LMFDB - Embedded newform 3750.2.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3750,2,Mod(1,3750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3750, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("3750.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3750 = 2 \cdot 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3750.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:	$29.9439007580$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.8.71684000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 18x^{6} + 10x^{5} + 101x^{4} + 40x^{3} - 132x^{2} - 96x - 4 $ x^8 - 2x^7 - 18x^6 + 10x^5 + 101x^4 + 40x^3 - 132x^2 - 96*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 150)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.20224$ of defining polynomial
Character	$\chi$	$=$	3750.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -4.63137 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -4.63137 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.53967 q^{11} -1.00000 q^{12} +0.143974 q^{13} +4.63137 q^{14} +1.00000 q^{16} -7.49100 q^{17} -1.00000 q^{18} -6.74065 q^{19} +4.63137 q^{21} +2.53967 q^{22} -1.67733 q^{23} +1.00000 q^{24} -0.143974 q^{26} -1.00000 q^{27} -4.63137 q^{28} -2.25493 q^{29} +1.00385 q^{31} -1.00000 q^{32} +2.53967 q^{33} +7.49100 q^{34} +1.00000 q^{36} +0.0889810 q^{37} +6.74065 q^{38} -0.143974 q^{39} +3.07386 q^{41} -4.63137 q^{42} -9.02860 q^{43} -2.53967 q^{44} +1.67733 q^{46} -10.8854 q^{47} -1.00000 q^{48} +14.4496 q^{49} +7.49100 q^{51} +0.143974 q^{52} +4.96506 q^{53} +1.00000 q^{54} +4.63137 q^{56} +6.74065 q^{57} +2.25493 q^{58} +5.25365 q^{59} -13.7007 q^{61} -1.00385 q^{62} -4.63137 q^{63} +1.00000 q^{64} -2.53967 q^{66} +7.64929 q^{67} -7.49100 q^{68} +1.67733 q^{69} -10.2647 q^{71} -1.00000 q^{72} -1.96580 q^{73} -0.0889810 q^{74} -6.74065 q^{76} +11.7622 q^{77} +0.143974 q^{78} +0.747233 q^{79} +1.00000 q^{81} -3.07386 q^{82} +3.10257 q^{83} +4.63137 q^{84} +9.02860 q^{86} +2.25493 q^{87} +2.53967 q^{88} +0.733865 q^{89} -0.666798 q^{91} -1.67733 q^{92} -1.00385 q^{93} +10.8854 q^{94} +1.00000 q^{96} +9.12044 q^{97} -14.4496 q^{98} -2.53967 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9	$ 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9} + 6 q^{11} - 8 q^{12} - 2 q^{13} + 4 q^{14} + 8 q^{16} - 14 q^{17} - 8 q^{18} + 10 q^{19} + 4 q^{21} - 6 q^{22} - 12 q^{23} + 8 q^{24} + 2 q^{26} - 8 q^{27} - 4 q^{28} + 10 q^{29} + 16 q^{31} - 8 q^{32} - 6 q^{33} + 14 q^{34} + 8 q^{36} + 6 q^{37} - 10 q^{38} + 2 q^{39} + 6 q^{41} - 4 q^{42} - 2 q^{43} + 6 q^{44} + 12 q^{46} - 14 q^{47} - 8 q^{48} + 26 q^{49} + 14 q^{51} - 2 q^{52} - 12 q^{53} + 8 q^{54} + 4 q^{56} - 10 q^{57} - 10 q^{58} + 16 q^{61} - 16 q^{62} - 4 q^{63} + 8 q^{64} + 6 q^{66} + 6 q^{67} - 14 q^{68} + 12 q^{69} + 6 q^{71} - 8 q^{72} + 8 q^{73} - 6 q^{74} + 10 q^{76} - 8 q^{77} - 2 q^{78} + 10 q^{79} + 8 q^{81} - 6 q^{82} - 22 q^{83} + 4 q^{84} + 2 q^{86} - 10 q^{87} - 6 q^{88} + 20 q^{89} + 6 q^{91} - 12 q^{92} - 16 q^{93} + 14 q^{94} + 8 q^{96} + 16 q^{97} - 26 q^{98} + 6 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9 + 6 * q^11 - 8 * q^12 - 2 * q^13 + 4 * q^14 + 8 * q^16 - 14 * q^17 - 8 * q^18 + 10 * q^19 + 4 * q^21 - 6 * q^22 - 12 * q^23 + 8 * q^24 + 2 * q^26 - 8 * q^27 - 4 * q^28 + 10 * q^29 + 16 * q^31 - 8 * q^32 - 6 * q^33 + 14 * q^34 + 8 * q^36 + 6 * q^37 - 10 * q^38 + 2 * q^39 + 6 * q^41 - 4 * q^42 - 2 * q^43 + 6 * q^44 + 12 * q^46 - 14 * q^47 - 8 * q^48 + 26 * q^49 + 14 * q^51 - 2 * q^52 - 12 * q^53 + 8 * q^54 + 4 * q^56 - 10 * q^57 - 10 * q^58 + 16 * q^61 - 16 * q^62 - 4 * q^63 + 8 * q^64 + 6 * q^66 + 6 * q^67 - 14 * q^68 + 12 * q^69 + 6 * q^71 - 8 * q^72 + 8 * q^73 - 6 * q^74 + 10 * q^76 - 8 * q^77 - 2 * q^78 + 10 * q^79 + 8 * q^81 - 6 * q^82 - 22 * q^83 + 4 * q^84 + 2 * q^86 - 10 * q^87 - 6 * q^88 + 20 * q^89 + 6 * q^91 - 12 * q^92 - 16 * q^93 + 14 * q^94 + 8 * q^96 + 16 * q^97 - 26 * q^98 + 6 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	−4.63137	−1.75049	−0.875247	−	0.483677i	$-0.839301\pi$
$7$	−4.63137	−1.75049	−0.875247	+	0.483677i	$0.839301\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−2.53967	−0.765741	−0.382870	−	0.923802i	$-0.625064\pi$
$11$	−2.53967	−0.765741	−0.382870	+	0.923802i	$0.625064\pi$
$12$	−1.00000	−0.288675
$13$	0.143974	0.0399313	0.0199656	−	0.999801i	$-0.493644\pi$
$13$	0.143974	0.0399313	0.0199656	+	0.999801i	$0.493644\pi$
$14$	4.63137	1.23779
$15$	0	0
$16$	1.00000	0.250000
$17$	−7.49100	−1.81683	−0.908417	−	0.418065i	$-0.862708\pi$
$17$	−7.49100	−1.81683	−0.908417	+	0.418065i	$0.862708\pi$
$18$	−1.00000	−0.235702
$19$	−6.74065	−1.54641	−0.773206	−	0.634155i	$-0.781348\pi$
$19$	−6.74065	−1.54641	−0.773206	+	0.634155i	$0.781348\pi$
$20$	0	0
$21$	4.63137	1.01065
$22$	2.53967	0.541460
$23$	−1.67733	−0.349748	−0.174874	−	0.984591i	$-0.555952\pi$
$23$	−1.67733	−0.349748	−0.174874	+	0.984591i	$0.555952\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	−0.143974	−0.0282357
$27$	−1.00000	−0.192450
$28$	−4.63137	−0.875247
$29$	−2.25493	−0.418730	−0.209365	−	0.977838i	$-0.567140\pi$
$29$	−2.25493	−0.418730	−0.209365	+	0.977838i	$0.567140\pi$
$30$	0	0
$31$	1.00385	0.180297	0.0901484	−	0.995928i	$-0.471266\pi$
$31$	1.00385	0.180297	0.0901484	+	0.995928i	$0.471266\pi$
$32$	−1.00000	−0.176777
$33$	2.53967	0.442101
$34$	7.49100	1.28470
$35$	0	0
$36$	1.00000	0.166667
$37$	0.0889810	0.0146284	0.00731419	−	0.999973i	$-0.497672\pi$
$37$	0.0889810	0.0146284	0.00731419	+	0.999973i	$0.497672\pi$
$38$	6.74065	1.09348
$39$	−0.143974	−0.0230543
$40$	0	0
$41$	3.07386	0.480056	0.240028	−	0.970766i	$-0.422843\pi$
$41$	3.07386	0.480056	0.240028	+	0.970766i	$0.422843\pi$
$42$	−4.63137	−0.714636
