LMFDB - Embedded newform 1617.2.a.x.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,2,Mod(1,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, 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("1617.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1617.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:	$12.9118100068$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.11344.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 4x + 3 $ x^4 - 2x^3 - 4x^2 + 4*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.78165$ of defining polynomial
Character	$\chi$	$=$	1617.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.78165 q^{2} -1.00000 q^{3} +5.73760 q^{4} -0.825711 q^{5} -2.78165 q^{6} +10.3967 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.78165 q^{2} -1.00000 q^{3} +5.73760 q^{4} -0.825711 q^{5} -2.78165 q^{6} +10.3967 q^{8} +1.00000 q^{9} -2.29684 q^{10} -1.00000 q^{11} -5.73760 q^{12} +0.296842 q^{13} +0.825711 q^{15} +17.4448 q^{16} +6.69354 q^{17} +2.78165 q^{18} +2.83339 q^{19} -4.73760 q^{20} -2.78165 q^{22} -3.96962 q^{23} -10.3967 q^{24} -4.31820 q^{25} +0.825711 q^{26} -1.00000 q^{27} -0.484812 q^{29} +2.29684 q^{30} +7.33128 q^{31} +27.7320 q^{32} +1.00000 q^{33} +18.6191 q^{34} +5.73760 q^{36} -5.73760 q^{37} +7.88151 q^{38} -0.296842 q^{39} -8.58467 q^{40} -0.645420 q^{41} +6.43308 q^{43} -5.73760 q^{44} -0.825711 q^{45} -11.0421 q^{46} -7.73760 q^{47} -17.4448 q^{48} -12.0117 q^{50} -6.69354 q^{51} +1.70316 q^{52} +7.11354 q^{53} -2.78165 q^{54} +0.825711 q^{55} -2.83339 q^{57} -1.34858 q^{58} +1.15699 q^{59} +4.73760 q^{60} -5.26647 q^{61} +20.3931 q^{62} +42.2513 q^{64} -0.245106 q^{65} +2.78165 q^{66} +3.01730 q^{67} +38.4048 q^{68} +3.96962 q^{69} +3.58061 q^{71} +10.3967 q^{72} -16.0325 q^{73} -15.9600 q^{74} +4.31820 q^{75} +16.2568 q^{76} -0.825711 q^{78} -4.32420 q^{79} -14.4044 q^{80} +1.00000 q^{81} -1.79533 q^{82} -2.37594 q^{83} -5.52693 q^{85} +17.8946 q^{86} +0.484812 q^{87} -10.3967 q^{88} -12.1723 q^{89} -2.29684 q^{90} -22.7761 q^{92} -7.33128 q^{93} -21.5233 q^{94} -2.33956 q^{95} -27.7320 q^{96} +10.7680 q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 2 q^{6} + 12 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 2 * q^6 + 12 * q^8 + 4 * q^9	$ 4 q + 2 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 2 q^{6} + 12 q^{8} + 4 q^{9} - 10 q^{10} - 4 q^{11} - 4 q^{12} + 2 q^{13} + 4 q^{15} + 12 q^{16} - 2 q^{17} + 2 q^{18} - 2 q^{22} + 4 q^{23} - 12 q^{24} + 4 q^{25} + 4 q^{26} - 4 q^{27} + 8 q^{29} + 10 q^{30} + 12 q^{31} + 26 q^{32} + 4 q^{33} + 16 q^{34} + 4 q^{36} - 4 q^{37} - 8 q^{38} - 2 q^{39} + 6 q^{40} - 2 q^{41} + 18 q^{43} - 4 q^{44} - 4 q^{45} - 14 q^{46} - 12 q^{47} - 12 q^{48} + 2 q^{50} + 2 q^{51} + 6 q^{52} - 12 q^{53} - 2 q^{54} + 4 q^{55} - 4 q^{58} - 12 q^{59} - 2 q^{61} + 26 q^{62} + 56 q^{64} - 4 q^{65} + 2 q^{66} + 28 q^{67} + 48 q^{68} - 4 q^{69} + 12 q^{71} + 12 q^{72} - 6 q^{73} - 16 q^{74} - 4 q^{75} + 18 q^{76} - 4 q^{78} + 2 q^{79} - 16 q^{80} + 4 q^{81} + 12 q^{82} + 12 q^{83} + 18 q^{85} + 36 q^{86} - 8 q^{87} - 12 q^{88} - 8 q^{89} - 10 q^{90} - 16 q^{92} - 12 q^{93} - 20 q^{94} + 34 q^{95} - 26 q^{96} + 44 q^{97} - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 2 * q^6 + 12 * q^8 + 4 * q^9 - 10 * q^10 - 4 * q^11 - 4 * q^12 + 2 * q^13 + 4 * q^15 + 12 * q^16 - 2 * q^17 + 2 * q^18 - 2 * q^22 + 4 * q^23 - 12 * q^24 + 4 * q^25 + 4 * q^26 - 4 * q^27 + 8 * q^29 + 10 * q^30 + 12 * q^31 + 26 * q^32 + 4 * q^33 + 16 * q^34 + 4 * q^36 - 4 * q^37 - 8 * q^38 - 2 * q^39 + 6 * q^40 - 2 * q^41 + 18 * q^43 - 4 * q^44 - 4 * q^45 - 14 * q^46 - 12 * q^47 - 12 * q^48 + 2 * q^50 + 2 * q^51 + 6 * q^52 - 12 * q^53 - 2 * q^54 + 4 * q^55 - 4 * q^58 - 12 * q^59 - 2 * q^61 + 26 * q^62 + 56 * q^64 - 4 * q^65 + 2 * q^66 + 28 * q^67 + 48 * q^68 - 4 * q^69 + 12 * q^71 + 12 * q^72 - 6 * q^73 - 16 * q^74 - 4 * q^75 + 18 * q^76 - 4 * q^78 + 2 * q^79 - 16 * q^80 + 4 * q^81 + 12 * q^82 + 12 * q^83 + 18 * q^85 + 36 * q^86 - 8 * q^87 - 12 * q^88 - 8 * q^89 - 10 * q^90 - 16 * q^92 - 12 * q^93 - 20 * q^94 + 34 * q^95 - 26 * q^96 + 44 * q^97 - 4 * 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 $

$2$	2.78165	1.96693	0.983463	−	0.181109i	$-0.0579687\pi$
$2$	2.78165	1.96693	0.983463	+	0.181109i	$0.0579687\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.73760	2.86880
$5$	−0.825711	−0.369269	−0.184635	−	0.982807i	$-0.559110\pi$
$5$	−0.825711	−0.369269	−0.184635	+	0.982807i	$0.559110\pi$
$6$	−2.78165	−1.13561
$7$	0	0
$7$	0	0
$8$	10.3967	3.67579
$9$	1.00000	0.333333
$10$	−2.29684	−0.726325
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−5.73760	−1.65630
$13$	0.296842	0.0823291	0.0411645	−	0.999152i	$-0.486893\pi$
$13$	0.296842	0.0823291	0.0411645	+	0.999152i	$0.486893\pi$
$14$	0	0
$15$	0.825711	0.213198
$16$	17.4448	4.36120
$17$	6.69354	1.62342	0.811711	−	0.584060i	$-0.198537\pi$
$17$	6.69354	1.62342	0.811711	+	0.584060i	$0.198537\pi$
$18$	2.78165	0.655642
$19$	2.83339	0.650024	0.325012	−	0.945710i	$-0.394632\pi$
$19$	2.83339	0.650024	0.325012	+	0.945710i	$0.394632\pi$
$20$	−4.73760	−1.05936
$21$	0	0
$22$	−2.78165	−0.593051
$23$	−3.96962	−0.827724	−0.413862	−	0.910340i	$-0.635820\pi$
$23$	−3.96962	−0.827724	−0.413862	+	0.910340i	$0.635820\pi$
$24$	−10.3967	−2.12222
$25$	−4.31820	−0.863640
$26$	0.825711	0.161935
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−0.484812	−0.0900273	−0.0450136	−	0.998986i	$-0.514333\pi$
$29$	−0.484812	−0.0900273	−0.0450136	+	0.998986i	$0.514333\pi$
$30$	2.29684	0.419344
$31$	7.33128	1.31674	0.658368	−	0.752696i	$-0.271247\pi$
$31$	7.33128	1.31674	0.658368	+	0.752696i	$0.271247\pi$
$32$	27.7320	4.90238
$33$	1.00000	0.174078
$34$	18.6191	3.19315
$35$	0	0
$36$	5.73760	0.956266
$37$	−5.73760	−0.943255	−0.471627	−	0.881798i	$-0.656333\pi$
