LMFDB - Embedded newform 5550.2.a.cj.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5550,2,Mod(1,5550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5550, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("5550.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5550 = 2 \cdot 3 \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5550.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:	$44.3169731218$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.54764.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 9x^{2} + 3x + 2 $ x^4 - x^3 - 9x^2 + 3x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 1110)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$3.36007$ of defining polynomial
Character	$\chi$	$=$	5550.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -0.487359 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -0.487359 q^{7} -1.00000 q^{8} +1.00000 q^{9} -5.20750 q^{11} -1.00000 q^{12} -4.12492 q^{13} +0.487359 q^{14} +1.00000 q^{16} -3.67781 q^{17} -1.00000 q^{18} +0.430057 q^{19} +0.487359 q^{21} +5.20750 q^{22} -7.31537 q^{23} +1.00000 q^{24} +4.12492 q^{26} -1.00000 q^{27} -0.487359 q^{28} -6.77745 q^{29} +7.80273 q^{31} -1.00000 q^{32} +5.20750 q^{33} +3.67781 q^{34} +1.00000 q^{36} +1.00000 q^{37} -0.430057 q^{38} +4.12492 q^{39} -9.80273 q^{41} -0.487359 q^{42} -4.77745 q^{43} -5.20750 q^{44} +7.31537 q^{46} -3.52969 q^{47} -1.00000 q^{48} -6.76248 q^{49} +3.67781 q^{51} -4.12492 q^{52} +7.67781 q^{53} +1.00000 q^{54} +0.487359 q^{56} -0.430057 q^{57} +6.77745 q^{58} -0.974718 q^{59} -14.5229 q^{61} -7.80273 q^{62} -0.487359 q^{63} +1.00000 q^{64} -5.20750 q^{66} +1.19045 q^{67} -3.67781 q^{68} +7.31537 q^{69} +8.58018 q^{71} -1.00000 q^{72} +7.15020 q^{73} -1.00000 q^{74} +0.430057 q^{76} +2.53792 q^{77} -4.12492 q^{78} +4.00000 q^{79} +1.00000 q^{81} +9.80273 q^{82} +16.5399 q^{83} +0.487359 q^{84} +4.77745 q^{86} +6.77745 q^{87} +5.20750 q^{88} +16.7051 q^{89} +2.01032 q^{91} -7.31537 q^{92} -7.80273 q^{93} +3.52969 q^{94} +1.00000 q^{96} +7.16726 q^{97} +6.76248 q^{98} -5.20750 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^9	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{9} + 2 q^{11} - 4 q^{12} + 3 q^{13} + 4 q^{14} + 4 q^{16} - 6 q^{17} - 4 q^{18} + 3 q^{19} + 4 q^{21} - 2 q^{22} + q^{23} + 4 q^{24} - 3 q^{26} - 4 q^{27} - 4 q^{28} - 3 q^{29} + 3 q^{31} - 4 q^{32} - 2 q^{33} + 6 q^{34} + 4 q^{36} + 4 q^{37} - 3 q^{38} - 3 q^{39} - 11 q^{41} - 4 q^{42} + 5 q^{43} + 2 q^{44} - q^{46} - 4 q^{48} + 14 q^{49} + 6 q^{51} + 3 q^{52} + 22 q^{53} + 4 q^{54} + 4 q^{56} - 3 q^{57} + 3 q^{58} - 8 q^{59} - 5 q^{61} - 3 q^{62} - 4 q^{63} + 4 q^{64} + 2 q^{66} - 6 q^{67} - 6 q^{68} - q^{69} - 18 q^{71} - 4 q^{72} + 5 q^{73} - 4 q^{74} + 3 q^{76} + 4 q^{77} + 3 q^{78} + 16 q^{79} + 4 q^{81} + 11 q^{82} + q^{83} + 4 q^{84} - 5 q^{86} + 3 q^{87} - 2 q^{88} - 5 q^{89} - 13 q^{91} + q^{92} - 3 q^{93} + 4 q^{96} - 7 q^{97} - 14 q^{98} + 2 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^9 + 2 * q^11 - 4 * q^12 + 3 * q^13 + 4 * q^14 + 4 * q^16 - 6 * q^17 - 4 * q^18 + 3 * q^19 + 4 * q^21 - 2 * q^22 + q^23 + 4 * q^24 - 3 * q^26 - 4 * q^27 - 4 * q^28 - 3 * q^29 + 3 * q^31 - 4 * q^32 - 2 * q^33 + 6 * q^34 + 4 * q^36 + 4 * q^37 - 3 * q^38 - 3 * q^39 - 11 * q^41 - 4 * q^42 + 5 * q^43 + 2 * q^44 - q^46 - 4 * q^48 + 14 * q^49 + 6 * q^51 + 3 * q^52 + 22 * q^53 + 4 * q^54 + 4 * q^56 - 3 * q^57 + 3 * q^58 - 8 * q^59 - 5 * q^61 - 3 * q^62 - 4 * q^63 + 4 * q^64 + 2 * q^66 - 6 * q^67 - 6 * q^68 - q^69 - 18 * q^71 - 4 * q^72 + 5 * q^73 - 4 * q^74 + 3 * q^76 + 4 * q^77 + 3 * q^78 + 16 * q^79 + 4 * q^81 + 11 * q^82 + q^83 + 4 * q^84 - 5 * q^86 + 3 * q^87 - 2 * q^88 - 5 * q^89 - 13 * q^91 + q^92 - 3 * q^93 + 4 * q^96 - 7 * q^97 - 14 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	−0.487359	−0.184204	−0.0921022	−	0.995750i	$-0.529359\pi$
$7$	−0.487359	−0.184204	−0.0921022	+	0.995750i	$0.529359\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−5.20750	−1.57012	−0.785061	−	0.619419i	$-0.787368\pi$
$11$	−5.20750	−1.57012	−0.785061	+	0.619419i	$0.787368\pi$
$12$	−1.00000	−0.288675
$13$	−4.12492	−1.14405	−0.572023	−	0.820237i	$-0.693841\pi$
$13$	−4.12492	−1.14405	−0.572023	+	0.820237i	$0.693841\pi$
$14$	0.487359	0.130252
$15$	0	0
$16$	1.00000	0.250000
$17$	−3.67781	−0.892000	−0.446000	−	0.895033i	$-0.647152\pi$
$17$	−3.67781	−0.892000	−0.446000	+	0.895033i	$0.647152\pi$
$18$	−1.00000	−0.235702
$19$	0.430057	0.0986618	0.0493309	−	0.998782i	$-0.484291\pi$
$19$	0.430057	0.0986618	0.0493309	+	0.998782i	$0.484291\pi$
$20$	0	0
$21$	0.487359	0.106350
$22$	5.20750	1.11024
$23$	−7.31537	−1.52536	−0.762680	−	0.646776i	$-0.776117\pi$
$23$	−7.31537	−1.52536	−0.762680	+	0.646776i	$0.776117\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	4.12492	0.808963
$27$	−1.00000	−0.192450
$28$	−0.487359	−0.0921022
$29$	−6.77745	−1.25854	−0.629270	−	0.777187i	$-0.716646\pi$
$29$	−6.77745	−1.25854	−0.629270	+	0.777187i	$0.716646\pi$
$30$	0	0
$31$	7.80273	1.40141	0.700706	−	0.713450i	$-0.252869\pi$
$31$	7.80273	1.40141	0.700706	+	0.713450i	$0.252869\pi$
$32$	−1.00000	−0.176777
$33$	5.20750	0.906510
$34$	3.67781	0.630739
$35$	0	0
$36$	1.00000	0.166667
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−0.430057	−0.0697645
$39$	4.12492	0.660516
$40$	0	0
$41$	−9.80273	−1.53093	−0.765465	−	0.643478i	$-0.777491\pi$
$41$	−9.80273	−1.53093	−0.765465	+	0.643478i	$0.777491\pi$
$42$	−0.487359	−0.0752011
$43$	−4.77745	−0.728554	−0.364277	−	0.931291i	$-0.618684\pi$
$43$	−4.77745	−0.728554	−0.364277	+	0.931291i	$0.618684\pi$
