LMFDB - Embedded newform 8281.2.a.bt.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8281,2,Mod(1,8281)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8281, 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("8281.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8281 = 7^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8281.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:	$66.1241179138$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.27004.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6x^{2} + 3x + 1 $ x^4 - x^3 - 6x^2 + 3x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.710287$ of defining polynomial
Character	$\chi$	$=$	8281.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.710287 q^{2} -2.40788 q^{3} -1.49549 q^{4} -1.28971 q^{5} -1.71029 q^{6} -2.48280 q^{8} +2.79790 q^{9} +O(q^{10})$	\(q+0.710287 q^{2} -2.40788 q^{3} -1.49549 q^{4} -1.28971 q^{5} -1.71029 q^{6} -2.48280 q^{8} +2.79790 q^{9} -0.916066 q^{10} +2.40788 q^{11} +3.60097 q^{12} +3.10548 q^{15} +1.22748 q^{16} -3.90338 q^{17} +1.98731 q^{18} -5.89068 q^{19} +1.92876 q^{20} +1.71029 q^{22} -6.32395 q^{23} +5.97829 q^{24} -3.33664 q^{25} +0.486640 q^{27} +5.61366 q^{29} +2.20578 q^{30} +2.20578 q^{31} +5.83747 q^{32} -5.79790 q^{33} -2.77252 q^{34} -4.18424 q^{36} +5.11817 q^{37} -4.18407 q^{38} +3.20210 q^{40} -7.78521 q^{41} +0.289713 q^{43} -3.60097 q^{44} -3.60849 q^{45} -4.49182 q^{46} +1.27702 q^{47} -2.95564 q^{48} -2.36997 q^{50} +9.39887 q^{51} -13.6225 q^{53} +0.345654 q^{54} -3.10548 q^{55} +14.1841 q^{57} +3.98731 q^{58} -4.03056 q^{59} -4.64422 q^{60} +4.60097 q^{61} +1.56674 q^{62} +1.69131 q^{64} -4.11817 q^{66} -7.57559 q^{67} +5.83747 q^{68} +15.2273 q^{69} -7.22732 q^{71} -6.94662 q^{72} -15.0125 q^{73} +3.63537 q^{74} +8.03424 q^{75} +8.80948 q^{76} -9.30758 q^{79} -1.58310 q^{80} -9.56546 q^{81} -5.52973 q^{82} -1.36463 q^{83} +5.03424 q^{85} +0.205780 q^{86} -13.5170 q^{87} -5.97829 q^{88} -0.899698 q^{89} -2.56306 q^{90} +9.45742 q^{92} -5.31126 q^{93} +0.907052 q^{94} +7.59729 q^{95} -14.0559 q^{96} +15.6658 q^{97} +6.73701 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} + 6 q^{8} + 7 q^{9}+O(q^{10}) $ 4 * q + q^2 - q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 + 6 * q^8 + 7 * q^9	$ 4 q + q^{2} - q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} + 6 q^{8} + 7 q^{9} + 11 q^{10} + q^{11} - 12 q^{12} - 3 q^{15} + 19 q^{16} + 4 q^{17} + 3 q^{18} + q^{19} - 2 q^{20} + 5 q^{22} - 2 q^{23} - 3 q^{24} + 5 q^{25} + 26 q^{27} + q^{29} - 4 q^{30} - 4 q^{31} + 33 q^{32} - 19 q^{33} + 3 q^{34} - 34 q^{36} + 10 q^{37} + 23 q^{38} + 17 q^{40} - 22 q^{41} + 3 q^{43} + 12 q^{44} - 11 q^{45} - 24 q^{46} + 2 q^{47} - 11 q^{48} - 43 q^{50} + 7 q^{51} + 2 q^{53} + 5 q^{54} + 3 q^{55} + 17 q^{57} + 11 q^{58} - 8 q^{59} + 11 q^{60} - 8 q^{61} + 5 q^{62} + 14 q^{64} - 6 q^{66} + 6 q^{67} + 33 q^{68} + 18 q^{69} + 14 q^{71} - 5 q^{72} - 8 q^{73} + 20 q^{74} + 7 q^{75} + 32 q^{76} - 26 q^{79} + 7 q^{80} + 24 q^{81} + 14 q^{82} - 5 q^{85} - 12 q^{86} - 13 q^{87} + 3 q^{88} - q^{89} - 26 q^{90} + 12 q^{92} + 7 q^{93} - 33 q^{94} + 21 q^{95} - 58 q^{96} + 3 q^{97} - 23 q^{99}+O(q^{100}) $ 4 * q + q^2 - q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 + 6 * q^8 + 7 * q^9 + 11 * q^10 + q^11 - 12 * q^12 - 3 * q^15 + 19 * q^16 + 4 * q^17 + 3 * q^18 + q^19 - 2 * q^20 + 5 * q^22 - 2 * q^23 - 3 * q^24 + 5 * q^25 + 26 * q^27 + q^29 - 4 * q^30 - 4 * q^31 + 33 * q^32 - 19 * q^33 + 3 * q^34 - 34 * q^36 + 10 * q^37 + 23 * q^38 + 17 * q^40 - 22 * q^41 + 3 * q^43 + 12 * q^44 - 11 * q^45 - 24 * q^46 + 2 * q^47 - 11 * q^48 - 43 * q^50 + 7 * q^51 + 2 * q^53 + 5 * q^54 + 3 * q^55 + 17 * q^57 + 11 * q^58 - 8 * q^59 + 11 * q^60 - 8 * q^61 + 5 * q^62 + 14 * q^64 - 6 * q^66 + 6 * q^67 + 33 * q^68 + 18 * q^69 + 14 * q^71 - 5 * q^72 - 8 * q^73 + 20 * q^74 + 7 * q^75 + 32 * q^76 - 26 * q^79 + 7 * q^80 + 24 * q^81 + 14 * q^82 - 5 * q^85 - 12 * q^86 - 13 * q^87 + 3 * q^88 - q^89 - 26 * q^90 + 12 * q^92 + 7 * q^93 - 33 * q^94 + 21 * q^95 - 58 * q^96 + 3 * q^97 - 23 * 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 $

$2$	0.710287	0.502249	0.251124	−	0.967955i	$-0.419200\pi$
$2$	0.710287	0.502249	0.251124	+	0.967955i	$0.419200\pi$
$3$	−2.40788	−1.39019	−0.695096	−	0.718917i	$-0.744638\pi$
$3$	−2.40788	−1.39019	−0.695096	+	0.718917i	$0.744638\pi$
$4$	−1.49549	−0.747746
$5$	−1.28971	−0.576777	−0.288389	−	0.957513i	$-0.593120\pi$
$5$	−1.28971	−0.576777	−0.288389	+	0.957513i	$0.593120\pi$
$6$	−1.71029	−0.698222
$7$	0	0
$7$	0	0
$8$	−2.48280	−0.877803
$9$	2.79790	0.932632
$10$	−0.916066	−0.289686
$11$	2.40788	0.726004	0.363002	−	0.931788i	$-0.381752\pi$
$11$	2.40788	0.726004	0.363002	+	0.931788i	$0.381752\pi$
$12$	3.60097	1.03951
$13$	0	0
$13$	0	0
$14$	0	0
$15$	3.10548	0.801831
$16$	1.22748	0.306871
$17$	−3.90338	−0.946708	−0.473354	−	0.880872i	$-0.656957\pi$
$17$	−3.90338	−0.946708	−0.473354	+	0.880872i	$0.656957\pi$
$18$	1.98731	0.468413
$19$	−5.89068	−1.35142	−0.675708	−	0.737170i	$-0.736162\pi$
$19$	−5.89068	−1.35142	−0.675708	+	0.737170i	$0.736162\pi$
$20$	1.92876	0.431283
$21$	0	0
$22$	1.71029	0.364634
$23$	−6.32395	−1.31863	−0.659317	−	0.751865i	$-0.729155\pi$
$23$	−6.32395	−1.31863	−0.659317	+	0.751865i	$0.729155\pi$
$24$	5.97829	1.22031
$25$	−3.33664	−0.667328
$26$	0	0
$27$	0.486640	0.0936539
$28$	0	0
$29$	5.61366	1.04243	0.521215	−	0.853425i	$-0.325479\pi$
$29$	5.61366	1.04243	0.521215	+	0.853425i	$0.325479\pi$
$30$	2.20578	0.402718
$31$	2.20578	0.396170	0.198085	−	0.980185i	$-0.436528\pi$
$31$	2.20578	0.396170	0.198085	+	0.980185i	$0.436528\pi$
$32$	5.83747	1.03193
$33$	−5.79790	−1.00928
$34$	−2.77252	−0.475482
$35$	0	0
$36$	−4.18424	−0.697373
$37$	5.11817	0.841422	0.420711	−	0.907195i	$-0.361781\pi$
