LMFDB - Embedded newform 5550.2.a.cf.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5550,2,Mod(1,5550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5550, 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("5550.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5550 = 2 \cdot 3 \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5550.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:	$44.3169731218$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x - 2 $ x^3 - x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1110)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$3.12489$ of defining polynomial
Character	$\chi$	$=$	5550.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +3.64002 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +3.64002 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.60975 q^{11} +1.00000 q^{12} +2.12489 q^{13} -3.64002 q^{14} +1.00000 q^{16} +0.609747 q^{17} -1.00000 q^{18} +3.48486 q^{19} +3.64002 q^{21} +4.60975 q^{22} -8.76491 q^{23} -1.00000 q^{24} -2.12489 q^{26} +1.00000 q^{27} +3.64002 q^{28} -8.15516 q^{29} -5.76491 q^{31} -1.00000 q^{32} -4.60975 q^{33} -0.609747 q^{34} +1.00000 q^{36} -1.00000 q^{37} -3.48486 q^{38} +2.12489 q^{39} -11.3747 q^{41} -3.64002 q^{42} -12.0147 q^{43} -4.60975 q^{44} +8.76491 q^{46} +1.60975 q^{47} +1.00000 q^{48} +6.24977 q^{49} +0.609747 q^{51} +2.12489 q^{52} -9.24977 q^{53} -1.00000 q^{54} -3.64002 q^{56} +3.48486 q^{57} +8.15516 q^{58} -3.67030 q^{59} +1.45459 q^{61} +5.76491 q^{62} +3.64002 q^{63} +1.00000 q^{64} +4.60975 q^{66} -3.75023 q^{67} +0.609747 q^{68} -8.76491 q^{69} +14.1698 q^{71} -1.00000 q^{72} +6.76491 q^{73} +1.00000 q^{74} +3.48486 q^{76} -16.7796 q^{77} -2.12489 q^{78} -6.64002 q^{79} +1.00000 q^{81} +11.3747 q^{82} -2.90539 q^{83} +3.64002 q^{84} +12.0147 q^{86} -8.15516 q^{87} +4.60975 q^{88} +10.3747 q^{89} +7.73463 q^{91} -8.76491 q^{92} -5.76491 q^{93} -1.60975 q^{94} -1.00000 q^{96} -16.5942 q^{97} -6.24977 q^{98} -4.60975 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - 5 q^{11} + 3 q^{12} - 2 q^{13} - 3 q^{14} + 3 q^{16} - 7 q^{17} - 3 q^{18} + 10 q^{19} + 3 q^{21} + 5 q^{22} - 10 q^{23} - 3 q^{24} + 2 q^{26} + 3 q^{27} + 3 q^{28} - 17 q^{29} - q^{31} - 3 q^{32} - 5 q^{33} + 7 q^{34} + 3 q^{36} - 3 q^{37} - 10 q^{38} - 2 q^{39} - 9 q^{41} - 3 q^{42} - 3 q^{43} - 5 q^{44} + 10 q^{46} - 4 q^{47} + 3 q^{48} + 2 q^{49} - 7 q^{51} - 2 q^{52} - 11 q^{53} - 3 q^{54} - 3 q^{56} + 10 q^{57} + 17 q^{58} - 4 q^{59} + 3 q^{61} + q^{62} + 3 q^{63} + 3 q^{64} + 5 q^{66} - 28 q^{67} - 7 q^{68} - 10 q^{69} + 2 q^{71} - 3 q^{72} + 4 q^{73} + 3 q^{74} + 10 q^{76} - q^{77} + 2 q^{78} - 12 q^{79} + 3 q^{81} + 9 q^{82} - 18 q^{83} + 3 q^{84} + 3 q^{86} - 17 q^{87} + 5 q^{88} + 6 q^{89} + 6 q^{91} - 10 q^{92} - q^{93} + 4 q^{94} - 3 q^{96} - 7 q^{97} - 2 q^{98} - 5 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - 5 * q^11 + 3 * q^12 - 2 * q^13 - 3 * q^14 + 3 * q^16 - 7 * q^17 - 3 * q^18 + 10 * q^19 + 3 * q^21 + 5 * q^22 - 10 * q^23 - 3 * q^24 + 2 * q^26 + 3 * q^27 + 3 * q^28 - 17 * q^29 - q^31 - 3 * q^32 - 5 * q^33 + 7 * q^34 + 3 * q^36 - 3 * q^37 - 10 * q^38 - 2 * q^39 - 9 * q^41 - 3 * q^42 - 3 * q^43 - 5 * q^44 + 10 * q^46 - 4 * q^47 + 3 * q^48 + 2 * q^49 - 7 * q^51 - 2 * q^52 - 11 * q^53 - 3 * q^54 - 3 * q^56 + 10 * q^57 + 17 * q^58 - 4 * q^59 + 3 * q^61 + q^62 + 3 * q^63 + 3 * q^64 + 5 * q^66 - 28 * q^67 - 7 * q^68 - 10 * q^69 + 2 * q^71 - 3 * q^72 + 4 * q^73 + 3 * q^74 + 10 * q^76 - q^77 + 2 * q^78 - 12 * q^79 + 3 * q^81 + 9 * q^82 - 18 * q^83 + 3 * q^84 + 3 * q^86 - 17 * q^87 + 5 * q^88 + 6 * q^89 + 6 * q^91 - 10 * q^92 - q^93 + 4 * q^94 - 3 * q^96 - 7 * q^97 - 2 * q^98 - 5 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	3.64002	1.37580	0.687900	−	0.725806i	$-0.258533\pi$
$7$	3.64002	1.37580	0.687900	+	0.725806i	$0.258533\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−4.60975	−1.38989	−0.694946	−	0.719062i	$-0.744572\pi$
$11$	−4.60975	−1.38989	−0.694946	+	0.719062i	$0.744572\pi$
$12$	1.00000	0.288675
$13$	2.12489	0.589337	0.294669	−	0.955600i	$-0.404791\pi$
$13$	2.12489	0.589337	0.294669	+	0.955600i	$0.404791\pi$
$14$	−3.64002	−0.972837
$15$	0	0
$16$	1.00000	0.250000
$17$	0.609747	0.147885	0.0739427	−	0.997262i	$-0.476442\pi$
$17$	0.609747	0.147885	0.0739427	+	0.997262i	$0.476442\pi$
$18$	−1.00000	−0.235702
$19$	3.48486	0.799482	0.399741	−	0.916628i	$-0.369100\pi$
$19$	3.48486	0.799482	0.399741	+	0.916628i	$0.369100\pi$
$20$	0	0
$21$	3.64002	0.794318
$22$	4.60975	0.982801
$23$	−8.76491	−1.82761	−0.913805	−	0.406153i	$-0.866870\pi$
$23$	−8.76491	−1.82761	−0.913805	+	0.406153i	$0.866870\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	−2.12489	−0.416724
$27$	1.00000	0.192450
$28$	3.64002	0.687900
$29$	−8.15516	−1.51438	−0.757188	−	0.653197i	$-0.773427\pi$
$29$	−8.15516	−1.51438	−0.757188	+	0.653197i	$0.773427\pi$
$30$	0	0
$31$	−5.76491	−1.03541	−0.517704	−	0.855560i	$-0.673213\pi$
$31$	−5.76491	−1.03541	−0.517704	+	0.855560i	$0.673213\pi$
$32$	−1.00000	−0.176777
$33$	−4.60975	−0.802454
$34$	−0.609747	−0.104571
$35$	0	0
$36$	1.00000	0.166667
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−3.48486	−0.565319
$39$	2.12489	0.340254
$40$	0	0
$41$	−11.3747	−1.77642	−0.888211	−	0.459435i	$-0.848052\pi$
$41$	−11.3747	−1.77642	−0.888211	+	0.459435i	$0.848052\pi$
$42$	−3.64002	−0.561668
$43$	−12.0147	−1.83222	−0.916111	−	0.400925i	$-0.868689\pi$
$43$	−12.0147	−1.83222	−0.916111	+	0.400925i	$0.868689\pi$
$44$	−4.60975	−0.694946
$45$	0	0
$46$	8.76491	1.29232
