Properties

Label 18.8.c.a.7.2
Level 1818
Weight 88
Character 18.7
Analytic conductor 5.6235.623
Analytic rank 00
Dimension 66
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [18,8,Mod(7,18)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(18, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("18.7");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: N N == 18=232 18 = 2 \cdot 3^{2}
Weight: k k == 8 8
Character orbit: [χ][\chi] == 18.c (of order 33, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 5.622930458715.62293045871
Analytic rank: 00
Dimension: 66
Relative dimension: 33 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: 6.0.14601465675.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x63x5+52x499x3+709x2660x+1872 x^{6} - 3x^{5} + 52x^{4} - 99x^{3} + 709x^{2} - 660x + 1872 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 2236 2^{2}\cdot 3^{6}
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 7.2
Root 0.500000+5.21243i0.500000 + 5.21243i of defining polynomial
Character χ\chi == 18.7
Dual form 18.8.c.a.13.2

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+(4.00000+6.92820i)q2+(11.781945.2569i)q3+(32.000055.4256i)q4+(187.789+325.261i)q5+(360.677+99.4005i)q6+(528.867+916.024i)q7+512.000q8+(1909.38+1066.42i)q93004.63q10+(849.965+1472.18i)q11+(2131.37+2101.24i)q12+(6256.75+10837.0i)q13+(4230.937328.19i)q14+(12507.812330.9i)q15+(2048.00+3547.24i)q16+16879.9q17+(249.11717494.2i)q1835281.9q19+(12018.520816.7i)q20+(47687.4+13142.4i)q21+(6799.7211777.5i)q22+(35482.761457.8i)q23+(6032.3123171.5i)q24+(31467.1+54502.6i)q25100108.q26+(70758.9+73848.0i)q27+67694.9q28+(38827.467251.0i)q29+(35400.1+135980.i)q30+(63093.8+109282.i)q31+(16384.028377.9i)q32+(76640.6+21121.7i)q33+(67519.4+116947.i)q34397262.q35+(120207.+71702.8i)q36528664.q37+(141128.244440.i)q38+(416733.410841.i)q39+(96148.1+166533.i)q40+(258960.+448533.i)q41+(281803.+277819.i)q42+(135830.235264.i)q43+108795.q44+(705425.420782.i)q45+567723.q46+(211814.366873.i)q47+(184666.+50893.0i)q48+(147628.255699.i)q49+(251737.436021.i)q50+(198876.763930.i)q51+(400432.693568.i)q52+1.24314e6q53+(794670.+194840.i)q54638457.q55+(270780.+469004.i)q56+(415687.+1.59675e6i)q57+(310619.+538008.i)q58+(1.34086e6+2.32244e6i)q59+(1.08370e6298661.i)q60+(377040.653052.i)q611.00950e6q62+(32937.42.31303e6i)q63+262144.q64+(2.34990e6+4.07014e6i)q65+(452898.+446495.i)q66+(131285.+227392.i)q67+(540156.935577.i)q68+(2.36334e6+2.32993e6i)q69+(1.58905e62.75231e6i)q70+990913.q71+(977600.+546008.i)q721.04389e6q73+(2.11466e63.66269e6i)q74+(2.83736e6+781961.i)q75+(1.12902e6+1.95552e6i)q76+(899036.1.55718e6i)q77+(1.17946e6+4.53058e6i)q78+(3.66860e66.35419e6i)q791.53837e6q80+(2.50846e64.07240e6i)q814.14337e6q82+(1.94611e63.37075e6i)q83+(797572.3.06366e6i)q84+(3.16986e6+5.49035e6i)q85+(1.08664e6+1.88211e6i)q86+(3.50103e6964865.i)q87+(435182.+753757.i)q88+675681.q89+(5.73696e63.20420e6i)q901.32359e7q91+(2.27089e6+3.93330e6i)q92+(4.20239e64.14298e6i)q93+(1.69452e6+2.93499e6i)q94+(6.62556e61.14758e7i)q95+(1.09126e6+1.07583e6i)q96+(8.12785e6+1.40779e7i)q97+2.36205e6q98+(52935.23.71737e6i)q99+O(q100)q+(-4.00000 + 6.92820i) q^{2} +(-11.7819 - 45.2569i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(187.789 + 325.261i) q^{5} +(360.677 + 99.4005i) q^{6} +(-528.867 + 916.024i) q^{7} +512.000 q^{8} +(-1909.38 + 1066.42i) q^{9} -3004.63 q^{10} +(-849.965 + 1472.18i) q^{11} +(-2131.37 + 2101.24i) q^{12} +(6256.75 + 10837.0i) q^{13} +(-4230.93 - 7328.19i) q^{14} +(12507.8 - 12330.9i) q^{15} +(-2048.00 + 3547.24i) q^{16} +16879.9 q^{17} +(249.117 - 17494.2i) q^{18} -35281.9 q^{19} +(12018.5 - 20816.7i) q^{20} +(47687.4 + 13142.4i) q^{21} +(-6799.72 - 11777.5i) q^{22} +(-35482.7 - 61457.8i) q^{23} +(-6032.31 - 23171.5i) q^{24} +(-31467.1 + 54502.6i) q^{25} -100108. q^{26} +(70758.9 + 73848.0i) q^{27} +67694.9 q^{28} +(38827.4 - 67251.0i) q^{29} +(35400.1 + 135980. i) q^{30} +(63093.8 + 109282. i) q^{31} +(-16384.0 - 28377.9i) q^{32} +(76640.6 + 21121.7i) q^{33} +(-67519.4 + 116947. i) q^{34} -397262. q^{35} +(120207. + 71702.8i) q^{36} -528664. q^{37} +(141128. - 244440. i) q^{38} +(416733. - 410841. i) q^{39} +(96148.1 + 166533. i) q^{40} +(258960. + 448533. i) q^{41} +(-281803. + 277819. i) q^{42} +(135830. - 235264. i) q^{43} +108795. q^{44} +(-705425. - 420782. i) q^{45} +567723. q^{46} +(211814. - 366873. i) q^{47} +(184666. + 50893.0i) q^{48} +(-147628. - 255699. i) q^{49} +(-251737. - 436021. i) q^{50} +(-198876. - 763930. i) q^{51} +(400432. - 693568. i) q^{52} +1.24314e6 q^{53} +(-794670. + 194840. i) q^{54} -638457. q^{55} +(-270780. + 469004. i) q^{56} +(415687. + 1.59675e6i) q^{57} +(310619. + 538008. i) q^{58} +(1.34086e6 + 2.32244e6i) q^{59} +(-1.08370e6 - 298661. i) q^{60} +(377040. - 653052. i) q^{61} -1.00950e6 q^{62} +(32937.4 - 2.31303e6i) q^{63} +262144. q^{64} +(-2.34990e6 + 4.07014e6i) q^{65} +(-452898. + 446495. i) q^{66} +(131285. + 227392. i) q^{67} +(-540156. - 935577. i) q^{68} +(-2.36334e6 + 2.32993e6i) q^{69} +(1.58905e6 - 2.75231e6i) q^{70} +990913. q^{71} +(-977600. + 546008. i) q^{72} -1.04389e6 q^{73} +(2.11466e6 - 3.66269e6i) q^{74} +(2.83736e6 + 781961. i) q^{75} +(1.12902e6 + 1.95552e6i) q^{76} +(-899036. - 1.55718e6i) q^{77} +(1.17946e6 + 4.53058e6i) q^{78} +(3.66860e6 - 6.35419e6i) q^{79} -1.53837e6 q^{80} +(2.50846e6 - 4.07240e6i) q^{81} -4.14337e6 q^{82} +(1.94611e6 - 3.37075e6i) q^{83} +(-797572. - 3.06366e6i) q^{84} +(3.16986e6 + 5.49035e6i) q^{85} +(1.08664e6 + 1.88211e6i) q^{86} +(-3.50103e6 - 964865. i) q^{87} +(-435182. + 753757. i) q^{88} +675681. q^{89} +(5.73696e6 - 3.20420e6i) q^{90} -1.32359e7 q^{91} +(-2.27089e6 + 3.93330e6i) q^{92} +(4.20239e6 - 4.14298e6i) q^{93} +(1.69452e6 + 2.93499e6i) q^{94} +(-6.62556e6 - 1.14758e7i) q^{95} +(-1.09126e6 + 1.07583e6i) q^{96} +(-8.12785e6 + 1.40779e7i) q^{97} +2.36205e6 q^{98} +(52935.2 - 3.71737e6i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q24q227q3192q4+54q5+792q6+210q7+3072q8+2295q9864q10+6579q114608q12+10092q13+1680q14+756q1512288q1629790q17+11453238q99+O(q100) 6 q - 24 q^{2} - 27 q^{3} - 192 q^{4} + 54 q^{5} + 792 q^{6} + 210 q^{7} + 3072 q^{8} + 2295 q^{9} - 864 q^{10} + 6579 q^{11} - 4608 q^{12} + 10092 q^{13} + 1680 q^{14} + 756 q^{15} - 12288 q^{16} - 29790 q^{17}+ \cdots - 11453238 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/18Z)×\left(\mathbb{Z}/18\mathbb{Z}\right)^\times.

