Properties

Label 150.8.e.a.143.2
Level 150150
Weight 88
Character 150.143
Analytic conductor 46.85846.858
Analytic rank 00
Dimension 1616
Inner twists 88

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [150,8,Mod(107,150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(150, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("150.107");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: N N == 150=2352 150 = 2 \cdot 3 \cdot 5^{2}
Weight: k k == 8 8
Character orbit: [χ][\chi] == 150.e (of order 44, degree 22, 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: 46.857753822646.8577538226
Analytic rank: 00
Dimension: 1616
Relative dimension: 88 over Q(i)\Q(i)
Coefficient field: Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x168x15+64x14308x13+1346x124436x11+12996x1030704x9++6793 x^{16} - 8 x^{15} + 64 x^{14} - 308 x^{13} + 1346 x^{12} - 4436 x^{11} + 12996 x^{10} - 30704 x^{9} + \cdots + 6793 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 25231658 2^{52}\cdot 3^{16}\cdot 5^{8}
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 143.2
Root 0.500000+0.415846i0.500000 + 0.415846i of defining polynomial
Character χ\chi == 150.143
Dual form 150.8.e.a.107.2

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+(5.656855.65685i)q2+(26.939838.2263i)q3+64.0000iq4+(63.8461+368.635i)q6+(6.12631+6.12631i)q7+(362.039362.039i)q8+(735.497+2059.61i)q9+2862.04iq11+(2446.481724.15i)q12+(2016.242016.24i)q13+69.3113q144096.00q16+(8719.44+8719.44i)q17+(15811.57490.34i)q18+1408.92iq19+(399.228+69.1446i)q21+(16190.116190.1i)q22+(52424.752424.7i)q23+(23592.64086.15i)q24+22811.2iq26+(98545.527370.3i)q27+(392.084392.084i)q2895838.3q29+125580.q31+(23170.5+23170.5i)q32+(109405.77102.7i)q3398649.2iq34+(131815.47071.8i)q36+(305427.305427.i)q37+(7970.057970.05i)q38+(22756.4+131391.i)q39609628.iq41+(1867.232649.51i)q42+(317725.+317725.i)q43183170.q44593118.q46+(435458.435458.i)q47+(110345.+156575.i)q48+823468.iq49+(98412.0568212.i)q51+(129040.129040.i)q52+(1.07335e6+1.07335e6i)q53+(712287.402628.i)q54+4435.92iq56+(53857.737956.0i)q57+(542143.+542143.i)q583.09673e6q59+1.62355e6q61+(710389.710389.i)q62+(8111.9617123.7i)q63262144.iq64+(1.05505e6182730.i)q66+(907865.+907865.i)q67+(558044.+558044.i)q68+(3.41631e6591692.i)q693.60524e6iq71+(479382.+1.01194e6i)q72+(2.84276e62.84276e6i)q733.45551e6q7490170.8q76+(17533.717533.7i)q77+(871988.614529.i)q78+4.14998e6iq79+(3.70106e63.02968e6i)q81+(3.44858e6+3.44858e6i)q82+(2.77023e62.77023e6i)q83+(4425.26+25550.6i)q843.59464e6iq86+(2.58186e6+3.66354e6i)q87+(1.03617e6+1.03617e6i)q881.02628e7q89+24704.3q91+(3.35518e6+3.35518e6i)q92+(3.38311e64.80047e6i)q93+4.92664e6iq94+(261514.1.50993e6i)q96+(2.22241e62.22241e6i)q97+(4.65824e64.65824e6i)q98+(5.89470e62.10502e6i)q99+O(q100)q+(-5.65685 - 5.65685i) q^{2} +(-26.9398 - 38.2263i) q^{3} +64.0000i q^{4} +(-63.8461 + 368.635i) q^{6} +(-6.12631 + 6.12631i) q^{7} +(362.039 - 362.039i) q^{8} +(-735.497 + 2059.61i) q^{9} +2862.04i q^{11} +(2446.48 - 1724.15i) q^{12} +(-2016.24 - 2016.24i) q^{13} +69.3113 q^{14} -4096.00 q^{16} +(8719.44 + 8719.44i) q^{17} +(15811.5 - 7490.34i) q^{18} +1408.92i q^{19} +(399.228 + 69.1446i) q^{21} +(16190.1 - 16190.1i) q^{22} +(52424.7 - 52424.7i) q^{23} +(-23592.6 - 4086.15i) q^{24} +22811.2i q^{26} +(98545.5 - 27370.3i) q^{27} +(-392.084 - 392.084i) q^{28} -95838.3 q^{29} +125580. q^{31} +(23170.5 + 23170.5i) q^{32} +(109405. - 77102.7i) q^{33} -98649.2i q^{34} +(-131815. - 47071.8i) q^{36} +(305427. - 305427. i) q^{37} +(7970.05 - 7970.05i) q^{38} +(-22756.4 + 131391. i) q^{39} -609628. i q^{41} +(-1867.23 - 2649.51i) q^{42} +(317725. + 317725. i) q^{43} -183170. q^{44} -593118. q^{46} +(-435458. - 435458. i) q^{47} +(110345. + 156575. i) q^{48} +823468. i q^{49} +(98412.0 - 568212. i) q^{51} +(129040. - 129040. i) q^{52} +(-1.07335e6 + 1.07335e6i) q^{53} +(-712287. - 402628. i) q^{54} +4435.92i q^{56} +(53857.7 - 37956.0i) q^{57} +(542143. + 542143. i) q^{58} -3.09673e6 q^{59} +1.62355e6 q^{61} +(-710389. - 710389. i) q^{62} +(-8111.96 - 17123.7i) q^{63} -262144. i q^{64} +(-1.05505e6 - 182730. i) q^{66} +(-907865. + 907865. i) q^{67} +(-558044. + 558044. i) q^{68} +(-3.41631e6 - 591692. i) q^{69} -3.60524e6i q^{71} +(479382. + 1.01194e6i) q^{72} +(-2.84276e6 - 2.84276e6i) q^{73} -3.45551e6 q^{74} -90170.8 q^{76} +(-17533.7 - 17533.7i) q^{77} +(871988. - 614529. i) q^{78} +4.14998e6i q^{79} +(-3.70106e6 - 3.02968e6i) q^{81} +(-3.44858e6 + 3.44858e6i) q^{82} +(2.77023e6 - 2.77023e6i) q^{83} +(-4425.26 + 25550.6i) q^{84} -3.59464e6i q^{86} +(2.58186e6 + 3.66354e6i) q^{87} +(1.03617e6 + 1.03617e6i) q^{88} -1.02628e7 q^{89} +24704.3 q^{91} +(3.35518e6 + 3.35518e6i) q^{92} +(-3.38311e6 - 4.80047e6i) q^{93} +4.92664e6i q^{94} +(261514. - 1.50993e6i) q^{96} +(2.22241e6 - 2.22241e6i) q^{97} +(4.65824e6 - 4.65824e6i) q^{98} +(-5.89470e6 - 2.10502e6i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q+2304q665536q16183168q21+1410688q31193536q36+2302464q46+1055808q51+21247904q614589568q66+13881344q7636589968q81+160819200q91+9437184q96+O(q100) 16 q + 2304 q^{6} - 65536 q^{16} - 183168 q^{21} + 1410688 q^{31} - 193536 q^{36} + 2302464 q^{46} + 1055808 q^{51} + 21247904 q^{61} - 4589568 q^{66} + 13881344 q^{76} - 36589968 q^{81} + 160819200 q^{91}+ \cdots - 9437184 q^{96}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/150Z)×\left(\mathbb{Z}/150\mathbb{Z}\right)^\times.

