LMFDB - Embedded newform 3525.2.a.bf.1.2

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			1.2
Root			$2.38580$ 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)

$f(q)$	$=$	$q-2.38580 q^{2} +1.00000 q^{3} +3.69205 q^{4} -2.38580 q^{6} +1.19234 q^{7} -4.03690 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.38580 q^{2} +1.00000 q^{3} +3.69205 q^{4} -2.38580 q^{6} +1.19234 q^{7} -4.03690 q^{8} +1.00000 q^{9} -2.68688 q^{11} +3.69205 q^{12} +5.12547 q^{13} -2.84469 q^{14} +2.24714 q^{16} +0.967149 q^{17} -2.38580 q^{18} +1.87461 q^{19} +1.19234 q^{21} +6.41037 q^{22} -7.60212 q^{23} -4.03690 q^{24} -12.2284 q^{26} +1.00000 q^{27} +4.40218 q^{28} -9.33467 q^{29} -7.48104 q^{31} +2.71257 q^{32} -2.68688 q^{33} -2.30743 q^{34} +3.69205 q^{36} -8.35311 q^{37} -4.47244 q^{38} +5.12547 q^{39} +0.858735 q^{41} -2.84469 q^{42} +6.69665 q^{43} -9.92010 q^{44} +18.1371 q^{46} -1.00000 q^{47} +2.24714 q^{48} -5.57833 q^{49} +0.967149 q^{51} +18.9235 q^{52} +8.42050 q^{53} -2.38580 q^{54} -4.81336 q^{56} +1.87461 q^{57} +22.2707 q^{58} -11.2142 q^{59} -10.7671 q^{61} +17.8483 q^{62} +1.19234 q^{63} -10.9659 q^{64} +6.41037 q^{66} -2.45600 q^{67} +3.57076 q^{68} -7.60212 q^{69} -7.42913 q^{71} -4.03690 q^{72} -5.18337 q^{73} +19.9289 q^{74} +6.92114 q^{76} -3.20368 q^{77} -12.2284 q^{78} +9.80667 q^{79} +1.00000 q^{81} -2.04877 q^{82} +4.00659 q^{83} +4.40218 q^{84} -15.9769 q^{86} -9.33467 q^{87} +10.8467 q^{88} +0.872329 q^{89} +6.11131 q^{91} -28.0674 q^{92} -7.48104 q^{93} +2.38580 q^{94} +2.71257 q^{96} -6.63229 q^{97} +13.3088 q^{98} -2.68688 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.38580	−1.68702	−0.843508	−	0.537116i	$-0.819514\pi$
$2$	−2.38580	−1.68702	−0.843508	+	0.537116i	$0.819514\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.69205	1.84603
$5$	0	0
$5$	0	0
$6$	−2.38580	−0.974000
$7$	1.19234	0.450662	0.225331	−	0.974282i	$-0.427654\pi$
$7$	1.19234	0.450662	0.225331	+	0.974282i	$0.427654\pi$
$8$	−4.03690	−1.42726
$9$	1.00000	0.333333
$10$	0	0
$11$	−2.68688	−0.810125	−0.405063	−	0.914289i	$-0.632750\pi$
$11$	−2.68688	−0.810125	−0.405063	+	0.914289i	$0.632750\pi$
$12$	3.69205	1.06580
$13$	5.12547	1.42155	0.710775	−	0.703419i	$-0.248344\pi$
$13$	5.12547	1.42155	0.710775	+	0.703419i	$0.248344\pi$
$14$	−2.84469	−0.760274
$15$	0	0
$16$	2.24714	0.561785
$17$	0.967149	0.234568	0.117284	−	0.993098i	$-0.462581\pi$
$17$	0.967149	0.234568	0.117284	+	0.993098i	$0.462581\pi$
$18$	−2.38580	−0.562339
$19$	1.87461	0.430064	0.215032	−	0.976607i	$-0.431014\pi$
$19$	1.87461	0.430064	0.215032	+	0.976607i	$0.431014\pi$
$20$	0	0
$21$	1.19234	0.260190
$22$	6.41037	1.36669
$23$	−7.60212	−1.58515	−0.792575	−	0.609774i	$-0.791260\pi$
$23$	−7.60212	−1.58515	−0.792575	+	0.609774i	$0.791260\pi$
$24$	−4.03690	−0.824029
$25$	0	0
$26$	−12.2284	−2.39818
$27$	1.00000	0.192450
$28$	4.40218	0.831934
$29$	−9.33467	−1.73341	−0.866703	−	0.498825i	$-0.833765\pi$
$29$	−9.33467	−1.73341	−0.866703	+	0.498825i	$0.833765\pi$
$30$	0	0
$31$	−7.48104	−1.34363	−0.671817	−	0.740717i	$-0.734486\pi$
$31$	−7.48104	−1.34363	−0.671817	+	0.740717i	$0.734486\pi$
$32$	2.71257	0.479519
$33$	−2.68688	−0.467726
$34$	−2.30743	−0.395720
$35$	0	0
$36$	3.69205	0.615342
$37$	−8.35311	−1.37324	−0.686622	−	0.727015i	$-0.740907\pi$
$37$	−8.35311	−1.37324	−0.686622	+	0.727015i	$0.740907\pi$
$38$	−4.47244	−0.725526
$39$	5.12547	0.820733
$40$	0	0
$41$	0.858735	0.134112	0.0670559	−	0.997749i	$-0.478639\pi$
$41$	0.858735	0.134112	0.0670559	+	0.997749i	$0.478639\pi$
$42$	−2.84469	−0.438945
$43$	6.69665	1.02123	0.510615	−	0.859810i	$-0.329418\pi$
$43$	6.69665	1.02123	0.510615	+	0.859810i	$0.329418\pi$
$44$	−9.92010	−1.49551
$45$	0	0
$46$	18.1371	2.67418
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	2.24714	0.324347
$49$	−5.57833	−0.796904
$50$	0	0
$51$	0.967149	0.135428
$52$	18.9235	2.62422
$53$	8.42050	1.15664	0.578322	−	0.815809i	$-0.303708\pi$
$53$	8.42050	1.15664	0.578322	+	0.815809i	$0.303708\pi$
$54$	−2.38580	−0.324667
$55$	0	0
$56$	−4.81336	−0.643212
$57$	1.87461	0.248298
$58$	22.2707	2.92428
$59$	−11.2142	−1.45996	−0.729980	−	0.683469i	$-0.760471\pi$
$59$	−11.2142	−1.45996	−0.729980	+	0.683469i	$0.760471\pi$
$60$	0	0
$61$	−10.7671	−1.37859	−0.689295	−	0.724481i	$-0.742080\pi$
$61$	−10.7671	−1.37859	−0.689295	+	0.724481i	$0.742080\pi$
$62$	17.8483	2.26673
$63$	1.19234	0.150221
$64$	−10.9659	−1.37074
$65$	0	0
$66$	6.41037	0.789062
$67$	−2.45600	−0.300048	−0.150024	−	0.988682i	$-0.547935\pi$
$67$	−2.45600	−0.300048	−0.150024	+	0.988682i	$0.547935\pi$
$68$	3.57076	0.433019
$69$	−7.60212	−0.915187
$70$	0	0
$71$	−7.42913	−0.881675	−0.440838	−	0.897587i	$-0.645319\pi$
$71$	−7.42913	−0.881675	−0.440838	+	0.897587i	$0.645319\pi$
$72$	−4.03690	−0.475753
$73$	−5.18337	−0.606667	−0.303334	−	0.952884i	$-0.598100\pi$
$73$	−5.18337	−0.606667	−0.303334	+	0.952884i	$0.598100\pi$
$74$	19.9289	2.31668
$75$	0	0
$76$	6.92114	0.793910
$77$	−3.20368	−0.365093
$78$	−12.2284	−1.38459
$79$	9.80667	1.10334	0.551669	−	0.834063i	$-0.313991\pi$
$79$	9.80667	1.10334	0.551669	+	0.834063i	$0.313991\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−2.04877	−0.226249
