LMFDB - Embedded newform 547.8.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,8,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("547.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	547.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:	$170.874608940$
Analytic rank:	$0$
Dimension:	$162$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-20.3517 q^{2} +46.7393 q^{3} +286.191 q^{4} +64.7634 q^{5} -951.224 q^{6} +714.717 q^{7} -3219.46 q^{8} -2.43807 q^{9} +O(q^{10})$	\(q-20.3517 q^{2} +46.7393 q^{3} +286.191 q^{4} +64.7634 q^{5} -951.224 q^{6} +714.717 q^{7} -3219.46 q^{8} -2.43807 q^{9} -1318.04 q^{10} -1947.92 q^{11} +13376.4 q^{12} +9286.00 q^{13} -14545.7 q^{14} +3027.00 q^{15} +28888.9 q^{16} +33760.0 q^{17} +49.6189 q^{18} -1213.16 q^{19} +18534.7 q^{20} +33405.4 q^{21} +39643.4 q^{22} +107948. q^{23} -150475. q^{24} -73930.7 q^{25} -188986. q^{26} -102333. q^{27} +204546. q^{28} +68435.4 q^{29} -61604.5 q^{30} +173879. q^{31} -175848. q^{32} -91044.2 q^{33} -687073. q^{34} +46287.5 q^{35} -697.755 q^{36} -131389. q^{37} +24689.8 q^{38} +434021. q^{39} -208503. q^{40} -197814. q^{41} -679856. q^{42} +708607. q^{43} -557477. q^{44} -157.898 q^{45} -2.19691e6 q^{46} -710410. q^{47} +1.35025e6 q^{48} -312722. q^{49} +1.50461e6 q^{50} +1.57792e6 q^{51} +2.65757e6 q^{52} -1.24889e6 q^{53} +2.08265e6 q^{54} -126154. q^{55} -2.30100e6 q^{56} -56702.2 q^{57} -1.39278e6 q^{58} +1.93469e6 q^{59} +866300. q^{60} +1.36509e6 q^{61} -3.53873e6 q^{62} -1742.53 q^{63} -118982. q^{64} +601393. q^{65} +1.85290e6 q^{66} +3.67065e6 q^{67} +9.66182e6 q^{68} +5.04539e6 q^{69} -942029. q^{70} +3.57528e6 q^{71} +7849.27 q^{72} -4.51261e6 q^{73} +2.67398e6 q^{74} -3.45547e6 q^{75} -347195. q^{76} -1.39221e6 q^{77} -8.83307e6 q^{78} -1.91241e6 q^{79} +1.87095e6 q^{80} -4.77763e6 q^{81} +4.02584e6 q^{82} +4.51489e6 q^{83} +9.56033e6 q^{84} +2.18641e6 q^{85} -1.44213e7 q^{86} +3.19862e6 q^{87} +6.27124e6 q^{88} +4.84291e6 q^{89} +3213.49 q^{90} +6.63687e6 q^{91} +3.08936e7 q^{92} +8.12697e6 q^{93} +1.44580e7 q^{94} -78568.3 q^{95} -8.21901e6 q^{96} -1599.81 q^{97} +6.36443e6 q^{98} +4749.16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q + 48 q^{2} + 310 q^{3} + 10650 q^{4} + 3999 q^{5} + 1998 q^{6} + 4301 q^{7} + 9216 q^{8} + 124464 q^{9}+O(q^{10}) $ 162 * q + 48 * q^2 + 310 * q^3 + 10650 * q^4 + 3999 * q^5 + 1998 * q^6 + 4301 * q^7 + 9216 * q^8 + 124464 * q^9	\( 162 q + 48 q^{2} + 310 q^{3} + 10650 q^{4} + 3999 q^{5} + 1998 q^{6} + 4301 q^{7} + 9216 q^{8} + 124464 q^{9} + 7430 q^{10} + 19840 q^{11} + 55737 q^{12} + 51223 q^{13} + 75679 q^{14} + 44609 q^{15} + 709506 q^{16} + 258906 q^{17} + 135171 q^{18} + 80362 q^{19} + 506432 q^{20} + 138572 q^{21} + 158320 q^{22} + 571410 q^{23} + 325871 q^{24} + 2732541 q^{25} + 488640 q^{26} + 772231 q^{27} + 699304 q^{28} + 968170 q^{29} + 301526 q^{30} + 348203 q^{31} + 1078196 q^{32} + 1536618 q^{33} + 870073 q^{34} + 1089291 q^{35} + 8775356 q^{36} + 2226256 q^{37} + 3884597 q^{38} + 923555 q^{39} + 2518352 q^{40} + 1825935 q^{41} + 3419892 q^{42} + 1582376 q^{43} + 4352040 q^{44} + 9457186 q^{45} + 1012278 q^{46} + 4801410 q^{47} + 9073674 q^{48} + 21448221 q^{49} + 2366848 q^{50} + 3749747 q^{51} + 7035334 q^{52} + 17191348 q^{53} + 5748697 q^{54} + 5271331 q^{55} + 14854657 q^{56} + 5393884 q^{57} + 4036260 q^{58} + 8263804 q^{59} + 10193498 q^{60} + 12366404 q^{61} + 18470554 q^{62} + 15526895 q^{63} + 49399626 q^{64} + 17325330 q^{65} + 11279868 q^{66} + 5477434 q^{67} + 44562265 q^{68} + 26851278 q^{69} + 9428823 q^{70} + 12108395 q^{71} + 22153063 q^{72} + 13995388 q^{73} + 13478769 q^{74} + 24654171 q^{75} + 8225460 q^{76} + 61240119 q^{77} + 17624449 q^{78} + 8215066 q^{79} + 65708461 q^{80} + 112675190 q^{81} + 29179962 q^{82} + 33597369 q^{83} + 13895447 q^{84} + 24308391 q^{85} + 22043075 q^{86} + 25661967 q^{87} + 32743591 q^{88} + 47538968 q^{89} + 46132321 q^{90} + 24574095 q^{91} + 108017386 q^{92} + 63765304 q^{93} + 41203657 q^{94} + 38032578 q^{95} + 41465754 q^{96} + 45954628 q^{97} + 37164970 q^{98} + 43882333 q^{99}+O(q^{100}) \) 162 * q + 48 * q^2 + 310 * q^3 + 10650 * q^4 + 3999 * q^5 + 1998 * q^6 + 4301 * q^7 + 9216 * q^8 + 124464 * q^9 + 7430 * q^10 + 19840 * q^11 + 55737 * q^12 + 51223 * q^13 + 75679 * q^14 + 44609 * q^15 + 709506 * q^16 + 258906 * q^17 + 135171 * q^18 + 80362 * q^19 + 506432 * q^20 + 138572 * q^21 + 158320 * q^22 + 571410 * q^23 + 325871 * q^24 + 2732541 * q^25 + 488640 * q^26 + 772231 * q^27 + 699304 * q^28 + 968170 * q^29 + 301526 * q^30 + 348203 * q^31 + 1078196 * q^32 + 1536618 * q^33 + 870073 * q^34 + 1089291 * q^35 + 8775356 * q^36 + 2226256 * q^37 + 3884597 * q^38 + 923555 * q^39 + 2518352 * q^40 + 1825935 * q^41 + 3419892 * q^42 + 1582376 * q^43 + 4352040 * q^44 + 9457186 * q^45 + 1012278 * q^46 + 4801410 * q^47 + 9073674 * q^48 + 21448221 * q^49 + 2366848 * q^50 + 3749747 * q^51 + 7035334 * q^52 + 17191348 * q^53 + 5748697 * q^54 + 5271331 * q^55 + 14854657 * q^56 + 5393884 * q^57 + 4036260 * q^58 + 8263804 * q^59 + 10193498 * q^60 + 12366404 * q^61 + 18470554 * q^62 + 15526895 * q^63 + 49399626 * q^64 + 17325330 * q^65 + 11279868 * q^66 + 5477434 * q^67 + 44562265 * q^68 + 26851278 * q^69 + 9428823 * q^70 + 12108395 * q^71 + 22153063 * q^72 + 13995388 * q^73 + 13478769 * q^74 + 24654171 * q^75 + 8225460 * q^76 + 61240119 * q^77 + 17624449 * q^78 + 8215066 * q^79 + 65708461 * q^80 + 112675190 * q^81 + 29179962 * q^82 + 33597369 * q^83 + 13895447 * q^84 + 24308391 * q^85 + 22043075 * q^86 + 25661967 * q^87 + 32743591 * q^88 + 47538968 * q^89 + 46132321 * q^90 + 24574095 * q^91 + 108017386 * q^92 + 63765304 * q^93 + 41203657 * q^94 + 38032578 * q^95 + 41465754 * q^96 + 45954628 * q^97 + 37164970 * q^98 + 43882333 * 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 $

$2$	−20.3517	−1.79885	−0.899426	−	0.437073i	$-0.856015\pi$
$2$	−20.3517	−1.79885	−0.899426	+	0.437073i	$0.856015\pi$
$3$	46.7393	0.999442	0.499721	−	0.866186i	$-0.333436\pi$
$3$	46.7393	0.999442	0.499721	+	0.866186i	$0.333436\pi$
$4$	286.191	2.23587
$5$	64.7634	0.231705	0.115852	−	0.993266i	$-0.463040\pi$
$5$	64.7634	0.231705	0.115852	+	0.993266i	$0.463040\pi$
$6$	−951.224	−1.79785
$7$	714.717	0.787573	0.393787	−	0.919202i	$-0.371165\pi$
$7$	714.717	0.787573	0.393787	+	0.919202i	$0.371165\pi$
$8$	−3219.46	−2.22315
$9$	−2.43807	−0.00111480
$10$	−1318.04	−0.416802
$11$	−1947.92	−0.441261	−0.220631	−	0.975357i	$-0.570812\pi$
$11$	−1947.92	−0.441261	−0.220631	+	0.975357i	$0.570812\pi$
$12$	13376.4	2.23462
$13$	9286.00	1.17227	0.586134	−	0.810214i	$-0.300649\pi$
$13$	9286.00	1.17227	0.586134	+	0.810214i	$0.300649\pi$
$14$	−14545.7	−1.41673
$15$	3027.00	0.231575
$16$	28888.9	1.76324
$17$	33760.0	1.66660	0.833300	−	0.552821i	$-0.186449\pi$