$37$	−5.73760	−0.943255	−0.471627	+	0.881798i	$0.656333\pi$
$38$	7.88151	1.27855
$39$	−0.296842	−0.0475327
$40$	−8.58467	−1.35735
$41$	−0.645420	−0.100798	−0.0503988	−	0.998729i	$-0.516049\pi$
$41$	−0.645420	−0.100798	−0.0503988	+	0.998729i	$0.516049\pi$
$42$	0	0
$43$	6.43308	0.981035	0.490517	−	0.871431i	$-0.336808\pi$
$43$	6.43308	0.981035	0.490517	+	0.871431i	$0.336808\pi$
$44$	−5.73760	−0.864975
$45$	−0.825711	−0.123090
$46$	−11.0421	−1.62807
$47$	−7.73760	−1.12864	−0.564322	−	0.825555i	$-0.690862\pi$
$47$	−7.73760	−1.12864	−0.564322	+	0.825555i	$0.690862\pi$
$48$	−17.4448	−2.51794
$49$	0	0
$50$	−12.0117	−1.69872
$51$	−6.69354	−0.937283
$52$	1.70316	0.236186
$53$	7.11354	0.977119	0.488560	−	0.872531i	$-0.337522\pi$
$53$	7.11354	0.977119	0.488560	+	0.872531i	$0.337522\pi$
$54$	−2.78165	−0.378535
$55$	0.825711	0.111339
$56$	0	0
$57$	−2.83339	−0.375292
$58$	−1.34858	−0.177077
$59$	1.15699	0.150627	0.0753137	−	0.997160i	$-0.476004\pi$
$59$	1.15699	0.150627	0.0753137	+	0.997160i	$0.476004\pi$
$60$	4.73760	0.611621
$61$	−5.26647	−0.674302	−0.337151	−	0.941451i	$-0.609463\pi$
$61$	−5.26647	−0.674302	−0.337151	+	0.941451i	$0.609463\pi$
$62$	20.3931	2.58992
$63$	0	0
$64$	42.2513	5.28141
$65$	−0.245106	−0.0304016
$66$	2.78165	0.342398
$67$	3.01730	0.368622	0.184311	−	0.982868i	$-0.440995\pi$
$67$	3.01730	0.368622	0.184311	+	0.982868i	$0.440995\pi$
$68$	38.4048	4.65727
$69$	3.96962	0.477886
$70$	0	0
$71$	3.58061	0.424940	0.212470	−	0.977168i	$-0.431849\pi$
$71$	3.58061	0.424940	0.212470	+	0.977168i	$0.431849\pi$
$72$	10.3967	1.22526
$73$	−16.0325	−1.87646	−0.938231	−	0.346010i	$-0.887536\pi$
$73$	−16.0325	−1.87646	−0.938231	+	0.346010i	$0.887536\pi$
$74$	−15.9600	−1.85531
$75$	4.31820	0.498623
$76$	16.2568	1.86479
$77$	0	0
$78$	−0.825711	−0.0934934
$79$	−4.32420	−0.486511	−0.243255	−	0.969962i	$-0.578215\pi$
$79$	−4.32420	−0.486511	−0.243255	+	0.969962i	$0.578215\pi$
$80$	−14.4044	−1.61046
$81$	1.00000	0.111111
$82$	−1.79533	−0.198262
$83$	−2.37594	−0.260793	−0.130397	−	0.991462i	$-0.541625\pi$
$83$	−2.37594	−0.260793	−0.130397	+	0.991462i	$0.541625\pi$
$84$	0	0
$85$	−5.52693	−0.599480
$86$	17.8946	1.92962
$87$	0.484812	0.0519773
$88$	−10.3967	−1.10829
$89$	−12.1723	−1.29027	−0.645133	−	0.764070i	$-0.723198\pi$
$89$	−12.1723	−1.29027	−0.645133	+	0.764070i	$0.723198\pi$
$90$	−2.29684	−0.242108
$91$	0	0
$92$	−22.7761	−2.37457
$93$	−7.33128	−0.760218
$94$	−21.5233	−2.21996
$95$	−2.33956	−0.240034
$96$	−27.7320	−2.83039
$97$	10.7680	1.09332	0.546661	−	0.837354i	$-0.315899\pi$
$97$	10.7680	1.09332	0.546661	+	0.837354i	$0.315899\pi$
$98$	0	0
$99$	−1.00000	−0.100504
$100$	−24.7761	−2.47761
$101$	−14.9904	−1.49160	−0.745799	−	0.666171i	$-0.767932\pi$
$101$	−14.9904	−1.49160	−0.745799	+	0.666171i	$0.767932\pi$
$102$	−18.6191	−1.84357
$103$	2.46405	0.242791	0.121395	−	0.992604i	$-0.461263\pi$
$103$	2.46405	0.242791	0.121395	+	0.992604i	$0.461263\pi$
$104$	3.08617	0.302624
$105$	0	0
$106$	19.7874	1.92192
$107$	−11.5804	−1.11952	−0.559762	−	0.828653i	$-0.689107\pi$
$107$	−11.5804	−1.11952	−0.559762	+	0.828653i	$0.689107\pi$
$108$	−5.73760	−0.552100
$109$	−5.42346	−0.519473	−0.259736	−	0.965680i	$-0.583636\pi$
$109$	−5.42346	−0.519473	−0.259736	+	0.965680i	$0.583636\pi$
$110$	2.29684	0.218995
$111$	5.73760	0.544589
$112$	0	0
$113$	−17.5156	−1.64773	−0.823866	−	0.566785i	$-0.808187\pi$
$113$	−17.5156	−1.64773	−0.823866	+	0.566785i	$0.808187\pi$
$114$	−7.88151	−0.738171
$115$	3.27776	0.305653
$116$	−2.78165	−0.258270
$117$	0.296842	0.0274430
$118$	3.21835	0.296273
$119$	0	0
$120$	8.58467	0.783669
$121$	1.00000	0.0909091
$122$	−14.6495	−1.32630
$123$	0.645420	0.0581955
$124$	42.0639	3.77745
$125$	7.69414	0.688185
$126$	0	0
$127$	5.97924	0.530572	0.265286	−	0.964170i	$-0.414534\pi$
$127$	5.97924	0.530572	0.265286	+	0.964170i	$0.414534\pi$
$128$	62.0644	5.48577
$129$	−6.43308	−0.566401
$130$	−0.681799	−0.0597977
$131$	−17.6424	−1.54142	−0.770712	−	0.637184i	$-0.780099\pi$
$131$	−17.6424	−1.54142	−0.770712	+	0.637184i	$0.780099\pi$
$132$	5.73760	0.499394
$133$	0	0
$134$	8.39308	0.725052
$135$	0.825711	0.0710659
$136$	69.5907	5.96735
$137$	9.35972	0.799654	0.399827	−	0.916591i	$-0.369070\pi$
$137$	9.35972	0.799654	0.399827	+	0.916591i	$0.369070\pi$
$138$	11.0421	0.939967
$139$	−7.40270	−0.627889	−0.313944	−	0.949441i	$-0.601651\pi$
$139$	−7.40270	−0.627889	−0.313944	+	0.949441i	$0.601651\pi$
$140$	0	0
$141$	7.73760	0.651623
$142$	9.96000	0.835825
$143$	−0.296842	−0.0248232
$144$	17.4448	1.45373
$145$	0.400314	0.0332443
$146$	−44.5968	−3.69086
$147$	0	0
$148$	−32.9200	−2.70601
$149$	−12.0117	−0.984040	−0.492020	−	0.870584i	$-0.663741\pi$
$149$	−12.0117	−0.984040	−0.492020	+	0.870584i	$0.663741\pi$
$150$	12.0117	0.980754
$151$	9.32182	0.758599	0.379299	−	0.925274i	$-0.376165\pi$
$151$	9.32182	0.758599	0.379299	+	0.925274i	$0.376165\pi$
$152$	29.4579	2.38935
$153$	6.69354	0.541141
$154$	0	0
$155$	−6.05352	−0.486230
$156$	−1.70316	−0.136362
$157$	5.10347	0.407301	0.203651	−	0.979044i	$-0.434719\pi$
$157$	5.10347	0.407301	0.203651	+	0.979044i	$0.434719\pi$
$158$	−12.0284	−0.956931
$159$	−7.11354	−0.564140
$160$	−22.8986	−1.81030
$161$	0	0
$162$	2.78165	0.218547
$163$	9.48827	0.743179	0.371589	−	0.928397i	$-0.378813\pi$
$163$	9.48827	0.743179	0.371589	+	0.928397i	$0.378813\pi$
$164$	−3.70316	−0.289168
$165$	−0.825711	−0.0642815
$166$	−6.60904	−0.512961
$167$	3.03850	0.235126	0.117563	−	0.993065i	$-0.462492\pi$
$167$	3.03850	0.235126	0.117563	+	0.993065i	$0.462492\pi$
$168$	0	0
$169$	−12.9119	−0.993222
$170$	−15.3740	−1.17913
$171$	2.83339	0.216675
$172$	36.9104	2.81439
$173$	5.77203	0.438840	0.219420	−	0.975631i	$-0.429584\pi$
$173$	5.77203	0.438840	0.219420	+	0.975631i	$0.429584\pi$
$174$	1.34858	0.102235
$175$	0	0
$176$	−17.4448	−1.31495
$177$	−1.15699	−0.0869647
