LMFDB - Embedded newform 2009.2.a.o.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2009,2,Mod(1,2009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2009, 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("2009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2009 = 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2009.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:	$16.0419457661$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.185257757.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 10x^{4} + 10x^{3} + 23x^{2} - 24x + 5 $ x^6 - x^5 - 10x^4 + 10x^3 + 23x^2 - 24x + 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 287)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.644787$ of defining polynomial
Character	$\chi$	$=$	2009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.644787 q^{2} +2.95586 q^{3} -1.58425 q^{4} +4.36552 q^{5} -1.90590 q^{6} +2.31108 q^{8} +5.73713 q^{9} +O(q^{10})$	\(q-0.644787 q^{2} +2.95586 q^{3} -1.58425 q^{4} +4.36552 q^{5} -1.90590 q^{6} +2.31108 q^{8} +5.73713 q^{9} -2.81483 q^{10} -4.65944 q^{11} -4.68283 q^{12} +0.769213 q^{13} +12.9039 q^{15} +1.67835 q^{16} -0.371615 q^{17} -3.69923 q^{18} +1.98942 q^{19} -6.91607 q^{20} +3.00434 q^{22} +1.04414 q^{23} +6.83123 q^{24} +14.0578 q^{25} -0.495979 q^{26} +8.09060 q^{27} -9.76819 q^{29} -8.32026 q^{30} +7.10875 q^{31} -5.70433 q^{32} -13.7727 q^{33} +0.239612 q^{34} -9.08905 q^{36} -0.873617 q^{37} -1.28275 q^{38} +2.27369 q^{39} +10.0891 q^{40} -1.00000 q^{41} +9.74596 q^{43} +7.38171 q^{44} +25.0456 q^{45} -0.673245 q^{46} +6.56785 q^{47} +4.96097 q^{48} -9.06426 q^{50} -1.09844 q^{51} -1.21863 q^{52} +10.2444 q^{53} -5.21671 q^{54} -20.3409 q^{55} +5.88047 q^{57} +6.29840 q^{58} +0.148022 q^{59} -20.4430 q^{60} -2.38647 q^{61} -4.58363 q^{62} +0.321384 q^{64} +3.35801 q^{65} +8.88044 q^{66} -4.27725 q^{67} +0.588730 q^{68} +3.08632 q^{69} -6.72656 q^{71} +13.2590 q^{72} -2.05099 q^{73} +0.563297 q^{74} +41.5528 q^{75} -3.15175 q^{76} -1.46605 q^{78} -4.82800 q^{79} +7.32686 q^{80} +6.70330 q^{81} +0.644787 q^{82} -1.55806 q^{83} -1.62229 q^{85} -6.28407 q^{86} -28.8734 q^{87} -10.7683 q^{88} +2.86975 q^{89} -16.1491 q^{90} -1.65417 q^{92} +21.0125 q^{93} -4.23486 q^{94} +8.68487 q^{95} -16.8612 q^{96} -16.2763 q^{97} -26.7318 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} + 4 q^{3} + 9 q^{4} + q^{5} + 4 q^{6} + 3 q^{8} + 14 q^{9}+O(q^{10}) $ 6 * q - q^2 + 4 * q^3 + 9 * q^4 + q^5 + 4 * q^6 + 3 * q^8 + 14 * q^9	$ 6 q - q^{2} + 4 q^{3} + 9 q^{4} + q^{5} + 4 q^{6} + 3 q^{8} + 14 q^{9} - 10 q^{10} + 6 q^{11} - 9 q^{12} - 7 q^{13} - 13 q^{15} + 7 q^{16} - 7 q^{17} - 5 q^{18} - 2 q^{19} - 11 q^{20} + 15 q^{22} + 20 q^{23} + 36 q^{24} + 29 q^{25} + 43 q^{26} - 2 q^{27} - 9 q^{29} + 13 q^{30} + 27 q^{31} - 10 q^{32} - 17 q^{33} - 6 q^{34} + 29 q^{36} + 19 q^{37} + 23 q^{38} + q^{39} - 23 q^{40} - 6 q^{41} + 19 q^{43} + 21 q^{44} + 35 q^{45} - 8 q^{46} + 19 q^{47} + 9 q^{48} - 58 q^{50} - 19 q^{51} + 5 q^{53} + 37 q^{54} - 3 q^{55} + 37 q^{57} + 13 q^{58} + 7 q^{59} - 110 q^{60} + 12 q^{61} - 37 q^{64} - 13 q^{65} + 54 q^{66} + 27 q^{67} - 31 q^{68} - 16 q^{69} - 6 q^{71} + 5 q^{72} - 52 q^{73} - 14 q^{74} + 46 q^{75} - 13 q^{76} - 45 q^{78} + 26 q^{80} - 22 q^{81} + q^{82} - 12 q^{83} + 25 q^{85} - 10 q^{86} - 42 q^{87} - 2 q^{88} + 38 q^{89} - 93 q^{90} + 45 q^{92} + 33 q^{93} + 8 q^{94} + q^{95} + 12 q^{96} - 8 q^{97} + q^{99}+O(q^{100}) $ 6 * q - q^2 + 4 * q^3 + 9 * q^4 + q^5 + 4 * q^6 + 3 * q^8 + 14 * q^9 - 10 * q^10 + 6 * q^11 - 9 * q^12 - 7 * q^13 - 13 * q^15 + 7 * q^16 - 7 * q^17 - 5 * q^18 - 2 * q^19 - 11 * q^20 + 15 * q^22 + 20 * q^23 + 36 * q^24 + 29 * q^25 + 43 * q^26 - 2 * q^27 - 9 * q^29 + 13 * q^30 + 27 * q^31 - 10 * q^32 - 17 * q^33 - 6 * q^34 + 29 * q^36 + 19 * q^37 + 23 * q^38 + q^39 - 23 * q^40 - 6 * q^41 + 19 * q^43 + 21 * q^44 + 35 * q^45 - 8 * q^46 + 19 * q^47 + 9 * q^48 - 58 * q^50 - 19 * q^51 + 5 * q^53 + 37 * q^54 - 3 * q^55 + 37 * q^57 + 13 * q^58 + 7 * q^59 - 110 * q^60 + 12 * q^61 - 37 * q^64 - 13 * q^65 + 54 * q^66 + 27 * q^67 - 31 * q^68 - 16 * q^69 - 6 * q^71 + 5 * q^72 - 52 * q^73 - 14 * q^74 + 46 * q^75 - 13 * q^76 - 45 * q^78 + 26 * q^80 - 22 * q^81 + q^82 - 12 * q^83 + 25 * q^85 - 10 * q^86 - 42 * q^87 - 2 * q^88 + 38 * q^89 - 93 * q^90 + 45 * q^92 + 33 * q^93 + 8 * q^94 + q^95 + 12 * q^96 - 8 * q^97 + 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 $

$2$	−0.644787	−0.455933	−0.227967	−	0.973669i	$-0.573208\pi$
$2$	−0.644787	−0.455933	−0.227967	+	0.973669i	$0.573208\pi$
$3$	2.95586	1.70657	0.853285	−	0.521446i	$-0.174607\pi$
$3$	2.95586	1.70657	0.853285	+	0.521446i	$0.174607\pi$
$4$	−1.58425	−0.792125
$5$	4.36552	1.95232	0.976160	−	0.217053i	$-0.0696444\pi$
$5$	4.36552	1.95232	0.976160	+	0.217053i	$0.0696444\pi$
$6$	−1.90590	−0.778082
$7$	0	0
$7$	0	0
$8$	2.31108	0.817089
$9$	5.73713	1.91238
$10$	−2.81483	−0.890127
$11$	−4.65944	−1.40487	−0.702437	−	0.711746i	$-0.747905\pi$
$11$	−4.65944	−1.40487	−0.702437	+	0.711746i	$0.747905\pi$
$12$	−4.68283	−1.35182
$13$	0.769213	0.213341	0.106671	−	0.994294i	$-0.465981\pi$
$13$	0.769213	0.213341	0.106671	+	0.994294i	$0.465981\pi$
$14$	0	0
$15$	12.9039	3.33177
$16$	1.67835	0.419587
$17$	−0.371615	−0.0901298	−0.0450649	−	0.998984i	$-0.514349\pi$
$17$	−0.371615	−0.0901298	−0.0450649	+	0.998984i	$0.514349\pi$
$18$	−3.69923	−0.871917
$19$	1.98942	0.456405	0.228203	−	0.973614i	$-0.426715\pi$
$19$	1.98942	0.456405	0.228203	+	0.973614i	$0.426715\pi$
$20$	−6.91607	−1.54648
$21$	0	0
$22$	3.00434	0.640528
$23$	1.04414	0.217717	0.108859	−	0.994057i	$-0.465280\pi$
$23$	1.04414	0.217717	0.108859	+	0.994057i	$0.465280\pi$
$24$	6.83123	1.39442
$25$	14.0578	2.81155
$26$	−0.495979	−0.0972694
$27$	8.09060	1.55704
$28$	0	0
$29$	−9.76819	−1.81391	−0.906953	−	0.421231i	$-0.861598\pi$
