Properties

Label 5.13.c.a.3.1
Level $5$
Weight $13$
Character 5.3
Analytic conductor $4.570$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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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 3.1
Root \(8.55327i\) of defining polynomial
Character \(\chi\) \(=\) 5.3
Dual form 5.13.c.a.2.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-61.7891 + 61.7891i) q^{2} +(877.187 + 877.187i) q^{3} -3539.78i q^{4} +(-13781.9 + 7362.02i) q^{5} -108401. q^{6} +(67595.3 - 67595.3i) q^{7} +(-34368.1 - 34368.1i) q^{8} +1.00747e6i q^{9} +O(q^{10})\) \(q+(-61.7891 + 61.7891i) q^{2} +(877.187 + 877.187i) q^{3} -3539.78i q^{4} +(-13781.9 + 7362.02i) q^{5} -108401. q^{6} +(67595.3 - 67595.3i) q^{7} +(-34368.1 - 34368.1i) q^{8} +1.00747e6i q^{9} +(396679. - 1.30646e6i) q^{10} -626262. q^{11} +(3.10505e6 - 3.10505e6i) q^{12} +(3.07386e6 + 3.07386e6i) q^{13} +8.35330e6i q^{14} +(-1.85472e7 - 5.63145e6i) q^{15} +1.87461e7 q^{16} +(-6.99904e6 + 6.99904e6i) q^{17} +(-6.22509e7 - 6.22509e7i) q^{18} +4.52415e7i q^{19} +(2.60600e7 + 4.87850e7i) q^{20} +1.18587e8 q^{21} +(3.86962e7 - 3.86962e7i) q^{22} +(5.22502e7 + 5.22502e7i) q^{23} -6.02945e7i q^{24} +(1.35742e8 - 2.02926e8i) q^{25} -3.79863e8 q^{26} +(-4.17569e8 + 4.17569e8i) q^{27} +(-2.39273e8 - 2.39273e8i) q^{28} +5.40006e8i q^{29} +(1.49398e9 - 7.98052e8i) q^{30} -2.02184e8 q^{31} +(-1.01753e9 + 1.01753e9i) q^{32} +(-5.49349e8 - 5.49349e8i) q^{33} -8.64929e8i q^{34} +(-4.33954e8 + 1.42923e9i) q^{35} +3.56624e9 q^{36} +(2.57578e9 - 2.57578e9i) q^{37} +(-2.79543e9 - 2.79543e9i) q^{38} +5.39271e9i q^{39} +(7.26677e8 + 2.20639e8i) q^{40} +2.72921e9 q^{41} +(-7.32741e9 + 7.32741e9i) q^{42} +(-4.70194e9 - 4.70194e9i) q^{43} +2.21683e9i q^{44} +(-7.41704e9 - 1.38849e10i) q^{45} -6.45699e9 q^{46} +(1.28054e10 - 1.28054e10i) q^{47} +(1.64438e10 + 1.64438e10i) q^{48} +4.70305e9i q^{49} +(4.15123e9 + 2.09260e10i) q^{50} -1.22789e10 q^{51} +(1.08808e10 - 1.08808e10i) q^{52} +(1.73523e10 + 1.73523e10i) q^{53} -5.16024e10i q^{54} +(8.63109e9 - 4.61056e9i) q^{55} -4.64624e9 q^{56} +(-3.96853e10 + 3.96853e10i) q^{57} +(-3.33665e10 - 3.33665e10i) q^{58} -1.93469e10i q^{59} +(-1.99341e10 + 6.56530e10i) q^{60} -1.74415e10 q^{61} +(1.24928e10 - 1.24928e10i) q^{62} +(6.81004e10 + 6.81004e10i) q^{63} -4.89608e10i q^{64} +(-6.49936e10 - 1.97339e10i) q^{65} +6.78875e10 q^{66} +(7.91041e10 - 7.91041e10i) q^{67} +(2.47751e10 + 2.47751e10i) q^{68} +9.16664e10i q^{69} +(-6.14972e10 - 1.15124e11i) q^{70} -1.08760e11 q^{71} +(3.46249e10 - 3.46249e10i) q^{72} +(-3.78162e10 - 3.78162e10i) q^{73} +3.18310e11i q^{74} +(2.97075e11 - 5.89328e10i) q^{75} +1.60145e11 q^{76} +(-4.23323e10 + 4.23323e10i) q^{77} +(-3.33211e11 - 3.33211e11i) q^{78} +4.17485e10i q^{79} +(-2.58357e11 + 1.38009e11i) q^{80} -1.97160e11 q^{81} +(-1.68635e11 + 1.68635e11i) q^{82} +(1.08002e11 + 1.08002e11i) q^{83} -4.19774e11i q^{84} +(4.49331e10 - 1.47987e11i) q^{85} +5.81057e11 q^{86} +(-4.73686e11 + 4.73686e11i) q^{87} +(2.15234e10 + 2.15234e10i) q^{88} -6.78885e11i q^{89} +(1.31623e12 + 3.99644e11i) q^{90} +4.15557e11 q^{91} +(1.84954e11 - 1.84954e11i) q^{92} +(-1.77353e11 - 1.77353e11i) q^{93} +1.58246e12i q^{94} +(-3.33069e11 - 6.23515e11i) q^{95} -1.78513e12 q^{96} +(-3.15626e10 + 3.15626e10i) q^{97} +(-2.90597e11 - 2.90597e11i) q^{98} -6.30942e11i 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 \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −61.7891 + 61.7891i −0.965455 + 0.965455i −0.999423 0.0339683i \(-0.989185\pi\)
0.0339683 + 0.999423i \(0.489185\pi\)
\(3\) 877.187 + 877.187i 1.20327 + 1.20327i 0.973165 + 0.230110i \(0.0739085\pi\)
0.230110 + 0.973165i \(0.426092\pi\)
\(4\) 3539.78i 0.864205i
\(5\) −13781.9 + 7362.02i −0.882043 + 0.471170i
\(6\) −108401. −2.32341
\(7\) 67595.3 67595.3i 0.574550 0.574550i −0.358846 0.933397i \(-0.616830\pi\)
0.933397 + 0.358846i \(0.116830\pi\)
\(8\) −34368.1 34368.1i −0.131104 0.131104i
\(9\) 1.00747e6i 1.89574i
\(10\) 396679. 1.30646e6i 0.396679 1.30646i
\(11\) −626262. −0.353509 −0.176754 0.984255i \(-0.556560\pi\)
−0.176754 + 0.984255i \(0.556560\pi\)
\(12\) 3.10505e6 3.10505e6i 1.03988 1.03988i
\(13\) 3.07386e6 + 3.07386e6i 0.636832 + 0.636832i 0.949773 0.312941i \(-0.101314\pi\)
−0.312941 + 0.949773i \(0.601314\pi\)
\(14\) 8.35330e6i 1.10940i
\(15\) −1.85472e7 5.63145e6i −1.62829 0.494393i
\(16\) 1.87461e7 1.11735
\(17\) −6.99904e6 + 6.99904e6i −0.289965 + 0.289965i −0.837066 0.547102i \(-0.815731\pi\)
0.547102 + 0.837066i \(0.315731\pi\)
\(18\) −6.22509e7 6.22509e7i −1.83025 1.83025i
\(19\) 4.52415e7i 0.961647i 0.876817 + 0.480824i \(0.159662\pi\)
−0.876817 + 0.480824i \(0.840338\pi\)
\(20\) 2.60600e7 + 4.87850e7i 0.407187 + 0.762266i
\(21\) 1.18587e8 1.38268
\(22\) 3.86962e7 3.86962e7i 0.341296 0.341296i
\(23\) 5.22502e7 + 5.22502e7i 0.352956 + 0.352956i 0.861208 0.508252i \(-0.169708\pi\)
−0.508252 + 0.861208i \(0.669708\pi\)
\(24\) 6.02945e7i 0.315508i
\(25\) 1.35742e8 2.02926e8i 0.555998 0.831183i
\(26\) −3.79863e8 −1.22966
\(27\) −4.17569e8 + 4.17569e8i −1.07782 + 1.07782i
\(28\) −2.39273e8 2.39273e8i −0.496529 0.496529i
\(29\) 5.40006e8i 0.907842i 0.891042 + 0.453921i \(0.149975\pi\)
−0.891042 + 0.453921i \(0.850025\pi\)
\(30\) 1.49398e9 7.98052e8i 2.04935 1.09472i
\(31\) −2.02184e8 −0.227812 −0.113906 0.993492i \(-0.536336\pi\)
−0.113906 + 0.993492i \(0.536336\pi\)
\(32\) −1.01753e9 + 1.01753e9i −0.947651 + 0.947651i
\(33\) −5.49349e8 5.49349e8i −0.425368 0.425368i
\(34\) 8.64929e8i 0.559895i
\(35\) −4.33954e8 + 1.42923e9i −0.236067 + 0.777488i
\(36\) 3.56624e9 1.63831
\(37\) 2.57578e9 2.57578e9i 1.00392 1.00392i 0.00392644 0.999992i \(-0.498750\pi\)
0.999992 0.00392644i \(-0.00124983\pi\)
\(38\) −2.79543e9 2.79543e9i −0.928427 0.928427i
\(39\) 5.39271e9i 1.53257i
\(40\) 7.26677e8 + 2.20639e8i 0.177411 + 0.0538670i
\(41\) 2.72921e9 0.574557 0.287279 0.957847i \(-0.407249\pi\)
0.287279 + 0.957847i \(0.407249\pi\)
\(42\) −7.32741e9 + 7.32741e9i −1.33492 + 1.33492i
\(43\) −4.70194e9 4.70194e9i −0.743817 0.743817i 0.229493 0.973310i \(-0.426293\pi\)
−0.973310 + 0.229493i \(0.926293\pi\)
\(44\) 2.21683e9i 0.305504i
\(45\) −7.41704e9 1.38849e10i −0.893214 1.67212i
\(46\) −6.45699e9 −0.681527
\(47\) 1.28054e10 1.28054e10i 1.18797 1.18797i 0.210340 0.977628i \(-0.432543\pi\)
0.977628 0.210340i \(-0.0674571\pi\)
\(48\) 1.64438e10 + 1.64438e10i 1.34448 + 1.34448i
\(49\) 4.70305e9i 0.339784i
\(50\) 4.15123e9 + 2.09260e10i 0.265679 + 1.33926i
\(51\) −1.22789e10 −0.697814
\(52\) 1.08808e10 1.08808e10i 0.550353 0.550353i
\(53\) 1.73523e10 + 1.73523e10i 0.782890 + 0.782890i 0.980317 0.197427i \(-0.0632587\pi\)
−0.197427 + 0.980317i \(0.563259\pi\)
\(54\) 5.16024e10i 2.08117i
\(55\) 8.63109e9 4.61056e9i 0.311810 0.166562i
\(56\) −4.64624e9 −0.150652
\(57\) −3.96853e10 + 3.96853e10i −1.15713 + 1.15713i
\(58\) −3.33665e10 3.33665e10i −0.876480 0.876480i
\(59\) 1.93469e10i 0.458670i −0.973348 0.229335i \(-0.926345\pi\)
0.973348 0.229335i \(-0.0736551\pi\)
\(60\) −1.99341e10 + 6.56530e10i −0.427257 + 1.40717i
\(61\) −1.74415e10 −0.338535 −0.169268 0.985570i \(-0.554140\pi\)
−0.169268 + 0.985570i \(0.554140\pi\)
\(62\) 1.24928e10 1.24928e10i 0.219942 0.219942i
\(63\) 6.81004e10 + 6.81004e10i 1.08920 + 1.08920i
\(64\) 4.89608e10i 0.712474i
\(65\) −6.49936e10 1.97339e10i −0.861768 0.261657i
\(66\) 6.78875e10 0.821347
\(67\) 7.91041e10 7.91041e10i 0.874480 0.874480i −0.118477 0.992957i \(-0.537801\pi\)
0.992957 + 0.118477i \(0.0378011\pi\)
