LMFDB - Embedded newform 3525.2.a.bi.1.11

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			1.11
Root			$2.57687$ 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)

$f(q)$	$=$	$q+2.57687 q^{2} +1.00000 q^{3} +4.64024 q^{4} +2.57687 q^{6} +1.51741 q^{7} +6.80354 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.57687 q^{2} +1.00000 q^{3} +4.64024 q^{4} +2.57687 q^{6} +1.51741 q^{7} +6.80354 q^{8} +1.00000 q^{9} -0.409552 q^{11} +4.64024 q^{12} +1.70509 q^{13} +3.91015 q^{14} +8.25132 q^{16} -3.62967 q^{17} +2.57687 q^{18} -0.485553 q^{19} +1.51741 q^{21} -1.05536 q^{22} +7.71926 q^{23} +6.80354 q^{24} +4.39379 q^{26} +1.00000 q^{27} +7.04112 q^{28} -1.53695 q^{29} +4.32311 q^{31} +7.65548 q^{32} -0.409552 q^{33} -9.35318 q^{34} +4.64024 q^{36} -2.44384 q^{37} -1.25121 q^{38} +1.70509 q^{39} -7.76866 q^{41} +3.91015 q^{42} -7.59452 q^{43} -1.90042 q^{44} +19.8915 q^{46} +1.00000 q^{47} +8.25132 q^{48} -4.69748 q^{49} -3.62967 q^{51} +7.91202 q^{52} +10.2033 q^{53} +2.57687 q^{54} +10.3237 q^{56} -0.485553 q^{57} -3.96052 q^{58} +0.118818 q^{59} +2.25962 q^{61} +11.1401 q^{62} +1.51741 q^{63} +3.22450 q^{64} -1.05536 q^{66} -15.7869 q^{67} -16.8426 q^{68} +7.71926 q^{69} -9.50172 q^{71} +6.80354 q^{72} +8.20986 q^{73} -6.29745 q^{74} -2.25308 q^{76} -0.621456 q^{77} +4.39379 q^{78} +13.2865 q^{79} +1.00000 q^{81} -20.0188 q^{82} +6.59494 q^{83} +7.04112 q^{84} -19.5701 q^{86} -1.53695 q^{87} -2.78640 q^{88} +17.7958 q^{89} +2.58731 q^{91} +35.8192 q^{92} +4.32311 q^{93} +2.57687 q^{94} +7.65548 q^{96} -5.61258 q^{97} -12.1048 q^{98} -0.409552 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.57687	1.82212	0.911060	−	0.412275i	$-0.135266\pi$
$2$	2.57687	1.82212	0.911060	+	0.412275i	$0.135266\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.64024	2.32012
$5$	0	0
$5$	0	0
$6$	2.57687	1.05200
$7$	1.51741	0.573525	0.286763	−	0.958002i	$-0.407421\pi$
$7$	1.51741	0.573525	0.286763	+	0.958002i	$0.407421\pi$
$8$	6.80354	2.40541
$9$	1.00000	0.333333
$10$	0	0
$11$	−0.409552	−0.123485	−0.0617423	−	0.998092i	$-0.519666\pi$
$11$	−0.409552	−0.123485	−0.0617423	+	0.998092i	$0.519666\pi$
$12$	4.64024	1.33952
$13$	1.70509	0.472907	0.236454	−	0.971643i	$-0.424015\pi$
$13$	1.70509	0.472907	0.236454	+	0.971643i	$0.424015\pi$
$14$	3.91015	1.04503
$15$	0	0
$16$	8.25132	2.06283
$17$	−3.62967	−0.880325	−0.440163	−	0.897918i	$-0.645079\pi$
$17$	−3.62967	−0.880325	−0.440163	+	0.897918i	$0.645079\pi$
$18$	2.57687	0.607373
$19$	−0.485553	−0.111394	−0.0556968	−	0.998448i	$-0.517738\pi$
$19$	−0.485553	−0.111394	−0.0556968	+	0.998448i	$0.517738\pi$
$20$	0	0
$21$	1.51741	0.331125
$22$	−1.05536	−0.225004
$23$	7.71926	1.60958	0.804789	−	0.593562i	$-0.202279\pi$
$23$	7.71926	1.60958	0.804789	+	0.593562i	$0.202279\pi$
$24$	6.80354	1.38877
$25$	0	0
$26$	4.39379	0.861693
$27$	1.00000	0.192450
$28$	7.04112	1.33065
$29$	−1.53695	−0.285405	−0.142702	−	0.989766i	$-0.545579\pi$
$29$	−1.53695	−0.285405	−0.142702	+	0.989766i	$0.545579\pi$
$30$	0	0
$31$	4.32311	0.776453	0.388226	−	0.921564i	$-0.373088\pi$
$31$	4.32311	0.776453	0.388226	+	0.921564i	$0.373088\pi$
$32$	7.65548	1.35331
$33$	−0.409552	−0.0712939
$34$	−9.35318	−1.60406
$35$	0	0
$36$	4.64024	0.773373
$37$	−2.44384	−0.401765	−0.200883	−	0.979615i	$-0.564381\pi$
$37$	−2.44384	−0.401765	−0.200883	+	0.979615i	$0.564381\pi$
$38$	−1.25121	−0.202972
$39$	1.70509	0.273033
$40$	0	0
$41$	−7.76866	−1.21326	−0.606630	−	0.794984i	$-0.707479\pi$
$41$	−7.76866	−1.21326	−0.606630	+	0.794984i	$0.707479\pi$
$42$	3.91015	0.603349
$43$	−7.59452	−1.15815	−0.579077	−	0.815273i	$-0.696587\pi$
$43$	−7.59452	−1.15815	−0.579077	+	0.815273i	$0.696587\pi$
$44$	−1.90042	−0.286499
$45$	0	0
$46$	19.8915	2.93284
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	8.25132	1.19098
$49$	−4.69748	−0.671069
$50$	0	0
$51$	−3.62967	−0.508256
$52$	7.91202	1.09720
$53$	10.2033	1.40153	0.700765	−	0.713392i	$-0.252842\pi$
$53$	10.2033	1.40153	0.700765	+	0.713392i	$0.252842\pi$
$54$	2.57687	0.350667
$55$	0	0
$56$	10.3237	1.37957
$57$	−0.485553	−0.0643131
$58$	−3.96052	−0.520042
$59$	0.118818	0.0154687	0.00773437	−	0.999970i	$-0.497538\pi$
$59$	0.118818	0.0154687	0.00773437	+	0.999970i	$0.497538\pi$
$60$	0	0
$61$	2.25962	0.289315	0.144658	−	0.989482i	$-0.453792\pi$
$61$	2.25962	0.289315	0.144658	+	0.989482i	$0.453792\pi$
$62$	11.1401	1.41479
$63$	1.51741	0.191175
$64$	3.22450	0.403063
$65$	0	0
$66$	−1.05536	−0.129906
$67$	−15.7869	−1.92868	−0.964338	−	0.264675i	$-0.914735\pi$
$67$	−15.7869	−1.92868	−0.964338	+	0.264675i	$0.914735\pi$
$68$	−16.8426	−2.04246
$69$	7.71926	0.929290
$70$	0	0
$71$	−9.50172	−1.12765	−0.563824	−	0.825895i	$-0.690670\pi$
$71$	−9.50172	−1.12765	−0.563824	+	0.825895i	$0.690670\pi$
$72$	6.80354	0.801804
$73$	8.20986	0.960891	0.480446	−	0.877025i	$-0.340475\pi$
$73$	8.20986	0.960891	0.480446	+	0.877025i	$0.340475\pi$
$74$	−6.29745	−0.732064
$75$	0	0
$76$	−2.25308	−0.258446
$77$	−0.621456	−0.0708215
$78$	4.39379	0.497499
$79$	13.2865	1.49485	0.747424	−	0.664348i	$-0.231291\pi$
$79$	13.2865	1.49485	0.747424	+	0.664348i	$0.231291\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−20.0188	−2.21071
