LMFDB - Embedded newform 2001.2.a.l.1.8

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:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 18 x^{9} + 30 x^{8} + 124 x^{7} - 152 x^{6} - 408 x^{5} + 285 x^{4} + 634 x^{3} + \cdots - 108 $ x^11 - 2x^10 - 18x^9 + 30x^8 + 124x^7 - 152x^6 - 408x^5 + 285x^4 + 634x^3 - 93x^2 - 369x - 108
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$1.76484$ 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)

$f(q)$	$=$	$q+1.76484 q^{2} -1.00000 q^{3} +1.11465 q^{4} -2.54815 q^{5} -1.76484 q^{6} -4.97592 q^{7} -1.56250 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.76484 q^{2} -1.00000 q^{3} +1.11465 q^{4} -2.54815 q^{5} -1.76484 q^{6} -4.97592 q^{7} -1.56250 q^{8} +1.00000 q^{9} -4.49707 q^{10} +0.283045 q^{11} -1.11465 q^{12} -0.170966 q^{13} -8.78168 q^{14} +2.54815 q^{15} -4.98686 q^{16} +5.92041 q^{17} +1.76484 q^{18} +4.65876 q^{19} -2.84029 q^{20} +4.97592 q^{21} +0.499527 q^{22} +1.00000 q^{23} +1.56250 q^{24} +1.49307 q^{25} -0.301727 q^{26} -1.00000 q^{27} -5.54640 q^{28} -1.00000 q^{29} +4.49707 q^{30} +8.96888 q^{31} -5.67599 q^{32} -0.283045 q^{33} +10.4486 q^{34} +12.6794 q^{35} +1.11465 q^{36} +0.201428 q^{37} +8.22195 q^{38} +0.170966 q^{39} +3.98148 q^{40} -6.77658 q^{41} +8.78168 q^{42} -2.97728 q^{43} +0.315495 q^{44} -2.54815 q^{45} +1.76484 q^{46} +7.64176 q^{47} +4.98686 q^{48} +17.7597 q^{49} +2.63502 q^{50} -5.92041 q^{51} -0.190567 q^{52} +2.22897 q^{53} -1.76484 q^{54} -0.721240 q^{55} +7.77487 q^{56} -4.65876 q^{57} -1.76484 q^{58} -15.2006 q^{59} +2.84029 q^{60} +1.08366 q^{61} +15.8286 q^{62} -4.97592 q^{63} -0.0434802 q^{64} +0.435647 q^{65} -0.499527 q^{66} -4.78799 q^{67} +6.59918 q^{68} -1.00000 q^{69} +22.3770 q^{70} +15.9000 q^{71} -1.56250 q^{72} +5.09595 q^{73} +0.355488 q^{74} -1.49307 q^{75} +5.19288 q^{76} -1.40841 q^{77} +0.301727 q^{78} +15.8153 q^{79} +12.7073 q^{80} +1.00000 q^{81} -11.9596 q^{82} -4.95563 q^{83} +5.54640 q^{84} -15.0861 q^{85} -5.25441 q^{86} +1.00000 q^{87} -0.442257 q^{88} -3.87577 q^{89} -4.49707 q^{90} +0.850713 q^{91} +1.11465 q^{92} -8.96888 q^{93} +13.4865 q^{94} -11.8712 q^{95} +5.67599 q^{96} -16.0439 q^{97} +31.3430 q^{98} +0.283045 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9} + 14 q^{10} + 11 q^{11} - 18 q^{12} - 5 q^{13} + 17 q^{14} - 2 q^{15} + 20 q^{16} + 15 q^{17} + 2 q^{18} - 6 q^{19} + 21 q^{20} - 3 q^{21} - 10 q^{22} + 11 q^{23} - 18 q^{24} + 3 q^{25} - 5 q^{26} - 11 q^{27} + 7 q^{28} - 11 q^{29} - 14 q^{30} + 35 q^{31} + 28 q^{32} - 11 q^{33} + 28 q^{34} + 15 q^{35} + 18 q^{36} - 28 q^{37} - 2 q^{38} + 5 q^{39} - q^{40} + 10 q^{41} - 17 q^{42} - 6 q^{43} + 18 q^{44} + 2 q^{45} + 2 q^{46} + 15 q^{47} - 20 q^{48} + 22 q^{49} + 15 q^{50} - 15 q^{51} - 36 q^{52} - 7 q^{53} - 2 q^{54} - 12 q^{55} + 56 q^{56} + 6 q^{57} - 2 q^{58} - 20 q^{59} - 21 q^{60} - 20 q^{61} - 11 q^{62} + 3 q^{63} + 36 q^{64} + 11 q^{65} + 10 q^{66} - 39 q^{67} + 35 q^{68} - 11 q^{69} + 38 q^{70} + 49 q^{71} + 18 q^{72} - 3 q^{73} + 37 q^{74} - 3 q^{75} - 18 q^{76} + 25 q^{77} + 5 q^{78} + 41 q^{79} + 51 q^{80} + 11 q^{81} - 19 q^{82} + 13 q^{83} - 7 q^{84} + 62 q^{86} + 11 q^{87} - 40 q^{88} + 34 q^{89} + 14 q^{90} + 2 q^{91} + 18 q^{92} - 35 q^{93} - 14 q^{94} + 25 q^{95} - 28 q^{96} - 11 q^{97} + 53 q^{98} + 11 q^{99}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9 + 14 * q^10 + 11 * q^11 - 18 * q^12 - 5 * q^13 + 17 * q^14 - 2 * q^15 + 20 * q^16 + 15 * q^17 + 2 * q^18 - 6 * q^19 + 21 * q^20 - 3 * q^21 - 10 * q^22 + 11 * q^23 - 18 * q^24 + 3 * q^25 - 5 * q^26 - 11 * q^27 + 7 * q^28 - 11 * q^29 - 14 * q^30 + 35 * q^31 + 28 * q^32 - 11 * q^33 + 28 * q^34 + 15 * q^35 + 18 * q^36 - 28 * q^37 - 2 * q^38 + 5 * q^39 - q^40 + 10 * q^41 - 17 * q^42 - 6 * q^43 + 18 * q^44 + 2 * q^45 + 2 * q^46 + 15 * q^47 - 20 * q^48 + 22 * q^49 + 15 * q^50 - 15 * q^51 - 36 * q^52 - 7 * q^53 - 2 * q^54 - 12 * q^55 + 56 * q^56 + 6 * q^57 - 2 * q^58 - 20 * q^59 - 21 * q^60 - 20 * q^61 - 11 * q^62 + 3 * q^63 + 36 * q^64 + 11 * q^65 + 10 * q^66 - 39 * q^67 + 35 * q^68 - 11 * q^69 + 38 * q^70 + 49 * q^71 + 18 * q^72 - 3 * q^73 + 37 * q^74 - 3 * q^75 - 18 * q^76 + 25 * q^77 + 5 * q^78 + 41 * q^79 + 51 * q^80 + 11 * q^81 - 19 * q^82 + 13 * q^83 - 7 * q^84 + 62 * q^86 + 11 * q^87 - 40 * q^88 + 34 * q^89 + 14 * q^90 + 2 * q^91 + 18 * q^92 - 35 * q^93 - 14 * q^94 + 25 * q^95 - 28 * q^96 - 11 * q^97 + 53 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.76484	1.24793	0.623964	−	0.781453i	$-0.285521\pi$
$2$	1.76484	1.24793	0.623964	+	0.781453i	$0.285521\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.11465	0.557325
$5$	−2.54815	−1.13957	−0.569784	−	0.821795i	$-0.692973\pi$
$5$	−2.54815	−1.13957	−0.569784	+	0.821795i	$0.692973\pi$
$6$	−1.76484	−0.720492
$7$	−4.97592	−1.88072	−0.940360	−	0.340182i	$-0.889511\pi$
$7$	−4.97592	−1.88072	−0.940360	+	0.340182i	$0.889511\pi$
$8$	−1.56250	−0.552427
$9$	1.00000	0.333333
$10$	−4.49707	−1.42210
$11$	0.283045	0.0853411	0.0426706	−	0.999089i	$-0.486413\pi$
$11$	0.283045	0.0853411	0.0426706	+	0.999089i	$0.486413\pi$
$12$	−1.11465	−0.321772
$13$	−0.170966	−0.0474175	−0.0237087	−	0.999719i	$-0.507547\pi$
$13$	−0.170966	−0.0474175	−0.0237087	+	0.999719i	$0.507547\pi$
$14$	−8.78168	−2.34700
$15$	2.54815	0.657929
$16$	−4.98686	−1.24671
$17$	5.92041	1.43591	0.717956	−	0.696089i	$-0.245078\pi$
$17$	5.92041	1.43591	0.717956	+	0.696089i	$0.245078\pi$
$18$	1.76484	0.415976
$19$	4.65876	1.06879	0.534396	−	0.845234i	$-0.320539\pi$
$19$	4.65876	1.06879	0.534396	+	0.845234i	$0.320539\pi$
$20$	−2.84029	−0.635109
$21$	4.97592	1.08583
$22$	0.499527	0.106500
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.56250	0.318944
$25$	1.49307	0.298613
$26$	−0.301727	−0.0591736
$27$	−1.00000	−0.192450
$28$	−5.54640	−1.04817
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	4.49707	0.821049
$31$	8.96888	1.61086	0.805429	−	0.592692i	$-0.201935\pi$
$31$	8.96888	1.61086	0.805429	+	0.592692i	$0.201935\pi$
$32$	−5.67599	−1.00338
$33$	−0.283045	−0.0492717
$34$	10.4486	1.79191
$35$	12.6794	2.14321
$36$	1.11465	0.185775
