LMFDB - Embedded newform 5775.2.a.ce.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5775,2,Mod(1,5775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5775, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("5775.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5775 = 3 \cdot 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5775.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:	$46.1136071673$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.457904.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 8x^{2} + 5x - 6 $ x^5 - 2x^4 - 5x^3 + 8x^2 + 5x - 6
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.788997$ of defining polynomial
Character	$\chi$	$=$	5775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.788997 q^{2} +1.00000 q^{3} -1.37748 q^{4} -0.788997 q^{6} -1.00000 q^{7} +2.66482 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.788997 q^{2} +1.00000 q^{3} -1.37748 q^{4} -0.788997 q^{6} -1.00000 q^{7} +2.66482 q^{8} +1.00000 q^{9} +1.00000 q^{11} -1.37748 q^{12} -4.93456 q^{13} +0.788997 q^{14} +0.652431 q^{16} -2.30636 q^{17} -0.788997 q^{18} +6.49754 q^{19} -1.00000 q^{21} -0.788997 q^{22} +2.76998 q^{23} +2.66482 q^{24} +3.89335 q^{26} +1.00000 q^{27} +1.37748 q^{28} +0.180289 q^{29} -3.81039 q^{31} -5.84441 q^{32} +1.00000 q^{33} +1.81971 q^{34} -1.37748 q^{36} -6.95216 q^{37} -5.12654 q^{38} -4.93456 q^{39} -5.90384 q^{41} +0.788997 q^{42} -2.42201 q^{43} -1.37748 q^{44} -2.18550 q^{46} +7.88672 q^{47} +0.652431 q^{48} +1.00000 q^{49} -2.30636 q^{51} +6.79728 q^{52} +12.8564 q^{53} -0.788997 q^{54} -2.66482 q^{56} +6.49754 q^{57} -0.142248 q^{58} -4.76018 q^{59} -8.82799 q^{61} +3.00638 q^{62} -1.00000 q^{63} +3.30636 q^{64} -0.788997 q^{66} -6.41719 q^{67} +3.17698 q^{68} +2.76998 q^{69} -1.34567 q^{71} +2.66482 q^{72} +5.13617 q^{73} +5.48523 q^{74} -8.95027 q^{76} -1.00000 q^{77} +3.89335 q^{78} +13.9466 q^{79} +1.00000 q^{81} +4.65811 q^{82} -3.53828 q^{83} +1.37748 q^{84} +1.91096 q^{86} +0.180289 q^{87} +2.66482 q^{88} +14.2197 q^{89} +4.93456 q^{91} -3.81560 q^{92} -3.81039 q^{93} -6.22260 q^{94} -5.84441 q^{96} -7.78568 q^{97} -0.788997 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} + 5 q^{3} + 4 q^{4} - 2 q^{6} - 5 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 + 5 * q^3 + 4 * q^4 - 2 * q^6 - 5 * q^7 - 6 * q^8 + 5 * q^9	$ 5 q - 2 q^{2} + 5 q^{3} + 4 q^{4} - 2 q^{6} - 5 q^{7} - 6 q^{8} + 5 q^{9} + 5 q^{11} + 4 q^{12} - 7 q^{13} + 2 q^{14} - 2 q^{16} - 15 q^{17} - 2 q^{18} + 3 q^{19} - 5 q^{21} - 2 q^{22} - 6 q^{24} + 5 q^{27} - 4 q^{28} - 4 q^{29} + 16 q^{31} - 14 q^{32} + 5 q^{33} + 14 q^{34} + 4 q^{36} - 7 q^{37} + 2 q^{38} - 7 q^{39} - 5 q^{41} + 2 q^{42} - 16 q^{43} + 4 q^{44} - 10 q^{46} - 6 q^{47} - 2 q^{48} + 5 q^{49} - 15 q^{51} - 18 q^{52} - 11 q^{53} - 2 q^{54} + 6 q^{56} + 3 q^{57} + 28 q^{58} - 6 q^{59} + q^{61} - 26 q^{62} - 5 q^{63} + 20 q^{64} - 2 q^{66} - 9 q^{67} - 2 q^{68} - 21 q^{71} - 6 q^{72} - 17 q^{73} + 4 q^{74} - 26 q^{76} - 5 q^{77} - 8 q^{79} + 5 q^{81} - 14 q^{82} - 26 q^{83} - 4 q^{84} - 20 q^{86} - 4 q^{87} - 6 q^{88} + 7 q^{91} + 12 q^{92} + 16 q^{93} + 4 q^{94} - 14 q^{96} - 24 q^{97} - 2 q^{98} + 5 q^{99}+O(q^{100}) $ 5 * q - 2 * q^2 + 5 * q^3 + 4 * q^4 - 2 * q^6 - 5 * q^7 - 6 * q^8 + 5 * q^9 + 5 * q^11 + 4 * q^12 - 7 * q^13 + 2 * q^14 - 2 * q^16 - 15 * q^17 - 2 * q^18 + 3 * q^19 - 5 * q^21 - 2 * q^22 - 6 * q^24 + 5 * q^27 - 4 * q^28 - 4 * q^29 + 16 * q^31 - 14 * q^32 + 5 * q^33 + 14 * q^34 + 4 * q^36 - 7 * q^37 + 2 * q^38 - 7 * q^39 - 5 * q^41 + 2 * q^42 - 16 * q^43 + 4 * q^44 - 10 * q^46 - 6 * q^47 - 2 * q^48 + 5 * q^49 - 15 * q^51 - 18 * q^52 - 11 * q^53 - 2 * q^54 + 6 * q^56 + 3 * q^57 + 28 * q^58 - 6 * q^59 + q^61 - 26 * q^62 - 5 * q^63 + 20 * q^64 - 2 * q^66 - 9 * q^67 - 2 * q^68 - 21 * q^71 - 6 * q^72 - 17 * q^73 + 4 * q^74 - 26 * q^76 - 5 * q^77 - 8 * q^79 + 5 * q^81 - 14 * q^82 - 26 * q^83 - 4 * q^84 - 20 * q^86 - 4 * q^87 - 6 * q^88 + 7 * q^91 + 12 * q^92 + 16 * q^93 + 4 * q^94 - 14 * q^96 - 24 * q^97 - 2 * q^98 + 5 * 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 $

$2$	−0.788997	−0.557905	−0.278952	−	0.960305i	$-0.589987\pi$
$2$	−0.788997	−0.557905	−0.278952	+	0.960305i	$0.589987\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.37748	−0.688742
$5$	0	0
$5$	0	0
$6$	−0.788997	−0.322107
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.66482	0.942158
$9$	1.00000	0.333333
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.37748	−0.397645
$13$	−4.93456	−1.36860	−0.684300	−	0.729200i	$-0.739892\pi$
$13$	−4.93456	−1.36860	−0.684300	+	0.729200i	$0.739892\pi$
$14$	0.788997	0.210868
$15$	0	0
$16$	0.652431	0.163108
$17$	−2.30636	−0.559375	−0.279687	−	0.960091i	$-0.590231\pi$
$17$	−2.30636	−0.559375	−0.279687	+	0.960091i	$0.590231\pi$
$18$	−0.788997	−0.185968
$19$	6.49754	1.49064	0.745319	−	0.666708i	$-0.232297\pi$
$19$	6.49754	1.49064	0.745319	+	0.666708i	$0.232297\pi$
$20$	0	0
$21$	−1.00000	−0.218218
$22$	−0.788997	−0.168215
$23$	2.76998	0.577580	0.288790	−	0.957392i	$-0.406747\pi$
$23$	2.76998	0.577580	0.288790	+	0.957392i	$0.406747\pi$
$24$	2.66482	0.543955
$25$	0	0
$26$	3.89335	0.763549
$27$	1.00000	0.192450
$28$	1.37748	0.260320
$29$	0.180289	0.0334789	0.0167394	−	0.999860i	$-0.494671\pi$
$29$	0.180289	0.0334789	0.0167394	+	0.999860i	$0.494671\pi$
$30$	0	0
$31$	−3.81039	−0.684365	−0.342183	−	0.939633i	$-0.611166\pi$
$31$	−3.81039	−0.684365	−0.342183	+	0.939633i	$0.611166\pi$
$32$	−5.84441	−1.03316
$33$	1.00000	0.174078
$34$	1.81971	0.312078
$35$	0	0
$36$	−1.37748	−0.229581
$37$	−6.95216	−1.14293	−0.571464	−	0.820627i	$-0.693624\pi$
$37$	−6.95216	−1.14293	−0.571464	+	0.820627i	$0.693624\pi$
