LMFDB - Embedded newform 850.2.a.p.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(1,850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(850, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.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:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x - 2 $ x^3 - x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 170)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.76156$ of defining polynomial
Character	$\chi$	$=$	850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.62620 q^{3} +1.00000 q^{4} -2.62620 q^{6} -0.864641 q^{7} -1.00000 q^{8} +3.89692 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.62620 q^{3} +1.00000 q^{4} -2.62620 q^{6} -0.864641 q^{7} -1.00000 q^{8} +3.89692 q^{9} +2.00000 q^{11} +2.62620 q^{12} +2.62620 q^{13} +0.864641 q^{14} +1.00000 q^{16} -1.00000 q^{17} -3.89692 q^{18} -0.896916 q^{19} -2.27072 q^{21} -2.00000 q^{22} +3.13536 q^{23} -2.62620 q^{24} -2.62620 q^{26} +2.35548 q^{27} -0.864641 q^{28} +9.49084 q^{29} +9.01395 q^{31} -1.00000 q^{32} +5.25240 q^{33} +1.00000 q^{34} +3.89692 q^{36} -10.1816 q^{37} +0.896916 q^{38} +6.89692 q^{39} +9.52311 q^{41} +2.27072 q^{42} -7.25240 q^{43} +2.00000 q^{44} -3.13536 q^{46} +10.4200 q^{47} +2.62620 q^{48} -6.25240 q^{49} -2.62620 q^{51} +2.62620 q^{52} -11.4017 q^{53} -2.35548 q^{54} +0.864641 q^{56} -2.35548 q^{57} -9.49084 q^{58} -4.14931 q^{59} +3.28467 q^{61} -9.01395 q^{62} -3.36943 q^{63} +1.00000 q^{64} -5.25240 q^{66} -1.25240 q^{67} -1.00000 q^{68} +8.23407 q^{69} -12.5371 q^{71} -3.89692 q^{72} +2.62620 q^{73} +10.1816 q^{74} -0.896916 q^{76} -1.72928 q^{77} -6.89692 q^{78} -7.91087 q^{79} -5.50479 q^{81} -9.52311 q^{82} +4.20617 q^{83} -2.27072 q^{84} +7.25240 q^{86} +24.9248 q^{87} -2.00000 q^{88} +4.14931 q^{89} -2.27072 q^{91} +3.13536 q^{92} +23.6724 q^{93} -10.4200 q^{94} -2.62620 q^{96} +6.14931 q^{97} +6.25240 q^{98} +7.79383 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - q^{3} + 3 q^{4} + q^{6} - 3 q^{8} + 8 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - q^3 + 3 * q^4 + q^6 - 3 * q^8 + 8 * q^9	$ 3 q - 3 q^{2} - q^{3} + 3 q^{4} + q^{6} - 3 q^{8} + 8 q^{9} + 6 q^{11} - q^{12} - q^{13} + 3 q^{16} - 3 q^{17} - 8 q^{18} + q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} + q^{24} + q^{26} - 7 q^{27} + 17 q^{29} + 3 q^{31} - 3 q^{32} - 2 q^{33} + 3 q^{34} + 8 q^{36} - 8 q^{37} - q^{38} + 17 q^{39} + 16 q^{41} + 12 q^{42} - 4 q^{43} + 6 q^{44} - 12 q^{46} + 15 q^{47} - q^{48} - q^{49} + q^{51} - q^{52} + 5 q^{53} + 7 q^{54} + 7 q^{57} - 17 q^{58} + 9 q^{59} - 9 q^{61} - 3 q^{62} + 28 q^{63} + 3 q^{64} + 2 q^{66} + 14 q^{67} - 3 q^{68} - 16 q^{69} - q^{71} - 8 q^{72} - q^{73} + 8 q^{74} + q^{76} - 17 q^{78} + 4 q^{79} + 19 q^{81} - 16 q^{82} + 20 q^{83} - 12 q^{84} + 4 q^{86} + 23 q^{87} - 6 q^{88} - 9 q^{89} - 12 q^{91} + 12 q^{92} + 37 q^{93} - 15 q^{94} + q^{96} - 3 q^{97} + q^{98} + 16 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - q^3 + 3 * q^4 + q^6 - 3 * q^8 + 8 * q^9 + 6 * q^11 - q^12 - q^13 + 3 * q^16 - 3 * q^17 - 8 * q^18 + q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 + q^24 + q^26 - 7 * q^27 + 17 * q^29 + 3 * q^31 - 3 * q^32 - 2 * q^33 + 3 * q^34 + 8 * q^36 - 8 * q^37 - q^38 + 17 * q^39 + 16 * q^41 + 12 * q^42 - 4 * q^43 + 6 * q^44 - 12 * q^46 + 15 * q^47 - q^48 - q^49 + q^51 - q^52 + 5 * q^53 + 7 * q^54 + 7 * q^57 - 17 * q^58 + 9 * q^59 - 9 * q^61 - 3 * q^62 + 28 * q^63 + 3 * q^64 + 2 * q^66 + 14 * q^67 - 3 * q^68 - 16 * q^69 - q^71 - 8 * q^72 - q^73 + 8 * q^74 + q^76 - 17 * q^78 + 4 * q^79 + 19 * q^81 - 16 * q^82 + 20 * q^83 - 12 * q^84 + 4 * q^86 + 23 * q^87 - 6 * q^88 - 9 * q^89 - 12 * q^91 + 12 * q^92 + 37 * q^93 - 15 * q^94 + q^96 - 3 * q^97 + 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.62620	1.51624	0.758118	−	0.652117i	$-0.226119\pi$
$3$	2.62620	1.51624	0.758118	+	0.652117i	$0.226119\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−2.62620	−1.07214
$7$	−0.864641	−0.326804	−0.163402	−	0.986560i	$-0.552247\pi$
$7$	−0.864641	−0.326804	−0.163402	+	0.986560i	$0.552247\pi$
$8$	−1.00000	−0.353553
$9$	3.89692	1.29897
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	2.62620	0.758118
$13$	2.62620	0.728376	0.364188	−	0.931325i	$-0.381347\pi$
$13$	2.62620	0.728376	0.364188	+	0.931325i	$0.381347\pi$
$14$	0.864641	0.231085
$15$	0	0
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−3.89692	−0.918512
$19$	−0.896916	−0.205767	−0.102883	−	0.994693i	$-0.532807\pi$
$19$	−0.896916	−0.205767	−0.102883	+	0.994693i	$0.532807\pi$
$20$	0	0
$21$	−2.27072	−0.495511
$22$	−2.00000	−0.426401
$23$	3.13536	0.653768	0.326884	−	0.945065i	$-0.394001\pi$
$23$	3.13536	0.653768	0.326884	+	0.945065i	$0.394001\pi$
$24$	−2.62620	−0.536070
$25$	0	0
$26$	−2.62620	−0.515040
$27$	2.35548	0.453312
$28$	−0.864641	−0.163402
$29$	9.49084	1.76240	0.881202	−	0.472739i	$-0.156735\pi$
$29$	9.49084	1.76240	0.881202	+	0.472739i	$0.156735\pi$
$30$	0	0
$31$	9.01395	1.61895	0.809477	−	0.587152i	$-0.199751\pi$
$31$	9.01395	1.61895	0.809477	+	0.587152i	$0.199751\pi$
$32$	−1.00000	−0.176777
$33$	5.25240	0.914325
$34$	1.00000	0.171499
$35$	0	0
$36$	3.89692	0.649486
$37$	−10.1816	−1.67384	−0.836921	−	0.547323i	$-0.815647\pi$
$37$	−10.1816	−1.67384	−0.836921	+	0.547323i	$0.815647\pi$
$38$	0.896916	0.145499
$39$	6.89692	1.10439
$40$	0	0
$41$	9.52311	1.48726	0.743630	−	0.668591i	$-0.233102\pi$
$41$	9.52311	1.48726	0.743630	+	0.668591i	$0.233102\pi$
$42$	2.27072	0.350379
$43$	−7.25240	−1.10598	−0.552990	−	0.833188i	$-0.686513\pi$
$43$	−7.25240	−1.10598	−0.552990	+	0.833188i	$0.686513\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	−3.13536	−0.462283
