LMFDB - Embedded newform 2001.2.a.n.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,2,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.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:	$15.9780654445$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} - 28 x^{14} + 27 x^{13} + 316 x^{12} - 295 x^{11} - 1835 x^{10} + 1665 x^{9} + \cdots - 192 $ x^16 - x^15 - 28x^14 + 27x^13 + 316x^12 - 295x^11 - 1835x^10 + 1665x^9 + 5778x^8 - 5124x^7 - 9405x^6 + 8288x^5 + 6405x^4 - 6032x^3 - 400x^2 + 1088x - 192
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.563182$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.563182 q^{2} +1.00000 q^{3} -1.68283 q^{4} -1.59433 q^{5} -0.563182 q^{6} +4.95339 q^{7} +2.07410 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.563182 q^{2} +1.00000 q^{3} -1.68283 q^{4} -1.59433 q^{5} -0.563182 q^{6} +4.95339 q^{7} +2.07410 q^{8} +1.00000 q^{9} +0.897897 q^{10} -0.616624 q^{11} -1.68283 q^{12} +6.48438 q^{13} -2.78966 q^{14} -1.59433 q^{15} +2.19756 q^{16} -1.67611 q^{17} -0.563182 q^{18} +2.69708 q^{19} +2.68298 q^{20} +4.95339 q^{21} +0.347272 q^{22} -1.00000 q^{23} +2.07410 q^{24} -2.45812 q^{25} -3.65188 q^{26} +1.00000 q^{27} -8.33570 q^{28} -1.00000 q^{29} +0.897897 q^{30} -3.94303 q^{31} -5.38583 q^{32} -0.616624 q^{33} +0.943955 q^{34} -7.89733 q^{35} -1.68283 q^{36} +5.81974 q^{37} -1.51895 q^{38} +6.48438 q^{39} -3.30680 q^{40} -6.01020 q^{41} -2.78966 q^{42} +0.472349 q^{43} +1.03767 q^{44} -1.59433 q^{45} +0.563182 q^{46} +4.27730 q^{47} +2.19756 q^{48} +17.5361 q^{49} +1.38437 q^{50} -1.67611 q^{51} -10.9121 q^{52} -7.82304 q^{53} -0.563182 q^{54} +0.983101 q^{55} +10.2738 q^{56} +2.69708 q^{57} +0.563182 q^{58} +11.6621 q^{59} +2.68298 q^{60} +10.3582 q^{61} +2.22064 q^{62} +4.95339 q^{63} -1.36191 q^{64} -10.3382 q^{65} +0.347272 q^{66} -6.36345 q^{67} +2.82060 q^{68} -1.00000 q^{69} +4.44764 q^{70} +8.81789 q^{71} +2.07410 q^{72} -2.13920 q^{73} -3.27757 q^{74} -2.45812 q^{75} -4.53872 q^{76} -3.05438 q^{77} -3.65188 q^{78} -11.9951 q^{79} -3.50362 q^{80} +1.00000 q^{81} +3.38484 q^{82} +10.2126 q^{83} -8.33570 q^{84} +2.67227 q^{85} -0.266019 q^{86} -1.00000 q^{87} -1.27894 q^{88} -6.30439 q^{89} +0.897897 q^{90} +32.1197 q^{91} +1.68283 q^{92} -3.94303 q^{93} -2.40890 q^{94} -4.30003 q^{95} -5.38583 q^{96} +11.9110 q^{97} -9.87603 q^{98} -0.616624 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9}+O(q^{10}) $ 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9	\( 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9} + 11 q^{10} + 8 q^{11} + 25 q^{12} + 19 q^{13} + 16 q^{14} + 3 q^{15} + 31 q^{16} - 4 q^{17} - q^{18} + 19 q^{19} + 16 q^{20} + 13 q^{21} + 6 q^{22} - 16 q^{23} + 23 q^{25} - 15 q^{26} + 16 q^{27} + 18 q^{28} - 16 q^{29} + 11 q^{30} + 24 q^{31} - 21 q^{32} + 8 q^{33} - 9 q^{34} - 13 q^{35} + 25 q^{36} + 26 q^{37} + 19 q^{39} - 22 q^{40} - 15 q^{41} + 16 q^{42} + 33 q^{43} + 6 q^{44} + 3 q^{45} + q^{46} + 13 q^{47} + 31 q^{48} + 41 q^{49} + 13 q^{50} - 4 q^{51} - 26 q^{52} + 5 q^{53} - q^{54} + 9 q^{55} + 40 q^{56} + 19 q^{57} + q^{58} + 2 q^{59} + 16 q^{60} + 29 q^{61} - 32 q^{62} + 13 q^{63} + 28 q^{64} + 18 q^{65} + 6 q^{66} + 32 q^{67} - 26 q^{68} - 16 q^{69} + 18 q^{70} + 29 q^{71} + 19 q^{73} - 16 q^{74} + 23 q^{75} + 64 q^{76} - 21 q^{77} - 15 q^{78} + 56 q^{79} + 16 q^{81} + 14 q^{82} + 5 q^{83} + 18 q^{84} + 16 q^{85} - 20 q^{86} - 16 q^{87} + q^{88} + 7 q^{89} + 11 q^{90} - 6 q^{91} - 25 q^{92} + 24 q^{93} - 11 q^{94} + 39 q^{95} - 21 q^{96} + 35 q^{97} - 109 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9 + 11 * q^10 + 8 * q^11 + 25 * q^12 + 19 * q^13 + 16 * q^14 + 3 * q^15 + 31 * q^16 - 4 * q^17 - q^18 + 19 * q^19 + 16 * q^20 + 13 * q^21 + 6 * q^22 - 16 * q^23 + 23 * q^25 - 15 * q^26 + 16 * q^27 + 18 * q^28 - 16 * q^29 + 11 * q^30 + 24 * q^31 - 21 * q^32 + 8 * q^33 - 9 * q^34 - 13 * q^35 + 25 * q^36 + 26 * q^37 + 19 * q^39 - 22 * q^40 - 15 * q^41 + 16 * q^42 + 33 * q^43 + 6 * q^44 + 3 * q^45 + q^46 + 13 * q^47 + 31 * q^48 + 41 * q^49 + 13 * q^50 - 4 * q^51 - 26 * q^52 + 5 * q^53 - q^54 + 9 * q^55 + 40 * q^56 + 19 * q^57 + q^58 + 2 * q^59 + 16 * q^60 + 29 * q^61 - 32 * q^62 + 13 * q^63 + 28 * q^64 + 18 * q^65 + 6 * q^66 + 32 * q^67 - 26 * q^68 - 16 * q^69 + 18 * q^70 + 29 * q^71 + 19 * q^73 - 16 * q^74 + 23 * q^75 + 64 * q^76 - 21 * q^77 - 15 * q^78 + 56 * q^79 + 16 * q^81 + 14 * q^82 + 5 * q^83 + 18 * q^84 + 16 * q^85 - 20 * q^86 - 16 * q^87 + q^88 + 7 * q^89 + 11 * q^90 - 6 * q^91 - 25 * q^92 + 24 * q^93 - 11 * q^94 + 39 * q^95 - 21 * q^96 + 35 * q^97 - 109 * q^98 + 8 * 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 $

$2$	−0.563182	−0.398230	−0.199115	−	0.979976i	$-0.563807\pi$
$2$	−0.563182	−0.398230	−0.199115	+	0.979976i	$0.563807\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.68283	−0.841413
$5$	−1.59433	−0.713005	−0.356503	−	0.934294i	$-0.616031\pi$
$5$	−1.59433	−0.713005	−0.356503	+	0.934294i	$0.616031\pi$
$6$	−0.563182	−0.229918
$7$	4.95339	1.87221	0.936104	−	0.351724i	$-0.114405\pi$
$7$	4.95339	1.87221	0.936104	+	0.351724i	$0.114405\pi$
$8$	2.07410	0.733306
$9$	1.00000	0.333333
$10$	0.897897	0.283940
$11$	−0.616624	−0.185919	−0.0929596	−	0.995670i	$-0.529633\pi$
$11$	−0.616624	−0.185919	−0.0929596	+	0.995670i	$0.529633\pi$
$12$	−1.68283	−0.485790
$13$	6.48438	1.79844	0.899221	−	0.437494i	$-0.144134\pi$
$13$	6.48438	1.79844	0.899221	+	0.437494i	$0.144134\pi$
$14$	−2.78966	−0.745569
$15$	−1.59433	−0.411654
$16$	2.19756	0.549389
$17$	−1.67611	−0.406516	−0.203258	−	0.979125i	$-0.565153\pi$
$17$	−1.67611	−0.406516	−0.203258	+	0.979125i	$0.565153\pi$
$18$	−0.563182	−0.132743
$19$	2.69708	0.618753	0.309376	−	0.950940i	$-0.399880\pi$
$19$	2.69708	0.618753	0.309376	+	0.950940i	$0.399880\pi$
$20$	2.68298	0.599932
$21$	4.95339	1.08092
$22$	0.347272	0.0740386
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.07410	0.423374
$25$	−2.45812	−0.491624
$26$	−3.65188	−0.716193
$27$	1.00000	0.192450
$28$	−8.33570	−1.57530
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0.897897	0.163933
$31$	−3.94303	−0.708188	−0.354094	−	0.935210i	$-0.615211\pi$