$29$	−9.76819	−1.81391	−0.906953	+	0.421231i	$0.861598\pi$
$30$	−8.32026	−1.51906
$31$	7.10875	1.27677	0.638384	−	0.769718i	$-0.279603\pi$
$31$	7.10875	1.27677	0.638384	+	0.769718i	$0.279603\pi$
$32$	−5.70433	−1.00839
$33$	−13.7727	−2.39751
$34$	0.239612	0.0410932
$35$	0	0
$36$	−9.08905	−1.51484
$37$	−0.873617	−0.143622	−0.0718109	−	0.997418i	$-0.522878\pi$
$37$	−0.873617	−0.143622	−0.0718109	+	0.997418i	$0.522878\pi$
$38$	−1.28275	−0.208090
$39$	2.27369	0.364082
$40$	10.0891	1.59522
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	9.74596	1.48624	0.743122	−	0.669155i	$-0.233344\pi$
$43$	9.74596	1.48624	0.743122	+	0.669155i	$0.233344\pi$
$44$	7.38171	1.11284
$45$	25.0456	3.73357
$46$	−0.673245	−0.0992646
$47$	6.56785	0.958019	0.479010	−	0.877810i	$-0.340996\pi$
$47$	6.56785	0.958019	0.479010	+	0.877810i	$0.340996\pi$
$48$	4.96097	0.716054
$49$	0	0
$50$	−9.06426	−1.28188
$51$	−1.09844	−0.153813
$52$	−1.21863	−0.168993
$53$	10.2444	1.40718	0.703591	−	0.710605i	$-0.251579\pi$
$53$	10.2444	1.40718	0.703591	+	0.710605i	$0.251579\pi$
$54$	−5.21671	−0.709904
$55$	−20.3409	−2.74276
$56$	0	0
$57$	5.88047	0.778887
$58$	6.29840	0.827020
$59$	0.148022	0.0192709	0.00963544	−	0.999954i	$-0.496933\pi$
$59$	0.148022	0.0192709	0.00963544	+	0.999954i	$0.496933\pi$
$60$	−20.4430	−2.63918
$61$	−2.38647	−0.305557	−0.152778	−	0.988260i	$-0.548822\pi$
$61$	−2.38647	−0.305557	−0.152778	+	0.988260i	$0.548822\pi$
$62$	−4.58363	−0.582121
$63$	0	0
$64$	0.321384	0.0401730
$65$	3.35801	0.416510
$66$	8.88044	1.09311
$67$	−4.27725	−0.522549	−0.261275	−	0.965265i	$-0.584143\pi$
$67$	−4.27725	−0.522549	−0.261275	+	0.965265i	$0.584143\pi$
$68$	0.588730	0.0713940
$69$	3.08632	0.371550
$70$	0	0
$71$	−6.72656	−0.798296	−0.399148	−	0.916887i	$-0.630694\pi$
$71$	−6.72656	−0.798296	−0.399148	+	0.916887i	$0.630694\pi$
$72$	13.2590	1.56258
$73$	−2.05099	−0.240050	−0.120025	−	0.992771i	$-0.538297\pi$
$73$	−2.05099	−0.240050	−0.120025	+	0.992771i	$0.538297\pi$
$74$	0.563297	0.0654819
$75$	41.5528	4.79811
$76$	−3.15175	−0.361530
$77$	0	0
$78$	−1.46605	−0.165997
$79$	−4.82800	−0.543192	−0.271596	−	0.962411i	$-0.587552\pi$
$79$	−4.82800	−0.543192	−0.271596	+	0.962411i	$0.587552\pi$
$80$	7.32686	0.819168
$81$	6.70330	0.744812
$82$	0.644787	0.0712048
$83$	−1.55806	−0.171019	−0.0855096	−	0.996337i	$-0.527252\pi$
$83$	−1.55806	−0.171019	−0.0855096	+	0.996337i	$0.527252\pi$
$84$	0	0
$85$	−1.62229	−0.175962
$86$	−6.28407	−0.677628
$87$	−28.8734	−3.09556
$88$	−10.7683	−1.14791
$89$	2.86975	0.304193	0.152096	−	0.988366i	$-0.451398\pi$
$89$	2.86975	0.304193	0.152096	+	0.988366i	$0.451398\pi$
$90$	−16.1491	−1.70226
$91$	0	0
$92$	−1.65417	−0.172459
$93$	21.0125	2.17889
$94$	−4.23486	−0.436793
$95$	8.68487	0.891049
$96$	−16.8612	−1.72089
$97$	−16.2763	−1.65260	−0.826302	−	0.563228i	$-0.809559\pi$
$97$	−16.2763	−1.65260	−0.826302	+	0.563228i	$0.809559\pi$
$98$	0	0
$99$	−26.7318	−2.68665
$100$	−22.2710	−2.22710
$101$	−15.5762	−1.54989	−0.774943	−	0.632031i	$-0.782222\pi$
$101$	−15.5762	−1.54989	−0.774943	+	0.632031i	$0.782222\pi$
$102$	0.708261	0.0701283
$103$	0.687958	0.0677866	0.0338933	−	0.999425i	$-0.489209\pi$
$103$	0.687958	0.0677866	0.0338933	+	0.999425i	$0.489209\pi$
$104$	1.77771	0.174319
$105$	0	0
$106$	−6.60548	−0.641581
$107$	−4.96393	−0.479881	−0.239941	−	0.970788i	$-0.577128\pi$
$107$	−4.96393	−0.479881	−0.239941	+	0.970788i	$0.577128\pi$
$108$	−12.8175	−1.23337
$109$	14.4041	1.37966	0.689832	−	0.723969i	$-0.257684\pi$
$109$	14.4041	1.37966	0.689832	+	0.723969i	$0.257684\pi$
$110$	13.1155	1.25052
$111$	−2.58229	−0.245100
$112$	0	0
$113$	−4.16902	−0.392188	−0.196094	−	0.980585i	$-0.562826\pi$
$113$	−4.16902	−0.392188	−0.196094	+	0.980585i	$0.562826\pi$
$114$	−3.79165	−0.355121
$115$	4.55819	0.425054
$116$	15.4752	1.43684
$117$	4.41308	0.407989
$118$	−0.0954429	−0.00878623
$119$	0	0
$120$	29.8219	2.72235
$121$	10.7104	0.973669
$122$	1.53877	0.139313
$123$	−2.95586	−0.266521
$124$	−11.2620	−1.01136
$125$	39.5418	3.53673
$126$	0	0
$127$	−5.65606	−0.501894	−0.250947	−	0.968001i	$-0.580742\pi$
$127$	−5.65606	−0.501894	−0.250947	+	0.968001i	$0.580742\pi$
$128$	11.2014	0.990077
$129$	28.8077	2.53638
$130$	−2.16520	−0.189901
$131$	−1.71925	−0.150212	−0.0751058	−	0.997176i	$-0.523929\pi$
$131$	−1.71925	−0.150212	−0.0751058	+	0.997176i	$0.523929\pi$
$132$	21.8193	1.89913
$133$	0	0
$134$	2.75791	0.238247
$135$	35.3197	3.03983
$136$	−0.858830	−0.0736441
$137$	−10.3832	−0.887094	−0.443547	−	0.896251i	$-0.646280\pi$
$137$	−10.3832	−0.887094	−0.443547	+	0.896251i	$0.646280\pi$
$138$	−1.99002	−0.169402
$139$	1.25229	0.106218	0.0531089	−	0.998589i	$-0.483087\pi$
$139$	1.25229	0.106218	0.0531089	+	0.998589i	$0.483087\pi$
$140$	0	0
$141$	19.4137	1.63493
$142$	4.33720	0.363969
$143$	−3.58410	−0.299718
$144$	9.62890	0.802409
$145$	−42.6432	−3.54133
$146$	1.32245	0.109447
$147$	0	0
$148$	1.38403	0.113766
$149$	−19.1563	−1.56935	−0.784673	−	0.619910i	$-0.787169\pi$
$149$	−19.1563	−1.56935	−0.784673	+	0.619910i	$0.787169\pi$
$150$	−26.7927	−2.18762
$151$	−4.78203	−0.389156	−0.194578	−	0.980887i	$-0.562334\pi$
$151$	−4.78203	−0.389156	−0.194578	+	0.980887i	$0.562334\pi$
$152$	4.59771	0.372924
$153$	−2.13200	−0.172362
$154$	0	0
$155$	31.0334	2.49266
$156$	−3.60209	−0.288398
$157$	−8.99825	−0.718139	−0.359069	−	0.933311i	$-0.616906\pi$
$157$	−8.99825	−0.718139	−0.359069	+	0.933311i	$0.616906\pi$
$158$	3.11303	0.247659
$159$	30.2812	2.40145
$160$	−24.9024	−1.96871
$161$	0	0
$162$	−4.32220	−0.339584
$163$	15.3390	1.20145	0.600723	−	0.799457i	$-0.294879\pi$
$163$	15.3390	1.20145	0.600723	+	0.799457i	$0.294879\pi$
$164$	1.58425	0.123709
$165$	−60.1248	−4.68071
$166$	1.00462	0.0779733
$167$	−1.01492	−0.0785369	−0.0392684	−	0.999229i	$-0.512503\pi$
$167$	−1.01492	−0.0785369	−0.0392684	+	0.999229i	$0.512503\pi$
$168$	0	0
$169$	−12.4083	−0.954485
