LMFDB - Embedded newform 3525.2.a.bf.1.1

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:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 9x^{8} + 29x^{7} + 25x^{6} - 91x^{5} - 21x^{4} + 101x^{3} + 6x^{2} - 30x - 4 $ x^10 - 3x^9 - 9x^8 + 29x^7 + 25x^6 - 91x^5 - 21x^4 + 101x^3 + 6x^2 - 30*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 705)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.56385$ 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)

$f(q)$	$=$	$q-2.56385 q^{2} +1.00000 q^{3} +4.57334 q^{4} -2.56385 q^{6} +4.44946 q^{7} -6.59766 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.56385 q^{2} +1.00000 q^{3} +4.57334 q^{4} -2.56385 q^{6} +4.44946 q^{7} -6.59766 q^{8} +1.00000 q^{9} -5.41232 q^{11} +4.57334 q^{12} -5.68352 q^{13} -11.4078 q^{14} +7.76874 q^{16} -0.388491 q^{17} -2.56385 q^{18} -5.51295 q^{19} +4.44946 q^{21} +13.8764 q^{22} +3.44228 q^{23} -6.59766 q^{24} +14.5717 q^{26} +1.00000 q^{27} +20.3489 q^{28} +1.30580 q^{29} +3.60752 q^{31} -6.72259 q^{32} -5.41232 q^{33} +0.996033 q^{34} +4.57334 q^{36} +10.8089 q^{37} +14.1344 q^{38} -5.68352 q^{39} -7.19471 q^{41} -11.4078 q^{42} +4.48698 q^{43} -24.7524 q^{44} -8.82551 q^{46} -1.00000 q^{47} +7.76874 q^{48} +12.7977 q^{49} -0.388491 q^{51} -25.9926 q^{52} -2.35896 q^{53} -2.56385 q^{54} -29.3560 q^{56} -5.51295 q^{57} -3.34787 q^{58} -11.6564 q^{59} -11.7400 q^{61} -9.24914 q^{62} +4.44946 q^{63} +1.69824 q^{64} +13.8764 q^{66} +1.24426 q^{67} -1.77670 q^{68} +3.44228 q^{69} +1.25192 q^{71} -6.59766 q^{72} +4.03934 q^{73} -27.7125 q^{74} -25.2126 q^{76} -24.0819 q^{77} +14.5717 q^{78} +1.18741 q^{79} +1.00000 q^{81} +18.4462 q^{82} -11.2594 q^{83} +20.3489 q^{84} -11.5039 q^{86} +1.30580 q^{87} +35.7086 q^{88} +5.78199 q^{89} -25.2886 q^{91} +15.7427 q^{92} +3.60752 q^{93} +2.56385 q^{94} -6.72259 q^{96} +5.11545 q^{97} -32.8115 q^{98} -5.41232 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{2} + 10 q^{3} + 7 q^{4} - 3 q^{6} - 9 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 3 * q^2 + 10 * q^3 + 7 * q^4 - 3 * q^6 - 9 * q^8 + 10 * q^9	$ 10 q - 3 q^{2} + 10 q^{3} + 7 q^{4} - 3 q^{6} - 9 q^{8} + 10 q^{9} - 16 q^{11} + 7 q^{12} - q^{13} - 12 q^{14} - 3 q^{16} - 14 q^{17} - 3 q^{18} - 26 q^{19} - 7 q^{23} - 9 q^{24} - 10 q^{26} + 10 q^{27} + 24 q^{28} - 14 q^{29} - 22 q^{31} - 11 q^{32} - 16 q^{33} - 12 q^{34} + 7 q^{36} - 2 q^{37} + 2 q^{38} - q^{39} - 22 q^{41} - 12 q^{42} + 11 q^{43} - 36 q^{44} - 14 q^{46} - 10 q^{47} - 3 q^{48} + 2 q^{49} - 14 q^{51} - 14 q^{52} - 22 q^{53} - 3 q^{54} - 48 q^{56} - 26 q^{57} + 20 q^{58} - 37 q^{59} - 25 q^{61} + 2 q^{62} - 7 q^{64} + 4 q^{67} - 8 q^{68} - 7 q^{69} - 27 q^{71} - 9 q^{72} - q^{73} + 4 q^{74} - 42 q^{76} - 34 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{81} + 32 q^{82} - 2 q^{83} + 24 q^{84} - 6 q^{86} - 14 q^{87} + 58 q^{88} + 9 q^{89} - 64 q^{91} - 34 q^{92} - 22 q^{93} + 3 q^{94} - 11 q^{96} + 40 q^{97} - 29 q^{98} - 16 q^{99}+O(q^{100}) $ 10 * q - 3 * q^2 + 10 * q^3 + 7 * q^4 - 3 * q^6 - 9 * q^8 + 10 * q^9 - 16 * q^11 + 7 * q^12 - q^13 - 12 * q^14 - 3 * q^16 - 14 * q^17 - 3 * q^18 - 26 * q^19 - 7 * q^23 - 9 * q^24 - 10 * q^26 + 10 * q^27 + 24 * q^28 - 14 * q^29 - 22 * q^31 - 11 * q^32 - 16 * q^33 - 12 * q^34 + 7 * q^36 - 2 * q^37 + 2 * q^38 - q^39 - 22 * q^41 - 12 * q^42 + 11 * q^43 - 36 * q^44 - 14 * q^46 - 10 * q^47 - 3 * q^48 + 2 * q^49 - 14 * q^51 - 14 * q^52 - 22 * q^53 - 3 * q^54 - 48 * q^56 - 26 * q^57 + 20 * q^58 - 37 * q^59 - 25 * q^61 + 2 * q^62 - 7 * q^64 + 4 * q^67 - 8 * q^68 - 7 * q^69 - 27 * q^71 - 9 * q^72 - q^73 + 4 * q^74 - 42 * q^76 - 34 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^81 + 32 * q^82 - 2 * q^83 + 24 * q^84 - 6 * q^86 - 14 * q^87 + 58 * q^88 + 9 * q^89 - 64 * q^91 - 34 * q^92 - 22 * q^93 + 3 * q^94 - 11 * q^96 + 40 * q^97 - 29 * q^98 - 16 * 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 $

$2$	−2.56385	−1.81292	−0.906459	−	0.422295i	$-0.861225\pi$
$2$	−2.56385	−1.81292	−0.906459	+	0.422295i	$0.861225\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.57334	2.28667
$5$	0	0
$5$	0	0
$6$	−2.56385	−1.04669
$7$	4.44946	1.68174	0.840870	−	0.541237i	$-0.182044\pi$
$7$	4.44946	1.68174	0.840870	+	0.541237i	$0.182044\pi$
$8$	−6.59766	−2.33262
$9$	1.00000	0.333333
$10$	0	0
$11$	−5.41232	−1.63188	−0.815938	−	0.578140i	$-0.803779\pi$
$11$	−5.41232	−1.63188	−0.815938	+	0.578140i	$0.803779\pi$
$12$	4.57334	1.32021
$13$	−5.68352	−1.57632	−0.788162	−	0.615468i	$-0.788967\pi$
$13$	−5.68352	−1.57632	−0.788162	+	0.615468i	$0.788967\pi$
$14$	−11.4078	−3.04885
$15$	0	0
$16$	7.76874	1.94218
$17$	−0.388491	−0.0942229	−0.0471114	−	0.998890i	$-0.515002\pi$
$17$	−0.388491	−0.0942229	−0.0471114	+	0.998890i	$0.515002\pi$
$18$	−2.56385	−0.604306
$19$	−5.51295	−1.26476	−0.632378	−	0.774660i	$-0.717921\pi$
$19$	−5.51295	−1.26476	−0.632378	+	0.774660i	$0.717921\pi$
$20$	0	0
$21$	4.44946	0.970953
$22$	13.8764	2.95845
$23$	3.44228	0.717766	0.358883	−	0.933383i	$-0.383158\pi$
$23$	3.44228	0.717766	0.358883	+	0.933383i	$0.383158\pi$
$24$	−6.59766	−1.34674
$25$	0	0
$26$	14.5717	2.85775
$27$	1.00000	0.192450
$28$	20.3489	3.84558
$29$	1.30580	0.242480	0.121240	−	0.992623i	$-0.461313\pi$
$29$	1.30580	0.242480	0.121240	+	0.992623i	$0.461313\pi$
$30$	0	0
$31$	3.60752	0.647929	0.323965	−	0.946069i	$-0.394984\pi$
$31$	3.60752	0.647929	0.323965	+	0.946069i	$0.394984\pi$
$32$	−6.72259	−1.18840
$33$	−5.41232	−0.942164
$34$	0.996033	0.170818
$35$	0	0
$36$	4.57334	0.762223
$37$	10.8089	1.77698	0.888490	−	0.458896i	$-0.151755\pi$
$37$	10.8089	1.77698	0.888490	+	0.458896i	$0.151755\pi$