$31$	−3.94303	−0.708188	−0.354094	+	0.935210i	$0.615211\pi$
$32$	−5.38583	−0.952089
$33$	−0.616624	−0.107341
$34$	0.943955	0.161887
$35$	−7.89733	−1.33489
$36$	−1.68283	−0.280471
$37$	5.81974	0.956759	0.478379	−	0.878153i	$-0.341224\pi$
$37$	5.81974	0.956759	0.478379	+	0.878153i	$0.341224\pi$
$38$	−1.51895	−0.246406
$39$	6.48438	1.03833
$40$	−3.30680	−0.522851
$41$	−6.01020	−0.938636	−0.469318	−	0.883029i	$-0.655500\pi$
$41$	−6.01020	−0.938636	−0.469318	+	0.883029i	$0.655500\pi$
$42$	−2.78966	−0.430454
$43$	0.472349	0.0720326	0.0360163	−	0.999351i	$-0.488533\pi$
$43$	0.472349	0.0720326	0.0360163	+	0.999351i	$0.488533\pi$
$44$	1.03767	0.156435
$45$	−1.59433	−0.237668
$46$	0.563182	0.0830367
$47$	4.27730	0.623909	0.311954	−	0.950097i	$-0.399016\pi$
$47$	4.27730	0.623909	0.311954	+	0.950097i	$0.399016\pi$
$48$	2.19756	0.317190
$49$	17.5361	2.50516
$50$	1.38437	0.195779
$51$	−1.67611	−0.234702
$52$	−10.9121	−1.51323
$53$	−7.82304	−1.07458	−0.537288	−	0.843399i	$-0.680551\pi$
$53$	−7.82304	−1.07458	−0.537288	+	0.843399i	$0.680551\pi$
$54$	−0.563182	−0.0766394
$55$	0.983101	0.132561
$56$	10.2738	1.37290
$57$	2.69708	0.357237
$58$	0.563182	0.0739494
$59$	11.6621	1.51827	0.759137	−	0.650930i	$-0.225621\pi$
$59$	11.6621	1.51827	0.759137	+	0.650930i	$0.225621\pi$
$60$	2.68298	0.346371
$61$	10.3582	1.32623	0.663115	−	0.748517i	$-0.269234\pi$
$61$	10.3582	1.32623	0.663115	+	0.748517i	$0.269234\pi$
$62$	2.22064	0.282022
$63$	4.95339	0.624069
$64$	−1.36191	−0.170239
$65$	−10.3382	−1.28230
$66$	0.347272	0.0427462
$67$	−6.36345	−0.777420	−0.388710	−	0.921360i	$-0.627079\pi$
$67$	−6.36345	−0.777420	−0.388710	+	0.921360i	$0.627079\pi$
$68$	2.82060	0.342048
$69$	−1.00000	−0.120386
$70$	4.44764	0.531594
$71$	8.81789	1.04649	0.523246	−	0.852182i	$-0.324721\pi$
$71$	8.81789	1.04649	0.523246	+	0.852182i	$0.324721\pi$
$72$	2.07410	0.244435
$73$	−2.13920	−0.250375	−0.125187	−	0.992133i	$-0.539953\pi$
$73$	−2.13920	−0.250375	−0.125187	+	0.992133i	$0.539953\pi$
$74$	−3.27757	−0.381010
$75$	−2.45812	−0.283839
$76$	−4.53872	−0.520626
$77$	−3.05438	−0.348079
$78$	−3.65188	−0.413494
$79$	−11.9951	−1.34956	−0.674780	−	0.738019i	$-0.735761\pi$
$79$	−11.9951	−1.34956	−0.674780	+	0.738019i	$0.735761\pi$
$80$	−3.50362	−0.391717
$81$	1.00000	0.111111
$82$	3.38484	0.373793
$83$	10.2126	1.12098	0.560490	−	0.828161i	$-0.310613\pi$
$83$	10.2126	1.12098	0.560490	+	0.828161i	$0.310613\pi$
$84$	−8.33570	−0.909500
$85$	2.67227	0.289848
$86$	−0.266019	−0.0286855
$87$	−1.00000	−0.107211
$88$	−1.27894	−0.136336
$89$	−6.30439	−0.668264	−0.334132	−	0.942526i	$-0.608443\pi$
$89$	−6.30439	−0.668264	−0.334132	+	0.942526i	$0.608443\pi$
$90$	0.897897	0.0946466
$91$	32.1197	3.36706
$92$	1.68283	0.175447
$93$	−3.94303	−0.408873
$94$	−2.40890	−0.248459
$95$	−4.30003	−0.441174
$96$	−5.38583	−0.549689
$97$	11.9110	1.20938	0.604691	−	0.796461i	$-0.293297\pi$
$97$	11.9110	1.20938	0.604691	+	0.796461i	$0.293297\pi$
$98$	−9.87603	−0.997630
$99$	−0.616624	−0.0619731
$100$	4.13659	0.413659
$101$	4.59685	0.457404	0.228702	−	0.973496i	$-0.426552\pi$
$101$	4.59685	0.457404	0.228702	+	0.973496i	$0.426552\pi$
$102$	0.943955	0.0934655
$103$	4.58092	0.451372	0.225686	−	0.974200i	$-0.427538\pi$
$103$	4.58092	0.451372	0.225686	+	0.974200i	$0.427538\pi$
$104$	13.4493	1.31881
$105$	−7.89733	−0.770701
$106$	4.40579	0.427929
$107$	9.04500	0.874413	0.437207	−	0.899361i	$-0.355968\pi$
$107$	9.04500	0.874413	0.437207	+	0.899361i	$0.355968\pi$
$108$	−1.68283	−0.161930
$109$	−16.0639	−1.53864	−0.769320	−	0.638864i	$-0.779405\pi$
$109$	−16.0639	−1.53864	−0.769320	+	0.638864i	$0.779405\pi$
$110$	−0.553665	−0.0527899
$111$	5.81974	0.552385
$112$	10.8854	1.02857
$113$	18.3897	1.72996	0.864978	−	0.501809i	$-0.167332\pi$
$113$	18.3897	1.72996	0.864978	+	0.501809i	$0.167332\pi$
$114$	−1.51895	−0.142262
$115$	1.59433	0.148672
$116$	1.68283	0.156246
$117$	6.48438	0.599481
$118$	−6.56788	−0.604622
$119$	−8.30243	−0.761083
$120$	−3.30680	−0.301868
$121$	−10.6198	−0.965434
$122$	−5.83355	−0.528144
$123$	−6.01020	−0.541922
$124$	6.63543	0.595879
$125$	11.8907	1.06354
$126$	−2.78966	−0.248523
$127$	4.34065	0.385171	0.192585	−	0.981280i	$-0.438313\pi$
$127$	4.34065	0.385171	0.192585	+	0.981280i	$0.438313\pi$
$128$	11.5387	1.01988
$129$	0.472349	0.0415880
$130$	5.82230	0.510650
$131$	14.2331	1.24355	0.621776	−	0.783195i	$-0.286411\pi$
$131$	14.2331	1.24355	0.621776	+	0.783195i	$0.286411\pi$
$132$	1.03767	0.0903177
$133$	13.3597	1.15843
$134$	3.58378	0.309592
$135$	−1.59433	−0.137218
$136$	−3.47642	−0.298101
$137$	10.4871	0.895977	0.447988	−	0.894039i	$-0.352141\pi$
$137$	10.4871	0.895977	0.447988	+	0.894039i	$0.352141\pi$
$138$	0.563182	0.0479412
$139$	−19.5982	−1.66230	−0.831151	−	0.556047i	$-0.812317\pi$
$139$	−19.5982	−1.66230	−0.831151	+	0.556047i	$0.812317\pi$
$140$	13.2898	1.12320
$141$	4.27730	0.360214
$142$	−4.96608	−0.416744
$143$	−3.99842	−0.334365
$144$	2.19756	0.183130
$145$	1.59433	0.132402
$146$	1.20476	0.0997067
$147$	17.5361	1.44635
$148$	−9.79360	−0.805029
$149$	−6.73460	−0.551720	−0.275860	−	0.961198i	$-0.588963\pi$
$149$	−6.73460	−0.551720	−0.275860	+	0.961198i	$0.588963\pi$
$150$	1.38437	0.113033
$151$	4.73376	0.385228	0.192614	−	0.981275i	$-0.438304\pi$
$151$	4.73376	0.385228	0.192614	+	0.981275i	$0.438304\pi$
$152$	5.59402	0.453735
$153$	−1.67611	−0.135505
$154$	1.72017	0.138616
$155$	6.28648	0.504942
$156$	−10.9121	−0.873665
$157$	21.3212	1.70162	0.850810	−	0.525473i	$-0.176112\pi$
$157$	21.3212	1.70162	0.850810	+	0.525473i	$0.176112\pi$
$158$	6.75545	0.537435
$159$	−7.82304	−0.620407
$160$	8.58677	0.678844
$161$	−4.95339	−0.390382
$162$	−0.563182	−0.0442478
$163$	4.09507	0.320750	0.160375	−	0.987056i	$-0.448730\pi$
$163$	4.09507	0.320750	0.160375	+	0.987056i	$0.448730\pi$
$164$	10.1141	0.789780
$165$	0.983101	0.0765343
$166$	−5.75156	−0.446408
$167$	−10.3928	−0.804217	−0.402108	−	0.915592i	$-0.631723\pi$
$167$	−10.3928	−0.804217	−0.402108	+	0.915592i	$0.631723\pi$
$168$	10.2738	0.792644
$169$	29.0471	2.23440
$170$	−1.50497	−0.115426
$171$	2.69708	0.206251
$172$	−0.794882	−0.0606091
$173$	−4.60624	−0.350206	−0.175103	−	0.984550i	$-0.556026\pi$
