LMFDB - Embedded newform 2013.2.a.f.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,2,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, 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("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2013.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$16.0738859269$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4 x^{12} - 11 x^{11} + 55 x^{10} + 32 x^{9} - 266 x^{8} + 13 x^{7} + 534 x^{6} - 141 x^{5} + \cdots - 11 $ x^13 - 4x^12 - 11x^11 + 55x^10 + 32x^9 - 266x^8 + 13x^7 + 534x^6 - 141x^5 - 404x^4 + 98x^3 + 118x^2 - 16x - 11
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$2.38255$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.38255 q^{2} +1.00000 q^{3} +3.67655 q^{4} +3.76064 q^{5} +2.38255 q^{6} -1.09133 q^{7} +3.99445 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.38255 q^{2} +1.00000 q^{3} +3.67655 q^{4} +3.76064 q^{5} +2.38255 q^{6} -1.09133 q^{7} +3.99445 q^{8} +1.00000 q^{9} +8.95992 q^{10} -1.00000 q^{11} +3.67655 q^{12} -1.78163 q^{13} -2.60015 q^{14} +3.76064 q^{15} +2.16390 q^{16} -3.04503 q^{17} +2.38255 q^{18} -3.42832 q^{19} +13.8262 q^{20} -1.09133 q^{21} -2.38255 q^{22} +6.13858 q^{23} +3.99445 q^{24} +9.14242 q^{25} -4.24483 q^{26} +1.00000 q^{27} -4.01233 q^{28} +3.50029 q^{29} +8.95992 q^{30} +6.38612 q^{31} -2.83332 q^{32} -1.00000 q^{33} -7.25493 q^{34} -4.10410 q^{35} +3.67655 q^{36} +1.67879 q^{37} -8.16815 q^{38} -1.78163 q^{39} +15.0217 q^{40} -3.11800 q^{41} -2.60015 q^{42} -1.12212 q^{43} -3.67655 q^{44} +3.76064 q^{45} +14.6255 q^{46} -0.248264 q^{47} +2.16390 q^{48} -5.80900 q^{49} +21.7823 q^{50} -3.04503 q^{51} -6.55025 q^{52} -14.3190 q^{53} +2.38255 q^{54} -3.76064 q^{55} -4.35927 q^{56} -3.42832 q^{57} +8.33961 q^{58} +10.2941 q^{59} +13.8262 q^{60} -1.00000 q^{61} +15.2153 q^{62} -1.09133 q^{63} -11.0783 q^{64} -6.70008 q^{65} -2.38255 q^{66} -4.06640 q^{67} -11.1952 q^{68} +6.13858 q^{69} -9.77824 q^{70} -13.8198 q^{71} +3.99445 q^{72} -0.212426 q^{73} +3.99981 q^{74} +9.14242 q^{75} -12.6044 q^{76} +1.09133 q^{77} -4.24483 q^{78} -5.71262 q^{79} +8.13764 q^{80} +1.00000 q^{81} -7.42880 q^{82} -11.1821 q^{83} -4.01233 q^{84} -11.4513 q^{85} -2.67351 q^{86} +3.50029 q^{87} -3.99445 q^{88} +8.41037 q^{89} +8.95992 q^{90} +1.94435 q^{91} +22.5688 q^{92} +6.38612 q^{93} -0.591500 q^{94} -12.8927 q^{95} -2.83332 q^{96} -6.22538 q^{97} -13.8402 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 5 q^{7} + 15 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 5 * q^7 + 15 * q^8 + 13 * q^9	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 5 q^{7} + 15 q^{8} + 13 q^{9} + 8 q^{10} - 13 q^{11} + 12 q^{12} - 9 q^{13} + 19 q^{14} + 7 q^{15} + 18 q^{16} + 7 q^{17} + 4 q^{18} + 2 q^{19} + 15 q^{20} + 5 q^{21} - 4 q^{22} + 23 q^{23} + 15 q^{24} + 10 q^{25} + 8 q^{26} + 13 q^{27} + 9 q^{28} + 16 q^{29} + 8 q^{30} + 9 q^{31} + 29 q^{32} - 13 q^{33} + 2 q^{34} + 16 q^{35} + 12 q^{36} + 14 q^{37} + 8 q^{38} - 9 q^{39} + 16 q^{40} + 19 q^{41} + 19 q^{42} + 7 q^{43} - 12 q^{44} + 7 q^{45} + 4 q^{46} + 26 q^{47} + 18 q^{48} + 8 q^{49} - 15 q^{50} + 7 q^{51} - 17 q^{52} + 18 q^{53} + 4 q^{54} - 7 q^{55} + 44 q^{56} + 2 q^{57} - q^{58} + 31 q^{59} + 15 q^{60} - 13 q^{61} - 5 q^{62} + 5 q^{63} - 17 q^{64} + 31 q^{65} - 4 q^{66} + 14 q^{67} - 32 q^{68} + 23 q^{69} - 20 q^{70} + 37 q^{71} + 15 q^{72} - 16 q^{73} - 6 q^{74} + 10 q^{75} - 7 q^{76} - 5 q^{77} + 8 q^{78} - 17 q^{79} - 2 q^{80} + 13 q^{81} - 2 q^{82} + 30 q^{83} + 9 q^{84} - 16 q^{85} - 22 q^{86} + 16 q^{87} - 15 q^{88} + 35 q^{89} + 8 q^{90} - q^{91} + 24 q^{92} + 9 q^{93} - 11 q^{94} + 13 q^{95} + 29 q^{96} - q^{97} - q^{98} - 13 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 5 * q^7 + 15 * q^8 + 13 * q^9 + 8 * q^10 - 13 * q^11 + 12 * q^12 - 9 * q^13 + 19 * q^14 + 7 * q^15 + 18 * q^16 + 7 * q^17 + 4 * q^18 + 2 * q^19 + 15 * q^20 + 5 * q^21 - 4 * q^22 + 23 * q^23 + 15 * q^24 + 10 * q^25 + 8 * q^26 + 13 * q^27 + 9 * q^28 + 16 * q^29 + 8 * q^30 + 9 * q^31 + 29 * q^32 - 13 * q^33 + 2 * q^34 + 16 * q^35 + 12 * q^36 + 14 * q^37 + 8 * q^38 - 9 * q^39 + 16 * q^40 + 19 * q^41 + 19 * q^42 + 7 * q^43 - 12 * q^44 + 7 * q^45 + 4 * q^46 + 26 * q^47 + 18 * q^48 + 8 * q^49 - 15 * q^50 + 7 * q^51 - 17 * q^52 + 18 * q^53 + 4 * q^54 - 7 * q^55 + 44 * q^56 + 2 * q^57 - q^58 + 31 * q^59 + 15 * q^60 - 13 * q^61 - 5 * q^62 + 5 * q^63 - 17 * q^64 + 31 * q^65 - 4 * q^66 + 14 * q^67 - 32 * q^68 + 23 * q^69 - 20 * q^70 + 37 * q^71 + 15 * q^72 - 16 * q^73 - 6 * q^74 + 10 * q^75 - 7 * q^76 - 5 * q^77 + 8 * q^78 - 17 * q^79 - 2 * q^80 + 13 * q^81 - 2 * q^82 + 30 * q^83 + 9 * q^84 - 16 * q^85 - 22 * q^86 + 16 * q^87 - 15 * q^88 + 35 * q^89 + 8 * q^90 - q^91 + 24 * q^92 + 9 * q^93 - 11 * q^94 + 13 * q^95 + 29 * q^96 - q^97 - q^98 - 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.38255	1.68472	0.842359	−	0.538917i	$-0.181166\pi$
$2$	2.38255	1.68472	0.842359	+	0.538917i	$0.181166\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.67655	1.83827
$5$	3.76064	1.68181	0.840905	−	0.541183i	$-0.182023\pi$
$5$	3.76064	1.68181	0.840905	+	0.541183i	$0.182023\pi$
$6$	2.38255	0.972672
$7$	−1.09133	−0.412484	−0.206242	−	0.978501i	$-0.566123\pi$
$7$	−1.09133	−0.412484	−0.206242	+	0.978501i	$0.566123\pi$
$8$	3.99445	1.41225
$9$	1.00000	0.333333
$10$	8.95992	2.83337
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	3.67655	1.06133
$13$	−1.78163	−0.494136	−0.247068	−	0.968998i	$-0.579467\pi$
$13$	−1.78163	−0.494136	−0.247068	+	0.968998i	$0.579467\pi$
$14$	−2.60015	−0.694920
$15$	3.76064	0.970993
$16$	2.16390	0.540974
$17$	−3.04503	−0.738528	−0.369264	−	0.929325i	$-0.620390\pi$
$17$	−3.04503	−0.738528	−0.369264	+	0.929325i	$0.620390\pi$
$18$	2.38255	0.561572
$19$	−3.42832	−0.786511	−0.393255	−	0.919429i	$-0.628651\pi$
$19$	−3.42832	−0.786511	−0.393255	+	0.919429i	$0.628651\pi$
$20$	13.8262	3.09163
$21$	−1.09133	−0.238148
$22$	−2.38255	−0.507961
$23$	6.13858	1.27998	0.639991	−	0.768382i	$-0.278938\pi$
$23$	6.13858	1.27998	0.639991	+	0.768382i	$0.278938\pi$
$24$	3.99445	0.815365
$25$	9.14242	1.82848
$26$	−4.24483	−0.832479
$27$	1.00000	0.192450
