Properties

Label 5.13.c.a.2.2
Level $5$
Weight $13$
Character 5.2
Analytic conductor $4.570$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5,13,Mod(2,5)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 13, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5.2");
 
S:= CuspForms(chi, 13);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 13 \)
Character orbit: \([\chi]\) \(=\) 5.c (of order \(4\), degree \(2\), 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: \(4.56996908638\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} + 7950x^{8} + 16939113x^{6} + 4574579500x^{4} + 337520899536x^{2} + 6615595526400 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{13}\cdot 3^{2}\cdot 5^{9} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 2.2
Root \(60.9123i\) of defining polynomial
Character \(\chi\) \(=\) 5.2
Dual form 5.13.c.a.3.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-54.8437 - 54.8437i) q^{2} +(-506.429 + 506.429i) q^{3} +1919.66i q^{4} +(15616.9 + 502.591i) q^{5} +55548.9 q^{6} +(78559.8 + 78559.8i) q^{7} +(-119359. + 119359. i) q^{8} +18500.3i q^{9} +O(q^{10})\) \(q+(-54.8437 - 54.8437i) q^{2} +(-506.429 + 506.429i) q^{3} +1919.66i q^{4} +(15616.9 + 502.591i) q^{5} +55548.9 q^{6} +(78559.8 + 78559.8i) q^{7} +(-119359. + 119359. i) q^{8} +18500.3i q^{9} +(-828925. - 884053. i) q^{10} +1.27194e6 q^{11} +(-972170. - 972170. i) q^{12} +(-3.53518e6 + 3.53518e6i) q^{13} -8.61702e6i q^{14} +(-8.16339e6 + 7.65433e6i) q^{15} +2.09550e7 q^{16} +(2.56603e7 + 2.56603e7i) q^{17} +(1.01463e6 - 1.01463e6i) q^{18} -5.31802e7i q^{19} +(-964803. + 2.99791e7i) q^{20} -7.95700e7 q^{21} +(-6.97580e7 - 6.97580e7i) q^{22} +(-1.16839e8 + 1.16839e8i) q^{23} -1.20893e8i q^{24} +(2.43635e8 + 1.56979e7i) q^{25} +3.87764e8 q^{26} +(-2.78506e8 - 2.78506e8i) q^{27} +(-1.50808e8 + 1.50808e8i) q^{28} +8.95459e8i q^{29} +(8.67502e8 + 2.79184e7i) q^{30} -1.69379e8 q^{31} +(-6.60359e8 - 6.60359e8i) q^{32} +(-6.44148e8 + 6.44148e8i) q^{33} -2.81461e9i q^{34} +(1.18738e9 + 1.26635e9i) q^{35} -3.55143e7 q^{36} +(-6.45104e8 - 6.45104e8i) q^{37} +(-2.91660e9 + 2.91660e9i) q^{38} -3.58063e9i q^{39} +(-1.92400e9 + 1.80402e9i) q^{40} +1.87299e9 q^{41} +(4.36391e9 + 4.36391e9i) q^{42} +(4.24875e9 - 4.24875e9i) q^{43} +2.44169e9i q^{44} +(-9.29811e6 + 2.88918e8i) q^{45} +1.28157e10 q^{46} +(-3.40998e9 - 3.40998e9i) q^{47} +(-1.06122e10 + 1.06122e10i) q^{48} -1.49799e9i q^{49} +(-1.25009e10 - 1.42228e10i) q^{50} -2.59903e10 q^{51} +(-6.78633e9 - 6.78633e9i) q^{52} +(2.01462e10 - 2.01462e10i) q^{53} +3.05486e10i q^{54} +(1.98638e10 + 6.39267e8i) q^{55} -1.87536e10 q^{56} +(2.69320e10 + 2.69320e10i) q^{57} +(4.91103e10 - 4.91103e10i) q^{58} +4.54399e10i q^{59} +(-1.46937e10 - 1.56709e10i) q^{60} -3.24024e10 q^{61} +(9.28937e9 + 9.28937e9i) q^{62} +(-1.45338e9 + 1.45338e9i) q^{63} -1.33989e10i q^{64} +(-5.69853e10 + 5.34318e10i) q^{65} +7.06549e10 q^{66} +(-1.79028e10 - 1.79028e10i) q^{67} +(-4.92590e10 + 4.92590e10i) q^{68} -1.18341e11i q^{69} +(4.33084e9 - 1.34571e11i) q^{70} -9.83693e9 q^{71} +(-2.20817e9 - 2.20817e9i) q^{72} +(-1.11985e10 + 1.11985e10i) q^{73} +7.07598e10i q^{74} +(-1.31334e11 + 1.15434e11i) q^{75} +1.02088e11 q^{76} +(9.99235e10 + 9.99235e10i) q^{77} +(-1.96375e11 + 1.96375e11i) q^{78} -1.98262e11i q^{79} +(3.27253e11 + 1.05318e10i) q^{80} +2.72255e11 q^{81} +(-1.02722e11 - 1.02722e11i) q^{82} +(1.02047e11 - 1.02047e11i) q^{83} -1.52747e11i q^{84} +(3.87838e11 + 4.13632e11i) q^{85} -4.66034e11 q^{86} +(-4.53487e11 - 4.53487e11i) q^{87} +(-1.51817e11 + 1.51817e11i) q^{88} +1.71978e11i q^{89} +(1.63553e10 - 1.53354e10i) q^{90} -5.55446e11 q^{91} +(-2.24291e11 - 2.24291e11i) q^{92} +(8.57785e10 - 8.57785e10i) q^{93} +3.74032e11i q^{94} +(2.67279e10 - 8.30511e11i) q^{95} +6.68850e11 q^{96} +(2.72426e11 + 2.72426e11i) q^{97} +(-8.21552e10 + 8.21552e10i) q^{98} +2.35313e10i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 2 q^{2} + 318 q^{3} - 4250 q^{5} - 175080 q^{6} + 279598 q^{7} - 469980 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 2 q^{2} + 318 q^{3} - 4250 q^{5} - 175080 q^{6} + 279598 q^{7} - 469980 q^{8} + 1552150 q^{10} + 312620 q^{11} - 2359992 q^{12} + 5290738 q^{13} - 5821650 q^{15} + 30547960 q^{16} - 41269502 q^{17} - 140573742 q^{18} + 334988100 q^{20} + 107493420 q^{21} - 155490544 q^{22} - 510099842 q^{23} + 942201250 q^{25} + 1475846420 q^{26} - 1993958640 q^{27} - 3562106488 q^{28} + 5922516000 q^{30} + 3077089820 q^{31} - 4623883832 q^{32} - 7503698004 q^{33} + 9330787150 q^{35} + 7760793660 q^{36} - 2599618502 q^{37} - 15310240920 q^{38} + 15901243500 q^{40} + 7412079020 q^{41} - 18593270064 q^{42} - 5784410402 q^{43} - 10510145100 q^{45} - 7382547880 q^{46} + 16053249598 q^{47} + 42572492208 q^{48} - 68314688750 q^{50} - 33139878180 q^{51} + 96763417228 q^{52} + 101763514618 q^{53} - 84180068500 q^{55} - 172002747600 q^{56} + 27733489920 q^{57} + 135238672320 q^{58} - 220124568600 q^{60} + 7731718220 q^{61} + 193287375176 q^{62} + 207465112158 q^{63} - 338075024150 q^{65} - 60815472960 q^{66} - 80010636002 q^{67} + 204699541412 q^{68} + 376969924200 q^{70} - 46557252580 q^{71} - 13986370620 q^{72} - 448527032342 q^{73} + 719724648750 q^{75} + 305095930800 q^{76} - 425580405844 q^{77} - 1690993241784 q^{78} + 873032236000 q^{80} + 1107831051810 q^{81} - 671946416464 q^{82} - 91118376722 q^{83} + 543768569650 q^{85} + 414117747320 q^{86} - 2078422804320 q^{87} - 1842434230560 q^{88} + 3098742811350 q^{90} + 2737742572220 q^{91} + 906853941448 q^{92} - 91295366484 q^{93} - 1044695070000 q^{95} - 3473259523680 q^{96} - 1409507601302 q^{97} - 1481746533298 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −54.8437 54.8437i −0.856932 0.856932i 0.134043 0.990976i \(-0.457204\pi\)
−0.990976 + 0.134043i \(0.957204\pi\)
\(3\) −506.429 + 506.429i −0.694690 + 0.694690i −0.963260 0.268570i \(-0.913449\pi\)
0.268570 + 0.963260i \(0.413449\pi\)
\(4\) 1919.66i 0.468666i
\(5\) 15616.9 + 502.591i 0.999483 + 0.0321658i
\(6\) 55548.9 1.19060
\(7\) 78559.8 + 78559.8i 0.667748 + 0.667748i 0.957194 0.289447i \(-0.0934712\pi\)
−0.289447 + 0.957194i \(0.593471\pi\)
\(8\) −119359. + 119359.i −0.455317 + 0.455317i
\(9\) 18500.3i 0.0348116i
\(10\) −828925. 884053.i −0.828925 0.884053i
\(11\) 1.27194e6 0.717978 0.358989 0.933342i \(-0.383122\pi\)
0.358989 + 0.933342i \(0.383122\pi\)
\(12\) −972170. 972170.i −0.325578 0.325578i
\(13\) −3.53518e6 + 3.53518e6i −0.732405 + 0.732405i −0.971096 0.238691i \(-0.923282\pi\)
0.238691 + 0.971096i \(0.423282\pi\)
\(14\) 8.61702e6i 1.14443i
\(15\) −8.16339e6 + 7.65433e6i −0.716676 + 0.671985i
\(16\) 2.09550e7 1.24902
\(17\) 2.56603e7 + 2.56603e7i 1.06309 + 1.06309i 0.997871 + 0.0652150i \(0.0207733\pi\)
0.0652150 + 0.997871i \(0.479227\pi\)
\(18\) 1.01463e6 1.01463e6i 0.0298312 0.0298312i
\(19\) 5.31802e7i 1.13039i −0.824957 0.565195i \(-0.808801\pi\)
0.824957 0.565195i \(-0.191199\pi\)
\(20\) −964803. + 2.99791e7i −0.0150750 + 0.468424i
\(21\) −7.95700e7 −0.927755
\(22\) −6.97580e7 6.97580e7i −0.615259 0.615259i
\(23\) −1.16839e8 + 1.16839e8i −0.789260 + 0.789260i −0.981373 0.192113i \(-0.938466\pi\)
0.192113 + 0.981373i \(0.438466\pi\)
\(24\) 1.20893e8i 0.632608i
\(25\) 2.43635e8 + 1.56979e7i 0.997931 + 0.0642984i
\(26\) 3.87764e8 1.25524
\(27\) −2.78506e8 2.78506e8i −0.718873 0.718873i
\(28\) −1.50808e8 + 1.50808e8i −0.312951 + 0.312951i
\(29\) 8.95459e8i 1.50542i 0.658352 + 0.752710i \(0.271254\pi\)
−0.658352 + 0.752710i \(0.728746\pi\)
\(30\) 8.67502e8 + 2.79184e7i 1.18999 + 0.0382968i
\(31\) −1.69379e8 −0.190849 −0.0954245 0.995437i \(-0.530421\pi\)
−0.0954245 + 0.995437i \(0.530421\pi\)
\(32\) −6.60359e8 6.60359e8i −0.615007 0.615007i
\(33\) −6.44148e8 + 6.44148e8i −0.498772 + 0.498772i
\(34\) 2.81461e9i 1.82199i
\(35\) 1.18738e9 + 1.26635e9i 0.645923 + 0.688881i
