LMFDB - Embedded newform 3525.2.a.bc.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, 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("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.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:	$28.1472667125$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 5x^{5} + 18x^{4} - 15x^{2} + 1 $ x^7 - 3x^6 - 5x^5 + 18x^4 - 15x^2 + 1
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			1.4
Root			$0.269111$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.269111 q^{2} +1.00000 q^{3} -1.92758 q^{4} +0.269111 q^{6} +3.07209 q^{7} -1.05695 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.269111 q^{2} +1.00000 q^{3} -1.92758 q^{4} +0.269111 q^{6} +3.07209 q^{7} -1.05695 q^{8} +1.00000 q^{9} +2.33362 q^{11} -1.92758 q^{12} +4.03372 q^{13} +0.826734 q^{14} +3.57072 q^{16} -2.84812 q^{17} +0.269111 q^{18} -0.180848 q^{19} +3.07209 q^{21} +0.628003 q^{22} +5.20976 q^{23} -1.05695 q^{24} +1.08552 q^{26} +1.00000 q^{27} -5.92170 q^{28} +1.32536 q^{29} +3.79820 q^{31} +3.07483 q^{32} +2.33362 q^{33} -0.766460 q^{34} -1.92758 q^{36} -10.3849 q^{37} -0.0486683 q^{38} +4.03372 q^{39} -2.42359 q^{41} +0.826734 q^{42} -10.2674 q^{43} -4.49824 q^{44} +1.40200 q^{46} -1.00000 q^{47} +3.57072 q^{48} +2.43775 q^{49} -2.84812 q^{51} -7.77531 q^{52} +11.6828 q^{53} +0.269111 q^{54} -3.24706 q^{56} -0.180848 q^{57} +0.356669 q^{58} -1.75227 q^{59} +7.23748 q^{61} +1.02214 q^{62} +3.07209 q^{63} -6.31397 q^{64} +0.628003 q^{66} +1.45422 q^{67} +5.48997 q^{68} +5.20976 q^{69} +13.8364 q^{71} -1.05695 q^{72} -1.85439 q^{73} -2.79469 q^{74} +0.348599 q^{76} +7.16910 q^{77} +1.08552 q^{78} -2.14604 q^{79} +1.00000 q^{81} -0.652215 q^{82} -5.31760 q^{83} -5.92170 q^{84} -2.76306 q^{86} +1.32536 q^{87} -2.46653 q^{88} -1.23507 q^{89} +12.3920 q^{91} -10.0422 q^{92} +3.79820 q^{93} -0.269111 q^{94} +3.07483 q^{96} +13.5727 q^{97} +0.656026 q^{98} +2.33362 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 3 q^{2} + 7 q^{3} + 5 q^{4} + 3 q^{6} + 5 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 3 * q^2 + 7 * q^3 + 5 * q^4 + 3 * q^6 + 5 * q^7 + 6 * q^8 + 7 * q^9	$ 7 q + 3 q^{2} + 7 q^{3} + 5 q^{4} + 3 q^{6} + 5 q^{7} + 6 q^{8} + 7 q^{9} + 4 q^{11} + 5 q^{12} + 5 q^{13} + 5 q^{14} + 9 q^{16} + 10 q^{17} + 3 q^{18} + q^{19} + 5 q^{21} + 10 q^{22} + 10 q^{23} + 6 q^{24} + 12 q^{26} + 7 q^{27} + 2 q^{28} + 9 q^{29} + 3 q^{31} + 4 q^{33} - 20 q^{34} + 5 q^{36} + 9 q^{37} - 2 q^{38} + 5 q^{39} + 20 q^{41} + 5 q^{42} + 16 q^{43} - 5 q^{44} - q^{46} - 7 q^{47} + 9 q^{48} - 10 q^{49} + 10 q^{51} + 21 q^{52} + 3 q^{54} + 21 q^{56} + q^{57} + 19 q^{58} + 18 q^{59} - 2 q^{62} + 5 q^{63} - 30 q^{64} + 10 q^{66} + 8 q^{67} + 20 q^{68} + 10 q^{69} + 14 q^{71} + 6 q^{72} + 4 q^{73} - 17 q^{74} + 12 q^{76} + 2 q^{77} + 12 q^{78} - 21 q^{79} + 7 q^{81} - 7 q^{82} + 22 q^{83} + 2 q^{84} + 35 q^{86} + 9 q^{87} + 14 q^{88} + 2 q^{89} - 2 q^{91} + 5 q^{92} + 3 q^{93} - 3 q^{94} + 12 q^{97} + 30 q^{98} + 4 q^{99}+O(q^{100}) $ 7 * q + 3 * q^2 + 7 * q^3 + 5 * q^4 + 3 * q^6 + 5 * q^7 + 6 * q^8 + 7 * q^9 + 4 * q^11 + 5 * q^12 + 5 * q^13 + 5 * q^14 + 9 * q^16 + 10 * q^17 + 3 * q^18 + q^19 + 5 * q^21 + 10 * q^22 + 10 * q^23 + 6 * q^24 + 12 * q^26 + 7 * q^27 + 2 * q^28 + 9 * q^29 + 3 * q^31 + 4 * q^33 - 20 * q^34 + 5 * q^36 + 9 * q^37 - 2 * q^38 + 5 * q^39 + 20 * q^41 + 5 * q^42 + 16 * q^43 - 5 * q^44 - q^46 - 7 * q^47 + 9 * q^48 - 10 * q^49 + 10 * q^51 + 21 * q^52 + 3 * q^54 + 21 * q^56 + q^57 + 19 * q^58 + 18 * q^59 - 2 * q^62 + 5 * q^63 - 30 * q^64 + 10 * q^66 + 8 * q^67 + 20 * q^68 + 10 * q^69 + 14 * q^71 + 6 * q^72 + 4 * q^73 - 17 * q^74 + 12 * q^76 + 2 * q^77 + 12 * q^78 - 21 * q^79 + 7 * q^81 - 7 * q^82 + 22 * q^83 + 2 * q^84 + 35 * q^86 + 9 * q^87 + 14 * q^88 + 2 * q^89 - 2 * q^91 + 5 * q^92 + 3 * q^93 - 3 * q^94 + 12 * q^97 + 30 * q^98 + 4 * 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 $

$2$	0.269111	0.190290	0.0951451	−	0.995463i	$-0.469668\pi$
$2$	0.269111	0.190290	0.0951451	+	0.995463i	$0.469668\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.92758	−0.963790
$5$	0	0
$5$	0	0
$6$	0.269111	0.109864
$7$	3.07209	1.16114	0.580571	−	0.814210i	$-0.302829\pi$
$7$	3.07209	1.16114	0.580571	+	0.814210i	$0.302829\pi$
$8$	−1.05695	−0.373690
$9$	1.00000	0.333333
$10$	0	0
$11$	2.33362	0.703613	0.351807	−	0.936073i	$-0.385567\pi$
$11$	2.33362	0.703613	0.351807	+	0.936073i	$0.385567\pi$
$12$	−1.92758	−0.556444
$13$	4.03372	1.11875	0.559376	−	0.828914i	$-0.311041\pi$
$13$	4.03372	1.11875	0.559376	+	0.828914i	$0.311041\pi$
$14$	0.826734	0.220954
$15$	0	0
$16$	3.57072	0.892680
$17$	−2.84812	−0.690770	−0.345385	−	0.938461i	$-0.612252\pi$
$17$	−2.84812	−0.690770	−0.345385	+	0.938461i	$0.612252\pi$
$18$	0.269111	0.0634301
$19$	−0.180848	−0.0414894	−0.0207447	−	0.999785i	$-0.506604\pi$
$19$	−0.180848	−0.0414894	−0.0207447	+	0.999785i	$0.506604\pi$
$20$	0	0
$21$	3.07209	0.670386
$22$	0.628003	0.133891
$23$	5.20976	1.08631	0.543155	−	0.839633i	$-0.317230\pi$
$23$	5.20976	1.08631	0.543155	+	0.839633i	$0.317230\pi$
$24$	−1.05695	−0.215750
$25$	0	0
$26$	1.08552	0.212888
$27$	1.00000	0.192450
$28$	−5.92170	−1.11910
$29$	1.32536	0.246113	0.123057	−	0.992400i	$-0.460730\pi$
$29$	1.32536	0.246113	0.123057	+	0.992400i	$0.460730\pi$
$30$	0	0
$31$	3.79820	0.682177	0.341089	−	0.940031i	$-0.389204\pi$
$31$	3.79820	0.682177	0.341089	+	0.940031i	$0.389204\pi$
$32$	3.07483	0.543558
$33$	2.33362	0.406231
$34$	−0.766460	−0.131447
$35$	0	0
$36$	−1.92758	−0.321263
$37$	−10.3849	−1.70727	−0.853635	−	0.520872i	$-0.825607\pi$
$37$	−10.3849	−1.70727	−0.853635	+	0.520872i	$0.825607\pi$
