Properties

Label 162.8.c.q.55.4
Level 162162
Weight 88
Character 162.55
Analytic conductor 50.60650.606
Analytic rank 00
Dimension 88
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [162,8,Mod(55,162)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(162, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 8, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("162.55"); S:= CuspForms(chi, 8); N := Newforms(S);
 
Level: N N == 162=234 162 = 2 \cdot 3^{4}
Weight: k k == 8 8
Character orbit: [χ][\chi] == 162.c (of order 33, degree 22, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [8,-32,0,-256,-528] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 50.606374128450.6063741284
Analytic rank: 00
Dimension: 88
Relative dimension: 44 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q[x]/(x8)\mathbb{Q}[x]/(x^{8} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x82x7+2x6+518x5+53377x4+11940x3+3528x2+1563408x+346406544 x^{8} - 2x^{7} + 2x^{6} + 518x^{5} + 53377x^{4} + 11940x^{3} + 3528x^{2} + 1563408x + 346406544 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 28318 2^{8}\cdot 3^{18}
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 55.4
Root 6.43942+6.43942i6.43942 + 6.43942i of defining polynomial
Character χ\chi == 162.55
Dual form 162.8.c.q.109.4

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(4.00000+6.92820i)q2+(32.000055.4256i)q4+(140.213+242.855i)q5+(82.1617142.308i)q7+512.000q82243.40q10+(1018.971764.91i)q11+(839.167+1453.48i)q13+(657.293+1138.47i)q14+(2048.00+3547.24i)q16+31685.7q1712641.8q19+(8973.6115542.7i)q20+(8151.75+14119.3i)q22+(24733.542839.6i)q23+(256.638+444.510i)q2513426.7q2610516.7q28+(3776.406540.91i)q29+(78017.6135131.i)q31+(16384.028377.9i)q32+(126743.+219525.i)q34+46080.4q35+541440.q37+(50567.287584.9i)q38+(71788.8+124342.i)q40+(268792.465561.i)q41+(100249.+173636.i)q43130428.q44+395735.q46+(205436.355825.i)q47+(398270.+689825.i)q49+(2053.103556.08i)q50+(53706.793022.7i)q52+1.36778e6q53+571489.q55+(42066.872861.8i)q56+(30211.2+52327.3i)q58+(399444.691858.i)q59+(284720.+493149.i)q61+1.24828e6q62+262144.q64+(235323.+407592.i)q65+(2.40226e6+4.16084e6i)q67+(1.01394e61.75620e6i)q68+(184322.+319254.i)q70+2.45714e6q71+1.60344e6q73+(2.16576e6+3.75121e6i)q74+(404537.+700679.i)q76+(167440.290015.i)q77+(2.79499e6+4.84107e6i)q791.14862e6q80+4.30067e6q82+(4.91453e6+8.51221e6i)q83+(4.44273e6+7.69504e6i)q85+(801990.1.38909e6i)q86+(521712.903632.i)q88117249.q89+275789.q91+(1.58294e6+2.74173e6i)q92+(1.64348e6+2.84660e6i)q94+(1.77254e63.07013e6i)q95+(3.89623e66.74846e6i)q976.37233e6q98+O(q100)q+(-4.00000 + 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(140.213 + 242.855i) q^{5} +(82.1617 - 142.308i) q^{7} +512.000 q^{8} -2243.40 q^{10} +(1018.97 - 1764.91i) q^{11} +(839.167 + 1453.48i) q^{13} +(657.293 + 1138.47i) q^{14} +(-2048.00 + 3547.24i) q^{16} +31685.7 q^{17} -12641.8 q^{19} +(8973.61 - 15542.7i) q^{20} +(8151.75 + 14119.3i) q^{22} +(-24733.5 - 42839.6i) q^{23} +(-256.638 + 444.510i) q^{25} -13426.7 q^{26} -10516.7 q^{28} +(3776.40 - 6540.91i) q^{29} +(-78017.6 - 135131. i) q^{31} +(-16384.0 - 28377.9i) q^{32} +(-126743. + 219525. i) q^{34} +46080.4 q^{35} +541440. q^{37} +(50567.2 - 87584.9i) q^{38} +(71788.8 + 124342. i) q^{40} +(-268792. - 465561. i) q^{41} +(-100249. + 173636. i) q^{43} -130428. q^{44} +395735. q^{46} +(205436. - 355825. i) q^{47} +(398270. + 689825. i) q^{49} +(-2053.10 - 3556.08i) q^{50} +(53706.7 - 93022.7i) q^{52} +1.36778e6 q^{53} +571489. q^{55} +(42066.8 - 72861.8i) q^{56} +(30211.2 + 52327.3i) q^{58} +(-399444. - 691858. i) q^{59} +(-284720. + 493149. i) q^{61} +1.24828e6 q^{62} +262144. q^{64} +(-235323. + 407592. i) q^{65} +(2.40226e6 + 4.16084e6i) q^{67} +(-1.01394e6 - 1.75620e6i) q^{68} +(-184322. + 319254. i) q^{70} +2.45714e6 q^{71} +1.60344e6 q^{73} +(-2.16576e6 + 3.75121e6i) q^{74} +(404537. + 700679. i) q^{76} +(-167440. - 290015. i) q^{77} +(-2.79499e6 + 4.84107e6i) q^{79} -1.14862e6 q^{80} +4.30067e6 q^{82} +(-4.91453e6 + 8.51221e6i) q^{83} +(4.44273e6 + 7.69504e6i) q^{85} +(-801990. - 1.38909e6i) q^{86} +(521712. - 903632. i) q^{88} -117249. q^{89} +275789. q^{91} +(-1.58294e6 + 2.74173e6i) q^{92} +(1.64348e6 + 2.84660e6i) q^{94} +(-1.77254e6 - 3.07013e6i) q^{95} +(3.89623e6 - 6.74846e6i) q^{97} -6.37233e6 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q32q2256q4528q5560q7+4096q8+8448q102160q1113460q134480q1416384q16+45120q17+73408q1933792q2017280q2262640q23++23190336q98+O(q100) 8 q - 32 q^{2} - 256 q^{4} - 528 q^{5} - 560 q^{7} + 4096 q^{8} + 8448 q^{10} - 2160 q^{11} - 13460 q^{13} - 4480 q^{14} - 16384 q^{16} + 45120 q^{17} + 73408 q^{19} - 33792 q^{20} - 17280 q^{22} - 62640 q^{23}+ \cdots + 23190336 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/162Z)×\left(\mathbb{Z}/162\mathbb{Z}\right)^\times.

nn 8383
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 0 0
44 −32.0000 55.4256i −0.250000 0.433013i
55 140.213 + 242.855i 0.501640 + 0.868866i 0.999998 + 0.00189451i 0.000603041π0.000603041\pi
−0.498358 + 0.866971i 0.666064π0.666064\pi
66 0 0
77 82.1617 142.308i 0.0905370 0.156815i −0.817200 0.576354i 0.804475π-0.804475\pi
0.907737 + 0.419539i 0.137808π0.137808\pi
88 512.000 0.353553
99 0 0
1010 −2243.40 −0.709426
1111 1018.97 1764.91i 0.230827 0.399804i −0.727225 0.686399i 0.759190π-0.759190\pi
0.958052 + 0.286595i 0.0925235π0.0925235\pi
1212 0 0
1313 839.167 + 1453.48i 0.105937 + 0.183488i 0.914121 0.405443i 0.132883π-0.132883\pi
−0.808184 + 0.588930i 0.799549π0.799549\pi
1414 657.293 + 1138.47i 0.0640193 + 0.110885i
1515 0 0
1616 −2048.00 + 3547.24i −0.125000 + 0.216506i
1717 31685.7 1.56420 0.782099 0.623154i 0.214149π-0.214149\pi
0.782099 + 0.623154i 0.214149π0.214149\pi
1818 0 0
1919 −12641.8 −0.422835 −0.211418 0.977396i 0.567808π-0.567808\pi
−0.211418 + 0.977396i 0.567808π0.567808\pi
2020 8973.61 15542.7i 0.250820 0.434433i
2121 0 0
2222 8151.75 + 14119.3i 0.163219 + 0.282704i
2323 −24733.5 42839.6i −0.423874 0.734172i 0.572440 0.819947i 0.305997π-0.305997\pi
−0.996315 + 0.0857744i 0.972664π0.972664\pi
2424 0 0
2525 −256.638 + 444.510i −0.00328497 + 0.00568973i
2626 −13426.7 −0.149817
2727 0 0
2828 −10516.7 −0.0905370
2929 3776.40 6540.91i 0.0287531 0.0498018i −0.851291 0.524694i 0.824180π-0.824180\pi
0.880044 + 0.474892i 0.157513π0.157513\pi
3030 0 0
3131 −78017.6 135131.i −0.470356 0.814681i 0.529069 0.848579i 0.322541π-0.322541\pi