$44$	−5.20750	−0.785061
$45$	0	0
$46$	7.31537	1.07859
$47$	−3.52969	−0.514859	−0.257429	−	0.966297i	$-0.582875\pi$
$47$	−3.52969	−0.514859	−0.257429	+	0.966297i	$0.582875\pi$
$48$	−1.00000	−0.144338
$49$	−6.76248	−0.966069
$50$	0	0
$51$	3.67781	0.514996
$52$	−4.12492	−0.572023
$53$	7.67781	1.05463	0.527314	−	0.849670i	$-0.323199\pi$
$53$	7.67781	1.05463	0.527314	+	0.849670i	$0.323199\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	0.487359	0.0651261
$57$	−0.430057	−0.0569624
$58$	6.77745	0.889922
$59$	−0.974718	−0.126897	−0.0634487	−	0.997985i	$-0.520210\pi$
$59$	−0.974718	−0.126897	−0.0634487	+	0.997985i	$0.520210\pi$
$60$	0	0
$61$	−14.5229	−1.85946	−0.929732	−	0.368237i	$-0.879961\pi$
$61$	−14.5229	−1.85946	−0.929732	+	0.368237i	$0.879961\pi$
$62$	−7.80273	−0.990948
$63$	−0.487359	−0.0614014
$64$	1.00000	0.125000
$65$	0	0
$66$	−5.20750	−0.640999
$67$	1.19045	0.145437	0.0727183	−	0.997353i	$-0.476833\pi$
$67$	1.19045	0.145437	0.0727183	+	0.997353i	$0.476833\pi$
$68$	−3.67781	−0.446000
$69$	7.31537	0.880667
$70$	0	0
$71$	8.58018	1.01828	0.509140	−	0.860684i	$-0.329964\pi$
$71$	8.58018	1.01828	0.509140	+	0.860684i	$0.329964\pi$
$72$	−1.00000	−0.117851
$73$	7.15020	0.836868	0.418434	−	0.908247i	$-0.362579\pi$
$73$	7.15020	0.836868	0.418434	+	0.908247i	$0.362579\pi$
$74$	−1.00000	−0.116248
$75$	0	0
$76$	0.430057	0.0493309
$77$	2.53792	0.289223
$78$	−4.12492	−0.467055
$79$	4.00000	0.450035	0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000	0.450035	0.225018	+	0.974355i	$0.427756\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	9.80273	1.08253
$83$	16.5399	1.81549	0.907747	−	0.419519i	$-0.137801\pi$
$83$	16.5399	1.81549	0.907747	+	0.419519i	$0.137801\pi$
$84$	0.487359	0.0531752
$85$	0	0
$86$	4.77745	0.515165
$87$	6.77745	0.726619
$88$	5.20750	0.555122
$89$	16.7051	1.77074	0.885368	−	0.464890i	$-0.153906\pi$
$89$	16.7051	1.77074	0.885368	+	0.464890i	$0.153906\pi$
$90$	0	0
$91$	2.01032	0.210738
$92$	−7.31537	−0.762680
$93$	−7.80273	−0.809105
$94$	3.52969	0.364060
$95$	0	0
$96$	1.00000	0.102062
$97$	7.16726	0.727725	0.363862	−	0.931453i	$-0.381458\pi$
$97$	7.16726	0.727725	0.363862	+	0.931453i	$0.381458\pi$
$98$	6.76248	0.683114
$99$	−5.20750	−0.523374
$100$	0	0
$101$	−13.7454	−1.36772	−0.683861	−	0.729613i	$-0.739700\pi$
$101$	−13.7454	−1.36772	−0.683861	+	0.729613i	$0.739700\pi$
$102$	−3.67781	−0.364157
$103$	3.52969	0.347791	0.173896	−	0.984764i	$-0.444364\pi$
$103$	3.52969	0.347791	0.173896	+	0.984764i	$0.444364\pi$
$104$	4.12492	0.404482
$105$	0	0
$106$	−7.67781	−0.745735
$107$	−7.09964	−0.686348	−0.343174	−	0.939272i	$-0.611502\pi$
$107$	−7.09964	−0.686348	−0.343174	+	0.939272i	$0.611502\pi$
$108$	−1.00000	−0.0962250
$109$	16.4321	1.57391	0.786953	−	0.617013i	$-0.211657\pi$
$109$	16.4321	1.57391	0.786953	+	0.617013i	$0.211657\pi$
$110$	0	0
$111$	−1.00000	−0.0949158
$112$	−0.487359	−0.0460511
$113$	1.22255	0.115008	0.0575040	−	0.998345i	$-0.481686\pi$
$113$	1.22255	0.115008	0.0575040	+	0.998345i	$0.481686\pi$
$114$	0.430057	0.0402785
$115$	0	0
$116$	−6.77745	−0.629270
$117$	−4.12492	−0.381349
$118$	0.974718	0.0897300
$119$	1.79241	0.164310
$120$	0	0
$121$	16.1181	1.46528
$122$	14.5229	1.31484
$123$	9.80273	0.883882
$124$	7.80273	0.700706
$125$	0	0
$126$	0.487359	0.0434174
$127$	−15.5652	−1.38119	−0.690595	−	0.723242i	$-0.742651\pi$
$127$	−15.5652	−1.38119	−0.690595	+	0.723242i	$0.742651\pi$
$128$	−1.00000	−0.0883883
$129$	4.77745	0.420631
$130$	0	0
$131$	−17.5549	−1.53378	−0.766889	−	0.641780i	$-0.778196\pi$
$131$	−17.5549	−1.53378	−0.766889	+	0.641780i	$0.778196\pi$
$132$	5.20750	0.453255
$133$	−0.209592	−0.0181739
$134$	−1.19045	−0.102839
$135$	0	0
$136$	3.67781	0.315370
$137$	21.2498	1.81549	0.907745	−	0.419523i	$-0.137803\pi$
$137$	21.2498	1.81549	0.907745	+	0.419523i	$0.137803\pi$
$138$	−7.31537	−0.622726
$139$	−15.4082	−1.30691	−0.653453	−	0.756967i	$-0.726680\pi$
$139$	−15.4082	−1.30691	−0.653453	+	0.756967i	$0.726680\pi$
$140$	0	0
$141$	3.52969	0.297254
$142$	−8.58018	−0.720032
$143$	21.4805	1.79629
$144$	1.00000	0.0833333
$145$	0	0
$146$	−7.15020	−0.591755
$147$	6.76248	0.557760
$148$	1.00000	0.0821995
$149$	−3.47913	−0.285021	−0.142511	−	0.989793i	$-0.545518\pi$
$149$	−3.47913	−0.285021	−0.142511	+	0.989793i	$0.545518\pi$
$150$	0	0
$151$	−17.7304	−1.44288	−0.721439	−	0.692478i	$-0.756519\pi$
$151$	−17.7304	−1.44288	−0.721439	+	0.692478i	$0.756519\pi$
$152$	−0.430057	−0.0348822
$153$	−3.67781	−0.297333
$154$	−2.53792	−0.204512
$155$	0	0
$156$	4.12492	0.330258
$157$	−11.8533	−0.945996	−0.472998	−	0.881064i	$-0.656828\pi$
$157$	−11.8533	−0.945996	−0.472998	+	0.881064i	$0.656828\pi$
$158$	−4.00000	−0.318223
$159$	−7.67781	−0.608890
$160$	0	0
$161$	3.56521	0.280978
$162$	−1.00000	−0.0785674
$163$	−5.89354	−0.461618	−0.230809	−	0.972999i	$-0.574137\pi$
$163$	−5.89354	−0.461618	−0.230809	+	0.972999i	$0.574137\pi$
$164$	−9.80273	−0.765465
$165$	0	0
$166$	−16.5399	−1.28375
$167$	−24.8362	−1.92188	−0.960940	−	0.276758i	$-0.910740\pi$
$167$	−24.8362	−1.92188	−0.960940	+	0.276758i	$0.910740\pi$
$168$	−0.487359	−0.0376006
$169$	4.01497	0.308844
$170$	0	0
$171$	0.430057	0.0328873
$172$	−4.77745	−0.364277
$173$	19.9276	1.51507	0.757536	−	0.652794i	$-0.226403\pi$
$173$	19.9276	1.51507	0.757536	+	0.652794i	$0.226403\pi$
$174$	−6.77745	−0.513797
$175$	0	0
$176$	−5.20750	−0.392530
$177$	0.974718	0.0732643
$178$	−16.7051	−1.25210
$179$	−4.33034	−0.323665	−0.161832	−	0.986818i	$-0.551740\pi$
$179$	−4.33034	−0.323665	−0.161832	+	0.986818i	$0.551740\pi$
$180$	0	0
