LMFDB - Embedded newform 5390.2.a.bz.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5390,2,Mod(1,5390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5390, 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("5390.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5390 = 2 \cdot 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5390.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:	$43.0393666895$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.892.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 8x + 10 $ x^3 - x^2 - 8*x + 10
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 770)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.59774$ of defining polynomial
Character	$\chi$	$=$	5390.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.34596 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.34596 q^{6} -1.00000 q^{8} +8.19547 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.34596 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.34596 q^{6} -1.00000 q^{8} +8.19547 q^{9} -1.00000 q^{10} +1.00000 q^{11} -3.34596 q^{12} -6.69193 q^{13} -3.34596 q^{15} +1.00000 q^{16} +7.19547 q^{17} -8.19547 q^{18} +1.84951 q^{19} +1.00000 q^{20} -1.00000 q^{22} +1.84951 q^{23} +3.34596 q^{24} +1.00000 q^{25} +6.69193 q^{26} -17.3839 q^{27} +6.84242 q^{29} +3.34596 q^{30} -6.00000 q^{31} -1.00000 q^{32} -3.34596 q^{33} -7.19547 q^{34} +8.19547 q^{36} -6.54143 q^{37} -1.84951 q^{38} +22.3909 q^{39} -1.00000 q^{40} +9.34596 q^{41} +0.503544 q^{43} +1.00000 q^{44} +8.19547 q^{45} -1.84951 q^{46} +1.49646 q^{47} -3.34596 q^{48} -1.00000 q^{50} -24.0758 q^{51} -6.69193 q^{52} +6.84242 q^{53} +17.3839 q^{54} +1.00000 q^{55} -6.18838 q^{57} -6.84242 q^{58} +7.88740 q^{59} -3.34596 q^{60} -4.50354 q^{61} +6.00000 q^{62} +1.00000 q^{64} -6.69193 q^{65} +3.34596 q^{66} +8.00000 q^{67} +7.19547 q^{68} -6.18838 q^{69} +0.300986 q^{71} -8.19547 q^{72} +10.1884 q^{73} +6.54143 q^{74} -3.34596 q^{75} +1.84951 q^{76} -22.3909 q^{78} -12.2404 q^{79} +1.00000 q^{80} +33.5793 q^{81} -9.34596 q^{82} +1.30807 q^{83} +7.19547 q^{85} -0.503544 q^{86} -22.8945 q^{87} -1.00000 q^{88} +8.69193 q^{89} -8.19547 q^{90} +1.84951 q^{92} +20.0758 q^{93} -1.49646 q^{94} +1.84951 q^{95} +3.34596 q^{96} -3.84951 q^{97} +8.19547 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{4} + 3 q^{5} - 3 q^{8} + 11 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^4 + 3 * q^5 - 3 * q^8 + 11 * q^9	$ 3 q - 3 q^{2} + 3 q^{4} + 3 q^{5} - 3 q^{8} + 11 q^{9} - 3 q^{10} + 3 q^{11} + 3 q^{16} + 8 q^{17} - 11 q^{18} + 2 q^{19} + 3 q^{20} - 3 q^{22} + 2 q^{23} + 3 q^{25} - 12 q^{27} + 4 q^{29} - 18 q^{31} - 3 q^{32} - 8 q^{34} + 11 q^{36} + 4 q^{37} - 2 q^{38} + 40 q^{39} - 3 q^{40} + 18 q^{41} + 8 q^{43} + 3 q^{44} + 11 q^{45} - 2 q^{46} - 2 q^{47} - 3 q^{50} - 12 q^{51} + 4 q^{53} + 12 q^{54} + 3 q^{55} + 8 q^{57} - 4 q^{58} - 10 q^{59} - 20 q^{61} + 18 q^{62} + 3 q^{64} + 24 q^{67} + 8 q^{68} + 8 q^{69} + 8 q^{71} - 11 q^{72} + 4 q^{73} - 4 q^{74} + 2 q^{76} - 40 q^{78} - 6 q^{79} + 3 q^{80} + 47 q^{81} - 18 q^{82} + 24 q^{83} + 8 q^{85} - 8 q^{86} - 48 q^{87} - 3 q^{88} + 6 q^{89} - 11 q^{90} + 2 q^{92} + 2 q^{94} + 2 q^{95} - 8 q^{97} + 11 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^4 + 3 * q^5 - 3 * q^8 + 11 * q^9 - 3 * q^10 + 3 * q^11 + 3 * q^16 + 8 * q^17 - 11 * q^18 + 2 * q^19 + 3 * q^20 - 3 * q^22 + 2 * q^23 + 3 * q^25 - 12 * q^27 + 4 * q^29 - 18 * q^31 - 3 * q^32 - 8 * q^34 + 11 * q^36 + 4 * q^37 - 2 * q^38 + 40 * q^39 - 3 * q^40 + 18 * q^41 + 8 * q^43 + 3 * q^44 + 11 * q^45 - 2 * q^46 - 2 * q^47 - 3 * q^50 - 12 * q^51 + 4 * q^53 + 12 * q^54 + 3 * q^55 + 8 * q^57 - 4 * q^58 - 10 * q^59 - 20 * q^61 + 18 * q^62 + 3 * q^64 + 24 * q^67 + 8 * q^68 + 8 * q^69 + 8 * q^71 - 11 * q^72 + 4 * q^73 - 4 * q^74 + 2 * q^76 - 40 * q^78 - 6 * q^79 + 3 * q^80 + 47 * q^81 - 18 * q^82 + 24 * q^83 + 8 * q^85 - 8 * q^86 - 48 * q^87 - 3 * q^88 + 6 * q^89 - 11 * q^90 + 2 * q^92 + 2 * q^94 + 2 * q^95 - 8 * q^97 + 11 * 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
$3$	−3.34596	−1.93179	−0.965896	−	0.258929i	$-0.916630\pi$
$3$	−3.34596	−1.93179	−0.965896	+	0.258929i	$0.916630\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	3.34596	1.36598
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	8.19547	2.73182
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.34596	−0.965896
$13$	−6.69193	−1.85601	−0.928003	−	0.372572i	$-0.878476\pi$
$13$	−6.69193	−1.85601	−0.928003	+	0.372572i	$0.878476\pi$
$14$	0	0
$15$	−3.34596	−0.863924
$16$	1.00000	0.250000
$17$	7.19547	1.74516	0.872579	−	0.488473i	$-0.162446\pi$
$17$	7.19547	1.74516	0.872579	+	0.488473i	$0.162446\pi$
$18$	−8.19547	−1.93169
$19$	1.84951	0.424306	0.212153	−	0.977236i	$-0.431952\pi$
$19$	1.84951	0.424306	0.212153	+	0.977236i	$0.431952\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	−1.00000	−0.213201
$23$	1.84951	0.385649	0.192824	−	0.981233i	$-0.438235\pi$
$23$	1.84951	0.385649	0.192824	+	0.981233i	$0.438235\pi$
$24$	3.34596	0.682992
$25$	1.00000	0.200000
$26$	6.69193	1.31239
$27$	−17.3839	−3.34552
$28$	0	0
$29$	6.84242	1.27061	0.635303	−	0.772263i	$-0.280875\pi$
$29$	6.84242	1.27061	0.635303	+	0.772263i	$0.280875\pi$
$30$	3.34596	0.610887
$31$	−6.00000	−1.07763	−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000	−1.07763	−0.538816	+	0.842424i	$0.681128\pi$
$32$	−1.00000	−0.176777
$33$	−3.34596	−0.582457
$34$	−7.19547	−1.23401
$35$	0	0
$36$	8.19547	1.36591
$37$	−6.54143	−1.07541	−0.537703	−	0.843135i	$-0.680708\pi$
$37$	−6.54143	−1.07541	−0.537703	+	0.843135i	$0.680708\pi$
$38$	−1.84951	−0.300030
$39$	22.3909	3.58542
$40$	−1.00000	−0.158114
$41$	9.34596	1.45959	0.729797	−	0.683664i	$-0.239615\pi$
