LMFDB - Embedded newform 2013.2.a.e.1.10

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} - 2 x^{12} - 19 x^{11} + 35 x^{10} + 136 x^{9} - 220 x^{8} - 469 x^{7} + 610 x^{6} + 841 x^{5} + \cdots - 47 $ x^13 - 2x^12 - 19x^11 + 35x^10 + 136x^9 - 220x^8 - 469x^7 + 610x^6 + 841x^5 - 760x^4 - 742x^3 + 366x^2 + 236x - 47
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			1.10
Root			$1.61181$ 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)

$f(q)$	$=$	$q+1.61181 q^{2} -1.00000 q^{3} +0.597924 q^{4} +4.27930 q^{5} -1.61181 q^{6} +1.98799 q^{7} -2.25988 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.61181 q^{2} -1.00000 q^{3} +0.597924 q^{4} +4.27930 q^{5} -1.61181 q^{6} +1.98799 q^{7} -2.25988 q^{8} +1.00000 q^{9} +6.89741 q^{10} +1.00000 q^{11} -0.597924 q^{12} +0.250746 q^{13} +3.20426 q^{14} -4.27930 q^{15} -4.83834 q^{16} +3.17083 q^{17} +1.61181 q^{18} -3.76446 q^{19} +2.55870 q^{20} -1.98799 q^{21} +1.61181 q^{22} +8.19125 q^{23} +2.25988 q^{24} +13.3124 q^{25} +0.404154 q^{26} -1.00000 q^{27} +1.18867 q^{28} -4.02069 q^{29} -6.89741 q^{30} +2.98063 q^{31} -3.27871 q^{32} -1.00000 q^{33} +5.11077 q^{34} +8.50721 q^{35} +0.597924 q^{36} -8.39318 q^{37} -6.06759 q^{38} -0.250746 q^{39} -9.67069 q^{40} -2.30573 q^{41} -3.20426 q^{42} +7.83567 q^{43} +0.597924 q^{44} +4.27930 q^{45} +13.2027 q^{46} +0.852827 q^{47} +4.83834 q^{48} -3.04789 q^{49} +21.4571 q^{50} -3.17083 q^{51} +0.149927 q^{52} -7.07558 q^{53} -1.61181 q^{54} +4.27930 q^{55} -4.49261 q^{56} +3.76446 q^{57} -6.48058 q^{58} +9.77116 q^{59} -2.55870 q^{60} -1.00000 q^{61} +4.80420 q^{62} +1.98799 q^{63} +4.39201 q^{64} +1.07302 q^{65} -1.61181 q^{66} -13.1758 q^{67} +1.89592 q^{68} -8.19125 q^{69} +13.7120 q^{70} +2.07157 q^{71} -2.25988 q^{72} -1.20929 q^{73} -13.5282 q^{74} -13.3124 q^{75} -2.25086 q^{76} +1.98799 q^{77} -0.404154 q^{78} +2.92819 q^{79} -20.7047 q^{80} +1.00000 q^{81} -3.71639 q^{82} +12.1817 q^{83} -1.18867 q^{84} +13.5689 q^{85} +12.6296 q^{86} +4.02069 q^{87} -2.25988 q^{88} -9.78144 q^{89} +6.89741 q^{90} +0.498480 q^{91} +4.89775 q^{92} -2.98063 q^{93} +1.37459 q^{94} -16.1093 q^{95} +3.27871 q^{96} +3.01824 q^{97} -4.91261 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9} + 6 q^{10} + 13 q^{11} - 16 q^{12} + 13 q^{13} + q^{14} - 3 q^{15} + 18 q^{16} + 17 q^{17} + 2 q^{18} + 14 q^{19} - 7 q^{20} - 11 q^{21} + 2 q^{22} + 7 q^{23} - 9 q^{24} + 18 q^{25} - 10 q^{26} - 13 q^{27} + 19 q^{28} - 6 q^{29} - 6 q^{30} + 27 q^{31} + 5 q^{32} - 13 q^{33} + 6 q^{34} + 14 q^{35} + 16 q^{36} + 10 q^{37} + 2 q^{38} - 13 q^{39} + 8 q^{40} + 3 q^{41} - q^{42} + 29 q^{43} + 16 q^{44} + 3 q^{45} - 24 q^{46} + 8 q^{47} - 18 q^{48} + 8 q^{49} - 27 q^{50} - 17 q^{51} + 37 q^{52} - 24 q^{53} - 2 q^{54} + 3 q^{55} + 24 q^{56} - 14 q^{57} - 5 q^{58} + 13 q^{59} + 7 q^{60} - 13 q^{61} + 39 q^{62} + 11 q^{63} + 47 q^{64} - 11 q^{65} - 2 q^{66} + 44 q^{67} - 8 q^{68} - 7 q^{69} - 12 q^{70} + 3 q^{71} + 9 q^{72} + 48 q^{73} - 22 q^{74} - 18 q^{75} + 47 q^{76} + 11 q^{77} + 10 q^{78} - 17 q^{79} - 26 q^{80} + 13 q^{81} + 56 q^{82} + 50 q^{83} - 19 q^{84} + 8 q^{85} + 18 q^{86} + 