$37$	5.11817	0.841422	0.420711	+	0.907195i	$0.361781\pi$
$38$	−4.18407	−0.678746
$39$	0	0
$40$	3.20210	0.506297
$41$	−7.78521	−1.21584	−0.607922	−	0.793996i	$-0.707997\pi$
$41$	−7.78521	−1.21584	−0.607922	+	0.793996i	$0.707997\pi$
$42$	0	0
$43$	0.289713	0.0441809	0.0220904	−	0.999756i	$-0.492968\pi$
$43$	0.289713	0.0441809	0.0220904	+	0.999756i	$0.492968\pi$
$44$	−3.60097	−0.542867
$45$	−3.60849	−0.537921
$46$	−4.49182	−0.662282
$47$	1.27702	0.186273	0.0931364	−	0.995653i	$-0.470311\pi$
$47$	1.27702	0.186273	0.0931364	+	0.995653i	$0.470311\pi$
$48$	−2.95564	−0.426610
$49$	0	0
$50$	−2.36997	−0.335164
$51$	9.39887	1.31610
$52$	0	0
$53$	−13.6225	−1.87120	−0.935598	−	0.353067i	$-0.885139\pi$
$53$	−13.6225	−1.87120	−0.935598	+	0.353067i	$0.885139\pi$
$54$	0.345654	0.0470375
$55$	−3.10548	−0.418743
$56$	0	0
$57$	14.1841	1.87873
$58$	3.98731	0.523559
$59$	−4.03056	−0.524734	−0.262367	−	0.964968i	$-0.584503\pi$
$59$	−4.03056	−0.524734	−0.262367	+	0.964968i	$0.584503\pi$
$60$	−4.64422	−0.599566
$61$	4.60097	0.589094	0.294547	−	0.955637i	$-0.404831\pi$
$61$	4.60097	0.589094	0.294547	+	0.955637i	$0.404831\pi$
$62$	1.56674	0.198976
$63$	0	0
$64$	1.69131	0.211413
$65$	0	0
$66$	−4.11817	−0.506912
$67$	−7.57559	−0.925505	−0.462753	−	0.886487i	$-0.653138\pi$
$67$	−7.57559	−0.925505	−0.462753	+	0.886487i	$0.653138\pi$
$68$	5.83747	0.707897
$69$	15.2273	1.83315
$70$	0	0
$71$	−7.22732	−0.857726	−0.428863	−	0.903370i	$-0.641086\pi$
$71$	−7.22732	−0.857726	−0.428863	+	0.903370i	$0.641086\pi$
$72$	−6.94662	−0.818668
$73$	−15.0125	−1.75708	−0.878542	−	0.477665i	$-0.841483\pi$
$73$	−15.0125	−1.75708	−0.878542	+	0.477665i	$0.841483\pi$
$74$	3.63537	0.422603
$75$	8.03424	0.927714
$76$	8.80948	1.01052
$77$	0	0
$78$	0	0
$79$	−9.30758	−1.04718	−0.523592	−	0.851969i	$-0.675408\pi$
$79$	−9.30758	−1.04718	−0.523592	+	0.851969i	$0.675408\pi$
$80$	−1.58310	−0.176996
$81$	−9.56546	−1.06283
$82$	−5.52973	−0.610656
$83$	−1.36463	−0.149788	−0.0748940	−	0.997192i	$-0.523862\pi$
$83$	−1.36463	−0.149788	−0.0748940	+	0.997192i	$0.523862\pi$
$84$	0	0
$85$	5.03424	0.546039
$86$	0.205780	0.0221898
$87$	−13.5170	−1.44918
$88$	−5.97829	−0.637288
$89$	−0.899698	−0.0953678	−0.0476839	−	0.998862i	$-0.515184\pi$
$89$	−0.899698	−0.0953678	−0.0476839	+	0.998862i	$0.515184\pi$
$90$	−2.56306	−0.270170
$91$	0	0
$92$	9.45742	0.986004
$93$	−5.31126	−0.550752
$94$	0.907052	0.0935553
$95$	7.59729	0.779466
$96$	−14.0559	−1.43458
$97$	15.6658	1.59062	0.795309	−	0.606205i	$-0.207309\pi$
$97$	15.6658	1.59062	0.795309	+	0.606205i	$0.207309\pi$
$98$	0	0
$99$	6.73701	0.677095
$100$	4.98992	0.498992
$101$	−0.684905	−0.0681506	−0.0340753	−	0.999419i	$-0.510849\pi$
$101$	−0.684905	−0.0681506	−0.0340753	+	0.999419i	$0.510849\pi$
$102$	6.67589	0.661012
$103$	−17.9249	−1.76619	−0.883097	−	0.469190i	$-0.844546\pi$
$103$	−17.9249	−1.76619	−0.883097	+	0.469190i	$0.844546\pi$
$104$	0	0
$105$	0	0
$106$	−9.67589	−0.939806
$107$	8.49549	0.821290	0.410645	−	0.911795i	$-0.365304\pi$
$107$	8.49549	0.821290	0.410645	+	0.911795i	$0.365304\pi$
$108$	−0.727766	−0.0700293
$109$	−12.0928	−1.15828	−0.579139	−	0.815228i	$-0.696611\pi$
$109$	−12.0928	−1.15828	−0.579139	+	0.815228i	$0.696611\pi$
$110$	−2.20578	−0.210313
$111$	−12.3239	−1.16974
$112$	0	0
$113$	−14.2527	−1.34078	−0.670391	−	0.742008i	$-0.733874\pi$
$113$	−14.2527	−1.34078	−0.670391	+	0.742008i	$0.733874\pi$
$114$	10.0748	0.943588
$115$	8.15608	0.760558
$116$	−8.39519	−0.779474
$117$	0	0
$118$	−2.86285	−0.263547
$119$	0	0
$120$	−7.71029	−0.703850
$121$	−5.20210	−0.472918
$122$	3.26801	0.295872
$123$	18.7459	1.69026
$124$	−3.29873	−0.296234
$125$	10.7519	0.961677
$126$	0	0
$127$	−8.82462	−0.783058	−0.391529	−	0.920166i	$-0.628054\pi$
$127$	−8.82462	−0.783058	−0.391529	+	0.920166i	$0.628054\pi$
$128$	−10.4736	−0.925747
$129$	−0.697596	−0.0614199
$130$	0	0
$131$	19.4294	1.69756	0.848778	−	0.528749i	$-0.177339\pi$
$131$	19.4294	1.69756	0.848778	+	0.528749i	$0.177339\pi$
$132$	8.67071	0.754689
$133$	0	0
$134$	−5.38084	−0.464834
$135$	−0.627626	−0.0540174
$136$	9.69131	0.831023
$137$	−10.2362	−0.874536	−0.437268	−	0.899331i	$-0.644054\pi$
$137$	−10.2362	−0.874536	−0.437268	+	0.899331i	$0.644054\pi$
$138$	10.8158	0.920699
$139$	−8.14723	−0.691039	−0.345519	−	0.938412i	$-0.612297\pi$
$139$	−8.14723	−0.691039	−0.345519	+	0.938412i	$0.612297\pi$
$140$	0	0
$141$	−3.07492	−0.258955
$142$	−5.13347	−0.430791
$143$	0	0
$144$	3.43438	0.286198
$145$	−7.24001	−0.601250
$146$	−10.6632	−0.882493
$147$	0	0
$148$	−7.65419	−0.629170
$149$	9.78888	0.801937	0.400968	−	0.916092i	$-0.368674\pi$
$149$	9.78888	0.801937	0.400968	+	0.916092i	$0.368674\pi$
$150$	5.70661	0.465943
$151$	−14.7407	−1.19958	−0.599790	−	0.800158i	$-0.704749\pi$
$151$	−14.7407	−1.19958	−0.599790	+	0.800158i	$0.704749\pi$
$152$	14.6254	1.18628
$153$	−10.9212	−0.882930
$154$	0	0
$155$	−2.84482	−0.228502
$156$	0	0
$157$	−20.5844	−1.64282	−0.821409	−	0.570340i	$-0.806811\pi$
$157$	−20.5844	−1.64282	−0.821409	+	0.570340i	$0.806811\pi$
$158$	−6.61105	−0.525947
$159$	32.8014	2.60132
$160$	−7.52866	−0.595193
$161$	0	0
$162$	−6.79422	−0.533804
$163$	3.98086	0.311805	0.155902	−	0.987772i	$-0.450171\pi$
$163$	3.98086	0.311805	0.155902	+	0.987772i	$0.450171\pi$
$164$	11.6427	0.909144
$165$	7.47763	0.582132
$166$	−0.969281	−0.0752308
$167$	8.67846	0.671559	0.335780	−	0.941941i	$-0.391000\pi$
$167$	8.67846	0.671559	0.335780	+	0.941941i	$0.391000\pi$
$168$	0	0
$169$	0	0
$170$	3.57575	0.274248
$171$	−16.4815	−1.26037
$172$	−0.433264	−0.0330361
$173$	−0.933934	−0.0710057	−0.0355028	−	0.999370i	$-0.511303\pi$
$173$	−0.933934	−0.0710057	−0.0355028	+	0.999370i	$0.511303\pi$
$174$	−9.60097	−0.727848
$175$	0	0
$176$	2.95564	0.222790
$177$	9.70511	0.729481
$178$	−0.639044	−0.0478984
$179$	13.5461	1.01248	0.506241	−	0.862392i	$-0.331034\pi$
