LMFDB - Embedded newform 931.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(1,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, 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("931.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.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:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{13}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3 $ x^2 - x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 133)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.30278$ of defining polynomial
Character	$\chi$	$=$	931.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.30278 q^{2} -0.302776 q^{3} +3.30278 q^{4} +3.00000 q^{5} +0.697224 q^{6} -3.00000 q^{8} -2.90833 q^{9} +O(q^{10})$	\(q-2.30278 q^{2} -0.302776 q^{3} +3.30278 q^{4} +3.00000 q^{5} +0.697224 q^{6} -3.00000 q^{8} -2.90833 q^{9} -6.90833 q^{10} -0.697224 q^{11} -1.00000 q^{12} +5.60555 q^{13} -0.908327 q^{15} +0.302776 q^{16} +5.30278 q^{17} +6.69722 q^{18} -1.00000 q^{19} +9.90833 q^{20} +1.60555 q^{22} -3.00000 q^{23} +0.908327 q^{24} +4.00000 q^{25} -12.9083 q^{26} +1.78890 q^{27} +9.90833 q^{29} +2.09167 q^{30} -1.30278 q^{31} +5.30278 q^{32} +0.211103 q^{33} -12.2111 q^{34} -9.60555 q^{36} +3.60555 q^{37} +2.30278 q^{38} -1.69722 q^{39} -9.00000 q^{40} -0.697224 q^{41} -10.0000 q^{43} -2.30278 q^{44} -8.72498 q^{45} +6.90833 q^{46} -6.21110 q^{47} -0.0916731 q^{48} -9.21110 q^{50} -1.60555 q^{51} +18.5139 q^{52} -6.90833 q^{53} -4.11943 q^{54} -2.09167 q^{55} +0.302776 q^{57} -22.8167 q^{58} +6.21110 q^{59} -3.00000 q^{60} +4.21110 q^{61} +3.00000 q^{62} -12.8167 q^{64} +16.8167 q^{65} -0.486122 q^{66} -1.90833 q^{67} +17.5139 q^{68} +0.908327 q^{69} +12.2111 q^{71} +8.72498 q^{72} -1.51388 q^{73} -8.30278 q^{74} -1.21110 q^{75} -3.30278 q^{76} +3.90833 q^{78} +11.2111 q^{79} +0.908327 q^{80} +8.18335 q^{81} +1.60555 q^{82} +12.9083 q^{83} +15.9083 q^{85} +23.0278 q^{86} -3.00000 q^{87} +2.09167 q^{88} +10.6056 q^{89} +20.0917 q^{90} -9.90833 q^{92} +0.394449 q^{93} +14.3028 q^{94} -3.00000 q^{95} -1.60555 q^{96} -9.60555 q^{97} +2.02776 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 3 q^{3} + 3 q^{4} + 6 q^{5} + 5 q^{6} - 6 q^{8} + 5 q^{9}+O(q^{10}) $ 2 * q - q^2 + 3 * q^3 + 3 * q^4 + 6 * q^5 + 5 * q^6 - 6 * q^8 + 5 * q^9	$ 2 q - q^{2} + 3 q^{3} + 3 q^{4} + 6 q^{5} + 5 q^{6} - 6 q^{8} + 5 q^{9} - 3 q^{10} - 5 q^{11} - 2 q^{12} + 4 q^{13} + 9 q^{15} - 3 q^{16} + 7 q^{17} + 17 q^{18} - 2 q^{19} + 9 q^{20} - 4 q^{22} - 6 q^{23} - 9 q^{24} + 8 q^{25} - 15 q^{26} + 18 q^{27} + 9 q^{29} + 15 q^{30} + q^{31} + 7 q^{32} - 14 q^{33} - 10 q^{34} - 12 q^{36} + q^{38} - 7 q^{39} - 18 q^{40} - 5 q^{41} - 20 q^{43} - q^{44} + 15 q^{45} + 3 q^{46} + 2 q^{47} - 11 q^{48} - 4 q^{50} + 4 q^{51} + 19 q^{52} - 3 q^{53} + 17 q^{54} - 15 q^{55} - 3 q^{57} - 24 q^{58} - 2 q^{59} - 6 q^{60} - 6 q^{61} + 6 q^{62} - 4 q^{64} + 12 q^{65} - 19 q^{66} + 7 q^{67} + 17 q^{68} - 9 q^{69} + 10 q^{71} - 15 q^{72} + 15 q^{73} - 13 q^{74} + 12 q^{75} - 3 q^{76} - 3 q^{78} + 8 q^{79} - 9 q^{80} + 38 q^{81} - 4 q^{82} + 15 q^{83} + 21 q^{85} + 10 q^{86} - 6 q^{87} + 15 q^{88} + 14 q^{89} + 51 q^{90} - 9 q^{92} + 8 q^{93} + 25 q^{94} - 6 q^{95} + 4 q^{96} - 12 q^{97} - 32 q^{99}+O(q^{100}) $ 2 * q - q^2 + 3 * q^3 + 3 * q^4 + 6 * q^5 + 5 * q^6 - 6 * q^8 + 5 * q^9 - 3 * q^10 - 5 * q^11 - 2 * q^12 + 4 * q^13 + 9 * q^15 - 3 * q^16 + 7 * q^17 + 17 * q^18 - 2 * q^19 + 9 * q^20 - 4 * q^22 - 6 * q^23 - 9 * q^24 + 8 * q^25 - 15 * q^26 + 18 * q^27 + 9 * q^29 + 15 * q^30 + q^31 + 7 * q^32 - 14 * q^33 - 10 * q^34 - 12 * q^36 + q^38 - 7 * q^39 - 18 * q^40 - 5 * q^41 - 20 * q^43 - q^44 + 15 * q^45 + 3 * q^46 + 2 * q^47 - 11 * q^48 - 4 * q^50 + 4 * q^51 + 19 * q^52 - 3 * q^53 + 17 * q^54 - 15 * q^55 - 3 * q^57 - 24 * q^58 - 2 * q^59 - 6 * q^60 - 6 * q^61 + 6 * q^62 - 4 * q^64 + 12 * q^65 - 19 * q^66 + 7 * q^67 + 17 * q^68 - 9 * q^69 + 10 * q^71 - 15 * q^72 + 15 * q^73 - 13 * q^74 + 12 * q^75 - 3 * q^76 - 3 * q^78 + 8 * q^79 - 9 * q^80 + 38 * q^81 - 4 * q^82 + 15 * q^83 + 21 * q^85 + 10 * q^86 - 6 * q^87 + 15 * q^88 + 14 * q^89 + 51 * q^90 - 9 * q^92 + 8 * q^93 + 25 * q^94 - 6 * q^95 + 4 * q^96 - 12 * q^97 - 32 * 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 $

$2$	−2.30278	−1.62831	−0.814154	−	0.580649i	$-0.802799\pi$
$2$	−2.30278	−1.62831	−0.814154	+	0.580649i	$0.802799\pi$
$3$	−0.302776	−0.174808	−0.0874038	−	0.996173i	$-0.527857\pi$
$3$	−0.302776	−0.174808	−0.0874038	+	0.996173i	$0.527857\pi$
$4$	3.30278	1.65139
$5$	3.00000	1.34164	0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000	1.34164	0.670820	+	0.741620i	$0.265942\pi$
$6$	0.697224	0.284641
$7$	0	0
$7$	0	0
$8$	−3.00000	−1.06066
$9$	−2.90833	−0.969442
$10$	−6.90833	−2.18460
$11$	−0.697224	−0.210221	−0.105111	−	0.994461i	$-0.533520\pi$
$11$	−0.697224	−0.210221	−0.105111	+	0.994461i	$0.533520\pi$
$12$	−1.00000	−0.288675
$13$	5.60555	1.55470	0.777350	−	0.629068i	$-0.216563\pi$
$13$	5.60555	1.55470	0.777350	+	0.629068i	$0.216563\pi$
$14$	0	0
$15$	−0.908327	−0.234529
$16$	0.302776	0.0756939
$17$	5.30278	1.28611	0.643056	−	0.765819i	$-0.277666\pi$
$17$	5.30278	1.28611	0.643056	+	0.765819i	$0.277666\pi$
$18$	6.69722	1.57855
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	9.90833	2.21557
$21$	0	0
$22$	1.60555	0.342305
$23$	−3.00000	−0.625543	−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000	−0.625543	−0.312772	+	0.949828i	$0.601257\pi$
$24$	0.908327	0.185411
$25$	4.00000	0.800000
$26$	−12.9083	−2.53153
$27$	1.78890	0.344273
$28$	0	0
$29$	9.90833	1.83993	0.919965	−	0.392000i	$-0.128217\pi$
$29$	9.90833	1.83993	0.919965	+	0.392000i	$0.128217\pi$
$30$	2.09167	0.381886
$31$	−1.30278	−0.233985	−0.116993	−	0.993133i	$-0.537325\pi$
$31$	−1.30278	−0.233985	−0.116993	+	0.993133i	$0.537325\pi$
$32$	5.30278	0.937407
$33$	0.211103	0.0367482
$34$	−12.2111	−2.09419