6 q^{87} + 9 q^{88} - 15 q^{89} + 6 q^{90} + 47 q^{91} + 14 q^{92} - 27 q^{93} + 45 q^{94} - q^{95} - 5 q^{96} + 27 q^{97} + 47 q^{98} + 13 q^{99}+O(q^{100}) \) 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9 + 6 * q^10 + 13 * q^11 - 16 * q^12 + 13 * q^13 + q^14 - 3 * q^15 + 18 * q^16 + 17 * q^17 + 2 * q^18 + 14 * q^19 - 7 * q^20 - 11 * q^21 + 2 * q^22 + 7 * q^23 - 9 * q^24 + 18 * q^25 - 10 * q^26 - 13 * q^27 + 19 * q^28 - 6 * q^29 - 6 * q^30 + 27 * q^31 + 5 * q^32 - 13 * q^33 + 6 * q^34 + 14 * q^35 + 16 * q^36 + 10 * q^37 + 2 * q^38 - 13 * q^39 + 8 * q^40 + 3 * q^41 - q^42 + 29 * q^43 + 16 * q^44 + 3 * q^45 - 24 * q^46 + 8 * q^47 - 18 * q^48 + 8 * q^49 - 27 * q^50 - 17 * q^51 + 37 * q^52 - 24 * q^53 - 2 * q^54 + 3 * q^55 + 24 * q^56 - 14 * q^57 - 5 * q^58 + 13 * q^59 + 7 * q^60 - 13 * q^61 + 39 * q^62 + 11 * q^63 + 47 * q^64 - 11 * q^65 - 2 * q^66 + 44 * q^67 - 8 * q^68 - 7 * q^69 - 12 * q^70 + 3 * q^71 + 9 * q^72 + 48 * q^73 - 22 * q^74 - 18 * q^75 + 47 * q^76 + 11 * q^77 + 10 * q^78 - 17 * q^79 - 26 * q^80 + 13 * q^81 + 56 * q^82 + 50 * q^83 - 19 * q^84 + 8 * q^85 + 18 * q^86 + 6 * q^87 + 9 * q^88 - 15 * q^89 + 6 * q^90 + 47 * q^91 + 14 * q^92 - 27 * q^93 + 45 * q^94 - q^95 - 5 * q^96 + 27 * q^97 + 47 * 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 $

$2$	1.61181	1.13972	0.569860	−	0.821742i	$-0.306997\pi$
$2$	1.61181	1.13972	0.569860	+	0.821742i	$0.306997\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.597924	0.298962
$5$	4.27930	1.91376	0.956881	−	0.290481i	$-0.0938153\pi$
$5$	4.27930	1.91376	0.956881	+	0.290481i	$0.0938153\pi$
$6$	−1.61181	−0.658018
$7$	1.98799	0.751390	0.375695	−	0.926743i	$-0.377404\pi$
$7$	1.98799	0.751390	0.375695	+	0.926743i	$0.377404\pi$
$8$	−2.25988	−0.798987
$9$	1.00000	0.333333
$10$	6.89741	2.18115
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.597924	−0.172606
$13$	0.250746	0.0695444	0.0347722	−	0.999395i	$-0.488929\pi$
$13$	0.250746	0.0695444	0.0347722	+	0.999395i	$0.488929\pi$
$14$	3.20426	0.856374
$15$	−4.27930	−1.10491
$16$	−4.83834	−1.20958
$17$	3.17083	0.769040	0.384520	−	0.923117i	$-0.374367\pi$
$17$	3.17083	0.769040	0.384520	+	0.923117i	$0.374367\pi$
$18$	1.61181	0.379907
$19$	−3.76446	−0.863627	−0.431814	−	0.901963i	$-0.642126\pi$
$19$	−3.76446	−0.863627	−0.431814	+	0.901963i	$0.642126\pi$
$20$	2.55870	0.572142
$21$	−1.98799	−0.433815
$22$	1.61181	0.343639
$23$	8.19125	1.70799	0.853997	−	0.520278i	$-0.174172\pi$
$23$	8.19125	1.70799	0.853997	+	0.520278i	$0.174172\pi$
$24$	2.25988	0.461295
$25$	13.3124	2.66248
$26$	0.404154	0.0792611
$27$	−1.00000	−0.192450
$28$	1.18867	0.224637
$29$	−4.02069	−0.746623	−0.373312	−	0.927706i	$-0.621778\pi$
$29$	−4.02069	−0.746623	−0.373312	+	0.927706i	$0.621778\pi$
$30$	−6.89741	−1.25929
$31$	2.98063	0.535337	0.267669	−	0.963511i	$-0.413747\pi$
$31$	2.98063	0.535337	0.267669	+	0.963511i	$0.413747\pi$
$32$	−3.27871	−0.579600
$33$	−1.00000	−0.174078
$34$	5.11077	0.876490
$35$	8.50721	1.43798
$36$	0.597924	0.0996541
$37$	−8.39318	−1.37983	−0.689916	−	0.723890i	$-0.742352\pi$
$37$	−8.39318	−1.37983	−0.689916	+	0.723890i	$0.742352\pi$
$38$	−6.06759	−0.984293