$179$	13.5461	1.01248	0.506241	+	0.862392i	$0.331034\pi$
$180$	5.39646	0.402229
$181$	8.86269	0.658759	0.329379	−	0.944198i	$-0.393161\pi$
$181$	8.86269	0.658759	0.329379	+	0.944198i	$0.393161\pi$
$182$	0	0
$183$	−11.0786	−0.818953
$184$	15.7011	1.15750
$185$	−6.60097	−0.485313
$186$	−3.77252	−0.276614
$187$	−9.39887	−0.687313
$188$	−1.90978	−0.139285
$189$	0	0
$190$	5.39626	0.391486
$191$	−15.3735	−1.11239	−0.556193	−	0.831053i	$-0.687739\pi$
$191$	−15.3735	−1.11239	−0.556193	+	0.831053i	$0.687739\pi$
$192$	−4.07247	−0.293905
$193$	24.4953	1.76321	0.881606	−	0.471986i	$-0.156463\pi$
$193$	24.4953	1.76321	0.881606	+	0.471986i	$0.156463\pi$
$194$	11.1272	0.798885
$195$	0	0
$196$	0	0
$197$	6.71412	0.478362	0.239181	−	0.970975i	$-0.423121\pi$
$197$	6.71412	0.478362	0.239181	+	0.970975i	$0.423121\pi$
$198$	4.78521	0.340070
$199$	4.87282	0.345425	0.172712	−	0.984972i	$-0.444747\pi$
$199$	4.87282	0.345425	0.172712	+	0.984972i	$0.444747\pi$
$200$	8.28421	0.585782
$201$	18.2411	1.28663
$202$	−0.486479	−0.0342285
$203$	0	0
$204$	−14.0559	−0.984113
$205$	10.0407	0.701272
$206$	−12.7318	−0.887069
$207$	−17.6938	−1.22980
$208$	0	0
$209$	−14.1841	−0.981133
$210$	0	0
$211$	3.68747	0.253856	0.126928	−	0.991912i	$-0.459488\pi$
$211$	3.68747	0.253856	0.126928	+	0.991912i	$0.459488\pi$
$212$	20.3724	1.39918
$213$	17.4025	1.19240
$214$	6.03424	0.412492
$215$	−0.373647	−0.0254825
$216$	−1.20823	−0.0822096
$217$	0	0
$218$	−8.58935	−0.581744
$219$	36.1484	2.44268
$220$	4.64422	0.313113
$221$	0	0
$222$	−8.75354	−0.587499
$223$	8.81426	0.590247	0.295123	−	0.955459i	$-0.404639\pi$
$223$	8.81426	0.590247	0.295123	+	0.955459i	$0.404639\pi$
$224$	0	0
$225$	−9.33557	−0.622372
$226$	−10.1235	−0.673406
$227$	−13.4511	−0.892783	−0.446391	−	0.894838i	$-0.647291\pi$
$227$	−13.4511	−0.892783	−0.446391	+	0.894838i	$0.647291\pi$
$228$	−21.2122	−1.40481
$229$	6.81576	0.450398	0.225199	−	0.974313i	$-0.427697\pi$
$229$	6.81576	0.450398	0.225199	+	0.974313i	$0.427697\pi$
$230$	5.79316	0.381989
$231$	0	0
$232$	−13.9376	−0.915049
$233$	−25.0672	−1.64221	−0.821105	−	0.570777i	$-0.806642\pi$
$233$	−25.0672	−1.64221	−0.821105	+	0.570777i	$0.806642\pi$
$234$	0	0
$235$	−1.64699	−0.107438
$236$	6.02767	0.392368
$237$	22.4116	1.45579
$238$	0	0
$239$	2.78521	0.180160	0.0900800	−	0.995935i	$-0.471288\pi$
$239$	2.78521	0.180160	0.0900800	+	0.995935i	$0.471288\pi$
$240$	3.81193	0.246059
$241$	6.97829	0.449511	0.224756	−	0.974415i	$-0.427842\pi$
$241$	6.97829	0.449511	0.224756	+	0.974415i	$0.427842\pi$
$242$	−3.69498	−0.237523
$243$	21.5726	1.38388
$244$	−6.88072	−0.440493
$245$	0	0
$246$	13.3149	0.848929
$247$	0	0
$248$	−5.47651	−0.347759
$249$	3.28588	0.208234
$250$	7.63691	0.483001
$251$	0.783029	0.0494244	0.0247122	−	0.999695i	$-0.492133\pi$
$251$	0.783029	0.0494244	0.0247122	+	0.999695i	$0.492133\pi$
$252$	0	0
$253$	−15.2273	−0.957334
$254$	−6.26801	−0.393290
$255$	−12.1218	−0.759099
$256$	−10.8219	−0.676368
$257$	−3.25804	−0.203231	−0.101616	−	0.994824i	$-0.532401\pi$
$257$	−3.25804	−0.203231	−0.101616	+	0.994824i	$0.532401\pi$
$258$	−0.495493	−0.0308480
$259$	0	0
$260$	0	0
$261$	15.7064	0.972205
$262$	13.8005	0.852595
$263$	29.5829	1.82416	0.912081	−	0.410010i	$-0.134475\pi$
$263$	29.5829	1.82416	0.912081	+	0.410010i	$0.134475\pi$
$264$	14.3950	0.885953
$265$	17.5691	1.07926
$266$	0	0
$267$	2.16637	0.132580
$268$	11.3292	0.692043
$269$	−1.23650	−0.0753907	−0.0376953	−	0.999289i	$-0.512002\pi$
$269$	−1.23650	−0.0753907	−0.0376953	+	0.999289i	$0.512002\pi$
$270$	−0.445794	−0.0271302
$271$	25.2071	1.53122	0.765612	−	0.643303i	$-0.222436\pi$
$271$	25.2071	1.53122	0.765612	+	0.643303i	$0.222436\pi$
$272$	−4.79133	−0.290517
$273$	0	0
$274$	−7.27062	−0.439234
$275$	−8.03424	−0.484483
$276$	−22.7724	−1.37073
$277$	9.53602	0.572964	0.286482	−	0.958086i	$-0.407514\pi$
$277$	9.53602	0.572964	0.286482	+	0.958086i	$0.407514\pi$
$278$	−5.78687	−0.347073
$279$	6.17154	0.369481
$280$	0	0
$281$	−9.56546	−0.570628	−0.285314	−	0.958434i	$-0.592098\pi$
$281$	−9.56546	−0.570628	−0.285314	+	0.958434i	$0.592098\pi$
$282$	−2.18407	−0.130060
$283$	−11.4320	−0.679564	−0.339782	−	0.940504i	$-0.610353\pi$
$283$	−11.4320	−0.679564	−0.339782	+	0.940504i	$0.610353\pi$
$284$	10.8084	0.641361
$285$	−18.2934	−1.08361
$286$	0	0
$287$	0	0
$288$	16.3326	0.962410
$289$	−1.76366	−0.103745
$290$	−5.14249	−0.301977
$291$	−37.7213	−2.21126
$292$	22.4511	1.31385
$293$	−9.35562	−0.546561	−0.273281	−	0.961934i	$-0.588109\pi$
$293$	−9.35562	−0.546561	−0.273281	+	0.961934i	$0.588109\pi$
$294$	0	0
$295$	5.19826	0.302655
$296$	−12.7074	−0.738603
$297$	1.17177	0.0679931
$298$	6.95291	0.402771
$299$	0	0
$300$	−12.0151	−0.693695
$301$	0	0
$302$	−10.4701	−0.602487
$303$	1.64917	0.0947423
$304$	−7.23072	−0.414711
$305$	−5.93393	−0.339776
$306$	−7.75721	−0.443450
$307$	8.11449	0.463119	0.231559	−	0.972821i	$-0.425617\pi$
$307$	8.11449	0.463119	0.231559	+	0.972821i	$0.425617\pi$
$308$	0	0
$309$	43.1611	2.45535
$310$	−2.02064	−0.114765
$311$	8.64016	0.489938	0.244969	−	0.969531i	$-0.421222\pi$
$311$	8.64016	0.489938	0.244969	+	0.969531i	$0.421222\pi$
$312$	0	0
$313$	5.22732	0.295466	0.147733	−	0.989027i	$-0.452802\pi$
$313$	5.22732	0.295466	0.147733	+	0.989027i	$0.452802\pi$
$314$	−14.6209	−0.825103
$315$	0	0
$316$	13.9194	0.783029
$317$	−11.1929	−0.628657	−0.314329	−	0.949314i	$-0.601779\pi$
$317$	−11.1929	−0.628657	−0.314329	+	0.949314i	$0.601779\pi$
$318$	23.2984	1.30651
$319$	13.5170	0.756809
$320$	−2.18130	−0.121938
$321$	−20.4561	−1.14175
$322$	0	0
$323$	22.9936	1.27940
$324$	14.3051	0.794727
$325$	0	0
$326$	2.82755	0.156604
$327$	29.1180	1.61023
$328$	19.3291	1.06727
$329$	0	0
$330$	5.31126	0.292375
$331$	−20.0468	−1.10187	−0.550935	−	0.834548i	$-0.685729\pi$
$331$	−20.0468	−1.10187	−0.550935	+	0.834548i	$0.685729\pi$
$332$	2.04080	0.112003
$333$	14.3201	0.784737