$47$	10.4200	1.51992	0.759959	−	0.649971i	$-0.225219\pi$
$47$	10.4200	1.51992	0.759959	+	0.649971i	$0.225219\pi$
$48$	2.62620	0.379059
$49$	−6.25240	−0.893199
$50$	0	0
$51$	−2.62620	−0.367741
$52$	2.62620	0.364188
$53$	−11.4017	−1.56615	−0.783073	−	0.621930i	$-0.786349\pi$
$53$	−11.4017	−1.56615	−0.783073	+	0.621930i	$0.786349\pi$
$54$	−2.35548	−0.320540
$55$	0	0
$56$	0.864641	0.115542
$57$	−2.35548	−0.311991
$58$	−9.49084	−1.24621
$59$	−4.14931	−0.540194	−0.270097	−	0.962833i	$-0.587056\pi$
$59$	−4.14931	−0.540194	−0.270097	+	0.962833i	$0.587056\pi$
$60$	0	0
$61$	3.28467	0.420559	0.210280	−	0.977641i	$-0.432563\pi$
$61$	3.28467	0.420559	0.210280	+	0.977641i	$0.432563\pi$
$62$	−9.01395	−1.14477
$63$	−3.36943	−0.424509
$64$	1.00000	0.125000
$65$	0	0
$66$	−5.25240	−0.646525
$67$	−1.25240	−0.153005	−0.0765023	−	0.997069i	$-0.524375\pi$
$67$	−1.25240	−0.153005	−0.0765023	+	0.997069i	$0.524375\pi$
$68$	−1.00000	−0.121268
$69$	8.23407	0.991266
$70$	0	0
$71$	−12.5371	−1.48788	−0.743938	−	0.668249i	$-0.767044\pi$
$71$	−12.5371	−1.48788	−0.743938	+	0.668249i	$0.767044\pi$
$72$	−3.89692	−0.459256
$73$	2.62620	0.307373	0.153687	−	0.988120i	$-0.450885\pi$
$73$	2.62620	0.307373	0.153687	+	0.988120i	$0.450885\pi$
$74$	10.1816	1.18359
$75$	0	0
$76$	−0.896916	−0.102883
$77$	−1.72928	−0.197070
$78$	−6.89692	−0.780922
$79$	−7.91087	−0.890042	−0.445021	−	0.895520i	$-0.646804\pi$
$79$	−7.91087	−0.890042	−0.445021	+	0.895520i	$0.646804\pi$
$80$	0	0
$81$	−5.50479	−0.611644
$82$	−9.52311	−1.05165
$83$	4.20617	0.461687	0.230843	−	0.972991i	$-0.425851\pi$
$83$	4.20617	0.461687	0.230843	+	0.972991i	$0.425851\pi$
$84$	−2.27072	−0.247756
$85$	0	0
$86$	7.25240	0.782046
$87$	24.9248	2.67222
$88$	−2.00000	−0.213201
$89$	4.14931	0.439826	0.219913	−	0.975519i	$-0.429423\pi$
$89$	4.14931	0.439826	0.219913	+	0.975519i	$0.429423\pi$
$90$	0	0
$91$	−2.27072	−0.238036
$92$	3.13536	0.326884
$93$	23.6724	2.45472
$94$	−10.4200	−1.07474
$95$	0	0
$96$	−2.62620	−0.268035
$97$	6.14931	0.624368	0.312184	−	0.950022i	$-0.398939\pi$
$97$	6.14931	0.624368	0.312184	+	0.950022i	$0.398939\pi$
$98$	6.25240	0.631587
$99$	7.79383	0.783310
$100$	0	0
$101$	0.206167	0.0205144	0.0102572	−	0.999947i	$-0.496735\pi$
$101$	0.206167	0.0205144	0.0102572	+	0.999947i	$0.496735\pi$
$102$	2.62620	0.260032
$103$	−4.77551	−0.470545	−0.235273	−	0.971929i	$-0.575598\pi$
$103$	−4.77551	−0.470545	−0.235273	+	0.971929i	$0.575598\pi$
$104$	−2.62620	−0.257520
$105$	0	0
$106$	11.4017	1.10743
$107$	−6.29862	−0.608911	−0.304456	−	0.952527i	$-0.598474\pi$
$107$	−6.29862	−0.608911	−0.304456	+	0.952527i	$0.598474\pi$
$108$	2.35548	0.226656
$109$	5.55539	0.532110	0.266055	−	0.963958i	$-0.414280\pi$
$109$	5.55539	0.532110	0.266055	+	0.963958i	$0.414280\pi$
$110$	0	0
$111$	−26.7389	−2.53794
$112$	−0.864641	−0.0817009
$113$	−10.6262	−0.999629	−0.499814	−	0.866133i	$-0.666598\pi$
$113$	−10.6262	−0.999629	−0.499814	+	0.866133i	$0.666598\pi$
$114$	2.35548	0.220611
$115$	0	0
$116$	9.49084	0.881202
$117$	10.2341	0.946140
$118$	4.14931	0.381975
$119$	0.864641	0.0792615
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−3.28467	−0.297380
$123$	25.0096	2.25504
$124$	9.01395	0.809477
$125$	0	0
$126$	3.36943	0.300173
$127$	14.3555	1.27384	0.636921	−	0.770929i	$-0.280208\pi$
$127$	14.3555	1.27384	0.636921	+	0.770929i	$0.280208\pi$
$128$	−1.00000	−0.0883883
$129$	−19.0462	−1.67693
$130$	0	0
$131$	17.0462	1.48934	0.744668	−	0.667435i	$-0.232608\pi$
$131$	17.0462	1.48934	0.744668	+	0.667435i	$0.232608\pi$
$132$	5.25240	0.457162
$133$	0.775511	0.0672453
$134$	1.25240	0.108191
$135$	0	0
$136$	1.00000	0.0857493
$137$	−14.5048	−1.23923	−0.619614	−	0.784907i	$-0.712711\pi$
$137$	−14.5048	−1.23923	−0.619614	+	0.784907i	$0.712711\pi$
$138$	−8.23407	−0.700931
$139$	−14.7110	−1.24777	−0.623884	−	0.781517i	$-0.714446\pi$
$139$	−14.7110	−1.24777	−0.623884	+	0.781517i	$0.714446\pi$
$140$	0	0
$141$	27.3651	2.30455
$142$	12.5371	1.05209
$143$	5.25240	0.439227
$144$	3.89692	0.324743
$145$	0	0
$146$	−2.62620	−0.217346
$147$	−16.4200	−1.35430
$148$	−10.1816	−0.836921
$149$	10.0000	0.819232	0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000	0.819232	0.409616	+	0.912258i	$0.365663\pi$
$150$	0	0
$151$	−5.18785	−0.422181	−0.211090	−	0.977467i	$-0.567701\pi$
$151$	−5.18785	−0.422181	−0.211090	+	0.977467i	$0.567701\pi$
$152$	0.896916	0.0727495
$153$	−3.89692	−0.315047
$154$	1.72928	0.139349
$155$	0	0
$156$	6.89692	0.552195
$157$	−10.2341	−0.816768	−0.408384	−	0.912810i	$-0.633908\pi$
$157$	−10.2341	−0.816768	−0.408384	+	0.912810i	$0.633908\pi$
$158$	7.91087	0.629355
$159$	−29.9431	−2.37465
$160$	0	0
$161$	−2.71096	−0.213654
$162$	5.50479	0.432497
$163$	−6.47689	−0.507309	−0.253654	−	0.967295i	$-0.581633\pi$
$163$	−6.47689	−0.507309	−0.253654	+	0.967295i	$0.581633\pi$
$164$	9.52311	0.743630
$165$	0	0
$166$	−4.20617	−0.326462
$167$	3.84632	0.297637	0.148819	−	0.988865i	$-0.452453\pi$
$167$	3.84632	0.297637	0.148819	+	0.988865i	$0.452453\pi$
$168$	2.27072	0.175190
$169$	−6.10308	−0.469468
$170$	0	0
$171$	−3.49521	−0.267285
$172$	−7.25240	−0.552990
$173$	23.9109	1.81791	0.908955	−	0.416895i	$-0.136882\pi$
$173$	23.9109	1.81791	0.908955	+	0.416895i	$0.136882\pi$
$174$	−24.9248	−1.88955
$175$	0	0
$176$	2.00000	0.150756
$177$	−10.8969	−0.819062
$178$	−4.14931	−0.311004
$179$	−14.7110	−1.09955	−0.549774	−	0.835313i	$-0.685286\pi$
$179$	−14.7110	−1.09955	−0.549774	+	0.835313i	$0.685286\pi$
$180$	0	0
$181$	−23.4340	−1.74183	−0.870917	−	0.491430i	$-0.836474\pi$
$181$	−23.4340	−1.74183	−0.870917	+	0.491430i	$0.836474\pi$
$182$	2.27072	0.168317
$183$	8.62620	0.637667
$184$	−3.13536	−0.231142
