LMFDB - Embedded newform 3525.2.a.bi.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$28.1472667125$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 3 x^{12} - 17 x^{11} + 51 x^{10} + 106 x^{9} - 316 x^{8} - 288 x^{7} + 852 x^{6} + 309 x^{5} + \cdots - 2 $ x^13 - 3x^12 - 17x^11 + 51x^10 + 106x^9 - 316x^8 - 288x^7 + 852x^6 + 309x^5 - 923x^4 - 107x^3 + 293x^2 + 12x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 705)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.0655745$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0655745 q^{2} +1.00000 q^{3} -1.99570 q^{4} +0.0655745 q^{6} +1.54896 q^{7} -0.262016 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.0655745 q^{2} +1.00000 q^{3} -1.99570 q^{4} +0.0655745 q^{6} +1.54896 q^{7} -0.262016 q^{8} +1.00000 q^{9} -1.06261 q^{11} -1.99570 q^{12} -2.81638 q^{13} +0.101572 q^{14} +3.97422 q^{16} +6.13170 q^{17} +0.0655745 q^{18} -1.66708 q^{19} +1.54896 q^{21} -0.0696802 q^{22} -1.16150 q^{23} -0.262016 q^{24} -0.184682 q^{26} +1.00000 q^{27} -3.09126 q^{28} -1.45219 q^{29} +2.64469 q^{31} +0.784639 q^{32} -1.06261 q^{33} +0.402083 q^{34} -1.99570 q^{36} +5.18954 q^{37} -0.109318 q^{38} -2.81638 q^{39} -7.11022 q^{41} +0.101572 q^{42} +4.61168 q^{43} +2.12065 q^{44} -0.0761650 q^{46} +1.00000 q^{47} +3.97422 q^{48} -4.60072 q^{49} +6.13170 q^{51} +5.62064 q^{52} +4.84221 q^{53} +0.0655745 q^{54} -0.405852 q^{56} -1.66708 q^{57} -0.0952267 q^{58} -2.40342 q^{59} +10.2873 q^{61} +0.173424 q^{62} +1.54896 q^{63} -7.89698 q^{64} -0.0696802 q^{66} -5.05399 q^{67} -12.2370 q^{68} -1.16150 q^{69} +10.7415 q^{71} -0.262016 q^{72} -3.43369 q^{73} +0.340301 q^{74} +3.32700 q^{76} -1.64594 q^{77} -0.184682 q^{78} +5.61624 q^{79} +1.00000 q^{81} -0.466249 q^{82} +4.31116 q^{83} -3.09126 q^{84} +0.302408 q^{86} -1.45219 q^{87} +0.278421 q^{88} +11.2875 q^{89} -4.36246 q^{91} +2.31801 q^{92} +2.64469 q^{93} +0.0655745 q^{94} +0.784639 q^{96} +6.69673 q^{97} -0.301690 q^{98} -1.06261 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 3 q^{2} + 13 q^{3} + 17 q^{4} + 3 q^{6} - 4 q^{7} + 15 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 3 * q^2 + 13 * q^3 + 17 * q^4 + 3 * q^6 - 4 * q^7 + 15 * q^8 + 13 * q^9	$ 13 q + 3 q^{2} + 13 q^{3} + 17 q^{4} + 3 q^{6} - 4 q^{7} + 15 q^{8} + 13 q^{9} + 16 q^{11} + 17 q^{12} - 8 q^{13} - 4 q^{14} + 29 q^{16} + 12 q^{17} + 3 q^{18} + 28 q^{19} - 4 q^{21} + 6 q^{23} + 15 q^{24} + 4 q^{26} + 13 q^{27} - 20 q^{28} + 12 q^{29} + 26 q^{31} + 53 q^{32} + 16 q^{33} + 8 q^{34} + 17 q^{36} - 4 q^{37} + 2 q^{38} - 8 q^{39} + 24 q^{41} - 4 q^{42} - 6 q^{43} + 4 q^{44} + 16 q^{46} + 13 q^{47} + 29 q^{48} + 21 q^{49} + 12 q^{51} - 32 q^{52} + 6 q^{53} + 3 q^{54} + 28 q^{57} - 4 q^{58} + 34 q^{59} + 24 q^{61} + 30 q^{62} - 4 q^{63} + 13 q^{64} - 24 q^{67} + 44 q^{68} + 6 q^{69} + 20 q^{71} + 15 q^{72} - 6 q^{73} + 20 q^{74} + 66 q^{76} - 2 q^{77} + 4 q^{78} + 6 q^{79} + 13 q^{81} + 20 q^{82} + 14 q^{83} - 20 q^{84} + 48 q^{86} + 12 q^{87} - 22 q^{88} + 36 q^{89} + 4 q^{91} + 4 q^{92} + 26 q^{93} + 3 q^{94} + 53 q^{96} - 32 q^{97} - 39 q^{98} + 16 q^{99}+O(q^{100}) $ 13 * q + 3 * q^2 + 13 * q^3 + 17 * q^4 + 3 * q^6 - 4 * q^7 + 15 * q^8 + 13 * q^9 + 16 * q^11 + 17 * q^12 - 8 * q^13 - 4 * q^14 + 29 * q^16 + 12 * q^17 + 3 * q^18 + 28 * q^19 - 4 * q^21 + 6 * q^23 + 15 * q^24 + 4 * q^26 + 13 * q^27 - 20 * q^28 + 12 * q^29 + 26 * q^31 + 53 * q^32 + 16 * q^33 + 8 * q^34 + 17 * q^36 - 4 * q^37 + 2 * q^38 - 8 * q^39 + 24 * q^41 - 4 * q^42 - 6 * q^43 + 4 * q^44 + 16 * q^46 + 13 * q^47 + 29 * q^48 + 21 * q^49 + 12 * q^51 - 32 * q^52 + 6 * q^53 + 3 * q^54 + 28 * q^57 - 4 * q^58 + 34 * q^59 + 24 * q^61 + 30 * q^62 - 4 * q^63 + 13 * q^64 - 24 * q^67 + 44 * q^68 + 6 * q^69 + 20 * q^71 + 15 * q^72 - 6 * q^73 + 20 * q^74 + 66 * q^76 - 2 * q^77 + 4 * q^78 + 6 * q^79 + 13 * q^81 + 20 * q^82 + 14 * q^83 - 20 * q^84 + 48 * q^86 + 12 * q^87 - 22 * q^88 + 36 * q^89 + 4 * q^91 + 4 * q^92 + 26 * q^93 + 3 * q^94 + 53 * q^96 - 32 * q^97 - 39 * 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 $

$2$	0.0655745	0.0463681	0.0231841	−	0.999731i	$-0.492620\pi$
$2$	0.0655745	0.0463681	0.0231841	+	0.999731i	$0.492620\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.99570	−0.997850
$5$	0	0
$5$	0	0
$6$	0.0655745	0.0267707
$7$	1.54896	0.585452	0.292726	−	0.956196i	$-0.405438\pi$
$7$	1.54896	0.585452	0.292726	+	0.956196i	$0.405438\pi$
$8$	−0.262016	−0.0926366
$9$	1.00000	0.333333
$10$	0	0
$11$	−1.06261	−0.320390	−0.160195	−	0.987085i	$-0.551212\pi$
$11$	−1.06261	−0.320390	−0.160195	+	0.987085i	$0.551212\pi$
$12$	−1.99570	−0.576109
$13$	−2.81638	−0.781123	−0.390561	−	0.920577i	$-0.627719\pi$
$13$	−2.81638	−0.781123	−0.390561	+	0.920577i	$0.627719\pi$
$14$	0.101572	0.0271463
$15$	0	0
$16$	3.97422	0.993555
$17$	6.13170	1.48716	0.743578	−	0.668649i	$-0.233127\pi$
$17$	6.13170	1.48716	0.743578	+	0.668649i	$0.233127\pi$
$18$	0.0655745	0.0154560
$19$	−1.66708	−0.382455	−0.191228	−	0.981546i	$-0.561247\pi$
$19$	−1.66708	−0.382455	−0.191228	+	0.981546i	$0.561247\pi$
$20$	0	0
$21$	1.54896	0.338011
$22$	−0.0696802	−0.0148559
$23$	−1.16150	−0.242190	−0.121095	−	0.992641i	$-0.538641\pi$
$23$	−1.16150	−0.242190	−0.121095	+	0.992641i	$0.538641\pi$
$24$	−0.262016	−0.0534838
$25$	0	0
$26$	−0.184682	−0.0362192
$27$	1.00000	0.192450
$28$	−3.09126	−0.584193
$29$	−1.45219	−0.269665	−0.134833	−	0.990868i	$-0.543050\pi$
$29$	−1.45219	−0.269665	−0.134833	+	0.990868i	$0.543050\pi$
$30$	0	0
$31$	2.64469	0.475001	0.237500	−	0.971387i	$-0.423672\pi$
$31$	2.64469	0.475001	0.237500	+	0.971387i	$0.423672\pi$
$32$	0.784639	0.138706
$33$	−1.06261	−0.184977
$34$	0.402083	0.0689566
$35$	0	0
$36$	−1.99570	−0.332617
$37$	5.18954	0.853155	0.426577	−	0.904451i	$-0.359719\pi$