\(68\) 2.47751e10 + 2.47751e10i 0.250589 + 0.250589i
\(69\) 9.16664e10i 0.849407i
\(70\) −6.14972e10 1.15124e11i −0.522718 0.978542i
\(71\) −1.08760e11 −0.849026 −0.424513 0.905422i \(-0.639555\pi\)
−0.424513 + 0.905422i \(0.639555\pi\)
\(72\) 3.46249e10 3.46249e10i 0.248539 0.248539i
\(73\) −3.78162e10 3.78162e10i −0.249885 0.249885i 0.571038 0.820923i \(-0.306541\pi\)
−0.820923 + 0.571038i \(0.806541\pi\)
\(74\) 3.18310e11i 1.93848i
\(75\) 2.97075e11 5.89328e10i 1.66916 0.331123i
\(76\) 1.60145e11 0.831061
\(77\) −4.23323e10 + 4.23323e10i −0.203108 + 0.203108i
\(78\) −3.33211e11 3.33211e11i −1.47962 1.47962i
\(79\) 4.17485e10i 0.171743i 0.996306 + 0.0858714i \(0.0273674\pi\)
−0.996306 + 0.0858714i \(0.972633\pi\)
\(80\) −2.58357e11 + 1.38009e11i −0.985554 + 0.526464i
\(81\) −1.97160e11 −0.698086
\(82\) −1.68635e11 + 1.68635e11i −0.554709 + 0.554709i
\(83\) 1.08002e11 + 1.08002e11i 0.330341 + 0.330341i 0.852716 0.522375i \(-0.174954\pi\)
−0.522375 + 0.852716i \(0.674954\pi\)
\(84\) 4.19774e11i 1.19492i
\(85\) 4.49331e10 1.47987e11i 0.119139 0.392384i
\(86\) 5.81057e11 1.43624
\(87\) −4.73686e11 + 4.73686e11i −1.09238 + 1.09238i
\(88\) 2.15234e10 + 2.15234e10i 0.0463463 + 0.0463463i
\(89\) 6.78885e11i 1.36602i −0.730411 0.683008i \(-0.760671\pi\)
0.730411 0.683008i \(-0.239329\pi\)
\(90\) 1.31623e12 + 3.99644e11i 2.47672 + 0.752000i
\(91\) 4.15557e11 0.731784
\(92\) 1.84954e11 1.84954e11i 0.305027 0.305027i
\(93\) −1.77353e11 1.77353e11i −0.274121 0.274121i
\(94\) 1.58246e12i 2.29386i
\(95\) −3.33069e11 6.23515e11i −0.453099 0.848214i
\(96\) −1.78513e12 −2.28057
\(97\) −3.15626e10 + 3.15626e10i −0.0378916 + 0.0378916i −0.725799 0.687907i \(-0.758530\pi\)
0.687907 + 0.725799i \(0.258530\pi\)
\(98\) −2.90597e11 2.90597e11i −0.328046 0.328046i
\(99\) 6.30942e11i 0.670160i
\(100\) −7.18313e11 4.80497e11i −0.718313 0.480497i
\(101\) 5.81967e11 0.548239 0.274120 0.961696i \(-0.411614\pi\)
0.274120 + 0.961696i \(0.411614\pi\)
\(102\) 7.58704e11 7.58704e11i 0.673708 0.673708i
\(103\) 1.06154e12 + 1.06154e12i 0.889023 + 0.889023i 0.994429 0.105406i \(-0.0336143\pi\)
−0.105406 + 0.994429i \(0.533614\pi\)
\(104\) 2.11286e11i 0.166982i
\(105\) −1.63436e12 + 8.73043e11i −1.21959 + 0.651478i
\(106\) −2.14436e12 −1.51169
\(107\) 7.60757e11 7.60757e11i 0.506924 0.506924i −0.406657 0.913581i \(-0.633305\pi\)
0.913581 + 0.406657i \(0.133305\pi\)
\(108\) 1.47810e12 + 1.47810e12i 0.931457 + 0.931457i
\(109\) 2.13246e12i 1.27152i 0.771887 + 0.635759i \(0.219313\pi\)
−0.771887 + 0.635759i \(0.780687\pi\)
\(110\) −2.48425e11 + 8.18189e11i −0.140230 + 0.461847i
\(111\) 4.51888e12 2.41598
\(112\) 1.26715e12 1.26715e12i 0.641976 0.641976i
\(113\) −2.60692e12 2.60692e12i −1.25215 1.25215i −0.954753 0.297401i \(-0.903880\pi\)
−0.297401 0.954753i \(-0.596120\pi\)
\(114\) 4.90424e12i 2.23430i
\(115\) −1.10478e12 3.35441e11i −0.477625 0.145020i
\(116\) 1.91150e12 0.784562
\(117\) −3.09684e12 + 3.09684e12i −1.20727 + 1.20727i
\(118\) 1.19543e12 + 1.19543e12i 0.442825 + 0.442825i
\(119\) 9.46204e11i 0.333198i
\(120\) 4.43889e11 + 8.30973e11i 0.148658 + 0.278291i
\(121\) −2.74622e12 −0.875032
\(122\) 1.07769e12 1.07769e12i 0.326841 0.326841i
\(123\) 2.39403e12 + 2.39403e12i 0.691350 + 0.691350i
\(124\) 7.15688e11i 0.196876i
\(125\) −3.76839e11 + 3.79604e12i −0.0987860 + 0.995109i
\(126\) −8.41573e12 −2.10314
\(127\) 2.09669e12 2.09669e12i 0.499703 0.499703i −0.411643 0.911345i \(-0.635045\pi\)
0.911345 + 0.411643i \(0.135045\pi\)
\(128\) −1.14257e12 1.14257e12i −0.259790 0.259790i
\(129\) 8.24896e12i 1.79003i
\(130\) 5.23524e12 2.79656e12i 1.08462 0.579380i
\(131\) −1.98696e12 −0.393153 −0.196577 0.980488i \(-0.562982\pi\)
−0.196577 + 0.980488i \(0.562982\pi\)
\(132\) −1.94458e12 + 1.94458e12i −0.367605 + 0.367605i
\(133\) 3.05811e12 + 3.05811e12i 0.552515 + 0.552515i
\(134\) 9.77554e12i 1.68854i
\(135\) 2.68075e12 8.82906e12i 0.442847 1.45852i
\(136\) 4.81087e11 0.0760309
\(137\) −7.17765e12 + 7.17765e12i −1.08557 + 1.08557i −0.0895941 + 0.995978i \(0.528557\pi\)
−0.995978 + 0.0895941i \(0.971443\pi\)
\(138\) −5.66399e12 5.66399e12i −0.820064 0.820064i
\(139\) 1.60028e11i 0.0221875i −0.999938 0.0110938i \(-0.996469\pi\)
0.999938 0.0110938i \(-0.00353132\pi\)
\(140\) 5.05917e12 + 1.53610e12i 0.671909 + 0.204010i
\(141\) 2.24654e13 2.85890
\(142\) 6.72021e12 6.72021e12i 0.819696 0.819696i
\(143\) −1.92504e12 1.92504e12i −0.225125 0.225125i
\(144\) 1.88862e13i 2.11821i
\(145\) −3.97553e12 7.44231e12i −0.427747 0.800755i
\(146\) 4.67325e12 0.482505
\(147\) −4.12545e12 + 4.12545e12i −0.408853 + 0.408853i
\(148\) −9.11771e12 9.11771e12i −0.867592 0.867592i
\(149\) 1.52562e13i 1.39422i −0.716966 0.697108i \(-0.754470\pi\)
0.716966 0.697108i \(-0.245530\pi\)
\(150\) −1.47146e13 + 2.19974e13i −1.29181 + 1.93118i
\(151\) −2.24188e13 −1.89126 −0.945631 0.325242i \(-0.894554\pi\)
−0.945631 + 0.325242i \(0.894554\pi\)
\(152\) 1.55487e12 1.55487e12i 0.126076 0.126076i
\(153\) −7.05134e12 7.05134e12i −0.549697 0.549697i
\(154\) 5.23135e12i 0.392184i
\(155\) 2.78648e12 1.48848e12i 0.200940 0.107338i
\(156\) 1.90890e13 1.32445
\(157\) −5.18200e12 + 5.18200e12i −0.346019 + 0.346019i −0.858624 0.512606i \(-0.828680\pi\)
0.512606 + 0.858624i \(0.328680\pi\)
\(158\) −2.57960e12 2.57960e12i −0.165810 0.165810i
\(159\) 3.04423e13i 1.88406i
\(160\) 6.53245e12 2.15147e13i 0.389364 1.28237i
\(161\) 7.06374e12 0.405582
\(162\) 1.21823e13 1.21823e13i 0.673970 0.673970i
\(163\) 2.32479e13 + 2.32479e13i 1.23954 + 1.23954i 0.960191 + 0.279344i \(0.0901171\pi\)
0.279344 + 0.960191i \(0.409883\pi\)
\(164\) 9.66081e12i 0.496535i
\(165\) 1.16154e13 + 3.52676e12i 0.575613 + 0.174772i
\(166\) −1.33467e13 −0.637859
\(167\) 6.01904e12 6.01904e12i 0.277478 0.277478i −0.554624 0.832101i \(-0.687138\pi\)
0.832101 + 0.554624i \(0.187138\pi\)
\(168\) −4.07562e12 4.07562e12i −0.181275 0.181275i
\(169\) 4.40079e12i 0.188891i
\(170\) 6.36763e12 + 1.19204e13i 0.263806 + 0.493851i
\(171\) −4.55796e13 −1.82303
\(172\) −1.66438e13 + 1.66438e13i −0.642810 + 0.642810i
\(173\) 2.55096e13 + 2.55096e13i 0.951538 + 0.951538i 0.998879 0.0473407i \(-0.0150746\pi\)
−0.0473407 + 0.998879i \(0.515075\pi\)
\(174\) 5.85372e13i 2.10929i
\(175\) −4.54131e12 2.28923e13i −0.158108 0.797006i
\(176\) −1.17400e13 −0.394994
\(177\) 1.69709e13 1.69709e13i 0.551906 0.551906i
\(178\) 4.19477e13 + 4.19477e13i 1.31883 + 1.31883i
\(179\) 2.62541e13i 0.798139i −0.916921 0.399070i \(-0.869333\pi\)
0.916921 0.399070i \(-0.130667\pi\)
\(180\) −4.91496e13 + 2.62547e13i −1.44506 + 0.771920i
\(181\) 9.97197e12 0.283602 0.141801 0.989895i \(-0.454711\pi\)
0.141801 + 0.989895i \(0.454711\pi\)
\(182\) −2.56769e13 + 2.56769e13i −0.706504 + 0.706504i
\(183\) −1.52994e13 1.52994e13i −0.407351 0.407351i
\(184\) 3.59148e12i 0.0925479i
\(185\) −1.65362e13 + 5.44622e13i −0.412483 + 1.35852i
\(186\) 2.19170e13 0.529302
\(187\) 4.38323e12 4.38323e12i 0.102505 0.102505i
\(188\) −4.53282e13 4.53282e13i −1.02665 1.02665i
\(189\) 5.64514e13i 1.23852i
\(190\) 5.91065e13 + 1.79464e13i 1.25636 + 0.381466i
\(191\) 1.36705e13 0.281568 0.140784 0.990040i \(-0.455038\pi\)
0.140784 + 0.990040i \(0.455038\pi\)
\(192\) 4.29478e13 4.29478e13i 0.857302 0.857302i
\(193\) −5.46179e13 5.46179e13i −1.05680 1.05680i −0.998287 0.0585082i \(-0.981366\pi\)
−0.0585082 0.998287i \(-0.518634\pi\)
\(194\) 3.90045e12i 0.0731652i
\(195\) −3.97013e13 7.43219e13i −0.722099 1.35179i
\(196\) 1.66478e13 0.293643
