == 6 6
Character orbit: [χ][\chi] == 195.bb (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: 31.274844863531.2748448635
Analytic rank: 00
Dimension: 4444
Relative dimension: 2222 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 166.16
Character χ\chi == 195.166
Dual form 195.6.bb.a.121.16

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+(4.519542.60936i)q2+(4.50000+7.79423i)q3+(2.38250+4.12662i)q4+25.0000iq5+(40.6759+23.4842i)q6+(51.9425+29.9890i)q7+191.866iq8+(40.5000+70.1481i)q9+(65.2339+112.989i)q10+(144.11883.2065i)q1142.8850q12+(603.169+86.4908i)q13+313.008q14+(194.856+112.500i)q15+(424.407+735.095i)q16+(192.295+333.064i)q17+422.716iq18+(1121.56647.531i)q19+(103.16559.5626i)q20+539.803iq21+(434.231752.111i)q22+(990.7191715.97i)q23+(1495.45+863.398i)q24625.000q25+(2500.36+1964.78i)q26729.000q27+(247.506+142.898i)q28+(637.665+1104.47i)q29+(587.106+1016.90i)q30+9337.36iq31+(1480.90854.997i)q32+(1297.06+748.859i)q33+2007.06iq34+(749.726+1298.56i)q35+(192.983334.256i)q36+(2352.11+1357.99i)q376758.57q38+(3388.394312.03i)q394796.65q40+(3703.17+2138.03i)q41+(1408.54+2439.66i)q42+(3226.35+5588.21i)q43+792.959iq44+(1753.701012.50i)q45+(8955.195170.28i)q46+12003.9iq47+(3819.67+6615.85i)q48+(6604.8211439.9i)q49+(2824.71+1630.85i)q503461.30q51+(1080.142695.11i)q52+8751.13q53+(3294.75+1902.22i)q54+(2080.16+3602.95i)q55+(5753.88+9966.01i)q5611655.6iq57+(5763.91+3327.79i)q58+(11693.8+6751.41i)q591072.13iq60+(6052.99+10484.1i)q61+(24364.5+42200.6i)q62+(4207.34+2429.11i)q6336086.0q64+(2162.2715079.2i)q65+7816.16q66+(30125.717393.1i)q67+(916.2851587.05i)q68+(8916.4715443.8i)q69+7825.21iq70+(21774.3+12571.4i)q71+(13459.07770.58i)q72+12638.3iq73+(7086.98+12275.0i)q74+(2812.504871.39i)q75+(5344.233085.49i)q76+9981.13q77+(26565.610646.9i)q78+38441.1q79+(18377.4+10610.2i)q80+(3280.505681.99i)q81+(11157.7+19325.8i)q82+51744.5iq83+(2227.561286.08i)q84+(8326.604807.37i)q85+33674.8iq86+(5738.99+9940.22i)q87+(15964.5+27651.3i)q88+(2134.331232.26i)q8910567.9q90+(33923.913595.9i)q91+9441.56q92+(72777.5+42018.1i)q93+(31322.5+54252.1i)q94+(16188.328038.9i)q9515389.9iq96+(47857.927630.8i)q97+(59701.534468.7i)q98+13479.5iq99+O(q100)q+(4.51954 - 2.60936i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-2.38250 + 4.12662i) q^{4} +25.0000i q^{5} +(40.6759 + 23.4842i) q^{6} +(51.9425 + 29.9890i) q^{7} +191.866i q^{8} +(-40.5000 + 70.1481i) q^{9} +(65.2339 + 112.989i) q^{10} +(144.118 - 83.2065i) q^{11} -42.8850 q^{12} +(-603.169 + 86.4908i) q^{13} +313.008 q^{14} +(-194.856 + 112.500i) q^{15} +(424.407 + 735.095i) q^{16} +(-192.295 + 333.064i) q^{17} +422.716i q^{18} +(-1121.56 - 647.531i) q^{19} +(-103.165 - 59.5626i) q^{20} +539.803i q^{21} +(434.231 - 752.111i) q^{22} +(-990.719 - 1715.97i) q^{23} +(-1495.45 + 863.398i) q^{24} -625.000 q^{25} +(-2500.36 + 1964.78i) q^{26} -729.000 q^{27} +(-247.506 + 142.898i) q^{28} +(637.665 + 1104.47i) q^{29} +(-587.106 + 1016.90i) q^{30} +9337.36i q^{31} +(-1480.90 - 854.997i) q^{32} +(1297.06 + 748.859i) q^{33} +2007.06i q^{34} +(-749.726 + 1298.56i) q^{35} +(-192.983 - 334.256i) q^{36} +(-2352.11 + 1357.99i) q^{37} -6758.57 q^{38} +(-3388.39 - 4312.03i) q^{39} -4796.65 q^{40} +(-3703.17 + 2138.03i) q^{41} +(1408.54 + 2439.66i) q^{42} +(-3226.35 + 5588.21i) q^{43} +792.959i q^{44} +(-1753.70 - 1012.50i) q^{45} +(-8955.19 - 5170.28i) q^{46} +12003.9i q^{47} +(-3819.67 + 6615.85i) q^{48} +(-6604.82 - 11439.9i) q^{49} +(-2824.71 + 1630.85i) q^{50} -3461.30 q^{51} +(1080.14 - 2695.11i) q^{52} +8751.13 q^{53} +(-3294.75 + 1902.22i) q^{54} +(2080.16 + 3602.95i) q^{55} +(-5753.88 + 9966.01i) q^{56} -11655.6i q^{57} +(5763.91 + 3327.79i) q^{58} +(11693.8 + 6751.41i) q^{59} -1072.13i q^{60} +(-6052.99 + 10484.1i) q^{61} +(24364.5 + 42200.6i) q^{62} +(-4207.34 + 2429.11i) q^{63} -36086.0 q^{64} +(-2162.27 - 15079.2i) q^{65} +7816.16 q^{66} +(30125.7 - 17393.1i) q^{67} +(-916.285 - 1587.05i) q^{68} +(8916.47 - 15443.8i) q^{69} +7825.21i q^{70} +(21774.3 + 12571.4i) q^{71} +(-13459.0 - 7770.58i) q^{72} +12638.3i q^{73} +(-7086.98 + 12275.0i) q^{74} +(-2812.50 - 4871.39i) q^{75} +(5344.23 - 3085.49i) q^{76} +9981.13 q^{77} +(-26565.6 - 10646.9i) q^{78} +38441.1 q^{79} +(-18377.4 + 10610.2i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-11157.7 + 19325.8i) q^{82} +51744.5i q^{83} +(-2227.56 - 1286.08i) q^{84} +(-8326.60 - 4807.37i) q^{85} +33674.8i q^{86} +(-5738.99 + 9940.22i) q^{87} +(15964.5 + 27651.3i) q^{88} +(2134.33 - 1232.26i) q^{89} -10567.9 q^{90} +(-33923.9 - 13595.9i) q^{91} +9441.56 q^{92} +(-72777.5 + 42018.1i) q^{93} +(31322.5 + 54252.1i) q^{94} +(16188.3 - 28038.9i) q^{95} -15389.9i q^{96} +(-47857.9 - 27630.8i) q^{97} +(-59701.5 - 34468.7i) q^{98} +13479.5i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 44q+198q3+320q4858q71782q9504q11+5760q121066q13+2708q143508q16+1380q17+7560q19+5700q20+1986q223188q2327500q25++408840q98+O(q100) 44 q + 198 q^{3} + 320 q^{4} - 858 q^{7} - 1782 q^{9} - 504 q^{11} + 5760 q^{12} - 1066 q^{13} + 2708 q^{14} - 3508 q^{16} + 1380 q^{17} + 7560 q^{19} + 5700 q^{20} + 1986 q^{22} - 3188 q^{23} - 27500 q^{25}+ \cdots + 408840 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/195Z)×\left(\mathbb{Z}/195\mathbb{Z}\right)^\times.

nn 106106 131131 157157
χ(n)\chi(n) e(56)e\left(\frac{5}{6}\right) 11 11

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 4.51954 2.60936i 0.798949 0.461274i −0.0441542 0.999025i 0.514059π-0.514059\pi
0.843104 + 0.537751i 0.180726π0.180726\pi
33 4.50000 + 7.79423i 0.288675 + 0.500000i
44 −2.38250 + 4.12662i −0.0744532 + 0.128957i
55 25.0000i 0.447214i
66 40.6759 + 23.4842i 0.461274 + 0.266316i
77 51.9425 + 29.9890i 0.400662 + 0.231322i 0.686770 0.726875i 0.259028π-0.259028\pi
−0.286108 + 0.958197i 0.592362π0.592362\pi
88 191.866i 1.05992i
99 −40.5000 + 70.1481i −0.166667 + 0.288675i
1010 65.2339 + 112.989i 0.206288 + 0.357301i
1111 144.118 83.2065i 0.359117 0.207336i −0.309576 0.950875i 0.600187π-0.600187\pi
0.668693 + 0.743538i 0.266854π0.266854\pi
1212 −42.8850 −0.0859711
1313 −603.169 + 86.4908i −0.989875 + 0.141942i
1414 313.008 0.426811
1515 −194.856 + 112.500i −0.223607 + 0.129099i
1616 424.407 + 735.095i 0.414460 + 0.717866i
1717 −192.295 + 333.064i −0.161378 + 0.279515i −0.935363 0.353689i 0.884927π-0.884927\pi
0.773985 + 0.633204i 0.218261π0.218261\pi
1818 422.716i 0.307516i
1919 −1121.56 647.531i −0.712750 0.411507i 0.0993282 0.995055i 0.468331π-0.468331\pi
−0.812079 + 0.583548i 0.801664π0.801664\pi
2020 −103.165 59.5626i −0.0576712 0.0332965i
2121 539.803i 0.267108i
2222 434.231 752.111i 0.191278 0.331303i
2323 −990.719 1715.97i −0.390509 0.676381i 0.602008 0.798490i 0.294368π-0.294368\pi
−0.992517 + 0.122109i 0.961034π0.961034\pi
2424 −1495.45 + 863.398i −0.529960 + 0.305973i
2525 −625.000 −0.200000
2626 −2500.36 + 1964.78i −0.725386 + 0.570008i
2727 −729.000 −0.192450
2828 −247.506 + 142.898i −0.0596611 + 0.0344454i
2929 637.665 + 1104.47i 0.140798 + 0.243870i 0.927798 0.373084i 0.121700π-0.121700\pi
−0.786999 + 0.616954i 0.788366π0.788366\pi
3030 −587.106 + 1016.90i −0.119100 + 0.206288i
3131 9337.36i 1.74510i 0.488527 + 0.872549i 0.337534π0.337534\pi
−0.488527 + 0.872549i 0.662466π0.662466\pi
3232 −1480.90 854.997i −0.255653 0.147601i
3333 1297.06 + 748.859i 0.207336 + 0.119706i
3434 2007.06i 0.297758i
3535 −749.726 + 1298.56i −0.103450 + 0.179181i
3636 −192.983 334.256i −0.0248177 0.0429856i
3737 −2352.11 + 1357.99i −0.282458 + 0.163077i −0.634536 0.772894i 0.718809π-0.718809\pi
0.352078 + 0.935971i 0.385475π0.385475\pi
3838 −6758.57 −0.759269
3939 −3388.39 4312.03i −0.356723 0.453962i
4040 −4796.65 −0.474011
