LMFDB - Embedded newform 2254.2.a.x.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2254,2,Mod(1,2254)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2254, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2254.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2254 = 2 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2254.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:	$17.9982806156$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.1957.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} - x + 1 $ x^4 - 4*x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 322)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.396339$ of defining polynomial
Character	$\chi$	$=$	2254.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.12676 q^{3} +1.00000 q^{4} -1.71616 q^{5} +1.12676 q^{6} +1.00000 q^{8} -1.73042 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.12676 q^{3} +1.00000 q^{4} -1.71616 q^{5} +1.12676 q^{6} +1.00000 q^{8} -1.73042 q^{9} -1.71616 q^{10} -3.64985 q^{11} +1.12676 q^{12} +3.79833 q^{13} -1.93369 q^{15} +1.00000 q^{16} -4.17700 q^{17} -1.73042 q^{18} -8.12271 q^{19} -1.71616 q^{20} -3.64985 q^{22} -1.00000 q^{23} +1.12676 q^{24} -2.05480 q^{25} +3.79833 q^{26} -5.33003 q^{27} +2.80694 q^{29} -1.93369 q^{30} -8.54301 q^{31} +1.00000 q^{32} -4.11250 q^{33} -4.17700 q^{34} -1.73042 q^{36} +8.93530 q^{37} -8.12271 q^{38} +4.27979 q^{39} -1.71616 q^{40} -10.0518 q^{41} +8.11069 q^{43} -3.64985 q^{44} +2.96967 q^{45} -1.00000 q^{46} +2.95137 q^{47} +1.12676 q^{48} -2.05480 q^{50} -4.70646 q^{51} +3.79833 q^{52} +3.05480 q^{53} -5.33003 q^{54} +6.26373 q^{55} -9.15232 q^{57} +2.80694 q^{58} -4.18902 q^{59} -1.93369 q^{60} +11.3156 q^{61} -8.54301 q^{62} +1.00000 q^{64} -6.51854 q^{65} -4.11250 q^{66} -13.2368 q^{67} -4.17700 q^{68} -1.12676 q^{69} +14.3054 q^{71} -1.73042 q^{72} +4.26097 q^{73} +8.93530 q^{74} -2.31526 q^{75} -8.12271 q^{76} +4.27979 q^{78} -13.4482 q^{79} -1.71616 q^{80} -0.814396 q^{81} -10.0518 q^{82} -9.43848 q^{83} +7.16839 q^{85} +8.11069 q^{86} +3.16274 q^{87} -3.64985 q^{88} -3.95837 q^{89} +2.96967 q^{90} -1.00000 q^{92} -9.62589 q^{93} +2.95137 q^{94} +13.9399 q^{95} +1.12676 q^{96} -0.121105 q^{97} +6.31577 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 3 q^{3} + 4 q^{4} - 7 q^{5} - 3 q^{6} + 4 q^{8} - q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 3 * q^3 + 4 * q^4 - 7 * q^5 - 3 * q^6 + 4 * q^8 - q^9	$ 4 q + 4 q^{2} - 3 q^{3} + 4 q^{4} - 7 q^{5} - 3 q^{6} + 4 q^{8} - q^{9} - 7 q^{10} + 2 q^{11} - 3 q^{12} - q^{13} + 9 q^{15} + 4 q^{16} - 5 q^{17} - q^{18} - 11 q^{19} - 7 q^{20} + 2 q^{22} - 4 q^{23} - 3 q^{24} + 3 q^{25} - q^{26} - 3 q^{27} + 2 q^{29} + 9 q^{30} - 6 q^{31} + 4 q^{32} - 15 q^{33} - 5 q^{34} - q^{36} - 8 q^{37} - 11 q^{38} + 3 q^{39} - 7 q^{40} - 9 q^{41} + 4 q^{43} + 2 q^{44} - 3 q^{45} - 4 q^{46} - 11 q^{47} - 3 q^{48} + 3 q^{50} - 18 q^{51} - q^{52} + q^{53} - 3 q^{54} - 10 q^{55} + 3 q^{57} + 2 q^{58} - 12 q^{59} + 9 q^{60} - 21 q^{61} - 6 q^{62} + 4 q^{64} - 24 q^{65} - 15 q^{66} - 3 q^{67} - 5 q^{68} + 3 q^{69} + 11 q^{71} - q^{72} + 16 q^{73} - 8 q^{74} - 18 q^{75} - 11 q^{76} + 3 q^{78} - 21 q^{79} - 7 q^{80} - 8 q^{81} - 9 q^{82} - 4 q^{83} + 10 q^{85} + 4 q^{86} + 7 q^{87} + 2 q^{88} - 27 q^{89} - 3 q^{90} - 4 q^{92} - 27 q^{93} - 11 q^{94} + 5 q^{95} - 3 q^{96} - 6 q^{97} + 13 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 3 * q^3 + 4 * q^4 - 7 * q^5 - 3 * q^6 + 4 * q^8 - q^9 - 7 * q^10 + 2 * q^11 - 3 * q^12 - q^13 + 9 * q^15 + 4 * q^16 - 5 * q^17 - q^18 - 11 * q^19 - 7 * q^20 + 2 * q^22 - 4 * q^23 - 3 * q^24 + 3 * q^25 - q^26 - 3 * q^27 + 2 * q^29 + 9 * q^30 - 6 * q^31 + 4 * q^32 - 15 * q^33 - 5 * q^34 - q^36 - 8 * q^37 - 11 * q^38 + 3 * q^39 - 7 * q^40 - 9 * q^41 + 4 * q^43 + 2 * q^44 - 3 * q^45 - 4 * q^46 - 11 * q^47 - 3 * q^48 + 3 * q^50 - 18 * q^51 - q^52 + q^53 - 3 * q^54 - 10 * q^55 + 3 * q^57 + 2 * q^58 - 12 * q^59 + 9 * q^60 - 21 * q^61 - 6 * q^62 + 4 * q^64 - 24 * q^65 - 15 * q^66 - 3 * q^67 - 5 * q^68 + 3 * q^69 + 11 * q^71 - q^72 + 16 * q^73 - 8 * q^74 - 18 * q^75 - 11 * q^76 + 3 * q^78 - 21 * q^79 - 7 * q^80 - 8 * q^81 - 9 * q^82 - 4 * q^83 + 10 * q^85 + 4 * q^86 + 7 * q^87 + 2 * q^88 - 27 * q^89 - 3 * q^90 - 4 * q^92 - 27 * q^93 - 11 * q^94 + 5 * q^95 - 3 * q^96 - 6 * q^97 + 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.12676	0.650533	0.325267	−	0.945622i	$-0.394546\pi$
$3$	1.12676	0.650533	0.325267	+	0.945622i	$0.394546\pi$
$4$	1.00000	0.500000
$5$	−1.71616	−0.767490	−0.383745	−	0.923439i	$-0.625366\pi$
$5$	−1.71616	−0.767490	−0.383745	+	0.923439i	$0.625366\pi$
$6$	1.12676	0.459997
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	−1.73042	−0.576806
$10$	−1.71616	−0.542697
$11$	−3.64985	−1.10047	−0.550236	−	0.835009i	$-0.685462\pi$
$11$	−3.64985	−1.10047	−0.550236	+	0.835009i	$0.685462\pi$
$12$	1.12676	0.325267
$13$	3.79833	1.05347	0.526733	−	0.850031i	$-0.323417\pi$
$13$	3.79833	1.05347	0.526733	+	0.850031i	$0.323417\pi$
$14$	0	0
$15$	−1.93369	−0.499278
$16$	1.00000	0.250000
$17$	−4.17700	−1.01307	−0.506535	−	0.862219i	$-0.669074\pi$
$17$	−4.17700	−1.01307	−0.506535	+	0.862219i	$0.669074\pi$
$18$	−1.73042	−0.407864
$19$	−8.12271	−1.86348	−0.931739	−	0.363129i	$-0.881708\pi$
$19$	−8.12271	−1.86348	−0.931739	+	0.363129i	$0.881708\pi$
$20$	−1.71616	−0.383745
$21$	0	0
$22$	−3.64985	−0.778151
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.12676	0.229998
$25$	−2.05480	−0.410960
$26$	3.79833	0.744914
$27$	−5.33003	−1.02577
$28$	0	0
$29$	2.80694	0.521235	0.260618	−	0.965442i	$-0.416074\pi$
$29$	2.80694	0.521235	0.260618	+	0.965442i	$0.416074\pi$
$30$	−1.93369	−0.353043
$31$	−8.54301	−1.53437	−0.767185	−	0.641426i	$-0.778343\pi$
$31$	−8.54301	−1.53437	−0.767185	+	0.641426i	$0.778343\pi$
$32$	1.00000	0.176777