nn 1111
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −4.00000 + 6.92820i −0.353553 + 0.612372i
33 −11.7819 45.2569i −0.251936 0.967744i
44 −32.0000 55.4256i −0.250000 0.433013i
55 187.789 + 325.261i 0.671855 + 1.16369i 0.977377 + 0.211502i 0.0678356π0.0678356\pi
−0.305522 + 0.952185i 0.598831π0.598831\pi
66 360.677 + 99.4005i 0.681692 + 0.187871i
77 −528.867 + 916.024i −0.582778 + 1.00940i 0.412371 + 0.911016i 0.364701π0.364701\pi
−0.995148 + 0.0983845i 0.968633π0.968633\pi
88 512.000 0.353553
99 −1909.38 + 1066.42i −0.873057 + 0.487618i
1010 −3004.63 −0.950147
1111 −849.965 + 1472.18i −0.192542 + 0.333493i −0.946092 0.323898i 0.895007π-0.895007\pi
0.753550 + 0.657391i 0.228340π0.228340\pi
1212 −2131.37 + 2101.24i −0.356062 + 0.351027i
1313 6256.75 + 10837.0i 0.789854 + 1.36807i 0.926056 + 0.377386i 0.123177π0.123177\pi
−0.136202 + 0.990681i 0.543490π0.543490\pi
1414 −4230.93 7328.19i −0.412086 0.713754i
1515 12507.8 12330.9i 0.956887 0.943358i
1616 −2048.00 + 3547.24i −0.125000 + 0.216506i
1717 16879.9 0.833293 0.416646 0.909069i 0.363205π-0.363205\pi
0.416646 + 0.909069i 0.363205π0.363205\pi
1818 249.117 17494.2i 0.0100682 0.707035i
1919 −35281.9 −1.18009 −0.590044 0.807371i 0.700890π-0.700890\pi
−0.590044 + 0.807371i 0.700890π0.700890\pi
2020 12018.5 20816.7i 0.335928 0.581844i
2121 47687.4 + 13142.4i 1.12366 + 0.309676i
2222 −6799.72 11777.5i −0.136148 0.235815i
2323 −35482.7 61457.8i −0.608092 1.05325i −0.991555 0.129690i 0.958602π-0.958602\pi
0.383463 0.923556i 0.374731π-0.374731\pi
2424 −6032.31 23171.5i −0.0890727 0.342149i
2525 −31467.1 + 54502.6i −0.402779 + 0.697634i
2626 −100108. −1.11702
2727 70758.9 + 73848.0i 0.691844 + 0.722047i
2828 67694.9 0.582778
2929 38827.4 67251.0i 0.295628 0.512042i −0.679503 0.733673i 0.737805π-0.737805\pi
0.975131 + 0.221631i 0.0711379π0.0711379\pi
3030 35400.1 + 135980.i 0.239376 + 0.919499i
3131 63093.8 + 109282.i 0.380383 + 0.658843i 0.991117 0.132993i 0.0424588π-0.0424588\pi
−0.610734 + 0.791836i 0.709126π0.709126\pi
3232 −16384.0 28377.9i −0.0883883 0.153093i
3333 76640.6 + 21121.7i 0.371244 + 0.102313i
3434 −67519.4 + 116947.i −0.294614 + 0.510286i
3535 −397262. −1.56617
3636 120207. + 71702.8i 0.429409 + 0.256140i
3737 −528664. −1.71583 −0.857914 0.513794i 0.828240π-0.828240\pi
−0.857914 + 0.513794i 0.828240π0.828240\pi
3838 141128. 244440.i 0.417224 0.722654i
3939 416733. 410841.i 1.12495 1.10904i
4040 96148.1 + 166533.i 0.237537 + 0.411426i
4141 258960. + 448533.i 0.586800 + 1.01637i 0.994648 + 0.103318i 0.0329458π0.0329458\pi
−0.407849 + 0.913050i 0.633721π0.633721\pi
4242 −281803. + 277819.i −0.586912 + 0.578614i
4343 135830. 235264.i 0.260529 0.451249i −0.705854 0.708358i 0.749436π-0.749436\pi
0.966383 + 0.257109i 0.0827698π0.0827698\pi
4444 108795. 0.192542
4545 −705425. 420782.i −1.15400 0.688356i
4646 567723. 0.859972
4747 211814. 366873.i 0.297586 0.515435i −0.677997 0.735065i 0.737152π-0.737152\pi
0.975583 + 0.219630i 0.0704850π0.0704850\pi
4848 184666. + 50893.0i 0.241015 + 0.0664223i
4949 −147628. 255699.i −0.179260 0.310487i
5050 −251737. 436021.i −0.284808 0.493301i
5151 −198876. 763930.i −0.209936 0.806414i
5252 400432. 693568.i 0.394927 0.684034i
5353 1.24314e6 1.14698 0.573490 0.819213i 0.305589π-0.305589\pi
0.573490 + 0.819213i 0.305589π0.305589\pi
5454 −794670. + 194840.i −0.686765 + 0.168384i
5555 −638457. −0.517443
5656 −270780. + 469004.i −0.206043 + 0.356877i
5757 415687. + 1.59675e6i 0.297306 + 1.14202i
5858 310619. + 538008.i 0.209040 + 0.362068i
5959 1.34086e6 + 2.32244e6i 0.849968 + 1.47219i 0.881236 + 0.472677i 0.156712π0.156712\pi
−0.0312678 + 0.999511i 0.509954π0.509954\pi
6060 −1.08370e6 298661.i −0.647708 0.178505i
6161 377040. 653052.i 0.212683 0.368378i −0.739870 0.672750i 0.765113π-0.765113\pi
0.952553 + 0.304372i 0.0984465π0.0984465\pi
6262 −1.00950e6 −0.537943
6363 32937.4 2.31303e6i 0.0165958 1.16544i
6464 262144. 0.125000
6565 −2.34990e6 + 4.07014e6i −1.06133 + 1.83829i
6666 −452898. + 446495.i −0.193908 + 0.191167i
6767 131285. + 227392.i 0.0533278 + 0.0923664i 0.891457 0.453105i 0.149684π-0.149684\pi
−0.838129 + 0.545472i 0.816351π0.816351\pi
6868 −540156. 935577.i −0.208323 0.360826i
6969 −2.36334e6 + 2.32993e6i −0.866073 + 0.853828i
7070 1.58905e6 2.75231e6i 0.553724 0.959079i
7171 990913. 0.328573 0.164286 0.986413i 0.447468π-0.447468\pi
0.164286 + 0.986413i 0.447468π0.447468\pi
7272 −977600. + 546008.i −0.308672 + 0.172399i
7373 −1.04389e6 −0.314068 −0.157034 0.987593i 0.550193π-0.550193\pi
−0.157034 + 0.987593i 0.550193π0.550193\pi
7474 2.11466e6 3.66269e6i 0.606637 1.05073i
7575 2.83736e6 + 781961.i 0.776605 + 0.214028i
7676 1.12902e6 + 1.95552e6i 0.295022 + 0.510993i
7777 −899036. 1.55718e6i −0.224419 0.388705i
7878 1.17946e6 + 4.53058e6i 0.281418 + 1.08099i
7979 3.66860e6 6.35419e6i 0.837153 1.44999i −0.0551117 0.998480i 0.517551π-0.517551\pi
0.892265 0.451512i 0.149115π-0.149115\pi
8080 −1.53837e6 −0.335928
8181 2.50846e6 4.07240e6i 0.524457 0.851437i
8282 −4.14337e6 −0.829860
8383 1.94611e6 3.37075e6i 0.373588 0.647074i −0.616526 0.787334i 0.711461π-0.711461\pi
0.990115 + 0.140260i 0.0447940π0.0447940\pi
8484 −797572. 3.06366e6i −0.146822 0.563980i
8585 3.16986e6 + 5.49035e6i 0.559852 + 0.969692i
8686 1.08664e6 + 1.88211e6i 0.184222 + 0.319081i
8787 −3.50103e6 964865.i −0.570005 0.157090i
8888 −435182. + 753757.i −0.0680740 + 0.117908i
8989 675681. 0.101596 0.0507980 0.998709i 0.483824π-0.483824\pi
0.0507980 + 0.998709i 0.483824π0.483824\pi
9090 5.73696e6 3.20420e6i 0.829532 0.463309i
9191 −1.32359e7 −1.84124
9292 −2.27089e6 + 3.93330e6i −0.304046 + 0.526623i
9393 4.20239e6 4.14298e6i 0.541759 0.534099i
9494 1.69452e6 + 2.93499e6i 0.210425 + 0.364467i
9595 −6.62556e6 1.14758e7i −0.792849 1.37325i
9696 −1.09126e6 + 1.07583e6i −0.125887 + 0.124107i
9797 −8.12785e6 + 1.40779e7i −0.904221 + 1.56616i −0.0822619 + 0.996611i 0.526214π0.526214\pi
−0.821959 + 0.569546i 0.807119π0.807119\pi
9898 2.36205e6 0.253512
9999 52935.2 3.71737e6i 0.00548304 0.385046i
100100 4.02779e6 0.402779
101101 212270. 367662.i 0.0205005 0.0355079i −0.855593 0.517649i 0.826807π-0.826807\pi
0.876094 + 0.482141i 0.160141π0.160141\pi
102102 6.08817e6 + 1.67787e6i 0.568049 + 0.156551i
103103 2.43167e6 + 4.21178e6i 0.219268 + 0.379783i 0.954584 0.297941i 0.0962999π-0.0962999\pi
−0.735317 + 0.677724i 0.762967π0.762967\pi
104104 3.20345e6 + 5.54854e6i 0.279256 + 0.483685i
105105 4.68048e6 + 1.79788e7i 0.394574 + 1.51565i
106106 −4.97257e6 + 8.61275e6i −0.405519 + 0.702379i
107107 2.83648e6 0.223839 0.111920 0.993717i 0.464300π-0.464300\pi
0.111920 + 0.993717i 0.464300π0.464300\pi
108108 1.82879e6 6.28499e6i 0.139695 0.480089i
109109 6.31389e6 0.466987 0.233493 0.972358i 0.424984π-0.424984\pi
0.233493 + 0.972358i 0.424984π0.424984\pi
110110 2.55383e6 4.42336e6i 0.182944 0.316868i
111111 6.22865e6 + 2.39257e7i 0.432278 + 1.66048i
112112 −2.16624e6 3.75203e6i −0.145694 0.252350i
113113 −1.07218e7 1.85708e7i −0.699029 1.21075i −0.968804 0.247830i 0.920283π-0.920283\pi
0.269775 0.962923i 0.413051π-0.413051\pi
114114 −1.27254e7 3.50704e6i −0.804457 0.221704i
115115 1.33265e7 2.30822e7i 0.817100 1.41526i
116116 −4.96990e6 −0.295628
117117 −2.35033e7 1.40196e7i −1.35668 0.809253i
118118 −2.14538e7 −1.20204
119119 −8.92719e6 + 1.54624e7i −0.485624 + 0.841126i
120120 6.40398e6 6.31344e6i 0.338311 0.333527i
121121 8.29871e6 + 1.43738e7i 0.425855 + 0.737602i
122122 3.01632e6 + 5.22442e6i 0.150390 + 0.260483i
123123 1.72482e7 1.70043e7i 0.835747 0.823931i
124124 4.03801e6 6.99403e6i 0.190191 0.329421i
125125 5.70534e6 0.261274
126126 1.58934e7 + 9.48031e6i 0.707814 + 0.422207i
127127 1.35681e7 0.587768 0.293884 0.955841i 0.405052π-0.405052\pi
0.293884 + 0.955841i 0.405052π0.405052\pi
128128 −1.04858e6 + 1.81619e6i −0.0441942 + 0.0765466i
129129 −1.22477e7 3.37539e6i −0.502330 0.138439i
130130 −1.87992e7 3.25612e7i −0.750477 1.29986i
131131 1.17657e7 + 2.03788e7i 0.457265 + 0.792005i 0.998815 0.0486627i 0.0154959π-0.0154959\pi
−0.541551 + 0.840668i 0.682163π0.682163\pi
132132 −1.28181e6 4.92375e6i −0.0485083 0.186332i
133133 1.86594e7 3.23191e7i 0.687729 1.19118i
134134 −2.10056e6 −0.0754169
135135 −1.07321e7 + 3.68829e7i −0.375418 + 1.29020i
136136 8.64249e6 0.294614
137137 1.39952e7 2.42405e7i 0.465006 0.805414i −0.534196 0.845361i 0.679385π-0.679385\pi
0.999202 + 0.0399467i 0.0127188π0.0127188\pi
138138 −6.68884e6 2.56934e7i −0.216658 0.832233i
139139 4.00094e6 + 6.92982e6i 0.126360 + 0.218862i 0.922264 0.386561i 0.126337π-0.126337\pi
