LMFDB - Embedded newform 3525.2.a.be.1.5

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:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 7x^{6} + 24x^{5} + 8x^{4} - 47x^{3} + 8x^{2} + 13x + 2 $ x^8 - 3x^7 - 7x^6 + 24x^5 + 8x^4 - 47x^3 + 8x^2 + 13*x + 2
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			1.5
Root			$0.936719$ 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)

$f(q)$	$=$	$q+0.936719 q^{2} -1.00000 q^{3} -1.12256 q^{4} -0.936719 q^{6} -3.65526 q^{7} -2.92496 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.936719 q^{2} -1.00000 q^{3} -1.12256 q^{4} -0.936719 q^{6} -3.65526 q^{7} -2.92496 q^{8} +1.00000 q^{9} -5.57376 q^{11} +1.12256 q^{12} -2.92869 q^{13} -3.42395 q^{14} -0.494746 q^{16} -2.26461 q^{17} +0.936719 q^{18} -2.64416 q^{19} +3.65526 q^{21} -5.22104 q^{22} +7.72850 q^{23} +2.92496 q^{24} -2.74336 q^{26} -1.00000 q^{27} +4.10324 q^{28} -7.79408 q^{29} -6.03466 q^{31} +5.38648 q^{32} +5.57376 q^{33} -2.12130 q^{34} -1.12256 q^{36} -6.60338 q^{37} -2.47683 q^{38} +2.92869 q^{39} -8.81927 q^{41} +3.42395 q^{42} +9.69632 q^{43} +6.25687 q^{44} +7.23943 q^{46} +1.00000 q^{47} +0.494746 q^{48} +6.36091 q^{49} +2.26461 q^{51} +3.28763 q^{52} -2.97538 q^{53} -0.936719 q^{54} +10.6915 q^{56} +2.64416 q^{57} -7.30086 q^{58} +0.571458 q^{59} +8.30187 q^{61} -5.65278 q^{62} -3.65526 q^{63} +6.03511 q^{64} +5.22104 q^{66} -8.03594 q^{67} +2.54216 q^{68} -7.72850 q^{69} +11.7268 q^{71} -2.92496 q^{72} +5.94373 q^{73} -6.18551 q^{74} +2.96822 q^{76} +20.3735 q^{77} +2.74336 q^{78} -16.6200 q^{79} +1.00000 q^{81} -8.26117 q^{82} +13.8354 q^{83} -4.10324 q^{84} +9.08272 q^{86} +7.79408 q^{87} +16.3030 q^{88} +4.31121 q^{89} +10.7051 q^{91} -8.67569 q^{92} +6.03466 q^{93} +0.936719 q^{94} -5.38648 q^{96} +5.24644 q^{97} +5.95838 q^{98} -5.57376 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - 8 q^{3} + 7 q^{4} - 3 q^{6} + 8 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 - 8 * q^3 + 7 * q^4 - 3 * q^6 + 8 * q^7 + 6 * q^8 + 8 * q^9	$ 8 q + 3 q^{2} - 8 q^{3} + 7 q^{4} - 3 q^{6} + 8 q^{7} + 6 q^{8} + 8 q^{9} - 8 q^{11} - 7 q^{12} + 10 q^{13} + q^{14} + 5 q^{16} + 6 q^{17} + 3 q^{18} - 2 q^{19} - 8 q^{21} + 10 q^{23} - 6 q^{24} - 14 q^{26} - 8 q^{27} + 44 q^{28} - 13 q^{29} + 10 q^{32} + 8 q^{33} + 28 q^{34} + 7 q^{36} + 3 q^{37} + 36 q^{38} - 10 q^{39} - 16 q^{41} - q^{42} + 25 q^{43} - 17 q^{44} - 5 q^{46} + 8 q^{47} - 5 q^{48} + 16 q^{49} - 6 q^{51} - 17 q^{52} + 4 q^{53} - 3 q^{54} + 37 q^{56} + 2 q^{57} + 15 q^{58} - 8 q^{59} + 15 q^{61} + 6 q^{62} + 8 q^{63} - 14 q^{64} + 27 q^{67} + 14 q^{68} - 10 q^{69} + 14 q^{71} + 6 q^{72} + 28 q^{73} - 21 q^{74} + 6 q^{76} + 4 q^{77} + 14 q^{78} + 7 q^{79} + 8 q^{81} - 53 q^{82} + 60 q^{83} - 44 q^{84} - 3 q^{86} + 13 q^{87} + 54 q^{88} - 34 q^{89} + 23 q^{91} - 43 q^{92} + 3 q^{94} - 10 q^{96} + 7 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) $ 8 * q + 3 * q^2 - 8 * q^3 + 7 * q^4 - 3 * q^6 + 8 * q^7 + 6 * q^8 + 8 * q^9 - 8 * q^11 - 7 * q^12 + 10 * q^13 + q^14 + 5 * q^16 + 6 * q^17 + 3 * q^18 - 2 * q^19 - 8 * q^21 + 10 * q^23 - 6 * q^24 - 14 * q^26 - 8 * q^27 + 44 * q^28 - 13 * q^29 + 10 * q^32 + 8 * q^33 + 28 * q^34 + 7 * q^36 + 3 * q^37 + 36 * q^38 - 10 * q^39 - 16 * q^41 - q^42 + 25 * q^43 - 17 * q^44 - 5 * q^46 + 8 * q^47 - 5 * q^48 + 16 * q^49 - 6 * q^51 - 17 * q^52 + 4 * q^53 - 3 * q^54 + 37 * q^56 + 2 * q^57 + 15 * q^58 - 8 * q^59 + 15 * q^61 + 6 * q^62 + 8 * q^63 - 14 * q^64 + 27 * q^67 + 14 * q^68 - 10 * q^69 + 14 * q^71 + 6 * q^72 + 28 * q^73 - 21 * q^74 + 6 * q^76 + 4 * q^77 + 14 * q^78 + 7 * q^79 + 8 * q^81 - 53 * q^82 + 60 * q^83 - 44 * q^84 - 3 * q^86 + 13 * q^87 + 54 * q^88 - 34 * q^89 + 23 * q^91 - 43 * q^92 + 3 * q^94 - 10 * q^96 + 7 * q^97 + 40 * q^98 - 8 * 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 $

$2$	0.936719	0.662360	0.331180	−	0.943568i	$-0.392553\pi$
$2$	0.936719	0.662360	0.331180	+	0.943568i	$0.392553\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.12256	−0.561279
$5$	0	0
$5$	0	0
$6$	−0.936719	−0.382414
$7$	−3.65526	−1.38156	−0.690779	−	0.723066i	$-0.742732\pi$
$7$	−3.65526	−1.38156	−0.690779	+	0.723066i	$0.742732\pi$
$8$	−2.92496	−1.03413
$9$	1.00000	0.333333
$10$	0	0
$11$	−5.57376	−1.68055	−0.840275	−	0.542160i	$-0.817607\pi$
$11$	−5.57376	−1.68055	−0.840275	+	0.542160i	$0.817607\pi$
$12$	1.12256	0.324055
$13$	−2.92869	−0.812274	−0.406137	−	0.913812i	$-0.633124\pi$
$13$	−2.92869	−0.812274	−0.406137	+	0.913812i	$0.633124\pi$
$14$	−3.42395	−0.915089
$15$	0	0
$16$	−0.494746	−0.123686
$17$	−2.26461	−0.549249	−0.274624	−	0.961552i	$-0.588554\pi$
$17$	−2.26461	−0.549249	−0.274624	+	0.961552i	$0.588554\pi$
$18$	0.936719	0.220787
$19$	−2.64416	−0.606612	−0.303306	−	0.952893i	$-0.598090\pi$
$19$	−2.64416	−0.606612	−0.303306	+	0.952893i	$0.598090\pi$
$20$	0	0
$21$	3.65526	0.797643
$22$	−5.22104	−1.11313
$23$	7.72850	1.61150	0.805751	−	0.592254i	$-0.201762\pi$
$23$	7.72850	1.61150	0.805751	+	0.592254i	$0.201762\pi$
$24$	2.92496	0.597055
$25$	0	0
$26$	−2.74336	−0.538018
$27$	−1.00000	−0.192450
$28$	4.10324	0.775440
$29$	−7.79408	−1.44732	−0.723662	−	0.690154i	$-0.757543\pi$
$29$	−7.79408	−1.44732	−0.723662	+	0.690154i	$0.757543\pi$
$30$	0	0
$31$	−6.03466	−1.08386	−0.541928	−	0.840425i	$-0.682306\pi$
$31$	−6.03466	−1.08386	−0.541928	+	0.840425i	$0.682306\pi$
$32$	5.38648	0.952204
$33$	5.57376	0.970266
$34$	−2.12130	−0.363801
$35$	0	0
$36$	−1.12256	−0.187093
$37$	−6.60338	−1.08559	−0.542794	−	0.839866i	$-0.682634\pi$
$37$	−6.60338	−1.08559	−0.542794	+	0.839866i	$0.682634\pi$
$38$	−2.47683	−0.401796
$39$	2.92869	0.468966