$38$	−5.12654	−0.831635
$39$	−4.93456	−0.790162
$40$	0	0
$41$	−5.90384	−0.922026	−0.461013	−	0.887393i	$-0.652514\pi$
$41$	−5.90384	−0.922026	−0.461013	+	0.887393i	$0.652514\pi$
$42$	0.788997	0.121745
$43$	−2.42201	−0.369353	−0.184676	−	0.982799i	$-0.559124\pi$
$43$	−2.42201	−0.369353	−0.184676	+	0.982799i	$0.559124\pi$
$44$	−1.37748	−0.207664
$45$	0	0
$46$	−2.18550	−0.322235
$47$	7.88672	1.15040	0.575198	−	0.818014i	$-0.304925\pi$
$47$	7.88672	1.15040	0.575198	+	0.818014i	$0.304925\pi$
$48$	0.652431	0.0941704
$49$	1.00000	0.142857
$50$	0	0
$51$	−2.30636	−0.322955
$52$	6.79728	0.942613
$53$	12.8564	1.76596	0.882982	−	0.469407i	$-0.155532\pi$
$53$	12.8564	1.76596	0.882982	+	0.469407i	$0.155532\pi$
$54$	−0.788997	−0.107369
$55$	0	0
$56$	−2.66482	−0.356102
$57$	6.49754	0.860621
$58$	−0.142248	−0.0186780
$59$	−4.76018	−0.619723	−0.309861	−	0.950782i	$-0.600283\pi$
$59$	−4.76018	−0.619723	−0.309861	+	0.950782i	$0.600283\pi$
$60$	0	0
$61$	−8.82799	−1.13031	−0.565154	−	0.824985i	$-0.691183\pi$
$61$	−8.82799	−1.13031	−0.565154	+	0.824985i	$0.691183\pi$
$62$	3.00638	0.381811
$63$	−1.00000	−0.125988
$64$	3.30636	0.413295
$65$	0	0
$66$	−0.788997	−0.0971188
$67$	−6.41719	−0.783985	−0.391993	−	0.919968i	$-0.628214\pi$
$67$	−6.41719	−0.783985	−0.391993	+	0.919968i	$0.628214\pi$
$68$	3.17698	0.385265
$69$	2.76998	0.333466
$70$	0	0
$71$	−1.34567	−0.159702	−0.0798508	−	0.996807i	$-0.525444\pi$
$71$	−1.34567	−0.159702	−0.0798508	+	0.996807i	$0.525444\pi$
$72$	2.66482	0.314053
$73$	5.13617	0.601143	0.300571	−	0.953759i	$-0.402823\pi$
$73$	5.13617	0.601143	0.300571	+	0.953759i	$0.402823\pi$
$74$	5.48523	0.637645
$75$	0	0
$76$	−8.95027	−1.02667
$77$	−1.00000	−0.113961
$78$	3.89335	0.440835
$79$	13.9466	1.56911	0.784555	−	0.620059i	$-0.212891\pi$
$79$	13.9466	1.56911	0.784555	+	0.620059i	$0.212891\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	4.65811	0.514403
$83$	−3.53828	−0.388377	−0.194188	−	0.980964i	$-0.562207\pi$
$83$	−3.53828	−0.388377	−0.194188	+	0.980964i	$0.562207\pi$
$84$	1.37748	0.150296
$85$	0	0
$86$	1.91096	0.206064
$87$	0.180289	0.0193290
$88$	2.66482	0.284071
$89$	14.2197	1.50728	0.753642	−	0.657285i	$-0.228295\pi$
$89$	14.2197	1.50728	0.753642	+	0.657285i	$0.228295\pi$
$90$	0	0
$91$	4.93456	0.517282
$92$	−3.81560	−0.397804
$93$	−3.81039	−0.395119
$94$	−6.22260	−0.641812
$95$	0	0
$96$	−5.84441	−0.596493
$97$	−7.78568	−0.790516	−0.395258	−	0.918570i	$-0.629345\pi$
$97$	−7.78568	−0.790516	−0.395258	+	0.918570i	$0.629345\pi$
$98$	−0.788997	−0.0797007
$99$	1.00000	0.100504
$100$	0	0
$101$	7.95864	0.791915	0.395957	−	0.918269i	$-0.370413\pi$
$101$	7.95864	0.791915	0.395957	+	0.918269i	$0.370413\pi$
$102$	1.81971	0.180178
$103$	−2.06544	−0.203514	−0.101757	−	0.994809i	$-0.532446\pi$
$103$	−2.06544	−0.203514	−0.101757	+	0.994809i	$0.532446\pi$
$104$	−13.1497	−1.28944
$105$	0	0
$106$	−10.1437	−0.985240
$107$	−17.7213	−1.71319	−0.856593	−	0.515992i	$-0.827423\pi$
$107$	−17.7213	−1.71319	−0.856593	+	0.515992i	$0.827423\pi$
$108$	−1.37748	−0.132548
$109$	11.8481	1.13484	0.567422	−	0.823427i	$-0.307941\pi$
$109$	11.8481	1.13484	0.567422	+	0.823427i	$0.307941\pi$
$110$	0	0
$111$	−6.95216	−0.659870
$112$	−0.652431	−0.0616490
$113$	−8.49754	−0.799382	−0.399691	−	0.916650i	$-0.630883\pi$
$113$	−8.49754	−0.799382	−0.399691	+	0.916650i	$0.630883\pi$
$114$	−5.12654	−0.480145
$115$	0	0
$116$	−0.248346	−0.0230583
$117$	−4.93456	−0.456200
$118$	3.75577	0.345746
$119$	2.30636	0.211424
$120$	0	0
$121$	1.00000	0.0909091
$122$	6.96526	0.630605
$123$	−5.90384	−0.532332
$124$	5.24875	0.471351
$125$	0	0
$126$	0.788997	0.0702894
$127$	−17.6996	−1.57059	−0.785294	−	0.619123i	$-0.787488\pi$
$127$	−17.6996	−1.57059	−0.785294	+	0.619123i	$0.787488\pi$
$128$	9.08012	0.802577
$129$	−2.42201	−0.213246
$130$	0	0
$131$	−3.50624	−0.306342	−0.153171	−	0.988200i	$-0.548948\pi$
$131$	−3.50624	−0.306342	−0.153171	+	0.988200i	$0.548948\pi$
$132$	−1.37748	−0.119895
$133$	−6.49754	−0.563409
$134$	5.06315	0.437389
$135$	0	0
$136$	−6.14604	−0.527019
$137$	−0.270365	−0.0230988	−0.0115494	−	0.999933i	$-0.503676\pi$
$137$	−0.270365	−0.0230988	−0.0115494	+	0.999933i	$0.503676\pi$
$138$	−2.18550	−0.186042
$139$	−5.78488	−0.490667	−0.245334	−	0.969439i	$-0.578898\pi$
$139$	−5.78488	−0.490667	−0.245334	+	0.969439i	$0.578898\pi$
$140$	0	0
$141$	7.88672	0.664182
$142$	1.06173	0.0890984
$143$	−4.93456	−0.412649
$144$	0.652431	0.0543693
$145$	0	0
$146$	−4.05242	−0.335381
$147$	1.00000	0.0824786
$148$	9.57650	0.787183
$149$	−19.8676	−1.62762	−0.813809	−	0.581133i	$-0.802610\pi$
$149$	−19.8676	−1.62762	−0.813809	+	0.581133i	$0.802610\pi$
$150$	0	0
$151$	−21.9589	−1.78699	−0.893497	−	0.449070i	$-0.851756\pi$
$151$	−21.9589	−1.78699	−0.893497	+	0.449070i	$0.851756\pi$
$152$	17.3148	1.40442
$153$	−2.30636	−0.186458
$154$	0.788997	0.0635792
$155$	0	0
$156$	6.79728	0.544218
$157$	−16.4411	−1.31214	−0.656071	−	0.754699i	$-0.727783\pi$
$157$	−16.4411	−1.31214	−0.656071	+	0.754699i	$0.727783\pi$
$158$	−11.0038	−0.875414
$159$	12.8564	1.01958
$160$	0	0
$161$	−2.76998	−0.218305
$162$	−0.788997	−0.0619894
$163$	−14.5561	−1.14012	−0.570062	−	0.821602i	$-0.693081\pi$
$163$	−14.5561	−1.14012	−0.570062	+	0.821602i	$0.693081\pi$
$164$	8.13245	0.635038
$165$	0	0
$166$	2.79169	0.216677
$167$	8.60868	0.666159	0.333080	−	0.942899i	$-0.391912\pi$
$167$	8.60868	0.666159	0.333080	+	0.942899i	$0.391912\pi$
$168$	−2.66482	−0.205596
$169$	11.3499	0.873067
$170$	0	0
$171$	6.49754	0.496880
$172$	3.33628	0.254389
$173$	−4.55306	−0.346163	−0.173081	−	0.984908i	$-0.555372\pi$
$173$	−4.55306	−0.346163	−0.173081	+	0.984908i	$0.555372\pi$
$174$	−0.142248	−0.0107838
$175$	0	0