$37$	0.201428	0.0331146	0.0165573	−	0.999863i	$-0.494729\pi$
$37$	0.201428	0.0331146	0.0165573	+	0.999863i	$0.494729\pi$
$38$	8.22195	1.33378
$39$	0.170966	0.0273765
$40$	3.98148	0.629528
$41$	−6.77658	−1.05832	−0.529162	−	0.848521i	$-0.677493\pi$
$41$	−6.77658	−1.05832	−0.529162	+	0.848521i	$0.677493\pi$
$42$	8.78168	1.35504
$43$	−2.97728	−0.454031	−0.227015	−	0.973891i	$-0.572897\pi$
$43$	−2.97728	−0.454031	−0.227015	+	0.973891i	$0.572897\pi$
$44$	0.315495	0.0475627
$45$	−2.54815	−0.379856
$46$	1.76484	0.260211
$47$	7.64176	1.11466	0.557332	−	0.830290i	$-0.311825\pi$
$47$	7.64176	1.11466	0.557332	+	0.830290i	$0.311825\pi$
$48$	4.98686	0.719791
$49$	17.7597	2.53711
$50$	2.63502	0.372648
$51$	−5.92041	−0.829024
$52$	−0.190567	−0.0264269
$53$	2.22897	0.306173	0.153087	−	0.988213i	$-0.451079\pi$
$53$	2.22897	0.306173	0.153087	+	0.988213i	$0.451079\pi$
$54$	−1.76484	−0.240164
$55$	−0.721240	−0.0972520
$56$	7.77487	1.03896
$57$	−4.65876	−0.617068
$58$	−1.76484	−0.231734
$59$	−15.2006	−1.97895	−0.989474	−	0.144711i	$-0.953775\pi$
$59$	−15.2006	−1.97895	−0.989474	+	0.144711i	$0.953775\pi$
$60$	2.84029	0.366680
$61$	1.08366	0.138748	0.0693741	−	0.997591i	$-0.477900\pi$
$61$	1.08366	0.138748	0.0693741	+	0.997591i	$0.477900\pi$
$62$	15.8286	2.01023
$63$	−4.97592	−0.626907
$64$	−0.0434802	−0.00543502
$65$	0.435647	0.0540354
$66$	−0.499527	−0.0614876
$67$	−4.78799	−0.584946	−0.292473	−	0.956274i	$-0.594478\pi$
$67$	−4.78799	−0.584946	−0.292473	+	0.956274i	$0.594478\pi$
$68$	6.59918	0.800269
$69$	−1.00000	−0.120386
$70$	22.3770	2.67457
$71$	15.9000	1.88698	0.943489	−	0.331404i	$-0.107522\pi$
$71$	15.9000	1.88698	0.943489	+	0.331404i	$0.107522\pi$
$72$	−1.56250	−0.184142
$73$	5.09595	0.596436	0.298218	−	0.954498i	$-0.403608\pi$
$73$	5.09595	0.596436	0.298218	+	0.954498i	$0.403608\pi$
$74$	0.355488	0.0413247
$75$	−1.49307	−0.172405
$76$	5.19288	0.595664
$77$	−1.40841	−0.160503
$78$	0.301727	0.0341639
$79$	15.8153	1.77936	0.889678	−	0.456588i	$-0.150929\pi$
$79$	15.8153	1.77936	0.889678	+	0.456588i	$0.150929\pi$
$80$	12.7073	1.42071
$81$	1.00000	0.111111
$82$	−11.9596	−1.32071
$83$	−4.95563	−0.543951	−0.271976	−	0.962304i	$-0.587677\pi$
$83$	−4.95563	−0.543951	−0.271976	+	0.962304i	$0.587677\pi$
$84$	5.54640	0.605162
$85$	−15.0861	−1.63632
$86$	−5.25441	−0.566597
$87$	1.00000	0.107211
$88$	−0.442257	−0.0471448
$89$	−3.87577	−0.410830	−0.205415	−	0.978675i	$-0.565854\pi$
$89$	−3.87577	−0.410830	−0.205415	+	0.978675i	$0.565854\pi$
$90$	−4.49707	−0.474033
$91$	0.850713	0.0891790
$92$	1.11465	0.116210
$93$	−8.96888	−0.930029
$94$	13.4865	1.39102
$95$	−11.8712	−1.21796
$96$	5.67599	0.579303
$97$	−16.0439	−1.62901	−0.814507	−	0.580154i	$-0.802992\pi$
$97$	−16.0439	−1.62901	−0.814507	+	0.580154i	$0.802992\pi$
$98$	31.3430	3.16613
$99$	0.283045	0.0284470
$100$	1.66425	0.166425
$101$	5.49297	0.546571	0.273285	−	0.961933i	$-0.411890\pi$
$101$	5.49297	0.546571	0.273285	+	0.961933i	$0.411890\pi$
$102$	−10.4486	−1.03456
$103$	−11.1030	−1.09401	−0.547004	−	0.837130i	$-0.684232\pi$
$103$	−11.1030	−1.09401	−0.547004	+	0.837130i	$0.684232\pi$
$104$	0.267135	0.0261947
$105$	−12.6794	−1.23738
$106$	3.93378	0.382082
$107$	4.19747	0.405785	0.202892	−	0.979201i	$-0.434966\pi$
$107$	4.19747	0.405785	0.202892	+	0.979201i	$0.434966\pi$
$108$	−1.11465	−0.107257
$109$	−1.34044	−0.128391	−0.0641954	−	0.997937i	$-0.520448\pi$
$109$	−1.34044	−0.128391	−0.0641954	+	0.997937i	$0.520448\pi$
$110$	−1.27287	−0.121363
$111$	−0.201428	−0.0191187
$112$	24.8142	2.34472
$113$	−6.13822	−0.577435	−0.288718	−	0.957414i	$-0.593229\pi$
$113$	−6.13822	−0.577435	−0.288718	+	0.957414i	$0.593229\pi$
$114$	−8.22195	−0.770056
$115$	−2.54815	−0.237616
$116$	−1.11465	−0.103493
$117$	−0.170966	−0.0158058
$118$	−26.8266	−2.46958
$119$	−29.4595	−2.70055
$120$	−3.98148	−0.363458
$121$	−10.9199	−0.992717
$122$	1.91248	0.173148
$123$	6.77658	0.611023
$124$	9.99715	0.897771
$125$	8.93619	0.799277
$126$	−8.78168	−0.782334
$127$	20.6626	1.83351	0.916755	−	0.399450i	$-0.130799\pi$
$127$	20.6626	1.83351	0.916755	+	0.399450i	$0.130799\pi$
$128$	11.2752	0.996600
$129$	2.97728	0.262135
$130$	0.768847	0.0674323
$131$	14.9676	1.30772	0.653861	−	0.756614i	$-0.273148\pi$
$131$	14.9676	1.30772	0.653861	+	0.756614i	$0.273148\pi$
$132$	−0.315495	−0.0274603
$133$	−23.1816	−2.01010
$134$	−8.45002	−0.729970
$135$	2.54815	0.219310
$136$	−9.25064	−0.793236
$137$	7.68590	0.656651	0.328326	−	0.944565i	$-0.393516\pi$
$137$	7.68590	0.656651	0.328326	+	0.944565i	$0.393516\pi$
$138$	−1.76484	−0.150233
$139$	18.0155	1.52806	0.764029	−	0.645182i	$-0.223218\pi$
$139$	18.0155	1.52806	0.764029	+	0.645182i	$0.223218\pi$
$140$	14.1331	1.19446
$141$	−7.64176	−0.643552
$142$	28.0608	2.35481
$143$	−0.0483910	−0.00404666
$144$	−4.98686	−0.415571
$145$	2.54815	0.211612
$146$	8.99353	0.744310
$147$	−17.7597	−1.46480
$148$	0.224522	0.0184556
$149$	19.5667	1.60297	0.801485	−	0.598015i	$-0.204044\pi$
$149$	19.5667	1.60297	0.801485	+	0.598015i	$0.204044\pi$
$150$	−2.63502	−0.215148
$151$	−3.32858	−0.270876	−0.135438	−	0.990786i	$-0.543244\pi$
$151$	−3.32858	−0.270876	−0.135438	+	0.990786i	$0.543244\pi$
$152$	−7.27931	−0.590430
$153$	5.92041	0.478637
$154$	−2.48561	−0.200296
$155$	−22.8540	−1.83568
$156$	0.190567	0.0152576
$157$	−18.4270	−1.47063	−0.735317	−	0.677723i	$-0.762967\pi$
$157$	−18.4270	−1.47063	−0.735317	+	0.677723i	$0.762967\pi$
$158$	27.9114	2.22051
$159$	−2.22897	−0.176769
$160$	14.4633	1.14342
$161$	−4.97592	−0.392157
$162$	1.76484	0.138659
$163$	2.52999	0.198164	0.0990822	−	0.995079i	$-0.468409\pi$
$163$	2.52999	0.198164	0.0990822	+	0.995079i	$0.468409\pi$
$164$	−7.55350	−0.589830
$165$	0.721240	0.0561484
$166$	−8.74588	−0.678812
$167$	−1.30974	−0.101350	−0.0506752	−	0.998715i	$-0.516137\pi$
$167$	−1.30974	−0.101350	−0.0506752	+	0.998715i	$0.516137\pi$
$168$	−7.77487	−0.599844
$169$	−12.9708	−0.997752
$170$	−26.6245	−2.04201
$171$	4.65876	0.356264
$172$	−3.31862	−0.253042
$173$	13.3226	1.01290	0.506451	−	0.862269i	$-0.330957\pi$
$173$	13.3226	1.01290	0.506451	+	0.862269i	$0.330957\pi$
$174$	1.76484	0.133792
$175$	−7.42938	−0.561608
$176$	−1.41150	−0.106396