$39$	−0.250746	−0.0401515
$40$	−9.67069	−1.52907
$41$	−2.30573	−0.360094	−0.180047	−	0.983658i	$-0.557625\pi$
$41$	−2.30573	−0.360094	−0.180047	+	0.983658i	$0.557625\pi$
$42$	−3.20426	−0.494428
$43$	7.83567	1.19493	0.597464	−	0.801896i	$-0.296175\pi$
$43$	7.83567	1.19493	0.597464	+	0.801896i	$0.296175\pi$
$44$	0.597924	0.0901405
$45$	4.27930	0.637921
$46$	13.2027	1.94663
$47$	0.852827	0.124398	0.0621988	−	0.998064i	$-0.480189\pi$
$47$	0.852827	0.124398	0.0621988	+	0.998064i	$0.480189\pi$
$48$	4.83834	0.698354
$49$	−3.04789	−0.435413
$50$	21.4571	3.03449
$51$	−3.17083	−0.444005
$52$	0.149927	0.0207911
$53$	−7.07558	−0.971906	−0.485953	−	0.873985i	$-0.661527\pi$
$53$	−7.07558	−0.971906	−0.485953	+	0.873985i	$0.661527\pi$
$54$	−1.61181	−0.219339
$55$	4.27930	0.577021
$56$	−4.49261	−0.600351
$57$	3.76446	0.498615
$58$	−6.48058	−0.850942
$59$	9.77116	1.27210	0.636048	−	0.771649i	$-0.280568\pi$
$59$	9.77116	1.27210	0.636048	+	0.771649i	$0.280568\pi$
$60$	−2.55870	−0.330327
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	4.80420	0.610135
$63$	1.98799	0.250463
$64$	4.39201	0.549002
$65$	1.07302	0.133091
$66$	−1.61181	−0.198400
$67$	−13.1758	−1.60968	−0.804841	−	0.593490i	$-0.797750\pi$
$67$	−13.1758	−1.60968	−0.804841	+	0.593490i	$0.797750\pi$
$68$	1.89592	0.229914
$69$	−8.19125	−0.986111
$70$	13.7120	1.63890
$71$	2.07157	0.245850	0.122925	−	0.992416i	$-0.460773\pi$
$71$	2.07157	0.245850	0.122925	+	0.992416i	$0.460773\pi$
$72$	−2.25988	−0.266329
$73$	−1.20929	−0.141537	−0.0707686	−	0.997493i	$-0.522545\pi$
$73$	−1.20929	−0.141537	−0.0707686	+	0.997493i	$0.522545\pi$
$74$	−13.5282	−1.57262
$75$	−13.3124	−1.53719
$76$	−2.25086	−0.258192
$77$	1.98799	0.226553
$78$	−0.404154	−0.0457614
$79$	2.92819	0.329447	0.164723	−	0.986340i	$-0.447327\pi$
$79$	2.92819	0.329447	0.164723	+	0.986340i	$0.447327\pi$
$80$	−20.7047	−2.31486
$81$	1.00000	0.111111
$82$	−3.71639	−0.410407
$83$	12.1817	1.33712	0.668558	−	0.743660i	$-0.266912\pi$
$83$	12.1817	1.33712	0.668558	+	0.743660i	$0.266912\pi$
$84$	−1.18867	−0.129694
$85$	13.5689	1.47176
$86$	12.6296	1.36188
$87$	4.02069	0.431063
$88$	−2.25988	−0.240904
$89$	−9.78144	−1.03683	−0.518415	−	0.855129i	$-0.673478\pi$
$89$	−9.78144	−1.03683	−0.518415	+	0.855129i	$0.673478\pi$
$90$	6.89741	0.727051
$91$	0.498480	0.0522549
$92$	4.89775	0.510626
$93$	−2.98063	−0.309077
$94$	1.37459	0.141778
$95$	−16.1093	−1.65278
$96$	3.27871	0.334632
$97$	3.01824	0.306456	0.153228	−	0.988191i	$-0.451033\pi$
$97$	3.01824	0.306456	0.153228	+	0.988191i	$0.451033\pi$
$98$	−4.91261	−0.496249
$99$	1.00000	0.100504
$100$	7.95982	0.795982
$101$	5.62832	0.560039	0.280020	−	0.959994i	$-0.409659\pi$
$101$	5.62832	0.560039	0.280020	+	0.959994i	$0.409659\pi$
$102$	−5.11077	−0.506042
$103$	−16.3398	−1.61001	−0.805003	−	0.593270i	$-0.797837\pi$
$103$	−16.3398	−1.61001	−0.805003	+	0.593270i	$0.797837\pi$
$104$	−0.566654	−0.0555650
$105$	−8.50721	−0.830219
$106$	−11.4045	−1.10770
$107$	13.4737	1.30255	0.651276	−	0.758841i	$-0.274234\pi$
$107$	13.4737	1.30255	0.651276	+	0.758841i	$0.274234\pi$
$108$	−0.597924	−0.0575353
$109$	13.5673	1.29951	0.649757	−	0.760142i	$-0.274871\pi$