$35$	0	0
$36$	−9.60555	−1.60093
$37$	3.60555	0.592749	0.296374	−	0.955072i	$-0.404222\pi$
$37$	3.60555	0.592749	0.296374	+	0.955072i	$0.404222\pi$
$38$	2.30278	0.373560
$39$	−1.69722	−0.271773
$40$	−9.00000	−1.42302
$41$	−0.697224	−0.108888	−0.0544441	−	0.998517i	$-0.517339\pi$
$41$	−0.697224	−0.108888	−0.0544441	+	0.998517i	$0.517339\pi$
$42$	0	0
$43$	−10.0000	−1.52499	−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000	−1.52499	−0.762493	+	0.646997i	$0.776025\pi$
$44$	−2.30278	−0.347156
$45$	−8.72498	−1.30064
$46$	6.90833	1.01858
$47$	−6.21110	−0.905982	−0.452991	−	0.891515i	$-0.649643\pi$
$47$	−6.21110	−0.905982	−0.452991	+	0.891515i	$0.649643\pi$
$48$	−0.0916731	−0.0132319
$49$	0	0
$50$	−9.21110	−1.30265
$51$	−1.60555	−0.224822
$52$	18.5139	2.56741
$53$	−6.90833	−0.948932	−0.474466	−	0.880274i	$-0.657359\pi$
$53$	−6.90833	−0.948932	−0.474466	+	0.880274i	$0.657359\pi$
$54$	−4.11943	−0.560583
$55$	−2.09167	−0.282041
$56$	0	0
$57$	0.302776	0.0401036
$58$	−22.8167	−2.99597
$59$	6.21110	0.808617	0.404308	−	0.914623i	$-0.367512\pi$
$59$	6.21110	0.808617	0.404308	+	0.914623i	$0.367512\pi$
$60$	−3.00000	−0.387298
$61$	4.21110	0.539176	0.269588	−	0.962976i	$-0.413112\pi$
$61$	4.21110	0.539176	0.269588	+	0.962976i	$0.413112\pi$
$62$	3.00000	0.381000
$63$	0	0
$64$	−12.8167	−1.60208
$65$	16.8167	2.08585
$66$	−0.486122	−0.0598375
$67$	−1.90833	−0.233139	−0.116570	−	0.993183i	$-0.537190\pi$
$67$	−1.90833	−0.233139	−0.116570	+	0.993183i	$0.537190\pi$
$68$	17.5139	2.12387
$69$	0.908327	0.109350
$70$	0	0
$71$	12.2111	1.44919	0.724596	−	0.689174i	$-0.242027\pi$
$71$	12.2111	1.44919	0.724596	+	0.689174i	$0.242027\pi$
$72$	8.72498	1.02825
$73$	−1.51388	−0.177186	−0.0885930	−	0.996068i	$-0.528237\pi$
$73$	−1.51388	−0.177186	−0.0885930	+	0.996068i	$0.528237\pi$
$74$	−8.30278	−0.965178
$75$	−1.21110	−0.139846
$76$	−3.30278	−0.378854
$77$	0	0
$78$	3.90833	0.442531
$79$	11.2111	1.26135	0.630674	−	0.776048i	$-0.282779\pi$
$79$	11.2111	1.26135	0.630674	+	0.776048i	$0.282779\pi$
$80$	0.908327	0.101554
$81$	8.18335	0.909261
$82$	1.60555	0.177303
$83$	12.9083	1.41687	0.708436	−	0.705775i	$-0.249401\pi$
$83$	12.9083	1.41687	0.708436	+	0.705775i	$0.249401\pi$
$84$	0	0
$85$	15.9083	1.72550
$86$	23.0278	2.48315
$87$	−3.00000	−0.321634
$88$	2.09167	0.222973
$89$	10.6056	1.12419	0.562093	−	0.827074i	$-0.309996\pi$
$89$	10.6056	1.12419	0.562093	+	0.827074i	$0.309996\pi$
$90$	20.0917	2.11785
$91$	0	0
$92$	−9.90833	−1.03301
$93$	0.394449	0.0409024
$94$	14.3028	1.47522
$95$	−3.00000	−0.307794
$96$	−1.60555	−0.163866
$97$	−9.60555	−0.975296	−0.487648	−	0.873040i	$-0.662145\pi$
$97$	−9.60555	−0.975296	−0.487648	+	0.873040i	$0.662145\pi$
$98$	0	0
$99$	2.02776	0.203797
$100$	13.2111	1.32111
$101$	4.39445	0.437264	0.218632	−	0.975807i	$-0.429841\pi$
$101$	4.39445	0.437264	0.218632	+	0.975807i	$0.429841\pi$
$102$	3.69722	0.366080
$103$	16.2111	1.59733	0.798664	−	0.601778i	$-0.205541\pi$
$103$	16.2111	1.59733	0.798664	+	0.601778i	$0.205541\pi$
$104$	−16.8167	−1.64901
$105$	0	0
$106$	15.9083	1.54515
$107$	−5.78890	−0.559634	−0.279817	−	0.960053i	$-0.590274\pi$
$107$	−5.78890	−0.559634	−0.279817	+	0.960053i	$0.590274\pi$
$108$	5.90833	0.568529
$109$	−10.2111	−0.978046	−0.489023	−	0.872271i	$-0.662647\pi$
$109$	−10.2111	−0.978046	−0.489023	+	0.872271i	$0.662647\pi$
$110$	4.81665	0.459250
$111$	−1.09167	−0.103617
$112$	0	0
$113$	9.69722	0.912238	0.456119	−	0.889919i	$-0.349239\pi$
$113$	9.69722	0.912238	0.456119	+	0.889919i	$0.349239\pi$
$114$	−0.697224	−0.0653010
$115$	−9.00000	−0.839254
$116$	32.7250	3.03844
$117$	−16.3028	−1.50719
$118$	−14.3028	−1.31668
$119$	0	0
$120$	2.72498	0.248756
$121$	−10.5139	−0.955807
$122$	−9.69722	−0.877945
$123$	0.211103	0.0190345
$124$	−4.30278	−0.386401
$125$	−3.00000	−0.268328
$126$	0	0
$127$	−11.8167	−1.04856	−0.524279	−	0.851546i	$-0.675665\pi$
$127$	−11.8167	−1.04856	−0.524279	+	0.851546i	$0.675665\pi$
$128$	18.9083	1.67128
$129$	3.02776	0.266579
$130$	−38.7250	−3.39641
$131$	20.5139	1.79231	0.896153	−	0.443745i	$-0.146351\pi$
$131$	20.5139	1.79231	0.896153	+	0.443745i	$0.146351\pi$
$132$	0.697224	0.0606856
$133$	0	0
$134$	4.39445	0.379623
$135$	5.36669	0.461891
$136$	−15.9083	−1.36413
$137$	21.6333	1.84826	0.924129	−	0.382080i	$-0.124792\pi$
$137$	21.6333	1.84826	0.924129	+	0.382080i	$0.124792\pi$
$138$	−2.09167	−0.178055
$139$	−5.00000	−0.424094	−0.212047	−	0.977259i	$-0.568013\pi$
$139$	−5.00000	−0.424094	−0.212047	+	0.977259i	$0.568013\pi$
$140$	0	0
$141$	1.88057	0.158373
$142$	−28.1194	−2.35973
$143$	−3.90833	−0.326831
$144$	−0.880571	−0.0733809
$145$	29.7250	2.46853
$146$	3.48612	0.288513
$147$	0	0
$148$	11.9083	0.978858
$149$	−6.21110	−0.508833	−0.254417	−	0.967095i	$-0.581883\pi$
$149$	−6.21110	−0.508833	−0.254417	+	0.967095i	$0.581883\pi$
$150$	2.78890	0.227713
$151$	5.90833	0.480813	0.240406	−	0.970672i	$-0.422719\pi$
$151$	5.90833	0.480813	0.240406	+	0.970672i	$0.422719\pi$
$152$	3.00000	0.243332
$153$	−15.4222	−1.24681
$154$	0	0
$155$	−3.90833	−0.313924
$156$	−5.60555	−0.448803
$157$	−4.51388	−0.360247	−0.180123	−	0.983644i	$-0.557650\pi$
$157$	−4.51388	−0.360247	−0.180123	+	0.983644i	$0.557650\pi$
$158$	−25.8167	−2.05386
$159$	2.09167	0.165880
$160$	15.9083	1.25766
$161$	0	0
$162$	−18.8444	−1.48056
$163$	5.69722	0.446241	0.223121	−	0.974791i	$-0.428376\pi$
$163$	5.69722	0.446241	0.223121	+	0.974791i	$0.428376\pi$
$164$	−2.30278	−0.179817
$165$	0.633308	0.0493029
$166$	−29.7250	−2.30711
$167$	−4.39445	−0.340053	−0.170026	−	0.985440i	$-0.554385\pi$
$167$	−4.39445	−0.340053	−0.170026	+	0.985440i	$0.554385\pi$
$168$	0	0
$169$	18.4222	1.41709
$170$	−36.6333	−2.80965
$171$	2.90833	0.222405
$172$	−33.0278	−2.51834
$173$	−7.81665	−0.594289	−0.297145	−	0.954832i	$-0.596034\pi$
$173$	−7.81665	−0.594289	−0.297145	+	0.954832i	$0.596034\pi$
$174$	6.90833	0.523719
$175$	0	0
$176$	−0.211103	−0.0159125
$177$	−1.88057	−0.141352
