Properties

Label 81.7.d.e.26.4
Level 8181
Weight 77
Character 81.26
Analytic conductor 18.63418.634
Analytic rank 00
Dimension 88
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [81,7,Mod(26,81)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(81, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("81.26");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: N N == 81=34 81 = 3^{4}
Weight: k k == 7 7
Character orbit: [χ][\chi] == 81.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: 18.634380773218.6343807732
Analytic rank: 00
Dimension: 88
Relative dimension: 44 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: 8.0.58594980096.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x821x6+341x42100x2+10000 x^{8} - 21x^{6} + 341x^{4} - 2100x^{2} + 10000 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 316 3^{16}
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 26.4
Root 3.20565+1.85078i3.20565 + 1.85078i of defining polynomial
Character χ\chi == 81.26
Dual form 81.7.d.e.53.4

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+(12.2150+7.05234i)q2+(67.4711+116.863i)q4+(119.00868.7094i)q5+(257.384445.803i)q7+1000.62iq8+1938.25q10+(1055.05+609.131i)q11+(85.2313+147.625i)q13+(6287.913630.33i)q14+(2738.55+4743.30i)q16+1574.10iq1711289.1q19+(16059.2+9271.79i)q20+(8591.60+14881.1i)q22+(9156.17+5286.32i)q23+(1629.462822.30i)q25+2404.32iq26+69464.0q28+(7504.484332.71i)q29+(13104.5+22697.7i)q31+(11442.9+6606.58i)q32+(11101.1+19227.7i)q3470738.9iq35+21866.9q37+(137896.79614.3i)q38+(68751.8+119082.i)q40+(33053.3+19083.3i)q41+(11947.5+20693.8i)q43+164395.iq44149124.q46+(23121.813349.4i)q47+(73668.9127598.i)q49+(39807.722983.0i)q50+(11501.3+19920.8i)q52213997.iq53+167412.q55+(446078.+257543.i)q56+(61111.5105848.i)q58+(141759.81844.5i)q59+(55538.9+96196.1i)q61+369671.iq62+164166.q64+(20286.4+11712.4i)q65+(190518.+329986.i)q67+(183955.+106206.i)q68+(498875.864076.i)q70675048.iq71762939.q73+(267105.+154213.i)q74+(761685.1.31928e6i)q76+(543105.313562.i)q77+(257854.+446616.i)q79+752655.iq80538328.q82+(782690.451887.i)q83+(108155.+187331.i)q85+(291879.+168516.i)q86+(609507.+1.05570e6i)q88+644278.iq89+87748.8q91+(1.23555e6713347.i)q92+(188289.326125.i)q94+(1.34349e6+775664.i)q95+(308235.533878.i)q972.07815e6iq98+O(q100)q+(12.2150 + 7.05234i) q^{2} +(67.4711 + 116.863i) q^{4} +(119.008 - 68.7094i) q^{5} +(257.384 - 445.803i) q^{7} +1000.62i q^{8} +1938.25 q^{10} +(1055.05 + 609.131i) q^{11} +(85.2313 + 147.625i) q^{13} +(6287.91 - 3630.33i) q^{14} +(-2738.55 + 4743.30i) q^{16} +1574.10i q^{17} -11289.1 q^{19} +(16059.2 + 9271.79i) q^{20} +(8591.60 + 14881.1i) q^{22} +(-9156.17 + 5286.32i) q^{23} +(1629.46 - 2822.30i) q^{25} +2404.32i q^{26} +69464.0 q^{28} +(-7504.48 - 4332.71i) q^{29} +(13104.5 + 22697.7i) q^{31} +(-11442.9 + 6606.58i) q^{32} +(-11101.1 + 19227.7i) q^{34} -70738.9i q^{35} +21866.9 q^{37} +(-137896. - 79614.3i) q^{38} +(68751.8 + 119082. i) q^{40} +(-33053.3 + 19083.3i) q^{41} +(-11947.5 + 20693.8i) q^{43} +164395. i q^{44} -149124. q^{46} +(-23121.8 - 13349.4i) q^{47} +(-73668.9 - 127598. i) q^{49} +(39807.7 - 22983.0i) q^{50} +(-11501.3 + 19920.8i) q^{52} -213997. i q^{53} +167412. q^{55} +(446078. + 257543. i) q^{56} +(-61111.5 - 105848. i) q^{58} +(141759. - 81844.5i) q^{59} +(-55538.9 + 96196.1i) q^{61} +369671. i q^{62} +164166. q^{64} +(20286.4 + 11712.4i) q^{65} +(190518. + 329986. i) q^{67} +(-183955. + 106206. i) q^{68} +(498875. - 864076. i) q^{70} -675048. i q^{71} -762939. q^{73} +(267105. + 154213. i) q^{74} +(-761685. - 1.31928e6i) q^{76} +(543105. - 313562. i) q^{77} +(-257854. + 446616. i) q^{79} +752655. i q^{80} -538328. q^{82} +(-782690. - 451887. i) q^{83} +(108155. + 187331. i) q^{85} +(-291879. + 168516. i) q^{86} +(-609507. + 1.05570e6i) q^{88} +644278. i q^{89} +87748.8 q^{91} +(-1.23555e6 - 713347. i) q^{92} +(-188289. - 326125. i) q^{94} +(-1.34349e6 + 775664. i) q^{95} +(308235. - 533878. i) q^{97} -2.07815e6i q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+194q4+676q7+6516q10+3448q1310498q167328q19+58014q2217392q25+304684q28+153244q3165988q34+257920q37+338058q40126008q43+975212q97+O(q100) 8 q + 194 q^{4} + 676 q^{7} + 6516 q^{10} + 3448 q^{13} - 10498 q^{16} - 7328 q^{19} + 58014 q^{22} - 17392 q^{25} + 304684 q^{28} + 153244 q^{31} - 65988 q^{34} + 257920 q^{37} + 338058 q^{40} - 126008 q^{43}+ \cdots - 975212 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/81Z)×\left(\mathbb{Z}/81\mathbb{Z}\right)^\times.

nn 22
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 12.2150 + 7.05234i 1.52688 + 0.881543i 0.999491 + 0.0319175i 0.0101614π0.0101614\pi
0.527387 + 0.849625i 0.323172π0.323172\pi
33 0 0
44 67.4711 + 116.863i 1.05424 + 1.82599i
55 119.008 68.7094i 0.952065 0.549675i 0.0583432 0.998297i 0.481418π-0.481418\pi
0.893722 + 0.448622i 0.148085π0.148085\pi
66 0 0
77 257.384 445.803i 0.750392 1.29972i −0.197241 0.980355i 0.563198π-0.563198\pi
0.947633 0.319362i 0.103468π-0.103468\pi
88 1000.62i 1.95433i
99 0 0
1010 1938.25 1.93825
1111 1055.05 + 609.131i 0.792672 + 0.457649i 0.840902 0.541187i 0.182025π-0.182025\pi
−0.0482305 + 0.998836i 0.515358π0.515358\pi
1212 0 0
1313 85.2313 + 147.625i 0.0387944 + 0.0671939i 0.884771 0.466027i 0.154315π-0.154315\pi
−0.845976 + 0.533221i 0.820982π0.820982\pi
1414 6287.91 3630.33i 2.29151 1.32300i
1515 0 0
1616 −2738.55 + 4743.30i −0.668590 + 1.15803i
1717 1574.10i 0.320395i 0.987085 + 0.160197i 0.0512131π0.0512131\pi
−0.987085 + 0.160197i 0.948787π0.948787\pi
1818 0 0
1919 −11289.1 −1.64588 −0.822938 0.568131i 0.807667π-0.807667\pi
−0.822938 + 0.568131i 0.807667π0.807667\pi
2020 16059.2 + 9271.79i 2.00740 + 1.15897i
2121 0 0
2222 8591.60 + 14881.1i 0.806875 + 1.39755i
2323 −9156.17 + 5286.32i −0.752542 + 0.434480i −0.826611 0.562773i 0.809735π-0.809735\pi
0.0740699 + 0.997253i 0.476401π0.476401\pi
2424 0 0
2525 1629.46 2822.30i 0.104285 0.180627i
2626 2404.32i 0.136796i
2727 0 0
2828 69464.0 3.16436
2929 −7504.48 4332.71i −0.307699 0.177650i 0.338197 0.941075i 0.390183π-0.390183\pi
−0.645896 + 0.763425i 0.723516π0.723516\pi
3030 0 0
3131 13104.5 + 22697.7i 0.439883 + 0.761899i 0.997680 0.0680779i 0.0216867π-0.0216867\pi
−0.557797 + 0.829977i 0.688353π0.688353\pi
3232 −11442.9 + 6606.58i −0.349211 + 0.201617i
3333 0 0
3434 −11101.1 + 19227.7i −0.282442 + 0.489204i
3535 70738.9i 1.64989i