$38$	14.1344	2.29290
$39$	−5.68352	−0.910091
$40$	0	0
$41$	−7.19471	−1.12362	−0.561812	−	0.827265i	$-0.689896\pi$
$41$	−7.19471	−1.12362	−0.561812	+	0.827265i	$0.689896\pi$
$42$	−11.4078	−1.76026
$43$	4.48698	0.684257	0.342129	−	0.939653i	$-0.388852\pi$
$43$	4.48698	0.684257	0.342129	+	0.939653i	$0.388852\pi$
$44$	−24.7524	−3.73156
$45$	0	0
$46$	−8.82551	−1.30125
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	7.76874	1.12132
$49$	12.7977	1.82825
$50$	0	0
$51$	−0.388491	−0.0543996
$52$	−25.9926	−3.60453
$53$	−2.35896	−0.324028	−0.162014	−	0.986788i	$-0.551799\pi$
$53$	−2.35896	−0.324028	−0.162014	+	0.986788i	$0.551799\pi$
$54$	−2.56385	−0.348896
$55$	0	0
$56$	−29.3560	−3.92287
$57$	−5.51295	−0.730208
$58$	−3.34787	−0.439597
$59$	−11.6564	−1.51753	−0.758767	−	0.651362i	$-0.774198\pi$
$59$	−11.6564	−1.51753	−0.758767	+	0.651362i	$0.774198\pi$
$60$	0	0
$61$	−11.7400	−1.50316	−0.751578	−	0.659644i	$-0.770707\pi$
$61$	−11.7400	−1.50316	−0.751578	+	0.659644i	$0.770707\pi$
$62$	−9.24914	−1.17464
$63$	4.44946	0.560580
$64$	1.69824	0.212280
$65$	0	0
$66$	13.8764	1.70806
$67$	1.24426	0.152010	0.0760051	−	0.997107i	$-0.475783\pi$
$67$	1.24426	0.152010	0.0760051	+	0.997107i	$0.475783\pi$
$68$	−1.77670	−0.215457
$69$	3.44228	0.414402
$70$	0	0
$71$	1.25192	0.148576	0.0742880	−	0.997237i	$-0.476332\pi$
$71$	1.25192	0.148576	0.0742880	+	0.997237i	$0.476332\pi$
$72$	−6.59766	−0.777541
$73$	4.03934	0.472769	0.236385	−	0.971660i	$-0.424037\pi$
$73$	4.03934	0.472769	0.236385	+	0.971660i	$0.424037\pi$
$74$	−27.7125	−3.22152
$75$	0	0
$76$	−25.2126	−2.89208
$77$	−24.0819	−2.74439
$78$	14.5717	1.64992
$79$	1.18741	0.133594	0.0667970	−	0.997767i	$-0.478722\pi$
$79$	1.18741	0.133594	0.0667970	+	0.997767i	$0.478722\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	18.4462	2.03704
$83$	−11.2594	−1.23588	−0.617940	−	0.786225i	$-0.712032\pi$
$83$	−11.2594	−1.23588	−0.617940	+	0.786225i	$0.712032\pi$
$84$	20.3489	2.22025
$85$	0	0
$86$	−11.5039	−1.24050
$87$	1.30580	0.139996
$88$	35.7086	3.80655
$89$	5.78199	0.612890	0.306445	−	0.951888i	$-0.400860\pi$
$89$	5.78199	0.612890	0.306445	+	0.951888i	$0.400860\pi$
$90$	0	0
$91$	−25.2886	−2.65097
$92$	15.7427	1.64129
$93$	3.60752	0.374082
$94$	2.56385	0.264441
$95$	0	0
$96$	−6.72259	−0.686121
$97$	5.11545	0.519395	0.259697	−	0.965690i	$-0.416377\pi$
$97$	5.11545	0.519395	0.259697	+	0.965690i	$0.416377\pi$
$98$	−32.8115	−3.31446
$99$	−5.41232	−0.543958
$100$	0	0
$101$	−3.91513	−0.389570	−0.194785	−	0.980846i	$-0.562401\pi$
$101$	−3.91513	−0.389570	−0.194785	+	0.980846i	$0.562401\pi$
$102$	0.996033	0.0986220
$103$	−3.19671	−0.314981	−0.157491	−	0.987520i	$-0.550340\pi$
$103$	−3.19671	−0.314981	−0.157491	+	0.987520i	$0.550340\pi$
$104$	37.4979	3.67697
$105$	0	0
$106$	6.04803	0.587436
$107$	0.333406	0.0322315	0.0161158	−	0.999870i	$-0.494870\pi$
$107$	0.333406	0.0322315	0.0161158	+	0.999870i	$0.494870\pi$
$108$	4.57334	0.440070
$109$	−10.9837	−1.05205	−0.526023	−	0.850470i	$-0.676318\pi$
$109$	−10.9837	−1.05205	−0.526023	+	0.850470i	$0.676318\pi$
$110$	0	0
$111$	10.8089	1.02594
$112$	34.5667	3.26625
$113$	−9.81554	−0.923369	−0.461684	−	0.887044i	$-0.652755\pi$
$113$	−9.81554	−0.923369	−0.461684	+	0.887044i	$0.652755\pi$
$114$	14.1344	1.32381
$115$	0	0
$116$	5.97185	0.554472
$117$	−5.68352	−0.525441
$118$	29.8853	2.75116
$119$	−1.72858	−0.158458
$120$	0	0
$121$	18.2932	1.66302
$122$	30.0997	2.72510
$123$	−7.19471	−0.648725
$124$	16.4984	1.48160
$125$	0	0
$126$	−11.4078	−1.01628
$127$	−15.9043	−1.41128	−0.705639	−	0.708572i	$-0.749340\pi$
$127$	−15.9043	−1.41128	−0.705639	+	0.708572i	$0.749340\pi$
$128$	9.09114	0.803551
$129$	4.48698	0.395056
$130$	0	0
$131$	9.79475	0.855772	0.427886	−	0.903833i	$-0.359259\pi$
$131$	9.79475	0.855772	0.427886	+	0.903833i	$0.359259\pi$
$132$	−24.7524	−2.15442
$133$	−24.5297	−2.12699
$134$	−3.19009	−0.275582
$135$	0	0
$136$	2.56313	0.219787
$137$	−10.0847	−0.861591	−0.430796	−	0.902450i	$-0.641767\pi$
$137$	−10.0847	−0.861591	−0.430796	+	0.902450i	$0.641767\pi$
$138$	−8.82551	−0.751277
$139$	−16.1731	−1.37179	−0.685894	−	0.727702i	$-0.740589\pi$
$139$	−16.1731	−1.37179	−0.685894	+	0.727702i	$0.740589\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	−3.20975	−0.269356
$143$	30.7610	2.57236
$144$	7.76874	0.647395
$145$	0	0
$146$	−10.3563	−0.857092
$147$	12.7977	1.05554
$148$	49.4330	4.06336
$149$	−17.4452	−1.42917	−0.714583	−	0.699551i	$-0.753383\pi$
$149$	−17.4452	−1.42917	−0.714583	+	0.699551i	$0.753383\pi$
$150$	0	0
$151$	−8.12004	−0.660799	−0.330400	−	0.943841i	$-0.607183\pi$
$151$	−8.12004	−0.660799	−0.330400	+	0.943841i	$0.607183\pi$
$152$	36.3725	2.95020
$153$	−0.388491	−0.0314076
$154$	61.7425	4.97535
$155$	0	0
$156$	−25.9926	−2.08108
$157$	−20.7690	−1.65755	−0.828773	−	0.559585i	$-0.810961\pi$
$157$	−20.7690	−1.65755	−0.828773	+	0.559585i	$0.810961\pi$
$158$	−3.04434	−0.242195
$159$	−2.35896	−0.187078
$160$	0	0
$161$	15.3163	1.20710
$162$	−2.56385	−0.201435
$163$	−7.96472	−0.623845	−0.311923	−	0.950108i	$-0.600973\pi$
$163$	−7.96472	−0.623845	−0.311923	+	0.950108i	$0.600973\pi$
$164$	−32.9038	−2.56936
$165$	0	0
$166$	28.8674	2.24055
$167$	−11.6273	−0.899751	−0.449875	−	0.893091i	$-0.648532\pi$
$167$	−11.6273	−0.899751	−0.449875	+	0.893091i	$0.648532\pi$
$168$	−29.3560	−2.26487
$169$	19.3024	1.48480
$170$	0	0
$171$	−5.51295	−0.421586
$172$	20.5205	1.56467
$173$	5.87914	0.446983	0.223492	−	0.974706i	$-0.428255\pi$
$173$	5.87914	0.446983	0.223492	+	0.974706i	$0.428255\pi$
$174$	−3.34787	−0.253801
$175$	0	0
$176$	−42.0469	−3.16940
$177$	−11.6564	−0.876149
$178$	−14.8242	−1.11112