$41$	9.34596	1.45959	0.729797	+	0.683664i	$0.239615\pi$
$42$	0	0
$43$	0.503544	0.0767897	0.0383949	−	0.999263i	$-0.487776\pi$
$43$	0.503544	0.0767897	0.0383949	+	0.999263i	$0.487776\pi$
$44$	1.00000	0.150756
$45$	8.19547	1.22171
$46$	−1.84951	−0.272695
$47$	1.49646	0.218281	0.109140	−	0.994026i	$-0.465190\pi$
$47$	1.49646	0.218281	0.109140	+	0.994026i	$0.465190\pi$
$48$	−3.34596	−0.482948
$49$	0	0
$50$	−1.00000	−0.141421
$51$	−24.0758	−3.37128
$52$	−6.69193	−0.928003
$53$	6.84242	0.939879	0.469939	−	0.882699i	$-0.344276\pi$
$53$	6.84242	0.939879	0.469939	+	0.882699i	$0.344276\pi$
$54$	17.3839	2.36564
$55$	1.00000	0.134840
$56$	0	0
$57$	−6.18838	−0.819671
$58$	−6.84242	−0.898454
$59$	7.88740	1.02685	0.513426	−	0.858134i	$-0.328376\pi$
$59$	7.88740	1.02685	0.513426	+	0.858134i	$0.328376\pi$
$60$	−3.34596	−0.431962
$61$	−4.50354	−0.576620	−0.288310	−	0.957537i	$-0.593093\pi$
$61$	−4.50354	−0.576620	−0.288310	+	0.957537i	$0.593093\pi$
$62$	6.00000	0.762001
$63$	0	0
$64$	1.00000	0.125000
$65$	−6.69193	−0.830031
$66$	3.34596	0.411860
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	7.19547	0.872579
$69$	−6.18838	−0.744994
$70$	0	0
$71$	0.300986	0.0357204	0.0178602	−	0.999840i	$-0.494315\pi$
$71$	0.300986	0.0357204	0.0178602	+	0.999840i	$0.494315\pi$
$72$	−8.19547	−0.965845
$73$	10.1884	1.19246	0.596230	−	0.802814i	$-0.296665\pi$
$73$	10.1884	1.19246	0.596230	+	0.802814i	$0.296665\pi$
$74$	6.54143	0.760426
$75$	−3.34596	−0.386359
$76$	1.84951	0.212153
$77$	0	0
$78$	−22.3909	−2.53527
$79$	−12.2404	−1.37716	−0.688579	−	0.725161i	$-0.741765\pi$
$79$	−12.2404	−1.37716	−0.688579	+	0.725161i	$0.741765\pi$
$80$	1.00000	0.111803
$81$	33.5793	3.73104
$82$	−9.34596	−1.03209
$83$	1.30807	0.143580	0.0717899	−	0.997420i	$-0.477129\pi$
$83$	1.30807	0.143580	0.0717899	+	0.997420i	$0.477129\pi$
$84$	0	0
$85$	7.19547	0.780458
$86$	−0.503544	−0.0542985
$87$	−22.8945	−2.45455
$88$	−1.00000	−0.106600
$89$	8.69193	0.921342	0.460671	−	0.887571i	$-0.347609\pi$
$89$	8.69193	0.921342	0.460671	+	0.887571i	$0.347609\pi$
$90$	−8.19547	−0.863878
$91$	0	0
$92$	1.84951	0.192824
$93$	20.0758	2.08176
$94$	−1.49646	−0.154348
$95$	1.84951	0.189755
$96$	3.34596	0.341496
$97$	−3.84951	−0.390858	−0.195429	−	0.980718i	$-0.562610\pi$
$97$	−3.84951	−0.390858	−0.195429	+	0.980718i	$0.562610\pi$
$98$	0	0
$99$	8.19547	0.823676
$100$	1.00000	0.100000
$101$	−6.89448	−0.686027	−0.343013	−	0.939331i	$-0.611448\pi$
$101$	−6.89448	−0.686027	−0.343013	+	0.939331i	$0.611448\pi$
$102$	24.0758	2.38386
$103$	10.5793	1.04241	0.521206	−	0.853431i	$-0.325482\pi$
$103$	10.5793	1.04241	0.521206	+	0.853431i	$0.325482\pi$
$104$	6.69193	0.656197
$105$	0	0
$106$	−6.84242	−0.664595
$107$	−7.49646	−0.724710	−0.362355	−	0.932040i	$-0.618027\pi$
$107$	−7.49646	−0.724710	−0.362355	+	0.932040i	$0.618027\pi$
$108$	−17.3839	−1.67276
$109$	1.45857	0.139705	0.0698527	−	0.997557i	$-0.477747\pi$
$109$	1.45857	0.139705	0.0698527	+	0.997557i	$0.477747\pi$
$110$	−1.00000	−0.0953463
$111$	21.8874	2.07746
$112$	0	0
$113$	−14.0000	−1.31701	−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000	−1.31701	−0.658505	+	0.752577i	$0.728811\pi$
$114$	6.18838	0.579595
$115$	1.84951	0.172467
$116$	6.84242	0.635303
$117$	−54.8435	−5.07028
$118$	−7.88740	−0.726094
$119$	0	0
$120$	3.34596	0.305443
$121$	1.00000	0.0909091
$122$	4.50354	0.407732
$123$	−31.2713	−2.81963
$124$	−6.00000	−0.538816
$125$	1.00000	0.0894427
$126$	0	0
$127$	−19.7748	−1.75473	−0.877365	−	0.479824i	$-0.840700\pi$
$127$	−19.7748	−1.75473	−0.877365	+	0.479824i	$0.840700\pi$
$128$	−1.00000	−0.0883883
$129$	−1.68484	−0.148342
$130$	6.69193	0.586921
$131$	−2.15049	−0.187889	−0.0939447	−	0.995577i	$-0.529948\pi$
$131$	−2.15049	−0.187889	−0.0939447	+	0.995577i	$0.529948\pi$
$132$	−3.34596	−0.291229
$133$	0	0
$134$	−8.00000	−0.691095
$135$	−17.3839	−1.49616
$136$	−7.19547	−0.617006
$137$	−8.39094	−0.716886	−0.358443	−	0.933552i	$-0.616692\pi$
$137$	−8.39094	−0.716886	−0.358443	+	0.933552i	$0.616692\pi$
$138$	6.18838	0.526790
$139$	−17.9253	−1.52040	−0.760201	−	0.649687i	$-0.774900\pi$
$139$	−17.9253	−1.52040	−0.760201	+	0.649687i	$0.774900\pi$
$140$	0	0
$141$	−5.00709	−0.421673
$142$	−0.300986	−0.0252582
$143$	−6.69193	−0.559607
$144$	8.19547	0.682956
$145$	6.84242	0.568232
$146$	−10.1884	−0.843197
$147$	0	0
$148$	−6.54143	−0.537703
$149$	−0.451479	−0.0369866	−0.0184933	−	0.999829i	$-0.505887\pi$
$149$	−0.451479	−0.0369866	−0.0184933	+	0.999829i	$0.505887\pi$
$150$	3.34596	0.273197
$151$	19.2334	1.56519	0.782594	−	0.622532i	$-0.213896\pi$
$151$	19.2334	1.56519	0.782594	+	0.622532i	$0.213896\pi$
$152$	−1.84951	−0.150015
$153$	58.9703	4.76746
$154$	0	0
$155$	−6.00000	−0.481932
$156$	22.3909	1.79271
$157$	9.69901	0.774066	0.387033	−	0.922066i	$-0.373500\pi$
$157$	9.69901	0.774066	0.387033	+	0.922066i	$0.373500\pi$
$158$	12.2404	0.973798
$159$	−22.8945	−1.81565
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	−33.5793	−2.63824
$163$	−8.00000	−0.626608	−0.313304	−	0.949653i	$-0.601436\pi$
$163$	−8.00000	−0.626608	−0.313304	+	0.949653i	$0.601436\pi$
$164$	9.34596	0.729797
$165$	−3.34596	−0.260483
$166$	−1.30807	−0.101526
$167$	−8.00000	−0.619059	−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000	−0.619059	−0.309529	+	0.950890i	$0.600171\pi$
$168$	0	0
$169$	31.7819	2.44476
$170$	−7.19547	−0.551867
$171$	15.1576	1.15913
$172$	0.503544	0.0383949
$173$	15.4965	1.17817	0.589087	−	0.808070i	$-0.299488\pi$
$173$	15.4965	1.17817	0.589087	+	0.808070i	$0.299488\pi$
$174$	22.8945	1.73563
$175$	0	0
$176$	1.00000	0.0753778
$177$	−26.3909	−1.98366
$178$	−8.69193	−0.651487
$179$	−13.8874	−1.03799	−0.518996	−	0.854776i	$-0.673694\pi$
$179$	−13.8874	−1.03799	−0.518996	+	0.854776i	$0.673694\pi$
$180$	8.19547	0.610854
$181$	−18.7819	−1.39605	−0.698023	−	0.716075i	$-0.745937\pi$
