LMFDB - Embedded newform 2793.2.a.bm.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2793,2,Mod(1,2793)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2793, 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("2793.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2793 = 3 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2793.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:	$22.3022172845$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 13x^{6} - x^{5} + 51x^{4} + 3x^{3} - 65x^{2} - 6x + 16 $ x^8 - 13x^6 - x^5 + 51x^4 + 3x^3 - 65x^2 - 6*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 399)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.24973$ of defining polynomial
Character	$\chi$	$=$	2793.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.24973 q^{2} -1.00000 q^{3} -0.438184 q^{4} +3.99593 q^{5} -1.24973 q^{6} -3.04706 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.24973 q^{2} -1.00000 q^{3} -0.438184 q^{4} +3.99593 q^{5} -1.24973 q^{6} -3.04706 q^{8} +1.00000 q^{9} +4.99382 q^{10} -2.36861 q^{11} +0.438184 q^{12} -2.18914 q^{13} -3.99593 q^{15} -2.93163 q^{16} -2.27220 q^{17} +1.24973 q^{18} -1.00000 q^{19} -1.75095 q^{20} -2.96011 q^{22} -8.59867 q^{23} +3.04706 q^{24} +10.9675 q^{25} -2.73582 q^{26} -1.00000 q^{27} -0.735824 q^{29} -4.99382 q^{30} -9.90898 q^{31} +2.43040 q^{32} +2.36861 q^{33} -2.83963 q^{34} -0.438184 q^{36} +8.19438 q^{37} -1.24973 q^{38} +2.18914 q^{39} -12.1759 q^{40} -8.35871 q^{41} -0.800311 q^{43} +1.03789 q^{44} +3.99593 q^{45} -10.7460 q^{46} -4.92130 q^{47} +2.93163 q^{48} +13.7063 q^{50} +2.27220 q^{51} +0.959247 q^{52} -3.27829 q^{53} -1.24973 q^{54} -9.46479 q^{55} +1.00000 q^{57} -0.919579 q^{58} -3.56096 q^{59} +1.75095 q^{60} +2.75619 q^{61} -12.3835 q^{62} +8.90058 q^{64} -8.74765 q^{65} +2.96011 q^{66} -3.70108 q^{67} +0.995642 q^{68} +8.59867 q^{69} +7.30367 q^{71} -3.04706 q^{72} -7.38246 q^{73} +10.2407 q^{74} -10.9675 q^{75} +0.438184 q^{76} +2.73582 q^{78} +0.916892 q^{79} -11.7146 q^{80} +1.00000 q^{81} -10.4461 q^{82} +4.91925 q^{83} -9.07955 q^{85} -1.00017 q^{86} +0.735824 q^{87} +7.21729 q^{88} +17.7015 q^{89} +4.99382 q^{90} +3.76780 q^{92} +9.90898 q^{93} -6.15028 q^{94} -3.99593 q^{95} -2.43040 q^{96} +13.3590 q^{97} -2.36861 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3} + 10 q^{4} - 5 q^{5} - 3 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^3 + 10 * q^4 - 5 * q^5 - 3 * q^8 + 8 * q^9	$ 8 q - 8 q^{3} + 10 q^{4} - 5 q^{5} - 3 q^{8} + 8 q^{9} - 3 q^{10} - 7 q^{11} - 10 q^{12} - 6 q^{13} + 5 q^{15} + 10 q^{16} - 8 q^{19} - 16 q^{20} + 18 q^{22} - 9 q^{23} + 3 q^{24} + 15 q^{25} - 12 q^{26} - 8 q^{27} + 4 q^{29} + 3 q^{30} - 11 q^{31} - 26 q^{32} + 7 q^{33} - 16 q^{34} + 10 q^{36} + 17 q^{37} + 6 q^{39} - 3 q^{40} - 17 q^{41} + 8 q^{43} - 31 q^{44} - 5 q^{45} + q^{46} - 29 q^{47} - 10 q^{48} + 30 q^{50} - 25 q^{52} - 6 q^{53} - 21 q^{55} + 8 q^{57} - 37 q^{58} - 7 q^{59} + 16 q^{60} - 2 q^{61} - 39 q^{62} + 29 q^{64} - 13 q^{65} - 18 q^{66} + 13 q^{67} + 14 q^{68} + 9 q^{69} + 18 q^{71} - 3 q^{72} - 20 q^{73} - 26 q^{74} - 15 q^{75} - 10 q^{76} + 12 q^{78} - 3 q^{79} - 35 q^{80} + 8 q^{81} - 5 q^{82} - 36 q^{83} + 5 q^{85} - 51 q^{86} - 4 q^{87} + 53 q^{88} - q^{89} - 3 q^{90} + 15 q^{92} + 11 q^{93} - 30 q^{94} + 5 q^{95} + 26 q^{96} + 3 q^{97} - 7 q^{99}+O(q^{100}) $ 8 * q - 8 * q^3 + 10 * q^4 - 5 * q^5 - 3 * q^8 + 8 * q^9 - 3 * q^10 - 7 * q^11 - 10 * q^12 - 6 * q^13 + 5 * q^15 + 10 * q^16 - 8 * q^19 - 16 * q^20 + 18 * q^22 - 9 * q^23 + 3 * q^24 + 15 * q^25 - 12 * q^26 - 8 * q^27 + 4 * q^29 + 3 * q^30 - 11 * q^31 - 26 * q^32 + 7 * q^33 - 16 * q^34 + 10 * q^36 + 17 * q^37 + 6 * q^39 - 3 * q^40 - 17 * q^41 + 8 * q^43 - 31 * q^44 - 5 * q^45 + q^46 - 29 * q^47 - 10 * q^48 + 30 * q^50 - 25 * q^52 - 6 * q^53 - 21 * q^55 + 8 * q^57 - 37 * q^58 - 7 * q^59 + 16 * q^60 - 2 * q^61 - 39 * q^62 + 29 * q^64 - 13 * q^65 - 18 * q^66 + 13 * q^67 + 14 * q^68 + 9 * q^69 + 18 * q^71 - 3 * q^72 - 20 * q^73 - 26 * q^74 - 15 * q^75 - 10 * q^76 + 12 * q^78 - 3 * q^79 - 35 * q^80 + 8 * q^81 - 5 * q^82 - 36 * q^83 + 5 * q^85 - 51 * q^86 - 4 * q^87 + 53 * q^88 - q^89 - 3 * q^90 + 15 * q^92 + 11 * q^93 - 30 * q^94 + 5 * q^95 + 26 * q^96 + 3 * q^97 - 7 * 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 $

$2$	1.24973	0.883690	0.441845	−	0.897091i	$-0.354324\pi$
$2$	1.24973	0.883690	0.441845	+	0.897091i	$0.354324\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.438184	−0.219092
$5$	3.99593	1.78703	0.893517	−	0.449029i	$-0.148230\pi$
$5$	3.99593	1.78703	0.893517	+	0.449029i	$0.148230\pi$
$6$	−1.24973	−0.510199
$7$	0	0
$7$	0	0
$8$	−3.04706	−1.07730
$9$	1.00000	0.333333
$10$	4.99382	1.57918
$11$	−2.36861	−0.714162	−0.357081	−	0.934073i	$-0.616228\pi$
$11$	−2.36861	−0.714162	−0.357081	+	0.934073i	$0.616228\pi$
$12$	0.438184	0.126493
$13$	−2.18914	−0.607158	−0.303579	−	0.952806i	$-0.598182\pi$
$13$	−2.18914	−0.607158	−0.303579	+	0.952806i	$0.598182\pi$
$14$	0	0
$15$	−3.99593	−1.03174
$16$	−2.93163	−0.732906
$17$	−2.27220	−0.551089	−0.275545	−	0.961288i	$-0.588858\pi$
$17$	−2.27220	−0.551089	−0.275545	+	0.961288i	$0.588858\pi$
$18$	1.24973	0.294563
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−1.75095	−0.391525
$21$	0	0
$22$	−2.96011	−0.631098
$23$	−8.59867	−1.79295	−0.896473	−	0.443098i	$-0.853879\pi$
$23$	−8.59867	−1.79295	−0.896473	+	0.443098i	$0.853879\pi$
$24$	3.04706	0.621979
$25$	10.9675	2.19349
$26$	−2.73582	−0.536539
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−0.735824	−0.136639	−0.0683196	−	0.997663i	$-0.521764\pi$
$29$	−0.735824	−0.136639	−0.0683196	+	0.997663i	$0.521764\pi$
$30$	−4.99382	−0.911742
$31$	−9.90898	−1.77971	−0.889853	−	0.456248i	$-0.849193\pi$
$31$	−9.90898	−1.77971	−0.889853	+	0.456248i	$0.849193\pi$
$32$	2.43040	0.429638
$33$	2.36861	0.412321