$28$	−4.01233	−0.758259
$29$	3.50029	0.649987	0.324993	−	0.945716i	$-0.394638\pi$
$29$	3.50029	0.649987	0.324993	+	0.945716i	$0.394638\pi$
$30$	8.95992	1.63585
$31$	6.38612	1.14698	0.573491	−	0.819212i	$-0.305589\pi$
$31$	6.38612	1.14698	0.573491	+	0.819212i	$0.305589\pi$
$32$	−2.83332	−0.500864
$33$	−1.00000	−0.174078
$34$	−7.25493	−1.24421
$35$	−4.10410	−0.693720
$36$	3.67655	0.612758
$37$	1.67879	0.275992	0.137996	−	0.990433i	$-0.455934\pi$
$37$	1.67879	0.275992	0.137996	+	0.990433i	$0.455934\pi$
$38$	−8.16815	−1.32505
$39$	−1.78163	−0.285289
$40$	15.0217	2.37514
$41$	−3.11800	−0.486951	−0.243475	−	0.969907i	$-0.578287\pi$
$41$	−3.11800	−0.486951	−0.243475	+	0.969907i	$0.578287\pi$
$42$	−2.60015	−0.401212
$43$	−1.12212	−0.171122	−0.0855608	−	0.996333i	$-0.527268\pi$
$43$	−1.12212	−0.171122	−0.0855608	+	0.996333i	$0.527268\pi$
$44$	−3.67655	−0.554260
$45$	3.76064	0.560603
$46$	14.6255	2.15641
$47$	−0.248264	−0.0362130	−0.0181065	−	0.999836i	$-0.505764\pi$
$47$	−0.248264	−0.0362130	−0.0181065	+	0.999836i	$0.505764\pi$
$48$	2.16390	0.312332
$49$	−5.80900	−0.829857
$50$	21.7823	3.08048
$51$	−3.04503	−0.426389
$52$	−6.55025	−0.908356
$53$	−14.3190	−1.96686	−0.983431	−	0.181284i	$-0.941975\pi$
$53$	−14.3190	−1.96686	−0.983431	+	0.181284i	$0.941975\pi$
$54$	2.38255	0.324224
$55$	−3.76064	−0.507085
$56$	−4.35927	−0.582532
$57$	−3.42832	−0.454092
$58$	8.33961	1.09504
$59$	10.2941	1.34018	0.670088	−	0.742282i	$-0.266256\pi$
$59$	10.2941	1.34018	0.670088	+	0.742282i	$0.266256\pi$
$60$	13.8262	1.78495
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	15.2153	1.93234
$63$	−1.09133	−0.137495
$64$	−11.0783	−1.38479
$65$	−6.70008	−0.831042
$66$	−2.38255	−0.293272
$67$	−4.06640	−0.496790	−0.248395	−	0.968659i	$-0.579903\pi$
$67$	−4.06640	−0.496790	−0.248395	+	0.968659i	$0.579903\pi$
$68$	−11.1952	−1.35762
$69$	6.13858	0.738998
$70$	−9.77824	−1.16872
$71$	−13.8198	−1.64011	−0.820055	−	0.572285i	$-0.806057\pi$
$71$	−13.8198	−1.64011	−0.820055	+	0.572285i	$0.806057\pi$
$72$	3.99445	0.470751
$73$	−0.212426	−0.0248626	−0.0124313	−	0.999923i	$-0.503957\pi$
$73$	−0.212426	−0.0248626	−0.0124313	+	0.999923i	$0.503957\pi$
$74$	3.99981	0.464968
$75$	9.14242	1.05568
$76$	−12.6044	−1.44582
$77$	1.09133	0.124369
$78$	−4.24483	−0.480632
$79$	−5.71262	−0.642720	−0.321360	−	0.946957i	$-0.604140\pi$
$79$	−5.71262	−0.642720	−0.321360	+	0.946957i	$0.604140\pi$
$80$	8.13764	0.909816
$81$	1.00000	0.111111
$82$	−7.42880	−0.820374
$83$	−11.1821	−1.22740	−0.613698	−	0.789541i	$-0.710319\pi$
$83$	−11.1821	−1.22740	−0.613698	+	0.789541i	$0.710319\pi$
$84$	−4.01233	−0.437781
$85$	−11.4513	−1.24206
$86$	−2.67351	−0.288292
$87$	3.50029	0.375270
$88$	−3.99445	−0.425810
$89$	8.41037	0.891498	0.445749	−	0.895158i	$-0.352937\pi$
$89$	8.41037	0.891498	0.445749	+	0.895158i	$0.352937\pi$
$90$	8.95992	0.944458
$91$	1.94435	0.203823
$92$	22.5688	2.35296
$93$	6.38612	0.662210
$94$	−0.591500	−0.0610086
$95$	−12.8927	−1.32276
$96$	−2.83332	−0.289174
$97$	−6.22538	−0.632091	−0.316046	−	0.948744i	$-0.602355\pi$
$97$	−6.22538	−0.632091	−0.316046	+	0.948744i	$0.602355\pi$
$98$	−13.8402	−1.39807
$99$	−1.00000	−0.100504
$100$	33.6125	3.36125
$101$	−15.7920	−1.57136	−0.785682	−	0.618631i	$-0.787688\pi$
$101$	−15.7920	−1.57136	−0.785682	+	0.618631i	$0.787688\pi$
$102$	−7.25493	−0.718345
$103$	17.4211	1.71655	0.858277	−	0.513186i	$-0.171535\pi$
$103$	17.4211	1.71655	0.858277	+	0.513186i	$0.171535\pi$
$104$	−7.11664	−0.697844
$105$	−4.10410	−0.400520
$106$	−34.1157	−3.31361
$107$	8.91707	0.862045	0.431023	−	0.902341i	$-0.358153\pi$
$107$	8.91707	0.862045	0.431023	+	0.902341i	$0.358153\pi$
$108$	3.67655	0.353776
$109$	−2.17652	−0.208473	−0.104236	−	0.994553i	$-0.533240\pi$
$109$	−2.17652	−0.208473	−0.104236	+	0.994553i	$0.533240\pi$
$110$	−8.95992	−0.854295
$111$	1.67879	0.159344
$112$	−2.36153	−0.223143
$113$	9.29620	0.874513	0.437256	−	0.899337i	$-0.355950\pi$
$113$	9.29620	0.874513	0.437256	+	0.899337i	$0.355950\pi$
$114$	−8.16815	−0.765017
$115$	23.0850	2.15269
$116$	12.8690	1.19485
$117$	−1.78163	−0.164712
$118$	24.5262	2.25782
$119$	3.32313	0.304631
$120$	15.0217	1.37129
$121$	1.00000	0.0909091
$122$	−2.38255	−0.215706
$123$	−3.11800	−0.281141
$124$	23.4789	2.10847
$125$	15.5782	1.39335
$126$	−2.60015	−0.231640
$127$	12.7608	1.13234	0.566168	−	0.824290i	$-0.308425\pi$
$127$	12.7608	1.13234	0.566168	+	0.824290i	$0.308425\pi$
$128$	−20.7280	−1.83211
$129$	−1.12212	−0.0987971
$130$	−15.9633	−1.40007
$131$	−11.5721	−1.01105	−0.505527	−	0.862811i	$-0.668702\pi$
$131$	−11.5721	−1.01105	−0.505527	+	0.862811i	$0.668702\pi$
$132$	−3.67655	−0.320002
$133$	3.74143	0.324423
$134$	−9.68841	−0.836951
$135$	3.76064	0.323664
$136$	−12.1632	−1.04299
$137$	−14.7352	−1.25891	−0.629457	−	0.777035i	$-0.716723\pi$
$137$	−14.7352	−1.25891	−0.629457	+	0.777035i	$0.716723\pi$
$138$	14.6255	1.24500
$139$	3.05691	0.259284	0.129642	−	0.991561i	$-0.458617\pi$
$139$	3.05691	0.259284	0.129642	+	0.991561i	$0.458617\pi$
$140$	−15.0889	−1.27525
$141$	−0.248264	−0.0209076
$142$	−32.9264	−2.76312
$143$	1.78163	0.148987
$144$	2.16390	0.180325
$145$	13.1633	1.09315
$146$	−0.506116	−0.0418865
$147$	−5.80900	−0.479118
$148$	6.17216	0.507348
$149$	18.3303	1.50167	0.750837	−	0.660487i	$-0.229650\pi$
$149$	18.3303	1.50167	0.750837	+	0.660487i	$0.229650\pi$
$150$	21.7823	1.77852
$151$	14.2446	1.15921	0.579604	−	0.814898i	$-0.303207\pi$
$151$	14.2446	1.15921	0.579604	+	0.814898i	$0.303207\pi$
$152$	−13.6943	−1.11075
$153$	−3.04503	−0.246176
$154$	2.60015	0.209526
$155$	24.0159	1.92901
$156$	−6.55025	−0.524440
$157$	7.76182	0.619461	0.309730	−	0.950824i	$-0.399761\pi$
$157$	7.76182	0.619461	0.309730	+	0.950824i	$0.399761\pi$
$158$	−13.6106	−1.08280
$159$	−14.3190	−1.13557
$160$	−10.6551	−0.842358
$161$	−6.69923	−0.527973
$162$	2.38255	0.187191
$163$	7.78441	0.609722	0.304861	−	0.952397i	$-0.401390\pi$
$163$	7.78441	0.609722	0.304861	+	0.952397i	$0.401390\pi$
$164$	−11.4635	−0.895148
$165$	−3.76064	−0.292766
$166$	−26.6419	−2.06782
$167$	8.91988	0.690241	0.345121	−	0.938558i	$-0.387838\pi$
$167$	8.91988	0.690241	0.345121	+	0.938558i	$0.387838\pi$
$168$	−4.35927	−0.336325
