LMFDB - Embedded newform 2013.2.a.g.1.7

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} + 57 x^{10} + 28 x^{9} - 290 x^{8} + 51 x^{7} + 644 x^{6} - 259 x^{5} + \cdots - 35 $ x^13 - 4x^12 - 11x^11 + 57x^10 + 28x^9 - 290x^8 + 51x^7 + 644x^6 - 259x^5 - 640x^4 + 274x^3 + 256x^2 - 74x - 35
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.669508$ 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)

$f(q)$	$=$	$q+0.669508 q^{2} +1.00000 q^{3} -1.55176 q^{4} +2.40049 q^{5} +0.669508 q^{6} +3.10183 q^{7} -2.37793 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.669508 q^{2} +1.00000 q^{3} -1.55176 q^{4} +2.40049 q^{5} +0.669508 q^{6} +3.10183 q^{7} -2.37793 q^{8} +1.00000 q^{9} +1.60715 q^{10} +1.00000 q^{11} -1.55176 q^{12} +5.50687 q^{13} +2.07670 q^{14} +2.40049 q^{15} +1.51147 q^{16} +3.36670 q^{17} +0.669508 q^{18} -5.54438 q^{19} -3.72498 q^{20} +3.10183 q^{21} +0.669508 q^{22} -0.208297 q^{23} -2.37793 q^{24} +0.762344 q^{25} +3.68689 q^{26} +1.00000 q^{27} -4.81330 q^{28} -2.24051 q^{29} +1.60715 q^{30} -4.06946 q^{31} +5.76781 q^{32} +1.00000 q^{33} +2.25404 q^{34} +7.44592 q^{35} -1.55176 q^{36} -0.189553 q^{37} -3.71201 q^{38} +5.50687 q^{39} -5.70820 q^{40} -8.03499 q^{41} +2.07670 q^{42} +2.64746 q^{43} -1.55176 q^{44} +2.40049 q^{45} -0.139457 q^{46} +4.25006 q^{47} +1.51147 q^{48} +2.62138 q^{49} +0.510395 q^{50} +3.36670 q^{51} -8.54533 q^{52} -1.22666 q^{53} +0.669508 q^{54} +2.40049 q^{55} -7.37595 q^{56} -5.54438 q^{57} -1.50004 q^{58} +12.5763 q^{59} -3.72498 q^{60} +1.00000 q^{61} -2.72454 q^{62} +3.10183 q^{63} +0.838654 q^{64} +13.2192 q^{65} +0.669508 q^{66} +6.00410 q^{67} -5.22431 q^{68} -0.208297 q^{69} +4.98510 q^{70} -5.05407 q^{71} -2.37793 q^{72} +2.08395 q^{73} -0.126908 q^{74} +0.762344 q^{75} +8.60353 q^{76} +3.10183 q^{77} +3.68689 q^{78} +4.33120 q^{79} +3.62827 q^{80} +1.00000 q^{81} -5.37950 q^{82} -5.39014 q^{83} -4.81330 q^{84} +8.08174 q^{85} +1.77250 q^{86} -2.24051 q^{87} -2.37793 q^{88} +16.0138 q^{89} +1.60715 q^{90} +17.0814 q^{91} +0.323227 q^{92} -4.06946 q^{93} +2.84545 q^{94} -13.3092 q^{95} +5.76781 q^{96} -11.4439 q^{97} +1.75503 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 7 q^{7} + 9 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 + 7 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 7 q^{7} + 9 q^{8} + 13 q^{9} + 2 q^{10} + 13 q^{11} + 12 q^{12} + 9 q^{13} + 7 q^{14} + 7 q^{15} + 2 q^{16} + 19 q^{17} + 4 q^{18} + 14 q^{19} + 19 q^{20} + 7 q^{21} + 4 q^{22} + 5 q^{23} + 9 q^{24} + 2 q^{25} - 4 q^{26} + 13 q^{27} + 7 q^{28} + 10 q^{29} + 2 q^{30} - q^{31} + 7 q^{32} + 13 q^{33} - 2 q^{34} + 16 q^{35} + 12 q^{36} - 8 q^{37} - 10 q^{38} + 9 q^{39} + 14 q^{40} + 21 q^{41} + 7 q^{42} + 11 q^{43} + 12 q^{44} + 7 q^{45} - 8 q^{46} + 22 q^{47} + 2 q^{48} + 19 q^{50} + 19 q^{51} - q^{52} + 16 q^{53} + 4 q^{54} + 7 q^{55} + 14 q^{57} - 13 q^{58} + 19 q^{59} + 19 q^{60} + 13 q^{61} + 3 q^{62} + 7 q^{63} - 13 q^{64} + 13 q^{65} + 4 q^{66} + 12 q^{67} + 36 q^{68} + 5 q^{69} - 20 q^{70} + 5 q^{71} + 9 q^{72} + 18 q^{73} + 6 q^{74} + 2 q^{75} - 5 q^{76} + 7 q^{77} - 4 q^{78} - q^{79} + 6 q^{80} + 13 q^{81} - 22 q^{82} + 48 q^{83} + 7 q^{84} - 2 q^{85} + 26 q^{86} + 10 q^{87} + 9 q^{88} + 15 q^{89} + 2 q^{90} - 11 q^{91} - 24 q^{92} - q^{93} - 23 q^{94} + 17 q^{95} + 7 q^{96} - 17 q^{97} - 15 q^{98} + 13 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 7 * q^7 + 9 * q^8 + 13 * q^9 + 2 * q^10 + 13 * q^11 + 12 * q^12 + 9 * q^13 + 7 * q^14 + 7 * q^15 + 2 * q^16 + 19 * q^17 + 4 * q^18 + 14 * q^19 + 19 * q^20 + 7 * q^21 + 4 * q^22 + 5 * q^23 + 9 * q^24 + 2 * q^25 - 4 * q^26 + 13 * q^27 + 7 * q^28 + 10 * q^29 + 2 * q^30 - q^31 + 7 * q^32 + 13 * q^33 - 2 * q^34 + 16 * q^35 + 12 * q^36 - 8 * q^37 - 10 * q^38 + 9 * q^39 + 14 * q^40 + 21 * q^41 + 7 * q^42 + 11 * q^43 + 12 * q^44 + 7 * q^45 - 8 * q^46 + 22 * q^47 + 2 * q^48 + 19 * q^50 + 19 * q^51 - q^52 + 16 * q^53 + 4 * q^54 + 7 * q^55 + 14 * q^57 - 13 * q^58 + 19 * q^59 + 19 * q^60 + 13 * q^61 + 3 * q^62 + 7 * q^63 - 13 * q^64 + 13 * q^65 + 4 * q^66 + 12 * q^67 + 36 * q^68 + 5 * q^69 - 20 * q^70 + 5 * q^71 + 9 * q^72 + 18 * q^73 + 6 * q^74 + 2 * q^75 - 5 * q^76 + 7 * q^77 - 4 * q^78 - q^79 + 6 * q^80 + 13 * q^81 - 22 * q^82 + 48 * q^83 + 7 * q^84 - 2 * q^85 + 26 * q^86 + 10 * q^87 + 9 * q^88 + 15 * q^89 + 2 * q^90 - 11 * q^91 - 24 * q^92 - q^93 - 23 * q^94 + 17 * q^95 + 7 * q^96 - 17 * q^97 - 15 * 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 $

$2$	0.669508	0.473414	0.236707	−	0.971581i	$-0.423932\pi$
$2$	0.669508	0.473414	0.236707	+	0.971581i	$0.423932\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.55176	−0.775879
$5$	2.40049	1.07353	0.536765	−	0.843731i	$-0.319646\pi$
$5$	2.40049	1.07353	0.536765	+	0.843731i	$0.319646\pi$
$6$	0.669508	0.273326
$7$	3.10183	1.17238	0.586192	−	0.810172i	$-0.300627\pi$
$7$	3.10183	1.17238	0.586192	+	0.810172i	$0.300627\pi$
$8$	−2.37793	−0.840726
$9$	1.00000	0.333333
$10$	1.60715	0.508225
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.55176	−0.447954
$13$	5.50687	1.52733	0.763665	−	0.645613i	$-0.223398\pi$
$13$	5.50687	1.52733	0.763665	+	0.645613i	$0.223398\pi$
$14$	2.07670	0.555023
$15$	2.40049	0.619803
$16$	1.51147	0.377868
$17$	3.36670	0.816546	0.408273	−	0.912860i	$-0.366131\pi$
$17$	3.36670	0.816546	0.408273	+	0.912860i	$0.366131\pi$
$18$	0.669508	0.157805
$19$	−5.54438	−1.27197	−0.635984	−	0.771702i	$-0.719405\pi$
$19$	−5.54438	−1.27197	−0.635984	+	0.771702i	$0.719405\pi$
$20$	−3.72498	−0.832930
$21$	3.10183	0.676876
$22$	0.669508	0.142740
$23$	−0.208297	−0.0434329	−0.0217165	−	0.999764i	$-0.506913\pi$
$23$	−0.208297	−0.0434329	−0.0217165	+	0.999764i	$0.506913\pi$
$24$	−2.37793	−0.485393
$25$	0.762344	0.152469
$26$	3.68689	0.723059
$27$	1.00000	0.192450
$28$	−4.81330	−0.909628
$29$	−2.24051	−0.416053	−0.208026	−	0.978123i	$-0.566704\pi$
$29$	−2.24051	−0.416053	−0.208026	+	0.978123i	$0.566704\pi$
$30$	1.60715	0.293424
$31$	−4.06946	−0.730897	−0.365449	−	0.930831i	$-0.619084\pi$
$31$	−4.06946	−0.730897	−0.365449	+	0.930831i	$0.619084\pi$
$32$	5.76781	1.01961
$33$	1.00000	0.174078
$34$	2.25404	0.386564