nn 101101 127127
χ(n)\chi(n) 1-1 e(34)e\left(\frac{3}{4}\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 −5.65685 5.65685i −0.500000 0.500000i
33 −26.9398 38.2263i −0.576063 0.817406i
44 64.0000i 0.500000i
55 0 0
66 −63.8461 + 368.635i −0.120672 + 0.696734i
77 −6.12631 + 6.12631i −0.00675081 + 0.00675081i −0.710474 0.703723i 0.751519π-0.751519\pi
0.703723 + 0.710474i 0.251519π0.251519\pi
88 362.039 362.039i 0.250000 0.250000i
99 −735.497 + 2059.61i −0.336304 + 0.941753i
1010 0 0
1111 2862.04i 0.648337i 0.945999 + 0.324169i 0.105085π0.105085\pi
−0.945999 + 0.324169i 0.894915π0.894915\pi
1212 2446.48 1724.15i 0.408703 0.288031i
1313 −2016.24 2016.24i −0.254531 0.254531i 0.568294 0.822826i 0.307604π-0.307604\pi
−0.822826 + 0.568294i 0.807604π0.807604\pi
1414 69.3113 0.00675081
1515 0 0
1616 −4096.00 −0.250000
1717 8719.44 + 8719.44i 0.430445 + 0.430445i 0.888780 0.458335i 0.151554π-0.151554\pi
−0.458335 + 0.888780i 0.651554π0.651554\pi
1818 15811.5 7490.34i 0.639029 0.302725i
1919 1408.92i 0.0471247i 0.999722 + 0.0235623i 0.00750082π0.00750082\pi
−0.999722 + 0.0235623i 0.992499π0.992499\pi
2020 0 0
2121 399.228 + 69.1446i 0.00940704 + 0.00162926i
2222 16190.1 16190.1i 0.324169 0.324169i
2323 52424.7 52424.7i 0.898440 0.898440i −0.0968586 0.995298i 0.530879π-0.530879\pi
0.995298 + 0.0968586i 0.0308794π0.0308794\pi
2424 −23592.6 4086.15i −0.348367 0.0603358i
2525 0 0
2626 22811.2i 0.254531i
2727 98545.5 27370.3i 0.963527 0.267612i
2828 −392.084 392.084i −0.00337541 0.00337541i
2929 −95838.3 −0.729703 −0.364852 0.931066i 0.618880π-0.618880\pi
−0.364852 + 0.931066i 0.618880π0.618880\pi
3030 0 0
3131 125580. 0.757104 0.378552 0.925580i 0.376422π-0.376422\pi
0.378552 + 0.925580i 0.376422π0.376422\pi
3232 23170.5 + 23170.5i 0.125000 + 0.125000i
3333 109405. 77102.7i 0.529955 0.373483i
3434 98649.2i 0.430445i
3535 0 0
3636 −131815. 47071.8i −0.470877 0.168152i
3737 305427. 305427.i 0.991292 0.991292i −0.00867015 0.999962i 0.502760π-0.502760\pi
0.999962 + 0.00867015i 0.00275983π0.00275983\pi
3838 7970.05 7970.05i 0.0235623 0.0235623i
3939 −22756.4 + 131391.i −0.0614294 + 0.354682i
4040 0 0
4141 609628.i 1.38141i −0.723138 0.690703i 0.757301π-0.757301\pi
0.723138 0.690703i 0.242699π-0.242699\pi
4242 −1867.23 2649.51i −0.00388889 0.00551815i
4343 317725. + 317725.i 0.609412 + 0.609412i 0.942792 0.333380i 0.108189π-0.108189\pi
−0.333380 + 0.942792i 0.608189π0.608189\pi
4444 −183170. −0.324169
4545 0 0
4646 −593118. −0.898440
4747 −435458. 435458.i −0.611791 0.611791i 0.331621 0.943413i 0.392404π-0.392404\pi
−0.943413 + 0.331621i 0.892404π0.892404\pi
4848 110345. + 156575.i 0.144016 + 0.204351i
4949 823468.i 0.999909i
5050 0 0
5151 98412.0 568212.i 0.103885 0.599811i
5252 129040. 129040.i 0.127266 0.127266i
5353 −1.07335e6 + 1.07335e6i −0.990318 + 0.990318i −0.999954 0.00963560i 0.996933π-0.996933\pi
0.00963560 + 0.999954i 0.496933π0.496933\pi
5454 −712287. 402628.i −0.615569 0.347957i
5555 0 0
5656 4435.92i 0.00337541i
5757 53857.7 37956.0i 0.0385200 0.0271468i
5858 542143. + 542143.i 0.364852 + 0.364852i
5959 −3.09673e6 −1.96300 −0.981501 0.191455i 0.938679π-0.938679\pi
−0.981501 + 0.191455i 0.938679π0.938679\pi
6060 0 0
6161 1.62355e6 0.915823 0.457912 0.888998i 0.348598π-0.348598\pi
0.457912 + 0.888998i 0.348598π0.348598\pi
6262 −710389. 710389.i −0.378552 0.378552i
6363 −8111.96 17123.7i −0.00408727 0.00862792i
6464 262144.i 0.125000i
6565 0 0
6666 −1.05505e6 182730.i −0.451719 0.0782359i
6767 −907865. + 907865.i −0.368773 + 0.368773i −0.867030 0.498256i 0.833974π-0.833974\pi
0.498256 + 0.867030i 0.333974π0.333974\pi
6868 −558044. + 558044.i −0.215222 + 0.215222i
6969 −3.41631e6 591692.i −1.25195 0.216832i
7070 0 0
7171 3.60524e6i 1.19545i −0.801703 0.597723i 0.796072π-0.796072\pi
0.801703 0.597723i 0.203928π-0.203928\pi
7272 479382. + 1.01194e6i 0.151362 + 0.319514i
7373 −2.84276e6 2.84276e6i −0.855284 0.855284i 0.135494 0.990778i 0.456738π-0.456738\pi
−0.990778 + 0.135494i 0.956738π0.956738\pi
7474 −3.45551e6 −0.991292
7575 0 0
7676 −90170.8 −0.0235623
7777 −17533.7 17533.7i −0.00437680 0.00437680i
7878 871988. 614529.i 0.208055 0.146626i
7979 4.14998e6i 0.947002i 0.880793 + 0.473501i 0.157010π0.157010\pi
−0.880793 + 0.473501i 0.842990π0.842990\pi
8080 0 0
8181 −3.70106e6 3.02968e6i −0.773799 0.633431i
8282 −3.44858e6 + 3.44858e6i −0.690703 + 0.690703i
8383 2.77023e6 2.77023e6i 0.531794 0.531794i −0.389312 0.921106i 0.627287π-0.627287\pi
0.921106 + 0.389312i 0.127287π0.127287\pi
8484 −4425.26 + 25550.6i −0.000814631 + 0.00470352i
8585 0 0
8686 3.59464e6i 0.609412i
8787 2.58186e6 + 3.66354e6i 0.420355 + 0.596463i
8888 1.03617e6 + 1.03617e6i 0.162084 + 0.162084i
8989 −1.02628e7 −1.54312 −0.771559 0.636158i 0.780523π-0.780523\pi
−0.771559 + 0.636158i 0.780523π0.780523\pi
9090 0 0
9191 24704.3 0.00343659
9292 3.35518e6 + 3.35518e6i 0.449220 + 0.449220i
9393 −3.38311e6 4.80047e6i −0.436139 0.618861i
9494 4.92664e6i 0.611791i
9595 0 0
9696 261514. 1.50993e6i 0.0301679 0.174184i
9797 2.22241e6 2.22241e6i 0.247242 0.247242i −0.572596 0.819838i 0.694064π-0.694064\pi
0.819838 + 0.572596i 0.194064π0.194064\pi
9898 4.65824e6 4.65824e6i 0.499954 0.499954i
9999 −5.89470e6 2.10502e6i −0.610574 0.218038i
100100 0 0
101101 6.99729e6i 0.675780i −0.941186 0.337890i 0.890287π-0.890287\pi
0.941186 0.337890i 0.109713π-0.109713\pi
102102 −3.77099e6 + 2.65759e6i −0.351848 + 0.247963i
103103 −7.72957e6 7.72957e6i −0.696988 0.696988i 0.266772 0.963760i 0.414043π-0.414043\pi
−0.963760 + 0.266772i 0.914043π0.914043\pi
104104 −1.45992e6 −0.127266
105105 0 0
106106 1.21435e7 0.990318
107107 −3.51399e6 3.51399e6i −0.277304 0.277304i 0.554728 0.832032i 0.312822π-0.312822\pi
−0.832032 + 0.554728i 0.812822π0.812822\pi
108108 1.75170e6 + 6.30691e6i 0.133806 + 0.481763i
109109 5.96074e6i 0.440867i −0.975402 0.220434i 0.929253π-0.929253\pi
0.975402 0.220434i 0.0707472π-0.0707472\pi
110110 0 0
111111 −1.99035e7 3.44721e6i −1.38133 0.239242i
112112 25093.4 25093.4i 0.00168770 0.00168770i
113113 936497. 936497.i 0.0610565 0.0610565i −0.675919 0.736976i 0.736253π-0.736253\pi
0.736976 + 0.675919i 0.236253π0.236253\pi
114114 −519377. 89954.0i −0.0328334 0.00568661i
115115 0 0
116116 6.13365e6i 0.364852i
117117 5.63563e6 2.66975e6i 0.325306 0.154106i
118118 1.75177e7 + 1.75177e7i 0.981501 + 0.981501i
119119 −106836. −0.00581170
120120 0 0
121121 1.12959e7 0.579659
122122 −9.18419e6 9.18419e6i −0.457912 0.457912i
123123 −2.33038e7 + 1.64232e7i −1.12917 + 0.795776i
124124 8.03714e6i 0.378552i
125125 0 0
126126 −50978.2 + 142755.i −0.00227032 + 0.00635760i
127127 1.66782e7 1.66782e7i 0.722497 0.722497i −0.246616 0.969113i 0.579319π-0.579319\pi
0.969113 + 0.246616i 0.0793187π0.0793187\pi
128128 −1.48291e6 + 1.48291e6i −0.0625000 + 0.0625000i
129129 3.58600e6 2.07049e7i 0.147077 0.849197i
130130 0 0
131131 2.82268e7i 1.09701i 0.836146 + 0.548506i 0.184803π0.184803\pi
−0.836146 + 0.548506i 0.815197π0.815197\pi
132132 4.93457e6 + 7.00192e6i 0.186741 + 0.264977i
133133 −8631.48 8631.48i −0.000318130 0.000318130i
134134 1.02713e7 0.368773
135135 0 0
136136 6.31355e6 0.215222
137137 −2.43514e7 2.43514e7i −0.809098 0.809098i 0.175399 0.984497i 0.443878π-0.443878\pi
−0.984497 + 0.175399i 0.943878π0.943878\pi
138138 1.59785e7 + 2.26727e7i 0.517557 + 0.734390i
139139 2.79446e7i 0.882563i 0.897369 + 0.441281i 0.145476π0.145476\pi