$37$	5.18954	0.853155	0.426577	+	0.904451i	$0.359719\pi$
$38$	−0.109318	−0.0177337
$39$	−2.81638	−0.450981
$40$	0	0
$41$	−7.11022	−1.11043	−0.555215	−	0.831707i	$-0.687364\pi$
$41$	−7.11022	−1.11043	−0.555215	+	0.831707i	$0.687364\pi$
$42$	0.101572	0.0156729
$43$	4.61168	0.703274	0.351637	−	0.936136i	$-0.385625\pi$
$43$	4.61168	0.703274	0.351637	+	0.936136i	$0.385625\pi$
$44$	2.12065	0.319701
$45$	0	0
$46$	−0.0761650	−0.0112299
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	3.97422	0.573629
$49$	−4.60072	−0.657246
$50$	0	0
$51$	6.13170	0.858610
$52$	5.62064	0.779443
$53$	4.84221	0.665129	0.332565	−	0.943080i	$-0.392086\pi$
$53$	4.84221	0.665129	0.332565	+	0.943080i	$0.392086\pi$
$54$	0.0655745	0.00892355
$55$	0	0
$56$	−0.405852	−0.0542343
$57$	−1.66708	−0.220811
$58$	−0.0952267	−0.0125039
$59$	−2.40342	−0.312899	−0.156449	−	0.987686i	$-0.550005\pi$
$59$	−2.40342	−0.312899	−0.156449	+	0.987686i	$0.550005\pi$
$60$	0	0
$61$	10.2873	1.31715	0.658576	−	0.752514i	$-0.271159\pi$
$61$	10.2873	1.31715	0.658576	+	0.752514i	$0.271159\pi$
$62$	0.173424	0.0220249
$63$	1.54896	0.195151
$64$	−7.89698	−0.987123
$65$	0	0
$66$	−0.0696802	−0.00857704
$67$	−5.05399	−0.617443	−0.308722	−	0.951152i	$-0.599901\pi$
$67$	−5.05399	−0.617443	−0.308722	+	0.951152i	$0.599901\pi$
$68$	−12.2370	−1.48396
$69$	−1.16150	−0.139829
$70$	0	0
$71$	10.7415	1.27478	0.637392	−	0.770540i	$-0.280013\pi$
$71$	10.7415	1.27478	0.637392	+	0.770540i	$0.280013\pi$
$72$	−0.262016	−0.0308789
$73$	−3.43369	−0.401883	−0.200941	−	0.979603i	$-0.564400\pi$
$73$	−3.43369	−0.401883	−0.200941	+	0.979603i	$0.564400\pi$
$74$	0.340301	0.0395592
$75$	0	0
$76$	3.32700	0.381633
$77$	−1.64594	−0.187573
$78$	−0.184682	−0.0209112
$79$	5.61624	0.631876	0.315938	−	0.948780i	$-0.397681\pi$
$79$	5.61624	0.631876	0.315938	+	0.948780i	$0.397681\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−0.466249	−0.0514886
$83$	4.31116	0.473211	0.236605	−	0.971606i	$-0.423965\pi$
$83$	4.31116	0.473211	0.236605	+	0.971606i	$0.423965\pi$
$84$	−3.09126	−0.337284
$85$	0	0
$86$	0.302408	0.0326095
$87$	−1.45219	−0.155691
$88$	0.278421	0.0296798
$89$	11.2875	1.19648	0.598239	−	0.801318i	$-0.295867\pi$
$89$	11.2875	1.19648	0.598239	+	0.801318i	$0.295867\pi$
$90$	0	0
$91$	−4.36246	−0.457310
$92$	2.31801	0.241670
$93$	2.64469	0.274242
$94$	0.0655745	0.00676349
$95$	0	0
$96$	0.784639	0.0800819
$97$	6.69673	0.679950	0.339975	−	0.940434i	$-0.389581\pi$
$97$	6.69673	0.679950	0.339975	+	0.940434i	$0.389581\pi$
$98$	−0.301690	−0.0304753
$99$	−1.06261	−0.106797
$100$	0	0
$101$	8.18433	0.814371	0.407186	−	0.913345i	$-0.366510\pi$
$101$	8.18433	0.814371	0.407186	+	0.913345i	$0.366510\pi$
$102$	0.402083	0.0398121
$103$	10.6872	1.05304	0.526522	−	0.850162i	$-0.323496\pi$
$103$	10.6872	1.05304	0.526522	+	0.850162i	$0.323496\pi$
$104$	0.737936	0.0723605
$105$	0	0
$106$	0.317526	0.0308408
$107$	7.96273	0.769787	0.384893	−	0.922961i	$-0.374238\pi$
$107$	7.96273	0.769787	0.384893	+	0.922961i	$0.374238\pi$
$108$	−1.99570	−0.192036
$109$	12.6645	1.21304	0.606521	−	0.795067i	$-0.292565\pi$
$109$	12.6645	1.21304	0.606521	+	0.795067i	$0.292565\pi$
$110$	0	0
$111$	5.18954	0.492569
$112$	6.15591	0.581679
$113$	7.39978	0.696113	0.348057	−	0.937474i	$-0.386842\pi$
$113$	7.39978	0.696113	0.348057	+	0.937474i	$0.386842\pi$
$114$	−0.109318	−0.0102386
$115$	0	0
$116$	2.89814	0.269086
$117$	−2.81638	−0.260374
$118$	−0.157603	−0.0145085
$119$	9.49776	0.870658
$120$	0	0
$121$	−9.87086	−0.897351
$122$	0.674584	0.0610739
$123$	−7.11022	−0.641107
$124$	−5.27801	−0.473979
$125$	0	0
$126$	0.101572	0.00904878
$127$	−9.24574	−0.820427	−0.410213	−	0.911990i	$-0.634546\pi$
$127$	−9.24574	−0.820427	−0.410213	+	0.911990i	$0.634546\pi$
$128$	−2.08712	−0.184477
$129$	4.61168	0.406036
$130$	0	0
$131$	0.889591	0.0777239	0.0388620	−	0.999245i	$-0.487627\pi$
$131$	0.889591	0.0777239	0.0388620	+	0.999245i	$0.487627\pi$
$132$	2.12065	0.184579
$133$	−2.58225	−0.223909
$134$	−0.331413	−0.0286297
$135$	0	0
$136$	−1.60660	−0.137765
$137$	−18.0787	−1.54457	−0.772284	−	0.635277i	$-0.780886\pi$
$137$	−18.0787	−1.54457	−0.772284	+	0.635277i	$0.780886\pi$
$138$	−0.0761650	−0.00648359
$139$	1.72846	0.146606	0.0733029	−	0.997310i	$-0.476646\pi$
$139$	1.72846	0.146606	0.0733029	+	0.997310i	$0.476646\pi$
$140$	0	0
$141$	1.00000	0.0842152
$142$	0.704369	0.0591094
$143$	2.99272	0.250263
$144$	3.97422	0.331185
$145$	0	0
$146$	−0.225162	−0.0186346
$147$	−4.60072	−0.379461
$148$	−10.3568	−0.851321
$149$	13.6868	1.12127	0.560634	−	0.828064i	$-0.310557\pi$
$149$	13.6868	1.12127	0.560634	+	0.828064i	$0.310557\pi$
$150$	0	0
$151$	9.67723	0.787522	0.393761	−	0.919213i	$-0.371174\pi$
$151$	9.67723	0.787522	0.393761	+	0.919213i	$0.371174\pi$
$152$	0.436802	0.0354294
$153$	6.13170	0.495719
$154$	−0.107932	−0.00869740
$155$	0	0
$156$	5.62064	0.450012
$157$	−10.6539	−0.850276	−0.425138	−	0.905129i	$-0.639774\pi$
$157$	−10.6539	−0.850276	−0.425138	+	0.905129i	$0.639774\pi$
$158$	0.368282	0.0292989
$159$	4.84221	0.384013
$160$	0	0
$161$	−1.79912	−0.141791
$162$	0.0655745	0.00515202
$163$	2.64395	0.207090	0.103545	−	0.994625i	$-0.466981\pi$
$163$	2.64395	0.207090	0.103545	+	0.994625i	$0.466981\pi$
$164$	14.1899	1.10804
$165$	0	0
$166$	0.282702	0.0219419
$167$	−14.0673	−1.08856	−0.544278	−	0.838905i	$-0.683196\pi$
$167$	−14.0673	−1.08856	−0.544278	+	0.838905i	$0.683196\pi$
$168$	−0.405852	−0.0313122
$169$	−5.06802	−0.389847
$170$	0	0
$171$	−1.66708	−0.127485
$172$	−9.20352	−0.701762
$173$	−0.851604	−0.0647463	−0.0323731	−	0.999476i	$-0.510306\pi$
$173$	−0.851604	−0.0647463	−0.0323731	+	0.999476i	$0.510306\pi$
$174$	−0.0952267	−0.00721912
$175$	0	0
$176$	−4.22305	−0.318324
$177$	−2.40342	−0.180652