$38$	−0.0486683	−0.00789503
$39$	4.03372	0.645912
$40$	0	0
$41$	−2.42359	−0.378501	−0.189251	−	0.981929i	$-0.560606\pi$
$41$	−2.42359	−0.378501	−0.189251	+	0.981929i	$0.560606\pi$
$42$	0.826734	0.127568
$43$	−10.2674	−1.56576	−0.782879	−	0.622175i	$-0.786249\pi$
$43$	−10.2674	−1.56576	−0.782879	+	0.622175i	$0.786249\pi$
$44$	−4.49824	−0.678135
$45$	0	0
$46$	1.40200	0.206714
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	3.57072	0.515389
$49$	2.43775	0.348250
$50$	0	0
$51$	−2.84812	−0.398816
$52$	−7.77531	−1.07824
$53$	11.6828	1.60475	0.802376	−	0.596818i	$-0.203569\pi$
$53$	11.6828	1.60475	0.802376	+	0.596818i	$0.203569\pi$
$54$	0.269111	0.0366214
$55$	0	0
$56$	−3.24706	−0.433907
$57$	−0.180848	−0.0239539
$58$	0.356669	0.0468330
$59$	−1.75227	−0.228126	−0.114063	−	0.993473i	$-0.536387\pi$
$59$	−1.75227	−0.228126	−0.114063	+	0.993473i	$0.536387\pi$
$60$	0	0
$61$	7.23748	0.926664	0.463332	−	0.886185i	$-0.346654\pi$
$61$	7.23748	0.926664	0.463332	+	0.886185i	$0.346654\pi$
$62$	1.02214	0.129812
$63$	3.07209	0.387047
$64$	−6.31397	−0.789246
$65$	0	0
$66$	0.628003	0.0773019
$67$	1.45422	0.177662	0.0888308	−	0.996047i	$-0.471687\pi$
$67$	1.45422	0.177662	0.0888308	+	0.996047i	$0.471687\pi$
$68$	5.48997	0.665757
$69$	5.20976	0.627181
$70$	0	0
$71$	13.8364	1.64208	0.821039	−	0.570872i	$-0.193395\pi$
$71$	13.8364	1.64208	0.821039	+	0.570872i	$0.193395\pi$
$72$	−1.05695	−0.124563
$73$	−1.85439	−0.217040	−0.108520	−	0.994094i	$-0.534611\pi$
$73$	−1.85439	−0.217040	−0.108520	+	0.994094i	$0.534611\pi$
$74$	−2.79469	−0.324877
$75$	0	0
$76$	0.348599	0.0399871
$77$	7.16910	0.816995
$78$	1.08552	0.122911
$79$	−2.14604	−0.241448	−0.120724	−	0.992686i	$-0.538522\pi$
$79$	−2.14604	−0.241448	−0.120724	+	0.992686i	$0.538522\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−0.652215	−0.0720251
$83$	−5.31760	−0.583682	−0.291841	−	0.956467i	$-0.594268\pi$
$83$	−5.31760	−0.583682	−0.291841	+	0.956467i	$0.594268\pi$
$84$	−5.92170	−0.646111
$85$	0	0
$86$	−2.76306	−0.297948
$87$	1.32536	0.142094
$88$	−2.46653	−0.262933
$89$	−1.23507	−0.130917	−0.0654583	−	0.997855i	$-0.520851\pi$
$89$	−1.23507	−0.130917	−0.0654583	+	0.997855i	$0.520851\pi$
$90$	0	0
$91$	12.3920	1.29903
$92$	−10.0422	−1.04697
$93$	3.79820	0.393855
$94$	−0.269111	−0.0277567
$95$	0	0
$96$	3.07483	0.313824
$97$	13.5727	1.37810	0.689052	−	0.724712i	$-0.258027\pi$
$97$	13.5727	1.37810	0.689052	+	0.724712i	$0.258027\pi$
$98$	0.656026	0.0662687
$99$	2.33362	0.234538
$100$	0	0
$101$	12.0737	1.20138	0.600690	−	0.799482i	$-0.294893\pi$
$101$	12.0737	1.20138	0.600690	+	0.799482i	$0.294893\pi$
$102$	−0.766460	−0.0758909
$103$	−0.439311	−0.0432866	−0.0216433	−	0.999766i	$-0.506890\pi$
$103$	−0.439311	−0.0432866	−0.0216433	+	0.999766i	$0.506890\pi$
$104$	−4.26346	−0.418066
$105$	0	0
$106$	3.14396	0.305369
$107$	14.4490	1.39684	0.698418	−	0.715690i	$-0.253888\pi$
$107$	14.4490	1.39684	0.698418	+	0.715690i	$0.253888\pi$
$108$	−1.92758	−0.185481
$109$	−1.21161	−0.116052	−0.0580258	−	0.998315i	$-0.518481\pi$
$109$	−1.21161	−0.116052	−0.0580258	+	0.998315i	$0.518481\pi$
$110$	0	0
$111$	−10.3849	−0.985692
$112$	10.9696	1.03653
$113$	9.13508	0.859356	0.429678	−	0.902982i	$-0.358627\pi$
$113$	9.13508	0.859356	0.429678	+	0.902982i	$0.358627\pi$
$114$	−0.0486683	−0.00455820
$115$	0	0
$116$	−2.55474	−0.237202
$117$	4.03372	0.372917
$118$	−0.471556	−0.0434102
$119$	−8.74968	−0.802082
$120$	0	0
$121$	−5.55421	−0.504928
$122$	1.94768	0.176335
$123$	−2.42359	−0.218528
$124$	−7.32134	−0.657476
$125$	0	0
$126$	0.826734	0.0736513
$127$	13.2747	1.17794	0.588970	−	0.808155i	$-0.299534\pi$
$127$	13.2747	1.17794	0.588970	+	0.808155i	$0.299534\pi$
$128$	−7.84882	−0.693744
$129$	−10.2674	−0.903990
$130$	0	0
$131$	−6.29299	−0.549821	−0.274911	−	0.961470i	$-0.588648\pi$
$131$	−6.29299	−0.549821	−0.274911	+	0.961470i	$0.588648\pi$
$132$	−4.49824	−0.391522
$133$	−0.555583	−0.0481751
$134$	0.391347	0.0338073
$135$	0	0
$136$	3.01033	0.258134
$137$	−15.2643	−1.30412	−0.652059	−	0.758168i	$-0.726095\pi$
$137$	−15.2643	−1.30412	−0.652059	+	0.758168i	$0.726095\pi$
$138$	1.40200	0.119346
$139$	−21.0862	−1.78851	−0.894253	−	0.447561i	$-0.852293\pi$
$139$	−21.0862	−1.78851	−0.894253	+	0.447561i	$0.852293\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	3.72353	0.312471
$143$	9.41317	0.787169
$144$	3.57072	0.297560
$145$	0	0
$146$	−0.499038	−0.0413007
$147$	2.43775	0.201062
$148$	20.0177	1.64545
$149$	13.7893	1.12967	0.564834	−	0.825205i	$-0.308940\pi$
$149$	13.7893	1.12967	0.564834	+	0.825205i	$0.308940\pi$
$150$	0	0
$151$	−0.957268	−0.0779014	−0.0389507	−	0.999241i	$-0.512402\pi$
$151$	−0.957268	−0.0779014	−0.0389507	+	0.999241i	$0.512402\pi$
$152$	0.191148	0.0155042
$153$	−2.84812	−0.230257
$154$	1.92928	0.155466
$155$	0	0
$156$	−7.77531	−0.622523
$157$	10.8705	0.867561	0.433780	−	0.901019i	$-0.357179\pi$
$157$	10.8705	0.867561	0.433780	+	0.901019i	$0.357179\pi$
$158$	−0.577523	−0.0459452
$159$	11.6828	0.926504
$160$	0	0
$161$	16.0049	1.26136
$162$	0.269111	0.0211434
$163$	18.3350	1.43611	0.718055	−	0.695987i	$-0.245033\pi$
$163$	18.3350	1.43611	0.718055	+	0.695987i	$0.245033\pi$
$164$	4.67166	0.364795
$165$	0	0
$166$	−1.43102	−0.111069
$167$	12.3710	0.957299	0.478649	−	0.878006i	$-0.341126\pi$
$167$	12.3710	0.957299	0.478649	+	0.878006i	$0.341126\pi$
$168$	−3.24706	−0.250516
$169$	3.27088	0.251606
$170$	0	0
$171$	−0.180848	−0.0138298
$172$	19.7911	1.50906
$173$	13.8192	1.05065	0.525326	−	0.850901i	$-0.323943\pi$
$173$	13.8192	1.05065	0.525326	+	0.850901i	$0.323943\pi$
$174$	0.356669	0.0270390
$175$	0	0
$176$	8.33271	0.628102
$177$	−1.75227	−0.131709
$178$	−0.332370	−0.0249122
