LMFDB - Embedded newform 3.14.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,14,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, 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("3.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	3.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:	$3.21692786856$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{1969}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 492 $ x^2 - x - 492
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-21.6867$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+106.120 q^{2} +729.000 q^{3} +3069.51 q^{4} +37397.4 q^{5} +77361.7 q^{6} -470568. q^{7} -543600. q^{8} +531441. q^{9} +O(q^{10})$	\(q+106.120 q^{2} +729.000 q^{3} +3069.51 q^{4} +37397.4 q^{5} +77361.7 q^{6} -470568. q^{7} -543600. q^{8} +531441. q^{9} +3.96862e6 q^{10} -4.53706e6 q^{11} +2.23767e6 q^{12} +2.07280e7 q^{13} -4.99367e7 q^{14} +2.72627e7 q^{15} -8.28324e7 q^{16} +5.16317e7 q^{17} +5.63966e7 q^{18} +2.30281e8 q^{19} +1.14792e8 q^{20} -3.43044e8 q^{21} -4.81474e8 q^{22} -6.24089e7 q^{23} -3.96285e8 q^{24} +1.77862e8 q^{25} +2.19966e9 q^{26} +3.87420e8 q^{27} -1.44441e9 q^{28} -1.55107e9 q^{29} +2.89312e9 q^{30} +1.67331e9 q^{31} -4.33702e9 q^{32} -3.30752e9 q^{33} +5.47917e9 q^{34} -1.75980e10 q^{35} +1.63126e9 q^{36} +1.13979e10 q^{37} +2.44375e10 q^{38} +1.51107e10 q^{39} -2.03292e10 q^{40} +2.06830e10 q^{41} -3.64039e10 q^{42} -4.71393e10 q^{43} -1.39265e10 q^{44} +1.98745e10 q^{45} -6.62285e9 q^{46} +5.74250e10 q^{47} -6.03848e10 q^{48} +1.24545e11 q^{49} +1.88747e10 q^{50} +3.76395e10 q^{51} +6.36246e10 q^{52} -2.87197e11 q^{53} +4.11132e10 q^{54} -1.69674e11 q^{55} +2.55801e11 q^{56} +1.67875e11 q^{57} -1.64600e11 q^{58} -5.16846e11 q^{59} +8.36830e10 q^{60} +2.96537e11 q^{61} +1.77572e11 q^{62} -2.50079e11 q^{63} +2.18317e11 q^{64} +7.75171e11 q^{65} -3.50995e11 q^{66} +4.61824e11 q^{67} +1.58484e11 q^{68} -4.54961e10 q^{69} -1.86750e12 q^{70} -1.04330e12 q^{71} -2.88891e11 q^{72} -1.68078e10 q^{73} +1.20955e12 q^{74} +1.29661e11 q^{75} +7.06849e11 q^{76} +2.13499e12 q^{77} +1.60355e12 q^{78} -4.91179e11 q^{79} -3.09772e12 q^{80} +2.82430e11 q^{81} +2.19488e12 q^{82} -2.48490e12 q^{83} -1.05298e12 q^{84} +1.93089e12 q^{85} -5.00244e12 q^{86} -1.13073e12 q^{87} +2.46635e12 q^{88} +4.61192e12 q^{89} +2.10909e12 q^{90} -9.75390e12 q^{91} -1.91565e11 q^{92} +1.21984e12 q^{93} +6.09396e12 q^{94} +8.61190e12 q^{95} -3.16169e12 q^{96} -9.87180e12 q^{97} +1.32167e13 q^{98} -2.41118e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 54 q^{2} + 1458 q^{3} + 20516 q^{4} + 40716 q^{5} - 39366 q^{6} - 21008 q^{7} - 2025432 q^{8} + 1062882 q^{9}+O(q^{10}) $ 2 * q - 54 * q^2 + 1458 * q^3 + 20516 * q^4 + 40716 * q^5 - 39366 * q^6 - 21008 * q^7 - 2025432 * q^8 + 1062882 * q^9	\( 2 q - 54 q^{2} + 1458 q^{3} + 20516 q^{4} + 40716 q^{5} - 39366 q^{6} - 21008 q^{7} - 2025432 q^{8} + 1062882 q^{9} + 3437244 q^{10} + 672408 q^{11} + 14956164 q^{12} + 17532604 q^{13} - 121920336 q^{14} + 29681964 q^{15} + 11517200 q^{16} + 83838564 q^{17} - 28697814 q^{18} + 256293544 q^{19} + 172689624 q^{20} - 15314832 q^{21} - 1315615752 q^{22} + 859581936 q^{23} - 1476539928 q^{24} - 1031828194 q^{25} + 2711296044 q^{26} + 774840978 q^{27} + 6398827744 q^{28} - 4728475332 q^{29} + 2505750876 q^{30} - 5982551648 q^{31} - 7305134688 q^{32} + 490185432 q^{33} + 322207092 q^{34} - 16106087520 q^{35} + 10903043556 q^{36} + 27411194092 q^{37} + 20272310856 q^{38} + 12781268316 q^{39} - 25246850832 q^{40} + 15258974292 q^{41} - 88879924944 q^{42} - 11314499240 q^{43} + 76960441008 q^{44} + 21638151756 q^{45} - 154252246608 q^{46} - 69035142240 q^{47} + 8396038800 q^{48} + 229759626930 q^{49} + 212570589654 q^{50} + 61118313156 q^{51} + 7876928824 q^{52} - 226336894164 q^{53} - 20920706406 q^{54} - 152386092144 q^{55} - 410370995520 q^{56} + 186837993576 q^{57} + 344167850412 q^{58} - 927820824264 q^{59} + 125890735896 q^{60} + 179395461340 q^{61} + 1403430184224 q^{62} - 11164512528 q^{63} - 79339420096 q^{64} + 764567325288 q^{65} - 959083883208 q^{66} - 698315061176 q^{67} + 720380180232 q^{68} + 626635231344 q^{69} - 2106389414880 q^{70} - 784458549936 q^{71} - 1076397607512 q^{72} + 1857400245076 q^{73} - 1354499801316 q^{74} - 752202753426 q^{75} + 1160678400976 q^{76} + 4476961329984 q^{77} + 1976534816076 q^{78} - 714025470080 q^{79} - 2784606024096 q^{80} + 564859072962 q^{81} + 3063378763044 q^{82} - 4574293917912 q^{83} + 4664745425376 q^{84} + 2037774070872 q^{85} - 10738721134152 q^{86} - 3447058517028 q^{87} - 5253209973792 q^{88} + 3270178701684 q^{89} + 1826692388604 q^{90} - 11190403944928 q^{91} + 15893942353632 q^{92} - 4361280151392 q^{93} + 26342795766816 q^{94} + 8698230246384 q^{95} - 5325443187552 q^{96} - 9874926156476 q^{97} - 3630291434694 q^{98} + 357345179928 q^{99}+O(q^{100}) \) 2 * q - 54 * q^2 + 1458 * q^3 + 20516 * q^4 + 40716 * q^5 - 39366 * q^6 - 21008 * q^7 - 2025432 * q^8 + 1062882 * q^9 + 3437244 * q^10 + 672408 * q^11 + 14956164 * q^12 + 17532604 * q^13 - 121920336 * q^14 + 29681964 * q^15 + 11517200 * q^16 + 83838564 * q^17 - 28697814 * q^18 + 256293544 * q^19 + 172689624 * q^20 - 15314832 * q^21 - 1315615752 * q^22 + 859581936 * q^23 - 1476539928 * q^24 - 1031828194 * q^25 + 2711296044 * q^26 + 774840978 * q^27 + 6398827744 * q^28 - 4728475332 * q^29 + 2505750876 * q^30 - 5982551648 * q^31 - 7305134688 * q^32 + 490185432 * q^33 + 322207092 * q^34 - 16106087520 * q^35 + 10903043556 * q^36 + 27411194092 * q^37 + 20272310856 * q^38 + 12781268316 * q^39 - 25246850832 * q^40 + 15258974292 * q^41 - 88879924944 * q^42 - 11314499240 * q^43 + 76960441008 * q^44 + 21638151756 * q^45 - 154252246608 * q^46 - 69035142240 * q^47 + 8396038800 * q^48 + 229759626930 * q^49 + 212570589654 * q^50 + 61118313156 * q^51 + 7876928824 * q^52 - 226336894164 * q^53 - 20920706406 * q^54 - 152386092144 * q^55 - 410370995520 * q^56 + 186837993576 * q^57 + 344167850412 * q^58 - 927820824264 * q^59 + 125890735896 * q^60 + 179395461340 * q^61 + 1403430184224 * q^62 - 11164512528 * q^63 - 79339420096 * q^64 + 764567325288 * q^65 - 959083883208 * q^66 - 698315061176 * q^67 + 720380180232 * q^68 + 626635231344 * q^69 - 2106389414880 * q^70 - 784458549936 * q^71 - 1076397607512 * q^72 + 1857400245076 * q^73 - 1354499801316 * q^74 - 752202753426 * q^75 + 1160678400976 * q^76 + 4476961329984 * q^77 + 1976534816076 * q^78 - 714025470080 * q^79 - 2784606024096 * q^80 + 564859072962 * q^81 + 3063378763044 * q^82 - 4574293917912 * q^83 + 4664745425376 * q^84 + 2037774070872 * q^85 - 10738721134152 * q^86 - 3447058517028 * q^87 - 5253209973792 * q^88 + 3270178701684 * q^89 + 1826692388604 * q^90 - 11190403944928 * q^91 + 15893942353632 * q^92 - 4361280151392 * q^93 + 26342795766816 * q^94 + 8698230246384 * q^95 - 5325443187552 * q^96 - 9874926156476 * q^97 - 3630291434694 * q^98 + 357345179928 * 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 $

$2$	106.120	1.17247	0.586237	−	0.810140i	$-0.300609\pi$
$2$	106.120	1.17247	0.586237	+	0.810140i	$0.300609\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	3069.51	0.374696
$5$	37397.4	1.07038	0.535188	−	0.844733i	$-0.320241\pi$