$169$	−9.82579	−0.755830
$170$	−27.2832	−2.09253
$171$	−3.42832	−0.262170
$172$	−4.12552	−0.314568
$173$	2.91340	0.221502	0.110751	−	0.993848i	$-0.464674\pi$
$173$	2.91340	0.221502	0.110751	+	0.993848i	$0.464674\pi$
$174$	8.33961	0.632224
$175$	−9.97741	−0.754221
$176$	−2.16390	−0.163110
$177$	10.2941	0.773751
$178$	20.0381	1.50192
$179$	−16.7081	−1.24882	−0.624412	−	0.781095i	$-0.714661\pi$
$179$	−16.7081	−1.24882	−0.624412	+	0.781095i	$0.714661\pi$
$180$	13.8262	1.03054
$181$	13.3870	0.995051	0.497526	−	0.867449i	$-0.334242\pi$
$181$	13.3870	0.995051	0.497526	+	0.867449i	$0.334242\pi$
$182$	4.63251	0.343384
$183$	−1.00000	−0.0739221
$184$	24.5203	1.80766
$185$	6.31334	0.464166
$186$	15.2153	1.11564
$187$	3.04503	0.222674
$188$	−0.912752	−0.0665693
$189$	−1.09133	−0.0793827
$190$	−30.7175	−2.22848
$191$	5.59555	0.404880	0.202440	−	0.979295i	$-0.435113\pi$
$191$	5.59555	0.404880	0.202440	+	0.979295i	$0.435113\pi$
$192$	−11.0783	−0.799508
$193$	−15.3064	−1.10178	−0.550888	−	0.834579i	$-0.685711\pi$
$193$	−15.3064	−1.10178	−0.550888	+	0.834579i	$0.685711\pi$
$194$	−14.8323	−1.06490
$195$	−6.70008	−0.479802
$196$	−21.3570	−1.52550
$197$	−4.73748	−0.337531	−0.168766	−	0.985656i	$-0.553978\pi$
$197$	−4.73748	−0.337531	−0.168766	+	0.985656i	$0.553978\pi$
$198$	−2.38255	−0.169320
$199$	−17.4265	−1.23533	−0.617666	−	0.786441i	$-0.711922\pi$
$199$	−17.4265	−1.23533	−0.617666	+	0.786441i	$0.711922\pi$
$200$	36.5190	2.58228
$201$	−4.06640	−0.286822
$202$	−37.6253	−2.64730
$203$	−3.81997	−0.268109
$204$	−11.1952	−0.783820
$205$	−11.7257	−0.818958
$206$	41.5067	2.89191
$207$	6.13858	0.426661
$208$	−3.85527	−0.267315
$209$	3.42832	0.237142
$210$	−9.77824	−0.674762
$211$	9.49083	0.653375	0.326688	−	0.945132i	$-0.394067\pi$
$211$	9.49083	0.653375	0.326688	+	0.945132i	$0.394067\pi$
$212$	−52.6443	−3.61563
$213$	−13.8198	−0.946918
$214$	21.2454	1.45230
$215$	−4.21989	−0.287794
$216$	3.99445	0.271788
$217$	−6.96937	−0.473112
$218$	−5.18567	−0.351218
$219$	−0.212426	−0.0143544
$220$	−13.8262	−0.932160
$221$	5.42512	0.364933
$222$	3.99981	0.268450
$223$	2.99644	0.200657	0.100328	−	0.994954i	$-0.468011\pi$
$223$	2.99644	0.200657	0.100328	+	0.994954i	$0.468011\pi$
$224$	3.09209	0.206599
$225$	9.14242	0.609495
$226$	22.1487	1.47331
$227$	−4.24273	−0.281600	−0.140800	−	0.990038i	$-0.544967\pi$
$227$	−4.24273	−0.281600	−0.140800	+	0.990038i	$0.544967\pi$
$228$	−12.6044	−0.834745
$229$	24.0042	1.58624	0.793122	−	0.609063i	$-0.208454\pi$
$229$	24.0042	1.58624	0.793122	+	0.609063i	$0.208454\pi$
$230$	55.0012	3.62667
$231$	1.09133	0.0718043
$232$	13.9817	0.917946
$233$	−22.5049	−1.47434	−0.737172	−	0.675705i	$-0.763839\pi$
$233$	−22.5049	−1.47434	−0.737172	+	0.675705i	$0.763839\pi$
$234$	−4.24483	−0.277493
$235$	−0.933630	−0.0609033
$236$	37.8467	2.46361
$237$	−5.71262	−0.371074
$238$	7.91753	0.513217
$239$	19.7406	1.27691	0.638457	−	0.769657i	$-0.279573\pi$
$239$	19.7406	1.27691	0.638457	+	0.769657i	$0.279573\pi$
$240$	8.13764	0.525282
$241$	−18.1850	−1.17140	−0.585700	−	0.810528i	$-0.699181\pi$
$241$	−18.1850	−1.17140	−0.585700	+	0.810528i	$0.699181\pi$
$242$	2.38255	0.153156
$243$	1.00000	0.0641500
$244$	−3.67655	−0.235367
$245$	−21.8456	−1.39566
$246$	−7.42880	−0.473643
$247$	6.10800	0.388643
$248$	25.5091	1.61983
$249$	−11.1821	−0.708638
$250$	37.1158	2.34741
$251$	10.6407	0.671633	0.335817	−	0.941927i	$-0.390988\pi$
$251$	10.6407	0.671633	0.335817	+	0.941927i	$0.390988\pi$
$252$	−4.01233	−0.252753
$253$	−6.13858	−0.385929
$254$	30.4032	1.90767
$255$	−11.4513	−0.717106
$256$	−27.2289	−1.70181
$257$	8.01772	0.500131	0.250066	−	0.968229i	$-0.419548\pi$
$257$	8.01772	0.500131	0.250066	+	0.968229i	$0.419548\pi$
$258$	−2.67351	−0.166445
$259$	−1.83212	−0.113842
$260$	−24.6331	−1.52768
$261$	3.50029	0.216662
$262$	−27.5710	−1.70334
$263$	15.3632	0.947335	0.473667	−	0.880704i	$-0.342930\pi$
$263$	15.3632	0.947335	0.473667	+	0.880704i	$0.342930\pi$
$264$	−3.99445	−0.245842
$265$	−53.8485	−3.30789
$266$	8.91415	0.546562
$267$	8.41037	0.514706
$268$	−14.9503	−0.913236
$269$	−5.07644	−0.309516	−0.154758	−	0.987952i	$-0.549460\pi$
$269$	−5.07644	−0.309516	−0.154758	+	0.987952i	$0.549460\pi$
$270$	8.95992	0.545283
$271$	−29.7407	−1.80662	−0.903310	−	0.428989i	$-0.858870\pi$
$271$	−29.7407	−1.80662	−0.903310	+	0.428989i	$0.858870\pi$
$272$	−6.58913	−0.399524
$273$	1.94435	0.117677
$274$	−35.1074	−2.12092
$275$	−9.14242	−0.551309
$276$	22.5688	1.35848
$277$	17.8468	1.07231	0.536156	−	0.844119i	$-0.319876\pi$
$277$	17.8468	1.07231	0.536156	+	0.844119i	$0.319876\pi$
$278$	7.28325	0.436820
$279$	6.38612	0.382327
$280$	−16.3937	−0.979708
$281$	21.6250	1.29004	0.645019	−	0.764167i	$-0.276850\pi$
$281$	21.6250	1.29004	0.645019	+	0.764167i	$0.276850\pi$
$282$	−0.591500	−0.0352233
$283$	16.6497	0.989720	0.494860	−	0.868973i	$-0.335219\pi$
$283$	16.6497	0.989720	0.494860	+	0.868973i	$0.335219\pi$
$284$	−50.8092	−3.01497
$285$	−12.8927	−0.763697
$286$	4.24483	0.251002
$287$	3.40278	0.200859
$288$	−2.83332	−0.166955
$289$	−7.72781	−0.454577
$290$	31.3623	1.84166
$291$	−6.22538	−0.364938
$292$	−0.780995	−0.0457043
$293$	20.3255	1.18743	0.593713	−	0.804677i	$-0.297661\pi$
$293$	20.3255	1.18743	0.593713	+	0.804677i	$0.297661\pi$
$294$	−13.8402	−0.807178
$295$	38.7124	2.25392
$296$	6.70586	0.389770
$297$	−1.00000	−0.0580259
$298$	43.6728	2.52990
$299$	−10.9367	−0.632485
$300$	33.6125	1.94062
$301$	1.22460	0.0705850
$302$	33.9385	1.95294
$303$	−15.7920	−0.907227
$304$	−7.41853	−0.425482
$305$	−3.76064	−0.215334
$306$	−7.25493	−0.414737
$307$	11.1880	0.638532	0.319266	−	0.947665i	$-0.396564\pi$
$307$	11.1880	0.638532	0.319266	+	0.947665i	$0.396564\pi$
$308$	4.01233	0.228624
$309$	17.4211	0.991053
$310$	57.2191	3.24983
$311$	2.01127	0.114049	0.0570243	−	0.998373i	$-0.481839\pi$
$311$	2.01127	0.114049	0.0570243	+	0.998373i	$0.481839\pi$
$312$	−7.11664	−0.402901
$313$	−20.1614	−1.13959	−0.569794	−	0.821788i	$-0.692977\pi$
$313$	−20.1614	−1.13959	−0.569794	+	0.821788i	$0.692977\pi$
$314$	18.4929	1.04362
$315$	−4.10410	−0.231240
$316$	−21.0027	−1.18149
$317$	−5.84041	−0.328030	−0.164015	−	0.986458i	$-0.552445\pi$
$317$	−5.84041	−0.328030	−0.164015	+	0.986458i	$0.552445\pi$
