LMFDB - Embedded newform 2013.2.a.f.1.2

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			1.2
Root			$-1.96783$ 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)

$f(q)$	$=$	$q-1.96783 q^{2} +1.00000 q^{3} +1.87234 q^{4} +3.39588 q^{5} -1.96783 q^{6} +0.824946 q^{7} +0.251204 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.96783 q^{2} +1.00000 q^{3} +1.87234 q^{4} +3.39588 q^{5} -1.96783 q^{6} +0.824946 q^{7} +0.251204 q^{8} +1.00000 q^{9} -6.68250 q^{10} -1.00000 q^{11} +1.87234 q^{12} -0.512752 q^{13} -1.62335 q^{14} +3.39588 q^{15} -4.23901 q^{16} -3.00809 q^{17} -1.96783 q^{18} +2.20200 q^{19} +6.35825 q^{20} +0.824946 q^{21} +1.96783 q^{22} -2.99290 q^{23} +0.251204 q^{24} +6.53198 q^{25} +1.00901 q^{26} +1.00000 q^{27} +1.54458 q^{28} +4.96873 q^{29} -6.68250 q^{30} +2.37886 q^{31} +7.83924 q^{32} -1.00000 q^{33} +5.91940 q^{34} +2.80141 q^{35} +1.87234 q^{36} +8.04878 q^{37} -4.33316 q^{38} -0.512752 q^{39} +0.853057 q^{40} -2.71322 q^{41} -1.62335 q^{42} -0.419884 q^{43} -1.87234 q^{44} +3.39588 q^{45} +5.88951 q^{46} +10.4722 q^{47} -4.23901 q^{48} -6.31946 q^{49} -12.8538 q^{50} -3.00809 q^{51} -0.960049 q^{52} +12.9007 q^{53} -1.96783 q^{54} -3.39588 q^{55} +0.207229 q^{56} +2.20200 q^{57} -9.77761 q^{58} +7.61029 q^{59} +6.35825 q^{60} -1.00000 q^{61} -4.68119 q^{62} +0.824946 q^{63} -6.94825 q^{64} -1.74124 q^{65} +1.96783 q^{66} -3.08954 q^{67} -5.63218 q^{68} -2.99290 q^{69} -5.51270 q^{70} +14.6212 q^{71} +0.251204 q^{72} -12.3982 q^{73} -15.8386 q^{74} +6.53198 q^{75} +4.12291 q^{76} -0.824946 q^{77} +1.00901 q^{78} +3.11221 q^{79} -14.3952 q^{80} +1.00000 q^{81} +5.33915 q^{82} +3.05573 q^{83} +1.54458 q^{84} -10.2151 q^{85} +0.826259 q^{86} +4.96873 q^{87} -0.251204 q^{88} -1.99709 q^{89} -6.68250 q^{90} -0.422993 q^{91} -5.60373 q^{92} +2.37886 q^{93} -20.6074 q^{94} +7.47773 q^{95} +7.83924 q^{96} -12.3600 q^{97} +12.4356 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.96783	−1.39146	−0.695732	−	0.718301i	$-0.744920\pi$
$2$	−1.96783	−1.39146	−0.695732	+	0.718301i	$0.744920\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.87234	0.936172
$5$	3.39588	1.51868	0.759341	−	0.650693i	$-0.225521\pi$
$5$	3.39588	1.51868	0.759341	+	0.650693i	$0.225521\pi$
$6$	−1.96783	−0.803362
$7$	0.824946	0.311800	0.155900	−	0.987773i	$-0.450172\pi$
$7$	0.824946	0.311800	0.155900	+	0.987773i	$0.450172\pi$
$8$	0.251204	0.0888140
$9$	1.00000	0.333333
$10$	−6.68250	−2.11319
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.87234	0.540499
$13$	−0.512752	−0.142212	−0.0711060	−	0.997469i	$-0.522653\pi$
$13$	−0.512752	−0.142212	−0.0711060	+	0.997469i	$0.522653\pi$
$14$	−1.62335	−0.433859
$15$	3.39588	0.876812
$16$	−4.23901	−1.05975
$17$	−3.00809	−0.729568	−0.364784	−	0.931092i	$-0.618857\pi$
$17$	−3.00809	−0.729568	−0.364784	+	0.931092i	$0.618857\pi$
$18$	−1.96783	−0.463821
$19$	2.20200	0.505174	0.252587	−	0.967574i	$-0.418719\pi$
$19$	2.20200	0.505174	0.252587	+	0.967574i	$0.418719\pi$
$20$	6.35825	1.42175
$21$	0.824946	0.180018
$22$	1.96783	0.419542
$23$	−2.99290	−0.624062	−0.312031	−	0.950072i	$-0.601009\pi$
$23$	−2.99290	−0.624062	−0.312031	+	0.950072i	$0.601009\pi$
$24$	0.251204	0.0512768
$25$	6.53198	1.30640
$26$	1.00901	0.197883
$27$	1.00000	0.192450
$28$	1.54458	0.291899
$29$	4.96873	0.922671	0.461335	−	0.887226i	$-0.347370\pi$
$29$	4.96873	0.922671	0.461335	+	0.887226i	$0.347370\pi$
$30$	−6.68250	−1.22005
$31$	2.37886	0.427256	0.213628	−	0.976915i	$-0.431472\pi$
$31$	2.37886	0.427256	0.213628	+	0.976915i	$0.431472\pi$
$32$	7.83924	1.38580
$33$	−1.00000	−0.174078
$34$	5.91940	1.01517
$35$	2.80141	0.473525
$36$	1.87234	0.312057
$37$	8.04878	1.32321	0.661606	−	0.749852i	$-0.269875\pi$
$37$	8.04878	1.32321	0.661606	+	0.749852i	$0.269875\pi$
$38$	−4.33316	−0.702932
$39$	−0.512752	−0.0821061
$40$	0.853057	0.134880
$41$	−2.71322	−0.423734	−0.211867	−	0.977299i	$-0.567954\pi$
$41$	−2.71322	−0.423734	−0.211867	+	0.977299i	$0.567954\pi$
$42$	−1.62335	−0.250488
$43$	−0.419884	−0.0640317	−0.0320158	−	0.999487i	$-0.510193\pi$
$43$	−0.419884	−0.0640317	−0.0320158	+	0.999487i	$0.510193\pi$
$44$	−1.87234	−0.282267
$45$	3.39588	0.506227
$46$	5.88951	0.868360
$47$	10.4722	1.52752	0.763762	−	0.645497i	$-0.223350\pi$
$47$	10.4722	1.52752	0.763762	+	0.645497i	$0.223350\pi$
$48$	−4.23901	−0.611849
$49$	−6.31946	−0.902781
$50$	−12.8538	−1.81780
$51$	−3.00809	−0.421217
$52$	−0.960049	−0.133135
$53$	12.9007	1.77205	0.886023	−	0.463640i	$-0.153457\pi$
$53$	12.9007	1.77205	0.886023	+	0.463640i	$0.153457\pi$
$54$	−1.96783	−0.267787
$55$	−3.39588	−0.457900
$56$	0.207229	0.0276922
$57$	2.20200	0.291662
$58$	−9.77761	−1.28386
$59$	7.61029	0.990776	0.495388	−	0.868672i	$-0.335026\pi$
$59$	7.61029	0.990776	0.495388	+	0.868672i	$0.335026\pi$
$60$	6.35825	0.820847
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−4.68119	−0.594512
$63$	0.824946	0.103933
$64$	−6.94825	−0.868531
$65$	−1.74124	−0.215975
$66$	1.96783	0.242223
$67$	−3.08954	−0.377447	−0.188724	−	0.982030i	$-0.560435\pi$
$67$	−3.08954	−0.377447	−0.188724	+	0.982030i	$0.560435\pi$
$68$	−5.63218	−0.683002
$69$	−2.99290	−0.360302
$70$	−5.51270	−0.658893
$71$	14.6212	1.73522	0.867611	−	0.497243i	$-0.165654\pi$
$71$	14.6212	1.73522	0.867611	+	0.497243i	$0.165654\pi$
$72$	0.251204	0.0296047
$73$	−12.3982	−1.45110	−0.725549	−	0.688171i	$-0.758414\pi$
$73$	−12.3982	−1.45110	−0.725549	+	0.688171i	$0.758414\pi$
$74$	−15.8386	−1.84120
$75$	6.53198	0.754248
$76$	4.12291	0.472930
$77$	−0.824946	−0.0940113
$78$	1.00901	0.114248