$181$	−18.7819	−1.39605	−0.698023	+	0.716075i	$0.745937\pi$
$182$	0	0
$183$	15.0687	1.11391
$184$	−1.84951	−0.136347
$185$	−6.54143	−0.480936
$186$	−20.0758	−1.47203
$187$	7.19547	0.526185
$188$	1.49646	0.109140
$189$	0	0
$190$	−1.84951	−0.134177
$191$	−6.39094	−0.462432	−0.231216	−	0.972902i	$-0.574270\pi$
$191$	−6.39094	−0.462432	−0.231216	+	0.972902i	$0.574270\pi$
$192$	−3.34596	−0.241474
$193$	−13.1955	−0.949831	−0.474915	−	0.880031i	$-0.657521\pi$
$193$	−13.1955	−0.949831	−0.474915	+	0.880031i	$0.657521\pi$
$194$	3.84951	0.276379
$195$	22.3909	1.60345
$196$	0	0
$197$	−4.69193	−0.334286	−0.167143	−	0.985933i	$-0.553454\pi$
$197$	−4.69193	−0.334286	−0.167143	+	0.985933i	$0.553454\pi$
$198$	−8.19547	−0.582427
$199$	9.49646	0.673186	0.336593	−	0.941650i	$-0.390725\pi$
$199$	9.49646	0.673186	0.336593	+	0.941650i	$0.390725\pi$
$200$	−1.00000	−0.0707107
$201$	−26.7677	−1.88805
$202$	6.89448	0.485094
$203$	0	0
$204$	−24.0758	−1.68564
$205$	9.34596	0.652750
$206$	−10.5793	−0.737096
$207$	15.1576	1.05352
$208$	−6.69193	−0.464002
$209$	1.84951	0.127933
$210$	0	0
$211$	−2.39094	−0.164599	−0.0822996	−	0.996608i	$-0.526226\pi$
$211$	−2.39094	−0.164599	−0.0822996	+	0.996608i	$0.526226\pi$
$212$	6.84242	0.469939
$213$	−1.00709	−0.0690045
$214$	7.49646	0.512447
$215$	0.503544	0.0343414
$216$	17.3839	1.18282
$217$	0	0
$218$	−1.45857	−0.0987866
$219$	−34.0900	−2.30359
$220$	1.00000	0.0674200
$221$	−48.1516	−3.23902
$222$	−21.8874	−1.46899
$223$	−0.188383	−0.0126150	−0.00630752	−	0.999980i	$-0.502008\pi$
$223$	−0.188383	−0.0126150	−0.00630752	+	0.999980i	$0.502008\pi$
$224$	0	0
$225$	8.19547	0.546365
$226$	14.0000	0.931266
$227$	6.99291	0.464136	0.232068	−	0.972700i	$-0.425451\pi$
$227$	6.99291	0.464136	0.232068	+	0.972700i	$0.425451\pi$
$228$	−6.18838	−0.409836
$229$	9.19547	0.607654	0.303827	−	0.952727i	$-0.401736\pi$
$229$	9.19547	0.607654	0.303827	+	0.952727i	$0.401736\pi$
$230$	−1.84951	−0.121953
$231$	0	0
$232$	−6.84242	−0.449227
$233$	−0.992912	−0.0650479	−0.0325239	−	0.999471i	$-0.510355\pi$
$233$	−0.992912	−0.0650479	−0.0325239	+	0.999471i	$0.510355\pi$
$234$	54.8435	3.58523
$235$	1.49646	0.0976180
$236$	7.88740	0.513426
$237$	40.9561	2.66038
$238$	0	0
$239$	−1.14341	−0.0739607	−0.0369804	−	0.999316i	$-0.511774\pi$
$239$	−1.14341	−0.0739607	−0.0369804	+	0.999316i	$0.511774\pi$
$240$	−3.34596	−0.215981
$241$	−8.33888	−0.537154	−0.268577	−	0.963258i	$-0.586553\pi$
$241$	−8.33888	−0.537154	−0.268577	+	0.963258i	$0.586553\pi$
$242$	−1.00000	−0.0642824
$243$	−60.2036	−3.86206
$244$	−4.50354	−0.288310
$245$	0	0
$246$	31.2713	1.99378
$247$	−12.3768	−0.787515
$248$	6.00000	0.381000
$249$	−4.37677	−0.277366
$250$	−1.00000	−0.0632456
$251$	−23.8874	−1.50776	−0.753880	−	0.657013i	$-0.771820\pi$
$251$	−23.8874	−1.50776	−0.753880	+	0.657013i	$0.771820\pi$
$252$	0	0
$253$	1.84951	0.116278
$254$	19.7748	1.24078
$255$	−24.0758	−1.50768
$256$	1.00000	0.0625000
$257$	31.6243	1.97267	0.986335	−	0.164753i	$-0.0526827\pi$
$257$	31.6243	1.97267	0.986335	+	0.164753i	$0.0526827\pi$
$258$	1.68484	0.104893
$259$	0	0
$260$	−6.69193	−0.415016
$261$	56.0768	3.47107
$262$	2.15049	0.132858
$263$	13.3839	0.825284	0.412642	−	0.910893i	$-0.364606\pi$
$263$	13.3839	0.825284	0.412642	+	0.910893i	$0.364606\pi$
$264$	3.34596	0.205930
$265$	6.84242	0.420326
$266$	0	0
$267$	−29.0829	−1.77984
$268$	8.00000	0.488678
$269$	−5.79744	−0.353476	−0.176738	−	0.984258i	$-0.556555\pi$
$269$	−5.79744	−0.353476	−0.176738	+	0.984258i	$0.556555\pi$
$270$	17.3839	1.05795
$271$	20.0758	1.21952	0.609758	−	0.792587i	$-0.291266\pi$
$271$	20.0758	1.21952	0.609758	+	0.792587i	$0.291266\pi$
$272$	7.19547	0.436289
$273$	0	0
$274$	8.39094	0.506915
$275$	1.00000	0.0603023
$276$	−6.18838	−0.372497
$277$	22.0000	1.32185	0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000	1.32185	0.660926	+	0.750451i	$0.270164\pi$
$278$	17.9253	1.07509
$279$	−49.1728	−2.94390
$280$	0	0
$281$	−6.30099	−0.375885	−0.187943	−	0.982180i	$-0.560182\pi$
$281$	−6.30099	−0.375885	−0.187943	+	0.982180i	$0.560182\pi$
$282$	5.00709	0.298168
$283$	−22.3909	−1.33100	−0.665502	−	0.746396i	$-0.731782\pi$
$283$	−22.3909	−1.33100	−0.665502	+	0.746396i	$0.731782\pi$
$284$	0.300986	0.0178602
$285$	−6.18838	−0.366568
$286$	6.69193	0.395702
$287$	0	0
$288$	−8.19547	−0.482923
$289$	34.7748	2.04558
$290$	−6.84242	−0.401801
$291$	12.8803	0.755057
$292$	10.1884	0.596230
$293$	10.6919	0.624629	0.312315	−	0.949979i	$-0.398896\pi$
$293$	10.6919	0.624629	0.312315	+	0.949979i	$0.398896\pi$
$294$	0	0
$295$	7.88740	0.459222
$296$	6.54143	0.380213
$297$	−17.3839	−1.00871
$298$	0.451479	0.0261535
$299$	−12.3768	−0.715767
$300$	−3.34596	−0.193179
$301$	0	0
$302$	−19.2334	−1.10676
$303$	23.0687	1.32526
$304$	1.84951	0.106077
$305$	−4.50354	−0.257872
$306$	−58.9703	−3.37111
$307$	9.08287	0.518387	0.259193	−	0.965825i	$-0.416543\pi$
$307$	9.08287	0.518387	0.259193	+	0.965825i	$0.416543\pi$
$308$	0	0
$309$	−35.3980	−2.01372
$310$	6.00000	0.340777
$311$	11.3839	0.645519	0.322760	−	0.946481i	$-0.395389\pi$
$311$	11.3839	0.645519	0.322760	+	0.946481i	$0.395389\pi$
$312$	−22.3909	−1.26764
$313$	23.6243	1.33532	0.667662	−	0.744464i	$-0.267295\pi$
$313$	23.6243	1.33532	0.667662	+	0.744464i	$0.267295\pi$
$314$	−9.69901	−0.547347
$315$	0	0
$316$	−12.2404	−0.688579
$317$	−9.53435	−0.535502	−0.267751	−	0.963488i	$-0.586280\pi$
$317$	−9.53435	−0.535502	−0.267751	+	0.963488i	$0.586280\pi$
$318$	22.8945	1.28386
$319$	6.84242	0.383102
$320$	1.00000	0.0559017
$321$	25.0829	1.39999
$322$	0	0
$323$	13.3081	0.740481
$324$	33.5793	1.86552
$325$	−6.69193	−0.371201
$326$	8.00000	0.443079
$327$	−4.88031	−0.269882
$328$	−9.34596	−0.516044
$329$	0	0
$330$	3.34596	0.184189
