LMFDB - Embedded newform 5.14.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,14,Mod(1,5)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 14, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	5.a (trivial)

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:	yes
Analytic conductor:	$5.36154644760$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{499}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 499 $ x^2 - 499
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-22.3383$ of defining polynomial
Character	$\chi$	$=$	5.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-129.353 q^{2} +1462.24 q^{3} +8540.26 q^{4} -15625.0 q^{5} -189145. q^{6} -454332. q^{7} -45048.4 q^{8} +543819. q^{9} +O(q^{10})$	\(q-129.353 q^{2} +1462.24 q^{3} +8540.26 q^{4} -15625.0 q^{5} -189145. q^{6} -454332. q^{7} -45048.4 q^{8} +543819. q^{9} +2.02114e6 q^{10} -8.29247e6 q^{11} +1.24879e7 q^{12} -8.65436e6 q^{13} +5.87693e7 q^{14} -2.28475e7 q^{15} -6.41346e7 q^{16} +9.15414e7 q^{17} -7.03448e7 q^{18} -2.26390e8 q^{19} -1.33442e8 q^{20} -6.64342e8 q^{21} +1.07266e9 q^{22} +1.16161e9 q^{23} -6.58715e7 q^{24} +2.44141e8 q^{25} +1.11947e9 q^{26} -1.53609e9 q^{27} -3.88011e9 q^{28} -2.27916e9 q^{29} +2.95540e9 q^{30} +2.87630e9 q^{31} +8.66506e9 q^{32} -1.21256e10 q^{33} -1.18412e10 q^{34} +7.09894e9 q^{35} +4.64436e9 q^{36} -6.89036e9 q^{37} +2.92843e10 q^{38} -1.26547e10 q^{39} +7.03881e8 q^{40} +1.94638e9 q^{41} +8.59347e10 q^{42} -2.23125e10 q^{43} -7.08199e10 q^{44} -8.49718e9 q^{45} -1.50258e11 q^{46} +7.41696e10 q^{47} -9.37802e10 q^{48} +1.09528e11 q^{49} -3.15804e10 q^{50} +1.33855e11 q^{51} -7.39105e10 q^{52} +5.95731e10 q^{53} +1.98698e11 q^{54} +1.29570e11 q^{55} +2.04669e10 q^{56} -3.31036e11 q^{57} +2.94817e11 q^{58} -1.27313e11 q^{59} -1.95123e11 q^{60} -1.48099e9 q^{61} -3.72058e11 q^{62} -2.47074e11 q^{63} -5.95462e11 q^{64} +1.35224e11 q^{65} +1.56848e12 q^{66} -1.18465e12 q^{67} +7.81787e11 q^{68} +1.69855e12 q^{69} -9.18270e11 q^{70} -1.21601e12 q^{71} -2.44982e10 q^{72} -9.43614e11 q^{73} +8.91290e11 q^{74} +3.56992e11 q^{75} -1.93343e12 q^{76} +3.76754e12 q^{77} +1.63693e12 q^{78} +1.30732e12 q^{79} +1.00210e12 q^{80} -3.11315e12 q^{81} -2.51771e11 q^{82} -3.10115e12 q^{83} -5.67365e12 q^{84} -1.43033e12 q^{85} +2.88620e12 q^{86} -3.33267e12 q^{87} +3.73562e11 q^{88} +3.81172e11 q^{89} +1.09914e12 q^{90} +3.93195e12 q^{91} +9.92045e12 q^{92} +4.20583e12 q^{93} -9.59407e12 q^{94} +3.53734e12 q^{95} +1.26704e13 q^{96} +6.84151e12 q^{97} -1.41679e13 q^{98} -4.50961e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 80 q^{2} + 780 q^{3} + 2784 q^{4} - 31250 q^{5} - 222816 q^{6} - 616300 q^{7} - 733440 q^{8} - 585054 q^{9}+O(q^{10}) $ 2 * q - 80 * q^2 + 780 * q^3 + 2784 * q^4 - 31250 * q^5 - 222816 * q^6 - 616300 * q^7 - 733440 * q^8 - 585054 * q^9	\( 2 q - 80 q^{2} + 780 q^{3} + 2784 q^{4} - 31250 q^{5} - 222816 q^{6} - 616300 q^{7} - 733440 q^{8} - 585054 q^{9} + 1250000 q^{10} - 2467136 q^{11} + 16415040 q^{12} + 6517860 q^{13} + 50775648 q^{14} - 12187500 q^{15} - 50953728 q^{16} + 633460 q^{17} - 126058320 q^{18} - 374063400 q^{19} - 43500000 q^{20} - 553840776 q^{21} + 1360157440 q^{22} + 621982140 q^{23} + 403776000 q^{24} + 488281250 q^{25} + 1868267104 q^{26} + 321782760 q^{27} - 2947781440 q^{28} - 7795134100 q^{29} + 3481500000 q^{30} - 4957819816 q^{31} + 14954885120 q^{32} - 16099847040 q^{33} - 16327772192 q^{34} + 9629687500 q^{35} + 11142443232 q^{36} + 21833071780 q^{37} + 21996120640 q^{38} - 23005812648 q^{39} + 11460000000 q^{40} + 5565813644 q^{41} + 91388324160 q^{42} - 52510877700 q^{43} - 104352013312 q^{44} + 9141468750 q^{45} - 176890366176 q^{46} + 92855886340 q^{47} - 102772700160 q^{48} + 38873112314 q^{49} - 19531250000 q^{50} + 195876254904 q^{51} - 161245659200 q^{52} + 266248876180 q^{53} + 290389752000 q^{54} + 38549000000 q^{55} + 131964403200 q^{56} - 230287741680 q^{57} + 22585283360 q^{58} + 253501607800 q^{59} - 256485000000 q^{60} - 377459239836 q^{61} - 758697351360 q^{62} - 64232955180 q^{63} - 393017368576 q^{64} - 101841562500 q^{65} + 1372339327488 q^{66} - 2375782313740 q^{67} + 1305076479680 q^{68} + 2066706001512 q^{69} - 793369500000 q^{70} - 556190102776 q^{71} + 752608730880 q^{72} - 556465382460 q^{73} + 2308883896928 q^{74} + 190429687500 q^{75} - 1083383024000 q^{76} + 2824016150400 q^{77} + 1126072161600 q^{78} - 2408230567600 q^{79} + 796152000000 q^{80} - 2580872423958 q^{81} - 73140129760 q^{82} - 3898295602980 q^{83} - 6309721809792 q^{84} - 9897812500 q^{85} + 1395814341664 q^{86} + 430538668680 q^{87} - 3636551086080 q^{88} + 106847675700 q^{89} + 1969661250000 q^{90} + 1474535181544 q^{91} + 13026685584960 q^{92} + 9550571999760 q^{93} - 8671844110112 q^{94} + 5844740625000 q^{95} + 8379224039424 q^{96} + 18744409451140 q^{97} - 17654928754960 q^{98} - 11085674027328 q^{99}+O(q^{100}) \) 2 * q - 80 * q^2 + 780 * q^3 + 2784 * q^4 - 31250 * q^5 - 222816 * q^6 - 616300 * q^7 - 733440 * q^8 - 585054 * q^9 + 1250000 * q^10 - 2467136 * q^11 + 16415040 * q^12 + 6517860 * q^13 + 50775648 * q^14 - 12187500 * q^15 - 50953728 * q^16 + 633460 * q^17 - 126058320 * q^18 - 374063400 * q^19 - 43500000 * q^20 - 553840776 * q^21 + 1360157440 * q^22 + 621982140 * q^23 + 403776000 * q^24 + 488281250 * q^25 + 1868267104 * q^26 + 321782760 * q^27 - 2947781440 * q^28 - 7795134100 * q^29 + 3481500000 * q^30 - 4957819816 * q^31 + 14954885120 * q^32 - 16099847040 * q^33 - 16327772192 * q^34 + 9629687500 * q^35 + 11142443232 * q^36 + 21833071780 * q^37 + 21996120640 * q^38 - 23005812648 * q^39 + 11460000000 * q^40 + 5565813644 * q^41 + 91388324160 * q^42 - 52510877700 * q^43 - 104352013312 * q^44 + 9141468750 * q^45 - 176890366176 * q^46 + 92855886340 * q^47 - 102772700160 * q^48 + 38873112314 * q^49 - 19531250000 * q^50 + 195876254904 * q^51 - 161245659200 * q^52 + 266248876180 * q^53 + 290389752000 * q^54 + 38549000000 * q^55 + 131964403200 * q^56 - 230287741680 * q^57 + 22585283360 * q^58 + 253501607800 * q^59 - 256485000000 * q^60 - 377459239836 * q^61 - 758697351360 * q^62 - 64232955180 * q^63 - 393017368576 * q^64 - 101841562500 * q^65 + 1372339327488 * q^66 - 2375782313740 * q^67 + 1305076479680 * q^68 + 2066706001512 * q^69 - 793369500000 * q^70 - 556190102776 * q^71 + 752608730880 * q^72 - 556465382460 * q^73 + 2308883896928 * q^74 + 190429687500 * q^75 - 1083383024000 * q^76 + 2824016150400 * q^77 + 1126072161600 * q^78 - 2408230567600 * q^79 + 796152000000 * q^80 - 2580872423958 * q^81 - 73140129760 * q^82 - 3898295602980 * q^83 - 6309721809792 * q^84 - 9897812500 * q^85 + 1395814341664 * q^86 + 430538668680 * q^87 - 3636551086080 * q^88 + 106847675700 * q^89 + 1969661250000 * q^90 + 1474535181544 * q^91 + 13026685584960 * q^92 + 9550571999760 * q^93 - 8671844110112 * q^94 + 5844740625000 * q^95 + 8379224039424 * q^96 + 18744409451140 * q^97 - 17654928754960 * q^98 - 11085674027328 * q^99

Display 100 coefficients 10 coefficients

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 $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−129.353	−1.42916	−0.714582	−	0.699551i	$-0.753383\pi$
$2$	−129.353	−1.42916	−0.714582	+	0.699551i	$0.753383\pi$