$178$	−24.4222	−1.83052
$179$	−11.7250	−0.876366	−0.438183	−	0.898886i	$-0.644378\pi$
$179$	−11.7250	−0.876366	−0.438183	+	0.898886i	$0.644378\pi$
$180$	−28.8167	−2.14787
$181$	10.6972	0.795118	0.397559	−	0.917577i	$-0.369857\pi$
$181$	10.6972	0.795118	0.397559	+	0.917577i	$0.369857\pi$
$182$	0	0
$183$	−1.27502	−0.0942521
$184$	9.00000	0.663489
$185$	10.8167	0.795256
$186$	−0.908327	−0.0666018
$187$	−3.69722	−0.270368
$188$	−20.5139	−1.49613
$189$	0	0
$190$	6.90833	0.501183
$191$	25.3305	1.83285	0.916426	−	0.400203i	$-0.131060\pi$
$191$	25.3305	1.83285	0.916426	+	0.400203i	$0.131060\pi$
$192$	3.88057	0.280056
$193$	−23.1194	−1.66417	−0.832086	−	0.554646i	$-0.812854\pi$
$193$	−23.1194	−1.66417	−0.832086	+	0.554646i	$0.812854\pi$
$194$	22.1194	1.58808
$195$	−5.09167	−0.364622
$196$	0	0
$197$	−6.90833	−0.492198	−0.246099	−	0.969245i	$-0.579149\pi$
$197$	−6.90833	−0.492198	−0.246099	+	0.969245i	$0.579149\pi$
$198$	−4.66947	−0.331845
$199$	13.4222	0.951475	0.475737	−	0.879587i	$-0.342181\pi$
$199$	13.4222	0.951475	0.475737	+	0.879587i	$0.342181\pi$
$200$	−12.0000	−0.848528
$201$	0.577795	0.0407545
$202$	−10.1194	−0.712001
$203$	0	0
$204$	−5.30278	−0.371269
$205$	−2.09167	−0.146089
$206$	−37.3305	−2.60094
$207$	8.72498	0.606428
$208$	1.69722	0.117681
$209$	0.697224	0.0482280
$210$	0	0
$211$	−7.69722	−0.529899	−0.264949	−	0.964262i	$-0.585355\pi$
$211$	−7.69722	−0.529899	−0.264949	+	0.964262i	$0.585355\pi$
$212$	−22.8167	−1.56705
$213$	−3.69722	−0.253330
$214$	13.3305	0.911256
$215$	−30.0000	−2.04598
$216$	−5.36669	−0.365157
$217$	0	0
$218$	23.5139	1.59256
$219$	0.458365	0.0309735
$220$	−6.90833	−0.465759
$221$	29.7250	1.99952
$222$	2.51388	0.168720
$223$	−12.8167	−0.858267	−0.429133	−	0.903241i	$-0.641181\pi$
$223$	−12.8167	−0.858267	−0.429133	+	0.903241i	$0.641181\pi$
$224$	0	0
$225$	−11.6333	−0.775554
$226$	−22.3305	−1.48540
$227$	25.1194	1.66724	0.833618	−	0.552342i	$-0.186266\pi$
$227$	25.1194	1.66724	0.833618	+	0.552342i	$0.186266\pi$
$228$	1.00000	0.0662266
$229$	0.788897	0.0521318	0.0260659	−	0.999660i	$-0.491702\pi$
$229$	0.788897	0.0521318	0.0260659	+	0.999660i	$0.491702\pi$
$230$	20.7250	1.36656
$231$	0	0
$232$	−29.7250	−1.95154
$233$	−2.09167	−0.137030	−0.0685150	−	0.997650i	$-0.521826\pi$
$233$	−2.09167	−0.137030	−0.0685150	+	0.997650i	$0.521826\pi$
$234$	37.5416	2.45417
$235$	−18.6333	−1.21550
$236$	20.5139	1.33534
$237$	−3.39445	−0.220493
$238$	0	0
$239$	−27.4222	−1.77379	−0.886897	−	0.461966i	$-0.847144\pi$
$239$	−27.4222	−1.77379	−0.886897	+	0.461966i	$0.847144\pi$
$240$	−0.275019	−0.0177524
$241$	20.6056	1.32732	0.663660	−	0.748034i	$-0.269002\pi$
$241$	20.6056	1.32732	0.663660	+	0.748034i	$0.269002\pi$
$242$	24.2111	1.55635
$243$	−7.84441	−0.503219
$244$	13.9083	0.890389
$245$	0	0
$246$	−0.486122	−0.0309940
$247$	−5.60555	−0.356673
$248$	3.90833	0.248179
$249$	−3.90833	−0.247680
$250$	6.90833	0.436921
$251$	15.9083	1.00412	0.502062	−	0.864831i	$-0.332575\pi$
$251$	15.9083	1.00412	0.502062	+	0.864831i	$0.332575\pi$
$252$	0	0
$253$	2.09167	0.131502
$254$	27.2111	1.70738
$255$	−4.81665	−0.301631
$256$	−17.9083	−1.11927
$257$	0.908327	0.0566599	0.0283299	−	0.999599i	$-0.490981\pi$
$257$	0.908327	0.0566599	0.0283299	+	0.999599i	$0.490981\pi$
$258$	−6.97224	−0.434073
$259$	0	0
$260$	55.5416	3.44455
$261$	−28.8167	−1.78371
$262$	−47.2389	−2.91843
$263$	−9.69722	−0.597956	−0.298978	−	0.954260i	$-0.596646\pi$
$263$	−9.69722	−0.597956	−0.298978	+	0.954260i	$0.596646\pi$
$264$	−0.633308	−0.0389774
$265$	−20.7250	−1.27313
$266$	0	0
$267$	−3.21110	−0.196516
$268$	−6.30278	−0.385003
$269$	−20.7250	−1.26362	−0.631812	−	0.775122i	$-0.717689\pi$
$269$	−20.7250	−1.26362	−0.631812	+	0.775122i	$0.717689\pi$
$270$	−12.3583	−0.752101
$271$	−17.9083	−1.08785	−0.543927	−	0.839133i	$-0.683063\pi$
$271$	−17.9083	−1.08785	−0.543927	+	0.839133i	$0.683063\pi$
$272$	1.60555	0.0973508
$273$	0	0
$274$	−49.8167	−3.00953
$275$	−2.78890	−0.168177
$276$	3.00000	0.180579
$277$	0.605551	0.0363840	0.0181920	−	0.999835i	$-0.494209\pi$
$277$	0.605551	0.0363840	0.0181920	+	0.999835i	$0.494209\pi$
$278$	11.5139	0.690557
$279$	3.78890	0.226835
$280$	0	0
$281$	3.00000	0.178965	0.0894825	−	0.995988i	$-0.471479\pi$
$281$	3.00000	0.178965	0.0894825	+	0.995988i	$0.471479\pi$
$282$	−4.33053	−0.257879
$283$	−27.3305	−1.62463	−0.812316	−	0.583218i	$-0.801793\pi$
$283$	−27.3305	−1.62463	−0.812316	+	0.583218i	$0.801793\pi$
$284$	40.3305	2.39318
$285$	0.908327	0.0538046
$286$	9.00000	0.532181
$287$	0	0
$288$	−15.4222	−0.908762
$289$	11.1194	0.654084
$290$	−68.4500	−4.01952
$291$	2.90833	0.170489
$292$	−5.00000	−0.292603
$293$	12.6333	0.738046	0.369023	−	0.929420i	$-0.379692\pi$
$293$	12.6333	0.738046	0.369023	+	0.929420i	$0.379692\pi$
$294$	0	0
$295$	18.6333	1.08487
$296$	−10.8167	−0.628705
$297$	−1.24726	−0.0723735
$298$	14.3028	0.828538
$299$	−16.8167	−0.972532
$300$	−4.00000	−0.230940
$301$	0	0
$302$	−13.6056	−0.782911
$303$	−1.33053	−0.0764371
$304$	−0.302776	−0.0173654
$305$	12.6333	0.723381
$306$	35.5139	2.03019
$307$	−14.6972	−0.838815	−0.419407	−	0.907798i	$-0.637762\pi$
$307$	−14.6972	−0.838815	−0.419407	+	0.907798i	$0.637762\pi$
$308$	0	0
$309$	−4.90833	−0.279225
$310$	9.00000	0.511166
$311$	2.51388	0.142549	0.0712745	−	0.997457i	$-0.477293\pi$
$311$	2.51388	0.142549	0.0712745	+	0.997457i	$0.477293\pi$
$312$	5.09167	0.288259
$313$	27.0278	1.52770	0.763850	−	0.645394i	$-0.223307\pi$
$313$	27.0278	1.52770	0.763850	+	0.645394i	$0.223307\pi$
$314$	10.3944	0.586593
$315$	0	0
$316$	37.0278	2.08297
$317$	8.78890	0.493634	0.246817	−	0.969062i	$-0.420615\pi$
$317$	8.78890	0.493634	0.246817	+	0.969062i	$0.420615\pi$
$318$	−4.81665	−0.270105
$319$	−6.90833	−0.386792
$320$	−38.4500	−2.14942
$321$	1.75274	0.0978282
$322$	0	0
$323$	−5.30278	−0.295054
$324$	27.0278	1.50154
$325$	22.4222	1.24376
$326$	−13.1194	−0.726618
$327$	3.09167	0.170970
$328$	2.09167	0.115493