$5$	37397.4	1.07038	0.535188	+	0.844733i	$0.320241\pi$
$6$	77361.7	0.676928
$7$	−470568.	−1.51177	−0.755883	−	0.654706i	$-0.772792\pi$
$7$	−470568.	−1.51177	−0.755883	+	0.654706i	$0.772792\pi$
$8$	−543600.	−0.733153
$9$	531441.	0.333333
$10$	3.96862e6	1.25499
$11$	−4.53706e6	−0.772187	−0.386093	−	0.922460i	$-0.626176\pi$
$11$	−4.53706e6	−0.772187	−0.386093	+	0.922460i	$0.626176\pi$
$12$	2.23767e6	0.216331
$13$	2.07280e7	1.19104	0.595518	−	0.803342i	$-0.296947\pi$
$13$	2.07280e7	1.19104	0.595518	+	0.803342i	$0.296947\pi$
$14$	−4.99367e7	−1.77251
$15$	2.72627e7	0.617982
$16$	−8.28324e7	−1.23430
$17$	5.16317e7	0.518799	0.259399	−	0.965770i	$-0.416475\pi$
$17$	5.16317e7	0.518799	0.259399	+	0.965770i	$0.416475\pi$
$18$	5.63966e7	0.390825
$19$	2.30281e8	1.12295	0.561474	−	0.827495i	$-0.310235\pi$
$19$	2.30281e8	1.12295	0.561474	+	0.827495i	$0.310235\pi$
$20$	1.14792e8	0.401065
$21$	−3.43044e8	−0.872819
$22$	−4.81474e8	−0.905369
$23$	−6.24089e7	−0.0879054	−0.0439527	−	0.999034i	$-0.513995\pi$
$23$	−6.24089e7	−0.0879054	−0.0439527	+	0.999034i	$0.513995\pi$
$24$	−3.96285e8	−0.423286
$25$	1.77862e8	0.145704
$26$	2.19966e9	1.39646
$27$	3.87420e8	0.192450
$28$	−1.44441e9	−0.566452
$29$	−1.55107e9	−0.484221	−0.242110	−	0.970249i	$-0.577840\pi$
$29$	−1.55107e9	−0.484221	−0.242110	+	0.970249i	$0.577840\pi$
$30$	2.89312e9	0.724568
$31$	1.67331e9	0.338630	0.169315	−	0.985562i	$-0.445845\pi$
$31$	1.67331e9	0.338630	0.169315	+	0.985562i	$0.445845\pi$
$32$	−4.33702e9	−0.714030
$33$	−3.30752e9	−0.445822
$34$	5.47917e9	0.608278
$35$	−1.75980e10	−1.61816
$36$	1.63126e9	0.124899
$37$	1.13979e10	0.730322	0.365161	−	0.930944i	$-0.381014\pi$
$37$	1.13979e10	0.730322	0.365161	+	0.930944i	$0.381014\pi$
$38$	2.44375e10	1.31663
$39$	1.51107e10	0.687645
$40$	−2.03292e10	−0.784749
$41$	2.06830e10	0.680015	0.340007	−	0.940423i	$-0.389570\pi$
$41$	2.06830e10	0.680015	0.340007	+	0.940423i	$0.389570\pi$
$42$	−3.64039e10	−1.02336
$43$	−4.71393e10	−1.13720	−0.568602	−	0.822613i	$-0.692516\pi$
$43$	−4.71393e10	−1.13720	−0.568602	+	0.822613i	$0.692516\pi$
$44$	−1.39265e10	−0.289335
$45$	1.98745e10	0.356792
$46$	−6.62285e9	−0.103067
$47$	5.74250e10	0.777079	0.388540	−	0.921432i	$-0.372980\pi$
$47$	5.74250e10	0.777079	0.388540	+	0.921432i	$0.372980\pi$
$48$	−6.03848e10	−0.712623
$49$	1.24545e11	1.28544
$50$	1.88747e10	0.170835
$51$	3.76395e10	0.299528
$52$	6.36246e10	0.446276
$53$	−2.87197e11	−1.77986	−0.889930	−	0.456096i	$-0.849247\pi$
$53$	−2.87197e11	−1.77986	−0.889930	+	0.456096i	$0.849247\pi$
$54$	4.11132e10	0.225643
$55$	−1.69674e11	−0.826530
$56$	2.55801e11	1.10836
$57$	1.67875e11	0.648334
$58$	−1.64600e11	−0.567736
$59$	−5.16846e11	−1.59523	−0.797615	−	0.603167i	$-0.793905\pi$
$59$	−5.16846e11	−1.59523	−0.797615	+	0.603167i	$0.793905\pi$
$60$	8.36830e10	0.231555
$61$	2.96537e11	0.736944	0.368472	−	0.929639i	$-0.379881\pi$
$61$	2.96537e11	0.736944	0.368472	+	0.929639i	$0.379881\pi$
$62$	1.77572e11	0.397035
$63$	−2.50079e11	−0.503922
$64$	2.18317e11	0.397117
$65$	7.75171e11	1.27486
$66$	−3.50995e11	−0.522715
$67$	4.61824e11	0.623721	0.311861	−	0.950128i	$-0.399048\pi$
$67$	4.61824e11	0.623721	0.311861	+	0.950128i	$0.399048\pi$
$68$	1.58484e11	0.194392
$69$	−4.54961e10	−0.0507522
$70$	−1.86750e12	−1.89725
$71$	−1.04330e12	−0.966558	−0.483279	−	0.875466i	$-0.660554\pi$
$71$	−1.04330e12	−0.966558	−0.483279	+	0.875466i	$0.660554\pi$
$72$	−2.88891e11	−0.244384
$73$	−1.68078e10	−0.0129991	−0.00649954	−	0.999979i	$-0.502069\pi$
$73$	−1.68078e10	−0.0129991	−0.00649954	+	0.999979i	$0.502069\pi$
$74$	1.20955e12	0.856284
$75$	1.29661e11	0.0841225
$76$	7.06849e11	0.420764
$77$	2.13499e12	1.16737
$78$	1.60355e12	0.806246
$79$	−4.91179e11	−0.227334	−0.113667	−	0.993519i	$-0.536260\pi$
$79$	−4.91179e11	−0.227334	−0.113667	+	0.993519i	$0.536260\pi$
$80$	−3.09772e12	−1.32116
$81$	2.82430e11	0.111111
$82$	2.19488e12	0.797300
$83$	−2.48490e12	−0.834259	−0.417129	−	0.908847i	$-0.636964\pi$
$83$	−2.48490e12	−0.834259	−0.417129	+	0.908847i	$0.636964\pi$
$84$	−1.05298e12	−0.327041
$85$	1.93089e12	0.555309
$86$	−5.00244e12	−1.33334
$87$	−1.13073e12	−0.279565
$88$	2.46635e12	0.566131
$89$	4.61192e12	0.983665	0.491832	−	0.870690i	$-0.336327\pi$
$89$	4.61192e12	0.983665	0.491832	+	0.870690i	$0.336327\pi$
$90$	2.10909e12	0.418329
$91$	−9.75390e12	−1.80057
$92$	−1.91565e11	−0.0329378
$93$	1.21984e12	0.195508
$94$	6.09396e12	0.911105
$95$	8.61190e12	1.20198
$96$	−3.16169e12	−0.412246
$97$	−9.87180e12	−1.20332	−0.601659	−	0.798753i	$-0.705493\pi$
$97$	−9.87180e12	−1.20332	−0.601659	+	0.798753i	$0.705493\pi$
$98$	1.32167e13	1.50714
$99$	−2.41118e12	−0.257396
$100$	5.45948e11	0.0545948
$101$	−1.13959e13	−1.06821	−0.534107	−	0.845417i	$-0.679352\pi$
$101$	−1.13959e13	−1.06821	−0.534107	+	0.845417i	$0.679352\pi$
$102$	3.99432e12	0.351189
$103$	1.46278e13	1.20708	0.603541	−	0.797332i	$-0.293756\pi$
$103$	1.46278e13	1.20708	0.603541	+	0.797332i	$0.293756\pi$
$104$	−1.12677e13	−0.873211
$105$	−1.28289e13	−0.934244
$106$	−3.04774e13	−2.08684
$107$	1.19546e13	0.770087	0.385043	−	0.922898i	$-0.374186\pi$
$107$	1.19546e13	0.770087	0.385043	+	0.922898i	$0.374186\pi$
$108$	1.18919e12	0.0721102
$109$	2.22849e13	1.27274	0.636369	−	0.771385i	$-0.280436\pi$
$109$	2.22849e13	1.27274	0.636369	+	0.771385i	$0.280436\pi$
$110$	−1.80059e13	−0.969085
$111$	8.30908e12	0.421652
$112$	3.89782e13	1.86597
$113$	4.91990e12	0.222304	0.111152	−	0.993803i	$-0.464546\pi$
$113$	4.91990e12	0.222304	0.111152	+	0.993803i	$0.464546\pi$
$114$	1.78149e13	0.760155
$115$	−2.33393e12	−0.0940918
$116$	−4.76101e12	−0.181435
$117$	1.10157e13	0.397012
$118$	−5.48478e13	−1.87037
$119$	−2.42962e13	−0.784302
$120$	−1.48200e13	−0.453075
$121$	−1.39378e13	−0.403728
$122$	3.14686e13	0.864048
$123$	1.50779e13	0.392607
$124$	5.13623e12	0.126883
$125$	−3.89995e13	−0.914417
$126$	−2.65384e13	−0.590836
$127$	3.57455e13	0.755957	0.377979	−	0.925814i	$-0.376619\pi$
$127$	3.57455e13	0.755957	0.377979	+	0.925814i	$0.376619\pi$
$128$	5.86968e13	1.17964
$129$	−3.43646e13	−0.656565
$130$	8.22614e13	1.49474
$131$	−7.90565e12	−0.136670	−0.0683352	−	0.997662i	$-0.521769\pi$
$131$	−7.90565e12	−0.136670	−0.0683352	+	0.997662i	$0.521769\pi$
$132$	−1.01524e13	−0.167048
$133$	−1.08363e14	−1.69763
$134$	4.90089e13	0.731297
$135$	1.44885e13	0.205994
$136$	−2.80670e13	−0.380359
$137$	7.11960e13	0.919967	0.459983	−	0.887928i	$-0.347855\pi$
$137$	7.11960e13	0.919967	0.459983	+	0.887928i	$0.347855\pi$
$138$	−4.82806e12	−0.0595057
$139$	7.98488e13	0.939015	0.469507	−	0.882929i	$-0.344432\pi$
$139$	7.98488e13	0.939015	0.469507	+	0.882929i	$0.344432\pi$
$140$	−5.40172e13	−0.606317
$141$	4.18629e13	0.448647
$142$	−1.10715e14	−1.13326
$143$	−9.40440e13	−0.919702
$144$	−4.40205e13	−0.411433
$145$	−5.80059e13	−0.518298
$146$	−1.78365e12	−0.0152411
$147$	9.07932e13	0.742148
$148$	3.49860e13	0.273648
$149$	−2.35761e13	−0.176507	−0.0882533	−	0.996098i	$-0.528128\pi$
$149$	−2.35761e13	−0.176507	−0.0882533	+	0.996098i	$0.528128\pi$
$150$	1.37597e13	0.0986314
$151$	1.11718e14	0.766960	0.383480	−	0.923549i	$-0.374725\pi$
$151$	1.11718e14	0.766960	0.383480	+	0.923549i	$0.374725\pi$
$152$	−1.25181e14	−0.823293
$153$	2.74392e13	0.172933
$154$	2.26566e14	1.36871
$155$	6.25774e13	0.362461