$179$	−2.70258	−0.202000	−0.101000	−	0.994886i	$-0.532204\pi$
$179$	−2.70258	−0.202000	−0.101000	+	0.994886i	$0.532204\pi$
$180$	0	0
$181$	−6.86851	−0.510532	−0.255266	−	0.966871i	$-0.582163\pi$
$181$	−6.86851	−0.510532	−0.255266	+	0.966871i	$0.582163\pi$
$182$	64.8363	4.80598
$183$	−11.7400	−0.867848
$184$	−22.7110	−1.67428
$185$	0	0
$186$	−9.24914	−0.678180
$187$	2.10264	0.153760
$188$	−4.57334	−0.333545
$189$	4.44946	0.323651
$190$	0	0
$191$	11.6279	0.841368	0.420684	−	0.907207i	$-0.361790\pi$
$191$	11.6279	0.841368	0.420684	+	0.907207i	$0.361790\pi$
$192$	1.69824	0.122560
$193$	−19.3617	−1.39368	−0.696842	−	0.717225i	$-0.745412\pi$
$193$	−19.3617	−1.39368	−0.696842	+	0.717225i	$0.745412\pi$
$194$	−13.1152	−0.941620
$195$	0	0
$196$	58.5284	4.18060
$197$	−8.23457	−0.586689	−0.293344	−	0.956007i	$-0.594768\pi$
$197$	−8.23457	−0.586689	−0.293344	+	0.956007i	$0.594768\pi$
$198$	13.8764	0.986151
$199$	−4.79311	−0.339775	−0.169887	−	0.985463i	$-0.554340\pi$
$199$	−4.79311	−0.339775	−0.169887	+	0.985463i	$0.554340\pi$
$200$	0	0
$201$	1.24426	0.0877631
$202$	10.0378	0.706258
$203$	5.81010	0.407789
$204$	−1.77670	−0.124394
$205$	0	0
$206$	8.19589	0.571035
$207$	3.44228	0.239255
$208$	−44.1538	−3.06151
$209$	29.8378	2.06392
$210$	0	0
$211$	12.5319	0.862728	0.431364	−	0.902178i	$-0.358032\pi$
$211$	12.5319	0.862728	0.431364	+	0.902178i	$0.358032\pi$
$212$	−10.7883	−0.740945
$213$	1.25192	0.0857804
$214$	−0.854803	−0.0584331
$215$	0	0
$216$	−6.59766	−0.448914
$217$	16.0515	1.08965
$218$	28.1606	1.90727
$219$	4.03934	0.272953
$220$	0	0
$221$	2.20800	0.148526
$222$	−27.7125	−1.85994
$223$	−5.49915	−0.368251	−0.184125	−	0.982903i	$-0.558945\pi$
$223$	−5.49915	−0.368251	−0.184125	+	0.982903i	$0.558945\pi$
$224$	−29.9119	−1.99857
$225$	0	0
$226$	25.1656	1.67399
$227$	−5.63051	−0.373710	−0.186855	−	0.982387i	$-0.559829\pi$
$227$	−5.63051	−0.373710	−0.186855	+	0.982387i	$0.559829\pi$
$228$	−25.2126	−1.66974
$229$	−3.65697	−0.241660	−0.120830	−	0.992673i	$-0.538556\pi$
$229$	−3.65697	−0.241660	−0.120830	+	0.992673i	$0.538556\pi$
$230$	0	0
$231$	−24.0819	−1.58447
$232$	−8.61520	−0.565616
$233$	−11.9353	−0.781908	−0.390954	−	0.920410i	$-0.627855\pi$
$233$	−11.9353	−0.781908	−0.390954	+	0.920410i	$0.627855\pi$
$234$	14.5717	0.952582
$235$	0	0
$236$	−53.3087	−3.47010
$237$	1.18741	0.0771305
$238$	4.43181	0.287272
$239$	0.0758088	0.00490366	0.00245183	−	0.999997i	$-0.499220\pi$
$239$	0.0758088	0.00490366	0.00245183	+	0.999997i	$0.499220\pi$
$240$	0	0
$241$	−3.57830	−0.230498	−0.115249	−	0.993337i	$-0.536767\pi$
$241$	−3.57830	−0.230498	−0.115249	+	0.993337i	$0.536767\pi$
$242$	−46.9010	−3.01491
$243$	1.00000	0.0641500
$244$	−53.6911	−3.43722
$245$	0	0
$246$	18.4462	1.17608
$247$	31.3329	1.99367
$248$	−23.8012	−1.51137
$249$	−11.2594	−0.713535
$250$	0	0
$251$	−15.5096	−0.978957	−0.489479	−	0.872015i	$-0.662813\pi$
$251$	−15.5096	−0.978957	−0.489479	+	0.872015i	$0.662813\pi$
$252$	20.3489	1.28186
$253$	−18.6307	−1.17130
$254$	40.7762	2.55853
$255$	0	0
$256$	−26.7048	−1.66905
$257$	23.5336	1.46799	0.733993	−	0.679157i	$-0.237655\pi$
$257$	23.5336	1.46799	0.733993	+	0.679157i	$0.237655\pi$
$258$	−11.5039	−0.716204
$259$	48.0940	2.98842
$260$	0	0
$261$	1.30580	0.0808268
$262$	−25.1123	−1.55144
$263$	16.3121	1.00585	0.502924	−	0.864331i	$-0.332258\pi$
$263$	16.3121	1.00585	0.502924	+	0.864331i	$0.332258\pi$
$264$	35.7086	2.19771
$265$	0	0
$266$	62.8904	3.85606
$267$	5.78199	0.353852
$268$	5.69041	0.347597
$269$	14.9008	0.908517	0.454259	−	0.890870i	$-0.349904\pi$
$269$	14.9008	0.908517	0.454259	+	0.890870i	$0.349904\pi$
$270$	0	0
$271$	−26.7855	−1.62710	−0.813552	−	0.581493i	$-0.802469\pi$
$271$	−26.7855	−1.62710	−0.813552	+	0.581493i	$0.802469\pi$
$272$	−3.01808	−0.182998
$273$	−25.2886	−1.53054
$274$	25.8556	1.56199
$275$	0	0
$276$	15.7427	0.947601
$277$	−23.6115	−1.41868	−0.709338	−	0.704868i	$-0.751006\pi$
$277$	−23.6115	−1.41868	−0.709338	+	0.704868i	$0.751006\pi$
$278$	41.4655	2.48694
$279$	3.60752	0.215976
$280$	0	0
$281$	31.9800	1.90776	0.953882	−	0.300182i	$-0.0970474\pi$
$281$	31.9800	1.90776	0.953882	+	0.300182i	$0.0970474\pi$
$282$	2.56385	0.152675
$283$	25.4820	1.51475	0.757374	−	0.652981i	$-0.226482\pi$
$283$	25.4820	1.51475	0.757374	+	0.652981i	$0.226482\pi$
$284$	5.72547	0.339744
$285$	0	0
$286$	−78.8667	−4.66348
$287$	−32.0126	−1.88964
$288$	−6.72259	−0.396132
$289$	−16.8491	−0.991122
$290$	0	0
$291$	5.11545	0.299873
$292$	18.4733	1.08107
$293$	23.2398	1.35768	0.678841	−	0.734285i	$-0.262483\pi$
$293$	23.2398	1.35768	0.678841	+	0.734285i	$0.262483\pi$
$294$	−32.8115	−1.91361
$295$	0	0
$296$	−71.3137	−4.14502
$297$	−5.41232	−0.314055
$298$	44.7269	2.59096
$299$	−19.5643	−1.13143
$300$	0	0
$301$	19.9646	1.15074
$302$	20.8186	1.19797
$303$	−3.91513	−0.224918
$304$	−42.8286	−2.45639
$305$	0	0
$306$	0.996033	0.0569394
$307$	−10.3925	−0.593132	−0.296566	−	0.955012i	$-0.595841\pi$
$307$	−10.3925	−0.593132	−0.296566	+	0.955012i	$0.595841\pi$
$308$	−110.135	−6.27551
$309$	−3.19671	−0.181854
$310$	0	0
$311$	−11.6060	−0.658115	−0.329058	−	0.944310i	$-0.606731\pi$
$311$	−11.6060	−0.658115	−0.329058	+	0.944310i	$0.606731\pi$
$312$	37.4979	2.12290
$313$	−18.7595	−1.06035	−0.530176	−	0.847888i	$-0.677874\pi$
$313$	−18.7595	−1.06035	−0.530176	+	0.847888i	$0.677874\pi$
$314$	53.2486	3.00499
$315$	0	0
$316$	5.43042	0.305485
$317$	2.09114	0.117450	0.0587251	−	0.998274i	$-0.481296\pi$
$317$	2.09114	0.117450	0.0587251	+	0.998274i	$0.481296\pi$
$318$	6.04803	0.339157
$319$	−7.06739	−0.395698
$320$	0	0
$321$	0.333406	0.0186089
$322$	−39.2688	−2.18836
$323$	2.14173	0.119169
