LMFDB - Embedded newform 187.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(1,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, 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("187.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.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:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	187.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +1.56155 q^{3} +2.00000 q^{4} -1.56155 q^{5} +3.12311 q^{6} -0.561553 q^{7} -0.561553 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +1.56155 q^{3} +2.00000 q^{4} -1.56155 q^{5} +3.12311 q^{6} -0.561553 q^{7} -0.561553 q^{9} -3.12311 q^{10} +1.00000 q^{11} +3.12311 q^{12} -1.12311 q^{14} -2.43845 q^{15} -4.00000 q^{16} -1.00000 q^{17} -1.12311 q^{18} +1.12311 q^{19} -3.12311 q^{20} -0.876894 q^{21} +2.00000 q^{22} +6.68466 q^{23} -2.56155 q^{25} -5.56155 q^{27} -1.12311 q^{28} +5.43845 q^{29} -4.87689 q^{30} +1.56155 q^{31} -8.00000 q^{32} +1.56155 q^{33} -2.00000 q^{34} +0.876894 q^{35} -1.12311 q^{36} +0.438447 q^{37} +2.24621 q^{38} +3.68466 q^{41} -1.75379 q^{42} +2.00000 q^{43} +2.00000 q^{44} +0.876894 q^{45} +13.3693 q^{46} +3.68466 q^{47} -6.24621 q^{48} -6.68466 q^{49} -5.12311 q^{50} -1.56155 q^{51} +3.43845 q^{53} -11.1231 q^{54} -1.56155 q^{55} +1.75379 q^{57} +10.8769 q^{58} -3.00000 q^{59} -4.87689 q^{60} -9.12311 q^{61} +3.12311 q^{62} +0.315342 q^{63} -8.00000 q^{64} +3.12311 q^{66} -4.12311 q^{67} -2.00000 q^{68} +10.4384 q^{69} +1.75379 q^{70} -2.68466 q^{71} +11.6847 q^{73} +0.876894 q^{74} -4.00000 q^{75} +2.24621 q^{76} -0.561553 q^{77} +9.36932 q^{79} +6.24621 q^{80} -7.00000 q^{81} +7.36932 q^{82} -8.24621 q^{83} -1.75379 q^{84} +1.56155 q^{85} +4.00000 q^{86} +8.49242 q^{87} -8.36932 q^{89} +1.75379 q^{90} +13.3693 q^{92} +2.43845 q^{93} +7.36932 q^{94} -1.75379 q^{95} -12.4924 q^{96} -14.6847 q^{97} -13.3693 q^{98} -0.561553 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} - q^{3} + 4 q^{4} + q^{5} - 2 q^{6} + 3 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q + 4 * q^2 - q^3 + 4 * q^4 + q^5 - 2 * q^6 + 3 * q^7 + 3 * q^9	$ 2 q + 4 q^{2} - q^{3} + 4 q^{4} + q^{5} - 2 q^{6} + 3 q^{7} + 3 q^{9} + 2 q^{10} + 2 q^{11} - 2 q^{12} + 6 q^{14} - 9 q^{15} - 8 q^{16} - 2 q^{17} + 6 q^{18} - 6 q^{19} + 2 q^{20} - 10 q^{21} + 4 q^{22} + q^{23} - q^{25} - 7 q^{27} + 6 q^{28} + 15 q^{29} - 18 q^{30} - q^{31} - 16 q^{32} - q^{33} - 4 q^{34} + 10 q^{35} + 6 q^{36} + 5 q^{37} - 12 q^{38} - 5 q^{41} - 20 q^{42} + 4 q^{43} + 4 q^{44} + 10 q^{45} + 2 q^{46} - 5 q^{47} + 4 q^{48} - q^{49} - 2 q^{50} + q^{51} + 11 q^{53} - 14 q^{54} + q^{55} + 20 q^{57} + 30 q^{58} - 6 q^{59} - 18 q^{60} - 10 q^{61} - 2 q^{62} + 13 q^{63} - 16 q^{64} - 2 q^{66} - 4 q^{68} + 25 q^{69} + 20 q^{70} + 7 q^{71} + 11 q^{73} + 10 q^{74} - 8 q^{75} - 12 q^{76} + 3 q^{77} - 6 q^{79} - 4 q^{80} - 14 q^{81} - 10 q^{82} - 20 q^{84} - q^{85} + 8 q^{86} - 16 q^{87} + 8 q^{89} + 20 q^{90} + 2 q^{92} + 9 q^{93} - 10 q^{94} - 20 q^{95} + 8 q^{96} - 17 q^{97} - 2 q^{98} + 3 q^{99}+O(q^{100}) $ 2 * q + 4 * q^2 - q^3 + 4 * q^4 + q^5 - 2 * q^6 + 3 * q^7 + 3 * q^9 + 2 * q^10 + 2 * q^11 - 2 * q^12 + 6 * q^14 - 9 * q^15 - 8 * q^16 - 2 * q^17 + 6 * q^18 - 6 * q^19 + 2 * q^20 - 10 * q^21 + 4 * q^22 + q^23 - q^25 - 7 * q^27 + 6 * q^28 + 15 * q^29 - 18 * q^30 - q^31 - 16 * q^32 - q^33 - 4 * q^34 + 10 * q^35 + 6 * q^36 + 5 * q^37 - 12 * q^38 - 5 * q^41 - 20 * q^42 + 4 * q^43 + 4 * q^44 + 10 * q^45 + 2 * q^46 - 5 * q^47 + 4 * q^48 - q^49 - 2 * q^50 + q^51 + 11 * q^53 - 14 * q^54 + q^55 + 20 * q^57 + 30 * q^58 - 6 * q^59 - 18 * q^60 - 10 * q^61 - 2 * q^62 + 13 * q^63 - 16 * q^64 - 2 * q^66 - 4 * q^68 + 25 * q^69 + 20 * q^70 + 7 * q^71 + 11 * q^73 + 10 * q^74 - 8 * q^75 - 12 * q^76 + 3 * q^77 - 6 * q^79 - 4 * q^80 - 14 * q^81 - 10 * q^82 - 20 * q^84 - q^85 + 8 * q^86 - 16 * q^87 + 8 * q^89 + 20 * q^90 + 2 * q^92 + 9 * q^93 - 10 * q^94 - 20 * q^95 + 8 * q^96 - 17 * q^97 - 2 * q^98 + 3 * 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 $

$2$	2.00000	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$2$	2.00000	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$3$	1.56155	0.901563	0.450781	−	0.892634i	$-0.351145\pi$
$3$	1.56155	0.901563	0.450781	+	0.892634i	$0.351145\pi$
$4$	2.00000	1.00000
$5$	−1.56155	−0.698348	−0.349174	−	0.937058i	$-0.613538\pi$
$5$	−1.56155	−0.698348	−0.349174	+	0.937058i	$0.613538\pi$
$6$	3.12311	1.27500
$7$	−0.561553	−0.212247	−0.106124	−	0.994353i	$-0.533844\pi$
$7$	−0.561553	−0.212247	−0.106124	+	0.994353i	$0.533844\pi$
$8$	0	0
$9$	−0.561553	−0.187184
$10$	−3.12311	−0.987613
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.12311	0.901563
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	−1.12311	−0.300163
$15$	−2.43845	−0.629604
$16$	−4.00000	−1.00000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.12311	−0.264719
$19$	1.12311	0.257658	0.128829	−	0.991667i	$-0.458878\pi$
$19$	1.12311	0.257658	0.128829	+	0.991667i	$0.458878\pi$
$20$	−3.12311	−0.698348
$21$	−0.876894	−0.191354
$22$	2.00000	0.426401
$23$	6.68466	1.39385	0.696924	−	0.717145i	$-0.254552\pi$
$23$	6.68466	1.39385	0.696924	+	0.717145i	$0.254552\pi$
$24$	0	0
$25$	−2.56155	−0.512311
$26$	0	0
$27$	−5.56155	−1.07032
$28$	−1.12311	−0.212247
$29$	5.43845	1.00989	0.504947	−	0.863150i	$-0.331512\pi$
$29$	5.43845	1.00989	0.504947	+	0.863150i	$0.331512\pi$
$30$	−4.87689	−0.890395
$31$	1.56155	0.280463	0.140232	−	0.990119i	$-0.455215\pi$
$31$	1.56155	0.280463	0.140232	+	0.990119i	$0.455215\pi$
$32$	−8.00000	−1.41421
$33$	1.56155	0.271831
$34$	−2.00000	−0.342997
$35$	0.876894	0.148222
$36$	−1.12311	−0.187184
$37$	0.438447	0.0720803	0.0360401	−	0.999350i	$-0.488526\pi$
$37$	0.438447	0.0720803	0.0360401	+	0.999350i	$0.488526\pi$
$38$	2.24621	0.364384
$39$	0	0
$40$	0	0