$177$	15.2006	1.14255
$178$	−6.84009	−0.512687
$179$	−6.31895	−0.472300	−0.236150	−	0.971717i	$-0.575886\pi$
$179$	−6.31895	−0.472300	−0.236150	+	0.971717i	$0.575886\pi$
$180$	−2.84029	−0.211703
$181$	−9.65286	−0.717491	−0.358746	−	0.933435i	$-0.616795\pi$
$181$	−9.65286	−0.717491	−0.358746	+	0.933435i	$0.616795\pi$
$182$	1.50137	0.111289
$183$	−1.08366	−0.0801063
$184$	−1.56250	−0.115189
$185$	−0.513270	−0.0377364
$186$	−15.8286	−1.16061
$187$	1.67574	0.122542
$188$	8.51788	0.621230
$189$	4.97592	0.361945
$190$	−20.9508	−1.51993
$191$	−1.31803	−0.0953691	−0.0476846	−	0.998862i	$-0.515184\pi$
$191$	−1.31803	−0.0953691	−0.0476846	+	0.998862i	$0.515184\pi$
$192$	0.0434802	0.00313791
$193$	21.0522	1.51537	0.757685	−	0.652620i	$-0.226330\pi$
$193$	21.0522	1.51537	0.757685	+	0.652620i	$0.226330\pi$
$194$	−28.3149	−2.03289
$195$	−0.435647	−0.0311974
$196$	19.7959	1.41399
$197$	6.15267	0.438359	0.219180	−	0.975684i	$-0.429662\pi$
$197$	6.15267	0.438359	0.219180	+	0.975684i	$0.429662\pi$
$198$	0.499527	0.0354999
$199$	12.2203	0.866274	0.433137	−	0.901328i	$-0.357407\pi$
$199$	12.2203	0.866274	0.433137	+	0.901328i	$0.357407\pi$
$200$	−2.33292	−0.164962
$201$	4.78799	0.337719
$202$	9.69419	0.682081
$203$	4.97592	0.349241
$204$	−6.59918	−0.462035
$205$	17.2677	1.20603
$206$	−19.5949	−1.36524
$207$	1.00000	0.0695048
$208$	0.852584	0.0591160
$209$	1.31864	0.0912120
$210$	−22.3770	−1.54416
$211$	4.47990	0.308409	0.154205	−	0.988039i	$-0.450719\pi$
$211$	4.47990	0.308409	0.154205	+	0.988039i	$0.450719\pi$
$212$	2.48452	0.170638
$213$	−15.9000	−1.08945
$214$	7.40785	0.506390
$215$	7.58655	0.517398
$216$	1.56250	0.106315
$217$	−44.6284	−3.02957
$218$	−2.36566	−0.160223
$219$	−5.09595	−0.344353
$220$	−0.803929	−0.0542009
$221$	−1.01219	−0.0680873
$222$	−0.355488	−0.0238588
$223$	2.63867	0.176699	0.0883493	−	0.996090i	$-0.471841\pi$
$223$	2.63867	0.176699	0.0883493	+	0.996090i	$0.471841\pi$
$224$	28.2432	1.88708
$225$	1.49307	0.0995378
$226$	−10.8330	−0.720598
$227$	14.3265	0.950885	0.475442	−	0.879747i	$-0.342288\pi$
$227$	14.3265	0.950885	0.475442	+	0.879747i	$0.342288\pi$
$228$	−5.19288	−0.343907
$229$	−24.0371	−1.58842	−0.794208	−	0.607647i	$-0.792114\pi$
$229$	−24.0371	−1.58842	−0.794208	+	0.607647i	$0.792114\pi$
$230$	−4.49707	−0.296528
$231$	1.40841	0.0926663
$232$	1.56250	0.102583
$233$	−0.647548	−0.0424223	−0.0212111	−	0.999775i	$-0.506752\pi$
$233$	−0.647548	−0.0424223	−0.0212111	+	0.999775i	$0.506752\pi$
$234$	−0.301727	−0.0197245
$235$	−19.4723	−1.27024
$236$	−16.9433	−1.10292
$237$	−15.8153	−1.02731
$238$	−51.9912	−3.37009
$239$	23.0226	1.48921	0.744603	−	0.667508i	$-0.232639\pi$
$239$	23.0226	1.48921	0.744603	+	0.667508i	$0.232639\pi$
$240$	−12.7073	−0.820250
$241$	4.27926	0.275652	0.137826	−	0.990456i	$-0.455989\pi$
$241$	4.27926	0.275652	0.137826	+	0.990456i	$0.455989\pi$
$242$	−19.2718	−1.23884
$243$	−1.00000	−0.0641500
$244$	1.20790	0.0773278
$245$	−45.2545	−2.89120
$246$	11.9596	0.762513
$247$	−0.796490	−0.0506795
$248$	−14.0139	−0.889881
$249$	4.95563	0.314050
$250$	15.7709	0.997440
$251$	−13.5637	−0.856132	−0.428066	−	0.903747i	$-0.640805\pi$
$251$	−13.5637	−0.856132	−0.428066	+	0.903747i	$0.640805\pi$
$252$	−5.54640	−0.349390
$253$	0.283045	0.0177949
$254$	36.4661	2.28809
$255$	15.0861	0.944728
$256$	19.9859	1.24912
$257$	−2.03382	−0.126866	−0.0634330	−	0.997986i	$-0.520205\pi$
$257$	−2.03382	−0.126866	−0.0634330	+	0.997986i	$0.520205\pi$
$258$	5.25441	0.327125
$259$	−1.00229	−0.0622793
$260$	0.485594	0.0301153
$261$	−1.00000	−0.0618984
$262$	26.4153	1.63194
$263$	11.9405	0.736283	0.368142	−	0.929770i	$-0.379994\pi$
$263$	11.9405	0.736283	0.368142	+	0.929770i	$0.379994\pi$
$264$	0.442257	0.0272190
$265$	−5.67976	−0.348905
$266$	−40.9117	−2.50846
$267$	3.87577	0.237193
$268$	−5.33693	−0.326005
$269$	15.1479	0.923587	0.461793	−	0.886988i	$-0.347206\pi$
$269$	15.1479	0.923587	0.461793	+	0.886988i	$0.347206\pi$
$270$	4.49707	0.273683
$271$	20.1868	1.22626	0.613132	−	0.789981i	$-0.289909\pi$
$271$	20.1868	1.22626	0.613132	+	0.789981i	$0.289909\pi$
$272$	−29.5242	−1.79017
$273$	−0.850713	−0.0514875
$274$	13.5644	0.819453
$275$	0.422604	0.0254840
$276$	−1.11465	−0.0670940
$277$	−2.22660	−0.133783	−0.0668917	−	0.997760i	$-0.521308\pi$
$277$	−2.22660	−0.133783	−0.0668917	+	0.997760i	$0.521308\pi$
$278$	31.7945	1.90691
$279$	8.96888	0.536953
$280$	−19.8115	−1.18397
$281$	21.9565	1.30981	0.654907	−	0.755710i	$-0.272708\pi$
$281$	21.9565	1.30981	0.654907	+	0.755710i	$0.272708\pi$
$282$	−13.4865	−0.803107
$283$	4.53617	0.269647	0.134824	−	0.990870i	$-0.456953\pi$
$283$	4.53617	0.269647	0.134824	+	0.990870i	$0.456953\pi$
$284$	17.7229	1.05166
$285$	11.8712	0.703190
$286$	−0.0854023	−0.00504994
$287$	33.7197	1.99041
$288$	−5.67599	−0.334461
$289$	18.0513	1.06184
$290$	4.49707	0.264077
$291$	16.0439	0.940511
$292$	5.68020	0.332409
$293$	−11.0848	−0.647581	−0.323790	−	0.946129i	$-0.604957\pi$
$293$	−11.0848	−0.647581	−0.323790	+	0.946129i	$0.604957\pi$
$294$	−31.3430	−1.82796
$295$	38.7334	2.25514
$296$	−0.314732	−0.0182934
$297$	−0.283045	−0.0164239
$298$	34.5321	2.00039
$299$	−0.170966	−0.00988723
$300$	−1.66425	−0.0960853
$301$	14.8147	0.853904
$302$	−5.87440	−0.338034
$303$	−5.49297	−0.315563
$304$	−23.2326	−1.33248
$305$	−2.76132	−0.158113
$306$	10.4486	0.597305
$307$	−11.6843	−0.666856	−0.333428	−	0.942776i	$-0.608205\pi$
$307$	−11.6843	−0.666856	−0.333428	+	0.942776i	$0.608205\pi$
$308$	−1.56988	−0.0894521
$309$	11.1030	0.631626
$310$	−40.3337	−2.29080
$311$	18.4799	1.04790	0.523949	−	0.851750i	$-0.324458\pi$
$311$	18.4799	1.04790	0.523949	+	0.851750i	$0.324458\pi$
$312$	−0.267135	−0.0151235
$313$	1.66419	0.0940656	0.0470328	−	0.998893i	$-0.485023\pi$
$313$	1.66419	0.0940656	0.0470328	+	0.998893i	$0.485023\pi$
$314$	−32.5206	−1.83525
$315$	12.6794	0.714402
$316$	17.6285	0.991679
$317$	6.66769	0.374495	0.187247	−	0.982313i	$-0.440043\pi$
$317$	6.66769	0.374495	0.187247	+	0.982313i	$0.440043\pi$
$318$	−3.93378	−0.220595
$319$	−0.283045	−0.0158475
$320$	0.110794	0.00619357
$321$	−4.19747	−0.234280
$322$	−8.78168	−0.489384
$323$	27.5818	1.53469
$324$	1.11465	0.0619250