4141 −3703.17 + 2138.03i −0.344044 + 0.198634i −0.662059 0.749452i 0.730317π-0.730317\pi
0.318015 + 0.948086i 0.396984π0.396984\pi
4242 1408.54 + 2439.66i 0.123210 + 0.213406i
4343 −3226.35 + 5588.21i −0.266098 + 0.460894i −0.967851 0.251526i 0.919068π-0.919068\pi
0.701753 + 0.712420i 0.252401π0.252401\pi
4444 792.959i 0.0617475i
4545 −1753.70 1012.50i −0.129099 0.0745356i
4646 −8955.19 5170.28i −0.623993 0.360263i
4747 12003.9i 0.792644i 0.918112 + 0.396322i 0.129714π0.129714\pi
−0.918112 + 0.396322i 0.870286π0.870286\pi
4848 −3819.67 + 6615.85i −0.239289 + 0.414460i
4949 −6604.82 11439.9i −0.392980 0.680661i
5050 −2824.71 + 1630.85i −0.159790 + 0.0922547i
5151 −3461.30 −0.186343
5252 1080.14 2695.11i 0.0553950 0.138219i
5353 8751.13 0.427932 0.213966 0.976841i 0.431362π-0.431362\pi
0.213966 + 0.976841i 0.431362π0.431362\pi
5454 −3294.75 + 1902.22i −0.153758 + 0.0887722i
5555 2080.16 + 3602.95i 0.0927237 + 0.160602i
5656 −5753.88 + 9966.01i −0.245183 + 0.424670i
5757 11655.6i 0.475167i
5858 5763.91 + 3327.79i 0.224982 + 0.129893i
5959 11693.8 + 6751.41i 0.437346 + 0.252502i 0.702471 0.711712i 0.252080π-0.252080\pi
−0.265125 + 0.964214i 0.585413π0.585413\pi
6060 1072.13i 0.0384475i
6161 −6052.99 + 10484.1i −0.208279 + 0.360750i −0.951172 0.308660i 0.900120π-0.900120\pi
0.742894 + 0.669410i 0.233453π0.233453\pi
6262 24364.5 + 42200.6i 0.804968 + 1.39424i
6363 −4207.34 + 2429.11i −0.133554 + 0.0771074i
6464 −36086.0 −1.10126
6565 −2162.27 15079.2i −0.0634785 0.442686i
6666 7816.16 0.220868
6767 30125.7 17393.1i 0.819880 0.473358i −0.0304952 0.999535i 0.509708π-0.509708\pi
0.850375 + 0.526177i 0.176375π0.176375\pi
6868 −916.285 1587.05i −0.0240302 0.0416216i
6969 8916.47 15443.8i 0.225460 0.390509i
7070 7825.21i 0.190876i
7171 21774.3 + 12571.4i 0.512623 + 0.295963i 0.733911 0.679245i 0.237693π-0.237693\pi
−0.221288 + 0.975208i 0.571026π0.571026\pi
7272 −13459.0 7770.58i −0.305973 0.176653i
7373 12638.3i 0.277575i 0.990322 + 0.138787i 0.0443205π0.0443205\pi
−0.990322 + 0.138787i 0.955680π0.955680\pi
7474 −7086.98 + 12275.0i −0.150446 + 0.260581i
7575 −2812.50 4871.39i −0.0577350 0.100000i
7676 5344.23 3085.49i 0.106133 0.0612760i
7777 9981.13 0.191846
7878 −26565.6 10646.9i −0.494405 0.198146i
7979 38441.1 0.692992 0.346496 0.938051i 0.387371π-0.387371\pi
0.346496 + 0.938051i 0.387371π0.387371\pi
8080 −18377.4 + 10610.2i −0.321040 + 0.185352i
8181 −3280.50 5681.99i −0.0555556 0.0962250i
8282 −11157.7 + 19325.8i −0.183249 + 0.317397i
8383 51744.5i 0.824459i 0.911080 + 0.412230i 0.135250π0.135250\pi
−0.911080 + 0.412230i 0.864750π0.864750\pi
8484 −2227.56 1286.08i −0.0344454 0.0198870i
8585 −8326.60 4807.37i −0.125003 0.0721705i
8686 33674.8i 0.490975i
8787 −5738.99 + 9940.22i −0.0812900 + 0.140798i
8888 15964.5 + 27651.3i 0.219760 + 0.380636i
8989 2134.33 1232.26i 0.0285618 0.0164902i −0.485651 0.874153i 0.661417π-0.661417\pi
0.514213 + 0.857663i 0.328084π0.328084\pi
9090 −10567.9 −0.137525
9191 −33923.9 13595.9i −0.429439 0.172109i
9292 9441.56 0.116298
9393 −72777.5 + 42018.1i −0.872549 + 0.503766i
9494 31322.5 + 54252.1i 0.365626 + 0.633282i
9595 16188.3 28038.9i 0.184031 0.318752i
9696 15389.9i 0.170435i
9797 −47857.9 27630.8i −0.516445 0.298170i 0.219034 0.975717i 0.429710π-0.429710\pi
−0.735479 + 0.677547i 0.763043π0.763043\pi
9898 −59701.5 34468.7i −0.627942 0.362543i
9999 13479.5i 0.138224i
100100 1489.06 2579.13i 0.0148906 0.0257913i
101101 54032.2 + 93586.5i 0.527047 + 0.912872i 0.999503 + 0.0315179i 0.0100341π0.0100341\pi
−0.472456 + 0.881354i 0.656633π0.656633\pi
102102 −15643.5 + 9031.78i −0.148879 + 0.0859553i
103103 189283. 1.75800 0.879001 0.476821i 0.158211π-0.158211\pi
0.879001 + 0.476821i 0.158211π0.158211\pi
104104 −16594.7 115728.i −0.150447 1.04919i
105105 −13495.1 −0.119454
106106 39551.1 22834.8i 0.341896 0.197394i
107107 −4400.02 7621.05i −0.0371531 0.0643510i 0.846851 0.531830i 0.178496π-0.178496\pi
−0.884004 + 0.467479i 0.845162π0.845162\pi
108108 1736.84 3008.30i 0.0143285 0.0248177i
109109 109262.i 0.880852i −0.897789 0.440426i 0.854827π-0.854827\pi
0.897789 0.440426i 0.145173π-0.145173\pi
110110 18802.8 + 10855.8i 0.148163 + 0.0855420i
111111 −21169.0 12221.9i −0.163077 0.0941526i
112112 50910.3i 0.383495i
113113 22817.2 39520.6i 0.168100 0.291157i −0.769652 0.638464i 0.779570π-0.779570\pi
0.937752 + 0.347306i 0.112904π0.112904\pi
114114 −30413.5 52677.8i −0.219182 0.379634i
115115 42899.4 24768.0i 0.302487 0.174641i
116116 −6076.95 −0.0419316
117117 18361.2 45814.0i 0.124004 0.309409i
118118 70467.4 0.465890
119119 −19976.5 + 11533.5i −0.129316 + 0.0746607i
120120 −21584.9 37386.2i −0.136835 0.237005i
121121 −66678.8 + 115491.i −0.414023 + 0.717109i
122122 63177.7i 0.384294i
123123 −33328.5 19242.2i −0.198634 0.114681i
124124 −38531.7 22246.3i −0.225042 0.129928i
125125 15625.0i 0.0894427i
126126 −12676.8 + 21956.9i −0.0711352 + 0.123210i
127127 538.345 + 932.441i 0.00296177 + 0.00512994i 0.867502 0.497433i 0.165724π-0.165724\pi
−0.864541 + 0.502563i 0.832391π0.832391\pi
128128 −115704. + 66801.5i −0.624197 + 0.360380i
129129 −58074.4 −0.307263
130130 −49119.5 62509.0i −0.254915 0.324402i
131131 −27169.4 −0.138325 −0.0691626 0.997605i 0.522033π-0.522033\pi
−0.0691626 + 0.997605i 0.522033π0.522033\pi
132132 −6180.50 + 3568.32i −0.0308737 + 0.0178250i
133133 −38837.7 67268.8i −0.190381 0.329750i
134134 90769.6 157218.i 0.436695 0.756378i
135135 18225.0i 0.0860663i
136136 −63903.7 36894.8i −0.296264 0.171048i
137137 110342. + 63705.8i 0.502271 + 0.289986i 0.729651 0.683820i 0.239683π-0.239683\pi
−0.227380 + 0.973806i 0.573016π0.573016\pi
138138 93065.0i 0.415996i
139139 133572. 231353.i 0.586378 1.01564i −0.408324 0.912837i 0.633887π-0.633887\pi
0.994702 0.102800i 0.0327801π-0.0327801\pi
140140 −3572.45 6187.66i −0.0154044 0.0266813i
141141 −93561.2 + 54017.6i −0.396322 + 0.228817i
142142 131213. 0.546080
143143 −79730.8 + 62652.4i −0.326051 + 0.256211i
144144 −68754.0 −0.276307
145145 −27611.7 + 15941.6i −0.109062 + 0.0629670i
146146 32977.7 + 57119.1i 0.128038 + 0.221768i
147147 59443.3 102959.i 0.226887 0.392980i
148148 12941.7i 0.0485664i
149149 −297875. 171978.i −1.09918 0.634611i −0.163173 0.986598i 0.552173π-0.552173\pi
−0.936005 + 0.351987i 0.885506π0.885506\pi
150150 −25422.4 14677.6i −0.0922547 0.0532633i
151151 399.575i 0.00142612i 1.00000 0.000713060i 0.000226974π0.000226974\pi
−1.00000 0.000713060i 0.999773π0.999773\pi
152152 124239. 215189.i 0.436164 0.755459i
153153 −15575.9 26978.2i −0.0537927 0.0931717i
154154 45110.1 26044.3i 0.153275 0.0884936i
155155 −233434. −0.780431
156156 25866.9 3709.16i 0.0851007 0.0122029i
157157 354487. 1.14776 0.573879 0.818940i 0.305438π-0.305438\pi
0.573879 + 0.818940i 0.305438π0.305438\pi
158158 173736. 100307.i 0.553666 0.319659i
159159 39380.1 + 68208.3i 0.123533 + 0.213966i
160160 21374.9 37022.4i 0.0660092 0.114331i
161161 118843.i 0.361333i
162162 −29652.7 17120.0i −0.0887722 0.0512526i
163163 294303. + 169916.i 0.867611 + 0.500916i 0.866554 0.499084i 0.166330π-0.166330\pi
0.00105751 + 0.999999i 0.499663π0.499663\pi
164164 20375.4i 0.0591557i
165165 −18721.5 + 32426.5i −0.0535340 + 0.0927237i
166166 135020. + 233861.i 0.380301 + 0.658701i
167167 182387. 105301.i 0.506061 0.292175i −0.225152 0.974324i 0.572288π-0.572288\pi
0.731213 + 0.682149i 0.238955π0.238955\pi
168168 −103570. −0.283113
169169 356332. 104337.i 0.959705 0.281010i
170170 −50176.5 −0.133161
171171 90846.1 52450.0i 0.237583 0.137169i
172172 −15373.6 26627.8i −0.0396236 0.0686301i
173173 −76009.6 + 131653.i −0.193087 + 0.334437i −0.946272 0.323372i 0.895183π-0.895183\pi
0.753185 + 0.657809i 0.228517π0.228517\pi
174174 59900.3i 0.149988i
175175 −32464.1 18743.1i −0.0801324 0.0462644i