$41$	3.68466	0.575447	0.287723	−	0.957714i	$-0.407102\pi$
$41$	3.68466	0.575447	0.287723	+	0.957714i	$0.407102\pi$
$42$	−1.75379	−0.270615
$43$	2.00000	0.304997	0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000	0.304997	0.152499	+	0.988304i	$0.451268\pi$
$44$	2.00000	0.301511
$45$	0.876894	0.130720
$46$	13.3693	1.97120
$47$	3.68466	0.537463	0.268731	−	0.963215i	$-0.413396\pi$
$47$	3.68466	0.537463	0.268731	+	0.963215i	$0.413396\pi$
$48$	−6.24621	−0.901563
$49$	−6.68466	−0.954951
$50$	−5.12311	−0.724517
$51$	−1.56155	−0.218661
$52$	0	0
$53$	3.43845	0.472307	0.236154	−	0.971716i	$-0.424113\pi$
$53$	3.43845	0.472307	0.236154	+	0.971716i	$0.424113\pi$
$54$	−11.1231	−1.51366
$55$	−1.56155	−0.210560
$56$	0	0
$57$	1.75379	0.232295
$58$	10.8769	1.42821
$59$	−3.00000	−0.390567	−0.195283	−	0.980747i	$-0.562563\pi$
$59$	−3.00000	−0.390567	−0.195283	+	0.980747i	$0.562563\pi$
$60$	−4.87689	−0.629604
$61$	−9.12311	−1.16809	−0.584047	−	0.811720i	$-0.698532\pi$
$61$	−9.12311	−1.16809	−0.584047	+	0.811720i	$0.698532\pi$
$62$	3.12311	0.396635
$63$	0.315342	0.0397293
$64$	−8.00000	−1.00000
$65$	0	0
$66$	3.12311	0.384428
$67$	−4.12311	−0.503718	−0.251859	−	0.967764i	$-0.581042\pi$
$67$	−4.12311	−0.503718	−0.251859	+	0.967764i	$0.581042\pi$
$68$	−2.00000	−0.242536
$69$	10.4384	1.25664
$70$	1.75379	0.209618
$71$	−2.68466	−0.318610	−0.159305	−	0.987229i	$-0.550925\pi$
$71$	−2.68466	−0.318610	−0.159305	+	0.987229i	$0.550925\pi$
$72$	0	0
$73$	11.6847	1.36759	0.683793	−	0.729676i	$-0.260329\pi$
$73$	11.6847	1.36759	0.683793	+	0.729676i	$0.260329\pi$
$74$	0.876894	0.101937
$75$	−4.00000	−0.461880
$76$	2.24621	0.257658
$77$	−0.561553	−0.0639949
$78$	0	0
$79$	9.36932	1.05413	0.527065	−	0.849825i	$-0.323292\pi$
$79$	9.36932	1.05413	0.527065	+	0.849825i	$0.323292\pi$
$80$	6.24621	0.698348
$81$	−7.00000	−0.777778
$82$	7.36932	0.813805
$83$	−8.24621	−0.905139	−0.452570	−	0.891729i	$-0.649493\pi$
$83$	−8.24621	−0.905139	−0.452570	+	0.891729i	$0.649493\pi$
$84$	−1.75379	−0.191354
$85$	1.56155	0.169374
$86$	4.00000	0.431331
$87$	8.49242	0.910483
$88$	0	0
$89$	−8.36932	−0.887146	−0.443573	−	0.896238i	$-0.646289\pi$
$89$	−8.36932	−0.887146	−0.443573	+	0.896238i	$0.646289\pi$
$90$	1.75379	0.184866
$91$	0	0
$92$	13.3693	1.39385
$93$	2.43845	0.252855
$94$	7.36932	0.760087
$95$	−1.75379	−0.179935
$96$	−12.4924	−1.27500
$97$	−14.6847	−1.49100	−0.745501	−	0.666505i	$-0.767790\pi$
$97$	−14.6847	−1.49100	−0.745501	+	0.666505i	$0.767790\pi$
$98$	−13.3693	−1.35050
$99$	−0.561553	−0.0564382
$100$	−5.12311	−0.512311
$101$	13.3693	1.33030	0.665148	−	0.746711i	$-0.268368\pi$
$101$	13.3693	1.33030	0.665148	+	0.746711i	$0.268368\pi$
$102$	−3.12311	−0.309234
$103$	−1.43845	−0.141734	−0.0708672	−	0.997486i	$-0.522577\pi$
$103$	−1.43845	−0.141734	−0.0708672	+	0.997486i	$0.522577\pi$
$104$	0	0
$105$	1.36932	0.133632
$106$	6.87689	0.667943
$107$	7.43845	0.719102	0.359551	−	0.933125i	$-0.382930\pi$
$107$	7.43845	0.719102	0.359551	+	0.933125i	$0.382930\pi$
$108$	−11.1231	−1.07032
$109$	17.6847	1.69388	0.846942	−	0.531686i	$-0.178441\pi$
$109$	17.6847	1.69388	0.846942	+	0.531686i	$0.178441\pi$
$110$	−3.12311	−0.297776
$111$	0.684658	0.0649849
$112$	2.24621	0.212247
$113$	11.5616	1.08762	0.543810	−	0.839209i	$-0.316981\pi$
$113$	11.5616	1.08762	0.543810	+	0.839209i	$0.316981\pi$
$114$	3.50758	0.328515
$115$	−10.4384	−0.973390
$116$	10.8769	1.00989
$117$	0	0
$118$	−6.00000	−0.552345
$119$	0.561553	0.0514775
$120$	0	0
$121$	1.00000	0.0909091
$122$	−18.2462	−1.65193
$123$	5.75379	0.518802
$124$	3.12311	0.280463
$125$	11.8078	1.05612
$126$	0.630683	0.0561857
$127$	−20.4924	−1.81841	−0.909204	−	0.416350i	$-0.863309\pi$
$127$	−20.4924	−1.81841	−0.909204	+	0.416350i	$0.863309\pi$
$128$	0	0
$129$	3.12311	0.274974
$130$	0	0
$131$	−15.9309	−1.39189	−0.695943	−	0.718097i	$-0.745014\pi$
$131$	−15.9309	−1.39189	−0.695943	+	0.718097i	$0.745014\pi$
$132$	3.12311	0.271831
$133$	−0.630683	−0.0546872
$134$	−8.24621	−0.712364
$135$	8.68466	0.747456
$136$	0	0
$137$	14.1231	1.20662	0.603309	−	0.797507i	$-0.293849\pi$
$137$	14.1231	1.20662	0.603309	+	0.797507i	$0.293849\pi$
$138$	20.8769	1.77716
$139$	−5.68466	−0.482166	−0.241083	−	0.970504i	$-0.577503\pi$
$139$	−5.68466	−0.482166	−0.241083	+	0.970504i	$0.577503\pi$
$140$	1.75379	0.148222
$141$	5.75379	0.484556
$142$	−5.36932	−0.450583
$143$	0	0
$144$	2.24621	0.187184
$145$	−8.49242	−0.705257
$146$	23.3693	1.93406
$147$	−10.4384	−0.860949
$148$	0.876894	0.0720803
$149$	14.4924	1.18727	0.593633	−	0.804736i	$-0.297693\pi$
$149$	14.4924	1.18727	0.593633	+	0.804736i	$0.297693\pi$
$150$	−8.00000	−0.653197
$151$	8.24621	0.671067	0.335534	−	0.942028i	$-0.391083\pi$
$151$	8.24621	0.671067	0.335534	+	0.942028i	$0.391083\pi$
$152$	0	0
$153$	0.561553	0.0453989
$154$	−1.12311	−0.0905024
$155$	−2.43845	−0.195861
$156$	0	0
$157$	−17.2462	−1.37640	−0.688199	−	0.725522i	$-0.741598\pi$
$157$	−17.2462	−1.37640	−0.688199	+	0.725522i	$0.741598\pi$
$158$	18.7386	1.49077
$159$	5.36932	0.425815
$160$	12.4924	0.987613
$161$	−3.75379	−0.295840
$162$	−14.0000	−1.09994
$163$	−6.87689	−0.538640	−0.269320	−	0.963051i	$-0.586799\pi$
$163$	−6.87689	−0.538640	−0.269320	+	0.963051i	$0.586799\pi$
$164$	7.36932	0.575447
$165$	−2.43845	−0.189833
$166$	−16.4924	−1.28006
$167$	−12.4924	−0.966693	−0.483346	−	0.875429i	$-0.660579\pi$
$167$	−12.4924	−0.966693	−0.483346	+	0.875429i	$0.660579\pi$
$168$	0	0
$169$	−13.0000	−1.00000
$170$	3.12311	0.239531
$171$	−0.630683	−0.0482295
$172$	4.00000	0.304997
$173$	11.4384	0.869649	0.434825	−	0.900515i	$-0.356810\pi$
$173$	11.4384	0.869649	0.434825	+	0.900515i	$0.356810\pi$
$174$	16.9848	1.28762
$175$	1.43845	0.108736
$176$	−4.00000	−0.301511
$177$	−4.68466	−0.352120
$178$	−16.7386	−1.25461
$179$	−22.3693	−1.67196	−0.835981	−	0.548759i	$-0.815100\pi$