$185$	0	0
$186$	−23.6724	−1.73575
$187$	−2.00000	−0.146254
$188$	10.4200	0.759959
$189$	−2.03664	−0.148144
$190$	0	0
$191$	18.5048	1.33896	0.669480	−	0.742830i	$-0.266517\pi$
$191$	18.5048	1.33896	0.669480	+	0.742830i	$0.266517\pi$
$192$	2.62620	0.189530
$193$	−5.45856	−0.392916	−0.196458	−	0.980512i	$-0.562944\pi$
$193$	−5.45856	−0.392916	−0.196458	+	0.980512i	$0.562944\pi$
$194$	−6.14931	−0.441495
$195$	0	0
$196$	−6.25240	−0.446600
$197$	13.9388	0.993097	0.496548	−	0.868009i	$-0.334601\pi$
$197$	13.9388	0.993097	0.496548	+	0.868009i	$0.334601\pi$
$198$	−7.79383	−0.553884
$199$	−11.2847	−0.799949	−0.399975	−	0.916526i	$-0.630981\pi$
$199$	−11.2847	−0.799949	−0.399975	+	0.916526i	$0.630981\pi$
$200$	0	0
$201$	−3.28904	−0.231991
$202$	−0.206167	−0.0145059
$203$	−8.20617	−0.575960
$204$	−2.62620	−0.183871
$205$	0	0
$206$	4.77551	0.332726
$207$	12.2182	0.849226
$208$	2.62620	0.182094
$209$	−1.79383	−0.124082
$210$	0	0
$211$	−14.8401	−1.02163	−0.510816	−	0.859690i	$-0.670657\pi$
$211$	−14.8401	−1.02163	−0.510816	+	0.859690i	$0.670657\pi$
$212$	−11.4017	−0.783073
$213$	−32.9248	−2.25597
$214$	6.29862	0.430565
$215$	0	0
$216$	−2.35548	−0.160270
$217$	−7.79383	−0.529080
$218$	−5.55539	−0.376258
$219$	6.89692	0.466050
$220$	0	0
$221$	−2.62620	−0.176657
$222$	26.7389	1.79460
$223$	3.30925	0.221604	0.110802	−	0.993843i	$-0.464658\pi$
$223$	3.30925	0.221604	0.110802	+	0.993843i	$0.464658\pi$
$224$	0.864641	0.0577712
$225$	0	0
$226$	10.6262	0.706844
$227$	−24.7187	−1.64063	−0.820317	−	0.571909i	$-0.806203\pi$
$227$	−24.7187	−1.64063	−0.820317	+	0.571909i	$0.806203\pi$
$228$	−2.35548	−0.155995
$229$	4.27072	0.282217	0.141109	−	0.989994i	$-0.454933\pi$
$229$	4.27072	0.282217	0.141109	+	0.989994i	$0.454933\pi$
$230$	0	0
$231$	−4.54144	−0.298805
$232$	−9.49084	−0.623104
$233$	0.832365	0.0545301	0.0272650	−	0.999628i	$-0.491320\pi$
$233$	0.832365	0.0545301	0.0272650	+	0.999628i	$0.491320\pi$
$234$	−10.2341	−0.669022
$235$	0	0
$236$	−4.14931	−0.270097
$237$	−20.7755	−1.34951
$238$	−0.864641	−0.0560463
$239$	−4.71096	−0.304727	−0.152363	−	0.988325i	$-0.548688\pi$
$239$	−4.71096	−0.304727	−0.152363	+	0.988325i	$0.548688\pi$
$240$	0	0
$241$	−23.4865	−1.51290	−0.756448	−	0.654054i	$-0.773067\pi$
$241$	−23.4865	−1.51290	−0.756448	+	0.654054i	$0.773067\pi$
$242$	7.00000	0.449977
$243$	−21.5231	−1.38071
$244$	3.28467	0.210280
$245$	0	0
$246$	−25.0096	−1.59455
$247$	−2.35548	−0.149876
$248$	−9.01395	−0.572387
$249$	11.0462	0.700026
$250$	0	0
$251$	−6.29862	−0.397566	−0.198783	−	0.980044i	$-0.563699\pi$
$251$	−6.29862	−0.397566	−0.198783	+	0.980044i	$0.563699\pi$
$252$	−3.36943	−0.212254
$253$	6.27072	0.394237
$254$	−14.3555	−0.900743
$255$	0	0
$256$	1.00000	0.0625000
$257$	−1.49521	−0.0932685	−0.0466342	−	0.998912i	$-0.514850\pi$
$257$	−1.49521	−0.0932685	−0.0466342	+	0.998912i	$0.514850\pi$
$258$	19.0462	1.18577
$259$	8.80342	0.547018
$260$	0	0
$261$	36.9850	2.28931
$262$	−17.0462	−1.05312
$263$	−9.94315	−0.613121	−0.306560	−	0.951851i	$-0.599178\pi$
$263$	−9.94315	−0.613121	−0.306560	+	0.951851i	$0.599178\pi$
$264$	−5.25240	−0.323263
$265$	0	0
$266$	−0.775511	−0.0475496
$267$	10.8969	0.666880
$268$	−1.25240	−0.0765023
$269$	1.96772	0.119974	0.0599871	−	0.998199i	$-0.480894\pi$
$269$	1.96772	0.119974	0.0599871	+	0.998199i	$0.480894\pi$
$270$	0	0
$271$	8.84006	0.536995	0.268498	−	0.963280i	$-0.413473\pi$
$271$	8.84006	0.536995	0.268498	+	0.963280i	$0.413473\pi$
$272$	−1.00000	−0.0606339
$273$	−5.96336	−0.360919
$274$	14.5048	0.876267
$275$	0	0
$276$	8.23407	0.495633
$277$	−19.8463	−1.19245	−0.596225	−	0.802817i	$-0.703333\pi$
$277$	−19.8463	−1.19245	−0.596225	+	0.802817i	$0.703333\pi$
$278$	14.7110	0.882305
$279$	35.1266	2.10298
$280$	0	0
$281$	−11.9065	−0.710282	−0.355141	−	0.934813i	$-0.615567\pi$
$281$	−11.9065	−0.710282	−0.355141	+	0.934813i	$0.615567\pi$
$282$	−27.3651	−1.62957
$283$	13.7370	0.816579	0.408289	−	0.912853i	$-0.366125\pi$
$283$	13.7370	0.816579	0.408289	+	0.912853i	$0.366125\pi$
$284$	−12.5371	−0.743938
$285$	0	0
$286$	−5.25240	−0.310581
$287$	−8.23407	−0.486042
$288$	−3.89692	−0.229628
$289$	1.00000	0.0588235
$290$	0	0
$291$	16.1493	0.946689
$292$	2.62620	0.153687
$293$	−12.1772	−0.711401	−0.355700	−	0.934600i	$-0.615758\pi$
$293$	−12.1772	−0.711401	−0.355700	+	0.934600i	$0.615758\pi$
$294$	16.4200	0.957636
$295$	0	0
$296$	10.1816	0.591793
$297$	4.71096	0.273358
$298$	−10.0000	−0.579284
$299$	8.23407	0.476189
$300$	0	0
$301$	6.27072	0.361438
$302$	5.18785	0.298527
$303$	0.541436	0.0311047
$304$	−0.896916	−0.0514417
$305$	0	0
$306$	3.89692	0.222772
$307$	23.7938	1.35799	0.678993	−	0.734145i	$-0.262417\pi$
$307$	23.7938	1.35799	0.678993	+	0.734145i	$0.262417\pi$
$308$	−1.72928	−0.0985350
$309$	−12.5414	−0.713457
$310$	0	0
$311$	32.9205	1.86675	0.933374	−	0.358906i	$-0.116850\pi$
$311$	32.9205	1.86675	0.933374	+	0.358906i	$0.116850\pi$
$312$	−6.89692	−0.390461
$313$	−29.0462	−1.64179	−0.820895	−	0.571079i	$-0.806525\pi$
$313$	−29.0462	−1.64179	−0.820895	+	0.571079i	$0.806525\pi$
$314$	10.2341	0.577542
$315$	0	0
$316$	−7.91087	−0.445021
$317$	20.6864	1.16186	0.580931	−	0.813953i	$-0.302688\pi$
$317$	20.6864	1.16186	0.580931	+	0.813953i	$0.302688\pi$
$318$	29.9431	1.67913
$319$	18.9817	1.06277
$320$	0	0
$321$	−16.5414	−0.923253
$322$	2.71096	0.151076
$323$	0.896916	0.0499058
$324$	−5.50479	−0.305822
$325$	0	0
$326$	6.47689	0.358722
$327$	14.5896	0.806804
$328$	−9.52311	−0.525826
$329$	−9.00958	−0.496714
$330$	0	0
$331$	4.02021	0.220971	0.110485	−	0.993878i	$-0.464759\pi$
$331$	4.02021	0.220971	0.110485	+	0.993878i	$0.464759\pi$
$332$	4.20617	0.230843
$333$	−39.6768	−2.17428
$334$	−3.84632	−0.210461