$329$	0	0
$330$	−1.45837	−0.0802804
$331$	11.6972	0.642938	0.321469	−	0.946920i	$-0.395823\pi$
$331$	11.6972	0.642938	0.321469	+	0.946920i	$0.395823\pi$
$332$	42.6333	2.33981
$333$	−10.4861	−0.574636
$334$	10.1194	0.553711
$335$	−5.72498	−0.312789
$336$	0	0
$337$	7.72498	0.420807	0.210403	−	0.977615i	$-0.432522\pi$
$337$	7.72498	0.420807	0.210403	+	0.977615i	$0.432522\pi$
$338$	−42.4222	−2.30746
$339$	−2.93608	−0.159466
$340$	52.5416	2.84947
$341$	0.908327	0.0491887
$342$	−6.69722	−0.362144
$343$	0	0
$344$	30.0000	1.61749
$345$	2.72498	0.146708
$346$	18.0000	0.967686
$347$	−28.5416	−1.53220	−0.766098	−	0.642724i	$-0.777804\pi$
$347$	−28.5416	−1.53220	−0.766098	+	0.642724i	$0.777804\pi$
$348$	−9.90833	−0.531142
$349$	−7.51388	−0.402209	−0.201104	−	0.979570i	$-0.564453\pi$
$349$	−7.51388	−0.402209	−0.201104	+	0.979570i	$0.564453\pi$
$350$	0	0
$351$	10.0278	0.535242
$352$	−3.69722	−0.197063
$353$	−9.90833	−0.527367	−0.263684	−	0.964609i	$-0.584937\pi$
$353$	−9.90833	−0.527367	−0.263684	+	0.964609i	$0.584937\pi$
$354$	4.33053	0.230165
$355$	36.6333	1.94429
$356$	35.0278	1.85647
$357$	0	0
$358$	27.0000	1.42699
$359$	−25.5416	−1.34804	−0.674018	−	0.738715i	$-0.735433\pi$
$359$	−25.5416	−1.34804	−0.674018	+	0.738715i	$0.735433\pi$
$360$	26.1749	1.37954
$361$	1.00000	0.0526316
$362$	−24.6333	−1.29470
$363$	3.18335	0.167082
$364$	0	0
$365$	−4.54163	−0.237720
$366$	2.93608	0.153472
$367$	0.0277564	0.00144887	0.000724436	−	1.00000i	$-0.499769\pi$
$367$	0.0277564	0.00144887	0.000724436		1.00000i	$0.499769\pi$
$368$	−0.908327	−0.0473498
$369$	2.02776	0.105561
$370$	−24.9083	−1.29492
$371$	0	0
$372$	1.30278	0.0675458
$373$	24.1194	1.24886	0.624428	−	0.781082i	$-0.285332\pi$
$373$	24.1194	1.24886	0.624428	+	0.781082i	$0.285332\pi$
$374$	8.51388	0.440242
$375$	0.908327	0.0469058
$376$	18.6333	0.960939
$377$	55.5416	2.86054
$378$	0	0
$379$	6.81665	0.350148	0.175074	−	0.984555i	$-0.443984\pi$
$379$	6.81665	0.350148	0.175074	+	0.984555i	$0.443984\pi$
$380$	−9.90833	−0.508286
$381$	3.57779	0.183296
$382$	−58.3305	−2.98445
$383$	−6.63331	−0.338946	−0.169473	−	0.985535i	$-0.554207\pi$
$383$	−6.63331	−0.338946	−0.169473	+	0.985535i	$0.554207\pi$
$384$	−5.72498	−0.292152
$385$	0	0
$386$	53.2389	2.70979
$387$	29.0833	1.47839
$388$	−31.7250	−1.61059
$389$	−24.1472	−1.22431	−0.612155	−	0.790737i	$-0.709697\pi$
$389$	−24.1472	−1.22431	−0.612155	+	0.790737i	$0.709697\pi$
$390$	11.7250	0.593717
$391$	−15.9083	−0.804519
$392$	0	0
$393$	−6.21110	−0.313309
$394$	15.9083	0.801450
$395$	33.6333	1.69228
$396$	6.69722	0.336548
$397$	−37.0278	−1.85837	−0.929185	−	0.369615i	$-0.879490\pi$
$397$	−37.0278	−1.85837	−0.929185	+	0.369615i	$0.879490\pi$
$398$	−30.9083	−1.54929
$399$	0	0
$400$	1.21110	0.0605551
$401$	−3.48612	−0.174089	−0.0870443	−	0.996204i	$-0.527742\pi$
$401$	−3.48612	−0.174089	−0.0870443	+	0.996204i	$0.527742\pi$
$402$	−1.33053	−0.0663609
$403$	−7.30278	−0.363777
$404$	14.5139	0.722092
$405$	24.5500	1.21990
$406$	0	0
$407$	−2.51388	−0.124608
$408$	4.81665	0.238460
$409$	−20.9083	−1.03385	−0.516925	−	0.856031i	$-0.672923\pi$
$409$	−20.9083	−1.03385	−0.516925	+	0.856031i	$0.672923\pi$
$410$	4.81665	0.237878
$411$	−6.55004	−0.323090
$412$	53.5416	2.63781
$413$	0	0
$414$	−20.0917	−0.987452
$415$	38.7250	1.90093
$416$	29.7250	1.45739
$417$	1.51388	0.0741349
$418$	−1.60555	−0.0785301
$419$	−15.0000	−0.732798	−0.366399	−	0.930458i	$-0.619409\pi$
$419$	−15.0000	−0.732798	−0.366399	+	0.930458i	$0.619409\pi$
$420$	0	0
$421$	−29.6056	−1.44289	−0.721443	−	0.692474i	$-0.756521\pi$
$421$	−29.6056	−1.44289	−0.721443	+	0.692474i	$0.756521\pi$
$422$	17.7250	0.862839
$423$	18.0639	0.878298
$424$	20.7250	1.00649
$425$	21.2111	1.02889
$426$	8.51388	0.412499
$427$	0	0
$428$	−19.1194	−0.924173
$429$	1.18335	0.0571325
$430$	69.0833	3.33149
$431$	−3.21110	−0.154673	−0.0773367	−	0.997005i	$-0.524642\pi$
$431$	−3.21110	−0.154673	−0.0773367	+	0.997005i	$0.524642\pi$
$432$	0.541635	0.0260594
$433$	0.577795	0.0277671	0.0138835	−	0.999904i	$-0.495581\pi$
$433$	0.577795	0.0277671	0.0138835	+	0.999904i	$0.495581\pi$
$434$	0	0
$435$	−9.00000	−0.431517
$436$	−33.7250	−1.61513
$437$	3.00000	0.143509
$438$	−1.05551	−0.0504344
$439$	−22.7889	−1.08765	−0.543827	−	0.839197i	$-0.683025\pi$
$439$	−22.7889	−1.08765	−0.543827	+	0.839197i	$0.683025\pi$
$440$	6.27502	0.299150
$441$	0	0
$442$	−68.4500	−3.25583
$443$	−16.1194	−0.765857	−0.382929	−	0.923778i	$-0.625084\pi$
$443$	−16.1194	−0.765857	−0.382929	+	0.923778i	$0.625084\pi$
$444$	−3.60555	−0.171112
$445$	31.8167	1.50825
$446$	29.5139	1.39752
$447$	1.88057	0.0889479
$448$	0	0
$449$	−0.486122	−0.0229415	−0.0114708	−	0.999934i	$-0.503651\pi$
$449$	−0.486122	−0.0229415	−0.0114708	+	0.999934i	$0.503651\pi$
$450$	26.7889	1.26284
$451$	0.486122	0.0228906
$452$	32.0278	1.50646
$453$	−1.78890	−0.0840497
$454$	−57.8444	−2.71477
$455$	0	0
$456$	−0.908327	−0.0425363
$457$	22.3028	1.04328	0.521640	−	0.853166i	$-0.325320\pi$
$457$	22.3028	1.04328	0.521640	+	0.853166i	$0.325320\pi$
$458$	−1.81665	−0.0848867
$459$	9.48612	0.442774
$460$	−29.7250	−1.38593
$461$	−0.908327	−0.0423050	−0.0211525	−	0.999776i	$-0.506734\pi$
$461$	−0.908327	−0.0423050	−0.0211525	+	0.999776i	$0.506734\pi$
$462$	0	0
$463$	−36.4500	−1.69397	−0.846987	−	0.531614i	$-0.821586\pi$
$463$	−36.4500	−1.69397	−0.846987	+	0.531614i	$0.821586\pi$
$464$	3.00000	0.139272
$465$	1.18335	0.0548764
$466$	4.81665	0.223127
$467$	−16.5416	−0.765456	−0.382728	−	0.923861i	$-0.625015\pi$
$467$	−16.5416	−0.765456	−0.382728	+	0.923861i	$0.625015\pi$
$468$	−53.8444	−2.48896
$469$	0	0
$470$	42.9083	1.97921
$471$	1.36669	0.0629739
$472$	−18.6333	−0.857668
$473$	6.97224	0.320584
$474$	7.81665	0.359031
$475$	−4.00000	−0.183533
$476$	0	0
$477$	20.0917	0.919935
$478$	63.1472	2.88829
$479$	0.697224	0.0318570	0.0159285	−	0.999873i	$-0.494930\pi$
$479$	0.697224	0.0318570	0.0159285	+	0.999873i	$0.494930\pi$