−0.999425 + 0.0338979i 0.989208π0.989208\pi
3232 −16384.0 28377.9i −0.0883883 0.153093i
3333 0 0
3434 −126743. + 219525.i −0.553028 + 0.957872i
3535 46080.4 0.181668
3636 0 0
3737 541440. 1.75729 0.878647 0.477472i 0.158447π-0.158447\pi
0.878647 + 0.477472i 0.158447π0.158447\pi
3838 50567.2 87584.9i 0.149495 0.258933i
3939 0 0
4040 71788.8 + 124342.i 0.177356 + 0.307190i
4141 −268792. 465561.i −0.609077 1.05495i −0.991393 0.130921i 0.958207π-0.958207\pi
0.382316 0.924032i 0.375127π-0.375127\pi
4242 0 0
4343 −100249. + 173636.i −0.192282 + 0.333043i −0.946006 0.324148i 0.894922π-0.894922\pi
0.753724 + 0.657191i 0.228256π0.228256\pi
4444 −130428. −0.230827
4545 0 0
4646 395735. 0.599449
4747 205436. 355825.i 0.288624 0.499912i −0.684857 0.728677i 0.740135π-0.740135\pi
0.973482 + 0.228765i 0.0734688π0.0734688\pi
4848 0 0
4949 398270. + 689825.i 0.483606 + 0.837630i
5050 −2053.10 3556.08i −0.00232282 0.00402324i
5151 0 0
5252 53706.7 93022.7i 0.0529684 0.0917439i
5353 1.36778e6 1.26198 0.630988 0.775792i 0.282650π-0.282650\pi
0.630988 + 0.775792i 0.282650π0.282650\pi
5454 0 0
5555 571489. 0.463168
5656 42066.8 72861.8i 0.0320097 0.0554424i
5757 0 0
5858 30211.2 + 52327.3i 0.0203315 + 0.0352152i
5959 −399444. 691858.i −0.253206 0.438566i 0.711201 0.702989i 0.248152π-0.248152\pi
−0.964407 + 0.264423i 0.914818π0.914818\pi
6060 0 0
6161 −284720. + 493149.i −0.160606 + 0.278179i −0.935086 0.354420i 0.884678π-0.884678\pi
0.774480 + 0.632599i 0.218012π0.218012\pi
6262 1.24828e6 0.665184
6363 0 0
6464 262144. 0.125000
6565 −235323. + 407592.i −0.106284 + 0.184090i
6666 0 0
6767 2.40226e6 + 4.16084e6i 0.975795 + 1.69013i 0.677285 + 0.735720i 0.263156π0.263156\pi
0.298510 + 0.954407i 0.403510π0.403510\pi
6868 −1.01394e6 1.75620e6i −0.391050 0.677318i
6969 0 0
7070 −184322. + 319254.i −0.0642293 + 0.111248i
7171 2.45714e6 0.814751 0.407376 0.913261i 0.366444π-0.366444\pi
0.407376 + 0.913261i 0.366444π0.366444\pi
7272 0 0
7373 1.60344e6 0.482418 0.241209 0.970473i 0.422456π-0.422456\pi
0.241209 + 0.970473i 0.422456π0.422456\pi
7474 −2.16576e6 + 3.75121e6i −0.621297 + 1.07612i
7575 0 0
7676 404537. + 700679.i 0.105709 + 0.183093i
7777 −167440. 290015.i −0.0417968 0.0723942i
7878 0 0
7979 −2.79499e6 + 4.84107e6i −0.637801 + 1.10470i 0.348113 + 0.937453i 0.386823π0.386823\pi
−0.985914 + 0.167252i 0.946511π0.946511\pi
8080 −1.14862e6 −0.250820
8181 0 0
8282 4.30067e6 0.861365
8383 −4.91453e6 + 8.51221e6i −0.943427 + 1.63406i −0.184556 + 0.982822i 0.559085π0.559085\pi
−0.758871 + 0.651241i 0.774249π0.774249\pi
8484 0 0
8585 4.44273e6 + 7.69504e6i 0.784664 + 1.35908i
8686 −801990. 1.38909e6i −0.135964 0.235497i
8787 0 0
8888 521712. 903632.i 0.0816097 0.141352i
8989 −117249. −0.0176296 −0.00881480 0.999961i 0.502806π-0.502806\pi
−0.00881480 + 0.999961i 0.502806π0.502806\pi
9090 0 0
9191 275789. 0.0383648
9292 −1.58294e6 + 2.74173e6i −0.211937 + 0.367086i
9393 0 0
9494 1.64348e6 + 2.84660e6i 0.204088 + 0.353491i
9595 −1.77254e6 3.07013e6i −0.212111 0.367387i
9696 0 0
9797 3.89623e6 6.74846e6i 0.433454 0.750765i −0.563714 0.825970i 0.690628π-0.690628\pi
0.997168 + 0.0752054i 0.0239613π0.0239613\pi
9898 −6.37233e6 −0.683922
9999 0 0
100100 32849.7 0.00328497
101101 −577424. + 1.00013e6i −0.0557661 + 0.0965897i −0.892561 0.450927i 0.851093π-0.851093\pi
0.836795 + 0.547517i 0.184427π0.184427\pi
102102 0 0
103103 8.49333e6 + 1.47109e7i 0.765857 + 1.32650i 0.939792 + 0.341746i 0.111018π0.111018\pi
−0.173935 + 0.984757i 0.555648π0.555648\pi
104104 429653. + 744181.i 0.0374543 + 0.0648727i
105105 0 0
106106 −5.47113e6 + 9.47627e6i −0.446176 + 0.772800i
107107 2.24189e7 1.76918 0.884589 0.466372i 0.154439π-0.154439\pi
0.884589 + 0.466372i 0.154439π0.154439\pi
108108 0 0
109109 1.75728e7 1.29971 0.649857 0.760056i 0.274829π-0.274829\pi
0.649857 + 0.760056i 0.274829π0.274829\pi
110110 −2.28596e6 + 3.95939e6i −0.163755 + 0.283631i
111111 0 0
112112 336534. + 582894.i 0.0226343 + 0.0392037i
113113 3.47819e6 + 6.02441e6i 0.226767 + 0.392772i 0.956848 0.290589i 0.0938512π-0.0938512\pi
−0.730081 + 0.683360i 0.760518π0.760518\pi
114114 0 0
115115 6.93588e6 1.20133e7i 0.425265 0.736580i
116116 −483379. −0.0287531
117117 0 0
118118 6.39111e6 0.358088
119119 2.60335e6 4.50913e6i 0.141618 0.245289i
120120 0 0
121121 7.66699e6 + 1.32796e7i 0.393438 + 0.681454i
122122 −2.27776e6 3.94519e6i −0.113566 0.196702i
123123 0 0
124124 −4.99313e6 + 8.64835e6i −0.235178 + 0.407340i
125125 2.17643e7 0.996688
126126 0 0
127127 −3.25050e7 −1.40811 −0.704057 0.710144i 0.748630π-0.748630\pi
−0.704057 + 0.710144i 0.748630π0.748630\pi
128128 −1.04858e6 + 1.81619e6i −0.0441942 + 0.0765466i
129129 0 0
130130 −1.88259e6 3.26074e6i −0.0751542 0.130171i
131131 −8.15697e6 1.41283e7i −0.317015 0.549085i 0.662849 0.748753i 0.269347π-0.269347\pi
−0.979864 + 0.199668i 0.936014π0.936014\pi
132132 0 0
133133 −1.03867e6 + 1.79903e6i −0.0382822 + 0.0663068i
134134 −3.84362e7 −1.37998
135135 0 0
136136 1.62231e7 0.553028
137137 1.80797e7 3.13150e7i 0.600716 1.04047i −0.391997 0.919967i 0.628215π-0.628215\pi
0.992713 0.120504i 0.0384512π-0.0384512\pi
138138 0 0
139139 −2.67592e7 4.63482e7i −0.845125 1.46380i −0.885513 0.464615i 0.846193π-0.846193\pi
0.0403883 0.999184i 0.487141π-0.487141\pi
140140 −1.47457e6 2.55404e6i −0.0454170 0.0786645i
141141 0 0
142142 −9.82854e6 + 1.70235e7i −0.288058 + 0.498931i
143143 3.42034e6 0.0978122
144144 0 0
145145 2.11799e6 0.0576948
146146 −6.41378e6 + 1.11090e7i −0.170561 + 0.295420i
147147 0 0
148148 −1.73261e7 3.00097e7i −0.439323 0.760931i
149149 2.72109e6 + 4.71307e6i 0.0673893 + 0.116722i 0.897751 0.440503i 0.145200π-0.145200\pi
−0.830362 + 0.557224i 0.811866π0.811866\pi
150150 0 0
151151 −1.09681e7 + 1.89972e7i −0.259245 + 0.449025i −0.966040 0.258393i 0.916807π-0.916807\pi
0.706795 + 0.707419i 0.250140π0.250140\pi
152152 −6.47260e6 −0.149495
153153 0 0
154154 2.67905e6 0.0591096
155155 2.18781e7 3.78940e7i 0.471899 0.817353i
156156 0 0
157157 −2.49533e6 4.32205e6i −0.0514612 0.0891334i 0.839147 0.543904i 0.183055π-0.183055\pi
−0.890609 + 0.454771i 0.849721π0.849721\pi
158158 −2.23599e7 3.87285e7i −0.450994 0.781144i
159159 0 0
160160 4.59449e6 7.95788e6i 0.0886782 0.153595i
161161 −8.12857e6 −0.153505
162162 0 0
163163 −4.47642e7 −0.809606 −0.404803 0.914404i 0.632660π-0.632660\pi
−0.404803 + 0.914404i 0.632660π0.632660\pi
164164 −1.72027e7 + 2.97959e7i −0.304539 + 0.527476i
165165 0 0