$179$	−22.3693	−1.67196	−0.835981	+	0.548759i	$0.815100\pi$
$180$	1.75379	0.130720
$181$	−9.31534	−0.692404	−0.346202	−	0.938160i	$-0.612529\pi$
$181$	−9.31534	−0.692404	−0.346202	+	0.938160i	$0.612529\pi$
$182$	0	0
$183$	−14.2462	−1.05311
$184$	0	0
$185$	−0.684658	−0.0503371
$186$	4.87689	0.357591
$187$	−1.00000	−0.0731272
$188$	7.36932	0.537463
$189$	3.12311	0.227173
$190$	−3.50758	−0.254466
$191$	2.43845	0.176440	0.0882199	−	0.996101i	$-0.471882\pi$
$191$	2.43845	0.176440	0.0882199	+	0.996101i	$0.471882\pi$
$192$	−12.4924	−0.901563
$193$	−7.36932	−0.530455	−0.265228	−	0.964186i	$-0.585447\pi$
$193$	−7.36932	−0.530455	−0.265228	+	0.964186i	$0.585447\pi$
$194$	−29.3693	−2.10859
$195$	0	0
$196$	−13.3693	−0.954951
$197$	−18.4924	−1.31753	−0.658765	−	0.752349i	$-0.728921\pi$
$197$	−18.4924	−1.31753	−0.658765	+	0.752349i	$0.728921\pi$
$198$	−1.12311	−0.0798156
$199$	−23.3693	−1.65661	−0.828303	−	0.560280i	$-0.810694\pi$
$199$	−23.3693	−1.65661	−0.828303	+	0.560280i	$0.810694\pi$
$200$	0	0
$201$	−6.43845	−0.454133
$202$	26.7386	1.88132
$203$	−3.05398	−0.214347
$204$	−3.12311	−0.218661
$205$	−5.75379	−0.401862
$206$	−2.87689	−0.200443
$207$	−3.75379	−0.260906
$208$	0	0
$209$	1.12311	0.0776868
$210$	2.73863	0.188984
$211$	2.56155	0.176345	0.0881723	−	0.996105i	$-0.471897\pi$
$211$	2.56155	0.176345	0.0881723	+	0.996105i	$0.471897\pi$
$212$	6.87689	0.472307
$213$	−4.19224	−0.287247
$214$	14.8769	1.01696
$215$	−3.12311	−0.212994
$216$	0	0
$217$	−0.876894	−0.0595275
$218$	35.3693	2.39551
$219$	18.2462	1.23296
$220$	−3.12311	−0.210560
$221$	0	0
$222$	1.36932	0.0919025
$223$	−26.9309	−1.80342	−0.901712	−	0.432337i	$-0.857689\pi$
$223$	−26.9309	−1.80342	−0.901712	+	0.432337i	$0.857689\pi$
$224$	4.49242	0.300163
$225$	1.43845	0.0958965
$226$	23.1231	1.53813
$227$	5.19224	0.344621	0.172310	−	0.985043i	$-0.444877\pi$
$227$	5.19224	0.344621	0.172310	+	0.985043i	$0.444877\pi$
$228$	3.50758	0.232295
$229$	3.49242	0.230786	0.115393	−	0.993320i	$-0.463187\pi$
$229$	3.49242	0.230786	0.115393	+	0.993320i	$0.463187\pi$
$230$	−20.8769	−1.37658
$231$	−0.876894	−0.0576954
$232$	0	0
$233$	24.1771	1.58389	0.791947	−	0.610590i	$-0.209068\pi$
$233$	24.1771	1.58389	0.791947	+	0.610590i	$0.209068\pi$
$234$	0	0
$235$	−5.75379	−0.375336
$236$	−6.00000	−0.390567
$237$	14.6307	0.950365
$238$	1.12311	0.0728001
$239$	0.876894	0.0567216	0.0283608	−	0.999598i	$-0.490971\pi$
$239$	0.876894	0.0567216	0.0283608	+	0.999598i	$0.490971\pi$
$240$	9.75379	0.629604
$241$	1.43845	0.0926585	0.0463293	−	0.998926i	$-0.485248\pi$
$241$	1.43845	0.0926585	0.0463293	+	0.998926i	$0.485248\pi$
$242$	2.00000	0.128565
$243$	5.75379	0.369106
$244$	−18.2462	−1.16809
$245$	10.4384	0.666888
$246$	11.5076	0.733696
$247$	0	0
$248$	0	0
$249$	−12.8769	−0.816040
$250$	23.6155	1.49358
$251$	26.4384	1.66878	0.834390	−	0.551175i	$-0.185820\pi$
$251$	26.4384	1.66878	0.834390	+	0.551175i	$0.185820\pi$
$252$	0.630683	0.0397293
$253$	6.68466	0.420261
$254$	−40.9848	−2.57162
$255$	2.43845	0.152701
$256$	16.0000	1.00000
$257$	−29.6847	−1.85168	−0.925839	−	0.377918i	$-0.876640\pi$
$257$	−29.6847	−1.85168	−0.925839	+	0.377918i	$0.876640\pi$
$258$	6.24621	0.388872
$259$	−0.246211	−0.0152988
$260$	0	0
$261$	−3.05398	−0.189036
$262$	−31.8617	−1.96842
$263$	17.3693	1.07104	0.535519	−	0.844523i	$-0.320116\pi$
$263$	17.3693	1.07104	0.535519	+	0.844523i	$0.320116\pi$
$264$	0	0
$265$	−5.36932	−0.329835
$266$	−1.26137	−0.0773393
$267$	−13.0691	−0.799818
$268$	−8.24621	−0.503718
$269$	17.3693	1.05903	0.529513	−	0.848302i	$-0.322375\pi$
$269$	17.3693	1.05903	0.529513	+	0.848302i	$0.322375\pi$
$270$	17.3693	1.05706
$271$	−1.12311	−0.0682238	−0.0341119	−	0.999418i	$-0.510860\pi$
$271$	−1.12311	−0.0682238	−0.0341119	+	0.999418i	$0.510860\pi$
$272$	4.00000	0.242536
$273$	0	0
$274$	28.2462	1.70642
$275$	−2.56155	−0.154467
$276$	20.8769	1.25664
$277$	22.8078	1.37039	0.685193	−	0.728362i	$-0.259718\pi$
$277$	22.8078	1.37039	0.685193	+	0.728362i	$0.259718\pi$
$278$	−11.3693	−0.681886
$279$	−0.876894	−0.0524983
$280$	0	0
$281$	4.87689	0.290931	0.145466	−	0.989363i	$-0.453532\pi$
$281$	4.87689	0.290931	0.145466	+	0.989363i	$0.453532\pi$
$282$	11.5076	0.685266
$283$	−18.2462	−1.08462	−0.542312	−	0.840177i	$-0.682451\pi$
$283$	−18.2462	−1.08462	−0.542312	+	0.840177i	$0.682451\pi$
$284$	−5.36932	−0.318610
$285$	−2.73863	−0.162223
$286$	0	0
$287$	−2.06913	−0.122137
$288$	4.49242	0.264719
$289$	1.00000	0.0588235
$290$	−16.9848	−0.997384
$291$	−22.9309	−1.34423
$292$	23.3693	1.36759
$293$	28.4924	1.66455	0.832273	−	0.554367i	$-0.187039\pi$
$293$	28.4924	1.66455	0.832273	+	0.554367i	$0.187039\pi$
$294$	−20.8769	−1.21757
$295$	4.68466	0.272751
$296$	0	0
$297$	−5.56155	−0.322714
$298$	28.9848	1.67905
$299$	0	0
$300$	−8.00000	−0.461880
$301$	−1.12311	−0.0647347
$302$	16.4924	0.949032
$303$	20.8769	1.19935
$304$	−4.49242	−0.257658
$305$	14.2462	0.815736
$306$	1.12311	0.0642037
$307$	30.2462	1.72624	0.863121	−	0.504997i	$-0.168506\pi$
$307$	30.2462	1.72624	0.863121	+	0.504997i	$0.168506\pi$
$308$	−1.12311	−0.0639949
$309$	−2.24621	−0.127782
$310$	−4.87689	−0.276989
$311$	−28.0000	−1.58773	−0.793867	−	0.608091i	$-0.791935\pi$
$311$	−28.0000	−1.58773	−0.793867	+	0.608091i	$0.791935\pi$
$312$	0	0
$313$	22.0540	1.24656	0.623282	−	0.781997i	$-0.285799\pi$
$313$	22.0540	1.24656	0.623282	+	0.781997i	$0.285799\pi$
$314$	−34.4924	−1.94652
$315$	−0.492423	−0.0277449
$316$	18.7386	1.05413
$317$	5.31534	0.298539	0.149270	−	0.988797i	$-0.452308\pi$
$317$	5.31534	0.298539	0.149270	+	0.988797i	$0.452308\pi$
$318$	10.7386	0.602193
$319$	5.43845	0.304495
$320$	12.4924	0.698348
$321$	11.6155	0.648316
$322$	−7.50758	−0.418381
$323$	−1.12311	−0.0624913
$324$	−14.0000	−0.777778
$325$	0	0
$326$	−13.7538	−0.761752
$327$	27.6155	1.52714
$328$	0	0
$329$	−2.06913	−0.114075
$330$	−4.87689	−0.268464
