Properties

Label 54.9.d.a.35.8
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 35.8
Root 147.3090.866025i-147.309 - 0.866025i of defining polynomial
Character χ\chi == 54.35
Dual form 54.9.d.a.17.8

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+(9.79796+5.65685i)q2+(64.0000+110.851i)q4+(719.139415.195i)q5+(1343.412326.85i)q7+1448.15iq8+9394.80q10+(21366.912336.2i)q11+(4848.778398.31i)q13+(26325.315198.9i)q14+(8192.00+14189.0i)q1642669.1iq17+101194.q19+(92049.8+53145.0i)q20+(139568.241739.i)q22+(396990.229203.i)q23+(149462.258875.i)q25109715.iq26+343913.q28+(577159.333223.i)q29+(709545.+1.22897e6i)q31+(160530.+92681.9i)q32+(241373.418071.i)q342.23111e6iq35+1.62583e6q37+(991496.+572441.i)q38+(601267.+1.04142e6i)q40+(1.99920e6+1.15424e6i)q41+(812997.1.40815e6i)q433.15806e6iq44+5.18626e6q46+(3.38272e6+1.95301e6i)q47+(727099.1.25937e6i)q49+(2.92884e61.69097e6i)q50+(620642.1.07498e6i)q526.96433e6iq532.04877e7q55+(3.36964e6+1.94547e6i)q56+(3.76999e66.52981e6i)q58+(5.94959e6+3.43500e6i)q59+(1.26576e62.19236e6i)q61+1.60552e7iq622.09715e6q64+(6.97388e64.02637e6i)q65+(1.58375e7+2.74313e7i)q67+(4.72993e62.73083e6i)q68+(1.26211e72.18603e7i)q70+1.75496e7iq712.86971e7q73+(1.59299e7+9.19711e6i)q74+(6.47643e6+1.12175e7i)q76+(5.74089e7+3.31451e7i)q77+(3.40323e7+5.89457e7i)q79+1.36051e7iq802.61174e7q82+(4.73759e72.73525e7i)q83+(1.77160e73.06851e7i)q85+(1.59314e79.19801e6i)q86+(1.78647e73.09425e7i)q88+7.04968e6iq892.60555e7q91+(5.08148e7+2.93379e7i)q92+(2.20958e7+3.82711e7i)q94+(7.27727e74.20153e7i)q95+(5.14341e78.90865e7i)q971.64524e7iq98+O(q100)q+(9.79796 + 5.65685i) q^{2} +(64.0000 + 110.851i) q^{4} +(719.139 - 415.195i) q^{5} +(1343.41 - 2326.85i) q^{7} +1448.15i q^{8} +9394.80 q^{10} +(-21366.9 - 12336.2i) q^{11} +(-4848.77 - 8398.31i) q^{13} +(26325.3 - 15198.9i) q^{14} +(-8192.00 + 14189.0i) q^{16} -42669.1i q^{17} +101194. q^{19} +(92049.8 + 53145.0i) q^{20} +(-139568. - 241739. i) q^{22} +(396990. - 229203. i) q^{23} +(149462. - 258875. i) q^{25} -109715. i q^{26} +343913. q^{28} +(-577159. - 333223. i) q^{29} +(709545. + 1.22897e6i) q^{31} +(-160530. + 92681.9i) q^{32} +(241373. - 418071. i) q^{34} -2.23111e6i q^{35} +1.62583e6 q^{37} +(991496. + 572441. i) q^{38} +(601267. + 1.04142e6i) q^{40} +(-1.99920e6 + 1.15424e6i) q^{41} +(812997. - 1.40815e6i) q^{43} -3.15806e6i q^{44} +5.18626e6 q^{46} +(3.38272e6 + 1.95301e6i) q^{47} +(-727099. - 1.25937e6i) q^{49} +(2.92884e6 - 1.69097e6i) q^{50} +(620642. - 1.07498e6i) q^{52} -6.96433e6i q^{53} -2.04877e7 q^{55} +(3.36964e6 + 1.94547e6i) q^{56} +(-3.76999e6 - 6.52981e6i) q^{58} +(-5.94959e6 + 3.43500e6i) q^{59} +(1.26576e6 - 2.19236e6i) q^{61} +1.60552e7i q^{62} -2.09715e6 q^{64} +(-6.97388e6 - 4.02637e6i) q^{65} +(1.58375e7 + 2.74313e7i) q^{67} +(4.72993e6 - 2.73083e6i) q^{68} +(1.26211e7 - 2.18603e7i) q^{70} +1.75496e7i q^{71} -2.86971e7 q^{73} +(1.59299e7 + 9.19711e6i) q^{74} +(6.47643e6 + 1.12175e7i) q^{76} +(-5.74089e7 + 3.31451e7i) q^{77} +(-3.40323e7 + 5.89457e7i) q^{79} +1.36051e7i q^{80} -2.61174e7 q^{82} +(-4.73759e7 - 2.73525e7i) q^{83} +(-1.77160e7 - 3.06851e7i) q^{85} +(1.59314e7 - 9.19801e6i) q^{86} +(1.78647e7 - 3.09425e7i) q^{88} +7.04968e6i q^{89} -2.60555e7 q^{91} +(5.08148e7 + 2.93379e7i) q^{92} +(2.20958e7 + 3.82711e7i) q^{94} +(7.27727e7 - 4.20153e7i) q^{95} +(5.14341e7 - 8.90865e7i) q^{97} -1.64524e7i 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
55 719.139 415.195i 1.15062 0.664312i 0.201584 0.979471i 0.435391π-0.435391\pi
0.949039 + 0.315159i 0.102058π0.102058\pi
66 0 0
77 1343.41 2326.85i 0.559521 0.969119i −0.438015 0.898967i 0.644318π-0.644318\pi
0.997536 0.0701513i 0.0223482π-0.0223482\pi
88 1448.15i 0.353553i
99 0 0
1010 9394.80 0.939480
1111 −21366.9 12336.2i −1.45939 0.842577i −0.460405 0.887709i 0.652296π-0.652296\pi
−0.998981 + 0.0451321i 0.985629π0.985629\pi
1212 0 0
1313 −4848.77 8398.31i −0.169769 0.294048i 0.768570 0.639766i 0.220969π-0.220969\pi
−0.938339 + 0.345718i 0.887635π0.887635\pi
1414 26325.3 15198.9i 0.685270 0.395641i
1515 0 0
1616 −8192.00 + 14189.0i −0.125000 + 0.216506i
1717 42669.1i 0.510879i −0.966825 0.255440i 0.917780π-0.917780\pi
0.966825 0.255440i 0.0822202π-0.0822202\pi
1818 0 0
1919 101194. 0.776499 0.388250 0.921554i 0.373080π-0.373080\pi
0.388250 + 0.921554i 0.373080π0.373080\pi
2020 92049.8 + 53145.0i 0.575311 + 0.332156i
2121 0 0
2222 −139568. 241739.i −0.595792 1.03194i
2323 396990. 229203.i 1.41863 0.819046i 0.422450 0.906386i 0.361170π-0.361170\pi
0.996179 + 0.0873406i 0.0278369π0.0278369\pi
2424 0 0
2525 149462. 258875.i 0.382622 0.662721i
2626 109715.i 0.240089i
2727 0 0
2828 343913. 0.559521
2929 −577159. 333223.i −0.816025 0.471132i 0.0330188 0.999455i 0.489488π-0.489488\pi
−0.849044 + 0.528322i 0.822821π0.822821\pi
3030 0 0
3131 709545. + 1.22897e6i 0.768305 + 1.33074i 0.938482 + 0.345329i 0.112233π0.112233\pi
−0.170177 + 0.985413i 0.554434π0.554434\pi
3232 −160530. + 92681.9i −0.153093 + 0.0883883i
3333 0 0
3434 241373. 418071.i 0.180623 0.312848i
3535 2.23111e6i 1.48679i
3636 0 0
3737 1.62583e6 0.867500 0.433750 0.901033i 0.357190π-0.357190\pi
0.433750 + 0.901033i 0.357190π0.357190\pi
3838 991496. + 572441.i 0.475507 + 0.274534i
3939 0 0
4040 601267. + 1.04142e6i 0.234870 + 0.406807i
4141 −1.99920e6 + 1.15424e6i −0.707491 + 0.408470i −0.810131 0.586249i 0.800604π-0.800604\pi
0.102641 + 0.994719i 0.467271π0.467271\pi
4242 0 0
4343 812997. 1.40815e6i 0.237802 0.411885i −0.722281 0.691599i 0.756906π-0.756906\pi
0.960083 + 0.279714i 0.0902398π0.0902398\pi
4444 3.15806e6i 0.842577i
4545 0 0
4646 5.18626e6 1.15831
4747 3.38272e6 + 1.95301e6i 0.693226 + 0.400234i 0.804819 0.593520i 0.202262π-0.202262\pi
−0.111594 + 0.993754i 0.535595π0.535595\pi
4848 0 0
4949 −727099. 1.25937e6i −0.126127 0.218459i
5050 2.92884e6 1.69097e6i 0.468614 0.270555i
5151 0 0
5252 620642. 1.07498e6i 0.0848844 0.147024i
5353 6.96433e6i 0.882624i −0.897354 0.441312i 0.854513π-0.854513\pi
0.897354 0.441312i 0.145487π-0.145487\pi
5454 0 0
5555 −2.04877e7 −2.23894
5656 3.36964e6 + 1.94547e6i 0.342635 + 0.197821i
5757 0 0
5858 −3.76999e6 6.52981e6i −0.333141 0.577017i
5959 −5.94959e6 + 3.43500e6i −0.490997 + 0.283477i −0.724988 0.688761i 0.758155π-0.758155\pi
0.233991 + 0.972239i 0.424821π0.424821\pi
6060 0 0
6161 1.26576e6 2.19236e6i 0.0914182 0.158341i −0.816690 0.577077i 0.804193π-0.804193\pi