$47$	1.60975	0.234806	0.117403	−	0.993084i	$-0.462543\pi$
$47$	1.60975	0.234806	0.117403	+	0.993084i	$0.462543\pi$
$48$	1.00000	0.144338
$49$	6.24977	0.892824
$50$	0	0
$51$	0.609747	0.0853817
$52$	2.12489	0.294669
$53$	−9.24977	−1.27055	−0.635277	−	0.772284i	$-0.719114\pi$
$53$	−9.24977	−1.27055	−0.635277	+	0.772284i	$0.719114\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−3.64002	−0.486419
$57$	3.48486	0.461581
$58$	8.15516	1.07083
$59$	−3.67030	−0.477832	−0.238916	−	0.971040i	$-0.576792\pi$
$59$	−3.67030	−0.477832	−0.238916	+	0.971040i	$0.576792\pi$
$60$	0	0
$61$	1.45459	0.186241	0.0931203	−	0.995655i	$-0.470316\pi$
$61$	1.45459	0.186241	0.0931203	+	0.995655i	$0.470316\pi$
$62$	5.76491	0.732144
$63$	3.64002	0.458600
$64$	1.00000	0.125000
$65$	0	0
$66$	4.60975	0.567421
$67$	−3.75023	−0.458163	−0.229082	−	0.973407i	$-0.573572\pi$
$67$	−3.75023	−0.458163	−0.229082	+	0.973407i	$0.573572\pi$
$68$	0.609747	0.0739427
$69$	−8.76491	−1.05517
$70$	0	0
$71$	14.1698	1.68165	0.840825	−	0.541306i	$-0.182070\pi$
$71$	14.1698	1.68165	0.840825	+	0.541306i	$0.182070\pi$
$72$	−1.00000	−0.117851
$73$	6.76491	0.791773	0.395886	−	0.918300i	$-0.370437\pi$
$73$	6.76491	0.791773	0.395886	+	0.918300i	$0.370437\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	3.48486	0.399741
$77$	−16.7796	−1.91221
$78$	−2.12489	−0.240596
$79$	−6.64002	−0.747061	−0.373531	−	0.927618i	$-0.621853\pi$
$79$	−6.64002	−0.747061	−0.373531	+	0.927618i	$0.621853\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	11.3747	1.25612
$83$	−2.90539	−0.318908	−0.159454	−	0.987205i	$-0.550973\pi$
$83$	−2.90539	−0.318908	−0.159454	+	0.987205i	$0.550973\pi$
$84$	3.64002	0.397159
$85$	0	0
$86$	12.0147	1.29558
$87$	−8.15516	−0.874325
$88$	4.60975	0.491401
$89$	10.3747	1.09971	0.549856	−	0.835260i	$-0.314683\pi$
$89$	10.3747	1.09971	0.549856	+	0.835260i	$0.314683\pi$
$90$	0	0
$91$	7.73463	0.810810
$92$	−8.76491	−0.913805
$93$	−5.76491	−0.597793
$94$	−1.60975	−0.166033
$95$	0	0
$96$	−1.00000	−0.102062
$97$	−16.5942	−1.68488	−0.842440	−	0.538790i	$-0.818882\pi$
$97$	−16.5942	−1.68488	−0.842440	+	0.538790i	$0.818882\pi$
$98$	−6.24977	−0.631322
$99$	−4.60975	−0.463297
$100$	0	0
$101$	4.06055	0.404040	0.202020	−	0.979381i	$-0.435249\pi$
$101$	4.06055	0.404040	0.202020	+	0.979381i	$0.435249\pi$
$102$	−0.609747	−0.0603740
$103$	3.13957	0.309351	0.154675	−	0.987965i	$-0.450567\pi$
$103$	3.13957	0.309351	0.154675	+	0.987965i	$0.450567\pi$
$104$	−2.12489	−0.208362
$105$	0	0
$106$	9.24977	0.898417
$107$	13.9045	1.34420	0.672098	−	0.740462i	$-0.265393\pi$
$107$	13.9045	1.34420	0.672098	+	0.740462i	$0.265393\pi$
$108$	1.00000	0.0962250
$109$	−6.85952	−0.657023	−0.328511	−	0.944500i	$-0.606547\pi$
$109$	−6.85952	−0.657023	−0.328511	+	0.944500i	$0.606547\pi$
$110$	0	0
$111$	−1.00000	−0.0949158
$112$	3.64002	0.343950
$113$	−10.9844	−1.03333	−0.516663	−	0.856189i	$-0.672826\pi$
$113$	−10.9844	−1.03333	−0.516663	+	0.856189i	$0.672826\pi$
$114$	−3.48486	−0.326387
$115$	0	0
$116$	−8.15516	−0.757188
$117$	2.12489	0.196446
$118$	3.67030	0.337878
$119$	2.21949	0.203461
$120$	0	0
$121$	10.2498	0.931797
$122$	−1.45459	−0.131692
$123$	−11.3747	−1.02562
$124$	−5.76491	−0.517704
$125$	0	0
$126$	−3.64002	−0.324279
$127$	−19.6547	−1.74407	−0.872036	−	0.489441i	$-0.837201\pi$
$127$	−19.6547	−1.74407	−0.872036	+	0.489441i	$0.837201\pi$
$128$	−1.00000	−0.0883883
$129$	−12.0147	−1.05783
$130$	0	0
$131$	−1.54920	−0.135354	−0.0676769	−	0.997707i	$-0.521559\pi$
$131$	−1.54920	−0.135354	−0.0676769	+	0.997707i	$0.521559\pi$
$132$	−4.60975	−0.401227
$133$	12.6850	1.09993
$134$	3.75023	0.323970
$135$	0	0
$136$	−0.609747	−0.0522854
$137$	−16.6400	−1.42165	−0.710827	−	0.703367i	$-0.751679\pi$
$137$	−16.6400	−1.42165	−0.710827	+	0.703367i	$0.751679\pi$
$138$	8.76491	0.746119
$139$	3.04496	0.258270	0.129135	−	0.991627i	$-0.458780\pi$
$139$	3.04496	0.258270	0.129135	+	0.991627i	$0.458780\pi$
$140$	0	0
$141$	1.60975	0.135565
$142$	−14.1698	−1.18911
$143$	−9.79518	−0.819115
$144$	1.00000	0.0833333
$145$	0	0
$146$	−6.76491	−0.559868
$147$	6.24977	0.515472
$148$	−1.00000	−0.0821995
$149$	19.8401	1.62537	0.812684	−	0.582705i	$-0.198006\pi$
$149$	19.8401	1.62537	0.812684	+	0.582705i	$0.198006\pi$
$150$	0	0
$151$	6.59507	0.536699	0.268349	−	0.963322i	$-0.413522\pi$
$151$	6.59507	0.536699	0.268349	+	0.963322i	$0.413522\pi$
$152$	−3.48486	−0.282660
$153$	0.609747	0.0492952
$154$	16.7796	1.35214
$155$	0	0
$156$	2.12489	0.170127
$157$	−10.6741	−0.851884	−0.425942	−	0.904750i	$-0.640057\pi$
$157$	−10.6741	−0.851884	−0.425942	+	0.904750i	$0.640057\pi$
$158$	6.64002	0.528252
$159$	−9.24977	−0.733555
$160$	0	0
$161$	−31.9045	−2.51442
$162$	−1.00000	−0.0785674
$163$	−7.00000	−0.548282	−0.274141	−	0.961689i	$-0.588394\pi$
$163$	−7.00000	−0.548282	−0.274141	+	0.961689i	$0.588394\pi$
$164$	−11.3747	−0.888211
$165$	0	0
$166$	2.90539	0.225502
$167$	−3.17454	−0.245653	−0.122827	−	0.992428i	$-0.539196\pi$
$167$	−3.17454	−0.245653	−0.122827	+	0.992428i	$0.539196\pi$
$168$	−3.64002	−0.280834
$169$	−8.48486	−0.652682
$170$	0	0
$171$	3.48486	0.266494
$172$	−12.0147	−0.916111
$173$	1.96972	0.149755	0.0748777	−	0.997193i	$-0.476143\pi$
$173$	1.96972	0.149755	0.0748777	+	0.997193i	$0.476143\pi$
$174$	8.15516	0.618241
$175$	0	0
$176$	−4.60975	−0.347473
$177$	−3.67030	−0.275877
$178$	−10.3747	−0.777613
$179$	22.7493	1.70036	0.850182	−	0.526489i	$-0.176492\pi$
$179$	22.7493	1.70036	0.850182	+	0.526489i	$0.176492\pi$
$180$	0	0
$181$	11.6703	0.867447	0.433723	−	0.901046i	$-0.357200\pi$
$181$	11.6703	0.867447	0.433723	+	0.901046i	$0.357200\pi$
$182$	−7.73463	−0.573329