$109$	13.5673	1.29951	0.649757	+	0.760142i	$0.274871\pi$
$110$	6.89741	0.657642
$111$	8.39318	0.796646
$112$	−9.61857	−0.908869
$113$	−0.0631308	−0.00593884	−0.00296942	−	0.999996i	$-0.500945\pi$
$113$	−0.0631308	−0.00593884	−0.00296942	+	0.999996i	$0.500945\pi$
$114$	6.06759	0.568282
$115$	35.0528	3.26869
$116$	−2.40407	−0.223212
$117$	0.250746	0.0231815
$118$	15.7492	1.44983
$119$	6.30359	0.577849
$120$	9.67069	0.882809
$121$	1.00000	0.0909091
$122$	−1.61181	−0.145926
$123$	2.30573	0.207900
$124$	1.78219	0.160046
$125$	35.5713	3.18160
$126$	3.20426	0.285458
$127$	5.04839	0.447972	0.223986	−	0.974592i	$-0.428093\pi$
$127$	5.04839	0.447972	0.223986	+	0.974592i	$0.428093\pi$
$128$	13.6365	1.20531
$129$	−7.83567	−0.689892
$130$	1.72950	0.151687
$131$	19.1064	1.66933	0.834665	−	0.550757i	$-0.185661\pi$
$131$	19.1064	1.66933	0.834665	+	0.550757i	$0.185661\pi$
$132$	−0.597924	−0.0520426
$133$	−7.48372	−0.648921
$134$	−21.2369	−1.83459
$135$	−4.27930	−0.368304
$136$	−7.16569	−0.614453
$137$	−8.39986	−0.717649	−0.358824	−	0.933405i	$-0.616822\pi$
$137$	−8.39986	−0.717649	−0.358824	+	0.933405i	$0.616822\pi$
$138$	−13.2027	−1.12389
$139$	7.05747	0.598607	0.299303	−	0.954158i	$-0.403246\pi$
$139$	7.05747	0.598607	0.299303	+	0.954158i	$0.403246\pi$
$140$	5.08667	0.429902
$141$	−0.852827	−0.0718210
$142$	3.33897	0.280200
$143$	0.250746	0.0209684
$144$	−4.83834	−0.403195
$145$	−17.2057	−1.42886
$146$	−1.94915	−0.161313
$147$	3.04789	0.251386
$148$	−5.01849	−0.412517
$149$	−19.9863	−1.63734	−0.818672	−	0.574262i	$-0.805289\pi$
$149$	−19.9863	−1.63734	−0.818672	+	0.574262i	$0.805289\pi$
$150$	−21.4571	−1.75196
$151$	−15.0434	−1.22421	−0.612107	−	0.790775i	$-0.709678\pi$
$151$	−15.0434	−1.22421	−0.612107	+	0.790775i	$0.709678\pi$
$152$	8.50722	0.690027
$153$	3.17083	0.256347
$154$	3.20426	0.258207
$155$	12.7550	1.02451
$156$	−0.149927	−0.0120038
$157$	−14.2863	−1.14017	−0.570086	−	0.821585i	$-0.693090\pi$
$157$	−14.2863	−1.14017	−0.570086	+	0.821585i	$0.693090\pi$
$158$	4.71967	0.375477
$159$	7.07558	0.561130
$160$	−14.0306	−1.10922
$161$	16.2841	1.28337
$162$	1.61181	0.126636
$163$	−12.0009	−0.939983	−0.469991	−	0.882671i	$-0.655743\pi$
$163$	−12.0009	−0.939983	−0.469991	+	0.882671i	$0.655743\pi$
$164$	−1.37865	−0.107655
$165$	−4.27930	−0.333143
$166$	19.6346	1.52394
$167$	−17.9733	−1.39082	−0.695408	−	0.718615i	$-0.744776\pi$
$167$	−17.9733	−1.39082	−0.695408	+	0.718615i	$0.744776\pi$
$168$	4.49261	0.346613
$169$	−12.9371	−0.995164
$170$	21.8705	1.67739
$171$	−3.76446	−0.287876
$172$	4.68514	0.357238
$173$	−5.97151	−0.454006	−0.227003	−	0.973894i	$-0.572893\pi$
$173$	−5.97151	−0.454006	−0.227003	+	0.973894i	$0.572893\pi$
$174$	6.48058	0.491291
$175$	26.4650	2.00056
$176$	−4.83834	−0.364703
$177$	−9.77116	−0.734445
$178$	−15.7658	−1.18170
$179$	22.5218	1.68336	0.841678	−	0.539980i	$-0.181568\pi$
$179$	22.5218	1.68336	0.841678	+	0.539980i	$0.181568\pi$
$180$	2.55870	0.190714
$181$	−16.7687	−1.24641	−0.623205	−	0.782058i	$-0.714170\pi$
$181$	−16.7687	−1.24641	−0.623205	+	0.782058i	$0.714170\pi$
$182$	0.803455	0.0595560
$183$	1.00000	0.0739221
$184$	−18.5112	−1.36466
$185$	−35.9170	−2.64067