$33$	−4.11250	−0.715894
$34$	−4.17700	−0.716349
$35$	0	0
$36$	−1.73042	−0.288403
$37$	8.93530	1.46895	0.734477	−	0.678634i	$-0.237428\pi$
$37$	8.93530	1.46895	0.734477	+	0.678634i	$0.237428\pi$
$38$	−8.12271	−1.31768
$39$	4.27979	0.685315
$40$	−1.71616	−0.271349
$41$	−10.0518	−1.56983	−0.784917	−	0.619601i	$-0.787294\pi$
$41$	−10.0518	−1.56983	−0.784917	+	0.619601i	$0.787294\pi$
$42$	0	0
$43$	8.11069	1.23687	0.618434	−	0.785837i	$-0.287767\pi$
$43$	8.11069	1.23687	0.618434	+	0.785837i	$0.287767\pi$
$44$	−3.64985	−0.550236
$45$	2.96967	0.442693
$46$	−1.00000	−0.147442
$47$	2.95137	0.430501	0.215250	−	0.976559i	$-0.430943\pi$
$47$	2.95137	0.430501	0.215250	+	0.976559i	$0.430943\pi$
$48$	1.12676	0.162633
$49$	0	0
$50$	−2.05480	−0.290593
$51$	−4.70646	−0.659036
$52$	3.79833	0.526733
$53$	3.05480	0.419609	0.209804	−	0.977743i	$-0.432717\pi$
$53$	3.05480	0.419609	0.209804	+	0.977743i	$0.432717\pi$
$54$	−5.33003	−0.725326
$55$	6.26373	0.844601
$56$	0	0
$57$	−9.15232	−1.21225
$58$	2.80694	0.368569
$59$	−4.18902	−0.545363	−0.272682	−	0.962104i	$-0.587911\pi$
$59$	−4.18902	−0.545363	−0.272682	+	0.962104i	$0.587911\pi$
$60$	−1.93369	−0.249639
$61$	11.3156	1.44881	0.724405	−	0.689375i	$-0.242115\pi$
$61$	11.3156	1.44881	0.724405	+	0.689375i	$0.242115\pi$
$62$	−8.54301	−1.08496
$63$	0	0
$64$	1.00000	0.125000
$65$	−6.51854	−0.808525
$66$	−4.11250	−0.506213
$67$	−13.2368	−1.61713	−0.808567	−	0.588404i	$-0.799756\pi$
$67$	−13.2368	−1.61713	−0.808567	+	0.588404i	$0.799756\pi$
$68$	−4.17700	−0.506535
$69$	−1.12676	−0.135646
$70$	0	0
$71$	14.3054	1.69773	0.848867	−	0.528607i	$-0.177285\pi$
$71$	14.3054	1.69773	0.848867	+	0.528607i	$0.177285\pi$
$72$	−1.73042	−0.203932
$73$	4.26097	0.498709	0.249355	−	0.968412i	$-0.419782\pi$
$73$	4.26097	0.498709	0.249355	+	0.968412i	$0.419782\pi$
$74$	8.93530	1.03871
$75$	−2.31526	−0.267343
$76$	−8.12271	−0.931739
$77$	0	0
$78$	4.27979	0.484591
$79$	−13.4482	−1.51304	−0.756519	−	0.653971i	$-0.773102\pi$
$79$	−13.4482	−1.51304	−0.756519	+	0.653971i	$0.773102\pi$
$80$	−1.71616	−0.191872
$81$	−0.814396	−0.0904885
$82$	−10.0518	−1.11004
$83$	−9.43848	−1.03601	−0.518004	−	0.855378i	$-0.673325\pi$
$83$	−9.43848	−1.03601	−0.518004	+	0.855378i	$0.673325\pi$
$84$	0	0
$85$	7.16839	0.777521
$86$	8.11069	0.874598
$87$	3.16274	0.339081
$88$	−3.64985	−0.389076
$89$	−3.95837	−0.419586	−0.209793	−	0.977746i	$-0.567279\pi$
$89$	−3.95837	−0.419586	−0.209793	+	0.977746i	$0.567279\pi$
$90$	2.96967	0.313031
$91$	0	0
$92$	−1.00000	−0.104257
$93$	−9.62589	−0.998159
$94$	2.95137	0.304410
$95$	13.9399	1.43020
$96$	1.12676	0.114999
$97$	−0.121105	−0.0122964	−0.00614819	−	0.999981i	$-0.501957\pi$
$97$	−0.121105	−0.0122964	−0.00614819	+	0.999981i	$0.501957\pi$
$98$	0	0
$99$	6.31577	0.634759
$100$	−2.05480	−0.205480
$101$	3.72296	0.370448	0.185224	−	0.982696i	$-0.440699\pi$
$101$	3.72296	0.370448	0.185224	+	0.982696i	$0.440699\pi$
$102$	−4.70646	−0.466009
$103$	−15.1284	−1.49064	−0.745321	−	0.666706i	$-0.767704\pi$
$103$	−15.1284	−1.49064	−0.745321	+	0.666706i	$0.767704\pi$
$104$	3.79833	0.372457
$105$	0	0
$106$	3.05480	0.296708
$107$	−13.7354	−1.32785	−0.663927	−	0.747797i	$-0.731112\pi$
$107$	−13.7354	−1.32785	−0.663927	+	0.747797i	$0.731112\pi$
$108$	−5.33003	−0.512883
$109$	9.38933	0.899335	0.449668	−	0.893196i	$-0.351542\pi$
$109$	9.38933	0.899335	0.449668	+	0.893196i	$0.351542\pi$
$110$	6.26373	0.597223
$111$	10.0679	0.955604
$112$	0	0
$113$	−9.39338	−0.883655	−0.441828	−	0.897100i	$-0.645670\pi$
$113$	−9.39338	−0.883655	−0.441828	+	0.897100i	$0.645670\pi$
$114$	−9.15232	−0.857193
$115$	1.71616	0.160033
$116$	2.80694	0.260618
$117$	−6.57270	−0.607646
$118$	−4.18902	−0.385630
$119$	0	0
$120$	−1.93369	−0.176521
$121$	2.32142	0.211039
$122$	11.3156	1.02446
$123$	−11.3260	−1.02123
$124$	−8.54301	−0.767185
$125$	12.1072	1.08290
$126$	0	0
$127$	2.53575	0.225012	0.112506	−	0.993651i	$-0.464112\pi$
$127$	2.53575	0.225012	0.112506	+	0.993651i	$0.464112\pi$
$128$	1.00000	0.0883883
$129$	9.13878	0.804624
$130$	−6.51854	−0.571713
$131$	5.26258	0.459794	0.229897	−	0.973215i	$-0.426161\pi$
$131$	5.26258	0.459794	0.229897	+	0.973215i	$0.426161\pi$
$132$	−4.11250	−0.357947
$133$	0	0
$134$	−13.2368	−1.14349
$135$	9.14718	0.787264
$136$	−4.17700	−0.358174
$137$	−13.8513	−1.18340	−0.591699	−	0.806159i	$-0.701543\pi$
$137$	−13.8513	−1.18340	−0.591699	+	0.806159i	$0.701543\pi$
$138$	−1.12676	−0.0959159
$139$	9.65665	0.819067	0.409533	−	0.912295i	$-0.365692\pi$
$139$	9.65665	0.819067	0.409533	+	0.912295i	$0.365692\pi$
$140$	0	0
$141$	3.32547	0.280055
$142$	14.3054	1.20048
$143$	−13.8633	−1.15931
$144$	−1.73042	−0.144202
$145$	−4.81715	−0.400042
$146$	4.26097	0.352641
$147$	0	0
$148$	8.93530	0.734477
$149$	−9.56131	−0.783293	−0.391647	−	0.920116i	$-0.628094\pi$
$149$	−9.56131	−0.783293	−0.391647	+	0.920116i	$0.628094\pi$
$150$	−2.31526	−0.189040
$151$	7.25672	0.590544	0.295272	−	0.955413i	$-0.404590\pi$
$151$	7.25672	0.590544	0.295272	+	0.955413i	$0.404590\pi$
$152$	−8.12271	−0.658839
$153$	7.22795	0.584345
$154$	0	0
$155$	14.6612	1.17761
$156$	4.27979	0.342658
$157$	2.75509	0.219880	0.109940	−	0.993938i	$-0.464934\pi$
$157$	2.75509	0.219880	0.109940	+	0.993938i	$0.464934\pi$
$158$	−13.4482	−1.06988
$159$	3.44202	0.272970
$160$	−1.71616	−0.135674
$161$	0	0
$162$	−0.814396	−0.0639850
$163$	20.2841	1.58877	0.794386	−	0.607413i	$-0.207793\pi$
$163$	20.2841	1.58877	0.794386	+	0.607413i	$0.207793\pi$
$164$	−10.0518	−0.784917
$165$	7.05770	0.549441
$166$	−9.43848	−0.732568
$167$	0.325472	0.0251858	0.0125929	−	0.999921i	$-0.495991\pi$
$167$	0.325472	0.0251858	0.0125929	+	0.999921i	$0.495991\pi$
$168$	0	0
$169$	1.42730	0.109792
$170$	7.16839	0.549790
$171$	14.0557	1.07487
$172$	8.11069	0.618434
$173$	−13.4018	−1.01892	−0.509459	−	0.860495i	$-0.670155\pi$
$173$	−13.4018	−1.01892	−0.509459	+	0.860495i	$0.670155\pi$