\(36\) −3.55143e7 −0.0163150
\(37\) −6.45104e8 6.45104e8i −0.251431 0.251431i 0.570126 0.821557i \(-0.306894\pi\)
−0.821557 + 0.570126i \(0.806894\pi\)
\(38\) −2.91660e9 + 2.91660e9i −0.968669 + 0.968669i
\(39\) 3.58063e9i 1.01759i
\(40\) −1.92400e9 + 1.80402e9i −0.469727 + 0.440436i
\(41\) 1.87299e9 0.394306 0.197153 0.980373i \(-0.436830\pi\)
0.197153 + 0.980373i \(0.436830\pi\)
\(42\) 4.36391e9 + 4.36391e9i 0.795024 + 0.795024i
\(43\) 4.24875e9 4.24875e9i 0.672125 0.672125i −0.286081 0.958206i \(-0.592353\pi\)
0.958206 + 0.286081i \(0.0923525\pi\)
\(44\) 2.44169e9i 0.336492i
\(45\) −9.29811e6 + 2.88918e8i −0.00111975 + 0.0347936i
\(46\) 1.28157e10 1.35269
\(47\) −3.40998e9 3.40998e9i −0.316348 0.316348i 0.531015 0.847363i \(-0.321811\pi\)
−0.847363 + 0.531015i \(0.821811\pi\)
\(48\) −1.06122e10 + 1.06122e10i −0.867680 + 0.867680i
\(49\) 1.49799e9i 0.108226i
\(50\) −1.25009e10 1.42228e10i −0.800060 0.910259i
\(51\) −2.59903e10 −1.47703
\(52\) −6.78633e9 6.78633e9i −0.343253 0.343253i
\(53\) 2.01462e10 2.01462e10i 0.908946 0.908946i −0.0872416 0.996187i \(-0.527805\pi\)
0.996187 + 0.0872416i \(0.0278052\pi\)
\(54\) 3.05486e10i 1.23205i
\(55\) 1.98638e10 + 6.39267e8i 0.717606 + 0.0230944i
\(56\) −1.87536e10 −0.608074
\(57\) 2.69320e10 + 2.69320e10i 0.785271 + 0.785271i
\(58\) 4.91103e10 4.91103e10i 1.29004 1.29004i
\(59\) 4.54399e10i 1.07727i 0.842539 + 0.538636i \(0.181060\pi\)
−0.842539 + 0.538636i \(0.818940\pi\)
\(60\) −1.46937e10 1.56709e10i −0.314937 0.335882i
\(61\) −3.24024e10 −0.628925 −0.314462 0.949270i \(-0.601824\pi\)
−0.314462 + 0.949270i \(0.601824\pi\)
\(62\) 9.28937e9 + 9.28937e9i 0.163545 + 0.163545i
\(63\) −1.45338e9 + 1.45338e9i −0.0232454 + 0.0232454i
\(64\) 1.33989e10i 0.194979i
\(65\) −5.69853e10 + 5.34318e10i −0.755584 + 0.708467i
\(66\) 7.06549e10 0.854828
\(67\) −1.79028e10 1.79028e10i −0.197912 0.197912i 0.601192 0.799104i \(-0.294693\pi\)
−0.799104 + 0.601192i \(0.794693\pi\)
\(68\) −4.92590e10 + 4.92590e10i −0.498233 + 0.498233i
\(69\) 1.18341e11i 1.09658i
\(70\) 4.33084e9 1.34571e11i 0.0368115 1.14384i
\(71\) −9.83693e9 −0.0767909 −0.0383954 0.999263i \(-0.512225\pi\)
−0.0383954 + 0.999263i \(0.512225\pi\)
\(72\) −2.20817e9 2.20817e9i −0.0158503 0.0158503i
\(73\) −1.11985e10 + 1.11985e10i −0.0739988 + 0.0739988i −0.743138 0.669139i \(-0.766663\pi\)
0.669139 + 0.743138i \(0.266663\pi\)
\(74\) 7.07598e10i 0.430919i
\(75\) −1.31334e11 + 1.15434e11i −0.737920 + 0.648585i
\(76\) 1.02088e11 0.529776
\(77\) 9.99235e10 + 9.99235e10i 0.479428 + 0.479428i
\(78\) −1.96375e11 + 1.96375e11i −0.872004 + 0.872004i
\(79\) 1.98262e11i 0.815598i −0.913072 0.407799i \(-0.866296\pi\)
0.913072 0.407799i \(-0.133704\pi\)
\(80\) 3.27253e11 + 1.05318e10i 1.24837 + 0.0401757i
\(81\) 2.72255e11 0.963977
\(82\) −1.02722e11 1.02722e11i −0.337893 0.337893i
\(83\) 1.02047e11 1.02047e11i 0.312128 0.312128i −0.533606 0.845733i \(-0.679163\pi\)
0.845733 + 0.533606i \(0.179163\pi\)
\(84\) 1.52747e11i 0.434808i
\(85\) 3.87838e11 + 4.13632e11i 1.02834 + 1.09673i
\(86\) −4.66034e11 −1.15193
\(87\) −4.53487e11 4.53487e11i −1.04580 1.04580i
\(88\) −1.51817e11 + 1.51817e11i −0.326908 + 0.326908i
\(89\) 1.71978e11i 0.346045i 0.984918 + 0.173023i \(0.0553534\pi\)
−0.984918 + 0.173023i \(0.944647\pi\)
\(90\) 1.63553e10 1.53354e10i 0.0307753 0.0288562i
\(91\) −5.55446e11 −0.978123
\(92\) −2.24291e11 2.24291e11i −0.369900 0.369900i
\(93\) 8.57785e10 8.57785e10i 0.132581 0.132581i
\(94\) 3.74032e11i 0.542178i
\(95\) 2.67279e10 8.30511e11i 0.0363600 1.12981i
\(96\) 6.68850e11 0.854479
\(97\) 2.72426e11 + 2.72426e11i 0.327053 + 0.327053i 0.851465 0.524412i \(-0.175715\pi\)
−0.524412 + 0.851465i \(0.675715\pi\)
\(98\) −8.21552e10 + 8.21552e10i −0.0927424 + 0.0927424i
\(99\) 2.35313e10i 0.0249940i
\(100\) −3.01345e10 + 4.67697e11i −0.0301345 + 0.467697i
\(101\) 1.74091e12 1.64001 0.820007 0.572354i \(-0.193970\pi\)
0.820007 + 0.572354i \(0.193970\pi\)
\(102\) 1.42540e12 + 1.42540e12i 1.26572 + 1.26572i
\(103\) −2.00256e11 + 2.00256e11i −0.167711 + 0.167711i −0.785973 0.618261i \(-0.787837\pi\)
0.618261 + 0.785973i \(0.287837\pi\)
\(104\) 8.43908e11i 0.666953i
\(105\) −1.24264e12 3.99912e10i −0.927275 0.0298420i
\(106\) −2.20978e12 −1.55781
\(107\) −1.27598e12 1.27598e12i −0.850237 0.850237i 0.139925 0.990162i \(-0.455314\pi\)
−0.990162 + 0.139925i \(0.955314\pi\)
\(108\) 5.34637e11 5.34637e11i 0.336912 0.336912i
\(109\) 1.64108e12i 0.978520i 0.872138 + 0.489260i \(0.162733\pi\)
−0.872138 + 0.489260i \(0.837267\pi\)
\(110\) −1.05434e12 1.12446e12i −0.595150 0.634731i
\(111\) 6.53399e11 0.349334
\(112\) 1.64623e12 + 1.64623e12i 0.834029 + 0.834029i
\(113\) 1.06785e12 1.06785e12i 0.512909 0.512909i −0.402507 0.915417i \(-0.631861\pi\)
0.915417 + 0.402507i \(0.131861\pi\)
\(114\) 2.95410e12i 1.34585i
\(115\) −1.88338e12 + 1.76594e12i −0.814239 + 0.763465i
\(116\) −1.71898e12 −0.705540
\(117\) −6.54020e10 6.54020e10i −0.0254962 0.0254962i
\(118\) 2.49209e12 2.49209e12i 0.923149 0.923149i
\(119\) 4.03174e12i 1.41975i
\(120\) 6.07599e10 1.88798e12i 0.0203484 0.632281i
\(121\) −1.52059e12 −0.484508
\(122\) 1.77707e12 + 1.77707e12i 0.538946 + 0.538946i
\(123\) −9.48538e11 + 9.48538e11i −0.273920 + 0.273920i
\(124\) 3.25150e11i 0.0894445i
\(125\) 3.79694e12 + 3.67601e11i 0.995346 + 0.0963644i
\(126\) 1.59418e11 0.0398395
\(127\) −3.25841e12 3.25841e12i −0.776574 0.776574i 0.202672 0.979247i \(-0.435037\pi\)
−0.979247 + 0.202672i \(0.935037\pi\)
\(128\) −3.43967e12 + 3.43967e12i −0.782091 + 0.782091i
\(129\) 4.30338e12i 0.933837i
\(130\) 6.05568e12 + 1.94887e11i 1.25459 + 0.0403759i
\(131\) 6.35834e12 1.25810 0.629051 0.777364i \(-0.283443\pi\)
0.629051 + 0.777364i \(0.283443\pi\)
\(132\) −1.23654e12 1.23654e12i −0.233758 0.233758i
\(133\) 4.17783e12 4.17783e12i 0.754816 0.754816i
\(134\) 1.96371e12i 0.339195i
\(135\) −4.20943e12 4.48938e12i −0.695378 0.741624i
\(136\) −6.12556e12 −0.968083
\(137\) −3.91400e12 3.91400e12i −0.591968 0.591968i 0.346195 0.938163i \(-0.387474\pi\)
−0.938163 + 0.346195i \(0.887474\pi\)
\(138\) −6.49026e12 + 6.49026e12i −0.939697 + 0.939697i
\(139\) 1.23384e13i 1.71068i −0.518063 0.855342i \(-0.673347\pi\)
0.518063 0.855342i \(-0.326653\pi\)
\(140\) −2.43095e12 + 2.27936e12i −0.322855 + 0.302723i
\(141\) 3.45383e12 0.439527
\(142\) 5.39494e11 + 5.39494e11i 0.0658046 + 0.0658046i
\(143\) −4.49654e12 + 4.49654e12i −0.525850 + 0.525850i
\(144\) 3.87675e11i 0.0434804i
\(145\) −4.50050e11 + 1.39843e13i −0.0484231 + 1.50464i
\(146\) 1.22834e12 0.126824
\(147\) 7.58625e11 + 7.58625e11i 0.0751836 + 0.0751836i
\(148\) 1.23838e12 1.23838e12i 0.117837 0.117837i
\(149\) 1.42078e13i 1.29840i −0.760617 0.649200i \(-0.775104\pi\)
0.760617 0.649200i \(-0.224896\pi\)
\(150\) 1.35337e13 + 8.71998e11i 1.18814 + 0.0765540i
\(151\) 9.94655e12 0.839095 0.419547 0.907733i \(-0.362189\pi\)
0.419547 + 0.907733i \(0.362189\pi\)
\(152\) 6.34752e12 + 6.34752e12i 0.514686 + 0.514686i
\(153\) −4.74724e11 + 4.74724e11i −0.0370078 + 0.0370078i
\(154\) 1.09603e13i 0.821675i
\(155\) −2.64518e12 8.51285e10i −0.190750 0.00613882i
\(156\) 6.87359e12 0.476909
\(157\) 8.04948e12 + 8.04948e12i 0.537489 + 0.537489i 0.922791 0.385301i \(-0.125902\pi\)
−0.385301 + 0.922791i \(0.625902\pi\)
\(158\) −1.08734e13 + 1.08734e13i −0.698912 + 0.698912i
\(159\) 2.04052e13i 1.26287i
\(160\) −9.98088e12 1.06447e13i −0.594907 0.634471i
\(161\) −1.83577e13 −1.05405
\(162\) −1.49315e13 1.49315e13i −0.826063 0.826063i
\(163\) 1.13523e13 1.13523e13i 0.605283 0.605283i −0.336426 0.941710i \(-0.609218\pi\)
0.941710 + 0.336426i \(0.109218\pi\)
\(164\) 3.59550e12i 0.184798i
\(165\) −1.03834e13 + 9.73586e12i −0.514557 + 0.482471i
\(166\) −1.11933e13 −0.534944
\(167\) −4.22185e12 4.22185e12i −0.194627 0.194627i 0.603065 0.797692i \(-0.293946\pi\)