$83$	4.00659	0.439781	0.219890	−	0.975525i	$-0.429430\pi$
$83$	4.00659	0.439781	0.219890	+	0.975525i	$0.429430\pi$
$84$	4.40218	0.480317
$85$	0	0
$86$	−15.9769	−1.72283
$87$	−9.33467	−1.00078
$88$	10.8467	1.15626
$89$	0.872329	0.0924667	0.0462333	−	0.998931i	$-0.485278\pi$
$89$	0.872329	0.0924667	0.0462333	+	0.998931i	$0.485278\pi$
$90$	0	0
$91$	6.11131	0.640639
$92$	−28.0674	−2.92623
$93$	−7.48104	−0.775747
$94$	2.38580	0.246077
$95$	0	0
$96$	2.71257	0.276850
$97$	−6.63229	−0.673407	−0.336704	−	0.941611i	$-0.609312\pi$
$97$	−6.63229	−0.673407	−0.336704	+	0.941611i	$0.609312\pi$
$98$	13.3088	1.34439
$99$	−2.68688	−0.270042
$100$	0	0
$101$	12.1860	1.21255	0.606274	−	0.795256i	$-0.292663\pi$
$101$	12.1860	1.21255	0.606274	+	0.795256i	$0.292663\pi$
$102$	−2.30743	−0.228469
$103$	−3.37168	−0.332222	−0.166111	−	0.986107i	$-0.553121\pi$
$103$	−3.37168	−0.332222	−0.166111	+	0.986107i	$0.553121\pi$
$104$	−20.6910	−2.02892
$105$	0	0
$106$	−20.0896	−1.95128
$107$	−11.7874	−1.13953	−0.569765	−	0.821808i	$-0.692966\pi$
$107$	−11.7874	−1.13953	−0.569765	+	0.821808i	$0.692966\pi$
$108$	3.69205	0.355268
$109$	3.50151	0.335384	0.167692	−	0.985839i	$-0.446369\pi$
$109$	3.50151	0.335384	0.167692	+	0.985839i	$0.446369\pi$
$110$	0	0
$111$	−8.35311	−0.792842
$112$	2.67935	0.253175
$113$	−4.70984	−0.443064	−0.221532	−	0.975153i	$-0.571106\pi$
$113$	−4.70984	−0.443064	−0.221532	+	0.975153i	$0.571106\pi$
$114$	−4.47244	−0.418882
$115$	0	0
$116$	−34.4641	−3.19991
$117$	5.12547	0.473850
$118$	26.7548	2.46298
$119$	1.15317	0.105711
$120$	0	0
$121$	−3.78067	−0.343697
$122$	25.6882	2.32570
$123$	0.858735	0.0774295
$124$	−27.6204	−2.48038
$125$	0	0
$126$	−2.84469	−0.253425
$127$	−1.51685	−0.134599	−0.0672994	−	0.997733i	$-0.521438\pi$
$127$	−1.51685	−0.134599	−0.0672994	+	0.997733i	$0.521438\pi$
$128$	20.7374	1.83294
$129$	6.69665	0.589607
$130$	0	0
$131$	−19.6769	−1.71918	−0.859591	−	0.510982i	$-0.829282\pi$
$131$	−19.6769	−1.71918	−0.859591	+	0.510982i	$0.829282\pi$
$132$	−9.92010	−0.863434
$133$	2.23517	0.193814
$134$	5.85954	0.506187
$135$	0	0
$136$	−3.90428	−0.334789
$137$	−14.4732	−1.23653	−0.618264	−	0.785971i	$-0.712164\pi$
$137$	−14.4732	−1.23653	−0.618264	+	0.785971i	$0.712164\pi$
$138$	18.1371	1.54394
$139$	0.397762	0.0337378	0.0168689	−	0.999858i	$-0.494630\pi$
$139$	0.397762	0.0337378	0.0168689	+	0.999858i	$0.494630\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	17.7244	1.48740
$143$	−13.7715	−1.15163
$144$	2.24714	0.187262
$145$	0	0
$146$	12.3665	1.02346
$147$	−5.57833	−0.460093
$148$	−30.8401	−2.53504
$149$	10.5936	0.867864	0.433932	−	0.900946i	$-0.357126\pi$
$149$	10.5936	0.867864	0.433932	+	0.900946i	$0.357126\pi$
$150$	0	0
$151$	16.7245	1.36102	0.680508	−	0.732740i	$-0.261759\pi$
$151$	16.7245	1.36102	0.680508	+	0.732740i	$0.261759\pi$
$152$	−7.56760	−0.613813
$153$	0.967149	0.0781893
$154$	7.64334	0.615918
$155$	0	0
$156$	18.9235	1.51509
$157$	15.7288	1.25529	0.627646	−	0.778499i	$-0.284019\pi$
$157$	15.7288	1.25529	0.627646	+	0.778499i	$0.284019\pi$
$158$	−23.3968	−1.86135
$159$	8.42050	0.667789
$160$	0	0
$161$	−9.06430	−0.714367
$162$	−2.38580	−0.187446
$163$	11.3372	0.887995	0.443998	−	0.896028i	$-0.353560\pi$
$163$	11.3372	0.887995	0.443998	+	0.896028i	$0.353560\pi$
$164$	3.17049	0.247574
$165$	0	0
$166$	−9.55894	−0.741917
$167$	−1.61989	−0.125351	−0.0626753	−	0.998034i	$-0.519963\pi$
$167$	−1.61989	−0.125351	−0.0626753	+	0.998034i	$0.519963\pi$
$168$	−4.81336	−0.371358
$169$	13.2705	1.02081
$170$	0	0
$171$	1.87461	0.143355
$172$	24.7244	1.88522
$173$	24.6582	1.87473	0.937364	−	0.348351i	$-0.113258\pi$
$173$	24.6582	1.87473	0.937364	+	0.348351i	$0.113258\pi$
$174$	22.2707	1.68834
$175$	0	0
$176$	−6.03780	−0.455116
$177$	−11.2142	−0.842908
$178$	−2.08120	−0.155993
$179$	−2.12475	−0.158811	−0.0794056	−	0.996842i	$-0.525302\pi$
$179$	−2.12475	−0.158811	−0.0794056	+	0.996842i	$0.525302\pi$
$180$	0	0
$181$	0.443183	0.0329415	0.0164708	−	0.999864i	$-0.494757\pi$
$181$	0.443183	0.0329415	0.0164708	+	0.999864i	$0.494757\pi$
$182$	−14.5804	−1.08077
$183$	−10.7671	−0.795929
$184$	30.6890	2.26242
$185$	0	0
$186$	17.8483	1.30870
$187$	−2.59861	−0.190029
$188$	−3.69205	−0.269271
$189$	1.19234	0.0867300
$190$	0	0
$191$	6.10367	0.441646	0.220823	−	0.975314i	$-0.429126\pi$
$191$	6.10367	0.441646	0.220823	+	0.975314i	$0.429126\pi$
$192$	−10.9659	−0.791398
$193$	3.79802	0.273387	0.136694	−	0.990613i	$-0.456352\pi$
$193$	3.79802	0.273387	0.136694	+	0.990613i	$0.456352\pi$
$194$	15.8233	1.13605
$195$	0	0
$196$	−20.5955	−1.47110
$197$	−3.25900	−0.232194	−0.116097	−	0.993238i	$-0.537038\pi$
$197$	−3.25900	−0.232194	−0.116097	+	0.993238i	$0.537038\pi$
$198$	6.41037	0.455565
$199$	−0.0824884	−0.00584745	−0.00292372	−	0.999996i	$-0.500931\pi$
$199$	−0.0824884	−0.00584745	−0.00292372	+	0.999996i	$0.500931\pi$
$200$	0	0
$201$	−2.45600	−0.173233
$202$	−29.0733	−2.04559
$203$	−11.1301	−0.781180
$204$	3.57076	0.250003
$205$	0	0
$206$	8.04417	0.560464
$207$	−7.60212	−0.528384
$208$	11.5177	0.798606
$209$	−5.03685	−0.348406
$210$	0	0