$331$	0.503544	0.0276773	0.0138386	−	0.999904i	$-0.495595\pi$
$331$	0.503544	0.0276773	0.0138386	+	0.999904i	$0.495595\pi$
$332$	1.30807	0.0717899
$333$	−53.6101	−2.93782
$334$	8.00000	0.437741
$335$	8.00000	0.437087
$336$	0	0
$337$	12.3909	0.674978	0.337489	−	0.941330i	$-0.390422\pi$
$337$	12.3909	0.674978	0.337489	+	0.941330i	$0.390422\pi$
$338$	−31.7819	−1.72871
$339$	46.8435	2.54419
$340$	7.19547	0.390229
$341$	−6.00000	−0.324918
$342$	−15.1576	−0.819628
$343$	0	0
$344$	−0.503544	−0.0271493
$345$	−6.18838	−0.333171
$346$	−15.4965	−0.833095
$347$	20.8803	1.12091	0.560457	−	0.828184i	$-0.310626\pi$
$347$	20.8803	1.12091	0.560457	+	0.828184i	$0.310626\pi$
$348$	−22.8945	−1.22727
$349$	22.1884	1.18772	0.593858	−	0.804570i	$-0.297604\pi$
$349$	22.1884	1.18772	0.593858	+	0.804570i	$0.297604\pi$
$350$	0	0
$351$	116.331	6.20931
$352$	−1.00000	−0.0533002
$353$	31.6243	1.68319	0.841596	−	0.540108i	$-0.181617\pi$
$353$	31.6243	1.68319	0.841596	+	0.540108i	$0.181617\pi$
$354$	26.3909	1.40266
$355$	0.300986	0.0159747
$356$	8.69193	0.460671
$357$	0	0
$358$	13.8874	0.733972
$359$	30.5273	1.61117	0.805584	−	0.592482i	$-0.201852\pi$
$359$	30.5273	1.61117	0.805584	+	0.592482i	$0.201852\pi$
$360$	−8.19547	−0.431939
$361$	−15.5793	−0.819964
$362$	18.7819	0.987154
$363$	−3.34596	−0.175618
$364$	0	0
$365$	10.1884	0.533284
$366$	−15.0687	−0.787653
$367$	10.5793	0.552236	0.276118	−	0.961124i	$-0.410952\pi$
$367$	10.5793	0.552236	0.276118	+	0.961124i	$0.410952\pi$
$368$	1.84951	0.0964122
$369$	76.5946	3.98735
$370$	6.54143	0.340073
$371$	0	0
$372$	20.0758	1.04088
$373$	36.4667	1.88818	0.944088	−	0.329695i	$-0.106946\pi$
$373$	36.4667	1.88818	0.944088	+	0.329695i	$0.106946\pi$
$374$	−7.19547	−0.372069
$375$	−3.34596	−0.172785
$376$	−1.49646	−0.0771738
$377$	−45.7890	−2.35825
$378$	0	0
$379$	14.9929	0.770134	0.385067	−	0.922889i	$-0.374178\pi$
$379$	14.9929	0.770134	0.385067	+	0.922889i	$0.374178\pi$
$380$	1.84951	0.0948777
$381$	66.1657	3.38977
$382$	6.39094	0.326989
$383$	−35.1813	−1.79768	−0.898840	−	0.438277i	$-0.855589\pi$
$383$	−35.1813	−1.79768	−0.898840	+	0.438277i	$0.855589\pi$
$384$	3.34596	0.170748
$385$	0	0
$386$	13.1955	0.671632
$387$	4.12678	0.209776
$388$	−3.84951	−0.195429
$389$	2.30099	0.116665	0.0583323	−	0.998297i	$-0.481422\pi$
$389$	2.30099	0.116665	0.0583323	+	0.998297i	$0.481422\pi$
$390$	−22.3909	−1.13381
$391$	13.3081	0.673018
$392$	0	0
$393$	7.19547	0.362963
$394$	4.69193	0.236376
$395$	−12.2404	−0.615884
$396$	8.19547	0.411838
$397$	−18.0758	−0.907197	−0.453599	−	0.891206i	$-0.649860\pi$
$397$	−18.0758	−0.907197	−0.453599	+	0.891206i	$0.649860\pi$
$398$	−9.49646	−0.476014
$399$	0	0
$400$	1.00000	0.0500000
$401$	22.5793	1.12756	0.563779	−	0.825926i	$-0.309347\pi$
$401$	22.5793	1.12756	0.563779	+	0.825926i	$0.309347\pi$
$402$	26.7677	1.33505
$403$	40.1516	2.00009
$404$	−6.89448	−0.343013
$405$	33.5793	1.66857
$406$	0	0
$407$	−6.54143	−0.324247
$408$	24.0758	1.19193
$409$	−1.04498	−0.0516708	−0.0258354	−	0.999666i	$-0.508225\pi$
$409$	−1.04498	−0.0516708	−0.0258354	+	0.999666i	$0.508225\pi$
$410$	−9.34596	−0.461564
$411$	28.0758	1.38488
$412$	10.5793	0.521206
$413$	0	0
$414$	−15.1576	−0.744954
$415$	1.30807	0.0642108
$416$	6.69193	0.328099
$417$	59.9774	2.93710
$418$	−1.84951	−0.0904623
$419$	−5.49646	−0.268519	−0.134260	−	0.990946i	$-0.542866\pi$
$419$	−5.49646	−0.268519	−0.134260	+	0.990946i	$0.542866\pi$
$420$	0	0
$421$	2.60197	0.126812	0.0634062	−	0.997988i	$-0.479804\pi$
$421$	2.60197	0.126812	0.0634062	+	0.997988i	$0.479804\pi$
$422$	2.39094	0.116389
$423$	12.2642	0.596304
$424$	−6.84242	−0.332297
$425$	7.19547	0.349032
$426$	1.00709	0.0487936
$427$	0	0
$428$	−7.49646	−0.362355
$429$	22.3909	1.08104
$430$	−0.503544	−0.0242830
$431$	19.2334	0.926438	0.463219	−	0.886244i	$-0.346694\pi$
$431$	19.2334	0.926438	0.463219	+	0.886244i	$0.346694\pi$
$432$	−17.3839	−0.836381
$433$	8.93237	0.429263	0.214631	−	0.976695i	$-0.431145\pi$
$433$	8.93237	0.429263	0.214631	+	0.976695i	$0.431145\pi$
$434$	0	0
$435$	−22.8945	−1.09771
$436$	1.45857	0.0698527
$437$	3.42068	0.163633
$438$	34.0900	1.62888
$439$	0.300986	0.0143653	0.00718264	−	0.999974i	$-0.497714\pi$
$439$	0.300986	0.0143653	0.00718264	+	0.999974i	$0.497714\pi$
$440$	−1.00000	−0.0476731
$441$	0	0
$442$	48.1516	2.29034
$443$	30.7677	1.46182	0.730909	−	0.682475i	$-0.239096\pi$
$443$	30.7677	1.46182	0.730909	+	0.682475i	$0.239096\pi$
$444$	21.8874	1.03873
$445$	8.69193	0.412037
$446$	0.188383	0.00892018
$447$	1.51063	0.0714504
$448$	0	0
$449$	−1.19547	−0.0564177	−0.0282089	−	0.999602i	$-0.508980\pi$
$449$	−1.19547	−0.0564177	−0.0282089	+	0.999602i	$0.508980\pi$
$450$	−8.19547	−0.386338
$451$	9.34596	0.440084
$452$	−14.0000	−0.658505
$453$	−64.3541	−3.02362
$454$	−6.99291	−0.328194
$455$	0	0
$456$	6.18838	0.289798
$457$	−25.7748	−1.20569	−0.602847	−	0.797857i	$-0.705967\pi$
$457$	−25.7748	−1.20569	−0.602847	+	0.797857i	$0.705967\pi$
$458$	−9.19547	−0.429676
$459$	−125.085	−5.83847
$460$	1.84951	0.0862337
$461$	−11.5722	−0.538973	−0.269486	−	0.963004i	$-0.586854\pi$
$461$	−11.5722	−0.538973	−0.269486	+	0.963004i	$0.586854\pi$
$462$	0	0
$463$	−32.9182	−1.52984	−0.764919	−	0.644126i	$-0.777221\pi$
$463$	−32.9182	−1.52984	−0.764919	+	0.644126i	$0.777221\pi$
$464$	6.84242	0.317651
$465$	20.0758	0.930992
$466$	0.992912	0.0459958
$467$	14.6399	0.677452	0.338726	−	0.940885i	$-0.390004\pi$
$467$	14.6399	0.677452	0.338726	+	0.940885i	$0.390004\pi$
$468$	−54.8435	−2.53514
$469$	0	0
$470$	−1.49646	−0.0690264
$471$	−32.4525	−1.49533
$472$	−7.88740	−0.363047
$473$	0.503544	0.0231530
$474$	−40.9561	−1.88118
$475$	1.84951	0.0848612
$476$	0	0
$477$	56.0768	2.56758
$478$	1.14341	0.0522981
$479$	−10.3909	−0.474774	−0.237387	−	0.971415i	$-0.576291\pi$
$479$	−10.3909	−0.474774	−0.237387	+	0.971415i	$0.576291\pi$