$176$	0.652431	0.0491789
$177$	−4.76018	−0.357797
$178$	−11.2193	−0.840921
$179$	0.0981232	0.00733407	0.00366703	−	0.999993i	$-0.498833\pi$
$179$	0.0981232	0.00733407	0.00366703	+	0.999993i	$0.498833\pi$
$180$	0	0
$181$	17.9212	1.33207	0.666037	−	0.745919i	$-0.267989\pi$
$181$	17.9212	1.33207	0.666037	+	0.745919i	$0.267989\pi$
$182$	−3.89335	−0.288594
$183$	−8.82799	−0.652584
$184$	7.38150	0.544171
$185$	0	0
$186$	3.00638	0.220439
$187$	−2.30636	−0.168658
$188$	−10.8638	−0.792327
$189$	−1.00000	−0.0727393
$190$	0	0
$191$	−5.93008	−0.429085	−0.214543	−	0.976715i	$-0.568826\pi$
$191$	−5.93008	−0.429085	−0.214543	+	0.976715i	$0.568826\pi$
$192$	3.30636	0.238616
$193$	2.56369	0.184538	0.0922691	−	0.995734i	$-0.470588\pi$
$193$	2.56369	0.184538	0.0922691	+	0.995734i	$0.470588\pi$
$194$	6.14288	0.441033
$195$	0	0
$196$	−1.37748	−0.0983917
$197$	14.3472	1.02220	0.511099	−	0.859522i	$-0.329238\pi$
$197$	14.3472	1.02220	0.511099	+	0.859522i	$0.329238\pi$
$198$	−0.788997	−0.0560716
$199$	−26.7371	−1.89534	−0.947672	−	0.319245i	$-0.896571\pi$
$199$	−26.7371	−1.89534	−0.947672	+	0.319245i	$0.896571\pi$
$200$	0	0
$201$	−6.41719	−0.452634
$202$	−6.27934	−0.441813
$203$	−0.180289	−0.0126538
$204$	3.17698	0.222433
$205$	0	0
$206$	1.62963	0.113541
$207$	2.76998	0.192527
$208$	−3.21946	−0.223229
$209$	6.49754	0.449445
$210$	0	0
$211$	1.43630	0.0988788	0.0494394	−	0.998777i	$-0.484257\pi$
$211$	1.43630	0.0988788	0.0494394	+	0.998777i	$0.484257\pi$
$212$	−17.7095	−1.21629
$213$	−1.34567	−0.0922038
$214$	13.9821	0.955795
$215$	0	0
$216$	2.66482	0.181318
$217$	3.81039	0.258666
$218$	−9.34812	−0.633135
$219$	5.13617	0.347070
$220$	0	0
$221$	11.3809	0.765560
$222$	5.48523	0.368145
$223$	17.2785	1.15705	0.578526	−	0.815664i	$-0.303628\pi$
$223$	17.2785	1.15705	0.578526	+	0.815664i	$0.303628\pi$
$224$	5.84441	0.390496
$225$	0	0
$226$	6.70453	0.445979
$227$	−7.73398	−0.513322	−0.256661	−	0.966501i	$-0.582622\pi$
$227$	−7.73398	−0.513322	−0.256661	+	0.966501i	$0.582622\pi$
$228$	−8.95027	−0.592746
$229$	26.5037	1.75141	0.875707	−	0.482843i	$-0.160396\pi$
$229$	26.5037	1.75141	0.875707	+	0.482843i	$0.160396\pi$
$230$	0	0
$231$	−1.00000	−0.0657952
$232$	0.480439	0.0315424
$233$	−18.0872	−1.18493	−0.592467	−	0.805595i	$-0.701846\pi$
$233$	−18.0872	−1.18493	−0.592467	+	0.805595i	$0.701846\pi$
$234$	3.89335	0.254516
$235$	0	0
$236$	6.55707	0.426829
$237$	13.9466	0.905926
$238$	−1.81971	−0.117954
$239$	−11.0395	−0.714089	−0.357044	−	0.934087i	$-0.616215\pi$
$239$	−11.0395	−0.714089	−0.357044	+	0.934087i	$0.616215\pi$
$240$	0	0
$241$	14.7187	0.948118	0.474059	−	0.880493i	$-0.342788\pi$
$241$	14.7187	0.948118	0.474059	+	0.880493i	$0.342788\pi$
$242$	−0.788997	−0.0507186
$243$	1.00000	0.0641500
$244$	12.1604	0.778491
$245$	0	0
$246$	4.65811	0.296990
$247$	−32.0625	−2.04009
$248$	−10.1540	−0.644780
$249$	−3.53828	−0.224230
$250$	0	0
$251$	18.4218	1.16277	0.581386	−	0.813628i	$-0.302511\pi$
$251$	18.4218	1.16277	0.581386	+	0.813628i	$0.302511\pi$
$252$	1.37748	0.0867734
$253$	2.76998	0.174147
$254$	13.9649	0.876239
$255$	0	0
$256$	−13.7769	−0.861057
$257$	−22.2539	−1.38816	−0.694079	−	0.719899i	$-0.744188\pi$
$257$	−22.2539	−1.38816	−0.694079	+	0.719899i	$0.744188\pi$
$258$	1.91096	0.118971
$259$	6.95216	0.431986
$260$	0	0
$261$	0.180289	0.0111596
$262$	2.76641	0.170909
$263$	−16.8138	−1.03678	−0.518391	−	0.855144i	$-0.673469\pi$
$263$	−16.8138	−1.03678	−0.518391	+	0.855144i	$0.673469\pi$
$264$	2.66482	0.164009
$265$	0	0
$266$	5.12654	0.314328
$267$	14.2197	0.870231
$268$	8.83958	0.539964
$269$	19.1425	1.16714	0.583571	−	0.812062i	$-0.301655\pi$
$269$	19.1425	1.16714	0.583571	+	0.812062i	$0.301655\pi$
$270$	0	0
$271$	−0.734995	−0.0446478	−0.0223239	−	0.999751i	$-0.507107\pi$
$271$	−0.734995	−0.0446478	−0.0223239	+	0.999751i	$0.507107\pi$
$272$	−1.50474	−0.0912384
$273$	4.93456	0.298653
$274$	0.213317	0.0128869
$275$	0	0
$276$	−3.81560	−0.229672
$277$	27.5241	1.65376	0.826881	−	0.562378i	$-0.190113\pi$
$277$	27.5241	1.65376	0.826881	+	0.562378i	$0.190113\pi$
$278$	4.56425	0.273746
$279$	−3.81039	−0.228122
$280$	0	0
$281$	−25.9444	−1.54771	−0.773857	−	0.633361i	$-0.781675\pi$
$281$	−25.9444	−1.54771	−0.773857	+	0.633361i	$0.781675\pi$
$282$	−6.22260	−0.370550
$283$	16.2878	0.968210	0.484105	−	0.875010i	$-0.339145\pi$
$283$	16.2878	0.968210	0.484105	+	0.875010i	$0.339145\pi$
$284$	1.85364	0.109993
$285$	0	0
$286$	3.89335	0.230219
$287$	5.90384	0.348493
$288$	−5.84441	−0.344385
$289$	−11.6807	−0.687100
$290$	0	0
$291$	−7.78568	−0.456405
$292$	−7.07499	−0.414032
$293$	−27.7255	−1.61974	−0.809871	−	0.586608i	$-0.800463\pi$
$293$	−27.7255	−1.61974	−0.809871	+	0.586608i	$0.800463\pi$
$294$	−0.788997	−0.0460152
$295$	0	0
$296$	−18.5263	−1.07682
$297$	1.00000	0.0580259
$298$	15.6755	0.908056
$299$	−13.6686	−0.790476
$300$	0	0
$301$	2.42201	0.139602
$302$	17.3255	0.996973
$303$	7.95864	0.457212
$304$	4.23920	0.243135
$305$	0	0
$306$	1.81971	0.104026
$307$	−13.4199	−0.765912	−0.382956	−	0.923767i	$-0.625094\pi$
$307$	−13.4199	−0.765912	−0.382956	+	0.923767i	$0.625094\pi$
$308$	1.37748	0.0784894
$309$	−2.06544	−0.117499
$310$	0	0
$311$	−1.04271	−0.0591266	−0.0295633	−	0.999563i	$-0.509412\pi$
$311$	−1.04271	−0.0591266	−0.0295633	+	0.999563i	$0.509412\pi$
$312$	−13.1497	−0.744457
$313$	−11.3495	−0.641509	−0.320755	−	0.947162i	$-0.603936\pi$
$313$	−11.3495	−0.641509	−0.320755	+	0.947162i	$0.603936\pi$
$314$	12.9720	0.732051
$315$	0	0
$316$	−19.2112	−1.08071
$317$	−26.8011	−1.50530	−0.752649	−	0.658422i	$-0.771224\pi$
$317$	−26.8011	−1.50530	−0.752649	+	0.658422i	$0.771224\pi$
$318$	−10.1437	−0.568828
$319$	0.180289	0.0100943
$320$	0	0
$321$	−17.7213	−0.989109
