Properties

Label 54.9.d.a.35.4
Level 5454
Weight 99
Character 54.35
Analytic conductor 21.99821.998
Analytic rank 00
Dimension 1616
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [54,9,Mod(17,54)]
 
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([5]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("54.17");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: N N == 54=233 54 = 2 \cdot 3^{3}
Weight: k k == 9 9
Character orbit: [χ][\chi] == 54.d (of order 66, 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: 21.998444943321.9984449433
Analytic rank: 00
Dimension: 1616
Relative dimension: 88 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x164x15150208x141927740x13+8702363206x12+239206241152x11++81 ⁣ ⁣61 x^{16} - 4 x^{15} - 150208 x^{14} - 1927740 x^{13} + 8702363206 x^{12} + 239206241152 x^{11} + \cdots + 81\!\cdots\!61 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 228336 2^{28}\cdot 3^{36}
Twist minimal: no (minimal twist has level 18)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 35.4
Root 197.4350.866025i-197.435 - 0.866025i of defining polynomial
Character χ\chi == 54.35
Dual form 54.9.d.a.17.4

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+(9.797965.65685i)q2+(64.0000+110.851i)q4+(944.709545.428i)q5+(1250.702166.27i)q71448.15iq812341.6q10+(3212.80+1854.91i)q11+(22409.9+38815.1i)q13+(24508.5+14150.0i)q14+(8192.00+14189.0i)q1654543.2iq17+125188.q19+(120923.+69814.8i)q20+(20985.936348.7i)q22+(266411.+153812.i)q23+(399671.692251.i)q25507078.iq26+320178.q28+(400230.231073.i)q29+(140570.243475.i)q31+(160530.92681.9i)q32+(308543.+534412.i)q342.72866e6iq35+159985.q37+(1.22659e6708173.i)q38+(789864.1.36808e6i)q40+(4.49810e62.59698e6i)q41+(2.49848e64.32750e6i)q43+474858.iq44+3.48037e6q46+(306798.+177130.i)q47+(246080.426223.i)q49+(7.83192e6+4.52176e6i)q50+(2.86847e6+4.96833e6i)q52+958543.iq53+4.04689e6q55+(3.13709e61.81120e6i)q56+(2.61429e6+4.52809e6i)q58+(1.38270e7+7.98300e6i)q59+(5.55708e6+9.62514e6i)q61+3.18074e6iq622.09715e6q64+(4.23417e7+2.44460e7i)q65+(1.22942e72.12942e7i)q67+(6.04618e63.49076e6i)q68+(1.54356e7+2.67353e7i)q701.67264e7iq71+4.77259e6q73+(1.56752e6905009.i)q74+(8.01206e6+1.38773e7i)q76+(8.03648e64.63986e6i)q77+(1.81889e7+3.15042e7i)q79+1.78726e7iq805.87630e7q82+(2.53425e71.46315e7i)q83+(2.97494e75.15274e7i)q85+(4.89601e7+2.82671e7i)q86+(2.68620e64.65264e6i)q88+6.26485e7iq89+1.12112e8q91+(3.41006e71.96880e7i)q92+(2.00399e63.47102e6i)q94+(1.18267e86.82813e7i)q95+(2.42081e74.19297e7i)q97+5.56815e6iq98+O(q100)q+(-9.79796 - 5.65685i) q^{2} +(64.0000 + 110.851i) q^{4} +(944.709 - 545.428i) q^{5} +(1250.70 - 2166.27i) q^{7} -1448.15i q^{8} -12341.6 q^{10} +(3212.80 + 1854.91i) q^{11} +(22409.9 + 38815.1i) q^{13} +(-24508.5 + 14150.0i) q^{14} +(-8192.00 + 14189.0i) q^{16} -54543.2i q^{17} +125188. q^{19} +(120923. + 69814.8i) q^{20} +(-20985.9 - 36348.7i) q^{22} +(-266411. + 153812. i) q^{23} +(399671. - 692251. i) q^{25} -507078. i q^{26} +320178. q^{28} +(-400230. - 231073. i) q^{29} +(-140570. - 243475. i) q^{31} +(160530. - 92681.9i) q^{32} +(-308543. + 534412. i) q^{34} -2.72866e6i q^{35} +159985. q^{37} +(-1.22659e6 - 708173. i) q^{38} +(-789864. - 1.36808e6i) q^{40} +(4.49810e6 - 2.59698e6i) q^{41} +(2.49848e6 - 4.32750e6i) q^{43} +474858. i q^{44} +3.48037e6 q^{46} +(306798. + 177130. i) q^{47} +(-246080. - 426223. i) q^{49} +(-7.83192e6 + 4.52176e6i) q^{50} +(-2.86847e6 + 4.96833e6i) q^{52} +958543. i q^{53} +4.04689e6 q^{55} +(-3.13709e6 - 1.81120e6i) q^{56} +(2.61429e6 + 4.52809e6i) q^{58} +(-1.38270e7 + 7.98300e6i) q^{59} +(-5.55708e6 + 9.62514e6i) q^{61} +3.18074e6i q^{62} -2.09715e6 q^{64} +(4.23417e7 + 2.44460e7i) q^{65} +(-1.22942e7 - 2.12942e7i) q^{67} +(6.04618e6 - 3.49076e6i) q^{68} +(-1.54356e7 + 2.67353e7i) q^{70} -1.67264e7i q^{71} +4.77259e6 q^{73} +(-1.56752e6 - 905009. i) q^{74} +(8.01206e6 + 1.38773e7i) q^{76} +(8.03648e6 - 4.63986e6i) q^{77} +(-1.81889e7 + 3.15042e7i) q^{79} +1.78726e7i q^{80} -5.87630e7 q^{82} +(-2.53425e7 - 1.46315e7i) q^{83} +(-2.97494e7 - 5.15274e7i) q^{85} +(-4.89601e7 + 2.82671e7i) q^{86} +(2.68620e6 - 4.65264e6i) q^{88} +6.26485e7i q^{89} +1.12112e8 q^{91} +(-3.41006e7 - 1.96880e7i) q^{92} +(-2.00399e6 - 3.47102e6i) q^{94} +(1.18267e8 - 6.82813e7i) q^{95} +(2.42081e7 - 4.19297e7i) q^{97} +5.56815e6i q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q+1024q4+882q51846q745756q113370q13+94464q14131072q16+362180q19+112896q2061824q221311138q23+963394q25472576q28+2851290q29+89415484q97+O(q100) 16 q + 1024 q^{4} + 882 q^{5} - 1846 q^{7} - 45756 q^{11} - 3370 q^{13} + 94464 q^{14} - 131072 q^{16} + 362180 q^{19} + 112896 q^{20} - 61824 q^{22} - 1311138 q^{23} + 963394 q^{25} - 472576 q^{28} + 2851290 q^{29}+ \cdots - 89415484 q^{97}+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(16)e\left(\frac{1}{6}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −9.79796 5.65685i −0.612372 0.353553i
33 0 0
44 64.0000 + 110.851i 0.250000 + 0.433013i
55 944.709 545.428i 1.51153 0.872685i 0.511625 0.859209i 0.329044π-0.329044\pi
0.999909 0.0134763i 0.00428977π-0.00428977\pi
66 0 0
77 1250.70 2166.27i 0.520906 0.902236i −0.478798 0.877925i 0.658927π-0.658927\pi
0.999704 0.0243111i 0.00773922π-0.00773922\pi
88 1448.15i 0.353553i
99 0 0
1010 −12341.6 −1.23416
1111 3212.80 + 1854.91i 0.219439 + 0.126693i 0.605690 0.795700i 0.292897π-0.292897\pi
−0.386252 + 0.922393i 0.626230π0.626230\pi
1212 0 0
1313 22409.9 + 38815.1i 0.784633 + 1.35902i 0.929218 + 0.369531i 0.120482π0.120482\pi
−0.144586 + 0.989492i 0.546185π0.546185\pi
1414 −24508.5 + 14150.0i −0.637977 + 0.368336i
1515 0 0
1616 −8192.00 + 14189.0i −0.125000 + 0.216506i
1717 54543.2i 0.653048i −0.945189 0.326524i 0.894123π-0.894123\pi
0.945189 0.326524i 0.105877π-0.105877\pi
1818 0 0
1919 125188. 0.960616 0.480308 0.877100i 0.340525π-0.340525\pi
0.480308 + 0.877100i 0.340525π0.340525\pi
2020 120923. + 69814.8i 0.755767 + 0.436342i
2121 0 0
2222 −20985.9 36348.7i −0.0895855 0.155167i
2323 −266411. + 153812.i −0.952007 + 0.549642i −0.893704 0.448657i 0.851902π-0.851902\pi
−0.0583033 + 0.998299i 0.518569π0.518569\pi
2424 0 0
2525 399671. 692251.i 1.02316 1.77216i
2626 507078.i 1.10964i
2727 0 0
2828 320178. 0.520906
2929 −400230. 231073.i −0.565872 0.326706i 0.189627 0.981856i 0.439272π-0.439272\pi
−0.755499 + 0.655150i 0.772605π0.772605\pi
3030 0 0
3131 −140570. 243475.i −0.152211 0.263638i 0.779829 0.625993i 0.215306π-0.215306\pi
−0.932040 + 0.362355i 0.881973π0.881973\pi
3232 160530. 92681.9i 0.153093 0.0883883i
3333 0 0
