Properties

Label 54.9.f.a.11.1
Level 5454
Weight 99
Character 54.11
Analytic conductor 21.99821.998
Analytic rank 00
Dimension 144144
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(5,54)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(54, base_ring=CyclotomicField(18))
 
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("54.5");
 
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.f (of order 1818, degree 66, 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: 144144
Relative dimension: 2424 over Q(ζ18)\Q(\zeta_{18})
Twist minimal: yes
Sato-Tate group: SU(2)[C18]\mathrm{SU}(2)[C_{18}]

Embedding invariants

Embedding label 11.1
Character χ\chi == 54.11
Dual form 54.9.f.a.5.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(7.27231+8.66680i)q2+(80.61837.85385i)q3+(22.2270126.055i)q4+(208.139571.857i)q5+(654.349641.588i)q6+(808.155+4583.27i)q7+(1254.14+724.077i)q8+(6437.63+1266.33i)q9+(3442.52+5962.62i)q10+(2304.876332.57i)q11+(801.881+10336.9i)q12+(28817.9+24181.1i)q13+(33845.240335.1i)q14+(21271.1+44467.4i)q15+(15395.9+5603.66i)q16+(25788.7+14889.1i)q17+(57791.5+46584.6i)q18+(36420.763082.5i)q19+(76711.913526.4i)q20+(101148.363149.i)q21+(71644.8+26076.6i)q22+(453226.79916.0i)q23+(95419.868223.7i)q24+(15537.9+13037.9i)q25425611.iq26+(509046.152649.i)q27+595709.q28+(488689.+582397.i)q29+(230701.507733.i)q30+(266191.1.50964e6i)q31+(63398.2174185.i)q32+(136079.+528623.i)q33+(58502.5331784.i)q34+(2.45277e6+1.41611e6i)q35+(16538.4839645.i)q36+(1.42819e62.47370e6i)q37+(281861.+774407.i)q38+(2.51316e61.72311e6i)q39+(675103.566479.i)q40+(2.69268e63.20902e6i)q41+(2.41176e6+3.51756e6i)q42+(2.67475e6973529.i)q43+(747024.+431294.i)q44+(2.06408e63.41783e6i)q45+(2.60338e6+4.50919e6i)q46+(390402.68838.4i)q47+(1.28520e6330840.i)q48+(1.49361e75.43631e6i)q49+(225993.+39848.7i)q50+(2.19598e6997795.i)q51+(3.68869e6+3.09518e6i)q52+34340.3iq53+(5.02492e63.30169e6i)q544.10105e6q55+(4.33218e6+5.16289e6i)q56+(3.43162e6+4.79956e6i)q57+(1.49362e68.47075e6i)q58+(5.31298e61.45973e7i)q59+(6.07815e6+1.69296e6i)q60+(669659.+3.79782e6i)q61+(1.50196e7+8.67158e6i)q62+(1.10065e7+2.84820e7i)q63+(1.04858e6+1.81619e6i)q64+(7.82999e6+2.15127e7i)q65+(5.57108e62.66494e6i)q66+(5.68875e64.77343e6i)q67+(2.45006e6+2.91987e6i)q68+(3.71660e7+2.88312e6i)q69+(3.01104e7+1.09593e7i)q70+(2.44321e7+1.41059e7i)q71+(7.15677e6+6.24950e6i)q72+(6.47054e61.12073e7i)q73+(3.18253e7+5.61166e6i)q74+(1.15024e61.17312e6i)q75+(8.76141e63.18889e6i)q76+(3.08866e75.44614e6i)q77+(3.34268e6+3.43121e7i)q78+(5.72766e6+4.80607e6i)q79+9.97060e6iq80+(3.98395e7+1.63043e7i)q81+4.73939e7q82+(2.51217e72.99388e7i)q83+(4.80251e74.67861e6i)q84+(3.14681e6+1.78464e7i)q85+(1.10142e7+3.02613e7i)q86+(4.39714e74.31138e7i)q87+(1.69465e69.61082e6i)q88+(2.94822e71.70215e7i)q89+(1.46110e7+4.27445e7i)q90+(8.75391e71.51622e8i)q91+(2.01477e75.53553e7i)q92+(9.60337e6+1.23796e8i)q93+(3.43573e62.88292e6i)q94+(2.84936e73.39573e7i)q95+(6.47908e6+1.35446e7i)q96+(1.27634e8+4.64551e7i)q97+(1.55736e88.99140e7i)q98+(6.81877e64.36855e7i)q99+O(q100)q+(-7.27231 + 8.66680i) q^{2} +(-80.6183 - 7.85385i) q^{3} +(-22.2270 - 126.055i) q^{4} +(208.139 - 571.857i) q^{5} +(654.349 - 641.588i) q^{6} +(-808.155 + 4583.27i) q^{7} +(1254.14 + 724.077i) q^{8} +(6437.63 + 1266.33i) q^{9} +(3442.52 + 5962.62i) q^{10} +(-2304.87 - 6332.57i) q^{11} +(801.881 + 10336.9i) q^{12} +(-28817.9 + 24181.1i) q^{13} +(-33845.2 - 40335.1i) q^{14} +(-21271.1 + 44467.4i) q^{15} +(-15395.9 + 5603.66i) q^{16} +(-25788.7 + 14889.1i) q^{17} +(-57791.5 + 46584.6i) q^{18} +(36420.7 - 63082.5i) q^{19} +(-76711.9 - 13526.4i) q^{20} +(101148. - 363149. i) q^{21} +(71644.8 + 26076.6i) q^{22} +(453226. - 79916.0i) q^{23} +(-95419.8 - 68223.7i) q^{24} +(15537.9 + 13037.9i) q^{25} -425611. i q^{26} +(-509046. - 152649. i) q^{27} +595709. q^{28} +(-488689. + 582397. i) q^{29} +(-230701. - 507733. i) q^{30} +(-266191. - 1.50964e6i) q^{31} +(63398.2 - 174185. i) q^{32} +(136079. + 528623. i) q^{33} +(58502.5 - 331784. i) q^{34} +(2.45277e6 + 1.41611e6i) q^{35} +(16538.4 - 839645. i) q^{36} +(-1.42819e6 - 2.47370e6i) q^{37} +(281861. + 774407. i) q^{38} +(2.51316e6 - 1.72311e6i) q^{39} +(675103. - 566479. i) q^{40} +(-2.69268e6 - 3.20902e6i) q^{41} +(2.41176e6 + 3.51756e6i) q^{42} +(2.67475e6 - 973529. i) q^{43} +(-747024. + 431294. i) q^{44} +(2.06408e6 - 3.41783e6i) q^{45} +(-2.60338e6 + 4.50919e6i) q^{46} +(-390402. - 68838.4i) q^{47} +(1.28520e6 - 330840. i) q^{48} +(-1.49361e7 - 5.43631e6i) q^{49} +(-225993. + 39848.7i) q^{50} +(2.19598e6 - 997795. i) q^{51} +(3.68869e6 + 3.09518e6i) q^{52} +34340.3i q^{53} +(5.02492e6 - 3.30169e6i) q^{54} -4.10105e6 q^{55} +(-4.33218e6 + 5.16289e6i) q^{56} +(-3.43162e6 + 4.79956e6i) q^{57} +(-1.49362e6 - 8.47075e6i) q^{58} +(5.31298e6 - 1.45973e7i) q^{59} +(6.07815e6 + 1.69296e6i) q^{60} +(-669659. + 3.79782e6i) q^{61} +(1.50196e7 + 8.67158e6i) q^{62} +(-1.10065e7 + 2.84820e7i) q^{63} +(1.04858e6 + 1.81619e6i) q^{64} +(7.82999e6 + 2.15127e7i) q^{65} +(-5.57108e6 - 2.66494e6i) q^{66} +(5.68875e6 - 4.77343e6i) q^{67} +(2.45006e6 + 2.91987e6i) q^{68} +(-3.71660e7 + 2.88312e6i) q^{69} +(-3.01104e7 + 1.09593e7i) q^{70} +(-2.44321e7 + 1.41059e7i) q^{71} +(7.15677e6 + 6.24950e6i) q^{72} +(6.47054e6 - 1.12073e7i) q^{73} +(3.18253e7 + 5.61166e6i) q^{74} +(-1.15024e6 - 1.17312e6i) q^{75} +(-8.76141e6 - 3.18889e6i) q^{76} +(3.08866e7 - 5.44614e6i) q^{77} +(-3.34268e6 + 3.43121e7i) q^{78} +(5.72766e6 + 4.80607e6i) q^{79} +9.97060e6i q^{80} +(3.98395e7 + 1.63043e7i) q^{81} +4.73939e7 q^{82} +(2.51217e7 - 2.99388e7i) q^{83} +(-4.80251e7 - 4.67861e6i) q^{84} +(3.14681e6 + 1.78464e7i) q^{85} +(-1.10142e7 + 3.02613e7i) q^{86} +(4.39714e7 - 4.31138e7i) q^{87} +(1.69465e6 - 9.61082e6i) q^{88} +(-2.94822e7 - 1.70215e7i) q^{89} +(1.46110e7 + 4.27445e7i) q^{90} +(-8.75391e7 - 1.51622e8i) q^{91} +(-2.01477e7 - 5.53553e7i) q^{92} +(9.60337e6 + 1.23796e8i) q^{93} +(3.43573e6 - 2.88292e6i) q^{94} +(-2.84936e7 - 3.39573e7i) q^{95} +(-6.47908e6 + 1.35446e7i) q^{96} +(-1.27634e8 + 4.64551e7i) q^{97} +(1.55736e8 - 8.99140e7i) q^{98} +(-6.81877e6 - 4.36855e7i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 144q+882q5+768q6+25908q945756q1121504q12+94464q1470002q15182784q18225792q202071668q21+185472q22+552996q231015182q25++26756370q99+O(q100) 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25}+ \cdots + 26756370 q^{99}+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(1318)e\left(\frac{13}{18}\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 −7.27231 + 8.66680i −0.454519 + 0.541675i
33 −80.6183 7.85385i −0.995288 0.0969611i
44 −22.2270 126.055i −0.0868241 0.492404i
55 208.139 571.857i 0.333022 0.914971i −0.654299 0.756236i 0.727036π-0.727036\pi
0.987321 0.158735i 0.0507415π-0.0507415\pi
66 654.349 641.588i 0.504899 0.495052i
77 −808.155 + 4583.27i −0.336591 + 1.90890i 0.0743355 + 0.997233i 0.476316π0.476316\pi
−0.410926 + 0.911669i 0.634795π0.634795\pi
88 1254.14 + 724.077i 0.306186 + 0.176777i
99 6437.63 + 1266.33i 0.981197 + 0.193008i
1010 3442.52 + 5962.62i 0.344252 + 0.596262i
1111 −2304.87 6332.57i −0.157425 0.432523i 0.835756 0.549101i 0.185030π-0.185030\pi
−0.993182 + 0.116578i 0.962807π0.962807\pi
1212 801.881 + 10336.9i 0.0386710 + 0.498502i
1313 −28817.9 + 24181.1i −1.00899 + 0.846646i −0.988205 0.153137i 0.951062π-0.951062\pi
−0.0207890 + 0.999784i 0.506618π0.506618\pi
1414 −33845.2 40335.1i −0.881018 1.04996i
1515 −21271.1 + 44467.4i −0.420169 + 0.878369i
1616 −15395.9 + 5603.66i −0.234923 + 0.0855050i
1717 −25788.7 + 14889.1i −0.308769 + 0.178268i −0.646376 0.763019i 0.723716π-0.723716\pi
0.337606 + 0.941287i 0.390383π0.390383\pi
1818 −57791.5 + 46584.6i −0.550521 + 0.443764i
1919 36420.7 63082.5i 0.279469 0.484055i −0.691784 0.722105i 0.743175π-0.743175\pi
0.971253 + 0.238050i 0.0765082π0.0765082\pi
2020 −76711.9 13526.4i −0.479449 0.0845399i
2121 101148. 363149.i 0.520094 1.86727i
2222 71644.8 + 26076.6i 0.305840 + 0.111317i
2323 453226. 79916.0i 1.61958 0.285576i 0.710973 0.703220i 0.248255π-0.248255\pi
0.908611 + 0.417643i 0.137144π0.137144\pi
2424 −95419.8 68223.7i −0.287603 0.205632i
2525 15537.9 + 13037.9i 0.0397771 + 0.0333769i
2626 425611.i 0.931364i
2727 −509046. 152649.i −0.957860 0.287237i
2828 595709. 0.969175
2929 −488689. + 582397.i −0.690941 + 0.823432i −0.991469 0.130341i 0.958393π-0.958393\pi
0.300528 + 0.953773i 0.402837π0.402837\pi
3030 −230701. 507733.i −0.284816 0.626831i
3131 −266191. 1.50964e6i −0.288235 1.63466i −0.693496 0.720461i 0.743930π-0.743930\pi
0.405261 0.914201i 0.367181π-0.367181\pi
3232 63398.2 174185.i 0.0604612 0.166116i
3333 136079. + 528623.i 0.114746 + 0.445749i
3434 58502.5 331784.i 0.0437783 0.248279i
3535 2.45277e6 + 1.41611e6i 1.63450 + 0.943677i
3636 16538.4 839645.i 0.00984656 0.499903i