$34$	−2.83963	−0.486992
$35$	0	0
$36$	−0.438184	−0.0730307
$37$	8.19438	1.34715	0.673574	−	0.739120i	$-0.264758\pi$
$37$	8.19438	1.34715	0.673574	+	0.739120i	$0.264758\pi$
$38$	−1.24973	−0.202732
$39$	2.18914	0.350543
$40$	−12.1759	−1.92517
$41$	−8.35871	−1.30541	−0.652705	−	0.757612i	$-0.726366\pi$
$41$	−8.35871	−1.30541	−0.652705	+	0.757612i	$0.726366\pi$
$42$	0	0
$43$	−0.800311	−0.122046	−0.0610232	−	0.998136i	$-0.519436\pi$
$43$	−0.800311	−0.122046	−0.0610232	+	0.998136i	$0.519436\pi$
$44$	1.03789	0.156467
$45$	3.99593	0.595678
$46$	−10.7460	−1.58441
$47$	−4.92130	−0.717846	−0.358923	−	0.933367i	$-0.616856\pi$
$47$	−4.92130	−0.717846	−0.358923	+	0.933367i	$0.616856\pi$
$48$	2.93163	0.423144
$49$	0	0
$50$	13.7063	1.93837
$51$	2.27220	0.318172
$52$	0.959247	0.133024
$53$	−3.27829	−0.450307	−0.225154	−	0.974323i	$-0.572288\pi$
$53$	−3.27829	−0.450307	−0.225154	+	0.974323i	$0.572288\pi$
$54$	−1.24973	−0.170066
$55$	−9.46479	−1.27623
$56$	0	0
$57$	1.00000	0.132453
$58$	−0.919579	−0.120747
$59$	−3.56096	−0.463598	−0.231799	−	0.972764i	$-0.574461\pi$
$59$	−3.56096	−0.463598	−0.231799	+	0.972764i	$0.574461\pi$
$60$	1.75095	0.226047
$61$	2.75619	0.352893	0.176447	−	0.984310i	$-0.443540\pi$
$61$	2.75619	0.352893	0.176447	+	0.984310i	$0.443540\pi$
$62$	−12.3835	−1.57271
$63$	0	0
$64$	8.90058	1.11257
$65$	−8.74765	−1.08501
$66$	2.96011	0.364364
$67$	−3.70108	−0.452159	−0.226080	−	0.974109i	$-0.572591\pi$
$67$	−3.70108	−0.452159	−0.226080	+	0.974109i	$0.572591\pi$
$68$	0.995642	0.120739
$69$	8.59867	1.03516
$70$	0	0
$71$	7.30367	0.866786	0.433393	−	0.901205i	$-0.357316\pi$
$71$	7.30367	0.866786	0.433393	+	0.901205i	$0.357316\pi$
$72$	−3.04706	−0.359100
$73$	−7.38246	−0.864052	−0.432026	−	0.901861i	$-0.642201\pi$
$73$	−7.38246	−0.864052	−0.432026	+	0.901861i	$0.642201\pi$
$74$	10.2407	1.19046
$75$	−10.9675	−1.26641
$76$	0.438184	0.0502632
$77$	0	0
$78$	2.73582	0.309771
$79$	0.916892	0.103158	0.0515792	−	0.998669i	$-0.483575\pi$
$79$	0.916892	0.103158	0.0515792	+	0.998669i	$0.483575\pi$
$80$	−11.7146	−1.30973
$81$	1.00000	0.111111
$82$	−10.4461	−1.15358
$83$	4.91925	0.539957	0.269979	−	0.962866i	$-0.412983\pi$
$83$	4.91925	0.539957	0.269979	+	0.962866i	$0.412983\pi$
$84$	0	0
$85$	−9.07955	−0.984815
$86$	−1.00017	−0.107851
$87$	0.735824	0.0788887
$88$	7.21729	0.769366
$89$	17.7015	1.87635	0.938176	−	0.346159i	$-0.112514\pi$
$89$	17.7015	1.87635	0.938176	+	0.346159i	$0.112514\pi$
$90$	4.99382	0.526395
$91$	0	0
$92$	3.76780	0.392821
$93$	9.90898	1.02751
$94$	−6.15028	−0.634353
$95$	−3.99593	−0.409974
$96$	−2.43040	−0.248051
$97$	13.3590	1.35640	0.678201	−	0.734877i	$-0.262760\pi$
$97$	13.3590	1.35640	0.678201	+	0.734877i	$0.262760\pi$
$98$	0	0
$99$	−2.36861	−0.238054
$100$	−4.80577	−0.480577
$101$	−11.2752	−1.12193	−0.560964	−	0.827840i	$-0.689569\pi$
$101$	−11.2752	−1.12193	−0.560964	+	0.827840i	$0.689569\pi$
$102$	2.83963	0.281165
$103$	−9.87999	−0.973504	−0.486752	−	0.873540i	$-0.661818\pi$
$103$	−9.87999	−0.973504	−0.486752	+	0.873540i	$0.661818\pi$
$104$	6.67044	0.654091
$105$	0	0
$106$	−4.09696	−0.397932
$107$	6.93760	0.670683	0.335342	−	0.942097i	$-0.391148\pi$
$107$	6.93760	0.670683	0.335342	+	0.942097i	$0.391148\pi$
$108$	0.438184	0.0421643
$109$	3.69992	0.354388	0.177194	−	0.984176i	$-0.443298\pi$
$109$	3.69992	0.354388	0.177194	+	0.984176i	$0.443298\pi$
$110$	−11.8284	−1.12779
$111$	−8.19438	−0.777776
$112$	0	0
$113$	−2.09680	−0.197250	−0.0986252	−	0.995125i	$-0.531445\pi$
$113$	−2.09680	−0.197250	−0.0986252	+	0.995125i	$0.531445\pi$
$114$	1.24973	0.117048
$115$	−34.3597	−3.20406
$116$	0.322427	0.0299366
$117$	−2.18914	−0.202386
$118$	−4.45023	−0.409677
$119$	0	0
$120$	12.1759	1.11150
$121$	−5.38970	−0.489973
$122$	3.44448	0.311848
$123$	8.35871	0.753679
$124$	4.34196	0.389920
$125$	23.8455	2.13281
$126$	0	0
$127$	10.7759	0.956206	0.478103	−	0.878304i	$-0.341325\pi$
$127$	10.7759	0.956206	0.478103	+	0.878304i	$0.341325\pi$
$128$	6.26250	0.553532
$129$	0.800311	0.0704635
$130$	−10.9322	−0.958814
$131$	−0.840542	−0.0734385	−0.0367192	−	0.999326i	$-0.511691\pi$
$131$	−0.840542	−0.0734385	−0.0367192	+	0.999326i	$0.511691\pi$
$132$	−1.03789	−0.0903364
$133$	0	0
$134$	−4.62534	−0.399569
$135$	−3.99593	−0.343915
$136$	6.92353	0.593688
$137$	2.56197	0.218884	0.109442	−	0.993993i	$-0.465094\pi$
$137$	2.56197	0.218884	0.109442	+	0.993993i	$0.465094\pi$
$138$	10.7460	0.914759
$139$	−10.8739	−0.922313	−0.461156	−	0.887319i	$-0.652565\pi$
$139$	−10.8739	−0.922313	−0.461156	+	0.887319i	$0.652565\pi$
$140$	0	0
$141$	4.92130	0.414449
$142$	9.12759	0.765970
$143$	5.18521	0.433609
$144$	−2.93163	−0.244302
$145$	−2.94030	−0.244179
$146$	−9.22605	−0.763554
$147$	0	0
$148$	−3.59065	−0.295149
$149$	−22.0617	−1.80737	−0.903684	−	0.428201i	$-0.859148\pi$
$149$	−22.0617	−1.80737	−0.903684	+	0.428201i	$0.859148\pi$
$150$	−13.7063	−1.11912
$151$	−3.17917	−0.258717	−0.129359	−	0.991598i	$-0.541292\pi$
$151$	−3.17917	−0.258717	−0.129359	+	0.991598i	$0.541292\pi$
$152$	3.04706	0.247149
$153$	−2.27220	−0.183696
$154$	0	0
$155$	−39.5956	−3.18040
$156$	−0.959247	−0.0768012
$157$	−22.6389	−1.80678	−0.903390	−	0.428819i	$-0.858930\pi$
$157$	−22.6389	−1.80678	−0.903390	+	0.428819i	$0.858930\pi$
$158$	1.14586	0.0911601
$159$	3.27829	0.259985
$160$	9.71170	0.767777
$161$	0	0
$162$	1.24973	0.0981878
$163$	−14.6296	−1.14588	−0.572940	−	0.819597i	$-0.694197\pi$
$163$	−14.6296	−1.14588	−0.572940	+	0.819597i	$0.694197\pi$
$164$	3.66266	0.286005
$165$	9.46479	0.736833
$166$	6.14771	0.477155
$167$	−17.8027	−1.37762	−0.688808	−	0.724944i	$-0.741866\pi$
$167$	−17.8027	−1.37762	−0.688808	+	0.724944i	$0.741866\pi$
$168$	0	0
$169$	−8.20767	−0.631359
$170$	−11.3469	−0.870271
$171$	−1.00000	−0.0764719
$172$	0.350684	0.0267394
$173$	−24.9345	−1.89573	−0.947866	−	0.318670i	$-0.896764\pi$
$173$	−24.9345	−1.89573	−0.947866	+	0.318670i	$0.896764\pi$