$331$	28.3002	1.55552	0.777759	−	0.628562i	$-0.216356\pi$
$331$	28.3002	1.55552	0.777759	+	0.628562i	$0.216356\pi$
$332$	−16.4924	−0.905139
$333$	−0.246211	−0.0134923
$334$	−24.9848	−1.36711
$335$	6.43845	0.351770
$336$	3.50758	0.191354
$337$	10.8078	0.588736	0.294368	−	0.955692i	$-0.404891\pi$
$337$	10.8078	0.588736	0.294368	+	0.955692i	$0.404891\pi$
$338$	−26.0000	−1.41421
$339$	18.0540	0.980557
$340$	3.12311	0.169374
$341$	1.56155	0.0845628
$342$	−1.26137	−0.0682069
$343$	7.68466	0.414933
$344$	0	0
$345$	−16.3002	−0.877573
$346$	22.8769	1.22987
$347$	−29.4384	−1.58034	−0.790169	−	0.612889i	$-0.790007\pi$
$347$	−29.4384	−1.58034	−0.790169	+	0.612889i	$0.790007\pi$
$348$	16.9848	0.910483
$349$	−9.36932	−0.501528	−0.250764	−	0.968048i	$-0.580682\pi$
$349$	−9.36932	−0.501528	−0.250764	+	0.968048i	$0.580682\pi$
$350$	2.87689	0.153776
$351$	0	0
$352$	−8.00000	−0.426401
$353$	8.75379	0.465917	0.232959	−	0.972487i	$-0.425159\pi$
$353$	8.75379	0.465917	0.232959	+	0.972487i	$0.425159\pi$
$354$	−9.36932	−0.497974
$355$	4.19224	0.222501
$356$	−16.7386	−0.887146
$357$	0.876894	0.0464102
$358$	−44.7386	−2.36451
$359$	−5.12311	−0.270387	−0.135194	−	0.990819i	$-0.543166\pi$
$359$	−5.12311	−0.270387	−0.135194	+	0.990819i	$0.543166\pi$
$360$	0	0
$361$	−17.7386	−0.933612
$362$	−18.6307	−0.979207
$363$	1.56155	0.0819603
$364$	0	0
$365$	−18.2462	−0.955050
$366$	−28.4924	−1.48932
$367$	9.56155	0.499109	0.249554	−	0.968361i	$-0.419716\pi$
$367$	9.56155	0.499109	0.249554	+	0.968361i	$0.419716\pi$
$368$	−26.7386	−1.39385
$369$	−2.06913	−0.107715
$370$	−1.36932	−0.0711874
$371$	−1.93087	−0.100246
$372$	4.87689	0.252855
$373$	20.2462	1.04831	0.524155	−	0.851623i	$-0.324381\pi$
$373$	20.2462	1.04831	0.524155	+	0.851623i	$0.324381\pi$
$374$	−2.00000	−0.103418
$375$	18.4384	0.952157
$376$	0	0
$377$	0	0
$378$	6.24621	0.321270
$379$	−0.192236	−0.00987450	−0.00493725	−	0.999988i	$-0.501572\pi$
$379$	−0.192236	−0.00987450	−0.00493725	+	0.999988i	$0.501572\pi$
$380$	−3.50758	−0.179935
$381$	−32.0000	−1.63941
$382$	4.87689	0.249524
$383$	18.0540	0.922515	0.461258	−	0.887266i	$-0.347398\pi$
$383$	18.0540	0.922515	0.461258	+	0.887266i	$0.347398\pi$
$384$	0	0
$385$	0.876894	0.0446907
$386$	−14.7386	−0.750177
$387$	−1.12311	−0.0570907
$388$	−29.3693	−1.49100
$389$	−27.4924	−1.39392	−0.696961	−	0.717109i	$-0.745465\pi$
$389$	−27.4924	−1.39392	−0.696961	+	0.717109i	$0.745465\pi$
$390$	0	0
$391$	−6.68466	−0.338058
$392$	0	0
$393$	−24.8769	−1.25487
$394$	−36.9848	−1.86327
$395$	−14.6307	−0.736150
$396$	−1.12311	−0.0564382
$397$	6.63068	0.332784	0.166392	−	0.986060i	$-0.446788\pi$
$397$	6.63068	0.332784	0.166392	+	0.986060i	$0.446788\pi$
$398$	−46.7386	−2.34280
$399$	−0.984845	−0.0493039
$400$	10.2462	0.512311
$401$	9.36932	0.467881	0.233941	−	0.972251i	$-0.424838\pi$
$401$	9.36932	0.467881	0.233941	+	0.972251i	$0.424838\pi$
$402$	−12.8769	−0.642241
$403$	0	0
$404$	26.7386	1.33030
$405$	10.9309	0.543159
$406$	−6.10795	−0.303133
$407$	0.438447	0.0217330
$408$	0	0
$409$	−23.1231	−1.14336	−0.571682	−	0.820475i	$-0.693709\pi$
$409$	−23.1231	−1.14336	−0.571682	+	0.820475i	$0.693709\pi$
$410$	−11.5076	−0.568319
$411$	22.0540	1.08784
$412$	−2.87689	−0.141734
$413$	1.68466	0.0828966
$414$	−7.50758	−0.368977
$415$	12.8769	0.632102
$416$	0	0
$417$	−8.87689	−0.434703
$418$	2.24621	0.109866
$419$	4.00000	0.195413	0.0977064	−	0.995215i	$-0.468849\pi$
$419$	4.00000	0.195413	0.0977064	+	0.995215i	$0.468849\pi$
$420$	2.73863	0.133632
$421$	19.3002	0.940634	0.470317	−	0.882498i	$-0.344140\pi$
$421$	19.3002	0.940634	0.470317	+	0.882498i	$0.344140\pi$
$422$	5.12311	0.249389
$423$	−2.06913	−0.100605
$424$	0	0
$425$	2.56155	0.124254
$426$	−8.38447	−0.406229
$427$	5.12311	0.247924
$428$	14.8769	0.719102
$429$	0	0
$430$	−6.24621	−0.301219
$431$	−6.80776	−0.327918	−0.163959	−	0.986467i	$-0.552427\pi$
$431$	−6.80776	−0.327918	−0.163959	+	0.986467i	$0.552427\pi$
$432$	22.2462	1.07032
$433$	−11.0000	−0.528626	−0.264313	−	0.964437i	$-0.585145\pi$
$433$	−11.0000	−0.528626	−0.264313	+	0.964437i	$0.585145\pi$
$434$	−1.75379	−0.0841846
$435$	−13.2614	−0.635834
$436$	35.3693	1.69388
$437$	7.50758	0.359136
$438$	36.4924	1.74368
$439$	11.1922	0.534176	0.267088	−	0.963672i	$-0.413939\pi$
$439$	11.1922	0.534176	0.267088	+	0.963672i	$0.413939\pi$
$440$	0	0
$441$	3.75379	0.178752
$442$	0	0
$443$	34.9309	1.65962	0.829808	−	0.558049i	$-0.188450\pi$
$443$	34.9309	1.65962	0.829808	+	0.558049i	$0.188450\pi$
$444$	1.36932	0.0649849
$445$	13.0691	0.619536
$446$	−53.8617	−2.55043
$447$	22.6307	1.07039
$448$	4.49242	0.212247
$449$	−30.9309	−1.45972	−0.729859	−	0.683598i	$-0.760414\pi$
$449$	−30.9309	−1.45972	−0.729859	+	0.683598i	$0.760414\pi$
$450$	2.87689	0.135618
$451$	3.68466	0.173504
$452$	23.1231	1.08762
$453$	12.8769	0.605009
$454$	10.3845	0.487367
$455$	0	0
$456$	0	0
$457$	18.2462	0.853522	0.426761	−	0.904365i	$-0.359655\pi$
$457$	18.2462	0.853522	0.426761	+	0.904365i	$0.359655\pi$
$458$	6.98485	0.326380
$459$	5.56155	0.259591
$460$	−20.8769	−0.973390
$461$	−27.3693	−1.27472	−0.637358	−	0.770568i	$-0.719973\pi$
$461$	−27.3693	−1.27472	−0.637358	+	0.770568i	$0.719973\pi$
$462$	−1.75379	−0.0815936
$463$	37.9848	1.76531	0.882653	−	0.470026i	$-0.155755\pi$
$463$	37.9848	1.76531	0.882653	+	0.470026i	$0.155755\pi$
$464$	−21.7538	−1.00989
$465$	−3.80776	−0.176581
$466$	48.3542	2.23996
$467$	20.3693	0.942580	0.471290	−	0.881978i	$-0.343789\pi$
$467$	20.3693	0.942580	0.471290	+	0.881978i	$0.343789\pi$
$468$	0	0
$469$	2.31534	0.106913
$470$	−11.5076	−0.530805
$471$	−26.9309	−1.24091
$472$	0	0
$473$	2.00000	0.0919601
$474$	29.2614	1.34402
$475$	−2.87689	−0.132001
$476$	1.12311	0.0514775
$477$	−1.93087	−0.0884084
$478$	1.75379	0.0802164
$479$	−8.31534	−0.379938	−0.189969	−	0.981790i	$-0.560839\pi$
$479$	−8.31534	−0.379938	−0.189969	+	0.981790i	$0.560839\pi$