$17$	33760.0	1.66660	0.833300	+	0.552821i	$0.186449\pi$
$18$	49.6189	0.00200537
$19$	−1213.16	−0.0405770	−0.0202885	−	0.999794i	$-0.506458\pi$
$19$	−1213.16	−0.0405770	−0.0202885	+	0.999794i	$0.506458\pi$
$20$	18534.7	0.518061
$21$	33405.4	0.787134
$22$	39643.4	0.793764
$23$	107948.	1.84997	0.924986	−	0.380001i	$-0.124076\pi$
$23$	107948.	1.84997	0.924986	+	0.380001i	$0.124076\pi$
$24$	−150475.	−2.22191
$25$	−73930.7	−0.946313
$26$	−188986.	−2.10874
$27$	−102333.	−1.00056
$28$	204546.	1.76091
$29$	68435.4	0.521060	0.260530	−	0.965466i	$-0.416103\pi$
$29$	68435.4	0.521060	0.260530	+	0.965466i	$0.416103\pi$
$30$	−61604.5	−0.416570
$31$	173879.	1.04829	0.524144	−	0.851630i	$-0.324385\pi$
$31$	173879.	1.04829	0.524144	+	0.851630i	$0.324385\pi$
$32$	−175848.	−0.948664
$33$	−91044.2	−0.441015
$34$	−687073.	−2.99797
$35$	46287.5	0.182484
$36$	−697.755	−0.00249255
$37$	−131389.	−0.426434	−0.213217	−	0.977005i	$-0.568394\pi$
$37$	−131389.	−0.426434	−0.213217	+	0.977005i	$0.568394\pi$
$38$	24689.8	0.0729920
$39$	434021.	1.17161
$40$	−208503.	−0.515113
$41$	−197814.	−0.448242	−0.224121	−	0.974561i	$-0.571951\pi$
$41$	−197814.	−0.448242	−0.224121	+	0.974561i	$0.571951\pi$
$42$	−679856.	−1.41594
$43$	708607.	1.35914	0.679572	−	0.733608i	$-0.262165\pi$
$43$	708607.	1.35914	0.679572	+	0.733608i	$0.262165\pi$
$44$	−557477.	−0.986603
$45$	−157.898	−0.000258305 0
$46$	−2.19691e6	−3.32783
$47$	−710410.	−0.998083	−0.499042	−	0.866578i	$-0.666314\pi$
$47$	−710410.	−0.998083	−0.499042	+	0.866578i	$0.666314\pi$
$48$	1.35025e6	1.76226
$49$	−312722.	−0.379728
$50$	1.50461e6	1.70228
$51$	1.57792e6	1.66567
$52$	2.65757e6	2.62104
$53$	−1.24889e6	−1.15228	−0.576140	−	0.817351i	$-0.695442\pi$
$53$	−1.24889e6	−1.15228	−0.576140	+	0.817351i	$0.695442\pi$
$54$	2.08265e6	1.79985
$55$	−126154.	−0.102242
$56$	−2.30100e6	−1.75089
$57$	−56702.2	−0.0405544
$58$	−1.39278e6	−0.937310
$59$	1.93469e6	1.22640	0.613198	−	0.789930i	$-0.289883\pi$
$59$	1.93469e6	1.22640	0.613198	+	0.789930i	$0.289883\pi$
$60$	866300.	0.517772
$61$	1.36509e6	0.770031	0.385016	−	0.922910i	$-0.374196\pi$
$61$	1.36509e6	0.770031	0.385016	+	0.922910i	$0.374196\pi$
$62$	−3.53873e6	−1.88572
$63$	−1742.53	−0.000877989 0
$64$	−118982.	−0.0567350
$65$	601393.	0.271620
$66$	1.85290e6	0.793321
$67$	3.67065e6	1.49101	0.745506	−	0.666498i	$-0.232208\pi$
$67$	3.67065e6	1.49101	0.745506	+	0.666498i	$0.232208\pi$
$68$	9.66182e6	3.72630
$69$	5.04539e6	1.84894
$70$	−942029.	−0.328262
$71$	3.57528e6	1.18551	0.592755	−	0.805383i	$-0.298040\pi$
$71$	3.57528e6	1.18551	0.592755	+	0.805383i	$0.298040\pi$
$72$	7849.27	0.00247837
$73$	−4.51261e6	−1.35768	−0.678840	−	0.734286i	$-0.737517\pi$
$73$	−4.51261e6	−1.35768	−0.678840	+	0.734286i	$0.737517\pi$
$74$	2.67398e6	0.767092
$75$	−3.45547e6	−0.945785
$76$	−347195.	−0.0907249
$77$	−1.39221e6	−0.347526
$78$	−8.83307e6	−2.10756
$79$	−1.91241e6	−0.436402	−0.218201	−	0.975904i	$-0.570019\pi$
$79$	−1.91241e6	−0.436402	−0.218201	+	0.975904i	$0.570019\pi$
$80$	1.87095e6	0.408551
$81$	−4.77763e6	−0.998884
$82$	4.02584e6	0.806321
$83$	4.51489e6	0.866710	0.433355	−	0.901223i	$-0.357330\pi$
$83$	4.51489e6	0.866710	0.433355	+	0.901223i	$0.357330\pi$
$84$	9.56033e6	1.75993
$85$	2.18641e6	0.386159
$86$	−1.44213e7	−2.44490
$87$	3.19862e6	0.520769
$88$	6.27124e6	0.980988
$89$	4.84291e6	0.728184	0.364092	−	0.931363i	$-0.381379\pi$
$89$	4.84291e6	0.728184	0.364092	+	0.931363i	$0.381379\pi$
$90$	3213.49	0.000464652 0
$91$	6.63687e6	0.923248
$92$	3.08936e7	4.13630
$93$	8.12697e6	1.04770
$94$	1.44580e7	1.79540
$95$	−78568.3	−0.00940188
$96$	−8.21901e6	−0.948135
$97$	−1599.81	−0.000177979 0	−8.89895e−5	−	1.00000i	$-0.500028\pi$
$97$	−1599.81	−0.000177979 0	−8.89895e−5		1.00000i	$0.500028\pi$
$98$	6.36443e6	0.683075
$99$	4749.16	0.000491919 0
$100$	−2.11583e7	−2.11583
$101$	8.99504e6	0.868716	0.434358	−	0.900740i	$-0.356975\pi$
$101$	8.99504e6	0.868716	0.434358	+	0.900740i	$0.356975\pi$
$102$	−3.21133e7	−2.99630
$103$	5.33636e6	0.481188	0.240594	−	0.970626i	$-0.422658\pi$
$103$	5.33636e6	0.481188	0.240594	+	0.970626i	$0.422658\pi$
$104$	−2.98959e7	−2.60612
$105$	2.16345e6	0.182383
$106$	2.54170e7	2.07278
$107$	1.82023e7	1.43643	0.718213	−	0.695824i	$-0.244960\pi$
$107$	1.82023e7	1.43643	0.718213	+	0.695824i	$0.244960\pi$
$108$	−2.92867e7	−2.23711
$109$	−1.64805e7	−1.21893	−0.609463	−	0.792815i	$-0.708615\pi$
$109$	−1.64805e7	−1.21893	−0.609463	+	0.792815i	$0.708615\pi$
$110$	2.56744e6	0.183919
$111$	−6.14101e6	−0.426196
$112$	2.06474e7	1.38868
$113$	−2.93338e7	−1.91246	−0.956232	−	0.292611i	$-0.905476\pi$
$113$	−2.93338e7	−1.91246	−0.956232	+	0.292611i	$0.905476\pi$
$114$	1.15399e6	0.0729514
$115$	6.99105e6	0.428647
$116$	1.95856e7	1.16502
$117$	−22640.0	−0.00130685
$118$	−3.93743e7	−2.20610
$119$	2.41289e7	1.31257
$120$	−9.74529e6	−0.514826
$121$	−1.56928e7	−0.805288
$122$	−2.77820e7	−1.38517
$123$	−9.24567e6	−0.447992
$124$	4.97626e7	2.34384
$125$	−9.84764e6	−0.450970
$126$	35463.5	0.00157937
$127$	1.04222e7	0.451489	0.225745	−	0.974187i	$-0.427518\pi$
$127$	1.04222e7	0.451489	0.225745	+	0.974187i	$0.427518\pi$
$128$	2.49300e7	1.05072
$129$	3.31198e7	1.35839
$130$	−1.22394e7	−0.488604
$131$	−1.10194e7	−0.428259	−0.214129	−	0.976805i	$-0.568691\pi$
$131$	−1.10194e7	−0.428259	−0.214129	+	0.976805i	$0.568691\pi$
$132$	−2.60561e7	−0.986052
$133$	−867066.	−0.0319574
$134$	−7.47040e7	−2.68211
$135$	−6.62742e6	−0.231834
$136$	−1.08689e8	−3.70509
$137$	−1.58435e7	−0.526418	−0.263209	−	0.964739i	$-0.584781\pi$
$137$	−1.58435e7	−0.526418	−0.263209	+	0.964739i	$0.584781\pi$
$138$	−1.02682e8	−3.32597
$139$	−1.66494e7	−0.525831	−0.262915	−	0.964819i	$-0.584684\pi$
$139$	−1.66494e7	−0.525831	−0.262915	+	0.964819i	$0.584684\pi$
$140$	1.32471e7	0.408011
$141$	−3.32041e7	−0.997527
$142$	−7.27629e7	−2.13256
$143$	−1.80884e7	−0.517277
$144$	−70433.3	−0.00196567
$145$	4.43211e6	0.120732
$146$	9.18392e7	2.44227
$147$	−1.46164e7	−0.379516
$148$	−3.76023e7	−0.953450
$149$	−2.84236e7	−0.703926	−0.351963	−	0.936014i	$-0.614486\pi$
$149$	−2.84236e7	−0.703926	−0.351963	+	0.936014i	$0.614486\pi$
$150$	7.03246e7	1.70133
$151$	6.31041e7	1.49155	0.745776	−	0.666197i	$-0.232079\pi$
$151$	6.31041e7	1.49155	0.745776	+	0.666197i	$0.232079\pi$
$152$	3.90571e6	0.0902086
$153$	−82309.4	−0.00185793
$154$	2.83338e7	0.625147
$155$	1.12610e7	0.242893
$156$	1.24213e8	2.61958
$157$	−8.16384e7	−1.68363	−0.841813	−	0.539769i	$-0.818511\pi$
$157$	−8.16384e7	−1.68363	−0.841813	+	0.539769i	$0.818511\pi$
$158$	3.89208e7	0.785022
$159$	−5.83722e7	−1.15164
$160$	−1.13885e7	−0.219810
$161$	7.71519e7	1.45699
$162$	9.72329e7	1.79684
$163$	−8.59527e7	−1.55454	−0.777272	−	0.629165i	$-0.783397\pi$
$163$	−8.59527e7	−1.55454	−0.777272	+	0.629165i	$0.783397\pi$