$83$	6.59494	0.723889	0.361944	−	0.932200i	$-0.382113\pi$
$83$	6.59494	0.723889	0.361944	+	0.932200i	$0.382113\pi$
$84$	7.04112	0.768249
$85$	0	0
$86$	−19.5701	−2.11029
$87$	−1.53695	−0.164779
$88$	−2.78640	−0.297031
$89$	17.7958	1.88635	0.943175	−	0.332296i	$-0.107823\pi$
$89$	17.7958	1.88635	0.943175	+	0.332296i	$0.107823\pi$
$90$	0	0
$91$	2.58731	0.271224
$92$	35.8192	3.73441
$93$	4.32311	0.448285
$94$	2.57687	0.265783
$95$	0	0
$96$	7.65548	0.781335
$97$	−5.61258	−0.569872	−0.284936	−	0.958547i	$-0.591972\pi$
$97$	−5.61258	−0.569872	−0.284936	+	0.958547i	$0.591972\pi$
$98$	−12.1048	−1.22277
$99$	−0.409552	−0.0411615
$100$	0	0
$101$	1.93695	0.192734	0.0963671	−	0.995346i	$-0.469278\pi$
$101$	1.93695	0.192734	0.0963671	+	0.995346i	$0.469278\pi$
$102$	−9.35318	−0.926103
$103$	−6.55151	−0.645540	−0.322770	−	0.946477i	$-0.604614\pi$
$103$	−6.55151	−0.645540	−0.322770	+	0.946477i	$0.604614\pi$
$104$	11.6006	1.13754
$105$	0	0
$106$	26.2925	2.55376
$107$	−0.241779	−0.0233737	−0.0116868	−	0.999932i	$-0.503720\pi$
$107$	−0.241779	−0.0233737	−0.0116868	+	0.999932i	$0.503720\pi$
$108$	4.64024	0.446507
$109$	−3.75817	−0.359968	−0.179984	−	0.983670i	$-0.557605\pi$
$109$	−3.75817	−0.359968	−0.179984	+	0.983670i	$0.557605\pi$
$110$	0	0
$111$	−2.44384	−0.231959
$112$	12.5206	1.18309
$113$	−3.00612	−0.282792	−0.141396	−	0.989953i	$-0.545159\pi$
$113$	−3.00612	−0.282792	−0.141396	+	0.989953i	$0.545159\pi$
$114$	−1.25121	−0.117186
$115$	0	0
$116$	−7.13183	−0.662173
$117$	1.70509	0.157636
$118$	0.306177	0.0281859
$119$	−5.50769	−0.504889
$120$	0	0
$121$	−10.8323	−0.984752
$122$	5.82275	0.527167
$123$	−7.76866	−0.700477
$124$	20.0602	1.80146
$125$	0	0
$126$	3.91015	0.348344
$127$	−9.77663	−0.867536	−0.433768	−	0.901025i	$-0.642816\pi$
$127$	−9.77663	−0.867536	−0.433768	+	0.901025i	$0.642816\pi$
$128$	−7.00185	−0.618882
$129$	−7.59452	−0.668661
$130$	0	0
$131$	−7.07155	−0.617844	−0.308922	−	0.951087i	$-0.599968\pi$
$131$	−7.07155	−0.617844	−0.308922	+	0.951087i	$0.599968\pi$
$132$	−1.90042	−0.165410
$133$	−0.736781	−0.0638870
$134$	−40.6807	−3.51428
$135$	0	0
$136$	−24.6946	−2.11755
$137$	0.552072	0.0471667	0.0235833	−	0.999722i	$-0.492492\pi$
$137$	0.552072	0.0471667	0.0235833	+	0.999722i	$0.492492\pi$
$138$	19.8915	1.69328
$139$	−3.52217	−0.298746	−0.149373	−	0.988781i	$-0.547726\pi$
$139$	−3.52217	−0.298746	−0.149373	+	0.988781i	$0.547726\pi$
$140$	0	0
$141$	1.00000	0.0842152
$142$	−24.4847	−2.05471
$143$	−0.698323	−0.0583967
$144$	8.25132	0.687610
$145$	0	0
$146$	21.1557	1.75086
$147$	−4.69748	−0.387442
$148$	−11.3400	−0.932143
$149$	−4.18581	−0.342915	−0.171458	−	0.985191i	$-0.554848\pi$
$149$	−4.18581	−0.342915	−0.171458	+	0.985191i	$0.554848\pi$
$150$	0	0
$151$	−15.9025	−1.29413	−0.647064	−	0.762436i	$-0.724003\pi$
$151$	−15.9025	−1.29413	−0.647064	+	0.762436i	$0.724003\pi$
$152$	−3.30348	−0.267948
$153$	−3.62967	−0.293442
$154$	−1.60141	−0.129045
$155$	0	0
$156$	7.91202	0.633469
$157$	13.1534	1.04976	0.524880	−	0.851177i	$-0.324110\pi$
$157$	13.1534	1.04976	0.524880	+	0.851177i	$0.324110\pi$
$158$	34.2375	2.72379
$159$	10.2033	0.809174
$160$	0	0
$161$	11.7132	0.923133
$162$	2.57687	0.202458
$163$	−2.82593	−0.221344	−0.110672	−	0.993857i	$-0.535300\pi$
$163$	−2.82593	−0.221344	−0.110672	+	0.993857i	$0.535300\pi$
$164$	−36.0484	−2.81491
$165$	0	0
$166$	16.9943	1.31901
$167$	−12.6036	−0.975296	−0.487648	−	0.873040i	$-0.662145\pi$
$167$	−12.6036	−0.975296	−0.487648	+	0.873040i	$0.662145\pi$
$168$	10.3237	0.796492
$169$	−10.0927	−0.776359
$170$	0	0
$171$	−0.485553	−0.0371312
$172$	−35.2404	−2.68705
$173$	15.3764	1.16905	0.584524	−	0.811377i	$-0.301281\pi$
$173$	15.3764	1.16905	0.584524	+	0.811377i	$0.301281\pi$
$174$	−3.96052	−0.300246
$175$	0	0
$176$	−3.37935	−0.254728
$177$	0.118818	0.00893088
$178$	45.8574	3.43715
$179$	−24.2359	−1.81147	−0.905737	−	0.423840i	$-0.860682\pi$
$179$	−24.2359	−1.81147	−0.905737	+	0.423840i	$0.860682\pi$
$180$	0	0
$181$	−7.51402	−0.558513	−0.279257	−	0.960217i	$-0.590088\pi$
$181$	−7.51402	−0.558513	−0.279257	+	0.960217i	$0.590088\pi$
$182$	6.66716	0.494203
$183$	2.25962	0.167036
$184$	52.5183	3.87170
$185$	0	0
$186$	11.1401	0.816829
$187$	1.48654	0.108707
$188$	4.64024	0.338424
$189$	1.51741	0.110375
$190$	0	0
$191$	14.6707	1.06154	0.530768	−	0.847517i	$-0.321903\pi$
$191$	14.6707	1.06154	0.530768	+	0.847517i	$0.321903\pi$
$192$	3.22450	0.232709
$193$	−4.00150	−0.288034	−0.144017	−	0.989575i	$-0.546002\pi$
$193$	−4.00150	−0.288034	−0.144017	+	0.989575i	$0.546002\pi$
$194$	−14.4629	−1.03837
$195$	0	0
$196$	−21.7974	−1.55696
$197$	17.1433	1.22141	0.610704	−	0.791859i	$-0.290886\pi$
$197$	17.1433	1.22141	0.610704	+	0.791859i	$0.290886\pi$
$198$	−1.05536	−0.0750012
$199$	−12.0104	−0.851392	−0.425696	−	0.904866i	$-0.639971\pi$
$199$	−12.0104	−0.851392	−0.425696	+	0.904866i	$0.639971\pi$
$200$	0	0
$201$	−15.7869	−1.11352
$202$	4.99127	0.351185
$203$	−2.33218	−0.163687
$204$	−16.8426	−1.17921
$205$	0	0
$206$	−16.8824	−1.17625
$207$	7.71926	0.536526
$208$	14.0693	0.975527
$209$	0.198859	0.0137554
$210$	0	0