$318$	−34.1157	−1.91311
$319$	−3.50029	−0.195978
$320$	−41.6616	−2.32895
$321$	8.91707	0.497702
$322$	−15.9612	−0.889485
$323$	10.4393	0.580860
$324$	3.67655	0.204253
$325$	−16.2884	−0.903519
$326$	18.5467	1.02721
$327$	−2.17652	−0.120362
$328$	−12.4547	−0.687697
$329$	0.270938	0.0149373
$330$	−8.95992	−0.493227
$331$	34.0931	1.87393	0.936964	−	0.349426i	$-0.113623\pi$
$331$	34.0931	1.87393	0.936964	+	0.349426i	$0.113623\pi$
$332$	−41.1115	−2.25629
$333$	1.67879	0.0919973
$334$	21.2521	1.16286
$335$	−15.2923	−0.835507
$336$	−2.36153	−0.128832
$337$	14.8883	0.811018	0.405509	−	0.914091i	$-0.367094\pi$
$337$	14.8883	0.811018	0.405509	+	0.914091i	$0.367094\pi$
$338$	−23.4104	−1.27336
$339$	9.29620	0.504900
$340$	−42.1011	−2.28325
$341$	−6.38612	−0.345828
$342$	−8.16815	−0.441683
$343$	13.9789	0.754787
$344$	−4.48226	−0.241667
$345$	23.0850	1.24286
$346$	6.94133	0.373168
$347$	−11.3131	−0.607321	−0.303660	−	0.952780i	$-0.598209\pi$
$347$	−11.3131	−0.607321	−0.303660	+	0.952780i	$0.598209\pi$
$348$	12.8690	0.689849
$349$	6.97921	0.373588	0.186794	−	0.982399i	$-0.440190\pi$
$349$	6.97921	0.373588	0.186794	+	0.982399i	$0.440190\pi$
$350$	−23.7717	−1.27065
$351$	−1.78163	−0.0950964
$352$	2.83332	0.151016
$353$	−3.67016	−0.195343	−0.0976715	−	0.995219i	$-0.531139\pi$
$353$	−3.67016	−0.195343	−0.0976715	+	0.995219i	$0.531139\pi$
$354$	24.5262	1.30355
$355$	−51.9714	−2.75835
$356$	30.9211	1.63882
$357$	3.32313	0.175879
$358$	−39.8079	−2.10391
$359$	17.3409	0.915219	0.457609	−	0.889153i	$-0.348706\pi$
$359$	17.3409	0.915219	0.457609	+	0.889153i	$0.348706\pi$
$360$	15.0217	0.791714
$361$	−7.24661	−0.381401
$362$	31.8953	1.67638
$363$	1.00000	0.0524864
$364$	7.14849	0.374683
$365$	−0.798859	−0.0418142
$366$	−2.38255	−0.124538
$367$	28.2723	1.47580	0.737902	−	0.674908i	$-0.235817\pi$
$367$	28.2723	1.47580	0.737902	+	0.674908i	$0.235817\pi$
$368$	13.2833	0.692438
$369$	−3.11800	−0.162317
$370$	15.0418	0.781988
$371$	15.6267	0.811300
$372$	23.4789	1.21732
$373$	2.61395	0.135345	0.0676725	−	0.997708i	$-0.478443\pi$
$373$	2.61395	0.135345	0.0676725	+	0.997708i	$0.478443\pi$
$374$	7.25493	0.375144
$375$	15.5782	0.804453
$376$	−0.991677	−0.0511418
$377$	−6.23622	−0.321182
$378$	−2.60015	−0.133737
$379$	−14.3196	−0.735550	−0.367775	−	0.929915i	$-0.619880\pi$
$379$	−14.3196	−0.735550	−0.367775	+	0.929915i	$0.619880\pi$
$380$	−47.4005	−2.43160
$381$	12.7608	0.653754
$382$	13.3317	0.682109
$383$	10.0006	0.511005	0.255503	−	0.966808i	$-0.417759\pi$
$383$	10.0006	0.511005	0.255503	+	0.966808i	$0.417759\pi$
$384$	−20.7280	−1.05777
$385$	4.10410	0.209165
$386$	−36.4682	−1.85618
$387$	−1.12212	−0.0570406
$388$	−22.8879	−1.16196
$389$	−7.94199	−0.402675	−0.201337	−	0.979522i	$-0.564529\pi$
$389$	−7.94199	−0.402675	−0.201337	+	0.979522i	$0.564529\pi$
$390$	−15.9633	−0.808331
$391$	−18.6922	−0.945303
$392$	−23.2038	−1.17197
$393$	−11.5721	−0.583733
$394$	−11.2873	−0.568645
$395$	−21.4831	−1.08093
$396$	−3.67655	−0.184753
$397$	1.62563	0.0815880	0.0407940	−	0.999168i	$-0.487011\pi$
$397$	1.62563	0.0815880	0.0407940	+	0.999168i	$0.487011\pi$
$398$	−41.5195	−2.08119
$399$	3.74143	0.187306
$400$	19.7833	0.989163
$401$	10.3906	0.518882	0.259441	−	0.965759i	$-0.416462\pi$
$401$	10.3906	0.518882	0.259441	+	0.965759i	$0.416462\pi$
$402$	−9.68841	−0.483214
$403$	−11.3777	−0.566764
$404$	−58.0600	−2.88859
$405$	3.76064	0.186868
$406$	−9.10127	−0.451689
$407$	−1.67879	−0.0832147
$408$	−12.1632	−0.602169
$409$	−12.4065	−0.613460	−0.306730	−	0.951797i	$-0.599235\pi$
$409$	−12.4065	−0.613460	−0.306730	+	0.951797i	$0.599235\pi$
$410$	−27.9371	−1.37971
$411$	−14.7352	−0.726835
$412$	64.0496	3.15550
$413$	−11.2343	−0.552801
$414$	14.6255	0.718803
$415$	−42.0519	−2.06425
$416$	5.04792	0.247495
$417$	3.05691	0.149698
$418$	8.16815	0.399517
$419$	14.6017	0.713338	0.356669	−	0.934231i	$-0.383912\pi$
$419$	14.6017	0.713338	0.356669	+	0.934231i	$0.383912\pi$
$420$	−15.0889	−0.736264
$421$	−0.0271310	−0.00132228	−0.000661142	−	1.00000i	$-0.500210\pi$
$421$	−0.0271310	−0.00132228	−0.000661142		1.00000i	$0.500210\pi$
$422$	22.6124	1.10075
$423$	−0.248264	−0.0120710
$424$	−57.1965	−2.77771
$425$	−27.8389	−1.35039
$426$	−32.9264	−1.59529
$427$	1.09133	0.0528132
$428$	32.7840	1.58467
$429$	1.78163	0.0860180
$430$	−10.0541	−0.484852
$431$	27.5140	1.32530	0.662652	−	0.748928i	$-0.269431\pi$
$431$	27.5140	1.32530	0.662652	+	0.748928i	$0.269431\pi$
$432$	2.16390	0.104111
$433$	1.06309	0.0510887	0.0255444	−	0.999674i	$-0.491868\pi$
$433$	1.06309	0.0510887	0.0255444	+	0.999674i	$0.491868\pi$
$434$	−16.6049	−0.797060
$435$	13.1633	0.631133
$436$	−8.00208	−0.383230
$437$	−21.0450	−1.00672
$438$	−0.506116	−0.0241832
$439$	−21.2618	−1.01477	−0.507386	−	0.861719i	$-0.669388\pi$
$439$	−21.2618	−1.01477	−0.507386	+	0.861719i	$0.669388\pi$
$440$	−15.0217	−0.716132
$441$	−5.80900	−0.276619
$442$	12.9256	0.614809
$443$	2.97641	0.141414	0.0707068	−	0.997497i	$-0.477475\pi$
$443$	2.97641	0.141414	0.0707068	+	0.997497i	$0.477475\pi$
$444$	6.17216	0.292918
$445$	31.6284	1.49933
$446$	7.13917	0.338050
$447$	18.3303	0.866992
$448$	12.0901	0.571204
$449$	−38.7013	−1.82643	−0.913215	−	0.407479i	$-0.866408\pi$
$449$	−38.7013	−1.82643	−0.913215	+	0.407479i	$0.866408\pi$
$450$	21.7823	1.02683
$451$	3.11800	0.146821
$452$	34.1779	1.60759
$453$	14.2446	0.669269
$454$	−10.1085	−0.474417
$455$	7.31200	0.342792
$456$	−13.6943	−0.641293
$457$	−11.8895	−0.556166	−0.278083	−	0.960557i	$-0.589699\pi$
$457$	−11.8895	−0.556166	−0.278083	+	0.960557i	$0.589699\pi$
$458$	57.1913	2.67237
$459$	−3.04503	−0.142130
$460$	84.8731	3.95723
$461$	−9.31132	−0.433671	−0.216836	−	0.976208i	$-0.569574\pi$
$461$	−9.31132	−0.433671	−0.216836	+	0.976208i	$0.569574\pi$
$462$	2.60015	0.120970
$463$	−33.6494	−1.56382	−0.781911	−	0.623390i	$-0.785755\pi$
$463$	−33.6494	−1.56382	−0.781911	+	0.623390i	$0.785755\pi$
$464$	7.57426	0.351626
$465$	24.0159	1.11371
$466$	−53.6190	−2.48385
$467$	−17.1794	−0.794966	−0.397483	−	0.917609i	$-0.630116\pi$
$467$	−17.1794	−0.794966	−0.397483	+	0.917609i	$0.630116\pi$
$468$	−6.55025	−0.302785
$469$	4.43779	0.204918
$470$	−2.22442	−0.102605