$174$	0.919579	0.0697131
$175$	0	0
$176$	6.94387	0.523414
$177$	3.56096	0.267658
$178$	22.1220	1.65811
$179$	13.6341	1.01906	0.509530	−	0.860453i	$-0.329819\pi$
$179$	13.6341	1.01906	0.509530	+	0.860453i	$0.329819\pi$
$180$	−1.75095	−0.130508
$181$	−3.79249	−0.281893	−0.140947	−	0.990017i	$-0.545015\pi$
$181$	−3.79249	−0.281893	−0.140947	+	0.990017i	$0.545015\pi$
$182$	0	0
$183$	−2.75619	−0.203743
$184$	26.2007	1.93154
$185$	32.7442	2.40740
$186$	12.3835	0.908003
$187$	5.38195	0.393567
$188$	2.15644	0.157274
$189$	0	0
$190$	−4.99382	−0.362290
$191$	10.0366	0.726222	0.363111	−	0.931746i	$-0.381715\pi$
$191$	10.0366	0.726222	0.363111	+	0.931746i	$0.381715\pi$
$192$	−8.90058	−0.642344
$193$	18.9894	1.36689	0.683444	−	0.730003i	$-0.260482\pi$
$193$	18.9894	1.36689	0.683444	+	0.730003i	$0.260482\pi$
$194$	16.6951	1.19864
$195$	8.74765	0.626432
$196$	0	0
$197$	3.08525	0.219815	0.109908	−	0.993942i	$-0.464945\pi$
$197$	3.08525	0.219815	0.109908	+	0.993942i	$0.464945\pi$
$198$	−2.96011	−0.210366
$199$	−18.8541	−1.33653	−0.668266	−	0.743923i	$-0.732963\pi$
$199$	−18.8541	−1.33653	−0.668266	+	0.743923i	$0.732963\pi$
$200$	−33.4185	−2.36305
$201$	3.70108	0.261054
$202$	−14.0910	−0.991436
$203$	0	0
$204$	−0.995642	−0.0697089
$205$	−33.4008	−2.33281
$206$	−12.3473	−0.860276
$207$	−8.59867	−0.597649
$208$	6.41774	0.444990
$209$	2.36861	0.163840
$210$	0	0
$211$	−19.9172	−1.37115	−0.685577	−	0.728000i	$-0.740450\pi$
$211$	−19.9172	−1.37115	−0.685577	+	0.728000i	$0.740450\pi$
$212$	1.43649	0.0986588
$213$	−7.30367	−0.500439
$214$	8.67010	0.592676
$215$	−3.19799	−0.218101
$216$	3.04706	0.207326
$217$	0	0
$218$	4.62389	0.313169
$219$	7.38246	0.498860
$220$	4.14732	0.279612
$221$	4.97416	0.334598
$222$	−10.2407	−0.687313
$223$	12.3503	0.827040	0.413520	−	0.910495i	$-0.364299\pi$
$223$	12.3503	0.827040	0.413520	+	0.910495i	$0.364299\pi$
$224$	0	0
$225$	10.9675	0.731164
$226$	−2.62043	−0.174308
$227$	10.5379	0.699428	0.349714	−	0.936857i	$-0.386279\pi$
$227$	10.5379	0.699428	0.349714	+	0.936857i	$0.386279\pi$
$228$	−0.438184	−0.0290195
$229$	21.9463	1.45025	0.725126	−	0.688616i	$-0.241781\pi$
$229$	21.9463	1.45025	0.725126	+	0.688616i	$0.241781\pi$
$230$	−42.9402	−2.83139
$231$	0	0
$232$	2.24210	0.147201
$233$	−6.61044	−0.433064	−0.216532	−	0.976275i	$-0.569475\pi$
$233$	−6.61044	−0.433064	−0.216532	+	0.976275i	$0.569475\pi$
$234$	−2.73582	−0.178846
$235$	−19.6652	−1.28282
$236$	1.56036	0.101571
$237$	−0.916892	−0.0595586
$238$	0	0
$239$	16.2362	1.05023	0.525115	−	0.851031i	$-0.324022\pi$
$239$	16.2362	1.05023	0.525115	+	0.851031i	$0.324022\pi$
$240$	11.7146	0.756172
$241$	14.1559	0.911859	0.455929	−	0.890016i	$-0.349307\pi$
$241$	14.1559	0.911859	0.455929	+	0.890016i	$0.349307\pi$
$242$	−6.73565	−0.432984
$243$	−1.00000	−0.0641500
$244$	−1.20772	−0.0773162
$245$	0	0
$246$	10.4461	0.666019
$247$	2.18914	0.139292
$248$	30.1933	1.91728
$249$	−4.91925	−0.311745
$250$	29.8004	1.88474
$251$	−14.5157	−0.916224	−0.458112	−	0.888895i	$-0.651474\pi$
$251$	−14.5157	−0.916224	−0.458112	+	0.888895i	$0.651474\pi$
$252$	0	0
$253$	20.3669	1.28045
$254$	13.4669	0.844989
$255$	9.07955	0.568583
$256$	−9.97476	−0.623422
$257$	3.33012	0.207727	0.103864	−	0.994592i	$-0.466879\pi$
$257$	3.33012	0.207727	0.103864	+	0.994592i	$0.466879\pi$
$258$	1.00017	0.0622679
$259$	0	0
$260$	3.83308	0.237718
$261$	−0.735824	−0.0455464
$262$	−1.05045	−0.0648969
$263$	23.9111	1.47442	0.737211	−	0.675662i	$-0.236142\pi$
$263$	23.9111	1.47442	0.737211	+	0.675662i	$0.236142\pi$
$264$	−7.21729	−0.444194
$265$	−13.0998	−0.804715
$266$	0	0
$267$	−17.7015	−1.08331
$268$	1.62176	0.0990646
$269$	−18.2581	−1.11321	−0.556607	−	0.830776i	$-0.687897\pi$
$269$	−18.2581	−1.11321	−0.556607	+	0.830776i	$0.687897\pi$
$270$	−4.99382	−0.303914
$271$	−9.10046	−0.552814	−0.276407	−	0.961041i	$-0.589144\pi$
$271$	−9.10046	−0.552814	−0.276407	+	0.961041i	$0.589144\pi$
$272$	6.66124	0.403897
$273$	0	0
$274$	3.20176	0.193425
$275$	−25.9776	−1.56651
$276$	−3.76780	−0.226795
$277$	12.9101	0.775690	0.387845	−	0.921725i	$-0.373220\pi$
$277$	12.9101	0.775690	0.387845	+	0.921725i	$0.373220\pi$
$278$	−13.5894	−0.815038
$279$	−9.90898	−0.593235
$280$	0	0
$281$	30.7965	1.83716	0.918582	−	0.395232i	$-0.129336\pi$
$281$	30.7965	1.83716	0.918582	+	0.395232i	$0.129336\pi$
$282$	6.15028	0.366244
$283$	23.2702	1.38327	0.691635	−	0.722247i	$-0.256891\pi$
$283$	23.2702	1.38327	0.691635	+	0.722247i	$0.256891\pi$
$284$	−3.20035	−0.189906
$285$	3.99593	0.236698
$286$	6.48009	0.383176
$287$	0	0
$288$	2.43040	0.143213
$289$	−11.8371	−0.696301
$290$	−3.67457	−0.215778
$291$	−13.3590	−0.783119
$292$	3.23488	0.189307
$293$	8.18298	0.478055	0.239027	−	0.971013i	$-0.423171\pi$
$293$	8.18298	0.478055	0.239027	+	0.971013i	$0.423171\pi$
$294$	0	0
$295$	−14.2294	−0.828466
$296$	−24.9688	−1.45128
$297$	2.36861	0.137440
$298$	−27.5711	−1.59715
$299$	18.8237	1.08860
$300$	4.80577	0.277461
$301$	0	0
$302$	−3.97309	−0.228626
$303$	11.2752	0.647745
$304$	2.93163	0.168140
$305$	11.0135	0.630633
$306$	−2.83963	−0.162331
$307$	19.1256	1.09156	0.545778	−	0.837930i	$-0.316234\pi$
$307$	19.1256	1.09156	0.545778	+	0.837930i	$0.316234\pi$
$308$	0	0
$309$	9.87999	0.562053
$310$	−49.4837	−2.81048
$311$	34.3142	1.94578	0.972890	−	0.231268i	$-0.0742874\pi$
$311$	34.3142	1.94578	0.972890	+	0.231268i	$0.0742874\pi$
$312$	−6.67044	−0.377640
$313$	−2.95548	−0.167054	−0.0835269	−	0.996506i	$-0.526618\pi$
$313$	−2.95548	−0.167054	−0.0835269	+	0.996506i	$0.526618\pi$
$314$	−28.2924	−1.59663
$315$	0	0
$316$	−0.401768	−0.0226012
$317$	−12.5218	−0.703293	−0.351646	−	0.936133i	$-0.614378\pi$
$317$	−12.5218	−0.703293	−0.351646	+	0.936133i	$0.614378\pi$
$318$	4.09696	0.229746
$319$	1.74288	0.0975825
$320$	35.5661	1.98821
$321$	−6.93760	−0.387219
$322$	0	0
$323$	2.27220	0.126429