$186$	−4.80420	−0.352261
$187$	3.17083	0.231874
$188$	0.509926	0.0371902
$189$	−1.98799	−0.144605
$190$	−25.9651	−1.88370
$191$	23.1333	1.67386	0.836932	−	0.547307i	$-0.184347\pi$
$191$	23.1333	1.67386	0.836932	+	0.547307i	$0.184347\pi$
$192$	−4.39201	−0.316966
$193$	1.54885	0.111489	0.0557443	−	0.998445i	$-0.482247\pi$
$193$	1.54885	0.111489	0.0557443	+	0.998445i	$0.482247\pi$
$194$	4.86482	0.349274
$195$	−1.07302	−0.0768403
$196$	−1.82241	−0.130172
$197$	−3.90674	−0.278344	−0.139172	−	0.990268i	$-0.544444\pi$
$197$	−3.90674	−0.278344	−0.139172	+	0.990268i	$0.544444\pi$
$198$	1.61181	0.114546
$199$	−11.2931	−0.800544	−0.400272	−	0.916396i	$-0.631084\pi$
$199$	−11.2931	−0.800544	−0.400272	+	0.916396i	$0.631084\pi$
$200$	−30.0844	−2.12729
$201$	13.1758	0.929351
$202$	9.07178	0.638288
$203$	−7.99309	−0.561005
$204$	−1.89592	−0.132741
$205$	−9.86690	−0.689134
$206$	−26.3366	−1.83496
$207$	8.19125	0.569331
$208$	−1.21319	−0.0841197
$209$	−3.76446	−0.260393
$210$	−13.7120	−0.946217
$211$	17.2658	1.18863	0.594314	−	0.804233i	$-0.297424\pi$
$211$	17.2658	1.18863	0.594314	+	0.804233i	$0.297424\pi$
$212$	−4.23066	−0.290563
$213$	−2.07157	−0.141941
$214$	21.7170	1.48454
$215$	33.5312	2.28681
$216$	2.25988	0.153765
$217$	5.92547	0.402247
$218$	21.8679	1.48108
$219$	1.20929	0.0817165
$220$	2.55870	0.172507
$221$	0.795073	0.0534824
$222$	13.5282	0.907953
$223$	−28.3241	−1.89672	−0.948362	−	0.317191i	$-0.897260\pi$
$223$	−28.3241	−1.89672	−0.948362	+	0.317191i	$0.897260\pi$
$224$	−6.51805	−0.435506
$225$	13.3124	0.887494
$226$	−0.101755	−0.00676862
$227$	−14.3403	−0.951800	−0.475900	−	0.879500i	$-0.657877\pi$
$227$	−14.3403	−0.951800	−0.475900	+	0.879500i	$0.657877\pi$
$228$	2.25086	0.149067
$229$	−9.21589	−0.609003	−0.304502	−	0.952512i	$-0.598490\pi$
$229$	−9.21589	−0.609003	−0.304502	+	0.952512i	$0.598490\pi$
$230$	56.4984	3.72540
$231$	−1.98799	−0.130800
$232$	9.08626	0.596542
$233$	−25.2945	−1.65710	−0.828550	−	0.559915i	$-0.810834\pi$
$233$	−25.2945	−1.65710	−0.828550	+	0.559915i	$0.810834\pi$
$234$	0.404154	0.0264204
$235$	3.64950	0.238067
$236$	5.84241	0.380309
$237$	−2.92819	−0.190206
$238$	10.1602	0.658586
$239$	−19.2893	−1.24772	−0.623860	−	0.781536i	$-0.714437\pi$
$239$	−19.2893	−1.24772	−0.623860	+	0.781536i	$0.714437\pi$
$240$	20.7047	1.33648
$241$	12.4108	0.799448	0.399724	−	0.916636i	$-0.369106\pi$
$241$	12.4108	0.799448	0.399724	+	0.916636i	$0.369106\pi$
$242$	1.61181	0.103611
$243$	−1.00000	−0.0641500
$244$	−0.597924	−0.0382782
$245$	−13.0428	−0.833277
$246$	3.71639	0.236948
$247$	−0.943924	−0.0600604
$248$	−6.73586	−0.427727
$249$	−12.1817	−0.771984
$250$	57.3342	3.62613
$251$	−13.9303	−0.879270	−0.439635	−	0.898176i	$-0.644892\pi$
$251$	−13.9303	−0.879270	−0.439635	+	0.898176i	$0.644892\pi$
$252$	1.18867	0.0748791
$253$	8.19125	0.514979
$254$	8.13703	0.510562
$255$	−13.5689	−0.849720
$256$	13.1954	0.824713
$257$	−8.15779	−0.508869	−0.254434	−	0.967090i	$-0.581889\pi$
$257$	−8.15779	−0.508869	−0.254434	+	0.967090i	$0.581889\pi$
$258$	−12.6296	−0.786284
$259$	−16.6856	−1.03679
$260$	0.641583	0.0397893
$261$	−4.02069	−0.248874
$262$	30.7958	1.90257