$179$	−15.4955	−1.15818	−0.579092	−	0.815262i	$-0.696593\pi$
$179$	−15.4955	−1.15818	−0.579092	+	0.815262i	$0.696593\pi$
$180$	0	0
$181$	6.32105	0.469840	0.234920	−	0.972015i	$-0.424517\pi$
$181$	6.32105	0.469840	0.234920	+	0.972015i	$0.424517\pi$
$182$	3.33481	0.247193
$183$	7.23748	0.535010
$184$	−5.50648	−0.405943
$185$	0	0
$186$	1.02214	0.0749468
$187$	−6.64643	−0.486035
$188$	1.92758	0.140583
$189$	3.07209	0.223462
$190$	0	0
$191$	−21.0324	−1.52185	−0.760924	−	0.648841i	$-0.775254\pi$
$191$	−21.0324	−1.52185	−0.760924	+	0.648841i	$0.775254\pi$
$192$	−6.31397	−0.455672
$193$	−16.7987	−1.20920	−0.604598	−	0.796531i	$-0.706666\pi$
$193$	−16.7987	−1.20920	−0.604598	+	0.796531i	$0.706666\pi$
$194$	3.65257	0.262240
$195$	0	0
$196$	−4.69896	−0.335640
$197$	−12.8136	−0.912930	−0.456465	−	0.889741i	$-0.650885\pi$
$197$	−12.8136	−0.912930	−0.456465	+	0.889741i	$0.650885\pi$
$198$	0.628003	0.0446303
$199$	−5.88646	−0.417280	−0.208640	−	0.977993i	$-0.566904\pi$
$199$	−5.88646	−0.417280	−0.208640	+	0.977993i	$0.566904\pi$
$200$	0	0
$201$	1.45422	0.102573
$202$	3.24917	0.228611
$203$	4.07163	0.285773
$204$	5.48997	0.384375
$205$	0	0
$206$	−0.118224	−0.00823702
$207$	5.20976	0.362103
$208$	14.4033	0.998688
$209$	−0.422031	−0.0291925
$210$	0	0
$211$	3.42885	0.236052	0.118026	−	0.993011i	$-0.462343\pi$
$211$	3.42885	0.236052	0.118026	+	0.993011i	$0.462343\pi$
$212$	−22.5195	−1.54664
$213$	13.8364	0.948054
$214$	3.88838	0.265804
$215$	0	0
$216$	−1.05695	−0.0719167
$217$	11.6684	0.792105
$218$	−0.326059	−0.0220835
$219$	−1.85439	−0.125308
$220$	0	0
$221$	−11.4885	−0.772800
$222$	−2.79469	−0.187568
$223$	5.22346	0.349789	0.174894	−	0.984587i	$-0.444042\pi$
$223$	5.22346	0.349789	0.174894	+	0.984587i	$0.444042\pi$
$224$	9.44616	0.631148
$225$	0	0
$226$	2.45835	0.163527
$227$	−4.05730	−0.269293	−0.134646	−	0.990894i	$-0.542990\pi$
$227$	−4.05730	−0.269293	−0.134646	+	0.990894i	$0.542990\pi$
$228$	0.348599	0.0230866
$229$	21.7638	1.43819	0.719097	−	0.694909i	$-0.244556\pi$
$229$	21.7638	1.43819	0.719097	+	0.694909i	$0.244556\pi$
$230$	0	0
$231$	7.16910	0.471692
$232$	−1.40085	−0.0919702
$233$	23.0827	1.51220	0.756099	−	0.654458i	$-0.227103\pi$
$233$	23.0827	1.51220	0.756099	+	0.654458i	$0.227103\pi$
$234$	1.08552	0.0709625
$235$	0	0
$236$	3.37764	0.219866
$237$	−2.14604	−0.139400
$238$	−2.35464	−0.152628
$239$	15.8168	1.02311	0.511553	−	0.859252i	$-0.329071\pi$
$239$	15.8168	1.02311	0.511553	+	0.859252i	$0.329071\pi$
$240$	0	0
$241$	−15.5213	−0.999815	−0.499908	−	0.866079i	$-0.666633\pi$
$241$	−15.5213	−0.999815	−0.499908	+	0.866079i	$0.666633\pi$
$242$	−1.49470	−0.0960829
$243$	1.00000	0.0641500
$244$	−13.9508	−0.893109
$245$	0	0
$246$	−0.652215	−0.0415837
$247$	−0.729491	−0.0464164
$248$	−4.01453	−0.254923
$249$	−5.31760	−0.336989
$250$	0	0
$251$	−16.3712	−1.03334	−0.516669	−	0.856185i	$-0.672828\pi$
$251$	−16.3712	−1.03334	−0.516669	+	0.856185i	$0.672828\pi$
$252$	−5.92170	−0.373032
$253$	12.1576	0.764342
$254$	3.57237	0.224150
$255$	0	0
$256$	10.5157	0.657233
$257$	11.3356	0.707092	0.353546	−	0.935417i	$-0.384976\pi$
$257$	11.3356	0.707092	0.353546	+	0.935417i	$0.384976\pi$
$258$	−2.76306	−0.172021
$259$	−31.9034	−1.98238
$260$	0	0
$261$	1.32536	0.0820378
$262$	−1.69351	−0.104626
$263$	13.4091	0.826840	0.413420	−	0.910541i	$-0.364334\pi$
$263$	13.4091	0.826840	0.413420	+	0.910541i	$0.364334\pi$
$264$	−2.46653	−0.151805
$265$	0	0
$266$	−0.149513	−0.00916726
$267$	−1.23507	−0.0755848
$268$	−2.80313	−0.171228
$269$	17.9856	1.09660	0.548301	−	0.836281i	$-0.315275\pi$
$269$	17.9856	1.09660	0.548301	+	0.836281i	$0.315275\pi$
$270$	0	0
$271$	−6.54923	−0.397837	−0.198919	−	0.980016i	$-0.563743\pi$
$271$	−6.54923	−0.397837	−0.198919	+	0.980016i	$0.563743\pi$
$272$	−10.1698	−0.616637
$273$	12.3920	0.749995
$274$	−4.10780	−0.248161
$275$	0	0
$276$	−10.0422	−0.604470
$277$	4.99751	0.300271	0.150136	−	0.988665i	$-0.452029\pi$
$277$	4.99751	0.300271	0.150136	+	0.988665i	$0.452029\pi$
$278$	−5.67452	−0.340335
$279$	3.79820	0.227392
$280$	0	0
$281$	19.0218	1.13475	0.567374	−	0.823460i	$-0.307960\pi$
$281$	19.0218	1.13475	0.567374	+	0.823460i	$0.307960\pi$
$282$	−0.269111	−0.0160253
$283$	7.20108	0.428060	0.214030	−	0.976827i	$-0.431341\pi$
$283$	7.20108	0.428060	0.214030	+	0.976827i	$0.431341\pi$
$284$	−26.6707	−1.58262
$285$	0	0
$286$	2.53319	0.149791
$287$	−7.44549	−0.439493
$288$	3.07483	0.181186
$289$	−8.88822	−0.522837
$290$	0	0
$291$	13.5727	0.795648
$292$	3.57449	0.209181
$293$	−14.3214	−0.836664	−0.418332	−	0.908294i	$-0.637385\pi$
$293$	−14.3214	−0.836664	−0.418332	+	0.908294i	$0.637385\pi$
$294$	0.656026	0.0382602
$295$	0	0
$296$	10.9764	0.637989
$297$	2.33362	0.135410
$298$	3.71087	0.214965
$299$	21.0147	1.21531
$300$	0	0
$301$	−31.5423	−1.81807
$302$	−0.257611	−0.0148239
$303$	12.0737	0.693617
$304$	−0.645758	−0.0370368
$305$	0	0
$306$	−0.766460	−0.0438156
$307$	9.78584	0.558507	0.279254	−	0.960217i	$-0.409913\pi$
$307$	9.78584	0.558507	0.279254	+	0.960217i	$0.409913\pi$
$308$	−13.8190	−0.787411
$309$	−0.439311	−0.0249915
$310$	0	0
$311$	−23.4310	−1.32865	−0.664326	−	0.747443i	$-0.731281\pi$
$311$	−23.4310	−1.32865	−0.664326	+	0.747443i	$0.731281\pi$
$312$	−4.26346	−0.241371
$313$	−23.4736	−1.32681	−0.663404	−	0.748261i	$-0.730889\pi$
$313$	−23.4736	−1.32681	−0.663404	+	0.748261i	$0.730889\pi$
$314$	2.92537	0.165088
$315$	0	0
$316$	4.13666	0.232705
$317$	−21.6990	−1.21874	−0.609368	−	0.792888i	$-0.708577\pi$
$317$	−21.6990	−1.21874	−0.609368	+	0.792888i	$0.708577\pi$
$318$	3.14396	0.176305
$319$	3.09289	0.173169
$320$	0	0
$321$	14.4490	0.806464
$322$	4.30708	0.240024
$323$	0.515077	0.0286597
$324$	−1.92758	−0.107088