0.908108 + 0.418736i 0.137527π0.137527\pi
6262 1.60552e7i 1.08655i
6363 0 0
6464 −2.09715e6 −0.125000
6565 −6.97388e6 4.02637e6i −0.390680 0.225559i
6666 0 0
6767 1.58375e7 + 2.74313e7i 0.785936 + 1.36128i 0.928439 + 0.371486i 0.121152π0.121152\pi
−0.142503 + 0.989794i 0.545515π0.545515\pi
6868 4.72993e6 2.73083e6i 0.221217 0.127720i
6969 0 0
7070 1.26211e7 2.18603e7i 0.525659 0.910467i
7171 1.75496e7i 0.690612i 0.938490 + 0.345306i 0.112225π0.112225\pi
−0.938490 + 0.345306i 0.887775π0.887775\pi
7272 0 0
7373 −2.86971e7 −1.01052 −0.505261 0.862966i 0.668604π-0.668604\pi
−0.505261 + 0.862966i 0.668604π0.668604\pi
7474 1.59299e7 + 9.19711e6i 0.531233 + 0.306707i
7575 0 0
7676 6.47643e6 + 1.12175e7i 0.194125 + 0.336234i
7777 −5.74089e7 + 3.31451e7i −1.63311 + 0.942879i
7878 0 0
7979 −3.40323e7 + 5.89457e7i −0.873741 + 1.51336i −0.0156441 + 0.999878i 0.504980π0.504980\pi
−0.858097 + 0.513487i 0.828353π0.828353\pi
8080 1.36051e7i 0.332156i
8181 0 0
8282 −2.61174e7 −0.577664
8383 −4.73759e7 2.73525e7i −0.998263 0.576347i −0.0905288 0.995894i 0.528856π-0.528856\pi
−0.907734 + 0.419547i 0.862189π0.862189\pi
8484 0 0
8585 −1.77160e7 3.06851e7i −0.339383 0.587829i
8686 1.59314e7 9.19801e6i 0.291247 0.168151i
8787 0 0
8888 1.78647e7 3.09425e7i 0.297896 0.515971i
8989 7.04968e6i 0.112359i 0.998421 + 0.0561797i 0.0178920π0.0178920\pi
−0.998421 + 0.0561797i 0.982108π0.982108\pi
9090 0 0
9191 −2.60555e7 −0.379957
9292 5.08148e7 + 2.93379e7i 0.709314 + 0.409523i
9393 0 0
9494 2.20958e7 + 3.82711e7i 0.283008 + 0.490185i
9595 7.27727e7 4.20153e7i 0.893458 0.515838i
9696 0 0
9797 5.14341e7 8.90865e7i 0.580984 1.00629i −0.414379 0.910104i 0.636001π-0.636001\pi
0.995363 0.0961894i 0.0306655π-0.0306655\pi
9898 1.64524e7i 0.178371i
9999 0 0
100100 3.82622e7 0.382622
101101 8.11338e7 + 4.68426e7i 0.779680 + 0.450148i 0.836317 0.548246i 0.184704π-0.184704\pi
−0.0566370 + 0.998395i 0.518038π0.518038\pi
102102 0 0
103103 4.68590e7 + 8.11622e7i 0.416336 + 0.721116i 0.995568 0.0940475i 0.0299806π-0.0299806\pi
−0.579231 + 0.815163i 0.696647π0.696647\pi
104104 1.21621e7 7.02177e6i 0.103962 0.0600224i
105105 0 0
106106 3.93962e7 6.82362e7i 0.312055 0.540495i
107107 1.34556e8i 1.02652i −0.858232 0.513262i 0.828437π-0.828437\pi
0.858232 0.513262i 0.171563π-0.171563\pi
108108 0 0
109109 −5.31868e7 −0.376788 −0.188394 0.982093i 0.560328π-0.560328\pi
−0.188394 + 0.982093i 0.560328π0.560328\pi
110110 −2.00737e8 1.15896e8i −1.37106 0.791584i
111111 0 0
112112 2.20104e7 + 3.81232e7i 0.139880 + 0.242280i
113113 1.14368e8 6.60307e7i 0.701443 0.404978i −0.106442 0.994319i 0.533946π-0.533946\pi
0.807885 + 0.589341i 0.200612π0.200612\pi
114114 0 0
115115 1.90328e8 3.29657e8i 1.08820 1.88483i
116116 8.53051e7i 0.471132i
117117 0 0
118118 −7.77251e7 −0.400897
119119 −9.92849e7 5.73222e7i −0.495103 0.285848i
120120 0 0
121121 1.97183e8 + 3.41530e8i 0.919872 + 1.59326i
122122 2.48038e7 1.43205e7i 0.111964 0.0646424i
123123 0 0
124124 −9.08218e7 + 1.57308e8i −0.384152 + 0.665371i
125125 7.61481e7i 0.311903i
126126 0 0
127127 5.72307e7 0.219996 0.109998 0.993932i 0.464916π-0.464916\pi
0.109998 + 0.993932i 0.464916π0.464916\pi
128128 −2.05478e7 1.18633e7i −0.0765466 0.0441942i
129129 0 0
130130 −4.55532e7 7.89004e7i −0.159494 0.276252i
131131 9.79607e7 5.65576e7i 0.332634 0.192046i −0.324376 0.945928i 0.605154π-0.605154\pi
0.657010 + 0.753882i 0.271821π0.271821\pi
132132 0 0
133133 1.35945e8 2.35464e8i 0.434468 0.752520i
134134 3.58361e8i 1.11148i
135135 0 0
136136 6.17915e7 0.180623
137137 1.19042e8 + 6.87289e7i 0.337923 + 0.195100i 0.659353 0.751833i 0.270830π-0.270830\pi
−0.321430 + 0.946933i 0.604164π0.604164\pi
138138 0 0
139139 −9.70841e7 1.68155e8i −0.260069 0.450453i 0.706191 0.708022i 0.250412π-0.250412\pi
−0.966260 + 0.257568i 0.917079π0.917079\pi
140140 2.47321e8 1.42791e8i 0.643798 0.371697i
141141 0 0
142142 −9.92757e7 + 1.71950e8i −0.244168 + 0.422912i
143143 2.39261e8i 0.572173i
144144 0 0
145145 −5.53410e8 −1.25192
146146 −2.81173e8 1.62335e8i −0.618816 0.357274i
147147 0 0
148148 1.04053e8 + 1.80226e8i 0.216875 + 0.375638i
149149 −6.70921e8 + 3.87357e8i −1.36121 + 0.785897i −0.989786 0.142564i 0.954465π-0.954465\pi
−0.371429 + 0.928461i 0.621132π0.621132\pi
150150 0 0
151151 −3.48071e8 + 6.02877e8i −0.669515 + 1.15963i 0.308525 + 0.951216i 0.400165π0.400165\pi
−0.978040 + 0.208418i 0.933169π0.933169\pi
152152 1.46545e8i 0.274534i
153153 0 0
154154 −7.49987e8 −1.33343
155155 1.02052e9 + 5.89200e8i 1.76806 + 1.02079i
156156 0 0
157157 −4.99364e6 8.64924e6i −0.00821900 0.0142357i 0.861887 0.507101i 0.169283π-0.169283\pi
−0.870106 + 0.492865i 0.835950π0.835950\pi
158158 −6.66894e8 + 3.85032e8i −1.07011 + 0.617829i
159159 0 0
160160 −7.69622e7 + 1.33302e8i −0.117435 + 0.203403i
161161 1.23165e9i 1.83309i
162162 0 0
163163 1.22877e9 1.74068 0.870340 0.492451i 0.163899π-0.163899\pi
0.870340 + 0.492451i 0.163899π0.163899\pi
164164 −2.55898e8 1.47743e8i −0.353745 0.204235i
165165 0 0
166166 −3.09458e8 5.35997e8i −0.407539 0.705878i
167167 −7.41092e8 + 4.27870e8i −0.952809 + 0.550105i −0.893953 0.448162i 0.852079π-0.852079\pi
−0.0588569 + 0.998266i 0.518746π0.518746\pi
168168 0 0
169169 3.60844e8 6.25001e8i 0.442357 0.766185i
170170 4.00868e8i 0.479961i
171171 0 0
172172 2.08127e8 0.237802
173173 3.96513e8 + 2.28927e8i 0.442663 + 0.255572i 0.704727 0.709479i 0.251070π-0.251070\pi
−0.262064 + 0.965051i 0.584403π0.584403\pi
174174 0 0
175175 −4.01577e8 6.95551e8i −0.428170 0.741612i
176176 3.50075e8 2.02116e8i 0.364846 0.210644i
177177 0 0
178178 −3.98790e7 + 6.90725e7i −0.0397250 + 0.0688058i
179179 1.46762e9i 1.42956i 0.699350 + 0.714779i 0.253473π0.253473\pi
−0.699350 + 0.714779i 0.746527π0.746527\pi
180180 0 0
181181 −1.59274e9 −1.48399 −0.741993 0.670408i 0.766119π-0.766119\pi
−0.741993 + 0.670408i 0.766119π0.766119\pi
182182 −2.55291e8 1.47392e8i −0.232675 0.134335i
183183 0 0
184184 3.31921e8 + 5.74904e8i 0.289576 + 0.501561i
185185 1.16920e9 6.75039e8i 0.998165 0.576291i
186186 0 0
187187 −5.26374e8 + 9.11706e8i −0.430455 + 0.745570i
188188 4.99972e8i 0.400234i
189189 0 0
190190 9.50699e8 0.729505
191191 1.60894e8 + 9.28923e7i 0.120895 + 0.0697985i 0.559228 0.829014i 0.311098π-0.311098\pi
−0.438333 + 0.898813i 0.644431π0.644431\pi
192192 0 0