$211$	−21.9720	−1.51261	−0.756307	−	0.654217i	$-0.772998\pi$
$211$	−21.9720	−1.51261	−0.756307	+	0.654217i	$0.772998\pi$
$212$	31.0889	2.13519
$213$	−7.42913	−0.509036
$214$	28.1224	1.92241
$215$	0	0
$216$	−4.03690	−0.274676
$217$	−8.91994	−0.605525
$218$	−8.35390	−0.565798
$219$	−5.18337	−0.350260
$220$	0	0
$221$	4.95710	0.333450
$222$	19.9289	1.33754
$223$	−2.78392	−0.186425	−0.0932126	−	0.995646i	$-0.529714\pi$
$223$	−2.78392	−0.186425	−0.0932126	+	0.995646i	$0.529714\pi$
$224$	3.23430	0.216101
$225$	0	0
$226$	11.2367	0.747457
$227$	−7.69378	−0.510654	−0.255327	−	0.966855i	$-0.582183\pi$
$227$	−7.69378	−0.510654	−0.255327	+	0.966855i	$0.582183\pi$
$228$	6.92114	0.458364
$229$	4.01668	0.265430	0.132715	−	0.991154i	$-0.457631\pi$
$229$	4.01668	0.265430	0.132715	+	0.991154i	$0.457631\pi$
$230$	0	0
$231$	−3.20368	−0.210786
$232$	37.6831	2.47402
$233$	−10.4924	−0.687377	−0.343688	−	0.939084i	$-0.611676\pi$
$233$	−10.4924	−0.687377	−0.343688	+	0.939084i	$0.611676\pi$
$234$	−12.2284	−0.799393
$235$	0	0
$236$	−41.4033	−2.69512
$237$	9.80667	0.637012
$238$	−2.75123	−0.178336
$239$	−27.4470	−1.77540	−0.887699	−	0.460425i	$-0.847697\pi$
$239$	−27.4470	−1.77540	−0.887699	+	0.460425i	$0.847697\pi$
$240$	0	0
$241$	23.2503	1.49768	0.748841	−	0.662749i	$-0.230611\pi$
$241$	23.2503	1.49768	0.748841	+	0.662749i	$0.230611\pi$
$242$	9.01993	0.579823
$243$	1.00000	0.0641500
$244$	−39.7528	−2.54491
$245$	0	0
$246$	−2.04877	−0.130625
$247$	9.60825	0.611358
$248$	30.2002	1.91771
$249$	4.00659	0.253907
$250$	0	0
$251$	28.2831	1.78522	0.892608	−	0.450833i	$-0.148873\pi$
$251$	28.2831	1.78522	0.892608	+	0.450833i	$0.148873\pi$
$252$	4.40218	0.277311
$253$	20.4260	1.28417
$254$	3.61891	0.227070
$255$	0	0
$256$	−27.5435	−1.72147
$257$	5.57969	0.348051	0.174026	−	0.984741i	$-0.444322\pi$
$257$	5.57969	0.348051	0.174026	+	0.984741i	$0.444322\pi$
$258$	−15.9769	−0.994677
$259$	−9.95975	−0.618869
$260$	0	0
$261$	−9.33467	−0.577802
$262$	46.9453	2.90029
$263$	12.8628	0.793156	0.396578	−	0.918001i	$-0.370198\pi$
$263$	12.8628	0.793156	0.396578	+	0.918001i	$0.370198\pi$
$264$	10.8467	0.667566
$265$	0	0
$266$	−5.33267	−0.326967
$267$	0.872329	0.0533857
$268$	−9.06769	−0.553897
$269$	−10.6101	−0.646908	−0.323454	−	0.946244i	$-0.604844\pi$
$269$	−10.6101	−0.646908	−0.323454	+	0.946244i	$0.604844\pi$
$270$	0	0
$271$	−20.2404	−1.22951	−0.614757	−	0.788716i	$-0.710746\pi$
$271$	−20.2404	−1.22951	−0.614757	+	0.788716i	$0.710746\pi$
$272$	2.17332	0.131777
$273$	6.11131	0.369873
$274$	34.5302	2.08604
$275$	0	0
$276$	−28.0674	−1.68946
$277$	−23.2449	−1.39665	−0.698324	−	0.715782i	$-0.746070\pi$
$277$	−23.2449	−1.39665	−0.698324	+	0.715782i	$0.746070\pi$
$278$	−0.948982	−0.0569162
$279$	−7.48104	−0.447878
$280$	0	0
$281$	31.5740	1.88355	0.941773	−	0.336249i	$-0.109158\pi$
$281$	31.5740	1.88355	0.941773	+	0.336249i	$0.109158\pi$
$282$	2.38580	0.142072
$283$	−8.21270	−0.488194	−0.244097	−	0.969751i	$-0.578492\pi$
$283$	−8.21270	−0.488194	−0.244097	+	0.969751i	$0.578492\pi$
$284$	−27.4287	−1.62760
$285$	0	0
$286$	32.8562	1.94283
$287$	1.02390	0.0604391
$288$	2.71257	0.159840
$289$	−16.0646	−0.944978
$290$	0	0
$291$	−6.63229	−0.388792
$292$	−19.1373	−1.11992
$293$	−30.4424	−1.77847	−0.889233	−	0.457454i	$-0.848761\pi$
$293$	−30.4424	−1.77847	−0.889233	+	0.457454i	$0.848761\pi$
$294$	13.3088	0.776184
$295$	0	0
$296$	33.7207	1.95997
$297$	−2.68688	−0.155909
$298$	−25.2743	−1.46410
$299$	−38.9645	−2.25337
$300$	0	0
$301$	7.98468	0.460229
$302$	−39.9012	−2.29606
$303$	12.1860	0.700065
$304$	4.21250	0.241604
$305$	0	0
$306$	−2.30743	−0.131907
$307$	9.63268	0.549766	0.274883	−	0.961478i	$-0.411361\pi$
$307$	9.63268	0.549766	0.274883	+	0.961478i	$0.411361\pi$
$308$	−11.8281	−0.673970
$309$	−3.37168	−0.191808
$310$	0	0
$311$	9.90510	0.561667	0.280833	−	0.959757i	$-0.409389\pi$
$311$	9.90510	0.561667	0.280833	+	0.959757i	$0.409389\pi$
$312$	−20.6910	−1.17140
$313$	28.5259	1.61238	0.806190	−	0.591657i	$-0.201526\pi$
$313$	28.5259	1.61238	0.806190	+	0.591657i	$0.201526\pi$
$314$	−37.5257	−2.11770
$315$	0	0
$316$	36.2067	2.03679
$317$	−4.98153	−0.279790	−0.139895	−	0.990166i	$-0.544677\pi$
$317$	−4.98153	−0.279790	−0.139895	+	0.990166i	$0.544677\pi$
$318$	−20.0896	−1.12657
$319$	25.0812	1.40428
$320$	0	0
$321$	−11.7874	−0.657908
$322$	21.6256	1.20515
$323$	1.81302	0.100879
$324$	3.69205	0.205114
$325$	0	0
$326$	−27.0482	−1.49806
$327$	3.50151	0.193634
$328$	−3.46663	−0.191412
$329$	−1.19234	−0.0657358
$330$	0	0
$331$	12.8791	0.707899	0.353949	−	0.935265i	$-0.384839\pi$
$331$	12.8791	0.707899	0.353949	+	0.935265i	$0.384839\pi$
$332$	14.7925	0.811846
$333$	−8.35311	−0.457748
$334$	3.86473	0.211469
$335$	0	0
$336$	2.67935	0.146171
$337$	22.6261	1.23252	0.616262	−	0.787541i	$-0.288646\pi$
$337$	22.6261	1.23252	0.616262	+	0.787541i	$0.288646\pi$
$338$	−31.6608	−1.72212
$339$	−4.70984	−0.255803
$340$	0	0
$341$	20.1007	1.08851
$342$	−4.47244	−0.241842
$343$	−14.9976	−0.809796
$344$	−27.0337	−1.45756
$345$	0	0
$346$	−58.8296	−3.16270
$347$	−6.32410	−0.339495	−0.169748	−	0.985488i	$-0.554295\pi$
$347$	−6.32410	−0.339495	−0.169748	+	0.985488i	$0.554295\pi$