−0.797692 + 0.603065i \(0.793946\pi\)
\(168\) 9.49736e12 9.49736e12i 0.422423 0.422423i
\(169\) 1.69687e12i 0.0728332i
\(170\) 1.41460e12 4.39556e13i 0.0586057 1.82104i
\(171\) 9.83852e11 0.0393508
\(172\) 8.15614e12 + 8.15614e12i 0.315002 + 0.315002i
\(173\) 8.20643e12 8.20643e12i 0.306110 0.306110i −0.537288 0.843399i \(-0.680551\pi\)
0.843399 + 0.537288i \(0.180551\pi\)
\(174\) 4.97417e13i 1.79236i
\(175\) 1.79067e13 + 2.03732e13i 0.623431 + 0.709301i
\(176\) 2.66536e13 0.896768
\(177\) −2.30121e13 2.30121e13i −0.748370 0.748370i
\(178\) 9.43191e12 9.43191e12i 0.296538 0.296538i
\(179\) 3.70781e13i 1.12719i 0.826050 + 0.563597i \(0.190583\pi\)
−0.826050 + 0.563597i \(0.809417\pi\)
\(180\) −5.54624e11 1.78492e10i −0.0163066 0.000524787i
\(181\) −4.86231e13 −1.38284 −0.691419 0.722454i \(-0.743014\pi\)
−0.691419 + 0.722454i \(0.743014\pi\)
\(182\) 3.04627e13 + 3.04627e13i 0.838185 + 0.838185i
\(183\) 1.64095e13 1.64095e13i 0.436908 0.436908i
\(184\) 2.78914e13i 0.718727i
\(185\) −9.75031e12 1.03988e13i −0.243214 0.259389i
\(186\) −9.40882e12 −0.227226
\(187\) 3.26384e13 + 3.26384e13i 0.763272 + 0.763272i
\(188\) 6.54600e12 6.54600e12i 0.148262 0.148262i
\(189\) 4.37588e13i 0.960052i
\(190\) −4.70141e13 + 4.40824e13i −0.999325 + 0.937009i
\(191\) 5.40605e12 0.111347 0.0556737 0.998449i \(-0.482269\pi\)
0.0556737 + 0.998449i \(0.482269\pi\)
\(192\) 6.78557e12 + 6.78557e12i 0.135450 + 0.135450i
\(193\) −8.58662e11 + 8.58662e11i −0.0166142 + 0.0166142i −0.715365 0.698751i \(-0.753740\pi\)
0.698751 + 0.715365i \(0.253740\pi\)
\(194\) 2.98817e13i 0.560525i
\(195\) 1.79959e12 5.59184e13i 0.0327316 1.01706i
\(196\) 2.87562e12 0.0507219
\(197\) 1.89377e13 + 1.89377e13i 0.323988 + 0.323988i 0.850295 0.526307i \(-0.176424\pi\)
−0.526307 + 0.850295i \(0.676424\pi\)
\(198\) 1.29055e12 1.29055e12i 0.0214182 0.0214182i
\(199\) 1.86991e13i 0.301094i 0.988603 + 0.150547i \(0.0481034\pi\)
−0.988603 + 0.150547i \(0.951897\pi\)
\(200\) −3.09537e13 + 2.72063e13i −0.483651 + 0.425099i
\(201\) 1.81330e13 0.274975
\(202\) −9.54777e13 9.54777e13i −1.40538 1.40538i
\(203\) −7.03472e13 + 7.03472e13i −1.00524 + 1.00524i
\(204\) 4.98924e13i 0.692235i
\(205\) 2.92504e13 + 9.41350e11i 0.394102 + 0.0126832i
\(206\) 2.19655e13 0.287434
\(207\) −2.16156e12 2.16156e12i −0.0274754 0.0274754i
\(208\) −7.40798e13 + 7.40798e13i −0.914787 + 0.914787i
\(209\) 6.76422e13i 0.811596i
\(210\) 6.59575e13 + 7.03441e13i 0.769040 + 0.820185i
\(211\) 1.46180e14 1.65651 0.828255 0.560352i \(-0.189334\pi\)
0.828255 + 0.560352i \(0.189334\pi\)
\(212\) 3.86738e13 + 3.86738e13i 0.425992 + 0.425992i
\(213\) 4.98171e12 4.98171e12i 0.0533458 0.0533458i
\(214\) 1.39958e14i 1.45719i
\(215\) 6.84877e13 6.42169e13i 0.693397 0.650158i
\(216\) 6.64842e13 0.654630
\(217\) −1.33064e13 1.33064e13i −0.127439 0.127439i
\(218\) 9.00026e13 9.00026e13i 0.838525 0.838525i
\(219\) 1.13425e13i 0.102812i
\(220\) −1.22717e12 + 3.81317e13i −0.0108236 + 0.336318i
\(221\) −1.81428e14 −1.55722
\(222\) −3.58348e13 3.58348e13i −0.299355 0.299355i
\(223\) −3.47224e13 + 3.47224e13i −0.282345 + 0.282345i −0.834044 0.551699i \(-0.813980\pi\)
0.551699 + 0.834044i \(0.313980\pi\)
\(224\) 1.03755e14i 0.821339i
\(225\) −2.90415e11 + 4.50734e12i −0.00223833 + 0.0347396i
\(226\) −1.17130e14 −0.879057
\(227\) −6.69134e13 6.69134e13i −0.489055 0.489055i 0.418953 0.908008i \(-0.362397\pi\)
−0.908008 + 0.418953i \(0.862397\pi\)
\(228\) −5.17002e13 + 5.17002e13i −0.368030 + 0.368030i
\(229\) 9.54919e13i 0.662146i 0.943605 + 0.331073i \(0.107411\pi\)
−0.943605 + 0.331073i \(0.892589\pi\)
\(230\) 2.00142e14 + 6.44108e12i 1.35199 + 0.0435103i
\(231\) −1.01208e14 −0.666108
\(232\) −1.06881e14 1.06881e14i −0.685444 0.685444i
\(233\) −7.83472e13 + 7.83472e13i −0.489653 + 0.489653i −0.908197 0.418544i \(-0.862541\pi\)
0.418544 + 0.908197i \(0.362541\pi\)
\(234\) 7.17377e12i 0.0436971i
\(235\) −5.15396e13 5.49672e13i −0.306009 0.326360i
\(236\) −8.72290e13 −0.504881
\(237\) 1.00405e14 + 1.00405e14i 0.566588 + 0.566588i
\(238\) 2.21116e14 2.21116e14i 1.21663 1.21663i
\(239\) 8.41630e13i 0.451579i −0.974176 0.225790i \(-0.927504\pi\)
0.974176 0.225790i \(-0.0724962\pi\)
\(240\) −1.71064e14 + 1.60397e14i −0.895141 + 0.839322i
\(241\) 3.63503e14 1.85527 0.927633 0.373493i \(-0.121840\pi\)
0.927633 + 0.373493i \(0.121840\pi\)
\(242\) 8.33949e13 + 8.33949e13i 0.415190 + 0.415190i
\(243\) 1.01316e13 1.01316e13i 0.0492085 0.0492085i
\(244\) 6.22016e13i 0.294756i
\(245\) 7.52876e11 2.33940e13i 0.00348118 0.108170i
\(246\) 1.04043e14 0.469462
\(247\) 1.88002e14 + 1.88002e14i 0.827904 + 0.827904i
\(248\) 2.02169e13 2.02169e13i 0.0868968 0.0868968i
\(249\) 1.03359e14i 0.433664i
\(250\) −1.88078e14 2.28399e14i −0.770367 0.935522i
\(251\) −2.32641e14 −0.930345 −0.465172 0.885220i \(-0.654008\pi\)
−0.465172 + 0.885220i \(0.654008\pi\)
\(252\) −2.79000e12 2.79000e12i −0.0108943 0.0108943i
\(253\) −1.48612e14 + 1.48612e14i −0.566671 + 0.566671i
\(254\) 3.57406e14i 1.33094i
\(255\) −4.05888e14 1.30625e13i −1.47627 0.0475099i
\(256\) 3.22407e14 1.14542
\(257\) 2.47701e14 + 2.47701e14i 0.859663 + 0.859663i 0.991298 0.131635i \(-0.0420227\pi\)
−0.131635 + 0.991298i \(0.542023\pi\)
\(258\) 2.36013e14 2.36013e14i 0.800235 0.800235i
\(259\) 1.01359e14i 0.335785i
\(260\) −1.02571e14 1.09392e14i −0.332035 0.354117i
\(261\) −1.65663e13 −0.0524062
\(262\) −3.48715e14 3.48715e14i −1.07811 1.07811i
\(263\) −2.08239e13 + 2.08239e13i −0.0629257 + 0.0629257i −0.737869 0.674944i \(-0.764168\pi\)
0.674944 + 0.737869i \(0.264168\pi\)
\(264\) 1.53769e14i 0.454199i
\(265\) 3.24747e14 3.04496e14i 0.937712 0.879238i
\(266\) −4.58255e14 −1.29365
\(267\) −8.70947e13 8.70947e13i −0.240394 0.240394i
\(268\) 3.43673e13 3.43673e13i 0.0927548 0.0927548i
\(269\) 2.87569e14i 0.758976i −0.925197 0.379488i \(-0.876100\pi\)
0.925197 0.379488i \(-0.123900\pi\)
\(270\) −1.53535e13 + 4.77075e14i −0.0396300 + 1.23141i
\(271\) −3.79499e14 −0.958066 −0.479033 0.877797i \(-0.659013\pi\)
−0.479033 + 0.877797i \(0.659013\pi\)
\(272\) 5.37713e14 + 5.37713e14i 1.32781 + 1.32781i
\(273\) 2.81294e14 2.81294e14i 0.679492 0.679492i
\(274\) 4.29317e14i 1.01455i
\(275\) 3.09890e14 + 1.99668e13i 0.716492 + 0.0461648i
\(276\) 2.27174e14 0.513931
\(277\) −4.24359e14 4.24359e14i −0.939410 0.939410i 0.0588562 0.998266i \(-0.481255\pi\)
−0.998266 + 0.0588562i \(0.981255\pi\)
\(278\) −6.76683e14 + 6.76683e14i −1.46594 + 1.46594i
\(279\) 3.13357e12i 0.00664376i
\(280\) −2.92873e14 9.42539e12i −0.607759 0.0195592i
\(281\) −1.56177e14 −0.317234 −0.158617 0.987340i \(-0.550704\pi\)
−0.158617 + 0.987340i \(0.550704\pi\)
\(282\) −1.89421e14 1.89421e14i −0.376645 0.376645i
\(283\) 6.95840e14 6.95840e14i 1.35454 1.35454i 0.474026 0.880511i \(-0.342800\pi\)
0.880511 0.474026i \(-0.157200\pi\)
\(284\) 1.88835e13i 0.0359893i
\(285\) 4.07059e14 + 4.34131e14i 0.759606 + 0.810124i
\(286\) 4.93214e14 0.901237
\(287\) 1.47142e14 + 1.47142e14i 0.263297 + 0.263297i
\(288\) 1.22169e13 1.22169e13i 0.0214094 0.0214094i
\(289\) 7.34282e14i 1.26030i
\(290\) 7.91634e14 7.42269e14i 1.33087 1.24788i
\(291\) −2.75929e14 −0.454401
\(292\) −2.14974e13 2.14974e13i −0.0346807 0.0346807i
\(293\) 4.29488e13 4.29488e13i 0.0678806 0.0678806i −0.672351 0.740232i \(-0.734716\pi\)
0.740232 + 0.672351i \(0.234716\pi\)
\(294\) 8.32115e13i 0.128854i
\(295\) −2.28377e13 + 7.09631e14i −0.0346514 + 1.07671i
\(296\) 1.53997e14 0.228962
\(297\) −3.54244e14 3.54244e14i −0.516135 0.516135i
\(298\) −7.79207e14 + 7.79207e14i −1.11264 + 1.11264i
\(299\) 8.26092e14i 1.15612i
\(300\) −2.21594e14 2.52116e14i −0.303970 0.345838i
\(301\) 6.67562e14 0.897620
\(302\) −5.45506e14 5.45506e14i −0.719047 0.719047i
\(303\) −8.81646e14 + 8.81646e14i −1.13930 + 1.13930i
\(304\) 1.11439e15i 1.41188i
\(305\) −5.06026e14 1.62852e13i −0.628599 0.0202299i