176176 122329. + 70626.9i 0.297680 + 0.171865i
177177 121525.i 0.291564i
178178 6430.79 11138.5i 0.0152130 0.0263497i
179179 −152608. 264325.i −0.355996 0.616603i 0.631292 0.775545i 0.282525π-0.282525\pi
−0.987288 + 0.158942i 0.949192π0.949192\pi
180180 8356.40 4824.57i 0.0192237 0.0110988i
181181 877478. 1.99086 0.995428 0.0955129i 0.0304491π-0.0304491\pi
0.995428 + 0.0955129i 0.0304491π0.0304491\pi
182182 −188797. + 27072.4i −0.422490 + 0.0605826i
183183 −108954. −0.240500
184184 329237. 190085.i 0.716910 0.413908i
185185 −33949.8 58802.8i −0.0729303 0.126319i
186186 −219281. + 379805.i −0.464748 + 0.804968i
187187 64000.7i 0.133838i
188188 −49535.5 28599.3i −0.102217 0.0590149i
189189 −37866.1 21862.0i −0.0771074 0.0445180i
190190 168964.i 0.339555i
191191 −67180.3 + 116360.i −0.133247 + 0.230791i −0.924927 0.380146i 0.875874π-0.875874\pi
0.791679 + 0.610937i 0.209207π0.209207\pi
192192 −162387. 281263.i −0.317906 0.550629i
193193 67321.2 38867.9i 0.130094 0.0751100i −0.433540 0.901134i 0.642736π-0.642736\pi
0.563635 + 0.826024i 0.309403π0.309403\pi
194194 −288394. −0.550152
195195 107801. 84709.7i 0.203018 0.159532i
196196 62944.0 0.117034
197197 −90820.3 + 52435.1i −0.166731 + 0.0962624i −0.581044 0.813872i 0.697355π-0.697355\pi
0.414312 + 0.910135i 0.364022π0.364022\pi
198198 35172.7 + 60921.0i 0.0637592 + 0.110434i
199199 −107055. + 185424.i −0.191634 + 0.331920i −0.945792 0.324773i 0.894712π-0.894712\pi
0.754158 + 0.656693i 0.228045π0.228045\pi
200200 119916.i 0.211984i
201201 271131. + 156538.i 0.473358 + 0.273293i
202202 488401. + 281979.i 0.842168 + 0.486226i
203203 76491.8i 0.130279i
204204 8246.56 14283.5i 0.0138739 0.0240302i
205205 −53450.6 92579.2i −0.0888318 0.153861i
206206 855473. 493908.i 1.40455 0.810920i
207207 160496. 0.260339
208208 −319568. 406679.i −0.512159 0.651768i
209209 −215515. −0.341281
210210 −60991.5 + 35213.5i −0.0954379 + 0.0551011i
211211 616088. + 1.06710e6i 0.952657 + 1.65005i 0.739641 + 0.673001i 0.234995π0.234995\pi
0.213016 + 0.977049i 0.431671π0.431671\pi
212212 −20849.6 + 36112.5i −0.0318609 + 0.0551847i
213213 226285.i 0.341749i
214214 −39772.1 22962.4i −0.0593669 0.0342755i
215215 −139705. 80658.8i −0.206118 0.119002i
216216 139870.i 0.203982i
217217 −280018. + 485006.i −0.403680 + 0.699194i
218218 −285104. 493814.i −0.406314 0.703756i
219219 −98505.4 + 56872.1i −0.138787 + 0.0801289i
220220 −19824.0 −0.0276143
221221 87179.1 217525.i 0.120069 0.299591i
222222 −127566. −0.173720
223223 −266218. + 153701.i −0.358489 + 0.206973i −0.668418 0.743786i 0.733028π-0.733028\pi
0.309929 + 0.950760i 0.399695π0.399695\pi
224224 −51281.0 88821.4i −0.0682868 0.118276i
225225 25312.5 43842.5i 0.0333333 0.0577350i
226226 238153.i 0.310160i
227227 −1.03194e6 595789.i −1.32919 0.767411i −0.344019 0.938963i 0.611788π-0.611788\pi
−0.985175 + 0.171552i 0.945122π0.945122\pi
228228 48098.0 + 27769.4i 0.0612760 + 0.0353777i
229229 298650.i 0.376334i −0.982137 0.188167i 0.939745π-0.939745\pi
0.982137 0.188167i 0.0602546π-0.0602546\pi
230230 129257. 223880.i 0.161114 0.279058i
231231 44915.1 + 77795.2i 0.0553812 + 0.0959231i
232232 −211910. + 122346.i −0.258483 + 0.149235i
233233 −1.07994e6 −1.30319 −0.651597 0.758566i 0.725901π-0.725901\pi
−0.651597 + 0.758566i 0.725901π0.725901\pi
234234 −36561.0 254969.i −0.0436495 0.304402i
235235 −300098. −0.354481
236236 −55721.0 + 32170.5i −0.0651236 + 0.0375992i
237237 172985. + 299619.i 0.200050 + 0.346496i
238238 −60189.8 + 104252.i −0.0688780 + 0.119300i
239239 1.33861e6i 1.51586i 0.652339 + 0.757928i 0.273788π0.273788\pi
−0.652339 + 0.757928i 0.726212π0.726212\pi
240240 −165396. 95491.6i −0.185352 0.107013i
241241 919850. + 531076.i 1.02017 + 0.588998i 0.914154 0.405366i 0.132856π-0.132856\pi
0.106020 + 0.994364i 0.466189π0.466189\pi
242242 695956.i 0.763912i
243243 29524.5 51137.9i 0.0320750 0.0555556i
244244 −28842.5 49956.7i −0.0310141 0.0537179i
245245 285997. 165120.i 0.304401 0.175746i
246246 −200839. −0.211598
247247 732494. + 293566.i 0.763944 + 0.306171i
248248 −1.79152e6 −1.84966
249249 −403309. + 232850.i −0.412230 + 0.238001i
250250 −40771.2 70617.8i −0.0412576 0.0714602i
251251 −588083. + 1.01859e6i −0.589189 + 1.02050i 0.405150 + 0.914250i 0.367219π0.367219\pi
−0.994339 + 0.106255i 0.966114π0.966114\pi
252252 23149.5i 0.0229636i
253253 −285561. 164868.i −0.280477 0.161933i
254254 4866.15 + 2809.47i 0.00473261 + 0.00273237i
255255 86532.6i 0.0833353i
256256 228759. 396221.i 0.218161 0.377866i
257257 486030. + 841828.i 0.459018 + 0.795043i 0.998909 0.0466919i 0.0148679π-0.0148679\pi
−0.539891 + 0.841735i 0.681535π0.681535\pi
258258 −262469. + 151537.i −0.245488 + 0.141732i
259259 −162899. −0.150893
260260 67377.7 + 27003.4i 0.0618135 + 0.0247734i
261261 −103302. −0.0938656
262262 −122793. + 70894.7i −0.110515 + 0.0638058i
263263 −403494. 698872.i −0.359706 0.623029i 0.628206 0.778047i 0.283790π-0.283790\pi
−0.987912 + 0.155018i 0.950456π0.950456\pi
264264 −143681. + 248862.i −0.126879 + 0.219760i
265265 218778.i 0.191377i
266266 −351057. 202683.i −0.304210 0.175636i
267267 19209.0 + 11090.3i 0.0164902 + 0.00952062i
268268 165756.i 0.140972i
269269 −895225. + 1.55057e6i −0.754313 + 1.30651i 0.191403 + 0.981512i 0.438696π0.438696\pi
−0.945715 + 0.324996i 0.894637π0.894637\pi
270270 −47555.5 82368.6i −0.0397001 0.0687626i
271271 1.06468e6 614693.i 0.880635 0.508435i 0.00976724 0.999952i 0.496891π-0.496891\pi
0.870868 + 0.491517i 0.163558π0.163558\pi
272272 −326445. −0.267539
273273 −46688.0 325592.i −0.0379139 0.264403i
274274 664925. 0.535053
275275 −90073.7 + 52004.1i −0.0718235 + 0.0414673i
276276 42487.0 + 73589.7i 0.0335725 + 0.0581492i
277277 −713522. + 1.23586e6i −0.558737 + 0.967761i 0.438865 + 0.898553i 0.355381π0.355381\pi
−0.997602 + 0.0692084i 0.977953π0.977953\pi
278278 1.39415e6i 1.08192i
279279 −654997. 378163.i −0.503766 0.290850i
280280 −249150. 143847.i −0.189918 0.109649i
281281 1.36246e6i 1.02934i 0.857389 + 0.514668i 0.172085π0.172085\pi
−0.857389 + 0.514668i 0.827915π0.827915\pi
282282 −281902. + 488269.i −0.211094 + 0.365626i
283283 −458620. 794353.i −0.340398 0.589587i 0.644109 0.764934i 0.277228π-0.277228\pi
−0.984507 + 0.175347i 0.943895π0.943895\pi
284284 −103755. + 59902.7i −0.0763328 + 0.0440708i
285285 291389. 0.212501
286286 −196864. + 491206.i −0.142315 + 0.355099i
287287 −256469. −0.183794
288288 119953. 69254.7i 0.0852175 0.0492004i
289289 635974. + 1.10154e6i 0.447914 + 0.775810i
290290 −83194.8 + 144098.i −0.0580900 + 0.100615i
291291 497354.i 0.344297i
292292 −52153.2 30110.7i −0.0357951 0.0206663i
293293 31692.1 + 18297.5i 0.0215666 + 0.0124515i 0.510745 0.859733i 0.329370π-0.329370\pi
−0.489178 + 0.872184i 0.662703π0.662703\pi
294294 620436.i 0.418628i
295295 −168785. + 292345.i −0.112922 + 0.195587i
296296 −260553. 451290.i −0.172849 0.299383i
297297 −105062. + 60657.6i −0.0691122 + 0.0399019i
298298 −1.79501e6 −1.17092
299299 745986. + 949334.i 0.482562 + 0.614103i
300300 26803.2 0.0171942
301301 −335170. + 193510.i −0.213230 + 0.123109i
302302 1042.64 + 1805.90i 0.000657832 + 0.00113940i
303303 −486290. + 842279.i −0.304291 + 0.527047i
304304 1.09927e6i 0.682213i
305305 −262102. 151325.i −0.161332 0.0931452i
306306 −140791. 81286.0i −0.0859553 0.0496263i
307307 2.09577e6i 1.26910i 0.772880 + 0.634552i 0.218815π0.218815\pi
−0.772880 + 0.634552i 0.781185π0.781185\pi
308308 −23780.1 + 41188.3i −0.0142836 + 0.0247398i
309309 851775. + 1.47532e6i 0.507491 + 0.879001i
310310 −1.05501e6 + 609113.i −0.623525 + 0.359992i
311311 729836. 0.427882 0.213941 0.976847i 0.431370π-0.431370\pi
0.213941 + 0.976847i 0.431370π0.431370\pi