$335$	0	0
$336$	−2.27072	−0.123878
$337$	2.21386	0.120597	0.0602984	−	0.998180i	$-0.480795\pi$
$337$	2.21386	0.120597	0.0602984	+	0.998180i	$0.480795\pi$
$338$	6.10308	0.331964
$339$	−27.9065	−1.51567
$340$	0	0
$341$	18.0279	0.976266
$342$	3.49521	0.188999
$343$	11.4586	0.618704
$344$	7.25240	0.391023
$345$	0	0
$346$	−23.9109	−1.28546
$347$	−1.37380	−0.0737496	−0.0368748	−	0.999320i	$-0.511740\pi$
$347$	−1.37380	−0.0737496	−0.0368748	+	0.999320i	$0.511740\pi$
$348$	24.9248	1.33611
$349$	−20.8680	−1.11704	−0.558518	−	0.829492i	$-0.688630\pi$
$349$	−20.8680	−1.11704	−0.558518	+	0.829492i	$0.688630\pi$
$350$	0	0
$351$	6.18596	0.330182
$352$	−2.00000	−0.106600
$353$	−13.7572	−0.732221	−0.366111	−	0.930571i	$-0.619311\pi$
$353$	−13.7572	−0.732221	−0.366111	+	0.930571i	$0.619311\pi$
$354$	10.8969	0.579165
$355$	0	0
$356$	4.14931	0.219913
$357$	2.27072	0.120179
$358$	14.7110	0.777498
$359$	9.31695	0.491730	0.245865	−	0.969304i	$-0.420928\pi$
$359$	9.31695	0.491730	0.245865	+	0.969304i	$0.420928\pi$
$360$	0	0
$361$	−18.1955	−0.957660
$362$	23.4340	1.23166
$363$	−18.3834	−0.964878
$364$	−2.27072	−0.119018
$365$	0	0
$366$	−8.62620	−0.450899
$367$	12.3878	0.646636	0.323318	−	0.946290i	$-0.395202\pi$
$367$	12.3878	0.646636	0.323318	+	0.946290i	$0.395202\pi$
$368$	3.13536	0.163442
$369$	37.1108	1.93191
$370$	0	0
$371$	9.85838	0.511822
$372$	23.6724	1.22736
$373$	−23.3169	−1.20731	−0.603653	−	0.797247i	$-0.706289\pi$
$373$	−23.3169	−1.20731	−0.603653	+	0.797247i	$0.706289\pi$
$374$	2.00000	0.103418
$375$	0	0
$376$	−10.4200	−0.537372
$377$	24.9248	1.28369
$378$	2.03664	0.104754
$379$	28.9817	1.48869	0.744344	−	0.667796i	$-0.232762\pi$
$379$	28.9817	1.48869	0.744344	+	0.667796i	$0.232762\pi$
$380$	0	0
$381$	37.7003	1.93145
$382$	−18.5048	−0.946788
$383$	14.9527	0.764049	0.382024	−	0.924152i	$-0.375227\pi$
$383$	14.9527	0.764049	0.382024	+	0.924152i	$0.375227\pi$
$384$	−2.62620	−0.134018
$385$	0	0
$386$	5.45856	0.277834
$387$	−28.2620	−1.43664
$388$	6.14931	0.312184
$389$	−19.3169	−0.979408	−0.489704	−	0.871889i	$-0.662895\pi$
$389$	−19.3169	−0.979408	−0.489704	+	0.871889i	$0.662895\pi$
$390$	0	0
$391$	−3.13536	−0.158562
$392$	6.25240	0.315794
$393$	44.7668	2.25818
$394$	−13.9388	−0.702225
$395$	0	0
$396$	7.79383	0.391655
$397$	9.57560	0.480586	0.240293	−	0.970700i	$-0.422757\pi$
$397$	9.57560	0.480586	0.240293	+	0.970700i	$0.422757\pi$
$398$	11.2847	0.565649
$399$	2.03664	0.101960
$400$	0	0
$401$	11.3169	0.565141	0.282571	−	0.959246i	$-0.408813\pi$
$401$	11.3169	0.565141	0.282571	+	0.959246i	$0.408813\pi$
$402$	3.28904	0.164042
$403$	23.6724	1.17921
$404$	0.206167	0.0102572
$405$	0	0
$406$	8.20617	0.407265
$407$	−20.3632	−1.00937
$408$	2.62620	0.130016
$409$	−9.10308	−0.450119	−0.225059	−	0.974345i	$-0.572258\pi$
$409$	−9.10308	−0.450119	−0.225059	+	0.974345i	$0.572258\pi$
$410$	0	0
$411$	−38.0925	−1.87896
$412$	−4.77551	−0.235273
$413$	3.58767	0.176537
$414$	−12.2182	−0.600493
$415$	0	0
$416$	−2.62620	−0.128760
$417$	−38.6339	−1.89191
$418$	1.79383	0.0877392
$419$	−4.02791	−0.196776	−0.0983881	−	0.995148i	$-0.531369\pi$
$419$	−4.02791	−0.196776	−0.0983881	+	0.995148i	$0.531369\pi$
$420$	0	0
$421$	15.2524	0.743356	0.371678	−	0.928362i	$-0.378782\pi$
$421$	15.2524	0.743356	0.371678	+	0.928362i	$0.378782\pi$
$422$	14.8401	0.722403
$423$	40.6060	1.97433
$424$	11.4017	0.553716
$425$	0	0
$426$	32.9248	1.59521
$427$	−2.84006	−0.137440
$428$	−6.29862	−0.304456
$429$	13.7938	0.665973
$430$	0	0
$431$	−4.45231	−0.214460	−0.107230	−	0.994234i	$-0.534198\pi$
$431$	−4.45231	−0.214460	−0.107230	+	0.994234i	$0.534198\pi$
$432$	2.35548	0.113328
$433$	10.7110	0.514736	0.257368	−	0.966313i	$-0.417145\pi$
$433$	10.7110	0.514736	0.257368	+	0.966313i	$0.417145\pi$
$434$	7.79383	0.374116
$435$	0	0
$436$	5.55539	0.266055
$437$	−2.81215	−0.134524
$438$	−6.89692	−0.329547
$439$	5.09871	0.243348	0.121674	−	0.992570i	$-0.461174\pi$
$439$	5.09871	0.243348	0.121674	+	0.992570i	$0.461174\pi$
$440$	0	0
$441$	−24.3651	−1.16024
$442$	2.62620	0.124916
$443$	10.8034	0.513286	0.256643	−	0.966506i	$-0.417384\pi$
$443$	10.8034	0.513286	0.256643	+	0.966506i	$0.417384\pi$
$444$	−26.7389	−1.26897
$445$	0	0
$446$	−3.30925	−0.156698
$447$	26.2620	1.24215
$448$	−0.864641	−0.0408504
$449$	−5.82174	−0.274745	−0.137372	−	0.990519i	$-0.543866\pi$
$449$	−5.82174	−0.274745	−0.137372	+	0.990519i	$0.543866\pi$
$450$	0	0
$451$	19.0462	0.896852
$452$	−10.6262	−0.499814
$453$	−13.6243	−0.640126
$454$	24.7187	1.16010
$455$	0	0
$456$	2.35548	0.110305
$457$	13.7014	0.640923	0.320462	−	0.947261i	$-0.396162\pi$
$457$	13.7014	0.640923	0.320462	+	0.947261i	$0.396162\pi$
$458$	−4.27072	−0.199558
$459$	−2.35548	−0.109944
$460$	0	0
$461$	−27.0741	−1.26097	−0.630484	−	0.776202i	$-0.717144\pi$
$461$	−27.0741	−1.26097	−0.630484	+	0.776202i	$0.717144\pi$
$462$	4.54144	0.211287
$463$	37.3372	1.73520	0.867602	−	0.497258i	$-0.165660\pi$
$463$	37.3372	1.73520	0.867602	+	0.497258i	$0.165660\pi$
$464$	9.49084	0.440601
$465$	0	0
$466$	−0.832365	−0.0385586
$467$	35.3449	1.63556	0.817782	−	0.575528i	$-0.195203\pi$
$467$	35.3449	1.63556	0.817782	+	0.575528i	$0.195203\pi$
$468$	10.2341	0.473070
$469$	1.08287	0.0500024
$470$	0	0
$471$	−26.8767	−1.23841
$472$	4.14931	0.190988
$473$	−14.5048	−0.666931
$474$	20.7755	0.954251
$475$	0	0
$476$	0.864641	0.0396308
$477$	−44.4315	−2.03438
$478$	4.71096	0.215474
$479$	31.0419	1.41834	0.709169	−	0.705038i	$-0.249070\pi$
$479$	31.0419	1.41834	0.709169	+	0.705038i	$0.249070\pi$
$480$	0	0
$481$	−26.7389	−1.21919
$482$	23.4865	1.06978
$483$	−7.11952	−0.323949
$484$	−7.00000	−0.318182
$485$	0	0
$486$	21.5231	0.976308
$487$	13.1633	0.596485	0.298242	−	0.954490i	$-0.403600\pi$