\(306\) 5.20713e13 0.0634263
\(307\) −2.37125e14 2.37125e14i −0.283235 0.283235i 0.551163 0.834398i \(-0.314184\pi\)
−0.834398 + 0.551163i \(0.814184\pi\)
\(308\) −1.91819e14 + 1.91819e14i −0.224692 + 0.224692i
\(309\) 2.02831e14i 0.233015i
\(310\) 1.40403e14 + 1.49740e14i 0.158199 + 0.168721i
\(311\) −1.33386e14 −0.147418 −0.0737088 0.997280i \(-0.523484\pi\)
−0.0737088 + 0.997280i \(0.523484\pi\)
\(312\) 4.27379e14 + 4.27379e14i 0.463325 + 0.463325i
\(313\) −8.27117e14 + 8.27117e14i −0.879632 + 0.879632i −0.993496 0.113865i \(-0.963677\pi\)
0.113865 + 0.993496i \(0.463677\pi\)
\(314\) 8.82926e14i 0.921184i
\(315\) −2.34278e13 + 2.19669e13i −0.0239811 + 0.0224857i
\(316\) 3.80594e14 0.382243
\(317\) 9.41830e14 + 9.41830e14i 0.928147 + 0.928147i 0.997586 0.0694392i \(-0.0221210\pi\)
−0.0694392 + 0.997586i \(0.522121\pi\)
\(318\) 1.11910e15 1.11910e15i 1.08219 1.08219i
\(319\) 1.13897e15i 1.08086i
\(320\) 6.73415e12 2.09249e14i 0.00627166 0.194878i
\(321\) 1.29238e15 1.18130
\(322\) 1.00680e15 + 1.00680e15i 0.903252 + 0.903252i
\(323\) 1.36462e15 1.36462e15i 1.20170 1.20170i
\(324\) 5.22637e14i 0.451783i
\(325\) −9.16789e14 + 8.05800e14i −0.777982 + 0.683797i
\(326\) −1.24521e15 −1.03737
\(327\) −8.31088e14 8.31088e14i −0.679768 0.679768i
\(328\) −2.23558e14 + 2.23558e14i −0.179534 + 0.179534i
\(329\) 5.35775e14i 0.422481i
\(330\) 1.10341e15 + 3.55105e13i 0.854386 + 0.0274963i
\(331\) −5.67388e14 −0.431432 −0.215716 0.976456i \(-0.569208\pi\)
−0.215716 + 0.976456i \(0.569208\pi\)
\(332\) 1.95895e14 + 1.95895e14i 0.146284 + 0.146284i
\(333\) 1.19346e13 1.19346e13i 0.00875274 0.00875274i
\(334\) 4.63083e14i 0.333565i
\(335\) −2.70589e14 2.88585e14i −0.191444 0.204176i
\(336\) −1.66739e15 −1.15878
\(337\) −1.09538e15 1.09538e15i −0.747800 0.747800i 0.226265 0.974066i \(-0.427348\pi\)
−0.974066 + 0.226265i \(0.927348\pi\)
\(338\) −9.30628e13 + 9.30628e13i −0.0624131 + 0.0624131i
\(339\) 1.08158e15i 0.712626i
\(340\) −7.94031e14 + 7.44517e14i −0.514001 + 0.481949i
\(341\) −2.15440e14 −0.137025
\(342\) −5.39581e13 5.39581e13i −0.0337209 0.0337209i
\(343\) 1.20505e15 1.20505e15i 0.740015 0.740015i
\(344\) 1.01425e15i 0.612060i
\(345\) 5.94772e13 1.84812e15i 0.0352725 1.09601i
\(346\) −9.00141e14 −0.524631
\(347\) 1.29045e15 + 1.29045e15i 0.739203 + 0.739203i 0.972424 0.233221i \(-0.0749265\pi\)
−0.233221 + 0.972424i \(0.574927\pi\)
\(348\) 8.70539e14 8.70539e14i 0.490132 0.490132i
\(349\) 1.00281e15i 0.554965i −0.960731 0.277483i \(-0.910500\pi\)
0.960731 0.277483i \(-0.0895001\pi\)
\(350\) 1.35269e14 2.09941e15i 0.0735850 1.14206i
\(351\) 1.96914e15 1.05301
\(352\) −8.39938e14 8.39938e14i −0.441562 0.441562i
\(353\) −1.87450e15 + 1.87450e15i −0.968807 + 0.968807i −0.999528 0.0307212i \(-0.990220\pi\)
0.0307212 + 0.999528i \(0.490220\pi\)
\(354\) 2.52413e15i 1.28260i
\(355\) −1.53623e14 4.94396e12i −0.0767511 0.00247004i
\(356\) −3.30139e14 −0.162180
\(357\) −2.04179e15 2.04179e15i −0.986284 0.986284i
\(358\) 2.03350e15 2.03350e15i 0.965930 0.965930i
\(359\) 2.74993e15i 1.28456i 0.766470 + 0.642280i \(0.222011\pi\)
−0.766470 + 0.642280i \(0.777989\pi\)
\(360\) −3.33751e13 3.55947e13i −0.0153323 0.0163520i
\(361\) −6.14823e14 −0.277784
\(362\) 2.66667e15 + 2.66667e15i 1.18500 + 1.18500i
\(363\) 7.70072e14 7.70072e14i 0.336583 0.336583i
\(364\) 1.06627e15i 0.458413i
\(365\) −1.80515e14 + 1.69258e14i −0.0763407 + 0.0715803i
\(366\) −1.79992e15 −0.748801
\(367\) 2.65693e15 + 2.65693e15i 1.08738 + 1.08738i 0.995797 + 0.0915878i \(0.0291942\pi\)
0.0915878 + 0.995797i \(0.470806\pi\)
\(368\) −2.44836e15 + 2.44836e15i −0.985800 + 0.985800i
\(369\) 3.46510e13i 0.0137264i
\(370\) −3.55632e13 + 1.10505e15i −0.0138609 + 0.430696i
\(371\) 3.16536e15 1.21389
\(372\) 1.64665e14 + 1.64665e14i 0.0621362 + 0.0621362i
\(373\) 2.12011e15 2.12011e15i 0.787236 0.787236i −0.193805 0.981040i \(-0.562083\pi\)
0.981040 + 0.193805i \(0.0620828\pi\)
\(374\) 3.58002e15i 1.30815i
\(375\) −2.10905e15 + 1.73672e15i −0.758400 + 0.624514i
\(376\) 8.14021e14 0.288077
\(377\) −3.16561e15 3.16561e15i −1.10258 1.10258i
\(378\) −2.39989e15 + 2.39989e15i −0.822700 + 0.822700i
\(379\) 3.54241e15i 1.19526i −0.801771 0.597632i \(-0.796109\pi\)
0.801771 0.597632i \(-0.203891\pi\)
\(380\) 1.59430e15 + 5.13085e13i 0.529502 + 0.0170407i
\(381\) 3.30030e15 1.07896
\(382\) −2.96488e14 2.96488e14i −0.0954171 0.0954171i
\(383\) −1.02345e15 + 1.02345e15i −0.324246 + 0.324246i −0.850394 0.526147i \(-0.823636\pi\)
0.526147 + 0.850394i \(0.323636\pi\)
\(384\) 3.48390e15i 1.08662i
\(385\) 1.51028e15 + 1.61072e15i 0.463759 + 0.494601i
\(386\) 9.41843e13 0.0284744
\(387\) 7.86032e13 + 7.86032e13i 0.0233978 + 0.0233978i
\(388\) −5.22965e14 + 5.22965e14i −0.153279 + 0.153279i
\(389\) 6.69264e14i 0.193152i −0.995326 0.0965761i \(-0.969211\pi\)
0.995326 0.0965761i \(-0.0307891\pi\)
\(390\) −3.16547e15 + 2.96808e15i −0.899602 + 0.843505i
\(391\) −5.99624e15 −1.67810
\(392\) 1.78798e14 + 1.78798e14i 0.0492772 + 0.0492772i
\(393\) −3.22005e15 + 3.22005e15i −0.873991 + 0.873991i
\(394\) 2.07722e15i 0.555272i
\(395\) 9.96445e13 3.09623e15i 0.0262344 0.815176i
\(396\) −4.51721e13 −0.0117138
\(397\) −8.67794e14 8.67794e14i −0.221653 0.221653i 0.587541 0.809194i \(-0.300096\pi\)
−0.809194 + 0.587541i \(0.800096\pi\)
\(398\) 1.02553e15 1.02553e15i 0.258017 0.258017i
\(399\) 4.23155e15i 1.04873i
\(400\) 5.10539e15 + 3.28949e14i 1.24643 + 0.0803099i
\(401\) −2.66825e15 −0.641743 −0.320871 0.947123i \(-0.603976\pi\)
−0.320871 + 0.947123i \(0.603976\pi\)
\(402\) −9.94481e14 9.94481e14i −0.235635 0.235635i
\(403\) 5.98785e14 5.98785e14i 0.139779 0.139779i
\(404\) 3.34195e15i 0.768619i
\(405\) 4.25179e15 + 1.36833e14i 0.963478 + 0.0310071i
\(406\) 7.71619e15 1.72285
\(407\) −8.20535e14 8.20535e14i −0.180522 0.180522i
\(408\) 3.10216e15 3.10216e15i 0.672517 0.672517i
\(409\) 1.11713e14i 0.0238652i 0.999929 + 0.0119326i \(0.00379836\pi\)
−0.999929 + 0.0119326i \(0.996202\pi\)
\(410\) −1.55257e15 1.65582e15i −0.326850 0.348587i
\(411\) 3.96433e15 0.822468
\(412\) −3.84423e14 3.84423e14i −0.0786006 0.0786006i
\(413\) −3.56975e15 + 3.56975e15i −0.719346 + 0.719346i
\(414\) 2.37095e14i 0.0470892i
\(415\) 1.64495e15 1.54237e15i 0.322006 0.301926i
\(416\) 4.66897e15 0.900868
\(417\) 6.24852e15 + 6.24852e15i 1.18840 + 1.18840i
\(418\) −3.70974e15 + 3.70974e15i −0.695483 + 0.695483i
\(419\) 9.60350e14i 0.177478i 0.996055 + 0.0887392i \(0.0282838\pi\)
−0.996055 + 0.0887392i \(0.971716\pi\)
\(420\) 7.67694e13 2.38544e15i 0.0139860 0.434583i
\(421\) −9.04099e15 −1.62377 −0.811883 0.583820i \(-0.801557\pi\)
−0.811883 + 0.583820i \(0.801557\pi\)
\(422\) −8.01706e15 8.01706e15i −1.41952 1.41952i
\(423\) 6.30858e13 6.30858e13i 0.0110126 0.0110126i
\(424\) 4.80925e15i 0.827717i
\(425\) 5.84895e15 + 6.65457e15i 0.992532 + 1.12924i
\(426\) −5.46430e14 −0.0914276
\(427\) −2.54553e15 2.54553e15i −0.419963 0.419963i
\(428\) 2.44944e15 2.44944e15i 0.398477 0.398477i
\(429\) 4.55436e15i 0.730606i
\(430\) −7.27801e15 2.34224e14i −1.15134 0.0370528i
\(431\) −7.59243e15 −1.18445 −0.592225 0.805772i \(-0.701750\pi\)
−0.592225 + 0.805772i \(0.701750\pi\)
\(432\) −5.83611e15 5.83611e15i −0.897886 0.897886i
\(433\) 6.95237e15 6.95237e15i 1.05489 1.05489i 0.0564825 0.998404i \(-0.482011\pi\)
0.998404 0.0564825i \(-0.0179885\pi\)
\(434\) 1.45954e15i 0.218413i
\(435\) −6.85414e15 7.30998e15i −1.01162 1.07890i
\(436\) −3.15030e15 −0.458599
\(437\) 6.21352e15 + 6.21352e15i 0.892172 + 0.892172i
\(438\) −6.22067e14 + 6.22067e14i −0.0881033 + 0.0881033i
\(439\) 2.99766e15i 0.418788i 0.977831 + 0.209394i \(0.0671492\pi\)
−0.977831 + 0.209394i \(0.932851\pi\)
\(440\) −2.44722e15 + 2.29461e15i −0.337254 + 0.316223i
\(441\) 2.77133e13 0.00376753
\(442\) 9.95015e15 + 9.95015e15i 1.33443 + 1.33443i
\(443\) 7.67450e15 7.67450e15i 1.01538 1.01538i 0.0154987 0.999880i \(-0.495066\pi\)