$324$	4.57334	0.254074
$325$	0	0
$326$	20.4204	1.13098
$327$	−10.9837	−0.607400
$328$	47.4682	2.62099
$329$	−4.44946	−0.245307
$330$	0	0
$331$	11.6448	0.640054	0.320027	−	0.947408i	$-0.396308\pi$
$331$	11.6448	0.640054	0.320027	+	0.947408i	$0.396308\pi$
$332$	−51.4930	−2.82605
$333$	10.8089	0.592327
$334$	29.8108	1.63117
$335$	0	0
$336$	34.5667	1.88577
$337$	22.3380	1.21683	0.608415	−	0.793619i	$-0.291806\pi$
$337$	22.3380	1.21683	0.608415	+	0.793619i	$0.291806\pi$
$338$	−49.4885	−2.69182
$339$	−9.81554	−0.533107
$340$	0	0
$341$	−19.5250	−1.05734
$342$	14.1344	0.764300
$343$	25.7968	1.39290
$344$	−29.6035	−1.59611
$345$	0	0
$346$	−15.0733	−0.810343
$347$	15.3213	0.822492	0.411246	−	0.911524i	$-0.365094\pi$
$347$	15.3213	0.822492	0.411246	+	0.911524i	$0.365094\pi$
$348$	5.97185	0.320125
$349$	−33.9945	−1.81969	−0.909843	−	0.414952i	$-0.863798\pi$
$349$	−33.9945	−1.81969	−0.909843	+	0.414952i	$0.863798\pi$
$350$	0	0
$351$	−5.68352	−0.303364
$352$	36.3848	1.93931
$353$	−15.9908	−0.851103	−0.425552	−	0.904934i	$-0.639920\pi$
$353$	−15.9908	−0.851103	−0.425552	+	0.904934i	$0.639920\pi$
$354$	29.8853	1.58839
$355$	0	0
$356$	26.4430	1.40148
$357$	−1.72858	−0.0914860
$358$	6.92902	0.366210
$359$	−11.8019	−0.622880	−0.311440	−	0.950266i	$-0.600811\pi$
$359$	−11.8019	−0.622880	−0.311440	+	0.950266i	$0.600811\pi$
$360$	0	0
$361$	11.3926	0.599610
$362$	17.6098	0.925552
$363$	18.2932	0.960143
$364$	−115.653	−6.06188
$365$	0	0
$366$	30.0997	1.57334
$367$	3.27624	0.171018	0.0855092	−	0.996337i	$-0.472748\pi$
$367$	3.27624	0.171018	0.0855092	+	0.996337i	$0.472748\pi$
$368$	26.7422	1.39403
$369$	−7.19471	−0.374541
$370$	0	0
$371$	−10.4961	−0.544931
$372$	16.4984	0.855402
$373$	−3.63848	−0.188393	−0.0941966	−	0.995554i	$-0.530028\pi$
$373$	−3.63848	−0.188393	−0.0941966	+	0.995554i	$0.530028\pi$
$374$	−5.39085	−0.278754
$375$	0	0
$376$	6.59766	0.340248
$377$	−7.42152	−0.382228
$378$	−11.4078	−0.586752
$379$	10.1069	0.519154	0.259577	−	0.965722i	$-0.416417\pi$
$379$	10.1069	0.519154	0.259577	+	0.965722i	$0.416417\pi$
$380$	0	0
$381$	−15.9043	−0.814802
$382$	−29.8123	−1.52533
$383$	−1.02945	−0.0526022	−0.0263011	−	0.999654i	$-0.508373\pi$
$383$	−1.02945	−0.0526022	−0.0263011	+	0.999654i	$0.508373\pi$
$384$	9.09114	0.463930
$385$	0	0
$386$	49.6405	2.52663
$387$	4.48698	0.228086
$388$	23.3947	1.18768
$389$	36.3853	1.84481	0.922404	−	0.386227i	$-0.126222\pi$
$389$	36.3853	1.84481	0.922404	+	0.386227i	$0.126222\pi$
$390$	0	0
$391$	−1.33730	−0.0676300
$392$	−84.4351	−4.26462
$393$	9.79475	0.494080
$394$	21.1122	1.06362
$395$	0	0
$396$	−24.7524	−1.24385
$397$	−22.9240	−1.15052	−0.575262	−	0.817969i	$-0.695100\pi$
$397$	−22.9240	−1.15052	−0.575262	+	0.817969i	$0.695100\pi$
$398$	12.2888	0.615983
$399$	−24.5297	−1.22802
$400$	0	0
$401$	3.85083	0.192301	0.0961505	−	0.995367i	$-0.469347\pi$
$401$	3.85083	0.192301	0.0961505	+	0.995367i	$0.469347\pi$
$402$	−3.19009	−0.159107
$403$	−20.5034	−1.02135
$404$	−17.9052	−0.890817
$405$	0	0
$406$	−14.8962	−0.739288
$407$	−58.5014	−2.89981
$408$	2.56313	0.126894
$409$	0.961361	0.0475362	0.0237681	−	0.999717i	$-0.492434\pi$
$409$	0.961361	0.0475362	0.0237681	+	0.999717i	$0.492434\pi$
$410$	0	0
$411$	−10.0847	−0.497440
$412$	−14.6196	−0.720257
$413$	−51.8648	−2.55210
$414$	−8.82551	−0.433750
$415$	0	0
$416$	38.2079	1.87330
$417$	−16.1731	−0.792002
$418$	−76.4997	−3.74173
$419$	9.31038	0.454842	0.227421	−	0.973797i	$-0.426971\pi$
$419$	9.31038	0.454842	0.227421	+	0.973797i	$0.426971\pi$
$420$	0	0
$421$	4.23569	0.206435	0.103217	−	0.994659i	$-0.467086\pi$
$421$	4.23569	0.206435	0.103217	+	0.994659i	$0.467086\pi$
$422$	−32.1298	−1.56405
$423$	−1.00000	−0.0486217
$424$	15.5636	0.755836
$425$	0	0
$426$	−3.20975	−0.155513
$427$	−52.2368	−2.52792
$428$	1.52478	0.0737029
$429$	30.7610	1.48516
$430$	0	0
$431$	0.947503	0.0456396	0.0228198	−	0.999740i	$-0.492736\pi$
$431$	0.947503	0.0456396	0.0228198	+	0.999740i	$0.492736\pi$
$432$	7.76874	0.373774
$433$	1.37171	0.0659202	0.0329601	−	0.999457i	$-0.489507\pi$
$433$	1.37171	0.0659202	0.0329601	+	0.999457i	$0.489507\pi$
$434$	−41.1537	−1.97544
$435$	0	0
$436$	−50.2321	−2.40568
$437$	−18.9771	−0.907799
$438$	−10.3563	−0.494842
$439$	−5.78963	−0.276324	−0.138162	−	0.990410i	$-0.544119\pi$
$439$	−5.78963	−0.276324	−0.138162	+	0.990410i	$0.544119\pi$
$440$	0	0
$441$	12.7977	0.609416
$442$	−5.66097	−0.269265
$443$	−15.0084	−0.713073	−0.356536	−	0.934281i	$-0.616042\pi$
$443$	−15.0084	−0.713073	−0.356536	+	0.934281i	$0.616042\pi$
$444$	49.4330	2.34598
$445$	0	0
$446$	14.0990	0.667608
$447$	−17.4452	−0.825129
$448$	7.55625	0.356999
$449$	−32.5601	−1.53661	−0.768303	−	0.640086i	$-0.778899\pi$
$449$	−32.5601	−1.53661	−0.768303	+	0.640086i	$0.778899\pi$
$450$	0	0
$451$	38.9400	1.83361
$452$	−44.8898	−2.11144
$453$	−8.12004	−0.381513
$454$	14.4358	0.677505
$455$	0	0
$456$	36.3725	1.70330
$457$	15.9755	0.747301	0.373650	−	0.927570i	$-0.378106\pi$
$457$	15.9755	0.747301	0.373650	+	0.927570i	$0.378106\pi$
$458$	9.37593	0.438109
$459$	−0.388491	−0.0181332
$460$	0	0
$461$	13.9359	0.649062	0.324531	−	0.945875i	$-0.394794\pi$
$461$	13.9359	0.649062	0.324531	+	0.945875i	$0.394794\pi$
$462$	61.7425	2.87252
$463$	21.1791	0.984277	0.492139	−	0.870517i	$-0.336215\pi$
$463$	21.1791	0.984277	0.492139	+	0.870517i	$0.336215\pi$
$464$	10.1444	0.470942
$465$	0	0
$466$	30.6004	1.41753
$467$	30.5700	1.41461	0.707304	−	0.706909i	$-0.249911\pi$
$467$	30.5700	1.41461	0.707304	+	0.706909i	$0.249911\pi$
$468$	−25.9926	−1.20151
$469$	5.53628	0.255642
$470$	0	0
$471$	−20.7690	−0.956985
$472$	76.9050	3.53984
$473$	−24.2849	−1.11662