$348$	−34.4641	−1.84747
$349$	0.105596	0.00565243	0.00282621	−	0.999996i	$-0.499100\pi$
$349$	0.105596	0.00565243	0.00282621	+	0.999996i	$0.499100\pi$
$350$	0	0
$351$	5.12547	0.273578
$352$	−7.28835	−0.388470
$353$	6.54957	0.348598	0.174299	−	0.984693i	$-0.444234\pi$
$353$	6.54957	0.348598	0.174299	+	0.984693i	$0.444234\pi$
$354$	26.7548	1.42200
$355$	0	0
$356$	3.22068	0.170696
$357$	1.15317	0.0610322
$358$	5.06923	0.267917
$359$	−19.0004	−1.00280	−0.501402	−	0.865214i	$-0.667182\pi$
$359$	−19.0004	−1.00280	−0.501402	+	0.865214i	$0.667182\pi$
$360$	0	0
$361$	−15.4858	−0.815045
$362$	−1.05735	−0.0555729
$363$	−3.78067	−0.198434
$364$	22.5633	1.18264
$365$	0	0
$366$	25.6882	1.34275
$367$	−2.42929	−0.126808	−0.0634038	−	0.997988i	$-0.520196\pi$
$367$	−2.42929	−0.126808	−0.0634038	+	0.997988i	$0.520196\pi$
$368$	−17.0830	−0.890514
$369$	0.858735	0.0447040
$370$	0	0
$371$	10.0401	0.521256
$372$	−27.6204	−1.43205
$373$	21.8107	1.12932	0.564659	−	0.825324i	$-0.309008\pi$
$373$	21.8107	1.12932	0.564659	+	0.825324i	$0.309008\pi$
$374$	6.19978	0.320583
$375$	0	0
$376$	4.03690	0.208187
$377$	−47.8446	−2.46412
$378$	−2.84469	−0.146315
$379$	−26.2597	−1.34887	−0.674434	−	0.738335i	$-0.735612\pi$
$379$	−26.2597	−1.34887	−0.674434	+	0.738335i	$0.735612\pi$
$380$	0	0
$381$	−1.51685	−0.0777106
$382$	−14.5622	−0.745065
$383$	−4.87094	−0.248893	−0.124447	−	0.992226i	$-0.539716\pi$
$383$	−4.87094	−0.248893	−0.124447	+	0.992226i	$0.539716\pi$
$384$	20.7374	1.05825
$385$	0	0
$386$	−9.06132	−0.461209
$387$	6.69665	0.340410
$388$	−24.4868	−1.24313
$389$	35.6058	1.80529	0.902643	−	0.430389i	$-0.141624\pi$
$389$	35.6058	1.80529	0.902643	+	0.430389i	$0.141624\pi$
$390$	0	0
$391$	−7.35238	−0.371826
$392$	22.5191	1.13739
$393$	−19.6769	−0.992570
$394$	7.77533	0.391715
$395$	0	0
$396$	−9.92010	−0.498504
$397$	−19.4097	−0.974146	−0.487073	−	0.873361i	$-0.661935\pi$
$397$	−19.4097	−0.974146	−0.487073	+	0.873361i	$0.661935\pi$
$398$	0.196801	0.00986474
$399$	2.23517	0.111898
$400$	0	0
$401$	2.51164	0.125425	0.0627126	−	0.998032i	$-0.480025\pi$
$401$	2.51164	0.125425	0.0627126	+	0.998032i	$0.480025\pi$
$402$	5.85954	0.292247
$403$	−38.3439	−1.91004
$404$	44.9912	2.23840
$405$	0	0
$406$	26.5542	1.31786
$407$	22.4438	1.11250
$408$	−3.90428	−0.193291
$409$	−23.3785	−1.15599	−0.577996	−	0.816040i	$-0.696165\pi$
$409$	−23.3785	−1.15599	−0.577996	+	0.816040i	$0.696165\pi$
$410$	0	0
$411$	−14.4732	−0.713910
$412$	−12.4484	−0.613290
$413$	−13.3711	−0.657949
$414$	18.1371	0.891392
$415$	0	0
$416$	13.9032	0.681660
$417$	0.397762	0.0194785
$418$	12.0169	0.587767
$419$	−26.4200	−1.29070	−0.645352	−	0.763886i	$-0.723289\pi$
$419$	−26.4200	−1.29070	−0.645352	+	0.763886i	$0.723289\pi$
$420$	0	0
$421$	7.81317	0.380791	0.190395	−	0.981708i	$-0.439023\pi$
$421$	7.81317	0.380791	0.190395	+	0.981708i	$0.439023\pi$
$422$	52.4208	2.55181
$423$	−1.00000	−0.0486217
$424$	−33.9927	−1.65083
$425$	0	0
$426$	17.7244	0.858751
$427$	−12.8381	−0.621278
$428$	−43.5196	−2.10360
$429$	−13.7715	−0.664896
$430$	0	0
$431$	14.5878	0.702670	0.351335	−	0.936250i	$-0.385728\pi$
$431$	14.5878	0.702670	0.351335	+	0.936250i	$0.385728\pi$
$432$	2.24714	0.108116
$433$	−36.0701	−1.73342	−0.866708	−	0.498816i	$-0.833768\pi$
$433$	−36.0701	−1.73342	−0.866708	+	0.498816i	$0.833768\pi$
$434$	21.2812	1.02153
$435$	0	0
$436$	12.9277	0.619127
$437$	−14.2510	−0.681717
$438$	12.3665	0.590894
$439$	−30.7826	−1.46918	−0.734588	−	0.678514i	$-0.762624\pi$
$439$	−30.7826	−1.46918	−0.734588	+	0.678514i	$0.762624\pi$
$440$	0	0
$441$	−5.57833	−0.265635
$442$	−11.8266	−0.562536
$443$	−34.0184	−1.61626	−0.808132	−	0.589002i	$-0.799521\pi$
$443$	−34.0184	−1.61626	−0.808132	+	0.589002i	$0.799521\pi$
$444$	−30.8401	−1.46361
$445$	0	0
$446$	6.64189	0.314502
$447$	10.5936	0.501062
$448$	−13.0751	−0.617741
$449$	0.223246	0.0105356	0.00526781	−	0.999986i	$-0.498323\pi$
$449$	0.223246	0.0105356	0.00526781	+	0.999986i	$0.498323\pi$
$450$	0	0
$451$	−2.30732	−0.108647
$452$	−17.3890	−0.817908
$453$	16.7245	0.785783
$454$	18.3558	0.861482
$455$	0	0
$456$	−7.56760	−0.354385
$457$	−27.1629	−1.27062	−0.635312	−	0.772255i	$-0.719129\pi$
$457$	−27.1629	−1.27062	−0.635312	+	0.772255i	$0.719129\pi$
$458$	−9.58300	−0.447784
$459$	0.967149	0.0451426
$460$	0	0
$461$	−16.7028	−0.777927	−0.388963	−	0.921253i	$-0.627167\pi$
$461$	−16.7028	−0.777927	−0.388963	+	0.921253i	$0.627167\pi$
$462$	7.64334	0.355600
$463$	−25.8498	−1.20134	−0.600672	−	0.799496i	$-0.705100\pi$
$463$	−25.8498	−1.20134	−0.600672	+	0.799496i	$0.705100\pi$
$464$	−20.9763	−0.973801
$465$	0	0
$466$	25.0327	1.15962
$467$	14.8478	0.687074	0.343537	−	0.939139i	$-0.388375\pi$
$467$	14.8478	0.687074	0.343537	+	0.939139i	$0.388375\pi$
$468$	18.9235	0.874740
$469$	−2.92839	−0.135220
$470$	0	0
$471$	15.7288	0.724743
$472$	45.2704	2.08374
$473$	−17.9931	−0.827324
$474$	−23.3968	−1.07465
$475$	0	0
$476$	4.25756	0.195145
$477$	8.42050	0.385548
$478$	65.4830	2.99512
$479$	30.8478	1.40947	0.704736	−	0.709469i	$-0.251065\pi$
$479$	30.8478	1.40947	0.704736	+	0.709469i	$0.251065\pi$
$480$	0	0
$481$	−42.8137	−1.95214