3737 −1.42819e6 2.47370e6i −0.762042 1.31990i −0.941796 0.336184i 0.890863π-0.890863\pi
0.179754 0.983712i 0.442470π-0.442470\pi
3838 281861. + 774407.i 0.135176 + 0.371394i
3939 2.51316e6 1.72311e6i 1.08633 0.744824i
4040 675103. 566479.i 0.263712 0.221281i
4141 −2.69268e6 3.20902e6i −0.952906 1.13563i −0.990662 0.136342i 0.956465π-0.956465\pi
0.0377562 0.999287i 0.487979π-0.487979\pi
4242 2.41176e6 + 3.51756e6i 0.775062 + 1.13043i
4343 2.67475e6 973529.i 0.782365 0.284757i 0.0802063 0.996778i 0.474442π-0.474442\pi
0.702158 + 0.712021i 0.252220π0.252220\pi
4444 −747024. + 431294.i −0.199308 + 0.115070i
4545 2.06408e6 3.41783e6i 0.503357 0.833490i
4646 −2.60338e6 + 4.50919e6i −0.581443 + 1.00709i
4747 −390402. 68838.4i −0.0800056 0.0141072i 0.133502 0.991049i 0.457378π-0.457378\pi
−0.213508 + 0.976941i 0.568489π0.568489\pi
4848 1.28520e6 330840.i 0.242107 0.0623237i
4949 −1.49361e7 5.43631e6i −2.59092 0.943018i
5050 −225993. + 39848.7i −0.0361589 + 0.00637579i
5151 2.19598e6 997795.i 0.324599 0.147489i
5252 3.68869e6 + 3.09518e6i 0.504497 + 0.423323i
5353 34340.3i 0.00435212i 0.999998 + 0.00217606i 0.000692662π0.000692662\pi
−0.999998 + 0.00217606i 0.999307π0.999307\pi
5454 5.02492e6 3.30169e6i 0.590955 0.388294i
5555 −4.10105e6 −0.448172
5656 −4.33218e6 + 5.16289e6i −0.440509 + 0.524978i
5757 −3.43162e6 + 4.79956e6i −0.325087 + 0.454676i
5858 −1.49362e6 8.47075e6i −0.131986 0.748531i
5959 5.31298e6 1.45973e7i 0.438460 1.20466i −0.502034 0.864848i 0.667415π-0.667415\pi
0.940494 0.339811i 0.110363π-0.110363\pi
6060 6.07815e6 + 1.69296e6i 0.468993 + 0.130629i
6161 −669659. + 3.79782e6i −0.0483653 + 0.274293i −0.999394 0.0348094i 0.988918π-0.988918\pi
0.951029 + 0.309103i 0.100029π0.100029\pi
6262 1.50196e7 + 8.67158e6i 1.01646 + 0.586856i
6363 −1.10065e7 + 2.84820e7i −0.698696 + 1.80804i
6464 1.04858e6 + 1.81619e6i 0.0625000 + 0.108253i
6565 7.82999e6 + 2.15127e7i 0.438639 + 1.20515i
6666 −5.57108e6 2.66494e6i −0.293605 0.140447i
6767 5.68875e6 4.77343e6i 0.282304 0.236882i −0.490629 0.871368i 0.663233π-0.663233\pi
0.772934 + 0.634487i 0.218789π0.218789\pi
6868 2.45006e6 + 2.91987e6i 0.114588 + 0.136561i
6969 −3.71660e7 + 2.88312e6i −1.63964 + 0.127194i
7070 −3.01104e7 + 1.09593e7i −1.25408 + 0.456447i
7171 −2.44321e7 + 1.41059e7i −0.961452 + 0.555094i −0.896620 0.442802i 0.853985π-0.853985\pi
−0.0648322 + 0.997896i 0.520651π0.520651\pi
7272 7.15677e6 + 6.24950e6i 0.266310 + 0.232549i
7373 6.47054e6 1.12073e7i 0.227850 0.394648i −0.729321 0.684172i 0.760164π-0.760164\pi
0.957171 + 0.289524i 0.0934970π0.0934970\pi
7474 3.18253e7 + 5.61166e6i 1.06132 + 0.187139i
7575 −1.15024e6 1.17312e6i −0.0363534 0.0370765i
7676 −8.76141e6 3.18889e6i −0.262615 0.0955841i
7777 3.08866e7 5.44614e6i 0.878631 0.154926i
7878 −3.34268e6 + 3.43121e7i −0.0903061 + 0.926976i
7979 5.72766e6 + 4.80607e6i 0.147051 + 0.123391i 0.713346 0.700812i 0.247179π-0.247179\pi
−0.566294 + 0.824203i 0.691623π0.691623\pi
8080 9.97060e6i 0.243423i
8181 3.98395e7 + 1.63043e7i 0.925495 + 0.378759i
8282 4.73939e7 1.04826
8383 2.51217e7 2.99388e7i 0.529341 0.630844i −0.433422 0.901191i 0.642694π-0.642694\pi
0.962763 + 0.270347i 0.0871384π0.0871384\pi
8484 −4.80251e7 4.67861e6i −0.964608 0.0939722i
8585 3.14681e6 + 1.78464e7i 0.0602830 + 0.341882i
8686 −1.10142e7 + 3.02613e7i −0.201354 + 0.553215i
8787 4.39714e7 4.31138e7i 0.767526 0.752557i
8888 1.69465e6 9.61082e6i 0.0282585 0.160262i
8989 −2.94822e7 1.70215e7i −0.469894 0.271293i 0.246301 0.969193i 0.420785π-0.420785\pi
−0.716195 + 0.697900i 0.754118π0.754118\pi
9090 1.46110e7 + 4.27445e7i 0.222695 + 0.651494i
9191 −8.75391e7 1.51622e8i −1.27655 2.21104i
9292 −2.01477e7 5.53553e7i −0.281238 0.772694i
9393 9.60337e6 + 1.23796e8i 0.128378 + 1.65491i
9494 3.43573e6 2.88292e6i 0.0440056 0.0369251i
9595 −2.84936e7 3.39573e7i −0.349826 0.416907i
9696 −6.47908e6 + 1.35446e7i −0.0762831 + 0.159471i
9797 −1.27634e8 + 4.64551e7i −1.44172 + 0.524743i −0.940266 0.340441i 0.889424π-0.889424\pi
−0.501454 + 0.865184i 0.667201π0.667201\pi
9898 1.55736e8 8.99140e7i 1.68843 0.974817i
9999 −6.81877e6 4.36855e7i −0.0709848 0.454775i
100100 1.29813e6 2.24843e6i 0.0129813 0.0224843i
101101 1.52432e8 + 2.68778e7i 1.46484 + 0.258291i 0.848503 0.529191i 0.177505π-0.177505\pi
0.616337 + 0.787482i 0.288616π0.288616\pi
102102 −7.32215e6 + 2.62884e7i −0.0676454 + 0.242864i
103103 8.46933e6 + 3.08258e6i 0.0752489 + 0.0273884i 0.379370 0.925245i 0.376141π-0.376141\pi
−0.304121 + 0.952633i 0.598363π0.598363\pi
104104 −5.36506e7 + 9.46004e6i −0.458607 + 0.0808649i
105105 −1.86616e8 1.33428e8i −1.53530 1.09771i
106106 −297621. 249734.i −0.00235744 0.00197812i
107107 1.30990e7i 0.0999319i −0.998751 0.0499659i 0.984089π-0.984089\pi
0.998751 0.0499659i 0.0159113π-0.0159113\pi
108108 −7.92775e6 + 6.75609e7i −0.0582713 + 0.496593i
109109 −3.69259e7 −0.261592 −0.130796 0.991409i 0.541753π-0.541753\pi
−0.130796 + 0.991409i 0.541753π0.541753\pi
110110 2.98241e7 3.55430e7i 0.203703 0.242764i
111111 9.57103e7 + 2.10642e8i 0.630473 + 1.38757i
112112 −1.32408e7 7.50923e7i −0.0841477 0.477225i
113113 1.96169e7 5.38970e7i 0.120314 0.330561i −0.864886 0.501968i 0.832609π-0.832609\pi
0.985200 + 0.171408i 0.0548316π0.0548316\pi
114114 −1.66411e7 6.46451e7i −0.0985286 0.382751i
115115 4.86334e7 2.75814e8i 0.278063 1.57697i
116116 8.42764e7 + 4.86570e7i 0.465451 + 0.268728i
117117 −2.16140e8 + 1.19176e8i −1.15343 + 0.635983i
118118 8.78742e7 + 1.52203e8i 0.453245 + 0.785044i
119119 −4.73996e7 1.30229e8i −0.236367 0.649413i
120120 −5.88747e7 + 4.03664e7i −0.283925 + 0.194668i
121121 1.29419e8 1.08596e8i 0.603751 0.506607i
122122 −2.80450e7 3.34228e7i −0.126595 0.150870i
123123 1.91877e8 + 2.79853e8i 0.838304 + 1.22267i
124124 −1.84382e8 + 6.71096e7i −0.779888 + 0.283856i
125125 2.16559e8 1.25031e8i 0.887027 0.512125i
126126 −1.66805e8 3.02522e8i −0.661802 1.20026i
127127 7.79555e7 1.35023e8i 0.299662 0.519030i −0.676396 0.736538i 0.736459π-0.736459\pi
0.976059 + 0.217508i 0.0697927π0.0697927\pi
128128 −2.33661e7 4.12008e6i −0.0870455 0.0153485i
129129 −2.23280e8 + 5.74772e7i −0.806289 + 0.207557i
130130 −2.43389e8 8.85862e7i −0.852171 0.310165i
131131 2.07082e8 3.65141e7i 0.703164 0.123987i 0.189377 0.981904i 0.439353π-0.439353\pi
0.513787 + 0.857918i 0.328242π0.328242\pi
132132 6.36112e7 2.89032e7i 0.209526 0.0952030i
133133 2.59691e8 + 2.17906e8i 0.829946 + 0.696408i
134134 8.40171e7i 0.260585i
135135 −1.93246e8 + 2.59329e8i −0.581802 + 0.780757i
136136 −4.31235e7 −0.126054
137137 1.86230e8 2.21940e8i 0.528649 0.630019i −0.433954 0.900935i 0.642882π-0.642882\pi
0.962603 + 0.270916i 0.0873265π0.0873265\pi
138138 2.45295e8 3.43077e8i 0.676352 0.945966i
139139 −5.40792e7 3.06699e8i −0.144868 0.821585i −0.967473 0.252973i 0.918592π-0.918592\pi
0.822606 0.568612i 0.192519π-0.192519\pi
140140 1.23990e8 3.40660e8i 0.322757 0.886766i
141141 3.09329e7 + 8.61580e6i 0.0782608 + 0.0217981i
142142 5.54250e7 3.14331e8i 0.136318 0.773096i
143143 2.19550e8 + 1.26757e8i 0.525035 + 0.303129i
144144 −1.06209e8 + 1.65780e7i −0.247009 + 0.0385551i
145145 2.31333e8 + 4.00680e8i 0.523317 + 0.906412i
146146 5.00757e7 + 1.37582e8i 0.110209 + 0.302796i
147147 1.16143e9 + 5.55572e8i 2.48728 + 1.18979i
148148 −2.80079e8 + 2.35014e8i −0.583758 + 0.489831i
149149 −1.85737e8 2.21353e8i −0.376838 0.449098i 0.543976 0.839101i 0.316918π-0.316918\pi
−0.920813 + 0.390003i 0.872474π0.872474\pi
150150 1.85322e7 1.43762e6i 0.0366067 0.00283974i
151151 −8.24893e8 + 3.00236e8i −1.58668 + 0.577505i −0.976643 0.214868i 0.931068π-0.931068\pi
−0.610038 + 0.792372i 0.708846π0.708846\pi
152152 9.13532e7 5.27428e7i 0.171139 0.0988073i
153153 −1.84873e8 + 6.31937e7i −0.337371 + 0.115321i
154154 −1.77416e8 + 3.07294e8i −0.315435 + 0.546350i
155155 −9.18705e8 1.61992e8i −1.59166 0.280652i
156156 −2.73067e8 2.78498e8i −0.461074 0.470245i
157157 −4.67660e8 1.70214e8i −0.769717 0.280154i −0.0728391 0.997344i 0.523206π-0.523206\pi
−0.696878 + 0.717190i 0.745428π0.745428\pi
158158 −8.33066e7 + 1.46892e7i −0.133675 + 0.0235706i
159159 269704. 2.76846e6i 0.000421986 0.00433161i
160160 −8.64132e7 7.25093e7i −0.131856 0.110640i
161161 2.14184e9i 3.18775i
162162 −4.31032e8 + 2.26711e8i −0.625820 + 0.329165i
163163 6.53890e8 0.926306 0.463153 0.886278i 0.346718π-0.346718\pi
0.463153 + 0.886278i 0.346718π0.346718\pi
164164 −3.44664e8 + 4.10754e8i −0.476453 + 0.567814i
165165 3.30620e8 + 3.22090e7i 0.446060 + 0.0434552i
166166 7.67814e7 + 4.35449e8i 0.101117 + 0.573462i
167167 −4.24548e8 + 1.16644e9i −0.545834 + 1.49967i 0.293450 + 0.955974i 0.405196π0.405196\pi
−0.839284 + 0.543693i 0.817026π0.817026\pi
168168 3.89802e8 3.82200e8i 0.489336 0.479792i
169169 1.04096e8 5.90356e8i 0.127610 0.723714i
170170 −1.77556e8 1.02512e8i −0.212589 0.122738i
171171 3.14346e8 3.59982e8i 0.367641 0.421013i