$79$	3.11221	0.350151	0.175076	−	0.984555i	$-0.443983\pi$
$79$	3.11221	0.350151	0.175076	+	0.984555i	$0.443983\pi$
$80$	−14.3952	−1.60943
$81$	1.00000	0.111111
$82$	5.33915	0.589610
$83$	3.05573	0.335410	0.167705	−	0.985837i	$-0.446364\pi$
$83$	3.05573	0.335410	0.167705	+	0.985837i	$0.446364\pi$
$84$	1.54458	0.168528
$85$	−10.2151	−1.10798
$86$	0.826259	0.0890978
$87$	4.96873	0.532704
$88$	−0.251204	−0.0267784
$89$	−1.99709	−0.211691	−0.105846	−	0.994383i	$-0.533755\pi$
$89$	−1.99709	−0.211691	−0.105846	+	0.994383i	$0.533755\pi$
$90$	−6.68250	−0.704397
$91$	−0.422993	−0.0443417
$92$	−5.60373	−0.584230
$93$	2.37886	0.246676
$94$	−20.6074	−2.12550
$95$	7.47773	0.767199
$96$	7.83924	0.800089
$97$	−12.3600	−1.25497	−0.627484	−	0.778630i	$-0.715915\pi$
$97$	−12.3600	−1.25497	−0.627484	+	0.778630i	$0.715915\pi$
$98$	12.4356	1.25619
$99$	−1.00000	−0.100504
$100$	12.2301	1.22301
$101$	9.32824	0.928195	0.464097	−	0.885784i	$-0.346379\pi$
$101$	9.32824	0.928195	0.464097	+	0.885784i	$0.346379\pi$
$102$	5.91940	0.586108
$103$	5.76118	0.567666	0.283833	−	0.958874i	$-0.408394\pi$
$103$	5.76118	0.567666	0.283833	+	0.958874i	$0.408394\pi$
$104$	−0.128805	−0.0126304
$105$	2.80141	0.273390
$106$	−25.3863	−2.46574
$107$	−8.73496	−0.844441	−0.422220	−	0.906493i	$-0.638749\pi$
$107$	−8.73496	−0.844441	−0.422220	+	0.906493i	$0.638749\pi$
$108$	1.87234	0.180166
$109$	−14.1506	−1.35538	−0.677692	−	0.735346i	$-0.737020\pi$
$109$	−14.1506	−1.35538	−0.677692	+	0.735346i	$0.737020\pi$
$110$	6.68250	0.637151
$111$	8.04878	0.763956
$112$	−3.49696	−0.330431
$113$	19.0500	1.79207	0.896037	−	0.443979i	$-0.146433\pi$
$113$	19.0500	1.79207	0.896037	+	0.443979i	$0.146433\pi$
$114$	−4.33316	−0.405838
$115$	−10.1635	−0.947752
$116$	9.30318	0.863779
$117$	−0.512752	−0.0474040
$118$	−14.9757	−1.37863
$119$	−2.48151	−0.227480
$120$	0.853057	0.0778731
$121$	1.00000	0.0909091
$122$	1.96783	0.178159
$123$	−2.71322	−0.244643
$124$	4.45405	0.399985
$125$	5.20241	0.465318
$126$	−1.62335	−0.144620
$127$	−2.51858	−0.223488	−0.111744	−	0.993737i	$-0.535644\pi$
$127$	−2.51858	−0.223488	−0.111744	+	0.993737i	$0.535644\pi$
$128$	−2.00554	−0.177266
$129$	−0.419884	−0.0369687
$130$	3.42647	0.300521
$131$	1.33904	0.116992	0.0584962	−	0.998288i	$-0.481369\pi$
$131$	1.33904	0.116992	0.0584962	+	0.998288i	$0.481369\pi$
$132$	−1.87234	−0.162967
$133$	1.81653	0.157513
$134$	6.07968	0.525204
$135$	3.39588	0.292271
$136$	−0.755643	−0.0647959
$137$	−8.62643	−0.737005	−0.368503	−	0.929627i	$-0.620129\pi$
$137$	−8.62643	−0.737005	−0.368503	+	0.929627i	$0.620129\pi$
$138$	5.88951	0.501348
$139$	−7.46494	−0.633168	−0.316584	−	0.948564i	$-0.602536\pi$
$139$	−7.46494	−0.633168	−0.316584	+	0.948564i	$0.602536\pi$
$140$	5.24521	0.443301
$141$	10.4722	0.881917
$142$	−28.7721	−2.41450
$143$	0.512752	0.0428785
$144$	−4.23901	−0.353251
$145$	16.8732	1.40124
$146$	24.3975	2.01915
$147$	−6.31946	−0.521221
$148$	15.0701	1.23875
$149$	−20.4973	−1.67920	−0.839602	−	0.543202i	$-0.817212\pi$
$149$	−20.4973	−1.67920	−0.839602	+	0.543202i	$0.817212\pi$
$150$	−12.8538	−1.04951
$151$	11.9828	0.975149	0.487575	−	0.873081i	$-0.337882\pi$
$151$	11.9828	0.975149	0.487575	+	0.873081i	$0.337882\pi$
$152$	0.553151	0.0448665
$153$	−3.00809	−0.243189
$154$	1.62335	0.130813
$155$	8.07832	0.648866
$156$	−0.960049	−0.0768655
$157$	23.7720	1.89721	0.948605	−	0.316463i	$-0.102495\pi$
$157$	23.7720	1.89721	0.948605	+	0.316463i	$0.102495\pi$
$158$	−6.12430	−0.487223
$159$	12.9007	1.02309
$160$	26.6211	2.10458
$161$	−2.46898	−0.194583
$162$	−1.96783	−0.154607
$163$	−15.8216	−1.23925	−0.619623	−	0.784900i	$-0.712714\pi$
$163$	−15.8216	−1.23925	−0.619623	+	0.784900i	$0.712714\pi$
$164$	−5.08008	−0.396688
$165$	−3.39588	−0.264369
$166$	−6.01316	−0.466711
$167$	16.6896	1.29148	0.645741	−	0.763556i	$-0.276548\pi$
$167$	16.6896	1.29148	0.645741	+	0.763556i	$0.276548\pi$
$168$	0.207229	0.0159881
$169$	−12.7371	−0.979776
$170$	20.1015	1.54172
$171$	2.20200	0.168391
$172$	−0.786167	−0.0599447
$173$	−24.1641	−1.83716	−0.918582	−	0.395229i	$-0.870665\pi$
$173$	−24.1641	−1.83716	−0.918582	+	0.395229i	$0.870665\pi$
$174$	−9.77761	−0.741239
$175$	5.38853	0.407334
$176$	4.23901	0.319528
$177$	7.61029	0.572025
$178$	3.92993	0.294561
$179$	7.62331	0.569793	0.284896	−	0.958558i	$-0.408041\pi$
$179$	7.62331	0.569793	0.284896	+	0.958558i	$0.408041\pi$
$180$	6.35825	0.473916
$181$	6.41642	0.476929	0.238464	−	0.971151i	$-0.423356\pi$
$181$	6.41642	0.476929	0.238464	+	0.971151i	$0.423356\pi$
$182$	0.832377	0.0616999
$183$	−1.00000	−0.0739221
$184$	−0.751827	−0.0554254
$185$	27.3327	2.00954
$186$	−4.68119	−0.343241
$187$	3.00809	0.219973
$188$	19.6075	1.43003
$189$	0.824946	0.0600060
$190$	−14.7149	−1.06753
$191$	−10.9960	−0.795640	−0.397820	−	0.917463i	$-0.630233\pi$
$191$	−10.9960	−0.795640	−0.397820	+	0.917463i	$0.630233\pi$
$192$	−6.94825	−0.501446
$193$	14.1984	1.02203	0.511013	−	0.859573i	$-0.329270\pi$
$193$	14.1984	1.02203	0.511013	+	0.859573i	$0.329270\pi$
$194$	24.3223	1.74624
$195$	−1.74124	−0.124693
$196$	−11.8322	−0.845158
$197$	10.8378	0.772165	0.386082	−	0.922464i	$-0.373828\pi$
$197$	10.8378	0.772165	0.386082	+	0.922464i	$0.373828\pi$
$198$	1.96783	0.139847
$199$	15.4077	1.09222	0.546111	−	0.837713i	$-0.316108\pi$
$199$	15.4077	1.09222	0.546111	+	0.837713i	$0.316108\pi$
$200$	1.64086	0.116026
$201$	−3.08954	−0.217919
$202$	−18.3564	−1.29155
$203$	4.09894	0.287689
$204$	−5.63218	−0.394331
$205$	−9.21376	−0.643517
$206$	−11.3370	−0.789887
$207$	−2.99290	−0.208021
$208$	2.17357	0.150710