$211$	26.1444	1.79986	0.899928	−	0.436039i	$-0.143619\pi$
$211$	26.1444	1.79986	0.899928	+	0.436039i	$0.143619\pi$
$212$	47.3457	3.25172
$213$	−9.50172	−0.651047
$214$	−0.623032	−0.0425896
$215$	0	0
$216$	6.80354	0.462922
$217$	6.55990	0.445315
$218$	−9.68430	−0.655904
$219$	8.20986	0.554771
$220$	0	0
$221$	−6.18892	−0.416312
$222$	−6.29745	−0.422657
$223$	8.60705	0.576371	0.288185	−	0.957575i	$-0.406948\pi$
$223$	8.60705	0.576371	0.288185	+	0.957575i	$0.406948\pi$
$224$	11.6165	0.776158
$225$	0	0
$226$	−7.74636	−0.515280
$227$	−29.0547	−1.92843	−0.964214	−	0.265124i	$-0.914587\pi$
$227$	−29.0547	−1.92843	−0.964214	+	0.265124i	$0.914587\pi$
$228$	−2.25308	−0.149214
$229$	5.27755	0.348750	0.174375	−	0.984679i	$-0.444209\pi$
$229$	5.27755	0.348750	0.174375	+	0.984679i	$0.444209\pi$
$230$	0	0
$231$	−0.621456	−0.0408888
$232$	−10.4567	−0.686517
$233$	−25.5165	−1.67164	−0.835821	−	0.549002i	$-0.815008\pi$
$233$	−25.5165	−1.67164	−0.835821	+	0.549002i	$0.815008\pi$
$234$	4.39379	0.287231
$235$	0	0
$236$	0.551342	0.0358893
$237$	13.2865	0.863051
$238$	−14.1926	−0.919968
$239$	23.0647	1.49193	0.745966	−	0.665984i	$-0.231988\pi$
$239$	23.0647	1.49193	0.745966	+	0.665984i	$0.231988\pi$
$240$	0	0
$241$	−21.2707	−1.37017	−0.685083	−	0.728465i	$-0.740234\pi$
$241$	−21.2707	−1.37017	−0.685083	+	0.728465i	$0.740234\pi$
$242$	−27.9133	−1.79433
$243$	1.00000	0.0641500
$244$	10.4852	0.671246
$245$	0	0
$246$	−20.0188	−1.27635
$247$	−0.827913	−0.0526788
$248$	29.4124	1.86769
$249$	6.59494	0.417937
$250$	0	0
$251$	18.9282	1.19474	0.597370	−	0.801966i	$-0.296213\pi$
$251$	18.9282	1.19474	0.597370	+	0.801966i	$0.296213\pi$
$252$	7.04112	0.443549
$253$	−3.16144	−0.198758
$254$	−25.1931	−1.58075
$255$	0	0
$256$	−24.4918	−1.53074
$257$	21.7891	1.35916	0.679582	−	0.733599i	$-0.262161\pi$
$257$	21.7891	1.35916	0.679582	+	0.733599i	$0.262161\pi$
$258$	−19.5701	−1.21838
$259$	−3.70830	−0.230423
$260$	0	0
$261$	−1.53695	−0.0951350
$262$	−18.2224	−1.12579
$263$	−11.1448	−0.687219	−0.343610	−	0.939113i	$-0.611650\pi$
$263$	−11.1448	−0.687219	−0.343610	+	0.939113i	$0.611650\pi$
$264$	−2.78640	−0.171491
$265$	0	0
$266$	−1.89859	−0.116410
$267$	17.7958	1.08908
$268$	−73.2549	−4.47475
$269$	25.8889	1.57848	0.789238	−	0.614088i	$-0.210476\pi$
$269$	25.8889	1.57848	0.789238	+	0.614088i	$0.210476\pi$
$270$	0	0
$271$	17.7769	1.07987	0.539934	−	0.841707i	$-0.318449\pi$
$271$	17.7769	1.07987	0.539934	+	0.841707i	$0.318449\pi$
$272$	−29.9496	−1.81596
$273$	2.58731	0.156591
$274$	1.42261	0.0859433
$275$	0	0
$276$	35.8192	2.15606
$277$	−23.2875	−1.39921	−0.699604	−	0.714531i	$-0.746640\pi$
$277$	−23.2875	−1.39921	−0.699604	+	0.714531i	$0.746640\pi$
$278$	−9.07615	−0.544351
$279$	4.32311	0.258818
$280$	0	0
$281$	18.6599	1.11316	0.556578	−	0.830795i	$-0.312114\pi$
$281$	18.6599	1.11316	0.556578	+	0.830795i	$0.312114\pi$
$282$	2.57687	0.153450
$283$	−25.1730	−1.49638	−0.748189	−	0.663486i	$-0.769076\pi$
$283$	−25.1730	−1.49638	−0.748189	+	0.663486i	$0.769076\pi$
$284$	−44.0902	−2.61627
$285$	0	0
$286$	−1.79949	−0.106406
$287$	−11.7882	−0.695836
$288$	7.65548	0.451104
$289$	−3.82546	−0.225027
$290$	0	0
$291$	−5.61258	−0.329016
$292$	38.0957	2.22938
$293$	28.6924	1.67622	0.838112	−	0.545497i	$-0.183659\pi$
$293$	28.6924	1.67622	0.838112	+	0.545497i	$0.183659\pi$
$294$	−12.1048	−0.705965
$295$	0	0
$296$	−16.6268	−0.966411
$297$	−0.409552	−0.0237646
$298$	−10.7863	−0.624833
$299$	13.1620	0.761180
$300$	0	0
$301$	−11.5240	−0.664231
$302$	−40.9786	−2.35806
$303$	1.93695	0.111275
$304$	−4.00646	−0.229786
$305$	0	0
$306$	−9.35318	−0.534686
$307$	8.58383	0.489905	0.244953	−	0.969535i	$-0.421228\pi$
$307$	8.58383	0.489905	0.244953	+	0.969535i	$0.421228\pi$
$308$	−2.88371	−0.164314
$309$	−6.55151	−0.372703
$310$	0	0
$311$	13.5732	0.769664	0.384832	−	0.922987i	$-0.374259\pi$
$311$	13.5732	0.769664	0.384832	+	0.922987i	$0.374259\pi$
$312$	11.6006	0.656757
$313$	−7.43322	−0.420151	−0.210075	−	0.977685i	$-0.567371\pi$
$313$	−7.43322	−0.420151	−0.210075	+	0.977685i	$0.567371\pi$
$314$	33.8947	1.91279
$315$	0	0
$316$	61.6525	3.46822
$317$	−16.1762	−0.908543	−0.454272	−	0.890863i	$-0.650100\pi$
$317$	−16.1762	−0.908543	−0.454272	+	0.890863i	$0.650100\pi$
$318$	26.2925	1.47441
$319$	0.629462	0.0352431
$320$	0	0
$321$	−0.241779	−0.0134948
$322$	30.1835	1.68206
$323$	1.76240	0.0980626
$324$	4.64024	0.257791
$325$	0	0
$326$	−7.28203	−0.403315
$327$	−3.75817	−0.207827
$328$	−52.8544	−2.91839
$329$	1.51741	0.0836573
$330$	0	0
$331$	23.9233	1.31494	0.657472	−	0.753479i	$-0.271626\pi$
$331$	23.9233	1.31494	0.657472	+	0.753479i	$0.271626\pi$
$332$	30.6021	1.67951
$333$	−2.44384	−0.133922
$334$	−32.4778	−1.77710
$335$	0	0
$336$	12.5206	0.683055
$337$	−0.151324	−0.00824317	−0.00412158	−	0.999992i	$-0.501312\pi$
$337$	−0.151324	−0.00824317	−0.00412158	+	0.999992i	$0.501312\pi$
$338$	−26.0074	−1.41462
$339$	−3.00612	−0.163270
$340$	0	0
$341$	−1.77054	−0.0958799
$342$	−1.25121	−0.0676575
$343$	−17.7498	−0.958400
$344$	−51.6696	−2.78584
$345$	0	0
$346$	39.6230	2.13014
$347$	−6.17087	−0.331270	−0.165635	−	0.986187i	$-0.552967\pi$
$347$	−6.17087	−0.331270	−0.165635	+	0.986187i	$0.552967\pi$