\(197\) 3.56213e13 3.56213e13i 0.609415 0.609415i −0.333378 0.942793i \(-0.608189\pi\)
0.942793 + 0.333378i \(0.108189\pi\)
\(198\) 3.89853e13 + 3.89853e13i 0.647009 + 0.647009i
\(199\) 4.38190e13i 0.705576i 0.935703 + 0.352788i \(0.114766\pi\)
−0.935703 + 0.352788i \(0.885234\pi\)
\(200\) −1.16394e13 + 2.30898e12i −0.181865 + 0.0360778i
\(201\) 1.38778e14 2.10448
\(202\) −3.59592e13 + 3.59592e13i −0.529300 + 0.529300i
\(203\) 3.65018e13 + 3.65018e13i 0.521601 + 0.521601i
\(204\) 4.34648e13i 0.603054i
\(205\) −3.76137e13 + 2.00925e13i −0.506784 + 0.270714i
\(206\) −1.31183e14 −1.71662
\(207\) −5.26407e13 + 5.26407e13i −0.669113 + 0.669113i
\(208\) 5.76230e13 + 5.76230e13i 0.711567 + 0.711567i
\(209\) 2.83331e13i 0.339951i
\(210\) 4.70412e13 1.54930e14i 0.548482 1.80643i
\(211\) −1.15325e14 −1.30686 −0.653430 0.756987i \(-0.726671\pi\)
−0.653430 + 0.756987i \(0.726671\pi\)
\(212\) 6.14232e13 6.14232e13i 0.676577 0.676577i
\(213\) −9.54033e13 9.54033e13i −1.02161 1.02161i
\(214\) 9.40129e13i 0.978825i
\(215\) 9.94175e13 + 3.01859e13i 1.00654 + 0.305614i
\(216\) 2.87021e13 0.282612
\(217\) −1.36667e13 + 1.36667e13i −0.130890 + 0.130890i
\(218\) −1.31763e14 1.31763e14i −1.22759 1.22759i
\(219\) 6.63437e13i 0.601360i
\(220\) −1.63204e13 3.05522e13i −0.143944 0.269467i
\(221\) −4.30282e13 −0.369317
\(222\) −2.79218e14 + 2.79218e14i −2.33252 + 2.33252i
\(223\) −4.25094e13 4.25094e13i −0.345666 0.345666i 0.512827 0.858492i \(-0.328598\pi\)
−0.858492 + 0.512827i \(0.828598\pi\)
\(224\) 1.37561e14i 1.08895i
\(225\) 2.04442e14 + 1.36756e14i 1.57571 + 1.05403i
\(226\) 3.22159e14 2.41779
\(227\) 1.56632e14 1.56632e14i 1.14479 1.14479i 0.157225 0.987563i \(-0.449745\pi\)
0.987563 0.157225i \(-0.0502547\pi\)
\(228\) 1.40477e14 + 1.40477e14i 0.999994 + 0.999994i
\(229\) 2.12425e14i 1.47297i −0.676456 0.736483i \(-0.736485\pi\)
0.676456 0.736483i \(-0.263515\pi\)
\(230\) 8.89897e13 4.75365e13i 0.601136 0.321115i
\(231\) −7.42668e13 −0.488790
\(232\) 1.85590e13 1.85590e13i 0.119022 0.119022i
\(233\) 3.32347e13 + 3.32347e13i 0.207709 + 0.207709i 0.803293 0.595584i \(-0.203079\pi\)
−0.595584 + 0.803293i \(0.703079\pi\)
\(234\) 3.82701e14i 2.33112i
\(235\) −8.22091e13 + 2.70756e14i −0.488104 + 1.60757i
\(236\) −6.84840e13 −0.396385
\(237\) −3.66213e13 + 3.66213e13i −0.206654 + 0.206654i
\(238\) −5.84651e13 5.84651e13i −0.321688 0.321688i
\(239\) 2.78396e14i 1.49374i 0.664969 + 0.746871i \(0.268445\pi\)
−0.664969 + 0.746871i \(0.731555\pi\)
\(240\) −3.47688e14 1.05568e14i −1.81937 0.552412i
\(241\) 1.17185e13 0.0598095 0.0299047 0.999553i \(-0.490480\pi\)
0.0299047 + 0.999553i \(0.490480\pi\)
\(242\) 1.69687e14 1.69687e14i 0.844803 0.844803i
\(243\) 4.89672e13 + 4.89672e13i 0.237830 + 0.237830i
\(244\) 6.17391e13i 0.292564i
\(245\) −3.46239e13 6.48170e13i −0.160096 0.299704i
\(246\) −2.95849e14 −1.33493
\(247\) −1.39066e14 + 1.39066e14i −0.612408 + 0.612408i
\(248\) 6.94868e12 + 6.94868e12i 0.0298671 + 0.0298671i
\(249\) 1.89476e14i 0.794982i
\(250\) −2.11269e14 2.57838e14i −0.865359 1.05611i
\(251\) 1.40981e14 0.563792 0.281896 0.959445i \(-0.409037\pi\)
0.281896 + 0.959445i \(0.409037\pi\)
\(252\) 2.41061e14 2.41061e14i 0.941290 0.941290i
\(253\) −3.27223e13 3.27223e13i −0.124773 0.124773i
\(254\) 2.59105e14i 0.964881i
\(255\) 1.69227e14 9.03978e13i 0.615502 0.328789i
\(256\) 3.41740e14 1.21411
\(257\) −1.00683e14 + 1.00683e14i −0.349428 + 0.349428i −0.859896 0.510469i \(-0.829472\pi\)
0.510469 + 0.859896i \(0.329472\pi\)
\(258\) 5.09695e14 + 5.09695e14i 1.72819 + 1.72819i
\(259\) 3.48221e14i 1.15360i
\(260\) −6.98537e13 + 2.30063e14i −0.226125 + 0.744745i
\(261\) −5.44041e14 −1.72103
\(262\) 1.22773e14 1.22773e14i 0.379572 0.379572i
\(263\) −1.47227e14 1.47227e14i −0.444889 0.444889i 0.448762 0.893651i \(-0.351865\pi\)
−0.893651 + 0.448762i \(0.851865\pi\)
\(264\) 3.77601e13i 0.111535i
\(265\) −3.66895e14 1.11400e14i −1.05942 0.321668i
\(266\) −3.77916e14 −1.06686
\(267\) 5.95509e14 5.95509e14i 1.64369 1.64369i
\(268\) −2.80011e14 2.80011e14i −0.755730 0.755730i
\(269\) 5.62680e13i 0.148507i 0.997239 + 0.0742536i \(0.0236574\pi\)
−0.997239 + 0.0742536i \(0.976343\pi\)
\(270\) 3.79898e14 + 7.11181e14i 0.980584 + 1.83568i
\(271\) 6.58674e14 1.66286 0.831429 0.555632i \(-0.187523\pi\)
0.831429 + 0.555632i \(0.187523\pi\)
\(272\) −1.31205e14 + 1.31205e14i −0.323993 + 0.323993i
\(273\) 3.64522e14 + 3.64522e14i 0.880537 + 0.880537i
\(274\) 8.87001e14i 2.09614i
\(275\) −8.50099e13 + 1.27085e14i −0.196550 + 0.293830i
\(276\) 3.24479e14 0.734062
\(277\) −2.01448e14 + 2.01448e14i −0.445949 + 0.445949i −0.894005 0.448056i \(-0.852116\pi\)
0.448056 + 0.894005i \(0.352116\pi\)
\(278\) 9.88801e12 + 9.88801e12i 0.0214210 + 0.0214210i
\(279\) 2.03695e14i 0.431872i
\(280\) 6.40341e13 3.42057e13i 0.132881 0.0709824i
\(281\) −4.59473e14 −0.933302 −0.466651 0.884442i \(-0.654540\pi\)
−0.466651 + 0.884442i \(0.654540\pi\)
\(282\) −1.38812e15 + 1.38812e15i −2.76014 + 2.76014i
\(283\) 7.88330e11 + 7.88330e11i 0.00153458 + 0.00153458i 0.707874 0.706339i \(-0.249655\pi\)
−0.706339 + 0.707874i \(0.749655\pi\)
\(284\) 3.84988e14i 0.733732i
\(285\) 2.54775e14 8.39104e14i 0.475432 1.56584i
\(286\) 2.37894e14 0.434697
\(287\) 1.84482e14 1.84482e14i 0.330112 0.330112i
\(288\) −1.02514e15 1.02514e15i −1.79650 1.79650i
\(289\) 4.84649e14i 0.831841i
\(290\) 7.05498e14 + 2.14209e14i 1.18606 + 0.360122i
\(291\) −5.53726e13 −0.0911879
\(292\) −1.33861e14 + 1.33861e14i −0.215952 + 0.215952i
\(293\) −4.07426e14 4.07426e14i −0.643937 0.643937i 0.307584 0.951521i \(-0.400480\pi\)
−0.951521 + 0.307584i \(0.900480\pi\)
\(294\) 5.09816e14i 0.789458i
\(295\) 1.42433e14 + 2.66638e14i 0.216111 + 0.404567i
\(296\) −1.77049e14 −0.263235
\(297\) 2.61508e14 2.61508e14i 0.381018 0.381018i
\(298\) 9.42670e14 + 9.42670e14i 1.34605 + 1.34605i
\(299\) 3.21220e14i 0.449548i
\(300\) −2.08609e14 1.05158e15i −0.286158 1.44250i
\(301\) −6.35657e14 −0.854720
\(302\) 1.38524e15 1.38524e15i 1.82593 1.82593i
\(303\) 5.10494e14 + 5.10494e14i 0.659683 + 0.659683i
\(304\) 8.48103e14i 1.07450i
\(305\) 2.40377e14 1.28405e14i 0.298603 0.159508i
\(306\) 8.71392e14 1.06141
\(307\) −8.39174e14 + 8.39174e14i −1.00236 + 1.00236i −0.00235845 + 0.999997i \(0.500751\pi\)
−0.999997 + 0.00235845i \(0.999249\pi\)
\(308\) 1.49847e14 + 1.49847e14i 0.175527 + 0.175527i
\(309\) 1.86234e15i 2.13948i
\(310\) −8.02023e13 + 2.64146e14i −0.0903684 + 0.297629i
\(311\) 4.19245e14 0.463346 0.231673 0.972794i \(-0.425580\pi\)
0.231673 + 0.972794i \(0.425580\pi\)
\(312\) 1.85337e14 1.85337e14i 0.200925 0.200925i
\(313\) −6.71824e14 6.71824e14i −0.714479 0.714479i 0.252990 0.967469i \(-0.418586\pi\)
−0.967469 + 0.252990i \(0.918586\pi\)
\(314\) 6.40382e14i 0.668131i
\(315\) −1.43991e15 4.37197e14i −1.47391 0.447522i
\(316\) 1.47781e14 0.148421
\(317\) 7.72397e14 7.72397e14i 0.761176 0.761176i −0.215359 0.976535i \(-0.569092\pi\)
0.976535 + 0.215359i \(0.0690922\pi\)
\(318\) −1.88101e15 1.88101e15i −1.81898 1.81898i
\(319\) 3.38185e14i 0.320930i
\(320\) 3.60451e14 + 6.74774e14i 0.335696 + 0.628432i
\(321\) 1.33465e15 1.21994
\(322\) −4.36462e14 + 4.36462e14i −0.391571 + 0.391571i
\(323\) −3.16647e14 3.16647e14i −0.278844 0.278844i
\(324\) 6.97904e14i 0.603289i
\(325\) 1.04102e15 2.06514e14i 0.883401 0.175246i
\(326\) −2.87294e15 −2.39343
\(327\) −1.87057e15 + 1.87057e15i −1.52999 + 1.52999i
\(328\) −9.37976e13 9.37976e13i −0.0753267 0.0753267i
\(329\) 1.73116e15i 1.36510i
\(330\) −9.35620e14 + 4.99790e14i −0.724463 + 0.386994i