$480$	3.34596	0.152722
$481$	43.7748	1.99596
$482$	8.33888	0.379825
$483$	0	0
$484$	1.00000	0.0454545
$485$	−3.84951	−0.174797
$486$	60.2036	2.73089
$487$	39.3091	1.78127	0.890634	−	0.454722i	$-0.150261\pi$
$487$	39.3091	1.78127	0.890634	+	0.454722i	$0.150261\pi$
$488$	4.50354	0.203866
$489$	26.7677	1.21048
$490$	0	0
$491$	23.7748	1.07294	0.536471	−	0.843919i	$-0.319757\pi$
$491$	23.7748	1.07294	0.536471	+	0.843919i	$0.319757\pi$
$492$	−31.2713	−1.40982
$493$	49.2344	2.21741
$494$	12.3768	0.556857
$495$	8.19547	0.368359
$496$	−6.00000	−0.269408
$497$	0	0
$498$	4.37677	0.196128
$499$	−6.11260	−0.273638	−0.136819	−	0.990596i	$-0.543688\pi$
$499$	−6.11260	−0.273638	−0.136819	+	0.990596i	$0.543688\pi$
$500$	1.00000	0.0447214
$501$	26.7677	1.19589
$502$	23.8874	1.06615
$503$	13.1586	0.586715	0.293358	−	0.956003i	$-0.405227\pi$
$503$	13.1586	0.586715	0.293358	+	0.956003i	$0.405227\pi$
$504$	0	0
$505$	−6.89448	−0.306801
$506$	−1.84951	−0.0822206
$507$	−106.341	−4.72277
$508$	−19.7748	−0.877365
$509$	−34.1799	−1.51500	−0.757499	−	0.652836i	$-0.773579\pi$
$509$	−34.1799	−1.51500	−0.757499	+	0.652836i	$0.773579\pi$
$510$	24.0758	1.06609
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−32.1516	−1.41953
$514$	−31.6243	−1.39489
$515$	10.5793	0.466181
$516$	−1.68484	−0.0741709
$517$	1.49646	0.0658141
$518$	0	0
$519$	−51.8506	−2.27599
$520$	6.69193	0.293460
$521$	26.6778	1.16877	0.584387	−	0.811475i	$-0.301335\pi$
$521$	26.6778	1.16877	0.584387	+	0.811475i	$0.301335\pi$
$522$	−56.0768	−2.45442
$523$	−25.4880	−1.11451	−0.557256	−	0.830341i	$-0.688146\pi$
$523$	−25.4880	−1.11451	−0.557256	+	0.830341i	$0.688146\pi$
$524$	−2.15049	−0.0939447
$525$	0	0
$526$	−13.3839	−0.583564
$527$	−43.1728	−1.88064
$528$	−3.34596	−0.145614
$529$	−19.5793	−0.851275
$530$	−6.84242	−0.297216
$531$	64.6409	2.80518
$532$	0	0
$533$	−62.5425	−2.70902
$534$	29.0829	1.25854
$535$	−7.49646	−0.324100
$536$	−8.00000	−0.345547
$537$	46.4667	2.00519
$538$	5.79744	0.249945
$539$	0	0
$540$	−17.3839	−0.748082
$541$	4.45148	0.191384	0.0956920	−	0.995411i	$-0.469494\pi$
$541$	4.45148	0.191384	0.0956920	+	0.995411i	$0.469494\pi$
$542$	−20.0758	−0.862329
$543$	62.8435	2.69687
$544$	−7.19547	−0.308503
$545$	1.45857	0.0624781
$546$	0	0
$547$	−1.38385	−0.0591693	−0.0295846	−	0.999562i	$-0.509418\pi$
$547$	−1.38385	−0.0591693	−0.0295846	+	0.999562i	$0.509418\pi$
$548$	−8.39094	−0.358443
$549$	−36.9087	−1.57522
$550$	−1.00000	−0.0426401
$551$	12.6551	0.539126
$552$	6.18838	0.263395
$553$	0	0
$554$	−22.0000	−0.934690
$555$	21.8874	0.929068
$556$	−17.9253	−0.760201
$557$	−6.70610	−0.284147	−0.142073	−	0.989856i	$-0.545377\pi$
$557$	−6.70610	−0.284147	−0.142073	+	0.989856i	$0.545377\pi$
$558$	49.1728	2.08165
$559$	−3.36968	−0.142522
$560$	0	0
$561$	−24.0758	−1.01648
$562$	6.30099	0.265791
$563$	−3.59488	−0.151506	−0.0757532	−	0.997127i	$-0.524136\pi$
$563$	−3.59488	−0.151506	−0.0757532	+	0.997127i	$0.524136\pi$
$564$	−5.00709	−0.210836
$565$	−14.0000	−0.588984
$566$	22.3909	0.941161
$567$	0	0
$568$	−0.300986	−0.0126291
$569$	31.7606	1.33147	0.665737	−	0.746186i	$-0.268117\pi$
$569$	31.7606	1.33147	0.665737	+	0.746186i	$0.268117\pi$
$570$	6.18838	0.259203
$571$	−5.68484	−0.237903	−0.118952	−	0.992900i	$-0.537953\pi$
$571$	−5.68484	−0.237903	−0.118952	+	0.992900i	$0.537953\pi$
$572$	−6.69193	−0.279804
$573$	21.3839	0.893323
$574$	0	0
$575$	1.84951	0.0771298
$576$	8.19547	0.341478
$577$	−13.5343	−0.563442	−0.281721	−	0.959496i	$-0.590905\pi$
$577$	−13.5343	−0.563442	−0.281721	+	0.959496i	$0.590905\pi$
$578$	−34.7748	−1.44644
$579$	44.1516	1.83488
$580$	6.84242	0.284116
$581$	0	0
$582$	−12.8803	−0.533906
$583$	6.84242	0.283384
$584$	−10.1884	−0.421598
$585$	−54.8435	−2.26750
$586$	−10.6919	−0.441679
$587$	0.0520650	0.00214895	0.00107448	−	0.999999i	$-0.499658\pi$
$587$	0.0520650	0.00214895	0.00107448	+	0.999999i	$0.499658\pi$
$588$	0	0
$589$	−11.0970	−0.457246
$590$	−7.88740	−0.324719
$591$	15.6990	0.645771
$592$	−6.54143	−0.268851
$593$	−31.9774	−1.31315	−0.656576	−	0.754260i	$-0.727996\pi$
$593$	−31.9774	−1.31315	−0.656576	+	0.754260i	$0.727996\pi$
$594$	17.3839	0.713268
$595$	0	0
$596$	−0.451479	−0.0184933
$597$	−31.7748	−1.30046
$598$	12.3768	0.506124
$599$	21.0829	0.861423	0.430711	−	0.902490i	$-0.358263\pi$
$599$	21.0829	0.861423	0.430711	+	0.902490i	$0.358263\pi$
$600$	3.34596	0.136598
$601$	21.6469	0.882997	0.441499	−	0.897262i	$-0.354447\pi$
$601$	21.6469	0.882997	0.441499	+	0.897262i	$0.354447\pi$
$602$	0	0
$603$	65.5638	2.66996
$604$	19.2334	0.782594
$605$	1.00000	0.0406558
$606$	−23.0687	−0.937102
$607$	−21.6622	−0.879241	−0.439621	−	0.898184i	$-0.644887\pi$
$607$	−21.6622	−0.879241	−0.439621	+	0.898184i	$0.644887\pi$
$608$	−1.84951	−0.0750074
$609$	0	0
$610$	4.50354	0.182343
$611$	−10.0142	−0.405130
$612$	58.9703	2.38373
$613$	8.31516	0.335846	0.167923	−	0.985800i	$-0.446294\pi$
$613$	8.31516	0.335846	0.167923	+	0.985800i	$0.446294\pi$
$614$	−9.08287	−0.366555
$615$	−31.2713	−1.26098
$616$	0	0
$617$	12.4667	0.501891	0.250946	−	0.968001i	$-0.419258\pi$
$617$	12.4667	0.501891	0.250946	+	0.968001i	$0.419258\pi$
$618$	35.3980	1.42392
$619$	−5.27125	−0.211869	−0.105935	−	0.994373i	$-0.533783\pi$
$619$	−5.27125	−0.211869	−0.105935	+	0.994373i	$0.533783\pi$
$620$	−6.00000	−0.240966
$621$	−32.1516	−1.29020
$622$	−11.3839	−0.456451
$623$	0	0
$624$	22.3909	0.896355
$625$	1.00000	0.0400000
$626$	−23.6243	−0.944217
$627$	−6.18838	−0.247140
$628$	9.69901	0.387033
$629$	−47.0687	−1.87675
$630$	0	0
$631$	−17.1586	−0.683075	−0.341537	−	0.939868i	$-0.610948\pi$
$631$	−17.1586	−0.683075	−0.341537	+	0.939868i	$0.610948\pi$
$632$	12.2404	0.486899
$633$	8.00000	0.317971
$634$	9.53435	0.378657
$635$	−19.7748	−0.784739
$636$	−22.8945	−0.907825