$348$	−7.13183	−0.382306
$349$	27.4329	1.46845	0.734226	−	0.678905i	$-0.237545\pi$
$349$	27.4329	1.46845	0.734226	+	0.678905i	$0.237545\pi$
$350$	0	0
$351$	1.70509	0.0910110
$352$	−3.13532	−0.167113
$353$	−30.5374	−1.62534	−0.812671	−	0.582723i	$-0.801987\pi$
$353$	−30.5374	−1.62534	−0.812671	+	0.582723i	$0.801987\pi$
$354$	0.306177	0.0162731
$355$	0	0
$356$	82.5767	4.37656
$357$	−5.50769	−0.291498
$358$	−62.4526	−3.30072
$359$	−2.99142	−0.157881	−0.0789406	−	0.996879i	$-0.525154\pi$
$359$	−2.99142	−0.157881	−0.0789406	+	0.996879i	$0.525154\pi$
$360$	0	0
$361$	−18.7642	−0.987591
$362$	−19.3626	−1.01768
$363$	−10.8323	−0.568547
$364$	12.0057	0.629272
$365$	0	0
$366$	5.82275	0.304360
$367$	−5.64402	−0.294615	−0.147308	−	0.989091i	$-0.547061\pi$
$367$	−5.64402	−0.294615	−0.147308	+	0.989091i	$0.547061\pi$
$368$	63.6941	3.32029
$369$	−7.76866	−0.404420
$370$	0	0
$371$	15.4825	0.803813
$372$	20.0602	1.04007
$373$	32.7211	1.69423	0.847116	−	0.531408i	$-0.178337\pi$
$373$	32.7211	1.69423	0.847116	+	0.531408i	$0.178337\pi$
$374$	3.83062	0.198076
$375$	0	0
$376$	6.80354	0.350866
$377$	−2.62064	−0.134970
$378$	3.91015	0.201116
$379$	−16.4931	−0.847194	−0.423597	−	0.905851i	$-0.639233\pi$
$379$	−16.4931	−0.847194	−0.423597	+	0.905851i	$0.639233\pi$
$380$	0	0
$381$	−9.77663	−0.500872
$382$	37.8045	1.93425
$383$	11.3694	0.580950	0.290475	−	0.956883i	$-0.406187\pi$
$383$	11.3694	0.580950	0.290475	+	0.956883i	$0.406187\pi$
$384$	−7.00185	−0.357312
$385$	0	0
$386$	−10.3113	−0.524833
$387$	−7.59452	−0.386051
$388$	−26.0437	−1.32217
$389$	−4.34727	−0.220415	−0.110208	−	0.993909i	$-0.535152\pi$
$389$	−4.34727	−0.220415	−0.110208	+	0.993909i	$0.535152\pi$
$390$	0	0
$391$	−28.0184	−1.41695
$392$	−31.9595	−1.61420
$393$	−7.07155	−0.356713
$394$	44.1759	2.22555
$395$	0	0
$396$	−1.90042	−0.0954996
$397$	−23.3610	−1.17245	−0.586227	−	0.810147i	$-0.699387\pi$
$397$	−23.3610	−1.17245	−0.586227	+	0.810147i	$0.699387\pi$
$398$	−30.9491	−1.55134
$399$	−0.736781	−0.0368852
$400$	0	0
$401$	−1.43302	−0.0715614	−0.0357807	−	0.999360i	$-0.511392\pi$
$401$	−1.43302	−0.0715614	−0.0357807	+	0.999360i	$0.511392\pi$
$402$	−40.6807	−2.02897
$403$	7.37129	0.367190
$404$	8.98793	0.447166
$405$	0	0
$406$	−6.00972	−0.298257
$407$	1.00088	0.0496118
$408$	−24.6946	−1.22257
$409$	10.2611	0.507378	0.253689	−	0.967286i	$-0.418356\pi$
$409$	10.2611	0.507378	0.253689	+	0.967286i	$0.418356\pi$
$410$	0	0
$411$	0.552072	0.0272317
$412$	−30.4006	−1.49773
$413$	0.180295	0.00887171
$414$	19.8915	0.977614
$415$	0	0
$416$	13.0533	0.639990
$417$	−3.52217	−0.172481
$418$	0.512434	0.0250640
$419$	4.69348	0.229291	0.114646	−	0.993406i	$-0.463427\pi$
$419$	4.69348	0.229291	0.114646	+	0.993406i	$0.463427\pi$
$420$	0	0
$421$	15.7878	0.769448	0.384724	−	0.923032i	$-0.374297\pi$
$421$	15.7878	0.769448	0.384724	+	0.923032i	$0.374297\pi$
$422$	67.3706	3.27955
$423$	1.00000	0.0486217
$424$	69.4185	3.37126
$425$	0	0
$426$	−24.4847	−1.18629
$427$	3.42877	0.165930
$428$	−1.12191	−0.0542297
$429$	−0.698323	−0.0337154
$430$	0	0
$431$	15.5978	0.751319	0.375659	−	0.926758i	$-0.377416\pi$
$431$	15.5978	0.751319	0.375659	+	0.926758i	$0.377416\pi$
$432$	8.25132	0.396992
$433$	−31.9312	−1.53452	−0.767259	−	0.641338i	$-0.778380\pi$
$433$	−31.9312	−1.53452	−0.767259	+	0.641338i	$0.778380\pi$
$434$	16.9040	0.811418
$435$	0	0
$436$	−17.4388	−0.835167
$437$	−3.74811	−0.179297
$438$	21.1557	1.01086
$439$	37.0698	1.76925	0.884623	−	0.466307i	$-0.154416\pi$
$439$	37.0698	1.76925	0.884623	+	0.466307i	$0.154416\pi$
$440$	0	0
$441$	−4.69748	−0.223690
$442$	−15.9480	−0.758570
$443$	−29.5069	−1.40192	−0.700958	−	0.713202i	$-0.747244\pi$
$443$	−29.5069	−1.40192	−0.700958	+	0.713202i	$0.747244\pi$
$444$	−11.3400	−0.538173
$445$	0	0
$446$	22.1792	1.05022
$447$	−4.18581	−0.197982
$448$	4.89288	0.231167
$449$	7.79984	0.368097	0.184049	−	0.982917i	$-0.441080\pi$
$449$	7.79984	0.368097	0.184049	+	0.982917i	$0.441080\pi$
$450$	0	0
$451$	3.18167	0.149819
$452$	−13.9491	−0.656110
$453$	−15.9025	−0.747165
$454$	−74.8701	−3.51383
$455$	0	0
$456$	−3.30348	−0.154700
$457$	−21.6451	−1.01252	−0.506258	−	0.862382i	$-0.668972\pi$
$457$	−21.6451	−1.01252	−0.506258	+	0.862382i	$0.668972\pi$
$458$	13.5995	0.635465
$459$	−3.62967	−0.169419
$460$	0	0
$461$	−35.0177	−1.63094	−0.815469	−	0.578801i	$-0.803521\pi$
$461$	−35.0177	−1.63094	−0.815469	+	0.578801i	$0.803521\pi$
$462$	−1.60141	−0.0745043
$463$	−13.1365	−0.610503	−0.305252	−	0.952272i	$-0.598741\pi$
$463$	−13.1365	−0.610503	−0.305252	+	0.952272i	$0.598741\pi$
$464$	−12.6819	−0.588742
$465$	0	0
$466$	−65.7526	−3.04593
$467$	−15.5109	−0.717757	−0.358878	−	0.933384i	$-0.616841\pi$
$467$	−15.5109	−0.717757	−0.358878	+	0.933384i	$0.616841\pi$
$468$	7.91202	0.365733
$469$	−23.9551	−1.10614
$470$	0	0
$471$	13.1534	0.606079
$472$	0.808380	0.0372087
$473$	3.11035	0.143014
$474$	34.2375	1.57258
$475$	0	0
$476$	−25.5570	−1.17140
$477$	10.2033	0.467177
$478$	59.4347	2.71848
$479$	18.6295	0.851204	0.425602	−	0.904910i	$-0.360062\pi$
$479$	18.6295	0.851204	0.425602	+	0.904910i	$0.360062\pi$
$480$	0	0
$481$	−4.16697	−0.189998
$482$	−54.8117	−2.49661