3636 0 0
3737 21866.9 0.431701 0.215850 0.976426i 0.430748π-0.430748\pi
0.215850 + 0.976426i 0.430748π0.430748\pi
3838 −137896. 79614.3i −2.51305 1.45091i
3939 0 0
4040 68751.8 + 119082.i 1.07425 + 1.86065i
4141 −33053.3 + 19083.3i −0.479582 + 0.276887i −0.720242 0.693723i 0.755969π-0.755969\pi
0.240660 + 0.970609i 0.422636π0.422636\pi
4242 0 0
4343 −11947.5 + 20693.8i −0.150270 + 0.260276i −0.931327 0.364185i 0.881348π-0.881348\pi
0.781056 + 0.624460i 0.214681π0.214681\pi
4444 164395.i 1.92988i
4545 0 0
4646 −149124. −1.53205
4747 −23121.8 13349.4i −0.222704 0.128578i 0.384498 0.923126i 0.374375π-0.374375\pi
−0.607202 + 0.794548i 0.707708π0.707708\pi
4848 0 0
4949 −73668.9 127598.i −0.626175 1.08457i
5050 39807.7 22983.0i 0.318461 0.183864i
5151 0 0
5252 −11501.3 + 19920.8i −0.0817969 + 0.141676i
5353 213997.i 1.43741i −0.695315 0.718705i 0.744735π-0.744735\pi
0.695315 0.718705i 0.255265π-0.255265\pi
5454 0 0
5555 167412. 1.00623
5656 446078. + 257543.i 2.54008 + 1.46651i
5757 0 0
5858 −61111.5 105848.i −0.313213 0.542500i
5959 141759. 81844.5i 0.690231 0.398505i −0.113468 0.993542i 0.536196π-0.536196\pi
0.803698 + 0.595037i 0.202863π0.202863\pi
6060 0 0
6161 −55538.9 + 96196.1i −0.244685 + 0.423807i −0.962043 0.272898i 0.912018π-0.912018\pi
0.717358 + 0.696705i 0.245351π0.245351\pi
6262 369671.i 1.55110i
6363 0 0
6464 164166. 0.626245
6565 20286.4 + 11712.4i 0.0738696 + 0.0426486i
6666 0 0
6767 190518. + 329986.i 0.633447 + 1.09716i 0.986842 + 0.161689i 0.0516941π0.0516941\pi
−0.353394 + 0.935474i 0.614973π0.614973\pi
6868 −183955. + 106206.i −0.585038 + 0.337772i
6969 0 0
7070 498875. 864076.i 1.45445 2.51917i
7171 675048.i 1.88608i −0.332682 0.943039i 0.607953π-0.607953\pi
0.332682 0.943039i 0.392047π-0.392047\pi
7272 0 0
7373 −762939. −1.96120 −0.980599 0.196025i 0.937197π-0.937197\pi
−0.980599 + 0.196025i 0.937197π0.937197\pi
7474 267105. + 154213.i 0.659154 + 0.380563i
7575 0 0
7676 −761685. 1.31928e6i −1.73514 3.00535i
7777 543105. 313562.i 1.18963 0.686832i
7878 0 0
7979 −257854. + 446616.i −0.522989 + 0.905843i 0.476653 + 0.879091i 0.341850π0.341850\pi
−0.999642 + 0.0267519i 0.991484π0.991484\pi
8080 752655.i 1.47003i
8181 0 0
8282 −538328. −0.976350
8383 −782690. 451887.i −1.36885 0.790306i −0.378068 0.925778i 0.623412π-0.623412\pi
−0.990781 + 0.135472i 0.956745π0.956745\pi
8484 0 0
8585 108155. + 187331.i 0.176113 + 0.305037i
8686 −291879. + 168516.i −0.458889 + 0.264940i
8787 0 0
8888 −609507. + 1.05570e6i −0.894398 + 1.54914i
8989 644278.i 0.913910i 0.889490 + 0.456955i 0.151060π0.151060\pi
−0.889490 + 0.456955i 0.848940π0.848940\pi
9090 0 0
9191 87748.8 0.116444
9292 −1.23555e6 713347.i −1.58671 0.916089i
9393 0 0
9494 −188289. 326125.i −0.226694 0.392646i
9595 −1.34349e6 + 775664.i −1.56698 + 0.904697i
9696 0 0
9797 308235. 533878.i 0.337728 0.584961i −0.646277 0.763103i 0.723675π-0.723675\pi
0.984005 + 0.178141i 0.0570084π0.0570084\pi
9898 2.07815e6i 2.20800i
9999 0 0
100100 439765. 0.439765
101101 −539557. 311514.i −0.523689 0.302352i 0.214754 0.976668i 0.431105π-0.431105\pi
−0.738443 + 0.674316i 0.764438π0.764438\pi
102102 0 0
103103 375348. + 650121.i 0.343496 + 0.594953i 0.985079 0.172101i 0.0550554π-0.0550554\pi
−0.641583 + 0.767053i 0.721722π0.721722\pi
104104 −147716. + 85283.9i −0.131319 + 0.0758171i
105105 0 0
106106 1.50918e6 2.61398e6i 1.26714 2.19475i
107107 345428.i 0.281973i 0.990012 + 0.140986i 0.0450273π0.0450273\pi
−0.990012 + 0.140986i 0.954973π0.954973\pi
108108 0 0
109109 1.17208e6 0.905061 0.452530 0.891749i 0.350521π-0.350521\pi
0.452530 + 0.891749i 0.350521π0.350521\pi
110110 2.04494e6 + 1.18065e6i 1.53639 + 0.887038i
111111 0 0
112112 1.40972e6 + 2.44170e6i 1.00341 + 1.73796i
113113 2.12463e6 1.22665e6i 1.47247 0.850132i 0.472952 0.881088i 0.343189π-0.343189\pi
0.999521 + 0.0309561i 0.00985519π0.00985519\pi
114114 0 0
115115 −726439. + 1.25823e6i −0.477646 + 0.827307i
116116 1.16933e6i 0.749141i
117117 0 0
118118 2.30878e6 1.40520
119119 701738. + 405149.i 0.416422 + 0.240422i
120120 0 0
121121 −143699. 248894.i −0.0811143 0.140494i
122122 −1.35682e6 + 783358.i −0.747208 + 0.431401i
123123 0 0
124124 −1.76836e6 + 3.06288e6i −0.927480 + 1.60644i
125125 1.69933e6i 0.870058i
126126 0 0
127127 −1.53816e6 −0.750913 −0.375456 0.926840i 0.622514π-0.622514\pi
−0.375456 + 0.926840i 0.622514π0.622514\pi
128128 2.73764e6 + 1.58058e6i 1.30541 + 0.753679i
129129 0 0
130130 165199. + 286134.i 0.0751932 + 0.130238i
131131 −976209. + 563615.i −0.434239 + 0.250708i −0.701151 0.713013i 0.747330π-0.747330\pi
0.266912 + 0.963721i 0.413997π0.413997\pi
132132 0 0
133133 −2.90563e6 + 5.03269e6i −1.23505 + 2.13917i
134134 5.37438e6i 2.23364i
135135 0 0
136136 −1.57507e6 −0.626157
137137 2.77647e6 + 1.60300e6i 1.07977 + 0.623406i 0.930834 0.365441i 0.119082π-0.119082\pi
0.148936 + 0.988847i 0.452415π0.452415\pi
138138 0 0
139139 33342.8 + 57751.4i 0.0124153 + 0.0215039i 0.872166 0.489210i 0.162715π-0.162715\pi
−0.859751 + 0.510713i 0.829381π0.829381\pi
140140 8.26678e6 4.77283e6i 3.01268 1.73937i
141141 0 0
142142 4.76067e6 8.24573e6i 1.66266 2.87981i
143143 207668.i 0.0710169i
144144 0 0
145145 −1.19079e6 −0.390600
146146 −9.31932e6 5.38051e6i −2.99451 1.72888i
147147 0 0
148148 1.47539e6 + 2.55544e6i 0.455114 + 0.788281i
149149 −1.41029e6 + 814231.i −0.426333 + 0.246144i −0.697783 0.716309i 0.745830π-0.745830\pi
0.271450 + 0.962453i 0.412497π0.412497\pi
150150 0 0
151151 182810. 316636.i 0.0530968 0.0919664i −0.838255 0.545278i 0.816424π-0.816424\pi
0.891352 + 0.453311i 0.149757π0.149757\pi
152152 1.12960e7i 3.21658i
153153 0 0
154154 8.84538e6 2.42189
155155 3.11910e6 + 1.80081e6i 0.837594 + 0.483585i
156156 0 0
157157 2.59463e6 + 4.49403e6i 0.670465 + 1.16128i 0.977772 + 0.209669i 0.0672387π0.0672387\pi
−0.307307 + 0.951610i 0.599428π0.599428\pi
158158 −6.29938e6 + 3.63695e6i −1.59708 + 0.922074i
159159 0 0
160160 −907868. + 1.57247e6i −0.221648 + 0.383905i
161161 5.44246e6i 1.30412i
162162 0 0
163163 −3.00726e6 −0.694397 −0.347199 0.937792i 0.612867π-0.612867\pi
−0.347199 + 0.937792i 0.612867π0.612867\pi
164164 −4.46028e6 2.57514e6i −1.01119 0.583808i
165165 0 0
166166 −6.37372e6 1.10396e7i −1.39338 2.41340i
167167 −4.14290e6 + 2.39191e6i −0.889519 + 0.513564i −0.873785 0.486312i 0.838342π-0.838342\pi
−0.0157339 + 0.999876i 0.505008π0.505008\pi
168168 0 0