172172 −1.82170e8 3.15528e8i −0.208144 0.360516i
173173 1.56927e8 + 4.31152e8i 0.175191 + 0.481334i 0.995947 0.0899458i 0.0286694π-0.0286694\pi
−0.820755 + 0.571280i 0.806447π0.806447\pi
174174 5.38853e7 + 6.94629e8i 0.0587860 + 0.757802i
175175 −7.23131e7 + 6.06779e7i −0.0771019 + 0.0646962i
176176 7.09711e7 + 8.45800e7i 0.0739658 + 0.0881490i
177177 −5.42968e8 + 1.13508e9i −0.553199 + 1.15647i
178178 3.61926e8 1.31730e8i 0.360529 0.131222i
179179 3.92103e8 2.26381e8i 0.381933 0.220509i −0.296726 0.954963i 0.595895π-0.595895\pi
0.678659 + 0.734453i 0.262561π0.262561\pi
180180 −4.76714e8 1.84220e8i −0.454117 0.175488i
181181 6.48174e8 1.12267e9i 0.603917 1.04602i −0.388304 0.921531i 0.626939π-0.626939\pi
0.992222 0.124484i 0.0397276π-0.0397276\pi
182182 1.95069e9 + 3.43960e8i 1.77788 + 0.313489i
183183 8.38143e7 3.00915e8i 0.0747332 0.268311i
184184 6.26274e8 + 2.27945e8i 0.546377 + 0.198865i
185185 −1.71186e9 + 3.01847e8i −1.46144 + 0.257692i
186186 −1.14275e9 8.17050e8i −0.954773 0.682648i
187187 1.53726e8 + 1.28991e8i 0.125713 + 0.105486i
188188 5.07423e7i 0.0406199i
189189 1.11102e9 2.20973e9i 0.870714 1.73178i
190190 5.01516e8 0.384831
191191 1.23458e8 1.47132e8i 0.0927655 0.110554i −0.717665 0.696389i 0.754789π-0.754789\pi
0.810430 + 0.585835i 0.199233π0.199233\pi
192192 −7.02704e7 1.54653e8i −0.0517092 0.113803i
193193 2.02415e7 + 1.14795e8i 0.0145886 + 0.0827361i 0.991233 0.132127i 0.0421806π-0.0421806\pi
−0.976644 + 0.214863i 0.931070π0.931070\pi
194194 5.25580e8 1.44402e9i 0.371049 1.01945i
195195 −4.62283e8 1.79581e9i −0.319720 1.24200i
196196 −3.53291e8 + 2.00361e9i −0.239391 + 1.35766i
197197 −1.96751e9 1.13594e9i −1.30633 0.754208i −0.324845 0.945767i 0.605312π-0.605312\pi
−0.981481 + 0.191559i 0.938646π0.938646\pi
198198 4.28202e8 + 2.58597e8i 0.278604 + 0.168253i
199199 −2.53993e8 4.39928e8i −0.161960 0.280524i 0.773611 0.633660i 0.218448π-0.218448\pi
−0.935572 + 0.353137i 0.885115π0.885115\pi
200200 1.00463e7 + 2.76019e7i 0.00627893 + 0.0172512i
201201 −4.96107e8 + 3.40147e8i −0.303943 + 0.208393i
202202 −1.34148e9 + 1.12563e9i −0.805708 + 0.676069i
203203 −2.27435e9 2.71046e9i −1.33929 1.59610i
204204 −1.74587e8 2.54637e8i −0.100807 0.147028i
205205 −2.39555e9 + 8.71908e8i −1.35641 + 0.493691i
206206 −8.83078e7 + 5.09845e7i −0.0490377 + 0.0283119i
207207 3.01890e9 + 5.94631e7i 1.64425 + 0.0323867i
208208 3.08175e8 5.33775e8i 0.164644 0.285171i
209209 −4.83419e8 8.52398e7i −0.253360 0.0446743i
210210 2.51352e9 6.47037e8i 1.29243 0.332699i
211211 1.98173e9 + 7.21292e8i 0.999806 + 0.363900i 0.789510 0.613738i 0.210335π-0.210335\pi
0.210296 + 0.977638i 0.432557π0.432557\pi
212212 4.32878e6 763281.i 0.00214300 0.000377869i
213213 2.08046e9 9.45307e8i 1.01074 0.459256i
214214 1.13527e8 + 9.52602e7i 0.0541306 + 0.0454210i
215215 1.73220e9i 0.810671i
216216 −5.27884e8 5.60032e8i −0.242507 0.257275i
217217 7.13424e9 3.21743
218218 2.68537e8 3.20030e8i 0.118899 0.141698i
219219 −6.09665e8 + 8.52696e8i −0.265042 + 0.370696i
220220 9.11539e7 + 5.16960e8i 0.0389121 + 0.220681i
221221 3.83141e8 1.05267e9i 0.160616 0.441290i
222222 −2.52163e9 7.02354e8i −1.03817 0.289164i
223223 −1.07941e8 + 6.12162e8i −0.0436481 + 0.247541i −0.998823 0.0485009i 0.984556π-0.984556\pi
0.955175 + 0.296042i 0.0956667π0.0956667\pi
224224 7.47102e8 + 4.31339e8i 0.296748 + 0.171328i
225225 8.35172e7 + 1.03609e8i 0.0325871 + 0.0404267i
226226 3.24455e8 + 5.61972e8i 0.124371 + 0.215417i
227227 −5.66505e8 1.55646e9i −0.213354 0.586184i 0.786138 0.618050i 0.212077π-0.212077\pi
−0.999492 + 0.0318660i 0.989855π0.989855\pi
228228 6.81285e8 + 3.25894e8i 0.252110 + 0.120597i
229229 1.41138e8 1.18429e8i 0.0513217 0.0430640i −0.616766 0.787147i 0.711558π-0.711558\pi
0.668088 + 0.744083i 0.267113π0.267113\pi
230230 2.03675e9 + 2.42730e9i 0.727823 + 0.867386i
231231 −2.53280e9 + 1.96480e8i −0.889513 + 0.0690034i
232232 −1.03459e9 + 3.76558e8i −0.357120 + 0.129981i
233233 −1.64102e9 + 9.47443e8i −0.556788 + 0.321462i −0.751855 0.659328i 0.770841π-0.770841\pi
0.195067 + 0.980790i 0.437508π0.437508\pi
234234 5.38963e8 2.73993e9i 0.179761 0.913852i
235235 −1.20623e8 + 2.08926e8i −0.0395513 + 0.0685048i
236236 −1.95816e9 3.45276e8i −0.631248 0.111306i
237237 −4.24008e8 4.32442e8i −0.134394 0.137067i
238238 1.47338e9 + 5.36266e8i 0.459205 + 0.167137i
239239 6.53182e7 1.15174e7i 0.0200190 0.00352989i −0.163630 0.986522i 0.552320π-0.552320\pi
0.183649 + 0.982992i 0.441209π0.441209\pi
240240 7.83076e7 8.03813e8i 0.0236025 0.242276i
241241 −3.35963e9 2.81906e9i −0.995917 0.835674i −0.00950371 0.999955i 0.503025π-0.503025\pi
−0.986414 + 0.164281i 0.947470π0.947470\pi
242242 1.91140e9i 0.557300i
243243 −3.08375e9 1.62732e9i −0.884410 0.466711i
244244 4.93621e8 0.139262
245245 −6.21758e9 + 7.40982e9i −1.72567 + 2.05657i
246246 −3.82082e9 3.72225e8i −1.04332 0.101640i
247247 4.75835e8 + 2.69860e9i 0.127841 + 0.725020i
248248 7.59259e8 2.08605e9i 0.200717 0.551464i
249249 −2.26040e9 + 2.21632e9i −0.588015 + 0.576547i
250250 −4.91271e8 + 2.78614e9i −0.125765 + 0.713251i
251251 5.21406e9 + 3.01034e9i 1.31366 + 0.758439i 0.982699 0.185207i 0.0592956π-0.0592956\pi
0.330956 + 0.943646i 0.392629π0.392629\pi
252252 3.83496e9 + 7.54363e8i 0.950952 + 0.187059i
253253 −1.55070e9 2.68589e9i −0.378482 0.655550i
254254 6.03300e8 + 1.65755e9i 0.144943 + 0.398229i
255255 −1.13527e8 1.46347e9i −0.0268497 0.346116i
256256 2.05633e8 1.72547e8i 0.0478778 0.0401742i
257257 −5.51616e9 6.57390e9i −1.26446 1.50692i −0.770505 0.637434i 0.779996π-0.779996\pi
−0.493953 0.869489i 0.664448π-0.664448\pi
258258 1.12562e9 2.35311e9i 0.254046 0.531085i
259259 1.24918e10 4.54665e9i 2.77605 1.01040i
260260 2.53776e9 1.46517e9i 0.555337 0.320624i
261261 −3.88351e9 + 3.13042e9i −0.836879 + 0.674591i
262262 −1.18950e9 + 2.06028e9i −0.252441 + 0.437241i
263263 −3.56775e9 6.29090e8i −0.745712 0.131489i −0.212135 0.977240i 0.568042π-0.568042\pi
−0.533577 + 0.845751i 0.679153π0.679153\pi
264264 −2.12101e8 + 7.61499e8i −0.0436644 + 0.156767i
265265 1.96377e7 + 7.14755e6i 0.00398206 + 0.00144935i
266266 −3.77711e9 + 6.66006e8i −0.754454 + 0.133031i
267267 2.24312e9 + 1.60380e9i 0.441375 + 0.315576i
268268 −7.28160e8 6.10999e8i −0.141152 0.118441i
269269 2.99749e9i 0.572465i 0.958160 + 0.286233i 0.0924030π0.0924030\pi
−0.958160 + 0.286233i 0.907597π0.907597\pi
270270 −8.42209e8 3.56074e9i −0.158477 0.670017i
271271 −4.06312e9 −0.753325 −0.376663 0.926351i 0.622928π-0.622928\pi
−0.376663 + 0.926351i 0.622928π0.622928\pi
272272 3.13607e8 3.73743e8i 0.0572942 0.0682806i
273273 5.86644e9 + 1.29111e10i 1.05615 + 2.32440i
274274 5.69190e8 + 3.22804e9i 0.100985 + 0.572712i
275275 4.67503e7 1.28445e8i 0.00817436 0.0224589i
276276 1.18952e9 + 4.62089e9i 0.204991 + 0.796323i
277277 5.01418e8 2.84368e9i 0.0851689 0.483017i −0.912151 0.409854i 0.865580π-0.865580\pi
0.997320 0.0731627i 0.0233092π-0.0233092\pi
278278 3.05138e9 + 1.76171e9i 0.510877 + 0.294955i
279279 1.98065e8 1.00556e10i 0.0326882 1.65956i
280280 2.05074e9 + 3.55199e9i 0.333640 + 0.577882i
281281 1.18431e9 + 3.25387e9i 0.189951 + 0.521885i 0.997711 0.0676261i 0.0215425π-0.0215425\pi
−0.807760 + 0.589512i 0.799320π0.799320\pi
282282 −2.99625e8 + 2.05433e8i −0.0473786 + 0.0324843i
283283 −5.07471e9 + 4.25819e9i −0.791163 + 0.663864i −0.946033 0.324070i 0.894949π-0.894949\pi
0.154870 + 0.987935i 0.450504π0.450504\pi
284284 2.32117e9 + 2.76627e9i 0.356808 + 0.425227i
285285 2.03041e9 + 2.96137e9i 0.307754 + 0.448862i
286286 −2.69521e9 + 9.80976e8i −0.402836 + 0.146620i
287287 1.68839e10 9.74792e9i 2.48854 1.43676i
288288 6.28710e8 1.04106e9i 0.0913861 0.151323i
289289 −3.04451e9 + 5.27324e9i −0.436441 + 0.755938i
290290 −5.15494e9 9.08954e8i −0.728838 0.128514i
291291 1.06545e10 2.74271e9i 1.48581 0.382480i
292292 −1.55656e9 5.66542e8i −0.214109 0.0779293i
293293 2.26858e9 4.00012e8i 0.307811 0.0542753i −0.0176092 0.999845i 0.505605π-0.505605\pi
0.325420 + 0.945570i 0.394494π0.394494\pi
294294 −1.32613e10 + 6.02560e9i −1.77500 + 0.806512i
295295 −7.24172e9 6.07652e9i −0.956211 0.802356i
296296 4.13648e9i 0.538845i
297297 2.06619e8 + 3.57540e9i 0.0265549 + 0.459514i
298298 3.26916e9 0.414545
299299 −1.11286e10 + 1.32625e10i −1.39237 + 1.65936i
300300 −1.22312e8 + 1.71069e8i −0.0151003 + 0.0211197i
301301 2.30034e9 + 1.30459e10i 0.280237 + 1.58930i
302302 3.39679e9 9.33259e9i 0.408357 1.12195i
303303 −1.20777e10 3.36402e9i −1.43289 0.399106i
304304 −2.07238e8 + 1.17530e9i −0.0242647 + 0.137612i
305305 2.03243e9 + 1.17342e9i 0.234864 + 0.135599i
306306 7.96765e8 2.06182e9i 0.0908750 0.235161i
307307 −3.93188e9 6.81021e9i −0.442636 0.766668i 0.555248 0.831685i 0.312623π-0.312623\pi
−0.997884 + 0.0650169i 0.979290π0.979290\pi
308308 −1.37303e9 3.77237e9i −0.152573 0.419190i
309309 −6.58573e8 3.15030e8i −0.0722387 0.0345555i