−0.795904 + 0.605423i 0.793004π0.793004\pi
140140 1.27124e7 + 2.20185e7i 0.391542 + 0.678171i
141141 −1.90991e7 5.26361e6i −0.573781 0.158131i
142142 −3.96365e6 + 6.86525e6i −0.116168 + 0.201209i
143143 −2.12721e7 −0.608322
144144 127548. 8.95704e6i 0.00355963 0.249975i
145145 2.91655e7 0.794476
146146 4.17555e6 7.23226e6i 0.111040 0.192327i
147147 −9.83283e6 + 9.69381e6i −0.255310 + 0.251700i
148148 1.69172e7 + 2.93015e7i 0.428957 + 0.742975i
149149 1.35829e7 + 2.35262e7i 0.336387 + 0.582639i 0.983750 0.179542i 0.0574617π-0.0574617\pi
−0.647363 + 0.762182i 0.724128π0.724128\pi
150150 −1.67670e7 + 1.65300e7i −0.405636 + 0.399901i
151151 −2.09932e7 + 3.63612e7i −0.496202 + 0.859447i −0.999990 0.00438023i 0.998606π-0.998606\pi
0.503789 + 0.863827i 0.331939π0.331939\pi
152152 −1.80643e7 −0.417224
153153 −3.22300e7 + 1.80010e7i −0.727512 + 0.406329i
154154 1.43846e7 0.317376
155155 −2.36967e7 + 4.10439e7i −0.511125 + 0.885294i
156156 −3.61066e7 9.95078e6i −0.761466 0.209856i
157157 −4.10239e7 7.10556e7i −0.846036 1.46538i −0.884719 0.466125i 0.845650π-0.845650\pi
0.0386831 0.999252i 0.487684π-0.487684\pi
158158 2.93488e7 + 5.08336e7i 0.591957 + 1.02530i
159159 −1.46465e7 5.62608e7i −0.288965 1.10998i
160160 6.15348e6 1.06581e7i 0.118768 0.205713i
161161 7.50625e7 1.41753
162162 1.81806e7 + 3.36687e7i 0.335973 + 0.622191i
163163 −2.89286e7 −0.523203 −0.261602 0.965176i 0.584251π-0.584251\pi
−0.261602 + 0.965176i 0.584251π0.584251\pi
164164 1.65735e7 2.87061e7i 0.293400 0.508184i
165165 7.52221e6 + 2.88946e7i 0.130362 + 0.500752i
166166 1.55688e7 + 2.69660e7i 0.264167 + 0.457550i
167167 −1.33585e7 2.31376e7i −0.221947 0.384424i 0.733452 0.679741i 0.237908π-0.237908\pi
−0.955399 + 0.295318i 0.904575π0.904575\pi
168168 2.44160e7 + 6.72891e6i 0.397275 + 0.109487i
169169 −4.69195e7 + 8.12669e7i −0.747738 + 1.29512i
170170 −5.07177e7 −0.791751
171171 6.73664e7 3.76254e7i 1.03028 0.575433i
172172 −1.73862e7 −0.260529
173173 1.31561e7 2.27871e7i 0.193182 0.334601i −0.753121 0.657882i 0.771453π-0.771453\pi
0.946303 + 0.323281i 0.104786π0.104786\pi
174174 2.06889e7 2.03964e7i 0.297725 0.293515i
175175 −3.32838e7 5.76492e7i −0.469461 0.813131i
176176 −3.48146e6 6.03006e6i −0.0481356 0.0833733i
177177 8.93088e7 8.80461e7i 1.21056 1.19345i
178178 −2.70272e6 + 4.68125e6i −0.0359196 + 0.0622146i
179179 −2.19724e7 −0.286347 −0.143174 0.989698i 0.545731π-0.545731\pi
−0.143174 + 0.989698i 0.545731π0.545731\pi
180180 −748504. + 5.25636e7i −0.00956623 + 0.671787i
181181 1.26202e8 1.58195 0.790975 0.611849i 0.209574π-0.209574\pi
0.790975 + 0.611849i 0.209574π0.209574\pi
182182 5.29437e7 9.17012e7i 0.650976 1.12752i
183183 −3.39974e7 9.36949e6i −0.410078 0.113015i
184184 −1.81671e7 3.14664e7i −0.214993 0.372379i
185185 −9.92774e7 1.71954e8i −1.15279 1.99669i
186186 1.18938e7 + 4.56869e7i 0.135527 + 0.520591i
187187 −1.43473e7 + 2.48502e7i −0.160444 + 0.277898i
188188 −2.71122e7 −0.297586
189189 −1.05069e8 + 2.57611e7i −1.13203 + 0.277555i
190190 1.06009e8 1.12126
191191 −8.97257e7 + 1.55409e8i −0.931752 + 1.61384i −0.151425 + 0.988469i 0.548386π0.548386\pi
−0.780326 + 0.625372i 0.784947π0.784947\pi
192192 −3.08854e6 1.18638e7i −0.0314920 0.120968i
193193 1.49157e7 + 2.58348e7i 0.149346 + 0.258675i 0.930986 0.365055i 0.118950π-0.118950\pi
−0.781640 + 0.623730i 0.785617π0.785617\pi
194194 −6.50228e7 1.12623e8i −0.639381 1.10744i
195195 2.11888e8 + 5.83953e7i 2.04638 + 0.563971i
196196 −9.44820e6 + 1.63648e7i −0.0896299 + 0.155243i
197197 6.70863e7 0.625176 0.312588 0.949889i 0.398804π-0.398804\pi
0.312588 + 0.949889i 0.398804π0.398804\pi
198198 2.55429e7 + 1.52362e7i 0.233853 + 0.139492i
199199 −1.18177e8 −1.06304 −0.531519 0.847046i 0.678379π-0.678379\pi
−0.531519 + 0.847046i 0.678379π0.678379\pi
200200 −1.61112e7 + 2.79053e7i −0.142404 + 0.246651i
201201 8.74429e6 8.62066e6i 0.0759519 0.0748780i
202202 1.69816e6 + 2.94130e6i 0.0144960 + 0.0251078i
203203 4.10690e7 + 7.11336e7i 0.344570 + 0.596813i
204204 −3.59773e7 + 3.54686e7i −0.296704 + 0.292509i
205205 −9.72600e7 + 1.68459e8i −0.788489 + 1.36570i
206206 −3.89067e7 −0.310091
207207 1.33290e8 + 7.95066e7i 1.04448 + 0.623027i
208208 −5.12553e7 −0.394927
209209 2.99884e7 5.19414e7i 0.227217 0.393552i
210210 −1.43283e8 3.94880e7i −1.06765 0.294237i
211211 −5.19927e7 9.00540e7i −0.381025 0.659955i 0.610184 0.792260i 0.291096π-0.291096\pi
−0.991209 + 0.132305i 0.957762π0.957762\pi
212212 −3.97806e7 6.89020e7i −0.286745 0.496657i
213213 −1.16748e7 4.48457e7i −0.0827791 0.317974i
214214 −1.13459e7 + 1.96517e7i −0.0791392 + 0.137073i
215215 1.02030e8 0.700150
216216 3.62286e7 + 3.78102e7i 0.244604 + 0.255282i
217217 −1.33473e8 −0.886715
218218 −2.52556e7 + 4.37439e7i −0.165105 + 0.285970i
219219 1.22989e7 + 4.72431e7i 0.0791249 + 0.303937i
220220 2.04306e7 + 3.53869e7i 0.129361 + 0.224059i
221221 1.05613e8 + 1.82927e8i 0.658180 + 1.14000i
222222 −1.90677e8 5.25495e7i −1.16967 0.322354i
223223 8.07648e7 1.39889e8i 0.487703 0.844726i −0.512197 0.858868i 0.671168π-0.671168\pi
0.999900 + 0.0141421i 0.00450171π0.00450171\pi
224224 3.46598e7 0.206043
225225 1.95975e6 1.37623e8i 0.0114700 0.805476i
226226 1.71550e8 0.988576
227227 −1.90267e7 + 3.29553e7i −0.107963 + 0.186997i −0.914945 0.403579i 0.867766π-0.867766\pi
0.806982 + 0.590576i 0.201099π0.201099\pi
228228 7.51989e7 7.41357e7i 0.420184 0.414243i
229229 1.44858e8 + 2.50901e8i 0.797110 + 1.38064i 0.921491 + 0.388401i 0.126972π0.126972\pi
−0.124381 + 0.992235i 0.539694π0.539694\pi
230230 1.06612e8 + 1.84658e8i 0.577777 + 1.00074i
231231 −5.98806e7 + 5.90340e7i −0.319628 + 0.315109i
232232 1.98796e7 3.44325e7i 0.104520 0.181034i
233233 −7.45094e7 −0.385892 −0.192946 0.981209i 0.561804π-0.561804\pi
−0.192946 + 0.981209i 0.561804π0.561804\pi
234234 1.91144e8 1.06757e8i 0.975224 0.544681i
235235 1.59106e8 0.799740
236236 8.58153e7 1.48636e8i 0.424984 0.736094i
237237 −3.30794e8 9.11650e7i −1.61413 0.444845i
238238 −7.14175e7 1.23699e8i −0.343388 0.594766i
239239 −8.98328e7 1.55595e8i −0.425640 0.737230i 0.570840 0.821061i 0.306618π-0.306618\pi
−0.996480 + 0.0838313i 0.973284π0.973284\pi
240240 1.81249e7 + 6.96218e7i 0.0846321 + 0.325092i
241241 3.04341e7 5.27134e7i 0.140056 0.242583i −0.787462 0.616364i 0.788605π-0.788605\pi
0.927517 + 0.373780i 0.121939π0.121939\pi
242242 −1.32779e8 −0.602250
243243 −2.13858e8 6.55447e7i −0.956103 0.293032i
244244 −4.82611e7 −0.212683
245245 5.54459e7 9.60352e7i 0.240873 0.417205i
246246 4.88166e7 + 1.87516e8i 0.209071 + 0.803092i
247247 −2.20750e8 3.82350e8i −0.932098 1.61444i
248248 3.23041e7 + 5.59523e7i 0.134486 + 0.232936i
249249 −1.75479e8 4.83610e7i −0.720322 0.198517i
250250 −2.28213e7 + 3.95277e7i −0.0923743 + 0.159997i
251251 2.14309e8 0.855426 0.427713 0.903915i 0.359319π-0.359319\pi
0.427713 + 0.903915i 0.359319π0.359319\pi
252252 −1.29255e8 + 7.21913e7i −0.508798 + 0.284173i
253253 1.20636e8 0.468334
254254 −5.42724e7 + 9.40025e7i −0.207807 + 0.359933i
255255 2.11130e8 2.08144e8i 0.797367 0.786094i
256256 −8.38861e6 1.45295e7i −0.0312500 0.0541266i
257257 2.63538e7 + 4.56461e7i 0.0968450 + 0.167740i 0.910377 0.413779i 0.135792π-0.135792\pi
−0.813532 + 0.581520i 0.802458π0.802458\pi
258258 7.23760e7 7.13527e7i 0.262377 0.258667i
259259 2.79593e8 4.84269e8i 0.999946 1.73196i
260260 3.00787e8 1.06133
261261 −2.41814e6 + 1.69814e8i −0.00841860 + 0.591195i
262262 −1.88251e8 −0.646670
263263 −2.44289e8 + 4.23121e8i −0.828055 + 1.43423i 0.0715077 + 0.997440i 0.477219π0.477219\pi
−0.899562 + 0.436793i 0.856114π0.856114\pi
264264 3.92400e7 + 1.08143e7i 0.131255 + 0.0361731i
265265 2.33449e8 + 4.04346e8i 0.770604 + 1.33473i
266266 1.49275e8 + 2.58553e8i 0.486298 + 0.842293i
267267 −7.96078e6 3.05792e7i −0.0255956 0.0983189i
268268 8.40224e6 1.45531e7i 0.0266639 0.0461832i
269269 −1.69083e8 −0.529622 −0.264811 0.964300i 0.585310π-0.585310\pi
−0.264811 + 0.964300i 0.585310π0.585310\pi
270270 −2.12604e8 2.21886e8i −0.657353 0.686051i
271271 −1.99531e8 −0.609001 −0.304501 0.952512i 0.598490π-0.598490\pi
−0.304501 + 0.952512i 0.598490π0.598490\pi
272272 −3.45700e7 + 5.98769e7i −0.104162 + 0.180413i
273273 1.55944e8 + 5.99017e8i 0.463873 + 1.78185i
274274 1.11962e8 + 1.93924e8i 0.328809 + 0.569514i
275275 −5.34919e7 9.26506e7i −0.155104 0.268648i
276276 2.04764e8 + 5.64320e7i 0.586236 + 0.161564i
277277 1.77438e8 3.07331e8i 0.501611 0.868816i −0.498387 0.866955i 0.666074π-0.666074\pi
0.999998 0.00186126i 0.000592457π-0.000592457\pi
278278 −6.40150e7 −0.178700
279279 −2.37010e8 1.41375e8i −0.653360 0.389725i
280280 −2.03398e8 −0.553724
