LMFDB - Embedded newform 2541.2.a.r.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2541,2,Mod(1,2541)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2541, 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("2541.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2541 = 3 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2541.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:	$20.2899871536$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	2541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.61803 q^{2} +1.00000 q^{3} +0.618034 q^{4} -4.23607 q^{5} -1.61803 q^{6} +1.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.61803 q^{2} +1.00000 q^{3} +0.618034 q^{4} -4.23607 q^{5} -1.61803 q^{6} +1.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} +6.85410 q^{10} +0.618034 q^{12} -6.23607 q^{13} -1.61803 q^{14} -4.23607 q^{15} -4.85410 q^{16} +4.47214 q^{17} -1.61803 q^{18} -3.00000 q^{19} -2.61803 q^{20} +1.00000 q^{21} +8.47214 q^{23} +2.23607 q^{24} +12.9443 q^{25} +10.0902 q^{26} +1.00000 q^{27} +0.618034 q^{28} +3.00000 q^{29} +6.85410 q^{30} +3.38197 q^{32} -7.23607 q^{34} -4.23607 q^{35} +0.618034 q^{36} +3.47214 q^{37} +4.85410 q^{38} -6.23607 q^{39} -9.47214 q^{40} -1.52786 q^{41} -1.61803 q^{42} -10.9443 q^{43} -4.23607 q^{45} -13.7082 q^{46} -3.00000 q^{47} -4.85410 q^{48} +1.00000 q^{49} -20.9443 q^{50} +4.47214 q^{51} -3.85410 q^{52} +8.94427 q^{53} -1.61803 q^{54} +2.23607 q^{56} -3.00000 q^{57} -4.85410 q^{58} -1.47214 q^{59} -2.61803 q^{60} -3.52786 q^{61} +1.00000 q^{63} +4.23607 q^{64} +26.4164 q^{65} -8.70820 q^{67} +2.76393 q^{68} +8.47214 q^{69} +6.85410 q^{70} +1.52786 q^{71} +2.23607 q^{72} -12.2361 q^{73} -5.61803 q^{74} +12.9443 q^{75} -1.85410 q^{76} +10.0902 q^{78} +13.4164 q^{79} +20.5623 q^{80} +1.00000 q^{81} +2.47214 q^{82} -6.00000 q^{83} +0.618034 q^{84} -18.9443 q^{85} +17.7082 q^{86} +3.00000 q^{87} -4.47214 q^{89} +6.85410 q^{90} -6.23607 q^{91} +5.23607 q^{92} +4.85410 q^{94} +12.7082 q^{95} +3.38197 q^{96} +2.00000 q^{97} -1.61803 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 2 q^{3} - q^{4} - 4 q^{5} - q^{6} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 + 2 * q^3 - q^4 - 4 * q^5 - q^6 + 2 * q^7 + 2 * q^9	$ 2 q - q^{2} + 2 q^{3} - q^{4} - 4 q^{5} - q^{6} + 2 q^{7} + 2 q^{9} + 7 q^{10} - q^{12} - 8 q^{13} - q^{14} - 4 q^{15} - 3 q^{16} - q^{18} - 6 q^{19} - 3 q^{20} + 2 q^{21} + 8 q^{23} + 8 q^{25} + 9 q^{26} + 2 q^{27} - q^{28} + 6 q^{29} + 7 q^{30} + 9 q^{32} - 10 q^{34} - 4 q^{35} - q^{36} - 2 q^{37} + 3 q^{38} - 8 q^{39} - 10 q^{40} - 12 q^{41} - q^{42} - 4 q^{43} - 4 q^{45} - 14 q^{46} - 6 q^{47} - 3 q^{48} + 2 q^{49} - 24 q^{50} - q^{52} - q^{54} - 6 q^{57} - 3 q^{58} + 6 q^{59} - 3 q^{60} - 16 q^{61} + 2 q^{63} + 4 q^{64} + 26 q^{65} - 4 q^{67} + 10 q^{68} + 8 q^{69} + 7 q^{70} + 12 q^{71} - 20 q^{73} - 9 q^{74} + 8 q^{75} + 3 q^{76} + 9 q^{78} + 21 q^{80} + 2 q^{81} - 4 q^{82} - 12 q^{83} - q^{84} - 20 q^{85} + 22 q^{86} + 6 q^{87} + 7 q^{90} - 8 q^{91} + 6 q^{92} + 3 q^{94} + 12 q^{95} + 9 q^{96} + 4 q^{97} - q^{98}+O(q^{100}) $ 2 * q - q^2 + 2 * q^3 - q^4 - 4 * q^5 - q^6 + 2 * q^7 + 2 * q^9 + 7 * q^10 - q^12 - 8 * q^13 - q^14 - 4 * q^15 - 3 * q^16 - q^18 - 6 * q^19 - 3 * q^20 + 2 * q^21 + 8 * q^23 + 8 * q^25 + 9 * q^26 + 2 * q^27 - q^28 + 6 * q^29 + 7 * q^30 + 9 * q^32 - 10 * q^34 - 4 * q^35 - q^36 - 2 * q^37 + 3 * q^38 - 8 * q^39 - 10 * q^40 - 12 * q^41 - q^42 - 4 * q^43 - 4 * q^45 - 14 * q^46 - 6 * q^47 - 3 * q^48 + 2 * q^49 - 24 * q^50 - q^52 - q^54 - 6 * q^57 - 3 * q^58 + 6 * q^59 - 3 * q^60 - 16 * q^61 + 2 * q^63 + 4 * q^64 + 26 * q^65 - 4 * q^67 + 10 * q^68 + 8 * q^69 + 7 * q^70 + 12 * q^71 - 20 * q^73 - 9 * q^74 + 8 * q^75 + 3 * q^76 + 9 * q^78 + 21 * q^80 + 2 * q^81 - 4 * q^82 - 12 * q^83 - q^84 - 20 * q^85 + 22 * q^86 + 6 * q^87 + 7 * q^90 - 8 * q^91 + 6 * q^92 + 3 * q^94 + 12 * q^95 + 9 * q^96 + 4 * q^97 - q^98

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 $

$2$	−1.61803	−1.14412	−0.572061	−	0.820211i	$-0.693856\pi$
$2$	−1.61803	−1.14412	−0.572061	+	0.820211i	$0.693856\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.618034	0.309017
$5$	−4.23607	−1.89443	−0.947214	−	0.320603i	$-0.896114\pi$
$5$	−4.23607	−1.89443	−0.947214	+	0.320603i	$0.896114\pi$
$6$	−1.61803	−0.660560
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.23607	0.790569
$9$	1.00000	0.333333
$10$	6.85410	2.16746
$11$	0	0
$11$	0	0
$12$	0.618034	0.178411
$13$	−6.23607	−1.72957	−0.864787	−	0.502139i	$-0.832547\pi$
$13$	−6.23607	−1.72957	−0.864787	+	0.502139i	$0.832547\pi$
$14$	−1.61803	−0.432438
$15$	−4.23607	−1.09375
$16$	−4.85410	−1.21353
$17$	4.47214	1.08465	0.542326	−	0.840168i	$-0.317544\pi$
$17$	4.47214	1.08465	0.542326	+	0.840168i	$0.317544\pi$
$18$	−1.61803	−0.381374
$19$	−3.00000	−0.688247	−0.344124	−	0.938924i	$-0.611824\pi$
$19$	−3.00000	−0.688247	−0.344124	+	0.938924i	$0.611824\pi$
$20$	−2.61803	−0.585410
$21$	1.00000	0.218218
$22$	0	0
$23$	8.47214	1.76656	0.883281	−	0.468844i	$-0.155329\pi$
$23$	8.47214	1.76656	0.883281	+	0.468844i	$0.155329\pi$
$24$	2.23607	0.456435
$25$	12.9443	2.58885
$26$	10.0902	1.97885
$27$	1.00000	0.192450
$28$	0.618034	0.116797
$29$	3.00000	0.557086	0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000	0.557086	0.278543	+	0.960424i	$0.410149\pi$
$30$	6.85410	1.25138
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	3.38197	0.597853
$33$	0	0
$34$	−7.23607	−1.24098
$35$	−4.23607	−0.716026
$36$	0.618034	0.103006
$37$	3.47214	0.570816	0.285408	−	0.958406i	$-0.407871\pi$
$37$	3.47214	0.570816	0.285408	+	0.958406i	$0.407871\pi$
$38$	4.85410	0.787439
$39$	−6.23607	−0.998570
$40$	−9.47214	−1.49768
$41$	−1.52786	−0.238612	−0.119306	−	0.992858i	$-0.538067\pi$