$487$	13.1633	0.596485	0.298242	+	0.954490i	$0.403600\pi$
$488$	−3.28467	−0.148690
$489$	−17.0096	−0.769200
$490$	0	0
$491$	24.3555	1.09915	0.549574	−	0.835445i	$-0.314790\pi$
$491$	24.3555	1.09915	0.549574	+	0.835445i	$0.314790\pi$
$492$	25.0096	1.12752
$493$	−9.49084	−0.427446
$494$	2.35548	0.105978
$495$	0	0
$496$	9.01395	0.404738
$497$	10.8401	0.486243
$498$	−11.0462	−0.494993
$499$	36.2620	1.62331	0.811655	−	0.584138i	$-0.198567\pi$
$499$	36.2620	1.62331	0.811655	+	0.584138i	$0.198567\pi$
$500$	0	0
$501$	10.1012	0.451288
$502$	6.29862	0.281121
$503$	−42.3511	−1.88834	−0.944171	−	0.329455i	$-0.893135\pi$
$503$	−42.3511	−1.88834	−0.944171	+	0.329455i	$0.893135\pi$
$504$	3.36943	0.150086
$505$	0	0
$506$	−6.27072	−0.278767
$507$	−16.0279	−0.711824
$508$	14.3555	0.636921
$509$	−1.70138	−0.0754121	−0.0377061	−	0.999289i	$-0.512005\pi$
$509$	−1.70138	−0.0754121	−0.0377061	+	0.999289i	$0.512005\pi$
$510$	0	0
$511$	−2.27072	−0.100451
$512$	−1.00000	−0.0441942
$513$	−2.11267	−0.0932766
$514$	1.49521	0.0659508
$515$	0	0
$516$	−19.0462	−0.838463
$517$	20.8401	0.916545
$518$	−8.80342	−0.386800
$519$	62.7947	2.75638
$520$	0	0
$521$	3.01832	0.132235	0.0661175	−	0.997812i	$-0.478939\pi$
$521$	3.01832	0.132235	0.0661175	+	0.997812i	$0.478939\pi$
$522$	−36.9850	−1.61879
$523$	−5.79383	−0.253347	−0.126673	−	0.991944i	$-0.540430\pi$
$523$	−5.79383	−0.253347	−0.126673	+	0.991944i	$0.540430\pi$
$524$	17.0462	0.744668
$525$	0	0
$526$	9.94315	0.433542
$527$	−9.01395	−0.392654
$528$	5.25240	0.228581
$529$	−13.1695	−0.572588
$530$	0	0
$531$	−16.1695	−0.701698
$532$	0.775511	0.0336226
$533$	25.0096	1.08329
$534$	−10.8969	−0.471556
$535$	0	0
$536$	1.25240	0.0540953
$537$	−38.6339	−1.66718
$538$	−1.96772	−0.0848346
$539$	−12.5048	−0.538620
$540$	0	0
$541$	0.258654	0.0111204	0.00556019	−	0.999985i	$-0.498230\pi$
$541$	0.258654	0.0111204	0.00556019	+	0.999985i	$0.498230\pi$
$542$	−8.84006	−0.379713
$543$	−61.5423	−2.64103
$544$	1.00000	0.0428746
$545$	0	0
$546$	5.96336	0.255208
$547$	32.4113	1.38581	0.692903	−	0.721030i	$-0.256331\pi$
$547$	32.4113	1.38581	0.692903	+	0.721030i	$0.256331\pi$
$548$	−14.5048	−0.619614
$549$	12.8001	0.546295
$550$	0	0
$551$	−8.51249	−0.362644
$552$	−8.23407	−0.350465
$553$	6.84006	0.290869
$554$	19.8463	0.843189
$555$	0	0
$556$	−14.7110	−0.623884
$557$	−22.9248	−0.971356	−0.485678	−	0.874138i	$-0.661427\pi$
$557$	−22.9248	−0.971356	−0.485678	+	0.874138i	$0.661427\pi$
$558$	−35.1266	−1.48703
$559$	−19.0462	−0.805570
$560$	0	0
$561$	−5.25240	−0.221756
$562$	11.9065	0.502245
$563$	17.8863	0.753817	0.376909	−	0.926250i	$-0.376987\pi$
$563$	17.8863	0.753817	0.376909	+	0.926250i	$0.376987\pi$
$564$	27.3651	1.15228
$565$	0	0
$566$	−13.7370	−0.577408
$567$	4.75967	0.199887
$568$	12.5371	0.526044
$569$	12.3555	0.517969	0.258984	−	0.965882i	$-0.416612\pi$
$569$	12.3555	0.517969	0.258984	+	0.965882i	$0.416612\pi$
$570$	0	0
$571$	−27.3169	−1.14318	−0.571589	−	0.820540i	$-0.693673\pi$
$571$	−27.3169	−1.14318	−0.571589	+	0.820540i	$0.693673\pi$
$572$	5.25240	0.219614
$573$	48.5972	2.03018
$574$	8.23407	0.343684
$575$	0	0
$576$	3.89692	0.162372
$577$	10.6339	0.442695	0.221347	−	0.975195i	$-0.428955\pi$
$577$	10.6339	0.442695	0.221347	+	0.975195i	$0.428955\pi$
$578$	−1.00000	−0.0415945
$579$	−14.3353	−0.595753
$580$	0	0
$581$	−3.63682	−0.150881
$582$	−16.1493	−0.669411
$583$	−22.8034	−0.944421
$584$	−2.62620	−0.108673
$585$	0	0
$586$	12.1772	0.503036
$587$	−22.3757	−0.923544	−0.461772	−	0.886999i	$-0.652786\pi$
$587$	−22.3757	−0.923544	−0.461772	+	0.886999i	$0.652786\pi$
$588$	−16.4200	−0.677151
$589$	−8.08476	−0.333127
$590$	0	0
$591$	36.6060	1.50577
$592$	−10.1816	−0.418461
$593$	12.1695	0.499742	0.249871	−	0.968279i	$-0.419612\pi$
$593$	12.1695	0.499742	0.249871	+	0.968279i	$0.419612\pi$
$594$	−4.71096	−0.193293
$595$	0	0
$596$	10.0000	0.409616
$597$	−29.6358	−1.21291
$598$	−8.23407	−0.336716
$599$	−25.1387	−1.02714	−0.513569	−	0.858048i	$-0.671677\pi$
$599$	−25.1387	−1.02714	−0.513569	+	0.858048i	$0.671677\pi$
$600$	0	0
$601$	−4.50479	−0.183754	−0.0918772	−	0.995770i	$-0.529287\pi$
$601$	−4.50479	−0.183754	−0.0918772	+	0.995770i	$0.529287\pi$
$602$	−6.27072	−0.255575
$603$	−4.88048	−0.198749
$604$	−5.18785	−0.211090
$605$	0	0
$606$	−0.541436	−0.0219944
$607$	7.00626	0.284375	0.142188	−	0.989840i	$-0.454586\pi$
$607$	7.00626	0.284375	0.142188	+	0.989840i	$0.454586\pi$
$608$	0.896916	0.0363748
$609$	−21.5510	−0.873291
$610$	0	0
$611$	27.3651	1.10707
$612$	−3.89692	−0.157524
$613$	−7.46626	−0.301559	−0.150780	−	0.988567i	$-0.548178\pi$
$613$	−7.46626	−0.301559	−0.150780	+	0.988567i	$0.548178\pi$
$614$	−23.7938	−0.960241
$615$	0	0
$616$	1.72928	0.0696747
$617$	−36.1772	−1.45644	−0.728220	−	0.685343i	$-0.759652\pi$
$617$	−36.1772	−1.45644	−0.728220	+	0.685343i	$0.759652\pi$
$618$	12.5414	0.504491
$619$	−4.27072	−0.171655	−0.0858273	−	0.996310i	$-0.527353\pi$
$619$	−4.27072	−0.171655	−0.0858273	+	0.996310i	$0.527353\pi$
$620$	0	0
$621$	7.38528	0.296361
$622$	−32.9205	−1.31999
$623$	−3.58767	−0.143737
$624$	6.89692	0.276098
$625$	0	0
$626$	29.0462	1.16092
$627$	−4.71096	−0.188138
$628$	−10.2341	−0.408384
$629$	10.1816	0.405966
$630$	0	0
$631$	26.0279	1.03615	0.518077	−	0.855334i	$-0.326648\pi$
$631$	26.0279	1.03615	0.518077	+	0.855334i	$0.326648\pi$
$632$	7.91087	0.314677
$633$	−38.9729	−1.54904
$634$	−20.6864	−0.821561
$635$	0	0
$636$	−29.9431	−1.18732
$637$	−16.4200	−0.650585
$638$	−18.9817	−0.751492
$639$	−48.8559	−1.93271
$640$	0	0
$641$	12.6831	0.500950	0.250475	−	0.968123i	$-0.419413\pi$
$641$	12.6831	0.500950	0.250475	+	0.968123i	$0.419413\pi$
$642$	16.5414	0.652838