$170$	1.04603	0.0802270
$171$	11.4136	0.872819
$172$	−15.4400	−1.17729
$173$	−10.1564	−0.772175	−0.386087	−	0.922462i	$-0.626174\pi$
$173$	−10.1564	−0.772175	−0.386087	+	0.922462i	$0.626174\pi$
$174$	18.6172	1.41137
$175$	0	0
$176$	−7.82015	−0.589466
$177$	0.437534	0.0328871
$178$	−1.85038	−0.138692
$179$	6.15617	0.460134	0.230067	−	0.973175i	$-0.426105\pi$
$179$	6.15617	0.460134	0.230067	+	0.973175i	$0.426105\pi$
$180$	−39.6784	−2.95746
$181$	−3.58270	−0.266300	−0.133150	−	0.991096i	$-0.542509\pi$
$181$	−3.58270	−0.266300	−0.133150	+	0.991096i	$0.542509\pi$
$182$	0	0
$183$	−7.05409	−0.521453
$184$	2.41308	0.177894
$185$	−3.81379	−0.280396
$186$	−13.5486	−0.993430
$187$	1.73151	0.126621
$188$	−10.4051	−0.758871
$189$	0	0
$190$	−5.59989	−0.406259
$191$	17.0157	1.23121	0.615605	−	0.788055i	$-0.288912\pi$
$191$	17.0157	1.23121	0.615605	+	0.788055i	$0.288912\pi$
$192$	0.949967	0.0685580
$193$	−0.147825	−0.0106407	−0.00532033	−	0.999986i	$-0.501694\pi$
$193$	−0.147825	−0.0106407	−0.00532033	+	0.999986i	$0.501694\pi$
$194$	10.4947	0.753477
$195$	9.92584	0.710804
$196$	0	0
$197$	0.534255	0.0380641	0.0190320	−	0.999819i	$-0.493942\pi$
$197$	0.534255	0.0380641	0.0190320	+	0.999819i	$0.493942\pi$
$198$	17.2363	1.22493
$199$	19.1515	1.35761	0.678806	−	0.734318i	$-0.262498\pi$
$199$	19.1515	1.35761	0.678806	+	0.734318i	$0.262498\pi$
$200$	32.4886	2.29729
$201$	−12.6430	−0.891766
$202$	10.0433	0.706645
$203$	0	0
$204$	1.74021	0.121839
$205$	−4.36552	−0.304901
$206$	−0.443587	−0.0309061
$207$	5.99035	0.416358
$208$	1.29101	0.0895152
$209$	−9.26960	−0.641192
$210$	0	0
$211$	−16.9039	−1.16371	−0.581856	−	0.813292i	$-0.697673\pi$
$211$	−16.9039	−1.16371	−0.581856	+	0.813292i	$0.697673\pi$
$212$	−16.2298	−1.11466
$213$	−19.8828	−1.36235
$214$	3.20068	0.218794
$215$	42.5462	2.90163
$216$	18.6980	1.27224
$217$	0	0
$218$	−9.28759	−0.629035
$219$	−6.06244	−0.409662
$220$	32.2250	2.17261
$221$	−0.285851	−0.0192284
$222$	1.66503	0.111749
$223$	6.58005	0.440633	0.220317	−	0.975428i	$-0.429291\pi$
$223$	6.58005	0.440633	0.220317	+	0.975428i	$0.429291\pi$
$224$	0	0
$225$	80.6513	5.37675
$226$	2.68813	0.178812
$227$	9.23817	0.613159	0.306580	−	0.951845i	$-0.400815\pi$
$227$	9.23817	0.613159	0.306580	+	0.951845i	$0.400815\pi$
$228$	−9.31613	−0.616976
$229$	7.85581	0.519126	0.259563	−	0.965726i	$-0.416421\pi$
$229$	7.85581	0.519126	0.259563	+	0.965726i	$0.416421\pi$
$230$	−2.93906	−0.193796
$231$	0	0
$232$	−22.5750	−1.48212
$233$	21.8736	1.43299	0.716493	−	0.697595i	$-0.245746\pi$
$233$	21.8736	1.43299	0.716493	+	0.697595i	$0.245746\pi$
$234$	−2.84550	−0.186016
$235$	28.6721	1.87036
$236$	−0.234504	−0.0152649
$237$	−14.2709	−0.926995
$238$	0	0
$239$	−19.3327	−1.25053	−0.625263	−	0.780414i	$-0.715008\pi$
$239$	−19.3327	−1.25053	−0.625263	+	0.780414i	$0.715008\pi$
$240$	21.6572	1.39797
$241$	−19.4467	−1.25267	−0.626335	−	0.779554i	$-0.715446\pi$
$241$	−19.4467	−1.25267	−0.626335	+	0.779554i	$0.715446\pi$
$242$	−6.90590	−0.443928
$243$	−4.45773	−0.285964
$244$	3.78077	0.242039
$245$	0	0
$246$	1.90590	0.121516
$247$	1.53029	0.0973701
$248$	16.4289	1.04323
$249$	−4.60541	−0.291856
$250$	−25.4961	−1.61251
$251$	−8.02675	−0.506644	−0.253322	−	0.967382i	$-0.581523\pi$
$251$	−8.02675	−0.506644	−0.253322	+	0.967382i	$0.581523\pi$
$252$	0	0
$253$	−4.86509	−0.305865
$254$	3.64695	0.228830
$255$	−4.79527	−0.300291
$256$	−7.86531	−0.491582
$257$	23.7181	1.47949	0.739746	−	0.672886i	$-0.234946\pi$
$257$	23.7181	1.47949	0.739746	+	0.672886i	$0.234946\pi$
$258$	−18.5748	−1.15642
$259$	0	0
$260$	−5.31993	−0.329928
$261$	−56.0414	−3.46888
$262$	1.10855	0.0684865
$263$	−5.42183	−0.334325	−0.167162	−	0.985929i	$-0.553460\pi$
$263$	−5.42183	−0.334325	−0.167162	+	0.985929i	$0.553460\pi$
$264$	−31.8297	−1.95898
$265$	44.7223	2.74727
$266$	0	0
$267$	8.48259	0.519126
$268$	6.77623	0.413924
$269$	−29.6431	−1.80737	−0.903685	−	0.428198i	$-0.859149\pi$
$269$	−29.6431	−1.80737	−0.903685	+	0.428198i	$0.859149\pi$
$270$	−22.7737	−1.38596
$271$	6.05790	0.367991	0.183995	−	0.982927i	$-0.441097\pi$
$271$	6.05790	0.367991	0.183995	+	0.982927i	$0.441097\pi$
$272$	−0.623698	−0.0378173
$273$	0	0
$274$	6.69493	0.404456
$275$	−65.5013	−3.94987
$276$	−4.88951	−0.294314
$277$	16.3855	0.984508	0.492254	−	0.870452i	$-0.336173\pi$
$277$	16.3855	0.984508	0.492254	+	0.870452i	$0.336173\pi$
$278$	−0.807461	−0.0484283
$279$	40.7838	2.44166
$280$	0	0
$281$	−2.10296	−0.125452	−0.0627259	−	0.998031i	$-0.519979\pi$
$281$	−2.10296	−0.125452	−0.0627259	+	0.998031i	$0.519979\pi$
$282$	−12.5177	−0.745417
$283$	12.5550	0.746319	0.373160	−	0.927767i	$-0.378274\pi$
$283$	12.5550	0.746319	0.373160	+	0.927767i	$0.378274\pi$
$284$	10.6565	0.632350
$285$	25.6713	1.52064
$286$	2.31098	0.136651
$287$	0	0
$288$	−32.7265	−1.92843
$289$	−16.8619	−0.991877
$290$	27.4958	1.61461
$291$	−48.1104	−2.82028
$292$	3.24928	0.190150
$293$	14.2895	0.834802	0.417401	−	0.908722i	$-0.362941\pi$
$293$	14.2895	0.834802	0.417401	+	0.908722i	$0.362941\pi$
$294$	0	0
$295$	0.646195	0.0376229
$296$	−2.01900	−0.117352
$297$	−37.6976	−2.18744
$298$	12.3517	0.715517
$299$	0.803163	0.0464481
$300$	−65.8301	−3.80070
$301$	0	0
$302$	3.08339	0.177429
$303$	−46.0410	−2.64499
$304$	3.33895	0.191502
$305$	−10.4182	−0.596544
$306$	1.37469	0.0785856
$307$	−7.38798	−0.421654	−0.210827	−	0.977523i	$-0.567616\pi$
$307$	−7.38798	−0.421654	−0.210827	+	0.977523i	$0.567616\pi$
$308$	0	0
$309$	2.03351	0.115682
$310$	−20.0099	−1.13649
$311$	−24.2305	−1.37399	−0.686993	−	0.726664i	$-0.741070\pi$
$311$	−24.2305	−1.37399	−0.686993	+	0.726664i	$0.741070\pi$
$312$	5.25467	0.297487
$313$	1.03705	0.0586174	0.0293087	−	0.999570i	$-0.490669\pi$
$313$	1.03705	0.0586174	0.0293087	+	0.999570i	$0.490669\pi$
$314$	5.80195	0.327423
$315$	0	0
$316$	7.64876	0.430276
$317$	−6.16355	−0.346179	−0.173090	−	0.984906i	$-0.555375\pi$