3434 −308543. + 534412.i −0.230887 + 0.399908i
3535 2.72866e6i 1.81835i
3636 0 0
3737 159985. 0.0853633 0.0426816 0.999089i 0.486410π-0.486410\pi
0.0426816 + 0.999089i 0.486410π0.486410\pi
3838 −1.22659e6 708173.i −0.588255 0.339629i
3939 0 0
4040 −789864. 1.36808e6i −0.308541 0.534408i
4141 4.49810e6 2.59698e6i 1.59182 0.919038i 0.598825 0.800880i 0.295635π-0.295635\pi
0.992995 0.118158i 0.0376988π-0.0376988\pi
4242 0 0
4343 2.49848e6 4.32750e6i 0.730807 1.26580i −0.225731 0.974190i 0.572477π-0.572477\pi
0.956539 0.291606i 0.0941895π-0.0941895\pi
4444 474858.i 0.126693i
4545 0 0
4646 3.48037e6 0.777311
4747 306798. + 177130.i 0.0628725 + 0.0362995i 0.531107 0.847305i 0.321776π-0.321776\pi
−0.468234 + 0.883604i 0.655110π0.655110\pi
4848 0 0
4949 −246080. 426223.i −0.0426866 0.0739354i
5050 −7.83192e6 + 4.52176e6i −1.25311 + 0.723482i
5151 0 0
5252 −2.86847e6 + 4.96833e6i −0.392316 + 0.679512i
5353 958543.i 0.121481i 0.998154 + 0.0607405i 0.0193462π0.0193462\pi
−0.998154 + 0.0607405i 0.980654π0.980654\pi
5454 0 0
5555 4.04689e6 0.442252
5656 −3.13709e6 1.81120e6i −0.318989 0.184168i
5757 0 0
5858 2.61429e6 + 4.52809e6i 0.231016 + 0.400132i
5959 −1.38270e7 + 7.98300e6i −1.14109 + 0.658807i −0.946700 0.322118i 0.895605π-0.895605\pi
−0.194387 + 0.980925i 0.562272π0.562272\pi
6060 0 0
6161 −5.55708e6 + 9.62514e6i −0.401354 + 0.695165i −0.993890 0.110379i 0.964793π-0.964793\pi
0.592536 + 0.805544i 0.298127π0.298127\pi
6262 3.18074e6i 0.215259i
6363 0 0
6464 −2.09715e6 −0.125000
6565 4.23417e7 + 2.44460e7i 2.37200 + 1.36947i
6666 0 0
6767 −1.22942e7 2.12942e7i −0.610102 1.05673i −0.991223 0.132202i 0.957795π-0.957795\pi
0.381121 0.924525i 0.375538π-0.375538\pi
6868 6.04618e6 3.49076e6i 0.282778 0.163262i
6969 0 0
7070 −1.54356e7 + 2.67353e7i −0.642883 + 1.11351i
7171 1.67264e7i 0.658215i −0.944292 0.329108i 0.893252π-0.893252\pi
0.944292 0.329108i 0.106748π-0.106748\pi
7272 0 0
7373 4.77259e6 0.168059 0.0840297 0.996463i 0.473221π-0.473221\pi
0.0840297 + 0.996463i 0.473221π0.473221\pi
7474 −1.56752e6 905009.i −0.0522741 0.0301805i
7575 0 0
7676 8.01206e6 + 1.38773e7i 0.240154 + 0.415959i
7777 8.03648e6 4.63986e6i 0.228614 0.131990i
7878 0 0
7979 −1.81889e7 + 3.15042e7i −0.466981 + 0.808835i −0.999288 0.0377164i 0.987992π-0.987992\pi
0.532308 + 0.846551i 0.321325π0.321325\pi
8080 1.78726e7i 0.436342i
8181 0 0
8282 −5.87630e7 −1.29972
8383 −2.53425e7 1.46315e7i −0.533994 0.308302i 0.208647 0.977991i 0.433094π-0.433094\pi
−0.742641 + 0.669689i 0.766427π0.766427\pi
8484 0 0
8585 −2.97494e7 5.15274e7i −0.569905 0.987104i
8686 −4.89601e7 + 2.82671e7i −0.895052 + 0.516759i
8787 0 0
8888 2.68620e6 4.65264e6i 0.0447927 0.0775833i
8989 6.26485e7i 0.998506i 0.866456 + 0.499253i 0.166392π0.166392\pi
−0.866456 + 0.499253i 0.833608π0.833608\pi
9090 0 0
9191 1.12112e8 1.63488
9292 −3.41006e7 1.96880e7i −0.476004 0.274821i
9393 0 0
9494 −2.00399e6 3.47102e6i −0.0256676 0.0444576i
9595 1.18267e8 6.82813e7i 1.45200 0.838315i
9696 0 0
9797 2.42081e7 4.19297e7i 0.273447 0.473625i −0.696295 0.717756i 0.745169π-0.745169\pi
0.969742 + 0.244131i 0.0785027π0.0785027\pi
9898 5.56815e6i 0.0603680i
9999 0 0
100100 1.02316e8 1.02316
101101 −4.53627e7 2.61902e7i −0.435927 0.251682i 0.265942 0.963989i 0.414317π-0.414317\pi
−0.701868 + 0.712307i 0.747651π0.747651\pi
102102 0 0
103103 −3.13984e7 5.43835e7i −0.278970 0.483191i 0.692159 0.721745i 0.256660π-0.256660\pi
−0.971129 + 0.238555i 0.923326π0.923326\pi
104104 5.62102e7 3.24530e7i 0.480487 0.277410i
105105 0 0
106106 5.42234e6 9.39177e6i 0.0429500 0.0743916i
107107 631989.i 0.00482142i 0.999997 + 0.00241071i 0.000767353π0.000767353\pi
−0.999997 + 0.00241071i 0.999233π0.999233\pi
108108 0 0
109109 3.60140e7 0.255132 0.127566 0.991830i 0.459284π-0.459284\pi
0.127566 + 0.991830i 0.459284π0.459284\pi
110110 −3.96512e7 2.28926e7i −0.270823 0.156360i
111111 0 0
112112 2.04914e7 + 3.54921e7i 0.130227 + 0.225559i
113113 −8.33220e7 + 4.81060e7i −0.511030 + 0.295043i −0.733257 0.679952i 0.762001π-0.762001\pi
0.222227 + 0.974995i 0.428667π0.428667\pi
114114 0 0
115115 −1.67787e8 + 2.90616e8i −0.959328 + 1.66160i
116116 5.91547e7i 0.326706i
117117 0 0
118118 1.80635e8 0.931694
119119 −1.18155e8 6.82169e7i −0.589203 0.340177i
120120 0 0
121121 −1.00298e8 1.73721e8i −0.467898 0.810423i
122122 1.08896e8 6.28712e7i 0.491556 0.283800i
123123 0 0
124124 1.79930e7 3.11648e7i 0.0761057 0.131819i
125125 4.45852e8i 1.82621i
126126 0 0
127127 3.67312e8 1.41195 0.705976 0.708235i 0.250508π-0.250508\pi
0.705976 + 0.708235i 0.250508π0.250508\pi
128128 2.05478e7 + 1.18633e7i 0.0765466 + 0.0441942i
129129 0 0
130130 −2.76575e8 4.79041e8i −0.968364 1.67726i
131131 −2.20534e8 + 1.27325e8i −0.748841 + 0.432343i −0.825275 0.564731i 0.808980π-0.808980\pi
0.0764341 + 0.997075i 0.475647π0.475647\pi
132132 0 0
133133 1.56573e8 2.71192e8i 0.500391 0.866702i
134134 2.78187e8i 0.862815i
135135 0 0
136136 −7.89870e7 −0.230887
137137 3.69065e8 + 2.13080e8i 1.04766 + 0.604868i 0.921994 0.387205i 0.126559π-0.126559\pi
0.125668 + 0.992072i 0.459893π0.459893\pi
138138 0 0
139139 1.03393e8 + 1.79082e8i 0.276969 + 0.479725i 0.970630 0.240577i 0.0773366π-0.0773366\pi
−0.693661 + 0.720302i 0.744003π0.744003\pi
140140 3.02475e8 1.74634e8i 0.787368 0.454587i
141141 0 0
142142 −9.46185e7 + 1.63884e8i −0.232714 + 0.403073i
143143 1.66274e8i 0.397630i
144144 0 0
145145 −5.04135e8 −1.14045
146146 −4.67616e7 2.69978e7i −0.102915 0.0594180i
147147 0 0
148148 1.02390e7 + 1.77345e7i 0.0213408 + 0.0369634i
149149 −5.73316e8 + 3.31004e8i −1.16319 + 0.671565i −0.952065 0.305895i 0.901044π-0.901044\pi
−0.211120 + 0.977460i 0.567711π0.567711\pi
150150 0 0
151151 −2.17181e8 + 3.76169e8i −0.417749 + 0.723562i −0.995713 0.0925004i 0.970514π-0.970514\pi
0.577964 + 0.816062i 0.303847π0.303847\pi
152152 1.81292e8i 0.339629i
153153 0 0
154154 −1.04988e8 −0.186663
155155 −2.65596e8 1.53342e8i −0.460145 0.265665i
156156 0 0
157157 5.96980e8 + 1.03400e9i 0.982565 + 1.70185i 0.652293 + 0.757967i 0.273807π0.273807\pi
0.330272 + 0.943886i 0.392860π0.392860\pi
158158 3.56429e8 2.05784e8i 0.571932 0.330205i
159159 0 0
160160 1.01103e8 1.75115e8i 0.154270 0.267204i
161161 7.69489e8i 1.14525i
162162 0 0
163163 −1.10437e9 −1.56446 −0.782232 0.622987i 0.785919π-0.785919\pi
−0.782232 + 0.622987i 0.785919π0.785919\pi
164164 5.75757e8 + 3.32414e8i 0.795910 + 0.459519i
165165 0 0
166166 1.65536e8 + 2.86717e8i 0.218002 + 0.377591i
167167 −2.37674e8 + 1.37221e8i −0.305573 + 0.176423i −0.644944 0.764230i 0.723119π-0.723119\pi