$471$	7.76182	0.357646
$472$	41.1192	1.89267
$473$	1.12212	0.0515951
$474$	−13.6106	−0.625155
$475$	−31.3432	−1.43812
$476$	12.2177	0.559995
$477$	−14.3190	−0.655620
$478$	47.0330	2.15124
$479$	16.1794	0.739255	0.369628	−	0.929180i	$-0.379485\pi$
$479$	16.1794	0.739255	0.369628	+	0.929180i	$0.379485\pi$
$480$	−10.6551	−0.486336
$481$	−2.99099	−0.136377
$482$	−43.3268	−1.97348
$483$	−6.69923	−0.304825
$484$	3.67655	0.167116
$485$	−23.4114	−1.06306
$486$	2.38255	0.108075
$487$	−26.0872	−1.18212	−0.591062	−	0.806626i	$-0.701291\pi$
$487$	−26.0872	−1.18212	−0.591062	+	0.806626i	$0.701291\pi$
$488$	−3.99445	−0.180820
$489$	7.78441	0.352023
$490$	−52.0481	−2.35129
$491$	29.5631	1.33416	0.667081	−	0.744985i	$-0.267543\pi$
$491$	29.5631	1.33416	0.667081	+	0.744985i	$0.267543\pi$
$492$	−11.4635	−0.516814
$493$	−10.6585	−0.480033
$494$	14.5526	0.654754
$495$	−3.76064	−0.169028
$496$	13.8189	0.620487
$497$	15.0820	0.676520
$498$	−26.6419	−1.19385
$499$	34.2316	1.53242	0.766209	−	0.642592i	$-0.222141\pi$
$499$	34.2316	1.53242	0.766209	+	0.642592i	$0.222141\pi$
$500$	57.2738	2.56136
$501$	8.91988	0.398511
$502$	25.3519	1.13151
$503$	17.2219	0.767885	0.383943	−	0.923357i	$-0.374566\pi$
$503$	17.2219	0.767885	0.383943	+	0.923357i	$0.374566\pi$
$504$	−4.35927	−0.194177
$505$	−59.3881	−2.64273
$506$	−14.6255	−0.650182
$507$	−9.82579	−0.436379
$508$	46.9156	2.08154
$509$	23.3711	1.03591	0.517954	−	0.855409i	$-0.326694\pi$
$509$	23.3711	1.03591	0.517954	+	0.855409i	$0.326694\pi$
$510$	−27.2832	−1.20812
$511$	0.231827	0.0102554
$512$	−23.4182	−1.03495
$513$	−3.42832	−0.151364
$514$	19.1026	0.842580
$515$	65.5146	2.88692
$516$	−4.12552	−0.181616
$517$	0.248264	0.0109186
$518$	−4.36511	−0.191792
$519$	2.91340	0.127884
$520$	−26.7631	−1.17364
$521$	−30.1377	−1.32036	−0.660179	−	0.751108i	$-0.729520\pi$
$521$	−30.1377	−1.32036	−0.660179	+	0.751108i	$0.729520\pi$
$522$	8.33961	0.365015
$523$	6.17259	0.269908	0.134954	−	0.990852i	$-0.456911\pi$
$523$	6.17259	0.269908	0.134954	+	0.990852i	$0.456911\pi$
$524$	−42.5452	−1.85859
$525$	−9.97741	−0.435450
$526$	36.6036	1.59599
$527$	−19.4459	−0.847078
$528$	−2.16390	−0.0941715
$529$	14.6822	0.638356
$530$	−128.297	−5.57286
$531$	10.2941	0.446725
$532$	13.7555	0.596379
$533$	5.55513	0.240620
$534$	20.0381	0.867135
$535$	33.5339	1.44980
$536$	−16.2431	−0.701593
$537$	−16.7081	−0.721009
$538$	−12.0949	−0.521447
$539$	5.80900	0.250211
$540$	13.8262	0.594984
$541$	−12.8447	−0.552237	−0.276118	−	0.961124i	$-0.589048\pi$
$541$	−12.8447	−0.552237	−0.276118	+	0.961124i	$0.589048\pi$
$542$	−70.8587	−3.04364
$543$	13.3870	0.574493
$544$	8.62753	0.369902
$545$	−8.18511	−0.350612
$546$	4.63251	0.198253
$547$	−1.96661	−0.0840864	−0.0420432	−	0.999116i	$-0.513387\pi$
$547$	−1.96661	−0.0840864	−0.0420432	+	0.999116i	$0.513387\pi$
$548$	−54.1747	−2.31423
$549$	−1.00000	−0.0426790
$550$	−21.7823	−0.928800
$551$	−12.0001	−0.511222
$552$	24.5203	1.04365
$553$	6.23435	0.265112
$554$	42.5209	1.80654
$555$	6.31334	0.267986
$556$	11.2389	0.476635
$557$	−5.69332	−0.241234	−0.120617	−	0.992699i	$-0.538487\pi$
$557$	−5.69332	−0.241234	−0.120617	+	0.992699i	$0.538487\pi$
$558$	15.2153	0.644113
$559$	1.99920	0.0845573
$560$	−8.88086	−0.375285
$561$	3.04503	0.128561
$562$	51.5226	2.17335
$563$	16.5808	0.698796	0.349398	−	0.936974i	$-0.386386\pi$
$563$	16.5808	0.698796	0.349398	+	0.936974i	$0.386386\pi$
$564$	−0.912752	−0.0384338
$565$	34.9597	1.47076
$566$	39.6687	1.66740
$567$	−1.09133	−0.0458316
$568$	−55.2026	−2.31625
$569$	43.7570	1.83439	0.917195	−	0.398438i	$-0.130447\pi$
$569$	43.7570	1.83439	0.917195	+	0.398438i	$0.130447\pi$
$570$	−30.7175	−1.28661
$571$	−33.9337	−1.42008	−0.710040	−	0.704161i	$-0.751323\pi$
$571$	−33.9337	−1.42008	−0.710040	+	0.704161i	$0.751323\pi$
$572$	6.55025	0.273880
$573$	5.59555	0.233758
$574$	8.10728	0.338391
$575$	56.1215	2.34043
$576$	−11.0783	−0.461596
$577$	4.51610	0.188008	0.0940039	−	0.995572i	$-0.470033\pi$
$577$	4.51610	0.188008	0.0940039	+	0.995572i	$0.470033\pi$
$578$	−18.4119	−0.765833
$579$	−15.3064	−0.636111
$580$	48.3955	2.00952
$581$	12.2034	0.506282
$582$	−14.8323	−0.614818
$583$	14.3190	0.593031
$584$	−0.848527	−0.0351123
$585$	−6.70008	−0.277014
$586$	48.4264	2.00048
$587$	44.9601	1.85570	0.927850	−	0.372953i	$-0.121655\pi$
$587$	44.9601	1.85570	0.927850	+	0.372953i	$0.121655\pi$
$588$	−21.3570	−0.880750
$589$	−21.8937	−0.902113
$590$	92.2341	3.79722
$591$	−4.73748	−0.194874
$592$	3.63273	0.149304
$593$	−2.10590	−0.0864790	−0.0432395	−	0.999065i	$-0.513768\pi$
$593$	−2.10590	−0.0864790	−0.0432395	+	0.999065i	$0.513768\pi$
$594$	−2.38255	−0.0977572
$595$	12.4971	0.512332
$596$	67.3921	2.76049
$597$	−17.4265	−0.713219
$598$	−26.0572	−1.06556
$599$	−3.19404	−0.130505	−0.0652526	−	0.997869i	$-0.520785\pi$
$599$	−3.19404	−0.130505	−0.0652526	+	0.997869i	$0.520785\pi$
$600$	36.5190	1.49088
$601$	−35.4191	−1.44478	−0.722388	−	0.691488i	$-0.756956\pi$
$601$	−35.4191	−1.44478	−0.722388	+	0.691488i	$0.756956\pi$
$602$	2.91768	0.118916
$603$	−4.06640	−0.165597
$604$	52.3709	2.13094
$605$	3.76064	0.152892
$606$	−37.6253	−1.52842
$607$	9.57307	0.388559	0.194279	−	0.980946i	$-0.437763\pi$
$607$	9.57307	0.388559	0.194279	+	0.980946i	$0.437763\pi$
$608$	9.71352	0.393935
$609$	−3.81997	−0.154793
$610$	−8.95992	−0.362776
$611$	0.442314	0.0178941
$612$	−11.1952	−0.452538
$613$	−28.7926	−1.16292	−0.581461	−	0.813574i	$-0.697519\pi$
$613$	−28.7926	−1.16292	−0.581461	+	0.813574i	$0.697519\pi$
$614$	26.6559	1.07575
$615$	−11.7257	−0.472826
$616$	4.35927	0.175640
$617$	3.17755	0.127923	0.0639617	−	0.997952i	$-0.479626\pi$
$617$	3.17755	0.127923	0.0639617	+	0.997952i	$0.479626\pi$
$618$	41.5067	1.66964
$619$	−24.2849	−0.976091	−0.488046	−	0.872818i	$-0.662290\pi$
$619$	−24.2849	−0.976091	−0.488046	+	0.872818i	$0.662290\pi$
$620$	88.2956	3.54604
$621$	6.13858	0.246333
$622$	4.79195	0.192140
$623$	−9.17850	−0.367729
$624$	−3.85527	−0.154334
$625$	12.8718	0.514872
$626$	−48.0355	−1.91988
$627$	3.42832	0.136914
$628$	28.5367	1.13874
$629$	−5.11197	−0.203828
$630$	−9.77824	−0.389574
$631$	1.14808	0.0457042	0.0228521	−	0.999739i	$-0.492725\pi$