$317$	−6.16355	−0.346179	−0.173090	+	0.984906i	$0.555375\pi$
$318$	−19.5249	−1.09490
$319$	45.5143	2.54831
$320$	1.40301	0.0784305
$321$	−14.6727	−0.818951
$322$	0	0
$323$	−0.739299	−0.0411357
$324$	−10.6197	−0.589984
$325$	10.8134	0.599820
$326$	−9.89041	−0.547779
$327$	42.5766	2.35449
$328$	−2.31108	−0.127608
$329$	0	0
$330$	38.7677	2.13409
$331$	7.81435	0.429516	0.214758	−	0.976667i	$-0.431104\pi$
$331$	7.81435	0.429516	0.214758	+	0.976667i	$0.431104\pi$
$332$	2.46835	0.135469
$333$	−5.01206	−0.274659
$334$	0.654407	0.0358076
$335$	−18.6724	−1.02018
$336$	0	0
$337$	20.8926	1.13809	0.569047	−	0.822305i	$-0.307312\pi$
$337$	20.8926	1.13809	0.569047	+	0.822305i	$0.307312\pi$
$338$	8.00072	0.435182
$339$	−12.3230	−0.669296
$340$	2.57011	0.139384
$341$	−33.1228	−1.79370
$342$	−7.35934	−0.397947
$343$	0	0
$344$	22.5237	1.21439
$345$	13.4734	0.725384
$346$	6.54870	0.352060
$347$	21.3183	1.14443	0.572214	−	0.820104i	$-0.306085\pi$
$347$	21.3183	1.14443	0.572214	+	0.820104i	$0.306085\pi$
$348$	45.7427	2.45207
$349$	−5.58983	−0.299217	−0.149608	−	0.988745i	$-0.547801\pi$
$349$	−5.58983	−0.299217	−0.149608	+	0.988745i	$0.547801\pi$
$350$	0	0
$351$	6.22339	0.332180
$352$	26.5790	1.41666
$353$	−15.0504	−0.801051	−0.400526	−	0.916286i	$-0.631172\pi$
$353$	−15.0504	−0.801051	−0.400526	+	0.916286i	$0.631172\pi$
$354$	−0.282116	−0.0149943
$355$	−29.3649	−1.55853
$356$	−4.54640	−0.240959
$357$	0	0
$358$	−3.96942	−0.209790
$359$	9.45849	0.499200	0.249600	−	0.968349i	$-0.419701\pi$
$359$	9.45849	0.499200	0.249600	+	0.968349i	$0.419701\pi$
$360$	57.8823	3.05066
$361$	−15.0422	−0.791694
$362$	2.31008	0.121415
$363$	31.6584	1.66163
$364$	0	0
$365$	−8.95363	−0.468654
$366$	4.54838	0.237748
$367$	4.08793	0.213388	0.106694	−	0.994292i	$-0.465973\pi$
$367$	4.08793	0.213388	0.106694	+	0.994292i	$0.465973\pi$
$368$	1.75242	0.0913513
$369$	−5.73713	−0.298663
$370$	2.45908	0.127842
$371$	0	0
$372$	−33.2890	−1.72596
$373$	−15.5933	−0.807392	−0.403696	−	0.914893i	$-0.632275\pi$
$373$	−15.5933	−0.807392	−0.403696	+	0.914893i	$0.632275\pi$
$374$	−1.11646	−0.0577307
$375$	116.880	6.03567
$376$	15.1788	0.782787
$377$	−7.51382	−0.386981
$378$	0	0
$379$	17.3850	0.893008	0.446504	−	0.894782i	$-0.352669\pi$
$379$	17.3850	0.893008	0.446504	+	0.894782i	$0.352669\pi$
$380$	−13.7590	−0.705822
$381$	−16.7185	−0.856517
$382$	−10.9715	−0.561349
$383$	−30.8083	−1.57423	−0.787115	−	0.616806i	$-0.788426\pi$
$383$	−30.8083	−1.57423	−0.787115	+	0.616806i	$0.788426\pi$
$384$	33.1099	1.68963
$385$	0	0
$386$	0.0953154	0.00485143
$387$	55.9139	2.84226
$388$	25.7857	1.30907
$389$	−27.6236	−1.40057	−0.700287	−	0.713862i	$-0.746944\pi$
$389$	−27.6236	−1.40057	−0.700287	+	0.713862i	$0.746944\pi$
$390$	−6.40005	−0.324079
$391$	−0.388016	−0.0196228
$392$	0	0
$393$	−5.08187	−0.256347
$394$	−0.344480	−0.0173547
$395$	−21.0767	−1.06049
$396$	42.3499	2.12816
$397$	2.09413	0.105101	0.0525506	−	0.998618i	$-0.483265\pi$
$397$	2.09413	0.105101	0.0525506	+	0.998618i	$0.483265\pi$
$398$	−12.3486	−0.618980
$399$	0	0
$400$	23.5938	1.17969
$401$	−13.7468	−0.686480	−0.343240	−	0.939248i	$-0.611524\pi$
$401$	−13.7468	−0.686480	−0.343240	+	0.939248i	$0.611524\pi$
$402$	8.15202	0.406586
$403$	5.46814	0.272388
$404$	24.6765	1.22770
$405$	29.2634	1.45411
$406$	0	0
$407$	4.07056	0.201770
$408$	−2.53858	−0.125679
$409$	28.7518	1.42169	0.710843	−	0.703351i	$-0.248314\pi$
$409$	28.7518	1.42169	0.710843	+	0.703351i	$0.248314\pi$
$410$	2.81483	0.139015
$411$	−30.6912	−1.51389
$412$	−1.08990	−0.0536954
$413$	0	0
$414$	−3.86250	−0.189831
$415$	−6.80174	−0.333884
$416$	−4.38785	−0.215132
$417$	3.70160	0.181268
$418$	5.97692	0.292341
$419$	−19.4060	−0.948045	−0.474023	−	0.880513i	$-0.657198\pi$
$419$	−19.4060	−0.948045	−0.474023	+	0.880513i	$0.657198\pi$
$420$	0	0
$421$	−32.2747	−1.57297	−0.786485	−	0.617609i	$-0.788101\pi$
$421$	−32.2747	−1.57297	−0.786485	+	0.617609i	$0.788101\pi$
$422$	10.8994	0.530575
$423$	37.6806	1.83209
$424$	23.6757	1.14979
$425$	−5.22407	−0.253405
$426$	12.8202	0.621139
$427$	0	0
$428$	7.86411	0.380126
$429$	−10.5941	−0.511489
$430$	−27.4332	−1.32295
$431$	37.7093	1.81639	0.908196	−	0.418545i	$-0.137460\pi$
$431$	37.7093	1.81639	0.908196	+	0.418545i	$0.137460\pi$
$432$	13.5788	0.653312
$433$	−18.1950	−0.874395	−0.437197	−	0.899366i	$-0.644029\pi$
$433$	−18.1950	−0.874395	−0.437197	+	0.899366i	$0.644029\pi$
$434$	0	0
$435$	−126.048	−6.04352
$436$	−22.8197	−1.09287
$437$	2.07723	0.0993673
$438$	3.90898	0.186778
$439$	−0.735065	−0.0350827	−0.0175414	−	0.999846i	$-0.505584\pi$
$439$	−0.735065	−0.0350827	−0.0175414	+	0.999846i	$0.505584\pi$
$440$	−47.0093	−2.24108
$441$	0	0
$442$	0.184313	0.00876687
$443$	23.2114	1.10281	0.551403	−	0.834239i	$-0.314093\pi$
$443$	23.2114	1.10281	0.551403	+	0.834239i	$0.314093\pi$
$444$	4.09100	0.194150
$445$	12.5279	0.593881
$446$	−4.24273	−0.200899
$447$	−56.6235	−2.67820
$448$	0	0
$449$	35.6413	1.68202	0.841009	−	0.541022i	$-0.181962\pi$
$449$	35.6413	1.68202	0.841009	+	0.541022i	$0.181962\pi$
$450$	−52.0029	−2.45144
$451$	4.65944	0.219404
$452$	6.60476	0.310662
$453$	−14.1350	−0.664121
$454$	−5.95665	−0.279560
$455$	0	0
$456$	13.5902	0.636420
$457$	2.93632	0.137355	0.0686776	−	0.997639i	$-0.478122\pi$
$457$	2.93632	0.137355	0.0686776	+	0.997639i	$0.478122\pi$
$458$	−5.06532	−0.236687
$459$	−3.00658	−0.140335
$460$	−7.22132	−0.336696
$461$	−30.5182	−1.42137	−0.710687	−	0.703508i	$-0.751616\pi$
$461$	−30.5182	−1.42137	−0.710687	+	0.703508i	$0.751616\pi$
$462$	0	0
$463$	13.3489	0.620377	0.310188	−	0.950675i	$-0.399608\pi$
$463$	13.3489	0.620377	0.310188	+	0.950675i	$0.399608\pi$
$464$	−16.3944	−0.761091
$465$	91.7305	4.25390
$466$	−14.1038	−0.653346
$467$	18.7897	0.869484	0.434742	−	0.900555i	$-0.356840\pi$
$467$	18.7897	0.869484	0.434742	+	0.900555i	$0.356840\pi$
$468$	−6.99142	−0.323178
$469$	0	0