−0.897369 + 0.441281i 0.854524π0.854524\pi
140140 0 0
141141 −4.91479e6 + 2.83771e7i −0.147652 + 0.852512i
142142 −2.03943e7 + 2.03943e7i −0.597723 + 0.597723i
143143 5.77057e6 5.77057e6i 0.165022 0.165022i
144144 3.01259e6 8.43618e6i 0.0840760 0.235438i
145145 0 0
146146 3.21622e7i 0.855284i
147147 3.14781e7 2.21840e7i 0.817331 0.576010i
148148 1.95473e7 + 1.95473e7i 0.495646 + 0.495646i
149149 4.77169e7 1.18174 0.590868 0.806768i 0.298785π-0.298785\pi
0.590868 + 0.806768i 0.298785π0.298785\pi
150150 0 0
151151 1.50380e7 0.355443 0.177722 0.984081i 0.443127π-0.443127\pi
0.177722 + 0.984081i 0.443127π0.443127\pi
152152 510083. + 510083.i 0.0117812 + 0.0117812i
153153 −2.43718e7 + 1.15456e7i −0.550133 + 0.260613i
154154 198372.i 0.00437680i
155155 0 0
156156 −8.40901e6 1.45641e6i −0.177341 0.0307147i
157157 3.59845e7 3.59845e7i 0.742107 0.742107i −0.230876 0.972983i 0.574159π-0.574159\pi
0.972983 + 0.230876i 0.0741591π0.0741591\pi
158158 2.34758e7 2.34758e7i 0.473501 0.473501i
159159 6.99458e7 + 1.21143e7i 1.37998 + 0.239006i
160160 0 0
161161 642341.i 0.0121304i
162162 3.79788e6 + 3.80748e7i 0.0701842 + 0.703615i
163163 −5.78634e7 5.78634e7i −1.04652 1.04652i −0.998864 0.0476564i 0.984825π-0.984825\pi
−0.0476564 0.998864i 0.515175π-0.515175\pi
164164 3.90162e7 0.690703
165165 0 0
166166 −3.13416e7 −0.531794
167167 −2.91589e7 2.91589e7i −0.484465 0.484465i 0.422089 0.906554i 0.361297π-0.361297\pi
−0.906554 + 0.422089i 0.861297π0.861297\pi
168168 169569. 119503.i 0.00275908 0.00194444i
169169 5.46180e7i 0.870427i
170170 0 0
171171 −2.90183e6 1.03626e6i −0.0443798 0.0158482i
172172 −2.03344e7 + 2.03344e7i −0.304706 + 0.304706i
173173 5.12770e7 5.12770e7i 0.752941 0.752941i −0.222086 0.975027i 0.571286π-0.571286\pi
0.975027 + 0.222086i 0.0712865π0.0712865\pi
174174 6.11890e6 3.53293e7i 0.0880544 0.508409i
175175 0 0
176176 1.17229e7i 0.162084i
177177 8.34251e7 + 1.18376e8i 1.13081 + 1.60457i
178178 5.80549e7 + 5.80549e7i 0.771559 + 0.771559i
179179 1.27198e8 1.65766 0.828828 0.559503i 0.189008π-0.189008\pi
0.828828 + 0.559503i 0.189008π0.189008\pi
180180 0 0
181181 1.10662e8 1.38715 0.693576 0.720383i 0.256034π-0.256034\pi
0.693576 + 0.720383i 0.256034π0.256034\pi
182182 −139749. 139749.i −0.00171829 0.00171829i
183183 −4.37381e7 6.20623e7i −0.527571 0.748599i
184184 3.79596e7i 0.449220i
185185 0 0
186186 −8.01781e6 + 4.62933e7i −0.0913609 + 0.527500i
187187 −2.49554e7 + 2.49554e7i −0.279073 + 0.279073i
188188 2.78693e7 2.78693e7i 0.305896 0.305896i
189189 −436042. + 771399.i −0.00469799 + 0.00831118i
190190 0 0
191191 8.53658e7i 0.886477i 0.896404 + 0.443238i 0.146170π0.146170\pi
−0.896404 + 0.443238i 0.853830π0.853830\pi
192192 −1.00208e7 + 7.06210e6i −0.102176 + 0.0720078i
193193 −8.56363e7 8.56363e7i −0.857447 0.857447i 0.133590 0.991037i 0.457349π-0.457349\pi
−0.991037 + 0.133590i 0.957349π0.957349\pi
194194 −2.51436e7 −0.247242
195195 0 0
196196 −5.27019e7 −0.499954
197197 −9.18117e7 9.18117e7i −0.855591 0.855591i 0.135224 0.990815i 0.456824π-0.456824\pi
−0.990815 + 0.135224i 0.956824π0.956824\pi
198198 2.14376e7 + 4.52532e7i 0.196268 + 0.414306i
199199 6.40625e7i 0.576259i 0.957591 + 0.288130i 0.0930334π0.0930334\pi
−0.957591 + 0.288130i 0.906967π0.906967\pi
200200 0 0
201201 5.91620e7 + 1.02466e7i 0.513874 + 0.0890009i
202202 −3.95827e7 + 3.95827e7i −0.337890 + 0.337890i
203203 587135. 587135.i 0.00492609 0.00492609i
204204 3.63655e7 + 6.29837e6i 0.299906 + 0.0519424i
205205 0 0
206206 8.74501e7i 0.696988i
207207 6.94165e7 + 1.46533e8i 0.543960 + 1.14826i
208208 8.25854e6 + 8.25854e6i 0.0636329 + 0.0636329i
209209 −4.03238e6 −0.0305527
210210 0 0
211211 −1.27578e8 −0.934949 −0.467475 0.884007i 0.654836π-0.654836\pi
−0.467475 + 0.884007i 0.654836π0.654836\pi
212212 −6.86942e7 6.86942e7i −0.495159 0.495159i
213213 −1.37815e8 + 9.71243e7i −0.977164 + 0.688651i
214214 3.97562e7i 0.277304i
215215 0 0
216216 2.57682e7 4.55864e7i 0.173979 0.307785i
217217 −769344. + 769344.i −0.00511107 + 0.00511107i
218218 −3.37191e7 + 3.37191e7i −0.220434 + 0.220434i
219219 −3.20848e7 + 1.85251e8i −0.206417 + 1.19181i
220220 0 0
221221 3.51611e7i 0.219123i
222222 9.30908e7 + 1.32091e8i 0.571046 + 0.810288i
223223 2.45541e7 + 2.45541e7i 0.148271 + 0.148271i 0.777345 0.629074i 0.216566π-0.216566\pi
−0.629074 + 0.777345i 0.716566π0.716566\pi
224224 −283899. −0.00168770
225225 0 0
226226 −1.05953e7 −0.0610565
227227 −2.09701e8 2.09701e8i −1.18990 1.18990i −0.977095 0.212805i 0.931740π-0.931740\pi
−0.212805 0.977095i 0.568260π-0.568260\pi
228228 2.42918e6 + 3.44689e6i 0.0135734 + 0.0192600i
229229 2.78948e8i 1.53497i −0.641070 0.767483i 0.721509π-0.721509\pi
0.641070 0.767483i 0.278491π-0.278491\pi
230230 0 0
231231 −197895. + 1.14260e6i −0.00105631 + 0.00609893i
232232 −3.46972e7 + 3.46972e7i −0.182426 + 0.182426i
233233 −2.11914e7 + 2.11914e7i −0.109752 + 0.109752i −0.759850 0.650098i 0.774728π-0.774728\pi
0.650098 + 0.759850i 0.274728π0.274728\pi
234234 −4.69823e7 1.67776e7i −0.239706 0.0856000i
235235 0 0
236236 1.98191e8i 0.981501i
237237 1.58638e8 1.11799e8i 0.774084 0.545532i
238238 604356. + 604356.i 0.00290585 + 0.00290585i
239239 −2.40754e8 −1.14073 −0.570363 0.821393i 0.693197π-0.693197\pi
−0.570363 + 0.821393i 0.693197π0.693197\pi
240240 0 0
241241 −1.04259e8 −0.479792 −0.239896 0.970799i 0.577113π-0.577113\pi
−0.239896 + 0.970799i 0.577113π0.577113\pi
242242 −6.38993e7 6.38993e7i −0.289829 0.289829i
243243 −1.61077e7 + 2.23097e8i −0.0720133 + 0.997404i
244244 1.03907e8i 0.457912i
245245 0 0
246246 2.24730e8 + 3.89224e7i 0.962473 + 0.166696i
247247 2.84073e6 2.84073e6i 0.0119947 0.0119947i
248248 4.54649e7 4.54649e7i 0.189276 0.189276i
249249 −1.80525e8 3.12663e7i −0.741038 0.128345i
250250 0 0
251251 1.88430e8i 0.752130i −0.926593 0.376065i 0.877277π-0.877277\pi
0.926593 0.376065i 0.122723π-0.122723\pi
252252 1.09592e6 519165.i 0.00431396 0.00204364i
253253 1.50042e8 + 1.50042e8i 0.582492 + 0.582492i
254254 −1.88692e8 −0.722497
255255 0 0
256256 1.67772e7 0.0625000
257257 −1.45638e8 1.45638e8i −0.535189 0.535189i 0.386923 0.922112i 0.373538π-0.373538\pi
−0.922112 + 0.386923i 0.873538π0.873538\pi
258258 −1.37410e8 + 9.68389e7i −0.498137 + 0.351060i
259259 3.74228e6i 0.0133841i
260260 0 0
261261 7.04888e7 1.97390e8i 0.245402 0.687200i
262262 1.59675e8 1.59675e8i 0.548506 0.548506i
263263 2.68726e8 2.68726e8i 0.910886 0.910886i −0.0854562 0.996342i 0.527235π-0.527235\pi
0.996342 + 0.0854562i 0.0272348π0.0272348\pi
264264 1.16947e7 6.75230e7i 0.0391179 0.225859i
265265 0 0
266266 97654.0i 0.000318130i
267267 2.76476e8 + 3.92307e8i 0.888932 + 1.26135i
268268 −5.81034e7 5.81034e7i −0.184387 0.184387i
269269 −4.82898e8 −1.51259 −0.756297 0.654228i 0.772994π-0.772994\pi
−0.756297 + 0.654228i 0.772994π0.772994\pi
270270 0 0
271271 −3.56999e8 −1.08962 −0.544810 0.838560i 0.683398π-0.683398\pi
−0.544810 + 0.838560i 0.683398π0.683398\pi
272272 −3.57148e7 3.57148e7i −0.107611 0.107611i
273273 −665528. 944353.i −0.00197969 0.00280909i
274274 2.75504e8i 0.809098i
275275 0 0
276276 3.78683e7 2.18644e8i 0.108416 0.625973i
277277 2.10083e8 2.10083e8i 0.593897 0.593897i −0.344785 0.938682i 0.612048π-0.612048\pi
0.938682 + 0.344785i 0.112048π0.112048\pi
278278 1.58078e8 1.58078e8i 0.441281 0.441281i
279279 −9.23639e7 + 2.58647e8i −0.254617 + 0.713005i