$322$	2.18550	0.121793
$323$	−14.9857	−0.833826
$324$	−1.37748	−0.0765269
$325$	0	0
$326$	11.4847	0.636081
$327$	11.8481	0.655202
$328$	−15.7327	−0.868693
$329$	−7.88672	−0.434809
$330$	0	0
$331$	−23.8648	−1.31173	−0.655865	−	0.754878i	$-0.727696\pi$
$331$	−23.8648	−1.31173	−0.655865	+	0.754878i	$0.727696\pi$
$332$	4.87393	0.267492
$333$	−6.95216	−0.380976
$334$	−6.79222	−0.371654
$335$	0	0
$336$	−0.652431	−0.0355930
$337$	0.968517	0.0527585	0.0263793	−	0.999652i	$-0.491602\pi$
$337$	0.968517	0.0527585	0.0263793	+	0.999652i	$0.491602\pi$
$338$	−8.95501	−0.487088
$339$	−8.49754	−0.461523
$340$	0	0
$341$	−3.81039	−0.206344
$342$	−5.12654	−0.277212
$343$	−1.00000	−0.0539949
$344$	−6.45422	−0.347988
$345$	0	0
$346$	3.59235	0.193126
$347$	−35.4959	−1.90552	−0.952759	−	0.303726i	$-0.901769\pi$
$347$	−35.4959	−1.90552	−0.952759	+	0.303726i	$0.901769\pi$
$348$	−0.248346	−0.0133127
$349$	−8.70753	−0.466104	−0.233052	−	0.972464i	$-0.574871\pi$
$349$	−8.70753	−0.466104	−0.233052	+	0.972464i	$0.574871\pi$
$350$	0	0
$351$	−4.93456	−0.263387
$352$	−5.84441	−0.311508
$353$	−20.5995	−1.09640	−0.548199	−	0.836348i	$-0.684687\pi$
$353$	−20.5995	−1.09640	−0.548199	+	0.836348i	$0.684687\pi$
$354$	3.75577	0.199617
$355$	0	0
$356$	−19.5874	−1.03813
$357$	2.30636	0.122066
$358$	−0.0774188	−0.00409171
$359$	−33.1190	−1.74796	−0.873978	−	0.485965i	$-0.838468\pi$
$359$	−33.1190	−1.74796	−0.873978	+	0.485965i	$0.838468\pi$
$360$	0	0
$361$	23.2181	1.22200
$362$	−14.1398	−0.743170
$363$	1.00000	0.0524864
$364$	−6.79728	−0.356274
$365$	0	0
$366$	6.96526	0.364080
$367$	−15.6639	−0.817650	−0.408825	−	0.912613i	$-0.634061\pi$
$367$	−15.6639	−0.817650	−0.408825	+	0.912613i	$0.634061\pi$
$368$	1.80722	0.0942078
$369$	−5.90384	−0.307342
$370$	0	0
$371$	−12.8564	−0.667471
$372$	5.24875	0.272135
$373$	−7.00048	−0.362471	−0.181236	−	0.983440i	$-0.558010\pi$
$373$	−7.00048	−0.362471	−0.181236	+	0.983440i	$0.558010\pi$
$374$	1.81971	0.0940950
$375$	0	0
$376$	21.0167	1.08385
$377$	−0.889648	−0.0458192
$378$	0.788997	0.0405816
$379$	−19.3416	−0.993513	−0.496757	−	0.867890i	$-0.665476\pi$
$379$	−19.3416	−0.993513	−0.496757	+	0.867890i	$0.665476\pi$
$380$	0	0
$381$	−17.6996	−0.906779
$382$	4.67881	0.239389
$383$	−5.25023	−0.268274	−0.134137	−	0.990963i	$-0.542826\pi$
$383$	−5.25023	−0.268274	−0.134137	+	0.990963i	$0.542826\pi$
$384$	9.08012	0.463368
$385$	0	0
$386$	−2.02274	−0.102955
$387$	−2.42201	−0.123118
$388$	10.7247	0.544462
$389$	13.4333	0.681094	0.340547	−	0.940228i	$-0.389388\pi$
$389$	13.4333	0.681094	0.340547	+	0.940228i	$0.389388\pi$
$390$	0	0
$391$	−6.38856	−0.323084
$392$	2.66482	0.134594
$393$	−3.50624	−0.176866
$394$	−11.3199	−0.570290
$395$	0	0
$396$	−1.37748	−0.0692212
$397$	16.1710	0.811597	0.405799	−	0.913962i	$-0.366993\pi$
$397$	16.1710	0.811597	0.405799	+	0.913962i	$0.366993\pi$
$398$	21.0955	1.05742
$399$	−6.49754	−0.325284
$400$	0	0
$401$	−4.03211	−0.201354	−0.100677	−	0.994919i	$-0.532101\pi$
$401$	−4.03211	−0.201354	−0.100677	+	0.994919i	$0.532101\pi$
$402$	5.06315	0.252527
$403$	18.8026	0.936623
$404$	−10.9629	−0.545425
$405$	0	0
$406$	0.142248	0.00705963
$407$	−6.95216	−0.344606
$408$	−6.14604	−0.304275
$409$	18.7138	0.925340	0.462670	−	0.886531i	$-0.346891\pi$
$409$	18.7138	0.925340	0.462670	+	0.886531i	$0.346891\pi$
$410$	0	0
$411$	−0.270365	−0.0133361
$412$	2.84511	0.140169
$413$	4.76018	0.234233
$414$	−2.18550	−0.107412
$415$	0	0
$416$	28.8396	1.41398
$417$	−5.78488	−0.283287
$418$	−5.12654	−0.250747
$419$	−0.434416	−0.0212226	−0.0106113	−	0.999944i	$-0.503378\pi$
$419$	−0.434416	−0.0212226	−0.0106113	+	0.999944i	$0.503378\pi$
$420$	0	0
$421$	3.60143	0.175523	0.0877614	−	0.996142i	$-0.472029\pi$
$421$	3.60143	0.175523	0.0877614	+	0.996142i	$0.472029\pi$
$422$	−1.13323	−0.0551650
$423$	7.88672	0.383466
$424$	34.2601	1.66382
$425$	0	0
$426$	1.06173	0.0514410
$427$	8.82799	0.427216
$428$	24.4109	1.17994
$429$	−4.93456	−0.238243
$430$	0	0
$431$	14.5285	0.699813	0.349906	−	0.936785i	$-0.386213\pi$
$431$	14.5285	0.699813	0.349906	+	0.936785i	$0.386213\pi$
$432$	0.652431	0.0313901
$433$	−18.0883	−0.869270	−0.434635	−	0.900607i	$-0.643123\pi$
$433$	−18.0883	−0.869270	−0.434635	+	0.900607i	$0.643123\pi$
$434$	−3.00638	−0.144311
$435$	0	0
$436$	−16.3206	−0.781614
$437$	17.9980	0.860963
$438$	−4.05242	−0.193632
$439$	35.1038	1.67541	0.837706	−	0.546121i	$-0.183896\pi$
$439$	35.1038	1.67541	0.837706	+	0.546121i	$0.183896\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	−8.97947	−0.427110
$443$	1.14786	0.0545364	0.0272682	−	0.999628i	$-0.491319\pi$
$443$	1.14786	0.0545364	0.0272682	+	0.999628i	$0.491319\pi$
$444$	9.57650	0.454480
$445$	0	0
$446$	−13.6327	−0.645525
$447$	−19.8676	−0.939705
$448$	−3.30636	−0.156211
$449$	−11.4825	−0.541895	−0.270948	−	0.962594i	$-0.587337\pi$
$449$	−11.4825	−0.541895	−0.270948	+	0.962594i	$0.587337\pi$
$450$	0	0
$451$	−5.90384	−0.278001
$452$	11.7052	0.550568
$453$	−21.9589	−1.03172
$454$	6.10208	0.286385
$455$	0	0
$456$	17.3148	0.810840
$457$	0.748159	0.0349974	0.0174987	−	0.999847i	$-0.494430\pi$
$457$	0.748159	0.0349974	0.0174987	+	0.999847i	$0.494430\pi$
$458$	−20.9113	−0.977123
$459$	−2.30636	−0.107652
$460$	0	0
$461$	0.0395629	0.00184263	0.000921315	−	1.00000i	$-0.499707\pi$
$461$	0.0395629	0.00184263	0.000921315		1.00000i	$0.499707\pi$
$462$	0.788997	0.0367074
$463$	23.7924	1.10573	0.552863	−	0.833272i	$-0.313535\pi$
$463$	23.7924	1.10573	0.552863	+	0.833272i	$0.313535\pi$
$464$	0.117626	0.00546067
$465$	0	0
$466$	14.2708	0.661080
$467$	−20.8572	−0.965156	−0.482578	−	0.875853i	$-0.660300\pi$
$467$	−20.8572	−0.965156	−0.482578	+	0.875853i	$0.660300\pi$
$468$	6.79728	0.314204