$334$	6.16419	0.337290
$335$	9.77034	0.533811
$336$	0	0
$337$	18.5866	1.01248	0.506239	−	0.862393i	$-0.331035\pi$
$337$	18.5866	1.01248	0.506239	+	0.862393i	$0.331035\pi$
$338$	0	0
$339$	34.3188	1.86394
$340$	−7.52866	−0.408299
$341$	5.31126	0.287621
$342$	−11.7066	−0.633021
$343$	0	0
$344$	−0.719301	−0.0387821
$345$	−19.6389	−1.05732
$346$	−0.663361	−0.0356625
$347$	22.3417	1.19936	0.599681	−	0.800239i	$-0.295294\pi$
$347$	22.3417	1.19936	0.599681	+	0.800239i	$0.295294\pi$
$348$	20.2146	1.08362
$349$	8.78632	0.470321	0.235160	−	0.971957i	$-0.424438\pi$
$349$	8.78632	0.470321	0.235160	+	0.971957i	$0.424438\pi$
$350$	0	0
$351$	0	0
$352$	14.0559	0.749184
$353$	7.71898	0.410840	0.205420	−	0.978674i	$-0.434144\pi$
$353$	7.71898	0.410840	0.205420	+	0.978674i	$0.434144\pi$
$354$	6.89341	0.366381
$355$	9.32118	0.494717
$356$	1.34549	0.0713110
$357$	0	0
$358$	9.62161	0.508518
$359$	10.5956	0.559216	0.279608	−	0.960114i	$-0.409795\pi$
$359$	10.5956	0.559216	0.279608	+	0.960114i	$0.409795\pi$
$360$	8.95915	0.472189
$361$	15.7002	0.826324
$362$	6.29505	0.330861
$363$	12.5261	0.657447
$364$	0	0
$365$	19.3619	1.01345
$366$	−7.86898	−0.411318
$367$	−5.82067	−0.303836	−0.151918	−	0.988393i	$-0.548545\pi$
$367$	−5.82067	−0.303836	−0.151918	+	0.988393i	$0.548545\pi$
$368$	−7.76255	−0.404651
$369$	−21.7822	−1.13394
$370$	−4.68858	−0.243748
$371$	0	0
$372$	7.94295	0.411823
$373$	26.0569	1.34917	0.674587	−	0.738195i	$-0.264322\pi$
$373$	26.0569	1.34917	0.674587	+	0.738195i	$0.264322\pi$
$374$	−6.67589	−0.345202
$375$	−25.8893	−1.33692
$376$	−3.17059	−0.163511
$377$	0	0
$378$	0	0
$379$	−15.6532	−0.804053	−0.402026	−	0.915628i	$-0.631694\pi$
$379$	−15.6532	−0.804053	−0.402026	+	0.915628i	$0.631694\pi$
$380$	−11.3617	−0.582843
$381$	21.2486	1.08860
$382$	−10.9196	−0.558694
$383$	−12.5588	−0.641724	−0.320862	−	0.947126i	$-0.603973\pi$
$383$	−12.5588	−0.641724	−0.320862	+	0.947126i	$0.603973\pi$
$384$	25.2193	1.28696
$385$	0	0
$386$	17.3987	0.885571
$387$	0.810588	0.0412045
$388$	−23.4280	−1.18938
$389$	−0.503007	−0.0255035	−0.0127517	−	0.999919i	$-0.504059\pi$
$389$	−0.503007	−0.0255035	−0.0127517	+	0.999919i	$0.504059\pi$
$390$	0	0
$391$	24.6847	1.24836
$392$	0	0
$393$	−46.7838	−2.35993
$394$	4.76895	0.240256
$395$	12.0041	0.603992
$396$	−10.0751	−0.506295
$397$	−2.35044	−0.117965	−0.0589827	−	0.998259i	$-0.518786\pi$
$397$	−2.35044	−0.117965	−0.0589827	+	0.998259i	$0.518786\pi$
$398$	3.46110	0.173489
$399$	0	0
$400$	−4.09567	−0.204784
$401$	34.6046	1.72807	0.864037	−	0.503429i	$-0.167928\pi$
$401$	34.6046	1.72807	0.864037	+	0.503429i	$0.167928\pi$
$402$	12.9564	0.646208
$403$	0	0
$404$	1.02427	0.0509593
$405$	12.3367	0.613016
$406$	0	0
$407$	12.3239	0.610875
$408$	−23.3355	−1.15528
$409$	−8.02411	−0.396767	−0.198383	−	0.980125i	$-0.563569\pi$
$409$	−8.02411	−0.396767	−0.198383	+	0.980125i	$0.563569\pi$
$410$	7.13176	0.352213
$411$	24.6475	1.21577
$412$	26.8066	1.32067
$413$	0	0
$414$	−12.5676	−0.617666
$415$	1.75999	0.0863943
$416$	0	0
$417$	19.6176	0.960676
$418$	−10.0748	−0.492773
$419$	11.6694	0.570090	0.285045	−	0.958514i	$-0.407992\pi$
$419$	11.6694	0.570090	0.285045	+	0.958514i	$0.407992\pi$
$420$	0	0
$421$	18.3381	0.893746	0.446873	−	0.894597i	$-0.352538\pi$
$421$	18.3381	0.893746	0.446873	+	0.894597i	$0.352538\pi$
$422$	2.61916	0.127499
$423$	3.57298	0.173724
$424$	33.8220	1.64254
$425$	13.0242	0.631764
$426$	12.3608	0.598882
$427$	0	0
$428$	−12.7049	−0.614117
$429$	0	0
$430$	−0.265397	−0.0127986
$431$	31.2435	1.50495	0.752474	−	0.658622i	$-0.228860\pi$
$431$	31.2435	1.50495	0.752474	+	0.658622i	$0.228860\pi$
$432$	0.597343	0.0287397
$433$	30.5513	1.46820	0.734100	−	0.679041i	$-0.237604\pi$
$433$	30.5513	1.46820	0.734100	+	0.679041i	$0.237604\pi$
$434$	0	0
$435$	17.4331	0.835853
$436$	18.0847	0.866099
$437$	37.2524	1.78202
$438$	25.6757	1.22683
$439$	12.1472	0.579756	0.289878	−	0.957064i	$-0.406385\pi$
$439$	12.1472	0.579756	0.289878	+	0.957064i	$0.406385\pi$
$440$	7.71029	0.367573
$441$	0	0
$442$	0	0
$443$	−8.46532	−0.402200	−0.201100	−	0.979571i	$-0.564452\pi$
$443$	−8.46532	−0.402200	−0.201100	+	0.979571i	$0.564452\pi$
$444$	18.4304	0.874667
$445$	1.16035	0.0550060
$446$	6.26065	0.296451
$447$	−23.5705	−1.11485
$448$	0	0
$449$	23.3264	1.10084	0.550420	−	0.834888i	$-0.314467\pi$
$449$	23.3264	1.10084	0.550420	+	0.834888i	$0.314467\pi$
$450$	−6.63093	−0.312585
$451$	−18.7459	−0.882708
$452$	21.3148	1.00256
$453$	35.4938	1.66765
$454$	−9.55416	−0.448399
$455$	0	0
$456$	−35.2162	−1.64915
$457$	−15.4866	−0.724434	−0.362217	−	0.932094i	$-0.617980\pi$
$457$	−15.4866	−0.724434	−0.362217	+	0.932094i	$0.617980\pi$
$458$	4.84115	0.226212
$459$	−1.89954	−0.0886628
$460$	−12.1974	−0.568705
$461$	−9.28204	−0.432308	−0.216154	−	0.976359i	$-0.569351\pi$
$461$	−9.28204	−0.432308	−0.216154	+	0.976359i	$0.569351\pi$
$462$	0	0
$463$	−28.8283	−1.33976	−0.669882	−	0.742467i	$-0.733655\pi$
$463$	−28.8283	−1.33976	−0.669882	+	0.742467i	$0.733655\pi$
$464$	6.89068	0.319892
$465$	6.85000	0.317661
$466$	−17.8049	−0.824797
$467$	2.87393	0.132990	0.0664948	−	0.997787i	$-0.478818\pi$
$467$	2.87393	0.132990	0.0664948	+	0.997787i	$0.478818\pi$
$468$	0	0
$469$	0	0
$470$	−1.16984	−0.0539606
$471$	49.5649	2.28383
$472$	10.0071	0.460613
$473$	0.697596	0.0320755
$474$	15.9186	0.731167
$475$	19.6551	0.901837
$476$	0	0
$477$	−38.1144	−1.74514
$478$	1.97829	0.0904851
$479$	−22.6082	−1.03299	−0.516497	−	0.856289i	$-0.672764\pi$
$479$	−22.6082	−1.03299	−0.516497	+	0.856289i	$0.672764\pi$
$480$	18.1281	0.827432
$481$	0	0
$482$	4.95659	0.225766
$483$	0	0
$484$	7.77971	0.353623
$485$	−20.2043	−0.917432
$486$	15.3227	0.695053
$487$	−2.86803	−0.129963	−0.0649814	−	0.997886i	$-0.520699\pi$
$487$	−2.86803	−0.129963	−0.0649814	+	0.997886i	$0.520699\pi$
$488$	−11.4233	−0.517108
$489$	−9.58544	−0.433469