$324$	−0.438184	−0.0243436
$325$	−24.0093	−1.33180
$326$	−18.2830	−1.01260
$327$	−3.69992	−0.204606
$328$	25.4695	1.40632
$329$	0	0
$330$	11.8284	0.651132
$331$	22.7383	1.24981	0.624906	−	0.780700i	$-0.285137\pi$
$331$	22.7383	1.24981	0.624906	+	0.780700i	$0.285137\pi$
$332$	−2.15554	−0.118300
$333$	8.19438	0.449049
$334$	−22.2485	−1.21739
$335$	−14.7893	−0.808024
$336$	0	0
$337$	4.05805	0.221056	0.110528	−	0.993873i	$-0.464746\pi$
$337$	4.05805	0.221056	0.110528	+	0.993873i	$0.464746\pi$
$338$	−10.2573	−0.557926
$339$	2.09680	0.113883
$340$	3.97852	0.215765
$341$	23.4705	1.27100
$342$	−1.24973	−0.0675775
$343$	0	0
$344$	2.43860	0.131480
$345$	34.3597	1.84986
$346$	−31.1612	−1.67524
$347$	−23.1052	−1.24035	−0.620175	−	0.784464i	$-0.712938\pi$
$347$	−23.1052	−1.24035	−0.620175	+	0.784464i	$0.712938\pi$
$348$	−0.322427	−0.0172839
$349$	17.9043	0.958394	0.479197	−	0.877707i	$-0.340928\pi$
$349$	17.9043	0.958394	0.479197	+	0.877707i	$0.340928\pi$
$350$	0	0
$351$	2.18914	0.116848
$352$	−5.75665	−0.306831
$353$	−8.91202	−0.474339	−0.237169	−	0.971468i	$-0.576220\pi$
$353$	−8.91202	−0.474339	−0.237169	+	0.971468i	$0.576220\pi$
$354$	4.45023	0.236527
$355$	29.1849	1.54898
$356$	−7.75651	−0.411094
$357$	0	0
$358$	17.0389	0.900534
$359$	12.2365	0.645819	0.322909	−	0.946430i	$-0.395339\pi$
$359$	12.2365	0.645819	0.322909	+	0.946430i	$0.395339\pi$
$360$	−12.1759	−0.641724
$361$	1.00000	0.0526316
$362$	−4.73957	−0.249106
$363$	5.38970	0.282886
$364$	0	0
$365$	−29.4998	−1.54409
$366$	−3.44448	−0.180046
$367$	−0.356848	−0.0186273	−0.00931366	−	0.999957i	$-0.502965\pi$
$367$	−0.356848	−0.0186273	−0.00931366	+	0.999957i	$0.502965\pi$
$368$	25.2081	1.31406
$369$	−8.35871	−0.435137
$370$	40.9212	2.12739
$371$	0	0
$372$	−4.34196	−0.225120
$373$	−12.4840	−0.646396	−0.323198	−	0.946331i	$-0.604758\pi$
$373$	−12.4840	−0.646396	−0.323198	+	0.946331i	$0.604758\pi$
$374$	6.72596	0.347791
$375$	−23.8455	−1.23138
$376$	14.9955	0.773335
$377$	1.61082	0.0829616
$378$	0	0
$379$	17.4065	0.894111	0.447056	−	0.894506i	$-0.352473\pi$
$379$	17.4065	0.894111	0.447056	+	0.894506i	$0.352473\pi$
$380$	1.75095	0.0898221
$381$	−10.7759	−0.552066
$382$	12.5430	0.641755
$383$	−26.9538	−1.37727	−0.688636	−	0.725107i	$-0.741790\pi$
$383$	−26.9538	−1.37727	−0.688636	+	0.725107i	$0.741790\pi$
$384$	−6.26250	−0.319582
$385$	0	0
$386$	23.7316	1.20790
$387$	−0.800311	−0.0406821
$388$	−5.85371	−0.297177
$389$	−34.6133	−1.75496	−0.877481	−	0.479611i	$-0.840778\pi$
$389$	−34.6133	−1.75496	−0.877481	+	0.479611i	$0.840778\pi$
$390$	10.9322	0.553572
$391$	19.5379	0.988073
$392$	0	0
$393$	0.840542	0.0423997
$394$	3.85572	0.194248
$395$	3.66384	0.184348
$396$	1.03789	0.0521558
$397$	−17.6794	−0.887306	−0.443653	−	0.896199i	$-0.646318\pi$
$397$	−17.6794	−0.887306	−0.443653	+	0.896199i	$0.646318\pi$
$398$	−23.5624	−1.18108
$399$	0	0
$400$	−32.1525	−1.60762
$401$	−13.9984	−0.699048	−0.349524	−	0.936927i	$-0.613657\pi$
$401$	−13.9984	−0.699048	−0.349524	+	0.936927i	$0.613657\pi$
$402$	4.62534	0.230691
$403$	21.6921	1.08056
$404$	4.94063	0.245806
$405$	3.99593	0.198559
$406$	0	0
$407$	−19.4093	−0.962081
$408$	−6.92353	−0.342766
$409$	30.5465	1.51043	0.755213	−	0.655480i	$-0.227534\pi$
$409$	30.5465	1.51043	0.755213	+	0.655480i	$0.227534\pi$
$410$	−41.7419	−2.06148
$411$	−2.56197	−0.126373
$412$	4.32926	0.213287
$413$	0	0
$414$	−10.7460	−0.528136
$415$	19.6570	0.964922
$416$	−5.32048	−0.260858
$417$	10.8739	0.532497
$418$	2.96011	0.144784
$419$	17.2075	0.840640	0.420320	−	0.907376i	$-0.361918\pi$
$419$	17.2075	0.840640	0.420320	+	0.907376i	$0.361918\pi$
$420$	0	0
$421$	−9.71684	−0.473570	−0.236785	−	0.971562i	$-0.576094\pi$
$421$	−9.71684	−0.473570	−0.236785	+	0.971562i	$0.576094\pi$
$422$	−24.8910	−1.21168
$423$	−4.92130	−0.239282
$424$	9.98915	0.485116
$425$	−24.9202	−1.20881
$426$	−9.12759	−0.442233
$427$	0	0
$428$	−3.03995	−0.146941
$429$	−5.18521	−0.250344
$430$	−3.99661	−0.192734
$431$	−18.5753	−0.894740	−0.447370	−	0.894349i	$-0.647639\pi$
$431$	−18.5753	−0.894740	−0.447370	+	0.894349i	$0.647639\pi$
$432$	2.93163	0.141048
$433$	−16.8441	−0.809474	−0.404737	−	0.914433i	$-0.632637\pi$
$433$	−16.8441	−0.809474	−0.404737	+	0.914433i	$0.632637\pi$
$434$	0	0
$435$	2.94030	0.140977
$436$	−1.62125	−0.0776437
$437$	8.59867	0.411330
$438$	9.22605	0.440838
$439$	−0.376355	−0.0179625	−0.00898123	−	0.999960i	$-0.502859\pi$
$439$	−0.376355	−0.0179625	−0.00898123	+	0.999960i	$0.502859\pi$
$440$	28.8398	1.37488
$441$	0	0
$442$	6.21634	0.295681
$443$	−32.5949	−1.54863	−0.774316	−	0.632800i	$-0.781906\pi$
$443$	−32.5949	−1.54863	−0.774316	+	0.632800i	$0.781906\pi$
$444$	3.59065	0.170405
$445$	70.7338	3.35311
$446$	15.4346	0.730847
$447$	22.0617	1.04348
$448$	0	0
$449$	16.7178	0.788964	0.394482	−	0.918904i	$-0.370924\pi$
$449$	16.7178	0.788964	0.394482	+	0.918904i	$0.370924\pi$
$450$	13.7063	0.646122
$451$	19.7985	0.932274
$452$	0.918786	0.0432160
$453$	3.17917	0.149370
$454$	13.1695	0.618077
$455$	0	0
$456$	−3.04706	−0.142692
$457$	17.5907	0.822857	0.411428	−	0.911442i	$-0.365030\pi$
$457$	17.5907	0.822857	0.411428	+	0.911442i	$0.365030\pi$
$458$	27.4269	1.28157
$459$	2.27220	0.106057
$460$	15.0559	0.701984
$461$	−1.81881	−0.0847103	−0.0423552	−	0.999103i	$-0.513486\pi$
$461$	−1.81881	−0.0847103	−0.0423552	+	0.999103i	$0.513486\pi$
$462$	0	0
$463$	−1.35124	−0.0627976	−0.0313988	−	0.999507i	$-0.509996\pi$
$463$	−1.35124	−0.0627976	−0.0313988	+	0.999507i	$0.509996\pi$
$464$	2.15716	0.100144
$465$	39.5956	1.83620
$466$	−8.26124	−0.382694
$467$	−15.9974	−0.740273	−0.370137	−	0.928977i	$-0.620689\pi$
$467$	−15.9974	−0.740273	−0.370137	+	0.928977i	$0.620689\pi$
$468$	0.959247	0.0443412
$469$	0	0
$470$	−24.5761	−1.13361
$471$	22.6389	1.04315
$472$	10.8505	0.499434
$473$	1.89562	0.0871608
$474$	−1.14586	−0.0526313
$475$	−10.9675	−0.503221
$476$	0	0
$477$	−3.27829	−0.150102