$35$	7.44592	1.25859
$36$	−1.55176	−0.258626
$37$	−0.189553	−0.0311624	−0.0155812	−	0.999879i	$-0.504960\pi$
$37$	−0.189553	−0.0311624	−0.0155812	+	0.999879i	$0.504960\pi$
$38$	−3.71201	−0.602167
$39$	5.50687	0.881804
$40$	−5.70820	−0.902545
$41$	−8.03499	−1.25486	−0.627428	−	0.778675i	$-0.715892\pi$
$41$	−8.03499	−1.25486	−0.627428	+	0.778675i	$0.715892\pi$
$42$	2.07670	0.320442
$43$	2.64746	0.403734	0.201867	−	0.979413i	$-0.435299\pi$
$43$	2.64746	0.403734	0.201867	+	0.979413i	$0.435299\pi$
$44$	−1.55176	−0.233936
$45$	2.40049	0.357844
$46$	−0.139457	−0.0205618
$47$	4.25006	0.619936	0.309968	−	0.950747i	$-0.399682\pi$
$47$	4.25006	0.619936	0.309968	+	0.950747i	$0.399682\pi$
$48$	1.51147	0.218162
$49$	2.62138	0.374482
$50$	0.510395	0.0721808
$51$	3.36670	0.471433
$52$	−8.54533	−1.18502
$53$	−1.22666	−0.168495	−0.0842475	−	0.996445i	$-0.526849\pi$
$53$	−1.22666	−0.168495	−0.0842475	+	0.996445i	$0.526849\pi$
$54$	0.669508	0.0911086
$55$	2.40049	0.323682
$56$	−7.37595	−0.985653
$57$	−5.54438	−0.734371
$58$	−1.50004	−0.196965
$59$	12.5763	1.63729	0.818644	−	0.574301i	$-0.194726\pi$
$59$	12.5763	1.63729	0.818644	+	0.574301i	$0.194726\pi$
$60$	−3.72498	−0.480893
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−2.72454	−0.346017
$63$	3.10183	0.390794
$64$	0.838654	0.104832
$65$	13.2192	1.63964
$66$	0.669508	0.0824108
$67$	6.00410	0.733518	0.366759	−	0.930316i	$-0.380467\pi$
$67$	6.00410	0.733518	0.366759	+	0.930316i	$0.380467\pi$
$68$	−5.22431	−0.633541
$69$	−0.208297	−0.0250760
$70$	4.98510	0.595834
$71$	−5.05407	−0.599808	−0.299904	−	0.953969i	$-0.596955\pi$
$71$	−5.05407	−0.599808	−0.299904	+	0.953969i	$0.596955\pi$
$72$	−2.37793	−0.280242
$73$	2.08395	0.243908	0.121954	−	0.992536i	$-0.461084\pi$
$73$	2.08395	0.243908	0.121954	+	0.992536i	$0.461084\pi$
$74$	−0.126908	−0.0147527
$75$	0.762344	0.0880278
$76$	8.60353	0.986893
$77$	3.10183	0.353487
$78$	3.68689	0.417459
$79$	4.33120	0.487298	0.243649	−	0.969863i	$-0.421655\pi$
$79$	4.33120	0.487298	0.243649	+	0.969863i	$0.421655\pi$
$80$	3.62827	0.405653
$81$	1.00000	0.111111
$82$	−5.37950	−0.594066
$83$	−5.39014	−0.591645	−0.295822	−	0.955243i	$-0.595594\pi$
$83$	−5.39014	−0.591645	−0.295822	+	0.955243i	$0.595594\pi$
$84$	−4.81330	−0.525174
$85$	8.08174	0.876587
$86$	1.77250	0.191134
$87$	−2.24051	−0.240208
$88$	−2.37793	−0.253488
$89$	16.0138	1.69746	0.848732	−	0.528823i	$-0.177366\pi$
$89$	16.0138	1.69746	0.848732	+	0.528823i	$0.177366\pi$
$90$	1.60715	0.169408
$91$	17.0814	1.79062
$92$	0.323227	0.0336987
$93$	−4.06946	−0.421984
$94$	2.84545	0.293486
$95$	−13.3092	−1.36550
$96$	5.76781	0.588674
$97$	−11.4439	−1.16196	−0.580978	−	0.813919i	$-0.697330\pi$
$97$	−11.4439	−1.16196	−0.580978	+	0.813919i	$0.697330\pi$
$98$	1.75503	0.177285
$99$	1.00000	0.100504
$100$	−1.18297	−0.118297
$101$	1.38330	0.137643	0.0688217	−	0.997629i	$-0.478076\pi$
$101$	1.38330	0.137643	0.0688217	+	0.997629i	$0.478076\pi$
$102$	2.25404	0.223183
$103$	12.4253	1.22430	0.612152	−	0.790740i	$-0.290304\pi$
$103$	12.4253	1.22430	0.612152	+	0.790740i	$0.290304\pi$
$104$	−13.0950	−1.28407
$105$	7.44592	0.726647
$106$	−0.821261	−0.0797679
$107$	3.79236	0.366621	0.183311	−	0.983055i	$-0.441319\pi$
$107$	3.79236	0.366621	0.183311	+	0.983055i	$0.441319\pi$
$108$	−1.55176	−0.149318
$109$	−19.0209	−1.82187	−0.910935	−	0.412551i	$-0.864638\pi$
$109$	−19.0209	−1.82187	−0.910935	+	0.412551i	$0.864638\pi$
$110$	1.60715	0.153235
$111$	−0.189553	−0.0179916
$112$	4.68833	0.443006
$113$	−11.2221	−1.05569	−0.527844	−	0.849341i	$-0.676999\pi$
$113$	−11.2221	−1.05569	−0.527844	+	0.849341i	$0.676999\pi$
$114$	−3.71201	−0.347661
$115$	−0.500015	−0.0466266
$116$	3.47674	0.322807
$117$	5.50687	0.509110
$118$	8.41991	0.775115
$119$	10.4430	0.957305
$120$	−5.70820	−0.521085
$121$	1.00000	0.0909091
$122$	0.669508	0.0606144
$123$	−8.03499	−0.724491
$124$	6.31483	0.567088
$125$	−10.1724	−0.909851
$126$	2.07670	0.185008
$127$	9.35013	0.829689	0.414845	−	0.909892i	$-0.363836\pi$
$127$	9.35013	0.829689	0.414845	+	0.909892i	$0.363836\pi$
$128$	−10.9741	−0.969985
$129$	2.64746	0.233096
$130$	8.85035	0.776227
$131$	−4.11912	−0.359889	−0.179945	−	0.983677i	$-0.557592\pi$
$131$	−4.11912	−0.359889	−0.179945	+	0.983677i	$0.557592\pi$
$132$	−1.55176	−0.135063
$133$	−17.1977	−1.49123
$134$	4.01980	0.347258
$135$	2.40049	0.206601
$136$	−8.00580	−0.686491
$137$	−8.46212	−0.722967	−0.361484	−	0.932378i	$-0.617730\pi$
$137$	−8.46212	−0.722967	−0.361484	+	0.932378i	$0.617730\pi$
$138$	−0.139457	−0.0118713
$139$	10.7026	0.907786	0.453893	−	0.891056i	$-0.350035\pi$
$139$	10.7026	0.907786	0.453893	+	0.891056i	$0.350035\pi$
$140$	−11.5543	−0.976514
$141$	4.25006	0.357920
$142$	−3.38374	−0.283957
$143$	5.50687	0.460507
$144$	1.51147	0.125956
$145$	−5.37833	−0.446646
$146$	1.39522	0.115469
$147$	2.62138	0.216208
$148$	0.294141	0.0241783
$149$	0.109199	0.00894597	0.00447298	−	0.999990i	$-0.498576\pi$
$149$	0.109199	0.00894597	0.00447298	+	0.999990i	$0.498576\pi$
$150$	0.510395	0.0416736
$151$	−6.32845	−0.515002	−0.257501	−	0.966278i	$-0.582899\pi$
$151$	−6.32845	−0.515002	−0.257501	+	0.966278i	$0.582899\pi$
$152$	13.1842	1.06938
$153$	3.36670	0.272182
$154$	2.07670	0.167346
$155$	−9.76870	−0.784641
$156$	−8.54533	−0.684174
$157$	−5.58034	−0.445360	−0.222680	−	0.974892i	$-0.571480\pi$
$157$	−5.58034	−0.445360	−0.222680	+	0.974892i	$0.571480\pi$
$158$	2.89978	0.230694
$159$	−1.22666	−0.0972806
$160$	13.8456	1.09459
$161$	−0.646103	−0.0509200
$162$	0.669508	0.0526016
$163$	−16.3793	−1.28292	−0.641461	−	0.767155i	$-0.721672\pi$
$163$	−16.3793	−1.28292	−0.641461	+	0.767155i	$0.721672\pi$
$164$	12.4684	0.973616
$165$	2.40049	0.186878
$166$	−3.60875	−0.280093
$167$	11.8885	0.919960	0.459980	−	0.887929i	$-0.347856\pi$
$167$	11.8885	0.919960	0.459980	+	0.887929i	$0.347856\pi$
$168$	−7.37595	−0.569067
$169$	17.3256	1.33274
$170$	5.41079	0.414989
$171$	−5.54438	−0.423989
$172$	−4.10822	−0.313249
$173$	−15.1858	−1.15455	−0.577277	−	0.816548i	$-0.695885\pi$
$173$	−15.1858	−1.15455	−0.577277	+	0.816548i	$0.695885\pi$
$174$	−1.50004	−0.113718
$175$	2.36466	0.178752
$176$	1.51147	0.113931
$177$	12.5763	0.945289