193193 −5.85324e8 1.01381e9i −0.421859 0.730681i 0.574262 0.818671i 0.305289π-0.305289\pi
−0.996121 + 0.0879903i 0.971956π0.971956\pi
194194 1.00790e9 5.81910e8i 0.711557 0.410818i
195195 0 0
196196 9.30687e7 1.61200e8i 0.0630637 0.109230i
197197 1.90415e9i 1.26426i −0.774864 0.632128i 0.782182π-0.782182\pi
0.774864 0.632128i 0.217818π-0.217818\pi
198198 0 0
199199 1.59363e9 1.01619 0.508096 0.861300i 0.330349π-0.330349\pi
0.508096 + 0.861300i 0.330349π0.330349\pi
200200 3.74891e8 + 2.16444e8i 0.234307 + 0.135277i
201201 0 0
202202 5.29964e8 + 9.17924e8i 0.318303 + 0.551317i
203203 −1.55072e9 + 8.95310e8i −0.913166 + 0.527217i
204204 0 0
205205 −9.58469e8 + 1.66012e9i −0.542703 + 0.939990i
206206 1.06030e9i 0.588788i
207207 0 0
208208 1.58884e8 0.0848844
209209 −2.16220e9 1.24835e9i −1.13321 0.654260i
210210 0 0
211211 4.36444e8 + 7.55944e8i 0.220191 + 0.381382i 0.954866 0.297038i 0.0959987π-0.0959987\pi
−0.734675 + 0.678419i 0.762665π0.762665\pi
212212 7.72004e8 4.45717e8i 0.382187 0.220656i
213213 0 0
214214 7.61166e8 1.31838e9i 0.362931 0.628615i
215215 1.35021e9i 0.631899i
216216 0 0
217217 3.81284e9 1.71953
218218 −5.21122e8 3.00870e8i −0.230735 0.133215i
219219 0 0
220220 −1.31121e9 2.27108e9i −0.559734 0.969488i
221221 −3.58349e8 + 2.06893e8i −0.150223 + 0.0867314i
222222 0 0
223223 1.69943e8 2.94349e8i 0.0687199 0.119026i −0.829618 0.558331i 0.811442π-0.811442\pi
0.898338 + 0.439305i 0.144775π0.144775\pi
224224 4.98039e8i 0.197821i
225225 0 0
226226 1.49410e9 0.572726
227227 7.86249e8 + 4.53941e8i 0.296113 + 0.170961i 0.640695 0.767795i 0.278646π-0.278646\pi
−0.344583 + 0.938756i 0.611980π0.611980\pi
228228 0 0
229229 1.91967e7 + 3.32497e7i 0.00698047 + 0.0120905i 0.869495 0.493943i 0.164445π-0.164445\pi
−0.862514 + 0.506033i 0.831111π0.831111\pi
230230 3.72964e9 2.15331e9i 1.33277 0.769477i
231231 0 0
232232 4.82558e8 8.35816e8i 0.166570 0.288508i
233233 3.39626e9i 1.15233i −0.817334 0.576165i 0.804549π-0.804549\pi
0.817334 0.576165i 0.195451π-0.195451\pi
234234 0 0
235235 3.24353e9 1.06352
236236 −7.61547e8 4.39680e8i −0.245499 0.141739i
237237 0 0
238238 −6.48526e8 1.12328e9i −0.202125 0.350090i
239239 2.60050e8 1.50140e8i 0.0797012 0.0460155i −0.459620 0.888116i 0.652014π-0.652014\pi
0.539321 + 0.842100i 0.318681π0.318681\pi
240240 0 0
241241 −2.67282e9 + 4.62946e9i −0.792321 + 1.37234i 0.132205 + 0.991222i 0.457794π0.457794\pi
−0.924526 + 0.381119i 0.875539π0.875539\pi
242242 4.46173e9i 1.30089i
243243 0 0
244244 3.24035e8 0.0914182
245245 −1.04577e9 6.03776e8i −0.290250 0.167576i
246246 0 0
247247 −4.90667e8 8.49860e8i −0.131825 0.228328i
248248 −1.77974e9 + 1.02753e9i −0.470489 + 0.271637i
249249 0 0
250250 −4.30759e8 + 7.46096e8i −0.110274 + 0.191001i
251251 2.15800e8i 0.0543696i 0.999630 + 0.0271848i 0.00865425π0.00865425\pi
−0.999630 + 0.0271848i 0.991346π0.991346\pi
252252 0 0
253253 −1.13099e10 −2.76044
254254 5.60744e8 + 3.23746e8i 0.134719 + 0.0777802i
255255 0 0
256256 −1.34218e8 2.32472e8i −0.0312500 0.0541266i
257257 −1.30255e9 + 7.52028e8i −0.298581 + 0.172386i −0.641805 0.766868i 0.721814π-0.721814\pi
0.343224 + 0.939254i 0.388481π0.388481\pi
258258 0 0
259259 2.18416e9 3.78308e9i 0.485384 0.840710i
260260 1.03075e9i 0.225559i
261261 0 0
262262 1.27975e9 0.271595
263263 4.86114e9 + 2.80658e9i 1.01605 + 0.586616i 0.912957 0.408055i 0.133793π-0.133793\pi
0.103092 + 0.994672i 0.467126π0.467126\pi
264264 0 0
265265 −2.89156e9 5.00832e9i −0.586338 1.01557i
266266 2.66397e9 1.53804e9i 0.532112 0.307215i
267267 0 0
268268 −2.02720e9 + 3.51121e9i −0.392968 + 0.680640i
269269 5.36842e9i 1.02527i 0.858607 + 0.512634i 0.171330π0.171330\pi
−0.858607 + 0.512634i 0.828670π0.828670\pi
270270 0 0
271271 −3.34972e9 −0.621056 −0.310528 0.950564i 0.600506π-0.600506\pi
−0.310528 + 0.950564i 0.600506π0.600506\pi
272272 6.05431e8 + 3.49546e8i 0.110609 + 0.0638599i
273273 0 0
274274 7.77578e8 + 1.34681e9i 0.137956 + 0.238948i
275275 −6.38706e9 + 3.68757e9i −1.11679 + 0.644777i
276276 0 0
277277 4.05893e8 7.03028e8i 0.0689434 0.119413i −0.829493 0.558517i 0.811371π-0.811371\pi
0.898436 + 0.439104i 0.144704π0.144704\pi
278278 2.19676e9i 0.367793i
279279 0 0
280280 3.23099e9 0.525659
281281 9.24159e8 + 5.33564e8i 0.148225 + 0.0855778i 0.572278 0.820060i 0.306060π-0.306060\pi
−0.424053 + 0.905637i 0.639393π0.639393\pi
282282 0 0
283283 4.18292e9 + 7.24503e9i 0.652130 + 1.12952i 0.982605 + 0.185707i 0.0594577π0.0594577\pi
−0.330475 + 0.943815i 0.607209π0.607209\pi
284284 −1.94540e9 + 1.12318e9i −0.299044 + 0.172653i
285285 0 0
286286 −1.35346e9 + 2.34427e9i −0.202294 + 0.350383i
287287 6.20246e9i 0.914190i
288288 0 0
289289 5.15510e9 0.739002
290290 −5.42229e9 3.13056e9i −0.766639 0.442619i
291291 0 0
292292 −1.83661e9 3.18111e9i −0.252631 0.437569i
293293 1.17267e9 6.77039e8i 0.159112 0.0918636i −0.418330 0.908295i 0.637384π-0.637384\pi
0.577442 + 0.816432i 0.304051π0.304051\pi
294294 0 0
295295 −2.85239e9 + 4.94048e9i −0.376635 + 0.652351i
296296 2.35446e9i 0.306707i
297297 0 0
298298 −8.76488e9 −1.11143
299299 −3.84983e9 2.22270e9i −0.481678 0.278097i
300300 0 0
301301 −2.18438e9 3.78345e9i −0.266110 0.460916i
302302 −6.82078e9 + 3.93798e9i −0.819985 + 0.473419i
303303 0 0
304304 −8.28983e8 + 1.43584e9i −0.0970624 + 0.168117i
305305 2.10215e9i 0.242921i
306306 0 0
307307 3.34624e9 0.376707 0.188354 0.982101i 0.439685π-0.439685\pi
0.188354 + 0.982101i 0.439685π0.439685\pi
308308 −7.34834e9 4.24257e9i −0.816557 0.471439i
309309 0 0
310310 6.66603e9 + 1.15459e10i 0.721806 + 1.25021i
311311 7.07501e9 4.08476e9i 0.756285 0.436641i −0.0716755 0.997428i 0.522835π-0.522835\pi
0.827960 + 0.560787i 0.189501π0.189501\pi
312312 0 0
313313 6.49273e9 1.12457e10i 0.676472 1.17168i −0.299564 0.954076i 0.596841π-0.596841\pi
0.976036 0.217608i 0.0698255π-0.0698255\pi
314314 1.12993e8i 0.0116234i
315315 0 0
316316 −8.71227e9 −0.873741
317317 2.27583e9 + 1.31395e9i 0.225374 + 0.130120i 0.608436 0.793603i 0.291797π-0.291797\pi
−0.383062 + 0.923723i 0.625131π0.625131\pi
318318 0 0
319319 8.22139e9 + 1.42399e10i 0.793930 + 1.37513i
320320 −1.50814e9 + 8.70728e8i −0.143828 + 0.0830391i
321321 0 0
322322 6.96727e9 1.20677e10i 0.648096 1.12254i
323323 4.31787e9i 0.396697i
324324 0 0
325325 −2.89882e9 −0.259829
326326 1.20394e10 + 6.95095e9i 1.06594 + 0.615423i
327327 0 0
328328 −1.67152e9 2.89515e9i −0.144416 0.250136i