$173$	−4.60624	−0.350206	−0.175103	+	0.984550i	$0.556026\pi$
$174$	0.563182	0.0426947
$175$	−12.1760	−0.920422
$176$	−1.35507	−0.102142
$177$	11.6621	0.876576
$178$	3.55052	0.266123
$179$	−25.3247	−1.89286	−0.946430	−	0.322910i	$-0.895339\pi$
$179$	−25.3247	−1.89286	−0.946430	+	0.322910i	$0.895339\pi$
$180$	2.68298	0.199977
$181$	−22.1243	−1.64449	−0.822245	−	0.569134i	$-0.807279\pi$
$181$	−22.1243	−1.64449	−0.822245	+	0.569134i	$0.807279\pi$
$182$	−18.0892	−1.34086
$183$	10.3582	0.765699
$184$	−2.07410	−0.152905
$185$	−9.27857	−0.682174
$186$	2.22064	0.162825
$187$	1.03353	0.0755792
$188$	−7.19796	−0.524965
$189$	4.95339	0.360306
$190$	2.42170	0.175689
$191$	−20.9666	−1.51709	−0.758545	−	0.651620i	$-0.774090\pi$
$191$	−20.9666	−1.51709	−0.758545	+	0.651620i	$0.774090\pi$
$192$	−1.36191	−0.0982874
$193$	20.7423	1.49306	0.746530	−	0.665351i	$-0.231718\pi$
$193$	20.7423	1.49306	0.746530	+	0.665351i	$0.231718\pi$
$194$	−6.70807	−0.481612
$195$	−10.3382	−0.740335
$196$	−29.5102	−2.10787
$197$	−22.2579	−1.58581	−0.792906	−	0.609344i	$-0.791433\pi$
$197$	−22.2579	−1.58581	−0.792906	+	0.609344i	$0.791433\pi$
$198$	0.347272	0.0246795
$199$	0.316336	0.0224245	0.0112122	−	0.999937i	$-0.496431\pi$
$199$	0.316336	0.0224245	0.0112122	+	0.999937i	$0.496431\pi$
$200$	−5.09839	−0.360511
$201$	−6.36345	−0.448843
$202$	−2.58887	−0.182152
$203$	−4.95339	−0.347660
$204$	2.82060	0.197482
$205$	9.58223	0.669252
$206$	−2.57989	−0.179750
$207$	−1.00000	−0.0695048
$208$	14.2498	0.988044
$209$	−1.66308	−0.115038
$210$	4.44764	0.306916
$211$	−0.730479	−0.0502883	−0.0251441	−	0.999684i	$-0.508004\pi$
$211$	−0.730479	−0.0502883	−0.0251441	+	0.999684i	$0.508004\pi$
$212$	13.1648	0.904163
$213$	8.81789	0.604192
$214$	−5.09398	−0.348217
$215$	−0.753079	−0.0513596
$216$	2.07410	0.141125
$217$	−19.5314	−1.32588
$218$	9.04688	0.612732
$219$	−2.13920	−0.144554
$220$	−1.65439	−0.111539
$221$	−10.8685	−0.731096
$222$	−3.27757	−0.219976
$223$	−0.992801	−0.0664829	−0.0332414	−	0.999447i	$-0.510583\pi$
$223$	−0.992801	−0.0664829	−0.0332414	+	0.999447i	$0.510583\pi$
$224$	−26.6781	−1.78251
$225$	−2.45812	−0.163875
$226$	−10.3567	−0.688920
$227$	−6.80592	−0.451725	−0.225862	−	0.974159i	$-0.572520\pi$
$227$	−6.80592	−0.451725	−0.225862	+	0.974159i	$0.572520\pi$
$228$	−4.53872	−0.300584
$229$	16.5937	1.09654	0.548272	−	0.836300i	$-0.315286\pi$
$229$	16.5937	1.09654	0.548272	+	0.836300i	$0.315286\pi$
$230$	−0.897897	−0.0592056
$231$	−3.05438	−0.200964
$232$	−2.07410	−0.136171
$233$	25.8874	1.69594	0.847971	−	0.530042i	$-0.177824\pi$
$233$	25.8874	1.69594	0.847971	+	0.530042i	$0.177824\pi$
$234$	−3.65188	−0.238731
$235$	−6.81942	−0.444850
$236$	−19.6253	−1.27750
$237$	−11.9951	−0.779168
$238$	4.67578	0.303086
$239$	6.18941	0.400360	0.200180	−	0.979759i	$-0.435847\pi$
$239$	6.18941	0.400360	0.200180	+	0.979759i	$0.435847\pi$
$240$	−3.50362	−0.226158
$241$	20.6273	1.32872	0.664360	−	0.747413i	$-0.268704\pi$
$241$	20.6273	1.32872	0.664360	+	0.747413i	$0.268704\pi$
$242$	5.98087	0.384465
$243$	1.00000	0.0641500
$244$	−17.4310	−1.11591
$245$	−27.9583	−1.78619
$246$	3.38484	0.215809
$247$	17.4889	1.11279
$248$	−8.17824	−0.519319
$249$	10.2126	0.647198
$250$	−6.69662	−0.423531
$251$	−16.1608	−1.02006	−0.510029	−	0.860157i	$-0.670365\pi$
$251$	−16.1608	−1.02006	−0.510029	+	0.860157i	$0.670365\pi$
$252$	−8.33570	−0.525100
$253$	0.616624	0.0387668
$254$	−2.44458	−0.153386
$255$	2.67227	0.167344
$256$	−3.77454	−0.235909
$257$	−7.71144	−0.481026	−0.240513	−	0.970646i	$-0.577316\pi$
$257$	−7.71144	−0.481026	−0.240513	+	0.970646i	$0.577316\pi$
$258$	−0.266019	−0.0165616
$259$	28.8275	1.79125
$260$	17.3974	1.07894
$261$	−1.00000	−0.0618984
$262$	−8.01583	−0.495220
$263$	−3.66457	−0.225967	−0.112984	−	0.993597i	$-0.536041\pi$
$263$	−3.66457	−0.225967	−0.112984	+	0.993597i	$0.536041\pi$
$264$	−1.27894	−0.0787134
$265$	12.4725	0.766179
$266$	−7.52394	−0.461323
$267$	−6.30439	−0.385823
$268$	10.7086	0.654131
$269$	18.5829	1.13302	0.566510	−	0.824055i	$-0.308293\pi$
$269$	18.5829	1.13302	0.566510	+	0.824055i	$0.308293\pi$
$270$	0.897897	0.0546443
$271$	−11.7264	−0.712326	−0.356163	−	0.934424i	$-0.615915\pi$
$271$	−11.7264	−0.712326	−0.356163	+	0.934424i	$0.615915\pi$
$272$	−3.68334	−0.223336
$273$	32.1197	1.94397
$274$	−5.90617	−0.356805
$275$	1.51574	0.0914023
$276$	1.68283	0.101294
$277$	−25.5590	−1.53569	−0.767846	−	0.640634i	$-0.778672\pi$
$277$	−25.5590	−1.53569	−0.767846	+	0.640634i	$0.778672\pi$
$278$	11.0374	0.661978
$279$	−3.94303	−0.236063
$280$	−16.3799	−0.978885
$281$	−7.56252	−0.451142	−0.225571	−	0.974227i	$-0.572425\pi$
$281$	−7.56252	−0.451142	−0.225571	+	0.974227i	$0.572425\pi$
$282$	−2.40890	−0.143448
$283$	15.6951	0.932980	0.466490	−	0.884527i	$-0.345518\pi$
$283$	15.6951	0.932980	0.466490	+	0.884527i	$0.345518\pi$
$284$	−14.8390	−0.880531
$285$	−4.30003	−0.254712
$286$	2.25184	0.133154
$287$	−29.7709	−1.75732
$288$	−5.38583	−0.317363
$289$	−14.1907	−0.834744
$290$	−0.897897	−0.0527263
$291$	11.9110	0.698236
$292$	3.59991	0.210669
$293$	27.4297	1.60246	0.801229	−	0.598358i	$-0.204180\pi$
$293$	27.4297	1.60246	0.801229	+	0.598358i	$0.204180\pi$
$294$	−9.87603	−0.575982
$295$	−18.5932	−1.08254
$296$	12.0707	0.701596
$297$	−0.616624	−0.0357802
$298$	3.79281	0.219711
$299$	−6.48438	−0.375001
$300$	4.13659	0.238826
$301$	2.33973	0.134860
$302$	−2.66597	−0.153409
$303$	4.59685	0.264082
$304$	5.92698	0.339936
$305$	−16.5143	−0.945609
$306$	0.943955	0.0539623
$307$	12.9197	0.737365	0.368683	−	0.929555i	$-0.379809\pi$
$307$	12.9197	0.737365	0.368683	+	0.929555i	$0.379809\pi$
$308$	5.14000	0.292878
$309$	4.58092	0.260600
$310$	−3.54043	−0.201083
$311$	−3.77938	−0.214309	−0.107155	−	0.994242i	$-0.534174\pi$
$311$	−3.77938	−0.214309	−0.107155	+	0.994242i	$0.534174\pi$
$312$	13.4493	0.761414
$313$	4.35313	0.246054	0.123027	−	0.992403i	$-0.460740\pi$
$313$	4.35313	0.246054	0.123027	+	0.992403i	$0.460740\pi$
$314$	−12.0077	−0.677636
$315$	−7.89733	−0.444964
$316$	20.1857	1.13554
$317$	0.496952	0.0279116	0.0139558	−	0.999903i	$-0.495558\pi$
$317$	0.496952	0.0279116	0.0139558	+	0.999903i	$0.495558\pi$
$318$	4.40579	0.247065
$319$	0.616624	0.0345243