$643$	−25.1108	−0.990272	−0.495136	−	0.868815i	$-0.664882\pi$
$643$	−25.1108	−0.990272	−0.495136	+	0.868815i	$0.664882\pi$
$644$	−2.71096	−0.106827
$645$	0	0
$646$	−0.896916	−0.0352887
$647$	−38.0635	−1.49643	−0.748215	−	0.663456i	$-0.769089\pi$
$647$	−38.0635	−1.49643	−0.748215	+	0.663456i	$0.769089\pi$
$648$	5.50479	0.216249
$649$	−8.29862	−0.325750
$650$	0	0
$651$	−20.4681	−0.802210
$652$	−6.47689	−0.253654
$653$	−45.2682	−1.77148	−0.885742	−	0.464179i	$-0.846350\pi$
$653$	−45.2682	−1.77148	−0.885742	+	0.464179i	$0.846350\pi$
$654$	−14.5896	−0.570497
$655$	0	0
$656$	9.52311	0.371815
$657$	10.2341	0.399269
$658$	9.00958	0.351230
$659$	40.7466	1.58726	0.793630	−	0.608400i	$-0.208188\pi$
$659$	40.7466	1.58726	0.793630	+	0.608400i	$0.208188\pi$
$660$	0	0
$661$	2.53270	0.0985106	0.0492553	−	0.998786i	$-0.484315\pi$
$661$	2.53270	0.0985106	0.0492553	+	0.998786i	$0.484315\pi$
$662$	−4.02021	−0.156250
$663$	−6.89692	−0.267854
$664$	−4.20617	−0.163231
$665$	0	0
$666$	39.6768	1.53744
$667$	29.7572	1.15220
$668$	3.84632	0.148819
$669$	8.69075	0.336004
$670$	0	0
$671$	6.56934	0.253607
$672$	2.27072	0.0875949
$673$	37.0818	1.42940	0.714700	−	0.699431i	$-0.246563\pi$
$673$	37.0818	1.42940	0.714700	+	0.699431i	$0.246563\pi$
$674$	−2.21386	−0.0852748
$675$	0	0
$676$	−6.10308	−0.234734
$677$	44.3790	1.70562	0.852812	−	0.522218i	$-0.174895\pi$
$677$	44.3790	1.70562	0.852812	+	0.522218i	$0.174895\pi$
$678$	27.9065	1.07174
$679$	−5.31695	−0.204046
$680$	0	0
$681$	−64.9161	−2.48759
$682$	−18.0279	−0.690324
$683$	−7.46626	−0.285688	−0.142844	−	0.989745i	$-0.545625\pi$
$683$	−7.46626	−0.285688	−0.142844	+	0.989745i	$0.545625\pi$
$684$	−3.49521	−0.133643
$685$	0	0
$686$	−11.4586	−0.437490
$687$	11.2158	0.427908
$688$	−7.25240	−0.276495
$689$	−29.9431	−1.14074
$690$	0	0
$691$	26.8959	1.02317	0.511584	−	0.859233i	$-0.329059\pi$
$691$	26.8959	1.02317	0.511584	+	0.859233i	$0.329059\pi$
$692$	23.9109	0.908955
$693$	−6.73887	−0.255988
$694$	1.37380	0.0521488
$695$	0	0
$696$	−24.9248	−0.944773
$697$	−9.52311	−0.360714
$698$	20.8680	0.789864
$699$	2.18596	0.0826805
$700$	0	0
$701$	23.7938	0.898681	0.449340	−	0.893361i	$-0.351659\pi$
$701$	23.7938	0.898681	0.449340	+	0.893361i	$0.351659\pi$
$702$	−6.18596	−0.233474
$703$	9.13203	0.344421
$704$	2.00000	0.0753778
$705$	0	0
$706$	13.7572	0.517759
$707$	−0.178261	−0.00670419
$708$	−10.8969	−0.409531
$709$	−17.0140	−0.638972	−0.319486	−	0.947591i	$-0.603510\pi$
$709$	−17.0140	−0.638972	−0.319486	+	0.947591i	$0.603510\pi$
$710$	0	0
$711$	−30.8280	−1.15614
$712$	−4.14931	−0.155502
$713$	28.2620	1.05842
$714$	−2.27072	−0.0849795
$715$	0	0
$716$	−14.7110	−0.549774
$717$	−12.3719	−0.462038
$718$	−9.31695	−0.347705
$719$	−23.8665	−0.890071	−0.445036	−	0.895513i	$-0.646809\pi$
$719$	−23.8665	−0.890071	−0.445036	+	0.895513i	$0.646809\pi$
$720$	0	0
$721$	4.12910	0.153776
$722$	18.1955	0.677168
$723$	−61.6801	−2.29391
$724$	−23.4340	−0.870917
$725$	0	0
$726$	18.3834	0.682271
$727$	28.3834	1.05268	0.526341	−	0.850274i	$-0.323564\pi$
$727$	28.3834	1.05268	0.526341	+	0.850274i	$0.323564\pi$
$728$	2.27072	0.0841584
$729$	−40.0096	−1.48184
$730$	0	0
$731$	7.25240	0.268240
$732$	8.62620	0.318833
$733$	28.2216	1.04239	0.521194	−	0.853439i	$-0.325487\pi$
$733$	28.2216	1.04239	0.521194	+	0.853439i	$0.325487\pi$
$734$	−12.3878	−0.457240
$735$	0	0
$736$	−3.13536	−0.115571
$737$	−2.50479	−0.0922652
$738$	−37.1108	−1.36607
$739$	0.226378	0.00832746	0.00416373	−	0.999991i	$-0.498675\pi$
$739$	0.226378	0.00832746	0.00416373	+	0.999991i	$0.498675\pi$
$740$	0	0
$741$	−6.18596	−0.227247
$742$	−9.85838	−0.361913
$743$	47.6035	1.74640	0.873202	−	0.487359i	$-0.162040\pi$
$743$	47.6035	1.74640	0.873202	+	0.487359i	$0.162040\pi$
$744$	−23.6724	−0.867873
$745$	0	0
$746$	23.3169	0.853694
$747$	16.3911	0.599718
$748$	−2.00000	−0.0731272
$749$	5.44605	0.198994
$750$	0	0
$751$	0.124733	0.00455157	0.00227578	−	0.999997i	$-0.499276\pi$
$751$	0.124733	0.00455157	0.00227578	+	0.999997i	$0.499276\pi$
$752$	10.4200	0.379979
$753$	−16.5414	−0.602803
$754$	−24.9248	−0.907709
$755$	0	0
$756$	−2.03664	−0.0740720
$757$	33.7774	1.22766	0.613830	−	0.789438i	$-0.289628\pi$
$757$	33.7774	1.22766	0.613830	+	0.789438i	$0.289628\pi$
$758$	−28.9817	−1.05266
$759$	16.4681	0.597756
$760$	0	0
$761$	11.4219	0.414044	0.207022	−	0.978336i	$-0.433623\pi$
$761$	11.4219	0.414044	0.207022	+	0.978336i	$0.433623\pi$
$762$	−37.7003	−1.36574
$763$	−4.80342	−0.173895
$764$	18.5048	0.669480
$765$	0	0
$766$	−14.9527	−0.540264
$767$	−10.8969	−0.393465
$768$	2.62620	0.0947648
$769$	12.1127	0.436794	0.218397	−	0.975860i	$-0.429917\pi$
$769$	12.1127	0.436794	0.218397	+	0.975860i	$0.429917\pi$
$770$	0	0
$771$	−3.92671	−0.141417
$772$	−5.45856	−0.196458
$773$	37.4586	1.34729	0.673645	−	0.739055i	$-0.264728\pi$
$773$	37.4586	1.34729	0.673645	+	0.739055i	$0.264728\pi$
$774$	28.2620	1.01586
$775$	0	0
$776$	−6.14931	−0.220747
$777$	23.1195	0.829408
$778$	19.3169	0.692546
$779$	−8.54144	−0.306029
$780$	0	0
$781$	−25.0741	−0.897223
$782$	3.13536	0.112120
$783$	22.3555	0.798920
$784$	−6.25240	−0.223300
$785$	0	0
$786$	−44.7668	−1.59678
$787$	−25.0664	−0.893522	−0.446761	−	0.894653i	$-0.647423\pi$
$787$	−25.0664	−0.893522	−0.446761	+	0.894653i	$0.647423\pi$
$788$	13.9388	0.496548
$789$	−26.1127	−0.929636
$790$	0	0
$791$	9.18785	0.326682
$792$	−7.79383	−0.276942
$793$	8.62620	0.306325
$794$	−9.57560	−0.339825
$795$	0	0
$796$	−11.2847	−0.399975
$797$	−19.5510	−0.692533	−0.346266	−	0.938136i	$-0.612551\pi$
$797$	−19.5510	−0.692533	−0.346266	+	0.938136i	$0.612551\pi$
$798$	−2.03664	−0.0720964
$799$	−10.4200	−0.368634
$800$	0	0
$801$	16.1695	0.571322
$802$	−11.3169	−0.399615