$325$	−0.255264	−0.0141595
$326$	4.46503	0.247295
$327$	1.34044	0.0741265
$328$	10.5884	0.584646
$329$	−38.0247	−2.09637
$330$	1.27287	0.0700692
$331$	19.8701	1.09216	0.546080	−	0.837733i	$-0.316119\pi$
$331$	19.8701	1.09216	0.546080	+	0.837733i	$0.316119\pi$
$332$	−5.52379	−0.303157
$333$	0.201428	0.0110382
$334$	−2.31147	−0.126478
$335$	12.2005	0.666585
$336$	−24.8142	−1.35372
$337$	−12.8728	−0.701228	−0.350614	−	0.936520i	$-0.614027\pi$
$337$	−12.8728	−0.701228	−0.350614	+	0.936520i	$0.614027\pi$
$338$	−22.8913	−1.24512
$339$	6.13822	0.333382
$340$	−16.8157	−0.911960
$341$	2.53859	0.137472
$342$	8.22195	0.444592
$343$	−53.5396	−2.89087
$344$	4.65199	0.250819
$345$	2.54815	0.137188
$346$	23.5123	1.26403
$347$	9.77259	0.524620	0.262310	−	0.964984i	$-0.415516\pi$
$347$	9.77259	0.524620	0.262310	+	0.964984i	$0.415516\pi$
$348$	1.11465	0.0597515
$349$	13.1699	0.704971	0.352486	−	0.935817i	$-0.385337\pi$
$349$	13.1699	0.704971	0.352486	+	0.935817i	$0.385337\pi$
$350$	−13.1116	−0.700846
$351$	0.170966	0.00912550
$352$	−1.60656	−0.0856298
$353$	−14.5533	−0.774593	−0.387297	−	0.921955i	$-0.626591\pi$
$353$	−14.5533	−0.774593	−0.387297	+	0.921955i	$0.626591\pi$
$354$	26.8266	1.42582
$355$	−40.5155	−2.15034
$356$	−4.32012	−0.228966
$357$	29.4595	1.55916
$358$	−11.1519	−0.589397
$359$	−11.6926	−0.617113	−0.308556	−	0.951206i	$-0.599846\pi$
$359$	−11.6926	−0.617113	−0.308556	+	0.951206i	$0.599846\pi$
$360$	3.98148	0.209843
$361$	2.70404	0.142318
$362$	−17.0357	−0.895378
$363$	10.9199	0.573145
$364$	0.948247	0.0497016
$365$	−12.9853	−0.679679
$366$	−1.91248	−0.0999669
$367$	−0.437440	−0.0228342	−0.0114171	−	0.999935i	$-0.503634\pi$
$367$	−0.437440	−0.0228342	−0.0114171	+	0.999935i	$0.503634\pi$
$368$	−4.98686	−0.259958
$369$	−6.77658	−0.352774
$370$	−0.905838	−0.0470923
$371$	−11.0912	−0.575826
$372$	−9.99715	−0.518328
$373$	14.7884	0.765714	0.382857	−	0.923808i	$-0.374940\pi$
$373$	14.7884	0.765714	0.382857	+	0.923808i	$0.374940\pi$
$374$	2.95741	0.152924
$375$	−8.93619	−0.461463
$376$	−11.9402	−0.615771
$377$	0.170966	0.00880521
$378$	8.78168	0.451681
$379$	−14.0767	−0.723073	−0.361537	−	0.932358i	$-0.617748\pi$
$379$	−14.0767	−0.723073	−0.361537	+	0.932358i	$0.617748\pi$
$380$	−13.2322	−0.678800
$381$	−20.6626	−1.05858
$382$	−2.32610	−0.119014
$383$	−14.7132	−0.751809	−0.375905	−	0.926658i	$-0.622668\pi$
$383$	−14.7132	−0.751809	−0.375905	+	0.926658i	$0.622668\pi$
$384$	−11.2752	−0.575387
$385$	3.58883	0.182904
$386$	37.1537	1.89107
$387$	−2.97728	−0.151344
$388$	−17.8833	−0.907889
$389$	11.4361	0.579835	0.289917	−	0.957052i	$-0.406372\pi$
$389$	11.4361	0.579835	0.289917	+	0.957052i	$0.406372\pi$
$390$	−0.768847	−0.0389321
$391$	5.92041	0.299408
$392$	−27.7496	−1.40157
$393$	−14.9676	−0.755014
$394$	10.8585	0.547041
$395$	−40.2997	−2.02770
$396$	0.315495	0.0158542
$397$	31.0202	1.55686	0.778430	−	0.627732i	$-0.216016\pi$
$397$	31.0202	1.55686	0.778430	+	0.627732i	$0.216016\pi$
$398$	21.5668	1.08105
$399$	23.1816	1.16053
$400$	−7.44571	−0.372285
$401$	−37.4659	−1.87096	−0.935480	−	0.353379i	$-0.885032\pi$
$401$	−37.4659	−1.87096	−0.935480	+	0.353379i	$0.885032\pi$
$402$	8.45002	0.421449
$403$	−1.53337	−0.0763828
$404$	6.12273	0.304617
$405$	−2.54815	−0.126619
$406$	8.78168	0.435827
$407$	0.0570132	0.00282604
$408$	9.25064	0.457975
$409$	−30.1554	−1.49109	−0.745544	−	0.666456i	$-0.767810\pi$
$409$	−30.1554	−1.49109	−0.745544	+	0.666456i	$0.767810\pi$
$410$	30.4747	1.50504
$411$	−7.68590	−0.379118
$412$	−12.3759	−0.609718
$413$	75.6369	3.72185
$414$	1.76484	0.0867370
$415$	12.6277	0.619869
$416$	0.970402	0.0475779
$417$	−18.0155	−0.882225
$418$	2.32718	0.113826
$419$	21.3187	1.04149	0.520745	−	0.853713i	$-0.325654\pi$
$419$	21.3187	1.04149	0.520745	+	0.853713i	$0.325654\pi$
$420$	−14.1331	−0.689623
$421$	−39.1557	−1.90833	−0.954165	−	0.299280i	$-0.903254\pi$
$421$	−39.1557	−1.90833	−0.954165	+	0.299280i	$0.903254\pi$
$422$	7.90629	0.384872
$423$	7.64176	0.371555
$424$	−3.48277	−0.169138
$425$	8.83957	0.428782
$426$	−28.0608	−1.35955
$427$	−5.39219	−0.260946
$428$	4.67871	0.226154
$429$	0.0483910	0.00233634
$430$	13.3890	0.645676
$431$	17.4143	0.838818	0.419409	−	0.907797i	$-0.362237\pi$
$431$	17.4143	0.838818	0.419409	+	0.907797i	$0.362237\pi$
$432$	4.98686	0.239930
$433$	−12.3095	−0.591555	−0.295778	−	0.955257i	$-0.595579\pi$
$433$	−12.3095	−0.591555	−0.295778	+	0.955257i	$0.595579\pi$
$434$	−78.7618	−3.78069
$435$	−2.54815	−0.122174
$436$	−1.49412	−0.0715554
$437$	4.65876	0.222859
$438$	−8.99353	−0.429727
$439$	−14.3065	−0.682814	−0.341407	−	0.939916i	$-0.610903\pi$
$439$	−14.3065	−0.682814	−0.341407	+	0.939916i	$0.610903\pi$
$440$	1.12694	0.0537246
$441$	17.7597	0.845702
$442$	−1.78635	−0.0849680
$443$	−13.9006	−0.660439	−0.330220	−	0.943904i	$-0.607123\pi$
$443$	−13.9006	−0.660439	−0.330220	+	0.943904i	$0.607123\pi$
$444$	−0.224522	−0.0106553
$445$	9.87603	0.468169
$446$	4.65683	0.220507
$447$	−19.5667	−0.925475
$448$	0.216354	0.0102217
$449$	29.6600	1.39974	0.699872	−	0.714268i	$-0.253240\pi$
$449$	29.6600	1.39974	0.699872	+	0.714268i	$0.253240\pi$
$450$	2.63502	0.124216
$451$	−1.91807	−0.0903185
$452$	−6.84196	−0.321819
$453$	3.32858	0.156390
$454$	25.2840	1.18664
$455$	−2.16774	−0.101625
$456$	7.27931	0.340885
$457$	38.3682	1.79479	0.897394	−	0.441230i	$-0.145458\pi$
$457$	38.3682	1.79479	0.897394	+	0.441230i	$0.145458\pi$
$458$	−42.4215	−1.98223
$459$	−5.92041	−0.276341
$460$	−2.84029	−0.132429
$461$	−28.6130	−1.33264	−0.666321	−	0.745665i	$-0.732132\pi$
$461$	−28.6130	−1.33264	−0.666321	+	0.745665i	$0.732132\pi$
$462$	2.48561	0.115641
$463$	6.51659	0.302852	0.151426	−	0.988469i	$-0.451614\pi$
$463$	6.51659	0.302852	0.151426	+	0.988469i	$0.451614\pi$
$464$	4.98686	0.231509
$465$	22.8540	1.05983
$466$	−1.14282	−0.0529400
$467$	−16.6592	−0.770895	−0.385448	−	0.922730i	$-0.625953\pi$
$467$	−16.6592	−0.770895	−0.385448	+	0.922730i	$0.625953\pi$
$468$	−0.190567	−0.00880898
$469$	23.8246	1.10012
$470$	−34.3655	−1.58516
$471$	18.4270	0.849071
$472$	23.7509	1.09322
$473$	−0.842702	−0.0387475
$474$	−27.9114	−1.28201
$475$	6.95584	0.319156