$480$	−4.81665	−0.219849
$481$	20.2111	0.921547
$482$	−47.4500	−2.16129
$483$	0	0
$484$	−34.7250	−1.57841
$485$	−28.8167	−1.30850
$486$	18.0639	0.819396
$487$	4.57779	0.207440	0.103720	−	0.994607i	$-0.466925\pi$
$487$	4.57779	0.207440	0.103720	+	0.994607i	$0.466925\pi$
$488$	−12.6333	−0.571883
$489$	−1.72498	−0.0780063
$490$	0	0
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	0.697224	0.0314333
$493$	52.5416	2.36636
$494$	12.9083	0.580773
$495$	6.08327	0.273423
$496$	−0.394449	−0.0177113
$497$	0	0
$498$	9.00000	0.403300
$499$	19.9361	0.892462	0.446231	−	0.894918i	$-0.352766\pi$
$499$	19.9361	0.892462	0.446231	+	0.894918i	$0.352766\pi$
$500$	−9.90833	−0.443114
$501$	1.33053	0.0594438
$502$	−36.6333	−1.63502
$503$	−6.42221	−0.286352	−0.143176	−	0.989697i	$-0.545731\pi$
$503$	−6.42221	−0.286352	−0.143176	+	0.989697i	$0.545731\pi$
$504$	0	0
$505$	13.1833	0.586651
$506$	−4.81665	−0.214126
$507$	−5.57779	−0.247719
$508$	−39.0278	−1.73158
$509$	−33.6333	−1.49077	−0.745385	−	0.666634i	$-0.767734\pi$
$509$	−33.6333	−1.49077	−0.745385	+	0.666634i	$0.767734\pi$
$510$	11.0917	0.491148
$511$	0	0
$512$	3.42221	0.151242
$513$	−1.78890	−0.0789818
$514$	−2.09167	−0.0922597
$515$	48.6333	2.14304
$516$	10.0000	0.440225
$517$	4.33053	0.190457
$518$	0	0
$519$	2.36669	0.103886
$520$	−50.4500	−2.21238
$521$	−36.6333	−1.60493	−0.802467	−	0.596696i	$-0.796480\pi$
$521$	−36.6333	−1.60493	−0.802467	+	0.596696i	$0.796480\pi$
$522$	66.3583	2.90442
$523$	−37.6611	−1.64680	−0.823402	−	0.567459i	$-0.807927\pi$
$523$	−37.6611	−1.64680	−0.823402	+	0.567459i	$0.807927\pi$
$524$	67.7527	2.95979
$525$	0	0
$526$	22.3305	0.973657
$527$	−6.90833	−0.300931
$528$	0.0639167	0.00278162
$529$	−14.0000	−0.608696
$530$	47.7250	2.07304
$531$	−18.0639	−0.783907
$532$	0	0
$533$	−3.90833	−0.169288
$534$	7.39445	0.319989
$535$	−17.3667	−0.750828
$536$	5.72498	0.247282
$537$	3.55004	0.153195
$538$	47.7250	2.05757
$539$	0	0
$540$	17.7250	0.762762
$541$	16.7889	0.721811	0.360906	−	0.932602i	$-0.382468\pi$
$541$	16.7889	0.721811	0.360906	+	0.932602i	$0.382468\pi$
$542$	41.2389	1.77136
$543$	−3.23886	−0.138993
$544$	28.1194	1.20561
$545$	−30.6333	−1.31219
$546$	0	0
$547$	−10.4861	−0.448354	−0.224177	−	0.974548i	$-0.571969\pi$
$547$	−10.4861	−0.448354	−0.224177	+	0.974548i	$0.571969\pi$
$548$	71.4500	3.05219
$549$	−12.2473	−0.522700
$550$	6.42221	0.273844
$551$	−9.90833	−0.422109
$552$	−2.72498	−0.115983
$553$	0	0
$554$	−1.39445	−0.0592444
$555$	−3.27502	−0.139017
$556$	−16.5139	−0.700344
$557$	−1.11943	−0.0474317	−0.0237159	−	0.999719i	$-0.507550\pi$
$557$	−1.11943	−0.0474317	−0.0237159	+	0.999719i	$0.507550\pi$
$558$	−8.72498	−0.369358
$559$	−56.0555	−2.37090
$560$	0	0
$561$	1.11943	0.0472623
$562$	−6.90833	−0.291410
$563$	24.2111	1.02038	0.510188	−	0.860063i	$-0.329576\pi$
$563$	24.2111	1.02038	0.510188	+	0.860063i	$0.329576\pi$
$564$	6.21110	0.261535
$565$	29.0917	1.22390
$566$	62.9361	2.64540
$567$	0	0
$568$	−36.6333	−1.53710
$569$	7.18335	0.301142	0.150571	−	0.988599i	$-0.451889\pi$
$569$	7.18335	0.301142	0.150571	+	0.988599i	$0.451889\pi$
$570$	−2.09167	−0.0876105
$571$	−2.39445	−0.100205	−0.0501023	−	0.998744i	$-0.515955\pi$
$571$	−2.39445	−0.100205	−0.0501023	+	0.998744i	$0.515955\pi$
$572$	−12.9083	−0.539724
$573$	−7.66947	−0.320397
$574$	0	0
$575$	−12.0000	−0.500435
$576$	37.2750	1.55313
$577$	−19.5139	−0.812373	−0.406187	−	0.913790i	$-0.633142\pi$
$577$	−19.5139	−0.812373	−0.406187	+	0.913790i	$0.633142\pi$
$578$	−25.6056	−1.06505
$579$	7.00000	0.290910
$580$	98.1749	4.07649
$581$	0	0
$582$	−6.69722	−0.277609
$583$	4.81665	0.199485
$584$	4.54163	0.187934
$585$	−48.9083	−2.02211
$586$	−29.0917	−1.20177
$587$	−0.422205	−0.0174263	−0.00871313	−	0.999962i	$-0.502774\pi$
$587$	−0.422205	−0.0174263	−0.00871313	+	0.999962i	$0.502774\pi$
$588$	0	0
$589$	1.30278	0.0536799
$590$	−42.9083	−1.76651
$591$	2.09167	0.0860399
$592$	1.09167	0.0448675
$593$	4.81665	0.197796	0.0988981	−	0.995098i	$-0.468468\pi$
$593$	4.81665	0.197796	0.0988981	+	0.995098i	$0.468468\pi$
$594$	2.87217	0.117846
$595$	0	0
$596$	−20.5139	−0.840281
$597$	−4.06392	−0.166325
$598$	38.7250	1.58358
$599$	−0.908327	−0.0371132	−0.0185566	−	0.999828i	$-0.505907\pi$
$599$	−0.908327	−0.0371132	−0.0185566	+	0.999828i	$0.505907\pi$
$600$	3.63331	0.148329
$601$	27.5139	1.12231	0.561157	−	0.827709i	$-0.310356\pi$
$601$	27.5139	1.12231	0.561157	+	0.827709i	$0.310356\pi$
$602$	0	0
$603$	5.55004	0.226015
$604$	19.5139	0.794008
$605$	−31.5416	−1.28235
$606$	3.06392	0.124463
$607$	13.0000	0.527654	0.263827	−	0.964570i	$-0.415015\pi$
$607$	13.0000	0.527654	0.263827	+	0.964570i	$0.415015\pi$
$608$	−5.30278	−0.215056
$609$	0	0
$610$	−29.0917	−1.17789
$611$	−34.8167	−1.40853
$612$	−50.9361	−2.05897
$613$	−0.724981	−0.0292817	−0.0146408	−	0.999893i	$-0.504660\pi$
$613$	−0.724981	−0.0292817	−0.0146408	+	0.999893i	$0.504660\pi$
$614$	33.8444	1.36585
$615$	0.633308	0.0255374
$616$	0	0
$617$	−10.8806	−0.438035	−0.219018	−	0.975721i	$-0.570285\pi$
$617$	−10.8806	−0.438035	−0.219018	+	0.975721i	$0.570285\pi$
$618$	11.3028	0.454664
$619$	41.3305	1.66121	0.830607	−	0.556859i	$-0.187994\pi$
$619$	41.3305	1.66121	0.830607	+	0.556859i	$0.187994\pi$
$620$	−12.9083	−0.518411
$621$	−5.36669	−0.215358
$622$	−5.78890	−0.232114
$623$	0	0
$624$	−0.513878	−0.0205716
$625$	−29.0000	−1.16000
$626$	−62.2389	−2.48757
$627$	−0.211103	−0.00843062
$628$	−14.9083	−0.594907
$629$	19.1194	0.762342
$630$	0	0
$631$	13.2389	0.527031	0.263515	−	0.964655i	$-0.415118\pi$
$631$	13.2389	0.527031	0.263515	+	0.964655i	$0.415118\pi$
$632$	−33.6333	−1.33786
$633$	2.33053	0.0926303
$634$	−20.2389	−0.803788
$635$	−35.4500	−1.40679
$636$	6.90833	0.273933
$637$	0	0
$638$	15.9083	0.629817
$639$	−35.5139	−1.40491
$640$	56.7250	2.24225
$641$	9.90833	0.391355	0.195678	−	0.980668i	$-0.437309\pi$
$641$	9.90833	0.391355	0.195678	+	0.980668i	$0.437309\pi$
$642$	−4.03616	−0.159295