$181$	−0.0505645	−0.00375843	−0.00187922	−	0.999998i	$-0.500598\pi$
$181$	−0.0505645	−0.00375843	−0.00187922	+	0.999998i	$0.500598\pi$
$182$	−2.01032	−0.149015
$183$	14.5229	1.07356
$184$	7.31537	0.539296
$185$	0	0
$186$	7.80273	0.572124
$187$	19.1522	1.40055
$188$	−3.52969	−0.257429
$189$	0.487359	0.0354501
$190$	0	0
$191$	−4.37276	−0.316401	−0.158201	−	0.987407i	$-0.550569\pi$
$191$	−4.37276	−0.316401	−0.158201	+	0.987407i	$0.550569\pi$
$192$	−1.00000	−0.0721688
$193$	2.47031	0.177816	0.0889082	−	0.996040i	$-0.471662\pi$
$193$	2.47031	0.177816	0.0889082	+	0.996040i	$0.471662\pi$
$194$	−7.16726	−0.514579
$195$	0	0
$196$	−6.76248	−0.483034
$197$	13.3154	0.948681	0.474340	−	0.880341i	$-0.342687\pi$
$197$	13.3154	0.948681	0.474340	+	0.880341i	$0.342687\pi$
$198$	5.20750	0.370081
$199$	21.4403	1.51986	0.759931	−	0.650004i	$-0.225233\pi$
$199$	21.4403	1.51986	0.759931	+	0.650004i	$0.225233\pi$
$200$	0	0
$201$	−1.19045	−0.0839679
$202$	13.7454	0.967125
$203$	3.30305	0.231829
$204$	3.67781	0.257498
$205$	0	0
$206$	−3.52969	−0.245925
$207$	−7.31537	−0.508453
$208$	−4.12492	−0.286012
$209$	−2.23952	−0.154911
$210$	0	0
$211$	13.9679	0.961590	0.480795	−	0.876833i	$-0.340348\pi$
$211$	13.9679	0.961590	0.480795	+	0.876833i	$0.340348\pi$
$212$	7.67781	0.527314
$213$	−8.58018	−0.587904
$214$	7.09964	0.485321
$215$	0	0
$216$	1.00000	0.0680414
$217$	−3.80273	−0.258146
$218$	−16.4321	−1.11292
$219$	−7.15020	−0.483166
$220$	0	0
$221$	15.1707	1.02049
$222$	1.00000	0.0671156
$223$	22.4335	1.50226	0.751128	−	0.660156i	$-0.229510\pi$
$223$	22.4335	1.50226	0.751128	+	0.660156i	$0.229510\pi$
$224$	0.487359	0.0325630
$225$	0	0
$226$	−1.22255	−0.0813230
$227$	−23.8368	−1.58211	−0.791053	−	0.611747i	$-0.790467\pi$
$227$	−23.8368	−1.58211	−0.791053	+	0.611747i	$0.790467\pi$
$228$	−0.430057	−0.0284812
$229$	10.2157	0.675075	0.337537	−	0.941312i	$-0.390406\pi$
$229$	10.2157	0.675075	0.337537	+	0.941312i	$0.390406\pi$
$230$	0	0
$231$	−2.53792	−0.166983
$232$	6.77745	0.444961
$233$	−2.07576	−0.135988	−0.0679939	−	0.997686i	$-0.521660\pi$
$233$	−2.07576	−0.135988	−0.0679939	+	0.997686i	$0.521660\pi$
$234$	4.12492	0.269654
$235$	0	0
$236$	−0.974718	−0.0634487
$237$	−4.00000	−0.259828
$238$	−1.79241	−0.116185
$239$	−28.2683	−1.82852	−0.914262	−	0.405123i	$-0.867229\pi$
$239$	−28.2683	−1.82852	−0.914262	+	0.405123i	$0.867229\pi$
$240$	0	0
$241$	20.4491	1.31724	0.658622	−	0.752474i	$-0.271140\pi$
$241$	20.4491	1.31724	0.658622	+	0.752474i	$0.271140\pi$
$242$	−16.1181	−1.03611
$243$	−1.00000	−0.0641500
$244$	−14.5229	−0.929732
$245$	0	0
$246$	−9.80273	−0.624999
$247$	−1.77395	−0.112874
$248$	−7.80273	−0.495474
$249$	−16.5399	−1.04818
$250$	0	0
$251$	−19.3092	−1.21879	−0.609394	−	0.792868i	$-0.708587\pi$
$251$	−19.3092	−1.21879	−0.609394	+	0.792868i	$0.708587\pi$
$252$	−0.487359	−0.0307007
$253$	38.0948	2.39500
$254$	15.5652	0.976648
$255$	0	0
$256$	1.00000	0.0625000
$257$	−0.735194	−0.0458601	−0.0229301	−	0.999737i	$-0.507300\pi$
$257$	−0.735194	−0.0458601	−0.0229301	+	0.999737i	$0.507300\pi$
$258$	−4.77745	−0.297431
$259$	−0.487359	−0.0302830
$260$	0	0
$261$	−6.77745	−0.419513
$262$	17.5549	1.08454
$263$	−6.47231	−0.399100	−0.199550	−	0.979888i	$-0.563948\pi$
$263$	−6.47231	−0.399100	−0.199550	+	0.979888i	$0.563948\pi$
$264$	−5.20750	−0.320500
$265$	0	0
$266$	0.209592	0.0128509
$267$	−16.7051	−1.02234
$268$	1.19045	0.0727183
$269$	−0.810958	−0.0494450	−0.0247225	−	0.999694i	$-0.507870\pi$
$269$	−0.810958	−0.0494450	−0.0247225	+	0.999694i	$0.507870\pi$
$270$	0	0
$271$	17.4403	1.05942	0.529711	−	0.848178i	$-0.322300\pi$
$271$	17.4403	1.05942	0.529711	+	0.848178i	$0.322300\pi$
$272$	−3.67781	−0.223000
$273$	−2.01032	−0.121670
$274$	−21.2498	−1.28374
$275$	0	0
$276$	7.31537	0.440334
$277$	1.46007	0.0877272	0.0438636	−	0.999038i	$-0.486033\pi$
$277$	1.46007	0.0877272	0.0438636	+	0.999038i	$0.486033\pi$
$278$	15.4082	0.924122
$279$	7.80273	0.467137
$280$	0	0
$281$	−12.1249	−0.723312	−0.361656	−	0.932312i	$-0.617789\pi$
$281$	−12.1249	−0.723312	−0.361656	+	0.932312i	$0.617789\pi$
$282$	−3.52969	−0.210190
$283$	−19.5652	−1.16303	−0.581516	−	0.813535i	$-0.697540\pi$
$283$	−19.5652	−1.16303	−0.581516	+	0.813535i	$0.697540\pi$
$284$	8.58018	0.509140
$285$	0	0
$286$	−21.4805	−1.27017
$287$	4.77745	0.282004
$288$	−1.00000	−0.0589256
$289$	−3.47372	−0.204336
$290$	0	0
$291$	−7.16726	−0.420152
$292$	7.15020	0.418434
$293$	17.5126	1.02310	0.511550	−	0.859254i	$-0.329072\pi$
$293$	17.5126	1.02310	0.511550	+	0.859254i	$0.329072\pi$
$294$	−6.76248	−0.394396
$295$	0	0
$296$	−1.00000	−0.0581238
$297$	5.20750	0.302170
$298$	3.47913	0.201541
$299$	30.1753	1.74508
$300$	0	0
$301$	2.32833	0.134203
$302$	17.7304	1.02027
$303$	13.7454	0.789654
$304$	0.430057	0.0246655
$305$	0	0
$306$	3.67781	0.210246
$307$	0.364444	0.0207999	0.0104000	−	0.999946i	$-0.496690\pi$
$307$	0.364444	0.0207999	0.0104000	+	0.999946i	$0.496690\pi$
$308$	2.53792	0.144612
$309$	−3.52969	−0.200797
$310$	0	0
$311$	−15.1583	−0.859551	−0.429776	−	0.902936i	$-0.641407\pi$
$311$	−15.1583	−0.859551	−0.429776	+	0.902936i	$0.641407\pi$
$312$	−4.12492	−0.233528
$313$	14.7201	0.832032	0.416016	−	0.909357i	$-0.363426\pi$
$313$	14.7201	0.832032	0.416016	+	0.909357i	$0.363426\pi$
$314$	11.8533	0.668920
$315$	0	0
$316$	4.00000	0.225018
$317$	0.942615	0.0529426	0.0264713	−	0.999650i	$-0.491573\pi$
$317$	0.942615	0.0529426	0.0264713	+	0.999650i	$0.491573\pi$
$318$	7.67781	0.430550
$319$	35.2936	1.97606
$320$	0	0
$321$	7.09964	0.396263
$322$	−3.56521	−0.198681
$323$	−1.58167	−0.0880063
$324$	1.00000	0.0555556
$325$	0	0
$326$	5.89354	0.326413