$178$	10.7214	0.803603
$179$	−15.5323	−1.16094	−0.580468	−	0.814283i	$-0.697130\pi$
$179$	−15.5323	−1.16094	−0.580468	+	0.814283i	$0.697130\pi$
$180$	−3.72498	−0.277643
$181$	4.80567	0.357202	0.178601	−	0.983922i	$-0.442843\pi$
$181$	4.80567	0.357202	0.178601	+	0.983922i	$0.442843\pi$
$182$	11.4361	0.847703
$183$	1.00000	0.0739221
$184$	0.495316	0.0365152
$185$	−0.455021	−0.0334538
$186$	−2.72454	−0.199773
$187$	3.36670	0.246198
$188$	−6.59507	−0.480995
$189$	3.10183	0.225625
$190$	−8.91063	−0.646445
$191$	13.2611	0.959539	0.479770	−	0.877395i	$-0.340720\pi$
$191$	13.2611	0.959539	0.479770	+	0.877395i	$0.340720\pi$
$192$	0.838654	0.0605246
$193$	−15.7974	−1.13712	−0.568559	−	0.822642i	$-0.692499\pi$
$193$	−15.7974	−1.13712	−0.568559	+	0.822642i	$0.692499\pi$
$194$	−7.66182	−0.550087
$195$	13.2192	0.946644
$196$	−4.06774	−0.290553
$197$	19.1056	1.36122	0.680610	−	0.732646i	$-0.261715\pi$
$197$	19.1056	1.36122	0.680610	+	0.732646i	$0.261715\pi$
$198$	0.669508	0.0475799
$199$	19.5760	1.38770	0.693852	−	0.720118i	$-0.255912\pi$
$199$	19.5760	1.38770	0.693852	+	0.720118i	$0.255912\pi$
$200$	−1.81280	−0.128184
$201$	6.00410	0.423497
$202$	0.926130	0.0651623
$203$	−6.94970	−0.487773
$204$	−5.22431	−0.365775
$205$	−19.2879	−1.34713
$206$	8.31886	0.579602
$207$	−0.208297	−0.0144776
$208$	8.32347	0.577129
$209$	−5.54438	−0.383513
$210$	4.98510	0.344005
$211$	−0.414444	−0.0285315	−0.0142658	−	0.999898i	$-0.504541\pi$
$211$	−0.414444	−0.0285315	−0.0142658	+	0.999898i	$0.504541\pi$
$212$	1.90348	0.130732
$213$	−5.05407	−0.346299
$214$	2.53902	0.173564
$215$	6.35521	0.433421
$216$	−2.37793	−0.161798
$217$	−12.6228	−0.856892
$218$	−12.7346	−0.862498
$219$	2.08395	0.140820
$220$	−3.72498	−0.251138
$221$	18.5400	1.24714
$222$	−0.126908	−0.00851748
$223$	−15.2013	−1.01795	−0.508976	−	0.860781i	$-0.669976\pi$
$223$	−15.2013	−1.01795	−0.508976	+	0.860781i	$0.669976\pi$
$224$	17.8908	1.19538
$225$	0.762344	0.0508229
$226$	−7.51330	−0.499777
$227$	6.12083	0.406254	0.203127	−	0.979152i	$-0.434890\pi$
$227$	6.12083	0.406254	0.203127	+	0.979152i	$0.434890\pi$
$228$	8.60353	0.569783
$229$	−0.461898	−0.0305231	−0.0152615	−	0.999884i	$-0.504858\pi$
$229$	−0.461898	−0.0305231	−0.0152615	+	0.999884i	$0.504858\pi$
$230$	−0.334764	−0.0220737
$231$	3.10183	0.204086
$232$	5.32779	0.349786
$233$	9.09033	0.595527	0.297764	−	0.954640i	$-0.403759\pi$
$233$	9.09033	0.595527	0.297764	+	0.954640i	$0.403759\pi$
$234$	3.68689	0.241020
$235$	10.2022	0.665520
$236$	−19.5153	−1.27034
$237$	4.33120	0.281342
$238$	6.99165	0.453201
$239$	28.5691	1.84798	0.923992	−	0.382412i	$-0.124907\pi$
$239$	28.5691	1.84798	0.923992	+	0.382412i	$0.124907\pi$
$240$	3.62827	0.234204
$241$	−25.0281	−1.61220	−0.806101	−	0.591778i	$-0.798426\pi$
$241$	−25.0281	−1.61220	−0.806101	+	0.591778i	$0.798426\pi$
$242$	0.669508	0.0430376
$243$	1.00000	0.0641500
$244$	−1.55176	−0.0993412
$245$	6.29258	0.402018
$246$	−5.37950	−0.342984
$247$	−30.5321	−1.94271
$248$	9.67691	0.614485
$249$	−5.39014	−0.341586
$250$	−6.81054	−0.430736
$251$	−23.4623	−1.48093	−0.740464	−	0.672096i	$-0.765394\pi$
$251$	−23.4623	−1.48093	−0.740464	+	0.672096i	$0.765394\pi$
$252$	−4.81330	−0.303209
$253$	−0.208297	−0.0130955
$254$	6.25999	0.392787
$255$	8.08174	0.506098
$256$	−9.02458	−0.564036
$257$	−15.8044	−0.985854	−0.492927	−	0.870071i	$-0.664073\pi$
$257$	−15.8044	−0.985854	−0.492927	+	0.870071i	$0.664073\pi$
$258$	1.77250	0.110351
$259$	−0.587963	−0.0365343
$260$	−20.5130	−1.27216
$261$	−2.24051	−0.138684
$262$	−2.75779	−0.170377
$263$	−3.47756	−0.214435	−0.107218	−	0.994236i	$-0.534194\pi$
$263$	−3.47756	−0.214435	−0.107218	+	0.994236i	$0.534194\pi$
$264$	−2.37793	−0.146352
$265$	−2.94459	−0.180885
$266$	−11.5140	−0.705971
$267$	16.0138	0.980032
$268$	−9.31692	−0.569121
$269$	−3.62064	−0.220755	−0.110377	−	0.993890i	$-0.535206\pi$
$269$	−3.62064	−0.220755	−0.110377	+	0.993890i	$0.535206\pi$
$270$	1.60715	0.0978079
$271$	0.153371	0.00931662	0.00465831	−	0.999989i	$-0.498517\pi$
$271$	0.153371	0.00931662	0.00465831	+	0.999989i	$0.498517\pi$
$272$	5.08868	0.308546
$273$	17.0814	1.03381
$274$	−5.66546	−0.342263
$275$	0.762344	0.0459710
$276$	0.323227	0.0194560
$277$	−15.6937	−0.942941	−0.471470	−	0.881882i	$-0.656277\pi$
$277$	−15.6937	−0.942941	−0.471470	+	0.881882i	$0.656277\pi$
$278$	7.16551	0.429759
$279$	−4.06946	−0.243632
$280$	−17.7059	−1.05813
$281$	0.314057	0.0187351	0.00936753	−	0.999956i	$-0.497018\pi$
$281$	0.314057	0.0187351	0.00936753	+	0.999956i	$0.497018\pi$
$282$	2.84545	0.169444
$283$	−12.0264	−0.714897	−0.357449	−	0.933933i	$-0.616353\pi$
$283$	−12.0264	−0.714897	−0.357449	+	0.933933i	$0.616353\pi$
$284$	7.84270	0.465378
$285$	−13.3092	−0.788370
$286$	3.68689	0.218011
$287$	−24.9232	−1.47117
$288$	5.76781	0.339871
$289$	−5.66530	−0.333253
$290$	−3.60083	−0.211448
$291$	−11.4439	−0.670856
$292$	−3.23379	−0.189243
$293$	9.39855	0.549069	0.274534	−	0.961577i	$-0.411476\pi$
$293$	9.39855	0.549069	0.274534	+	0.961577i	$0.411476\pi$
$294$	1.75503	0.102356
$295$	30.1891	1.75768
$296$	0.450745	0.0261990
$297$	1.00000	0.0580259
$298$	0.0731100	0.00423515
$299$	−1.14706	−0.0663364
$300$	−1.18297	−0.0682990
$301$	8.21199	0.473331
$302$	−4.23695	−0.243809
$303$	1.38330	0.0794684
$304$	−8.38017	−0.480635
$305$	2.40049	0.137452
$306$	2.25404	0.128855
$307$	0.917582	0.0523692	0.0261846	−	0.999657i	$-0.491664\pi$
$307$	0.917582	0.0523692	0.0261846	+	0.999657i	$0.491664\pi$
$308$	−4.81330	−0.274263
$309$	12.4253	0.706852
$310$	−6.54023	−0.371460
$311$	−19.2784	−1.09318	−0.546590	−	0.837400i	$-0.684074\pi$
$311$	−19.2784	−1.09318	−0.546590	+	0.837400i	$0.684074\pi$
$312$	−13.0950	−0.741356
$313$	−26.3200	−1.48770	−0.743848	−	0.668349i	$-0.767001\pi$
$313$	−26.3200	−1.48770	−0.743848	+	0.668349i	$0.767001\pi$
$314$	−3.73609	−0.210840
$315$	7.44592	0.419530
$316$	−6.72098	−0.378085
$317$	27.9967	1.57245	0.786225	−	0.617940i	$-0.212033\pi$
$317$	27.9967	1.57245	0.786225	+	0.617940i	$0.212033\pi$
$318$	−0.821261	−0.0460540
$319$	−2.24051	−0.125445
$320$	2.01318	0.112540
$321$	3.79236	0.211669
$322$	−0.432571	−0.0241063
$323$	−18.6663	−1.03862
$324$	−1.55176	−0.0862088