$174$	3.16274	0.239766
$175$	0	0
$176$	−3.64985	−0.275118
$177$	−4.72000	−0.354777
$178$	−3.95837	−0.296692
$179$	20.8545	1.55874	0.779370	−	0.626564i	$-0.215539\pi$
$179$	20.8545	1.55874	0.779370	+	0.626564i	$0.215539\pi$
$180$	2.96967	0.221346
$181$	−1.57738	−0.117246	−0.0586229	−	0.998280i	$-0.518671\pi$
$181$	−1.57738	−0.117246	−0.0586229	+	0.998280i	$0.518671\pi$
$182$	0	0
$183$	12.7499	0.942500
$184$	−1.00000	−0.0737210
$185$	−15.3344	−1.12741
$186$	−9.62589	−0.705805
$187$	15.2454	1.11486
$188$	2.95137	0.215250
$189$	0	0
$190$	13.9399	1.01130
$191$	6.26097	0.453028	0.226514	−	0.974008i	$-0.427267\pi$
$191$	6.26097	0.453028	0.226514	+	0.974008i	$0.427267\pi$
$192$	1.12676	0.0813167
$193$	13.0358	0.938336	0.469168	−	0.883109i	$-0.344554\pi$
$193$	13.0358	0.938336	0.469168	+	0.883109i	$0.344554\pi$
$194$	−0.121105	−0.00869486
$195$	−7.34481	−0.525972
$196$	0	0
$197$	−21.2551	−1.51436	−0.757182	−	0.653204i	$-0.773425\pi$
$197$	−21.2551	−1.51436	−0.757182	+	0.653204i	$0.773425\pi$
$198$	6.31577	0.448842
$199$	−4.73724	−0.335814	−0.167907	−	0.985803i	$-0.553701\pi$
$199$	−4.73724	−0.335814	−0.167907	+	0.985803i	$0.553701\pi$
$200$	−2.05480	−0.145296
$201$	−14.9147	−1.05200
$202$	3.72296	0.261947
$203$	0	0
$204$	−4.70646	−0.329518
$205$	17.2506	1.20483
$206$	−15.1284	−1.05404
$207$	1.73042	0.120272
$208$	3.79833	0.263367
$209$	29.6467	2.05070
$210$	0	0
$211$	16.7617	1.15392	0.576962	−	0.816771i	$-0.304238\pi$
$211$	16.7617	1.15392	0.576962	+	0.816771i	$0.304238\pi$
$212$	3.05480	0.209804
$213$	16.1187	1.10443
$214$	−13.7354	−0.938935
$215$	−13.9192	−0.949284
$216$	−5.33003	−0.362663
$217$	0	0
$218$	9.38933	0.635926
$219$	4.80108	0.324427
$220$	6.26373	0.422300
$221$	−15.8656	−1.06724
$222$	10.0679	0.675714
$223$	−1.23469	−0.0826812	−0.0413406	−	0.999145i	$-0.513163\pi$
$223$	−1.23469	−0.0826812	−0.0413406	+	0.999145i	$0.513163\pi$
$224$	0	0
$225$	3.55566	0.237044
$226$	−9.39338	−0.624838
$227$	−23.0421	−1.52936	−0.764678	−	0.644413i	$-0.777102\pi$
$227$	−23.0421	−1.52936	−0.764678	+	0.644413i	$0.777102\pi$
$228$	−9.15232	−0.606127
$229$	4.83663	0.319613	0.159807	−	0.987148i	$-0.448913\pi$
$229$	4.83663	0.319613	0.159807	+	0.987148i	$0.448913\pi$
$230$	1.71616	0.113160
$231$	0	0
$232$	2.80694	0.184284
$233$	−13.2545	−0.868330	−0.434165	−	0.900833i	$-0.642957\pi$
$233$	−13.2545	−0.868330	−0.434165	+	0.900833i	$0.642957\pi$
$234$	−6.57270	−0.429671
$235$	−5.06501	−0.330405
$236$	−4.18902	−0.272682
$237$	−15.1528	−0.984282
$238$	0	0
$239$	−5.40250	−0.349459	−0.174729	−	0.984616i	$-0.555905\pi$
$239$	−5.40250	−0.349459	−0.174729	+	0.984616i	$0.555905\pi$
$240$	−1.93369	−0.124819
$241$	17.2207	1.10929	0.554643	−	0.832089i	$-0.312855\pi$
$241$	17.2207	1.10929	0.554643	+	0.832089i	$0.312855\pi$
$242$	2.32142	0.149227
$243$	15.0725	0.966899
$244$	11.3156	0.724405
$245$	0	0
$246$	−11.3260	−0.722118
$247$	−30.8527	−1.96311
$248$	−8.54301	−0.542481
$249$	−10.6349	−0.673958
$250$	12.1072	0.765724
$251$	−16.9165	−1.06776	−0.533879	−	0.845561i	$-0.679266\pi$
$251$	−16.9165	−1.06776	−0.533879	+	0.845561i	$0.679266\pi$
$252$	0	0
$253$	3.64985	0.229464
$254$	2.53575	0.159107
$255$	8.07703	0.505803
$256$	1.00000	0.0625000
$257$	12.2662	0.765143	0.382571	−	0.923926i	$-0.375039\pi$
$257$	12.2662	0.765143	0.382571	+	0.923926i	$0.375039\pi$
$258$	9.13878	0.568955
$259$	0	0
$260$	−6.51854	−0.404262
$261$	−4.85718	−0.300652
$262$	5.26258	0.325123
$263$	13.0580	0.805191	0.402596	−	0.915378i	$-0.368108\pi$
$263$	13.0580	0.805191	0.402596	+	0.915378i	$0.368108\pi$
$264$	−4.11250	−0.253107
$265$	−5.24252	−0.322045
$266$	0	0
$267$	−4.46012	−0.272955
$268$	−13.2368	−0.808567
$269$	−3.56705	−0.217487	−0.108743	−	0.994070i	$-0.534683\pi$
$269$	−3.56705	−0.217487	−0.108743	+	0.994070i	$0.534683\pi$
$270$	9.14718	0.556680
$271$	−1.97719	−0.120106	−0.0600529	−	0.998195i	$-0.519127\pi$
$271$	−1.97719	−0.120106	−0.0600529	+	0.998195i	$0.519127\pi$
$272$	−4.17700	−0.253268
$273$	0	0
$274$	−13.8513	−0.836789
$275$	7.49971	0.452250
$276$	−1.12676	−0.0678228
$277$	−10.9364	−0.657104	−0.328552	−	0.944486i	$-0.606561\pi$
$277$	−10.9364	−0.657104	−0.328552	+	0.944486i	$0.606561\pi$
$278$	9.65665	0.579168
$279$	14.7830	0.885034
$280$	0	0
$281$	−4.58034	−0.273240	−0.136620	−	0.990624i	$-0.543624\pi$
$281$	−4.58034	−0.273240	−0.136620	+	0.990624i	$0.543624\pi$
$282$	3.32547	0.198029
$283$	15.0809	0.896465	0.448233	−	0.893917i	$-0.352054\pi$
$283$	15.0809	0.896465	0.448233	+	0.893917i	$0.352054\pi$
$284$	14.3054	0.848867
$285$	15.7068	0.930393
$286$	−13.8633	−0.819757
$287$	0	0
$288$	−1.73042	−0.101966
$289$	0.447294	0.0263114
$290$	−4.81715	−0.282873
$291$	−0.136456	−0.00799921
$292$	4.26097	0.249355
$293$	−14.5555	−0.850344	−0.425172	−	0.905113i	$-0.639786\pi$
$293$	−14.5555	−0.850344	−0.425172	+	0.905113i	$0.639786\pi$
$294$	0	0
$295$	7.18902	0.418561
$296$	8.93530	0.519354
$297$	19.4538	1.12883
$298$	−9.56131	−0.553872
$299$	−3.79833	−0.219663
$300$	−2.31526	−0.133672
$301$	0	0
$302$	7.25672	0.417577
$303$	4.19487	0.240989
$304$	−8.12271	−0.465869
$305$	−19.4193	−1.11195
$306$	7.22795	0.413194
$307$	12.7024	0.724965	0.362482	−	0.931991i	$-0.381929\pi$
$307$	12.7024	0.724965	0.362482	+	0.931991i	$0.381929\pi$
$308$	0	0
$309$	−17.0460	−0.969712
$310$	14.6612	0.832698
$311$	9.21894	0.522758	0.261379	−	0.965236i	$-0.415823\pi$
$311$	9.21894	0.522758	0.261379	+	0.965236i	$0.415823\pi$
$312$	4.27979	0.242296
$313$	15.6567	0.884966	0.442483	−	0.896777i	$-0.354098\pi$
$313$	15.6567	0.884966	0.442483	+	0.896777i	$0.354098\pi$
$314$	2.75509	0.155479
$315$	0	0
$316$	−13.4482	−0.756519
$317$	11.0382	0.619968	0.309984	−	0.950742i	$-0.399676\pi$
$317$	11.0382	0.619968	0.309984	+	0.950742i	$0.399676\pi$
$318$	3.44202	0.193019
$319$	−10.2449	−0.573605
$320$	−1.71616	−0.0959362
$321$	−15.4765	−0.863814