$474$	−3.04434	−0.139831
$475$	0	0
$476$	−7.90536	−0.362342
$477$	−2.35896	−0.108009
$478$	−0.194363	−0.00888993
$479$	−23.2628	−1.06290	−0.531452	−	0.847088i	$-0.678353\pi$
$479$	−23.2628	−1.06290	−0.531452	+	0.847088i	$0.678353\pi$
$480$	0	0
$481$	−61.4328	−2.80110
$482$	9.17423	0.417875
$483$	15.3163	0.696917
$484$	83.6609	3.80277
$485$	0	0
$486$	−2.56385	−0.116299
$487$	25.9833	1.17742	0.588709	−	0.808345i	$-0.299637\pi$
$487$	25.9833	1.17742	0.588709	+	0.808345i	$0.299637\pi$
$488$	77.4566	3.50630
$489$	−7.96472	−0.360177
$490$	0	0
$491$	−14.9131	−0.673019	−0.336510	−	0.941680i	$-0.609246\pi$
$491$	−14.9131	−0.673019	−0.336510	+	0.941680i	$0.609246\pi$
$492$	−32.9038	−1.48342
$493$	−0.507290	−0.0228472
$494$	−80.3330	−3.61435
$495$	0	0
$496$	28.0259	1.25840
$497$	5.57039	0.249866
$498$	28.8674	1.29358
$499$	−18.0434	−0.807731	−0.403866	−	0.914818i	$-0.632334\pi$
$499$	−18.0434	−0.807731	−0.403866	+	0.914818i	$0.632334\pi$
$500$	0	0
$501$	−11.6273	−0.519471
$502$	39.7643	1.77477
$503$	9.18628	0.409596	0.204798	−	0.978804i	$-0.434346\pi$
$503$	9.18628	0.409596	0.204798	+	0.978804i	$0.434346\pi$
$504$	−29.3560	−1.30762
$505$	0	0
$506$	47.7664	2.12348
$507$	19.3024	0.857249
$508$	−72.7357	−3.22712
$509$	−28.5440	−1.26519	−0.632595	−	0.774483i	$-0.718010\pi$
$509$	−28.5440	−1.26519	−0.632595	+	0.774483i	$0.718010\pi$
$510$	0	0
$511$	17.9729	0.795075
$512$	50.2849	2.22230
$513$	−5.51295	−0.243403
$514$	−60.3367	−2.66134
$515$	0	0
$516$	20.5205	0.903363
$517$	5.41232	0.238033
$518$	−123.306	−5.41775
$519$	5.87914	0.258066
$520$	0	0
$521$	1.25898	0.0551569	0.0275784	−	0.999620i	$-0.491220\pi$
$521$	1.25898	0.0551569	0.0275784	+	0.999620i	$0.491220\pi$
$522$	−3.34787	−0.146532
$523$	31.9071	1.39520	0.697600	−	0.716488i	$-0.254251\pi$
$523$	31.9071	1.39520	0.697600	+	0.716488i	$0.254251\pi$
$524$	44.7947	1.95687
$525$	0	0
$526$	−41.8218	−1.82352
$527$	−1.40149	−0.0610497
$528$	−42.0469	−1.82986
$529$	−11.1507	−0.484812
$530$	0	0
$531$	−11.6564	−0.505845
$532$	−112.182	−4.86373
$533$	40.8912	1.77120
$534$	−14.8242	−0.641505
$535$	0	0
$536$	−8.20918	−0.354583
$537$	−2.70258	−0.116625
$538$	−38.2034	−1.64707
$539$	−69.2654	−2.98347
$540$	0	0
$541$	17.1961	0.739319	0.369659	−	0.929167i	$-0.379474\pi$
$541$	17.1961	0.739319	0.369659	+	0.929167i	$0.379474\pi$
$542$	68.6741	2.94980
$543$	−6.86851	−0.294756
$544$	2.61166	0.111974
$545$	0	0
$546$	64.8363	2.77474
$547$	11.6411	0.497736	0.248868	−	0.968537i	$-0.419941\pi$
$547$	11.6411	0.497736	0.248868	+	0.968537i	$0.419941\pi$
$548$	−46.1206	−1.97017
$549$	−11.7400	−0.501052
$550$	0	0
$551$	−7.19879	−0.306679
$552$	−22.7110	−0.966645
$553$	5.28334	0.224670
$554$	60.5364	2.57194
$555$	0	0
$556$	−73.9652	−3.13682
$557$	10.4346	0.442127	0.221063	−	0.975259i	$-0.429047\pi$
$557$	10.4346	0.442127	0.221063	+	0.975259i	$0.429047\pi$
$558$	−9.24914	−0.391547
$559$	−25.5018	−1.07861
$560$	0	0
$561$	2.10264	0.0887734
$562$	−81.9919	−3.45862
$563$	14.4936	0.610832	0.305416	−	0.952219i	$-0.401205\pi$
$563$	14.4936	0.610832	0.305416	+	0.952219i	$0.401205\pi$
$564$	−4.57334	−0.192572
$565$	0	0
$566$	−65.3321	−2.74611
$567$	4.44946	0.186860
$568$	−8.25976	−0.346572
$569$	11.1294	0.466569	0.233284	−	0.972409i	$-0.425053\pi$
$569$	11.1294	0.466569	0.233284	+	0.972409i	$0.425053\pi$
$570$	0	0
$571$	10.8000	0.451968	0.225984	−	0.974131i	$-0.427440\pi$
$571$	10.8000	0.451968	0.225984	+	0.974131i	$0.427440\pi$
$572$	140.680	5.88215
$573$	11.6279	0.485764
$574$	82.0756	3.42577
$575$	0	0
$576$	1.69824	0.0707599
$577$	30.0642	1.25159	0.625794	−	0.779988i	$-0.284775\pi$
$577$	30.0642	1.25159	0.625794	+	0.779988i	$0.284775\pi$
$578$	43.1985	1.79682
$579$	−19.3617	−0.804644
$580$	0	0
$581$	−50.0983	−2.07843
$582$	−13.1152	−0.543645
$583$	12.7674	0.528774
$584$	−26.6502	−1.10279
$585$	0	0
$586$	−59.5833	−2.46136
$587$	−8.40815	−0.347041	−0.173521	−	0.984830i	$-0.555514\pi$
$587$	−8.40815	−0.347041	−0.173521	+	0.984830i	$0.555514\pi$
$588$	58.5284	2.41367
$589$	−19.8880	−0.819473
$590$	0	0
$591$	−8.23457	−0.338725
$592$	83.9719	3.45122
$593$	−45.4627	−1.86693	−0.933464	−	0.358672i	$-0.883230\pi$
$593$	−45.4627	−1.86693	−0.933464	+	0.358672i	$0.883230\pi$
$594$	13.8764	0.569355
$595$	0	0
$596$	−79.7827	−3.26803
$597$	−4.79311	−0.196169
$598$	50.1599	2.05119
$599$	19.8866	0.812543	0.406271	−	0.913753i	$-0.366829\pi$
$599$	19.8866	0.812543	0.406271	+	0.913753i	$0.366829\pi$
$600$	0	0
$601$	16.0378	0.654196	0.327098	−	0.944990i	$-0.393929\pi$
$601$	16.0378	0.654196	0.327098	+	0.944990i	$0.393929\pi$
$602$	−51.1864	−2.08620
$603$	1.24426	0.0506701
$604$	−37.1357	−1.51103
$605$	0	0
$606$	10.0378	0.407758
$607$	−9.28626	−0.376918	−0.188459	−	0.982081i	$-0.560349\pi$
$607$	−9.28626	−0.376918	−0.188459	+	0.982081i	$0.560349\pi$
$608$	37.0613	1.50303
$609$	5.81010	0.235437
$610$	0	0
$611$	5.68352	0.229931
$612$	−1.77670	−0.0718188
$613$	32.5268	1.31374	0.656872	−	0.754002i	$-0.271879\pi$
$613$	32.5268	1.31374	0.656872	+	0.754002i	$0.271879\pi$
$614$	26.6449	1.07530
$615$	0	0
$616$	158.884	6.40163
$617$	−4.09330	−0.164790	−0.0823950	−	0.996600i	$-0.526257\pi$
$617$	−4.09330	−0.164790	−0.0823950	+	0.996600i	$0.526257\pi$
$618$	8.19589	0.329687
$619$	15.5105	0.623419	0.311709	−	0.950177i	$-0.399098\pi$
$619$	15.5105	0.623419	0.311709	+	0.950177i	$0.399098\pi$
$620$	0	0
$621$	3.44228	0.138134
$622$	29.7560	1.19311
$623$	25.7268	1.03072
$624$	−44.1538	−1.76757
$625$	0	0
$626$	48.0967	1.92233
$627$	29.8378	1.19161
$628$	−94.9836	−3.79026
$629$	−4.19918	−0.167432
$630$	0	0
$631$	17.5274	0.697754	0.348877	−	0.937169i	$-0.386563\pi$