0.339371 + 0.940653i 0.389786π0.389786\pi
168168 0 0
169169 −5.96541e8 + 1.03324e9i −0.731297 + 1.26664i
170170 6.73152e8i 0.805967i
171171 0 0
172172 6.39612e8 0.730807
173173 7.56506e8 + 4.36769e8i 0.844555 + 0.487604i 0.858810 0.512294i 0.171204π-0.171204\pi
−0.0142547 + 0.999898i 0.504538π0.504538\pi
174174 0 0
175175 −9.99734e8 1.73159e9i −1.06594 1.84626i
176176 −5.26386e7 + 3.03909e7i −0.0548597 + 0.0316733i
177177 0 0
178178 3.54393e8 6.13827e8i 0.353025 0.611457i
179179 6.23780e8i 0.607602i −0.952736 0.303801i 0.901744π-0.901744\pi
0.952736 0.303801i 0.0982558π-0.0982558\pi
180180 0 0
181181 1.47088e9 1.37045 0.685227 0.728330i 0.259703π-0.259703\pi
0.685227 + 0.728330i 0.259703π0.259703\pi
182182 −1.09847e9 6.34200e8i −1.00116 0.578017i
183183 0 0
184184 2.22744e8 + 3.85804e8i 0.194328 + 0.336585i
185185 1.51139e8 8.72601e7i 0.129030 0.0744952i
186186 0 0
187187 1.01173e8 1.75236e8i 0.0827366 0.143304i
188188 4.53452e7i 0.0362995i
189189 0 0
190190 −1.54503e9 −1.18556
191191 8.99674e8 + 5.19427e8i 0.676007 + 0.390293i 0.798349 0.602195i 0.205707π-0.205707\pi
−0.122342 + 0.992488i 0.539040π0.539040\pi
192192 0 0
193193 1.19815e9 + 2.07527e9i 0.863543 + 1.49570i 0.868487 + 0.495712i 0.165093π0.165093\pi
−0.00494446 + 0.999988i 0.501574π0.501574\pi
194194 −4.74380e8 + 2.73883e8i −0.334903 + 0.193356i
195195 0 0
196196 3.14982e7 5.45565e7i 0.0213433 0.0369677i
197197 1.61075e9i 1.06945i −0.845025 0.534727i 0.820414π-0.820414\pi
0.845025 0.534727i 0.179586π-0.179586\pi
198198 0 0
199199 −5.25183e8 −0.334887 −0.167444 0.985882i 0.553551π-0.553551\pi
−0.167444 + 0.985882i 0.553551π0.553551\pi
200200 −1.00249e9 5.78786e8i −0.626554 0.361741i
201201 0 0
202202 2.96308e8 + 5.13221e8i 0.177966 + 0.308247i
203203 −1.00113e9 + 5.78004e8i −0.589532 + 0.340367i
204204 0 0
205205 2.83293e9 4.90678e9i 1.60406 2.77831i
206206 7.10464e8i 0.394524i
207207 0 0
208208 −7.34327e8 −0.392316
209209 4.02206e8 + 2.32214e8i 0.210796 + 0.121703i
210210 0 0
211211 −8.85159e8 1.53314e9i −0.446572 0.773485i 0.551588 0.834117i 0.314022π-0.314022\pi
−0.998160 + 0.0606312i 0.980689π0.980689\pi
212212 −1.06256e8 + 6.13468e7i −0.0526028 + 0.0303702i
213213 0 0
214214 3.57507e6 6.19220e6i 0.00170463 0.00295250i
215215 5.45097e9i 2.55106i
216216 0 0
217217 −7.03243e8 −0.317151
218218 −3.52863e8 2.03726e8i −0.156236 0.0902028i
219219 0 0
220220 2.59001e8 + 4.48602e8i 0.110563 + 0.191501i
221221 2.11710e9 1.22231e9i 0.887507 0.512402i
222222 0 0
223223 −2.52764e8 + 4.37800e8i −0.102210 + 0.177034i −0.912595 0.408865i 0.865925π-0.865925\pi
0.810385 + 0.585898i 0.199258π0.199258\pi
224224 4.63667e8i 0.184168i
225225 0 0
226226 1.08851e9 0.417254
227227 −6.53594e8 3.77352e8i −0.246153 0.142116i 0.371849 0.928293i 0.378724π-0.378724\pi
−0.618001 + 0.786177i 0.712057π0.712057\pi
228228 0 0
229229 −2.78927e8 4.83115e8i −0.101426 0.175675i 0.810847 0.585259i 0.199007π-0.199007\pi
−0.912272 + 0.409584i 0.865674π0.865674\pi
230230 3.28794e9 1.89829e9i 1.17493 0.678347i
231231 0 0
232232 −3.34630e8 + 5.79595e8i −0.115508 + 0.200066i
233233 3.55157e9i 1.20503i 0.798108 + 0.602514i 0.205834π0.205834\pi
−0.798108 + 0.602514i 0.794166π0.794166\pi
234234 0 0
235235 3.86446e8 0.126712
236236 −1.76985e9 1.02182e9i −0.570543 0.329403i
237237 0 0
238238 7.71787e8 + 1.33677e9i 0.240541 + 0.416629i
239239 −7.71502e8 + 4.45427e8i −0.236453 + 0.136516i −0.613546 0.789659i 0.710257π-0.710257\pi
0.377092 + 0.926176i 0.376924π0.376924\pi
240240 0 0
241241 1.71946e9 2.97819e9i 0.509710 0.882844i −0.490227 0.871595i 0.663086π-0.663086\pi
0.999937 0.0112489i 0.00358072π-0.00358072\pi
242242 2.26949e9i 0.661707i
243243 0 0
244244 −1.42261e9 −0.401354
245245 −4.64948e8 2.68438e8i −0.129045 0.0745039i
246246 0 0
247247 2.80546e9 + 4.85920e9i 0.753731 + 1.30550i
248248 −3.52589e8 + 2.03568e8i −0.0932100 + 0.0538148i
249249 0 0
250250 −2.52212e9 + 4.36844e9i −0.645662 + 1.11832i
251251 6.42022e9i 1.61754i 0.588124 + 0.808770i 0.299867π0.299867\pi
−0.588124 + 0.808770i 0.700133π0.700133\pi
252252 0 0
253253 −1.14123e9 −0.278543
254254 −3.59891e9 2.07783e9i −0.864641 0.499201i
255255 0 0
256256 −1.34218e8 2.32472e8i −0.0312500 0.0541266i
257257 −8.30896e8 + 4.79718e8i −0.190464 + 0.109965i −0.592200 0.805791i 0.701740π-0.701740\pi
0.401736 + 0.915756i 0.368407π0.368407\pi
258258 0 0
259259 2.00092e8 3.46570e8i 0.0444663 0.0770178i
260260 6.25817e9i 1.36947i
261261 0 0
262262 2.88104e9 0.611426
263263 2.47754e9 + 1.43041e9i 0.517842 + 0.298976i 0.736051 0.676926i 0.236688π-0.236688\pi
−0.218209 + 0.975902i 0.570022π0.570022\pi
264264 0 0
265265 5.22816e8 + 9.05545e8i 0.106015 + 0.183623i
266266 −3.06819e9 + 1.77142e9i −0.612851 + 0.353830i
267267 0 0
268268 1.57366e9 2.72566e9i 0.305051 0.528364i
269269 1.20245e9i 0.229646i −0.993386 0.114823i 0.963370π-0.963370\pi
0.993386 0.114823i 0.0366301π-0.0366301\pi
270270 0 0
271271 −8.98794e9 −1.66641 −0.833207 0.552961i 0.813498π-0.813498\pi
−0.833207 + 0.552961i 0.813498π0.813498\pi
272272 7.73911e8 + 4.46818e8i 0.141389 + 0.0816309i
273273 0 0
274274 −2.41072e9 4.17550e9i −0.427706 0.740809i
275275 2.56813e9 1.48271e9i 0.449041 0.259254i
276276 0 0
277277 −8.05272e8 + 1.39477e9i −0.136780 + 0.236911i −0.926276 0.376845i 0.877009π-0.877009\pi
0.789496 + 0.613756i 0.210342π0.210342\pi
278278 2.33952e9i 0.391694i
279279 0 0
280280 −3.95152e9 −0.642883
281281 1.00668e10 + 5.81207e9i 1.61461 + 0.932193i 0.988284 + 0.152628i 0.0487736π0.0487736\pi
0.626322 + 0.779565i 0.284560π0.284560\pi
282282 0 0
283283 7.70868e8 + 1.33518e9i 0.120181 + 0.208159i 0.919839 0.392297i 0.128319π-0.128319\pi
−0.799658 + 0.600455i 0.794986π0.794986\pi
284284 1.85414e9 1.07049e9i 0.285015 0.164554i
285285 0 0
286286 9.40585e8 1.62914e9i 0.140583 0.243498i
287287 1.29921e10i 1.91493i
288288 0 0
289289 4.00080e9 0.573529
290290 4.93949e9 + 2.85182e9i 0.698378 + 0.403209i
291291 0 0
292292 3.05446e8 + 5.29048e8i 0.0420148 + 0.0727718i
293293 −4.98204e9 + 2.87638e9i −0.675984 + 0.390280i −0.798340 0.602207i 0.794288π-0.794288\pi
0.122356 + 0.992486i 0.460955π0.460955\pi
294294 0 0
295295 −8.70831e9 + 1.50832e10i −1.14986 + 1.99162i
296296 2.31682e8i 0.0301805i
297297 0 0
298298 7.48977e9 0.949737
299299 −1.19405e10 6.89383e9i −1.49395 0.862533i
300300 0 0
301301 −6.24969e9 1.08248e10i −0.761364 1.31872i
302302 4.25587e9 2.45713e9i 0.511635 0.295393i
303303 0 0
304304 −1.02554e9 + 1.77629e9i −0.120077 + 0.207979i
305305 1.21239e10i 1.40102i
306306 0 0
307307 −6.49769e9 −0.731486 −0.365743 0.930716i 0.619185π-0.619185\pi