$41$	−1.52786	−0.238612	−0.119306	+	0.992858i	$0.538067\pi$
$42$	−1.61803	−0.249668
$43$	−10.9443	−1.66899	−0.834493	−	0.551019i	$-0.814239\pi$
$43$	−10.9443	−1.66899	−0.834493	+	0.551019i	$0.814239\pi$
$44$	0	0
$45$	−4.23607	−0.631476
$46$	−13.7082	−2.02116
$47$	−3.00000	−0.437595	−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000	−0.437595	−0.218797	+	0.975770i	$0.570213\pi$
$48$	−4.85410	−0.700629
$49$	1.00000	0.142857
$50$	−20.9443	−2.96197
$51$	4.47214	0.626224
$52$	−3.85410	−0.534468
$53$	8.94427	1.22859	0.614295	−	0.789076i	$-0.289440\pi$
$53$	8.94427	1.22859	0.614295	+	0.789076i	$0.289440\pi$
$54$	−1.61803	−0.220187
$55$	0	0
$56$	2.23607	0.298807
$57$	−3.00000	−0.397360
$58$	−4.85410	−0.637375
$59$	−1.47214	−0.191656	−0.0958279	−	0.995398i	$-0.530550\pi$
$59$	−1.47214	−0.191656	−0.0958279	+	0.995398i	$0.530550\pi$
$60$	−2.61803	−0.337987
$61$	−3.52786	−0.451697	−0.225848	−	0.974162i	$-0.572515\pi$
$61$	−3.52786	−0.451697	−0.225848	+	0.974162i	$0.572515\pi$
$62$	0	0
$63$	1.00000	0.125988
$64$	4.23607	0.529508
$65$	26.4164	3.27655
$66$	0	0
$67$	−8.70820	−1.06388	−0.531938	−	0.846783i	$-0.678536\pi$
$67$	−8.70820	−1.06388	−0.531938	+	0.846783i	$0.678536\pi$
$68$	2.76393	0.335176
$69$	8.47214	1.01993
$70$	6.85410	0.819222
$71$	1.52786	0.181324	0.0906621	−	0.995882i	$-0.471102\pi$
$71$	1.52786	0.181324	0.0906621	+	0.995882i	$0.471102\pi$
$72$	2.23607	0.263523
$73$	−12.2361	−1.43212	−0.716062	−	0.698037i	$-0.754057\pi$
$73$	−12.2361	−1.43212	−0.716062	+	0.698037i	$0.754057\pi$
$74$	−5.61803	−0.653083
$75$	12.9443	1.49468
$76$	−1.85410	−0.212680
$77$	0	0
$78$	10.0902	1.14249
$79$	13.4164	1.50946	0.754732	−	0.656033i	$-0.227767\pi$
$79$	13.4164	1.50946	0.754732	+	0.656033i	$0.227767\pi$
$80$	20.5623	2.29894
$81$	1.00000	0.111111
$82$	2.47214	0.273002
$83$	−6.00000	−0.658586	−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000	−0.658586	−0.329293	+	0.944228i	$0.606810\pi$
$84$	0.618034	0.0674330
$85$	−18.9443	−2.05479
$86$	17.7082	1.90952
$87$	3.00000	0.321634
$88$	0	0
$89$	−4.47214	−0.474045	−0.237023	−	0.971504i	$-0.576172\pi$
$89$	−4.47214	−0.474045	−0.237023	+	0.971504i	$0.576172\pi$
$90$	6.85410	0.722486
$91$	−6.23607	−0.653718
$92$	5.23607	0.545898
$93$	0	0
$94$	4.85410	0.500662
$95$	12.7082	1.30383
$96$	3.38197	0.345170
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	−1.61803	−0.163446
$99$	0	0
$100$	8.00000	0.800000
$101$	16.9443	1.68602	0.843009	−	0.537899i	$-0.180782\pi$
$101$	16.9443	1.68602	0.843009	+	0.537899i	$0.180782\pi$
$102$	−7.23607	−0.716477
$103$	6.47214	0.637719	0.318859	−	0.947802i	$-0.396700\pi$
$103$	6.47214	0.637719	0.318859	+	0.947802i	$0.396700\pi$
$104$	−13.9443	−1.36735
$105$	−4.23607	−0.413398
$106$	−14.4721	−1.40566
$107$	−9.76393	−0.943915	−0.471957	−	0.881621i	$-0.656452\pi$
$107$	−9.76393	−0.943915	−0.471957	+	0.881621i	$0.656452\pi$
$108$	0.618034	0.0594703
$109$	0	0		−	1.00000i	$-0.5\pi$
$109$	0	0			1.00000i	$0.5\pi$
$110$	0	0
$111$	3.47214	0.329561
$112$	−4.85410	−0.458670
$113$	−6.47214	−0.608847	−0.304424	−	0.952537i	$-0.598464\pi$
$113$	−6.47214	−0.608847	−0.304424	+	0.952537i	$0.598464\pi$
$114$	4.85410	0.454628
$115$	−35.8885	−3.34662
$116$	1.85410	0.172149
$117$	−6.23607	−0.576525
$118$	2.38197	0.219278
$119$	4.47214	0.409960
$120$	−9.47214	−0.864684
$121$	0	0
$122$	5.70820	0.516797
$123$	−1.52786	−0.137763
$124$	0	0
$125$	−33.6525	−3.00997
$126$	−1.61803	−0.144146
$127$	−2.00000	−0.177471	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000	−0.177471	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	−13.6180	−1.20368
$129$	−10.9443	−0.963589
$130$	−42.7426	−3.74878
$131$	−2.47214	−0.215992	−0.107996	−	0.994151i	$-0.534443\pi$
$131$	−2.47214	−0.215992	−0.107996	+	0.994151i	$0.534443\pi$
$132$	0	0
$133$	−3.00000	−0.260133
$134$	14.0902	1.21721
$135$	−4.23607	−0.364583
$136$	10.0000	0.857493
$137$	2.94427	0.251546	0.125773	−	0.992059i	$-0.459859\pi$
$137$	2.94427	0.251546	0.125773	+	0.992059i	$0.459859\pi$
$138$	−13.7082	−1.16692
$139$	0.944272	0.0800921	0.0400460	−	0.999198i	$-0.487250\pi$
$139$	0.944272	0.0800921	0.0400460	+	0.999198i	$0.487250\pi$
$140$	−2.61803	−0.221264
$141$	−3.00000	−0.252646
$142$	−2.47214	−0.207457
$143$	0	0
$144$	−4.85410	−0.404508
$145$	−12.7082	−1.05536
$146$	19.7984	1.63853
$147$	1.00000	0.0824786
$148$	2.14590	0.176392
$149$	−17.9443	−1.47005	−0.735026	−	0.678039i	$-0.762830\pi$
$149$	−17.9443	−1.47005	−0.735026	+	0.678039i	$0.762830\pi$
$150$	−20.9443	−1.71009
$151$	−17.4164	−1.41733	−0.708664	−	0.705547i	$-0.750702\pi$
$151$	−17.4164	−1.41733	−0.708664	+	0.705547i	$0.750702\pi$
$152$	−6.70820	−0.544107
$153$	4.47214	0.361551
$154$	0	0
$155$	0	0
$156$	−3.85410	−0.308575
$157$	−13.4164	−1.07075	−0.535373	−	0.844616i	$-0.679829\pi$
$157$	−13.4164	−1.07075	−0.535373	+	0.844616i	$0.679829\pi$
$158$	−21.7082	−1.72701
$159$	8.94427	0.709327
$160$	−14.3262	−1.13259
$161$	8.47214	0.667698
$162$	−1.61803	−0.127125
$163$	7.29180	0.571138	0.285569	−	0.958358i	$-0.407818\pi$
$163$	7.29180	0.571138	0.285569	+	0.958358i	$0.407818\pi$
$164$	−0.944272	−0.0737352
$165$	0	0
$166$	9.70820	0.753503
$167$	−18.9443	−1.46595	−0.732976	−	0.680255i	$-0.761869\pi$
$167$	−18.9443	−1.46595	−0.732976	+	0.680255i	$0.761869\pi$
$168$	2.23607	0.172516
$169$	25.8885	1.99143
$170$	30.6525	2.35094
$171$	−3.00000	−0.229416
$172$	−6.76393	−0.515745
$173$	−7.52786	−0.572333	−0.286166	−	0.958180i	$-0.592381\pi$
$173$	−7.52786	−0.572333	−0.286166	+	0.958180i	$0.592381\pi$
$174$	−4.85410	−0.367989
$175$	12.9443	0.978495
$176$	0	0
$177$	−1.47214	−0.110653
$178$	7.23607	0.542366
$179$	−16.4721	−1.23119	−0.615593	−	0.788065i	$-0.711083\pi$
$179$	−16.4721	−1.23119	−0.615593	+	0.788065i	$0.711083\pi$
$180$	−2.61803	−0.195137