$156$	4.63823e13	0.257657
$157$	1.74687e14	0.930919	0.465459	−	0.885069i	$-0.345889\pi$
$157$	1.74687e14	0.930919	0.465459	+	0.885069i	$0.345889\pi$
$158$	−5.21240e13	−0.266543
$159$	−2.09366e14	−1.02760
$160$	−1.62193e14	−0.764281
$161$	2.93676e13	0.132892
$162$	2.99715e13	0.130275
$163$	−3.21979e14	−1.34465	−0.672323	−	0.740257i	$-0.734704\pi$
$163$	−3.21979e14	−1.34465	−0.672323	+	0.740257i	$0.734704\pi$
$164$	6.34866e13	0.254799
$165$	−1.23693e14	−0.477197
$166$	−2.63698e14	−0.978147
$167$	−7.75401e13	−0.276611	−0.138305	−	0.990390i	$-0.544166\pi$
$167$	−7.75401e13	−0.276611	−0.138305	+	0.990390i	$0.544166\pi$
$168$	1.86479e14	0.639910
$169$	1.26773e14	0.418565
$170$	2.04907e14	0.651086
$171$	1.22381e14	0.374316
$172$	−1.44695e14	−0.426106
$173$	6.49312e14	1.84142	0.920711	−	0.390244i	$-0.127609\pi$
$173$	6.49312e14	1.84142	0.920711	+	0.390244i	$0.127609\pi$
$174$	−1.19993e14	−0.327783
$175$	−8.36960e13	−0.220271
$176$	3.75816e14	0.953109
$177$	−3.76781e14	−0.921006
$178$	4.89419e14	1.15332
$179$	−6.14630e14	−1.39659	−0.698295	−	0.715810i	$-0.746058\pi$
$179$	−6.14630e14	−1.39659	−0.698295	+	0.715810i	$0.746058\pi$
$180$	6.10049e13	0.133688
$181$	1.29251e14	0.273227	0.136614	−	0.990624i	$-0.456378\pi$
$181$	1.29251e14	0.273227	0.136614	+	0.990624i	$0.456378\pi$
$182$	−1.03509e15	−2.11112
$183$	2.16175e14	0.425475
$184$	3.39255e13	0.0644481
$185$	4.26252e14	0.781719
$186$	1.29450e14	0.229228
$187$	−2.34256e14	−0.400609
$188$	1.76267e14	0.291168
$189$	−1.82308e14	−0.290940
$190$	9.13897e14	1.40929
$191$	−8.47295e14	−1.26275	−0.631376	−	0.775477i	$-0.717509\pi$
$191$	−8.47295e14	−1.26275	−0.631376	+	0.775477i	$0.717509\pi$
$192$	1.59153e14	0.229275
$193$	−1.19513e15	−1.66454	−0.832269	−	0.554372i	$-0.812958\pi$
$193$	−1.19513e15	−1.66454	−0.832269	+	0.554372i	$0.812958\pi$
$194$	−1.04760e15	−1.41086
$195$	5.65100e14	0.736038
$196$	3.82291e14	0.481648
$197$	1.47869e15	1.80238	0.901190	−	0.433424i	$-0.142695\pi$
$197$	1.47869e15	1.80238	0.901190	+	0.433424i	$0.142695\pi$
$198$	−2.55875e14	−0.301790
$199$	7.93030e14	0.905201	0.452600	−	0.891714i	$-0.350496\pi$
$199$	7.93030e14	0.905201	0.452600	+	0.891714i	$0.350496\pi$
$200$	−9.66857e13	−0.106824
$201$	3.36670e14	0.360106
$202$	−1.20933e15	−1.25245
$203$	7.29882e14	0.732029
$204$	1.15535e14	0.112232
$205$	7.73490e14	0.727871
$206$	1.55231e15	1.41527
$207$	−3.31666e13	−0.0293018
$208$	−1.71695e15	−1.47009
$209$	−1.04480e15	−0.867125
$210$	−1.36141e15	−1.09538
$211$	5.43968e14	0.424363	0.212181	−	0.977230i	$-0.431943\pi$
$211$	5.43968e14	0.424363	0.212181	+	0.977230i	$0.431943\pi$
$212$	−8.81552e14	−0.666906
$213$	−7.60562e14	−0.558043
$214$	1.26862e15	0.902907
$215$	−1.76289e15	−1.21724
$216$	−2.10602e14	−0.141095
$217$	−7.87405e14	−0.511929
$218$	2.36488e15	1.49225
$219$	−1.22529e13	−0.00750502
$220$	−5.20816e14	−0.309697
$221$	1.07022e15	0.617907
$222$	8.81762e14	0.494376
$223$	1.39680e15	0.760594	0.380297	−	0.924864i	$-0.375822\pi$
$223$	1.39680e15	0.760594	0.380297	+	0.924864i	$0.375822\pi$
$224$	2.04086e15	1.07945
$225$	9.45230e13	0.0485681
$226$	5.22101e14	0.260645
$227$	−1.15094e15	−0.558321	−0.279161	−	0.960244i	$-0.590056\pi$
$227$	−1.15094e15	−0.558321	−0.279161	+	0.960244i	$0.590056\pi$
$228$	5.15293e14	0.242928
$229$	−3.06221e15	−1.40315	−0.701576	−	0.712594i	$-0.747520\pi$
$229$	−3.06221e15	−1.40315	−0.701576	+	0.712594i	$0.747520\pi$
$230$	−2.47677e14	−0.110320
$231$	1.55641e15	0.673979
$232$	8.43160e14	0.355008
$233$	−4.36428e15	−1.78690	−0.893448	−	0.449167i	$-0.851721\pi$
$233$	−4.36428e15	−1.78690	−0.893448	+	0.449167i	$0.851721\pi$
$234$	1.16899e15	0.465486
$235$	2.14755e15	0.831767
$236$	−1.58646e15	−0.597726
$237$	−3.58069e14	−0.131251
$238$	−2.57832e15	−0.919574
$239$	9.94091e13	0.0345016	0.0172508	−	0.999851i	$-0.494509\pi$
$239$	9.94091e13	0.0345016	0.0172508	+	0.999851i	$0.494509\pi$
$240$	−2.25823e15	−0.762774
$241$	1.36764e15	0.449637	0.224818	−	0.974401i	$-0.427821\pi$
$241$	1.36764e15	0.449637	0.224818	+	0.974401i	$0.427821\pi$
$242$	−1.47908e15	−0.473360
$243$	2.05891e14	0.0641500
$244$	9.10222e14	0.276130
$245$	4.65765e15	1.37590
$246$	1.60007e15	0.460321
$247$	4.77325e15	1.33747
$248$	−9.09611e14	−0.248267
$249$	−1.81149e15	−0.481659
$250$	−4.13864e15	−1.07213
$251$	−4.56390e15	−1.15201	−0.576006	−	0.817445i	$-0.695390\pi$
$251$	−4.56390e15	−1.15201	−0.576006	+	0.817445i	$0.695390\pi$
$252$	−7.67619e14	−0.188817
$253$	2.83153e14	0.0678794
$254$	3.79332e15	0.886340
$255$	1.40762e15	0.320608
$256$	4.44046e15	0.985980
$257$	6.09990e15	1.32056	0.660279	−	0.751021i	$-0.270438\pi$
$257$	6.09990e15	1.32056	0.660279	+	0.751021i	$0.270438\pi$
$258$	−3.64678e15	−0.769806
$259$	−5.36349e15	−1.10408
$260$	2.37939e15	0.477683
$261$	−8.24300e14	−0.161407
$262$	−8.38950e14	−0.160242
$263$	7.60447e15	1.41696	0.708478	−	0.705733i	$-0.249382\pi$
$263$	7.60447e15	1.41696	0.708478	+	0.705733i	$0.249382\pi$
$264$	1.79797e15	0.326856
$265$	−1.07404e16	−1.90512
$266$	−1.14995e16	−1.99043
$267$	3.36209e15	0.567919
$268$	1.41757e15	0.233706
$269$	2.61338e15	0.420545	0.210272	−	0.977643i	$-0.432565\pi$
$269$	2.61338e15	0.420545	0.210272	+	0.977643i	$0.432565\pi$
$270$	1.53752e15	0.241523
$271$	−8.38856e15	−1.28643	−0.643216	−	0.765685i	$-0.722400\pi$
$271$	−8.38856e15	−1.28643	−0.643216	+	0.765685i	$0.722400\pi$
$272$	−4.27678e15	−0.640352
$273$	−7.11060e15	−1.03956
$274$	7.55534e15	1.07864
$275$	−8.06970e14	−0.112511
$276$	−1.39651e14	−0.0190166
$277$	1.22863e16	1.63419	0.817094	−	0.576505i	$-0.195584\pi$
$277$	1.22863e16	1.63419	0.817094	+	0.576505i	$0.195584\pi$
$278$	8.47358e15	1.10097
$279$	8.89265e14	0.112877
$280$	9.56628e15	1.18636
$281$	−9.27241e15	−1.12357	−0.561787	−	0.827282i	$-0.689886\pi$
$281$	−9.27241e15	−1.12357	−0.561787	+	0.827282i	$0.689886\pi$
$282$	4.44250e15	0.526027
$283$	1.33488e16	1.54465	0.772325	−	0.635227i	$-0.219094\pi$
$283$	1.33488e16	1.54465	0.772325	+	0.635227i	$0.219094\pi$
$284$	−3.20240e15	−0.362165
$285$	6.27808e15	0.693961
$286$	−9.97997e15	−1.07833
$287$	−9.73274e15	−1.02802
$288$	−2.30487e15	−0.238010
$289$	−7.23874e15	−0.730848
$290$	−6.15560e15	−0.607691
$291$	−7.19654e15	−0.694736
$292$	−5.15917e13	−0.00487070
$293$	1.27873e16	1.18070	0.590350	−	0.807147i	$-0.298990\pi$
$293$	1.27873e16	1.18070	0.590350	+	0.807147i	$0.298990\pi$
$294$	9.63499e15	0.870149
$295$	−1.93287e16	−1.70749
$296$	−6.19591e15	−0.535438
$297$	−1.75775e15	−0.148607
$298$	−2.50190e15	−0.206949
$299$	−1.29361e15	−0.104698
$300$	3.97996e14	0.0315203
$301$	2.21822e16	1.71919
$302$	1.18555e16	0.899241
$303$	−8.30758e15	−0.616733
$304$	−1.90747e16	−1.38605
$305$	1.10897e16	0.788807
$306$	2.91186e15	0.202759
$307$	1.53370e15	0.104554	0.0522769	−	0.998633i	$-0.483352\pi$
$307$	1.53370e15	0.104554	0.0522769	+	0.998633i	$0.483352\pi$
$308$	6.55338e15	0.437407
$309$	1.06637e16	0.696909
$310$	6.64073e15	0.424976
$311$	−5.36723e15	−0.336362	−0.168181	−	0.985756i	$-0.553789\pi$
$311$	−5.36723e15	−0.336362	−0.168181	+	0.985756i	$0.553789\pi$
$312$	−8.21417e15	−0.504149
$313$	−1.61530e15	−0.0970990	−0.0485495	−	0.998821i	$-0.515460\pi$
$313$	−1.61530e15	−0.0970990	−0.0485495	+	0.998821i	$0.515460\pi$
$314$	1.85378e16	1.09148
$315$	−9.35230e15	−0.539386