$469$	6.41719	0.296319
$470$	0	0
$471$	−16.4411	−0.757566
$472$	−12.6850	−0.583876
$473$	−2.42201	−0.111364
$474$	−11.0038	−0.505421
$475$	0	0
$476$	−3.17698	−0.145616
$477$	12.8564	0.588655
$478$	8.71016	0.398394
$479$	−37.1983	−1.69963	−0.849816	−	0.527079i	$-0.823287\pi$
$479$	−37.1983	−1.69963	−0.849816	+	0.527079i	$0.823287\pi$
$480$	0	0
$481$	34.3059	1.56421
$482$	−11.6130	−0.528959
$483$	−2.76998	−0.126038
$484$	−1.37748	−0.0626129
$485$	0	0
$486$	−0.788997	−0.0357896
$487$	2.47835	0.112305	0.0561524	−	0.998422i	$-0.482117\pi$
$487$	2.47835	0.112305	0.0561524	+	0.998422i	$0.482117\pi$
$488$	−23.5250	−1.06493
$489$	−14.5561	−0.658251
$490$	0	0
$491$	20.0107	0.903068	0.451534	−	0.892254i	$-0.350877\pi$
$491$	20.0107	0.903068	0.451534	+	0.892254i	$0.350877\pi$
$492$	8.13245	0.366639
$493$	−0.415812	−0.0187272
$494$	25.2972	1.13818
$495$	0	0
$496$	−2.48602	−0.111625
$497$	1.34567	0.0603616
$498$	2.79169	0.125099
$499$	29.4147	1.31678	0.658391	−	0.752676i	$-0.271237\pi$
$499$	29.4147	1.31678	0.658391	+	0.752676i	$0.271237\pi$
$500$	0	0
$501$	8.60868	0.384607
$502$	−14.5347	−0.648716
$503$	9.54600	0.425635	0.212818	−	0.977092i	$-0.431736\pi$
$503$	9.54600	0.425635	0.212818	+	0.977092i	$0.431736\pi$
$504$	−2.66482	−0.118701
$505$	0	0
$506$	−2.18550	−0.0971574
$507$	11.3499	0.504065
$508$	24.3810	1.08173
$509$	−29.9387	−1.32701	−0.663506	−	0.748171i	$-0.730932\pi$
$509$	−29.9387	−1.32701	−0.663506	+	0.748171i	$0.730932\pi$
$510$	0	0
$511$	−5.13617	−0.227211
$512$	−7.29031	−0.322189
$513$	6.49754	0.286874
$514$	17.5582	0.774460
$515$	0	0
$516$	3.33628	0.146871
$517$	7.88672	0.346858
$518$	−5.48523	−0.241007
$519$	−4.55306	−0.199857
$520$	0	0
$521$	−11.3719	−0.498211	−0.249105	−	0.968476i	$-0.580137\pi$
$521$	−11.3719	−0.498211	−0.249105	+	0.968476i	$0.580137\pi$
$522$	−0.142248	−0.00622601
$523$	−27.7214	−1.21217	−0.606087	−	0.795399i	$-0.707262\pi$
$523$	−27.7214	−1.21217	−0.606087	+	0.795399i	$0.707262\pi$
$524$	4.82979	0.210990
$525$	0	0
$526$	13.2660	0.578426
$527$	8.78812	0.382817
$528$	0.652431	0.0283934
$529$	−15.3272	−0.666401
$530$	0	0
$531$	−4.76018	−0.206574
$532$	8.95027	0.388043
$533$	29.1329	1.26188
$534$	−11.2193	−0.485506
$535$	0	0
$536$	−17.1007	−0.738637
$537$	0.0981232	0.00423433
$538$	−15.1034	−0.651154
$539$	1.00000	0.0430730
$540$	0	0
$541$	−17.5860	−0.756080	−0.378040	−	0.925789i	$-0.623402\pi$
$541$	−17.5860	−0.756080	−0.378040	+	0.925789i	$0.623402\pi$
$542$	0.579909	0.0249092
$543$	17.9212	0.769073
$544$	13.4793	0.577921
$545$	0	0
$546$	−3.89335	−0.166620
$547$	17.0283	0.728078	0.364039	−	0.931384i	$-0.381397\pi$
$547$	17.0283	0.728078	0.364039	+	0.931384i	$0.381397\pi$
$548$	0.372423	0.0159091
$549$	−8.82799	−0.376769
$550$	0	0
$551$	1.17144	0.0499049
$552$	7.38150	0.314177
$553$	−13.9466	−0.593068
$554$	−21.7164	−0.922641
$555$	0	0
$556$	7.96859	0.337943
$557$	12.1787	0.516027	0.258013	−	0.966141i	$-0.416932\pi$
$557$	12.1787	0.516027	0.258013	+	0.966141i	$0.416932\pi$
$558$	3.00638	0.127270
$559$	11.9515	0.505496
$560$	0	0
$561$	−2.30636	−0.0973746
$562$	20.4701	0.863477
$563$	−12.2616	−0.516764	−0.258382	−	0.966043i	$-0.583189\pi$
$563$	−12.2616	−0.516764	−0.258382	+	0.966043i	$0.583189\pi$
$564$	−10.8638	−0.457450
$565$	0	0
$566$	−12.8510	−0.540169
$567$	−1.00000	−0.0419961
$568$	−3.58597	−0.150464
$569$	−2.17352	−0.0911188	−0.0455594	−	0.998962i	$-0.514507\pi$
$569$	−2.17352	−0.0911188	−0.0455594	+	0.998962i	$0.514507\pi$
$570$	0	0
$571$	−11.4507	−0.479198	−0.239599	−	0.970872i	$-0.577016\pi$
$571$	−11.4507	−0.479198	−0.239599	+	0.970872i	$0.577016\pi$
$572$	6.79728	0.284208
$573$	−5.93008	−0.247732
$574$	−4.65811	−0.194426
$575$	0	0
$576$	3.30636	0.137765
$577$	7.68068	0.319751	0.159876	−	0.987137i	$-0.448891\pi$
$577$	7.68068	0.319751	0.159876	+	0.987137i	$0.448891\pi$
$578$	9.21603	0.383337
$579$	2.56369	0.106543
$580$	0	0
$581$	3.53828	0.146793
$582$	6.14288	0.254630
$583$	12.8564	0.532458
$584$	13.6870	0.566371
$585$	0	0
$586$	21.8753	0.903662
$587$	2.36400	0.0975729	0.0487865	−	0.998809i	$-0.484465\pi$
$587$	2.36400	0.0975729	0.0487865	+	0.998809i	$0.484465\pi$
$588$	−1.37748	−0.0568065
$589$	−24.7582	−1.02014
$590$	0	0
$591$	14.3472	0.590167
$592$	−4.53581	−0.186421
$593$	−22.6352	−0.929518	−0.464759	−	0.885437i	$-0.653859\pi$
$593$	−22.6352	−0.929518	−0.464759	+	0.885437i	$0.653859\pi$
$594$	−0.788997	−0.0323729
$595$	0	0
$596$	27.3673	1.12101
$597$	−26.7371	−1.09428
$598$	10.7845	0.441010
$599$	−21.7852	−0.890119	−0.445060	−	0.895501i	$-0.646818\pi$
$599$	−21.7852	−0.890119	−0.445060	+	0.895501i	$0.646818\pi$
$600$	0	0
$601$	−8.09948	−0.330385	−0.165192	−	0.986261i	$-0.552825\pi$
$601$	−8.09948	−0.330385	−0.165192	+	0.986261i	$0.552825\pi$
$602$	−1.91096	−0.0778847
$603$	−6.41719	−0.261328
$604$	30.2481	1.23078
$605$	0	0
$606$	−6.27934	−0.255081
$607$	−31.8459	−1.29258	−0.646292	−	0.763090i	$-0.723681\pi$
$607$	−31.8459	−1.29258	−0.646292	+	0.763090i	$0.723681\pi$
$608$	−37.9743	−1.54006
$609$	−0.180289	−0.00730569
$610$	0	0
$611$	−38.9175	−1.57443
$612$	3.17698	0.128422
$613$	−12.7298	−0.514152	−0.257076	−	0.966391i	$-0.582759\pi$
$613$	−12.7298	−0.514152	−0.257076	+	0.966391i	$0.582759\pi$
$614$	10.5882	0.427306
$615$	0	0
$616$	−2.66482	−0.107369
$617$	27.3911	1.10272	0.551362	−	0.834266i	$-0.314108\pi$
$617$	27.3911	1.10272	0.551362	+	0.834266i	$0.314108\pi$
$618$	1.62963	0.0655532
$619$	31.7576	1.27645	0.638223	−	0.769851i	$-0.279670\pi$
$619$	31.7576	1.27645	0.638223	+	0.769851i	$0.279670\pi$
$620$	0	0
$621$	2.76998	0.111155
$622$	0.822694	0.0329870
$623$	−14.2197	−0.569700
$624$	−3.21946	−0.128882
$625$	0	0
$626$	8.95468	0.357901
$627$	6.49754	0.259487