$327$	−16.4321	−0.908695
$328$	9.80273	0.541265
$329$	1.72023	0.0948392
$330$	0	0
$331$	15.8600	0.871746	0.435873	−	0.900008i	$-0.356440\pi$
$331$	15.8600	0.871746	0.435873	+	0.900008i	$0.356440\pi$
$332$	16.5399	0.907747
$333$	1.00000	0.0547997
$334$	24.8362	1.35897
$335$	0	0
$336$	0.487359	0.0265876
$337$	−16.9549	−0.923594	−0.461797	−	0.886986i	$-0.652795\pi$
$337$	−16.9549	−0.923594	−0.461797	+	0.886986i	$0.652795\pi$
$338$	−4.01497	−0.218385
$339$	−1.22255	−0.0664000
$340$	0	0
$341$	−40.6327	−2.20039
$342$	−0.430057	−0.0232548
$343$	6.70727	0.362158
$344$	4.77745	0.257583
$345$	0	0
$346$	−19.9276	−1.07132
$347$	5.44029	0.292050	0.146025	−	0.989281i	$-0.453352\pi$
$347$	5.44029	0.292050	0.146025	+	0.989281i	$0.453352\pi$
$348$	6.77745	0.363309
$349$	23.1262	1.23792	0.618960	−	0.785423i	$-0.287554\pi$
$349$	23.1262	1.23792	0.618960	+	0.785423i	$0.287554\pi$
$350$	0	0
$351$	4.12492	0.220172
$352$	5.20750	0.277561
$353$	−24.7638	−1.31804	−0.659022	−	0.752123i	$-0.729030\pi$
$353$	−24.7638	−1.31804	−0.659022	+	0.752123i	$0.729030\pi$
$354$	−0.974718	−0.0518057
$355$	0	0
$356$	16.7051	0.885368
$357$	−1.79241	−0.0948646
$358$	4.33034	0.228865
$359$	−17.5549	−0.926512	−0.463256	−	0.886225i	$-0.653319\pi$
$359$	−17.5549	−0.926512	−0.463256	+	0.886225i	$0.653319\pi$
$360$	0	0
$361$	−18.8151	−0.990266
$362$	0.0505645	0.00265761
$363$	−16.1181	−0.845981
$364$	2.01032	0.105369
$365$	0	0
$366$	−14.5229	−0.759123
$367$	8.17331	0.426644	0.213322	−	0.976982i	$-0.431572\pi$
$367$	8.17331	0.426644	0.213322	+	0.976982i	$0.431572\pi$
$368$	−7.31537	−0.381340
$369$	−9.80273	−0.510310
$370$	0	0
$371$	−3.74185	−0.194267
$372$	−7.80273	−0.404553
$373$	6.00000	0.310668	0.155334	−	0.987862i	$-0.450355\pi$
$373$	6.00000	0.310668	0.155334	+	0.987862i	$0.450355\pi$
$374$	−19.1522	−0.990337
$375$	0	0
$376$	3.52969	0.182030
$377$	27.9564	1.43983
$378$	−0.487359	−0.0250670
$379$	26.1993	1.34577	0.672883	−	0.739749i	$-0.265056\pi$
$379$	26.1993	1.34577	0.672883	+	0.739749i	$0.265056\pi$
$380$	0	0
$381$	15.5652	0.797430
$382$	4.37276	0.223730
$383$	5.87508	0.300203	0.150101	−	0.988671i	$-0.452040\pi$
$383$	5.87508	0.300203	0.150101	+	0.988671i	$0.452040\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−2.47031	−0.125735
$387$	−4.77745	−0.242851
$388$	7.16726	0.363862
$389$	33.8368	1.71560	0.857798	−	0.513987i	$-0.171832\pi$
$389$	33.8368	1.71560	0.857798	+	0.513987i	$0.171832\pi$
$390$	0	0
$391$	26.9045	1.36062
$392$	6.76248	0.341557
$393$	17.5549	0.885527
$394$	−13.3154	−0.670819
$395$	0	0
$396$	−5.20750	−0.261687
$397$	1.75016	0.0878380	0.0439190	−	0.999035i	$-0.486016\pi$
$397$	1.75016	0.0878380	0.0439190	+	0.999035i	$0.486016\pi$
$398$	−21.4403	−1.07470
$399$	0.209592	0.0104927
$400$	0	0
$401$	24.7051	1.23371	0.616857	−	0.787075i	$-0.288406\pi$
$401$	24.7051	1.23371	0.616857	+	0.787075i	$0.288406\pi$
$402$	1.19045	0.0593743
$403$	−32.1856	−1.60328
$404$	−13.7454	−0.683861
$405$	0	0
$406$	−3.30305	−0.163928
$407$	−5.20750	−0.258126
$408$	−3.67781	−0.182079
$409$	6.75899	0.334210	0.167105	−	0.985939i	$-0.446558\pi$
$409$	6.75899	0.334210	0.167105	+	0.985939i	$0.446558\pi$
$410$	0	0
$411$	−21.2498	−1.04817
$412$	3.52969	0.173896
$413$	0.475037	0.0233751
$414$	7.31537	0.359531
$415$	0	0
$416$	4.12492	0.202241
$417$	15.4082	0.754542
$418$	2.23952	0.109539
$419$	12.2143	0.596709	0.298354	−	0.954455i	$-0.403562\pi$
$419$	12.2143	0.596709	0.298354	+	0.954455i	$0.403562\pi$
$420$	0	0
$421$	−8.91942	−0.434706	−0.217353	−	0.976093i	$-0.569742\pi$
$421$	−8.91942	−0.434706	−0.217353	+	0.976093i	$0.569742\pi$
$422$	−13.9679	−0.679947
$423$	−3.52969	−0.171620
$424$	−7.67781	−0.372867
$425$	0	0
$426$	8.58018	0.415711
$427$	7.07785	0.342521
$428$	−7.09964	−0.343174
$429$	−21.4805	−1.03709
$430$	0	0
$431$	4.98704	0.240217	0.120109	−	0.992761i	$-0.461676\pi$
$431$	4.98704	0.240217	0.120109	+	0.992761i	$0.461676\pi$
$432$	−1.00000	−0.0481125
$433$	−15.4805	−0.743947	−0.371974	−	0.928243i	$-0.621319\pi$
$433$	−15.4805	−0.743947	−0.371974	+	0.928243i	$0.621319\pi$
$434$	3.80273	0.182537
$435$	0	0
$436$	16.4321	0.786953
$437$	−3.14603	−0.150495
$438$	7.15020	0.341650
$439$	−21.4929	−1.02580	−0.512899	−	0.858449i	$-0.671429\pi$
$439$	−21.4929	−1.02580	−0.512899	+	0.858449i	$0.671429\pi$
$440$	0	0
$441$	−6.76248	−0.322023
$442$	−15.1707	−0.721595
$443$	32.4355	1.54106	0.770528	−	0.637406i	$-0.219993\pi$
$443$	32.4355	1.54106	0.770528	+	0.637406i	$0.219993\pi$
$444$	−1.00000	−0.0474579
$445$	0	0
$446$	−22.4335	−1.06226
$447$	3.47913	0.164557
$448$	−0.487359	−0.0230255
$449$	15.8348	0.747292	0.373646	−	0.927571i	$-0.378108\pi$
$449$	15.8348	0.747292	0.373646	+	0.927571i	$0.378108\pi$
$450$	0	0
$451$	51.0478	2.40374
$452$	1.22255	0.0575040
$453$	17.7304	0.833046
$454$	23.8368	1.11872
$455$	0	0
$456$	0.430057	0.0201393
$457$	29.4470	1.37747	0.688737	−	0.725011i	$-0.258166\pi$
$457$	29.4470	1.37747	0.688737	+	0.725011i	$0.258166\pi$
$458$	−10.2157	−0.477350
$459$	3.67781	0.171665
$460$	0	0
$461$	18.4975	0.861515	0.430757	−	0.902468i	$-0.358246\pi$
$461$	18.4975	0.861515	0.430757	+	0.902468i	$0.358246\pi$
$462$	2.53792	0.118075
$463$	7.46549	0.346951	0.173475	−	0.984838i	$-0.444500\pi$
$463$	7.46549	0.346951	0.173475	+	0.984838i	$0.444500\pi$
$464$	−6.77745	−0.314635
$465$	0	0
$466$	2.07576	0.0961579
$467$	−33.3917	−1.54519	−0.772593	−	0.634902i	$-0.781040\pi$
$467$	−33.3917	−1.54519	−0.772593	+	0.634902i	$0.781040\pi$
$468$	−4.12492	−0.190674
$469$	−0.580177	−0.0267901
$470$	0	0
$471$	11.8533	0.546171
$472$	0.974718	0.0448650
$473$	24.8786	1.14392
$474$	4.00000	0.183726