$470$	−18.4874	−0.852759
$471$	−26.5976	−1.22555
$472$	0.342091	0.0157460
$473$	−45.4107	−2.08799
$474$	9.20170	0.422648
$475$	27.9669	1.28321
$476$	0	0
$477$	58.7738	2.69107
$478$	12.4654	0.570156
$479$	−18.2465	−0.833706	−0.416853	−	0.908974i	$-0.636867\pi$
$479$	−18.2465	−0.833706	−0.416853	+	0.908974i	$0.636867\pi$
$480$	−73.6080	−3.35973
$481$	−0.671997	−0.0306404
$482$	12.5389	0.571133
$483$	0	0
$484$	−16.9679	−0.771268
$485$	−71.0543	−3.22641
$486$	2.87429	0.130380
$487$	−6.61097	−0.299572	−0.149786	−	0.988718i	$-0.547858\pi$
$487$	−6.61097	−0.299572	−0.149786	+	0.988718i	$0.547858\pi$
$488$	−5.51532	−0.249667
$489$	45.3401	2.05035
$490$	0	0
$491$	36.7888	1.66026	0.830129	−	0.557572i	$-0.188267\pi$
$491$	36.7888	1.66026	0.830129	+	0.557572i	$0.188267\pi$
$492$	4.68283	0.211118
$493$	3.63000	0.163487
$494$	−0.986712	−0.0443943
$495$	−116.698	−5.24520
$496$	11.9309	0.535715
$497$	0	0
$498$	2.96951	0.133067
$499$	30.1361	1.34908	0.674539	−	0.738239i	$-0.264342\pi$
$499$	30.1361	1.34908	0.674539	+	0.738239i	$0.264342\pi$
$500$	−62.6441	−2.80153
$501$	−2.99997	−0.134029
$502$	5.17554	0.230996
$503$	−13.6149	−0.607058	−0.303529	−	0.952822i	$-0.598165\pi$
$503$	−13.6149	−0.607058	−0.303529	+	0.952822i	$0.598165\pi$
$504$	0	0
$505$	−67.9980	−3.02587
$506$	3.13694	0.139454
$507$	−36.6773	−1.62890
$508$	8.96061	0.397563
$509$	−24.9162	−1.10439	−0.552195	−	0.833715i	$-0.686209\pi$
$509$	−24.9162	−1.10439	−0.552195	+	0.833715i	$0.686209\pi$
$510$	3.09193	0.136913
$511$	0	0
$512$	−17.3314	−0.765948
$513$	16.0956	0.710640
$514$	−15.2931	−0.674550
$515$	3.00330	0.132341
$516$	−45.6386	−2.00913
$517$	−30.6025	−1.34590
$518$	0	0
$519$	−30.0209	−1.31777
$520$	7.76063	0.340326
$521$	−28.2228	−1.23646	−0.618232	−	0.785996i	$-0.712151\pi$
$521$	−28.2228	−1.23646	−0.618232	+	0.785996i	$0.712151\pi$
$522$	36.1348	1.58158
$523$	−1.39226	−0.0608792	−0.0304396	−	0.999537i	$-0.509691\pi$
$523$	−1.39226	−0.0608792	−0.0304396	+	0.999537i	$0.509691\pi$
$524$	2.72372	0.118986
$525$	0	0
$526$	3.49593	0.152430
$527$	−2.64171	−0.115075
$528$	−23.1153	−1.00597
$529$	−21.9098	−0.952599
$530$	−28.8364	−1.25257
$531$	0.849224	0.0368532
$532$	0	0
$533$	−0.769213	−0.0333183
$534$	−5.46946	−0.236687
$535$	−21.6701	−0.936882
$536$	−9.88505	−0.426969
$537$	18.1968	0.785251
$538$	19.1135	0.824040
$539$	0	0
$540$	−55.9552	−2.40793
$541$	−40.2432	−1.73019	−0.865095	−	0.501608i	$-0.832742\pi$
$541$	−40.2432	−1.73019	−0.865095	+	0.501608i	$0.832742\pi$
$542$	−3.90605	−0.167779
$543$	−10.5900	−0.454459
$544$	2.11981	0.0908862
$545$	62.8815	2.69355
$546$	0	0
$547$	−31.5963	−1.35096	−0.675481	−	0.737378i	$-0.736064\pi$
$547$	−31.5963	−1.35096	−0.675481	+	0.737378i	$0.736064\pi$
$548$	16.4495	0.702689
$549$	−13.6915	−0.584340
$550$	42.2344	1.80088
$551$	−19.4331	−0.827877
$552$	7.13273	0.303589
$553$	0	0
$554$	−10.5651	−0.448870
$555$	−11.2730	−0.478514
$556$	−1.98394	−0.0841378
$557$	−25.2292	−1.06900	−0.534498	−	0.845169i	$-0.679499\pi$
$557$	−25.2292	−1.06900	−0.534498	+	0.845169i	$0.679499\pi$
$558$	−26.2969	−1.11324
$559$	7.49672	0.317077
$560$	0	0
$561$	5.11812	0.216087
$562$	1.35596	0.0571977
$563$	−18.8091	−0.792710	−0.396355	−	0.918097i	$-0.629725\pi$
$563$	−18.8091	−0.792710	−0.396355	+	0.918097i	$0.629725\pi$
$564$	−30.7561	−1.29507
$565$	−18.1999	−0.765677
$566$	−8.09532	−0.340272
$567$	0	0
$568$	−15.5456	−0.652279
$569$	14.7098	0.616669	0.308334	−	0.951278i	$-0.400228\pi$
$569$	14.7098	0.616669	0.308334	+	0.951278i	$0.400228\pi$
$570$	−16.5525	−0.693309
$571$	−32.7371	−1.37001	−0.685003	−	0.728540i	$-0.740199\pi$
$571$	−32.7371	−1.37001	−0.685003	+	0.728540i	$0.740199\pi$
$572$	5.67811	0.237414
$573$	50.2960	2.10114
$574$	0	0
$575$	14.6782	0.612124
$576$	1.84382	0.0768259
$577$	0.488761	0.0203474	0.0101737	−	0.999948i	$-0.496762\pi$
$577$	0.488761	0.0203474	0.0101737	+	0.999948i	$0.496762\pi$
$578$	10.8723	0.452229
$579$	−0.436950	−0.0181590
$580$	67.5575	2.80517
$581$	0	0
$582$	31.0210	1.28586
$583$	−47.7334	−1.97691
$584$	−4.73999	−0.196142
$585$	19.2654	0.796525
$586$	−9.21369	−0.380614
$587$	28.4557	1.17449	0.587247	−	0.809408i	$-0.300212\pi$
$587$	28.4557	1.17449	0.587247	+	0.809408i	$0.300212\pi$
$588$	0	0
$589$	14.1423	0.582724
$590$	−0.416658	−0.0171535
$591$	1.57918	0.0649590
$592$	−1.46623	−0.0602618
$593$	8.08361	0.331954	0.165977	−	0.986130i	$-0.446922\pi$
$593$	8.08361	0.331954	0.165977	+	0.986130i	$0.446922\pi$
$594$	24.3069	0.997326
$595$	0	0
$596$	30.3484	1.24312
$597$	56.6092	2.31686
$598$	−0.517869	−0.0211772
$599$	−2.82862	−0.115574	−0.0577872	−	0.998329i	$-0.518404\pi$
$599$	−2.82862	−0.115574	−0.0577872	+	0.998329i	$0.518404\pi$
$600$	96.0318	3.92048
$601$	−5.18459	−0.211484	−0.105742	−	0.994394i	$-0.533722\pi$
$601$	−5.18459	−0.211484	−0.105742	+	0.994394i	$0.533722\pi$
$602$	0	0
$603$	−24.5391	−0.999311
$604$	7.57593	0.308260
$605$	46.7563	1.90091
$606$	29.6867	1.20594
$607$	28.3184	1.14941	0.574704	−	0.818361i	$-0.305117\pi$
$607$	28.3184	1.14941	0.574704	+	0.818361i	$0.305117\pi$
$608$	−11.3483	−0.460236
$609$	0	0
$610$	6.71751	0.271984
$611$	5.05207	0.204385
$612$	3.37762	0.136532
$613$	−4.40474	−0.177906	−0.0889530	−	0.996036i	$-0.528352\pi$
$613$	−4.40474	−0.177906	−0.0889530	+	0.996036i	$0.528352\pi$
$614$	4.76367	0.192246
$615$	−12.9039	−0.520335
$616$	0	0
$617$	30.9019	1.24406	0.622031	−	0.782993i	$-0.286308\pi$
$617$	30.9019	1.24406	0.622031	+	0.782993i	$0.286308\pi$
$618$	−1.31118	−0.0527435
$619$	−39.2610	−1.57803	−0.789016	−	0.614373i	$-0.789409\pi$
$619$	−39.2610	−1.57803	−0.789016	+	0.614373i	$0.789409\pi$
$620$	−49.1646	−1.97450
$621$	8.44768	0.338994
$622$	15.6235	0.626446
$623$	0	0
$624$	3.81604	0.152764
$625$	102.332	4.09327
$626$	−0.668675	−0.0267256
$627$	−27.3997	−1.09424
$628$	14.2555	0.568855
$629$	0.324649	0.0129446
$630$	0	0
$631$	5.39267	0.214679	0.107339	−	0.994222i	$-0.465767\pi$