$322$	0	0
$323$	33.9285	1.88783
$324$	−0.814396	−0.0452442
$325$	−7.80480	−0.432933
$326$	20.2841	1.12343
$327$	10.5795	0.585048
$328$	−10.0518	−0.555020
$329$	0	0
$330$	7.05770	0.388513
$331$	−15.6915	−0.862482	−0.431241	−	0.902237i	$-0.641924\pi$
$331$	−15.6915	−0.862482	−0.431241	+	0.902237i	$0.641924\pi$
$332$	−9.43848	−0.518004
$333$	−15.4618	−0.847302
$334$	0.325472	0.0178090
$335$	22.7165	1.24113
$336$	0	0
$337$	5.18787	0.282601	0.141301	−	0.989967i	$-0.454872\pi$
$337$	5.18787	0.282601	0.141301	+	0.989967i	$0.454872\pi$
$338$	1.42730	0.0776350
$339$	−10.5841	−0.574847
$340$	7.16839	0.388760
$341$	31.1807	1.68853
$342$	14.0557	0.760045
$343$	0	0
$344$	8.11069	0.437299
$345$	1.93369	0.104107
$346$	−13.4018	−0.720485
$347$	−17.7594	−0.953374	−0.476687	−	0.879073i	$-0.658163\pi$
$347$	−17.7594	−0.953374	−0.476687	+	0.879073i	$0.658163\pi$
$348$	3.16274	0.169540
$349$	15.3654	0.822488	0.411244	−	0.911525i	$-0.365094\pi$
$349$	15.3654	0.822488	0.411244	+	0.911525i	$0.365094\pi$
$350$	0	0
$351$	−20.2452	−1.08061
$352$	−3.64985	−0.194538
$353$	26.4646	1.40857	0.704283	−	0.709919i	$-0.251269\pi$
$353$	26.4646	1.40857	0.704283	+	0.709919i	$0.251269\pi$
$354$	−4.72000	−0.250865
$355$	−24.5503	−1.30299
$356$	−3.95837	−0.209793
$357$	0	0
$358$	20.8545	1.10220
$359$	7.50002	0.395836	0.197918	−	0.980219i	$-0.436582\pi$
$359$	7.50002	0.395836	0.197918	+	0.980219i	$0.436582\pi$
$360$	2.96967	0.156516
$361$	46.9784	2.47255
$362$	−1.57738	−0.0829053
$363$	2.61568	0.137288
$364$	0	0
$365$	−7.31251	−0.382754
$366$	12.7499	0.666448
$367$	1.61092	0.0840892	0.0420446	−	0.999116i	$-0.486613\pi$
$367$	1.61092	0.0840892	0.0420446	+	0.999116i	$0.486613\pi$
$368$	−1.00000	−0.0521286
$369$	17.3939	0.905490
$370$	−15.3344	−0.797197
$371$	0	0
$372$	−9.62589	−0.499079
$373$	18.1008	0.937223	0.468612	−	0.883404i	$-0.344754\pi$
$373$	18.1008	0.937223	0.468612	+	0.883404i	$0.344754\pi$
$374$	15.2454	0.788322
$375$	13.6418	0.704461
$376$	2.95137	0.152205
$377$	10.6617	0.549104
$378$	0	0
$379$	−10.3909	−0.533747	−0.266873	−	0.963732i	$-0.585991\pi$
$379$	−10.3909	−0.533747	−0.266873	+	0.963732i	$0.585991\pi$
$380$	13.9399	0.715100
$381$	2.85718	0.146378
$382$	6.26097	0.320339
$383$	7.39562	0.377899	0.188949	−	0.981987i	$-0.439492\pi$
$383$	7.39562	0.377899	0.188949	+	0.981987i	$0.439492\pi$
$384$	1.12676	0.0574996
$385$	0	0
$386$	13.0358	0.663504
$387$	−14.0349	−0.713433
$388$	−0.121105	−0.00614819
$389$	4.07942	0.206835	0.103417	−	0.994638i	$-0.467022\pi$
$389$	4.07942	0.206835	0.103417	+	0.994638i	$0.467022\pi$
$390$	−7.34481	−0.371919
$391$	4.17700	0.211240
$392$	0	0
$393$	5.92965	0.299111
$394$	−21.2551	−1.07082
$395$	23.0792	1.16124
$396$	6.31577	0.317380
$397$	−8.86110	−0.444726	−0.222363	−	0.974964i	$-0.571377\pi$
$397$	−8.86110	−0.444726	−0.222363	+	0.974964i	$0.571377\pi$
$398$	−4.73724	−0.237456
$399$	0	0
$400$	−2.05480	−0.102740
$401$	16.6035	0.829137	0.414569	−	0.910018i	$-0.363933\pi$
$401$	16.6035	0.829137	0.414569	+	0.910018i	$0.363933\pi$
$402$	−14.9147	−0.743876
$403$	−32.4491	−1.61641
$404$	3.72296	0.185224
$405$	1.39763	0.0694489
$406$	0	0
$407$	−32.6125	−1.61654
$408$	−4.70646	−0.233004
$409$	−33.7434	−1.66851	−0.834253	−	0.551382i	$-0.814101\pi$
$409$	−33.7434	−1.66851	−0.834253	+	0.551382i	$0.814101\pi$
$410$	17.2506	0.851944
$411$	−15.6071	−0.769840
$412$	−15.1284	−0.745321
$413$	0	0
$414$	1.73042	0.0850454
$415$	16.1979	0.795125
$416$	3.79833	0.186228
$417$	10.8807	0.532830
$418$	29.6467	1.45007
$419$	−36.5806	−1.78708	−0.893539	−	0.448985i	$-0.851786\pi$
$419$	−36.5806	−1.78708	−0.893539	+	0.448985i	$0.851786\pi$
$420$	0	0
$421$	−32.7603	−1.59664	−0.798321	−	0.602233i	$-0.794278\pi$
$421$	−32.7603	−1.59664	−0.798321	+	0.602233i	$0.794278\pi$
$422$	16.7617	0.815947
$423$	−5.10710	−0.248316
$424$	3.05480	0.148354
$425$	8.58289	0.416331
$426$	16.1187	0.780952
$427$	0	0
$428$	−13.7354	−0.663927
$429$	−15.6206	−0.754170
$430$	−13.9192	−0.671245
$431$	−17.7194	−0.853512	−0.426756	−	0.904367i	$-0.640344\pi$
$431$	−17.7194	−0.853512	−0.426756	+	0.904367i	$0.640344\pi$
$432$	−5.33003	−0.256441
$433$	4.51989	0.217212	0.108606	−	0.994085i	$-0.465361\pi$
$433$	4.51989	0.217212	0.108606	+	0.994085i	$0.465361\pi$
$434$	0	0
$435$	−5.42776	−0.260241
$436$	9.38933	0.449668
$437$	8.12271	0.388562
$438$	4.80108	0.229405
$439$	−6.39794	−0.305357	−0.152679	−	0.988276i	$-0.548790\pi$
$439$	−6.39794	−0.305357	−0.152679	+	0.988276i	$0.548790\pi$
$440$	6.26373	0.298611
$441$	0	0
$442$	−15.8656	−0.754650
$443$	−17.1369	−0.814198	−0.407099	−	0.913384i	$-0.633460\pi$
$443$	−17.1369	−0.814198	−0.407099	+	0.913384i	$0.633460\pi$
$444$	10.0679	0.477802
$445$	6.79319	0.322028
$446$	−1.23469	−0.0584644
$447$	−10.7733	−0.509559
$448$	0	0
$449$	−13.2695	−0.626226	−0.313113	−	0.949716i	$-0.601372\pi$
$449$	−13.2695	−0.626226	−0.313113	+	0.949716i	$0.601372\pi$
$450$	3.55566	0.167616
$451$	36.6877	1.72756
$452$	−9.39338	−0.441828
$453$	8.17656	0.384168
$454$	−23.0421	−1.08142
$455$	0	0
$456$	−9.15232	−0.428597
$457$	−30.4628	−1.42499	−0.712494	−	0.701678i	$-0.752435\pi$
$457$	−30.4628	−1.42499	−0.712494	+	0.701678i	$0.752435\pi$
$458$	4.83663	0.226001
$459$	22.2635	1.03917
$460$	1.71616	0.0800163
$461$	−13.1239	−0.611239	−0.305620	−	0.952154i	$-0.598864\pi$
$461$	−13.1239	−0.611239	−0.305620	+	0.952154i	$0.598864\pi$
$462$	0	0
$463$	−21.3453	−0.991998	−0.495999	−	0.868323i	$-0.665198\pi$
$463$	−21.3453	−0.991998	−0.495999	+	0.868323i	$0.665198\pi$
$464$	2.80694	0.130309
$465$	16.5196	0.766076
$466$	−13.2545	−0.614002
$467$	−22.3604	−1.03472	−0.517358	−	0.855769i	$-0.673084\pi$
$467$	−22.3604	−1.03472	−0.517358	+	0.855769i	$0.673084\pi$
$468$	−6.57270	−0.303823
$469$	0	0
$470$	−5.06501	−0.233632
$471$	3.10432	0.143040
$472$	−4.18902	−0.192815
$473$	−29.6028	−1.36114
$474$	−15.1528	−0.695993