$3$	1462.24	1.15806	0.579029	−	0.815307i	$-0.303432\pi$
$3$	1462.24	1.15806	0.579029	+	0.815307i	$0.303432\pi$
$4$	8540.26	1.04251
$5$	−15625.0	−0.447214
$5$	−15625.0	−0.447214
$6$	−189145.	−1.65506
$7$	−454332.	−1.45961	−0.729804	−	0.683657i	$-0.760388\pi$
$7$	−454332.	−1.45961	−0.729804	+	0.683657i	$0.760388\pi$
$8$	−45048.4	−0.0607567
$9$	543819.	0.341097
$10$	2.02114e6	0.639142
$11$	−8.29247e6	−1.41134	−0.705670	−	0.708541i	$-0.749354\pi$
$11$	−8.29247e6	−1.41134	−0.705670	+	0.708541i	$0.749354\pi$
$12$	1.24879e7	1.20729
$13$	−8.65436e6	−0.497282	−0.248641	−	0.968596i	$-0.579984\pi$
$13$	−8.65436e6	−0.497282	−0.248641	+	0.968596i	$0.579984\pi$
$14$	5.87693e7	2.08602
$15$	−2.28475e7	−0.517899
$16$	−6.41346e7	−0.955681
$17$	9.15414e7	0.919813	0.459906	−	0.887967i	$-0.347883\pi$
$17$	9.15414e7	0.919813	0.459906	+	0.887967i	$0.347883\pi$
$18$	−7.03448e7	−0.487484
$19$	−2.26390e8	−1.10397	−0.551987	−	0.833853i	$-0.686130\pi$
$19$	−2.26390e8	−1.10397	−0.551987	+	0.833853i	$0.686130\pi$
$20$	−1.33442e8	−0.466226
$21$	−6.64342e8	−1.69031
$22$	1.07266e9	2.01704
$23$	1.16161e9	1.63617	0.818087	−	0.575095i	$-0.195035\pi$
$23$	1.16161e9	1.63617	0.818087	+	0.575095i	$0.195035\pi$
$24$	−6.58715e7	−0.0703597
$25$	2.44141e8	0.200000
$26$	1.11947e9	0.710698
$27$	−1.53609e9	−0.763047
$28$	−3.88011e9	−1.52166
$29$	−2.27916e9	−0.711521	−0.355760	−	0.934577i	$-0.615778\pi$
$29$	−2.27916e9	−0.711521	−0.355760	+	0.934577i	$0.615778\pi$
$30$	2.95540e9	0.740163
$31$	2.87630e9	0.582080	0.291040	−	0.956711i	$-0.405999\pi$
$31$	2.87630e9	0.582080	0.291040	+	0.956711i	$0.405999\pi$
$32$	8.66506e9	1.42658
$33$	−1.21256e10	−1.63441
$34$	−1.18412e10	−1.31456
$35$	7.09894e9	0.652756
$36$	4.64436e9	0.355598
$37$	−6.89036e9	−0.441500	−0.220750	−	0.975330i	$-0.570850\pi$
$37$	−6.89036e9	−0.441500	−0.220750	+	0.975330i	$0.570850\pi$
$38$	2.92843e10	1.57776
$39$	−1.26547e10	−0.575882
$40$	7.03881e8	0.0271712
$41$	1.94638e9	0.0639931	0.0319965	−	0.999488i	$-0.489813\pi$
$41$	1.94638e9	0.0639931	0.0319965	+	0.999488i	$0.489813\pi$
$42$	8.59347e10	2.41573
$43$	−2.23125e10	−0.538275	−0.269137	−	0.963102i	$-0.586739\pi$
$43$	−2.23125e10	−0.538275	−0.269137	+	0.963102i	$0.586739\pi$
$44$	−7.08199e10	−1.47134
$45$	−8.49718e9	−0.152543
$46$	−1.50258e11	−2.33836
$47$	7.41696e10	1.00367	0.501834	−	0.864964i	$-0.332659\pi$
$47$	7.41696e10	1.00367	0.501834	+	0.864964i	$0.332659\pi$
$48$	−9.37802e10	−1.10673
$49$	1.09528e11	1.13045
$50$	−3.15804e10	−0.285833
$51$	1.33855e11	1.06520
$52$	−7.39105e10	−0.518423
$53$	5.95731e10	0.369196	0.184598	−	0.982814i	$-0.440902\pi$
$53$	5.95731e10	0.369196	0.184598	+	0.982814i	$0.440902\pi$
$54$	1.98698e11	1.09052
$55$	1.29570e11	0.631170
$56$	2.04669e10	0.0886809
$57$	−3.31036e11	−1.27847
$58$	2.94817e11	1.01688
$59$	−1.27313e11	−0.392948	−0.196474	−	0.980509i	$-0.562949\pi$
$59$	−1.27313e11	−0.392948	−0.196474	+	0.980509i	$0.562949\pi$
$60$	−1.95123e11	−0.539916
$61$	−1.48099e9	−0.00368051	−0.00184025	−	0.999998i	$-0.500586\pi$
$61$	−1.48099e9	−0.00368051	−0.00184025	+	0.999998i	$0.500586\pi$
$62$	−3.72058e11	−0.831888
$63$	−2.47074e11	−0.497868
$64$	−5.95462e11	−1.08314
$65$	1.35224e11	0.222391
$66$	1.56848e12	2.33585
$67$	−1.18465e12	−1.59994	−0.799969	−	0.600041i	$-0.795151\pi$
$67$	−1.18465e12	−1.59994	−0.799969	+	0.600041i	$0.795151\pi$
$68$	7.81787e11	0.958916
$69$	1.69855e12	1.89478
$70$	−9.18270e11	−0.932896
$71$	−1.21601e12	−1.12657	−0.563283	−	0.826264i	$-0.690462\pi$
$71$	−1.21601e12	−1.12657	−0.563283	+	0.826264i	$0.690462\pi$
$72$	−2.44982e10	−0.0207239
$73$	−9.43614e11	−0.729786	−0.364893	−	0.931049i	$-0.618894\pi$
$73$	−9.43614e11	−0.729786	−0.364893	+	0.931049i	$0.618894\pi$
$74$	8.91290e11	0.630976
$75$	3.56992e11	0.231612
$76$	−1.93343e12	−1.15091
$77$	3.76754e12	2.06000
$78$	1.63693e12	0.823030
$79$	1.30732e12	0.605068	0.302534	−	0.953139i	$-0.402167\pi$
$79$	1.30732e12	0.605068	0.302534	+	0.953139i	$0.402167\pi$
$80$	1.00210e12	0.427393
$81$	−3.11315e12	−1.22475
$82$	−2.51771e11	−0.0914567
$83$	−3.10115e12	−1.04115	−0.520577	−	0.853815i	$-0.674283\pi$
$83$	−3.10115e12	−1.04115	−0.520577	+	0.853815i	$0.674283\pi$
$84$	−5.67365e12	−1.76217
$85$	−1.43033e12	−0.411353
$86$	2.88620e12	0.769284
$87$	−3.33267e12	−0.823982
$88$	3.73562e11	0.0857483
$89$	3.81172e11	0.0812991	0.0406495	−	0.999173i	$-0.487057\pi$
$89$	3.81172e11	0.0812991	0.0406495	+	0.999173i	$0.487057\pi$
$90$	1.09914e12	0.218010
$91$	3.93195e12	0.725837
$92$	9.92045e12	1.70573
$93$	4.20583e12	0.674082
$94$	−9.59407e12	−1.43441
$95$	3.53734e12	0.493712
$96$	1.26704e13	1.65206
$97$	6.84151e12	0.833942	0.416971	−	0.908920i	$-0.363092\pi$
$97$	6.84151e12	0.833942	0.416971	+	0.908920i	$0.363092\pi$
$98$	−1.41679e13	−1.61560
$99$	−4.50961e12	−0.481404
$100$	2.08502e12	0.208502
$101$	−1.10253e13	−1.03347	−0.516737	−	0.856144i	$-0.672854\pi$
$101$	−1.10253e13	−1.03347	−0.516737	+	0.856144i	$0.672854\pi$
$102$	−1.73146e13	−1.52234
$103$	1.05655e13	0.871863	0.435932	−	0.899980i	$-0.356419\pi$
$103$	1.05655e13	0.871863	0.435932	+	0.899980i	$0.356419\pi$
$104$	3.89865e11	0.0302132
$105$	1.03803e13	0.755929
$106$	−7.70597e12	−0.527642
$107$	−8.98111e12	−0.578543	−0.289271	−	0.957247i	$-0.593413\pi$
$107$	−8.98111e12	−0.578543	−0.289271	+	0.957247i	$0.593413\pi$
$108$	−1.31186e13	−0.795486
$109$	1.81433e13	1.03620	0.518099	−	0.855320i	$-0.326640\pi$
$109$	1.81433e13	1.03620	0.518099	+	0.855320i	$0.326640\pi$
$110$	−1.67603e13	−0.902047
$111$	−1.00753e13	−0.511282
$112$	2.91384e13	1.39492
$113$	1.36451e13	0.616546	0.308273	−	0.951298i	$-0.400249\pi$
$113$	1.36451e13	0.616546	0.308273	+	0.951298i	$0.400249\pi$
$114$	4.28206e13	1.82714
$115$	−1.81502e13	−0.731719
$116$	−1.94646e13	−0.741769
$117$	−4.70641e12	−0.169622
$118$	1.64684e13	0.561587
$119$	−4.15902e13	−1.34257
$120$	1.02924e12	0.0314658
$121$	3.42424e13	0.991880
$122$	1.91571e11	0.00526005
$123$	2.84608e12	0.0741077
$124$	2.45643e13	0.606826
$125$	−3.81470e12	−0.0894427
$126$	3.19599e13	0.711535
$127$	−5.29887e13	−1.12062	−0.560311	−	0.828282i	$-0.689318\pi$
$127$	−5.29887e13	−1.12062	−0.560311	+	0.828282i	$0.689318\pi$
$128$	6.04083e12	0.121404
$129$	−3.26263e13	−0.623353
$130$	−1.74917e13	−0.317834
$131$	−4.71441e13	−0.815012	−0.407506	−	0.913203i	$-0.633601\pi$
$131$	−4.71441e13	−0.815012	−0.407506	+	0.913203i	$0.633601\pi$
$132$	−1.03556e14	−1.70390
$133$	1.02856e14	1.61137
$134$	1.53238e14	2.28657
$135$	2.40014e13	0.341245
$136$	−4.12379e12	−0.0558848
$137$	−7.03376e13	−0.908874	−0.454437	−	0.890779i	$-0.650159\pi$
$137$	−7.03376e13	−0.908874	−0.454437	+	0.890779i	$0.650159\pi$
$138$	−2.19713e14	−2.70796
$139$	−1.59447e14	−1.87509	−0.937543	−	0.347868i	$-0.886906\pi$
$139$	−1.59447e14	−1.87509	−0.937543	+	0.347868i	$0.886906\pi$
$140$	6.06267e13	0.680506
$141$	1.08454e14	1.16230
$142$	1.57294e14	1.61005
$143$	7.17660e13	0.701834
$144$	−3.48777e13	−0.325980
$145$	3.56119e13	0.318202
$146$	1.22059e14	1.04298
$147$	1.60157e14	1.30913
$148$	−5.88454e13	−0.460269
$149$	2.14372e14	1.60493	0.802467	−	0.596697i	$-0.203520\pi$
$149$	2.14372e14	1.60493	0.802467	+	0.596697i	$0.203520\pi$
$150$	−4.61781e13	−0.331011
$151$	−1.66039e14	−1.13988	−0.569942	−	0.821685i	$-0.693034\pi$