$43$	−9.02860	−1.37685	−0.688424	−	0.725308i	$-0.741697\pi$
$43$	−9.02860	−1.37685	−0.688424	+	0.725308i	$0.741697\pi$
$44$	−2.53967	−0.382870
$45$	0	0
$46$	1.67733	0.247309
$47$	−10.8854	−1.58779	−0.793896	−	0.608053i	$-0.791951\pi$
$47$	−10.8854	−1.58779	−0.793896	+	0.608053i	$0.791951\pi$
$48$	−1.00000	−0.144338
$49$	14.4496	2.06423
$50$	0	0
$51$	7.49100	1.04895
$52$	0.143974	0.0199656
$53$	4.96506	0.682003	0.341002	−	0.940063i	$-0.389234\pi$
$53$	4.96506	0.682003	0.341002	+	0.940063i	$0.389234\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	4.63137	0.618893
$57$	6.74065	0.892821
$58$	2.25493	0.296087
$59$	5.25365	0.683967	0.341984	−	0.939706i	$-0.388901\pi$
$59$	5.25365	0.683967	0.341984	+	0.939706i	$0.388901\pi$
$60$	0	0
$61$	−13.7007	−1.75419	−0.877096	−	0.480316i	$-0.840522\pi$
$61$	−13.7007	−1.75419	−0.877096	+	0.480316i	$0.840522\pi$
$62$	−1.00385	−0.127489
$63$	−4.63137	−0.583498
$64$	1.00000	0.125000
$65$	0	0
$66$	−2.53967	−0.312612
$67$	7.64929	0.934509	0.467255	−	0.884123i	$-0.345243\pi$
$67$	7.64929	0.934509	0.467255	+	0.884123i	$0.345243\pi$
$68$	−7.49100	−0.908417
$69$	1.67733	0.201927
$70$	0	0
$71$	−10.2647	−1.21819	−0.609096	−	0.793097i	$-0.708468\pi$
$71$	−10.2647	−1.21819	−0.609096	+	0.793097i	$0.708468\pi$
$72$	−1.00000	−0.117851
$73$	−1.96580	−0.230079	−0.115040	−	0.993361i	$-0.536699\pi$
$73$	−1.96580	−0.230079	−0.115040	+	0.993361i	$0.536699\pi$
$74$	−0.0889810	−0.0103438
$75$	0	0
$76$	−6.74065	−0.773206
$77$	11.7622	1.34042
$78$	0.143974	0.0163019
$79$	0.747233	0.0840703	0.0420352	−	0.999116i	$-0.486616\pi$
$79$	0.747233	0.0840703	0.0420352	+	0.999116i	$0.486616\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−3.07386	−0.339451
$83$	3.10257	0.340551	0.170275	−	0.985397i	$-0.445534\pi$
$83$	3.10257	0.340551	0.170275	+	0.985397i	$0.445534\pi$
$84$	4.63137	0.505324
$85$	0	0
$86$	9.02860	0.973579
$87$	2.25493	0.241754
$88$	2.53967	0.270730
$89$	0.733865	0.0777896	0.0388948	−	0.999243i	$-0.487616\pi$
$89$	0.733865	0.0777896	0.0388948	+	0.999243i	$0.487616\pi$
$90$	0	0
$91$	−0.666798	−0.0698995
$92$	−1.67733	−0.174874
$93$	−1.00385	−0.104094
$94$	10.8854	1.12274
$95$	0	0
$96$	1.00000	0.102062
$97$	9.12044	0.926041	0.463020	−	0.886348i	$-0.346766\pi$
$97$	9.12044	0.926041	0.463020	+	0.886348i	$0.346766\pi$
$98$	−14.4496	−1.45963
$99$	−2.53967	−0.255247
$100$	0	0
$101$	−2.88013	−0.286583	−0.143292	−	0.989680i	$-0.545769\pi$
$101$	−2.88013	−0.286583	−0.143292	+	0.989680i	$0.545769\pi$
$102$	−7.49100	−0.741720
$103$	11.1713	1.10075	0.550373	−	0.834919i	$-0.314486\pi$
$103$	11.1713	1.10075	0.550373	+	0.834919i	$0.314486\pi$
$104$	−0.143974	−0.0141178
$105$	0	0
$106$	−4.96506	−0.482249
$107$	−14.0538	−1.35863	−0.679316	−	0.733846i	$-0.737723\pi$
$107$	−14.0538	−1.35863	−0.679316	+	0.733846i	$0.737723\pi$
$108$	−1.00000	−0.0962250
$109$	6.71867	0.643532	0.321766	−	0.946819i	$-0.395724\pi$
$109$	6.71867	0.643532	0.321766	+	0.946819i	$0.395724\pi$
$110$	0	0
$111$	−0.0889810	−0.00844570
$112$	−4.63137	−0.437623
$113$	−0.997621	−0.0938483	−0.0469241	−	0.998898i	$-0.514942\pi$
$113$	−0.997621	−0.0938483	−0.0469241	+	0.998898i	$0.514942\pi$
$114$	−6.74065	−0.631320
$115$	0	0
$116$	−2.25493	−0.209365
$117$	0.143974	0.0133104
$118$	−5.25365	−0.483638
$119$	34.6936	3.18036
$120$	0	0
$121$	−4.55005	−0.413641
$122$	13.7007	1.24040
$123$	−3.07386	−0.277160
$124$	1.00385	0.0901484
$125$	0	0
$126$	4.63137	0.412595
$127$	−11.5217	−1.02238	−0.511192	−	0.859467i	$-0.670796\pi$
$127$	−11.5217	−1.02238	−0.511192	+	0.859467i	$0.670796\pi$
$128$	−1.00000	−0.0883883
$129$	9.02860	0.794924
$130$	0	0
$131$	−1.78409	−0.155877	−0.0779385	−	0.996958i	$-0.524834\pi$
$131$	−1.78409	−0.155877	−0.0779385	+	0.996958i	$0.524834\pi$
$132$	2.53967	0.221050
$133$	31.2184	2.70698
$134$	−7.64929	−0.660798
$135$	0	0
$136$	7.49100	0.642348
$137$	−16.0233	−1.36897	−0.684483	−	0.729029i	$-0.739972\pi$
$137$	−16.0233	−1.36897	−0.684483	+	0.729029i	$0.739972\pi$
$138$	−1.67733	−0.142784
$139$	−3.70400	−0.314169	−0.157085	−	0.987585i	$-0.550210\pi$
$139$	−3.70400	−0.314169	−0.157085	+	0.987585i	$0.550210\pi$
$140$	0	0
$141$	10.8854	0.916712
$142$	10.2647	0.861392
$143$	−0.365648	−0.0305770
$144$	1.00000	0.0833333
$145$	0	0
$146$	1.96580	0.162690
$147$	−14.4496	−1.19178
$148$	0.0889810	0.00731419
$149$	1.88534	0.154453	0.0772267	−	0.997014i	$-0.475393\pi$
$149$	1.88534	0.154453	0.0772267	+	0.997014i	$0.475393\pi$
$150$	0	0
$151$	−6.15090	−0.500553	−0.250276	−	0.968174i	$-0.580522\pi$
$151$	−6.15090	−0.500553	−0.250276	+	0.968174i	$0.580522\pi$
$152$	6.74065	0.546739
$153$	−7.49100	−0.605611
$154$	−11.7622	−0.947823
$155$	0	0
$156$	−0.143974	−0.0115272
$157$	23.4830	1.87414	0.937072	−	0.349137i	$-0.113525\pi$
$157$	23.4830	1.87414	0.937072	+	0.349137i	$0.113525\pi$
$158$	−0.747233	−0.0594467
$159$	−4.96506	−0.393755
$160$	0	0
$161$	7.76834	0.612231
$162$	−1.00000	−0.0785674
$163$	15.7773	1.23577	0.617887	−	0.786267i	$-0.287989\pi$
$163$	15.7773	1.23577	0.617887	+	0.786267i	$0.287989\pi$
$164$	3.07386	0.240028
$165$	0	0
$166$	−3.10257	−0.240806
$167$	4.03980	0.312609	0.156305	−	0.987709i	$-0.450042\pi$
$167$	4.03980	0.312609	0.156305	+	0.987709i	$0.450042\pi$
$168$	−4.63137	−0.357318
$169$	−12.9793	−0.998405
$170$	0	0
$171$	−6.74065	−0.515470
$172$	−9.02860	−0.688424
$173$	−20.1595	−1.53270	−0.766351	−	0.642422i	$-0.777930\pi$
$173$	−20.1595	−1.53270	−0.766351	+	0.642422i	$0.777930\pi$
$174$	−2.25493	−0.170946
$175$	0	0
$176$	−2.53967	−0.191435
$177$	−5.25365	−0.394889
$178$	−0.733865	−0.0550055
$179$	−7.76067	−0.580060	−0.290030	−	0.957018i	$-0.593665\pi$
$179$	−7.76067	−0.580060	−0.290030	+	0.957018i	$0.593665\pi$
$180$	0	0
$181$	11.7909	0.876409	0.438205	−	0.898875i	$-0.355615\pi$