$628$	22.6474	0.903728
$629$	16.0342	0.639325
$630$	0	0
$631$	−5.07364	−0.201978	−0.100989	−	0.994888i	$-0.532201\pi$
$631$	−5.07364	−0.201978	−0.100989	+	0.994888i	$0.532201\pi$
$632$	37.1651	1.47835
$633$	1.43630	0.0570877
$634$	21.1459	0.839813
$635$	0	0
$636$	−17.7095	−0.702227
$637$	−4.93456	−0.195514
$638$	−0.142248	−0.00563164
$639$	−1.34567	−0.0532339
$640$	0	0
$641$	24.0828	0.951213	0.475607	−	0.879658i	$-0.342229\pi$
$641$	24.0828	0.951213	0.475607	+	0.879658i	$0.342229\pi$
$642$	13.9821	0.551829
$643$	27.7846	1.09572	0.547858	−	0.836571i	$-0.315443\pi$
$643$	27.7846	1.09572	0.547858	+	0.836571i	$0.315443\pi$
$644$	3.81560	0.150356
$645$	0	0
$646$	11.8237	0.465195
$647$	25.1682	0.989464	0.494732	−	0.869046i	$-0.335266\pi$
$647$	25.1682	0.989464	0.494732	+	0.869046i	$0.335266\pi$
$648$	2.66482	0.104684
$649$	−4.76018	−0.186853
$650$	0	0
$651$	3.81039	0.149341
$652$	20.0508	0.785251
$653$	−34.2015	−1.33841	−0.669205	−	0.743078i	$-0.733365\pi$
$653$	−34.2015	−1.33841	−0.669205	+	0.743078i	$0.733365\pi$
$654$	−9.34812	−0.365540
$655$	0	0
$656$	−3.85185	−0.150390
$657$	5.13617	0.200381
$658$	6.22260	0.242582
$659$	−7.41861	−0.288988	−0.144494	−	0.989506i	$-0.546155\pi$
$659$	−7.41861	−0.288988	−0.144494	+	0.989506i	$0.546155\pi$
$660$	0	0
$661$	7.51976	0.292485	0.146242	−	0.989249i	$-0.453282\pi$
$661$	7.51976	0.292485	0.146242	+	0.989249i	$0.453282\pi$
$662$	18.8293	0.731821
$663$	11.3809	0.441996
$664$	−9.42890	−0.365912
$665$	0	0
$666$	5.48523	0.212548
$667$	0.499397	0.0193367
$668$	−11.8583	−0.458812
$669$	17.2785	0.668025
$670$	0	0
$671$	−8.82799	−0.340801
$672$	5.84441	0.225453
$673$	−13.5425	−0.522026	−0.261013	−	0.965335i	$-0.584057\pi$
$673$	−13.5425	−0.522026	−0.261013	+	0.965335i	$0.584057\pi$
$674$	−0.764157	−0.0294342
$675$	0	0
$676$	−15.6343	−0.601318
$677$	14.1926	0.545466	0.272733	−	0.962090i	$-0.412072\pi$
$677$	14.1926	0.545466	0.272733	+	0.962090i	$0.412072\pi$
$678$	6.70453	0.257486
$679$	7.78568	0.298787
$680$	0	0
$681$	−7.73398	−0.296367
$682$	3.00638	0.115120
$683$	−27.7046	−1.06009	−0.530043	−	0.847971i	$-0.677824\pi$
$683$	−27.7046	−1.06009	−0.530043	+	0.847971i	$0.677824\pi$
$684$	−8.95027	−0.342222
$685$	0	0
$686$	0.788997	0.0301240
$687$	26.5037	1.01118
$688$	−1.58019	−0.0602443
$689$	−63.4407	−2.41690
$690$	0	0
$691$	14.1225	0.537245	0.268623	−	0.963246i	$-0.413432\pi$
$691$	14.1225	0.537245	0.268623	+	0.963246i	$0.413432\pi$
$692$	6.27177	0.238417
$693$	−1.00000	−0.0379869
$694$	28.0061	1.06310
$695$	0	0
$696$	0.480439	0.0182110
$697$	13.6164	0.515758
$698$	6.87021	0.260041
$699$	−18.0872	−0.684122
$700$	0	0
$701$	3.95123	0.149236	0.0746180	−	0.997212i	$-0.476226\pi$
$701$	3.95123	0.149236	0.0746180	+	0.997212i	$0.476226\pi$
$702$	3.89335	0.146945
$703$	−45.1720	−1.70369
$704$	3.30636	0.124613
$705$	0	0
$706$	16.2529	0.611686
$707$	−7.95864	−0.299316
$708$	6.55707	0.246430
$709$	2.26082	0.0849070	0.0424535	−	0.999098i	$-0.486483\pi$
$709$	2.26082	0.0849070	0.0424535	+	0.999098i	$0.486483\pi$
$710$	0	0
$711$	13.9466	0.523037
$712$	37.8930	1.42010
$713$	−10.5547	−0.395276
$714$	−1.81971	−0.0681010
$715$	0	0
$716$	−0.135163	−0.00505128
$717$	−11.0395	−0.412279
$718$	26.1308	0.975193
$719$	34.7622	1.29641	0.648206	−	0.761465i	$-0.275520\pi$
$719$	34.7622	1.29641	0.648206	+	0.761465i	$0.275520\pi$
$720$	0	0
$721$	2.06544	0.0769211
$722$	−18.3190	−0.681762
$723$	14.7187	0.547396
$724$	−24.6862	−0.917455
$725$	0	0
$726$	−0.788997	−0.0292824
$727$	−10.7652	−0.399257	−0.199629	−	0.979872i	$-0.563974\pi$
$727$	−10.7652	−0.399257	−0.199629	+	0.979872i	$0.563974\pi$
$728$	13.1497	0.487361
$729$	1.00000	0.0370370
$730$	0	0
$731$	5.58602	0.206606
$732$	12.1604	0.449462
$733$	−44.7894	−1.65433	−0.827167	−	0.561956i	$-0.810049\pi$
$733$	−44.7894	−1.65433	−0.827167	+	0.561956i	$0.810049\pi$
$734$	12.3588	0.456171
$735$	0	0
$736$	−16.1889	−0.596730
$737$	−6.41719	−0.236380
$738$	4.65811	0.171468
$739$	45.9645	1.69083	0.845415	−	0.534110i	$-0.179353\pi$
$739$	45.9645	1.69083	0.845415	+	0.534110i	$0.179353\pi$
$740$	0	0
$741$	−32.0625	−1.17785
$742$	10.1437	0.372386
$743$	35.8254	1.31431	0.657154	−	0.753757i	$-0.271760\pi$
$743$	35.8254	1.31431	0.657154	+	0.753757i	$0.271760\pi$
$744$	−10.1540	−0.372264
$745$	0	0
$746$	5.52336	0.202224
$747$	−3.53828	−0.129459
$748$	3.17698	0.116162
$749$	17.7213	0.647524
$750$	0	0
$751$	39.1841	1.42985	0.714925	−	0.699202i	$-0.246461\pi$
$751$	39.1841	1.42985	0.714925	+	0.699202i	$0.246461\pi$
$752$	5.14554	0.187639
$753$	18.4218	0.671326
$754$	0.701929	0.0255628
$755$	0	0
$756$	1.37748	0.0500986
$757$	−31.3245	−1.13851	−0.569254	−	0.822162i	$-0.692768\pi$
$757$	−31.3245	−1.13851	−0.569254	+	0.822162i	$0.692768\pi$
$758$	15.2605	0.554286
$759$	2.76998	0.100544
$760$	0	0
$761$	−9.03351	−0.327465	−0.163732	−	0.986505i	$-0.552353\pi$
$761$	−9.03351	−0.327465	−0.163732	+	0.986505i	$0.552353\pi$
$762$	13.9649	0.505897
$763$	−11.8481	−0.428930
$764$	8.16859	0.295529
$765$	0	0
$766$	4.14241	0.149671
$767$	23.4894	0.848153
$768$	−13.7769	−0.497131
$769$	−36.1186	−1.30247	−0.651234	−	0.758877i	$-0.725748\pi$
$769$	−36.1186	−1.30247	−0.651234	+	0.758877i	$0.725748\pi$
$770$	0	0
$771$	−22.2539	−0.801453
$772$	−3.53144	−0.127099
$773$	24.7785	0.891222	0.445611	−	0.895227i	$-0.352986\pi$
$773$	24.7785	0.891222	0.445611	+	0.895227i	$0.352986\pi$
$774$	1.91096	0.0686879
$775$	0	0
$776$	−20.7475	−0.744791
$777$	6.95216	0.249407
$778$	−10.5988	−0.379986
$779$	−38.3605	−1.37441
$780$	0	0
$781$	−1.34567	−0.0481519
$782$	5.04055	0.180250
$783$	0.180289	0.00644301
$784$	0.652431	0.0233011
$785$	0	0
$786$	2.76641	0.0986746
$787$	36.2621	1.29261	0.646303	−	0.763081i	$-0.276314\pi$