$325$	4.19812	0.232870
$326$	−10.9661	−0.607353
$327$	−19.0209	−1.05186
$328$	19.1067	1.05499
$329$	13.1830	0.726802
$330$	1.60715	0.0884705
$331$	−32.8151	−1.80368	−0.901841	−	0.432067i	$-0.857784\pi$
$331$	−32.8151	−1.80368	−0.901841	+	0.432067i	$0.857784\pi$
$332$	8.36420	0.459045
$333$	−0.189553	−0.0103875
$334$	7.95946	0.435522
$335$	14.4128	0.787454
$336$	4.68833	0.255770
$337$	−6.45779	−0.351778	−0.175889	−	0.984410i	$-0.556280\pi$
$337$	−6.45779	−0.351778	−0.175889	+	0.984410i	$0.556280\pi$
$338$	11.5996	0.630936
$339$	−11.2221	−0.609502
$340$	−12.5409	−0.680126
$341$	−4.06946	−0.220374
$342$	−3.71201	−0.200722
$343$	−13.5818	−0.733346
$344$	−6.29549	−0.339430
$345$	−0.500015	−0.0269199
$346$	−10.1670	−0.546582
$347$	11.4612	0.615272	0.307636	−	0.951504i	$-0.400462\pi$
$347$	11.4612	0.615272	0.307636	+	0.951504i	$0.400462\pi$
$348$	3.47674	0.186373
$349$	−23.5832	−1.26238	−0.631190	−	0.775628i	$-0.717433\pi$
$349$	−23.5832	−1.26238	−0.631190	+	0.775628i	$0.717433\pi$
$350$	1.58316	0.0846236
$351$	5.50687	0.293935
$352$	5.76781	0.307425
$353$	−5.22492	−0.278094	−0.139047	−	0.990286i	$-0.544404\pi$
$353$	−5.22492	−0.278094	−0.139047	+	0.990286i	$0.544404\pi$
$354$	8.41991	0.447513
$355$	−12.1322	−0.643912
$356$	−24.8496	−1.31703
$357$	10.4430	0.552700
$358$	−10.3990	−0.549603
$359$	11.2344	0.592927	0.296463	−	0.955044i	$-0.404193\pi$
$359$	11.2344	0.592927	0.296463	+	0.955044i	$0.404193\pi$
$360$	−5.70820	−0.300848
$361$	11.7401	0.617901
$362$	3.21744	0.169105
$363$	1.00000	0.0524864
$364$	−26.5062	−1.38930
$365$	5.00250	0.261843
$366$	0.669508	0.0349958
$367$	−21.0350	−1.09802	−0.549010	−	0.835816i	$-0.684995\pi$
$367$	−21.0350	−1.09802	−0.549010	+	0.835816i	$0.684995\pi$
$368$	−0.314835	−0.0164119
$369$	−8.03499	−0.418285
$370$	−0.304640	−0.0158375
$371$	−3.80490	−0.197541
$372$	6.31483	0.327408
$373$	−10.4988	−0.543606	−0.271803	−	0.962353i	$-0.587620\pi$
$373$	−10.4988	−0.543606	−0.271803	+	0.962353i	$0.587620\pi$
$374$	2.25404	0.116554
$375$	−10.1724	−0.525303
$376$	−10.1064	−0.521196
$377$	−12.3382	−0.635450
$378$	2.07670	0.106814
$379$	−8.03928	−0.412950	−0.206475	−	0.978452i	$-0.566199\pi$
$379$	−8.03928	−0.412950	−0.206475	+	0.978452i	$0.566199\pi$
$380$	20.6527	1.05946
$381$	9.35013	0.479021
$382$	8.87842	0.454259
$383$	3.98184	0.203462	0.101731	−	0.994812i	$-0.467562\pi$
$383$	3.98184	0.203462	0.101731	+	0.994812i	$0.467562\pi$
$384$	−10.9741	−0.560021
$385$	7.44592	0.379479
$386$	−10.5765	−0.538328
$387$	2.64746	0.134578
$388$	17.7582	0.901538
$389$	21.7703	1.10380	0.551900	−	0.833910i	$-0.313903\pi$
$389$	21.7703	1.10380	0.551900	+	0.833910i	$0.313903\pi$
$390$	8.85035	0.448155
$391$	−0.701275	−0.0354650
$392$	−6.23346	−0.314837
$393$	−4.11912	−0.207782
$394$	12.7914	0.644421
$395$	10.3970	0.523130
$396$	−1.55176	−0.0779788
$397$	17.3160	0.869066	0.434533	−	0.900656i	$-0.356913\pi$
$397$	17.3160	0.869066	0.434533	+	0.900656i	$0.356913\pi$
$398$	13.1063	0.656958
$399$	−17.1977	−0.860964
$400$	1.15226	0.0576130
$401$	0.892389	0.0445638	0.0222819	−	0.999752i	$-0.492907\pi$
$401$	0.892389	0.0445638	0.0222819	+	0.999752i	$0.492907\pi$
$402$	4.01980	0.200489
$403$	−22.4100	−1.11632
$404$	−2.14654	−0.106795
$405$	2.40049	0.119281
$406$	−4.65288	−0.230919
$407$	−0.189553	−0.00939582
$408$	−8.00580	−0.396346
$409$	8.72225	0.431287	0.215644	−	0.976472i	$-0.430815\pi$
$409$	8.72225	0.431287	0.215644	+	0.976472i	$0.430815\pi$
$410$	−12.9134	−0.637748
$411$	−8.46212	−0.417405
$412$	−19.2811	−0.949912
$413$	39.0095	1.91953
$414$	−0.139457	−0.00685392
$415$	−12.9390	−0.635149
$416$	31.7625	1.55729
$417$	10.7026	0.524111
$418$	−3.71201	−0.181560
$419$	−4.28525	−0.209348	−0.104674	−	0.994507i	$-0.533380\pi$
$419$	−4.28525	−0.209348	−0.104674	+	0.994507i	$0.533380\pi$
$420$	−11.5543	−0.563790
$421$	9.20694	0.448719	0.224359	−	0.974506i	$-0.427971\pi$
$421$	9.20694	0.448719	0.224359	+	0.974506i	$0.427971\pi$
$422$	−0.277474	−0.0135072
$423$	4.25006	0.206645
$424$	2.91692	0.141658
$425$	2.56659	0.124498
$426$	−3.38374	−0.163943
$427$	3.10183	0.150108
$428$	−5.88483	−0.284454
$429$	5.50687	0.265874
$430$	4.25486	0.205188
$431$	39.0802	1.88243	0.941215	−	0.337809i	$-0.109686\pi$
$431$	39.0802	1.88243	0.941215	+	0.337809i	$0.109686\pi$
$432$	1.51147	0.0727207
$433$	−12.5376	−0.602517	−0.301259	−	0.953542i	$-0.597407\pi$
$433$	−12.5376	−0.602517	−0.301259	+	0.953542i	$0.597407\pi$
$434$	−8.45108	−0.405665
$435$	−5.37833	−0.257871
$436$	29.5158	1.41355
$437$	1.15488	0.0552453
$438$	1.39522	0.0666663
$439$	−21.5773	−1.02983	−0.514913	−	0.857242i	$-0.672176\pi$
$439$	−21.5773	−1.02983	−0.514913	+	0.857242i	$0.672176\pi$
$440$	−5.70820	−0.272128
$441$	2.62138	0.124827
$442$	12.4127	0.590411
$443$	16.3415	0.776406	0.388203	−	0.921574i	$-0.373096\pi$
$443$	16.3415	0.776406	0.388203	+	0.921574i	$0.373096\pi$
$444$	0.294141	0.0139593
$445$	38.4411	1.82228
$446$	−10.1774	−0.481912
$447$	0.109199	0.00516496
$448$	2.60137	0.122903
$449$	8.73314	0.412142	0.206071	−	0.978537i	$-0.433932\pi$
$449$	8.73314	0.412142	0.206071	+	0.978537i	$0.433932\pi$
$450$	0.510395	0.0240603
$451$	−8.03499	−0.378353
$452$	17.4140	0.819086
$453$	−6.32845	−0.297336
$454$	4.09795	0.192326
$455$	41.0037	1.92228
$456$	13.1842	0.617405
$457$	6.31648	0.295472	0.147736	−	0.989027i	$-0.452801\pi$
$457$	6.31648	0.295472	0.147736	+	0.989027i	$0.452801\pi$
$458$	−0.309245	−0.0144500
$459$	3.36670	0.157144
$460$	0.775902	0.0361766
$461$	33.4128	1.55619	0.778095	−	0.628147i	$-0.216186\pi$
$461$	33.4128	1.55619	0.778095	+	0.628147i	$0.216186\pi$
$462$	2.07670	0.0966170
$463$	−30.6547	−1.42464	−0.712322	−	0.701853i	$-0.752356\pi$
$463$	−30.6547	−1.42464	−0.712322	+	0.701853i	$0.752356\pi$
$464$	−3.38647	−0.157213
$465$	−9.76870	−0.453013
$466$	6.08605	0.281931
$467$	−19.3938	−0.897440	−0.448720	−	0.893672i	$-0.648120\pi$
$467$	−19.3938	−0.897440	−0.448720	+	0.893672i	$0.648120\pi$
$468$	−8.54533	−0.395008
$469$	18.6237	0.859964
$470$	6.83048	0.315067
$471$	−5.58034	−0.257129
$472$	−29.9055	−1.37651
$473$	2.64746	0.121731
$474$	2.89978	0.133191
$475$	−4.22672	−0.193935
$476$	−16.2050	−0.742753
$477$	−1.22666	−0.0561650