310310 8.08507e9 6.78418e9i 0.875461 0.734599i
311311 −1.55726e9 1.85588e9i −0.166464 0.198384i 0.676363 0.736568i 0.263555π-0.263555\pi
−0.842827 + 0.538184i 0.819111π0.819111\pi
312312 4.39952e9 3.41290e8i 0.464287 0.0360168i
313313 −7.11159e9 + 2.58841e9i −0.740951 + 0.269684i −0.684793 0.728738i 0.740107π-0.740107\pi
−0.0561581 + 0.998422i 0.517885π0.517885\pi
314314 4.87618e9 2.81526e9i 0.501604 0.289601i
315315 1.39968e10 + 1.22224e10i 1.42163 + 1.24140i
316316 4.78523e8 8.28826e8i 0.0479904 0.0831219i
317317 1.30171e10 + 2.29527e9i 1.28907 + 0.227298i 0.775829 0.630944i 0.217332π-0.217332\pi
0.513245 + 0.858242i 0.328443π0.328443\pi
318318 2.20323e7 + 2.24706e7i 0.00215453 + 0.00219738i
319319 4.81443e9 + 1.75231e9i 0.464925 + 0.169219i
320320 1.25685e9 2.21616e8i 0.119862 0.0211350i
321321 −1.02878e8 + 1.05602e9i −0.00968950 + 0.0994610i
322322 −1.85629e10 1.55761e10i −1.72672 1.44889i
323323 2.16909e9i 0.199282i
324324 1.16973e9 5.38439e9i 0.106147 0.488603i
325325 −7.63039e8 −0.0683933
326326 −4.75529e9 + 5.66714e9i −0.421024 + 0.501757i
327327 2.97691e9 + 2.90010e8i 0.260360 + 0.0253643i
328328 −1.05342e9 5.97426e9i −0.0910139 0.516165i
329329 6.31010e8 1.73369e9i 0.0538583 0.147975i
330330 −2.68352e9 + 2.63118e9i −0.226282 + 0.221868i
331331 3.15619e9 1.78997e10i 0.262937 1.49119i −0.511909 0.859040i 0.671062π-0.671062\pi
0.774846 0.632150i 0.217827π-0.217827\pi
332332 −4.33233e9 2.50127e9i −0.356590 0.205877i
333333 −6.06165e9 1.77333e10i −0.492963 1.44216i
334334 −7.02182e9 1.21622e10i −0.564240 0.977293i
335335 −1.54567e9 4.24669e9i −0.122726 0.337187i
336336 4.77688e8 + 6.15781e9i 0.0374789 + 0.483136i
337337 −1.14032e10 + 9.56846e9i −0.884115 + 0.741861i −0.967021 0.254697i 0.918024π-0.918024\pi
0.0829057 + 0.996557i 0.473580π0.473580\pi
338338 4.35948e9 + 5.19543e9i 0.334017 + 0.398066i
339339 −2.00478e9 + 4.19102e9i −0.151799 + 0.317337i
340340 2.17970e9 7.93345e8i 0.163110 0.0593672i
341341 −8.94639e9 + 5.16520e9i −0.661653 + 0.382006i
342342 8.33865e8 + 5.34228e9i 0.0609525 + 0.390501i
343343 2.35722e10 4.08282e10i 1.70303 2.94974i
344344 4.05942e9 + 7.15785e8i 0.289888 + 0.0511150i
345345 −6.08695e9 + 2.18537e10i −0.429658 + 1.54258i
346346 −4.87793e9 1.77542e9i −0.340354 0.123879i
347347 2.42670e10 4.27893e9i 1.67378 0.295132i 0.745359 0.666664i 0.232278π-0.232278\pi
0.928420 + 0.371531i 0.121167π0.121167\pi
348348 −6.41208e9 4.58454e9i −0.437202 0.312593i
349349 −1.55872e10 1.30792e10i −1.05067 0.881618i −0.0575079 0.998345i 0.518315π-0.518315\pi
−0.993164 + 0.116727i 0.962760π0.962760\pi
350350 1.06799e9i 0.0711698i
351351 1.83608e10 7.91024e9i 1.20966 0.521148i
352352 −1.24916e9 −0.0813670
353353 6.55825e9 7.81582e9i 0.422366 0.503357i −0.512337 0.858784i 0.671220π-0.671220\pi
0.934704 + 0.355428i 0.115665π0.115665\pi
354354 −5.88890e9 1.29605e10i −0.374991 0.825292i
355355 2.98127e9 + 1.69076e10i 0.187710 + 1.06456i
356356 −1.49036e9 + 4.09473e9i −0.0927878 + 0.254932i
357357 2.79848e9 + 1.08711e10i 0.172286 + 0.669272i
358358 −8.89497e8 + 5.04459e9i −0.0541517 + 0.307110i
359359 1.49833e10 + 8.65060e9i 0.902047 + 0.520797i 0.877864 0.478910i 0.158968π-0.158968\pi
0.0241833 + 0.999708i 0.492301π0.492301\pi
360360 5.06342e9 2.79188e9i 0.301463 0.166221i
361361 5.83885e9 + 1.01132e10i 0.343794 + 0.595469i
362362 5.01624e9 + 1.37820e10i 0.292108 + 0.802561i
363363 −1.12865e10 + 7.73837e9i −0.650028 + 0.445680i
364364 −1.71671e10 + 1.44049e10i −0.977892 + 0.820548i
365365 −5.06220e9 6.03290e9i −0.285212 0.339903i
366366 1.99845e9 + 2.91475e9i 0.111370 + 0.162434i
367367 −2.63458e10 + 9.58908e9i −1.45227 + 0.528583i −0.943224 0.332158i 0.892223π-0.892223\pi
−0.509045 + 0.860740i 0.670001π0.670001\pi
368368 −6.53001e9 + 3.77010e9i −0.356060 + 0.205571i
369369 −1.32708e10 2.40683e10i −0.715802 1.29819i
370370 9.83314e9 1.70315e10i 0.524669 0.908753i
371371 −1.57391e8 2.77523e7i −0.00830777 0.00146488i
372372 1.53917e10 3.96216e9i 0.803736 0.206900i
373373 1.95992e10 + 7.13352e9i 1.01252 + 0.368526i 0.794399 0.607396i 0.207786π-0.207786\pi
0.218118 + 0.975922i 0.430008π0.430008\pi
374374 −2.23588e9 + 3.94247e8i −0.114278 + 0.0201503i
375375 −1.84406e10 + 8.37893e9i −0.932504 + 0.423705i
376376 −4.39774e8 3.69014e8i −0.0220028 0.0184625i
377377 2.86005e10i 1.41582i
378378 1.10716e10 + 2.56989e10i 0.542305 + 1.25877i
379379 −9.38168e9 −0.454699 −0.227350 0.973813i 0.573006π-0.573006\pi
−0.227350 + 0.973813i 0.573006π0.573006\pi
380380 −3.64718e9 + 4.34654e9i −0.174913 + 0.208453i
381381 −7.34509e9 + 1.02731e10i −0.348576 + 0.487529i
382382 3.77336e8 + 2.13998e9i 0.0177204 + 0.100498i
383383 −1.93666e9 + 5.32094e9i −0.0900034 + 0.247282i −0.976525 0.215405i 0.930893π-0.930893\pi
0.886521 + 0.462688i 0.153115π0.153115\pi
384384 1.85138e9 + 5.15667e8i 0.0851472 + 0.0237162i
385385 3.31428e9 1.87962e10i 0.150851 0.855516i
386386 −1.14211e9 6.59398e8i −0.0514469 0.0297029i
387387 1.84519e10 2.88011e9i 0.822614 0.128400i
388388 8.69285e9 + 1.50564e10i 0.383562 + 0.664348i
389389 −6.25611e9 1.71885e10i −0.273216 0.750655i −0.998090 0.0617737i 0.980324π-0.980324\pi
0.724874 0.688881i 0.241898π-0.241898\pi
390390 1.89258e10 + 9.05321e9i 0.818082 + 0.391331i
391391 −1.04982e10 + 8.80906e9i −0.449168 + 0.376897i
392392 −1.47957e10 1.76328e10i −0.626600 0.746753i
393393 −1.69814e10 + 1.31732e9i −0.711873 + 0.0552231i
394394 2.41533e10 8.79109e9i 1.00229 0.364802i
395395 3.94053e9 2.27507e9i 0.161870 0.0934557i
396396 −5.35523e9 + 1.83054e9i −0.217770 + 0.0744386i
397397 −2.05364e10 + 3.55700e10i −0.826726 + 1.43193i 0.0738664 + 0.997268i 0.476466π0.476466\pi
−0.900593 + 0.434664i 0.856867π0.856867\pi
398398 5.65988e9 + 9.97990e8i 0.225567 + 0.0397735i
399399 −1.92244e10 1.96068e10i −0.758511 0.773599i
400400 −3.12280e8 1.13661e8i −0.0121985 0.00443987i
401401 5.68533e9 1.00248e9i 0.219876 0.0387701i −0.0626247 0.998037i 0.519947π-0.519947\pi
0.282501 + 0.959267i 0.408836π0.408836\pi
402402 6.59858e8 6.77332e9i 0.0252666 0.259357i
403403 4.41759e10 + 3.70680e10i 1.67481 + 1.40533i
404404 1.98123e10i 0.743719i
405405 1.76159e10 1.93889e10i 0.654763 0.720666i
406406 4.00308e10 1.47330
407407 −1.23731e10 + 1.47456e10i −0.450920 + 0.537386i
408408 3.47654e9 + 3.38685e8i 0.125461 + 0.0122224i
409409 −3.40118e9 1.92890e10i −0.121545 0.689314i −0.983300 0.181990i 0.941746π-0.941746\pi
0.861756 0.507324i 0.169365π-0.169365\pi
410410 9.86452e9 2.71025e10i 0.349092 0.959123i
411411 −1.67566e10 + 1.64298e10i −0.587245 + 0.575792i
412412 2.00329e8 1.13612e9i 0.00695272 0.0394308i
413413 6.26096e10 + 3.61477e10i 2.15199 + 1.24245i
414414 −2.24698e10 + 2.57318e10i −0.764887 + 0.875929i
415415 −1.18919e10 2.05974e10i −0.400922 0.694417i
416416 2.38498e9 + 6.55268e9i 0.0796363 + 0.218799i
417417 1.95101e9 + 2.51503e10i 0.0645232 + 0.831760i
418418 4.25433e9 3.56981e9i 0.139356 0.116934i
419419 −4.21037e9 5.01772e9i −0.136604 0.162798i 0.693405 0.720548i 0.256110π-0.256110\pi
−0.830010 + 0.557749i 0.811665π0.811665\pi
420420 −1.26714e10 + 2.64897e10i −0.407218 + 0.851293i
421421 −4.93249e10 + 1.79528e10i −1.57014 + 0.571483i −0.973030 0.230678i 0.925905π-0.925905\pi
−0.597107 + 0.802162i 0.703683π0.703683\pi
422422 −2.06631e10 + 1.19298e10i −0.651547 + 0.376171i
423423 −2.42609e9 9.37534e8i −0.0757785 0.0292837i
424424 −2.48651e7 + 4.30675e7i −0.000769353 + 0.00133256i
425425 −5.94825e8 1.04884e8i −0.0182320 0.00321479i
426426 −6.93697e9 + 2.49055e10i −0.210636 + 0.756236i
427427 −1.68653e10 6.13846e9i −0.507320 0.184649i
428428 −1.65120e9 + 2.91152e8i −0.0492068 + 0.00867649i
429429 −1.67042e10 1.19432e10i −0.493170 0.352609i
430430 1.50127e10 + 1.25971e10i 0.439120 + 0.368466i
431431 5.46765e9i 0.158450i 0.996857 + 0.0792248i 0.0252445π0.0252445\pi
−0.996857 + 0.0792248i 0.974755π0.974755\pi
432432 8.69263e9 5.02339e8i 0.249584 0.0144232i
433433 5.74008e10 1.63292 0.816462 0.577399i 0.195932π-0.195932\pi
0.816462 + 0.577399i 0.195932π0.195932\pi
434434 −5.18824e10 + 6.18310e10i −1.46238 + 1.74280i
435435 −1.55028e10 3.41190e10i −0.432965 0.952882i
436436 8.20751e8 + 4.65471e9i 0.0227125 + 0.128809i
437437 1.14655e10 3.15012e10i 0.314389 0.863777i
438438 −2.95648e9 1.14849e10i −0.0803300 0.312055i
439439 4.09034e8 2.31975e9i 0.0110129 0.0624572i −0.978806 0.204789i 0.934349π-0.934349\pi
0.989819 + 0.142332i 0.0454601π0.0454601\pi
440440 −5.14329e9 2.96948e9i −0.137224 0.0792263i
441441 −8.92692e10 5.39110e10i −2.36019 1.42536i
442442 6.33697e9 + 1.09760e10i 0.166032 + 0.287577i
443443 −9.87952e8 2.71438e9i −0.0256520 0.0704782i 0.926206 0.377019i 0.123051π-0.123051\pi
−0.951858 + 0.306540i 0.900829π0.900829\pi
444444 2.44252e10 1.67467e10i 0.628502 0.430922i
445445 −1.58703e10 + 1.33167e10i −0.404710 + 0.339592i
446446 −4.52051e9 5.38733e9i −0.114248 0.136155i
447447 1.32354e10 + 1.93039e10i 0.331517 + 0.483520i