$483$	11.7132	0.532971
$484$	−50.2643	−2.28474
$485$	0	0
$486$	2.57687	0.116889
$487$	36.0131	1.63191	0.815955	−	0.578115i	$-0.196212\pi$
$487$	36.0131	1.63191	0.815955	+	0.578115i	$0.196212\pi$
$488$	15.3734	0.695923
$489$	−2.82593	−0.127793
$490$	0	0
$491$	17.0040	0.767379	0.383690	−	0.923462i	$-0.374653\pi$
$491$	17.0040	0.767379	0.383690	+	0.923462i	$0.374653\pi$
$492$	−36.0484	−1.62519
$493$	5.57864	0.251249
$494$	−2.13342	−0.0959871
$495$	0	0
$496$	35.6714	1.60169
$497$	−14.4180	−0.646734
$498$	16.9943	0.761531
$499$	−20.0215	−0.896283	−0.448142	−	0.893963i	$-0.647914\pi$
$499$	−20.0215	−0.896283	−0.448142	+	0.893963i	$0.647914\pi$
$500$	0	0
$501$	−12.6036	−0.563087
$502$	48.7755	2.17696
$503$	1.34377	0.0599159	0.0299579	−	0.999551i	$-0.490463\pi$
$503$	1.34377	0.0599159	0.0299579	+	0.999551i	$0.490463\pi$
$504$	10.3237	0.459855
$505$	0	0
$506$	−8.14660	−0.362161
$507$	−10.0927	−0.448231
$508$	−45.3659	−2.01279
$509$	37.6244	1.66767	0.833837	−	0.552011i	$-0.186139\pi$
$509$	37.6244	1.66767	0.833837	+	0.552011i	$0.186139\pi$
$510$	0	0
$511$	12.4577	0.551095
$512$	−49.1085	−2.17031
$513$	−0.485553	−0.0214377
$514$	56.1475	2.47656
$515$	0	0
$516$	−35.2404	−1.55137
$517$	−0.409552	−0.0180121
$518$	−9.55579	−0.419857
$519$	15.3764	0.674950
$520$	0	0
$521$	−23.1702	−1.01510	−0.507551	−	0.861621i	$-0.669449\pi$
$521$	−23.1702	−1.01510	−0.507551	+	0.861621i	$0.669449\pi$
$522$	−3.96052	−0.173347
$523$	41.1342	1.79867	0.899335	−	0.437259i	$-0.144051\pi$
$523$	41.1342	1.79867	0.899335	+	0.437259i	$0.144051\pi$
$524$	−32.8137	−1.43347
$525$	0	0
$526$	−28.7187	−1.25220
$527$	−15.6915	−0.683531
$528$	−3.37935	−0.147067
$529$	36.5870	1.59074
$530$	0	0
$531$	0.118818	0.00515625
$532$	−3.41884	−0.148226
$533$	−13.2463	−0.573760
$534$	45.8574	1.98444
$535$	0	0
$536$	−107.407	−4.63926
$537$	−24.2359	−1.04586
$538$	66.7123	2.87617
$539$	1.92386	0.0828666
$540$	0	0
$541$	7.92870	0.340882	0.170441	−	0.985368i	$-0.445481\pi$
$541$	7.92870	0.340882	0.170441	+	0.985368i	$0.445481\pi$
$542$	45.8086	1.96765
$543$	−7.51402	−0.322458
$544$	−27.7869	−1.19135
$545$	0	0
$546$	6.66716	0.285328
$547$	18.6294	0.796537	0.398268	−	0.917269i	$-0.369611\pi$
$547$	18.6294	0.796537	0.398268	+	0.917269i	$0.369611\pi$
$548$	2.56174	0.109432
$549$	2.25962	0.0964384
$550$	0	0
$551$	0.746273	0.0317923
$552$	52.5183	2.23533
$553$	20.1610	0.857333
$554$	−60.0087	−2.54952
$555$	0	0
$556$	−16.3437	−0.693127
$557$	−13.1979	−0.559214	−0.279607	−	0.960115i	$-0.590204\pi$
$557$	−13.1979	−0.559214	−0.279607	+	0.960115i	$0.590204\pi$
$558$	11.1401	0.471597
$559$	−12.9494	−0.547699
$560$	0	0
$561$	1.48654	0.0627618
$562$	48.0840	2.02830
$563$	6.28490	0.264877	0.132438	−	0.991191i	$-0.457719\pi$
$563$	6.28490	0.264877	0.132438	+	0.991191i	$0.457719\pi$
$564$	4.64024	0.195389
$565$	0	0
$566$	−64.8674	−2.72658
$567$	1.51741	0.0637250
$568$	−64.6453	−2.71246
$569$	−0.393539	−0.0164980	−0.00824900	−	0.999966i	$-0.502626\pi$
$569$	−0.393539	−0.0164980	−0.00824900	+	0.999966i	$0.502626\pi$
$570$	0	0
$571$	26.3529	1.10284	0.551418	−	0.834229i	$-0.314087\pi$
$571$	26.3529	1.10284	0.551418	+	0.834229i	$0.314087\pi$
$572$	−3.24039	−0.135487
$573$	14.6707	0.612879
$574$	−30.3766	−1.26790
$575$	0	0
$576$	3.22450	0.134354
$577$	−29.8939	−1.24450	−0.622249	−	0.782819i	$-0.713781\pi$
$577$	−29.8939	−1.24450	−0.622249	+	0.782819i	$0.713781\pi$
$578$	−9.85770	−0.410026
$579$	−4.00150	−0.166297
$580$	0	0
$581$	10.0072	0.415168
$582$	−14.4629	−0.599506
$583$	−4.17878	−0.173067
$584$	55.8561	2.31134
$585$	0	0
$586$	73.9363	3.05428
$587$	−33.5669	−1.38545	−0.692727	−	0.721200i	$-0.743591\pi$
$587$	−33.5669	−1.38545	−0.692727	+	0.721200i	$0.743591\pi$
$588$	−21.7974	−0.898911
$589$	−2.09910	−0.0864919
$590$	0	0
$591$	17.1433	0.705181
$592$	−20.1649	−0.828774
$593$	−16.7068	−0.686067	−0.343033	−	0.939323i	$-0.611454\pi$
$593$	−16.7068	−0.686067	−0.343033	+	0.939323i	$0.611454\pi$
$594$	−1.05536	−0.0433020
$595$	0	0
$596$	−19.4232	−0.795604
$597$	−12.0104	−0.491551
$598$	33.9168	1.38696
$599$	−31.9754	−1.30648	−0.653241	−	0.757150i	$-0.726591\pi$
$599$	−31.9754	−1.30648	−0.653241	+	0.757150i	$0.726591\pi$
$600$	0	0
$601$	11.4369	0.466520	0.233260	−	0.972414i	$-0.425061\pi$
$601$	11.4369	0.466520	0.233260	+	0.972414i	$0.425061\pi$
$602$	−29.6957	−1.21031
$603$	−15.7869	−0.642892
$604$	−73.7914	−3.00253
$605$	0	0
$606$	4.99127	0.202756
$607$	−0.310562	−0.0126053	−0.00630266	−	0.999980i	$-0.502006\pi$
$607$	−0.310562	−0.0126053	−0.00630266	+	0.999980i	$0.502006\pi$
$608$	−3.71715	−0.150750
$609$	−2.33218	−0.0945047
$610$	0	0
$611$	1.70509	0.0689806
$612$	−16.8426	−0.680820
$613$	−11.6310	−0.469770	−0.234885	−	0.972023i	$-0.575471\pi$
$613$	−11.6310	−0.469770	−0.234885	+	0.972023i	$0.575471\pi$
$614$	22.1194	0.892665
$615$	0	0
$616$	−4.22810	−0.170355
$617$	13.0457	0.525199	0.262599	−	0.964905i	$-0.415420\pi$
$617$	13.0457	0.525199	0.262599	+	0.964905i	$0.415420\pi$
$618$	−16.8824	−0.679108
$619$	23.8892	0.960190	0.480095	−	0.877217i	$-0.340602\pi$
$619$	23.8892	0.960190	0.480095	+	0.877217i	$0.340602\pi$
$620$	0	0
$621$	7.71926	0.309763