\(331\) 1.14681e15 0.872017 0.436009 0.899942i \(-0.356392\pi\)
0.436009 + 0.899942i \(0.356392\pi\)
\(332\) 3.82303e14 3.82303e14i 0.285482 0.285482i
\(333\) 2.59503e15 + 2.59503e15i 1.90317 + 1.90317i
\(334\) 7.43821e14i 0.535784i
\(335\) −5.07840e14 + 1.67257e15i −0.359300 + 1.18336i
\(336\) 2.22305e15 1.54495
\(337\) −3.55515e14 + 3.55515e14i −0.242705 + 0.242705i −0.817968 0.575263i \(-0.804900\pi\)
0.575263 + 0.817968i \(0.304900\pi\)
\(338\) 2.71921e14 + 2.71921e14i 0.182366 + 0.182366i
\(339\) 4.57352e15i 3.01337i
\(340\) −5.23843e14 1.59053e14i −0.339100 0.102960i
\(341\) 1.26620e14 0.0805336
\(342\) 2.81632e15 2.81632e15i 1.76005 1.76005i
\(343\) 1.25351e15 + 1.25351e15i 0.769773 + 0.769773i
\(344\) 3.23193e14i 0.195035i
\(345\) −6.74851e14 1.26334e15i −0.400215 0.749213i
\(346\) −3.15242e15 −1.83733
\(347\) −5.71227e14 + 5.71227e14i −0.327214 + 0.327214i −0.851526 0.524312i \(-0.824323\pi\)
0.524312 + 0.851526i \(0.324323\pi\)
\(348\) 1.67675e15 + 1.67675e15i 0.944043 + 0.944043i
\(349\) 9.84765e14i 0.544980i −0.962159 0.272490i \(-0.912153\pi\)
0.962159 0.272490i \(-0.0878471\pi\)
\(350\) 1.69510e15 + 1.13389e15i 0.922118 + 0.616827i
\(351\) −2.56710e15 −1.37278
\(352\) 6.37242e14 6.37242e14i 0.335003 0.335003i
\(353\) −1.69093e15 1.69093e15i −0.873930 0.873930i 0.118968 0.992898i \(-0.462041\pi\)
−0.992898 + 0.118968i \(0.962041\pi\)
\(354\) 2.09723e15i 1.06568i
\(355\) 1.49893e15 8.00697e14i 0.748877 0.400035i
\(356\) −2.40311e15 −1.18052
\(357\) −8.29998e14 + 8.29998e14i −0.400929 + 0.400929i
\(358\) 1.62222e15 + 1.62222e15i 0.770567 + 0.770567i
\(359\) 1.01974e15i 0.476345i 0.971223 + 0.238173i \(0.0765484\pi\)
−0.971223 + 0.238173i \(0.923452\pi\)
\(360\) −2.22288e14 + 7.32107e14i −0.102118 + 0.336325i
\(361\) 1.66517e14 0.0752343
\(362\) −6.16159e14 + 6.16159e14i −0.273805 + 0.273805i
\(363\) −2.40895e15 2.40895e15i −1.05290 1.05290i
\(364\) 1.47098e15i 0.632411i
\(365\) 7.99583e14 + 2.42776e14i 0.338147 + 0.102671i
\(366\) 1.89068e15 0.786558
\(367\) 1.52100e15 1.52100e15i 0.622490 0.622490i −0.323677 0.946168i \(-0.604919\pi\)
0.946168 + 0.323677i \(0.104919\pi\)
\(368\) 9.79488e14 + 9.79488e14i 0.394378 + 0.394378i
\(369\) 2.74960e15i 1.08921i
\(370\) −2.34341e15 4.38693e15i −0.913351 1.70982i
\(371\) 2.34586e15 0.899619
\(372\) −6.27792e14 + 6.27792e14i −0.236896 + 0.236896i
\(373\) 4.81109e14 + 4.81109e14i 0.178645 + 0.178645i 0.790765 0.612120i \(-0.209683\pi\)
−0.612120 + 0.790765i \(0.709683\pi\)
\(374\) 5.41672e14i 0.197928i
\(375\) −3.66039e15 + 2.99928e15i −1.31626 + 1.07852i
\(376\) −8.80192e14 −0.311494
\(377\) −1.65990e15 + 1.65990e15i −0.578142 + 0.578142i
\(378\) −3.48808e15 3.48808e15i −1.19574 1.19574i
\(379\) 7.77243e14i 0.262254i −0.991366 0.131127i \(-0.958141\pi\)
0.991366 0.131127i \(-0.0418595\pi\)
\(380\) −2.20711e15 + 1.17899e15i −0.733031 + 0.391570i
\(381\) 3.67838e15 1.20256
\(382\) −8.44686e14 + 8.44686e14i −0.271841 + 0.271841i
\(383\) 2.57180e14 + 2.57180e14i 0.0814787 + 0.0814787i 0.746672 0.665193i \(-0.231651\pi\)
−0.665193 + 0.746672i \(0.731651\pi\)
\(384\) 2.00449e15i 0.625198i
\(385\) 2.71769e14 8.95073e14i 0.0834518 0.274849i
\(386\) 6.74958e15 2.04058
\(387\) 4.73707e15 4.73707e15i 1.41008 1.41008i
\(388\) 1.11725e14 + 1.11725e14i 0.0327461 + 0.0327461i
\(389\) 1.28470e15i 0.370769i 0.982666 + 0.185384i \(0.0593531\pi\)
−0.982666 + 0.185384i \(0.940647\pi\)
\(390\) 7.04538e15 + 2.13918e15i 2.00224 + 0.607937i
\(391\) −7.31403e14 −0.204690
\(392\) 1.61635e14 1.61635e14i 0.0445470 0.0445470i
\(393\) −1.74294e15 1.74294e15i −0.473071 0.473071i
\(394\) 4.40202e15i 1.17672i
\(395\) −3.07354e14 5.75375e14i −0.0809200 0.151485i
\(396\) −2.23340e15 −0.579156
\(397\) −7.12595e14 + 7.12595e14i −0.182012 + 0.182012i −0.792232 0.610220i \(-0.791081\pi\)
0.610220 + 0.792232i \(0.291081\pi\)
\(398\) −2.70754e15 2.70754e15i −0.681202 0.681202i
\(399\) 5.36508e15i 1.32965i
\(400\) 2.54463e15 3.80406e15i 0.621247 0.928727i
\(401\) 4.12594e15 0.992332 0.496166 0.868228i \(-0.334741\pi\)
0.496166 + 0.868228i \(0.334741\pi\)
\(402\) −8.57497e15 + 8.57497e15i −2.03178 + 2.03178i
\(403\) −6.21487e14 6.21487e14i −0.145078 0.145078i
\(404\) 2.06004e15i 0.473791i
\(405\) 2.71724e15 1.45150e15i 0.615741 0.328917i
\(406\) −4.51083e15 −1.00716
\(407\) −1.61311e15 + 1.61311e15i −0.354894 + 0.354894i
\(408\) 4.22003e14 + 4.22003e14i 0.0914861 + 0.0914861i
\(409\) 7.37449e14i 0.157541i −0.996893 0.0787703i \(-0.974901\pi\)
0.996893 0.0787703i \(-0.0250994\pi\)
\(410\) 1.08262e15 3.56561e15i 0.227915 0.750639i
\(411\) −1.25923e16 −2.61248
\(412\) 3.75762e15 3.75762e15i 0.768298 0.768298i
\(413\) −1.30776e15 1.30776e15i −0.263529 0.263529i
\(414\) 6.50524e15i 1.29200i
\(415\) −2.28358e15 6.93360e14i −0.447022 0.135728i
\(416\) −6.25552e15 −1.20699
\(417\) 1.40375e14 1.40375e14i 0.0266977 0.0266977i
\(418\) 1.75067e15 + 1.75067e15i 0.328207 + 0.328207i
\(419\) 1.89487e15i 0.350183i 0.984552 + 0.175092i \(0.0560222\pi\)
−0.984552 + 0.175092i \(0.943978\pi\)
\(420\) 3.09038e15 + 5.78529e15i 0.563011 + 1.05397i
\(421\) 7.70049e14 0.138301 0.0691506 0.997606i \(-0.477971\pi\)
0.0691506 + 0.997606i \(0.477971\pi\)
\(422\) 7.12583e15 7.12583e15i 1.26171 1.26171i
\(423\) 1.29011e16 + 1.29011e16i 2.25208 + 2.25208i
\(424\) 1.19273e15i 0.205280i
\(425\) 4.70222e14 + 2.37035e15i 0.0797939 + 0.402234i
\(426\) 1.17898e16 1.97264
\(427\) −1.17896e15 + 1.17896e15i −0.194506 + 0.194506i
\(428\) −2.69291e15 2.69291e15i −0.438087 0.438087i
\(429\) 3.37725e15i 0.541775i
\(430\) −8.00808e15 + 4.27775e15i −1.26683 + 0.676714i
\(431\) 1.23954e15 0.193373 0.0966867 0.995315i \(-0.469175\pi\)
0.0966867 + 0.995315i \(0.469175\pi\)
\(432\) −7.82779e15 + 7.82779e15i −1.20431 + 1.20431i
\(433\) −4.00108e15 4.00108e15i −0.607085 0.607085i 0.335098 0.942183i \(-0.391231\pi\)
−0.942183 + 0.335098i \(0.891231\pi\)
\(434\) 1.68890e15i 0.252736i
\(435\) 3.04101e15 1.00156e16i 0.448831 1.47823i
\(436\) 7.54846e15 1.09885
\(437\) −2.36388e15 + 2.36388e15i −0.339420 + 0.339420i
\(438\) 4.09932e15 + 4.09932e15i 0.580586 + 0.580586i
\(439\) 2.05585e15i 0.287213i 0.989635 + 0.143607i \(0.0458700\pi\)
−0.989635 + 0.143607i \(0.954130\pi\)
\(440\) −4.55090e14 1.38178e14i −0.0627164 0.0190425i
\(441\) −4.73819e15 −0.644141
\(442\) 2.65867e15 2.65867e15i 0.356559 0.356559i
\(443\) −4.86246e14 4.86246e14i −0.0643330 0.0643330i 0.674208 0.738541i \(-0.264485\pi\)
−0.738541 + 0.674208i \(0.764485\pi\)
\(444\) 1.59959e16i 2.08790i
\(445\) 4.99797e15 + 9.35633e15i 0.643626 + 1.20488i
\(446\) 5.25324e15 0.667449
\(447\) 1.33826e16 1.33826e16i 1.67762 1.67762i
\(448\) −3.30952e15 3.30952e15i −0.409352 0.409352i
\(449\) 7.06392e15i 0.862120i 0.902323 + 0.431060i \(0.141860\pi\)
−0.902323 + 0.431060i \(0.858140\pi\)
\(450\) −2.10823e16 + 4.18225e15i −2.53889 + 0.503657i
\(451\) −1.70920e15 −0.203111
\(452\) −9.22794e15 + 9.22794e15i −1.08212 + 1.08212i
\(453\) −1.96655e16 1.96655e16i −2.27571 2.27571i
\(454\) 1.93563e16i 2.21048i
\(455\) −5.72718e15 + 3.05934e15i −0.645464 + 0.344794i
\(456\) 2.72782e15 0.303407
\(457\) 7.02310e15 7.02310e15i 0.770959 0.770959i −0.207315 0.978274i \(-0.566472\pi\)
0.978274 + 0.207315i \(0.0664725\pi\)
\(458\) 1.31256e16 + 1.31256e16i 1.42208 + 1.42208i
\(459\) 5.84517e15i 0.625059i
\(460\) −1.18739e15 + 3.91067e15i −0.125327 + 0.412766i
\(461\) −1.41503e16 −1.47422 −0.737109 0.675774i \(-0.763809\pi\)
−0.737109 + 0.675774i \(0.763809\pi\)
\(462\) 4.58888e15 4.58888e15i 0.471905 0.471905i