448448 −9.17149e9 + 3.33815e9i −0.227682 + 0.0828693i
449449 −1.65503e10 + 9.55529e9i −0.407211 + 0.235103i −0.689591 0.724199i 0.742210π-0.742210\pi
0.282380 + 0.959303i 0.408876π0.408876\pi
450450 −1.50532e9 2.96502e7i −0.0367096 0.000723067i
451451 −1.41150e10 + 2.44479e10i −0.341174 + 0.590930i
452452 −7.23003e9 1.27485e9i −0.173215 0.0305426i
453453 6.88595e10 1.77260e10i 1.63520 0.420937i
454454 1.76093e10 + 6.40927e9i 0.414495 + 0.150864i
455455 −1.04926e11 + 1.85014e10i −2.44816 + 0.431676i
456456 −7.77898e9 + 3.53456e9i −0.179913 + 0.0817479i
457457 1.70069e10 + 1.42705e10i 0.389907 + 0.327171i 0.816577 0.577237i 0.195869π-0.195869\pi
−0.426670 + 0.904407i 0.640313π0.640313\pi
458458 2.08446e9i 0.0473731i
459459 1.54005e10 3.64261e9i 0.346963 0.0820658i
460460 −3.58488e10 −0.800651
461461 1.08079e10 1.28803e10i 0.239297 0.285183i −0.633008 0.774145i 0.718180π-0.718180\pi
0.872305 + 0.488963i 0.162625π0.162625\pi
462462 1.67164e10 2.33801e10i 0.366924 0.513191i
463463 3.11709e9 + 1.76779e10i 0.0678305 + 0.384686i 0.999757 + 0.0220390i 0.00701580π0.00701580\pi
−0.931927 + 0.362647i 0.881873π0.881873\pi
464464 4.26027e9 1.17050e10i 0.0919105 0.252522i
465465 7.27922e10 + 2.02749e10i 1.55694 + 0.433658i
466466 3.72270e9 2.11125e10i 0.0789432 0.447709i
467467 1.26576e10 + 7.30789e9i 0.266125 + 0.153647i 0.627125 0.778918i 0.284231π-0.284231\pi
−0.361000 + 0.932566i 0.617565π0.617565\pi
468468 1.98269e10 + 2.45967e10i 0.413306 + 0.512736i
469469 1.72805e10 + 2.99308e10i 0.357163 + 0.618624i
470470 −9.33509e8 2.56480e9i −0.0191305 0.0525607i
471471 3.63651e10 + 1.73953e10i 0.738926 + 0.353467i
472472 1.72328e10 1.44600e10i 0.347206 0.291340i
473473 −1.23299e10 1.46942e10i −0.246328 0.293562i
474474 6.83141e9 5.29942e8i 0.135331 0.0104982i
475475 1.38836e9 5.05323e8i 0.0272727 0.00992646i
476476 −1.53626e10 + 8.86958e9i −0.299251 + 0.172773i
477477 −4.34861e7 + 2.21070e8i −0.000839996 + 0.00427029i
478478 −3.75196e8 + 6.49858e8i −0.00718698 + 0.0124482i
479479 −9.35117e9 1.64886e9i −0.177633 0.0313215i 0.0841240 0.996455i 0.473191π-0.473191\pi
−0.261757 + 0.965134i 0.584302π0.584302\pi
480480 6.39701e9 + 6.52426e9i 0.120507 + 0.122904i
481481 1.00974e11 + 3.67516e10i 1.88638 + 0.686587i
482482 4.88646e10 8.61614e9i 0.905328 0.159634i
483483 1.68217e10 1.72672e11i 0.309088 3.17273i
484484 −1.65657e10 1.39003e10i −0.301876 0.253304i
485485 8.26577e10i 1.49388i
486486 3.65296e10 1.48918e10i 0.654787 0.266934i
487487 −1.09510e11 −1.94687 −0.973435 0.228964i 0.926466π-0.926466\pi
−0.973435 + 0.228964i 0.926466π0.926466\pi
488488 −3.58976e9 + 4.27811e9i −0.0632975 + 0.0754350i
489489 −5.27155e10 5.13555e9i −0.921941 0.0898156i
490490 −1.90033e10 1.07773e11i −0.329644 1.86950i
491491 −1.59722e10 + 4.38833e10i −0.274814 + 0.755045i 0.723116 + 0.690727i 0.242709π0.242709\pi
−0.997929 + 0.0643180i 0.979513π0.979513\pi
492492 3.10122e10 3.04074e10i 0.529264 0.518942i
493493 3.93129e9 2.22954e10i 0.0665498 0.377423i
494494 −2.68486e10 1.55011e10i −0.450831 0.260288i
495495 −2.64011e10 5.19328e9i −0.439745 0.0865009i
496496 1.25578e10 + 2.17507e10i 0.207485 + 0.359374i
497497 −4.49062e10 1.23379e11i −0.736005 2.02216i
498498 −2.77004e9 3.57082e10i −0.0450369 0.580565i
499499 −1.51236e10 + 1.26902e10i −0.243923 + 0.204676i −0.756550 0.653936i 0.773117π-0.773117\pi
0.512627 + 0.858611i 0.328672π0.328672\pi
500500 −2.05742e10 2.45194e10i −0.329188 0.392311i
501501 4.33873e10 9.07018e10i 0.688672 1.43968i
502502 −6.40083e10 + 2.32971e10i −1.00791 + 0.366849i
503503 1.03427e11 5.97137e10i 1.61571 0.932828i 0.627692 0.778462i 0.284000π-0.284000\pi
0.988014 0.154367i 0.0493337π-0.0493337\pi
504504 −3.44269e10 + 2.77509e10i −0.533551 + 0.430085i
505505 4.70972e10 8.15748e10i 0.724152 1.25427i
506506 3.45552e10 + 6.09302e9i 0.527123 + 0.0929459i
507507 −1.30286e10 + 4.67760e10i −0.197181 + 0.707931i
508508 −1.87531e10 6.82556e9i −0.281590 0.102491i
509509 −4.55739e10 + 8.03591e9i −0.678962 + 0.119719i −0.502486 0.864586i 0.667581π-0.667581\pi
−0.176476 + 0.984305i 0.556470π0.556470\pi
510510 1.35092e10 + 9.65886e9i 0.199686 + 0.142773i
511511 4.61370e10 + 3.87135e10i 0.676652 + 0.567778i
512512 3.03700e9i 0.0441942i
513513 −2.81693e10 + 2.65523e10i −0.406731 + 0.383383i
514514 9.70900e10 1.39098
515515 3.52559e9 4.20164e9i 0.0501191 0.0597296i
516516 1.22081e10 + 2.68681e10i 0.172207 + 0.378999i
517517 4.63900e8 + 2.63091e9i 0.00649326 + 0.0368251i
518518 −5.14395e10 + 1.41329e11i −0.714460 + 1.96296i
519519 −9.26496e9 3.59913e10i −0.127695 0.496053i
520520 −5.75698e9 + 3.26494e10i −0.0787374 + 0.446542i
521521 −1.06319e11 6.13835e10i −1.44298 0.833106i −0.444935 0.895563i 0.646773π-0.646773\pi
−0.998048 + 0.0624566i 0.980106π0.980106\pi
522522 1.11136e9 5.64230e10i 0.0149683 0.759931i
523523 8.51271e9 + 1.47445e10i 0.113779 + 0.197071i 0.917291 0.398218i 0.130371π-0.130371\pi
−0.803512 + 0.595288i 0.797038π0.797038\pi
524524 −9.20560e9 2.52922e10i −0.122103 0.335476i
525525 6.30632e9 4.32382e9i 0.0830116 0.0569154i
526526 3.13980e10 2.63460e10i 0.410165 0.344169i
527527 2.93420e10 + 3.49684e10i 0.380406 + 0.453350i
528528 −5.05729e9 7.37610e9i −0.0650702 0.0949054i
529529 1.25439e11 4.56560e10i 1.60181 0.583009i
530530 −2.04758e8 + 1.18217e8i −0.00259500 + 0.00149823i
531531 5.26880e10 8.72440e10i 0.662725 1.09738i
532532 2.16961e10 3.75788e10i 0.270855 0.469134i
533533 1.55195e11 + 2.73650e10i 1.92295 + 0.339068i
534534 −3.02125e10 + 7.77737e9i −0.371553 + 0.0956462i
535535 −7.49077e9 2.72642e9i −0.0914347 0.0332795i
536536 1.05908e10 1.86745e9i 0.128313 0.0226250i
537537 −3.33886e10 + 1.51709e10i −0.401515 + 0.182438i
538538 −2.59787e10 2.17987e10i −0.310090 0.260197i
539539 1.07114e11i 1.26909i
540540 3.69851e10 + 1.85956e10i 0.434962 + 0.218693i
541541 −4.41827e10 −0.515778 −0.257889 0.966175i 0.583027π-0.583027\pi
−0.257889 + 0.966175i 0.583027π0.583027\pi
542542 2.95483e10 3.52143e10i 0.342401 0.408058i
543543 −6.10720e10 + 8.54172e10i −0.702495 + 0.982530i
544544 9.58504e8 + 5.43595e9i 0.0109446 + 0.0620697i
545545 −7.68571e9 + 2.11163e10i −0.0871161 + 0.239349i
546546 −1.54560e11 4.30499e10i −1.73911 0.484397i
547547 −1.14275e10 + 6.48085e10i −0.127644 + 0.723907i 0.852058 + 0.523448i 0.175355π0.175355\pi
−0.979702 + 0.200459i 0.935757π0.935757\pi
548548 −3.21161e10 1.85422e10i −0.356123 0.205608i
549549 −9.12031e9 + 2.36010e10i −0.100397 + 0.259801i
550550 7.73228e8 + 1.33927e9i 0.00845001 + 0.0146358i
551551 1.89407e10 + 5.20391e10i 0.205489 + 0.564577i
552552 −4.86989e10 2.32952e10i −0.524521 0.250905i
553553 −2.66564e10 + 2.23674e10i −0.285037 + 0.239174i
554554 2.09992e10 + 2.50258e10i 0.222927 + 0.265674i
555555 1.40378e11 1.08897e10i 1.47954 0.114775i
556556 −3.74590e10 + 1.36340e10i −0.391974 + 0.142667i
557557 −1.45491e11 + 8.39991e10i −1.51152 + 0.872678i −0.511613 + 0.859216i 0.670952π0.670952\pi
−0.999909 + 0.0134620i 0.995715π0.995715\pi
558558 8.57097e10 + 7.48442e10i 0.884084 + 0.772008i
559559 −5.35396e10 + 9.27333e10i −0.548312 + 0.949705i
560560 −4.56980e10 8.05779e9i −0.464670 0.0819339i
561561 −1.13800e10 1.16064e10i −0.114893 0.117178i
562562 −3.68134e10 1.33990e10i −0.369029 0.134315i
563563 −4.17694e10 + 7.36508e9i −0.415743 + 0.0733067i −0.377607 0.925966i 0.623253π-0.623253\pi
−0.0381357 + 0.999273i 0.512142π0.512142\pi
564564 3.98523e8 4.09076e9i 0.00393855 0.0404285i
565565 −2.67383e10 2.24361e10i −0.262386 0.220168i
566566 7.49484e10i 0.730293i
567567 −1.06924e11 + 1.69419e11i −1.03453 + 1.63919i
568568 −4.08550e10 −0.392511
569569 4.96494e9 5.91699e9i 0.0473658 0.0564484i −0.741841 0.670575i 0.766047π-0.766047\pi
0.789207 + 0.614127i 0.210492π0.210492\pi
570570 −4.04314e10 3.93883e9i −0.383018 0.0373136i
571571 −1.20307e9 6.82293e9i −0.0113174 0.0641839i 0.978626 0.205648i 0.0659302π-0.0659302\pi
−0.989943 + 0.141464i 0.954819π0.954819\pi
572572 1.10985e10 3.04928e10i 0.103676 0.284848i
573573 −1.11085e10 + 1.08919e10i −0.103048 + 0.101038i
574574 −3.83016e10 + 2.17219e11i −0.352833 + 2.00102i
575575 8.08412e9 + 4.66737e9i 0.0739540 + 0.0426973i
576576 4.45046e9 + 1.30198e10i 0.0404310 + 0.118281i
577577 3.42329e9 + 5.92932e9i 0.0308845 + 0.0534936i 0.881055 0.473015i 0.156834π-0.156834\pi
−0.850170 + 0.526508i 0.823501π0.823501\pi
578578 −2.35615e10 6.47348e10i −0.211102 0.579998i
579579 −7.30252e8 9.41358e9i −0.00649769 0.0837608i
580580 4.53660e10 3.80666e10i 0.400884 0.336382i
581581 1.16916e11 + 1.39335e11i 1.02605 + 1.22280i
582582 −5.37125e10 + 1.12287e11i −0.468148 + 0.978669i
583583 2.17462e8 7.91498e7i 0.00188239 0.000685134i
584584 1.62299e10 9.37035e9i 0.139529 0.0805572i
585585 2.31644e10 + 1.48406e11i 0.197787 + 1.26715i
586586 −1.30310e10 + 2.25703e10i −0.110506 + 0.191403i
587587 1.17881e11 + 2.07856e10i 0.992867 + 0.175069i 0.646405 0.762995i 0.276272π-0.276272\pi