281281 1.40245e8 2.42912e8i 0.377065 0.653096i −0.613569 0.789641i 0.710267π-0.710267\pi
0.990634 + 0.136545i 0.0436000π0.0436000\pi
282282 1.12864e8 1.11268e8i 0.299697 0.295460i
283283 7.95244e7 + 1.37740e8i 0.208568 + 0.361251i 0.951264 0.308379i 0.0997863π-0.0997863\pi
−0.742696 + 0.669629i 0.766453π0.766453\pi
284284 −3.17092e7 5.49220e7i −0.0821431 0.142276i
285285 −4.41298e8 + 4.35059e8i −1.12921 + 1.11325i
286286 8.50882e7 1.47377e8i 0.215074 0.372519i
287287 −5.47822e8 −1.36790
288288 6.15460e7 + 3.67119e7i 0.151819 + 0.0905592i
289289 −1.25409e8 −0.305623
290290 −1.16662e8 + 2.02064e8i −0.280890 + 0.486515i
291291 7.32881e8 + 2.01978e8i 1.74344 + 0.480484i
292292 3.34044e7 + 5.78581e7i 0.0785170 + 0.135995i
293293 −1.72190e8 2.98242e8i −0.399918 0.692679i 0.593797 0.804615i 0.297628π-0.297628\pi
−0.993715 + 0.111936i 0.964295π0.964295\pi
294294 −2.78293e7 1.06899e8i −0.0638686 0.245334i
295295 −5.03600e8 + 8.72260e8i −1.14211 + 1.97819i
296296 −2.70676e8 −0.606637
297297 −1.68860e8 + 4.14019e7i −0.374007 + 0.0917006i
298298 −2.17326e8 −0.475723
299299 4.44013e8 7.69052e8i 0.960608 1.66382i
300300 −4.74549e7 1.82285e8i −0.101474 0.389787i
301301 1.43672e8 + 2.48847e8i 0.303661 + 0.525956i
302302 −1.67945e8 2.90890e8i −0.350868 0.607721i
303303 −1.91402e7 5.27494e6i −0.0395273 0.0108935i
304304 7.22574e7 1.25153e8i 0.147511 0.255497i
305305 2.83216e8 0.571569
306306 4.20506e6 2.95300e8i 0.00838972 0.589167i
307307 5.28744e8 1.04294 0.521472 0.853269i 0.325383π-0.325383\pi
0.521472 + 0.853269i 0.325383π0.325383\pi
308308 −5.75383e7 + 9.96592e7i −0.112209 + 0.194352i
309309 1.61962e8 1.59673e8i 0.312291 0.307876i
310310 −1.89574e8 3.28351e8i −0.361420 0.625997i
311311 1.43382e8 + 2.48345e8i 0.270292 + 0.468159i 0.968937 0.247310i 0.0795465π-0.0795465\pi
−0.698645 + 0.715469i 0.746213π0.746213\pi
312312 2.13367e8 2.10351e8i 0.397729 0.392105i
313313 −1.25124e7 + 2.16722e7i −0.0230641 + 0.0399482i −0.877327 0.479893i 0.840676π-0.840676\pi
0.854263 + 0.519841i 0.174009π0.174009\pi
314314 6.56383e8 1.19648
315315 7.58522e8 4.23648e8i 1.36735 0.763693i
316316 −4.69580e8 −0.837153
317317 2.60137e8 4.50570e8i 0.458663 0.794428i −0.540227 0.841519i 0.681662π-0.681662\pi
0.998891 + 0.0470910i 0.0149951π0.0149951\pi
318318 4.48373e8 + 1.23569e8i 0.781887 + 0.215484i
319319 6.60038e7 + 1.14322e8i 0.113842 + 0.197180i
320320 4.92278e7 + 8.52651e7i 0.0839819 + 0.145461i
321321 −3.34190e7 1.28370e8i −0.0563931 0.216619i
322322 −3.00250e8 + 5.20048e8i −0.501172 + 0.868056i
323323 −5.95554e8 −0.983359
324324 −3.05986e8 8.71622e6i −0.499797 0.0142371i
325325 −7.87527e8 −1.27255
326326 1.15714e8 2.00423e8i 0.184980 0.320395i
327327 −7.43894e7 2.85747e8i −0.117651 0.451924i
328328 1.32588e8 + 2.29649e8i 0.207465 + 0.359340i
329329 2.24043e8 + 3.88054e8i 0.346853 + 0.600768i
330330 −2.30276e8 6.34629e7i −0.352737 0.0972123i
331331 2.52520e8 4.37377e8i 0.382734 0.662915i −0.608718 0.793387i 0.708316π-0.708316\pi
0.991452 + 0.130472i 0.0416492π0.0416492\pi
332332 −2.49102e8 −0.373588
333333 1.00942e9 5.63779e8i 1.49802 0.836669i
334334 2.13736e8 0.313881
335335 −4.93078e7 + 8.54037e7i −0.0716571 + 0.124114i
336336 −1.44283e8 + 1.42243e8i −0.207505 + 0.204571i
337337 9.18750e7 + 1.59132e8i 0.130765 + 0.226492i 0.923972 0.382461i 0.124923π-0.124923\pi
−0.793206 + 0.608953i 0.791590π0.791590\pi
338338 −3.75356e8 6.50135e8i −0.528731 0.915789i
339339 −7.14133e8 + 7.04036e8i −0.995589 + 0.981513i
340340 2.02871e8 3.51383e8i 0.279926 0.484846i
341341 −2.14510e8 −0.292960
342342 −8.78933e6 + 6.17230e8i −0.0118813 + 0.834364i
343343 −5.58786e8 −0.747681
344344 6.95449e7 1.20455e8i 0.0921108 0.159541i
345345 −1.20164e9 3.31166e8i −1.57546 0.434189i
346346 1.05249e8 + 1.82296e8i 0.136600 + 0.236598i
347347 1.43066e8 + 2.47797e8i 0.183816 + 0.318378i 0.943177 0.332291i 0.107822π-0.107822\pi
−0.759361 + 0.650670i 0.774488π0.774488\pi
348348 5.85547e7 + 2.24922e8i 0.0744791 + 0.286092i
349349 1.83182e7 3.17281e7i 0.0230672 0.0399535i −0.854261 0.519844i 0.825990π-0.825990\pi
0.877329 + 0.479890i 0.159324π0.159324\pi
350350 5.32541e8 0.663918
351351 −3.57570e8 + 1.22886e9i −0.441353 + 1.51680i
352352 5.57033e7 0.0680740
353353 −2.38469e8 + 4.13040e8i −0.288549 + 0.499782i −0.973464 0.228841i 0.926506π-0.926506\pi
0.684914 + 0.728624i 0.259840π0.259840\pi
354354 2.52766e8 + 9.70934e8i 0.302836 + 1.16326i
355355 1.86083e8 + 3.22305e8i 0.220753 + 0.382356i
356356 −2.16218e7 3.74500e7i −0.0253990 0.0439923i
357357 8.04957e8 + 2.21842e8i 0.936341 + 0.258050i
358358 8.78898e7 1.52230e8i 0.101239 0.175351i
359359 −3.73983e8 −0.426600 −0.213300 0.976987i 0.568421π-0.568421\pi
−0.213300 + 0.976987i 0.568421π0.568421\pi
360360 −3.61178e8 2.15440e8i −0.408002 0.243371i
361361 3.50942e8 0.392609
362362 −5.04809e8 + 8.74356e8i −0.559303 + 0.968742i
363363 5.52739e8 5.44924e8i 0.606522 0.597947i
364364 4.23550e8 + 7.33610e8i 0.460309 + 0.797279i
365365 −1.96031e8 3.39535e8i −0.211008 0.365477i
366366 2.00903e8 1.98063e8i 0.214192 0.211164i
367367 2.91624e8 5.05107e8i 0.307958 0.533399i −0.669957 0.742400i 0.733688π-0.733688\pi
0.977916 + 0.209000i 0.0670209π0.0670209\pi
368368 2.90674e8 0.304046
369369 −9.72778e8 5.80256e8i −1.00791 0.601212i
370370 1.58844e9 1.63029
371371 −6.57457e8 + 1.13875e9i −0.668434 + 1.15776i
372372 −3.64104e8 1.00345e8i −0.366712 0.101064i
373373 −7.38605e8 1.27930e9i −0.736939 1.27642i −0.953867 0.300228i 0.902937π-0.902937\pi
0.216928 0.976188i 0.430396π-0.430396\pi
374374 −1.14778e8 1.98802e8i −0.113451 0.196503i
375375 −6.72195e7 2.58206e8i −0.0658242 0.252846i
376376 1.08449e8 1.87839e8i 0.105213 0.182234i
377377 9.71732e8 0.934011
378378 2.41796e8 8.30981e8i 0.230265 0.791352i
379379 −6.08958e8 −0.574580 −0.287290 0.957844i 0.592754π-0.592754\pi
−0.287290 + 0.957844i 0.592754π0.592754\pi
380380 −4.24036e8 + 7.34452e8i −0.396424 + 0.686627i
381381 −1.59857e8 6.14050e8i −0.148080 0.568809i
382382 −7.17806e8 1.24328e9i −0.658848 1.14116i
383383 4.24357e8 + 7.35008e8i 0.385954 + 0.668492i 0.991901 0.127013i 0.0405390π-0.0405390\pi
−0.605947 + 0.795505i 0.707206π0.707206\pi
384384 9.45492e7 + 2.60572e7i 0.0852116 + 0.0234838i
385385 3.37659e8 5.84842e8i 0.301554 0.522307i
386386 −2.38651e8 −0.211207
387387 −8.45939e6 + 5.94060e8i −0.00741909 + 0.521005i
388388 1.04036e9 0.904221
389389 1.26651e8 2.19367e8i 0.109090 0.188950i −0.806312 0.591491i 0.798540π-0.798540\pi
0.915402 + 0.402541i 0.131873π0.131873\pi
390390 −1.25213e9 + 1.23442e9i −1.06886 + 1.05375i
391391 −5.98943e8 1.03740e9i −0.506719 0.877662i
392392 −7.55856e7 1.30918e8i −0.0633779 0.109774i
393393 7.83658e8 7.72578e8i 0.651257 0.642049i
394394 −2.68345e8 + 4.64788e8i −0.221033 + 0.382841i
395395 2.75569e9 2.24978
396396 −2.07731e8 + 1.16022e8i −0.168101 + 0.0938872i
397397 9.92215e8 0.795865 0.397932 0.917415i 0.369728π-0.369728\pi
0.397932 + 0.917415i 0.369728π0.369728\pi
398398 4.72710e8 8.18758e8i 0.375841 0.650975i
399399 −1.68250e9 4.63689e8i −1.32602 0.365445i
400400 −1.28889e8 2.23243e8i −0.100695 0.174408i
401401 4.74376e8 + 8.21644e8i 0.367382 + 0.636324i 0.989155 0.146873i 0.0469209π-0.0469209\pi
−0.621774 + 0.783197i 0.713588π0.713588\pi
402402 2.47485e7 + 9.50649e7i 0.0190002 + 0.0729842i
403403 −7.89524e8 + 1.36750e9i −0.600894 + 1.04078i
404404 −2.71706e7 −0.0205005
405405 1.79565e9 + 5.11504e7i 1.34317 + 0.0382610i
406406 −6.57104e8 −0.487296
407407 4.49346e8 7.78290e8i 0.330370 0.572217i
408408 −1.01825e8 3.91132e8i −0.0742236 0.285110i
409409 −3.88383e8 6.72699e8i −0.280691 0.486171i 0.690864 0.722985i 0.257230π-0.257230\pi
−0.971555 + 0.236813i 0.923897π0.923897\pi
410410 −7.78080e8 1.34767e9i −0.557546 0.965698i
411411 −1.26194e9 3.47784e8i −0.896586 0.247094i
412412 1.55627e8 2.69554e8i 0.109634 0.189891i
413413 −2.83655e9 −1.98137
414414 −1.08400e9 + 6.05432e8i −0.750804 + 0.419338i
415415 1.46183e9 1.00399
416416 2.05021e8 3.55107e8i 0.139628 0.241842i
417417 2.66484e8 2.62716e8i 0.179968 0.177423i
418418 2.39907e8 + 4.15531e8i 0.160667 + 0.278283i
419419 3.14943e8 + 5.45498e8i 0.209162 + 0.362280i 0.951451 0.307801i 0.0995930π-0.0995930\pi
−0.742289 + 0.670080i 0.766260π0.766260\pi
420420 8.46713e8 8.34742e8i 0.557653 0.549768i
421421 −5.52425e8 + 9.56829e8i −0.360816 + 0.624952i −0.988095 0.153842i 0.950835π-0.950835\pi
0.627279 + 0.778795i 0.284169π0.284169\pi
422422 8.31883e8 0.538851
423423 −1.31917e7 + 9.26382e8i −0.00847438 + 0.595112i
424424 6.36490e8 0.405519
425425 −5.31160e8 + 9.19997e8i −0.335633 + 0.581333i