$787$	36.2621	1.29261	0.646303	+	0.763081i	$0.276314\pi$
$788$	−19.7631	−0.704031
$789$	−16.8138	−0.598586
$790$	0	0
$791$	8.49754	0.302138
$792$	2.66482	0.0946904
$793$	43.5622	1.54694
$794$	−12.7588	−0.452794
$795$	0	0
$796$	36.8300	1.30540
$797$	−49.5097	−1.75372	−0.876862	−	0.480742i	$-0.840367\pi$
$797$	−49.5097	−1.75372	−0.876862	+	0.480742i	$0.840367\pi$
$798$	5.12654	0.181478
$799$	−18.1896	−0.643503
$800$	0	0
$801$	14.2197	0.502428
$802$	3.18132	0.112336
$803$	5.13617	0.181251
$804$	8.83958	0.311748
$805$	0	0
$806$	−14.8352	−0.522546
$807$	19.1425	0.673850
$808$	21.2084	0.746108
$809$	2.07952	0.0731121	0.0365560	−	0.999332i	$-0.488361\pi$
$809$	2.07952	0.0731121	0.0365560	+	0.999332i	$0.488361\pi$
$810$	0	0
$811$	−27.3273	−0.959590	−0.479795	−	0.877381i	$-0.659289\pi$
$811$	−27.3273	−0.959590	−0.479795	+	0.877381i	$0.659289\pi$
$812$	0.248346	0.00871522
$813$	−0.734995	−0.0257774
$814$	5.48523	0.192257
$815$	0	0
$816$	−1.50474	−0.0526765
$817$	−15.7371	−0.550571
$818$	−14.7652	−0.516252
$819$	4.93456	0.172427
$820$	0	0
$821$	−15.7423	−0.549411	−0.274706	−	0.961528i	$-0.588580\pi$
$821$	−15.7423	−0.549411	−0.274706	+	0.961528i	$0.588580\pi$
$822$	0.213317	0.00744028
$823$	18.7280	0.652816	0.326408	−	0.945229i	$-0.394162\pi$
$823$	18.7280	0.652816	0.326408	+	0.945229i	$0.394162\pi$
$824$	−5.50404	−0.191742
$825$	0	0
$826$	−3.75577	−0.130680
$827$	−38.2250	−1.32921	−0.664606	−	0.747194i	$-0.731401\pi$
$827$	−38.2250	−1.32921	−0.664606	+	0.747194i	$0.731401\pi$
$828$	−3.81560	−0.132601
$829$	10.4180	0.361832	0.180916	−	0.983499i	$-0.442094\pi$
$829$	10.4180	0.361832	0.180916	+	0.983499i	$0.442094\pi$
$830$	0	0
$831$	27.5241	0.954799
$832$	−16.3154	−0.565636
$833$	−2.30636	−0.0799107
$834$	4.56425	0.158047
$835$	0	0
$836$	−8.95027	−0.309551
$837$	−3.81039	−0.131706
$838$	0.342753	0.0118402
$839$	−33.0843	−1.14220	−0.571099	−	0.820881i	$-0.693483\pi$
$839$	−33.0843	−1.14220	−0.571099	+	0.820881i	$0.693483\pi$
$840$	0	0
$841$	−28.9675	−0.998879
$842$	−2.84151	−0.0979251
$843$	−25.9444	−0.893573
$844$	−1.97848	−0.0681020
$845$	0	0
$846$	−6.22260	−0.213937
$847$	−1.00000	−0.0343604
$848$	8.38792	0.288042
$849$	16.2878	0.558996
$850$	0	0
$851$	−19.2573	−0.660133
$852$	1.85364	0.0635047
$853$	40.7088	1.39384	0.696921	−	0.717148i	$-0.254553\pi$
$853$	40.7088	1.39384	0.696921	+	0.717148i	$0.254553\pi$
$854$	−6.96526	−0.238346
$855$	0	0
$856$	−47.2243	−1.61409
$857$	−22.0388	−0.752832	−0.376416	−	0.926451i	$-0.622844\pi$
$857$	−22.0388	−0.752832	−0.376416	+	0.926451i	$0.622844\pi$
$858$	3.89335	0.132917
$859$	−16.9544	−0.578478	−0.289239	−	0.957257i	$-0.593402\pi$
$859$	−16.9544	−0.578478	−0.289239	+	0.957257i	$0.593402\pi$
$860$	0	0
$861$	5.90384	0.201202
$862$	−11.4629	−0.390429
$863$	56.8946	1.93671	0.968357	−	0.249567i	$-0.0802884\pi$
$863$	56.8946	1.93671	0.968357	+	0.249567i	$0.0802884\pi$
$864$	−5.84441	−0.198831
$865$	0	0
$866$	14.2716	0.484970
$867$	−11.6807	−0.396697
$868$	−5.24875	−0.178154
$869$	13.9466	0.473104
$870$	0	0
$871$	31.6660	1.07296
$872$	31.5731	1.06920
$873$	−7.78568	−0.263505
$874$	−14.2004	−0.480336
$875$	0	0
$876$	−7.07499	−0.239042
$877$	−15.3027	−0.516734	−0.258367	−	0.966047i	$-0.583184\pi$
$877$	−15.3027	−0.516734	−0.258367	+	0.966047i	$0.583184\pi$
$878$	−27.6968	−0.934721
$879$	−27.7255	−0.935158
$880$	0	0
$881$	33.9292	1.14310	0.571551	−	0.820566i	$-0.306342\pi$
$881$	33.9292	1.14310	0.571551	+	0.820566i	$0.306342\pi$
$882$	−0.788997	−0.0265669
$883$	−24.6417	−0.829259	−0.414629	−	0.909990i	$-0.636089\pi$
$883$	−24.6417	−0.829259	−0.414629	+	0.909990i	$0.636089\pi$
$884$	−15.6770	−0.527274
$885$	0	0
$886$	−0.905656	−0.0304261
$887$	−5.23942	−0.175922	−0.0879612	−	0.996124i	$-0.528035\pi$
$887$	−5.23942	−0.175922	−0.0879612	+	0.996124i	$0.528035\pi$
$888$	−18.5263	−0.621702
$889$	17.6996	0.593626
$890$	0	0
$891$	1.00000	0.0335013
$892$	−23.8008	−0.796911
$893$	51.2443	1.71483
$894$	15.6755	0.524266
$895$	0	0
$896$	−9.08012	−0.303346
$897$	−13.6686	−0.456382
$898$	9.05969	0.302326
$899$	−0.686972	−0.0229118
$900$	0	0
$901$	−29.6515	−0.987835
$902$	4.65811	0.155098
$903$	2.42201	0.0805993
$904$	−22.6445	−0.753144
$905$	0	0
$906$	17.3255	0.575602
$907$	−9.46660	−0.314333	−0.157167	−	0.987572i	$-0.550236\pi$
$907$	−9.46660	−0.314333	−0.157167	+	0.987572i	$0.550236\pi$
$908$	10.6534	0.353547
$909$	7.95864	0.263972
$910$	0	0
$911$	41.9347	1.38936	0.694680	−	0.719319i	$-0.255546\pi$
$911$	41.9347	1.38936	0.694680	+	0.719319i	$0.255546\pi$
$912$	4.23920	0.140374
$913$	−3.53828	−0.117100
$914$	−0.590295	−0.0195252
$915$	0	0
$916$	−36.5084	−1.20627
$917$	3.50624	0.115786
$918$	1.81971	0.0600594
$919$	−4.24437	−0.140009	−0.0700044	−	0.997547i	$-0.522301\pi$
$919$	−4.24437	−0.140009	−0.0700044	+	0.997547i	$0.522301\pi$
$920$	0	0
$921$	−13.4199	−0.442199
$922$	−0.0312150	−0.00102801
$923$	6.64029	0.218568
$924$	1.37748	0.0453159
$925$	0	0
$926$	−18.7721	−0.616890
$927$	−2.06544	−0.0678380
$928$	−1.05369	−0.0345889
$929$	−14.9040	−0.488984	−0.244492	−	0.969651i	$-0.578621\pi$
$929$	−14.9040	−0.488984	−0.244492	+	0.969651i	$0.578621\pi$
$930$	0	0
$931$	6.49754	0.212948
$932$	24.9149	0.816114
$933$	−1.04271	−0.0341367
$934$	16.4563	0.538466
$935$	0	0
$936$	−13.1497	−0.429812
$937$	30.0582	0.981957	0.490979	−	0.871172i	$-0.336639\pi$
$937$	30.0582	0.981957	0.490979	+	0.871172i	$0.336639\pi$
$938$	−5.06315	−0.165318
$939$	−11.3495	−0.370375
$940$	0	0
$941$	43.5348	1.41919	0.709596	−	0.704608i	$-0.248877\pi$
$941$	43.5348	1.41919	0.709596	+	0.704608i	$0.248877\pi$
$942$	12.9720	0.422650
$943$	−16.3535	−0.532543
$944$	−3.10569	−0.101082
$945$	0	0
$946$	1.91096	0.0621305