0.346462 + 0.938064i 0.387383π0.387383\pi
588588 4.42178e10 1.58753e11i 0.369903 1.32805i
589589 −1.04927e11 3.81903e10i −0.871819 0.317316i
590590 1.05328e11 1.85722e10i 0.869233 0.153269i
591591 1.49696e11 + 1.07030e11i 1.22704 + 0.877317i
592592 3.58501e10 + 3.00818e10i 0.291879 + 0.244916i
593593 1.43481e11i 1.16031i −0.814506 0.580155i 0.802992π-0.802992\pi
0.814506 0.580155i 0.197008π-0.197008\pi
594594 −3.24899e10 2.42107e10i −0.260977 0.194474i
595595 −8.43382e10 −0.672910
596596 −2.37744e10 + 2.83332e10i −0.188419 + 0.224549i
597597 1.70213e10 + 3.74611e10i 0.133997 + 0.294906i
598598 −3.40131e10 1.92898e11i −0.265976 1.50842i
599599 3.73399e10 1.02591e11i 0.290046 0.796894i −0.706013 0.708199i 0.749508π-0.749508\pi
0.996059 0.0886950i 0.0282696π-0.0282696\pi
600600 −5.93133e8 2.30412e9i −0.00457665 0.0177787i
601601 1.76969e9 1.00364e10i 0.0135644 0.0769275i −0.977274 0.211979i 0.932009π-0.932009\pi
0.990839 + 0.135052i 0.0431201π0.0431201\pi
602602 −1.29795e11 7.49370e10i −0.988260 0.570572i
603603 4.26668e10 2.35258e10i 0.322716 0.177940i
604604 5.61813e10 + 9.73088e10i 0.422128 + 0.731147i
605605 −3.51640e10 9.66124e10i −0.262468 0.721126i
606606 1.16988e11 8.02109e10i 0.867464 0.594761i
607607 −6.80673e10 + 5.71152e10i −0.501399 + 0.420724i −0.858090 0.513499i 0.828349π-0.828349\pi
0.356691 + 0.934222i 0.383905π0.383905\pi
608608 −8.67902e9 1.03433e10i −0.0635121 0.0756908i
609609 1.62067e11 + 2.36376e11i 1.17822 + 1.71844i
610610 −2.49503e10 + 9.08116e9i −0.180201 + 0.0655876i
611611 1.29151e10 7.45656e9i 0.0926690 0.0535025i
612612 1.20751e10 + 2.18996e10i 0.0860764 + 0.156110i
613613 4.78807e10 8.29318e10i 0.339093 0.587326i −0.645170 0.764039i 0.723213π-0.723213\pi
0.984262 + 0.176713i 0.0565466π0.0565466\pi
614614 8.76166e10 + 1.54492e10i 0.616472 + 0.108701i
615615 1.99973e11 5.14775e10i 1.39788 0.359846i
616616 4.26795e10 + 1.55341e10i 0.296412 + 0.107885i
617617 −1.02462e11 + 1.80668e10i −0.707004 + 0.124664i −0.515577 0.856843i 0.672423π-0.672423\pi
−0.191427 + 0.981507i 0.561311π0.561311\pi
618618 7.51965e9 3.41673e9i 0.0515518 0.0234238i
619619 −8.74309e10 7.33632e10i −0.595528 0.499708i 0.294477 0.955659i 0.404855π-0.404855\pi
−0.890005 + 0.455951i 0.849299π0.849299\pi
620620 1.19408e11i 0.808105i
621621 −2.42912e11 2.85038e10i −1.63336 0.191662i
622622 2.74094e10 0.183121
623623 1.01841e11 1.21369e11i 0.676034 0.805666i
624624 −2.90368e10 + 4.06117e10i −0.191518 + 0.267863i
625625 −2.50493e10 1.42062e11i −0.164163 0.931016i
626626 2.92845e10 8.04585e10i 0.190695 0.523931i
627627 3.83030e10 + 1.06686e10i 0.247835 + 0.0690298i
628628 −1.10618e10 + 6.27344e10i −0.0711190 + 0.403336i
629629 7.36624e10 + 4.25290e10i 0.470590 + 0.271695i
630630 −2.07718e11 + 3.24222e10i −1.31859 + 0.205817i
631631 −8.73812e10 1.51349e11i −0.551189 0.954688i −0.998189 0.0601538i 0.980841π-0.980841\pi
0.447000 0.894534i 0.352492π-0.352492\pi
632632 3.70331e9 + 1.01748e10i 0.0232125 + 0.0637757i
633633 −1.54099e11 7.37136e10i −0.959811 0.459127i
634634 −1.14557e11 + 9.61249e10i −0.709031 + 0.594948i
635635 −6.09882e10 7.26829e10i −0.375103 0.447031i
636636 −3.54974e8 + 2.75369e7i −0.00216954 + 0.000168301i
637637 5.61884e11 2.04509e11i 3.41263 1.24209i
638638 −5.01990e10 + 2.89824e10i −0.302979 + 0.174925i
639639 −1.75148e11 + 5.98694e10i −1.05051 + 0.359089i
640640 −7.21948e9 + 1.25045e10i −0.0430315 + 0.0745327i
641641 7.99764e9 + 1.41020e9i 0.0473729 + 0.00835312i 0.197284 0.980346i 0.436788π-0.436788\pi
−0.149911 + 0.988699i 0.547899π0.547899\pi
642642 −8.40418e9 8.57134e9i −0.0494715 0.0504555i
643643 1.09381e11 + 3.98115e10i 0.639880 + 0.232897i 0.641526 0.767101i 0.278302π-0.278302\pi
−0.00164564 + 0.999999i 0.500524π0.500524\pi
644644 2.69991e11 4.76067e10i 1.56966 0.276773i
645645 −1.36044e10 + 1.39647e11i −0.0786035 + 0.806851i
646646 −1.87991e10 1.57743e10i −0.107946 0.0905774i
647647 2.68470e11i 1.53207i 0.642800 + 0.766034i 0.277773π0.277773\pi
−0.642800 + 0.766034i 0.722227π0.722227\pi
648648 3.81587e10 + 4.92948e10i 0.216418 + 0.279577i
649649 −1.04684e11 −0.590067
650650 5.54906e9 6.61311e9i 0.0310861 0.0370469i
651651 −5.75150e11 5.60312e10i −3.20227 0.311965i
652652 −1.45340e10 8.24264e10i −0.0804257 0.456117i
653653 1.68626e10 4.63295e10i 0.0927408 0.254803i −0.884646 0.466264i 0.845600π-0.845600\pi
0.977387 + 0.211461i 0.0678220π0.0678220\pi
654654 −2.41625e10 + 2.36912e10i −0.132078 + 0.129502i
655655 2.22209e10 1.26021e11i 0.120725 0.684665i
656656 5.94386e10 + 3.43169e10i 0.320962 + 0.185307i
657657 5.58471e10 6.39547e10i 0.299736 0.343250i
658658 1.04366e10 + 1.80768e10i 0.0556745 + 0.0964311i
659659 −5.50314e10 1.51198e11i −0.291789 0.801684i −0.995805 0.0914998i 0.970834π-0.970834\pi
0.704016 0.710184i 0.251388π-0.251388\pi
660660 −3.28856e9 4.23923e10i −0.0173312 0.223415i
661661 −1.27976e10 + 1.07385e10i −0.0670384 + 0.0562519i −0.675691 0.737185i 0.736155π-0.736155\pi
0.608653 + 0.793437i 0.291710π0.291710\pi
662662 1.32180e11 + 1.57526e11i 0.688231 + 0.820201i
663663 −3.91557e10 + 8.18555e10i −0.202647 + 0.423637i
664664 5.31841e10 1.93574e10i 0.273596 0.0995807i
665665 1.78663e11 1.03151e11i 0.913583 0.527457i
666666 1.97773e11 + 7.64271e10i 1.00524 + 0.388464i
667667 −1.74944e11 + 3.03012e11i −0.883884 + 1.53093i
668668 1.56472e11 + 2.75902e10i 0.785833 + 0.138564i
669669 1.35098e10 4.85037e10i 0.0674443 0.242142i
670670 4.80458e10 + 1.74872e10i 0.238427 + 0.0867804i
671671 2.55934e10 4.51281e9i 0.126252 0.0222616i
672672 −5.68424e10 4.06415e10i −0.278738 0.199293i
673673 1.65026e11 + 1.38473e11i 0.804435 + 0.675001i 0.949273 0.314455i 0.101822π-0.101822\pi
−0.144838 + 0.989455i 0.546266π0.546266\pi
674674 1.68415e11i 0.816094i
675675 −5.91929e9 9.00872e9i −0.0285138 0.0433959i
676676 −7.67313e10 −0.367439
677677 1.44588e11 1.72314e11i 0.688302 0.820286i −0.302847 0.953039i 0.597937π-0.597937\pi
0.991149 + 0.132753i 0.0423817π0.0423817\pi
678678 −2.17433e10 4.78535e10i −0.102898 0.226462i
679679 −1.09768e11 6.22526e11i −0.516413 2.92873i
680680 −8.97567e9 + 2.46605e10i −0.0419789 + 0.115336i
681681 3.34465e10 + 1.29928e11i 0.155511 + 0.604109i
682682 2.02952e10 1.15100e11i 0.0938113 0.532030i
683683 −2.85374e11 1.64761e11i −1.31139 0.757131i −0.329063 0.944308i 0.606733π-0.606733\pi
−0.982326 + 0.187177i 0.940066π0.940066\pi
684684 −5.23646e10 3.16238e10i −0.239229 0.144474i
685685 −8.81563e10 1.52691e11i −0.400397 0.693508i
686686 1.82426e11 + 5.01211e11i 0.823740 + 2.26321i
687687 −1.23084e10 + 8.43904e9i −0.0552554 + 0.0378849i
688688 −3.57249e10 + 2.99768e10i −0.159447 + 0.133792i
689689 −8.30386e8 9.89615e8i −0.00368471 0.00439126i
690690 −1.45136e11 2.11681e11i −0.640291 0.933869i
691691 −2.25153e10 + 8.19488e9i −0.0987563 + 0.0359443i −0.390926 0.920422i 0.627845π-0.627845\pi
0.292169 + 0.956367i 0.405623π0.405623\pi
692692 5.08611e10 2.93647e10i 0.221800 0.128056i
693693 2.05733e11 + 4.05231e9i 0.892013 + 0.0175699i
694694 −1.39393e11 + 2.41435e11i −0.600899 + 1.04079i
695695 −1.86644e11 3.29103e10i −0.799970 0.141056i
696696 8.63640e10 2.22320e10i 0.368041 0.0947419i
697697 1.17220e11 + 4.26647e10i 0.496674 + 0.180775i
698698 2.26710e11 3.99752e10i 0.955102 0.168410i
699699 1.39737e11 6.34930e10i 0.585334 0.265960i
700700 9.25608e9 + 7.76677e9i 0.0385509 + 0.0323481i
701701 4.21785e11i 1.74670i −0.487091 0.873351i 0.661942π-0.661942\pi
0.487091 0.873351i 0.338058π-0.338058\pi
702702 −6.49693e10 + 2.16656e11i −0.267522 + 0.892116i
703703 −2.08063e11 −0.851869
704704 9.08430e9 1.08262e10i 0.0369829 0.0440745i
705705 1.13653e10 1.58959e10i 0.0460072 0.0643471i
706706 2.00445e10 + 1.13678e11i 0.0806821 + 0.457571i
707707 −2.46377e11 + 6.76915e11i −0.986104 + 2.70930i
708708 1.55152e11 + 4.32147e10i 0.617481 + 0.171988i
709709 −1.96979e10 + 1.11712e11i −0.0779533 + 0.442095i 0.920703 + 0.390265i 0.127617π0.127617\pi
−0.998656 + 0.0518302i 0.983495π0.983495\pi
710710 −1.68216e11 9.71195e10i −0.661963 0.382185i
711711 3.07865e10 + 3.81928e10i 0.120471 + 0.149453i
712712 −2.46498e10 4.26948e10i −0.0959167 0.166133i
713713 −2.41289e11 6.62937e11i −0.933642 2.56516i
714714 −1.14570e11 5.48045e10i −0.440835 0.210874i
715715 1.18184e11 9.91678e10i 0.452203 0.379443i
716716 −3.72517e10 4.43949e10i −0.141741 0.168920i
717717 −5.35630e9 + 4.15511e8i −0.0202670 + 0.00157219i
718718 −1.83936e11 + 6.69473e10i −0.692101 + 0.251904i
719719 −1.50686e11 + 8.69985e10i −0.563841 + 0.325534i −0.754686 0.656086i 0.772211π-0.772211\pi
0.190845 + 0.981620i 0.438877π0.438877\pi
720720 −1.26261e10 + 6.41871e10i −0.0469827 + 0.238846i
721721 −2.09729e10 + 3.63260e10i −0.0776098 + 0.134424i
722722 −1.30111e11 2.29421e10i −0.478812 0.0844274i
723723 2.48707e11 + 2.53654e11i 0.910197 + 0.928301i
724724 −1.55926e11 5.67523e10i −0.567497 0.206552i