$178$	0.740175	0.0554784
$179$	5.79978	0.433496	0.216748	−	0.976228i	$-0.430455\pi$
$179$	5.79978	0.433496	0.216748	+	0.976228i	$0.430455\pi$
$180$	0	0
$181$	4.53580	0.337143	0.168572	−	0.985689i	$-0.446085\pi$
$181$	4.53580	0.337143	0.168572	+	0.985689i	$0.446085\pi$
$182$	−0.286066	−0.0212046
$183$	10.2873	0.760459
$184$	0.304332	0.0224357
$185$	0	0
$186$	0.173424	0.0127161
$187$	−6.51562	−0.476469
$188$	−1.99570	−0.145551
$189$	1.54896	0.112670
$190$	0	0
$191$	16.5775	1.19951	0.599753	−	0.800185i	$-0.295265\pi$
$191$	16.5775	1.19951	0.599753	+	0.800185i	$0.295265\pi$
$192$	−7.89698	−0.569916
$193$	7.26754	0.523129	0.261564	−	0.965186i	$-0.415762\pi$
$193$	7.26754	0.523129	0.261564	+	0.965186i	$0.415762\pi$
$194$	0.439135	0.0315280
$195$	0	0
$196$	9.18166	0.655833
$197$	5.81105	0.414020	0.207010	−	0.978339i	$-0.433627\pi$
$197$	5.81105	0.414020	0.207010	+	0.978339i	$0.433627\pi$
$198$	−0.0696802	−0.00495196
$199$	21.2679	1.50764	0.753822	−	0.657078i	$-0.228208\pi$
$199$	21.2679	1.50764	0.753822	+	0.657078i	$0.228208\pi$
$200$	0	0
$201$	−5.05399	−0.356481
$202$	0.536683	0.0377609
$203$	−2.24939	−0.157876
$204$	−12.2370	−0.856764
$205$	0	0
$206$	0.700809	0.0488277
$207$	−1.16150	−0.0807301
$208$	−11.1929	−0.776088
$209$	1.77146	0.122535
$210$	0	0
$211$	3.79411	0.261197	0.130599	−	0.991435i	$-0.458310\pi$
$211$	3.79411	0.261197	0.130599	+	0.991435i	$0.458310\pi$
$212$	−9.66361	−0.663699
$213$	10.7415	0.735997
$214$	0.522152	0.0356936
$215$	0	0
$216$	−0.262016	−0.0178279
$217$	4.09652	0.278090
$218$	0.830470	0.0562465
$219$	−3.43369	−0.232027
$220$	0	0
$221$	−17.2692	−1.16165
$222$	0.340301	0.0228395
$223$	−13.2239	−0.885539	−0.442770	−	0.896635i	$-0.646004\pi$
$223$	−13.2239	−0.885539	−0.442770	+	0.896635i	$0.646004\pi$
$224$	1.21537	0.0812057
$225$	0	0
$226$	0.485237	0.0322775
$227$	4.81241	0.319411	0.159706	−	0.987165i	$-0.448946\pi$
$227$	4.81241	0.319411	0.159706	+	0.987165i	$0.448946\pi$
$228$	3.32700	0.220336
$229$	11.8693	0.784343	0.392172	−	0.919892i	$-0.371724\pi$
$229$	11.8693	0.784343	0.392172	+	0.919892i	$0.371724\pi$
$230$	0	0
$231$	−1.64594	−0.108295
$232$	0.380497	0.0249809
$233$	7.67172	0.502591	0.251296	−	0.967910i	$-0.419143\pi$
$233$	7.67172	0.502591	0.251296	+	0.967910i	$0.419143\pi$
$234$	−0.184682	−0.0120731
$235$	0	0
$236$	4.79651	0.312226
$237$	5.61624	0.364814
$238$	0.622811	0.0403708
$239$	5.66300	0.366309	0.183155	−	0.983084i	$-0.441369\pi$
$239$	5.66300	0.366309	0.183155	+	0.983084i	$0.441369\pi$
$240$	0	0
$241$	22.6462	1.45877	0.729384	−	0.684104i	$-0.239807\pi$
$241$	22.6462	1.45877	0.729384	+	0.684104i	$0.239807\pi$
$242$	−0.647276	−0.0416085
$243$	1.00000	0.0641500
$244$	−20.5304	−1.31432
$245$	0	0
$246$	−0.466249	−0.0297269
$247$	4.69514	0.298744
$248$	−0.692951	−0.0440024
$249$	4.31116	0.273208
$250$	0	0
$251$	29.9890	1.89289	0.946445	−	0.322865i	$-0.104646\pi$
$251$	29.9890	1.89289	0.946445	+	0.322865i	$0.104646\pi$
$252$	−3.09126	−0.194731
$253$	1.23423	0.0775952
$254$	−0.606285	−0.0380417
$255$	0	0
$256$	15.6571	0.978569
$257$	1.95068	0.121680	0.0608401	−	0.998148i	$-0.480622\pi$
$257$	1.95068	0.121680	0.0608401	+	0.998148i	$0.480622\pi$
$258$	0.302408	0.0188271
$259$	8.03839	0.499481
$260$	0	0
$261$	−1.45219	−0.0898885
$262$	0.0583345	0.00360391
$263$	−0.280153	−0.0172750	−0.00863750	−	0.999963i	$-0.502749\pi$
$263$	−0.280153	−0.0172750	−0.00863750	+	0.999963i	$0.502749\pi$
$264$	0.278421	0.0171356
$265$	0	0
$266$	−0.169329	−0.0103823
$267$	11.2875	0.690787
$268$	10.0862	0.616116
$269$	−21.7483	−1.32602	−0.663008	−	0.748612i	$-0.730721\pi$
$269$	−21.7483	−1.32602	−0.663008	+	0.748612i	$0.730721\pi$
$270$	0	0
$271$	−21.5923	−1.31164	−0.655820	−	0.754917i	$-0.727677\pi$
$271$	−21.5923	−1.31164	−0.655820	+	0.754917i	$0.727677\pi$
$272$	24.3687	1.47757
$273$	−4.36246	−0.264028
$274$	−1.18550	−0.0716188
$275$	0	0
$276$	2.31801	0.139528
$277$	−19.9667	−1.19968	−0.599842	−	0.800118i	$-0.704770\pi$
$277$	−19.9667	−1.19968	−0.599842	+	0.800118i	$0.704770\pi$
$278$	0.113343	0.00679784
$279$	2.64469	0.158334
$280$	0	0
$281$	−29.3734	−1.75227	−0.876137	−	0.482063i	$-0.839888\pi$
$281$	−29.3734	−1.75227	−0.876137	+	0.482063i	$0.839888\pi$
$282$	0.0655745	0.00390490
$283$	−22.5990	−1.34337	−0.671686	−	0.740836i	$-0.734430\pi$
$283$	−22.5990	−1.34337	−0.671686	+	0.740836i	$0.734430\pi$
$284$	−21.4369	−1.27204
$285$	0	0
$286$	0.196246	0.0116043
$287$	−11.0135	−0.650104
$288$	0.784639	0.0462353
$289$	20.5977	1.21163
$290$	0	0
$291$	6.69673	0.392569
$292$	6.85261	0.401019
$293$	15.0205	0.877507	0.438753	−	0.898608i	$-0.355420\pi$
$293$	15.0205	0.877507	0.438753	+	0.898608i	$0.355420\pi$
$294$	−0.301690	−0.0175949
$295$	0	0
$296$	−1.35974	−0.0790334
$297$	−1.06261	−0.0616590
$298$	0.897506	0.0519911
$299$	3.27123	0.189180
$300$	0	0
$301$	7.14331	0.411733
$302$	0.634579	0.0365159
$303$	8.18433	0.470177
$304$	−6.62535	−0.379990
$305$	0	0
$306$	0.402083	0.0229855
$307$	29.4609	1.68143	0.840713	−	0.541482i	$-0.182136\pi$
$307$	29.4609	1.68143	0.840713	+	0.541482i	$0.182136\pi$
$308$	3.28481	0.187169
$309$	10.6872	0.607975
$310$	0	0
$311$	30.4080	1.72428	0.862141	−	0.506669i	$-0.169123\pi$
$311$	30.4080	1.72428	0.862141	+	0.506669i	$0.169123\pi$
$312$	0.737936	0.0417774
$313$	−16.5641	−0.936260	−0.468130	−	0.883660i	$-0.655072\pi$
$313$	−16.5641	−0.936260	−0.468130	+	0.883660i	$0.655072\pi$
$314$	−0.698625	−0.0394257
$315$	0	0
$316$	−11.2083	−0.630517
$317$	24.7720	1.39133	0.695667	−	0.718364i	$-0.255109\pi$
$317$	24.7720	1.39133	0.695667	+	0.718364i	$0.255109\pi$
$318$	0.317526	0.0178059
$319$	1.54312	0.0863980
$320$	0	0
$321$	7.96273	0.444437
$322$	−0.117977	−0.00657458
$323$	−10.2221	−0.568770
$324$	−1.99570	−0.110872
$325$	0	0
$326$	0.173376	0.00960239