$475$	0	0
$476$	1.79241	0.0821551
$477$	7.67781	0.351543
$478$	28.2683	1.29296
$479$	26.7051	1.22019	0.610094	−	0.792329i	$-0.291132\pi$
$479$	26.7051	1.22019	0.610094	+	0.792329i	$0.291132\pi$
$480$	0	0
$481$	−4.12492	−0.188080
$482$	−20.4491	−0.931432
$483$	−3.56521	−0.162223
$484$	16.1181	0.732641
$485$	0	0
$486$	1.00000	0.0453609
$487$	1.61437	0.0731539	0.0365770	−	0.999331i	$-0.488355\pi$
$487$	1.61437	0.0731539	0.0365770	+	0.999331i	$0.488355\pi$
$488$	14.5229	0.657420
$489$	5.89354	0.266515
$490$	0	0
$491$	1.40477	0.0633966	0.0316983	−	0.999497i	$-0.489908\pi$
$491$	1.40477	0.0633966	0.0316983	+	0.999497i	$0.489908\pi$
$492$	9.80273	0.441941
$493$	24.9262	1.12262
$494$	1.77395	0.0798138
$495$	0	0
$496$	7.80273	0.350353
$497$	−4.18163	−0.187572
$498$	16.5399	0.741172
$499$	−9.98495	−0.446988	−0.223494	−	0.974705i	$-0.571746\pi$
$499$	−9.98495	−0.446988	−0.223494	+	0.974705i	$0.571746\pi$
$500$	0	0
$501$	24.8362	1.10960
$502$	19.3092	0.861813
$503$	20.8300	0.928765	0.464382	−	0.885635i	$-0.346276\pi$
$503$	20.8300	0.928765	0.464382	+	0.885635i	$0.346276\pi$
$504$	0.487359	0.0217087
$505$	0	0
$506$	−38.0948	−1.69352
$507$	−4.01497	−0.178311
$508$	−15.5652	−0.690595
$509$	26.5816	1.17821	0.589104	−	0.808057i	$-0.299481\pi$
$509$	26.5816	1.17821	0.589104	+	0.808057i	$0.299481\pi$
$510$	0	0
$511$	−3.48471	−0.154155
$512$	−1.00000	−0.0441942
$513$	−0.430057	−0.0189875
$514$	0.735194	0.0324280
$515$	0	0
$516$	4.77745	0.210315
$517$	18.3809	0.808391
$518$	0.487359	0.0214133
$519$	−19.9276	−0.874727
$520$	0	0
$521$	−9.91733	−0.434486	−0.217243	−	0.976118i	$-0.569706\pi$
$521$	−9.91733	−0.434486	−0.217243	+	0.976118i	$0.569706\pi$
$522$	6.77745	0.296641
$523$	−5.61910	−0.245706	−0.122853	−	0.992425i	$-0.539204\pi$
$523$	−5.61910	−0.245706	−0.122853	+	0.992425i	$0.539204\pi$
$524$	−17.5549	−0.766889
$525$	0	0
$526$	6.47231	0.282206
$527$	−28.6970	−1.25006
$528$	5.20750	0.226628
$529$	30.5146	1.32672
$530$	0	0
$531$	−0.974718	−0.0422991
$532$	−0.209592	−0.00908697
$533$	40.4355	1.75145
$534$	16.7051	0.722900
$535$	0	0
$536$	−1.19045	−0.0514196
$537$	4.33034	0.186868
$538$	0.810958	0.0349629
$539$	35.2156	1.51685
$540$	0	0
$541$	−0.315288	−0.0135553	−0.00677764	−	0.999977i	$-0.502157\pi$
$541$	−0.315288	−0.0135553	−0.00677764	+	0.999977i	$0.502157\pi$
$542$	−17.4403	−0.749125
$543$	0.0505645	0.00216993
$544$	3.67781	0.157685
$545$	0	0
$546$	2.01032	0.0860336
$547$	−22.1133	−0.945496	−0.472748	−	0.881198i	$-0.656738\pi$
$547$	−22.1133	−0.945496	−0.472748	+	0.881198i	$0.656738\pi$
$548$	21.2498	0.907745
$549$	−14.5229	−0.619821
$550$	0	0
$551$	−2.91469	−0.124170
$552$	−7.31537	−0.311363
$553$	−1.94944	−0.0828984
$554$	−1.46007	−0.0620325
$555$	0	0
$556$	−15.4082	−0.653453
$557$	−24.9611	−1.05763	−0.528817	−	0.848736i	$-0.677364\pi$
$557$	−24.9611	−1.05763	−0.528817	+	0.848736i	$0.677364\pi$
$558$	−7.80273	−0.330316
$559$	19.7066	0.833500
$560$	0	0
$561$	−19.1522	−0.808607
$562$	12.1249	0.511459
$563$	29.0642	1.22491	0.612455	−	0.790505i	$-0.290182\pi$
$563$	29.0642	1.22491	0.612455	+	0.790505i	$0.290182\pi$
$564$	3.52969	0.148627
$565$	0	0
$566$	19.5652	0.822387
$567$	−0.487359	−0.0204671
$568$	−8.58018	−0.360016
$569$	34.5740	1.44942	0.724709	−	0.689055i	$-0.241974\pi$
$569$	34.5740	1.44942	0.724709	+	0.689055i	$0.241974\pi$
$570$	0	0
$571$	−40.4539	−1.69294	−0.846472	−	0.532433i	$-0.821278\pi$
$571$	−40.4539	−1.69294	−0.846472	+	0.532433i	$0.821278\pi$
$572$	21.4805	0.898146
$573$	4.37276	0.182674
$574$	−4.77745	−0.199407
$575$	0	0
$576$	1.00000	0.0416667
$577$	15.5803	0.648615	0.324307	−	0.945952i	$-0.394869\pi$
$577$	15.5803	0.648615	0.324307	+	0.945952i	$0.394869\pi$
$578$	3.47372	0.144488
$579$	−2.47031	−0.102662
$580$	0	0
$581$	−8.06088	−0.334422
$582$	7.16726	0.297092
$583$	−39.9822	−1.65589
$584$	−7.15020	−0.295877
$585$	0	0
$586$	−17.5126	−0.723441
$587$	−25.6717	−1.05958	−0.529792	−	0.848128i	$-0.677730\pi$
$587$	−25.6717	−1.05958	−0.529792	+	0.848128i	$0.677730\pi$
$588$	6.76248	0.278880
$589$	3.35562	0.138266
$590$	0	0
$591$	−13.3154	−0.547721
$592$	1.00000	0.0410997
$593$	−22.9399	−0.942028	−0.471014	−	0.882126i	$-0.656112\pi$
$593$	−22.9399	−0.942028	−0.471014	+	0.882126i	$0.656112\pi$
$594$	−5.20750	−0.213666
$595$	0	0
$596$	−3.47913	−0.142511
$597$	−21.4403	−0.877493
$598$	−30.1753	−1.23396
$599$	−10.9583	−0.447742	−0.223871	−	0.974619i	$-0.571869\pi$
$599$	−10.9583	−0.447742	−0.223871	+	0.974619i	$0.571869\pi$
$600$	0	0
$601$	38.0123	1.55055	0.775277	−	0.631621i	$-0.217610\pi$
$601$	38.0123	1.55055	0.775277	+	0.631621i	$0.217610\pi$
$602$	−2.32833	−0.0948957
$603$	1.19045	0.0484789
$604$	−17.7304	−0.721439
$605$	0	0
$606$	−13.7454	−0.558370
$607$	5.16509	0.209644	0.104822	−	0.994491i	$-0.466573\pi$
$607$	5.16509	0.209644	0.104822	+	0.994491i	$0.466573\pi$
$608$	−0.430057	−0.0174411
$609$	−3.30305	−0.133846
$610$	0	0
$611$	14.5597	0.589023
$612$	−3.67781	−0.148667
$613$	−35.6075	−1.43817	−0.719086	−	0.694921i	$-0.755439\pi$
$613$	−35.6075	−1.43817	−0.719086	+	0.694921i	$0.755439\pi$
$614$	−0.364444	−0.0147078
$615$	0	0
$616$	−2.53792	−0.102256
$617$	−32.0799	−1.29149	−0.645745	−	0.763553i	$-0.723453\pi$
$617$	−32.0799	−1.29149	−0.645745	+	0.763553i	$0.723453\pi$
$618$	3.52969	0.141985
$619$	24.6628	0.991283	0.495642	−	0.868527i	$-0.334933\pi$
$619$	24.6628	0.991283	0.495642	+	0.868527i	$0.334933\pi$
$620$	0	0
$621$	7.31537	0.293556
$622$	15.1583	0.607794
$623$	−8.14138	−0.326177
$624$	4.12492	0.165129
$625$	0	0
$626$	−14.7201	−0.588335
$627$	2.23952	0.0894380
$628$	−11.8533	−0.472998