$40$	0	0
$41$	−8.81927	−1.37734	−0.688669	−	0.725076i	$-0.741805\pi$
$41$	−8.81927	−1.37734	−0.688669	+	0.725076i	$0.741805\pi$
$42$	3.42395	0.528327
$43$	9.69632	1.47867	0.739337	−	0.673335i	$-0.235139\pi$
$43$	9.69632	1.47867	0.739337	+	0.673335i	$0.235139\pi$
$44$	6.25687	0.943258
$45$	0	0
$46$	7.23943	1.06740
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	0.494746	0.0714104
$49$	6.36091	0.908702
$50$	0	0
$51$	2.26461	0.317109
$52$	3.28763	0.455912
$53$	−2.97538	−0.408700	−0.204350	−	0.978898i	$-0.565508\pi$
$53$	−2.97538	−0.408700	−0.204350	+	0.978898i	$0.565508\pi$
$54$	−0.936719	−0.127471
$55$	0	0
$56$	10.6915	1.42871
$57$	2.64416	0.350228
$58$	−7.30086	−0.958650
$59$	0.571458	0.0743975	0.0371987	−	0.999308i	$-0.488157\pi$
$59$	0.571458	0.0743975	0.0371987	+	0.999308i	$0.488157\pi$
$60$	0	0
$61$	8.30187	1.06295	0.531473	−	0.847075i	$-0.321639\pi$
$61$	8.30187	1.06295	0.531473	+	0.847075i	$0.321639\pi$
$62$	−5.65278	−0.717903
$63$	−3.65526	−0.460519
$64$	6.03511	0.754388
$65$	0	0
$66$	5.22104	0.642666
$67$	−8.03594	−0.981746	−0.490873	−	0.871231i	$-0.663322\pi$
$67$	−8.03594	−0.981746	−0.490873	+	0.871231i	$0.663322\pi$
$68$	2.54216	0.308282
$69$	−7.72850	−0.930402
$70$	0	0
$71$	11.7268	1.39171	0.695855	−	0.718183i	$-0.255026\pi$
$71$	11.7268	1.39171	0.695855	+	0.718183i	$0.255026\pi$
$72$	−2.92496	−0.344710
$73$	5.94373	0.695661	0.347830	−	0.937558i	$-0.386919\pi$
$73$	5.94373	0.695661	0.347830	+	0.937558i	$0.386919\pi$
$74$	−6.18551	−0.719050
$75$	0	0
$76$	2.96822	0.340479
$77$	20.3735	2.32178
$78$	2.74336	0.310625
$79$	−16.6200	−1.86990	−0.934950	−	0.354780i	$-0.884556\pi$
$79$	−16.6200	−1.86990	−0.934950	+	0.354780i	$0.884556\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−8.26117	−0.912294
$83$	13.8354	1.51863	0.759316	−	0.650722i	$-0.225534\pi$
$83$	13.8354	1.51863	0.759316	+	0.650722i	$0.225534\pi$
$84$	−4.10324	−0.447700
$85$	0	0
$86$	9.08272	0.979415
$87$	7.79408	0.835613
$88$	16.3030	1.73791
$89$	4.31121	0.456988	0.228494	−	0.973545i	$-0.426620\pi$
$89$	4.31121	0.456988	0.228494	+	0.973545i	$0.426620\pi$
$90$	0	0
$91$	10.7051	1.12220
$92$	−8.67569	−0.904503
$93$	6.03466	0.625765
$94$	0.936719	0.0966151
$95$	0	0
$96$	−5.38648	−0.549755
$97$	5.24644	0.532696	0.266348	−	0.963877i	$-0.414183\pi$
$97$	5.24644	0.532696	0.266348	+	0.963877i	$0.414183\pi$
$98$	5.95838	0.601888
$99$	−5.57376	−0.560184
$100$	0	0
$101$	−17.9567	−1.78675	−0.893377	−	0.449308i	$-0.851671\pi$
$101$	−17.9567	−1.78675	−0.893377	+	0.449308i	$0.851671\pi$
$102$	2.12130	0.210040
$103$	13.8334	1.36305	0.681525	−	0.731795i	$-0.261317\pi$
$103$	13.8334	1.36305	0.681525	+	0.731795i	$0.261317\pi$
$104$	8.56631	0.839996
$105$	0	0
$106$	−2.78710	−0.270707
$107$	6.17861	0.597309	0.298655	−	0.954361i	$-0.403462\pi$
$107$	6.17861	0.597309	0.298655	+	0.954361i	$0.403462\pi$
$108$	1.12256	0.108018
$109$	14.0831	1.34892	0.674458	−	0.738314i	$-0.264378\pi$
$109$	14.0831	1.34892	0.674458	+	0.738314i	$0.264378\pi$
$110$	0	0
$111$	6.60338	0.626765
$112$	1.80842	0.170880
$113$	−16.6357	−1.56496	−0.782480	−	0.622676i	$-0.786045\pi$
$113$	−16.6357	−1.56496	−0.782480	+	0.622676i	$0.786045\pi$
$114$	2.47683	0.231977
$115$	0	0
$116$	8.74931	0.812353
$117$	−2.92869	−0.270758
$118$	0.535295	0.0492779
$119$	8.27774	0.758819
$120$	0	0
$121$	20.0668	1.82425
$122$	7.77652	0.704053
$123$	8.81927	0.795207
$124$	6.77426	0.608346
$125$	0	0
$126$	−3.42395	−0.305030
$127$	−12.1084	−1.07445	−0.537225	−	0.843439i	$-0.680527\pi$
$127$	−12.1084	−1.07445	−0.537225	+	0.843439i	$0.680527\pi$
$128$	−5.11976	−0.452527
$129$	−9.69632	−0.853713
$130$	0	0
$131$	1.58271	0.138282	0.0691409	−	0.997607i	$-0.477974\pi$
$131$	1.58271	0.138282	0.0691409	+	0.997607i	$0.477974\pi$
$132$	−6.25687	−0.544590
$133$	9.66509	0.838069
$134$	−7.52741	−0.650269
$135$	0	0
$136$	6.62389	0.567994
$137$	−20.5052	−1.75188	−0.875938	−	0.482424i	$-0.839757\pi$
$137$	−20.5052	−1.75188	−0.875938	+	0.482424i	$0.839757\pi$
$138$	−7.23943	−0.616261
$139$	−16.7180	−1.41800	−0.709002	−	0.705207i	$-0.750854\pi$
$139$	−16.7180	−1.41800	−0.709002	+	0.705207i	$0.750854\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	10.9847	0.921813
$143$	16.3238	1.36507
$144$	−0.494746	−0.0412288
$145$	0	0
$146$	5.56760	0.460778
$147$	−6.36091	−0.524639
$148$	7.41268	0.609318
$149$	10.2172	0.837025	0.418513	−	0.908211i	$-0.362552\pi$
$149$	10.2172	0.837025	0.418513	+	0.908211i	$0.362552\pi$
$150$	0	0
$151$	−20.9048	−1.70121	−0.850603	−	0.525808i	$-0.823763\pi$
$151$	−20.9048	−1.70121	−0.850603	+	0.525808i	$0.823763\pi$
$152$	7.73406	0.627315
$153$	−2.26461	−0.183083
$154$	19.0843	1.53785
$155$	0	0
$156$	−3.28763	−0.263221
$157$	−22.8938	−1.82712	−0.913561	−	0.406702i	$-0.866679\pi$
$157$	−22.8938	−1.82712	−0.913561	+	0.406702i	$0.866679\pi$
$158$	−15.5683	−1.23855
$159$	2.97538	0.235963
$160$	0	0
$161$	−28.2496	−2.22638
$162$	0.936719	0.0735956
$163$	11.2612	0.882042	0.441021	−	0.897497i	$-0.354616\pi$
$163$	11.2612	0.882042	0.441021	+	0.897497i	$0.354616\pi$
$164$	9.90014	0.773071
$165$	0	0
$166$	12.9599	1.00588
$167$	16.8461	1.30359	0.651794	−	0.758396i	$-0.274017\pi$
$167$	16.8461	1.30359	0.651794	+	0.758396i	$0.274017\pi$
$168$	−10.6915	−0.824865
$169$	−4.42275	−0.340212
$170$	0	0
$171$	−2.64416	−0.202204
$172$	−10.8847	−0.829949
$173$	13.5553	1.03059	0.515294	−	0.857014i	$-0.327683\pi$
$173$	13.5553	1.03059	0.515294	+	0.857014i	$0.327683\pi$
$174$	7.30086	0.553477
$175$	0	0
$176$	2.75759	0.207861
$177$	−0.571458	−0.0429534
$178$	4.03839	0.302690
$179$	−5.29177	−0.395525	−0.197763	−	0.980250i	$-0.563368\pi$