$178$	−33.8593	−2.53786
$179$	−3.02844	−0.226356	−0.113178	−	0.993575i	$-0.536103\pi$
$179$	−3.02844	−0.226356	−0.113178	+	0.993575i	$0.536103\pi$
$180$	−4.73760	−0.353120
$181$	9.67878	0.719418	0.359709	−	0.933064i	$-0.382876\pi$
$181$	9.67878	0.719418	0.359709	+	0.933064i	$0.382876\pi$
$182$	0	0
$183$	5.26647	0.389308
$184$	−41.2710	−3.04254
$185$	4.73760	0.348315
$186$	−20.3931	−1.49529
$187$	−6.69354	−0.489480
$188$	−44.3952	−3.23785
$189$	0	0
$190$	−6.50785	−0.472129
$191$	−1.29084	−0.0934019	−0.0467009	−	0.998909i	$-0.514871\pi$
$191$	−1.29084	−0.0934019	−0.0467009	+	0.998909i	$0.514871\pi$
$192$	−42.2513	−3.04922
$193$	−20.9777	−1.51001	−0.755006	−	0.655718i	$-0.772366\pi$
$193$	−20.9777	−1.51001	−0.755006	+	0.655718i	$0.772366\pi$
$194$	29.9528	2.15048
$195$	0.245106	0.0175524
$196$	0	0
$197$	15.0836	1.07466	0.537332	−	0.843371i	$-0.319432\pi$
$197$	15.0836	1.07466	0.537332	+	0.843371i	$0.319432\pi$
$198$	−2.78165	−0.197684
$199$	25.7203	1.82326	0.911632	−	0.411008i	$-0.134823\pi$
$199$	25.7203	1.82326	0.911632	+	0.411008i	$0.134823\pi$
$200$	−44.8950	−3.17456
$201$	−3.01730	−0.212824
$202$	−41.6980	−2.93386
$203$	0	0
$204$	−38.4048	−2.68888
$205$	0.532930	0.0372215
$206$	6.85415	0.477551
$207$	−3.96962	−0.275908
$208$	5.17835	0.359054
$209$	−2.83339	−0.195990
$210$	0	0
$211$	1.84814	0.127232	0.0636158	−	0.997974i	$-0.479737\pi$
$211$	1.84814	0.127232	0.0636158	+	0.997974i	$0.479737\pi$
$212$	40.8146	2.80316
$213$	−3.58061	−0.245339
$214$	−32.2128	−2.20202
$215$	−5.31186	−0.362266
$216$	−10.3967	−0.707406
$217$	0	0
$218$	−15.0862	−1.02176
$219$	16.0325	1.08338
$220$	4.73760	0.319409
$221$	1.98692	0.133655
$222$	15.9600	1.07117
$223$	6.17851	0.413744	0.206872	−	0.978368i	$-0.433672\pi$
$223$	6.17851	0.413744	0.206872	+	0.978368i	$0.433672\pi$
$224$	0	0
$225$	−4.31820	−0.287880
$226$	−48.7224	−3.24097
$227$	−5.01114	−0.332601	−0.166300	−	0.986075i	$-0.553182\pi$
$227$	−5.01114	−0.332601	−0.166300	+	0.986075i	$0.553182\pi$
$228$	−16.2568	−1.07664
$229$	−22.4328	−1.48240	−0.741201	−	0.671283i	$-0.765743\pi$
$229$	−22.4328	−1.48240	−0.741201	+	0.671283i	$0.765743\pi$
$230$	9.11760	0.601197
$231$	0	0
$232$	−5.04044	−0.330921
$233$	4.83339	0.316646	0.158323	−	0.987387i	$-0.449391\pi$
$233$	4.83339	0.316646	0.158323	+	0.987387i	$0.449391\pi$
$234$	0.825711	0.0539784
$235$	6.38902	0.416774
$236$	6.63834	0.432119
$237$	4.32420	0.280887
$238$	0	0
$239$	−2.58467	−0.167188	−0.0835941	−	0.996500i	$-0.526640\pi$
$239$	−2.58467	−0.167188	−0.0835941	+	0.996500i	$0.526640\pi$
$240$	14.4044	0.929798
$241$	−2.77804	−0.178949	−0.0894745	−	0.995989i	$-0.528519\pi$
$241$	−2.77804	−0.178949	−0.0894745	+	0.995989i	$0.528519\pi$
$242$	2.78165	0.178811
$243$	−1.00000	−0.0641500
$244$	−30.2168	−1.93444
$245$	0	0
$246$	1.79533	0.114466
$247$	0.841068	0.0535159
$248$	76.2211	4.84004
$249$	2.37594	0.150569
$250$	21.4024	1.35361
$251$	−0.936967	−0.0591409	−0.0295704	−	0.999563i	$-0.509414\pi$
$251$	−0.936967	−0.0591409	−0.0295704	+	0.999563i	$0.509414\pi$
$252$	0	0
$253$	3.96962	0.249568
$254$	16.6322	1.04360
$255$	5.52693	0.346110
$256$	88.1390	5.50869
$257$	18.0343	1.12495	0.562474	−	0.826815i	$-0.309850\pi$
$257$	18.0343	1.12495	0.562474	+	0.826815i	$0.309850\pi$
$258$	−17.8946	−1.11407
$259$	0	0
$260$	−1.40632	−0.0872160
$261$	−0.484812	−0.0300091
$262$	−49.0751	−3.03187
$263$	7.89653	0.486921	0.243460	−	0.969911i	$-0.421717\pi$
$263$	7.89653	0.486921	0.243460	+	0.969911i	$0.421717\pi$
$264$	10.3967	0.639872
$265$	−5.87372	−0.360820
$266$	0	0
$267$	12.1723	0.744936
$268$	17.3120	1.05750
$269$	−17.2170	−1.04974	−0.524870	−	0.851183i	$-0.675886\pi$
$269$	−17.2170	−1.04974	−0.524870	+	0.851183i	$0.675886\pi$
$270$	2.29684	0.139781
$271$	9.33534	0.567082	0.283541	−	0.958960i	$-0.408491\pi$
$271$	9.33534	0.567082	0.283541	+	0.958960i	$0.408491\pi$
$272$	116.768	7.08007
$273$	0	0
$274$	26.0355	1.57286
$275$	4.31820	0.260397
$276$	22.7761	1.37096
$277$	5.47519	0.328972	0.164486	−	0.986379i	$-0.447403\pi$
$277$	5.47519	0.328972	0.164486	+	0.986379i	$0.447403\pi$
$278$	−20.5917	−1.23501
$279$	7.33128	0.438912
$280$	0	0
$281$	−18.3501	−1.09467	−0.547337	−	0.836912i	$-0.684359\pi$
$281$	−18.3501	−1.09467	−0.547337	+	0.836912i	$0.684359\pi$
$282$	21.5233	1.28169
$283$	−26.0406	−1.54795	−0.773977	−	0.633214i	$-0.781735\pi$
$283$	−26.0406	−1.54795	−0.773977	+	0.633214i	$0.781735\pi$
$284$	20.5441	1.21907
$285$	2.33956	0.138584
$286$	−0.825711	−0.0488253
$287$	0	0
$288$	27.7320	1.63413
$289$	27.8035	1.63550
$290$	1.11354	0.0653891
$291$	−10.7680	−0.631230
$292$	−91.9880	−5.38319
$293$	−21.3317	−1.24621	−0.623106	−	0.782137i	$-0.714130\pi$
$293$	−21.3317	−1.24621	−0.623106	+	0.782137i	$0.714130\pi$
$294$	0	0
$295$	−0.955340	−0.0556220
$296$	−59.6520	−3.46720
$297$	1.00000	0.0580259
$298$	−33.4125	−1.93553
$299$	−1.17835	−0.0681457
$300$	24.7761	1.43045
$301$	0	0
$302$	25.9301	1.49211
$303$	14.9904	0.861175
$304$	49.4280	2.83489
$305$	4.34858	0.248999
$306$	18.6191	1.06438
$307$	6.88329	0.392850	0.196425	−	0.980519i	$-0.437067\pi$
$307$	6.88329	0.392850	0.196425	+	0.980519i	$0.437067\pi$
$308$	0	0
$309$	−2.46405	−0.140175
$310$	−16.8388	−0.956379
$311$	3.79728	0.215324	0.107662	−	0.994188i	$-0.465664\pi$
$311$	3.79728	0.215324	0.107662	+	0.994188i	$0.465664\pi$
$312$	−3.08617	−0.174720
$313$	−2.61910	−0.148041	−0.0740203	−	0.997257i	$-0.523583\pi$
$313$	−2.61910	−0.148041	−0.0740203	+	0.997257i	$0.523583\pi$
$314$	14.1961	0.801132
$315$	0	0
$316$	−24.8105	−1.39570
$317$	−27.8642	−1.56501	−0.782505	−	0.622644i	$-0.786058\pi$
$317$	−27.8642	−1.56501	−0.782505	+	0.622644i	$0.786058\pi$
$318$	−19.7874	−1.10962
$319$	0.484812	0.0271442
$320$	−34.8874	−1.95026
$321$	11.5804	0.646357
$322$	0	0
$323$	18.9654	1.05526
$324$	5.73760	0.318755
$325$	−1.28182	−0.0711027