329329 9.08876e9 5.24740e9i 0.775749 0.447879i
330330 0 0
331331 5.38121e9 9.32053e9i 0.448299 0.776477i −0.549976 0.835180i 0.685363π-0.685363\pi
0.998275 + 0.0587032i 0.0186965π0.0186965\pi
332332 7.00223e9i 0.576347i
333333 0 0
334334 −9.68158e9 −0.777966
335335 2.27787e10 + 1.31513e10i 1.80863 + 1.04421i
336336 0 0
337337 −6.49324e9 1.12466e10i −0.503433 0.871972i −0.999992 0.00396864i 0.998737π-0.998737\pi
0.496559 0.868003i 0.334597π-0.334597\pi
338338 7.07107e9 4.08249e9i 0.541775 0.312794i
339339 0 0
340340 2.26765e9 3.92769e9i 0.169692 0.293915i
341341 3.50123e10i 2.58942i
342342 0 0
343343 1.15818e10 0.836758
344344 2.03922e9 + 1.17735e9i 0.145623 + 0.0840757i
345345 0 0
346346 2.59001e9 + 4.48603e9i 0.180716 + 0.313010i
347347 −2.11272e9 + 1.21978e9i −0.145722 + 0.0841324i −0.571088 0.820889i 0.693479π-0.693479\pi
0.425366 + 0.905021i 0.360145π0.360145\pi
348348 0 0
349349 1.08992e10 1.88779e10i 0.734669 1.27248i −0.220200 0.975455i 0.570671π-0.570671\pi
0.954869 0.297029i 0.0959957π-0.0959957\pi
350350 9.08664e9i 0.605524i
351351 0 0
352352 4.57336e9 0.297896
353353 −1.22820e10 7.09100e9i −0.790987 0.456677i 0.0493227 0.998783i 0.484294π-0.484294\pi
−0.840310 + 0.542106i 0.817627π0.817627\pi
354354 0 0
355355 7.28652e9 + 1.26206e10i 0.458782 + 0.794634i
356356 −7.81466e8 + 4.51180e8i −0.0486530 + 0.0280898i
357357 0 0
358358 −8.30212e9 + 1.43797e10i −0.505425 + 0.875422i
359359 1.62366e10i 0.977499i 0.872424 + 0.488750i 0.162547π0.162547\pi
−0.872424 + 0.488750i 0.837453π0.837453\pi
360360 0 0
361361 −6.74331e9 −0.397049
362362 −1.56056e10 9.00988e9i −0.908752 0.524668i
363363 0 0
364364 −1.66755e9 2.88829e9i −0.0949892 0.164526i
365365 −2.06372e10 + 1.19149e10i −1.16273 + 0.671303i
366366 0 0
367367 4.72220e9 8.17909e9i 0.260303 0.450859i −0.706019 0.708193i 0.749511π-0.749511\pi
0.966323 + 0.257334i 0.0828440π0.0828440\pi
368368 7.51051e9i 0.409523i
369369 0 0
370370 1.52744e10 0.814998
371371 −1.62050e10 9.35595e9i −0.855367 0.493847i
372372 0 0
373373 6.87407e9 + 1.19062e10i 0.355123 + 0.615091i 0.987139 0.159864i 0.0511056π-0.0511056\pi
−0.632016 + 0.774955i 0.717772π0.717772\pi
374374 −1.03148e10 + 5.95524e9i −0.527198 + 0.304378i
375375 0 0
376376 −2.82827e9 + 4.89870e9i −0.141504 + 0.245092i
377377 6.46288e9i 0.319934i
378378 0 0
379379 −8.10058e9 −0.392608 −0.196304 0.980543i 0.562894π-0.562894\pi
−0.196304 + 0.980543i 0.562894π0.562894\pi
380380 9.31490e9 + 5.37796e9i 0.446729 + 0.257919i
381381 0 0
382382 1.05096e9 + 1.82031e9i 0.0493550 + 0.0854854i
383383 3.26313e10 1.88397e10i 1.51649 0.875544i 0.516675 0.856182i 0.327170π-0.327170\pi
0.999813 0.0193625i 0.00616365π-0.00616365\pi
384384 0 0
385385 −2.75233e10 + 4.76718e10i −1.25273 + 2.16980i
386386 1.32444e10i 0.596599i
387387 0 0
388388 1.31671e10 0.580984
389389 7.44708e9 + 4.29957e9i 0.325228 + 0.187770i 0.653720 0.756736i 0.273207π-0.273207\pi
−0.328493 + 0.944507i 0.606541π0.606541\pi
390390 0 0
391391 −9.77988e9 1.69392e10i −0.418433 0.724748i
392392 1.82377e9 1.05295e9i 0.0772369 0.0445928i
393393 0 0
394394 1.07715e10 1.86567e10i 0.446982 0.774196i
395395 5.65202e10i 2.32175i
396396 0 0
397397 −7.53858e9 −0.303478 −0.151739 0.988421i 0.548487π-0.548487\pi
−0.151739 + 0.988421i 0.548487π0.548487\pi
398398 1.56144e10 + 9.01495e9i 0.622289 + 0.359278i
399399 0 0
400400 2.44878e9 + 4.24141e9i 0.0956555 + 0.165680i
401401 2.42910e9 1.40244e9i 0.0939436 0.0542384i −0.452292 0.891870i 0.649394π-0.649394\pi
0.546236 + 0.837631i 0.316060π0.316060\pi
402402 0 0
403403 6.88084e9 1.19180e10i 0.260868 0.451837i
404404 1.19917e10i 0.450148i
405405 0 0
406406 −2.02585e10 −0.745597
407407 −3.47390e10 2.00566e10i −1.26602 0.730935i
408408 0 0
409409 4.31779e9 + 7.47864e9i 0.154301 + 0.267257i 0.932804 0.360383i 0.117354π-0.117354\pi
−0.778503 + 0.627641i 0.784021π0.784021\pi
410410 −1.87821e10 + 1.08438e10i −0.664673 + 0.383749i
411411 0 0
412412 −5.99795e9 + 1.03888e10i −0.208168 + 0.360558i
413413 1.84584e10i 0.634446i
414414 0 0
415415 −4.54265e10 −1.53150
416416 1.55674e9 + 8.98786e8i 0.0519809 + 0.0300112i
417417 0 0
418418 −1.41234e10 2.44625e10i −0.462632 0.801302i
419419 −2.20697e10 + 1.27420e10i −0.716046 + 0.413409i −0.813296 0.581851i 0.802329π-0.802329\pi
0.0972497 + 0.995260i 0.468995π0.468995\pi
420420 0 0
421421 7.22114e7 1.25074e8i 0.00229867 0.00398142i −0.864874 0.501989i 0.832602π-0.832602\pi
0.867172 + 0.498008i 0.165935π0.165935\pi
422422 9.87561e9i 0.311397i
423423 0 0
424424 1.00854e10 0.312055
425425 −1.10460e10 6.37740e9i −0.338570 0.195474i
426426 0 0
427427 −3.40087e9 5.89049e9i −0.102301 0.177190i
428428 1.49157e10 8.61161e9i 0.444498 0.256631i
429429 0 0
430430 7.63794e9 1.32293e10i 0.223410 0.386957i
431431 6.31640e9i 0.183046i −0.995803 0.0915231i 0.970826π-0.970826\pi
0.995803 0.0915231i 0.0291735π-0.0291735\pi
432432 0 0
433433 −3.96241e10 −1.12722 −0.563609 0.826042i 0.690587π-0.690587\pi
−0.563609 + 0.826042i 0.690587π0.690587\pi
434434 3.73581e10 + 2.15687e10i 1.05299 + 0.607946i
435435 0 0
436436 −3.40395e9 5.89582e9i −0.0941971 0.163154i
437437 4.01731e10 2.31940e10i 1.10156 0.635988i
438438 0 0
439439 −1.57438e10 + 2.72691e10i −0.423889 + 0.734196i −0.996316 0.0857589i 0.972669π-0.972669\pi
0.572427 + 0.819955i 0.306002π0.306002\pi
440440 2.96693e10i 0.791584i
441441 0 0
442442 −4.68145e9 −0.122657
443443 −3.86111e10 2.22921e10i −1.00253 0.578810i −0.0935330 0.995616i 0.529816π-0.529816\pi
−0.908995 + 0.416806i 0.863149π0.863149\pi
444444 0 0
445445 2.92699e9 + 5.06970e9i 0.0746417 + 0.129283i
446446 3.33018e9 1.92268e9i 0.0841644 0.0485923i
447447 0 0
448448 −2.81733e9 + 4.87977e9i −0.0699401 + 0.121140i
449449 2.35548e10i 0.579553i 0.957094 + 0.289777i 0.0935810π0.0935810\pi
−0.957094 + 0.289777i 0.906419π0.906419\pi
450450 0 0
451451 5.69555e10 1.37667
452452 1.46392e10 + 8.45192e9i 0.350722 + 0.202489i
453453 0 0
454454 5.13576e9 + 8.89540e9i 0.120887 + 0.209383i
455455 −1.87376e10 + 1.08181e10i −0.437187 + 0.252410i
456456 0 0
457457 −2.05058e10 + 3.55170e10i −0.470122 + 0.814276i −0.999416 0.0341626i 0.989124π-0.989124\pi
0.529294 + 0.848439i 0.322457π0.322457\pi
458458 4.34372e8i 0.00987188i
459459 0 0
460460 4.87239e10 1.08820
461461 3.37174e9 + 1.94668e9i 0.0746536 + 0.0431013i 0.536862 0.843670i 0.319610π-0.319610\pi
−0.462209 + 0.886771i 0.652943π0.652943\pi