\(463\) 1.23030e16 + 1.23030e16i 1.24889 + 1.24889i 0.956212 + 0.292676i \(0.0945458\pi\)
0.292676 + 0.956212i \(0.405454\pi\)
\(464\) 1.01230e16i 1.01438i
\(465\) 3.74995e15 + 1.13859e15i 0.370943 + 0.112629i
\(466\) −4.10708e15 −0.401068
\(467\) 1.13770e16 1.13770e16i 1.09679 1.09679i 0.102011 0.994783i \(-0.467472\pi\)
0.994783 0.102011i \(-0.0325277\pi\)
\(468\) 1.09621e16 + 1.09621e16i 1.04333 + 1.04333i
\(469\) 1.06941e16i 1.00487i
\(470\) −1.16501e16 2.18094e16i −1.08080 2.02328i
\(471\) −9.09117e15 −0.832711
\(472\) −6.64918e14 + 6.64918e14i −0.0601334 + 0.0601334i
\(473\) 2.94464e15 + 2.94464e15i 0.262946 + 0.262946i
\(474\) 4.52559e15i 0.399030i
\(475\) 9.18067e15 + 6.14117e15i 0.799305 + 0.534674i
\(476\) 3.34936e15 0.287952
\(477\) −1.74819e16 + 1.74819e16i −1.48415 + 1.48415i
\(478\) −1.72018e16 1.72018e16i −1.44214 1.44214i
\(479\) 2.02648e16i 1.67776i −0.544316 0.838880i \(-0.683211\pi\)
0.544316 0.838880i \(-0.316789\pi\)
\(480\) 2.46026e16 1.31422e16i 2.01156 1.07453i
\(481\) 1.58352e16 1.27865
\(482\) −7.24076e14 + 7.24076e14i −0.0577433 + 0.0577433i
\(483\) 6.19622e15 + 6.19622e15i 0.488027 + 0.488027i
\(484\) 9.72104e15i 0.756207i
\(485\) 2.02629e14 6.67358e14i 0.0155686 0.0512753i
\(486\) −6.05127e15 −0.459229
\(487\) −1.19627e16 + 1.19627e16i −0.896721 + 0.896721i −0.995145 0.0984239i \(-0.968620\pi\)
0.0984239 + 0.995145i \(0.468620\pi\)
\(488\) 5.99430e14 + 5.99430e14i 0.0443833 + 0.0443833i
\(489\) 4.07856e16i 2.98300i
\(490\) 6.14437e15 + 1.86560e15i 0.443916 + 0.134785i
\(491\) 4.72173e15 0.336986 0.168493 0.985703i \(-0.446110\pi\)
0.168493 + 0.985703i \(0.446110\pi\)
\(492\) 8.47433e15 8.47433e15i 0.597468 0.597468i
\(493\) −3.77952e15 3.77952e15i −0.263242 0.263242i
\(494\) 1.71856e16i 1.18250i
\(495\) 4.64501e15 + 8.69559e15i 0.315759 + 0.591110i
\(496\) −3.79016e15 −0.254547
\(497\) −7.35169e15 + 7.35169e15i −0.487808 + 0.487808i
\(498\) −1.17075e16 1.17075e16i −0.767519 0.767519i
\(499\) 1.86387e16i 1.20729i −0.797253 0.603646i \(-0.793714\pi\)
0.797253 0.603646i \(-0.206286\pi\)
\(500\) 1.34372e16 + 1.33393e15i 0.859978 + 0.0853714i
\(501\) 1.05596e16 0.667764
\(502\) −8.71110e15 + 8.71110e15i −0.544315 + 0.544315i
\(503\) −4.21542e15 4.21542e15i −0.260275 0.260275i 0.564890 0.825166i \(-0.308918\pi\)
−0.825166 + 0.564890i \(0.808918\pi\)
\(504\) 4.68096e15i 0.285596i
\(505\) −8.02062e15 + 4.28446e15i −0.483571 + 0.258314i
\(506\) 4.04377e15 0.240926
\(507\) 3.86032e15 3.86032e15i 0.227287 0.227287i
\(508\) −7.42183e15 7.42183e15i −0.431846 0.431846i
\(509\) 7.67307e15i 0.441228i −0.975361 0.220614i \(-0.929194\pi\)
0.975361 0.220614i \(-0.0708061\pi\)
\(510\) −4.87080e15 + 1.60420e16i −0.276808 + 0.911669i
\(511\) −5.11239e15 −0.287143
\(512\) −1.64359e16 + 1.64359e16i −0.912373 + 0.912373i
\(513\) −1.88915e16 1.88915e16i −1.03648 1.03648i
\(514\) 1.24422e16i 0.674713i
\(515\) −2.24451e16 6.81497e15i −1.20304 0.365276i
\(516\) −2.91995e16 −1.54695
\(517\) −8.01951e15 + 8.01951e15i −0.419957 + 0.419957i
\(518\) 2.15163e16 + 2.15163e16i 1.11375 + 1.11375i
\(519\) 4.47533e16i 2.28992i
\(520\) 1.55549e15 + 2.91192e15i 0.0786769 + 0.147285i
\(521\) 2.97878e16 1.48940 0.744701 0.667398i \(-0.232592\pi\)
0.744701 + 0.667398i \(0.232592\pi\)
\(522\) 3.36158e16 3.36158e16i 1.66158 1.66158i
\(523\) −3.43245e15 3.43245e15i −0.167723 0.167723i 0.618255 0.785978i \(-0.287840\pi\)
−0.785978 + 0.618255i \(0.787840\pi\)
\(524\) 7.03342e15i 0.339765i
\(525\) 1.60973e16 2.40644e16i 0.768770 1.14926i
\(526\) 1.81940e16 0.859040
\(527\) 1.41509e15 1.41509e15i 0.0660575 0.0660575i
\(528\) −1.02982e16 1.02982e16i −0.475287 0.475287i
\(529\) 1.64545e16i 0.750843i
\(530\) 2.95534e16 1.57868e16i 1.33337 0.712262i
\(531\) 1.94915e16 0.869518
\(532\) 1.08251e16 1.08251e16i 0.477486 0.477486i
\(533\) 8.38922e15 + 8.38922e15i 0.365896 + 0.365896i
\(534\) 7.35919e16i 3.17382i
\(535\) −4.88398e15 + 1.60854e16i −0.208282 + 0.685976i
\(536\) −5.43731e15 −0.229295
\(537\) 2.30297e16 2.30297e16i 0.960380 0.960380i
\(538\) −3.47675e15 3.47675e15i −0.143377 0.143377i
\(539\) 2.94534e15i 0.120117i
\(540\) −3.12530e16 9.48927e15i −1.26046 0.382710i
\(541\) 6.03588e15 0.240745 0.120372 0.992729i \(-0.461591\pi\)
0.120372 + 0.992729i \(0.461591\pi\)
\(542\) −4.06989e16 + 4.06989e16i −1.60541 + 1.60541i
\(543\) 8.74728e15 + 8.74728e15i 0.341251 + 0.341251i
\(544\) 1.42435e16i 0.549571i
\(545\) −1.56993e16 2.93894e16i −0.599101 1.12153i
\(546\) −4.50469e16 −1.70024
\(547\) 1.37352e16 1.37352e16i 0.512755 0.512755i −0.402615 0.915370i \(-0.631899\pi\)
0.915370 + 0.402615i \(0.131899\pi\)
\(548\) 2.54073e16 + 2.54073e16i 0.938157 + 0.938157i
\(549\) 1.75718e16i 0.641775i
\(550\) −2.59976e15 1.31051e16i −0.0939196 0.473440i
\(551\) −2.44307e16 −0.873024
\(552\) 3.15040e15 3.15040e15i 0.111361 0.111361i
\(553\) 2.82200e15 + 2.82200e15i 0.0986749 + 0.0986749i
\(554\) 2.48946e16i 0.861087i
\(555\) −6.22789e16 + 3.32681e16i −2.13100 + 1.13834i
\(556\) −5.66466e14 −0.0191746
\(557\) −2.30649e15 + 2.30649e15i −0.0772362 + 0.0772362i −0.744670 0.667433i \(-0.767393\pi\)
0.667433 + 0.744670i \(0.267393\pi\)
\(558\) 1.25861e16 + 1.25861e16i 0.416953 + 0.416953i
\(559\) 2.89062e16i 0.947372i
\(560\) −8.13495e15 + 2.67925e16i −0.263771 + 0.868730i
\(561\) 7.68983e15 0.246683
\(562\) 2.83904e16 2.83904e16i 0.901060 0.901060i
\(563\) −1.89176e15 1.89176e15i −0.0594040 0.0594040i 0.676781 0.736185i \(-0.263375\pi\)
−0.736185 + 0.676781i \(0.763375\pi\)
\(564\) 7.95227e16i 2.47068i
\(565\) 5.51206e16 + 1.67362e16i 1.69443 + 0.514476i
\(566\) −9.74204e13 −0.00296314
\(567\) −1.33271e16 + 1.33271e16i −0.401085 + 0.401085i
\(568\) 3.73789e15 + 3.73789e15i 0.111311 + 0.111311i
\(569\) 6.48056e16i 1.90959i 0.297273 + 0.954793i \(0.403923\pi\)
−0.297273 + 0.954793i \(0.596077\pi\)
\(570\) 3.61051e16 + 6.75898e16i 1.05274 + 1.97075i
\(571\) −6.74108e16 −1.94497 −0.972485 0.232967i \(-0.925157\pi\)
−0.972485 + 0.232967i \(0.925157\pi\)
\(572\) −6.81424e15 + 6.81424e15i −0.194555 + 0.194555i
\(573\) 1.19916e16 + 1.19916e16i 0.338803 + 0.338803i
\(574\) 2.27979e16i 0.637417i
\(575\) 1.76954e16 3.51037e15i 0.489615 0.0971283i
\(576\) 4.93267e16 1.35066
\(577\) −2.36489e16 + 2.36489e16i −0.640849 + 0.640849i −0.950764 0.309915i \(-0.899699\pi\)
0.309915 + 0.950764i \(0.399699\pi\)
\(578\) −2.99460e16 2.99460e16i −0.803105 0.803105i
\(579\) 9.58201e16i 2.54323i
\(580\) −2.63442e16 + 1.40725e16i −0.692017 + 0.369662i
\(581\) 1.46008e16 0.379595
\(582\) 3.42142e15 3.42142e15i 0.0880378 0.0880378i
\(583\) −1.08671e16 1.08671e16i −0.276758 0.276758i
\(584\) 2.59934e15i 0.0655218i
\(585\) 1.98814e16 6.54793e16i 0.496033 1.63369i
\(586\) 5.03490e16 1.24338
\(587\) −1.75615e16 + 1.75615e16i −0.429273 + 0.429273i −0.888381 0.459108i \(-0.848169\pi\)
0.459108 + 0.888381i \(0.348169\pi\)
\(588\) 1.46032e16 + 1.46032e16i 0.353333 + 0.353333i
\(589\) 9.14712e15i 0.219075i
\(590\) −2.52761e16 7.67453e15i −0.599236 0.181945i
\(591\) 6.24932e16 1.46659
\(592\) 4.82858e16 4.82858e16i 1.12173 1.12173i
\(593\) 1.59726e16 + 1.59726e16i 0.367322 + 0.367322i 0.866500 0.499177i \(-0.166364\pi\)
−0.499177 + 0.866500i \(0.666364\pi\)
\(594\) 3.23167e16i 0.735712i
\(595\) −6.96598e15 1.30405e16i −0.156993 0.293895i
\(596\) −5.40038e16 −1.20489
\(597\) −3.84375e16 + 3.84375e16i −0.849002 + 0.849002i
\(598\) −1.98479e16 1.98479e16i −0.434018 0.434018i
\(599\) 5.40452e14i 0.0117003i −0.999983 0.00585014i \(-0.998138\pi\)
0.999983 0.00585014i \(-0.00186217\pi\)