426426 3.57399e8 + 9.84972e7i 0.223985 + 0.0617292i
427427 3.98808e8 + 6.90755e8i 0.247894 + 0.429365i
428428 −9.07674e7 1.57214e8i −0.0559599 0.0969253i
429429 2.50624e8 + 9.62707e8i 0.153258 + 0.588700i
430430 −4.08118e8 + 7.06881e8i −0.247541 + 0.428753i
431431 −2.85661e8 −0.171863 −0.0859313 0.996301i 0.527387π-0.527387\pi
−0.0859313 + 0.996301i 0.527387π0.527387\pi
432432 −4.06871e8 + 9.97582e7i −0.242808 + 0.0595327i
433433 4.76788e8 0.282239 0.141120 0.989993i 0.454930π-0.454930\pi
0.141120 + 0.989993i 0.454930π0.454930\pi
434434 5.33892e8 9.24727e8i 0.313501 0.543000i
435435 −3.43623e8 1.31994e9i −0.200157 0.768849i
436436 −2.02045e8 3.49952e8i −0.116747 0.202211i
437437 1.25190e9 + 2.16835e9i 0.717602 + 1.24292i
438438 −3.76506e8 1.03763e8i −0.214098 0.0590042i
439439 −1.25879e9 + 2.18029e9i −0.710112 + 1.22995i 0.254703 + 0.967019i 0.418022π0.418022\pi
−0.964815 + 0.262931i 0.915311π0.915311\pi
440440 −3.26890e8 −0.182944
441441 5.54561e8 + 3.30792e8i 0.307903 + 0.183662i
442442 −1.68981e9 −0.930807
443443 2.29324e8 3.97201e8i 0.125325 0.217069i −0.796535 0.604592i 0.793336π-0.793336\pi
0.921860 + 0.387523i 0.126669π0.126669\pi
444444 1.12678e9 1.11085e9i 0.610940 0.602302i
445445 1.26886e8 + 2.19772e8i 0.0682578 + 0.118226i
446446 6.46118e8 + 1.11911e9i 0.344858 + 0.597311i
447447 9.04691e8 8.91900e8i 0.479098 0.472324i
448448 −1.38639e8 + 2.40130e8i −0.0728472 + 0.126175i
449449 −1.46433e9 −0.763444 −0.381722 0.924277i 0.624669π-0.624669\pi
−0.381722 + 0.924277i 0.624669π0.624669\pi
450450 9.45642e8 + 5.64070e8i 0.489196 + 0.291803i
451451 −8.80429e8 −0.451936
452452 −6.86198e8 + 1.18853e9i −0.349514 + 0.605377i
453453 1.89293e9 + 5.21682e8i 0.956735 + 0.263671i
454454 −1.52214e8 2.63642e8i −0.0763411 0.132227i
455455 −2.48557e9 4.30513e9i −1.23704 2.14262i
456456 2.12832e8 + 8.17536e8i 0.105114 + 0.403766i
457457 −6.98299e8 + 1.20949e9i −0.342243 + 0.592783i −0.984849 0.173414i 0.944520π-0.944520\pi
0.642606 + 0.766197i 0.277853π0.277853\pi
458458 −2.31773e9 −1.12728
459459 1.19440e9 + 1.24654e9i 0.576509 + 0.601677i
460460 −1.70580e9 −0.817100
461461 1.98110e9 3.43137e9i 0.941789 1.63123i 0.179733 0.983715i 0.442476π-0.442476\pi
0.762056 0.647511i 0.224190π-0.224190\pi
462462 −1.69477e8 6.51001e8i −0.0799584 0.307139i
463463 9.40813e8 + 1.62954e9i 0.440524 + 0.763010i 0.997728 0.0673653i 0.0214593π-0.0214593\pi
−0.557204 + 0.830375i 0.688126π0.688126\pi
464464 1.59037e8 + 2.75460e8i 0.0739069 + 0.128011i
465465 2.13671e9 + 5.88866e8i 0.985508 + 0.271601i
466466 2.98038e8 5.16217e8i 0.136433 0.236310i
467467 9.69518e8 0.440501 0.220250 0.975443i 0.429313π-0.429313\pi
0.220250 + 0.975443i 0.429313π0.429313\pi
468468 −2.49386e7 + 1.75131e9i −0.0112464 + 0.789774i
469469 −2.77729e8 −0.124313
470470 −6.36424e8 + 1.10232e9i −0.282751 + 0.489739i
471471 −2.73242e9 + 2.69378e9i −1.20496 + 1.18793i
472472 6.86522e8 + 1.18909e9i 0.300509 + 0.520497i
473473 2.30901e8 + 3.99933e8i 0.100326 + 0.173769i
474474 1.95479e9 1.92715e9i 0.843092 0.831172i
475475 1.11022e9 1.92296e9i 0.475315 0.823269i
476476 1.14268e9 0.485624
477477 −2.37363e9 + 1.32571e9i −1.00138 + 0.559288i
478478 1.43733e9 0.601946
479479 1.00435e9 1.73959e9i 0.417552 0.723222i −0.578140 0.815937i 0.696221π-0.696221\pi
0.995693 + 0.0927156i 0.0295547π0.0295547\pi
480480 −5.54854e8 1.52915e8i −0.228999 0.0631110i
481481 −3.30772e9 5.72913e9i −1.35525 2.34737i
482482 2.43473e8 + 4.21707e8i 0.0990343 + 0.171532i
483483 −8.84376e8 3.39709e9i −0.357126 1.37181i
484484 5.31117e8 9.19922e8i 0.212927 0.368801i
485485 −6.10529e9 −2.43002
486486 1.30954e9 1.21948e9i 0.517478 0.481888i
487487 3.02884e9 1.18830 0.594148 0.804356i 0.297490π-0.297490\pi
0.594148 + 0.804356i 0.297490π0.297490\pi
488488 1.93044e8 3.34363e8i 0.0751948 0.130241i
489489 3.40833e8 + 1.30922e9i 0.131814 + 0.506327i
490490 4.43567e8 + 7.68281e8i 0.170323 + 0.295008i
491491 −2.25862e9 3.91204e9i −0.861107 1.49148i −0.870861 0.491529i 0.836438π-0.836438\pi
0.00975413 0.999952i 0.496895π-0.496895\pi
492492 −1.49442e9 4.11853e8i −0.565709 0.155906i
493493 6.55401e8 1.13519e9i 0.246344 0.426681i
494494 3.53200e9 1.31819
495495 1.21905e9 6.80864e8i 0.451757 0.252315i
496496 −5.16865e8 −0.190191
497497 −5.24061e8 + 9.07700e8i −0.191485 + 0.331661i
498498 1.03697e9 1.02231e9i 0.376239 0.370919i
499499 2.32832e9 + 4.03277e9i 0.838862 + 1.45295i 0.890846 + 0.454305i 0.150112π0.150112\pi
−0.0519839 + 0.998648i 0.516554π0.516554\pi
500500 −1.82571e8 3.16222e8i −0.0653185 0.113135i
501501 −8.89747e8 + 8.77167e8i −0.316107 + 0.311638i
502502 −8.57236e8 + 1.48478e9i −0.302439 + 0.523840i
503503 2.88413e9 1.01048 0.505239 0.862980i 0.331404π-0.331404\pi
0.505239 + 0.862980i 0.331404π0.331404\pi
504504 1.68640e7 1.18427e9i 0.00586750 0.412044i
505505 1.59448e8 0.0550934
506506 −4.82545e8 + 8.35792e8i −0.165581 + 0.286795i
507507 4.23069e9 + 1.16595e9i 1.44173 + 0.397332i
508508 −4.34179e8 7.52020e8i −0.146942 0.254511i
509509 6.60362e8 + 1.14378e9i 0.221957 + 0.384442i 0.955402 0.295307i 0.0954221π-0.0954221\pi
−0.733445 + 0.679749i 0.762089π0.762089\pi
510510 5.97549e8 + 2.29533e9i 0.199470 + 0.766212i
511511 5.52077e8 9.56225e8i 0.183032 0.317020i
512512 1.34218e8 0.0441942
513513 −2.49651e9 2.60550e9i −0.816437 0.852079i
514514 −4.21661e8 −0.136960
515515 −9.13283e8 + 1.58185e9i −0.294632 + 0.510318i
516516 2.04842e8 + 7.86847e8i 0.0656365 + 0.252125i
517517 3.60070e8 + 6.23659e8i 0.114596 + 0.198486i
518518 2.23674e9 + 3.87415e9i 0.707069 + 1.22468i
519519 −1.18628e9 3.26931e8i −0.372477 0.102653i
520520 −1.20315e9 + 2.08391e9i −0.375239 + 0.649932i
521521 5.14654e9 1.59435 0.797175 0.603749i 0.206327π-0.206327\pi
0.797175 + 0.603749i 0.206327π0.206327\pi
522522 −1.16683e9 6.96008e8i −0.359055 0.214174i
523523 −2.17050e9 −0.663444 −0.331722 0.943377i 0.607630π-0.607630\pi
−0.331722 + 0.943377i 0.607630π0.607630\pi
524524 7.53004e8 1.30424e9i 0.228632 0.396003i
525525 −2.21688e9 + 2.18554e9i −0.668628 + 0.659175i
526526 −1.95431e9 3.38497e9i −0.585523 1.01416i
527527 1.06502e9 + 1.84466e9i 0.316970 + 0.549009i
528528 −2.31884e8 + 2.28605e8i −0.0685570 + 0.0675877i
529529 −8.15632e8 + 1.41272e9i −0.239552 + 0.414916i
530530 −3.73518e9 −1.08980
531531 −5.03692e9 3.00449e9i −1.45994 0.870844i
532532 −2.38841e9 −0.687729
533533 −3.24050e9 + 5.61271e9i −0.926972 + 1.60556i
534534 2.43702e8 + 6.71630e7i 0.0692572 + 0.0190869i
535535 5.32661e8 + 9.22595e8i 0.150388 + 0.260479i
536536 6.72180e7 + 1.16425e8i 0.0188542 + 0.0326565i
537537 2.58876e8 + 9.94405e8i 0.0721410 + 0.277111i
538538 6.76330e8 1.17144e9i 0.187250 0.324326i
539539 5.01915e8 0.138060
540540 2.38769e9 5.85423e8i 0.652528 0.159989i
541541 −9.27955e7 −0.0251963 −0.0125981 0.999921i 0.504010π-0.504010\pi
−0.0125981 + 0.999921i 0.504010π0.504010\pi
542542 7.98125e8 1.38239e9i 0.215314 0.372936i
543543 −1.48690e9 5.71153e9i −0.398549 1.53092i
544544 −2.76560e8 4.79015e8i −0.0736534 0.127571i
545545 1.18568e9 + 2.05366e9i 0.313747 + 0.543427i
546546 −4.77389e9 1.31566e9i −1.25516 0.345915i
547547 2.73518e9 4.73747e9i 0.714547 1.23763i −0.248588 0.968609i 0.579966π-0.579966\pi
0.963134 0.269022i 0.0867003π-0.0867003\pi
548548 −1.79139e9 −0.465006
549549 −2.34818e7 + 1.64901e9i −0.00605659 + 0.425323i
550550 8.55870e8 0.219350
551551 −1.36990e9 + 2.37274e9i −0.348867 + 0.604255i
552552 −1.21003e9 + 1.19292e9i −0.306203 + 0.301874i
553553 3.88039e9 + 6.72104e9i 0.975749 + 1.69005i
554554 1.41950e9 + 2.45865e9i 0.354693 + 0.614346i
555555 −6.61241e9 + 6.51892e9i −1.64185 + 1.61864i
556556 2.56060e8 4.43509e8i 0.0631800 0.109431i
557557 4.50060e9 1.10351 0.551756 0.834006i 0.313958π-0.313958\pi
0.551756 + 0.834006i 0.313958π0.313958\pi
558558 1.92752e9 1.07655e9i 0.469655 0.262311i
559559 3.39941e9 0.823119
560560 8.13592e8 1.40918e9i 0.195771 0.339086i
561561 1.29368e9 + 3.56532e8i 0.309355 + 0.0852567i
562562 1.12196e9 + 1.94330e9i 0.266625 + 0.461809i
563563 −3.06529e9 5.30923e9i −0.723922 1.25387i −0.959416 0.281994i 0.909004π-0.909004\pi
0.235494 0.971876i 0.424329π-0.424329\pi
564564 3.19433e8 + 1.22702e9i 0.0749726 + 0.287987i
565565 4.02690e9 6.97479e9i 0.939292 1.62690i
566566 −1.27239e9 −0.294960
567567 2.40377e9 + 4.45156e9i 0.553800 + 1.02559i
568568 5.07347e8 0.116168
569569 1.71059e9 2.96282e9i 0.389271 0.674238i −0.603080 0.797680i 0.706060π-0.706060\pi
0.992352 + 0.123443i 0.0393935π0.0393935\pi
570570 −1.24898e9 4.79764e9i −0.282485 1.08509i
571571 −1.14292e9 1.97960e9i −0.256916 0.444991i 0.708498 0.705712i 0.249373π-0.249373\pi