$151$	−1.66039e14	−1.13988	−0.569942	+	0.821685i	$0.693034\pi$
$152$	1.01985e13	0.0670738
$153$	4.97820e13	0.313746
$154$	−4.87343e14	−2.94408
$155$	−4.49421e13	−0.260314
$156$	−1.08075e14	−0.600363
$157$	4.14094e13	0.220674	0.110337	−	0.993894i	$-0.464807\pi$
$157$	4.14094e13	0.220674	0.110337	+	0.993894i	$0.464807\pi$
$158$	−1.69105e14	−0.864742
$159$	8.71101e13	0.427550
$160$	−1.35392e14	−0.637987
$161$	−5.27756e14	−2.38817
$162$	4.02696e14	1.75037
$163$	4.21175e14	1.75891	0.879454	−	0.475983i	$-0.157908\pi$
$163$	4.21175e14	1.75891	0.879454	+	0.475983i	$0.157908\pi$
$164$	1.66226e13	0.0667136
$165$	1.89462e14	0.730932
$166$	4.01143e14	1.48798
$167$	5.37662e13	0.191802	0.0959009	−	0.995391i	$-0.469427\pi$
$167$	5.37662e13	0.191802	0.0959009	+	0.995391i	$0.469427\pi$
$168$	2.99275e13	0.102698
$169$	−2.27977e14	−0.752710
$170$	1.85018e14	0.587891
$171$	−1.23115e14	−0.376563
$172$	−1.90555e14	−0.561158
$173$	−6.07901e14	−1.72398	−0.861992	−	0.506921i	$-0.830783\pi$
$173$	−6.07901e14	−1.72398	−0.861992	+	0.506921i	$0.830783\pi$
$174$	4.31092e14	1.17761
$175$	−1.10921e14	−0.291921
$176$	5.31835e14	1.34879
$177$	−1.86162e14	−0.455056
$178$	−4.93058e13	−0.116190
$179$	2.62554e14	0.596586	0.298293	−	0.954474i	$-0.403583\pi$
$179$	2.62554e14	0.596586	0.298293	+	0.954474i	$0.403583\pi$
$180$	−7.25681e13	−0.159028
$181$	3.32412e14	0.702693	0.351346	−	0.936246i	$-0.385724\pi$
$181$	3.32412e14	0.702693	0.351346	+	0.936246i	$0.385724\pi$
$182$	−5.08611e14	−1.03734
$183$	−2.16556e12	−0.00426224
$184$	−5.23286e13	−0.0994085
$185$	1.07662e14	0.197445
$186$	−5.44038e14	−0.963375
$187$	−7.59104e14	−1.29817
$188$	6.33427e14	1.04634
$189$	6.97893e14	1.11375
$190$	−4.57567e14	−0.705596
$191$	6.81892e14	1.01625	0.508123	−	0.861285i	$-0.330340\pi$
$191$	6.81892e14	1.01625	0.508123	+	0.861285i	$0.330340\pi$
$192$	−8.70708e14	−1.25434
$193$	−2.12512e14	−0.295979	−0.147990	−	0.988989i	$-0.547280\pi$
$193$	−2.12512e14	−0.295979	−0.147990	+	0.988989i	$0.547280\pi$
$194$	−8.84972e14	−1.19184
$195$	1.97730e14	0.257542
$196$	9.35401e14	1.17851
$197$	4.45359e13	0.0542850	0.0271425	−	0.999632i	$-0.491359\pi$
$197$	4.45359e13	0.0542850	0.0271425	+	0.999632i	$0.491359\pi$
$198$	5.83332e14	0.688006
$199$	−8.49745e14	−0.969937	−0.484968	−	0.874532i	$-0.661169\pi$
$199$	−8.49745e14	−0.969937	−0.484968	+	0.874532i	$0.661169\pi$
$200$	−1.09981e13	−0.0121513
$201$	−1.73224e15	−1.85282
$202$	1.42615e15	1.47701
$203$	1.03549e15	1.03854
$204$	1.14316e15	1.11048
$205$	−3.04122e13	−0.0286186
$206$	−1.36668e15	−1.24604
$207$	6.31706e14	0.558094
$208$	5.55044e14	0.475243
$209$	1.87733e15	1.55808
$210$	−1.34273e15	−1.08035
$211$	7.44243e14	0.580602	0.290301	−	0.956935i	$-0.406245\pi$
$211$	7.44243e14	0.580602	0.290301	+	0.956935i	$0.406245\pi$
$212$	5.08770e14	0.384891
$213$	−1.77809e15	−1.30463
$214$	1.16174e15	0.826833
$215$	3.48634e14	0.240724
$216$	6.91982e13	0.0463602
$217$	−1.30679e15	−0.849608
$218$	−2.34689e15	−1.48090
$219$	−1.37979e15	−0.845134
$220$	1.10656e15	0.658003
$221$	−7.92232e14	−0.457407
$222$	1.30328e15	0.730706
$223$	4.27532e14	0.232802	0.116401	−	0.993202i	$-0.462864\pi$
$223$	4.27532e14	0.232802	0.116401	+	0.993202i	$0.462864\pi$
$224$	−3.93681e15	−2.08225
$225$	1.32768e14	0.0682195
$226$	−1.76503e15	−0.881146
$227$	1.49794e15	0.726650	0.363325	−	0.931663i	$-0.381642\pi$
$227$	1.49794e15	0.726650	0.363325	+	0.931663i	$0.381642\pi$
$228$	−2.82714e15	−1.33282
$229$	−6.49186e14	−0.297467	−0.148733	−	0.988877i	$-0.547520\pi$
$229$	−6.49186e14	−0.297467	−0.148733	+	0.988877i	$0.547520\pi$
$230$	2.34778e15	1.04575
$231$	5.50904e15	2.38560
$232$	1.02672e14	0.0432296
$233$	3.00477e15	1.23026	0.615131	−	0.788425i	$-0.289103\pi$
$233$	3.00477e15	1.23026	0.615131	+	0.788425i	$0.289103\pi$
$234$	6.08789e14	0.242417
$235$	−1.15890e15	−0.448854
$236$	−1.08729e15	−0.409653
$237$	1.91161e15	0.700704
$238$	5.37982e15	1.91875
$239$	−2.78947e15	−0.968135	−0.484067	−	0.875031i	$-0.660841\pi$
$239$	−2.78947e15	−0.968135	−0.484067	+	0.875031i	$0.660841\pi$
$240$	1.46532e15	0.494946
$241$	2.33877e15	0.768911	0.384456	−	0.923144i	$-0.374389\pi$
$241$	2.33877e15	0.768911	0.384456	+	0.923144i	$0.374389\pi$
$242$	−4.42937e15	−1.41756
$243$	−2.10315e15	−0.655284
$244$	−1.26480e13	−0.00383697
$245$	−1.71138e15	−0.505554
$246$	−3.68149e14	−0.105912
$247$	1.95926e15	0.548987
$248$	−1.29572e14	−0.0353653
$249$	−4.53462e15	−1.20572
$250$	4.93443e14	0.127828
$251$	−2.64944e15	−0.668766	−0.334383	−	0.942437i	$-0.608528\pi$
$251$	−2.64944e15	−0.668766	−0.334383	+	0.942437i	$0.608528\pi$
$252$	−2.11008e15	−0.519033
$253$	−9.63262e15	−2.30920
$254$	6.85426e15	1.60155
$255$	−2.09149e15	−0.476370
$256$	4.09663e15	0.909634
$257$	−4.78165e14	−0.103517	−0.0517586	−	0.998660i	$-0.516483\pi$
$257$	−4.78165e14	−0.103517	−0.0517586	+	0.998660i	$0.516483\pi$
$258$	4.22031e15	0.890875
$259$	3.13051e15	0.644416
$260$	1.15485e15	0.231846
$261$	−1.23945e15	−0.242698
$262$	6.09824e15	1.16479
$263$	6.01585e15	1.12095	0.560473	−	0.828173i	$-0.310619\pi$
$263$	6.01585e15	1.12095	0.560473	+	0.828173i	$0.310619\pi$
$264$	5.46237e14	0.0993015
$265$	−9.30829e14	−0.165109
$266$	−1.33048e16	−2.30291
$267$	5.57364e14	0.0941490
$268$	−1.01172e16	−1.66795
$269$	8.12278e15	1.30712	0.653559	−	0.756875i	$-0.273275\pi$
$269$	8.12278e15	1.30712	0.653559	+	0.756875i	$0.273275\pi$
$270$	−3.10465e15	−0.487695
$271$	−1.19305e16	−1.82962	−0.914808	−	0.403889i	$-0.867658\pi$
$271$	−1.19305e16	−1.82962	−0.914808	+	0.403889i	$0.867658\pi$
$272$	−5.87097e15	−0.879047
$273$	5.74945e15	0.840561
$274$	9.09839e15	1.29893
$275$	−2.02453e15	−0.282268
$276$	1.45061e16	1.97533
$277$	−2.49011e15	−0.331208	−0.165604	−	0.986192i	$-0.552957\pi$
$277$	−2.49011e15	−0.331208	−0.165604	+	0.986192i	$0.552957\pi$
$278$	2.06250e16	2.67981
$279$	1.56419e15	0.198546
$280$	−3.19795e14	−0.0396593
$281$	1.61666e16	1.95897	0.979486	−	0.201515i	$-0.0645863\pi$
$281$	1.61666e16	1.95897	0.979486	+	0.201515i	$0.0645863\pi$
$282$	−1.40288e16	−1.66112
$283$	−9.63373e15	−1.11476	−0.557382	−	0.830256i	$-0.688194\pi$
$283$	−9.63373e15	−1.11476	−0.557382	+	0.830256i	$0.688194\pi$
$284$	−1.03850e16	−1.17446
$285$	5.17244e15	0.571747
$286$	−9.28317e15	−1.00304
$287$	−8.84303e14	−0.0934047
$288$	4.71223e15	0.486603
$289$	−1.52475e15	−0.153944
$290$	−4.60651e15	−0.454763
$291$	1.00039e16	0.965753
$292$	−8.05870e15	−0.760811
$293$	1.07504e15	0.0992625	0.0496312	−	0.998768i	$-0.484195\pi$
$293$	1.07504e15	0.0992625	0.0496312	+	0.998768i	$0.484195\pi$
$294$	−2.07168e16	−1.87096
$295$	1.98927e15	0.175732
$296$	3.10399e14	0.0268241
$297$	1.27380e16	1.07692
$298$	−2.77297e16	−2.29371
$299$	−1.00530e16	−0.813640
$300$	3.04880e15	0.241458
$301$	1.01373e16	0.785670
$302$	2.14777e16	1.62908
$303$	−1.61216e16	−1.19682
$304$	1.45194e16	1.05505
$305$	2.31404e13	0.00164597
$306$	−6.43946e15	−0.448394
$307$	−1.75534e16	−1.19664	−0.598319	−	0.801258i	$-0.704164\pi$
$307$	−1.75534e16	−1.19664	−0.598319	+	0.801258i	$0.704164\pi$
$308$	3.21757e16	2.14758
$309$	1.54493e16	1.00967
$310$	5.81341e15	0.372032
$311$	−5.98832e15	−0.375286	−0.187643	−	0.982237i	$-0.560085\pi$
$311$	−5.98832e15	−0.375286	−0.187643	+	0.982237i	$0.560085\pi$
$312$	5.70075e14	0.0349887