$327$	12.6645	0.700350
$328$	1.86299	0.102866
$329$	1.54896	0.0853970
$330$	0	0
$331$	34.4304	1.89246	0.946232	−	0.323488i	$-0.104855\pi$
$331$	34.4304	1.89246	0.946232	+	0.323488i	$0.104855\pi$
$332$	−8.60377	−0.472193
$333$	5.18954	0.284385
$334$	−0.922452	−0.0504744
$335$	0	0
$336$	6.15591	0.335832
$337$	11.0332	0.601017	0.300508	−	0.953779i	$-0.402844\pi$
$337$	11.0332	0.601017	0.300508	+	0.953779i	$0.402844\pi$
$338$	−0.332332	−0.0180765
$339$	7.39978	0.401901
$340$	0	0
$341$	−2.81028	−0.152185
$342$	−0.109318	−0.00591125
$343$	−17.9691	−0.970238
$344$	−1.20833	−0.0651489
$345$	0	0
$346$	−0.0558435	−0.00300217
$347$	−16.8298	−0.903470	−0.451735	−	0.892152i	$-0.649195\pi$
$347$	−16.8298	−0.903470	−0.451735	+	0.892152i	$0.649195\pi$
$348$	2.89814	0.155357
$349$	−11.7920	−0.631212	−0.315606	−	0.948890i	$-0.602208\pi$
$349$	−11.7920	−0.631212	−0.315606	+	0.948890i	$0.602208\pi$
$350$	0	0
$351$	−2.81638	−0.150327
$352$	−0.833767	−0.0444399
$353$	30.6239	1.62995	0.814973	−	0.579498i	$-0.196751\pi$
$353$	30.6239	1.62995	0.814973	+	0.579498i	$0.196751\pi$
$354$	−0.157603	−0.00837651
$355$	0	0
$356$	−22.5266	−1.19391
$357$	9.49776	0.502675
$358$	0.380317	0.0201004
$359$	−3.82869	−0.202070	−0.101035	−	0.994883i	$-0.532215\pi$
$359$	−3.82869	−0.202070	−0.101035	+	0.994883i	$0.532215\pi$
$360$	0	0
$361$	−16.2208	−0.853728
$362$	0.297433	0.0156327
$363$	−9.87086	−0.518086
$364$	8.70616	0.456327
$365$	0	0
$366$	0.674584	0.0352611
$367$	−31.1252	−1.62472	−0.812362	−	0.583153i	$-0.801819\pi$
$367$	−31.1252	−1.62472	−0.812362	+	0.583153i	$0.801819\pi$
$368$	−4.61607	−0.240629
$369$	−7.11022	−0.370143
$370$	0	0
$371$	7.50040	0.389401
$372$	−5.27801	−0.273652
$373$	−33.0735	−1.71248	−0.856241	−	0.516577i	$-0.827206\pi$
$373$	−33.0735	−1.71248	−0.856241	+	0.516577i	$0.827206\pi$
$374$	−0.427258	−0.0220930
$375$	0	0
$376$	−0.262016	−0.0135124
$377$	4.08992	0.210642
$378$	0.101572	0.00522431
$379$	3.47466	0.178481	0.0892405	−	0.996010i	$-0.471556\pi$
$379$	3.47466	0.178481	0.0892405	+	0.996010i	$0.471556\pi$
$380$	0	0
$381$	−9.24574	−0.473674
$382$	1.08706	0.0556189
$383$	3.68658	0.188375	0.0941876	−	0.995554i	$-0.469975\pi$
$383$	3.68658	0.188375	0.0941876	+	0.995554i	$0.469975\pi$
$384$	−2.08712	−0.106508
$385$	0	0
$386$	0.476565	0.0242565
$387$	4.61168	0.234425
$388$	−13.3647	−0.678488
$389$	−22.9043	−1.16129	−0.580647	−	0.814155i	$-0.697200\pi$
$389$	−22.9043	−1.16129	−0.580647	+	0.814155i	$0.697200\pi$
$390$	0	0
$391$	−7.12199	−0.360175
$392$	1.20546	0.0608850
$393$	0.889591	0.0448739
$394$	0.381056	0.0191973
$395$	0	0
$396$	2.12065	0.106567
$397$	−24.7423	−1.24178	−0.620891	−	0.783897i	$-0.713229\pi$
$397$	−24.7423	−1.24178	−0.620891	+	0.783897i	$0.713229\pi$
$398$	1.39463	0.0699067
$399$	−2.58225	−0.129274
$400$	0	0
$401$	4.81836	0.240617	0.120309	−	0.992737i	$-0.461612\pi$
$401$	4.81836	0.240617	0.120309	+	0.992737i	$0.461612\pi$
$402$	−0.331413	−0.0165294
$403$	−7.44845	−0.371034
$404$	−16.3335	−0.812620
$405$	0	0
$406$	−0.147502	−0.00732042
$407$	−5.51446	−0.273342
$408$	−1.60660	−0.0795387
$409$	32.1271	1.58858	0.794291	−	0.607537i	$-0.207842\pi$
$409$	32.1271	1.58858	0.794291	+	0.607537i	$0.207842\pi$
$410$	0	0
$411$	−18.0787	−0.891757
$412$	−21.3285	−1.05078
$413$	−3.72281	−0.183187
$414$	−0.0761650	−0.00374330
$415$	0	0
$416$	−2.20984	−0.108346
$417$	1.72846	0.0846429
$418$	0.116163	0.00568170
$419$	−31.8673	−1.55682	−0.778410	−	0.627756i	$-0.783973\pi$
$419$	−31.8673	−1.55682	−0.778410	+	0.627756i	$0.783973\pi$
$420$	0	0
$421$	−29.7646	−1.45064	−0.725319	−	0.688413i	$-0.758308\pi$
$421$	−29.7646	−1.45064	−0.725319	+	0.688413i	$0.758308\pi$
$422$	0.248797	0.0121112
$423$	1.00000	0.0486217
$424$	−1.26874	−0.0616153
$425$	0	0
$426$	0.704369	0.0341268
$427$	15.9346	0.771130
$428$	−15.8912	−0.768132
$429$	2.99272	0.144490
$430$	0	0
$431$	19.3630	0.932681	0.466341	−	0.884605i	$-0.345572\pi$
$431$	19.3630	0.932681	0.466341	+	0.884605i	$0.345572\pi$
$432$	3.97422	0.191210
$433$	−0.639376	−0.0307264	−0.0153632	−	0.999882i	$-0.504890\pi$
$433$	−0.639376	−0.0307264	−0.0153632	+	0.999882i	$0.504890\pi$
$434$	0.268627	0.0128945
$435$	0	0
$436$	−25.2746	−1.21043
$437$	1.93632	0.0926269
$438$	−0.225162	−0.0107587
$439$	−31.0844	−1.48358	−0.741788	−	0.670635i	$-0.766022\pi$
$439$	−31.0844	−1.48358	−0.741788	+	0.670635i	$0.766022\pi$
$440$	0	0
$441$	−4.60072	−0.219082
$442$	−1.13242	−0.0538636
$443$	14.4077	0.684531	0.342266	−	0.939603i	$-0.388806\pi$
$443$	14.4077	0.684531	0.342266	+	0.939603i	$0.388806\pi$
$444$	−10.3568	−0.491510
$445$	0	0
$446$	−0.867152	−0.0410608
$447$	13.6868	0.647365
$448$	−12.2321	−0.577913
$449$	−8.13215	−0.383780	−0.191890	−	0.981416i	$-0.561462\pi$
$449$	−8.13215	−0.383780	−0.191890	+	0.981416i	$0.561462\pi$
$450$	0	0
$451$	7.55540	0.355770
$452$	−14.7677	−0.694617
$453$	9.67723	0.454676
$454$	0.315571	0.0148105
$455$	0	0
$456$	0.436802	0.0204551
$457$	−5.94507	−0.278098	−0.139049	−	0.990285i	$-0.544405\pi$
$457$	−5.94507	−0.278098	−0.139049	+	0.990285i	$0.544405\pi$
$458$	0.778321	0.0363685
$459$	6.13170	0.286203
$460$	0	0
$461$	21.5784	1.00501	0.502503	−	0.864576i	$-0.332413\pi$
$461$	21.5784	1.00501	0.502503	+	0.864576i	$0.332413\pi$
$462$	−0.107932	−0.00502145
$463$	−36.9770	−1.71847	−0.859233	−	0.511584i	$-0.829059\pi$
$463$	−36.9770	−1.71847	−0.859233	+	0.511584i	$0.829059\pi$
$464$	−5.77133	−0.267927
$465$	0	0
$466$	0.503069	0.0233042
$467$	19.6603	0.909769	0.454885	−	0.890550i	$-0.349680\pi$
$467$	19.6603	0.909769	0.454885	+	0.890550i	$0.349680\pi$
$468$	5.62064	0.259814
$469$	−7.82843	−0.361483
$470$	0	0
$471$	−10.6539	−0.490907
$472$	0.629735	0.0289859
$473$	−4.90042	−0.225322
$474$	0.368282	0.0169157
$475$	0	0
$476$	−18.9547	−0.868786