$478$	20.2908	0.928078
$479$	−14.3648	−0.656343	−0.328171	−	0.944618i	$-0.606432\pi$
$479$	−14.3648	−0.656343	−0.328171	+	0.944618i	$0.606432\pi$
$480$	−9.71170	−0.443276
$481$	−17.9386	−0.817931
$482$	17.6909	0.805800
$483$	0	0
$484$	2.36168	0.107349
$485$	53.3816	2.42394
$486$	−1.24973	−0.0566887
$487$	−15.6958	−0.711243	−0.355621	−	0.934630i	$-0.615731\pi$
$487$	−15.6958	−0.711243	−0.355621	+	0.934630i	$0.615731\pi$
$488$	−8.39827	−0.380172
$489$	14.6296	0.661575
$490$	0	0
$491$	38.8742	1.75437	0.877183	−	0.480156i	$-0.159420\pi$
$491$	38.8742	1.75437	0.877183	+	0.480156i	$0.159420\pi$
$492$	−3.66266	−0.165125
$493$	1.67194	0.0753004
$494$	2.73582	0.123091
$495$	−9.46479	−0.425411
$496$	29.0494	1.30436
$497$	0	0
$498$	−6.14771	−0.275485
$499$	43.9616	1.96799	0.983997	−	0.178187i	$-0.0570232\pi$
$499$	43.9616	1.96799	0.983997	+	0.178187i	$0.0570232\pi$
$500$	−10.4487	−0.467282
$501$	17.8027	0.795367
$502$	−18.1407	−0.809658
$503$	−23.9459	−1.06770	−0.533848	−	0.845580i	$-0.679255\pi$
$503$	−23.9459	−1.06770	−0.533848	+	0.845580i	$0.679255\pi$
$504$	0	0
$505$	−45.0551	−2.00492
$506$	25.4530	1.13152
$507$	8.20767	0.364515
$508$	−4.72183	−0.209497
$509$	−18.3847	−0.814887	−0.407444	−	0.913230i	$-0.633580\pi$
$509$	−18.3847	−0.814887	−0.407444	+	0.913230i	$0.633580\pi$
$510$	11.3469	0.502451
$511$	0	0
$512$	−24.9907	−1.10444
$513$	1.00000	0.0441511
$514$	4.16174	0.183567
$515$	−39.4797	−1.73969
$516$	−0.350684	−0.0154380
$517$	11.6566	0.512658
$518$	0	0
$519$	24.9345	1.09450
$520$	26.6546	1.16888
$521$	1.42014	0.0622174	0.0311087	−	0.999516i	$-0.490096\pi$
$521$	1.42014	0.0622174	0.0311087	+	0.999516i	$0.490096\pi$
$522$	−0.919579	−0.0402489
$523$	23.3835	1.02249	0.511245	−	0.859435i	$-0.329184\pi$
$523$	23.3835	1.02249	0.511245	+	0.859435i	$0.329184\pi$
$524$	0.368312	0.0160898
$525$	0	0
$526$	29.8823	1.30293
$527$	22.5152	0.980777
$528$	−6.94387	−0.302193
$529$	50.9371	2.21466
$530$	−16.3712	−0.711118
$531$	−3.56096	−0.154533
$532$	0	0
$533$	18.2984	0.792591
$534$	−22.1220	−0.957312
$535$	27.7222	1.19853
$536$	11.2774	0.487111
$537$	−13.6341	−0.588355
$538$	−22.8176	−0.983737
$539$	0	0
$540$	1.75095	0.0753491
$541$	35.8128	1.53971	0.769856	−	0.638218i	$-0.220328\pi$
$541$	35.8128	1.53971	0.769856	+	0.638218i	$0.220328\pi$
$542$	−11.3731	−0.488516
$543$	3.79249	0.162751
$544$	−5.52235	−0.236769
$545$	14.7846	0.633304
$546$	0	0
$547$	13.7734	0.588909	0.294455	−	0.955665i	$-0.404862\pi$
$547$	13.7734	0.588909	0.294455	+	0.955665i	$0.404862\pi$
$548$	−1.12262	−0.0479557
$549$	2.75619	0.117631
$550$	−32.4649	−1.38431
$551$	0.735824	0.0313472
$552$	−26.2007	−1.11518
$553$	0	0
$554$	16.1340	0.685470
$555$	−32.7442	−1.38991
$556$	4.76478	0.202072
$557$	11.7750	0.498925	0.249462	−	0.968385i	$-0.419746\pi$
$557$	11.7750	0.498925	0.249462	+	0.968385i	$0.419746\pi$
$558$	−12.3835	−0.524236
$559$	1.75199	0.0741014
$560$	0	0
$561$	−5.38195	−0.227226
$562$	38.4871	1.62348
$563$	11.5981	0.488802	0.244401	−	0.969674i	$-0.421409\pi$
$563$	11.5981	0.488802	0.244401	+	0.969674i	$0.421409\pi$
$564$	−2.15644	−0.0908025
$565$	−8.37867	−0.352493
$566$	29.0814	1.22238
$567$	0	0
$568$	−22.2547	−0.933788
$569$	16.2064	0.679409	0.339705	−	0.940532i	$-0.389673\pi$
$569$	16.2064	0.679409	0.339705	+	0.940532i	$0.389673\pi$
$570$	4.99382	0.209168
$571$	−17.9918	−0.752934	−0.376467	−	0.926430i	$-0.622861\pi$
$571$	−17.9918	−0.752934	−0.376467	+	0.926430i	$0.622861\pi$
$572$	−2.27208	−0.0950004
$573$	−10.0366	−0.419284
$574$	0	0
$575$	−94.3055	−3.93281
$576$	8.90058	0.370858
$577$	−23.9012	−0.995019	−0.497509	−	0.867459i	$-0.665752\pi$
$577$	−23.9012	−0.995019	−0.497509	+	0.867459i	$0.665752\pi$
$578$	−14.7931	−0.615314
$579$	−18.9894	−0.789173
$580$	1.28840	0.0534977
$581$	0	0
$582$	−16.6951	−0.692034
$583$	7.76497	0.321592
$584$	22.4948	0.930842
$585$	−8.74765	−0.361671
$586$	10.2265	0.422452
$587$	−15.6293	−0.645091	−0.322545	−	0.946554i	$-0.604539\pi$
$587$	−15.6293	−0.645091	−0.322545	+	0.946554i	$0.604539\pi$
$588$	0	0
$589$	9.90898	0.408293
$590$	−17.7828	−0.732107
$591$	−3.08525	−0.126910
$592$	−24.0228	−0.987333
$593$	8.24862	0.338730	0.169365	−	0.985553i	$-0.445828\pi$
$593$	8.24862	0.338730	0.169365	+	0.985553i	$0.445828\pi$
$594$	2.96011	0.121455
$595$	0	0
$596$	9.66711	0.395980
$597$	18.8541	0.771647
$598$	23.5244	0.961986
$599$	−8.41697	−0.343908	−0.171954	−	0.985105i	$-0.555008\pi$
$599$	−8.41697	−0.343908	−0.171954	+	0.985105i	$0.555008\pi$
$600$	33.4185	1.36431
$601$	−15.3330	−0.625446	−0.312723	−	0.949844i	$-0.601241\pi$
$601$	−15.3330	−0.625446	−0.312723	+	0.949844i	$0.601241\pi$
$602$	0	0
$603$	−3.70108	−0.150720
$604$	1.39306	0.0566829
$605$	−21.5369	−0.875599
$606$	14.0910	0.572406
$607$	−3.76356	−0.152758	−0.0763790	−	0.997079i	$-0.524336\pi$
$607$	−3.76356	−0.152758	−0.0763790	+	0.997079i	$0.524336\pi$
$608$	−2.43040	−0.0985656
$609$	0	0
$610$	13.7639	0.557284
$611$	10.7734	0.435846
$612$	0.995642	0.0402465
$613$	17.5257	0.707858	0.353929	−	0.935272i	$-0.384845\pi$
$613$	17.5257	0.707858	0.353929	+	0.935272i	$0.384845\pi$
$614$	23.9018	0.964598
$615$	33.4008	1.34685
$616$	0	0
$617$	−12.0057	−0.483330	−0.241665	−	0.970360i	$-0.577694\pi$
$617$	−12.0057	−0.483330	−0.241665	+	0.970360i	$0.577694\pi$
$618$	12.3473	0.496680
$619$	27.8728	1.12030	0.560150	−	0.828391i	$-0.310743\pi$
$619$	27.8728	1.12030	0.560150	+	0.828391i	$0.310743\pi$
$620$	17.3502	0.696800
$621$	8.59867	0.345053
$622$	42.8834	1.71947
$623$	0	0
$624$	−6.41774	−0.256915
$625$	40.4478	1.61791
$626$	−3.69354	−0.147624
$627$	−2.36861	−0.0945930
$628$	9.92001	0.395852
$629$	−18.6193	−0.742398
$630$	0	0
$631$	46.7972	1.86297	0.931483	−	0.363784i	$-0.118515\pi$
$631$	46.7972	1.86297	0.931483	+	0.363784i	$0.118515\pi$
$632$	−2.79383	−0.111133
$633$	19.9172	0.791636
$634$	−15.6488	−0.621493
$635$	43.0597	1.70877