312312 827332. 650117.i 0.481164 0.378098i
313313 −2.02399e6 −1.16775 −0.583873 0.811845i 0.698464π-0.698464\pi
−0.583873 + 0.811845i 0.698464π0.698464\pi
314314 1.60212e6 924982.i 0.917001 0.529431i
315315 −60727.8 105184.i −0.0344835 0.0597271i
316316 −91586.0 + 158632.i −0.0515955 + 0.0893660i
317317 170968.i 0.0955578i −0.998858 0.0477789i 0.984786π-0.984786\pi
0.998858 0.0477789i 0.0152143π-0.0152143\pi
318318 355960. + 205513.i 0.197394 + 0.113965i
319319 183798. + 106116.i 0.101126 + 0.0583853i
320320 902151.i 0.492498i
321321 39600.1 68589.5i 0.0214503 0.0371531i
322322 −310103. 537115.i −0.166674 0.288687i
323323 431339. 249034.i 0.230045 0.132816i
324324 31263.2 0.0165452
325325 376980. 54056.8i 0.197975 0.0283884i
326326 1.77348e6 0.924237
327327 851613. 491679.i 0.440426 0.254280i
328328 −410215. 710513.i −0.210536 0.364659i
329329 −359986. + 623513.i −0.183356 + 0.317582i
330330 195404.i 0.0987754i
331331 1.32868e6 + 767114.i 0.666578 + 0.384849i 0.794779 0.606899i 0.207587π-0.207587\pi
−0.128201 + 0.991748i 0.540920π0.540920\pi
332332 −213530. 123281.i −0.106320 0.0613836i
333333 219995.i 0.108718i
334334 549537. 951826.i 0.269545 0.466865i
335335 434827. + 753143.i 0.211692 + 0.366661i
336336 −396806. + 229096.i −0.191748 + 0.110706i
337337 31943.4 0.0153217 0.00766083 0.999971i 0.497561π-0.497561\pi
0.00766083 + 0.999971i 0.497561π0.497561\pi
338338 1.33820e6 1.40135e6i 0.637133 0.667199i
339339 410710. 0.194105
340340 39676.3 22907.1i 0.0186137 0.0107467i
341341 776929. + 1.34568e6i 0.361822 + 0.626695i
342342 273722. 474100.i 0.126545 0.219182i
343343 1.80034e6i 0.826264i
344344 −1.07219e6 619028.i −0.488511 0.282042i
345345 386094. + 222912.i 0.174641 + 0.100829i
346346 793345.i 0.356264i
347347 1.41178e6 2.44528e6i 0.629424 1.09019i −0.358243 0.933628i 0.616624π-0.616624\pi
0.987667 0.156567i 0.0500426π-0.0500426\pi
348348 −27346.3 47365.2i −0.0121046 0.0209658i
349349 850966. 491306.i 0.373980 0.215918i −0.301216 0.953556i 0.597392π-0.597392\pi
0.675196 + 0.737638i 0.264059π0.264059\pi
350350 −195630. −0.0853623
351351 439710. 63051.8i 0.190502 0.0273168i
352352 −284565. −0.122412
353353 2.11683e6 1.22215e6i 0.904168 0.522022i 0.0256180 0.999672i 0.491845π-0.491845\pi
0.878550 + 0.477650i 0.158511π0.158511\pi
354354 317103. + 549239.i 0.134491 + 0.232945i
355355 −314285. + 544357.i −0.132359 + 0.229252i
356356 11743.4i 0.00491099i
357357 −179789. 103801.i −0.0746607 0.0431054i
358358 −1.37944e6 796418.i −0.568846 0.328423i
359359 3.34651e6i 1.37043i 0.728342 + 0.685214i 0.240291π0.240291\pi
−0.728342 + 0.685214i 0.759709π0.759709\pi
360360 194264. 336476.i 0.0790018 0.136835i
361361 −399456. 691877.i −0.161325 0.279422i
362362 3.96580e6 2.28965e6i 1.59059 0.918330i
363363 −1.20022e6 −0.478073
364364 136929. 107599.i 0.0541678 0.0425650i
365365 −315956. −0.124135
366366 −492421. + 284299.i −0.192147 + 0.110936i
367367 −60415.6 104643.i −0.0234144 0.0405550i 0.854081 0.520140i 0.174120π-0.174120\pi
−0.877495 + 0.479585i 0.840787π0.840787\pi
368368 840936. 1.45654e6i 0.323701 0.560666i
369369 346360.i 0.132423i
370370 −306875. 177174.i −0.116535 0.0672817i
371371 454556. + 262438.i 0.171456 + 0.0989901i
372372 400433.i 0.150028i
373373 2.36847e6 4.10230e6i 0.881445 1.52671i 0.0317096 0.999497i 0.489905π-0.489905\pi
0.849735 0.527210i 0.176762π-0.176762\pi
374374 167001. + 289254.i 0.0617361 + 0.106930i
375375 121785. 70312.5i 0.0447214 0.0258199i
376376 −2.30314e6 −0.840139
377377 −480146. 611028.i −0.173988 0.221416i
378378 −228183. −0.0821399
379379 3.14885e6 1.81799e6i 1.12604 0.650119i 0.183104 0.983094i 0.441386π-0.441386\pi
0.942936 + 0.332974i 0.108052π0.108052\pi
380380 77137.3 + 133606.i 0.0274034 + 0.0474642i
381381 −4845.11 + 8391.97i −0.00170998 + 0.00296177i
382382 701190.i 0.245854i
383383 −2.49640e6 1.44130e6i −0.869596 0.502061i −0.00238185 0.999997i 0.500758π-0.500758\pi
−0.867214 + 0.497936i 0.834092π0.834092\pi
384384 −1.04133e6 601213.i −0.360380 0.208066i
385385 249528.i 0.0857962i
386386 202841. 351330.i 0.0692926 0.120018i
387387 −261335. 452645.i −0.0886992 0.153631i
388388 228043. 131661.i 0.0769020 0.0443994i
389389 1.85772e6 0.622452 0.311226 0.950336i 0.399260π-0.399260\pi
0.311226 + 0.950336i 0.399260π0.399260\pi
390390 266171. 664139.i 0.0886135 0.221105i
391391 762039. 0.252078
392392 2.19492e6 1.26724e6i 0.721447 0.416528i
393393 −122262. 211764.i −0.0399311 0.0691626i
394394 −273644. + 473965.i −0.0888066 + 0.153818i
395395 961028.i 0.309915i
396396 −55624.5 32114.8i −0.0178250 0.0102912i
397397 −922605. 532666.i −0.293792 0.169621i 0.345859 0.938287i 0.387588π-0.387588\pi
−0.639651 + 0.768666i 0.720921π0.720921\pi
398398 1.11738e6i 0.353584i
399399 349539. 605420.i 0.109917 0.190381i
400400 −265255. 459434.i −0.0828920 0.143573i
401401 1.68649e6 973694.i 0.523748 0.302386i −0.214719 0.976676i 0.568884π-0.568884\pi
0.738467 + 0.674290i 0.235550π0.235550\pi
402402 1.63385e6 0.504252
403403 −807596. 5.63200e6i −0.247703 1.72743i
404404 −514927. −0.156961
405405 142050. 82012.5i 0.0430331 0.0248452i
406406 199595. + 345708.i 0.0600944 + 0.104086i
407407 −225988. + 391422.i −0.0676237 + 0.117128i
408408 664107.i 0.197509i
409409 −2.09310e6 1.20845e6i −0.618704 0.357209i 0.157660 0.987493i 0.449605π-0.449605\pi
−0.776364 + 0.630285i 0.782938π0.782938\pi
410410 −483145. 278944.i −0.141944 0.0819515i
411411 1.14670e6i 0.334848i
412412 −450968. + 781099.i −0.130889 + 0.226706i
413413 404937. + 701371.i 0.116819 + 0.202336i
414414 725370. 418793.i 0.207998 0.120088i
415415 −1.29361e6 −0.368709
416416 967180. + 387623.i 0.274015 + 0.109819i
417417 2.40429e6 0.677091
418418 −974030. + 562357.i −0.272667 + 0.157424i
419419 1.71640e6 + 2.97289e6i 0.477621 + 0.827265i 0.999671 0.0256506i 0.00816573π-0.00816573\pi
−0.522050 + 0.852915i 0.674832π0.674832\pi
420420 32152.0 55688.9i 0.00889375 0.0154044i
421421 6.32471e6i 1.73914i −0.493806 0.869572i 0.664395π-0.664395\pi
0.493806 0.869572i 0.335605π-0.335605\pi
422422 5.56887e6 + 3.21519e6i 1.52225 + 0.878871i
423423 −842051. 486158.i −0.228817 0.132107i
424424 1.67904e6i 0.453574i
425425 120184. 208165.i 0.0322756 0.0559030i
426426 590458. + 1.02270e6i 0.157640 + 0.273040i
427427 −628815. + 363047.i −0.166899 + 0.0963591i
428428 41932.2 0.0110647
429429 −847116. 339504.i −0.222228 0.0890639i
430430 −841871. −0.219571
431431 3.52739e6 2.03654e6i 0.914662 0.528080i 0.0327339 0.999464i 0.489579π-0.489579\pi
0.881928 + 0.471384i 0.156245π0.156245\pi
432432 −309393. 535884.i −0.0797629 0.138153i
433433 −1.18073e6 + 2.04508e6i −0.302643 + 0.524193i −0.976734 0.214455i 0.931202π-0.931202\pi
0.674091 + 0.738649i 0.264536π0.264536\pi
434434 2.92267e6i 0.744828i
435435 −248505. 143475.i −0.0629670 0.0363540i
436436 450882. + 260317.i 0.113592 + 0.0655822i
437437 2.56609e6i 0.642788i
438438 −296800. + 514072.i −0.0739227 + 0.128038i
439439 −495600. 858404.i −0.122735 0.212584i 0.798110 0.602512i 0.205833π-0.205833\pi
−0.920845 + 0.389928i 0.872500π0.872500\pi
440440 −691284. + 399113.i −0.170226 + 0.0982797i
441441 1.06998e6 0.261987
442442 −173592. 1.21060e6i −0.0422644 0.294743i
443443 −7.82126e6 −1.89351 −0.946754 0.321958i 0.895659π-0.895659\pi
−0.946754 + 0.321958i 0.895659π0.895659\pi
444444 100870. 58237.6i 0.0242832 0.0140199i
445445 30806.4 + 53358.2i 0.00737464 + 0.0127732i
446446 −802122. + 1.38932e6i −0.190943 + 0.330723i
447447 3.09560e6i 0.732785i
448448 −1.87440e6 1.08219e6i −0.441232 0.254746i
449449 6.07750e6 + 3.50884e6i 1.42269 + 0.821388i 0.996528 0.0832613i 0.0265336π-0.0265336\pi
0.426157 + 0.904649i 0.359867π0.359867\pi
450450 264197.i 0.0615032i
451451 −355795. + 616256.i −0.0823681 + 0.142666i