462462 0 0
463463 −2.67932e10 4.64073e10i −0.583044 1.00986i −0.995116 0.0987107i 0.968528π-0.968528\pi
0.412072 0.911151i 0.364805π-0.364805\pi
464464 9.45617e9 5.45952e9i 0.204006 0.117783i
465465 0 0
466466 1.92121e10 3.32764e10i 0.407410 0.705655i
467467 4.53162e10i 0.952766i −0.879238 0.476383i 0.841948π-0.841948\pi
0.879238 0.476383i 0.158052π-0.158052\pi
468468 0 0
469469 8.51049e10 1.75899
470470 3.17800e10 + 1.83482e10i 0.651272 + 0.376012i
471471 0 0
472472 −4.97441e9 8.61593e9i −0.100224 0.173594i
473473 −3.47424e10 + 2.00585e10i −0.694089 + 0.400733i
474474 0 0
475475 1.51247e10 2.61967e10i 0.297106 0.514602i
476476 1.46745e10i 0.285848i
477477 0 0
478478 3.39728e9 0.0650758
479479 −4.92416e9 2.84297e9i −0.0935385 0.0540045i 0.452501 0.891764i 0.350532π-0.350532\pi
−0.546040 + 0.837759i 0.683865π0.683865\pi
480480 0 0
481481 −7.88329e9 1.36543e10i −0.147274 0.255087i
482482 −5.23763e10 + 3.02395e10i −0.970392 + 0.560256i
483483 0 0
484484 −2.52394e10 + 4.37159e10i −0.459936 + 0.796632i
485485 8.54208e10i 1.54382i
486486 0 0
487487 3.64760e10 0.648472 0.324236 0.945976i 0.394893π-0.394893\pi
0.324236 + 0.945976i 0.394893π0.394893\pi
488488 3.17488e9 + 1.83302e9i 0.0559820 + 0.0323212i
489489 0 0
490490 −6.83095e9 1.18316e10i −0.118494 0.205238i
491491 5.07409e10 2.92952e10i 0.873035 0.504047i 0.00467962 0.999989i 0.498510π-0.498510\pi
0.868356 + 0.495942i 0.165177π0.165177\pi
492492 0 0
493493 −1.42183e10 + 2.46269e10i −0.240692 + 0.416890i
494494 1.11025e10i 0.186429i
495495 0 0
496496 −2.32504e10 −0.384152
497497 4.08354e10 + 2.35763e10i 0.669285 + 0.386412i
498498 0 0
499499 3.18425e10 + 5.51528e10i 0.513576 + 0.889541i 0.999876 + 0.0157483i 0.00501306π0.00501306\pi
−0.486300 + 0.873792i 0.661654π0.661654\pi
500500 −8.44112e9 + 4.87348e9i −0.135058 + 0.0779757i
501501 0 0
502502 −1.22075e9 + 2.11440e9i −0.0192225 + 0.0332944i
503503 1.09134e10i 0.170486i −0.996360 0.0852430i 0.972833π-0.972833\pi
0.996360 0.0852430i 0.0271667π-0.0271667\pi
504504 0 0
505505 7.77953e10 1.19616
506506 −1.10814e11 6.39786e10i −1.69041 0.975961i
507507 0 0
508508 3.66277e9 + 6.34410e9i 0.0549989 + 0.0952609i
509509 9.71431e9 5.60856e9i 0.144724 0.0835565i −0.425889 0.904775i 0.640039π-0.640039\pi
0.570614 + 0.821219i 0.306705π0.306705\pi
510510 0 0
511511 −3.85519e10 + 6.67739e10i −0.565409 + 0.979316i
512512 3.03700e9i 0.0441942i
513513 0 0
514514 −1.70165e10 −0.243790
515515 6.73963e10 + 3.89113e10i 0.958092 + 0.553155i
516516 0 0
517517 −4.81854e10 8.34596e10i −0.674456 1.16819i
518518 4.28006e10 2.47110e10i 0.594472 0.343218i
519519 0 0
520520 5.83081e9 1.00993e10i 0.0797472 0.138126i
521521 1.03375e11i 1.40302i 0.712658 + 0.701511i 0.247491π0.247491\pi
−0.712658 + 0.701511i 0.752509π0.752509\pi
522522 0 0
523523 −6.50405e10 −0.869314 −0.434657 0.900596i 0.643130π-0.643130\pi
−0.434657 + 0.900596i 0.643130π0.643130\pi
524524 1.25390e10 + 7.23938e9i 0.166317 + 0.0960232i
525525 0 0
526526 3.17528e10 + 5.49975e10i 0.414800 + 0.718456i
527527 5.24390e10 3.02757e10i 0.679849 0.392511i
528528 0 0
529529 6.59121e10 1.14163e11i 0.841671 1.45782i
530530 6.54284e10i 0.829207i
531531 0 0
532532 3.48020e10 0.434468
533533 1.93873e10 + 1.11933e10i 0.240220 + 0.138691i
534534 0 0
535535 −5.58672e10 9.67648e10i −0.681933 1.18114i
536536 −3.97248e10 + 2.29351e10i −0.481285 + 0.277870i
537537 0 0
538538 −3.03684e10 + 5.25995e10i −0.362487 + 0.627845i
539539 3.58785e10i 0.425088i
540540 0 0
541541 9.26356e10 1.08141 0.540703 0.841214i 0.318158π-0.318158\pi
0.540703 + 0.841214i 0.318158π0.318158\pi
542542 −3.28204e10 1.89489e10i −0.380318 0.219577i
543543 0 0
544544 3.95466e9 + 6.84967e9i 0.0451558 + 0.0782121i
545545 −3.82487e10 + 2.20829e10i −0.433541 + 0.250305i
546546 0 0
547547 −6.17442e9 + 1.06944e10i −0.0689679 + 0.119456i −0.898447 0.439081i 0.855304π-0.855304\pi
0.829479 + 0.558537i 0.188637π0.188637\pi
548548 1.75946e10i 0.195100i
549549 0 0
550550 −8.34402e10 −0.911852
551551 −5.84051e10 3.37202e10i −0.633643 0.365834i
552552 0 0
553553 9.14387e10 + 1.58376e11i 0.977753 + 1.69352i
554554 7.95385e9 4.59216e9i 0.0844381 0.0487503i
555555 0 0
556556 1.24268e10 2.15238e10i 0.130035 0.225227i
557557 1.17871e9i 0.0122458i 0.999981 + 0.00612290i 0.00194899π0.00194899\pi
−0.999981 + 0.00612290i 0.998051π0.998051\pi
558558 0 0
559559 −1.57681e10 −0.161485
560560 3.16571e10 + 1.82772e10i 0.321899 + 0.185848i
561561 0 0
562562 6.03658e9 + 1.04557e10i 0.0605126 + 0.104811i
563563 4.60975e10 2.66144e10i 0.458822 0.264901i −0.252727 0.967538i 0.581327π-0.581327\pi
0.711549 + 0.702637i 0.247994π0.247994\pi
564564 0 0
565565 5.48312e10 9.49705e10i 0.538064 0.931955i
566566 9.46487e10i 0.922251i
567567 0 0
568568 −2.54146e10 −0.244168
569569 7.89230e9 + 4.55662e9i 0.0752930 + 0.0434704i 0.537174 0.843472i 0.319492π-0.319492\pi
−0.461881 + 0.886942i 0.652825π0.652825\pi
570570 0 0
571571 −8.93207e10 1.54708e11i −0.840248 1.45535i −0.889685 0.456575i 0.849076π-0.849076\pi
0.0494367 0.998777i 0.484257π-0.484257\pi
572572 −2.65224e10 + 1.53127e10i −0.247758 + 0.143043i
573573 0 0
574574 −3.50864e10 + 6.07715e10i −0.323215 + 0.559825i
575575 1.37028e11i 1.25354i
576576 0 0
577577 −1.57035e11 −1.41675 −0.708374 0.705837i 0.750571π-0.750571\pi
−0.708374 + 0.705837i 0.750571π0.750571\pi
578578 5.05095e10 + 2.91617e10i 0.452545 + 0.261277i
579579 0 0
580580 −3.54183e10 6.13462e10i −0.312979 0.542096i
581581 −1.27290e11 + 7.34911e10i −1.11710 + 0.644957i
582582 0 0
583583 −8.59131e10 + 1.48806e11i −0.743679 + 1.28809i
584584 4.15578e10i 0.357274i
585585 0 0
586586 1.53197e10 0.129915
587587 −7.02172e10 4.05399e10i −0.591413 0.341452i 0.174243 0.984703i 0.444252π-0.444252\pi
−0.765656 + 0.643250i 0.777586π0.777586\pi
588588 0 0
589589 7.18018e10 + 1.24364e11i 0.596588 + 1.03332i
590590 −5.58952e10 + 3.22711e10i −0.461282 + 0.266321i
591591 0 0
592592 −1.33188e10 + 2.30689e10i −0.108437 + 0.187819i
593593 2.32095e11i 1.87693i 0.345379 + 0.938463i 0.387750π0.387750\pi
−0.345379 + 0.938463i 0.612250π0.612250\pi
594594 0 0
595595 −9.51995e10 −0.759569
596596 −8.58779e10 4.95816e10i −0.680607 0.392949i
597597 0 0
598598 −2.51470e10 4.35558e10i −0.196644 0.340598i
599599 6.67859e9 3.85589e9i 0.0518773 0.0299514i −0.473837 0.880613i 0.657131π-0.657131\pi
0.525714 + 0.850661i 0.323798π0.323798\pi
600600 0 0