$631$	17.5274	0.697754	0.348877	+	0.937169i	$0.386563\pi$
$632$	−7.83412	−0.311625
$633$	12.5319	0.498096
$634$	−5.36137	−0.212927
$635$	0	0
$636$	−10.7883	−0.427785
$637$	−72.7362	−2.88191
$638$	18.1197	0.717367
$639$	1.25192	0.0495253
$640$	0	0
$641$	4.35859	0.172154	0.0860770	−	0.996288i	$-0.472567\pi$
$641$	4.35859	0.172154	0.0860770	+	0.996288i	$0.472567\pi$
$642$	−0.854803	−0.0337364
$643$	−16.8991	−0.666435	−0.333218	−	0.942850i	$-0.608134\pi$
$643$	−16.8991	−0.666435	−0.333218	+	0.942850i	$0.608134\pi$
$644$	70.0467	2.76023
$645$	0	0
$646$	−5.49108	−0.216044
$647$	38.5085	1.51392	0.756962	−	0.653459i	$-0.226683\pi$
$647$	38.5085	1.51392	0.756962	+	0.653459i	$0.226683\pi$
$648$	−6.59766	−0.259180
$649$	63.0882	2.47643
$650$	0	0
$651$	16.0515	0.629109
$652$	−36.4254	−1.42653
$653$	13.5535	0.530389	0.265194	−	0.964195i	$-0.414564\pi$
$653$	13.5535	0.530389	0.265194	+	0.964195i	$0.414564\pi$
$654$	28.1606	1.10117
$655$	0	0
$656$	−55.8938	−2.18229
$657$	4.03934	0.157590
$658$	11.4078	0.444721
$659$	40.2724	1.56879	0.784396	−	0.620260i	$-0.212973\pi$
$659$	40.2724	1.56879	0.784396	+	0.620260i	$0.212973\pi$
$660$	0	0
$661$	−42.9627	−1.67106	−0.835528	−	0.549448i	$-0.814838\pi$
$661$	−42.9627	−1.67106	−0.835528	+	0.549448i	$0.814838\pi$
$662$	−29.8555	−1.16037
$663$	2.20800	0.0857514
$664$	74.2856	2.88284
$665$	0	0
$666$	−27.7125	−1.07384
$667$	4.49492	0.174044
$668$	−53.1758	−2.05743
$669$	−5.49915	−0.212610
$670$	0	0
$671$	63.5407	2.45296
$672$	−29.9119	−1.15388
$673$	28.3904	1.09437	0.547184	−	0.837012i	$-0.315700\pi$
$673$	28.3904	1.09437	0.547184	+	0.837012i	$0.315700\pi$
$674$	−57.2714	−2.20601
$675$	0	0
$676$	88.2763	3.39524
$677$	−21.5641	−0.828777	−0.414388	−	0.910100i	$-0.636005\pi$
$677$	−21.5641	−0.828777	−0.414388	+	0.910100i	$0.636005\pi$
$678$	25.1656	0.966479
$679$	22.7610	0.873487
$680$	0	0
$681$	−5.63051	−0.215762
$682$	50.0593	1.91687
$683$	0.307265	0.0117572	0.00587858	−	0.999983i	$-0.498129\pi$
$683$	0.307265	0.0117572	0.00587858	+	0.999983i	$0.498129\pi$
$684$	−25.2126	−0.964027
$685$	0	0
$686$	−66.1393	−2.52521
$687$	−3.65697	−0.139522
$688$	34.8581	1.32895
$689$	13.4072	0.510774
$690$	0	0
$691$	−18.9810	−0.722073	−0.361037	−	0.932552i	$-0.617577\pi$
$691$	−18.9810	−0.722073	−0.361037	+	0.932552i	$0.617577\pi$
$692$	26.8873	1.02210
$693$	−24.0819	−0.914796
$694$	−39.2816	−1.49111
$695$	0	0
$696$	−8.61520	−0.326558
$697$	2.79508	0.105871
$698$	87.1570	3.29894
$699$	−11.9353	−0.451435
$700$	0	0
$701$	−3.97267	−0.150046	−0.0750229	−	0.997182i	$-0.523903\pi$
$701$	−3.97267	−0.150046	−0.0750229	+	0.997182i	$0.523903\pi$
$702$	14.5717	0.549973
$703$	−59.5891	−2.24745
$704$	−9.19140	−0.346414
$705$	0	0
$706$	40.9980	1.54298
$707$	−17.4202	−0.655155
$708$	−53.3087	−2.00346
$709$	24.0929	0.904828	0.452414	−	0.891808i	$-0.350563\pi$
$709$	24.0929	0.904828	0.452414	+	0.891808i	$0.350563\pi$
$710$	0	0
$711$	1.18741	0.0445313
$712$	−38.1476	−1.42964
$713$	12.4181	0.465061
$714$	4.43181	0.165856
$715$	0	0
$716$	−12.3598	−0.461908
$717$	0.0758088	0.00283113
$718$	30.2583	1.12923
$719$	−50.4457	−1.88131	−0.940654	−	0.339366i	$-0.889787\pi$
$719$	−50.4457	−1.88131	−0.940654	+	0.339366i	$0.889787\pi$
$720$	0	0
$721$	−14.2236	−0.529716
$722$	−29.2089	−1.08704
$723$	−3.57830	−0.133078
$724$	−31.4120	−1.16742
$725$	0	0
$726$	−46.9010	−1.74066
$727$	−23.6456	−0.876966	−0.438483	−	0.898739i	$-0.644484\pi$
$727$	−23.6456	−0.876966	−0.438483	+	0.898739i	$0.644484\pi$
$728$	166.846	6.18371
$729$	1.00000	0.0370370
$730$	0	0
$731$	−1.74315	−0.0644727
$732$	−53.6911	−1.98448
$733$	−16.3808	−0.605039	−0.302520	−	0.953143i	$-0.597828\pi$
$733$	−16.3808	−0.605039	−0.302520	+	0.953143i	$0.597828\pi$
$734$	−8.39979	−0.310042
$735$	0	0
$736$	−23.1411	−0.852991
$737$	−6.73432	−0.248062
$738$	18.4462	0.679013
$739$	−0.667363	−0.0245494	−0.0122747	−	0.999925i	$-0.503907\pi$
$739$	−0.667363	−0.0245494	−0.0122747	+	0.999925i	$0.503907\pi$
$740$	0	0
$741$	31.3329	1.15104
$742$	26.9105	0.987915
$743$	−37.1829	−1.36411	−0.682054	−	0.731302i	$-0.738913\pi$
$743$	−37.1829	−1.36411	−0.682054	+	0.731302i	$0.738913\pi$
$744$	−23.8012	−0.872593
$745$	0	0
$746$	9.32852	0.341541
$747$	−11.2594	−0.411960
$748$	9.61606	0.351598
$749$	1.48348	0.0542051
$750$	0	0
$751$	48.0300	1.75264	0.876319	−	0.481731i	$-0.159992\pi$
$751$	48.0300	1.75264	0.876319	+	0.481731i	$0.159992\pi$
$752$	−7.76874	−0.283297
$753$	−15.5096	−0.565201
$754$	19.0277	0.692947
$755$	0	0
$756$	20.3489	0.740082
$757$	28.8757	1.04950	0.524752	−	0.851255i	$-0.324158\pi$
$757$	28.8757	1.04950	0.524752	+	0.851255i	$0.324158\pi$
$758$	−25.9125	−0.941184
$759$	−18.6307	−0.676253
$760$	0	0
$761$	4.57497	0.165843	0.0829213	−	0.996556i	$-0.473575\pi$
$761$	4.57497	0.165843	0.0829213	+	0.996556i	$0.473575\pi$
$762$	40.7762	1.47717
$763$	−48.8716	−1.76927
$764$	53.1785	1.92393
$765$	0	0
$766$	2.63935	0.0953635
$767$	66.2494	2.39213
$768$	−26.7048	−0.963627
$769$	−41.2805	−1.48861	−0.744307	−	0.667838i	$-0.767220\pi$
$769$	−41.2805	−1.48861	−0.744307	+	0.667838i	$0.767220\pi$
$770$	0	0
$771$	23.5336	0.847542
$772$	−88.5475	−3.18689
$773$	42.0756	1.51335	0.756677	−	0.653789i	$-0.226822\pi$
$773$	42.0756	1.51335	0.756677	+	0.653789i	$0.226822\pi$
$774$	−11.5039	−0.413501
$775$	0	0
$776$	−33.7500	−1.21155
$777$	48.0940	1.72536
$778$	−93.2865	−3.34448
$779$	39.6640	1.42111
$780$	0	0
$781$	−6.77581	−0.242458
$782$	3.42863	0.122608
$783$	1.30580	0.0466654
$784$	99.4223	3.55080
$785$	0	0
$786$	−25.1123	−0.895726
$787$	15.6360	0.557362	0.278681	−	0.960384i	$-0.410103\pi$
$787$	15.6360	0.557362	0.278681	+	0.960384i	$0.410103\pi$