0.999880 0.0154987i \(-0.00493357\pi\)
\(444\) 1.25430e15i 0.163721i
\(445\) −8.64347e13 + 2.68577e15i −0.0111308 + 0.345866i
\(446\) 3.80860e15 0.483901
\(447\) 7.19523e15 + 7.19523e15i 0.901986 + 0.901986i
\(448\) 1.05261e15 1.05261e15i 0.130197 0.130197i
\(449\) 1.03992e16i 1.26918i −0.772849 0.634589i \(-0.781169\pi\)
0.772849 0.634589i \(-0.218831\pi\)
\(450\) 2.63126e14 2.31271e14i 0.0316876 0.0278514i
\(451\) 2.38234e15 0.283103
\(452\) 2.04991e15 + 2.04991e15i 0.240383 + 0.240383i
\(453\) −5.03722e15 + 5.03722e15i −0.582911 + 0.582911i
\(454\) 7.33955e15i 0.838174i
\(455\) −8.67435e15 2.79162e14i −0.977617 0.0314622i
\(456\) −6.42914e15 −0.715095
\(457\) −4.53331e15 4.53331e15i −0.497643 0.497643i 0.413060 0.910704i \(-0.364460\pi\)
−0.910704 + 0.413060i \(0.864460\pi\)
\(458\) 5.23713e15 5.23713e15i 0.567414 0.567414i
\(459\) 1.42931e16i 1.52845i
\(460\) −3.39000e15 3.61545e15i −0.357810 0.381606i
\(461\) 1.21557e16 1.26641 0.633206 0.773983i \(-0.281739\pi\)
0.633206 + 0.773983i \(0.281739\pi\)
\(462\) 5.55064e15 + 5.55064e15i 0.570809 + 0.570809i
\(463\) −1.12434e16 + 1.12434e16i −1.14133 + 1.14133i −0.153127 + 0.988207i \(0.548934\pi\)
−0.988207 + 0.153127i \(0.951066\pi\)
\(464\) 1.87644e16i 1.88030i
\(465\) 1.38271e15 1.29648e15i 0.136777 0.128248i
\(466\) 8.59370e15 0.839199
\(467\) 1.79243e15 + 1.79243e15i 0.172799 + 0.172799i 0.788208 0.615409i \(-0.211009\pi\)
−0.615409 + 0.788208i \(0.711009\pi\)
\(468\) 1.25549e14 1.25549e14i 0.0119492 0.0119492i
\(469\) 2.81289e15i 0.264311i
\(470\) −1.87985e14 + 5.84122e15i −0.0174396 + 0.541897i
\(471\) −8.15298e15 −0.746777
\(472\) −5.42364e15 5.42364e15i −0.490500 0.490500i
\(473\) 5.40416e15 5.40416e15i 0.482571 0.482571i
\(474\) 1.10132e16i 0.971055i
\(475\) 8.34815e14 1.29566e16i 0.0726823 1.12805i
\(476\) −7.73956e15 −0.665388
\(477\) 3.72711e14 + 3.72711e14i 0.0316419 + 0.0316419i
\(478\) −4.61581e15 + 4.61581e15i −0.386973 + 0.386973i
\(479\) 1.64145e16i 1.35898i 0.733683 + 0.679492i \(0.237800\pi\)
−0.733683 + 0.679492i \(0.762200\pi\)
\(480\) 1.04454e16 + 3.36158e14i 0.854037 + 0.0274850i
\(481\) 4.56111e15 0.368299
\(482\) −1.99359e16 1.99359e16i −1.58984 1.58984i
\(483\) 9.29686e15 9.29686e15i 0.732240 0.732240i
\(484\) 2.91902e15i 0.227072i
\(485\) 4.11754e15 + 4.39138e15i 0.316364 + 0.337404i
\(486\) −1.11131e15 −0.0843366
\(487\) −2.19609e15 2.19609e15i −0.164618 0.164618i 0.619991 0.784609i \(-0.287136\pi\)
−0.784609 + 0.619991i \(0.787136\pi\)
\(488\) 3.86751e15 3.86751e15i 0.286360 0.286360i
\(489\) 1.14983e16i 0.840969i
\(490\) −1.32430e15 + 1.24172e15i −0.0956776 + 0.0897113i
\(491\) −7.85269e15 −0.560441 −0.280220 0.959936i \(-0.590408\pi\)
−0.280220 + 0.959936i \(0.590408\pi\)
\(492\) −1.82087e15 1.82087e15i −0.128377 0.128377i
\(493\) −2.29778e16 + 2.29778e16i −1.60039 + 1.60039i
\(494\) 2.06214e16i 1.41891i
\(495\) −1.18266e13 + 3.67487e14i −0.000803953 + 0.0249811i
\(496\) −3.54935e15 −0.238374
\(497\) −7.72788e14 7.72788e14i −0.0512769 0.0512769i
\(498\) 5.66860e15 5.66860e15i 0.371621 0.371621i
\(499\) 2.19424e16i 1.42129i 0.703553 + 0.710643i \(0.251596\pi\)
−0.703553 + 0.710643i \(0.748404\pi\)
\(500\) −7.05668e14 + 7.28883e15i −0.0451628 + 0.466485i
\(501\) 4.27613e15 0.270411
\(502\) 1.27589e16 + 1.27589e16i 0.797243 + 0.797243i
\(503\) −6.63707e14 + 6.63707e14i −0.0409797 + 0.0409797i −0.727300 0.686320i \(-0.759225\pi\)
0.686320 + 0.727300i \(0.259225\pi\)
\(504\) 3.46948e14i 0.0211680i
\(505\) 2.71876e16 + 8.74965e14i 1.63916 + 0.0527524i
\(506\) 1.63009e16 0.971198
\(507\) 8.59346e14 + 8.59346e14i 0.0505965 + 0.0505965i
\(508\) 6.25503e15 6.25503e15i 0.363954 0.363954i
\(509\) 3.01064e16i 1.73122i −0.500718 0.865610i \(-0.666931\pi\)
0.500718 0.865610i \(-0.333069\pi\)
\(510\) 2.15440e16 + 2.29768e16i 1.22435 + 1.30577i
\(511\) −1.75951e15 −0.0988250
\(512\) −3.59308e15 3.59308e15i −0.199456 0.199456i
\(513\) −1.48110e16 + 1.48110e16i −0.812608 + 0.812608i
\(514\) 2.71696e16i 1.47335i
\(515\) −3.22803e15 + 3.02673e15i −0.173019 + 0.162230i
\(516\) −8.26101e15 −0.437658
\(517\) −4.33730e15 4.33730e15i −0.227131 0.227131i
\(518\) −5.55888e15 + 5.55888e15i −0.287745 + 0.287745i
\(519\) 8.31195e15i 0.425303i
\(520\) 4.24141e14 1.31792e16i 0.0214531 0.666607i
\(521\) 3.81010e15 0.190507 0.0952534 0.995453i \(-0.469634\pi\)
0.0952534 + 0.995453i \(0.469634\pi\)
\(522\) 9.08557e14 + 9.08557e14i 0.0449085 + 0.0449085i
\(523\) 1.30804e16 1.30804e16i 0.639160 0.639160i −0.311188 0.950348i \(-0.600727\pi\)
0.950348 + 0.311188i \(0.100727\pi\)
\(524\) 1.22058e16i 0.589631i
\(525\) −1.93861e16 1.24908e15i −0.925835 0.0596532i
\(526\) 2.28412e15 0.107846
\(527\) −4.34632e15 4.34632e15i −0.202889 0.202889i
\(528\) −1.34982e16 + 1.34982e16i −0.622975 + 0.622975i
\(529\) 5.38800e15i 0.245863i
\(530\) −3.45100e16 1.11062e15i −1.55700 0.0501083i
\(531\) −8.40653e14 −0.0375016
\(532\) 8.02001e15 + 8.02001e15i 0.353757 + 0.353757i
\(533\) −6.62136e15 + 6.62136e15i −0.288791 + 0.288791i
\(534\) 9.55319e15i 0.412003i
\(535\) −1.92855e16 2.05681e16i −0.822448 0.877145i
\(536\) 4.27371e15 0.180226
\(537\) −1.87774e16 1.87774e16i −0.783051 0.783051i
\(538\) −1.57713e16 + 1.57713e16i −0.650391 + 0.650391i
\(539\) 1.90535e15i 0.0777039i
\(540\) 8.61808e15 8.08067e15i 0.347574 0.325900i
\(541\) 2.39081e16 0.953588 0.476794 0.879015i \(-0.341799\pi\)
0.476794 + 0.879015i \(0.341799\pi\)
\(542\) 2.08131e16 + 2.08131e16i 0.820998 + 0.820998i
\(543\) 2.46242e16 2.46242e16i 0.960644 0.960644i
\(544\) 3.38900e16i 1.30761i
\(545\) −8.24790e14 + 2.56285e16i −0.0314749 + 0.978013i
\(546\) −3.08544e16 −1.16456
\(547\) 1.06673e16 + 1.06673e16i 0.398229 + 0.398229i 0.877608 0.479379i \(-0.159138\pi\)
−0.479379 + 0.877608i \(0.659138\pi\)
\(548\) 7.51355e15 7.51355e15i 0.277435 0.277435i
\(549\) 5.99456e14i 0.0218939i
\(550\) −1.59005e16 1.80906e16i −0.574425 0.653546i
\(551\) 4.76207e16 1.70171
\(552\) 1.41250e16 + 1.41250e16i 0.499293 + 0.499293i
\(553\) 1.55754e16 1.55754e16i 0.544614 0.544614i
\(554\) 4.65469e16i 1.61002i
\(555\) 1.02041e16 + 3.28393e14i 0.349153 + 0.0112366i
\(556\) 2.36855e16 0.801740
\(557\) −1.90227e16 1.90227e16i −0.637001 0.637001i 0.312813 0.949815i \(-0.398729\pi\)
−0.949815 + 0.312813i \(0.898729\pi\)
\(558\) −1.71857e14 + 1.71857e14i −0.00569326 + 0.00569326i
\(559\) 3.00401e16i 0.984535i
\(560\) 2.48816e16 + 2.65363e16i 0.806770 + 0.860425i
\(561\) −3.30581e16 −1.06048
\(562\) 8.56533e15 + 8.56533e15i 0.271848 + 0.271848i
\(563\) 1.18877e16 1.18877e16i 0.373292 0.373292i −0.495383 0.868675i \(-0.664972\pi\)
0.868675 + 0.495383i \(0.164972\pi\)
\(564\) 6.63017e15i 0.205992i
\(565\) 1.72133e16 1.61399e16i 0.529142 0.496146i
\(566\) −7.63249e16 −2.32149
\(567\) 2.13883e16 + 2.13883e16i 0.643693 + 0.643693i
\(568\) 1.17412e15 1.17412e15i 0.0349642 0.0349642i
\(569\) 2.74494e16i 0.808834i 0.914575 + 0.404417i \(0.132526\pi\)
−0.914575 + 0.404417i \(0.867474\pi\)
\(570\) 1.48471e15 4.61339e16i 0.0432904 1.34515i
\(571\) −3.96327e16 −1.14350 −0.571750 0.820428i \(-0.693735\pi\)
−0.571750 + 0.820428i \(0.693735\pi\)
\(572\) −8.63182e15 8.63182e15i −0.246448 0.246448i
\(573\) −2.73778e15 + 2.73778e15i −0.0773519 + 0.0773519i
\(574\) 1.61396e16i 0.451255i
\(575\) −3.03002e16 + 2.66320e16i −0.838375 + 0.736879i
\(576\) 2.47883e14 0.00678754
\(577\) −2.68681e16 2.68681e16i −0.728084 0.728084i 0.242154 0.970238i \(-0.422146\pi\)
−0.970238 + 0.242154i \(0.922146\pi\)
\(578\) 4.02707e16 4.02707e16i 1.08000 1.08000i
\(579\) 8.69702e14i 0.0230834i
\(580\) −2.68451e16 8.63942e14i −0.705175 0.0226943i
\(581\) 1.60336e16 0.416845
\(582\) 1.51330e16 + 1.51330e16i 0.389391 + 0.389391i
\(583\) 2.56248e16 2.56248e16i 0.652603 0.652603i
\(584\) 2.67329e15i 0.0673858i
\(585\) −9.88506e14 1.05425e15i −0.0246629 0.0263031i