725725 −1.51864e10 + 2.67778e9i −0.0549672 + 0.00969220i
726726 1.50118e10 1.54094e11i 0.0540364 0.554674i
727727 −2.31003e11 1.93835e11i −0.826953 0.693896i 0.127636 0.991821i 0.459261π-0.459261\pi
−0.954589 + 0.297925i 0.903705π0.903705\pi
728728 2.53540e11i 0.902655i
729729 2.35826e11 + 1.55411e11i 0.834990 + 0.550265i
730730 8.90998e10 0.313751
731731 −5.44833e10 + 6.49307e10i −0.190807 + 0.227395i
732732 −3.97949e10 3.87682e9i −0.138606 0.0135030i
733733 5.67847e10 + 3.22042e11i 0.196705 + 1.11557i 0.909970 + 0.414675i 0.136105π0.136105\pi
−0.713265 + 0.700895i 0.752784π0.752784\pi
734734 1.08488e11 2.98069e11i 0.373764 1.02691i
735735 5.59447e11 5.48536e11i 1.91694 1.87956i
736736 1.48135e10 8.40117e10i 0.0504832 0.286305i
737737 −4.33399e10 2.50223e10i −0.146899 0.0848119i
738738 3.05105e11 + 6.00163e10i 1.02855 + 0.202322i
739739 −1.78330e11 3.08877e11i −0.597925 1.03564i −0.993127 0.117042i 0.962659π-0.962659\pi
0.395202 0.918594i 0.370675π-0.370675\pi
740740 7.60990e10 + 2.09080e11i 0.253777 + 0.697246i
741741 −1.71667e10 2.21293e11i −0.0569395 0.733999i
742742 1.38512e9 1.16225e9i 0.00456954 0.00383430i
743743 3.85547e11 + 4.59477e11i 1.26509 + 1.50768i 0.768749 + 0.639551i 0.220880π0.220880\pi
0.496343 + 0.868127i 0.334676π0.334676\pi
744744 −7.75937e10 + 1.62211e11i −0.253241 + 0.529404i
745745 −1.65241e11 + 6.01430e10i −0.536406 + 0.195236i
746746 −2.04356e11 + 1.17985e11i −0.659831 + 0.380953i
747747 1.99636e11 1.60923e11i 0.641147 0.516815i
748748 1.28432e10 2.22451e10i 0.0410267 0.0710603i
749749 6.00364e10 + 1.05860e10i 0.190760 + 0.0336362i
750750 6.14874e10 2.20755e11i 0.194331 0.697696i
751751 5.82770e11 + 2.12111e11i 1.83205 + 0.666812i 0.992302 + 0.123838i 0.0395202π0.0395202\pi
0.839749 + 0.542975i 0.182702π0.182702\pi
752752 6.39635e9 1.12785e9i 0.0200014 0.00352679i
753753 −3.96706e11 2.83639e11i −1.23393 0.882239i
754754 2.47875e11 + 2.07992e11i 0.766915 + 0.643518i
755755 5.34211e11i 1.64409i
756756 −3.03243e11 9.09347e10i −0.928333 0.278383i
757757 −1.73730e11 −0.529042 −0.264521 0.964380i 0.585214π-0.585214\pi
−0.264521 + 0.964380i 0.585214π0.585214\pi
758758 6.82265e10 8.13092e10i 0.206670 0.246299i
759759 1.03920e11 + 2.28711e11i 0.313136 + 0.689159i
760760 −1.11472e10 6.32188e10i −0.0334126 0.189492i
761761 −1.65093e11 + 4.53591e11i −0.492256 + 1.35246i 0.406354 + 0.913716i 0.366800π0.366800\pi
−0.898610 + 0.438747i 0.855422π0.855422\pi
762762 −3.56189e10 1.38367e11i −0.105648 0.410406i
763763 2.98419e10 1.69242e11i 0.0880496 0.499354i
764764 −2.12909e10 1.22923e10i −0.0624913 0.0360794i
765765 −2.34145e9 + 1.18874e11i −0.00683658 + 0.347089i
766766 −3.20315e10 5.54802e10i −0.0930384 0.161147i
767767 1.99869e11 + 5.49136e11i 0.577517 + 1.58671i
768768 −1.79330e10 + 1.22954e10i −0.0515475 + 0.0353427i
769769 −4.15701e11 + 3.48815e11i −1.18871 + 0.997446i −0.188829 + 0.982010i 0.560469π0.560469\pi
−0.999881 + 0.0154358i 0.995086π0.995086\pi
770770 1.38801e11 + 1.65416e11i 0.394847 + 0.470561i
771771 3.93073e11 + 5.73300e11i 1.11239 + 1.62243i
772772 1.40207e10 5.10310e9i 0.0394729 0.0143670i
773773 1.22712e11 7.08481e10i 0.343693 0.198431i −0.318211 0.948020i 0.603082π-0.603082\pi
0.661904 + 0.749589i 0.269749π0.269749\pi
774774 −1.09226e11 + 1.80864e11i −0.304343 + 0.503950i
775775 1.55465e10 2.69273e10i 0.0430948 0.0746425i
776776 −1.93708e11 3.41560e10i −0.534197 0.0941934i
777777 −1.04278e12 + 2.68435e11i −2.86094 + 0.736470i
778778 1.94466e11 + 7.07799e10i 0.530793 + 0.193193i
779779 −3.00502e11 + 5.29866e10i −0.816014 + 0.143885i
780780 −2.16097e11 + 9.81888e10i −0.583808 + 0.265267i
781781 1.45639e11 + 1.22206e11i 0.391448 + 0.328464i
782782 1.55048e11i 0.414610i
783783 3.37668e11 2.21869e11i 0.898344 0.590268i
784784 2.60419e11 0.689300
785785 −1.94676e11 + 2.32006e11i −0.512666 + 0.610971i
786786 1.12077e11 1.56754e11i 0.293647 0.410704i
787787 −5.17348e10 2.93403e11i −0.134860 0.764830i −0.974957 0.222394i 0.928613π-0.928613\pi
0.840097 0.542437i 0.182498π-0.182498\pi
788788 −9.94598e10 + 2.73264e11i −0.257954 + 0.708724i
789789 2.82685e11 + 7.87368e10i 0.729449 + 0.203175i
790790 −8.93922e9 + 5.06968e10i −0.0229504 + 0.130158i
791791 2.31171e11 + 1.33467e11i 0.590511 + 0.340932i
792792 2.30800e10 5.97249e10i 0.0586590 0.151794i
793793 −7.25373e10 1.25638e11i −0.183429 0.317709i
794794 −1.58932e11 4.36661e11i −0.399879 1.09866i
795795 −1.52703e9 7.30456e8i −0.00382277 0.00182863i
796796 −4.98098e10 + 4.17954e10i −0.124069 + 0.104106i
797797 −1.47296e11 1.75541e11i −0.365055 0.435056i 0.551983 0.833856i 0.313871π-0.313871\pi
−0.917038 + 0.398799i 0.869427π0.869427\pi
798798 3.09735e11 2.40275e10i 0.763797 0.0592511i
799799 1.10929e10 4.03749e9i 0.0272181 0.00990659i
800800 3.25608e9 1.87990e9i 0.00794940 0.00458959i
801801 −1.68241e11 1.46913e11i −0.408697 0.356886i
802802 −3.26572e10 + 5.65640e10i −0.0789372 + 0.136723i
803803 −8.58847e10 1.51438e10i −0.206564 0.0364227i
804804 5.39044e10 + 5.49766e10i 0.129003 + 0.131569i
805805 1.22483e12 + 4.45801e11i 2.91670 + 1.06159i
806806 −6.42522e11 + 1.13294e11i −1.52247 + 0.268452i
807807 2.35419e10 2.41653e11i 0.0555068 0.569768i
808808 1.71709e11 + 1.44081e11i 0.402854 + 0.338035i
809809 8.80448e10i 0.205546i −0.994705 0.102773i 0.967228π-0.967228\pi
0.994705 0.102773i 0.0327716π-0.0327716\pi
810810 3.99320e10 + 2.93676e11i 0.0927643 + 0.682226i
811811 3.75493e8 0.000867998 0.000433999 1.00000i 0.499862π-0.499862\pi
0.000433999 1.00000i 0.499862π0.499862\pi
812812 −2.91117e11 + 3.46939e11i −0.669643 + 0.798049i
813813 3.27562e11 + 3.19111e10i 0.749776 + 0.0730432i
814814 −3.78168e10 2.14470e11i −0.0861366 0.488505i
815815 1.36100e11 3.73931e11i 0.308480 0.847543i
816816 −2.82178e10 + 2.76675e10i −0.0636448 + 0.0624036i
817817 3.60036e10 2.04186e11i 0.0808086 0.458288i
818818 1.91909e11 + 1.10798e11i 0.428629 + 0.247469i
819819 −3.71541e11 1.08694e12i −0.825794 2.41585i
820820 1.63155e11 + 2.82592e11i 0.360864 + 0.625035i
821821 −6.98628e10 1.91946e11i −0.153771 0.422481i 0.838756 0.544507i 0.183283π-0.183283\pi
−0.992527 + 0.122026i 0.961061π0.961061\pi
822822 −2.05346e10 2.64709e11i −0.0449780 0.579805i
823823 −4.68555e11 + 3.93165e11i −1.02132 + 0.856989i −0.989793 0.142514i 0.954481π-0.954481\pi
−0.0315268 + 0.999503i 0.510037π0.510037\pi
824824 8.38969e9 + 9.99844e9i 0.0181986 + 0.0216882i
825825 −4.77772e9 + 9.98789e9i −0.0103135 + 0.0215604i
826826 −7.68602e11 + 2.79748e11i −1.65113 + 0.600962i
827827 −4.31359e11 + 2.49045e11i −0.922183 + 0.532422i −0.884331 0.466861i 0.845385π-0.845385\pi
−0.0378519 + 0.999283i 0.512052π0.512052\pi
828828 −5.96054e10 3.81871e11i −0.126813 0.812447i
829829 −2.91062e11 + 5.04134e11i −0.616265 + 1.06740i 0.373896 + 0.927471i 0.378022π0.378022\pi
−0.990161 + 0.139932i 0.955312π0.955312\pi
830830 2.64995e11 + 4.67259e10i 0.558375 + 0.0984566i
831831 −6.27573e10 + 2.25315e11i −0.131601 + 0.472483i
832832 −7.41351e10 2.69830e10i −0.154714 0.0563114i
833833 4.66126e11 8.21905e10i 0.968106 0.170703i
834834 −2.32161e11 1.65991e11i −0.479871 0.343101i
835835 5.78669e11 + 4.85561e11i 1.19038 + 0.998844i
836836 6.28322e10i 0.128634i
837837 −9.49430e10 + 8.09112e11i −0.193447 + 1.64857i
838838 7.41067e10 0.150273
839839 4.52293e11 5.39022e11i 0.912793 1.08782i −0.0830329 0.996547i 0.526461π-0.526461\pi
0.995826 0.0912770i 0.0290949π-0.0290949\pi
840840 −1.37430e11 3.02461e11i −0.276036 0.607509i
841841 −1.35025e10 7.65765e10i −0.0269917 0.153078i
842842 2.03113e11 5.58047e11i 0.404100 1.11025i
843843 −6.99219e10 2.71623e11i −0.138453 0.537844i
844844 4.68748e10 2.65840e11i 0.0923783 0.523904i
845845 −3.15933e11 1.82404e11i −0.619680 0.357773i
846846 2.57687e10 1.42084e10i 0.0503050 0.0277373i
847847 3.93133e11 + 6.80927e11i 0.763847 + 1.32302i
848848 −1.92431e8 5.28701e8i −0.000372128 0.00102241i
849849 4.42558e11 3.03432e11i 0.851804 0.584024i
850850 5.23476e9 4.39249e9i 0.0100282 0.00841462i
851851 −8.44981e11 1.00701e12i −1.61112 1.92006i
852852 −1.65403e11 2.41242e11i −0.313896 0.457820i
853853 6.49207e11 2.36292e11i 1.22627 0.446327i 0.353954 0.935263i 0.384837π-0.384837\pi
0.872320 + 0.488936i 0.162615π0.162615\pi
854854 1.75850e11 1.01527e11i 0.330607 0.190876i
855855 −1.40430e11 2.54687e11i −0.262782 0.476587i
856856 9.48471e9 1.64280e10i 0.0176656 0.0305978i
857857 −6.63284e11 1.16955e11i −1.22963 0.216818i −0.479166 0.877724i 0.659061π-0.659061\pi
−0.750468 + 0.660906i 0.770172π0.770172\pi
858858 2.24988e11 5.79169e10i 0.415155 0.106870i
859859 −3.76675e11 1.37098e11i −0.691821 0.251802i −0.0279066 0.999611i 0.508884π-0.508884\pi
−0.663915 + 0.747808i 0.731106π0.731106\pi
860860 −2.18353e11 + 3.85016e10i −0.399178 + 0.0703858i
861861 −1.43771e12 + 6.53258e11i −2.61613 + 1.18870i
862862 −4.73870e10 3.97624e10i −0.0858283 0.0720185i