$482$	−55.4706	−2.52662
$483$	−9.06430	−0.412440
$484$	−13.9584	−0.634474
$485$	0	0
$486$	−2.38580	−0.108222
$487$	−36.9060	−1.67237	−0.836184	−	0.548449i	$-0.815219\pi$
$487$	−36.9060	−1.67237	−0.836184	+	0.548449i	$0.815219\pi$
$488$	43.4658	1.96761
$489$	11.3372	0.512684
$490$	0	0
$491$	−9.98900	−0.450797	−0.225399	−	0.974267i	$-0.572368\pi$
$491$	−9.98900	−0.450797	−0.225399	+	0.974267i	$0.572368\pi$
$492$	3.17049	0.142937
$493$	−9.02802	−0.406601
$494$	−22.9234	−1.03137
$495$	0	0
$496$	−16.8109	−0.754833
$497$	−8.85805	−0.397338
$498$	−9.55894	−0.428346
$499$	−22.0497	−0.987082	−0.493541	−	0.869723i	$-0.664298\pi$
$499$	−22.0497	−0.987082	−0.493541	+	0.869723i	$0.664298\pi$
$500$	0	0
$501$	−1.61989	−0.0723712
$502$	−67.4780	−3.01169
$503$	25.9351	1.15639	0.578195	−	0.815899i	$-0.303757\pi$
$503$	25.9351	1.15639	0.578195	+	0.815899i	$0.303757\pi$
$504$	−4.81336	−0.214404
$505$	0	0
$506$	−48.7324	−2.16642
$507$	13.2705	0.589363
$508$	−5.60029	−0.248473
$509$	−2.02078	−0.0895693	−0.0447847	−	0.998997i	$-0.514260\pi$
$509$	−2.02078	−0.0895693	−0.0447847	+	0.998997i	$0.514260\pi$
$510$	0	0
$511$	−6.18034	−0.273402
$512$	24.2385	1.07120
$513$	1.87461	0.0827659
$514$	−13.3120	−0.587169
$515$	0	0
$516$	24.7244	1.08843
$517$	2.68688	0.118169
$518$	23.7620	1.04404
$519$	24.6582	1.08237
$520$	0	0
$521$	−34.5368	−1.51308	−0.756542	−	0.653945i	$-0.773113\pi$
$521$	−34.5368	−1.51308	−0.756542	+	0.653945i	$0.773113\pi$
$522$	22.2707	0.974761
$523$	−10.4466	−0.456796	−0.228398	−	0.973568i	$-0.573349\pi$
$523$	−10.4466	−0.456796	−0.228398	+	0.973568i	$0.573349\pi$
$524$	−72.6483	−3.17365
$525$	0	0
$526$	−30.6881	−1.33807
$527$	−7.23527	−0.315173
$528$	−6.03780	−0.262761
$529$	34.7922	1.51270
$530$	0	0
$531$	−11.2142	−0.486653
$532$	8.25236	0.357785
$533$	4.40143	0.190647
$534$	−2.08120	−0.0900625
$535$	0	0
$536$	9.91463	0.428247
$537$	−2.12475	−0.0916897
$538$	25.3135	1.09134
$539$	14.9883	0.645592
$540$	0	0
$541$	6.16979	0.265260	0.132630	−	0.991166i	$-0.457658\pi$
$541$	6.16979	0.265260	0.132630	+	0.991166i	$0.457658\pi$
$542$	48.2895	2.07421
$543$	0.443183	0.0190188
$544$	2.62346	0.112480
$545$	0	0
$546$	−14.5804	−0.623982
$547$	−0.944715	−0.0403931	−0.0201965	−	0.999796i	$-0.506429\pi$
$547$	−0.944715	−0.0403931	−0.0201965	+	0.999796i	$0.506429\pi$
$548$	−53.4357	−2.28266
$549$	−10.7671	−0.459530
$550$	0	0
$551$	−17.4988	−0.745476
$552$	30.6890	1.30621
$553$	11.6929	0.497232
$554$	55.4576	2.35617
$555$	0	0
$556$	1.46856	0.0622808
$557$	−11.0339	−0.467520	−0.233760	−	0.972294i	$-0.575103\pi$
$557$	−11.0339	−0.467520	−0.233760	+	0.972294i	$0.575103\pi$
$558$	17.8483	0.755578
$559$	34.3235	1.45173
$560$	0	0
$561$	−2.59861	−0.109714
$562$	−75.3293	−3.17757
$563$	−6.64368	−0.279998	−0.139999	−	0.990152i	$-0.544710\pi$
$563$	−6.64368	−0.279998	−0.139999	+	0.990152i	$0.544710\pi$
$564$	−3.69205	−0.155463
$565$	0	0
$566$	19.5939	0.823592
$567$	1.19234	0.0500736
$568$	29.9906	1.25838
$569$	0.879548	0.0368726	0.0184363	−	0.999830i	$-0.494131\pi$
$569$	0.879548	0.0368726	0.0184363	+	0.999830i	$0.494131\pi$
$570$	0	0
$571$	−7.30539	−0.305721	−0.152860	−	0.988248i	$-0.548849\pi$
$571$	−7.30539	−0.305721	−0.152860	+	0.988248i	$0.548849\pi$
$572$	−50.8452	−2.12595
$573$	6.10367	0.254985
$574$	−2.44283	−0.101962
$575$	0	0
$576$	−10.9659	−0.456914
$577$	−12.0868	−0.503179	−0.251589	−	0.967834i	$-0.580953\pi$
$577$	−12.0868	−0.503179	−0.251589	+	0.967834i	$0.580953\pi$
$578$	38.3270	1.59419
$579$	3.79802	0.157840
$580$	0	0
$581$	4.77722	0.198192
$582$	15.8233	0.655898
$583$	−22.6249	−0.937027
$584$	20.9247	0.865872
$585$	0	0
$586$	72.6296	3.00030
$587$	41.5536	1.71510	0.857551	−	0.514399i	$-0.171985\pi$
$587$	41.5536	1.71510	0.857551	+	0.514399i	$0.171985\pi$
$588$	−20.5955	−0.849343
$589$	−14.0240	−0.577849
$590$	0	0
$591$	−3.25900	−0.134057
$592$	−18.7706	−0.771467
$593$	−36.4434	−1.49655	−0.748276	−	0.663388i	$-0.769118\pi$
$593$	−36.4434	−1.49655	−0.748276	+	0.663388i	$0.769118\pi$
$594$	6.41037	0.263021
$595$	0	0
$596$	39.1122	1.60210
$597$	−0.0824884	−0.00337602
$598$	92.9615	3.80148
$599$	−43.0297	−1.75815	−0.879073	−	0.476688i	$-0.841837\pi$
$599$	−43.0297	−1.75815	−0.879073	+	0.476688i	$0.841837\pi$
$600$	0	0
$601$	26.1555	1.06690	0.533452	−	0.845830i	$-0.320894\pi$
$601$	26.1555	1.06690	0.533452	+	0.845830i	$0.320894\pi$
$602$	−19.0499	−0.776415
$603$	−2.45600	−0.100016
$604$	61.7475	2.51247
$605$	0	0
$606$	−29.0733	−1.18102
$607$	14.2392	0.577953	0.288976	−	0.957336i	$-0.406685\pi$
$607$	14.2392	0.577953	0.288976	+	0.957336i	$0.406685\pi$
$608$	5.08500	0.206224
$609$	−11.1301	−0.451014
$610$	0	0
$611$	−5.12547	−0.207355
$612$	3.57076	0.144340
$613$	9.75780	0.394114	0.197057	−	0.980392i	$-0.436862\pi$
$613$	9.75780	0.394114	0.197057	+	0.980392i	$0.436862\pi$
$614$	−22.9817	−0.927465
$615$	0	0
$616$	12.9329	0.521082
$617$	36.3651	1.46400	0.732002	−	0.681303i	$-0.238586\pi$
$617$	36.3651	1.46400	0.732002	+	0.681303i	$0.238586\pi$
$618$	8.04417	0.323584
$619$	0.982621	0.0394949	0.0197474	−	0.999805i	$-0.493714\pi$
$619$	0.982621	0.0394949	0.0197474	+	0.999805i	$0.493714\pi$
$620$	0	0