$181$	−3.41641	−0.253940	−0.126970	−	0.991907i	$-0.540525\pi$
$181$	−3.41641	−0.253940	−0.126970	+	0.991907i	$0.540525\pi$
$182$	10.0902	0.747933
$183$	−3.52786	−0.260787
$184$	18.9443	1.39659
$185$	−14.7082	−1.08137
$186$	0	0
$187$	0	0
$188$	−1.85410	−0.135224
$189$	1.00000	0.0727393
$190$	−20.5623	−1.49175
$191$	2.94427	0.213040	0.106520	−	0.994311i	$-0.466029\pi$
$191$	2.94427	0.213040	0.106520	+	0.994311i	$0.466029\pi$
$192$	4.23607	0.305712
$193$	−12.0000	−0.863779	−0.431889	−	0.901927i	$-0.642153\pi$
$193$	−12.0000	−0.863779	−0.431889	+	0.901927i	$0.642153\pi$
$194$	−3.23607	−0.232336
$195$	26.4164	1.89172
$196$	0.618034	0.0441453
$197$	1.05573	0.0752175	0.0376088	−	0.999293i	$-0.488026\pi$
$197$	1.05573	0.0752175	0.0376088	+	0.999293i	$0.488026\pi$
$198$	0	0
$199$	−12.4721	−0.884126	−0.442063	−	0.896984i	$-0.645753\pi$
$199$	−12.4721	−0.884126	−0.442063	+	0.896984i	$0.645753\pi$
$200$	28.9443	2.04667
$201$	−8.70820	−0.614229
$202$	−27.4164	−1.92901
$203$	3.00000	0.210559
$204$	2.76393	0.193514
$205$	6.47214	0.452034
$206$	−10.4721	−0.729628
$207$	8.47214	0.588854
$208$	30.2705	2.09888
$209$	0	0
$210$	6.85410	0.472978
$211$	1.41641	0.0975095	0.0487548	−	0.998811i	$-0.484475\pi$
$211$	1.41641	0.0975095	0.0487548	+	0.998811i	$0.484475\pi$
$212$	5.52786	0.379655
$213$	1.52786	0.104688
$214$	15.7984	1.07995
$215$	46.3607	3.16177
$216$	2.23607	0.152145
$217$	0	0
$218$	0	0
$219$	−12.2361	−0.826837
$220$	0	0
$221$	−27.8885	−1.87599
$222$	−5.61803	−0.377058
$223$	6.00000	0.401790	0.200895	−	0.979613i	$-0.435615\pi$
$223$	6.00000	0.401790	0.200895	+	0.979613i	$0.435615\pi$
$224$	3.38197	0.225967
$225$	12.9443	0.862951
$226$	10.4721	0.696596
$227$	15.5279	1.03062	0.515310	−	0.857004i	$-0.327677\pi$
$227$	15.5279	1.03062	0.515310	+	0.857004i	$0.327677\pi$
$228$	−1.85410	−0.122791
$229$	−24.4721	−1.61716	−0.808582	−	0.588383i	$-0.799765\pi$
$229$	−24.4721	−1.61716	−0.808582	+	0.588383i	$0.799765\pi$
$230$	58.0689	3.82895
$231$	0	0
$232$	6.70820	0.440415
$233$	−19.8885	−1.30294	−0.651471	−	0.758674i	$-0.725848\pi$
$233$	−19.8885	−1.30294	−0.651471	+	0.758674i	$0.725848\pi$
$234$	10.0902	0.659615
$235$	12.7082	0.828992
$236$	−0.909830	−0.0592249
$237$	13.4164	0.871489
$238$	−7.23607	−0.469045
$239$	−12.7082	−0.822025	−0.411013	−	0.911630i	$-0.634825\pi$
$239$	−12.7082	−0.822025	−0.411013	+	0.911630i	$0.634825\pi$
$240$	20.5623	1.32729
$241$	−12.7082	−0.818607	−0.409304	−	0.912398i	$-0.634228\pi$
$241$	−12.7082	−0.818607	−0.409304	+	0.912398i	$0.634228\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	−2.18034	−0.139582
$245$	−4.23607	−0.270632
$246$	2.47214	0.157618
$247$	18.7082	1.19037
$248$	0	0
$249$	−6.00000	−0.380235
$250$	54.4508	3.44377
$251$	−16.4164	−1.03619	−0.518097	−	0.855322i	$-0.673359\pi$
$251$	−16.4164	−1.03619	−0.518097	+	0.855322i	$0.673359\pi$
$252$	0.618034	0.0389325
$253$	0	0
$254$	3.23607	0.203049
$255$	−18.9443	−1.18634
$256$	13.5623	0.847644
$257$	0.347524	0.0216780	0.0108390	−	0.999941i	$-0.496550\pi$
$257$	0.347524	0.0216780	0.0108390	+	0.999941i	$0.496550\pi$
$258$	17.7082	1.10246
$259$	3.47214	0.215748
$260$	16.3262	1.01251
$261$	3.00000	0.185695
$262$	4.00000	0.247121
$263$	−0.236068	−0.0145566	−0.00727829	−	0.999974i	$-0.502317\pi$
$263$	−0.236068	−0.0145566	−0.00727829	+	0.999974i	$0.502317\pi$
$264$	0	0
$265$	−37.8885	−2.32747
$266$	4.85410	0.297624
$267$	−4.47214	−0.273690
$268$	−5.38197	−0.328756
$269$	−19.5279	−1.19063	−0.595317	−	0.803491i	$-0.702974\pi$
$269$	−19.5279	−1.19063	−0.595317	+	0.803491i	$0.702974\pi$
$270$	6.85410	0.417127
$271$	3.47214	0.210917	0.105459	−	0.994424i	$-0.466369\pi$
$271$	3.47214	0.210917	0.105459	+	0.994424i	$0.466369\pi$
$272$	−21.7082	−1.31625
$273$	−6.23607	−0.377424
$274$	−4.76393	−0.287800
$275$	0	0
$276$	5.23607	0.315174
$277$	12.4721	0.749378	0.374689	−	0.927151i	$-0.377749\pi$
$277$	12.4721	0.749378	0.374689	+	0.927151i	$0.377749\pi$
$278$	−1.52786	−0.0916352
$279$	0	0
$280$	−9.47214	−0.566068
$281$	−16.4164	−0.979321	−0.489660	−	0.871913i	$-0.662879\pi$
$281$	−16.4164	−0.979321	−0.489660	+	0.871913i	$0.662879\pi$
$282$	4.85410	0.289058
$283$	18.8885	1.12281	0.561404	−	0.827542i	$-0.310262\pi$
$283$	18.8885	1.12281	0.561404	+	0.827542i	$0.310262\pi$
$284$	0.944272	0.0560322
$285$	12.7082	0.752769
$286$	0	0
$287$	−1.52786	−0.0901870
$288$	3.38197	0.199284
$289$	3.00000	0.176471
$290$	20.5623	1.20746
$291$	2.00000	0.117242
$292$	−7.56231	−0.442550
$293$	−9.88854	−0.577695	−0.288847	−	0.957375i	$-0.593272\pi$
$293$	−9.88854	−0.577695	−0.288847	+	0.957375i	$0.593272\pi$
$294$	−1.61803	−0.0943657
$295$	6.23607	0.363078
$296$	7.76393	0.451269
$297$	0	0
$298$	29.0344	1.68192
$299$	−52.8328	−3.05540
$300$	8.00000	0.461880
$301$	−10.9443	−0.630817
$302$	28.1803	1.62160
$303$	16.9443	0.973423
$304$	14.5623	0.835206
$305$	14.9443	0.855707
$306$	−7.23607	−0.413658
$307$	−16.9443	−0.967061	−0.483530	−	0.875328i	$-0.660646\pi$
$307$	−16.9443	−0.967061	−0.483530	+	0.875328i	$0.660646\pi$
$308$	0	0
$309$	6.47214	0.368187
$310$	0	0
$311$	−17.8885	−1.01437	−0.507183	−	0.861838i	$-0.669313\pi$
$311$	−17.8885	−1.01437	−0.507183	+	0.861838i	$0.669313\pi$
$312$	−13.9443	−0.789439
$313$	−20.4721	−1.15715	−0.578577	−	0.815628i	$-0.696392\pi$
$313$	−20.4721	−1.15715	−0.578577	+	0.815628i	$0.696392\pi$
$314$	21.7082	1.22506
$315$	−4.23607	−0.238675
$316$	8.29180	0.466450
$317$	30.4721	1.71149	0.855743	−	0.517401i	$-0.173101\pi$
$317$	30.4721	1.71149	0.855743	+	0.517401i	$0.173101\pi$
$318$	−14.4721	−0.811557
$319$	0	0
$320$	−17.9443	−1.00312
$321$	−9.76393	−0.544970
$322$	−13.7082	−0.763928
$323$	−13.4164	−0.746509
$324$	0.618034	0.0343352
$325$	−80.7214	−4.47762
$326$	−11.7984	−0.653451
$327$	0	0
$328$	−3.41641	−0.188640
$329$	−3.00000	−0.165395