$181$	11.7909	0.876409	0.438205	+	0.898875i	$0.355615\pi$
$182$	0.666798	0.0494264
$183$	13.7007	1.01278
$184$	1.67733	0.123654
$185$	0	0
$186$	1.00385	0.0736058
$187$	19.0247	1.39122
$188$	−10.8854	−0.793896
$189$	4.63137	0.336883
$190$	0	0
$191$	4.88438	0.353422	0.176711	−	0.984263i	$-0.443454\pi$
$191$	4.88438	0.353422	0.176711	+	0.984263i	$0.443454\pi$
$192$	−1.00000	−0.0721688
$193$	18.7342	1.34852	0.674258	−	0.738496i	$-0.264464\pi$
$193$	18.7342	1.34852	0.674258	+	0.738496i	$0.264464\pi$
$194$	−9.12044	−0.654810
$195$	0	0
$196$	14.4496	1.03211
$197$	1.25454	0.0893822	0.0446911	−	0.999001i	$-0.485770\pi$
$197$	1.25454	0.0893822	0.0446911	+	0.999001i	$0.485770\pi$
$198$	2.53967	0.180487
$199$	19.3703	1.37312	0.686562	−	0.727071i	$-0.259119\pi$
$199$	19.3703	1.37312	0.686562	+	0.727071i	$0.259119\pi$
$200$	0	0
$201$	−7.64929	−0.539539
$202$	2.88013	0.202645
$203$	10.4434	0.732985
$204$	7.49100	0.524475
$205$	0	0
$206$	−11.1713	−0.778345
$207$	−1.67733	−0.116583
$208$	0.143974	0.00998282
$209$	17.1191	1.18415
$210$	0	0
$211$	−1.24920	−0.0859983	−0.0429991	−	0.999075i	$-0.513691\pi$
$211$	−1.24920	−0.0859983	−0.0429991	+	0.999075i	$0.513691\pi$
$212$	4.96506	0.341002
$213$	10.2647	0.703323
$214$	14.0538	0.960698
$215$	0	0
$216$	1.00000	0.0680414
$217$	−4.64920	−0.315608
$218$	−6.71867	−0.455046
$219$	1.96580	0.132836
$220$	0	0
$221$	−1.07851	−0.0725485
$222$	0.0889810	0.00597201
$223$	−21.8855	−1.46556	−0.732782	−	0.680463i	$-0.761779\pi$
$223$	−21.8855	−1.46556	−0.732782	+	0.680463i	$0.761779\pi$
$224$	4.63137	0.309446
$225$	0	0
$226$	0.997621	0.0663607
$227$	−14.5034	−0.962621	−0.481311	−	0.876550i	$-0.659839\pi$
$227$	−14.5034	−0.962621	−0.481311	+	0.876550i	$0.659839\pi$
$228$	6.74065	0.446410
$229$	4.70079	0.310637	0.155318	−	0.987864i	$-0.450360\pi$
$229$	4.70079	0.310637	0.155318	+	0.987864i	$0.450360\pi$
$230$	0	0
$231$	−11.7622	−0.773894
$232$	2.25493	0.148044
$233$	11.8187	0.774269	0.387135	−	0.922023i	$-0.373465\pi$
$233$	11.8187	0.774269	0.387135	+	0.922023i	$0.373465\pi$
$234$	−0.143974	−0.00941189
$235$	0	0
$236$	5.25365	0.341984
$237$	−0.747233	−0.0485380
$238$	−34.6936	−2.24885
$239$	9.71363	0.628323	0.314161	−	0.949370i	$-0.398277\pi$
$239$	9.71363	0.628323	0.314161	+	0.949370i	$0.398277\pi$
$240$	0	0
$241$	6.68035	0.430319	0.215159	−	0.976579i	$-0.430973\pi$
$241$	6.68035	0.430319	0.215159	+	0.976579i	$0.430973\pi$
$242$	4.55005	0.292488
$243$	−1.00000	−0.0641500
$244$	−13.7007	−0.877096
$245$	0	0
$246$	3.07386	0.195982
$247$	−0.970480	−0.0617502
$248$	−1.00385	−0.0637445
$249$	−3.10257	−0.196617
$250$	0	0
$251$	−19.6023	−1.23729	−0.618644	−	0.785672i	$-0.712317\pi$
$251$	−19.6023	−1.23729	−0.618644	+	0.785672i	$0.712317\pi$
$252$	−4.63137	−0.291749
$253$	4.25987	0.267816
$254$	11.5217	0.722934
$255$	0	0
$256$	1.00000	0.0625000
$257$	−9.46931	−0.590679	−0.295340	−	0.955392i	$-0.595433\pi$
$257$	−9.46931	−0.590679	−0.295340	+	0.955392i	$0.595433\pi$
$258$	−9.02860	−0.562096
$259$	−0.412104	−0.0256069
$260$	0	0
$261$	−2.25493	−0.139577
$262$	1.78409	0.110222
$263$	21.1465	1.30395	0.651974	−	0.758241i	$-0.273941\pi$
$263$	21.1465	1.30395	0.651974	+	0.758241i	$0.273941\pi$
$264$	−2.53967	−0.156306
$265$	0	0
$266$	−31.2184	−1.91413
$267$	−0.733865	−0.0449118
$268$	7.64929	0.467255
$269$	−1.95250	−0.119046	−0.0595230	−	0.998227i	$-0.518958\pi$
$269$	−1.95250	−0.119046	−0.0595230	+	0.998227i	$0.518958\pi$
$270$	0	0
$271$	−15.9059	−0.966217	−0.483109	−	0.875560i	$-0.660492\pi$
$271$	−15.9059	−0.966217	−0.483109	+	0.875560i	$0.660492\pi$
$272$	−7.49100	−0.454209
$273$	0.666798	0.0403565
$274$	16.0233	0.968006
$275$	0	0
$276$	1.67733	0.100963
$277$	1.99048	0.119596	0.0597982	−	0.998210i	$-0.480954\pi$
$277$	1.99048	0.119596	0.0597982	+	0.998210i	$0.480954\pi$
$278$	3.70400	0.222151
$279$	1.00385	0.0600989
$280$	0	0
$281$	−25.1864	−1.50249	−0.751247	−	0.660021i	$-0.770547\pi$
$281$	−25.1864	−1.50249	−0.751247	+	0.660021i	$0.770547\pi$
$282$	−10.8854	−0.648214
$283$	−11.2601	−0.669346	−0.334673	−	0.942334i	$-0.608626\pi$
$283$	−11.2601	−0.669346	−0.334673	+	0.942334i	$0.608626\pi$
$284$	−10.2647	−0.609096
$285$	0	0
$286$	0.365648	0.0216212
$287$	−14.2362	−0.840335
$288$	−1.00000	−0.0589256
$289$	39.1151	2.30089
$290$	0	0
$291$	−9.12044	−0.534650
$292$	−1.96580	−0.115040
$293$	−20.0482	−1.17123	−0.585613	−	0.810591i	$-0.699146\pi$
$293$	−20.0482	−1.17123	−0.585613	+	0.810591i	$0.699146\pi$
$294$	14.4496	0.842717
$295$	0	0
$296$	−0.0889810	−0.00517192
$297$	2.53967	0.147367
$298$	−1.88534	−0.109215
$299$	−0.241492	−0.0139659
$300$	0	0
$301$	41.8148	2.41016
$302$	6.15090	0.353944
$303$	2.88013	0.165459
$304$	−6.74065	−0.386603
$305$	0	0
$306$	7.49100	0.428232
$307$	14.4493	0.824668	0.412334	−	0.911033i	$-0.364714\pi$
$307$	14.4493	0.824668	0.412334	+	0.911033i	$0.364714\pi$
$308$	11.7622	0.670212
$309$	−11.1713	−0.635516
$310$	0	0
$311$	−23.5815	−1.33718	−0.668592	−	0.743630i	$-0.733103\pi$
$311$	−23.5815	−1.33718	−0.668592	+	0.743630i	$0.733103\pi$
$312$	0.143974	0.00815094
$313$	27.4927	1.55398	0.776988	−	0.629515i	$-0.216746\pi$
$313$	27.4927	1.55398	0.776988	+	0.629515i	$0.216746\pi$
$314$	−23.4830	−1.32522
$315$	0	0
$316$	0.747233	0.0420352
$317$	−6.04575	−0.339563	−0.169782	−	0.985482i	$-0.554306\pi$
$317$	−6.04575	−0.339563	−0.169782	+	0.985482i	$0.554306\pi$
$318$	4.96506	0.278427
$319$	5.72679	0.320639
$320$	0	0
$321$	14.0538	0.784406
$322$	−7.76834	−0.432913
$323$	50.4942	2.80957
$324$	1.00000	0.0555556
$325$	0	0
$326$	−15.7773	−0.873824
$327$	−6.71867	−0.371543
$328$	−3.07386	−0.169725
$329$	50.4141	2.77942
$330$	0	0
$331$	16.9315	0.930637	0.465319	−	0.885143i	$-0.345940\pi$
$331$	16.9315	0.930637	0.465319	+	0.885143i	$0.345940\pi$
$332$	3.10257	0.170275