601601 8.64971e10 1.49817e11i 0.662985 1.14832i −0.316842 0.948478i 0.602623π-0.602623\pi
0.979827 0.199846i 0.0640441π-0.0640441\pi
602602 4.94268e10i 0.376337i
603603 0 0
604604 −8.91062e10 −0.669515
605605 2.83604e11 + 1.63739e11i 2.11685 + 1.22216i
606606 0 0
607607 6.33224e10 + 1.09678e11i 0.466448 + 0.807911i 0.999266 0.0383189i 0.0122003π-0.0122003\pi
−0.532818 + 0.846230i 0.678867π0.678867\pi
608608 −1.62447e10 + 9.37887e9i −0.118877 + 0.0686335i
609609 0 0
610610 1.18916e10 2.05968e10i 0.0858855 0.148758i
611611 3.78789e10i 0.271789i
612612 0 0
613613 −1.90947e11 −1.35230 −0.676148 0.736765i 0.736352π-0.736352\pi
−0.676148 + 0.736765i 0.736352π0.736352\pi
614614 3.27863e10 + 1.89292e10i 0.230685 + 0.133186i
615615 0 0
616616 −4.79992e10 8.31370e10i −0.333358 0.577393i
617617 −3.94255e10 + 2.27623e10i −0.272043 + 0.157064i −0.629816 0.776745i 0.716870π-0.716870\pi
0.357773 + 0.933809i 0.383536π0.383536\pi
618618 0 0
619619 2.52527e10 4.37390e10i 0.172007 0.297925i −0.767114 0.641510i 0.778308π-0.778308\pi
0.939121 + 0.343585i 0.111642π0.111642\pi
620620 1.50835e11i 1.02079i
621621 0 0
622622 9.24275e10 0.617504
623623 1.64036e10 + 9.47061e9i 0.108890 + 0.0628674i
624624 0 0
625625 8.99998e10 + 1.55884e11i 0.589823 + 1.02160i
626626 1.27231e11 7.34569e10i 0.828506 0.478338i
627627 0 0
628628 6.39186e8 1.10710e9i 0.00410950 0.00711786i
629629 6.93730e10i 0.443188i
630630 0 0
631631 7.46120e10 0.470642 0.235321 0.971918i 0.424386π-0.424386\pi
0.235321 + 0.971918i 0.424386π0.424386\pi
632632 −8.53625e10 4.92840e10i −0.535055 0.308914i
633633 0 0
634634 1.48657e10 + 2.57481e10i 0.0920085 + 0.159363i
635635 4.11568e10 2.37619e10i 0.253132 0.146146i
636636 0 0
637637 −7.05107e9 + 1.22128e10i −0.0428250 + 0.0741751i
638638 1.86029e11i 1.12279i
639639 0 0
640640 −1.97023e10 −0.117435
641641 −2.44739e11 1.41300e11i −1.44968 0.836972i −0.451215 0.892415i 0.649009π-0.649009\pi
−0.998462 + 0.0554435i 0.982343π0.982343\pi
642642 0 0
643643 8.57408e10 + 1.48507e11i 0.501584 + 0.868769i 0.999998 + 0.00183012i 0.000582545π0.000582545\pi
−0.498414 + 0.866939i 0.666084π0.666084\pi
644644 1.36530e11 7.88257e10i 0.793752 0.458273i
645645 0 0
646646 2.44256e10 4.23063e10i 0.140254 0.242927i
647647 6.51359e10i 0.371709i 0.982577 + 0.185855i 0.0595053π0.0595053\pi
−0.982577 + 0.185855i 0.940495π0.940495\pi
648648 0 0
649649 1.69499e11 0.955406
650650 −2.84025e10 1.63982e10i −0.159112 0.0918635i
651651 0 0
652652 7.86411e10 + 1.36210e11i 0.435170 + 0.753737i
653653 −2.27135e10 + 1.31137e10i −0.124920 + 0.0721226i −0.561158 0.827709i 0.689644π-0.689644\pi
0.436238 + 0.899831i 0.356311π0.356311\pi
654654 0 0
655655 4.69649e10 8.13456e10i 0.255158 0.441946i
656656 3.78221e10i 0.204235i
657657 0 0
658658 1.18735e11 0.633396
659659 −2.34946e11 1.35646e11i −1.24574 0.719228i −0.275483 0.961306i 0.588838π-0.588838\pi
−0.970257 + 0.242078i 0.922171π0.922171\pi
660660 0 0
661661 −1.12700e11 1.95203e11i −0.590364 1.02254i −0.994183 0.107702i 0.965651π-0.965651\pi
0.403819 0.914839i 0.367682π-0.367682\pi
662662 1.05450e11 6.08815e10i 0.549052 0.316995i
663663 0 0
664664 3.96106e10 6.86076e10i 0.203769 0.352939i
665665 2.25775e11i 1.15449i
666666 0 0
667667 −3.05502e11 −1.54352
668668 −9.48597e10 5.47673e10i −0.476405 0.275052i
669669 0 0
670670 1.48790e11 + 2.57712e11i 0.738370 + 1.27890i
671671 −5.40907e10 + 3.12293e10i −0.266829 + 0.154054i
672672 0 0
673673 −7.58538e10 + 1.31383e11i −0.369757 + 0.640439i −0.989527 0.144345i 0.953893π-0.953893\pi
0.619770 + 0.784784i 0.287226π0.287226\pi
674674 1.46925e11i 0.711962i
675675 0 0
676676 9.23761e10 0.442357
677677 2.20192e11 + 1.27128e11i 1.04821 + 0.605183i 0.922147 0.386839i 0.126433π-0.126433\pi
0.126061 + 0.992023i 0.459767π0.459767\pi
678678 0 0
679679 −1.38194e11 2.39359e11i −0.650145 1.12608i
680680 4.44367e10 2.56555e10i 0.207829 0.119990i
681681 0 0
682682 1.98059e11 3.43049e11i 0.915499 1.58569i
683683 2.98251e11i 1.37056i −0.728279 0.685281i 0.759679π-0.759679\pi
0.728279 0.685281i 0.240321π-0.240321\pi
684684 0 0
685685 1.14144e11 0.518429
686686 1.13478e11 + 6.55166e10i 0.512408 + 0.295839i
687687 0 0
688688 1.33201e10 + 2.30712e10i 0.0594505 + 0.102971i
689689 −5.84886e10 + 3.37684e10i −0.259534 + 0.149842i
690690 0 0
691691 1.50423e11 2.60541e11i 0.659785 1.14278i −0.320886 0.947118i 0.603981π-0.603981\pi
0.980671 0.195663i 0.0626860π-0.0626860\pi
692692 5.86053e10i 0.255572i
693693 0 0
694694 −2.76005e10 −0.118981
695695 −1.39634e11 8.06177e10i −0.598483 0.345534i
696696 0 0
697697 4.92504e10 + 8.53041e10i 0.208679 + 0.361442i
698698 2.13579e11 1.23310e11i 0.899782 0.519489i
699699 0 0
700700 5.14018e10 8.90305e10i 0.214085 0.370806i
701701 2.33302e11i 0.966156i −0.875577 0.483078i 0.839519π-0.839519\pi
0.875577 0.483078i 0.160481π-0.160481\pi
702702 0 0
703703 1.64525e11 0.673613
704704 4.48096e10 + 2.58708e10i 0.182423 + 0.105322i
705705 0 0
706706 −8.02255e10 1.38955e11i −0.322919 0.559312i
707707 2.17992e11 1.25858e11i 0.872494 0.503735i
708708 0 0
709709 −1.36103e11 + 2.35737e11i −0.538620 + 0.932918i 0.460358 + 0.887733i 0.347721π0.347721\pi
−0.998979 + 0.0451845i 0.985612π0.985612\pi
710710 1.64875e11i 0.648816i
711711 0 0
712712 −1.02090e10 −0.0397250
713713 5.63365e11 + 3.25259e11i 2.17988 + 1.25855i
714714 0 0
715715 9.93400e10 + 1.72062e11i 0.380102 + 0.658356i
716716 −1.62688e11 + 9.39278e10i −0.619017 + 0.357390i
717717 0 0
718718 −9.18479e10 + 1.59085e11i −0.345598 + 0.598594i
719719 4.94299e11i 1.84958i 0.380473 + 0.924792i 0.375761π0.375761\pi
−0.380473 + 0.924792i 0.624239π0.624239\pi
720720 0 0
721721 2.51803e11 0.931796
722722 −6.60706e10 3.81459e10i −0.243142 0.140378i
723723 0 0
724724 −1.01935e11 1.76557e11i −0.370996 0.642585i
725725 −1.72526e11 + 9.96081e10i −0.624458 + 0.360531i
726726 0 0
727727 7.37697e10 1.27773e11i 0.264083 0.457405i −0.703240 0.710952i 0.748264π-0.748264\pi
0.967323 + 0.253548i 0.0815974π0.0815974\pi
728728 3.77324e10i 0.134335i
729729 0 0
730730 −2.69603e11 −0.949365
731731 −6.00847e10 3.46899e10i −0.210423 0.121488i
732732 0 0
733733 2.03374e10 + 3.52254e10i 0.0704497 + 0.122022i 0.899098 0.437746i 0.144223π-0.144223\pi
−0.828649 + 0.559769i 0.810890π0.810890\pi
734734 9.25358e10 5.34256e10i 0.318805 0.184062i
735735 0 0
736736 −4.24859e10 + 7.35877e10i −0.144788 + 0.250780i