$947$	−23.9271	−0.777527	−0.388763	−	0.921338i	$-0.627098\pi$
$947$	−23.9271	−0.777527	−0.388763	+	0.921338i	$0.627098\pi$
$948$	−19.2112	−0.623949
$949$	−25.3447	−0.822724
$950$	0	0
$951$	−26.8011	−0.869084
$952$	6.14604	0.199194
$953$	37.0720	1.20088	0.600440	−	0.799670i	$-0.294992\pi$
$953$	37.0720	1.20088	0.600440	+	0.799670i	$0.294992\pi$
$954$	−10.1437	−0.328413
$955$	0	0
$956$	15.2068	0.491823
$957$	0.180289	0.00582793
$958$	29.3493	0.948233
$959$	0.270365	0.00873053
$960$	0	0
$961$	−16.4810	−0.531644
$962$	−27.0672	−0.872682
$963$	−17.7213	−0.571062
$964$	−20.2748	−0.653009
$965$	0	0
$966$	2.18550	0.0703174
$967$	−18.7632	−0.603383	−0.301692	−	0.953406i	$-0.597551\pi$
$967$	−18.7632	−0.603383	−0.301692	+	0.953406i	$0.597551\pi$
$968$	2.66482	0.0856507
$969$	−14.9857	−0.481409
$970$	0	0
$971$	27.9800	0.897919	0.448960	−	0.893552i	$-0.351795\pi$
$971$	27.9800	0.897919	0.448960	+	0.893552i	$0.351795\pi$
$972$	−1.37748	−0.0441828
$973$	5.78488	0.185455
$974$	−1.95541	−0.0626554
$975$	0	0
$976$	−5.75966	−0.184362
$977$	−17.3992	−0.556650	−0.278325	−	0.960487i	$-0.589779\pi$
$977$	−17.3992	−0.556650	−0.278325	+	0.960487i	$0.589779\pi$
$978$	11.4847	0.367241
$979$	14.2197	0.454463
$980$	0	0
$981$	11.8481	0.378281
$982$	−15.7883	−0.503826
$983$	19.2647	0.614447	0.307224	−	0.951637i	$-0.400600\pi$
$983$	19.2647	0.614447	0.307224	+	0.951637i	$0.400600\pi$
$984$	−15.7327	−0.501540
$985$	0	0
$986$	0.328074	0.0104480
$987$	−7.88672	−0.251037
$988$	44.1656	1.40510
$989$	−6.70890	−0.213331
$990$	0	0
$991$	51.2302	1.62738	0.813690	−	0.581299i	$-0.197455\pi$
$991$	51.2302	1.62738	0.813690	+	0.581299i	$0.197455\pi$
$992$	22.2695	0.707056
$993$	−23.8648	−0.757328
$994$	−1.06173	−0.0336760
$995$	0	0
$996$	4.87393	0.154436
$997$	−2.78554	−0.0882189	−0.0441095	−	0.999027i	$-0.514045\pi$
$997$	−2.78554	−0.0882189	−0.0441095	+	0.999027i	$0.514045\pi$
$998$	−23.2081	−0.734639
$999$	−6.95216	−0.219957

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5775.2.a.ce.1.3	✓	5
5.4	even	2		5775.2.a.cl.1.3	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5775.2.a.ce.1.3	✓	5	1.1	even	1	trivial
5775.2.a.cl.1.3	yes	5	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5775 = 3 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5775.a (trivial)

\(f(q)\)	\(=\)	\(q-0.788997 q^{2} +1.00000 q^{3} -1.37748 q^{4} -0.788997 q^{6} -1.00000 q^{7} +2.66482 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.788997 q^{2} +1.00000 q^{3} -1.37748 q^{4} -0.788997 q^{6} -1.00000 q^{7} +2.66482 q^{8} +1.00000 q^{9} +1.00000 q^{11} -1.37748 q^{12} -4.93456 q^{13} +0.788997 q^{14} +0.652431 q^{16} -2.30636 q^{17} -0.788997 q^{18} +6.49754 q^{19} -1.00000 q^{21} -0.788997 q^{22} +2.76998 q^{23} +2.66482 q^{24} +3.89335 q^{26} +1.00000 q^{27} +1.37748 q^{28} +0.180289 q^{29} -3.81039 q^{31} -5.84441 q^{32} +1.00000 q^{33} +1.81971 q^{34} -1.37748 q^{36} -6.95216 q^{37} -5.12654 q^{38} -4.93456 q^{39} -5.90384 q^{41} +0.788997 q^{42} -2.42201 q^{43} -1.37748 q^{44} -2.18550 q^{46} +7.88672 q^{47} +0.652431 q^{48} +1.00000 q^{49} -2.30636 q^{51} +6.79728 q^{52} +12.8564 q^{53} -0.788997 q^{54} -2.66482 q^{56} +6.49754 q^{57} -0.142248 q^{58} -4.76018 q^{59} -8.82799 q^{61} +3.00638 q^{62} -1.00000 q^{63} +3.30636 q^{64} -0.788997 q^{66} -6.41719 q^{67} +3.17698 q^{68} +2.76998 q^{69} -1.34567 q^{71} +2.66482 q^{72} +5.13617 q^{73} +5.48523 q^{74} -8.95027 q^{76} -1.00000 q^{77} +3.89335 q^{78} +13.9466 q^{79} +1.00000 q^{81} +4.65811 q^{82} -3.53828 q^{83} +1.37748 q^{84} +1.91096 q^{86} +0.180289 q^{87} +2.66482 q^{88} +14.2197 q^{89} +4.93456 q^{91} -3.81560 q^{92} -3.81039 q^{93} -6.22260 q^{94} -5.84441 q^{96} -7.78568 q^{97} -0.788997 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} + 5 q^{3} + 4 q^{4} - 2 q^{6} - 5 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 + 5 * q^3 + 4 * q^4 - 2 * q^6 - 5 * q^7 - 6 * q^8 + 5 * q^9	\( 5 q - 2 q^{2} + 5 q^{3} + 4 q^{4} - 2 q^{6} - 5 q^{7} - 6 q^{8} + 5 q^{9} + 5 q^{11} + 4 q^{12} - 7 q^{13} + 2 q^{14} - 2 q^{16} - 15 q^{17} - 2 q^{18} + 3 q^{19} - 5 q^{21} - 2 q^{22} - 6 q^{24} + 5 q^{27} - 4 q^{28} - 4 q^{29} + 16 q^{31} - 14 q^{32} + 5 q^{33} + 14 q^{34} + 4 q^{36} - 7 q^{37} + 2 q^{38} - 7 q^{39} - 5 q^{41} + 2 q^{42} - 16 q^{43} + 4 q^{44} - 10 q^{46} - 6 q^{47} - 2 q^{48} + 5 q^{49} - 15 q^{51} - 18 q^{52} - 11 q^{53} - 2 q^{54} + 6 q^{56} + 3 q^{57} + 28 q^{58} - 6 q^{59} + q^{61} - 26 q^{62} - 5 q^{63} + 20 q^{64} - 2 q^{66} - 9 q^{67} - 2 q^{68} - 21 q^{71} - 6 q^{72} - 17 q^{73} + 4 q^{74} - 26 q^{76} - 5 q^{77} - 8 q^{79} + 5 q^{81} - 14 q^{82} - 26 q^{83} - 4 q^{84} - 20 q^{86} - 4 q^{87} - 6 q^{88} + 7 q^{91} + 12 q^{92} + 16 q^{93} + 4 q^{94} - 14 q^{96} - 24 q^{97} - 2 q^{98} + 5 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 + 5 * q^3 + 4 * q^4 - 2 * q^6 - 5 * q^7 - 6 * q^8 + 5 * q^9 + 5 * q^11 + 4 * q^12 - 7 * q^13 + 2 * q^14 - 2 * q^16 - 15 * q^17 - 2 * q^18 + 3 * q^19 - 5 * q^21 - 2 * q^22 - 6 * q^24 + 5 * q^27 - 4 * q^28 - 4 * q^29 + 16 * q^31 - 14 * q^32 + 5 * q^33 + 14 * q^34 + 4 * q^36 - 7 * q^37 + 2 * q^38 - 7 * q^39 - 5 * q^41 + 2 * q^42 - 16 * q^43 + 4 * q^44 - 10 * q^46 - 6 * q^47 - 2 * q^48 + 5 * q^49 - 15 * q^51 - 18 * q^52 - 11 * q^53 - 2 * q^54 + 6 * q^56 + 3 * q^57 + 28 * q^58 - 6 * q^59 + q^61 - 26 * q^62 - 5 * q^63 + 20 * q^64 - 2 * q^66 - 9 * q^67 - 2 * q^68 - 21 * q^71 - 6 * q^72 - 17 * q^73 + 4 * q^74 - 26 * q^76 - 5 * q^77 - 8 * q^79 + 5 * q^81 - 14 * q^82 - 26 * q^83 - 4 * q^84 - 20 * q^86 - 4 * q^87 - 6 * q^88 + 7 * q^91 + 12 * q^92 + 16 * q^93 + 4 * q^94 - 14 * q^96 - 24 * q^97 - 2 * q^98 + 5 * q^99

Introduction

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