$330$	0	0
$331$	24.0000	1.31916	0.659580	−	0.751635i	$-0.270734\pi$
$331$	24.0000	1.31916	0.659580	+	0.751635i	$0.270734\pi$
$332$	−3.70820	−0.203514
$333$	3.47214	0.190272
$334$	30.6525	1.67723
$335$	36.8885	2.01544
$336$	−4.85410	−0.264813
$337$	−24.8328	−1.35273	−0.676365	−	0.736567i	$-0.736446\pi$
$337$	−24.8328	−1.35273	−0.676365	+	0.736567i	$0.736446\pi$
$338$	−41.8885	−2.27844
$339$	−6.47214	−0.351518
$340$	−11.7082	−0.634967
$341$	0	0
$342$	4.85410	0.262480
$343$	1.00000	0.0539949
$344$	−24.4721	−1.31945
$345$	−35.8885	−1.93217
$346$	12.1803	0.654819
$347$	3.05573	0.164040	0.0820200	−	0.996631i	$-0.473863\pi$
$347$	3.05573	0.164040	0.0820200	+	0.996631i	$0.473863\pi$
$348$	1.85410	0.0993903
$349$	22.7082	1.21554	0.607771	−	0.794112i	$-0.292064\pi$
$349$	22.7082	1.21554	0.607771	+	0.794112i	$0.292064\pi$
$350$	−20.9443	−1.11952
$351$	−6.23607	−0.332857
$352$	0	0
$353$	32.5967	1.73495	0.867475	−	0.497481i	$-0.165742\pi$
$353$	32.5967	1.73495	0.867475	+	0.497481i	$0.165742\pi$
$354$	2.38197	0.126600
$355$	−6.47214	−0.343505
$356$	−2.76393	−0.146488
$357$	4.47214	0.236691
$358$	26.6525	1.40863
$359$	19.0557	1.00572	0.502861	−	0.864367i	$-0.332281\pi$
$359$	19.0557	1.00572	0.502861	+	0.864367i	$0.332281\pi$
$360$	−9.47214	−0.499225
$361$	−10.0000	−0.526316
$362$	5.52786	0.290538
$363$	0	0
$364$	−3.85410	−0.202010
$365$	51.8328	2.71305
$366$	5.70820	0.298373
$367$	−22.8328	−1.19186	−0.595932	−	0.803035i	$-0.703217\pi$
$367$	−22.8328	−1.19186	−0.595932	+	0.803035i	$0.703217\pi$
$368$	−41.1246	−2.14377
$369$	−1.52786	−0.0795374
$370$	23.7984	1.23722
$371$	8.94427	0.464363
$372$	0	0
$373$	−2.58359	−0.133773	−0.0668867	−	0.997761i	$-0.521307\pi$
$373$	−2.58359	−0.133773	−0.0668867	+	0.997761i	$0.521307\pi$
$374$	0	0
$375$	−33.6525	−1.73781
$376$	−6.70820	−0.345949
$377$	−18.7082	−0.963522
$378$	−1.61803	−0.0832227
$379$	−4.23607	−0.217592	−0.108796	−	0.994064i	$-0.534700\pi$
$379$	−4.23607	−0.217592	−0.108796	+	0.994064i	$0.534700\pi$
$380$	7.85410	0.402907
$381$	−2.00000	−0.102463
$382$	−4.76393	−0.243744
$383$	13.8885	0.709671	0.354836	−	0.934929i	$-0.384537\pi$
$383$	13.8885	0.709671	0.354836	+	0.934929i	$0.384537\pi$
$384$	−13.6180	−0.694942
$385$	0	0
$386$	19.4164	0.988269
$387$	−10.9443	−0.556329
$388$	1.23607	0.0627518
$389$	28.3607	1.43794	0.718972	−	0.695039i	$-0.244613\pi$
$389$	28.3607	1.43794	0.718972	+	0.695039i	$0.244613\pi$
$390$	−42.7426	−2.16436
$391$	37.8885	1.91611
$392$	2.23607	0.112938
$393$	−2.47214	−0.124703
$394$	−1.70820	−0.0860581
$395$	−56.8328	−2.85957
$396$	0	0
$397$	12.4721	0.625959	0.312979	−	0.949760i	$-0.398673\pi$
$397$	12.4721	0.625959	0.312979	+	0.949760i	$0.398673\pi$
$398$	20.1803	1.01155
$399$	−3.00000	−0.150188
$400$	−62.8328	−3.14164
$401$	−10.3607	−0.517388	−0.258694	−	0.965959i	$-0.583292\pi$
$401$	−10.3607	−0.517388	−0.258694	+	0.965959i	$0.583292\pi$
$402$	14.0902	0.702754
$403$	0	0
$404$	10.4721	0.521008
$405$	−4.23607	−0.210492
$406$	−4.85410	−0.240905
$407$	0	0
$408$	10.0000	0.495074
$409$	−2.58359	−0.127750	−0.0638752	−	0.997958i	$-0.520346\pi$
$409$	−2.58359	−0.127750	−0.0638752	+	0.997958i	$0.520346\pi$
$410$	−10.4721	−0.517182
$411$	2.94427	0.145230
$412$	4.00000	0.197066
$413$	−1.47214	−0.0724391
$414$	−13.7082	−0.673721
$415$	25.4164	1.24764
$416$	−21.0902	−1.03403
$417$	0.944272	0.0462412
$418$	0	0
$419$	24.5279	1.19826	0.599132	−	0.800650i	$-0.295512\pi$
$419$	24.5279	1.19826	0.599132	+	0.800650i	$0.295512\pi$
$420$	−2.61803	−0.127747
$421$	−16.4164	−0.800087	−0.400043	−	0.916496i	$-0.631005\pi$
$421$	−16.4164	−0.800087	−0.400043	+	0.916496i	$0.631005\pi$
$422$	−2.29180	−0.111563
$423$	−3.00000	−0.145865
$424$	20.0000	0.971286
$425$	57.8885	2.80801
$426$	−2.47214	−0.119775
$427$	−3.52786	−0.170725
$428$	−6.03444	−0.291686
$429$	0	0
$430$	−75.0132	−3.61746
$431$	18.5967	0.895774	0.447887	−	0.894090i	$-0.352177\pi$
$431$	18.5967	0.895774	0.447887	+	0.894090i	$0.352177\pi$
$432$	−4.85410	−0.233543
$433$	9.41641	0.452524	0.226262	−	0.974067i	$-0.427349\pi$
$433$	9.41641	0.452524	0.226262	+	0.974067i	$0.427349\pi$
$434$	0	0
$435$	−12.7082	−0.609312
$436$	0	0
$437$	−25.4164	−1.21583
$438$	19.7984	0.946003
$439$	9.36068	0.446761	0.223380	−	0.974731i	$-0.428291\pi$
$439$	9.36068	0.446761	0.223380	+	0.974731i	$0.428291\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	45.1246	2.14636
$443$	−7.88854	−0.374796	−0.187398	−	0.982284i	$-0.560005\pi$
$443$	−7.88854	−0.374796	−0.187398	+	0.982284i	$0.560005\pi$
$444$	2.14590	0.101840
$445$	18.9443	0.898045
$446$	−9.70820	−0.459697
$447$	−17.9443	−0.848735
$448$	4.23607	0.200135
$449$	28.4721	1.34368	0.671842	−	0.740695i	$-0.265504\pi$
$449$	28.4721	1.34368	0.671842	+	0.740695i	$0.265504\pi$
$450$	−20.9443	−0.987322
$451$	0	0
$452$	−4.00000	−0.188144
$453$	−17.4164	−0.818294
$454$	−25.1246	−1.17916
$455$	26.4164	1.23842
$456$	−6.70820	−0.314140
$457$	−26.0000	−1.21623	−0.608114	−	0.793849i	$-0.708074\pi$
$457$	−26.0000	−1.21623	−0.608114	+	0.793849i	$0.708074\pi$
$458$	39.5967	1.85023
$459$	4.47214	0.208741
$460$	−22.1803	−1.03416
$461$	−26.9443	−1.25492	−0.627460	−	0.778649i	$-0.715905\pi$
$461$	−26.9443	−1.25492	−0.627460	+	0.778649i	$0.715905\pi$
$462$	0	0
$463$	−32.1246	−1.49296	−0.746479	−	0.665409i	$-0.768257\pi$
$463$	−32.1246	−1.49296	−0.746479	+	0.665409i	$0.768257\pi$
$464$	−14.5623	−0.676038
$465$	0	0
$466$	32.1803	1.49073
$467$	15.4721	0.715965	0.357983	−	0.933728i	$-0.383465\pi$
$467$	15.4721	0.715965	0.357983	+	0.933728i	$0.383465\pi$
$468$	−3.85410	−0.178156
$469$	−8.70820	−0.402107
$470$	−20.5623	−0.948468
$471$	−13.4164	−0.618195
$472$	−3.29180	−0.151517
$473$	0	0
$474$	−21.7082	−0.997091
$475$	−38.8328	−1.78177
$476$	2.76393	0.126685
$477$	8.94427	0.409530