$326$	26.3931	1.46178
$327$	5.42346	0.299918
$328$	−6.71023	−0.370511
$329$	0	0
$330$	−2.29684	−0.126437
$331$	−8.04151	−0.442002	−0.221001	−	0.975274i	$-0.570932\pi$
$331$	−8.04151	−0.442002	−0.221001	+	0.975274i	$0.570932\pi$
$332$	−13.6322	−0.748163
$333$	−5.73760	−0.314418
$334$	8.45205	0.462476
$335$	−2.49142	−0.136121
$336$	0	0
$337$	26.2686	1.43094	0.715471	−	0.698643i	$-0.246212\pi$
$337$	26.2686	1.43094	0.715471	+	0.698643i	$0.246212\pi$
$338$	−35.9164	−1.95359
$339$	17.5156	0.951319
$340$	−31.7113	−1.71979
$341$	−7.33128	−0.397011
$342$	7.88151	0.426183
$343$	0	0
$344$	66.8827	3.60608
$345$	−3.27776	−0.176469
$346$	16.0558	0.863165
$347$	8.48843	0.455683	0.227841	−	0.973698i	$-0.426833\pi$
$347$	8.48843	0.455683	0.227841	+	0.973698i	$0.426833\pi$
$348$	2.78165	0.149112
$349$	31.9290	1.70912	0.854561	−	0.519351i	$-0.173826\pi$
$349$	31.9290	1.70912	0.854561	+	0.519351i	$0.173826\pi$
$350$	0	0
$351$	−0.296842	−0.0158442
$352$	−27.7320	−1.47812
$353$	−0.143912	−0.00765968	−0.00382984	−	0.999993i	$-0.501219\pi$
$353$	−0.143912	−0.00765968	−0.00382984	+	0.999993i	$0.501219\pi$
$354$	−3.21835	−0.171053
$355$	−2.95655	−0.156917
$356$	−69.8400	−3.70151
$357$	0	0
$358$	−8.42406	−0.445225
$359$	8.23488	0.434621	0.217310	−	0.976103i	$-0.430272\pi$
$359$	8.23488	0.434621	0.217310	+	0.976103i	$0.430272\pi$
$360$	−8.58467	−0.452452
$361$	−10.9719	−0.577469
$362$	26.9230	1.41504
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	13.2382	0.692919
$366$	14.6495	0.765741
$367$	−16.6302	−0.868092	−0.434046	−	0.900891i	$-0.642914\pi$
$367$	−16.6302	−0.868092	−0.434046	+	0.900891i	$0.642914\pi$
$368$	−69.2493	−3.60987
$369$	−0.645420	−0.0335992
$370$	13.1784	0.685110
$371$	0	0
$372$	−42.0639	−2.18091
$373$	−5.12483	−0.265354	−0.132677	−	0.991159i	$-0.542357\pi$
$373$	−5.12483	−0.265354	−0.132677	+	0.991159i	$0.542357\pi$
$374$	−18.6191	−0.962771
$375$	−7.69414	−0.397324
$376$	−80.4454	−4.14866
$377$	−0.143912	−0.00741186
$378$	0	0
$379$	−19.6383	−1.00875	−0.504377	−	0.863484i	$-0.668278\pi$
$379$	−19.6383	−1.00875	−0.504377	+	0.863484i	$0.668278\pi$
$380$	−13.4235	−0.688609
$381$	−5.97924	−0.306326
$382$	−3.59067	−0.183715
$383$	10.7703	0.550334	0.275167	−	0.961396i	$-0.411267\pi$
$383$	10.7703	0.550334	0.275167	+	0.961396i	$0.411267\pi$
$384$	−62.0644	−3.16721
$385$	0	0
$386$	−58.3528	−2.97008
$387$	6.43308	0.327012
$388$	61.7823	3.13652
$389$	32.6788	1.65688	0.828441	−	0.560077i	$-0.189228\pi$
$389$	32.6788	1.65688	0.828441	+	0.560077i	$0.189228\pi$
$390$	0.681799	0.0345242
$391$	−26.5708	−1.34374
$392$	0	0
$393$	17.6424	0.889942
$394$	41.9574	2.11378
$395$	3.57054	0.179653
$396$	−5.73760	−0.288325
$397$	32.9484	1.65363	0.826817	−	0.562470i	$-0.190149\pi$
$397$	32.9484	1.65363	0.826817	+	0.562470i	$0.190149\pi$
$398$	71.5450	3.58622
$399$	0	0
$400$	−75.3302	−3.76651
$401$	−19.3586	−0.966724	−0.483362	−	0.875420i	$-0.660585\pi$
$401$	−19.3586	−0.966724	−0.483362	+	0.875420i	$0.660585\pi$
$402$	−8.39308	−0.418609
$403$	2.17623	0.108406
$404$	−86.0087	−4.27909
$405$	−0.825711	−0.0410299
$406$	0	0
$407$	5.73760	0.284402
$408$	−69.5907	−3.44525
$409$	30.1146	1.48907	0.744535	−	0.667583i	$-0.232671\pi$
$409$	30.1146	1.48907	0.744535	+	0.667583i	$0.232671\pi$
$410$	1.48243	0.0732119
$411$	−9.35972	−0.461681
$412$	14.1378	0.696517
$413$	0	0
$414$	−11.0421	−0.542690
$415$	1.96184	0.0963029
$416$	8.23203	0.403608
$417$	7.40270	0.362512
$418$	−7.88151	−0.385497
$419$	2.70722	0.132256	0.0661282	−	0.997811i	$-0.478935\pi$
$419$	2.70722	0.132256	0.0661282	+	0.997811i	$0.478935\pi$
$420$	0	0
$421$	−30.1501	−1.46943	−0.734713	−	0.678378i	$-0.762683\pi$
$421$	−30.1501	−1.46943	−0.734713	+	0.678378i	$0.762683\pi$
$422$	5.14090	0.250255
$423$	−7.73760	−0.376215
$424$	73.9573	3.59168
$425$	−28.9040	−1.40205
$426$	−9.96000	−0.482564
$427$	0	0
$428$	−66.4439	−3.21169
$429$	0.296842	0.0143317
$430$	−14.7758	−0.712550
$431$	32.6809	1.57418	0.787092	−	0.616836i	$-0.211586\pi$
$431$	32.6809	1.57418	0.787092	+	0.616836i	$0.211586\pi$
$432$	−17.4448	−0.839314
$433$	26.2432	1.26117	0.630583	−	0.776122i	$-0.282816\pi$
$433$	26.2432	1.26117	0.630583	+	0.776122i	$0.282816\pi$
$434$	0	0
$435$	−0.400314	−0.0191936
$436$	−31.1176	−1.49026
$437$	−11.2475	−0.538040
$438$	44.5968	2.13092
$439$	27.6905	1.32160	0.660798	−	0.750564i	$-0.270218\pi$
$439$	27.6905	1.32160	0.660798	+	0.750564i	$0.270218\pi$
$440$	8.58467	0.409258
$441$	0	0
$442$	5.52693	0.262889
$443$	−20.8939	−0.992697	−0.496348	−	0.868123i	$-0.665326\pi$
$443$	−20.8939	−0.992697	−0.496348	+	0.868123i	$0.665326\pi$
$444$	32.9200	1.56231
$445$	10.0508	0.476456
$446$	17.1865	0.813803
$447$	12.0117	0.568136
$448$	0	0
$449$	23.9615	1.13081	0.565407	−	0.824812i	$-0.308719\pi$
$449$	23.9615	1.13081	0.565407	+	0.824812i	$0.308719\pi$
$450$	−12.0117	−0.566239
$451$	0.645420	0.0303916
$452$	−100.498	−4.72701
$453$	−9.32182	−0.437977
$454$	−13.9392	−0.654201
$455$	0	0
$456$	−29.4579	−1.37949
$457$	18.6108	0.870578	0.435289	−	0.900291i	$-0.356646\pi$
$457$	18.6108	0.870578	0.435289	+	0.900291i	$0.356646\pi$
$458$	−62.4003	−2.91577
$459$	−6.69354	−0.312428
$460$	18.8065	0.876856
$461$	6.88513	0.320672	0.160336	−	0.987062i	$-0.448742\pi$
$461$	6.88513	0.320672	0.160336	+	0.987062i	$0.448742\pi$
$462$	0	0
$463$	2.73532	0.127121	0.0635605	−	0.997978i	$-0.479754\pi$
$463$	2.73532	0.127121	0.0635605	+	0.997978i	$0.479754\pi$
$464$	−8.45745	−0.392627
$465$	6.05352	0.280725
$466$	13.4448	0.622819
$467$	−35.6361	−1.64904	−0.824521	−	0.565832i	$-0.808555\pi$
$467$	−35.6361	−1.64904	−0.824521	+	0.565832i	$0.808555\pi$
$468$	1.70316	0.0787285
$469$	0	0
$470$	17.7720	0.819763
$471$	−5.10347	−0.235156
$472$	12.0289	0.553674
$473$	−6.43308	−0.295793
$474$	12.0284	0.552484
$475$	−12.2351	−0.561387
$476$	0	0
$477$	7.11354	0.325706
$478$	−7.18965	−0.328847