$164$	−5.66125e7	−1.00221
$165$	−5.89634e6	−0.102185
$166$	−9.18856e7	−1.55908
$167$	2.79792e7	0.464866	0.232433	−	0.972612i	$-0.425331\pi$
$167$	2.79792e7	0.464866	0.232433	+	0.972612i	$0.425331\pi$
$168$	−1.07547e8	−1.74991
$169$	2.34813e7	0.374214
$170$	−4.44972e7	−0.694643
$171$	2957.77	4.52354e−5 0
$172$	2.02797e8	3.03887
$173$	6.65496e7	0.977201	0.488601	−	0.872508i	$-0.337508\pi$
$173$	6.65496e7	0.977201	0.488601	+	0.872508i	$0.337508\pi$
$174$	−6.50974e7	−0.936787
$175$	−5.28395e7	−0.745291
$176$	−5.62732e7	−0.778050
$177$	9.04263e7	1.22571
$178$	−9.85613e7	−1.30990
$179$	8.93281e7	1.16413	0.582066	−	0.813141i	$-0.302244\pi$
$179$	8.93281e7	1.16413	0.582066	+	0.813141i	$0.302244\pi$
$180$	−45189.0	−0.000577536 0
$181$	−2.76415e7	−0.346487	−0.173244	−	0.984879i	$-0.555425\pi$
$181$	−2.76415e7	−0.346487	−0.173244	+	0.984879i	$0.555425\pi$
$182$	−1.35071e8	−1.66079
$183$	6.38036e7	0.769602
$184$	−3.47533e8	−4.11276
$185$	−8.50917e6	−0.0988067
$186$	−1.65398e8	−1.88466
$187$	−6.57617e7	−0.735406
$188$	−2.03313e8	−2.23158
$189$	−7.31390e7	−0.788012
$190$	1.59900e6	0.0169126
$191$	−4.39940e7	−0.456853	−0.228426	−	0.973561i	$-0.573358\pi$
$191$	−4.39940e7	−0.456853	−0.228426	+	0.973561i	$0.573358\pi$
$192$	−5.56113e6	−0.0567034
$193$	−5.92988e7	−0.593738	−0.296869	−	0.954918i	$-0.595943\pi$
$193$	−5.92988e7	−0.593738	−0.296869	+	0.954918i	$0.595943\pi$
$194$	32558.9	0.000320158 0
$195$	2.81087e7	0.271469
$196$	−8.94984e7	−0.849022
$197$	1.14757e8	1.06942	0.534711	−	0.845035i	$-0.320421\pi$
$197$	1.14757e8	1.06942	0.534711	+	0.845035i	$0.320421\pi$
$198$	−96653.5	−0.000884890 0
$199$	1.42870e8	1.28515	0.642575	−	0.766223i	$-0.277866\pi$
$199$	1.42870e8	1.28515	0.642575	+	0.766223i	$0.277866\pi$
$200$	2.38017e8	2.10379
$201$	1.71564e8	1.49018
$202$	−1.83064e8	−1.56269
$203$	4.89119e7	0.410373
$204$	4.51587e8	3.72422
$205$	−1.28111e7	−0.103860
$206$	−1.08604e8	−0.865586
$207$	−263184.	−0.00206235
$208$	2.68263e8	2.06699
$209$	2.36313e6	0.0179051
$210$	−4.40298e7	−0.328079
$211$	1.29375e8	0.948114	0.474057	−	0.880494i	$-0.342789\pi$
$211$	1.29375e8	0.948114	0.474057	+	0.880494i	$0.342789\pi$
$212$	−3.57421e8	−2.57635
$213$	1.67106e8	1.18485
$214$	−3.70448e8	−2.58392
$215$	4.58918e7	0.314920
$216$	3.29456e8	2.22438
$217$	1.24274e8	0.825604
$218$	3.35406e8	2.19267
$219$	−2.10916e8	−1.35692
$220$	−3.61041e7	−0.228600
$221$	3.13496e8	1.95370
$222$	1.24980e8	0.766664
$223$	−2.70265e8	−1.63201	−0.816004	−	0.578046i	$-0.803815\pi$
$223$	−2.70265e8	−1.63201	−0.816004	+	0.578046i	$0.803815\pi$
$224$	−1.25681e8	−0.747142
$225$	180248.	0.00105495
$226$	5.96991e8	3.44024
$227$	−2.62079e8	−1.48711	−0.743553	−	0.668677i	$-0.766861\pi$
$227$	−2.62079e8	−1.48711	−0.743553	+	0.668677i	$0.766861\pi$
$228$	−1.62277e7	−0.0906743
$229$	−1.49979e6	−0.00825291	−0.00412646	−	0.999991i	$-0.501313\pi$
$229$	−1.49979e6	−0.00825291	−0.00412646	+	0.999991i	$0.501313\pi$
$230$	−1.42280e8	−0.771073
$231$	−6.50709e7	−0.347332
$232$	−2.20325e8	−1.15839
$233$	−9.34000e7	−0.483728	−0.241864	−	0.970310i	$-0.577759\pi$
$233$	−9.34000e7	−0.483728	−0.241864	+	0.970310i	$0.577759\pi$
$234$	460761.	0.00235083
$235$	−4.60086e7	−0.231260
$236$	5.53693e8	2.74206
$237$	−8.93848e7	−0.436159
$238$	−4.91063e8	−2.36112
$239$	2.41851e8	1.14592	0.572962	−	0.819582i	$-0.305794\pi$
$239$	2.41851e8	1.14592	0.572962	+	0.819582i	$0.305794\pi$
$240$	8.74467e7	0.408323
$241$	1.91711e8	0.882241	0.441120	−	0.897448i	$-0.354581\pi$
$241$	1.91711e8	0.882241	0.441120	+	0.897448i	$0.354581\pi$
$242$	3.19375e8	1.44859
$243$	498712.	0.00222960
$244$	3.90678e8	1.72169
$245$	−2.02530e7	−0.0879847
$246$	1.88165e8	0.805872
$247$	−1.12654e7	−0.0475672
$248$	−5.59796e8	−2.33050
$249$	2.11023e8	0.866226
$250$	2.00416e8	0.811228
$251$	2.90793e7	0.116072	0.0580358	−	0.998315i	$-0.481516\pi$
$251$	2.90793e7	0.116072	0.0580358	+	0.998315i	$0.481516\pi$
$252$	−498698.	−0.00196307
$253$	−2.10273e8	−0.816321
$254$	−2.12110e8	−0.812162
$255$	1.02191e8	0.385944
$256$	−4.92138e8	−1.83336
$257$	4.59700e8	1.68931	0.844653	−	0.535313i	$-0.179807\pi$
$257$	4.59700e8	1.68931	0.844653	+	0.535313i	$0.179807\pi$
$258$	−6.74044e8	−2.44354
$259$	−9.39057e7	−0.335848
$260$	1.72113e8	0.607307
$261$	−166850.	−0.000580879 0
$262$	2.24262e8	0.770375
$263$	5.14846e8	1.74515	0.872573	−	0.488483i	$-0.162450\pi$
$263$	5.14846e8	1.74515	0.872573	+	0.488483i	$0.162450\pi$
$264$	2.93113e8	0.980441
$265$	−8.08823e7	−0.266989
$266$	1.76462e7	0.0574866
$267$	2.26354e8	0.727778
$268$	1.05051e9	3.33371
$269$	−4.14382e8	−1.29798	−0.648989	−	0.760798i	$-0.724808\pi$
$269$	−4.14382e8	−1.29798	−0.648989	+	0.760798i	$0.724808\pi$
$270$	1.34879e8	0.417034
$271$	4.41452e8	1.34738	0.673692	−	0.739013i	$-0.264708\pi$
$271$	4.41452e8	1.34738	0.673692	+	0.739013i	$0.264708\pi$
$272$	9.75291e8	2.93862
$273$	3.10202e8	0.922733
$274$	3.22443e8	0.946947
$275$	1.44011e8	0.417571
$276$	1.44395e9	4.13399
$277$	−2.75656e8	−0.779270	−0.389635	−	0.920969i	$-0.627399\pi$
$277$	−2.75656e8	−0.779270	−0.389635	+	0.920969i	$0.627399\pi$
$278$	3.38843e8	0.945891
$279$	−423929.	−0.00116863
$280$	−1.49021e8	−0.405689
$281$	3.69915e8	0.994558	0.497279	−	0.867591i	$-0.334333\pi$
$281$	3.69915e8	0.994558	0.497279	+	0.867591i	$0.334333\pi$
$282$	6.75759e8	1.79440
$283$	−6.81926e8	−1.78848	−0.894241	−	0.447586i	$-0.852284\pi$
$283$	−6.81926e8	−1.78848	−0.894241	+	0.447586i	$0.852284\pi$
$284$	1.02321e9	2.65065
$285$	−3.67223e6	−0.00939664
$286$	3.68129e8	0.930505
$287$	−1.41381e8	−0.353024
$288$	428730.	0.00105757
$289$	7.29400e8	1.77756
$290$	−9.02009e7	−0.217179
$291$	−74774.2	−0.000177880 0
$292$	−1.29147e9	−3.03560
$293$	5.03961e8	1.17047	0.585235	−	0.810864i	$-0.301002\pi$
$293$	5.03961e8	1.17047	0.585235	+	0.810864i	$0.301002\pi$
$294$	2.97469e8	0.682694
$295$	1.25297e8	0.284161
$296$	4.23000e8	0.948024
$297$	1.99336e8	0.441507
$298$	5.78468e8	1.26626
$299$	1.00240e9	2.16866
$300$	−9.88925e8	−2.11465
$301$	5.06454e8	1.07043
$302$	−1.28427e9	−2.68308
$303$	4.20422e8	0.868232
$304$	−3.50469e7	−0.0715470
$305$	8.84082e7	0.178420
$306$	1.67514e6	0.00334214
$307$	−2.37079e8	−0.467636	−0.233818	−	0.972280i	$-0.575122\pi$
$307$	−2.37079e8	−0.467636	−0.233818	+	0.972280i	$0.575122\pi$
$308$	−3.98438e8	−0.777022
$309$	2.49418e8	0.480919
$310$	−2.29180e8	−0.436929
$311$	2.03946e7	0.0384462	0.0192231	−	0.999815i	$-0.493881\pi$
$311$	2.03946e7	0.0384462	0.0192231	+	0.999815i	$0.493881\pi$
$312$	−1.39731e9	−2.60467
$313$	9.70264e7	0.178848	0.0894242	−	0.995994i	$-0.471497\pi$
$313$	9.70264e7	0.178848	0.0894242	+	0.995994i	$0.471497\pi$
$314$	1.66148e9	3.02859
$315$	−112852.	−0.000203434 0
$316$	−5.47315e8	−0.975737
$317$	−2.80138e8	−0.493929	−0.246965	−	0.969025i	$-0.579433\pi$
$317$	−2.80138e8	−0.493929	−0.246965	+	0.969025i	$0.579433\pi$