$478$	19.1273	0.874861
$479$	−10.7976	−0.493355	−0.246678	−	0.969098i	$-0.579339\pi$
$479$	−10.7976	−0.493355	−0.246678	+	0.969098i	$0.579339\pi$
$480$	13.8456	0.631960
$481$	−1.04385	−0.0475953
$482$	−16.7565	−0.763239
$483$	−0.646103	−0.0293987
$484$	−1.55176	−0.0705345
$485$	−27.4711	−1.24740
$486$	0.669508	0.0303695
$487$	−12.5043	−0.566622	−0.283311	−	0.959028i	$-0.591433\pi$
$487$	−12.5043	−0.566622	−0.283311	+	0.959028i	$0.591433\pi$
$488$	−2.37793	−0.107644
$489$	−16.3793	−0.740696
$490$	4.21294	0.190321
$491$	−21.4476	−0.967915	−0.483957	−	0.875092i	$-0.660801\pi$
$491$	−21.4476	−0.967915	−0.483957	+	0.875092i	$0.660801\pi$
$492$	12.4684	0.562118
$493$	−7.54315	−0.339726
$494$	−20.4415	−0.919708
$495$	2.40049	0.107894
$496$	−6.15088	−0.276183
$497$	−15.6769	−0.703205
$498$	−3.60875	−0.161712
$499$	−4.46283	−0.199784	−0.0998918	−	0.994998i	$-0.531850\pi$
$499$	−4.46283	−0.199784	−0.0998918	+	0.994998i	$0.531850\pi$
$500$	15.7852	0.705935
$501$	11.8885	0.531139
$502$	−15.7082	−0.701092
$503$	19.1647	0.854512	0.427256	−	0.904131i	$-0.359480\pi$
$503$	19.1647	0.854512	0.427256	+	0.904131i	$0.359480\pi$
$504$	−7.37595	−0.328551
$505$	3.32059	0.147764
$506$	−0.139457	−0.00619960
$507$	17.3256	0.769456
$508$	−14.5091	−0.643739
$509$	−28.3803	−1.25794	−0.628968	−	0.777431i	$-0.716522\pi$
$509$	−28.3803	−1.25794	−0.628968	+	0.777431i	$0.716522\pi$
$510$	5.41079	0.239594
$511$	6.46407	0.285953
$512$	15.9062	0.702962
$513$	−5.54438	−0.244790
$514$	−10.5812	−0.466717
$515$	29.8268	1.31433
$516$	−4.10822	−0.180854
$517$	4.25006	0.186918
$518$	−0.393647	−0.0172958
$519$	−15.1858	−0.666582
$520$	−31.4343	−1.37848
$521$	−42.2672	−1.85176	−0.925881	−	0.377816i	$-0.876675\pi$
$521$	−42.2672	−1.85176	−0.925881	+	0.377816i	$0.876675\pi$
$522$	−1.50004	−0.0656551
$523$	23.8026	1.04082	0.520408	−	0.853918i	$-0.325780\pi$
$523$	23.8026	1.04082	0.520408	+	0.853918i	$0.325780\pi$
$524$	6.39188	0.279230
$525$	2.36466	0.103202
$526$	−2.32825	−0.101517
$527$	−13.7007	−0.596811
$528$	1.51147	0.0657783
$529$	−22.9566	−0.998114
$530$	−1.97143	−0.0856333
$531$	12.5763	0.545763
$532$	26.6867	1.15702
$533$	−44.2476	−1.91658
$534$	10.7214	0.463961
$535$	9.10352	0.393579
$536$	−14.2774	−0.616688
$537$	−15.5323	−0.670267
$538$	−2.42405	−0.104508
$539$	2.62138	0.112911
$540$	−3.72498	−0.160298
$541$	39.0431	1.67859	0.839297	−	0.543673i	$-0.182967\pi$
$541$	39.0431	1.67859	0.839297	+	0.543673i	$0.182967\pi$
$542$	0.102683	0.00441062
$543$	4.80567	0.206231
$544$	19.4185	0.832562
$545$	−45.6594	−1.95583
$546$	11.4361	0.489421
$547$	−22.3042	−0.953657	−0.476828	−	0.878996i	$-0.658214\pi$
$547$	−22.3042	−0.953657	−0.476828	+	0.878996i	$0.658214\pi$
$548$	13.1312	0.560935
$549$	1.00000	0.0426790
$550$	0.510395	0.0217633
$551$	12.4223	0.529206
$552$	0.495316	0.0210821
$553$	13.4347	0.571300
$554$	−10.5070	−0.446401
$555$	−0.455021	−0.0193146
$556$	−16.6079	−0.704332
$557$	−6.85079	−0.290277	−0.145139	−	0.989411i	$-0.546363\pi$
$557$	−6.85079	−0.290277	−0.145139	+	0.989411i	$0.546363\pi$
$558$	−2.72454	−0.115339
$559$	14.5792	0.616636
$560$	11.2543	0.475580
$561$	3.36670	0.142142
$562$	0.210264	0.00886944
$563$	20.4627	0.862400	0.431200	−	0.902256i	$-0.358090\pi$
$563$	20.4627	0.862400	0.431200	+	0.902256i	$0.358090\pi$
$564$	−6.59507	−0.277703
$565$	−26.9386	−1.13331
$566$	−8.05180	−0.338442
$567$	3.10183	0.130265
$568$	12.0182	0.504274
$569$	10.0983	0.423344	0.211672	−	0.977341i	$-0.432109\pi$
$569$	10.0983	0.423344	0.211672	+	0.977341i	$0.432109\pi$
$570$	−8.91063	−0.373225
$571$	45.3377	1.89732	0.948662	−	0.316291i	$-0.102438\pi$
$571$	45.3377	1.89732	0.948662	+	0.316291i	$0.102438\pi$
$572$	−8.54533	−0.357298
$573$	13.2611	0.553990
$574$	−16.6863	−0.696473
$575$	−0.158794	−0.00662216
$576$	0.838654	0.0349439
$577$	15.0975	0.628516	0.314258	−	0.949338i	$-0.398244\pi$
$577$	15.0975	0.628516	0.314258	+	0.949338i	$0.398244\pi$
$578$	−3.79297	−0.157767
$579$	−15.7974	−0.656516
$580$	8.34586	0.346543
$581$	−16.7193	−0.693635
$582$	−7.66182	−0.317593
$583$	−1.22666	−0.0508032
$584$	−4.95549	−0.205060
$585$	13.2192	0.546545
$586$	6.29241	0.259937
$587$	−4.15308	−0.171416	−0.0857079	−	0.996320i	$-0.527315\pi$
$587$	−4.15308	−0.171416	−0.0857079	+	0.996320i	$0.527315\pi$
$588$	−4.06774	−0.167751
$589$	22.5626	0.929678
$590$	20.2119	0.832110
$591$	19.1056	0.785901
$592$	−0.286505	−0.0117753
$593$	−3.00061	−0.123220	−0.0616102	−	0.998100i	$-0.519624\pi$
$593$	−3.00061	−0.123220	−0.0616102	+	0.998100i	$0.519624\pi$
$594$	0.669508	0.0274703
$595$	25.0682	1.02770
$596$	−0.169451	−0.00694099
$597$	19.5760	0.801191
$598$	−0.767969	−0.0314046
$599$	6.34871	0.259401	0.129701	−	0.991553i	$-0.458598\pi$
$599$	6.34871	0.259401	0.129701	+	0.991553i	$0.458598\pi$
$600$	−1.81280	−0.0740073
$601$	42.5871	1.73716	0.868581	−	0.495547i	$-0.165032\pi$
$601$	42.5871	1.73716	0.868581	+	0.495547i	$0.165032\pi$
$602$	5.49800	0.224082
$603$	6.00410	0.244506
$604$	9.82022	0.399579
$605$	2.40049	0.0975937
$606$	0.926130	0.0376215
$607$	−35.5536	−1.44308	−0.721539	−	0.692374i	$-0.756565\pi$
$607$	−35.5536	−1.44308	−0.721539	+	0.692374i	$0.756565\pi$
$608$	−31.9789	−1.29692
$609$	−6.94970	−0.281616
$610$	1.60715	0.0650715
$611$	23.4045	0.946846
$612$	−5.22431	−0.211180
$613$	−44.4527	−1.79543	−0.897714	−	0.440578i	$-0.854774\pi$
$613$	−44.4527	−1.79543	−0.897714	+	0.440578i	$0.854774\pi$
$614$	0.614329	0.0247923
$615$	−19.2879	−0.777764
$616$	−7.37595	−0.297186
$617$	−14.3101	−0.576101	−0.288050	−	0.957615i	$-0.593007\pi$
$617$	−14.3101	−0.576101	−0.288050	+	0.957615i	$0.593007\pi$
$618$	8.31886	0.334634
$619$	36.9549	1.48534	0.742671	−	0.669656i	$-0.233559\pi$
$619$	36.9549	1.48534	0.742671	+	0.669656i	$0.233559\pi$
$620$	15.1587	0.608787
$621$	−0.208297	−0.00835867
$622$	−12.9071	−0.517527
$623$	49.6723	1.99008
$624$	8.32347	0.333205
$625$	−28.2305	−1.12922
$626$	−17.6215	−0.704296
$627$	−5.54438	−0.221421
$628$	8.65934	0.345545
$629$	−0.638171	−0.0254455
$630$	4.98510	0.198611
$631$	2.14575	0.0854211	0.0427106	−	0.999087i	$-0.486401\pi$
$631$	2.14575	0.0854211	0.0427106	+	0.999087i	$0.486401\pi$
$632$	−10.2993	−0.409684