$179$	−5.29177	−0.395525	−0.197763	+	0.980250i	$0.563368\pi$
$180$	0	0
$181$	−6.93711	−0.515632	−0.257816	−	0.966194i	$-0.583003\pi$
$181$	−6.93711	−0.515632	−0.257816	+	0.966194i	$0.583003\pi$
$182$	10.0277	0.743302
$183$	−8.30187	−0.613692
$184$	−22.6055	−1.66650
$185$	0	0
$186$	5.65278	0.414482
$187$	12.6224	0.923041
$188$	−1.12256	−0.0818710
$189$	3.65526	0.265881
$190$	0	0
$191$	3.27524	0.236988	0.118494	−	0.992955i	$-0.462193\pi$
$191$	3.27524	0.236988	0.118494	+	0.992955i	$0.462193\pi$
$192$	−6.03511	−0.435546
$193$	−6.91822	−0.497984	−0.248992	−	0.968506i	$-0.580099\pi$
$193$	−6.91822	−0.497984	−0.248992	+	0.968506i	$0.580099\pi$
$194$	4.91444	0.352836
$195$	0	0
$196$	−7.14050	−0.510035
$197$	13.2026	0.940650	0.470325	−	0.882493i	$-0.344137\pi$
$197$	13.2026	0.940650	0.470325	+	0.882493i	$0.344137\pi$
$198$	−5.22104	−0.371043
$199$	−10.3855	−0.736210	−0.368105	−	0.929784i	$-0.619993\pi$
$199$	−10.3855	−0.736210	−0.368105	+	0.929784i	$0.619993\pi$
$200$	0	0
$201$	8.03594	0.566811
$202$	−16.8203	−1.18347
$203$	28.4894	1.99956
$204$	−2.54216	−0.177987
$205$	0	0
$206$	12.9580	0.902830
$207$	7.72850	0.537168
$208$	1.44896	0.100467
$209$	14.7379	1.01944
$210$	0	0
$211$	19.5002	1.34245	0.671226	−	0.741253i	$-0.265768\pi$
$211$	19.5002	1.34245	0.671226	+	0.741253i	$0.265768\pi$
$212$	3.34004	0.229395
$213$	−11.7268	−0.803504
$214$	5.78762	0.395634
$215$	0	0
$216$	2.92496	0.199018
$217$	22.0582	1.49741
$218$	13.1919	0.893467
$219$	−5.94373	−0.401640
$220$	0	0
$221$	6.63235	0.446140
$222$	6.18551	0.415144
$223$	−5.43059	−0.363659	−0.181830	−	0.983330i	$-0.558202\pi$
$223$	−5.43059	−0.363659	−0.181830	+	0.983330i	$0.558202\pi$
$224$	−19.6890	−1.31552
$225$	0	0
$226$	−15.5830	−1.03657
$227$	2.68717	0.178354	0.0891770	−	0.996016i	$-0.471576\pi$
$227$	2.68717	0.178354	0.0891770	+	0.996016i	$0.471576\pi$
$228$	−2.96822	−0.196575
$229$	17.6212	1.16444	0.582221	−	0.813030i	$-0.302184\pi$
$229$	17.6212	1.16444	0.582221	+	0.813030i	$0.302184\pi$
$230$	0	0
$231$	−20.3735	−1.34048
$232$	22.7974	1.49672
$233$	14.3094	0.937437	0.468719	−	0.883348i	$-0.344716\pi$
$233$	14.3094	0.937437	0.468719	+	0.883348i	$0.344716\pi$
$234$	−2.74336	−0.179339
$235$	0	0
$236$	−0.641495	−0.0417578
$237$	16.6200	1.07959
$238$	7.75391	0.502611
$239$	−0.608101	−0.0393348	−0.0196674	−	0.999807i	$-0.506261\pi$
$239$	−0.608101	−0.0393348	−0.0196674	+	0.999807i	$0.506261\pi$
$240$	0	0
$241$	−0.888912	−0.0572598	−0.0286299	−	0.999590i	$-0.509114\pi$
$241$	−0.888912	−0.0572598	−0.0286299	+	0.999590i	$0.509114\pi$
$242$	18.7969	1.20831
$243$	−1.00000	−0.0641500
$244$	−9.31934	−0.596609
$245$	0	0
$246$	8.26117	0.526713
$247$	7.74394	0.492735
$248$	17.6511	1.12085
$249$	−13.8354	−0.876782
$250$	0	0
$251$	−0.0483724	−0.00305324	−0.00152662	−	0.999999i	$-0.500486\pi$
$251$	−0.0483724	−0.00305324	−0.00152662	+	0.999999i	$0.500486\pi$
$252$	4.10324	0.258480
$253$	−43.0768	−2.70821
$254$	−11.3422	−0.711672
$255$	0	0
$256$	−16.8660	−1.05412
$257$	−3.58017	−0.223325	−0.111662	−	0.993746i	$-0.535618\pi$
$257$	−3.58017	−0.223325	−0.111662	+	0.993746i	$0.535618\pi$
$258$	−9.08272	−0.565465
$259$	24.1370	1.49980
$260$	0	0
$261$	−7.79408	−0.482441
$262$	1.48255	0.0915924
$263$	−17.6132	−1.08608	−0.543040	−	0.839707i	$-0.682727\pi$
$263$	−17.6132	−1.08608	−0.543040	+	0.839707i	$0.682727\pi$
$264$	−16.3030	−1.00338
$265$	0	0
$266$	9.05347	0.555104
$267$	−4.31121	−0.263842
$268$	9.02081	0.551034
$269$	−14.7262	−0.897870	−0.448935	−	0.893564i	$-0.648196\pi$
$269$	−14.7262	−0.897870	−0.448935	+	0.893564i	$0.648196\pi$
$270$	0	0
$271$	7.26580	0.441366	0.220683	−	0.975346i	$-0.429171\pi$
$271$	7.26580	0.441366	0.220683	+	0.975346i	$0.429171\pi$
$272$	1.12041	0.0679347
$273$	−10.7051	−0.647904
$274$	−19.2076	−1.16037
$275$	0	0
$276$	8.67569	0.522215
$277$	16.0913	0.966833	0.483416	−	0.875391i	$-0.339396\pi$
$277$	16.0913	0.966833	0.483416	+	0.875391i	$0.339396\pi$
$278$	−15.6601	−0.939229
$279$	−6.03466	−0.361286
$280$	0	0
$281$	−2.13975	−0.127647	−0.0638234	−	0.997961i	$-0.520329\pi$
$281$	−2.13975	−0.127647	−0.0638234	+	0.997961i	$0.520329\pi$
$282$	−0.936719	−0.0557808
$283$	23.8300	1.41655	0.708274	−	0.705937i	$-0.249474\pi$
$283$	23.8300	1.41655	0.708274	+	0.705937i	$0.249474\pi$
$284$	−13.1640	−0.781138
$285$	0	0
$286$	15.2908	0.904166
$287$	32.2367	1.90287
$288$	5.38648	0.317401
$289$	−11.8715	−0.698326
$290$	0	0
$291$	−5.24644	−0.307552
$292$	−6.67218	−0.390460
$293$	17.5931	1.02780	0.513901	−	0.857850i	$-0.328200\pi$
$293$	17.5931	1.02780	0.513901	+	0.857850i	$0.328200\pi$
$294$	−5.95838	−0.347500
$295$	0	0
$296$	19.3146	1.12264
$297$	5.57376	0.323422
$298$	9.57064	0.554412
$299$	−22.6344	−1.30898
$300$	0	0
$301$	−35.4425	−2.04287
$302$	−19.5819	−1.12681
$303$	17.9567	1.03158
$304$	1.30819	0.0750297
$305$	0	0
$306$	−2.12130	−0.121267
$307$	20.7229	1.18272	0.591360	−	0.806407i	$-0.298591\pi$
$307$	20.7229	1.18272	0.591360	+	0.806407i	$0.298591\pi$
$308$	−22.8705	−1.30317
$309$	−13.8334	−0.786957
$310$	0	0
$311$	−24.3065	−1.37829	−0.689146	−	0.724622i	$-0.742014\pi$
$311$	−24.3065	−1.37829	−0.689146	+	0.724622i	$0.742014\pi$
$312$	−8.56631	−0.484972
$313$	−17.3665	−0.981615	−0.490808	−	0.871268i	$-0.663298\pi$
$313$	−17.3665	−0.981615	−0.490808	+	0.871268i	$0.663298\pi$
$314$	−21.4450	−1.21021
$315$	0	0
$316$	18.6570	1.04954
$317$	−2.00730	−0.112741	−0.0563706	−	0.998410i	$-0.517953\pi$
$317$	−2.00730	−0.112741	−0.0563706	+	0.998410i	$0.517953\pi$
$318$	2.78710	0.156293
$319$	43.4423	2.43230
$320$	0	0
$321$	−6.17861	−0.344857
$322$	−26.4620	−1.47467
$323$	5.98799	0.333181
$324$	−1.12256	−0.0623644
$325$	0	0
$326$	10.5485	0.584230