$318$	1.18797e9	2.07163
$319$	−1.33306e8	−0.229924
$320$	−7.70568e6	−0.0131458
$321$	8.50763e8	1.43562
$322$	−1.57017e9	−2.62091
$323$	−4.09563e7	−0.0676257
$324$	−1.36732e9	−2.23337
$325$	−6.86521e8	−1.10933
$326$	1.74928e9	2.79639
$327$	−7.70286e8	−1.21825
$328$	6.36853e8	0.996507
$329$	−5.07742e8	−0.786064
$330$	1.20000e8	0.183816
$331$	−1.08711e9	−1.64769	−0.823846	−	0.566814i	$-0.808176\pi$
$331$	−1.08711e9	−1.64769	−0.823846	+	0.566814i	$0.808176\pi$
$332$	1.29212e9	1.93785
$333$	320335.	0.000475390 0
$334$	−5.69424e8	−0.836224
$335$	2.37724e8	0.345475
$336$	9.65046e8	1.38791
$337$	1.61614e8	0.230025	0.115012	−	0.993364i	$-0.463309\pi$
$337$	1.61614e8	0.230025	0.115012	+	0.993364i	$0.463309\pi$
$338$	−4.77885e8	−0.673155
$339$	−1.37104e9	−1.91140
$340$	6.25732e8	0.863401
$341$	−3.38701e8	−0.462569
$342$	−60195.6	−8.13717e−5 0
$343$	−8.12108e8	−1.08664
$344$	−2.28133e9	−3.02158
$345$	3.26757e8	0.428408
$346$	−1.35440e9	−1.75784
$347$	4.79684e8	0.616314	0.308157	−	0.951336i	$-0.400288\pi$
$347$	4.79684e8	0.616314	0.308157	+	0.951336i	$0.400288\pi$
$348$	9.15417e8	1.16437
$349$	−4.25786e8	−0.536170	−0.268085	−	0.963395i	$-0.586391\pi$
$349$	−4.25786e8	−0.536170	−0.268085	+	0.963395i	$0.586391\pi$
$350$	1.07537e9	1.34067
$351$	−9.50263e8	−1.17292
$352$	3.42537e8	0.418609
$353$	−1.04239e9	−1.26131	−0.630653	−	0.776065i	$-0.717213\pi$
$353$	−1.04239e9	−1.26131	−0.630653	+	0.776065i	$0.717213\pi$
$354$	−1.84033e9	−2.20487
$355$	2.31547e8	0.274688
$356$	1.38600e9	1.62812
$357$	1.12777e9	1.31184
$358$	−1.81798e9	−2.09410
$359$	6.47045e7	0.0738081	0.0369041	−	0.999319i	$-0.488250\pi$
$359$	6.47045e7	0.0738081	0.0369041	+	0.999319i	$0.488250\pi$
$360$	508346.	0.000574249 0
$361$	−8.92400e8	−0.998354
$362$	5.62552e8	0.623279
$363$	−7.33470e8	−0.804839
$364$	1.89941e9	2.06426
$365$	−2.92252e8	−0.314581
$366$	−1.29851e9	−1.38440
$367$	1.17718e9	1.24311	0.621557	−	0.783369i	$-0.286500\pi$
$367$	1.17718e9	1.24311	0.621557	+	0.783369i	$0.286500\pi$
$368$	3.11849e9	3.26195
$369$	482284.	0.000499702 0
$370$	1.73176e8	0.177739
$371$	−8.92602e8	−0.907506
$372$	2.32587e9	2.34253
$373$	1.58429e9	1.58072	0.790360	−	0.612643i	$-0.209894\pi$
$373$	1.58429e9	1.58072	0.790360	+	0.612643i	$0.209894\pi$
$374$	1.33836e9	1.32289
$375$	−4.60272e8	−0.450718
$376$	2.28714e9	2.21888
$377$	6.35491e8	0.610822
$378$	1.48850e9	1.41752
$379$	1.15571e9	1.09047	0.545234	−	0.838284i	$-0.316441\pi$
$379$	1.15571e9	1.09047	0.545234	+	0.838284i	$0.316441\pi$
$380$	−2.24856e7	−0.0210214
$381$	4.87128e8	0.451238
$382$	8.95351e8	0.821810
$383$	−8.92766e8	−0.811974	−0.405987	−	0.913879i	$-0.633072\pi$
$383$	−8.92766e8	−0.811974	−0.405987	+	0.913879i	$0.633072\pi$
$384$	1.16521e9	1.05014
$385$	−9.01642e7	−0.0805233
$386$	1.20683e9	1.06805
$387$	−1.72764e6	−0.00151518
$388$	−457853.	−0.000397938 0
$389$	−3.66231e8	−0.315451	−0.157726	−	0.987483i	$-0.550416\pi$
$389$	−3.66231e8	−0.315451	−0.157726	+	0.987483i	$0.550416\pi$
$390$	−5.72059e8	−0.488332
$391$	3.64431e9	3.08316
$392$	1.00680e9	0.844191
$393$	−5.15037e8	−0.428020
$394$	−2.33551e9	−1.92373
$395$	−1.23854e8	−0.101116
$396$	1.35917e6	0.00109987
$397$	−1.33417e9	−1.07015	−0.535076	−	0.844804i	$-0.679717\pi$
$397$	−1.33417e9	−1.07015	−0.535076	+	0.844804i	$0.679717\pi$
$398$	−2.90764e9	−2.31180
$399$	−4.05260e7	−0.0319396
$400$	−2.13578e9	−1.66858
$401$	−4.15260e6	−0.00321599	−0.00160800	−	0.999999i	$-0.500512\pi$
$401$	−4.15260e6	−0.00321599	−0.00160800	+	0.999999i	$0.500512\pi$
$402$	−3.49161e9	−2.68062
$403$	1.61464e9	1.22888
$404$	2.57430e9	1.94234
$405$	−3.09416e8	−0.231446
$406$	−9.95441e8	−0.738200
$407$	2.55934e8	0.188169
$408$	−5.08005e9	−3.70303
$409$	1.74884e9	1.26391	0.631957	−	0.775003i	$-0.282252\pi$
$409$	1.74884e9	1.26391	0.631957	+	0.775003i	$0.282252\pi$
$410$	2.60727e8	0.186828
$411$	−7.40516e8	−0.526124
$412$	1.52722e9	1.07587
$413$	1.38276e9	0.965876
$414$	5.35624e6	0.00370987
$415$	2.92399e8	0.200821
$416$	−1.63292e9	−1.11209
$417$	−7.78179e8	−0.525537
$418$	−4.80937e7	−0.0322086
$419$	−1.39252e9	−0.924812	−0.462406	−	0.886668i	$-0.653014\pi$
$419$	−1.39252e9	−0.924812	−0.462406	+	0.886668i	$0.653014\pi$
$420$	6.19159e8	0.407784
$421$	1.10043e9	0.718748	0.359374	−	0.933194i	$-0.382990\pi$
$421$	1.10043e9	0.718748	0.359374	+	0.933194i	$0.382990\pi$
$422$	−2.63299e9	−1.70552
$423$	1.73203e6	0.00111267
$424$	4.02075e9	2.56169
$425$	−2.49590e9	−1.57713
$426$	−3.40089e9	−2.13137
$427$	9.75657e8	0.606456
$428$	5.20934e9	3.21166
$429$	−8.45437e8	−0.516988
$430$	−9.33975e8	−0.566495
$431$	−3.15271e9	−1.89676	−0.948382	−	0.317129i	$-0.897281\pi$
$431$	−3.15271e9	−1.89676	−0.948382	+	0.317129i	$0.897281\pi$
$432$	−2.95629e9	−1.76422
$433$	1.94972e9	1.15416	0.577078	−	0.816689i	$-0.304193\pi$
$433$	1.94972e9	1.15416	0.577078	+	0.816689i	$0.304193\pi$
$434$	−2.52919e9	−1.48514
$435$	2.07154e8	0.120665
$436$	−4.71657e9	−2.72536
$437$	−1.30958e8	−0.0750664
$438$	4.29250e9	2.44090
$439$	2.16001e9	1.21851	0.609256	−	0.792973i	$-0.291468\pi$
$439$	2.16001e9	1.21851	0.609256	+	0.792973i	$0.291468\pi$
$440$	4.06147e8	0.227299
$441$	762440.	0.000423322 0
$442$	−6.38017e9	−3.51442
$443$	3.16519e9	1.72977	0.864883	−	0.501973i	$-0.167392\pi$
$443$	3.16519e9	1.72977	0.864883	+	0.501973i	$0.167392\pi$
$444$	−1.75750e9	−0.952919
$445$	3.13643e8	0.168724
$446$	5.50034e9	2.93574
$447$	−1.32850e9	−0.703533
$448$	−8.50385e7	−0.0446830
$449$	1.40005e9	0.729932	0.364966	−	0.931021i	$-0.381081\pi$
$449$	1.40005e9	0.729932	0.364966	+	0.931021i	$0.381081\pi$
$450$	−3.66836e6	−0.00189770
$451$	3.85324e8	0.197792
$452$	−8.39506e9	−4.27602
$453$	2.94944e9	1.49072
$454$	5.33375e9	2.67508
$455$	4.29826e8	0.213921
$456$	1.82550e8	0.0901583
$457$	−3.99919e9	−1.96004	−0.980021	−	0.198892i	$-0.936266\pi$
$457$	−3.99919e9	−1.96004	−0.980021	+	0.198892i	$0.936266\pi$
$458$	3.05233e7	0.0148458
$459$	−3.45476e9	−1.66753
$460$	2.00078e9	0.958399
$461$	−3.86771e8	−0.183865	−0.0919327	−	0.995765i	$-0.529304\pi$
$461$	−3.86771e8	−0.183865	−0.0919327	+	0.995765i	$0.529304\pi$
$462$	1.32430e9	0.624799
$463$	−1.52657e9	−0.714796	−0.357398	−	0.933952i	$-0.616336\pi$
$463$	−1.52657e9	−0.714796	−0.357398	+	0.933952i	$0.616336\pi$
$464$	1.97703e9	0.918754
$465$	5.26331e8	0.242758
$466$	1.90085e9	0.870155
$467$	8.25613e8	0.375117	0.187559	−	0.982253i	$-0.439943\pi$
$467$	8.25613e8	0.375117	0.187559	+	0.982253i	$0.439943\pi$
$468$	−6.47936e6	−0.00292194
$469$	2.62348e9	1.17428
$470$	9.36352e8	0.416003
$471$	−3.81572e9	−1.68269
$472$	−6.22867e9	−2.72645
$473$	−1.38031e9	−0.599738
$474$	1.81913e9	0.784585
$475$	8.96897e7	0.0383986
$476$	6.90547e9	2.93473
$477$	3.04488e6	0.00128457
$478$	−4.92208e9	−2.06135
$479$	1.40159e9	0.582701	0.291350	−	0.956616i	$-0.405895\pi$
$479$	1.40159e9	0.582701	0.291350	+	0.956616i	$0.405895\pi$