$183$	1.45459	0.107526
$184$	8.76491	0.646158
$185$	0	0
$186$	5.76491	0.422704
$187$	−2.81078	−0.205545
$188$	1.60975	0.117403
$189$	3.64002	0.264773
$190$	0	0
$191$	10.2800	0.743838	0.371919	−	0.928265i	$-0.378700\pi$
$191$	10.2800	0.743838	0.371919	+	0.928265i	$0.378700\pi$
$192$	1.00000	0.0721688
$193$	6.00000	0.431889	0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000	0.431889	0.215945	+	0.976406i	$0.430717\pi$
$194$	16.5942	1.19139
$195$	0	0
$196$	6.24977	0.446412
$197$	22.4839	1.60191	0.800957	−	0.598721i	$-0.204324\pi$
$197$	22.4839	1.60191	0.800957	+	0.598721i	$0.204324\pi$
$198$	4.60975	0.327600
$199$	26.5601	1.88280	0.941398	−	0.337299i	$-0.109513\pi$
$199$	26.5601	1.88280	0.941398	+	0.337299i	$0.109513\pi$
$200$	0	0
$201$	−3.75023	−0.264521
$202$	−4.06055	−0.285699
$203$	−29.6850	−2.08348
$204$	0.609747	0.0426909
$205$	0	0
$206$	−3.13957	−0.218744
$207$	−8.76491	−0.609203
$208$	2.12489	0.147334
$209$	−16.0643	−1.11119
$210$	0	0
$211$	17.7455	1.22165	0.610826	−	0.791765i	$-0.290837\pi$
$211$	17.7455	1.22165	0.610826	+	0.791765i	$0.290837\pi$
$212$	−9.24977	−0.635277
$213$	14.1698	0.970902
$214$	−13.9045	−0.950490
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	−20.9844	−1.42451
$218$	6.85952	0.464585
$219$	6.76491	0.457130
$220$	0	0
$221$	1.29564	0.0871544
$222$	1.00000	0.0671156
$223$	5.20482	0.348540	0.174270	−	0.984698i	$-0.444243\pi$
$223$	5.20482	0.348540	0.174270	+	0.984698i	$0.444243\pi$
$224$	−3.64002	−0.243209
$225$	0	0
$226$	10.9844	0.730672
$227$	16.3856	1.08755	0.543774	−	0.839232i	$-0.316995\pi$
$227$	16.3856	1.08755	0.543774	+	0.839232i	$0.316995\pi$
$228$	3.48486	0.230791
$229$	−20.6694	−1.36587	−0.682936	−	0.730479i	$-0.739297\pi$
$229$	−20.6694	−1.36587	−0.682936	+	0.730479i	$0.739297\pi$
$230$	0	0
$231$	−16.7796	−1.10402
$232$	8.15516	0.535413
$233$	3.28005	0.214883	0.107442	−	0.994211i	$-0.465734\pi$
$233$	3.28005	0.214883	0.107442	+	0.994211i	$0.465734\pi$
$234$	−2.12489	−0.138908
$235$	0	0
$236$	−3.67030	−0.238916
$237$	−6.64002	−0.431316
$238$	−2.21949	−0.143868
$239$	−23.3553	−1.51073	−0.755364	−	0.655306i	$-0.772540\pi$
$239$	−23.3553	−1.51073	−0.755364	+	0.655306i	$0.772540\pi$
$240$	0	0
$241$	−11.7309	−0.755651	−0.377825	−	0.925877i	$-0.623328\pi$
$241$	−11.7309	−0.755651	−0.377825	+	0.925877i	$0.623328\pi$
$242$	−10.2498	−0.658880
$243$	1.00000	0.0641500
$244$	1.45459	0.0931203
$245$	0	0
$246$	11.3747	0.725222
$247$	7.40493	0.471165
$248$	5.76491	0.366072
$249$	−2.90539	−0.184122
$250$	0	0
$251$	18.6888	1.17962	0.589812	−	0.807541i	$-0.299202\pi$
$251$	18.6888	1.17962	0.589812	+	0.807541i	$0.299202\pi$
$252$	3.64002	0.229300
$253$	40.4040	2.54018
$254$	19.6547	1.23325
$255$	0	0
$256$	1.00000	0.0625000
$257$	30.1542	1.88097	0.940485	−	0.339835i	$-0.110371\pi$
$257$	30.1542	1.88097	0.940485	+	0.339835i	$0.110371\pi$
$258$	12.0147	0.748001
$259$	−3.64002	−0.226180
$260$	0	0
$261$	−8.15516	−0.504792
$262$	1.54920	0.0957096
$263$	15.3141	0.944308	0.472154	−	0.881516i	$-0.343477\pi$
$263$	15.3141	0.944308	0.472154	+	0.881516i	$0.343477\pi$
$264$	4.60975	0.283710
$265$	0	0
$266$	−12.6850	−0.777766
$267$	10.3747	0.634919
$268$	−3.75023	−0.229082
$269$	7.98440	0.486818	0.243409	−	0.969924i	$-0.421734\pi$
$269$	7.98440	0.486818	0.243409	+	0.969924i	$0.421734\pi$
$270$	0	0
$271$	−13.3094	−0.808489	−0.404244	−	0.914651i	$-0.632465\pi$
$271$	−13.3094	−0.808489	−0.404244	+	0.914651i	$0.632465\pi$
$272$	0.609747	0.0369714
$273$	7.73463	0.468121
$274$	16.6400	1.00526
$275$	0	0
$276$	−8.76491	−0.527586
$277$	0.435208	0.0261491	0.0130746	−	0.999915i	$-0.495838\pi$
$277$	0.435208	0.0261491	0.0130746	+	0.999915i	$0.495838\pi$
$278$	−3.04496	−0.182624
$279$	−5.76491	−0.345136
$280$	0	0
$281$	−4.65562	−0.277731	−0.138865	−	0.990311i	$-0.544346\pi$
$281$	−4.65562	−0.277731	−0.138865	+	0.990311i	$0.544346\pi$
$282$	−1.60975	−0.0958591
$283$	−10.2947	−0.611958	−0.305979	−	0.952038i	$-0.598984\pi$
$283$	−10.2947	−0.611958	−0.305979	+	0.952038i	$0.598984\pi$
$284$	14.1698	0.840825
$285$	0	0
$286$	9.79518	0.579201
$287$	−41.4040	−2.44400
$288$	−1.00000	−0.0589256
$289$	−16.6282	−0.978130
$290$	0	0
$291$	−16.5942	−0.972766
$292$	6.76491	0.395886
$293$	−11.9092	−0.695741	−0.347871	−	0.937543i	$-0.613095\pi$
$293$	−11.9092	−0.695741	−0.347871	+	0.937543i	$0.613095\pi$
$294$	−6.24977	−0.364494
$295$	0	0
$296$	1.00000	0.0581238
$297$	−4.60975	−0.267485
$298$	−19.8401	−1.14931
$299$	−18.6244	−1.07708
$300$	0	0
$301$	−43.7337	−2.52077
$302$	−6.59507	−0.379503
$303$	4.06055	0.233273
$304$	3.48486	0.199871
$305$	0	0
$306$	−0.609747	−0.0348569
$307$	−13.8595	−0.791004	−0.395502	−	0.918465i	$-0.629429\pi$
$307$	−13.8595	−0.791004	−0.395502	+	0.918465i	$0.629429\pi$
$308$	−16.7796	−0.956106
$309$	3.13957	0.178604
$310$	0	0
$311$	7.54450	0.427809	0.213905	−	0.976855i	$-0.431382\pi$
$311$	7.54450	0.427809	0.213905	+	0.976855i	$0.431382\pi$
$312$	−2.12489	−0.120298
$313$	4.64002	0.262270	0.131135	−	0.991365i	$-0.458138\pi$
$313$	4.64002	0.262270	0.131135	+	0.991365i	$0.458138\pi$
$314$	10.6741	0.602373
$315$	0	0
$316$	−6.64002	−0.373531
$317$	−10.5142	−0.590538	−0.295269	−	0.955414i	$-0.595409\pi$
$317$	−10.5142	−0.590538	−0.295269	+	0.955414i	$0.595409\pi$
$318$	9.24977	0.518701
$319$	37.5932	2.10482
$320$	0	0
$321$	13.9045	0.776072
$322$	31.9045	1.77797
$323$	2.12489	0.118232
$324$	1.00000	0.0555556
$325$	0	0
$326$	7.00000	0.387694
$327$	−6.85952	−0.379332
$328$	11.3747	0.628060
$329$	5.85952	0.323046
$330$	0	0
$331$	−1.34060	−0.0736860	−0.0368430	−	0.999321i	$-0.511730\pi$
$331$	−1.34060	−0.0736860	−0.0368430	+	0.999321i	$0.511730\pi$