\(600\) −1.22353e16 8.18448e15i −0.262245 0.175422i
\(601\) −9.10704e16 −1.93255 −0.966274 0.257515i \(-0.917096\pi\)
−0.966274 + 0.257515i \(0.917096\pi\)
\(602\) 3.92767e16 3.92767e16i 0.825194 0.825194i
\(603\) 7.96952e16 + 7.96952e16i 1.65779 + 1.65779i
\(604\) 7.93579e16i 1.63444i
\(605\) 3.78482e16 2.02178e16i 0.771815 0.412288i
\(606\) −6.30859e16 −1.27379
\(607\) −2.28805e16 + 2.28805e16i −0.457440 + 0.457440i −0.897814 0.440374i \(-0.854846\pi\)
0.440374 + 0.897814i \(0.354846\pi\)
\(608\) −4.60348e16 4.60348e16i −0.911306 0.911306i
\(609\) 6.40378e16i 1.25526i
\(610\) −6.91867e15 + 2.27867e16i −0.134290 + 0.442285i
\(611\) 7.87239e16 1.51307
\(612\) −2.49602e16 + 2.49602e16i −0.475051 + 0.475051i
\(613\) 5.03246e16 + 5.03246e16i 0.948456 + 0.948456i 0.998735 0.0502791i \(-0.0160111\pi\)
−0.0502791 + 0.998735i \(0.516011\pi\)
\(614\) 1.03704e17i 1.93546i
\(615\) −5.06191e16 1.53694e16i −0.935544 0.284057i
\(616\) 2.90976e15 0.0532566
\(617\) 5.26298e16 5.26298e16i 0.953939 0.953939i −0.0450463 0.998985i \(-0.514344\pi\)
0.998985 + 0.0450463i \(0.0143435\pi\)
\(618\) −1.15072e17 1.15072e17i −2.06557 2.06557i
\(619\) 5.70602e16i 1.01435i 0.861842 + 0.507177i \(0.169311\pi\)
−0.861842 + 0.507177i \(0.830689\pi\)
\(620\) −5.26891e15 9.86355e15i −0.0927622 0.173653i
\(621\) −4.36362e16 −0.760846
\(622\) −2.59048e16 + 2.59048e16i −0.447340 + 0.447340i
\(623\) −4.58894e16 4.58894e16i −0.784845 0.784845i
\(624\) 1.01092e17i 1.71242i
\(625\) −2.27530e16 5.50910e16i −0.381731 0.924273i
\(626\) 8.30228e16 1.37959
\(627\) 2.48534e16 2.48534e16i 0.409054 0.409054i
\(628\) 1.83432e16 + 1.83432e16i 0.299031 + 0.299031i
\(629\) 3.60560e16i 0.582202i
\(630\) 1.15985e17 6.19568e16i 1.85506 0.990936i
\(631\) 2.30258e16 0.364786 0.182393 0.983226i \(-0.441616\pi\)
0.182393 + 0.983226i \(0.441616\pi\)
\(632\) 1.43482e15 1.43482e15i 0.0225162 0.0225162i
\(633\) −1.01162e17 1.01162e17i −1.57251 1.57251i
\(634\) 9.54514e16i 1.46976i
\(635\) −1.34605e16 + 4.43323e16i −0.205314 + 0.676204i
\(636\) 1.07759e17 1.62822
\(637\) −1.44565e16 + 1.44565e16i −0.216385 + 0.216385i
\(638\) 2.08961e16 + 2.08961e16i 0.309843 + 0.309843i
\(639\) 1.09573e17i 1.60953i
\(640\) 2.41584e16 + 7.33517e15i 0.351551 + 0.106741i
\(641\) 3.74181e15 0.0539429 0.0269714 0.999636i \(-0.491414\pi\)
0.0269714 + 0.999636i \(0.491414\pi\)
\(642\) −8.24669e16 + 8.24669e16i −1.17779 + 1.17779i
\(643\) 1.66526e16 + 1.66526e16i 0.235622 + 0.235622i 0.815035 0.579412i \(-0.196718\pi\)
−0.579412 + 0.815035i \(0.696718\pi\)
\(644\) 2.50041e16i 0.350506i
\(645\) 6.07290e16 + 1.13686e17i 0.843408 + 1.57888i
\(646\) 3.91307e16 0.538422
\(647\) −1.95135e16 + 1.95135e16i −0.266017 + 0.266017i −0.827493 0.561476i \(-0.810234\pi\)
0.561476 + 0.827493i \(0.310234\pi\)
\(648\) 6.77601e15 + 6.77601e15i 0.0915217 + 0.0915217i
\(649\) 1.21163e16i 0.162144i
\(650\) −5.15632e16 + 7.70839e16i −0.683691 + 1.02208i
\(651\) −2.39765e16 −0.314992
\(652\) 8.22927e16 8.22927e16i 1.07121 1.07121i
\(653\) 1.75698e16 + 1.75698e16i 0.226615 + 0.226615i 0.811277 0.584662i \(-0.198773\pi\)
−0.584662 + 0.811277i \(0.698773\pi\)
\(654\) 2.31162e17i 2.95426i
\(655\) 2.73842e16 1.46281e16i 0.346778 0.185242i
\(656\) 5.11620e16 0.641984
\(657\) 3.80988e16 3.80988e16i 0.473717 0.473717i
\(658\) 1.06967e17 + 1.06967e17i 1.31794 + 1.31794i
\(659\) 3.81081e16i 0.465269i 0.972564 + 0.232635i \(0.0747346\pi\)
−0.972564 + 0.232635i \(0.925265\pi\)
\(660\) 1.24840e16 4.11160e16i 0.151039 0.497448i
\(661\) −8.15161e16 −0.977315 −0.488657 0.872476i \(-0.662513\pi\)
−0.488657 + 0.872476i \(0.662513\pi\)
\(662\) −7.08606e16 + 7.08606e16i −0.841893 + 0.841893i
\(663\) −3.77438e16 3.77438e16i −0.444390 0.444390i
\(664\) 7.42363e15i 0.0866180i
\(665\) −6.46606e16 1.96328e16i −0.747670 0.227013i
\(666\) −3.20689e17 −3.67484
\(667\) −2.82154e16 + 2.82154e16i −0.320429 + 0.320429i
\(668\) −2.13061e16 2.13061e16i −0.239798 0.239798i
\(669\) 7.45774e16i 0.831861i
\(670\) −7.19677e16 1.34726e17i −0.795590 1.48937i
\(671\) 1.09229e16 0.119675
\(672\) −1.20667e17 + 1.20667e17i −1.31030 + 1.31030i
\(673\) −7.90609e16 7.90609e16i −0.850886 0.850886i 0.139356 0.990242i \(-0.455497\pi\)
−0.990242 + 0.139356i \(0.955497\pi\)
\(674\) 4.39339e16i 0.468641i
\(675\) 2.80539e16 + 1.41417e17i 0.296600 + 1.49513i
\(676\) −1.55779e16 −0.163240
\(677\) 2.97497e16 2.97497e16i 0.308995 0.308995i −0.535525 0.844519i \(-0.679886\pi\)
0.844519 + 0.535525i \(0.179886\pi\)
\(678\) 2.82594e17 + 2.82594e17i 2.90927 + 2.90927i
\(679\) 4.26697e15i 0.0435412i
\(680\) −6.63030e15 + 3.54178e15i −0.0670625 + 0.0358235i
\(681\) 2.74791e17 2.75499
\(682\) −7.82375e15 + 7.82375e15i −0.0777515 + 0.0777515i
\(683\) −5.51641e15 5.51641e15i −0.0543415 0.0543415i 0.679414 0.733755i \(-0.262234\pi\)
−0.733755 + 0.679414i \(0.762234\pi\)
\(684\) 1.61342e17i 1.57547i
\(685\) 4.60797e16 1.51764e17i 0.446032 1.46901i
\(686\) −1.54906e17 −1.48636
\(687\) 1.86337e17 1.86337e17i 1.77238 1.77238i
\(688\) −8.81430e16 8.81430e16i −0.831107 0.831107i
\(689\) 1.06677e17i 0.997138i
\(690\) 1.19759e17 + 3.63622e16i 1.10972 + 0.336942i
\(691\) −9.43544e16 −0.866750 −0.433375 0.901214i \(-0.642677\pi\)
−0.433375 + 0.901214i \(0.642677\pi\)
\(692\) 9.02983e16 9.02983e16i 0.822324 0.822324i
\(693\) −4.26487e16 4.26487e16i −0.385041 0.385041i
\(694\) 7.05912e16i 0.631821i
\(695\) 1.17813e15 + 2.20550e15i 0.0104541 + 0.0195703i
\(696\) 3.25594e16 0.286431
\(697\) −1.91018e16 + 1.91018e16i −0.166601 + 0.166601i
\(698\) 6.08478e16 + 6.08478e16i 0.526153 + 0.526153i
\(699\) 5.83061e16i 0.499863i
\(700\) −8.10339e16 + 1.60752e16i −0.688776 + 0.136637i
\(701\) −6.88565e16 −0.580279 −0.290140 0.956984i \(-0.593702\pi\)
−0.290140 + 0.956984i \(0.593702\pi\)
\(702\) 1.58619e17 1.58619e17i 1.32536 1.32536i
\(703\) 1.16532e17 + 1.16532e17i 0.965416 + 0.965416i
\(704\) 3.06623e16i 0.251866i
\(705\) −3.09616e17 + 1.65391e17i −2.52167 + 1.34703i
\(706\) 2.08962e17 1.68748
\(707\) 3.93382e16 3.93382e16i 0.314991 0.314991i
\(708\) −6.00733e16 6.00733e16i −0.476960 0.476960i
\(709\) 1.81196e17i 1.42650i −0.700909 0.713251i \(-0.747222\pi\)
0.700909 0.713251i \(-0.252778\pi\)
\(710\) −4.31430e16 + 1.42092e17i −0.336791 + 1.10922i
\(711\) −4.20605e16 −0.325580
\(712\) −2.33320e16 + 2.33320e16i −0.179090 + 0.179090i
\(713\) −1.05642e16 1.05642e16i −0.0804078 0.0804078i
\(714\) 1.02570e17i 0.774158i
\(715\) 4.07030e16 + 1.23586e16i 0.304643 + 0.0924980i
\(716\) −9.29338e16 −0.689756
\(717\) −2.44205e17 + 2.44205e17i −1.79738 + 1.79738i
\(718\) −6.30087e16 6.30087e16i −0.459890 0.459890i
\(719\) 5.00769e16i 0.362464i −0.983440 0.181232i \(-0.941992\pi\)
0.983440 0.181232i \(-0.0580084\pi\)
\(720\) −1.39041e17 2.60288e17i −0.998037 1.86835i
\(721\) 1.43510e17 1.02158
\(722\) −1.02889e16 + 1.02889e16i −0.0726353 + 0.0726353i
\(723\) 1.02793e16 + 1.02793e16i 0.0719672 + 0.0719672i
\(724\) 3.52986e16i 0.245090i
\(725\) 1.09581e17 + 7.33013e16i 0.754583 + 0.504759i
\(726\) 2.97694e17 2.03306
\(727\) 9.59203e16 9.59203e16i 0.649687 0.649687i −0.303231 0.952917i \(-0.598065\pi\)
0.952917 + 0.303231i \(0.0980652\pi\)
\(728\) −1.42819e16 1.42819e16i −0.0959397 0.0959397i
\(729\) 1.90686e17i 1.27044i
\(730\) −6.44064e16 + 3.44046e16i −0.425590 + 0.227342i
\(731\) 6.58181e16 0.431361
\(732\) −5.41567e16 + 5.41567e16i −0.352035 + 0.352035i
\(733\) −4.57264e16 4.57264e16i −0.294811 0.294811i 0.544166 0.838977i \(-0.316846\pi\)
−0.838977 + 0.544166i \(0.816846\pi\)
\(734\) 1.87962e17i 1.20197i