−0.965414 + 0.260721i 0.916040π0.916040\pi
572572 6.80706e8 + 1.17902e9i 0.152080 + 0.263411i
573573 8.09049e9 + 2.22969e9i 1.79653 + 0.495113i
574574 2.19129e9 3.79542e9i 0.483624 0.837661i
575575 4.46615e9 0.979706
576576 −5.00531e8 + 2.79556e8i −0.109132 + 0.0609523i
577577 −7.03121e9 −1.52375 −0.761877 0.647722i 0.775722π-0.775722\pi
−0.761877 + 0.647722i 0.775722π0.775722\pi
578578 5.01636e8 8.68859e8i 0.108054 0.187155i
579579 9.93467e8 9.79420e8i 0.212705 0.209698i
580580 −9.33295e8 1.61651e9i −0.198619 0.344018i
581581 2.05846e9 + 3.56536e9i 0.435438 + 0.754200i
582582 −4.33087e9 + 4.26964e9i −0.910636 + 0.897761i
583583 −1.05663e9 + 1.83013e9i −0.220842 + 0.382510i
584584 −5.34470e8 −0.111040
585585 1.46350e8 1.02774e10i 0.0302237 2.12245i
586586 2.75504e9 0.565570
587587 4.47158e8 7.74500e8i 0.0912488 0.158048i −0.816788 0.576938i 0.804247π-0.804247\pi
0.908037 + 0.418890i 0.137581π0.137581\pi
588588 8.51936e8 + 2.34789e8i 0.172817 + 0.0476274i
589589 −2.22607e9 3.85567e9i −0.448886 0.777493i
590590 −4.02880e9 6.97808e9i −0.807594 1.39879i
591591 −7.90402e8 3.03612e9i −0.157504 0.605010i
592592 1.08270e9 1.87530e9i 0.214478 0.371488i
593593 −8.80907e9 −1.73476 −0.867379 0.497649i 0.834197π-0.834197\pi
−0.867379 + 0.497649i 0.834197π0.834197\pi
594594 3.88601e8 1.33551e9i 0.0760766 0.261453i
595595 −6.70572e9 −1.30508
596596 8.69302e8 1.50568e9i 0.168193 0.291320i
597597 1.39235e9 + 5.34835e9i 0.267817 + 1.02875i
598598 3.55210e9 + 6.15242e9i 0.679252 + 1.17650i
599599 −4.91595e8 8.51468e8i −0.0934574 0.161873i 0.815506 0.578748i 0.196459π-0.196459\pi
−0.908964 + 0.416875i 0.863125π0.863125\pi
600600 1.45273e9 + 4.00364e8i 0.274571 + 0.0756704i
601601 −1.02236e9 + 1.77078e9i −0.192107 + 0.332739i −0.945948 0.324317i 0.894865π-0.894865\pi
0.753841 + 0.657056i 0.228199π0.228199\pi
602602 −2.29875e9 −0.429441
603603 −4.93169e8 2.94172e8i −0.0915978 0.0546375i
604604 2.68712e9 0.496202
605605 −3.11682e9 + 5.39848e9i −0.572226 + 0.991124i
606606 1.13107e8 1.11507e8i 0.0206459 0.0203540i
607607 −1.78806e9 3.09701e9i −0.324505 0.562059i 0.656907 0.753971i 0.271864π-0.271864\pi
−0.981412 + 0.191913i 0.938531π0.938531\pi
608608 5.78059e8 + 1.00123e9i 0.104306 + 0.180663i
609609 2.73542e9 2.69674e9i 0.490753 0.483815i
610610 −1.13286e9 + 1.96218e9i −0.202080 + 0.350013i
611611 5.30108e9 0.940199
612612 2.02908e9 + 1.21033e9i 0.357824 + 0.213440i
613613 1.22567e9 0.214913 0.107457 0.994210i 0.465729π-0.465729\pi
0.107457 + 0.994210i 0.465729π0.465729\pi
614614 −2.11497e9 + 3.66324e9i −0.368736 + 0.638670i
615615 8.76985e9 + 2.41692e9i 1.52030 + 0.418986i
616616 −4.60306e8 7.97274e8i −0.0793441 0.137428i
617617 −3.80166e9 6.58468e9i −0.651592 1.12859i −0.982737 0.185010i 0.940768π-0.940768\pi
0.331145 0.943580i 0.392565π-0.392565\pi
618618 4.58394e8 + 1.76080e9i 0.0781230 + 0.300089i
619619 −2.87850e9 + 4.98571e9i −0.487808 + 0.844908i −0.999902 0.0140213i 0.995537π-0.995537\pi
0.512094 + 0.858930i 0.328870π0.328870\pi
620620 3.03318e9 0.511125
621621 2.02782e9 6.96902e9i 0.339789 1.16775i
622622 −2.29411e9 −0.382250
623623 −3.57345e8 + 6.18940e8i −0.0592079 + 0.102551i
624624 6.03883e8 + 2.31965e9i 0.0994962 + 0.382188i
625625 3.52977e9 + 6.11374e9i 0.578317 + 1.00167i
626626 −1.00099e8 1.73377e8i −0.0163088 0.0282476i
627627 −2.70403e9 7.45215e8i −0.438101 0.120738i
628628 −2.62553e9 + 4.54756e9i −0.423018 + 0.732688i
629629 −8.92377e9 −1.42979
630630 −9.89647e7 + 6.94979e9i −0.0157684 + 1.10734i
631631 −2.41912e9 −0.383313 −0.191657 0.981462i 0.561386π-0.561386\pi
−0.191657 + 0.981462i 0.561386π0.561386\pi
632632 1.87832e9 3.25335e9i 0.295978 0.512650i
633633 −3.46299e9 + 3.41403e9i −0.542674 + 0.535001i
634634 2.08109e9 + 3.60456e9i 0.324324 + 0.561746i
635635 2.54794e9 + 4.41316e9i 0.394895 + 0.683978i
636636 −2.64960e9 + 2.61214e9i −0.408395 + 0.402621i
637637 1.84734e9 3.19969e9i 0.283178 0.490479i
638638 −1.05606e9 −0.160997
639639 −1.89202e9 + 1.05673e9i −0.286863 + 0.160218i
640640 −7.87645e8 −0.118768
641641 3.95891e9 6.85703e9i 0.593707 1.02833i −0.400021 0.916506i 0.630997π-0.630997\pi
0.993728 0.111825i 0.0356696π-0.0356696\pi
642642 1.02305e9 + 2.81948e8i 0.152590 + 0.0420529i
643643 5.35854e9 + 9.28126e9i 0.794891 + 1.37679i 0.922908 + 0.385020i 0.125805π0.125805\pi
−0.128017 + 0.991772i 0.540861π0.540861\pi
644644 −2.40200e9 4.16038e9i −0.354382 0.613808i
645645 −1.20210e9 4.61754e9i −0.176393 0.677566i
646646 2.38222e9 4.12612e9i 0.347670 0.602182i
647647 8.06643e9 1.17089 0.585446 0.810712i 0.300920π-0.300920\pi
0.585446 + 0.810712i 0.300920π0.300920\pi
648648 1.28433e9 2.08507e9i 0.185423 0.301029i
649649 −4.55875e9 −0.654620
650650 3.15011e9 5.45614e9i 0.449913 0.779272i
651651 1.57256e9 + 6.04057e9i 0.223395 + 0.858113i
652652 9.25715e8 + 1.60338e9i 0.130801 + 0.226554i
653653 −5.00680e9 8.67202e9i −0.703661 1.21878i −0.967172 0.254121i 0.918214π-0.918214\pi
0.263511 0.964656i 0.415119π-0.415119\pi
654654 2.27727e9 + 6.27604e8i 0.318341 + 0.0877331i
655655 −4.41894e9 + 7.65382e9i −0.614431 + 1.06423i
656656 −2.12140e9 −0.293400
657657 1.99317e9 1.11322e9i 0.274199 0.153145i
658658 −3.58469e9 −0.490525
659659 −7.05570e9 + 1.22208e10i −0.960376 + 1.66342i −0.238821 + 0.971064i 0.576761π0.576761\pi
−0.721555 + 0.692357i 0.756572π0.756572\pi
660660 1.36079e9 1.34155e9i 0.184241 0.181637i
661661 −4.81075e9 8.33246e9i −0.647899 1.12219i −0.983624 0.180234i 0.942315π-0.942315\pi
0.335725 0.941960i 0.391019π-0.391019\pi
662662 2.02016e9 + 3.49902e9i 0.270634 + 0.468752i
663663 7.03440e9 6.93494e9i 0.937410 0.924156i
664664 9.96406e8 1.72583e9i 0.132083 0.228775i
665665 1.40162e10 1.84822
666666 −1.31699e8 + 9.24857e9i −0.0172752 + 1.21315i
667667 −5.51080e9 −0.719075
668668 −8.54943e8 + 1.48080e9i −0.110974 + 0.192212i
669669 −7.28249e9 2.00701e9i −0.940348 0.259155i
670670 −3.94463e8 6.83230e8i −0.0506692 0.0877617i
671671 6.40941e8 + 1.11014e9i 0.0819011 + 0.141857i
672672 −4.08357e8 1.56860e9i −0.0519096 0.199397i
673673 −5.84290e9 + 1.01202e10i −0.738884 + 1.27978i 0.214115 + 0.976808i 0.431313π0.431313\pi
−0.952998 + 0.302975i 0.902020π0.902020\pi
674674 −1.47000e9 −0.184930
675675 −6.25149e9 + 1.53276e9i −0.782384 + 0.191828i
676676 6.00569e9 0.747738
677677 5.55719e9 9.62534e9i 0.688327 1.19222i −0.284051 0.958809i 0.591679π-0.591679\pi
0.972379 0.233409i 0.0749881π-0.0749881\pi
678678 −2.02117e9 7.76380e9i −0.249058 0.956688i
679679 −8.59710e9 1.48906e10i −1.05392 1.82544i
680680 1.62297e9 + 2.81106e9i 0.197938 + 0.342838i
681681 1.71562e9 + 4.72817e8i 0.208165 + 0.0573691i
682682 8.58041e8 1.48617e9i 0.103577 0.179400i
683683 −1.61450e10 −1.93894 −0.969472 0.245201i 0.921146π-0.921146\pi
−0.969472 + 0.245201i 0.921146π0.921146\pi
684684 −4.24114e9 2.52981e9i −0.506741 0.302268i
685685 1.05126e10 1.24967
686686 2.23515e9 3.87139e9i 0.264345 0.457859i
687687 9.64833e9 9.51191e9i 1.13528 1.11923i
688688 5.56359e8 + 9.63642e8i 0.0651322 + 0.112812i
689689 7.77803e9 + 1.34719e10i 0.905946 + 1.56915i
690690 7.10096e9 7.00056e9i 0.822896 0.811262i
691691 6.98902e8 1.21053e9i 0.0805829 0.139574i −0.822918 0.568161i 0.807655π-0.807655\pi
0.903500 + 0.428587i 0.140988π0.140988\pi
692692 −1.68398e9 −0.193182
693693 3.37720e9 + 2.01448e9i 0.385470 + 0.229931i
694694 −2.28905e9 −0.259955
695695 −1.50267e9 + 2.60269e9i −0.169791 + 0.294087i
696696 −1.79253e9 4.94011e8i −0.201527 0.0555398i
697697 4.37122e9 + 7.57117e9i 0.488976 + 0.846931i
698698 1.46546e8 + 2.53825e8i 0.0163110 + 0.0282514i
699699 8.77860e8 + 3.37207e9i 0.0972199 + 0.373445i
700700 −2.13016e9 + 3.68955e9i −0.234731 + 0.406565i
701701 −1.34244e9 −0.147191 −0.0735956 0.997288i 0.523447π-0.523447\pi
−0.0735956 + 0.997288i 0.523447π0.523447\pi
702702 −7.08353e9 7.39277e9i −0.772805 0.806543i
703703 1.86523e10 2.02483
704704 −2.22813e8 + 3.85924e8i −0.0240678 + 0.0416867i
705705 −1.87456e9 7.20064e9i −0.201483 0.773943i
706706 −1.90775e9 3.30432e9i −0.204035 0.353399i
707707 2.24525e8 + 3.88889e8i 0.0238944 + 0.0413864i
708708 −7.73789e9 2.13252e9i −0.819419 0.225827i
709709 7.93153e9 1.37378e10i 0.835786 1.44762i −0.0576025 0.998340i 0.518346π-0.518346\pi
0.893389 0.449285i 0.148321π-0.148321\pi
710710 −2.97732e9 −0.312192
711711 −2.28478e8 + 1.60448e10i −0.0238397 + 1.67414i
712712 3.45949e8 0.0359196
713713 4.47748e9 7.75522e9i 0.462616 0.801274i
714714 −4.75679e9 + 4.68954e9i −0.489070 + 0.482155i
715715 −3.99466e9 6.91896e9i −0.408704 0.707896i
716716 7.03118e8 + 1.21784e9i 0.0715868 + 0.123992i
717717 −5.98335e9 + 5.89875e9i −0.606216 + 0.597645i