$621$	−7.60212	−0.305062
$622$	−23.6316	−0.947541
$623$	1.04011	0.0416712
$624$	11.5177	0.461075
$625$	0	0
$626$	−68.0572	−2.72011
$627$	−5.03685	−0.201152
$628$	58.0714	2.31730
$629$	−8.07870	−0.322119
$630$	0	0
$631$	−20.4904	−0.815709	−0.407855	−	0.913047i	$-0.633723\pi$
$631$	−20.4904	−0.815709	−0.407855	+	0.913047i	$0.633723\pi$
$632$	−39.5886	−1.57475
$633$	−21.9720	−0.873308
$634$	11.8849	0.472011
$635$	0	0
$636$	31.0889	1.23276
$637$	−28.5916	−1.13284
$638$	−59.8387	−2.36904
$639$	−7.42913	−0.293892
$640$	0	0
$641$	19.9400	0.787585	0.393792	−	0.919199i	$-0.371163\pi$
$641$	19.9400	0.787585	0.393792	+	0.919199i	$0.371163\pi$
$642$	28.1224	1.10990
$643$	50.4839	1.99089	0.995446	−	0.0953270i	$-0.0303897\pi$
$643$	50.4839	1.99089	0.995446	+	0.0953270i	$0.0303897\pi$
$644$	−33.4659	−1.31874
$645$	0	0
$646$	−4.32552	−0.170185
$647$	23.8703	0.938438	0.469219	−	0.883082i	$-0.344536\pi$
$647$	23.8703	0.938438	0.469219	+	0.883082i	$0.344536\pi$
$648$	−4.03690	−0.158584
$649$	30.1311	1.18275
$650$	0	0
$651$	−8.91994	−0.349600
$652$	41.8574	1.63926
$653$	−20.3088	−0.794746	−0.397373	−	0.917657i	$-0.630078\pi$
$653$	−20.3088	−0.794746	−0.397373	+	0.917657i	$0.630078\pi$
$654$	−8.35390	−0.326663
$655$	0	0
$656$	1.92970	0.0753420
$657$	−5.18337	−0.202222
$658$	2.84469	0.110897
$659$	32.5448	1.26777	0.633883	−	0.773429i	$-0.281460\pi$
$659$	32.5448	1.26777	0.633883	+	0.773429i	$0.281460\pi$
$660$	0	0
$661$	10.8368	0.421504	0.210752	−	0.977540i	$-0.432409\pi$
$661$	10.8368	0.421504	0.210752	+	0.977540i	$0.432409\pi$
$662$	−30.7270	−1.19424
$663$	4.95710	0.192518
$664$	−16.1742	−0.627681
$665$	0	0
$666$	19.9289	0.772228
$667$	70.9633	2.74771
$668$	−5.98071	−0.231401
$669$	−2.78392	−0.107633
$670$	0	0
$671$	28.9300	1.11683
$672$	3.23430	0.124766
$673$	−21.4323	−0.826156	−0.413078	−	0.910696i	$-0.635546\pi$
$673$	−21.4323	−0.826156	−0.413078	+	0.910696i	$0.635546\pi$
$674$	−53.9815	−2.07929
$675$	0	0
$676$	48.9953	1.88444
$677$	2.47078	0.0949597	0.0474799	−	0.998872i	$-0.484881\pi$
$677$	2.47078	0.0949597	0.0474799	+	0.998872i	$0.484881\pi$
$678$	11.2367	0.431544
$679$	−7.90794	−0.303479
$680$	0	0
$681$	−7.69378	−0.294826
$682$	−47.9562	−1.83634
$683$	35.0933	1.34281	0.671403	−	0.741092i	$-0.265692\pi$
$683$	35.0933	1.34281	0.671403	+	0.741092i	$0.265692\pi$
$684$	6.92114	0.264637
$685$	0	0
$686$	35.7814	1.36614
$687$	4.01668	0.153246
$688$	15.0483	0.573711
$689$	43.1590	1.64423
$690$	0	0
$691$	−30.0956	−1.14489	−0.572445	−	0.819943i	$-0.694005\pi$
$691$	−30.0956	−1.14489	−0.572445	+	0.819943i	$0.694005\pi$
$692$	91.0393	3.46080
$693$	−3.20368	−0.121698
$694$	15.0881	0.572735
$695$	0	0
$696$	37.6831	1.42838
$697$	0.830525	0.0314584
$698$	−0.251931	−0.00953574
$699$	−10.4924	−0.396857
$700$	0	0
$701$	42.6929	1.61249	0.806244	−	0.591583i	$-0.201497\pi$
$701$	42.6929	1.61249	0.806244	+	0.591583i	$0.201497\pi$
$702$	−12.2284	−0.461530
$703$	−15.6588	−0.590583
$704$	29.4642	1.11047
$705$	0	0
$706$	−15.6260	−0.588091
$707$	14.5298	0.546450
$708$	−41.4033	−1.55603
$709$	14.9760	0.562434	0.281217	−	0.959644i	$-0.409262\pi$
$709$	14.9760	0.562434	0.281217	+	0.959644i	$0.409262\pi$
$710$	0	0
$711$	9.80667	0.367779
$712$	−3.52150	−0.131974
$713$	56.8717	2.12986
$714$	−2.75123	−0.102962
$715$	0	0
$716$	−7.84468	−0.293169
$717$	−27.4470	−1.02503
$718$	45.3313	1.69175
$719$	−16.9803	−0.633257	−0.316629	−	0.948550i	$-0.602551\pi$
$719$	−16.9803	−0.633257	−0.316629	+	0.948550i	$0.602551\pi$
$720$	0	0
$721$	−4.02019	−0.149720
$722$	36.9462	1.37499
$723$	23.2503	0.864687
$724$	1.63625	0.0608109
$725$	0	0
$726$	9.01993	0.334761
$727$	21.1613	0.784828	0.392414	−	0.919789i	$-0.371640\pi$
$727$	21.1613	0.784828	0.392414	+	0.919789i	$0.371640\pi$
$728$	−24.6707	−0.914358
$729$	1.00000	0.0370370
$730$	0	0
$731$	6.47665	0.239548
$732$	−39.7528	−1.46931
$733$	17.7710	0.656387	0.328194	−	0.944611i	$-0.393560\pi$
$733$	17.7710	0.656387	0.328194	+	0.944611i	$0.393560\pi$
$734$	5.79579	0.213927
$735$	0	0
$736$	−20.6213	−0.760110
$737$	6.59899	0.243077
$738$	−2.04877	−0.0754163
$739$	−7.02220	−0.258316	−0.129158	−	0.991624i	$-0.541227\pi$
$739$	−7.02220	−0.258316	−0.129158	+	0.991624i	$0.541227\pi$
$740$	0	0
$741$	9.60825	0.352968
$742$	−23.9537	−0.879367
$743$	−11.4581	−0.420358	−0.210179	−	0.977663i	$-0.567405\pi$
$743$	−11.4581	−0.420358	−0.210179	+	0.977663i	$0.567405\pi$
$744$	30.2002	1.10719
$745$	0	0
$746$	−52.0361	−1.90518
$747$	4.00659	0.146594
$748$	−9.59421	−0.350799
$749$	−14.0546	−0.513543
$750$	0	0
$751$	−20.7268	−0.756332	−0.378166	−	0.925738i	$-0.623445\pi$
$751$	−20.7268	−0.756332	−0.378166	+	0.925738i	$0.623445\pi$
$752$	−2.24714	−0.0819447
$753$	28.2831	1.03070
$754$	114.148	4.15702
$755$	0	0
$756$	4.40218	0.160106
$757$	10.9366	0.397498	0.198749	−	0.980050i	$-0.436312\pi$
$757$	10.9366	0.397498	0.198749	+	0.980050i	$0.436312\pi$
$758$	62.6504	2.27556
$759$	20.4260	0.741416
$760$	0	0
$761$	6.68955	0.242496	0.121248	−	0.992622i	$-0.461310\pi$
$761$	6.68955	0.242496	0.121248	+	0.992622i	$0.461310\pi$
$762$	3.61891	0.131099
$763$	4.17499	0.151145
$764$	22.5351	0.815290
$765$	0	0