$327$	−14.0831	−0.778797
$328$	25.7960	1.42435
$329$	−3.65526	−0.201521
$330$	0	0
$331$	23.0557	1.26725	0.633627	−	0.773638i	$-0.281565\pi$
$331$	23.0557	1.26725	0.633627	+	0.773638i	$0.281565\pi$
$332$	−15.5310	−0.852376
$333$	−6.60338	−0.361863
$334$	15.7800	0.863445
$335$	0	0
$336$	−1.80842	−0.0986576
$337$	−0.977276	−0.0532356	−0.0266178	−	0.999646i	$-0.508474\pi$
$337$	−0.977276	−0.0532356	−0.0266178	+	0.999646i	$0.508474\pi$
$338$	−4.14287	−0.225343
$339$	16.6357	0.903530
$340$	0	0
$341$	33.6357	1.82148
$342$	−2.47683	−0.133932
$343$	2.33603	0.126134
$344$	−28.3613	−1.52914
$345$	0	0
$346$	12.6975	0.682620
$347$	−9.11111	−0.489110	−0.244555	−	0.969635i	$-0.578642\pi$
$347$	−9.11111	−0.489110	−0.244555	+	0.969635i	$0.578642\pi$
$348$	−8.74931	−0.469012
$349$	2.64665	0.141672	0.0708359	−	0.997488i	$-0.477433\pi$
$349$	2.64665	0.141672	0.0708359	+	0.997488i	$0.477433\pi$
$350$	0	0
$351$	2.92869	0.156322
$352$	−30.0229	−1.60023
$353$	−15.8458	−0.843386	−0.421693	−	0.906739i	$-0.638564\pi$
$353$	−15.8458	−0.843386	−0.421693	+	0.906739i	$0.638564\pi$
$354$	−0.535295	−0.0284506
$355$	0	0
$356$	−4.83959	−0.256498
$357$	−8.27774	−0.438104
$358$	−4.95690	−0.261980
$359$	11.8670	0.626318	0.313159	−	0.949701i	$-0.398613\pi$
$359$	11.8670	0.626318	0.313159	+	0.949701i	$0.398613\pi$
$360$	0	0
$361$	−12.0084	−0.632022
$362$	−6.49812	−0.341534
$363$	−20.0668	−1.05323
$364$	−12.0171	−0.629869
$365$	0	0
$366$	−7.77652	−0.406485
$367$	5.06080	0.264172	0.132086	−	0.991238i	$-0.457833\pi$
$367$	5.06080	0.264172	0.132086	+	0.991238i	$0.457833\pi$
$368$	−3.82364	−0.199321
$369$	−8.81927	−0.459113
$370$	0	0
$371$	10.8758	0.564643
$372$	−6.77426	−0.351229
$373$	−1.19434	−0.0618405	−0.0309203	−	0.999522i	$-0.509844\pi$
$373$	−1.19434	−0.0618405	−0.0309203	+	0.999522i	$0.509844\pi$
$374$	11.8236	0.611385
$375$	0	0
$376$	−2.92496	−0.150843
$377$	22.8265	1.17562
$378$	3.42395	0.176109
$379$	16.0321	0.823511	0.411756	−	0.911294i	$-0.364916\pi$
$379$	16.0321	0.823511	0.411756	+	0.911294i	$0.364916\pi$
$380$	0	0
$381$	12.1084	0.620334
$382$	3.06798	0.156972
$383$	−23.4599	−1.19875	−0.599374	−	0.800469i	$-0.704584\pi$
$383$	−23.4599	−1.19875	−0.599374	+	0.800469i	$0.704584\pi$
$384$	5.11976	0.261267
$385$	0	0
$386$	−6.48042	−0.329845
$387$	9.69632	0.492891
$388$	−5.88944	−0.298991
$389$	−27.8951	−1.41434	−0.707169	−	0.707045i	$-0.750028\pi$
$389$	−27.8951	−1.41434	−0.707169	+	0.707045i	$0.750028\pi$
$390$	0	0
$391$	−17.5020	−0.885116
$392$	−18.6054	−0.939715
$393$	−1.58271	−0.0798371
$394$	12.3672	0.623049
$395$	0	0
$396$	6.25687	0.314419
$397$	11.3412	0.569199	0.284600	−	0.958646i	$-0.408139\pi$
$397$	11.3412	0.569199	0.284600	+	0.958646i	$0.408139\pi$
$398$	−9.72830	−0.487636
$399$	−9.66509	−0.483860
$400$	0	0
$401$	−12.6214	−0.630283	−0.315142	−	0.949045i	$-0.602052\pi$
$401$	−12.6214	−0.630283	−0.315142	+	0.949045i	$0.602052\pi$
$402$	7.52741	0.375433
$403$	17.6737	0.880388
$404$	20.1574	1.00287
$405$	0	0
$406$	26.6865	1.32443
$407$	36.8056	1.82439
$408$	−6.62389	−0.327932
$409$	−2.98302	−0.147501	−0.0737505	−	0.997277i	$-0.523497\pi$
$409$	−2.98302	−0.147501	−0.0737505	+	0.997277i	$0.523497\pi$
$410$	0	0
$411$	20.5052	1.01145
$412$	−15.5288	−0.765051
$413$	−2.08883	−0.102784
$414$	7.23943	0.355798
$415$	0	0
$416$	−15.7754	−0.773450
$417$	16.7180	0.818685
$418$	13.8053	0.675238
$419$	15.5076	0.757595	0.378798	−	0.925480i	$-0.376338\pi$
$419$	15.5076	0.757595	0.378798	+	0.925480i	$0.376338\pi$
$420$	0	0
$421$	−22.2089	−1.08240	−0.541198	−	0.840895i	$-0.682029\pi$
$421$	−22.2089	−1.08240	−0.541198	+	0.840895i	$0.682029\pi$
$422$	18.2662	0.889186
$423$	1.00000	0.0486217
$424$	8.70287	0.422649
$425$	0	0
$426$	−10.9847	−0.532209
$427$	−30.3455	−1.46852
$428$	−6.93585	−0.335257
$429$	−16.3238	−0.788122
$430$	0	0
$431$	−20.1349	−0.969865	−0.484932	−	0.874552i	$-0.661156\pi$
$431$	−20.1349	−0.969865	−0.484932	+	0.874552i	$0.661156\pi$
$432$	0.494746	0.0238035
$433$	−17.8238	−0.856557	−0.428278	−	0.903647i	$-0.640880\pi$
$433$	−17.8238	−0.856557	−0.428278	+	0.903647i	$0.640880\pi$
$434$	20.6624	0.991825
$435$	0	0
$436$	−15.8091	−0.757118
$437$	−20.4354	−0.977557
$438$	−5.56760	−0.266030
$439$	11.9909	0.572293	0.286146	−	0.958186i	$-0.407626\pi$
$439$	11.9909	0.572293	0.286146	+	0.958186i	$0.407626\pi$
$440$	0	0
$441$	6.36091	0.302901
$442$	6.21265	0.295506
$443$	25.2442	1.19939	0.599694	−	0.800230i	$-0.295289\pi$
$443$	25.2442	1.19939	0.599694	+	0.800230i	$0.295289\pi$
$444$	−7.41268	−0.351790
$445$	0	0
$446$	−5.08693	−0.240873
$447$	−10.2172	−0.483257
$448$	−22.0599	−1.04223
$449$	−37.0349	−1.74778	−0.873891	−	0.486121i	$-0.838411\pi$
$449$	−37.0349	−1.74778	−0.873891	+	0.486121i	$0.838411\pi$
$450$	0	0
$451$	49.1564	2.31469
$452$	18.6746	0.878379
$453$	20.9048	0.982192
$454$	2.51712	0.118134
$455$	0	0
$456$	−7.73406	−0.362180
$457$	−13.9630	−0.653162	−0.326581	−	0.945169i	$-0.605897\pi$
$457$	−13.9630	−0.653162	−0.326581	+	0.945169i	$0.605897\pi$
$458$	16.5061	0.771280
$459$	2.26461	0.105703
$460$	0	0
$461$	−41.9963	−1.95596	−0.977982	−	0.208689i	$-0.933080\pi$
$461$	−41.9963	−1.95596	−0.977982	+	0.208689i	$0.933080\pi$
$462$	−19.0843	−0.887880
$463$	−23.1267	−1.07479	−0.537394	−	0.843331i	$-0.680591\pi$
$463$	−23.1267	−1.07479	−0.537394	+	0.843331i	$0.680591\pi$
$464$	3.85609	0.179014
$465$	0	0
$466$	13.4038	0.620921
$467$	−13.4945	−0.624451	−0.312225	−	0.950008i	$-0.601074\pi$
$467$	−13.4945	−0.624451	−0.312225	+	0.950008i	$0.601074\pi$
$468$	3.28763	0.151971
$469$	29.3734	1.35634
$470$	0	0
$471$	22.8938	1.05489
$472$	−1.67149	−0.0769366
$473$	−54.0449	−2.48499