452452 108724. + 188316.i 0.0250311 + 0.0433552i
453453 −3114.38 + 1798.09i −0.000713060 + 0.000411686i
454454 −6.21851e6 −1.41595
455455 339897. 848097.i 0.0769696 0.192051i
456456 2.23631e6 0.503639
457457 −5.51398e6 + 3.18350e6i −1.23502 + 0.713041i −0.968073 0.250669i 0.919349π-0.919349\pi
−0.266950 + 0.963710i 0.586016π0.586016\pi
458458 −779284. 1.34976e6i −0.173593 0.300672i
459459 140183. 242804.i 0.0310572 0.0537927i
460460 236039.i 0.0520103i
461461 −1.20272e6 694388.i −0.263579 0.152177i 0.362387 0.932028i 0.381962π-0.381962\pi
−0.625966 + 0.779850i 0.715295π0.715295\pi
462462 405991. + 234399.i 0.0884936 + 0.0510918i
463463 799163.i 0.173254i −0.996241 0.0866269i 0.972391π-0.972391\pi
0.996241 0.0866269i 0.0276088π-0.0276088\pi
464464 −541259. + 937489.i −0.116711 + 0.202149i
465465 −1.05045e6 1.81944e6i −0.225291 0.390216i
466466 −4.88082e6 + 2.81794e6i −1.04119 + 0.601129i
467467 −5.06728e6 −1.07518 −0.537592 0.843205i 0.680666π-0.680666\pi
−0.537592 + 0.843205i 0.680666π0.680666\pi
468468 145311. + 184921.i 0.0306679 + 0.0390277i
469469 2.08641e6 0.437993
470470 −1.35630e6 + 783062.i −0.283212 + 0.163513i
471471 1.59519e6 + 2.76295e6i 0.331329 + 0.573879i
472472 −1.29537e6 + 2.24364e6i −0.267632 + 0.463552i
473473 1.07381e6i 0.220687i
474474 1.56363e6 + 902760.i 0.319659 + 0.184555i
475475 700973. + 404707.i 0.142550 + 0.0823013i
476476 109914.i 0.0222349i
477477 −354421. + 613875.i −0.0713219 + 0.123533i
478478 3.49290e6 + 6.04988e6i 0.699224 + 1.21109i
479479 −2.79367e6 + 1.61292e6i −0.556334 + 0.321200i −0.751673 0.659536i 0.770753π-0.770753\pi
0.195339 + 0.980736i 0.437419π0.437419\pi
480480 384749. 0.0762209
481481 1.30127e6 1.02253e6i 0.256450 0.201519i
482482 5.54307e6 1.08676
483483 926288. 534792.i 0.180667 0.104308i
484484 −317725. 550316.i −0.0616507 0.106782i
485485 690770. 1.19645e6i 0.133346 0.230961i
486486 308160.i 0.0591814i
487487 −4.20416e6 2.42727e6i −0.803261 0.463763i 0.0413489 0.999145i 0.486834π-0.486834\pi
−0.844610 + 0.535382i 0.820168π0.820168\pi
488488 −2.01154e6 1.16136e6i −0.382366 0.220759i
489489 3.05848e6i 0.578407i
490490 861716. 1.49254e6i 0.162134 0.280824i
491491 −2.82546e6 4.89385e6i −0.528915 0.916108i −0.999431 0.0337164i 0.989266π-0.989266\pi
0.470516 0.882391i 0.344068π-0.344068\pi
492492 158811. 91689.3i 0.0295779 0.0170768i
493493 −490478. −0.0908871
494494 4.07655e6 584554.i 0.751581 0.107772i
495495 −336986. −0.0618158
496496 −6.86384e6 + 3.96284e6i −1.25275 + 0.723274i
497497 754007. + 1.30598e6i 0.136926 + 0.237162i
498498 −1.21518e6 + 2.10475e6i −0.219567 + 0.380301i
499499 1.00718e7i 1.81074i −0.424623 0.905370i 0.639593π-0.639593\pi
0.424623 0.905370i 0.360407π-0.360407\pi
500500 64478.4 + 37226.6i 0.0115342 + 0.00665930i
501501 1.64148e6 + 947711.i 0.292175 + 0.168687i
502502 6.13808e6i 1.08711i
503503 1.50537e6 2.60738e6i 0.265292 0.459499i −0.702348 0.711834i 0.747865π-0.747865\pi
0.967640 + 0.252335i 0.0811984π0.0811984\pi
504504 −466064. 807247.i −0.0817277 0.141557i
505505 −2.33966e6 + 1.35081e6i −0.408249 + 0.235703i
506506 −1.72080e6 −0.298782
507507 2.41672e6 + 2.30781e6i 0.417548 + 0.398732i
508508 −5130.43 −0.000882053
509509 −8.43937e6 + 4.87247e6i −1.44383 + 0.833595i −0.998102 0.0615747i 0.980388π-0.980388\pi
−0.445726 + 0.895169i 0.647054π0.647054\pi
510510 −225794. 391087.i −0.0384404 0.0665807i
511511 −379009. + 656463.i −0.0642092 + 0.111214i
512512 6.66295e6i 1.12329i
513513 817615. + 472050.i 0.137169 + 0.0791945i
514514 4.39326e6 + 2.53645e6i 0.733465 + 0.423466i
515515 4.73208e6i 0.786202i
516516 138362. 239651.i 0.0228767 0.0396236i
517517 998804. + 1.72998e6i 0.164344 + 0.284652i
518518 −736231. + 425063.i −0.120556 + 0.0696032i
519519 −1.36817e6 −0.222958
520520 2.89319e6 414866.i 0.469211 0.0672822i
521521 134535. 0.0217140 0.0108570 0.999941i 0.496544π-0.496544\pi
0.0108570 + 0.999941i 0.496544π0.496544\pi
522522 −466876. + 269551.i −0.0749939 + 0.0432977i
523523 927891. + 1.60716e6i 0.148335 + 0.256923i 0.930612 0.366007i 0.119275π-0.119275\pi
−0.782277 + 0.622930i 0.785942π0.785942\pi
524524 64731.1 112118.i 0.0102988 0.0178380i
525525 337377.i 0.0534216i
526526 −3.64721e6 2.10572e6i −0.574774 0.331846i
527527 −3.10994e6 1.79552e6i −0.487781 0.281621i
528528 1.27128e6i 0.198453i
529529 1.25513e6 2.17394e6i 0.195006 0.337760i
530530 570871. + 988777.i 0.0882771 + 0.152900i
531531 −947197. + 546865.i −0.145782 + 0.0841673i
532532 370123. 0.0566980
533533 2.04872e6 1.60988e6i 0.312366 0.245457i
534534 115754. 0.0175664
535535 190526. 110000.i 0.0287786 0.0166154i
536536 3.33714e6 + 5.78010e6i 0.501722 + 0.869008i
537537 1.37347e6 2.37893e6i 0.205534 0.355996i
538538 9.34385e6i 1.39178i
539539 −1.90374e6 1.09913e6i −0.282252 0.162958i
540540 75207.6 + 43421.1i 0.0110988 + 0.00640791i
541541 7.51174e6i 1.10344i 0.834031 + 0.551718i 0.186028π0.186028\pi
−0.834031 + 0.551718i 0.813972π0.813972\pi
542542 3.20791e6 5.55626e6i 0.469055 0.812427i
543543 3.94865e6 + 6.83927e6i 0.574711 + 0.995428i
544544 569537. 328823.i 0.0825135 0.0476392i
545545 2.73155e6 0.393929
546546 −1.06059e6 1.34970e6i −0.152254 0.193756i
547547 −1.27898e7 −1.82766 −0.913829 0.406099i 0.866889π-0.866889\pi
−0.913829 + 0.406099i 0.866889π0.866889\pi
548548 −525779. + 303559.i −0.0747914 + 0.0431808i
549549 −490292. 849211.i −0.0694263 0.120250i
550550 −271395. + 470069.i −0.0382555 + 0.0662605i
551551 1.65163e6i 0.231758i
552552 2.96314e6 + 1.71077e6i 0.413908 + 0.238970i
553553 1.99673e6 + 1.15281e6i 0.277655 + 0.160304i
554554 7.44733e6i 1.03092i
555555 305548. 529225.i 0.0421063 0.0729303i
556556 636470. + 1.10240e6i 0.0873155 + 0.151235i
557557 3.85138e6 2.22360e6i 0.525991 0.303681i −0.213391 0.976967i 0.568451π-0.568451\pi
0.739383 + 0.673286i 0.235118π0.235118\pi
558558 −3.94705e6 −0.536645
559559 1.46271e6 3.64968e6i 0.197983 0.493998i
560560 −1.27276e6 −0.171504
561561 −498836. + 288003.i −0.0669192 + 0.0386358i
562562 3.55514e6 + 6.15769e6i 0.474806 + 0.822388i
563563 3.75805e6 6.50913e6i 0.499679 0.865470i −0.500321 0.865840i 0.666785π-0.666785\pi
1.00000 0.000370381i 0.000117896π0.000117896\pi
564564 514788.i 0.0681445i
565565 988015. + 570431.i 0.130209 + 0.0751765i
566566 −4.14550e6 2.39341e6i −0.543922 0.314033i
567567 393516.i 0.0514049i
568568 −2.41202e6 + 4.17775e6i −0.313697 + 0.543339i
569569 −7.19533e6 1.24627e7i −0.931688 1.61373i −0.780437 0.625235i 0.785003π-0.785003\pi
−0.151251 0.988495i 0.548330π-0.548330\pi
570570 1.31695e6 760339.i 0.169778 0.0980212i
571571 3.62318e6 0.465050 0.232525 0.972590i 0.425301π-0.425301\pi
0.232525 + 0.972590i 0.425301π0.425301\pi
572572 −68583.7 478288.i −0.00876457 0.0611223i
573573 −1.20925e6 −0.153861
574574 −1.15912e6 + 669220.i −0.146842 + 0.0847792i
575575 619199. + 1.07248e6i 0.0781017 + 0.135276i
576576 1.46148e6 2.53137e6i 0.183543 0.317906i
577577 3.39602e6i 0.424649i −0.977199 0.212325i 0.931897π-0.931897\pi
0.977199 0.212325i 0.0681034π-0.0681034\pi
578578 5.74862e6 + 3.31897e6i 0.715722 + 0.413222i
579579 605891. + 349811.i 0.0751100 + 0.0433648i
580580 151924.i 0.0187524i
581581 −1.55177e6 + 2.68774e6i −0.190716 + 0.330329i
582582 −1.29777e6 2.24781e6i −0.158815 0.275076i
583583 1.26119e6 728151.i 0.153678 0.0887258i
584584 −2.42485e6 −0.294207
585585 1.14535e6 + 459029.i 0.138372 + 0.0554563i
586586 190978. 0.0229742
587587 −8.17357e6 + 4.71901e6i −0.979076 + 0.565270i −0.901991 0.431755i 0.857895π-0.857895\pi
−0.0770848 + 0.997025i 0.524561π0.524561\pi
588588 283248. + 490600.i 0.0337849 + 0.0585172i
589589 6.04623e6 1.04724e7i 0.718119 1.24382i
590590 1.76169e6i 0.208352i
591591 −817383. 471916.i −0.0962624 0.0555771i