$643$	−30.3944	−1.19864	−0.599320	−	0.800510i	$-0.704562\pi$
$643$	−30.3944	−1.19864	−0.599320	+	0.800510i	$0.704562\pi$
$644$	0	0
$645$	9.08327	0.357653
$646$	12.2111	0.480439
$647$	−15.4222	−0.606309	−0.303155	−	0.952941i	$-0.598040\pi$
$647$	−15.4222	−0.606309	−0.303155	+	0.952941i	$0.598040\pi$
$648$	−24.5500	−0.964417
$649$	−4.33053	−0.169988
$650$	−51.6333	−2.02522
$651$	0	0
$652$	18.8167	0.736917
$653$	−16.8167	−0.658087	−0.329043	−	0.944315i	$-0.606726\pi$
$653$	−16.8167	−0.658087	−0.329043	+	0.944315i	$0.606726\pi$
$654$	−7.11943	−0.278392
$655$	61.5416	2.40463
$656$	−0.211103	−0.00824217
$657$	4.40285	0.171772
$658$	0	0
$659$	16.3305	0.636147	0.318074	−	0.948066i	$-0.396964\pi$
$659$	16.3305	0.636147	0.318074	+	0.948066i	$0.396964\pi$
$660$	2.09167	0.0814183
$661$	0.788897	0.0306846	0.0153423	−	0.999882i	$-0.495116\pi$
$661$	0.788897	0.0306846	0.0153423	+	0.999882i	$0.495116\pi$
$662$	−26.9361	−1.04690
$663$	−9.00000	−0.349531
$664$	−38.7250	−1.50282
$665$	0	0
$666$	24.1472	0.935684
$667$	−29.7250	−1.15096
$668$	−14.5139	−0.561559
$669$	3.88057	0.150032
$670$	13.1833	0.509317
$671$	−2.93608	−0.113346
$672$	0	0
$673$	14.9083	0.574674	0.287337	−	0.957830i	$-0.407230\pi$
$673$	14.9083	0.574674	0.287337	+	0.957830i	$0.407230\pi$
$674$	−17.7889	−0.685203
$675$	7.15559	0.275419
$676$	60.8444	2.34017
$677$	−17.9361	−0.689340	−0.344670	−	0.938724i	$-0.612009\pi$
$677$	−17.9361	−0.689340	−0.344670	+	0.938724i	$0.612009\pi$
$678$	6.76114	0.259660
$679$	0	0
$680$	−47.7250	−1.83017
$681$	−7.60555	−0.291445
$682$	−2.09167	−0.0800943
$683$	12.2111	0.467245	0.233622	−	0.972327i	$-0.424942\pi$
$683$	12.2111	0.467245	0.233622	+	0.972327i	$0.424942\pi$
$684$	9.60555	0.367277
$685$	64.8999	2.47970
$686$	0	0
$687$	−0.238859	−0.00911304
$688$	−3.02776	−0.115432
$689$	−38.7250	−1.47530
$690$	−6.27502	−0.238886
$691$	41.8167	1.59078	0.795390	−	0.606098i	$-0.207266\pi$
$691$	41.8167	1.59078	0.795390	+	0.606098i	$0.207266\pi$
$692$	−25.8167	−0.981402
$693$	0	0
$694$	65.7250	2.49489
$695$	−15.0000	−0.568982
$696$	9.00000	0.341144
$697$	−3.69722	−0.140042
$698$	17.3028	0.654920
$699$	0.633308	0.0239539
$700$	0	0
$701$	21.2111	0.801132	0.400566	−	0.916268i	$-0.368813\pi$
$701$	21.2111	0.801132	0.400566	+	0.916268i	$0.368813\pi$
$702$	−23.0917	−0.871539
$703$	−3.60555	−0.135986
$704$	8.93608	0.336791
$705$	5.64171	0.212479
$706$	22.8167	0.858716
$707$	0	0
$708$	−6.21110	−0.233428
$709$	−11.6056	−0.435856	−0.217928	−	0.975965i	$-0.569930\pi$
$709$	−11.6056	−0.435856	−0.217928	+	0.975965i	$0.569930\pi$
$710$	−84.3583	−3.16591
$711$	−32.6056	−1.22280
$712$	−31.8167	−1.19238
$713$	3.90833	0.146368
$714$	0	0
$715$	−11.7250	−0.438489
$716$	−38.7250	−1.44722
$717$	8.30278	0.310073
$718$	58.8167	2.19502
$719$	27.6333	1.03055	0.515274	−	0.857025i	$-0.327690\pi$
$719$	27.6333	1.03055	0.515274	+	0.857025i	$0.327690\pi$
$720$	−2.64171	−0.0984508
$721$	0	0
$722$	−2.30278	−0.0857004
$723$	−6.23886	−0.232026
$724$	35.3305	1.31305
$725$	39.6333	1.47194
$726$	−7.33053	−0.272062
$727$	27.6611	1.02589	0.512946	−	0.858421i	$-0.328554\pi$
$727$	27.6611	1.02589	0.512946	+	0.858421i	$0.328554\pi$
$728$	0	0
$729$	−22.1749	−0.821294
$730$	10.4584	0.387081
$731$	−53.0278	−1.96130
$732$	−4.21110	−0.155647
$733$	−32.0000	−1.18195	−0.590973	−	0.806691i	$-0.701256\pi$
$733$	−32.0000	−1.18195	−0.590973	+	0.806691i	$0.701256\pi$
$734$	−0.0639167	−0.00235921
$735$	0	0
$736$	−15.9083	−0.586389
$737$	1.33053	0.0490108
$738$	−4.66947	−0.171885
$739$	−18.5778	−0.683395	−0.341698	−	0.939810i	$-0.611002\pi$
$739$	−18.5778	−0.683395	−0.341698	+	0.939810i	$0.611002\pi$
$740$	35.7250	1.31328
$741$	1.69722	0.0623491
$742$	0	0
$743$	−12.6333	−0.463471	−0.231736	−	0.972779i	$-0.574440\pi$
$743$	−12.6333	−0.463471	−0.231736	+	0.972779i	$0.574440\pi$
$744$	−1.18335	−0.0433836
$745$	−18.6333	−0.682672
$746$	−55.5416	−2.03352
$747$	−37.5416	−1.37358
$748$	−12.2111	−0.446482
$749$	0	0
$750$	−2.09167	−0.0763771
$751$	26.3583	0.961828	0.480914	−	0.876768i	$-0.340305\pi$
$751$	26.3583	0.961828	0.480914	+	0.876768i	$0.340305\pi$
$752$	−1.88057	−0.0685774
$753$	−4.81665	−0.175529
$754$	−127.900	−4.65784
$755$	17.7250	0.645078
$756$	0	0
$757$	2.00000	0.0726912	0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000	0.0726912	0.0363456	+	0.999339i	$0.488428\pi$
$758$	−15.6972	−0.570149
$759$	−0.633308	−0.0229876
$760$	9.00000	0.326464
$761$	24.2111	0.877652	0.438826	−	0.898572i	$-0.355394\pi$
$761$	24.2111	0.877652	0.438826	+	0.898572i	$0.355394\pi$
$762$	−8.23886	−0.298462
$763$	0	0
$764$	83.6611	3.02675
$765$	−46.2666	−1.67277
$766$	15.2750	0.551909
$767$	34.8167	1.25716
$768$	5.42221	0.195657
$769$	25.2111	0.909136	0.454568	−	0.890712i	$-0.349794\pi$
$769$	25.2111	0.909136	0.454568	+	0.890712i	$0.349794\pi$
$770$	0	0
$771$	−0.275019	−0.00990458
$772$	−76.3583	−2.74819
$773$	22.1833	0.797880	0.398940	−	0.916977i	$-0.369378\pi$
$773$	22.1833	0.797880	0.398940	+	0.916977i	$0.369378\pi$
$774$	−66.9722	−2.40727
$775$	−5.21110	−0.187188
$776$	28.8167	1.03446
$777$	0	0
$778$	55.6056	1.99356
$779$	0.697224	0.0249807
$780$	−16.8167	−0.602133
$781$	−8.51388	−0.304651
$782$	36.6333	1.31000
$783$	17.7250	0.633439
$784$	0	0
$785$	−13.5416	−0.483322
$786$	14.3028	0.510163
$787$	31.6333	1.12761	0.563803	−	0.825909i	$-0.309338\pi$
$787$	31.6333	1.12761	0.563803	+	0.825909i	$0.309338\pi$
$788$	−22.8167	−0.812810
$789$	2.93608	0.104527
$790$	−77.4500	−2.75555
$791$	0	0
$792$	−6.08327	−0.216160
$793$	23.6056	0.838258
$794$	85.2666	3.02600
$795$	6.27502	0.222552
$796$	44.3305	1.57125
$797$	−26.0917	−0.924214	−0.462107	−	0.886824i	$-0.652906\pi$
$797$	−26.0917	−0.924214	−0.462107	+	0.886824i	$0.652906\pi$
$798$	0	0
$799$	−32.9361	−1.16519
$800$	21.2111	0.749926
$801$	−30.8444	−1.08983
$802$	8.02776	0.283470
$803$	1.05551	0.0372482
$804$	1.90833	0.0673015
$805$	0	0
$806$	16.8167	0.592341
$807$	6.27502	0.220891