$475$	16.6905	0.765814
$476$	0	0
$477$	−5.28608	−0.242033
$478$	−5.40250	−0.247105
$479$	17.4670	0.798088	0.399044	−	0.916932i	$-0.369342\pi$
$479$	17.4670	0.798088	0.399044	+	0.916932i	$0.369342\pi$
$480$	−1.93369	−0.0882606
$481$	33.9392	1.54749
$482$	17.2207	0.784383
$483$	0	0
$484$	2.32142	0.105519
$485$	0.207836	0.00943735
$486$	15.0725	0.683701
$487$	−5.79067	−0.262400	−0.131200	−	0.991356i	$-0.541883\pi$
$487$	−5.79067	−0.262400	−0.131200	+	0.991356i	$0.541883\pi$
$488$	11.3156	0.512232
$489$	22.8552	1.03355
$490$	0	0
$491$	−8.47054	−0.382270	−0.191135	−	0.981564i	$-0.561217\pi$
$491$	−8.47054	−0.382270	−0.191135	+	0.981564i	$0.561217\pi$
$492$	−11.3260	−0.510615
$493$	−11.7246	−0.528048
$494$	−30.8527	−1.38813
$495$	−10.8389	−0.487171
$496$	−8.54301	−0.383592
$497$	0	0
$498$	−10.6349	−0.476560
$499$	−2.52200	−0.112900	−0.0564502	−	0.998405i	$-0.517978\pi$
$499$	−2.52200	−0.112900	−0.0564502	+	0.998405i	$0.517978\pi$
$500$	12.1072	0.541448
$501$	0.366728	0.0163842
$502$	−16.9165	−0.755019
$503$	−8.34455	−0.372065	−0.186033	−	0.982544i	$-0.559563\pi$
$503$	−8.34455	−0.372065	−0.186033	+	0.982544i	$0.559563\pi$
$504$	0	0
$505$	−6.38919	−0.284315
$506$	3.64985	0.162256
$507$	1.60822	0.0714236
$508$	2.53575	0.112506
$509$	16.8755	0.747993	0.373996	−	0.927430i	$-0.377987\pi$
$509$	16.8755	0.747993	0.373996	+	0.927430i	$0.377987\pi$
$510$	8.07703	0.357657
$511$	0	0
$512$	1.00000	0.0441942
$513$	43.2943	1.91149
$514$	12.2662	0.541038
$515$	25.9627	1.14405
$516$	9.13878	0.402312
$517$	−10.7720	−0.473754
$518$	0	0
$519$	−15.1006	−0.662841
$520$	−6.51854	−0.285857
$521$	−6.87941	−0.301392	−0.150696	−	0.988580i	$-0.548152\pi$
$521$	−6.87941	−0.301392	−0.150696	+	0.988580i	$0.548152\pi$
$522$	−4.85718	−0.212593
$523$	−21.2855	−0.930750	−0.465375	−	0.885114i	$-0.654081\pi$
$523$	−21.2855	−0.930750	−0.465375	+	0.885114i	$0.654081\pi$
$524$	5.26258	0.229897
$525$	0	0
$526$	13.0580	0.569356
$527$	35.6841	1.55442
$528$	−4.11250	−0.178973
$529$	1.00000	0.0434783
$530$	−5.24252	−0.227721
$531$	7.24875	0.314569
$532$	0	0
$533$	−38.1802	−1.65377
$534$	−4.46012	−0.193008
$535$	23.5722	1.01911
$536$	−13.2368	−0.571743
$537$	23.4980	1.01401
$538$	−3.56705	−0.153786
$539$	0	0
$540$	9.14718	0.393632
$541$	−44.5055	−1.91344	−0.956721	−	0.291006i	$-0.906010\pi$
$541$	−44.5055	−1.91344	−0.956721	+	0.291006i	$0.906010\pi$
$542$	−1.97719	−0.0849276
$543$	−1.77733	−0.0762724
$544$	−4.17700	−0.179087
$545$	−16.1136	−0.690230
$546$	0	0
$547$	4.70118	0.201008	0.100504	−	0.994937i	$-0.467954\pi$
$547$	4.70118	0.201008	0.100504	+	0.994937i	$0.467954\pi$
$548$	−13.8513	−0.591699
$549$	−19.5807	−0.835683
$550$	7.49971	0.319789
$551$	−22.7999	−0.971310
$552$	−1.12676	−0.0479580
$553$	0	0
$554$	−10.9364	−0.464643
$555$	−17.2781	−0.733416
$556$	9.65665	0.409533
$557$	23.3153	0.987902	0.493951	−	0.869490i	$-0.335552\pi$
$557$	23.3153	0.987902	0.493951	+	0.869490i	$0.335552\pi$
$558$	14.7830	0.625813
$559$	30.8071	1.30300
$560$	0	0
$561$	17.1779	0.725251
$562$	−4.58034	−0.193210
$563$	−39.2614	−1.65467	−0.827335	−	0.561708i	$-0.810144\pi$
$563$	−39.2614	−1.65467	−0.827335	+	0.561708i	$0.810144\pi$
$564$	3.32547	0.140028
$565$	16.1205	0.678196
$566$	15.0809	0.633896
$567$	0	0
$568$	14.3054	0.600239
$569$	28.5241	1.19579	0.597895	−	0.801574i	$-0.296004\pi$
$569$	28.5241	1.19579	0.597895	+	0.801574i	$0.296004\pi$
$570$	15.7068	0.657887
$571$	11.4778	0.480333	0.240167	−	0.970732i	$-0.422798\pi$
$571$	11.4778	0.480333	0.240167	+	0.970732i	$0.422798\pi$
$572$	−13.8633	−0.579655
$573$	7.05460	0.294710
$574$	0	0
$575$	2.05480	0.0856911
$576$	−1.73042	−0.0721008
$577$	−22.8183	−0.949940	−0.474970	−	0.880002i	$-0.657541\pi$
$577$	−22.8183	−0.949940	−0.474970	+	0.880002i	$0.657541\pi$
$578$	0.447294	0.0186050
$579$	14.6882	0.610419
$580$	−4.81715	−0.200021
$581$	0	0
$582$	−0.136456	−0.00565630
$583$	−11.1496	−0.461768
$584$	4.26097	0.176320
$585$	11.2798	0.466362
$586$	−14.5555	−0.601284
$587$	−20.6525	−0.852422	−0.426211	−	0.904624i	$-0.640152\pi$
$587$	−20.6525	−0.852422	−0.426211	+	0.904624i	$0.640152\pi$
$588$	0	0
$589$	69.3924	2.85926
$590$	7.18902	0.295967
$591$	−23.9494	−0.985145
$592$	8.93530	0.367238
$593$	7.66752	0.314867	0.157434	−	0.987530i	$-0.449678\pi$
$593$	7.66752	0.314867	0.157434	+	0.987530i	$0.449678\pi$
$594$	19.4538	0.798200
$595$	0	0
$596$	−9.56131	−0.391647
$597$	−5.33772	−0.218458
$598$	−3.79833	−0.155325
$599$	37.5460	1.53409	0.767043	−	0.641596i	$-0.221727\pi$
$599$	37.5460	1.53409	0.767043	+	0.641596i	$0.221727\pi$
$600$	−2.31526	−0.0945201
$601$	16.2537	0.663003	0.331501	−	0.943455i	$-0.392445\pi$
$601$	16.2537	0.663003	0.331501	+	0.943455i	$0.392445\pi$
$602$	0	0
$603$	22.9052	0.932773
$604$	7.25672	0.295272
$605$	−3.98393	−0.161970
$606$	4.19487	0.170405
$607$	−4.32270	−0.175453	−0.0877264	−	0.996145i	$-0.527960\pi$
$607$	−4.32270	−0.175453	−0.0877264	+	0.996145i	$0.527960\pi$
$608$	−8.12271	−0.329419
$609$	0	0
$610$	−19.4193	−0.786265
$611$	11.2103	0.453518
$612$	7.22795	0.292173
$613$	40.1450	1.62144	0.810720	−	0.585433i	$-0.199076\pi$
$613$	40.1450	1.62144	0.810720	+	0.585433i	$0.199076\pi$
$614$	12.7024	0.512628
$615$	19.4372	0.783783
$616$	0	0
$617$	−27.7668	−1.11785	−0.558925	−	0.829218i	$-0.688786\pi$
$617$	−27.7668	−1.11785	−0.558925	+	0.829218i	$0.688786\pi$
$618$	−17.0460	−0.685690
$619$	16.7330	0.672555	0.336277	−	0.941763i	$-0.390832\pi$
$619$	16.7330	0.672555	0.336277	+	0.941763i	$0.390832\pi$
$620$	14.6612	0.588806
$621$	5.33003	0.213887
$622$	9.21894	0.369646
$623$	0	0
$624$	4.27979	0.171329
$625$	−10.5038	−0.420152
$626$	15.6567	0.625766
$627$	33.4046	1.33405
$628$	2.75509	0.109940
$629$	−37.3227	−1.48815
$630$	0	0
$631$	16.4804	0.656073	0.328037	−	0.944665i	$-0.393613\pi$
$631$	16.4804	0.656073	0.328037	+	0.944665i	$0.393613\pi$
$632$	−13.4482	−0.534940