$209$	−2.20200	−0.152316
$210$	−5.51270	−0.380412
$211$	−0.600314	−0.0413273	−0.0206636	−	0.999786i	$-0.506578\pi$
$211$	−0.600314	−0.0413273	−0.0206636	+	0.999786i	$0.506578\pi$
$212$	24.1545	1.65894
$213$	14.6212	1.00183
$214$	17.1889	1.17501
$215$	−1.42587	−0.0972438
$216$	0.251204	0.0170923
$217$	1.96243	0.133219
$218$	27.8460	1.88597
$219$	−12.3982	−0.837792
$220$	−6.35825	−0.428673
$221$	1.54240	0.103753
$222$	−15.8386	−1.06302
$223$	−4.55023	−0.304706	−0.152353	−	0.988326i	$-0.548685\pi$
$223$	−4.55023	−0.304706	−0.152353	+	0.988326i	$0.548685\pi$
$224$	6.46695	0.432091
$225$	6.53198	0.435465
$226$	−37.4871	−2.49361
$227$	−13.5313	−0.898107	−0.449053	−	0.893505i	$-0.648239\pi$
$227$	−13.5313	−0.898107	−0.449053	+	0.893505i	$0.648239\pi$
$228$	4.12291	0.273046
$229$	1.66111	0.109769	0.0548846	−	0.998493i	$-0.482521\pi$
$229$	1.66111	0.109769	0.0548846	+	0.998493i	$0.482521\pi$
$230$	20.0000	1.31876
$231$	−0.824946	−0.0542774
$232$	1.24817	0.0819461
$233$	14.1053	0.924067	0.462033	−	0.886863i	$-0.347120\pi$
$233$	14.1053	0.924067	0.462033	+	0.886863i	$0.347120\pi$
$234$	1.00901	0.0659609
$235$	35.5622	2.31982
$236$	14.2491	0.927537
$237$	3.11221	0.202160
$238$	4.88318	0.316530
$239$	12.7753	0.826367	0.413183	−	0.910648i	$-0.364417\pi$
$239$	12.7753	0.826367	0.413183	+	0.910648i	$0.364417\pi$
$240$	−14.3952	−0.929204
$241$	−4.74459	−0.305626	−0.152813	−	0.988255i	$-0.548833\pi$
$241$	−4.74459	−0.305626	−0.152813	+	0.988255i	$0.548833\pi$
$242$	−1.96783	−0.126497
$243$	1.00000	0.0641500
$244$	−1.87234	−0.119865
$245$	−21.4601	−1.37104
$246$	5.33915	0.340412
$247$	−1.12908	−0.0718418
$248$	0.597579	0.0379463
$249$	3.05573	0.193649
$250$	−10.2375	−0.647473
$251$	−10.0520	−0.634480	−0.317240	−	0.948345i	$-0.602756\pi$
$251$	−10.0520	−0.634480	−0.317240	+	0.948345i	$0.602756\pi$
$252$	1.54458	0.0972995
$253$	2.99290	0.188162
$254$	4.95614	0.310976
$255$	−10.2151	−0.639694
$256$	17.8430	1.11519
$257$	5.41228	0.337609	0.168804	−	0.985650i	$-0.446009\pi$
$257$	5.41228	0.337609	0.168804	+	0.985650i	$0.446009\pi$
$258$	0.826259	0.0514406
$259$	6.63981	0.412577
$260$	−3.26021	−0.202190
$261$	4.96873	0.307557
$262$	−2.63500	−0.162791
$263$	8.59046	0.529710	0.264855	−	0.964288i	$-0.414676\pi$
$263$	8.59046	0.529710	0.264855	+	0.964288i	$0.414676\pi$
$264$	−0.251204	−0.0154605
$265$	43.8092	2.69118
$266$	−3.57462	−0.219174
$267$	−1.99709	−0.122220
$268$	−5.78468	−0.353355
$269$	−0.207922	−0.0126772	−0.00633860	−	0.999980i	$-0.502018\pi$
$269$	−0.207922	−0.0126772	−0.00633860	+	0.999980i	$0.502018\pi$
$270$	−6.68250	−0.406684
$271$	−19.5846	−1.18968	−0.594838	−	0.803845i	$-0.702784\pi$
$271$	−19.5846	−1.18968	−0.594838	+	0.803845i	$0.702784\pi$
$272$	12.7513	0.773163
$273$	−0.422993	−0.0256007
$274$	16.9753	1.02552
$275$	−6.53198	−0.393893
$276$	−5.60373	−0.337305
$277$	−17.7601	−1.06710	−0.533550	−	0.845768i	$-0.679142\pi$
$277$	−17.7601	−1.06710	−0.533550	+	0.845768i	$0.679142\pi$
$278$	14.6897	0.881030
$279$	2.37886	0.142419
$280$	0.703726	0.0420557
$281$	7.71906	0.460480	0.230240	−	0.973134i	$-0.426049\pi$
$281$	7.71906	0.460480	0.230240	+	0.973134i	$0.426049\pi$
$282$	−20.6074	−1.22716
$283$	7.01833	0.417196	0.208598	−	0.978001i	$-0.433110\pi$
$283$	7.01833	0.417196	0.208598	+	0.978001i	$0.433110\pi$
$284$	27.3760	1.62447
$285$	7.47773	0.442942
$286$	−1.00901	−0.0596639
$287$	−2.23826	−0.132120
$288$	7.83924	0.461932
$289$	−7.95141	−0.467730
$290$	−33.2036	−1.94978
$291$	−12.3600	−0.724556
$292$	−23.2137	−1.35848
$293$	−0.967349	−0.0565131	−0.0282566	−	0.999601i	$-0.508996\pi$
$293$	−0.967349	−0.0565131	−0.0282566	+	0.999601i	$0.508996\pi$
$294$	12.4356	0.725260
$295$	25.8436	1.50467
$296$	2.02188	0.117520
$297$	−1.00000	−0.0580259
$298$	40.3351	2.33655
$299$	1.53462	0.0887491
$300$	12.2301	0.706106
$301$	−0.346381	−0.0199651
$302$	−23.5801	−1.35688
$303$	9.32824	0.535893
$304$	−9.33432	−0.535360
$305$	−3.39588	−0.194447
$306$	5.91940	0.338389
$307$	24.1462	1.37810	0.689048	−	0.724716i	$-0.258029\pi$
$307$	24.1462	1.37810	0.689048	+	0.724716i	$0.258029\pi$
$308$	−1.54458	−0.0880108
$309$	5.76118	0.327742
$310$	−15.8967	−0.902874
$311$	−2.44837	−0.138834	−0.0694171	−	0.997588i	$-0.522114\pi$
$311$	−2.44837	−0.138834	−0.0694171	+	0.997588i	$0.522114\pi$
$312$	−0.128805	−0.00729217
$313$	−16.2454	−0.918245	−0.459122	−	0.888373i	$-0.651836\pi$
$313$	−16.2454	−0.918245	−0.459122	+	0.888373i	$0.651836\pi$
$314$	−46.7791	−2.63990
$315$	2.80141	0.157842
$316$	5.82713	0.327802
$317$	−14.1481	−0.794634	−0.397317	−	0.917681i	$-0.630059\pi$
$317$	−14.1481	−0.794634	−0.397317	+	0.917681i	$0.630059\pi$
$318$	−25.3863	−1.42360
$319$	−4.96873	−0.278196
$320$	−23.5954	−1.31902
$321$	−8.73496	−0.487538
$322$	4.85852	0.270755
$323$	−6.62382	−0.368559
$324$	1.87234	0.104019
$325$	−3.34929	−0.185785
$326$	31.1342	1.72437
$327$	−14.1506	−0.782531
$328$	−0.681571	−0.0376335
$329$	8.63898	0.476282
$330$	6.68250	0.367859
$331$	−9.83670	−0.540674	−0.270337	−	0.962766i	$-0.587135\pi$
$331$	−9.83670	−0.540674	−0.270337	+	0.962766i	$0.587135\pi$
$332$	5.72139	0.314002
$333$	8.04878	0.441070
$334$	−32.8423	−1.79705
$335$	−10.4917	−0.573222
$336$	−3.49696	−0.190775
$337$	−14.3438	−0.781357	−0.390678	−	0.920527i	$-0.627760\pi$
$337$	−14.3438	−0.781357	−0.390678	+	0.920527i	$0.627760\pi$
$338$	25.0644	1.36332
$339$	19.0500	1.03465
$340$	−19.1262	−1.03726
$341$	−2.37886	−0.128823
$342$	−4.33316	−0.234311
$343$	−10.9878	−0.593287
$344$	−0.105476	−0.00568691
$345$	−10.1635	−0.547185
$346$	47.5508	2.55635
