Properties

Label 8.12.b.a.5.9
Level 88
Weight 1212
Character 8.5
Analytic conductor 6.1476.147
Analytic rank 00
Dimension 1010
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8,12,Mod(5,8)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 12, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8.5");
 
S:= CuspForms(chi, 12);
 
N := Newforms(S);
 
Level: N N == 8=23 8 = 2^{3}
Weight: k k == 12 12
Character orbit: [χ][\chi] == 8.b (of order 22, degree 11, 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: 6.146745444486.14674544448
Analytic rank: 00
Dimension: 1010
Coefficient field: Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x10x948x8+8836x792554x62200342x588894588x4++34431558027300 x^{10} - x^{9} - 48 x^{8} + 8836 x^{7} - 92554 x^{6} - 2200342 x^{5} - 88894588 x^{4} + \cdots + 34431558027300 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 245327 2^{45}\cdot 3^{2}\cdot 7
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 5.9
Root 20.84725.89062i20.8472 - 5.89062i of defining polynomial
Character χ\chi == 8.5
Dual form 8.12.b.a.5.10

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+(43.694411.7812i)q2+381.717iq3+(1770.401029.55i)q4+8937.55iq5+(4497.10+16678.9i)q6+10175.0q7+(65227.565843.1i)q8+31439.0q9+(105295.+390521.i)q10+408594.iq11+(392996.+675794.i)q121.94255e6iq13+(444591.119874.i)q143.41162e6q15+(2.07436e63.64544e6i)q169.64991e6q17+(1.37371e6370391.i)q181.27489e7iq19+(9.20165e6+1.58231e7i)q20+3.88398e6iq21+(4.81374e6+1.78533e7i)q22+2.34581e7q23+(2.51334e7+2.48984e7i)q243.10517e7q25+(2.28857e78.48786e7i)q26+7.96209e7iq27+(1.80139e71.04757e7i)q284.83134e7iq29+(1.49069e8+4.01931e7i)q30+2.63557e8q31+(4.76903e71.83724e8i)q321.55967e8q33+(4.21647e8+1.13688e8i)q34+9.09397e7iq35+(5.56598e73.23680e7i)q367.91290e7iq37+(1.50198e85.57057e8i)q38+7.41505e8q39+(5.88476e8+5.82974e8i)q406.96380e8q41+(4.57581e7+1.69708e8i)q42+4.03606e8iq43+(4.20667e8+7.23376e8i)q44+2.80988e8iq45+(1.02499e92.76365e8i)q465.59625e8q47+(1.39153e9+7.91820e8i)q481.87380e9q49+(1.35679e9+3.65828e8i)q503.68354e9iq51+(1.99995e93.43910e9i)q522.88775e9iq53+(9.38032e8+3.47899e9i)q543.65183e9q55+(6.63690e86.69954e8i)q56+4.86648e9q57+(5.69191e82.11102e9i)q58+9.84523e9iq59+(6.03994e9+3.51243e9i)q60+5.65364e9iq61+(1.15160e103.10503e9i)q62+3.19892e8q63+(8.06933e78.58956e9i)q64+1.73617e10q65+(6.81489e9+1.83749e9i)q661.28196e10iq67+(1.70842e10+9.93505e9i)q68+8.95435e9iq69+(1.07138e9+3.97356e9i)q703.63445e9q71+(2.05069e92.07004e9i)q722.56732e9q73+(9.32237e83.45749e9i)q741.18530e10iq75+(1.31256e102.25707e10i)q76+4.15744e9iq77+(3.23996e108.73585e9i)q782.59475e10q79+(3.25813e10+1.85397e10i)q802.48233e10q81+(3.04279e10+8.20422e9i)q82+3.80496e10iq83+(3.99874e9+6.87621e9i)q848.62466e10iq85+(4.75498e9+1.76353e10i)q86+1.84420e10q87+(2.69031e10+2.66515e10i)q882.00557e10q89+(3.31039e9+1.22776e10i)q901.97655e10iq91+(4.15303e102.41512e10i)q92+1.00604e11iq93+(2.44525e10+6.59307e9i)q94+1.13944e11q95+(7.01305e10+1.82042e10i)q966.90643e10q97+(8.18744e10+2.20756e10i)q98+1.28458e10iq99+O(q100)q+(43.6944 - 11.7812i) q^{2} +381.717i q^{3} +(1770.40 - 1029.55i) q^{4} +8937.55i q^{5} +(4497.10 + 16678.9i) q^{6} +10175.0 q^{7} +(65227.5 - 65843.1i) q^{8} +31439.0 q^{9} +(105295. + 390521. i) q^{10} +408594. i q^{11} +(392996. + 675794. i) q^{12} -1.94255e6i q^{13} +(444591. - 119874. i) q^{14} -3.41162e6 q^{15} +(2.07436e6 - 3.64544e6i) q^{16} -9.64991e6 q^{17} +(1.37371e6 - 370391. i) q^{18} -1.27489e7i q^{19} +(9.20165e6 + 1.58231e7i) q^{20} +3.88398e6i q^{21} +(4.81374e6 + 1.78533e7i) q^{22} +2.34581e7 q^{23} +(2.51334e7 + 2.48984e7i) q^{24} -3.10517e7 q^{25} +(-2.28857e7 - 8.48786e7i) q^{26} +7.96209e7i q^{27} +(1.80139e7 - 1.04757e7i) q^{28} -4.83134e7i q^{29} +(-1.49069e8 + 4.01931e7i) q^{30} +2.63557e8 q^{31} +(4.76903e7 - 1.83724e8i) q^{32} -1.55967e8 q^{33} +(-4.21647e8 + 1.13688e8i) q^{34} +9.09397e7i q^{35} +(5.56598e7 - 3.23680e7i) q^{36} -7.91290e7i q^{37} +(-1.50198e8 - 5.57057e8i) q^{38} +7.41505e8 q^{39} +(5.88476e8 + 5.82974e8i) q^{40} -6.96380e8 q^{41} +(4.57581e7 + 1.69708e8i) q^{42} +4.03606e8i q^{43} +(4.20667e8 + 7.23376e8i) q^{44} +2.80988e8i q^{45} +(1.02499e9 - 2.76365e8i) q^{46} -5.59625e8 q^{47} +(1.39153e9 + 7.91820e8i) q^{48} -1.87380e9 q^{49} +(-1.35679e9 + 3.65828e8i) q^{50} -3.68354e9i q^{51} +(-1.99995e9 - 3.43910e9i) q^{52} -2.88775e9i q^{53} +(9.38032e8 + 3.47899e9i) q^{54} -3.65183e9 q^{55} +(6.63690e8 - 6.69954e8i) q^{56} +4.86648e9 q^{57} +(-5.69191e8 - 2.11102e9i) q^{58} +9.84523e9i q^{59} +(-6.03994e9 + 3.51243e9i) q^{60} +5.65364e9i q^{61} +(1.15160e10 - 3.10503e9i) q^{62} +3.19892e8 q^{63} +(-8.06933e7 - 8.58956e9i) q^{64} +1.73617e10 q^{65} +(-6.81489e9 + 1.83749e9i) q^{66} -1.28196e10i q^{67} +(-1.70842e10 + 9.93505e9i) q^{68} +8.95435e9i q^{69} +(1.07138e9 + 3.97356e9i) q^{70} -3.63445e9 q^{71} +(2.05069e9 - 2.07004e9i) q^{72} -2.56732e9 q^{73} +(-9.32237e8 - 3.45749e9i) q^{74} -1.18530e10i q^{75} +(-1.31256e10 - 2.25707e10i) q^{76} +4.15744e9i q^{77} +(3.23996e10 - 8.73585e9i) q^{78} -2.59475e10 q^{79} +(3.25813e10 + 1.85397e10i) q^{80} -2.48233e10 q^{81} +(-3.04279e10 + 8.20422e9i) q^{82} +3.80496e10i q^{83} +(3.99874e9 + 6.87621e9i) q^{84} -8.62466e10i q^{85} +(4.75498e9 + 1.76353e10i) q^{86} +1.84420e10 q^{87} +(2.69031e10 + 2.66515e10i) q^{88} -2.00557e10 q^{89} +(3.31039e9 + 1.22776e10i) q^{90} -1.97655e10i q^{91} +(4.15303e10 - 2.41512e10i) q^{92} +1.00604e11i q^{93} +(-2.44525e10 + 6.59307e9i) q^{94} +1.13944e11 q^{95} +(7.01305e10 + 1.82042e10i) q^{96} -6.90643e10 q^{97} +(-8.18744e10 + 2.20756e10i) q^{98} +1.28458e10i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 10q+22q2+436q424308q633616q7208472q8472394q9+29864q10476216q12+2264272q14+3391792q15+3757072q16+2639732q17+2329130q18+6194726778q98+O(q100) 10 q + 22 q^{2} + 436 q^{4} - 24308 q^{6} - 33616 q^{7} - 208472 q^{8} - 472394 q^{9} + 29864 q^{10} - 476216 q^{12} + 2264272 q^{14} + 3391792 q^{15} + 3757072 q^{16} + 2639732 q^{17} + 2329130 q^{18}+ \cdots - 6194726778 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/8Z)×\left(\mathbb{Z}/8\mathbb{Z}\right)^\times.