592592 −1.99651e6 1.15268e6i −0.234135 0.135178i
593593 7.96111e6i 0.929688i −0.885393 0.464844i 0.846110π-0.846110\pi
0.885393 0.464844i 0.153890π-0.153890\pi
594594 −316555. + 548289.i −0.0368114 + 0.0637592i
595595 −288336. 499413.i −0.0333893 0.0578319i
596596 1.41937e6 819476.i 0.163675 0.0944976i
597597 −1.92699e6 −0.221280
598598 5.84867e6 + 2.34401e6i 0.668812 + 0.268044i
599599 −1.15336e7 −1.31341 −0.656703 0.754149i 0.728050π-0.728050\pi
−0.656703 + 0.754149i 0.728050π0.728050\pi
600600 934655. 539623.i 0.105992 0.0611945i
601601 −302621. 524156.i −0.0341754 0.0591935i 0.848432 0.529305i 0.177547π-0.177547\pi
−0.882607 + 0.470111i 0.844214π0.844214\pi
602602 −1.00988e6 + 1.74916e6i −0.113573 + 0.196715i
603603 2.81768e6i 0.315572i
604604 −1648.89 951.989i −0.000183908 0.000106179i
605605 −2.88728e6 1.66697e6i −0.320701 0.185157i
606606 5.07562e6i 0.561445i
607607 537341. 930702.i 0.0591941 0.102527i −0.834910 0.550387i 0.814480π-0.814480\pi
0.894104 + 0.447860i 0.147814π0.147814\pi
608608 1.10727e6 + 1.91786e6i 0.121478 + 0.210405i
609609 −596195. + 344213.i −0.0651396 + 0.0376084i
610610 −1.57944e6 −0.171862
611611 −1.03823e6 7.24038e6i −0.112510 0.784618i
612612 148438. 0.0160202
613613 4.71726e6 2.72351e6i 0.507036 0.292737i −0.224579 0.974456i 0.572101π-0.572101\pi
0.731614 + 0.681719i 0.238767π0.238767\pi
614614 5.46861e6 + 9.47190e6i 0.585404 + 1.01395i
615615 481056. 833213.i 0.0512870 0.0888318i
616616 1.91504e6i 0.203342i
617617 −5.81016e6 3.35450e6i −0.614434 0.354744i 0.160265 0.987074i 0.448765π-0.448765\pi
−0.774699 + 0.632330i 0.782099π0.782099\pi
618618 7.69926e6 + 4.44517e6i 0.810920 + 0.468185i
619619 4.89152e6i 0.513118i −0.966529 0.256559i 0.917411π-0.917411\pi
0.966529 0.256559i 0.0825889π-0.0825889\pi
620620 556157. 963292.i 0.0581056 0.100642i
621621 722234. + 1.25095e6i 0.0751534 + 0.130170i
622622 3.29852e6 1.90440e6i 0.341856 0.197371i
623623 147817. 0.0152582
624624 1.73169e6 4.32084e6i 0.178037 0.444229i
625625 390625. 0.0400000
626626 −9.14753e6 + 5.28133e6i −0.932970 + 0.538651i
627627 −969819. 1.67978e6i −0.0985194 0.170641i
628628 −844565. + 1.46283e6i −0.0854543 + 0.148011i
629629 1.04454e6i 0.105268i
630630 −548923. 316921.i −0.0551011 0.0318126i
631631 −4.34348e6 2.50771e6i −0.434275 0.250729i 0.266891 0.963727i 0.414004π-0.414004\pi
−0.701166 + 0.712998i 0.747337π0.747337\pi
632632 7.37555e6i 0.734516i
633633 −5.54479e6 + 9.60386e6i −0.550017 + 0.952657i
634634 −446116. 772696.i −0.0440783 0.0763459i
635635 −23311.0 + 13458.6i −0.00229418 + 0.00132454i
636636 −375293. −0.0367898
637637 4.97326e6 + 6.32892e6i 0.485616 + 0.617989i
638638 1.10758e6 0.107726
639639 −1.76372e6 + 1.01828e6i −0.170874 + 0.0986543i
640640 −1.67004e6 2.89259e6i −0.161167 0.279150i
641641 2.33486e6 4.04409e6i 0.224448 0.388755i −0.731706 0.681620i 0.761276π-0.761276\pi
0.956154 + 0.292866i 0.0946089π0.0946089\pi
642642 413324.i 0.0395779i
643643 1.25679e7 + 7.25609e6i 1.19877 + 0.692110i 0.960281 0.279035i 0.0900146π-0.0900146\pi
0.238489 + 0.971145i 0.423348π0.423348\pi
644644 490418. + 283143.i 0.0465964 + 0.0269024i
645645 1.45186e6i 0.137412i
646646 1.29964e6 2.25103e6i 0.122529 0.212227i
647647 −3.81368e6 6.60549e6i −0.358166 0.620361i 0.629489 0.777010i 0.283264π-0.283264\pi
−0.987654 + 0.156648i 0.949931π0.949931\pi
648648 1.09018e6 629417.i 0.101991 0.0588845i
649649 2.24705e6 0.209411
650650 1.56272e6 1.22799e6i 0.145077 0.114002i
651651 −5.04033e6 −0.466129
652652 −1.40235e6 + 809649.i −0.129193 + 0.0745895i
653653 8.85402e6 + 1.53356e7i 0.812564 + 1.40740i 0.911064 + 0.412265i 0.135262π0.135262\pi
−0.0985004 + 0.995137i 0.531405π0.531405\pi
654654 2.56593e6 4.44433e6i 0.234585 0.406314i
655655 679235.i 0.0618610i
656656 −3.14330e6 1.81479e6i −0.285185 0.164652i
657657 −886549. 511849.i −0.0801289 0.0462625i
658658 3.75732e6i 0.338309i
659659 −256484. + 444243.i −0.0230063 + 0.0398480i −0.877299 0.479944i 0.840657π-0.840657\pi
0.854293 + 0.519792i 0.173990π0.173990\pi
660660 −89207.9 154513.i −0.00797156 0.0138071i
661661 1.61427e7 9.32002e6i 1.43706 0.829685i 0.439412 0.898286i 0.355187π-0.355187\pi
0.997644 + 0.0686013i 0.0218536π0.0218536\pi
662662 8.00670e6 0.710082
663663 2.08775e6 299371.i 0.184457 0.0264500i
664664 −9.92802e6 −0.873861
665665 1.68172e6 970942.i 0.147469 0.0851411i
666666 −574045. 994275.i −0.0501488 0.0868602i
667667 1.26349e6 2.18843e6i 0.109966 0.190467i
668668 1.00352e6i 0.0870133i
669669 −2.39596e6 1.38331e6i −0.206973 0.119496i
670670 3.93044e6 + 2.26924e6i 0.338263 + 0.195296i
671671 2.01459e6i 0.172735i
672672 461529. 799392.i 0.0394254 0.0682868i
673673 3.16996e6 + 5.49053e6i 0.269784 + 0.467280i 0.968806 0.247821i 0.0797143π-0.0797143\pi
−0.699022 + 0.715100i 0.746381π0.746381\pi
674674 144369. 83351.7i 0.0122412 0.00706748i
675675 455625. 0.0384900
676676 −418402. + 1.71903e6i −0.0352150 + 0.144682i
677677 −8.47267e6 −0.710475 −0.355237 0.934776i 0.615600π-0.615600\pi
−0.355237 + 0.934776i 0.615600π0.615600\pi
678678 1.85622e6 1.07169e6i 0.155080 0.0895354i
679679 −1.65724e6 2.87043e6i −0.137947 0.238931i
680680 922370. 1.59759e6i 0.0764950 0.132493i
681681 1.07242e7i 0.886129i
682682 7.02272e6 + 4.05457e6i 0.578156 + 0.333798i
683683 806023. + 465357.i 0.0661143 + 0.0381711i 0.532693 0.846309i 0.321180π-0.321180\pi
−0.466578 + 0.884480i 0.654513π0.654513\pi
684684 499849.i 0.0408506i
685685 −1.59265e6 + 2.75854e6i −0.129686 + 0.224623i
686686 −4.69773e6 8.13671e6i −0.381134 0.660144i
687687 2.32775e6 1.34392e6i 0.188167 0.108638i
688688 −5.47715e6 −0.441147
689689 −5.27841e6 + 756892.i −0.423599 + 0.0607416i
690690 2.32663e6 0.186039
691691 2.89151e6 1.66942e6i 0.230372 0.133006i −0.380371 0.924834i 0.624204π-0.624204\pi
0.610744 + 0.791828i 0.290871π0.290871\pi
692692 −362186. 627325.i −0.0287519 0.0497998i
693693 −404236. + 700157.i −0.0319744 + 0.0553812i
694694 1.47354e7i 1.16135i
695695 5.78383e6 + 3.33930e6i 0.454207 + 0.262236i
696696 −1.90719e6 1.10112e6i −0.149235 0.0861609i
697697 1.64452e6i 0.128221i
698698 2.56399e6 4.44095e6i 0.199194 0.345015i
699699 −4.85972e6 8.41728e6i −0.376200 0.651597i
700700 154691. 89311.2i 0.0119322 0.00688907i
701701 −7.31359e6 −0.562128 −0.281064 0.959689i 0.590687π-0.590687\pi
−0.281064 + 0.959689i 0.590687π0.590687\pi
702702 1.82276e6 1.43233e6i 0.139601 0.109698i
703703 3.51737e6 0.268429
704704 −5.20065e6 + 3.00259e6i −0.395481 + 0.228331i
705705 −1.35044e6 2.33903e6i −0.102330 0.177241i
706706 6.37807e6 1.10471e7i 0.481590 0.834138i
707707 6.48149e6i 0.487671i
708708 −501489. 289535.i −0.0375992 0.0217079i
709709 4.35669e6 + 2.51534e6i 0.325492 + 0.187923i 0.653838 0.756634i 0.273158π-0.273158\pi
−0.328346 + 0.944558i 0.606491π0.606491\pi
710710 3.28032e6i 0.244214i
711711 −1.55687e6 + 2.69657e6i −0.115499 + 0.200050i
712712 236428. + 409505.i 0.0174783 + 0.0302733i
713713 1.60227e7 9.25069e6i 1.18035 0.681476i
714714 −1.08342e6 −0.0795335
715715 −1.56631e6 1.99327e6i −0.114581 0.145815i
716716 1.45436e6 0.106020
717717 −1.04334e7 + 6.02372e6i −0.757928 + 0.437590i
718718 8.73225e6 + 1.51247e7i 0.632143 + 1.09490i
719719 −5.16627e6 + 8.94823e6i −0.372696 + 0.645528i −0.989979 0.141213i 0.954900π-0.954900\pi
0.617283 + 0.786741i 0.288233π0.288233\pi
720720 1.71885e6i 0.123568i
721721 9.83185e6 + 5.67642e6i 0.704364 + 0.406665i
722722 −3.61071e6 2.08465e6i −0.257780 0.148830i
723723 9.55936e6i 0.680116i
724724 −2.09059e6 + 3.62102e6i −0.148226 + 0.256734i
725725 −398541. 690293.i −0.0281597 0.0487740i
726726 −5.42444e6 + 3.13180e6i −0.381956 + 0.220522i
727727 −2.49303e7 −1.74941 −0.874706 0.484654i 0.838945π-0.838945\pi
−0.874706 + 0.484654i 0.838945π0.838945\pi