737737 7.81495e11i 2.64884i
738738 0 0
739739 −4.39058e11 −1.47212 −0.736062 0.676915i 0.763317π-0.763317\pi
−0.736062 + 0.676915i 0.763317π0.763317\pi
740740 1.49658e11 + 8.64049e10i 0.499082 + 0.288145i
741741 0 0
742742 −1.05850e11 1.83338e11i −0.349202 0.604836i
743743 −2.39798e11 + 1.38447e11i −0.786846 + 0.454286i −0.838851 0.544361i 0.816772π-0.816772\pi
0.0520049 + 0.998647i 0.483439π0.483439\pi
744744 0 0
745745 −3.21657e11 + 5.57127e11i −1.04416 + 1.80854i
746746 1.55543e11i 0.502220i
747747 0 0
748748 −1.34752e11 −0.430455
749749 −3.13093e11 1.80764e11i −0.994824 0.574362i
750750 0 0
751751 −2.18499e10 3.78451e10i −0.0686893 0.118973i 0.829635 0.558306i 0.188548π-0.188548\pi
−0.898325 + 0.439332i 0.855215π0.855215\pi
752752 −5.54225e10 + 3.19982e10i −0.173306 + 0.100059i
753753 0 0
754754 −3.65596e10 + 6.33231e10i −0.113114 + 0.195919i
755755 5.78070e11i 1.77907i
756756 0 0
757757 −2.44223e11 −0.743708 −0.371854 0.928291i 0.621278π-0.621278\pi
−0.371854 + 0.928291i 0.621278π0.621278\pi
758758 −7.93691e10 4.58238e10i −0.240422 0.138808i
759759 0 0
760760 6.08447e10 + 1.05386e11i 0.182376 + 0.315885i
761761 −3.60019e11 + 2.07857e11i −1.07346 + 0.619764i −0.929125 0.369765i 0.879438π-0.879438\pi
−0.144337 + 0.989529i 0.546105π0.546105\pi
762762 0 0
763763 −7.14516e10 + 1.23758e11i −0.210821 + 0.365153i
764764 2.37804e10i 0.0697985i
765765 0 0
766766 4.26293e11 1.23821
767767 5.76964e10 + 3.33110e10i 0.166712 + 0.0962512i
768768 0 0
769769 −5.75903e10 9.97493e10i −0.164681 0.285236i 0.771861 0.635792i 0.219326π-0.219326\pi
−0.936542 + 0.350555i 0.885993π0.885993\pi
770770 −5.39345e11 + 3.11391e11i −1.53428 + 0.885815i
771771 0 0
772772 7.49215e10 1.29768e11i 0.210929 0.365340i
773773 1.78665e11i 0.500406i 0.968193 + 0.250203i 0.0804973π0.0804973\pi
−0.968193 + 0.250203i 0.919503π0.919503\pi
774774 0 0
775775 4.24199e11 1.17588
776776 1.29011e11 + 7.44845e10i 0.355779 + 0.205409i
777777 0 0
778778 4.86441e10 + 8.42541e10i 0.132774 + 0.229971i
779779 −2.02307e11 + 1.16802e11i −0.549366 + 0.317177i
780780 0 0
781781 2.16495e11 3.74981e11i 0.581894 1.00787i
782782 2.21293e11i 0.591754i
783783 0 0
784784 2.38256e10 0.0630637
785785 −7.18225e9 4.14667e9i −0.0189139 0.0109200i
786786 0 0
787787 2.61255e11 + 4.52507e11i 0.681029 + 1.17958i 0.974667 + 0.223660i 0.0718005π0.0718005\pi
−0.293638 + 0.955917i 0.594866π0.594866\pi
788788 2.11077e11 1.21865e11i 0.547439 0.316064i
789789 0 0
790790 −3.19727e11 + 5.53783e11i −0.820862 + 1.42178i
791791 3.54825e11i 0.906376i
792792 0 0
793793 −2.45495e10 −0.0620798
794794 −7.38627e10 4.26446e10i −0.185842 0.107296i
795795 0 0
796796 1.01993e11 + 1.76656e11i 0.254048 + 0.440024i
797797 −1.67664e11 + 9.68008e10i −0.415534 + 0.239908i −0.693165 0.720779i 0.743784π-0.743784\pi
0.277631 + 0.960688i 0.410451π0.410451\pi
798798 0 0
799799 8.33335e10 1.44338e11i 0.204471 0.354155i
800800 5.54096e10i 0.135277i
801801 0 0
802802 3.17336e10 0.0767047
803803 6.13166e11 + 3.54012e11i 1.47474 + 0.851443i
804804 0 0
805805 −5.11376e11 8.85729e11i −1.21775 2.10920i
806806 1.34836e11 7.78478e10i 0.319497 0.184462i
807807 0 0
808808 −6.78354e10 + 1.17494e11i −0.159151 + 0.275658i
809809 4.05968e11i 0.947760i 0.880590 + 0.473880i 0.157147π0.157147\pi
−0.880590 + 0.473880i 0.842853π0.842853\pi
810810 0 0
811811 −3.49637e11 −0.808229 −0.404115 0.914708i 0.632420π-0.632420\pi
−0.404115 + 0.914708i 0.632420π0.632420\pi
812812 −1.98492e11 1.14600e11i −0.456583 0.263608i
813813 0 0
814814 −2.26914e11 3.93027e11i −0.516849 0.895209i
815815 8.83654e11 5.10178e11i 2.00287 1.15636i
816816 0 0
817817 8.22706e10 1.42497e11i 0.184653 0.319828i
818818 9.77005e10i 0.218215i
819819 0 0
820820 −2.45368e11 −0.542703
821821 1.48992e11 + 8.60206e10i 0.327937 + 0.189334i 0.654925 0.755694i 0.272700π-0.272700\pi
−0.326988 + 0.945029i 0.606034π0.606034\pi
822822 0 0
823823 −1.51520e11 2.62440e11i −0.330271 0.572046i 0.652294 0.757966i 0.273807π-0.273807\pi
−0.982565 + 0.185920i 0.940473π0.940473\pi
824824 −1.17535e11 + 6.78591e10i −0.254953 + 0.147197i
825825 0 0
826826 −1.04417e11 + 1.80855e11i −0.224311 + 0.388517i
827827 7.71110e11i 1.64852i 0.566211 + 0.824260i 0.308409π0.308409\pi
−0.566211 + 0.824260i 0.691591π0.691591\pi
828828 0 0
829829 1.56682e11 0.331742 0.165871 0.986147i 0.446956π-0.446956\pi
0.165871 + 0.986147i 0.446956π0.446956\pi
830830 −4.45087e11 2.56971e11i −0.937847 0.541466i
831831 0 0
832832 1.01686e10 + 1.76125e10i 0.0212211 + 0.0367560i
833833 −5.37364e10 + 3.10247e10i −0.111606 + 0.0644359i
834834 0 0
835835 −3.55299e11 + 6.15396e11i −0.730883 + 1.26593i
836836 3.19577e11i 0.654260i
837837 0 0
838838 −2.88318e11 −0.584649
839839 −4.22447e11 2.43900e11i −0.852559 0.492225i 0.00895468 0.999960i 0.497150π-0.497150\pi
−0.861513 + 0.507735i 0.830483π0.830483\pi
840840 0 0
841841 −2.80482e10 4.85809e10i −0.0560688 0.0971140i
842842 1.41505e9 8.16978e8i 0.00281529 0.00162541i
843843 0 0
844844 −5.58649e10 + 9.67608e10i −0.110095 + 0.190691i
845845 5.99283e11i 1.17545i
846846 0 0
847847 1.05959e12 2.05875
848848 9.88166e10 + 5.70518e10i 0.191094 + 0.110328i
849849 0 0
850850 −7.21521e10 1.24971e11i −0.138221 0.239405i
851851 6.45441e11 3.72645e11i 1.23066 0.710522i
852852 0 0
853853 −5.07020e10 + 8.78185e10i −0.0957699 + 0.165878i −0.909930 0.414763i 0.863865π-0.863865\pi
0.814160 + 0.580641i 0.197198π0.197198\pi
854854 7.69530e10i 0.144675i
855855 0 0
856856 1.94859e11 0.362931
857857 −2.37864e11 1.37331e11i −0.440967 0.254592i 0.263041 0.964785i 0.415275π-0.415275\pi
−0.704008 + 0.710192i 0.748608π0.748608\pi
858858 0 0
859859 −2.10607e11 3.64783e11i −0.386813 0.669980i 0.605206 0.796069i 0.293091π-0.293091\pi
−0.992019 + 0.126089i 0.959757π0.959757\pi
860860 1.49673e11 8.64135e10i 0.273620 0.157975i
861861 0 0
862862 3.57310e10 6.18879e10i 0.0647166 0.112092i
863863 8.61056e11i 1.55235i 0.630520 + 0.776173i 0.282842π0.282842\pi
−0.630520 + 0.776173i 0.717158π0.717158\pi
864864 0 0
865865 3.80198e11 0.679117
866866 −3.88235e11 2.24148e11i −0.690277 0.398532i
867867 0 0
868868 2.44022e11 + 4.22658e11i 0.429882 + 0.744578i
869869 1.45433e12 8.39656e11i 2.55025 1.47239i
870870 0 0
871871 1.53585e11 2.66016e11i 0.266855 0.462206i
872872 7.70227e10i 0.133215i
873873 0 0
874874 5.24819e11 0.899423
875875 1.77186e11 + 1.02298e11i 0.302271 + 0.174516i
876876 0 0