$477$	4.84221	0.221710
$478$	0.371348	0.0169851
$479$	−29.1545	−1.33210	−0.666051	−	0.745907i	$-0.732017\pi$
$479$	−29.1545	−1.33210	−0.666051	+	0.745907i	$0.732017\pi$
$480$	0	0
$481$	−14.6157	−0.666419
$482$	1.48501	0.0676404
$483$	−1.79912	−0.0818630
$484$	19.6993	0.895421
$485$	0	0
$486$	0.0655745	0.00297452
$487$	−29.9821	−1.35862	−0.679309	−	0.733852i	$-0.737720\pi$
$487$	−29.9821	−1.35862	−0.679309	+	0.733852i	$0.737720\pi$
$488$	−2.69543	−0.122017
$489$	2.64395	0.119564
$490$	0	0
$491$	9.52510	0.429862	0.214931	−	0.976629i	$-0.431047\pi$
$491$	9.52510	0.429862	0.214931	+	0.976629i	$0.431047\pi$
$492$	14.1899	0.639729
$493$	−8.90441	−0.401034
$494$	0.307881	0.0138522
$495$	0	0
$496$	10.5106	0.471939
$497$	16.6382	0.746325
$498$	0.282702	0.0126682
$499$	−5.96880	−0.267200	−0.133600	−	0.991035i	$-0.542654\pi$
$499$	−5.96880	−0.267200	−0.133600	+	0.991035i	$0.542654\pi$
$500$	0	0
$501$	−14.0673	−0.628478
$502$	1.96651	0.0877698
$503$	16.2717	0.725519	0.362760	−	0.931883i	$-0.381835\pi$
$503$	16.2717	0.725519	0.362760	+	0.931883i	$0.381835\pi$
$504$	−0.405852	−0.0180781
$505$	0	0
$506$	0.0809338	0.00359795
$507$	−5.06802	−0.225079
$508$	18.4517	0.818663
$509$	−8.97733	−0.397913	−0.198956	−	0.980008i	$-0.563755\pi$
$509$	−8.97733	−0.397913	−0.198956	+	0.980008i	$0.563755\pi$
$510$	0	0
$511$	−5.31865	−0.235283
$512$	5.20094	0.229851
$513$	−1.66708	−0.0736035
$514$	0.127915	0.00564209
$515$	0	0
$516$	−9.20352	−0.405163
$517$	−1.06261	−0.0467336
$518$	0.527113	0.0231600
$519$	−0.851604	−0.0373813
$520$	0	0
$521$	−0.0674323	−0.00295426	−0.00147713	−	0.999999i	$-0.500470\pi$
$521$	−0.0674323	−0.00295426	−0.00147713	+	0.999999i	$0.500470\pi$
$522$	−0.0952267	−0.00416796
$523$	−44.0470	−1.92604	−0.963021	−	0.269425i	$-0.913166\pi$
$523$	−44.0470	−1.92604	−0.963021	+	0.269425i	$0.913166\pi$
$524$	−1.77536	−0.0775568
$525$	0	0
$526$	−0.0183709	−0.000801010 0
$527$	16.2165	0.706400
$528$	−4.22305	−0.183785
$529$	−21.6509	−0.941344
$530$	0	0
$531$	−2.40342	−0.104300
$532$	5.15339	0.223428
$533$	20.0251	0.867382
$534$	0.740175	0.0320305
$535$	0	0
$536$	1.32423	0.0571978
$537$	5.79978	0.250279
$538$	−1.42613	−0.0614849
$539$	4.88878	0.210575
$540$	0	0
$541$	14.5985	0.627640	0.313820	−	0.949482i	$-0.398391\pi$
$541$	14.5985	0.627640	0.313820	+	0.949482i	$0.398391\pi$
$542$	−1.41590	−0.0608183
$543$	4.53580	0.194650
$544$	4.81117	0.206277
$545$	0	0
$546$	−0.286066	−0.0122425
$547$	−0.542549	−0.0231977	−0.0115989	−	0.999933i	$-0.503692\pi$
$547$	−0.542549	−0.0231977	−0.0115989	+	0.999933i	$0.503692\pi$
$548$	36.0797	1.54125
$549$	10.2873	0.439051
$550$	0	0
$551$	2.42093	0.103135
$552$	0.304332	0.0129532
$553$	8.69933	0.369933
$554$	−1.30931	−0.0556271
$555$	0	0
$556$	−3.44948	−0.146291
$557$	−24.4526	−1.03609	−0.518045	−	0.855354i	$-0.673340\pi$
$557$	−24.4526	−1.03609	−0.518045	+	0.855354i	$0.673340\pi$
$558$	0.173424	0.00734163
$559$	−12.9882	−0.549343
$560$	0	0
$561$	−6.51562	−0.275090
$562$	−1.92615	−0.0812497
$563$	−24.2105	−1.02035	−0.510175	−	0.860071i	$-0.670419\pi$
$563$	−24.2105	−1.02035	−0.510175	+	0.860071i	$0.670419\pi$
$564$	−1.99570	−0.0840341
$565$	0	0
$566$	−1.48192	−0.0622897
$567$	1.54896	0.0650502
$568$	−2.81445	−0.118092
$569$	3.60360	0.151071	0.0755354	−	0.997143i	$-0.475933\pi$
$569$	3.60360	0.151071	0.0755354	+	0.997143i	$0.475933\pi$
$570$	0	0
$571$	−40.4067	−1.69097	−0.845484	−	0.534001i	$-0.820688\pi$
$571$	−40.4067	−1.69097	−0.845484	+	0.534001i	$0.820688\pi$
$572$	−5.97256	−0.249725
$573$	16.5775	0.692536
$574$	−0.722201	−0.0301441
$575$	0	0
$576$	−7.89698	−0.329041
$577$	−10.0507	−0.418416	−0.209208	−	0.977871i	$-0.567089\pi$
$577$	−10.0507	−0.418416	−0.209208	+	0.977871i	$0.567089\pi$
$578$	1.35069	0.0561811
$579$	7.26754	0.302028
$580$	0	0
$581$	6.67781	0.277042
$582$	0.439135	0.0182027
$583$	−5.14539	−0.213100
$584$	0.899681	0.0372290
$585$	0	0
$586$	0.984961	0.0406884
$587$	40.5631	1.67422	0.837109	−	0.547036i	$-0.184244\pi$
$587$	40.5631	1.67422	0.837109	+	0.547036i	$0.184244\pi$
$588$	9.18166	0.378645
$589$	−4.40892	−0.181666
$590$	0	0
$591$	5.81105	0.239035
$592$	20.6244	0.847656
$593$	17.3655	0.713116	0.356558	−	0.934273i	$-0.383950\pi$
$593$	17.3655	0.713116	0.356558	+	0.934273i	$0.383950\pi$
$594$	−0.0696802	−0.00285901
$595$	0	0
$596$	−27.3148	−1.11886
$597$	21.2679	0.870439
$598$	0.214509	0.00877194
$599$	16.1610	0.660320	0.330160	−	0.943925i	$-0.392897\pi$
$599$	16.1610	0.660320	0.330160	+	0.943925i	$0.392897\pi$
$600$	0	0
$601$	24.9111	1.01615	0.508073	−	0.861314i	$-0.330358\pi$
$601$	24.9111	1.01615	0.508073	+	0.861314i	$0.330358\pi$
$602$	0.468419	0.0190913
$603$	−5.05399	−0.205814
$604$	−19.3128	−0.785829
$605$	0	0
$606$	0.536683	0.0218013
$607$	11.5798	0.470009	0.235005	−	0.971994i	$-0.424489\pi$
$607$	11.5798	0.470009	0.235005	+	0.971994i	$0.424489\pi$
$608$	−1.30806	−0.0530488
$609$	−2.24939	−0.0911498
$610$	0	0
$611$	−2.81638	−0.113938
$612$	−12.2370	−0.494653
$613$	37.5509	1.51667	0.758333	−	0.651867i	$-0.226014\pi$
$613$	37.5509	1.51667	0.758333	+	0.651867i	$0.226014\pi$
$614$	1.93189	0.0779646
$615$	0	0
$616$	0.431263	0.0173761
$617$	−10.0491	−0.404560	−0.202280	−	0.979328i	$-0.564835\pi$
$617$	−10.0491	−0.404560	−0.202280	+	0.979328i	$0.564835\pi$
$618$	0.700809	0.0281907
$619$	16.7432	0.672967	0.336484	−	0.941689i	$-0.390762\pi$
$619$	16.7432	0.672967	0.336484	+	0.941689i	$0.390762\pi$
$620$	0	0
$621$	−1.16150	−0.0466095
$622$	1.99399	0.0799517
$623$	17.4840	0.700480
$624$	−11.1929	−0.448075
$625$	0	0
$626$	−1.08618	−0.0434126
$627$	1.77146	0.0707454
$628$	21.2620	0.848448
$629$	31.8207	1.26877
$630$	0	0
$631$	−16.2491	−0.646865	−0.323432	−	0.946251i	$-0.604837\pi$
$631$	−16.2491	−0.646865	−0.323432	+	0.946251i	$0.604837\pi$