$808$	−13.1833	−0.463788
$809$	−26.0278	−0.915087	−0.457544	−	0.889187i	$-0.651271\pi$
$809$	−26.0278	−0.915087	−0.457544	+	0.889187i	$0.651271\pi$
$810$	−56.5332	−1.98638
$811$	32.0555	1.12562	0.562811	−	0.826586i	$-0.309720\pi$
$811$	32.0555	1.12562	0.562811	+	0.826586i	$0.309720\pi$
$812$	0	0
$813$	5.42221	0.190165
$814$	5.78890	0.202901
$815$	17.0917	0.598695
$816$	−0.486122	−0.0170177
$817$	10.0000	0.349856
$818$	48.1472	1.68343
$819$	0	0
$820$	−6.90833	−0.241249
$821$	−51.6333	−1.80201	−0.901007	−	0.433804i	$-0.857171\pi$
$821$	−51.6333	−1.80201	−0.901007	+	0.433804i	$0.857171\pi$
$822$	15.0833	0.526089
$823$	16.2389	0.566051	0.283026	−	0.959112i	$-0.408662\pi$
$823$	16.2389	0.566051	0.283026	+	0.959112i	$0.408662\pi$
$824$	−48.6333	−1.69422
$825$	0.844410	0.0293986
$826$	0	0
$827$	−45.0000	−1.56480	−0.782402	−	0.622774i	$-0.786006\pi$
$827$	−45.0000	−1.56480	−0.782402	+	0.622774i	$0.786006\pi$
$828$	28.8167	1.00145
$829$	−54.0555	−1.87743	−0.938713	−	0.344700i	$-0.887981\pi$
$829$	−54.0555	−1.87743	−0.938713	+	0.344700i	$0.887981\pi$
$830$	−89.1749	−3.09531
$831$	−0.183346	−0.00636021
$832$	−71.8444	−2.49076
$833$	0	0
$834$	−3.48612	−0.120715
$835$	−13.1833	−0.456229
$836$	2.30278	0.0796432
$837$	−2.33053	−0.0805550
$838$	34.5416	1.19322
$839$	2.78890	0.0962834	0.0481417	−	0.998841i	$-0.484670\pi$
$839$	2.78890	0.0962834	0.0481417	+	0.998841i	$0.484670\pi$
$840$	0	0
$841$	69.1749	2.38534
$842$	68.1749	2.34946
$843$	−0.908327	−0.0312844
$844$	−25.4222	−0.875068
$845$	55.2666	1.90123
$846$	−41.5971	−1.43014
$847$	0	0
$848$	−2.09167	−0.0718283
$849$	8.27502	0.283998
$850$	−48.8444	−1.67535
$851$	−10.8167	−0.370790
$852$	−12.2111	−0.418345
$853$	−3.33053	−0.114035	−0.0570176	−	0.998373i	$-0.518159\pi$
$853$	−3.33053	−0.114035	−0.0570176	+	0.998373i	$0.518159\pi$
$854$	0	0
$855$	8.72498	0.298388
$856$	17.3667	0.593581
$857$	−32.0917	−1.09623	−0.548115	−	0.836403i	$-0.684655\pi$
$857$	−32.0917	−1.09623	−0.548115	+	0.836403i	$0.684655\pi$
$858$	−2.72498	−0.0930293
$859$	27.3028	0.931559	0.465779	−	0.884901i	$-0.345774\pi$
$859$	27.3028	0.931559	0.465779	+	0.884901i	$0.345774\pi$
$860$	−99.0833	−3.37871
$861$	0	0
$862$	7.39445	0.251856
$863$	−16.5416	−0.563084	−0.281542	−	0.959549i	$-0.590846\pi$
$863$	−16.5416	−0.563084	−0.281542	+	0.959549i	$0.590846\pi$
$864$	9.48612	0.322724
$865$	−23.4500	−0.797323
$866$	−1.33053	−0.0452133
$867$	−3.36669	−0.114339
$868$	0	0
$869$	−7.81665	−0.265162
$870$	20.7250	0.702643
$871$	−10.6972	−0.362462
$872$	30.6333	1.03737
$873$	27.9361	0.945493
$874$	−6.90833	−0.233678
$875$	0	0
$876$	1.51388	0.0511492
$877$	−8.18335	−0.276332	−0.138166	−	0.990409i	$-0.544121\pi$
$877$	−8.18335	−0.276332	−0.138166	+	0.990409i	$0.544121\pi$
$878$	52.4777	1.77104
$879$	−3.82506	−0.129016
$880$	−0.633308	−0.0213488
$881$	19.7527	0.665487	0.332743	−	0.943017i	$-0.392026\pi$
$881$	19.7527	0.665487	0.332743	+	0.943017i	$0.392026\pi$
$882$	0	0
$883$	−46.2111	−1.55513	−0.777564	−	0.628804i	$-0.783545\pi$
$883$	−46.2111	−1.55513	−0.777564	+	0.628804i	$0.783545\pi$
$884$	98.1749	3.30198
$885$	−5.64171	−0.189644
$886$	37.1194	1.24705
$887$	−19.1833	−0.644114	−0.322057	−	0.946720i	$-0.604374\pi$
$887$	−19.1833	−0.644114	−0.322057	+	0.946720i	$0.604374\pi$
$888$	3.27502	0.109902
$889$	0	0
$890$	−73.2666	−2.45590
$891$	−5.70563	−0.191146
$892$	−42.3305	−1.41733
$893$	6.21110	0.207847
$894$	−4.33053	−0.144835
$895$	−35.1749	−1.17577
$896$	0	0
$897$	5.09167	0.170006
$898$	1.11943	0.0373558
$899$	−12.9083	−0.430517
$900$	−38.4222	−1.28074
$901$	−36.6333	−1.22043
$902$	−1.11943	−0.0372729
$903$	0	0
$904$	−29.0917	−0.967575
$905$	32.0917	1.06676
$906$	4.11943	0.136859
$907$	−5.18335	−0.172110	−0.0860551	−	0.996290i	$-0.527426\pi$
$907$	−5.18335	−0.172110	−0.0860551	+	0.996290i	$0.527426\pi$
$908$	82.9638	2.75325
$909$	−12.7805	−0.423902
$910$	0	0
$911$	−6.00000	−0.198789	−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000	−0.198789	−0.0993944	+	0.995048i	$0.531691\pi$
$912$	0.0916731	0.00303560
$913$	−9.00000	−0.297857
$914$	−51.3583	−1.69878
$915$	−3.82506	−0.126453
$916$	2.60555	0.0860898
$917$	0	0
$918$	−21.8444	−0.720973
$919$	−7.97224	−0.262980	−0.131490	−	0.991317i	$-0.541976\pi$
$919$	−7.97224	−0.262980	−0.131490	+	0.991317i	$0.541976\pi$
$920$	27.0000	0.890164
$921$	4.44996	0.146631
$922$	2.09167	0.0688856
$923$	68.4500	2.25306
$924$	0	0
$925$	14.4222	0.474199
$926$	83.9361	2.75831
$927$	−47.1472	−1.54852
$928$	52.5416	1.72476
$929$	−11.5139	−0.377758	−0.188879	−	0.982000i	$-0.560485\pi$
$929$	−11.5139	−0.377758	−0.188879	+	0.982000i	$0.560485\pi$
$930$	−2.72498	−0.0893556
$931$	0	0
$932$	−6.90833	−0.226290
$933$	−0.761141	−0.0249186
$934$	38.0917	1.24640
$935$	−11.0917	−0.362736
$936$	48.9083	1.59862
$937$	−21.1194	−0.689942	−0.344971	−	0.938613i	$-0.612111\pi$
$937$	−21.1194	−0.689942	−0.344971	+	0.938613i	$0.612111\pi$
$938$	0	0
$939$	−8.18335	−0.267053
$940$	−61.5416	−2.00727
$941$	−6.00000	−0.195594	−0.0977972	−	0.995206i	$-0.531180\pi$
$941$	−6.00000	−0.195594	−0.0977972	+	0.995206i	$0.531180\pi$
$942$	−3.14719	−0.102541
$943$	2.09167	0.0681142
$944$	1.88057	0.0612074
$945$	0	0
$946$	−16.0555	−0.522010
$947$	36.9083	1.19936	0.599680	−	0.800240i	$-0.295295\pi$
$947$	36.9083	1.19936	0.599680	+	0.800240i	$0.295295\pi$
$948$	−11.2111	−0.364120
$949$	−8.48612	−0.275471
$950$	9.21110	0.298848
$951$	−2.66106	−0.0862909
$952$	0	0
$953$	4.33053	0.140280	0.0701398	−	0.997537i	$-0.477655\pi$
$953$	4.33053	0.140280	0.0701398	+	0.997537i	$0.477655\pi$
$954$	−46.2666	−1.49794
$955$	75.9916	2.45903
$956$	−90.5694	−2.92922
$957$	2.09167	0.0676142
$958$	−1.60555	−0.0518730
$959$	0	0
$960$	11.6417	0.375735
$961$	−29.3028	−0.945251
$962$	−46.5416	−1.50056
$963$	16.8360	0.542533
$964$	68.0555	2.19192
$965$	−69.3583	−2.23272
$966$	0	0
$967$	26.6972	0.858525	0.429262	−	0.903180i	$-0.358774\pi$
$967$	26.6972	0.858525	0.429262	+	0.903180i	$0.358774\pi$