169169 2.39888e6 4.15497e6i 0.496990 0.860812i
170170 3.05100e6i 0.621005i
171171 0 0
172172 −3.22446e6 −0.633681
173173 −3.06223e6 1.76798e6i −0.591425 0.341459i 0.174236 0.984704i 0.444254π-0.444254\pi
−0.765661 + 0.643245i 0.777588π0.777588\pi
174174 0 0
175175 −838793. 1.45283e6i −0.156509 0.271082i
176176 −5.77858e6 + 3.33627e6i −1.05995 + 0.611960i
177177 0 0
178178 −4.54367e6 + 7.86987e6i −0.805651 + 1.39543i
179179 8.57291e6i 1.49475i −0.664401 0.747376i 0.731313π-0.731313\pi
0.664401 0.747376i 0.268687π-0.268687\pi
180180 0 0
181181 1.79208e6 0.302219 0.151110 0.988517i 0.451715π-0.451715\pi
0.151110 + 0.988517i 0.451715π0.451715\pi
182182 1.07185e6 + 618835.i 0.177796 + 0.102650i
183183 0 0
184184 −5.28958e6 9.16182e6i −0.849118 1.47071i
185185 2.60234e6 1.50246e6i 0.411007 0.237295i
186186 0 0
187187 −958833. + 1.66075e6i −0.146628 + 0.253968i
188188 3.60278e6i 0.542206i
189189 0 0
190190 −2.18810e7 −3.19012
191191 8.75348e6 + 5.05382e6i 1.25626 + 0.725304i 0.972346 0.233545i 0.0750327π-0.0750327\pi
0.283917 + 0.958849i 0.408366π0.408366\pi
192192 0 0
193193 3.82329e6 + 6.62213e6i 0.531820 + 0.921140i 0.999310 + 0.0371413i 0.0118252π0.0118252\pi
−0.467490 + 0.883999i 0.654842π0.654842\pi
194194 7.53019e6 4.34755e6i 1.03134 0.595443i
195195 0 0
196196 9.94104e6 1.72184e7i 1.32027 2.28678i
197197 4.94403e6i 0.646669i 0.946285 + 0.323335i 0.104804π0.104804\pi
−0.946285 + 0.323335i 0.895196π0.895196\pi
198198 0 0
199199 −1.96814e6 −0.249745 −0.124872 0.992173i 0.539852π-0.539852\pi
−0.124872 + 0.992173i 0.539852π0.539852\pi
200200 2.82404e6 + 1.63046e6i 0.353005 + 0.203808i
201201 0 0
202202 −4.39380e6 7.61029e6i −0.533073 0.923309i
203203 −3.86307e6 + 2.23034e6i −0.461790 + 0.266615i
204204 0 0
205205 −2.62241e6 + 4.54214e6i −0.304396 + 0.527229i
206206 1.05883e7i 1.21123i
207207 0 0
208208 −933639. −0.103750
209209 −1.19105e7 6.87652e6i −1.30464 0.753234i
210210 0 0
211211 −4.14983e6 7.18771e6i −0.441756 0.765144i 0.556064 0.831140i 0.312311π-0.312311\pi
−0.997820 + 0.0659953i 0.978978π0.978978\pi
212212 2.50085e7 1.44386e7i 2.62470 1.51537i
213213 0 0
214214 −2.43608e6 + 4.21941e6i −0.248571 + 0.430537i
215215 3.28363e6i 0.330399i
216216 0 0
217217 1.34916e7 1.32034
218218 1.43170e7 + 8.26591e6i 1.38192 + 0.797850i
219219 0 0
220220 1.12955e7 + 1.95643e7i 1.06081 + 1.83737i
221221 −232376. + 134163.i −0.0215286 + 0.0124295i
222222 0 0
223223 −4.68890e6 + 8.12141e6i −0.422821 + 0.732347i −0.996214 0.0869334i 0.972293π-0.972293\pi
0.573394 + 0.819280i 0.305627π0.305627\pi
224224 6.80172e6i 0.605167i
225225 0 0
226226 3.46031e7 2.99771
227227 3.17328e6 + 1.83209e6i 0.271288 + 0.156628i 0.629473 0.777022i 0.283271π-0.283271\pi
−0.358185 + 0.933651i 0.616604π0.616604\pi
228228 0 0
229229 −2.49452e6 4.32063e6i −0.207721 0.359783i 0.743275 0.668986i 0.233271π-0.233271\pi
−0.950996 + 0.309202i 0.899938π0.899938\pi
230230 −1.77469e7 + 1.02462e7i −1.45861 + 0.842130i
231231 0 0
232232 4.33539e6 7.50911e6i 0.347187 0.601346i
233233 5.00370e6i 0.395570i −0.980245 0.197785i 0.936625π-0.936625\pi
0.980245 0.197785i 0.0633749π-0.0633749\pi
234234 0 0
235235 −3.66890e6 −0.282705
236236 1.91293e7 + 1.10443e7i 1.45533 + 0.840236i
237237 0 0
238238 5.71449e6 + 9.89780e6i 0.423884 + 0.734189i
239239 1.63810e7 9.45757e6i 1.19990 0.692765i 0.239370 0.970928i 0.423059π-0.423059\pi
0.960534 + 0.278163i 0.0897256π0.0897256\pi
240240 0 0
241241 7.62573e6 1.32081e7i 0.544791 0.943606i −0.453829 0.891089i 0.649942π-0.649942\pi
0.998620 0.0525173i 0.0167245π-0.0167245\pi
242242 4.05366e6i 0.286023i
243243 0 0
244244 −1.49891e7 −1.03182
245245 −1.75344e7 1.01235e7i −1.19232 0.688386i
246246 0 0
247247 −962181. 1.66655e6i −0.0638508 0.110593i
248248 −2.27118e7 + 1.31126e7i −1.48900 + 0.859676i
249249 0 0
250250 −1.19843e7 + 2.07574e7i −0.766994 + 1.32847i
251251 1.44796e7i 0.915661i −0.889040 0.457830i 0.848627π-0.848627\pi
0.889040 0.457830i 0.151373π-0.151373\pi
252252 0 0
253253 −1.28802e7 −0.795358
254254 −1.87886e7 1.08476e7i −1.14655 0.661962i
255255 0 0
256256 1.70402e7 + 2.95146e7i 1.01568 + 1.75921i
257257 1.03463e7 5.97342e6i 0.609515 0.351904i −0.163261 0.986583i 0.552201π-0.552201\pi
0.772776 + 0.634679i 0.218868π0.218868\pi
258258 0 0
259259 5.62821e6 9.74834e6i 0.323945 0.561089i
260260 3.16099e6i 0.179847i
261261 0 0
262262 −1.58992e7 −0.884040
263263 −1.31116e7 7.56999e6i −0.720757 0.416129i 0.0942745 0.995546i 0.469947π-0.469947\pi
−0.815031 + 0.579417i 0.803280π0.803280\pi
264264 0 0
265265 −1.47036e7 2.54674e7i −0.790109 1.36851i
266266 −7.09846e7 + 4.09830e7i −3.77154 + 2.17750i
267267 0 0
268268 −2.57089e7 + 4.45290e7i −1.33561 + 2.31334i
269269 3.37864e7i 1.73574i −0.496789 0.867871i 0.665488π-0.665488\pi
0.496789 0.867871i 0.334512π-0.334512\pi
270270 0 0
271271 −292052. −0.0146741 −0.00733707 0.999973i 0.502335π-0.502335\pi
−0.00733707 + 0.999973i 0.502335π0.502335\pi
272272 −7.46643e6 4.31074e6i −0.371028 0.214213i
273273 0 0
274274 2.26098e7 + 3.91612e7i 1.09912 + 1.90373i
275275 3.43830e6 1.98510e6i 0.165328 0.0954521i
276276 0 0
277277 5.92330e6 1.02595e7i 0.278692 0.482708i −0.692368 0.721545i 0.743433π-0.743433\pi
0.971060 + 0.238836i 0.0767659π0.0767659\pi
278278 940578.i 0.0437785i
279279 0 0
280280 7.07825e7 3.22442
281281 −2.31829e6 1.33847e6i −0.104484 0.0603238i 0.446847 0.894610i 0.352547π-0.352547\pi
−0.551331 + 0.834286i 0.685880π0.685880\pi
282282 0 0
283283 1.55551e7 + 2.69422e7i 0.686298 + 1.18870i 0.973027 + 0.230691i 0.0740987π0.0740987\pi
−0.286729 + 0.958012i 0.592568π0.592568\pi
284284 7.88884e7 4.55462e7i 3.44396 1.98837i
285285 0 0
286286 −1.46455e6 + 2.53667e6i −0.0626044 + 0.108434i
287287 1.96470e7i 0.831094i
288288 0 0
289289 2.16598e7 0.897347
290290 −1.45455e7 8.39787e6i −0.596397 0.344330i
291291 0 0
292292 −5.14763e7 8.91596e7i −2.06756 3.58113i
293293 2.03856e6 1.17696e6i 0.0810438 0.0467906i −0.458930 0.888472i 0.651767π-0.651767\pi
0.539974 + 0.841682i 0.318434π0.318434\pi
294294 0 0
295295 1.12470e7 1.94803e7i 0.438096 0.758805i
296296 2.18804e7i 0.843686i
297297 0 0
298298 −2.29689e7 −0.867945
299299 −1.56078e6 901120.i −0.0583888 0.0337108i
300300 0 0
301301 6.15022e6 + 1.06525e7i 0.225523 + 0.390618i
302302 4.46605e6 2.57848e6i 0.162145 0.0936143i
303303 0 0
304304 3.09156e7 5.35474e7i 1.10042 1.90598i
305305 1.52642e7i 0.537989i
306306 0 0