280280 0 0
281281 3.10671e8i 0.835272i −0.908614 0.417636i 0.862859π-0.862859\pi
0.908614 0.417636i 0.137141π-0.137141\pi
282282 1.88327e8 1.32723e8i 0.500082 0.352430i
283283 9.09536e7 + 9.09536e7i 0.238543 + 0.238543i 0.816247 0.577703i 0.196051π-0.196051\pi
−0.577703 + 0.816247i 0.696051π0.696051\pi
284284 2.30735e8 0.597723
285285 0 0
286286 −6.52865e7 −0.165022
287287 3.73477e6 + 3.73477e6i 0.00932561 + 0.00932561i
288288 −6.47641e7 + 3.06804e7i −0.159757 + 0.0756812i
289289 2.58281e8i 0.629435i
290290 0 0
291291 −1.44825e8 2.50832e7i −0.344524 0.0596701i
292292 1.81937e8 1.81937e8i 0.427642 0.427642i
293293 4.86060e8 4.86060e8i 1.12889 1.12889i 0.138536 0.990357i 0.455760π-0.455760\pi
0.990357 0.138536i 0.0442396π-0.0442396\pi
294294 −3.03559e8 5.25752e7i −0.696671 0.120661i
295295 0 0
296296 2.21153e8i 0.495646i
297297 7.83347e7 + 2.82041e8i 0.173503 + 0.624690i
298298 −2.69928e8 2.69928e8i −0.590868 0.590868i
299299 −2.11402e8 −0.457362
300300 0 0
301301 −3.89296e6 −0.00822805
302302 −8.50677e7 8.50677e7i −0.177722 0.177722i
303303 −2.67480e8 + 1.88505e8i −0.552386 + 0.389291i
304304 5.77093e6i 0.0117812i
305305 0 0
306306 2.03179e8 + 7.25562e7i 0.405373 + 0.144760i
307307 −3.34862e8 + 3.34862e8i −0.660514 + 0.660514i −0.955501 0.294987i 0.904685π-0.904685\pi
0.294987 + 0.955501i 0.404685π0.404685\pi
308308 1.12216e6 1.12216e6i 0.00218840 0.00218840i
309309 −8.72398e7 + 5.03706e8i −0.168213 + 0.971230i
310310 0 0
311311 2.15028e7i 0.0405353i 0.999795 + 0.0202676i 0.00645183π0.00645183\pi
−0.999795 + 0.0202676i 0.993548π0.993548\pi
312312 3.93298e7 + 5.58072e7i 0.0733130 + 0.104028i
313313 2.82789e8 + 2.82789e8i 0.521263 + 0.521263i 0.917953 0.396690i 0.129841π-0.129841\pi
−0.396690 + 0.917953i 0.629841π0.629841\pi
314314 −4.07118e8 −0.742107
315315 0 0
316316 −2.65598e8 −0.473501
317317 −1.32636e8 1.32636e8i −0.233860 0.233860i 0.580442 0.814302i 0.302880π-0.302880\pi
−0.814302 + 0.580442i 0.802880π0.802880\pi
318318 −3.27144e8 4.64202e8i −0.570485 0.809492i
319319 2.74293e8i 0.473094i
320320 0 0
321321 −3.96606e7 + 2.28993e8i −0.0669255 + 0.386415i
322322 3.63363e6 3.63363e6i 0.00606520 0.00606520i
323323 −1.22850e7 + 1.22850e7i −0.0202846 + 0.0202846i
324324 1.93900e8 2.36868e8i 0.316715 0.386900i
325325 0 0
326326 6.54650e8i 1.04652i
327327 −2.27857e8 + 1.60581e8i −0.360367 + 0.253967i
328328 −2.20709e8 2.20709e8i −0.345352 0.345352i
329329 5.33550e6 0.00826017
330330 0 0
331331 9.99204e8 1.51445 0.757227 0.653152i 0.226554π-0.226554\pi
0.757227 + 0.653152i 0.226554π0.226554\pi
332332 1.77295e8 + 1.77295e8i 0.265897 + 0.265897i
333333 4.04422e8 + 8.53703e8i 0.600177 + 1.26693i
334334 3.29895e8i 0.484465i
335335 0 0
336336 −1.63524e6 283216.i −0.00235176 0.000407315i
337337 −5.14283e8 + 5.14283e8i −0.731977 + 0.731977i −0.971011 0.239034i 0.923169π-0.923169\pi
0.239034 + 0.971011i 0.423169π0.423169\pi
338338 −3.08966e8 + 3.08966e8i −0.435214 + 0.435214i
339339 −6.10278e7 1.05698e7i −0.0850803 0.0147356i
340340 0 0
341341 3.59416e8i 0.490859i
342342 1.05533e7 + 2.22772e7i 0.0142658 + 0.0301140i
343343 −1.00901e7 1.00901e7i −0.0135010 0.0135010i
344344 2.30057e8 0.304706
345345 0 0
346346 −5.80133e8 −0.752941
347347 −2.23304e8 2.23304e8i −0.286908 0.286908i 0.548948 0.835856i 0.315028π-0.315028\pi
−0.835856 + 0.548948i 0.815028π0.815028\pi
348348 −2.34467e8 + 1.65239e8i −0.298232 + 0.210177i
349349 6.32133e6i 0.00796012i −0.999992 0.00398006i 0.998733π-0.998733\pi
0.999992 0.00398006i 0.00126690π-0.00126690\pi
350350 0 0
351351 −2.53877e8 1.43507e8i −0.313364 0.177132i
352352 −6.63148e7 + 6.63148e7i −0.0810422 + 0.0810422i
353353 −4.03328e8 + 4.03328e8i −0.488030 + 0.488030i −0.907684 0.419654i 0.862151π-0.862151\pi
0.419654 + 0.907684i 0.362151π0.362151\pi
354354 1.97714e8 1.14156e9i 0.236879 1.36769i
355355 0 0
356356 6.56816e8i 0.771559i
357357 2.87814e6 + 4.08394e6i 0.00334790 + 0.00475052i
358358 −7.19540e8 7.19540e8i −0.828828 0.828828i
359359 1.25329e9 1.42962 0.714810 0.699319i 0.246513π-0.246513\pi
0.714810 + 0.699319i 0.246513π0.246513\pi
360360 0 0
361361 8.91887e8 0.997779
362362 −6.26000e8 6.26000e8i −0.693576 0.693576i
363363 −3.04309e8 4.31801e8i −0.333920 0.473816i
364364 1.58107e6i 0.00171829i
365365 0 0
366366 −1.03657e8 + 5.98498e8i −0.110514 + 0.638085i
367367 −8.33720e8 + 8.33720e8i −0.880419 + 0.880419i −0.993577 0.113158i 0.963903π-0.963903\pi
0.113158 + 0.993577i 0.463903π0.463903\pi
368368 −2.14732e8 + 2.14732e8i −0.224610 + 0.224610i
369369 1.25560e9 + 4.48379e8i 1.30094 + 0.464572i
370370 0 0
371371 1.31513e7i 0.0133709i
372372 3.07230e8 2.16519e8i 0.309431 0.218070i
373373 7.65695e8 + 7.65695e8i 0.763968 + 0.763968i 0.977037 0.213069i 0.0683460π-0.0683460\pi
−0.213069 + 0.977037i 0.568346π0.568346\pi
374374 2.82338e8 0.279073
375375 0 0
376376 −3.15305e8 −0.305896
377377 1.93233e8 + 1.93233e8i 0.185732 + 0.185732i
378378 6.83032e6 1.89707e6i 0.00650459 0.00180660i
379379 4.88370e8i 0.460799i −0.973096 0.230400i 0.925997π-0.925997\pi
0.973096 0.230400i 0.0740033π-0.0740033\pi
380380 0 0
381381 −1.08685e9 1.88238e8i −1.00678 0.174370i
382382 4.82902e8 4.82902e8i 0.443238 0.443238i
383383 −4.76741e8 + 4.76741e8i −0.433597 + 0.433597i −0.889850 0.456253i 0.849191π-0.849191\pi
0.456253 + 0.889850i 0.349191π0.349191\pi
384384 9.66354e7 + 1.67369e7i 0.0870918 + 0.0150839i
385385 0 0
386386 9.68864e8i 0.857447i
387387 −8.88076e8 + 4.20705e8i −0.778864 + 0.368968i
388388 1.42234e8 + 1.42234e8i 0.123621 + 0.123621i
389389 1.98819e9 1.71251 0.856257 0.516550i 0.172784π-0.172784\pi
0.856257 + 0.516550i 0.172784π0.172784\pi
390390 0 0
391391 9.14229e8 0.773457
392392 2.98127e8 + 2.98127e8i 0.249977 + 0.249977i
393393 1.07900e9 7.60423e8i 0.896704 0.631948i
394394 1.03873e9i 0.855591i
395395 0 0
396396 1.34721e8 3.77261e8i 0.109019 0.305287i
397397 9.69093e8 9.69093e8i 0.777318 0.777318i −0.202056 0.979374i 0.564762π-0.564762\pi
0.979374 + 0.202056i 0.0647623π0.0647623\pi
398398 3.62392e8 3.62392e8i 0.288130 0.288130i
399399 −97419.2 + 562479.i −7.67784e−5 + 0.000443304i
400400 0 0
401401 1.62528e9i 1.25871i 0.777120 + 0.629353i 0.216680π0.216680\pi
−0.777120 + 0.629353i 0.783320π0.783320\pi
402402 −2.76707e8 3.92635e8i −0.212437 0.301438i
403403 −2.53201e8 2.53201e8i −0.192707 0.192707i
404404 4.47827e8 0.337890
405405 0 0
406406 −6.64268e6 −0.00492609
407407 8.74144e8 + 8.74144e8i 0.642692 + 0.642692i
408408 −1.70086e8 2.41344e8i −0.123982 0.175924i
409409 5.83288e8i 0.421553i 0.977534 + 0.210776i 0.0675992π0.0675992\pi
−0.977534 + 0.210776i 0.932401π0.932401\pi
410410 0 0
411411 −2.74842e8 + 1.58688e9i −0.195270 + 1.12745i
412412 4.94692e8 4.94692e8i 0.348494 0.348494i
413413 1.89715e7 1.89715e7i 0.0132519 0.0132519i
414414 4.36237e8 1.22160e9i 0.302149 0.846109i
415415 0 0
416416 9.34347e7i 0.0636329i
417417 1.06822e9 7.52821e8i 0.721412 0.508411i
418418 2.28106e7 + 2.28106e7i 0.0152763 + 0.0152763i
419419 2.63830e8 0.175217 0.0876083 0.996155i 0.472078π-0.472078\pi
0.0876083 + 0.996155i 0.472078π0.472078\pi
420420 0 0
421421 2.33804e8 0.152709 0.0763545 0.997081i 0.475672π-0.475672\pi
0.0763545 + 0.997081i 0.475672π0.475672\pi
422422 7.21691e8 + 7.21691e8i 0.467475 + 0.467475i
423423 1.21715e9 5.76597e8i 0.781905 0.370409i
424424 7.77186e8i 0.495159i
425425 0 0
426426 1.32902e9 + 2.30180e8i 0.832907 + 0.144256i