$633$	−0.414444	−0.0164727
$634$	18.7440	0.744420
$635$	22.4449	0.890697
$636$	1.90348	0.0754780
$637$	14.4356	0.571958
$638$	−1.50004	−0.0593873
$639$	−5.05407	−0.199936
$640$	−26.3433	−1.04131
$641$	19.9594	0.788348	0.394174	−	0.919036i	$-0.371031\pi$
$641$	19.9594	0.788348	0.394174	+	0.919036i	$0.371031\pi$
$642$	2.53902	0.100207
$643$	−0.643354	−0.0253714	−0.0126857	−	0.999920i	$-0.504038\pi$
$643$	−0.643354	−0.0253714	−0.0126857	+	0.999920i	$0.504038\pi$
$644$	1.00260	0.0395078
$645$	6.35521	0.250236
$646$	−12.4972	−0.491697
$647$	37.0147	1.45520	0.727600	−	0.686002i	$-0.240636\pi$
$647$	37.0147	1.45520	0.727600	+	0.686002i	$0.240636\pi$
$648$	−2.37793	−0.0934140
$649$	12.5763	0.493661
$650$	2.81068	0.110244
$651$	−12.6228	−0.494727
$652$	25.4167	0.995393
$653$	−5.08355	−0.198935	−0.0994673	−	0.995041i	$-0.531714\pi$
$653$	−5.08355	−0.198935	−0.0994673	+	0.995041i	$0.531714\pi$
$654$	−12.7346	−0.497964
$655$	−9.88790	−0.386352
$656$	−12.1447	−0.474169
$657$	2.08395	0.0813026
$658$	8.82613	0.344078
$659$	−20.1734	−0.785844	−0.392922	−	0.919572i	$-0.628536\pi$
$659$	−20.1734	−0.785844	−0.392922	+	0.919572i	$0.628536\pi$
$660$	−3.72498	−0.144995
$661$	−44.4385	−1.72846	−0.864230	−	0.503098i	$-0.832194\pi$
$661$	−44.4385	−1.72846	−0.864230	+	0.503098i	$0.832194\pi$
$662$	−21.9700	−0.853889
$663$	18.5400	0.720034
$664$	12.8174	0.497411
$665$	−41.2830	−1.60089
$666$	−0.126908	−0.00491757
$667$	0.466692	0.0180704
$668$	−18.4481	−0.713778
$669$	−15.2013	−0.587714
$670$	9.64948	0.372792
$671$	1.00000	0.0386046
$672$	17.8908	0.690152
$673$	15.7260	0.606193	0.303097	−	0.952960i	$-0.401980\pi$
$673$	15.7260	0.606193	0.303097	+	0.952960i	$0.401980\pi$
$674$	−4.32354	−0.166537
$675$	0.762344	0.0293426
$676$	−26.8851	−1.03404
$677$	19.9128	0.765311	0.382656	−	0.923891i	$-0.375010\pi$
$677$	19.9128	0.765311	0.382656	+	0.923891i	$0.375010\pi$
$678$	−7.51330	−0.288547
$679$	−35.4972	−1.36226
$680$	−19.2178	−0.736970
$681$	6.12083	0.234551
$682$	−2.72454	−0.104328
$683$	−42.3059	−1.61879	−0.809396	−	0.587264i	$-0.800205\pi$
$683$	−42.3059	−1.61879	−0.809396	+	0.587264i	$0.800205\pi$
$684$	8.60353	0.328964
$685$	−20.3132	−0.776128
$686$	−9.09311	−0.347176
$687$	−0.461898	−0.0176225
$688$	4.00156	0.152558
$689$	−6.75507	−0.257347
$690$	−0.334764	−0.0127442
$691$	9.24183	0.351576	0.175788	−	0.984428i	$-0.443753\pi$
$691$	9.24183	0.351576	0.175788	+	0.984428i	$0.443753\pi$
$692$	23.5647	0.895795
$693$	3.10183	0.117829
$694$	7.67340	0.291278
$695$	25.6916	0.974536
$696$	5.32779	0.201949
$697$	−27.0515	−1.02465
$698$	−15.7892	−0.597629
$699$	9.09033	0.343828
$700$	−3.66939	−0.138690
$701$	−36.6771	−1.38528	−0.692638	−	0.721285i	$-0.743552\pi$
$701$	−36.6771	−1.38528	−0.692638	+	0.721285i	$0.743552\pi$
$702$	3.68689	0.139153
$703$	1.05096	0.0396376
$704$	0.838654	0.0316080
$705$	10.2022	0.384238
$706$	−3.49813	−0.131654
$707$	4.29076	0.161371
$708$	−19.5153	−0.733430
$709$	31.3476	1.17729	0.588643	−	0.808393i	$-0.299663\pi$
$709$	31.3476	1.17729	0.588643	+	0.808393i	$0.299663\pi$
$710$	−8.12264	−0.304837
$711$	4.33120	0.162433
$712$	−38.0798	−1.42710
$713$	0.847657	0.0317450
$714$	6.99165	0.261656
$715$	13.2192	0.494369
$716$	24.1023	0.900746
$717$	28.5691	1.06693
$718$	7.52150	0.280700
$719$	−37.0436	−1.38149	−0.690746	−	0.723097i	$-0.742718\pi$
$719$	−37.0436	−1.38149	−0.690746	+	0.723097i	$0.742718\pi$
$720$	3.62827	0.135218
$721$	38.5413	1.43535
$722$	7.86011	0.292523
$723$	−25.0281	−0.930805
$724$	−7.45723	−0.277146
$725$	−1.70804	−0.0634350
$726$	0.669508	0.0248478
$727$	9.66723	0.358538	0.179269	−	0.983800i	$-0.442627\pi$
$727$	9.66723	0.358538	0.179269	+	0.983800i	$0.442627\pi$
$728$	−40.6184	−1.50542
$729$	1.00000	0.0370370
$730$	3.34921	0.123960
$731$	8.91323	0.329668
$732$	−1.55176	−0.0573546
$733$	−20.9221	−0.772777	−0.386388	−	0.922336i	$-0.626278\pi$
$733$	−20.9221	−0.772777	−0.386388	+	0.922336i	$0.626278\pi$
$734$	−14.0831	−0.519818
$735$	6.29258	0.232105
$736$	−1.20142	−0.0442848
$737$	6.00410	0.221164
$738$	−5.37950	−0.198022
$739$	42.2616	1.55462	0.777309	−	0.629118i	$-0.216584\pi$
$739$	42.2616	1.55462	0.777309	+	0.629118i	$0.216584\pi$
$740$	0.706082	0.0259561
$741$	−30.5321	−1.12163
$742$	−2.54741	−0.0935185
$743$	−2.04185	−0.0749083	−0.0374542	−	0.999298i	$-0.511925\pi$
$743$	−2.04185	−0.0749083	−0.0374542	+	0.999298i	$0.511925\pi$
$744$	9.67691	0.354773
$745$	0.262132	0.00960377
$746$	−7.02901	−0.257350
$747$	−5.39014	−0.197215
$748$	−5.22431	−0.191020
$749$	11.7633	0.429821
$750$	−6.81054	−0.248686
$751$	24.7484	0.903080	0.451540	−	0.892251i	$-0.350875\pi$
$751$	24.7484	0.903080	0.451540	+	0.892251i	$0.350875\pi$
$752$	6.42385	0.234254
$753$	−23.4623	−0.855014
$754$	−8.26053	−0.300831
$755$	−15.1914	−0.552870
$756$	−4.81330	−0.175058
$757$	−38.8731	−1.41287	−0.706433	−	0.707780i	$-0.749697\pi$
$757$	−38.8731	−1.41287	−0.706433	+	0.707780i	$0.749697\pi$
$758$	−5.38236	−0.195496
$759$	−0.208297	−0.00756070
$760$	31.6484	1.14801
$761$	0.589810	0.0213806	0.0106903	−	0.999943i	$-0.496597\pi$
$761$	0.589810	0.0213806	0.0106903	+	0.999943i	$0.496597\pi$
$762$	6.25999	0.226775
$763$	−58.9996	−2.13593
$764$	−20.5780	−0.744486
$765$	8.08174	0.292196
$766$	2.66587	0.0963219
$767$	69.2558	2.50068
$768$	−9.02458	−0.325646
$769$	10.6963	0.385718	0.192859	−	0.981227i	$-0.438224\pi$
$769$	10.6963	0.385718	0.192859	+	0.981227i	$0.438224\pi$
$770$	4.98510	0.179651
$771$	−15.8044	−0.569183
$772$	24.5137	0.882267
$773$	−17.9902	−0.647063	−0.323531	−	0.946217i	$-0.604870\pi$
$773$	−17.9902	−0.647063	−0.323531	+	0.946217i	$0.604870\pi$
$774$	1.77250	0.0637112
$775$	−3.10233	−0.111439
$776$	27.2129	0.976887
$777$	−0.587963	−0.0210931
$778$	14.5754	0.522554
$779$	44.5490	1.59614
$780$	−20.5130	−0.734482
$781$	−5.05407	−0.180849
$782$	−0.469509	−0.0167896
$783$	−2.24051	−0.0800694
$784$	3.96213	0.141505
$785$	−13.3955	−0.478108
$786$	−2.75779	−0.0983669
$787$	−14.6929	−0.523746	−0.261873	−	0.965102i	$-0.584340\pi$
$787$	−14.6929	−0.523746	−0.261873	+	0.965102i	$0.584340\pi$
$788$	−29.6473	−1.05614
$789$	−3.47756	−0.123804
$790$	6.96088	0.247657
$791$	−34.8091	−1.23767
$792$	−2.37793	−0.0844961