$479$	27.3798	1.25102	0.625508	−	0.780217i	$-0.284892\pi$
$479$	27.3798	1.25102	0.625508	+	0.780217i	$0.284892\pi$
$480$	22.8986	1.04518
$481$	−1.70316	−0.0776573
$482$	−7.72753	−0.351979
$483$	0	0
$484$	5.73760	0.260800
$485$	−8.89123	−0.403730
$486$	−2.78165	−0.126178
$487$	29.3706	1.33091	0.665455	−	0.746438i	$-0.268237\pi$
$487$	29.3706	1.33091	0.665455	+	0.746438i	$0.268237\pi$
$488$	−54.7538	−2.47859
$489$	−9.48827	−0.429074
$490$	0	0
$491$	−1.69115	−0.0763207	−0.0381604	−	0.999272i	$-0.512150\pi$
$491$	−1.69115	−0.0763207	−0.0381604	+	0.999272i	$0.512150\pi$
$492$	3.70316	0.166951
$493$	−3.24511	−0.146152
$494$	2.33956	0.105262
$495$	0.825711	0.0371129
$496$	127.893	5.74256
$497$	0	0
$498$	6.60904	0.296158
$499$	29.5965	1.32492	0.662461	−	0.749096i	$-0.269512\pi$
$499$	29.5965	1.32492	0.662461	+	0.749096i	$0.269512\pi$
$500$	44.1459	1.97426
$501$	−3.03850	−0.135750
$502$	−2.60632	−0.116326
$503$	−28.2737	−1.26066	−0.630331	−	0.776326i	$-0.717081\pi$
$503$	−28.2737	−1.26066	−0.630331	+	0.776326i	$0.717081\pi$
$504$	0	0
$505$	12.3777	0.550801
$506$	11.0421	0.490882
$507$	12.9119	0.573437
$508$	34.3065	1.52210
$509$	−10.9007	−0.483167	−0.241584	−	0.970380i	$-0.577667\pi$
$509$	−10.9007	−0.483167	−0.241584	+	0.970380i	$0.577667\pi$
$510$	15.3740	0.680772
$511$	0	0
$512$	121.043	5.34941
$513$	−2.83339	−0.125097
$514$	50.1651	2.21269
$515$	−2.03460	−0.0896551
$516$	−36.9104	−1.62489
$517$	7.73760	0.340299
$518$	0	0
$519$	−5.77203	−0.253364
$520$	−2.54829	−0.111750
$521$	−5.63606	−0.246920	−0.123460	−	0.992350i	$-0.539399\pi$
$521$	−5.63606	−0.246920	−0.123460	+	0.992350i	$0.539399\pi$
$522$	−1.34858	−0.0590257
$523$	26.8225	1.17287	0.586434	−	0.809997i	$-0.300531\pi$
$523$	26.8225	1.17287	0.586434	+	0.809997i	$0.300531\pi$
$524$	−101.225	−4.42203
$525$	0	0
$526$	21.9654	0.957737
$527$	49.0722	2.13762
$528$	17.4448	0.759188
$529$	−7.24209	−0.314874
$530$	−16.3387	−0.709706
$531$	1.15699	0.0502091
$532$	0	0
$533$	−0.191588	−0.00829858
$534$	33.8593	1.46523
$535$	9.56210	0.413406
$536$	31.3699	1.35497
$537$	3.02844	0.130687
$538$	−47.8918	−2.06476
$539$	0	0
$540$	4.73760	0.203874
$541$	6.06709	0.260845	0.130422	−	0.991459i	$-0.458367\pi$
$541$	6.06709	0.260845	0.130422	+	0.991459i	$0.458367\pi$
$542$	25.9677	1.11541
$543$	−9.67878	−0.415356
$544$	185.625	7.95863
$545$	4.47821	0.191825
$546$	0	0
$547$	−13.7115	−0.586263	−0.293132	−	0.956072i	$-0.594697\pi$
$547$	−13.7115	−0.586263	−0.293132	+	0.956072i	$0.594697\pi$
$548$	53.7023	2.29405
$549$	−5.26647	−0.224767
$550$	12.0117	0.512182
$551$	−1.37366	−0.0585199
$552$	41.2710	1.75661
$553$	0	0
$554$	15.2301	0.647064
$555$	−4.73760	−0.201100
$556$	−42.4737	−1.80129
$557$	−11.0956	−0.470137	−0.235069	−	0.971979i	$-0.575531\pi$
$557$	−11.0956	−0.470137	−0.235069	+	0.971979i	$0.575531\pi$
$558$	20.3931	0.863308
$559$	1.90961	0.0807677
$560$	0	0
$561$	6.69354	0.282601
$562$	−51.0436	−2.15314
$563$	−4.35157	−0.183397	−0.0916983	−	0.995787i	$-0.529230\pi$
$563$	−4.35157	−0.183397	−0.0916983	+	0.995787i	$0.529230\pi$
$564$	44.3952	1.86938
$565$	14.4628	0.608457
$566$	−72.4360	−3.04471
$567$	0	0
$568$	37.2265	1.56199
$569$	9.14224	0.383262	0.191631	−	0.981467i	$-0.438622\pi$
$569$	9.14224	0.383262	0.191631	+	0.981467i	$0.438622\pi$
$570$	6.50785	0.272584
$571$	4.76451	0.199389	0.0996944	−	0.995018i	$-0.468213\pi$
$571$	4.76451	0.199389	0.0996944	+	0.995018i	$0.468213\pi$
$572$	−1.70316	−0.0712126
$573$	1.29084	0.0539256
$574$	0	0
$575$	17.1416	0.714856
$576$	42.2513	1.76047
$577$	17.6096	0.733097	0.366548	−	0.930399i	$-0.380539\pi$
$577$	17.6096	0.733097	0.366548	+	0.930399i	$0.380539\pi$
$578$	77.3396	3.21690
$579$	20.9777	0.871805
$580$	2.29684	0.0953712
$581$	0	0
$582$	−29.9528	−1.24158
$583$	−7.11354	−0.294613
$584$	−166.685	−6.89747
$585$	−0.245106	−0.0101339
$586$	−59.3375	−2.45121
$587$	−33.3405	−1.37611	−0.688054	−	0.725659i	$-0.741535\pi$
$587$	−33.3405	−1.37611	−0.688054	+	0.725659i	$0.741535\pi$
$588$	0	0
$589$	20.7724	0.855911
$590$	−2.65742	−0.109404
$591$	−15.0836	−0.620458
$592$	−100.091	−4.11373
$593$	3.73414	0.153343	0.0766713	−	0.997056i	$-0.475571\pi$
$593$	3.73414	0.153343	0.0766713	+	0.997056i	$0.475571\pi$
$594$	2.78165	0.114133
$595$	0	0
$596$	−68.9185	−2.82301
$597$	−25.7203	−1.05266
$598$	−3.27776	−0.134038
$599$	14.1651	0.578771	0.289385	−	0.957213i	$-0.406549\pi$
$599$	14.1651	0.578771	0.289385	+	0.957213i	$0.406549\pi$
$600$	44.8950	1.83283
$601$	18.3032	0.746602	0.373301	−	0.927710i	$-0.378226\pi$
$601$	18.3032	0.746602	0.373301	+	0.927710i	$0.378226\pi$
$602$	0	0
$603$	3.01730	0.122874
$604$	53.4848	2.17627
$605$	−0.825711	−0.0335699
$606$	41.6980	1.69387
$607$	45.2626	1.83715	0.918576	−	0.395245i	$-0.129340\pi$
$607$	45.2626	1.83715	0.918576	+	0.395245i	$0.129340\pi$
$608$	78.5757	3.18666
$609$	0	0
$610$	12.0962	0.489762
$611$	−2.29684	−0.0929203
$612$	38.4048	1.55242
$613$	−14.5744	−0.588656	−0.294328	−	0.955704i	$-0.595096\pi$
$613$	−14.5744	−0.588656	−0.294328	+	0.955704i	$0.595096\pi$
$614$	19.1469	0.772707
$615$	−0.532930	−0.0214898
$616$	0	0
$617$	−39.8257	−1.60332	−0.801662	−	0.597778i	$-0.796050\pi$
$617$	−39.8257	−1.60332	−0.801662	+	0.597778i	$0.796050\pi$
$618$	−6.85415	−0.275714
$619$	0.437767	0.0175953	0.00879767	−	0.999961i	$-0.497200\pi$
$619$	0.437767	0.0175953	0.00879767	+	0.999961i	$0.497200\pi$
$620$	−34.7326	−1.39490
$621$	3.96962	0.159295
$622$	10.5627	0.423526
$623$	0	0
$624$	−5.17835	−0.207300
$625$	15.2379	0.609515
$626$	−7.28544	−0.291185
$627$	2.83339	0.113155
$628$	29.2817	1.16847
$629$	−38.4048	−1.53130
$630$	0	0
$631$	29.1632	1.16097	0.580484	−	0.814272i	$-0.302863\pi$
$631$	29.1632	1.16097	0.580484	+	0.814272i	$0.302863\pi$
$632$	−44.9574	−1.78831
$633$	−1.84814	−0.0734571
$634$	−77.5086	−3.07826
$635$	−4.93713	−0.195924
$636$	−40.8146	−1.61840