$332$	−2.90539	−0.159454
$333$	−1.00000	−0.0547997
$334$	3.17454	0.173703
$335$	0	0
$336$	3.64002	0.198580
$337$	20.1055	1.09522	0.547608	−	0.836735i	$-0.315538\pi$
$337$	20.1055	1.09522	0.547608	+	0.836735i	$0.315538\pi$
$338$	8.48486	0.461516
$339$	−10.9844	−0.596591
$340$	0	0
$341$	26.5748	1.43910
$342$	−3.48486	−0.188440
$343$	−2.73085	−0.147452
$344$	12.0147	0.647788
$345$	0	0
$346$	−1.96972	−0.105893
$347$	−4.70058	−0.252340	−0.126170	−	0.992009i	$-0.540269\pi$
$347$	−4.70058	−0.252340	−0.126170	+	0.992009i	$0.540269\pi$
$348$	−8.15516	−0.437163
$349$	−9.54920	−0.511157	−0.255578	−	0.966788i	$-0.582266\pi$
$349$	−9.54920	−0.511157	−0.255578	+	0.966788i	$0.582266\pi$
$350$	0	0
$351$	2.12489	0.113418
$352$	4.60975	0.245700
$353$	14.4537	0.769291	0.384646	−	0.923064i	$-0.374324\pi$
$353$	14.4537	0.769291	0.384646	+	0.923064i	$0.374324\pi$
$354$	3.67030	0.195074
$355$	0	0
$356$	10.3747	0.549856
$357$	2.21949	0.117468
$358$	−22.7493	−1.20234
$359$	−11.0790	−0.584728	−0.292364	−	0.956307i	$-0.594442\pi$
$359$	−11.0790	−0.584728	−0.292364	+	0.956307i	$0.594442\pi$
$360$	0	0
$361$	−6.85574	−0.360828
$362$	−11.6703	−0.613377
$363$	10.2498	0.537973
$364$	7.73463	0.405405
$365$	0	0
$366$	−1.45459	−0.0760324
$367$	−10.9201	−0.570023	−0.285012	−	0.958524i	$-0.591997\pi$
$367$	−10.9201	−0.570023	−0.285012	+	0.958524i	$0.591997\pi$
$368$	−8.76491	−0.456902
$369$	−11.3747	−0.592141
$370$	0	0
$371$	−33.6694	−1.74803
$372$	−5.76491	−0.298897
$373$	−5.92007	−0.306530	−0.153265	−	0.988185i	$-0.548979\pi$
$373$	−5.92007	−0.306530	−0.153265	+	0.988185i	$0.548979\pi$
$374$	2.81078	0.145342
$375$	0	0
$376$	−1.60975	−0.0830164
$377$	−17.3288	−0.892478
$378$	−3.64002	−0.187223
$379$	22.5189	1.15672	0.578360	−	0.815782i	$-0.303693\pi$
$379$	22.5189	1.15672	0.578360	+	0.815782i	$0.303693\pi$
$380$	0	0
$381$	−19.6547	−1.00694
$382$	−10.2800	−0.525973
$383$	−27.2039	−1.39005	−0.695027	−	0.718984i	$-0.744608\pi$
$383$	−27.2039	−1.39005	−0.695027	+	0.718984i	$0.744608\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−6.00000	−0.305392
$387$	−12.0147	−0.610740
$388$	−16.5942	−0.842440
$389$	−0.295643	−0.0149897	−0.00749486	−	0.999972i	$-0.502386\pi$
$389$	−0.295643	−0.0149897	−0.00749486	+	0.999972i	$0.502386\pi$
$390$	0	0
$391$	−5.34438	−0.270277
$392$	−6.24977	−0.315661
$393$	−1.54920	−0.0781466
$394$	−22.4839	−1.13272
$395$	0	0
$396$	−4.60975	−0.231649
$397$	14.1287	0.709097	0.354549	−	0.935038i	$-0.384635\pi$
$397$	14.1287	0.709097	0.354549	+	0.935038i	$0.384635\pi$
$398$	−26.5601	−1.33134
$399$	12.6850	0.635043
$400$	0	0
$401$	17.2838	0.863113	0.431557	−	0.902086i	$-0.357965\pi$
$401$	17.2838	0.863113	0.431557	+	0.902086i	$0.357965\pi$
$402$	3.75023	0.187044
$403$	−12.2498	−0.610205
$404$	4.06055	0.202020
$405$	0	0
$406$	29.6850	1.47324
$407$	4.60975	0.228497
$408$	−0.609747	−0.0301870
$409$	5.73085	0.283372	0.141686	−	0.989912i	$-0.454748\pi$
$409$	5.73085	0.283372	0.141686	+	0.989912i	$0.454748\pi$
$410$	0	0
$411$	−16.6400	−0.820792
$412$	3.13957	0.154675
$413$	−13.3600	−0.657401
$414$	8.76491	0.430772
$415$	0	0
$416$	−2.12489	−0.104181
$417$	3.04496	0.149112
$418$	16.0643	0.785732
$419$	4.06433	0.198556	0.0992778	−	0.995060i	$-0.468347\pi$
$419$	4.06433	0.198556	0.0992778	+	0.995060i	$0.468347\pi$
$420$	0	0
$421$	34.7493	1.69358	0.846789	−	0.531929i	$-0.178533\pi$
$421$	34.7493	1.69358	0.846789	+	0.531929i	$0.178533\pi$
$422$	−17.7455	−0.863839
$423$	1.60975	0.0782686
$424$	9.24977	0.449209
$425$	0	0
$426$	−14.1698	−0.686531
$427$	5.29473	0.256230
$428$	13.9045	0.672098
$429$	−9.79518	−0.472916
$430$	0	0
$431$	−9.68120	−0.466327	−0.233163	−	0.972438i	$-0.574908\pi$
$431$	−9.68120	−0.466327	−0.233163	+	0.972438i	$0.574908\pi$
$432$	1.00000	0.0481125
$433$	−23.7346	−1.14061	−0.570307	−	0.821432i	$-0.693176\pi$
$433$	−23.7346	−1.14061	−0.570307	+	0.821432i	$0.693176\pi$
$434$	20.9844	1.00728
$435$	0	0
$436$	−6.85952	−0.328511
$437$	−30.5445	−1.46114
$438$	−6.76491	−0.323240
$439$	7.49576	0.357753	0.178877	−	0.983872i	$-0.442754\pi$
$439$	7.49576	0.357753	0.178877	+	0.983872i	$0.442754\pi$
$440$	0	0
$441$	6.24977	0.297608
$442$	−1.29564	−0.0616275
$443$	27.1202	1.28852	0.644260	−	0.764807i	$-0.277166\pi$
$443$	27.1202	1.28852	0.644260	+	0.764807i	$0.277166\pi$
$444$	−1.00000	−0.0474579
$445$	0	0
$446$	−5.20482	−0.246455
$447$	19.8401	0.938406
$448$	3.64002	0.171975
$449$	−33.2489	−1.56911	−0.784555	−	0.620059i	$-0.787109\pi$
$449$	−33.2489	−1.56911	−0.784555	+	0.620059i	$0.787109\pi$
$450$	0	0
$451$	52.4343	2.46903
$452$	−10.9844	−0.516663
$453$	6.59507	0.309863
$454$	−16.3856	−0.769012
$455$	0	0
$456$	−3.48486	−0.163194
$457$	−37.2635	−1.74311	−0.871557	−	0.490294i	$-0.836890\pi$
$457$	−37.2635	−1.74311	−0.871557	+	0.490294i	$0.836890\pi$
$458$	20.6694	0.965817
$459$	0.609747	0.0284606
$460$	0	0
$461$	−23.5151	−1.09521	−0.547605	−	0.836737i	$-0.684460\pi$
$461$	−23.5151	−1.09521	−0.547605	+	0.836737i	$0.684460\pi$
$462$	16.7796	0.780657
$463$	−32.4196	−1.50667	−0.753334	−	0.657639i	$-0.771555\pi$
$463$	−32.4196	−1.50667	−0.753334	+	0.657639i	$0.771555\pi$
$464$	−8.15516	−0.378594
$465$	0	0
$466$	−3.28005	−0.151945
$467$	−33.6244	−1.55595	−0.777976	−	0.628293i	$-0.783754\pi$
$467$	−33.6244	−1.55595	−0.777976	+	0.628293i	$0.783754\pi$
$468$	2.12489	0.0982229
$469$	−13.6509	−0.630341
$470$	0	0
$471$	−10.6741	−0.491836
$472$	3.67030	0.168939
$473$	55.3846	2.54659
$474$	6.64002	0.304986
$475$	0	0
$476$	2.21949	0.101730
$477$	−9.24977	−0.423518
$478$	23.3553	1.06825
$479$	13.7952	0.630318	0.315159	−	0.949039i	$-0.397942\pi$