$480$	19.5076	0.890395
$481$	0	0
$482$	2.87689	0.131039
$483$	−5.86174	−0.266718
$484$	2.00000	0.0909091
$485$	22.9309	1.04124
$486$	11.5076	0.521994
$487$	6.68466	0.302911	0.151455	−	0.988464i	$-0.451604\pi$
$487$	6.68466	0.302911	0.151455	+	0.988464i	$0.451604\pi$
$488$	0	0
$489$	−10.7386	−0.485618
$490$	20.8769	0.943122
$491$	−37.6155	−1.69757	−0.848783	−	0.528742i	$-0.822664\pi$
$491$	−37.6155	−1.69757	−0.848783	+	0.528742i	$0.822664\pi$
$492$	11.5076	0.518802
$493$	−5.43845	−0.244935
$494$	0	0
$495$	0.876894	0.0394135
$496$	−6.24621	−0.280463
$497$	1.50758	0.0676241
$498$	−25.7538	−1.15405
$499$	19.3693	0.867090	0.433545	−	0.901132i	$-0.357263\pi$
$499$	19.3693	0.867090	0.433545	+	0.901132i	$0.357263\pi$
$500$	23.6155	1.05612
$501$	−19.5076	−0.871534
$502$	52.8769	2.36001
$503$	18.8078	0.838597	0.419298	−	0.907848i	$-0.362276\pi$
$503$	18.8078	0.838597	0.419298	+	0.907848i	$0.362276\pi$
$504$	0	0
$505$	−20.8769	−0.929010
$506$	13.3693	0.594339
$507$	−20.3002	−0.901563
$508$	−40.9848	−1.81841
$509$	3.49242	0.154799	0.0773995	−	0.997000i	$-0.475338\pi$
$509$	3.49242	0.154799	0.0773995	+	0.997000i	$0.475338\pi$
$510$	4.87689	0.215953
$511$	−6.56155	−0.290266
$512$	32.0000	1.41421
$513$	−6.24621	−0.275777
$514$	−59.3693	−2.61867
$515$	2.24621	0.0989799
$516$	6.24621	0.274974
$517$	3.68466	0.162051
$518$	−0.492423	−0.0216358
$519$	17.8617	0.784043
$520$	0	0
$521$	−3.31534	−0.145248	−0.0726239	−	0.997359i	$-0.523137\pi$
$521$	−3.31534	−0.145248	−0.0726239	+	0.997359i	$0.523137\pi$
$522$	−6.10795	−0.267338
$523$	2.24621	0.0982200	0.0491100	−	0.998793i	$-0.484362\pi$
$523$	2.24621	0.0982200	0.0491100	+	0.998793i	$0.484362\pi$
$524$	−31.8617	−1.39189
$525$	2.24621	0.0980327
$526$	34.7386	1.51468
$527$	−1.56155	−0.0680223
$528$	−6.24621	−0.271831
$529$	21.6847	0.942811
$530$	−10.7386	−0.466456
$531$	1.68466	0.0731079
$532$	−1.26137	−0.0546872
$533$	0	0
$534$	−26.1383	−1.13111
$535$	−11.6155	−0.502183
$536$	0	0
$537$	−34.9309	−1.50738
$538$	34.7386	1.49769
$539$	−6.68466	−0.287929
$540$	17.3693	0.747456
$541$	−15.0540	−0.647221	−0.323610	−	0.946190i	$-0.604897\pi$
$541$	−15.0540	−0.647221	−0.323610	+	0.946190i	$0.604897\pi$
$542$	−2.24621	−0.0964830
$543$	−14.5464	−0.624246
$544$	8.00000	0.342997
$545$	−27.6155	−1.18292
$546$	0	0
$547$	−18.7386	−0.801206	−0.400603	−	0.916252i	$-0.631199\pi$
$547$	−18.7386	−0.801206	−0.400603	+	0.916252i	$0.631199\pi$
$548$	28.2462	1.20662
$549$	5.12311	0.218649
$550$	−5.12311	−0.218450
$551$	6.10795	0.260207
$552$	0	0
$553$	−5.26137	−0.223736
$554$	45.6155	1.93802
$555$	−1.06913	−0.0453821
$556$	−11.3693	−0.482166
$557$	39.6155	1.67856	0.839282	−	0.543697i	$-0.182976\pi$
$557$	39.6155	1.67856	0.839282	+	0.543697i	$0.182976\pi$
$558$	−1.75379	−0.0742438
$559$	0	0
$560$	−3.50758	−0.148222
$561$	−1.56155	−0.0659288
$562$	9.75379	0.411439
$563$	−21.7538	−0.916813	−0.458406	−	0.888743i	$-0.651580\pi$
$563$	−21.7538	−0.916813	−0.458406	+	0.888743i	$0.651580\pi$
$564$	11.5076	0.484556
$565$	−18.0540	−0.759536
$566$	−36.4924	−1.53389
$567$	3.93087	0.165081
$568$	0	0
$569$	26.2462	1.10030	0.550149	−	0.835066i	$-0.314571\pi$
$569$	26.2462	1.10030	0.550149	+	0.835066i	$0.314571\pi$
$570$	−5.47727	−0.229417
$571$	−11.6847	−0.488988	−0.244494	−	0.969651i	$-0.578622\pi$
$571$	−11.6847	−0.488988	−0.244494	+	0.969651i	$0.578622\pi$
$572$	0	0
$573$	3.80776	0.159072
$574$	−4.13826	−0.172728
$575$	−17.1231	−0.714083
$576$	4.49242	0.187184
$577$	16.3693	0.681464	0.340732	−	0.940161i	$-0.389325\pi$
$577$	16.3693	0.681464	0.340732	+	0.940161i	$0.389325\pi$
$578$	2.00000	0.0831890
$579$	−11.5076	−0.478239
$580$	−16.9848	−0.705257
$581$	4.63068	0.192113
$582$	−45.8617	−1.90103
$583$	3.43845	0.142406
$584$	0	0
$585$	0	0
$586$	56.9848	2.35402
$587$	40.4924	1.67130	0.835651	−	0.549261i	$-0.185091\pi$
$587$	40.4924	1.67130	0.835651	+	0.549261i	$0.185091\pi$
$588$	−20.8769	−0.860949
$589$	1.75379	0.0722636
$590$	9.36932	0.385729
$591$	−28.8769	−1.18784
$592$	−1.75379	−0.0720803
$593$	−23.3693	−0.959663	−0.479831	−	0.877361i	$-0.659302\pi$
$593$	−23.3693	−0.959663	−0.479831	+	0.877361i	$0.659302\pi$
$594$	−11.1231	−0.456387
$595$	−0.876894	−0.0359492
$596$	28.9848	1.18727
$597$	−36.4924	−1.49354
$598$	0	0
$599$	−21.9309	−0.896071	−0.448036	−	0.894016i	$-0.647876\pi$
$599$	−21.9309	−0.896071	−0.448036	+	0.894016i	$0.647876\pi$
$600$	0	0
$601$	−16.2462	−0.662697	−0.331348	−	0.943508i	$-0.607504\pi$
$601$	−16.2462	−0.662697	−0.331348	+	0.943508i	$0.607504\pi$
$602$	−2.24621	−0.0915487
$603$	2.31534	0.0942880
$604$	16.4924	0.671067
$605$	−1.56155	−0.0634861
$606$	41.7538	1.69613
$607$	−3.12311	−0.126763	−0.0633815	−	0.997989i	$-0.520188\pi$
$607$	−3.12311	−0.126763	−0.0633815	+	0.997989i	$0.520188\pi$
$608$	−8.98485	−0.364384
$609$	−4.76894	−0.193247
$610$	28.4924	1.15362
$611$	0	0
$612$	1.12311	0.0453989
$613$	−35.8617	−1.44844	−0.724221	−	0.689568i	$-0.757800\pi$
$613$	−35.8617	−1.44844	−0.724221	+	0.689568i	$0.757800\pi$
$614$	60.4924	2.44128
$615$	−8.98485	−0.362304
$616$	0	0
$617$	19.6155	0.789691	0.394846	−	0.918747i	$-0.370798\pi$
$617$	19.6155	0.789691	0.394846	+	0.918747i	$0.370798\pi$
$618$	−4.49242	−0.180712
$619$	38.6847	1.55487	0.777434	−	0.628965i	$-0.216521\pi$
$619$	38.6847	1.55487	0.777434	+	0.628965i	$0.216521\pi$
$620$	−4.87689	−0.195861
$621$	−37.1771	−1.49186
$622$	−56.0000	−2.24540
$623$	4.69981	0.188294
$624$	0	0
$625$	−5.63068	−0.225227
$626$	44.1080	1.76291
$627$	1.75379	0.0700396
$628$	−34.4924	−1.37640
$629$	−0.438447	−0.0174820
$630$	−0.984845	−0.0392372
$631$	−11.2462	−0.447705	−0.223852	−	0.974623i	$-0.571863\pi$
$631$	−11.2462	−0.447705	−0.223852	+	0.974623i	$0.571863\pi$
$632$	0	0
$633$	4.00000	0.158986
$634$	10.6307	0.422198
$635$	32.0000	1.26988
$636$	10.7386	0.425815
$637$	0	0
$638$	10.8769	0.430620