$637$	0	0
$638$	1.34858	0.0533907
$639$	3.58061	0.141647
$640$	−51.2472	−2.02572
$641$	−5.38600	−0.212734	−0.106367	−	0.994327i	$-0.533922\pi$
$641$	−5.38600	−0.212734	−0.106367	+	0.994327i	$0.533922\pi$
$642$	32.2128	1.27134
$643$	2.19971	0.0867481	0.0433740	−	0.999059i	$-0.486189\pi$
$643$	2.19971	0.0867481	0.0433740	+	0.999059i	$0.486189\pi$
$644$	0	0
$645$	5.31186	0.209154
$646$	52.7552	2.07562
$647$	17.2421	0.677857	0.338928	−	0.940812i	$-0.389936\pi$
$647$	17.2421	0.677857	0.338928	+	0.940812i	$0.389936\pi$
$648$	10.3967	0.408421
$649$	−1.15699	−0.0454158
$650$	−3.56559	−0.139854
$651$	0	0
$652$	54.4399	2.13203
$653$	40.7669	1.59533	0.797666	−	0.603099i	$-0.206068\pi$
$653$	40.7669	1.59533	0.797666	+	0.603099i	$0.206068\pi$
$654$	15.0862	0.589916
$655$	14.5675	0.569200
$656$	−11.2592	−0.439599
$657$	−16.0325	−0.625487
$658$	0	0
$659$	33.9747	1.32347	0.661734	−	0.749739i	$-0.269821\pi$
$659$	33.9747	1.32347	0.661734	+	0.749739i	$0.269821\pi$
$660$	−4.73760	−0.184411
$661$	29.9158	1.16359	0.581795	−	0.813336i	$-0.302351\pi$
$661$	29.9158	1.16359	0.581795	+	0.813336i	$0.302351\pi$
$662$	−22.3687	−0.869384
$663$	−1.98692	−0.0771657
$664$	−24.7019	−0.958621
$665$	0	0
$666$	−15.9600	−0.618438
$667$	1.92452	0.0745177
$668$	17.4337	0.674529
$669$	−6.17851	−0.238875
$670$	−6.93026	−0.267739
$671$	5.26647	0.203310
$672$	0	0
$673$	11.3711	0.438325	0.219163	−	0.975688i	$-0.429667\pi$
$673$	11.3711	0.438325	0.219163	+	0.975688i	$0.429667\pi$
$674$	73.0701	2.81456
$675$	4.31820	0.166208
$676$	−74.0832	−2.84935
$677$	−9.71191	−0.373259	−0.186630	−	0.982430i	$-0.559756\pi$
$677$	−9.71191	−0.373259	−0.186630	+	0.982430i	$0.559756\pi$
$678$	48.7224	1.87117
$679$	0	0
$680$	−57.4618	−2.20356
$681$	5.01114	0.192027
$682$	−20.3931	−0.780891
$683$	9.71023	0.371552	0.185776	−	0.982592i	$-0.440520\pi$
$683$	9.71023	0.371552	0.185776	+	0.982592i	$0.440520\pi$
$684$	16.2568	0.621596
$685$	−7.72842	−0.295288
$686$	0	0
$687$	22.4328	0.855865
$688$	112.224	4.27849
$689$	2.11159	0.0804453
$690$	−9.11760	−0.347101
$691$	3.93804	0.149810	0.0749051	−	0.997191i	$-0.476135\pi$
$691$	3.93804	0.149810	0.0749051	+	0.997191i	$0.476135\pi$
$692$	33.1176	1.25894
$693$	0	0
$694$	23.6119	0.896294
$695$	6.11249	0.231860
$696$	5.04044	0.191057
$697$	−4.32014	−0.163637
$698$	88.8155	3.36172
$699$	−4.83339	−0.182816
$700$	0	0
$701$	11.7432	0.443533	0.221766	−	0.975100i	$-0.428818\pi$
$701$	11.7432	0.443533	0.221766	+	0.975100i	$0.428818\pi$
$702$	−0.825711	−0.0311645
$703$	−16.2568	−0.613139
$704$	−42.2513	−1.59241
$705$	−6.38902	−0.240624
$706$	−0.400314	−0.0150660
$707$	0	0
$708$	−6.63834	−0.249484
$709$	−6.53487	−0.245422	−0.122711	−	0.992442i	$-0.539159\pi$
$709$	−6.53487	−0.245422	−0.122711	+	0.992442i	$0.539159\pi$
$710$	−8.22408	−0.308644
$711$	−4.32420	−0.162170
$712$	−126.552	−4.74274
$713$	−29.1024	−1.08989
$714$	0	0
$715$	0.245106	0.00916643
$716$	−17.3759	−0.649369
$717$	2.58467	0.0965261
$718$	22.9066	0.854866
$719$	3.68764	0.137526	0.0687629	−	0.997633i	$-0.478095\pi$
$719$	3.68764	0.137526	0.0687629	+	0.997633i	$0.478095\pi$
$720$	−14.4044	−0.536819
$721$	0	0
$722$	−30.5200	−1.13584
$723$	2.77804	0.103316
$724$	55.5329	2.06387
$725$	2.09351	0.0777512
$726$	−2.78165	−0.103237
$727$	0.674563	0.0250182	0.0125091	−	0.999922i	$-0.496018\pi$
$727$	0.674563	0.0250182	0.0125091	+	0.999922i	$0.496018\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	36.8241	1.36292
$731$	43.0600	1.59263
$732$	30.2168	1.11685
$733$	−17.3392	−0.640439	−0.320219	−	0.947343i	$-0.603757\pi$
$733$	−17.3392	−0.640439	−0.320219	+	0.947343i	$0.603757\pi$
$734$	−46.2596	−1.70747
$735$	0	0
$736$	−110.086	−4.05781
$737$	−3.01730	−0.111144
$738$	−1.79533	−0.0660872
$739$	36.5390	1.34411	0.672054	−	0.740503i	$-0.265412\pi$
$739$	36.5390	1.34411	0.672054	+	0.740503i	$0.265412\pi$
$740$	27.1824	0.999245
$741$	−0.841068	−0.0308974
$742$	0	0
$743$	9.83489	0.360807	0.180404	−	0.983593i	$-0.442260\pi$
$743$	9.83489	0.360807	0.180404	+	0.983593i	$0.442260\pi$
$744$	−76.2211	−2.79440
$745$	9.91823	0.363376
$746$	−14.2555	−0.521931
$747$	−2.37594	−0.0869311
$748$	−38.4048	−1.40422
$749$	0	0
$750$	−21.4024	−0.781506
$751$	−28.6968	−1.04716	−0.523581	−	0.851976i	$-0.675404\pi$
$751$	−28.6968	−1.04716	−0.523581	+	0.851976i	$0.675404\pi$
$752$	−134.981	−4.92225
$753$	0.936967	0.0341450
$754$	−0.400314	−0.0145786
$755$	−7.69713	−0.280127
$756$	0	0
$757$	−50.9435	−1.85157	−0.925786	−	0.378047i	$-0.876596\pi$
$757$	−50.9435	−1.85157	−0.925786	+	0.378047i	$0.876596\pi$
$758$	−54.6271	−1.98414
$759$	−3.96962	−0.144088
$760$	−24.3237	−0.882314
$761$	−43.9179	−1.59202	−0.796011	−	0.605282i	$-0.793061\pi$
$761$	−43.9179	−1.59202	−0.796011	+	0.605282i	$0.793061\pi$
$762$	−16.6322	−0.602520
$763$	0	0
$764$	−7.40632	−0.267951
$765$	−5.52693	−0.199827
$766$	29.9591	1.08247
$767$	0.343443	0.0124010
$768$	−88.1390	−3.18044
$769$	−4.82343	−0.173937	−0.0869687	−	0.996211i	$-0.527718\pi$
$769$	−4.82343	−0.173937	−0.0869687	+	0.996211i	$0.527718\pi$
$770$	0	0
$771$	−18.0343	−0.649489
$772$	−120.362	−4.33192
$773$	−7.29084	−0.262233	−0.131117	−	0.991367i	$-0.541856\pi$
$773$	−7.29084	−0.262233	−0.131117	+	0.991367i	$0.541856\pi$
$774$	17.8946	0.643208
$775$	−31.6579	−1.13719
$776$	111.951	4.01882
$777$	0	0
$778$	90.9011	3.25896
$779$	−1.82873	−0.0655209
$780$	1.40632	0.0503542
$781$	−3.58061	−0.128124
$782$	−73.9108	−2.64305
$783$	0.484812	0.0173258
$784$	0	0
$785$	−4.21399	−0.150404
$786$	49.0751	1.75045
$787$	28.9814	1.03307	0.516537	−	0.856265i	$-0.327221\pi$
$787$	28.9814	1.03307	0.516537	+	0.856265i	$0.327221\pi$
$788$	86.5438	3.08299
$789$	−7.89653	−0.281124
$790$	9.93201	0.353365
$791$	0	0
$792$	−10.3967	−0.369431
$793$	−1.56331	−0.0555147
$794$	91.6511	3.25258
$795$	5.87372	0.208320
$796$	147.573	5.23057