−0.365743 + 0.930716i 0.619185π0.619185\pi
308308 1.02867e9 + 5.93902e8i 0.114307 + 0.0659952i
309309 0 0
310310 1.73487e9 + 3.00488e9i 0.187854 + 0.325372i
311311 −1.18485e10 + 6.84076e9i −1.26655 + 0.731245i −0.974334 0.225106i 0.927727π-0.927727\pi
−0.292219 + 0.956351i 0.594394π0.594394\pi
312312 0 0
313313 −3.58243e9 + 6.20496e9i −0.373251 + 0.646489i −0.990064 0.140620i 0.955090π-0.955090\pi
0.616813 + 0.787110i 0.288424π0.288424\pi
314314 1.35081e10i 1.38956i
315315 0 0
316316 −4.65637e9 −0.466981
317317 9.86964e9 + 5.69824e9i 0.977382 + 0.564292i 0.901479 0.432824i 0.142483π-0.142483\pi
0.0759031 + 0.997115i 0.475816π0.475816\pi
318318 0 0
319319 −8.57241e8 1.48478e9i −0.0827828 0.143384i
320320 −1.98120e9 + 1.14385e9i −0.188942 + 0.109086i
321321 0 0
322322 4.35289e9 7.53943e9i 0.404906 0.701318i
323323 6.82818e9i 0.627328i
324324 0 0
325325 3.58263e10 3.21121
326326 1.08206e10 + 6.24728e9i 0.958035 + 0.553122i
327327 0 0
328328 −3.76083e9 6.51395e9i −0.324929 0.562793i
329329 7.67421e8 4.43071e8i 0.0655014 0.0378172i
330330 0 0
331331 8.59454e9 1.48862e10i 0.715996 1.24014i −0.246578 0.969123i 0.579306π-0.579306\pi
0.962574 0.271018i 0.0873604π-0.0873604\pi
332332 3.74566e9i 0.308302i
333333 0 0
334334 3.10496e9 0.249499
335335 −2.32290e10 1.34112e10i −1.84438 1.06485i
336336 0 0
337337 1.61156e9 + 2.79131e9i 0.124947 + 0.216415i 0.921712 0.387874i 0.126790π-0.126790\pi
−0.796765 + 0.604289i 0.793457π0.793457\pi
338338 1.16898e10 6.74909e9i 0.895652 0.517105i
339339 0 0
340340 3.80792e9 6.59551e9i 0.284952 0.493552i
341341 1.04298e9i 0.0771364i
342342 0 0
343343 1.31889e10 0.952870
344344 −6.26689e9 3.61819e9i −0.447526 0.258379i
345345 0 0
346346 −4.94148e9 8.55889e9i −0.344788 0.597191i
347347 2.16831e9 1.25187e9i 0.149556 0.0863461i −0.423355 0.905964i 0.639148π-0.639148\pi
0.572911 + 0.819618i 0.305814π0.305814\pi
348348 0 0
349349 −8.92317e9 + 1.54554e10i −0.601475 + 1.04178i 0.391123 + 0.920338i 0.372087π0.372087\pi
−0.992598 + 0.121446i 0.961247π0.961247\pi
350350 2.26214e10i 1.50746i
351351 0 0
352352 6.87667e8 0.0447927
353353 −2.33322e9 1.34709e9i −0.150265 0.0867555i 0.422982 0.906138i 0.360983π-0.360983\pi
−0.573247 + 0.819382i 0.694317π0.694317\pi
354354 0 0
355355 −9.12302e9 1.58015e10i −0.574414 0.994915i
356356 −6.94466e9 + 4.00950e9i −0.432366 + 0.249626i
357357 0 0
358358 −3.52863e9 + 6.11177e9i −0.214820 + 0.372079i
359359 4.46773e8i 0.0268973i −0.999910 0.0134487i 0.995719π-0.995719\pi
0.999910 0.0134487i 0.00428097π-0.00428097\pi
360360 0 0
361361 −1.31142e9 −0.0772168
362362 −1.44117e10 8.32058e9i −0.839228 0.484529i
363363 0 0
364364 7.17516e9 + 1.24277e10i 0.408720 + 0.707924i
365365 4.50871e9 2.60310e9i 0.254028 0.146663i
366366 0 0
367367 −4.50312e9 + 7.79963e9i −0.248227 + 0.429942i −0.963034 0.269380i 0.913181π-0.913181\pi
0.714807 + 0.699322i 0.246515π0.246515\pi
368368 5.04012e9i 0.274821i
369369 0 0
370370 −1.97447e9 −0.105352
371371 2.07646e9 + 1.19885e9i 0.109605 + 0.0632802i
372372 0 0
373373 3.61769e9 + 6.26602e9i 0.186894 + 0.323710i 0.944213 0.329335i 0.106825π-0.106825\pi
−0.757319 + 0.653045i 0.773491π0.773491\pi
374374 −1.98257e9 + 1.14464e9i −0.101331 + 0.0585036i
375375 0 0
376376 2.56511e8 4.44291e8i 0.0128338 0.0222288i
377377 2.07133e10i 1.02538i
378378 0 0
379379 −2.18940e10 −1.06113 −0.530566 0.847644i 0.678020π-0.678020\pi
−0.530566 + 0.847644i 0.678020π0.678020\pi
380380 1.51381e10 + 8.74001e9i 0.726002 + 0.419158i
381381 0 0
382382 −5.87664e9 1.01786e10i −0.275979 0.478009i
383383 1.99158e10 1.14984e10i 0.925555 0.534369i 0.0401518 0.999194i 0.487216π-0.487216\pi
0.885403 + 0.464824i 0.153883π0.153883\pi
384384 0 0
385385 5.06142e9 8.76664e9i 0.230372 0.399016i
386386 2.71112e10i 1.22123i
387387 0 0
388388 6.19727e9 0.273447
389389 1.71912e10 + 9.92532e9i 0.750770 + 0.433457i 0.825972 0.563711i 0.190627π-0.190627\pi
−0.0752021 + 0.997168i 0.523960π0.523960\pi
390390 0 0
391391 8.38941e9 + 1.45309e10i 0.358942 + 0.621706i
392392 −6.17236e8 + 3.56362e8i −0.0261401 + 0.0150920i
393393 0 0
394394 −9.11175e9 + 1.57820e10i −0.378109 + 0.654904i
395395 3.96830e10i 1.63011i
396396 0 0
397397 −2.22799e10 −0.896915 −0.448458 0.893804i 0.648026π-0.648026\pi
−0.448458 + 0.893804i 0.648026π0.648026\pi
398398 5.14572e9 + 2.97089e9i 0.205076 + 0.118401i
399399 0 0
400400 6.54821e9 + 1.13418e10i 0.255789 + 0.443040i
401401 2.03685e10 1.17598e10i 0.787738 0.454801i −0.0514274 0.998677i 0.516377π-0.516377\pi
0.839166 + 0.543876i 0.183044π0.183044\pi
402402 0 0
403403 6.30033e9 1.09125e10i 0.238860 0.413718i
404404 6.70469e9i 0.251682i
405405 0 0
406406 1.30787e10 0.481351
407407 5.13999e8 + 2.96757e8i 0.0187320 + 0.0108149i
408408 0 0
409409 −2.32825e10 4.03265e10i −0.832025 1.44111i −0.896430 0.443186i 0.853848π-0.853848\pi
0.0644044 0.997924i 0.479485π-0.479485\pi
410410 −5.55139e10 + 3.20510e10i −1.96456 + 1.13424i
411411 0 0
412412 4.01899e9 6.96109e9i 0.139485 0.241595i
413413 3.99372e10i 1.37271i
414414 0 0
415415 −3.19217e10 −1.07620
416416 7.19491e9 + 4.15398e9i 0.240244 + 0.138705i
417417 0 0
418418 −2.62720e9 4.55044e9i −0.0860573 0.149056i
419419 −3.95877e9 + 2.28560e9i −0.128441 + 0.0741556i −0.562844 0.826563i 0.690293π-0.690293\pi
0.434403 + 0.900719i 0.356959π0.356959\pi
420420 0 0
421421 6.62653e9 1.14775e10i 0.210939 0.365358i −0.741069 0.671428i 0.765681π-0.765681\pi
0.952009 + 0.306071i 0.0990144π0.0990144\pi
422422 2.00289e10i 0.631548i
423423 0 0
424424 1.38812e9 0.0429500
425425 −3.77576e10 2.17993e10i −1.15731 0.668171i
426426 0 0
427427 1.39004e10 + 2.40762e10i 0.418135 + 0.724231i
428428 −7.00568e7 + 4.04473e7i −0.00208773 + 0.00120535i
429429 0 0
430430 −3.08354e10 + 5.34084e10i −0.901935 + 1.56220i
431431 2.64178e10i 0.765575i 0.923836 + 0.382787i 0.125036π0.125036\pi
−0.923836 + 0.382787i 0.874964π0.874964\pi
432432 0 0
433433 4.70683e10 1.33899 0.669494 0.742817i 0.266511π-0.266511\pi
0.669494 + 0.742817i 0.266511π0.266511\pi
434434 6.89035e9 + 3.97814e9i 0.194215 + 0.112130i
435435 0 0
436436 2.30489e9 + 3.99219e9i 0.0637830 + 0.110475i
437437 −3.33515e10 + 1.92555e10i −0.914513 + 0.527995i
438438 0 0
439439 −1.60624e10 + 2.78209e10i −0.432467 + 0.749055i −0.997085 0.0762974i 0.975690π-0.975690\pi
0.564618 + 0.825352i 0.309023π0.309023\pi
440440 5.86052e9i 0.156360i
441441 0 0
442442 −2.76576e10 −0.724646
443443 4.36195e10 + 2.51837e10i 1.13257 + 0.653891i 0.944581 0.328279i 0.106469π-0.106469\pi
0.187992 + 0.982171i 0.439802π0.439802\pi
444444 0 0
445445 3.41702e10 + 5.91846e10i 0.871381 + 1.50928i