\(735\) 2.64849e16 8.72283e16i 0.167987 0.553265i
\(736\) −1.06333e17 −0.668959
\(737\) −4.95399e16 + 4.95399e16i −0.309136 + 0.309136i
\(738\) −1.69895e17 1.69895e17i −1.05158 1.05158i
\(739\) 1.18384e17i 0.726818i 0.931630 + 0.363409i \(0.118387\pi\)
−0.931630 + 0.363409i \(0.881613\pi\)
\(740\) 1.92784e17 + 5.85347e16i 1.17404 + 0.356470i
\(741\) −2.43975e17 −1.47379
\(742\) −1.44949e17 + 1.44949e17i −0.868542 + 0.868542i
\(743\) −8.36175e16 8.36175e16i −0.497009 0.497009i 0.413497 0.910506i \(-0.364307\pi\)
−0.910506 + 0.413497i \(0.864307\pi\)
\(744\) 1.21906e16i 0.0718765i
\(745\) 1.12317e17 + 2.10260e17i 0.656912 + 1.22976i
\(746\) −5.94545e16 −0.344947
\(747\) −1.08809e17 + 1.08809e17i −0.626240 + 0.626240i
\(748\) −1.55157e16 1.55157e16i −0.0885853 0.0885853i
\(749\) 1.02847e17i 0.582507i
\(750\) 4.08498e16 4.11495e17i 0.229521 2.31205i
\(751\) −5.34118e16 −0.297713 −0.148856 0.988859i \(-0.547559\pi\)
−0.148856 + 0.988859i \(0.547559\pi\)
\(752\) 2.40051e17 2.40051e17i 1.32738 1.32738i
\(753\) 1.23667e17 + 1.23667e17i 0.678396 + 0.678396i
\(754\) 2.05128e17i 1.11634i
\(755\) 3.08975e17 1.65048e17i 1.66817 0.891105i
\(756\) 1.99826e17 1.07034
\(757\) 8.74072e16 8.74072e16i 0.464485 0.464485i −0.435637 0.900122i \(-0.643477\pi\)
0.900122 + 0.435637i \(0.143477\pi\)
\(758\) 4.80251e16 + 4.80251e16i 0.253194 + 0.253194i
\(759\) 5.74072e16i 0.300273i
\(760\) −9.98207e15 + 3.28760e16i −0.0518011 + 0.170607i
\(761\) −1.69256e17 −0.871439 −0.435720 0.900083i \(-0.643506\pi\)
−0.435720 + 0.900083i \(0.643506\pi\)
\(762\) −2.27284e17 + 2.27284e17i −1.16102 + 1.16102i
\(763\) 1.44144e17 + 1.44144e17i 0.730551 + 0.730551i
\(764\) 4.83905e16i 0.243332i
\(765\) 1.49093e17 + 4.52689e16i 0.743857 + 0.225856i
\(766\) −3.17818e16 −0.157328
\(767\) 5.94699e16 5.94699e16i 0.292096 0.292096i
\(768\) 2.99770e17 + 2.99770e17i 1.46090 + 1.46090i
\(769\) 1.92021e17i 0.928521i −0.885699 0.464260i \(-0.846320\pi\)
0.885699 0.464260i \(-0.153680\pi\)
\(770\) 3.85134e16 + 7.20981e16i 0.184785 + 0.345923i
\(771\) −1.76636e17 −0.840915
\(772\) −1.93335e17 + 1.93335e17i −0.913288 + 0.913288i
\(773\) −1.91520e17 1.91520e17i −0.897714 0.897714i 0.0975192 0.995234i \(-0.468909\pi\)
−0.995234 + 0.0975192i \(0.968909\pi\)
\(774\) 5.85399e17i 2.72274i
\(775\) −2.74448e16 + 4.10283e16i −0.126663 + 0.189354i
\(776\) 2.16949e15 0.00993546
\(777\) 3.05455e17 3.05455e17i 1.38810 1.38810i
\(778\) −7.93803e16 7.93803e16i −0.357961 0.357961i
\(779\) 1.23474e17i 0.552522i
\(780\) −2.63083e17 + 1.40534e17i −1.16822 + 0.624041i
\(781\) 6.81125e16 0.300138
\(782\) 4.51927e16 4.51927e16i 0.197619 0.197619i
\(783\) −2.25490e17 2.25490e17i −0.978489 0.978489i
\(784\) 8.81638e16i 0.379659i
\(785\) 3.32679e16 1.09568e17i 0.142170 0.468237i
\(786\) 2.15389e17 0.913458
\(787\) −1.82035e17 + 1.82035e17i −0.766138 + 0.766138i −0.977424 0.211287i \(-0.932235\pi\)
0.211287 + 0.977424i \(0.432235\pi\)
\(788\) −1.26092e17 1.26092e17i −0.526659 0.526659i
\(789\) 2.58290e17i 1.07065i
\(790\) 5.45430e16 + 1.65608e16i 0.224376 + 0.0681268i
\(791\) −3.52431e17 −1.43885
\(792\) −2.16843e16 + 2.16843e16i −0.0878605 + 0.0878605i
\(793\) −5.36127e16 5.36127e16i −0.215590 0.215590i
\(794\) 8.80613e16i 0.351449i
\(795\) −2.24117e17 4.19554e17i −0.887713 1.66182i
\(796\) 1.55110e17 0.609763
\(797\) −6.96241e16 + 6.96241e16i −0.271650 + 0.271650i −0.829764 0.558114i \(-0.811525\pi\)
0.558114 + 0.829764i \(0.311525\pi\)
\(798\) −3.31503e17 3.31503e17i −1.28372 1.28372i
\(799\) 1.79251e17i 0.688937i
\(800\) 6.83617e16 + 3.44605e17i 0.260779 + 1.31456i
\(801\) 6.83958e17 2.58961
\(802\) −2.54938e17 + 2.54938e17i −0.958052 + 0.958052i
\(803\) 2.36828e16 + 2.36828e16i 0.0883365 + 0.0883365i
\(804\) 4.91245e17i 1.81870i
\(805\) −9.73518e16 + 5.20034e16i −0.357741 + 0.191098i
\(806\) 7.68022e16 0.280132
\(807\) −4.93575e16 + 4.93575e16i −0.178695 + 0.178695i
\(808\) −2.00011e16 2.00011e16i −0.0718763 0.0718763i
\(809\) 4.08047e17i 1.45552i 0.685829 + 0.727762i \(0.259440\pi\)
−0.685829 + 0.727762i \(0.740560\pi\)
\(810\) −7.82093e16 + 2.57583e17i −0.276916 + 0.912025i
\(811\) 2.99530e17 1.05272 0.526362 0.850260i \(-0.323556\pi\)
0.526362 + 0.850260i \(0.323556\pi\)
\(812\) 1.29209e17 1.29209e17i 0.450770 0.450770i
\(813\) 5.77781e17 + 5.77781e17i 2.00087 + 2.00087i
\(814\) 1.99346e17i 0.685268i
\(815\) −4.91553e17 1.49249e17i −1.67735 0.509292i
\(816\) −2.30182e17 −0.779706
\(817\) 2.12723e17 2.12723e17i 0.715290 0.715290i
\(818\) 4.55663e16 + 4.55663e16i 0.152098 + 0.152098i
\(819\) 4.18663e17i 1.38727i
\(820\) 7.11231e16 + 1.33144e17i 0.233952 + 0.437965i
\(821\) −2.94278e17 −0.960945 −0.480473 0.877010i \(-0.659535\pi\)
−0.480473 + 0.877010i \(0.659535\pi\)
\(822\) 7.78066e17 7.78066e17i 2.52223 2.52223i
\(823\) 3.30432e17 + 3.30432e17i 1.06337 + 1.06337i 0.997852 + 0.0655141i \(0.0208687\pi\)
0.0655141 + 0.997852i \(0.479131\pi\)
\(824\) 7.29662e16i 0.233109i
\(825\) −1.86047e17 + 3.69074e16i −0.590062 + 0.117055i
\(826\) 1.61611e17 0.508851
\(827\) −1.15770e17 + 1.15770e17i −0.361880 + 0.361880i −0.864505 0.502625i \(-0.832368\pi\)
0.502625 + 0.864505i \(0.332368\pi\)
\(828\) 1.86337e17 + 1.86337e17i 0.578251 + 0.578251i
\(829\) 5.47006e17i 1.68525i −0.538500 0.842626i \(-0.681009\pi\)
0.538500 0.842626i \(-0.318991\pi\)
\(830\) 1.83943e17 9.82585e16i 0.562619 0.300540i
\(831\) −3.53416e17 −1.07320
\(832\) 1.50499e17 1.50499e17i 0.453726 0.453726i
\(833\) −3.29168e16 3.29168e16i −0.0985253 0.0985253i
\(834\) 1.73473e16i 0.0515507i
\(835\) −3.86416e16 + 1.27266e17i −0.114008 + 0.375486i
\(836\) −1.00293e17 −0.293787
\(837\) 8.44259e16 8.44259e16i 0.245540 0.245540i
\(838\) −1.17082e17 1.17082e17i −0.338086 0.338086i
\(839\) 2.08823e17i 0.598697i −0.954144 0.299348i \(-0.903231\pi\)
0.954144 0.299348i \(-0.0967693\pi\)
\(840\) 8.61747e16 + 2.61650e16i 0.245304 + 0.0744811i
\(841\) 6.22088e16 0.175823
\(842\) −4.75806e16 + 4.75806e16i −0.133523 + 0.133523i
\(843\) −4.03044e17 4.03044e17i −1.12302 1.12302i
\(844\) 4.08226e17i 1.12939i
\(845\) 3.23988e16 + 6.06514e16i 0.0889996 + 0.166610i
\(846\) −1.59429e18 −4.34856
\(847\) −1.85632e17 + 1.85632e17i −0.502750 + 0.502750i
\(848\) 3.25287e17 + 3.25287e17i 0.874766 + 0.874766i
\(849\) 1.38303e15i 0.00369304i
\(850\) −1.75516e17 1.17407e17i −0.465376 0.311301i
\(851\) 2.69170e17 0.708679
\(852\) −3.37707e17 + 3.37707e17i −0.882881 + 0.882881i
\(853\) 4.48811e16 + 4.48811e16i 0.116512 + 0.116512i 0.762959 0.646447i \(-0.223746\pi\)
−0.646447 + 0.762959i \(0.723746\pi\)
\(854\) 1.45694e17i 0.375573i
\(855\) 6.28175e17 3.35558e17i 1.60799 0.858957i
\(856\) −5.22915e16 −0.132919
\(857\) −1.35142e17 + 1.35142e17i −0.341118 + 0.341118i −0.856788 0.515669i \(-0.827543\pi\)
0.515669 + 0.856788i \(0.327543\pi\)
\(858\) 2.08677e17 + 2.08677e17i 0.523060 + 0.523060i
\(859\) 5.20411e17i 1.29535i 0.761916 + 0.647676i \(0.224259\pi\)
−0.761916 + 0.647676i \(0.775741\pi\)
\(860\) 1.06852e17 3.51916e17i 0.264113 0.869859i
\(861\) 3.23650e17 0.794431
\(862\) −7.65901e16 + 7.65901e16i −0.186693 + 0.186693i
\(863\) 3.52137e16 + 3.52137e16i 0.0852407 + 0.0852407i 0.748441 0.663201i \(-0.230802\pi\)
−0.663201 + 0.748441i \(0.730802\pi\)
\(864\) 8.49781e17i 2.04279i
\(865\) −5.39372e17 1.63769e17i −1.28763 0.390961i
\(866\) 4.94446e17 1.17223
\(867\) −4.25128e17 + 4.25128e17i −1.00093 + 1.00093i
\(868\) 4.83771e16 + 4.83771e16i 0.113115 + 0.113115i
\(869\) 2.61455e16i 0.0607126i
\(870\) 4.30953e17 + 8.06755e17i 0.993834 + 1.86049i
\(871\) 4.86310e17 1.11379