$347$	6.22591	0.334224	0.167112	−	0.985938i	$-0.446556\pi$
$347$	6.22591	0.334224	0.167112	+	0.985938i	$0.446556\pi$
$348$	9.30318	0.498703
$349$	9.56337	0.511916	0.255958	−	0.966688i	$-0.417609\pi$
$349$	9.56337	0.511916	0.255958	+	0.966688i	$0.417609\pi$
$350$	−10.6037	−0.566791
$351$	−0.512752	−0.0273687
$352$	−7.83924	−0.417833
$353$	−16.2348	−0.864093	−0.432046	−	0.901851i	$-0.642208\pi$
$353$	−16.2348	−0.864093	−0.432046	+	0.901851i	$0.642208\pi$
$354$	−14.9757	−0.795952
$355$	49.6519	2.63525
$356$	−3.73924	−0.198180
$357$	−2.48151	−0.131335
$358$	−15.0014	−0.792846
$359$	26.4116	1.39395	0.696975	−	0.717095i	$-0.254529\pi$
$359$	26.4116	1.39395	0.696975	+	0.717095i	$0.254529\pi$
$360$	0.853057	0.0449601
$361$	−14.1512	−0.744799
$362$	−12.6264	−0.663629
$363$	1.00000	0.0524864
$364$	−0.791988	−0.0415115
$365$	−42.1027	−2.20376
$366$	1.96783	0.102860
$367$	−13.4336	−0.701230	−0.350615	−	0.936520i	$-0.614027\pi$
$367$	−13.4336	−0.701230	−0.350615	+	0.936520i	$0.614027\pi$
$368$	12.6869	0.661352
$369$	−2.71322	−0.141245
$370$	−53.7860	−2.79620
$371$	10.6424	0.552524
$372$	4.45405	0.230932
$373$	17.3525	0.898480	0.449240	−	0.893411i	$-0.351695\pi$
$373$	17.3525	0.898480	0.449240	+	0.893411i	$0.351695\pi$
$374$	−5.91940	−0.306085
$375$	5.20241	0.268652
$376$	2.63065	0.135666
$377$	−2.54773	−0.131215
$378$	−1.62335	−0.0834961
$379$	−36.7962	−1.89009	−0.945047	−	0.326935i	$-0.893984\pi$
$379$	−36.7962	−1.89009	−0.945047	+	0.326935i	$0.893984\pi$
$380$	14.0009	0.718230
$381$	−2.51858	−0.129031
$382$	21.6382	1.10711
$383$	−7.02641	−0.359033	−0.179516	−	0.983755i	$-0.557453\pi$
$383$	−7.02641	−0.359033	−0.179516	+	0.983755i	$0.557453\pi$
$384$	−2.00554	−0.102345
$385$	−2.80141	−0.142773
$386$	−27.9401	−1.42211
$387$	−0.419884	−0.0213439
$388$	−23.1422	−1.17487
$389$	−13.9638	−0.707994	−0.353997	−	0.935247i	$-0.615178\pi$
$389$	−13.9638	−0.707994	−0.353997	+	0.935247i	$0.615178\pi$
$390$	3.42647	0.173506
$391$	9.00290	0.455296
$392$	−1.58747	−0.0801795
$393$	1.33904	0.0675456
$394$	−21.3270	−1.07444
$395$	10.5687	0.531769
$396$	−1.87234	−0.0940889
$397$	0.390617	0.0196045	0.00980225	−	0.999952i	$-0.496880\pi$
$397$	0.390617	0.0196045	0.00980225	+	0.999952i	$0.496880\pi$
$398$	−30.3197	−1.51979
$399$	1.81653	0.0909404
$400$	−27.6892	−1.38446
$401$	−20.7827	−1.03784	−0.518918	−	0.854824i	$-0.673665\pi$
$401$	−20.7827	−1.03784	−0.518918	+	0.854824i	$0.673665\pi$
$402$	6.07968	0.303227
$403$	−1.21977	−0.0607609
$404$	17.4657	0.868950
$405$	3.39588	0.168742
$406$	−8.06600	−0.400309
$407$	−8.04878	−0.398963
$408$	−0.755643	−0.0374099
$409$	−18.3158	−0.905656	−0.452828	−	0.891598i	$-0.649585\pi$
$409$	−18.3158	−0.905656	−0.452828	+	0.891598i	$0.649585\pi$
$410$	18.1311	0.895430
$411$	−8.62643	−0.425510
$412$	10.7869	0.531433
$413$	6.27808	0.308924
$414$	5.88951	0.289453
$415$	10.3769	0.509382
$416$	−4.01959	−0.197077
$417$	−7.46494	−0.365560
$418$	4.33316	0.211942
$419$	22.9716	1.12224	0.561118	−	0.827736i	$-0.310371\pi$
$419$	22.9716	1.12224	0.561118	+	0.827736i	$0.310371\pi$
$420$	5.24521	0.255940
$421$	8.76867	0.427359	0.213679	−	0.976904i	$-0.431455\pi$
$421$	8.76867	0.427359	0.213679	+	0.976904i	$0.431455\pi$
$422$	1.18131	0.0575054
$423$	10.4722	0.509175
$424$	3.24070	0.157383
$425$	−19.6488	−0.953105
$426$	−28.7721	−1.39401
$427$	−0.824946	−0.0399219
$428$	−16.3549	−0.790542
$429$	0.512752	0.0247559
$430$	2.80587	0.135311
$431$	1.97653	0.0952063	0.0476031	−	0.998866i	$-0.484842\pi$
$431$	1.97653	0.0952063	0.0476031	+	0.998866i	$0.484842\pi$
$432$	−4.23901	−0.203950
$433$	−31.2877	−1.50359	−0.751796	−	0.659396i	$-0.770812\pi$
$433$	−31.2877	−1.50359	−0.751796	+	0.659396i	$0.770812\pi$
$434$	−3.86173	−0.185369
$435$	16.8732	0.809009
$436$	−26.4948	−1.26887
$437$	−6.59037	−0.315260
$438$	24.3975	1.16576
$439$	21.5841	1.03015	0.515077	−	0.857144i	$-0.327763\pi$
$439$	21.5841	1.03015	0.515077	+	0.857144i	$0.327763\pi$
$440$	−0.853057	−0.0406679
$441$	−6.31946	−0.300927
$442$	−3.03519	−0.144369
$443$	8.25486	0.392200	0.196100	−	0.980584i	$-0.437172\pi$
$443$	8.25486	0.392200	0.196100	+	0.980584i	$0.437172\pi$
$444$	15.0701	0.715195
$445$	−6.78188	−0.321492
$446$	8.95406	0.423987
$447$	−20.4973	−0.969489
$448$	−5.73192	−0.270808
$449$	13.0926	0.617879	0.308940	−	0.951082i	$-0.400026\pi$
$449$	13.0926	0.617879	0.308940	+	0.951082i	$0.400026\pi$
$450$	−12.8538	−0.605934
$451$	2.71322	0.127760
$452$	35.6682	1.67769
$453$	11.9828	0.563003
$454$	26.6274	1.24968
$455$	−1.43643	−0.0673410
$456$	0.553151	0.0259037
$457$	23.5287	1.10063	0.550314	−	0.834958i	$-0.314508\pi$
$457$	23.5287	1.10063	0.550314	+	0.834958i	$0.314508\pi$
$458$	−3.26878	−0.152740
$459$	−3.00809	−0.140406
$460$	−19.0296	−0.887259
$461$	−23.5920	−1.09879	−0.549394	−	0.835563i	$-0.685141\pi$
$461$	−23.5920	−1.09879	−0.549394	+	0.835563i	$0.685141\pi$
$462$	1.62335	0.0755251
$463$	24.6266	1.14449	0.572247	−	0.820082i	$-0.306072\pi$
$463$	24.6266	1.14449	0.572247	+	0.820082i	$0.306072\pi$
$464$	−21.0625	−0.977804
$465$	8.07832	0.374623
$466$	−27.7567	−1.28581
$467$	14.9987	0.694058	0.347029	−	0.937854i	$-0.387190\pi$
$467$	14.9987	0.694058	0.347029	+	0.937854i	$0.387190\pi$
$468$	−0.960049	−0.0443783
$469$	−2.54870	−0.117688
$470$	−69.9804	−3.22795
$471$	23.7720	1.09535
$472$	1.91173	0.0879947
$473$	0.419884	0.0193063
$474$	−6.12430	−0.281298
$475$	14.3834	0.659957
$476$	−4.64624	−0.212960
$477$	12.9007	0.590682
$478$	−25.1396	−1.14986
$479$	−21.2429	−0.970612	−0.485306	−	0.874344i	$-0.661292\pi$
$479$	−21.2429	−0.970612	−0.485306	+	0.874344i	$0.661292\pi$