$263$	−16.6378	−1.02593	−0.512966	−	0.858409i	$-0.671453\pi$
$263$	−16.6378	−1.02593	−0.512966	+	0.858409i	$0.671453\pi$
$264$	2.25988	0.139086
$265$	−30.2785	−1.86000
$266$	−12.0623	−0.739588
$267$	9.78144	0.598615
$268$	−7.87815	−0.481234
$269$	1.23389	0.0752315	0.0376158	−	0.999292i	$-0.488024\pi$
$269$	1.23389	0.0752315	0.0376158	+	0.999292i	$0.488024\pi$
$270$	−6.89741	−0.419763
$271$	4.48114	0.272210	0.136105	−	0.990694i	$-0.456542\pi$
$271$	4.48114	0.272210	0.136105	+	0.990694i	$0.456542\pi$
$272$	−15.3415	−0.930218
$273$	−0.498480	−0.0301694
$274$	−13.5390	−0.817919
$275$	13.3124	0.802769
$276$	−4.89775	−0.294810
$277$	22.3235	1.34129	0.670644	−	0.741779i	$-0.266018\pi$
$277$	22.3235	1.34129	0.670644	+	0.741779i	$0.266018\pi$
$278$	11.3753	0.682244
$279$	2.98063	0.178446
$280$	−19.2252	−1.14893
$281$	1.20667	0.0719840	0.0359920	−	0.999352i	$-0.488541\pi$
$281$	1.20667	0.0719840	0.0359920	+	0.999352i	$0.488541\pi$
$282$	−1.37459	−0.0818558
$283$	−12.8779	−0.765509	−0.382755	−	0.923850i	$-0.625025\pi$
$283$	−12.8779	−0.765509	−0.382755	+	0.923850i	$0.625025\pi$
$284$	1.23864	0.0734997
$285$	16.1093	0.954231
$286$	0.404154	0.0238981
$287$	−4.58377	−0.270571
$288$	−3.27871	−0.193200
$289$	−6.94583	−0.408578
$290$	−27.7323	−1.62850
$291$	−3.01824	−0.176932
$292$	−0.723066	−0.0423142
$293$	3.55779	0.207848	0.103924	−	0.994585i	$-0.466860\pi$
$293$	3.55779	0.207848	0.103924	+	0.994585i	$0.466860\pi$
$294$	4.91261	0.286510
$295$	41.8137	2.43449
$296$	18.9676	1.10247
$297$	−1.00000	−0.0580259
$298$	−32.2141	−1.86611
$299$	2.05392	0.118781
$300$	−7.95982	−0.459560
$301$	15.5772	0.897857
$302$	−24.2471	−1.39526
$303$	−5.62832	−0.323339
$304$	18.2137	1.04463
$305$	−4.27930	−0.245032
$306$	5.11077	0.292163
$307$	15.7013	0.896118	0.448059	−	0.894004i	$-0.352115\pi$
$307$	15.7013	0.896118	0.448059	+	0.894004i	$0.352115\pi$
$308$	1.18867	0.0677307
$309$	16.3398	0.929538
$310$	20.5586	1.16765
$311$	−20.3629	−1.15467	−0.577336	−	0.816507i	$-0.695908\pi$
$311$	−20.3629	−1.15467	−0.577336	+	0.816507i	$0.695908\pi$
$312$	0.566654	0.0320805
$313$	5.37471	0.303797	0.151898	−	0.988396i	$-0.451461\pi$
$313$	5.37471	0.303797	0.151898	+	0.988396i	$0.451461\pi$
$314$	−23.0268	−1.29948
$315$	8.50721	0.479327
$316$	1.75083	0.0984921
$317$	−3.60000	−0.202196	−0.101098	−	0.994876i	$-0.532236\pi$
$317$	−3.60000	−0.202196	−0.101098	+	0.994876i	$0.532236\pi$
$318$	11.4045	0.639531
$319$	−4.02069	−0.225115
$320$	18.7948	1.05066
$321$	−13.4737	−0.752029
$322$	26.2469	1.46268
$323$	−11.9365	−0.664164
$324$	0.597924	0.0332180
$325$	3.33803	0.185161
$326$	−19.3431	−1.07132
$327$	−13.5673	−0.750274
$328$	5.21066	0.287710
$329$	1.69541	0.0934711
$330$	−6.89741	−0.379690
$331$	35.9801	1.97765	0.988823	−	0.149092i	$-0.0476351\pi$
$331$	35.9801	1.97765	0.988823	+	0.149092i	$0.0476351\pi$
$332$	7.28374	0.399747
$333$	−8.39318	−0.459944
$334$	−28.9695	−1.58514
$335$	−56.3833	−3.08055
$336$	9.61857	0.524736
$337$	4.79883	0.261409	0.130704	−	0.991421i	$-0.458276\pi$
$337$	4.79883	0.261409	0.130704	+	0.991421i	$0.458276\pi$
$338$	−20.8522	−1.13421
$339$	0.0631308	0.00342879
$340$	8.11320	0.440000