$333$	0.0889810	0.00487613
$334$	−4.03980	−0.221048
$335$	0	0
$336$	4.63137	0.252662
$337$	22.6622	1.23449	0.617246	−	0.786771i	$-0.288249\pi$
$337$	22.6622	1.23449	0.617246	+	0.786771i	$0.288249\pi$
$338$	12.9793	0.705979
$339$	0.997621	0.0541833
$340$	0	0
$341$	−2.54945	−0.138061
$342$	6.74065	0.364493
$343$	−34.5018	−1.86292
$344$	9.02860	0.486789
$345$	0	0
$346$	20.1595	1.08378
$347$	10.2520	0.550357	0.275179	−	0.961393i	$-0.411263\pi$
$347$	10.2520	0.550357	0.275179	+	0.961393i	$0.411263\pi$
$348$	2.25493	0.120877
$349$	1.38746	0.0742691	0.0371346	−	0.999310i	$-0.488177\pi$
$349$	1.38746	0.0742691	0.0371346	+	0.999310i	$0.488177\pi$
$350$	0	0
$351$	−0.143974	−0.00768478
$352$	2.53967	0.135365
$353$	−12.9180	−0.687558	−0.343779	−	0.939051i	$-0.611707\pi$
$353$	−12.9180	−0.687558	−0.343779	+	0.939051i	$0.611707\pi$
$354$	5.25365	0.279228
$355$	0	0
$356$	0.733865	0.0388948
$357$	−34.6936	−1.83618
$358$	7.76067	0.410164
$359$	9.87465	0.521164	0.260582	−	0.965452i	$-0.416086\pi$
$359$	9.87465	0.521164	0.260582	+	0.965452i	$0.416086\pi$
$360$	0	0
$361$	26.4364	1.39139
$362$	−11.7909	−0.619715
$363$	4.55005	0.238816
$364$	−0.666798	−0.0349497
$365$	0	0
$366$	−13.7007	−0.716146
$367$	−5.31920	−0.277660	−0.138830	−	0.990316i	$-0.544334\pi$
$367$	−5.31920	−0.277660	−0.138830	+	0.990316i	$0.544334\pi$
$368$	−1.67733	−0.0874369
$369$	3.07386	0.160019
$370$	0	0
$371$	−22.9950	−1.19384
$372$	−1.00385	−0.0520472
$373$	9.68458	0.501449	0.250724	−	0.968059i	$-0.419331\pi$
$373$	9.68458	0.501449	0.250724	+	0.968059i	$0.419331\pi$
$374$	−19.0247	−0.983744
$375$	0	0
$376$	10.8854	0.561369
$377$	−0.324652	−0.0167204
$378$	−4.63137	−0.238212
$379$	−22.5220	−1.15688	−0.578439	−	0.815726i	$-0.696338\pi$
$379$	−22.5220	−1.15688	−0.578439	+	0.815726i	$0.696338\pi$
$380$	0	0
$381$	11.5217	0.590273
$382$	−4.88438	−0.249907
$383$	7.21160	0.368495	0.184248	−	0.982880i	$-0.441015\pi$
$383$	7.21160	0.368495	0.184248	+	0.982880i	$0.441015\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−18.7342	−0.953544
$387$	−9.02860	−0.458949
$388$	9.12044	0.463020
$389$	13.2431	0.671453	0.335726	−	0.941960i	$-0.391018\pi$
$389$	13.2431	0.671453	0.335726	+	0.941960i	$0.391018\pi$
$390$	0	0
$391$	12.5649	0.635433
$392$	−14.4496	−0.729815
$393$	1.78409	0.0899957
$394$	−1.25454	−0.0632027
$395$	0	0
$396$	−2.53967	−0.127623
$397$	29.2626	1.46865	0.734325	−	0.678798i	$-0.237499\pi$
$397$	29.2626	1.46865	0.734325	+	0.678798i	$0.237499\pi$
$398$	−19.3703	−0.970945
$399$	−31.2184	−1.56288
$400$	0	0
$401$	27.4005	1.36832	0.684158	−	0.729334i	$-0.260170\pi$
$401$	27.4005	1.36832	0.684158	+	0.729334i	$0.260170\pi$
$402$	7.64929	0.381512
$403$	0.144529	0.00719948
$404$	−2.88013	−0.143292
$405$	0	0
$406$	−10.4434	−0.518298
$407$	−0.225983	−0.0112016
$408$	−7.49100	−0.370860
$409$	10.0026	0.494596	0.247298	−	0.968939i	$-0.420457\pi$
$409$	10.0026	0.494596	0.247298	+	0.968939i	$0.420457\pi$
$410$	0	0
$411$	16.0233	0.790373
$412$	11.1713	0.550373
$413$	−24.3316	−1.19728
$414$	1.67733	0.0824363
$415$	0	0
$416$	−0.143974	−0.00705892
$417$	3.70400	0.181386
$418$	−17.1191	−0.837320
$419$	−8.05118	−0.393326	−0.196663	−	0.980471i	$-0.563010\pi$
$419$	−8.05118	−0.393326	−0.196663	+	0.980471i	$0.563010\pi$
$420$	0	0
$421$	10.0532	0.489965	0.244982	−	0.969528i	$-0.421218\pi$
$421$	10.0532	0.489965	0.244982	+	0.969528i	$0.421218\pi$
$422$	1.24920	0.0608100
$423$	−10.8854	−0.529264
$424$	−4.96506	−0.241125
$425$	0	0
$426$	−10.2647	−0.497325
$427$	63.4529	3.07070
$428$	−14.0538	−0.679316
$429$	0.365648	0.0176536
$430$	0	0
$431$	22.9694	1.10640	0.553198	−	0.833049i	$-0.313407\pi$
$431$	22.9694	1.10640	0.553198	+	0.833049i	$0.313407\pi$
$432$	−1.00000	−0.0481125
$433$	−17.9964	−0.864854	−0.432427	−	0.901669i	$-0.642343\pi$
$433$	−17.9964	−0.864854	−0.432427	+	0.901669i	$0.642343\pi$
$434$	4.64920	0.223169
$435$	0	0
$436$	6.71867	0.321766
$437$	11.3063	0.540854
$438$	−1.96580	−0.0939294
$439$	−26.1564	−1.24838	−0.624188	−	0.781274i	$-0.714570\pi$
$439$	−26.1564	−1.24838	−0.624188	+	0.781274i	$0.714570\pi$
$440$	0	0
$441$	14.4496	0.688076
$442$	1.07851	0.0512996
$443$	40.5689	1.92749	0.963743	−	0.266833i	$-0.0859772\pi$
$443$	40.5689	1.92749	0.963743	+	0.266833i	$0.0859772\pi$
$444$	−0.0889810	−0.00422285
$445$	0	0
$446$	21.8855	1.03631
$447$	−1.88534	−0.0891737
$448$	−4.63137	−0.218812
$449$	−23.1589	−1.09294	−0.546468	−	0.837480i	$-0.684028\pi$
$449$	−23.1589	−1.09294	−0.546468	+	0.837480i	$0.684028\pi$
$450$	0	0
$451$	−7.80660	−0.367598
$452$	−0.997621	−0.0469241
$453$	6.15090	0.288994
$454$	14.5034	0.680676
$455$	0	0
$456$	−6.74065	−0.315660
$457$	38.3997	1.79626	0.898131	−	0.439728i	$-0.144925\pi$
$457$	38.3997	1.79626	0.898131	+	0.439728i	$0.144925\pi$
$458$	−4.70079	−0.219653
$459$	7.49100	0.349650
$460$	0	0
$461$	−32.5913	−1.51793	−0.758965	−	0.651131i	$-0.774295\pi$
$461$	−32.5913	−1.51793	−0.758965	+	0.651131i	$0.774295\pi$
$462$	11.7622	0.547226
$463$	2.53778	0.117941	0.0589703	−	0.998260i	$-0.481218\pi$
$463$	2.53778	0.117941	0.0589703	+	0.998260i	$0.481218\pi$
$464$	−2.25493	−0.104683
$465$	0	0
$466$	−11.8187	−0.547491
$467$	−1.49654	−0.0692516	−0.0346258	−	0.999400i	$-0.511024\pi$
$467$	−1.49654	−0.0692516	−0.0346258	+	0.999400i	$0.511024\pi$
$468$	0.143974	0.00665521
$469$	−35.4267	−1.63585
$470$	0	0
$471$	−23.4830	−1.08204
$472$	−5.25365	−0.241819
$473$	22.9297	1.05431
$474$	0.747233	0.0343216
$475$	0	0
$476$	34.6936	1.59018
$477$	4.96506	0.227334
$478$	−9.71363	−0.444291
$479$	24.2990	1.11025	0.555125	−	0.831767i	$-0.312670\pi$
$479$	24.2990	1.11025	0.555125	+	0.831767i	$0.312670\pi$
$480$	0	0
$481$	0.0128110	0.000584130 0
$482$	−6.68035	−0.304281
$483$	−7.76834	−0.353472
$484$	−4.55005	−0.206821
$485$	0	0