$325$	0	0
$326$	4.93416	0.273278
$327$	−1.21161	−0.0670024
$328$	2.56162	0.141442
$329$	−3.07209	−0.169370
$330$	0	0
$331$	−11.9299	−0.655729	−0.327864	−	0.944725i	$-0.606329\pi$
$331$	−11.9299	−0.655729	−0.327864	+	0.944725i	$0.606329\pi$
$332$	10.2501	0.562547
$333$	−10.3849	−0.569090
$334$	3.32918	0.182165
$335$	0	0
$336$	10.9696	0.598440
$337$	−4.25723	−0.231906	−0.115953	−	0.993255i	$-0.536992\pi$
$337$	−4.25723	−0.231906	−0.115953	+	0.993255i	$0.536992\pi$
$338$	0.880229	0.0478781
$339$	9.13508	0.496150
$340$	0	0
$341$	8.86357	0.479989
$342$	−0.0486683	−0.00263168
$343$	−14.0156	−0.756774
$344$	10.8521	0.585108
$345$	0	0
$346$	3.71889	0.199929
$347$	13.1514	0.706005	0.353003	−	0.935622i	$-0.385161\pi$
$347$	13.1514	0.706005	0.353003	+	0.935622i	$0.385161\pi$
$348$	−2.55474	−0.136948
$349$	−22.5552	−1.20735	−0.603675	−	0.797230i	$-0.706298\pi$
$349$	−22.5552	−1.20735	−0.603675	+	0.797230i	$0.706298\pi$
$350$	0	0
$351$	4.03372	0.215304
$352$	7.17549	0.382455
$353$	34.4438	1.83326	0.916628	−	0.399741i	$-0.130900\pi$
$353$	34.4438	1.83326	0.916628	+	0.399741i	$0.130900\pi$
$354$	−0.471556	−0.0250629
$355$	0	0
$356$	2.38069	0.126176
$357$	−8.74968	−0.463082
$358$	−4.17000	−0.220391
$359$	−1.38690	−0.0731980	−0.0365990	−	0.999330i	$-0.511652\pi$
$359$	−1.38690	−0.0731980	−0.0365990	+	0.999330i	$0.511652\pi$
$360$	0	0
$361$	−18.9673	−0.998279
$362$	1.70107	0.0894060
$363$	−5.55421	−0.291520
$364$	−23.8865	−1.25199
$365$	0	0
$366$	1.94768	0.101807
$367$	−16.9782	−0.886256	−0.443128	−	0.896458i	$-0.646131\pi$
$367$	−16.9782	−0.886256	−0.443128	+	0.896458i	$0.646131\pi$
$368$	18.6026	0.969726
$369$	−2.42359	−0.126167
$370$	0	0
$371$	35.8906	1.86335
$372$	−7.32134	−0.379594
$373$	7.42332	0.384365	0.192182	−	0.981359i	$-0.438443\pi$
$373$	7.42332	0.384365	0.192182	+	0.981359i	$0.438443\pi$
$374$	−1.78863	−0.0924877
$375$	0	0
$376$	1.05695	0.0545083
$377$	5.34613	0.275340
$378$	0.826734	0.0425226
$379$	21.5273	1.10578	0.552892	−	0.833253i	$-0.313524\pi$
$379$	21.5273	1.10578	0.552892	+	0.833253i	$0.313524\pi$
$380$	0	0
$381$	13.2747	0.680084
$382$	−5.66004	−0.289593
$383$	0.299985	0.0153285	0.00766426	−	0.999971i	$-0.497560\pi$
$383$	0.299985	0.0153285	0.00766426	+	0.999971i	$0.497560\pi$
$384$	−7.84882	−0.400533
$385$	0	0
$386$	−4.52071	−0.230098
$387$	−10.2674	−0.521919
$388$	−26.1625	−1.32820
$389$	−4.12137	−0.208962	−0.104481	−	0.994527i	$-0.533318\pi$
$389$	−4.12137	−0.208962	−0.104481	+	0.994527i	$0.533318\pi$
$390$	0	0
$391$	−14.8380	−0.750390
$392$	−2.57660	−0.130138
$393$	−6.29299	−0.317440
$394$	−3.44828	−0.173722
$395$	0	0
$396$	−4.49824	−0.226045
$397$	31.6904	1.59049	0.795247	−	0.606286i	$-0.207341\pi$
$397$	31.6904	1.59049	0.795247	+	0.606286i	$0.207341\pi$
$398$	−1.58411	−0.0794043
$399$	−0.555583	−0.0278139
$400$	0	0
$401$	−13.2406	−0.661204	−0.330602	−	0.943770i	$-0.607252\pi$
$401$	−13.2406	−0.661204	−0.330602	+	0.943770i	$0.607252\pi$
$402$	0.391347	0.0195186
$403$	15.3209	0.763187
$404$	−23.2730	−1.15788
$405$	0	0
$406$	1.09572	0.0543798
$407$	−24.2345	−1.20126
$408$	3.01033	0.149034
$409$	5.41092	0.267553	0.133777	−	0.991012i	$-0.457290\pi$
$409$	5.41092	0.267553	0.133777	+	0.991012i	$0.457290\pi$
$410$	0	0
$411$	−15.2643	−0.752933
$412$	0.846807	0.0417192
$413$	−5.38314	−0.264887
$414$	1.40200	0.0689047
$415$	0	0
$416$	12.4030	0.608107
$417$	−21.0862	−1.03259
$418$	−0.113573	−0.00555505
$419$	−0.633923	−0.0309692	−0.0154846	−	0.999880i	$-0.504929\pi$
$419$	−0.633923	−0.0309692	−0.0154846	+	0.999880i	$0.504929\pi$
$420$	0	0
$421$	−7.91157	−0.385586	−0.192793	−	0.981239i	$-0.561755\pi$
$421$	−7.91157	−0.385586	−0.192793	+	0.981239i	$0.561755\pi$
$422$	0.922742	0.0449184
$423$	−1.00000	−0.0486217
$424$	−12.3482	−0.599680
$425$	0	0
$426$	3.72353	0.180405
$427$	22.2342	1.07599
$428$	−27.8516	−1.34626
$429$	9.41317	0.454472
$430$	0	0
$431$	16.2778	0.784073	0.392037	−	0.919950i	$-0.371771\pi$
$431$	16.2778	0.784073	0.392037	+	0.919950i	$0.371771\pi$
$432$	3.57072	0.171796
$433$	−37.2585	−1.79053	−0.895266	−	0.445533i	$-0.853014\pi$
$433$	−37.2585	−1.79053	−0.895266	+	0.445533i	$0.853014\pi$
$434$	3.14010	0.150730
$435$	0	0
$436$	2.33548	0.111849
$437$	−0.942175	−0.0450703
$438$	−0.499038	−0.0238450
$439$	−5.55330	−0.265045	−0.132522	−	0.991180i	$-0.542308\pi$
$439$	−5.55330	−0.265045	−0.132522	+	0.991180i	$0.542308\pi$
$440$	0	0
$441$	2.43775	0.116083
$442$	−3.09168	−0.147056
$443$	−25.4320	−1.20831	−0.604156	−	0.796866i	$-0.706490\pi$
$443$	−25.4320	−1.20831	−0.604156	+	0.796866i	$0.706490\pi$
$444$	20.0177	0.950000
$445$	0	0
$446$	1.40569	0.0665614
$447$	13.7893	0.652214
$448$	−19.3971	−0.916427
$449$	−25.8864	−1.22166	−0.610828	−	0.791763i	$-0.709163\pi$
$449$	−25.8864	−1.22166	−0.610828	+	0.791763i	$0.709163\pi$
$450$	0	0
$451$	−5.65574	−0.266318
$452$	−17.6086	−0.828239
$453$	−0.957268	−0.0449764
$454$	−1.09187	−0.0512438
$455$	0	0
$456$	0.191148	0.00895135
$457$	−20.0977	−0.940132	−0.470066	−	0.882631i	$-0.655770\pi$
$457$	−20.0977	−0.940132	−0.470066	+	0.882631i	$0.655770\pi$
$458$	5.85689	0.273674
$459$	−2.84812	−0.132939
$460$	0	0
$461$	31.8716	1.48441	0.742205	−	0.670173i	$-0.233780\pi$
$461$	31.8716	1.48441	0.742205	+	0.670173i	$0.233780\pi$
$462$	1.92928	0.0897584
$463$	−8.67661	−0.403236	−0.201618	−	0.979464i	$-0.564620\pi$
$463$	−8.67661	−0.403236	−0.201618	+	0.979464i	$0.564620\pi$
$464$	4.73250	0.219701
$465$	0	0
$466$	6.21181	0.287756
$467$	3.44978	0.159637	0.0798184	−	0.996809i	$-0.474566\pi$
$467$	3.44978	0.159637	0.0798184	+	0.996809i	$0.474566\pi$
$468$	−7.77531	−0.359414
$469$	4.46751	0.206290
$470$	0	0
$471$	10.8705	0.500886
$472$	1.85207	0.0852486