$476$	−32.8370	−1.50508
$477$	2.22897	0.102058
$478$	40.6310	1.85842
$479$	−9.73200	−0.444666	−0.222333	−	0.974971i	$-0.571367\pi$
$479$	−9.73200	−0.444666	−0.222333	+	0.974971i	$0.571367\pi$
$480$	−14.4633	−0.660155
$481$	−0.0344375	−0.00157021
$482$	7.55220	0.343993
$483$	4.97592	0.226412
$484$	−12.1718	−0.553266
$485$	40.8823	1.85637
$486$	−1.76484	−0.0800546
$487$	−10.4945	−0.475551	−0.237775	−	0.971320i	$-0.576418\pi$
$487$	−10.4945	−0.475551	−0.237775	+	0.971320i	$0.576418\pi$
$488$	−1.69321	−0.0766482
$489$	−2.52999	−0.114410
$490$	−79.8668	−3.60801
$491$	31.9404	1.44145	0.720726	−	0.693220i	$-0.243809\pi$
$491$	31.9404	1.44145	0.720726	+	0.693220i	$0.243809\pi$
$492$	7.55350	0.340538
$493$	−5.92041	−0.266642
$494$	−1.40568	−0.0632443
$495$	−0.721240	−0.0324173
$496$	−44.7265	−2.00828
$497$	−79.1169	−3.54888
$498$	8.74588	0.391912
$499$	2.06782	0.0925684	0.0462842	−	0.998928i	$-0.485262\pi$
$499$	2.06782	0.0925684	0.0462842	+	0.998928i	$0.485262\pi$
$500$	9.96072	0.445457
$501$	1.30974	0.0585147
$502$	−23.9377	−1.06839
$503$	−39.4576	−1.75933	−0.879663	−	0.475598i	$-0.842232\pi$
$503$	−39.4576	−1.75933	−0.879663	+	0.475598i	$0.842232\pi$
$504$	7.77487	0.346320
$505$	−13.9969	−0.622854
$506$	0.499527	0.0222067
$507$	12.9708	0.576052
$508$	23.0316	1.02186
$509$	26.0870	1.15629	0.578143	−	0.815935i	$-0.303777\pi$
$509$	26.0870	1.15629	0.578143	+	0.815935i	$0.303777\pi$
$510$	26.6245	1.17895
$511$	−25.3570	−1.12173
$512$	12.7214	0.562212
$513$	−4.65876	−0.205689
$514$	−3.58936	−0.158320
$515$	28.2920	1.24670
$516$	3.31862	0.146094
$517$	2.16296	0.0951267
$518$	−1.76888	−0.0777202
$519$	−13.3226	−0.584799
$520$	−0.680699	−0.0298506
$521$	35.0010	1.53342	0.766711	−	0.641992i	$-0.221892\pi$
$521$	35.0010	1.53342	0.766711	+	0.641992i	$0.221892\pi$
$522$	−1.76484	−0.0772448
$523$	−14.5683	−0.637026	−0.318513	−	0.947919i	$-0.603183\pi$
$523$	−14.5683	−0.637026	−0.318513	+	0.947919i	$0.603183\pi$
$524$	16.6836	0.728826
$525$	7.42938	0.324245
$526$	21.0730	0.918828
$527$	53.0995	2.31305
$528$	1.41150	0.0614277
$529$	1.00000	0.0434783
$530$	−10.0238	−0.435408
$531$	−15.2006	−0.659649
$532$	−25.8393	−1.12028
$533$	1.15857	0.0501830
$534$	6.84009	0.296000
$535$	−10.6958	−0.462419
$536$	7.48123	0.323140
$537$	6.31895	0.272683
$538$	26.7337	1.15257
$539$	5.02680	0.216519
$540$	2.84029	0.122227
$541$	−25.5258	−1.09744	−0.548719	−	0.836007i	$-0.684884\pi$
$541$	−25.5258	−1.09744	−0.548719	+	0.836007i	$0.684884\pi$
$542$	35.6265	1.53029
$543$	9.65286	0.414244
$544$	−33.6042	−1.44077
$545$	3.41564	0.146310
$546$	−1.50137	−0.0642527
$547$	8.84906	0.378358	0.189179	−	0.981943i	$-0.439417\pi$
$547$	8.84906	0.378358	0.189179	+	0.981943i	$0.439417\pi$
$548$	8.56709	0.365968
$549$	1.08366	0.0462494
$550$	0.745828	0.0318022
$551$	−4.65876	−0.198470
$552$	1.56250	0.0665044
$553$	−78.6955	−3.34647
$554$	−3.92959	−0.166952
$555$	0.513270	0.0217871
$556$	20.0810	0.851625
$557$	26.6759	1.13029	0.565147	−	0.824990i	$-0.308819\pi$
$557$	26.6759	1.13029	0.565147	+	0.824990i	$0.308819\pi$
$558$	15.8286	0.670078
$559$	0.509014	0.0215290
$560$	−63.2302	−2.67197
$561$	−1.67574	−0.0707498
$562$	38.7496	1.63455
$563$	−16.5834	−0.698906	−0.349453	−	0.936954i	$-0.613633\pi$
$563$	−16.5834	−0.698906	−0.349453	+	0.936954i	$0.613633\pi$
$564$	−8.51788	−0.358667
$565$	15.6411	0.658026
$566$	8.00560	0.336501
$567$	−4.97592	−0.208969
$568$	−24.8437	−1.04242
$569$	24.5455	1.02900	0.514500	−	0.857491i	$-0.327978\pi$
$569$	24.5455	1.02900	0.514500	+	0.857491i	$0.327978\pi$
$570$	20.9508	0.877531
$571$	−26.4099	−1.10522	−0.552611	−	0.833439i	$-0.686368\pi$
$571$	−26.4099	−1.10522	−0.552611	+	0.833439i	$0.686368\pi$
$572$	−0.0539390	−0.00225530
$573$	1.31803	0.0550614
$574$	59.5097	2.48389
$575$	1.49307	0.0622652
$576$	−0.0434802	−0.00181167
$577$	−20.0446	−0.834469	−0.417234	−	0.908799i	$-0.637001\pi$
$577$	−20.0446	−0.834469	−0.417234	+	0.908799i	$0.637001\pi$
$578$	31.8576	1.32510
$579$	−21.0522	−0.874900
$580$	2.84029	0.117937
$581$	24.6588	1.02302
$582$	28.3149	1.17369
$583$	0.630899	0.0261292
$584$	−7.96243	−0.329488
$585$	0.435647	0.0180118
$586$	−19.5629	−0.808134
$587$	2.29610	0.0947702	0.0473851	−	0.998877i	$-0.484911\pi$
$587$	2.29610	0.0947702	0.0473851	+	0.998877i	$0.484911\pi$
$588$	−19.7959	−0.816368
$589$	41.7838	1.72167
$590$	68.3581	2.81426
$591$	−6.15267	−0.253087
$592$	−1.00449	−0.0412845
$593$	−12.5883	−0.516940	−0.258470	−	0.966019i	$-0.583218\pi$
$593$	−12.5883	−0.516940	−0.258470	+	0.966019i	$0.583218\pi$
$594$	−0.499527	−0.0204959
$595$	75.0672	3.07745
$596$	21.8101	0.893375
$597$	−12.2203	−0.500144
$598$	−0.301727	−0.0123386
$599$	26.0338	1.06371	0.531857	−	0.846834i	$-0.321494\pi$
$599$	26.0338	1.06371	0.531857	+	0.846834i	$0.321494\pi$
$600$	2.33292	0.0952409
$601$	14.9942	0.611628	0.305814	−	0.952091i	$-0.401071\pi$
$601$	14.9942	0.611628	0.305814	+	0.952091i	$0.401071\pi$
$602$	26.1455	1.06561
$603$	−4.78799	−0.194982
$604$	−3.71020	−0.150966
$605$	27.8255	1.13127
$606$	−9.69419	−0.393800
$607$	−6.38075	−0.258987	−0.129493	−	0.991580i	$-0.541335\pi$
$607$	−6.38075	−0.258987	−0.129493	+	0.991580i	$0.541335\pi$
$608$	−26.4431	−1.07241
$609$	−4.97592	−0.201634
$610$	−4.87328	−0.197313
$611$	−1.30648	−0.0528546
$612$	6.59918	0.266756
$613$	−21.4514	−0.866413	−0.433206	−	0.901295i	$-0.642618\pi$
$613$	−21.4514	−0.866413	−0.433206	+	0.901295i	$0.642618\pi$
$614$	−20.6208	−0.832188
$615$	−17.2677	−0.696302
$616$	2.20063	0.0886661
$617$	27.6955	1.11498	0.557489	−	0.830184i	$-0.311765\pi$
$617$	27.6955	1.11498	0.557489	+	0.830184i	$0.311765\pi$
$618$	19.5949	0.788224
$619$	11.3783	0.457332	0.228666	−	0.973505i	$-0.426564\pi$
$619$	11.3783	0.457332	0.228666	+	0.973505i	$0.426564\pi$
$620$	−25.4742	−1.02307
$621$	−1.00000	−0.0401286
$622$	32.6140	1.30770
$623$	19.2855	0.772657
$624$	−0.852584	−0.0341307
$625$	−30.2361	−1.20944
$626$	2.93702	0.117387
$627$	−1.31864	−0.0526613
$628$	−20.5396	−0.819621
$629$	1.19254	0.0475497
$630$	22.3770	0.891522
$631$	−45.9809	−1.83047	−0.915235	−	0.402921i	$-0.867995\pi$
$631$	−45.9809	−1.83047	−0.915235	+	0.402921i	$0.867995\pi$
$632$	−24.7114	−0.982965