$631$	5.39267	0.214679	0.107339	+	0.994222i	$0.465767\pi$
$632$	−11.1579	−0.443837
$633$	−49.9656	−1.98595
$634$	3.97417	0.157835
$635$	−24.6916	−0.979857
$636$	−47.9730	−1.90225
$637$	0	0
$638$	−29.3470	−1.16186
$639$	−38.5912	−1.52664
$640$	48.9001	1.93295
$641$	−28.1660	−1.11249	−0.556244	−	0.831019i	$-0.687758\pi$
$641$	−28.1660	−1.11249	−0.556244	+	0.831019i	$0.687758\pi$
$642$	9.46077	0.373387
$643$	−1.56000	−0.0615205	−0.0307603	−	0.999527i	$-0.509793\pi$
$643$	−1.56000	−0.0615205	−0.0307603	+	0.999527i	$0.509793\pi$
$644$	0	0
$645$	125.761	4.95182
$646$	0.476690	0.0187551
$647$	−20.5264	−0.806978	−0.403489	−	0.914985i	$-0.632203\pi$
$647$	−20.5264	−0.806978	−0.403489	+	0.914985i	$0.632203\pi$
$648$	15.4919	0.608578
$649$	−0.689701	−0.0270731
$650$	−6.97235	−0.273478
$651$	0	0
$652$	−24.3009	−0.951695
$653$	3.82662	0.149747	0.0748736	−	0.997193i	$-0.476145\pi$
$653$	3.82662	0.149747	0.0748736	+	0.997193i	$0.476145\pi$
$654$	−27.4529	−1.07349
$655$	−7.50543	−0.293261
$656$	−1.67835	−0.0655284
$657$	−11.7668	−0.459066
$658$	0	0
$659$	−36.5446	−1.42358	−0.711788	−	0.702395i	$-0.752114\pi$
$659$	−36.5446	−1.42358	−0.711788	+	0.702395i	$0.752114\pi$
$660$	95.2528	3.70771
$661$	35.4153	1.37750	0.688748	−	0.725001i	$-0.258161\pi$
$661$	35.4153	1.37750	0.688748	+	0.725001i	$0.258161\pi$
$662$	−5.03859	−0.195830
$663$	−0.844936	−0.0328146
$664$	−3.60079	−0.139738
$665$	0	0
$666$	3.23171	0.125226
$667$	−10.1993	−0.394919
$668$	1.60789	0.0622110
$669$	19.4497	0.751971
$670$	12.0397	0.465135
$671$	11.1196	0.429268
$672$	0	0
$673$	−6.11351	−0.235658	−0.117829	−	0.993034i	$-0.537594\pi$
$673$	−6.11351	−0.235658	−0.117829	+	0.993034i	$0.537594\pi$
$674$	−13.4713	−0.518894
$675$	113.736	4.37769
$676$	19.6579	0.756072
$677$	−4.62306	−0.177679	−0.0888393	−	0.996046i	$-0.528316\pi$
$677$	−4.62306	−0.177679	−0.0888393	+	0.996046i	$0.528316\pi$
$678$	7.94574	0.305154
$679$	0	0
$680$	−3.74924	−0.143777
$681$	27.3068	1.04640
$682$	21.3571	0.817807
$683$	−5.59818	−0.214209	−0.107104	−	0.994248i	$-0.534158\pi$
$683$	−5.59818	−0.214209	−0.107104	+	0.994248i	$0.534158\pi$
$684$	−18.0820	−0.691382
$685$	−45.3279	−1.73189
$686$	0	0
$687$	23.2207	0.885925
$688$	16.3571	0.623609
$689$	7.88016	0.300210
$690$	−8.68748	−0.330727
$691$	−26.6730	−1.01469	−0.507344	−	0.861744i	$-0.669373\pi$
$691$	−26.6730	−1.01469	−0.507344	+	0.861744i	$0.669373\pi$
$692$	16.0902	0.611659
$693$	0	0
$694$	−13.7458	−0.521783
$695$	5.46690	0.207371
$696$	−66.7287	−2.52935
$697$	0.371615	0.0140759
$698$	3.60425	0.136423
$699$	64.6553	2.44549
$700$	0	0
$701$	−20.3641	−0.769141	−0.384571	−	0.923096i	$-0.625650\pi$
$701$	−20.3641	−0.769141	−0.384571	+	0.923096i	$0.625650\pi$
$702$	−4.01276	−0.151452
$703$	−1.73799	−0.0655497
$704$	−1.49747	−0.0564380
$705$	84.7508	3.19190
$706$	9.70429	0.365226
$707$	0	0
$708$	−0.693163	−0.0260507
$709$	0.454399	0.0170653	0.00853265	−	0.999964i	$-0.497284\pi$
$709$	0.454399	0.0170653	0.00853265	+	0.999964i	$0.497284\pi$
$710$	18.9341	0.710585
$711$	−27.6989	−1.03879
$712$	6.63221	0.248553
$713$	7.42250	0.277975
$714$	0	0
$715$	−15.6465	−0.585144
$716$	−9.75292	−0.364484
$717$	−57.1447	−2.13411
$718$	−6.09871	−0.227602
$719$	−7.23912	−0.269974	−0.134987	−	0.990847i	$-0.543099\pi$
$719$	−7.23912	−0.269974	−0.134987	+	0.990847i	$0.543099\pi$
$720$	42.0352	1.56656
$721$	0	0
$722$	9.69901	0.360960
$723$	−57.4817	−2.13777
$724$	5.67589	0.210943
$725$	−137.319	−5.09989
$726$	−20.4129	−0.757594
$727$	40.3129	1.49512	0.747561	−	0.664193i	$-0.231225\pi$
$727$	40.3129	1.49512	0.747561	+	0.664193i	$0.231225\pi$
$728$	0	0
$729$	−33.2864	−1.23283
$730$	5.77318	0.213675
$731$	−3.62174	−0.133955
$732$	11.1754	0.413056
$733$	−0.541451	−0.0199989	−0.00999947	−	0.999950i	$-0.503183\pi$
$733$	−0.541451	−0.0199989	−0.00999947	+	0.999950i	$0.503183\pi$
$734$	−2.63584	−0.0972908
$735$	0	0
$736$	−5.95610	−0.219545
$737$	19.9296	0.734115
$738$	3.69923	0.136171
$739$	29.1238	1.07134	0.535668	−	0.844429i	$-0.320060\pi$
$739$	29.1238	1.07134	0.535668	+	0.844429i	$0.320060\pi$
$740$	6.04200	0.222108
$741$	4.52333	0.166169
$742$	0	0
$743$	43.7759	1.60598	0.802991	−	0.595991i	$-0.203240\pi$
$743$	43.7759	1.60598	0.802991	+	0.595991i	$0.203240\pi$
$744$	48.5615	1.78035
$745$	−83.6272	−3.06387
$746$	10.0544	0.368117
$747$	−8.93879	−0.327053
$748$	−2.74315	−0.100300
$749$	0	0
$750$	−75.3629	−2.75186
$751$	16.4783	0.601301	0.300650	−	0.953734i	$-0.402796\pi$
$751$	16.4783	0.601301	0.300650	+	0.953734i	$0.402796\pi$
$752$	11.0231	0.401972
$753$	−23.7260	−0.864623
$754$	4.84481	0.176438
$755$	−20.8760	−0.759757
$756$	0	0
$757$	38.6380	1.40432	0.702161	−	0.712018i	$-0.252218\pi$
$757$	38.6380	1.40432	0.702161	+	0.712018i	$0.252218\pi$
$758$	−11.2096	−0.407152
$759$	−14.3805	−0.521980
$760$	20.0714	0.728067
$761$	4.95857	0.179748	0.0898741	−	0.995953i	$-0.471354\pi$
$761$	4.95857	0.179748	0.0898741	+	0.995953i	$0.471354\pi$
$762$	10.7799	0.390514
$763$	0	0
$764$	−26.9571	−0.975272
$765$	−9.30730	−0.336506
$766$	19.8648	0.717744
$767$	0.113861	0.00411127
$768$	−23.2488	−0.838918
$769$	−31.4465	−1.13399	−0.566995	−	0.823721i	$-0.691894\pi$
$769$	−31.4465	−1.13399	−0.566995	+	0.823721i	$0.691894\pi$
$770$	0	0
$771$	70.1074	2.52486
$772$	0.234191	0.00842872
$773$	39.1351	1.40759	0.703796	−	0.710402i	$-0.251487\pi$
$773$	39.1351	1.40759	0.703796	+	0.710402i	$0.251487\pi$
$774$	−36.0525	−1.29588
$775$	99.9331	3.58970
$776$	−37.6157	−1.35032
$777$	0	0
$778$	17.8114	0.638568
$779$	−1.98942	−0.0712785
$780$	−15.7250	−0.563045
$781$	31.3420	1.12150
$782$	0.250188	0.00894669
$783$	−79.0305	−2.82432
$784$	0	0
$785$	−39.2820	−1.40204
$786$	3.27673	0.116877
$787$	−39.9046	−1.42245	−0.711223	−	0.702967i	$-0.751858\pi$
$787$	−39.9046	−1.42245	−0.711223	+	0.702967i	$0.751858\pi$
$788$	−0.846393	−0.0301515
$789$	−16.0262	−0.570548