$474$	15.5683	0.715075
$475$	0	0
$476$	−9.29224	−0.425909
$477$	−2.97538	−0.136233
$478$	−0.569620	−0.0260538
$479$	6.69141	0.305739	0.152869	−	0.988246i	$-0.451149\pi$
$479$	6.69141	0.305739	0.152869	+	0.988246i	$0.451149\pi$
$480$	0	0
$481$	19.3393	0.881795
$482$	−0.832660	−0.0379266
$483$	28.2496	1.28540
$484$	−22.5261	−1.02391
$485$	0	0
$486$	−0.936719	−0.0424904
$487$	28.6972	1.30039	0.650197	−	0.759765i	$-0.274686\pi$
$487$	28.6972	1.30039	0.650197	+	0.759765i	$0.274686\pi$
$488$	−24.2826	−1.09922
$489$	−11.2612	−0.509247
$490$	0	0
$491$	−6.00762	−0.271120	−0.135560	−	0.990769i	$-0.543283\pi$
$491$	−6.00762	−0.271120	−0.135560	+	0.990769i	$0.543283\pi$
$492$	−9.90014	−0.446333
$493$	17.6506	0.794941
$494$	7.25389	0.326368
$495$	0	0
$496$	2.98562	0.134058
$497$	−42.8643	−1.92273
$498$	−12.9599	−0.580746
$499$	40.6329	1.81898	0.909489	−	0.415727i	$-0.136473\pi$
$499$	40.6329	1.81898	0.909489	+	0.415727i	$0.136473\pi$
$500$	0	0
$501$	−16.8461	−0.752627
$502$	−0.0453114	−0.00202235
$503$	−15.2536	−0.680124	−0.340062	−	0.940403i	$-0.610448\pi$
$503$	−15.2536	−0.680124	−0.340062	+	0.940403i	$0.610448\pi$
$504$	10.6915	0.476236
$505$	0	0
$506$	−40.3508	−1.79381
$507$	4.42275	0.196421
$508$	13.5924	0.603066
$509$	−12.9027	−0.571904	−0.285952	−	0.958244i	$-0.592310\pi$
$509$	−12.9027	−0.571904	−0.285952	+	0.958244i	$0.592310\pi$
$510$	0	0
$511$	−21.7259	−0.961095
$512$	−5.55916	−0.245683
$513$	2.64416	0.116743
$514$	−3.35361	−0.147921
$515$	0	0
$516$	10.8847	0.479171
$517$	−5.57376	−0.245134
$518$	22.6096	0.993410
$519$	−13.5553	−0.595010
$520$	0	0
$521$	8.30560	0.363875	0.181937	−	0.983310i	$-0.441763\pi$
$521$	8.30560	0.363875	0.181937	+	0.983310i	$0.441763\pi$
$522$	−7.30086	−0.319550
$523$	−36.5557	−1.59847	−0.799235	−	0.601019i	$-0.794762\pi$
$523$	−36.5557	−1.59847	−0.799235	+	0.601019i	$0.794762\pi$
$524$	−1.77668	−0.0776147
$525$	0	0
$526$	−16.4987	−0.719375
$527$	13.6662	0.595307
$528$	−2.75759	−0.120009
$529$	36.7297	1.59694
$530$	0	0
$531$	0.571458	0.0247992
$532$	−10.8496	−0.470391
$533$	25.8289	1.11878
$534$	−4.03839	−0.174758
$535$	0	0
$536$	23.5048	1.01525
$537$	5.29177	0.228357
$538$	−13.7943	−0.594713
$539$	−35.4542	−1.52712
$540$	0	0
$541$	17.6937	0.760713	0.380356	−	0.924840i	$-0.375801\pi$
$541$	17.6937	0.760713	0.380356	+	0.924840i	$0.375801\pi$
$542$	6.80601	0.292343
$543$	6.93711	0.297700
$544$	−12.1983	−0.522997
$545$	0	0
$546$	−10.0277	−0.429146
$547$	15.8840	0.679150	0.339575	−	0.940579i	$-0.389717\pi$
$547$	15.8840	0.679150	0.339575	+	0.940579i	$0.389717\pi$
$548$	23.0183	0.983291
$549$	8.30187	0.354315
$550$	0	0
$551$	20.6088	0.877964
$552$	22.6055	0.962155
$553$	60.7505	2.58337
$554$	15.0730	0.640391
$555$	0	0
$556$	18.7669	0.795896
$557$	8.53325	0.361566	0.180783	−	0.983523i	$-0.442137\pi$
$557$	8.53325	0.361566	0.180783	+	0.983523i	$0.442137\pi$
$558$	−5.65278	−0.239301
$559$	−28.3975	−1.20109
$560$	0	0
$561$	−12.6224	−0.532918
$562$	−2.00434	−0.0845482
$563$	−20.6854	−0.871785	−0.435893	−	0.899999i	$-0.643567\pi$
$563$	−20.6854	−0.871785	−0.435893	+	0.899999i	$0.643567\pi$
$564$	1.12256	0.0472682
$565$	0	0
$566$	22.3220	0.938265
$567$	−3.65526	−0.153506
$568$	−34.3003	−1.43921
$569$	10.7355	0.450057	0.225029	−	0.974352i	$-0.427752\pi$
$569$	10.7355	0.450057	0.225029	+	0.974352i	$0.427752\pi$
$570$	0	0
$571$	−11.4293	−0.478303	−0.239152	−	0.970982i	$-0.576869\pi$
$571$	−11.4293	−0.478303	−0.239152	+	0.970982i	$0.576869\pi$
$572$	−18.3245	−0.766184
$573$	−3.27524	−0.136825
$574$	30.1967	1.26039
$575$	0	0
$576$	6.03511	0.251463
$577$	18.3590	0.764296	0.382148	−	0.924101i	$-0.375184\pi$
$577$	18.3590	0.764296	0.382148	+	0.924101i	$0.375184\pi$
$578$	−11.1203	−0.462543
$579$	6.91822	0.287511
$580$	0	0
$581$	−50.5719	−2.09808
$582$	−4.91444	−0.203710
$583$	16.5841	0.686841
$584$	−17.3852	−0.719403
$585$	0	0
$586$	16.4798	0.680774
$587$	−15.6571	−0.646237	−0.323119	−	0.946358i	$-0.604731\pi$
$587$	−15.6571	−0.646237	−0.323119	+	0.946358i	$0.604731\pi$
$588$	7.14050	0.294469
$589$	15.9566	0.657480
$590$	0	0
$591$	−13.2026	−0.543084
$592$	3.26699	0.134273
$593$	−15.5623	−0.639067	−0.319533	−	0.947575i	$-0.603526\pi$
$593$	−15.5623	−0.639067	−0.319533	+	0.947575i	$0.603526\pi$
$594$	5.22104	0.214222
$595$	0	0
$596$	−11.4694	−0.469805
$597$	10.3855	0.425051
$598$	−21.2021	−0.867017
$599$	−30.3904	−1.24172	−0.620859	−	0.783922i	$-0.713216\pi$
$599$	−30.3904	−1.24172	−0.620859	+	0.783922i	$0.713216\pi$
$600$	0	0
$601$	−30.1251	−1.22883	−0.614414	−	0.788984i	$-0.710608\pi$
$601$	−30.1251	−1.22883	−0.614414	+	0.788984i	$0.710608\pi$
$602$	−33.1997	−1.35312
$603$	−8.03594	−0.327249
$604$	23.4668	0.954852
$605$	0	0
$606$	16.8203	0.683279
$607$	−44.1714	−1.79286	−0.896430	−	0.443184i	$-0.853849\pi$
$607$	−44.1714	−1.79286	−0.896430	+	0.443184i	$0.853849\pi$
$608$	−14.2427	−0.577618
$609$	−28.4894	−1.15445
$610$	0	0
$611$	−2.92869	−0.118482
$612$	2.54216	0.102761
$613$	−24.8671	−1.00437	−0.502186	−	0.864759i	$-0.667471\pi$
$613$	−24.8671	−1.00437	−0.502186	+	0.864759i	$0.667471\pi$
$614$	19.4116	0.783387
$615$	0	0
$616$	−59.5917	−2.40102
$617$	−24.8433	−1.00015	−0.500077	−	0.865981i	$-0.666695\pi$
$617$	−24.8433	−1.00015	−0.500077	+	0.865981i	$0.666695\pi$
$618$	−12.9580	−0.521249
$619$	18.9581	0.761988	0.380994	−	0.924577i	$-0.375582\pi$
$619$	18.9581	0.761988	0.380994	+	0.924577i	$0.375582\pi$
$620$	0	0
$621$	−7.72850	−0.310134
$622$	−22.7683	−0.912926
$623$	−15.7586	−0.631355
$624$	−1.44896	−0.0580048
$625$	0	0
$626$	−16.2676	−0.650183
$627$	−14.7379	−0.588575
$628$	25.6996	1.02553
$629$	14.9541	0.596258
$630$	0	0