$320$	2.17133	0.121381
$321$	9.04500	0.504843
$322$	2.78966	0.155462
$323$	−4.52060	−0.251533
$324$	−1.68283	−0.0934903
$325$	−15.9394	−0.884157
$326$	−2.30627	−0.127732
$327$	−16.0639	−0.888334
$328$	−12.4658	−0.688307
$329$	21.1872	1.16809
$330$	−0.553665	−0.0304782
$331$	−5.64763	−0.310422	−0.155211	−	0.987881i	$-0.549606\pi$
$331$	−5.64763	−0.310422	−0.155211	+	0.987881i	$0.549606\pi$
$332$	−17.1861	−0.943207
$333$	5.81974	0.318920
$334$	5.85302	0.320263
$335$	10.1454	0.554304
$336$	10.8854	0.593845
$337$	−7.46517	−0.406654	−0.203327	−	0.979111i	$-0.565175\pi$
$337$	−7.46517	−0.406654	−0.203327	+	0.979111i	$0.565175\pi$
$338$	−16.3588	−0.889803
$339$	18.3897	0.998791
$340$	−4.49696	−0.243882
$341$	2.43137	0.131666
$342$	−1.51895	−0.0821352
$343$	52.1896	2.81797
$344$	0.979700	0.0528219
$345$	1.59433	0.0858357
$346$	2.59415	0.139462
$347$	14.1931	0.761923	0.380961	−	0.924591i	$-0.375593\pi$
$347$	14.1931	0.761923	0.380961	+	0.924591i	$0.375593\pi$
$348$	1.68283	0.0902089
$349$	−18.3724	−0.983455	−0.491727	−	0.870749i	$-0.663634\pi$
$349$	−18.3724	−0.983455	−0.491727	+	0.870749i	$0.663634\pi$
$350$	6.85732	0.366539
$351$	6.48438	0.346110
$352$	3.32103	0.177012
$353$	−29.4962	−1.56992	−0.784962	−	0.619544i	$-0.787318\pi$
$353$	−29.4962	−1.56992	−0.784962	+	0.619544i	$0.787318\pi$
$354$	−6.56788	−0.349079
$355$	−14.0586	−0.746154
$356$	10.6092	0.562286
$357$	−8.30243	−0.439411
$358$	14.2624	0.753793
$359$	1.45373	0.0767248	0.0383624	−	0.999264i	$-0.487786\pi$
$359$	1.45373	0.0767248	0.0383624	+	0.999264i	$0.487786\pi$
$360$	−3.30680	−0.174284
$361$	−11.7258	−0.617145
$362$	12.4600	0.654885
$363$	−10.6198	−0.557394
$364$	−54.0518	−2.83309
$365$	3.41059	0.178518
$366$	−5.83355	−0.304924
$367$	−10.1531	−0.529990	−0.264995	−	0.964250i	$-0.585370\pi$
$367$	−10.1531	−0.529990	−0.264995	+	0.964250i	$0.585370\pi$
$368$	−2.19756	−0.114555
$369$	−6.01020	−0.312879
$370$	5.22552	0.271662
$371$	−38.7506	−2.01183
$372$	6.63543	0.344031
$373$	10.0893	0.522406	0.261203	−	0.965284i	$-0.415881\pi$
$373$	10.0893	0.522406	0.261203	+	0.965284i	$0.415881\pi$
$374$	−0.582065	−0.0300979
$375$	11.8907	0.614032
$376$	8.87156	0.457516
$377$	−6.48438	−0.333962
$378$	−2.78966	−0.143485
$379$	−14.5482	−0.747293	−0.373646	−	0.927571i	$-0.621893\pi$
$379$	−14.5482	−0.747293	−0.373646	+	0.927571i	$0.621893\pi$
$380$	7.23620	0.371209
$381$	4.34065	0.222378
$382$	11.8080	0.604151
$383$	14.7357	0.752960	0.376480	−	0.926425i	$-0.377134\pi$
$383$	14.7357	0.752960	0.376480	+	0.926425i	$0.377134\pi$
$384$	11.5387	0.588830
$385$	4.86969	0.248182
$386$	−11.6817	−0.594581
$387$	0.472349	0.0240109
$388$	−20.0442	−1.01759
$389$	−5.48698	−0.278201	−0.139101	−	0.990278i	$-0.544421\pi$
$389$	−5.48698	−0.278201	−0.139101	+	0.990278i	$0.544421\pi$
$390$	5.82230	0.294824
$391$	1.67611	0.0847645
$392$	36.3717	1.83705
$393$	14.2331	0.717965
$394$	12.5353	0.631518
$395$	19.1242	0.962243
$396$	1.03767	0.0521450
$397$	−8.85454	−0.444397	−0.222198	−	0.975002i	$-0.571323\pi$
$397$	−8.85454	−0.444397	−0.222198	+	0.975002i	$0.571323\pi$
$398$	−0.178155	−0.00893009
$399$	13.3597	0.668822
$400$	−5.40185	−0.270093
$401$	−1.93901	−0.0968298	−0.0484149	−	0.998827i	$-0.515417\pi$
$401$	−1.93901	−0.0968298	−0.0484149	+	0.998827i	$0.515417\pi$
$402$	3.58378	0.178743
$403$	−25.5681	−1.27364
$404$	−7.73571	−0.384866
$405$	−1.59433	−0.0792228
$406$	2.78966	0.138449
$407$	−3.58859	−0.177880
$408$	−3.47642	−0.172109
$409$	6.64781	0.328713	0.164357	−	0.986401i	$-0.447445\pi$
$409$	6.64781	0.328713	0.164357	+	0.986401i	$0.447445\pi$
$410$	−5.39654	−0.266516
$411$	10.4871	0.517292
$412$	−7.70890	−0.379790
$413$	57.7669	2.84253
$414$	0.563182	0.0276789
$415$	−16.2823	−0.799264
$416$	−34.9237	−1.71228
$417$	−19.5982	−0.959730
$418$	0.936620	0.0458116
$419$	0.802297	0.0391948	0.0195974	−	0.999808i	$-0.493762\pi$
$419$	0.802297	0.0391948	0.0195974	+	0.999808i	$0.493762\pi$
$420$	13.2898	0.648478
$421$	21.2976	1.03798	0.518990	−	0.854781i	$-0.326308\pi$
$421$	21.2976	1.03798	0.518990	+	0.854781i	$0.326308\pi$
$422$	0.411393	0.0200263
$423$	4.27730	0.207970
$424$	−16.2258	−0.787993
$425$	4.12008	0.199853
$426$	−4.96608	−0.240607
$427$	51.3082	2.48298
$428$	−15.2212	−0.735743
$429$	−3.99842	−0.193046
$430$	0.424121	0.0204529
$431$	−21.0438	−1.01364	−0.506822	−	0.862051i	$-0.669180\pi$
$431$	−21.0438	−1.01364	−0.506822	+	0.862051i	$0.669180\pi$
$432$	2.19756	0.105730
$433$	3.07000	0.147535	0.0737675	−	0.997275i	$-0.476498\pi$
$433$	3.07000	0.147535	0.0737675	+	0.997275i	$0.476498\pi$
$434$	10.9997	0.528003
$435$	1.59433	0.0764422
$436$	27.0327	1.29463
$437$	−2.69708	−0.129019
$438$	1.20476	0.0575657
$439$	22.8075	1.08854	0.544271	−	0.838909i	$-0.316806\pi$
$439$	22.8075	1.08854	0.544271	+	0.838909i	$0.316806\pi$
$440$	2.03905	0.0972080
$441$	17.5361	0.835053
$442$	6.12096	0.291144
$443$	1.82887	0.0868922	0.0434461	−	0.999056i	$-0.486166\pi$
$443$	1.82887	0.0868922	0.0434461	+	0.999056i	$0.486166\pi$
$444$	−9.79360	−0.464784
$445$	10.0513	0.476476
$446$	0.559128	0.0264755
$447$	−6.73460	−0.318536
$448$	−6.74608	−0.318722
$449$	32.1557	1.51752	0.758760	−	0.651371i	$-0.225806\pi$
$449$	32.1557	1.51752	0.758760	+	0.651371i	$0.225806\pi$
$450$	1.38437	0.0652598
$451$	3.70604	0.174510
$452$	−30.9466	−1.45561
$453$	4.73376	0.222411
$454$	3.83297	0.179890
$455$	−51.2093	−2.40073
$456$	5.59402	0.261964
$457$	−17.6731	−0.826714	−0.413357	−	0.910569i	$-0.635644\pi$
$457$	−17.6731	−0.826714	−0.413357	+	0.910569i	$0.635644\pi$
$458$	−9.34528	−0.436676
$459$	−1.67611	−0.0782341
$460$	−2.68298	−0.125094
$461$	35.1978	1.63932	0.819662	−	0.572848i	$-0.194161\pi$
$461$	35.1978	1.63932	0.819662	+	0.572848i	$0.194161\pi$
$462$	1.72017	0.0800297
$463$	−9.53381	−0.443074	−0.221537	−	0.975152i	$-0.571107\pi$
$463$	−9.53381	−0.443074	−0.221537	+	0.975152i	$0.571107\pi$
$464$	−2.19756	−0.102019
$465$	6.28648	0.291528
$466$	−14.5793	−0.675375
$467$	−20.9801	−0.970841	−0.485421	−	0.874281i	$-0.661333\pi$
$467$	−20.9801	−0.970841	−0.485421	+	0.874281i	$0.661333\pi$
$468$	−10.9121	−0.504411
$469$	−31.5207	−1.45549
$470$	3.84058	0.177153
$471$	21.3212	0.982431
$472$	24.1884	1.11336