nn 55 77
χ(n)\chi(n) 1-1 11

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 43.6944 11.7812i 0.965519 0.260331i
33 381.717i 0.906932i 0.891274 + 0.453466i 0.149813π0.149813\pi
−0.891274 + 0.453466i 0.850187π0.850187\pi
44 1770.40 1029.55i 0.864455 0.502709i
55 8937.55i 1.27904i 0.768775 + 0.639519i 0.220867π0.220867\pi
−0.768775 + 0.639519i 0.779133π0.779133\pi
66 4497.10 + 16678.9i 0.236103 + 0.875661i
77 10175.0 0.228821 0.114410 0.993434i 0.463502π-0.463502\pi
0.114410 + 0.993434i 0.463502π0.463502\pi
88 65227.5 65843.1i 0.703778 0.710420i
99 31439.0 0.177474
1010 105295. + 390521.i 0.332973 + 1.23494i
1111 408594.i 0.764948i 0.923966 + 0.382474i 0.124928π0.124928\pi
−0.923966 + 0.382474i 0.875072π0.875072\pi
1212 392996. + 675794.i 0.455923 + 0.784002i
1313 1.94255e6i 1.45106i −0.688193 0.725528i 0.741596π-0.741596\pi
0.688193 0.725528i 0.258404π-0.258404\pi
1414 444591. 119874.i 0.220931 0.0595692i
1515 −3.41162e6 −1.16000
1616 2.07436e6 3.64544e6i 0.494567 0.869140i
1717 −9.64991e6 −1.64837 −0.824184 0.566322i 0.808366π-0.808366\pi
−0.824184 + 0.566322i 0.808366π0.808366\pi
1818 1.37371e6 370391.i 0.171355 0.0462020i
1919 1.27489e7i 1.18121i −0.806959 0.590607i 0.798888π-0.798888\pi
0.806959 0.590607i 0.201112π-0.201112\pi
2020 9.20165e6 + 1.58231e7i 0.642985 + 1.10567i
2121 3.88398e6i 0.207525i
2222 4.81374e6 + 1.78533e7i 0.199140 + 0.738572i
2323 2.34581e7 0.759957 0.379979 0.924995i 0.375931π-0.375931\pi
0.379979 + 0.924995i 0.375931π0.375931\pi
2424 2.51334e7 + 2.48984e7i 0.644303 + 0.638279i
2525 −3.10517e7 −0.635939
2626 −2.28857e7 8.48786e7i −0.377755 1.40102i
2727 7.96209e7i 1.06789i
2828 1.80139e7 1.04757e7i 0.197805 0.115030i
2929 4.83134e7i 0.437400i −0.975792 0.218700i 0.929818π-0.929818\pi
0.975792 0.218700i 0.0701815π-0.0701815\pi
3030 −1.49069e8 + 4.01931e7i −1.12000 + 0.301984i
3131 2.63557e8 1.65343 0.826714 0.562622i 0.190207π-0.190207\pi
0.826714 + 0.562622i 0.190207π0.190207\pi
3232 4.76903e7 1.83724e8i 0.251250 0.967922i
3333 −1.55967e8 −0.693756
3434 −4.21647e8 + 1.13688e8i −1.59153 + 0.429121i
3535 9.09397e7i 0.292671i
3636 5.56598e7 3.23680e7i 0.153419 0.0892179i
3737 7.91290e7i 0.187597i −0.995591 0.0937985i 0.970099π-0.970099\pi
0.995591 0.0937985i 0.0299010π-0.0299010\pi
3838 −1.50198e8 5.57057e8i −0.307507 1.14048i
3939 7.41505e8 1.31601
4040 5.88476e8 + 5.82974e8i 0.908655 + 0.900159i
4141 −6.96380e8 −0.938718 −0.469359 0.883008i 0.655515π-0.655515\pi
−0.469359 + 0.883008i 0.655515π0.655515\pi
4242 4.57581e7 + 1.69708e8i 0.0540252 + 0.200369i
4343 4.03606e8i 0.418679i 0.977843 + 0.209339i 0.0671314π0.0671314\pi
−0.977843 + 0.209339i 0.932869π0.932869\pi
4444 4.20667e8 + 7.23376e8i 0.384546 + 0.661263i
4545 2.80988e8i 0.226996i
4646 1.02499e9 2.76365e8i 0.733753 0.197840i
4747 −5.59625e8 −0.355925 −0.177963 0.984037i 0.556951π-0.556951\pi
−0.177963 + 0.984037i 0.556951π0.556951\pi
4848 1.39153e9 + 7.91820e8i 0.788251 + 0.448538i
4949 −1.87380e9 −0.947641
5050 −1.35679e9 + 3.65828e8i −0.614012 + 0.165555i
5151 3.68354e9i 1.49496i
5252 −1.99995e9 3.43910e9i −0.729459 1.25437i
5353 2.88775e9i 0.948510i −0.880388 0.474255i 0.842717π-0.842717\pi
0.880388 0.474255i 0.157283π-0.157283\pi
5454 9.38032e8 + 3.47899e9i 0.278005 + 1.03107i
5555 −3.65183e9 −0.978397
5656 6.63690e8 6.69954e8i 0.161039 0.162559i
5757 4.86648e9 1.07128
5858 −5.69191e8 2.11102e9i −0.113869 0.422318i
5959 9.84523e9i 1.79283i 0.443213 + 0.896417i 0.353839π0.353839\pi
−0.443213 + 0.896417i 0.646161π0.646161\pi
6060 −6.03994e9 + 3.51243e9i −1.00277 + 0.583143i
6161 5.65364e9i 0.857066i 0.903526 + 0.428533i 0.140969π0.140969\pi
−0.903526 + 0.428533i 0.859031π0.859031\pi
6262 1.15160e10 3.10503e9i 1.59642 0.430439i
6363 3.19892e8 0.0406098
6464 −8.06933e7 8.58956e9i −0.00939394 0.999956i
6565 1.73617e10 1.85596
6666 −6.81489e9 + 1.83749e9i −0.669834 + 0.180606i
6767 1.28196e10i 1.16001i −0.814613 0.580005i 0.803051π-0.803051\pi
0.814613 0.580005i 0.196949π-0.196949\pi
6868 −1.70842e10 + 9.93505e9i −1.42494 + 0.828650i
6969 8.95435e9i 0.689230i
7070 1.07138e9 + 3.97356e9i 0.0761913 + 0.282579i
7171 −3.63445e9 −0.239066 −0.119533 0.992830i 0.538140π-0.538140\pi
−0.119533 + 0.992830i 0.538140π0.538140\pi
7272 2.05069e9 2.07004e9i 0.124902 0.126081i
7373 −2.56732e9 −0.144945 −0.0724727 0.997370i 0.523089π-0.523089\pi
−0.0724727 + 0.997370i 0.523089π0.523089\pi
7474 −9.32237e8 3.45749e9i −0.0488373 0.181129i
7575 1.18530e10i 0.576754i
7676 −1.31256e10 2.25707e10i −0.593807 1.02111i
7777 4.15744e9i 0.175036i
7878 3.23996e10 8.73585e9i 1.27063 0.342598i
7979 −2.59475e10 −0.948739 −0.474370 0.880326i 0.657324π-0.657324\pi
−0.474370 + 0.880326i 0.657324π0.657324\pi
8080 3.25813e10 + 1.85397e10i 1.11166 + 0.632570i
8181 −2.48233e10 −0.791029
8282 −3.04279e10 + 8.20422e9i −0.906350 + 0.244377i
8383 3.80496e10i 1.06028i 0.847910 + 0.530140i 0.177860π0.177860\pi
−0.847910 + 0.530140i 0.822140π0.822140\pi
8484 3.99874e9 + 6.87621e9i 0.104325 + 0.179396i
8585 8.62466e10i 2.10833i
8686 4.75498e9 + 1.76353e10i 0.108995 + 0.404243i
8787 1.84420e10 0.396692
8888 2.69031e10 + 2.66515e10i 0.543434 + 0.538353i
8989 −2.00557e10 −0.380709 −0.190354 0.981715i 0.560964π-0.560964\pi
−0.190354 + 0.981715i 0.560964π0.560964\pi
9090 3.31039e9 + 1.22776e10i 0.0590942 + 0.219169i
9191 1.97655e10i 0.332032i
9292 4.15303e10 2.41512e10i 0.656949 0.382038i
9393 1.00604e11i 1.49955i
9494 −2.44525e10 + 6.59307e9i −0.343653 + 0.0926584i
9595 1.13944e11 1.51082
9696 7.01305e10 + 1.82042e10i 0.877840 + 0.227866i
9797 −6.90643e10 −0.816600 −0.408300 0.912848i 0.633878π-0.633878\pi
−0.408300 + 0.912848i 0.633878π0.633878\pi
9898 −8.18744e10 + 2.20756e10i −0.914966 + 0.246700i
9999 1.28458e10i 0.135758i
100100 −5.49741e10 + 3.19693e10i −0.549741 + 0.319693i
101101 3.00032e10i 0.284053i −0.989863 0.142027i 0.954638π-0.954638\pi
0.989863 0.142027i 0.0453619π-0.0453619\pi
102102 −4.33966e10 1.60950e11i −0.389184 1.44341i
103103 4.46196e10 0.379246 0.189623 0.981857i 0.439273π-0.439273\pi
0.189623 + 0.981857i 0.439273π0.439273\pi
104104 −1.27904e11 1.26708e11i −1.03086 1.02122i
105105 −3.47132e10 −0.265432
106106 −3.40212e10 1.26178e11i −0.246927 0.915805i
107107 1.84556e10i 0.127209i −0.997975 0.0636044i 0.979740π-0.979740\pi
0.997975 0.0636044i 0.0202596π-0.0202596\pi
108108 8.19736e10 + 1.40961e11i 0.536838 + 0.923143i
109109 9.05577e8i 0.00563741i −0.999996 0.00281871i 0.999103π-0.999103\pi
0.999996 0.00281871i 0.000897223π-0.000897223\pi
110110 −1.59564e11 + 4.30230e10i −0.944662 + 0.254707i
111111 3.02049e10 0.170138
112112 2.11067e10 3.70924e10i 0.113167 0.198877i
113113 1.77827e11 0.907957 0.453978 0.891013i 0.350004π-0.350004\pi
0.453978 + 0.891013i 0.350004π0.350004\pi
114114 2.12638e11 5.73332e10i 1.03434 0.278888i
115115 2.09658e11i 0.972014i
116116 −4.97410e10 8.55342e10i −0.219885 0.378112i
117117 6.10719e10i 0.257525i
118118 1.15989e11 + 4.30182e11i 0.466730 + 1.73102i
119119 −9.81879e10 −0.377181
120120 −2.22531e11 + 2.24631e11i −0.816383 + 0.824088i
121121 1.18363e11 0.414855
122122 6.66069e10 + 2.47033e11i 0.223121 + 0.827514i
123123 2.65820e11i 0.851353i
124124 4.66603e11 2.71345e11i 1.42932 0.831194i
125125 1.58877e11i 0.465648i
126126 1.39775e10 3.76873e9i 0.0392095 0.0105720i
127127 −5.40179e11 −1.45083 −0.725417 0.688310i 0.758353π-0.758353\pi
−0.725417 + 0.688310i 0.758353π0.758353\pi
128128 −1.04721e11 3.74365e11i −0.269390 0.963031i
129129 −1.54063e11 −0.379713
130130 7.58607e11 2.04542e11i 1.79196 0.483163i
131131 2.23934e11i 0.507141i −0.967317 0.253570i 0.918395π-0.918395\pi
0.967317 0.253570i 0.0816049π-0.0816049\pi
132132 −2.76125e11 + 1.60576e11i −0.599721 + 0.348757i
133133 1.29720e11i 0.270286i
134134 −1.51030e11 5.60143e11i −0.301986 1.12001i
135135 −7.11616e11 −1.36587
136136 −6.29439e11 + 6.35380e11i −1.16008 + 1.17103i
137137 3.35319e11 0.593602 0.296801 0.954939i 0.404080π-0.404080\pi