$313$	9.18443e15	0.552095	0.276048	−	0.961144i	$-0.410975\pi$
$313$	9.18443e15	0.552095	0.276048	+	0.961144i	$0.410975\pi$
$314$	−5.35644e15	−0.315380
$315$	3.86054e15	0.222653
$316$	1.11648e16	0.630791
$317$	−1.40350e16	−0.776831	−0.388415	−	0.921484i	$-0.626977\pi$
$317$	−1.40350e16	−0.776831	−0.388415	+	0.921484i	$0.626977\pi$
$318$	−1.12680e16	−0.611040
$319$	1.88999e16	1.00420
$320$	9.30410e15	0.484395
$321$	−1.31325e16	−0.669986
$322$	6.82670e16	3.41309
$323$	−2.07241e16	−1.01545
$324$	−2.65871e16	−1.27682
$325$	−2.11288e15	−0.0994565
$326$	−5.44804e16	−2.51377
$327$	2.65298e16	1.19998
$328$	−8.76813e13	−0.00388801
$329$	−3.36976e16	−1.46496
$330$	−2.45075e16	−1.04462
$331$	−2.30699e16	−0.964194	−0.482097	−	0.876118i	$-0.660125\pi$
$331$	−2.30699e16	−0.964194	−0.482097	+	0.876118i	$0.660125\pi$
$332$	−2.64846e16	−1.08542
$333$	−3.74711e15	−0.150594
$334$	−6.95484e15	−0.274116
$335$	1.85101e16	0.715514
$336$	4.26073e16	1.61540
$337$	6.69098e15	0.248826	0.124413	−	0.992231i	$-0.460295\pi$
$337$	6.69098e15	0.248826	0.124413	+	0.992231i	$0.460295\pi$
$338$	2.94896e16	1.07575
$339$	1.99523e16	0.713996
$340$	−1.22154e16	−0.428840
$341$	−2.38516e16	−0.821513
$342$	1.59254e16	0.538170
$343$	−5.74250e15	−0.190410
$344$	1.00514e15	0.0327038
$345$	−2.65399e16	−0.847373
$346$	7.86340e16	2.46386
$347$	−1.02492e15	−0.0315172	−0.0157586	−	0.999876i	$-0.505016\pi$
$347$	−1.02492e15	−0.0315172	−0.0157586	+	0.999876i	$0.505016\pi$
$348$	−2.84619e16	−0.859011
$349$	8.02611e15	0.237761	0.118880	−	0.992909i	$-0.462070\pi$
$349$	8.02611e15	0.237761	0.118880	+	0.992909i	$0.462070\pi$
$350$	1.43480e16	0.417204
$351$	1.32938e16	0.379450
$352$	−7.18548e16	−2.01339
$353$	6.40637e16	1.76228	0.881142	−	0.472851i	$-0.156775\pi$
$353$	6.40637e16	1.76228	0.881142	+	0.472851i	$0.156775\pi$
$354$	2.40807e16	0.650351
$355$	1.90001e16	0.503816
$356$	3.25531e15	0.0847553
$357$	−6.08148e16	−1.55477
$358$	−3.39622e16	−0.852620
$359$	−9.00708e15	−0.222060	−0.111030	−	0.993817i	$-0.535415\pi$
$359$	−9.00708e15	−0.222060	−0.111030	+	0.993817i	$0.535415\pi$
$360$	3.82784e14	0.00926803
$361$	9.19945e15	0.218759
$362$	−4.29985e16	−1.00426
$363$	5.00706e16	1.14865
$364$	3.35799e16	0.756694
$365$	1.47440e16	0.326370
$366$	2.80122e14	0.00609144
$367$	1.43497e15	0.0306559	0.0153280	−	0.999883i	$-0.495121\pi$
$367$	1.43497e15	0.0306559	0.0153280	+	0.999883i	$0.495121\pi$
$368$	−7.44994e16	−1.56366
$369$	1.05848e15	0.0218279
$370$	−1.39264e16	−0.282181
$371$	−2.70660e16	−0.538881
$372$	3.59189e16	0.702739
$373$	6.67663e16	1.28366	0.641830	−	0.766847i	$-0.278176\pi$
$373$	6.67663e16	1.28366	0.641830	+	0.766847i	$0.278176\pi$
$374$	9.81926e16	1.85530
$375$	−5.57800e15	−0.103580
$376$	−3.34122e15	−0.0609795
$377$	1.97247e16	0.353827
$378$	−9.02748e16	−1.59173
$379$	−9.24716e16	−1.60270	−0.801352	−	0.598193i	$-0.795886\pi$
$379$	−9.24716e16	−1.60270	−0.801352	+	0.598193i	$0.795886\pi$
$380$	3.02098e16	0.514701
$381$	−7.74821e16	−1.29774
$382$	−8.82050e16	−1.45238
$383$	3.75824e16	0.608405	0.304203	−	0.952607i	$-0.401610\pi$
$383$	3.75824e16	0.608405	0.304203	+	0.952607i	$0.401610\pi$
$384$	8.83313e15	0.140592
$385$	−5.88677e16	−0.921261
$386$	2.74891e16	0.423003
$387$	−1.21340e16	−0.183604
$388$	5.84283e16	0.869395
$389$	−1.17206e16	−0.171505	−0.0857523	−	0.996316i	$-0.527329\pi$
$389$	−1.17206e16	−0.171505	−0.0857523	+	0.996316i	$0.527329\pi$
$390$	−2.55770e16	−0.368070
$391$	1.06335e17	1.50497
$392$	−4.93408e15	−0.0686826
$393$	−6.89359e16	−0.943831
$394$	−5.76086e15	−0.0775822
$395$	−2.04268e16	−0.270595
$396$	−3.85132e16	−0.501870
$397$	1.24323e17	1.59373	0.796864	−	0.604158i	$-0.206491\pi$
$397$	1.24323e17	1.59373	0.796864	+	0.604158i	$0.206491\pi$
$398$	1.09917e17	1.38620
$399$	1.50400e17	1.86606
$400$	−1.56579e16	−0.191136
$401$	1.28256e16	0.154043	0.0770213	−	0.997029i	$-0.475459\pi$
$401$	1.28256e16	0.154043	0.0770213	+	0.997029i	$0.475459\pi$
$402$	2.24071e17	2.64799
$403$	−2.48925e16	−0.289458
$404$	−9.41585e16	−1.07741
$405$	4.86430e16	0.547725
$406$	−1.33945e17	−1.48425
$407$	5.71381e16	0.623106
$408$	−6.02996e15	−0.0647178
$409$	−1.74483e17	−1.84311	−0.921554	−	0.388250i	$-0.873080\pi$
$409$	−1.74483e17	−1.84311	−0.921554	+	0.388250i	$0.873080\pi$
$410$	3.93392e15	0.0409007
$411$	−1.02850e17	−1.05253
$412$	9.02322e16	0.908928
$413$	5.78424e16	0.573550
$414$	−8.17132e16	−0.797609
$415$	4.84554e16	0.465618
$416$	−7.49905e16	−0.709414
$417$	−2.33150e17	−2.17146
$418$	−2.42839e17	−2.22676
$419$	−2.23061e16	−0.201388	−0.100694	−	0.994917i	$-0.532106\pi$
$419$	−2.23061e16	−0.201388	−0.100694	+	0.994917i	$0.532106\pi$
$420$	8.86508e16	0.788065
$421$	1.09818e17	0.961259	0.480629	−	0.876924i	$-0.340408\pi$
$421$	1.09818e17	0.961259	0.480629	+	0.876924i	$0.340408\pi$
$422$	−9.62702e16	−0.829776
$423$	4.03348e16	0.342348
$424$	−2.68367e15	−0.0224311
$425$	2.23490e16	0.183963
$426$	2.30002e17	1.86453
$427$	6.72860e14	0.00537209
$428$	−7.67010e16	−0.603138
$429$	1.04939e17	0.812765
$430$	−4.50969e16	−0.344034
$431$	−5.24100e16	−0.393833	−0.196916	−	0.980420i	$-0.563093\pi$
$431$	−5.24100e16	−0.393833	−0.196916	+	0.980420i	$0.563093\pi$
$432$	9.85164e16	0.729230
$433$	−6.38582e16	−0.465635	−0.232817	−	0.972520i	$-0.574794\pi$
$433$	−6.38582e16	−0.465635	−0.232817	+	0.972520i	$0.574794\pi$
$434$	1.69038e17	1.21423
$435$	5.20730e16	0.368496
$436$	1.54948e17	1.08025
$437$	−2.62977e17	−1.80629
$438$	1.78480e17	1.20784
$439$	−2.08151e17	−1.38791	−0.693953	−	0.720020i	$-0.744132\pi$
$439$	−2.08151e17	−1.38791	−0.693953	+	0.720020i	$0.744132\pi$
$440$	−5.83691e15	−0.0383478
$441$	5.95637e16	0.385594
$442$	1.02478e17	0.653710
$443$	−1.74659e17	−1.09791	−0.548954	−	0.835853i	$-0.684974\pi$
$443$	−1.74659e17	−1.09791	−0.548954	+	0.835853i	$0.684974\pi$
$444$	−8.60461e16	−0.533018
$445$	−5.95581e15	−0.0363581
$446$	−5.53027e16	−0.332713
$447$	3.13463e17	1.85861
$448$	2.70538e17	1.58096
$449$	2.06717e17	1.19063	0.595313	−	0.803494i	$-0.297028\pi$
$449$	2.06717e17	1.19063	0.595313	+	0.803494i	$0.297028\pi$
$450$	−1.71740e16	−0.0974968
$451$	−1.61403e16	−0.0903160
$452$	1.16532e17	0.642757
$453$	−2.42789e17	−1.32005
$454$	−1.93763e17	−1.03850
$455$	−6.14367e16	−0.324604
$456$	1.49126e16	0.0776753
$457$	−1.22509e17	−0.629091	−0.314545	−	0.949242i	$-0.601852\pi$
$457$	−1.22509e17	−0.629091	−0.314545	+	0.949242i	$0.601852\pi$
$458$	8.39743e16	0.425129
$459$	−1.40616e17	−0.701861
$460$	−1.55007e17	−0.762826
$461$	−6.18077e15	−0.0299907	−0.0149954	−	0.999888i	$-0.504773\pi$
$461$	−6.18077e15	−0.0299907	−0.0149954	+	0.999888i	$0.504773\pi$
$462$	−7.12612e17	−3.40942
$463$	3.40854e17	1.60802	0.804010	−	0.594615i	$-0.202696\pi$
$463$	3.40854e17	1.60802	0.804010	+	0.594615i	$0.202696\pi$
$464$	1.46173e17	0.679987
$465$	−6.57161e16	−0.301459
$466$	−3.88676e17	−1.75825
$467$	3.26578e17	1.45689	0.728447	−	0.685103i	$-0.240243\pi$
$467$	3.26578e17	1.45689	0.728447	+	0.685103i	$0.240243\pi$
$468$	−4.01939e16	−0.176833
$469$	5.38223e17	2.33528
$470$	1.49907e17	0.641486
$471$	6.05505e16	0.255553
$472$	5.73525e15	0.0238742
$473$	1.85026e17	0.759689
$474$	−2.47273e17	−1.00142
$475$	−5.52710e16	−0.220795
$476$	−3.55191e17	−1.39964
$477$	3.23970e16	0.125932
$478$	3.60827e17	1.38362