$631$	39.5889	1.57601	0.788004	−	0.615670i	$-0.211115\pi$
$631$	39.5889	1.57601	0.788004	+	0.615670i	$0.211115\pi$
$632$	48.6129	1.93372
$633$	−19.5002	−0.775065
$634$	−1.88027	−0.0746752
$635$	0	0
$636$	−3.34004	−0.132441
$637$	−18.6292	−0.738114
$638$	40.6932	1.61106
$639$	11.7268	0.463903
$640$	0	0
$641$	−7.69114	−0.303782	−0.151891	−	0.988397i	$-0.548536\pi$
$641$	−7.69114	−0.303782	−0.151891	+	0.988397i	$0.548536\pi$
$642$	−5.78762	−0.228419
$643$	32.5033	1.28180	0.640902	−	0.767623i	$-0.278561\pi$
$643$	32.5033	1.28180	0.640902	+	0.767623i	$0.278561\pi$
$644$	31.7119	1.24962
$645$	0	0
$646$	5.60907	0.220686
$647$	33.1357	1.30270	0.651349	−	0.758778i	$-0.274203\pi$
$647$	33.1357	1.30270	0.651349	+	0.758778i	$0.274203\pi$
$648$	−2.92496	−0.114903
$649$	−3.18517	−0.125029
$650$	0	0
$651$	−22.0582	−0.864530
$652$	−12.6413	−0.495072
$653$	−1.78903	−0.0700102	−0.0350051	−	0.999387i	$-0.511145\pi$
$653$	−1.78903	−0.0700102	−0.0350051	+	0.999387i	$0.511145\pi$
$654$	−13.1919	−0.515844
$655$	0	0
$656$	4.36330	0.170358
$657$	5.94373	0.231887
$658$	−3.42395	−0.133479
$659$	−13.1926	−0.513912	−0.256956	−	0.966423i	$-0.582720\pi$
$659$	−13.1926	−0.513912	−0.256956	+	0.966423i	$0.582720\pi$
$660$	0	0
$661$	48.8401	1.89966	0.949830	−	0.312766i	$-0.101256\pi$
$661$	48.8401	1.89966	0.949830	+	0.312766i	$0.101256\pi$
$662$	21.5967	0.839379
$663$	−6.63235	−0.257579
$664$	−40.4679	−1.57046
$665$	0	0
$666$	−6.18551	−0.239683
$667$	−60.2365	−2.33237
$668$	−18.9107	−0.731677
$669$	5.43059	0.209959
$670$	0	0
$671$	−46.2726	−1.78633
$672$	19.6890	0.759519
$673$	7.24521	0.279282	0.139641	−	0.990202i	$-0.455405\pi$
$673$	7.24521	0.279282	0.139641	+	0.990202i	$0.455405\pi$
$674$	−0.915433	−0.0352611
$675$	0	0
$676$	4.96479	0.190954
$677$	−17.0194	−0.654109	−0.327054	−	0.945006i	$-0.606056\pi$
$677$	−17.0194	−0.654109	−0.327054	+	0.945006i	$0.606056\pi$
$678$	15.5830	0.598462
$679$	−19.1771	−0.735950
$680$	0	0
$681$	−2.68717	−0.102973
$682$	31.5072	1.20647
$683$	−1.41734	−0.0542331	−0.0271166	−	0.999632i	$-0.508633\pi$
$683$	−1.41734	−0.0542331	−0.0271166	+	0.999632i	$0.508633\pi$
$684$	2.96822	0.113493
$685$	0	0
$686$	2.18820	0.0835460
$687$	−17.6212	−0.672291
$688$	−4.79721	−0.182892
$689$	8.71398	0.331976
$690$	0	0
$691$	8.82922	0.335879	0.167940	−	0.985797i	$-0.446289\pi$
$691$	8.82922	0.335879	0.167940	+	0.985797i	$0.446289\pi$
$692$	−15.2166	−0.578447
$693$	20.3735	0.773926
$694$	−8.53455	−0.323967
$695$	0	0
$696$	−22.7974	−0.864132
$697$	19.9722	0.756501
$698$	2.47916	0.0938377
$699$	−14.3094	−0.541230
$700$	0	0
$701$	−29.1496	−1.10096	−0.550482	−	0.834847i	$-0.685556\pi$
$701$	−29.1496	−1.10096	−0.550482	+	0.834847i	$0.685556\pi$
$702$	2.74336	0.103542
$703$	17.4604	0.658531
$704$	−33.6382	−1.26779
$705$	0	0
$706$	−14.8430	−0.558625
$707$	65.6362	2.46850
$708$	0.641495	0.0241088
$709$	−19.7491	−0.741694	−0.370847	−	0.928694i	$-0.620933\pi$
$709$	−19.7491	−0.741694	−0.370847	+	0.928694i	$0.620933\pi$
$710$	0	0
$711$	−16.6200	−0.623300
$712$	−12.6101	−0.472584
$713$	−46.6388	−1.74664
$714$	−7.75391	−0.290183
$715$	0	0
$716$	5.94032	0.222000
$717$	0.608101	0.0227100
$718$	11.1161	0.414848
$719$	16.8239	0.627426	0.313713	−	0.949518i	$-0.398427\pi$
$719$	16.8239	0.627426	0.313713	+	0.949518i	$0.398427\pi$
$720$	0	0
$721$	−50.5648	−1.88313
$722$	−11.2485	−0.418626
$723$	0.888912	0.0330590
$724$	7.78732	0.289413
$725$	0	0
$726$	−18.7969	−0.697619
$727$	−21.9005	−0.812244	−0.406122	−	0.913819i	$-0.633119\pi$
$727$	−21.9005	−0.812244	−0.406122	+	0.913819i	$0.633119\pi$
$728$	−31.3121	−1.16050
$729$	1.00000	0.0370370
$730$	0	0
$731$	−21.9584	−0.812160
$732$	9.31934	0.344453
$733$	36.6289	1.35292	0.676460	−	0.736479i	$-0.263513\pi$
$733$	36.6289	1.35292	0.676460	+	0.736479i	$0.263513\pi$
$734$	4.74055	0.174977
$735$	0	0
$736$	41.6294	1.53448
$737$	44.7904	1.64987
$738$	−8.26117	−0.304098
$739$	−9.51491	−0.350011	−0.175006	−	0.984567i	$-0.555994\pi$
$739$	−9.51491	−0.350011	−0.175006	+	0.984567i	$0.555994\pi$
$740$	0	0
$741$	−7.74394	−0.284481
$742$	10.1876	0.373997
$743$	4.47470	0.164161	0.0820805	−	0.996626i	$-0.473844\pi$
$743$	4.47470	0.164161	0.0820805	+	0.996626i	$0.473844\pi$
$744$	−17.6511	−0.647122
$745$	0	0
$746$	−1.11876	−0.0409607
$747$	13.8354	0.506211
$748$	−14.1694	−0.518084
$749$	−22.5844	−0.825217
$750$	0	0
$751$	33.1075	1.20811	0.604055	−	0.796943i	$-0.293551\pi$
$751$	33.1075	1.20811	0.604055	+	0.796943i	$0.293551\pi$
$752$	−0.494746	−0.0180415
$753$	0.0483724	0.00176279
$754$	21.3820	0.778686
$755$	0	0
$756$	−4.10324	−0.149233
$757$	−12.0208	−0.436902	−0.218451	−	0.975848i	$-0.570100\pi$
$757$	−12.0208	−0.436902	−0.218451	+	0.975848i	$0.570100\pi$
$758$	15.0175	0.545461
$759$	43.0768	1.56359
$760$	0	0
$761$	26.4998	0.960616	0.480308	−	0.877100i	$-0.340525\pi$
$761$	26.4998	0.960616	0.480308	+	0.877100i	$0.340525\pi$
$762$	11.3422	0.410884
$763$	−51.4773	−1.86360
$764$	−3.67665	−0.133017
$765$	0	0
$766$	−21.9754	−0.794002
$767$	−1.67363	−0.0604311
$768$	16.8660	0.608599
$769$	−7.70999	−0.278029	−0.139015	−	0.990290i	$-0.544394\pi$
$769$	−7.70999	−0.278029	−0.139015	+	0.990290i	$0.544394\pi$
$770$	0	0
$771$	3.58017	0.128937
$772$	7.76610	0.279508
$773$	20.8018	0.748190	0.374095	−	0.927390i	$-0.377953\pi$
$773$	20.8018	0.748190	0.374095	+	0.927390i	$0.377953\pi$
$774$	9.08272	0.326472
$775$	0	0
$776$	−15.3456	−0.550876
$777$	−24.1370	−0.865912
$778$	−26.1299	−0.936801
$779$	23.3196	0.835510
$780$	0	0
$781$	−65.3621	−2.33884
$782$	−16.3945	−0.586266
$783$	7.79408	0.278538
$784$	−3.14704	−0.112394
$785$	0	0
$786$	−1.48255	−0.0528809
$787$	46.7576	1.66673	0.833364	−	0.552725i	$-0.186412\pi$