$316$	−1.50768e15	−0.0851809
$317$	−1.24129e16	−0.687052	−0.343526	−	0.939143i	$-0.611621\pi$
$317$	−1.24129e16	−0.687052	−0.343526	+	0.939143i	$0.611621\pi$
$318$	−2.22180e16	−1.20484
$319$	7.03729e15	0.373909
$320$	8.16450e15	0.425064
$321$	8.71489e15	0.444610
$322$	3.11650e15	0.155813
$323$	1.18898e16	0.582584
$324$	8.66919e14	0.0416328
$325$	3.68671e15	0.173539
$326$	−3.41685e16	−1.57656
$327$	1.62457e16	0.734815
$328$	−1.12433e16	−0.498555
$329$	−2.70224e16	−1.17476
$330$	−1.31263e16	−0.559501
$331$	1.49215e16	0.623636	0.311818	−	0.950142i	$-0.399062\pi$
$331$	1.49215e16	0.623636	0.311818	+	0.950142i	$0.399062\pi$
$332$	−7.62741e15	−0.312593
$333$	6.05732e15	0.243441
$334$	−8.22858e15	−0.324319
$335$	1.72710e16	0.667616
$336$	2.84151e16	1.07732
$337$	−3.14737e16	−1.17045	−0.585226	−	0.810870i	$-0.698994\pi$
$337$	−3.14737e16	−1.17045	−0.585226	+	0.810870i	$0.698994\pi$
$338$	1.34532e16	0.490757
$339$	3.58661e15	0.128347
$340$	5.92689e15	0.208072
$341$	−7.59191e15	−0.261485
$342$	1.29871e16	0.438876
$343$	−1.30139e16	−0.431516
$344$	2.56250e16	0.833745
$345$	−1.70143e15	−0.0543239
$346$	6.89051e16	2.15902
$347$	−2.42512e16	−0.745749	−0.372874	−	0.927882i	$-0.621628\pi$
$347$	−2.42512e16	−0.745749	−0.372874	+	0.927882i	$0.621628\pi$
$348$	−3.47078e15	−0.104752
$349$	1.87440e16	0.555261	0.277630	−	0.960688i	$-0.410451\pi$
$349$	1.87440e16	0.555261	0.277630	+	0.960688i	$0.410451\pi$
$350$	−8.88184e15	−0.258262
$351$	8.03043e15	0.229215
$352$	1.96773e16	0.551365
$353$	−3.15037e16	−0.866615	−0.433307	−	0.901246i	$-0.642654\pi$
$353$	−3.15037e16	−0.866615	−0.433307	+	0.901246i	$0.642654\pi$
$354$	−3.99841e16	−1.07986
$355$	−3.90165e16	−1.03458
$356$	1.41563e16	0.368575
$357$	−1.77119e16	−0.452817
$358$	−6.52247e16	−1.63747
$359$	−2.33985e15	−0.0576866	−0.0288433	−	0.999584i	$-0.509182\pi$
$359$	−2.33985e15	−0.0576866	−0.0288433	+	0.999584i	$0.509182\pi$
$360$	−1.08038e16	−0.261583
$361$	1.09763e16	0.261011
$362$	1.37162e16	0.320352
$363$	−1.01606e16	−0.233092
$364$	−2.99397e16	−0.674665
$365$	−6.28568e14	−0.0139139
$366$	2.29406e16	0.498858
$367$	4.74616e16	1.01394	0.506971	−	0.861963i	$-0.330765\pi$
$367$	4.74616e16	1.01394	0.506971	+	0.861963i	$0.330765\pi$
$368$	5.16948e15	0.108502
$369$	1.09918e16	0.226672
$370$	4.52340e16	0.916545
$371$	1.35145e17	2.69073
$372$	3.74431e15	0.0732560
$373$	−1.04515e16	−0.200942	−0.100471	−	0.994940i	$-0.532035\pi$
$373$	−1.04515e16	−0.200942	−0.100471	+	0.994940i	$0.532035\pi$
$374$	−2.48593e16	−0.469704
$375$	−2.84307e16	−0.527939
$376$	−3.12163e16	−0.569718
$377$	−3.21504e16	−0.576724
$378$	−1.93465e16	−0.341119
$379$	−3.86703e16	−0.670228	−0.335114	−	0.942178i	$-0.608775\pi$
$379$	−3.86703e16	−0.670228	−0.335114	+	0.942178i	$0.608775\pi$
$380$	2.64343e16	0.450375
$381$	2.60585e16	0.436452
$382$	−8.99152e16	−1.48054
$383$	1.08413e17	1.75505	0.877526	−	0.479529i	$-0.159193\pi$
$383$	1.08413e17	1.75505	0.877526	+	0.479529i	$0.159193\pi$
$384$	4.27899e16	0.681065
$385$	7.98432e16	1.24952
$386$	−1.26828e17	−1.95163
$387$	−2.50518e16	−0.379068
$388$	−3.03016e16	−0.450878
$389$	−9.68885e16	−1.41775	−0.708875	−	0.705334i	$-0.750797\pi$
$389$	−9.68885e16	−1.41775	−0.708875	+	0.705334i	$0.750797\pi$
$390$	5.99685e16	0.862986
$391$	−3.22228e15	−0.0456052
$392$	−6.77026e16	−0.942423
$393$	−5.76322e15	−0.0789067
$394$	1.56919e17	2.11324
$395$	−1.83688e16	−0.243332
$396$	−7.40114e15	−0.0964450
$397$	−1.94128e16	−0.248857	−0.124429	−	0.992229i	$-0.539710\pi$
$397$	−1.94128e16	−0.248857	−0.124429	+	0.992229i	$0.539710\pi$
$398$	8.41566e16	1.06132
$399$	−7.89964e16	−0.980130
$400$	−1.47327e16	−0.179843
$401$	−1.00109e17	−1.20235	−0.601177	−	0.799116i	$-0.705301\pi$
$401$	−1.00109e17	−1.20235	−0.601177	+	0.799116i	$0.705301\pi$
$402$	3.57275e16	0.422214
$403$	3.46843e16	0.403320
$404$	−3.49797e16	−0.400255
$405$	1.05621e16	0.118931
$406$	7.74552e16	0.858285
$407$	−5.17131e16	−0.563945
$408$	−2.04609e16	−0.219600
$409$	−2.18636e16	−0.230951	−0.115476	−	0.993310i	$-0.536839\pi$
$409$	−2.18636e16	−0.230951	−0.115476	+	0.993310i	$0.536839\pi$
$410$	8.20829e16	0.853410
$411$	5.19019e16	0.531143
$412$	4.49001e16	0.452288
$413$	2.43211e17	2.41161
$414$	−3.51965e15	−0.0343556
$415$	−9.29286e16	−0.892970
$416$	−8.98976e16	−0.850435
$417$	5.82098e16	0.542140
$418$	−1.10874e17	−1.01668
$419$	−7.42101e15	−0.0669995	−0.0334998	−	0.999439i	$-0.510665\pi$
$419$	−7.42101e15	−0.0669995	−0.0334998	+	0.999439i	$0.510665\pi$
$420$	−3.93785e16	−0.350057
$421$	−1.07950e17	−0.944911	−0.472455	−	0.881355i	$-0.656632\pi$
$421$	−1.07950e17	−0.944911	−0.472455	+	0.881355i	$0.656632\pi$
$422$	5.77260e16	0.497555
$423$	3.05180e16	0.259026
$424$	1.56120e17	1.30491
$425$	9.18331e15	0.0755912
$426$	−8.07111e16	−0.654291
$427$	−1.39541e17	−1.11409
$428$	3.66947e16	0.288548
$429$	−6.85581e16	−0.530990
$430$	−1.87078e17	−1.42718
$431$	3.48021e16	0.261519	0.130760	−	0.991414i	$-0.458258\pi$
$431$	3.48021e16	0.261519	0.130760	+	0.991414i	$0.458258\pi$
$432$	−3.20910e16	−0.237541
$433$	−1.72361e16	−0.125680	−0.0628401	−	0.998024i	$-0.520016\pi$
$433$	−1.72361e16	−0.125680	−0.0628401	+	0.998024i	$0.520016\pi$
$434$	−8.35596e16	−0.600224
$435$	−4.22863e16	−0.299240
$436$	6.84037e16	0.476889
$437$	−1.43716e16	−0.0987132
$438$	−1.30028e15	−0.00879944
$439$	2.42982e17	1.62015	0.810073	−	0.586329i	$-0.199428\pi$
$439$	2.42982e17	1.62015	0.810073	+	0.586329i	$0.199428\pi$
$440$	9.22350e16	0.605973
$441$	6.61882e16	0.428479
$442$	1.13572e17	0.724480
$443$	−1.12613e17	−0.707887	−0.353943	−	0.935267i	$-0.615159\pi$
$443$	−1.12613e17	−0.707887	−0.353943	+	0.935267i	$0.615159\pi$
$444$	2.55048e16	0.157991
$445$	1.72474e17	1.05289
$446$	1.48229e17	0.891776
$447$	−1.71870e16	−0.101906
$448$	−1.02733e17	−0.600348
$449$	1.36479e17	0.786074	0.393037	−	0.919523i	$-0.371424\pi$
$449$	1.36479e17	0.786074	0.393037	+	0.919523i	$0.371424\pi$
$450$	1.00308e16	0.0569449
$451$	−9.38400e16	−0.525098
$452$	1.51017e16	0.0832962
$453$	8.14424e16	0.442805
$454$	−1.22138e17	−0.654617
$455$	−3.64771e17	−1.92728
$456$	−9.12568e16	−0.475328
$457$	3.10661e17	1.59526	0.797631	−	0.603146i	$-0.206086\pi$
$457$	3.10661e17	1.59526	0.797631	+	0.603146i	$0.206086\pi$
$458$	−3.24963e17	−1.64516
$459$	2.00032e16	0.0998428
$460$	−7.16401e15	−0.0352558
$461$	−2.41345e17	−1.17107	−0.585535	−	0.810647i	$-0.699115\pi$
$461$	−2.41345e17	−1.17107	−0.585535	+	0.810647i	$0.699115\pi$
$462$	1.65167e17	0.790223
$463$	−1.56064e16	−0.0736254	−0.0368127	−	0.999322i	$-0.511720\pi$
$463$	−1.56064e16	−0.0736254	−0.0368127	+	0.999322i	$0.511720\pi$
$464$	1.28479e17	0.597673
$465$	4.56189e16	0.209267
$466$	−4.63139e17	−2.09509
$467$	1.12327e17	0.501100	0.250550	−	0.968104i	$-0.419389\pi$
$467$	1.12327e17	0.501100	0.250550	+	0.968104i	$0.419389\pi$
$468$	3.38127e16	0.148759
$469$	−2.17319e17	−0.942921
$470$	2.27898e17	0.975225
$471$	1.27346e17	0.537466
$472$	2.80958e17	1.16955
$473$	2.13874e17	0.878134
$474$	−3.79984e16	−0.153888
$475$	4.09582e16	0.163618
$476$	−7.45774e16	−0.293875
$477$	−1.52628e17	−0.593287
$478$	1.05493e16	0.0404523
$479$	2.07000e16	0.0783051	0.0391525	−	0.999233i	$-0.487534\pi$
$479$	2.07000e16	0.0783051	0.0391525	+	0.999233i	$0.487534\pi$
$480$	−1.18239e17	−0.441258
$481$	2.36256e17	0.869839