$633$	18.8864	0.750666
$634$	11.0382	0.438384
$635$	−4.35175	−0.172694
$636$	3.44202	0.136485
$637$	0	0
$638$	−10.2449	−0.405600
$639$	−24.7543	−0.979263
$640$	−1.71616	−0.0678371
$641$	1.76510	0.0697174	0.0348587	−	0.999392i	$-0.488902\pi$
$641$	1.76510	0.0697174	0.0348587	+	0.999392i	$0.488902\pi$
$642$	−15.4765	−0.610809
$643$	8.26706	0.326021	0.163010	−	0.986624i	$-0.447880\pi$
$643$	8.26706	0.326021	0.163010	+	0.986624i	$0.447880\pi$
$644$	0	0
$645$	−15.6836	−0.617541
$646$	33.9285	1.33490
$647$	15.5237	0.610301	0.305150	−	0.952304i	$-0.401293\pi$
$647$	15.5237	0.610301	0.305150	+	0.952304i	$0.401293\pi$
$648$	−0.814396	−0.0319925
$649$	15.2893	0.600157
$650$	−7.80480	−0.306130
$651$	0	0
$652$	20.2841	0.794386
$653$	19.8592	0.777152	0.388576	−	0.921417i	$-0.372967\pi$
$653$	19.8592	0.777152	0.388576	+	0.921417i	$0.372967\pi$
$654$	10.5795	0.413691
$655$	−9.03142	−0.352887
$656$	−10.0518	−0.392459
$657$	−7.37327	−0.287659
$658$	0	0
$659$	−1.62164	−0.0631702	−0.0315851	−	0.999501i	$-0.510056\pi$
$659$	−1.62164	−0.0631702	−0.0315851	+	0.999501i	$0.510056\pi$
$660$	7.05770	0.274721
$661$	9.06300	0.352510	0.176255	−	0.984345i	$-0.443602\pi$
$661$	9.06300	0.352510	0.176255	+	0.984345i	$0.443602\pi$
$662$	−15.6915	−0.609867
$663$	−17.8767	−0.694273
$664$	−9.43848	−0.366284
$665$	0	0
$666$	−15.4618	−0.599133
$667$	−2.80694	−0.108685
$668$	0.325472	0.0125929
$669$	−1.39120	−0.0537869
$670$	22.7165	0.877614
$671$	−41.3002	−1.59438
$672$	0	0
$673$	8.45539	0.325931	0.162966	−	0.986632i	$-0.447894\pi$
$673$	8.45539	0.325931	0.162966	+	0.986632i	$0.447894\pi$
$674$	5.18787	0.199829
$675$	10.9521	0.421548
$676$	1.42730	0.0548962
$677$	30.6385	1.17753	0.588767	−	0.808303i	$-0.299613\pi$
$677$	30.6385	1.17753	0.588767	+	0.808303i	$0.299613\pi$
$678$	−10.5841	−0.406478
$679$	0	0
$680$	7.16839	0.274895
$681$	−25.9628	−0.994897
$682$	31.1807	1.19397
$683$	−29.0305	−1.11082	−0.555410	−	0.831577i	$-0.687439\pi$
$683$	−29.0305	−1.11082	−0.555410	+	0.831577i	$0.687439\pi$
$684$	14.0557	0.537433
$685$	23.7711	0.908246
$686$	0	0
$687$	5.44971	0.207919
$688$	8.11069	0.309217
$689$	11.6031	0.442044
$690$	1.93369	0.0736145
$691$	−22.2112	−0.844953	−0.422477	−	0.906374i	$-0.638839\pi$
$691$	−22.2112	−0.844953	−0.422477	+	0.906374i	$0.638839\pi$
$692$	−13.4018	−0.509459
$693$	0	0
$694$	−17.7594	−0.674137
$695$	−16.5723	−0.628625
$696$	3.16274	0.119883
$697$	41.9865	1.59035
$698$	15.3654	0.581587
$699$	−14.9346	−0.564878
$700$	0	0
$701$	−2.49593	−0.0942699	−0.0471350	−	0.998889i	$-0.515009\pi$
$701$	−2.49593	−0.0942699	−0.0471350	+	0.998889i	$0.515009\pi$
$702$	−20.2452	−0.764106
$703$	−72.5788	−2.73736
$704$	−3.64985	−0.137559
$705$	−5.70704	−0.214939
$706$	26.4646	0.996007
$707$	0	0
$708$	−4.72000	−0.177389
$709$	−40.1275	−1.50702	−0.753510	−	0.657436i	$-0.771641\pi$
$709$	−40.1275	−1.50702	−0.753510	+	0.657436i	$0.771641\pi$
$710$	−24.5503	−0.921355
$711$	23.2710	0.872730
$712$	−3.95837	−0.148346
$713$	8.54301	0.319938
$714$	0	0
$715$	23.7917	0.889759
$716$	20.8545	0.779370
$717$	−6.08731	−0.227335
$718$	7.50002	0.279898
$719$	−11.3918	−0.424844	−0.212422	−	0.977178i	$-0.568135\pi$
$719$	−11.3918	−0.424844	−0.212422	+	0.977178i	$0.568135\pi$
$720$	2.96967	0.110673
$721$	0	0
$722$	46.9784	1.74836
$723$	19.4036	0.721627
$724$	−1.57738	−0.0586229
$725$	−5.76769	−0.214207
$726$	2.61568	0.0970770
$727$	22.5154	0.835051	0.417526	−	0.908665i	$-0.362897\pi$
$727$	22.5154	0.835051	0.417526	+	0.908665i	$0.362897\pi$
$728$	0	0
$729$	19.4262	0.719489
$730$	−7.31251	−0.270648
$731$	−33.8783	−1.25303
$732$	12.7499	0.471250
$733$	12.3494	0.456134	0.228067	−	0.973645i	$-0.426759\pi$
$733$	12.3494	0.456134	0.228067	+	0.973645i	$0.426759\pi$
$734$	1.61092	0.0594600
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	48.3124	1.77961
$738$	17.3939	0.640278
$739$	−9.49624	−0.349325	−0.174662	−	0.984628i	$-0.555883\pi$
$739$	−9.49624	−0.349325	−0.174662	+	0.984628i	$0.555883\pi$
$740$	−15.3344	−0.563703
$741$	−34.7635	−1.27707
$742$	0	0
$743$	−31.7348	−1.16424	−0.582118	−	0.813104i	$-0.697776\pi$
$743$	−31.7348	−1.16424	−0.582118	+	0.813104i	$0.697776\pi$
$744$	−9.62589	−0.352902
$745$	16.4087	0.601169
$746$	18.1008	0.662717
$747$	16.3325	0.597576
$748$	15.2454	0.557428
$749$	0	0
$750$	13.6418	0.498129
$751$	−1.45892	−0.0532369	−0.0266184	−	0.999646i	$-0.508474\pi$
$751$	−1.45892	−0.0532369	−0.0266184	+	0.999646i	$0.508474\pi$
$752$	2.95137	0.107625
$753$	−19.0608	−0.694613
$754$	10.6617	0.388275
$755$	−12.4537	−0.453236
$756$	0	0
$757$	13.7895	0.501186	0.250593	−	0.968092i	$-0.419374\pi$
$757$	13.7895	0.501186	0.250593	+	0.968092i	$0.419374\pi$
$758$	−10.3909	−0.377416
$759$	4.11250	0.149274
$760$	13.9399	0.505652
$761$	5.27416	0.191188	0.0955942	−	0.995420i	$-0.469525\pi$
$761$	5.27416	0.191188	0.0955942	+	0.995420i	$0.469525\pi$
$762$	2.85718	0.103505
$763$	0	0
$764$	6.26097	0.226514
$765$	−12.4043	−0.448479
$766$	7.39562	0.267215
$767$	−15.9113	−0.574522
$768$	1.12676	0.0406583
$769$	4.68371	0.168899	0.0844495	−	0.996428i	$-0.473087\pi$
$769$	4.68371	0.168899	0.0844495	+	0.996428i	$0.473087\pi$
$770$	0	0
$771$	13.8210	0.497751
$772$	13.0358	0.469168
$773$	8.40316	0.302241	0.151120	−	0.988515i	$-0.451712\pi$
$773$	8.40316	0.302241	0.151120	+	0.988515i	$0.451712\pi$
$774$	−14.0349	−0.504474
$775$	17.5542	0.630564
$776$	−0.121105	−0.00434743
$777$	0	0
$778$	4.07942	0.146254
$779$	81.6482	2.92535
$780$	−7.34481	−0.262986
$781$	−52.2124	−1.86831
$782$	4.17700	0.149369
$783$	−14.9611	−0.534665
$784$	0	0
$785$	−4.72818	−0.168756
$786$	5.92965	0.211503
$787$	−24.9364	−0.888888	−0.444444	−	0.895807i	$-0.646599\pi$
$787$	−24.9364	−0.888888	−0.444444	+	0.895807i	$0.646599\pi$
$788$	−21.2551	−0.757182
$789$	14.7132	0.523804
$790$	23.0792	0.821122
$791$	0	0
$792$	6.31577	0.224421
$793$	42.9803	1.52627