$479$	1.64950e17	0.623981	0.311991	−	0.950085i	$-0.399004\pi$
$479$	1.64950e17	0.623981	0.311991	+	0.950085i	$0.399004\pi$
$480$	−1.97975e17	−0.738825
$481$	5.96316e16	0.219550
$482$	−3.02527e17	−1.09890
$483$	−7.71706e17	−2.76564
$484$	2.92439e17	1.03405
$485$	−1.06899e17	−0.372950
$486$	2.72049e17	0.936508
$487$	−1.14620e17	−0.389333	−0.194667	−	0.980869i	$-0.562362\pi$
$487$	−1.14620e17	−0.389333	−0.194667	+	0.980869i	$0.562362\pi$
$488$	6.67161e13	0.000223615 0
$489$	6.15859e17	2.03692
$490$	2.21373e17	0.722520
$491$	−8.38999e16	−0.270229	−0.135114	−	0.990830i	$-0.543140\pi$
$491$	−8.38999e16	−0.270229	−0.135114	+	0.990830i	$0.543140\pi$
$492$	2.43062e16	0.0772581
$493$	−2.08637e17	−0.654466
$494$	−2.53437e17	−0.784593
$495$	7.04626e16	0.215291
$496$	−1.84470e17	−0.556283
$497$	5.52471e17	1.64434
$498$	5.86568e17	1.72317
$499$	−4.79739e17	−1.39108	−0.695540	−	0.718488i	$-0.744835\pi$
$499$	−4.79739e17	−1.39108	−0.695540	+	0.718488i	$0.744835\pi$
$500$	−3.25785e16	−0.0932451
$501$	7.86191e16	0.222118
$502$	3.42713e17	0.955777
$503$	−3.54862e17	−0.976939	−0.488470	−	0.872581i	$-0.662445\pi$
$503$	−3.54862e17	−0.976939	−0.488470	+	0.872581i	$0.662445\pi$
$504$	1.11303e16	0.0302488
$505$	1.72270e17	0.462184
$506$	1.24601e18	3.30022
$507$	−3.33357e17	−0.871682
$508$	−4.52537e17	−1.16826
$509$	−5.38826e17	−1.37335	−0.686677	−	0.726962i	$-0.740931\pi$
$509$	−5.38826e17	−1.37335	−0.686677	+	0.726962i	$0.740931\pi$
$510$	2.70541e17	0.680812
$511$	4.28714e17	1.06520
$512$	−5.79399e17	−1.42142
$513$	3.47755e17	0.842384
$514$	6.18521e16	0.147943
$515$	−1.65086e17	−0.389909
$516$	−2.78637e17	−0.649853
$517$	−6.15049e17	−1.41652
$518$	−4.04941e17	−0.920977
$519$	−8.88897e17	−1.99647
$520$	−6.09164e15	−0.0135118
$521$	−6.16165e17	−1.34974	−0.674872	−	0.737935i	$-0.735801\pi$
$521$	−6.16165e17	−1.34974	−0.674872	+	0.737935i	$0.735801\pi$
$522$	1.60327e17	0.346855
$523$	5.15681e17	1.10184	0.550922	−	0.834557i	$-0.314276\pi$
$523$	5.15681e17	1.10184	0.550922	+	0.834557i	$0.314276\pi$
$524$	−4.02623e17	−0.849660
$525$	−1.62193e17	−0.338062
$526$	−7.78170e17	−1.60202
$527$	2.63300e17	0.535405
$528$	7.77670e17	1.56198
$529$	8.45301e17	1.67706
$530$	1.20406e17	0.235969
$531$	−6.92353e16	−0.134033
$532$	8.78419e17	1.67987
$533$	−1.68447e16	−0.0318226
$534$	−7.20969e16	−0.134554
$535$	1.40330e17	0.258732
$536$	5.33665e16	0.0972069
$537$	3.83916e17	0.690881
$538$	−1.05071e18	−1.86809
$539$	−9.08262e17	−1.59545
$540$	2.04978e17	0.355752
$541$	1.06233e18	1.82171	0.910855	−	0.412727i	$-0.135424\pi$
$541$	1.06233e18	1.82171	0.910855	+	0.412727i	$0.135424\pi$
$542$	1.54325e18	2.61482
$543$	4.86065e17	0.813759
$544$	7.93212e17	1.31219
$545$	−2.83488e17	−0.463402
$546$	−7.43710e17	−1.20130
$547$	2.68384e17	0.428390	0.214195	−	0.976791i	$-0.431287\pi$
$547$	2.68384e17	0.428390	0.214195	+	0.976791i	$0.431287\pi$
$548$	−6.00701e17	−0.947512
$549$	−8.05390e14	−0.00125541
$550$	2.61879e17	0.403407
$551$	5.15979e17	0.785500
$552$	−7.65169e16	−0.115121
$553$	−5.93955e17	−0.883162
$554$	3.22104e17	0.473351
$555$	1.57427e17	0.228652
$556$	−1.36172e18	−1.95480
$557$	−5.88867e17	−0.835523	−0.417762	−	0.908557i	$-0.637185\pi$
$557$	−5.88867e17	−0.835523	−0.417762	+	0.908557i	$0.637185\pi$
$558$	−2.02332e17	−0.283755
$559$	1.93101e17	0.267675
$560$	−4.55288e17	−0.623826
$561$	−1.10999e18	−1.50335
$562$	−2.09120e18	−2.79969
$563$	1.58197e17	0.209360	0.104680	−	0.994506i	$-0.466618\pi$
$563$	1.58197e17	0.209360	0.104680	+	0.994506i	$0.466618\pi$
$564$	9.26222e17	1.21172
$565$	−2.13204e17	−0.275728
$566$	1.24615e18	1.59318
$567$	1.41440e18	1.78765
$568$	5.47791e16	0.0684464
$569$	3.03974e16	0.0375498	0.0187749	−	0.999824i	$-0.494023\pi$
$569$	3.03974e16	0.0375498	0.0187749	+	0.999824i	$0.494023\pi$
$570$	−6.69072e17	−0.817121
$571$	−3.35151e17	−0.404674	−0.202337	−	0.979316i	$-0.564854\pi$
$571$	−3.35151e17	−0.404674	−0.202337	+	0.979316i	$0.564854\pi$
$572$	6.12900e17	0.731671
$573$	9.97089e17	1.17687
$574$	1.14387e17	0.133491
$575$	2.83596e17	0.327235
$576$	−3.23824e17	−0.369456
$577$	−1.43971e18	−1.62417	−0.812086	−	0.583538i	$-0.801668\pi$
$577$	−1.43971e18	−1.62417	−0.812086	+	0.583538i	$0.801668\pi$
$578$	1.97232e17	0.220012
$579$	−3.10743e17	−0.342761
$580$	3.04134e17	0.331729
$581$	1.40895e18	1.51968
$582$	−1.29404e18	−1.38022
$583$	−4.94008e17	−0.521061
$584$	4.25082e16	0.0443394
$585$	7.35376e16	0.0758571
$586$	−1.39060e17	−0.141862
$587$	−4.52894e17	−0.456929	−0.228464	−	0.973552i	$-0.573370\pi$
$587$	−4.52894e17	−0.456929	−0.228464	+	0.973552i	$0.573370\pi$
$588$	1.36778e18	1.36478
$589$	−6.51165e17	−0.642601
$590$	−2.57318e17	−0.251150
$591$	6.51221e16	0.0628651
$592$	4.41911e17	0.421933
$593$	4.65868e17	0.439954	0.219977	−	0.975505i	$-0.429402\pi$
$593$	4.65868e17	0.439954	0.219977	+	0.975505i	$0.429402\pi$
$594$	−1.64770e18	−1.53909
$595$	6.49846e17	0.600413
$596$	1.83079e18	1.67316
$597$	−1.24253e18	−1.12324
$598$	1.30039e18	1.16283
$599$	2.03999e18	1.80449	0.902246	−	0.431223i	$-0.141918\pi$
$599$	2.03999e18	1.80449	0.902246	+	0.431223i	$0.141918\pi$
$600$	−1.60819e16	−0.0140719
$601$	−6.44187e16	−0.0557607	−0.0278803	−	0.999611i	$-0.508876\pi$
$601$	−6.44187e16	−0.0557607	−0.0278803	+	0.999611i	$0.508876\pi$
$602$	−1.31129e18	−1.12285
$603$	−6.44234e17	−0.545734
$604$	−1.41802e18	−1.18834
$605$	−5.35038e17	−0.443582
$606$	2.08538e18	1.71046
$607$	9.71795e17	0.788584	0.394292	−	0.918985i	$-0.370990\pi$
$607$	9.71795e17	0.788584	0.394292	+	0.918985i	$0.370990\pi$
$608$	−1.96168e18	−1.57491
$609$	1.51414e18	1.20269
$610$	−2.99329e15	−0.00235237
$611$	−6.41890e17	−0.499106
$612$	4.25151e17	0.327084
$613$	8.50151e17	0.647147	0.323573	−	0.946203i	$-0.395116\pi$
$613$	8.50151e17	0.647147	0.323573	+	0.946203i	$0.395116\pi$
$614$	2.27059e18	1.71019
$615$	−4.44699e16	−0.0331420
$616$	−1.69721e17	−0.125159
$617$	−1.65584e18	−1.20827	−0.604137	−	0.796880i	$-0.706482\pi$
$617$	−1.65584e18	−1.20827	−0.604137	+	0.796880i	$0.706482\pi$
$618$	−1.99842e18	−1.44298
$619$	−1.20464e18	−0.860730	−0.430365	−	0.902655i	$-0.641615\pi$
$619$	−1.20464e18	−0.860730	−0.430365	+	0.902655i	$0.641615\pi$
$620$	−3.83818e17	−0.271381
$621$	−1.78433e18	−1.24848
$622$	7.74608e17	0.536346
$623$	−1.73178e17	−0.118665
$624$	8.11607e17	0.550359
$625$	5.96046e16	0.0400000
$626$	−1.18804e18	−0.789035
$627$	2.74511e18	1.80435
$628$	3.53647e17	0.230055
$629$	−6.30753e17	−0.406097
$630$	−4.99373e17	−0.318208
$631$	−2.84776e18	−1.79602	−0.898012	−	0.439970i	$-0.854989\pi$
$631$	−2.84776e18	−1.79602	−0.898012	+	0.439970i	$0.854989\pi$
$632$	−5.88924e16	−0.0367619
$633$	1.08826e18	0.672371
$634$	1.81547e18	1.11022
$635$	8.27948e17	0.501157
$636$	7.43943e17	0.445726
$637$	−9.47898e17	−0.562154
$638$	−2.44476e18	−1.43516
$639$	−6.61288e17	−0.384269
$640$	−9.43879e16	−0.0542933
$641$	−1.99743e18	−1.13735	−0.568675	−	0.822563i	$-0.692544\pi$
$641$	−1.99743e18	−1.13735	−0.568675	+	0.822563i	$0.692544\pi$
$642$	1.69873e18	0.957520
$643$	2.44248e17	0.136288	0.0681442	−	0.997675i	$-0.478292\pi$
$643$	2.44248e17	0.136288	0.0681442	+	0.997675i	$0.478292\pi$
$644$	−4.50718e18	−2.48970
$645$	5.09785e17	0.278772
$646$	2.68072e18	1.45124
$647$	2.57933e18	1.38239	0.691193	−	0.722670i	$-0.257085\pi$