0.296801 + 0.954939i 0.404080π0.404080\pi
138138 1.05493e11 + 3.91255e11i 0.179428 + 0.665465i
139139 2.72700e10i 0.0445763i 0.999752 + 0.0222881i 0.00709512π0.00709512\pi
−0.999752 + 0.0222881i 0.992905π0.992905\pi
140140 9.36269e10 + 1.61000e11i 0.147128 + 0.253001i
141141 2.13618e11i 0.322800i
142142 −1.58805e11 + 4.28184e10i −0.230823 + 0.0622363i
143143 7.93714e11 1.10998
144144 6.52159e10 1.14609e11i 0.0877728 0.154250i
145145 4.31803e11 0.559451
146146 −1.12178e11 + 3.02462e10i −0.139948 + 0.0377338i
147147 7.15260e11i 0.859446i
148148 −8.14671e10 1.40090e11i −0.0943068 0.162169i
149149 1.14880e12i 1.28151i 0.767747 + 0.640753i 0.221378π0.221378\pi
−0.767747 + 0.640753i 0.778622π0.778622\pi
150150 −1.39643e11 5.17909e11i −0.150147 0.556867i
151151 4.51160e11 0.467689 0.233845 0.972274i 0.424869π-0.424869\pi
0.233845 + 0.972274i 0.424869π0.424869\pi
152152 −8.39428e11 8.31579e11i −0.839158 0.831312i
153153 −3.03384e11 −0.292543
154154 4.89798e10 + 1.81657e11i 0.0455673 + 0.169001i
155155 2.35556e12i 2.11480i
156156 1.31276e12 7.63416e11i 1.13763 0.661570i
157157 8.98082e10i 0.0751395i −0.999294 0.0375697i 0.988038π-0.988038\pi
0.999294 0.0375697i 0.0119616π-0.0119616\pi
158158 −1.13376e12 + 3.05694e11i −0.916026 + 0.246986i
159159 1.10230e12 0.860234
160160 1.64204e12 + 4.26235e11i 1.23801 + 0.321358i
161161 2.38686e11 0.173894
162162 −1.08464e12 + 2.92449e11i −0.763754 + 0.205929i
163163 3.45737e11i 0.235350i −0.993052 0.117675i 0.962456π-0.962456\pi
0.993052 0.117675i 0.0375441π-0.0375441\pi
164164 −1.23287e12 + 7.16957e11i −0.811480 + 0.471902i
165165 1.39396e12i 0.887340i
166166 4.48271e11 + 1.66255e12i 0.276024 + 1.02372i
167167 6.61651e11 0.394174 0.197087 0.980386i 0.436852π-0.436852\pi
0.197087 + 0.980386i 0.436852π0.436852\pi
168168 2.55733e11 + 2.53342e11i 0.147430 + 0.146051i
169169 −1.98134e12 −1.10556
170170 −1.01609e12 3.76849e12i −0.548863 2.03563i
171171 4.00813e11i 0.209635i
172172 4.15532e11 + 7.14546e11i 0.210474 + 0.361929i
173173 2.94318e12i 1.44399i −0.691900 0.721993i 0.743226π-0.743226\pi
0.691900 0.721993i 0.256774π-0.256774\pi
174174 8.05814e11 2.17270e11i 0.383014 0.103271i
175175 −3.15952e11 −0.145516
176176 1.48950e12 + 8.47571e11i 0.664846 + 0.378318i
177177 −3.75809e12 −1.62598
178178 −8.76322e11 + 2.36281e11i −0.367582 + 0.0991103i
179179 8.70295e11i 0.353977i −0.984213 0.176988i 0.943364π-0.943364\pi
0.984213 0.176988i 0.0566355π-0.0566355\pi
180180 2.89291e11 + 4.97462e11i 0.114113 + 0.196228i
181181 4.02698e12i 1.54080i 0.637559 + 0.770401i 0.279944π0.279944\pi
−0.637559 + 0.770401i 0.720056π0.720056\pi
182182 −2.32862e11 8.63641e11i −0.0864382 0.320583i
183183 −2.15809e12 −0.777301
184184 1.53011e12 1.54455e12i 0.534841 0.539889i
185185 7.07219e11 0.239944
186186 1.18524e12 + 4.39585e12i 0.390379 + 1.44784i
187187 3.94289e12i 1.26092i
188188 −9.90762e11 + 5.76161e11i −0.307681 + 0.178927i
189189 8.10143e11i 0.244355i
190190 4.97872e12 1.34240e12i 1.45872 0.393313i
191191 5.16393e12 1.46993 0.734965 0.678105i 0.237199π-0.237199\pi
0.734965 + 0.678105i 0.237199π0.237199\pi
192192 3.27878e12 3.08020e10i 0.906892 0.00851966i
193193 2.61981e12 0.704214 0.352107 0.935960i 0.385465π-0.385465\pi
0.352107 + 0.935960i 0.385465π0.385465\pi
194194 −3.01773e12 + 8.13663e11i −0.788443 + 0.212586i
195195 6.62724e12i 1.68323i
196196 −3.31738e12 + 1.92916e12i −0.819193 + 0.476388i
197197 9.51398e11i 0.228453i 0.993455 + 0.114227i 0.0364390π0.0364390\pi
−0.993455 + 0.114227i 0.963561π0.963561\pi
198198 1.51339e11 + 5.61289e11i 0.0353421 + 0.131077i
199199 −7.34864e12 −1.66923 −0.834613 0.550837i 0.814309π-0.814309\pi
−0.834613 + 0.550837i 0.814309π0.814309\pi
200200 −2.02543e12 + 2.04454e12i −0.447560 + 0.451784i
201201 4.89344e12 1.05205
202202 −3.53475e11 1.31097e12i −0.0739479 0.274259i
203203 4.91589e11i 0.100086i
204204 −3.79238e12 6.52135e12i −0.751529 1.29232i
205205 6.22393e12i 1.20066i
206206 1.94963e12 5.25674e11i 0.366169 0.0987294i
207207 7.37499e11 0.134873
208208 −7.08145e12 4.02956e12i −1.26117 0.717644i
209209 5.20912e12 0.903567
210210 −1.51678e12 + 4.08965e11i −0.256280 + 0.0691003i
211211 6.80722e11i 0.112051i −0.998429 0.0560256i 0.982157π-0.982157\pi
0.998429 0.0560256i 0.0178428π-0.0178428\pi
212212 −2.97308e12 5.11248e12i −0.476825 0.819945i
213213 1.38733e12i 0.216817i
214214 −2.17430e11 8.06406e11i −0.0331164 0.122823i
215215 −3.60725e12 −0.535506
216216 5.24248e12 + 5.19347e12i 0.758650 + 0.751557i
217217 2.68170e12 0.378339
218218 −1.06688e10 3.95687e10i −0.00146759 0.00544303i
219219 9.79991e11i 0.131456i
220220 −6.46521e12 + 3.75973e12i −0.845781 + 0.491850i
221221 1.87454e13i 2.39187i
222222 1.31979e12 3.55851e11i 0.164271 0.0442922i
223223 −1.19442e12 −0.145037 −0.0725187 0.997367i 0.523104π-0.523104\pi
−0.0725187 + 0.997367i 0.523104π0.523104\pi
224224 4.85249e11 1.86939e12i 0.0574911 0.221481i
225225 −9.76236e11 −0.112863
226226 7.77003e12 2.09502e12i 0.876650 0.236369i
227227 5.02675e12i 0.553535i −0.960937 0.276768i 0.910737π-0.910737\pi
0.960937 0.276768i 0.0892632π-0.0892632\pi
228228 8.61564e12 5.01028e12i 0.926074 0.538543i
229229 2.86620e12i 0.300754i −0.988629 0.150377i 0.951951π-0.951951\pi
0.988629 0.150377i 0.0480487π-0.0480487\pi
230230 2.47003e12 + 9.16087e12i 0.253046 + 0.938499i
231231 −1.58697e12 −0.158746
232232 −3.18110e12 3.15136e12i −0.310737 0.307832i
233233 −9.05833e12 −0.864153 −0.432077 0.901837i 0.642219π-0.642219\pi
−0.432077 + 0.901837i 0.642219π0.642219\pi
234234 −7.19503e11 2.66850e12i −0.0670417 0.248645i
235235 5.00168e12i 0.455242i
236236 1.01361e13 + 1.74300e13i 0.901274 + 1.54982i
237237 9.90461e12i 0.860442i
238238 −4.29026e12 + 1.15678e12i −0.364176 + 0.0981919i
239239 1.48753e13 1.23389 0.616947 0.787005i 0.288369π-0.288369\pi
0.616947 + 0.787005i 0.288369π0.288369\pi
240240 −7.07693e12 + 1.24368e13i −0.573698 + 1.00820i
241241 1.65832e12 0.131394 0.0656969 0.997840i 0.479073π-0.479073\pi
0.0656969 + 0.997840i 0.479073π0.479073\pi
242242 5.17180e12 1.39446e12i 0.400551 0.108000i
243243 4.62911e12i 0.350480i
244244 5.82070e12 + 1.00092e13i 0.430855 + 0.740896i
245245 1.67472e13i 1.21207i
246246 −3.13169e12 1.16149e13i −0.221634 0.821998i
247247 −2.47654e13 −1.71401
248248 1.71912e13 1.73534e13i 1.16365 1.17463i
249249 −1.45242e13 −0.961601
250250 1.87177e12 + 6.94206e12i 0.121223 + 0.449592i
251251 1.60614e13i 1.01760i 0.860883 + 0.508802i 0.169912π0.169912\pi
−0.860883 + 0.508802i 0.830088π0.830088\pi
252252 5.66339e11 3.29345e11i 0.0351054 0.0204149i
253253 9.58481e12i 0.581327i
254254 −2.36028e13 + 6.36398e12i −1.40081 + 0.377697i
255255 3.29218e13 1.91211
256256 −8.98623e12 1.51239e13i −0.510808 0.859695i
257257 −2.90477e13 −1.61614 −0.808072 0.589084i 0.799489π-0.799489\pi
−0.808072 + 0.589084i 0.799489π0.799489\pi
258258 −6.73171e12 + 1.81506e12i −0.366621 + 0.0988512i
259259 8.05138e11i 0.0429261i
260260 3.07372e13 1.78747e13i 1.60439 0.933006i
261261 1.51892e12i 0.0776271i
262262 −2.63822e12 9.78468e12i −0.132024 0.489654i
263263 −7.15627e12 −0.350695 −0.175348 0.984507i 0.556105π-0.556105\pi
−0.175348 + 0.984507i 0.556105π0.556105\pi
264264 −1.01733e13 + 1.02694e13i −0.488250 + 0.492858i
265265 2.58094e13 1.21318
266266 −1.52827e12 5.66806e12i −0.0703639 0.260967i
267267 7.65561e12i 0.345277i
268268 −1.31984e13 2.26958e13i −0.583147 1.00278i
269269 9.77777e12i 0.423255i −0.977350 0.211627i 0.932124π-0.932124\pi
0.977350 0.211627i 0.0678764π-0.0678764\pi
270270 −3.10936e13 + 8.38371e12i −1.31878 + 0.355579i
271271 3.73866e13 1.55376 0.776882 0.629647i 0.216800π-0.216800\pi
0.776882 + 0.629647i 0.216800π0.216800\pi
272272 −2.00174e13 + 3.51781e13i −0.815228 + 1.43266i
273273 7.54482e12 0.301130
274274 1.46516e13 3.95048e12i 0.573134 0.154533i
275275 1.26875e13i 0.486460i
276276 9.21894e12 + 1.58528e13i 0.346482 + 0.595808i