$790$	13.5900	0.483510
$791$	0	0
$792$	−61.7793	−2.19523
$793$	−1.83571	−0.0651878
$794$	−1.35027	−0.0479191
$795$	132.193	4.68841
$796$	−30.3407	−1.07540
$797$	50.4521	1.78710	0.893552	−	0.448960i	$-0.148206\pi$
$797$	50.4521	1.78710	0.893552	+	0.448960i	$0.148206\pi$
$798$	0	0
$799$	−2.44071	−0.0863460
$800$	−80.1901	−2.83515
$801$	16.4641	0.581731
$802$	8.86373	0.312989
$803$	9.55645	0.337240
$804$	20.0296	0.706390
$805$	0	0
$806$	−3.52579	−0.124191
$807$	−87.6209	−3.08440
$808$	−35.9977	−1.26640
$809$	15.3353	0.539162	0.269581	−	0.962978i	$-0.413115\pi$
$809$	15.3353	0.539162	0.269581	+	0.962978i	$0.413115\pi$
$810$	−18.8687	−0.662977
$811$	−18.0593	−0.634147	−0.317074	−	0.948401i	$-0.602700\pi$
$811$	−18.0593	−0.634147	−0.317074	+	0.948401i	$0.602700\pi$
$812$	0	0
$813$	17.9063	0.628002
$814$	−2.62465	−0.0919938
$815$	66.9629	2.34561
$816$	−1.84357	−0.0645378
$817$	19.3889	0.678330
$818$	−18.5388	−0.648194
$819$	0	0
$820$	6.91607	0.241520
$821$	−14.3533	−0.500933	−0.250467	−	0.968125i	$-0.580584\pi$
$821$	−14.3533	−0.500933	−0.250467	+	0.968125i	$0.580584\pi$
$822$	19.7893	0.690232
$823$	16.2866	0.567716	0.283858	−	0.958866i	$-0.408386\pi$
$823$	16.2866	0.567716	0.283858	+	0.958866i	$0.408386\pi$
$824$	1.58993	0.0553877
$825$	−193.613	−6.74073
$826$	0	0
$827$	−39.4877	−1.37312	−0.686561	−	0.727072i	$-0.740881\pi$
$827$	−39.4877	−1.37312	−0.686561	+	0.727072i	$0.740881\pi$
$828$	−9.49020	−0.329807
$829$	54.5376	1.89417	0.947084	−	0.320985i	$-0.104014\pi$
$829$	54.5376	1.89417	0.947084	+	0.320985i	$0.104014\pi$
$830$	4.38567	0.152229
$831$	48.4333	1.68013
$832$	0.247213	0.00857056
$833$	0	0
$834$	−2.38674	−0.0826462
$835$	−4.43065	−0.153329
$836$	14.6854	0.507904
$837$	57.5140	1.98798
$838$	12.5127	0.432245
$839$	−40.3930	−1.39452	−0.697260	−	0.716818i	$-0.745598\pi$
$839$	−40.3930	−1.39452	−0.697260	+	0.716818i	$0.745598\pi$
$840$	0	0
$841$	66.4175	2.29026
$842$	20.8103	0.717169
$843$	−6.21605	−0.214092
$844$	26.7800	0.921805
$845$	−54.1687	−1.86346
$846$	−24.2960	−0.835313
$847$	0	0
$848$	17.1937	0.590435
$849$	37.1110	1.27365
$850$	3.36841	0.115536
$851$	−0.912174	−0.0312689
$852$	31.4993	1.07915
$853$	46.2729	1.58435	0.792177	−	0.610292i	$-0.208948\pi$
$853$	46.2729	1.58435	0.792177	+	0.610292i	$0.208948\pi$
$854$	0	0
$855$	49.8263	1.70402
$856$	−11.4720	−0.392106
$857$	−14.3855	−0.491398	−0.245699	−	0.969346i	$-0.579017\pi$
$857$	−14.3855	−0.491398	−0.245699	+	0.969346i	$0.579017\pi$
$858$	6.83095	0.233205
$859$	24.1886	0.825303	0.412652	−	0.910889i	$-0.364603\pi$
$859$	24.1886	0.825303	0.412652	+	0.910889i	$0.364603\pi$
$860$	−67.4038	−2.29845
$861$	0	0
$862$	−24.3145	−0.828154
$863$	39.5689	1.34694	0.673470	−	0.739215i	$-0.264803\pi$
$863$	39.5689	1.34694	0.673470	+	0.739215i	$0.264803\pi$
$864$	−46.1514	−1.57010
$865$	−44.3378	−1.50753
$866$	11.7319	0.398666
$867$	−49.8415	−1.69271
$868$	0	0
$869$	22.4958	0.763117
$870$	81.2738	2.75544
$871$	−3.29012	−0.111481
$872$	33.2890	1.12731
$873$	−93.3791	−3.16040
$874$	−1.33937	−0.0453049
$875$	0	0
$876$	9.60442	0.324503
$877$	42.4365	1.43298	0.716489	−	0.697598i	$-0.245748\pi$
$877$	42.4365	1.43298	0.716489	+	0.697598i	$0.245748\pi$
$878$	0.473960	0.0159954
$879$	42.2379	1.42465
$880$	−34.1390	−1.15083
$881$	52.4981	1.76871	0.884353	−	0.466818i	$-0.154600\pi$
$881$	52.4981	1.76871	0.884353	+	0.466818i	$0.154600\pi$
$882$	0	0
$883$	−22.0554	−0.742225	−0.371112	−	0.928588i	$-0.621024\pi$
$883$	−22.0554	−0.742225	−0.371112	+	0.928588i	$0.621024\pi$
$884$	0.452859	0.0152313
$885$	1.91006	0.0642061
$886$	−14.9664	−0.502806
$887$	15.7621	0.529240	0.264620	−	0.964353i	$-0.414753\pi$
$887$	15.7621	0.529240	0.264620	+	0.964353i	$0.414753\pi$
$888$	−5.96788	−0.200269
$889$	0	0
$890$	−8.07785	−0.270770
$891$	−31.2336	−1.04637
$892$	−10.4244	−0.349036
$893$	13.0662	0.437245
$894$	36.5101	1.22108
$895$	26.8749	0.898329
$896$	0	0
$897$	2.37404	0.0792669
$898$	−22.9810	−0.766887
$899$	−69.4396	−2.31594
$900$	−127.772	−4.25906
$901$	−3.80698	−0.126829
$902$	−3.00434	−0.100034
$903$	0	0
$904$	−9.63492	−0.320453
$905$	−15.6403	−0.519902
$906$	9.11408	0.302795
$907$	−46.9887	−1.56024	−0.780118	−	0.625633i	$-0.784841\pi$
$907$	−46.9887	−1.56024	−0.780118	+	0.625633i	$0.784841\pi$
$908$	−14.6356	−0.485699
$909$	−89.3625	−2.96397
$910$	0	0
$911$	12.9195	0.428041	0.214021	−	0.976829i	$-0.431344\pi$
$911$	12.9195	0.428041	0.214021	+	0.976829i	$0.431344\pi$
$912$	9.86947	0.326811
$913$	7.25968	0.240260
$914$	−1.89330	−0.0626248
$915$	−30.7948	−1.01804
$916$	−12.4456	−0.411213
$917$	0	0
$918$	1.93861	0.0639835
$919$	42.0587	1.38739	0.693695	−	0.720269i	$-0.255982\pi$
$919$	42.0587	1.38739	0.693695	+	0.720269i	$0.255982\pi$
$920$	10.5343	0.347307
$921$	−21.8379	−0.719582
$922$	19.6777	0.648052
$923$	−5.17416	−0.170309
$924$	0	0
$925$	−12.2811	−0.403800
$926$	−8.60721	−0.282850
$927$	3.94691	0.129634
$928$	55.7210	1.82913
$929$	12.4186	0.407442	0.203721	−	0.979029i	$-0.434697\pi$
$929$	12.4186	0.407442	0.203721	+	0.979029i	$0.434697\pi$
$930$	−59.1466	−1.93949
$931$	0	0
$932$	−34.6532	−1.13510
$933$	−71.6221	−2.34480
$934$	−12.1154	−0.396426
$935$	7.55896	0.247204
$936$	10.1990	0.333364
$937$	44.1369	1.44189	0.720945	−	0.692992i	$-0.243708\pi$
$937$	44.1369	1.44189	0.720945	+	0.692992i	$0.243708\pi$
$938$	0	0
$939$	3.06537	0.100035
$940$	−45.4237	−1.48156
$941$	37.0967	1.20932	0.604659	−	0.796484i	$-0.293309\pi$
$941$	37.0967	1.20932	0.604659	+	0.796484i	$0.293309\pi$
$942$	17.1498	0.558770
$943$	−1.04414	−0.0340017
$944$	0.248433	0.00808580
$945$	0	0
$946$	29.2802	0.951982
$947$	39.3959	1.28020	0.640098	−	0.768294i	$-0.278894\pi$
$947$	39.3959	1.28020	0.640098	+	0.768294i	$0.278894\pi$
$948$	22.6087	0.734296
$949$	−1.57765	−0.0512126
$950$	−18.0327	−0.585057
$951$	−18.2186	−0.590779
$952$	0	0
$953$	−5.41687	−0.175470	−0.0877348	−	0.996144i	$-0.527963\pi$