$490$	0	0
$491$	−22.7201	−1.02534	−0.512672	−	0.858585i	$-0.671344\pi$
$491$	−22.7201	−1.02534	−0.512672	+	0.858585i	$0.671344\pi$
$492$	−28.0343	−1.26388
$493$	−21.9122	−0.986877
$494$	0	0
$495$	−8.68881	−0.390533
$496$	2.70756	0.121573
$497$	0	0
$498$	2.33391	0.104585
$499$	18.0151	0.806466	0.403233	−	0.915097i	$-0.367886\pi$
$499$	18.0151	0.806466	0.403233	+	0.915097i	$0.367886\pi$
$500$	−16.0794	−0.719091
$501$	−20.8967	−0.933596
$502$	0.556175	0.0248233
$503$	31.1496	1.38889	0.694447	−	0.719544i	$-0.255649\pi$
$503$	31.1496	1.38889	0.694447	+	0.719544i	$0.255649\pi$
$504$	0	0
$505$	0.883331	0.0393077
$506$	−10.8158	−0.480819
$507$	0	0
$508$	13.1972	0.585529
$509$	−39.5018	−1.75089	−0.875444	−	0.483319i	$-0.839431\pi$
$509$	−39.5018	−1.75089	−0.875444	+	0.483319i	$0.839431\pi$
$510$	−8.60999	−0.381257
$511$	0	0
$512$	13.2606	0.586042
$513$	−2.86664	−0.126565
$514$	−2.31414	−0.102073
$515$	23.1180	1.01870
$516$	1.04325	0.0459265
$517$	3.07492	0.135235
$518$	0	0
$519$	2.24880	0.0987115
$520$	0	0
$521$	17.7672	0.778394	0.389197	−	0.921155i	$-0.372753\pi$
$521$	17.7672	0.778394	0.389197	+	0.921155i	$0.372753\pi$
$522$	11.1561	0.488288
$523$	1.78904	0.0782294	0.0391147	−	0.999235i	$-0.487546\pi$
$523$	1.78904	0.0782294	0.0391147	+	0.999235i	$0.487546\pi$
$524$	−29.0566	−1.26934
$525$	0	0
$526$	21.0124	0.916183
$527$	−8.60999	−0.375057
$528$	−7.11683	−0.309720
$529$	16.9923	0.738797
$530$	12.4791	0.542059
$531$	−11.2771	−0.489384
$532$	0	0
$533$	0	0
$534$	1.53874	0.0665879
$535$	−10.9568	−0.473702
$536$	18.8087	0.812412
$537$	−32.6174	−1.40754
$538$	−0.878269	−0.0378649
$539$	0	0
$540$	0.938610	0.0403913
$541$	−15.4027	−0.662214	−0.331107	−	0.943593i	$-0.607422\pi$
$541$	−15.4027	−0.662214	−0.331107	+	0.943593i	$0.607422\pi$
$542$	17.9043	0.769055
$543$	−21.3403	−0.915801
$544$	−22.7858	−0.976935
$545$	15.5962	0.668069
$546$	0	0
$547$	−3.96944	−0.169721	−0.0848605	−	0.996393i	$-0.527044\pi$
$547$	−3.96944	−0.169721	−0.0848605	+	0.996393i	$0.527044\pi$
$548$	15.3081	0.653931
$549$	12.8730	0.549408
$550$	−5.70661	−0.243331
$551$	−33.0683	−1.40876
$552$	−37.8064	−1.60915
$553$	0	0
$554$	6.77331	0.287770
$555$	15.8944	0.674678
$556$	12.1841	0.516722
$557$	−18.6901	−0.791924	−0.395962	−	0.918267i	$-0.629589\pi$
$557$	−18.6901	−0.791924	−0.395962	+	0.918267i	$0.629589\pi$
$558$	4.38357	0.185571
$559$	0	0
$560$	0	0
$561$	22.6314	0.955497
$562$	−6.79422	−0.286597
$563$	−36.3059	−1.53011	−0.765056	−	0.643964i	$-0.777289\pi$
$563$	−36.3059	−1.53011	−0.765056	+	0.643964i	$0.777289\pi$
$564$	4.59852	0.193633
$565$	18.3819	0.773333
$566$	−8.12002	−0.341310
$567$	0	0
$568$	17.9440	0.752914
$569$	10.9760	0.460136	0.230068	−	0.973175i	$-0.426105\pi$
$569$	10.9760	0.460136	0.230068	+	0.973175i	$0.426105\pi$
$570$	−12.9936	−0.544240
$571$	31.3363	1.31138	0.655692	−	0.755028i	$-0.272377\pi$
$571$	31.3363	1.31138	0.655692	+	0.755028i	$0.272377\pi$
$572$	0	0
$573$	37.0175	1.54643
$574$	0	0
$575$	21.1007	0.879962
$576$	4.73210	0.197171
$577$	−42.7876	−1.78127	−0.890636	−	0.454717i	$-0.849740\pi$
$577$	−42.7876	−1.78127	−0.890636	+	0.454717i	$0.849740\pi$
$578$	−1.25271	−0.0521057
$579$	−58.9819	−2.45120
$580$	10.8274	0.449583
$581$	0	0
$582$	−26.7929	−1.11060
$583$	−32.8014	−1.35850
$584$	37.2731	1.54237
$585$	0	0
$586$	−6.64517	−0.274509
$587$	−38.7886	−1.60098	−0.800488	−	0.599349i	$-0.795426\pi$
$587$	−38.7886	−1.60098	−0.800488	+	0.599349i	$0.795426\pi$
$588$	0	0
$589$	−12.9936	−0.535390
$590$	3.69226	0.152008
$591$	−16.1668	−0.665014
$592$	6.28247	0.258208
$593$	−29.9564	−1.23016	−0.615081	−	0.788464i	$-0.710877\pi$
$593$	−29.9564	−1.23016	−0.615081	+	0.788464i	$0.710877\pi$
$594$	0.832293	0.0341494
$595$	0	0
$596$	−14.6392	−0.599645
$597$	−11.7332	−0.480207
$598$	0	0
$599$	41.2539	1.68559	0.842794	−	0.538236i	$-0.180909\pi$
$599$	41.2539	1.68559	0.842794	+	0.538236i	$0.180909\pi$
$600$	−19.9474	−0.814350
$601$	−6.61089	−0.269664	−0.134832	−	0.990868i	$-0.543049\pi$
$601$	−6.61089	−0.269664	−0.134832	+	0.990868i	$0.543049\pi$
$602$	0	0
$603$	−21.1957	−0.863156
$604$	22.0446	0.896982
$605$	6.70922	0.272769
$606$	1.17138	0.0475842
$607$	20.8832	0.847622	0.423811	−	0.905751i	$-0.360692\pi$
$607$	20.8832	0.847622	0.423811	+	0.905751i	$0.360692\pi$
$608$	−34.3867	−1.39456
$609$	0	0
$610$	−4.21479	−0.170652
$611$	0	0
$612$	16.3326	0.660208
$613$	4.29655	0.173536	0.0867680	−	0.996229i	$-0.472346\pi$
$613$	4.29655	0.173536	0.0867680	+	0.996229i	$0.472346\pi$
$614$	5.76362	0.232601
$615$	−24.1768	−0.974902
$616$	0	0
$617$	30.7380	1.23746	0.618732	−	0.785602i	$-0.287647\pi$
$617$	30.7380	1.23746	0.618732	+	0.785602i	$0.287647\pi$
$618$	30.6568	1.23320
$619$	−20.6417	−0.829658	−0.414829	−	0.909899i	$-0.636159\pi$
$619$	−20.6417	−0.829658	−0.414829	+	0.909899i	$0.636159\pi$
$620$	4.25441	0.170861
$621$	−3.07748	−0.123495
$622$	6.13699	0.246071
$623$	0	0
$624$	0	0
$625$	2.81636	0.112654
$626$	3.71290	0.148397
$627$	34.1536	1.36396
$628$	30.7839	1.22841
$629$	−19.9781	−0.796580
$630$	0	0
$631$	−29.3366	−1.16787	−0.583937	−	0.811799i	$-0.698488\pi$
$631$	−29.3366	−1.16787	−0.583937	+	0.811799i	$0.698488\pi$
$632$	23.1089	0.919222
$633$	−8.87899	−0.352908
$634$	−7.95019	−0.315742
$635$	11.3812	0.451650
$636$	−49.0543	−1.94513
$637$	0	0
$638$	9.60097	0.380106
$639$	−20.2213	−0.799943
$640$	13.5080	0.533950
$641$	−4.01680	−0.158654	−0.0793271	−	0.996849i	$-0.525277\pi$
$641$	−4.01680	−0.158654	−0.0793271	+	0.996849i	$0.525277\pi$
$642$	−14.5297	−0.573443
$643$	−6.87282	−0.271037	−0.135519	−	0.990775i	$-0.543270\pi$
$643$	−6.87282	−0.271037	−0.135519	+	0.990775i	$0.543270\pi$
$644$	0	0
$645$	0.899698	0.0354256
$646$	16.3320	0.642574
$647$	33.7431	1.32658	0.663289	−	0.748363i	$-0.269160\pi$
$647$	33.7431	1.32658	0.663289	+	0.748363i	$0.269160\pi$
$648$	23.7491	0.932955