$473$	−23.9601	−1.10169
$474$	−0.577523	−0.0265265
$475$	0	0
$476$	16.8657	0.773038
$477$	11.6828	0.534918
$478$	4.25648	0.194687
$479$	−24.1901	−1.10527	−0.552637	−	0.833422i	$-0.686378\pi$
$479$	−24.1901	−1.10527	−0.552637	+	0.833422i	$0.686378\pi$
$480$	0	0
$481$	−41.8898	−1.91001
$482$	−4.17696	−0.190255
$483$	16.0049	0.728246
$484$	10.7062	0.486645
$485$	0	0
$486$	0.269111	0.0122071
$487$	14.1816	0.642630	0.321315	−	0.946972i	$-0.395875\pi$
$487$	14.1816	0.642630	0.321315	+	0.946972i	$0.395875\pi$
$488$	−7.64969	−0.346285
$489$	18.3350	0.829138
$490$	0	0
$491$	−22.9889	−1.03748	−0.518738	−	0.854933i	$-0.673598\pi$
$491$	−22.9889	−1.03748	−0.518738	+	0.854933i	$0.673598\pi$
$492$	4.67166	0.210615
$493$	−3.77479	−0.170008
$494$	−0.196314	−0.00883258
$495$	0	0
$496$	13.5623	0.608966
$497$	42.5067	1.90668
$498$	−1.43102	−0.0641257
$499$	−19.6805	−0.881021	−0.440510	−	0.897748i	$-0.645203\pi$
$499$	−19.6805	−0.881021	−0.440510	+	0.897748i	$0.645203\pi$
$500$	0	0
$501$	12.3710	0.552697
$502$	−4.40566	−0.196634
$503$	−5.60473	−0.249903	−0.124951	−	0.992163i	$-0.539877\pi$
$503$	−5.60473	−0.249903	−0.124951	+	0.992163i	$0.539877\pi$
$504$	−3.24706	−0.144636
$505$	0	0
$506$	3.27174	0.145447
$507$	3.27088	0.145265
$508$	−25.5880	−1.13529
$509$	−14.1116	−0.625488	−0.312744	−	0.949838i	$-0.601248\pi$
$509$	−14.1116	−0.625488	−0.312744	+	0.949838i	$0.601248\pi$
$510$	0	0
$511$	−5.69687	−0.252015
$512$	18.5275	0.818809
$513$	−0.180848	−0.00798464
$514$	3.05052	0.134553
$515$	0	0
$516$	19.7911	0.871256
$517$	−2.33362	−0.102633
$518$	−8.58556	−0.377228
$519$	13.8192	0.606594
$520$	0	0
$521$	−5.65414	−0.247712	−0.123856	−	0.992300i	$-0.539526\pi$
$521$	−5.65414	−0.247712	−0.123856	+	0.992300i	$0.539526\pi$
$522$	0.356669	0.0156110
$523$	−29.1013	−1.27251	−0.636256	−	0.771478i	$-0.719518\pi$
$523$	−29.1013	−1.27251	−0.636256	+	0.771478i	$0.719518\pi$
$524$	12.1302	0.529912
$525$	0	0
$526$	3.60853	0.157340
$527$	−10.8177	−0.471228
$528$	8.33271	0.362635
$529$	4.14155	0.180067
$530$	0	0
$531$	−1.75227	−0.0760422
$532$	1.07093	0.0464307
$533$	−9.77607	−0.423449
$534$	−0.332370	−0.0143830
$535$	0	0
$536$	−1.53705	−0.0663904
$537$	−15.4955	−0.668678
$538$	4.84013	0.208673
$539$	5.68879	0.245034
$540$	0	0
$541$	−2.47200	−0.106280	−0.0531399	−	0.998587i	$-0.516923\pi$
$541$	−2.47200	−0.106280	−0.0531399	+	0.998587i	$0.516923\pi$
$542$	−1.76247	−0.0757045
$543$	6.32105	0.271262
$544$	−8.75748	−0.375474
$545$	0	0
$546$	3.33481	0.142717
$547$	16.9960	0.726698	0.363349	−	0.931653i	$-0.381633\pi$
$547$	16.9960	0.726698	0.363349	+	0.931653i	$0.381633\pi$
$548$	29.4232	1.25690
$549$	7.23748	0.308888
$550$	0	0
$551$	−0.239689	−0.0102111
$552$	−5.50648	−0.234371
$553$	−6.59283	−0.280356
$554$	1.34488	0.0571387
$555$	0	0
$556$	40.6453	1.72374
$557$	−31.4855	−1.33408	−0.667041	−	0.745021i	$-0.732439\pi$
$557$	−31.4855	−1.33408	−0.667041	+	0.745021i	$0.732439\pi$
$558$	1.02214	0.0432706
$559$	−41.4156	−1.75169
$560$	0	0
$561$	−6.64643	−0.280612
$562$	5.11899	0.215931
$563$	6.31185	0.266013	0.133006	−	0.991115i	$-0.457537\pi$
$563$	6.31185	0.266013	0.133006	+	0.991115i	$0.457537\pi$
$564$	1.92758	0.0811657
$565$	0	0
$566$	1.93789	0.0814556
$567$	3.07209	0.129016
$568$	−14.6244	−0.613628
$569$	34.7205	1.45556	0.727780	−	0.685810i	$-0.240552\pi$
$569$	34.7205	1.45556	0.727780	+	0.685810i	$0.240552\pi$
$570$	0	0
$571$	−29.3106	−1.22661	−0.613304	−	0.789847i	$-0.710160\pi$
$571$	−29.3106	−1.22661	−0.613304	+	0.789847i	$0.710160\pi$
$572$	−18.1446	−0.758665
$573$	−21.0324	−0.878639
$574$	−2.00366	−0.0836313
$575$	0	0
$576$	−6.31397	−0.263082
$577$	−10.1096	−0.420868	−0.210434	−	0.977608i	$-0.567488\pi$
$577$	−10.1096	−0.420868	−0.210434	+	0.977608i	$0.567488\pi$
$578$	−2.39192	−0.0994907
$579$	−16.7987	−0.698130
$580$	0	0
$581$	−16.3362	−0.677738
$582$	3.65257	0.151404
$583$	27.2632	1.12913
$584$	1.96001	0.0811059
$585$	0	0
$586$	−3.85404	−0.159209
$587$	4.61631	0.190535	0.0952677	−	0.995452i	$-0.469629\pi$
$587$	4.61631	0.190535	0.0952677	+	0.995452i	$0.469629\pi$
$588$	−4.69896	−0.193782
$589$	−0.686898	−0.0283032
$590$	0	0
$591$	−12.8136	−0.527080
$592$	−37.0816	−1.52405
$593$	16.8938	0.693745	0.346873	−	0.937912i	$-0.387244\pi$
$593$	16.8938	0.693745	0.346873	+	0.937912i	$0.387244\pi$
$594$	0.628003	0.0257673
$595$	0	0
$596$	−26.5801	−1.08876
$597$	−5.88646	−0.240917
$598$	5.65528	0.231262
$599$	31.4438	1.28476	0.642380	−	0.766386i	$-0.277947\pi$
$599$	31.4438	1.28476	0.642380	+	0.766386i	$0.277947\pi$
$600$	0	0
$601$	−45.9702	−1.87516	−0.937581	−	0.347766i	$-0.886940\pi$
$601$	−45.9702	−1.87516	−0.937581	+	0.347766i	$0.886940\pi$
$602$	−8.48837	−0.345960
$603$	1.45422	0.0592205
$604$	1.84521	0.0750806
$605$	0	0
$606$	3.24917	0.131989
$607$	−33.8605	−1.37436	−0.687178	−	0.726489i	$-0.741151\pi$
$607$	−33.8605	−1.37436	−0.687178	+	0.726489i	$0.741151\pi$
$608$	−0.556078	−0.0225519
$609$	4.07163	0.164991
$610$	0	0
$611$	−4.03372	−0.163187
$612$	5.48997	0.221919
$613$	37.2269	1.50358	0.751791	−	0.659402i	$-0.229190\pi$
$613$	37.2269	1.50358	0.751791	+	0.659402i	$0.229190\pi$
$614$	2.63348	0.106279
$615$	0	0
$616$	−7.57742	−0.305303
$617$	−33.0605	−1.33097	−0.665483	−	0.746413i	$-0.731774\pi$
$617$	−33.0605	−1.33097	−0.665483	+	0.746413i	$0.731774\pi$
$618$	−0.118224	−0.00475565
$619$	−11.9550	−0.480512	−0.240256	−	0.970710i	$-0.577231\pi$
$619$	−11.9550	−0.480512	−0.240256	+	0.970710i	$0.577231\pi$
$620$	0	0
$621$	5.20976	0.209060
$622$	−6.30555	−0.252830
$623$	−3.79424	−0.152013
$624$	14.4033	0.576592
$625$	0	0
$626$	−6.31702	−0.252479
$627$	−0.422031	−0.0168543
$628$	−20.9538	−0.836146
$629$	29.5775	1.17933
$630$	0	0