\(586\) −4.71094e15 −0.116338
\(587\) 6.86096e15 + 6.86096e15i 0.167709 + 0.167709i 0.785972 0.618263i \(-0.212163\pi\)
−0.618263 + 0.785972i \(0.712163\pi\)
\(588\) −1.45630e15 + 1.45630e15i −0.0352360 + 0.0352360i
\(589\) 9.00762e15i 0.215734i
\(590\) 4.01713e16 3.76663e16i 0.952365 0.892978i
\(591\) −1.91812e16 −0.450143
\(592\) −1.35182e16 1.35182e16i −0.314042 0.314042i
\(593\) −2.02985e16 + 2.02985e16i −0.466806 + 0.466806i −0.900878 0.434072i \(-0.857076\pi\)
0.434072 + 0.900878i \(0.357076\pi\)
\(594\) 3.88561e16i 0.884586i
\(595\) −2.02632e15 + 6.29634e16i −0.0456674 + 1.41901i
\(596\) 2.72741e16 0.608517
\(597\) −9.46976e15 9.46976e15i −0.209167 0.209167i
\(598\) −4.53059e16 + 4.53059e16i −0.990713 + 0.990713i
\(599\) 6.80430e16i 1.47307i −0.676401 0.736534i \(-0.736461\pi\)
0.676401 0.736534i \(-0.263539\pi\)
\(600\) 1.89777e15 2.94539e16i 0.0406757 0.631299i
\(601\) −4.04277e15 −0.0857892 −0.0428946 0.999080i \(-0.513658\pi\)
−0.0428946 + 0.999080i \(0.513658\pi\)
\(602\) −3.66115e16 3.66115e16i −0.769199 0.769199i
\(603\) 3.31208e14 3.31208e14i 0.00688965 0.00688965i
\(604\) 1.90940e16i 0.393255i
\(605\) −2.37470e16 7.64237e14i −0.484257 0.0155846i
\(606\) 9.67054e16 1.95261
\(607\) 5.23645e16 + 5.23645e16i 1.04690 + 1.04690i 0.998845 + 0.0480536i \(0.0153018\pi\)
0.0480536 + 0.998845i \(0.484698\pi\)
\(608\) −3.51180e16 + 3.51180e16i −0.695199 + 0.695199i
\(609\) 7.12517e16i 1.39666i
\(610\) 2.68592e16 + 2.86455e16i 0.521332 + 0.556003i
\(611\) 2.41098e16 0.463389
\(612\) −9.11308e14 9.11308e14i −0.0173443 0.0173443i
\(613\) −2.42437e15 + 2.42437e15i −0.0456916 + 0.0456916i −0.729583 0.683892i \(-0.760286\pi\)
0.683892 + 0.729583i \(0.260286\pi\)
\(614\) 2.60096e16i 0.485426i
\(615\) −1.52900e16 + 1.43365e16i −0.282589 + 0.264968i
\(616\) −2.38535e16 −0.436584
\(617\) −3.51410e16 3.51410e16i −0.636947 0.636947i 0.312854 0.949801i \(-0.398715\pi\)
−0.949801 + 0.312854i \(0.898715\pi\)
\(618\) −1.11240e16 + 1.11240e16i −0.199678 + 0.199678i
\(619\) 4.72208e16i 0.839440i 0.907654 + 0.419720i \(0.137872\pi\)
−0.907654 + 0.419720i \(0.862128\pi\)
\(620\) 1.63418e14 5.07784e15i 0.00287706 0.0893982i
\(621\) 6.50807e16 1.13476
\(622\) 7.31540e15 + 7.31540e15i 0.126327 + 0.126327i
\(623\) −1.35106e16 + 1.35106e16i −0.231071 + 0.231071i
\(624\) 7.50323e16i 1.27099i
\(625\) 5.91118e16 + 7.64910e15i 0.991731 + 0.128331i
\(626\) 9.07243e16 1.50757
\(627\) 3.42560e16 + 3.42560e16i 0.563807 + 0.563807i
\(628\) −1.54522e16 + 1.54522e16i −0.251903 + 0.251903i
\(629\) 3.31071e16i 0.534586i
\(630\) 2.48961e15 + 8.01220e13i 0.0398188 + 0.00128147i
\(631\) −7.96886e16 −1.26247 −0.631234 0.775593i \(-0.717451\pi\)
−0.631234 + 0.775593i \(0.717451\pi\)
\(632\) 2.36642e16 + 2.36642e16i 0.371356 + 0.371356i
\(633\) −7.40299e16 + 7.40299e16i −1.15076 + 1.15076i
\(634\) 1.03307e17i 1.59072i
\(635\) −4.92486e16 5.25239e16i −0.751193 0.801152i
\(636\) −3.91711e16 −0.591865
\(637\) 5.29565e15 + 5.29565e15i 0.0792653 + 0.0792653i
\(638\) 6.24654e16 6.24654e16i 0.926223 0.926223i
\(639\) 1.81987e14i 0.00267322i
\(640\) −5.54458e16 + 5.19883e16i −0.806843 + 0.756530i
\(641\) −5.08846e16 −0.733565 −0.366782 0.930307i \(-0.619541\pi\)
−0.366782 + 0.930307i \(0.619541\pi\)
\(642\) −7.08790e16 7.08790e16i −1.01230 1.01230i
\(643\) 5.83086e16 5.83086e16i 0.825024 0.825024i −0.161799 0.986824i \(-0.551730\pi\)
0.986824 + 0.161799i \(0.0517298\pi\)
\(644\) 3.52405e16i 0.493999i
\(645\) −2.16284e15 + 6.72055e16i −0.0300377 + 0.933354i
\(646\) −1.49682e17 −2.05956
\(647\) −5.50175e16 5.50175e16i −0.750025 0.750025i 0.224459 0.974484i \(-0.427939\pi\)
−0.974484 + 0.224459i \(0.927939\pi\)
\(648\) −3.24960e16 + 3.24960e16i −0.438915 + 0.438915i
\(649\) 5.77969e16i 0.773457i
\(650\) 9.44731e16 + 6.08707e15i 1.25265 + 0.0807101i
\(651\) 1.34775e16 0.177061
\(652\) 2.17926e16 + 2.17926e16i 0.283676 + 0.283676i
\(653\) −2.74560e16 + 2.74560e16i −0.354126 + 0.354126i −0.861642 0.507516i \(-0.830564\pi\)
0.507516 + 0.861642i \(0.330564\pi\)
\(654\) 9.11599e16i 1.16503i
\(655\) 9.92977e16 + 3.19565e15i 1.25745 + 0.0404679i
\(656\) 3.92486e16 0.492495
\(657\) −2.07177e14 2.07177e14i −0.00257602 0.00257602i
\(658\) −2.93839e16 + 2.93839e16i −0.362038 + 0.362038i
\(659\) 5.54245e16i 0.676690i 0.941022 + 0.338345i \(0.109867\pi\)
−0.941022 + 0.338345i \(0.890133\pi\)
\(660\) −1.86895e16 1.99325e16i −0.226118 0.241156i
\(661\) 1.40923e17 1.68956 0.844781 0.535113i \(-0.179731\pi\)
0.844781 + 0.535113i \(0.179731\pi\)
\(662\) 3.11176e16 + 3.11176e16i 0.369708 + 0.369708i
\(663\) 9.18802e16 9.18802e16i 1.08178 1.08178i
\(664\) 2.43604e16i 0.284234i
\(665\) 6.73446e16 6.31451e16i 0.778705 0.730146i
\(666\) −1.30908e15 −0.0150010
\(667\) −1.04624e17 1.04624e17i −1.18817 1.18817i
\(668\) 8.10450e15 8.10450e15i 0.0912153 0.0912153i
\(669\) 3.51688e16i 0.392284i
\(670\) −9.86945e14 + 3.06671e16i −0.0109105 + 0.339019i
\(671\) −4.12140e16 −0.451554
\(672\) 5.25447e16 + 5.25447e16i 0.570576 + 0.570576i
\(673\) 4.92874e16 4.92874e16i 0.530451 0.530451i −0.390255 0.920707i \(-0.627613\pi\)
0.920707 + 0.390255i \(0.127613\pi\)
\(674\) 1.20149e17i 1.28163i
\(675\) −6.34820e16 7.22259e16i −0.671163 0.763608i
\(676\) 3.25742e15 0.0341345
\(677\) 1.12156e17 + 1.12156e17i 1.16491 + 1.16491i 0.983387 + 0.181521i \(0.0581020\pi\)
0.181521 + 0.983387i \(0.441898\pi\)
\(678\) 5.93180e16 5.93180e16i 0.610672 0.610672i
\(679\) 4.28035e16i 0.436778i
\(680\) −9.56624e16 3.07865e15i −0.967582 0.0311392i
\(681\) 6.77738e16 0.679483
\(682\) 1.18155e16 + 1.18155e16i 0.117421 + 0.117421i
\(683\) −9.50390e16 + 9.50390e16i −0.936219 + 0.936219i −0.998084 0.0618654i \(-0.980295\pi\)
0.0618654 + 0.998084i \(0.480295\pi\)
\(684\) 1.88866e15i 0.0184424i
\(685\) −5.91575e16 6.30918e16i −0.572620 0.610702i
\(686\) −1.32179e17 −1.26829
\(687\) −4.83599e16 4.83599e16i −0.459986 0.459986i
\(688\) 8.90327e16 8.90327e16i 0.839496 0.839496i
\(689\) 1.42441e17i 1.33143i
\(690\) −1.04620e17 + 9.80959e16i −0.969437 + 0.908984i
\(691\) −1.49400e17 −1.37240 −0.686201 0.727412i \(-0.740723\pi\)
−0.686201 + 0.727412i \(0.740723\pi\)
\(692\) 1.57535e16 + 1.57535e16i 0.143463 + 0.143463i
\(693\) −1.84862e15 + 1.84862e15i −0.0166897 + 0.0166897i
\(694\) 1.41546e17i 1.26689i
\(695\) 6.20117e15 1.92688e17i 0.0550256 1.70980i
\(696\) 1.08255e17 0.952342
\(697\) 4.80616e16 + 4.80616e16i 0.419181 + 0.419181i
\(698\) −5.49978e16 + 5.49978e16i −0.475568 + 0.475568i
\(699\) 7.93546e16i 0.680314i
\(700\) −3.91095e16 + 3.43748e16i −0.332426 + 0.292181i
\(701\) −9.64381e16 −0.812719 −0.406360 0.913713i \(-0.633202\pi\)
−0.406360 + 0.913713i \(0.633202\pi\)
\(702\) −1.07995e17 1.07995e17i −0.902360 0.902360i
\(703\) −3.43068e16 + 3.43068e16i −0.284216 + 0.284216i
\(704\) 1.70426e16i 0.139991i
\(705\) 5.39381e16 + 1.73586e15i 0.439300 + 0.0141378i
\(706\) 2.05609e17 1.66040
\(707\) 1.36765e17 + 1.36765e17i 1.09511 + 1.09511i
\(708\) 4.41753e16 4.41753e16i 0.350736 0.350736i
\(709\) 1.96501e17i 1.54699i −0.633801 0.773496i \(-0.718506\pi\)
0.633801 0.773496i \(-0.281494\pi\)
\(710\) 8.15408e15 + 8.69637e15i 0.0636539 + 0.0678872i
\(711\) 3.66791e15 0.0283923
\(712\) −2.05271e16 2.05271e16i −0.157560 0.157560i
\(713\) 1.97901e16 1.97901e16i 0.150629 0.150629i
\(714\) 2.23959e17i 1.69036i
\(715\) −7.24820e16 + 6.79622e16i −0.542493 + 0.508664i
\(716\) −7.11772e16 −0.528278
\(717\) 4.26226e16 + 4.26226e16i 0.313708 + 0.313708i
\(718\) 1.50816e17 1.50816e17i 1.10078 1.10078i
\(719\) 1.00539e17i 0.727714i −0.931455 0.363857i \(-0.881460\pi\)
0.931455 0.363857i \(-0.118540\pi\)
\(720\) −1.94842e14 + 6.05429e15i −0.00139858 + 0.0434579i
\(721\) −3.14642e16 −0.223978
\(722\) 3.37191e16 + 3.37191e16i 0.238042 + 0.238042i
\(723\) −1.84089e17 + 1.84089e17i −1.28883 + 1.28883i
\(724\) 9.33397e16i 0.648090i