446446 4.95314e9 2.85969e9i 0.125182 0.0722737i
447447 0 0
448448 −2.62290e9 + 4.54299e9i −0.0651133 + 0.112780i
449449 2.09633e10i 0.515792i −0.966173 0.257896i 0.916971π-0.916971\pi
0.966173 0.257896i 0.0830293π-0.0830293\pi
450450 0 0
451451 1.92687e10 0.465743
452452 −1.06652e10 6.15757e9i −0.255515 0.147522i
453453 0 0
454454 4.26926e9 + 7.39457e9i 0.100491 + 0.174056i
455455 1.05913e11 6.11489e10i 2.47118 1.42674i
456456 0 0
457457 2.27460e10 3.93972e10i 0.521482 0.903234i −0.478206 0.878248i 0.658713π-0.658713\pi
0.999688 0.0249858i 0.00795405π-0.00795405\pi
458458 6.31139e9i 0.143438i
459459 0 0
460460 −4.29535e10 −0.959328
461461 −3.76919e10 2.17614e10i −0.834534 0.481818i 0.0208685 0.999782i 0.493357π-0.493357\pi
−0.855403 + 0.517964i 0.826690π0.826690\pi
462462 0 0
463463 −1.88669e10 3.26784e10i −0.410560 0.711111i 0.584391 0.811472i 0.301333π-0.301333\pi
−0.994951 + 0.100361i 0.968000π0.968000\pi
464464 6.55737e9 3.78590e9i 0.141468 0.0816765i
465465 0 0
466466 2.00907e10 3.47982e10i 0.426042 0.737926i
467467 1.94089e10i 0.408068i 0.978964 + 0.204034i 0.0654053π0.0654053\pi
−0.978964 + 0.204034i 0.934595π0.934595\pi
468468 0 0
469469 −6.15054e10 −1.27122
470470 −3.78638e9 2.18607e9i −0.0775949 0.0447994i
471471 0 0
472472 1.15606e10 + 2.00236e10i 0.232923 + 0.403435i
473473 1.60543e10 9.26894e9i 0.320735 0.185176i
474474 0 0
475475 5.00342e10 8.66618e10i 0.982862 1.70237i
476476 1.74635e10i 0.340177i
477477 0 0
478478 1.00789e10 0.193063
479479 −1.20390e10 6.95073e9i −0.228691 0.132035i 0.381277 0.924461i 0.375484π-0.375484\pi
−0.609968 + 0.792426i 0.708818π0.708818\pi
480480 0 0
481481 3.58524e9 + 6.20981e9i 0.0669788 + 0.116011i
482482 −3.36944e10 + 1.94534e10i −0.624265 + 0.360420i
483483 0 0
484484 1.28381e10 2.22363e10i 0.233949 0.405211i
485485 5.28151e10i 0.954534i
486486 0 0
487487 3.69205e10 0.656374 0.328187 0.944613i 0.393562π-0.393562\pi
0.328187 + 0.944613i 0.393562π0.393562\pi
488488 1.39387e10 + 8.04751e9i 0.245778 + 0.141900i
489489 0 0
490490 3.03703e9 + 5.26028e9i 0.0526822 + 0.0912483i
491491 −5.69924e10 + 3.29046e10i −0.980598 + 0.566149i −0.902451 0.430793i 0.858234π-0.858234\pi
−0.0781474 + 0.996942i 0.524900π0.524900\pi
492492 0 0
493493 −1.26035e10 + 2.18298e10i −0.213355 + 0.369541i
494494 6.34803e10i 1.06594i
495495 0 0
496496 4.60621e9 0.0761057
497497 −3.62338e10 2.09196e10i −0.593865 0.342868i
498498 0 0
499499 −4.81781e9 8.34469e9i −0.0777047 0.134589i 0.824555 0.565782i 0.191426π-0.191426\pi
−0.902259 + 0.431194i 0.858092π0.858092\pi
500500 4.94232e10 2.85345e10i 0.790771 0.456552i
501501 0 0
502502 3.63183e10 6.29051e10i 0.571887 0.990537i
503503 2.91551e10i 0.455452i −0.973725 0.227726i 0.926871π-0.926871\pi
0.973725 0.227726i 0.0731291π-0.0731291\pi
504504 0 0
505505 −5.71394e10 −0.878558
506506 1.11818e10 + 6.45579e9i 0.170572 + 0.0984798i
507507 0 0
508508 2.35080e10 + 4.07170e10i 0.352988 + 0.611393i
509509 −6.14696e10 + 3.54895e10i −0.915776 + 0.528723i −0.882285 0.470716i 0.843996π-0.843996\pi
−0.0334907 + 0.999439i 0.510662π0.510662\pi
510510 0 0
511511 5.96906e9 1.03387e10i 0.0875432 0.151629i
512512 3.03700e9i 0.0441942i
513513 0 0
514514 1.08548e10 0.155514
515515 −5.93246e10 3.42511e10i −0.843347 0.486906i
516516 0 0
517517 6.57120e8 + 1.13817e9i 0.00919778 + 0.0159310i
518518 −3.92099e9 + 2.26378e9i −0.0544598 + 0.0314424i
519519 0 0
520520 3.54015e10 6.13173e10i 0.484182 0.838628i
521521 6.08836e10i 0.826323i −0.910658 0.413161i 0.864425π-0.864425\pi
0.910658 0.413161i 0.135575π-0.135575\pi
522522 0 0
523523 2.81890e10 0.376768 0.188384 0.982095i 0.439675π-0.439675\pi
0.188384 + 0.982095i 0.439675π0.439675\pi
524524 −2.82283e10 1.62976e10i −0.374420 0.216172i
525525 0 0
526526 −1.61832e10 2.80301e10i −0.211408 0.366170i
527527 −1.32799e10 + 7.66716e9i −0.172168 + 0.0994012i
528528 0 0
529529 8.16093e9 1.41351e10i 0.104212 0.180500i
530530 1.18300e10i 0.149927i
531531 0 0
532532 4.00826e10 0.500391
533533 2.01604e11 + 1.16396e11i 2.49799 + 1.44221i
534534 0 0
535535 3.44705e8 + 5.97046e8i 0.00420758 + 0.00728774i
536536 −3.08374e10 + 1.78040e10i −0.373610 + 0.215704i
537537 0 0
538538 −6.80210e9 + 1.17816e10i −0.0811921 + 0.140629i
539539 1.82583e9i 0.0216324i
540540 0 0
541541 −1.20219e11 −1.40341 −0.701703 0.712470i 0.747577π-0.747577\pi
−0.701703 + 0.712470i 0.747577π0.747577\pi
542542 8.80634e10 + 5.08435e10i 1.02047 + 0.589166i
543543 0 0
544544 −5.05517e9 8.75580e9i −0.0577218 0.0999771i
545545 3.40227e10 1.96430e10i 0.385641 0.222650i
546546 0 0
547547 −6.82534e10 + 1.18218e11i −0.762386 + 1.32049i 0.179231 + 0.983807i 0.442639π0.442639\pi
−0.941617 + 0.336685i 0.890694π0.890694\pi
548548 5.45485e10i 0.604868i
549549 0 0
550550 −3.35499e10 −0.366640
551551 −5.01042e10 2.89277e10i −0.543585 0.313839i
552552 0 0
553553 4.54977e10 + 7.88043e10i 0.486506 + 0.842654i
554554 1.57801e10 9.11062e9i 0.167521 0.0967183i
555555 0 0
556556 −1.32343e10 + 2.29225e10i −0.138485 + 0.239862i
557557 1.72931e10i 0.179660i −0.995957 0.0898300i 0.971368π-0.971368\pi
0.995957 0.0898300i 0.0286324π-0.0286324\pi
558558 0 0
559559 2.23963e11 2.29366
560560 3.87168e10 + 2.23532e10i 0.393684 + 0.227294i
561561 0 0
562562 −6.57561e10 1.13893e11i −0.659160 1.14170i
563563 −4.39485e10 + 2.53737e10i −0.437432 + 0.252552i −0.702508 0.711676i 0.747936π-0.747936\pi
0.265076 + 0.964228i 0.414603π0.414603\pi
564564 0 0
565565 −5.24767e10 + 9.08923e10i −0.514959 + 0.891936i
566566 1.74427e10i 0.169961i
567567 0 0
568568 −2.42223e10 −0.232714
569569 −7.23149e10 4.17510e10i −0.689888 0.398307i 0.113682 0.993517i 0.463735π-0.463735\pi
−0.803570 + 0.595210i 0.797069π0.797069\pi
570570 0 0
571571 6.95426e10 + 1.20451e11i 0.654194 + 1.13310i 0.982095 + 0.188385i 0.0603254π0.0603254\pi
−0.327901 + 0.944712i 0.606341π0.606341\pi
572572 −1.84316e10 + 1.06415e10i −0.172179 + 0.0994075i
573573 0 0
574574 −7.34946e10 + 1.27296e11i −0.677030 + 1.17265i
575575 2.45897e11i 2.24948i
576576 0 0
577577 −1.25735e11 −1.13437 −0.567184 0.823591i 0.691967π-0.691967\pi
−0.567184 + 0.823591i 0.691967π0.691967\pi
578578 −3.91997e10 2.26319e10i −0.351213 0.202773i
579579 0 0
580580 −3.22646e10 5.58840e10i −0.285112 0.493828i
581581 −6.33915e10 + 3.65991e10i −0.556322 + 0.321193i
582582 0 0
583583 −1.77801e9 + 3.07961e9i −0.0153908 + 0.0266576i
584584 6.91145e9i 0.0594180i
585585 0 0
586586 6.50851e10 0.551939
587587 6.44083e10 + 3.71861e10i 0.542487 + 0.313205i 0.746086 0.665849i 0.231931π-0.231931\pi
−0.203599 + 0.979054i 0.565264π0.565264\pi
588588 0 0
