Properties

Label 54.8.c.a.19.1
Level 5454
Weight 88
Character 54.19
Analytic conductor 16.86916.869
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] = [54,8,Mod(19,54)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(54, 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("54.19");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: N N == 54=233 54 = 2 \cdot 3^{3}
Weight: k k == 8 8
Character orbit: [χ][\chi] == 54.c (of order 33, degree 22, not 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: 16.868791376116.8687913761
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,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 2239 2^{2}\cdot 3^{9}
Twist minimal: no (minimal twist has level 18)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 19.1
Root 0.500000+5.21243i0.500000 + 5.21243i of defining polynomial
Character χ\chi == 54.19
Dual form 54.8.c.a.37.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(4.000006.92820i)q2+(32.000055.4256i)q4+(187.789325.261i)q5+(528.867+916.024i)q7512.000q83004.63q10+(849.9651472.18i)q11+(6256.75+10837.0i)q13+(4230.93+7328.19i)q14+(2048.00+3547.24i)q1616879.9q1735281.9q19+(12018.5+20816.7i)q20+(6799.7211777.5i)q22+(35482.7+61457.8i)q23+(31467.1+54502.6i)q25+100108.q26+67694.9q28+(38827.4+67251.0i)q29+(63093.8+109282.i)q31+(16384.0+28377.9i)q32+(67519.4+116947.i)q34+397262.q35528664.q37+(141128.+244440.i)q38+(96148.1+166533.i)q40+(258960.448533.i)q41+(135830.235264.i)q43108795.q44+567723.q46+(211814.+366873.i)q47+(147628.255699.i)q49+(251737.+436021.i)q50+(400432.693568.i)q521.24314e6q53638457.q55+(270780.469004.i)q56+(310619.+538008.i)q58+(1.34086e62.32244e6i)q59+(377040.653052.i)q61+1.00950e6q62+262144.q64+(2.34990e64.07014e6i)q65+(131285.+227392.i)q67+(540156.+935577.i)q68+(1.58905e62.75231e6i)q70990913.q711.04389e6q73+(2.11466e6+3.66269e6i)q74+(1.12902e6+1.95552e6i)q76+(899036.+1.55718e6i)q77+(3.66860e66.35419e6i)q79+1.53837e6q804.14337e6q82+(1.94611e6+3.37075e6i)q83+(3.16986e6+5.49035e6i)q85+(1.08664e61.88211e6i)q86+(435182.+753757.i)q88675681.q891.32359e7q91+(2.27089e63.93330e6i)q92+(1.69452e6+2.93499e6i)q94+(6.62556e6+1.14758e7i)q95+(8.12785e6+1.40779e7i)q972.36205e6q98+O(q100)q+(4.00000 - 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(-187.789 - 325.261i) q^{5} +(-528.867 + 916.024i) q^{7} -512.000 q^{8} -3004.63 q^{10} +(849.965 - 1472.18i) q^{11} +(6256.75 + 10837.0i) q^{13} +(4230.93 + 7328.19i) q^{14} +(-2048.00 + 3547.24i) q^{16} -16879.9 q^{17} -35281.9 q^{19} +(-12018.5 + 20816.7i) q^{20} +(-6799.72 - 11777.5i) q^{22} +(35482.7 + 61457.8i) q^{23} +(-31467.1 + 54502.6i) q^{25} +100108. q^{26} +67694.9 q^{28} +(-38827.4 + 67251.0i) q^{29} +(63093.8 + 109282. i) q^{31} +(16384.0 + 28377.9i) q^{32} +(-67519.4 + 116947. i) q^{34} +397262. q^{35} -528664. q^{37} +(-141128. + 244440. i) q^{38} +(96148.1 + 166533. i) q^{40} +(-258960. - 448533. i) q^{41} +(135830. - 235264. i) q^{43} -108795. q^{44} +567723. q^{46} +(-211814. + 366873. i) q^{47} +(-147628. - 255699. i) q^{49} +(251737. + 436021. i) q^{50} +(400432. - 693568. i) q^{52} -1.24314e6 q^{53} -638457. q^{55} +(270780. - 469004. i) q^{56} +(310619. + 538008. i) q^{58} +(-1.34086e6 - 2.32244e6i) q^{59} +(377040. - 653052. i) q^{61} +1.00950e6 q^{62} +262144. q^{64} +(2.34990e6 - 4.07014e6i) q^{65} +(131285. + 227392. i) q^{67} +(540156. + 935577. i) q^{68} +(1.58905e6 - 2.75231e6i) q^{70} -990913. q^{71} -1.04389e6 q^{73} +(-2.11466e6 + 3.66269e6i) q^{74} +(1.12902e6 + 1.95552e6i) q^{76} +(899036. + 1.55718e6i) q^{77} +(3.66860e6 - 6.35419e6i) q^{79} +1.53837e6 q^{80} -4.14337e6 q^{82} +(-1.94611e6 + 3.37075e6i) q^{83} +(3.16986e6 + 5.49035e6i) q^{85} +(-1.08664e6 - 1.88211e6i) q^{86} +(-435182. + 753757. i) q^{88} -675681. q^{89} -1.32359e7 q^{91} +(2.27089e6 - 3.93330e6i) q^{92} +(1.69452e6 + 2.93499e6i) q^{94} +(6.62556e6 + 1.14758e7i) q^{95} +(-8.12785e6 + 1.40779e7i) q^{97} -2.36205e6 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q+24q2192q454q5+210q73072q8864q106579q11+10092q131680q1412288q16+29790q17137490q193456q20+52632q22+39654q23++7714800q98+O(q100) 6 q + 24 q^{2} - 192 q^{4} - 54 q^{5} + 210 q^{7} - 3072 q^{8} - 864 q^{10} - 6579 q^{11} + 10092 q^{13} - 1680 q^{14} - 12288 q^{16} + 29790 q^{17} - 137490 q^{19} - 3456 q^{20} + 52632 q^{22} + 39654 q^{23}+ \cdots + 7714800 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/54Z)×\left(\mathbb{Z}/54\mathbb{Z}\right)^\times.