307307 3.99249e6 0.137984 0.0689920 0.997617i 0.478022π-0.478022\pi
0.0689920 + 0.997617i 0.478022π0.478022\pi
308308 7.32877e7 + 4.23127e7i 2.50830 + 1.44817i
309309 0 0
310310 2.53999e7 + 4.39939e7i 0.852602 + 1.47675i
311311 −2.61007e7 + 1.50692e7i −0.867703 + 0.500969i −0.866584 0.499031i 0.833689π-0.833689\pi
−0.00111874 + 0.999999i 0.500356π0.500356\pi
312312 0 0
313313 1.89456e7 3.28147e7i 0.617838 1.07013i −0.372041 0.928216i 0.621342π-0.621342\pi
0.989879 0.141911i 0.0453246π-0.0453246\pi
314314 7.31928e7i 2.36417i
315315 0 0
316316 −6.95907e7 −2.20541
317317 3.00895e7 + 1.73722e7i 0.944577 + 0.545352i 0.891392 0.453233i 0.149729π-0.149729\pi
0.0531849 + 0.998585i 0.483063π0.483063\pi
318318 0 0
319319 −5.27838e6 9.14242e6i −0.162603 0.281637i
320320 1.95371e7 1.12798e7i 0.596226 0.344231i
321321 0 0
322322 −3.83821e7 + 6.64798e7i −1.14964 + 1.99123i
323323 1.77701e7i 0.527330i
324324 0 0
325325 555522. 0.0161827
326326 −3.67337e7 2.12082e7i −1.06026 0.612141i
327327 0 0
328328 −1.90951e7 3.30737e7i −0.541128 0.937262i
329329 −1.19024e7 + 6.87183e6i −0.334230 + 0.192968i
330330 0 0
331331 −1.83106e7 + 3.17150e7i −0.504917 + 0.874541i 0.495067 + 0.868855i 0.335143π0.335143\pi
−0.999984 + 0.00568670i 0.998190π0.998190\pi
332332 1.21957e8i 3.33267i
333333 0 0
334334 −6.74742e7 −1.81092
335335 4.53463e7 + 2.61807e7i 1.20617 + 0.696380i
336336 0 0
337337 −2.26572e7 3.92434e7i −0.591992 1.02536i −0.993964 0.109709i 0.965008π-0.965008\pi
0.401971 0.915652i 0.368325π-0.368325\pi
338338 5.86046e7 3.38354e7i 1.51769 0.876236i
339339 0 0
340340 −1.45947e7 + 2.52788e7i −0.371329 + 0.643161i
341341 3.19296e7i 0.805248i
342342 0 0
343343 −1.52829e7 −0.378724
344344 −2.07065e7 1.19549e7i −0.508665 0.293678i
345345 0 0
346346 −2.49368e7 4.31918e7i −0.602022 1.04273i
347347 2.53109e7 1.46133e7i 0.605787 0.349751i −0.165528 0.986205i 0.552933π-0.552933\pi
0.771315 + 0.636454i 0.219599π0.219599\pi
348348 0 0
349349 4.80635e6 8.32484e6i 0.113068 0.195839i −0.803938 0.594713i 0.797266π-0.797266\pi
0.917006 + 0.398874i 0.130599π0.130599\pi
350350 2.36618e7i 0.551879i
351351 0 0
352352 −1.60971e7 −0.369079
353353 2.60926e7 + 1.50646e7i 0.593189 + 0.342478i 0.766357 0.642415i 0.222067π-0.222067\pi
−0.173169 + 0.984892i 0.555401π0.555401\pi
354354 0 0
355355 −4.63821e7 8.03362e7i −1.03673 1.79567i
356356 −7.52925e7 + 4.34702e7i −1.66879 + 0.963477i
357357 0 0
358358 6.04591e7 1.04718e8i 1.31769 2.28230i
359359 3.63910e7i 0.786521i 0.919427 + 0.393260i 0.128653π0.128653\pi
−0.919427 + 0.393260i 0.871347π0.871347\pi
360360 0 0
361361 8.03970e7 1.70891
362362 2.18903e7 + 1.26384e7i 0.461452 + 0.266419i
363363 0 0
364364 5.92051e6 + 1.02546e7i 0.122759 + 0.212626i
365365 −9.07960e7 + 5.24211e7i −1.86719 + 1.07802i
366366 0 0
367367 −2.52979e7 + 4.38173e7i −0.511784 + 0.886436i 0.488123 + 0.872775i 0.337682π0.337682\pi
−0.999907 + 0.0136607i 0.995652π0.995652\pi
368368 5.79073e7i 1.16196i
369369 0 0
370370 4.23836e7 0.836743
371371 −9.54007e7 5.50796e7i −1.86823 1.07862i
372372 0 0
373373 4.72498e7 + 8.18391e7i 0.910487 + 1.57701i 0.813378 + 0.581736i 0.197626π0.197626\pi
0.0971089 + 0.995274i 0.469040π0.469040\pi
374374 −2.34243e7 + 1.35240e7i −0.447767 + 0.258519i
375375 0 0
376376 1.33576e7 2.31360e7i 0.251284 0.435237i
377377 1.47713e6i 0.0275673i
378378 0 0
379379 −5.62274e7 −1.03283 −0.516417 0.856337i 0.672734π-0.672734\pi
−0.516417 + 0.856337i 0.672734π0.672734\pi
380380 −1.81293e8 1.04670e8i −3.30393 1.90753i
381381 0 0
382382 7.12826e7 + 1.23465e8i 1.27877 + 2.21490i
383383 −1.83955e7 + 1.06206e7i −0.327427 + 0.189040i −0.654698 0.755890i 0.727204π-0.727204\pi
0.327271 + 0.944930i 0.393871π0.393871\pi
384384 0 0
385385 4.30892e7 7.46328e7i 0.755069 1.30782i
386386 1.07853e8i 1.87529i
387387 0 0
388388 8.31877e7 1.42418
389389 8.33267e7 + 4.81087e7i 1.41558 + 0.817288i 0.995907 0.0903860i 0.0288101π-0.0288101\pi
0.419677 + 0.907674i 0.362143π0.362143\pi
390390 0 0
391391 −8.32119e6 1.44127e7i −0.139205 0.241110i
392392 1.27677e8 7.37144e7i 2.11960 1.22375i
393393 0 0
394394 −3.48670e7 + 6.03914e7i −0.570067 + 0.987384i
395395 7.08679e7i 1.14990i
396396 0 0
397397 2.71686e7 0.434206 0.217103 0.976149i 0.430339π-0.430339\pi
0.217103 + 0.976149i 0.430339π0.430339\pi
398398 −2.40409e7 1.38800e7i −0.381330 0.220161i
399399 0 0
400400 8.92468e6 + 1.54580e7i 0.139448 + 0.241531i
401401 1.33304e7 7.69630e6i 0.206733 0.119357i −0.393059 0.919513i 0.628583π-0.628583\pi
0.599792 + 0.800156i 0.295250π0.295250\pi
402402 0 0
403403 −2.23384e6 + 3.86912e6i −0.0341300 + 0.0591148i
404404 8.40727e7i 1.27500i
405405 0 0
406406 −6.29166e7 −0.940129
407407 2.30706e7 + 1.33198e7i 0.342197 + 0.197568i
408408 0 0
409409 1.63204e7 + 2.82678e7i 0.238540 + 0.413164i 0.960296 0.278985i 0.0899978π-0.0899978\pi
−0.721755 + 0.692148i 0.756664π0.756664\pi
410410 −6.40655e7 + 3.69882e7i −0.929549 + 0.536675i
411411 0 0
412412 −5.06502e7 + 8.77288e7i −0.724252 + 1.25444i
413413 8.42620e7i 1.19614i
414414 0 0
415415 −1.24195e8 −1.73765
416416 −1.95059e6 1.12618e6i −0.0270948 0.0156432i
417417 0 0
418418 −9.69911e7 1.67994e8i −1.32802 2.30019i
419419 7.67514e7 4.43125e7i 1.04338 0.602398i 0.122595 0.992457i 0.460878π-0.460878\pi
0.920790 + 0.390058i 0.127545π0.127545\pi
420420 0 0
421421 −4.75587e7 + 8.23740e7i −0.637358 + 1.10394i 0.348652 + 0.937252i 0.386639π0.386639\pi
−0.986010 + 0.166684i 0.946694π0.946694\pi
422422 1.17064e8i 1.55771i
423423 0 0
424424 2.14130e8 2.80918
425425 4.44258e6 + 2.56493e6i 0.0578720 + 0.0334124i
426426 0 0
427427 2.85897e7 + 4.95188e7i 0.367219 + 0.636043i
428428 −4.03679e7 + 2.33064e7i −0.514879 + 0.297266i
429429 0 0
430430 −2.31573e7 + 4.01096e7i −0.291261 + 0.504479i
431431 8.05617e7i 1.00623i 0.864220 + 0.503115i 0.167813π0.167813\pi
−0.864220 + 0.503115i 0.832187π0.832187\pi
432432 0 0
433433 3.50511e7 0.431755 0.215878 0.976420i 0.430739π-0.430739\pi
0.215878 + 0.976420i 0.430739π0.430739\pi
434434 1.64800e8 + 9.51475e7i 2.01599 + 1.16393i
435435 0 0
436436 7.90815e7 + 1.36973e8i 0.954147 + 1.65263i
437437 1.03365e8 5.96776e7i 1.23859 0.715100i
438438 0 0
439439 2.31531e7 4.01023e7i 0.273663 0.473998i −0.696134 0.717912i 0.745098π-0.745098\pi
0.969797 + 0.243914i 0.0784315π0.0784315\pi
440440 1.67515e8i 1.96651i
441441 0 0
442442 −3.78464e6 −0.0438286
443443 −1.03092e8 5.95204e7i −1.18581 0.684628i −0.228458 0.973554i 0.573369π-0.573369\pi