$629$	−3.67781	−0.146644
$630$	0	0
$631$	8.89205	0.353987	0.176993	−	0.984212i	$-0.443363\pi$
$631$	8.89205	0.353987	0.176993	+	0.984212i	$0.443363\pi$
$632$	−4.00000	−0.159111
$633$	−13.9679	−0.555174
$634$	−0.942615	−0.0374360
$635$	0	0
$636$	−7.67781	−0.304445
$637$	27.8947	1.10523
$638$	−35.2936	−1.39729
$639$	8.58018	0.339427
$640$	0	0
$641$	41.5775	1.64221	0.821107	−	0.570774i	$-0.193357\pi$
$641$	41.5775	1.64221	0.821107	+	0.570774i	$0.193357\pi$
$642$	−7.09964	−0.280200
$643$	−43.1522	−1.70176	−0.850878	−	0.525363i	$-0.823930\pi$
$643$	−43.1522	−1.70176	−0.850878	+	0.525363i	$0.823930\pi$
$644$	3.56521	0.140489
$645$	0	0
$646$	1.58167	0.0622299
$647$	15.4641	0.607956	0.303978	−	0.952679i	$-0.401685\pi$
$647$	15.4641	0.607956	0.303978	+	0.952679i	$0.401685\pi$
$648$	−1.00000	−0.0392837
$649$	5.07585	0.199244
$650$	0	0
$651$	3.80273	0.149041
$652$	−5.89354	−0.230809
$653$	−17.3556	−0.679178	−0.339589	−	0.940574i	$-0.610288\pi$
$653$	−17.3556	−0.679178	−0.339589	+	0.940574i	$0.610288\pi$
$654$	16.4321	0.642544
$655$	0	0
$656$	−9.80273	−0.382732
$657$	7.15020	0.278956
$658$	−1.72023	−0.0670615
$659$	−15.3509	−0.597986	−0.298993	−	0.954255i	$-0.596651\pi$
$659$	−15.3509	−0.597986	−0.298993	+	0.954255i	$0.596651\pi$
$660$	0	0
$661$	−23.8218	−0.926560	−0.463280	−	0.886212i	$-0.653328\pi$
$661$	−23.8218	−0.926560	−0.463280	+	0.886212i	$0.653328\pi$
$662$	−15.8600	−0.616418
$663$	−15.1707	−0.589180
$664$	−16.5399	−0.641874
$665$	0	0
$666$	−1.00000	−0.0387492
$667$	49.5795	1.91973
$668$	−24.8362	−0.960940
$669$	−22.4335	−0.867328
$670$	0	0
$671$	75.6279	2.91958
$672$	−0.487359	−0.0188003
$673$	37.3523	1.43983	0.719913	−	0.694065i	$-0.244182\pi$
$673$	37.3523	1.43983	0.719913	+	0.694065i	$0.244182\pi$
$674$	16.9549	0.653080
$675$	0	0
$676$	4.01497	0.154422
$677$	−40.0143	−1.53788	−0.768938	−	0.639324i	$-0.779214\pi$
$677$	−40.0143	−1.53788	−0.768938	+	0.639324i	$0.779214\pi$
$678$	1.22255	0.0469519
$679$	−3.49303	−0.134050
$680$	0	0
$681$	23.8368	0.913430
$682$	40.6327	1.55591
$683$	−7.25948	−0.277776	−0.138888	−	0.990308i	$-0.544353\pi$
$683$	−7.25948	−0.277776	−0.138888	+	0.990308i	$0.544353\pi$
$684$	0.430057	0.0164436
$685$	0	0
$686$	−6.70727	−0.256085
$687$	−10.2157	−0.389755
$688$	−4.77745	−0.182138
$689$	−31.6703	−1.20654
$690$	0	0
$691$	7.91733	0.301190	0.150595	−	0.988596i	$-0.451881\pi$
$691$	7.91733	0.301190	0.150595	+	0.988596i	$0.451881\pi$
$692$	19.9276	0.757536
$693$	2.53792	0.0964077
$694$	−5.44029	−0.206511
$695$	0	0
$696$	−6.77745	−0.256898
$697$	36.0526	1.36559
$698$	−23.1262	−0.875341
$699$	2.07576	0.0785126
$700$	0	0
$701$	−39.1303	−1.47793	−0.738965	−	0.673744i	$-0.764685\pi$
$701$	−39.1303	−1.47793	−0.738965	+	0.673744i	$0.764685\pi$
$702$	−4.12492	−0.155685
$703$	0.430057	0.0162199
$704$	−5.20750	−0.196265
$705$	0	0
$706$	24.7638	0.931998
$707$	6.69896	0.251940
$708$	0.974718	0.0366321
$709$	−40.6478	−1.52656	−0.763280	−	0.646068i	$-0.776412\pi$
$709$	−40.6478	−1.52656	−0.763280	+	0.646068i	$0.776412\pi$
$710$	0	0
$711$	4.00000	0.150012
$712$	−16.7051	−0.626050
$713$	−57.0799	−2.13766
$714$	1.79241	0.0670794
$715$	0	0
$716$	−4.33034	−0.161832
$717$	28.2683	1.05570
$718$	17.5549	0.655143
$719$	−34.9147	−1.30210	−0.651049	−	0.759036i	$-0.725671\pi$
$719$	−34.9147	−1.30210	−0.651049	+	0.759036i	$0.725671\pi$
$720$	0	0
$721$	−1.72023	−0.0640646
$722$	18.8151	0.700224
$723$	−20.4491	−0.760511
$724$	−0.0505645	−0.00187922
$725$	0	0
$726$	16.1181	0.598199
$727$	16.1741	0.599863	0.299932	−	0.953961i	$-0.403036\pi$
$727$	16.1741	0.599863	0.299932	+	0.953961i	$0.403036\pi$
$728$	−2.01032	−0.0745073
$729$	1.00000	0.0370370
$730$	0	0
$731$	17.5705	0.649870
$732$	14.5229	0.536781
$733$	−50.0895	−1.85010	−0.925049	−	0.379848i	$-0.875976\pi$
$733$	−50.0895	−1.85010	−0.925049	+	0.379848i	$0.875976\pi$
$734$	−8.17331	−0.301683
$735$	0	0
$736$	7.31537	0.269648
$737$	−6.19928	−0.228353
$738$	9.80273	0.360843
$739$	−4.01846	−0.147822	−0.0739108	−	0.997265i	$-0.523548\pi$
$739$	−4.01846	−0.147822	−0.0739108	+	0.997265i	$0.523548\pi$
$740$	0	0
$741$	1.77395	0.0651677
$742$	3.74185	0.137368
$743$	14.4382	0.529686	0.264843	−	0.964292i	$-0.414680\pi$
$743$	14.4382	0.529686	0.264843	+	0.964292i	$0.414680\pi$
$744$	7.80273	0.286062
$745$	0	0
$746$	−6.00000	−0.219676
$747$	16.5399	0.605164
$748$	19.1522	0.700274
$749$	3.46007	0.126428
$750$	0	0
$751$	25.0088	0.912585	0.456292	−	0.889830i	$-0.349177\pi$
$751$	25.0088	0.912585	0.456292	+	0.889830i	$0.349177\pi$
$752$	−3.52969	−0.128715
$753$	19.3092	0.703667
$754$	−27.9564	−1.01811
$755$	0	0
$756$	0.487359	0.0177251
$757$	16.4049	0.596245	0.298122	−	0.954528i	$-0.403640\pi$
$757$	16.4049	0.596245	0.298122	+	0.954528i	$0.403640\pi$
$758$	−26.1993	−0.951601
$759$	−38.0948	−1.38275
$760$	0	0
$761$	19.3877	0.702804	0.351402	−	0.936225i	$-0.385705\pi$
$761$	19.3877	0.702804	0.351402	+	0.936225i	$0.385705\pi$
$762$	−15.5652	−0.563868
$763$	−8.00831	−0.289920
$764$	−4.37276	−0.158201
$765$	0	0
$766$	−5.87508	−0.212275
$767$	4.02063	0.145177
$768$	−1.00000	−0.0360844
$769$	14.1693	0.510960	0.255480	−	0.966814i	$-0.417767\pi$
$769$	14.1693	0.510960	0.255480	+	0.966814i	$0.417767\pi$
$770$	0	0
$771$	0.735194	0.0264774
$772$	2.47031	0.0889082
$773$	9.58367	0.344701	0.172350	−	0.985036i	$-0.444864\pi$
$773$	9.58367	0.344701	0.172350	+	0.985036i	$0.444864\pi$
$774$	4.77745	0.171722
$775$	0	0
$776$	−7.16726	−0.257289
$777$	0.487359	0.0174839
$778$	−33.8368	−1.21311
$779$	−4.21573	−0.151044
$780$	0	0
$781$	−44.6813	−1.59882
$782$	−26.9045	−0.962104
$783$	6.77745	0.242206
$784$	−6.76248	−0.241517