nn 2929
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 −187.789 325.261i −0.671855 1.16369i −0.977377 0.211502i 0.932164π-0.932164\pi
0.305522 0.952185i 0.401169π-0.401169\pi
66 0 0
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 0 0
1010 −3004.63 −0.950147
1111 849.965 1472.18i 0.192542 0.333493i −0.753550 0.657391i 0.771660π-0.771660\pi
0.946092 + 0.323898i 0.104993π0.104993\pi
1212 0 0
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 0 0
1616 −2048.00 + 3547.24i −0.125000 + 0.216506i
1717 −16879.9 −0.833293 −0.416646 0.909069i 0.636795π-0.636795\pi
−0.416646 + 0.909069i 0.636795π0.636795\pi
1818 0 0
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 0 0
2222 −6799.72 11777.5i −0.136148 0.235815i
2323 35482.7 + 61457.8i 0.608092 + 1.05325i 0.991555 + 0.129690i 0.0413981π0.0413981\pi
−0.383463 + 0.923556i 0.625269π0.625269\pi
2424 0 0
2525 −31467.1 + 54502.6i −0.402779 + 0.697634i
2626 100108. 1.11702
2727 0 0
2828 67694.9 0.582778
2929 −38827.4 + 67251.0i −0.295628 + 0.512042i −0.975131 0.221631i 0.928862π-0.928862\pi
0.679503 + 0.733673i 0.262195π0.262195\pi
3030 0 0
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 0 0
3434 −67519.4 + 116947.i −0.294614 + 0.510286i
3535 397262. 1.56617
3636 0 0
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 0 0
4040 96148.1 + 166533.i 0.237537 + 0.411426i
4141 −258960. 448533.i −0.586800 1.01637i −0.994648 0.103318i 0.967054π-0.967054\pi
0.407849 0.913050i 0.366279π-0.366279\pi
4242 0 0
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 0 0
4646 567723. 0.859972
4747 −211814. + 366873.i −0.297586 + 0.515435i −0.975583 0.219630i 0.929515π-0.929515\pi
0.677997 + 0.735065i 0.262848π0.262848\pi
4848 0 0
4949 −147628. 255699.i −0.179260 0.310487i
5050 251737. + 436021.i 0.284808 + 0.493301i
5151 0 0
5252 400432. 693568.i 0.394927 0.684034i
5353 −1.24314e6 −1.14698 −0.573490 0.819213i 0.694411π-0.694411\pi
−0.573490 + 0.819213i 0.694411π0.694411\pi
5454 0 0
5555 −638457. −0.517443
5656 270780. 469004.i 0.206043 0.356877i
5757 0 0
5858 310619. + 538008.i 0.209040 + 0.362068i
5959 −1.34086e6 2.32244e6i −0.849968 1.47219i −0.881236 0.472677i 0.843288π-0.843288\pi
0.0312678 0.999511i 0.490046π-0.490046\pi
6060 0 0
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 0 0
6464 262144. 0.125000
6565 2.34990e6 4.07014e6i 1.06133 1.83829i
6666 0 0
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 0 0
7070 1.58905e6 2.75231e6i 0.553724 0.959079i
7171 −990913. −0.328573 −0.164286 0.986413i 0.552532π-0.552532\pi
−0.164286 + 0.986413i 0.552532π0.552532\pi
7272 0 0
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 0 0
7676 1.12902e6 + 1.95552e6i 0.295022 + 0.510993i
7777 899036. + 1.55718e6i 0.224419 + 0.388705i
7878 0 0
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 0 0
8282 −4.14337e6 −0.829860
8383 −1.94611e6 + 3.37075e6i −0.373588 + 0.647074i −0.990115 0.140260i 0.955206π-0.955206\pi
0.616526 + 0.787334i 0.288539π0.288539\pi
8484 0 0
8585 3.16986e6 + 5.49035e6i 0.559852 + 0.969692i
8686 −1.08664e6 1.88211e6i −0.184222 0.319081i
8787 0 0
8888 −435182. + 753757.i −0.0680740 + 0.117908i
8989 −675681. −0.101596 −0.0507980 0.998709i 0.516176π-0.516176\pi
−0.0507980 + 0.998709i 0.516176π0.516176\pi
9090 0 0
9191 −1.32359e7 −1.84124
9292 2.27089e6 3.93330e6i 0.304046 0.526623i
9393 0 0
9494 1.69452e6 + 2.93499e6i 0.210425 + 0.364467i
9595 6.62556e6 + 1.14758e7i 0.792849 + 1.37325i
9696 0 0
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 0 0
100100 4.02779e6 0.402779
101101 −212270. + 367662.i −0.0205005 + 0.0355079i −0.876094 0.482141i 0.839859π-0.839859\pi
0.855593 + 0.517649i 0.173193π0.173193\pi
102102 0 0
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 0 0
106106 −4.97257e6 + 8.61275e6i −0.405519 + 0.702379i
107107 −2.83648e6 −0.223839 −0.111920 0.993717i 0.535700π-0.535700\pi
−0.111920 + 0.993717i 0.535700π0.535700\pi
108108 0 0
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 0 0
112112 −2.16624e6 3.75203e6i −0.145694 0.252350i
113113 1.07218e7 + 1.85708e7i 0.699029 + 1.21075i 0.968804 + 0.247830i 0.0797174π0.0797174\pi
−0.269775 + 0.962923i 0.586949π0.586949\pi
114114 0 0
115115 1.33265e7 2.30822e7i 0.817100 1.41526i
116116 4.96990e6 0.295628
117117 0 0
118118 −2.14538e7 −1.20204
119119 8.92719e6 1.54624e7i 0.485624 0.841126i
120120 0 0
121121 8.29871e6 + 1.43738e7i 0.425855 + 0.737602i
122122 −3.01632e6 5.22442e6i −0.150390 0.260483i
123123 0 0
124124 4.03801e6 6.99403e6i 0.190191 0.329421i
125125 −5.70534e6 −0.261274
126126 0 0
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 0 0
130130 −1.87992e7 3.25612e7i −0.750477 1.29986i
131131 −1.17657e7 2.03788e7i −0.457265 0.792005i 0.541551 0.840668i 0.317837π-0.317837\pi
−0.998815 + 0.0486627i 0.984504π0.984504\pi
132132 0 0
133133 1.86594e7 3.23191e7i 0.687729 1.19118i
134134 2.10056e6 0.0754169
135135 0 0
136136 8.64249e6 0.294614
137137 −1.39952e7 + 2.42405e7i −0.465006 + 0.805414i −0.999202 0.0399467i 0.987281π-0.987281\pi
0.534196 + 0.845361i 0.320615π0.320615\pi
138138 0 0
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 0 0
142142 −3.96365e6 + 6.86525e6i −0.116168 + 0.201209i
143143 2.12721e7 0.608322
144144 0 0
145145 2.91655e7 0.794476
146146 −4.17555e6 + 7.23226e6i −0.111040 + 0.192327i