$482$	1.45135e17	0.527188
$483$	2.14090e16	0.0767255
$484$	−4.27821e16	−0.151275
$485$	−3.69180e17	−1.28800
$486$	2.18492e16	0.0752143
$487$	−2.68533e16	−0.0912137	−0.0456069	−	0.998959i	$-0.514522\pi$
$487$	−2.68533e16	−0.0912137	−0.0456069	+	0.998959i	$0.514522\pi$
$488$	−1.61197e17	−0.540293
$489$	−2.34723e17	−0.776332
$490$	4.94271e17	1.61321
$491$	1.53444e17	0.494219	0.247110	−	0.968988i	$-0.420519\pi$
$491$	1.53444e17	0.494219	0.247110	+	0.968988i	$0.420519\pi$
$492$	4.62817e16	0.147108
$493$	−8.00843e16	−0.251213
$494$	5.06539e17	1.56815
$495$	−9.01719e16	−0.275510
$496$	−1.38604e17	−0.417970
$497$	4.90941e17	1.46121
$498$	−1.92236e17	−0.564733
$499$	−2.29906e17	−0.666649	−0.333325	−	0.942812i	$-0.608170\pi$
$499$	−2.29906e17	−0.666649	−0.333325	+	0.942812i	$0.608170\pi$
$500$	−1.19709e17	−0.342628
$501$	−5.65268e16	−0.159701
$502$	−4.84322e17	−1.35070
$503$	−3.30439e17	−0.909704	−0.454852	−	0.890567i	$-0.650308\pi$
$503$	−3.30439e17	−0.909704	−0.454852	+	0.890567i	$0.650308\pi$
$504$	1.35943e17	0.369452
$505$	−4.26175e17	−1.14339
$506$	3.00483e16	0.0795868
$507$	9.24175e16	0.241659
$508$	1.09721e17	0.283254
$509$	−5.12719e17	−1.30681	−0.653407	−	0.757007i	$-0.726661\pi$
$509$	−5.12719e17	−1.30681	−0.653407	+	0.757007i	$0.726661\pi$
$510$	1.49377e17	0.375905
$511$	7.90921e15	0.0196516
$512$	−9.62121e15	−0.0236034
$513$	8.92155e16	0.216111
$514$	6.47323e17	1.54832
$515$	5.47041e17	1.29203
$516$	−1.05482e17	−0.246012
$517$	−2.60541e17	−0.600050
$518$	−5.69175e17	−1.29450
$519$	4.73348e17	1.06315
$520$	−4.21383e17	−0.934664
$521$	5.83466e17	1.27812	0.639058	−	0.769159i	$-0.279324\pi$
$521$	5.83466e17	1.27812	0.639058	+	0.769159i	$0.279324\pi$
$522$	−8.74750e16	−0.189245
$523$	8.94634e17	1.91154	0.955772	−	0.294108i	$-0.0950227\pi$
$523$	8.94634e17	1.91154	0.955772	+	0.294108i	$0.0950227\pi$
$524$	−2.42665e16	−0.0512098
$525$	−6.10144e16	−0.127174
$526$	8.06988e17	1.66134
$527$	8.63958e16	0.175681
$528$	2.73970e17	0.550278
$529$	−5.00141e17	−0.992273
$530$	−1.13977e18	−2.23370
$531$	−2.74673e17	−0.531743
$532$	−3.32620e17	−0.636096
$533$	4.28716e17	0.809921
$534$	3.56786e17	0.665871
$535$	4.47070e17	0.824282
$536$	−2.51048e17	−0.457283
$537$	−4.48065e17	−0.806322
$538$	2.77332e17	0.493078
$539$	−5.65068e17	−0.992598
$540$	4.44726e16	0.0771850
$541$	−8.44775e17	−1.44863	−0.724317	−	0.689467i	$-0.757845\pi$
$541$	−8.44775e17	−1.44863	−0.724317	+	0.689467i	$0.757845\pi$
$542$	−8.90196e17	−1.50831
$543$	9.42241e16	0.157748
$544$	−2.23928e17	−0.370438
$545$	8.33398e17	1.36231
$546$	−7.54578e17	−1.21886
$547$	6.65614e17	1.06244	0.531221	−	0.847233i	$-0.321733\pi$
$547$	6.65614e17	1.06244	0.531221	+	0.847233i	$0.321733\pi$
$548$	2.18537e17	0.344707
$549$	1.57592e17	0.245648
$550$	−8.56358e16	−0.131916
$551$	−3.57181e17	−0.543755
$552$	2.47317e16	0.0372091
$553$	2.31133e17	0.343675
$554$	1.30382e18	1.91604
$555$	3.10738e17	0.451326
$556$	2.45097e17	0.351845
$557$	9.21860e16	0.130800	0.0653998	−	0.997859i	$-0.479168\pi$
$557$	9.21860e16	0.130800	0.0653998	+	0.997859i	$0.479168\pi$
$558$	9.43690e16	0.132345
$559$	−9.77102e17	−1.35445
$560$	1.45768e18	1.99729
$561$	−1.70773e17	−0.231292
$562$	−9.83990e17	−1.31736
$563$	−7.50885e17	−0.993731	−0.496865	−	0.867828i	$-0.665516\pi$
$563$	−7.50885e17	−0.993731	−0.496865	+	0.867828i	$0.665516\pi$
$564$	1.28498e17	0.168106
$565$	1.83991e17	0.237948
$566$	1.41658e18	1.81106
$567$	−1.32902e17	−0.167974
$568$	5.67136e17	0.708635
$569$	−7.78377e17	−0.961524	−0.480762	−	0.876851i	$-0.659640\pi$
$569$	−7.78377e17	−0.961524	−0.480762	+	0.876851i	$0.659640\pi$
$570$	6.66231e17	0.813651
$571$	−5.69592e17	−0.687747	−0.343874	−	0.939016i	$-0.611739\pi$
$571$	−5.69592e17	−0.687747	−0.343874	+	0.939016i	$0.611739\pi$
$572$	−2.88669e17	−0.344608
$573$	−6.17678e17	−0.729050
$574$	−1.03284e18	−1.20533
$575$	−1.11002e16	−0.0128082
$576$	1.16023e17	0.132372
$577$	7.10905e17	0.801990	0.400995	−	0.916080i	$-0.368664\pi$
$577$	7.10905e17	0.801990	0.400995	+	0.916080i	$0.368664\pi$
$578$	−7.68177e17	−0.856900
$579$	−8.71252e17	−0.961021
$580$	−1.78049e17	−0.194204
$581$	1.16931e18	1.26120
$582$	−7.63699e17	−0.814559
$583$	1.30303e18	1.37438
$584$	9.13673e15	0.00953031
$585$	4.11958e17	0.424952
$586$	1.35699e18	1.38434
$587$	−8.96183e17	−0.904167	−0.452084	−	0.891976i	$-0.649319\pi$
$587$	−8.96183e17	−0.904167	−0.452084	+	0.891976i	$0.649319\pi$
$588$	2.78690e17	0.278080
$589$	3.85331e17	0.380263
$590$	−2.05117e18	−2.00199
$591$	1.07796e18	1.04060
$592$	−9.44117e17	−0.901435
$593$	−1.63665e18	−1.54562	−0.772808	−	0.634640i	$-0.781148\pi$
$593$	−1.63665e18	−1.54562	−0.772808	+	0.634640i	$0.781148\pi$
$594$	−1.86533e17	−0.174238
$595$	−9.08615e17	−0.839498
$596$	−7.23669e16	−0.0661362
$597$	5.78119e17	0.522618
$598$	−1.37278e17	−0.122756
$599$	9.33817e17	0.826014	0.413007	−	0.910728i	$-0.364478\pi$
$599$	9.33817e17	0.826014	0.413007	+	0.910728i	$0.364478\pi$
$600$	−7.04839e16	−0.0616746
$601$	1.29644e18	1.12219	0.561096	−	0.827751i	$-0.310380\pi$
$601$	1.29644e18	1.12219	0.561096	+	0.827751i	$0.310380\pi$
$602$	2.35399e18	2.01570
$603$	2.45432e17	0.207907
$604$	3.42919e17	0.287377
$605$	−5.21237e17	−0.432141
$606$	−8.81602e17	−0.723104
$607$	−1.81706e17	−0.147449	−0.0737245	−	0.997279i	$-0.523489\pi$
$607$	−1.81706e17	−0.147449	−0.0737245	+	0.997279i	$0.523489\pi$
$608$	−9.98733e17	−0.801819
$609$	5.32084e17	0.422637
$610$	1.17684e18	0.924856
$611$	1.19030e18	0.925529
$612$	8.42249e16	0.0647972
$613$	−3.24753e17	−0.247207	−0.123603	−	0.992332i	$-0.539445\pi$
$613$	−3.24753e17	−0.247207	−0.123603	+	0.992332i	$0.539445\pi$
$614$	1.62756e17	0.122587
$615$	5.63874e17	0.420237
$616$	−1.16058e18	−0.855858
$617$	1.75871e17	0.128334	0.0641668	−	0.997939i	$-0.479561\pi$
$617$	1.75871e17	0.128334	0.0641668	+	0.997939i	$0.479561\pi$
$618$	1.13163e18	0.817108
$619$	−6.84471e17	−0.489064	−0.244532	−	0.969641i	$-0.578634\pi$
$619$	−6.84471e17	−0.489064	−0.244532	+	0.969641i	$0.578634\pi$
$620$	1.92082e17	0.135813
$621$	−2.41785e16	−0.0169174
$622$	−5.69571e17	−0.394376
$623$	−2.17022e18	−1.48707
$624$	−1.25165e18	−0.848759
$625$	−1.67560e18	−1.12447
$626$	−1.71416e17	−0.113846
$627$	−7.61658e17	−0.500635
$628$	5.36202e17	0.348811
$629$	5.88494e17	0.378890
$630$	−9.92468e17	−0.632416
$631$	−1.20083e18	−0.757341	−0.378671	−	0.925531i	$-0.623619\pi$
$631$	−1.20083e18	−0.757341	−0.378671	+	0.925531i	$0.623619\pi$
$632$	2.67005e17	0.166670
$633$	3.96553e17	0.245006
$634$	−1.31727e18	−0.805551
$635$	1.33679e18	0.809158
$636$	−6.42651e17	−0.385038
$637$	2.58156e18	1.53100
$638$	7.46799e17	0.438398
$639$	−5.54450e17	−0.322186
$640$	2.19511e18	1.26266
$641$	2.97598e18	1.69454	0.847272	−	0.531159i	$-0.178243\pi$
$641$	2.97598e18	1.69454	0.847272	+	0.531159i	$0.178243\pi$
$642$	9.24826e17	0.521293
$643$	−2.44863e17	−0.136632	−0.0683158	−	0.997664i	$-0.521763\pi$
$643$	−2.44863e17	−0.136632	−0.0683158	+	0.997664i	$0.521763\pi$
$644$	9.01441e16	0.0497942
$645$	−1.28515e18	−0.702772
$646$	1.26175e18	0.683064
$647$	−2.81360e18	−1.50794	−0.753970	−	0.656909i	$-0.771864\pi$
$647$	−2.81360e18	−1.50794	−0.753970	+	0.656909i	$0.771864\pi$
$648$	−1.53529e17	−0.0814615
$649$	2.34496e18	1.23181
$650$	3.91235e17	0.203470
$651$	−5.74018e17	−0.295562