$766$	11.6211	0.419887
$767$	−57.4779	−2.07541
$768$	−27.5435	−0.993889
$769$	−29.7060	−1.07122	−0.535612	−	0.844464i	$-0.679919\pi$
$769$	−29.7060	−1.07122	−0.535612	+	0.844464i	$0.679919\pi$
$770$	0	0
$771$	5.57969	0.200948
$772$	14.0225	0.504680
$773$	50.0327	1.79955	0.899775	−	0.436354i	$-0.143731\pi$
$773$	50.0327	1.79955	0.899775	+	0.436354i	$0.143731\pi$
$774$	−15.9769	−0.574277
$775$	0	0
$776$	26.7739	0.961127
$777$	−9.95975	−0.357304
$778$	−84.9484	−3.04555
$779$	1.60979	0.0576767
$780$	0	0
$781$	19.9612	0.714267
$782$	17.5413	0.627276
$783$	−9.33467	−0.333594
$784$	−12.5353	−0.447688
$785$	0	0
$786$	46.9453	1.67448
$787$	55.2085	1.96797	0.983985	−	0.178253i	$-0.0570444\pi$
$787$	55.2085	1.96797	0.983985	+	0.178253i	$0.0570444\pi$
$788$	−12.0324	−0.428636
$789$	12.8628	0.457929
$790$	0	0
$791$	−5.61573	−0.199672
$792$	10.8467	0.385420
$793$	−55.1867	−1.95974
$794$	46.3078	1.64340
$795$	0	0
$796$	−0.304551	−0.0107945
$797$	−9.23096	−0.326977	−0.163489	−	0.986545i	$-0.552275\pi$
$797$	−9.23096	−0.326977	−0.163489	+	0.986545i	$0.552275\pi$
$798$	−5.33267	−0.188774
$799$	−0.967149	−0.0342153
$800$	0	0
$801$	0.872329	0.0308222
$802$	−5.99227	−0.211594
$803$	13.9271	0.491477
$804$	−9.06769	−0.319793
$805$	0	0
$806$	91.4809	3.22228
$807$	−10.6101	−0.373492
$808$	−49.1935	−1.73062
$809$	21.2914	0.748566	0.374283	−	0.927314i	$-0.377889\pi$
$809$	21.2914	0.748566	0.374283	+	0.927314i	$0.377889\pi$
$810$	0	0
$811$	−44.5854	−1.56560	−0.782802	−	0.622270i	$-0.786210\pi$
$811$	−44.5854	−1.56560	−0.782802	+	0.622270i	$0.786210\pi$
$812$	−41.0929	−1.44208
$813$	−20.2404	−0.709861
$814$	−53.5465	−1.87680
$815$	0	0
$816$	2.17332	0.0760813
$817$	12.5536	0.439194
$818$	55.7764	1.95018
$819$	6.11131	0.213546
$820$	0	0
$821$	−35.6050	−1.24262	−0.621312	−	0.783563i	$-0.713400\pi$
$821$	−35.6050	−1.24262	−0.621312	+	0.783563i	$0.713400\pi$
$822$	34.5302	1.20438
$823$	10.7836	0.375892	0.187946	−	0.982179i	$-0.439817\pi$
$823$	10.7836	0.375892	0.187946	+	0.982179i	$0.439817\pi$
$824$	13.6111	0.474167
$825$	0	0
$826$	31.9008	1.10997
$827$	−32.9146	−1.14455	−0.572277	−	0.820061i	$-0.693940\pi$
$827$	−32.9146	−1.14455	−0.572277	+	0.820061i	$0.693940\pi$
$828$	−28.0674	−0.975410
$829$	−25.8865	−0.899074	−0.449537	−	0.893262i	$-0.648411\pi$
$829$	−25.8865	−0.899074	−0.449537	+	0.893262i	$0.648411\pi$
$830$	0	0
$831$	−23.2449	−0.806355
$832$	−56.2056	−1.94858
$833$	−5.39507	−0.186928
$834$	−0.948982	−0.0328606
$835$	0	0
$836$	−18.5963	−0.643166
$837$	−7.48104	−0.258582
$838$	63.0330	2.17744
$839$	28.2987	0.976980	0.488490	−	0.872569i	$-0.337548\pi$
$839$	28.2987	0.976980	0.488490	+	0.872569i	$0.337548\pi$
$840$	0	0
$841$	58.1361	2.00469
$842$	−18.6407	−0.642400
$843$	31.5740	1.08747
$844$	−81.1217	−2.79232
$845$	0	0
$846$	2.38580	0.0820256
$847$	−4.50784	−0.154891
$848$	18.9220	0.649785
$849$	−8.21270	−0.281859
$850$	0	0
$851$	63.5013	2.17680
$852$	−27.4287	−0.939693
$853$	14.7962	0.506614	0.253307	−	0.967386i	$-0.418482\pi$
$853$	14.7962	0.506614	0.253307	+	0.967386i	$0.418482\pi$
$854$	30.6291	1.04811
$855$	0	0
$856$	47.5845	1.62640
$857$	−2.96468	−0.101272	−0.0506358	−	0.998717i	$-0.516125\pi$
$857$	−2.96468	−0.101272	−0.0506358	+	0.998717i	$0.516125\pi$
$858$	32.8562	1.12169
$859$	31.3340	1.06910	0.534551	−	0.845136i	$-0.320481\pi$
$859$	31.3340	1.06910	0.534551	+	0.845136i	$0.320481\pi$
$860$	0	0
$861$	1.02390	0.0348946
$862$	−34.8036	−1.18542
$863$	12.6764	0.431509	0.215755	−	0.976448i	$-0.430779\pi$
$863$	12.6764	0.431509	0.215755	+	0.976448i	$0.430779\pi$
$864$	2.71257	0.0922834
$865$	0	0
$866$	86.0560	2.92430
$867$	−16.0646	−0.545583
$868$	−32.9329	−1.11781
$869$	−26.3494	−0.893841
$870$	0	0
$871$	−12.5882	−0.426534
$872$	−14.1352	−0.478679
$873$	−6.63229	−0.224469
$874$	34.0000	1.15007
$875$	0	0
$876$	−19.1373	−0.646588
$877$	−27.3080	−0.922125	−0.461063	−	0.887368i	$-0.652532\pi$
$877$	−27.3080	−0.922125	−0.461063	+	0.887368i	$0.652532\pi$
$878$	73.4413	2.47852
$879$	−30.4424	−1.02680
$880$	0	0
$881$	−48.1526	−1.62230	−0.811151	−	0.584836i	$-0.801159\pi$
$881$	−48.1526	−1.62230	−0.811151	+	0.584836i	$0.801159\pi$
$882$	13.3088	0.448130
$883$	37.5633	1.26411	0.632053	−	0.774925i	$-0.282213\pi$
$883$	37.5633	1.26411	0.632053	+	0.774925i	$0.282213\pi$
$884$	18.3019	0.615558
$885$	0	0
$886$	81.1612	2.72666
$887$	53.6172	1.80029	0.900144	−	0.435592i	$-0.143461\pi$
$887$	53.6172	1.80029	0.900144	+	0.435592i	$0.143461\pi$
$888$	33.7207	1.13159
$889$	−1.80860	−0.0606585
$890$	0	0
$891$	−2.68688	−0.0900139
$892$	−10.2784	−0.344146
$893$	−1.87461	−0.0627313
$894$	−25.2743	−0.845299
$895$	0	0
$896$	24.7260	0.826039
$897$	−38.9645	−1.30099
$898$	−0.532621	−0.0177738
$899$	69.8330	2.32906
$900$	0	0
$901$	8.14387	0.271312
$902$	5.50481	0.183290
$903$	7.98468	0.265714
$904$	19.0131	0.632368
$905$	0	0
$906$	−39.9012	−1.32563
$907$	31.6933	1.05236	0.526180	−	0.850373i	$-0.323624\pi$
$907$	31.6933	1.05236	0.526180	+	0.850373i	$0.323624\pi$
$908$	−28.4058	−0.942681
$909$	12.1860	0.404183
$910$	0	0
$911$	13.9704	0.462859	0.231429	−	0.972852i	$-0.425660\pi$
$911$	13.9704	0.462859	0.231429	+	0.972852i	$0.425660\pi$