$803$	5.25240	0.185353
$804$	−3.28904	−0.115996
$805$	0	0
$806$	−23.6724	−0.833826
$807$	5.16763	0.181909
$808$	−0.206167	−0.00725294
$809$	20.1974	0.710104	0.355052	−	0.934847i	$-0.384463\pi$
$809$	20.1974	0.710104	0.355052	+	0.934847i	$0.384463\pi$
$810$	0	0
$811$	28.1570	0.988726	0.494363	−	0.869255i	$-0.335401\pi$
$811$	28.1570	0.988726	0.494363	+	0.869255i	$0.335401\pi$
$812$	−8.20617	−0.287980
$813$	23.2158	0.814212
$814$	20.3632	0.713729
$815$	0	0
$816$	−2.62620	−0.0919353
$817$	6.50479	0.227574
$818$	9.10308	0.318282
$819$	−8.84880	−0.309202
$820$	0	0
$821$	−51.2759	−1.78954	−0.894771	−	0.446525i	$-0.852661\pi$
$821$	−51.2759	−1.78954	−0.894771	+	0.446525i	$0.852661\pi$
$822$	38.0925	1.32863
$823$	52.9850	1.84694	0.923471	−	0.383669i	$-0.125340\pi$
$823$	52.9850	1.84694	0.923471	+	0.383669i	$0.125340\pi$
$824$	4.77551	0.166363
$825$	0	0
$826$	−3.58767	−0.124831
$827$	39.7205	1.38122	0.690609	−	0.723228i	$-0.257342\pi$
$827$	39.7205	1.38122	0.690609	+	0.723228i	$0.257342\pi$
$828$	12.2182	0.424613
$829$	23.0096	0.799156	0.399578	−	0.916699i	$-0.369157\pi$
$829$	23.0096	0.799156	0.399578	+	0.916699i	$0.369157\pi$
$830$	0	0
$831$	−52.1204	−1.80804
$832$	2.62620	0.0910470
$833$	6.25240	0.216633
$834$	38.6339	1.33778
$835$	0	0
$836$	−1.79383	−0.0620410
$837$	21.2322	0.733892
$838$	4.02791	0.139142
$839$	2.39545	0.0827002	0.0413501	−	0.999145i	$-0.486834\pi$
$839$	2.39545	0.0827002	0.0413501	+	0.999145i	$0.486834\pi$
$840$	0	0
$841$	61.0760	2.10607
$842$	−15.2524	−0.525632
$843$	−31.2688	−1.07696
$844$	−14.8401	−0.510816
$845$	0	0
$846$	−40.6060	−1.39606
$847$	6.05249	0.207966
$848$	−11.4017	−0.391536
$849$	36.0760	1.23813
$850$	0	0
$851$	−31.9229	−1.09430
$852$	−32.9248	−1.12799
$853$	−2.24614	−0.0769063	−0.0384532	−	0.999260i	$-0.512243\pi$
$853$	−2.24614	−0.0769063	−0.0384532	+	0.999260i	$0.512243\pi$
$854$	2.84006	0.0971849
$855$	0	0
$856$	6.29862	0.215283
$857$	−18.3188	−0.625760	−0.312880	−	0.949793i	$-0.601294\pi$
$857$	−18.3188	−0.625760	−0.312880	+	0.949793i	$0.601294\pi$
$858$	−13.7938	−0.470914
$859$	−42.1127	−1.43687	−0.718433	−	0.695596i	$-0.755140\pi$
$859$	−42.1127	−1.43687	−0.718433	+	0.695596i	$0.755140\pi$
$860$	0	0
$861$	−21.6243	−0.736954
$862$	4.45231	0.151646
$863$	44.8313	1.52608	0.763038	−	0.646354i	$-0.223707\pi$
$863$	44.8313	1.52608	0.763038	+	0.646354i	$0.223707\pi$
$864$	−2.35548	−0.0801351
$865$	0	0
$866$	−10.7110	−0.363973
$867$	2.62620	0.0891904
$868$	−7.79383	−0.264540
$869$	−15.8217	−0.536716
$870$	0	0
$871$	−3.28904	−0.111445
$872$	−5.55539	−0.188129
$873$	23.9634	0.811037
$874$	2.81215	0.0951226
$875$	0	0
$876$	6.89692	0.233025
$877$	2.29530	0.0775067	0.0387533	−	0.999249i	$-0.487661\pi$
$877$	2.29530	0.0775067	0.0387533	+	0.999249i	$0.487661\pi$
$878$	−5.09871	−0.172073
$879$	−31.9798	−1.07865
$880$	0	0
$881$	−20.9171	−0.704716	−0.352358	−	0.935865i	$-0.614620\pi$
$881$	−20.9171	−0.704716	−0.352358	+	0.935865i	$0.614620\pi$
$882$	24.3651	0.820414
$883$	−26.6743	−0.897662	−0.448831	−	0.893617i	$-0.648160\pi$
$883$	−26.6743	−0.897662	−0.448831	+	0.893617i	$0.648160\pi$
$884$	−2.62620	−0.0883286
$885$	0	0
$886$	−10.8034	−0.362948
$887$	−29.1633	−0.979207	−0.489603	−	0.871945i	$-0.662858\pi$
$887$	−29.1633	−0.979207	−0.489603	+	0.871945i	$0.662858\pi$
$888$	26.7389	0.897298
$889$	−12.4123	−0.416296
$890$	0	0
$891$	−11.0096	−0.368835
$892$	3.30925	0.110802
$893$	−9.34590	−0.312748
$894$	−26.2620	−0.878332
$895$	0	0
$896$	0.864641	0.0288856
$897$	21.6243	0.722015
$898$	5.82174	0.194274
$899$	85.5500	2.85325
$900$	0	0
$901$	11.4017	0.379846
$902$	−19.0462	−0.634170
$903$	16.4681	0.548026
$904$	10.6262	0.353422
$905$	0	0
$906$	13.6243	0.452637
$907$	23.2322	0.771412	0.385706	−	0.922622i	$-0.373958\pi$
$907$	23.2322	0.771412	0.385706	+	0.922622i	$0.373958\pi$
$908$	−24.7187	−0.820317
$909$	0.803417	0.0266477
$910$	0	0
$911$	−20.8646	−0.691276	−0.345638	−	0.938368i	$-0.612338\pi$
$911$	−20.8646	−0.691276	−0.345638	+	0.938368i	$0.612338\pi$
$912$	−2.35548	−0.0779977
$913$	8.41233	0.278408
$914$	−13.7014	−0.453201
$915$	0	0
$916$	4.27072	0.141109
$917$	−14.7389	−0.486720
$918$	2.35548	0.0777424
$919$	18.2062	0.600566	0.300283	−	0.953850i	$-0.402919\pi$
$919$	18.2062	0.600566	0.300283	+	0.953850i	$0.402919\pi$
$920$	0	0
$921$	62.4873	2.05903
$922$	27.0741	0.891639
$923$	−32.9248	−1.08373
$924$	−4.54144	−0.149402
$925$	0	0
$926$	−37.3372	−1.22698
$927$	−18.6098	−0.611225
$928$	−9.49084	−0.311552
$929$	17.2803	0.566948	0.283474	−	0.958980i	$-0.408513\pi$
$929$	17.2803	0.566948	0.283474	+	0.958980i	$0.408513\pi$
$930$	0	0
$931$	5.60788	0.183791
$932$	0.832365	0.0272650
$933$	86.4556	2.83043
$934$	−35.3449	−1.15652
$935$	0	0
$936$	−10.2341	−0.334511
$937$	50.2986	1.64318	0.821592	−	0.570076i	$-0.193086\pi$
$937$	50.2986	1.64318	0.821592	+	0.570076i	$0.193086\pi$
$938$	−1.08287	−0.0353571
$939$	−76.2811	−2.48934
$940$	0	0
$941$	20.7153	0.675300	0.337650	−	0.941272i	$-0.390368\pi$
$941$	20.7153	0.675300	0.337650	+	0.941272i	$0.390368\pi$
$942$	26.8767	0.875690
$943$	29.8584	0.972323
$944$	−4.14931	−0.135049
$945$	0	0
$946$	14.5048	0.471591
$947$	−8.89692	−0.289111	−0.144555	−	0.989497i	$-0.546175\pi$
$947$	−8.89692	−0.289111	−0.144555	+	0.989497i	$0.546175\pi$
$948$	−20.7755	−0.674757
$949$	6.89692	0.223883
$950$	0	0
$951$	54.3265	1.76166
$952$	−0.864641	−0.0280232
$953$	17.2158	0.557673	0.278836	−	0.960339i	$-0.410051\pi$
$953$	17.2158	0.557673	0.278836	+	0.960339i	$0.410051\pi$
$954$	44.4315	1.43852
$955$	0	0
$956$	−4.71096	−0.152363
$957$	49.8496	1.61141
$958$	−31.0419	−1.00292
$959$	12.5414	0.404984
$960$	0	0
$961$	50.2514	1.62101
$962$	26.7389	0.862096
$963$	−24.5452	−0.790958