$785$	0	0
$786$	−17.5549	−0.626162
$787$	−2.47921	−0.0883744	−0.0441872	−	0.999023i	$-0.514070\pi$
$787$	−2.47921	−0.0883744	−0.0441872	+	0.999023i	$0.514070\pi$
$788$	13.3154	0.474340
$789$	6.47231	0.230420
$790$	0	0
$791$	−0.595822	−0.0211850
$792$	5.20750	0.185041
$793$	59.9057	2.12731
$794$	−1.75016	−0.0621108
$795$	0	0
$796$	21.4403	0.759931
$797$	47.0961	1.66823	0.834116	−	0.551590i	$-0.185979\pi$
$797$	47.0961	1.66823	0.834116	+	0.551590i	$0.185979\pi$
$798$	−0.209592	−0.00741948
$799$	12.9815	0.459254
$800$	0	0
$801$	16.7051	0.590246
$802$	−24.7051	−0.872367
$803$	−37.2347	−1.31398
$804$	−1.19045	−0.0419840
$805$	0	0
$806$	32.1856	1.13369
$807$	0.810958	0.0285471
$808$	13.7454	0.483562
$809$	36.6409	1.28823	0.644113	−	0.764931i	$-0.277227\pi$
$809$	36.6409	1.28823	0.644113	+	0.764931i	$0.277227\pi$
$810$	0	0
$811$	12.4997	0.438923	0.219462	−	0.975621i	$-0.429570\pi$
$811$	12.4997	0.438923	0.219462	+	0.975621i	$0.429570\pi$
$812$	3.30305	0.115914
$813$	−17.4403	−0.611658
$814$	5.20750	0.182523
$815$	0	0
$816$	3.67781	0.128749
$817$	−2.05457	−0.0718805
$818$	−6.75899	−0.236322
$819$	2.01032	0.0702461
$820$	0	0
$821$	−11.7351	−0.409558	−0.204779	−	0.978808i	$-0.565648\pi$
$821$	−11.7351	−0.409558	−0.204779	+	0.978808i	$0.565648\pi$
$822$	21.2498	0.741170
$823$	−40.5058	−1.41194	−0.705972	−	0.708240i	$-0.749490\pi$
$823$	−40.5058	−1.41194	−0.705972	+	0.708240i	$0.749490\pi$
$824$	−3.52969	−0.122963
$825$	0	0
$826$	−0.475037	−0.0165287
$827$	6.51115	0.226415	0.113207	−	0.993571i	$-0.463888\pi$
$827$	6.51115	0.226415	0.113207	+	0.993571i	$0.463888\pi$
$828$	−7.31537	−0.254227
$829$	11.0422	0.383510	0.191755	−	0.981443i	$-0.438582\pi$
$829$	11.0422	0.383510	0.191755	+	0.981443i	$0.438582\pi$
$830$	0	0
$831$	−1.46007	−0.0506493
$832$	−4.12492	−0.143006
$833$	24.8711	0.861733
$834$	−15.4082	−0.533542
$835$	0	0
$836$	−2.23952	−0.0774555
$837$	−7.80273	−0.269702
$838$	−12.2143	−0.421937
$839$	3.12641	0.107936	0.0539679	−	0.998543i	$-0.482813\pi$
$839$	3.12641	0.107936	0.0539679	+	0.998543i	$0.482813\pi$
$840$	0	0
$841$	16.9338	0.583924
$842$	8.91942	0.307384
$843$	12.1249	0.417604
$844$	13.9679	0.480795
$845$	0	0
$846$	3.52969	0.121353
$847$	−7.85530	−0.269911
$848$	7.67781	0.263657
$849$	19.5652	0.671476
$850$	0	0
$851$	−7.31537	−0.250768
$852$	−8.58018	−0.293952
$853$	8.98503	0.307642	0.153821	−	0.988099i	$-0.450842\pi$
$853$	8.98503	0.307642	0.153821	+	0.988099i	$0.450842\pi$
$854$	−7.07785	−0.242199
$855$	0	0
$856$	7.09964	0.242661
$857$	−5.59314	−0.191058	−0.0955290	−	0.995427i	$-0.530454\pi$
$857$	−5.59314	−0.191058	−0.0955290	+	0.995427i	$0.530454\pi$
$858$	21.4805	0.733334
$859$	−18.8110	−0.641822	−0.320911	−	0.947109i	$-0.603989\pi$
$859$	−18.8110	−0.641822	−0.320911	+	0.947109i	$0.603989\pi$
$860$	0	0
$861$	−4.77745	−0.162815
$862$	−4.98704	−0.169859
$863$	29.8116	1.01480	0.507400	−	0.861711i	$-0.330607\pi$
$863$	29.8116	1.01480	0.507400	+	0.861711i	$0.330607\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	15.4805	0.526050
$867$	3.47372	0.117974
$868$	−3.80273	−0.129073
$869$	−20.8300	−0.706610
$870$	0	0
$871$	−4.91051	−0.166386
$872$	−16.4321	−0.556460
$873$	7.16726	0.242575
$874$	3.14603	0.106416
$875$	0	0
$876$	−7.15020	−0.241583
$877$	9.96806	0.336598	0.168299	−	0.985736i	$-0.446173\pi$
$877$	9.96806	0.336598	0.168299	+	0.985736i	$0.446173\pi$
$878$	21.4929	0.725349
$879$	−17.5126	−0.590687
$880$	0	0
$881$	27.7387	0.934540	0.467270	−	0.884115i	$-0.345238\pi$
$881$	27.7387	0.934540	0.467270	+	0.884115i	$0.345238\pi$
$882$	6.76248	0.227705
$883$	−7.79659	−0.262376	−0.131188	−	0.991358i	$-0.541879\pi$
$883$	−7.79659	−0.262376	−0.131188	+	0.991358i	$0.541879\pi$
$884$	15.1707	0.510245
$885$	0	0
$886$	−32.4355	−1.08969
$887$	−19.1536	−0.643115	−0.321558	−	0.946890i	$-0.604206\pi$
$887$	−19.1536	−0.643115	−0.321558	+	0.946890i	$0.604206\pi$
$888$	1.00000	0.0335578
$889$	7.58584	0.254421
$890$	0	0
$891$	−5.20750	−0.174458
$892$	22.4335	0.751128
$893$	−1.51797	−0.0507969
$894$	−3.47913	−0.116360
$895$	0	0
$896$	0.487359	0.0162815
$897$	−30.1753	−1.00752
$898$	−15.8348	−0.528415
$899$	−52.8826	−1.76373
$900$	0	0
$901$	−28.2375	−0.940728
$902$	−51.0478	−1.69970
$903$	−2.32833	−0.0774820
$904$	−1.22255	−0.0406615
$905$	0	0
$906$	−17.7304	−0.589052
$907$	−1.34530	−0.0446700	−0.0223350	−	0.999751i	$-0.507110\pi$
$907$	−1.34530	−0.0446700	−0.0223350	+	0.999751i	$0.507110\pi$
$908$	−23.8368	−0.791053
$909$	−13.7454	−0.455907
$910$	0	0
$911$	2.95826	0.0980116	0.0490058	−	0.998798i	$-0.484395\pi$
$911$	2.95826	0.0980116	0.0490058	+	0.998798i	$0.484395\pi$
$912$	−0.430057	−0.0142406
$913$	−86.1317	−2.85054
$914$	−29.4470	−0.974021
$915$	0	0
$916$	10.2157	0.337537
$917$	8.55553	0.282529
$918$	−3.67781	−0.121386
$919$	16.0504	0.529454	0.264727	−	0.964323i	$-0.414718\pi$
$919$	16.0504	0.529454	0.264727	+	0.964323i	$0.414718\pi$
$920$	0	0
$921$	−0.364444	−0.0120088
$922$	−18.4975	−0.609183
$923$	−35.3925	−1.16496
$924$	−2.53792	−0.0834915
$925$	0	0
$926$	−7.46549	−0.245331
$927$	3.52969	0.115930
$928$	6.77745	0.222481
$929$	−2.20009	−0.0721825	−0.0360913	−	0.999348i	$-0.511491\pi$
$929$	−2.20009	−0.0721825	−0.0360913	+	0.999348i	$0.511491\pi$
$930$	0	0
$931$	−2.90825	−0.0953141
$932$	−2.07576	−0.0679939
$933$	15.1583	0.496262
$934$	33.3917	1.09261
$935$	0	0
$936$	4.12492	0.134827
$937$	15.9030	0.519530	0.259765	−	0.965672i	$-0.416355\pi$
$937$	15.9030	0.519530	0.259765	+	0.965672i	$0.416355\pi$
$938$	0.580177	0.0189434
$939$	−14.7201	−0.480374
$940$	0	0
$941$	50.0021	1.63002	0.815011	−	0.579446i	$-0.196731\pi$