427427 −9.94638e6 + 9.94638e6i −0.00618255 + 0.00618255i
428428 2.24895e8 2.24895e8i 0.138652 0.138652i
429429 −3.76045e8 6.51295e7i −0.229953 0.0398270i
430430 0 0
431431 2.44883e8i 0.147329i 0.997283 + 0.0736645i 0.0234694π0.0234694\pi
−0.997283 + 0.0736645i 0.976531π0.976531\pi
432432 −4.03643e8 + 1.12109e8i −0.240882 + 0.0669030i
433433 7.71156e8 + 7.71156e8i 0.456493 + 0.456493i 0.897503 0.441009i 0.145379π-0.145379\pi
−0.441009 + 0.897503i 0.645379π0.645379\pi
434434 8.70413e6 0.00511107
435435 0 0
436436 3.81488e8 0.220434
437437 7.38622e7 + 7.38622e7i 0.0423387 + 0.0423387i
438438 1.22944e9 8.66442e8i 0.699114 0.492697i
439439 3.41238e9i 1.92501i −0.271272 0.962503i 0.587444π-0.587444\pi
0.271272 0.962503i 0.412556π-0.412556\pi
440440 0 0
441441 −1.69603e9 6.05658e8i −0.941668 0.336273i
442442 −1.98901e8 + 1.98901e8i −0.109562 + 0.109562i
443443 4.85626e8 4.85626e8i 0.265393 0.265393i −0.561848 0.827241i 0.689909π-0.689909\pi
0.827241 + 0.561848i 0.189909π0.189909\pi
444444 2.20621e8 1.27382e9i 0.119621 0.690667i
445445 0 0
446446 2.77798e8i 0.148271i
447447 −1.28548e9 1.82404e9i −0.680754 0.965958i
448448 1.60598e6 + 1.60598e6i 0.000843851 + 0.000843851i
449449 −5.78436e8 −0.301573 −0.150787 0.988566i 0.548181π-0.548181\pi
−0.150787 + 0.988566i 0.548181π0.548181\pi
450450 0 0
451451 1.74478e9 0.895617
452452 5.99358e7 + 5.99358e7i 0.0305282 + 0.0305282i
453453 −4.05120e8 5.74846e8i −0.204757 0.290541i
454454 2.37250e9i 1.18990i
455455 0 0
456456 5.75705e6 3.32401e7i 0.00284330 0.0164167i
457457 2.70022e9 2.70022e9i 1.32340 1.32340i 0.412402 0.911002i 0.364690π-0.364690\pi
0.911002 0.412402i 0.135310π-0.135310\pi
458458 −1.57797e9 + 1.57797e9i −0.767483 + 0.767483i
459459 1.09792e9 + 6.20609e8i 0.529937 + 0.299553i
460460 0 0
461461 8.51165e7i 0.0404632i 0.999795 + 0.0202316i 0.00644036π0.00644036\pi
−0.999795 + 0.0202316i 0.993560π0.993560\pi
462462 7.58301e6 5.34409e6i 0.00357762 0.00252131i
463463 −1.02911e9 1.02911e9i −0.481868 0.481868i 0.423860 0.905728i 0.360675π-0.360675\pi
−0.905728 + 0.423860i 0.860675π0.860675\pi
464464 3.92554e8 0.182426
465465 0 0
466466 2.39753e8 0.109752
467467 2.36415e9 + 2.36415e9i 1.07415 + 1.07415i 0.997021 + 0.0771326i 0.0245765π0.0245765\pi
0.0771326 + 0.997021i 0.475424π0.475424\pi
468468 1.70864e8 + 3.60680e8i 0.0770530 + 0.162653i
469469 1.11237e7i 0.00497904i
470470 0 0
471471 −2.34497e9 4.06139e8i −1.03410 0.179103i
472472 −1.12113e9 + 1.12113e9i −0.490751 + 0.490751i
473473 −9.09340e8 + 9.09340e8i −0.395105 + 0.395105i
474474 −1.52983e9 2.64960e8i −0.659808 0.114276i
475475 0 0
476476 6.83751e6i 0.00290585i
477477 −1.42124e9 3.00013e9i −0.599588 1.26568i
478478 1.36191e9 + 1.36191e9i 0.570363 + 0.570363i
479479 −3.12651e9 −1.29983 −0.649914 0.760008i 0.725195π-0.725195\pi
−0.649914 + 0.760008i 0.725195π0.725195\pi
480480 0 0
481481 −1.23163e9 −0.504630
482482 5.89776e8 + 5.89776e8i 0.239896 + 0.239896i
483483 2.45543e7 1.73045e7i 0.00991545 0.00698786i
484484 7.22938e8i 0.289829i
485485 0 0
486486 1.35314e9 1.17091e9i 0.534708 0.462695i
487487 −2.97686e9 + 2.97686e9i −1.16790 + 1.16790i −0.185204 + 0.982700i 0.559294π0.559294\pi
−0.982700 + 0.185204i 0.940706π0.940706\pi
488488 5.87788e8 5.87788e8i 0.228956 0.228956i
489489 −6.53076e8 + 3.77073e9i −0.252570 + 1.45829i
490490 0 0
491491 1.72819e9i 0.658880i −0.944177 0.329440i 0.893140π-0.893140\pi
0.944177 0.329440i 0.106860π-0.106860\pi
492492 −1.05109e9 1.49144e9i −0.397888 0.564585i
493493 −8.35657e8 8.35657e8i −0.314097 0.314097i
494494 −3.21391e7 −0.0119947
495495 0 0
496496 −5.14377e8 −0.189276
497497 2.20868e7 + 2.20868e7i 0.00807022 + 0.00807022i
498498 8.44336e8 + 1.19807e9i 0.306346 + 0.434691i
499499 7.15257e8i 0.257698i −0.991664 0.128849i 0.958872π-0.958872\pi
0.991664 0.128849i 0.0411282π-0.0411282\pi
500500 0 0
501501 −3.29101e8 + 1.90017e9i −0.116922 + 0.675087i
502502 −1.06592e9 + 1.06592e9i −0.376065 + 0.376065i
503503 −3.37593e9 + 3.37593e9i −1.18279 + 1.18279i −0.203765 + 0.979020i 0.565318π0.565318\pi
−0.979020 + 0.203765i 0.934682π0.934682\pi
504504 −9.13629e6 3.26261e6i −0.00317880 0.00113516i
505505 0 0
506506 1.69753e9i 0.582492i
507507 −2.08784e9 + 1.47140e9i −0.711492 + 0.501421i
508508 1.06740e9 + 1.06740e9i 0.361248 + 0.361248i
509509 −1.54439e9 −0.519094 −0.259547 0.965730i 0.583573π-0.583573\pi
−0.259547 + 0.965730i 0.583573π0.583573\pi
510510 0 0
511511 3.48313e7 0.0115477
512512 −9.49063e7 9.49063e7i −0.0312500 0.0312500i
513513 3.85625e7 + 1.38843e8i 0.0126111 + 0.0454059i
514514 1.64770e9i 0.535189i
515515 0 0
516516 1.32511e9 + 2.29504e8i 0.424598 + 0.0735387i
517517 1.24630e9 1.24630e9i 0.396647 0.396647i
518518 2.11696e7 2.11696e7i 0.00669203 0.00669203i
519519 −3.34152e9 5.78738e8i −1.04920 0.181717i
520520 0 0
521521 4.27492e9i 1.32433i −0.749358 0.662165i 0.769638π-0.769638\pi
0.749358 0.662165i 0.230362π-0.230362\pi
522522 −1.51535e9 + 7.17862e8i −0.466301 + 0.220899i
523523 −3.59310e9 3.59310e9i −1.09828 1.09828i −0.994612 0.103670i 0.966941π-0.966941\pi
−0.103670 0.994612i 0.533059π-0.533059\pi
524524 −1.80651e9 −0.548506
525525 0 0
526526 −3.04028e9 −0.910886
527527 1.09499e9 + 1.09499e9i 0.325891 + 0.325891i
528528 −4.48123e8 + 3.15813e8i −0.132489 + 0.0933707i
529529 2.09188e9i 0.614387i
530530 0 0
531531 2.27763e9 6.37806e9i 0.660166 1.84866i
532532 552414. 552414.i 0.000159065 0.000159065i
533533 −1.22916e9 + 1.22916e9i −0.351611 + 0.351611i
534534 6.55237e8 3.78321e9i 0.186210 1.07514i
535535 0 0
536536 6.57365e8i 0.184387i
537537 −3.42668e9 4.86230e9i −0.954914 1.35498i
538538 2.73168e9 + 2.73168e9i 0.756297 + 0.756297i
539539 −2.35680e9 −0.648278
540540 0 0
541541 −1.34240e9 −0.364495 −0.182247 0.983253i 0.558337π-0.558337\pi
−0.182247 + 0.983253i 0.558337π0.558337\pi
542542 2.01949e9 + 2.01949e9i 0.544810 + 0.544810i
543543 −2.98122e9 4.23020e9i −0.799087 1.13387i
544544 4.04067e8i 0.107611i
545545 0 0
546546 −1.57727e6 + 9.10686e6i −0.000414698 + 0.00239439i
547547 −2.35698e9 + 2.35698e9i −0.615745 + 0.615745i −0.944437 0.328692i 0.893392π-0.893392\pi
0.328692 + 0.944437i 0.393392π0.393392\pi
548548 1.55849e9 1.55849e9i 0.404549 0.404549i
549549 −1.19412e9 + 3.34389e9i −0.307995 + 0.862480i
550550 0 0
551551 1.35028e8i 0.0343870i
552552 −1.45105e9 + 1.02262e9i −0.367195 + 0.258779i
553553 −2.54240e7 2.54240e7i −0.00639303 0.00639303i
554554 −2.37681e9 −0.593897
555555 0 0
556556 −1.78845e9 −0.441281
557557 5.24979e9 + 5.24979e9i 1.28721 + 1.28721i 0.936476 + 0.350732i 0.114067π0.114067\pi
0.350732 + 0.936476i 0.385933π0.385933\pi
558558 1.98562e9 9.40639e8i 0.483811 0.229194i
559559 1.28122e9i 0.310229i
560560 0 0
561561 1.62624e9 + 2.81659e8i 0.388880 + 0.0673525i
562562 −1.75742e9 + 1.75742e9i −0.417636 + 0.417636i
563563 3.18694e8 3.18694e8i 0.0752654 0.0752654i −0.668472 0.743737i 0.733051π-0.733051\pi
0.743737 + 0.668472i 0.233051π0.233051\pi
564564 −1.81613e9 3.14547e8i −0.426256 0.0738258i
565565 0 0
566566 1.02902e9i 0.238543i
567567 4.12346e7 4.11307e6i 0.00949994 0.000947600i
568568 −1.30524e9 1.30524e9i −0.298861 0.298861i
569569 −2.87684e9 −0.654671 −0.327336 0.944908i 0.606151π-0.606151\pi
−0.327336 + 0.944908i 0.606151π0.606151\pi
570570 0 0
571571 3.80780e9 0.855948 0.427974 0.903791i 0.359227π-0.359227\pi
0.427974 + 0.903791i 0.359227π0.359227\pi
572572 3.69316e8 + 3.69316e8i 0.0825111 + 0.0825111i