166166 −3.93162e7 6.80977e7i −0.667104 1.15546i
167167 3.07391e7 + 5.32416e7i 0.510720 + 0.884593i 0.999923 + 0.0124229i 0.00395445π0.00395445\pi
−0.489203 + 0.872170i 0.662712π0.662712\pi
168168 0 0
169169 2.99659e7 5.19024e7i 0.477555 0.827149i
170170 −7.10837e7 −1.10968
171171 0 0
172172 1.28318e7 0.192282
173173 5.12455e7 8.87599e7i 0.752479 1.30333i −0.194138 0.980974i 0.562191π-0.562191\pi
0.946618 0.322358i 0.104476π-0.104476\pi
174174 0 0
175175 42171.6 + 73043.4i 0.000594822 + 0.00103026i
176176 4.17370e6 + 7.22906e6i 0.0577068 + 0.0999511i
177177 0 0
178178 468994. 812322.i 0.00623301 0.0107959i
179179 6.08971e7 0.793617 0.396809 0.917901i 0.370118π-0.370118\pi
0.396809 + 0.917901i 0.370118π0.370118\pi
180180 0 0
181181 −9.62195e7 −1.20611 −0.603057 0.797698i 0.706051π-0.706051\pi
−0.603057 + 0.797698i 0.706051π0.706051\pi
182182 −1.10316e6 + 1.91072e6i −0.0135640 + 0.0234935i
183183 0 0
184184 −1.26635e7 2.19339e7i −0.149862 0.259569i
185185 7.59167e7 + 1.31492e8i 0.881528 + 1.52685i
186186 0 0
187187 3.22867e7 5.59223e7i 0.361059 0.625373i
188188 −2.62957e7 −0.288624
189189 0 0
190190 2.83606e7 0.299970
191191 3.69604e7 6.40172e7i 0.383813 0.664783i −0.607791 0.794097i 0.707944π-0.707944\pi
0.991604 + 0.129314i 0.0412774π0.0412774\pi
192192 0 0
193193 −4.07347e7 7.05546e7i −0.407863 0.706440i 0.586787 0.809741i 0.300393π-0.300393\pi
−0.994650 + 0.103302i 0.967059π0.967059\pi
194194 3.11698e7 + 5.39877e7i 0.306498 + 0.530871i
195195 0 0
196196 2.54893e7 4.41488e7i 0.241803 0.418815i
197197 −2.44033e7 −0.227414 −0.113707 0.993514i 0.536272π-0.536272\pi
−0.113707 + 0.993514i 0.536272π0.536272\pi
198198 0 0
199199 −1.52134e8 −1.36848 −0.684241 0.729256i 0.739867π-0.739867\pi
−0.684241 + 0.729256i 0.739867π0.739867\pi
200200 −131399. + 227589.i −0.00116141 + 0.00201162i
201201 0 0
202202 −4.61940e6 8.00103e6i −0.0394326 0.0682993i
203203 −620550. 1.07482e6i −0.00520644 0.00901781i
204204 0 0
205205 7.53760e7 1.30555e8i 0.611075 1.05841i
206206 −1.35893e8 −1.08309
207207 0 0
208208 −6.87445e6 −0.0529684
209209 −1.28816e7 + 2.23116e7i −0.0976018 + 0.169051i
210210 0 0
211211 2.93912e7 + 5.09071e7i 0.215392 + 0.373069i 0.953394 0.301729i 0.0975639π-0.0975639\pi
−0.738002 + 0.674799i 0.764231π0.764231\pi
212212 −4.37690e7 7.58102e7i −0.315494 0.546452i
213213 0 0
214214 −8.96757e7 + 1.55323e8i −0.625499 + 1.08340i
215215 −5.62246e7 −0.385826
216216 0 0
217217 −2.56402e7 −0.170339
218218 −7.02912e7 + 1.21748e8i −0.459518 + 0.795909i
219219 0 0
220220 −1.82877e7 3.16752e7i −0.115792 0.200558i
221221 2.65896e7 + 4.60545e7i 0.165706 + 0.287011i
222222 0 0
223223 1.65907e7 2.87360e7i 0.100184 0.173524i −0.811576 0.584246i 0.801390π-0.801390\pi
0.911760 + 0.410722i 0.134723π0.134723\pi
224224 −5.38455e6 −0.0320097
225225 0 0
226226 −5.56511e7 −0.320697
227227 −6.92959e7 + 1.20024e8i −0.393203 + 0.681048i −0.992870 0.119202i 0.961966π-0.961966\pi
0.599667 + 0.800250i 0.295300π0.295300\pi
228228 0 0
229229 −3.35184e7 5.80556e7i −0.184442 0.319463i 0.758946 0.651153i 0.225714π-0.225714\pi
−0.943388 + 0.331690i 0.892381π0.892381\pi
230230 5.54871e7 + 9.61064e7i 0.300707 + 0.520841i
231231 0 0
232232 1.93351e6 3.34894e6i 0.0101658 0.0176076i
233233 1.30899e8 0.677940 0.338970 0.940797i 0.389922π-0.389922\pi
0.338970 + 0.940797i 0.389922π0.389922\pi
234234 0 0
235235 1.15219e8 0.579142
236236 −2.55644e7 + 4.42789e7i −0.126603 + 0.219283i
237237 0 0
238238 2.08268e7 + 3.60731e7i 0.100139 + 0.173446i
239239 −9.63707e6 1.66919e7i −0.0456617 0.0790884i 0.842291 0.539023i 0.181206π-0.181206\pi
−0.887953 + 0.459934i 0.847873π0.847873\pi
240240 0 0
241241 −3.42495e7 + 5.93219e7i −0.157614 + 0.272995i −0.934008 0.357253i 0.883714π-0.883714\pi
0.776394 + 0.630248i 0.217047π0.217047\pi
242242 −1.22672e8 −0.556405
243243 0 0
244244 3.64441e7 0.160606
245245 −1.11685e8 + 1.93444e8i −0.485192 + 0.840377i
246246 0 0
247247 −1.06086e7 1.83746e7i −0.0447938 0.0775851i
248248 −3.99450e7 6.91868e7i −0.166296 0.288033i
249249 0 0
250250 −8.70571e7 + 1.50787e8i −0.352382 + 0.610344i
251251 2.45365e7 0.0979387 0.0489693 0.998800i 0.484406π-0.484406\pi
0.0489693 + 0.998800i 0.484406π0.484406\pi
252252 0 0
253253 −1.00811e8 −0.391367
254254 1.30020e8 2.25202e8i 0.497843 0.862290i
255255 0 0
256256 −8.38861e6 1.45295e7i −0.0312500 0.0541266i
257257 −1.66362e8 2.88148e8i −0.611349 1.05889i −0.991013 0.133763i 0.957294π-0.957294\pi
0.379664 0.925124i 0.376039π-0.376039\pi
258258 0 0
259259 4.44856e7 7.70514e7i 0.159100 0.275570i
260260 3.01214e7 0.106284
261261 0 0
262262 1.30512e8 0.448326
263263 1.85275e8 3.20907e8i 0.628019 1.08776i −0.359930 0.932979i 0.617199π-0.617199\pi
0.987949 0.154781i 0.0494673π-0.0494673\pi
264264 0 0
265265 1.91780e8 + 3.32173e8i 0.633058 + 1.09649i
266266 −8.30937e6 1.43922e7i −0.0270696 0.0468860i
267267 0 0
268268 1.53745e8 2.66294e8i 0.487898 0.845063i
269269 4.30980e8 1.34997 0.674985 0.737831i 0.264150π-0.264150\pi
0.674985 + 0.737831i 0.264150π0.264150\pi
270270 0 0
271271 3.41000e8 1.04079 0.520394 0.853927i 0.325785π-0.325785\pi
0.520394 + 0.853927i 0.325785π0.325785\pi
272272 −6.48923e7 + 1.12397e8i −0.195525 + 0.338659i
273273 0 0
274274 1.44638e8 + 2.50520e8i 0.424771 + 0.735724i
275275 523012. + 905884.i 0.00151652 + 0.00262669i
276276 0 0
277277 −3.41041e8 + 5.90701e8i −0.964112 + 1.66989i −0.252130 + 0.967693i 0.581131π0.581131\pi
−0.711982 + 0.702198i 0.752202π0.752202\pi
278278 4.28147e8 1.19519
279279 0 0
280280 2.35932e7 0.0642293
281281 −3.37119e7 + 5.83907e7i −0.0906382 + 0.156990i −0.907780 0.419447i 0.862224π-0.862224\pi
0.817142 + 0.576437i 0.195557π0.195557\pi
282282 0 0
283283 2.57861e8 + 4.46628e8i 0.676290 + 1.17137i 0.976090 + 0.217366i 0.0697466π0.0697466\pi
−0.299800 + 0.954002i 0.596920π0.596920\pi
284284 −7.86284e7 1.36188e8i −0.203688 0.352798i
285285 0 0
286286 −1.36814e7 + 2.36968e7i −0.0345818 + 0.0598975i
287287 −8.83375e7 −0.220576
288288 0 0
289289 5.93644e8 1.44672
290290 −8.47197e6 + 1.46739e7i −0.0203982 + 0.0353307i
291291 0 0
292292 −5.13102e7 8.88719e7i −0.120605 0.208893i
293293 −4.03009e7 6.98032e7i −0.0936005 0.162121i 0.815423 0.578865i 0.196504π-0.196504\pi
−0.909024 + 0.416744i 0.863171π0.863171\pi
294294 0 0
295295 1.12014e8 1.94014e8i 0.254037 0.440004i
296296 2.77217e8 0.621297
297297 0 0
298298 −4.35374e7 −0.0953029
299299 4.15110e7 7.18991e7i 0.0898077 0.155552i
300300 0 0
301301 1.64732e7 + 2.85324e7i 0.0348173 + 0.0603054i