$486$	1.00000	0.0453609
$487$	10.0016	0.453214	0.226607	−	0.973986i	$-0.427237\pi$
$487$	10.0016	0.453214	0.226607	+	0.973986i	$0.427237\pi$
$488$	13.7007	0.620200
$489$	−15.7773	−0.713474
$490$	0	0
$491$	4.17992	0.188637	0.0943186	−	0.995542i	$-0.469933\pi$
$491$	4.17992	0.188637	0.0943186	+	0.995542i	$0.469933\pi$
$492$	−3.07386	−0.138580
$493$	16.8917	0.760764
$494$	0.970480	0.0436640
$495$	0	0
$496$	1.00385	0.0450742
$497$	47.5395	2.13244
$498$	3.10257	0.139029
$499$	1.70548	0.0763476	0.0381738	−	0.999271i	$-0.487846\pi$
$499$	1.70548	0.0763476	0.0381738	+	0.999271i	$0.487846\pi$
$500$	0	0
$501$	−4.03980	−0.180485
$502$	19.6023	0.874894
$503$	30.9409	1.37958	0.689792	−	0.724007i	$-0.257702\pi$
$503$	30.9409	1.37958	0.689792	+	0.724007i	$0.257702\pi$
$504$	4.63137	0.206298
$505$	0	0
$506$	−4.25987	−0.189374
$507$	12.9793	0.576430
$508$	−11.5217	−0.511192
$509$	−36.1157	−1.60080	−0.800399	−	0.599467i	$-0.795379\pi$
$509$	−36.1157	−1.60080	−0.800399	+	0.599467i	$0.795379\pi$
$510$	0	0
$511$	9.10433	0.402752
$512$	−1.00000	−0.0441942
$513$	6.74065	0.297607
$514$	9.46931	0.417673
$515$	0	0
$516$	9.02860	0.397462
$517$	27.6453	1.21584
$518$	0.412104	0.0181068
$519$	20.1595	0.884906
$520$	0	0
$521$	4.47000	0.195834	0.0979171	−	0.995195i	$-0.468782\pi$
$521$	4.47000	0.195834	0.0979171	+	0.995195i	$0.468782\pi$
$522$	2.25493	0.0986957
$523$	30.6490	1.34019	0.670093	−	0.742277i	$-0.266254\pi$
$523$	30.6490	1.34019	0.670093	+	0.742277i	$0.266254\pi$
$524$	−1.78409	−0.0779385
$525$	0	0
$526$	−21.1465	−0.922030
$527$	−7.51984	−0.327569
$528$	2.53967	0.110525
$529$	−20.1866	−0.877677
$530$	0	0
$531$	5.25365	0.227989
$532$	31.2184	1.35349
$533$	0.442556	0.0191692
$534$	0.733865	0.0317575
$535$	0	0
$536$	−7.64929	−0.330399
$537$	7.76067	0.334898
$538$	1.95250	0.0841782
$539$	−36.6973	−1.58066
$540$	0	0
$541$	14.7172	0.632742	0.316371	−	0.948636i	$-0.397536\pi$
$541$	14.7172	0.632742	0.316371	+	0.948636i	$0.397536\pi$
$542$	15.9059	0.683219
$543$	−11.7909	−0.505995
$544$	7.49100	0.321174
$545$	0	0
$546$	−0.666798	−0.0285363
$547$	−10.6678	−0.456123	−0.228061	−	0.973647i	$-0.573239\pi$
$547$	−10.6678	−0.456123	−0.228061	+	0.973647i	$0.573239\pi$
$548$	−16.0233	−0.684483
$549$	−13.7007	−0.584730
$550$	0	0
$551$	15.1997	0.647529
$552$	−1.67733	−0.0713919
$553$	−3.46071	−0.147165
$554$	−1.99048	−0.0845674
$555$	0	0
$556$	−3.70400	−0.157085
$557$	16.1652	0.684942	0.342471	−	0.939528i	$-0.388736\pi$
$557$	16.1652	0.684942	0.342471	+	0.939528i	$0.388736\pi$
$558$	−1.00385	−0.0424963
$559$	−1.29989	−0.0549793
$560$	0	0
$561$	−19.0247	−0.803224
$562$	25.1864	1.06242
$563$	−43.4782	−1.83239	−0.916195	−	0.400733i	$-0.868755\pi$
$563$	−43.4782	−1.83239	−0.916195	+	0.400733i	$0.868755\pi$
$564$	10.8854	0.458356
$565$	0	0
$566$	11.2601	0.473299
$567$	−4.63137	−0.194499
$568$	10.2647	0.430696
$569$	12.0279	0.504237	0.252118	−	0.967696i	$-0.418873\pi$
$569$	12.0279	0.504237	0.252118	+	0.967696i	$0.418873\pi$
$570$	0	0
$571$	18.7799	0.785915	0.392958	−	0.919557i	$-0.371452\pi$
$571$	18.7799	0.785915	0.392958	+	0.919557i	$0.371452\pi$
$572$	−0.365648	−0.0152885
$573$	−4.88438	−0.204048
$574$	14.2362	0.594206
$575$	0	0
$576$	1.00000	0.0416667
$577$	−21.2351	−0.884029	−0.442015	−	0.897008i	$-0.645736\pi$
$577$	−21.2351	−0.884029	−0.442015	+	0.897008i	$0.645736\pi$
$578$	−39.1151	−1.62697
$579$	−18.7342	−0.778566
$580$	0	0
$581$	−14.3691	−0.596132
$582$	9.12044	0.378055
$583$	−12.6096	−0.522238
$584$	1.96580	0.0813452
$585$	0	0
$586$	20.0482	0.828182
$587$	−32.6278	−1.34669	−0.673346	−	0.739327i	$-0.735144\pi$
$587$	−32.6278	−1.34669	−0.673346	+	0.739327i	$0.735144\pi$
$588$	−14.4496	−0.595891
$589$	−6.76660	−0.278813
$590$	0	0
$591$	−1.25454	−0.0516048
$592$	0.0889810	0.00365710
$593$	−0.911868	−0.0374460	−0.0187230	−	0.999825i	$-0.505960\pi$
$593$	−0.911868	−0.0374460	−0.0187230	+	0.999825i	$0.505960\pi$
$594$	−2.53967	−0.104204
$595$	0	0
$596$	1.88534	0.0772267
$597$	−19.3703	−0.792773
$598$	0.241492	0.00987536
$599$	−35.5516	−1.45260	−0.726300	−	0.687378i	$-0.758762\pi$
$599$	−35.5516	−1.45260	−0.726300	+	0.687378i	$0.758762\pi$
$600$	0	0
$601$	−42.8608	−1.74833	−0.874164	−	0.485630i	$-0.838590\pi$
$601$	−42.8608	−1.74833	−0.874164	+	0.485630i	$0.838590\pi$
$602$	−41.8148	−1.70424
$603$	7.64929	0.311503
$604$	−6.15090	−0.250276
$605$	0	0
$606$	−2.88013	−0.116997
$607$	−47.7389	−1.93766	−0.968831	−	0.247724i	$-0.920317\pi$
$607$	−47.7389	−1.93766	−0.968831	+	0.247724i	$0.920317\pi$
$608$	6.74065	0.273369
$609$	−10.4434	−0.423189
$610$	0	0
$611$	−1.56721	−0.0634026
$612$	−7.49100	−0.302806
$613$	−24.5031	−0.989670	−0.494835	−	0.868987i	$-0.664771\pi$
$613$	−24.5031	−0.989670	−0.494835	+	0.868987i	$0.664771\pi$
$614$	−14.4493	−0.583128
$615$	0	0
$616$	−11.7622	−0.473911
$617$	−2.62056	−0.105500	−0.0527498	−	0.998608i	$-0.516799\pi$
$617$	−2.62056	−0.105500	−0.0527498	+	0.998608i	$0.516799\pi$
$618$	11.1713	0.449378
$619$	−6.75533	−0.271519	−0.135760	−	0.990742i	$-0.543348\pi$
$619$	−6.75533	−0.271519	−0.135760	+	0.990742i	$0.543348\pi$
$620$	0	0
$621$	1.67733	0.0673089
$622$	23.5815	0.945531
$623$	−3.39880	−0.136170
$624$	−0.143974	−0.00576358
$625$	0	0
$626$	−27.4927	−1.09883
$627$	−17.1191	−0.683669
$628$	23.4830	0.937072
$629$	−0.666557	−0.0265774
$630$	0	0
$631$	−30.1555	−1.20047	−0.600235	−	0.799823i	$-0.704926\pi$
$631$	−30.1555	−1.20047	−0.600235	+	0.799823i	$0.704926\pi$
$632$	−0.747233	−0.0297234
$633$	1.24920	0.0496511
$634$	6.04575	0.240107
$635$	0	0
$636$	−4.96506	−0.196877
$637$	2.08037	0.0824272
$638$	−5.72679	−0.226726
$639$	−10.2647	−0.406064
$640$	0	0
$641$	20.5260	0.810727	0.405364	−	0.914156i	$-0.367145\pi$
$641$	20.5260	0.810727	0.405364	+	0.914156i	$0.367145\pi$
$642$	−14.0538	−0.554659