573573 3.26322e9 2.29974e9i 0.724611 0.510666i
574574 4.22541e7i 0.00932561i
575575 0 0
576576 5.39916e8 + 1.92806e8i 0.117719 + 0.0420380i
577577 6.47107e9 6.47107e9i 1.40236 1.40236i 0.609839 0.792525i 0.291234π-0.291234\pi
0.792525 0.609839i 0.208766π-0.208766\pi
578578 −1.46106e9 + 1.46106e9i −0.314717 + 0.314717i
579579 −9.66534e8 + 5.58058e9i −0.206939 + 1.19482i
580580 0 0
581581 3.39426e7i 0.00718008i
582582 6.77364e8 + 9.61148e8i 0.142427 + 0.202097i
583583 −3.07196e9 3.07196e9i −0.642060 0.642060i
584584 −2.05838e9 −0.427642
585585 0 0
586586 −5.49914e9 −1.12889
587587 −1.02779e9 1.02779e9i −0.209734 0.209734i 0.594420 0.804155i 0.297382π-0.297382\pi
−0.804155 + 0.594420i 0.797382π0.797382\pi
588588 1.41978e9 + 2.01460e9i 0.288005 + 0.408666i
589589 1.76932e8i 0.0356783i
590590 0 0
591591 −1.03623e9 + 5.98300e9i −0.206491 + 1.19224i
592592 −1.25103e9 + 1.25103e9i −0.247823 + 0.247823i
593593 3.31531e9 3.31531e9i 0.652880 0.652880i −0.300806 0.953685i 0.597256π-0.597256\pi
0.953685 + 0.300806i 0.0972556π0.0972556\pi
594594 1.15234e9 2.03859e9i 0.225594 0.399097i
595595 0 0
596596 3.05388e9i 0.590868i
597597 2.44887e9 1.72583e9i 0.471038 0.331961i
598598 1.19587e9 + 1.19587e9i 0.228681 + 0.228681i
599599 4.59959e8 0.0874430 0.0437215 0.999044i 0.486079π-0.486079\pi
0.0437215 + 0.999044i 0.486079π0.486079\pi
600600 0 0
601601 2.14425e9 0.402917 0.201458 0.979497i 0.435432π-0.435432\pi
0.201458 + 0.979497i 0.435432π0.435432\pi
602602 2.20219e7 + 2.20219e7i 0.00411403 + 0.00411403i
603603 −1.20212e9 2.53759e9i −0.223274 0.471314i
604604 9.62431e8i 0.177722i
605605 0 0
606606 2.57945e9 + 4.46750e8i 0.470839 + 0.0815474i
607607 −1.08733e8 + 1.08733e8i −0.0197333 + 0.0197333i −0.716905 0.697171i 0.754442π-0.754442\pi
0.697171 + 0.716905i 0.254442π0.254442\pi
608608 −3.26453e7 + 3.26453e7i −0.00589059 + 0.00589059i
609609 −3.82613e7 6.62670e6i −0.00686434 0.00118888i
610610 0 0
611611 1.75598e9i 0.311440i
612612 −7.38916e8 1.55980e9i −0.130306 0.275067i
613613 3.55732e9 + 3.55732e9i 0.623751 + 0.623751i 0.946488 0.322738i 0.104603π-0.104603\pi
−0.322738 + 0.946488i 0.604603π0.604603\pi
614614 3.78853e9 0.660514
615615 0 0
616616 −1.26958e7 −0.00218840
617617 −8.21616e8 8.21616e8i −0.140822 0.140822i 0.633181 0.774003i 0.281749π-0.281749\pi
−0.774003 + 0.633181i 0.781749π0.781749\pi
618618 3.34289e9 2.35589e9i 0.569722 0.401508i
619619 7.57610e8i 0.128389i −0.997937 0.0641946i 0.979552π-0.979552\pi
0.997937 0.0641946i 0.0204478π-0.0204478\pi
620620 0 0
621621 3.73135e9 6.60110e9i 0.625237 1.10610i
622622 1.21638e8 1.21638e8i 0.0202676 0.0202676i
623623 6.28728e7 6.28728e7i 0.0104173 0.0104173i
624624 9.32100e7 5.38176e8i 0.0153574 0.0886704i
625625 0 0
626626 3.19939e9i 0.521263i
627627 1.08631e8 + 1.54143e8i 0.0176003 + 0.0249739i
628628 2.30301e9 + 2.30301e9i 0.371054 + 0.371054i
629629 5.32631e9 0.853393
630630 0 0
631631 −8.92366e9 −1.41397 −0.706985 0.707228i 0.749945π-0.749945\pi
−0.706985 + 0.707228i 0.749945π0.749945\pi
632632 1.50245e9 + 1.50245e9i 0.236750 + 0.236750i
633633 3.43693e9 + 4.87684e9i 0.538589 + 0.764233i
634634 1.50061e9i 0.233860i
635635 0 0
636636 −7.75317e8 + 4.47653e9i −0.119503 + 0.689988i
637637 1.66031e9 1.66031e9i 0.254508 0.254508i
638638 −1.55164e9 + 1.55164e9i −0.236547 + 0.236547i
639639 7.42540e9 + 2.65164e9i 1.12581 + 0.402033i
640640 0 0
641641 2.03499e8i 0.0305182i 0.999884 + 0.0152591i 0.00485731π0.00485731\pi
−0.999884 + 0.0152591i 0.995143π0.995143\pi
642642 1.51973e9 1.07102e9i 0.226670 0.159745i
643643 −3.94941e9 3.94941e9i −0.585859 0.585859i 0.350648 0.936507i 0.385961π-0.385961\pi
−0.936507 + 0.350648i 0.885961π0.885961\pi
644644 −4.11098e7 −0.00606520
645645 0 0
646646 1.38989e8 0.0202846
647647 7.82378e7 + 7.82378e7i 0.0113567 + 0.0113567i 0.712762 0.701406i 0.247444π-0.247444\pi
−0.701406 + 0.712762i 0.747444π0.747444\pi
648648 −2.43679e9 + 2.43065e8i −0.351808 + 0.0350921i
649649 8.86295e9i 1.27269i
650650 0 0
651651 5.01351e7 + 8.68320e6i 0.00712211 + 0.00123352i
652652 3.70326e9 3.70326e9i 0.523260 0.523260i
653653 −6.05012e9 + 6.05012e9i −0.850292 + 0.850292i −0.990169 0.139877i 0.955329π-0.955329\pi
0.139877 + 0.990169i 0.455329π0.455329\pi
654654 2.19734e9 + 3.80570e8i 0.307167 + 0.0532001i
655655 0 0
656656 2.49704e9i 0.345352i
657657 7.94583e9 3.76415e9i 1.09310 0.517831i
658658 −3.01821e7 3.01821e7i −0.00413009 0.00413009i
659659 1.01449e10 1.38085 0.690427 0.723402i 0.257423π-0.257423\pi
0.690427 + 0.723402i 0.257423π0.257423\pi
660660 0 0
661661 1.59862e9 0.215298 0.107649 0.994189i 0.465668π-0.465668\pi
0.107649 + 0.994189i 0.465668π0.465668\pi
662662 −5.65235e9 5.65235e9i −0.757227 0.757227i
663663 −1.34408e9 + 9.47231e8i −0.179113 + 0.126229i
664664 2.00586e9i 0.265897i
665665 0 0
666666 2.54152e9 7.11703e9i 0.333376 0.933553i
667667 −5.02430e9 + 5.02430e9i −0.655594 + 0.655594i
668668 1.86617e9 1.86617e9i 0.242233 0.242233i
669669 2.77130e8 1.60010e9i 0.0357843 0.206612i
670670 0 0
671671 4.64667e9i 0.593762i
672672 7.64818e6 + 1.08524e7i 0.000972222 + 0.00137954i
673673 7.66102e9 + 7.66102e9i 0.968799 + 0.968799i 0.999528 0.0307286i 0.00978276π-0.00978276\pi
−0.0307286 + 0.999528i 0.509783π0.509783\pi
674674 5.81845e9 0.731977
675675 0 0
676676 3.49555e9 0.435214
677677 −9.34134e9 9.34134e9i −1.15704 1.15704i −0.985109 0.171932i 0.944999π-0.944999\pi
−0.171932 0.985109i 0.555001π-0.555001\pi
678678 2.85434e8 + 4.05017e8i 0.0351724 + 0.0499079i
679679 2.72303e7i 0.00333817i
680680 0 0
681681 −2.36679e9 + 1.36654e10i −0.287174 + 1.65809i
682682 2.03316e9 2.03316e9i 0.245429 0.245429i
683683 −6.10846e9 + 6.10846e9i −0.733600 + 0.733600i −0.971331 0.237731i 0.923596π-0.923596\pi
0.237731 + 0.971331i 0.423596π0.423596\pi
684684 6.63203e7 1.85717e8i 0.00792411 0.0221899i
685685 0 0
686686 1.14156e8i 0.0135010i
687687 −1.06631e10 + 7.51479e9i −1.25469 + 0.884236i
688688 −1.30140e9 1.30140e9i −0.152353 0.152353i
689689 4.32826e9 0.504134
690690 0 0
691691 7.53547e9 0.868835 0.434417 0.900712i 0.356954π-0.356954\pi
0.434417 + 0.900712i 0.356954π0.356954\pi
692692 3.28173e9 + 3.28173e9i 0.376471 + 0.376471i
693693 4.90088e7 2.32167e7i 0.00559381 0.00264993i
694694 2.52639e9i 0.286908i
695695 0 0
696696 2.26108e9 + 3.91610e8i 0.254204 + 0.0440272i
697697 5.31562e9 5.31562e9i 0.594619 0.594619i
698698 −3.57588e7 + 3.57588e7i −0.00398006 + 0.00398006i
699699 1.38096e9 + 2.39176e8i 0.152936 + 0.0264879i
700700 0 0
701701 7.80912e9i 0.856228i 0.903725 + 0.428114i 0.140822π0.140822\pi
−0.903725 + 0.428114i 0.859178π0.859178\pi
702702 6.24349e8 + 2.24794e9i 0.0681157 + 0.245248i
703703 4.30322e8 + 4.30322e8i 0.0467143 + 0.0467143i
704704 7.50266e8 0.0810422
705705 0 0
706706 4.56314e9 0.488030
707707 4.28676e7 + 4.28676e7i 0.00456206 + 0.00456206i
708708 −7.57609e9 + 5.33921e9i −0.802285 + 0.565406i
709709 1.35196e10i 1.42463i −0.701859 0.712316i 0.747647π-0.747647\pi
0.701859 0.712316i 0.252353π-0.252353\pi
710710 0 0
711711 −8.54735e9 3.05229e9i −0.891842 0.318480i
712712 −3.71551e9 + 3.71551e9i −0.385779 + 0.385779i
713713 6.58351e9 6.58351e9i 0.680212 0.680212i
714714 6.82106e6 3.93835e7i 0.000701307 0.00404921i
715715 0 0
716716 8.14067e9i 0.828828i
717717 6.48586e9 + 9.20314e9i 0.657129 + 0.932435i
718718 −7.08967e9 7.08967e9i −0.714810 0.714810i
719719 1.42659e9 0.143136 0.0715679 0.997436i 0.477200π-0.477200\pi