863863 3.60967e11i 0.650766i −0.945582 0.325383i 0.894507π-0.894507\pi
0.945582 0.325383i 0.105493π-0.105493\pi
864864 −5.88618e10 + 7.89905e10i −0.105628 + 0.141749i
865865 2.79220e11 0.498749
866866 −4.17436e11 + 4.97481e11i −0.742196 + 0.884515i
867867 2.86858e11 4.01209e11i 0.507681 0.710058i
868868 −1.58572e11 8.99309e11i −0.279350 1.58427i
869869 1.72333e10 4.73481e10i 0.0302197 0.0830278i
870870 4.08444e11 + 1.13764e11i 0.712943 + 0.198577i
871871 −4.85111e10 + 2.75120e11i −0.0842885 + 0.478024i
872872 −4.63102e10 2.67372e10i −0.0800960 0.0462435i
873873 −8.80491e11 + 1.37434e11i −1.51589 + 0.236612i
874874 1.89634e11 + 3.28456e11i 0.324991 + 0.562900i
875875 3.98036e11 + 1.09359e12i 0.679032 + 1.86562i
876876 1.21038e11 + 5.78987e10i 0.205544 + 0.0983224i
877877 −2.12214e11 + 1.78069e11i −0.358737 + 0.301016i −0.804287 0.594241i 0.797453π-0.797453\pi
0.445550 + 0.895257i 0.353008π0.353008\pi
878878 1.71302e10 + 2.04149e10i 0.0288259 + 0.0343534i
879879 −1.86031e11 + 1.44312e10i −0.311623 + 0.0241739i
880880 6.31395e10 2.29809e10i 0.105286 0.0383209i
881881 −7.06464e10 + 4.07877e10i −0.117270 + 0.0677058i −0.557488 0.830185i 0.688235π-0.688235\pi
0.440218 + 0.897891i 0.354901π0.354901\pi
882882 1.11643e12 3.81621e11i 1.84483 0.630606i
883883 3.99517e11 6.91984e11i 0.657192 1.13829i −0.324147 0.946007i 0.605077π-0.605077\pi
0.981339 0.192284i 0.0615893π-0.0615893\pi
884884 −1.41211e11 2.48993e10i −0.231238 0.0407735i
885885 5.36091e11 + 5.46755e11i 0.873908 + 0.891291i
886886 3.07097e10 + 1.11774e10i 0.0498356 + 0.0181387i
887887 7.75909e11 1.36814e11i 1.25348 0.221022i 0.492794 0.870146i 0.335975π-0.335975\pi
0.760683 + 0.649124i 0.224864π0.224864\pi
888888 −3.24873e10 + 3.33476e11i −0.0522470 + 0.536306i
889889 5.55847e11 + 4.66411e11i 0.889914 + 0.746727i
890890 2.34388e11i 0.373573i
891891 1.14234e10 2.89866e11i 0.0181252 0.459924i
892892 7.95655e10 0.125680
893893 −1.85612e10 + 2.21204e10i −0.0291877 + 0.0347846i
894894 −2.63555e11 2.56755e10i −0.412592 0.0401947i
895895 −4.78454e10 2.71345e11i −0.0745673 0.422892i
896896 3.77669e10 1.03764e11i 0.0585975 0.160995i
897897 1.00133e12 9.81798e11i 1.54670 1.51654i
898898 3.75448e10 2.12927e11i 0.0577356 0.327435i
899899 1.00930e12 + 5.82718e11i 1.54519 + 0.892113i
900900 1.12042e10 1.28307e10i 0.0170769 0.0195560i
901901 −5.11297e8 8.85593e8i −0.000775844 0.00134380i
902902 −1.09237e11 3.00125e11i −0.165022 0.453395i
903903 −8.29892e10 1.06980e12i −0.124816 1.60899i
904904 6.36279e10 5.33902e10i 0.0952739 0.0799443i
905905 −5.07096e11 6.04334e11i −0.755956 0.900913i
906906 −3.47140e11 + 7.25700e11i −0.515219 + 1.07707i
907907 −7.06335e10 + 2.57085e10i −0.104371 + 0.0379881i −0.393678 0.919248i 0.628798π-0.628798\pi
0.289307 + 0.957236i 0.406575π0.406575\pi
908908 −1.83608e11 + 1.06006e11i −0.270115 + 0.155951i
909909 9.47264e11 + 3.66058e11i 1.38744 + 0.536161i
910910 6.02710e11 1.04392e12i 0.878907 1.52231i
911911 −5.26413e10 9.28208e9i −0.0764281 0.0134763i 0.135303 0.990804i 0.456799π-0.456799\pi
−0.211731 + 0.977328i 0.567910π0.567910\pi
912912 2.59378e10 9.31233e10i 0.0374933 0.134611i
913913 −2.47492e11 9.00796e10i −0.356186 0.129641i
914914 −2.47359e11 + 4.36161e10i −0.354441 + 0.0624974i
915915 −1.54635e11 1.10562e11i −0.220609 0.157732i
916916 −1.80656e10 1.51589e10i −0.0256608 0.0215320i
917917 9.78622e11i 1.38400i
918918 −8.04271e10 + 1.59963e11i −0.113248 + 0.225242i
919919 1.85878e11 0.260595 0.130297 0.991475i 0.458407π-0.458407\pi
0.130297 + 0.991475i 0.458407π0.458407\pi
920920 2.60704e11 3.10694e11i 0.363911 0.433693i
921921 2.63495e11 + 5.79908e11i 0.366213 + 0.805974i
922922 3.30330e10 + 1.87339e11i 0.0457114 + 0.259242i
923923 3.62986e11 9.97296e11i 0.500130 1.37410i
924924 8.10638e10 + 3.14906e11i 0.111209 + 0.432009i
925925 1.00606e10 5.70567e10i 0.0137423 0.0779362i
926926 −1.75879e11 1.01544e11i −0.239205 0.138105i
927927 5.06189e10 + 3.05695e10i 0.0685478 + 0.0413971i
928928 7.04629e10 + 1.22045e11i 0.0950098 + 0.164562i
929929 1.17933e11 + 3.24018e11i 0.158333 + 0.435017i 0.993340 0.115223i 0.0367584π-0.0367584\pi
−0.835006 + 0.550240i 0.814536π0.814536\pi
930930 −7.05086e11 + 4.83430e11i −0.942563 + 0.646252i
931931 −8.86921e11 + 7.44215e11i −1.18055 + 0.990603i
932932 1.55905e11 + 1.85801e11i 0.206632 + 0.246254i
933933 1.10968e11 + 1.61848e11i 0.146444 + 0.213590i
934934 −1.55386e11 + 5.65560e10i −0.204186 + 0.0743176i
935935 1.05761e11 6.10610e10i 0.138382 0.0798947i
936936 −3.57362e11 7.03894e9i −0.465592 0.00917073i
937937 2.26937e11 3.93066e11i 0.294406 0.509926i −0.680441 0.732803i 0.738212π-0.738212\pi
0.974846 + 0.222878i 0.0715450π0.0715450\pi
938938 −3.85074e11 6.78989e10i −0.497430 0.0877104i
939939 5.93654e11 1.52820e11i 0.763609 0.196570i
940940 2.90173e10 + 1.05614e10i 0.0371660 + 0.0135273i
941941 −9.58616e11 + 1.69030e11i −1.22260 + 0.215578i −0.747446 0.664322i 0.768720π-0.768720\pi
−0.475158 + 0.879900i 0.657609π0.657609\pi
942942 −4.15220e11 + 1.88665e11i −0.527321 + 0.239601i
943943 −1.47685e12 1.23922e12i −1.86762 1.56712i
944944 2.54511e11i 0.320493i
945945 −1.03240e12 1.09528e12i −1.29456 1.37340i
946946 2.17018e11 0.270976
947947 8.00877e11 9.54448e11i 0.995786 1.18673i 0.0133915 0.999910i 0.495737π-0.495737\pi
0.982394 0.186821i 0.0598183π-0.0598183\pi
948948 −4.50872e10 + 6.30604e10i −0.0558239 + 0.0780770i
949949 8.45374e10 + 4.79435e11i 0.104228 + 0.591106i
950950 −5.71707e9 + 1.57075e10i −0.00701907 + 0.0192847i
951951 −1.03139e12 2.87275e11i −1.26096 0.351217i
952952 3.48505e10 1.97647e11i 0.0424288 0.240626i
953953 5.26504e11 + 3.03977e11i 0.638308 + 0.368527i 0.783962 0.620808i 0.213196π-0.213196\pi
−0.145655 + 0.989335i 0.546529π0.546529\pi
954954 −1.59973e9 1.98458e9i −0.00193131 0.00239593i
955955 −5.84418e10 1.01224e11i −0.0702604 0.121694i
956956 −2.90365e9 7.97772e9i −0.00347627 0.00955096i
957957 −3.74369e11 1.79080e11i −0.446326 0.213501i
958958 8.22950e10 6.90537e10i 0.0977038 0.0819832i
959959 8.66710e11 + 1.03290e12i 1.02471 + 1.22120i
960960 −1.03066e11 + 7.99524e9i −0.121347 + 0.00941340i
961961 −1.40671e12 + 5.12002e11i −1.64935 + 0.600314i
962962 −1.05283e12 + 6.07854e11i −1.22930 + 0.709739i
963963 1.65877e10 8.43268e10i 0.0192877 0.0980529i
964964 −2.80684e11 + 4.86159e11i −0.325019 + 0.562950i
965965 6.98595e10 + 1.23181e10i 0.0805594 + 0.0142048i
966966 1.37418e12 + 1.40151e12i 1.57810 + 1.60949i
967967 −1.17995e11 4.29467e10i −0.134945 0.0491161i 0.273665 0.961825i 0.411764π-0.411764\pi
−0.408610 + 0.912709i 0.633986π0.633986\pi
968968 2.40942e11 4.24845e10i 0.274417 0.0483871i
969969 1.70357e10 1.74868e11i 0.0193226 0.198343i
970970 −7.16378e11 6.01112e11i −0.809199 0.678999i
971971 7.98948e11i 0.898755i −0.893342 0.449378i 0.851646π-0.851646\pi
0.893342 0.449378i 0.148354π-0.148354\pi
972972 −1.36590e11 + 4.24893e11i −0.153022 + 0.476009i
973973 1.44939e12 1.61709
974974 7.96389e11 9.49099e11i 0.884890 1.05457i
975975 6.15150e10 + 5.99279e9i 0.0680710 + 0.00663149i
976976 −1.09717e10 6.22235e10i −0.0120913 0.0685733i
977977 −1.25204e11 + 3.43994e11i −0.137416 + 0.377549i −0.989244 0.146273i 0.953272π-0.953272\pi
0.851828 + 0.523822i 0.175494π0.175494\pi
978978 4.27873e11 4.19528e11i 0.467691 0.458570i
979979 −3.98376e10 + 2.25930e11i −0.0433673 + 0.245948i
980980 1.07225e12 + 6.19061e11i 1.16249 + 0.671165i
981981 −2.37716e11 4.67603e10i −0.256674 0.0504896i
982982 −2.64173e11 4.57561e11i −0.284081 0.492043i
983983 1.21663e11 + 3.34265e11i 0.130300 + 0.357995i 0.987637 0.156760i 0.0501050π-0.0501050\pi
−0.857337 + 0.514755i 0.827883π0.827883\pi
984984 3.80043e10 + 4.89909e11i 0.0405371 + 0.522558i
985985 −1.05911e12 + 8.88699e11i −1.12511 + 0.944082i
986986 1.64641e11 + 1.96211e11i 0.174192 + 0.207594i
987987 −6.44871e10 + 1.34811e11i −0.0679523 + 0.142055i
988988 3.29596e11 1.19963e11i 0.345903 0.125898i
989989 1.13447e12 6.54984e11i 1.18579 0.684613i
990990 2.37006e11 1.91046e11i 0.246728 0.198883i
991991 1.76447e11 3.05615e11i 0.182945 0.316869i −0.759937 0.649996i 0.774770π-0.774770\pi
0.942882 + 0.333127i 0.108104π0.108104\pi
992992 −2.79833e11 4.93422e10i −0.288970 0.0509532i
993993 −3.95028e11 + 1.41825e12i −0.406285 + 1.45867i
994994 1.39587e12 + 5.08056e11i 1.42988 + 0.520434i
995995 −3.04441e11 + 5.36812e10i −0.310607 + 0.0547684i
996996 3.29620e11 + 2.35674e11i 0.334948 + 0.239483i
997997 −9.75186e11 8.18279e11i −0.986977 0.828172i −0.00184966 0.999998i 0.500589π-0.500589\pi
−0.985127 + 0.171826i 0.945033π0.945033\pi
998998 2.23360e11i 0.225156i
999999 3.49406e11 + 1.47724e12i 0.350807 + 1.48316i
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.f.a.11.1 yes 144
27.5 odd 18 inner 54.9.f.a.5.1 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
54.9.f.a.5.1 144 27.5 odd 18 inner
54.9.f.a.11.1 yes 144 1.1 even 1 trivial