$479$	13.7952	0.630318	0.315159	+	0.949039i	$0.397942\pi$
$480$	0	0
$481$	−2.12489	−0.0968864
$482$	11.7309	0.534326
$483$	−31.9045	−1.45170
$484$	10.2498	0.465899
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	−9.03028	−0.409201	−0.204600	−	0.978846i	$-0.565589\pi$
$487$	−9.03028	−0.409201	−0.204600	+	0.978846i	$0.565589\pi$
$488$	−1.45459	−0.0658460
$489$	−7.00000	−0.316551
$490$	0	0
$491$	−27.3737	−1.23536	−0.617680	−	0.786430i	$-0.711927\pi$
$491$	−27.3737	−1.23536	−0.617680	+	0.786430i	$0.711927\pi$
$492$	−11.3747	−0.512809
$493$	−4.97259	−0.223954
$494$	−7.40493	−0.333164
$495$	0	0
$496$	−5.76491	−0.258852
$497$	51.5786	2.31361
$498$	2.90539	0.130194
$499$	0.333481	0.0149287	0.00746434	−	0.999972i	$-0.497624\pi$
$499$	0.333481	0.0149287	0.00746434	+	0.999972i	$0.497624\pi$
$500$	0	0
$501$	−3.17454	−0.141828
$502$	−18.6888	−0.834120
$503$	−12.4390	−0.554627	−0.277314	−	0.960779i	$-0.589444\pi$
$503$	−12.4390	−0.554627	−0.277314	+	0.960779i	$0.589444\pi$
$504$	−3.64002	−0.162140
$505$	0	0
$506$	−40.4040	−1.79618
$507$	−8.48486	−0.376826
$508$	−19.6547	−0.872036
$509$	−36.4234	−1.61444	−0.807219	−	0.590252i	$-0.799028\pi$
$509$	−36.4234	−1.61444	−0.807219	+	0.590252i	$0.799028\pi$
$510$	0	0
$511$	24.6244	1.08932
$512$	−1.00000	−0.0441942
$513$	3.48486	0.153860
$514$	−30.1542	−1.33005
$515$	0	0
$516$	−12.0147	−0.528917
$517$	−7.42053	−0.326354
$518$	3.64002	0.159933
$519$	1.96972	0.0864613
$520$	0	0
$521$	40.8733	1.79069	0.895345	−	0.445372i	$-0.146929\pi$
$521$	40.8733	1.79069	0.895345	+	0.445372i	$0.146929\pi$
$522$	8.15516	0.356942
$523$	19.4693	0.851332	0.425666	−	0.904880i	$-0.360040\pi$
$523$	19.4693	0.851332	0.425666	+	0.904880i	$0.360040\pi$
$524$	−1.54920	−0.0676769
$525$	0	0
$526$	−15.3141	−0.667727
$527$	−3.51514	−0.153122
$528$	−4.60975	−0.200614
$529$	53.8236	2.34016
$530$	0	0
$531$	−3.67030	−0.159277
$532$	12.6850	0.549964
$533$	−24.1698	−1.04691
$534$	−10.3747	−0.448955
$535$	0	0
$536$	3.75023	0.161985
$537$	22.7493	0.981705
$538$	−7.98440	−0.344232
$539$	−28.8099	−1.24093
$540$	0	0
$541$	1.15516	0.0496643	0.0248321	−	0.999692i	$-0.492095\pi$
$541$	1.15516	0.0496643	0.0248321	+	0.999692i	$0.492095\pi$
$542$	13.3094	0.571688
$543$	11.6703	0.500820
$544$	−0.609747	−0.0261427
$545$	0	0
$546$	−7.73463	−0.331012
$547$	7.59885	0.324903	0.162452	−	0.986717i	$-0.448060\pi$
$547$	7.59885	0.324903	0.162452	+	0.986717i	$0.448060\pi$
$548$	−16.6400	−0.710827
$549$	1.45459	0.0620802
$550$	0	0
$551$	−28.4196	−1.21072
$552$	8.76491	0.373059
$553$	−24.1698	−1.02781
$554$	−0.435208	−0.0184902
$555$	0	0
$556$	3.04496	0.129135
$557$	3.73841	0.158402	0.0792008	−	0.996859i	$-0.474763\pi$
$557$	3.73841	0.158402	0.0792008	+	0.996859i	$0.474763\pi$
$558$	5.76491	0.244048
$559$	−25.5298	−1.07980
$560$	0	0
$561$	−2.81078	−0.118671
$562$	4.65562	0.196385
$563$	−23.5033	−0.990547	−0.495273	−	0.868737i	$-0.664932\pi$
$563$	−23.5033	−0.990547	−0.495273	+	0.868737i	$0.664932\pi$
$564$	1.60975	0.0677826
$565$	0	0
$566$	10.2947	0.432720
$567$	3.64002	0.152867
$568$	−14.1698	−0.594553
$569$	−45.2526	−1.89709	−0.948545	−	0.316644i	$-0.897444\pi$
$569$	−45.2526	−1.89709	−0.948545	+	0.316644i	$0.897444\pi$
$570$	0	0
$571$	20.4655	0.856454	0.428227	−	0.903671i	$-0.359138\pi$
$571$	20.4655	0.856454	0.428227	+	0.903671i	$0.359138\pi$
$572$	−9.79518	−0.409557
$573$	10.2800	0.429455
$574$	41.4040	1.72817
$575$	0	0
$576$	1.00000	0.0416667
$577$	23.7796	0.989957	0.494979	−	0.868905i	$-0.335176\pi$
$577$	23.7796	0.989957	0.494979	+	0.868905i	$0.335176\pi$
$578$	16.6282	0.691642
$579$	6.00000	0.249351
$580$	0	0
$581$	−10.5757	−0.438754
$582$	16.5942	0.687850
$583$	42.6391	1.76593
$584$	−6.76491	−0.279934
$585$	0	0
$586$	11.9092	0.491963
$587$	−10.8633	−0.448376	−0.224188	−	0.974546i	$-0.571973\pi$
$587$	−10.8633	−0.448376	−0.224188	+	0.974546i	$0.571973\pi$
$588$	6.24977	0.257736
$589$	−20.0899	−0.827790
$590$	0	0
$591$	22.4839	0.924866
$592$	−1.00000	−0.0410997
$593$	11.5005	0.472267	0.236134	−	0.971721i	$-0.424120\pi$
$593$	11.5005	0.472267	0.236134	+	0.971721i	$0.424120\pi$
$594$	4.60975	0.189140
$595$	0	0
$596$	19.8401	0.812684
$597$	26.5601	1.08703
$598$	18.6244	0.761609
$599$	32.7905	1.33978	0.669891	−	0.742459i	$-0.266341\pi$
$599$	32.7905	1.33978	0.669891	+	0.742459i	$0.266341\pi$
$600$	0	0
$601$	−13.4390	−0.548188	−0.274094	−	0.961703i	$-0.588378\pi$
$601$	−13.4390	−0.548188	−0.274094	+	0.961703i	$0.588378\pi$
$602$	43.7337	1.78245
$603$	−3.75023	−0.152721
$604$	6.59507	0.268349
$605$	0	0
$606$	−4.06055	−0.164949
$607$	−27.9007	−1.13245	−0.566227	−	0.824249i	$-0.691597\pi$
$607$	−27.9007	−1.13245	−0.566227	+	0.824249i	$0.691597\pi$
$608$	−3.48486	−0.141330
$609$	−29.6850	−1.20290
$610$	0	0
$611$	3.42053	0.138380
$612$	0.609747	0.0246476
$613$	−27.3553	−1.10487	−0.552435	−	0.833556i	$-0.686301\pi$
$613$	−27.3553	−1.10487	−0.552435	+	0.833556i	$0.686301\pi$
$614$	13.8595	0.559325
$615$	0	0
$616$	16.7796	0.676069
$617$	38.2985	1.54184	0.770920	−	0.636932i	$-0.219797\pi$
$617$	38.2985	1.54184	0.770920	+	0.636932i	$0.219797\pi$
$618$	−3.13957	−0.126292
$619$	−26.4948	−1.06492	−0.532459	−	0.846456i	$-0.678732\pi$
$619$	−26.4948	−1.06492	−0.532459	+	0.846456i	$0.678732\pi$
$620$	0	0
$621$	−8.76491	−0.351724
$622$	−7.54450	−0.302507
$623$	37.7640	1.51298
$624$	2.12489	0.0850635
$625$	0	0
$626$	−4.64002	−0.185453
$627$	−16.0643	−0.641548
$628$	−10.6741	−0.425942
$629$	−0.609747	−0.0243122
$630$	0	0
$631$	0.666519	0.0265337	0.0132668	−	0.999912i	$-0.495777\pi$
$631$	0.666519	0.0265337	0.0132668	+	0.999912i	$0.495777\pi$
$632$	6.64002	0.264126