277277 2.28097e13i 0.840391i 0.907433 + 0.420196i 0.138039π0.138039\pi
−0.907433 + 0.420196i 0.861961π0.861961\pi
278278 3.21274e11 + 1.19155e12i 0.0116046 + 0.0430392i
279279 8.28598e12 0.293441
280280 5.98775e12 + 5.93176e12i 0.207919 + 0.205975i
281281 −8.47235e12 −0.288482 −0.144241 0.989543i 0.546074π-0.546074\pi
−0.144241 + 0.989543i 0.546074π0.546074\pi
282282 −2.51669e12 9.33393e12i −0.0840349 0.311670i
283283 5.48093e13i 1.79485i 0.441163 + 0.897427i 0.354566π0.354566\pi
−0.441163 + 0.897427i 0.645434π0.645434\pi
284284 −6.43445e12 + 3.74185e12i −0.206662 + 0.120181i
285285 4.34944e13i 1.37021i
286286 3.46809e13 9.35093e12i 1.07171 0.288963i
287287 −7.08567e12 −0.214798
288288 1.49934e12 5.77610e12i 0.0445903 0.171781i
289289 5.88488e13 1.71712
290290 1.88674e13 5.08718e12i 0.540161 0.145642i
291291 2.63630e13i 0.740601i
292292 −4.54520e12 + 2.64318e12i −0.125299 + 0.0728655i
293293 5.59919e13i 1.51479i −0.652955 0.757396i 0.726471π-0.726471\pi
0.652955 0.757396i 0.273529π-0.273529\pi
294294 −8.42665e12 3.12529e13i −0.223740 0.829812i
295295 −8.79923e13 −2.29310
296296 −5.21010e12 5.16138e12i −0.133273 0.132027i
297297 −3.25326e13 −0.816879
298298 1.35343e13 + 5.01962e13i 0.333616 + 1.23732i
299299 4.55685e13i 1.10274i
300300 −1.22032e13 2.09846e13i −0.289940 0.498578i
301301 4.10670e12i 0.0958025i
302302 1.97132e13 5.31522e12i 0.451563 0.121754i
303303 1.14527e13 0.257617
304304 −4.64754e13 2.64459e13i −1.02664 0.584189i
305305 −5.05297e13 −1.09622
306306 −1.32562e13 + 3.57423e12i −0.282456 + 0.0761580i
307307 3.49392e13i 0.731226i −0.930767 0.365613i 0.880859π-0.880859\pi
0.930767 0.365613i 0.119141π-0.119141\pi
308308 4.28029e12 + 7.36036e12i 0.0879922 + 0.151311i
309309 1.70321e13i 0.343950i
310310 2.77514e13 + 1.02925e14i 0.550548 + 2.04188i
311311 −8.77394e13 −1.71006 −0.855032 0.518575i 0.826463π-0.826463\pi
−0.855032 + 0.518575i 0.826463π0.826463\pi
312312 4.83665e13 4.88230e13i 0.926178 0.934919i
313313 9.47630e13 1.78297 0.891487 0.453046i 0.149663π-0.149663\pi
0.891487 + 0.453046i 0.149663π0.149663\pi
314314 −1.05805e12 3.92412e12i −0.0195611 0.0725486i
315315 2.85905e12i 0.0519415i
316316 −4.59376e13 + 2.67142e13i −0.820143 + 0.476940i
317317 7.45724e13i 1.30844i −0.756306 0.654218i 0.772998π-0.772998\pi
0.756306 0.654218i 0.227002π-0.227002\pi
318318 4.81645e13 1.29865e13i 0.830573 0.223946i
319319 1.97405e13 0.334588
320320 7.67696e13 7.21201e11i 1.27898 0.0120152i
321321 7.04482e12 0.115370
322322 1.04293e13 2.81202e12i 0.167898 0.0452700i
323323 1.23026e14i 1.94707i
324324 −4.39473e13 + 2.55568e13i −0.683809 + 0.397658i
325325 6.03196e13i 0.922783i
326326 −4.07321e12 1.51068e13i −0.0612688 0.227235i
327327 3.45674e11 0.00511275
328328 −4.54231e13 + 4.58518e13i −0.660649 + 0.666884i
329329 −5.69419e12 −0.0814431
330330 −1.64226e13 6.09085e13i −0.231002 0.856744i
331331 9.05611e13i 1.25282i −0.779495 0.626409i 0.784524π-0.784524\pi
0.779495 0.626409i 0.215476π-0.215476\pi
332332 3.91739e13 + 6.73631e13i 0.533012 + 0.916564i
333333 2.48774e12i 0.0332936i
334334 2.89105e13 7.79507e12i 0.380583 0.102616i
335335 1.14575e14 1.48370
336336 1.41588e13 + 8.05677e12i 0.180368 + 0.102635i
337337 3.77207e13 0.472733 0.236366 0.971664i 0.424043π-0.424043\pi
0.236366 + 0.971664i 0.424043π0.424043\pi
338338 −8.65737e13 + 2.33427e13i −1.06744 + 0.287812i
339339 6.78794e13i 0.823455i
340340 −8.87950e13 1.52691e14i −1.05988 1.82255i
341341 1.07688e14i 1.26479i
342342 −4.72208e12 1.75133e13i −0.0545745 0.202407i
343343 −3.91852e13 −0.445661
344344 2.65747e13 + 2.63262e13i 0.297438 + 0.294657i
345345 −8.00299e13 −0.881551
346346 −3.46743e13 1.28601e14i −0.375915 1.39420i
347347 4.95297e13i 0.528510i −0.964453 0.264255i 0.914874π-0.914874\pi
0.964453 0.264255i 0.0851261π-0.0851261\pi
348348 3.26499e13 1.89870e13i 0.342922 0.199421i
349349 4.22844e13i 0.437160i −0.975819 0.218580i 0.929858π-0.929858\pi
0.975819 0.218580i 0.0701425π-0.0701425\pi
350350 −1.38053e13 + 3.72230e12i −0.140499 + 0.0378824i
351351 1.54668e14 1.54957
352352 7.50684e13 + 1.94860e13i 0.740410 + 0.192193i
353353 −5.42310e13 −0.526607 −0.263304 0.964713i 0.584812π-0.584812\pi
−0.263304 + 0.964713i 0.584812π0.584812\pi
354354 −1.64208e14 + 4.42750e13i −1.56991 + 0.423293i
355355 3.24831e13i 0.305775i
356356 −3.55067e13 + 2.06483e13i −0.329106 + 0.191386i
357357 3.74800e13i 0.342078i
358358 −1.02532e13 3.80270e13i −0.0921512 0.341771i
359359 1.11001e14 0.982441 0.491220 0.871035i 0.336551π-0.336551\pi
0.491220 + 0.871035i 0.336551π0.336551\pi
360360 1.85011e13 + 1.83281e13i 0.161263 + 0.159755i
361361 −4.60446e13 −0.395266
362362 4.74428e13 + 1.75956e14i 0.401119 + 1.48767i
363363 4.51812e13i 0.376245i
364364 −2.03495e13 3.49929e13i −0.166915 0.287027i
365365 2.29456e13i 0.185391i
366366 −9.42966e13 + 2.54250e13i −0.750499 + 0.202356i
367367 −1.37111e14 −1.07500 −0.537502 0.843262i 0.680632π-0.680632\pi
−0.537502 + 0.843262i 0.680632π0.680632\pi
368368 4.86605e13 8.55149e13i 0.375849 0.660509i
369369 −2.18935e13 −0.166598
370370 3.09015e13 8.33192e12i 0.231670 0.0624648i
371371 2.93829e13i 0.217039i
372372 1.03577e14 + 1.78110e14i 0.753837 + 1.29629i
373373 1.24348e14i 0.891744i −0.895097 0.445872i 0.852894π-0.852894\pi
0.895097 0.445872i 0.147106π-0.147106\pi
374374 −4.64521e13 1.72282e14i −0.328255 1.21744i
375375 −6.06463e13 −0.422311
376376 −3.65029e13 + 3.68474e13i −0.250492 + 0.252856i
377377 −9.38512e13 −0.634691
378378 9.54449e12 + 3.53987e13i 0.0636133 + 0.235930i
379379 2.76010e14i 1.81305i 0.422157 + 0.906523i 0.361273π0.361273\pi
−0.422157 + 0.906523i 0.638727π0.638727\pi
380380 2.01727e14 1.17311e14i 1.30603 0.759502i
381381 2.06196e14i 1.31581i
382382 2.25635e14 6.08374e13i 1.41925 0.382668i
383383 1.30866e14 0.811396 0.405698 0.914007i 0.367028π-0.367028\pi
0.405698 + 0.914007i 0.367028π0.367028\pi
384384 1.42902e14 3.99740e13i 0.873404 0.244318i
385385 −3.71574e13 −0.223878
386386 1.14471e14 3.08646e13i 0.679933 0.183329i
387387 1.26890e13i 0.0743047i
388388 −1.22272e14 + 7.11051e13i −0.705914 + 0.410512i
389389 2.65449e14i 1.51098i 0.655161 + 0.755489i 0.272601π0.272601\pi
−0.655161 + 0.755489i 0.727399π0.727399\pi
390390 7.80771e13 + 2.89573e14i 0.438196 + 1.62519i
391391 −2.26368e14 −1.25269
392392 −1.22223e14 + 1.23377e14i −0.666929 + 0.673223i
393393 8.54795e13 0.459942
394394 1.12086e13 + 4.15708e13i 0.0594735 + 0.220576i
395395 2.31907e14i 1.21347i
396396 1.32254e13 + 2.27422e13i 0.0682470 + 0.117357i
397397 2.55728e14i 1.30146i 0.759309 + 0.650730i 0.225537π0.225537\pi
−0.759309 + 0.650730i 0.774463π0.774463\pi
398398 −3.21095e14 + 8.65761e13i −1.61167 + 0.434551i
399399 4.95165e13 0.245131
400400 −6.44125e13 + 1.13197e14i −0.314514 + 0.552720i
401401 4.93538e13 0.237698 0.118849 0.992912i 0.462079π-0.462079\pi
0.118849 + 0.992912i 0.462079π0.462079\pi
402402 2.13816e14 5.76508e13i 1.01577 0.273881i
403403 5.11973e14i 2.39922i
404404 −3.08898e13 5.31178e13i −0.142796 0.245551i
405405 2.21860e14i 1.01176i
406406 −5.79153e12 2.14797e13i −0.0260555 0.0966351i
407407 3.23316e13 0.143502
408408 −2.42535e14 2.40268e14i −1.06205 1.05212i
409409 2.01464e14 0.870400 0.435200 0.900334i 0.356678π-0.356678\pi
0.435200 + 0.900334i 0.356678π0.356678\pi
410410 −7.33256e13 2.71951e14i −0.312568 1.15926i
411411 1.27997e14i 0.538357i
412412 7.89947e13 4.59380e13i 0.327841 0.190650i
413413 1.00175e14i 0.410238i
414414 3.22246e13 8.68865e12i 0.130222 0.0351116i
415415 −3.40070e14 −1.35614
416416 −3.56893e14 9.26409e13i −1.40451 0.364577i
417417 −1.04094e13 −0.0404276
418418 2.27610e14 6.13699e13i 0.872411 0.235226i
419419 3.36722e14i 1.27378i 0.770954 + 0.636891i 0.219780π0.219780\pi
−0.770954 + 0.636891i 0.780220π0.780220\pi
420420 −6.14565e13 + 3.57390e13i −0.229455 + 0.133435i
421421 1.20703e12i 0.00444800i 0.999998 + 0.00222400i 0.000707922π0.000707922\pi
−0.999998 + 0.00222400i 0.999292π0.999292\pi