0.0715679 + 0.997436i 0.477200π0.477200\pi
720720 0 0
721721 9.47075e7 0.00941046
722722 −5.04527e9 5.04527e9i −0.498890 0.498890i
723723 2.80871e9 + 3.98542e9i 0.276390 + 0.392184i
724724 7.08238e9i 0.693576i
725725 0 0
726726 −7.21200e8 + 4.16407e9i −0.0699483 + 0.403868i
727727 −9.45672e9 + 9.45672e9i −0.912789 + 0.912789i −0.996491 0.0837022i 0.973326π-0.973326\pi
0.0837022 + 0.996491i 0.473326π0.473326\pi
728728 8.94391e6 8.94391e6i 0.000859147 0.000859147i
729729 8.96209e9 5.39443e9i 0.856768 0.515703i
730730 0 0
731731 5.54076e9i 0.524637i
732732 3.97199e9 2.79924e9i 0.374299 0.263786i
733733 3.48961e9 + 3.48961e9i 0.327275 + 0.327275i 0.851549 0.524274i 0.175663π-0.175663\pi
−0.524274 + 0.851549i 0.675663π0.675663\pi
734734 9.43247e9 0.880419
735735 0 0
736736 2.42941e9 0.224610
737737 −2.59835e9 2.59835e9i −0.239090 0.239090i
738738 −4.56632e9 9.63916e9i −0.418186 0.882758i
739739 2.10615e10i 1.91970i 0.280512 + 0.959850i 0.409496π0.409496\pi
−0.280512 + 0.959850i 0.590504π0.590504\pi
740740 0 0
741741 −1.85119e8 3.20619e7i −0.0167143 0.00289484i
742742 −7.43951e7 + 7.43951e7i −0.00668545 + 0.00668545i
743743 1.14614e10 1.14614e10i 1.02512 1.02512i 0.0254470 0.999676i 0.491899π-0.491899\pi
0.999676 0.0254470i 0.00810090π-0.00810090\pi
744744 −2.96277e9 5.13140e8i −0.263750 0.0456805i
745745 0 0
746746 8.66285e9i 0.763968i
747747 3.66812e9 + 7.74311e9i 0.321974 + 0.679663i
748748 −1.59714e9 1.59714e9i −0.139537 0.139537i
749749 4.30555e7 0.00374406
750750 0 0
751751 −1.54716e10 −1.33289 −0.666447 0.745553i 0.732186π-0.732186\pi
−0.666447 + 0.745553i 0.732186π0.732186\pi
752752 1.78363e9 + 1.78363e9i 0.152948 + 0.152948i
753753 −7.20299e9 + 5.07627e9i −0.614795 + 0.433274i
754754 2.18619e9i 0.185732i
755755 0 0
756756 −4.93696e7 2.79067e7i −0.00415559 0.00234899i
757757 1.08146e9 1.08146e9i 0.0906096 0.0906096i −0.660349 0.750959i 0.729592π-0.729592\pi
0.750959 + 0.660349i 0.229592π0.229592\pi
758758 −2.76264e9 + 2.76264e9i −0.230400 + 0.230400i
759759 1.69345e9 9.77762e9i 0.140580 0.811684i
760760 0 0
761761 2.19606e9i 0.180633i −0.995913 0.0903166i 0.971212π-0.971212\pi
0.995913 0.0903166i 0.0287879π-0.0287879\pi
762762 5.08333e9 + 7.21300e9i 0.416203 + 0.590573i
763763 3.65174e7 + 3.65174e7i 0.00297621 + 0.00297621i
764764 −5.46341e9 −0.443238
765765 0 0
766766 5.39370e9 0.433597
767767 6.24376e9 + 6.24376e9i 0.499646 + 0.499646i
768768 −4.51974e8 6.41331e8i −0.0360039 0.0510879i
769769 8.38646e9i 0.665023i 0.943099 + 0.332511i 0.107896π0.107896\pi
−0.943099 + 0.332511i 0.892104π0.892104\pi
770770 0 0
771771 −1.64374e9 + 9.49062e9i −0.129164 + 0.745769i
772772 5.48072e9 5.48072e9i 0.428723 0.428723i
773773 1.32895e10 1.32895e10i 1.03486 1.03486i 0.0354850 0.999370i 0.488702π-0.488702\pi
0.999370 0.0354850i 0.0112976π-0.0112976\pi
774774 7.40358e9 + 2.64385e9i 0.573916 + 0.204948i
775775 0 0
776776 1.60919e9i 0.123621i
777777 1.43054e8 1.00816e8i 0.0109402 0.00771005i
778778 −1.12469e10 1.12469e10i −0.856257 0.856257i
779779 8.58916e8 0.0650983
780780 0 0
781781 1.03183e10 0.775052
782782 −5.17166e9 5.17166e9i −0.386729 0.386729i
783783 −9.44444e9 + 2.62312e9i −0.703088 + 0.195277i
784784 3.37292e9i 0.249977i
785785 0 0
786786 −1.04054e10 1.80217e9i −0.764326 0.132378i
787787 −1.62056e10 + 1.62056e10i −1.18510 + 1.18510i −0.206691 + 0.978406i 0.566269π0.566269\pi
−0.978406 + 0.206691i 0.933731π0.933731\pi
788788 5.87595e9 5.87595e9i 0.427795 0.427795i
789789 −1.75118e10 3.03297e9i −1.26929 0.219836i
790790 0 0
791791 1.14745e7i 0.000824361i
792792 −2.89621e9 + 1.37201e9i −0.207153 + 0.0981339i
793793 −3.27348e9 3.27348e9i −0.233106 0.233106i
794794 −1.09640e10 −0.777318
795795 0 0
796796 −4.10000e9 −0.288130
797797 −9.60911e9 9.60911e9i −0.672325 0.672325i 0.285927 0.958251i 0.407699π-0.407699\pi
−0.958251 + 0.285927i 0.907699π0.907699\pi
798798 3.73295e6 2.63078e6i 0.000260041 0.000183263i
799799 7.59389e9i 0.526685i
800800 0 0
801801 7.54823e9 2.11373e10i 0.518957 1.45324i
802802 9.19400e9 9.19400e9i 0.629353 0.629353i
803803 8.13609e9 8.13609e9i 0.554512 0.554512i
804804 −6.55784e8 + 3.78637e9i −0.0445005 + 0.256937i
805805 0 0
806806 2.86464e9i 0.192707i
807807 1.30092e10 + 1.84594e10i 0.871349 + 1.23640i
808808 −2.53329e9 2.53329e9i −0.168945 0.168945i
809809 −1.28712e10 −0.854670 −0.427335 0.904093i 0.640547π-0.640547\pi
−0.427335 + 0.904093i 0.640547π0.640547\pi
810810 0 0
811811 2.57707e10 1.69650 0.848250 0.529597i 0.177657π-0.177657\pi
0.848250 + 0.529597i 0.177657π0.177657\pi
812812 3.75767e7 + 3.75767e7i 0.00246304 + 0.00246304i
813813 9.61749e9 + 1.36468e10i 0.627689 + 0.890662i
814814 9.88982e9i 0.642692i
815815 0 0
816816 −4.03096e8 + 2.32739e9i −0.0259712 + 0.149953i
817817 −4.47648e8 + 4.47648e8i −0.0287184 + 0.0287184i
818818 3.29958e9 3.29958e9i 0.210776 0.210776i
819819 −1.81699e7 + 5.08813e7i −0.00115574 + 0.00323642i
820820 0 0
821821 1.40840e10i 0.888231i −0.895970 0.444115i 0.853518π-0.853518\pi
0.895970 0.444115i 0.146482π-0.146482\pi
822822 1.05315e10 7.42202e9i 0.661362 0.466091i
823823 1.00043e10 + 1.00043e10i 0.625585 + 0.625585i 0.946954 0.321369i 0.104143π-0.104143\pi
−0.321369 + 0.946954i 0.604143π0.604143\pi
824824 −5.59681e9 −0.348494
825825 0 0
826826 −2.14638e8 −0.0132519
827827 −9.81003e9 9.81003e9i −0.603116 0.603116i 0.338022 0.941138i 0.390242π-0.390242\pi
−0.941138 + 0.338022i 0.890242π0.890242\pi
828828 −9.37811e9 + 4.44266e9i −0.574129 + 0.271980i
829829 1.01779e10i 0.620465i 0.950661 + 0.310232i 0.100407π0.100407\pi
−0.950661 + 0.310232i 0.899593π0.899593\pi
830830 0 0
831831 −1.36903e10 2.37110e9i −0.827577 0.143333i
832832 −5.28546e8 + 5.28546e8i −0.0318164 + 0.0318164i
833833 −7.18018e9 + 7.18018e9i −0.430406 + 0.430406i
834834 −1.03013e10 1.78415e9i −0.614912 0.106500i
835835 0 0
836836 2.58072e8i 0.0152763i
837837 1.23754e10 3.43717e9i 0.729490 0.202610i
838838 −1.49245e9 1.49245e9i −0.0876083 0.0876083i
839839 −8.79408e9 −0.514071 −0.257036 0.966402i 0.582746π-0.582746\pi
−0.257036 + 0.966402i 0.582746π0.582746\pi
840840 0 0
841841 −8.06489e9 −0.467533
842842 −1.32259e9 1.32259e9i −0.0763545 0.0763545i
843843 −1.18758e10 + 8.36940e9i −0.682756 + 0.481169i
844844 8.16501e9i 0.467475i
845845 0 0
846846 −1.01470e10 3.62353e9i −0.576157 0.205748i
847847 −6.92022e7 + 6.92022e7i −0.00391317 + 0.00391317i
848848 4.39643e9 4.39643e9i 0.247579 0.247579i
849849 1.02655e9 5.92709e9i 0.0575708 0.332403i
850850 0 0
851851 3.20239e10i 1.78123i
852852 −6.21595e9 8.82015e9i −0.344326 0.488582i
853853 1.44455e10 + 1.44455e10i 0.796914 + 0.796914i 0.982608 0.185694i 0.0594533π-0.0594533\pi
−0.185694 + 0.982608i 0.559453π0.559453\pi
854854 1.12530e8 0.00618255
855855 0 0
856856 −2.54440e9 −0.138652
857857 −3.96978e9 3.96978e9i −0.215443 0.215443i 0.591132 0.806575i 0.298681π-0.298681\pi
−0.806575 + 0.591132i 0.798681π0.798681\pi
858858 1.75881e9 + 2.49566e9i 0.0950631 + 0.134890i
859859 3.68048e10i 1.98120i 0.136791 + 0.990600i 0.456321π0.456321\pi
−0.136791 + 0.990600i 0.543679π0.543679\pi
860860 0 0
861861 4.21525e7 2.43380e8i 0.00225067 0.0129949i
862862 1.38527e9 1.38527e9i 0.0736645 0.0736645i
863863 1.52667e9 1.52667e9i 0.0808550 0.0808550i −0.665523 0.746378i 0.731791π-0.731791\pi
0.746378 + 0.665523i 0.231791π0.231791\pi
864864 2.91753e9 + 1.64916e9i 0.153892 + 0.0869893i