$647$	2.57933e18	1.38239	0.691193	+	0.722670i	$0.257085\pi$
$648$	1.40242e17	0.0744118
$649$	1.05574e18	0.554583
$650$	2.73308e17	0.142140
$651$	−1.91084e18	−0.983895
$652$	3.59694e18	1.83368
$653$	1.24017e18	0.625956	0.312978	−	0.949760i	$-0.398673\pi$
$653$	1.24017e18	0.625956	0.312978	+	0.949760i	$0.398673\pi$
$654$	−3.43171e18	−1.71497
$655$	7.36627e17	0.364484
$656$	−1.24831e17	−0.0611569
$657$	−5.13155e17	−0.248928
$658$	4.35889e18	2.09367
$659$	1.90004e18	0.903665	0.451832	−	0.892103i	$-0.350771\pi$
$659$	1.90004e18	0.903665	0.451832	+	0.892103i	$0.350771\pi$
$660$	1.61806e18	0.762005
$661$	2.94946e18	1.37541	0.687707	−	0.725988i	$-0.258617\pi$
$661$	2.94946e18	1.37541	0.687707	+	0.725988i	$0.258617\pi$
$662$	2.98417e18	1.37799
$663$	−1.15843e18	−0.529703
$664$	1.39702e17	0.0632571
$665$	−1.60713e18	−0.720626
$666$	4.84701e17	0.215224
$667$	−2.64749e18	−1.16417
$668$	4.59178e17	0.199956
$669$	6.25154e17	0.269599
$670$	−2.39434e18	−1.02259
$671$	1.22811e16	0.00519445
$672$	−5.75656e18	−2.41136
$673$	−2.86981e18	−1.19057	−0.595284	−	0.803515i	$-0.702961\pi$
$673$	−2.86981e18	−1.19057	−0.595284	+	0.803515i	$0.702961\pi$
$674$	−8.65500e17	−0.355613
$675$	−3.75021e17	−0.152609
$676$	−1.94698e18	−0.784709
$677$	−1.86148e17	−0.0743073	−0.0371536	−	0.999310i	$-0.511829\pi$
$677$	−1.86148e17	−0.0743073	−0.0371536	+	0.999310i	$0.511829\pi$
$678$	−2.58090e18	−1.02042
$679$	−3.10832e18	−1.21723
$680$	6.44342e16	0.0249924
$681$	2.19034e18	0.841502
$682$	3.08528e18	1.17408
$683$	−3.62762e18	−1.36738	−0.683688	−	0.729775i	$-0.739625\pi$
$683$	−3.62762e18	−1.36738	−0.683688	+	0.729775i	$0.739625\pi$
$684$	−1.05144e18	−0.392571
$685$	1.09902e18	0.406461
$686$	7.42811e17	0.272127
$687$	−9.49265e17	−0.344484
$688$	1.43101e18	0.514419
$689$	−5.15567e17	−0.183595
$690$	3.43302e18	1.21104
$691$	5.46531e18	1.90989	0.954943	−	0.296790i	$-0.0959160\pi$
$691$	5.46531e18	1.90989	0.954943	+	0.296790i	$0.0959160\pi$
$692$	−5.19163e18	−1.79727
$693$	2.04886e18	0.702661
$694$	1.32576e17	0.0450433
$695$	2.49137e18	0.838564
$696$	1.50132e17	0.0500624
$697$	1.78174e17	0.0588616
$698$	−1.03820e18	−0.339799
$699$	4.39369e18	1.42471
$700$	−9.47293e17	−0.304332
$701$	1.84528e18	0.587349	0.293674	−	0.955906i	$-0.405122\pi$
$701$	1.84528e18	0.587349	0.293674	+	0.955906i	$0.405122\pi$
$702$	−1.71960e18	−0.542296
$703$	1.55991e18	0.487404
$704$	4.93786e18	1.52868
$705$	−1.69459e18	−0.519798
$706$	−8.28684e18	−2.51860
$707$	5.00912e18	1.50847
$708$	−1.58987e18	−0.474402
$709$	−3.81299e18	−1.12737	−0.563684	−	0.825991i	$-0.690616\pi$
$709$	−3.81299e18	−1.12737	−0.563684	+	0.825991i	$0.690616\pi$
$710$	−2.45773e18	−0.720036
$711$	7.10943e17	0.206387
$712$	−1.71712e16	−0.00493946
$713$	3.34114e18	0.952384
$714$	7.86658e18	2.22202
$715$	−1.12134e18	−0.313870
$716$	2.24228e18	0.621948
$717$	−4.07888e18	−1.12116
$718$	1.16509e18	0.317360
$719$	−1.07835e18	−0.291086	−0.145543	−	0.989352i	$-0.546493\pi$
$719$	−1.07835e18	−0.291086	−0.145543	+	0.989352i	$0.546493\pi$
$720$	5.44963e17	0.145783
$721$	−4.80025e18	−1.27258
$722$	−1.18998e18	−0.312642
$723$	3.41984e18	0.890443
$724$	2.83888e18	0.732566
$725$	−5.56435e17	−0.142304
$726$	−6.47679e18	−1.64162
$727$	−6.25979e18	−1.57248	−0.786241	−	0.617920i	$-0.787976\pi$
$727$	−6.25979e18	−1.57248	−0.786241	+	0.617920i	$0.787976\pi$
$728$	−1.77128e17	−0.0440994
$729$	1.88806e18	0.465894
$730$	−1.90718e18	−0.466437
$731$	−2.04252e18	−0.495112
$732$	−1.84944e16	−0.00444343
$733$	6.46173e18	1.53877	0.769383	−	0.638787i	$-0.220564\pi$
$733$	6.46173e18	1.53877	0.769383	+	0.638787i	$0.220564\pi$
$734$	−1.85619e17	−0.0438124
$735$	−2.50245e18	−0.585460
$736$	1.00654e19	2.33414
$737$	9.82366e18	2.25806
$738$	−1.36918e17	−0.0311956
$739$	−7.08319e18	−1.59971	−0.799853	−	0.600196i	$-0.795089\pi$
$739$	−7.08319e18	−1.59971	−0.799853	+	0.600196i	$0.795089\pi$
$740$	9.19460e17	0.205838
$741$	2.86491e18	0.635758
$742$	3.50107e18	0.770150
$743$	−6.25475e18	−1.36390	−0.681950	−	0.731399i	$-0.738868\pi$
$743$	−6.25475e18	−1.36390	−0.681950	+	0.731399i	$0.738868\pi$
$744$	−1.89466e17	−0.0409550
$745$	−3.34956e18	−0.717748
$746$	−8.63643e18	−1.83456
$747$	−1.68646e18	−0.355135
$748$	−6.48295e18	−1.35336
$749$	4.08040e18	0.844445
$750$	7.21532e17	0.148033
$751$	2.66182e18	0.541401	0.270700	−	0.962664i	$-0.412745\pi$
$751$	2.66182e18	0.541401	0.270700	+	0.962664i	$0.412745\pi$
$752$	−4.75684e18	−0.959185
$753$	−3.87411e18	−0.774470
$754$	−2.55145e18	−0.505677
$755$	2.59436e18	0.509771
$756$	5.96019e18	1.16110
$757$	−4.76964e18	−0.921218	−0.460609	−	0.887603i	$-0.652369\pi$
$757$	−4.76964e18	−0.921218	−0.460609	+	0.887603i	$0.652369\pi$
$758$	1.19615e19	2.29053
$759$	−1.40852e19	−2.67418
$760$	−1.59352e17	−0.0299963
$761$	−1.33157e18	−0.248521	−0.124260	−	0.992250i	$-0.539656\pi$
$761$	−1.33157e18	−0.248521	−0.124260	+	0.992250i	$0.539656\pi$
$762$	1.00226e19	1.85469
$763$	−8.24306e18	−1.51244
$764$	5.82354e18	1.05945
$765$	−7.77843e17	−0.140311
$766$	−4.86141e18	−0.869512
$767$	1.10181e18	0.195406
$768$	5.99025e18	1.05341
$769$	9.22797e18	1.60911	0.804553	−	0.593881i	$-0.202405\pi$
$769$	9.22797e18	1.60911	0.804553	+	0.593881i	$0.202405\pi$
$770$	7.61473e18	1.31663
$771$	−6.99191e17	−0.119879
$772$	−1.81491e18	−0.308562
$773$	−5.62993e18	−0.949154	−0.474577	−	0.880214i	$-0.657399\pi$
$773$	−5.62993e18	−0.949154	−0.474577	+	0.880214i	$0.657399\pi$
$774$	1.56957e18	0.262401
$775$	7.02221e17	0.116416
$776$	−3.08199e17	−0.0506676
$777$	4.57755e18	0.746271
$778$	1.51609e18	0.245108
$779$	−4.40641e17	−0.0706467
$780$	1.68867e18	0.268491
$781$	1.00837e19	1.58997
$782$	−1.37548e19	−2.15085
$783$	3.50099e18	0.542924
$784$	−7.02457e18	−1.08035
$785$	−6.47022e17	−0.0986885
$786$	8.91709e18	1.34889
$787$	1.04786e19	1.57206	0.786028	−	0.618190i	$-0.212134\pi$
$787$	1.04786e19	1.57206	0.786028	+	0.618190i	$0.212134\pi$
$788$	3.80348e17	0.0565927
$789$	8.79661e18	1.29812
$790$	2.64227e18	0.386724
$791$	−6.19939e18	−0.899915
$792$	2.03150e17	0.0292485
$793$	1.28170e16	0.00183025
$794$	−1.60816e19	−2.27770
$795$	−1.36109e18	−0.191206
$796$	−7.25704e18	−1.01117
$797$	−1.12696e19	−1.55750	−0.778752	−	0.627332i	$-0.784147\pi$
$797$	−1.12696e19	−1.55750	−0.778752	+	0.627332i	$0.784147\pi$
$798$	−1.94548e19	−2.66690
$799$	6.78958e18	0.923186
$800$	2.11549e18	0.285316
$801$	2.07289e17	0.0277309
$802$	−1.65904e18	−0.220152
$803$	7.82489e18	1.02998
$804$	−1.47938e19	−1.93159
$805$	8.24619e18	1.06802
$806$	3.21993e18	0.413683
$807$	1.18774e19	1.51372
$808$	4.96670e17	0.0627905
$809$	−5.35863e18	−0.672030	−0.336015	−	0.941857i	$-0.609079\pi$
$809$	−5.35863e18	−0.672030	−0.336015	+	0.941857i	$0.609079\pi$
$810$	−6.29213e18	−0.782789
$811$	8.99608e18	1.11024	0.555121	−	0.831769i	$-0.312672\pi$
$811$	8.99608e18	1.11024	0.555121	+	0.831769i	$0.312672\pi$
$812$	8.84339e18	1.08269
$813$	−1.74453e19	−2.11880
$814$	−7.39100e18	−0.890522
$815$	−6.58086e18	−0.786608
$816$	−8.58477e18	−1.01799
$817$	5.05134e18	0.594242
$818$	2.25699e19	2.63411
$819$	2.13827e18	0.247581
$820$	−2.59728e17	−0.0298352
$821$	−7.77887e18	−0.886515	−0.443257	−	0.896394i	$-0.646177\pi$
$821$	−7.77887e18	−0.886515	−0.443257	+	0.896394i	$0.646177\pi$
$822$	1.33040e19	1.50424