422422 −8.01975e12 2.97438e13i −0.0291704 0.108188i
423423 −1.75941e13 −0.0631675
424424 −1.90138e14 1.88360e14i −0.673841 0.667540i
425425 2.99646e14 1.04826
426426 −1.63445e13 6.06187e13i −0.0564441 0.209341i
427427 5.75259e13i 0.196115i
428428 −1.90009e13 3.26739e13i −0.0639491 0.109966i
429429 3.02974e14i 1.00668i
430430 −1.57617e14 + 4.24979e13i −0.517042 + 0.139409i
431431 −1.87948e13 −0.0608714 −0.0304357 0.999537i 0.509689π-0.509689\pi
−0.0304357 + 0.999537i 0.509689π0.509689\pi
432432 2.90253e14 + 1.65163e14i 0.928145 + 0.528142i
433433 3.13621e14 0.990197 0.495098 0.868837i 0.335132π-0.335132\pi
0.495098 + 0.868837i 0.335132π0.335132\pi
434434 1.17175e14 3.15937e13i 0.365294 0.0984934i
435435 1.64827e14i 0.507384i
436436 −9.32336e11 1.60324e12i −0.00283398 0.00487329i
437437 2.99065e14i 0.897672i
438438 −1.15455e13 4.28201e13i −0.0342220 0.126923i
439439 4.95205e14 1.44954 0.724771 0.688990i 0.241946π-0.241946\pi
0.724771 + 0.688990i 0.241946π0.241946\pi
440440 −2.38199e14 + 2.40448e14i −0.688574 + 0.695073i
441441 −5.89103e13 −0.168182
442442 2.20845e14 + 8.19071e14i 0.622679 + 2.30940i
443443 2.99673e14i 0.834500i 0.908792 + 0.417250i 0.137006π0.137006\pi
−0.908792 + 0.417250i 0.862994π0.862994\pi
444444 5.34749e13 3.10974e13i 0.147077 0.0855299i
445445 1.79249e14i 0.486941i
446446 −5.21894e13 + 1.40717e13i −0.140036 + 0.0377577i
447447 −4.38517e14 −1.16224
448448 −8.21055e11 8.73988e13i −0.00214953 0.228811i
449449 2.49937e14 0.646362 0.323181 0.946337i 0.395248π-0.395248\pi
0.323181 + 0.946337i 0.395248π0.395248\pi
450450 −4.26561e13 + 1.15013e13i −0.108971 + 0.0293817i
451451 2.84536e14i 0.718070i
452452 3.14825e14 1.83081e14i 0.784888 0.456438i
453453 1.72215e14i 0.424162i
454454 −5.92214e13 2.19641e14i −0.144102 0.534449i
455455 1.76655e14 0.424681
456456 3.17428e14 3.20424e14i 0.753943 0.761059i
457457 −7.22584e14 −1.69570 −0.847851 0.530235i 0.822104π-0.822104\pi
−0.847851 + 0.530235i 0.822104π0.822104\pi
458458 −3.37674e13 1.25237e14i −0.0782955 0.290383i
459459 7.68334e14i 1.76027i
460460 2.15853e14 + 3.71179e14i 0.488641 + 0.840263i
461461 2.69171e13i 0.0602107i 0.999547 + 0.0301054i 0.00958428π0.00958428\pi
−0.999547 + 0.0301054i 0.990416π0.990416\pi
462462 −6.93416e13 + 1.86964e13i −0.153272 + 0.0413265i
463463 −6.06138e13 −0.132396 −0.0661982 0.997806i 0.521087π-0.521087\pi
−0.0661982 + 0.997806i 0.521087π0.521087\pi
464464 −1.76123e14 1.00219e14i −0.380161 0.216323i
465465 −8.99156e14 −1.91798
466466 −3.95799e14 + 1.06718e14i −0.834357 + 0.224966i
467467 2.97151e13i 0.0619063i 0.999521 + 0.0309531i 0.00985426π0.00985426\pi
−0.999521 + 0.0309531i 0.990146π0.990146\pi
468468 −6.28765e13 1.08122e14i −0.129460 0.222619i
469469 1.30439e14i 0.265434i
470470 −5.89259e13 2.18545e14i −0.118514 0.439545i
471471 3.42813e13 0.0681464
472472 6.48241e14 + 6.42179e14i 1.27366 + 1.26176i
473473 −1.64911e14 −0.320267
474474 −1.16689e14 4.32776e14i −0.224000 0.830774i
475475 3.95876e14i 0.751180i
476476 −1.73832e14 + 1.01089e14i −0.326056 + 0.189612i
477477 9.07879e13i 0.168336i
478478 6.49968e14 1.75250e14i 1.19135 0.321221i
479479 1.21025e14 0.219296 0.109648 0.993970i 0.465028π-0.465028\pi
0.109648 + 0.993970i 0.465028π0.465028\pi
480480 −1.62701e14 + 6.26795e14i −0.291450 + 1.12279i
481481 −1.53712e14 −0.272214
482482 7.24594e13 1.95371e13i 0.126863 0.0342059i
483483 9.11106e13i 0.157710i
484484 2.09550e14 1.21860e14i 0.358624 0.208552i
485485 6.17266e14i 1.04446i
486486 5.45366e13 + 2.02266e14i 0.0912408 + 0.338395i
487487 6.01563e14 0.995111 0.497556 0.867432i 0.334231π-0.334231\pi
0.497556 + 0.867432i 0.334231π0.334231\pi
488488 3.72253e14 + 3.68773e14i 0.608877 + 0.603184i
489489 1.31974e14 0.213446
490490 −1.97302e14 7.31757e14i −0.315539 1.17028i
491491 8.74926e13i 0.138364i −0.997604 0.0691820i 0.977961π-0.977961\pi
0.997604 0.0691820i 0.0220389π-0.0220389\pi
492492 −2.73675e14 4.70609e14i −0.427983 0.735957i
493493 4.66220e14i 0.720995i
494494 −1.08211e15 + 2.91767e14i −1.65491 + 0.446209i
495495 −1.14810e14 −0.173640
496496 5.46713e14 9.60781e14i 0.817730 1.43706i
497497 −3.69806e13 −0.0547033
498498 −6.34625e14 + 1.71113e14i −0.928445 + 0.250335i
499499 8.99853e14i 1.30202i 0.759068 + 0.651011i 0.225655π0.225655\pi
−0.759068 + 0.651011i 0.774345π0.774345\pi
500500 1.63572e14 + 2.81277e14i 0.234085 + 0.402532i
501501 2.52564e14i 0.357489i
502502 1.89224e14 + 7.01796e14i 0.264914 + 0.982517i
503503 6.87292e14 0.951738 0.475869 0.879516i 0.342134π-0.342134\pi
0.475869 + 0.879516i 0.342134π0.342134\pi
504504 2.08658e13 2.10627e13i 0.0285803 0.0288500i
505505 2.68155e14 0.363315
506506 1.12921e14 + 4.18803e14i 0.151338 + 0.561283i
507507 7.56313e14i 1.00267i
508508 −9.56336e14 + 5.56141e14i −1.25418 + 0.729347i
509509 1.78689e14i 0.231819i 0.993260 + 0.115910i 0.0369783π0.0369783\pi
−0.993260 + 0.115910i 0.963022π0.963022\pi
510510 1.43850e15 3.87860e14i 1.84618 0.497781i
511511 −2.61225e13 −0.0331666
512512 −5.70826e14 5.54962e14i −0.717000 0.697073i
513513 1.01508e15 1.26141
514514 −1.26922e15 + 3.42218e14i −1.56042 + 0.420732i
515515 3.98790e14i 0.485070i
516516 −2.72754e14 + 1.58616e14i −0.328245 + 0.190885i
517517 2.28659e14i 0.272264i
518518 −9.48553e12 3.51800e13i −0.0111750 0.0414460i
519519 1.12346e15 1.30960
520520 1.13246e15 1.14315e15i 1.30618 1.31851i
521521 3.87660e14 0.442429 0.221215 0.975225i 0.428998π-0.428998\pi
0.221215 + 0.975225i 0.428998π0.428998\pi
522522 −1.78948e13 6.63685e13i −0.0202088 0.0749505i
523523 3.70738e14i 0.414293i 0.978310 + 0.207146i 0.0664177π0.0664177\pi
−0.978310 + 0.207146i 0.933582π0.933582\pi
524524 −2.30551e14 3.96454e14i −0.254944 0.438400i
525525 1.20604e14i 0.131973i
526526 −3.12689e14 + 8.43097e13i −0.338603 + 0.0912969i
527527 −2.54330e15 −2.72546
528528 −3.23532e14 + 5.68568e14i −0.343108 + 0.602971i
529529 −4.02529e14 −0.422465
530530 1.12773e15 3.04067e14i 1.17135 0.315829i
531531 3.09524e14i 0.318182i
532532 −1.33553e14 2.29658e14i −0.135875 0.233651i
533533 1.35275e15i 1.36213i
534534 −9.01925e13 3.34507e14i −0.0898863 0.333372i
535535 1.64948e14 0.162705
536536 −8.44079e14 8.36187e14i −0.824094 0.816388i
537537 3.32207e14 0.321033
538538 −1.15194e14 4.27234e14i −0.110186 0.408661i
539539 7.65621e14i 0.724896i
540540 −1.25985e15 + 7.32643e14i −1.18073 + 0.686636i
541541 1.32152e15i 1.22599i −0.790086 0.612995i 0.789964π-0.789964\pi
0.790086 0.612995i 0.210036π-0.210036\pi
542542 1.63359e15 4.40460e14i 1.50019 0.404493i
543543 −1.53717e15 −1.39740
544544 −4.60207e14 + 1.77292e15i −0.414152 + 1.59549i
545545 8.09364e12 0.00721046
546546 3.29667e14 8.88874e13i 0.290747 0.0783936i
547547 1.58642e15i 1.38513i −0.721357 0.692563i 0.756481π-0.756481\pi
0.721357 0.692563i 0.243519π-0.243519\pi
548548 5.93651e14 3.45228e14i 0.513143 0.298409i
549549 1.77745e14i 0.152107i
550550 −1.49475e14 5.54375e14i −0.126641 0.469687i
551551 −6.15943e14 −0.516662
552552 5.89582e14 + 5.84069e14i 0.489643 + 0.485064i
553553 −2.64016e14 −0.217091
554554 2.68727e14 + 9.96658e14i 0.218780 + 0.811414i
555555 2.69958e14i 0.217613i
556556 2.80758e13 + 4.82789e13i 0.0224089 + 0.0385342i
557557 1.21582e15i 0.960869i −0.877031 0.480435i 0.840479π-0.840479\pi
0.877031 0.480435i 0.159521π-0.159521\pi
558558 3.62051e14 9.76191e13i 0.283323 0.0763918i
559559 7.84025e14 0.607526
560560 3.31515e14 + 1.88642e14i 0.254372 + 0.144745i
561561 1.50507e15 1.14356
562562 −3.70194e14 + 9.98148e13i −0.278535 + 0.0751009i
563563 2.27297e15i 1.69355i −0.531951 0.846775i 0.678541π-0.678541\pi
0.531951 0.846775i 0.321459π-0.321459\pi
564564 −2.19931e14 3.78191e14i −0.162275 0.279046i
565565 1.58933e15i 1.16131i
566566 6.45722e14 + 2.39486e15i 0.467256 + 1.73297i
567567 −2.52578e14 −0.181004
568568 −2.37066e14 + 2.39304e14i −0.168249 + 0.169837i
569569 −3.01866e14 −0.212176 −0.106088 0.994357i 0.533833π-0.533833\pi
−0.106088 + 0.994357i 0.533833π0.533833\pi