−0.957351 + 0.288926i 0.906702π0.906702\pi
444444 0 0
445445 4.42680e7 + 7.66744e7i 0.502354 + 0.870102i
446446 −1.14550e8 + 6.61354e7i −1.29119 + 0.745469i
447447 0 0
448448 4.22538e7 7.31858e7i 0.469929 0.813941i
449449 9.75546e7i 1.07773i 0.842393 + 0.538864i 0.181146π0.181146\pi
−0.842393 + 0.538864i 0.818854π0.818854\pi
450450 0 0
451451 −4.64970e7 −0.506868
452452 2.86702e8 + 1.65527e8i 3.10467 + 1.79248i
453453 0 0
454454 2.58411e7 + 4.47581e7i 0.276149 + 0.478304i
455455 1.04428e7 6.02917e6i 0.110862 0.0640063i
456456 0 0
457457 4.06870e6 7.04719e6i 0.0426292 0.0738359i −0.843924 0.536463i 0.819760π-0.819760\pi
0.886553 + 0.462628i 0.153093π0.153093\pi
458458 7.03688e7i 0.732460i
459459 0 0
460460 −1.96055e8 −2.01420
461461 1.34509e8 + 7.76590e7i 1.37293 + 0.792664i 0.991297 0.131648i 0.0420269π-0.0420269\pi
0.381638 + 0.924312i 0.375360π0.375360\pi
462462 0 0
463463 −3.81492e7 6.60764e7i −0.384364 0.665738i 0.607317 0.794460i 0.292246π-0.292246\pi
−0.991681 + 0.128722i 0.958913π0.958913\pi
464464 4.11027e7 2.37307e7i 0.411449 0.237550i
465465 0 0
466466 3.52878e7 6.11203e7i 0.348712 0.603987i
467467 1.85842e8i 1.82470i −0.409408 0.912352i 0.634265π-0.634265\pi
0.409408 0.912352i 0.365735π-0.365735\pi
468468 0 0
469469 1.96145e8 1.90133
470470 −4.48157e7 2.58744e7i −0.431655 0.249216i
471471 0 0
472472 8.18950e7 + 1.41846e8i 0.778810 + 1.34894i
473473 −2.52104e7 + 1.45552e7i −0.238230 + 0.137542i
474474 0 0
475475 −1.83950e7 + 3.18611e7i −0.171640 + 0.297290i
476476 1.09343e8i 1.01384i
477477 0 0
478478 2.66792e8 2.44281
479479 −1.07230e8 6.19095e7i −0.975689 0.563314i −0.0747229 0.997204i 0.523807π-0.523807\pi
−0.900966 + 0.433890i 0.857141π0.857141\pi
480480 0 0
481481 1.86375e6 + 3.22811e6i 0.0167476 + 0.0290076i
482482 1.86297e8 1.07559e8i 1.66366 0.960514i
483483 0 0
484484 1.93911e7 3.35863e7i 0.171027 0.296228i
485485 8.47145e7i 0.742561i
486486 0 0
487487 −6.09360e7 −0.527578 −0.263789 0.964580i 0.584972π-0.584972\pi
−0.263789 + 0.964580i 0.584972π0.584972\pi
488488 −9.62555e7 5.55731e7i −0.828259 0.478196i
489489 0 0
490490 −1.42789e8 2.47317e8i −1.21368 2.10216i
491491 −5.61243e7 + 3.24034e7i −0.474140 + 0.273745i −0.717971 0.696073i 0.754929π-0.754929\pi
0.243831 + 0.969818i 0.421596π0.421596\pi
492492 0 0
493493 6.82012e6 1.18128e7i 0.0569182 0.0985852i
494494 2.71425e7i 0.225149i
495495 0 0
496496 −1.43550e8 −1.17641
497497 −3.00938e8 1.73747e8i −2.45137 1.41530i
498498 0 0
499499 −1.43548e7 2.48633e7i −0.115530 0.200104i 0.802461 0.596704i 0.203523π-0.203523\pi
−0.917992 + 0.396600i 0.870190π0.870190\pi
500500 −1.98590e8 + 1.14656e8i −1.58872 + 0.917246i
501501 0 0
502502 1.02115e8 1.76868e8i 0.807194 1.39810i
503503 1.12463e8i 0.883702i 0.897088 + 0.441851i 0.145678π0.145678\pi
−0.897088 + 0.441851i 0.854322π0.854322\pi
504504 0 0
505505 −8.56156e7 −0.664781
506506 −1.57332e8 9.08359e7i −1.21441 0.701142i
507507 0 0
508508 −1.03781e8 1.79754e8i −0.791639 1.37116i
509509 −4.86521e7 + 2.80893e7i −0.368934 + 0.213004i −0.672993 0.739649i 0.734991π-0.734991\pi
0.304059 + 0.952653i 0.401658π0.401658\pi
510510 0 0
511511 −1.96369e8 + 3.40120e8i −1.47167 + 2.54900i
512512 2.78380e8i 2.07410i
513513 0 0
514514 1.68506e8 1.24087
515515 8.93388e7 + 5.15798e7i 0.654061 + 0.377623i
516516 0 0
517517 −1.62630e7 2.81684e7i −0.117687 0.203840i
518518 1.37497e8 7.93841e7i 0.989247 0.571142i
519519 0 0
520520 −1.17196e7 + 2.02990e7i −0.0833495 + 0.144366i
521521 1.68861e8i 1.19403i −0.802230 0.597015i 0.796353π-0.796353\pi
0.802230 0.597015i 0.203647π-0.203647\pi
522522 0 0
523523 −2.39748e8 −1.67591 −0.837955 0.545739i 0.816249π-0.816249\pi
−0.837955 + 0.545739i 0.816249π0.816249\pi
524524 −1.31732e8 7.60554e7i −0.915581 0.528611i
525525 0 0
526526 −1.06772e8 1.84935e8i −0.733671 1.27076i
527527 −3.57285e7 + 2.06279e7i −0.244109 + 0.140936i
528528 0 0
529529 −1.81276e7 + 3.13979e7i −0.122454 + 0.212097i
530530 4.14780e8i 2.78606i
531531 0 0
532532 −7.84183e8 −5.20814
533533 −5.63435e6 3.25299e6i −0.0372102 0.0214833i
534534 0 0
535535 2.37342e7 + 4.11088e7i 0.154993 + 0.268456i
536536 −3.30190e8 + 1.90635e8i −2.14422 + 1.23797i
537537 0 0
538538 2.38273e8 4.12702e8i 1.53013 2.65027i
539539 1.79496e8i 1.14627i
540540 0 0
541541 1.85322e8 1.17040 0.585200 0.810889i 0.301016π-0.301016\pi
0.585200 + 0.810889i 0.301016π0.301016\pi
542542 −3.56742e6 2.05965e6i −0.0224056 0.0129359i
543543 0 0
544544 −1.03994e7 1.80123e7i −0.0645970 0.111885i
545545 1.39487e8 8.05329e7i 0.861676 0.497489i
546546 0 0
547547 −1.26423e8 + 2.18971e8i −0.772438 + 1.33790i 0.163785 + 0.986496i 0.447630π0.447630\pi
−0.936223 + 0.351406i 0.885704π0.885704\pi
548548 4.32624e8i 2.62887i
549549 0 0
550550 5.59986e7 0.336580
551551 8.47185e7 + 4.89122e7i 0.506435 + 0.292390i
552552 0 0
553553 1.32735e8 + 2.29904e8i 0.784893 + 1.35947i
554554 1.44706e8 8.35463e7i 0.851056 0.491358i
555555 0 0
556556 −4.49934e6 + 7.79309e6i −0.0261773 + 0.0453404i
557557 1.01472e8i 0.587194i −0.955929 0.293597i 0.905148π-0.905148\pi
0.955929 0.293597i 0.0948524π-0.0948524\pi
558558 0 0
559559 −4.07322e6 −0.0233186
560560 3.35536e8 + 1.93722e8i 1.91062 + 1.10310i
561561 0 0
562562 −1.88787e7 3.26988e7i −0.106356 0.184214i
563563 1.00331e8 5.79262e7i 0.562225 0.324601i −0.191813 0.981431i 0.561437π-0.561437\pi
0.754038 + 0.656831i 0.228103π0.228103\pi
564564 0 0
565565 1.68565e8 2.91963e8i 0.934593 1.61876i
566566 4.38799e8i 2.42000i
567567 0 0
568568 6.75465e8 3.68602
569569 6.32337e7 + 3.65080e7i 0.343251 + 0.198176i 0.661709 0.749761i 0.269832π-0.269832\pi
−0.318458 + 0.947937i 0.603165π0.603165\pi
570570 0 0
571571 4.87571e7 + 8.44498e7i 0.261897 + 0.453618i 0.966746 0.255739i 0.0823187π-0.0823187\pi
−0.704849 + 0.709357i 0.748985π0.748985\pi
572572 −2.42688e7 + 1.40116e7i −0.129676 + 0.0748686i
573573 0 0
574574 −1.38557e8 + 2.39988e8i −0.732645 + 1.26898i
575575 3.44553e7i 0.181239i
576576 0 0
577577 8.90080e7 0.463342 0.231671 0.972794i 0.425581π-0.425581\pi
0.231671 + 0.972794i 0.425581π0.425581\pi
578578 2.64575e8 + 1.52752e8i 1.37014 + 0.791050i
579579 0 0
580580 −8.03440e7 1.39160e8i −0.411784 0.713231i
581581 −4.02905e8 + 2.32617e8i −2.05435 + 1.18608i
582582 0 0
583583 1.30353e8 2.25777e8i 0.657830 1.13940i
584584 7.63410e8i 3.83283i
585585 0 0
586586 3.32013e7 0.164992