$632$	−1.47154	−0.0585348
$633$	3.79411	0.150802
$634$	1.62441	0.0645136
$635$	0	0
$636$	−9.66361	−0.383187
$637$	12.9574	0.513390
$638$	0.101189	0.00400611
$639$	10.7415	0.424928
$640$	0	0
$641$	−37.4547	−1.47937	−0.739687	−	0.672951i	$-0.765026\pi$
$641$	−37.4547	−1.47937	−0.739687	+	0.672951i	$0.765026\pi$
$642$	0.522152	0.0206077
$643$	−44.3288	−1.74816	−0.874078	−	0.485786i	$-0.838534\pi$
$643$	−44.3288	−1.74816	−0.874078	+	0.485786i	$0.838534\pi$
$644$	3.59051	0.141486
$645$	0	0
$646$	−0.670306	−0.0263728
$647$	−32.3755	−1.27281	−0.636407	−	0.771354i	$-0.719580\pi$
$647$	−32.3755	−1.27281	−0.636407	+	0.771354i	$0.719580\pi$
$648$	−0.262016	−0.0102930
$649$	2.55390	0.100250
$650$	0	0
$651$	4.09652	0.160555
$652$	−5.27654	−0.206645
$653$	35.5017	1.38929	0.694644	−	0.719353i	$-0.255562\pi$
$653$	35.5017	1.38929	0.694644	+	0.719353i	$0.255562\pi$
$654$	0.830470	0.0324739
$655$	0	0
$656$	−28.2576	−1.10327
$657$	−3.43369	−0.133961
$658$	0.101572	0.00395970
$659$	34.2016	1.33231	0.666153	−	0.745815i	$-0.267940\pi$
$659$	34.2016	1.33231	0.666153	+	0.745815i	$0.267940\pi$
$660$	0	0
$661$	−21.6211	−0.840962	−0.420481	−	0.907301i	$-0.638139\pi$
$661$	−21.6211	−0.840962	−0.420481	+	0.907301i	$0.638139\pi$
$662$	2.25775	0.0877501
$663$	−17.2692	−0.670679
$664$	−1.12959	−0.0438366
$665$	0	0
$666$	0.340301	0.0131864
$667$	1.68673	0.0653103
$668$	28.0740	1.08622
$669$	−13.2239	−0.511266
$670$	0	0
$671$	−10.9314	−0.422002
$672$	1.21537	0.0468841
$673$	37.2879	1.43734	0.718672	−	0.695349i	$-0.244750\pi$
$673$	37.2879	1.43734	0.718672	+	0.695349i	$0.244750\pi$
$674$	0.723496	0.0278680
$675$	0	0
$676$	10.1142	0.389009
$677$	−18.1830	−0.698828	−0.349414	−	0.936968i	$-0.613619\pi$
$677$	−18.1830	−0.698828	−0.349414	+	0.936968i	$0.613619\pi$
$678$	0.485237	0.0186354
$679$	10.3730	0.398078
$680$	0	0
$681$	4.81241	0.184412
$682$	−0.184283	−0.00705655
$683$	39.4379	1.50905	0.754526	−	0.656271i	$-0.227867\pi$
$683$	39.4379	1.50905	0.754526	+	0.656271i	$0.227867\pi$
$684$	3.32700	0.127211
$685$	0	0
$686$	−1.17831	−0.0449881
$687$	11.8693	0.452841
$688$	18.3278	0.698741
$689$	−13.6375	−0.519547
$690$	0	0
$691$	−34.2400	−1.30255	−0.651275	−	0.758842i	$-0.725765\pi$
$691$	−34.2400	−1.30255	−0.651275	+	0.758842i	$0.725765\pi$
$692$	1.69955	0.0646071
$693$	−1.64594	−0.0625242
$694$	−1.10360	−0.0418922
$695$	0	0
$696$	0.380497	0.0144227
$697$	−43.5977	−1.65138
$698$	−0.773255	−0.0292681
$699$	7.67172	0.290171
$700$	0	0
$701$	24.5453	0.927062	0.463531	−	0.886081i	$-0.346582\pi$
$701$	24.5453	0.927062	0.463531	+	0.886081i	$0.346582\pi$
$702$	−0.184682	−0.00697039
$703$	−8.65139	−0.326294
$704$	8.39143	0.316264
$705$	0	0
$706$	2.00815	0.0755776
$707$	12.6772	0.476775
$708$	4.79651	0.180264
$709$	−8.37005	−0.314344	−0.157172	−	0.987571i	$-0.550238\pi$
$709$	−8.37005	−0.314344	−0.157172	+	0.987571i	$0.550238\pi$
$710$	0	0
$711$	5.61624	0.210625
$712$	−2.95752	−0.110838
$713$	−3.07182	−0.115041
$714$	0.622811	0.0233081
$715$	0	0
$716$	−11.5746	−0.432564
$717$	5.66300	0.211489
$718$	−0.251064	−0.00936963
$719$	31.4224	1.17186	0.585928	−	0.810363i	$-0.300730\pi$
$719$	31.4224	1.17186	0.585928	+	0.810363i	$0.300730\pi$
$720$	0	0
$721$	16.5541	0.616507
$722$	−1.06367	−0.0395858
$723$	22.6462	0.842221
$724$	−9.05210	−0.336419
$725$	0	0
$726$	−0.647276	−0.0240227
$727$	−32.3545	−1.19996	−0.599982	−	0.800014i	$-0.704825\pi$
$727$	−32.3545	−1.19996	−0.599982	+	0.800014i	$0.704825\pi$
$728$	1.14303	0.0423636
$729$	1.00000	0.0370370
$730$	0	0
$731$	28.2774	1.04588
$732$	−20.5304	−0.758824
$733$	0.209606	0.00774196	0.00387098	−	0.999993i	$-0.498768\pi$
$733$	0.209606	0.00774196	0.00387098	+	0.999993i	$0.498768\pi$
$734$	−2.04102	−0.0753355
$735$	0	0
$736$	−0.911361	−0.0335932
$737$	5.37043	0.197822
$738$	−0.466249	−0.0171629
$739$	−11.0919	−0.408023	−0.204011	−	0.978969i	$-0.565398\pi$
$739$	−11.0919	−0.408023	−0.204011	+	0.978969i	$0.565398\pi$
$740$	0	0
$741$	4.69514	0.172480
$742$	0.491835	0.0180558
$743$	−49.0382	−1.79904	−0.899519	−	0.436882i	$-0.856083\pi$
$743$	−49.0382	−1.79904	−0.899519	+	0.436882i	$0.856083\pi$
$744$	−0.692951	−0.0254048
$745$	0	0
$746$	−2.16878	−0.0794046
$747$	4.31116	0.157737
$748$	13.0032	0.475445
$749$	12.3340	0.450673
$750$	0	0
$751$	−39.3975	−1.43763	−0.718817	−	0.695199i	$-0.755316\pi$
$751$	−39.3975	−1.43763	−0.718817	+	0.695199i	$0.755316\pi$
$752$	3.97422	0.144925
$753$	29.9890	1.09286
$754$	0.268194	0.00976707
$755$	0	0
$756$	−3.09126	−0.112428
$757$	−19.6838	−0.715421	−0.357710	−	0.933833i	$-0.616442\pi$
$757$	−19.6838	−0.715421	−0.357710	+	0.933833i	$0.616442\pi$
$758$	0.227849	0.00827584
$759$	1.23423	0.0447996
$760$	0	0
$761$	−16.1875	−0.586798	−0.293399	−	0.955990i	$-0.594786\pi$
$761$	−16.1875	−0.586798	−0.293399	+	0.955990i	$0.594786\pi$
$762$	−0.606285	−0.0219634
$763$	19.6169	0.710178
$764$	−33.0837	−1.19693
$765$	0	0
$766$	0.241745	0.00873461
$767$	6.76894	0.244412
$768$	15.6571	0.564977
$769$	4.44031	0.160122	0.0800609	−	0.996790i	$-0.474489\pi$
$769$	4.44031	0.160122	0.0800609	+	0.996790i	$0.474489\pi$
$770$	0	0
$771$	1.95068	0.0702521
$772$	−14.5038	−0.522004
$773$	−32.5841	−1.17197	−0.585984	−	0.810323i	$-0.699292\pi$
$773$	−32.5841	−1.17197	−0.585984	+	0.810323i	$0.699292\pi$
$774$	0.302408	0.0108698
$775$	0	0
$776$	−1.75465	−0.0629883
$777$	8.03839	0.288376
$778$	−1.50194	−0.0538471
$779$	11.8533	0.424690
$780$	0	0
$781$	−11.4141	−0.408427
$782$	−0.467021	−0.0167006
$783$	−1.45219	−0.0518971
$784$	−18.2843	−0.653010
$785$	0	0
$786$	0.0583345	0.00208072
$787$	32.3944	1.15474	0.577368	−	0.816484i	$-0.304080\pi$
$787$	32.3944	1.15474	0.577368	+	0.816484i	$0.304080\pi$
$788$	−11.5971	−0.413130
$789$	−0.280153	−0.00997373
$790$	0	0
$791$	11.4620	0.407541