$797$	18.5564	0.657302	0.328651	−	0.944451i	$-0.393406\pi$
$797$	18.5564	0.657302	0.328651	+	0.944451i	$0.393406\pi$
$798$	0	0
$799$	−51.7919	−1.83227
$800$	−119.753	−4.23389
$801$	−12.1723	−0.430089
$802$	−53.8490	−1.90148
$803$	16.0325	0.565775
$804$	−17.3120	−0.610549
$805$	0	0
$806$	6.05352	0.213226
$807$	17.2170	0.606067
$808$	−155.850	−5.48280
$809$	−51.7802	−1.82049	−0.910247	−	0.414066i	$-0.864108\pi$
$809$	−51.7802	−1.82049	−0.910247	+	0.414066i	$0.864108\pi$
$810$	−2.29684	−0.0807028
$811$	33.1104	1.16266	0.581331	−	0.813667i	$-0.302532\pi$
$811$	33.1104	1.16266	0.581331	+	0.813667i	$0.302532\pi$
$812$	0	0
$813$	−9.33534	−0.327405
$814$	15.9600	0.559398
$815$	−7.83457	−0.274433
$816$	−116.768	−4.08768
$817$	18.2274	0.637696
$818$	83.7683	2.92889
$819$	0	0
$820$	3.05774	0.106781
$821$	−10.5381	−0.367781	−0.183891	−	0.982947i	$-0.558869\pi$
$821$	−10.5381	−0.367781	−0.183891	+	0.982947i	$0.558869\pi$
$822$	−26.0355	−0.908092
$823$	5.03266	0.175427	0.0877137	−	0.996146i	$-0.472044\pi$
$823$	5.03266	0.175427	0.0877137	+	0.996146i	$0.472044\pi$
$824$	25.6180	0.892446
$825$	−4.31820	−0.150340
$826$	0	0
$827$	−37.6214	−1.30822	−0.654112	−	0.756398i	$-0.726957\pi$
$827$	−37.6214	−1.30822	−0.654112	+	0.756398i	$0.726957\pi$
$828$	−22.7761	−0.791524
$829$	−17.7102	−0.615102	−0.307551	−	0.951532i	$-0.599509\pi$
$829$	−17.7102	−0.615102	−0.307551	+	0.951532i	$0.599509\pi$
$830$	5.45716	0.189421
$831$	−5.47519	−0.189932
$832$	12.5419	0.434814
$833$	0	0
$834$	20.5917	0.713034
$835$	−2.50892	−0.0868248
$836$	−16.2568	−0.562255
$837$	−7.33128	−0.253406
$838$	7.53055	0.260138
$839$	4.81384	0.166192	0.0830961	−	0.996542i	$-0.473519\pi$
$839$	4.81384	0.166192	0.0830961	+	0.996542i	$0.473519\pi$
$840$	0	0
$841$	−28.7650	−0.991895
$842$	−83.8671	−2.89025
$843$	18.3501	0.632011
$844$	10.6039	0.365002
$845$	10.6615	0.366766
$846$	−21.5233	−0.739987
$847$	0	0
$848$	124.094	4.26142
$849$	26.0406	0.893712
$850$	−80.4010	−2.75773
$851$	22.7761	0.780754
$852$	−20.5441	−0.703828
$853$	−50.3883	−1.72526	−0.862631	−	0.505833i	$-0.831185\pi$
$853$	−50.3883	−1.72526	−0.862631	+	0.505833i	$0.831185\pi$
$854$	0	0
$855$	−2.33956	−0.0800113
$856$	−120.398	−4.11513
$857$	−17.7077	−0.604882	−0.302441	−	0.953168i	$-0.597802\pi$
$857$	−17.7077	−0.604882	−0.302441	+	0.953168i	$0.597802\pi$
$858$	0.825711	0.0281893
$859$	−7.16933	−0.244614	−0.122307	−	0.992492i	$-0.539029\pi$
$859$	−7.16933	−0.244614	−0.122307	+	0.992492i	$0.539029\pi$
$860$	−30.4773	−1.03927
$861$	0	0
$862$	90.9069	3.09630
$863$	8.80928	0.299871	0.149936	−	0.988696i	$-0.452093\pi$
$863$	8.80928	0.299871	0.149936	+	0.988696i	$0.452093\pi$
$864$	−27.7320	−0.943463
$865$	−4.76603	−0.162050
$866$	72.9994	2.48062
$867$	−27.8035	−0.944255
$868$	0	0
$869$	4.32420	0.146689
$870$	−1.11354	−0.0377524
$871$	0.895660	0.0303483
$872$	−56.3860	−1.90947
$873$	10.7680	0.364441
$874$	−31.2866	−1.05829
$875$	0	0
$876$	91.9880	3.10799
$877$	2.11249	0.0713337	0.0356669	−	0.999364i	$-0.488644\pi$
$877$	2.11249	0.0713337	0.0356669	+	0.999364i	$0.488644\pi$
$878$	77.0254	2.59948
$879$	21.3317	0.719501
$880$	14.4044	0.485571
$881$	−32.9967	−1.11169	−0.555843	−	0.831287i	$-0.687604\pi$
$881$	−32.9967	−1.11169	−0.555843	+	0.831287i	$0.687604\pi$
$882$	0	0
$883$	−28.3648	−0.954552	−0.477276	−	0.878753i	$-0.658376\pi$
$883$	−28.3648	−0.954552	−0.477276	+	0.878753i	$0.658376\pi$
$884$	11.4002	0.383429
$885$	0.955340	0.0321134
$886$	−58.1195	−1.95256
$887$	−29.4208	−0.987853	−0.493927	−	0.869504i	$-0.664439\pi$
$887$	−29.4208	−0.987853	−0.493927	+	0.869504i	$0.664439\pi$
$888$	59.6520	2.00179
$889$	0	0
$890$	27.9580	0.937153
$891$	−1.00000	−0.0335013
$892$	35.4498	1.18695
$893$	−21.9236	−0.733646
$894$	33.4125	1.11748
$895$	2.50061	0.0835863
$896$	0	0
$897$	1.17835	0.0393440
$898$	66.6526	2.22423
$899$	−3.55429	−0.118542
$900$	−24.7761	−0.825870
$901$	47.6147	1.58628
$902$	1.79533	0.0597781
$903$	0	0
$904$	−182.105	−6.05671
$905$	−7.99188	−0.265659
$906$	−25.9301	−0.861469
$907$	9.37615	0.311330	0.155665	−	0.987810i	$-0.450248\pi$
$907$	9.37615	0.311330	0.155665	+	0.987810i	$0.450248\pi$
$908$	−28.7519	−0.954165
$909$	−14.9904	−0.497200
$910$	0	0
$911$	−23.7992	−0.788504	−0.394252	−	0.919002i	$-0.628996\pi$
$911$	−23.7992	−0.788504	−0.394252	+	0.919002i	$0.628996\pi$
$912$	−49.4280	−1.63672
$913$	2.37594	0.0786321
$914$	51.7689	1.71236
$915$	−4.34858	−0.143760
$916$	−128.710	−4.25271
$917$	0	0
$918$	−18.6191	−0.614522
$919$	−8.34407	−0.275245	−0.137623	−	0.990485i	$-0.543946\pi$
$919$	−8.34407	−0.275245	−0.137623	+	0.990485i	$0.543946\pi$
$920$	34.0779	1.12351
$921$	−6.88329	−0.226812
$922$	19.1520	0.630739
$923$	1.06287	0.0349849
$924$	0	0
$925$	24.7761	0.814633
$926$	7.60870	0.250037
$927$	2.46405	0.0809302
$928$	−13.4448	−0.441348
$929$	−42.7966	−1.40411	−0.702055	−	0.712123i	$-0.747734\pi$
$929$	−42.7966	−1.40411	−0.702055	+	0.712123i	$0.747734\pi$
$930$	16.8388	0.552166
$931$	0	0
$932$	27.7320	0.908393
$933$	−3.79728	−0.124317
$934$	−99.1272	−3.24354
$935$	5.52693	0.180750
$936$	3.08617	0.100875
$937$	15.5047	0.506517	0.253258	−	0.967399i	$-0.418498\pi$
$937$	15.5047	0.506517	0.253258	+	0.967399i	$0.418498\pi$
$938$	0	0
$939$	2.61910	0.0854712
$940$	36.6576	1.19564
$941$	−9.37356	−0.305569	−0.152785	−	0.988260i	$-0.548824\pi$
$941$	−9.37356	−0.305569	−0.152785	+	0.988260i	$0.548824\pi$
$942$	−14.1961	−0.462534
$943$	2.56207	0.0834326
$944$	20.1835	0.656916
$945$	0	0
$946$	−17.8946	−0.581803
$947$	56.3668	1.83167	0.915837	−	0.401551i	$-0.131529\pi$
$947$	56.3668	1.83167	0.915837	+	0.401551i	$0.131529\pi$
$948$	24.8105	0.805809
$949$	−4.75911	−0.154487
$950$	−34.0339	−1.10421
$951$	27.8642	0.903559
$952$	0	0
$953$	17.5555	0.568678	0.284339	−	0.958724i	$-0.408226\pi$
$953$	17.5555	0.568678	0.284339	+	0.958724i	$0.408226\pi$
$954$	19.7874	0.640640