$480$	−5.32291e8	−0.219687
$481$	−1.22008e9	−0.499895
$482$	−3.90164e9	−1.58702
$483$	3.60603e9	1.45618
$484$	−4.49114e9	−1.80052
$485$	−103609.	−4.12385e−5 0
$486$	−1.01496e7	−0.00401073
$487$	5.29470e8	0.207725	0.103863	−	0.994592i	$-0.466880\pi$
$487$	5.29470e8	0.207725	0.103863	+	0.994592i	$0.466880\pi$
$488$	−4.39486e9	−1.71189
$489$	−4.01737e9	−1.55368
$490$	4.12182e8	0.158272
$491$	7.59968e8	0.289741	0.144871	−	0.989451i	$-0.453723\pi$
$491$	7.59968e8	0.289741	0.144871	+	0.989451i	$0.453723\pi$
$492$	−2.64603e9	−1.00165
$493$	2.31038e9	0.868399
$494$	2.29270e8	0.0855663
$495$	307572.	0.000113980 0
$496$	5.02317e9	1.84838
$497$	2.55531e9	0.933676
$498$	−4.29467e9	−1.55821
$499$	3.07280e9	1.10709	0.553544	−	0.832820i	$-0.313275\pi$
$499$	3.07280e9	1.10709	0.553544	+	0.832820i	$0.313275\pi$
$500$	−2.81831e9	−1.00831
$501$	1.30773e9	0.464606
$502$	−5.91813e8	−0.208796
$503$	−8.48359e8	−0.297229	−0.148615	−	0.988895i	$-0.547481\pi$
$503$	−8.48359e8	−0.297229	−0.148615	+	0.988895i	$0.547481\pi$
$504$	5.61001e6	0.00195190
$505$	5.82549e8	0.201286
$506$	4.27941e9	1.46844
$507$	1.09750e9	0.374005
$508$	2.98275e9	1.00947
$509$	6.06732e8	0.203932	0.101966	−	0.994788i	$-0.467487\pi$
$509$	6.06732e8	0.203932	0.101966	+	0.994788i	$0.467487\pi$
$510$	−2.07977e9	−0.694256
$511$	−3.22524e9	−1.06927
$512$	6.82480e9	2.24722
$513$	1.24146e8	0.0405996
$514$	−9.35567e9	−3.03881
$515$	3.45601e8	0.111493
$516$	9.47859e9	3.03718
$517$	1.38382e9	0.440416
$518$	1.91114e9	0.604141
$519$	3.11048e9	0.976656
$520$	−1.93616e9	−0.603851
$521$	3.17620e9	0.983956	0.491978	−	0.870608i	$-0.336274\pi$
$521$	3.17620e9	0.983956	0.491978	+	0.870608i	$0.336274\pi$
$522$	3.39569e6	0.00104492
$523$	5.22433e9	1.59689	0.798444	−	0.602069i	$-0.205657\pi$
$523$	5.22433e9	1.59689	0.798444	+	0.602069i	$0.205657\pi$
$524$	−3.15364e9	−0.957531
$525$	−2.46968e9	−0.744875
$526$	−1.04780e10	−3.13926
$527$	5.87015e9	1.74708
$528$	−2.63017e9	−0.777616
$529$	8.24784e9	2.42240
$530$	1.64609e9	0.480273
$531$	−4.71693e6	−0.00136719
$532$	−2.48147e8	−0.0714525
$533$	−1.83690e9	−0.525460
$534$	−4.60669e9	−1.30916
$535$	1.17884e9	0.332826
$536$	−1.18175e10	−3.31474
$537$	4.17513e9	1.16348
$538$	8.43336e9	2.33487
$539$	6.09157e8	0.167559
$540$	−1.89671e9	−0.518349
$541$	−6.84908e9	−1.85970	−0.929848	−	0.367945i	$-0.880061\pi$
$541$	−6.84908e9	−1.85970	−0.929848	+	0.367945i	$0.880061\pi$
$542$	−8.98430e9	−2.42374
$543$	−1.29195e9	−0.346294
$544$	−5.93663e9	−1.58104
$545$	−1.06733e9	−0.282431
$546$	−6.31314e9	−1.65986
$547$	−1.63667e8	−0.0427569
$547$	−1.63667e8	−0.0427569
$548$	−4.53428e9	−1.17700
$549$	−3.32820e6	−0.000858433 0
$550$	−2.93086e9	−0.751149
$551$	−8.30230e7	−0.0211431
$552$	−1.62434e10	−4.11046
$553$	−1.36683e9	−0.343699
$554$	5.61006e9	1.40179
$555$	−3.97713e8	−0.0987516
$556$	−4.76490e9	−1.17569
$557$	5.50826e9	1.35058	0.675291	−	0.737551i	$-0.264018\pi$
$557$	5.50826e9	1.35058	0.675291	+	0.737551i	$0.264018\pi$
$558$	8.62768e6	0.00210220
$559$	6.58013e9	1.59328
$560$	1.33720e9	0.321764
$561$	−3.07366e9	−0.734996
$562$	−7.52840e9	−1.78906
$563$	6.10193e9	1.44108	0.720539	−	0.693414i	$-0.243894\pi$
$563$	6.10193e9	1.44108	0.720539	+	0.693414i	$0.243894\pi$
$564$	−9.50271e9	−2.23034
$565$	−1.89975e9	−0.443127
$566$	1.38783e10	3.21721
$567$	−3.41465e9	−0.786695
$568$	−1.15105e10	−2.63556
$569$	−1.29701e9	−0.295156	−0.147578	−	0.989050i	$-0.547148\pi$
$569$	−1.29701e9	−0.295156	−0.147578	+	0.989050i	$0.547148\pi$
$570$	7.47360e7	0.0169032
$571$	7.68317e7	0.0172709	0.00863543	−	0.999963i	$-0.497251\pi$
$571$	7.68317e7	0.0172709	0.00863543	+	0.999963i	$0.497251\pi$
$572$	−5.17673e9	−1.15656
$573$	−2.05625e9	−0.456598
$574$	2.87734e9	0.635037
$575$	−7.98064e9	−1.75065
$576$	290087.	6.32484e−5 0
$577$	3.61729e9	0.783913	0.391956	−	0.919984i	$-0.371798\pi$
$577$	3.61729e9	0.783913	0.391956	+	0.919984i	$0.371798\pi$
$578$	−1.48445e10	−3.19756
$579$	−2.77158e9	−0.593407
$580$	1.26843e9	0.269941
$581$	3.22687e9	0.682597
$582$	1.52178e6	0.000319979 0
$583$	2.43273e9	0.508457
$584$	1.45282e10	3.01832
$585$	−1.46624e6	−0.000302803 0
$586$	−1.02565e10	−2.10550
$587$	8.96645e9	1.82973	0.914865	−	0.403759i	$-0.132297\pi$
$587$	8.96645e9	1.82973	0.914865	+	0.403759i	$0.132297\pi$
$588$	−4.18309e9	−0.848549
$589$	−2.10943e8	−0.0425364
$590$	−2.55001e9	−0.511164
$591$	5.36368e9	1.06883
$592$	−3.79568e9	−0.751905
$593$	9.58053e9	1.88668	0.943340	−	0.331829i	$-0.107666\pi$
$593$	9.58053e9	1.88668	0.943340	+	0.331829i	$0.107666\pi$
$594$	−4.05682e9	−0.794206
$595$	1.56267e9	0.304129
$596$	−8.13458e9	−1.57389
$597$	6.67762e9	1.28443
$598$	−2.04006e10	−3.90111
$599$	−9.77869e9	−1.85903	−0.929516	−	0.368782i	$-0.879775\pi$
$599$	−9.77869e9	−1.85903	−0.929516	+	0.368782i	$0.879775\pi$
$600$	1.11247e10	2.10262
$601$	4.45341e9	0.836821	0.418410	−	0.908258i	$-0.362587\pi$
$601$	4.45341e9	0.836821	0.418410	+	0.908258i	$0.362587\pi$
$602$	−1.03072e10	−1.92554
$603$	−8.94932e6	−0.00166218
$604$	1.80598e10	3.33491
$605$	−1.01632e9	−0.186589
$606$	−8.55629e9	−1.56182
$607$	−7.70424e9	−1.39820	−0.699100	−	0.715024i	$-0.746416\pi$
$607$	−7.70424e9	−1.39820	−0.699100	+	0.715024i	$0.746416\pi$
$608$	2.13331e8	0.0384939
$609$	2.28611e9	0.410144
$610$	−1.79926e9	−0.320951
$611$	−6.59687e9	−1.17002
$612$	−2.35562e7	−0.00415409
$613$	−4.27060e9	−0.748819	−0.374409	−	0.927263i	$-0.622155\pi$
$613$	−4.27060e9	−0.748819	−0.374409	+	0.927263i	$0.622155\pi$
$614$	4.82495e9	0.841208
$615$	−5.98781e8	−0.103802
$616$	4.48216e9	0.772600
$617$	−1.13245e10	−1.94097	−0.970486	−	0.241158i	$-0.922473\pi$
$617$	−1.13245e10	−1.94097	−0.970486	+	0.241158i	$0.922473\pi$
$618$	−5.07607e9	−0.865103
$619$	7.90097e9	1.33895	0.669473	−	0.742837i	$-0.266520\pi$
$619$	7.90097e9	1.33895	0.669473	+	0.742837i	$0.266520\pi$
$620$	3.22280e9	0.543077
$621$	−1.10466e10	−1.85100
$622$	−4.15064e8	−0.0691590
$623$	3.46131e9	0.573498
$624$	1.25384e10	2.06584
$625$	5.13807e9	0.841821
$626$	−1.97465e9	−0.321722
$627$	1.10451e8	0.0178951
$628$	−2.33642e10	−3.76437
$629$	−4.43568e9	−0.710695
$630$	2.29674e6	0.000365948 0
$631$	5.20176e9	0.824228	0.412114	−	0.911132i	$-0.364791\pi$
$631$	5.20176e9	0.824228	0.412114	+	0.911132i	$0.364791\pi$
$632$	6.15693e9	0.970185
$633$	6.04688e9	0.947585
$634$	5.70128e9	0.888505
$635$	6.74979e8	0.104612
$636$	−1.67056e10	−2.57491
$637$	−2.90394e9	−0.445143
$638$	2.71301e9	0.413599
$639$	−8.71678e6	−0.00132161
$640$	1.61455e9	0.243457
$641$	−4.03302e8	−0.0604822	−0.0302411	−	0.999543i	$-0.509628\pi$
$641$	−4.03302e8	−0.0604822	−0.0302411	+	0.999543i	$0.509628\pi$
$642$	−1.73145e10	−2.58248
$643$	1.48024e9	0.219581	0.109790	−	0.993955i	$-0.464982\pi$
$643$	1.48024e9	0.219581	0.109790	+	0.993955i	$0.464982\pi$
$644$	2.20802e10	3.25764