$787$	46.7576	1.66673	0.833364	+	0.552725i	$0.186412\pi$
$788$	−14.8207	−0.527967
$789$	17.6132	0.627048
$790$	0	0
$791$	60.8079	2.16208
$792$	16.3030	0.579302
$793$	−24.3136	−0.863403
$794$	10.6235	0.377015
$795$	0	0
$796$	11.6583	0.413219
$797$	−24.6265	−0.872314	−0.436157	−	0.899870i	$-0.643661\pi$
$797$	−24.6265	−0.872314	−0.436157	+	0.899870i	$0.643661\pi$
$798$	−9.05347	−0.320489
$799$	−2.26461	−0.0801162
$800$	0	0
$801$	4.31121	0.152329
$802$	−11.8227	−0.417474
$803$	−33.1289	−1.16909
$804$	−9.02081	−0.318139
$805$	0	0
$806$	16.5553	0.583134
$807$	14.7262	0.518385
$808$	52.5225	1.84773
$809$	32.1274	1.12954	0.564770	−	0.825248i	$-0.308965\pi$
$809$	32.1274	1.12954	0.564770	+	0.825248i	$0.308965\pi$
$810$	0	0
$811$	−0.000411906 0	−1.44640e−5 0	−7.23199e−6	−	1.00000i	$-0.500002\pi$
$811$	−0.000411906 0	−1.44640e−5 0	−7.23199e−6		1.00000i	$0.500002\pi$
$812$	−31.9810	−1.12231
$813$	−7.26580	−0.254823
$814$	34.4765	1.20840
$815$	0	0
$816$	−1.12041	−0.0392221
$817$	−25.6386	−0.896981
$818$	−2.79425	−0.0976988
$819$	10.7051	0.374068
$820$	0	0
$821$	53.7005	1.87416	0.937081	−	0.349113i	$-0.113517\pi$
$821$	53.7005	1.87416	0.937081	+	0.349113i	$0.113517\pi$
$822$	19.2076	0.669941
$823$	30.1058	1.04942	0.524711	−	0.851280i	$-0.324173\pi$
$823$	30.1058	1.04942	0.524711	+	0.851280i	$0.324173\pi$
$824$	−40.4622	−1.40957
$825$	0	0
$826$	−1.95664	−0.0680803
$827$	−4.74104	−0.164862	−0.0824310	−	0.996597i	$-0.526268\pi$
$827$	−4.74104	−0.164862	−0.0824310	+	0.996597i	$0.526268\pi$
$828$	−8.67569	−0.301501
$829$	24.2241	0.841337	0.420669	−	0.907214i	$-0.361796\pi$
$829$	24.2241	0.841337	0.420669	+	0.907214i	$0.361796\pi$
$830$	0	0
$831$	−16.0913	−0.558201
$832$	−17.6750	−0.612770
$833$	−14.4050	−0.499103
$834$	15.6601	0.542264
$835$	0	0
$836$	−16.5442	−0.572192
$837$	6.03466	0.208588
$838$	14.5262	0.501801
$839$	13.1024	0.452345	0.226172	−	0.974087i	$-0.427379\pi$
$839$	13.1024	0.452345	0.226172	+	0.974087i	$0.427379\pi$
$840$	0	0
$841$	31.7477	1.09475
$842$	−20.8035	−0.716936
$843$	2.13975	0.0736969
$844$	−21.8902	−0.753490
$845$	0	0
$846$	0.936719	0.0322050
$847$	−73.3492	−2.52031
$848$	1.47206	0.0505507
$849$	−23.8300	−0.817845
$850$	0	0
$851$	−51.0342	−1.74943
$852$	13.1640	0.450990
$853$	50.2328	1.71994	0.859969	−	0.510347i	$-0.170483\pi$
$853$	50.2328	1.71994	0.859969	+	0.510347i	$0.170483\pi$
$854$	−28.4252	−0.972690
$855$	0	0
$856$	−18.0722	−0.617695
$857$	−11.5763	−0.395438	−0.197719	−	0.980259i	$-0.563353\pi$
$857$	−11.5763	−0.395438	−0.197719	+	0.980259i	$0.563353\pi$
$858$	−15.2908	−0.522020
$859$	5.35315	0.182647	0.0913236	−	0.995821i	$-0.470890\pi$
$859$	5.35315	0.182647	0.0913236	+	0.995821i	$0.470890\pi$
$860$	0	0
$861$	−32.2367	−1.09862
$862$	−18.8608	−0.642400
$863$	−27.8072	−0.946569	−0.473285	−	0.880910i	$-0.656932\pi$
$863$	−27.8072	−0.946569	−0.473285	+	0.880910i	$0.656932\pi$
$864$	−5.38648	−0.183252
$865$	0	0
$866$	−16.6959	−0.567349
$867$	11.8715	0.403178
$868$	−24.7617	−0.840465
$869$	92.6360	3.14246
$870$	0	0
$871$	23.5348	0.797447
$872$	−41.1924	−1.39495
$873$	5.24644	0.177565
$874$	−19.1422	−0.647495
$875$	0	0
$876$	6.67218	0.225432
$877$	24.8181	0.838048	0.419024	−	0.907975i	$-0.362372\pi$
$877$	24.8181	0.838048	0.419024	+	0.907975i	$0.362372\pi$
$878$	11.2321	0.379064
$879$	−17.5931	−0.593401
$880$	0	0
$881$	35.1845	1.18540	0.592698	−	0.805424i	$-0.298063\pi$
$881$	35.1845	1.18540	0.592698	+	0.805424i	$0.298063\pi$
$882$	5.95838	0.200629
$883$	−18.2761	−0.615039	−0.307520	−	0.951542i	$-0.599499\pi$
$883$	−18.2761	−0.615039	−0.307520	+	0.951542i	$0.599499\pi$
$884$	−7.44520	−0.250409
$885$	0	0
$886$	23.6467	0.794426
$887$	−21.5403	−0.723254	−0.361627	−	0.932323i	$-0.617779\pi$
$887$	−21.5403	−0.723254	−0.361627	+	0.932323i	$0.617779\pi$
$888$	−19.3146	−0.648156
$889$	44.2594	1.48441
$890$	0	0
$891$	−5.57376	−0.186728
$892$	6.09615	0.204114
$893$	−2.64416	−0.0884834
$894$	−9.57064	−0.320090
$895$	0	0
$896$	18.7140	0.625193
$897$	22.6344	0.755741
$898$	−34.6912	−1.15766
$899$	47.0346	1.56869
$900$	0	0
$901$	6.73808	0.224478
$902$	46.0458	1.53316
$903$	35.4425	1.17945
$904$	48.6589	1.61837
$905$	0	0
$906$	19.5819	0.650565
$907$	17.7267	0.588605	0.294302	−	0.955712i	$-0.404913\pi$
$907$	17.7267	0.588605	0.294302	+	0.955712i	$0.404913\pi$
$908$	−3.01651	−0.100106
$909$	−17.9567	−0.595585
$910$	0	0
$911$	−5.58606	−0.185074	−0.0925372	−	0.995709i	$-0.529498\pi$
$911$	−5.58606	−0.185074	−0.0925372	+	0.995709i	$0.529498\pi$
$912$	−1.30819	−0.0433184
$913$	−77.1151	−2.55214
$914$	−13.0794	−0.432628
$915$	0	0
$916$	−19.7808	−0.653577
$917$	−5.78521	−0.191044
$918$	2.12130	0.0700134
$919$	9.14763	0.301752	0.150876	−	0.988553i	$-0.451791\pi$
$919$	9.14763	0.301752	0.150876	+	0.988553i	$0.451791\pi$
$920$	0	0
$921$	−20.7229	−0.682844
$922$	−39.3387	−1.29555
$923$	−34.3441	−1.13045
$924$	22.8705	0.752383
$925$	0	0
$926$	−21.6632	−0.711896
$927$	13.8334	0.454350
$928$	−41.9826	−1.37815
$929$	19.9482	0.654480	0.327240	−	0.944941i	$-0.393881\pi$
$929$	19.9482	0.654480	0.327240	+	0.944941i	$0.393881\pi$
$930$	0	0
$931$	−16.8193	−0.551229
$932$	−16.0631	−0.526164
$933$	24.3065	0.795758
$934$	−12.6405	−0.413611
$935$	0	0
$936$	8.56631	0.279999
$937$	28.6210	0.935007	0.467504	−	0.883991i	$-0.345153\pi$
$937$	28.6210	0.935007	0.467504	+	0.883991i	$0.345153\pi$
$938$	27.5146	0.898385
$939$	17.3665	0.566736
$940$	0	0
$941$	17.6221	0.574464	0.287232	−	0.957861i	$-0.407265\pi$
$941$	17.6221	0.574464	0.287232	+	0.957861i	$0.407265\pi$
$942$	21.4450	0.698716
$943$	−68.1597	−2.21958
$944$	−0.282726	−0.00920196
$945$	0	0
$946$	−50.6249	−1.64596