$631$	1.14808	0.0457042	0.0228521	+	0.999739i	$0.492725\pi$
$632$	−22.8188	−0.907682
$633$	9.49083	0.377226
$634$	−13.9151	−0.552638
$635$	47.9887	1.90437
$636$	−52.6443	−2.08748
$637$	10.3495	0.410062
$638$	−8.33961	−0.330168
$639$	−13.8198	−0.546703
$640$	−77.9506	−3.08127
$641$	14.3245	0.565784	0.282892	−	0.959152i	$-0.408706\pi$
$641$	14.3245	0.565784	0.282892	+	0.959152i	$0.408706\pi$
$642$	21.2454	0.838488
$643$	36.3946	1.43526	0.717632	−	0.696422i	$-0.245226\pi$
$643$	36.3946	1.43526	0.717632	+	0.696422i	$0.245226\pi$
$644$	−24.6300	−0.970558
$645$	−4.21989	−0.166158
$646$	24.8722	0.978585
$647$	15.9182	0.625811	0.312905	−	0.949784i	$-0.398698\pi$
$647$	15.9182	0.625811	0.312905	+	0.949784i	$0.398698\pi$
$648$	3.99445	0.156917
$649$	−10.2941	−0.404078
$650$	−38.8080	−1.52217
$651$	−6.96937	−0.273151
$652$	28.6197	1.12084
$653$	14.5026	0.567532	0.283766	−	0.958894i	$-0.408416\pi$
$653$	14.5026	0.567532	0.283766	+	0.958894i	$0.408416\pi$
$654$	−5.18567	−0.202776
$655$	−43.5183	−1.70040
$656$	−6.74704	−0.263428
$657$	−0.212426	−0.00828754
$658$	0.645523	0.0251651
$659$	−39.1669	−1.52573	−0.762863	−	0.646560i	$-0.776207\pi$
$659$	−39.1669	−1.52573	−0.762863	+	0.646560i	$0.776207\pi$
$660$	−13.8262	−0.538183
$661$	13.7606	0.535226	0.267613	−	0.963527i	$-0.413765\pi$
$661$	13.7606	0.535226	0.267613	+	0.963527i	$0.413765\pi$
$662$	81.2286	3.15704
$663$	5.42512	0.210694
$664$	−44.6664	−1.73339
$665$	14.0702	0.545618
$666$	3.99981	0.154989
$667$	21.4868	0.831972
$668$	32.7943	1.26885
$669$	2.99644	0.115849
$670$	−36.4346	−1.40759
$671$	1.00000	0.0386046
$672$	3.09209	0.119280
$673$	4.50630	0.173705	0.0868526	−	0.996221i	$-0.472319\pi$
$673$	4.50630	0.173705	0.0868526	+	0.996221i	$0.472319\pi$
$674$	35.4722	1.36634
$675$	9.14242	0.351892
$676$	−36.1250	−1.38942
$677$	7.83478	0.301115	0.150558	−	0.988601i	$-0.451893\pi$
$677$	7.83478	0.301115	0.150558	+	0.988601i	$0.451893\pi$
$678$	22.1487	0.850614
$679$	6.79395	0.260728
$680$	−45.7415	−1.75411
$681$	−4.24273	−0.162582
$682$	−15.2153	−0.582622
$683$	2.51023	0.0960512	0.0480256	−	0.998846i	$-0.484707\pi$
$683$	2.51023	0.0960512	0.0480256	+	0.998846i	$0.484707\pi$
$684$	−12.6044	−0.481940
$685$	−55.4139	−2.11726
$686$	33.3053	1.27160
$687$	24.0042	0.915819
$688$	−2.42815	−0.0925724
$689$	25.5111	0.971896
$690$	55.0012	2.09386
$691$	17.4304	0.663083	0.331542	−	0.943441i	$-0.392431\pi$
$691$	17.4304	0.663083	0.331542	+	0.943441i	$0.392431\pi$
$692$	10.7113	0.407181
$693$	1.09133	0.0414562
$694$	−26.9541	−1.02316
$695$	11.4960	0.436067
$696$	13.9817	0.529976
$697$	9.49441	0.359626
$698$	16.6283	0.629391
$699$	−22.5049	−0.851213
$700$	−36.6824	−1.38646
$701$	1.14666	0.0433089	0.0216544	−	0.999766i	$-0.493107\pi$
$701$	1.14666	0.0433089	0.0216544	+	0.999766i	$0.493107\pi$
$702$	−4.24483	−0.160211
$703$	−5.75544	−0.217071
$704$	11.0783	0.417530
$705$	−0.933630	−0.0351625
$706$	−8.74435	−0.329098
$707$	17.2343	0.648163
$708$	37.8467	1.42236
$709$	−45.6285	−1.71361	−0.856807	−	0.515638i	$-0.827555\pi$
$709$	−45.6285	−1.71361	−0.856807	+	0.515638i	$0.827555\pi$
$710$	−123.824	−4.64705
$711$	−5.71262	−0.214240
$712$	33.5948	1.25902
$713$	39.2017	1.46812
$714$	7.91753	0.296306
$715$	6.70008	0.250569
$716$	−61.4282	−2.29568
$717$	19.7406	0.737227
$718$	41.3156	1.54188
$719$	−0.752375	−0.0280588	−0.0140294	−	0.999902i	$-0.504466\pi$
$719$	−0.752375	−0.0280588	−0.0140294	+	0.999902i	$0.504466\pi$
$720$	8.13764	0.303272
$721$	−19.0122	−0.708052
$722$	−17.2654	−0.642553
$723$	−18.1850	−0.676309
$724$	49.2181	1.82918
$725$	32.0011	1.18849
$726$	2.38255	0.0884247
$727$	10.1178	0.375248	0.187624	−	0.982241i	$-0.439921\pi$
$727$	10.1178	0.375248	0.187624	+	0.982241i	$0.439921\pi$
$728$	7.76661	0.287850
$729$	1.00000	0.0370370
$730$	−1.90332	−0.0704451
$731$	3.41689	0.126378
$732$	−3.67655	−0.135889
$733$	−33.2720	−1.22893	−0.614465	−	0.788944i	$-0.710628\pi$
$733$	−33.2720	−1.22893	−0.614465	+	0.788944i	$0.710628\pi$
$734$	67.3602	2.48631
$735$	−21.8456	−0.805785
$736$	−17.3925	−0.641098
$737$	4.06640	0.149788
$738$	−7.42880	−0.273458
$739$	−51.5128	−1.89493	−0.947464	−	0.319861i	$-0.896364\pi$
$739$	−51.5128	−1.89493	−0.947464	+	0.319861i	$0.896364\pi$
$740$	23.2113	0.853263
$741$	6.10800	0.224383
$742$	37.2315	1.36681
$743$	35.6438	1.30764	0.653822	−	0.756649i	$-0.273165\pi$
$743$	35.6438	1.30764	0.653822	+	0.756649i	$0.273165\pi$
$744$	25.5091	0.935208
$745$	68.9336	2.52553
$746$	6.22786	0.228018
$747$	−11.1821	−0.409132
$748$	11.1952	0.409336
$749$	−9.73147	−0.355580
$750$	37.1158	1.35528
$751$	27.8095	1.01478	0.507391	−	0.861716i	$-0.330610\pi$
$751$	27.8095	1.01478	0.507391	+	0.861716i	$0.330610\pi$
$752$	−0.537217	−0.0195903
$753$	10.6407	0.387768
$754$	−14.8581	−0.541100
$755$	53.5688	1.94957
$756$	−4.01233	−0.145927
$757$	18.5695	0.674922	0.337461	−	0.941340i	$-0.390432\pi$
$757$	18.5695	0.674922	0.337461	+	0.941340i	$0.390432\pi$
$758$	−34.1172	−1.23919
$759$	−6.13858	−0.222816
$760$	−51.4992	−1.86807
$761$	40.3005	1.46089	0.730447	−	0.682970i	$-0.239312\pi$
$761$	40.3005	1.46089	0.730447	+	0.682970i	$0.239312\pi$
$762$	30.4032	1.10139
$763$	2.37530	0.0859918
$764$	20.5723	0.744280
$765$	−11.4513	−0.414021
$766$	23.8269	0.860900
$767$	−18.3403	−0.662228
$768$	−27.2289	−0.982538
$769$	−20.8170	−0.750682	−0.375341	−	0.926887i	$-0.622474\pi$
$769$	−20.8170	−0.750682	−0.375341	+	0.926887i	$0.622474\pi$
$770$	9.77824	0.352383
$771$	8.01772	0.288751
$772$	−56.2745	−2.02537
$773$	−45.2846	−1.62877	−0.814386	−	0.580323i	$-0.802926\pi$
$773$	−45.2846	−1.62877	−0.814386	+	0.580323i	$0.802926\pi$
$774$	−2.67351	−0.0960972
$775$	58.3846	2.09724
$776$	−24.8670	−0.892673
$777$	−1.83212	−0.0657269
$778$	−18.9222	−0.678393
$779$	10.6895	0.382992
$780$	−24.6331	−0.882008
$781$	13.8198	0.494512
$782$	−44.5350	−1.59257
$783$	3.50029	0.125090
$784$	−12.5701	−0.448931
$785$	29.1894	1.04182
$786$	−27.5710	−0.983425
$787$	−50.5578	−1.80219	−0.901096	−	0.433620i	$-0.857236\pi$
$787$	−50.5578	−1.80219	−0.901096	+	0.433620i	$0.857236\pi$
$788$	−17.4175	−0.620474
$789$	15.3632	0.546944
$790$	−51.1846	−1.82107
$791$	−10.1452	−0.360723
$792$	−3.99445	−0.141937
$793$	1.78163	0.0632676
$794$	3.87314	0.137453