865865 0 0
866866 8.72463e9i 0.456493i
867867 −9.87314e9 + 6.95804e9i −0.514503 + 0.362594i
868868 −4.92380e7 4.92380e7i −0.00255553 0.00255553i
869869 −1.18774e10 −0.613977
870870 0 0
871871 3.66096e9 0.187729
872872 −2.15802e9 2.15802e9i −0.110217 0.110217i
873873 2.94273e9 + 6.21187e9i 0.149693 + 0.315989i
874874 8.35656e8i 0.0423387i
875875 0 0
876876 −1.18561e10 2.05343e9i −0.595905 0.103208i
877877 1.62907e10 1.62907e10i 0.815535 0.815535i −0.169923 0.985457i 0.554352π-0.554352\pi
0.985457 + 0.169923i 0.0543519π0.0543519\pi
878878 −1.93034e10 + 1.93034e10i −0.962503 + 0.962503i
879879 −3.16746e10 5.48591e9i −1.57308 0.272451i
880880 0 0
881881 4.54066e9i 0.223719i 0.993724 + 0.111860i 0.0356807π0.0356807\pi
−0.993724 + 0.111860i 0.964319π0.964319\pi
882882 6.16806e9 + 1.30203e10i 0.302697 + 0.638970i
883883 6.30625e9 + 6.30625e9i 0.308254 + 0.308254i 0.844232 0.535978i 0.180057π-0.180057\pi
−0.535978 + 0.844232i 0.680057π0.680057\pi
884884 2.25031e9 0.109562
885885 0 0
886886 −5.49423e9 −0.265393
887887 −2.62069e10 2.62069e10i −1.26091 1.26091i −0.950654 0.310253i 0.899586π-0.899586\pi
−0.310253 0.950654i 0.600414π-0.600414\pi
888888 −8.45385e9 + 5.95781e9i −0.405144 + 0.285523i
889889 2.04352e8i 0.00975488i
890890 0 0
891891 8.67106e9 1.05926e10i 0.410677 0.501683i
892892 −1.57146e9 + 1.57146e9i −0.0741357 + 0.0741357i
893893 6.13524e8 6.13524e8i 0.0288305 0.0288305i
894894 −3.04654e9 + 1.75901e10i −0.142602 + 0.823356i
895895 0 0
896896 1.81695e7i 0.000843851i
897897 5.69513e9 + 8.08112e9i 0.263469 + 0.373851i
898898 3.27213e9 + 3.27213e9i 0.150787 + 0.150787i
899899 −1.20354e10 −0.552461
900900 0 0
901901 −1.87180e10 −0.852554
902902 −9.86996e9 9.86996e9i −0.447809 0.447809i
903903 1.04875e8 + 1.48813e8i 0.00473987 + 0.00672566i
904904 6.78096e8i 0.0305282i
905905 0 0
906906 −9.60116e8 + 5.54352e9i −0.0428919 + 0.247649i
907907 1.46368e10 1.46368e10i 0.651359 0.651359i −0.301962 0.953320i 0.597641π-0.597641\pi
0.953320 + 0.301962i 0.0976414π0.0976414\pi
908908 1.34209e10 1.34209e10i 0.594950 0.594950i
909909 1.44117e10 + 5.14649e9i 0.636418 + 0.227267i
910910 0 0
911911 1.17472e10i 0.514779i 0.966308 + 0.257389i 0.0828623π0.0828623\pi
−0.966308 + 0.257389i 0.917138π0.917138\pi
912912 −2.20601e8 + 1.55468e8i −0.00962999 + 0.00678669i
913913 7.92852e9 + 7.92852e9i 0.344782 + 0.344782i
914914 −3.05495e10 −1.32340
915915 0 0
916916 1.78527e10 0.767483
917917 −1.72926e8 1.72926e8i −0.00740572 0.00740572i
918918 −2.70005e9 9.72144e9i −0.115192 0.414745i
919919 6.14798e8i 0.0261293i −0.999915 0.0130647i 0.995841π-0.995841\pi
0.999915 0.0130647i 0.00415873π-0.00415873\pi
920920 0 0
921921 2.18217e10 + 3.77942e9i 0.920405 + 0.159410i
922922 4.81491e8 4.81491e8i 0.0202316 0.0202316i
923923 −7.26904e9 + 7.26904e9i −0.304278 + 0.304278i
924924 −7.31267e7 1.26653e7i −0.00304947 0.000528156i
925925 0 0
926926 1.16430e10i 0.481868i
927927 2.16050e10 1.02349e10i 0.890790 0.421991i
928928 −2.22062e9 2.22062e9i −0.0912129 0.0912129i
929929 −2.52842e10 −1.03465 −0.517325 0.855789i 0.673072π-0.673072\pi
−0.517325 + 0.855789i 0.673072π0.673072\pi
930930 0 0
931931 −1.16020e9 −0.0471204
932932 −1.35625e9 1.35625e9i −0.0548761 0.0548761i
933933 8.21971e8 5.79280e8i 0.0331338 0.0233509i
934934 2.67473e10i 1.07415i
935935 0 0
936936 1.07376e9 3.00687e9i 0.0428000 0.119853i
937937 −7.18729e9 + 7.18729e9i −0.285415 + 0.285415i −0.835264 0.549849i 0.814685π-0.814685\pi
0.549849 + 0.835264i 0.314685π0.314685\pi
938938 −6.29253e7 + 6.29253e7i −0.00248952 + 0.00248952i
939939 3.19170e9 1.84282e10i 0.125803 0.726364i
940940 0 0
941941 6.79467e9i 0.265830i 0.991127 + 0.132915i 0.0424338π0.0424338\pi
−0.991127 + 0.132915i 0.957566π0.957566\pi
942942 1.09677e10 + 1.55626e10i 0.427500 + 0.606603i
943943 −3.19596e10 3.19596e10i −1.24111 1.24111i
944944 1.26842e10 0.490751
945945 0 0
946946 1.02880e10 0.395105
947947 1.06210e10 + 1.06210e10i 0.406387 + 0.406387i 0.880476 0.474090i 0.157223π-0.157223\pi
−0.474090 + 0.880476i 0.657223π0.657223\pi
948948 7.15516e9 + 1.01528e10i 0.272766 + 0.387042i
949949 1.14634e10i 0.435393i
950950 0 0
951951 −1.49700e9 + 8.64339e9i −0.0564404 + 0.325876i
952952 −3.86788e7 + 3.86788e7i −0.00145293 + 0.00145293i
953953 1.21090e10 1.21090e10i 0.453195 0.453195i −0.443219 0.896413i 0.646164π-0.646164\pi
0.896413 + 0.443219i 0.146164π0.146164\pi
954954 −8.93153e9 + 2.50110e10i −0.333048 + 0.932635i
955955 0 0
956956 1.54083e10i 0.570363i
957957 −1.04852e10 + 7.38939e9i −0.386710 + 0.272532i
958958 1.76862e10 + 1.76862e10i 0.649914 + 0.649914i
959959 2.98368e8 0.0109241
960960 0 0
961961 −1.17422e10 −0.426793
962962 6.96716e9 + 6.96716e9i 0.252315 + 0.252315i
963963 9.82198e9 4.65293e9i 0.354411 0.167894i
964964 6.67256e9i 0.239896i
965965 0 0
966966 −2.36789e8 4.10109e7i −0.00845166 0.00146379i
967967 −1.11474e10 + 1.11474e10i −0.396443 + 0.396443i −0.876977 0.480533i 0.840443π-0.840443\pi
0.480533 + 0.876977i 0.340443π0.340443\pi
968968 4.08956e9 4.08956e9i 0.144915 0.144915i
969969 8.00564e8 + 1.38655e8i 0.0282659 + 0.00489554i
970970 0 0
971971 2.00122e10i 0.701501i −0.936469 0.350750i 0.885927π-0.885927\pi
0.936469 0.350750i 0.114073π-0.114073\pi
972972 −1.42782e10 1.03090e9i −0.498702 0.0360066i
973973 −1.71197e8 1.71197e8i −0.00595801 0.00595801i
974974 3.36793e10 1.16790
975975 0 0
976976 −6.65007e9 −0.228956
977977 1.36208e10 + 1.36208e10i 0.467273 + 0.467273i 0.901030 0.433757i 0.142812π-0.142812\pi
−0.433757 + 0.901030i 0.642812π0.642812\pi
978978 2.50248e10 1.76361e10i 0.855431 0.602861i
979979 2.93724e10i 1.00046i
980980 0 0
981981 1.22768e10 + 4.38411e9i 0.415188 + 0.148265i
982982 −9.77612e9 + 9.77612e9i −0.329440 + 0.329440i
983983 −1.66058e9 + 1.66058e9i −0.0557598 + 0.0557598i −0.734437 0.678677i 0.762554π-0.762554\pi
0.678677 + 0.734437i 0.262554π0.262554\pi
984984 −2.49103e9 + 1.43827e10i −0.0833482 + 0.481236i
985985 0 0
986986 9.45437e9i 0.314097i
987987 −1.43737e8 2.03956e8i −0.00475838 0.00675191i
988988 1.81806e8 + 1.81806e8i 0.00599736 + 0.00599736i
989989 3.33133e10 1.09504
990990 0 0
991991 −4.37565e10 −1.42819 −0.714093 0.700050i 0.753161π-0.753161\pi
−0.714093 + 0.700050i 0.753161π0.753161\pi
992992 2.90976e9 + 2.90976e9i 0.0946380 + 0.0946380i
993993 −2.69183e10 3.81958e10i −0.872420 1.23792i
994994 2.49884e8i 0.00807022i
995995 0 0
996996 2.00104e9 1.15536e10i 0.0641724 0.370519i
997997 −6.81579e9 + 6.81579e9i −0.217813 + 0.217813i −0.807576 0.589763i 0.799221π-0.799221\pi
0.589763 + 0.807576i 0.299221π0.299221\pi
998998 −4.04611e9 + 4.04611e9i −0.128849 + 0.128849i
999999 2.17389e10 3.84581e10i 0.689855 1.22042i
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 150.8.e.a.143.2 yes 16
3.2 odd 2 inner 150.8.e.a.143.5 yes 16
5.2 odd 4 inner 150.8.e.a.107.5 yes 16
5.3 odd 4 inner 150.8.e.a.107.4 yes 16
5.4 even 2 inner 150.8.e.a.143.7 yes 16
15.2 even 4 inner 150.8.e.a.107.2 16
15.8 even 4 inner 150.8.e.a.107.7 yes 16
15.14 odd 2 inner 150.8.e.a.143.4 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.8.e.a.107.2 16 15.2 even 4 inner
150.8.e.a.107.4 yes 16 5.3 odd 4 inner
150.8.e.a.107.5 yes 16 5.2 odd 4 inner
150.8.e.a.107.7 yes 16 15.8 even 4 inner
150.8.e.a.143.2 yes 16 1.1 even 1 trivial
150.8.e.a.143.4 yes 16 15.14 odd 2 inner
150.8.e.a.143.5 yes 16 3.2 odd 2 inner
150.8.e.a.143.7 yes 16 5.4 even 2 inner