$788$	−37.6595	−1.34156
$789$	16.3121	0.580727
$790$	0	0
$791$	−43.6739	−1.55287
$792$	35.7086	1.26885
$793$	66.7246	2.36946
$794$	58.7738	2.08580
$795$	0	0
$796$	−21.9205	−0.776952
$797$	12.1532	0.430489	0.215244	−	0.976560i	$-0.430945\pi$
$797$	12.1532	0.430489	0.215244	+	0.976560i	$0.430945\pi$
$798$	62.8904	2.22630
$799$	0.388491	0.0137438
$800$	0	0
$801$	5.78199	0.204297
$802$	−9.87295	−0.348626
$803$	−21.8622	−0.771500
$804$	5.69041	0.200685
$805$	0	0
$806$	52.5676	1.85162
$807$	14.9008	0.524533
$808$	25.8307	0.908720
$809$	47.3802	1.66580	0.832899	−	0.553425i	$-0.186680\pi$
$809$	47.3802	1.66580	0.832899	+	0.553425i	$0.186680\pi$
$810$	0	0
$811$	41.8183	1.46844	0.734220	−	0.678912i	$-0.237548\pi$
$811$	41.8183	1.46844	0.734220	+	0.678912i	$0.237548\pi$
$812$	26.5715	0.932478
$813$	−26.7855	−0.939409
$814$	149.989	5.25711
$815$	0	0
$816$	−3.01808	−0.105654
$817$	−24.7365	−0.865419
$818$	−2.46479	−0.0861792
$819$	−25.2886	−0.883656
$820$	0	0
$821$	46.4075	1.61963	0.809817	−	0.586683i	$-0.199567\pi$
$821$	46.4075	1.61963	0.809817	+	0.586683i	$0.199567\pi$
$822$	25.8556	0.901817
$823$	−11.0131	−0.383891	−0.191945	−	0.981406i	$-0.561480\pi$
$823$	−11.0131	−0.383891	−0.191945	+	0.981406i	$0.561480\pi$
$824$	21.0908	0.734732
$825$	0	0
$826$	132.974	4.62674
$827$	−25.7424	−0.895150	−0.447575	−	0.894246i	$-0.647712\pi$
$827$	−25.7424	−0.895150	−0.447575	+	0.894246i	$0.647712\pi$
$828$	15.7427	0.547098
$829$	−41.6421	−1.44629	−0.723146	−	0.690696i	$-0.757304\pi$
$829$	−41.6421	−1.44629	−0.723146	+	0.690696i	$0.757304\pi$
$830$	0	0
$831$	−23.6115	−0.819074
$832$	−9.65196	−0.334622
$833$	−4.97180	−0.172263
$834$	41.4655	1.43583
$835$	0	0
$836$	136.458	4.71951
$837$	3.60752	0.124694
$838$	−23.8704	−0.824590
$839$	54.7499	1.89018	0.945088	−	0.326817i	$-0.105976\pi$
$839$	54.7499	1.89018	0.945088	+	0.326817i	$0.105976\pi$
$840$	0	0
$841$	−27.2949	−0.941203
$842$	−10.8597	−0.374249
$843$	31.9800	1.10145
$844$	57.3124	1.97277
$845$	0	0
$846$	2.56385	0.0881470
$847$	81.3949	2.79676
$848$	−18.3262	−0.629323
$849$	25.4820	0.874540
$850$	0	0
$851$	37.2075	1.27546
$852$	5.72547	0.196151
$853$	46.5465	1.59372	0.796861	−	0.604162i	$-0.206492\pi$
$853$	46.5465	1.59372	0.796861	+	0.604162i	$0.206492\pi$
$854$	133.928	4.58290
$855$	0	0
$856$	−2.19970	−0.0751841
$857$	54.8204	1.87263	0.936314	−	0.351164i	$-0.114214\pi$
$857$	54.8204	1.87263	0.936314	+	0.351164i	$0.114214\pi$
$858$	−78.8667	−2.69246
$859$	−21.0358	−0.717733	−0.358867	−	0.933389i	$-0.616837\pi$
$859$	−21.0358	−0.717733	−0.358867	+	0.933389i	$0.616837\pi$
$860$	0	0
$861$	−32.0126	−1.09099
$862$	−2.42926	−0.0827408
$863$	25.5797	0.870744	0.435372	−	0.900251i	$-0.356617\pi$
$863$	25.5797	0.870744	0.435372	+	0.900251i	$0.356617\pi$
$864$	−6.72259	−0.228707
$865$	0	0
$866$	−3.51686	−0.119508
$867$	−16.8491	−0.572225
$868$	73.4090	2.49166
$869$	−6.42664	−0.218009
$870$	0	0
$871$	−7.07176	−0.239617
$872$	72.4666	2.45403
$873$	5.11545	0.173132
$874$	48.6546	1.64576
$875$	0	0
$876$	18.4733	0.624154
$877$	8.38347	0.283090	0.141545	−	0.989932i	$-0.454793\pi$
$877$	8.38347	0.283090	0.141545	+	0.989932i	$0.454793\pi$
$878$	14.8437	0.500952
$879$	23.2398	0.783858
$880$	0	0
$881$	10.0997	0.340268	0.170134	−	0.985421i	$-0.445580\pi$
$881$	10.0997	0.340268	0.170134	+	0.985421i	$0.445580\pi$
$882$	−32.8115	−1.10482
$883$	−14.9068	−0.501653	−0.250826	−	0.968032i	$-0.580702\pi$
$883$	−14.9068	−0.501653	−0.250826	+	0.968032i	$0.580702\pi$
$884$	10.0979	0.339629
$885$	0	0
$886$	38.4794	1.29274
$887$	−53.1637	−1.78506	−0.892532	−	0.450985i	$-0.851073\pi$
$887$	−53.1637	−1.78506	−0.892532	+	0.450985i	$0.851073\pi$
$888$	−71.3137	−2.39313
$889$	−70.7656	−2.37340
$890$	0	0
$891$	−5.41232	−0.181319
$892$	−25.1495	−0.842067
$893$	5.51295	0.184484
$894$	44.7269	1.49589
$895$	0	0
$896$	40.4507	1.35136
$897$	−19.5643	−0.653233
$898$	83.4793	2.78574
$899$	4.71068	0.157110
$900$	0	0
$901$	0.916435	0.0305309
$902$	−99.8365	−3.32419
$903$	19.9646	0.664382
$904$	64.7596	2.15387
$905$	0	0
$906$	20.8186	0.691651
$907$	−23.0456	−0.765218	−0.382609	−	0.923910i	$-0.624974\pi$
$907$	−23.0456	−0.765218	−0.382609	+	0.923910i	$0.624974\pi$
$908$	−25.7502	−0.854551
$909$	−3.91513	−0.129857
$910$	0	0
$911$	−4.85366	−0.160809	−0.0804044	−	0.996762i	$-0.525621\pi$
$911$	−4.85366	−0.160809	−0.0804044	+	0.996762i	$0.525621\pi$
$912$	−42.8286	−1.41820
$913$	60.9394	2.01680
$914$	−40.9587	−1.35479
$915$	0	0
$916$	−16.7246	−0.552595
$917$	43.5814	1.43919
$918$	0.996033	0.0328740
$919$	12.5252	0.413168	0.206584	−	0.978429i	$-0.433765\pi$
$919$	12.5252	0.413168	0.206584	+	0.978429i	$0.433765\pi$
$920$	0	0
$921$	−10.3925	−0.342445
$922$	−35.7297	−1.17670
$923$	−7.11533	−0.234204
$924$	−110.135	−3.62317
$925$	0	0
$926$	−54.3001	−1.78441
$927$	−3.19671	−0.104994
$928$	−8.77833	−0.288163
$929$	27.2535	0.894158	0.447079	−	0.894495i	$-0.352464\pi$
$929$	27.2535	0.894158	0.447079	+	0.894495i	$0.352464\pi$
$930$	0	0
$931$	−70.5533	−2.31229
$932$	−54.5842	−1.78796
$933$	−11.6060	−0.379963
$934$	−78.3768	−2.56457
$935$	0	0
$936$	37.4979	1.22566
$937$	−38.4858	−1.25728	−0.628638	−	0.777698i	$-0.716387\pi$
$937$	−38.4858	−1.25728	−0.628638	+	0.777698i	$0.716387\pi$
$938$	−14.1942	−0.463457
$939$	−18.7595	−0.612194
$940$	0	0
$941$	−14.6800	−0.478555	−0.239277	−	0.970951i	$-0.576911\pi$
$941$	−14.6800	−0.478555	−0.239277	+	0.970951i	$0.576911\pi$
$942$	53.2486	1.73493
$943$	−24.7662	−0.806499
$944$	−90.5556	−2.94733
$945$	0	0
$946$	62.2630	2.02434
$947$	−47.5318	−1.54458	−0.772288	−	0.635272i	$-0.780888\pi$
$947$	−47.5318	−1.54458	−0.772288	+	0.635272i	$0.780888\pi$