$478$	20.5623	0.940498
$479$	28.4721	1.30093	0.650463	−	0.759538i	$-0.274575\pi$
$479$	28.4721	1.30093	0.650463	+	0.759538i	$0.274575\pi$
$480$	−14.3262	−0.653900
$481$	−21.6525	−0.987268
$482$	20.5623	0.936587
$483$	8.47214	0.385496
$484$	0	0
$485$	−8.47214	−0.384700
$486$	−1.61803	−0.0733955
$487$	13.8885	0.629350	0.314675	−	0.949199i	$-0.398104\pi$
$487$	13.8885	0.629350	0.314675	+	0.949199i	$0.398104\pi$
$488$	−7.88854	−0.357098
$489$	7.29180	0.329746
$490$	6.85410	0.309637
$491$	−20.5967	−0.929518	−0.464759	−	0.885437i	$-0.653859\pi$
$491$	−20.5967	−0.929518	−0.464759	+	0.885437i	$0.653859\pi$
$492$	−0.944272	−0.0425711
$493$	13.4164	0.604245
$494$	−30.2705	−1.36193
$495$	0	0
$496$	0	0
$497$	1.52786	0.0685341
$498$	9.70820	0.435035
$499$	−23.2918	−1.04268	−0.521342	−	0.853348i	$-0.674568\pi$
$499$	−23.2918	−1.04268	−0.521342	+	0.853348i	$0.674568\pi$
$500$	−20.7984	−0.930132
$501$	−18.9443	−0.846368
$502$	26.5623	1.18553
$503$	19.4164	0.865735	0.432867	−	0.901458i	$-0.357502\pi$
$503$	19.4164	0.865735	0.432867	+	0.901458i	$0.357502\pi$
$504$	2.23607	0.0996024
$505$	−71.7771	−3.19404
$506$	0	0
$507$	25.8885	1.14975
$508$	−1.23607	−0.0548416
$509$	26.3607	1.16842	0.584208	−	0.811604i	$-0.301405\pi$
$509$	26.3607	1.16842	0.584208	+	0.811604i	$0.301405\pi$
$510$	30.6525	1.35731
$511$	−12.2361	−0.541292
$512$	5.29180	0.233867
$513$	−3.00000	−0.132453
$514$	−0.562306	−0.0248022
$515$	−27.4164	−1.20811
$516$	−6.76393	−0.297766
$517$	0	0
$518$	−5.61803	−0.246842
$519$	−7.52786	−0.330437
$520$	59.0689	2.59034
$521$	14.2361	0.623693	0.311847	−	0.950132i	$-0.399052\pi$
$521$	14.2361	0.623693	0.311847	+	0.950132i	$0.399052\pi$
$522$	−4.85410	−0.212458
$523$	3.00000	0.131181	0.0655904	−	0.997847i	$-0.479107\pi$
$523$	3.00000	0.131181	0.0655904	+	0.997847i	$0.479107\pi$
$524$	−1.52786	−0.0667451
$525$	12.9443	0.564934
$526$	0.381966	0.0166545
$527$	0	0
$528$	0	0
$529$	48.7771	2.12074
$530$	61.3050	2.66292
$531$	−1.47214	−0.0638853
$532$	−1.85410	−0.0803855
$533$	9.52786	0.412698
$534$	7.23607	0.313135
$535$	41.3607	1.78818
$536$	−19.4721	−0.841068
$537$	−16.4721	−0.710825
$538$	31.5967	1.36223
$539$	0	0
$540$	−2.61803	−0.112662
$541$	−15.4164	−0.662803	−0.331402	−	0.943490i	$-0.607521\pi$
$541$	−15.4164	−0.662803	−0.331402	+	0.943490i	$0.607521\pi$
$542$	−5.61803	−0.241315
$543$	−3.41641	−0.146612
$544$	15.1246	0.648462
$545$	0	0
$546$	10.0902	0.431819
$547$	−36.8328	−1.57486	−0.787429	−	0.616406i	$-0.788588\pi$
$547$	−36.8328	−1.57486	−0.787429	+	0.616406i	$0.788588\pi$
$548$	1.81966	0.0777320
$549$	−3.52786	−0.150566
$550$	0	0
$551$	−9.00000	−0.383413
$552$	18.9443	0.806322
$553$	13.4164	0.570524
$554$	−20.1803	−0.857380
$555$	−14.7082	−0.624328
$556$	0.583592	0.0247498
$557$	39.0000	1.65248	0.826242	−	0.563316i	$-0.190475\pi$
$557$	39.0000	1.65248	0.826242	+	0.563316i	$0.190475\pi$
$558$	0	0
$559$	68.2492	2.88663
$560$	20.5623	0.868916
$561$	0	0
$562$	26.5623	1.12046
$563$	2.47214	0.104188	0.0520941	−	0.998642i	$-0.483410\pi$
$563$	2.47214	0.104188	0.0520941	+	0.998642i	$0.483410\pi$
$564$	−1.85410	−0.0780718
$565$	27.4164	1.15342
$566$	−30.5623	−1.28463
$567$	1.00000	0.0419961
$568$	3.41641	0.143349
$569$	8.11146	0.340050	0.170025	−	0.985440i	$-0.445615\pi$
$569$	8.11146	0.340050	0.170025	+	0.985440i	$0.445615\pi$
$570$	−20.5623	−0.861260
$571$	−22.9443	−0.960188	−0.480094	−	0.877217i	$-0.659397\pi$
$571$	−22.9443	−0.960188	−0.480094	+	0.877217i	$0.659397\pi$
$572$	0	0
$573$	2.94427	0.122999
$574$	2.47214	0.103185
$575$	109.666	4.57337
$576$	4.23607	0.176503
$577$	−24.0000	−0.999133	−0.499567	−	0.866276i	$-0.666507\pi$
$577$	−24.0000	−0.999133	−0.499567	+	0.866276i	$0.666507\pi$
$578$	−4.85410	−0.201904
$579$	−12.0000	−0.498703
$580$	−7.85410	−0.326124
$581$	−6.00000	−0.248922
$582$	−3.23607	−0.134139
$583$	0	0
$584$	−27.3607	−1.13219
$585$	26.4164	1.09218
$586$	16.0000	0.660954
$587$	−0.639320	−0.0263876	−0.0131938	−	0.999913i	$-0.504200\pi$
$587$	−0.639320	−0.0263876	−0.0131938	+	0.999913i	$0.504200\pi$
$588$	0.618034	0.0254873
$589$	0	0
$590$	−10.0902	−0.415406
$591$	1.05573	0.0434269
$592$	−16.8541	−0.692699
$593$	29.7771	1.22280	0.611399	−	0.791322i	$-0.290607\pi$
$593$	29.7771	1.22280	0.611399	+	0.791322i	$0.290607\pi$
$594$	0	0
$595$	−18.9443	−0.776639
$596$	−11.0902	−0.454271
$597$	−12.4721	−0.510451
$598$	85.4853	3.49575
$599$	1.41641	0.0578729	0.0289364	−	0.999581i	$-0.490788\pi$
$599$	1.41641	0.0578729	0.0289364	+	0.999581i	$0.490788\pi$
$600$	28.9443	1.18164
$601$	−9.18034	−0.374474	−0.187237	−	0.982315i	$-0.559953\pi$
$601$	−9.18034	−0.374474	−0.187237	+	0.982315i	$0.559953\pi$
$602$	17.7082	0.721733
$603$	−8.70820	−0.354625
$604$	−10.7639	−0.437978
$605$	0	0
$606$	−27.4164	−1.11372
$607$	43.2492	1.75543	0.877716	−	0.479181i	$-0.159066\pi$
$607$	43.2492	1.75543	0.877716	+	0.479181i	$0.159066\pi$
$608$	−10.1459	−0.411470
$609$	3.00000	0.121566
$610$	−24.1803	−0.979033
$611$	18.7082	0.756853
$612$	2.76393	0.111725
$613$	17.5279	0.707944	0.353972	−	0.935256i	$-0.384831\pi$
$613$	17.5279	0.707944	0.353972	+	0.935256i	$0.384831\pi$
$614$	27.4164	1.10644
$615$	6.47214	0.260982
$616$	0	0
$617$	−29.8885	−1.20327	−0.601634	−	0.798772i	$-0.705483\pi$
$617$	−29.8885	−1.20327	−0.601634	+	0.798772i	$0.705483\pi$
$618$	−10.4721	−0.421251
$619$	46.2492	1.85891	0.929457	−	0.368931i	$-0.120276\pi$
$619$	46.2492	1.85891	0.929457	+	0.368931i	$0.120276\pi$
$620$	0	0
$621$	8.47214	0.339975
$622$	28.9443	1.16056
$623$	−4.47214	−0.179172
$624$	30.2705	1.21179
$625$	77.8328	3.11331
$626$	33.1246	1.32393
$627$	0	0
$628$	−8.29180	−0.330879
$629$	15.5279	0.619136
$630$	6.85410	0.273074
$631$	−12.0000	−0.477712	−0.238856	−	0.971055i	$-0.576772\pi$
$631$	−12.0000	−0.477712	−0.238856	+	0.971055i	$0.576772\pi$