$643$	33.4413	1.31880	0.659399	−	0.751793i	$-0.270811\pi$
$643$	33.4413	1.31880	0.659399	+	0.751793i	$0.270811\pi$
$644$	7.76834	0.306115
$645$	0	0
$646$	−50.4942	−1.98667
$647$	−18.0858	−0.711024	−0.355512	−	0.934672i	$-0.615694\pi$
$647$	−18.0858	−0.711024	−0.355512	+	0.934672i	$0.615694\pi$
$648$	−1.00000	−0.0392837
$649$	−13.3426	−0.523742
$650$	0	0
$651$	4.64920	0.182217
$652$	15.7773	0.617887
$653$	−30.9940	−1.21289	−0.606444	−	0.795126i	$-0.707404\pi$
$653$	−30.9940	−1.21289	−0.606444	+	0.795126i	$0.707404\pi$
$654$	6.71867	0.262721
$655$	0	0
$656$	3.07386	0.120014
$657$	−1.96580	−0.0766930
$658$	−50.4141	−1.96535
$659$	−21.6253	−0.842403	−0.421202	−	0.906967i	$-0.638392\pi$
$659$	−21.6253	−0.842403	−0.421202	+	0.906967i	$0.638392\pi$
$660$	0	0
$661$	−36.7601	−1.42980	−0.714902	−	0.699225i	$-0.753529\pi$
$661$	−36.7601	−1.42980	−0.714902	+	0.699225i	$0.753529\pi$
$662$	−16.9315	−0.658060
$663$	1.07851	0.0418859
$664$	−3.10257	−0.120403
$665$	0	0
$666$	−0.0889810	−0.00344794
$667$	3.78227	0.146450
$668$	4.03980	0.156305
$669$	21.8855	0.846144
$670$	0	0
$671$	34.7953	1.34326
$672$	−4.63137	−0.178659
$673$	−30.8335	−1.18854	−0.594272	−	0.804264i	$-0.702560\pi$
$673$	−30.8335	−1.18854	−0.594272	+	0.804264i	$0.702560\pi$
$674$	−22.6622	−0.872917
$675$	0	0
$676$	−12.9793	−0.499203
$677$	25.8101	0.991963	0.495981	−	0.868333i	$-0.334808\pi$
$677$	25.8101	0.991963	0.495981	+	0.868333i	$0.334808\pi$
$678$	−0.997621	−0.0383134
$679$	−42.2402	−1.62103
$680$	0	0
$681$	14.5034	0.555770
$682$	2.54945	0.0976235
$683$	−20.8802	−0.798959	−0.399479	−	0.916742i	$-0.630809\pi$
$683$	−20.8802	−0.798959	−0.399479	+	0.916742i	$0.630809\pi$
$684$	−6.74065	−0.257735
$685$	0	0
$686$	34.5018	1.31729
$687$	−4.70079	−0.179346
$688$	−9.02860	−0.344212
$689$	0.714841	0.0272333
$690$	0	0
$691$	20.6464	0.785427	0.392714	−	0.919661i	$-0.371536\pi$
$691$	20.6464	0.785427	0.392714	+	0.919661i	$0.371536\pi$
$692$	−20.1595	−0.766351
$693$	11.7622	0.446808
$694$	−10.2520	−0.389162
$695$	0	0
$696$	−2.25493	−0.0854730
$697$	−23.0263	−0.872182
$698$	−1.38746	−0.0525162
$699$	−11.8187	−0.447025
$700$	0	0
$701$	−12.3050	−0.464752	−0.232376	−	0.972626i	$-0.574650\pi$
$701$	−12.3050	−0.464752	−0.232376	+	0.972626i	$0.574650\pi$
$702$	0.143974	0.00543396
$703$	−0.599790	−0.0226215
$704$	−2.53967	−0.0957176
$705$	0	0
$706$	12.9180	0.486177
$707$	13.3389	0.501662
$708$	−5.25365	−0.197444
$709$	−24.6984	−0.927566	−0.463783	−	0.885949i	$-0.653508\pi$
$709$	−24.6984	−0.927566	−0.463783	+	0.885949i	$0.653508\pi$
$710$	0	0
$711$	0.747233	0.0280234
$712$	−0.733865	−0.0275028
$713$	−1.68379	−0.0630583
$714$	34.6936	1.29838
$715$	0	0
$716$	−7.76067	−0.290030
$717$	−9.71363	−0.362762
$718$	−9.87465	−0.368519
$719$	−21.0231	−0.784030	−0.392015	−	0.919959i	$-0.628222\pi$
$719$	−21.0231	−0.784030	−0.392015	+	0.919959i	$0.628222\pi$
$720$	0	0
$721$	−51.7387	−1.92685
$722$	−26.4364	−0.983860
$723$	−6.68035	−0.248445
$724$	11.7909	0.438205
$725$	0	0
$726$	−4.55005	−0.168868
$727$	−8.67125	−0.321599	−0.160799	−	0.986987i	$-0.551407\pi$
$727$	−8.67125	−0.321599	−0.160799	+	0.986987i	$0.551407\pi$
$728$	0.666798	0.0247132
$729$	1.00000	0.0370370
$730$	0	0
$731$	67.6332	2.50151
$732$	13.7007	0.506391
$733$	33.9376	1.25351	0.626757	−	0.779214i	$-0.284382\pi$
$733$	33.9376	1.25351	0.626757	+	0.779214i	$0.284382\pi$
$734$	5.31920	0.196335
$735$	0	0
$736$	1.67733	0.0618272
$737$	−19.4267	−0.715592
$738$	−3.07386	−0.113150
$739$	−16.4126	−0.603747	−0.301874	−	0.953348i	$-0.597612\pi$
$739$	−16.4126	−0.603747	−0.301874	+	0.953348i	$0.597612\pi$
$740$	0	0
$741$	0.970480	0.0356515
$742$	22.9950	0.844174
$743$	3.98742	0.146284	0.0731422	−	0.997322i	$-0.476697\pi$
$743$	3.98742	0.146284	0.0731422	+	0.997322i	$0.476697\pi$
$744$	1.00385	0.0368029
$745$	0	0
$746$	−9.68458	−0.354578
$747$	3.10257	0.113517
$748$	19.0247	0.695612
$749$	65.0883	2.37828
$750$	0	0
$751$	37.5827	1.37141	0.685706	−	0.727879i	$-0.259494\pi$
$751$	37.5827	1.37141	0.685706	+	0.727879i	$0.259494\pi$
$752$	−10.8854	−0.396948
$753$	19.6023	0.714348
$754$	0.324652	0.0118231
$755$	0	0
$756$	4.63137	0.168441
$757$	−31.2749	−1.13671	−0.568353	−	0.822785i	$-0.692419\pi$
$757$	−31.2749	−1.13671	−0.568353	+	0.822785i	$0.692419\pi$
$758$	22.5220	0.818036
$759$	−4.25987	−0.154624
$760$	0	0
$761$	29.9489	1.08565	0.542823	−	0.839847i	$-0.317355\pi$
$761$	29.9489	1.08565	0.542823	+	0.839847i	$0.317355\pi$
$762$	−11.5217	−0.417386
$763$	−31.1167	−1.12650
$764$	4.88438	0.176711
$765$	0	0
$766$	−7.21160	−0.260566
$767$	0.756391	0.0273117
$768$	−1.00000	−0.0360844
$769$	−36.9037	−1.33078	−0.665391	−	0.746495i	$-0.731735\pi$
$769$	−36.9037	−1.33078	−0.665391	+	0.746495i	$0.731735\pi$
$770$	0	0
$771$	9.46931	0.341029
$772$	18.7342	0.674258
$773$	44.2386	1.59115	0.795576	−	0.605853i	$-0.207168\pi$
$773$	44.2386	1.59115	0.795576	+	0.605853i	$0.207168\pi$
$774$	9.02860	0.324526
$775$	0	0
$776$	−9.12044	−0.327405
$777$	0.412104	0.0147841
$778$	−13.2431	−0.474789
$779$	−20.7198	−0.742364
$780$	0	0
$781$	26.0689	0.932819
$782$	−12.5649	−0.449319
$783$	2.25493	0.0805847
$784$	14.4496	0.516057
$785$	0	0
$786$	−1.78409	−0.0636365
$787$	−40.0500	−1.42763	−0.713813	−	0.700336i	$-0.753034\pi$
$787$	−40.0500	−1.42763	−0.713813	+	0.700336i	$0.753034\pi$
$788$	1.25454	0.0446911
$789$	−21.1465	−0.752834
$790$	0	0
$791$	4.62035	0.164281
$792$	2.53967	0.0902434
$793$	−1.97254	−0.0700471
$794$	−29.2626	−1.03849
$795$	0	0
$796$	19.3703	0.686562
$797$	−44.4781	−1.57549	−0.787747	−	0.615999i	$-0.788753\pi$
$797$	−44.4781	−1.57549	−0.787747	+	0.615999i	$0.788753\pi$
$798$	31.2184	1.10512
$799$	81.5422	2.88476
$800$	0	0
$801$	0.733865	0.0259299
$802$	−27.4005	−0.967545
$803$	4.99248	0.176181