570570 5.12418e14 + 1.90046e15i 0.356708 + 1.32296i
571571 2.23731e15i 1.54251i 0.636529 + 0.771253i 0.280370π0.280370\pi
−0.636529 + 0.771253i 0.719630π0.719630\pi
572572 1.40519e15 8.17167e14i 0.959530 0.557998i
573573 1.97116e15i 1.33313i
574574 −3.09604e14 + 8.34780e13i −0.207392 + 0.0559186i
575575 −7.28414e14 −0.483287
576576 −2.53692e12 2.70047e14i −0.00166718 0.177466i
577577 −1.67626e15 −1.09113 −0.545564 0.838069i 0.683684π-0.683684\pi
−0.545564 + 0.838069i 0.683684π0.683684\pi
578578 2.57137e15 6.93312e14i 1.65791 0.447019i
579579 1.00003e15i 0.638675i
580580 7.64467e14 4.44563e14i 0.483620 0.281241i
581581 3.87155e14i 0.242614i
582582 −3.10589e14 1.15192e15i −0.192801 0.715064i
583583 1.17991e15 0.725561
584584 −1.67460e14 + 1.69040e14i −0.102009 + 0.102972i
585585 5.45833e14 0.329384
586586 −6.59654e14 2.44653e15i −0.394348 1.46256i
587587 1.50304e15i 0.890144i 0.895495 + 0.445072i 0.146822π0.146822\pi
−0.895495 + 0.445072i 0.853178π0.853178\pi
588588 −7.36395e14 1.26630e15i −0.432052 0.742953i
589589 3.36007e15i 1.95305i
590590 −3.84477e15 + 1.03666e15i −2.21403 + 0.596966i
591591 −3.63165e14 −0.207192
592592 −2.88460e14 1.64142e14i −0.163048 0.0927792i
593593 −1.38749e14 −0.0777015 −0.0388507 0.999245i 0.512370π-0.512370\pi
−0.0388507 + 0.999245i 0.512370π0.512370\pi
594594 −1.42149e15 + 3.83274e14i −0.788713 + 0.212659i
595595 8.77560e14i 0.482429i
596596 1.18275e15 + 2.03384e15i 0.644225 + 1.10780i
597597 2.80510e15i 1.51387i
598598 −5.36853e14 1.99109e15i −0.287077 1.06472i
599599 1.44893e15 0.767717 0.383859 0.923392i 0.374595π-0.374595\pi
0.383859 + 0.923392i 0.374595π0.374595\pi
600600 −7.80437e14 7.73140e14i −0.409738 0.405906i
601601 −7.86748e13 −0.0409285 −0.0204643 0.999791i 0.506514π-0.506514\pi
−0.0204643 + 0.999791i 0.506514π0.506514\pi
602602 4.83820e13 + 1.79440e14i 0.0249404 + 0.0924992i
603603 4.03034e14i 0.205872i
604604 7.98735e14 4.64491e14i 0.404296 0.235112i
605605 1.05788e15i 0.530616i
606606 5.00421e14 1.34927e14i 0.248734 0.0670657i
607607 1.57249e15 0.774550 0.387275 0.921964i 0.373416π-0.373416\pi
0.387275 + 0.921964i 0.373416π0.373416\pi
608608 −2.34228e15 6.08000e14i −1.14332 0.296779i
609609 1.87648e14 0.0907713
610610 −2.20787e15 + 5.95303e14i −1.05842 + 0.285380i
611611 1.08710e15i 0.516467i
612612 −5.37112e14 + 3.12348e14i −0.252890 + 0.147064i
613613 8.60982e14i 0.401755i 0.979616 + 0.200878i 0.0643794π0.0643794\pi
−0.979616 + 0.200878i 0.935621π0.935621\pi
614614 −4.11627e14 1.52665e15i −0.190361 0.706013i
615615 2.37578e15 1.08891
616616 2.73739e14 + 2.71179e14i 0.124349 + 0.123186i
617617 −9.54957e14 −0.429947 −0.214974 0.976620i 0.568967π-0.568967\pi
−0.214974 + 0.976620i 0.568967π0.568967\pi
618618 2.00659e14 + 7.44206e14i 0.0895409 + 0.332090i
619619 1.65458e13i 0.00731793i 0.999993 + 0.00365896i 0.00116469π0.00116469\pi
−0.999993 + 0.00365896i 0.998835π0.998835\pi
620620 2.42516e15 + 4.17029e15i 1.06313 + 1.82815i
621621 1.86775e15i 0.811550i
622622 −3.83372e15 + 1.03368e15i −1.65110 + 0.445183i
623623 −2.04067e14 −0.0871141
624624 1.53815e15 2.70311e15i 0.650854 1.14380i
625625 −2.93617e15 −1.23152
626626 4.14062e15 1.11643e15i 1.72150 0.464164i
627627 1.98841e15i 0.819474i
628628 −9.24620e13 1.58997e14i −0.0377733 0.0649547i
629629 7.63587e14i 0.309229i
630630 3.36832e13 + 1.24925e14i 0.0135220 + 0.0501505i
631631 2.66470e15 1.06044 0.530221 0.847859i 0.322109π-0.322109\pi
0.530221 + 0.847859i 0.322109π0.322109\pi
632632 −1.69249e15 + 1.70847e15i −0.667702 + 0.674004i
633633 2.59843e14 0.101623
634634 −8.78556e14 3.25840e15i −0.340626 1.26332i
635635 4.82788e15i 1.85567i
636636 1.95152e15 1.13487e15i 0.743634 0.432448i
637637 3.63994e15i 1.37508i
638638 8.62551e14 2.32568e14i 0.323051 0.0871036i
639639 −1.14264e14 −0.0424281
640640 3.34591e15 9.35954e14i 1.23175 0.344560i
641641 2.68473e15 0.979901 0.489951 0.871750i 0.337015π-0.337015\pi
0.489951 + 0.871750i 0.337015π0.337015\pi
642642 3.07819e14 8.29967e13i 0.111392 0.0300343i
643643 4.42246e14i 0.158673i −0.996848 0.0793367i 0.974720π-0.974720\pi
0.996848 0.0793367i 0.0252802π-0.0252802\pi
644644 4.22571e14 2.45739e14i 0.150324 0.0874182i
645645 1.37695e15i 0.485668i
646646 1.44940e15 + 5.37554e15i 0.506884 + 1.87994i
647647 −3.79844e15 −1.31714 −0.658570 0.752520i 0.728838π-0.728838\pi
−0.658570 + 0.752520i 0.728838π0.728838\pi
648648 −1.61916e15 + 1.63444e15i −0.556708 + 0.561963i
649649 −4.02270e15 −1.37142
650650 7.10639e14 + 2.63563e15i 0.240229 + 0.890965i
651651 1.02365e15i 0.343128i
652652 −3.55953e14 6.12094e14i −0.118313 0.203449i
653653 5.25844e15i 1.73314i −0.499052 0.866572i 0.666318π-0.666318\pi
0.499052 0.866572i 0.333682π-0.333682\pi
654654 1.51040e13 4.07247e12i 0.00493646 0.00133101i
655655 2.00142e15 0.648652
656656 −1.44454e15 + 2.53861e15i −0.464258 + 0.815877i
657657 −8.07141e13 −0.0257241
658658 −2.48804e14 + 6.70846e13i −0.0786349 + 0.0212022i
659659 3.68455e15i 1.15482i 0.816454 + 0.577410i 0.195937π0.195937\pi
−0.816454 + 0.577410i 0.804063π0.804063\pi
660660 −1.43515e15 2.46788e15i −0.446074 0.767066i
661661 1.45382e15i 0.448130i −0.974574 0.224065i 0.928067π-0.928067\pi
0.974574 0.224065i 0.0719327π-0.0719327\pi
662662 −1.06692e15 3.95702e15i −0.326147 1.20962i
663663 −7.15546e15 −2.16927
664664 2.50530e15 + 2.48188e15i 0.753244 + 0.746201i
665665 1.15938e15 0.345707
666666 −2.93086e13 1.08700e14i −0.00866737 0.0321457i
667667 1.13334e15i 0.332405i
668668 1.17139e15 6.81202e14i 0.340746 0.198155i
669669 4.55930e14i 0.131539i
670670 5.00631e15 1.34984e15i 1.43254 0.386252i
671671 −2.31004e15 −0.655611
672672 7.13579e14 + 1.85228e14i 0.200868 + 0.0521406i
673673 4.59102e15 1.28182 0.640909 0.767617i 0.278557π-0.278557\pi
0.640909 + 0.767617i 0.278557π0.278557\pi
674674 1.64818e15 4.44397e14i 0.456432 0.123067i
675675 2.47237e15i 0.679113i
676676 −3.50778e15 + 2.03989e15i −0.955709 + 0.555776i
677677 2.08953e15i 0.564691i −0.959313 0.282345i 0.908888π-0.908888\pi
0.959313 0.282345i 0.0911124π-0.0911124\pi
678678 7.99704e14 + 2.96595e15i 0.214371 + 0.795062i
679679 −7.02730e14 −0.186855
680680 −5.67874e15 5.62564e15i −1.49780 1.48379i
681681 1.91880e15 0.502019
682682 1.26869e15 + 4.70535e15i 0.329263 + 1.22118i
683683 3.35863e14i 0.0864667i 0.999065 + 0.0432333i 0.0137659π0.0137659\pi
−0.999065 + 0.0432333i 0.986234π0.986234\pi
684684 −4.12657e14 7.09602e14i −0.105385 0.181220i
685685 2.99693e15i 0.759240i
686686 −1.71218e15 + 4.61650e14i −0.430294 + 0.116019i
687687 1.09408e15 0.272763
688688 1.47132e15 + 8.37225e14i 0.363891 + 0.207065i
689689 −5.60960e15 −1.37634
690690 −3.49686e15 + 9.42852e14i −0.851155 + 0.229495i
691691 6.13314e14i 0.148099i −0.997255 0.0740497i 0.976408π-0.976408\pi
0.997255 0.0740497i 0.0235923π-0.0235923\pi
692692 −3.03015e15 5.21062e15i −0.725906 1.24826i
693693 1.30706e14i 0.0310644i
694694 −5.83521e14 2.16417e15i −0.137588 0.510287i
695695 −2.43727e14 −0.0570148
696696 1.20293e15 1.21428e15i 0.279183 0.281818i
697697 6.72000e15 1.54735
698698 −4.98163e14 1.84759e15i −0.113806 0.422087i
699699 3.45772e15i 0.783728i
700700 −5.59362e14 + 3.25288e14i −0.125792 + 0.0731524i
701701 7.14041e15i 1.59321i 0.604498 + 0.796606i 0.293374π0.293374\pi
−0.604498 + 0.796606i 0.706626π0.706626\pi
702702 6.75811e15 1.82218e15i 1.49614 0.403400i
703703 −1.00881e15 −0.221592
704704 3.50964e15 3.29708e13i 0.764914 0.00718587i
705705 1.90923e15 0.412874
706706 −2.36959e15 + 6.38909e14i −0.508450 + 0.137092i
707707 3.05283e14i 0.0649973i
708708 −6.65335e15 + 3.86914e15i −1.40559 + 0.817394i
709709 1.70696e15i 0.357823i 0.983865 + 0.178911i 0.0572576π0.0572576\pi
−0.983865 + 0.178911i 0.942742π0.942742\pi
710710 −3.82691e14 1.41933e15i −0.0796027 0.295231i
711711 −8.15765e14 −0.168377
712712 −1.30818e15 + 1.32053e15i −0.267934 + 0.270463i
713713 6.18254e15 1.25653
714714 −4.41561e14 1.63767e15i −0.0890534 0.330282i