$793$	5.50687	0.195555
$794$	11.5932	0.411428
$795$	−2.94459	−0.104434
$796$	−30.3772	−1.07669
$797$	−11.5431	−0.408878	−0.204439	−	0.978879i	$-0.565537\pi$
$797$	−11.5431	−0.408878	−0.204439	+	0.978879i	$0.565537\pi$
$798$	−11.5140	−0.407592
$799$	14.3087	0.506206
$800$	4.39705	0.155459
$801$	16.0138	0.565821
$802$	0.597462	0.0210971
$803$	2.08395	0.0735410
$804$	−9.31692	−0.328582
$805$	−1.55096	−0.0546642
$806$	−15.0037	−0.528482
$807$	−3.62064	−0.127453
$808$	−3.28939	−0.115720
$809$	−19.8269	−0.697075	−0.348538	−	0.937295i	$-0.613322\pi$
$809$	−19.8269	−0.697075	−0.348538	+	0.937295i	$0.613322\pi$
$810$	1.60715	0.0564694
$811$	−46.7411	−1.64130	−0.820651	−	0.571430i	$-0.806389\pi$
$811$	−46.7411	−1.64130	−0.820651	+	0.571430i	$0.806389\pi$
$812$	10.7843	0.378453
$813$	0.153371	0.00537896
$814$	−0.126908	−0.00444811
$815$	−39.3182	−1.37726
$816$	5.08868	0.178139
$817$	−14.6785	−0.513537
$818$	5.83962	0.204178
$819$	17.0814	0.596872
$820$	29.9302	1.04521
$821$	−28.5707	−0.997123	−0.498562	−	0.866854i	$-0.666138\pi$
$821$	−28.5707	−0.997123	−0.498562	+	0.866854i	$0.666138\pi$
$822$	−5.66546	−0.197606
$823$	17.4103	0.606886	0.303443	−	0.952850i	$-0.401864\pi$
$823$	17.4103	0.606886	0.303443	+	0.952850i	$0.401864\pi$
$824$	−29.5466	−1.02930
$825$	0.762344	0.0265414
$826$	26.1172	0.908732
$827$	33.5234	1.16572	0.582862	−	0.812571i	$-0.301933\pi$
$827$	33.5234	1.16572	0.582862	+	0.812571i	$0.301933\pi$
$828$	0.323227	0.0112329
$829$	29.1955	1.01400	0.507001	−	0.861946i	$-0.330754\pi$
$829$	29.1955	1.01400	0.507001	+	0.861946i	$0.330754\pi$
$830$	−8.66275	−0.300688
$831$	−15.6937	−0.544407
$832$	4.61836	0.160113
$833$	8.82540	0.305782
$834$	7.16551	0.248121
$835$	28.5382	0.987606
$836$	8.60353	0.297559
$837$	−4.06946	−0.140661
$838$	−2.86901	−0.0991084
$839$	20.7091	0.714958	0.357479	−	0.933921i	$-0.383636\pi$
$839$	20.7091	0.714958	0.357479	+	0.933921i	$0.383636\pi$
$840$	−17.7059	−0.610911
$841$	−23.9801	−0.826900
$842$	6.16412	0.212430
$843$	0.314057	0.0108167
$844$	0.643117	0.0221370
$845$	41.5899	1.43073
$846$	2.84545	0.0978287
$847$	3.10183	0.106580
$848$	−1.85406	−0.0636688
$849$	−12.0264	−0.412746
$850$	1.71835	0.0589389
$851$	0.0394834	0.00135347
$852$	7.84270	0.268686
$853$	41.4913	1.42064	0.710318	−	0.703881i	$-0.248551\pi$
$853$	41.4913	1.42064	0.710318	+	0.703881i	$0.248551\pi$
$854$	2.07670	0.0710634
$855$	−13.3092	−0.455165
$856$	−9.01798	−0.308228
$857$	50.4444	1.72315	0.861575	−	0.507631i	$-0.169479\pi$
$857$	50.4444	1.72315	0.861575	+	0.507631i	$0.169479\pi$
$858$	3.68689	0.125868
$859$	−1.95442	−0.0666838	−0.0333419	−	0.999444i	$-0.510615\pi$
$859$	−1.95442	−0.0666838	−0.0333419	+	0.999444i	$0.510615\pi$
$860$	−9.86174	−0.336283
$861$	−24.9232	−0.849381
$862$	26.1646	0.891168
$863$	23.4035	0.796664	0.398332	−	0.917241i	$-0.369589\pi$
$863$	23.4035	0.796664	0.398332	+	0.917241i	$0.369589\pi$
$864$	5.76781	0.196225
$865$	−36.4533	−1.23945
$866$	−8.39401	−0.285240
$867$	−5.66530	−0.192404
$868$	19.5875	0.664845
$869$	4.33120	0.146926
$870$	−3.60083	−0.122080
$871$	33.0638	1.12032
$872$	45.2303	1.53169
$873$	−11.4439	−0.387319
$874$	0.773200	0.0261539
$875$	−31.5532	−1.06669
$876$	−3.23379	−0.109260
$877$	−23.3528	−0.788568	−0.394284	−	0.918989i	$-0.629007\pi$
$877$	−23.3528	−0.788568	−0.394284	+	0.918989i	$0.629007\pi$
$878$	−14.4462	−0.487534
$879$	9.39855	0.317005
$880$	3.62827	0.122309
$881$	32.2691	1.08717	0.543587	−	0.839353i	$-0.317066\pi$
$881$	32.2691	1.08717	0.543587	+	0.839353i	$0.317066\pi$
$882$	1.75503	0.0590951
$883$	−0.364962	−0.0122820	−0.00614098	−	0.999981i	$-0.501955\pi$
$883$	−0.364962	−0.0122820	−0.00614098	+	0.999981i	$0.501955\pi$
$884$	−28.7696	−0.967626
$885$	30.1891	1.01480
$886$	10.9407	0.367562
$887$	−41.6216	−1.39752	−0.698758	−	0.715358i	$-0.746264\pi$
$887$	−41.6216	−1.39752	−0.698758	+	0.715358i	$0.746264\pi$
$888$	0.450745	0.0151260
$889$	29.0025	0.972714
$890$	25.7366	0.862693
$891$	1.00000	0.0335013
$892$	23.5887	0.789807
$893$	−23.5640	−0.788538
$894$	0.0731100	0.00244516
$895$	−37.2850	−1.24630
$896$	−34.0399	−1.13719
$897$	−1.14706	−0.0382994
$898$	5.84691	0.195114
$899$	9.11769	0.304092
$900$	−1.18297	−0.0394324
$901$	−4.12981	−0.137584
$902$	−5.37950	−0.179118
$903$	8.21199	0.273278
$904$	26.6854	0.887544
$905$	11.5359	0.383468
$906$	−4.23695	−0.140763
$907$	18.0787	0.600294	0.300147	−	0.953893i	$-0.402964\pi$
$907$	18.0787	0.600294	0.300147	+	0.953893i	$0.402964\pi$
$908$	−9.49805	−0.315204
$909$	1.38330	0.0458811
$910$	27.4523	0.910035
$911$	39.8952	1.32179	0.660893	−	0.750480i	$-0.270178\pi$
$911$	39.8952	1.32179	0.660893	+	0.750480i	$0.270178\pi$
$912$	−8.38017	−0.277495
$913$	−5.39014	−0.178388
$914$	4.22894	0.139881
$915$	2.40049	0.0793577
$916$	0.716754	0.0236822
$917$	−12.7768	−0.421928
$918$	2.25404	0.0743943
$919$	15.0057	0.494993	0.247496	−	0.968889i	$-0.420392\pi$
$919$	15.0057	0.494993	0.247496	+	0.968889i	$0.420392\pi$
$920$	1.18900	0.0392002
$921$	0.917582	0.0302354
$922$	22.3702	0.736722
$923$	−27.8321	−0.916105
$924$	−4.81330	−0.158346
$925$	−0.144505	−0.00475129
$926$	−20.5236	−0.674446
$927$	12.4253	0.408101
$928$	−12.9228	−0.424213
$929$	9.86000	0.323496	0.161748	−	0.986832i	$-0.448287\pi$
$929$	9.86000	0.323496	0.161748	+	0.986832i	$0.448287\pi$
$930$	−6.54023	−0.214463
$931$	−14.5339	−0.476329
$932$	−14.1060	−0.462057
$933$	−19.2784	−0.631148
$934$	−12.9843	−0.424861
$935$	8.08174	0.264301
$936$	−13.0950	−0.428022
$937$	−44.9222	−1.46754	−0.733772	−	0.679395i	$-0.762242\pi$
$937$	−44.9222	−1.46754	−0.733772	+	0.679395i	$0.762242\pi$
$938$	12.4688	0.407119
$939$	−26.3200	−0.858922
$940$	−15.8314	−0.516363
$941$	24.8779	0.810997	0.405498	−	0.914096i	$-0.367098\pi$
$941$	24.8779	0.810997	0.405498	+	0.914096i	$0.367098\pi$
$942$	−3.73609	−0.121728
$943$	1.67367	0.0545020
$944$	19.0086	0.618679
$945$	7.44592	0.242216
$946$	1.77250	0.0576289
$947$	52.8229	1.71651	0.858256	−	0.513222i	$-0.171548\pi$
$947$	52.8229	1.71651	0.858256	+	0.513222i	$0.171548\pi$
$948$	−6.72098	−0.218287
$949$	11.4760	0.372528
$950$	−2.82983	−0.0918116
$951$	27.9967	0.907854
$952$	−24.8327	−0.804831