$632$	30.0000	1.19334
$633$	1.41641	0.0562972
$634$	−49.3050	−1.95815
$635$	8.47214	0.336206
$636$	5.52786	0.219194
$637$	−6.23607	−0.247082
$638$	0	0
$639$	1.52786	0.0604414
$640$	57.6869	2.28028
$641$	−38.8328	−1.53380	−0.766902	−	0.641764i	$-0.778203\pi$
$641$	−38.8328	−1.53380	−0.766902	+	0.641764i	$0.778203\pi$
$642$	15.7984	0.623512
$643$	−1.41641	−0.0558577	−0.0279288	−	0.999610i	$-0.508891\pi$
$643$	−1.41641	−0.0558577	−0.0279288	+	0.999610i	$0.508891\pi$
$644$	5.23607	0.206330
$645$	46.3607	1.82545
$646$	21.7082	0.854098
$647$	4.88854	0.192188	0.0960942	−	0.995372i	$-0.469365\pi$
$647$	4.88854	0.192188	0.0960942	+	0.995372i	$0.469365\pi$
$648$	2.23607	0.0878410
$649$	0	0
$650$	130.610	5.12294
$651$	0	0
$652$	4.50658	0.176491
$653$	−44.9443	−1.75881	−0.879403	−	0.476079i	$-0.842058\pi$
$653$	−44.9443	−1.75881	−0.879403	+	0.476079i	$0.842058\pi$
$654$	0	0
$655$	10.4721	0.409180
$656$	7.41641	0.289562
$657$	−12.2361	−0.477374
$658$	4.85410	0.189233
$659$	−25.7639	−1.00362	−0.501810	−	0.864978i	$-0.667332\pi$
$659$	−25.7639	−1.00362	−0.501810	+	0.864978i	$0.667332\pi$
$660$	0	0
$661$	30.8328	1.19926	0.599629	−	0.800278i	$-0.295315\pi$
$661$	30.8328	1.19926	0.599629	+	0.800278i	$0.295315\pi$
$662$	−38.8328	−1.50928
$663$	−27.8885	−1.08310
$664$	−13.4164	−0.520658
$665$	12.7082	0.492803
$666$	−5.61803	−0.217694
$667$	25.4164	0.984127
$668$	−11.7082	−0.453004
$669$	6.00000	0.231973
$670$	−59.6869	−2.30591
$671$	0	0
$672$	3.38197	0.130462
$673$	−33.3050	−1.28381	−0.641906	−	0.766784i	$-0.721856\pi$
$673$	−33.3050	−1.28381	−0.641906	+	0.766784i	$0.721856\pi$
$674$	40.1803	1.54769
$675$	12.9443	0.498225
$676$	16.0000	0.615385
$677$	−28.3607	−1.08999	−0.544995	−	0.838439i	$-0.683468\pi$
$677$	−28.3607	−1.08999	−0.544995	+	0.838439i	$0.683468\pi$
$678$	10.4721	0.402180
$679$	2.00000	0.0767530
$680$	−42.3607	−1.62446
$681$	15.5279	0.595029
$682$	0	0
$683$	−9.52786	−0.364574	−0.182287	−	0.983245i	$-0.558350\pi$
$683$	−9.52786	−0.364574	−0.182287	+	0.983245i	$0.558350\pi$
$684$	−1.85410	−0.0708934
$685$	−12.4721	−0.476536
$686$	−1.61803	−0.0617768
$687$	−24.4721	−0.933670
$688$	53.1246	2.02536
$689$	−55.7771	−2.12494
$690$	58.0689	2.21064
$691$	−32.0000	−1.21734	−0.608669	−	0.793424i	$-0.708296\pi$
$691$	−32.0000	−1.21734	−0.608669	+	0.793424i	$0.708296\pi$
$692$	−4.65248	−0.176861
$693$	0	0
$694$	−4.94427	−0.187682
$695$	−4.00000	−0.151729
$696$	6.70820	0.254274
$697$	−6.83282	−0.258811
$698$	−36.7426	−1.39073
$699$	−19.8885	−0.752254
$700$	8.00000	0.302372
$701$	−6.94427	−0.262282	−0.131141	−	0.991364i	$-0.541864\pi$
$701$	−6.94427	−0.262282	−0.131141	+	0.991364i	$0.541864\pi$
$702$	10.0902	0.380829
$703$	−10.4164	−0.392862
$704$	0	0
$705$	12.7082	0.478619
$706$	−52.7426	−1.98500
$707$	16.9443	0.637255
$708$	−0.909830	−0.0341935
$709$	11.5836	0.435031	0.217515	−	0.976057i	$-0.430205\pi$
$709$	11.5836	0.435031	0.217515	+	0.976057i	$0.430205\pi$
$710$	10.4721	0.393012
$711$	13.4164	0.503155
$712$	−10.0000	−0.374766
$713$	0	0
$714$	−7.23607	−0.270803
$715$	0	0
$716$	−10.1803	−0.380457
$717$	−12.7082	−0.474597
$718$	−30.8328	−1.15067
$719$	−24.7771	−0.924029	−0.462015	−	0.886872i	$-0.652873\pi$
$719$	−24.7771	−0.924029	−0.462015	+	0.886872i	$0.652873\pi$
$720$	20.5623	0.766312
$721$	6.47214	0.241035
$722$	16.1803	0.602170
$723$	−12.7082	−0.472623
$724$	−2.11146	−0.0784717
$725$	38.8328	1.44221
$726$	0	0
$727$	44.8328	1.66276	0.831379	−	0.555706i	$-0.187552\pi$
$727$	44.8328	1.66276	0.831379	+	0.555706i	$0.187552\pi$
$728$	−13.9443	−0.516809
$729$	1.00000	0.0370370
$730$	−83.8673	−3.10407
$731$	−48.9443	−1.81027
$732$	−2.18034	−0.0805877
$733$	−24.4721	−0.903899	−0.451949	−	0.892044i	$-0.649271\pi$
$733$	−24.4721	−0.903899	−0.451949	+	0.892044i	$0.649271\pi$
$734$	36.9443	1.36364
$735$	−4.23607	−0.156250
$736$	28.6525	1.05614
$737$	0	0
$738$	2.47214	0.0910006
$739$	−51.3050	−1.88728	−0.943642	−	0.330969i	$-0.892624\pi$
$739$	−51.3050	−1.88728	−0.943642	+	0.330969i	$0.892624\pi$
$740$	−9.09017	−0.334161
$741$	18.7082	0.687263
$742$	−14.4721	−0.531289
$743$	15.7639	0.578323	0.289161	−	0.957280i	$-0.406624\pi$
$743$	15.7639	0.578323	0.289161	+	0.957280i	$0.406624\pi$
$744$	0	0
$745$	76.0132	2.78491
$746$	4.18034	0.153053
$747$	−6.00000	−0.219529
$748$	0	0
$749$	−9.76393	−0.356766
$750$	54.4508	1.98826
$751$	−18.2361	−0.665444	−0.332722	−	0.943025i	$-0.607967\pi$
$751$	−18.2361	−0.665444	−0.332722	+	0.943025i	$0.607967\pi$
$752$	14.5623	0.531033
$753$	−16.4164	−0.598247
$754$	30.2705	1.10239
$755$	73.7771	2.68502
$756$	0.618034	0.0224777
$757$	24.4164	0.887429	0.443715	−	0.896168i	$-0.353660\pi$
$757$	24.4164	0.887429	0.443715	+	0.896168i	$0.353660\pi$
$758$	6.85410	0.248952
$759$	0	0
$760$	28.4164	1.03077
$761$	−6.36068	−0.230574	−0.115287	−	0.993332i	$-0.536779\pi$
$761$	−6.36068	−0.230574	−0.115287	+	0.993332i	$0.536779\pi$
$762$	3.23607	0.117230
$763$	0	0
$764$	1.81966	0.0658330
$765$	−18.9443	−0.684932
$766$	−22.4721	−0.811951
$767$	9.18034	0.331483
$768$	13.5623	0.489388
$769$	14.1246	0.509347	0.254673	−	0.967027i	$-0.418032\pi$
$769$	14.1246	0.509347	0.254673	+	0.967027i	$0.418032\pi$
$770$	0	0
$771$	0.347524	0.0125158
$772$	−7.41641	−0.266922
$773$	−11.2918	−0.406138	−0.203069	−	0.979164i	$-0.565092\pi$
$773$	−11.2918	−0.406138	−0.203069	+	0.979164i	$0.565092\pi$
$774$	17.7082	0.636508
$775$	0	0
$776$	4.47214	0.160540
$777$	3.47214	0.124562
$778$	−45.8885	−1.64518
$779$	4.58359	0.164224
$780$	16.3262	0.584573
$781$	0	0
$782$	−61.3050	−2.19226
$783$	3.00000	0.107211
$784$	−4.85410	−0.173361
$785$	56.8328	2.02845
$786$	4.00000	0.142675
$787$	27.0000	0.962446	0.481223	−	0.876598i	$-0.340193\pi$
$787$	27.0000	0.962446	0.481223	+	0.876598i	$0.340193\pi$
$788$	0.652476	0.0232435