$636$	−1.43649	−0.0569607
$637$	0	0
$638$	2.17812	0.0862326
$639$	7.30367	0.288929
$640$	25.0245	0.989180
$641$	17.7307	0.700321	0.350161	−	0.936690i	$-0.386127\pi$
$641$	17.7307	0.700321	0.350161	+	0.936690i	$0.386127\pi$
$642$	−8.67010	−0.342182
$643$	−42.2257	−1.66522	−0.832609	−	0.553862i	$-0.813154\pi$
$643$	−42.2257	−1.66522	−0.832609	+	0.553862i	$0.813154\pi$
$644$	0	0
$645$	3.19799	0.125921
$646$	2.83963	0.111724
$647$	−40.5904	−1.59577	−0.797886	−	0.602808i	$-0.794049\pi$
$647$	−40.5904	−1.59577	−0.797886	+	0.602808i	$0.794049\pi$
$648$	−3.04706	−0.119700
$649$	8.43452	0.331084
$650$	−30.0050	−1.17689
$651$	0	0
$652$	6.41048	0.251054
$653$	8.64161	0.338172	0.169086	−	0.985601i	$-0.445918\pi$
$653$	8.64161	0.338172	0.169086	+	0.985601i	$0.445918\pi$
$654$	−4.62389	−0.180808
$655$	−3.35875	−0.131237
$656$	24.5046	0.956744
$657$	−7.38246	−0.288017
$658$	0	0
$659$	−43.2307	−1.68403	−0.842015	−	0.539454i	$-0.818631\pi$
$659$	−43.2307	−1.68403	−0.842015	+	0.539454i	$0.818631\pi$
$660$	−4.14732	−0.161434
$661$	8.75358	0.340475	0.170237	−	0.985403i	$-0.445547\pi$
$661$	8.75358	0.340475	0.170237	+	0.985403i	$0.445547\pi$
$662$	28.4167	1.10445
$663$	−4.97416	−0.193180
$664$	−14.9893	−0.581696
$665$	0	0
$666$	10.2407	0.396820
$667$	6.32711	0.244987
$668$	7.80088	0.301825
$669$	−12.3503	−0.477492
$670$	−18.4825	−0.714043
$671$	−6.52832	−0.252023
$672$	0	0
$673$	0.331699	0.0127861	0.00639304	−	0.999980i	$-0.497965\pi$
$673$	0.331699	0.0127861	0.00639304	+	0.999980i	$0.497965\pi$
$674$	5.07146	0.195345
$675$	−10.9675	−0.422138
$676$	3.59647	0.138326
$677$	−27.8630	−1.07086	−0.535432	−	0.844579i	$-0.679851\pi$
$677$	−27.8630	−1.07086	−0.535432	+	0.844579i	$0.679851\pi$
$678$	2.62043	0.100637
$679$	0	0
$680$	27.6660	1.06094
$681$	−10.5379	−0.403815
$682$	29.3317	1.12317
$683$	16.7798	0.642062	0.321031	−	0.947069i	$-0.395971\pi$
$683$	16.7798	0.642062	0.321031	+	0.947069i	$0.395971\pi$
$684$	0.438184	0.0167544
$685$	10.2374	0.391153
$686$	0	0
$687$	−21.9463	−0.837303
$688$	2.34621	0.0894485
$689$	7.17663	0.273408
$690$	42.9402	1.63471
$691$	−25.8058	−0.981700	−0.490850	−	0.871244i	$-0.663314\pi$
$691$	−25.8058	−0.981700	−0.490850	+	0.871244i	$0.663314\pi$
$692$	10.9259	0.415340
$693$	0	0
$694$	−28.8751	−1.09608
$695$	−43.4514	−1.64820
$696$	−2.24210	−0.0849867
$697$	18.9926	0.719398
$698$	22.3754	0.846923
$699$	6.61044	0.250030
$700$	0	0
$701$	14.8949	0.562573	0.281287	−	0.959624i	$-0.409239\pi$
$701$	14.8949	0.562573	0.281287	+	0.959624i	$0.409239\pi$
$702$	2.73582	0.103257
$703$	−8.19438	−0.309057
$704$	−21.0820	−0.794557
$705$	19.6652	0.740634
$706$	−11.1376	−0.419168
$707$	0	0
$708$	−1.56036	−0.0586419
$709$	6.58894	0.247453	0.123726	−	0.992316i	$-0.460515\pi$
$709$	6.58894	0.247453	0.123726	+	0.992316i	$0.460515\pi$
$710$	36.4732	1.36881
$711$	0.916892	0.0343861
$712$	−53.9375	−2.02139
$713$	85.2041	3.19092
$714$	0	0
$715$	20.7197	0.774874
$716$	−5.97425	−0.223268
$717$	−16.2362	−0.606351
$718$	15.2923	0.570703
$719$	−32.8771	−1.22611	−0.613055	−	0.790040i	$-0.710060\pi$
$719$	−32.8771	−1.22611	−0.613055	+	0.790040i	$0.710060\pi$
$720$	−11.7146	−0.436576
$721$	0	0
$722$	1.24973	0.0465100
$723$	−14.1559	−0.526462
$724$	1.66181	0.0617606
$725$	−8.07012	−0.299717
$726$	6.73565	0.249984
$727$	−15.7724	−0.584966	−0.292483	−	0.956271i	$-0.594481\pi$
$727$	−15.7724	−0.584966	−0.292483	+	0.956271i	$0.594481\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−36.8667	−1.36450
$731$	1.81847	0.0672584
$732$	1.20772	0.0446385
$733$	5.99791	0.221538	0.110769	−	0.993846i	$-0.464669\pi$
$733$	5.99791	0.221538	0.110769	+	0.993846i	$0.464669\pi$
$734$	−0.445962	−0.0164608
$735$	0	0
$736$	−20.8982	−0.770317
$737$	8.76641	0.322915
$738$	−10.4461	−0.384526
$739$	11.0065	0.404882	0.202441	−	0.979294i	$-0.435112\pi$
$739$	11.0065	0.404882	0.202441	+	0.979294i	$0.435112\pi$
$740$	−14.3480	−0.527442
$741$	−2.18914	−0.0804200
$742$	0	0
$743$	23.7308	0.870598	0.435299	−	0.900286i	$-0.356643\pi$
$743$	23.7308	0.870598	0.435299	+	0.900286i	$0.356643\pi$
$744$	−30.1933	−1.10694
$745$	−88.1571	−3.22983
$746$	−15.6016	−0.571214
$747$	4.91925	0.179986
$748$	−2.35829	−0.0862274
$749$	0	0
$750$	−29.8004	−1.08816
$751$	−32.5972	−1.18949	−0.594745	−	0.803915i	$-0.702747\pi$
$751$	−32.5972	−1.18949	−0.594745	+	0.803915i	$0.702747\pi$
$752$	14.4274	0.526114
$753$	14.5157	0.528982
$754$	2.01309	0.0733123
$755$	−12.7037	−0.462336
$756$	0	0
$757$	−15.3780	−0.558923	−0.279461	−	0.960157i	$-0.590156\pi$
$757$	−15.3780	−0.558923	−0.279461	+	0.960157i	$0.590156\pi$
$758$	21.7533	0.790117
$759$	−20.3669	−0.739270
$760$	12.1759	0.441665
$761$	46.5251	1.68653	0.843266	−	0.537496i	$-0.180630\pi$
$761$	46.5251	1.68653	0.843266	+	0.537496i	$0.180630\pi$
$762$	−13.4669	−0.487855
$763$	0	0
$764$	−4.39788	−0.159110
$765$	−9.07955	−0.328272
$766$	−33.6848	−1.21708
$767$	7.79545	0.281477
$768$	9.97476	0.359933
$769$	−41.6203	−1.50086	−0.750432	−	0.660947i	$-0.770155\pi$
$769$	−41.6203	−1.50086	−0.750432	+	0.660947i	$0.770155\pi$
$770$	0	0
$771$	−3.33012	−0.119932
$772$	−8.32086	−0.299474
$773$	13.0309	0.468690	0.234345	−	0.972153i	$-0.424705\pi$
$773$	13.0309	0.468690	0.234345	+	0.972153i	$0.424705\pi$
$774$	−1.00017	−0.0359504
$775$	−108.676	−3.90377
$776$	−40.7057	−1.46125
$777$	0	0
$778$	−43.2571	−1.55084
$779$	8.35871	0.299482
$780$	−3.83308	−0.137246
$781$	−17.2995	−0.619025
$782$	24.4170	0.873150
$783$	0.735824	0.0262962
$784$	0	0
$785$	−90.4634	−3.22878
$786$	1.05045	0.0374682
$787$	10.8246	0.385854	0.192927	−	0.981213i	$-0.438202\pi$
$787$	10.8246	0.385854	0.192927	+	0.981213i	$0.438202\pi$
$788$	−1.35191	−0.0481598
$789$	−23.9111	−0.851258
$790$	4.57879	0.162906
$791$	0	0
$792$	7.21729	0.256455
$793$	−6.03367	−0.214262
$794$	−22.0945	−0.784103
$795$	13.0998	0.464602
$796$	8.26157	0.292824
$797$	1.01586	0.0359836	0.0179918	−	0.999838i	$-0.494273\pi$