$633$	−4.47990	−0.178060
$634$	11.7674	0.467342
$635$	−52.6514	−2.08941
$636$	−2.48452	−0.0985178
$637$	−3.03632	−0.120303
$638$	−0.499527	−0.0197765
$639$	15.9000	0.628993
$640$	−28.7310	−1.13569
$641$	8.77087	0.346428	0.173214	−	0.984884i	$-0.444585\pi$
$641$	8.77087	0.346428	0.173214	+	0.984884i	$0.444585\pi$
$642$	−7.40785	−0.292365
$643$	−42.4849	−1.67544	−0.837721	−	0.546098i	$-0.816113\pi$
$643$	−42.4849	−1.67544	−0.837721	+	0.546098i	$0.816113\pi$
$644$	−5.54640	−0.218559
$645$	−7.58655	−0.298720
$646$	48.6773	1.91518
$647$	−7.83180	−0.307900	−0.153950	−	0.988079i	$-0.549199\pi$
$647$	−7.83180	−0.307900	−0.153950	+	0.988079i	$0.549199\pi$
$648$	−1.56250	−0.0613808
$649$	−4.30244	−0.168886
$650$	−0.450499	−0.0176700
$651$	44.6284	1.74912
$652$	2.82006	0.110442
$653$	−19.9384	−0.780248	−0.390124	−	0.920762i	$-0.627568\pi$
$653$	−19.9384	−0.780248	−0.390124	+	0.920762i	$0.627568\pi$
$654$	2.36566	0.0925046
$655$	−38.1396	−1.49024
$656$	33.7938	1.31943
$657$	5.09595	0.198812
$658$	−67.1075	−2.61612
$659$	13.1611	0.512684	0.256342	−	0.966586i	$-0.417483\pi$
$659$	13.1611	0.512684	0.256342	+	0.966586i	$0.417483\pi$
$660$	0.803929	0.0312929
$661$	−9.99619	−0.388807	−0.194403	−	0.980922i	$-0.562277\pi$
$661$	−9.99619	−0.388807	−0.194403	+	0.980922i	$0.562277\pi$
$662$	35.0675	1.36294
$663$	1.01219	0.0393102
$664$	7.74317	0.300493
$665$	59.0702	2.29064
$666$	0.355488	0.0137749
$667$	−1.00000	−0.0387202
$668$	−1.45990	−0.0564851
$669$	−2.63867	−0.102017
$670$	21.5319	0.831850
$671$	0.306723	0.0118409
$672$	−28.2432	−1.08951
$673$	−44.4817	−1.71464	−0.857322	−	0.514781i	$-0.827873\pi$
$673$	−44.4817	−1.71464	−0.857322	+	0.514781i	$0.827873\pi$
$674$	−22.7185	−0.875082
$675$	−1.49307	−0.0574682
$676$	−14.4579	−0.556071
$677$	23.2960	0.895339	0.447670	−	0.894199i	$-0.352254\pi$
$677$	23.2960	0.895339	0.447670	+	0.894199i	$0.352254\pi$
$678$	10.8330	0.416037
$679$	79.8332	3.06372
$680$	23.5720	0.903946
$681$	−14.3265	−0.548993
$682$	4.48020	0.171556
$683$	46.6962	1.78678	0.893391	−	0.449280i	$-0.148320\pi$
$683$	46.6962	1.78678	0.893391	+	0.449280i	$0.148320\pi$
$684$	5.19288	0.198555
$685$	−19.5848	−0.748298
$686$	−94.4886	−3.60759
$687$	24.0371	0.917072
$688$	14.8473	0.566046
$689$	−0.381079	−0.0145180
$690$	4.49707	0.171200
$691$	−47.2859	−1.79884	−0.899421	−	0.437084i	$-0.856011\pi$
$691$	−47.2859	−1.79884	−0.899421	+	0.437084i	$0.856011\pi$
$692$	14.8501	0.564515
$693$	−1.40841	−0.0535009
$694$	17.2470	0.654688
$695$	−45.9063	−1.74133
$696$	−1.56250	−0.0592264
$697$	−40.1201	−1.51966
$698$	23.2428	0.879753
$699$	0.647548	0.0244925
$700$	−8.28115	−0.312998
$701$	46.4140	1.75303	0.876517	−	0.481371i	$-0.159861\pi$
$701$	46.4140	1.75303	0.876517	+	0.481371i	$0.159861\pi$
$702$	0.301727	0.0113880
$703$	0.938407	0.0353927
$704$	−0.0123068	−0.000463831 0
$705$	19.4723	0.733371
$706$	−25.6842	−0.966637
$707$	−27.3326	−1.02795
$708$	16.9433	0.636769
$709$	11.3444	0.426047	0.213024	−	0.977047i	$-0.431669\pi$
$709$	11.3444	0.426047	0.213024	+	0.977047i	$0.431669\pi$
$710$	−71.5032	−2.68347
$711$	15.8153	0.593119
$712$	6.05588	0.226954
$713$	8.96888	0.335887
$714$	51.9912	1.94572
$715$	0.123308	0.00461144
$716$	−7.04341	−0.263225
$717$	−23.0226	−0.859793
$718$	−20.6356	−0.770112
$719$	37.1842	1.38674	0.693369	−	0.720582i	$-0.256126\pi$
$719$	37.1842	1.38674	0.693369	+	0.720582i	$0.256126\pi$
$720$	12.7073	0.473571
$721$	55.2475	2.05752
$722$	4.77218	0.177602
$723$	−4.27926	−0.159147
$724$	−10.7596	−0.399876
$725$	−1.49307	−0.0554511
$726$	19.2718	0.715244
$727$	16.0657	0.595843	0.297922	−	0.954590i	$-0.403707\pi$
$727$	16.0657	0.595843	0.297922	+	0.954590i	$0.403707\pi$
$728$	−1.32924	−0.0492649
$729$	1.00000	0.0370370
$730$	−22.9169	−0.848191
$731$	−17.6267	−0.651948
$732$	−1.20790	−0.0446452
$733$	35.3061	1.30406	0.652031	−	0.758193i	$-0.273917\pi$
$733$	35.3061	1.30406	0.652031	+	0.758193i	$0.273917\pi$
$734$	−0.772009	−0.0284954
$735$	45.2545	1.66924
$736$	−5.67599	−0.209220
$737$	−1.35521	−0.0499199
$738$	−11.9596	−0.440237
$739$	−3.60959	−0.132781	−0.0663905	−	0.997794i	$-0.521148\pi$
$739$	−3.60959	−0.132781	−0.0663905	+	0.997794i	$0.521148\pi$
$740$	−0.572116	−0.0210314
$741$	0.796490	0.0292598
$742$	−19.5741	−0.718589
$743$	31.2299	1.14572	0.572858	−	0.819655i	$-0.305835\pi$
$743$	31.2299	1.14572	0.572858	+	0.819655i	$0.305835\pi$
$744$	14.0139	0.513773
$745$	−49.8590	−1.82669
$746$	26.0991	0.955556
$747$	−4.95563	−0.181317
$748$	1.86786	0.0682958
$749$	−20.8863	−0.763167
$750$	−15.7709	−0.575873
$751$	20.0119	0.730246	0.365123	−	0.930959i	$-0.381027\pi$
$751$	20.0119	0.730246	0.365123	+	0.930959i	$0.381027\pi$
$752$	−38.1083	−1.38967
$753$	13.5637	0.494288
$754$	0.301727	0.0109883
$755$	8.48172	0.308681
$756$	5.54640	0.201721
$757$	31.3437	1.13921	0.569604	−	0.821920i	$-0.307097\pi$
$757$	31.3437	1.13921	0.569604	+	0.821920i	$0.307097\pi$
$758$	−24.8431	−0.902343
$759$	−0.283045	−0.0102739
$760$	18.5488	0.672835
$761$	14.4059	0.522215	0.261107	−	0.965310i	$-0.415912\pi$
$761$	14.4059	0.522215	0.261107	+	0.965310i	$0.415912\pi$
$762$	−36.4661	−1.32103
$763$	6.66992	0.241467
$764$	−1.46914	−0.0531516
$765$	−15.0861	−0.545439
$766$	−25.9664	−0.938204
$767$	2.59879	0.0938367
$768$	−19.9859	−0.721180
$769$	−19.9701	−0.720140	−0.360070	−	0.932925i	$-0.617247\pi$
$769$	−19.9701	−0.720140	−0.360070	+	0.932925i	$0.617247\pi$
$770$	6.33370	0.228251
$771$	2.03382	0.0732461
$772$	23.4658	0.844553
$773$	−9.65289	−0.347190	−0.173595	−	0.984817i	$-0.555538\pi$
$773$	−9.65289	−0.347190	−0.173595	+	0.984817i	$0.555538\pi$
$774$	−5.25441	−0.188866
$775$	13.3911	0.481024
$776$	25.0686	0.899911
$777$	1.00229	0.0359570
$778$	20.1829	0.723592
$779$	−31.5704	−1.13113
$780$	−0.485594	−0.0173871
$781$	4.50040	0.161037
$782$	10.4486	0.373640
$783$	1.00000	0.0357371
$784$	−88.5653	−3.16305
$785$	46.9547	1.67589
$786$	−26.4153	−0.942203
$787$	37.1608	1.32464	0.662320	−	0.749221i	$-0.269572\pi$
$787$	37.1608	1.32464	0.662320	+	0.749221i	$0.269572\pi$
$788$	6.85807	0.244309
$789$	−11.9405	−0.425093
$790$	−71.1223	−2.53042
$791$	30.5433	1.08599
$792$	−0.442257	−0.0157149