$947$	−41.9598	−1.36351	−0.681754	−	0.731581i	$-0.738783\pi$
$947$	−41.9598	−1.36351	−0.681754	+	0.731581i	$0.738783\pi$
$948$	−18.6570	−0.605950
$949$	−17.4074	−0.565067
$950$	0	0
$951$	2.00730	0.0650911
$952$	−24.2120	−0.784717
$953$	26.1334	0.846545	0.423273	−	0.906002i	$-0.360881\pi$
$953$	26.1334	0.846545	0.423273	+	0.906002i	$0.360881\pi$
$954$	−2.78710	−0.0902355
$955$	0	0
$956$	0.682629	0.0220778
$957$	−43.4423	−1.40429
$958$	6.26797	0.202509
$959$	74.9517	2.42032
$960$	0	0
$961$	5.41711	0.174745
$962$	18.1155	0.584066
$963$	6.17861	0.199103
$964$	0.997855	0.0321388
$965$	0	0
$966$	26.4620	0.851400
$967$	−9.86542	−0.317251	−0.158625	−	0.987339i	$-0.550706\pi$
$967$	−9.86542	−0.317251	−0.158625	+	0.987339i	$0.550706\pi$
$968$	−58.6944	−1.88651
$969$	−5.98799	−0.192362
$970$	0	0
$971$	3.91113	0.125514	0.0627571	−	0.998029i	$-0.480011\pi$
$971$	3.91113	0.125514	0.0627571	+	0.998029i	$0.480011\pi$
$972$	1.12256	0.0360061
$973$	61.1087	1.95905
$974$	26.8812	0.861329
$975$	0	0
$976$	−4.10732	−0.131472
$977$	−8.80390	−0.281662	−0.140831	−	0.990034i	$-0.544977\pi$
$977$	−8.80390	−0.281662	−0.140831	+	0.990034i	$0.544977\pi$
$978$	−10.5485	−0.337305
$979$	−24.0297	−0.767991
$980$	0	0
$981$	14.0831	0.449638
$982$	−5.62745	−0.179579
$983$	2.42901	0.0774735	0.0387368	−	0.999249i	$-0.487667\pi$
$983$	2.42901	0.0774735	0.0387368	+	0.999249i	$0.487667\pi$
$984$	−25.7960	−0.822346
$985$	0	0
$986$	16.5336	0.526537
$987$	3.65526	0.116348
$988$	−8.69302	−0.276562
$989$	74.9379	2.38289
$990$	0	0
$991$	−12.4176	−0.394459	−0.197230	−	0.980357i	$-0.563194\pi$
$991$	−12.4176	−0.394459	−0.197230	+	0.980357i	$0.563194\pi$
$992$	−32.5056	−1.03205
$993$	−23.0557	−0.731650
$994$	−40.1518	−1.27354
$995$	0	0
$996$	15.5310	0.492120
$997$	14.3515	0.454518	0.227259	−	0.973834i	$-0.427024\pi$
$997$	14.3515	0.454518	0.227259	+	0.973834i	$0.427024\pi$
$998$	38.0616	1.20482
$999$	6.60338	0.208922

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.be.1.5	yes	8
5.4	even	2		3525.2.a.bd.1.4	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.2.a.bd.1.4	✓	8	5.4	even	2
3525.2.a.be.1.5	yes	8	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)

\(f(q)\)	\(=\)	\(q+0.936719 q^{2} -1.00000 q^{3} -1.12256 q^{4} -0.936719 q^{6} -3.65526 q^{7} -2.92496 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.936719 q^{2} -1.00000 q^{3} -1.12256 q^{4} -0.936719 q^{6} -3.65526 q^{7} -2.92496 q^{8} +1.00000 q^{9} -5.57376 q^{11} +1.12256 q^{12} -2.92869 q^{13} -3.42395 q^{14} -0.494746 q^{16} -2.26461 q^{17} +0.936719 q^{18} -2.64416 q^{19} +3.65526 q^{21} -5.22104 q^{22} +7.72850 q^{23} +2.92496 q^{24} -2.74336 q^{26} -1.00000 q^{27} +4.10324 q^{28} -7.79408 q^{29} -6.03466 q^{31} +5.38648 q^{32} +5.57376 q^{33} -2.12130 q^{34} -1.12256 q^{36} -6.60338 q^{37} -2.47683 q^{38} +2.92869 q^{39} -8.81927 q^{41} +3.42395 q^{42} +9.69632 q^{43} +6.25687 q^{44} +7.23943 q^{46} +1.00000 q^{47} +0.494746 q^{48} +6.36091 q^{49} +2.26461 q^{51} +3.28763 q^{52} -2.97538 q^{53} -0.936719 q^{54} +10.6915 q^{56} +2.64416 q^{57} -7.30086 q^{58} +0.571458 q^{59} +8.30187 q^{61} -5.65278 q^{62} -3.65526 q^{63} +6.03511 q^{64} +5.22104 q^{66} -8.03594 q^{67} +2.54216 q^{68} -7.72850 q^{69} +11.7268 q^{71} -2.92496 q^{72} +5.94373 q^{73} -6.18551 q^{74} +2.96822 q^{76} +20.3735 q^{77} +2.74336 q^{78} -16.6200 q^{79} +1.00000 q^{81} -8.26117 q^{82} +13.8354 q^{83} -4.10324 q^{84} +9.08272 q^{86} +7.79408 q^{87} +16.3030 q^{88} +4.31121 q^{89} +10.7051 q^{91} -8.67569 q^{92} +6.03466 q^{93} +0.936719 q^{94} -5.38648 q^{96} +5.24644 q^{97} +5.95838 q^{98} -5.57376 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - 8 q^{3} + 7 q^{4} - 3 q^{6} + 8 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 - 8 * q^3 + 7 * q^4 - 3 * q^6 + 8 * q^7 + 6 * q^8 + 8 * q^9	\( 8 q + 3 q^{2} - 8 q^{3} + 7 q^{4} - 3 q^{6} + 8 q^{7} + 6 q^{8} + 8 q^{9} - 8 q^{11} - 7 q^{12} + 10 q^{13} + q^{14} + 5 q^{16} + 6 q^{17} + 3 q^{18} - 2 q^{19} - 8 q^{21} + 10 q^{23} - 6 q^{24} - 14 q^{26} - 8 q^{27} + 44 q^{28} - 13 q^{29} + 10 q^{32} + 8 q^{33} + 28 q^{34} + 7 q^{36} + 3 q^{37} + 36 q^{38} - 10 q^{39} - 16 q^{41} - q^{42} + 25 q^{43} - 17 q^{44} - 5 q^{46} + 8 q^{47} - 5 q^{48} + 16 q^{49} - 6 q^{51} - 17 q^{52} + 4 q^{53} - 3 q^{54} + 37 q^{56} + 2 q^{57} + 15 q^{58} - 8 q^{59} + 15 q^{61} + 6 q^{62} + 8 q^{63} - 14 q^{64} + 27 q^{67} + 14 q^{68} - 10 q^{69} + 14 q^{71} + 6 q^{72} + 28 q^{73} - 21 q^{74} + 6 q^{76} + 4 q^{77} + 14 q^{78} + 7 q^{79} + 8 q^{81} - 53 q^{82} + 60 q^{83} - 44 q^{84} - 3 q^{86} + 13 q^{87} + 54 q^{88} - 34 q^{89} + 23 q^{91} - 43 q^{92} + 3 q^{94} - 10 q^{96} + 7 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 - 8 * q^3 + 7 * q^4 - 3 * q^6 + 8 * q^7 + 6 * q^8 + 8 * q^9 - 8 * q^11 - 7 * q^12 + 10 * q^13 + q^14 + 5 * q^16 + 6 * q^17 + 3 * q^18 - 2 * q^19 - 8 * q^21 + 10 * q^23 - 6 * q^24 - 14 * q^26 - 8 * q^27 + 44 * q^28 - 13 * q^29 + 10 * q^32 + 8 * q^33 + 28 * q^34 + 7 * q^36 + 3 * q^37 + 36 * q^38 - 10 * q^39 - 16 * q^41 - q^42 + 25 * q^43 - 17 * q^44 - 5 * q^46 + 8 * q^47 - 5 * q^48 + 16 * q^49 - 6 * q^51 - 17 * q^52 + 4 * q^53 - 3 * q^54 + 37 * q^56 + 2 * q^57 + 15 * q^58 - 8 * q^59 + 15 * q^61 + 6 * q^62 + 8 * q^63 - 14 * q^64 + 27 * q^67 + 14 * q^68 - 10 * q^69 + 14 * q^71 + 6 * q^72 + 28 * q^73 - 21 * q^74 + 6 * q^76 + 4 * q^77 + 14 * q^78 + 7 * q^79 + 8 * q^81 - 53 * q^82 + 60 * q^83 - 44 * q^84 - 3 * q^86 + 13 * q^87 + 54 * q^88 - 34 * q^89 + 23 * q^91 - 43 * q^92 + 3 * q^94 - 10 * q^96 + 7 * q^97 + 40 * q^98 - 8 * q^99

Introduction

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