$652$	−9.88317e17	−0.503833
$653$	3.48454e17	0.175877	0.0879387	−	0.996126i	$-0.471972\pi$
$653$	3.48454e17	0.175877	0.0879387	+	0.996126i	$0.471972\pi$
$654$	1.72400e18	0.861552
$655$	−2.95651e17	−0.146289
$656$	−1.71322e18	−0.839341
$657$	−8.93236e15	−0.00433303
$658$	−2.86762e18	−1.37738
$659$	2.51341e18	1.19539	0.597693	−	0.801725i	$-0.296084\pi$
$659$	2.51341e18	1.19539	0.597693	+	0.801725i	$0.296084\pi$
$660$	−3.79675e17	−0.178804
$661$	−3.35502e18	−1.56453	−0.782267	−	0.622943i	$-0.785937\pi$
$661$	−3.35502e18	−1.56453	−0.782267	+	0.622943i	$0.785937\pi$
$662$	1.58348e18	0.731197
$663$	7.80191e17	0.356749
$664$	1.35079e18	0.611639
$665$	−4.05248e18	−1.81711
$666$	6.42804e17	0.285428
$667$	9.68004e16	0.0425656
$668$	−2.38010e17	−0.103645
$669$	1.01827e18	0.439129
$670$	1.83280e18	0.782762
$671$	−1.34541e18	−0.569059
$672$	1.48779e18	0.623219
$673$	−4.63099e18	−1.92121	−0.960607	−	0.277910i	$-0.910358\pi$
$673$	−4.63099e18	−1.92121	−0.960607	+	0.277910i	$0.910358\pi$
$674$	−3.34000e18	−1.37233
$675$	6.89073e16	0.0280408
$676$	3.89131e17	0.156835
$677$	1.21324e18	0.484308	0.242154	−	0.970238i	$-0.422146\pi$
$677$	1.21324e18	0.484308	0.242154	+	0.970238i	$0.422146\pi$
$678$	3.80612e17	0.150484
$679$	4.64535e18	1.81913
$680$	−1.04963e18	−0.407127
$681$	−8.39034e17	−0.322347
$682$	−8.05655e17	−0.306585
$683$	4.64732e18	1.75173	0.875866	−	0.482554i	$-0.160291\pi$
$683$	4.64732e18	1.75173	0.875866	+	0.482554i	$0.160291\pi$
$684$	3.75648e17	0.140255
$685$	2.66255e18	0.984710
$686$	−1.38104e18	−0.505941
$687$	−2.23235e18	−0.810110
$688$	3.90466e18	1.40365
$689$	−5.95300e18	−2.11988
$690$	−1.80557e17	−0.0636934
$691$	−1.93103e18	−0.674809	−0.337404	−	0.941360i	$-0.609549\pi$
$691$	−1.93103e18	−0.674809	−0.337404	+	0.941360i	$0.609549\pi$
$692$	1.99307e18	0.689973
$693$	1.13462e18	0.389122
$694$	−2.57355e18	−0.874371
$695$	2.98614e18	1.00510
$696$	6.14664e17	0.204964
$697$	1.06790e18	0.352791
$698$	1.98912e18	0.651029
$699$	−3.18156e18	−1.03166
$700$	−2.56905e17	−0.0825346
$701$	−2.49665e17	−0.0794678	−0.0397339	−	0.999210i	$-0.512651\pi$
$701$	−2.49665e17	−0.0794678	−0.0397339	+	0.999210i	$0.512651\pi$
$702$	8.52192e17	0.268749
$703$	2.62472e18	0.820113
$704$	−9.90519e17	−0.306648
$705$	1.56556e18	0.480221
$706$	−3.34318e18	−1.01608
$707$	5.36252e18	1.61489
$708$	−1.15653e18	−0.345097
$709$	4.33975e18	1.28311	0.641556	−	0.767076i	$-0.278289\pi$
$709$	4.33975e18	1.28311	0.641556	+	0.767076i	$0.278289\pi$
$710$	−4.14044e18	−1.21302
$711$	−2.61033e17	−0.0757778
$712$	−2.50704e18	−0.721177
$713$	−1.04429e17	−0.0297674
$714$	−1.87960e18	−0.530916
$715$	−3.51700e18	−0.984426
$716$	−1.88661e18	−0.523296
$717$	7.24692e16	0.0199195
$718$	−2.48306e17	−0.0676360
$719$	3.75211e18	1.01283	0.506417	−	0.862289i	$-0.330970\pi$
$719$	3.75211e18	1.01283	0.506417	+	0.862289i	$0.330970\pi$
$720$	−1.64625e18	−0.440388
$721$	−6.88337e18	−1.82483
$722$	1.16481e18	0.306029
$723$	9.97012e17	0.259598
$724$	3.96737e17	0.102377
$725$	−2.75875e17	−0.0705531
$726$	−1.07825e18	−0.273295
$727$	−4.18999e18	−1.05254	−0.526271	−	0.850317i	$-0.676410\pi$
$727$	−4.18999e18	−1.05254	−0.526271	+	0.850317i	$0.676410\pi$
$728$	5.30222e18	1.32009
$729$	1.50095e17	0.0370370
$730$	−6.67038e16	−0.0163137
$731$	−2.43389e18	−0.589980
$732$	6.63552e17	0.159424
$733$	2.05157e18	0.488551	0.244275	−	0.969706i	$-0.421450\pi$
$733$	2.05157e18	0.488551	0.244275	+	0.969706i	$0.421450\pi$
$734$	5.03663e18	1.18882
$735$	3.39543e18	0.794377
$736$	2.70669e17	0.0627671
$737$	−2.09532e18	−0.481629
$738$	1.16645e18	0.265767
$739$	2.09599e18	0.473369	0.236684	−	0.971587i	$-0.423939\pi$
$739$	2.09599e18	0.473369	0.236684	+	0.971587i	$0.423939\pi$
$740$	1.30838e18	0.292907
$741$	3.47970e18	0.772189
$742$	1.43417e19	3.15482
$743$	−4.70979e18	−1.02701	−0.513505	−	0.858087i	$-0.671653\pi$
$743$	−4.70979e18	−1.02701	−0.513505	+	0.858087i	$0.671653\pi$
$744$	−6.63106e17	−0.143337
$745$	−8.81684e17	−0.188928
$746$	−1.10912e18	−0.235600
$747$	−1.32058e18	−0.278086
$748$	−7.19052e17	−0.150107
$749$	−5.62544e18	−1.16419
$750$	−3.01707e18	−0.618995
$751$	3.98453e18	0.810433	0.405217	−	0.914221i	$-0.367196\pi$
$751$	3.98453e18	0.810433	0.405217	+	0.914221i	$0.367196\pi$
$752$	−4.75665e18	−0.959148
$753$	−3.32708e18	−0.665114
$754$	−3.41181e18	−0.676194
$755$	4.17796e18	0.820936
$756$	−5.59594e17	−0.109014
$757$	8.61547e17	0.166401	0.0832005	−	0.996533i	$-0.473486\pi$
$757$	8.61547e17	0.166401	0.0832005	+	0.996533i	$0.473486\pi$
$758$	−4.10370e18	−0.785825
$759$	2.06419e17	0.0391902
$760$	−4.68143e18	−0.881232
$761$	−3.07962e18	−0.574773	−0.287387	−	0.957815i	$-0.592786\pi$
$761$	−3.07962e18	−0.574773	−0.287387	+	0.957815i	$0.592786\pi$
$762$	2.76533e18	0.511729
$763$	−1.04866e19	−1.92408
$764$	−2.60078e18	−0.473148
$765$	1.02616e18	0.185103
$766$	1.15048e19	2.05775
$767$	−1.07132e19	−1.89997
$768$	3.23709e18	0.569256
$769$	6.89987e18	1.20315	0.601574	−	0.798817i	$-0.294540\pi$
$769$	6.89987e18	1.20315	0.601574	+	0.798817i	$0.294540\pi$
$770$	8.47298e18	1.46503
$771$	4.44682e18	0.762424
$772$	−3.66847e18	−0.623695
$773$	3.78025e18	0.637315	0.318657	−	0.947870i	$-0.396768\pi$
$773$	3.78025e18	0.637315	0.318657	+	0.947870i	$0.396768\pi$
$774$	−2.65850e18	−0.444448
$775$	2.97618e17	0.0493398
$776$	5.36631e18	0.882216
$777$	−3.90998e18	−0.637439
$778$	−1.02818e19	−1.66228
$779$	4.76290e18	0.763621
$780$	1.73458e18	0.275790
$781$	4.73350e18	0.746363
$782$	−3.41949e17	−0.0534709
$783$	−6.00915e17	−0.0931884
$784$	−1.03163e19	−1.58661
$785$	6.53282e18	0.996433
$786$	−6.11594e17	−0.0925160
$787$	2.62786e18	0.394245	0.197123	−	0.980379i	$-0.436840\pi$
$787$	2.62786e18	0.394245	0.197123	+	0.980379i	$0.436840\pi$
$788$	4.53885e18	0.675344
$789$	5.54366e18	0.818080
$790$	−1.94930e18	−0.285301
$791$	−2.31515e18	−0.336071
$792$	1.31072e18	0.188710
$793$	6.14660e18	0.877727
$794$	−2.06009e18	−0.291779
$795$	−7.82975e18	−1.09992
$796$	2.43421e18	0.339175
$797$	−9.06963e16	−0.0125346	−0.00626730	−	0.999980i	$-0.501995\pi$
$797$	−9.06963e16	−0.0125346	−0.00626730	+	0.999980i	$0.501995\pi$
$798$	−8.38312e18	−1.14918
$799$	2.96495e18	0.403148
$800$	−7.71390e17	−0.104037
$801$	2.45097e18	0.327888
$802$	−1.06235e19	−1.40973
$803$	7.62581e16	0.0100377
$804$	1.03341e18	0.134930
$805$	1.09827e18	0.142245
$806$	3.68070e18	0.472882
$807$	1.90515e18	0.242802
$808$	6.19479e18	0.783164
$809$	7.46650e18	0.936379	0.468190	−	0.883628i	$-0.344906\pi$
$809$	7.46650e18	0.936379	0.468190	+	0.883628i	$0.344906\pi$
$810$	1.12086e18	0.139443
$811$	4.21029e16	0.00519609	0.00259804	−	0.999997i	$-0.499173\pi$
$811$	4.21029e16	0.00519609	0.00259804	+	0.999997i	$0.499173\pi$
$812$	2.24038e18	0.274288
$813$	−6.11526e18	−0.742722
$814$	−5.48780e18	−0.661211
$815$	−1.20412e19	−1.43928
$816$	−3.11777e18	−0.369708
$817$	−1.08553e19	−1.27702
$818$	−2.32017e18	−0.270784
$819$	−5.18362e18	−0.600189
$820$	2.37423e18	0.272730
$821$	−9.93002e17	−0.113167	−0.0565835	−	0.998398i	$-0.518021\pi$
$821$	−9.93002e17	−0.113167	−0.0565835	+	0.998398i	$0.518021\pi$
$822$	5.50784e18	0.622751
$823$	1.95194e18	0.218962	0.109481	−	0.993989i	$-0.465081\pi$
$823$	1.95194e18	0.218962	0.109481	+	0.993989i	$0.465081\pi$
$824$	−7.95167e18	−0.884976