$631$	−14.6560	−0.583444	−0.291722	−	0.956503i	$-0.594228\pi$
$631$	−14.6560	−0.583444	−0.291722	+	0.956503i	$0.594228\pi$
$632$	2.26827	0.0902268
$633$	3.42885	0.136285
$634$	−5.83943	−0.231913
$635$	0	0
$636$	−22.5195	−0.892955
$637$	9.83321	0.389606
$638$	0.832332	0.0329523
$639$	13.8364	0.547359
$640$	0	0
$641$	6.39030	0.252402	0.126201	−	0.992005i	$-0.459722\pi$
$641$	6.39030	0.252402	0.126201	+	0.992005i	$0.459722\pi$
$642$	3.88838	0.153462
$643$	44.7579	1.76508	0.882539	−	0.470239i	$-0.155832\pi$
$643$	44.7579	1.76508	0.882539	+	0.470239i	$0.155832\pi$
$644$	−30.8506	−1.21568
$645$	0	0
$646$	0.138613	0.00545365
$647$	29.8691	1.17427	0.587137	−	0.809488i	$-0.300255\pi$
$647$	29.8691	1.17427	0.587137	+	0.809488i	$0.300255\pi$
$648$	−1.05695	−0.0415211
$649$	−4.08914	−0.160513
$650$	0	0
$651$	11.6684	0.457322
$652$	−35.3422	−1.38411
$653$	−38.7945	−1.51815	−0.759073	−	0.651005i	$-0.774348\pi$
$653$	−38.7945	−1.51815	−0.759073	+	0.651005i	$0.774348\pi$
$654$	−0.326059	−0.0127499
$655$	0	0
$656$	−8.65396	−0.337880
$657$	−1.85439	−0.0723468
$658$	−0.826734	−0.0322295
$659$	10.6542	0.415031	0.207515	−	0.978232i	$-0.433462\pi$
$659$	10.6542	0.415031	0.207515	+	0.978232i	$0.433462\pi$
$660$	0	0
$661$	22.8616	0.889212	0.444606	−	0.895726i	$-0.353344\pi$
$661$	22.8616	0.889212	0.444606	+	0.895726i	$0.353344\pi$
$662$	−3.21048	−0.124779
$663$	−11.4885	−0.446176
$664$	5.62046	0.218116
$665$	0	0
$666$	−2.79469	−0.108292
$667$	6.90481	0.267355
$668$	−23.8461	−0.922635
$669$	5.22346	0.201951
$670$	0	0
$671$	16.8895	0.652013
$672$	9.44616	0.364394
$673$	0.850575	0.0327873	0.0163936	−	0.999866i	$-0.494782\pi$
$673$	0.850575	0.0327873	0.0163936	+	0.999866i	$0.494782\pi$
$674$	−1.14567	−0.0441295
$675$	0	0
$676$	−6.30487	−0.242495
$677$	50.7049	1.94875	0.974374	−	0.224932i	$-0.0722160\pi$
$677$	50.7049	1.94875	0.974374	+	0.224932i	$0.0722160\pi$
$678$	2.45835	0.0944124
$679$	41.6967	1.60017
$680$	0	0
$681$	−4.05730	−0.155476
$682$	2.38528	0.0913373
$683$	−37.8723	−1.44914	−0.724572	−	0.689199i	$-0.757963\pi$
$683$	−37.8723	−1.44914	−0.724572	+	0.689199i	$0.757963\pi$
$684$	0.348599	0.0133290
$685$	0	0
$686$	−3.77176	−0.144007
$687$	21.7638	0.830342
$688$	−36.6619	−1.39772
$689$	47.1250	1.79532
$690$	0	0
$691$	−30.0800	−1.14430	−0.572149	−	0.820150i	$-0.693890\pi$
$691$	−30.0800	−1.14430	−0.572149	+	0.820150i	$0.693890\pi$
$692$	−26.6376	−1.01261
$693$	7.16910	0.272332
$694$	3.53919	0.134346
$695$	0	0
$696$	−1.40085	−0.0530990
$697$	6.90267	0.261457
$698$	−6.06985	−0.229747
$699$	23.0827	0.873067
$700$	0	0
$701$	−45.5069	−1.71877	−0.859387	−	0.511326i	$-0.829154\pi$
$701$	−45.5069	−1.71877	−0.859387	+	0.511326i	$0.829154\pi$
$702$	1.08552	0.0409702
$703$	1.87809	0.0708336
$704$	−14.7344	−0.555324
$705$	0	0
$706$	9.26920	0.348851
$707$	37.0916	1.39497
$708$	3.37764	0.126940
$709$	−4.21814	−0.158416	−0.0792078	−	0.996858i	$-0.525239\pi$
$709$	−4.21814	−0.158416	−0.0792078	+	0.996858i	$0.525239\pi$
$710$	0	0
$711$	−2.14604	−0.0804828
$712$	1.30541	0.0489223
$713$	19.7877	0.741056
$714$	−2.35464	−0.0881200
$715$	0	0
$716$	29.8687	1.11625
$717$	15.8168	0.590690
$718$	−0.373231	−0.0139289
$719$	5.37482	0.200447	0.100224	−	0.994965i	$-0.468044\pi$
$719$	5.37482	0.200447	0.100224	+	0.994965i	$0.468044\pi$
$720$	0	0
$721$	−1.34960	−0.0502619
$722$	−5.10431	−0.189963
$723$	−15.5213	−0.577244
$724$	−12.1843	−0.452827
$725$	0	0
$726$	−1.49470	−0.0554735
$727$	−0.811084	−0.0300814	−0.0150407	−	0.999887i	$-0.504788\pi$
$727$	−0.811084	−0.0300814	−0.0150407	+	0.999887i	$0.504788\pi$
$728$	−13.0977	−0.485434
$729$	1.00000	0.0370370
$730$	0	0
$731$	29.2426	1.08158
$732$	−13.9508	−0.515637
$733$	−41.9719	−1.55027	−0.775134	−	0.631797i	$-0.782318\pi$
$733$	−41.9719	−1.55027	−0.775134	+	0.631797i	$0.782318\pi$
$734$	−4.56903	−0.168646
$735$	0	0
$736$	16.0191	0.590472
$737$	3.39360	0.125005
$738$	−0.652215	−0.0240084
$739$	2.42442	0.0891837	0.0445919	−	0.999005i	$-0.485801\pi$
$739$	2.42442	0.0891837	0.0445919	+	0.999005i	$0.485801\pi$
$740$	0	0
$741$	−0.729491	−0.0267985
$742$	9.65855	0.354577
$743$	−42.3197	−1.55256	−0.776280	−	0.630389i	$-0.782896\pi$
$743$	−42.3197	−1.55256	−0.776280	+	0.630389i	$0.782896\pi$
$744$	−4.01453	−0.147180
$745$	0	0
$746$	1.99770	0.0731409
$747$	−5.31760	−0.194561
$748$	12.8115	0.468436
$749$	44.3886	1.62193
$750$	0	0
$751$	32.2537	1.17695	0.588477	−	0.808514i	$-0.299728\pi$
$751$	32.2537	1.17695	0.588477	+	0.808514i	$0.299728\pi$
$752$	−3.57072	−0.130211
$753$	−16.3712	−0.596598
$754$	1.43870	0.0523945
$755$	0	0
$756$	−5.92170	−0.215370
$757$	−35.1624	−1.27800	−0.639000	−	0.769207i	$-0.720652\pi$
$757$	−35.1624	−1.27800	−0.639000	+	0.769207i	$0.720652\pi$
$758$	5.79323	0.210420
$759$	12.1576	0.441293
$760$	0	0
$761$	−37.1524	−1.34677	−0.673386	−	0.739291i	$-0.735161\pi$
$761$	−37.1524	−1.34677	−0.673386	+	0.739291i	$0.735161\pi$
$762$	3.57237	0.129413
$763$	−3.72219	−0.134752
$764$	40.5415	1.46674
$765$	0	0
$766$	0.0807293	0.00291687
$767$	−7.06817	−0.255217
$768$	10.5157	0.379454
$769$	31.6222	1.14033	0.570163	−	0.821532i	$-0.306880\pi$
$769$	31.6222	1.14033	0.570163	+	0.821532i	$0.306880\pi$
$770$	0	0
$771$	11.3356	0.408240
$772$	32.3808	1.16541
$773$	12.3229	0.443224	0.221612	−	0.975135i	$-0.428868\pi$
$773$	12.3229	0.443224	0.221612	+	0.975135i	$0.428868\pi$
$774$	−2.76306	−0.0993161
$775$	0	0
$776$	−14.3458	−0.514983
$777$	−31.9034	−1.14453
$778$	−1.10910	−0.0397633
$779$	0.438302	0.0157038
$780$	0	0
$781$	32.2889	1.15539
$782$	−3.99307	−0.142792
$783$	1.32536	0.0473646
$784$	8.70453	0.310876
$785$	0	0
$786$	−1.69351	−0.0604057
$787$	−1.81944	−0.0648561	−0.0324281	−	0.999474i	$-0.510324\pi$