$480$	26.6211	1.21508
$481$	−4.12703	−0.188176
$482$	9.33654	0.425268
$483$	−2.46898	−0.112342
$484$	1.87234	0.0851066
$485$	−41.9730	−1.90590
$486$	−1.96783	−0.0892625
$487$	−23.7201	−1.07486	−0.537431	−	0.843308i	$-0.680605\pi$
$487$	−23.7201	−1.07486	−0.537431	+	0.843308i	$0.680605\pi$
$488$	−0.251204	−0.0113715
$489$	−15.8216	−0.715479
$490$	42.2298	1.90775
$491$	−34.7640	−1.56888	−0.784439	−	0.620206i	$-0.787049\pi$
$491$	−34.7640	−1.56888	−0.784439	+	0.620206i	$0.787049\pi$
$492$	−5.08008	−0.229028
$493$	−14.9464	−0.673152
$494$	2.22184	0.0999653
$495$	−3.39588	−0.152633
$496$	−10.0840	−0.452786
$497$	12.0617	0.541043
$498$	−6.01316	−0.269456
$499$	−24.4706	−1.09546	−0.547728	−	0.836657i	$-0.684507\pi$
$499$	−24.4706	−1.09546	−0.547728	+	0.836657i	$0.684507\pi$
$500$	9.74071	0.435618
$501$	16.6896	0.745638
$502$	19.7807	0.882856
$503$	37.5547	1.67448	0.837240	−	0.546836i	$-0.184168\pi$
$503$	37.5547	1.67448	0.837240	+	0.546836i	$0.184168\pi$
$504$	0.207229	0.00923074
$505$	31.6776	1.40963
$506$	−5.88951	−0.261820
$507$	−12.7371	−0.565674
$508$	−4.71566	−0.209223
$509$	−8.43169	−0.373728	−0.186864	−	0.982386i	$-0.559832\pi$
$509$	−8.43169	−0.373728	−0.186864	+	0.982386i	$0.559832\pi$
$510$	20.1015	0.890111
$511$	−10.2278	−0.452452
$512$	−31.1010	−1.37448
$513$	2.20200	0.0972208
$514$	−10.6504	−0.469770
$515$	19.5643	0.862104
$516$	−0.786167	−0.0346091
$517$	−10.4722	−0.460566
$518$	−13.0660	−0.574087
$519$	−24.1641	−1.06069
$520$	−0.437407	−0.0191816
$521$	−5.16158	−0.226133	−0.113066	−	0.993587i	$-0.536067\pi$
$521$	−5.16158	−0.226133	−0.113066	+	0.993587i	$0.536067\pi$
$522$	−9.77761	−0.427954
$523$	−23.1206	−1.01099	−0.505497	−	0.862828i	$-0.668691\pi$
$523$	−23.1206	−1.01099	−0.505497	+	0.862828i	$0.668691\pi$
$524$	2.50714	0.109525
$525$	5.38853	0.235175
$526$	−16.9045	−0.737073
$527$	−7.15582	−0.311713
$528$	4.23901	0.184479
$529$	−14.0426	−0.610546
$530$	−86.2089	−3.74468
$531$	7.61029	0.330259
$532$	3.40117	0.147460
$533$	1.39121	0.0602600
$534$	3.92993	0.170065
$535$	−29.6629	−1.28244
$536$	−0.776104	−0.0335226
$537$	7.62331	0.328970
$538$	0.409154	0.0176399
$539$	6.31946	0.272199
$540$	6.35825	0.273616
$541$	−18.9923	−0.816542	−0.408271	−	0.912861i	$-0.633868\pi$
$541$	−18.9923	−0.816542	−0.408271	+	0.912861i	$0.633868\pi$
$542$	38.5390	1.65539
$543$	6.41642	0.275355
$544$	−23.5811	−1.01103
$545$	−48.0538	−2.05840
$546$	0.832377	0.0356224
$547$	−39.2317	−1.67743	−0.838713	−	0.544574i	$-0.816691\pi$
$547$	−39.2317	−1.67743	−0.838713	+	0.544574i	$0.816691\pi$
$548$	−16.1516	−0.689964
$549$	−1.00000	−0.0426790
$550$	12.8538	0.548088
$551$	10.9412	0.466109
$552$	−0.751827	−0.0319999
$553$	2.56741	0.109177
$554$	34.9488	1.48483
$555$	27.3327	1.16021
$556$	−13.9769	−0.592754
$557$	−29.0192	−1.22958	−0.614792	−	0.788690i	$-0.710760\pi$
$557$	−29.0192	−1.22958	−0.614792	+	0.788690i	$0.710760\pi$
$558$	−4.68119	−0.198171
$559$	0.215296	0.00910607
$560$	−11.8752	−0.501820
$561$	3.00809	0.127002
$562$	−15.1898	−0.640742
$563$	18.0152	0.759250	0.379625	−	0.925140i	$-0.376053\pi$
$563$	18.0152	0.759250	0.379625	+	0.925140i	$0.376053\pi$
$564$	19.6075	0.825626
$565$	64.6915	2.72159
$566$	−13.8109	−0.580514
$567$	0.824946	0.0346445
$568$	3.67291	0.154112
$569$	−32.7949	−1.37483	−0.687417	−	0.726263i	$-0.741255\pi$
$569$	−32.7949	−1.37483	−0.687417	+	0.726263i	$0.741255\pi$
$570$	−14.7149	−0.616339
$571$	15.7903	0.660804	0.330402	−	0.943840i	$-0.392816\pi$
$571$	15.7903	0.660804	0.330402	+	0.943840i	$0.392816\pi$
$572$	0.960049	0.0401417
$573$	−10.9960	−0.459363
$574$	4.40451	0.183841
$575$	−19.5495	−0.815272
$576$	−6.94825	−0.289510
$577$	−19.2762	−0.802477	−0.401239	−	0.915974i	$-0.631420\pi$
$577$	−19.2762	−0.802477	−0.401239	+	0.915974i	$0.631420\pi$
$578$	15.6470	0.650829
$579$	14.1984	0.590067
$580$	31.5925	1.31181
$581$	2.52081	0.104581
$582$	24.3223	1.00819
$583$	−12.9007	−0.534292
$584$	−3.11447	−0.128878
$585$	−1.74124	−0.0719916
$586$	1.90358	0.0786360
$587$	−26.7775	−1.10523	−0.552613	−	0.833438i	$-0.686369\pi$
$587$	−26.7775	−1.10523	−0.552613	+	0.833438i	$0.686369\pi$
$588$	−11.8322	−0.487952
$589$	5.23826	0.215839
$590$	−50.8558	−2.09370
$591$	10.8378	0.445810
$592$	−34.1189	−1.40228
$593$	35.4499	1.45575	0.727876	−	0.685709i	$-0.240508\pi$
$593$	35.4499	1.45575	0.727876	+	0.685709i	$0.240508\pi$
$594$	1.96783	0.0807409
$595$	−8.42690	−0.345469
$596$	−38.3780	−1.57202
$597$	15.4077	0.630595
$598$	−3.01986	−0.123491
$599$	−34.4469	−1.40746	−0.703732	−	0.710466i	$-0.748484\pi$
$599$	−34.4469	−1.40746	−0.703732	+	0.710466i	$0.748484\pi$
$600$	1.64086	0.0669878
$601$	6.76744	0.276050	0.138025	−	0.990429i	$-0.455925\pi$
$601$	6.76744	0.276050	0.138025	+	0.990429i	$0.455925\pi$
$602$	0.681619	0.0277807
$603$	−3.08954	−0.125816
$604$	22.4360	0.912908
$605$	3.39588	0.138062
$606$	−18.3564	−0.745676
$607$	17.5431	0.712054	0.356027	−	0.934476i	$-0.384131\pi$
$607$	17.5431	0.712054	0.356027	+	0.934476i	$0.384131\pi$
$608$	17.2620	0.700068
$609$	4.09894	0.166097
$610$	6.68250	0.270566
$611$	−5.36964	−0.217232
$612$	−5.63218	−0.227667
$613$	16.7573	0.676822	0.338411	−	0.940998i	$-0.390111\pi$
$613$	16.7573	0.676822	0.338411	+	0.940998i	$0.390111\pi$
$614$	−47.5155	−1.91757
$615$	−9.21376	−0.371535
$616$	−0.207229	−0.00834951
$617$	−29.4118	−1.18408	−0.592038	−	0.805910i	$-0.701677\pi$
$617$	−29.4118	−1.18408	−0.592038	+	0.805910i	$0.701677\pi$
$618$	−11.3370	−0.456041
$619$	−24.8691	−0.999573	−0.499787	−	0.866149i	$-0.666588\pi$
$619$	−24.8691	−0.999573	−0.499787	+	0.866149i	$0.666588\pi$