$964$	−23.4865	−0.756448
$965$	0	0
$966$	7.11952	0.229067
$967$	1.90754	0.0613424	0.0306712	−	0.999530i	$-0.490236\pi$
$967$	1.90754	0.0613424	0.0306712	+	0.999530i	$0.490236\pi$
$968$	7.00000	0.224989
$969$	2.35548	0.0756689
$970$	0	0
$971$	−4.97398	−0.159623	−0.0798113	−	0.996810i	$-0.525432\pi$
$971$	−4.97398	−0.159623	−0.0798113	+	0.996810i	$0.525432\pi$
$972$	−21.5231	−0.690354
$973$	12.7197	0.407775
$974$	−13.1633	−0.421778
$975$	0	0
$976$	3.28467	0.105140
$977$	51.2716	1.64032	0.820161	−	0.572132i	$-0.193884\pi$
$977$	51.2716	1.64032	0.820161	+	0.572132i	$0.193884\pi$
$978$	17.0096	0.543907
$979$	8.29862	0.265225
$980$	0	0
$981$	21.6489	0.691196
$982$	−24.3555	−0.777215
$983$	9.88296	0.315218	0.157609	−	0.987502i	$-0.449622\pi$
$983$	9.88296	0.315218	0.157609	+	0.987502i	$0.449622\pi$
$984$	−25.0096	−0.797276
$985$	0	0
$986$	9.49084	0.302250
$987$	−23.6610	−0.753136
$988$	−2.35548	−0.0749378
$989$	−22.7389	−0.723054
$990$	0	0
$991$	−37.7807	−1.20014	−0.600072	−	0.799946i	$-0.704861\pi$
$991$	−37.7807	−1.20014	−0.600072	+	0.799946i	$0.704861\pi$
$992$	−9.01395	−0.286193
$993$	10.5579	0.335044
$994$	−10.8401	−0.343826
$995$	0	0
$996$	11.0462	0.350013
$997$	−8.14494	−0.257953	−0.128976	−	0.991648i	$-0.541169\pi$
$997$	−8.14494	−0.257953	−0.128976	+	0.991648i	$0.541169\pi$
$998$	−36.2620	−1.14785
$999$	−23.9825	−0.758774

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.a.p.1.3		3
3.2	odd	2		7650.2.a.do.1.2		3
4.3	odd	2		6800.2.a.bp.1.1		3
5.2	odd	4		170.2.c.b.69.1	✓	6
5.3	odd	4		170.2.c.b.69.6	yes	6
5.4	even	2		850.2.a.q.1.1		3
15.2	even	4		1530.2.d.g.919.6		6
15.8	even	4		1530.2.d.g.919.3		6
15.14	odd	2		7650.2.a.dj.1.2		3
20.3	even	4		1360.2.e.c.1089.2		6
20.7	even	4		1360.2.e.c.1089.5		6
20.19	odd	2		6800.2.a.bk.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.c.b.69.1	✓	6	5.2	odd	4
170.2.c.b.69.6	yes	6	5.3	odd	4
850.2.a.p.1.3		3	1.1	even	1	trivial
850.2.a.q.1.1		3	5.4	even	2
1360.2.e.c.1089.2		6	20.3	even	4
1360.2.e.c.1089.5		6	20.7	even	4
1530.2.d.g.919.3		6	15.8	even	4
1530.2.d.g.919.6		6	15.2	even	4
6800.2.a.bk.1.3		3	20.19	odd	2
6800.2.a.bp.1.1		3	4.3	odd	2
7650.2.a.dj.1.2		3	15.14	odd	2
7650.2.a.do.1.2		3	3.2	odd	2

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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:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.62620 q^{3} +1.00000 q^{4} -2.62620 q^{6} -0.864641 q^{7} -1.00000 q^{8} +3.89692 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.62620 q^{3} +1.00000 q^{4} -2.62620 q^{6} -0.864641 q^{7} -1.00000 q^{8} +3.89692 q^{9} +2.00000 q^{11} +2.62620 q^{12} +2.62620 q^{13} +0.864641 q^{14} +1.00000 q^{16} -1.00000 q^{17} -3.89692 q^{18} -0.896916 q^{19} -2.27072 q^{21} -2.00000 q^{22} +3.13536 q^{23} -2.62620 q^{24} -2.62620 q^{26} +2.35548 q^{27} -0.864641 q^{28} +9.49084 q^{29} +9.01395 q^{31} -1.00000 q^{32} +5.25240 q^{33} +1.00000 q^{34} +3.89692 q^{36} -10.1816 q^{37} +0.896916 q^{38} +6.89692 q^{39} +9.52311 q^{41} +2.27072 q^{42} -7.25240 q^{43} +2.00000 q^{44} -3.13536 q^{46} +10.4200 q^{47} +2.62620 q^{48} -6.25240 q^{49} -2.62620 q^{51} +2.62620 q^{52} -11.4017 q^{53} -2.35548 q^{54} +0.864641 q^{56} -2.35548 q^{57} -9.49084 q^{58} -4.14931 q^{59} +3.28467 q^{61} -9.01395 q^{62} -3.36943 q^{63} +1.00000 q^{64} -5.25240 q^{66} -1.25240 q^{67} -1.00000 q^{68} +8.23407 q^{69} -12.5371 q^{71} -3.89692 q^{72} +2.62620 q^{73} +10.1816 q^{74} -0.896916 q^{76} -1.72928 q^{77} -6.89692 q^{78} -7.91087 q^{79} -5.50479 q^{81} -9.52311 q^{82} +4.20617 q^{83} -2.27072 q^{84} +7.25240 q^{86} +24.9248 q^{87} -2.00000 q^{88} +4.14931 q^{89} -2.27072 q^{91} +3.13536 q^{92} +23.6724 q^{93} -10.4200 q^{94} -2.62620 q^{96} +6.14931 q^{97} +6.25240 q^{98} +7.79383 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - q^{3} + 3 q^{4} + q^{6} - 3 q^{8} + 8 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - q^3 + 3 * q^4 + q^6 - 3 * q^8 + 8 * q^9	\( 3 q - 3 q^{2} - q^{3} + 3 q^{4} + q^{6} - 3 q^{8} + 8 q^{9} + 6 q^{11} - q^{12} - q^{13} + 3 q^{16} - 3 q^{17} - 8 q^{18} + q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} + q^{24} + q^{26} - 7 q^{27} + 17 q^{29} + 3 q^{31} - 3 q^{32} - 2 q^{33} + 3 q^{34} + 8 q^{36} - 8 q^{37} - q^{38} + 17 q^{39} + 16 q^{41} + 12 q^{42} - 4 q^{43} + 6 q^{44} - 12 q^{46} + 15 q^{47} - q^{48} - q^{49} + q^{51} - q^{52} + 5 q^{53} + 7 q^{54} + 7 q^{57} - 17 q^{58} + 9 q^{59} - 9 q^{61} - 3 q^{62} + 28 q^{63} + 3 q^{64} + 2 q^{66} + 14 q^{67} - 3 q^{68} - 16 q^{69} - q^{71} - 8 q^{72} - q^{73} + 8 q^{74} + q^{76} - 17 q^{78} + 4 q^{79} + 19 q^{81} - 16 q^{82} + 20 q^{83} - 12 q^{84} + 4 q^{86} + 23 q^{87} - 6 q^{88} - 9 q^{89} - 12 q^{91} + 12 q^{92} + 37 q^{93} - 15 q^{94} + q^{96} - 3 q^{97} + q^{98} + 16 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - q^3 + 3 * q^4 + q^6 - 3 * q^8 + 8 * q^9 + 6 * q^11 - q^12 - q^13 + 3 * q^16 - 3 * q^17 - 8 * q^18 + q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 + q^24 + q^26 - 7 * q^27 + 17 * q^29 + 3 * q^31 - 3 * q^32 - 2 * q^33 + 3 * q^34 + 8 * q^36 - 8 * q^37 - q^38 + 17 * q^39 + 16 * q^41 + 12 * q^42 - 4 * q^43 + 6 * q^44 - 12 * q^46 + 15 * q^47 - q^48 - q^49 + q^51 - q^52 + 5 * q^53 + 7 * q^54 + 7 * q^57 - 17 * q^58 + 9 * q^59 - 9 * q^61 - 3 * q^62 + 28 * q^63 + 3 * q^64 + 2 * q^66 + 14 * q^67 - 3 * q^68 - 16 * q^69 - q^71 - 8 * q^72 - q^73 + 8 * q^74 + q^76 - 17 * q^78 + 4 * q^79 + 19 * q^81 - 16 * q^82 + 20 * q^83 - 12 * q^84 + 4 * q^86 + 23 * q^87 - 6 * q^88 - 9 * q^89 - 12 * q^91 + 12 * q^92 + 37 * q^93 - 15 * q^94 + q^96 - 3 * q^97 + q^98 + 16 * q^99

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