$645$	2.14495e9	0.314745
$646$	8.33529e8	0.121649
$647$	1.11342e10	1.61620	0.808098	−	0.589048i	$-0.200497\pi$
$647$	1.11342e10	1.61620	0.808098	+	0.589048i	$0.200497\pi$
$648$	1.53814e10	2.22066
$649$	−3.76862e9	−0.541161
$650$	1.39719e10	1.99553
$651$	5.80849e9	0.825144
$652$	−2.45989e10	−3.47576
$653$	−1.55119e9	−0.218006	−0.109003	−	0.994041i	$-0.534766\pi$
$653$	−1.55119e9	−0.218006	−0.109003	+	0.994041i	$0.534766\pi$
$654$	1.56766e10	2.19144
$655$	−7.13651e8	−0.0992296
$656$	−5.71462e9	−0.790359
$657$	1.10021e7	0.00151355
$658$	1.03334e10	1.41401
$659$	6.82646e9	0.929173	0.464587	−	0.885528i	$-0.346203\pi$
$659$	6.82646e9	0.929173	0.464587	+	0.885528i	$0.346203\pi$
$660$	−1.68748e9	−0.228473
$661$	1.19286e9	0.160652	0.0803260	−	0.996769i	$-0.474404\pi$
$661$	1.19286e9	0.160652	0.0803260	+	0.996769i	$0.474404\pi$
$662$	2.21245e10	2.96395
$663$	1.46526e10	1.95261
$664$	−1.45355e10	−1.92682
$665$	−5.61541e7	−0.00740467
$666$	−6.51936e6	−0.000855156 0
$667$	7.38743e9	0.963947
$668$	8.00740e9	1.03938
$669$	−1.26320e10	−1.63110
$670$	−4.83808e9	−0.621458
$671$	−2.65909e9	−0.339785
$672$	−5.87426e9	−0.746726
$673$	9.02790e9	1.14165	0.570826	−	0.821071i	$-0.306623\pi$
$673$	9.02790e9	1.14165	0.570826	+	0.821071i	$0.306623\pi$
$674$	−3.28912e9	−0.413781
$675$	7.56554e9	0.946840
$676$	6.72015e9	0.836692
$677$	−7.15401e9	−0.886113	−0.443057	−	0.896494i	$-0.646106\pi$
$677$	−7.15401e9	−0.886113	−0.443057	+	0.896494i	$0.646106\pi$
$678$	2.79030e10	3.43832
$679$	−1.14342e6	−0.000140171 0
$680$	−7.03907e9	−0.858487
$681$	−1.22494e10	−1.48628
$682$	6.89315e9	0.832094
$683$	1.46986e10	1.76524	0.882619	−	0.470090i	$-0.155778\pi$
$683$	1.46986e10	1.76524	0.882619	+	0.470090i	$0.155778\pi$
$684$	846488.	0.000101140 0
$685$	−1.02608e9	−0.121973
$686$	1.65278e10	1.95470
$687$	−7.00993e7	−0.00824831
$688$	2.04709e10	2.39650
$689$	−1.15972e10	−1.35078
$690$	−6.65005e9	−0.770643
$691$	−1.25130e10	−1.44274	−0.721370	−	0.692550i	$-0.756487\pi$
$691$	−1.25130e10	−1.44274	−0.721370	+	0.692550i	$0.756487\pi$
$692$	1.90459e10	2.18489
$693$	3.39431e6	0.000387423 0
$694$	−9.76238e9	−1.10866
$695$	−1.07827e9	−0.121837
$696$	−1.02978e10	−1.15775
$697$	−6.67819e9	−0.747041
$698$	8.66547e9	0.964491
$699$	−4.36545e9	−0.483458
$700$	−1.51222e10	−1.66637
$701$	6.74423e9	0.739467	0.369734	−	0.929138i	$-0.379449\pi$
$701$	6.74423e9	0.739467	0.369734	+	0.929138i	$0.379449\pi$
$702$	1.93395e10	2.10991
$703$	1.59395e8	0.0173034
$704$	2.31767e8	0.0250350
$705$	−2.15041e9	−0.231131
$706$	2.12145e10	2.26890
$707$	6.42891e9	0.684178
$708$	2.58792e10	2.74053
$709$	3.34650e9	0.352638	0.176319	−	0.984333i	$-0.443581\pi$
$709$	3.34650e9	0.352638	0.176319	+	0.984333i	$0.443581\pi$
$710$	−4.71237e9	−0.494123
$711$	4.66260e6	0.000486502 0
$712$	−1.55915e10	−1.61886
$713$	1.87698e10	1.93930
$714$	−2.29519e10	−2.35980
$715$	−1.17146e9	−0.119855
$716$	2.55649e10	2.60285
$717$	1.13040e10	1.14528
$718$	−1.31685e9	−0.132770
$719$	2.29135e9	0.229901	0.114950	−	0.993371i	$-0.463329\pi$
$719$	2.29135e9	0.229901	0.114950	+	0.993371i	$0.463329\pi$
$720$	−4.56150e6	−0.000455454 0
$721$	3.81399e9	0.378971
$722$	1.81618e10	1.79589
$723$	8.96043e9	0.881749
$724$	−7.91076e9	−0.774700
$725$	−5.05948e9	−0.493086
$726$	1.49274e10	1.44779
$727$	−4.47357e9	−0.431801	−0.215901	−	0.976415i	$-0.569269\pi$
$727$	−4.47357e9	−0.431801	−0.215901	+	0.976415i	$0.569269\pi$
$728$	−2.13671e10	−2.05251
$729$	1.04720e10	1.00111
$730$	5.94782e9	0.565884
$731$	2.39226e10	2.26515
$732$	1.82600e10	1.72073
$733$	−5.59681e9	−0.524900	−0.262450	−	0.964946i	$-0.584531\pi$
$733$	−5.59681e9	−0.524900	−0.262450	+	0.964946i	$0.584531\pi$
$734$	−2.39576e10	−2.23618
$735$	−9.46609e8	−0.0879357
$736$	−1.89823e10	−1.75500
$737$	−7.15012e9	−0.657926
$738$	−9.81530e6	−0.000898889 0
$739$	1.28352e10	1.16989	0.584946	−	0.811072i	$-0.301116\pi$
$739$	1.28352e10	1.16989	0.584946	+	0.811072i	$0.301116\pi$
$740$	−2.43525e9	−0.220919
$741$	−5.26537e8	−0.0475406
$742$	1.81660e10	1.63247
$743$	−2.48576e9	−0.222330	−0.111165	−	0.993802i	$-0.535458\pi$
$743$	−2.48576e9	−0.222330	−0.111165	+	0.993802i	$0.535458\pi$
$744$	−2.61645e10	−2.32920
$745$	−1.84081e9	−0.163103
$746$	−3.22430e10	−2.84348
$747$	−1.10076e7	−0.000966210 0
$748$	−1.88204e10	−1.64427
$749$	1.30095e10	1.13129
$750$	9.36731e9	0.810775
$751$	−9.71168e9	−0.836671	−0.418335	−	0.908293i	$-0.637386\pi$
$751$	−9.71168e9	−0.836671	−0.418335	+	0.908293i	$0.637386\pi$
$752$	−2.05230e10	−1.75986
$753$	1.35915e9	0.116007
$754$	−1.29333e10	−1.09878
$755$	4.08684e9	0.345599
$756$	−2.09317e10	−1.76189
$757$	1.31624e10	1.10281	0.551404	−	0.834239i	$-0.314092\pi$
$757$	1.31624e10	1.10281	0.551404	+	0.834239i	$0.314092\pi$
$758$	−2.35207e10	−1.96159
$759$	−9.82800e9	−0.815866
$760$	2.52947e8	0.0209017
$761$	−2.67188e9	−0.219771	−0.109885	−	0.993944i	$-0.535048\pi$
$761$	−2.67188e9	−0.219771	−0.109885	+	0.993944i	$0.535048\pi$
$762$	−9.91387e9	−0.811710
$763$	−1.17789e10	−0.959993
$764$	−1.25907e10	−1.02146
$765$	−5.33064e6	−0.000430491 0
$766$	1.81693e10	1.46062
$767$	1.79656e10	1.43766
$768$	−2.30022e10	−1.83234
$769$	1.45087e9	0.115050	0.0575251	−	0.998344i	$-0.481679\pi$
$769$	1.45087e9	0.115050	0.0575251	+	0.998344i	$0.481679\pi$
$770$	1.83499e9	0.144850
$771$	2.14861e10	1.68837
$772$	−1.69708e10	−1.32752
$773$	9.57886e9	0.745908	0.372954	−	0.927850i	$-0.378345\pi$
$773$	9.57886e9	0.745908	0.372954	+	0.927850i	$0.378345\pi$
$774$	3.51603e7	0.00272558
$775$	−1.28550e10	−0.992009
$776$	5.15054e6	0.000395673 0
$777$	−4.38909e9	−0.335661
$778$	7.45343e9	0.567450
$779$	2.39979e8	0.0181883
$780$	8.04446e9	0.606968
$781$	−6.96434e9	−0.523120
$782$	−7.41679e10	−5.54616
$783$	−7.00318e9	−0.521350
$784$	−9.03421e9	−0.669552
$785$	−5.28718e9	−0.390104
$786$	1.04819e10	0.769945
$787$	4.06719e9	0.297428	0.148714	−	0.988880i	$-0.452487\pi$
$787$	4.06719e9	0.297428	0.148714	+	0.988880i	$0.452487\pi$
$788$	3.28426e10	2.39109
$789$	2.40635e10	1.74417
$790$	2.52064e9	0.181893
$791$	−2.09653e10	−1.50621
$792$	−1.52897e7	−0.00109361
$793$	1.26763e10	0.902683
$794$	2.71527e10	1.92505
$795$	−3.78038e9	−0.266840
$796$	4.08880e10	2.87343
$797$	−1.59324e10	−1.11475	−0.557374	−	0.830261i	$-0.688191\pi$
$797$	−1.59324e10	−1.11475	−0.557374	+	0.830261i	$0.688191\pi$
$798$	8.24773e8	0.0574545
$799$	−2.39835e10	−1.66341
$800$	1.30006e10	0.897733
$801$	−1.18074e7	−0.000811781 0
$802$	8.45125e7	0.00578509
$803$	8.79018e9	0.599092
$804$	4.91000e10	3.33185
$805$	4.99662e9	0.337591
$806$	−3.28606e10	−2.21057
$807$	−1.93679e10	−1.29725
$808$	−2.89591e10	−1.93128
$809$	4.03374e8	0.0267848	0.0133924	−	0.999910i	$-0.495737\pi$
$809$	4.03374e8	0.0267848	0.0133924	+	0.999910i	$0.495737\pi$
$810$	6.29713e9	0.416337
$811$	1.11896e10	0.736616	0.368308	−	0.929704i	$-0.379937\pi$