$787$	−1.81944	−0.0648561	−0.0324281	+	0.999474i	$0.510324\pi$
$788$	24.6992	0.879872
$789$	13.4091	0.477376
$790$	0	0
$791$	28.0638	0.997835
$792$	−2.46653	−0.0876444
$793$	29.1939	1.03671
$794$	8.52823	0.302655
$795$	0	0
$796$	11.3466	0.402170
$797$	23.7251	0.840388	0.420194	−	0.907434i	$-0.361962\pi$
$797$	23.7251	0.840388	0.420194	+	0.907434i	$0.361962\pi$
$798$	−0.149513	−0.00529272
$799$	2.84812	0.100759
$800$	0	0
$801$	−1.23507	−0.0436389
$802$	−3.56319	−0.125821
$803$	−4.32746	−0.152713
$804$	−2.80313	−0.0988587
$805$	0	0
$806$	4.12302	0.145227
$807$	17.9856	0.633123
$808$	−12.7614	−0.448944
$809$	17.4354	0.612995	0.306497	−	0.951872i	$-0.400843\pi$
$809$	17.4354	0.612995	0.306497	+	0.951872i	$0.400843\pi$
$810$	0	0
$811$	3.04319	0.106861	0.0534304	−	0.998572i	$-0.482984\pi$
$811$	3.04319	0.106861	0.0534304	+	0.998572i	$0.482984\pi$
$812$	−7.84840	−0.275425
$813$	−6.54923	−0.229691
$814$	−6.52176	−0.228588
$815$	0	0
$816$	−10.1698	−0.356015
$817$	1.85683	0.0649624
$818$	1.45614	0.0509127
$819$	12.3920	0.433010
$820$	0	0
$821$	41.0168	1.43150	0.715748	−	0.698359i	$-0.246086\pi$
$821$	41.0168	1.43150	0.715748	+	0.698359i	$0.246086\pi$
$822$	−4.10780	−0.143276
$823$	−9.60083	−0.334664	−0.167332	−	0.985901i	$-0.553515\pi$
$823$	−9.60083	−0.334664	−0.167332	+	0.985901i	$0.553515\pi$
$824$	0.464332	0.0161758
$825$	0	0
$826$	−1.44866	−0.0504055
$827$	−39.2745	−1.36571	−0.682854	−	0.730555i	$-0.739262\pi$
$827$	−39.2745	−1.36571	−0.682854	+	0.730555i	$0.739262\pi$
$828$	−10.0422	−0.348991
$829$	−6.83966	−0.237551	−0.118776	−	0.992921i	$-0.537897\pi$
$829$	−6.83966	−0.237551	−0.118776	+	0.992921i	$0.537897\pi$
$830$	0	0
$831$	4.99751	0.173362
$832$	−25.4688	−0.882971
$833$	−6.94301	−0.240561
$834$	−5.67452	−0.196493
$835$	0	0
$836$	0.813499	0.0281354
$837$	3.79820	0.131285
$838$	−0.170596	−0.00589313
$839$	48.5498	1.67612	0.838062	−	0.545575i	$-0.183689\pi$
$839$	48.5498	1.67612	0.838062	+	0.545575i	$0.183689\pi$
$840$	0	0
$841$	−27.2434	−0.939428
$842$	−2.12909	−0.0733733
$843$	19.0218	0.655147
$844$	−6.60939	−0.227504
$845$	0	0
$846$	−0.269111	−0.00925223
$847$	−17.0631	−0.586293
$848$	41.7159	1.43253
$849$	7.20108	0.247140
$850$	0	0
$851$	−54.1029	−1.85462
$852$	−26.6707	−0.913724
$853$	−43.0900	−1.47537	−0.737686	−	0.675144i	$-0.764081\pi$
$853$	−43.0900	−1.47537	−0.737686	+	0.675144i	$0.764081\pi$
$854$	5.98347	0.204750
$855$	0	0
$856$	−15.2719	−0.521984
$857$	50.0184	1.70860	0.854298	−	0.519783i	$-0.173987\pi$
$857$	50.0184	1.70860	0.854298	+	0.519783i	$0.173987\pi$
$858$	2.53319	0.0864816
$859$	−50.2512	−1.71455	−0.857274	−	0.514861i	$-0.827843\pi$
$859$	−50.2512	−1.71455	−0.857274	+	0.514861i	$0.827843\pi$
$860$	0	0
$861$	−7.44549	−0.253742
$862$	4.38053	0.149202
$863$	34.5585	1.17638	0.588192	−	0.808721i	$-0.299840\pi$
$863$	34.5585	1.17638	0.588192	+	0.808721i	$0.299840\pi$
$864$	3.07483	0.104608
$865$	0	0
$866$	−10.0267	−0.340721
$867$	−8.88822	−0.301860
$868$	−22.4918	−0.763422
$869$	−5.00804	−0.169886
$870$	0	0
$871$	5.86592	0.198759
$872$	1.28062	0.0433673
$873$	13.5727	0.459368
$874$	−0.253550	−0.00857645
$875$	0	0
$876$	3.57449	0.120771
$877$	2.72357	0.0919684	0.0459842	−	0.998942i	$-0.485358\pi$
$877$	2.72357	0.0919684	0.0459842	+	0.998942i	$0.485358\pi$
$878$	−1.49446	−0.0504354
$879$	−14.3214	−0.483048
$880$	0	0
$881$	23.3704	0.787369	0.393685	−	0.919246i	$-0.371200\pi$
$881$	23.3704	0.787369	0.393685	+	0.919246i	$0.371200\pi$
$882$	0.656026	0.0220896
$883$	7.39960	0.249016	0.124508	−	0.992219i	$-0.460265\pi$
$883$	7.39960	0.249016	0.124508	+	0.992219i	$0.460265\pi$
$884$	22.1450	0.744817
$885$	0	0
$886$	−6.84404	−0.229930
$887$	26.5701	0.892135	0.446068	−	0.894999i	$-0.352824\pi$
$887$	26.5701	0.892135	0.446068	+	0.894999i	$0.352824\pi$
$888$	10.9764	0.368343
$889$	40.7811	1.36775
$890$	0	0
$891$	2.33362	0.0781793
$892$	−10.0686	−0.337123
$893$	0.180848	0.00605186
$894$	3.71087	0.124110
$895$	0	0
$896$	−24.1123	−0.805535
$897$	21.0147	0.701660
$898$	−6.96633	−0.232469
$899$	5.03399	0.167893
$900$	0	0
$901$	−33.2739	−1.10852
$902$	−1.52202	−0.0506778
$903$	−31.5423	−1.04966
$904$	−9.65537	−0.321133
$905$	0	0
$906$	−0.257611	−0.00855857
$907$	20.4866	0.680246	0.340123	−	0.940381i	$-0.389531\pi$
$907$	20.4866	0.680246	0.340123	+	0.940381i	$0.389531\pi$
$908$	7.82078	0.259542
$909$	12.0737	0.400460
$910$	0	0
$911$	7.98661	0.264608	0.132304	−	0.991209i	$-0.457762\pi$
$911$	7.98661	0.264608	0.132304	+	0.991209i	$0.457762\pi$
$912$	−0.645758	−0.0213832
$913$	−12.4093	−0.410687
$914$	−5.40852	−0.178898
$915$	0	0
$916$	−41.9515	−1.38612
$917$	−19.3327	−0.638421
$918$	−0.766460	−0.0252970
$919$	−25.6366	−0.845672	−0.422836	−	0.906206i	$-0.638965\pi$
$919$	−25.6366	−0.845672	−0.422836	+	0.906206i	$0.638965\pi$
$920$	0	0
$921$	9.78584	0.322454
$922$	8.57701	0.282469
$923$	55.8121	1.83708
$924$	−13.8190	−0.454612
$925$	0	0
$926$	−2.33497	−0.0767320
$927$	−0.439311	−0.0144289
$928$	4.07526	0.133777
$929$	27.5880	0.905133	0.452566	−	0.891731i	$-0.350509\pi$
$929$	27.5880	0.905133	0.452566	+	0.891731i	$0.350509\pi$
$930$	0	0
$931$	−0.440863	−0.0144487
$932$	−44.4937	−1.45744
$933$	−23.4310	−0.767098
$934$	0.928374	0.0303773
$935$	0	0
$936$	−4.26346	−0.139355
$937$	34.5636	1.12914	0.564572	−	0.825384i	$-0.309041\pi$
$937$	34.5636	1.12914	0.564572	+	0.825384i	$0.309041\pi$
$938$	1.20226	0.0392550
$939$	−23.4736	−0.766033
$940$	0	0
$941$	12.8521	0.418968	0.209484	−	0.977812i	$-0.432822\pi$
$941$	12.8521	0.418968	0.209484	+	0.977812i	$0.432822\pi$
$942$	2.92537	0.0953138
$943$	−12.6263	−0.411169
$944$	−6.25688	−0.203644
$945$	0	0
$946$	−6.44793	−0.209640