$797$	1.01586	0.0359836	0.0179918	+	0.999838i	$0.494273\pi$
$798$	0	0
$799$	11.1822	0.395597
$800$	26.6553	0.942406
$801$	17.7015	0.625451
$802$	−17.4942	−0.617742
$803$	17.4861	0.617073
$804$	−1.62176	−0.0571950
$805$	0	0
$806$	27.1092	0.954882
$807$	18.2581	0.642715
$808$	34.3564	1.20865
$809$	−14.5235	−0.510617	−0.255309	−	0.966860i	$-0.582177\pi$
$809$	−14.5235	−0.510617	−0.255309	+	0.966860i	$0.582177\pi$
$810$	4.99382	0.175465
$811$	−8.72354	−0.306325	−0.153162	−	0.988201i	$-0.548946\pi$
$811$	−8.72354	−0.306325	−0.153162	+	0.988201i	$0.548946\pi$
$812$	0	0
$813$	9.10046	0.319167
$814$	−24.2563	−0.850181
$815$	−58.4590	−2.04773
$816$	−6.66124	−0.233190
$817$	0.800311	0.0279993
$818$	38.1747	1.33475
$819$	0	0
$820$	14.6357	0.511101
$821$	−23.8497	−0.832361	−0.416181	−	0.909282i	$-0.636632\pi$
$821$	−23.8497	−0.832361	−0.416181	+	0.909282i	$0.636632\pi$
$822$	−3.20176	−0.111674
$823$	−24.4498	−0.852268	−0.426134	−	0.904660i	$-0.640125\pi$
$823$	−24.4498	−0.852268	−0.426134	+	0.904660i	$0.640125\pi$
$824$	30.1049	1.04876
$825$	25.9776	0.904424
$826$	0	0
$827$	−17.8924	−0.622179	−0.311090	−	0.950381i	$-0.600694\pi$
$827$	−17.8924	−0.622179	−0.311090	+	0.950381i	$0.600694\pi$
$828$	3.76780	0.130940
$829$	15.5522	0.540151	0.270076	−	0.962839i	$-0.412951\pi$
$829$	15.5522	0.540151	0.270076	+	0.962839i	$0.412951\pi$
$830$	24.5658	0.852692
$831$	−12.9101	−0.447845
$832$	−19.4846	−0.675507
$833$	0	0
$834$	13.5894	0.470563
$835$	−71.1384	−2.46185
$836$	−1.03789	−0.0358961
$837$	9.90898	0.342505
$838$	21.5046	0.742865
$839$	−2.07381	−0.0715959	−0.0357979	−	0.999359i	$-0.511397\pi$
$839$	−2.07381	−0.0715959	−0.0357979	+	0.999359i	$0.511397\pi$
$840$	0	0
$841$	−28.4586	−0.981330
$842$	−12.1434	−0.418489
$843$	−30.7965	−1.06069
$844$	8.72739	0.300409
$845$	−32.7973	−1.12826
$846$	−6.15028	−0.211451
$847$	0	0
$848$	9.61071	0.330033
$849$	−23.2702	−0.798632
$850$	−31.1435	−1.06821
$851$	−70.4607	−2.41536
$852$	3.20035	0.109642
$853$	14.2407	0.487594	0.243797	−	0.969826i	$-0.421607\pi$
$853$	14.2407	0.487594	0.243797	+	0.969826i	$0.421607\pi$
$854$	0	0
$855$	−3.99593	−0.136658
$856$	−21.1393	−0.722527
$857$	25.3887	0.867261	0.433630	−	0.901091i	$-0.357232\pi$
$857$	25.3887	0.867261	0.433630	+	0.901091i	$0.357232\pi$
$858$	−6.48009	−0.221227
$859$	−39.1225	−1.33484	−0.667421	−	0.744680i	$-0.732602\pi$
$859$	−39.1225	−1.33484	−0.667421	+	0.744680i	$0.732602\pi$
$860$	1.40131	0.0477842
$861$	0	0
$862$	−23.2140	−0.790673
$863$	1.63557	0.0556755	0.0278377	−	0.999612i	$-0.491138\pi$
$863$	1.63557	0.0556755	0.0278377	+	0.999612i	$0.491138\pi$
$864$	−2.43040	−0.0826838
$865$	−99.6364	−3.38774
$866$	−21.0505	−0.715324
$867$	11.8371	0.402009
$868$	0	0
$869$	−2.17176	−0.0736718
$870$	3.67457	0.124580
$871$	8.10218	0.274532
$872$	−11.2739	−0.381782
$873$	13.3590	0.452134
$874$	10.7460	0.363488
$875$	0	0
$876$	−3.23488	−0.109296
$877$	−5.23936	−0.176920	−0.0884602	−	0.996080i	$-0.528195\pi$
$877$	−5.23936	−0.176920	−0.0884602	+	0.996080i	$0.528195\pi$
$878$	−0.470341	−0.0158732
$879$	−8.18298	−0.276005
$880$	27.7472	0.935358
$881$	−23.6123	−0.795520	−0.397760	−	0.917489i	$-0.630212\pi$
$881$	−23.6123	−0.795520	−0.397760	+	0.917489i	$0.630212\pi$
$882$	0	0
$883$	−22.5324	−0.758277	−0.379138	−	0.925340i	$-0.623780\pi$
$883$	−22.5324	−0.758277	−0.379138	+	0.925340i	$0.623780\pi$
$884$	−2.17960	−0.0733079
$885$	14.2294	0.478315
$886$	−40.7347	−1.36851
$887$	19.1279	0.642252	0.321126	−	0.947037i	$-0.395939\pi$
$887$	19.1279	0.642252	0.321126	+	0.947037i	$0.395939\pi$
$888$	24.9688	0.837897
$889$	0	0
$890$	88.3979	2.96311
$891$	−2.36861	−0.0793513
$892$	−5.41173	−0.181198
$893$	4.92130	0.164685
$894$	27.5711	0.922116
$895$	54.4809	1.82110
$896$	0	0
$897$	−18.8237	−0.628504
$898$	20.8927	0.697199
$899$	7.29127	0.243178
$900$	−4.80577	−0.160192
$901$	7.44892	0.248159
$902$	24.7427	0.823841
$903$	0	0
$904$	6.38909	0.212498
$905$	−15.1545	−0.503753
$906$	3.97309	0.131997
$907$	−23.6795	−0.786264	−0.393132	−	0.919482i	$-0.628608\pi$
$907$	−23.6795	−0.786264	−0.393132	+	0.919482i	$0.628608\pi$
$908$	−4.61756	−0.153239
$909$	−11.2752	−0.373976
$910$	0	0
$911$	−55.7299	−1.84641	−0.923207	−	0.384302i	$-0.874442\pi$
$911$	−55.7299	−1.84641	−0.923207	+	0.384302i	$0.874442\pi$
$912$	−2.93163	−0.0970758
$913$	−11.6518	−0.385617
$914$	21.9835	0.727150
$915$	−11.0135	−0.364096
$916$	−9.61653	−0.317739
$917$	0	0
$918$	2.83963	0.0937216
$919$	−18.0208	−0.594452	−0.297226	−	0.954807i	$-0.596062\pi$
$919$	−18.0208	−0.594452	−0.297226	+	0.954807i	$0.596062\pi$
$920$	104.696	3.45173
$921$	−19.1256	−0.630211
$922$	−2.27301	−0.0748577
$923$	−15.9887	−0.526276
$924$	0	0
$925$	89.8715	2.95496
$926$	−1.68868	−0.0554936
$927$	−9.87999	−0.324501
$928$	−1.78835	−0.0587053
$929$	12.5409	0.411452	0.205726	−	0.978610i	$-0.434044\pi$
$929$	12.5409	0.411452	0.205726	+	0.978610i	$0.434044\pi$
$930$	49.4837	1.62263
$931$	0	0
$932$	2.89659	0.0948810
$933$	−34.3142	−1.12340
$934$	−19.9924	−0.654172
$935$	21.5059	0.703317
$936$	6.67044	0.218030
$937$	−31.4153	−1.02629	−0.513147	−	0.858301i	$-0.671520\pi$
$937$	−31.4153	−1.02629	−0.513147	+	0.858301i	$0.671520\pi$
$938$	0	0
$939$	2.95548	0.0964485
$940$	8.61698	0.281055
$941$	14.9001	0.485730	0.242865	−	0.970060i	$-0.421913\pi$
$941$	14.9001	0.485730	0.242865	+	0.970060i	$0.421913\pi$
$942$	28.2924	0.921817
$943$	71.8738	2.34053
$944$	10.4394	0.339774
$945$	0	0
$946$	2.36901	0.0770231
$947$	9.37613	0.304683	0.152342	−	0.988328i	$-0.451319\pi$
$947$	9.37613	0.304683	0.152342	+	0.988328i	$0.451319\pi$
$948$	0.401768	0.0130488
$949$	16.1612	0.524616
$950$	−13.7063	−0.444692
$951$	12.5218	0.406046
$952$	0	0
$953$	−11.0785	−0.358868	−0.179434	−	0.983770i	$-0.557427\pi$
$953$	−11.0785	−0.358868	−0.179434	+	0.983770i	$0.557427\pi$
$954$	−4.09696	−0.132644
$955$	40.1055	1.29778