302302 −8.77444e7 1.51978e8i −0.183314 0.317509i
303303 0 0
304304 2.58904e7 4.48435e7i 0.0528544 0.0915465i
305305 −1.59685e8 −0.322266
306306 0 0
307307 3.87201e8 0.763752 0.381876 0.924214i 0.375278π-0.375278\pi
0.381876 + 0.924214i 0.375278π0.375278\pi
308308 −1.07162e7 + 1.85610e7i −0.0208984 + 0.0361971i
309309 0 0
310310 1.75025e8 + 3.03152e8i 0.333683 + 0.577956i
311311 −3.15388e8 5.46268e8i −0.594543 1.02978i −0.993611 0.112858i 0.964000π-0.964000\pi
0.399068 0.916921i 0.369334π-0.369334\pi
312312 0 0
313313 −2.37475e8 + 4.11320e8i −0.437737 + 0.758183i −0.997515 0.0704598i 0.977553π-0.977553\pi
0.559777 + 0.828643i 0.310887π0.310887\pi
314314 3.99254e7 0.0727772
315315 0 0
316316 3.57759e8 0.637801
317317 −1.45155e8 + 2.51415e8i −0.255931 + 0.443286i −0.965148 0.261704i 0.915715π-0.915715\pi
0.709217 + 0.704991i 0.249049π0.249049\pi
318318 0 0
319319 −7.69606e6 1.33300e7i −0.0132740 0.0229912i
320320 3.67559e7 + 6.36631e7i 0.0627050 + 0.108608i
321321 0 0
322322 3.25143e7 5.63164e7i 0.0542723 0.0940024i
323323 −4.00564e8 −0.661398
324324 0 0
325325 −861448. −0.00139199
326326 1.79057e8 3.10135e8i 0.286239 0.495781i
327327 0 0
328328 −1.37621e8 2.38367e8i −0.215341 0.372982i
329329 −3.37579e7 5.84703e7i −0.0522624 0.0905211i
330330 0 0
331331 −5.24913e8 + 9.09175e8i −0.795589 + 1.37800i 0.126875 + 0.991919i 0.459505π0.459505\pi
−0.922464 + 0.386083i 0.873828π0.873828\pi
332332 6.29059e8 0.943427
333333 0 0
334334 −4.91825e8 −0.722267
335335 −6.73655e8 + 1.16680e9i −0.978995 + 1.69567i
336336 0 0
337337 −2.54630e8 4.41032e8i −0.362414 0.627719i 0.625944 0.779868i 0.284714π-0.284714\pi
−0.988358 + 0.152149i 0.951381π0.951381\pi
338338 2.39727e8 + 4.15219e8i 0.337682 + 0.584883i
339339 0 0
340340 2.84335e8 4.92482e8i 0.392332 0.679539i
341341 −3.17990e8 −0.434284
342342 0 0
343343 2.66218e8 0.356211
344344 −5.13274e7 + 8.89016e7i −0.0679821 + 0.117748i
345345 0 0
346346 4.09964e8 + 7.10079e8i 0.532083 + 0.921595i
347347 −2.34537e8 4.06230e8i −0.301341 0.521938i 0.675099 0.737727i 0.264101π-0.264101\pi
−0.976440 + 0.215789i 0.930768π0.930768\pi
348348 0 0
349349 1.09391e8 1.89470e8i 0.137750 0.238590i −0.788895 0.614529i 0.789346π-0.789346\pi
0.926645 + 0.375938i 0.122680π0.122680\pi
350350 −674746. −0.000841205
351351 0 0
352352 −6.67792e7 −0.0816097
353353 −2.21516e8 + 3.83677e8i −0.268036 + 0.464252i −0.968355 0.249578i 0.919708π-0.919708\pi
0.700318 + 0.713831i 0.253041π0.253041\pi
354354 0 0
355355 3.44521e8 + 5.96729e8i 0.408712 + 0.707909i
356356 3.75195e6 + 6.49857e6i 0.00440740 + 0.00763384i
357357 0 0
358358 −2.43588e8 + 4.21908e8i −0.280586 + 0.485989i
359359 −4.34672e8 −0.495828 −0.247914 0.968782i 0.579745π-0.579745\pi
−0.247914 + 0.968782i 0.579745π0.579745\pi
360360 0 0
361361 −7.34057e8 −0.821210
362362 3.84878e8 6.66628e8i 0.426426 0.738591i
363363 0 0
364364 −8.82526e6 1.52858e7i −0.00959119 0.0166124i
365365 2.24823e8 + 3.89405e8i 0.242000 + 0.419157i
366366 0 0
367367 8.23673e8 1.42664e9i 0.869809 1.50655i 0.00761697 0.999971i 0.497575π-0.497575\pi
0.862192 0.506582i 0.169091π-0.169091\pi
368368 2.02616e8 0.211937
369369 0 0
370370 −1.21467e9 −1.24667
371371 1.12379e8 1.94647e8i 0.114256 0.197896i
372372 0 0
373373 −2.85414e8 4.94351e8i −0.284770 0.493235i 0.687784 0.725916i 0.258584π-0.258584\pi
−0.972553 + 0.232680i 0.925250π0.925250\pi
374374 2.58294e8 + 4.47378e8i 0.255308 + 0.442206i
375375 0 0
376376 1.05183e8 1.82182e8i 0.102044 0.176746i
377377 1.26761e7 0.0121840
378378 0 0
379379 −1.71431e8 −0.161753 −0.0808763 0.996724i 0.525772π-0.525772\pi
−0.0808763 + 0.996724i 0.525772π0.525772\pi
380380 −1.13442e8 + 1.96488e8i −0.106055 + 0.183693i
381381 0 0
382382 2.95683e8 + 5.12138e8i 0.271397 + 0.470073i
383383 3.33432e8 + 5.77522e8i 0.303258 + 0.525258i 0.976872 0.213825i 0.0685924π-0.0685924\pi
−0.673614 + 0.739083i 0.735259π0.735259\pi
384384 0 0
385385 4.69545e7 8.13276e7i 0.0419339 0.0726316i
386386 6.51756e8 0.576806
387387 0 0
388388 −4.98717e8 −0.433454
389389 −2.54407e8 + 4.40646e8i −0.219132 + 0.379547i −0.954543 0.298074i 0.903656π-0.903656\pi
0.735411 + 0.677621i 0.236989π0.236989\pi
390390 0 0
391391 −7.83696e8 1.35740e9i −0.663024 1.14839i
392392 2.03914e8 + 3.53190e8i 0.170981 + 0.296147i
393393 0 0
394394 9.76133e7 1.69071e8i 0.0804030 0.139262i
395395 −1.56757e9 −1.27979
396396 0 0
397397 9.18742e8 0.736931 0.368466 0.929641i 0.379883π-0.379883\pi
0.368466 + 0.929641i 0.379883π0.379883\pi
398398 6.08534e8 1.05401e9i 0.483832 0.838021i
399399 0 0
400400 −1.05119e6 1.82071e6i −0.000821241 0.00142243i
401401 9.88625e8 + 1.71235e9i 0.765643 + 1.32613i 0.939906 + 0.341433i 0.110912π0.110912\pi
−0.174264 + 0.984699i 0.555754π0.555754\pi
402402 0 0
403403 1.30940e8 2.26794e8i 0.0996560 0.172609i
404404 7.39103e7 0.0557661
405405 0 0
406406 9.92880e6 0.00736301
407407 5.51711e8 9.55591e8i 0.405631 0.702573i
408408 0 0
409409 −1.24460e9 2.15572e9i −0.899497 1.55797i −0.828139 0.560523i 0.810600π-0.810600\pi
−0.0713582 0.997451i 0.522733π-0.522733\pi
410410 6.03008e8 + 1.04444e9i 0.432095 + 0.748411i
411411 0 0
412412 5.43573e8 9.41496e8i 0.382928 0.663252i
413413 −1.31276e8 −0.0916981
414414 0 0
415415 −2.75631e9 −1.89304
416416 2.74978e7 4.76276e7i 0.0187271 0.0324364i
417417 0 0
418418 −1.03053e8 1.78493e8i −0.0690149 0.119537i
419419 −8.95795e8 1.55156e9i −0.594921 1.03043i −0.993558 0.113325i 0.963850π-0.963850\pi
0.398637 0.917109i 0.369483π-0.369483\pi
420420 0 0
421421 6.98308e6 1.20950e7i 0.00456099 0.00789987i −0.863736 0.503945i 0.831882π-0.831882\pi
0.868297 + 0.496045i 0.165215π0.165215\pi
422422 −4.70259e8 −0.304610
423423 0 0
424424 7.00304e8 0.446176
425425 −8.13175e6 + 1.40846e7i −0.00513834 + 0.00889986i
426426 0 0
427427 4.67861e7 + 8.10359e7i 0.0290817 + 0.0503709i
428428 −7.17405e8 1.24258e9i −0.442294 0.766076i
429429 0 0
430430 2.24898e8 3.89535e8i 0.136410 0.236269i
431431 −2.57849e9 −1.55129 −0.775647 0.631166i 0.782577π-0.782577\pi
−0.775647 + 0.631166i 0.782577π0.782577\pi
432432 0 0
433433 1.82232e9 1.07874 0.539372 0.842068i 0.318662π-0.318662\pi
0.539372 + 0.842068i 0.318662π0.318662\pi
434434 1.02561e8 1.77641e8i 0.0602238 0.104311i
435435 0 0
436436 −5.62329e8 9.73983e8i −0.324929 0.562793i
437437 3.12675e8 + 5.41569e8i 0.179229 + 0.310434i
438438 0 0
439439 −6.65655e8 + 1.15295e9i −0.375512 + 0.650405i −0.990403 0.138206i 0.955866π-0.955866\pi
0.614892 + 0.788611i 0.289200π0.289200\pi
440440 2.92603e8 0.163755