$633$	17.7455	0.705322
$634$	10.5142	0.417573
$635$	0	0
$636$	−9.24977	−0.366777
$637$	13.2800	0.526175
$638$	−37.5932	−1.48833
$639$	14.1698	0.560550
$640$	0	0
$641$	22.5436	0.890418	0.445209	−	0.895427i	$-0.353129\pi$
$641$	22.5436	0.890418	0.445209	+	0.895427i	$0.353129\pi$
$642$	−13.9045	−0.548766
$643$	6.52982	0.257511	0.128755	−	0.991676i	$-0.458902\pi$
$643$	6.52982	0.257511	0.128755	+	0.991676i	$0.458902\pi$
$644$	−31.9045	−1.25721
$645$	0	0
$646$	−2.12489	−0.0836025
$647$	−0.294727	−0.0115869	−0.00579345	−	0.999983i	$-0.501844\pi$
$647$	−0.294727	−0.0115869	−0.00579345	+	0.999983i	$0.501844\pi$
$648$	−1.00000	−0.0392837
$649$	16.9192	0.664135
$650$	0	0
$651$	−20.9844	−0.822444
$652$	−7.00000	−0.274141
$653$	−7.68968	−0.300920	−0.150460	−	0.988616i	$-0.548076\pi$
$653$	−7.68968	−0.300920	−0.150460	+	0.988616i	$0.548076\pi$
$654$	6.85952	0.268228
$655$	0	0
$656$	−11.3747	−0.444106
$657$	6.76491	0.263924
$658$	−5.85952	−0.228428
$659$	−2.22041	−0.0864949	−0.0432475	−	0.999064i	$-0.513770\pi$
$659$	−2.22041	−0.0864949	−0.0432475	+	0.999064i	$0.513770\pi$
$660$	0	0
$661$	7.76869	0.302167	0.151084	−	0.988521i	$-0.451724\pi$
$661$	7.76869	0.302167	0.151084	+	0.988521i	$0.451724\pi$
$662$	1.34060	0.0521039
$663$	1.29564	0.0503186
$664$	2.90539	0.112751
$665$	0	0
$666$	1.00000	0.0387492
$667$	71.4792	2.76769
$668$	−3.17454	−0.122827
$669$	5.20482	0.201230
$670$	0	0
$671$	−6.70527	−0.258854
$672$	−3.64002	−0.140417
$673$	−10.9853	−0.423453	−0.211726	−	0.977329i	$-0.567909\pi$
$673$	−10.9853	−0.423453	−0.211726	+	0.977329i	$0.567909\pi$
$674$	−20.1055	−0.774435
$675$	0	0
$676$	−8.48486	−0.326341
$677$	32.9229	1.26533	0.632666	−	0.774425i	$-0.281961\pi$
$677$	32.9229	1.26533	0.632666	+	0.774425i	$0.281961\pi$
$678$	10.9844	0.421853
$679$	−60.4031	−2.31806
$680$	0	0
$681$	16.3856	0.627896
$682$	−26.5748	−1.01760
$683$	−34.4343	−1.31759	−0.658796	−	0.752322i	$-0.728934\pi$
$683$	−34.4343	−1.31759	−0.658796	+	0.752322i	$0.728934\pi$
$684$	3.48486	0.133247
$685$	0	0
$686$	2.73085	0.104264
$687$	−20.6694	−0.788586
$688$	−12.0147	−0.458055
$689$	−19.6547	−0.748785
$690$	0	0
$691$	7.02558	0.267266	0.133633	−	0.991031i	$-0.457336\pi$
$691$	7.02558	0.267266	0.133633	+	0.991031i	$0.457336\pi$
$692$	1.96972	0.0748777
$693$	−16.7796	−0.637404
$694$	4.70058	0.178431
$695$	0	0
$696$	8.15516	0.309121
$697$	−6.93567	−0.262707
$698$	9.54920	0.361442
$699$	3.28005	0.124063
$700$	0	0
$701$	19.6509	0.742205	0.371103	−	0.928592i	$-0.378980\pi$
$701$	19.6509	0.742205	0.371103	+	0.928592i	$0.378980\pi$
$702$	−2.12489	−0.0801986
$703$	−3.48486	−0.131434
$704$	−4.60975	−0.173736
$705$	0	0
$706$	−14.4537	−0.543971
$707$	14.7805	0.555878
$708$	−3.67030	−0.137938
$709$	−28.7990	−1.08157	−0.540784	−	0.841162i	$-0.681872\pi$
$709$	−28.7990	−1.08157	−0.540784	+	0.841162i	$0.681872\pi$
$710$	0	0
$711$	−6.64002	−0.249020
$712$	−10.3747	−0.388807
$713$	50.5289	1.89232
$714$	−2.21949	−0.0830625
$715$	0	0
$716$	22.7493	0.850182
$717$	−23.3553	−0.872219
$718$	11.0790	0.413465
$719$	−52.2598	−1.94896	−0.974480	−	0.224475i	$-0.927933\pi$
$719$	−52.2598	−1.94896	−0.974480	+	0.224475i	$0.927933\pi$
$720$	0	0
$721$	11.4281	0.425604
$722$	6.85574	0.255144
$723$	−11.7309	−0.436275
$724$	11.6703	0.433723
$725$	0	0
$726$	−10.2498	−0.380405
$727$	20.3591	0.755076	0.377538	−	0.925994i	$-0.376771\pi$
$727$	20.3591	0.755076	0.377538	+	0.925994i	$0.376771\pi$
$728$	−7.73463	−0.286665
$729$	1.00000	0.0370370
$730$	0	0
$731$	−7.32592	−0.270959
$732$	1.45459	0.0537630
$733$	22.1433	0.817883	0.408942	−	0.912561i	$-0.365898\pi$
$733$	22.1433	0.817883	0.408942	+	0.912561i	$0.365898\pi$
$734$	10.9201	0.403067
$735$	0	0
$736$	8.76491	0.323079
$737$	17.2876	0.636797
$738$	11.3747	0.418707
$739$	34.6429	1.27436	0.637180	−	0.770715i	$-0.280101\pi$
$739$	34.6429	1.27436	0.637180	+	0.770715i	$0.280101\pi$
$740$	0	0
$741$	7.40493	0.272027
$742$	33.6694	1.23604
$743$	46.4049	1.70243	0.851216	−	0.524816i	$-0.175866\pi$
$743$	46.4049	1.70243	0.851216	+	0.524816i	$0.175866\pi$
$744$	5.76491	0.211352
$745$	0	0
$746$	5.92007	0.216749
$747$	−2.90539	−0.106303
$748$	−2.81078	−0.102772
$749$	50.6126	1.84934
$750$	0	0
$751$	−25.6585	−0.936291	−0.468146	−	0.883651i	$-0.655078\pi$
$751$	−25.6585	−0.936291	−0.468146	+	0.883651i	$0.655078\pi$
$752$	1.60975	0.0587014
$753$	18.6888	0.681056
$754$	17.3288	0.631077
$755$	0	0
$756$	3.64002	0.132386
$757$	−21.2157	−0.771098	−0.385549	−	0.922687i	$-0.625988\pi$
$757$	−21.2157	−0.771098	−0.385549	+	0.922687i	$0.625988\pi$
$758$	−22.5189	−0.817924
$759$	40.4040	1.46657
$760$	0	0
$761$	−41.2654	−1.49587	−0.747934	−	0.663773i	$-0.768954\pi$
$761$	−41.2654	−1.49587	−0.747934	+	0.663773i	$0.768954\pi$
$762$	19.6547	0.712015
$763$	−24.9688	−0.903932
$764$	10.2800	0.371919
$765$	0	0
$766$	27.2039	0.982917
$767$	−7.79897	−0.281604
$768$	1.00000	0.0360844
$769$	15.2607	0.550314	0.275157	−	0.961399i	$-0.411270\pi$
$769$	15.2607	0.550314	0.275157	+	0.961399i	$0.411270\pi$
$770$	0	0
$771$	30.1542	1.08598
$772$	6.00000	0.215945
$773$	−26.4693	−0.952033	−0.476017	−	0.879436i	$-0.657920\pi$
$773$	−26.4693	−0.952033	−0.476017	+	0.879436i	$0.657920\pi$
$774$	12.0147	0.431859
$775$	0	0
$776$	16.5942	0.595695
$777$	−3.64002	−0.130585
$778$	0.295643	0.0105993
$779$	−39.6391	−1.42022
$780$	0	0
$781$	−65.3194	−2.33731
$782$	5.34438	0.191115
$783$	−8.15516	−0.291442
$784$	6.24977	0.223206
$785$	0	0
$786$	1.54920	0.0552580
$787$	−37.7190	−1.34454	−0.672269	−	0.740307i	$-0.734680\pi$
$787$	−37.7190	−1.34454	−0.672269	+	0.740307i	$0.734680\pi$
$788$	22.4839	0.800957
$789$	15.3141	0.545197