$622$	34.9763	1.40242
$623$	27.0034	1.08187
$624$	14.0693	0.563221
$625$	0	0
$626$	−19.1544	−0.765565
$627$	0.198859	0.00794168
$628$	61.0351	2.43557
$629$	8.87035	0.353684
$630$	0	0
$631$	−3.97907	−0.158404	−0.0792022	−	0.996859i	$-0.525237\pi$
$631$	−3.97907	−0.158404	−0.0792022	+	0.996859i	$0.525237\pi$
$632$	90.3952	3.59573
$633$	26.1444	1.03915
$634$	−41.6838	−1.65547
$635$	0	0
$636$	47.3457	1.87738
$637$	−8.00963	−0.317353
$638$	1.62204	0.0642172
$639$	−9.50172	−0.375882
$640$	0	0
$641$	16.7620	0.662060	0.331030	−	0.943620i	$-0.392604\pi$
$641$	16.7620	0.662060	0.331030	+	0.943620i	$0.392604\pi$
$642$	−0.623032	−0.0245891
$643$	1.13421	0.0447289	0.0223644	−	0.999750i	$-0.492881\pi$
$643$	1.13421	0.0447289	0.0223644	+	0.999750i	$0.492881\pi$
$644$	54.3522	2.14178
$645$	0	0
$646$	4.54147	0.178682
$647$	24.1301	0.948652	0.474326	−	0.880349i	$-0.342692\pi$
$647$	24.1301	0.948652	0.474326	+	0.880349i	$0.342692\pi$
$648$	6.80354	0.267268
$649$	−0.0486620	−0.00191015
$650$	0	0
$651$	6.55990	0.257103
$652$	−13.1130	−0.513543
$653$	−3.75913	−0.147106	−0.0735531	−	0.997291i	$-0.523434\pi$
$653$	−3.75913	−0.147106	−0.0735531	+	0.997291i	$0.523434\pi$
$654$	−9.68430	−0.378686
$655$	0	0
$656$	−64.1017	−2.50275
$657$	8.20986	0.320297
$658$	3.91015	0.152434
$659$	−10.4017	−0.405193	−0.202597	−	0.979262i	$-0.564938\pi$
$659$	−10.4017	−0.405193	−0.202597	+	0.979262i	$0.564938\pi$
$660$	0	0
$661$	−7.27614	−0.283009	−0.141505	−	0.989938i	$-0.545194\pi$
$661$	−7.27614	−0.283009	−0.141505	+	0.989938i	$0.545194\pi$
$662$	61.6472	2.39598
$663$	−6.18892	−0.240358
$664$	44.8689	1.74125
$665$	0	0
$666$	−6.29745	−0.244021
$667$	−11.8641	−0.459381
$668$	−58.4837	−2.26280
$669$	8.60705	0.332768
$670$	0	0
$671$	−0.925434	−0.0357260
$672$	11.6165	0.448115
$673$	−31.4216	−1.21121	−0.605607	−	0.795764i	$-0.707070\pi$
$673$	−31.4216	−1.21121	−0.605607	+	0.795764i	$0.707070\pi$
$674$	−0.389943	−0.0150200
$675$	0	0
$676$	−46.8324	−1.80124
$677$	−19.6313	−0.754493	−0.377247	−	0.926113i	$-0.623129\pi$
$677$	−19.6313	−0.754493	−0.377247	+	0.926113i	$0.623129\pi$
$678$	−7.74636	−0.297497
$679$	−8.51657	−0.326836
$680$	0	0
$681$	−29.0547	−1.11338
$682$	−4.56244	−0.174705
$683$	3.80221	0.145487	0.0727437	−	0.997351i	$-0.476824\pi$
$683$	3.80221	0.145487	0.0727437	+	0.997351i	$0.476824\pi$
$684$	−2.25308	−0.0861488
$685$	0	0
$686$	−45.7389	−1.74632
$687$	5.27755	0.201351
$688$	−62.6649	−2.38908
$689$	17.3975	0.662794
$690$	0	0
$691$	47.0061	1.78819	0.894097	−	0.447873i	$-0.147818\pi$
$691$	47.0061	1.78819	0.894097	+	0.447873i	$0.147818\pi$
$692$	71.3502	2.71233
$693$	−0.621456	−0.0236072
$694$	−15.9015	−0.603613
$695$	0	0
$696$	−10.4567	−0.396361
$697$	28.1977	1.06806
$698$	70.6910	2.67569
$699$	−25.5165	−0.965123
$700$	0	0
$701$	37.4539	1.41461	0.707307	−	0.706906i	$-0.249910\pi$
$701$	37.4539	1.41461	0.707307	+	0.706906i	$0.249910\pi$
$702$	4.39379	0.165833
$703$	1.18662	0.0447541
$704$	−1.32060	−0.0497721
$705$	0	0
$706$	−78.6907	−2.96157
$707$	2.93914	0.110538
$708$	0.551342	0.0207207
$709$	34.7204	1.30395	0.651976	−	0.758240i	$-0.273940\pi$
$709$	34.7204	1.30395	0.651976	+	0.758240i	$0.273940\pi$
$710$	0	0
$711$	13.2865	0.498283
$712$	121.074	4.53745
$713$	33.3712	1.24976
$714$	−14.1926	−0.531144
$715$	0	0
$716$	−112.460	−4.20284
$717$	23.0647	0.861368
$718$	−7.70850	−0.287679
$719$	−15.7765	−0.588363	−0.294181	−	0.955750i	$-0.595047\pi$
$719$	−15.7765	−0.588363	−0.294181	+	0.955750i	$0.595047\pi$
$720$	0	0
$721$	−9.94130	−0.370233
$722$	−48.3529	−1.79951
$723$	−21.2707	−0.791066
$724$	−34.8669	−1.29582
$725$	0	0
$726$	−27.9133	−1.03596
$727$	−9.80778	−0.363750	−0.181875	−	0.983322i	$-0.558217\pi$
$727$	−9.80778	−0.363750	−0.181875	+	0.983322i	$0.558217\pi$
$728$	17.6029	0.652406
$729$	1.00000	0.0370370
$730$	0	0
$731$	27.5657	1.01955
$732$	10.4852	0.387544
$733$	29.9733	1.10709	0.553544	−	0.832820i	$-0.313275\pi$
$733$	29.9733	1.10709	0.553544	+	0.832820i	$0.313275\pi$
$734$	−14.5439	−0.536824
$735$	0	0
$736$	59.0947	2.17826
$737$	6.46555	0.238162
$738$	−20.0188	−0.736902
$739$	20.7720	0.764109	0.382055	−	0.924140i	$-0.375217\pi$
$739$	20.7720	0.764109	0.382055	+	0.924140i	$0.375217\pi$
$740$	0	0
$741$	−0.827913	−0.0304141
$742$	39.8964	1.46464
$743$	30.5350	1.12022	0.560110	−	0.828418i	$-0.310759\pi$
$743$	30.5350	1.12022	0.560110	+	0.828418i	$0.310759\pi$
$744$	29.4124	1.07831
$745$	0	0
$746$	84.3178	3.08709
$747$	6.59494	0.241296
$748$	6.89790	0.252212
$749$	−0.366877	−0.0134054
$750$	0	0
$751$	−30.9000	−1.12756	−0.563779	−	0.825926i	$-0.690653\pi$
$751$	−30.9000	−1.12756	−0.563779	+	0.825926i	$0.690653\pi$
$752$	8.25132	0.300895
$753$	18.9282	0.689783
$754$	−6.75305	−0.245931
$755$	0	0
$756$	7.04112	0.256083
$757$	9.99773	0.363374	0.181687	−	0.983356i	$-0.441844\pi$
$757$	9.99773	0.363374	0.181687	+	0.983356i	$0.441844\pi$
$758$	−42.5005	−1.54369
$759$	−3.16144	−0.114753
$760$	0	0
$761$	18.0677	0.654953	0.327476	−	0.944859i	$-0.393802\pi$
$761$	18.0677	0.654953	0.327476	+	0.944859i	$0.393802\pi$
$762$	−25.1931	−0.912648
$763$	−5.70267	−0.206451
$764$	68.0757	2.46289
$765$	0	0
$766$	29.2975	1.05856