147147 0 0
148148 1.69172e7 + 2.93015e7i 0.428957 + 0.742975i
149149 −1.35829e7 2.35262e7i −0.336387 0.582639i 0.647363 0.762182i 0.275872π-0.275872\pi
−0.983750 + 0.179542i 0.942538π0.942538\pi
150150 0 0
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 0 0
154154 1.43846e7 0.317376
155155 2.36967e7 4.10439e7i 0.511125 0.885294i
156156 0 0
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 0 0
160160 6.15348e6 1.06581e7i 0.118768 0.205713i
161161 −7.50625e7 −1.41753
162162 0 0
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 0 0
166166 1.55688e7 + 2.69660e7i 0.264167 + 0.457550i
167167 1.33585e7 + 2.31376e7i 0.221947 + 0.384424i 0.955399 0.295318i 0.0954254π-0.0954254\pi
−0.733452 + 0.679741i 0.762092π0.762092\pi
168168 0 0
169169 −4.69195e7 + 8.12669e7i −0.747738 + 1.29512i
170170 5.07177e7 0.791751
171171 0 0
172172 −1.73862e7 −0.260529
173173 −1.31561e7 + 2.27871e7i −0.193182 + 0.334601i −0.946303 0.323281i 0.895214π-0.895214\pi
0.753121 + 0.657882i 0.228547π0.228547\pi
174174 0 0
175175 −3.32838e7 5.76492e7i −0.469461 0.813131i
176176 3.48146e6 + 6.03006e6i 0.0481356 + 0.0833733i
177177 0 0
178178 −2.70272e6 + 4.68125e6i −0.0359196 + 0.0622146i
179179 2.19724e7 0.286347 0.143174 0.989698i 0.454269π-0.454269\pi
0.143174 + 0.989698i 0.454269π0.454269\pi
180180 0 0
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 0 0
184184 −1.81671e7 3.14664e7i −0.214993 0.372379i
185185 9.92774e7 + 1.71954e8i 1.15279 + 1.99669i
186186 0 0
187187 −1.43473e7 + 2.48502e7i −0.160444 + 0.277898i
188188 2.71122e7 0.297586
189189 0 0
190190 1.06009e8 1.12126
191191 8.97257e7 1.55409e8i 0.931752 1.61384i 0.151425 0.988469i 0.451614π-0.451614\pi
0.780326 0.625372i 0.215053π-0.215053\pi
192192 0 0
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 0 0
196196 −9.44820e6 + 1.63648e7i −0.0896299 + 0.155243i
197197 −6.70863e7 −0.625176 −0.312588 0.949889i 0.601196π-0.601196\pi
−0.312588 + 0.949889i 0.601196π0.601196\pi
198198 0 0
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 0 0
202202 1.69816e6 + 2.94130e6i 0.0144960 + 0.0251078i
203203 −4.10690e7 7.11336e7i −0.344570 0.596813i
204204 0 0
205205 −9.72600e7 + 1.68459e8i −0.788489 + 1.36570i
206206 3.89067e7 0.310091
207207 0 0
208208 −5.12553e7 −0.394927
209209 −2.99884e7 + 5.19414e7i −0.227217 + 0.393552i
210210 0 0
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 0 0
214214 −1.13459e7 + 1.96517e7i −0.0791392 + 0.137073i
215215 −1.02030e8 −0.700150
216216 0 0
217217 −1.33473e8 −0.886715
218218 2.52556e7 4.37439e7i 0.165105 0.285970i
219219 0 0
220220 2.04306e7 + 3.53869e7i 0.129361 + 0.224059i
221221 −1.05613e8 1.82927e8i −0.658180 1.14000i
222222 0 0
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 0 0
226226 1.71550e8 0.988576
227227 1.90267e7 3.29553e7i 0.107963 0.186997i −0.806982 0.590576i 0.798901π-0.798901\pi
0.914945 + 0.403579i 0.132234π0.132234\pi
228228 0 0
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 0 0
232232 1.98796e7 3.44325e7i 0.104520 0.181034i
233233 7.45094e7 0.385892 0.192946 0.981209i 0.438196π-0.438196\pi
0.192946 + 0.981209i 0.438196π0.438196\pi
234234 0 0
235235 1.59106e8 0.799740
236236 −8.58153e7 + 1.48636e8i −0.424984 + 0.736094i
237237 0 0
238238 −7.14175e7 1.23699e8i −0.343388 0.594766i
239239 8.98328e7 + 1.55595e8i 0.425640 + 0.737230i 0.996480 0.0838313i 0.0267157π-0.0267157\pi
−0.570840 + 0.821061i 0.693382π0.693382\pi
240240 0 0
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 0 0
244244 −4.82611e7 −0.212683
245245 −5.54459e7 + 9.60352e7i −0.240873 + 0.417205i
246246 0 0
247247 −2.20750e8 3.82350e8i −0.932098 1.61444i
248248 −3.23041e7 5.59523e7i −0.134486 0.232936i
249249 0 0
250250 −2.28213e7 + 3.95277e7i −0.0923743 + 0.159997i
251251 −2.14309e8 −0.855426 −0.427713 0.903915i 0.640681π-0.640681\pi
−0.427713 + 0.903915i 0.640681π0.640681\pi
252252 0 0
253253 1.20636e8 0.468334
254254 5.42724e7 9.40025e7i 0.207807 0.359933i
255255 0 0
256256 −8.38861e6 1.45295e7i −0.0312500 0.0541266i
257257 −2.63538e7 4.56461e7i −0.0968450 0.167740i 0.813532 0.581520i 0.197542π-0.197542\pi
−0.910377 + 0.413779i 0.864208π0.864208\pi
258258 0 0
259259 2.79593e8 4.84269e8i 0.999946 1.73196i
260260 −3.00787e8 −1.06133
261261 0 0
262262 −1.88251e8 −0.646670
263263 2.44289e8 4.23121e8i 0.828055 1.43423i −0.0715077 0.997440i 0.522781π-0.522781\pi
0.899562 0.436793i 0.143886π-0.143886\pi
264264 0 0
265265 2.33449e8 + 4.04346e8i 0.770604 + 1.33473i
266266 −1.49275e8 2.58553e8i −0.486298 0.842293i
267267 0 0
268268 8.40224e6 1.45531e7i 0.0266639 0.0461832i
269269 1.69083e8 0.529622 0.264811 0.964300i 0.414690π-0.414690\pi
0.264811 + 0.964300i 0.414690π0.414690\pi
270270 0 0
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 0 0
274274 1.11962e8 + 1.93924e8i 0.328809 + 0.569514i
275275 5.34919e7 + 9.26506e7i 0.155104 + 0.268648i
276276 0 0
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 0 0
280280 −2.03398e8 −0.553724
281281 −1.40245e8 + 2.42912e8i −0.377065 + 0.653096i −0.990634 0.136545i 0.956400π-0.956400\pi
0.613569 + 0.789641i 0.289733π0.289733\pi
282282 0 0
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 0 0
286286 8.50882e7 1.47377e8i 0.215074 0.372519i
287287 5.47822e8 1.36790
288288 0 0