$790$	0	0
$791$	−39.9835	−1.42165
$792$	4.60975	0.163800
$793$	3.09083	0.109759
$794$	−14.1287	−0.501408
$795$	0	0
$796$	26.5601	0.941398
$797$	26.6013	0.942265	0.471133	−	0.882062i	$-0.343845\pi$
$797$	26.6013	0.942265	0.471133	+	0.882062i	$0.343845\pi$
$798$	−12.6850	−0.449043
$799$	0.981539	0.0347244
$800$	0	0
$801$	10.3747	0.366570
$802$	−17.2838	−0.610313
$803$	−31.1845	−1.10048
$804$	−3.75023	−0.132260
$805$	0	0
$806$	12.2498	0.431480
$807$	7.98440	0.281064
$808$	−4.06055	−0.142850
$809$	−39.7834	−1.39871	−0.699354	−	0.714775i	$-0.746529\pi$
$809$	−39.7834	−1.39871	−0.699354	+	0.714775i	$0.746529\pi$
$810$	0	0
$811$	−3.62156	−0.127170	−0.0635851	−	0.997976i	$-0.520253\pi$
$811$	−3.62156	−0.127170	−0.0635851	+	0.997976i	$0.520253\pi$
$812$	−29.6850	−1.04174
$813$	−13.3094	−0.466781
$814$	−4.60975	−0.161572
$815$	0	0
$816$	0.609747	0.0213454
$817$	−41.8695	−1.46483
$818$	−5.73085	−0.200375
$819$	7.73463	0.270270
$820$	0	0
$821$	29.4537	1.02794	0.513970	−	0.857808i	$-0.328174\pi$
$821$	29.4537	1.02794	0.513970	+	0.857808i	$0.328174\pi$
$822$	16.6400	0.580387
$823$	−31.6159	−1.10206	−0.551031	−	0.834485i	$-0.685766\pi$
$823$	−31.6159	−1.10206	−0.551031	+	0.834485i	$0.685766\pi$
$824$	−3.13957	−0.109372
$825$	0	0
$826$	13.3600	0.464853
$827$	−27.3359	−0.950562	−0.475281	−	0.879834i	$-0.657654\pi$
$827$	−27.3359	−0.950562	−0.475281	+	0.879834i	$0.657654\pi$
$828$	−8.76491	−0.304602
$829$	14.6391	0.508437	0.254219	−	0.967147i	$-0.418182\pi$
$829$	14.6391	0.508437	0.254219	+	0.967147i	$0.418182\pi$
$830$	0	0
$831$	0.435208	0.0150972
$832$	2.12489	0.0736671
$833$	3.81078	0.132036
$834$	−3.04496	−0.105438
$835$	0	0
$836$	−16.0643	−0.555597
$837$	−5.76491	−0.199264
$838$	−4.06433	−0.140400
$839$	16.1386	0.557168	0.278584	−	0.960412i	$-0.410135\pi$
$839$	16.1386	0.557168	0.278584	+	0.960412i	$0.410135\pi$
$840$	0	0
$841$	37.5067	1.29333
$842$	−34.7493	−1.19754
$843$	−4.65562	−0.160348
$844$	17.7455	0.610826
$845$	0	0
$846$	−1.60975	−0.0553443
$847$	37.3094	1.28197
$848$	−9.24977	−0.317638
$849$	−10.2947	−0.353314
$850$	0	0
$851$	8.76491	0.300457
$852$	14.1698	0.485451
$853$	9.44369	0.323346	0.161673	−	0.986844i	$-0.448311\pi$
$853$	9.44369	0.323346	0.161673	+	0.986844i	$0.448311\pi$
$854$	−5.29473	−0.181182
$855$	0	0
$856$	−13.9045	−0.475245
$857$	−40.0091	−1.36668	−0.683342	−	0.730099i	$-0.739474\pi$
$857$	−40.0091	−1.36668	−0.683342	+	0.730099i	$0.739474\pi$
$858$	9.79518	0.334402
$859$	24.5739	0.838449	0.419225	−	0.907883i	$-0.362302\pi$
$859$	24.5739	0.838449	0.419225	+	0.907883i	$0.362302\pi$
$860$	0	0
$861$	−41.4040	−1.41105
$862$	9.68120	0.329743
$863$	−2.43613	−0.0829267	−0.0414633	−	0.999140i	$-0.513202\pi$
$863$	−2.43613	−0.0829267	−0.0414633	+	0.999140i	$0.513202\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	23.7346	0.806536
$867$	−16.6282	−0.564724
$868$	−20.9844	−0.712257
$869$	30.6088	1.03833
$870$	0	0
$871$	−7.96881	−0.270013
$872$	6.85952	0.232293
$873$	−16.5942	−0.561627
$874$	30.5445	1.03318
$875$	0	0
$876$	6.76491	0.228565
$877$	13.0861	0.441887	0.220944	−	0.975287i	$-0.429086\pi$
$877$	13.0861	0.441887	0.220944	+	0.975287i	$0.429086\pi$
$878$	−7.49576	−0.252970
$879$	−11.9092	−0.401686
$880$	0	0
$881$	−38.8539	−1.30902	−0.654511	−	0.756053i	$-0.727125\pi$
$881$	−38.8539	−1.30902	−0.654511	+	0.756053i	$0.727125\pi$
$882$	−6.24977	−0.210441
$883$	9.40023	0.316343	0.158172	−	0.987412i	$-0.449440\pi$
$883$	9.40023	0.316343	0.158172	+	0.987412i	$0.449440\pi$
$884$	1.29564	0.0435772
$885$	0	0
$886$	−27.1202	−0.911121
$887$	23.0156	0.772788	0.386394	−	0.922334i	$-0.373720\pi$
$887$	23.0156	0.772788	0.386394	+	0.922334i	$0.373720\pi$
$888$	1.00000	0.0335578
$889$	−71.5436	−2.39949
$890$	0	0
$891$	−4.60975	−0.154432
$892$	5.20482	0.174270
$893$	5.60975	0.187723
$894$	−19.8401	−0.663554
$895$	0	0
$896$	−3.64002	−0.121605
$897$	−18.6244	−0.621852
$898$	33.2489	1.10953
$899$	47.0138	1.56800
$900$	0	0
$901$	−5.64002	−0.187896
$902$	−52.4343	−1.74587
$903$	−43.7337	−1.45537
$904$	10.9844	0.365336
$905$	0	0
$906$	−6.59507	−0.219106
$907$	24.8860	0.826327	0.413163	−	0.910657i	$-0.364424\pi$
$907$	24.8860	0.826327	0.413163	+	0.910657i	$0.364424\pi$
$908$	16.3856	0.543774
$909$	4.06055	0.134680
$910$	0	0
$911$	−5.49863	−0.182178	−0.0910888	−	0.995843i	$-0.529035\pi$
$911$	−5.49863	−0.182178	−0.0910888	+	0.995843i	$0.529035\pi$
$912$	3.48486	0.115395
$913$	13.3931	0.443247
$914$	37.2635	1.23257
$915$	0	0
$916$	−20.6694	−0.682936
$917$	−5.63911	−0.186220
$918$	−0.609747	−0.0201247
$919$	−29.0790	−0.959228	−0.479614	−	0.877480i	$-0.659223\pi$
$919$	−29.0790	−0.959228	−0.479614	+	0.877480i	$0.659223\pi$
$920$	0	0
$921$	−13.8595	−0.456687
$922$	23.5151	0.774430
$923$	30.1093	0.991059
$924$	−16.7796	−0.552008
$925$	0	0
$926$	32.4196	1.06537
$927$	3.13957	0.103117
$928$	8.15516	0.267706
$929$	−48.3931	−1.58773	−0.793863	−	0.608096i	$-0.791933\pi$
$929$	−48.3931	−1.58773	−0.793863	+	0.608096i	$0.791933\pi$
$930$	0	0
$931$	21.7796	0.713797
$932$	3.28005	0.107442
$933$	7.54450	0.246996
$934$	33.6244	1.10022
$935$	0	0
$936$	−2.12489	−0.0694541
$937$	13.4399	0.439063	0.219531	−	0.975605i	$-0.429547\pi$
$937$	13.4399	0.439063	0.219531	+	0.975605i	$0.429547\pi$
$938$	13.6509	0.445718
$939$	4.64002	0.151421
$940$	0	0
$941$	−29.3482	−0.956723	−0.478361	−	0.878163i	$-0.658769\pi$
$941$	−29.3482	−0.956723	−0.478361	+	0.878163i	$0.658769\pi$
$942$	10.6741	0.347780
$943$	99.6978	3.24661
$944$	−3.67030	−0.119458
$945$	0	0
$946$	−55.3846	−1.80071
$947$	21.3435	0.693569	0.346785	−	0.937945i	$-0.387273\pi$
$947$	21.3435	0.693569	0.346785	+	0.937945i	$0.387273\pi$