715715 7.09386e15i 1.41971i
716716 −8.96011e14 1.54077e15i −0.177947 0.305997i
717717 5.67816e15i 1.11906i
718718 4.85011e15 1.30773e15i 0.948566 0.255760i
719719 7.81443e15 1.51666 0.758330 0.651870i 0.226015π-0.226015\pi
0.758330 + 0.651870i 0.226015π0.226015\pi
720720 1.02432e15 + 5.82871e14i 0.197292 + 0.112265i
721721 4.54005e14 0.0867793
722722 −2.01189e15 + 5.42463e14i −0.381637 + 0.102900i
723723 6.33009e14i 0.119165i
724724 4.14597e15 + 7.12938e15i 0.774576 + 1.33196i
725725 1.50021e15i 0.278160i
726726 5.32290e14 + 1.97417e15i 0.0979484 + 0.363272i
727727 9.77013e12 0.00178427 0.000892136 1.00000i 0.499716π-0.499716\pi
0.000892136 1.00000i 0.499716π0.499716\pi
728728 −1.30142e15 1.28925e15i −0.235882 0.233677i
729729 −6.16439e15 −1.10889
730730 −2.70327e14 1.00259e15i −0.0482630 0.178998i
731731 3.89476e15i 0.690137i
732732 −3.82070e15 + 2.22186e15i −0.671942 + 0.390756i
733733 1.07577e16i 1.87780i −0.344191 0.938900i 0.611847π-0.611847\pi
0.344191 0.938900i 0.388153π-0.388153\pi
734734 −5.99100e15 + 1.61534e15i −1.03794 + 0.279857i
735735 6.39267e15 1.09926
736736 1.11872e15 4.30981e15i 0.190939 0.735580i
737737 5.23799e15 0.887346
738738 −9.56624e14 + 2.57933e14i −0.160854 + 0.0433707i
739739 1.55149e14i 0.0258944i −0.999916 0.0129472i 0.995879π-0.995879\pi
0.999916 0.0129472i 0.00412133π-0.00412133\pi
740740 1.25206e15 7.28117e14i 0.207421 0.120622i
741741 9.45339e15i 1.55449i
742742 −3.46167e14 1.28387e15i −0.0565020 0.209555i
743743 −6.27422e15 −1.01653 −0.508266 0.861200i 0.669713π-0.669713\pi
−0.508266 + 0.861200i 0.669713π0.669713\pi
744744 6.62410e15 + 6.56216e15i 1.06531 + 1.05535i
745745 −1.02675e16 −1.63910
746746 −1.46497e15 5.43332e15i −0.232149 0.860996i
747747 1.19624e15i 0.188172i
748748 −4.05940e15 6.98051e15i −0.633874 1.09000i
749749 1.87786e14i 0.0291080i
750750 −2.64990e15 + 7.14488e14i −0.407749 + 0.109941i
751751 −6.57869e15 −1.00489 −0.502447 0.864608i 0.667567π-0.667567\pi
−0.502447 + 0.864608i 0.667567π0.667567\pi
752752 −1.16086e15 + 2.04008e15i −0.176029 + 0.309349i
753753 −6.13093e15 −0.922898
754754 −4.10077e15 + 1.10568e15i −0.612806 + 0.165230i
755755 4.03226e15i 0.598192i
756756 8.34082e14 + 1.43428e15i 0.122840 + 0.211234i
757757 2.54343e15i 0.371871i 0.982562 + 0.185935i 0.0595315π0.0595315\pi
−0.982562 + 0.185935i 0.940468π0.940468\pi
758758 3.25174e15 + 1.20601e16i 0.471992 + 1.75053i
759759 −3.65869e15 −0.527225
760760 7.43228e15 7.50243e15i 1.06328 1.07332i
761761 −5.98810e15 −0.850498 −0.425249 0.905076i 0.639813π-0.639813\pi
−0.425249 + 0.905076i 0.639813π0.639813\pi
762762 −2.42924e15 9.00960e15i −0.342545 1.27044i
763763 9.21426e12i 0.00128996i
764764 9.14224e15 5.31651e15i 1.27069 0.738947i
765765 2.71151e15i 0.374173i
766766 5.71810e15 1.54176e15i 0.783418 0.211232i
767767 1.91249e16 2.60150
768768 5.77306e15 3.43020e15i 0.779685 0.463268i
769769 −7.50045e15 −1.00576 −0.502878 0.864358i 0.667725π-0.667725\pi
−0.502878 + 0.864358i 0.667725π0.667725\pi
770770 −1.62357e15 + 4.37760e14i −0.216158 + 0.0582823i
771771 1.10880e16i 1.46573i
772772 4.63813e15 2.69722e15i 0.608762 0.354015i
773773 6.98863e15i 0.910762i 0.890297 + 0.455381i 0.150497π0.150497\pi
−0.890297 + 0.455381i 0.849503π0.849503\pi
774774 1.49492e14 + 5.54437e14i 0.0193438 + 0.0717426i
775775 −8.18390e15 −1.05148
776776 −4.50489e15 + 4.54741e15i −0.574705 + 0.580129i
777777 3.07335e14 0.0389311
778778 3.12732e15 + 1.15986e16i 0.393355 + 1.45888i
779779 8.87809e15i 1.10883i
780780 6.82307e15 + 1.17329e16i 0.846173 + 1.45507i
781781 1.48501e15i 0.182873i
782782 −9.89103e15 + 2.66690e15i −1.20950 + 0.326114i
783783 3.84675e15 0.467094
784784 −3.88693e15 + 6.83080e15i −0.468672 + 0.823632i
785785 8.02666e14 0.0961063
786786 3.73498e15 1.00705e15i 0.444083 0.119737i
787787 2.82969e15i 0.334102i −0.985948 0.167051i 0.946576π-0.946576\pi
0.985948 0.167051i 0.0534244π-0.0534244\pi
788788 9.79510e14 + 1.68436e15i 0.114846 + 0.197488i
789789 2.73167e15i 0.318057i
790790 −2.73216e15 1.01331e16i −0.315905 1.17163i
791791 1.80939e15 0.207759
792792 8.45806e14 + 8.37897e14i 0.0964456 + 0.0955438i
793793 1.09825e16 1.24365
794794 3.01280e15 + 1.11739e16i 0.338811 + 1.25659i
795795 9.85189e15i 1.10027i
796796 −1.30101e16 + 7.56578e15i −1.44297 + 0.839136i
797797 7.15437e15i 0.788044i −0.919101 0.394022i 0.871083π-0.871083\pi
0.919101 0.394022i 0.128917π-0.128917\pi
798798 2.16359e15 5.83366e14i 0.236679 0.0638153i
799799 5.40033e15 0.586696
800800 −1.48087e15 + 5.70494e15i −0.159779 + 0.615540i
801801 −6.30532e14 −0.0675660
802802 2.15648e15 5.81449e14i 0.229502 0.0618803i
803803 1.04899e15i 0.110876i
804804 8.66337e15 5.03804e15i 0.909450 0.528875i
805805 2.13327e15i 0.222417i
806806 −6.03168e15 2.23704e16i −0.624591 2.31649i
807807 3.73234e15 0.383864
808808 −1.97550e15 1.95703e15i −0.201797 0.199910i
809809 −6.06373e15 −0.615209 −0.307605 0.951514i 0.599527π-0.599527\pi
−0.307605 + 0.951514i 0.599527π0.599527\pi
810810 −2.61378e15 9.69403e15i −0.263392 0.976870i
811811 1.25004e16i 1.25115i −0.780164 0.625576i 0.784864π-0.784864\pi
0.780164 0.625576i 0.215136π-0.215136\pi
812812 −5.06115e14 8.70312e14i −0.0503142 0.0865200i
813813 1.42711e16i 1.40916i
814814 1.41271e15 3.80906e14i 0.138554 0.0373580i
815815 3.09004e15 0.301021
816816 −1.34281e16 7.64099e15i −1.29933 0.739356i
817817 5.14554e15 0.494549
818818 8.80284e15 2.37349e15i 0.840388 0.226592i
819819 6.21407e14i 0.0589271i
820820 −6.40784e15 1.10189e16i −0.603581 1.03791i
821821 9.11023e15i 0.852397i 0.904630 + 0.426198i 0.140147π0.140147\pi
−0.904630 + 0.426198i 0.859853π0.859853\pi
822822 1.50796e15 + 5.59276e15i 0.140151 + 0.519794i
823823 −1.90354e16 −1.75737 −0.878683 0.477407i 0.841577π-0.841577\pi
−0.878683 + 0.477407i 0.841577π0.841577\pi
824824 2.91042e15 2.93789e15i 0.266905 0.269424i
825825 4.84305e15 0.441187
826826 1.18019e15 + 4.37710e15i 0.106798 + 0.396092i
827827 6.03027e15i 0.542071i 0.962569 + 0.271036i 0.0873661π0.0873661\pi
−0.962569 + 0.271036i 0.912634π0.912634\pi
828828 1.30567e15 7.59291e14i 0.116592 0.0678018i
829829 1.35457e16i 1.20158i −0.799408 0.600788i 0.794854π-0.794854\pi
0.799408 0.600788i 0.205146π-0.205146\pi
830830 −1.48592e16 + 4.00645e15i −1.30938 + 0.353045i
831831 −8.70687e15 −0.762178
832832 −1.66857e16 + 1.56751e14i −1.45099 + 0.0136311i
833833 1.80820e16 1.56206
834834 −4.54834e14 + 1.22636e14i −0.0390337 + 0.0105246i
835835 5.91354e15i 0.504164i
836836 9.22226e15 5.36305e15i 0.781093 0.454231i
837837 2.09846e16i 1.76568i
838838 3.96701e15 + 1.47129e16i 0.331605 + 1.22986i
839839 5.63944e15 0.468322 0.234161 0.972198i 0.424766π-0.424766\pi
0.234161 + 0.972198i 0.424766π0.424766\pi
840840 −2.26426e15 + 2.28563e15i −0.186805 + 0.188569i
841841 9.86633e15 0.808682
842842 1.42203e13 + 5.27403e13i 0.00115795 + 0.00429463i
843843 3.23404e15i 0.261634i
844844 −7.00837e14 1.20515e15i −0.0563292 0.0968633i
845845 1.77084e16i 1.41406i
846846 −7.68762e14 + 2.07280e14i −0.0609895 + 0.0164445i
847847 1.20434e15 0.0949275
848848 −1.05271e16 5.99023e15i −0.824388 0.469101i
849849 −2.09217e16 −1.62781
850850 1.30929e16 3.53020e15i 1.01212 0.272895i
851851 1.85621e15i 0.142566i
852852 −1.42833e15 2.45614e15i −0.108996 0.187428i
853853 2.66012e15i 0.201689i −0.994902 0.100844i 0.967846π-0.967846\pi
0.994902 0.100844i 0.0321544π-0.0321544\pi
854854 6.77726e14 + 2.51356e15i 0.0510547 + 0.189353i
855855 3.58229e15 0.268131
856856 −1.21517e15 1.20381e15i −0.0903717 0.0895267i
857857 6.62417e15 0.489482 0.244741 0.969588i 0.421297π-0.421297\pi
0.244741 + 0.969588i 0.421297π0.421297\pi
858858 3.56941e15 + 1.32383e16i 0.262070 + 0.971967i
859859 2.28112e16i 1.66412i −0.554683 0.832062i 0.687161π-0.687161\pi
0.554683 0.832062i 0.312839π-0.312839\pi
860860 −6.38629e15 + 3.71384e15i −0.462922 + 0.269204i
861861 2.70472e15i 0.194807i
862862 −8.21229e14 + 2.21426e14i −0.0587725 + 0.0158467i