441441 0 0
442442 −4.25433e8 −0.234344
443443 1.85680e7 3.21607e7i 0.0101473 0.0175757i −0.860907 0.508762i 0.830103π-0.830103\pi
0.871054 + 0.491186i 0.163437π0.163437\pi
444444 0 0
445445 −1.64397e7 2.84744e7i −0.00884371 0.0153178i
446446 1.32726e8 + 2.29888e8i 0.0708409 + 0.122700i
447447 0 0
448448 2.15382e7 3.73052e7i 0.0113171 0.0196018i
449449 −1.95772e9 −1.02068 −0.510338 0.859974i 0.670480π-0.670480\pi
−0.510338 + 0.859974i 0.670480π0.670480\pi
450450 0 0
451451 −1.09556e9 −0.562366
452452 2.22604e8 3.85562e8i 0.113383 0.196386i
453453 0 0
454454 −5.54367e8 9.60192e8i −0.278037 0.481574i
455455 3.86691e7 + 6.69769e7i 0.0192453 + 0.0333338i
456456 0 0
457457 −4.99589e8 + 8.65314e8i −0.244854 + 0.424099i −0.962090 0.272731i 0.912073π-0.912073\pi
0.717237 + 0.696829i 0.245407π0.245407\pi
458458 5.36295e8 0.260840
459459 0 0
460460 −8.87793e8 −0.425265
461461 8.24033e8 1.42727e9i 0.391734 0.678503i −0.600944 0.799291i 0.705209π-0.705209\pi
0.992678 + 0.120788i 0.0385420π0.0385420\pi
462462 0 0
463463 −1.73531e9 3.00564e9i −0.812538 1.40736i −0.911083 0.412224i 0.864752π-0.864752\pi
0.0985450 0.995133i 0.468581π-0.468581\pi
464464 1.54681e7 + 2.67916e7i 0.00718827 + 0.0124505i
465465 0 0
466466 −5.23597e8 + 9.06896e8i −0.239688 + 0.415152i
467467 2.49926e9 1.13554 0.567769 0.823188i 0.307807π-0.307807\pi
0.567769 + 0.823188i 0.307807π0.307807\pi
468468 0 0
469469 7.89496e8 0.353382
470470 −4.60874e8 + 7.98258e8i −0.204758 + 0.354651i
471471 0 0
472472 −2.04516e8 3.54231e8i −0.0895219 0.155056i
473473 2.04301e8 + 3.53859e8i 0.0887680 + 0.153751i
474474 0 0
475475 3.24436e6 5.61940e6i 0.00138900 0.00240582i
476476 −3.33229e8 −0.141618
477477 0 0
478478 1.54193e8 0.0645754
479479 2.19805e9 3.80714e9i 0.913827 1.58280i 0.105219 0.994449i 0.466446π-0.466446\pi
0.808609 0.588347i 0.200221π-0.200221\pi
480480 0 0
481481 4.54358e8 + 7.86972e8i 0.186162 + 0.322442i
482482 −2.73996e8 4.74575e8i −0.111450 0.193037i
483483 0 0
484484 4.90687e8 8.49895e8i 0.196719 0.340727i
485485 2.18520e9 0.869752
486486 0 0
487487 −2.82989e9 −1.11025 −0.555123 0.831769i 0.687329π-0.687329\pi
−0.555123 + 0.831769i 0.687329π0.687329\pi
488488 −1.45776e8 + 2.52492e8i −0.0567830 + 0.0983510i
489489 0 0
490490 −8.93480e8 1.54755e9i −0.343083 0.594237i
491491 −1.22921e9 2.12905e9i −0.468641 0.811710i 0.530716 0.847550i 0.321923π-0.321923\pi
−0.999358 + 0.0358390i 0.988590π0.988590\pi
492492 0 0
493493 1.19658e8 2.07253e8i 0.0449755 0.0778999i
494494 1.69737e8 0.0633480
495495 0 0
496496 6.39121e8 0.235178
497497 2.01882e8 3.49671e8i 0.0737651 0.127765i
498498 0 0
499499 1.50302e9 + 2.60331e9i 0.541518 + 0.937938i 0.998817 + 0.0486243i 0.0154837π0.0154837\pi
−0.457299 + 0.889313i 0.651183π0.651183\pi
500500 −6.96457e8 1.20630e9i −0.249172 0.431579i
501501 0 0
502502 −9.81459e7 + 1.69994e8i −0.0346266 + 0.0599750i
503503 −2.43279e8 −0.0852348 −0.0426174 0.999091i 0.513570π-0.513570\pi
−0.0426174 + 0.999091i 0.513570π0.513570\pi
504504 0 0
505505 −3.23849e8 −0.111898
506506 4.03242e8 6.98436e8i 0.138369 0.239662i
507507 0 0
508508 1.04016e9 + 1.80161e9i 0.352028 + 0.609731i
509509 2.00216e9 + 3.46785e9i 0.672956 + 1.16559i 0.977062 + 0.212956i 0.0683092π0.0683092\pi
−0.304105 + 0.952638i 0.598357π0.598357\pi
510510 0 0
511511 1.31742e8 2.28183e8i 0.0436767 0.0756503i
512512 1.34218e8 0.0441942
513513 0 0
514514 2.66180e9 0.864578
515515 −2.38174e9 + 4.12530e9i −0.768369 + 1.33085i
516516 0 0
517517 −4.18665e8 7.25149e8i −0.133245 0.230786i
518518 3.55885e8 + 6.16411e8i 0.112501 + 0.194857i
519519 0 0
520520 −1.20486e8 + 2.08687e8i −0.0375771 + 0.0650855i
521521 5.72614e9 1.77390 0.886951 0.461864i 0.152819π-0.152819\pi
0.886951 + 0.461864i 0.152819π0.152819\pi
522522 0 0
523523 1.53753e9 0.469966 0.234983 0.971999i 0.424497π-0.424497\pi
0.234983 + 0.971999i 0.424497π0.424497\pi
524524 −5.22046e8 + 9.04210e8i −0.158507 + 0.274543i
525525 0 0
526526 1.48220e9 + 2.56725e9i 0.444077 + 0.769163i
527527 −2.47204e9 4.28170e9i −0.735731 1.27432i
528528 0 0
529529 4.78926e8 8.29523e8i 0.140661 0.243632i
530530 −3.06848e9 −0.895279
531531 0 0
532532 1.32950e8 0.0382822
533533 4.51122e8 7.81366e8i 0.129047 0.223516i
534534 0 0
535535 3.14341e9 + 5.44455e9i 0.887490 + 1.53718i
536536 1.22996e9 + 2.13035e9i 0.344996 + 0.597550i
537537 0 0
538538 −1.72392e9 + 2.98592e9i −0.477287 + 0.826685i
539539 1.62330e9 0.446518
540540 0 0
541541 3.90611e9 1.06061 0.530303 0.847808i 0.322078π-0.322078\pi
0.530303 + 0.847808i 0.322078π0.322078\pi
542542 −1.36400e9 + 2.36252e9i −0.367974 + 0.637349i
543543 0 0
544544 −5.19138e8 8.99174e8i −0.138257 0.239468i
545545 2.46393e9 + 4.26764e9i 0.651988 + 1.12928i
546546 0 0
547547 2.50427e9 4.33752e9i 0.654222 1.13315i −0.327866 0.944724i 0.606330π-0.606330\pi
0.982088 0.188422i 0.0603372π-0.0603372\pi
548548 −2.31420e9 −0.600716
549549 0 0
550550 −8.36820e6 −0.00214468
551551 −4.77404e7 + 8.26888e7i −0.0121578 + 0.0210580i
552552 0 0
553553 4.59282e8 + 7.95500e8i 0.115489 + 0.200033i
554554 −2.72833e9 4.72560e9i −0.681730 1.18079i
555555 0 0
556556 −1.71259e9 + 2.96629e9i −0.422562 + 0.731899i
557557 −1.45387e9 −0.356479 −0.178239 0.983987i 0.557040π-0.557040\pi
−0.178239 + 0.983987i 0.557040π0.557040\pi
558558 0 0
559559 −3.36502e8 −0.0814790
560560 −9.43727e7 + 1.63458e8i −0.0227085 + 0.0393323i
561561 0 0
562562 −2.69695e8 4.67126e8i −0.0640909 0.111009i
563563 −2.95600e9 5.11994e9i −0.698111 1.20916i −0.969121 0.246587i 0.920691π-0.920691\pi
0.271009 0.962577i 0.412643π-0.412643\pi
564564 0 0
565565 −9.75373e8 + 1.68940e9i −0.227510 + 0.394060i
566566 −4.12577e9 −0.956418
567567 0 0
568568 1.25805e9 0.288058
569569 −3.81277e9 + 6.60392e9i −0.867657 + 1.50283i −0.00327263 + 0.999995i 0.501042π0.501042\pi
−0.864384 + 0.502831i 0.832292π0.832292\pi
570570 0 0
571571 3.68647e9 + 6.38515e9i 0.828675 + 1.43531i 0.899078 + 0.437788i 0.144238π0.144238\pi
−0.0704037 + 0.997519i 0.522429π0.522429\pi
572572 −1.09451e8 1.89574e8i −0.0244531 0.0423539i
573573 0 0
574574 3.53350e8 6.12020e8i 0.0779854 0.135075i
575575 2.53902e7 0.00556965
576576 0 0
577577 1.95790e9 0.424302 0.212151 0.977237i 0.431953π-0.431953\pi
0.212151 + 0.977237i 0.431953π0.431953\pi
578578 −2.37458e9 + 4.11289e9i −0.511492 + 0.885930i
579579 0 0
580580 −6.77758e7 1.17391e8i −0.0144237 0.0249826i
581581 8.07571e8 + 1.39875e9i 0.170830 + 0.295886i
582582 0 0
583583 1.39373e9 2.41401e9i 0.291298 0.504543i