$620$	15.1254	0.607451
$621$	−2.99290	−0.120101
$622$	4.81797	0.193183
$623$	−1.64749	−0.0660054
$624$	2.17357	0.0870122
$625$	−14.9931	−0.599726
$626$	31.9682	1.27770
$627$	−2.20200	−0.0879395
$628$	44.5093	1.77612
$629$	−24.2114	−0.965373
$630$	−5.51270	−0.219631
$631$	−46.7531	−1.86121	−0.930605	−	0.366024i	$-0.880719\pi$
$631$	−46.7531	−1.86121	−0.930605	+	0.366024i	$0.880719\pi$
$632$	0.781800	0.0310983
$633$	−0.600314	−0.0238603
$634$	27.8409	1.10570
$635$	−8.55280	−0.339408
$636$	24.1545	0.957790
$637$	3.24032	0.128386
$638$	9.77761	0.387099
$639$	14.6212	0.578407
$640$	−6.81056	−0.269211
$641$	20.8899	0.825103	0.412552	−	0.910934i	$-0.364638\pi$
$641$	20.8899	0.825103	0.412552	+	0.910934i	$0.364638\pi$
$642$	17.1889	0.678392
$643$	9.99820	0.394291	0.197145	−	0.980374i	$-0.436833\pi$
$643$	9.99820	0.394291	0.197145	+	0.980374i	$0.436833\pi$
$644$	−4.62278	−0.182163
$645$	−1.42587	−0.0561437
$646$	13.0345	0.512837
$647$	12.5451	0.493200	0.246600	−	0.969117i	$-0.420687\pi$
$647$	12.5451	0.493200	0.246600	+	0.969117i	$0.420687\pi$
$648$	0.251204	0.00986822
$649$	−7.61029	−0.298730
$650$	6.59082	0.258513
$651$	1.96243	0.0769137
$652$	−29.6235	−1.16015
$653$	13.7401	0.537694	0.268847	−	0.963183i	$-0.413357\pi$
$653$	13.7401	0.537694	0.268847	+	0.963183i	$0.413357\pi$
$654$	27.8460	1.08886
$655$	4.54721	0.177674
$656$	11.5014	0.449053
$657$	−12.3982	−0.483699
$658$	−17.0000	−0.662730
$659$	10.2185	0.398057	0.199028	−	0.979994i	$-0.436221\pi$
$659$	10.2185	0.398057	0.199028	+	0.979994i	$0.436221\pi$
$660$	−6.35825	−0.247495
$661$	12.6939	0.493735	0.246867	−	0.969049i	$-0.420599\pi$
$661$	12.6939	0.493735	0.246867	+	0.969049i	$0.420599\pi$
$662$	19.3569	0.752328
$663$	1.54240	0.0599020
$664$	0.767612	0.0297891
$665$	6.16872	0.239213
$666$	−15.8386	−0.613734
$667$	−14.8709	−0.575804
$668$	31.2488	1.20905
$669$	−4.55023	−0.175922
$670$	20.6458	0.797618
$671$	1.00000	0.0386046
$672$	6.46695	0.249468
$673$	15.5429	0.599133	0.299567	−	0.954075i	$-0.403158\pi$
$673$	15.5429	0.599133	0.299567	+	0.954075i	$0.403158\pi$
$674$	28.2261	1.08723
$675$	6.53198	0.251416
$676$	−23.8482	−0.917239
$677$	−30.7857	−1.18319	−0.591596	−	0.806235i	$-0.701502\pi$
$677$	−30.7857	−1.18319	−0.591596	+	0.806235i	$0.701502\pi$
$678$	−37.4871	−1.43968
$679$	−10.1963	−0.391299
$680$	−2.56607	−0.0984043
$681$	−13.5313	−0.518522
$682$	4.68119	0.179252
$683$	17.6485	0.675300	0.337650	−	0.941272i	$-0.390368\pi$
$683$	17.6485	0.675300	0.337650	+	0.941272i	$0.390368\pi$
$684$	4.12291	0.157643
$685$	−29.2943	−1.11928
$686$	21.6222	0.825538
$687$	1.66111	0.0633753
$688$	1.77989	0.0678578
$689$	−6.61486	−0.252006
$690$	20.0000	0.761388
$691$	14.0926	0.536107	0.268054	−	0.963404i	$-0.413620\pi$
$691$	14.0926	0.536107	0.268054	+	0.963404i	$0.413620\pi$
$692$	−45.2436	−1.71990
$693$	−0.824946	−0.0313371
$694$	−12.2515	−0.465061
$695$	−25.3500	−0.961581
$696$	1.24817	0.0473116
$697$	8.16160	0.309143
$698$	−18.8191	−0.712312
$699$	14.1053	0.533510
$700$	10.0892	0.381335
$701$	−30.8377	−1.16472	−0.582361	−	0.812930i	$-0.697871\pi$
$701$	−30.8377	−1.16472	−0.582361	+	0.812930i	$0.697871\pi$
$702$	1.00901	0.0380826
$703$	17.7234	0.668452
$704$	6.94825	0.261872
$705$	35.5622	1.33935
$706$	31.9473	1.20235
$707$	7.69529	0.289411
$708$	14.2491	0.535514
$709$	33.3097	1.25097	0.625486	−	0.780236i	$-0.284901\pi$
$709$	33.3097	1.25097	0.625486	+	0.780236i	$0.284901\pi$
$710$	−97.7064	−3.66686
$711$	3.11221	0.116717
$712$	−0.501677	−0.0188011
$713$	−7.11969	−0.266634
$714$	4.88318	0.182748
$715$	1.74124	0.0651188
$716$	14.2735	0.533424
$717$	12.7753	0.477103
$718$	−51.9735	−1.93963
$719$	17.9880	0.670839	0.335419	−	0.942069i	$-0.391122\pi$
$719$	17.9880	0.670839	0.335419	+	0.942069i	$0.391122\pi$
$720$	−14.3952	−0.536476
$721$	4.75266	0.176998
$722$	27.8471	1.03636
$723$	−4.74459	−0.176453
$724$	12.0137	0.446487
$725$	32.4557	1.20537
$726$	−1.96783	−0.0730329
$727$	20.5015	0.760359	0.380179	−	0.924913i	$-0.375862\pi$
$727$	20.5015	0.760359	0.380179	+	0.924913i	$0.375862\pi$
$728$	−0.106257	−0.00393816
$729$	1.00000	0.0370370
$730$	82.8509	3.06645
$731$	1.26305	0.0467155
$732$	−1.87234	−0.0692038
$733$	4.48158	0.165531	0.0827655	−	0.996569i	$-0.473625\pi$
$733$	4.48158	0.165531	0.0827655	+	0.996569i	$0.473625\pi$
$734$	26.4351	0.975737
$735$	−21.4601	−0.791569
$736$	−23.4620	−0.864822
$737$	3.08954	0.113805
$738$	5.33915	0.196537
$739$	−7.19025	−0.264498	−0.132249	−	0.991217i	$-0.542220\pi$
$739$	−7.19025	−0.264498	−0.132249	+	0.991217i	$0.542220\pi$
$740$	51.1762	1.88127
$741$	−1.12908	−0.0414779
$742$	−20.9424	−0.768818
$743$	37.8137	1.38725	0.693624	−	0.720337i	$-0.256013\pi$
$743$	37.8137	1.38725	0.693624	+	0.720337i	$0.256013\pi$
$744$	0.597579	0.0219083
$745$	−69.6063	−2.55018
$746$	−34.1468	−1.25020
$747$	3.05573	0.111803
$748$	5.63218	0.205933
$749$	−7.20587	−0.263297
$750$	−10.2375	−0.373819
$751$	45.2299	1.65046	0.825231	−	0.564796i	$-0.191045\pi$
$751$	45.2299	1.65046	0.825231	+	0.564796i	$0.191045\pi$
$752$	−44.3917	−1.61880
$753$	−10.0520	−0.366317
$754$	5.01349	0.182581
$755$	40.6922	1.48094
$756$	1.54458	0.0561759
$757$	12.7093	0.461928	0.230964	−	0.972962i	$-0.425812\pi$
$757$	12.7093	0.461928	0.230964	+	0.972962i	$0.425812\pi$
$758$	72.4086	2.63000
$759$	2.99290	0.108635
$760$	1.87843	0.0681380
$761$	20.3875	0.739048	0.369524	−	0.929221i	$-0.379521\pi$
$761$	20.3875	0.739048	0.369524	+	0.929221i	$0.379521\pi$
$762$	4.95614	0.179542
$763$	−11.6735	−0.422609
$764$	−20.5882	−0.744856
$765$	−10.2151	−0.369328