$473$	−0.291262	−0.0133922
$474$	6.75545	0.310288
$475$	−6.62974	−0.304194
$476$	13.9716	0.640385
$477$	−7.82304	−0.358192
$478$	−3.48577	−0.159435
$479$	−29.5362	−1.34954	−0.674772	−	0.738027i	$-0.735758\pi$
$479$	−29.5362	−1.34954	−0.674772	+	0.738027i	$0.735758\pi$
$480$	8.58677	0.391931
$481$	37.7374	1.72068
$482$	−11.6169	−0.529136
$483$	−4.95339	−0.225387
$484$	17.8712	0.812329
$485$	−18.9901	−0.862295
$486$	−0.563182	−0.0255465
$487$	−4.69157	−0.212595	−0.106298	−	0.994334i	$-0.533900\pi$
$487$	−4.69157	−0.212595	−0.106298	+	0.994334i	$0.533900\pi$
$488$	21.4839	0.972532
$489$	4.09507	0.185185
$490$	15.7456	0.711315
$491$	−17.4315	−0.786674	−0.393337	−	0.919394i	$-0.628679\pi$
$491$	−17.4315	−0.786674	−0.393337	+	0.919394i	$0.628679\pi$
$492$	10.1141	0.455980
$493$	1.67611	0.0754882
$494$	−9.84942	−0.443147
$495$	0.983101	0.0441871
$496$	−8.66502	−0.389071
$497$	43.6785	1.95925
$498$	−5.75156	−0.257734
$499$	9.04617	0.404962	0.202481	−	0.979286i	$-0.435100\pi$
$499$	9.04617	0.404962	0.202481	+	0.979286i	$0.435100\pi$
$500$	−20.0100	−0.894872
$501$	−10.3928	−0.464315
$502$	9.10145	0.406217
$503$	25.7136	1.14651	0.573255	−	0.819377i	$-0.305680\pi$
$503$	25.7136	1.14651	0.573255	+	0.819377i	$0.305680\pi$
$504$	10.2738	0.457633
$505$	−7.32889	−0.326131
$506$	−0.347272	−0.0154381
$507$	29.0471	1.29003
$508$	−7.30456	−0.324088
$509$	−10.4056	−0.461220	−0.230610	−	0.973046i	$-0.574072\pi$
$509$	−10.4056	−0.461220	−0.230610	+	0.973046i	$0.574072\pi$
$510$	−1.50497	−0.0666413
$511$	−10.5963	−0.468753
$512$	−20.9516	−0.925937
$513$	2.69708	0.119079
$514$	4.34294	0.191559
$515$	−7.30349	−0.321830
$516$	−0.794882	−0.0349927
$517$	−2.63749	−0.115997
$518$	−16.2351	−0.713329
$519$	−4.60624	−0.202191
$520$	−21.4425	−0.940317
$521$	−44.3130	−1.94139	−0.970693	−	0.240323i	$-0.922747\pi$
$521$	−44.3130	−1.94139	−0.970693	+	0.240323i	$0.922747\pi$
$522$	0.563182	0.0246498
$523$	2.54821	0.111425	0.0557127	−	0.998447i	$-0.482257\pi$
$523$	2.54821	0.111425	0.0557127	+	0.998447i	$0.482257\pi$
$524$	−23.9518	−1.04634
$525$	−12.1760	−0.531406
$526$	2.06382	0.0899869
$527$	6.60894	0.287890
$528$	−1.35507	−0.0589717
$529$	1.00000	0.0434783
$530$	−7.02428	−0.305115
$531$	11.6621	0.506092
$532$	−22.4821	−0.974721
$533$	−38.9724	−1.68808
$534$	3.55052	0.153646
$535$	−14.4207	−0.623461
$536$	−13.1984	−0.570086
$537$	−25.3247	−1.09284
$538$	−10.4656	−0.451203
$539$	−10.8132	−0.465757
$540$	2.68298	0.115457
$541$	−9.57940	−0.411851	−0.205925	−	0.978568i	$-0.566020\pi$
$541$	−9.57940	−0.411851	−0.205925	+	0.978568i	$0.566020\pi$
$542$	6.60408	0.283670
$543$	−22.1243	−0.949447
$544$	9.02724	0.387040
$545$	25.6111	1.09706
$546$	−18.0892	−0.774147
$547$	7.62918	0.326200	0.163100	−	0.986610i	$-0.447851\pi$
$547$	7.62918	0.326200	0.163100	+	0.986610i	$0.447851\pi$
$548$	−17.6480	−0.753887
$549$	10.3582	0.442077
$550$	−0.853635	−0.0363991
$551$	−2.69708	−0.114899
$552$	−2.07410	−0.0882796
$553$	−59.4167	−2.52665
$554$	14.3944	0.611559
$555$	−9.27857	−0.393853
$556$	32.9804	1.39868
$557$	−29.7588	−1.26092	−0.630460	−	0.776222i	$-0.717134\pi$
$557$	−29.7588	−1.26092	−0.630460	+	0.776222i	$0.717134\pi$
$558$	2.22064	0.0940073
$559$	3.06289	0.129546
$560$	−17.3548	−0.733375
$561$	1.03353	0.0436357
$562$	4.25907	0.179658
$563$	35.5508	1.49829	0.749145	−	0.662407i	$-0.230465\pi$
$563$	35.5508	1.49829	0.749145	+	0.662407i	$0.230465\pi$
$564$	−7.19796	−0.303089
$565$	−29.3192	−1.23347
$566$	−8.83923	−0.371540
$567$	4.95339	0.208023
$568$	18.2892	0.767398
$569$	−16.4596	−0.690023	−0.345011	−	0.938599i	$-0.612125\pi$
$569$	−16.4596	−0.690023	−0.345011	+	0.938599i	$0.612125\pi$
$570$	2.42170	0.101434
$571$	−32.1451	−1.34523	−0.672616	−	0.739992i	$-0.734829\pi$
$571$	−32.1451	−1.34523	−0.672616	+	0.739992i	$0.734829\pi$
$572$	6.72865	0.281339
$573$	−20.9666	−0.875893
$574$	16.7664	0.699818
$575$	2.45812	0.102511
$576$	−1.36191	−0.0567463
$577$	−22.2212	−0.925080	−0.462540	−	0.886598i	$-0.653062\pi$
$577$	−22.2212	−0.925080	−0.462540	+	0.886598i	$0.653062\pi$
$578$	7.99192	0.332420
$579$	20.7423	0.862019
$580$	−2.68298	−0.111405
$581$	50.5871	2.09871
$582$	−6.70807	−0.278059
$583$	4.82387	0.199784
$584$	−4.43692	−0.183601
$585$	−10.3382	−0.427433
$586$	−15.4479	−0.638146
$587$	8.38053	0.345902	0.172951	−	0.984930i	$-0.444670\pi$
$587$	8.38053	0.345902	0.172951	+	0.984930i	$0.444670\pi$
$588$	−29.5102	−1.21698
$589$	−10.6347	−0.438193
$590$	10.4714	0.431099
$591$	−22.2579	−0.915569
$592$	12.7892	0.525633
$593$	41.5343	1.70561	0.852805	−	0.522230i	$-0.174900\pi$
$593$	41.5343	1.70561	0.852805	+	0.522230i	$0.174900\pi$
$594$	0.347272	0.0142487
$595$	13.2368	0.542656
$596$	11.3332	0.464224
$597$	0.316336	0.0129468
$598$	3.65188	0.149337
$599$	−41.6783	−1.70293	−0.851465	−	0.524412i	$-0.824285\pi$
$599$	−41.6783	−1.70293	−0.851465	+	0.524412i	$0.824285\pi$
$600$	−5.09839	−0.208141
$601$	−15.7600	−0.642862	−0.321431	−	0.946933i	$-0.604164\pi$
$601$	−15.7600	−0.642862	−0.321431	+	0.946933i	$0.604164\pi$
$602$	−1.31770	−0.0537052
$603$	−6.36345	−0.259140
$604$	−7.96609	−0.324136
$605$	16.9314	0.688359
$606$	−2.58887	−0.105165
$607$	−28.2457	−1.14646	−0.573229	−	0.819395i	$-0.694309\pi$
$607$	−28.2457	−1.14646	−0.573229	+	0.819395i	$0.694309\pi$
$608$	−14.5260	−0.589107
$609$	−4.95339	−0.200722
$610$	9.30058	0.376570
$611$	27.7356	1.12206
$612$	2.82060	0.114016
$613$	37.9241	1.53174	0.765870	−	0.642996i	$-0.222309\pi$
$613$	37.9241	1.53174	0.765870	+	0.642996i	$0.222309\pi$
$614$	−7.27613	−0.293641
$615$	9.58223	0.386393
$616$	−6.33510	−0.255249
$617$	12.9445	0.521128	0.260564	−	0.965457i	$-0.416092\pi$
$617$	12.9445	0.521128	0.260564	+	0.965457i	$0.416092\pi$
$618$	−2.57989	−0.103779
$619$	−44.2979	−1.78048	−0.890242	−	0.455487i	$-0.849465\pi$
$619$	−44.2979	−1.78048	−0.890242	+	0.455487i	$0.849465\pi$
$620$	−10.5790	−0.424865
$621$	−1.00000	−0.0401286
$622$	2.12848	0.0853443
$623$	−31.2281	−1.25113
$624$	14.2498	0.570448
$625$	−6.66705	−0.266682
$626$	−2.45161	−0.0979859
$627$	−1.66308	−0.0664172
$628$	−35.8800	−1.43177
$629$	−9.75452	−0.388938
$630$	4.44764	0.177198
$631$	1.21447	0.0483474	0.0241737	−	0.999708i	$-0.492305\pi$