728728 2.60859e6 6.50884e6i 0.182422 0.455172i
729729 531441. 0.0370370
730730 −1.42798e6 + 824443.i −0.0991777 + 0.0572603i
731731 −1.24082e6 2.14916e6i −0.0858847 0.148757i
732732 259583. 449610.i 0.0179060 0.0310141i
733733 7.08686e6i 0.487185i 0.969878 + 0.243593i 0.0783260π0.0783260\pi
−0.969878 + 0.243593i 0.921674π0.921674\pi
734734 −546101. 315292.i −0.0374139 0.0216009i
735735 2.57397e6 + 1.48608e6i 0.175746 + 0.101467i
736736 3.38824e6i 0.230558i
737737 2.89444e6 5.01331e6i 0.196289 0.339982i
738738 −903778. 1.56539e6i −0.0610830 0.105799i
739739 2.32084e6 1.33994e6i 0.156327 0.0902553i −0.419796 0.907619i 0.637898π-0.637898\pi
0.576123 + 0.817363i 0.304565π0.304565\pi
740740 323542. 0.0217196
741741 1.00810e6 + 7.03027e6i 0.0674463 + 0.470356i
742742 2.73918e6 0.182646
743743 −1.18974e7 + 6.86897e6i −0.790643 + 0.456478i −0.840189 0.542294i 0.817556π-0.817556\pi
0.0495461 + 0.998772i 0.484223π0.484223\pi
744744 −8.06185e6 1.39635e7i −0.533952 0.924832i
745745 4.29945e6 7.44687e6i 0.283806 0.491567i
746746 2.47207e7i 1.62635i
747747 −3.62978e6 2.09565e6i −0.238001 0.137410i
748748 −264106. 152482.i −0.0172594 0.00996469i
749749 527809.i 0.0343773i
750750 366941. 635560.i 0.0238201 0.0412576i
751751 −2.59564e6 4.49579e6i −0.167937 0.290875i 0.769758 0.638336i 0.220377π-0.220377\pi
−0.937694 + 0.347462i 0.887044π0.887044\pi
752752 −8.82401e6 + 5.09455e6i −0.569012 + 0.328519i
753753 −1.05855e7 −0.680337
754754 −3.76443e6 1.50870e6i −0.241141 0.0966436i
755755 −9989.38 −0.000637781
756756 180432. 104173.i 0.0114818 0.00662901i
757757 −3.81097e6 6.60080e6i −0.241711 0.418656i 0.719491 0.694502i 0.244375π-0.244375\pi
−0.961202 + 0.275846i 0.911042π0.911042\pi
758758 9.48756e6 1.64329e7i 0.599766 1.03882i
759759 2.96763e6i 0.186985i
760760 5.37972e6 + 3.10598e6i 0.337851 + 0.195059i
761761 1.01723e7 + 5.87296e6i 0.636731 + 0.367617i 0.783354 0.621576i 0.213507π-0.213507\pi
−0.146623 + 0.989192i 0.546840π0.546840\pi
762762 50570.5i 0.00315507i
763763 3.27666e6 5.67534e6i 0.203761 0.352924i
764764 −320114. 554455.i −0.0198414 0.0343663i
765765 674455. 389397.i 0.0416677 0.0240568i
766766 −1.50434e7 −0.926351
767767 −7.63726e6 3.06084e6i −0.468759 0.187867i
768768 4.11765e6 0.251911
769769 1.92883e7 1.11361e7i 1.17619 0.679074i 0.221060 0.975260i 0.429048π-0.429048\pi
0.955130 + 0.296186i 0.0957149π0.0957149\pi
770770 651109. + 1.12775e6i 0.0395755 + 0.0685468i
771771 −4.37427e6 + 7.57645e6i −0.265014 + 0.459018i
772772 370412.i 0.0223687i
773773 1.65192e7 + 9.53738e6i 0.994354 + 0.574090i 0.906573 0.422049i 0.138689π-0.138689\pi
0.0877810 + 0.996140i 0.472022π0.472022\pi
774774 −2.36223e6 1.36383e6i −0.141732 0.0818292i
775775 5.83585e6i 0.349020i
776776 5.30141e6 9.18231e6i 0.316036 0.547391i
777777 −733048. 1.26968e6i −0.0435592 0.0754467i
778778 8.39603e6 4.84745e6i 0.497308 0.287121i
779779 5.53776e6 0.326957
780780 92729.1 + 646673.i 0.00545732 + 0.0380582i
781781 4.18409e6 0.245456
782782 3.44407e6 1.98843e6i 0.201398 0.116277i
783783 −464858. 805157.i −0.0270967 0.0469328i
784784 5.60626e6 9.71033e6i 0.325749 0.564214i
785785 8.86217e6i 0.513293i
786786 −1.10514e6 638052.i −0.0638058 0.0368383i
787787 1.20781e7 + 6.97327e6i 0.695121 + 0.401328i 0.805528 0.592558i 0.201882π-0.201882\pi
−0.110407 + 0.993886i 0.535215π0.535215\pi
788788 499707.i 0.0286682i
789789 3.63145e6 6.28985e6i 0.207676 0.359706i
790790 2.50767e6 + 4.34340e6i 0.142956 + 0.247607i
791791 2.37037e6 1.36853e6i 0.134702 0.0777704i
792792 −2.58625e6 −0.146507
793793 2.74420e6 6.84720e6i 0.154964 0.386661i
794794 −5.55967e6 −0.312966
795795 −1.70521e6 + 984502.i −0.0956884 + 0.0552457i
796796 −510117. 883548.i −0.0285356 0.0494251i
797797 1.63419e7 2.83050e7i 0.911290 1.57840i 0.0990448 0.995083i 0.468421π-0.468421\pi
0.812245 0.583317i 0.198245π-0.198245\pi
798798 3.64829e6i 0.202807i
799799 −3.99807e6 2.30829e6i −0.221556 0.127915i
800800 925561. + 534373.i 0.0511305 + 0.0295202i
801801 199625.i 0.0109935i
802802 5.08143e6 8.80130e6i 0.278965 0.483182i
803803 1.05159e6 + 1.82140e6i 0.0575514 + 0.0996819i
804804 −1.29194e6 + 745903.i −0.0704860 + 0.0406951i
805805 2.97107e6 0.161593
806806 −1.83459e7 2.33467e7i −0.994719 1.26587i
807807 −1.61140e7 −0.871005
808808 −1.79561e7 + 1.03669e7i −0.967572 + 0.558628i
809809 9.71774e6 + 1.68316e7i 0.522028 + 0.904179i 0.999672 + 0.0256256i 0.00815779π0.00815779\pi
−0.477643 + 0.878554i 0.658509π0.658509\pi
810810 428000. 741318.i 0.0229209 0.0397001i
811811 151625.i 0.00809503i −0.999992 0.00404751i 0.998712π-0.998712\pi
0.999992 0.00404751i 0.00128837π-0.00128837\pi
812812 −315652. 182242.i −0.0168004 0.00969970i
813813 9.58212e6 + 5.53224e6i 0.508435 + 0.293545i
814814 2.35873e6i 0.124772i
815815 −4.24789e6 + 7.35757e6i −0.224016 + 0.388008i
816816 −1.46900e6 2.54439e6i −0.0772320 0.133770i
817817 7.23708e6 4.17833e6i 0.379322 0.219002i
818818 −1.26132e7 −0.659084
819819 2.32764e6 1.82906e6i 0.121257 0.0952836i
820820 509385. 0.0264552
821821 −1.13403e6 + 654735.i −0.0587176 + 0.0339006i −0.529071 0.848577i 0.677460π-0.677460\pi
0.470354 + 0.882478i 0.344126π0.344126\pi
822822 2.99216e6 + 5.18258e6i 0.154456 + 0.267526i
823823 3.30306e6 5.72107e6i 0.169988 0.294427i −0.768428 0.639937i 0.778961π-0.778961\pi
0.938415 + 0.345510i 0.112294π0.112294\pi
824824 3.63170e7i 1.86334i
825825 −810663. 468037.i −0.0414673 0.0239412i
826826 3.66026e6 + 2.11325e6i 0.186664 + 0.107771i
827827 2.30238e7i 1.17062i 0.810811 + 0.585308i 0.199026π0.199026\pi
−0.810811 + 0.585308i 0.800974π0.800974\pi
828828 −382383. + 662307.i −0.0193831 + 0.0335725i
829829 −7.29332e6 1.26324e7i −0.368586 0.638410i 0.620759 0.784002i 0.286825π-0.286825\pi
−0.989345 + 0.145592i 0.953491π0.953491\pi
830830 −5.84654e6 + 3.37550e6i −0.294580 + 0.170076i
831831 −1.28434e7 −0.645174
832832 2.17660e7 3.12111e6i 1.09011 0.156315i
833833 5.08028e6 0.253674
834834 1.08663e7 6.27366e6i 0.540962 0.312324i
835835 2.63253e6 + 4.55968e6i 0.130664 + 0.226317i
836836 513466. 889349.i 0.0254095 0.0440105i
837837 6.80693e6i 0.335844i
838838 1.55147e7 + 8.95741e6i 0.763191 + 0.440628i
839839 1.31511e7 + 7.59280e6i 0.644997 + 0.372389i 0.786537 0.617543i 0.211872π-0.211872\pi
−0.141540 + 0.989933i 0.545205π0.545205\pi
840840 2.58925e6i 0.126612i
841841 9.44234e6 1.63546e7i 0.460352 0.797352i
842842 −1.65034e7 2.85848e7i −0.802221 1.38949i
843843 −1.06193e7 + 6.13106e6i −0.514668 + 0.297144i
844844 −5.87132e6 −0.283713
845845 2.60843e6 + 8.90829e6i 0.125672 + 0.429193i
846846 −5.07424e6 −0.243750
847847 −6.92694e6 + 3.99927e6i −0.331767 + 0.191546i
848848 3.71404e6 + 6.43291e6i 0.177361 + 0.307198i
849849 4.12758e6 7.14918e6i 0.196529 0.340398i
850850 1.25441e6i 0.0595516i
851851 4.66056e6 + 2.69078e6i 0.220604 + 0.127366i
852852 −933791. 539124.i −0.0440708 0.0254443i
853853 1.91131e7i 0.899412i 0.893177 + 0.449706i 0.148471π0.148471\pi
−0.893177 + 0.449706i 0.851529π0.851529\pi
854854 −1.89464e6 + 3.28161e6i −0.0888958 + 0.153972i
855855 1.31125e6 + 2.27115e6i 0.0613438 + 0.106251i
856856 1.46222e6 844214.i 0.0682070 0.0393793i
857857 −694424. −0.0322978 −0.0161489 0.999870i 0.505141π-0.505141\pi
−0.0161489 + 0.999870i 0.505141π0.505141\pi
858858 −4.71446e6 + 676026.i −0.218632 + 0.0313506i
859859 3.06363e7 1.41662 0.708310 0.705902i 0.249458π-0.249458\pi
0.708310 + 0.705902i 0.249458π0.249458\pi
860860 665696. 384340.i 0.0306923 0.0177202i
861861 −1.15411e6 1.99898e6i −0.0530567 0.0918968i
862862 1.06281e7 1.84085e7i 0.487179 0.843819i
863863 1.30948e6i 0.0598511i −0.999552 0.0299255i 0.990473π-0.990473\pi
0.999552 0.0299255i 0.00952702π-0.00952702\pi
864864 1.07957e6 + 623293.i 0.0492004 + 0.0284058i