$341$	2.98063	0.161410
$342$	−6.06759	−0.328098
$343$	−19.9751	−1.07856
$344$	−17.7076	−0.954732
$345$	−35.0528	−1.88718
$346$	−9.62493	−0.517439
$347$	3.83919	0.206099	0.103049	−	0.994676i	$-0.467140\pi$
$347$	3.83919	0.206099	0.103049	+	0.994676i	$0.467140\pi$
$348$	2.40407	0.128872
$349$	0.105346	0.00563902	0.00281951	−	0.999996i	$-0.499103\pi$
$349$	0.105346	0.00563902	0.00281951	+	0.999996i	$0.499103\pi$
$350$	42.6564	2.28008
$351$	−0.250746	−0.0133838
$352$	−3.27871	−0.174756
$353$	−34.3508	−1.82831	−0.914155	−	0.405364i	$-0.867145\pi$
$353$	−34.3508	−1.82831	−0.914155	+	0.405364i	$0.867145\pi$
$354$	−15.7492	−0.837062
$355$	8.86485	0.470497
$356$	−5.84856	−0.309973
$357$	−6.30359	−0.333621
$358$	36.3007	1.91855
$359$	−13.8877	−0.732965	−0.366483	−	0.930425i	$-0.619438\pi$
$359$	−13.8877	−0.732965	−0.366483	+	0.930425i	$0.619438\pi$
$360$	−9.67069	−0.509690
$361$	−4.82881	−0.254148
$362$	−27.0280	−1.42056
$363$	−1.00000	−0.0524864
$364$	0.298054	0.0156223
$365$	−5.17493	−0.270868
$366$	1.61181	0.0842505
$367$	−12.2286	−0.638330	−0.319165	−	0.947699i	$-0.603402\pi$
$367$	−12.2286	−0.638330	−0.319165	+	0.947699i	$0.603402\pi$
$368$	−39.6320	−2.06596
$369$	−2.30573	−0.120031
$370$	−57.8912	−3.00962
$371$	−14.0662	−0.730280
$372$	−1.78219	−0.0924024
$373$	24.3245	1.25948	0.629738	−	0.776808i	$-0.283162\pi$
$373$	24.3245	1.25948	0.629738	+	0.776808i	$0.283162\pi$
$374$	5.11077	0.264272
$375$	−35.5713	−1.83690
$376$	−1.92728	−0.0993921
$377$	−1.00817	−0.0519234
$378$	−3.20426	−0.164809
$379$	2.33650	0.120018	0.0600090	−	0.998198i	$-0.480887\pi$
$379$	2.33650	0.120018	0.0600090	+	0.998198i	$0.480887\pi$
$380$	−9.63213	−0.494118
$381$	−5.04839	−0.258637
$382$	37.2864	1.90774
$383$	−29.8315	−1.52432	−0.762160	−	0.647389i	$-0.775861\pi$
$383$	−29.8315	−1.52432	−0.762160	+	0.647389i	$0.775861\pi$
$384$	−13.6365	−0.695885
$385$	8.50721	0.433568
$386$	2.49645	0.127066
$387$	7.83567	0.398309
$388$	1.80468	0.0916187
$389$	4.92145	0.249528	0.124764	−	0.992186i	$-0.460183\pi$
$389$	4.92145	0.249528	0.124764	+	0.992186i	$0.460183\pi$
$390$	−1.72950	−0.0875765
$391$	25.9731	1.31351
$392$	6.88786	0.347889
$393$	−19.1064	−0.963789
$394$	−6.29692	−0.317234
$395$	12.5306	0.630482
$396$	0.597924	0.0300468
$397$	−5.06135	−0.254022	−0.127011	−	0.991901i	$-0.540538\pi$
$397$	−5.06135	−0.254022	−0.127011	+	0.991901i	$0.540538\pi$
$398$	−18.2023	−0.912396
$399$	7.48372	0.374655
$400$	−64.4099	−3.22050
$401$	1.55341	0.0775736	0.0387868	−	0.999248i	$-0.487651\pi$
$401$	1.55341	0.0775736	0.0387868	+	0.999248i	$0.487651\pi$
$402$	21.2369	1.05920
$403$	0.747381	0.0372297
$404$	3.36531	0.167431
$405$	4.27930	0.212640
$406$	−12.8833	−0.639389
$407$	−8.39318	−0.416035
$408$	7.16569	0.354754
$409$	−8.42819	−0.416747	−0.208373	−	0.978049i	$-0.566817\pi$
$409$	−8.42819	−0.416747	−0.208373	+	0.978049i	$0.566817\pi$
$410$	−15.9035	−0.785420
$411$	8.39986	0.414335
$412$	−9.76995	−0.481331
$413$	19.4250	0.955841
$414$	13.2027	0.648878
$415$	52.1292	2.55892
$416$	−0.822124	−0.0403079
$417$	−7.05747	−0.345606
$418$	−6.06759	−0.296776
$419$	−32.6335	−1.59425	−0.797125	−	0.603814i	$-0.793647\pi$