589589 −1.75978e10 3.04803e10i −0.146217 0.253255i
590590 1.70647e11 9.85232e10i 1.40829 0.813075i
591591 0 0
592592 −1.31059e9 + 2.27001e9i −0.0106704 + 0.0184817i
593593 7.64545e10i 0.618279i 0.951017 + 0.309139i 0.100041π0.100041\pi
−0.951017 + 0.309139i 0.899959π0.899959\pi
594594 0 0
595595 −1.48830e11 −1.18747
596596 −7.33844e10 4.23685e10i −0.581593 0.335783i
597597 0 0
598598 7.79948e10 + 1.35091e11i 0.609903 + 1.05638i
599599 −6.63143e10 + 3.82866e10i −0.515110 + 0.297399i −0.734932 0.678141i 0.762786π-0.762786\pi
0.219822 + 0.975540i 0.429452π0.429452\pi
600600 0 0
601601 −2.39823e10 + 4.15386e10i −0.183820 + 0.318386i −0.943178 0.332287i 0.892180π-0.892180\pi
0.759358 + 0.650673i 0.225513π0.225513\pi
602602 1.41414e11i 1.07673i
603603 0 0
604604 −5.55985e10 −0.417749
605605 −1.89505e11 1.09411e11i −1.41449 0.816655i
606606 0 0
607607 −1.02320e11 1.77223e11i −0.753710 1.30546i −0.946013 0.324128i 0.894929π-0.894929\pi
0.192303 0.981336i 0.438404π-0.438404\pi
608608 2.00965e10 1.16027e10i 0.147064 0.0849073i
609609 0 0
610610 6.85834e10 1.18790e11i 0.495336 0.857946i
611611 1.58778e10i 0.113927i
612612 0 0
613613 4.26255e10 0.301876 0.150938 0.988543i 0.451771π-0.451771\pi
0.150938 + 0.988543i 0.451771π0.451771\pi
614614 6.36641e10 + 3.67565e10i 0.447942 + 0.258619i
615615 0 0
616616 −6.71924e9 1.16381e10i −0.0466656 0.0808273i
617617 2.80277e9 1.61818e9i 0.0193396 0.0111657i −0.490299 0.871554i 0.663112π-0.663112\pi
0.509639 + 0.860389i 0.329779π0.329779\pi
618618 0 0
619619 7.34200e10 1.27167e11i 0.500094 0.866189i −0.499906 0.866080i 0.666632π-0.666632\pi
1.00000 0.000108934i 3.46746e5π-3.46746e-5\pi
620620 3.92556e10i 0.265665i
621621 0 0
622622 1.54789e11 1.03414
623623 1.35713e11 + 7.83542e10i 0.900888 + 0.520128i
624624 0 0
625625 −8.70585e10 1.50790e11i −0.570546 0.988215i
626626 7.02011e10 4.05306e10i 0.457137 0.263928i
627627 0 0
628628 −7.64135e10 + 1.32352e11i −0.491283 + 0.850926i
629629 8.72607e9i 0.0557463i
630630 0 0
631631 2.39192e11 1.50879 0.754397 0.656419i 0.227929π-0.227929\pi
0.754397 + 0.656419i 0.227929π0.227929\pi
632632 4.56229e10 + 2.63404e10i 0.285966 + 0.165103i
633633 0 0
634634 −6.44682e10 1.11662e11i −0.399014 0.691113i
635635 3.47003e11 2.00342e11i 2.13422 1.23219i
636636 0 0
637637 1.10292e10 1.91032e10i 0.0669866 0.116024i
638638 1.93971e10i 0.117073i
639639 0 0
640640 2.58823e10 0.154270
641641 7.33197e8 + 4.23311e8i 0.00434299 + 0.00250742i 0.502170 0.864769i 0.332535π-0.332535\pi
−0.497827 + 0.867276i 0.665869π0.665869\pi
642642 0 0
643643 5.89225e10 + 1.02057e11i 0.344697 + 0.597033i 0.985299 0.170841i 0.0546483π-0.0546483\pi
−0.640602 + 0.767873i 0.721315π0.721315\pi
644644 −8.52989e10 + 4.92473e10i −0.495906 + 0.286312i
645645 0 0
646646 −3.86260e10 + 6.69022e10i −0.221794 + 0.384158i
647647 2.63434e11i 1.50333i −0.659546 0.751665i 0.729251π-0.729251\pi
0.659546 0.751665i 0.270749π-0.270749\pi
648648 0 0
649649 −5.92311e10 −0.333865
650650 −3.51025e11 2.02664e11i −1.96646 1.13534i
651651 0 0
652652 −7.06799e10 1.22421e11i −0.391116 0.677433i
653653 −1.08870e11 + 6.28559e10i −0.598761 + 0.345695i −0.768554 0.639785i 0.779024π-0.779024\pi
0.169793 + 0.985480i 0.445690π0.445690\pi
654654 0 0
655655 −1.38893e11 + 2.40570e11i −0.754599 + 1.30700i
656656 8.50979e10i 0.459519i
657657 0 0
658658 −1.00256e10 −0.0534816
659659 3.14417e10 + 1.81529e10i 0.166711 + 0.0962506i 0.581034 0.813879i 0.302648π-0.302648\pi
−0.414323 + 0.910130i 0.635982π0.635982\pi
660660 0 0
661661 −6.52457e10 1.13009e11i −0.341779 0.591979i 0.642984 0.765880i 0.277696π-0.277696\pi
−0.984763 + 0.173901i 0.944363π0.944363\pi
662662 −1.68418e11 + 9.72361e10i −0.876912 + 0.506286i
663663 0 0
664664 −2.11887e10 + 3.66998e10i −0.109001 + 0.188796i
665665 3.41597e11i 1.74673i
666666 0 0
667667 1.42167e11 0.718285
668668 −3.04222e10 1.75643e10i −0.152787 0.0882114i
669669 0 0
670670 1.51731e11 + 2.62806e11i 0.752965 + 1.30417i
671671 −3.57076e10 + 2.06158e10i −0.176145 + 0.101697i
672672 0 0
673673 −1.99070e10 + 3.44799e10i −0.0970388 + 0.168076i −0.910458 0.413602i 0.864270π-0.864270\pi
0.813419 + 0.581678i 0.197604π0.197604\pi
674674 3.64655e10i 0.176702i
675675 0 0
676676 −1.52715e11 −0.731297
677677 2.31655e11 + 1.33746e11i 1.10277 + 0.636687i 0.936948 0.349468i 0.113638π-0.113638\pi
0.165826 + 0.986155i 0.446971π0.446971\pi
678678 0 0
679679 −6.05539e10 1.04882e11i −0.284881 0.493428i
680680 −7.46197e10 + 4.30817e10i −0.348994 + 0.201492i
681681 0 0
682682 −5.90000e9 + 1.02191e10i −0.0272719 + 0.0472362i
683683 3.82963e10i 0.175984i −0.996121 0.0879922i 0.971955π-0.971955\pi
0.996121 0.0879922i 0.0280451π-0.0280451\pi
684684 0 0
685685 4.64879e11 2.11144
686686 −1.29225e11 7.46079e10i −0.583511 0.336890i
687687 0 0
688688 4.09352e10 + 7.09018e10i 0.182702 + 0.316449i
689689 −3.72059e10 + 2.14809e10i −0.165096 + 0.0953179i
690690 0 0
691691 2.01386e11 3.48810e11i 0.883316 1.52995i 0.0356843 0.999363i 0.488639π-0.488639\pi
0.847632 0.530585i 0.178028π-0.178028\pi
692692 1.11813e11i 0.487604i
693693 0 0
694694 −2.83267e10 −0.122112
695695 1.95353e11 + 1.12787e11i 0.837297 + 0.483414i
696696 0 0
697697 −1.41648e11 2.45341e11i −0.600175 1.03953i
698698 1.74858e11 1.00954e11i 0.736653 0.425307i
699699 0 0
700700 1.27966e11 2.21644e11i 0.532969 0.923130i
701701 4.49866e11i 1.86299i −0.363750 0.931497i 0.618504π-0.618504\pi
0.363750 0.931497i 0.381496π-0.381496\pi
702702 0 0
703703 2.00282e10 0.0820013
704704 −6.73774e9 3.89003e9i −0.0274298 0.0158366i
705705 0 0
706706 1.52405e10 + 2.63974e10i 0.0613454 + 0.106253i
707707 −1.13470e11 + 6.55119e10i −0.454154 + 0.262206i
708708 0 0
709709 1.26945e11 2.19875e11i 0.502378 0.870145i −0.497618 0.867396i 0.665792π-0.665792\pi
0.999996 0.00274839i 0.000874840π-0.000874840\pi
710710 2.06430e11i 0.812345i
711711 0 0
712712 9.07247e10 0.353025
713713 7.48989e10 + 4.32429e10i 0.289813 + 0.167323i
714714 0 0
715715 9.06903e10 + 1.57080e11i 0.347006 + 0.601031i
716716 6.91468e10 3.99219e10i 0.263099 0.151901i
717717 0 0
718718 −2.52733e9 + 4.37746e9i −0.00950964 + 0.0164712i
719719 5.21386e11i 1.95094i 0.220134 + 0.975470i 0.429351π0.429351\pi
−0.220134 + 0.975470i 0.570649π0.570649\pi
720720 0 0
721721 −1.57079e11 −0.581269
722722 1.28492e10 + 7.41849e9i 0.0472854 + 0.0273003i
723723 0 0
724724 9.41366e10 + 1.63049e11i 0.342613 + 0.593424i
725725 −3.19921e11 + 1.84706e11i −1.15795 + 0.668544i
726726 0 0
727727 2.86428e9 4.96107e9i 0.0102536 0.0177598i −0.860853 0.508854i 0.830069π-0.830069\pi
0.871107 + 0.491094i 0.163403π0.163403\pi