$631$	1.21447	0.0483474	0.0241737	+	0.999708i	$0.492305\pi$
$632$	−24.8791	−0.989639
$633$	−0.730479	−0.0290340
$634$	−0.279875	−0.0111152
$635$	−6.92042	−0.274629
$636$	13.1648	0.522019
$637$	113.711	4.50539
$638$	−0.347272	−0.0137486
$639$	8.81789	0.348830
$640$	−18.3964	−0.727182
$641$	−41.6001	−1.64310	−0.821552	−	0.570134i	$-0.806891\pi$
$641$	−41.6001	−1.64310	−0.821552	+	0.570134i	$0.806891\pi$
$642$	−5.09398	−0.201043
$643$	−33.3387	−1.31475	−0.657374	−	0.753564i	$-0.728333\pi$
$643$	−33.3387	−1.31475	−0.657374	+	0.753564i	$0.728333\pi$
$644$	8.33570	0.328473
$645$	−0.753079	−0.0296525
$646$	2.54592	0.100168
$647$	−16.2174	−0.637570	−0.318785	−	0.947827i	$-0.603275\pi$
$647$	−16.2174	−0.637570	−0.318785	+	0.947827i	$0.603275\pi$
$648$	2.07410	0.0814784
$649$	−7.19113	−0.282276
$650$	8.97677	0.352098
$651$	−19.5314	−0.765495
$652$	−6.89128	−0.269883
$653$	−19.3624	−0.757708	−0.378854	−	0.925456i	$-0.623682\pi$
$653$	−19.3624	−0.757708	−0.378854	+	0.925456i	$0.623682\pi$
$654$	9.04688	0.353761
$655$	−22.6922	−0.886659
$656$	−13.2078	−0.515676
$657$	−2.13920	−0.0834583
$658$	−11.9322	−0.465167
$659$	−29.7211	−1.15777	−0.578885	−	0.815409i	$-0.696512\pi$
$659$	−29.7211	−1.15777	−0.578885	+	0.815409i	$0.696512\pi$
$660$	−1.65439	−0.0643970
$661$	16.5459	0.643562	0.321781	−	0.946814i	$-0.395719\pi$
$661$	16.5459	0.643562	0.321781	+	0.946814i	$0.395719\pi$
$662$	3.18065	0.123619
$663$	−10.8685	−0.422099
$664$	21.1820	0.822021
$665$	−21.2997	−0.825969
$666$	−3.27757	−0.127003
$667$	1.00000	0.0387202
$668$	17.4892	0.676679
$669$	−0.992801	−0.0383839
$670$	−5.71372	−0.220740
$671$	−6.38711	−0.246572
$672$	−26.6781	−1.02913
$673$	−34.0750	−1.31349	−0.656746	−	0.754112i	$-0.728068\pi$
$673$	−34.0750	−1.31349	−0.656746	+	0.754112i	$0.728068\pi$
$674$	4.20425	0.161942
$675$	−2.45812	−0.0946131
$676$	−48.8813	−1.88005
$677$	−20.9027	−0.803357	−0.401678	−	0.915781i	$-0.631573\pi$
$677$	−20.9027	−0.803357	−0.401678	+	0.915781i	$0.631573\pi$
$678$	−10.3567	−0.397748
$679$	59.0000	2.26421
$680$	5.54255	0.212547
$681$	−6.80592	−0.260803
$682$	−1.36930	−0.0524333
$683$	47.7573	1.82738	0.913692	−	0.406408i	$-0.133219\pi$
$683$	47.7573	1.82738	0.913692	+	0.406408i	$0.133219\pi$
$684$	−4.53872	−0.173542
$685$	−16.7199	−0.638836
$686$	−29.3922	−1.12220
$687$	16.5937	0.633090
$688$	1.03801	0.0395739
$689$	−50.7275	−1.93256
$690$	−0.897897	−0.0341823
$691$	−0.154264	−0.00586849	−0.00293424	−	0.999996i	$-0.500934\pi$
$691$	−0.154264	−0.00586849	−0.00293424	+	0.999996i	$0.500934\pi$
$692$	7.75150	0.294668
$693$	−3.05438	−0.116026
$694$	−7.99327	−0.303420
$695$	31.2460	1.18523
$696$	−2.07410	−0.0786186
$697$	10.0738	0.381571
$698$	10.3470	0.391641
$699$	25.8874	0.979153
$700$	20.4901	0.774455
$701$	−30.8317	−1.16450	−0.582248	−	0.813011i	$-0.697827\pi$
$701$	−30.8317	−1.16450	−0.582248	+	0.813011i	$0.697827\pi$
$702$	−3.65188	−0.137831
$703$	15.6963	0.591997
$704$	0.839787	0.0316507
$705$	−6.81942	−0.256834
$706$	16.6117	0.625191
$707$	22.7700	0.856355
$708$	−19.6253	−0.737563
$709$	−3.56458	−0.133871	−0.0669353	−	0.997757i	$-0.521322\pi$
$709$	−3.56458	−0.133871	−0.0669353	+	0.997757i	$0.521322\pi$
$710$	7.91756	0.297141
$711$	−11.9951	−0.449853
$712$	−13.0759	−0.490042
$713$	3.94303	0.147667
$714$	4.67578	0.174987
$715$	6.37480	0.238404
$716$	42.6171	1.59268
$717$	6.18941	0.231148
$718$	−0.818713	−0.0305541
$719$	20.9959	0.783016	0.391508	−	0.920175i	$-0.371954\pi$
$719$	20.9959	0.783016	0.391508	+	0.920175i	$0.371954\pi$
$720$	−3.50362	−0.130572
$721$	22.6911	0.845062
$722$	6.60374	0.245766
$723$	20.6273	0.767137
$724$	37.2314	1.38370
$725$	2.45812	0.0912923
$726$	5.98087	0.221971
$727$	19.3196	0.716524	0.358262	−	0.933621i	$-0.383369\pi$
$727$	19.3196	0.716524	0.358262	+	0.933621i	$0.383369\pi$
$728$	66.6195	2.46908
$729$	1.00000	0.0370370
$730$	−1.92078	−0.0710914
$731$	−0.791709	−0.0292824
$732$	−17.4310	−0.644269
$733$	0.320498	0.0118379	0.00591893	−	0.999982i	$-0.498116\pi$
$733$	0.320498	0.0118379	0.00591893	+	0.999982i	$0.498116\pi$
$734$	5.71807	0.211058
$735$	−27.9583	−1.03126
$736$	5.38583	0.198524
$737$	3.92386	0.144537
$738$	3.38484	0.124598
$739$	−29.9692	−1.10243	−0.551217	−	0.834362i	$-0.685837\pi$
$739$	−29.9692	−1.10243	−0.551217	+	0.834362i	$0.685837\pi$
$740$	15.6142	0.573990
$741$	17.4889	0.642470
$742$	21.8236	0.801171
$743$	14.3052	0.524808	0.262404	−	0.964958i	$-0.415485\pi$
$743$	14.3052	0.524808	0.262404	+	0.964958i	$0.415485\pi$
$744$	−8.17824	−0.299829
$745$	10.7372	0.393379
$746$	−5.68214	−0.208038
$747$	10.2126	0.373660
$748$	−1.73925	−0.0635933
$749$	44.8035	1.63708
$750$	−6.69662	−0.244526
$751$	40.9102	1.49283	0.746417	−	0.665479i	$-0.231773\pi$
$751$	40.9102	1.49283	0.746417	+	0.665479i	$0.231773\pi$
$752$	9.39961	0.342769
$753$	−16.1608	−0.588931
$754$	3.65188	0.132994
$755$	−7.54716	−0.274669
$756$	−8.33570	−0.303167
$757$	−6.22635	−0.226300	−0.113150	−	0.993578i	$-0.536094\pi$
$757$	−6.22635	−0.226300	−0.113150	+	0.993578i	$0.536094\pi$
$758$	8.19331	0.297594
$759$	0.616624	0.0223820
$760$	−8.91870	−0.323515
$761$	−13.1589	−0.477011	−0.238505	−	0.971141i	$-0.576657\pi$
$761$	−13.1589	−0.477011	−0.238505	+	0.971141i	$0.576657\pi$
$762$	−2.44458	−0.0885577
$763$	−79.5707	−2.88065
$764$	35.2832	1.27650
$765$	2.67227	0.0966161
$766$	−8.29889	−0.299851
$767$	75.6214	2.73053
$768$	−3.77454	−0.136202
$769$	15.8580	0.571854	0.285927	−	0.958251i	$-0.407698\pi$
$769$	15.8580	0.571854	0.285927	+	0.958251i	$0.407698\pi$
$770$	−2.74252	−0.0988336
$771$	−7.71144	−0.277721
$772$	−34.9056	−1.25628
$773$	25.0338	0.900402	0.450201	−	0.892927i	$-0.351352\pi$
$773$	25.0338	0.900402	0.450201	+	0.892927i	$0.351352\pi$
$774$	−0.266019	−0.00956184
$775$	9.69243	0.348162
$776$	24.7047	0.886846
$777$	28.8275	1.03418
$778$	3.09017	0.110788
$779$	−16.2100	−0.580783
$780$	17.3974	0.622928
$781$	−5.43733	−0.194563
$782$	−0.943955	−0.0337558
$783$	−1.00000	−0.0357371
$784$	38.5366	1.37631
$785$	−33.9931	−1.21326
$786$	−8.01583	−0.285915
$787$	−22.1812	−0.790674	−0.395337	−	0.918536i	$-0.629372\pi$
$787$	−22.1812	−0.790674	−0.395337	+	0.918536i	$0.629372\pi$
$788$	37.4562	1.33432