$804$	−7.64929	−0.269770
$805$	0	0
$806$	−0.144529	−0.00509080
$807$	1.95250	0.0687312
$808$	2.88013	0.101323
$809$	−34.2539	−1.20430	−0.602151	−	0.798382i	$-0.705689\pi$
$809$	−34.2539	−1.20430	−0.602151	+	0.798382i	$0.705689\pi$
$810$	0	0
$811$	10.6488	0.373930	0.186965	−	0.982367i	$-0.440135\pi$
$811$	10.6488	0.373930	0.186965	+	0.982367i	$0.440135\pi$
$812$	10.4434	0.366492
$813$	15.9059	0.557846
$814$	0.225983	0.00792069
$815$	0	0
$816$	7.49100	0.262237
$817$	60.8586	2.12917
$818$	−10.0026	−0.349732
$819$	−0.666798	−0.0232998
$820$	0	0
$821$	−14.7387	−0.514384	−0.257192	−	0.966360i	$-0.582797\pi$
$821$	−14.7387	−0.514384	−0.257192	+	0.966360i	$0.582797\pi$
$822$	−16.0233	−0.558878
$823$	−2.83258	−0.0987377	−0.0493688	−	0.998781i	$-0.515721\pi$
$823$	−2.83258	−0.0987377	−0.0493688	+	0.998781i	$0.515721\pi$
$824$	−11.1713	−0.389172
$825$	0	0
$826$	24.3316	0.846605
$827$	−21.8116	−0.758463	−0.379231	−	0.925302i	$-0.623812\pi$
$827$	−21.8116	−0.758463	−0.379231	+	0.925302i	$0.623812\pi$
$828$	−1.67733	−0.0582913
$829$	−40.6037	−1.41023	−0.705113	−	0.709095i	$-0.749104\pi$
$829$	−40.6037	−1.41023	−0.705113	+	0.709095i	$0.749104\pi$
$830$	0	0
$831$	−1.99048	−0.0690490
$832$	0.143974	0.00499141
$833$	−108.242	−3.75036
$834$	−3.70400	−0.128259
$835$	0	0
$836$	17.1191	0.592075
$837$	−1.00385	−0.0346981
$838$	8.05118	0.278123
$839$	28.8888	0.997353	0.498676	−	0.866788i	$-0.333820\pi$
$839$	28.8888	0.997353	0.498676	+	0.866788i	$0.333820\pi$
$840$	0	0
$841$	−23.9153	−0.824665
$842$	−10.0532	−0.346458
$843$	25.1864	0.867465
$844$	−1.24920	−0.0429991
$845$	0	0
$846$	10.8854	0.374246
$847$	21.0730	0.724076
$848$	4.96506	0.170501
$849$	11.2601	0.386447
$850$	0	0
$851$	−0.149251	−0.00511624
$852$	10.2647	0.351662
$853$	−24.8092	−0.849450	−0.424725	−	0.905322i	$-0.639629\pi$
$853$	−24.8092	−0.849450	−0.424725	+	0.905322i	$0.639629\pi$
$854$	−63.4529	−2.17131
$855$	0	0
$856$	14.0538	0.480349
$857$	20.0312	0.684251	0.342126	−	0.939654i	$-0.388853\pi$
$857$	20.0312	0.684251	0.342126	+	0.939654i	$0.388853\pi$
$858$	−0.365648	−0.0124830
$859$	−31.7856	−1.08451	−0.542255	−	0.840214i	$-0.682429\pi$
$859$	−31.7856	−1.08451	−0.542255	+	0.840214i	$0.682429\pi$
$860$	0	0
$861$	14.2362	0.485167
$862$	−22.9694	−0.782341
$863$	−23.8998	−0.813560	−0.406780	−	0.913526i	$-0.633348\pi$
$863$	−23.8998	−0.813560	−0.406780	+	0.913526i	$0.633348\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	17.9964	0.611544
$867$	−39.1151	−1.32842
$868$	−4.64920	−0.157804
$869$	−1.89773	−0.0643761
$870$	0	0
$871$	1.10130	0.0373162
$872$	−6.71867	−0.227523
$873$	9.12044	0.308680
$874$	−11.3063	−0.382441
$875$	0	0
$876$	1.96580	0.0664181
$877$	4.70430	0.158853	0.0794265	−	0.996841i	$-0.474691\pi$
$877$	4.70430	0.158853	0.0794265	+	0.996841i	$0.474691\pi$
$878$	26.1564	0.882735
$879$	20.0482	0.676208
$880$	0	0
$881$	−44.6262	−1.50349	−0.751747	−	0.659452i	$-0.770789\pi$
$881$	−44.6262	−1.50349	−0.751747	+	0.659452i	$0.770789\pi$
$882$	−14.4496	−0.486543
$883$	−32.2048	−1.08378	−0.541888	−	0.840450i	$-0.682290\pi$
$883$	−32.2048	−1.08378	−0.541888	+	0.840450i	$0.682290\pi$
$884$	−1.07851	−0.0362743
$885$	0	0
$886$	−40.5689	−1.36294
$887$	43.0250	1.44464	0.722319	−	0.691560i	$-0.243076\pi$
$887$	43.0250	1.44464	0.722319	+	0.691560i	$0.243076\pi$
$888$	0.0889810	0.00298601
$889$	53.3611	1.78968
$890$	0	0
$891$	−2.53967	−0.0850823
$892$	−21.8855	−0.732782
$893$	73.3744	2.45538
$894$	1.88534	0.0630554
$895$	0	0
$896$	4.63137	0.154723
$897$	0.241492	0.00806320
$898$	23.1589	0.772823
$899$	−2.26361	−0.0754957
$900$	0	0
$901$	−37.1933	−1.23909
$902$	7.80660	0.259931
$903$	−41.8148	−1.39151
$904$	0.997621	0.0331804
$905$	0	0
$906$	−6.15090	−0.204350
$907$	−39.3398	−1.30626	−0.653129	−	0.757247i	$-0.726544\pi$
$907$	−39.3398	−1.30626	−0.653129	+	0.757247i	$0.726544\pi$
$908$	−14.5034	−0.481311
$909$	−2.88013	−0.0955278
$910$	0	0
$911$	−13.6023	−0.450664	−0.225332	−	0.974282i	$-0.572347\pi$
$911$	−13.6023	−0.450664	−0.225332	+	0.974282i	$0.572347\pi$
$912$	6.74065	0.223205
$913$	−7.87951	−0.260774
$914$	−38.3997	−1.27015
$915$	0	0
$916$	4.70079	0.155318
$917$	8.26280	0.272862
$918$	−7.49100	−0.247240
$919$	−14.2048	−0.468572	−0.234286	−	0.972168i	$-0.575275\pi$
$919$	−14.2048	−0.468572	−0.234286	+	0.972168i	$0.575275\pi$
$920$	0	0
$921$	−14.4493	−0.476122
$922$	32.5913	1.07334
$923$	−1.47785	−0.0486440
$924$	−11.7622	−0.386947
$925$	0	0
$926$	−2.53778	−0.0833966
$927$	11.1713	0.366915
$928$	2.25493	0.0740218
$929$	8.10960	0.266067	0.133034	−	0.991112i	$-0.457528\pi$
$929$	8.10960	0.266067	0.133034	+	0.991112i	$0.457528\pi$
$930$	0	0
$931$	−97.3996	−3.19214
$932$	11.8187	0.387135
$933$	23.5815	0.772023
$934$	1.49654	0.0489683
$935$	0	0
$936$	−0.143974	−0.00470595
$937$	−10.5255	−0.343854	−0.171927	−	0.985110i	$-0.554999\pi$
$937$	−10.5255	−0.343854	−0.171927	+	0.985110i	$0.554999\pi$
$938$	35.4267	1.15672
$939$	−27.4927	−0.897189
$940$	0	0
$941$	−49.5406	−1.61498	−0.807489	−	0.589882i	$-0.799174\pi$
$941$	−49.5406	−1.61498	−0.807489	+	0.589882i	$0.799174\pi$
$942$	23.4830	0.765116
$943$	−5.15587	−0.167898
$944$	5.25365	0.170992
$945$	0	0
$946$	−22.9297	−0.745509
$947$	−10.5814	−0.343849	−0.171925	−	0.985110i	$-0.554999\pi$
$947$	−10.5814	−0.343849	−0.171925	+	0.985110i	$0.554999\pi$
$948$	−0.747233	−0.0242690
$949$	−0.283024	−0.00918735
$950$	0	0
$951$	6.04575	0.196047
$952$	−34.6936	−1.12443
$953$	26.0143	0.842686	0.421343	−	0.906901i	$-0.361559\pi$
$953$	26.0143	0.842686	0.421343	+	0.906901i	$0.361559\pi$
$954$	−4.96506	−0.160750
$955$	0	0
$956$	9.71363	0.314161
$957$	−5.72679	−0.185121
$958$	−24.2990	−0.785065
$959$	74.2100	2.39637
$960$	0	0
$961$	−29.9923	−0.967493
$962$	−0.0128110	−0.000413043 0
$963$	−14.0538	−0.452877