$793$	−0.185269	−0.00657909
$794$	54.7456	1.94285
$795$	5.67976	0.201440
$796$	13.6213	0.482796
$797$	−18.0087	−0.637900	−0.318950	−	0.947772i	$-0.603330\pi$
$797$	−18.0087	−0.637900	−0.318950	+	0.947772i	$0.603330\pi$
$798$	40.9117	1.44826
$799$	45.2424	1.60056
$800$	−8.47463	−0.299623
$801$	−3.87577	−0.136943
$802$	−66.1213	−2.33482
$803$	1.44238	0.0509006
$804$	5.33693	0.188219
$805$	12.6794	0.446889
$806$	−2.70616	−0.0953203
$807$	−15.1479	−0.533233
$808$	−8.58276	−0.301941
$809$	4.86545	0.171060	0.0855301	−	0.996336i	$-0.472742\pi$
$809$	4.86545	0.171060	0.0855301	+	0.996336i	$0.472742\pi$
$810$	−4.49707	−0.158011
$811$	13.8980	0.488025	0.244012	−	0.969772i	$-0.421536\pi$
$811$	13.8980	0.488025	0.244012	+	0.969772i	$0.421536\pi$
$812$	5.54640	0.194641
$813$	−20.1868	−0.707984
$814$	0.100619	0.00352670
$815$	−6.44680	−0.225822
$816$	29.5242	1.03356
$817$	−13.8704	−0.485264
$818$	−53.2193	−1.86077
$819$	0.850713	0.0297263
$820$	19.2475	0.672150
$821$	−45.1277	−1.57497	−0.787483	−	0.616336i	$-0.788616\pi$
$821$	−45.1277	−1.57497	−0.787483	+	0.616336i	$0.788616\pi$
$822$	−13.5644	−0.473112
$823$	−20.1767	−0.703315	−0.351658	−	0.936129i	$-0.614382\pi$
$823$	−20.1767	−0.703315	−0.351658	+	0.936129i	$0.614382\pi$
$824$	17.3484	0.604360
$825$	−0.422604	−0.0147132
$826$	133.487	4.64460
$827$	54.0105	1.87813	0.939064	−	0.343742i	$-0.111695\pi$
$827$	54.0105	1.87813	0.939064	+	0.343742i	$0.111695\pi$
$828$	1.11465	0.0387367
$829$	−15.7634	−0.547485	−0.273742	−	0.961803i	$-0.588262\pi$
$829$	−15.7634	−0.547485	−0.273742	+	0.961803i	$0.588262\pi$
$830$	22.2858	0.773552
$831$	2.22660	0.0772399
$832$	0.00743364	0.000257715 0
$833$	105.145	3.64306
$834$	−31.7945	−1.10095
$835$	3.33740	0.115496
$836$	1.46982	0.0508347
$837$	−8.96888	−0.310010
$838$	37.6241	1.29970
$839$	19.8149	0.684086	0.342043	−	0.939684i	$-0.388881\pi$
$839$	19.8149	0.684086	0.342043	+	0.939684i	$0.388881\pi$
$840$	19.8115	0.683563
$841$	1.00000	0.0344828
$842$	−69.1034	−2.38146
$843$	−21.9565	−0.756221
$844$	4.99352	0.171884
$845$	33.0515	1.13700
$846$	13.4865	0.463674
$847$	54.3364	1.86702
$848$	−11.1156	−0.381710
$849$	−4.53617	−0.155681
$850$	15.6004	0.535089
$851$	0.201428	0.00690488
$852$	−17.7229	−0.607176
$853$	−28.3860	−0.971918	−0.485959	−	0.873982i	$-0.661529\pi$
$853$	−28.3860	−0.971918	−0.485959	+	0.873982i	$0.661529\pi$
$854$	−9.51634	−0.325642
$855$	−11.8712	−0.405987
$856$	−6.55855	−0.224167
$857$	−46.0087	−1.57163	−0.785814	−	0.618462i	$-0.787756\pi$
$857$	−46.0087	−1.57163	−0.785814	+	0.618462i	$0.787756\pi$
$858$	0.0854023	0.00291559
$859$	46.3189	1.58038	0.790191	−	0.612861i	$-0.209982\pi$
$859$	46.3189	1.58038	0.790191	+	0.612861i	$0.209982\pi$
$860$	8.45634	0.288359
$861$	−33.7197	−1.14916
$862$	30.7334	1.04678
$863$	17.1707	0.584497	0.292249	−	0.956342i	$-0.405597\pi$
$863$	17.1707	0.584497	0.292249	+	0.956342i	$0.405597\pi$
$864$	5.67599	0.193101
$865$	−33.9481	−1.15427
$866$	−21.7242	−0.738219
$867$	−18.0513	−0.613054
$868$	−49.7450	−1.68845
$869$	4.47642	0.151852
$870$	−4.49707	−0.152465
$871$	0.818584	0.0277367
$872$	2.09444	0.0709266
$873$	−16.0439	−0.543004
$874$	8.22195	0.278112
$875$	−44.4657	−1.50322
$876$	−5.68020	−0.191916
$877$	−41.0178	−1.38507	−0.692537	−	0.721383i	$-0.743507\pi$
$877$	−41.0178	−1.38507	−0.692537	+	0.721383i	$0.743507\pi$
$878$	−25.2487	−0.852103
$879$	11.0848	0.373881
$880$	3.59672	0.121245
$881$	−12.1431	−0.409111	−0.204556	−	0.978855i	$-0.565575\pi$
$881$	−12.1431	−0.409111	−0.204556	+	0.978855i	$0.565575\pi$
$882$	31.3430	1.05538
$883$	13.3621	0.449669	0.224835	−	0.974397i	$-0.427816\pi$
$883$	13.3621	0.449669	0.224835	+	0.974397i	$0.427816\pi$
$884$	−1.12824	−0.0379467
$885$	−38.7334	−1.30201
$886$	−24.5324	−0.824181
$887$	5.50891	0.184971	0.0924856	−	0.995714i	$-0.470519\pi$
$887$	5.50891	0.184971	0.0924856	+	0.995714i	$0.470519\pi$
$888$	0.314732	0.0105617
$889$	−102.815	−3.44832
$890$	17.4296	0.584241
$891$	0.283045	0.00948235
$892$	2.94119	0.0984785
$893$	35.6011	1.19135
$894$	−34.5321	−1.15493
$895$	16.1016	0.538218
$896$	−56.1046	−1.87432
$897$	0.170966	0.00570839
$898$	52.3451	1.74678
$899$	−8.96888	−0.299129
$900$	1.66425	0.0554749
$901$	13.1964	0.439637
$902$	−3.38509	−0.112711
$903$	−14.8147	−0.493002
$904$	9.59097	0.318991
$905$	24.5969	0.817630
$906$	5.87440	0.195164
$907$	−19.7017	−0.654184	−0.327092	−	0.944993i	$-0.606069\pi$
$907$	−19.7017	−0.654184	−0.327092	+	0.944993i	$0.606069\pi$
$908$	15.9690	0.529951
$909$	5.49297	0.182190
$910$	−3.82572	−0.126821
$911$	43.9735	1.45691	0.728453	−	0.685096i	$-0.240240\pi$
$911$	43.9735	1.45691	0.728453	+	0.685096i	$0.240240\pi$
$912$	23.2326	0.769307
$913$	−1.40266	−0.0464214
$914$	67.7136	2.23977
$915$	2.76132	0.0912865
$916$	−26.7929	−0.885263
$917$	−74.4774	−2.45946
$918$	−10.4486	−0.344854
$919$	27.3654	0.902703	0.451351	−	0.892346i	$-0.350942\pi$
$919$	27.3654	0.902703	0.451351	+	0.892346i	$0.350942\pi$
$920$	3.98148	0.131266
$921$	11.6843	0.385009
$922$	−50.4973	−1.66304
$923$	−2.71835	−0.0894757
$924$	1.56988	0.0516452
$925$	0.300746	0.00988847
$926$	11.5007	0.377937
$927$	−11.1030	−0.364670
$928$	5.67599	0.186323
$929$	48.2798	1.58401	0.792004	−	0.610516i	$-0.209038\pi$
$929$	48.2798	1.58401	0.792004	+	0.610516i	$0.209038\pi$
$930$	40.3337	1.32259
$931$	82.7384	2.71164
$932$	−0.721789	−0.0236430
$933$	−18.4799	−0.605004
$934$	−29.4007	−0.962022
$935$	−4.27004	−0.139645
$936$	0.267135	0.00873157
$937$	24.8928	0.813213	0.406607	−	0.913603i	$-0.366712\pi$
$937$	24.8928	0.813213	0.406607	+	0.913603i	$0.366712\pi$
$938$	42.0466	1.37287
$939$	−1.66419	−0.0543088
$940$	−21.7048	−0.707933
$941$	−5.98909	−0.195239	−0.0976193	−	0.995224i	$-0.531123\pi$
$941$	−5.98909	−0.195239	−0.0976193	+	0.995224i	$0.531123\pi$
$942$	32.5206	1.05958
$943$	−6.77658	−0.220676
$944$	75.8031	2.46718
$945$	−12.6794	−0.412460
$946$	−1.48723	−0.0483541
$947$	−45.5443	−1.47999	−0.739995	−	0.672613i	$-0.765172\pi$
$947$	−45.5443	−1.47999	−0.739995	+	0.672613i	$0.765172\pi$
$948$	−17.6285	−0.572546
$949$	−0.871236	−0.0282815
$950$	12.2759	0.398283
$951$	−6.66769	−0.216215
$952$	46.0304	1.49185