$811$	1.11896e10	0.736616	0.368308	+	0.929704i	$0.379937\pi$
$812$	1.39982e10	0.917540
$813$	2.06332e10	1.34663
$814$	−5.20869e9	−0.338488
$815$	−5.56659e9	−0.360195
$816$	4.55844e10	2.93698
$817$	−8.59653e8	−0.0551500
$818$	−3.55918e10	−2.27360
$819$	−1.61812e7	−0.00102924
$820$	−3.66642e9	−0.232217
$821$	−1.18417e10	−0.746816	−0.373408	−	0.927667i	$-0.621811\pi$
$821$	−1.18417e10	−0.746816	−0.373408	+	0.927667i	$0.621811\pi$
$822$	1.50708e10	0.946419
$823$	9.22245e9	0.576696	0.288348	−	0.957526i	$-0.406894\pi$
$823$	9.22245e9	0.576696	0.288348	+	0.957526i	$0.406894\pi$
$824$	−1.71802e10	−1.06975
$825$	6.73096e9	0.417339
$826$	−2.81415e10	−1.73747
$827$	1.35264e10	0.831594	0.415797	−	0.909457i	$-0.363503\pi$
$827$	1.35264e10	0.831594	0.415797	+	0.909457i	$0.363503\pi$
$828$	−7.53209e7	−0.00461115
$829$	−1.62388e10	−0.989953	−0.494976	−	0.868906i	$-0.664823\pi$
$829$	−1.62388e10	−0.989953	−0.494976	+	0.868906i	$0.664823\pi$
$830$	−5.95082e9	−0.361247
$831$	−1.28840e10	−0.778836
$832$	−1.10487e9	−0.0665087
$833$	−1.05575e10	−0.632855
$834$	1.58373e10	0.945364
$835$	1.81203e9	0.107711
$836$	6.76308e8	0.0400334
$837$	−1.77935e10	−1.04887
$838$	2.83402e10	1.66360
$839$	9.08956e9	0.531344	0.265672	−	0.964063i	$-0.414406\pi$
$839$	9.08956e9	0.531344	0.265672	+	0.964063i	$0.414406\pi$
$840$	−6.96512e9	−0.405463
$841$	−1.25665e10	−0.728497
$842$	−2.23957e10	−1.29292
$843$	1.72896e10	0.994003
$844$	3.70259e10	2.11986
$845$	1.52073e9	0.0867070
$846$	−3.52498e7	−0.00200152
$847$	−1.12159e10	−0.634224
$848$	−3.60791e10	−2.03175
$849$	−3.18727e10	−1.78748
$850$	5.07958e10	2.83702
$851$	−1.41831e10	−0.788891
$852$	4.78242e10	2.64917
$853$	−2.41384e10	−1.33164	−0.665819	−	0.746114i	$-0.731918\pi$
$853$	−2.41384e10	−1.33164	−0.665819	+	0.746114i	$0.731918\pi$
$854$	−1.98563e10	−1.09092
$855$	191555.	1.04812e−5 0
$856$	−5.86015e10	−3.19338
$857$	3.17960e10	1.72560	0.862800	−	0.505546i	$-0.168709\pi$
$857$	3.17960e10	1.72560	0.862800	+	0.505546i	$0.168709\pi$
$858$	1.72061e10	0.929986
$859$	1.47226e10	0.792514	0.396257	−	0.918140i	$-0.370309\pi$
$859$	1.47226e10	0.792514	0.396257	+	0.918140i	$0.370309\pi$
$860$	1.31338e10	0.704120
$861$	−6.60804e9	−0.352827
$862$	6.41630e10	3.41200
$863$	−1.32263e10	−0.700486	−0.350243	−	0.936659i	$-0.613901\pi$
$863$	−1.32263e10	−0.700486	−0.350243	+	0.936659i	$0.613901\pi$
$864$	1.79950e10	0.949192
$865$	4.30998e9	0.226422
$866$	−3.96801e10	−2.07616
$867$	3.40917e10	1.77657
$868$	3.55662e10	1.84594
$869$	3.72522e9	0.192567
$870$	−4.21593e9	−0.217058
$871$	3.40857e10	1.74787
$872$	5.30582e10	2.70985
$873$	3900.47	1.98411e−7 0
$874$	2.66521e9	0.135033
$875$	−7.03828e9	−0.355172
$876$	−6.03623e10	−3.03390
$877$	−1.94307e10	−0.972724	−0.486362	−	0.873757i	$-0.661676\pi$
$877$	−1.94307e10	−0.972724	−0.486362	+	0.873757i	$0.661676\pi$
$878$	−4.39598e10	−2.19192
$879$	2.35548e10	1.16982
$880$	−3.64445e9	−0.180278
$881$	1.70330e10	0.839217	0.419609	−	0.907705i	$-0.362167\pi$
$881$	1.70330e10	0.839217	0.419609	+	0.907705i	$0.362167\pi$
$882$	−1.55169e7	−0.000761493 0
$883$	−2.15185e10	−1.05184	−0.525920	−	0.850534i	$-0.676279\pi$
$883$	−2.15185e10	−1.05184	−0.525920	+	0.850534i	$0.676279\pi$
$884$	8.97197e10	4.36822
$885$	5.85631e9	0.284003
$886$	−6.44171e10	−3.11159
$887$	−3.20294e10	−1.54105	−0.770523	−	0.637412i	$-0.780005\pi$
$887$	−3.20294e10	−1.54105	−0.770523	+	0.637412i	$0.780005\pi$
$888$	1.97707e10	0.947496
$889$	7.44894e9	0.355581
$890$	−6.38317e9	−0.303509
$891$	9.30643e9	0.440769
$892$	−7.73474e10	−3.64896
$893$	8.61840e8	0.0404992
$894$	2.70372e10	1.26555
$895$	5.78519e9	0.269735
$896$	1.78179e10	0.827520
$897$	4.68515e10	2.16746
$898$	−2.84935e10	−1.31304
$899$	1.18995e10	0.546221
$900$	5.15855e7	0.00235873
$901$	−4.21625e10	−1.92039
$902$	−7.84200e9	−0.355799
$903$	2.36713e10	1.06983
$904$	9.44388e10	4.25168
$905$	−1.79016e9	−0.0802827
$906$	−6.00261e10	−2.68158
$907$	−2.66345e10	−1.18527	−0.592637	−	0.805470i	$-0.701913\pi$
$907$	−2.66345e10	−1.18527	−0.592637	+	0.805470i	$0.701913\pi$
$908$	−7.50047e10	−3.32497
$909$	−2.19306e7	−0.000968447 0
$910$	−8.74769e9	−0.384812
$911$	2.71359e10	1.18913	0.594565	−	0.804047i	$-0.297324\pi$
$911$	2.71359e10	1.18913	0.594565	+	0.804047i	$0.297324\pi$
$912$	−1.63807e9	−0.0715071
$913$	−8.79462e9	−0.382445
$914$	8.13903e10	3.52583
$915$	4.13214e9	0.178320
$916$	−4.29228e8	−0.0184524
$917$	−7.87572e9	−0.337285
$918$	7.03101e10	2.99964
$919$	−1.36155e9	−0.0578668	−0.0289334	−	0.999581i	$-0.509211\pi$
$919$	−1.36155e9	−0.0578668	−0.0289334	+	0.999581i	$0.509211\pi$
$920$	−2.25074e10	−0.952945
$921$	−1.10809e10	−0.467375
$922$	7.87143e9	0.330747
$923$	3.32000e10	1.38974
$924$	−1.86227e10	−0.776589
$925$	9.71365e9	0.403540
$926$	3.10682e10	1.28581
$927$	−1.30104e7	−0.000536429 0
$928$	−1.20342e10	−0.494311
$929$	−4.92364e9	−0.201480	−0.100740	−	0.994913i	$-0.532121\pi$
$929$	−4.92364e9	−0.201480	−0.100740	+	0.994913i	$0.532121\pi$
$930$	−1.07117e10	−0.436685
$931$	3.79382e8	0.0154082
$932$	−2.67303e10	−1.08155
$933$	9.53228e8	0.0384248
$934$	−1.68026e10	−0.674781
$935$	−4.25895e9	−0.170397
$936$	7.28884e7	0.00290531
$937$	−8.86692e8	−0.0352115	−0.0176057	−	0.999845i	$-0.505604\pi$
$937$	−8.86692e8	−0.0352115	−0.0176057	+	0.999845i	$0.505604\pi$
$938$	−5.33922e10	−2.11236
$939$	4.53495e9	0.178749
$940$	−1.31673e10	−0.517068
$941$	−2.28786e10	−0.895087	−0.447543	−	0.894262i	$-0.647701\pi$
$941$	−2.28786e10	−0.895087	−0.447543	+	0.894262i	$0.647701\pi$
$942$	7.76563e10	3.02691
$943$	−2.13535e10	−0.829236
$944$	5.58913e10	2.16243
$945$	−4.73673e9	−0.182586
$946$	2.80916e10	1.07884
$947$	1.31876e10	0.504594	0.252297	−	0.967650i	$-0.418814\pi$
$947$	1.31876e10	0.504594	0.252297	+	0.967650i	$0.418814\pi$
$948$	−2.55811e10	−0.975193
$949$	−4.19041e10	−1.59157
$950$	−1.82534e9	−0.0690733
$951$	−1.30935e10	−0.493654
$952$	−7.76819e10	−2.91803
$953$	−1.68677e10	−0.631292	−0.315646	−	0.948877i	$-0.602221\pi$
$953$	−1.68677e10	−0.631292	−0.315646	+	0.948877i	$0.602221\pi$
$954$	−6.19685e7	−0.00231074
$955$	−2.84920e9	−0.105855
$956$	6.92157e10	2.56213
$957$	−6.23065e9	−0.229795
$958$	−2.85246e10	−1.04819
$959$	−1.13237e10	−0.414592
$960$	−3.60158e8	−0.0131384
$961$	2.72124e9	0.0989087
$962$	2.48306e10	0.899237
$963$	−4.43785e7	−0.00160133
$964$	5.48660e10	1.97257
$965$	−3.84039e9	−0.137572
$966$	−7.33888e10	−2.61945
$967$	−5.24431e10	−1.86507	−0.932536	−	0.361078i	$-0.882409\pi$
$967$	−5.24431e10	−1.86507	−0.932536	+	0.361078i	$0.882409\pi$
$968$	5.05223e10	1.79027
$969$	−1.91427e9	−0.0675880
$970$	2.10863e6	7.41820e−5 0
$971$	−4.26915e10	−1.49649	−0.748245	−	0.663422i	$-0.769103\pi$
$971$	−4.26915e10	−1.49649	−0.748245	+	0.663422i	$0.769103\pi$
$972$	1.42727e8	0.00498510
$973$	−1.18996e10	−0.414130
$974$	−1.07756e10	−0.373667