$637$	0	0
$638$	−6.84242	−0.270894
$639$	2.46672	0.0975820
$640$	−1.00000	−0.0395285
$641$	24.7677	0.978266	0.489133	−	0.872209i	$-0.337313\pi$
$641$	24.7677	0.978266	0.489133	+	0.872209i	$0.337313\pi$
$642$	−25.0829	−0.989942
$643$	−1.03080	−0.0406509	−0.0203254	−	0.999793i	$-0.506470\pi$
$643$	−1.03080	−0.0406509	−0.0203254	+	0.999793i	$0.506470\pi$
$644$	0	0
$645$	−1.68484	−0.0663405
$646$	−13.3081	−0.523599
$647$	−12.7904	−0.502841	−0.251420	−	0.967878i	$-0.580898\pi$
$647$	−12.7904	−0.502841	−0.251420	+	0.967878i	$0.580898\pi$
$648$	−33.5793	−1.31912
$649$	7.88740	0.309607
$650$	6.69193	0.262479
$651$	0	0
$652$	−8.00000	−0.313304
$653$	−22.3162	−0.873301	−0.436651	−	0.899631i	$-0.643835\pi$
$653$	−22.3162	−0.873301	−0.436651	+	0.899631i	$0.643835\pi$
$654$	4.88031	0.190835
$655$	−2.15049	−0.0840267
$656$	9.34596	0.364899
$657$	83.4986	3.25759
$658$	0	0
$659$	22.6919	0.883952	0.441976	−	0.897027i	$-0.354278\pi$
$659$	22.6919	0.883952	0.441976	+	0.897027i	$0.354278\pi$
$660$	−3.34596	−0.130241
$661$	−43.5638	−1.69443	−0.847217	−	0.531247i	$-0.821724\pi$
$661$	−43.5638	−1.69443	−0.847217	+	0.531247i	$0.821724\pi$
$662$	−0.503544	−0.0195708
$663$	161.113	6.25712
$664$	−1.30807	−0.0507631
$665$	0	0
$666$	53.6101	2.07735
$667$	12.6551	0.490008
$668$	−8.00000	−0.309529
$669$	0.630322	0.0243697
$670$	−8.00000	−0.309067
$671$	−4.50354	−0.173857
$672$	0	0
$673$	38.0000	1.46479	0.732396	−	0.680879i	$-0.238402\pi$
$673$	38.0000	1.46479	0.732396	+	0.680879i	$0.238402\pi$
$674$	−12.3909	−0.477281
$675$	−17.3839	−0.669105
$676$	31.7819	1.22238
$677$	16.0984	0.618713	0.309356	−	0.950946i	$-0.399886\pi$
$677$	16.0984	0.618713	0.309356	+	0.950946i	$0.399886\pi$
$678$	−46.8435	−1.79901
$679$	0	0
$680$	−7.19547	−0.275934
$681$	−23.3980	−0.896614
$682$	6.00000	0.229752
$683$	29.0829	1.11282	0.556412	−	0.830906i	$-0.312177\pi$
$683$	29.0829	1.11282	0.556412	+	0.830906i	$0.312177\pi$
$684$	15.1576	0.579565
$685$	−8.39094	−0.320601
$686$	0	0
$687$	−30.7677	−1.17386
$688$	0.503544	0.0191974
$689$	−45.7890	−1.74442
$690$	6.18838	0.235588
$691$	−7.58641	−0.288601	−0.144300	−	0.989534i	$-0.546093\pi$
$691$	−7.58641	−0.288601	−0.144300	+	0.989534i	$0.546093\pi$
$692$	15.4965	0.589087
$693$	0	0
$694$	−20.8803	−0.792606
$695$	−17.9253	−0.679945
$696$	22.8945	0.867813
$697$	67.2486	2.54722
$698$	−22.1884	−0.839843
$699$	3.32225	0.125659
$700$	0	0
$701$	4.07471	0.153900	0.0769499	−	0.997035i	$-0.475482\pi$
$701$	4.07471	0.153900	0.0769499	+	0.997035i	$0.475482\pi$
$702$	−116.331	−4.39065
$703$	−12.0984	−0.456301
$704$	1.00000	0.0376889
$705$	−5.00709	−0.188578
$706$	−31.6243	−1.19020
$707$	0	0
$708$	−26.3909	−0.991832
$709$	−46.4525	−1.74456	−0.872281	−	0.489005i	$-0.837360\pi$
$709$	−46.4525	−1.74456	−0.872281	+	0.489005i	$0.837360\pi$
$710$	−0.300986	−0.0112958
$711$	−100.316	−3.76215
$712$	−8.69193	−0.325744
$713$	−11.0970	−0.415588
$714$	0	0
$715$	−6.69193	−0.250264
$716$	−13.8874	−0.518996
$717$	3.82579	0.142877
$718$	−30.5273	−1.13927
$719$	17.8732	0.666559	0.333279	−	0.942828i	$-0.391845\pi$
$719$	17.8732	0.666559	0.333279	+	0.942828i	$0.391845\pi$
$720$	8.19547	0.305427
$721$	0	0
$722$	15.5793	0.579802
$723$	27.9016	1.03767
$724$	−18.7819	−0.698023
$725$	6.84242	0.254121
$726$	3.34596	0.124180
$727$	11.8874	0.440879	0.220440	−	0.975401i	$-0.429251\pi$
$727$	11.8874	0.440879	0.220440	+	0.975401i	$0.429251\pi$
$728$	0	0
$729$	100.701	3.72967
$730$	−10.1884	−0.377089
$731$	3.62323	0.134010
$732$	15.0687	0.556955
$733$	31.6764	1.16999	0.584997	−	0.811036i	$-0.301096\pi$
$733$	31.6764	1.16999	0.584997	+	0.811036i	$0.301096\pi$
$734$	−10.5793	−0.390490
$735$	0	0
$736$	−1.84951	−0.0681737
$737$	8.00000	0.294684
$738$	−76.5946	−2.81948
$739$	28.5567	1.05047	0.525237	−	0.850956i	$-0.323977\pi$
$739$	28.5567	1.05047	0.525237	+	0.850956i	$0.323977\pi$
$740$	−6.54143	−0.240468
$741$	41.4122	1.52132
$742$	0	0
$743$	13.9858	0.513090	0.256545	−	0.966532i	$-0.417416\pi$
$743$	13.9858	0.513090	0.256545	+	0.966532i	$0.417416\pi$
$744$	−20.0758	−0.736014
$745$	−0.451479	−0.0165409
$746$	−36.4667	−1.33514
$747$	10.7203	0.392234
$748$	7.19547	0.263092
$749$	0	0
$750$	3.34596	0.122177
$751$	18.9171	0.690296	0.345148	−	0.938548i	$-0.387829\pi$
$751$	18.9171	0.690296	0.345148	+	0.938548i	$0.387829\pi$
$752$	1.49646	0.0545701
$753$	79.9264	2.91268
$754$	45.7890	1.66754
$755$	19.2334	0.699974
$756$	0	0
$757$	10.9182	0.396829	0.198414	−	0.980118i	$-0.436421\pi$
$757$	10.9182	0.396829	0.198414	+	0.980118i	$0.436421\pi$
$758$	−14.9929	−0.544567
$759$	−6.18838	−0.224624
$760$	−1.84951	−0.0670887
$761$	30.3531	1.10030	0.550149	−	0.835067i	$-0.314571\pi$
$761$	30.3531	1.10030	0.550149	+	0.835067i	$0.314571\pi$
$762$	−66.1657	−2.39693
$763$	0	0
$764$	−6.39094	−0.231216
$765$	58.9703	2.13207
$766$	35.1813	1.27115
$767$	−52.7819	−1.90584
$768$	−3.34596	−0.120737
$769$	19.7369	0.711731	0.355865	−	0.934537i	$-0.384186\pi$
$769$	19.7369	0.711731	0.355865	+	0.934537i	$0.384186\pi$
$770$	0	0
$771$	−105.814	−3.81079
$772$	−13.1955	−0.474915
$773$	24.3909	0.877281	0.438641	−	0.898663i	$-0.355460\pi$
$773$	24.3909	0.877281	0.438641	+	0.898663i	$0.355460\pi$
$774$	−4.12678	−0.148334
$775$	−6.00000	−0.215526
$776$	3.84951	0.138189
$777$	0	0
$778$	−2.30099	−0.0824943
$779$	17.2854	0.619315
$780$	22.3909	0.801724
$781$	0.300986	0.0107701
$782$	−13.3081	−0.475896
$783$	−118.948	−4.25084
$784$	0	0
$785$	9.69901	0.346173
$786$	−7.19547	−0.256654
$787$	−33.7890	−1.20445	−0.602223	−	0.798328i	$-0.705718\pi$
$787$	−33.7890	−1.20445	−0.602223	+	0.798328i	$0.705718\pi$
$788$	−4.69193	−0.167143
$789$	−44.7819	−1.59428
$790$	12.2404	0.435496
$791$	0	0
$792$	−8.19547	−0.291213
$793$	30.1374	1.07021
$794$	18.0758	0.641485
$795$	−22.8945	−0.811984