$766$	13.8268	0.499581
$767$	−3.90220	−0.140900
$768$	17.8430	0.643855
$769$	50.3730	1.81650	0.908249	−	0.418430i	$-0.137419\pi$
$769$	50.3730	1.81650	0.908249	+	0.418430i	$0.137419\pi$
$770$	5.51270	0.198664
$771$	5.41228	0.194919
$772$	26.5844	0.956792
$773$	7.57782	0.272555	0.136278	−	0.990671i	$-0.456486\pi$
$773$	7.57782	0.272555	0.136278	+	0.990671i	$0.456486\pi$
$774$	0.826259	0.0296993
$775$	15.5387	0.558166
$776$	−3.10488	−0.111459
$777$	6.63981	0.238202
$778$	27.4784	0.985148
$779$	−5.97452	−0.214059
$780$	−3.26021	−0.116734
$781$	−14.6212	−0.523189
$782$	−17.7161	−0.633528
$783$	4.96873	0.177568
$784$	26.7883	0.956725
$785$	80.7267	2.88126
$786$	−2.63500	−0.0939873
$787$	33.8561	1.20684	0.603420	−	0.797424i	$-0.293804\pi$
$787$	33.8561	1.20684	0.603420	+	0.797424i	$0.293804\pi$
$788$	20.2922	0.722879
$789$	8.59046	0.305828
$790$	−20.7974	−0.739937
$791$	15.7152	0.558769
$792$	−0.251204	−0.00892614
$793$	0.512752	0.0182084
$794$	−0.768666	−0.0272789
$795$	43.8092	1.55375
$796$	28.8485	1.02251
$797$	24.7221	0.875702	0.437851	−	0.899047i	$-0.355740\pi$
$797$	24.7221	0.875702	0.437851	+	0.899047i	$0.355740\pi$
$798$	−3.57462	−0.126540
$799$	−31.5012	−1.11443
$800$	51.2058	1.81040
$801$	−1.99709	−0.0705638
$802$	40.8967	1.44411
$803$	12.3982	0.437522
$804$	−5.78468	−0.204010
$805$	−8.38434	−0.295509
$806$	2.40029	0.0845466
$807$	−0.207922	−0.00731918
$808$	2.34329	0.0824366
$809$	−18.8921	−0.664212	−0.332106	−	0.943242i	$-0.607759\pi$
$809$	−18.8921	−0.664212	−0.332106	+	0.943242i	$0.607759\pi$
$810$	−6.68250	−0.234799
$811$	14.0291	0.492630	0.246315	−	0.969190i	$-0.420780\pi$
$811$	14.0291	0.492630	0.246315	+	0.969190i	$0.420780\pi$
$812$	7.67462	0.269326
$813$	−19.5846	−0.686860
$814$	15.8386	0.555143
$815$	−53.7283	−1.88202
$816$	12.7513	0.446386
$817$	−0.924585	−0.0323471
$818$	36.0423	1.26019
$819$	−0.422993	−0.0147806
$820$	−17.2513	−0.602443
$821$	11.8330	0.412976	0.206488	−	0.978449i	$-0.433797\pi$
$821$	11.8330	0.412976	0.206488	+	0.978449i	$0.433797\pi$
$822$	16.9753	0.592082
$823$	28.3210	0.987209	0.493605	−	0.869686i	$-0.335679\pi$
$823$	28.3210	0.987209	0.493605	+	0.869686i	$0.335679\pi$
$824$	1.44723	0.0504167
$825$	−6.53198	−0.227414
$826$	−12.3542	−0.429857
$827$	6.75795	0.234997	0.117499	−	0.993073i	$-0.462512\pi$
$827$	6.75795	0.234997	0.117499	+	0.993073i	$0.462512\pi$
$828$	−5.60373	−0.194743
$829$	−11.0072	−0.382296	−0.191148	−	0.981561i	$-0.561221\pi$
$829$	−11.0072	−0.382296	−0.191148	+	0.981561i	$0.561221\pi$
$830$	−20.4199	−0.708786
$831$	−17.7601	−0.616091
$832$	3.56273	0.123515
$833$	19.0095	0.658640
$834$	14.6897	0.508663
$835$	56.6760	1.96135
$836$	−4.12291	−0.142594
$837$	2.37886	0.0822255
$838$	−45.2042	−1.56155
$839$	−40.2176	−1.38847	−0.694233	−	0.719750i	$-0.744256\pi$
$839$	−40.2176	−1.38847	−0.694233	+	0.719750i	$0.744256\pi$
$840$	0.703726	0.0242808
$841$	−4.31168	−0.148678
$842$	−17.2552	−0.594654
$843$	7.71906	0.265858
$844$	−1.12399	−0.0386895
$845$	−43.2536	−1.48797
$846$	−20.6074	−0.708499
$847$	0.824946	0.0283455
$848$	−54.6862	−1.87793
$849$	7.01833	0.240868
$850$	38.6654	1.32621
$851$	−24.0892	−0.825766
$852$	27.3760	0.937886
$853$	23.3944	0.801011	0.400505	−	0.916294i	$-0.368835\pi$
$853$	23.3944	0.801011	0.400505	+	0.916294i	$0.368835\pi$
$854$	1.62335	0.0555499
$855$	7.47773	0.255733
$856$	−2.19426	−0.0749981
$857$	−8.34037	−0.284901	−0.142451	−	0.989802i	$-0.545498\pi$
$857$	−8.34037	−0.284901	−0.142451	+	0.989802i	$0.545498\pi$
$858$	−1.00901	−0.0344470
$859$	−1.41932	−0.0484266	−0.0242133	−	0.999707i	$-0.507708\pi$
$859$	−1.41932	−0.0484266	−0.0242133	+	0.999707i	$0.507708\pi$
$860$	−2.66973	−0.0910369
$861$	−2.23826	−0.0762796
$862$	−3.88948	−0.132476
$863$	11.5657	0.393701	0.196851	−	0.980433i	$-0.436929\pi$
$863$	11.5657	0.393701	0.196851	+	0.980433i	$0.436929\pi$
$864$	7.83924	0.266696
$865$	−82.0584	−2.79007
$866$	61.5688	2.09219
$867$	−7.95141	−0.270044
$868$	3.67435	0.124715
$869$	−3.11221	−0.105575
$870$	−33.2036	−1.12571
$871$	1.58417	0.0536775
$872$	−3.55469	−0.120377
$873$	−12.3600	−0.418323
$874$	12.9687	0.438673
$875$	4.29171	0.145086
$876$	−23.2137	−0.784317
$877$	−19.8788	−0.671260	−0.335630	−	0.941994i	$-0.608949\pi$
$877$	−19.8788	−0.671260	−0.335630	+	0.941994i	$0.608949\pi$
$878$	−42.4738	−1.43342
$879$	−0.967349	−0.0326279
$880$	14.3952	0.485261
$881$	−33.1952	−1.11838	−0.559188	−	0.829041i	$-0.688887\pi$
$881$	−33.1952	−1.11838	−0.559188	+	0.829041i	$0.688887\pi$
$882$	12.4356	0.418729
$883$	−7.41174	−0.249425	−0.124712	−	0.992193i	$-0.539801\pi$
$883$	−7.41174	−0.249425	−0.124712	+	0.992193i	$0.539801\pi$
$884$	2.88791	0.0971310
$885$	25.8436	0.868724
$886$	−16.2441	−0.545733
$887$	−44.7099	−1.50121	−0.750606	−	0.660750i	$-0.770238\pi$
$887$	−44.7099	−1.50121	−0.750606	+	0.660750i	$0.770238\pi$
$888$	2.02188	0.0678500
$889$	−2.07769	−0.0696836
$890$	13.3456	0.447344
$891$	−1.00000	−0.0335013
$892$	−8.51959	−0.285257
$893$	23.0598	0.771666
$894$	40.3351	1.34901
$895$	25.8878	0.865334
$896$	−1.65446	−0.0552716
$897$	1.53462	0.0512393
$898$	−25.7640	−0.859757
$899$	11.8199	0.394217
$900$	12.2301	0.407671
$901$	−38.8064	−1.29283
$902$	−5.33915	−0.177774
$903$	−0.346381	−0.0115268
$904$	4.78544	0.159161
$905$	21.7894	0.724303
$906$	−23.5801	−0.783398
$907$	22.4391	0.745079	0.372539	−	0.928016i	$-0.378487\pi$
$907$	22.4391	0.745079	0.372539	+	0.928016i	$0.378487\pi$
$908$	−25.3353	−0.840783
$909$	9.32824	0.309398
$910$	2.82665	0.0937025
$911$	47.8433	1.58512	0.792560	−	0.609794i	$-0.208748\pi$