584584 8.20964e8 0.170561
585585 0 0
586586 6.44815e8 0.132371
587587 1.09928e9 1.90401e9i 0.224324 0.388541i −0.731792 0.681528i 0.761316π-0.761316\pi
0.956117 + 0.292987i 0.0946492π0.0946492\pi
588588 0 0
589589 9.86283e8 + 1.70829e9i 0.198883 + 0.344476i
590590 8.96114e8 + 1.55212e9i 0.179631 + 0.311130i
591591 0 0
592592 −1.10887e9 + 1.92062e9i −0.219662 + 0.380465i
593593 6.54769e9 1.28943 0.644713 0.764425i 0.276977π-0.276977\pi
0.644713 + 0.764425i 0.276977π0.276977\pi
594594 0 0
595595 1.46009e9 0.284165
596596 1.74150e8 3.01636e8i 0.0336946 0.0583608i
597597 0 0
598598 3.32088e8 + 5.75193e8i 0.0635037 + 0.109992i
599599 2.63642e9 + 4.56641e9i 0.501210 + 0.868122i 0.999999 + 0.00139803i 0.000445007π0.000445007\pi
−0.498789 + 0.866724i 0.666222π0.666222\pi
600600 0 0
601601 −2.59635e9 + 4.49701e9i −0.487869 + 0.845013i −0.999903 0.0139518i 0.995559π-0.995559\pi
0.512034 + 0.858965i 0.328892π0.328892\pi
602602 −2.63571e8 −0.0492392
603603 0 0
604604 1.40391e9 0.259245
605605 −2.15002e9 + 3.72394e9i −0.394728 + 0.683689i
606606 0 0
607607 1.21854e9 + 2.11058e9i 0.221147 + 0.383037i 0.955156 0.296102i 0.0956868π-0.0956868\pi
−0.734010 + 0.679139i 0.762353π0.762353\pi
608608 2.07123e8 + 3.58748e8i 0.0373737 + 0.0647332i
609609 0 0
610610 6.38741e8 1.10633e9i 0.113938 0.197347i
611611 6.89579e8 0.122304
612612 0 0
613613 −3.31215e9 −0.580763 −0.290382 0.956911i 0.593782π-0.593782\pi
−0.290382 + 0.956911i 0.593782π0.593782\pi
614614 −1.54880e9 + 2.68261e9i −0.270027 + 0.467700i
615615 0 0
616616 −8.57295e7 1.48488e8i −0.0147774 0.0255952i
617617 −1.63565e9 2.83303e9i −0.280345 0.485572i 0.691125 0.722736i 0.257116π-0.257116\pi
−0.971470 + 0.237164i 0.923782π0.923782\pi
618618 0 0
619619 7.18024e8 1.24365e9i 0.121681 0.210757i −0.798750 0.601663i 0.794505π-0.794505\pi
0.920431 + 0.390906i 0.127838π0.127838\pi
620620 −2.80040e9 −0.471899
621621 0 0
622622 5.04620e9 0.840811
623623 −9.63334e6 + 1.66854e7i −0.00159613 + 0.00276458i
624624 0 0
625625 3.07168e9 + 5.32030e9i 0.503263 + 0.871678i
626626 −1.89980e9 3.29056e9i −0.309527 0.536117i
627627 0 0
628628 −1.59701e8 + 2.76611e8i −0.0257306 + 0.0445667i
629629 1.71559e10 2.74876
630630 0 0
631631 −7.26152e9 −1.15060 −0.575301 0.817942i 0.695115π-0.695115\pi
−0.575301 + 0.817942i 0.695115π0.695115\pi
632632 −1.43104e9 + 2.47863e9i −0.225497 + 0.390572i
633633 0 0
634634 −1.16124e9 2.01132e9i −0.180971 0.313451i
635635 −4.55762e9 7.89402e9i −0.706366 1.22346i
636636 0 0
637637 −6.68430e8 + 1.15776e9i −0.102463 + 0.177472i
638638 1.23137e8 0.0187722
639639 0 0
640640 −5.88094e8 −0.0886782
641641 4.47848e9 7.75695e9i 0.671625 1.16329i −0.305818 0.952090i 0.598930π-0.598930\pi
0.977443 0.211199i 0.0677369π-0.0677369\pi
642642 0 0
643643 1.29774e9 + 2.24774e9i 0.192508 + 0.333433i 0.946081 0.323931i 0.105005π-0.105005\pi
−0.753573 + 0.657364i 0.771671π0.771671\pi
644644 2.60114e8 + 4.50531e8i 0.0383763 + 0.0664698i
645645 0 0
646646 1.60226e9 2.77519e9i 0.233840 0.405022i
647647 −9.11067e9 −1.32247 −0.661234 0.750180i 0.729967π-0.729967\pi
−0.661234 + 0.750180i 0.729967π0.729967\pi
648648 0 0
649649 −1.62809e9 −0.233787
650650 3.44579e6 5.96829e6i 0.000492144 0.000852418i
651651 0 0
652652 1.43245e9 + 2.48108e9i 0.202402 + 0.350570i
653653 5.11670e9 + 8.86238e9i 0.719107 + 1.24553i 0.961354 + 0.275315i 0.0887823π0.0887823\pi
−0.242247 + 0.970215i 0.577884π0.577884\pi
654654 0 0
655655 2.28742e9 3.96193e9i 0.318054 0.550886i
656656 2.20194e9 0.304539
657657 0 0
658658 5.40126e8 0.0739102
659659 5.37910e9 9.31688e9i 0.732168 1.26815i −0.223786 0.974638i 0.571842π-0.571842\pi
0.955955 0.293515i 0.0948249π-0.0948249\pi
660660 0 0
661661 −3.02911e9 5.24658e9i −0.407953 0.706596i 0.586707 0.809799i 0.300424π-0.300424\pi
−0.994660 + 0.103204i 0.967091π0.967091\pi
662662 −4.19930e9 7.27340e9i −0.562567 0.974394i
663663 0 0
664664 −2.51624e9 + 4.35825e9i −0.333552 + 0.577729i
665665 −5.82539e8 −0.0768156
666666 0 0
667667 −3.73613e8 −0.0487508
668668 1.96730e9 3.40746e9i 0.255360 0.442296i
669669 0 0
670670 −5.38924e9 9.33444e9i −0.692254 1.19902i
671671 5.80241e8 + 1.00501e9i 0.0741446 + 0.128422i
672672 0 0
673673 −2.11743e9 + 3.66750e9i −0.267767 + 0.463786i −0.968285 0.249849i 0.919619π-0.919619\pi
0.700518 + 0.713635i 0.252952π0.252952\pi
674674 4.07408e9 0.512530
675675 0 0
676676 −3.83563e9 −0.477555
677677 −9.92582e8 + 1.71920e9i −0.122944 + 0.212945i −0.920927 0.389735i 0.872567π-0.872567\pi
0.797984 + 0.602679i 0.205900π0.205900\pi
678678 0 0
679679 −6.40241e8 1.10893e9i −0.0784873 0.135944i
680680 2.27468e9 + 3.93986e9i 0.277421 + 0.480507i
681681 0 0
682682 1.27196e9 2.20310e9i 0.153543 0.265943i
683683 −2.07576e9 −0.249290 −0.124645 0.992201i 0.539779π-0.539779\pi
−0.124645 + 0.992201i 0.539779π0.539779\pi
684684 0 0
685685 1.01400e10 1.20537
686686 −1.06487e9 + 1.84441e9i −0.125940 + 0.218134i
687687 0 0
688688 −4.10619e8 7.11213e8i −0.0480706 0.0832607i
689689 1.14780e9 + 1.98804e9i 0.133690 + 0.231557i
690690 0 0
691691 −7.28221e8 + 1.26132e9i −0.0839634 + 0.145429i −0.904949 0.425520i 0.860091π-0.860091\pi
0.820986 + 0.570949i 0.193425π0.193425\pi
692692 −6.55943e9 −0.752479
693693 0 0
694694 3.75259e9 0.426160
695695 7.50394e9 1.29972e10i 0.847896 1.46860i
696696 0 0
697697 −8.51685e9 1.47516e10i −0.952718 1.65016i
698698 8.75127e8 + 1.51576e9i 0.0974040 + 0.168709i
699699 0 0
700700 2.69898e6 4.67478e6i 0.000297411 0.000515131i
701701 −6.55669e9 −0.718905 −0.359452 0.933163i 0.617036π-0.617036\pi
−0.359452 + 0.933163i 0.617036π0.617036\pi
702702 0 0
703703 −6.84477e9 −0.743046
704704 2.67117e8 4.62660e8i 0.0288534 0.0499755i
705705 0 0
706706 −1.77213e9 3.06941e9i −0.189530 0.328276i
707707 9.48843e7 + 1.64344e8i 0.0100978 + 0.0174899i
708708 0 0
709709 −3.20151e9 + 5.54518e9i −0.337360 + 0.584324i −0.983935 0.178526i 0.942867π-0.942867\pi
0.646576 + 0.762850i 0.276200π0.276200\pi
710710 −5.51234e9 −0.578005
711711 0 0
712712 −6.00313e7 −0.00623301
713713 −3.85929e9 + 6.68449e9i −0.398744 + 0.690645i
714714 0 0
715715 4.79575e8 + 8.30648e8i 0.0490665 + 0.0849857i
716716 −1.94871e9 3.37526e9i −0.198404 0.343646i
717717 0 0
718718 1.73869e9 3.01150e9i 0.175302 0.303631i
719719 −1.33984e10 −1.34432 −0.672158 0.740408i 0.734632π-0.734632\pi
−0.672158 + 0.740408i 0.734632π0.734632\pi
720720 0 0
721721 2.79130e9 0.277354
722722 2.93623e9 5.08569e9i 0.290342 0.502887i
723723 0 0
724724 3.07902e9 + 5.33303e9i 0.301528 + 0.522262i