$953$	−36.5769	−1.18484	−0.592422	−	0.805628i	$-0.701828\pi$
$953$	−36.5769	−1.18484	−0.592422	+	0.805628i	$0.701828\pi$
$954$	3.93378	0.127361
$955$	3.35853	0.108680
$956$	25.6621	0.829971
$957$	0.283045	0.00914953
$958$	−17.1754	−0.554912
$959$	−38.2444	−1.23498
$960$	−0.110794	−0.00357586
$961$	49.4407	1.59486
$962$	−0.0607765	−0.00195951
$963$	4.19747	0.135262
$964$	4.76988	0.153627
$965$	−53.6442	−1.72687
$966$	8.78168	0.282546
$967$	4.29341	0.138067	0.0690334	−	0.997614i	$-0.478009\pi$
$967$	4.29341	0.138067	0.0690334	+	0.997614i	$0.478009\pi$
$968$	17.0623	0.548404
$969$	−27.5818	−0.886054
$970$	72.1506	2.31662
$971$	12.3990	0.397902	0.198951	−	0.980009i	$-0.436246\pi$
$971$	12.3990	0.397902	0.198951	+	0.980009i	$0.436246\pi$
$972$	−1.11465	−0.0357524
$973$	−89.6438	−2.87385
$974$	−18.5211	−0.593453
$975$	0.255264	0.00817499
$976$	−5.40404	−0.172979
$977$	5.07082	0.162230	0.0811150	−	0.996705i	$-0.474152\pi$
$977$	5.07082	0.162230	0.0811150	+	0.996705i	$0.474152\pi$
$978$	−4.46503	−0.142776
$979$	−1.09701	−0.0350607
$980$	−50.4429	−1.61134
$981$	−1.34044	−0.0427970
$982$	56.3697	1.79883
$983$	7.83628	0.249939	0.124969	−	0.992161i	$-0.460117\pi$
$983$	7.83628	0.249939	0.124969	+	0.992161i	$0.460117\pi$
$984$	−10.5884	−0.337546
$985$	−15.6779	−0.499540
$986$	−10.4486	−0.332750
$987$	38.0247	1.21034
$988$	−0.887807	−0.0282449
$989$	−2.97728	−0.0946719
$990$	−1.27287	−0.0404545
$991$	58.1336	1.84667	0.923337	−	0.383990i	$-0.125450\pi$
$991$	58.1336	1.84667	0.923337	+	0.383990i	$0.125450\pi$
$992$	−50.9072	−1.61631
$993$	−19.8701	−0.630559
$994$	−139.628	−4.42874
$995$	−31.1392	−0.987178
$996$	5.52379	0.175028
$997$	−62.9965	−1.99512	−0.997560	−	0.0698195i	$-0.977758\pi$
$997$	−62.9965	−1.99512	−0.997560	+	0.0698195i	$0.977758\pi$
$998$	3.64937	0.115519
$999$	−0.201428	−0.00637292

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.l.1.8	✓	11
3.2	odd	2		6003.2.a.m.1.4		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.l.1.8	✓	11	1.1	even	1	trivial
6003.2.a.m.1.4		11	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)

\(f(q)\)	\(=\)	\(q+1.76484 q^{2} -1.00000 q^{3} +1.11465 q^{4} -2.54815 q^{5} -1.76484 q^{6} -4.97592 q^{7} -1.56250 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.76484 q^{2} -1.00000 q^{3} +1.11465 q^{4} -2.54815 q^{5} -1.76484 q^{6} -4.97592 q^{7} -1.56250 q^{8} +1.00000 q^{9} -4.49707 q^{10} +0.283045 q^{11} -1.11465 q^{12} -0.170966 q^{13} -8.78168 q^{14} +2.54815 q^{15} -4.98686 q^{16} +5.92041 q^{17} +1.76484 q^{18} +4.65876 q^{19} -2.84029 q^{20} +4.97592 q^{21} +0.499527 q^{22} +1.00000 q^{23} +1.56250 q^{24} +1.49307 q^{25} -0.301727 q^{26} -1.00000 q^{27} -5.54640 q^{28} -1.00000 q^{29} +4.49707 q^{30} +8.96888 q^{31} -5.67599 q^{32} -0.283045 q^{33} +10.4486 q^{34} +12.6794 q^{35} +1.11465 q^{36} +0.201428 q^{37} +8.22195 q^{38} +0.170966 q^{39} +3.98148 q^{40} -6.77658 q^{41} +8.78168 q^{42} -2.97728 q^{43} +0.315495 q^{44} -2.54815 q^{45} +1.76484 q^{46} +7.64176 q^{47} +4.98686 q^{48} +17.7597 q^{49} +2.63502 q^{50} -5.92041 q^{51} -0.190567 q^{52} +2.22897 q^{53} -1.76484 q^{54} -0.721240 q^{55} +7.77487 q^{56} -4.65876 q^{57} -1.76484 q^{58} -15.2006 q^{59} +2.84029 q^{60} +1.08366 q^{61} +15.8286 q^{62} -4.97592 q^{63} -0.0434802 q^{64} +0.435647 q^{65} -0.499527 q^{66} -4.78799 q^{67} +6.59918 q^{68} -1.00000 q^{69} +22.3770 q^{70} +15.9000 q^{71} -1.56250 q^{72} +5.09595 q^{73} +0.355488 q^{74} -1.49307 q^{75} +5.19288 q^{76} -1.40841 q^{77} +0.301727 q^{78} +15.8153 q^{79} +12.7073 q^{80} +1.00000 q^{81} -11.9596 q^{82} -4.95563 q^{83} +5.54640 q^{84} -15.0861 q^{85} -5.25441 q^{86} +1.00000 q^{87} -0.442257 q^{88} -3.87577 q^{89} -4.49707 q^{90} +0.850713 q^{91} +1.11465 q^{92} -8.96888 q^{93} +13.4865 q^{94} -11.8712 q^{95} +5.67599 q^{96} -16.0439 q^{97} +31.3430 q^{98} +0.283045 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9} + 14 q^{10} + 11 q^{11} - 18 q^{12} - 5 q^{13} + 17 q^{14} - 2 q^{15} + 20 q^{16} + 15 q^{17} + 2 q^{18} - 6 q^{19} + 21 q^{20} - 3 q^{21} - 10 q^{22} + 11 q^{23} - 18 q^{24} + 3 q^{25} - 5 q^{26} - 11 q^{27} + 7 q^{28} - 11 q^{29} - 14 q^{30} + 35 q^{31} + 28 q^{32} - 11 q^{33} + 28 q^{34} + 15 q^{35} + 18 q^{36} - 28 q^{37} - 2 q^{38} + 5 q^{39} - q^{40} + 10 q^{41} - 17 q^{42} - 6 q^{43} + 18 q^{44} + 2 q^{45} + 2 q^{46} + 15 q^{47} - 20 q^{48} + 22 q^{49} + 15 q^{50} - 15 q^{51} - 36 q^{52} - 7 q^{53} - 2 q^{54} - 12 q^{55} + 56 q^{56} + 6 q^{57} - 2 q^{58} - 20 q^{59} - 21 q^{60} - 20 q^{61} - 11 q^{62} + 3 q^{63} + 36 q^{64} + 11 q^{65} + 10 q^{66} - 39 q^{67} + 35 q^{68} - 11 q^{69} + 38 q^{70} + 49 q^{71} + 18 q^{72} - 3 q^{73} + 37 q^{74} - 3 q^{75} - 18 q^{76} + 25 q^{77} + 5 q^{78} + 41 q^{79} + 51 q^{80} + 11 q^{81} - 19 q^{82} + 13 q^{83} - 7 q^{84} + 62 q^{86} + 11 q^{87} - 40 q^{88} + 34 q^{89} + 14 q^{90} + 2 q^{91} + 18 q^{92} - 35 q^{93} - 14 q^{94} + 25 q^{95} - 28 q^{96} - 11 q^{97} + 53 q^{98} + 11 q^{99}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9 + 14 * q^10 + 11 * q^11 - 18 * q^12 - 5 * q^13 + 17 * q^14 - 2 * q^15 + 20 * q^16 + 15 * q^17 + 2 * q^18 - 6 * q^19 + 21 * q^20 - 3 * q^21 - 10 * q^22 + 11 * q^23 - 18 * q^24 + 3 * q^25 - 5 * q^26 - 11 * q^27 + 7 * q^28 - 11 * q^29 - 14 * q^30 + 35 * q^31 + 28 * q^32 - 11 * q^33 + 28 * q^34 + 15 * q^35 + 18 * q^36 - 28 * q^37 - 2 * q^38 + 5 * q^39 - q^40 + 10 * q^41 - 17 * q^42 - 6 * q^43 + 18 * q^44 + 2 * q^45 + 2 * q^46 + 15 * q^47 - 20 * q^48 + 22 * q^49 + 15 * q^50 - 15 * q^51 - 36 * q^52 - 7 * q^53 - 2 * q^54 - 12 * q^55 + 56 * q^56 + 6 * q^57 - 2 * q^58 - 20 * q^59 - 21 * q^60 - 20 * q^61 - 11 * q^62 + 3 * q^63 + 36 * q^64 + 11 * q^65 + 10 * q^66 - 39 * q^67 + 35 * q^68 - 11 * q^69 + 38 * q^70 + 49 * q^71 + 18 * q^72 - 3 * q^73 + 37 * q^74 - 3 * q^75 - 18 * q^76 + 25 * q^77 + 5 * q^78 + 41 * q^79 + 51 * q^80 + 11 * q^81 - 19 * q^82 + 13 * q^83 - 7 * q^84 + 62 * q^86 + 11 * q^87 - 40 * q^88 + 34 * q^89 + 14 * q^90 + 2 * q^91 + 18 * q^92 - 35 * q^93 - 14 * q^94 + 25 * q^95 - 28 * q^96 - 11 * q^97 + 53 * q^98 + 11 * q^99

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