$649$	−9.70511	−0.380959
$650$	0	0
$651$	0	0
$652$	−5.95335	−0.233151
$653$	32.4002	1.26792	0.633958	−	0.773367i	$-0.281429\pi$
$653$	32.4002	1.26792	0.633958	+	0.773367i	$0.281429\pi$
$654$	20.6821	0.808735
$655$	−25.0584	−0.979112
$656$	−9.55622	−0.373108
$657$	−42.0035	−1.63871
$658$	0	0
$659$	4.01035	0.156221	0.0781106	−	0.996945i	$-0.475111\pi$
$659$	4.01035	0.156221	0.0781106	+	0.996945i	$0.475111\pi$
$660$	−11.1827	−0.435287
$661$	−1.81794	−0.0707097	−0.0353549	−	0.999375i	$-0.511256\pi$
$661$	−1.81794	−0.0707097	−0.0353549	+	0.999375i	$0.511256\pi$
$662$	−14.2389	−0.553412
$663$	0	0
$664$	3.38811	0.131484
$665$	0	0
$666$	10.1714	0.394133
$667$	−35.5005	−1.37459
$668$	−12.9786	−0.502156
$669$	−21.2237	−0.820556
$670$	6.93974	0.268106
$671$	11.0786	0.427684
$672$	0	0
$673$	−22.9743	−0.885594	−0.442797	−	0.896622i	$-0.646014\pi$
$673$	−22.9743	−0.885594	−0.442797	+	0.896622i	$0.646014\pi$
$674$	13.2018	0.508515
$675$	−1.62374	−0.0624978
$676$	0	0
$677$	−38.0276	−1.46152	−0.730760	−	0.682634i	$-0.760834\pi$
$677$	−38.0276	−1.46152	−0.730760	+	0.682634i	$0.760834\pi$
$678$	24.3762	0.936163
$679$	0	0
$680$	−12.4990	−0.479315
$681$	32.3887	1.24114
$682$	3.77252	0.144457
$683$	40.7786	1.56035	0.780176	−	0.625560i	$-0.215130\pi$
$683$	40.7786	1.56035	0.780176	+	0.625560i	$0.215130\pi$
$684$	24.6480	0.942440
$685$	13.2017	0.504412
$686$	0	0
$687$	−16.4116	−0.626140
$688$	0.355619	0.0135578
$689$	0	0
$690$	−13.9492	−0.531038
$691$	−3.12868	−0.119021	−0.0595104	−	0.998228i	$-0.518954\pi$
$691$	−3.12868	−0.119021	−0.0595104	+	0.998228i	$0.518954\pi$
$692$	1.39669	0.0530942
$693$	0	0
$694$	15.8690	0.602378
$695$	10.5076	0.398576
$696$	33.5601	1.27209
$697$	30.3886	1.15105
$698$	6.24080	0.236218
$699$	60.3590	2.28299
$700$	0	0
$701$	9.61382	0.363109	0.181555	−	0.983381i	$-0.441887\pi$
$701$	9.61382	0.363109	0.181555	+	0.983381i	$0.441887\pi$
$702$	0	0
$703$	−30.1495	−1.13711
$704$	4.07247	0.153487
$705$	3.96576	0.149359
$706$	5.48269	0.206344
$707$	0	0
$708$	−14.5139	−0.545467
$709$	−28.1294	−1.05642	−0.528211	−	0.849113i	$-0.677137\pi$
$709$	−28.1294	−1.05642	−0.528211	+	0.849113i	$0.677137\pi$
$710$	6.62071	0.248471
$711$	−26.0417	−0.976638
$712$	2.23377	0.0837142
$713$	−13.9492	−0.522403
$714$	0	0
$715$	0	0
$716$	−20.2581	−0.757080
$717$	−6.70645	−0.250457
$718$	7.52594	0.280865
$719$	−24.9044	−0.928779	−0.464389	−	0.885631i	$-0.653726\pi$
$719$	−24.9044	−0.928779	−0.464389	+	0.885631i	$0.653726\pi$
$720$	−4.42936	−0.165073
$721$	0	0
$722$	11.1516	0.415020
$723$	−16.8029	−0.624907
$724$	−13.2541	−0.492584
$725$	−18.7308	−0.695643
$726$	8.89709	0.330202
$727$	24.2120	0.897974	0.448987	−	0.893538i	$-0.351785\pi$
$727$	24.2120	0.897974	0.448987	+	0.893538i	$0.351785\pi$
$728$	0	0
$729$	−23.2479	−0.861032
$730$	13.7525	0.509002
$731$	−1.13086	−0.0418264
$732$	16.5680	0.612369
$733$	−12.3989	−0.457963	−0.228981	−	0.973431i	$-0.573539\pi$
$733$	−12.3989	−0.457963	−0.228981	+	0.973431i	$0.573539\pi$
$734$	−4.13434	−0.152601
$735$	0	0
$736$	−36.9159	−1.36074
$737$	−18.2411	−0.671921
$738$	−15.4716	−0.569518
$739$	10.9604	0.403184	0.201592	−	0.979470i	$-0.435388\pi$
$739$	10.9604	0.403184	0.201592	+	0.979470i	$0.435388\pi$
$740$	9.87170	0.362891
$741$	0	0
$742$	0	0
$743$	−40.6925	−1.49286	−0.746431	−	0.665463i	$-0.768234\pi$
$743$	−40.6925	−1.49286	−0.746431	+	0.665463i	$0.768234\pi$
$744$	13.1868	0.483452
$745$	−12.6249	−0.462539
$746$	18.5079	0.677621
$747$	−3.81810	−0.139697
$748$	14.0559	0.513936
$749$	0	0
$750$	−18.3888	−0.671464
$751$	9.40472	0.343183	0.171592	−	0.985168i	$-0.445109\pi$
$751$	9.40472	0.343183	0.171592	+	0.985168i	$0.445109\pi$
$752$	1.56753	0.0571618
$753$	−1.88544	−0.0687093
$754$	0	0
$755$	19.0113	0.691890
$756$	0	0
$757$	−29.5808	−1.07513	−0.537566	−	0.843222i	$-0.680656\pi$
$757$	−29.5808	−1.07513	−0.537566	+	0.843222i	$0.680656\pi$
$758$	−11.1183	−0.403834
$759$	36.6656	1.33088
$760$	−18.8626	−0.684218
$761$	16.9417	0.614137	0.307068	−	0.951687i	$-0.400652\pi$
$761$	16.9417	0.614137	0.307068	+	0.951687i	$0.400652\pi$
$762$	15.0926	0.546748
$763$	0	0
$764$	22.9909	0.831783
$765$	14.0853	0.509254
$766$	−8.92034	−0.322305
$767$	0	0
$768$	26.0578	0.940281
$769$	7.36574	0.265616	0.132808	−	0.991142i	$-0.457601\pi$
$769$	7.36574	0.265616	0.132808	+	0.991142i	$0.457601\pi$
$770$	0	0
$771$	7.84498	0.282530
$772$	−36.6326	−1.31844
$773$	−44.7734	−1.61039	−0.805194	−	0.593012i	$-0.797939\pi$
$773$	−44.7734	−1.61039	−0.805194	+	0.593012i	$0.797939\pi$
$774$	0.575750	0.0206949
$775$	−7.35989	−0.264375
$776$	−38.8950	−1.39625
$777$	0	0
$778$	−0.357279	−0.0128091
$779$	45.8602	1.64311
$780$	0	0
$781$	−17.4025	−0.622712
$782$	17.5332	0.626988
$783$	2.73183	0.0976277
$784$	0	0
$785$	26.5480	0.947540
$786$	−33.2299	−1.18527
$787$	−18.7682	−0.669016	−0.334508	−	0.942393i	$-0.608570\pi$
$787$	−18.7682	−0.669016	−0.334508	+	0.942393i	$0.608570\pi$
$788$	−10.0409	−0.357693
$789$	−71.2322	−2.53594
$790$	8.52636	0.303354
$791$	0	0
$792$	−16.7267	−0.594356
$793$	0	0
$794$	−1.66949	−0.0592479
$795$	−42.3044	−1.50038
$796$	−7.28726	−0.258290
$797$	−7.21697	−0.255638	−0.127819	−	0.991797i	$-0.540798\pi$
$797$	−7.21697	−0.255638	−0.127819	+	0.991797i	$0.540798\pi$
$798$	0	0
$799$	−4.98470	−0.176346
$800$	−19.4775	−0.688635
$801$	−2.51726	−0.0889431
$802$	24.5792	0.867922
$803$	−36.1484	−1.27565
$804$	−27.2795	−0.962073
$805$	0	0
$806$	0	0
$807$	2.97734	0.104807
$808$	1.70048	0.0598228
$809$	14.8318	0.521459	0.260729	−	0.965412i	$-0.416037\pi$
$809$	14.8318	0.521459	0.260729	+	0.965412i	$0.416037\pi$
$810$	8.76260	0.307886
$811$	18.5831	0.652541	0.326271	−	0.945276i	$-0.394208\pi$
$811$	18.5831	0.652541	0.326271	+	0.945276i	$0.394208\pi$
$812$	0	0
$813$	−60.6958	−2.12869
$814$	8.75354	0.306811
$815$	−5.13417	−0.179842
$816$	11.5370	0.403875