728728 1.62355e11i 0.578017i
729729 0 0
730730 −5.89015e10 −0.207413
731731 −2.36036e11 1.36275e11i −0.826625 0.477252i
732732 0 0
733733 1.60850e11 + 2.78600e11i 0.557192 + 0.965084i 0.997729 + 0.0673502i 0.0214545π0.0214545\pi
−0.440538 + 0.897734i 0.645212π0.645212\pi
734734 8.82427e10 5.09469e10i 0.304015 0.175523i
735735 0 0
736736 −2.85112e10 + 4.93829e10i −0.0971638 + 0.168293i
737737 9.12190e10i 0.309183i
738738 0 0
739739 −5.10308e11 −1.71102 −0.855508 0.517789i 0.826755π-0.826755\pi
−0.855508 + 0.517789i 0.826755π0.826755\pi
740740 1.93458e10 + 1.11693e10i 0.0645148 + 0.0372476i
741741 0 0
742742 −1.35634e10 2.34925e10i −0.0447459 0.0775021i
743743 3.85768e11 2.22723e11i 1.26582 0.730819i 0.291622 0.956533i 0.405805π-0.405805\pi
0.974194 + 0.225714i 0.0724716π0.0724716\pi
744744 0 0
745745 −3.61078e11 + 6.25405e11i −1.17213 + 2.03019i
746746 8.18589e10i 0.264308i
747747 0 0
748748 2.59002e10 0.0827366
749749 1.36906e9 + 7.90426e8i 0.00435005 + 0.00251151i
750750 0 0
751751 −2.49914e11 4.32864e11i −0.785654 1.36079i −0.928608 0.371063i 0.878993π-0.878993\pi
0.142954 0.989729i 0.454340π-0.454340\pi
752752 −5.02657e9 + 2.90209e9i −0.0157181 + 0.00907486i
753753 0 0
754754 −1.17172e11 + 2.02948e11i −0.362526 + 0.627913i
755755 4.73828e11i 1.45825i
756756 0 0
757757 4.42799e11 1.34841 0.674207 0.738542i 0.264485π-0.264485\pi
0.674207 + 0.738542i 0.264485π0.264485\pi
758758 2.14517e11 + 1.23851e11i 0.649808 + 0.375167i
759759 0 0
760760 −9.88819e10 1.71268e11i −0.296389 0.513361i
761761 −4.15275e11 + 2.39759e11i −1.23822 + 0.714885i −0.968730 0.248119i 0.920188π-0.920188\pi
−0.269488 + 0.963004i 0.586854π0.586854\pi
762762 0 0
763763 4.50425e10 7.80159e10i 0.132900 0.230189i
764764 1.32973e11i 0.390293i
765765 0 0
766766 −2.60179e11 −0.755712
767767 −6.19721e11 3.57796e11i −1.79067 1.03384i
768768 0 0
769769 1.36289e10 + 2.36059e10i 0.0389722 + 0.0675018i 0.884854 0.465869i 0.154258π-0.154258\pi
−0.845881 + 0.533371i 0.820925π0.820925\pi
770770 −9.91832e10 + 5.72635e10i −0.282147 + 0.162898i
771771 0 0
772772 −1.53364e11 + 2.65634e11i −0.431771 + 0.747850i
773773 2.36838e11i 0.663336i −0.943396 0.331668i 0.892389π-0.892389\pi
0.943396 0.331668i 0.107611π-0.107611\pi
774774 0 0
775775 −2.24728e11 −0.622945
776776 −6.07206e10 3.50571e10i −0.167452 0.0966782i
777777 0 0
778778 −1.12292e11 1.94496e11i −0.306501 0.530875i
779779 5.63110e11 3.25112e11i 1.52913 0.882842i
780780 0 0
781781 3.10259e10 5.37385e10i 0.0833913 0.144438i
782782 1.89831e11i 0.507621i
783783 0 0
784784 8.06354e9 0.0213433
785785 1.12795e12 + 6.51220e11i 2.97036 + 1.71494i
786786 0 0
787787 1.75898e11 + 3.04664e11i 0.458523 + 0.794185i 0.998883 0.0472487i 0.0150453π-0.0150453\pi
−0.540360 + 0.841434i 0.681712π0.681712\pi
788788 1.78553e11 1.03088e11i 0.463087 0.267363i
789789 0 0
790790 2.24481e11 3.88813e11i 0.576330 0.998234i
791791 2.40664e11i 0.614759i
792792 0 0
793793 −4.98134e11 −1.25966
794794 2.18298e11 + 1.26034e11i 0.549246 + 0.317107i
795795 0 0
796796 −3.36117e10 5.82172e10i −0.0837218 0.145010i
797797 1.21936e11 7.03995e10i 0.302202 0.174476i −0.341230 0.939980i 0.610843π-0.610843\pi
0.643432 + 0.765504i 0.277510π0.277510\pi
798798 0 0
799799 9.66122e9 1.67337e10i 0.0237053 0.0410587i
800800 1.48169e11i 0.361741i
801801 0 0
802802 −2.66093e11 −0.643186
803803 1.53334e10 + 8.85274e9i 0.0368787 + 0.0212919i
804804 0 0
805805 4.19701e11 + 7.26944e11i 0.999440 + 1.73108i
806806 −1.23461e11 + 7.12801e10i −0.292542 + 0.168899i
807807 0 0
808808 −3.79274e10 + 6.56922e10i −0.0889832 + 0.154123i
809809 5.70685e10i 0.133230i −0.997779 0.0666151i 0.978780π-0.978780\pi
0.997779 0.0666151i 0.0212199π-0.0212199\pi
810810 0 0
811811 −5.81519e11 −1.34425 −0.672126 0.740437i 0.734619π-0.734619\pi
−0.672126 + 0.740437i 0.734619π0.734619\pi
812812 −1.28145e11 7.39845e10i −0.294766 0.170183i
813813 0 0
814814 −3.35743e9 5.81523e9i −0.00764731 0.0132455i
815815 −1.04331e12 + 6.02356e11i −2.36474 + 1.36528i
816816 0 0
817817 3.12781e11 5.41753e11i 0.702025 1.21594i
818818 5.26823e11i 1.17666i
819819 0 0
820820 7.25231e11 1.60406
821821 −2.88515e11 1.66574e11i −0.635031 0.366636i 0.147667 0.989037i 0.452824π-0.452824\pi
−0.782698 + 0.622402i 0.786157π0.786157\pi
822822 0 0
823823 4.11950e11 + 7.13518e11i 0.897935 + 1.55527i 0.830129 + 0.557571i 0.188266π0.188266\pi
0.0678057 + 0.997699i 0.478400π0.478400\pi
824824 −7.87558e10 + 4.54697e10i −0.170834 + 0.0986309i
825825 0 0
826826 2.25919e11 3.91303e11i 0.485325 0.840608i
827827 8.92051e11i 1.90708i −0.301274 0.953538i 0.597412π-0.597412\pi
0.301274 0.953538i 0.402588π-0.402588\pi
828828 0 0
829829 −1.53632e11 −0.325284 −0.162642 0.986685i 0.552002π-0.552002\pi
−0.162642 + 0.986685i 0.552002π0.552002\pi
830830 3.12767e11 + 1.80576e11i 0.659036 + 0.380495i
831831 0 0
832832 −4.69970e10 8.14011e10i −0.0980791 0.169878i
833833 −2.32475e10 + 1.34220e10i −0.0482833 + 0.0278764i
834834 0 0
835835 −1.49688e11 + 2.59268e11i −0.307923 + 0.533338i
836836 5.94467e10i 0.121703i
837837 0 0
838838 5.17172e10 0.104872
839839 −2.64665e11 1.52805e11i −0.534133 0.308382i 0.208565 0.978009i 0.433121π-0.433121\pi
−0.742698 + 0.669627i 0.766454π0.766454\pi
840840 0 0
841841 −1.43334e11 2.48261e11i −0.286526 0.496278i
842842 −1.29853e11 + 7.49706e10i −0.258347 + 0.149157i
843843 0 0
844844 1.13300e11 1.96242e11i 0.223286 0.386743i
845845 1.30148e12i 2.55277i
846846 0 0
847847 −5.01769e11 −0.974923
848848 −1.36007e10 7.85239e9i −0.0263014 0.0151851i
849849 0 0
850850 2.46631e11 + 4.27178e11i 0.472468 + 0.818339i
851851 −4.26216e10 + 2.46076e10i −0.0812665 + 0.0469192i
852852 0 0
853853 −2.22811e11 + 3.85919e11i −0.420862 + 0.728955i −0.996024 0.0890849i 0.971606π-0.971606\pi
0.575162 + 0.818040i 0.304939π0.304939\pi
854854 3.14531e11i 0.591332i
855855 0 0
856856 9.15218e8 0.00170463
857857 8.02066e10 + 4.63073e10i 0.148692 + 0.0858472i 0.572500 0.819905i 0.305974π-0.305974\pi
−0.423808 + 0.905752i 0.639307π0.639307\pi
858858 0 0
859859 1.29899e11 + 2.24992e11i 0.238580 + 0.413233i 0.960307 0.278945i 0.0899847π-0.0899847\pi
−0.721727 + 0.692178i 0.756651π0.756651\pi
860860 6.04247e11 3.48862e11i 1.10464 0.637765i
861861 0 0
862862 1.49442e11 2.58841e11i 0.270672 0.468817i
863863 8.28592e10i 0.149382i −0.997207 0.0746909i 0.976203π-0.976203\pi
0.997207 0.0746909i 0.0237970π-0.0237970\pi
864864 0 0
865865 9.52905e11 1.70210
866866 −4.61173e11 2.66259e11i −0.819960 0.473404i
867867 0 0
868868 −4.50076e10 7.79554e10i −0.0792878 0.137331i
869869 −1.16875e11 + 6.74778e10i −0.204947 + 0.118326i