$941$	50.0021	1.63002	0.815011	+	0.579446i	$0.196731\pi$
$942$	−11.8533	−0.386201
$943$	71.7106	2.33522
$944$	−0.974718	−0.0317244
$945$	0	0
$946$	−24.8786	−0.808872
$947$	−8.11677	−0.263760	−0.131880	−	0.991266i	$-0.542101\pi$
$947$	−8.11677	−0.263760	−0.131880	+	0.991266i	$0.542101\pi$
$948$	−4.00000	−0.129914
$949$	−29.4940	−0.957416
$950$	0	0
$951$	−0.942615	−0.0305664
$952$	−1.79241	−0.0580924
$953$	34.2451	1.10931	0.554654	−	0.832081i	$-0.312851\pi$
$953$	34.2451	1.10931	0.554654	+	0.832081i	$0.312851\pi$
$954$	−7.67781	−0.248578
$955$	0	0
$956$	−28.2683	−0.914262
$957$	−35.2936	−1.14088
$958$	−26.7051	−0.862803
$959$	−10.3563	−0.334421
$960$	0	0
$961$	29.8826	0.963954
$962$	4.12492	0.132993
$963$	−7.09964	−0.228783
$964$	20.4491	0.658622
$965$	0	0
$966$	3.56521	0.114709
$967$	7.49960	0.241171	0.120585	−	0.992703i	$-0.461523\pi$
$967$	7.49960	0.241171	0.120585	+	0.992703i	$0.461523\pi$
$968$	−16.1181	−0.518055
$969$	1.58167	0.0508105
$970$	0	0
$971$	55.6327	1.78534	0.892669	−	0.450714i	$-0.148830\pi$
$971$	55.6327	1.78534	0.892669	+	0.450714i	$0.148830\pi$
$972$	−1.00000	−0.0320750
$973$	7.50932	0.240738
$974$	−1.61437	−0.0517277
$975$	0	0
$976$	−14.5229	−0.464866
$977$	−33.1685	−1.06115	−0.530577	−	0.847637i	$-0.678025\pi$
$977$	−33.1685	−1.06115	−0.530577	+	0.847637i	$0.678025\pi$
$978$	−5.89354	−0.188455
$979$	−86.9919	−2.78027
$980$	0	0
$981$	16.4321	0.524635
$982$	−1.40477	−0.0448282
$983$	−55.2178	−1.76117	−0.880587	−	0.473884i	$-0.842852\pi$
$983$	−55.2178	−1.76117	−0.880587	+	0.473884i	$0.842852\pi$
$984$	−9.80273	−0.312500
$985$	0	0
$986$	−24.9262	−0.793811
$987$	−1.72023	−0.0547555
$988$	−1.77395	−0.0564369
$989$	34.9488	1.11131
$990$	0	0
$991$	−36.7815	−1.16840	−0.584201	−	0.811609i	$-0.698592\pi$
$991$	−36.7815	−1.16840	−0.584201	+	0.811609i	$0.698592\pi$
$992$	−7.80273	−0.247737
$993$	−15.8600	−0.503303
$994$	4.18163	0.132633
$995$	0	0
$996$	−16.5399	−0.524088
$997$	42.5058	1.34617	0.673086	−	0.739564i	$-0.264968\pi$
$997$	42.5058	1.34617	0.673086	+	0.739564i	$0.264968\pi$
$998$	9.98495	0.316068
$999$	−1.00000	−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5550.2.a.cj.1.3		4
5.4	even	2		1110.2.a.s.1.2	✓	4
15.14	odd	2		3330.2.a.bj.1.2		4
20.19	odd	2		8880.2.a.cg.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.a.s.1.2	✓	4	5.4	even	2
3330.2.a.bj.1.2		4	15.14	odd	2
5550.2.a.cj.1.3		4	1.1	even	1	trivial
8880.2.a.cg.1.3		4	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5550 = 2 \cdot 3 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5550.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -0.487359 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -0.487359 q^{7} -1.00000 q^{8} +1.00000 q^{9} -5.20750 q^{11} -1.00000 q^{12} -4.12492 q^{13} +0.487359 q^{14} +1.00000 q^{16} -3.67781 q^{17} -1.00000 q^{18} +0.430057 q^{19} +0.487359 q^{21} +5.20750 q^{22} -7.31537 q^{23} +1.00000 q^{24} +4.12492 q^{26} -1.00000 q^{27} -0.487359 q^{28} -6.77745 q^{29} +7.80273 q^{31} -1.00000 q^{32} +5.20750 q^{33} +3.67781 q^{34} +1.00000 q^{36} +1.00000 q^{37} -0.430057 q^{38} +4.12492 q^{39} -9.80273 q^{41} -0.487359 q^{42} -4.77745 q^{43} -5.20750 q^{44} +7.31537 q^{46} -3.52969 q^{47} -1.00000 q^{48} -6.76248 q^{49} +3.67781 q^{51} -4.12492 q^{52} +7.67781 q^{53} +1.00000 q^{54} +0.487359 q^{56} -0.430057 q^{57} +6.77745 q^{58} -0.974718 q^{59} -14.5229 q^{61} -7.80273 q^{62} -0.487359 q^{63} +1.00000 q^{64} -5.20750 q^{66} +1.19045 q^{67} -3.67781 q^{68} +7.31537 q^{69} +8.58018 q^{71} -1.00000 q^{72} +7.15020 q^{73} -1.00000 q^{74} +0.430057 q^{76} +2.53792 q^{77} -4.12492 q^{78} +4.00000 q^{79} +1.00000 q^{81} +9.80273 q^{82} +16.5399 q^{83} +0.487359 q^{84} +4.77745 q^{86} +6.77745 q^{87} +5.20750 q^{88} +16.7051 q^{89} +2.01032 q^{91} -7.31537 q^{92} -7.80273 q^{93} +3.52969 q^{94} +1.00000 q^{96} +7.16726 q^{97} +6.76248 q^{98} -5.20750 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{9} + 2 q^{11} - 4 q^{12} + 3 q^{13} + 4 q^{14} + 4 q^{16} - 6 q^{17} - 4 q^{18} + 3 q^{19} + 4 q^{21} - 2 q^{22} + q^{23} + 4 q^{24} - 3 q^{26} - 4 q^{27} - 4 q^{28} - 3 q^{29} + 3 q^{31} - 4 q^{32} - 2 q^{33} + 6 q^{34} + 4 q^{36} + 4 q^{37} - 3 q^{38} - 3 q^{39} - 11 q^{41} - 4 q^{42} + 5 q^{43} + 2 q^{44} - q^{46} - 4 q^{48} + 14 q^{49} + 6 q^{51} + 3 q^{52} + 22 q^{53} + 4 q^{54} + 4 q^{56} - 3 q^{57} + 3 q^{58} - 8 q^{59} - 5 q^{61} - 3 q^{62} - 4 q^{63} + 4 q^{64} + 2 q^{66} - 6 q^{67} - 6 q^{68} - q^{69} - 18 q^{71} - 4 q^{72} + 5 q^{73} - 4 q^{74} + 3 q^{76} + 4 q^{77} + 3 q^{78} + 16 q^{79} + 4 q^{81} + 11 q^{82} + q^{83} + 4 q^{84} - 5 q^{86} + 3 q^{87} - 2 q^{88} - 5 q^{89} - 13 q^{91} + q^{92} - 3 q^{93} + 4 q^{96} - 7 q^{97} - 14 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^9 + 2 * q^11 - 4 * q^12 + 3 * q^13 + 4 * q^14 + 4 * q^16 - 6 * q^17 - 4 * q^18 + 3 * q^19 + 4 * q^21 - 2 * q^22 + q^23 + 4 * q^24 - 3 * q^26 - 4 * q^27 - 4 * q^28 - 3 * q^29 + 3 * q^31 - 4 * q^32 - 2 * q^33 + 6 * q^34 + 4 * q^36 + 4 * q^37 - 3 * q^38 - 3 * q^39 - 11 * q^41 - 4 * q^42 + 5 * q^43 + 2 * q^44 - q^46 - 4 * q^48 + 14 * q^49 + 6 * q^51 + 3 * q^52 + 22 * q^53 + 4 * q^54 + 4 * q^56 - 3 * q^57 + 3 * q^58 - 8 * q^59 - 5 * q^61 - 3 * q^62 - 4 * q^63 + 4 * q^64 + 2 * q^66 - 6 * q^67 - 6 * q^68 - q^69 - 18 * q^71 - 4 * q^72 + 5 * q^73 - 4 * q^74 + 3 * q^76 + 4 * q^77 + 3 * q^78 + 16 * q^79 + 4 * q^81 + 11 * q^82 + q^83 + 4 * q^84 - 5 * q^86 + 3 * q^87 - 2 * q^88 - 5 * q^89 - 13 * q^91 + q^92 - 3 * q^93 + 4 * q^96 - 7 * q^97 - 14 * q^98 + 2 * q^99

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