$964$	6.68035	0.215159
$965$	0	0
$966$	7.76834	0.249942
$967$	−29.5512	−0.950304	−0.475152	−	0.879904i	$-0.657607\pi$
$967$	−29.5512	−0.950304	−0.475152	+	0.879904i	$0.657607\pi$
$968$	4.55005	0.146244
$969$	−50.4942	−1.62211
$970$	0	0
$971$	35.8718	1.15118	0.575590	−	0.817739i	$-0.304773\pi$
$971$	35.8718	1.15118	0.575590	+	0.817739i	$0.304773\pi$
$972$	−1.00000	−0.0320750
$973$	17.1546	0.549952
$974$	−10.0016	−0.320470
$975$	0	0
$976$	−13.7007	−0.438548
$977$	−21.6261	−0.691881	−0.345940	−	0.938256i	$-0.612440\pi$
$977$	−21.6261	−0.691881	−0.345940	+	0.938256i	$0.612440\pi$
$978$	15.7773	0.504502
$979$	−1.86378	−0.0595666
$980$	0	0
$981$	6.71867	0.214511
$982$	−4.17992	−0.133387
$983$	14.6180	0.466243	0.233122	−	0.972448i	$-0.425106\pi$
$983$	14.6180	0.466243	0.233122	+	0.972448i	$0.425106\pi$
$984$	3.07386	0.0979910
$985$	0	0
$986$	−16.8917	−0.537941
$987$	−50.4141	−1.60470
$988$	−0.970480	−0.0308751
$989$	15.1439	0.481549
$990$	0	0
$991$	−13.0741	−0.415313	−0.207656	−	0.978202i	$-0.566584\pi$
$991$	−13.0741	−0.415313	−0.207656	+	0.978202i	$0.566584\pi$
$992$	−1.00385	−0.0318723
$993$	−16.9315	−0.537304
$994$	−47.5395	−1.50786
$995$	0	0
$996$	−3.10257	−0.0983086
$997$	12.1968	0.386275	0.193138	−	0.981172i	$-0.438134\pi$
$997$	12.1968	0.386275	0.193138	+	0.981172i	$0.438134\pi$
$998$	−1.70548	−0.0539859
$999$	−0.0889810	−0.00281523

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3750.2.a.u.1.1		8
5.2	odd	4		3750.2.c.k.1249.1		16
5.3	odd	4		3750.2.c.k.1249.16		16
5.4	even	2		3750.2.a.v.1.8		8
25.3	odd	20		750.2.h.d.49.4		16
25.4	even	10		750.2.g.f.451.4		16
25.6	even	5		750.2.g.g.301.1		16
25.8	odd	20		150.2.h.b.139.1	yes	16
25.17	odd	20		750.2.h.d.199.3		16
25.19	even	10		750.2.g.f.301.4		16
25.21	even	5		750.2.g.g.451.1		16
25.22	odd	20		150.2.h.b.109.1	✓	16
75.8	even	20		450.2.l.c.289.4		16
75.47	even	20		450.2.l.c.109.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.109.1	✓	16	25.22	odd	20
150.2.h.b.139.1	yes	16	25.8	odd	20
450.2.l.c.109.4		16	75.47	even	20
450.2.l.c.289.4		16	75.8	even	20
750.2.g.f.301.4		16	25.19	even	10
750.2.g.f.451.4		16	25.4	even	10
750.2.g.g.301.1		16	25.6	even	5
750.2.g.g.451.1		16	25.21	even	5
750.2.h.d.49.4		16	25.3	odd	20
750.2.h.d.199.3		16	25.17	odd	20
3750.2.a.u.1.1		8	1.1	even	1	trivial
3750.2.a.v.1.8		8	5.4	even	2
3750.2.c.k.1249.1		16	5.2	odd	4
3750.2.c.k.1249.16		16	5.3	odd	4

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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:	\( N \)	\(=\)	\( 3750 = 2 \cdot 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3750.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -4.63137 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -4.63137 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.53967 q^{11} -1.00000 q^{12} +0.143974 q^{13} +4.63137 q^{14} +1.00000 q^{16} -7.49100 q^{17} -1.00000 q^{18} -6.74065 q^{19} +4.63137 q^{21} +2.53967 q^{22} -1.67733 q^{23} +1.00000 q^{24} -0.143974 q^{26} -1.00000 q^{27} -4.63137 q^{28} -2.25493 q^{29} +1.00385 q^{31} -1.00000 q^{32} +2.53967 q^{33} +7.49100 q^{34} +1.00000 q^{36} +0.0889810 q^{37} +6.74065 q^{38} -0.143974 q^{39} +3.07386 q^{41} -4.63137 q^{42} -9.02860 q^{43} -2.53967 q^{44} +1.67733 q^{46} -10.8854 q^{47} -1.00000 q^{48} +14.4496 q^{49} +7.49100 q^{51} +0.143974 q^{52} +4.96506 q^{53} +1.00000 q^{54} +4.63137 q^{56} +6.74065 q^{57} +2.25493 q^{58} +5.25365 q^{59} -13.7007 q^{61} -1.00385 q^{62} -4.63137 q^{63} +1.00000 q^{64} -2.53967 q^{66} +7.64929 q^{67} -7.49100 q^{68} +1.67733 q^{69} -10.2647 q^{71} -1.00000 q^{72} -1.96580 q^{73} -0.0889810 q^{74} -6.74065 q^{76} +11.7622 q^{77} +0.143974 q^{78} +0.747233 q^{79} +1.00000 q^{81} -3.07386 q^{82} +3.10257 q^{83} +4.63137 q^{84} +9.02860 q^{86} +2.25493 q^{87} +2.53967 q^{88} +0.733865 q^{89} -0.666798 q^{91} -1.67733 q^{92} -1.00385 q^{93} +10.8854 q^{94} +1.00000 q^{96} +9.12044 q^{97} -14.4496 q^{98} -2.53967 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9} + 6 q^{11} - 8 q^{12} - 2 q^{13} + 4 q^{14} + 8 q^{16} - 14 q^{17} - 8 q^{18} + 10 q^{19} + 4 q^{21} - 6 q^{22} - 12 q^{23} + 8 q^{24} + 2 q^{26} - 8 q^{27} - 4 q^{28} + 10 q^{29} + 16 q^{31} - 8 q^{32} - 6 q^{33} + 14 q^{34} + 8 q^{36} + 6 q^{37} - 10 q^{38} + 2 q^{39} + 6 q^{41} - 4 q^{42} - 2 q^{43} + 6 q^{44} + 12 q^{46} - 14 q^{47} - 8 q^{48} + 26 q^{49} + 14 q^{51} - 2 q^{52} - 12 q^{53} + 8 q^{54} + 4 q^{56} - 10 q^{57} - 10 q^{58} + 16 q^{61} - 16 q^{62} - 4 q^{63} + 8 q^{64} + 6 q^{66} + 6 q^{67} - 14 q^{68} + 12 q^{69} + 6 q^{71} - 8 q^{72} + 8 q^{73} - 6 q^{74} + 10 q^{76} - 8 q^{77} - 2 q^{78} + 10 q^{79} + 8 q^{81} - 6 q^{82} - 22 q^{83} + 4 q^{84} + 2 q^{86} - 10 q^{87} - 6 q^{88} + 20 q^{89} + 6 q^{91} - 12 q^{92} - 16 q^{93} + 14 q^{94} + 8 q^{96} + 16 q^{97} - 26 q^{98} + 6 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9 + 6 * q^11 - 8 * q^12 - 2 * q^13 + 4 * q^14 + 8 * q^16 - 14 * q^17 - 8 * q^18 + 10 * q^19 + 4 * q^21 - 6 * q^22 - 12 * q^23 + 8 * q^24 + 2 * q^26 - 8 * q^27 - 4 * q^28 + 10 * q^29 + 16 * q^31 - 8 * q^32 - 6 * q^33 + 14 * q^34 + 8 * q^36 + 6 * q^37 - 10 * q^38 + 2 * q^39 + 6 * q^41 - 4 * q^42 - 2 * q^43 + 6 * q^44 + 12 * q^46 - 14 * q^47 - 8 * q^48 + 26 * q^49 + 14 * q^51 - 2 * q^52 - 12 * q^53 + 8 * q^54 + 4 * q^56 - 10 * q^57 - 10 * q^58 + 16 * q^61 - 16 * q^62 - 4 * q^63 + 8 * q^64 + 6 * q^66 + 6 * q^67 - 14 * q^68 + 12 * q^69 + 6 * q^71 - 8 * q^72 + 8 * q^73 - 6 * q^74 + 10 * q^76 - 8 * q^77 - 2 * q^78 + 10 * q^79 + 8 * q^81 - 6 * q^82 - 22 * q^83 + 4 * q^84 + 2 * q^86 - 10 * q^87 - 6 * q^88 + 20 * q^89 + 6 * q^91 - 12 * q^92 - 16 * q^93 + 14 * q^94 + 8 * q^96 + 16 * q^97 - 26 * q^98 + 6 * q^99

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