$796$	9.49646	0.336593
$797$	−36.8435	−1.30506	−0.652532	−	0.757761i	$-0.726293\pi$
$797$	−36.8435	−1.30506	−0.652532	+	0.757761i	$0.726293\pi$
$798$	0	0
$799$	10.7677	0.380934
$800$	−1.00000	−0.0353553
$801$	71.2344	2.51694
$802$	−22.5793	−0.797304
$803$	10.1884	0.359540
$804$	−26.7677	−0.944024
$805$	0	0
$806$	−40.1516	−1.41428
$807$	19.3980	0.682843
$808$	6.89448	0.242547
$809$	37.6990	1.32543	0.662713	−	0.748873i	$-0.269405\pi$
$809$	37.6990	1.32543	0.662713	+	0.748873i	$0.269405\pi$
$810$	−33.5793	−1.17986
$811$	−38.3304	−1.34596	−0.672981	−	0.739660i	$-0.734987\pi$
$811$	−38.3304	−1.34596	−0.672981	+	0.739660i	$0.734987\pi$
$812$	0	0
$813$	−67.1728	−2.35585
$814$	6.54143	0.229277
$815$	−8.00000	−0.280228
$816$	−24.0758	−0.842821
$817$	0.931308	0.0325823
$818$	1.04498	0.0365368
$819$	0	0
$820$	9.34596	0.326375
$821$	−18.1363	−0.632962	−0.316481	−	0.948599i	$-0.602501\pi$
$821$	−18.1363	−0.632962	−0.316481	+	0.948599i	$0.602501\pi$
$822$	−28.0758	−0.979255
$823$	−7.86368	−0.274111	−0.137055	−	0.990563i	$-0.543764\pi$
$823$	−7.86368	−0.274111	−0.137055	+	0.990563i	$0.543764\pi$
$824$	−10.5793	−0.368548
$825$	−3.34596	−0.116491
$826$	0	0
$827$	12.0000	0.417281	0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000	0.417281	0.208640	+	0.977992i	$0.433096\pi$
$828$	15.1576	0.526762
$829$	−2.80453	−0.0974053	−0.0487027	−	0.998813i	$-0.515509\pi$
$829$	−2.80453	−0.0974053	−0.0487027	+	0.998813i	$0.515509\pi$
$830$	−1.30807	−0.0454039
$831$	−73.6112	−2.55354
$832$	−6.69193	−0.232001
$833$	0	0
$834$	−59.9774	−2.07685
$835$	−8.00000	−0.276851
$836$	1.84951	0.0639665
$837$	104.303	3.60524
$838$	5.49646	0.189872
$839$	−36.9929	−1.27714	−0.638569	−	0.769565i	$-0.720473\pi$
$839$	−36.9929	−1.27714	−0.638569	+	0.769565i	$0.720473\pi$
$840$	0	0
$841$	17.8187	0.614438
$842$	−2.60197	−0.0896699
$843$	21.0829	0.726133
$844$	−2.39094	−0.0822996
$845$	31.7819	1.09333
$846$	−12.2642	−0.421651
$847$	0	0
$848$	6.84242	0.234970
$849$	74.9193	2.57122
$850$	−7.19547	−0.246803
$851$	−12.0984	−0.414729
$852$	−1.00709	−0.0345023
$853$	49.2571	1.68653	0.843265	−	0.537498i	$-0.180630\pi$
$853$	49.2571	1.68653	0.843265	+	0.537498i	$0.180630\pi$
$854$	0	0
$855$	15.1576	0.518378
$856$	7.49646	0.256224
$857$	20.3541	0.695283	0.347642	−	0.937627i	$-0.386983\pi$
$857$	20.3541	0.695283	0.347642	+	0.937627i	$0.386983\pi$
$858$	−22.3909	−0.764414
$859$	34.2783	1.16956	0.584781	−	0.811191i	$-0.301180\pi$
$859$	34.2783	1.16956	0.584781	+	0.811191i	$0.301180\pi$
$860$	0.503544	0.0171707
$861$	0	0
$862$	−19.2334	−0.655091
$863$	−12.4373	−0.423371	−0.211685	−	0.977338i	$-0.567895\pi$
$863$	−12.4373	−0.423371	−0.211685	+	0.977338i	$0.567895\pi$
$864$	17.3839	0.591411
$865$	15.4965	0.526895
$866$	−8.93237	−0.303534
$867$	−116.355	−3.95163
$868$	0	0
$869$	−12.2404	−0.415229
$870$	22.8945	0.776196
$871$	−53.5354	−1.81398
$872$	−1.45857	−0.0493933
$873$	−31.5485	−1.06776
$874$	−3.42068	−0.115706
$875$	0	0
$876$	−34.0900	−1.15179
$877$	34.4809	1.16434	0.582169	−	0.813068i	$-0.302204\pi$
$877$	34.4809	1.16434	0.582169	+	0.813068i	$0.302204\pi$
$878$	−0.300986	−0.0101578
$879$	−35.7748	−1.20665
$880$	1.00000	0.0337100
$881$	−27.3839	−0.922585	−0.461293	−	0.887248i	$-0.652614\pi$
$881$	−27.3839	−0.922585	−0.461293	+	0.887248i	$0.652614\pi$
$882$	0	0
$883$	22.0900	0.743386	0.371693	−	0.928356i	$-0.378777\pi$
$883$	22.0900	0.743386	0.371693	+	0.928356i	$0.378777\pi$
$884$	−48.1516	−1.61951
$885$	−26.3909	−0.887122
$886$	−30.7677	−1.03366
$887$	−25.7890	−0.865909	−0.432954	−	0.901416i	$-0.642529\pi$
$887$	−25.7890	−0.865909	−0.432954	+	0.901416i	$0.642529\pi$
$888$	−21.8874	−0.734493
$889$	0	0
$890$	−8.69193	−0.291354
$891$	33.5793	1.12495
$892$	−0.188383	−0.00630752
$893$	2.76771	0.0926178
$894$	−1.51063	−0.0505231
$895$	−13.8874	−0.464204
$896$	0	0
$897$	41.4122	1.38271
$898$	1.19547	0.0398934
$899$	−41.0545	−1.36924
$900$	8.19547	0.273182
$901$	49.2344	1.64024
$902$	−9.34596	−0.311187
$903$	0	0
$904$	14.0000	0.465633
$905$	−18.7819	−0.624331
$906$	64.3541	2.13802
$907$	−45.4596	−1.50946	−0.754731	−	0.656034i	$-0.772233\pi$
$907$	−45.4596	−1.50946	−0.754731	+	0.656034i	$0.772233\pi$
$908$	6.99291	0.232068
$909$	−56.5035	−1.87410
$910$	0	0
$911$	−15.8506	−0.525153	−0.262576	−	0.964911i	$-0.584572\pi$
$911$	−15.8506	−0.525153	−0.262576	+	0.964911i	$0.584572\pi$
$912$	−6.18838	−0.204918
$913$	1.30807	0.0432909
$914$	25.7748	0.852554
$915$	15.0687	0.498156
$916$	9.19547	0.303827
$917$	0	0
$918$	125.085	4.12842
$919$	18.6314	0.614593	0.307296	−	0.951614i	$-0.400576\pi$
$919$	18.6314	0.614593	0.307296	+	0.951614i	$0.400576\pi$
$920$	−1.84951	−0.0609764
$921$	−30.3909	−1.00142
$922$	11.5722	0.381111
$923$	−2.01418	−0.0662974
$924$	0	0
$925$	−6.54143	−0.215081
$926$	32.9182	1.08176
$927$	86.7025	2.84768
$928$	−6.84242	−0.224613
$929$	29.2486	0.959616	0.479808	−	0.877374i	$-0.340706\pi$
$929$	29.2486	0.959616	0.479808	+	0.877374i	$0.340706\pi$
$930$	−20.0758	−0.658311
$931$	0	0
$932$	−0.992912	−0.0325239
$933$	−38.0900	−1.24701
$934$	−14.6399	−0.479031
$935$	7.19547	0.235317
$936$	54.8435	1.79262
$937$	46.4441	1.51726	0.758631	−	0.651521i	$-0.225869\pi$
$937$	46.4441	1.51726	0.758631	+	0.651521i	$0.225869\pi$
$938$	0	0
$939$	−79.0460	−2.57957
$940$	1.49646	0.0488090
$941$	39.2713	1.28021	0.640103	−	0.768289i	$-0.278892\pi$
$941$	39.2713	1.28021	0.640103	+	0.768289i	$0.278892\pi$
$942$	32.4525	1.05736
$943$	17.2854	0.562891
$944$	7.88740	0.256713
$945$	0	0
$946$	−0.503544	−0.0163716
$947$	54.2415	1.76261	0.881306	−	0.472546i	$-0.156665\pi$
$947$	54.2415	1.76261	0.881306	+	0.472546i	$0.156665\pi$
$948$	40.9561	1.33019
$949$	−68.1799	−2.21321
$950$	−1.84951	−0.0600059
$951$	31.9016	1.03448
$952$	0	0
$953$	59.3612	1.92290	0.961449	−	0.274983i	$-0.0886723\pi$