718718 1.49593e9 2.59103e9i 0.150826 0.261238i
719719 2.14766e9 0.215483 0.107742 0.994179i 0.465638π-0.465638\pi
0.107742 + 0.994179i 0.465638π0.465638\pi
720720 2.93732e9 1.64055e9i 0.293284 0.163804i
721721 −5.14412e9 −0.511137
722722 −1.40377e9 + 2.43140e9i −0.138808 + 0.240423i
723723 −2.74421e9 7.56291e8i −0.270044 0.0744226i
724724 −4.03848e9 6.99485e9i −0.395487 0.685004i
725725 2.44357e9 + 4.23239e9i 0.238145 + 0.412480i
726726 1.56439e9 + 6.00918e9i 0.151728 + 0.582823i
727727 5.14336e9 8.90856e9i 0.496451 0.859879i −0.503540 0.863972i 0.667969π-0.667969\pi
0.999992 + 0.00409288i 0.00130281π0.00130281\pi
728728 −6.77680e9 −0.650976
729729 −4.46699e8 + 1.04508e10i −0.0427040 + 0.999088i
730730 3.13649e9 0.298411
731731 2.29279e9 3.97123e9i 0.217097 0.376023i
732732 5.68606e8 + 2.18415e9i 0.0535825 + 0.205823i
733733 1.60210e9 + 2.77493e9i 0.150254 + 0.260248i 0.931321 0.364200i 0.118657π-0.118657\pi
−0.781067 + 0.624448i 0.785324π0.785324\pi
734734 2.33299e9 + 4.04086e9i 0.217759 + 0.377170i
735735 −4.99951e9 1.37784e9i −0.464432 0.127995i
736736 −1.16270e9 + 2.01385e9i −0.107496 + 0.186189i
737737 −4.46351e8 −0.0410715
738738 7.91124e9 4.41858e9i 0.724515 0.404655i
739739 1.29766e10 1.18279 0.591394 0.806383i 0.298578π-0.298578\pi
0.591394 + 0.806383i 0.298578π0.298578\pi
740740 −6.35375e9 + 1.10050e10i −0.576394 + 0.998343i
741741 −1.47031e10 + 1.44953e10i −1.32754 + 1.30877i
742742 −5.25966e9 9.10999e9i −0.472654 0.818661i
743743 −3.62353e9 6.27614e9i −0.324094 0.561348i 0.657234 0.753686i 0.271726π-0.271726\pi
−0.981329 + 0.192339i 0.938393π0.938393\pi
744744 2.15162e9 2.12120e9i 0.191541 0.188833i
745745 −5.10143e9 + 8.83593e9i −0.452007 + 0.782898i
746746 1.18177e10 1.04219
747747 −1.21202e8 + 8.51141e9i −0.0106387 + 0.747101i
748748 1.83645e9 0.160444
749749 −1.50012e9 + 2.59828e9i −0.130449 + 0.225944i
750750 2.05778e9 + 5.67113e8i 0.178109 + 0.0490857i
751751 4.47123e9 + 7.74440e9i 0.385201 + 0.667188i 0.991797 0.127822i 0.0407988π-0.0407988\pi
−0.606596 + 0.795010i 0.707465π0.707465\pi
752752 8.67592e8 + 1.50271e9i 0.0743966 + 0.128859i
753753 −2.52496e9 9.69897e9i −0.215512 0.827834i
754754 −3.88693e9 + 6.73236e9i −0.330223 + 0.571962i
755755 −1.57692e10 −1.33350
756756 4.79002e9 + 4.99913e9i 0.403191 + 0.420793i
757757 1.36108e10 1.14037 0.570187 0.821515i 0.306871π-0.306871\pi
0.570187 + 0.821515i 0.306871π0.306871\pi
758758 2.43583e9 4.21899e9i 0.203145 0.351857i
759759 −1.42132e9 5.45962e9i −0.117990 0.453228i
760760 −3.39229e9 5.87562e9i −0.280314 0.485519i
761761 1.10122e10 + 1.90738e10i 0.905794 + 1.56888i 0.819848 + 0.572582i 0.194058π0.194058\pi
0.0859464 + 0.996300i 0.472609π0.472609\pi
762762 4.89369e9 + 1.34867e9i 0.400677 + 0.110424i
763763 −3.33921e9 + 5.78368e9i −0.272149 + 0.471377i
764764 1.14849e10 0.931752
765765 −1.19075e10 7.10274e9i −0.961623 0.573602i
766766 −6.78971e9 −0.545821
767767 −1.67789e10 + 2.90619e10i −1.34270 + 2.32563i
768768 −5.58727e8 + 5.50827e8i −0.0445077 + 0.0438784i
769769 −5.17112e9 8.95663e9i −0.410055 0.710236i 0.584840 0.811148i 0.301157π-0.301157\pi
−0.994895 + 0.100912i 0.967824π0.967824\pi
770770 2.70127e9 + 4.67873e9i 0.213231 + 0.369327i
771771 1.75531e9 1.73049e9i 0.137931 0.135981i
772772 9.54605e8 1.65342e9i 0.0746729 0.129337i
773773 3.65169e9 0.284358 0.142179 0.989841i 0.454589π-0.454589\pi
0.142179 + 0.989841i 0.454589π0.454589\pi
774774 −4.08193e9 2.43485e9i −0.316426 0.188746i
775775 −7.94152e9 −0.612841
776776 −4.16146e9 + 7.20786e9i −0.319690 + 0.553720i
777777 −2.52106e10 6.94791e9i −1.92801 0.531350i
778778 1.01321e9 + 1.75493e9i 0.0771385 + 0.133608i
779779 −9.13662e9 1.58251e10i −0.692476 1.19940i
780780 −3.54383e9 1.36127e10i −0.267388 1.02710i
781781 −8.42241e8 + 1.45880e9i −0.0632642 + 0.109577i
782782 9.58309e9 0.716608
783783 7.71373e9 1.89128e9i 0.574247 0.140796i
784784 1.20937e9 0.0896299
785785 1.54077e10 2.66869e10i 1.13683 1.96904i
786786 2.21795e9 + 8.51965e9i 0.162919 + 0.625811i
787787 −1.19537e10 2.07044e10i −0.874158 1.51409i −0.857657 0.514222i 0.828081π-0.828081\pi
−0.0165008 0.999864i 0.505253π-0.505253\pi
788788 −2.14676e9 3.71830e9i −0.156294 0.270709i
789789 2.20273e10 + 6.07061e9i 1.59659 + 0.440011i
790790 −1.10228e10 + 1.90920e10i −0.795419 + 1.37771i
791791 2.26817e10 1.62951
792792 2.71028e7 1.90329e9i 0.00193855 0.136134i
793793 9.43617e9 0.671954
794794 −3.96886e9 + 6.87427e9i −0.281381 + 0.487366i
795795 1.55490e10 1.53291e10i 1.09753 1.08201i
796796 3.78168e9 + 6.55006e9i 0.265760 + 0.460309i
797797 −1.36082e10 2.35700e10i −0.952128 1.64913i −0.740807 0.671718i 0.765557π-0.765557\pi
−0.211321 0.977417i 0.567777π-0.567777\pi
798798 9.94255e9 9.80197e9i 0.692608 0.682816i
799799 3.57540e9 6.19277e9i 0.247977 0.429508i
800800 2.06223e9 0.142404
801801 −1.29013e9 + 7.20560e8i −0.0886991 + 0.0495401i
802802 −7.59002e9 −0.519556
803803 8.87267e8 1.53679e9i 0.0604714 0.104740i
804804 −7.57623e8 2.08797e8i −0.0514111 0.0141686i
805805 1.40959e10 + 2.44149e10i 0.952375 + 1.64956i
806806 −6.31619e9 1.09400e10i −0.424896 0.735942i
807807 1.99211e9 + 7.65216e9i 0.133431 + 0.512538i
808808 1.08682e8 1.88243e8i 0.00724801 0.0125539i
809809 −2.09999e10 −1.39443 −0.697216 0.716861i 0.745578π-0.745578\pi
−0.697216 + 0.716861i 0.745578π0.745578\pi
810810 −7.53699e9 + 1.22360e10i −0.498311 + 0.808990i
811811 −1.21414e10 −0.799276 −0.399638 0.916673i 0.630864π-0.630864\pi
−0.399638 + 0.916673i 0.630864π0.630864\pi
812812 2.62842e9 4.55255e9i 0.172285 0.298407i
813813 2.35085e9 + 9.03016e9i 0.153429 + 0.589357i
814814 3.59477e9 + 6.22632e9i 0.233607 + 0.404619i
815815 −5.43248e9 9.40933e9i −0.351517 0.608845i
816816 3.11714e9 + 8.59068e8i 0.200836 + 0.0553493i
817817 −4.79234e9 + 8.30057e9i −0.307447 + 0.532514i
818818 6.21413e9 0.396957
819819 2.52724e10 1.41151e10i 1.60750 0.897821i
820820 1.24493e10 0.788489
821821 5.66101e9 9.80516e9i 0.357020 0.618377i −0.630441 0.776237i 0.717126π-0.717126\pi
0.987462 + 0.157860i 0.0504593π0.0504593\pi
822822 7.45727e9 7.35184e9i 0.468305 0.461684i
823823 2.91399e9 + 5.04718e9i 0.182217 + 0.315609i 0.942635 0.333825i 0.108339π-0.108339\pi
−0.760418 + 0.649434i 0.775006π0.775006\pi
824824 1.24502e9 + 2.15643e9i 0.0775228 + 0.134273i
825825 −3.56285e9 + 3.51247e9i −0.220906 + 0.217783i
826826 1.13462e10 1.96522e10i 0.700520 1.21334i
827827 2.11794e10 1.30210 0.651050 0.759034i 0.274329π-0.274329\pi
0.651050 + 0.759034i 0.274329π0.274329\pi
828828 1.41430e8 9.93188e9i 0.00865833 0.608030i
829829 −1.77492e10 −1.08203 −0.541013 0.841014i 0.681959π-0.681959\pi
−0.541013 + 0.841014i 0.681959π0.681959\pi
830830 −5.84733e9 + 1.01279e10i −0.354964 + 0.614815i
831831 −1.59994e10 4.40935e9i −0.967165 0.266545i
832832 1.64017e9 + 2.84085e9i 0.0987317 + 0.171008i
833833 −2.49194e9 4.31617e9i −0.149376 0.258727i
834834 7.54216e8 + 2.89712e9i 0.0450209 + 0.172936i
835835 5.01716e9 8.68997e9i 0.298233 0.516554i
836836 −3.83851e9 −0.227217
837837 −3.60578e9 + 1.23920e10i −0.212550 + 0.730471i
838838 −5.03909e9 −0.295800
839839 1.31911e10 2.28476e10i 0.771104 1.33559i −0.165855 0.986150i 0.553038π-0.553038\pi
0.936959 0.349441i 0.113628π-0.113628\pi
840840 2.39641e9 + 9.20517e9i 0.139503 + 0.535863i
841841 5.60981e9 + 9.71647e9i 0.325209 + 0.563278i
842842 −4.41940e9 7.65463e9i −0.255136 0.441908i
843843 −1.26458e10 3.48511e9i −0.727026 0.200364i
844844 −3.32753e9 + 5.76345e9i −0.190513 + 0.329977i
845845 −3.52439e10 −2.00949
846846 −6.36540e9 3.79692e9i −0.361434 0.215593i
847847 −1.75556e10 −0.992715
848848 −2.54596e9 + 4.40973e9i −0.143372 + 0.248328i
849849 5.29676e9 5.22187e9i 0.297052 0.292853i
850850 −4.24928e9 7.35997e9i −0.237328 0.411065i
851851 1.87584e10 + 3.24905e10i 1.04338 + 1.80719i
852852 −2.11200e9 + 2.08214e9i −0.116992 + 0.115338i
853853 −1.33903e10 + 2.31927e10i −0.738701 + 1.27947i 0.214379 + 0.976750i 0.431227π0.431227\pi
−0.953080 + 0.302717i 0.902106π0.902106\pi
854854 −6.38092e9 −0.350575
855855 2.48887e10 + 1.48460e10i 1.36183 + 0.812321i
856856 1.45228e9 0.0791392
857857 −6.44399e9 + 1.11613e10i −0.349721 + 0.605735i −0.986200 0.165560i 0.947057π-0.947057\pi
0.636479 + 0.771294i 0.280390π0.280390\pi
858858 −7.67233e9 2.11445e9i −0.414688 0.114286i
859859 −2.13794e9 3.70302e9i −0.115085 0.199333i 0.802729 0.596344i 0.203381π-0.203381\pi
−0.917814 + 0.397011i 0.870047π0.870047\pi
860860 −3.26495e9 5.65505e9i −0.175038 0.303174i
861861 6.45437e9 + 2.47927e10i 0.344622 + 1.32377i
862862 1.14265e9 1.97912e9i 0.0607626 0.105244i
863863 −2.63998e10 −1.39818 −0.699089 0.715035i 0.746411π-0.746411\pi