289289 −1.25409e8 −0.305623
290290 1.16662e8 2.02064e8i 0.280890 0.486515i
291291 0 0
292292 3.34044e7 + 5.78581e7i 0.0785170 + 0.135995i
293293 1.72190e8 + 2.98242e8i 0.399918 + 0.692679i 0.993715 0.111936i 0.0357051π-0.0357051\pi
−0.593797 + 0.804615i 0.702372π0.702372\pi
294294 0 0
295295 −5.03600e8 + 8.72260e8i −1.14211 + 1.97819i
296296 2.70676e8 0.606637
297297 0 0
298298 −2.17326e8 −0.475723
299299 −4.44013e8 + 7.69052e8i −0.960608 + 1.66382i
300300 0 0
301301 1.43672e8 + 2.48847e8i 0.303661 + 0.525956i
302302 1.67945e8 + 2.90890e8i 0.350868 + 0.607721i
303303 0 0
304304 7.22574e7 1.25153e8i 0.147511 0.255497i
305305 −2.83216e8 −0.571569
306306 0 0
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 0 0
310310 −1.89574e8 3.28351e8i −0.361420 0.625997i
311311 −1.43382e8 2.48345e8i −0.270292 0.468159i 0.698645 0.715469i 0.253787π-0.253787\pi
−0.968937 + 0.247310i 0.920454π0.920454\pi
312312 0 0
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 0 0
316316 −4.69580e8 −0.837153
317317 −2.60137e8 + 4.50570e8i −0.458663 + 0.794428i −0.998891 0.0470910i 0.985005π-0.985005\pi
0.540227 + 0.841519i 0.318338π0.318338\pi
318318 0 0
319319 6.60038e7 + 1.14322e8i 0.113842 + 0.197180i
320320 −4.92278e7 8.52651e7i −0.0839819 0.145461i
321321 0 0
322322 −3.00250e8 + 5.20048e8i −0.501172 + 0.868056i
323323 5.95554e8 0.983359
324324 0 0
325325 −7.87527e8 −1.27255
326326 −1.15714e8 + 2.00423e8i −0.184980 + 0.320395i
327327 0 0
328328 1.32588e8 + 2.29649e8i 0.207465 + 0.359340i
329329 −2.24043e8 3.88054e8i −0.346853 0.600768i
330330 0 0
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 0 0
334334 2.13736e8 0.313881
335335 4.93078e7 8.54037e7i 0.0716571 0.124114i
336336 0 0
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 0 0
340340 2.02871e8 3.51383e8i 0.279926 0.484846i
341341 2.14510e8 0.292960
342342 0 0
343343 −5.58786e8 −0.747681
344344 −6.95449e7 + 1.20455e8i −0.0921108 + 0.159541i
345345 0 0
346346 1.05249e8 + 1.82296e8i 0.136600 + 0.236598i
347347 −1.43066e8 2.47797e8i −0.183816 0.318378i 0.759361 0.650670i 0.225512π-0.225512\pi
−0.943177 + 0.332291i 0.892178π0.892178\pi
348348 0 0
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 0 0
352352 5.57033e7 0.0680740
353353 2.38469e8 4.13040e8i 0.288549 0.499782i −0.684914 0.728624i 0.740160π-0.740160\pi
0.973464 + 0.228841i 0.0734937π0.0734937\pi
354354 0 0
355355 1.86083e8 + 3.22305e8i 0.220753 + 0.382356i
356356 2.16218e7 + 3.74500e7i 0.0253990 + 0.0439923i
357357 0 0
358358 8.78898e7 1.52230e8i 0.101239 0.175351i
359359 3.73983e8 0.426600 0.213300 0.976987i 0.431579π-0.431579\pi
0.213300 + 0.976987i 0.431579π0.431579\pi
360360 0 0
361361 3.50942e8 0.392609
362362 5.04809e8 8.74356e8i 0.559303 0.968742i
363363 0 0
364364 4.23550e8 + 7.33610e8i 0.460309 + 0.797279i
365365 1.96031e8 + 3.39535e8i 0.211008 + 0.365477i
366366 0 0
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 0 0
370370 1.58844e9 1.63029
371371 6.57457e8 1.13875e9i 0.668434 1.15776i
372372 0 0
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 0 0
376376 1.08449e8 1.87839e8i 0.105213 0.182234i
377377 −9.71732e8 −0.934011
378378 0 0
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 0 0
382382 −7.17806e8 1.24328e9i −0.658848 1.14116i
383383 −4.24357e8 7.35008e8i −0.385954 0.668492i 0.605947 0.795505i 0.292794π-0.292794\pi
−0.991901 + 0.127013i 0.959461π0.959461\pi
384384 0 0
385385 3.37659e8 5.84842e8i 0.301554 0.522307i
386386 2.38651e8 0.211207
387387 0 0
388388 1.04036e9 0.904221
389389 −1.26651e8 + 2.19367e8i −0.109090 + 0.188950i −0.915402 0.402541i 0.868127π-0.868127\pi
0.806312 + 0.591491i 0.201460π0.201460\pi
390390 0 0
391391 −5.98943e8 1.03740e9i −0.506719 0.877662i
392392 7.55856e7 + 1.30918e8i 0.0633779 + 0.109774i
393393 0 0
394394 −2.68345e8 + 4.64788e8i −0.221033 + 0.382841i
395395 −2.75569e9 −2.24978
396396 0 0
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 0 0
400400 −1.28889e8 2.23243e8i −0.100695 0.174408i
401401 −4.74376e8 8.21644e8i −0.367382 0.636324i 0.621774 0.783197i 0.286412π-0.286412\pi
−0.989155 + 0.146873i 0.953079π0.953079\pi
402402 0 0
403403 −7.89524e8 + 1.36750e9i −0.600894 + 1.04078i
404404 2.71706e7 0.0205005
405405 0 0
406406 −6.57104e8 −0.487296
407407 −4.49346e8 + 7.78290e8i −0.330370 + 0.572217i
408408 0 0
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 0 0
412412 1.55627e8 2.69554e8i 0.109634 0.189891i
413413 2.83655e9 1.98137
414414 0 0
415415 1.46183e9 1.00399
416416 −2.05021e8 + 3.55107e8i −0.139628 + 0.241842i
417417 0 0
418418 2.39907e8 + 4.15531e8i 0.160667 + 0.278283i
419419 −3.14943e8 5.45498e8i −0.209162 0.362280i 0.742289 0.670080i 0.233740π-0.233740\pi
−0.951451 + 0.307801i 0.900407π0.900407\pi
420420 0 0
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 0 0
424424 6.36490e8 0.405519
425425 5.31160e8 9.19997e8i 0.335633 0.581333i
426426 0 0
427427 3.98808e8 + 6.90755e8i 0.247894 + 0.429365i
428428 9.07674e7 + 1.57214e8i 0.0559599 + 0.0969253i
429429 0 0
430430 −4.08118e8 + 7.06881e8i −0.247541 + 0.428753i
431431 2.85661e8 0.171863 0.0859313 0.996301i 0.472613π-0.472613\pi
0.0859313 + 0.996301i 0.472613π0.472613\pi
432432 0 0
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 0 0
436436 −2.02045e8 3.49952e8i −0.116747 0.202211i