$953$	−5.41687	−0.175470	−0.0877348	+	0.996144i	$0.527963\pi$
$954$	−37.8965	−1.22695
$955$	74.2822	2.40371
$956$	30.6278	0.990572
$957$	134.534	4.34887
$958$	11.7651	0.380114
$959$	0	0
$960$	4.14710	0.133847
$961$	19.5343	0.630139
$962$	0.433295	0.0139700
$963$	−28.4787	−0.917715
$964$	30.8084	0.992270
$965$	−0.645331	−0.0207740
$966$	0	0
$967$	10.5433	0.339048	0.169524	−	0.985526i	$-0.445777\pi$
$967$	10.5433	0.339048	0.169524	+	0.985526i	$0.445777\pi$
$968$	24.7525	0.795575
$969$	−2.18527	−0.0702009
$970$	45.8149	1.47103
$971$	−11.7624	−0.377473	−0.188736	−	0.982028i	$-0.560439\pi$
$971$	−11.7624	−0.377473	−0.188736	+	0.982028i	$0.560439\pi$
$972$	7.06216	0.226519
$973$	0	0
$974$	4.26267	0.136585
$975$	31.9630	1.02363
$976$	−4.00533	−0.128207
$977$	14.9836	0.479369	0.239685	−	0.970851i	$-0.422956\pi$
$977$	14.9836	0.479369	0.239685	+	0.970851i	$0.422956\pi$
$978$	−29.2347	−0.934823
$979$	−13.3714	−0.427352
$980$	0	0
$981$	82.6384	2.63844
$982$	−23.7210	−0.756967
$983$	30.3743	0.968791	0.484396	−	0.874849i	$-0.339040\pi$
$983$	30.3743	0.968791	0.484396	+	0.874849i	$0.339040\pi$
$984$	−6.83123	−0.217772
$985$	2.33230	0.0743132
$986$	−2.34058	−0.0745391
$987$	0	0
$988$	−2.42436	−0.0771293
$989$	10.1761	0.323581
$990$	75.2455	2.39146
$991$	−62.0328	−1.97054	−0.985268	−	0.171019i	$-0.945294\pi$
$991$	−62.0328	−1.97054	−0.985268	+	0.171019i	$0.945294\pi$
$992$	−40.5507	−1.28748
$993$	23.0982	0.732998
$994$	0	0
$995$	83.6061	2.65049
$996$	7.29612	0.231186
$997$	8.39532	0.265882	0.132941	−	0.991124i	$-0.457558\pi$
$997$	8.39532	0.265882	0.132941	+	0.991124i	$0.457558\pi$
$998$	−19.4314	−0.615090
$999$	−7.06808	−0.223624

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.o.1.3		6
7.6	odd	2		287.2.a.f.1.3	✓	6
21.20	even	2		2583.2.a.t.1.4		6
28.27	even	2		4592.2.a.bg.1.6		6
35.34	odd	2		7175.2.a.p.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.a.f.1.3	✓	6	7.6	odd	2
2009.2.a.o.1.3		6	1.1	even	1	trivial
2583.2.a.t.1.4		6	21.20	even	2
4592.2.a.bg.1.6		6	28.27	even	2
7175.2.a.p.1.4		6	35.34	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:	\( N \)	\(=\)	\( 2009 = 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2009.a (trivial)

\(f(q)\)	\(=\)	\(q-0.644787 q^{2} +2.95586 q^{3} -1.58425 q^{4} +4.36552 q^{5} -1.90590 q^{6} +2.31108 q^{8} +5.73713 q^{9} +O(q^{10})\)	\(q-0.644787 q^{2} +2.95586 q^{3} -1.58425 q^{4} +4.36552 q^{5} -1.90590 q^{6} +2.31108 q^{8} +5.73713 q^{9} -2.81483 q^{10} -4.65944 q^{11} -4.68283 q^{12} +0.769213 q^{13} +12.9039 q^{15} +1.67835 q^{16} -0.371615 q^{17} -3.69923 q^{18} +1.98942 q^{19} -6.91607 q^{20} +3.00434 q^{22} +1.04414 q^{23} +6.83123 q^{24} +14.0578 q^{25} -0.495979 q^{26} +8.09060 q^{27} -9.76819 q^{29} -8.32026 q^{30} +7.10875 q^{31} -5.70433 q^{32} -13.7727 q^{33} +0.239612 q^{34} -9.08905 q^{36} -0.873617 q^{37} -1.28275 q^{38} +2.27369 q^{39} +10.0891 q^{40} -1.00000 q^{41} +9.74596 q^{43} +7.38171 q^{44} +25.0456 q^{45} -0.673245 q^{46} +6.56785 q^{47} +4.96097 q^{48} -9.06426 q^{50} -1.09844 q^{51} -1.21863 q^{52} +10.2444 q^{53} -5.21671 q^{54} -20.3409 q^{55} +5.88047 q^{57} +6.29840 q^{58} +0.148022 q^{59} -20.4430 q^{60} -2.38647 q^{61} -4.58363 q^{62} +0.321384 q^{64} +3.35801 q^{65} +8.88044 q^{66} -4.27725 q^{67} +0.588730 q^{68} +3.08632 q^{69} -6.72656 q^{71} +13.2590 q^{72} -2.05099 q^{73} +0.563297 q^{74} +41.5528 q^{75} -3.15175 q^{76} -1.46605 q^{78} -4.82800 q^{79} +7.32686 q^{80} +6.70330 q^{81} +0.644787 q^{82} -1.55806 q^{83} -1.62229 q^{85} -6.28407 q^{86} -28.8734 q^{87} -10.7683 q^{88} +2.86975 q^{89} -16.1491 q^{90} -1.65417 q^{92} +21.0125 q^{93} -4.23486 q^{94} +8.68487 q^{95} -16.8612 q^{96} -16.2763 q^{97} -26.7318 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} + 4 q^{3} + 9 q^{4} + q^{5} + 4 q^{6} + 3 q^{8} + 14 q^{9}+O(q^{10}) \) 6 * q - q^2 + 4 * q^3 + 9 * q^4 + q^5 + 4 * q^6 + 3 * q^8 + 14 * q^9	\( 6 q - q^{2} + 4 q^{3} + 9 q^{4} + q^{5} + 4 q^{6} + 3 q^{8} + 14 q^{9} - 10 q^{10} + 6 q^{11} - 9 q^{12} - 7 q^{13} - 13 q^{15} + 7 q^{16} - 7 q^{17} - 5 q^{18} - 2 q^{19} - 11 q^{20} + 15 q^{22} + 20 q^{23} + 36 q^{24} + 29 q^{25} + 43 q^{26} - 2 q^{27} - 9 q^{29} + 13 q^{30} + 27 q^{31} - 10 q^{32} - 17 q^{33} - 6 q^{34} + 29 q^{36} + 19 q^{37} + 23 q^{38} + q^{39} - 23 q^{40} - 6 q^{41} + 19 q^{43} + 21 q^{44} + 35 q^{45} - 8 q^{46} + 19 q^{47} + 9 q^{48} - 58 q^{50} - 19 q^{51} + 5 q^{53} + 37 q^{54} - 3 q^{55} + 37 q^{57} + 13 q^{58} + 7 q^{59} - 110 q^{60} + 12 q^{61} - 37 q^{64} - 13 q^{65} + 54 q^{66} + 27 q^{67} - 31 q^{68} - 16 q^{69} - 6 q^{71} + 5 q^{72} - 52 q^{73} - 14 q^{74} + 46 q^{75} - 13 q^{76} - 45 q^{78} + 26 q^{80} - 22 q^{81} + q^{82} - 12 q^{83} + 25 q^{85} - 10 q^{86} - 42 q^{87} - 2 q^{88} + 38 q^{89} - 93 q^{90} + 45 q^{92} + 33 q^{93} + 8 q^{94} + q^{95} + 12 q^{96} - 8 q^{97} + q^{99}+O(q^{100}) \) 6 * q - q^2 + 4 * q^3 + 9 * q^4 + q^5 + 4 * q^6 + 3 * q^8 + 14 * q^9 - 10 * q^10 + 6 * q^11 - 9 * q^12 - 7 * q^13 - 13 * q^15 + 7 * q^16 - 7 * q^17 - 5 * q^18 - 2 * q^19 - 11 * q^20 + 15 * q^22 + 20 * q^23 + 36 * q^24 + 29 * q^25 + 43 * q^26 - 2 * q^27 - 9 * q^29 + 13 * q^30 + 27 * q^31 - 10 * q^32 - 17 * q^33 - 6 * q^34 + 29 * q^36 + 19 * q^37 + 23 * q^38 + q^39 - 23 * q^40 - 6 * q^41 + 19 * q^43 + 21 * q^44 + 35 * q^45 - 8 * q^46 + 19 * q^47 + 9 * q^48 - 58 * q^50 - 19 * q^51 + 5 * q^53 + 37 * q^54 - 3 * q^55 + 37 * q^57 + 13 * q^58 + 7 * q^59 - 110 * q^60 + 12 * q^61 - 37 * q^64 - 13 * q^65 + 54 * q^66 + 27 * q^67 - 31 * q^68 - 16 * q^69 - 6 * q^71 + 5 * q^72 - 52 * q^73 - 14 * q^74 + 46 * q^75 - 13 * q^76 - 45 * q^78 + 26 * q^80 - 22 * q^81 + q^82 - 12 * q^83 + 25 * q^85 - 10 * q^86 - 42 * q^87 - 2 * q^88 + 38 * q^89 - 93 * q^90 + 45 * q^92 + 33 * q^93 + 8 * q^94 + q^95 + 12 * q^96 - 8 * q^97 + q^99

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