$823$	−1.04773e19	−1.17530	−0.587652	−	0.809114i	$-0.699948\pi$
$823$	−1.04773e19	−1.17530	−0.587652	+	0.809114i	$0.699948\pi$
$824$	−4.75959e17	−0.0529715
$825$	−2.96035e18	−0.326883
$826$	−7.48210e18	−0.819697
$827$	9.57739e17	0.104103	0.0520513	−	0.998644i	$-0.483424\pi$
$827$	9.57739e17	0.104103	0.0520513	+	0.998644i	$0.483424\pi$
$828$	5.39493e18	0.581820
$829$	2.87451e18	0.307581	0.153790	−	0.988104i	$-0.450852\pi$
$829$	2.87451e18	0.307581	0.153790	+	0.988104i	$0.450852\pi$
$830$	−6.26787e18	−0.665445
$831$	−3.64114e18	−0.383558
$832$	5.15335e18	0.538626
$833$	1.00264e19	1.03980
$834$	3.01587e19	3.10337
$835$	−8.40098e17	−0.0857764
$836$	1.60329e19	1.62432
$837$	−4.41824e18	−0.444155
$838$	2.88537e18	0.287816
$839$	9.34410e18	0.924879	0.462440	−	0.886651i	$-0.346974\pi$
$839$	9.34410e18	0.924879	0.462440	+	0.886651i	$0.346974\pi$
$840$	−4.67617e17	−0.0459278
$841$	−5.06607e18	−0.493738
$842$	−1.42053e19	−1.37380
$843$	2.36395e19	2.26860
$844$	6.35603e18	0.605285
$845$	3.56214e18	0.336622
$846$	−5.21744e18	−0.489272
$847$	−1.55574e19	−1.44776
$848$	−3.82070e18	−0.352833
$849$	−1.40868e19	−1.29096
$850$	−2.89091e18	−0.262913
$851$	−8.00391e18	−0.722370
$852$	−1.51854e19	−1.36009
$853$	−1.49241e19	−1.32654	−0.663268	−	0.748382i	$-0.730831\pi$
$853$	−1.49241e19	−1.32654	−0.663268	+	0.748382i	$0.730831\pi$
$854$	−8.70366e16	−0.00767761
$855$	1.92368e18	0.168404
$856$	4.04584e17	0.0351503
$857$	1.48475e18	0.128020	0.0640102	−	0.997949i	$-0.479611\pi$
$857$	1.48475e18	0.128020	0.0640102	+	0.997949i	$0.479611\pi$
$858$	−1.35742e19	−1.16157
$859$	1.08123e19	0.918256	0.459128	−	0.888370i	$-0.348162\pi$
$859$	1.08123e19	0.918256	0.459128	+	0.888370i	$0.348162\pi$
$860$	2.97742e18	0.250958
$861$	−1.29306e18	−0.108168
$862$	6.77940e18	0.562852
$863$	−1.45004e18	−0.119484	−0.0597422	−	0.998214i	$-0.519028\pi$
$863$	−1.45004e18	−0.119484	−0.0597422	+	0.998214i	$0.519028\pi$
$864$	−1.33103e19	−1.08855
$865$	9.49846e18	0.770989
$866$	8.26026e18	0.665469
$867$	−2.22956e18	−0.178277
$868$	−1.11604e19	−0.885727
$869$	−1.08409e19	−0.853957
$870$	−6.73581e18	−0.526641
$871$	1.02524e19	0.795621
$872$	−8.17324e17	−0.0629560
$873$	3.72055e18	0.284455
$874$	3.40169e19	2.58149
$875$	1.73314e18	0.130551
$876$	−1.17837e19	−0.881063
$877$	−8.42309e18	−0.625136	−0.312568	−	0.949895i	$-0.601189\pi$
$877$	−8.42309e18	−0.625136	−0.312568	+	0.949895i	$0.601189\pi$
$878$	2.69251e19	1.98355
$879$	1.57196e18	0.114952
$880$	−8.30992e18	−0.603197
$881$	−7.10005e18	−0.511585	−0.255793	−	0.966732i	$-0.582336\pi$
$881$	−7.10005e18	−0.511585	−0.255793	+	0.966732i	$0.582336\pi$
$882$	−7.70475e18	−0.551078
$883$	−6.44311e17	−0.0457458	−0.0228729	−	0.999738i	$-0.507281\pi$
$883$	−6.44311e17	−0.0457458	−0.0228729	+	0.999738i	$0.507281\pi$
$884$	−6.76586e18	−0.476852
$885$	2.90878e18	0.203507
$886$	2.25927e19	1.56909
$887$	−1.62161e19	−1.11800	−0.559002	−	0.829166i	$-0.688816\pi$
$887$	−1.62161e19	−1.11800	−0.559002	+	0.829166i	$0.688816\pi$
$888$	4.53878e17	0.0310638
$889$	2.40745e19	1.63567
$890$	7.70403e17	0.0519617
$891$	2.58157e19	1.72854
$892$	3.65124e18	0.242699
$893$	−1.67913e19	−1.10802
$894$	−4.05474e19	−2.65625
$895$	−4.10240e18	−0.266802
$896$	−2.74454e18	−0.177202
$897$	−1.46999e19	−0.942242
$898$	−2.67395e19	−1.70160
$899$	−6.55554e18	−0.414162
$900$	1.13388e18	0.0711196
$901$	5.45340e18	0.339591
$902$	2.08780e18	0.129076
$903$	1.48232e19	0.909851
$904$	−6.14688e17	−0.0374593
$905$	−5.19393e18	−0.314254
$906$	3.14055e19	1.88657
$907$	3.19866e18	0.190775	0.0953874	−	0.995440i	$-0.469591\pi$
$907$	3.19866e18	0.190775	0.0953874	+	0.995440i	$0.469591\pi$
$908$	1.27928e19	0.757541
$909$	−5.99575e18	−0.352515
$910$	7.94704e18	0.463913
$911$	−9.72950e18	−0.563925	−0.281962	−	0.959425i	$-0.590985\pi$
$911$	−9.72950e18	−0.563925	−0.281962	+	0.959425i	$0.590985\pi$
$912$	2.12309e19	1.22180
$913$	2.57162e19	1.46942
$914$	1.58470e19	0.899074
$915$	3.38368e16	0.00190613
$916$	−5.54421e18	−0.310113
$917$	2.14191e19	1.18960
$918$	1.81891e19	1.00307
$919$	−3.16982e19	−1.73574	−0.867868	−	0.496796i	$-0.834510\pi$
$919$	−3.16982e19	−1.73574	−0.867868	+	0.496796i	$0.834510\pi$
$920$	8.17635e17	0.0444568
$921$	−2.56673e19	−1.38577
$922$	7.99503e17	0.0428617
$923$	1.05238e19	0.560222
$924$	4.70486e19	2.48702
$925$	−1.68222e18	−0.0883000
$926$	−4.40905e19	−2.29813
$927$	5.74573e18	0.297390
$928$	−1.97490e19	−1.01504
$929$	−3.17387e19	−1.61990	−0.809948	−	0.586502i	$-0.800505\pi$
$929$	−3.17387e19	−1.61990	−0.809948	+	0.586502i	$0.800505\pi$
$930$	8.50060e18	0.430834
$931$	−2.47961e19	−1.24799
$932$	2.56615e19	1.28256
$933$	−8.75635e18	−0.434603
$934$	−4.22440e19	−2.08214
$935$	1.18610e19	0.580559
$936$	2.12016e17	0.0103057
$937$	2.75535e19	1.33006	0.665028	−	0.746818i	$-0.268419\pi$
$937$	2.75535e19	1.33006	0.665028	+	0.746818i	$0.268419\pi$
$938$	−6.96209e19	−3.33750
$939$	1.34298e19	0.639358
$940$	−9.89730e18	−0.467935
$941$	2.25920e19	1.06077	0.530386	−	0.847756i	$-0.322047\pi$
$941$	2.25920e19	1.06077	0.530386	+	0.847756i	$0.322047\pi$
$942$	−7.83240e18	−0.365228
$943$	2.26094e18	0.104704
$944$	8.16518e18	0.375533
$945$	−1.09046e19	−0.498084
$946$	−2.39337e19	−1.08572
$947$	7.87113e18	0.354619	0.177310	−	0.984155i	$-0.443261\pi$
$947$	7.87113e18	0.354619	0.177310	+	0.984155i	$0.443261\pi$
$948$	1.63256e19	0.730492
$949$	8.16637e18	0.362910
$950$	7.14948e18	0.315552
$951$	−2.05225e19	−0.899615
$952$	1.87357e18	0.0815698
$953$	1.27474e19	0.551210	0.275605	−	0.961271i	$-0.411122\pi$
$953$	1.27474e19	0.551210	0.275605	+	0.961271i	$0.411122\pi$
$954$	−4.19066e18	−0.179977
$955$	−1.06546e19	−0.454479
$956$	−2.38228e19	−1.00929
$957$	2.76361e19	1.16292
$958$	−2.13368e19	−0.891772
$959$	3.19566e19	1.32660
$960$	1.36048e19	0.560957
$961$	−1.61445e19	−0.661183
$962$	−7.71354e18	−0.313773
$963$	−4.88410e18	−0.197339
$964$	1.99737e19	0.801599
$965$	3.32050e18	0.132366
$966$	9.98227e19	3.95255
$967$	−3.41837e19	−1.34446	−0.672228	−	0.740344i	$-0.734663\pi$
$967$	−3.41837e19	−1.34446	−0.672228	+	0.740344i	$0.734663\pi$
$968$	−1.54256e18	−0.0602634
$969$	−3.03035e19	−1.17595
$970$	1.38277e19	0.533007
$971$	4.07103e19	1.55876	0.779381	−	0.626551i	$-0.215534\pi$
$971$	4.07103e19	1.55876	0.779381	+	0.626551i	$0.215534\pi$
$972$	−1.79614e19	−0.683141
$973$	7.24421e19	2.73689
$974$	1.48264e19	0.556421
$975$	−3.08954e18	−0.115176
$976$	9.49826e16	0.00351739
$977$	1.65613e19	0.609228	0.304614	−	0.952476i	$-0.401473\pi$
$977$	1.65613e19	0.609228	0.304614	+	0.952476i	$0.401473\pi$
$978$	−7.96633e19	−2.91109
$979$	−3.16086e18	−0.114741
$980$	−1.46156e19	−0.527046
$981$	9.86665e18	0.353445
$982$	1.08527e19	0.386202
$983$	2.68368e19	0.948709	0.474354	−	0.880334i	$-0.342682\pi$
$983$	2.68368e19	0.948709	0.474354	+	0.880334i	$0.342682\pi$
$984$	−1.28211e17	−0.00450254
$985$	−6.95873e17	−0.0242770
$986$	2.69879e19	0.935340
$987$	−4.92739e19	−1.69651
$988$	1.67326e19	0.572325
$989$	−2.59185e19	−0.880711
$990$	−9.11457e18	−0.307686
$991$	−2.74102e19	−0.919251	−0.459625	−	0.888113i	$-0.652016\pi$
$991$	−2.74102e19	−0.919251	−0.459625	+	0.888113i	$0.652016\pi$
$992$	2.49233e19	0.830385
$993$	−3.37338e19	−1.11659
$994$	−7.14639e19	−2.35004
$995$	1.32773e19	0.433769
$996$	−3.87268e19	−1.25697