437437 −1.25190e9 2.16835e9i −0.717602 1.24292i
438438 0 0
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 0 0
442442 −1.68981e9 −0.930807
443443 −2.29324e8 + 3.97201e8i −0.125325 + 0.217069i −0.921860 0.387523i 0.873331π-0.873331\pi
0.796535 + 0.604592i 0.206664π0.206664\pi
444444 0 0
445445 1.26886e8 + 2.19772e8i 0.0682578 + 0.118226i
446446 −6.46118e8 1.11911e9i −0.344858 0.597311i
447447 0 0
448448 −1.38639e8 + 2.40130e8i −0.0728472 + 0.126175i
449449 1.46433e9 0.763444 0.381722 0.924277i 0.375331π-0.375331\pi
0.381722 + 0.924277i 0.375331π0.375331\pi
450450 0 0
451451 −8.80429e8 −0.451936
452452 6.86198e8 1.18853e9i 0.349514 0.605377i
453453 0 0
454454 −1.52214e8 2.63642e8i −0.0763411 0.132227i
455455 2.48557e9 + 4.30513e9i 1.23704 + 2.14262i
456456 0 0
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 0 0
460460 −1.70580e9 −0.817100
461461 −1.98110e9 + 3.43137e9i −0.941789 + 1.63123i −0.179733 + 0.983715i 0.557524π0.557524\pi
−0.762056 + 0.647511i 0.775810π0.775810\pi
462462 0 0
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 0 0
466466 2.98038e8 5.16217e8i 0.136433 0.236310i
467467 −9.69518e8 −0.440501 −0.220250 0.975443i 0.570687π-0.570687\pi
−0.220250 + 0.975443i 0.570687π0.570687\pi
468468 0 0
469469 −2.77729e8 −0.124313
470470 6.36424e8 1.10232e9i 0.282751 0.489739i
471471 0 0
472472 6.86522e8 + 1.18909e9i 0.300509 + 0.520497i
473473 −2.30901e8 3.99933e8i −0.100326 0.173769i
474474 0 0
475475 1.11022e9 1.92296e9i 0.475315 0.823269i
476476 −1.14268e9 −0.485624
477477 0 0
478478 1.43733e9 0.601946
479479 −1.00435e9 + 1.73959e9i −0.417552 + 0.723222i −0.995693 0.0927156i 0.970445π-0.970445\pi
0.578140 + 0.815937i 0.303779π0.303779\pi
480480 0 0
481481 −3.30772e9 5.72913e9i −1.35525 2.34737i
482482 −2.43473e8 4.21707e8i −0.0990343 0.171532i
483483 0 0
484484 5.31117e8 9.19922e8i 0.212927 0.368801i
485485 6.10529e9 2.43002
486486 0 0
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 0 0
490490 4.43567e8 + 7.68281e8i 0.170323 + 0.295008i
491491 2.25862e9 + 3.91204e9i 0.861107 + 1.49148i 0.870861 + 0.491529i 0.163562π0.163562\pi
−0.00975413 + 0.999952i 0.503105π0.503105\pi
492492 0 0
493493 6.55401e8 1.13519e9i 0.246344 0.426681i
494494 −3.53200e9 −1.31819
495495 0 0
496496 −5.16865e8 −0.190191
497497 5.24061e8 9.07700e8i 0.191485 0.331661i
498498 0 0
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 0 0
502502 −8.57236e8 + 1.48478e9i −0.302439 + 0.523840i
503503 −2.88413e9 −1.01048 −0.505239 0.862980i 0.668596π-0.668596\pi
−0.505239 + 0.862980i 0.668596π0.668596\pi
504504 0 0
505505 1.59448e8 0.0550934
506506 4.82545e8 8.35792e8i 0.165581 0.286795i
507507 0 0
508508 −4.34179e8 7.52020e8i −0.146942 0.254511i
509509 −6.60362e8 1.14378e9i −0.221957 0.384442i 0.733445 0.679749i 0.237911π-0.237911\pi
−0.955402 + 0.295307i 0.904578π0.904578\pi
510510 0 0
511511 5.52077e8 9.56225e8i 0.183032 0.317020i
512512 −1.34218e8 −0.0441942
513513 0 0
514514 −4.21661e8 −0.136960
515515 9.13283e8 1.58185e9i 0.294632 0.510318i
516516 0 0
517517 3.60070e8 + 6.23659e8i 0.114596 + 0.198486i
518518 −2.23674e9 3.87415e9i −0.707069 1.22468i
519519 0 0
520520 −1.20315e9 + 2.08391e9i −0.375239 + 0.649932i
521521 −5.14654e9 −1.59435 −0.797175 0.603749i 0.793673π-0.793673\pi
−0.797175 + 0.603749i 0.793673π0.793673\pi
522522 0 0
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 0 0
526526 −1.95431e9 3.38497e9i −0.585523 1.01416i
527527 −1.06502e9 1.84466e9i −0.316970 0.549009i
528528 0 0
529529 −8.15632e8 + 1.41272e9i −0.239552 + 0.414916i
530530 3.73518e9 1.08980
531531 0 0
532532 −2.38841e9 −0.687729
533533 3.24050e9 5.61271e9i 0.926972 1.60556i
534534 0 0
535535 5.32661e8 + 9.22595e8i 0.150388 + 0.260479i
536536 −6.72180e7 1.16425e8i −0.0188542 0.0326565i
537537 0 0
538538 6.76330e8 1.17144e9i 0.187250 0.324326i
539539 −5.01915e8 −0.138060
540540 0 0
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 0 0
544544 −2.76560e8 4.79015e8i −0.0736534 0.127571i
545545 −1.18568e9 2.05366e9i −0.313747 0.543427i
546546 0 0
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 0 0
550550 8.55870e8 0.219350
551551 1.36990e9 2.37274e9i 0.348867 0.604255i
552552 0 0
553553 3.88039e9 + 6.72104e9i 0.975749 + 1.69005i
554554 −1.41950e9 2.45865e9i −0.354693 0.614346i
555555 0 0
556556 2.56060e8 4.43509e8i 0.0631800 0.109431i
557557 −4.50060e9 −1.10351 −0.551756 0.834006i 0.686042π-0.686042\pi
−0.551756 + 0.834006i 0.686042π0.686042\pi
558558 0 0
559559 3.39941e9 0.823119
560560 −8.13592e8 + 1.40918e9i −0.195771 + 0.339086i
561561 0 0
562562 1.12196e9 + 1.94330e9i 0.266625 + 0.461809i
563563 3.06529e9 + 5.30923e9i 0.723922 + 1.25387i 0.959416 + 0.281994i 0.0909957π0.0909957\pi
−0.235494 + 0.971876i 0.575671π0.575671\pi
564564 0 0
565565 4.02690e9 6.97479e9i 0.939292 1.62690i
566566 1.27239e9 0.294960
567567 0 0
568568 5.07347e8 0.116168
569569 −1.71059e9 + 2.96282e9i −0.389271 + 0.674238i −0.992352 0.123443i 0.960606π-0.960606\pi
0.603080 + 0.797680i 0.293940π0.293940\pi
570570 0 0
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 0 0
574574 2.19129e9 3.79542e9i 0.483624 0.837661i
575575 −4.46615e9 −0.979706
576576 0 0
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 0 0
580580 −9.33295e8 1.61651e9i −0.198619 0.344018i