$947$	−30.1220	−0.978833	−0.489417	−	0.872050i	$-0.662790\pi$
$947$	−30.1220	−0.978833	−0.489417	+	0.872050i	$0.662790\pi$
$948$	4.13666	0.134352
$949$	−7.48010	−0.242814
$950$	0	0
$951$	−21.6990	−0.703637
$952$	9.24802	0.299730
$953$	−32.7745	−1.06167	−0.530834	−	0.847476i	$-0.678121\pi$
$953$	−32.7745	−1.06167	−0.530834	+	0.847476i	$0.678121\pi$
$954$	3.14396	0.101790
$955$	0	0
$956$	−30.4882	−0.986058
$957$	3.09289	0.0999790
$958$	−6.50982	−0.210323
$959$	−46.8934	−1.51427
$960$	0	0
$961$	−16.5737	−0.534634
$962$	−11.2730	−0.363456
$963$	14.4490	0.465612
$964$	29.9185	0.963612
$965$	0	0
$966$	4.30708	0.138578
$967$	17.9841	0.578328	0.289164	−	0.957280i	$-0.406623\pi$
$967$	17.9841	0.578328	0.289164	+	0.957280i	$0.406623\pi$
$968$	5.87055	0.188687
$969$	0.515077	0.0165467
$970$	0	0
$971$	−46.4939	−1.49206	−0.746030	−	0.665912i	$-0.768043\pi$
$971$	−46.4939	−1.49206	−0.746030	+	0.665912i	$0.768043\pi$
$972$	−1.92758	−0.0618271
$973$	−64.7787	−2.07671
$974$	3.81643	0.122286
$975$	0	0
$976$	25.8430	0.827214
$977$	34.5606	1.10569	0.552845	−	0.833284i	$-0.313542\pi$
$977$	34.5606	1.10569	0.552845	+	0.833284i	$0.313542\pi$
$978$	4.93416	0.157777
$979$	−2.88218	−0.0921147
$980$	0	0
$981$	−1.21161	−0.0386839
$982$	−6.18658	−0.197422
$983$	−3.84407	−0.122607	−0.0613034	−	0.998119i	$-0.519526\pi$
$983$	−3.84407	−0.122607	−0.0613034	+	0.998119i	$0.519526\pi$
$984$	2.56162	0.0816616
$985$	0	0
$986$	−1.01584	−0.0323508
$987$	−3.07209	−0.0977858
$988$	1.40615	0.0447356
$989$	−53.4904	−1.70090
$990$	0	0
$991$	−31.2979	−0.994210	−0.497105	−	0.867690i	$-0.665604\pi$
$991$	−31.2979	−0.994210	−0.497105	+	0.867690i	$0.665604\pi$
$992$	11.6788	0.370803
$993$	−11.9299	−0.378585
$994$	11.4390	0.362824
$995$	0	0
$996$	10.2501	0.324787
$997$	37.7423	1.19531	0.597655	−	0.801754i	$-0.296099\pi$
$997$	37.7423	1.19531	0.597655	+	0.801754i	$0.296099\pi$
$998$	−5.29624	−0.167650
$999$	−10.3849	−0.328564

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bc.1.4	yes	7
5.4	even	2		3525.2.a.x.1.4	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.2.a.x.1.4	✓	7	5.4	even	2
3525.2.a.bc.1.4	yes	7	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q+0.269111 q^{2} +1.00000 q^{3} -1.92758 q^{4} +0.269111 q^{6} +3.07209 q^{7} -1.05695 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.269111 q^{2} +1.00000 q^{3} -1.92758 q^{4} +0.269111 q^{6} +3.07209 q^{7} -1.05695 q^{8} +1.00000 q^{9} +2.33362 q^{11} -1.92758 q^{12} +4.03372 q^{13} +0.826734 q^{14} +3.57072 q^{16} -2.84812 q^{17} +0.269111 q^{18} -0.180848 q^{19} +3.07209 q^{21} +0.628003 q^{22} +5.20976 q^{23} -1.05695 q^{24} +1.08552 q^{26} +1.00000 q^{27} -5.92170 q^{28} +1.32536 q^{29} +3.79820 q^{31} +3.07483 q^{32} +2.33362 q^{33} -0.766460 q^{34} -1.92758 q^{36} -10.3849 q^{37} -0.0486683 q^{38} +4.03372 q^{39} -2.42359 q^{41} +0.826734 q^{42} -10.2674 q^{43} -4.49824 q^{44} +1.40200 q^{46} -1.00000 q^{47} +3.57072 q^{48} +2.43775 q^{49} -2.84812 q^{51} -7.77531 q^{52} +11.6828 q^{53} +0.269111 q^{54} -3.24706 q^{56} -0.180848 q^{57} +0.356669 q^{58} -1.75227 q^{59} +7.23748 q^{61} +1.02214 q^{62} +3.07209 q^{63} -6.31397 q^{64} +0.628003 q^{66} +1.45422 q^{67} +5.48997 q^{68} +5.20976 q^{69} +13.8364 q^{71} -1.05695 q^{72} -1.85439 q^{73} -2.79469 q^{74} +0.348599 q^{76} +7.16910 q^{77} +1.08552 q^{78} -2.14604 q^{79} +1.00000 q^{81} -0.652215 q^{82} -5.31760 q^{83} -5.92170 q^{84} -2.76306 q^{86} +1.32536 q^{87} -2.46653 q^{88} -1.23507 q^{89} +12.3920 q^{91} -10.0422 q^{92} +3.79820 q^{93} -0.269111 q^{94} +3.07483 q^{96} +13.5727 q^{97} +0.656026 q^{98} +2.33362 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 3 q^{2} + 7 q^{3} + 5 q^{4} + 3 q^{6} + 5 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 3 * q^2 + 7 * q^3 + 5 * q^4 + 3 * q^6 + 5 * q^7 + 6 * q^8 + 7 * q^9	\( 7 q + 3 q^{2} + 7 q^{3} + 5 q^{4} + 3 q^{6} + 5 q^{7} + 6 q^{8} + 7 q^{9} + 4 q^{11} + 5 q^{12} + 5 q^{13} + 5 q^{14} + 9 q^{16} + 10 q^{17} + 3 q^{18} + q^{19} + 5 q^{21} + 10 q^{22} + 10 q^{23} + 6 q^{24} + 12 q^{26} + 7 q^{27} + 2 q^{28} + 9 q^{29} + 3 q^{31} + 4 q^{33} - 20 q^{34} + 5 q^{36} + 9 q^{37} - 2 q^{38} + 5 q^{39} + 20 q^{41} + 5 q^{42} + 16 q^{43} - 5 q^{44} - q^{46} - 7 q^{47} + 9 q^{48} - 10 q^{49} + 10 q^{51} + 21 q^{52} + 3 q^{54} + 21 q^{56} + q^{57} + 19 q^{58} + 18 q^{59} - 2 q^{62} + 5 q^{63} - 30 q^{64} + 10 q^{66} + 8 q^{67} + 20 q^{68} + 10 q^{69} + 14 q^{71} + 6 q^{72} + 4 q^{73} - 17 q^{74} + 12 q^{76} + 2 q^{77} + 12 q^{78} - 21 q^{79} + 7 q^{81} - 7 q^{82} + 22 q^{83} + 2 q^{84} + 35 q^{86} + 9 q^{87} + 14 q^{88} + 2 q^{89} - 2 q^{91} + 5 q^{92} + 3 q^{93} - 3 q^{94} + 12 q^{97} + 30 q^{98} + 4 q^{99}+O(q^{100}) \) 7 * q + 3 * q^2 + 7 * q^3 + 5 * q^4 + 3 * q^6 + 5 * q^7 + 6 * q^8 + 7 * q^9 + 4 * q^11 + 5 * q^12 + 5 * q^13 + 5 * q^14 + 9 * q^16 + 10 * q^17 + 3 * q^18 + q^19 + 5 * q^21 + 10 * q^22 + 10 * q^23 + 6 * q^24 + 12 * q^26 + 7 * q^27 + 2 * q^28 + 9 * q^29 + 3 * q^31 + 4 * q^33 - 20 * q^34 + 5 * q^36 + 9 * q^37 - 2 * q^38 + 5 * q^39 + 20 * q^41 + 5 * q^42 + 16 * q^43 - 5 * q^44 - q^46 - 7 * q^47 + 9 * q^48 - 10 * q^49 + 10 * q^51 + 21 * q^52 + 3 * q^54 + 21 * q^56 + q^57 + 19 * q^58 + 18 * q^59 - 2 * q^62 + 5 * q^63 - 30 * q^64 + 10 * q^66 + 8 * q^67 + 20 * q^68 + 10 * q^69 + 14 * q^71 + 6 * q^72 + 4 * q^73 - 17 * q^74 + 12 * q^76 + 2 * q^77 + 12 * q^78 - 21 * q^79 + 7 * q^81 - 7 * q^82 + 22 * q^83 + 2 * q^84 + 35 * q^86 + 9 * q^87 + 14 * q^88 + 2 * q^89 - 2 * q^91 + 5 * q^92 + 3 * q^93 - 3 * q^94 + 12 * q^97 + 30 * q^98 + 4 * q^99

Introduction

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Database

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