$955$	1.06586	0.0344904
$956$	−14.8298	−0.479629
$957$	−0.484812	−0.0156717
$958$	76.1612	2.46066
$959$	0	0
$960$	34.8874	1.12598
$961$	22.7477	0.733795
$962$	−4.73760	−0.152746
$963$	−11.5804	−0.373175
$964$	−15.9392	−0.513369
$965$	17.3216	0.557601
$966$	0	0
$967$	52.7796	1.69728	0.848638	−	0.528974i	$-0.177423\pi$
$967$	52.7796	1.69728	0.848638	+	0.528974i	$0.177423\pi$
$968$	10.3967	0.334162
$969$	−18.9654	−0.609257
$970$	−24.7323	−0.794107
$971$	53.2656	1.70937	0.854687	−	0.519144i	$-0.173749\pi$
$971$	53.2656	1.70937	0.854687	+	0.519144i	$0.173749\pi$
$972$	−5.73760	−0.184033
$973$	0	0
$974$	81.6990	2.61780
$975$	1.28182	0.0410512
$976$	−91.8725	−2.94077
$977$	5.10662	0.163375	0.0816876	−	0.996658i	$-0.473969\pi$
$977$	5.10662	0.163375	0.0816876	+	0.996658i	$0.473969\pi$
$978$	−26.3931	−0.843958
$979$	12.1723	0.389030
$980$	0	0
$981$	−5.42346	−0.173158
$982$	−4.70420	−0.150117
$983$	−33.2878	−1.06172	−0.530858	−	0.847461i	$-0.678130\pi$
$983$	−33.2878	−1.06172	−0.530858	+	0.847461i	$0.678130\pi$
$984$	6.71023	0.213914
$985$	−12.4547	−0.396840
$986$	−9.02676	−0.287471
$987$	0	0
$988$	4.82571	0.153526
$989$	−25.5369	−0.812026
$990$	2.29684	0.0729984
$991$	37.9808	1.20650	0.603249	−	0.797553i	$-0.293872\pi$
$991$	37.9808	1.20650	0.603249	+	0.797553i	$0.293872\pi$
$992$	203.311	6.45514
$993$	8.04151	0.255190
$994$	0	0
$995$	−21.2375	−0.673275
$996$	13.6322	0.431952
$997$	−26.9470	−0.853421	−0.426711	−	0.904388i	$-0.640328\pi$
$997$	−26.9470	−0.853421	−0.426711	+	0.904388i	$0.640328\pi$
$998$	82.3272	2.60602
$999$	5.73760	0.181530

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.a.x.1.4		4
3.2	odd	2		4851.2.a.bu.1.1		4
7.3	odd	6		231.2.i.e.100.1	yes	8
7.5	odd	6		231.2.i.e.67.1	✓	8
7.6	odd	2		1617.2.a.z.1.4		4
21.5	even	6		693.2.i.i.298.4		8
21.17	even	6		693.2.i.i.100.4		8
21.20	even	2		4851.2.a.bt.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.i.e.67.1	✓	8	7.5	odd	6
231.2.i.e.100.1	yes	8	7.3	odd	6
693.2.i.i.100.4		8	21.17	even	6
693.2.i.i.298.4		8	21.5	even	6
1617.2.a.x.1.4		4	1.1	even	1	trivial
1617.2.a.z.1.4		4	7.6	odd	2
4851.2.a.bt.1.1		4	21.20	even	2
4851.2.a.bu.1.1		4	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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q+2.78165 q^{2} -1.00000 q^{3} +5.73760 q^{4} -0.825711 q^{5} -2.78165 q^{6} +10.3967 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.78165 q^{2} -1.00000 q^{3} +5.73760 q^{4} -0.825711 q^{5} -2.78165 q^{6} +10.3967 q^{8} +1.00000 q^{9} -2.29684 q^{10} -1.00000 q^{11} -5.73760 q^{12} +0.296842 q^{13} +0.825711 q^{15} +17.4448 q^{16} +6.69354 q^{17} +2.78165 q^{18} +2.83339 q^{19} -4.73760 q^{20} -2.78165 q^{22} -3.96962 q^{23} -10.3967 q^{24} -4.31820 q^{25} +0.825711 q^{26} -1.00000 q^{27} -0.484812 q^{29} +2.29684 q^{30} +7.33128 q^{31} +27.7320 q^{32} +1.00000 q^{33} +18.6191 q^{34} +5.73760 q^{36} -5.73760 q^{37} +7.88151 q^{38} -0.296842 q^{39} -8.58467 q^{40} -0.645420 q^{41} +6.43308 q^{43} -5.73760 q^{44} -0.825711 q^{45} -11.0421 q^{46} -7.73760 q^{47} -17.4448 q^{48} -12.0117 q^{50} -6.69354 q^{51} +1.70316 q^{52} +7.11354 q^{53} -2.78165 q^{54} +0.825711 q^{55} -2.83339 q^{57} -1.34858 q^{58} +1.15699 q^{59} +4.73760 q^{60} -5.26647 q^{61} +20.3931 q^{62} +42.2513 q^{64} -0.245106 q^{65} +2.78165 q^{66} +3.01730 q^{67} +38.4048 q^{68} +3.96962 q^{69} +3.58061 q^{71} +10.3967 q^{72} -16.0325 q^{73} -15.9600 q^{74} +4.31820 q^{75} +16.2568 q^{76} -0.825711 q^{78} -4.32420 q^{79} -14.4044 q^{80} +1.00000 q^{81} -1.79533 q^{82} -2.37594 q^{83} -5.52693 q^{85} +17.8946 q^{86} +0.484812 q^{87} -10.3967 q^{88} -12.1723 q^{89} -2.29684 q^{90} -22.7761 q^{92} -7.33128 q^{93} -21.5233 q^{94} -2.33956 q^{95} -27.7320 q^{96} +10.7680 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 2 q^{6} + 12 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 2 * q^6 + 12 * q^8 + 4 * q^9	\( 4 q + 2 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 2 q^{6} + 12 q^{8} + 4 q^{9} - 10 q^{10} - 4 q^{11} - 4 q^{12} + 2 q^{13} + 4 q^{15} + 12 q^{16} - 2 q^{17} + 2 q^{18} - 2 q^{22} + 4 q^{23} - 12 q^{24} + 4 q^{25} + 4 q^{26} - 4 q^{27} + 8 q^{29} + 10 q^{30} + 12 q^{31} + 26 q^{32} + 4 q^{33} + 16 q^{34} + 4 q^{36} - 4 q^{37} - 8 q^{38} - 2 q^{39} + 6 q^{40} - 2 q^{41} + 18 q^{43} - 4 q^{44} - 4 q^{45} - 14 q^{46} - 12 q^{47} - 12 q^{48} + 2 q^{50} + 2 q^{51} + 6 q^{52} - 12 q^{53} - 2 q^{54} + 4 q^{55} - 4 q^{58} - 12 q^{59} - 2 q^{61} + 26 q^{62} + 56 q^{64} - 4 q^{65} + 2 q^{66} + 28 q^{67} + 48 q^{68} - 4 q^{69} + 12 q^{71} + 12 q^{72} - 6 q^{73} - 16 q^{74} - 4 q^{75} + 18 q^{76} - 4 q^{78} + 2 q^{79} - 16 q^{80} + 4 q^{81} + 12 q^{82} + 12 q^{83} + 18 q^{85} + 36 q^{86} - 8 q^{87} - 12 q^{88} - 8 q^{89} - 10 q^{90} - 16 q^{92} - 12 q^{93} - 20 q^{94} + 34 q^{95} - 26 q^{96} + 44 q^{97} - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 2 * q^6 + 12 * q^8 + 4 * q^9 - 10 * q^10 - 4 * q^11 - 4 * q^12 + 2 * q^13 + 4 * q^15 + 12 * q^16 - 2 * q^17 + 2 * q^18 - 2 * q^22 + 4 * q^23 - 12 * q^24 + 4 * q^25 + 4 * q^26 - 4 * q^27 + 8 * q^29 + 10 * q^30 + 12 * q^31 + 26 * q^32 + 4 * q^33 + 16 * q^34 + 4 * q^36 - 4 * q^37 - 8 * q^38 - 2 * q^39 + 6 * q^40 - 2 * q^41 + 18 * q^43 - 4 * q^44 - 4 * q^45 - 14 * q^46 - 12 * q^47 - 12 * q^48 + 2 * q^50 + 2 * q^51 + 6 * q^52 - 12 * q^53 - 2 * q^54 + 4 * q^55 - 4 * q^58 - 12 * q^59 - 2 * q^61 + 26 * q^62 + 56 * q^64 - 4 * q^65 + 2 * q^66 + 28 * q^67 + 48 * q^68 - 4 * q^69 + 12 * q^71 + 12 * q^72 - 6 * q^73 - 16 * q^74 - 4 * q^75 + 18 * q^76 - 4 * q^78 + 2 * q^79 - 16 * q^80 + 4 * q^81 + 12 * q^82 + 12 * q^83 + 18 * q^85 + 36 * q^86 - 8 * q^87 - 12 * q^88 - 8 * q^89 - 10 * q^90 - 16 * q^92 - 12 * q^93 - 20 * q^94 + 34 * q^95 - 26 * q^96 + 44 * q^97 - 4 * q^99

Introduction

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