$956$	−7.11444	−0.230097
$957$	−1.74288	−0.0563393
$958$	−17.9520	−0.580004
$959$	0	0
$960$	−35.5661	−1.14789
$961$	67.1879	2.16735
$962$	−22.4184	−0.722797
$963$	6.93760	0.223561
$964$	−6.20287	−0.199781
$965$	75.8803	2.44267
$966$	0	0
$967$	51.5512	1.65778	0.828888	−	0.559415i	$-0.188974\pi$
$967$	51.5512	1.65778	0.828888	+	0.559415i	$0.188974\pi$
$968$	16.4228	0.527848
$969$	−2.27220	−0.0729935
$970$	66.7124	2.14201
$971$	−13.5264	−0.434084	−0.217042	−	0.976162i	$-0.569641\pi$
$971$	−13.5264	−0.434084	−0.217042	+	0.976162i	$0.569641\pi$
$972$	0.438184	0.0140548
$973$	0	0
$974$	−19.6154	−0.628518
$975$	24.0093	0.768913
$976$	−8.08010	−0.258638
$977$	−44.5581	−1.42554	−0.712771	−	0.701397i	$-0.752560\pi$
$977$	−44.5581	−1.42554	−0.712771	+	0.701397i	$0.752560\pi$
$978$	18.2830	0.584627
$979$	−41.9278	−1.34002
$980$	0	0
$981$	3.69992	0.118129
$982$	48.5820	1.55032
$983$	−10.2145	−0.325792	−0.162896	−	0.986643i	$-0.552083\pi$
$983$	−10.2145	−0.325792	−0.162896	+	0.986643i	$0.552083\pi$
$984$	−25.4695	−0.811938
$985$	12.3285	0.392817
$986$	2.08947	0.0665422
$987$	0	0
$988$	−0.959247	−0.0305177
$989$	6.88161	0.218823
$990$	−11.8284	−0.375931
$991$	−18.9187	−0.600974	−0.300487	−	0.953786i	$-0.597149\pi$
$991$	−18.9187	−0.600974	−0.300487	+	0.953786i	$0.597149\pi$
$992$	−24.0828	−0.764628
$993$	−22.7383	−0.721580
$994$	0	0
$995$	−75.3396	−2.38843
$996$	2.15554	0.0683008
$997$	15.3433	0.485928	0.242964	−	0.970035i	$-0.421880\pi$
$997$	15.3433	0.485928	0.242964	+	0.970035i	$0.421880\pi$
$998$	54.9400	1.73910
$999$	−8.19438	−0.259259

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2793.2.a.bm.1.6		8
3.2	odd	2		8379.2.a.cr.1.3		8
7.2	even	3		399.2.j.g.172.3	yes	16
7.4	even	3		399.2.j.g.58.3	✓	16
7.6	odd	2		2793.2.a.bn.1.6		8
21.2	odd	6		1197.2.j.m.172.6		16
21.11	odd	6		1197.2.j.m.856.6		16
21.20	even	2		8379.2.a.cq.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.j.g.58.3	✓	16	7.4	even	3
399.2.j.g.172.3	yes	16	7.2	even	3
1197.2.j.m.172.6		16	21.2	odd	6
1197.2.j.m.856.6		16	21.11	odd	6
2793.2.a.bm.1.6		8	1.1	even	1	trivial
2793.2.a.bn.1.6		8	7.6	odd	2
8379.2.a.cq.1.3		8	21.20	even	2
8379.2.a.cr.1.3		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2793 = 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2793.a (trivial)

\(f(q)\)	\(=\)	\(q+1.24973 q^{2} -1.00000 q^{3} -0.438184 q^{4} +3.99593 q^{5} -1.24973 q^{6} -3.04706 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.24973 q^{2} -1.00000 q^{3} -0.438184 q^{4} +3.99593 q^{5} -1.24973 q^{6} -3.04706 q^{8} +1.00000 q^{9} +4.99382 q^{10} -2.36861 q^{11} +0.438184 q^{12} -2.18914 q^{13} -3.99593 q^{15} -2.93163 q^{16} -2.27220 q^{17} +1.24973 q^{18} -1.00000 q^{19} -1.75095 q^{20} -2.96011 q^{22} -8.59867 q^{23} +3.04706 q^{24} +10.9675 q^{25} -2.73582 q^{26} -1.00000 q^{27} -0.735824 q^{29} -4.99382 q^{30} -9.90898 q^{31} +2.43040 q^{32} +2.36861 q^{33} -2.83963 q^{34} -0.438184 q^{36} +8.19438 q^{37} -1.24973 q^{38} +2.18914 q^{39} -12.1759 q^{40} -8.35871 q^{41} -0.800311 q^{43} +1.03789 q^{44} +3.99593 q^{45} -10.7460 q^{46} -4.92130 q^{47} +2.93163 q^{48} +13.7063 q^{50} +2.27220 q^{51} +0.959247 q^{52} -3.27829 q^{53} -1.24973 q^{54} -9.46479 q^{55} +1.00000 q^{57} -0.919579 q^{58} -3.56096 q^{59} +1.75095 q^{60} +2.75619 q^{61} -12.3835 q^{62} +8.90058 q^{64} -8.74765 q^{65} +2.96011 q^{66} -3.70108 q^{67} +0.995642 q^{68} +8.59867 q^{69} +7.30367 q^{71} -3.04706 q^{72} -7.38246 q^{73} +10.2407 q^{74} -10.9675 q^{75} +0.438184 q^{76} +2.73582 q^{78} +0.916892 q^{79} -11.7146 q^{80} +1.00000 q^{81} -10.4461 q^{82} +4.91925 q^{83} -9.07955 q^{85} -1.00017 q^{86} +0.735824 q^{87} +7.21729 q^{88} +17.7015 q^{89} +4.99382 q^{90} +3.76780 q^{92} +9.90898 q^{93} -6.15028 q^{94} -3.99593 q^{95} -2.43040 q^{96} +13.3590 q^{97} -2.36861 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} + 10 q^{4} - 5 q^{5} - 3 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^3 + 10 * q^4 - 5 * q^5 - 3 * q^8 + 8 * q^9	\( 8 q - 8 q^{3} + 10 q^{4} - 5 q^{5} - 3 q^{8} + 8 q^{9} - 3 q^{10} - 7 q^{11} - 10 q^{12} - 6 q^{13} + 5 q^{15} + 10 q^{16} - 8 q^{19} - 16 q^{20} + 18 q^{22} - 9 q^{23} + 3 q^{24} + 15 q^{25} - 12 q^{26} - 8 q^{27} + 4 q^{29} + 3 q^{30} - 11 q^{31} - 26 q^{32} + 7 q^{33} - 16 q^{34} + 10 q^{36} + 17 q^{37} + 6 q^{39} - 3 q^{40} - 17 q^{41} + 8 q^{43} - 31 q^{44} - 5 q^{45} + q^{46} - 29 q^{47} - 10 q^{48} + 30 q^{50} - 25 q^{52} - 6 q^{53} - 21 q^{55} + 8 q^{57} - 37 q^{58} - 7 q^{59} + 16 q^{60} - 2 q^{61} - 39 q^{62} + 29 q^{64} - 13 q^{65} - 18 q^{66} + 13 q^{67} + 14 q^{68} + 9 q^{69} + 18 q^{71} - 3 q^{72} - 20 q^{73} - 26 q^{74} - 15 q^{75} - 10 q^{76} + 12 q^{78} - 3 q^{79} - 35 q^{80} + 8 q^{81} - 5 q^{82} - 36 q^{83} + 5 q^{85} - 51 q^{86} - 4 q^{87} + 53 q^{88} - q^{89} - 3 q^{90} + 15 q^{92} + 11 q^{93} - 30 q^{94} + 5 q^{95} + 26 q^{96} + 3 q^{97} - 7 q^{99}+O(q^{100}) \) 8 * q - 8 * q^3 + 10 * q^4 - 5 * q^5 - 3 * q^8 + 8 * q^9 - 3 * q^10 - 7 * q^11 - 10 * q^12 - 6 * q^13 + 5 * q^15 + 10 * q^16 - 8 * q^19 - 16 * q^20 + 18 * q^22 - 9 * q^23 + 3 * q^24 + 15 * q^25 - 12 * q^26 - 8 * q^27 + 4 * q^29 + 3 * q^30 - 11 * q^31 - 26 * q^32 + 7 * q^33 - 16 * q^34 + 10 * q^36 + 17 * q^37 + 6 * q^39 - 3 * q^40 - 17 * q^41 + 8 * q^43 - 31 * q^44 - 5 * q^45 + q^46 - 29 * q^47 - 10 * q^48 + 30 * q^50 - 25 * q^52 - 6 * q^53 - 21 * q^55 + 8 * q^57 - 37 * q^58 - 7 * q^59 + 16 * q^60 - 2 * q^61 - 39 * q^62 + 29 * q^64 - 13 * q^65 - 18 * q^66 + 13 * q^67 + 14 * q^68 + 9 * q^69 + 18 * q^71 - 3 * q^72 - 20 * q^73 - 26 * q^74 - 15 * q^75 - 10 * q^76 + 12 * q^78 - 3 * q^79 - 35 * q^80 + 8 * q^81 - 5 * q^82 - 36 * q^83 + 5 * q^85 - 51 * q^86 - 4 * q^87 + 53 * q^88 - q^89 - 3 * q^90 + 15 * q^92 + 11 * q^93 - 30 * q^94 + 5 * q^95 + 26 * q^96 + 3 * q^97 - 7 * q^99

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