$975$	−3.20875e10	−1.10871
$976$	3.94361e10	1.35775
$977$	9.84684e9	0.337805	0.168903	−	0.985633i	$-0.445978\pi$
$977$	9.84684e9	0.337805	0.168903	+	0.985633i	$0.445978\pi$
$978$	8.17603e10	2.79484
$979$	−9.43358e9	−0.321319
$980$	−5.79622e9	−0.196722
$981$	4.01806e7	0.00135886
$982$	−1.54666e10	−0.521202
$983$	5.65736e9	0.189966	0.0949832	−	0.995479i	$-0.469720\pi$
$983$	5.65736e9	0.189966	0.0949832	+	0.995479i	$0.469720\pi$
$984$	2.97660e10	0.995952
$985$	7.43208e9	0.247790
$986$	−4.70201e10	−1.56212
$987$	−2.37315e10	−0.785625
$988$	−3.22406e9	−0.106354
$989$	7.64924e10	2.51438
$990$	−6.25961e6	−0.000205033 0
$991$	−3.43679e10	−1.12175	−0.560874	−	0.827901i	$-0.689535\pi$
$991$	−3.43679e10	−1.12175	−0.560874	+	0.827901i	$0.689535\pi$
$992$	−3.05762e10	−0.994473
$993$	−5.08108e10	−1.64677
$994$	−5.20049e10	−1.67955
$995$	9.25272e9	0.297775
$996$	6.03928e10	1.93677
$997$	1.57284e10	0.502635	0.251317	−	0.967905i	$-0.419136\pi$
$997$	1.57284e10	0.502635	0.251317	+	0.967905i	$0.419136\pi$
$998$	−6.25367e10	−1.99149
$999$	1.34454e10	0.426671

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.8.a.b.1.10	✓	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.8.a.b.1.10	✓	162	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-20.3517 q^{2} +46.7393 q^{3} +286.191 q^{4} +64.7634 q^{5} -951.224 q^{6} +714.717 q^{7} -3219.46 q^{8} -2.43807 q^{9} +O(q^{10})\)	\(q-20.3517 q^{2} +46.7393 q^{3} +286.191 q^{4} +64.7634 q^{5} -951.224 q^{6} +714.717 q^{7} -3219.46 q^{8} -2.43807 q^{9} -1318.04 q^{10} -1947.92 q^{11} +13376.4 q^{12} +9286.00 q^{13} -14545.7 q^{14} +3027.00 q^{15} +28888.9 q^{16} +33760.0 q^{17} +49.6189 q^{18} -1213.16 q^{19} +18534.7 q^{20} +33405.4 q^{21} +39643.4 q^{22} +107948. q^{23} -150475. q^{24} -73930.7 q^{25} -188986. q^{26} -102333. q^{27} +204546. q^{28} +68435.4 q^{29} -61604.5 q^{30} +173879. q^{31} -175848. q^{32} -91044.2 q^{33} -687073. q^{34} +46287.5 q^{35} -697.755 q^{36} -131389. q^{37} +24689.8 q^{38} +434021. q^{39} -208503. q^{40} -197814. q^{41} -679856. q^{42} +708607. q^{43} -557477. q^{44} -157.898 q^{45} -2.19691e6 q^{46} -710410. q^{47} +1.35025e6 q^{48} -312722. q^{49} +1.50461e6 q^{50} +1.57792e6 q^{51} +2.65757e6 q^{52} -1.24889e6 q^{53} +2.08265e6 q^{54} -126154. q^{55} -2.30100e6 q^{56} -56702.2 q^{57} -1.39278e6 q^{58} +1.93469e6 q^{59} +866300. q^{60} +1.36509e6 q^{61} -3.53873e6 q^{62} -1742.53 q^{63} -118982. q^{64} +601393. q^{65} +1.85290e6 q^{66} +3.67065e6 q^{67} +9.66182e6 q^{68} +5.04539e6 q^{69} -942029. q^{70} +3.57528e6 q^{71} +7849.27 q^{72} -4.51261e6 q^{73} +2.67398e6 q^{74} -3.45547e6 q^{75} -347195. q^{76} -1.39221e6 q^{77} -8.83307e6 q^{78} -1.91241e6 q^{79} +1.87095e6 q^{80} -4.77763e6 q^{81} +4.02584e6 q^{82} +4.51489e6 q^{83} +9.56033e6 q^{84} +2.18641e6 q^{85} -1.44213e7 q^{86} +3.19862e6 q^{87} +6.27124e6 q^{88} +4.84291e6 q^{89} +3213.49 q^{90} +6.63687e6 q^{91} +3.08936e7 q^{92} +8.12697e6 q^{93} +1.44580e7 q^{94} -78568.3 q^{95} -8.21901e6 q^{96} -1599.81 q^{97} +6.36443e6 q^{98} +4749.16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q + 48 q^{2} + 310 q^{3} + 10650 q^{4} + 3999 q^{5} + 1998 q^{6} + 4301 q^{7} + 9216 q^{8} + 124464 q^{9}+O(q^{10}) \) 162 * q + 48 * q^2 + 310 * q^3 + 10650 * q^4 + 3999 * q^5 + 1998 * q^6 + 4301 * q^7 + 9216 * q^8 + 124464 * q^9	\( 162 q + 48 q^{2} + 310 q^{3} + 10650 q^{4} + 3999 q^{5} + 1998 q^{6} + 4301 q^{7} + 9216 q^{8} + 124464 q^{9} + 7430 q^{10} + 19840 q^{11} + 55737 q^{12} + 51223 q^{13} + 75679 q^{14} + 44609 q^{15} + 709506 q^{16} + 258906 q^{17} + 135171 q^{18} + 80362 q^{19} + 506432 q^{20} + 138572 q^{21} + 158320 q^{22} + 571410 q^{23} + 325871 q^{24} + 2732541 q^{25} + 488640 q^{26} + 772231 q^{27} + 699304 q^{28} + 968170 q^{29} + 301526 q^{30} + 348203 q^{31} + 1078196 q^{32} + 1536618 q^{33} + 870073 q^{34} + 1089291 q^{35} + 8775356 q^{36} + 2226256 q^{37} + 3884597 q^{38} + 923555 q^{39} + 2518352 q^{40} + 1825935 q^{41} + 3419892 q^{42} + 1582376 q^{43} + 4352040 q^{44} + 9457186 q^{45} + 1012278 q^{46} + 4801410 q^{47} + 9073674 q^{48} + 21448221 q^{49} + 2366848 q^{50} + 3749747 q^{51} + 7035334 q^{52} + 17191348 q^{53} + 5748697 q^{54} + 5271331 q^{55} + 14854657 q^{56} + 5393884 q^{57} + 4036260 q^{58} + 8263804 q^{59} + 10193498 q^{60} + 12366404 q^{61} + 18470554 q^{62} + 15526895 q^{63} + 49399626 q^{64} + 17325330 q^{65} + 11279868 q^{66} + 5477434 q^{67} + 44562265 q^{68} + 26851278 q^{69} + 9428823 q^{70} + 12108395 q^{71} + 22153063 q^{72} + 13995388 q^{73} + 13478769 q^{74} + 24654171 q^{75} + 8225460 q^{76} + 61240119 q^{77} + 17624449 q^{78} + 8215066 q^{79} + 65708461 q^{80} + 112675190 q^{81} + 29179962 q^{82} + 33597369 q^{83} + 13895447 q^{84} + 24308391 q^{85} + 22043075 q^{86} + 25661967 q^{87} + 32743591 q^{88} + 47538968 q^{89} + 46132321 q^{90} + 24574095 q^{91} + 108017386 q^{92} + 63765304 q^{93} + 41203657 q^{94} + 38032578 q^{95} + 41465754 q^{96} + 45954628 q^{97} + 37164970 q^{98} + 43882333 q^{99}+O(q^{100}) \) 162 * q + 48 * q^2 + 310 * q^3 + 10650 * q^4 + 3999 * q^5 + 1998 * q^6 + 4301 * q^7 + 9216 * q^8 + 124464 * q^9 + 7430 * q^10 + 19840 * q^11 + 55737 * q^12 + 51223 * q^13 + 75679 * q^14 + 44609 * q^15 + 709506 * q^16 + 258906 * q^17 + 135171 * q^18 + 80362 * q^19 + 506432 * q^20 + 138572 * q^21 + 158320 * q^22 + 571410 * q^23 + 325871 * q^24 + 2732541 * q^25 + 488640 * q^26 + 772231 * q^27 + 699304 * q^28 + 968170 * q^29 + 301526 * q^30 + 348203 * q^31 + 1078196 * q^32 + 1536618 * q^33 + 870073 * q^34 + 1089291 * q^35 + 8775356 * q^36 + 2226256 * q^37 + 3884597 * q^38 + 923555 * q^39 + 2518352 * q^40 + 1825935 * q^41 + 3419892 * q^42 + 1582376 * q^43 + 4352040 * q^44 + 9457186 * q^45 + 1012278 * q^46 + 4801410 * q^47 + 9073674 * q^48 + 21448221 * q^49 + 2366848 * q^50 + 3749747 * q^51 + 7035334 * q^52 + 17191348 * q^53 + 5748697 * q^54 + 5271331 * q^55 + 14854657 * q^56 + 5393884 * q^57 + 4036260 * q^58 + 8263804 * q^59 + 10193498 * q^60 + 12366404 * q^61 + 18470554 * q^62 + 15526895 * q^63 + 49399626 * q^64 + 17325330 * q^65 + 11279868 * q^66 + 5477434 * q^67 + 44562265 * q^68 + 26851278 * q^69 + 9428823 * q^70 + 12108395 * q^71 + 22153063 * q^72 + 13995388 * q^73 + 13478769 * q^74 + 24654171 * q^75 + 8225460 * q^76 + 61240119 * q^77 + 17624449 * q^78 + 8215066 * q^79 + 65708461 * q^80 + 112675190 * q^81 + 29179962 * q^82 + 33597369 * q^83 + 13895447 * q^84 + 24308391 * q^85 + 22043075 * q^86 + 25661967 * q^87 + 32743591 * q^88 + 47538968 * q^89 + 46132321 * q^90 + 24574095 * q^91 + 108017386 * q^92 + 63765304 * q^93 + 41203657 * q^94 + 38032578 * q^95 + 41465754 * q^96 + 45954628 * q^97 + 37164970 * q^98 + 43882333 * q^99

Introduction

L-functions

Modular forms

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