863863 −2.00538e16 −1.42606 −0.713031 0.701133i 0.752678π-0.752678\pi
−0.713031 + 0.701133i 0.752678π0.752678\pi
864864 1.46282e16 + 3.79714e15i 1.03363 + 0.268307i
865865 2.63048e16 1.84691
866866 1.37035e16 3.69484e15i 0.956054 0.257779i
867867 2.24636e16i 1.55731i
868868 4.74769e15 2.76094e15i 0.327057 0.190195i
869869 1.06020e16i 0.725736i
870870 1.94186e15 + 7.20201e15i 0.132088 + 0.489889i
871871 −2.49026e16 −1.68324
872872 −5.96260e13 5.90685e13i −0.00400493 0.00396748i
873873 −2.17131e15 −0.144925
874874 −3.52336e15 1.30675e16i −0.233692 0.866720i
875875 1.61658e15i 0.106550i
876876 −1.00895e15 1.73498e15i −0.0660840 0.113638i
877877 2.76399e16i 1.79903i 0.436887 + 0.899516i 0.356081π0.356081\pi
−0.436887 + 0.899516i 0.643919π0.643919\pi
878878 2.16377e16 5.83413e15i 1.39956 0.377361i
879879 2.13731e16 1.37381
880880 −7.57521e15 + 1.33125e16i −0.483883 + 0.850364i
881881 −2.51486e16 −1.59642 −0.798208 0.602382i 0.794218π-0.794218\pi
−0.798208 + 0.602382i 0.794218π0.794218\pi
882882 −2.57405e15 + 6.94036e14i −0.162383 + 0.0437829i
883883 1.31245e16i 0.822810i 0.911453 + 0.411405i 0.134962π0.134962\pi
−0.911453 + 0.411405i 0.865038π0.865038\pi
884884 1.92993e16 + 3.31870e16i 1.20242 + 2.06767i
885885 3.35882e16i 2.07969i
886886 3.53051e15 + 1.30940e16i 0.217246 + 0.805726i
887887 −5.71207e15 −0.349312 −0.174656 0.984630i 0.555881π-0.555881\pi
−0.174656 + 0.984630i 0.555881π0.555881\pi
888888 1.97019e15 1.98878e15i 0.119739 0.120869i
889889 −5.49633e15 −0.331981
890890 −2.11177e15 7.83218e15i −0.126766 0.470151i
891891 1.01426e16i 0.605096i
892892 −2.11460e15 + 1.22971e15i −0.125378 + 0.0729116i
893893 7.13461e15i 0.420424i
894894 −1.91608e16 + 5.16628e15i −1.12216 + 0.302567i
895895 7.77831e15 0.452750
896896 −1.06554e15 3.80917e15i −0.0616420 0.220362i
897897 1.73943e16 1.00011
898898 1.09208e16 2.94457e15i 0.624075 0.168268i
899899 1.27333e16i 0.723209i
900900 −1.72833e15 + 1.00508e15i −0.0975649 + 0.0567372i
901901 2.78665e16i 1.56349i
902902 −3.35219e15 1.24327e16i −0.186936 0.693310i
903903 −1.56760e15 −0.0868864
904904 1.15992e16 1.17086e16i 0.639000 0.645031i
905905 −3.59913e16 −1.97075
906906 2.02891e15 + 7.52485e15i 0.110423 + 0.409537i
907907 1.52922e16i 0.827235i −0.910451 0.413618i 0.864265π-0.864265\pi
0.910451 0.413618i 0.135735π-0.135735\pi
908908 −5.17529e15 8.89938e15i −0.278267 0.478506i
909909 9.43271e14i 0.0504121i
910910 7.71884e15 2.08121e15i 0.410038 0.110558i
911911 −5.29684e14 −0.0279683 −0.0139842 0.999902i 0.504451π-0.504451\pi
−0.0139842 + 0.999902i 0.504451π0.504451\pi
912912 1.00948e16 1.77404e16i 0.529820 0.931093i
913913 −1.55468e16 −0.811058
914914 −3.15729e16 + 8.51294e15i −1.63723 + 0.441444i
915915 1.92881e16i 0.994198i
916916 −2.95089e15 5.07433e15i −0.151192 0.259988i
917917 2.27853e15i 0.116044i
918918 −9.05193e15 3.35719e16i −0.458254 1.69958i
919919 2.61618e16 1.31654 0.658268 0.752783i 0.271289π-0.271289\pi
0.658268 + 0.752783i 0.271289π0.271289\pi
920920 1.38045e16 + 1.36754e16i 0.690539 + 0.684082i
921921 1.33369e16 0.663173
922922 3.17117e14 + 1.17613e15i 0.0156747 + 0.0581346i
923923 7.06011e15i 0.346898i
924924 −2.80957e15 + 1.63386e15i −0.137229 + 0.0798030i
925925 2.45709e15i 0.119300i
926926 −2.64848e15 + 7.14105e14i −0.127831 + 0.0344669i
927927 1.40280e15 0.0673063
928928 −8.87631e15 2.30408e15i −0.423369 0.109896i
929929 −2.14173e16 −1.01550 −0.507749 0.861505i 0.669522π-0.669522\pi
−0.507749 + 0.861505i 0.669522π0.669522\pi
930930 −3.92881e16 + 1.05932e16i −1.85185 + 0.499309i
931931 2.38889e16i 1.11937i
932932 −1.60369e16 + 9.32600e15i −0.747022 + 0.434418i
933933 3.34916e16i 1.55091i
934934 3.50081e14 + 1.29838e15i 0.0161161 + 0.0597717i
935935 3.52398e16 1.61276
936936 −4.02116e15 3.98356e15i −0.182951 0.181240i
937937 1.84540e16 0.834685 0.417343 0.908749i 0.362961π-0.362961\pi
0.417343 + 0.908749i 0.362961π0.362961\pi
938938 −1.53673e15 5.69946e15i −0.0691008 0.256282i
939939 3.61727e16i 1.61704i
940940 −5.14947e15 8.85499e15i −0.228854 0.393536i
941941 1.10663e16i 0.488946i −0.969656 0.244473i 0.921385π-0.921385\pi
0.969656 0.244473i 0.0786149π-0.0786149\pi
942942 1.49790e15 4.03877e14i 0.0657967 0.0177406i
943943 −1.63357e16 −0.713385
944944 3.58902e16 + 2.04226e16i 1.55822 + 0.886675i
945945 −7.24070e15 −0.312540
946946 −7.20568e15 + 1.94285e15i −0.309224 + 0.0833756i
947947 1.56625e16i 0.668244i −0.942530 0.334122i 0.891560π-0.891560\pi
0.942530 0.334122i 0.108440π-0.108440\pi
948948 −1.01973e16 1.75352e16i −0.432552 0.743814i
949949 4.98715e15i 0.210324i
950950 4.66391e15 + 1.72976e16i 0.195556 + 0.725279i
951951 2.84656e16 1.18666
952952 −6.40455e15 + 6.46500e15i −0.265452 + 0.267957i
953953 2.46314e16 1.01503 0.507515 0.861643i 0.330564π-0.330564\pi
0.507515 + 0.861643i 0.330564π0.330564\pi
954954 −1.06959e15 3.96693e15i −0.0438231 0.162532i
955955 4.61529e16i 1.88010i
956956 2.63353e16 1.53149e16i 1.06665 0.620290i
957957 7.53530e15i 0.303448i
958958 5.28812e15 1.42583e15i 0.211734 0.0570895i
959959 3.41188e15 0.135829
960960 2.75295e14 + 2.93043e16i 0.0108970 + 1.15995i
961961 4.40539e16 1.73383
962962 −6.71636e15 + 1.81092e15i −0.262828 + 0.0708657i
963963 5.80226e14i 0.0225763i
964964 2.93590e15 1.70732e15i 0.113584 0.0660529i
965965 2.34147e16i 0.900717i
966966 1.07340e15 + 3.98102e15i 0.0410568 + 0.152272i
967967 1.75674e16 0.668130 0.334065 0.942550i 0.391579π-0.391579\pi
0.334065 + 0.942550i 0.391579π0.391579\pi
968968 7.72052e15 7.79339e15i 0.291966 0.294721i
969969 −4.69611e16 −1.76586
970970 −7.27216e15 2.69711e16i −0.271906 1.00845i
971971 1.47579e15i 0.0548679i −0.999624 0.0274339i 0.991266π-0.991266\pi
0.999624 0.0274339i 0.00873359π-0.00873359\pi
972972 4.76589e15 + 8.19540e15i 0.176189 + 0.302974i
973973 2.77472e14i 0.0102000i
974974 2.62849e16 7.08715e15i 0.960799 0.259058i
975975 −2.30250e16 −0.836902
976976 2.06100e16 + 1.17277e16i 0.744910 + 0.423876i
977977 −3.43891e16 −1.23595 −0.617975 0.786198i 0.712047π-0.712047\pi
−0.617975 + 0.786198i 0.712047π0.712047\pi
978978 5.76651e15 1.55481e15i 0.206086 0.0555667i
979979 8.19463e15i 0.291222i
980980 −1.72420e16 2.96492e16i −0.609319 1.04778i
981981 2.84705e13i 0.00100049i
982982 −1.03077e15 3.82294e15i −0.0360204 0.133593i
983983 −3.64560e16 −1.26685 −0.633424 0.773805i 0.718351π-0.718351\pi
−0.633424 + 0.773805i 0.718351π0.718351\pi
984984 −1.75024e16 1.73388e16i −0.604819 0.599163i
985985 −8.50317e15 −0.292201
986986 5.49264e15 + 2.03712e16i 0.187697 + 0.696135i
987987 2.17357e15i 0.0738634i
988988 −4.38448e16 + 2.54972e16i −1.48168 + 0.861647i
989989 9.46782e15i 0.318178i
990990 −5.01655e15 + 1.35260e15i −0.167653 + 0.0452040i
991991 −1.42245e16 −0.472750 −0.236375 0.971662i 0.575959π-0.575959\pi
−0.236375 + 0.971662i 0.575959π0.575959\pi
992992 1.25691e16 4.84217e16i 0.415423 1.60039i
993993 3.45687e16 1.13622
994994 −1.61585e15 + 4.35677e14i −0.0528171 + 0.0142410i
995995 6.56789e16i 2.13500i
996996 −2.57137e16 + 1.49533e16i −0.831261 + 0.483406i
997997 6.02174e16i 1.93597i −0.251009 0.967985i 0.580762π-0.580762\pi
0.251009 0.967985i 0.419238π-0.419238\pi
998998 1.06014e16 + 3.93185e16i 0.338957 + 1.25713i
999999 6.30032e15 0.200333
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 8.12.b.a.5.9 10
3.2 odd 2 72.12.d.b.37.2 10
4.3 odd 2 32.12.b.a.17.3 10
8.3 odd 2 32.12.b.a.17.8 10
8.5 even 2 inner 8.12.b.a.5.10 yes 10
16.3 odd 4 256.12.a.o.1.8 10
16.5 even 4 256.12.a.p.1.8 10
16.11 odd 4 256.12.a.o.1.3 10
16.13 even 4 256.12.a.p.1.3 10
24.5 odd 2 72.12.d.b.37.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8.12.b.a.5.9 10 1.1 even 1 trivial
8.12.b.a.5.10 yes 10 8.5 even 2 inner
32.12.b.a.17.3 10 4.3 odd 2
32.12.b.a.17.8 10 8.3 odd 2
72.12.d.b.37.1 10 24.5 odd 2
72.12.d.b.37.2 10 3.2 odd 2
256.12.a.o.1.3 10 16.11 odd 4
256.12.a.o.1.8 10 16.3 odd 4
256.12.a.p.1.3 10 16.13 even 4
256.12.a.p.1.8 10 16.5 even 4