$789$	−3.66457	−0.130462
$790$	−10.7704	−0.383194
$791$	91.0914	3.23884
$792$	−1.27894	−0.0454452
$793$	67.1664	2.38515
$794$	4.98672	0.176972
$795$	12.4725	0.442353
$796$	−0.532338	−0.0188682
$797$	−30.2552	−1.07169	−0.535846	−	0.844315i	$-0.680007\pi$
$797$	−30.2552	−1.07169	−0.535846	+	0.844315i	$0.680007\pi$
$798$	−7.52394	−0.266345
$799$	−7.16923	−0.253629
$800$	13.2390	0.468069
$801$	−6.30439	−0.222755
$802$	1.09202	0.0385605
$803$	1.31908	0.0465495
$804$	10.7086	0.377663
$805$	7.89733	0.278344
$806$	14.3995	0.507200
$807$	18.5829	0.654150
$808$	9.53434	0.335417
$809$	−32.5292	−1.14367	−0.571833	−	0.820370i	$-0.693767\pi$
$809$	−32.5292	−1.14367	−0.571833	+	0.820370i	$0.693767\pi$
$810$	0.897897	0.0315489
$811$	−17.2748	−0.606599	−0.303300	−	0.952895i	$-0.598088\pi$
$811$	−17.2748	−0.606599	−0.303300	+	0.952895i	$0.598088\pi$
$812$	8.33570	0.292526
$813$	−11.7264	−0.411262
$814$	2.02103	0.0708371
$815$	−6.52888	−0.228697
$816$	−3.68334	−0.128943
$817$	1.27396	0.0445703
$818$	−3.74393	−0.130903
$819$	32.1197	1.12235
$820$	−16.1252	−0.563117
$821$	11.3961	0.397728	0.198864	−	0.980027i	$-0.436275\pi$
$821$	11.3961	0.397728	0.198864	+	0.980027i	$0.436275\pi$
$822$	−5.90617	−0.206001
$823$	16.8758	0.588255	0.294128	−	0.955766i	$-0.404971\pi$
$823$	16.8758	0.588255	0.294128	+	0.955766i	$0.404971\pi$
$824$	9.50130	0.330993
$825$	1.51574	0.0527712
$826$	−32.5333	−1.13198
$827$	−45.9867	−1.59911	−0.799557	−	0.600590i	$-0.794932\pi$
$827$	−45.9867	−1.59911	−0.799557	+	0.600590i	$0.794932\pi$
$828$	1.68283	0.0584822
$829$	−53.2178	−1.84833	−0.924165	−	0.381995i	$-0.875237\pi$
$829$	−53.2178	−1.84833	−0.924165	+	0.381995i	$0.875237\pi$
$830$	9.16987	0.318291
$831$	−25.5590	−0.886633
$832$	−8.83114	−0.306165
$833$	−29.3925	−1.01839
$834$	11.0374	0.382193
$835$	16.5695	0.573411
$836$	2.79868	0.0967945
$837$	−3.94303	−0.136291
$838$	−0.451839	−0.0156085
$839$	13.5867	0.469064	0.234532	−	0.972108i	$-0.424644\pi$
$839$	13.5867	0.469064	0.234532	+	0.972108i	$0.424644\pi$
$840$	−16.3799	−0.565159
$841$	1.00000	0.0344828
$842$	−11.9944	−0.413354
$843$	−7.56252	−0.260467
$844$	1.22927	0.0423132
$845$	−46.3107	−1.59314
$846$	−2.40890	−0.0828197
$847$	−52.6039	−1.80749
$848$	−17.1916	−0.590361
$849$	15.6951	0.538656
$850$	−2.32035	−0.0795875
$851$	−5.81974	−0.199498
$852$	−14.8390	−0.508375
$853$	−6.73050	−0.230448	−0.115224	−	0.993340i	$-0.536759\pi$
$853$	−6.73050	−0.230448	−0.115224	+	0.993340i	$0.536759\pi$
$854$	−28.8959	−0.988796
$855$	−4.30003	−0.147058
$856$	18.7603	0.641212
$857$	35.0261	1.19647	0.598234	−	0.801321i	$-0.295869\pi$
$857$	35.0261	1.19647	0.598234	+	0.801321i	$0.295869\pi$
$858$	2.25184	0.0768766
$859$	1.65393	0.0564314	0.0282157	−	0.999602i	$-0.491017\pi$
$859$	1.65393	0.0564314	0.0282157	+	0.999602i	$0.491017\pi$
$860$	1.26730	0.0432146
$861$	−29.7709	−1.01459
$862$	11.8515	0.403663
$863$	31.4926	1.07202	0.536010	−	0.844212i	$-0.319931\pi$
$863$	31.4926	1.07202	0.536010	+	0.844212i	$0.319931\pi$
$864$	−5.38583	−0.183230
$865$	7.34385	0.249698
$866$	−1.72897	−0.0587528
$867$	−14.1907	−0.481940
$868$	32.8679	1.11561
$869$	7.39650	0.250909
$870$	−0.897897	−0.0304415
$871$	−41.2630	−1.39814
$872$	−33.3181	−1.12829
$873$	11.9110	0.403127
$874$	1.51895	0.0513791
$875$	58.8993	1.99116
$876$	3.59991	0.121630
$877$	42.2692	1.42733	0.713665	−	0.700487i	$-0.247034\pi$
$877$	42.2692	1.42733	0.713665	+	0.700487i	$0.247034\pi$
$878$	−12.8448	−0.433490
$879$	27.4297	0.925179
$880$	2.16042	0.0728277
$881$	−32.5253	−1.09581	−0.547903	−	0.836542i	$-0.684574\pi$
$881$	−32.5253	−1.09581	−0.547903	+	0.836542i	$0.684574\pi$
$882$	−9.87603	−0.332543
$883$	−20.9256	−0.704202	−0.352101	−	0.935962i	$-0.614533\pi$
$883$	−20.9256	−0.704202	−0.352101	+	0.935962i	$0.614533\pi$
$884$	18.2898	0.615154
$885$	−18.5932	−0.625003
$886$	−1.02999	−0.0346031
$887$	3.39320	0.113933	0.0569663	−	0.998376i	$-0.481857\pi$
$887$	3.39320	0.113933	0.0569663	+	0.998376i	$0.481857\pi$
$888$	12.0707	0.405067
$889$	21.5010	0.721119
$890$	−5.66069	−0.189747
$891$	−0.616624	−0.0206577
$892$	1.67071	0.0559395
$893$	11.5362	0.386045
$894$	3.79281	0.126850
$895$	40.3759	1.34962
$896$	57.1555	1.90943
$897$	−6.48438	−0.216507
$898$	−18.1095	−0.604321
$899$	3.94303	0.131507
$900$	4.13659	0.137886
$901$	13.1123	0.436833
$902$	−2.08717	−0.0694953
$903$	2.33973	0.0778614
$904$	38.1421	1.26859
$905$	35.2735	1.17253
$906$	−2.66597	−0.0885708
$907$	46.3463	1.53890	0.769452	−	0.638704i	$-0.220529\pi$
$907$	46.3463	1.53890	0.769452	+	0.638704i	$0.220529\pi$
$908$	11.4532	0.380087
$909$	4.59685	0.152468
$910$	28.8402	0.956042
$911$	34.0270	1.12737	0.563683	−	0.825991i	$-0.309384\pi$
$911$	34.0270	1.12737	0.563683	+	0.825991i	$0.309384\pi$
$912$	5.92698	0.196262
$913$	−6.29735	−0.208412
$914$	9.95319	0.329222
$915$	−16.5143	−0.545948
$916$	−27.9243	−0.922646
$917$	70.5022	2.32819
$918$	0.943955	0.0311552
$919$	8.92150	0.294293	0.147147	−	0.989115i	$-0.452991\pi$
$919$	8.92150	0.294293	0.147147	+	0.989115i	$0.452991\pi$
$920$	3.30680	0.109022
$921$	12.9197	0.425718
$922$	−19.8227	−0.652827
$923$	57.1785	1.88205
$924$	5.14000	0.169093
$925$	−14.3056	−0.470365
$926$	5.36927	0.176445
$927$	4.58092	0.150457
$928$	5.38583	0.176798
$929$	−3.51706	−0.115391	−0.0576955	−	0.998334i	$-0.518375\pi$
$929$	−3.51706	−0.115391	−0.0576955	+	0.998334i	$0.518375\pi$
$930$	−3.54043	−0.116095
$931$	47.2963	1.55007
$932$	−43.5641	−1.42699
$933$	−3.77938	−0.123731
$934$	11.8156	0.386618
$935$	−1.64779	−0.0538883
$936$	13.4493	0.439603
$937$	16.7996	0.548819	0.274409	−	0.961613i	$-0.411518\pi$
$937$	16.7996	0.548819	0.274409	+	0.961613i	$0.411518\pi$
$938$	17.7519	0.579620
$939$	4.35313	0.142059
$940$	11.4759	0.374303
$941$	2.96990	0.0968159	0.0484080	−	0.998828i	$-0.484585\pi$
$941$	2.96990	0.0968159	0.0484080	+	0.998828i	$0.484585\pi$
$942$	−12.0077	−0.391233
$943$	6.01020	0.195719
$944$	25.6281	0.834123
$945$	−7.89733	−0.256900
$946$	0.164034	0.00533319
$947$	−25.1490	−0.817233	−0.408617	−	0.912706i	$-0.633989\pi$
$947$	−25.1490	−0.817233	−0.408617	+	0.912706i	$0.633989\pi$
$948$	20.1857	0.655602
$949$	−13.8714	−0.450285
$950$	3.73375	0.121139
$951$	0.496952	0.0161148