$968$	31.5416	1.01379
$969$	1.60555	0.0515777
$970$	66.3583	2.13064
$971$	18.6333	0.597971	0.298986	−	0.954258i	$-0.403352\pi$
$971$	18.6333	0.597971	0.298986	+	0.954258i	$0.403352\pi$
$972$	−25.9083	−0.831010
$973$	0	0
$974$	−10.5416	−0.337776
$975$	−6.78890	−0.217419
$976$	1.27502	0.0408124
$977$	−17.4500	−0.558274	−0.279137	−	0.960251i	$-0.590048\pi$
$977$	−17.4500	−0.558274	−0.279137	+	0.960251i	$0.590048\pi$
$978$	3.97224	0.127018
$979$	−7.39445	−0.236328
$980$	0	0
$981$	29.6972	0.948159
$982$	27.6333	0.881814
$983$	49.0555	1.56463	0.782314	−	0.622884i	$-0.214039\pi$
$983$	49.0555	1.56463	0.782314	+	0.622884i	$0.214039\pi$
$984$	−0.633308	−0.0201891
$985$	−20.7250	−0.660353
$986$	−120.992	−3.85316
$987$	0	0
$988$	−18.5139	−0.589005
$989$	30.0000	0.953945
$990$	−14.0084	−0.445216
$991$	−16.9722	−0.539141	−0.269571	−	0.962981i	$-0.586882\pi$
$991$	−16.9722	−0.539141	−0.269571	+	0.962981i	$0.586882\pi$
$992$	−6.90833	−0.219340
$993$	−3.54163	−0.112390
$994$	0	0
$995$	40.2666	1.27654
$996$	−12.9083	−0.409016
$997$	−5.27502	−0.167062	−0.0835308	−	0.996505i	$-0.526620\pi$
$997$	−5.27502	−0.167062	−0.0835308	+	0.996505i	$0.526620\pi$
$998$	−45.9083	−1.45320
$999$	6.44996	0.204068

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.a.g.1.1		2
3.2	odd	2		8379.2.a.bf.1.2		2
7.2	even	3		931.2.f.g.704.2		4
7.3	odd	6		931.2.f.h.324.2		4
7.4	even	3		931.2.f.g.324.2		4
7.5	odd	6		931.2.f.h.704.2		4
7.6	odd	2		133.2.a.b.1.1	✓	2
21.20	even	2		1197.2.a.h.1.2		2
28.27	even	2		2128.2.a.l.1.1		2
35.34	odd	2		3325.2.a.n.1.2		2
56.13	odd	2		8512.2.a.bh.1.1		2
56.27	even	2		8512.2.a.l.1.2		2
133.132	even	2		2527.2.a.d.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.a.b.1.1	✓	2	7.6	odd	2
931.2.a.g.1.1		2	1.1	even	1	trivial
931.2.f.g.324.2		4	7.4	even	3
931.2.f.g.704.2		4	7.2	even	3
931.2.f.h.324.2		4	7.3	odd	6
931.2.f.h.704.2		4	7.5	odd	6
1197.2.a.h.1.2		2	21.20	even	2
2128.2.a.l.1.1		2	28.27	even	2
2527.2.a.d.1.2		2	133.132	even	2
3325.2.a.n.1.2		2	35.34	odd	2
8379.2.a.bf.1.2		2	3.2	odd	2
8512.2.a.l.1.2		2	56.27	even	2
8512.2.a.bh.1.1		2	56.13	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:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.a (trivial)

\(f(q)\)	\(=\)	\(q-2.30278 q^{2} -0.302776 q^{3} +3.30278 q^{4} +3.00000 q^{5} +0.697224 q^{6} -3.00000 q^{8} -2.90833 q^{9} +O(q^{10})\)	\(q-2.30278 q^{2} -0.302776 q^{3} +3.30278 q^{4} +3.00000 q^{5} +0.697224 q^{6} -3.00000 q^{8} -2.90833 q^{9} -6.90833 q^{10} -0.697224 q^{11} -1.00000 q^{12} +5.60555 q^{13} -0.908327 q^{15} +0.302776 q^{16} +5.30278 q^{17} +6.69722 q^{18} -1.00000 q^{19} +9.90833 q^{20} +1.60555 q^{22} -3.00000 q^{23} +0.908327 q^{24} +4.00000 q^{25} -12.9083 q^{26} +1.78890 q^{27} +9.90833 q^{29} +2.09167 q^{30} -1.30278 q^{31} +5.30278 q^{32} +0.211103 q^{33} -12.2111 q^{34} -9.60555 q^{36} +3.60555 q^{37} +2.30278 q^{38} -1.69722 q^{39} -9.00000 q^{40} -0.697224 q^{41} -10.0000 q^{43} -2.30278 q^{44} -8.72498 q^{45} +6.90833 q^{46} -6.21110 q^{47} -0.0916731 q^{48} -9.21110 q^{50} -1.60555 q^{51} +18.5139 q^{52} -6.90833 q^{53} -4.11943 q^{54} -2.09167 q^{55} +0.302776 q^{57} -22.8167 q^{58} +6.21110 q^{59} -3.00000 q^{60} +4.21110 q^{61} +3.00000 q^{62} -12.8167 q^{64} +16.8167 q^{65} -0.486122 q^{66} -1.90833 q^{67} +17.5139 q^{68} +0.908327 q^{69} +12.2111 q^{71} +8.72498 q^{72} -1.51388 q^{73} -8.30278 q^{74} -1.21110 q^{75} -3.30278 q^{76} +3.90833 q^{78} +11.2111 q^{79} +0.908327 q^{80} +8.18335 q^{81} +1.60555 q^{82} +12.9083 q^{83} +15.9083 q^{85} +23.0278 q^{86} -3.00000 q^{87} +2.09167 q^{88} +10.6056 q^{89} +20.0917 q^{90} -9.90833 q^{92} +0.394449 q^{93} +14.3028 q^{94} -3.00000 q^{95} -1.60555 q^{96} -9.60555 q^{97} +2.02776 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 3 q^{3} + 3 q^{4} + 6 q^{5} + 5 q^{6} - 6 q^{8} + 5 q^{9}+O(q^{10}) \) 2 * q - q^2 + 3 * q^3 + 3 * q^4 + 6 * q^5 + 5 * q^6 - 6 * q^8 + 5 * q^9	\( 2 q - q^{2} + 3 q^{3} + 3 q^{4} + 6 q^{5} + 5 q^{6} - 6 q^{8} + 5 q^{9} - 3 q^{10} - 5 q^{11} - 2 q^{12} + 4 q^{13} + 9 q^{15} - 3 q^{16} + 7 q^{17} + 17 q^{18} - 2 q^{19} + 9 q^{20} - 4 q^{22} - 6 q^{23} - 9 q^{24} + 8 q^{25} - 15 q^{26} + 18 q^{27} + 9 q^{29} + 15 q^{30} + q^{31} + 7 q^{32} - 14 q^{33} - 10 q^{34} - 12 q^{36} + q^{38} - 7 q^{39} - 18 q^{40} - 5 q^{41} - 20 q^{43} - q^{44} + 15 q^{45} + 3 q^{46} + 2 q^{47} - 11 q^{48} - 4 q^{50} + 4 q^{51} + 19 q^{52} - 3 q^{53} + 17 q^{54} - 15 q^{55} - 3 q^{57} - 24 q^{58} - 2 q^{59} - 6 q^{60} - 6 q^{61} + 6 q^{62} - 4 q^{64} + 12 q^{65} - 19 q^{66} + 7 q^{67} + 17 q^{68} - 9 q^{69} + 10 q^{71} - 15 q^{72} + 15 q^{73} - 13 q^{74} + 12 q^{75} - 3 q^{76} - 3 q^{78} + 8 q^{79} - 9 q^{80} + 38 q^{81} - 4 q^{82} + 15 q^{83} + 21 q^{85} + 10 q^{86} - 6 q^{87} + 15 q^{88} + 14 q^{89} + 51 q^{90} - 9 q^{92} + 8 q^{93} + 25 q^{94} - 6 q^{95} + 4 q^{96} - 12 q^{97} - 32 q^{99}+O(q^{100}) \) 2 * q - q^2 + 3 * q^3 + 3 * q^4 + 6 * q^5 + 5 * q^6 - 6 * q^8 + 5 * q^9 - 3 * q^10 - 5 * q^11 - 2 * q^12 + 4 * q^13 + 9 * q^15 - 3 * q^16 + 7 * q^17 + 17 * q^18 - 2 * q^19 + 9 * q^20 - 4 * q^22 - 6 * q^23 - 9 * q^24 + 8 * q^25 - 15 * q^26 + 18 * q^27 + 9 * q^29 + 15 * q^30 + q^31 + 7 * q^32 - 14 * q^33 - 10 * q^34 - 12 * q^36 + q^38 - 7 * q^39 - 18 * q^40 - 5 * q^41 - 20 * q^43 - q^44 + 15 * q^45 + 3 * q^46 + 2 * q^47 - 11 * q^48 - 4 * q^50 + 4 * q^51 + 19 * q^52 - 3 * q^53 + 17 * q^54 - 15 * q^55 - 3 * q^57 - 24 * q^58 - 2 * q^59 - 6 * q^60 - 6 * q^61 + 6 * q^62 - 4 * q^64 + 12 * q^65 - 19 * q^66 + 7 * q^67 + 17 * q^68 - 9 * q^69 + 10 * q^71 - 15 * q^72 + 15 * q^73 - 13 * q^74 + 12 * q^75 - 3 * q^76 - 3 * q^78 + 8 * q^79 - 9 * q^80 + 38 * q^81 - 4 * q^82 + 15 * q^83 + 21 * q^85 + 10 * q^86 - 6 * q^87 + 15 * q^88 + 14 * q^89 + 51 * q^90 - 9 * q^92 + 8 * q^93 + 25 * q^94 - 6 * q^95 + 4 * q^96 - 12 * q^97 - 32 * q^99

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