$825$	−5.88281e17	−0.0649582
$826$	2.58096e19	2.82756
$827$	3.37892e18	0.367276	0.183638	−	0.982994i	$-0.441213\pi$
$827$	3.37892e18	0.367276	0.183638	+	0.982994i	$0.441213\pi$
$828$	−1.01805e17	−0.0109793
$829$	−5.71188e18	−0.611188	−0.305594	−	0.952162i	$-0.598855\pi$
$829$	−5.71188e18	−0.611188	−0.305594	+	0.952162i	$0.598855\pi$
$830$	−9.86161e18	−1.04698
$831$	8.95670e18	0.943499
$832$	4.52527e18	0.472980
$833$	6.43047e18	0.666883
$834$	6.17724e18	0.635646
$835$	−2.89980e18	−0.296078
$836$	−3.20702e18	−0.324908
$837$	6.48274e17	0.0651693
$838$	−7.87519e17	−0.0785552
$839$	7.14822e18	0.707530	0.353765	−	0.935334i	$-0.384901\pi$
$839$	7.14822e18	0.707530	0.353765	+	0.935334i	$0.384901\pi$
$840$	6.97382e18	0.684944
$841$	−7.85482e18	−0.765530
$842$	−1.14557e19	−1.10788
$843$	−6.75958e18	−0.648695
$844$	1.66971e18	0.159007
$845$	4.74098e18	0.448022
$846$	3.23858e18	0.303702
$847$	6.55867e18	0.610342
$848$	2.37892e19	2.19688
$849$	9.73127e18	0.891804
$850$	9.74535e17	0.0886287
$851$	−7.11331e17	−0.0641992
$852$	−2.33455e18	−0.209096
$853$	−1.20618e19	−1.07212	−0.536059	−	0.844181i	$-0.680087\pi$
$853$	−1.20618e19	−1.07212	−0.536059	+	0.844181i	$0.680087\pi$
$854$	−1.48081e19	−1.30624
$855$	4.57672e18	0.400659
$856$	−6.49851e18	−0.564592
$857$	−5.17845e18	−0.446503	−0.223252	−	0.974761i	$-0.571667\pi$
$857$	−5.17845e18	−0.446503	−0.223252	+	0.974761i	$0.571667\pi$
$858$	−7.27540e18	−0.622572
$859$	−1.69719e19	−1.44136	−0.720682	−	0.693266i	$-0.756171\pi$
$859$	−1.69719e19	−1.44136	−0.720682	+	0.693266i	$0.756171\pi$
$860$	−5.41120e18	−0.456093
$861$	−7.09517e18	−0.593530
$862$	3.69321e18	0.306625
$863$	−1.91435e19	−1.57743	−0.788716	−	0.614757i	$-0.789254\pi$
$863$	−1.91435e19	−1.57743	−0.788716	+	0.614757i	$0.789254\pi$
$864$	−1.68025e18	−0.137415
$865$	2.42826e19	1.97101
$866$	−1.82910e18	−0.147357
$867$	−5.27704e18	−0.421955
$868$	−2.41694e18	−0.191818
$869$	2.22851e18	0.175544
$870$	−4.48743e18	−0.350851
$871$	9.57267e18	0.742874
$872$	−1.21141e19	−0.933111
$873$	−5.24628e18	−0.401106
$874$	−1.52512e18	−0.115739
$875$	1.83519e19	1.38239
$876$	−3.76103e16	−0.00281210
$877$	−3.79419e18	−0.281593	−0.140796	−	0.990039i	$-0.544966\pi$
$877$	−3.79419e18	−0.281593	−0.140796	+	0.990039i	$0.544966\pi$
$878$	2.57853e19	1.89958
$879$	9.32195e18	0.681678
$880$	1.40545e19	1.02018
$881$	3.75862e18	0.270823	0.135411	−	0.990789i	$-0.456764\pi$
$881$	3.75862e18	0.270823	0.135411	+	0.990789i	$0.456764\pi$
$882$	7.02391e18	0.502381
$883$	9.89604e18	0.702614	0.351307	−	0.936260i	$-0.385737\pi$
$883$	9.89604e18	0.702614	0.351307	+	0.936260i	$0.385737\pi$
$884$	3.28505e18	0.231527
$885$	−1.40906e19	−0.985823
$886$	−1.19505e19	−0.829979
$887$	1.15647e19	0.797319	0.398659	−	0.917099i	$-0.369476\pi$
$887$	1.15647e19	0.797319	0.398659	+	0.917099i	$0.369476\pi$
$888$	−4.51682e18	−0.309135
$889$	−1.68207e19	−1.14283
$890$	1.83030e19	1.23449
$891$	−1.28140e18	−0.0857985
$892$	4.28749e18	0.284991
$893$	1.32239e19	0.872619
$894$	−1.82388e18	−0.119482
$895$	−2.29856e19	−1.49488
$896$	−2.76208e19	−1.78334
$897$	−9.43041e17	−0.0604477
$898$	1.44831e19	0.921651
$899$	−2.59541e18	−0.163972
$900$	2.90139e17	0.0181983
$901$	−1.48285e19	−0.923389
$902$	−9.95832e18	−0.615664
$903$	1.61709e19	0.992573
$904$	−2.67446e18	−0.162983
$905$	4.83366e18	0.292456
$906$	8.64269e18	0.519177
$907$	2.70445e19	1.61299	0.806495	−	0.591242i	$-0.201362\pi$
$907$	2.70445e19	1.61299	0.806495	+	0.591242i	$0.201362\pi$
$908$	−3.53281e18	−0.209200
$909$	−6.05623e18	−0.356071
$910$	−3.87095e19	−2.25969
$911$	−2.72678e19	−1.58045	−0.790224	−	0.612818i	$-0.790036\pi$
$911$	−2.72678e19	−1.58045	−0.790224	+	0.612818i	$0.790036\pi$
$912$	−1.39055e19	−0.800238
$913$	1.12741e19	0.644203
$914$	3.29675e19	1.87040
$915$	8.08439e18	0.455418
$916$	−9.39948e18	−0.525755
$917$	3.72014e18	0.206614
$918$	2.12274e18	0.117063
$919$	2.66506e19	1.45934	0.729669	−	0.683801i	$-0.239674\pi$
$919$	2.66506e19	1.45934	0.729669	+	0.683801i	$0.239674\pi$
$920$	1.26872e18	0.0689837
$921$	1.11806e18	0.0603642
$922$	−2.56116e19	−1.37305
$923$	−2.16254e19	−1.15121
$924$	4.77741e18	0.252537
$925$	2.02725e18	0.106411
$926$	−1.65616e18	−0.0863239
$927$	7.77381e18	0.402361
$928$	6.72701e18	0.345748
$929$	−1.93311e19	−0.986630	−0.493315	−	0.869851i	$-0.664215\pi$
$929$	−1.93311e19	−0.986630	−0.493315	+	0.869851i	$0.664215\pi$
$930$	4.84109e18	0.245360
$931$	2.86803e19	1.44348
$932$	−1.33962e19	−0.669542
$933$	−3.91271e18	−0.194199
$934$	1.19202e19	0.587527
$935$	−8.76058e18	−0.428802
$936$	−5.98813e18	−0.291070
$937$	7.58240e18	0.366015	0.183008	−	0.983111i	$-0.441417\pi$
$937$	7.58240e18	0.366015	0.183008	+	0.983111i	$0.441417\pi$
$938$	−2.30620e19	−1.10555
$939$	−1.17755e18	−0.0560601
$940$	6.59191e18	0.311659
$941$	−1.02516e19	−0.481348	−0.240674	−	0.970606i	$-0.577369\pi$
$941$	−1.02516e19	−0.481348	−0.240674	+	0.970606i	$0.577369\pi$
$942$	1.35140e19	0.630165
$943$	−1.29080e18	−0.0597770
$944$	4.28116e19	1.96899
$945$	−6.81783e18	−0.311415
$946$	2.26964e19	1.02959
$947$	3.01069e19	1.35641	0.678204	−	0.734873i	$-0.262758\pi$
$947$	3.01069e19	1.35641	0.678204	+	0.734873i	$0.262758\pi$
$948$	−1.09910e18	−0.0491792
$949$	−3.48391e17	−0.0154824
$950$	4.34649e18	0.191838
$951$	−9.04904e18	−0.396670
$952$	1.32074e19	0.575014
$953$	−2.39687e17	−0.0103643	−0.00518215	−	0.999987i	$-0.501650\pi$
$953$	−2.39687e17	−0.0103643	−0.00518215	+	0.999987i	$0.501650\pi$
$954$	−1.61969e19	−0.695614
$955$	−3.16866e19	−1.35162
$956$	3.05137e17	0.0129276
$957$	5.13018e18	0.215876
$958$	2.19669e18	0.0918107
$959$	−3.35025e19	−1.39077
$960$	5.95192e18	0.245411
$961$	−2.16176e19	−0.885330
$962$	2.50715e19	1.01986
$963$	6.35315e18	0.256696
$964$	4.19799e18	0.168477
$965$	−4.46949e19	−1.78168
$966$	2.27193e18	0.0899587
$967$	−9.70726e18	−0.381790	−0.190895	−	0.981610i	$-0.561139\pi$
$967$	−9.70726e18	−0.381790	−0.190895	+	0.981610i	$0.561139\pi$
$968$	7.57658e18	0.295994
$969$	8.66767e18	0.336355
$970$	−3.91774e19	−1.51015
$971$	2.19064e19	0.838778	0.419389	−	0.907807i	$-0.362244\pi$
$971$	2.19064e19	0.838778	0.419389	+	0.907807i	$0.362244\pi$
$972$	6.31984e17	0.0240367
$973$	−3.75743e19	−1.41957
$974$	−2.84968e18	−0.106946
$975$	2.68761e18	0.100193
$976$	−2.45629e19	−0.909609
$977$	5.36297e19	1.97284	0.986418	−	0.164256i	$-0.0525224\pi$
$977$	5.36297e19	1.97284	0.986418	+	0.164256i	$0.0525224\pi$
$978$	−2.49088e19	−0.910230
$979$	−2.09246e19	−0.759573
$980$	1.42967e19	0.515544
$981$	1.18431e19	0.424246
$982$	1.62835e19	0.579459
$983$	1.52241e19	0.538189	0.269095	−	0.963114i	$-0.413276\pi$
$983$	1.52241e19	0.538189	0.269095	+	0.963114i	$0.413276\pi$
$984$	−8.19635e18	−0.287841
$985$	5.52991e19	1.92922
$986$	−8.49856e18	−0.294541
$987$	−1.96993e19	−0.678249
$988$	1.46515e19	0.501144
$989$	2.94191e18	0.0999664
$990$	−9.56906e18	−0.323028
$991$	5.37733e18	0.180338	0.0901691	−	0.995926i	$-0.471259\pi$
$991$	5.37733e18	0.180338	0.0901691	+	0.995926i	$0.471259\pi$
$992$	−7.25717e18	−0.241792
$993$	1.08778e19	0.360056
$994$	5.20988e19	1.71323
$995$	2.96573e19	0.968905
$996$	−5.56038e18	−0.180476
$997$	−2.84463e18	−0.0917292	−0.0458646	−	0.998948i	$-0.514604\pi$
$997$	−2.84463e18	−0.0917292	−0.0458646	+	0.998948i	$0.514604\pi$
$998$	−2.43977e19	−0.781629