587587 1.09392e8 + 6.31572e7i 0.540841 + 0.312255i 0.745420 0.666596i 0.232249π-0.232249\pi
−0.204579 + 0.978850i 0.565582π0.565582\pi
588588 0 0
589589 −1.47938e8 2.56236e8i −0.723992 1.25399i
590590 2.74764e8 1.58635e8i 1.33784 0.772401i
591591 0 0
592592 −5.98836e7 + 1.03721e8i −0.288631 + 0.499923i
593593 1.59275e8i 0.763805i 0.924203 + 0.381902i 0.124731π0.124731\pi
−0.924203 + 0.381902i 0.875269π0.875269\pi
594594 0 0
595595 1.11350e8 0.528615
596596 −1.90308e8 1.09874e8i −0.898912 0.518987i
597597 0 0
598598 −1.27100e7 2.20144e7i −0.0594350 0.102944i
599599 1.23461e8 7.12804e7i 0.574448 0.331658i −0.184476 0.982837i 0.559059π-0.559059\pi
0.758924 + 0.651179i 0.225725π0.225725\pi
600600 0 0
601601 5.92447e7 1.02615e8i 0.272914 0.472701i −0.696693 0.717370i 0.745346π-0.745346\pi
0.969607 + 0.244669i 0.0786792π0.0786792\pi
602602 1.73494e8i 0.795234i
603603 0 0
604604 4.93375e7 0.223906
605605 −3.42027e7 1.97469e7i −0.154452 0.0891730i
606606 0 0
607607 4.03021e7 + 6.98052e7i 0.180203 + 0.312120i 0.941949 0.335755i 0.108991π-0.108991\pi
−0.761747 + 0.647875i 0.775658π0.775658\pi
608608 1.29180e8 7.45821e7i 0.574757 0.331836i
609609 0 0
610610 −1.07648e8 + 1.86452e8i −0.474260 + 0.821443i
611611 4.55113e6i 0.0199524i
612612 0 0
613613 −2.49459e8 −1.08297 −0.541486 0.840710i 0.682138π-0.682138\pi
−0.541486 + 0.840710i 0.682138π0.682138\pi
614614 4.87683e7 + 2.81564e7i 0.210685 + 0.121639i
615615 0 0
616616 3.13755e8 + 5.43440e8i 1.34230 + 2.32493i
617617 2.98160e8 1.72143e8i 1.26939 0.732880i 0.294514 0.955647i 0.404842π-0.404842\pi
0.974872 + 0.222767i 0.0715088π0.0715088\pi
618618 0 0
619619 −2.29719e7 + 3.97886e7i −0.0968558 + 0.167759i −0.910382 0.413770i 0.864212π-0.864212\pi
0.813526 + 0.581529i 0.197545π0.197545\pi
620620 4.86011e8i 2.03925i
621621 0 0
622622 −4.25094e8 −1.76650
623623 2.87221e8 + 1.65827e8i 1.18782 + 0.685791i
624624 0 0
625625 1.42220e8 + 2.46333e8i 0.582534 + 1.00898i
626626 4.62841e8 2.67221e8i 1.88673 1.08930i
627627 0 0
628628 −3.50125e8 + 6.06434e8i −1.41366 + 2.44852i
629629 3.44207e7i 0.138315i
630630 0 0
631631 −2.71320e8 −1.07993 −0.539963 0.841689i 0.681562π-0.681562\pi
−0.539963 + 0.841689i 0.681562π0.681562\pi
632632 −4.46892e8 2.58013e8i −1.77032 1.02209i
633633 0 0
634634 2.45029e8 + 4.24403e8i 0.961502 + 1.66537i
635635 −1.83053e8 + 1.05686e8i −0.714918 + 0.412758i
636636 0 0
637637 1.25578e7 2.17507e7i 0.0485842 0.0841503i
638638 1.48900e8i 0.573366i
639639 0 0
640640 4.34402e8 1.65711
641641 −2.71512e8 1.56757e8i −1.03089 0.595187i −0.113654 0.993520i 0.536255π-0.536255\pi
−0.917241 + 0.398333i 0.869589π0.869589\pi
642642 0 0
643643 −2.97289e7 5.14920e7i −0.111827 0.193690i 0.804680 0.593709i 0.202337π-0.202337\pi
−0.916507 + 0.400019i 0.869004π0.869004\pi
644644 −6.36024e8 + 3.67209e8i −2.38131 + 1.37485i
645645 0 0
646646 1.25321e8 2.17062e8i 0.464864 0.805168i
647647 2.04779e8i 0.756089i −0.925787 0.378045i 0.876597π-0.876597\pi
0.925787 0.378045i 0.123403π-0.123403\pi
648648 0 0
649649 1.99416e8 0.729502
650650 6.78572e6 + 3.91774e6i 0.0247090 + 0.0142658i
651651 0 0
652652 −2.02903e8 3.51438e8i −0.732058 1.26796i
653653 2.94479e7 1.70017e7i 0.105758 0.0610596i −0.446188 0.894939i 0.647219π-0.647219\pi
0.551946 + 0.833880i 0.313885π0.313885\pi
654654 0 0
655655 −7.74512e7 + 1.34149e8i −0.275616 + 0.477381i
656656 2.09042e8i 0.740495i
657657 0 0
658658 −1.93850e8 −0.680438
659659 2.10570e8 + 1.21573e8i 0.735766 + 0.424795i 0.820528 0.571606i 0.193680π-0.193680\pi
−0.0847616 + 0.996401i 0.527013π0.527013\pi
660660 0 0
661661 −2.25986e8 3.91420e8i −0.782488 1.35531i −0.930488 0.366322i 0.880617π-0.880617\pi
0.148000 0.988987i 0.452717π-0.452717\pi
662662 −4.47330e8 + 2.58266e8i −1.54189 + 0.890212i
663663 0 0
664664 4.52165e8 7.83174e8i 1.54452 2.67518i
665665 7.98575e8i 2.71551i
666666 0 0
667667 9.16164e7 0.308742
668668 −5.59052e8 3.22769e8i −1.87553 1.08284i
669669 0 0
670670 3.69270e8 + 6.39595e8i 1.22778 + 2.12657i
671671 −1.17192e8 + 6.76609e7i −0.387910 + 0.223960i
672672 0 0
673673 −1.58780e8 + 2.75015e8i −0.520896 + 0.902217i 0.478809 + 0.877919i 0.341069π0.341069\pi
−0.999705 + 0.0242985i 0.992265π0.992265\pi
674674 6.39145e8i 2.08747i
675675 0 0
676676 6.47419e8 2.09578
677677 −5.80706e7 3.35271e7i −0.187150 0.108051i 0.403498 0.914981i 0.367794π-0.367794\pi
−0.590648 + 0.806930i 0.701128π0.701128\pi
678678 0 0
679679 −1.58670e8 2.74824e8i −0.506856 0.877900i
680680 −1.87446e8 + 1.08222e8i −0.596142 + 0.344183i
681681 0 0
682682 −2.25178e8 + 3.90020e8i −0.709861 + 1.22951i
683683 1.51437e8i 0.475303i 0.971350 + 0.237652i 0.0763777π0.0763777\pi
−0.971350 + 0.237652i 0.923622π0.923622\pi
684684 0 0
685685 4.40563e8 1.37068
686686 −1.86681e8 1.07780e8i −0.578265 0.333861i
687687 0 0
688688 −6.54378e7 1.13342e8i −0.200939 0.348036i
689689 3.15914e7 1.82393e7i 0.0965852 0.0557635i
690690 0 0
691691 −4.73402e7 + 8.19956e7i −0.143482 + 0.248517i −0.928805 0.370568i 0.879163π-0.879163\pi
0.785324 + 0.619085i 0.212496π0.212496\pi
692692 4.77150e8i 1.43991i
693693 0 0
694694 4.12231e8 1.23328
695695 7.93612e6 + 4.58192e6i 0.0236403 + 0.0136488i
696696 0 0
697697 −3.00390e7 5.20292e7i −0.0887131 0.153656i
698698 1.17419e8 6.77921e7i 0.345281 0.199348i
699699 0 0
700700 1.13189e8 1.96048e8i 0.329996 0.571569i
701701 7.92713e6i 0.0230124i −0.999934 0.0115062i 0.996337π-0.996337\pi
0.999934 0.0115062i 0.00366262π-0.00366262\pi
702702 0 0
703703 −2.46857e8 −0.710526
704704 1.73203e8 + 9.99988e7i 0.496407 + 0.286600i
705705 0 0
706706 2.12481e8 + 3.68028e8i 0.603817 + 1.04584i
707707 −2.77747e8 + 1.60357e8i −0.785944 + 0.453765i
708708 0 0
709709 3.32737e8 5.76317e8i 0.933603 1.61705i 0.156496 0.987679i 0.449980π-0.449980\pi
0.777107 0.629369i 0.216687π-0.216687\pi
710710 1.30841e9i 3.65569i
711711 0 0
712712 −6.44676e8 −1.78608
713713 −2.39975e8 1.38550e8i −0.662060 0.382241i
714714 0 0
715715 1.42687e7 + 2.47142e7i 0.0390362 + 0.0676127i
716716 1.00186e9 5.78424e8i 2.72940 1.57582i
717717 0 0
718718 −2.56642e8 + 4.44516e8i −0.693352 + 1.20092i
719719 4.90198e8i 1.31882i 0.751784 + 0.659409i 0.229194π0.229194\pi
−0.751784 + 0.659409i 0.770806π0.770806\pi
720720 0 0
721721 3.86434e8 1.03103
722722 9.82051e8 + 5.66987e8i 2.60929 + 1.50647i
723723 0 0
724724 1.20914e8 + 2.09429e8i 0.318610 + 0.551849i
725725 −2.44564e7 + 1.41199e7i −0.0641769 + 0.0370526i
726726 0 0