$948$	5.43042	0.176372
$949$	−22.9577	−0.745238
$950$	0	0
$951$	2.09114	0.0678099
$952$	11.4046	0.369624
$953$	5.10181	0.165264	0.0826319	−	0.996580i	$-0.473667\pi$
$953$	5.10181	0.165264	0.0826319	+	0.996580i	$0.473667\pi$
$954$	6.04803	0.195812
$955$	0	0
$956$	0.346699	0.0112131
$957$	−7.06739	−0.228456
$958$	59.6424	1.92696
$959$	−44.8714	−1.44897
$960$	0	0
$961$	−17.9858	−0.580188
$962$	157.505	5.07816
$963$	0.333406	0.0107438
$964$	−16.3648	−0.527074
$965$	0	0
$966$	−39.2688	−1.26345
$967$	29.0391	0.933834	0.466917	−	0.884301i	$-0.345365\pi$
$967$	29.0391	0.933834	0.466917	+	0.884301i	$0.345365\pi$
$968$	−120.692	−3.87919
$969$	2.14173	0.0688023
$970$	0	0
$971$	14.6097	0.468847	0.234424	−	0.972135i	$-0.424680\pi$
$971$	14.6097	0.468847	0.234424	+	0.972135i	$0.424680\pi$
$972$	4.57334	0.146690
$973$	−71.9618	−2.30699
$974$	−66.6174	−2.13456
$975$	0	0
$976$	−91.2052	−2.91941
$977$	−42.2424	−1.35145	−0.675727	−	0.737152i	$-0.736170\pi$
$977$	−42.2424	−1.35145	−0.675727	+	0.737152i	$0.736170\pi$
$978$	20.4204	0.652971
$979$	−31.2940	−1.00016
$980$	0	0
$981$	−10.9837	−0.350682
$982$	38.2350	1.22013
$983$	−34.0427	−1.08579	−0.542897	−	0.839799i	$-0.682673\pi$
$983$	−34.0427	−1.08579	−0.542897	+	0.839799i	$0.682673\pi$
$984$	47.4682	1.51323
$985$	0	0
$986$	1.30062	0.0414201
$987$	−4.44946	−0.141628
$988$	143.296	4.55886
$989$	15.4454	0.491137
$990$	0	0
$991$	53.4086	1.69658	0.848290	−	0.529533i	$-0.177633\pi$
$991$	53.4086	1.69658	0.848290	+	0.529533i	$0.177633\pi$
$992$	−24.2518	−0.769997
$993$	11.6448	0.369535
$994$	−14.2817	−0.452987
$995$	0	0
$996$	−51.4930	−1.63162
$997$	14.7959	0.468590	0.234295	−	0.972166i	$-0.424722\pi$
$997$	14.7959	0.468590	0.234295	+	0.972166i	$0.424722\pi$
$998$	46.2605	1.46435
$999$	10.8089	0.341980

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bf.1.1		10
5.2	odd	4		705.2.c.b.424.1	✓	20
5.3	odd	4		705.2.c.b.424.20	yes	20
5.4	even	2		3525.2.a.bg.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.2.c.b.424.1	✓	20	5.2	odd	4
705.2.c.b.424.20	yes	20	5.3	odd	4
3525.2.a.bf.1.1		10	1.1	even	1	trivial
3525.2.a.bg.1.10		10	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.56385 q^{2} +1.00000 q^{3} +4.57334 q^{4} -2.56385 q^{6} +4.44946 q^{7} -6.59766 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.56385 q^{2} +1.00000 q^{3} +4.57334 q^{4} -2.56385 q^{6} +4.44946 q^{7} -6.59766 q^{8} +1.00000 q^{9} -5.41232 q^{11} +4.57334 q^{12} -5.68352 q^{13} -11.4078 q^{14} +7.76874 q^{16} -0.388491 q^{17} -2.56385 q^{18} -5.51295 q^{19} +4.44946 q^{21} +13.8764 q^{22} +3.44228 q^{23} -6.59766 q^{24} +14.5717 q^{26} +1.00000 q^{27} +20.3489 q^{28} +1.30580 q^{29} +3.60752 q^{31} -6.72259 q^{32} -5.41232 q^{33} +0.996033 q^{34} +4.57334 q^{36} +10.8089 q^{37} +14.1344 q^{38} -5.68352 q^{39} -7.19471 q^{41} -11.4078 q^{42} +4.48698 q^{43} -24.7524 q^{44} -8.82551 q^{46} -1.00000 q^{47} +7.76874 q^{48} +12.7977 q^{49} -0.388491 q^{51} -25.9926 q^{52} -2.35896 q^{53} -2.56385 q^{54} -29.3560 q^{56} -5.51295 q^{57} -3.34787 q^{58} -11.6564 q^{59} -11.7400 q^{61} -9.24914 q^{62} +4.44946 q^{63} +1.69824 q^{64} +13.8764 q^{66} +1.24426 q^{67} -1.77670 q^{68} +3.44228 q^{69} +1.25192 q^{71} -6.59766 q^{72} +4.03934 q^{73} -27.7125 q^{74} -25.2126 q^{76} -24.0819 q^{77} +14.5717 q^{78} +1.18741 q^{79} +1.00000 q^{81} +18.4462 q^{82} -11.2594 q^{83} +20.3489 q^{84} -11.5039 q^{86} +1.30580 q^{87} +35.7086 q^{88} +5.78199 q^{89} -25.2886 q^{91} +15.7427 q^{92} +3.60752 q^{93} +2.56385 q^{94} -6.72259 q^{96} +5.11545 q^{97} -32.8115 q^{98} -5.41232 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} + 10 q^{3} + 7 q^{4} - 3 q^{6} - 9 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 3 * q^2 + 10 * q^3 + 7 * q^4 - 3 * q^6 - 9 * q^8 + 10 * q^9	\( 10 q - 3 q^{2} + 10 q^{3} + 7 q^{4} - 3 q^{6} - 9 q^{8} + 10 q^{9} - 16 q^{11} + 7 q^{12} - q^{13} - 12 q^{14} - 3 q^{16} - 14 q^{17} - 3 q^{18} - 26 q^{19} - 7 q^{23} - 9 q^{24} - 10 q^{26} + 10 q^{27} + 24 q^{28} - 14 q^{29} - 22 q^{31} - 11 q^{32} - 16 q^{33} - 12 q^{34} + 7 q^{36} - 2 q^{37} + 2 q^{38} - q^{39} - 22 q^{41} - 12 q^{42} + 11 q^{43} - 36 q^{44} - 14 q^{46} - 10 q^{47} - 3 q^{48} + 2 q^{49} - 14 q^{51} - 14 q^{52} - 22 q^{53} - 3 q^{54} - 48 q^{56} - 26 q^{57} + 20 q^{58} - 37 q^{59} - 25 q^{61} + 2 q^{62} - 7 q^{64} + 4 q^{67} - 8 q^{68} - 7 q^{69} - 27 q^{71} - 9 q^{72} - q^{73} + 4 q^{74} - 42 q^{76} - 34 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{81} + 32 q^{82} - 2 q^{83} + 24 q^{84} - 6 q^{86} - 14 q^{87} + 58 q^{88} + 9 q^{89} - 64 q^{91} - 34 q^{92} - 22 q^{93} + 3 q^{94} - 11 q^{96} + 40 q^{97} - 29 q^{98} - 16 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 + 10 * q^3 + 7 * q^4 - 3 * q^6 - 9 * q^8 + 10 * q^9 - 16 * q^11 + 7 * q^12 - q^13 - 12 * q^14 - 3 * q^16 - 14 * q^17 - 3 * q^18 - 26 * q^19 - 7 * q^23 - 9 * q^24 - 10 * q^26 + 10 * q^27 + 24 * q^28 - 14 * q^29 - 22 * q^31 - 11 * q^32 - 16 * q^33 - 12 * q^34 + 7 * q^36 - 2 * q^37 + 2 * q^38 - q^39 - 22 * q^41 - 12 * q^42 + 11 * q^43 - 36 * q^44 - 14 * q^46 - 10 * q^47 - 3 * q^48 + 2 * q^49 - 14 * q^51 - 14 * q^52 - 22 * q^53 - 3 * q^54 - 48 * q^56 - 26 * q^57 + 20 * q^58 - 37 * q^59 - 25 * q^61 + 2 * q^62 - 7 * q^64 + 4 * q^67 - 8 * q^68 - 7 * q^69 - 27 * q^71 - 9 * q^72 - q^73 + 4 * q^74 - 42 * q^76 - 34 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^81 + 32 * q^82 - 2 * q^83 + 24 * q^84 - 6 * q^86 - 14 * q^87 + 58 * q^88 + 9 * q^89 - 64 * q^91 - 34 * q^92 - 22 * q^93 + 3 * q^94 - 11 * q^96 + 40 * q^97 - 29 * q^98 - 16 * q^99

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