$999$	4.41579e18	0.140551

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.14.a.b.1.2	✓	2
3.2	odd	2		9.14.a.c.1.1		2
4.3	odd	2		48.14.a.g.1.2		2
5.2	odd	4		75.14.b.c.49.3		4
5.3	odd	4		75.14.b.c.49.2		4
5.4	even	2		75.14.a.e.1.1		2
7.6	odd	2		147.14.a.b.1.2		2
8.3	odd	2		192.14.a.o.1.1		2
8.5	even	2		192.14.a.k.1.1		2
12.11	even	2		144.14.a.m.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.14.a.b.1.2	✓	2	1.1	even	1	trivial
9.14.a.c.1.1		2	3.2	odd	2
48.14.a.g.1.2		2	4.3	odd	2
75.14.a.e.1.1		2	5.4	even	2
75.14.b.c.49.2		4	5.3	odd	4
75.14.b.c.49.3		4	5.2	odd	4
144.14.a.m.1.1		2	12.11	even	2
147.14.a.b.1.2		2	7.6	odd	2
192.14.a.k.1.1		2	8.5	even	2
192.14.a.o.1.1		2	8.3	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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q+106.120 q^{2} +729.000 q^{3} +3069.51 q^{4} +37397.4 q^{5} +77361.7 q^{6} -470568. q^{7} -543600. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+106.120 q^{2} +729.000 q^{3} +3069.51 q^{4} +37397.4 q^{5} +77361.7 q^{6} -470568. q^{7} -543600. q^{8} +531441. q^{9} +3.96862e6 q^{10} -4.53706e6 q^{11} +2.23767e6 q^{12} +2.07280e7 q^{13} -4.99367e7 q^{14} +2.72627e7 q^{15} -8.28324e7 q^{16} +5.16317e7 q^{17} +5.63966e7 q^{18} +2.30281e8 q^{19} +1.14792e8 q^{20} -3.43044e8 q^{21} -4.81474e8 q^{22} -6.24089e7 q^{23} -3.96285e8 q^{24} +1.77862e8 q^{25} +2.19966e9 q^{26} +3.87420e8 q^{27} -1.44441e9 q^{28} -1.55107e9 q^{29} +2.89312e9 q^{30} +1.67331e9 q^{31} -4.33702e9 q^{32} -3.30752e9 q^{33} +5.47917e9 q^{34} -1.75980e10 q^{35} +1.63126e9 q^{36} +1.13979e10 q^{37} +2.44375e10 q^{38} +1.51107e10 q^{39} -2.03292e10 q^{40} +2.06830e10 q^{41} -3.64039e10 q^{42} -4.71393e10 q^{43} -1.39265e10 q^{44} +1.98745e10 q^{45} -6.62285e9 q^{46} +5.74250e10 q^{47} -6.03848e10 q^{48} +1.24545e11 q^{49} +1.88747e10 q^{50} +3.76395e10 q^{51} +6.36246e10 q^{52} -2.87197e11 q^{53} +4.11132e10 q^{54} -1.69674e11 q^{55} +2.55801e11 q^{56} +1.67875e11 q^{57} -1.64600e11 q^{58} -5.16846e11 q^{59} +8.36830e10 q^{60} +2.96537e11 q^{61} +1.77572e11 q^{62} -2.50079e11 q^{63} +2.18317e11 q^{64} +7.75171e11 q^{65} -3.50995e11 q^{66} +4.61824e11 q^{67} +1.58484e11 q^{68} -4.54961e10 q^{69} -1.86750e12 q^{70} -1.04330e12 q^{71} -2.88891e11 q^{72} -1.68078e10 q^{73} +1.20955e12 q^{74} +1.29661e11 q^{75} +7.06849e11 q^{76} +2.13499e12 q^{77} +1.60355e12 q^{78} -4.91179e11 q^{79} -3.09772e12 q^{80} +2.82430e11 q^{81} +2.19488e12 q^{82} -2.48490e12 q^{83} -1.05298e12 q^{84} +1.93089e12 q^{85} -5.00244e12 q^{86} -1.13073e12 q^{87} +2.46635e12 q^{88} +4.61192e12 q^{89} +2.10909e12 q^{90} -9.75390e12 q^{91} -1.91565e11 q^{92} +1.21984e12 q^{93} +6.09396e12 q^{94} +8.61190e12 q^{95} -3.16169e12 q^{96} -9.87180e12 q^{97} +1.32167e13 q^{98} -2.41118e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 54 q^{2} + 1458 q^{3} + 20516 q^{4} + 40716 q^{5} - 39366 q^{6} - 21008 q^{7} - 2025432 q^{8} + 1062882 q^{9}+O(q^{10}) \) 2 * q - 54 * q^2 + 1458 * q^3 + 20516 * q^4 + 40716 * q^5 - 39366 * q^6 - 21008 * q^7 - 2025432 * q^8 + 1062882 * q^9	\( 2 q - 54 q^{2} + 1458 q^{3} + 20516 q^{4} + 40716 q^{5} - 39366 q^{6} - 21008 q^{7} - 2025432 q^{8} + 1062882 q^{9} + 3437244 q^{10} + 672408 q^{11} + 14956164 q^{12} + 17532604 q^{13} - 121920336 q^{14} + 29681964 q^{15} + 11517200 q^{16} + 83838564 q^{17} - 28697814 q^{18} + 256293544 q^{19} + 172689624 q^{20} - 15314832 q^{21} - 1315615752 q^{22} + 859581936 q^{23} - 1476539928 q^{24} - 1031828194 q^{25} + 2711296044 q^{26} + 774840978 q^{27} + 6398827744 q^{28} - 4728475332 q^{29} + 2505750876 q^{30} - 5982551648 q^{31} - 7305134688 q^{32} + 490185432 q^{33} + 322207092 q^{34} - 16106087520 q^{35} + 10903043556 q^{36} + 27411194092 q^{37} + 20272310856 q^{38} + 12781268316 q^{39} - 25246850832 q^{40} + 15258974292 q^{41} - 88879924944 q^{42} - 11314499240 q^{43} + 76960441008 q^{44} + 21638151756 q^{45} - 154252246608 q^{46} - 69035142240 q^{47} + 8396038800 q^{48} + 229759626930 q^{49} + 212570589654 q^{50} + 61118313156 q^{51} + 7876928824 q^{52} - 226336894164 q^{53} - 20920706406 q^{54} - 152386092144 q^{55} - 410370995520 q^{56} + 186837993576 q^{57} + 344167850412 q^{58} - 927820824264 q^{59} + 125890735896 q^{60} + 179395461340 q^{61} + 1403430184224 q^{62} - 11164512528 q^{63} - 79339420096 q^{64} + 764567325288 q^{65} - 959083883208 q^{66} - 698315061176 q^{67} + 720380180232 q^{68} + 626635231344 q^{69} - 2106389414880 q^{70} - 784458549936 q^{71} - 1076397607512 q^{72} + 1857400245076 q^{73} - 1354499801316 q^{74} - 752202753426 q^{75} + 1160678400976 q^{76} + 4476961329984 q^{77} + 1976534816076 q^{78} - 714025470080 q^{79} - 2784606024096 q^{80} + 564859072962 q^{81} + 3063378763044 q^{82} - 4574293917912 q^{83} + 4664745425376 q^{84} + 2037774070872 q^{85} - 10738721134152 q^{86} - 3447058517028 q^{87} - 5253209973792 q^{88} + 3270178701684 q^{89} + 1826692388604 q^{90} - 11190403944928 q^{91} + 15893942353632 q^{92} - 4361280151392 q^{93} + 26342795766816 q^{94} + 8698230246384 q^{95} - 5325443187552 q^{96} - 9874926156476 q^{97} - 3630291434694 q^{98} + 357345179928 q^{99}+O(q^{100}) \) 2 * q - 54 * q^2 + 1458 * q^3 + 20516 * q^4 + 40716 * q^5 - 39366 * q^6 - 21008 * q^7 - 2025432 * q^8 + 1062882 * q^9 + 3437244 * q^10 + 672408 * q^11 + 14956164 * q^12 + 17532604 * q^13 - 121920336 * q^14 + 29681964 * q^15 + 11517200 * q^16 + 83838564 * q^17 - 28697814 * q^18 + 256293544 * q^19 + 172689624 * q^20 - 15314832 * q^21 - 1315615752 * q^22 + 859581936 * q^23 - 1476539928 * q^24 - 1031828194 * q^25 + 2711296044 * q^26 + 774840978 * q^27 + 6398827744 * q^28 - 4728475332 * q^29 + 2505750876 * q^30 - 5982551648 * q^31 - 7305134688 * q^32 + 490185432 * q^33 + 322207092 * q^34 - 16106087520 * q^35 + 10903043556 * q^36 + 27411194092 * q^37 + 20272310856 * q^38 + 12781268316 * q^39 - 25246850832 * q^40 + 15258974292 * q^41 - 88879924944 * q^42 - 11314499240 * q^43 + 76960441008 * q^44 + 21638151756 * q^45 - 154252246608 * q^46 - 69035142240 * q^47 + 8396038800 * q^48 + 229759626930 * q^49 + 212570589654 * q^50 + 61118313156 * q^51 + 7876928824 * q^52 - 226336894164 * q^53 - 20920706406 * q^54 - 152386092144 * q^55 - 410370995520 * q^56 + 186837993576 * q^57 + 344167850412 * q^58 - 927820824264 * q^59 + 125890735896 * q^60 + 179395461340 * q^61 + 1403430184224 * q^62 - 11164512528 * q^63 - 79339420096 * q^64 + 764567325288 * q^65 - 959083883208 * q^66 - 698315061176 * q^67 + 720380180232 * q^68 + 626635231344 * q^69 - 2106389414880 * q^70 - 784458549936 * q^71 - 1076397607512 * q^72 + 1857400245076 * q^73 - 1354499801316 * q^74 - 752202753426 * q^75 + 1160678400976 * q^76 + 4476961329984 * q^77 + 1976534816076 * q^78 - 714025470080 * q^79 - 2784606024096 * q^80 + 564859072962 * q^81 + 3063378763044 * q^82 - 4574293917912 * q^83 + 4664745425376 * q^84 + 2037774070872 * q^85 - 10738721134152 * q^86 - 3447058517028 * q^87 - 5253209973792 * q^88 + 3270178701684 * q^89 + 1826692388604 * q^90 - 11190403944928 * q^91 + 15893942353632 * q^92 - 4361280151392 * q^93 + 26342795766816 * q^94 + 8698230246384 * q^95 - 5325443187552 * q^96 - 9874926156476 * q^97 - 3630291434694 * q^98 + 357345179928 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more