727727 1.04654e8 1.81265e8i 0.272365 0.471750i −0.697102 0.716972i 0.745528π-0.745528\pi
0.969467 + 0.245222i 0.0788609π0.0788609\pi
728728 8.78030e7i 0.227570i
729729 0 0
730730 −1.47877e9 −3.80129
731731 −3.25740e7 1.88066e7i −0.0833910 0.0481458i
732732 0 0
733733 1.83336e8 + 3.17547e8i 0.465517 + 0.806299i 0.999225 0.0393698i 0.0125350π-0.0125350\pi
−0.533708 + 0.845669i 0.679202π0.679202\pi
734734 −6.18029e8 + 3.56819e8i −1.56286 + 0.902319i
735735 0 0
736736 6.98490e7 1.20982e8i 0.175197 0.303450i
737737 4.64201e8i 1.15959i
738738 0 0
739739 −6.11387e8 −1.51490 −0.757449 0.652895i 0.773554π-0.773554\pi
−0.757449 + 0.652895i 0.773554π0.773554\pi
740740 3.51166e8 + 2.02746e8i 0.866597 + 0.500330i
741741 0 0
742742 −7.76880e8 1.34560e9i −1.90170 3.29384i
743743 −1.81962e8 + 1.05056e8i −0.443623 + 0.256126i −0.705133 0.709075i 0.749113π-0.749113\pi
0.261510 + 0.965201i 0.415779π0.415779\pi
744744 0 0
745745 −1.11891e8 + 1.93800e8i −0.270598 + 0.468690i
746746 1.33289e9i 3.21053i
747747 0 0
748748 −2.58774e8 −0.618324
749749 1.53993e8 + 8.89079e7i 0.366484 + 0.211590i
750750 0 0
751751 −2.52848e8 4.37946e8i −0.596953 1.03395i −0.993268 0.115839i 0.963044π-0.963044\pi
0.396315 0.918115i 0.370289π-0.370289\pi
752752 1.26640e8 7.31157e7i 0.297795 0.171932i
753753 0 0
754754 1.04172e7 1.80432e7i 0.0243018 0.0420919i
755755 5.02430e7i 0.116744i
756756 0 0
757757 4.19839e8 0.967822 0.483911 0.875117i 0.339216π-0.339216\pi
0.483911 + 0.875117i 0.339216π0.339216\pi
758758 −6.86819e8 3.96535e8i −1.57701 0.910487i
759759 0 0
760760 −7.76143e8 1.34432e9i −1.76808 3.06240i
761761 6.34065e8 3.66078e8i 1.43873 0.830653i 0.440971 0.897521i 0.354634π-0.354634\pi
0.997762 + 0.0668687i 0.0213009π0.0213009\pi
762762 0 0
763763 3.01675e8 5.22516e8i 0.679150 1.17632i
764764 1.36395e9i 3.05856i
765765 0 0
766766 −2.99601e8 −0.666588
767767 2.41646e7 + 1.39514e7i 0.0535542 + 0.0309195i
768768 0 0
769769 1.26647e8 + 2.19359e8i 0.278494 + 0.482366i 0.971011 0.239036i 0.0768314π-0.0768314\pi
−0.692517 + 0.721402i 0.743498π0.743498\pi
770770 1.05267e9 6.07760e8i 2.30580 1.33125i
771771 0 0
772772 −5.15923e8 + 8.93604e8i −1.12133 + 1.94220i
773773 7.82197e8i 1.69347i −0.532014 0.846735i 0.678565π-0.678565\pi
0.532014 0.846735i 0.321435π-0.321435\pi
774774 0 0
775775 8.54131e7 0.183493
776776 5.34208e8 + 3.08425e8i 1.14321 + 0.660031i
777777 0 0
778778 6.78558e8 + 1.17530e9i 1.44095 + 2.49580i
779779 3.73140e8 2.15433e8i 0.789332 0.455721i
780780 0 0
781781 4.11193e8 7.12207e8i 0.863162 1.49504i
782782 2.34736e8i 0.490861i
783783 0 0
784784 8.06983e8 1.67462
785785 6.17564e8 + 3.56550e8i 1.27665 + 0.737076i
786786 0 0
787787 −3.40918e8 5.90488e8i −0.699401 1.21140i −0.968674 0.248334i 0.920117π-0.920117\pi
0.269274 0.963064i 0.413216π-0.413216\pi
788788 −5.77775e8 + 3.33579e8i −1.18081 + 0.681742i
789789 0 0
790790 −4.99785e8 + 8.65653e8i −1.01368 + 1.75575i
791791 1.26289e9i 2.55173i
792792 0 0
793793 −1.89346e7 −0.0379696
794794 3.31865e8 + 1.91602e8i 0.662980 + 0.382771i
795795 0 0
796796 −1.32793e8 2.30003e8i −0.263290 0.456032i
797797 −4.40332e7 + 2.54226e7i −0.0869772 + 0.0502163i −0.542858 0.839825i 0.682658π-0.682658\pi
0.455881 + 0.890041i 0.349324π0.349324\pi
798798 0 0
799799 2.10132e7 3.63960e7i 0.0411957 0.0713531i
800800 4.30605e7i 0.0841026i
801801 0 0
802802 2.17108e8 0.420874
803803 −8.04936e8 4.64730e8i −1.55459 0.897541i
804804 0 0
805805 3.73948e8 + 6.47697e8i 0.716843 + 1.24161i
806806 −5.45727e7 + 3.15075e7i −0.104225 + 0.0601741i
807807 0 0
808808 3.11706e8 5.39890e8i 0.590896 1.02346i
809809 1.02851e7i 0.0194251i −0.999953 0.00971257i 0.996908π-0.996908\pi
0.999953 0.00971257i 0.00309166π-0.00309166\pi
810810 0 0
811811 4.84952e8 0.909152 0.454576 0.890708i 0.349791π-0.349791\pi
0.454576 + 0.890708i 0.349791π0.349791\pi
812812 −5.21291e8 3.00968e8i −0.973671 0.562149i
813813 0 0
814814 1.87872e8 + 3.25404e8i 0.348329 + 0.603323i
815815 −3.57888e8 + 2.06627e8i −0.661111 + 0.381693i
816816 0 0
817817 1.34877e8 2.33613e8i 0.247326 0.428382i
818818 4.60389e8i 0.841133i
819819 0 0
820820 −7.07746e8 −1.28362
821821 4.29688e8 + 2.48080e8i 0.776468 + 0.448294i 0.835177 0.549981i 0.185365π-0.185365\pi
−0.0587089 + 0.998275i 0.518698π0.518698\pi
822822 0 0
823823 1.60742e8 + 2.78412e8i 0.288356 + 0.499447i 0.973417 0.229038i 0.0735581π-0.0735581\pi
−0.685062 + 0.728485i 0.740225π0.740225\pi
824824 −6.50522e8 + 3.75579e8i −1.16273 + 0.671305i
825825 0 0
826826 5.94245e8 1.02926e9i 1.05445 1.82636i
827827 7.54902e8i 1.33467i 0.744757 + 0.667336i 0.232565π0.232565\pi
−0.744757 + 0.667336i 0.767435π0.767435\pi
828828 0 0
829829 −5.82262e8 −1.02201 −0.511004 0.859578i 0.670726π-0.670726\pi
−0.511004 + 0.859578i 0.670726π0.670726\pi
830830 −1.51705e9 8.75868e8i −2.65317 1.53181i
831831 0 0
832832 1.39921e7 + 2.42350e7i 0.0242948 + 0.0420798i
833833 2.00852e8 1.15962e8i 0.347490 0.200623i
834834 0 0
835835 −3.28693e8 + 5.69312e8i −0.564587 + 0.977893i
836836 1.85586e9i 3.17634i
837837 0 0
838838 1.25003e9 2.12416
839839 −5.75163e8 3.32071e8i −0.973879 0.562270i −0.0734627 0.997298i 0.523405π-0.523405\pi
−0.900417 + 0.435028i 0.856738π0.856738\pi
840840 0 0
841841 −2.59867e8 4.50103e8i −0.436881 0.756700i
842842 −1.16186e9 + 6.70800e8i −1.94633 + 1.12372i
843843 0 0
844844 5.59987e8 9.69926e8i 0.931431 1.61329i
845845 6.59301e8i 1.09273i
846846 0 0
847847 −1.47943e8 −0.243470
848848 1.01505e9 + 5.86042e8i 1.66457 + 0.961039i
849849 0 0
850850 3.61775e7 + 6.26612e7i 0.0589090 + 0.102033i
851851 −2.00217e8 + 1.15596e8i −0.324873 + 0.187565i
852852 0 0
853853 −3.93890e8 + 6.82237e8i −0.634640 + 1.09923i 0.351951 + 0.936018i 0.385518π0.385518\pi
−0.986591 + 0.163211i 0.947815π0.947815\pi
854854 8.06497e8i 1.29488i
855855 0 0
856856 −3.45642e8 −0.551067
857857 −8.35866e8 4.82588e8i −1.32799 0.766715i −0.343000 0.939335i 0.611443π-0.611443\pi
−0.984988 + 0.172621i 0.944776π0.944776\pi
858858 0 0
859859 2.97728e8 + 5.15681e8i 0.469722 + 0.813582i 0.999401 0.0346161i 0.0110208π-0.0110208\pi
−0.529679 + 0.848198i 0.677688π0.677688\pi
860860 −3.83736e8 + 2.21550e8i −0.603306 + 0.348319i
861861 0 0
862862 −5.68149e8 + 9.84063e8i −0.887034 + 1.53639i
863863 9.85551e8i 1.53337i −0.642024 0.766684i 0.721905π-0.721905\pi
0.642024 0.766684i 0.278095π-0.278095\pi
864864 0 0
865865 −4.85907e8 −0.750766