865865 −3.29131e6 1.90024e6i −0.149565 0.0863512i
866866 1.23238e7i 0.558405i
867867 −5.72377e6 + 9.91385e6i −0.258603 + 0.447914i
868868 −1.33429e6 2.31106e6i −0.0601105 0.104114i
869869 5.54005e6 3.19855e6i 0.248865 0.143683i
870870 −1.49751e6 −0.0670765
871871 −1.66665e7 + 1.30966e7i −0.744389 + 0.584941i
872872 2.09637e7 0.933633
873873 3.87649e6 2.23809e6i 0.172148 0.0993900i
874874 6.69584e6 + 1.15975e7i 0.296501 + 0.513555i
875875 468579. 811602.i 0.0206901 0.0358363i
876876 541992.i 0.0238634i
877877 3.04731e7 + 1.75936e7i 1.33788 + 0.772426i 0.986493 0.163804i 0.0523764π-0.0523764\pi
0.351388 + 0.936230i 0.385710π0.385710\pi
878878 −4.47977e6 2.58639e6i −0.196119 0.113229i
879879 329354.i 0.0143778i
880880 −1.76567e6 + 3.05824e6i −0.0768606 + 0.133126i
881881 −2.41552e6 4.18380e6i −0.104850 0.181606i 0.808827 0.588047i 0.200103π-0.200103\pi
−0.913677 + 0.406441i 0.866770π0.866770\pi
882882 4.83582e6 2.79196e6i 0.209314 0.120848i
883883 −4.01230e7 −1.73178 −0.865888 0.500238i 0.833246π-0.833246\pi
−0.865888 + 0.500238i 0.833246π0.833246\pi
884884 689940. + 878009.i 0.0296948 + 0.0377893i
885885 −3.03814e6 −0.130391
886886 −3.53485e7 + 2.04085e7i −1.51282 + 0.873425i
887887 653107. + 1.13122e6i 0.0278725 + 0.0482765i 0.879625 0.475667i 0.157793π-0.157793\pi
−0.851753 + 0.523944i 0.824460π0.824460\pi
888888 2.34497e6 4.06161e6i 0.0997943 0.172849i
889889 64577.8i 0.00274049i
890890 278461. + 160770.i 0.0117839 + 0.00680345i
891891 −945558. 545918.i −0.0399019 0.0230374i
892892 1.46477e6i 0.0616394i
893893 7.77291e6 1.34631e7i 0.326178 0.564957i
894894 −8.07754e6 1.39907e7i −0.338014 0.585458i
895895 6.60813e6 3.81520e6i 0.275753 0.159206i
896896 −8.01325e6 −0.333456
897897 −4.04239e6 + 1.00864e7i −0.167748 + 0.418557i
898898 3.66233e7 1.51554
899899 −1.03128e7 + 5.95411e6i −0.425577 + 0.245707i
900900 120614. + 208910.i 0.00496355 + 0.00859711i
901901 −1.68279e6 + 2.91469e6i −0.0690588 + 0.119613i
902902 3.71359e6i 0.151977i
903903 −3.01653e6 1.74159e6i −0.123109 0.0710767i
904904 7.58266e6 + 4.37785e6i 0.308603 + 0.178172i
905905 2.19370e7i 0.890338i
906906 −9383.72 + 16253.1i −0.000379799 + 0.000657832i
907907 5.75673e6 + 9.97095e6i 0.232358 + 0.402456i 0.958502 0.285087i 0.0920225π-0.0920225\pi
−0.726143 + 0.687543i 0.758689π0.758689\pi
908908 4.91718e6 2.83894e6i 0.197926 0.114272i
909909 −8.75322e6 −0.351365
910910 −676809. 4.71992e6i −0.0270933 0.188943i
911911 −2.93959e7 −1.17352 −0.586760 0.809761i 0.699597π-0.699597\pi
−0.586760 + 0.809761i 0.699597π0.699597\pi
912912 8.56795e6 4.94671e6i 0.341106 0.196938i
913913 4.30548e6 + 7.45731e6i 0.170940 + 0.296078i
914914 −1.66138e7 + 2.87759e7i −0.657814 + 1.13937i
915915 2.72384e6i 0.107555i
916916 1.23241e6 + 711534.i 0.0485308 + 0.0280193i
917917 −1.41125e6 814784.i −0.0554217 0.0319977i
918918 1.46315e6i 0.0573036i
919919 −2.02023e7 + 3.49914e7i −0.789063 + 1.36670i 0.137479 + 0.990505i 0.456100π0.456100\pi
−0.926542 + 0.376192i 0.877233π0.877233\pi
920920 4.75213e6 + 8.23094e6i 0.185105 + 0.320612i
921921 −1.63349e7 + 9.43095e6i −0.634552 + 0.366359i
922922 −7.24763e6 −0.280782
923923 −1.42209e7 5.69939e6i −0.549442 0.220203i
924924 −428041. −0.0164932
925925 1.47007e6 848745.i 0.0564916 0.0326154i
926926 −2.08530e6 3.61185e6i −0.0799174 0.138421i
927927 −7.66597e6 + 1.32779e7i −0.293000 + 0.507491i
928928 2.18081e6i 0.0831280i
929929 4.33856e7 + 2.50487e7i 1.64933 + 0.952239i 0.977340 + 0.211674i 0.0678917π0.0678917\pi
0.671986 + 0.740564i 0.265442π0.265442\pi
930930 −9.49513e6 5.48201e6i −0.359992 0.207842i
931931 1.71073e7i 0.646856i
932932 2.57295e6 4.45649e6i 0.0970269 0.168056i
933933 3.28426e6 + 5.68851e6i 0.123519 + 0.213941i
934934 −2.29018e7 + 1.32223e7i −0.859017 + 0.495954i
935935 −1.60002e6 −0.0598543
936936 8.79015e6 + 3.52289e6i 0.327949 + 0.131434i
937937 −1.74797e7 −0.650408 −0.325204 0.945644i 0.605433π-0.605433\pi
−0.325204 + 0.945644i 0.605433π0.605433\pi
938938 9.42960e6 5.44418e6i 0.349934 0.202035i
939939 −9.10798e6 1.57755e7i −0.337099 0.583873i
940940 714983. 1.23839e6i 0.0263922 0.0457127i
941941 2.44440e7i 0.899907i 0.893052 + 0.449954i 0.148560π0.148560\pi
−0.893052 + 0.449954i 0.851440π0.851440\pi
942942 1.44190e7 + 8.32484e6i 0.529431 + 0.305667i
943943 7.33760e6 + 4.23636e6i 0.268704 + 0.155136i
944944 1.14614e7i 0.418608i
945945 546550. 946653.i 0.0199090 0.0344835i
946946 2.80197e6 + 4.85315e6i 0.101797 + 0.176318i
947947 −4.15382e7 + 2.39821e7i −1.50513 + 0.868986i −0.505145 + 0.863035i 0.668561π0.668561\pi
−0.999982 + 0.00595105i 0.998106π0.998106\pi
948948 −1.64855e6 −0.0595773
949949 −1.09309e6 7.62300e6i −0.0393996 0.274764i
950950 4.22410e6 0.151854
951951 1.33256e6 769355.i 0.0477789 0.0275852i
952952 −2.21288e6 3.83282e6i −0.0791344 0.137065i
953953 2.01944e7 3.49778e7i 0.720277 1.24756i −0.240612 0.970621i 0.577348π-0.577348\pi
0.960889 0.276934i 0.0893185π-0.0893185\pi
954954 3.69924e6i 0.131596i
955955 −2.90899e6 1.67951e6i −0.103213 0.0595900i
956956 −5.52391e6 3.18923e6i −0.195480 0.112860i
957957 1.91008e6i 0.0674175i
958958 −8.41739e6 + 1.45794e7i −0.296322 + 0.513245i
959959 3.82095e6 + 6.61808e6i 0.134161 + 0.232373i
960960 7.03157e6 4.05968e6i 0.246249 0.142172i
961961 −5.85571e7 −2.04537
962962 3.21297e6 8.01685e6i 0.111936 0.279297i
963963 712802. 0.0247687
964964 −4.38309e6 + 2.53058e6i −0.151910 + 0.0877055i
965965 971698. + 1.68303e6i 0.0335902 + 0.0581800i
966966 2.79093e6 4.83403e6i 0.0962290 0.166674i
967967 4.79161e7i 1.64784i −0.566706 0.823920i 0.691782π-0.691782\pi
0.566706 0.823920i 0.308218π-0.308218\pi
968968 −2.21588e7 1.27934e7i −0.760079 0.438832i
969969 3.88205e6 + 2.24130e6i 0.132816 + 0.0766816i
970970 7.20986e6i 0.246035i
971971 1.18520e7 2.05282e7i 0.403406 0.698720i −0.590728 0.806871i 0.701159π-0.701159\pi
0.994135 + 0.108150i 0.0344928π0.0344928\pi
972972 140684. + 243672.i 0.00477617 + 0.00827258i
973973 1.38761e7 8.01138e6i 0.469879 0.271285i
974974 −2.53345e7 −0.855687
975975 2.11774e6 + 2.69502e6i 0.0713447 + 0.0907925i
976976 −1.02757e7 −0.345293
977977 −2.09892e7 + 1.21181e7i −0.703493 + 0.406162i −0.808647 0.588294i 0.799800π-0.799800\pi
0.105154 + 0.994456i 0.466467π0.466467\pi
978978 7.98068e6 + 1.38229e7i 0.266804 + 0.462118i
979979 205063. 355180.i 0.00683804 0.0118438i
980980 1.57360e6i 0.0523394i
981981 7.66452e6 + 4.42511e6i 0.254280 + 0.146809i
982982 −2.55396e7 1.47453e7i −0.845153 0.487949i
983983 3.71789e6i 0.122719i 0.998116 + 0.0613597i 0.0195437π0.0195437\pi
−0.998116 + 0.0613597i 0.980456π0.980456\pi
984984 3.69193e6 6.39461e6i 0.121553 0.210536i
985985 −1.31088e6 2.27051e6i −0.0430499 0.0745645i
986986 −2.21674e6 + 1.27983e6i −0.0726142 + 0.0419238i
987987 −6.47974e6 −0.211721
988988 −2.95660e6 + 2.32330e6i −0.0963608 + 0.0757203i
989989 1.27856e7 0.415654
990990 −1.52302e6 + 879318.i −0.0493877 + 0.0285140i
991991 −8.13116e6 1.40836e7i −0.263008 0.455543i 0.704032 0.710168i 0.251381π-0.251381\pi
−0.967040 + 0.254626i 0.918048π0.918048\pi
992992 7.98341e6 1.38277e7i 0.257578 0.446139i
993993 1.38081e7i 0.444385i
994994 6.81553e6 + 3.93495e6i 0.218793 + 0.126320i
995995 −4.63561e6 2.67637e6i −0.148439 0.0857015i
996996 2.21907e6i 0.0708797i
997997 1.07275e6 1.85806e6i 0.0341791 0.0592000i −0.848430 0.529308i 0.822452π-0.822452\pi
0.882609 + 0.470108i 0.155785π0.155785\pi
998998 −2.62810e7 4.55200e7i −0.835247 1.44669i
999999 1.71469e6 989976.i 0.0543590 0.0313842i
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 195.6.bb.a.166.16 yes 44
13.4 even 6 inner 195.6.bb.a.121.16 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
195.6.bb.a.121.16 44 13.4 even 6 inner
195.6.bb.a.166.16 yes 44 1.1 even 1 trivial