\(725\) −1.40568e16 + 2.18166e17i −0.0967961 + 1.50231i
\(726\) −8.44672e16 −0.576857
\(727\) 5.83551e16 + 5.83551e16i 0.395251 + 0.395251i 0.876554 0.481303i \(-0.159836\pi\)
−0.481303 + 0.876554i \(0.659836\pi\)
\(728\) 6.62973e16 6.62973e16i 0.445356 0.445356i
\(729\) 1.54950e17i 1.03235i
\(730\) 1.91829e16 + 6.17353e14i 0.126758 + 0.00407940i
\(731\) 2.18048e17 1.42905
\(732\) 3.15007e16 + 3.15007e16i 0.204764 + 0.204764i
\(733\) −5.61155e16 + 5.61155e16i −0.361792 + 0.361792i −0.864472 0.502680i \(-0.832347\pi\)
0.502680 + 0.864472i \(0.332347\pi\)
\(734\) 2.91431e17i 1.86363i
\(735\) 1.14661e16 + 1.22287e16i 0.0727263 + 0.0775630i
\(736\) 1.54311e17 0.970801
\(737\) −2.27713e16 2.27713e16i −0.142097 0.142097i
\(738\) 1.90039e15 1.90039e15i 0.0117626 0.0117626i
\(739\) 2.64833e17i 1.62594i 0.582304 + 0.812971i \(0.302151\pi\)
−0.582304 + 0.812971i \(0.697849\pi\)
\(740\) 1.99621e16 1.87173e16i 0.121567 0.113986i
\(741\) −1.90419e17 −1.15027
\(742\) −1.73600e17 1.73600e17i −1.04022 1.04022i
\(743\) 3.73128e16 3.73128e16i 0.221781 0.221781i −0.587467 0.809248i \(-0.699875\pi\)
0.809248 + 0.587467i \(0.199875\pi\)
\(744\) 2.04768e16i 0.120733i
\(745\) 7.14071e15 2.21882e17i 0.0417642 1.29773i
\(746\) −2.32549e17 −1.34922
\(747\) 1.88790e15 + 1.88790e15i 0.0108657 + 0.0108657i
\(748\) −6.26546e16 + 6.26546e16i −0.357720 + 0.357720i
\(749\) 2.00481e17i 1.13549i
\(750\) 2.10916e17 + 2.04198e16i 1.18506 + 0.114732i
\(751\) 2.04607e17 1.14046 0.570230 0.821485i \(-0.306854\pi\)
0.570230 + 0.821485i \(0.306854\pi\)
\(752\) −7.14563e16 7.14563e16i −0.395124 0.395124i
\(753\) 1.17816e17 1.17816e17i 0.646301 0.646301i
\(754\) 3.47227e17i 1.88967i
\(755\) 1.55334e17 + 4.99905e15i 0.838661 + 0.0269902i
\(756\) 8.40019e16 0.449944
\(757\) −8.24902e16 8.24902e16i −0.438356 0.438356i 0.453102 0.891458i \(-0.350317\pi\)
−0.891458 + 0.453102i \(0.850317\pi\)
\(758\) −1.94279e17 + 1.94279e17i −1.02426 + 1.02426i
\(759\) 1.50523e17i 0.787322i
\(760\) 9.59385e16 + 1.02319e17i 0.497865 + 0.530975i
\(761\) −3.10515e16 −0.159873 −0.0799364 0.996800i \(-0.525472\pi\)
−0.0799364 + 0.996800i \(0.525472\pi\)
\(762\) −1.81001e17 1.81001e17i −0.924593 0.924593i
\(763\) −1.28923e17 + 1.28923e17i −0.653404 + 0.653404i
\(764\) 1.03778e16i 0.0521847i
\(765\) −7.65232e15 + 7.17514e15i −0.0381790 + 0.0357982i
\(766\) 1.12260e17 0.555715
\(767\) −1.60638e17 1.60638e17i −0.788999 0.788999i
\(768\) −1.63276e17 + 1.63276e17i −0.795711 + 0.795711i
\(769\) 2.27421e16i 0.109970i −0.998487 0.0549849i \(-0.982489\pi\)
0.998487 0.0549849i \(-0.0175111\pi\)
\(770\) 5.50858e15 1.71167e17i 0.0264299 0.821250i
\(771\) −2.50886e17 −1.19440
\(772\) −1.64834e15 1.64834e15i −0.00778650 0.00778650i
\(773\) −5.77419e16 + 5.77419e16i −0.270654 + 0.270654i −0.829363 0.558710i \(-0.811297\pi\)
0.558710 + 0.829363i \(0.311297\pi\)
\(774\) 8.62178e15i 0.0401006i
\(775\) −4.12668e16 2.65889e15i −0.190454 0.0122713i
\(776\) −6.50328e16 −0.297826
\(777\) 5.13309e16 + 5.13309e16i 0.233267 + 0.233267i
\(778\) −3.67049e16 + 3.67049e16i −0.165518 + 0.165518i
\(779\) 9.96062e16i 0.445719i
\(780\) 1.07344e17 + 3.45461e15i 0.476663 + 0.0153402i
\(781\) −1.25120e16 −0.0551341
\(782\) 3.28856e17 + 3.28856e17i 1.43802 + 1.43802i
\(783\) 2.49391e17 2.49391e17i 1.08221 1.08221i
\(784\) 3.13904e16i 0.135176i
\(785\) 1.21662e17 + 1.29754e17i 0.519923 + 0.554500i
\(786\) 3.53199e17 1.49790
\(787\) −6.51691e16 6.51691e16i −0.274279 0.274279i 0.556541 0.830820i \(-0.312128\pi\)
−0.830820 + 0.556541i \(0.812128\pi\)
\(788\) −3.63539e16 + 3.63539e16i −0.151842 + 0.151842i
\(789\) 2.10917e16i 0.0874277i
\(790\) −1.75274e17 + 1.64344e17i −0.721032 + 0.676069i
\(791\) 1.67781e17 0.684988
\(792\) −2.80867e15 2.80867e15i −0.0113802 0.0113802i
\(793\) 1.14548e17 1.14548e17i 0.460627 0.460627i
\(794\) 9.51861e16i 0.379883i
\(795\) −1.02555e16 + 3.18667e17i −0.0406213 + 1.26222i
\(796\) −3.58958e16 −0.141113
\(797\) 1.98343e17 + 1.98343e17i 0.773870 + 0.773870i 0.978781 0.204911i \(-0.0656905\pi\)
−0.204911 + 0.978781i \(0.565690\pi\)
\(798\) 2.32074e17 2.32074e17i 0.898687 0.898687i
\(799\) 1.75002e17i 0.672610i
\(800\) −1.50521e17 1.71253e17i −0.574191 0.653279i
\(801\) −3.18165e15 −0.0120464
\(802\) 1.46337e17 + 1.46337e17i 0.549930 + 0.549930i
\(803\) −1.42439e16 + 1.42439e16i −0.0531295 + 0.0531295i
\(804\) 3.48092e16i 0.128872i
\(805\) −2.86690e17 9.22641e15i −1.05351 0.0339045i
\(806\) −6.56792e16 −0.239562
\(807\) 1.45633e17 + 1.45633e17i 0.527253 + 0.527253i
\(808\) −2.07792e17 + 2.07792e17i −0.746726 + 0.746726i
\(809\) 1.40004e17i 0.499400i −0.968323 0.249700i \(-0.919668\pi\)
0.968323 0.249700i \(-0.0803320\pi\)
\(810\) −2.25679e17 2.40688e17i −0.799064 0.852206i
\(811\) −2.46705e16 −0.0867067 −0.0433533 0.999060i \(-0.513804\pi\)
−0.0433533 + 0.999060i \(0.513804\pi\)
\(812\) −1.35042e17 1.35042e17i −0.471123 0.471123i
\(813\) 1.92189e17 1.92189e17i 0.665559 0.665559i
\(814\) 9.00023e16i 0.309391i
\(815\) 1.82994e17 1.71583e17i 0.624440 0.585501i
\(816\) −5.44627e17 −1.84484
\(817\) −2.25949e17 2.25949e17i −0.759764 0.759764i
\(818\) 6.12677e15 6.12677e15i 0.0204509 0.0204509i
\(819\) 1.02759e16i 0.0340501i
\(820\) −1.80707e15 + 5.61507e16i −0.00594418 + 0.184702i
\(821\) −3.46019e17 −1.12990 −0.564951 0.825124i \(-0.691105\pi\)
−0.564951 + 0.825124i \(0.691105\pi\)
\(822\) −2.17418e17 2.17418e17i −0.704799 0.704799i
\(823\) −1.95945e17 + 1.95945e17i −0.630572 + 0.630572i −0.948212 0.317639i \(-0.897110\pi\)
0.317639 + 0.948212i \(0.397110\pi\)
\(824\) 4.78046e16i 0.152724i
\(825\) −1.67049e17 + 1.46826e17i −0.529810 + 0.465670i
\(826\) 3.91557e17 1.23286
\(827\) 2.49398e17 + 2.49398e17i 0.779578 + 0.779578i 0.979759 0.200181i \(-0.0641531\pi\)
−0.200181 + 0.979759i \(0.564153\pi\)
\(828\) 4.14945e15 4.14945e15i 0.0128768 0.0128768i
\(829\) 3.97547e17i 1.22479i 0.790553 + 0.612394i \(0.209793\pi\)
−0.790553 + 0.612394i \(0.790207\pi\)
\(830\) −1.74804e17 5.62564e15i −0.534668 0.0172069i
\(831\) 4.29816e17 1.30520
\(832\) 4.73673e16 + 4.73673e16i 0.142804 + 0.142804i
\(833\) 3.84388e16 3.84388e16i 0.115054 0.115054i
\(834\) 6.85384e17i 2.03675i
\(835\) −6.38104e16 6.80541e16i −0.188266 0.200787i
\(836\) 1.29850e17 0.380368
\(837\) 4.71731e16 + 4.71731e16i 0.137196 + 0.137196i
\(838\) 5.26691e16 5.26691e16i 0.152087 0.152087i
\(839\) 1.84102e17i 0.527820i 0.964547 + 0.263910i \(0.0850123\pi\)
−0.964547 + 0.263910i \(0.914988\pi\)
\(840\) 1.53093e17 1.43546e17i 0.435792 0.408617i
\(841\) −4.48033e17 −1.26629
\(842\) 4.95841e17 + 4.95841e17i 1.39146 + 1.39146i
\(843\) 7.90927e16 7.90927e16i 0.220379 0.220379i
\(844\) 2.80616e17i 0.776350i
\(845\) 8.52834e14 2.64999e16i 0.00234274 0.0727955i
\(846\) −6.91971e15 −0.0188741
\(847\) −1.19458e17 1.19458e17i −0.323529 0.323529i
\(848\) 4.22165e17 4.22165e17i 1.13529 1.13529i
\(849\) 7.04787e17i 1.88197i
\(850\) 4.41834e16 6.85739e17i 0.117151 1.81822i
\(851\) 1.50746e17 0.396889
\(852\) 9.56317e15 + 9.56317e15i 0.0250014 + 0.0250014i
\(853\) 2.86257e17 2.86257e17i 0.743125 0.743125i −0.230053 0.973178i \(-0.573890\pi\)
0.973178 + 0.230053i \(0.0738901\pi\)
\(854\) 2.79213e17i 0.719760i
\(855\) 1.53647e16 + 4.94475e14i 0.0393304 + 0.00126575i
\(856\) 3.04597e17 0.774254
\(857\) −5.33346e17 5.33346e17i −1.34624 1.34624i −0.889701 0.456543i \(-0.849087\pi\)
−0.456543 0.889701i \(-0.650913\pi\)
\(858\) −2.49778e17 + 2.49778e17i −0.626080 + 0.626080i
\(859\) 3.79011e17i 0.943395i 0.881761 + 0.471697i \(0.156358\pi\)
−0.881761 + 0.471697i \(0.843642\pi\)
\(860\) 1.23274e17 + 1.31473e17i 0.304707 + 0.324972i
\(861\) −1.49034e17 −0.365819
\(862\) 4.16396e17 + 4.16396e17i 1.01499 + 1.01499i
\(863\) −2.54509e17 + 2.54509e17i −0.616082 + 0.616082i −0.944524 0.328442i \(-0.893476\pi\)
0.328442 + 0.944524i \(0.393476\pi\)
\(864\) 3.67828e17i 0.884225i