\(872\) 7.32887e16 7.32887e16i 0.166701 0.166701i
\(873\) −3.17985e16 3.17985e16i −0.0718325 0.0718325i
\(874\) 2.92124e17i 0.655389i
\(875\) 2.31122e17 + 2.82067e17i 0.514982 + 0.628498i
\(876\) −2.34842e17 −0.519699
\(877\) −1.54663e17 + 1.54663e17i −0.339930 + 0.339930i −0.856341 0.516411i \(-0.827268\pi\)
0.516411 + 0.856341i \(0.327268\pi\)
\(878\) −1.27029e17 1.27029e17i −0.277291 0.277291i
\(879\) 7.14778e17i 1.54967i
\(880\) 1.61799e17 8.64300e16i 0.348402 0.186109i
\(881\) 7.40343e16 0.158335 0.0791676 0.996861i \(-0.474774\pi\)
0.0791676 + 0.996861i \(0.474774\pi\)
\(882\) 2.92769e17 2.92769e17i 0.621889 0.621889i
\(883\) −3.54003e17 3.54003e17i −0.746866 0.746866i 0.227024 0.973889i \(-0.427101\pi\)
−0.973889 + 0.227024i \(0.927101\pi\)
\(884\) 1.52311e17i 0.319166i
\(885\) −1.08951e17 + 3.58832e17i −0.226763 + 0.746846i
\(886\) 6.00895e16 0.124221
\(887\) 5.57483e17 5.57483e17i 1.14469 1.14469i 0.157114 0.987580i \(-0.449781\pi\)
0.987580 0.157114i \(-0.0502191\pi\)
\(888\) −1.55305e17 1.55305e17i −0.316744 0.316744i
\(889\) 2.83453e17i 0.574209i
\(890\) −8.86939e17 2.69299e17i −1.78465 0.541870i
\(891\) 1.23474e17 0.246779
\(892\) −1.50474e17 + 1.50474e17i −0.298726 + 0.298726i
\(893\) 5.79335e17 + 5.79335e17i 1.14241 + 1.14241i
\(894\) 1.65380e18i 3.23934i
\(895\) 1.93283e17 + 3.61831e17i 0.376059 + 0.703993i
\(896\) −1.54465e17 −0.298525
\(897\) −2.81770e17 + 2.81770e17i −0.540929 + 0.540929i
\(898\) −4.36473e17 4.36473e17i −0.832337 0.832337i
\(899\) 1.09181e17i 0.206817i
\(900\) 4.84087e17 7.23681e17i 0.910896 1.36173i
\(901\) −2.42898e17 −0.454021
\(902\) 1.05610e17 1.05610e17i 0.196094 0.196094i
\(903\) −5.57590e17 5.57590e17i −1.02846 1.02846i
\(904\) 1.79190e17i 0.328324i
\(905\) −1.37433e17 + 7.34139e16i −0.250149 + 0.133625i
\(906\) 2.43023e18 4.39418
\(907\) 3.40011e17 3.40011e17i 0.610730 0.610730i −0.332406 0.943136i \(-0.607860\pi\)
0.943136 + 0.332406i \(0.107860\pi\)
\(908\) −5.54443e17 5.54443e17i −0.989331 0.989331i
\(909\) 5.86316e17i 1.03932i
\(910\) 1.64843e17 5.42911e17i 0.290283 0.956050i
\(911\) 5.97092e17 1.04455 0.522277 0.852776i \(-0.325083\pi\)
0.522277 + 0.852776i \(0.325083\pi\)
\(912\) −7.43945e17 + 7.43945e17i −1.29292 + 1.29292i
\(913\) −6.76375e16 6.76375e16i −0.116778 0.116778i
\(914\) 8.67902e17i 1.48865i
\(915\) 3.23490e17 + 9.82207e16i 0.551232 + 0.167370i
\(916\) −7.51939e17 −1.27295
\(917\) −1.34309e17 + 1.34309e17i −0.225886 + 0.225886i
\(918\) 3.61168e17 + 3.61168e17i 0.603466 + 0.603466i
\(919\) 7.95352e16i 0.132028i −0.997819 0.0660140i \(-0.978972\pi\)
0.997819 0.0660140i \(-0.0210282\pi\)
\(920\) 2.64406e16 + 4.94975e16i 0.0436058 + 0.0816312i
\(921\) −1.47223e18 −2.41222
\(922\) 8.74337e17 8.74337e17i 1.42329 1.42329i
\(923\) −3.34315e17 3.34315e17i −0.540687 0.540687i
\(924\) 2.62888e17i 0.422415i
\(925\) −1.73051e17 8.72333e17i −0.276263 1.39262i
\(926\) −1.52038e18 −2.41149
\(927\) −1.06947e18 + 1.06947e18i −1.68535 + 1.68535i
\(928\) −5.49473e17 5.49473e17i −0.860318 0.860318i
\(929\) 2.12697e17i 0.330877i −0.986220 0.165439i \(-0.947096\pi\)
0.986220 0.165439i \(-0.0529040\pi\)
\(930\) −3.02058e17 + 1.61353e17i −0.466867 + 0.249391i
\(931\) −2.12773e17 −0.326752
\(932\) 1.17644e17 1.17644e17i 0.179504 0.179504i
\(933\) 3.67756e17 + 3.67756e17i 0.557533 + 0.557533i
\(934\) 1.40594e18i 2.11781i
\(935\) −2.81399e16 + 9.26788e16i −0.0421165 + 0.138711i
\(936\) 2.12865e17 0.316555
\(937\) 8.07752e17 8.07752e17i 1.19355 1.19355i 0.217485 0.976064i \(-0.430215\pi\)
0.976064 0.217485i \(-0.0697855\pi\)
\(938\) 6.60780e17 + 6.60780e17i 0.970152 + 0.970152i
\(939\) 1.17863e18i 1.71943i
\(940\) 9.58417e17 + 2.91002e17i 1.38927 + 0.421822i
\(941\) 6.87254e17 0.989873 0.494936 0.868929i \(-0.335191\pi\)
0.494936 + 0.868929i \(0.335191\pi\)
\(942\) 5.61735e17 5.61735e17i 0.803944 0.803944i
\(943\) 1.42602e17 + 1.42602e17i 0.202794 + 0.202794i
\(944\) 3.62680e17i 0.512497i
\(945\) −4.15597e17 7.78009e17i −0.583554 1.09243i
\(946\) −3.63894e17 −0.507724
\(947\) −4.36393e17 + 4.36393e17i −0.605031 + 0.605031i −0.941643 0.336612i \(-0.890719\pi\)
0.336612 + 0.941643i \(0.390719\pi\)
\(948\) 1.29631e17 + 1.29631e17i 0.178591 + 0.178591i
\(949\) 2.32484e17i 0.318269i
\(950\) −9.46723e17 + 1.87808e17i −1.28790 + 0.255489i
\(951\) 1.35507e18 1.83181
\(952\) 3.25192e16 3.25192e16i 0.0436836 0.0436836i
\(953\) −4.05844e16 4.05844e16i −0.0541753 0.0541753i 0.679500 0.733675i \(-0.262197\pi\)
−0.733675 + 0.679500i \(0.762197\pi\)
\(954\) 2.16039e18i 2.86577i
\(955\) −1.88405e17 + 1.00642e17i −0.248355 + 0.132666i
\(956\) 9.85462e17 1.29090
\(957\) 2.96651e17 2.96651e17i 0.386167 0.386167i
\(958\) 1.25215e18 + 1.25215e18i 1.61980 + 1.61980i
\(959\) 9.70350e17i 1.24743i
\(960\) −2.75720e17 + 9.08086e17i −0.352242 + 1.16011i
\(961\) −7.46784e17 −0.948102
\(962\) −9.78443e17 + 9.78443e17i −1.23448 + 1.23448i
\(963\) 7.66442e17 + 7.66442e17i 0.960996 + 0.960996i
\(964\) 4.14810e16i 0.0516876i
\(965\) 1.15484e18 + 3.50641e17i 1.43007 + 0.434209i
\(966\) −7.65717e17 −0.942336
\(967\) −2.16577e17 + 2.16577e17i −0.264883 + 0.264883i −0.827034 0.562152i \(-0.809974\pi\)
0.562152 + 0.827034i \(0.309974\pi\)
\(968\) 9.43825e16 + 9.43825e16i 0.114720 + 0.114720i
\(969\) 5.55518e17i 0.671051i
\(970\) 2.87152e16 + 5.37557e16i 0.0344732 + 0.0645348i
\(971\) 1.15067e18 1.37289 0.686445 0.727181i \(-0.259170\pi\)
0.686445 + 0.727181i \(0.259170\pi\)
\(972\) 1.73333e17 1.73333e17i 0.205534 0.205534i
\(973\) −1.08172e16 1.08172e16i −0.0127478 0.0127478i
\(974\) 1.47833e18i 1.73149i
\(975\) 1.09432e18 + 7.32016e17i 1.27384 + 0.852105i
\(976\) −3.26960e17 −0.378264
\(977\) −8.74046e17 + 8.74046e17i −1.00500 + 1.00500i −0.00501491 + 0.999987i \(0.501596\pi\)
−0.999987 + 0.00501491i \(0.998404\pi\)
\(978\) −2.52010e18 2.52010e18i −2.87995 2.87995i
\(979\) 4.25160e17i 0.482899i
\(980\) −2.29438e17 + 1.22561e17i −0.259006 + 0.138356i
\(981\) −2.14840e18 −2.41047
\(982\) −2.91752e17 + 2.91752e17i −0.325345 + 0.325345i
\(983\) −1.16627e18 1.16627e18i −1.29264 1.29264i −0.933149 0.359490i \(-0.882951\pi\)
−0.359490 0.933149i \(-0.617049\pi\)
\(984\) 1.64556e17i 0.181277i
\(985\) −2.28685e17 + 7.53176e17i −0.250392 + 0.824667i
\(986\) 4.67066e17 0.508296
\(987\) 1.51855e18 1.51855e18i 1.64258 1.64258i
\(988\) 4.92265e17 + 4.92265e17i 0.529246 + 0.529246i
\(989\) 4.91354e17i 0.525070i
\(990\) −8.24304e17 2.50282e17i −0.875540 0.265838i
\(991\) −1.00175e18 −1.05759 −0.528793 0.848751i \(-0.677355\pi\)
−0.528793 + 0.848751i \(0.677355\pi\)
\(992\) 2.05729e17 2.05729e17i 0.215887 0.215887i
\(993\) 1.00597e18 + 1.00597e18i 1.04928 + 1.04928i
\(994\) 9.08509e17i 0.941913i
\(995\) −3.22597e17 6.03910e17i −0.332446 0.622348i
\(996\) 6.70703e17 0.687027
\(997\) 8.25301e17 8.25301e17i 0.840314 0.840314i −0.148585 0.988900i \(-0.547472\pi\)
0.988900 + 0.148585i \(0.0474720\pi\)
\(998\) 1.15167e18 + 1.15167e18i 1.16559 + 1.16559i
\(999\) 2.15113e18i 2.16409i
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.3.1 yes 10
3.2 odd 2 45.13.g.a.28.5 10
4.3 odd 2 80.13.p.c.33.1 10
5.2 odd 4 inner 5.13.c.a.2.1 10
5.3 odd 4 25.13.c.b.7.5 10
5.4 even 2 25.13.c.b.18.5 10
15.2 even 4 45.13.g.a.37.5 10
20.7 even 4 80.13.p.c.17.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5.13.c.a.2.1 10 5.2 odd 4 inner
5.13.c.a.3.1 yes 10 1.1 even 1 trivial
25.13.c.b.7.5 10 5.3 odd 4
25.13.c.b.18.5 10 5.4 even 2
45.13.g.a.28.5 10 3.2 odd 2
45.13.g.a.37.5 10 15.2 even 4
80.13.p.c.17.1 10 20.7 even 4
80.13.p.c.33.1 10 4.3 odd 2