$767$	0.202595	0.00731528
$768$	−24.4918	−0.883773
$769$	5.15329	0.185832	0.0929162	−	0.995674i	$-0.470381\pi$
$769$	5.15329	0.185832	0.0929162	+	0.995674i	$0.470381\pi$
$770$	0	0
$771$	21.7891	0.784714
$772$	−18.5679	−0.668273
$773$	−16.5239	−0.594322	−0.297161	−	0.954827i	$-0.596040\pi$
$773$	−16.5239	−0.594322	−0.297161	+	0.954827i	$0.596040\pi$
$774$	−19.5701	−0.703432
$775$	0	0
$776$	−38.1854	−1.37078
$777$	−3.70830	−0.133035
$778$	−11.2023	−0.401623
$779$	3.77210	0.135149
$780$	0	0
$781$	3.89145	0.139247
$782$	−72.1997	−2.58186
$783$	−1.53695	−0.0549262
$784$	−38.7604	−1.38430
$785$	0	0
$786$	−18.2224	−0.649973
$787$	−2.05263	−0.0731684	−0.0365842	−	0.999331i	$-0.511648\pi$
$787$	−2.05263	−0.0731684	−0.0365842	+	0.999331i	$0.511648\pi$
$788$	79.5489	2.83381
$789$	−11.1448	−0.396766
$790$	0	0
$791$	−4.56150	−0.162188
$792$	−2.78640	−0.0990105
$793$	3.85286	0.136819
$794$	−60.1981	−2.13635
$795$	0	0
$796$	−55.7309	−1.97533
$797$	37.3883	1.32436	0.662180	−	0.749345i	$-0.269631\pi$
$797$	37.3883	1.32436	0.662180	+	0.749345i	$0.269631\pi$
$798$	−1.89859	−0.0672092
$799$	−3.62967	−0.128409
$800$	0	0
$801$	17.7958	0.628783
$802$	−3.69269	−0.130393
$803$	−3.36236	−0.118655
$804$	−73.2549	−2.58350
$805$	0	0
$806$	18.9948	0.669064
$807$	25.8889	0.911333
$808$	13.1781	0.463605
$809$	−23.1030	−0.812257	−0.406128	−	0.913816i	$-0.633121\pi$
$809$	−23.1030	−0.812257	−0.406128	+	0.913816i	$0.633121\pi$
$810$	0	0
$811$	−23.6977	−0.832140	−0.416070	−	0.909333i	$-0.636593\pi$
$811$	−23.6977	−0.832140	−0.416070	+	0.909333i	$0.636593\pi$
$812$	−10.8219	−0.379773
$813$	17.7769	0.623462
$814$	2.57914	0.0903986
$815$	0	0
$816$	−29.9496	−1.04845
$817$	3.68755	0.129011
$818$	26.4414	0.924503
$819$	2.58731	0.0904081
$820$	0	0
$821$	42.8599	1.49582	0.747911	−	0.663799i	$-0.231057\pi$
$821$	42.8599	1.49582	0.747911	+	0.663799i	$0.231057\pi$
$822$	1.42261	0.0496194
$823$	22.2558	0.775788	0.387894	−	0.921704i	$-0.373203\pi$
$823$	22.2558	0.775788	0.387894	+	0.921704i	$0.373203\pi$
$824$	−44.5735	−1.55279
$825$	0	0
$826$	0.464595	0.0161653
$827$	−25.8507	−0.898917	−0.449459	−	0.893301i	$-0.648383\pi$
$827$	−25.8507	−0.898917	−0.449459	+	0.893301i	$0.648383\pi$
$828$	35.8192	1.24480
$829$	−8.19269	−0.284544	−0.142272	−	0.989828i	$-0.545441\pi$
$829$	−8.19269	−0.284544	−0.142272	+	0.989828i	$0.545441\pi$
$830$	0	0
$831$	−23.2875	−0.807833
$832$	5.49807	0.190611
$833$	17.0503	0.590759
$834$	−9.07615	−0.314281
$835$	0	0
$836$	0.922755	0.0319141
$837$	4.32311	0.149428
$838$	12.0945	0.417796
$839$	−13.6146	−0.470027	−0.235013	−	0.971992i	$-0.575513\pi$
$839$	−13.6146	−0.470027	−0.235013	+	0.971992i	$0.575513\pi$
$840$	0	0
$841$	−26.6378	−0.918544
$842$	40.6829	1.40203
$843$	18.6599	0.642681
$844$	121.316	4.17588
$845$	0	0
$846$	2.57687	0.0885945
$847$	−16.4369	−0.564780
$848$	84.1907	2.89112
$849$	−25.1730	−0.863934
$850$	0	0
$851$	−18.8647	−0.646672
$852$	−44.0902	−1.51051
$853$	19.4589	0.666261	0.333130	−	0.942881i	$-0.391895\pi$
$853$	19.4589	0.666261	0.333130	+	0.942881i	$0.391895\pi$
$854$	8.83547	0.302344
$855$	0	0
$856$	−1.64495	−0.0562233
$857$	18.3188	0.625758	0.312879	−	0.949793i	$-0.398707\pi$
$857$	18.3188	0.625758	0.312879	+	0.949793i	$0.398707\pi$
$858$	−1.79949	−0.0614334
$859$	−57.3781	−1.95772	−0.978858	−	0.204540i	$-0.934430\pi$
$859$	−57.3781	−1.95772	−0.978858	+	0.204540i	$0.934430\pi$
$860$	0	0
$861$	−11.7882	−0.401741
$862$	40.1934	1.36899
$863$	18.0524	0.614510	0.307255	−	0.951627i	$-0.400590\pi$
$863$	18.0524	0.614510	0.307255	+	0.951627i	$0.400590\pi$
$864$	7.65548	0.260445
$865$	0	0
$866$	−82.2825	−2.79607
$867$	−3.82546	−0.129919
$868$	30.4395	1.03318
$869$	−5.44151	−0.184591
$870$	0	0
$871$	−26.9181	−0.912084
$872$	−25.5689	−0.865871
$873$	−5.61258	−0.189957
$874$	−9.65838	−0.326700
$875$	0	0
$876$	38.0957	1.28713
$877$	−14.4579	−0.488209	−0.244105	−	0.969749i	$-0.578494\pi$
$877$	−14.4579	−0.488209	−0.244105	+	0.969749i	$0.578494\pi$
$878$	95.5240	3.22378
$879$	28.6924	0.967769
$880$	0	0
$881$	56.1913	1.89313	0.946567	−	0.322509i	$-0.104526\pi$
$881$	56.1913	1.89313	0.946567	+	0.322509i	$0.104526\pi$
$882$	−12.1048	−0.407589
$883$	−41.7329	−1.40443	−0.702213	−	0.711967i	$-0.747804\pi$
$883$	−41.7329	−1.40443	−0.702213	+	0.711967i	$0.747804\pi$
$884$	−28.7181	−0.965893
$885$	0	0
$886$	−76.0354	−2.55446
$887$	32.3399	1.08587	0.542933	−	0.839776i	$-0.317314\pi$
$887$	32.3399	1.08587	0.542933	+	0.839776i	$0.317314\pi$
$888$	−16.6268	−0.557958
$889$	−14.8351	−0.497554
$890$	0	0
$891$	−0.409552	−0.0137205
$892$	39.9388	1.33725
$893$	−0.485553	−0.0162484
$894$	−10.7863	−0.360747
$895$	0	0
$896$	−10.6246	−0.354945
$897$	13.1620	0.439468
$898$	20.0991	0.670717
$899$	−6.64441	−0.221603
$900$	0	0
$901$	−37.0347	−1.23380
$902$	8.19874	0.272988
$903$	−11.5240	−0.383494
$904$	−20.4522	−0.680231
$905$	0	0
$906$	−40.9786	−1.36142
$907$	8.06590	0.267824	0.133912	−	0.990993i	$-0.457246\pi$
$907$	8.06590	0.267824	0.133912	+	0.990993i	$0.457246\pi$
$908$	−134.821	−4.47418
$909$	1.93695	0.0642447
$910$	0	0
$911$	−10.8121	−0.358222	−0.179111	−	0.983829i	$-0.557322\pi$
$911$	−10.8121	−0.358222	−0.179111	+	0.983829i	$0.557322\pi$