\(865\) 1.32284e17 1.24035e17i 0.315798 0.296105i
\(866\) −7.62587e17 −1.80793
\(867\) −3.71862e17 3.71862e17i −0.875521 0.875521i
\(868\) 2.55437e16 2.55437e16i 0.0597263 0.0597263i
\(869\) 2.52177e17i 0.585581i
\(870\) −2.49998e16 + 7.76813e17i −0.0576528 + 1.79143i
\(871\) 1.26579e17 0.289904
\(872\) −1.95877e17 1.95877e17i −0.445537 0.445537i
\(873\) −5.03998e15 + 5.03998e15i −0.0113853 + 0.0113853i
\(874\) 6.81544e17i 1.52906i
\(875\) 2.69409e17 + 3.27166e17i 0.600293 + 0.728987i
\(876\) 2.17738e16 0.0481847
\(877\) 3.87525e16 + 3.87525e16i 0.0851731 + 0.0851731i 0.748410 0.663237i \(-0.230818\pi\)
−0.663237 + 0.748410i \(0.730818\pi\)
\(878\) 1.64402e17 1.64402e17i 0.358873 0.358873i
\(879\) 4.35011e16i 0.0943119i
\(880\) 4.16247e17 + 1.33959e16i 0.896303 + 0.0288453i
\(881\) 4.97245e17 1.06345 0.531723 0.846918i \(-0.321545\pi\)
0.531723 + 0.846918i \(0.321545\pi\)
\(882\) −1.51990e15 1.51990e15i −0.00322852 0.00322852i
\(883\) 7.18425e16 7.18425e16i 0.151571 0.151571i −0.627248 0.778820i \(-0.715819\pi\)
0.778820 + 0.627248i \(0.215819\pi\)
\(884\) 3.48279e17i 0.729816i
\(885\) −3.47812e17 3.70943e17i −0.723911 0.772055i
\(886\) −8.41796e17 −1.74022
\(887\) −2.66493e17 2.66493e17i −0.547198 0.547198i 0.378431 0.925629i \(-0.376464\pi\)
−0.925629 + 0.378431i \(0.876464\pi\)
\(888\) −7.79888e16 + 7.79888e16i −0.159058 + 0.159058i
\(889\) 5.11960e17i 1.03711i
\(890\) 1.52038e17 1.42557e17i 0.305923 0.286846i
\(891\) 3.46293e17 0.692114
\(892\) −6.66550e16 6.66550e16i −0.132326 0.132326i
\(893\) −1.81344e17 + 1.81344e17i −0.357597 + 0.357597i
\(894\) 7.89226e17i 1.54588i
\(895\) −1.86351e16 + 5.79045e17i −0.0362572 + 1.12661i
\(896\) −5.40440e17 −1.04448
\(897\) 4.18357e17 + 4.18357e17i 0.803142 + 0.803142i
\(898\) −5.70332e17 + 5.70332e17i −1.08760 + 1.08760i
\(899\) 1.51672e17i 0.287308i
\(900\) −8.65254e15 5.57498e14i −0.0162813 0.00104903i
\(901\) 1.03392e18 1.93258
\(902\) −1.30656e17 1.30656e17i −0.242600 0.242600i
\(903\) −3.38073e17 + 3.38073e17i −0.623567 + 0.623567i
\(904\) 2.54915e17i 0.467073i
\(905\) −7.59343e17 2.44375e16i −1.38212 0.0444801i
\(906\) 5.52520e17 0.999030
\(907\) −2.37100e17 2.37100e17i −0.425880 0.425880i 0.461342 0.887222i \(-0.347368\pi\)
−0.887222 + 0.461342i \(0.847368\pi\)
\(908\) 1.28451e17 1.28451e17i 0.229204 0.229204i
\(909\) 3.22074e16i 0.0570915i
\(910\) 4.60423e17 + 4.91044e17i 0.810791 + 0.864713i
\(911\) −3.66360e17 −0.640911 −0.320455 0.947264i \(-0.603836\pi\)
−0.320455 + 0.947264i \(0.603836\pi\)
\(912\) 5.64362e17 + 5.64362e17i 0.980818 + 0.980818i
\(913\) 1.29798e17 1.29798e17i 0.224101 0.224101i
\(914\) 4.97247e17i 0.852893i
\(915\) 2.64514e17 2.48019e17i 0.450735 0.422628i
\(916\) −1.83312e17 −0.310325
\(917\) 4.99510e17 + 4.99510e17i 0.840095 + 0.840095i
\(918\) −7.83887e17 + 7.83887e17i −1.30978 + 1.30978i
\(919\) 8.08608e17i 1.34229i −0.741328 0.671143i \(-0.765804\pi\)
0.741328 0.671143i \(-0.234196\pi\)
\(920\) 1.40180e16 4.35578e17i 0.0231185 0.718355i
\(921\) 2.40174e17 0.393521
\(922\) −6.66664e17 6.66664e17i −1.08523 1.08523i
\(923\) 3.47753e16 3.47753e16i 0.0562420 0.0562420i
\(924\) 1.94285e17i 0.312182i
\(925\) −1.47043e17 1.67297e17i −0.234744 0.267078i
\(926\) 1.23326e18 1.95609
\(927\) −3.70480e15 3.70480e15i −0.00583830 0.00583830i
\(928\) 5.91325e17 5.91325e17i 0.925845 0.925845i
\(929\) 8.97555e17i 1.39626i 0.715971 + 0.698130i \(0.245984\pi\)
−0.715971 + 0.698130i \(0.754016\pi\)
\(930\) −1.46937e17 4.72879e15i −0.227108 0.00730890i
\(931\) −7.96634e16 −0.122338
\(932\) −1.50400e17 1.50400e17i −0.229484 0.229484i
\(933\) 6.75507e16 6.75507e16i 0.102410 0.102410i
\(934\) 1.96607e17i 0.296154i
\(935\) 4.93308e17 + 5.26115e17i 0.738326 + 0.787429i
\(936\) 1.56126e16 0.0232177
\(937\) 4.23872e17 + 4.23872e17i 0.626321 + 0.626321i 0.947140 0.320819i \(-0.103958\pi\)
−0.320819 + 0.947140i \(0.603958\pi\)
\(938\) −1.54269e17 + 1.54269e17i −0.226497 + 0.226497i
\(939\) 8.37752e17i 1.22214i
\(940\) 1.05518e17 9.89383e16i 0.152954 0.143416i
\(941\) 5.70273e17 0.821382 0.410691 0.911775i \(-0.365288\pi\)
0.410691 + 0.911775i \(0.365288\pi\)
\(942\) 4.47139e17 + 4.47139e17i 0.639938 + 0.639938i
\(943\) −2.18838e17 + 2.18838e17i −0.311210 + 0.311210i
\(944\) 9.52195e17i 1.34553i
\(945\) 2.19928e16 6.83378e17i 0.0308809 0.959555i
\(946\) −5.92768e17 −0.827061
\(947\) −9.45403e17 9.45403e17i −1.31074 1.31074i −0.920869 0.389872i \(-0.872519\pi\)
−0.389872 0.920869i \(-0.627481\pi\)
\(948\) −1.92744e17 + 1.92744e17i −0.265541 + 0.265541i
\(949\) 7.91777e16i 0.108394i
\(950\) −7.56371e17 + 6.64803e17i −1.02895 + 0.904380i
\(951\) −9.53940e17 −1.28955
\(952\) −4.81223e17 4.81223e17i −0.646435 0.646435i
\(953\) −3.20563e17 + 3.20563e17i −0.427913 + 0.427913i −0.887917 0.460004i \(-0.847848\pi\)
0.460004 + 0.887917i \(0.347848\pi\)
\(954\) 4.08817e16i 0.0542299i
\(955\) 8.44258e16 + 2.71703e15i 0.111290 + 0.00358158i
\(956\) 1.61564e17 0.211640
\(957\) −5.76809e17 5.76809e17i −0.750862 0.750862i
\(958\) 9.00230e17 9.00230e17i 1.16456 1.16456i
\(959\) 6.14967e17i 0.790570i
\(960\) 1.02559e17 + 1.09380e17i 0.131023 + 0.139737i
\(961\) −7.58973e17 −0.963577
\(962\) −2.50148e17 2.50148e17i −0.315607 0.315607i
\(963\) 2.36060e16 2.36060e16i 0.0295981 0.0295981i
\(964\) 6.97802e17i 0.869501i
\(965\) −1.38412e16 + 1.29781e16i −0.0171400 + 0.0160711i
\(966\) −1.01975e18 −1.25496
\(967\) 1.12164e18 + 1.12164e18i 1.37182 + 1.37182i 0.857750 + 0.514067i \(0.171862\pi\)
0.514067 + 0.857750i \(0.328138\pi\)
\(968\) 1.81496e17 1.81496e17i 0.220605 0.220605i
\(969\) 1.38217e18i 1.66962i
\(970\) 1.50183e16 4.66660e17i 0.0180298 0.560235i
\(971\) −3.15230e17 −0.376107 −0.188054 0.982159i \(-0.560218\pi\)
−0.188054 + 0.982159i \(0.560218\pi\)
\(972\) 1.94492e16 + 1.94492e16i 0.0230623 + 0.0230623i
\(973\) 9.69303e17 9.69303e17i 1.14231 1.14231i
\(974\) 2.40883e17i 0.282132i
\(975\) 5.62082e16 8.72369e17i 0.0654293 1.01548i
\(976\) −6.78995e17 −0.785539
\(977\) 3.08755e17 + 3.08755e17i 0.355015 + 0.355015i 0.861971 0.506957i \(-0.169230\pi\)
−0.506957 + 0.861971i \(0.669230\pi\)
\(978\) 6.30608e17 6.30608e17i 0.720653 0.720653i
\(979\) 2.18746e17i 0.248453i
\(980\) 4.49084e16 + 1.44526e15i 0.0506957 + 0.00163151i
\(981\) −3.03604e16 −0.0340639
\(982\) 4.30671e17 + 4.30671e17i 0.480260 + 0.480260i
\(983\) 3.09500e17 3.09500e17i 0.343036 0.343036i −0.514472 0.857507i \(-0.672012\pi\)
0.857507 + 0.514472i \(0.172012\pi\)
\(984\) 2.26432e17i 0.249441i
\(985\) 2.86230e17 + 3.05266e17i 0.313399 + 0.334242i
\(986\) 2.52037e18 2.74286
\(987\) 2.71332e17 + 2.71332e17i 0.293493 + 0.293493i
\(988\) −3.60899e17 + 3.60899e17i −0.388011 + 0.388011i
\(989\) 9.92837e17i 1.06096i
\(990\) 2.08030e16 1.95057e16i 0.0220960 0.0207181i
\(991\) −1.26513e18 −1.33565 −0.667826 0.744318i \(-0.732775\pi\)
−0.667826 + 0.744318i \(0.732775\pi\)
\(992\) 1.11851e17 + 1.11851e17i 0.117373 + 0.117373i
\(993\) 2.87342e17 2.87342e17i 0.299711 0.299711i
\(994\) 8.47651e16i 0.0878817i
\(995\) −9.39799e15 + 2.92022e17i −0.00968493 + 0.300938i
\(996\) −1.98414e17 −0.203244
\(997\) 1.13579e18 + 1.13579e18i 1.15645 + 1.15645i 0.985233 + 0.171220i \(0.0547710\pi\)
0.171220 + 0.985233i \(0.445229\pi\)
\(998\) 1.20340e18 1.20340e18i 1.21795 1.21795i
\(999\) 3.59331e17i 0.361495i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 5.13.c.a.2.2 10
3.2 odd 2 45.13.g.a.37.4 10
4.3 odd 2 80.13.p.c.17.5 10
5.2 odd 4 25.13.c.b.18.4 10
5.3 odd 4 inner 5.13.c.a.3.2 yes 10
5.4 even 2 25.13.c.b.7.4 10
15.8 even 4 45.13.g.a.28.4 10
20.3 even 4 80.13.p.c.33.5 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5.13.c.a.2.2 10 1.1 even 1 trivial
5.13.c.a.3.2 yes 10 5.3 odd 4 inner
25.13.c.b.7.4 10 5.4 even 2
25.13.c.b.18.4 10 5.2 odd 4
45.13.g.a.28.4 10 15.8 even 4
45.13.g.a.37.4 10 3.2 odd 2
80.13.p.c.17.5 10 4.3 odd 2
80.13.p.c.33.5 10 20.3 even 4