$952$	−17.2201	−0.558106
$953$	−0.976881	−0.0316443	−0.0158221	−	0.999875i	$-0.505037\pi$
$953$	−0.976881	−0.0316443	−0.0158221	+	0.999875i	$0.505037\pi$
$954$	4.40579	0.142643
$955$	33.4276	1.08169
$956$	−10.4157	−0.336868
$957$	0.616624	0.0199326
$958$	16.6343	0.537428
$959$	51.9469	1.67745
$960$	2.17133	0.0700794
$961$	−15.4525	−0.498469
$962$	−21.2530	−0.685224
$963$	9.04500	0.291471
$964$	−34.7121	−1.11800
$965$	−33.0700	−1.06456
$966$	2.78966	0.0897559
$967$	−50.3884	−1.62038	−0.810191	−	0.586166i	$-0.800637\pi$
$967$	−50.3884	−1.62038	−0.810191	+	0.586166i	$0.800637\pi$
$968$	−22.0265	−0.707958
$969$	−4.52060	−0.145223
$970$	10.6949	0.343391
$971$	47.9179	1.53776	0.768879	−	0.639394i	$-0.220815\pi$
$971$	47.9179	1.53776	0.768879	+	0.639394i	$0.220815\pi$
$972$	−1.68283	−0.0539767
$973$	−97.0779	−3.11217
$974$	2.64221	0.0846617
$975$	−15.9394	−0.510468
$976$	22.7627	0.728616
$977$	25.9762	0.831053	0.415527	−	0.909581i	$-0.363597\pi$
$977$	25.9762	0.831053	0.415527	+	0.909581i	$0.363597\pi$
$978$	−2.30627	−0.0737463
$979$	3.88744	0.124243
$980$	47.0490	1.50293
$981$	−16.0639	−0.512880
$982$	9.81712	0.313277
$983$	50.0104	1.59509	0.797543	−	0.603263i	$-0.206133\pi$
$983$	50.0104	1.59509	0.797543	+	0.603263i	$0.206133\pi$
$984$	−12.4658	−0.397394
$985$	35.4865	1.13069
$986$	−0.943955	−0.0300616
$987$	21.1872	0.674395
$988$	−29.4307	−0.936317
$989$	−0.472349	−0.0150198
$990$	−0.553665	−0.0175966
$991$	−47.1683	−1.49835	−0.749176	−	0.662371i	$-0.769550\pi$
$991$	−47.1683	−1.49835	−0.749176	+	0.662371i	$0.769550\pi$
$992$	21.2365	0.674258
$993$	−5.64763	−0.179222
$994$	−24.5989	−0.780231
$995$	−0.504343	−0.0159888
$996$	−17.1861	−0.544561
$997$	−5.86063	−0.185608	−0.0928040	−	0.995684i	$-0.529583\pi$
$997$	−5.86063	−0.185608	−0.0928040	+	0.995684i	$0.529583\pi$
$998$	−5.09464	−0.161268
$999$	5.81974	0.184128

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.n.1.7	✓	16
3.2	odd	2		6003.2.a.r.1.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.n.1.7	✓	16	1.1	even	1	trivial
6003.2.a.r.1.10		16	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q-0.563182 q^{2} +1.00000 q^{3} -1.68283 q^{4} -1.59433 q^{5} -0.563182 q^{6} +4.95339 q^{7} +2.07410 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.563182 q^{2} +1.00000 q^{3} -1.68283 q^{4} -1.59433 q^{5} -0.563182 q^{6} +4.95339 q^{7} +2.07410 q^{8} +1.00000 q^{9} +0.897897 q^{10} -0.616624 q^{11} -1.68283 q^{12} +6.48438 q^{13} -2.78966 q^{14} -1.59433 q^{15} +2.19756 q^{16} -1.67611 q^{17} -0.563182 q^{18} +2.69708 q^{19} +2.68298 q^{20} +4.95339 q^{21} +0.347272 q^{22} -1.00000 q^{23} +2.07410 q^{24} -2.45812 q^{25} -3.65188 q^{26} +1.00000 q^{27} -8.33570 q^{28} -1.00000 q^{29} +0.897897 q^{30} -3.94303 q^{31} -5.38583 q^{32} -0.616624 q^{33} +0.943955 q^{34} -7.89733 q^{35} -1.68283 q^{36} +5.81974 q^{37} -1.51895 q^{38} +6.48438 q^{39} -3.30680 q^{40} -6.01020 q^{41} -2.78966 q^{42} +0.472349 q^{43} +1.03767 q^{44} -1.59433 q^{45} +0.563182 q^{46} +4.27730 q^{47} +2.19756 q^{48} +17.5361 q^{49} +1.38437 q^{50} -1.67611 q^{51} -10.9121 q^{52} -7.82304 q^{53} -0.563182 q^{54} +0.983101 q^{55} +10.2738 q^{56} +2.69708 q^{57} +0.563182 q^{58} +11.6621 q^{59} +2.68298 q^{60} +10.3582 q^{61} +2.22064 q^{62} +4.95339 q^{63} -1.36191 q^{64} -10.3382 q^{65} +0.347272 q^{66} -6.36345 q^{67} +2.82060 q^{68} -1.00000 q^{69} +4.44764 q^{70} +8.81789 q^{71} +2.07410 q^{72} -2.13920 q^{73} -3.27757 q^{74} -2.45812 q^{75} -4.53872 q^{76} -3.05438 q^{77} -3.65188 q^{78} -11.9951 q^{79} -3.50362 q^{80} +1.00000 q^{81} +3.38484 q^{82} +10.2126 q^{83} -8.33570 q^{84} +2.67227 q^{85} -0.266019 q^{86} -1.00000 q^{87} -1.27894 q^{88} -6.30439 q^{89} +0.897897 q^{90} +32.1197 q^{91} +1.68283 q^{92} -3.94303 q^{93} -2.40890 q^{94} -4.30003 q^{95} -5.38583 q^{96} +11.9110 q^{97} -9.87603 q^{98} -0.616624 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9}+O(q^{10}) \) 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9	\( 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9} + 11 q^{10} + 8 q^{11} + 25 q^{12} + 19 q^{13} + 16 q^{14} + 3 q^{15} + 31 q^{16} - 4 q^{17} - q^{18} + 19 q^{19} + 16 q^{20} + 13 q^{21} + 6 q^{22} - 16 q^{23} + 23 q^{25} - 15 q^{26} + 16 q^{27} + 18 q^{28} - 16 q^{29} + 11 q^{30} + 24 q^{31} - 21 q^{32} + 8 q^{33} - 9 q^{34} - 13 q^{35} + 25 q^{36} + 26 q^{37} + 19 q^{39} - 22 q^{40} - 15 q^{41} + 16 q^{42} + 33 q^{43} + 6 q^{44} + 3 q^{45} + q^{46} + 13 q^{47} + 31 q^{48} + 41 q^{49} + 13 q^{50} - 4 q^{51} - 26 q^{52} + 5 q^{53} - q^{54} + 9 q^{55} + 40 q^{56} + 19 q^{57} + q^{58} + 2 q^{59} + 16 q^{60} + 29 q^{61} - 32 q^{62} + 13 q^{63} + 28 q^{64} + 18 q^{65} + 6 q^{66} + 32 q^{67} - 26 q^{68} - 16 q^{69} + 18 q^{70} + 29 q^{71} + 19 q^{73} - 16 q^{74} + 23 q^{75} + 64 q^{76} - 21 q^{77} - 15 q^{78} + 56 q^{79} + 16 q^{81} + 14 q^{82} + 5 q^{83} + 18 q^{84} + 16 q^{85} - 20 q^{86} - 16 q^{87} + q^{88} + 7 q^{89} + 11 q^{90} - 6 q^{91} - 25 q^{92} + 24 q^{93} - 11 q^{94} + 39 q^{95} - 21 q^{96} + 35 q^{97} - 109 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9 + 11 * q^10 + 8 * q^11 + 25 * q^12 + 19 * q^13 + 16 * q^14 + 3 * q^15 + 31 * q^16 - 4 * q^17 - q^18 + 19 * q^19 + 16 * q^20 + 13 * q^21 + 6 * q^22 - 16 * q^23 + 23 * q^25 - 15 * q^26 + 16 * q^27 + 18 * q^28 - 16 * q^29 + 11 * q^30 + 24 * q^31 - 21 * q^32 + 8 * q^33 - 9 * q^34 - 13 * q^35 + 25 * q^36 + 26 * q^37 + 19 * q^39 - 22 * q^40 - 15 * q^41 + 16 * q^42 + 33 * q^43 + 6 * q^44 + 3 * q^45 + q^46 + 13 * q^47 + 31 * q^48 + 41 * q^49 + 13 * q^50 - 4 * q^51 - 26 * q^52 + 5 * q^53 - q^54 + 9 * q^55 + 40 * q^56 + 19 * q^57 + q^58 + 2 * q^59 + 16 * q^60 + 29 * q^61 - 32 * q^62 + 13 * q^63 + 28 * q^64 + 18 * q^65 + 6 * q^66 + 32 * q^67 - 26 * q^68 - 16 * q^69 + 18 * q^70 + 29 * q^71 + 19 * q^73 - 16 * q^74 + 23 * q^75 + 64 * q^76 - 21 * q^77 - 15 * q^78 + 56 * q^79 + 16 * q^81 + 14 * q^82 + 5 * q^83 + 18 * q^84 + 16 * q^85 - 20 * q^86 - 16 * q^87 + q^88 + 7 * q^89 + 11 * q^90 - 6 * q^91 - 25 * q^92 + 24 * q^93 - 11 * q^94 + 39 * q^95 - 21 * q^96 + 35 * q^97 - 109 * q^98 + 8 * q^99

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