581581 −2.05846e9 3.56536e9i −0.435438 0.754200i
582582 0 0
583583 −1.05663e9 + 1.83013e9i −0.220842 + 0.382510i
584584 5.34470e8 0.111040
585585 0 0
586586 2.75504e9 0.565570
587587 −4.47158e8 + 7.74500e8i −0.0912488 + 0.158048i −0.908037 0.418890i 0.862419π-0.862419\pi
0.816788 + 0.576938i 0.195753π0.195753\pi
588588 0 0
589589 −2.22607e9 3.85567e9i −0.448886 0.777493i
590590 4.02880e9 + 6.97808e9i 0.807594 + 1.39879i
591591 0 0
592592 1.08270e9 1.87530e9i 0.214478 0.371488i
593593 8.80907e9 1.73476 0.867379 0.497649i 0.165803π-0.165803\pi
0.867379 + 0.497649i 0.165803π0.165803\pi
594594 0 0
595595 −6.70572e9 −1.30508
596596 −8.69302e8 + 1.50568e9i −0.168193 + 0.291320i
597597 0 0
598598 3.55210e9 + 6.15242e9i 0.679252 + 1.17650i
599599 4.91595e8 + 8.51468e8i 0.0934574 + 0.161873i 0.908964 0.416875i 0.136875π-0.136875\pi
−0.815506 + 0.578748i 0.803541π0.803541\pi
600600 0 0
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 0 0
604604 2.68712e9 0.496202
605605 3.11682e9 5.39848e9i 0.572226 0.991124i
606606 0 0
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 0 0
610610 −1.13286e9 + 1.96218e9i −0.202080 + 0.350013i
611611 −5.30108e9 −0.940199
612612 0 0
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 0 0
616616 −4.60306e8 7.97274e8i −0.0793441 0.137428i
617617 3.80166e9 + 6.58468e9i 0.651592 + 1.12859i 0.982737 + 0.185010i 0.0592319π0.0592319\pi
−0.331145 + 0.943580i 0.607435π0.607435\pi
618618 0 0
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 0 0
622622 −2.29411e9 −0.382250
623623 3.57345e8 6.18940e8i 0.0592079 0.102551i
624624 0 0
625625 3.52977e9 + 6.11374e9i 0.578317 + 1.00167i
626626 1.00099e8 + 1.73377e8i 0.0163088 + 0.0282476i
627627 0 0
628628 −2.62553e9 + 4.54756e9i −0.423018 + 0.732688i
629629 8.92377e9 1.42979
630630 0 0
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 0 0
634634 2.08109e9 + 3.60456e9i 0.324324 + 0.561746i
635635 −2.54794e9 4.41316e9i −0.394895 0.683978i
636636 0 0
637637 1.84734e9 3.19969e9i 0.283178 0.490479i
638638 1.05606e9 0.160997
639639 0 0
640640 −7.87645e8 −0.118768
641641 −3.95891e9 + 6.85703e9i −0.593707 + 1.02833i 0.400021 + 0.916506i 0.369003π0.369003\pi
−0.993728 + 0.111825i 0.964330π0.964330\pi
642642 0 0
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 0 0
646646 2.38222e9 4.12612e9i 0.347670 0.602182i
647647 −8.06643e9 −1.17089 −0.585446 0.810712i 0.699080π-0.699080\pi
−0.585446 + 0.810712i 0.699080π0.699080\pi
648648 0 0
649649 −4.55875e9 −0.654620
650650 −3.15011e9 + 5.45614e9i −0.449913 + 0.779272i
651651 0 0
652652 9.25715e8 + 1.60338e9i 0.130801 + 0.226554i
653653 5.00680e9 + 8.67202e9i 0.703661 + 1.21878i 0.967172 + 0.254121i 0.0817861π0.0817861\pi
−0.263511 + 0.964656i 0.584881π0.584881\pi
654654 0 0
655655 −4.41894e9 + 7.65382e9i −0.614431 + 1.06423i
656656 2.12140e9 0.293400
657657 0 0
658658 −3.58469e9 −0.490525
659659 7.05570e9 1.22208e10i 0.960376 1.66342i 0.238821 0.971064i 0.423239π-0.423239\pi
0.721555 0.692357i 0.243428π-0.243428\pi
660660 0 0
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 0 0
664664 9.96406e8 1.72583e9i 0.132083 0.228775i
665665 −1.40162e10 −1.84822
666666 0 0
667667 −5.51080e9 −0.719075
668668 8.54943e8 1.48080e9i 0.110974 0.192212i
669669 0 0
670670 −3.94463e8 6.83230e8i −0.0506692 0.0877617i
671671 −6.40941e8 1.11014e9i −0.0819011 0.141857i
672672 0 0
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 0 0
676676 6.00569e9 0.747738
677677 −5.55719e9 + 9.62534e9i −0.688327 + 1.19222i 0.284051 + 0.958809i 0.408321π0.408321\pi
−0.972379 + 0.233409i 0.925012π0.925012\pi
678678 0 0
679679 −8.59710e9 1.48906e10i −1.05392 1.82544i
680680 −1.62297e9 2.81106e9i −0.197938 0.342838i
681681 0 0
682682 8.58041e8 1.48617e9i 0.103577 0.179400i
683683 1.61450e10 1.93894 0.969472 0.245201i 0.0788539π-0.0788539\pi
0.969472 + 0.245201i 0.0788539π0.0788539\pi
684684 0 0
685685 1.05126e10 1.24967
686686 −2.23515e9 + 3.87139e9i −0.264345 + 0.457859i
687687 0 0
688688 5.56359e8 + 9.63642e8i 0.0651322 + 0.112812i
689689 −7.77803e9 1.34719e10i −0.905946 1.56915i
690690 0 0
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 0 0
694694 −2.28905e9 −0.259955
695695 1.50267e9 2.60269e9i 0.169791 0.294087i
696696 0 0
697697 4.37122e9 + 7.57117e9i 0.488976 + 0.846931i
698698 −1.46546e8 2.53825e8i −0.0163110 0.0282514i
699699 0 0
700700 −2.13016e9 + 3.68955e9i −0.234731 + 0.406565i
701701 1.34244e9 0.147191 0.0735956 0.997288i 0.476553π-0.476553\pi
0.0735956 + 0.997288i 0.476553π0.476553\pi
702702 0 0
703703 1.86523e10 2.02483
704704 2.22813e8 3.85924e8i 0.0240678 0.0416867i
705705 0 0
706706 −1.90775e9 3.30432e9i −0.204035 0.353399i
707707 −2.24525e8 3.88889e8i −0.0238944 0.0413864i
708708 0 0
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 0 0
712712 3.45949e8 0.0359196
713713 −4.47748e9 + 7.75522e9i −0.462616 + 0.801274i
714714 0 0
715715 −3.99466e9 6.91896e9i −0.408704 0.707896i
716716 −7.03118e8 1.21784e9i −0.0715868 0.123992i
717717 0 0
718718 1.49593e9 2.59103e9i 0.150826 0.261238i
719719 −2.14766e9 −0.215483 −0.107742 0.994179i 0.534362π-0.534362\pi
−0.107742 + 0.994179i 0.534362π0.534362\pi
720720 0 0
721721 −5.14412e9 −0.511137
722722 1.40377e9 2.43140e9i 0.138808 0.240423i
723723 0 0