$911$	47.8433	1.58512	0.792560	+	0.609794i	$0.208748\pi$
$912$	−9.33432	−0.309090
$913$	−3.05573	−0.101130
$914$	−46.3005	−1.53148
$915$	−3.39588	−0.112264
$916$	3.11017	0.102763
$917$	1.10463	0.0364783
$918$	5.91940	0.195369
$919$	−26.7802	−0.883396	−0.441698	−	0.897164i	$-0.645624\pi$
$919$	−26.7802	−0.883396	−0.441698	+	0.897164i	$0.645624\pi$
$920$	−2.55311	−0.0841736
$921$	24.1462	0.795644
$922$	46.4250	1.52892
$923$	−7.49708	−0.246769
$924$	−1.54458	−0.0508130
$925$	52.5745	1.72864
$926$	−48.4608	−1.59252
$927$	5.76118	0.189222
$928$	38.9511	1.27863
$929$	−24.6892	−0.810028	−0.405014	−	0.914311i	$-0.632733\pi$
$929$	−24.6892	−0.810028	−0.405014	+	0.914311i	$0.632733\pi$
$930$	−15.8967	−0.521275
$931$	−13.9155	−0.456061
$932$	26.4099	0.865086
$933$	−2.44837	−0.0801560
$934$	−29.5149	−0.965757
$935$	10.2151	0.334069
$936$	−0.128805	−0.00421014
$937$	17.3650	0.567290	0.283645	−	0.958929i	$-0.408456\pi$
$937$	17.3650	0.567290	0.283645	+	0.958929i	$0.408456\pi$
$938$	5.01540	0.163759
$939$	−16.2454	−0.530149
$940$	66.5848	2.17176
$941$	−60.3494	−1.96734	−0.983668	−	0.179994i	$-0.942392\pi$
$941$	−60.3494	−1.96734	−0.983668	+	0.179994i	$0.942392\pi$
$942$	−46.7791	−1.52415
$943$	8.12039	0.264436
$944$	−32.2601	−1.04998
$945$	2.80141	0.0911300
$946$	−0.826259	−0.0268640
$947$	−29.4432	−0.956777	−0.478388	−	0.878148i	$-0.658779\pi$
$947$	−29.4432	−0.956777	−0.478388	+	0.878148i	$0.658779\pi$
$948$	5.82713	0.189257
$949$	6.35720	0.206363
$950$	−28.3041	−0.918307
$951$	−14.1481	−0.458782
$952$	−0.623364	−0.0202034
$953$	−26.5777	−0.860936	−0.430468	−	0.902606i	$-0.641651\pi$
$953$	−26.5777	−0.860936	−0.430468	+	0.902606i	$0.641651\pi$
$954$	−25.3863	−0.821913
$955$	−37.3410	−1.20833
$956$	23.9198	0.773622
$957$	−4.96873	−0.160616
$958$	41.8023	1.35057
$959$	−7.11633	−0.229798
$960$	−23.5954	−0.761538
$961$	−25.3410	−0.817452
$962$	8.12129	0.261841
$963$	−8.73496	−0.281480
$964$	−8.88351	−0.286119
$965$	48.2161	1.55213
$966$	4.85852	0.156320
$967$	38.3331	1.23271	0.616355	−	0.787468i	$-0.288609\pi$
$967$	38.3331	1.23271	0.616355	+	0.787468i	$0.288609\pi$
$968$	0.251204	0.00807400
$969$	−6.62382	−0.212788
$970$	82.5957	2.65199
$971$	−54.3703	−1.74483	−0.872414	−	0.488769i	$-0.837446\pi$
$971$	−54.3703	−1.74483	−0.872414	+	0.488769i	$0.837446\pi$
$972$	1.87234	0.0600555
$973$	−6.15817	−0.197422
$974$	46.6771	1.49563
$975$	−3.34929	−0.107263
$976$	4.23901	0.135688
$977$	24.8775	0.795902	0.397951	−	0.917407i	$-0.369721\pi$
$977$	24.8775	0.795902	0.397951	+	0.917407i	$0.369721\pi$
$978$	31.1342	0.995563
$979$	1.99709	0.0638273
$980$	−40.1807	−1.28353
$981$	−14.1506	−0.451794
$982$	68.4096	2.18304
$983$	−1.73808	−0.0554360	−0.0277180	−	0.999616i	$-0.508824\pi$
$983$	−1.73808	−0.0554360	−0.0277180	+	0.999616i	$0.508824\pi$
$984$	−0.681571	−0.0217277
$985$	36.8040	1.17267
$986$	29.4119	0.936666
$987$	8.63898	0.274982
$988$	−2.11403	−0.0672563
$989$	1.25667	0.0399598
$990$	6.68250	0.212384
$991$	−41.3165	−1.31246	−0.656231	−	0.754560i	$-0.727850\pi$
$991$	−41.3165	−1.31246	−0.656231	+	0.754560i	$0.727850\pi$
$992$	18.6485	0.592090
$993$	−9.83670	−0.312158
$994$	−23.7354	−0.752841
$995$	52.3226	1.65874
$996$	5.72139	0.181289
$997$	23.6330	0.748463	0.374232	−	0.927335i	$-0.377907\pi$
$997$	23.6330	0.748463	0.374232	+	0.927335i	$0.377907\pi$
$998$	48.1540	1.52429
$999$	8.04878	0.254652

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.f.1.2	✓	13
3.2	odd	2		6039.2.a.g.1.12		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.f.1.2	✓	13	1.1	even	1	trivial
6039.2.a.g.1.12		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)

\(f(q)\)	\(=\)	\(q-1.96783 q^{2} +1.00000 q^{3} +1.87234 q^{4} +3.39588 q^{5} -1.96783 q^{6} +0.824946 q^{7} +0.251204 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.96783 q^{2} +1.00000 q^{3} +1.87234 q^{4} +3.39588 q^{5} -1.96783 q^{6} +0.824946 q^{7} +0.251204 q^{8} +1.00000 q^{9} -6.68250 q^{10} -1.00000 q^{11} +1.87234 q^{12} -0.512752 q^{13} -1.62335 q^{14} +3.39588 q^{15} -4.23901 q^{16} -3.00809 q^{17} -1.96783 q^{18} +2.20200 q^{19} +6.35825 q^{20} +0.824946 q^{21} +1.96783 q^{22} -2.99290 q^{23} +0.251204 q^{24} +6.53198 q^{25} +1.00901 q^{26} +1.00000 q^{27} +1.54458 q^{28} +4.96873 q^{29} -6.68250 q^{30} +2.37886 q^{31} +7.83924 q^{32} -1.00000 q^{33} +5.91940 q^{34} +2.80141 q^{35} +1.87234 q^{36} +8.04878 q^{37} -4.33316 q^{38} -0.512752 q^{39} +0.853057 q^{40} -2.71322 q^{41} -1.62335 q^{42} -0.419884 q^{43} -1.87234 q^{44} +3.39588 q^{45} +5.88951 q^{46} +10.4722 q^{47} -4.23901 q^{48} -6.31946 q^{49} -12.8538 q^{50} -3.00809 q^{51} -0.960049 q^{52} +12.9007 q^{53} -1.96783 q^{54} -3.39588 q^{55} +0.207229 q^{56} +2.20200 q^{57} -9.77761 q^{58} +7.61029 q^{59} +6.35825 q^{60} -1.00000 q^{61} -4.68119 q^{62} +0.824946 q^{63} -6.94825 q^{64} -1.74124 q^{65} +1.96783 q^{66} -3.08954 q^{67} -5.63218 q^{68} -2.99290 q^{69} -5.51270 q^{70} +14.6212 q^{71} +0.251204 q^{72} -12.3982 q^{73} -15.8386 q^{74} +6.53198 q^{75} +4.12291 q^{76} -0.824946 q^{77} +1.00901 q^{78} +3.11221 q^{79} -14.3952 q^{80} +1.00000 q^{81} +5.33915 q^{82} +3.05573 q^{83} +1.54458 q^{84} -10.2151 q^{85} +0.826259 q^{86} +4.96873 q^{87} -0.251204 q^{88} -1.99709 q^{89} -6.68250 q^{90} -0.422993 q^{91} -5.60373 q^{92} +2.37886 q^{93} -20.6074 q^{94} +7.47773 q^{95} +7.83924 q^{96} -12.3600 q^{97} +12.4356 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 5 q^{7} + 15 q^{8} + 13 q^{9}+O(q^{10}) \) 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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