$789$	−0.236068	−0.00840424
$790$	91.9574	3.27170
$791$	−6.47214	−0.230123
$792$	0	0
$793$	22.0000	0.781243
$794$	−20.1803	−0.716173
$795$	−37.8885	−1.34377
$796$	−7.70820	−0.273210
$797$	−14.8197	−0.524939	−0.262470	−	0.964940i	$-0.584537\pi$
$797$	−14.8197	−0.524939	−0.262470	+	0.964940i	$0.584537\pi$
$798$	4.85410	0.171833
$799$	−13.4164	−0.474638
$800$	43.7771	1.54775
$801$	−4.47214	−0.158015
$802$	16.7639	0.591955
$803$	0	0
$804$	−5.38197	−0.189807
$805$	−35.8885	−1.26490
$806$	0	0
$807$	−19.5279	−0.687413
$808$	37.8885	1.33291
$809$	31.3607	1.10258	0.551291	−	0.834313i	$-0.314135\pi$
$809$	31.3607	1.10258	0.551291	+	0.834313i	$0.314135\pi$
$810$	6.85410	0.240829
$811$	−55.8328	−1.96056	−0.980278	−	0.197625i	$-0.936677\pi$
$811$	−55.8328	−1.96056	−0.980278	+	0.197625i	$0.936677\pi$
$812$	1.85410	0.0650662
$813$	3.47214	0.121773
$814$	0	0
$815$	−30.8885	−1.08198
$816$	−21.7082	−0.759939
$817$	32.8328	1.14867
$818$	4.18034	0.146162
$819$	−6.23607	−0.217906
$820$	4.00000	0.139686
$821$	17.9443	0.626259	0.313130	−	0.949710i	$-0.398623\pi$
$821$	17.9443	0.626259	0.313130	+	0.949710i	$0.398623\pi$
$822$	−4.76393	−0.166161
$823$	−15.1803	−0.529153	−0.264577	−	0.964365i	$-0.585232\pi$
$823$	−15.1803	−0.529153	−0.264577	+	0.964365i	$0.585232\pi$
$824$	14.4721	0.504161
$825$	0	0
$826$	2.38197	0.0828792
$827$	20.1246	0.699801	0.349901	−	0.936787i	$-0.386215\pi$
$827$	20.1246	0.699801	0.349901	+	0.936787i	$0.386215\pi$
$828$	5.23607	0.181966
$829$	−38.8328	−1.34872	−0.674360	−	0.738403i	$-0.735580\pi$
$829$	−38.8328	−1.34872	−0.674360	+	0.738403i	$0.735580\pi$
$830$	−41.1246	−1.42746
$831$	12.4721	0.432654
$832$	−26.4164	−0.915824
$833$	4.47214	0.154950
$834$	−1.52786	−0.0529056
$835$	80.2492	2.77714
$836$	0	0
$837$	0	0
$838$	−39.6869	−1.37096
$839$	−6.05573	−0.209067	−0.104533	−	0.994521i	$-0.533335\pi$
$839$	−6.05573	−0.209067	−0.104533	+	0.994521i	$0.533335\pi$
$840$	−9.47214	−0.326820
$841$	−20.0000	−0.689655
$842$	26.5623	0.915398
$843$	−16.4164	−0.565411
$844$	0.875388	0.0301321
$845$	−109.666	−3.77261
$846$	4.85410	0.166887
$847$	0	0
$848$	−43.4164	−1.49093
$849$	18.8885	0.648253
$850$	−93.6656	−3.21270
$851$	29.4164	1.00838
$852$	0.944272	0.0323502
$853$	−22.5836	−0.773247	−0.386624	−	0.922238i	$-0.626359\pi$
$853$	−22.5836	−0.773247	−0.386624	+	0.922238i	$0.626359\pi$
$854$	5.70820	0.195331
$855$	12.7082	0.434611
$856$	−21.8328	−0.746230
$857$	28.4721	0.972590	0.486295	−	0.873795i	$-0.338348\pi$
$857$	28.4721	0.972590	0.486295	+	0.873795i	$0.338348\pi$
$858$	0	0
$859$	37.7771	1.28894	0.644469	−	0.764631i	$-0.277079\pi$
$859$	37.7771	1.28894	0.644469	+	0.764631i	$0.277079\pi$
$860$	28.6525	0.977041
$861$	−1.52786	−0.0520695
$862$	−30.0902	−1.02488
$863$	7.63932	0.260045	0.130023	−	0.991511i	$-0.458495\pi$
$863$	7.63932	0.260045	0.130023	+	0.991511i	$0.458495\pi$
$864$	3.38197	0.115057
$865$	31.8885	1.08424
$866$	−15.2361	−0.517743
$867$	3.00000	0.101885
$868$	0	0
$869$	0	0
$870$	20.5623	0.697127
$871$	54.3050	1.84005
$872$	0	0
$873$	2.00000	0.0676897
$874$	41.1246	1.39106
$875$	−33.6525	−1.13766
$876$	−7.56231	−0.255507
$877$	2.83282	0.0956574	0.0478287	−	0.998856i	$-0.484770\pi$
$877$	2.83282	0.0956574	0.0478287	+	0.998856i	$0.484770\pi$
$878$	−15.1459	−0.511149
$879$	−9.88854	−0.333532
$880$	0	0
$881$	−26.4853	−0.892312	−0.446156	−	0.894955i	$-0.647207\pi$
$881$	−26.4853	−0.892312	−0.446156	+	0.894955i	$0.647207\pi$
$882$	−1.61803	−0.0544820
$883$	40.7082	1.36994	0.684970	−	0.728571i	$-0.259815\pi$
$883$	40.7082	1.36994	0.684970	+	0.728571i	$0.259815\pi$
$884$	−17.2361	−0.579712
$885$	6.23607	0.209623
$886$	12.7639	0.428813
$887$	−7.41641	−0.249019	−0.124509	−	0.992218i	$-0.539736\pi$
$887$	−7.41641	−0.249019	−0.124509	+	0.992218i	$0.539736\pi$
$888$	7.76393	0.260540
$889$	−2.00000	−0.0670778
$890$	−30.6525	−1.02747
$891$	0	0
$892$	3.70820	0.124160
$893$	9.00000	0.301174
$894$	29.0344	0.971057
$895$	69.7771	2.33239
$896$	−13.6180	−0.454947
$897$	−52.8328	−1.76404
$898$	−46.0689	−1.53734
$899$	0	0
$900$	8.00000	0.266667
$901$	40.0000	1.33259
$902$	0	0
$903$	−10.9443	−0.364203
$904$	−14.4721	−0.481336
$905$	14.4721	0.481070
$906$	28.1803	0.936229
$907$	−12.0000	−0.398453	−0.199227	−	0.979953i	$-0.563843\pi$
$907$	−12.0000	−0.398453	−0.199227	+	0.979953i	$0.563843\pi$
$908$	9.59675	0.318479
$909$	16.9443	0.562006
$910$	−42.7426	−1.41690
$911$	−21.3050	−0.705865	−0.352932	−	0.935649i	$-0.614815\pi$
$911$	−21.3050	−0.705865	−0.352932	+	0.935649i	$0.614815\pi$
$912$	14.5623	0.482206
$913$	0	0
$914$	42.0689	1.39151
$915$	14.9443	0.494042
$916$	−15.1246	−0.499731
$917$	−2.47214	−0.0816371
$918$	−7.23607	−0.238826
$919$	23.0557	0.760538	0.380269	−	0.924876i	$-0.375831\pi$
$919$	23.0557	0.760538	0.380269	+	0.924876i	$0.375831\pi$
$920$	−80.2492	−2.64574
$921$	−16.9443	−0.558333
$922$	43.5967	1.43578
$923$	−9.52786	−0.313613
$924$	0	0
$925$	44.9443	1.47776
$926$	51.9787	1.70813
$927$	6.47214	0.212573
$928$	10.1459	0.333055
$929$	−29.0689	−0.953719	−0.476860	−	0.878979i	$-0.658225\pi$
$929$	−29.0689	−0.953719	−0.476860	+	0.878979i	$0.658225\pi$
$930$	0	0
$931$	−3.00000	−0.0983210
$932$	−12.2918	−0.402631
$933$	−17.8885	−0.585645
$934$	−25.0344	−0.819152
$935$	0	0
$936$	−13.9443	−0.455783
$937$	29.4164	0.960992	0.480496	−	0.876997i	$-0.340457\pi$
$937$	29.4164	0.960992	0.480496	+	0.876997i	$0.340457\pi$
$938$	14.0902	0.460060
$939$	−20.4721	−0.668083
$940$	7.85410	0.256173
$941$	22.3607	0.728937	0.364469	−	0.931216i	$-0.381251\pi$
$941$	22.3607	0.728937	0.364469	+	0.931216i	$0.381251\pi$
$942$	21.7082	0.707292
$943$	−12.9443	−0.421523
$944$	7.14590	0.232579
$945$	−4.23607	−0.137799
$946$	0	0
$947$	−36.0000	−1.16984	−0.584921	−	0.811090i	$-0.698875\pi$
$947$	−36.0000	−1.16984	−0.584921	+	0.811090i	$0.698875\pi$