724724 −4.03848e9 6.99485e9i −0.395487 0.685004i
725725 −2.44357e9 4.23239e9i −0.238145 0.412480i
726726 0 0
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 0 0
730730 3.13649e9 0.298411
731731 −2.29279e9 + 3.97123e9i −0.217097 + 0.376023i
732732 0 0
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 0 0
736736 −1.16270e9 + 2.01385e9i −0.107496 + 0.186189i
737737 4.46351e8 0.0410715
738738 0 0
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 0 0
742742 −5.25966e9 9.10999e9i −0.472654 0.818661i
743743 3.62353e9 + 6.27614e9i 0.324094 + 0.561348i 0.981329 0.192339i 0.0616072π-0.0616072\pi
−0.657234 + 0.753686i 0.728274π0.728274\pi
744744 0 0
745745 −5.10143e9 + 8.83593e9i −0.452007 + 0.782898i
746746 −1.18177e10 −1.04219
747747 0 0
748748 1.83645e9 0.160444
749749 1.50012e9 2.59828e9i 0.130449 0.225944i
750750 0 0
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 0 0
754754 −3.88693e9 + 6.73236e9i −0.330223 + 0.571962i
755755 1.57692e10 1.33350
756756 0 0
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 0 0
760760 −3.39229e9 5.87562e9i −0.280314 0.485519i
761761 −1.10122e10 1.90738e10i −0.905794 1.56888i −0.819848 0.572582i 0.805942π-0.805942\pi
−0.0859464 0.996300i 0.527391π-0.527391\pi
762762 0 0
763763 −3.33921e9 + 5.78368e9i −0.272149 + 0.471377i
764764 −1.14849e10 −0.931752
765765 0 0
766766 −6.78971e9 −0.545821
767767 1.67789e10 2.90619e10i 1.34270 2.32563i
768768 0 0
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 0 0
772772 9.54605e8 1.65342e9i 0.0746729 0.129337i
773773 −3.65169e9 −0.284358 −0.142179 0.989841i 0.545411π-0.545411\pi
−0.142179 + 0.989841i 0.545411π0.545411\pi
774774 0 0
775775 −7.94152e9 −0.612841
776776 4.16146e9 7.20786e9i 0.319690 0.553720i
777777 0 0
778778 1.01321e9 + 1.75493e9i 0.0771385 + 0.133608i
779779 9.13662e9 + 1.58251e10i 0.692476 + 1.19940i
780780 0 0
781781 −8.42241e8 + 1.45880e9i −0.0632642 + 0.109577i
782782 −9.58309e9 −0.716608
783783 0 0
784784 1.20937e9 0.0896299
785785 −1.54077e10 + 2.66869e10i −1.13683 + 1.96904i
786786 0 0
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 0 0
790790 −1.10228e10 + 1.90920e10i −0.795419 + 1.37771i
791791 −2.26817e10 −1.62951
792792 0 0
793793 9.43617e9 0.671954
794794 3.96886e9 6.87427e9i 0.281381 0.487366i
795795 0 0
796796 3.78168e9 + 6.55006e9i 0.265760 + 0.460309i
797797 1.36082e10 + 2.35700e10i 0.952128 + 1.64913i 0.740807 + 0.671718i 0.234443π0.234443\pi
0.211321 + 0.977417i 0.432223π0.432223\pi
798798 0 0
799799 3.57540e9 6.19277e9i 0.247977 0.429508i
800800 −2.06223e9 −0.142404
801801 0 0
802802 −7.59002e9 −0.519556
803803 −8.87267e8 + 1.53679e9i −0.0604714 + 0.104740i
804804 0 0
805805 1.40959e10 + 2.44149e10i 0.952375 + 1.64956i
806806 6.31619e9 + 1.09400e10i 0.424896 + 0.735942i
807807 0 0
808808 1.08682e8 1.88243e8i 0.00724801 0.0125539i
809809 2.09999e10 1.39443 0.697216 0.716861i 0.254422π-0.254422\pi
0.697216 + 0.716861i 0.254422π0.254422\pi
810810 0 0
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 0 0
814814 3.59477e9 + 6.22632e9i 0.233607 + 0.404619i
815815 5.43248e9 + 9.40933e9i 0.351517 + 0.608845i
816816 0 0
817817 −4.79234e9 + 8.30057e9i −0.307447 + 0.532514i
818818 −6.21413e9 −0.396957
819819 0 0
820820 1.24493e10 0.788489
821821 −5.66101e9 + 9.80516e9i −0.357020 + 0.618377i −0.987462 0.157860i 0.949541π-0.949541\pi
0.630441 + 0.776237i 0.282874π0.282874\pi
822822 0 0
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 0 0
826826 1.13462e10 1.96522e10i 0.700520 1.21334i
827827 −2.11794e10 −1.30210 −0.651050 0.759034i 0.725671π-0.725671\pi
−0.651050 + 0.759034i 0.725671π0.725671\pi
828828 0 0
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 0 0
832832 1.64017e9 + 2.84085e9i 0.0987317 + 0.171008i
833833 2.49194e9 + 4.31617e9i 0.149376 + 0.258727i
834834 0 0
835835 5.01716e9 8.68997e9i 0.298233 0.516554i
836836 3.83851e9 0.227217
837837 0 0
838838 −5.03909e9 −0.295800
839839 −1.31911e10 + 2.28476e10i −0.771104 + 1.33559i 0.165855 + 0.986150i 0.446962π0.446962\pi
−0.936959 + 0.349441i 0.886372π0.886372\pi
840840 0 0
841841 5.60981e9 + 9.71647e9i 0.325209 + 0.563278i
842842 4.41940e9 + 7.65463e9i 0.255136 + 0.441908i
843843 0 0
844844 −3.32753e9 + 5.76345e9i −0.190513 + 0.329977i
845845 3.52439e10 2.00949
846846 0 0
847847 −1.75556e10 −0.992715
848848 2.54596e9 4.40973e9i 0.143372 0.248328i
849849 0 0
850850 −4.24928e9 7.35997e9i −0.237328 0.411065i
851851 −1.87584e10 3.24905e10i −1.04338 1.80719i
852852 0 0
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 0 0
856856 1.45228e9 0.0791392
857857 6.44399e9 1.11613e10i 0.349721 0.605735i −0.636479 0.771294i 0.719610π-0.719610\pi
0.986200 + 0.165560i 0.0529430π0.0529430\pi
858858 0 0
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 0 0
862862 1.14265e9 1.97912e9i 0.0607626 0.105244i
863863 2.63998e10 1.39818 0.699089 0.715035i 0.253589π-0.253589\pi
0.699089 + 0.715035i 0.253589π0.253589\pi
864864 0 0
865865 9.88231e9 0.519161
866866 1.90715e9 3.30328e9i 0.0997867 0.172836i
867867 0 0
868868 4.27113e9 + 7.39782e9i 0.221679 + 0.383959i
869869 −6.23635e9 1.08017e10i −0.322375 0.558370i
870870 0 0
871871 −1.64283e9 + 2.84547e9i −0.0842423 + 0.145912i
872872 −3.23271e9 −0.165105
873873 0 0
874874 −2.00304e10 −1.01484
875875 3.01736e9 5.22622e9i 0.152265 0.263730i