$997$	−6.38878e18	−0.206015	−0.103008	−	0.994681i	$-0.532847\pi$
$997$	−6.38878e18	−0.206015	−0.103008	+	0.994681i	$0.532847\pi$
$998$	6.20558e19	1.98808
$999$	1.05842e19	0.336885

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.14.a.a.1.1	✓	2
3.2	odd	2		45.14.a.d.1.2		2
4.3	odd	2		80.14.a.d.1.1		2
5.2	odd	4		25.14.b.a.24.1		4
5.3	odd	4		25.14.b.a.24.4		4
5.4	even	2		25.14.a.a.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.14.a.a.1.1	✓	2	1.1	even	1	trivial
25.14.a.a.1.2		2	5.4	even	2
25.14.b.a.24.1		4	5.2	odd	4
25.14.b.a.24.4		4	5.3	odd	4
45.14.a.d.1.2		2	3.2	odd	2
80.14.a.d.1.1		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	5.a (trivial)

\(f(q)\)	\(=\)	\(q-129.353 q^{2} +1462.24 q^{3} +8540.26 q^{4} -15625.0 q^{5} -189145. q^{6} -454332. q^{7} -45048.4 q^{8} +543819. q^{9} +O(q^{10})\)	\(q-129.353 q^{2} +1462.24 q^{3} +8540.26 q^{4} -15625.0 q^{5} -189145. q^{6} -454332. q^{7} -45048.4 q^{8} +543819. q^{9} +2.02114e6 q^{10} -8.29247e6 q^{11} +1.24879e7 q^{12} -8.65436e6 q^{13} +5.87693e7 q^{14} -2.28475e7 q^{15} -6.41346e7 q^{16} +9.15414e7 q^{17} -7.03448e7 q^{18} -2.26390e8 q^{19} -1.33442e8 q^{20} -6.64342e8 q^{21} +1.07266e9 q^{22} +1.16161e9 q^{23} -6.58715e7 q^{24} +2.44141e8 q^{25} +1.11947e9 q^{26} -1.53609e9 q^{27} -3.88011e9 q^{28} -2.27916e9 q^{29} +2.95540e9 q^{30} +2.87630e9 q^{31} +8.66506e9 q^{32} -1.21256e10 q^{33} -1.18412e10 q^{34} +7.09894e9 q^{35} +4.64436e9 q^{36} -6.89036e9 q^{37} +2.92843e10 q^{38} -1.26547e10 q^{39} +7.03881e8 q^{40} +1.94638e9 q^{41} +8.59347e10 q^{42} -2.23125e10 q^{43} -7.08199e10 q^{44} -8.49718e9 q^{45} -1.50258e11 q^{46} +7.41696e10 q^{47} -9.37802e10 q^{48} +1.09528e11 q^{49} -3.15804e10 q^{50} +1.33855e11 q^{51} -7.39105e10 q^{52} +5.95731e10 q^{53} +1.98698e11 q^{54} +1.29570e11 q^{55} +2.04669e10 q^{56} -3.31036e11 q^{57} +2.94817e11 q^{58} -1.27313e11 q^{59} -1.95123e11 q^{60} -1.48099e9 q^{61} -3.72058e11 q^{62} -2.47074e11 q^{63} -5.95462e11 q^{64} +1.35224e11 q^{65} +1.56848e12 q^{66} -1.18465e12 q^{67} +7.81787e11 q^{68} +1.69855e12 q^{69} -9.18270e11 q^{70} -1.21601e12 q^{71} -2.44982e10 q^{72} -9.43614e11 q^{73} +8.91290e11 q^{74} +3.56992e11 q^{75} -1.93343e12 q^{76} +3.76754e12 q^{77} +1.63693e12 q^{78} +1.30732e12 q^{79} +1.00210e12 q^{80} -3.11315e12 q^{81} -2.51771e11 q^{82} -3.10115e12 q^{83} -5.67365e12 q^{84} -1.43033e12 q^{85} +2.88620e12 q^{86} -3.33267e12 q^{87} +3.73562e11 q^{88} +3.81172e11 q^{89} +1.09914e12 q^{90} +3.93195e12 q^{91} +9.92045e12 q^{92} +4.20583e12 q^{93} -9.59407e12 q^{94} +3.53734e12 q^{95} +1.26704e13 q^{96} +6.84151e12 q^{97} -1.41679e13 q^{98} -4.50961e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 80 q^{2} + 780 q^{3} + 2784 q^{4} - 31250 q^{5} - 222816 q^{6} - 616300 q^{7} - 733440 q^{8} - 585054 q^{9}+O(q^{10}) \) 2 * q - 80 * q^2 + 780 * q^3 + 2784 * q^4 - 31250 * q^5 - 222816 * q^6 - 616300 * q^7 - 733440 * q^8 - 585054 * q^9	\( 2 q - 80 q^{2} + 780 q^{3} + 2784 q^{4} - 31250 q^{5} - 222816 q^{6} - 616300 q^{7} - 733440 q^{8} - 585054 q^{9} + 1250000 q^{10} - 2467136 q^{11} + 16415040 q^{12} + 6517860 q^{13} + 50775648 q^{14} - 12187500 q^{15} - 50953728 q^{16} + 633460 q^{17} - 126058320 q^{18} - 374063400 q^{19} - 43500000 q^{20} - 553840776 q^{21} + 1360157440 q^{22} + 621982140 q^{23} + 403776000 q^{24} + 488281250 q^{25} + 1868267104 q^{26} + 321782760 q^{27} - 2947781440 q^{28} - 7795134100 q^{29} + 3481500000 q^{30} - 4957819816 q^{31} + 14954885120 q^{32} - 16099847040 q^{33} - 16327772192 q^{34} + 9629687500 q^{35} + 11142443232 q^{36} + 21833071780 q^{37} + 21996120640 q^{38} - 23005812648 q^{39} + 11460000000 q^{40} + 5565813644 q^{41} + 91388324160 q^{42} - 52510877700 q^{43} - 104352013312 q^{44} + 9141468750 q^{45} - 176890366176 q^{46} + 92855886340 q^{47} - 102772700160 q^{48} + 38873112314 q^{49} - 19531250000 q^{50} + 195876254904 q^{51} - 161245659200 q^{52} + 266248876180 q^{53} + 290389752000 q^{54} + 38549000000 q^{55} + 131964403200 q^{56} - 230287741680 q^{57} + 22585283360 q^{58} + 253501607800 q^{59} - 256485000000 q^{60} - 377459239836 q^{61} - 758697351360 q^{62} - 64232955180 q^{63} - 393017368576 q^{64} - 101841562500 q^{65} + 1372339327488 q^{66} - 2375782313740 q^{67} + 1305076479680 q^{68} + 2066706001512 q^{69} - 793369500000 q^{70} - 556190102776 q^{71} + 752608730880 q^{72} - 556465382460 q^{73} + 2308883896928 q^{74} + 190429687500 q^{75} - 1083383024000 q^{76} + 2824016150400 q^{77} + 1126072161600 q^{78} - 2408230567600 q^{79} + 796152000000 q^{80} - 2580872423958 q^{81} - 73140129760 q^{82} - 3898295602980 q^{83} - 6309721809792 q^{84} - 9897812500 q^{85} + 1395814341664 q^{86} + 430538668680 q^{87} - 3636551086080 q^{88} + 106847675700 q^{89} + 1969661250000 q^{90} + 1474535181544 q^{91} + 13026685584960 q^{92} + 9550571999760 q^{93} - 8671844110112 q^{94} + 5844740625000 q^{95} + 8379224039424 q^{96} + 18744409451140 q^{97} - 17654928754960 q^{98} - 11085674027328 q^{99}+O(q^{100}) \) 2 * q - 80 * q^2 + 780 * q^3 + 2784 * q^4 - 31250 * q^5 - 222816 * q^6 - 616300 * q^7 - 733440 * q^8 - 585054 * q^9 + 1250000 * q^10 - 2467136 * q^11 + 16415040 * q^12 + 6517860 * q^13 + 50775648 * q^14 - 12187500 * q^15 - 50953728 * q^16 + 633460 * q^17 - 126058320 * q^18 - 374063400 * q^19 - 43500000 * q^20 - 553840776 * q^21 + 1360157440 * q^22 + 621982140 * q^23 + 403776000 * q^24 + 488281250 * q^25 + 1868267104 * q^26 + 321782760 * q^27 - 2947781440 * q^28 - 7795134100 * q^29 + 3481500000 * q^30 - 4957819816 * q^31 + 14954885120 * q^32 - 16099847040 * q^33 - 16327772192 * q^34 + 9629687500 * q^35 + 11142443232 * q^36 + 21833071780 * q^37 + 21996120640 * q^38 - 23005812648 * q^39 + 11460000000 * q^40 + 5565813644 * q^41 + 91388324160 * q^42 - 52510877700 * q^43 - 104352013312 * q^44 + 9141468750 * q^45 - 176890366176 * q^46 + 92855886340 * q^47 - 102772700160 * q^48 + 38873112314 * q^49 - 19531250000 * q^50 + 195876254904 * q^51 - 161245659200 * q^52 + 266248876180 * q^53 + 290389752000 * q^54 + 38549000000 * q^55 + 131964403200 * q^56 - 230287741680 * q^57 + 22585283360 * q^58 + 253501607800 * q^59 - 256485000000 * q^60 - 377459239836 * q^61 - 758697351360 * q^62 - 64232955180 * q^63 - 393017368576 * q^64 - 101841562500 * q^65 + 1372339327488 * q^66 - 2375782313740 * q^67 + 1305076479680 * q^68 + 2066706001512 * q^69 - 793369500000 * q^70 - 556190102776 * q^71 + 752608730880 * q^72 - 556465382460 * q^73 + 2308883896928 * q^74 + 190429687500 * q^75 - 1083383024000 * q^76 + 2824016150400 * q^77 + 1126072161600 * q^78 - 2408230567600 * q^79 + 796152000000 * q^80 - 2580872423958 * q^81 - 73140129760 * q^82 - 3898295602980 * q^83 - 6309721809792 * q^84 - 9897812500 * q^85 + 1395814341664 * q^86 + 430538668680 * q^87 - 3636551086080 * q^88 + 106847675700 * q^89 + 1969661250000 * q^90 + 1474535181544 * q^91 + 13026685584960 * q^92 + 9550571999760 * q^93 - 8671844110112 * q^94 + 5844740625000 * q^95 + 8379224039424 * q^96 + 18744409451140 * q^97 - 17654928754960 * q^98 - 11085674027328 * q^99

Introduction

L-functions

Modular forms

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Database

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