$795$	−53.8485	−1.90981
$796$	−64.0693	−2.27088
$797$	−1.62429	−0.0575352	−0.0287676	−	0.999586i	$-0.509158\pi$
$797$	−1.62429	−0.0575352	−0.0287676	+	0.999586i	$0.509158\pi$
$798$	8.91415	0.315558
$799$	0.755969	0.0267443
$800$	−25.9034	−0.915823
$801$	8.41037	0.297166
$802$	24.7561	0.874169
$803$	0.212426	0.00749636
$804$	−14.9503	−0.527257
$805$	−25.1934	−0.887950
$806$	−27.1080	−0.954838
$807$	−5.07644	−0.178699
$808$	−63.0805	−2.21916
$809$	−23.0904	−0.811817	−0.405908	−	0.913914i	$-0.633045\pi$
$809$	−23.0904	−0.811817	−0.405908	+	0.913914i	$0.633045\pi$
$810$	8.95992	0.314819
$811$	4.77528	0.167683	0.0838414	−	0.996479i	$-0.473281\pi$
$811$	4.77528	0.167683	0.0838414	+	0.996479i	$0.473281\pi$
$812$	−14.0443	−0.492858
$813$	−29.7407	−1.04305
$814$	−3.99981	−0.140193
$815$	29.2744	1.02544
$816$	−6.58913	−0.230666
$817$	3.84699	0.134589
$818$	−29.5590	−1.03351
$819$	1.94435	0.0679411
$820$	−43.1101	−1.50547
$821$	43.5463	1.51978	0.759888	−	0.650054i	$-0.225254\pi$
$821$	43.5463	1.51978	0.759888	+	0.650054i	$0.225254\pi$
$822$	−35.1074	−1.22451
$823$	−46.1469	−1.60858	−0.804290	−	0.594237i	$-0.797454\pi$
$823$	−46.1469	−1.60858	−0.804290	+	0.594237i	$0.797454\pi$
$824$	69.5879	2.42421
$825$	−9.14242	−0.318298
$826$	−26.7662	−0.931314
$827$	3.65250	0.127010	0.0635048	−	0.997982i	$-0.479772\pi$
$827$	3.65250	0.127010	0.0635048	+	0.997982i	$0.479772\pi$
$828$	22.5688	0.784319
$829$	10.3486	0.359420	0.179710	−	0.983720i	$-0.442484\pi$
$829$	10.3486	0.359420	0.179710	+	0.983720i	$0.442484\pi$
$830$	−100.191	−3.47767
$831$	17.8468	0.619099
$832$	19.7375	0.684273
$833$	17.6886	0.612872
$834$	7.28325	0.252198
$835$	33.5445	1.16085
$836$	12.6044	0.435932
$837$	6.38612	0.220737
$838$	34.7892	1.20177
$839$	−28.9001	−0.997743	−0.498871	−	0.866676i	$-0.666252\pi$
$839$	−28.9001	−0.997743	−0.498871	+	0.866676i	$0.666252\pi$
$840$	−16.3937	−0.565635
$841$	−16.7480	−0.577517
$842$	−0.0646409	−0.00222767
$843$	21.6250	0.744803
$844$	34.8935	1.20108
$845$	−36.9513	−1.27116
$846$	−0.591500	−0.0203362
$847$	−1.09133	−0.0374986
$848$	−30.9848	−1.06402
$849$	16.6497	0.571415
$850$	−66.3277	−2.27502
$851$	10.3054	0.353265
$852$	−50.8092	−1.74069
$853$	43.6457	1.49440	0.747200	−	0.664600i	$-0.231398\pi$
$853$	43.6457	1.49440	0.747200	+	0.664600i	$0.231398\pi$
$854$	2.60015	0.0889753
$855$	−12.8927	−0.440921
$856$	35.6188	1.21743
$857$	22.4032	0.765280	0.382640	−	0.923898i	$-0.375015\pi$
$857$	22.4032	0.765280	0.382640	+	0.923898i	$0.375015\pi$
$858$	4.24483	0.144916
$859$	−9.82217	−0.335128	−0.167564	−	0.985861i	$-0.553590\pi$
$859$	−9.82217	−0.335128	−0.167564	+	0.985861i	$0.553590\pi$
$860$	−15.5146	−0.529044
$861$	3.40278	0.115966
$862$	65.5535	2.23276
$863$	−45.5474	−1.55045	−0.775226	−	0.631684i	$-0.782364\pi$
$863$	−45.5474	−1.55045	−0.775226	+	0.631684i	$0.782364\pi$
$864$	−2.83332	−0.0963914
$865$	10.9563	0.372524
$866$	2.53286	0.0860701
$867$	−7.72781	−0.262450
$868$	−25.6232	−0.869709
$869$	5.71262	0.193787
$870$	31.3623	1.06328
$871$	7.24483	0.245482
$872$	−8.69401	−0.294416
$873$	−6.22538	−0.210697
$874$	−50.1408	−1.69604
$875$	−17.0009	−0.574737
$876$	−0.780995	−0.0263874
$877$	−7.92039	−0.267453	−0.133726	−	0.991018i	$-0.542694\pi$
$877$	−7.92039	−0.267453	−0.133726	+	0.991018i	$0.542694\pi$
$878$	−50.6574	−1.70960
$879$	20.3255	0.685561
$880$	−8.13764	−0.274320
$881$	25.2749	0.851532	0.425766	−	0.904833i	$-0.360005\pi$
$881$	25.2749	0.851532	0.425766	+	0.904833i	$0.360005\pi$
$882$	−13.8402	−0.466025
$883$	−36.0684	−1.21380	−0.606899	−	0.794779i	$-0.707587\pi$
$883$	−36.0684	−1.21380	−0.606899	+	0.794779i	$0.707587\pi$
$884$	19.9457	0.670846
$885$	38.7124	1.30130
$886$	7.09145	0.238242
$887$	33.9350	1.13942	0.569712	−	0.821844i	$-0.307055\pi$
$887$	33.9350	1.13942	0.569712	+	0.821844i	$0.307055\pi$
$888$	6.70586	0.225034
$889$	−13.9262	−0.467071
$890$	75.3562	2.52595
$891$	−1.00000	−0.0335013
$892$	11.0166	0.368862
$893$	0.851127	0.0284819
$894$	43.6728	1.46064
$895$	−62.8333	−2.10028
$896$	22.6211	0.755718
$897$	−10.9367	−0.365165
$898$	−92.2079	−3.07702
$899$	22.3533	0.745523
$900$	33.6125	1.12042
$901$	43.6017	1.45258
$902$	7.42880	0.247352
$903$	1.22460	0.0407523
$904$	37.1332	1.23503
$905$	50.3439	1.67349
$906$	33.9385	1.12753
$907$	16.9564	0.563028	0.281514	−	0.959557i	$-0.409163\pi$
$907$	16.9564	0.563028	0.281514	+	0.959557i	$0.409163\pi$
$908$	−15.5986	−0.517658
$909$	−15.7920	−0.523788
$910$	17.4212	0.577507
$911$	−40.0259	−1.32612	−0.663059	−	0.748567i	$-0.730742\pi$
$911$	−40.0259	−1.32612	−0.663059	+	0.748567i	$0.730742\pi$
$912$	−7.41853	−0.245652
$913$	11.1821	0.370074
$914$	−28.3273	−0.936983
$915$	−3.76064	−0.124323
$916$	88.2527	2.91595
$917$	12.6289	0.417044
$918$	−7.25493	−0.239448
$919$	42.7155	1.40905	0.704526	−	0.709678i	$-0.251159\pi$
$919$	42.7155	1.40905	0.704526	+	0.709678i	$0.251159\pi$
$920$	92.2120	3.04014
$921$	11.1880	0.368657
$922$	−22.1847	−0.730614
$923$	24.6218	0.810437
$924$	4.01233	0.131996
$925$	15.3482	0.504647
$926$	−80.1715	−2.63460
$927$	17.4211	0.572185
$928$	−9.91742	−0.325555
$929$	−10.2750	−0.337111	−0.168555	−	0.985692i	$-0.553910\pi$
$929$	−10.2750	−0.337111	−0.168555	+	0.985692i	$0.553910\pi$
$930$	57.2191	1.87629
$931$	19.9151	0.652691
$932$	−82.7402	−2.71025
$933$	2.01127	0.0658459
$934$	−40.9307	−1.33929
$935$	11.4513	0.374496
$936$	−7.11664	−0.232615
$937$	53.8161	1.75809	0.879047	−	0.476735i	$-0.158180\pi$
$937$	53.8161	1.75809	0.879047	+	0.476735i	$0.158180\pi$
$938$	10.5733	0.345229
$939$	−20.1614	−0.657941
$940$	−3.43253	−0.111957
$941$	−5.64514	−0.184026	−0.0920132	−	0.995758i	$-0.529330\pi$
$941$	−5.64514	−0.184026	−0.0920132	+	0.995758i	$0.529330\pi$
$942$	18.4929	0.602532
$943$	−19.1401	−0.623288
$944$	22.2753	0.725000
$945$	−4.10410	−0.133507
$946$	2.67351	0.0869232
$947$	0.163966	0.00532817	0.00266408	−	0.999996i	$-0.499152\pi$
$947$	0.163966	0.00532817	0.00266408	+	0.999996i	$0.499152\pi$
$948$	−21.0027	−0.682136
$949$	0.378465	0.0122855
$950$	−74.6767	−2.42283
$951$	−5.84041	−0.189388
$952$	13.2741	0.430216
$953$	44.8258	1.45205	0.726025	−	0.687669i	$-0.241366\pi$
$953$	44.8258	1.45205	0.726025	+	0.687669i	$0.241366\pi$