$912$	4.21250	0.139490
$913$	−10.7652	−0.356277
$914$	64.8052	2.14357
$915$	0	0
$916$	14.8298	0.489990
$917$	−23.4616	−0.774770
$918$	−2.30743	−0.0761564
$919$	−34.9368	−1.15246	−0.576229	−	0.817288i	$-0.695477\pi$
$919$	−34.9368	−1.15246	−0.576229	+	0.817288i	$0.695477\pi$
$920$	0	0
$921$	9.63268	0.317408
$922$	39.8496	1.31238
$923$	−38.0778	−1.25335
$924$	−11.8281	−0.389117
$925$	0	0
$926$	61.6726	2.02669
$927$	−3.37168	−0.110741
$928$	−25.3209	−0.831201
$929$	25.4857	0.836157	0.418079	−	0.908411i	$-0.362704\pi$
$929$	25.4857	0.836157	0.418079	+	0.908411i	$0.362704\pi$
$930$	0	0
$931$	−10.4572	−0.342720
$932$	−38.7383	−1.26892
$933$	9.90510	0.324278
$934$	−35.4239	−1.15911
$935$	0	0
$936$	−20.6910	−0.676307
$937$	12.1188	0.395904	0.197952	−	0.980212i	$-0.436571\pi$
$937$	12.1188	0.395904	0.197952	+	0.980212i	$0.436571\pi$
$938$	6.98656	0.228119
$939$	28.5259	0.930908
$940$	0	0
$941$	14.9260	0.486573	0.243286	−	0.969955i	$-0.421775\pi$
$941$	14.9260	0.486573	0.243286	+	0.969955i	$0.421775\pi$
$942$	−37.5257	−1.22265
$943$	−6.52820	−0.212588
$944$	−25.1998	−0.820183
$945$	0	0
$946$	42.9280	1.39571
$947$	−10.8787	−0.353509	−0.176755	−	0.984255i	$-0.556560\pi$
$947$	−10.8787	−0.353509	−0.176755	+	0.984255i	$0.556560\pi$
$948$	36.2067	1.17594
$949$	−26.5672	−0.862409
$950$	0	0
$951$	−4.98153	−0.161537
$952$	−4.65523	−0.150877
$953$	−40.6292	−1.31611	−0.658054	−	0.752970i	$-0.728620\pi$
$953$	−40.6292	−1.31611	−0.658054	+	0.752970i	$0.728620\pi$
$954$	−20.0896	−0.650426
$955$	0	0
$956$	−101.336	−3.27743
$957$	25.0812	0.810759
$958$	−73.5968	−2.37780
$959$	−17.2570	−0.557256
$960$	0	0
$961$	24.9659	0.805352
$962$	102.145	3.29329
$963$	−11.7874	−0.379843
$964$	85.8412	2.76476
$965$	0	0
$966$	21.6256	0.695793
$967$	−8.36117	−0.268877	−0.134438	−	0.990922i	$-0.542923\pi$
$967$	−8.36117	−0.268877	−0.134438	+	0.990922i	$0.542923\pi$
$968$	15.2622	0.490545
$969$	1.81302	0.0582427
$970$	0	0
$971$	−18.4198	−0.591120	−0.295560	−	0.955324i	$-0.595506\pi$
$971$	−18.4198	−0.591120	−0.295560	+	0.955324i	$0.595506\pi$
$972$	3.69205	0.118423
$973$	0.474268	0.0152043
$974$	88.0503	2.82131
$975$	0	0
$976$	−24.1952	−0.774471
$977$	−0.448275	−0.0143416	−0.00717080	−	0.999974i	$-0.502283\pi$
$977$	−0.448275	−0.0143416	−0.00717080	+	0.999974i	$0.502283\pi$
$978$	−27.0482	−0.864907
$979$	−2.34384	−0.0749096
$980$	0	0
$981$	3.50151	0.111795
$982$	23.8318	0.760503
$983$	40.7150	1.29861	0.649303	−	0.760529i	$-0.275061\pi$
$983$	40.7150	1.29861	0.649303	+	0.760529i	$0.275061\pi$
$984$	−3.46663	−0.110512
$985$	0	0
$986$	21.5391	0.685943
$987$	−1.19234	−0.0379526
$988$	35.4742	1.12858
$989$	−50.9087	−1.61880
$990$	0	0
$991$	−7.49645	−0.238133	−0.119066	−	0.992886i	$-0.537990\pi$
$991$	−7.49645	−0.238133	−0.119066	+	0.992886i	$0.537990\pi$
$992$	−20.2928	−0.644298
$993$	12.8791	0.408705
$994$	21.1335	0.670315
$995$	0	0
$996$	14.7925	0.468720
$997$	33.1196	1.04891	0.524455	−	0.851438i	$-0.324269\pi$
$997$	33.1196	1.04891	0.524455	+	0.851438i	$0.324269\pi$
$998$	52.6063	1.66522
$999$	−8.35311	−0.264281

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bf.1.2		10
5.2	odd	4		705.2.c.b.424.2	✓	20
5.3	odd	4		705.2.c.b.424.19	yes	20
5.4	even	2		3525.2.a.bg.1.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.2.c.b.424.2	✓	20	5.2	odd	4
705.2.c.b.424.19	yes	20	5.3	odd	4
3525.2.a.bf.1.2		10	1.1	even	1	trivial
3525.2.a.bg.1.9		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)

\(f(q)\)	\(=\)	\(q-2.38580 q^{2} +1.00000 q^{3} +3.69205 q^{4} -2.38580 q^{6} +1.19234 q^{7} -4.03690 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.38580 q^{2} +1.00000 q^{3} +3.69205 q^{4} -2.38580 q^{6} +1.19234 q^{7} -4.03690 q^{8} +1.00000 q^{9} -2.68688 q^{11} +3.69205 q^{12} +5.12547 q^{13} -2.84469 q^{14} +2.24714 q^{16} +0.967149 q^{17} -2.38580 q^{18} +1.87461 q^{19} +1.19234 q^{21} +6.41037 q^{22} -7.60212 q^{23} -4.03690 q^{24} -12.2284 q^{26} +1.00000 q^{27} +4.40218 q^{28} -9.33467 q^{29} -7.48104 q^{31} +2.71257 q^{32} -2.68688 q^{33} -2.30743 q^{34} +3.69205 q^{36} -8.35311 q^{37} -4.47244 q^{38} +5.12547 q^{39} +0.858735 q^{41} -2.84469 q^{42} +6.69665 q^{43} -9.92010 q^{44} +18.1371 q^{46} -1.00000 q^{47} +2.24714 q^{48} -5.57833 q^{49} +0.967149 q^{51} +18.9235 q^{52} +8.42050 q^{53} -2.38580 q^{54} -4.81336 q^{56} +1.87461 q^{57} +22.2707 q^{58} -11.2142 q^{59} -10.7671 q^{61} +17.8483 q^{62} +1.19234 q^{63} -10.9659 q^{64} +6.41037 q^{66} -2.45600 q^{67} +3.57076 q^{68} -7.60212 q^{69} -7.42913 q^{71} -4.03690 q^{72} -5.18337 q^{73} +19.9289 q^{74} +6.92114 q^{76} -3.20368 q^{77} -12.2284 q^{78} +9.80667 q^{79} +1.00000 q^{81} -2.04877 q^{82} +4.00659 q^{83} +4.40218 q^{84} -15.9769 q^{86} -9.33467 q^{87} +10.8467 q^{88} +0.872329 q^{89} +6.11131 q^{91} -28.0674 q^{92} -7.48104 q^{93} +2.38580 q^{94} +2.71257 q^{96} -6.63229 q^{97} +13.3088 q^{98} -2.68688 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} + 10 q^{3} + 7 q^{4} - 3 q^{6} - 9 q^{8} + 10 q^{9}+O(q^{10}) \) 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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