$948$	−6.64002	−0.215658
$949$	14.3747	0.466621
$950$	0	0
$951$	−10.5142	−0.340947
$952$	−2.21949	−0.0719342
$953$	−19.2389	−0.623208	−0.311604	−	0.950212i	$-0.600866\pi$
$953$	−19.2389	−0.623208	−0.311604	+	0.950212i	$0.600866\pi$
$954$	9.24977	0.299472
$955$	0	0
$956$	−23.3553	−0.755364
$957$	37.5932	1.21522
$958$	−13.7952	−0.445702
$959$	−60.5701	−1.95591
$960$	0	0
$961$	2.23417	0.0720701
$962$	2.12489	0.0685091
$963$	13.9045	0.448065
$964$	−11.7309	−0.377825
$965$	0	0
$966$	31.9045	1.02651
$967$	21.8813	0.703656	0.351828	−	0.936065i	$-0.385560\pi$
$967$	21.8813	0.703656	0.351828	+	0.936065i	$0.385560\pi$
$968$	−10.2498	−0.329440
$969$	2.12489	0.0682612
$970$	0	0
$971$	−49.8236	−1.59892	−0.799458	−	0.600722i	$-0.794880\pi$
$971$	−49.8236	−1.59892	−0.799458	+	0.600722i	$0.794880\pi$
$972$	1.00000	0.0320750
$973$	11.0837	0.355327
$974$	9.03028	0.289349
$975$	0	0
$976$	1.45459	0.0465602
$977$	−1.98910	−0.0636370	−0.0318185	−	0.999494i	$-0.510130\pi$
$977$	−1.98910	−0.0636370	−0.0318185	+	0.999494i	$0.510130\pi$
$978$	7.00000	0.223835
$979$	−47.8245	−1.52848
$980$	0	0
$981$	−6.85952	−0.219008
$982$	27.3737	0.873531
$983$	−35.6950	−1.13849	−0.569246	−	0.822167i	$-0.692765\pi$
$983$	−35.6950	−1.13849	−0.569246	+	0.822167i	$0.692765\pi$
$984$	11.3747	0.362611
$985$	0	0
$986$	4.97259	0.158359
$987$	5.85952	0.186511
$988$	7.40493	0.235582
$989$	105.308	3.34859
$990$	0	0
$991$	50.2333	1.59571	0.797856	−	0.602848i	$-0.205967\pi$
$991$	50.2333	1.59571	0.797856	+	0.602848i	$0.205967\pi$
$992$	5.76491	0.183036
$993$	−1.34060	−0.0425426
$994$	−51.5786	−1.63597
$995$	0	0
$996$	−2.90539	−0.0920608
$997$	−36.9036	−1.16875	−0.584374	−	0.811485i	$-0.698660\pi$
$997$	−36.9036	−1.16875	−0.584374	+	0.811485i	$0.698660\pi$
$998$	−0.333481	−0.0105562
$999$	−1.00000	−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5550.2.a.cf.1.3		3
5.2	odd	4		1110.2.d.i.889.3	✓	6
5.3	odd	4		1110.2.d.i.889.6	yes	6
5.4	even	2		5550.2.a.cg.1.1		3
15.2	even	4		3330.2.d.n.1999.4		6
15.8	even	4		3330.2.d.n.1999.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.d.i.889.3	✓	6	5.2	odd	4
1110.2.d.i.889.6	yes	6	5.3	odd	4
3330.2.d.n.1999.1		6	15.8	even	4
3330.2.d.n.1999.4		6	15.2	even	4
5550.2.a.cf.1.3		3	1.1	even	1	trivial
5550.2.a.cg.1.1		3	5.4	even	2

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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5550 = 2 \cdot 3 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5550.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +3.64002 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +3.64002 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.60975 q^{11} +1.00000 q^{12} +2.12489 q^{13} -3.64002 q^{14} +1.00000 q^{16} +0.609747 q^{17} -1.00000 q^{18} +3.48486 q^{19} +3.64002 q^{21} +4.60975 q^{22} -8.76491 q^{23} -1.00000 q^{24} -2.12489 q^{26} +1.00000 q^{27} +3.64002 q^{28} -8.15516 q^{29} -5.76491 q^{31} -1.00000 q^{32} -4.60975 q^{33} -0.609747 q^{34} +1.00000 q^{36} -1.00000 q^{37} -3.48486 q^{38} +2.12489 q^{39} -11.3747 q^{41} -3.64002 q^{42} -12.0147 q^{43} -4.60975 q^{44} +8.76491 q^{46} +1.60975 q^{47} +1.00000 q^{48} +6.24977 q^{49} +0.609747 q^{51} +2.12489 q^{52} -9.24977 q^{53} -1.00000 q^{54} -3.64002 q^{56} +3.48486 q^{57} +8.15516 q^{58} -3.67030 q^{59} +1.45459 q^{61} +5.76491 q^{62} +3.64002 q^{63} +1.00000 q^{64} +4.60975 q^{66} -3.75023 q^{67} +0.609747 q^{68} -8.76491 q^{69} +14.1698 q^{71} -1.00000 q^{72} +6.76491 q^{73} +1.00000 q^{74} +3.48486 q^{76} -16.7796 q^{77} -2.12489 q^{78} -6.64002 q^{79} +1.00000 q^{81} +11.3747 q^{82} -2.90539 q^{83} +3.64002 q^{84} +12.0147 q^{86} -8.15516 q^{87} +4.60975 q^{88} +10.3747 q^{89} +7.73463 q^{91} -8.76491 q^{92} -5.76491 q^{93} -1.60975 q^{94} -1.00000 q^{96} -16.5942 q^{97} -6.24977 q^{98} -4.60975 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - 5 q^{11} + 3 q^{12} - 2 q^{13} - 3 q^{14} + 3 q^{16} - 7 q^{17} - 3 q^{18} + 10 q^{19} + 3 q^{21} + 5 q^{22} - 10 q^{23} - 3 q^{24} + 2 q^{26} + 3 q^{27} + 3 q^{28} - 17 q^{29} - q^{31} - 3 q^{32} - 5 q^{33} + 7 q^{34} + 3 q^{36} - 3 q^{37} - 10 q^{38} - 2 q^{39} - 9 q^{41} - 3 q^{42} - 3 q^{43} - 5 q^{44} + 10 q^{46} - 4 q^{47} + 3 q^{48} + 2 q^{49} - 7 q^{51} - 2 q^{52} - 11 q^{53} - 3 q^{54} - 3 q^{56} + 10 q^{57} + 17 q^{58} - 4 q^{59} + 3 q^{61} + q^{62} + 3 q^{63} + 3 q^{64} + 5 q^{66} - 28 q^{67} - 7 q^{68} - 10 q^{69} + 2 q^{71} - 3 q^{72} + 4 q^{73} + 3 q^{74} + 10 q^{76} - q^{77} + 2 q^{78} - 12 q^{79} + 3 q^{81} + 9 q^{82} - 18 q^{83} + 3 q^{84} + 3 q^{86} - 17 q^{87} + 5 q^{88} + 6 q^{89} + 6 q^{91} - 10 q^{92} - q^{93} + 4 q^{94} - 3 q^{96} - 7 q^{97} - 2 q^{98} - 5 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - 5 * q^11 + 3 * q^12 - 2 * q^13 - 3 * q^14 + 3 * q^16 - 7 * q^17 - 3 * q^18 + 10 * q^19 + 3 * q^21 + 5 * q^22 - 10 * q^23 - 3 * q^24 + 2 * q^26 + 3 * q^27 + 3 * q^28 - 17 * q^29 - q^31 - 3 * q^32 - 5 * q^33 + 7 * q^34 + 3 * q^36 - 3 * q^37 - 10 * q^38 - 2 * q^39 - 9 * q^41 - 3 * q^42 - 3 * q^43 - 5 * q^44 + 10 * q^46 - 4 * q^47 + 3 * q^48 + 2 * q^49 - 7 * q^51 - 2 * q^52 - 11 * q^53 - 3 * q^54 - 3 * q^56 + 10 * q^57 + 17 * q^58 - 4 * q^59 + 3 * q^61 + q^62 + 3 * q^63 + 3 * q^64 + 5 * q^66 - 28 * q^67 - 7 * q^68 - 10 * q^69 + 2 * q^71 - 3 * q^72 + 4 * q^73 + 3 * q^74 + 10 * q^76 - q^77 + 2 * q^78 - 12 * q^79 + 3 * q^81 + 9 * q^82 - 18 * q^83 + 3 * q^84 + 3 * q^86 - 17 * q^87 + 5 * q^88 + 6 * q^89 + 6 * q^91 - 10 * q^92 - q^93 + 4 * q^94 - 3 * q^96 - 7 * q^97 - 2 * q^98 - 5 * q^99

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