$954$	−34.1157	−1.10454
$955$	21.0429	0.680931
$956$	72.5773	2.34732
$957$	−3.50029	−0.113148
$958$	38.5482	1.24544
$959$	16.0810	0.519283
$960$	−41.6616	−1.34462
$961$	9.78257	0.315567
$962$	−7.12618	−0.229757
$963$	8.91707	0.287348
$964$	−66.8581	−2.15335
$965$	−57.5617	−1.85298
$966$	−15.9612	−0.513545
$967$	−37.1280	−1.19396	−0.596979	−	0.802257i	$-0.703632\pi$
$967$	−37.1280	−1.19396	−0.596979	+	0.802257i	$0.703632\pi$
$968$	3.99445	0.128387
$969$	10.4393	0.335360
$970$	−55.7789	−1.79095
$971$	27.3839	0.878793	0.439396	−	0.898293i	$-0.355192\pi$
$971$	27.3839	0.878793	0.439396	+	0.898293i	$0.355192\pi$
$972$	3.67655	0.117925
$973$	−3.33611	−0.106951
$974$	−62.1540	−1.99154
$975$	−16.2884	−0.521647
$976$	−2.16390	−0.0692646
$977$	37.5915	1.20266	0.601330	−	0.799001i	$-0.294638\pi$
$977$	37.5915	1.20266	0.601330	+	0.799001i	$0.294638\pi$
$978$	18.5467	0.593060
$979$	−8.41037	−0.268797
$980$	−80.3162	−2.56561
$981$	−2.17652	−0.0694910
$982$	70.4355	2.24769
$983$	−58.1131	−1.85352	−0.926759	−	0.375656i	$-0.877418\pi$
$983$	−58.1131	−1.85352	−0.926759	+	0.375656i	$0.877418\pi$
$984$	−12.4547	−0.397042
$985$	−17.8159	−0.567663
$986$	−25.3943	−0.808720
$987$	0.270938	0.00862404
$988$	22.4564	0.714432
$989$	−6.88823	−0.219033
$990$	−8.95992	−0.284765
$991$	57.1597	1.81574	0.907869	−	0.419254i	$-0.137708\pi$
$991$	57.1597	1.81574	0.907869	+	0.419254i	$0.137708\pi$
$992$	−18.0939	−0.574482
$993$	34.0931	1.08191
$994$	35.9336	1.13974
$995$	−65.5348	−2.07759
$996$	−41.1115	−1.30267
$997$	−9.58068	−0.303423	−0.151712	−	0.988425i	$-0.548478\pi$
$997$	−9.58068	−0.303423	−0.151712	+	0.988425i	$0.548478\pi$
$998$	81.5585	2.58169
$999$	1.67879	0.0531147

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.f.1.11	✓	13
3.2	odd	2		6039.2.a.g.1.3		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.f.1.11	✓	13	1.1	even	1	trivial
6039.2.a.g.1.3		13	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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q+2.38255 q^{2} +1.00000 q^{3} +3.67655 q^{4} +3.76064 q^{5} +2.38255 q^{6} -1.09133 q^{7} +3.99445 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.38255 q^{2} +1.00000 q^{3} +3.67655 q^{4} +3.76064 q^{5} +2.38255 q^{6} -1.09133 q^{7} +3.99445 q^{8} +1.00000 q^{9} +8.95992 q^{10} -1.00000 q^{11} +3.67655 q^{12} -1.78163 q^{13} -2.60015 q^{14} +3.76064 q^{15} +2.16390 q^{16} -3.04503 q^{17} +2.38255 q^{18} -3.42832 q^{19} +13.8262 q^{20} -1.09133 q^{21} -2.38255 q^{22} +6.13858 q^{23} +3.99445 q^{24} +9.14242 q^{25} -4.24483 q^{26} +1.00000 q^{27} -4.01233 q^{28} +3.50029 q^{29} +8.95992 q^{30} +6.38612 q^{31} -2.83332 q^{32} -1.00000 q^{33} -7.25493 q^{34} -4.10410 q^{35} +3.67655 q^{36} +1.67879 q^{37} -8.16815 q^{38} -1.78163 q^{39} +15.0217 q^{40} -3.11800 q^{41} -2.60015 q^{42} -1.12212 q^{43} -3.67655 q^{44} +3.76064 q^{45} +14.6255 q^{46} -0.248264 q^{47} +2.16390 q^{48} -5.80900 q^{49} +21.7823 q^{50} -3.04503 q^{51} -6.55025 q^{52} -14.3190 q^{53} +2.38255 q^{54} -3.76064 q^{55} -4.35927 q^{56} -3.42832 q^{57} +8.33961 q^{58} +10.2941 q^{59} +13.8262 q^{60} -1.00000 q^{61} +15.2153 q^{62} -1.09133 q^{63} -11.0783 q^{64} -6.70008 q^{65} -2.38255 q^{66} -4.06640 q^{67} -11.1952 q^{68} +6.13858 q^{69} -9.77824 q^{70} -13.8198 q^{71} +3.99445 q^{72} -0.212426 q^{73} +3.99981 q^{74} +9.14242 q^{75} -12.6044 q^{76} +1.09133 q^{77} -4.24483 q^{78} -5.71262 q^{79} +8.13764 q^{80} +1.00000 q^{81} -7.42880 q^{82} -11.1821 q^{83} -4.01233 q^{84} -11.4513 q^{85} -2.67351 q^{86} +3.50029 q^{87} -3.99445 q^{88} +8.41037 q^{89} +8.95992 q^{90} +1.94435 q^{91} +22.5688 q^{92} +6.38612 q^{93} -0.591500 q^{94} -12.8927 q^{95} -2.83332 q^{96} -6.22538 q^{97} -13.8402 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 5 q^{7} + 15 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 5 * q^7 + 15 * q^8 + 13 * q^9	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 5 q^{7} + 15 q^{8} + 13 q^{9} + 8 q^{10} - 13 q^{11} + 12 q^{12} - 9 q^{13} + 19 q^{14} + 7 q^{15} + 18 q^{16} + 7 q^{17} + 4 q^{18} + 2 q^{19} + 15 q^{20} + 5 q^{21} - 4 q^{22} + 23 q^{23} + 15 q^{24} + 10 q^{25} + 8 q^{26} + 13 q^{27} + 9 q^{28} + 16 q^{29} + 8 q^{30} + 9 q^{31} + 29 q^{32} - 13 q^{33} + 2 q^{34} + 16 q^{35} + 12 q^{36} + 14 q^{37} + 8 q^{38} - 9 q^{39} + 16 q^{40} + 19 q^{41} + 19 q^{42} + 7 q^{43} - 12 q^{44} + 7 q^{45} + 4 q^{46} + 26 q^{47} + 18 q^{48} + 8 q^{49} - 15 q^{50} + 7 q^{51} - 17 q^{52} + 18 q^{53} + 4 q^{54} - 7 q^{55} + 44 q^{56} + 2 q^{57} - q^{58} + 31 q^{59} + 15 q^{60} - 13 q^{61} - 5 q^{62} + 5 q^{63} - 17 q^{64} + 31 q^{65} - 4 q^{66} + 14 q^{67} - 32 q^{68} + 23 q^{69} - 20 q^{70} + 37 q^{71} + 15 q^{72} - 16 q^{73} - 6 q^{74} + 10 q^{75} - 7 q^{76} - 5 q^{77} + 8 q^{78} - 17 q^{79} - 2 q^{80} + 13 q^{81} - 2 q^{82} + 30 q^{83} + 9 q^{84} - 16 q^{85} - 22 q^{86} + 16 q^{87} - 15 q^{88} + 35 q^{89} + 8 q^{90} - q^{91} + 24 q^{92} + 9 q^{93} - 11 q^{94} + 13 q^{95} + 29 q^{96} - q^{97} - q^{98} - 13 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 5 * q^7 + 15 * q^8 + 13 * q^9 + 8 * q^10 - 13 * q^11 + 12 * q^12 - 9 * q^13 + 19 * q^14 + 7 * q^15 + 18 * q^16 + 7 * q^17 + 4 * q^18 + 2 * q^19 + 15 * q^20 + 5 * q^21 - 4 * q^22 + 23 * q^23 + 15 * q^24 + 10 * q^25 + 8 * q^26 + 13 * q^27 + 9 * q^28 + 16 * q^29 + 8 * q^30 + 9 * q^31 + 29 * q^32 - 13 * q^33 + 2 * q^34 + 16 * q^35 + 12 * q^36 + 14 * q^37 + 8 * q^38 - 9 * q^39 + 16 * q^40 + 19 * q^41 + 19 * q^42 + 7 * q^43 - 12 * q^44 + 7 * q^45 + 4 * q^46 + 26 * q^47 + 18 * q^48 + 8 * q^49 - 15 * q^50 + 7 * q^51 - 17 * q^52 + 18 * q^53 + 4 * q^54 - 7 * q^55 + 44 * q^56 + 2 * q^57 - q^58 + 31 * q^59 + 15 * q^60 - 13 * q^61 - 5 * q^62 + 5 * q^63 - 17 * q^64 + 31 * q^65 - 4 * q^66 + 14 * q^67 - 32 * q^68 + 23 * q^69 - 20 * q^70 + 37 * q^71 + 15 * q^72 - 16 * q^73 - 6 * q^74 + 10 * q^75 - 7 * q^76 - 5 * q^77 + 8 * q^78 - 17 * q^79 - 2 * q^80 + 13 * q^81 - 2 * q^82 + 30 * q^83 + 9 * q^84 - 16 * q^85 - 22 * q^86 + 16 * q^87 - 15 * q^88 + 35 * q^89 + 8 * q^90 - q^91 + 24 * q^92 + 9 * q^93 - 11 * q^94 + 13 * q^95 + 29 * q^96 - q^97 - q^98 - 13 * q^99

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