876876 0 0
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 0 0
880880 1.30756e9 2.26476e9i 0.0646803 0.112030i
881881 −2.86878e10 −1.41345 −0.706727 0.707487i 0.749829π-0.749829\pi
−0.706727 + 0.707487i 0.749829π0.749829\pi
882882 0 0
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 0 0
886886 1.83459e9 + 3.17761e9i 0.0886180 + 0.153491i
887887 8.77534e9 + 1.51993e10i 0.422213 + 0.731294i 0.996156 0.0876014i 0.0279202π-0.0279202\pi
−0.573943 + 0.818895i 0.694587π0.694587\pi
888888 0 0
889889 −7.17571e9 + 1.24287e10i −0.342538 + 0.593293i
890890 2.03017e9 0.0965311
891891 0 0
892892 −1.03379e10 −0.487703
893893 7.47322e9 1.29440e10i 0.351178 0.608259i
894894 0 0
895895 −4.12619e9 7.14677e9i −0.192384 0.333218i
896896 1.10911e9 + 1.92104e9i 0.0515108 + 0.0892193i
897897 0 0
898898 5.85733e9 1.01452e10i 0.269918 0.467512i
899899 −9.79907e9 −0.449807
900900 0 0
901901 2.09841e10 0.955770
902902 −3.52172e9 + 6.09979e9i −0.159783 + 0.276753i
903903 0 0
904904 −5.48959e9 9.50824e9i −0.247144 0.428066i
905905 −2.36994e10 4.10486e10i −1.06284 1.84089i
906906 0 0
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 0 0
910910 3.97691e10 1.74945
911911 7.36357e9 1.27541e10i 0.322682 0.558901i −0.658359 0.752704i 0.728749π-0.728749\pi
0.981040 + 0.193803i 0.0620823π0.0620823\pi
912912 0 0
913913 3.30824e9 + 5.73005e9i 0.143863 + 0.249178i
914914 5.58639e9 + 9.67592e9i 0.242003 + 0.419161i
915915 0 0
916916 9.27091e9 1.60577e10i 0.398555 0.690318i
917917 2.48899e10 1.06593
918918 0 0
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 0 0
922922 1.58488e10 + 2.74510e10i 0.665946 + 1.15345i
923923 −6.19989e9 1.07385e10i −0.259524 0.449509i
924924 0 0
925925 1.66355e10 2.88136e10i 0.691099 1.19702i
926926 1.50530e10 0.622995
927927 0 0
928928 −2.54459e9 −0.104520
929929 −1.69702e10 + 2.93933e10i −0.694437 + 1.20280i 0.275933 + 0.961177i 0.411013π0.411013\pi
−0.970370 + 0.241624i 0.922320π0.922320\pi
930930 0 0
931931 5.20860e9 + 9.02156e9i 0.211542 + 0.366402i
932932 −2.38430e9 4.12973e9i −0.0964730 0.167096i
933933 0 0
934934 −3.87807e9 + 6.71702e9i −0.155741 + 0.269751i
935935 1.07771e10 0.431181
936936 0 0
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 0 0
940940 −5.09139e9 8.81854e9i −0.199935 0.346298i
941941 8.44461e9 + 1.46265e10i 0.330382 + 0.572238i 0.982587 0.185805i 0.0594892π-0.0594892\pi
−0.652205 + 0.758043i 0.726156π0.726156\pi
942942 0 0
943943 1.83772e10 3.18303e10i 0.713657 1.23609i
944944 1.09844e10 0.424984
945945 0 0
946946 −3.69442e9 −0.141882
947947 5.84561e9 1.01249e10i 0.223668 0.387405i −0.732251 0.681035i 0.761530π-0.761530\pi
0.955919 + 0.293630i 0.0948634π0.0948634\pi
948948 0 0
949949 −6.53134e9 1.13126e10i −0.248068 0.429666i
950950 −8.88176e9 1.53837e10i −0.336098 0.582139i
951951 0 0
952952 −4.57072e9 + 7.91672e9i −0.171694 + 0.297383i
953953 −5.10551e10 −1.91079 −0.955397 0.295323i 0.904573π-0.904573\pi
−0.955397 + 0.295323i 0.904573π0.904573\pi
954954 0 0
955955 −6.73981e10 −2.50401
956956 5.74930e9 9.95808e9i 0.212820 0.368615i
957957 0 0
958958 8.03480e9 + 1.39167e10i 0.295254 + 0.511395i
959959 −1.48032e10 2.56400e10i −0.541990 0.938755i
960960 0 0
961961 5.79464e9 1.00366e10i 0.210618 0.364800i
962962 −5.29235e10 −1.91662
963963 0 0
964964 −3.89556e9 −0.140056
965965 5.60202e9 9.70298e9i 0.200678 0.347584i
966966 0 0
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 0 0
970970 2.44212e10 4.22987e10i 0.859143 1.48808i
971971 −3.91347e10 −1.37181 −0.685906 0.727690i 0.740594π-0.740594\pi
−0.685906 + 0.727690i 0.740594π0.740594\pi
972972 0 0
973973 −8.46384e9 −0.294559
974974 1.21153e10 2.09844e10i 0.420126 0.727679i
975975 0 0
976976 1.54436e9 + 2.67490e9i 0.0531708 + 0.0920945i
977977 −1.36255e10 2.36001e10i −0.467437 0.809624i 0.531871 0.846825i 0.321489π-0.321489\pi
−0.999308 + 0.0372010i 0.988156π0.988156\pi
978978 0 0
979979 −5.74305e8 + 9.94725e8i −0.0195615 + 0.0338816i
980980 7.09708e9 0.240873
981981 0 0
982982 3.61379e10 1.21779
983983 3.56677e9 6.17782e9i 0.119767 0.207443i −0.799908 0.600122i 0.795119π-0.795119\pi
0.919675 + 0.392680i 0.128452π0.128452\pi
984984 0 0
985985 1.25981e10 + 2.18205e10i 0.420028 + 0.727509i
986986 −5.24321e9 9.08150e9i −0.174192 0.301709i
987987 0 0
988988 −1.41280e10 + 2.44704e10i −0.466049 + 0.807220i
989989 1.92784e10 0.633702
990990 0 0
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 0 0
994994 −4.19249e9 7.26160e9i −0.135400 0.234520i
995995 2.21925e10 + 3.84385e10i 0.714208 + 1.23704i
996996 0 0
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 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 54.8.c.a.19.1 6
3.2 odd 2 18.8.c.a.7.2 6
4.3 odd 2 432.8.i.a.289.1 6
9.2 odd 6 162.8.a.f.1.1 3
9.4 even 3 inner 54.8.c.a.37.1 6
9.5 odd 6 18.8.c.a.13.2 yes 6
9.7 even 3 162.8.a.e.1.3 3
12.11 even 2 144.8.i.a.97.2 6
36.23 even 6 144.8.i.a.49.2 6
36.31 odd 6 432.8.i.a.145.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
18.8.c.a.7.2 6 3.2 odd 2
18.8.c.a.13.2 yes 6 9.5 odd 6
54.8.c.a.19.1 6 1.1 even 1 trivial
54.8.c.a.37.1 6 9.4 even 3 inner
144.8.i.a.49.2 6 36.23 even 6
144.8.i.a.97.2 6 12.11 even 2
162.8.a.e.1.3 3 9.7 even 3
162.8.a.f.1.1 3 9.2 odd 6
432.8.i.a.145.1 6 36.31 odd 6
432.8.i.a.289.1 6 4.3 odd 2