$948$	8.29180	0.269305
$949$	76.3050	2.47696
$950$	62.8328	2.03857
$951$	30.4721	0.988127
$952$	10.0000	0.324102
$953$	11.3607	0.368009	0.184004	−	0.982925i	$-0.441094\pi$
$953$	11.3607	0.368009	0.184004	+	0.982925i	$0.441094\pi$
$954$	−14.4721	−0.468553
$955$	−12.4721	−0.403589
$956$	−7.85410	−0.254020
$957$	0	0
$958$	−46.0689	−1.48842
$959$	2.94427	0.0950755
$960$	−17.9443	−0.579149
$961$	−31.0000	−1.00000
$962$	35.0344	1.12956
$963$	−9.76393	−0.314638
$964$	−7.85410	−0.252964
$965$	50.8328	1.63637
$966$	−13.7082	−0.441054
$967$	29.5279	0.949552	0.474776	−	0.880107i	$-0.342529\pi$
$967$	29.5279	0.949552	0.474776	+	0.880107i	$0.342529\pi$
$968$	0	0
$969$	−13.4164	−0.430997
$970$	13.7082	0.440144
$971$	−23.4721	−0.753257	−0.376628	−	0.926364i	$-0.622917\pi$
$971$	−23.4721	−0.753257	−0.376628	+	0.926364i	$0.622917\pi$
$972$	0.618034	0.0198234
$973$	0.944272	0.0302720
$974$	−22.4721	−0.720054
$975$	−80.7214	−2.58515
$976$	17.1246	0.548145
$977$	57.7771	1.84845	0.924226	−	0.381845i	$-0.124711\pi$
$977$	57.7771	1.84845	0.924226	+	0.381845i	$0.124711\pi$
$978$	−11.7984	−0.377270
$979$	0	0
$980$	−2.61803	−0.0836300
$981$	0	0
$982$	33.3262	1.06348
$983$	41.8885	1.33604	0.668019	−	0.744145i	$-0.267143\pi$
$983$	41.8885	1.33604	0.668019	+	0.744145i	$0.267143\pi$
$984$	−3.41641	−0.108911
$985$	−4.47214	−0.142494
$986$	−21.7082	−0.691330
$987$	−3.00000	−0.0954911
$988$	11.5623	0.367846
$989$	−92.7214	−2.94837
$990$	0	0
$991$	−54.2361	−1.72287	−0.861433	−	0.507872i	$-0.830432\pi$
$991$	−54.2361	−1.72287	−0.861433	+	0.507872i	$0.830432\pi$
$992$	0	0
$993$	24.0000	0.761617
$994$	−2.47214	−0.0784114
$995$	52.8328	1.67491
$996$	−3.70820	−0.117499
$997$	10.5836	0.335186	0.167593	−	0.985856i	$-0.446401\pi$
$997$	10.5836	0.335186	0.167593	+	0.985856i	$0.446401\pi$
$998$	37.6869	1.19296
$999$	3.47214	0.109854

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.r.1.1	✓	2
3.2	odd	2		7623.2.a.bq.1.2		2
11.10	odd	2		2541.2.a.ba.1.2	yes	2
33.32	even	2		7623.2.a.bb.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2541.2.a.r.1.1	✓	2	1.1	even	1	trivial
2541.2.a.ba.1.2	yes	2	11.10	odd	2
7623.2.a.bb.1.1		2	33.32	even	2
7623.2.a.bq.1.2		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2541.a (trivial)

\(f(q)\)	\(=\)	\(q-1.61803 q^{2} +1.00000 q^{3} +0.618034 q^{4} -4.23607 q^{5} -1.61803 q^{6} +1.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.61803 q^{2} +1.00000 q^{3} +0.618034 q^{4} -4.23607 q^{5} -1.61803 q^{6} +1.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} +6.85410 q^{10} +0.618034 q^{12} -6.23607 q^{13} -1.61803 q^{14} -4.23607 q^{15} -4.85410 q^{16} +4.47214 q^{17} -1.61803 q^{18} -3.00000 q^{19} -2.61803 q^{20} +1.00000 q^{21} +8.47214 q^{23} +2.23607 q^{24} +12.9443 q^{25} +10.0902 q^{26} +1.00000 q^{27} +0.618034 q^{28} +3.00000 q^{29} +6.85410 q^{30} +3.38197 q^{32} -7.23607 q^{34} -4.23607 q^{35} +0.618034 q^{36} +3.47214 q^{37} +4.85410 q^{38} -6.23607 q^{39} -9.47214 q^{40} -1.52786 q^{41} -1.61803 q^{42} -10.9443 q^{43} -4.23607 q^{45} -13.7082 q^{46} -3.00000 q^{47} -4.85410 q^{48} +1.00000 q^{49} -20.9443 q^{50} +4.47214 q^{51} -3.85410 q^{52} +8.94427 q^{53} -1.61803 q^{54} +2.23607 q^{56} -3.00000 q^{57} -4.85410 q^{58} -1.47214 q^{59} -2.61803 q^{60} -3.52786 q^{61} +1.00000 q^{63} +4.23607 q^{64} +26.4164 q^{65} -8.70820 q^{67} +2.76393 q^{68} +8.47214 q^{69} +6.85410 q^{70} +1.52786 q^{71} +2.23607 q^{72} -12.2361 q^{73} -5.61803 q^{74} +12.9443 q^{75} -1.85410 q^{76} +10.0902 q^{78} +13.4164 q^{79} +20.5623 q^{80} +1.00000 q^{81} +2.47214 q^{82} -6.00000 q^{83} +0.618034 q^{84} -18.9443 q^{85} +17.7082 q^{86} +3.00000 q^{87} -4.47214 q^{89} +6.85410 q^{90} -6.23607 q^{91} +5.23607 q^{92} +4.85410 q^{94} +12.7082 q^{95} +3.38197 q^{96} +2.00000 q^{97} -1.61803 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 2 q^{3} - q^{4} - 4 q^{5} - q^{6} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 + 2 * q^3 - q^4 - 4 * q^5 - q^6 + 2 * q^7 + 2 * q^9	\( 2 q - q^{2} + 2 q^{3} - q^{4} - 4 q^{5} - q^{6} + 2 q^{7} + 2 q^{9} + 7 q^{10} - q^{12} - 8 q^{13} - q^{14} - 4 q^{15} - 3 q^{16} - q^{18} - 6 q^{19} - 3 q^{20} + 2 q^{21} + 8 q^{23} + 8 q^{25} + 9 q^{26} + 2 q^{27} - q^{28} + 6 q^{29} + 7 q^{30} + 9 q^{32} - 10 q^{34} - 4 q^{35} - q^{36} - 2 q^{37} + 3 q^{38} - 8 q^{39} - 10 q^{40} - 12 q^{41} - q^{42} - 4 q^{43} - 4 q^{45} - 14 q^{46} - 6 q^{47} - 3 q^{48} + 2 q^{49} - 24 q^{50} - q^{52} - q^{54} - 6 q^{57} - 3 q^{58} + 6 q^{59} - 3 q^{60} - 16 q^{61} + 2 q^{63} + 4 q^{64} + 26 q^{65} - 4 q^{67} + 10 q^{68} + 8 q^{69} + 7 q^{70} + 12 q^{71} - 20 q^{73} - 9 q^{74} + 8 q^{75} + 3 q^{76} + 9 q^{78} + 21 q^{80} + 2 q^{81} - 4 q^{82} - 12 q^{83} - q^{84} - 20 q^{85} + 22 q^{86} + 6 q^{87} + 7 q^{90} - 8 q^{91} + 6 q^{92} + 3 q^{94} + 12 q^{95} + 9 q^{96} + 4 q^{97} - q^{98}+O(q^{100}) \) 2 * q - q^2 + 2 * q^3 - q^4 - 4 * q^5 - q^6 + 2 * q^7 + 2 * q^9 + 7 * q^10 - q^12 - 8 * q^13 - q^14 - 4 * q^15 - 3 * q^16 - q^18 - 6 * q^19 - 3 * q^20 + 2 * q^21 + 8 * q^23 + 8 * q^25 + 9 * q^26 + 2 * q^27 - q^28 + 6 * q^29 + 7 * q^30 + 9 * q^32 - 10 * q^34 - 4 * q^35 - q^36 - 2 * q^37 + 3 * q^38 - 8 * q^39 - 10 * q^40 - 12 * q^41 - q^42 - 4 * q^43 - 4 * q^45 - 14 * q^46 - 6 * q^47 - 3 * q^48 + 2 * q^49 - 24 * q^50 - q^52 - q^54 - 6 * q^57 - 3 * q^58 + 6 * q^59 - 3 * q^60 - 16 * q^61 + 2 * q^63 + 4 * q^64 + 26 * q^65 - 4 * q^67 + 10 * q^68 + 8 * q^69 + 7 * q^70 + 12 * q^71 - 20 * q^73 - 9 * q^74 + 8 * q^75 + 3 * q^76 + 9 * q^78 + 21 * q^80 + 2 * q^81 - 4 * q^82 - 12 * q^83 - q^84 - 20 * q^85 + 22 * q^86 + 6 * q^87 + 7 * q^90 - 8 * q^91 + 6 * q^92 + 3 * q^94 + 12 * q^95 + 9 * q^96 + 4 * q^97 - q^98

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