$953$	42.4260	1.37431	0.687157	−	0.726509i	$-0.258859\pi$
$953$	42.4260	1.37431	0.687157	+	0.726509i	$0.258859\pi$
$954$	−0.821261	−0.0265893
$955$	31.8331	1.03009
$956$	−44.3324	−1.43381
$957$	−2.24051	−0.0724255
$958$	−7.22909	−0.233561
$959$	−26.2481	−0.847595
$960$	2.01318	0.0649751
$961$	−14.4395	−0.465789
$962$	−0.698864	−0.0225323
$963$	3.79236	0.122207
$964$	38.8376	1.25087
$965$	−37.9214	−1.22073
$966$	−0.432571	−0.0139178
$967$	51.5229	1.65687	0.828433	−	0.560089i	$-0.189233\pi$
$967$	51.5229	1.65687	0.828433	+	0.560089i	$0.189233\pi$
$968$	−2.37793	−0.0764296
$969$	−18.6663	−0.599647
$970$	−18.3921	−0.590535
$971$	−14.4771	−0.464593	−0.232296	−	0.972645i	$-0.574624\pi$
$971$	−14.4771	−0.464593	−0.232296	+	0.972645i	$0.574624\pi$
$972$	−1.55176	−0.0497727
$973$	33.1978	1.06427
$974$	−8.37170	−0.268247
$975$	4.19812	0.134448
$976$	1.51147	0.0483810
$977$	−8.98759	−0.287539	−0.143769	−	0.989611i	$-0.545922\pi$
$977$	−8.98759	−0.287539	−0.143769	+	0.989611i	$0.545922\pi$
$978$	−10.9661	−0.350656
$979$	16.0138	0.511805
$980$	−9.76457	−0.311918
$981$	−19.0209	−0.607290
$982$	−14.3593	−0.458224
$983$	−10.8871	−0.347244	−0.173622	−	0.984812i	$-0.555547\pi$
$983$	−10.8871	−0.347244	−0.173622	+	0.984812i	$0.555547\pi$
$984$	19.1067	0.609098
$985$	45.8629	1.46131
$986$	−5.05020	−0.160831
$987$	13.1830	0.419619
$988$	47.3785	1.50731
$989$	−0.551459	−0.0175354
$990$	1.60715	0.0510785
$991$	55.7155	1.76986	0.884931	−	0.465723i	$-0.154206\pi$
$991$	55.7155	1.76986	0.884931	+	0.465723i	$0.154206\pi$
$992$	−23.4719	−0.745233
$993$	−32.8151	−1.04136
$994$	−10.4958	−0.332907
$995$	46.9919	1.48974
$996$	8.36420	0.265030
$997$	26.9347	0.853031	0.426515	−	0.904480i	$-0.359741\pi$
$997$	26.9347	0.853031	0.426515	+	0.904480i	$0.359741\pi$
$998$	−2.98790	−0.0945804
$999$	−0.189553	−0.00599721

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.g.1.7	✓	13
3.2	odd	2		6039.2.a.h.1.7		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.g.1.7	✓	13	1.1	even	1	trivial
6039.2.a.h.1.7		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)

\(f(q)\)	\(=\)	\(q+0.669508 q^{2} +1.00000 q^{3} -1.55176 q^{4} +2.40049 q^{5} +0.669508 q^{6} +3.10183 q^{7} -2.37793 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.669508 q^{2} +1.00000 q^{3} -1.55176 q^{4} +2.40049 q^{5} +0.669508 q^{6} +3.10183 q^{7} -2.37793 q^{8} +1.00000 q^{9} +1.60715 q^{10} +1.00000 q^{11} -1.55176 q^{12} +5.50687 q^{13} +2.07670 q^{14} +2.40049 q^{15} +1.51147 q^{16} +3.36670 q^{17} +0.669508 q^{18} -5.54438 q^{19} -3.72498 q^{20} +3.10183 q^{21} +0.669508 q^{22} -0.208297 q^{23} -2.37793 q^{24} +0.762344 q^{25} +3.68689 q^{26} +1.00000 q^{27} -4.81330 q^{28} -2.24051 q^{29} +1.60715 q^{30} -4.06946 q^{31} +5.76781 q^{32} +1.00000 q^{33} +2.25404 q^{34} +7.44592 q^{35} -1.55176 q^{36} -0.189553 q^{37} -3.71201 q^{38} +5.50687 q^{39} -5.70820 q^{40} -8.03499 q^{41} +2.07670 q^{42} +2.64746 q^{43} -1.55176 q^{44} +2.40049 q^{45} -0.139457 q^{46} +4.25006 q^{47} +1.51147 q^{48} +2.62138 q^{49} +0.510395 q^{50} +3.36670 q^{51} -8.54533 q^{52} -1.22666 q^{53} +0.669508 q^{54} +2.40049 q^{55} -7.37595 q^{56} -5.54438 q^{57} -1.50004 q^{58} +12.5763 q^{59} -3.72498 q^{60} +1.00000 q^{61} -2.72454 q^{62} +3.10183 q^{63} +0.838654 q^{64} +13.2192 q^{65} +0.669508 q^{66} +6.00410 q^{67} -5.22431 q^{68} -0.208297 q^{69} +4.98510 q^{70} -5.05407 q^{71} -2.37793 q^{72} +2.08395 q^{73} -0.126908 q^{74} +0.762344 q^{75} +8.60353 q^{76} +3.10183 q^{77} +3.68689 q^{78} +4.33120 q^{79} +3.62827 q^{80} +1.00000 q^{81} -5.37950 q^{82} -5.39014 q^{83} -4.81330 q^{84} +8.08174 q^{85} +1.77250 q^{86} -2.24051 q^{87} -2.37793 q^{88} +16.0138 q^{89} +1.60715 q^{90} +17.0814 q^{91} +0.323227 q^{92} -4.06946 q^{93} +2.84545 q^{94} -13.3092 q^{95} +5.76781 q^{96} -11.4439 q^{97} +1.75503 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 7 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 7 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 7 q^{7} + 9 q^{8} + 13 q^{9} + 2 q^{10} + 13 q^{11} + 12 q^{12} + 9 q^{13} + 7 q^{14} + 7 q^{15} + 2 q^{16} + 19 q^{17} + 4 q^{18} + 14 q^{19} + 19 q^{20} + 7 q^{21} + 4 q^{22} + 5 q^{23} + 9 q^{24} + 2 q^{25} - 4 q^{26} + 13 q^{27} + 7 q^{28} + 10 q^{29} + 2 q^{30} - q^{31} + 7 q^{32} + 13 q^{33} - 2 q^{34} + 16 q^{35} + 12 q^{36} - 8 q^{37} - 10 q^{38} + 9 q^{39} + 14 q^{40} + 21 q^{41} + 7 q^{42} + 11 q^{43} + 12 q^{44} + 7 q^{45} - 8 q^{46} + 22 q^{47} + 2 q^{48} + 19 q^{50} + 19 q^{51} - q^{52} + 16 q^{53} + 4 q^{54} + 7 q^{55} + 14 q^{57} - 13 q^{58} + 19 q^{59} + 19 q^{60} + 13 q^{61} + 3 q^{62} + 7 q^{63} - 13 q^{64} + 13 q^{65} + 4 q^{66} + 12 q^{67} + 36 q^{68} + 5 q^{69} - 20 q^{70} + 5 q^{71} + 9 q^{72} + 18 q^{73} + 6 q^{74} + 2 q^{75} - 5 q^{76} + 7 q^{77} - 4 q^{78} - q^{79} + 6 q^{80} + 13 q^{81} - 22 q^{82} + 48 q^{83} + 7 q^{84} - 2 q^{85} + 26 q^{86} + 10 q^{87} + 9 q^{88} + 15 q^{89} + 2 q^{90} - 11 q^{91} - 24 q^{92} - q^{93} - 23 q^{94} + 17 q^{95} + 7 q^{96} - 17 q^{97} - 15 q^{98} + 13 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 7 * q^7 + 9 * q^8 + 13 * q^9 + 2 * q^10 + 13 * q^11 + 12 * q^12 + 9 * q^13 + 7 * q^14 + 7 * q^15 + 2 * q^16 + 19 * q^17 + 4 * q^18 + 14 * q^19 + 19 * q^20 + 7 * q^21 + 4 * q^22 + 5 * q^23 + 9 * q^24 + 2 * q^25 - 4 * q^26 + 13 * q^27 + 7 * q^28 + 10 * q^29 + 2 * q^30 - q^31 + 7 * q^32 + 13 * q^33 - 2 * q^34 + 16 * q^35 + 12 * q^36 - 8 * q^37 - 10 * q^38 + 9 * q^39 + 14 * q^40 + 21 * q^41 + 7 * q^42 + 11 * q^43 + 12 * q^44 + 7 * q^45 - 8 * q^46 + 22 * q^47 + 2 * q^48 + 19 * q^50 + 19 * q^51 - q^52 + 16 * q^53 + 4 * q^54 + 7 * q^55 + 14 * q^57 - 13 * q^58 + 19 * q^59 + 19 * q^60 + 13 * q^61 + 3 * q^62 + 7 * q^63 - 13 * q^64 + 13 * q^65 + 4 * q^66 + 12 * q^67 + 36 * q^68 + 5 * q^69 - 20 * q^70 + 5 * q^71 + 9 * q^72 + 18 * q^73 + 6 * q^74 + 2 * q^75 - 5 * q^76 + 7 * q^77 - 4 * q^78 - q^79 + 6 * q^80 + 13 * q^81 - 22 * q^82 + 48 * q^83 + 7 * q^84 - 2 * q^85 + 26 * q^86 + 10 * q^87 + 9 * q^88 + 15 * q^89 + 2 * q^90 - 11 * q^91 - 24 * q^92 - q^93 - 23 * q^94 + 17 * q^95 + 7 * q^96 - 17 * q^97 - 15 * q^98 + 13 * q^99

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