$792$	0.278421	0.00989327
$793$	−28.9729	−1.02886
$794$	−1.62246	−0.0575791
$795$	0	0
$796$	−42.4444	−1.50440
$797$	−2.96470	−0.105015	−0.0525076	−	0.998621i	$-0.516721\pi$
$797$	−2.96470	−0.105015	−0.0525076	+	0.998621i	$0.516721\pi$
$798$	−0.169329	−0.00599420
$799$	6.13170	0.216924
$800$	0	0
$801$	11.2875	0.398826
$802$	0.315961	0.0111570
$803$	3.64868	0.128759
$804$	10.0862	0.355714
$805$	0	0
$806$	−0.488428	−0.0172041
$807$	−21.7483	−0.765576
$808$	−2.14442	−0.0754406
$809$	42.6643	1.50000	0.749998	−	0.661440i	$-0.230055\pi$
$809$	42.6643	1.50000	0.749998	+	0.661440i	$0.230055\pi$
$810$	0	0
$811$	11.1214	0.390524	0.195262	−	0.980751i	$-0.437444\pi$
$811$	11.1214	0.390524	0.195262	+	0.980751i	$0.437444\pi$
$812$	4.48911	0.157537
$813$	−21.5923	−0.757276
$814$	−0.361608	−0.0126744
$815$	0	0
$816$	24.3687	0.853076
$817$	−7.68805	−0.268971
$818$	2.10672	0.0736596
$819$	−4.36246	−0.152437
$820$	0	0
$821$	12.8893	0.449838	0.224919	−	0.974377i	$-0.427788\pi$
$821$	12.8893	0.449838	0.224919	+	0.974377i	$0.427788\pi$
$822$	−1.18550	−0.0413491
$823$	−27.4785	−0.957841	−0.478920	−	0.877858i	$-0.658972\pi$
$823$	−27.4785	−0.957841	−0.478920	+	0.877858i	$0.658972\pi$
$824$	−2.80022	−0.0975504
$825$	0	0
$826$	−0.244121	−0.00849406
$827$	19.5586	0.680119	0.340060	−	0.940404i	$-0.389553\pi$
$827$	19.5586	0.680119	0.340060	+	0.940404i	$0.389553\pi$
$828$	2.31801	0.0805565
$829$	26.3805	0.916234	0.458117	−	0.888892i	$-0.348524\pi$
$829$	26.3805	0.916234	0.458117	+	0.888892i	$0.348524\pi$
$830$	0	0
$831$	−19.9667	−0.692638
$832$	22.2409	0.771064
$833$	−28.2102	−0.977427
$834$	0.113343	0.00392473
$835$	0	0
$836$	−3.53531	−0.122271
$837$	2.64469	0.0914139
$838$	−2.08968	−0.0721868
$839$	−26.8770	−0.927897	−0.463948	−	0.885862i	$-0.653568\pi$
$839$	−26.8770	−0.927897	−0.463948	+	0.885862i	$0.653568\pi$
$840$	0	0
$841$	−26.8911	−0.927281
$842$	−1.95180	−0.0672634
$843$	−29.3734	−1.01168
$844$	−7.57191	−0.260636
$845$	0	0
$846$	0.0655745	0.00225450
$847$	−15.2896	−0.525356
$848$	19.2440	0.660842
$849$	−22.5990	−0.775597
$850$	0	0
$851$	−6.02767	−0.206626
$852$	−21.4369	−0.734415
$853$	−48.6578	−1.66601	−0.833005	−	0.553265i	$-0.813382\pi$
$853$	−48.6578	−1.66601	−0.833005	+	0.553265i	$0.813382\pi$
$854$	1.04490	0.0357559
$855$	0	0
$856$	−2.08636	−0.0713104
$857$	52.5065	1.79359	0.896794	−	0.442449i	$-0.145890\pi$
$857$	52.5065	1.79359	0.896794	+	0.442449i	$0.145890\pi$
$858$	0.196246	0.00669972
$859$	2.68186	0.0915037	0.0457519	−	0.998953i	$-0.485432\pi$
$859$	2.68186	0.0915037	0.0457519	+	0.998953i	$0.485432\pi$
$860$	0	0
$861$	−11.0135	−0.375337
$862$	1.26972	0.0432467
$863$	−9.92665	−0.337907	−0.168954	−	0.985624i	$-0.554039\pi$
$863$	−9.92665	−0.337907	−0.168954	+	0.985624i	$0.554039\pi$
$864$	0.784639	0.0266940
$865$	0	0
$866$	−0.0419267	−0.00142473
$867$	20.5977	0.699536
$868$	−8.17543	−0.277492
$869$	−5.96788	−0.202446
$870$	0	0
$871$	14.2339	0.482299
$872$	−3.31831	−0.112372
$873$	6.69673	0.226650
$874$	0.126973	0.00429494
$875$	0	0
$876$	6.85261	0.231528
$877$	−9.80929	−0.331236	−0.165618	−	0.986190i	$-0.552962\pi$
$877$	−9.80929	−0.331236	−0.165618	+	0.986190i	$0.552962\pi$
$878$	−2.03834	−0.0687906
$879$	15.0205	0.506629
$880$	0	0
$881$	−49.1883	−1.65720	−0.828598	−	0.559844i	$-0.810861\pi$
$881$	−49.1883	−1.65720	−0.828598	+	0.559844i	$0.810861\pi$
$882$	−0.301690	−0.0101584
$883$	21.7949	0.733457	0.366729	−	0.930328i	$-0.380478\pi$
$883$	21.7949	0.733457	0.366729	+	0.930328i	$0.380478\pi$
$884$	34.4641	1.15915
$885$	0	0
$886$	0.944778	0.0317404
$887$	−40.1876	−1.34937	−0.674684	−	0.738107i	$-0.735720\pi$
$887$	−40.1876	−1.34937	−0.674684	+	0.738107i	$0.735720\pi$
$888$	−1.35974	−0.0456299
$889$	−14.3213	−0.480321
$890$	0	0
$891$	−1.06261	−0.0355988
$892$	26.3910	0.883636
$893$	−1.66708	−0.0557868
$894$	0.897506	0.0300171
$895$	0	0
$896$	−3.23286	−0.108002
$897$	3.27123	0.109223
$898$	−0.533262	−0.0177952
$899$	−3.84060	−0.128091
$900$	0	0
$901$	29.6910	0.989151
$902$	0.495442	0.0164964
$903$	7.14331	0.237714
$904$	−1.93886	−0.0644856
$905$	0	0
$906$	0.634579	0.0210825
$907$	−10.5387	−0.349932	−0.174966	−	0.984574i	$-0.555982\pi$
$907$	−10.5387	−0.349932	−0.174966	+	0.984574i	$0.555982\pi$
$908$	−9.60413	−0.318724
$909$	8.18433	0.271457
$910$	0	0
$911$	−21.9686	−0.727852	−0.363926	−	0.931428i	$-0.618564\pi$
$911$	−21.9686	−0.727852	−0.363926	+	0.931428i	$0.618564\pi$
$912$	−6.62535	−0.219387
$913$	−4.58108	−0.151612
$914$	−0.389844	−0.0128949
$915$	0	0
$916$	−23.6875	−0.782657
$917$	1.37794	0.0455036
$918$	0.402083	0.0132707
$919$	−23.2897	−0.768257	−0.384129	−	0.923280i	$-0.625498\pi$
$919$	−23.2897	−0.768257	−0.384129	+	0.923280i	$0.625498\pi$
$920$	0	0
$921$	29.4609	0.970771
$922$	1.41499	0.0466002
$923$	−30.2522	−0.995763
$924$	3.28481	0.108062
$925$	0	0
$926$	−2.42475	−0.0796821
$927$	10.6872	0.351015
$928$	−1.13945	−0.0374042
$929$	−39.1118	−1.28322	−0.641608	−	0.767033i	$-0.721732\pi$
$929$	−39.1118	−1.28322	−0.641608	+	0.767033i	$0.721732\pi$
$930$	0	0
$931$	7.66979	0.251367
$932$	−15.3105	−0.501511
$933$	30.4080	0.995514
$934$	1.28921	0.0421843
$935$	0	0
$936$	0.737936	0.0241202
$937$	−19.0221	−0.621425	−0.310713	−	0.950504i	$-0.600568\pi$
$937$	−19.0221	−0.621425	−0.310713	+	0.950504i	$0.600568\pi$
$938$	−0.513345	−0.0167613
$939$	−16.5641	−0.540550
$940$	0	0
$941$	−44.9937	−1.46675	−0.733377	−	0.679823i	$-0.762057\pi$
$941$	−44.9937	−1.46675	−0.733377	+	0.679823i	$0.762057\pi$
$942$	−0.698625	−0.0227624
$943$	8.25855	0.268935
$944$	−9.55172	−0.310882
$945$	0	0
$946$	−0.321343	−0.0104477
$947$	14.5223	0.471911	0.235955	−	0.971764i	$-0.424178\pi$
$947$	14.5223	0.471911	0.235955	+	0.971764i	$0.424178\pi$
$948$	−11.2083	−0.364029
$949$	9.67056	0.313920
$950$	0	0
$951$	24.7720	0.803288