$639$	1.50758	0.0596388
$640$	0	0
$641$	−4.19224	−0.165583	−0.0827917	−	0.996567i	$-0.526384\pi$
$641$	−4.19224	−0.165583	−0.0827917	+	0.996567i	$0.526384\pi$
$642$	23.2311	0.916857
$643$	−44.3002	−1.74703	−0.873514	−	0.486798i	$-0.838165\pi$
$643$	−44.3002	−1.74703	−0.873514	+	0.486798i	$0.838165\pi$
$644$	−7.50758	−0.295840
$645$	−4.87689	−0.192028
$646$	−2.24621	−0.0883760
$647$	0.369317	0.0145193	0.00725967	−	0.999974i	$-0.497689\pi$
$647$	0.369317	0.0145193	0.00725967	+	0.999974i	$0.497689\pi$
$648$	0	0
$649$	−3.00000	−0.117760
$650$	0	0
$651$	−1.36932	−0.0536678
$652$	−13.7538	−0.538640
$653$	7.94602	0.310952	0.155476	−	0.987840i	$-0.450309\pi$
$653$	7.94602	0.310952	0.155476	+	0.987840i	$0.450309\pi$
$654$	55.2311	2.15971
$655$	24.8769	0.972021
$656$	−14.7386	−0.575447
$657$	−6.56155	−0.255991
$658$	−4.13826	−0.161326
$659$	−7.12311	−0.277477	−0.138738	−	0.990329i	$-0.544305\pi$
$659$	−7.12311	−0.277477	−0.138738	+	0.990329i	$0.544305\pi$
$660$	−4.87689	−0.189833
$661$	12.3693	0.481111	0.240555	−	0.970635i	$-0.422670\pi$
$661$	12.3693	0.481111	0.240555	+	0.970635i	$0.422670\pi$
$662$	56.6004	2.19984
$663$	0	0
$664$	0	0
$665$	0.984845	0.0381907
$666$	−0.492423	−0.0190810
$667$	36.3542	1.40764
$668$	−24.9848	−0.966693
$669$	−42.0540	−1.62590
$670$	12.8769	0.497478
$671$	−9.12311	−0.352194
$672$	7.01515	0.270615
$673$	−33.0540	−1.27414	−0.637069	−	0.770807i	$-0.719853\pi$
$673$	−33.0540	−1.27414	−0.637069	+	0.770807i	$0.719853\pi$
$674$	21.6155	0.832599
$675$	14.2462	0.548337
$676$	−26.0000	−1.00000
$677$	34.8078	1.33777	0.668886	−	0.743365i	$-0.266772\pi$
$677$	34.8078	1.33777	0.668886	+	0.743365i	$0.266772\pi$
$678$	36.1080	1.38672
$679$	8.24621	0.316461
$680$	0	0
$681$	8.10795	0.310697
$682$	3.12311	0.119590
$683$	38.7386	1.48229	0.741146	−	0.671344i	$-0.234282\pi$
$683$	38.7386	1.48229	0.741146	+	0.671344i	$0.234282\pi$
$684$	−1.26137	−0.0482295
$685$	−22.0540	−0.842639
$686$	15.3693	0.586803
$687$	5.45360	0.208068
$688$	−8.00000	−0.304997
$689$	0	0
$690$	−32.6004	−1.24107
$691$	18.9309	0.720164	0.360082	−	0.932921i	$-0.382749\pi$
$691$	18.9309	0.720164	0.360082	+	0.932921i	$0.382749\pi$
$692$	22.8769	0.869649
$693$	0.315342	0.0119788
$694$	−58.8769	−2.23494
$695$	8.87689	0.336720
$696$	0	0
$697$	−3.68466	−0.139566
$698$	−18.7386	−0.709268
$699$	37.7538	1.42798
$700$	2.87689	0.108736
$701$	−8.87689	−0.335276	−0.167638	−	0.985849i	$-0.553614\pi$
$701$	−8.87689	−0.335276	−0.167638	+	0.985849i	$0.553614\pi$
$702$	0	0
$703$	0.492423	0.0185721
$704$	−8.00000	−0.301511
$705$	−8.98485	−0.338389
$706$	17.5076	0.658906
$707$	−7.50758	−0.282352
$708$	−9.36932	−0.352120
$709$	32.3002	1.21306	0.606529	−	0.795061i	$-0.292561\pi$
$709$	32.3002	1.21306	0.606529	+	0.795061i	$0.292561\pi$
$710$	8.38447	0.314664
$711$	−5.26137	−0.197317
$712$	0	0
$713$	10.4384	0.390923
$714$	1.75379	0.0656339
$715$	0	0
$716$	−44.7386	−1.67196
$717$	1.36932	0.0511381
$718$	−10.2462	−0.382385
$719$	−39.4233	−1.47024	−0.735120	−	0.677937i	$-0.762874\pi$
$719$	−39.4233	−1.47024	−0.735120	+	0.677937i	$0.762874\pi$
$720$	−3.50758	−0.130720
$721$	0.807764	0.0300827
$722$	−35.4773	−1.32033
$723$	2.24621	0.0835375
$724$	−18.6307	−0.692404
$725$	−13.9309	−0.517380
$726$	3.12311	0.115909
$727$	−13.0000	−0.482143	−0.241072	−	0.970507i	$-0.577499\pi$
$727$	−13.0000	−0.482143	−0.241072	+	0.970507i	$0.577499\pi$
$728$	0	0
$729$	29.9848	1.11055
$730$	−36.4924	−1.35065
$731$	−2.00000	−0.0739727
$732$	−28.4924	−1.05311
$733$	13.6155	0.502901	0.251451	−	0.967870i	$-0.419092\pi$
$733$	13.6155	0.502901	0.251451	+	0.967870i	$0.419092\pi$
$734$	19.1231	0.705847
$735$	16.3002	0.601241
$736$	−53.4773	−1.97120
$737$	−4.12311	−0.151877
$738$	−4.13826	−0.152331
$739$	9.86174	0.362770	0.181385	−	0.983412i	$-0.441942\pi$
$739$	9.86174	0.362770	0.181385	+	0.983412i	$0.441942\pi$
$740$	−1.36932	−0.0503371
$741$	0	0
$742$	−3.86174	−0.141769
$743$	−44.1771	−1.62070	−0.810350	−	0.585946i	$-0.800723\pi$
$743$	−44.1771	−1.62070	−0.810350	+	0.585946i	$0.800723\pi$
$744$	0	0
$745$	−22.6307	−0.829124
$746$	40.4924	1.48253
$747$	4.63068	0.169428
$748$	−2.00000	−0.0731272
$749$	−4.17708	−0.152627
$750$	36.8769	1.34655
$751$	−9.56155	−0.348906	−0.174453	−	0.984666i	$-0.555816\pi$
$751$	−9.56155	−0.348906	−0.174453	+	0.984666i	$0.555816\pi$
$752$	−14.7386	−0.537463
$753$	41.2850	1.50451
$754$	0	0
$755$	−12.8769	−0.468638
$756$	6.24621	0.227173
$757$	24.7386	0.899141	0.449570	−	0.893245i	$-0.351577\pi$
$757$	24.7386	0.899141	0.449570	+	0.893245i	$0.351577\pi$
$758$	−0.384472	−0.0139646
$759$	10.4384	0.378892
$760$	0	0
$761$	−38.1080	−1.38141	−0.690706	−	0.723136i	$-0.742700\pi$
$761$	−38.1080	−1.38141	−0.690706	+	0.723136i	$0.742700\pi$
$762$	−64.0000	−2.31848
$763$	−9.93087	−0.359522
$764$	4.87689	0.176440
$765$	−0.876894	−0.0317042
$766$	36.1080	1.30463
$767$	0	0
$768$	24.9848	0.901563
$769$	−20.0000	−0.721218	−0.360609	−	0.932717i	$-0.617431\pi$
$769$	−20.0000	−0.721218	−0.360609	+	0.932717i	$0.617431\pi$
$770$	1.75379	0.0632022
$771$	−46.3542	−1.66940
$772$	−14.7386	−0.530455
$773$	10.0000	0.359675	0.179838	−	0.983696i	$-0.442443\pi$
$773$	10.0000	0.359675	0.179838	+	0.983696i	$0.442443\pi$
$774$	−2.24621	−0.0807384
$775$	−4.00000	−0.143684
$776$	0	0
$777$	−0.384472	−0.0137929
$778$	−54.9848	−1.97130
$779$	4.13826	0.148269
$780$	0	0
$781$	−2.68466	−0.0960646
$782$	−13.3693	−0.478086
$783$	−30.2462	−1.08091
$784$	26.7386	0.954951
$785$	26.9309	0.961204
$786$	−49.7538	−1.77466
$787$	34.5616	1.23199	0.615993	−	0.787752i	$-0.288755\pi$
$787$	34.5616	1.23199	0.615993	+	0.787752i	$0.288755\pi$
$788$	−36.9848	−1.31753
$789$	27.1231	0.965608
$790$	−29.2614	−1.04107
$791$	−6.49242	−0.230844
$792$	0	0
$793$	0	0
$794$	13.2614	0.470628
$795$	−8.38447	−0.297367
$796$	−46.7386	−1.65661
$797$	−6.68466	−0.236783	−0.118391	−	0.992967i	$-0.537774\pi$