$794$	−8.86110	−0.314469
$795$	−5.90705	−0.209501
$796$	−4.73724	−0.167907
$797$	5.67934	0.201173	0.100586	−	0.994928i	$-0.467928\pi$
$797$	5.67934	0.201173	0.100586	+	0.994928i	$0.467928\pi$
$798$	0	0
$799$	−12.3278	−0.436128
$800$	−2.05480	−0.0726481
$801$	6.84964	0.242020
$802$	16.6035	0.586288
$803$	−15.5519	−0.548816
$804$	−14.9147	−0.526000
$805$	0	0
$806$	−32.4491	−1.14297
$807$	−4.01920	−0.141482
$808$	3.72296	0.130973
$809$	−18.2121	−0.640303	−0.320151	−	0.947366i	$-0.603734\pi$
$809$	−18.2121	−0.640303	−0.320151	+	0.947366i	$0.603734\pi$
$810$	1.39763	0.0491078
$811$	−39.0257	−1.37038	−0.685188	−	0.728366i	$-0.740280\pi$
$811$	−39.0257	−1.37038	−0.685188	+	0.728366i	$0.740280\pi$
$812$	0	0
$813$	−2.22781	−0.0781328
$814$	−32.6125	−1.14307
$815$	−34.8107	−1.21937
$816$	−4.70646	−0.164759
$817$	−65.8808	−2.30488
$818$	−33.7434	−1.17981
$819$	0	0
$820$	17.2506	0.602416
$821$	11.6602	0.406943	0.203472	−	0.979081i	$-0.434778\pi$
$821$	11.6602	0.406943	0.203472	+	0.979081i	$0.434778\pi$
$822$	−15.6071	−0.544359
$823$	−53.6427	−1.86987	−0.934934	−	0.354823i	$-0.884541\pi$
$823$	−53.6427	−1.86987	−0.934934	+	0.354823i	$0.884541\pi$
$824$	−15.1284	−0.527021
$825$	8.45036	0.294204
$826$	0	0
$827$	−8.37095	−0.291086	−0.145543	−	0.989352i	$-0.546493\pi$
$827$	−8.37095	−0.291086	−0.145543	+	0.989352i	$0.546493\pi$
$828$	1.73042	0.0601362
$829$	43.7276	1.51872	0.759362	−	0.650668i	$-0.225511\pi$
$829$	43.7276	1.51872	0.759362	+	0.650668i	$0.225511\pi$
$830$	16.1979	0.562238
$831$	−12.3227	−0.427468
$832$	3.79833	0.131683
$833$	0	0
$834$	10.8807	0.376768
$835$	−0.558561	−0.0193298
$836$	29.6467	1.02535
$837$	45.5345	1.57390
$838$	−36.5806	−1.26366
$839$	20.3471	0.702460	0.351230	−	0.936289i	$-0.385764\pi$
$839$	20.3471	0.702460	0.351230	+	0.936289i	$0.385764\pi$
$840$	0	0
$841$	−21.1211	−0.728314
$842$	−32.7603	−1.12900
$843$	−5.16093	−0.177752
$844$	16.7617	0.576962
$845$	−2.44948	−0.0842645
$846$	−5.10710	−0.175586
$847$	0	0
$848$	3.05480	0.104902
$849$	16.9925	0.583181
$850$	8.58289	0.294391
$851$	−8.93530	−0.306298
$852$	16.1187	0.552216
$853$	−10.3309	−0.353724	−0.176862	−	0.984236i	$-0.556595\pi$
$853$	−10.3309	−0.353724	−0.176862	+	0.984236i	$0.556595\pi$
$854$	0	0
$855$	−24.1218	−0.824948
$856$	−13.7354	−0.469467
$857$	−46.6217	−1.59257	−0.796283	−	0.604924i	$-0.793204\pi$
$857$	−46.6217	−1.59257	−0.796283	+	0.604924i	$0.793204\pi$
$858$	−15.6206	−0.533279
$859$	10.2552	0.349904	0.174952	−	0.984577i	$-0.444023\pi$
$859$	10.2552	0.349904	0.174952	+	0.984577i	$0.444023\pi$
$860$	−13.9192	−0.474642
$861$	0	0
$862$	−17.7194	−0.603524
$863$	−39.3903	−1.34086	−0.670431	−	0.741972i	$-0.733891\pi$
$863$	−39.3903	−1.34086	−0.670431	+	0.741972i	$0.733891\pi$
$864$	−5.33003	−0.181331
$865$	22.9996	0.782010
$866$	4.51989	0.153592
$867$	0.503991	0.0171164
$868$	0	0
$869$	49.0839	1.66506
$870$	−5.42776	−0.184018
$871$	−50.2778	−1.70360
$872$	9.38933	0.317963
$873$	0.209563	0.00709263
$874$	8.12271	0.274755
$875$	0	0
$876$	4.80108	0.162214
$877$	43.2618	1.46085	0.730424	−	0.682994i	$-0.239322\pi$
$877$	43.2618	1.46085	0.730424	+	0.682994i	$0.239322\pi$
$878$	−6.39794	−0.215920
$879$	−16.4006	−0.553177
$880$	6.26373	0.211150
$881$	−27.5229	−0.927272	−0.463636	−	0.886026i	$-0.653455\pi$
$881$	−27.5229	−0.927272	−0.463636	+	0.886026i	$0.653455\pi$
$882$	0	0
$883$	−20.9321	−0.704421	−0.352210	−	0.935921i	$-0.614570\pi$
$883$	−20.9321	−0.704421	−0.352210	+	0.935921i	$0.614570\pi$
$884$	−15.8656	−0.533618
$885$	8.10027	0.272288
$886$	−17.1369	−0.575725
$887$	50.1285	1.68315	0.841575	−	0.540141i	$-0.181629\pi$
$887$	50.1285	1.68315	0.841575	+	0.540141i	$0.181629\pi$
$888$	10.0679	0.337857
$889$	0	0
$890$	6.79319	0.227708
$891$	2.97243	0.0995800
$892$	−1.23469	−0.0413406
$893$	−23.9731	−0.802229
$894$	−10.7733	−0.360312
$895$	−35.7897	−1.19632
$896$	0	0
$897$	−4.27979	−0.142898
$898$	−13.2695	−0.442809
$899$	−23.9797	−0.799767
$900$	3.55566	0.118522
$901$	−12.7599	−0.425093
$902$	36.6877	1.22157
$903$	0	0
$904$	−9.39338	−0.312419
$905$	2.70704	0.0899850
$906$	8.17656	0.271648
$907$	−41.7226	−1.38538	−0.692689	−	0.721237i	$-0.743574\pi$
$907$	−41.7226	−1.38538	−0.692689	+	0.721237i	$0.743574\pi$
$908$	−23.0421	−0.764678
$909$	−6.44228	−0.213677
$910$	0	0
$911$	28.5662	0.946440	0.473220	−	0.880944i	$-0.343092\pi$
$911$	28.5662	0.946440	0.473220	+	0.880944i	$0.343092\pi$
$912$	−9.15232	−0.303064
$913$	34.4491	1.14010
$914$	−30.4628	−1.00762
$915$	−21.8808	−0.723359
$916$	4.83663	0.159807
$917$	0	0
$918$	22.2635	0.734806
$919$	16.9708	0.559814	0.279907	−	0.960027i	$-0.409696\pi$
$919$	16.9708	0.559814	0.279907	+	0.960027i	$0.409696\pi$
$920$	1.71616	0.0565801
$921$	14.3125	0.471614
$922$	−13.1239	−0.432211
$923$	54.3364	1.78851
$924$	0	0
$925$	−18.3602	−0.603681
$926$	−21.3453	−0.701449
$927$	26.1784	0.859811
$928$	2.80694	0.0921422
$929$	−34.7733	−1.14088	−0.570438	−	0.821341i	$-0.693226\pi$
$929$	−34.7733	−1.14088	−0.570438	+	0.821341i	$0.693226\pi$
$930$	16.5196	0.541698
$931$	0	0
$932$	−13.2545	−0.434165
$933$	10.3875	0.340072
$934$	−22.3604	−0.731655
$935$	−26.1636	−0.855640
$936$	−6.57270	−0.214835
$937$	49.0341	1.60187	0.800937	−	0.598749i	$-0.204335\pi$
$937$	49.0341	1.60187	0.800937	+	0.598749i	$0.204335\pi$
$938$	0	0
$939$	17.6412	0.575700
$940$	−5.06501	−0.165202
$941$	−34.9264	−1.13857	−0.569285	−	0.822140i	$-0.692780\pi$
$941$	−34.9264	−1.13857	−0.569285	+	0.822140i	$0.692780\pi$
$942$	3.10432	0.101144
$943$	10.0518	0.327333
$944$	−4.18902	−0.136341
$945$	0	0
$946$	−29.6028	−0.962471
$947$	−0.367593	−0.0119452	−0.00597258	−	0.999982i	$-0.501901\pi$
$947$	−0.367593	−0.0119452	−0.00597258	+	0.999982i	$0.501901\pi$
$948$	−15.1528	−0.492141
$949$	16.1846	0.525374
$950$	16.6905	0.541513
$951$	12.4374	0.403310
$952$	0	0
$953$	39.2201	1.27047	0.635233	−	0.772321i	$-0.280904\pi$