$953$	59.3612	1.92290	0.961449	+	0.274983i	$0.0886723\pi$
$954$	−56.0768	−1.81555
$955$	−6.39094	−0.206806
$956$	−1.14341	−0.0369804
$957$	−22.8945	−0.740074
$958$	10.3909	0.335716
$959$	0	0
$960$	−3.34596	−0.107991
$961$	5.00000	0.161290
$962$	−43.7748	−1.41136
$963$	−61.4370	−1.97978
$964$	−8.33888	−0.268577
$965$	−13.1955	−0.424777
$966$	0	0
$967$	−18.7677	−0.603529	−0.301764	−	0.953383i	$-0.597576\pi$
$967$	−18.7677	−0.603529	−0.301764	+	0.953383i	$0.597576\pi$
$968$	−1.00000	−0.0321412
$969$	−44.5283	−1.43046
$970$	3.84951	0.123600
$971$	59.4370	1.90742	0.953712	−	0.300722i	$-0.0972277\pi$
$971$	59.4370	1.90742	0.953712	+	0.300722i	$0.0972277\pi$
$972$	−60.2036	−1.93103
$973$	0	0
$974$	−39.3091	−1.25955
$975$	22.3909	0.717084
$976$	−4.50354	−0.144155
$977$	−32.7677	−1.04833	−0.524166	−	0.851616i	$-0.675623\pi$
$977$	−32.7677	−1.04833	−0.524166	+	0.851616i	$0.675623\pi$
$978$	−26.7677	−0.855937
$979$	8.69193	0.277795
$980$	0	0
$981$	11.9536	0.381650
$982$	−23.7748	−0.758684
$983$	−13.4207	−0.428053	−0.214027	−	0.976828i	$-0.568658\pi$
$983$	−13.4207	−0.428053	−0.214027	+	0.976828i	$0.568658\pi$
$984$	31.2713	0.996891
$985$	−4.69193	−0.149497
$986$	−49.2344	−1.56794
$987$	0	0
$988$	−12.3768	−0.393757
$989$	0.931308	0.0296139
$990$	−8.19547	−0.260469
$991$	−38.1657	−1.21237	−0.606187	−	0.795322i	$-0.707302\pi$
$991$	−38.1657	−1.21237	−0.606187	+	0.795322i	$0.707302\pi$
$992$	6.00000	0.190500
$993$	−1.68484	−0.0534668
$994$	0	0
$995$	9.49646	0.301058
$996$	−4.37677	−0.138683
$997$	33.6622	1.06609	0.533046	−	0.846086i	$-0.321047\pi$
$997$	33.6622	1.06609	0.533046	+	0.846086i	$0.321047\pi$
$998$	6.11260	0.193491
$999$	113.715	3.59779

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5390.2.a.bz.1.1		3
7.6	odd	2		770.2.a.l.1.3	✓	3
21.20	even	2		6930.2.a.cl.1.3		3
28.27	even	2		6160.2.a.bi.1.1		3
35.13	even	4		3850.2.c.z.1849.6		6
35.27	even	4		3850.2.c.z.1849.1		6
35.34	odd	2		3850.2.a.bu.1.1		3
77.76	even	2		8470.2.a.cl.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.l.1.3	✓	3	7.6	odd	2
3850.2.a.bu.1.1		3	35.34	odd	2
3850.2.c.z.1849.1		6	35.27	even	4
3850.2.c.z.1849.6		6	35.13	even	4
5390.2.a.bz.1.1		3	1.1	even	1	trivial
6160.2.a.bi.1.1		3	28.27	even	2
6930.2.a.cl.1.3		3	21.20	even	2
8470.2.a.cl.1.3		3	77.76	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5390 = 2 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5390.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.34596 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.34596 q^{6} -1.00000 q^{8} +8.19547 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.34596 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.34596 q^{6} -1.00000 q^{8} +8.19547 q^{9} -1.00000 q^{10} +1.00000 q^{11} -3.34596 q^{12} -6.69193 q^{13} -3.34596 q^{15} +1.00000 q^{16} +7.19547 q^{17} -8.19547 q^{18} +1.84951 q^{19} +1.00000 q^{20} -1.00000 q^{22} +1.84951 q^{23} +3.34596 q^{24} +1.00000 q^{25} +6.69193 q^{26} -17.3839 q^{27} +6.84242 q^{29} +3.34596 q^{30} -6.00000 q^{31} -1.00000 q^{32} -3.34596 q^{33} -7.19547 q^{34} +8.19547 q^{36} -6.54143 q^{37} -1.84951 q^{38} +22.3909 q^{39} -1.00000 q^{40} +9.34596 q^{41} +0.503544 q^{43} +1.00000 q^{44} +8.19547 q^{45} -1.84951 q^{46} +1.49646 q^{47} -3.34596 q^{48} -1.00000 q^{50} -24.0758 q^{51} -6.69193 q^{52} +6.84242 q^{53} +17.3839 q^{54} +1.00000 q^{55} -6.18838 q^{57} -6.84242 q^{58} +7.88740 q^{59} -3.34596 q^{60} -4.50354 q^{61} +6.00000 q^{62} +1.00000 q^{64} -6.69193 q^{65} +3.34596 q^{66} +8.00000 q^{67} +7.19547 q^{68} -6.18838 q^{69} +0.300986 q^{71} -8.19547 q^{72} +10.1884 q^{73} +6.54143 q^{74} -3.34596 q^{75} +1.84951 q^{76} -22.3909 q^{78} -12.2404 q^{79} +1.00000 q^{80} +33.5793 q^{81} -9.34596 q^{82} +1.30807 q^{83} +7.19547 q^{85} -0.503544 q^{86} -22.8945 q^{87} -1.00000 q^{88} +8.69193 q^{89} -8.19547 q^{90} +1.84951 q^{92} +20.0758 q^{93} -1.49646 q^{94} +1.84951 q^{95} +3.34596 q^{96} -3.84951 q^{97} +8.19547 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{4} + 3 q^{5} - 3 q^{8} + 11 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^4 + 3 * q^5 - 3 * q^8 + 11 * q^9	\( 3 q - 3 q^{2} + 3 q^{4} + 3 q^{5} - 3 q^{8} + 11 q^{9} - 3 q^{10} + 3 q^{11} + 3 q^{16} + 8 q^{17} - 11 q^{18} + 2 q^{19} + 3 q^{20} - 3 q^{22} + 2 q^{23} + 3 q^{25} - 12 q^{27} + 4 q^{29} - 18 q^{31} - 3 q^{32} - 8 q^{34} + 11 q^{36} + 4 q^{37} - 2 q^{38} + 40 q^{39} - 3 q^{40} + 18 q^{41} + 8 q^{43} + 3 q^{44} + 11 q^{45} - 2 q^{46} - 2 q^{47} - 3 q^{50} - 12 q^{51} + 4 q^{53} + 12 q^{54} + 3 q^{55} + 8 q^{57} - 4 q^{58} - 10 q^{59} - 20 q^{61} + 18 q^{62} + 3 q^{64} + 24 q^{67} + 8 q^{68} + 8 q^{69} + 8 q^{71} - 11 q^{72} + 4 q^{73} - 4 q^{74} + 2 q^{76} - 40 q^{78} - 6 q^{79} + 3 q^{80} + 47 q^{81} - 18 q^{82} + 24 q^{83} + 8 q^{85} - 8 q^{86} - 48 q^{87} - 3 q^{88} + 6 q^{89} - 11 q^{90} + 2 q^{92} + 2 q^{94} + 2 q^{95} - 8 q^{97} + 11 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^4 + 3 * q^5 - 3 * q^8 + 11 * q^9 - 3 * q^10 + 3 * q^11 + 3 * q^16 + 8 * q^17 - 11 * q^18 + 2 * q^19 + 3 * q^20 - 3 * q^22 + 2 * q^23 + 3 * q^25 - 12 * q^27 + 4 * q^29 - 18 * q^31 - 3 * q^32 - 8 * q^34 + 11 * q^36 + 4 * q^37 - 2 * q^38 + 40 * q^39 - 3 * q^40 + 18 * q^41 + 8 * q^43 + 3 * q^44 + 11 * q^45 - 2 * q^46 - 2 * q^47 - 3 * q^50 - 12 * q^51 + 4 * q^53 + 12 * q^54 + 3 * q^55 + 8 * q^57 - 4 * q^58 - 10 * q^59 - 20 * q^61 + 18 * q^62 + 3 * q^64 + 24 * q^67 + 8 * q^68 + 8 * q^69 + 8 * q^71 - 11 * q^72 + 4 * q^73 - 4 * q^74 + 2 * q^76 - 40 * q^78 - 6 * q^79 + 3 * q^80 + 47 * q^81 - 18 * q^82 + 24 * q^83 + 8 * q^85 - 8 * q^86 - 48 * q^87 - 3 * q^88 + 6 * q^89 - 11 * q^90 + 2 * q^92 + 2 * q^94 + 2 * q^95 - 8 * q^97 + 11 * q^99

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