$797$	−6.68466	−0.236783	−0.118391	+	0.992967i	$0.537774\pi$
$798$	−1.96969	−0.0697263
$799$	−3.68466	−0.130354
$800$	20.4924	0.724517
$801$	4.69981	0.166060
$802$	18.7386	0.661684
$803$	11.6847	0.412343
$804$	−12.8769	−0.454133
$805$	5.86174	0.206599
$806$	0	0
$807$	27.1231	0.954779
$808$	0	0
$809$	−12.1771	−0.428123	−0.214062	−	0.976820i	$-0.568669\pi$
$809$	−12.1771	−0.428123	−0.214062	+	0.976820i	$0.568669\pi$
$810$	21.8617	0.768143
$811$	8.87689	0.311710	0.155855	−	0.987780i	$-0.450187\pi$
$811$	8.87689	0.311710	0.155855	+	0.987780i	$0.450187\pi$
$812$	−6.10795	−0.214347
$813$	−1.75379	−0.0615081
$814$	0.876894	0.0307351
$815$	10.7386	0.376158
$816$	6.24621	0.218661
$817$	2.24621	0.0785850
$818$	−46.2462	−1.61696
$819$	0	0
$820$	−11.5076	−0.401862
$821$	−8.24621	−0.287795	−0.143897	−	0.989593i	$-0.545964\pi$
$821$	−8.24621	−0.287795	−0.143897	+	0.989593i	$0.545964\pi$
$822$	44.1080	1.53844
$823$	−41.6695	−1.45251	−0.726254	−	0.687427i	$-0.758740\pi$
$823$	−41.6695	−1.45251	−0.726254	+	0.687427i	$0.758740\pi$
$824$	0	0
$825$	−4.00000	−0.139262
$826$	3.36932	0.117234
$827$	39.5464	1.37516	0.687581	−	0.726107i	$-0.258672\pi$
$827$	39.5464	1.37516	0.687581	+	0.726107i	$0.258672\pi$
$828$	−7.50758	−0.260906
$829$	−32.4384	−1.12663	−0.563317	−	0.826241i	$-0.690475\pi$
$829$	−32.4384	−1.12663	−0.563317	+	0.826241i	$0.690475\pi$
$830$	25.7538	0.893927
$831$	35.6155	1.23549
$832$	0	0
$833$	6.68466	0.231610
$834$	−17.7538	−0.614763
$835$	19.5076	0.675088
$836$	2.24621	0.0776868
$837$	−8.68466	−0.300186
$838$	8.00000	0.276355
$839$	29.5616	1.02058	0.510289	−	0.860003i	$-0.329538\pi$
$839$	29.5616	1.02058	0.510289	+	0.860003i	$0.329538\pi$
$840$	0	0
$841$	0.576708	0.0198865
$842$	38.6004	1.33026
$843$	7.61553	0.262293
$844$	5.12311	0.176345
$845$	20.3002	0.698348
$846$	−4.13826	−0.142276
$847$	−0.561553	−0.0192952
$848$	−13.7538	−0.472307
$849$	−28.4924	−0.977857
$850$	5.12311	0.175721
$851$	2.93087	0.100469
$852$	−8.38447	−0.287247
$853$	35.4384	1.21339	0.606695	−	0.794935i	$-0.292495\pi$
$853$	35.4384	1.21339	0.606695	+	0.794935i	$0.292495\pi$
$854$	10.2462	0.350618
$855$	0.984845	0.0336810
$856$	0	0
$857$	−22.8769	−0.781460	−0.390730	−	0.920505i	$-0.627777\pi$
$857$	−22.8769	−0.781460	−0.390730	+	0.920505i	$0.627777\pi$
$858$	0	0
$859$	−2.86174	−0.0976413	−0.0488206	−	0.998808i	$-0.515546\pi$
$859$	−2.86174	−0.0976413	−0.0488206	+	0.998808i	$0.515546\pi$
$860$	−6.24621	−0.212994
$861$	−3.23106	−0.110114
$862$	−13.6155	−0.463747
$863$	−36.4924	−1.24222	−0.621108	−	0.783725i	$-0.713317\pi$
$863$	−36.4924	−1.24222	−0.621108	+	0.783725i	$0.713317\pi$
$864$	44.4924	1.51366
$865$	−17.8617	−0.607317
$866$	−22.0000	−0.747590
$867$	1.56155	0.0530331
$868$	−1.75379	−0.0595275
$869$	9.36932	0.317832
$870$	−26.5227	−0.899205
$871$	0	0
$872$	0	0
$873$	8.24621	0.279092
$874$	15.0152	0.507895
$875$	−6.63068	−0.224158
$876$	36.4924	1.23296
$877$	1.61553	0.0545525	0.0272763	−	0.999628i	$-0.491317\pi$
$877$	1.61553	0.0545525	0.0272763	+	0.999628i	$0.491317\pi$
$878$	22.3845	0.755439
$879$	44.4924	1.50069
$880$	6.24621	0.210560
$881$	−57.4233	−1.93464	−0.967320	−	0.253559i	$-0.918399\pi$
$881$	−57.4233	−1.93464	−0.967320	+	0.253559i	$0.918399\pi$
$882$	7.50758	0.252793
$883$	−43.5464	−1.46545	−0.732726	−	0.680523i	$-0.761753\pi$
$883$	−43.5464	−1.46545	−0.732726	+	0.680523i	$0.761753\pi$
$884$	0	0
$885$	7.31534	0.245903
$886$	69.8617	2.34705
$887$	15.1231	0.507784	0.253892	−	0.967233i	$-0.418289\pi$
$887$	15.1231	0.507784	0.253892	+	0.967233i	$0.418289\pi$
$888$	0	0
$889$	11.5076	0.385952
$890$	26.1383	0.876156
$891$	−7.00000	−0.234509
$892$	−53.8617	−1.80342
$893$	4.13826	0.138482
$894$	45.2614	1.51377
$895$	34.9309	1.16761
$896$	0	0
$897$	0	0
$898$	−61.8617	−2.06435
$899$	8.49242	0.283238
$900$	2.87689	0.0958965
$901$	−3.43845	−0.114551
$902$	7.36932	0.245371
$903$	−1.75379	−0.0583624
$904$	0	0
$905$	14.5464	0.483539
$906$	25.7538	0.855612
$907$	18.3845	0.610446	0.305223	−	0.952281i	$-0.401269\pi$
$907$	18.3845	0.610446	0.305223	+	0.952281i	$0.401269\pi$
$908$	10.3845	0.344621
$909$	−7.50758	−0.249011
$910$	0	0
$911$	−17.7538	−0.588209	−0.294105	−	0.955773i	$-0.595021\pi$
$911$	−17.7538	−0.588209	−0.294105	+	0.955773i	$0.595021\pi$
$912$	−7.01515	−0.232295
$913$	−8.24621	−0.272910
$914$	36.4924	1.20706
$915$	22.2462	0.735437
$916$	6.98485	0.230786
$917$	8.94602	0.295424
$918$	11.1231	0.367117
$919$	−39.6155	−1.30680	−0.653398	−	0.757015i	$-0.726657\pi$
$919$	−39.6155	−1.30680	−0.653398	+	0.757015i	$0.726657\pi$
$920$	0	0
$921$	47.2311	1.55632
$922$	−54.7386	−1.80272
$923$	0	0
$924$	−1.75379	−0.0576954
$925$	−1.12311	−0.0369275
$926$	75.9697	2.49652
$927$	0.807764	0.0265305
$928$	−43.5076	−1.42821
$929$	−6.00000	−0.196854	−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000	−0.196854	−0.0984268	+	0.995144i	$0.531381\pi$
$930$	−7.61553	−0.249723
$931$	−7.50758	−0.246051
$932$	48.3542	1.58389
$933$	−43.7235	−1.43144
$934$	40.7386	1.33301
$935$	1.56155	0.0510682
$936$	0	0
$937$	9.12311	0.298039	0.149019	−	0.988834i	$-0.452388\pi$
$937$	9.12311	0.298039	0.149019	+	0.988834i	$0.452388\pi$
$938$	4.63068	0.151197
$939$	34.4384	1.12386
$940$	−11.5076	−0.375336
$941$	39.3002	1.28115	0.640575	−	0.767896i	$-0.278696\pi$
$941$	39.3002	1.28115	0.640575	+	0.767896i	$0.278696\pi$
$942$	−53.8617	−1.75491
$943$	24.6307	0.802085
$944$	12.0000	0.390567
$945$	−4.87689	−0.158645
$946$	4.00000	0.130051
$947$	−30.1922	−0.981116	−0.490558	−	0.871409i	$-0.663207\pi$
$947$	−30.1922	−0.981116	−0.490558	+	0.871409i	$0.663207\pi$
$948$	29.2614	0.950365
$949$	0	0
$950$	−5.75379	−0.186678
$951$	8.30019	0.269152
$952$	0	0
$953$	−25.8617	−0.837744	−0.418872	−	0.908045i	$-0.637574\pi$
$953$	−25.8617	−0.837744	−0.418872	+	0.908045i	$0.637574\pi$
$954$	−3.86174	−0.125028
$955$	−3.80776	−0.123216