$953$	39.2201	1.27047	0.635233	+	0.772321i	$0.280904\pi$
$954$	−5.28608	−0.171143
$955$	−10.7448	−0.347694
$956$	−5.40250	−0.174729
$957$	−11.5435	−0.373149
$958$	17.4670	0.564333
$959$	0	0
$960$	−1.93369	−0.0624097
$961$	41.9830	1.35429
$962$	33.9392	1.09424
$963$	23.7681	0.765915
$964$	17.2207	0.554643
$965$	−22.3715	−0.720163
$966$	0	0
$967$	20.3070	0.653030	0.326515	−	0.945192i	$-0.394126\pi$
$967$	20.3070	0.653030	0.326515	+	0.945192i	$0.394126\pi$
$968$	2.32142	0.0746134
$969$	38.2292	1.22810
$970$	0.207836	0.00667321
$971$	−23.9384	−0.768219	−0.384110	−	0.923288i	$-0.625492\pi$
$971$	−23.9384	−0.768219	−0.384110	+	0.923288i	$0.625492\pi$
$972$	15.0725	0.483450
$973$	0	0
$974$	−5.79067	−0.185545
$975$	−8.79412	−0.281637
$976$	11.3156	0.362203
$977$	8.54283	0.273309	0.136655	−	0.990619i	$-0.456365\pi$
$977$	8.54283	0.273309	0.136655	+	0.990619i	$0.456365\pi$
$978$	22.8552	0.730830
$979$	14.4475	0.461743
$980$	0	0
$981$	−16.2475	−0.518742
$982$	−8.47054	−0.270306
$983$	−30.3024	−0.966496	−0.483248	−	0.875483i	$-0.660543\pi$
$983$	−30.3024	−0.966496	−0.483248	+	0.875483i	$0.660543\pi$
$984$	−11.3260	−0.361059
$985$	36.4772	1.16226
$986$	−11.7246	−0.373386
$987$	0	0
$988$	−30.8527	−0.981556
$989$	−8.11069	−0.257905
$990$	−10.8389	−0.344482
$991$	−32.5810	−1.03497	−0.517486	−	0.855692i	$-0.673132\pi$
$991$	−32.5810	−1.03497	−0.517486	+	0.855692i	$0.673132\pi$
$992$	−8.54301	−0.271241
$993$	−17.6805	−0.561073
$994$	0	0
$995$	8.12986	0.257734
$996$	−10.6349	−0.336979
$997$	0.931121	0.0294889	0.0147445	−	0.999891i	$-0.495307\pi$
$997$	0.931121	0.0294889	0.0147445	+	0.999891i	$0.495307\pi$
$998$	−2.52200	−0.0798327
$999$	−47.6254	−1.50680

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2254.2.a.x.1.4		4
7.3	odd	6		322.2.e.a.93.4	✓	8
7.5	odd	6		322.2.e.a.277.4	yes	8
7.6	odd	2		2254.2.a.z.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.e.a.93.4	✓	8	7.3	odd	6
322.2.e.a.277.4	yes	8	7.5	odd	6
2254.2.a.x.1.4		4	1.1	even	1	trivial
2254.2.a.z.1.1		4	7.6	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:	\( N \)	\(=\)	\( 2254 = 2 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2254.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.12676 q^{3} +1.00000 q^{4} -1.71616 q^{5} +1.12676 q^{6} +1.00000 q^{8} -1.73042 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.12676 q^{3} +1.00000 q^{4} -1.71616 q^{5} +1.12676 q^{6} +1.00000 q^{8} -1.73042 q^{9} -1.71616 q^{10} -3.64985 q^{11} +1.12676 q^{12} +3.79833 q^{13} -1.93369 q^{15} +1.00000 q^{16} -4.17700 q^{17} -1.73042 q^{18} -8.12271 q^{19} -1.71616 q^{20} -3.64985 q^{22} -1.00000 q^{23} +1.12676 q^{24} -2.05480 q^{25} +3.79833 q^{26} -5.33003 q^{27} +2.80694 q^{29} -1.93369 q^{30} -8.54301 q^{31} +1.00000 q^{32} -4.11250 q^{33} -4.17700 q^{34} -1.73042 q^{36} +8.93530 q^{37} -8.12271 q^{38} +4.27979 q^{39} -1.71616 q^{40} -10.0518 q^{41} +8.11069 q^{43} -3.64985 q^{44} +2.96967 q^{45} -1.00000 q^{46} +2.95137 q^{47} +1.12676 q^{48} -2.05480 q^{50} -4.70646 q^{51} +3.79833 q^{52} +3.05480 q^{53} -5.33003 q^{54} +6.26373 q^{55} -9.15232 q^{57} +2.80694 q^{58} -4.18902 q^{59} -1.93369 q^{60} +11.3156 q^{61} -8.54301 q^{62} +1.00000 q^{64} -6.51854 q^{65} -4.11250 q^{66} -13.2368 q^{67} -4.17700 q^{68} -1.12676 q^{69} +14.3054 q^{71} -1.73042 q^{72} +4.26097 q^{73} +8.93530 q^{74} -2.31526 q^{75} -8.12271 q^{76} +4.27979 q^{78} -13.4482 q^{79} -1.71616 q^{80} -0.814396 q^{81} -10.0518 q^{82} -9.43848 q^{83} +7.16839 q^{85} +8.11069 q^{86} +3.16274 q^{87} -3.64985 q^{88} -3.95837 q^{89} +2.96967 q^{90} -1.00000 q^{92} -9.62589 q^{93} +2.95137 q^{94} +13.9399 q^{95} +1.12676 q^{96} -0.121105 q^{97} +6.31577 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 3 q^{3} + 4 q^{4} - 7 q^{5} - 3 q^{6} + 4 q^{8} - q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 3 * q^3 + 4 * q^4 - 7 * q^5 - 3 * q^6 + 4 * q^8 - q^9	\( 4 q + 4 q^{2} - 3 q^{3} + 4 q^{4} - 7 q^{5} - 3 q^{6} + 4 q^{8} - q^{9} - 7 q^{10} + 2 q^{11} - 3 q^{12} - q^{13} + 9 q^{15} + 4 q^{16} - 5 q^{17} - q^{18} - 11 q^{19} - 7 q^{20} + 2 q^{22} - 4 q^{23} - 3 q^{24} + 3 q^{25} - q^{26} - 3 q^{27} + 2 q^{29} + 9 q^{30} - 6 q^{31} + 4 q^{32} - 15 q^{33} - 5 q^{34} - q^{36} - 8 q^{37} - 11 q^{38} + 3 q^{39} - 7 q^{40} - 9 q^{41} + 4 q^{43} + 2 q^{44} - 3 q^{45} - 4 q^{46} - 11 q^{47} - 3 q^{48} + 3 q^{50} - 18 q^{51} - q^{52} + q^{53} - 3 q^{54} - 10 q^{55} + 3 q^{57} + 2 q^{58} - 12 q^{59} + 9 q^{60} - 21 q^{61} - 6 q^{62} + 4 q^{64} - 24 q^{65} - 15 q^{66} - 3 q^{67} - 5 q^{68} + 3 q^{69} + 11 q^{71} - q^{72} + 16 q^{73} - 8 q^{74} - 18 q^{75} - 11 q^{76} + 3 q^{78} - 21 q^{79} - 7 q^{80} - 8 q^{81} - 9 q^{82} - 4 q^{83} + 10 q^{85} + 4 q^{86} + 7 q^{87} + 2 q^{88} - 27 q^{89} - 3 q^{90} - 4 q^{92} - 27 q^{93} - 11 q^{94} + 5 q^{95} - 3 q^{96} - 6 q^{97} + 13 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 3 * q^3 + 4 * q^4 - 7 * q^5 - 3 * q^6 + 4 * q^8 - q^9 - 7 * q^10 + 2 * q^11 - 3 * q^12 - q^13 + 9 * q^15 + 4 * q^16 - 5 * q^17 - q^18 - 11 * q^19 - 7 * q^20 + 2 * q^22 - 4 * q^23 - 3 * q^24 + 3 * q^25 - q^26 - 3 * q^27 + 2 * q^29 + 9 * q^30 - 6 * q^31 + 4 * q^32 - 15 * q^33 - 5 * q^34 - q^36 - 8 * q^37 - 11 * q^38 + 3 * q^39 - 7 * q^40 - 9 * q^41 + 4 * q^43 + 2 * q^44 - 3 * q^45 - 4 * q^46 - 11 * q^47 - 3 * q^48 + 3 * q^50 - 18 * q^51 - q^52 + q^53 - 3 * q^54 - 10 * q^55 + 3 * q^57 + 2 * q^58 - 12 * q^59 + 9 * q^60 - 21 * q^61 - 6 * q^62 + 4 * q^64 - 24 * q^65 - 15 * q^66 - 3 * q^67 - 5 * q^68 + 3 * q^69 + 11 * q^71 - q^72 + 16 * q^73 - 8 * q^74 - 18 * q^75 - 11 * q^76 + 3 * q^78 - 21 * q^79 - 7 * q^80 - 8 * q^81 - 9 * q^82 - 4 * q^83 + 10 * q^85 + 4 * q^86 + 7 * q^87 + 2 * q^88 - 27 * q^89 - 3 * q^90 - 4 * q^92 - 27 * q^93 - 11 * q^94 + 5 * q^95 - 3 * q^96 - 6 * q^97 + 13 * q^99

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