$817$	−1.70661	−0.0597067
$818$	−5.69942	−0.199275
$819$	0	0
$820$	−15.0158	−0.524374
$821$	26.6236	0.929169	0.464585	−	0.885529i	$-0.346204\pi$
$821$	26.6236	0.929169	0.464585	+	0.885529i	$0.346204\pi$
$822$	17.5068	0.610620
$823$	6.75136	0.235338	0.117669	−	0.993053i	$-0.462458\pi$
$823$	6.75136	0.235338	0.117669	+	0.993053i	$0.462458\pi$
$824$	44.5040	1.55037
$825$	19.3455	0.673524
$826$	0	0
$827$	21.7430	0.756079	0.378039	−	0.925789i	$-0.376598\pi$
$827$	21.7430	0.756079	0.378039	+	0.925789i	$0.376598\pi$
$828$	26.4609	0.919579
$829$	14.6216	0.507828	0.253914	−	0.967227i	$-0.418282\pi$
$829$	14.6216	0.507828	0.253914	+	0.967227i	$0.418282\pi$
$830$	1.25009	0.0433914
$831$	−22.9616	−0.796529
$832$	0	0
$833$	0	0
$834$	13.9341	0.482498
$835$	−11.1927	−0.387340
$836$	21.2122	0.733639
$837$	1.07342	0.0371028
$838$	8.28865	0.286327
$839$	−10.7469	−0.371023	−0.185511	−	0.982642i	$-0.559394\pi$
$839$	−10.7469	−0.371023	−0.185511	+	0.982642i	$0.559394\pi$
$840$	0	0
$841$	2.51320	0.0866620
$842$	13.0253	0.448883
$843$	23.0325	0.793282
$844$	−5.51458	−0.189820
$845$	0	0
$846$	2.53784	0.0872527
$847$	0	0
$848$	−16.7214	−0.574216
$849$	27.5270	0.944724
$850$	9.25088	0.317303
$851$	−32.3670	−1.10953
$852$	−26.0254	−0.891615
$853$	−31.7709	−1.08782	−0.543908	−	0.839145i	$-0.683056\pi$
$853$	−31.7709	−1.08782	−0.543908	+	0.839145i	$0.683056\pi$
$854$	0	0
$855$	21.2564	0.726955
$856$	−21.0926	−0.720931
$857$	0.648105	0.0221388	0.0110694	−	0.999939i	$-0.496476\pi$
$857$	0.648105	0.0221388	0.0110694	+	0.999939i	$0.496476\pi$
$858$	0	0
$859$	43.1902	1.47363	0.736815	−	0.676095i	$-0.236329\pi$
$859$	43.1902	1.47363	0.736815	+	0.676095i	$0.236329\pi$
$860$	0.558787	0.0190545
$861$	0	0
$862$	22.1919	0.755858
$863$	−21.6094	−0.735592	−0.367796	−	0.929906i	$-0.619888\pi$
$863$	−21.6094	−0.735592	−0.367796	+	0.929906i	$0.619888\pi$
$864$	2.84074	0.0966441
$865$	1.20451	0.0409545
$866$	21.7002	0.737401
$867$	4.24669	0.144225
$868$	0	0
$869$	−22.4116	−0.760260
$870$	12.3825	0.419806
$871$	0	0
$872$	30.0240	1.01674
$873$	43.8312	1.48346
$874$	26.4599	0.895018
$875$	0	0
$876$	−54.0597	−1.82651
$877$	0.880766	0.0297413	0.0148707	−	0.999889i	$-0.495266\pi$
$877$	0.880766	0.0297413	0.0148707	+	0.999889i	$0.495266\pi$
$878$	8.62801	0.291181
$879$	22.5272	0.759825
$880$	−3.81193	−0.128500
$881$	0.140035	0.00471791	0.00235895	−	0.999997i	$-0.499249\pi$
$881$	0.140035	0.00471791	0.00235895	+	0.999997i	$0.499249\pi$
$882$	0	0
$883$	−18.8253	−0.633522	−0.316761	−	0.948505i	$-0.602595\pi$
$883$	−18.8253	−0.633522	−0.316761	+	0.948505i	$0.602595\pi$
$884$	0	0
$885$	−12.5168	−0.420748
$886$	−6.01281	−0.202004
$887$	33.3010	1.11814	0.559069	−	0.829121i	$-0.311159\pi$
$887$	33.3010	1.11814	0.559069	+	0.829121i	$0.311159\pi$
$888$	30.5979	1.02680
$889$	0	0
$890$	0.824183	0.0276267
$891$	−23.0325	−0.771618
$892$	−13.1817	−0.441355
$893$	−7.52254	−0.251732
$894$	−16.7418	−0.559929
$895$	−17.4706	−0.583977
$896$	0	0
$897$	0	0
$898$	16.5684	0.552896
$899$	12.3825	0.412980
$900$	13.9613	0.465376
$901$	53.1738	1.77148
$902$	−13.3149	−0.443339
$903$	0	0
$904$	35.3866	1.17694
$905$	−11.4303	−0.379957
$906$	25.2108	0.837573
$907$	11.5870	0.384740	0.192370	−	0.981322i	$-0.438383\pi$
$907$	11.5870	0.384740	0.192370	+	0.981322i	$0.438383\pi$
$908$	20.1161	0.667575
$909$	−1.91629	−0.0635594
$910$	0	0
$911$	52.5489	1.74102	0.870512	−	0.492147i	$-0.163788\pi$
$911$	52.5489	1.74102	0.870512	+	0.492147i	$0.163788\pi$
$912$	17.4107	0.576527
$913$	−3.28588	−0.108747
$914$	−11.0000	−0.363846
$915$	14.2882	0.472354
$916$	−10.1929	−0.336784
$917$	0	0
$918$	−1.34922	−0.0445308
$919$	−20.0534	−0.661502	−0.330751	−	0.943718i	$-0.607302\pi$
$919$	−20.0534	−0.661502	−0.330751	+	0.943718i	$0.607302\pi$
$920$	−20.2499	−0.667621
$921$	−19.5387	−0.643823
$922$	−6.59291	−0.217126
$923$	0	0
$924$	0	0
$925$	−17.0775	−0.561504
$926$	−20.4764	−0.672895
$927$	−50.1521	−1.64721
$928$	32.7696	1.07571
$929$	−15.9085	−0.521941	−0.260971	−	0.965347i	$-0.584043\pi$
$929$	−15.9085	−0.521941	−0.260971	+	0.965347i	$0.584043\pi$
$930$	4.86546	0.159545
$931$	0	0
$932$	37.4879	1.22796
$933$	−20.8045	−0.681108
$934$	2.04131	0.0667938
$935$	12.1218	0.396427
$936$	0	0
$937$	−26.1978	−0.855846	−0.427923	−	0.903815i	$-0.640755\pi$
$937$	−26.1978	−0.855846	−0.427923	+	0.903815i	$0.640755\pi$
$938$	0	0
$939$	−12.5868	−0.410754
$940$	2.46307	0.0803364
$941$	−36.3059	−1.18354	−0.591769	−	0.806108i	$-0.701570\pi$
$941$	−36.3059	−1.18354	−0.591769	+	0.806108i	$0.701570\pi$
$942$	35.2053	1.14705
$943$	49.2332	1.60325
$944$	−4.94745	−0.161026
$945$	0	0
$946$	0.495493	0.0161099
$947$	0.918839	0.0298582	0.0149291	−	0.999889i	$-0.495248\pi$
$947$	0.918839	0.0298582	0.0149291	+	0.999889i	$0.495248\pi$
$948$	−33.5163	−1.08856
$949$	0	0
$950$	13.9607	0.452946
$951$	26.9513	0.873954
$952$	0	0
$953$	−18.3589	−0.594702	−0.297351	−	0.954768i	$-0.596103\pi$
$953$	−18.3589	−0.594702	−0.297351	+	0.954768i	$0.596103\pi$
$954$	−27.0721	−0.876493
$955$	19.8274	0.641599
$956$	−4.16526	−0.134714
$957$	−32.5474	−1.05211
$958$	−16.0583	−0.518819
$959$	0	0
$960$	5.25232	0.169518
$961$	−26.1345	−0.843050
$962$	0	0
$963$	23.7695	0.765962
$964$	−10.4360	−0.336121
$965$	−31.5920	−1.01698
$966$	0	0
$967$	−12.5923	−0.404940	−0.202470	−	0.979288i	$-0.564897\pi$
$967$	−12.5923	−0.404940	−0.202470	+	0.979288i	$0.564897\pi$
$968$	12.9158	0.415129
$969$	−55.3658	−1.77860
$970$	−14.3509	−0.460779
$971$	21.3308	0.684537	0.342269	−	0.939602i	$-0.388805\pi$
$971$	21.3308	0.684537	0.342269	+	0.939602i	$0.388805\pi$
$972$	−32.2617	−1.03479
$973$	0	0
$974$	−2.03712	−0.0652736
$975$	0	0
$976$	5.64762	0.180776
$977$	42.4279	1.35739	0.678695	−	0.734420i	$-0.262546\pi$
$977$	42.4279	1.35739	0.678695	+	0.734420i	$0.262546\pi$
$978$	−6.80841	−0.217709
$979$	−2.16637	−0.0692374
$980$	0	0