$952$	−2.48856	−0.0806548
$953$	−19.1701	−0.620981	−0.310490	−	0.950576i	$-0.600493\pi$
$953$	−19.1701	−0.620981	−0.310490	+	0.950576i	$0.600493\pi$
$954$	0.317526	0.0102803
$955$	0	0
$956$	−11.3017	−0.365522
$957$	1.54312	0.0498819
$958$	−1.91179	−0.0617671
$959$	−28.0032	−0.904271
$960$	0	0
$961$	−24.0056	−0.774374
$962$	−0.958417	−0.0309006
$963$	7.96273	0.256596
$964$	−45.1950	−1.45563
$965$	0	0
$966$	−0.117977	−0.00379583
$967$	8.39807	0.270064	0.135032	−	0.990841i	$-0.456886\pi$
$967$	8.39807	0.270064	0.135032	+	0.990841i	$0.456886\pi$
$968$	2.58632	0.0831275
$969$	−10.2221	−0.328380
$970$	0	0
$971$	18.0117	0.578024	0.289012	−	0.957325i	$-0.406673\pi$
$971$	18.0117	0.578024	0.289012	+	0.957325i	$0.406673\pi$
$972$	−1.99570	−0.0640121
$973$	2.67731	0.0858307
$974$	−1.96606	−0.0629966
$975$	0	0
$976$	40.8839	1.30866
$977$	38.9218	1.24522	0.622609	−	0.782533i	$-0.286073\pi$
$977$	38.9218	1.24522	0.622609	+	0.782533i	$0.286073\pi$
$978$	0.173376	0.00554394
$979$	−11.9943	−0.383339
$980$	0	0
$981$	12.6645	0.404347
$982$	0.624603	0.0199319
$983$	11.8082	0.376622	0.188311	−	0.982109i	$-0.439699\pi$
$983$	11.8082	0.376622	0.188311	+	0.982109i	$0.439699\pi$
$984$	1.86299	0.0593900
$985$	0	0
$986$	−0.583902	−0.0185952
$987$	1.54896	0.0493040
$988$	−9.37009	−0.298102
$989$	−5.35648	−0.170326
$990$	0	0
$991$	15.2565	0.484640	0.242320	−	0.970196i	$-0.422092\pi$
$991$	15.2565	0.484640	0.242320	+	0.970196i	$0.422092\pi$
$992$	2.07513	0.0658854
$993$	34.4304	1.09262
$994$	1.09104	0.0346057
$995$	0	0
$996$	−8.60377	−0.272621
$997$	1.53355	0.0485679	0.0242840	−	0.999705i	$-0.492269\pi$
$997$	1.53355	0.0485679	0.0242840	+	0.999705i	$0.492269\pi$
$998$	−0.391401	−0.0123896
$999$	5.18954	0.164190

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bi.1.7		13
5.2	odd	4		705.2.c.c.424.14	yes	26
5.3	odd	4		705.2.c.c.424.13	✓	26
5.4	even	2		3525.2.a.bh.1.7		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.2.c.c.424.13	✓	26	5.3	odd	4
705.2.c.c.424.14	yes	26	5.2	odd	4
3525.2.a.bh.1.7		13	5.4	even	2
3525.2.a.bi.1.7		13	1.1	even	1	trivial

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Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.0655745 q^{2} +1.00000 q^{3} -1.99570 q^{4} +0.0655745 q^{6} +1.54896 q^{7} -0.262016 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.0655745 q^{2} +1.00000 q^{3} -1.99570 q^{4} +0.0655745 q^{6} +1.54896 q^{7} -0.262016 q^{8} +1.00000 q^{9} -1.06261 q^{11} -1.99570 q^{12} -2.81638 q^{13} +0.101572 q^{14} +3.97422 q^{16} +6.13170 q^{17} +0.0655745 q^{18} -1.66708 q^{19} +1.54896 q^{21} -0.0696802 q^{22} -1.16150 q^{23} -0.262016 q^{24} -0.184682 q^{26} +1.00000 q^{27} -3.09126 q^{28} -1.45219 q^{29} +2.64469 q^{31} +0.784639 q^{32} -1.06261 q^{33} +0.402083 q^{34} -1.99570 q^{36} +5.18954 q^{37} -0.109318 q^{38} -2.81638 q^{39} -7.11022 q^{41} +0.101572 q^{42} +4.61168 q^{43} +2.12065 q^{44} -0.0761650 q^{46} +1.00000 q^{47} +3.97422 q^{48} -4.60072 q^{49} +6.13170 q^{51} +5.62064 q^{52} +4.84221 q^{53} +0.0655745 q^{54} -0.405852 q^{56} -1.66708 q^{57} -0.0952267 q^{58} -2.40342 q^{59} +10.2873 q^{61} +0.173424 q^{62} +1.54896 q^{63} -7.89698 q^{64} -0.0696802 q^{66} -5.05399 q^{67} -12.2370 q^{68} -1.16150 q^{69} +10.7415 q^{71} -0.262016 q^{72} -3.43369 q^{73} +0.340301 q^{74} +3.32700 q^{76} -1.64594 q^{77} -0.184682 q^{78} +5.61624 q^{79} +1.00000 q^{81} -0.466249 q^{82} +4.31116 q^{83} -3.09126 q^{84} +0.302408 q^{86} -1.45219 q^{87} +0.278421 q^{88} +11.2875 q^{89} -4.36246 q^{91} +2.31801 q^{92} +2.64469 q^{93} +0.0655745 q^{94} +0.784639 q^{96} +6.69673 q^{97} -0.301690 q^{98} -1.06261 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 3 q^{2} + 13 q^{3} + 17 q^{4} + 3 q^{6} - 4 q^{7} + 15 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 3 * q^2 + 13 * q^3 + 17 * q^4 + 3 * q^6 - 4 * q^7 + 15 * q^8 + 13 * q^9	\( 13 q + 3 q^{2} + 13 q^{3} + 17 q^{4} + 3 q^{6} - 4 q^{7} + 15 q^{8} + 13 q^{9} + 16 q^{11} + 17 q^{12} - 8 q^{13} - 4 q^{14} + 29 q^{16} + 12 q^{17} + 3 q^{18} + 28 q^{19} - 4 q^{21} + 6 q^{23} + 15 q^{24} + 4 q^{26} + 13 q^{27} - 20 q^{28} + 12 q^{29} + 26 q^{31} + 53 q^{32} + 16 q^{33} + 8 q^{34} + 17 q^{36} - 4 q^{37} + 2 q^{38} - 8 q^{39} + 24 q^{41} - 4 q^{42} - 6 q^{43} + 4 q^{44} + 16 q^{46} + 13 q^{47} + 29 q^{48} + 21 q^{49} + 12 q^{51} - 32 q^{52} + 6 q^{53} + 3 q^{54} + 28 q^{57} - 4 q^{58} + 34 q^{59} + 24 q^{61} + 30 q^{62} - 4 q^{63} + 13 q^{64} - 24 q^{67} + 44 q^{68} + 6 q^{69} + 20 q^{71} + 15 q^{72} - 6 q^{73} + 20 q^{74} + 66 q^{76} - 2 q^{77} + 4 q^{78} + 6 q^{79} + 13 q^{81} + 20 q^{82} + 14 q^{83} - 20 q^{84} + 48 q^{86} + 12 q^{87} - 22 q^{88} + 36 q^{89} + 4 q^{91} + 4 q^{92} + 26 q^{93} + 3 q^{94} + 53 q^{96} - 32 q^{97} - 39 q^{98} + 16 q^{99}+O(q^{100}) \) 13 * q + 3 * q^2 + 13 * q^3 + 17 * q^4 + 3 * q^6 - 4 * q^7 + 15 * q^8 + 13 * q^9 + 16 * q^11 + 17 * q^12 - 8 * q^13 - 4 * q^14 + 29 * q^16 + 12 * q^17 + 3 * q^18 + 28 * q^19 - 4 * q^21 + 6 * q^23 + 15 * q^24 + 4 * q^26 + 13 * q^27 - 20 * q^28 + 12 * q^29 + 26 * q^31 + 53 * q^32 + 16 * q^33 + 8 * q^34 + 17 * q^36 - 4 * q^37 + 2 * q^38 - 8 * q^39 + 24 * q^41 - 4 * q^42 - 6 * q^43 + 4 * q^44 + 16 * q^46 + 13 * q^47 + 29 * q^48 + 21 * q^49 + 12 * q^51 - 32 * q^52 + 6 * q^53 + 3 * q^54 + 28 * q^57 - 4 * q^58 + 34 * q^59 + 24 * q^61 + 30 * q^62 - 4 * q^63 + 13 * q^64 - 24 * q^67 + 44 * q^68 + 6 * q^69 + 20 * q^71 + 15 * q^72 - 6 * q^73 + 20 * q^74 + 66 * q^76 - 2 * q^77 + 4 * q^78 + 6 * q^79 + 13 * q^81 + 20 * q^82 + 14 * q^83 - 20 * q^84 + 48 * q^86 + 12 * q^87 - 22 * q^88 + 36 * q^89 + 4 * q^91 + 4 * q^92 + 26 * q^93 + 3 * q^94 + 53 * q^96 - 32 * q^97 - 39 * q^98 + 16 * q^99

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