877877 −3.14825e11 5.45294e11i −0.532196 0.921790i −0.999293 0.0375845i 0.988034π-0.988034\pi
0.467098 0.884206i 0.345300π-0.345300\pi
878878 −3.08514e11 + 1.78121e11i −0.519155 + 0.299734i
879879 0 0
880880 1.67835e11 2.90699e11i 0.279867 0.484744i
881881 8.26944e11i 1.37269i −0.727276 0.686345i 0.759214π-0.759214\pi
0.727276 0.686345i 0.240786π-0.240786\pi
882882 0 0
883883 1.00813e12 1.65834 0.829168 0.558999i 0.188815π-0.188815\pi
0.829168 + 0.558999i 0.188815π0.188815\pi
884884 −4.58687e10 2.64823e10i −0.0751116 0.0433657i
885885 0 0
886886 −2.52206e11 4.36834e11i −0.409281 0.708895i
887887 −8.45160e11 + 4.87954e11i −1.36535 + 0.788286i −0.990330 0.138730i 0.955698π-0.955698\pi
−0.375022 + 0.927016i 0.622365π0.622365\pi
888888 0 0
889889 7.68843e10 1.33167e11i 0.123092 0.213202i
890890 6.62303e10i 0.105559i
891891 0 0
892892 4.35053e10 0.0687199
893893 3.42312e11 + 1.97634e11i 0.538289 + 0.310781i
894894 0 0
895895 6.09349e11 + 1.05542e12i 0.949673 + 1.64488i
896896 −5.52083e10 + 3.18745e10i −0.0856588 + 0.0494551i
897897 0 0
898898 −1.33246e11 + 2.30789e11i −0.204903 + 0.354902i
899899 9.45747e11i 1.44789i
900900 0 0
901901 −2.97162e11 −0.450914
902902 5.58048e11 + 3.22189e11i 0.843034 + 0.486726i
903903 0 0
904904 9.56226e10 + 1.65623e11i 0.143181 + 0.247998i
905905 −1.14540e12 + 6.61297e11i −1.70751 + 0.985830i
906906 0 0
907907 2.98209e11 5.16514e11i 0.440648 0.763225i −0.557089 0.830453i 0.688082π-0.688082\pi
0.997738 + 0.0672273i 0.0214153π0.0214153\pi
908908 1.16209e11i 0.170961i
909909 0 0
910910 −2.44786e11 −0.356962
911911 −1.16083e12 6.70203e11i −1.68536 0.973045i −0.957989 0.286804i 0.907407π-0.907407\pi
−0.727374 0.686241i 0.759259π-0.759259\pi
912912 0 0
913913 6.74849e11 + 1.16887e12i 0.971234 + 1.68223i
914914 −4.01829e11 + 2.31996e11i −0.575780 + 0.332427i
915915 0 0
916916 −2.45718e9 + 4.25596e9i −0.00349024 + 0.00604527i
917917 3.03920e11i 0.429816i
918918 0 0
919919 −3.60905e11 −0.505977 −0.252988 0.967469i 0.581413π-0.581413\pi
−0.252988 + 0.967469i 0.581413π0.581413\pi
920920 4.77394e11 + 2.75624e11i 0.666386 + 0.384738i
921921 0 0
922922 2.20241e10 + 3.81469e10i 0.0304772 + 0.0527880i
923923 1.47387e11 8.50941e10i 0.203073 0.117244i
924924 0 0
925925 2.43000e11 4.20888e11i 0.331924 0.574910i
926926 6.06262e11i 0.824549i
927927 0 0
928928 1.23535e11 0.166570
929929 −8.27772e10 4.77914e10i −0.111134 0.0641634i 0.443403 0.896323i 0.353771π-0.353771\pi
−0.554537 + 0.832159i 0.687105π0.687105\pi
930930 0 0
931931 −7.35782e10 1.27441e11i −0.0979378 0.169633i
932932 3.76479e11 2.17360e11i 0.498973 0.288082i
933933 0 0
934934 2.56347e11 4.44006e11i 0.336854 0.583448i
935935 8.74192e11i 1.14383i
936936 0 0
937937 −1.26218e12 −1.63743 −0.818714 0.574201i 0.805313π-0.805313\pi
−0.818714 + 0.574201i 0.805313π0.805313\pi
938938 8.33855e11 + 4.81426e11i 1.07716 + 0.621897i
939939 0 0
940940 2.07586e11 + 3.59549e11i 0.265880 + 0.460519i
941941 5.84641e11 3.37543e11i 0.745643 0.430497i −0.0784743 0.996916i 0.525005π-0.525005\pi
0.824118 + 0.566419i 0.191672π0.191672\pi
942942 0 0
943943 −5.29109e11 + 9.16443e11i −0.669111 + 1.15893i
944944 1.12558e11i 0.141739i
945945 0 0
946946 −4.53873e11 −0.566722
947947 −4.41361e11 2.54820e11i −0.548775 0.316835i 0.199853 0.979826i 0.435954π-0.435954\pi
−0.748628 + 0.662991i 0.769287π0.769287\pi
948948 0 0
949949 1.39145e11 + 2.41007e11i 0.171555 + 0.297142i
950950 2.96381e11 1.71116e11i 0.363879 0.210085i
951951 0 0
952952 8.30113e10 1.43780e11i 0.101062 0.175045i
953953 1.54025e12i 1.86732i 0.358160 + 0.933660i 0.383404π0.383404\pi
−0.358160 + 0.933660i 0.616596π0.616596\pi
954954 0 0
955955 1.54274e11 0.185472
956956 3.32864e10 + 1.92179e10i 0.0398506 + 0.0230078i
957957 0 0
958958 −3.21645e10 5.57106e10i −0.0381869 0.0661417i
959959 3.19844e11 1.84662e11i 0.378150 0.218325i
960960 0 0
961961 −5.80464e11 + 1.00539e12i −0.680584 + 1.17881i
962962 1.78379e11i 0.208277i
963963 0 0
964964 −6.84242e11 −0.792321
965965 −8.41859e11 4.86048e11i −0.970801 0.560492i
966966 0 0
967967 −4.00962e11 6.94486e11i −0.458561 0.794251i 0.540324 0.841457i 0.318302π-0.318302\pi
−0.998885 + 0.0472059i 0.984968π0.984968\pi
968968 −4.94589e11 + 2.85551e11i −0.563304 + 0.325224i
969969 0 0
970970 4.83213e11 8.36949e11i 0.545823 0.945393i
971971 5.82235e11i 0.654970i 0.944856 + 0.327485i 0.106201π0.106201\pi
−0.944856 + 0.327485i 0.893799π0.893799\pi
972972 0 0
973973 −5.21695e11 −0.582057
974974 3.57390e11 + 2.06339e11i 0.397106 + 0.229269i
975975 0 0
976976 2.07382e10 + 3.59197e10i 0.0228545 + 0.0395852i
977977 −1.00625e12 + 5.80962e11i −1.10441 + 0.637631i −0.937375 0.348321i 0.886752π-0.886752\pi
−0.167033 + 0.985951i 0.553419π0.553419\pi
978978 0 0
979979 8.69660e10 1.50630e11i 0.0946714 0.163976i
980980 1.54567e11i 0.167576i
981981 0 0
982982 6.62876e11 0.712830
983983 1.19414e12 + 6.89439e11i 1.27892 + 0.738383i 0.976649 0.214840i 0.0689230π-0.0689230\pi
0.302268 + 0.953223i 0.402256π0.402256\pi
984984 0 0
985985 −7.90592e11 1.36935e12i −0.839861 1.45468i
986986 −2.78621e11 + 1.60862e11i −0.294786 + 0.170195i
987987 0 0
988988 6.28054e10 1.08782e11i 0.0659127 0.114164i
989989 7.45364e11i 0.779082i
990990 0 0
991991 −8.57390e11 −0.888963 −0.444482 0.895788i 0.646612π-0.646612\pi
−0.444482 + 0.895788i 0.646612π0.646612\pi
992992 −2.27806e11 1.31524e11i −0.235244 0.135818i
993993 0 0
994994 2.66736e11 + 4.62000e11i 0.273235 + 0.473256i
995995 1.14604e12 6.61669e11i 1.16925 0.675070i
996996 0 0
997997 7.94454e11 1.37603e12i 0.804060 1.39267i −0.112865 0.993610i 0.536003π-0.536003\pi
0.916924 0.399062i 0.130664π-0.130664\pi
998998 7.20514e11i 0.726307i
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.35.8 16
3.2 odd 2 18.9.d.a.11.1 yes 16
4.3 odd 2 432.9.q.c.305.7 16
9.2 odd 6 162.9.b.c.161.10 16
9.4 even 3 18.9.d.a.5.1 16
9.5 odd 6 inner 54.9.d.a.17.8 16
9.7 even 3 162.9.b.c.161.7 16
12.11 even 2 144.9.q.b.65.8 16
36.23 even 6 432.9.q.c.17.7 16
36.31 odd 6 144.9.q.b.113.8 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
18.9.d.a.5.1 16 9.4 even 3
18.9.d.a.11.1 yes 16 3.2 odd 2
54.9.d.a.17.8 16 9.5 odd 6 inner
54.9.d.a.35.8 16 1.1 even 1 trivial
144.9.q.b.65.8 16 12.11 even 2
144.9.q.b.113.8 16 36.31 odd 6
162.9.b.c.161.7 16 9.7 even 3
162.9.b.c.161.10 16 9.2 odd 6
432.9.q.c.17.7 16 36.23 even 6
432.9.q.c.305.7 16 4.3 odd 2