$981$	−33.8344	−1.08025
$982$	−16.1378	−0.514977
$983$	2.09758	0.0669023	0.0334511	−	0.999440i	$-0.489350\pi$
$983$	2.09758	0.0669023	0.0334511	+	0.999440i	$0.489350\pi$
$984$	−46.5423	−1.48371
$985$	−8.65930	−0.275908
$986$	−15.5640	−0.495658
$987$	0	0
$988$	0	0
$989$	−1.83213	−0.0582584
$990$	−6.17154	−0.196145
$991$	−27.6349	−0.877851	−0.438926	−	0.898523i	$-0.644641\pi$
$991$	−27.6349	−0.877851	−0.438926	+	0.898523i	$0.644641\pi$
$992$	12.8762	0.408819
$993$	48.2703	1.53181
$994$	0	0
$995$	−6.28454	−0.199233
$996$	−4.91400	−0.155706
$997$	2.02783	0.0642221	0.0321110	−	0.999484i	$-0.489777\pi$
$997$	2.02783	0.0642221	0.0321110	+	0.999484i	$0.489777\pi$
$998$	12.7959	0.405047
$999$	2.49070	0.0788024

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8281.2.a.bt.1.3		4
7.6	odd	2		1183.2.a.l.1.3		4
13.4	even	6		637.2.f.i.393.3		8
13.10	even	6		637.2.f.i.295.3		8
13.12	even	2		8281.2.a.bp.1.2		4
91.4	even	6		637.2.h.i.471.2		8
91.10	odd	6		637.2.g.k.373.3		8
91.17	odd	6		637.2.h.h.471.2		8
91.23	even	6		637.2.h.i.165.2		8
91.30	even	6		637.2.g.j.263.3		8
91.34	even	4		1183.2.c.g.337.6		8
91.62	odd	6		91.2.f.c.22.3	✓	8
91.69	odd	6		91.2.f.c.29.3	yes	8
91.75	odd	6		637.2.h.h.165.2		8
91.82	odd	6		637.2.g.k.263.3		8
91.83	even	4		1183.2.c.g.337.3		8
91.88	even	6		637.2.g.j.373.3		8
91.90	odd	2		1183.2.a.k.1.2		4
273.62	even	6		819.2.o.h.568.2		8
273.251	even	6		819.2.o.h.757.2		8
364.251	even	6		1456.2.s.q.1121.4		8
364.335	even	6		1456.2.s.q.113.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.c.22.3	✓	8	91.62	odd	6
91.2.f.c.29.3	yes	8	91.69	odd	6
637.2.f.i.295.3		8	13.10	even	6
637.2.f.i.393.3		8	13.4	even	6
637.2.g.j.263.3		8	91.30	even	6
637.2.g.j.373.3		8	91.88	even	6
637.2.g.k.263.3		8	91.82	odd	6
637.2.g.k.373.3		8	91.10	odd	6
637.2.h.h.165.2		8	91.75	odd	6
637.2.h.h.471.2		8	91.17	odd	6
637.2.h.i.165.2		8	91.23	even	6
637.2.h.i.471.2		8	91.4	even	6
819.2.o.h.568.2		8	273.62	even	6
819.2.o.h.757.2		8	273.251	even	6
1183.2.a.k.1.2		4	91.90	odd	2
1183.2.a.l.1.3		4	7.6	odd	2
1183.2.c.g.337.3		8	91.83	even	4
1183.2.c.g.337.6		8	91.34	even	4
1456.2.s.q.113.4		8	364.335	even	6
1456.2.s.q.1121.4		8	364.251	even	6
8281.2.a.bp.1.2		4	13.12	even	2
8281.2.a.bt.1.3		4	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:	\( N \)	\(=\)	\( 8281 = 7^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8281.a (trivial)

\(f(q)\)	\(=\)	\(q+0.710287 q^{2} -2.40788 q^{3} -1.49549 q^{4} -1.28971 q^{5} -1.71029 q^{6} -2.48280 q^{8} +2.79790 q^{9} +O(q^{10})\)	\(q+0.710287 q^{2} -2.40788 q^{3} -1.49549 q^{4} -1.28971 q^{5} -1.71029 q^{6} -2.48280 q^{8} +2.79790 q^{9} -0.916066 q^{10} +2.40788 q^{11} +3.60097 q^{12} +3.10548 q^{15} +1.22748 q^{16} -3.90338 q^{17} +1.98731 q^{18} -5.89068 q^{19} +1.92876 q^{20} +1.71029 q^{22} -6.32395 q^{23} +5.97829 q^{24} -3.33664 q^{25} +0.486640 q^{27} +5.61366 q^{29} +2.20578 q^{30} +2.20578 q^{31} +5.83747 q^{32} -5.79790 q^{33} -2.77252 q^{34} -4.18424 q^{36} +5.11817 q^{37} -4.18407 q^{38} +3.20210 q^{40} -7.78521 q^{41} +0.289713 q^{43} -3.60097 q^{44} -3.60849 q^{45} -4.49182 q^{46} +1.27702 q^{47} -2.95564 q^{48} -2.36997 q^{50} +9.39887 q^{51} -13.6225 q^{53} +0.345654 q^{54} -3.10548 q^{55} +14.1841 q^{57} +3.98731 q^{58} -4.03056 q^{59} -4.64422 q^{60} +4.60097 q^{61} +1.56674 q^{62} +1.69131 q^{64} -4.11817 q^{66} -7.57559 q^{67} +5.83747 q^{68} +15.2273 q^{69} -7.22732 q^{71} -6.94662 q^{72} -15.0125 q^{73} +3.63537 q^{74} +8.03424 q^{75} +8.80948 q^{76} -9.30758 q^{79} -1.58310 q^{80} -9.56546 q^{81} -5.52973 q^{82} -1.36463 q^{83} +5.03424 q^{85} +0.205780 q^{86} -13.5170 q^{87} -5.97829 q^{88} -0.899698 q^{89} -2.56306 q^{90} +9.45742 q^{92} -5.31126 q^{93} +0.907052 q^{94} +7.59729 q^{95} -14.0559 q^{96} +15.6658 q^{97} +6.73701 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} + 6 q^{8} + 7 q^{9}+O(q^{10}) \) 4 * q + q^2 - q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 + 6 * q^8 + 7 * q^9	\( 4 q + q^{2} - q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} + 6 q^{8} + 7 q^{9} + 11 q^{10} + q^{11} - 12 q^{12} - 3 q^{15} + 19 q^{16} + 4 q^{17} + 3 q^{18} + q^{19} - 2 q^{20} + 5 q^{22} - 2 q^{23} - 3 q^{24} + 5 q^{25} + 26 q^{27} + q^{29} - 4 q^{30} - 4 q^{31} + 33 q^{32} - 19 q^{33} + 3 q^{34} - 34 q^{36} + 10 q^{37} + 23 q^{38} + 17 q^{40} - 22 q^{41} + 3 q^{43} + 12 q^{44} - 11 q^{45} - 24 q^{46} + 2 q^{47} - 11 q^{48} - 43 q^{50} + 7 q^{51} + 2 q^{53} + 5 q^{54} + 3 q^{55} + 17 q^{57} + 11 q^{58} - 8 q^{59} + 11 q^{60} - 8 q^{61} + 5 q^{62} + 14 q^{64} - 6 q^{66} + 6 q^{67} + 33 q^{68} + 18 q^{69} + 14 q^{71} - 5 q^{72} - 8 q^{73} + 20 q^{74} + 7 q^{75} + 32 q^{76} - 26 q^{79} + 7 q^{80} + 24 q^{81} + 14 q^{82} - 5 q^{85} - 12 q^{86} - 13 q^{87} + 3 q^{88} - q^{89} - 26 q^{90} + 12 q^{92} + 7 q^{93} - 33 q^{94} + 21 q^{95} - 58 q^{96} + 3 q^{97} - 23 q^{99}+O(q^{100}) \) 4 * q + q^2 - q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 + 6 * q^8 + 7 * q^9 + 11 * q^10 + q^11 - 12 * q^12 - 3 * q^15 + 19 * q^16 + 4 * q^17 + 3 * q^18 + q^19 - 2 * q^20 + 5 * q^22 - 2 * q^23 - 3 * q^24 + 5 * q^25 + 26 * q^27 + q^29 - 4 * q^30 - 4 * q^31 + 33 * q^32 - 19 * q^33 + 3 * q^34 - 34 * q^36 + 10 * q^37 + 23 * q^38 + 17 * q^40 - 22 * q^41 + 3 * q^43 + 12 * q^44 - 11 * q^45 - 24 * q^46 + 2 * q^47 - 11 * q^48 - 43 * q^50 + 7 * q^51 + 2 * q^53 + 5 * q^54 + 3 * q^55 + 17 * q^57 + 11 * q^58 - 8 * q^59 + 11 * q^60 - 8 * q^61 + 5 * q^62 + 14 * q^64 - 6 * q^66 + 6 * q^67 + 33 * q^68 + 18 * q^69 + 14 * q^71 - 5 * q^72 - 8 * q^73 + 20 * q^74 + 7 * q^75 + 32 * q^76 - 26 * q^79 + 7 * q^80 + 24 * q^81 + 14 * q^82 - 5 * q^85 - 12 * q^86 - 13 * q^87 + 3 * q^88 - q^89 - 26 * q^90 + 12 * q^92 + 7 * q^93 - 33 * q^94 + 21 * q^95 - 58 * q^96 + 3 * q^97 - 23 * q^99

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