870870 0 0
871871 5.51025e11 9.54404e11i 0.957412 1.65829i
872872 5.21538e10i 0.0902028i
873873 0 0
874874 4.35703e11 0.746697
875875 −9.65834e11 5.57625e11i −1.64767 0.951283i
876876 0 0
877877 −1.71742e11 2.97466e11i −0.290321 0.502851i 0.683564 0.729890i 0.260429π-0.260429\pi
−0.973886 + 0.227039i 0.927096π0.927096\pi
878878 3.14758e11 1.81726e11i 0.529662 0.305800i
879879 0 0
880880 −3.31521e10 + 5.74211e10i −0.0552815 + 0.0957504i
881881 7.74337e11i 1.28537i −0.766132 0.642683i 0.777821π-0.777821\pi
0.766132 0.642683i 0.222179π-0.222179\pi
882882 0 0
883883 −3.73068e11 −0.613685 −0.306842 0.951760i 0.599272π-0.599272\pi
−0.306842 + 0.951760i 0.599272π0.599272\pi
884884 2.70989e11 + 1.56455e11i 0.443754 + 0.256201i
885885 0 0
886886 −2.84922e11 4.93499e11i −0.462371 0.800850i
887887 5.41302e11 3.12521e11i 0.874471 0.504876i 0.00563925 0.999984i 0.498205π-0.498205\pi
0.868831 + 0.495108i 0.164872π0.164872\pi
888888 0 0
889889 4.59395e11 7.95696e11i 0.735495 1.27391i
890890 7.73184e11i 1.23232i
891891 0 0
892892 −6.47075e10 −0.102210
893893 3.84075e10 + 2.21746e10i 0.0603963 + 0.0348698i
894894 0 0
895895 −3.40227e11 5.89291e11i −0.530245 0.918412i
896896 5.13981e10 2.96747e10i 0.0797472 0.0460420i
897897 0 0
898898 −1.18587e11 + 2.05398e11i −0.182360 + 0.315857i
899899 1.29928e11i 0.198914i
900900 0 0
901901 5.22820e10 0.0793329
902902 −1.88794e11 1.09000e11i −0.285208 0.164665i
903903 0 0
904904 6.96649e10 + 1.20663e11i 0.104313 + 0.180676i
905905 1.38956e12 8.02262e11i 2.07149 1.19597i
906906 0 0
907907 −4.55030e11 + 7.88136e11i −0.672375 + 1.16459i 0.304854 + 0.952399i 0.401392π0.401392\pi
−0.977229 + 0.212188i 0.931941π0.931941\pi
908908 9.66022e10i 0.142116i
909909 0 0
910910 −1.38364e12 −2.01771
911911 −9.63591e10 5.56330e10i −0.139901 0.0807716i 0.428416 0.903582i 0.359072π-0.359072\pi
−0.568317 + 0.822810i 0.692405π0.692405\pi
912912 0 0
913913 −5.42802e10 9.40162e10i −0.0781194 0.135307i
914914 −4.45728e11 + 2.57341e11i −0.638683 + 0.368744i
915915 0 0
916916 3.57026e10 6.18388e10i 0.0507129 0.0878373i
917917 6.36980e11i 0.900842i
918918 0 0
919919 1.32576e12 1.85867 0.929333 0.369243i 0.120383π-0.120383\pi
0.929333 + 0.369243i 0.120383π0.120383\pi
920920 4.20856e11 + 2.42982e11i 0.587466 + 0.339174i
921921 0 0
922922 2.46202e11 + 4.26435e11i 0.340697 + 0.590105i
923923 6.49235e11 3.74836e11i 0.894530 0.516457i
924924 0 0
925925 6.39412e10 1.10749e11i 0.0873401 0.151278i
926926 4.26909e11i 0.580620i
927927 0 0
928928 −8.56652e10 −0.115508
929929 −1.11339e12 6.42815e11i −1.49480 0.863024i −0.494819 0.868996i 0.664766π-0.664766\pi
−0.999982 + 0.00597212i 0.998099π0.998099\pi
930930 0 0
931931 −3.08063e10 5.33582e10i −0.0410054 0.0710235i
932932 −3.93696e11 + 2.27301e11i −0.521792 + 0.301257i
933933 0 0
934934 1.09793e11 1.90167e11i 0.144274 0.249890i
935935 2.20730e11i 0.288812i
936936 0 0
937937 −3.48380e11 −0.451955 −0.225977 0.974133i 0.572558π-0.572558\pi
−0.225977 + 0.974133i 0.572558π0.572558\pi
938938 6.02628e11 + 3.47927e11i 0.778462 + 0.449446i
939939 0 0
940940 2.47326e10 + 4.28380e10i 0.0316780 + 0.0548679i
941941 −7.29969e11 + 4.21448e11i −0.930992 + 0.537508i −0.887125 0.461529i 0.847301π-0.847301\pi
−0.0438668 + 0.999037i 0.513968π0.513968\pi
942942 0 0
943943 −7.98895e11 + 1.38373e12i −1.01028 + 1.74986i
944944 2.61587e11i 0.329403i
945945 0 0
946946 −2.09732e11 −0.261879
947947 −1.07702e12 6.21820e11i −1.33914 0.773152i −0.352459 0.935827i 0.614655π-0.614655\pi
−0.986680 + 0.162675i 0.947988π0.947988\pi
948948 0 0
949949 1.06953e11 + 1.85248e11i 0.131865 + 0.228397i
950950 −9.80466e11 + 5.66072e11i −1.20376 + 0.694988i
951951 0 0
952952 −9.87887e10 + 1.71107e11i −0.120271 + 0.208315i
953953 2.58906e11i 0.313885i 0.987608 + 0.156942i 0.0501637π0.0501637\pi
−0.987608 + 0.156942i 0.949836π0.949836\pi
954954 0 0
955955 1.13324e12 1.36241
956956 −9.87523e10 5.70146e10i −0.118227 0.0682582i
957957 0 0
958958 7.86385e10 + 1.36206e11i 0.0933626 + 0.161709i
959959 9.23177e11 5.32996e11i 1.09147 0.630159i
960960 0 0
961961 3.86925e11 6.70175e11i 0.453663 0.785768i
962962 8.11246e10i 0.0947224i
963963 0 0
964964 4.40181e11 0.509710
965965 2.26382e12 + 1.30701e12i 2.61055 + 1.50720i
966966 0 0
967967 −5.06389e11 8.77092e11i −0.579133 1.00309i −0.995579 0.0939280i 0.970058π-0.970058\pi
0.416446 0.909161i 0.363276π-0.363276\pi
968968 −2.51575e11 + 1.45247e11i −0.286528 + 0.165427i
969969 0 0
970970 −2.98767e11 + 5.17480e11i −0.337479 + 0.584530i
971971 6.44723e11i 0.725265i 0.931932 + 0.362632i 0.118122π0.118122\pi
−0.931932 + 0.362632i 0.881878π0.881878\pi
972972 0 0
973973 5.17253e11 0.577100
974974 −3.61745e11 2.08854e11i −0.401945 0.232063i
975975 0 0
976976 −9.10472e10 1.57698e11i −0.100338 0.173791i
977977 −1.30863e12 + 7.55535e11i −1.43627 + 0.829233i −0.997588 0.0694077i 0.977889π-0.977889\pi
−0.438685 + 0.898641i 0.644556π0.644556\pi
978978 0 0
979979 −1.16207e11 + 2.01277e11i −0.126504 + 0.219111i
980980 6.87200e10i 0.0745039i
981981 0 0
982982 7.44546e11 0.800655
983983 9.28316e11 + 5.35963e11i 0.994218 + 0.574012i 0.906532 0.422136i 0.138720π-0.138720\pi
0.0876854 + 0.996148i 0.472053π0.472053\pi
984984 0 0
985985 −8.78546e11 1.52169e12i −0.933296 1.61652i
986986 2.46976e11 1.42592e11i 0.261305 0.150865i
987987 0 0
988988 −3.59099e11 + 6.21977e11i −0.376865 + 0.652750i
989989 1.53719e12i 1.60673i
990990 0 0
991991 −8.67927e11 −0.899888 −0.449944 0.893057i 0.648556π-0.648556\pi
−0.449944 + 0.893057i 0.648556π0.648556\pi
992992 −4.51314e10 2.60567e10i −0.0466050 0.0269074i
993993 0 0
994994 2.36678e11 + 4.09938e11i 0.242445 + 0.419926i
995995 −4.96146e11 + 2.86450e11i −0.506194 + 0.292251i
996996 0 0
997997 1.19459e11 2.06909e11i 0.120903 0.209411i −0.799221 0.601037i 0.794754π-0.794754\pi
0.920124 + 0.391627i 0.128088π0.128088\pi
998998 1.09015e11i 0.109891i
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 54.9.d.a.35.4 16
3.2 odd 2 18.9.d.a.11.7 yes 16
4.3 odd 2 432.9.q.c.305.8 16
9.2 odd 6 162.9.b.c.161.1 16
9.4 even 3 18.9.d.a.5.7 16
9.5 odd 6 inner 54.9.d.a.17.4 16
9.7 even 3 162.9.b.c.161.16 16
12.11 even 2 144.9.q.b.65.3 16
36.23 even 6 432.9.q.c.17.8 16
36.31 odd 6 144.9.q.b.113.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
18.9.d.a.5.7 16 9.4 even 3
18.9.d.a.11.7 yes 16 3.2 odd 2
54.9.d.a.17.4 16 9.5 odd 6 inner
54.9.d.a.35.4 16 1.1 even 1 trivial
144.9.q.b.65.3 16 12.11 even 2
144.9.q.b.113.3 16 36.31 odd 6
162.9.b.c.161.1 16 9.2 odd 6
162.9.b.c.161.16 16 9.7 even 3
432.9.q.c.17.8 16 36.23 even 6
432.9.q.c.305.8 16 4.3 odd 2