$956$	1.75379	0.0567216
$957$	8.49242	0.274521
$958$	−16.6307	−0.537313
$959$	−7.93087	−0.256101
$960$	19.5076	0.629604
$961$	−28.5616	−0.921340
$962$	0	0
$963$	−4.17708	−0.134605
$964$	2.87689	0.0926585
$965$	11.5076	0.370442
$966$	−11.7235	−0.377197
$967$	−38.2462	−1.22992	−0.614958	−	0.788560i	$-0.710827\pi$
$967$	−38.2462	−1.22992	−0.614958	+	0.788560i	$0.710827\pi$
$968$	0	0
$969$	−1.75379	−0.0563398
$970$	45.8617	1.47253
$971$	−44.6847	−1.43400	−0.716999	−	0.697074i	$-0.754485\pi$
$971$	−44.6847	−1.43400	−0.716999	+	0.697074i	$0.754485\pi$
$972$	11.5076	0.369106
$973$	3.19224	0.102338
$974$	13.3693	0.428381
$975$	0	0
$976$	36.4924	1.16809
$977$	−36.6155	−1.17143	−0.585717	−	0.810515i	$-0.699187\pi$
$977$	−36.6155	−1.17143	−0.585717	+	0.810515i	$0.699187\pi$
$978$	−21.4773	−0.686767
$979$	−8.36932	−0.267485
$980$	20.8769	0.666888
$981$	−9.93087	−0.317068
$982$	−75.2311	−2.40072
$983$	18.1922	0.580242	0.290121	−	0.956990i	$-0.406304\pi$
$983$	18.1922	0.580242	0.290121	+	0.956990i	$0.406304\pi$
$984$	0	0
$985$	28.8769	0.920094
$986$	−10.8769	−0.346391
$987$	−3.23106	−0.102846
$988$	0	0
$989$	13.3693	0.425120
$990$	1.75379	0.0557391
$991$	25.6155	0.813704	0.406852	−	0.913494i	$-0.366626\pi$
$991$	25.6155	0.813704	0.406852	+	0.913494i	$0.366626\pi$
$992$	−12.4924	−0.396635
$993$	44.1922	1.40240
$994$	3.01515	0.0956349
$995$	36.4924	1.15689
$996$	−25.7538	−0.816040
$997$	31.9309	1.01126	0.505630	−	0.862750i	$-0.331260\pi$
$997$	31.9309	1.01126	0.505630	+	0.862750i	$0.331260\pi$
$998$	38.7386	1.22625
$999$	−2.43845	−0.0771491

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.a.d.1.2	✓	2
3.2	odd	2		1683.2.a.k.1.2		2
4.3	odd	2		2992.2.a.m.1.1		2
5.4	even	2		4675.2.a.u.1.1		2
7.6	odd	2		9163.2.a.i.1.1		2
11.10	odd	2		2057.2.a.f.1.2		2
17.16	even	2		3179.2.a.o.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.a.d.1.2	✓	2	1.1	even	1	trivial
1683.2.a.k.1.2		2	3.2	odd	2
2057.2.a.f.1.2		2	11.10	odd	2
2992.2.a.m.1.1		2	4.3	odd	2
3179.2.a.o.1.1		2	17.16	even	2
4675.2.a.u.1.1		2	5.4	even	2
9163.2.a.i.1.1		2	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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +1.56155 q^{3} +2.00000 q^{4} -1.56155 q^{5} +3.12311 q^{6} -0.561553 q^{7} -0.561553 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +1.56155 q^{3} +2.00000 q^{4} -1.56155 q^{5} +3.12311 q^{6} -0.561553 q^{7} -0.561553 q^{9} -3.12311 q^{10} +1.00000 q^{11} +3.12311 q^{12} -1.12311 q^{14} -2.43845 q^{15} -4.00000 q^{16} -1.00000 q^{17} -1.12311 q^{18} +1.12311 q^{19} -3.12311 q^{20} -0.876894 q^{21} +2.00000 q^{22} +6.68466 q^{23} -2.56155 q^{25} -5.56155 q^{27} -1.12311 q^{28} +5.43845 q^{29} -4.87689 q^{30} +1.56155 q^{31} -8.00000 q^{32} +1.56155 q^{33} -2.00000 q^{34} +0.876894 q^{35} -1.12311 q^{36} +0.438447 q^{37} +2.24621 q^{38} +3.68466 q^{41} -1.75379 q^{42} +2.00000 q^{43} +2.00000 q^{44} +0.876894 q^{45} +13.3693 q^{46} +3.68466 q^{47} -6.24621 q^{48} -6.68466 q^{49} -5.12311 q^{50} -1.56155 q^{51} +3.43845 q^{53} -11.1231 q^{54} -1.56155 q^{55} +1.75379 q^{57} +10.8769 q^{58} -3.00000 q^{59} -4.87689 q^{60} -9.12311 q^{61} +3.12311 q^{62} +0.315342 q^{63} -8.00000 q^{64} +3.12311 q^{66} -4.12311 q^{67} -2.00000 q^{68} +10.4384 q^{69} +1.75379 q^{70} -2.68466 q^{71} +11.6847 q^{73} +0.876894 q^{74} -4.00000 q^{75} +2.24621 q^{76} -0.561553 q^{77} +9.36932 q^{79} +6.24621 q^{80} -7.00000 q^{81} +7.36932 q^{82} -8.24621 q^{83} -1.75379 q^{84} +1.56155 q^{85} +4.00000 q^{86} +8.49242 q^{87} -8.36932 q^{89} +1.75379 q^{90} +13.3693 q^{92} +2.43845 q^{93} +7.36932 q^{94} -1.75379 q^{95} -12.4924 q^{96} -14.6847 q^{97} -13.3693 q^{98} -0.561553 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - q^{3} + 4 q^{4} + q^{5} - 2 q^{6} + 3 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q + 4 * q^2 - q^3 + 4 * q^4 + q^5 - 2 * q^6 + 3 * q^7 + 3 * q^9	\( 2 q + 4 q^{2} - q^{3} + 4 q^{4} + q^{5} - 2 q^{6} + 3 q^{7} + 3 q^{9} + 2 q^{10} + 2 q^{11} - 2 q^{12} + 6 q^{14} - 9 q^{15} - 8 q^{16} - 2 q^{17} + 6 q^{18} - 6 q^{19} + 2 q^{20} - 10 q^{21} + 4 q^{22} + q^{23} - q^{25} - 7 q^{27} + 6 q^{28} + 15 q^{29} - 18 q^{30} - q^{31} - 16 q^{32} - q^{33} - 4 q^{34} + 10 q^{35} + 6 q^{36} + 5 q^{37} - 12 q^{38} - 5 q^{41} - 20 q^{42} + 4 q^{43} + 4 q^{44} + 10 q^{45} + 2 q^{46} - 5 q^{47} + 4 q^{48} - q^{49} - 2 q^{50} + q^{51} + 11 q^{53} - 14 q^{54} + q^{55} + 20 q^{57} + 30 q^{58} - 6 q^{59} - 18 q^{60} - 10 q^{61} - 2 q^{62} + 13 q^{63} - 16 q^{64} - 2 q^{66} - 4 q^{68} + 25 q^{69} + 20 q^{70} + 7 q^{71} + 11 q^{73} + 10 q^{74} - 8 q^{75} - 12 q^{76} + 3 q^{77} - 6 q^{79} - 4 q^{80} - 14 q^{81} - 10 q^{82} - 20 q^{84} - q^{85} + 8 q^{86} - 16 q^{87} + 8 q^{89} + 20 q^{90} + 2 q^{92} + 9 q^{93} - 10 q^{94} - 20 q^{95} + 8 q^{96} - 17 q^{97} - 2 q^{98} + 3 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 - q^3 + 4 * q^4 + q^5 - 2 * q^6 + 3 * q^7 + 3 * q^9 + 2 * q^10 + 2 * q^11 - 2 * q^12 + 6 * q^14 - 9 * q^15 - 8 * q^16 - 2 * q^17 + 6 * q^18 - 6 * q^19 + 2 * q^20 - 10 * q^21 + 4 * q^22 + q^23 - q^25 - 7 * q^27 + 6 * q^28 + 15 * q^29 - 18 * q^30 - q^31 - 16 * q^32 - q^33 - 4 * q^34 + 10 * q^35 + 6 * q^36 + 5 * q^37 - 12 * q^38 - 5 * q^41 - 20 * q^42 + 4 * q^43 + 4 * q^44 + 10 * q^45 + 2 * q^46 - 5 * q^47 + 4 * q^48 - q^49 - 2 * q^50 + q^51 + 11 * q^53 - 14 * q^54 + q^55 + 20 * q^57 + 30 * q^58 - 6 * q^59 - 18 * q^60 - 10 * q^61 - 2 * q^62 + 13 * q^63 - 16 * q^64 - 2 * q^66 - 4 * q^68 + 25 * q^69 + 20 * q^70 + 7 * q^71 + 11 * q^73 + 10 * q^74 - 8 * q^75 - 12 * q^76 + 3 * q^77 - 6 * q^79 - 4 * q^80 - 14 * q^81 - 10 * q^82 - 20 * q^84 - q^85 + 8 * q^86 - 16 * q^87 + 8 * q^89 + 20 * q^90 + 2 * q^92 + 9 * q^93 - 10 * q^94 - 20 * q^95 + 8 * q^96 - 17 * q^97 - 2 * q^98 + 3 * q^99

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