−0.699089 + 0.715035i 0.746411π0.746411\pi
864864 9.36338e8 3.21792e9i 0.0493895 0.169737i
865865 9.88231e9 0.519161
866866 −1.90715e9 + 3.30328e9i −0.0997867 + 0.172836i
867867 1.47755e9 + 5.67562e9i 0.0769973 + 0.295765i
868868 4.27113e9 + 7.39782e9i 0.221679 + 0.383959i
869869 6.23635e9 + 1.08017e10i 0.322375 + 0.558370i
870870 1.05193e10 + 2.89906e9i 0.541588 + 0.149259i
871871 −1.64283e9 + 2.84547e9i −0.0842423 + 0.145912i
872872 3.23271e9 0.165105
873873 5.06197e8 3.55476e10i 0.0257495 1.80826i
874874 −2.00304e10 −1.01484
875875 −3.01736e9 + 5.22622e9i −0.152265 + 0.263730i
876876 2.22491e9 2.19346e9i 0.111827 0.110246i
877877 −7.19624e9 1.24642e10i −0.360252 0.623975i 0.627750 0.778415i 0.283976π-0.283976\pi
−0.988002 + 0.154440i 0.950643π0.950643\pi
878878 −1.00703e10 1.74423e10i −0.502125 0.869706i
879879 −1.14688e10 + 1.13066e10i −0.569582 + 0.561529i
880880 1.30756e9 2.26476e9i 0.0646803 0.112030i
881881 2.86878e10 1.41345 0.706727 0.707487i 0.250171π-0.250171\pi
0.706727 + 0.707487i 0.250171π0.250171\pi
882882 −4.51004e9 + 2.51894e9i −0.221330 + 0.123617i
883883 1.10176e10 0.538550 0.269275 0.963063i 0.413216π-0.413216\pi
0.269275 + 0.963063i 0.413216π0.413216\pi
884884 6.75923e9 1.17073e10i 0.329090 0.570000i
885885 4.54091e10 + 1.25145e10i 2.20212 + 0.606893i
886886 1.83459e9 + 3.17761e9i 0.0886180 + 0.153491i
887887 −8.77534e9 1.51993e10i −0.422213 0.731294i 0.573943 0.818895i 0.305413π-0.305413\pi
−0.996156 + 0.0876014i 0.972080π0.972080\pi
888888 3.18907e9 + 1.22500e10i 0.152833 + 0.587069i
889889 −7.17571e9 + 1.24287e10i −0.342538 + 0.593293i
890890 −2.03017e9 −0.0965311
891891 3.86321e9 + 7.15430e9i 0.182968 + 0.338841i
892892 −1.03379e10 −0.487703
893893 −7.47322e9 + 1.29440e10i −0.351178 + 0.608259i
894894 2.56050e9 + 9.83549e9i 0.119852 + 0.460378i
895895 −4.12619e9 7.14677e9i −0.192384 0.333218i
896896 −1.10911e9 1.92104e9i −0.0515108 0.0892193i
897897 −4.00362e10 1.10338e10i −1.85216 0.510446i
898898 5.85733e9 1.01452e10i 0.269918 0.467512i
899899 9.79907e9 0.449807
900900 −7.69056e9 + 4.29532e9i −0.351649 + 0.196402i
901901 2.09841e10 0.955770
902902 3.52172e9 6.09979e9i 0.159783 0.276753i
903903 9.56931e9 9.43402e9i 0.432488 0.426373i
904904 −5.48959e9 9.50824e9i −0.247144 0.428066i
905905 2.36994e10 + 4.10486e10i 1.06284 + 1.84089i
906906 −1.11861e10 + 1.10279e10i −0.499722 + 0.492657i
907907 8.42225e9 1.45878e10i 0.374803 0.649177i −0.615495 0.788141i 0.711044π-0.711044\pi
0.990297 + 0.138964i 0.0443771π0.0443771\pi
908908 2.43542e9 0.107963
909909 −1.32200e7 + 9.28375e8i −0.000583793 + 0.0409968i
910910 3.97691e10 1.74945
911911 −7.36357e9 + 1.27541e10i −0.322682 + 0.558901i −0.981040 0.193803i 0.937918π-0.937918\pi
0.658359 + 0.752704i 0.271251π0.271251\pi
912912 −6.51538e9 1.79560e9i −0.284419 0.0783842i
913913 3.30824e9 + 5.73005e9i 0.143863 + 0.249178i
914914 −5.58639e9 9.67592e9i −0.242003 0.419161i
915915 −3.33682e9 1.28175e10i −0.143999 0.553133i
916916 9.27091e9 1.60577e10i 0.398555 0.690318i
917917 −2.48899e10 −1.06593
918918 −1.34139e10 + 3.28888e9i −0.572277 + 0.140313i
919919 7.11506e9 0.302395 0.151197 0.988504i 0.451687π-0.451687\pi
0.151197 + 0.988504i 0.451687π0.451687\pi
920920 6.82319e9 1.18181e10i 0.288888 0.500369i
921921 −6.22958e9 2.39293e10i −0.262755 1.00930i
922922 1.58488e10 + 2.74510e10i 0.665946 + 1.15345i
923923 6.19989e9 + 1.07385e10i 0.259524 + 0.449509i
924924 5.18818e9 + 1.42983e9i 0.216353 + 0.0596257i
925925 1.66355e10 2.88136e10i 0.691099 1.19702i
926926 −1.50530e10 −0.622995
927927 −9.13450e9 5.44868e9i −0.376622 0.224653i
928928 −2.54459e9 −0.104520
929929 1.69702e10 2.93933e10i 0.694437 1.20280i −0.275933 0.961177i 0.588987π-0.588987\pi
0.970370 0.241624i 0.0776799π-0.0776799\pi
930930 −1.26266e10 + 1.24481e10i −0.514751 + 0.507473i
931931 5.20860e9 + 9.02156e9i 0.211542 + 0.366402i
932932 2.38430e9 + 4.12973e9i 0.0964730 + 0.167096i
933933 9.55001e9 9.41499e9i 0.384962 0.379519i
934934 −3.87807e9 + 6.71702e9i −0.155741 + 0.269751i
935935 −1.07771e10 −0.431181
936936 −1.20337e10 7.17802e9i −0.479660 0.286114i
937937 −3.78364e10 −1.50252 −0.751261 0.660005i 0.770554π-0.770554\pi
−0.751261 + 0.660005i 0.770554π0.770554\pi
938938 1.11092e9 1.92416e9i 0.0439513 0.0761258i
939939 1.12823e9 + 3.10935e8i 0.0444703 + 0.0122558i
940940 −5.09139e9 8.81854e9i −0.199935 0.346298i
941941 −8.44461e9 1.46265e10i −0.330382 0.572238i 0.652205 0.758043i 0.273844π-0.273844\pi
−0.982587 + 0.185805i 0.940511π0.940511\pi
942942 −7.73342e9 2.97059e10i −0.301435 1.15788i
943943 1.83772e10 3.18303e10i 0.713657 1.23609i
944944 −1.09844e10 −0.424984
945945 −2.81098e10 2.93370e10i −1.08354 1.13085i
946946 −3.69442e9 −0.141882
947947 −5.84561e9 + 1.01249e10i −0.223668 + 0.387405i −0.955919 0.293630i 0.905137π-0.905137\pi
0.732251 + 0.681035i 0.238470π0.238470\pi
948948 5.53253e9 + 2.12517e10i 0.210909 + 0.810150i
949949 −6.53134e9 1.13126e10i −0.248068 0.429666i
950950 8.88176e9 + 1.53837e10i 0.336098 + 0.582139i
951951 −2.34563e10 6.46443e9i −0.884357 0.243724i
952952 −4.57072e9 + 7.91672e9i −0.171694 + 0.297383i
953953 5.10551e10 1.91079 0.955397 0.295323i 0.0954274π-0.0954274\pi
0.955397 + 0.295323i 0.0954274π0.0954274\pi
954954 3.09688e8 2.17478e10i 0.0115480 0.810955i
955955 −6.73981e10 −2.50401
956956 −5.74930e9 + 9.95808e9i −0.212820 + 0.368615i
957957 4.39621e9 4.33405e9i 0.162139 0.159846i
958958 8.03480e9 + 1.39167e10i 0.295254 + 0.511395i
959959 1.48032e10 + 2.56400e10i 0.541990 + 0.938755i
960960 3.27884e9 3.23248e9i 0.119611 0.117920i
961961 5.79464e9 1.00366e10i 0.210618 0.364800i
962962 5.29235e10 1.91662
963963 −5.41591e9 + 3.02488e9i −0.195425 + 0.109148i
964964 −3.89556e9 −0.140056
965965 −5.60202e9 + 9.70298e9i −0.200678 + 0.347584i
966966 2.70733e10 + 7.46124e9i 0.966319 + 0.266312i
967967 4.34365e9 + 7.52343e9i 0.154476 + 0.267561i 0.932868 0.360218i 0.117298π-0.117298\pi
−0.778392 + 0.627779i 0.783964π0.783964\pi
968968 4.24894e9 + 7.35937e9i 0.150562 + 0.260782i
969969 7.01673e9 + 2.69529e10i 0.247743 + 0.951640i
970970 2.44212e10 4.22987e10i 0.859143 1.48808i
971971 3.91347e10 1.37181 0.685906 0.727690i 0.259406π-0.259406\pi
0.685906 + 0.727690i 0.259406π0.259406\pi
972972 3.21061e9 + 1.39507e10i 0.112139 + 0.487263i
973973 −8.46384e9 −0.294559
974974 −1.21153e10 + 2.09844e10i −0.420126 + 0.727679i
975975 9.27853e9 + 3.56410e10i 0.320600 + 1.23150i
976976 1.54436e9 + 2.67490e9i 0.0531708 + 0.0920945i
977977 1.36255e10 + 2.36001e10i 0.467437 + 0.809624i 0.999308 0.0372010i 0.0118442π-0.0118442\pi
−0.531871 + 0.846825i 0.678511π0.678511\pi
978978 −1.04339e10 2.87552e9i −0.356664 0.0982946i
979979 −5.74305e8 + 9.94725e8i −0.0195615 + 0.0338816i
980980 −7.09708e9 −0.240873
981981 −1.20556e10 + 6.73327e9i −0.407706 + 0.227711i
982982 3.61379e10 1.21779
983983 −3.56677e9 + 6.17782e9i −0.119767 + 0.207443i −0.919675 0.392680i 0.871548π-0.871548\pi
0.799908 + 0.600122i 0.204881π0.204881\pi
984984 8.83106e9 8.70620e9i 0.295481 0.291304i
985985 1.25981e10 + 2.18205e10i 0.420028 + 0.727509i
986986 5.24321e9 + 9.08150e9i 0.174192 + 0.301709i
987987 1.49225e10 1.47115e10i 0.494005 0.487020i
988988 −1.41280e10 + 2.44704e10i −0.466049 + 0.807220i
989989 −1.92784e10 −0.633702
990990 −1.59051e8 + 1.11693e10i −0.00520969 + 0.365850i
991991 −1.99378e10 −0.650760 −0.325380 0.945583i 0.605492π-0.605492\pi
−0.325380 + 0.945583i 0.605492π0.605492\pi
992992 2.06746e9 3.58094e9i 0.0672428 0.116468i
993993 −2.27695e10 6.27514e9i −0.737956 0.203377i
994994 −4.19249e9 7.26160e9i −0.135400 0.234520i
995995 −2.21925e10 3.84385e10i −0.714208 1.23704i
996996 2.93488e9 + 1.12736e10i 0.0941202 + 0.361538i
997997 6.37020e9 1.10335e10i 0.203573 0.352598i −0.746104 0.665829i 0.768078π-0.768078\pi
0.949677 + 0.313231i 0.101411π0.101411\pi
998998 −3.72531e10 −1.18633
999999 −3.74077e10 3.90408e10i −1.18708 1.23891i
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 18.8.c.a.7.2 6
3.2 odd 2 54.8.c.a.19.1 6
4.3 odd 2 144.8.i.a.97.2 6
9.2 odd 6 162.8.a.e.1.3 3
9.4 even 3 inner 18.8.c.a.13.2 yes 6
9.5 odd 6 54.8.c.a.37.1 6
9.7 even 3 162.8.a.f.1.1 3
12.11 even 2 432.8.i.a.289.1 6
36.23 even 6 432.8.i.a.145.1 6
36.31 odd 6 144.8.i.a.49.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
18.8.c.a.7.2 6 1.1 even 1 trivial
18.8.c.a.13.2 yes 6 9.4 even 3 inner
54.8.c.a.19.1 6 3.2 odd 2
54.8.c.a.37.1 6 9.5 odd 6
144.8.i.a.49.2 6 36.31 odd 6
144.8.i.a.97.2 6 4.3 odd 2
162.8.a.e.1.3 3 9.2 odd 6
162.8.a.f.1.1 3 9.7 even 3
432.8.i.a.145.1 6 36.23 even 6
432.8.i.a.289.1 6 12.11 even 2