866866 4.28150e8 + 2.47192e8i 0.659237 + 0.380611i
867867 0 0
868868 9.10294e8 + 1.57668e9i 1.39195 + 2.41092i
869869 −5.44096e8 + 3.14134e8i −0.829117 + 0.478691i
870870 0 0
871871 −3.24761e7 + 5.62503e7i −0.0491484 + 0.0851276i
872872 1.17280e9i 1.76879i
873873 0 0
874874 1.68347e9 2.52157
875875 7.57567e8 + 4.37382e8i 1.13083 + 0.652884i
876876 0 0
877877 −1.84340e8 3.19286e8i −0.273288 0.473349i 0.696413 0.717641i 0.254778π-0.254778\pi
−0.969702 + 0.244291i 0.921445π0.921445\pi
878878 5.65631e8 3.26567e8i 0.835698 0.482491i
879879 0 0
880880 −4.58466e8 + 7.94086e8i −0.672758 + 1.16525i
881881 7.29792e8i 1.06726i −0.845717 0.533632i 0.820827π-0.820827\pi
0.845717 0.533632i 0.179173π-0.179173\pi
882882 0 0
883883 −7.12900e7 −0.103549 −0.0517746 0.998659i 0.516488π-0.516488\pi
−0.0517746 + 0.998659i 0.516488π0.516488\pi
884884 −3.13574e7 1.81042e7i −0.0453924 0.0262073i
885885 0 0
886886 −8.39516e8 1.45408e9i −1.20706 2.09068i
887887 2.73062e8 1.57653e8i 0.391283 0.225907i −0.291433 0.956591i 0.594132π-0.594132\pi
0.682716 + 0.730684i 0.260799π0.260799\pi
888888 0 0
889889 −3.95897e8 + 6.85715e8i −0.563479 + 0.975974i
890890 1.24877e9i 1.77139i
891891 0 0
892892 −1.26546e9 −1.78301
893893 2.61023e8 + 1.50702e8i 0.366543 + 0.211624i
894894 0 0
895895 −5.89039e8 1.02025e9i −0.821628 1.42310i
896896 1.40925e9 8.13632e8i 1.95914 1.13111i
897897 0 0
898898 −6.87989e8 + 1.19163e9i −0.950063 + 1.64556i
899899 2.27113e8i 0.312581i
900900 0 0
901901 3.36853e8 0.460539
902902 −5.67961e8 3.27913e8i −0.773925 0.446826i
903903 0 0
904904 1.22741e9 + 2.12594e9i 1.66144 + 2.87770i
905905 2.13272e8 1.23133e8i 0.287732 0.166122i
906906 0 0
907907 2.85210e8 4.93997e8i 0.382245 0.662068i −0.609137 0.793065i 0.708484π-0.708484\pi
0.991383 + 0.130996i 0.0418176π0.0418176\pi
908908 4.94454e8i 0.660493i
909909 0 0
910910 1.70079e8 0.225697
911911 −2.97529e8 1.71779e8i −0.393527 0.227203i 0.290160 0.956978i 0.406291π-0.406291\pi
−0.683687 + 0.729775i 0.739625π0.739625\pi
912912 0 0
913913 −5.50516e8 9.53522e8i −0.723366 1.25291i
914914 9.93984e7 5.73877e7i 0.130179 0.0751589i
915915 0 0
916916 3.36616e8 5.83036e8i 0.437974 0.758593i
917917 5.80262e8i 0.752517i
918918 0 0
919919 7.92851e8 1.02152 0.510758 0.859725i 0.329365π-0.329365\pi
0.510758 + 0.859725i 0.329365π0.329365\pi
920920 −1.25901e9 7.26888e8i −1.61683 0.933477i
921921 0 0
922922 1.09536e9 + 1.89721e9i 1.39753 + 2.42060i
923923 9.96539e7 5.75352e7i 0.126733 0.0731693i
924924 0 0
925925 3.56312e7 6.17151e7i 0.0450200 0.0779769i
926926 1.07617e9i 1.35533i
927927 0 0
928928 1.14498e8 0.143269
929929 −1.57986e8 9.12134e7i −0.197048 0.113766i 0.398230 0.917286i 0.369625π-0.369625\pi
−0.595278 + 0.803520i 0.702958π0.702958\pi
930930 0 0
931931 8.31653e8 + 1.44047e9i 1.03061 + 1.78506i
932932 5.84750e8 3.37605e8i 0.722308 0.417025i
933933 0 0
934934 1.31062e9 2.27006e9i 1.60855 2.78610i
935935 2.63523e8i 0.322392i
936936 0 0
937937 −3.34488e8 −0.406594 −0.203297 0.979117i 0.565166π-0.565166\pi
−0.203297 + 0.979117i 0.565166π0.565166\pi
938938 2.39591e9 + 1.38328e9i 2.90310 + 1.67611i
939939 0 0
940940 −2.47545e8 4.28760e8i −0.298037 0.516216i
941941 −2.52152e8 + 1.45580e8i −0.302618 + 0.174716i −0.643618 0.765347i 0.722567π-0.722567\pi
0.341001 + 0.940063i 0.389234π0.389234\pi
942942 0 0
943943 2.01761e8 3.49460e8i 0.240604 0.416738i
944944 8.96540e8i 1.06575i
945945 0 0
946946 −4.10594e8 −0.484997
947947 −1.46907e8 8.48169e7i −0.172979 0.0998694i 0.411011 0.911630i 0.365176π-0.365176\pi
−0.583990 + 0.811761i 0.698509π0.698509\pi
948948 0 0
949949 −6.50263e7 1.12629e8i −0.0760835 0.131780i
950950 −4.49391e8 + 2.59456e8i −0.524148 + 0.302617i
951951 0 0
952952 −4.05399e8 + 7.02171e8i −0.469863 + 0.813827i
953953 5.17958e8i 0.598434i 0.954185 + 0.299217i 0.0967254π0.0967254\pi
−0.954185 + 0.299217i 0.903275π0.903275\pi
954954 0 0
955955 1.38898e9 1.59473
956956 2.21049e9 + 1.27623e9i 2.52996 + 1.46068i
957957 0 0
958958 −8.73214e8 1.51245e9i −0.993171 1.72022i
959959 1.42924e9 8.25172e8i 1.62050 0.935597i
960960 0 0
961961 1.00294e8 1.73713e8i 0.113006 0.195733i
962962 5.25751e7i 0.0590548i
963963 0 0
964964 2.05806e9 2.29735
965965 9.10004e8 + 5.25391e8i 1.01266 + 0.584657i
966966 0 0
967967 6.87108e8 + 1.19011e9i 0.759881 + 1.31615i 0.942911 + 0.333046i 0.108076π0.108076\pi
−0.183029 + 0.983107i 0.558590π0.558590\pi
968968 2.49048e8 1.43788e8i 0.274572 0.158524i
969969 0 0
970970 5.97436e8 1.03479e9i 0.654600 1.13380i
971971 7.45510e8i 0.814321i 0.913357 + 0.407160i 0.133481π0.133481\pi
−0.913357 + 0.407160i 0.866519π0.866519\pi
972972 0 0
973973 3.43276e7 0.0372653
974974 −7.44334e8 4.29742e8i −0.805547 0.465083i
975975 0 0
976976 −3.04191e8 5.26875e8i −0.327188 0.566707i
977977 −8.48899e8 + 4.90112e8i −0.910274 + 0.525547i −0.880519 0.474010i 0.842806π-0.842806\pi
−0.0297550 + 0.999557i 0.509473π0.509473\pi
978978 0 0
979979 −3.92450e8 + 6.79743e8i −0.418250 + 0.724431i
980980 2.73217e9i 2.90288i
981981 0 0
982982 −9.14080e8 −0.965272
983983 −8.77524e8 5.06639e8i −0.923844 0.533381i −0.0389845 0.999240i 0.512412π-0.512412\pi
−0.884859 + 0.465858i 0.845746π0.845746\pi
984984 0 0
985985 3.39701e8 + 5.88379e8i 0.355458 + 0.615671i
986986 1.66616e8 9.61957e7i 0.173814 0.100352i
987987 0 0
988988 1.29839e8 2.24887e8i 0.134627 0.233182i
989989 2.52634e8i 0.261158i
990990 0 0
991991 −1.85231e9 −1.90324 −0.951620 0.307279i 0.900582π-0.900582\pi
−0.951620 + 0.307279i 0.900582π0.900582\pi
992992 −2.99909e8 1.73153e8i −0.307224 0.177376i
993993 0 0
994994 −2.45064e9 4.24464e9i −2.49529 4.32197i
995995 −2.34225e8 + 1.35230e8i −0.237773 + 0.137279i
996996 0 0
997997 −6.28324e8 + 1.08829e9i −0.634013 + 1.09814i 0.352710 + 0.935733i 0.385260π0.385260\pi
−0.986723 + 0.162410i 0.948073π0.948073\pi
998998 4.04941e8i 0.407380i
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 81.7.d.e.26.4 8
3.2 odd 2 inner 81.7.d.e.26.1 8
9.2 odd 6 27.7.b.c.26.4 yes 4
9.4 even 3 inner 81.7.d.e.53.1 8
9.5 odd 6 inner 81.7.d.e.53.4 8
9.7 even 3 27.7.b.c.26.1 4
36.7 odd 6 432.7.e.j.161.4 4
36.11 even 6 432.7.e.j.161.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.7.b.c.26.1 4 9.7 even 3
27.7.b.c.26.4 yes 4 9.2 odd 6
81.7.d.e.26.1 8 3.2 odd 2 inner
81.7.d.e.26.4 8 1.1 even 1 trivial
81.7.d.e.53.1 8 9.4 even 3 inner
81.7.d.e.53.4 8 9.5 odd 6 inner
432.7.e.j.161.1 4 36.11 even 6
432.7.e.j.161.4 4 36.7 odd 6