725725 1.93833e6 + 3.35729e6i 0.000188906 + 0.000327194i
726726 0 0
727727 7.20401e9 1.24777e10i 0.695351 1.20438i −0.274711 0.961527i 0.588582π-0.588582\pi
0.970062 0.242856i 0.0780844π-0.0780844\pi
728728 1.41204e8 0.0135640
729729 0 0
730730 −3.59717e9 −0.342240
731731 −3.17645e9 + 5.50178e9i −0.300768 + 0.520945i
732732 0 0
733733 −5.60638e9 9.71053e9i −0.525797 0.910708i −0.999548 0.0300489i 0.990434π-0.990434\pi
0.473751 0.880659i 0.342900π-0.342900\pi
734734 6.58939e9 + 1.14132e10i 0.615048 + 1.06529i
735735 0 0
736736 −8.10466e8 + 1.40377e9i −0.0749311 + 0.129785i
737737 9.79133e9 0.900960
738738 0 0
739739 7.79784e9 0.710753 0.355377 0.934723i 0.384353π-0.384353\pi
0.355377 + 0.934723i 0.384353π0.384353\pi
740740 4.85867e9 8.41546e9i 0.440764 0.763426i
741741 0 0
742742 8.99034e8 + 1.55717e9i 0.0807909 + 0.139934i
743743 −7.80793e9 1.35237e10i −0.698353 1.20958i −0.969037 0.246915i 0.920583π-0.920583\pi
0.270684 0.962668i 0.412750π-0.412750\pi
744744 0 0
745745 −7.63062e8 + 1.32166e9i −0.0676103 + 0.117104i
746746 4.56662e9 0.402725
747747 0 0
748748 −4.13270e9 −0.361059
749749 1.84198e9 3.19040e9i 0.160176 0.277433i
750750 0 0
751751 −6.37283e9 1.10381e10i −0.549025 0.950940i −0.998342 0.0575671i 0.981666π-0.981666\pi
0.449316 0.893373i 0.351668π-0.351668\pi
752752 8.41464e8 + 1.45746e9i 0.0721561 + 0.124978i
753753 0 0
754754 −5.07044e7 + 8.78226e7i −0.00430770 + 0.00746116i
755755 −6.15144e9 −0.520190
756756 0 0
757757 −2.31819e10 −1.94229 −0.971144 0.238492i 0.923347π-0.923347\pi
−0.971144 + 0.238492i 0.923347π0.923347\pi
758758 6.85722e8 1.18771e9i 0.0571882 0.0990528i
759759 0 0
760760 −9.07540e8 1.57191e9i −0.0749926 0.129891i
761761 1.11016e10 + 1.92286e10i 0.913148 + 1.58162i 0.809591 + 0.586995i 0.199689π0.199689\pi
0.103557 + 0.994624i 0.466978π0.466978\pi
762762 0 0
763763 1.44381e9 2.50075e9i 0.117672 0.203814i
764764 −4.73093e9 −0.383813
765765 0 0
766766 −5.33492e9 −0.428871
767767 6.70401e8 1.16117e9i 0.0536477 0.0929205i
768768 0 0
769769 −1.09956e10 1.90449e10i −0.871916 1.51020i −0.860012 0.510275i 0.829544π-0.829544\pi
−0.0119049 0.999929i 0.503790π-0.503790\pi
770770 3.75636e8 + 6.50621e8i 0.0296517 + 0.0513583i
771771 0 0
772772 −2.60702e9 + 4.51550e9i −0.203932 + 0.353220i
773773 −1.12771e10 −0.878151 −0.439075 0.898450i 0.644694π-0.644694\pi
−0.439075 + 0.898450i 0.644694π0.644694\pi
774774 0 0
775775 8.00891e7 0.00618042
776776 1.99487e9 3.45521e9i 0.153249 0.265435i
777777 0 0
778778 −2.03525e9 3.52516e9i −0.154950 0.268380i
779779 3.39801e9 + 5.88553e9i 0.257539 + 0.446071i
780780 0 0
781781 2.50375e9 4.33662e9i 0.188067 0.325741i
782782 1.25391e10 0.937657
783783 0 0
784784 −3.26263e9 −0.241803
785785 6.99755e8 1.21201e9i 0.0516300 0.0894258i
786786 0 0
787787 9.17090e9 + 1.58845e10i 0.670657 + 1.16161i 0.977718 + 0.209922i 0.0673210π0.0673210\pi
−0.307061 + 0.951690i 0.599346π0.599346\pi
788788 7.80906e8 + 1.35257e9i 0.0568535 + 0.0984731i
789789 0 0
790790 6.27029e9 1.08605e10i 0.452473 0.783706i
791791 1.14310e9 0.0821231
792792 0 0
793793 −9.55709e8 −0.0680565
794794 −3.67497e9 + 6.36523e9i −0.260544 + 0.451276i
795795 0 0
796796 4.86827e9 + 8.43210e9i 0.342121 + 0.592570i
797797 −7.85176e8 1.35997e9i −0.0549368 0.0951533i 0.837249 0.546822i 0.184162π-0.184162\pi
−0.892186 + 0.451668i 0.850829π0.850829\pi
798798 0 0
799799 6.50937e9 1.12746e10i 0.451466 0.781962i
800800 1.68190e7 0.00116141
801801 0 0
802802 −1.58180e10 −1.08278
803803 1.63386e9 2.82993e9i 0.111355 0.192873i
804804 0 0
805805 −1.13973e9 1.97407e9i −0.0770044 0.133376i
806806 1.04752e9 + 1.81435e9i 0.0704674 + 0.122053i
807807 0 0
808808 −2.95641e8 + 5.12066e8i −0.0197163 + 0.0341496i
809809 −3.66110e9 −0.243104 −0.121552 0.992585i 0.538787π-0.538787\pi
−0.121552 + 0.992585i 0.538787π0.538787\pi
810810 0 0
811811 −2.32307e10 −1.52929 −0.764645 0.644451i 0.777086π-0.777086\pi
−0.764645 + 0.644451i 0.777086π0.777086\pi
812812 −3.97152e7 + 6.87887e7i −0.00260322 + 0.00450891i
813813 0 0
814814 4.41369e9 + 7.64473e9i 0.286824 + 0.496794i
815815 −6.27650e9 1.08712e10i −0.406131 0.703439i
816816 0 0
817817 1.26732e9 2.19507e9i 0.0813038 0.140822i
818818 1.99137e10 1.27208
819819 0 0
820820 −9.64812e9 −0.611075
821821 −1.26531e10 + 2.19157e10i −0.797984 + 1.38215i 0.122943 + 0.992414i 0.460767π0.460767\pi
−0.920927 + 0.389736i 0.872566π0.872566\pi
822822 0 0
823823 −4.14339e9 7.17655e9i −0.259093 0.448763i 0.706906 0.707307i 0.250090π-0.250090\pi
−0.965999 + 0.258545i 0.916757π0.916757\pi
824824 4.34858e9 + 7.53197e9i 0.270771 + 0.468990i
825825 0 0
826826 5.25104e8 9.09507e8i 0.0324202 0.0561534i
827827 −3.06921e10 −1.88694 −0.943470 0.331459i 0.892459π-0.892459\pi
−0.943470 + 0.331459i 0.892459π0.892459\pi
828828 0 0
829829 1.83150e10 1.11652 0.558260 0.829666i 0.311469π-0.311469\pi
0.558260 + 0.829666i 0.311469π0.311469\pi
830830 1.10253e10 1.90963e10i 0.669291 1.15925i
831831 0 0
832832 2.19982e8 + 3.81021e8i 0.0132421 + 0.0229360i
833833 1.26195e10 + 2.18576e10i 0.756456 + 1.31022i
834834 0 0
835835 −8.62000e9 + 1.49303e10i −0.512395 + 0.887494i
836836 1.64885e9 0.0976018
837837 0 0
838838 1.43327e10 0.841346
839839 −1.50106e10 + 2.59991e10i −0.877466 + 1.51982i −0.0233529 + 0.999727i 0.507434π0.507434\pi
−0.854113 + 0.520088i 0.825899π0.825899\pi
840840 0 0
841841 8.59642e9 + 1.48894e10i 0.498347 + 0.863161i
842842 5.58646e7 + 9.67603e7i 0.00322511 + 0.00558605i
843843 0 0
844844 1.88104e9 3.25805e9i 0.107696 0.186535i
845845 1.68064e10 0.958242
846846 0 0
847847 2.51973e9 0.142483
848848 −2.80122e9 + 4.85185e9i −0.157747 + 0.273226i
849849 0 0
850850 −6.50540e7 1.12677e8i −0.00363335 0.00629315i
851851 −1.33917e10 2.31951e10i −0.744872 1.29016i
852852 0 0
853853 −1.39325e10 + 2.41319e10i −0.768615 + 1.33128i 0.169699 + 0.985496i 0.445720π0.445720\pi
−0.938314 + 0.345784i 0.887613π0.887613\pi
854854 −7.48578e8 −0.0411277
855855 0 0
856856 1.14785e10 0.625499
857857 1.70531e9 2.95369e9i 0.0925488 0.160299i −0.816034 0.578004i 0.803832π-0.803832\pi
0.908583 + 0.417704i 0.137165π0.137165\pi
858858 0 0
859859 −4.50766e9 7.80749e9i −0.242647 0.420277i 0.718820 0.695196i 0.244682π-0.244682\pi
−0.961467 + 0.274919i 0.911349π0.911349\pi
860860 1.79919e9 + 3.11628e9i 0.0964565 + 0.167068i
861861 0 0
862862 1.03139e10 1.78643e10i 0.548466 0.949970i
863863 −2.43096e9 −0.128748 −0.0643739 0.997926i 0.520505π-0.520505\pi
−0.0643739 + 0.997926i 0.520505π0.520505\pi