$912$	−4.00646	−0.132667
$913$	−2.70097	−0.0893891
$914$	−55.7766	−1.84493
$915$	0	0
$916$	24.4891	0.809142
$917$	−10.7304	−0.354349
$918$	−9.35318	−0.308701
$919$	46.7910	1.54349	0.771747	−	0.635930i	$-0.219383\pi$
$919$	46.7910	1.54349	0.771747	+	0.635930i	$0.219383\pi$
$920$	0	0
$921$	8.58383	0.282847
$922$	−90.2360	−2.97176
$923$	−16.2013	−0.533272
$924$	−2.88371	−0.0948669
$925$	0	0
$926$	−33.8509	−1.11241
$927$	−6.55151	−0.215180
$928$	−11.7661	−0.386242
$929$	−6.27773	−0.205966	−0.102983	−	0.994683i	$-0.532839\pi$
$929$	−6.27773	−0.205966	−0.102983	+	0.994683i	$0.532839\pi$
$930$	0	0
$931$	2.28088	0.0747527
$932$	−118.403	−3.87841
$933$	13.5732	0.444366
$934$	−39.9694	−1.30784
$935$	0	0
$936$	11.6006	0.379179
$937$	23.1765	0.757145	0.378572	−	0.925572i	$-0.376415\pi$
$937$	23.1765	0.757145	0.378572	+	0.925572i	$0.376415\pi$
$938$	−61.7291	−2.01553
$939$	−7.43322	−0.242574
$940$	0	0
$941$	−46.6445	−1.52057	−0.760283	−	0.649592i	$-0.774940\pi$
$941$	−46.6445	−1.52057	−0.760283	+	0.649592i	$0.774940\pi$
$942$	33.8947	1.10435
$943$	−59.9683	−1.95284
$944$	0.980403	0.0319094
$945$	0	0
$946$	8.01496	0.260589
$947$	26.5370	0.862336	0.431168	−	0.902272i	$-0.358102\pi$
$947$	26.5370	0.862336	0.431168	+	0.902272i	$0.358102\pi$
$948$	61.6525	2.00238
$949$	13.9986	0.454412
$950$	0	0
$951$	−16.1762	−0.524548
$952$	−37.4718	−1.21447
$953$	−3.25613	−0.105476	−0.0527381	−	0.998608i	$-0.516795\pi$
$953$	−3.25613	−0.105476	−0.0527381	+	0.998608i	$0.516795\pi$
$954$	26.2925	0.851252
$955$	0	0
$956$	107.026	3.46146
$957$	0.629462	0.0203476
$958$	48.0058	1.55100
$959$	0.837716	0.0270513
$960$	0	0
$961$	−12.3108	−0.397121
$962$	−10.7377	−0.346198
$963$	−0.241779	−0.00779122
$964$	−98.7010	−3.17895
$965$	0	0
$966$	30.1835	0.971137
$967$	−57.0081	−1.83326	−0.916629	−	0.399739i	$-0.869101\pi$
$967$	−57.0081	−1.83326	−0.916629	+	0.399739i	$0.869101\pi$
$968$	−73.6977	−2.36873
$969$	1.76240	0.0566165
$970$	0	0
$971$	48.7556	1.56464	0.782321	−	0.622876i	$-0.214036\pi$
$971$	48.7556	1.56464	0.782321	+	0.622876i	$0.214036\pi$
$972$	4.64024	0.148836
$973$	−5.34456	−0.171339
$974$	92.8010	2.97354
$975$	0	0
$976$	18.6449	0.596809
$977$	39.3330	1.25838	0.629188	−	0.777253i	$-0.283388\pi$
$977$	39.3330	1.25838	0.629188	+	0.777253i	$0.283388\pi$
$978$	−7.28203	−0.232854
$979$	−7.28830	−0.232935
$980$	0	0
$981$	−3.75817	−0.119989
$982$	43.8170	1.39826
$983$	46.2193	1.47417	0.737083	−	0.675802i	$-0.236203\pi$
$983$	46.2193	1.47417	0.737083	+	0.675802i	$0.236203\pi$
$984$	−52.8544	−1.68494
$985$	0	0
$986$	14.3754	0.457806
$987$	1.51741	0.0482995
$988$	−3.84171	−0.122221
$989$	−58.6241	−1.86414
$990$	0	0
$991$	−25.4629	−0.808856	−0.404428	−	0.914570i	$-0.632529\pi$
$991$	−25.4629	−0.808856	−0.404428	+	0.914570i	$0.632529\pi$
$992$	33.0955	1.05078
$993$	23.9233	0.759183
$994$	−37.1532	−1.17843
$995$	0	0
$996$	30.6021	0.969664
$997$	−39.1066	−1.23852	−0.619260	−	0.785186i	$-0.712567\pi$
$997$	−39.1066	−1.23852	−0.619260	+	0.785186i	$0.712567\pi$
$998$	−51.5926	−1.63314
$999$	−2.44384	−0.0773198

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bi.1.11		13
5.2	odd	4		705.2.c.c.424.24	yes	26
5.3	odd	4		705.2.c.c.424.3	✓	26
5.4	even	2		3525.2.a.bh.1.3		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.2.c.c.424.3	✓	26	5.3	odd	4
705.2.c.c.424.24	yes	26	5.2	odd	4
3525.2.a.bh.1.3		13	5.4	even	2
3525.2.a.bi.1.11		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)

\(f(q)\)	\(=\)	\(q+2.57687 q^{2} +1.00000 q^{3} +4.64024 q^{4} +2.57687 q^{6} +1.51741 q^{7} +6.80354 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.57687 q^{2} +1.00000 q^{3} +4.64024 q^{4} +2.57687 q^{6} +1.51741 q^{7} +6.80354 q^{8} +1.00000 q^{9} -0.409552 q^{11} +4.64024 q^{12} +1.70509 q^{13} +3.91015 q^{14} +8.25132 q^{16} -3.62967 q^{17} +2.57687 q^{18} -0.485553 q^{19} +1.51741 q^{21} -1.05536 q^{22} +7.71926 q^{23} +6.80354 q^{24} +4.39379 q^{26} +1.00000 q^{27} +7.04112 q^{28} -1.53695 q^{29} +4.32311 q^{31} +7.65548 q^{32} -0.409552 q^{33} -9.35318 q^{34} +4.64024 q^{36} -2.44384 q^{37} -1.25121 q^{38} +1.70509 q^{39} -7.76866 q^{41} +3.91015 q^{42} -7.59452 q^{43} -1.90042 q^{44} +19.8915 q^{46} +1.00000 q^{47} +8.25132 q^{48} -4.69748 q^{49} -3.62967 q^{51} +7.91202 q^{52} +10.2033 q^{53} +2.57687 q^{54} +10.3237 q^{56} -0.485553 q^{57} -3.96052 q^{58} +0.118818 q^{59} +2.25962 q^{61} +11.1401 q^{62} +1.51741 q^{63} +3.22450 q^{64} -1.05536 q^{66} -15.7869 q^{67} -16.8426 q^{68} +7.71926 q^{69} -9.50172 q^{71} +6.80354 q^{72} +8.20986 q^{73} -6.29745 q^{74} -2.25308 q^{76} -0.621456 q^{77} +4.39379 q^{78} +13.2865 q^{79} +1.00000 q^{81} -20.0188 q^{82} +6.59494 q^{83} +7.04112 q^{84} -19.5701 q^{86} -1.53695 q^{87} -2.78640 q^{88} +17.7958 q^{89} +2.58731 q^{91} +35.8192 q^{92} +4.32311 q^{93} +2.57687 q^{94} +7.65548 q^{96} -5.61258 q^{97} -12.1048 q^{98} -0.409552 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 3 q^{2} + 13 q^{3} + 17 q^{4} + 3 q^{6} - 4 q^{7} + 15 q^{8} + 13 q^{9}+O(q^{10}) \) 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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