864864 0 0
865865 2.87411e10 1.50989
866866 −7.28930e9 + 1.26254e10i −0.381393 + 0.660593i
867867 0 0
868868 8.20488e8 + 1.42113e9i 0.0425847 + 0.0737588i
869869 5.69602e9 + 9.86579e9i 0.294444 + 0.509991i
870870 0 0
871871 −4.03180e9 + 6.98328e9i −0.206745 + 0.358093i
872872 8.99727e9 0.459518
873873 0 0
874874 −5.00280e9 −0.253468
875875 1.78819e9 3.09724e9i 0.0902372 0.156295i
876876 0 0
877877 4.99117e9 + 8.64495e9i 0.249864 + 0.432777i 0.963488 0.267752i 0.0862808π-0.0862808\pi
−0.713624 + 0.700529i 0.752947π0.752947\pi
878878 −5.32524e9 9.22359e9i −0.265527 0.459906i
879879 0 0
880880 −1.17041e9 + 2.02721e9i −0.0578960 + 0.100279i
881881 −2.89122e10 −1.42451 −0.712256 0.701920i 0.752327π-0.752327\pi
−0.712256 + 0.701920i 0.752327π0.752327\pi
882882 0 0
883883 −8.55345e9 −0.418099 −0.209049 0.977905i 0.567037π-0.567037\pi
−0.209049 + 0.977905i 0.567037π0.567037\pi
884884 1.70173e9 2.94749e9i 0.0828530 0.143506i
885885 0 0
886886 1.48544e8 + 2.57286e8i 0.00717525 + 0.0124279i
887887 −8.91592e9 1.54428e10i −0.428977 0.743009i 0.567806 0.823162i 0.307792π-0.307792\pi
−0.996783 + 0.0801531i 0.974459π0.974459\pi
888888 0 0
889889 −2.67067e9 + 4.62573e9i −0.127486 + 0.220813i
890890 2.63036e8 0.0125069
891891 0 0
892892 −2.12362e9 −0.100184
893893 −2.59707e9 + 4.49826e9i −0.122041 + 0.211380i
894894 0 0
895895 8.53854e9 + 1.47892e10i 0.398110 + 0.689547i
896896 1.72306e8 + 2.98442e8i 0.00800242 + 0.0138606i
897897 0 0
898898 7.83088e9 1.35635e10i 0.360864 0.625034i
899899 −1.17850e9 −0.0540968
900900 0 0
901901 4.33391e10 1.97398
902902 4.38225e9 7.59028e9i 0.198826 0.344377i
903903 0 0
904904 1.78084e9 + 3.08450e9i 0.0801742 + 0.138866i
905905 −1.34912e10 2.33674e10i −0.605035 1.04795i
906906 0 0
907907 3.21315e8 5.56534e8i 0.0142990 0.0247666i −0.858787 0.512332i 0.828782π-0.828782\pi
0.873086 + 0.487566i 0.162115π0.162115\pi
908908 8.86988e9 0.393203
909909 0 0
910910 −6.18706e8 −0.0272170
911911 4.61488e9 7.99321e9i 0.202230 0.350273i −0.747016 0.664806i 0.768514π-0.768514\pi
0.949247 + 0.314533i 0.101848π0.101848\pi
912912 0 0
913913 1.00155e10 + 1.73474e10i 0.435537 + 0.754372i
914914 −3.99671e9 6.92251e9i −0.173138 0.299883i
915915 0 0
916916 −2.14518e9 + 3.71556e9i −0.0922209 + 0.159731i
917917 −2.68076e9 −0.114806
918918 0 0
919919 1.03928e10 0.441701 0.220850 0.975308i 0.429117π-0.429117\pi
0.220850 + 0.975308i 0.429117π0.429117\pi
920920 3.55117e9 6.15081e9i 0.150354 0.260420i
921921 0 0
922922 6.59226e9 + 1.14181e10i 0.276998 + 0.479774i
923923 2.06195e9 + 3.57140e9i 0.0863120 + 0.149497i
924924 0 0
925925 −1.38954e8 + 2.40675e8i −0.00577265 + 0.00999852i
926926 2.77650e10 1.14910
927927 0 0
928928 −2.47490e8 −0.0101658
929929 −8.38051e9 + 1.45155e10i −0.342938 + 0.593986i −0.984977 0.172686i 0.944755π-0.944755\pi
0.642039 + 0.766672i 0.278089π0.278089\pi
930930 0 0
931931 −5.03485e9 8.72062e9i −0.204486 0.354180i
932932 −4.18877e9 7.25517e9i −0.169485 0.293557i
933933 0 0
934934 −9.99702e9 + 1.73153e10i −0.401473 + 0.695372i
935935 1.81080e10 0.724487
936936 0 0
937937 2.27134e9 0.0901973 0.0450987 0.998983i 0.485640π-0.485640\pi
0.0450987 + 0.998983i 0.485640π0.485640\pi
938938 −3.15798e9 + 5.46979e9i −0.124940 + 0.216402i
939939 0 0
940940 −3.68699e9 6.38606e9i −0.144785 0.250776i
941941 9.34719e8 + 1.61898e9i 0.0365694 + 0.0633400i 0.883731 0.467996i 0.155024π-0.155024\pi
−0.847161 + 0.531336i 0.821690π0.821690\pi
942942 0 0
943943 −1.32963e10 + 2.30299e10i −0.516345 + 0.894335i
944944 3.27225e9 0.126603
945945 0 0
946946 −3.26881e9 −0.125537
947947 2.49897e9 4.32834e9i 0.0956171 0.165614i −0.814249 0.580516i 0.802851π-0.802851\pi
0.909866 + 0.414902i 0.136184π0.136184\pi
948948 0 0
949949 1.34556e9 + 2.33057e9i 0.0511058 + 0.0885179i
950950 2.59549e7 + 4.49552e7i 0.000982171 + 0.00170117i
951951 0 0
952952 1.33291e9 2.30868e9i 0.0500695 0.0867229i
953953 4.30036e10 1.60946 0.804730 0.593641i 0.202310π-0.202310\pi
0.804730 + 0.593641i 0.202310π0.202310\pi
954954 0 0
955955 2.07292e10 0.770143
956956 −6.16772e8 + 1.06828e9i −0.0228309 + 0.0395442i
957957 0 0
958958 1.75844e10 + 3.04571e10i 0.646174 + 1.11921i
959959 −2.97092e9 5.14578e9i −0.108774 0.188402i
960960 0 0
961961 1.58280e9 2.74149e9i 0.0575300 0.0996449i
962962 −7.26973e9 −0.263273
963963 0 0
964964 4.38394e9 0.157614
965965 1.14230e10 1.97853e10i 0.409201 0.708756i
966966 0 0
967967 2.30180e10 + 3.98684e10i 0.818607 + 1.41787i 0.906709 + 0.421758i 0.138587π0.138587\pi
−0.0881016 + 0.996111i 0.528080π0.528080\pi
968968 3.92550e9 + 6.79916e9i 0.139101 + 0.240930i
969969 0 0
970970 −8.74080e9 + 1.51395e10i −0.307504 + 0.532612i
971971 3.33640e10 1.16953 0.584765 0.811203i 0.301187π-0.301187\pi
0.584765 + 0.811203i 0.301187π0.301187\pi
972972 0 0
973973 −8.79431e9 −0.306060
974974 1.13196e10 1.96061e10i 0.392531 0.679884i
975975 0 0
976976 −1.16621e9 2.01994e9i −0.0401516 0.0695446i
977977 −1.39320e10 2.41309e10i −0.477950 0.827833i 0.521731 0.853110i 0.325287π-0.325287\pi
−0.999680 + 0.0252770i 0.991953π0.991953\pi
978978 0 0
979979 −1.19473e8 + 2.06933e8i −0.00406939 + 0.00704839i
980980 1.42957e10 0.485192
981981 0 0
982982 1.96673e10 0.662759
983983 −1.54698e10 + 2.67945e10i −0.519455 + 0.899722i 0.480290 + 0.877110i 0.340532π0.340532\pi
−0.999744 + 0.0226119i 0.992802π0.992802\pi
984984 0 0
985985 −3.42165e9 5.92647e9i −0.114080 0.197592i
986986 9.57261e8 + 1.65803e9i 0.0318025 + 0.0550836i
987987 0 0
988988 −6.78949e8 + 1.17597e9i −0.0223969 + 0.0387925i
989989 9.91799e9 0.326014
990990 0 0
991991 −1.80515e10 −0.589192 −0.294596 0.955622i 0.595185π-0.595185\pi
−0.294596 + 0.955622i 0.595185π0.595185\pi
992992 −2.55648e9 + 4.42796e9i −0.0831480 + 0.144017i
993993 0 0
994994 1.61506e9 + 2.79737e9i 0.0521598 + 0.0903435i
995995 −2.13310e10 3.69465e10i −0.686485 1.18903i
996996 0 0
997997 −1.31421e9 + 2.27627e9i −0.0419982 + 0.0727429i −0.886260 0.463187i 0.846706π-0.846706\pi
0.844262 + 0.535930i 0.180039π0.180039\pi
998998 −2.40483e10 −0.765823
999999 0 0
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 162.8.c.q.55.4 8
3.2 odd 2 162.8.c.r.55.1 8
9.2 odd 6 162.8.a.g.1.4 4
9.4 even 3 inner 162.8.c.q.109.4 8
9.5 odd 6 162.8.c.r.109.1 8
9.7 even 3 162.8.a.j.1.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
162.8.a.g.1.4 4 9.2 odd 6
162.8.a.j.1.1 yes 4 9.7 even 3
162.8.c.q.55.4 8 1.1 even 1 trivial
162.8.c.q.109.4 8 9.4 even 3 inner
162.8.c.r.55.1 8 3.2 odd 2
162.8.c.r.109.1 8 9.5 odd 6