$419$	−32.6335	−1.59425	−0.797125	+	0.603814i	$0.793647\pi$
$420$	−5.08667	−0.248204
$421$	−5.65215	−0.275469	−0.137735	−	0.990469i	$-0.543982\pi$
$421$	−5.65215	−0.275469	−0.137735	+	0.990469i	$0.543982\pi$
$422$	27.8292	1.35470
$423$	0.852827	0.0414659
$424$	15.9899	0.776540
$425$	42.2114	2.04756
$426$	−3.33897	−0.161773
$427$	−1.98799	−0.0962056
$428$	8.05625	0.389414
$429$	−0.250746	−0.0121061
$430$	54.0458	2.60632
$431$	−23.6079	−1.13715	−0.568576	−	0.822631i	$-0.692505\pi$
$431$	−23.6079	−1.13715	−0.568576	+	0.822631i	$0.692505\pi$
$432$	4.83834	0.232785
$433$	11.9983	0.576600	0.288300	−	0.957540i	$-0.406910\pi$
$433$	11.9983	0.576600	0.288300	+	0.957540i	$0.406910\pi$
$434$	9.55072	0.458449
$435$	17.2057	0.824952
$436$	8.11223	0.388505
$437$	−30.8357	−1.47507
$438$	1.94915	0.0931339
$439$	−9.34054	−0.445799	−0.222900	−	0.974841i	$-0.571552\pi$
$439$	−9.34054	−0.445799	−0.222900	+	0.974841i	$0.571552\pi$
$440$	−9.67069	−0.461032
$441$	−3.04789	−0.145138
$442$	1.28150	0.0609550
$443$	26.2123	1.24538	0.622692	−	0.782467i	$-0.286039\pi$
$443$	26.2123	1.24538	0.622692	+	0.782467i	$0.286039\pi$
$444$	5.01849	0.238167
$445$	−41.8577	−1.98425
$446$	−45.6530	−2.16173
$447$	19.9863	0.945321
$448$	8.73129	0.412514
$449$	−11.4987	−0.542658	−0.271329	−	0.962487i	$-0.587463\pi$
$449$	−11.4987	−0.542658	−0.271329	+	0.962487i	$0.587463\pi$
$450$	21.4571	1.01150
$451$	−2.30573	−0.108572
$452$	−0.0377474	−0.00177549
$453$	15.0434	0.706800
$454$	−23.1138	−1.08479
$455$	2.13315	0.100004
$456$	−8.50722	−0.398387
$457$	34.8251	1.62905	0.814525	−	0.580128i	$-0.196997\pi$
$457$	34.8251	1.62905	0.814525	+	0.580128i	$0.196997\pi$
$458$	−14.8543	−0.694094
$459$	−3.17083	−0.148002
$460$	20.9589	0.977216
$461$	30.9884	1.44327	0.721637	−	0.692272i	$-0.243390\pi$
$461$	30.9884	1.44327	0.721637	+	0.692272i	$0.243390\pi$
$462$	−3.20426	−0.149076
$463$	−3.65194	−0.169720	−0.0848599	−	0.996393i	$-0.527044\pi$
$463$	−3.65194	−0.169720	−0.0848599	+	0.996393i	$0.527044\pi$
$464$	19.4534	0.903103
$465$	−12.7550	−0.591500
$466$	−40.7699	−1.88863
$467$	33.6723	1.55817	0.779084	−	0.626920i	$-0.215685\pi$
$467$	33.6723	1.55817	0.779084	+	0.626920i	$0.215685\pi$
$468$	0.149927	0.00693038
$469$	−26.1934	−1.20950
$470$	5.88230	0.271330
$471$	14.2863	0.658278
$472$	−22.0816	−1.01639
$473$	7.83567	0.360284
$474$	−4.71967	−0.216782
$475$	−50.1141	−2.29939
$476$	3.76907	0.172755
$477$	−7.07558	−0.323969
$478$	−31.0906	−1.42205
$479$	−0.0546621	−0.00249757	−0.00124879	−	0.999999i	$-0.500398\pi$
$479$	−0.0546621	−0.00249757	−0.00124879	+	0.999999i	$0.500398\pi$
$480$	14.0306	0.640406
$481$	−2.10456	−0.0959595
$482$	20.0038	0.911147
$483$	−16.2841	−0.740954
$484$	0.597924	0.0271784
$485$	12.9160	0.586484
$486$	−1.61181	−0.0731131
$487$	16.1791	0.733145	0.366573	−	0.930389i	$-0.380531\pi$
$487$	16.1791	0.733145	0.366573	+	0.930389i	$0.380531\pi$
$488$	2.25988	0.102300
$489$	12.0009	0.542699
$490$	−21.0226	−0.949702
$491$	−0.996030	−0.0449502	−0.0224751	−	0.999747i	$-0.507155\pi$
$491$	−0.996030	−0.0449502	−0.0224751	+	0.999747i	$0.507155\pi$
$492$	1.37865	0.0621544
$493$	−12.7489	−0.574183
$494$	−1.52142	−0.0684521
$495$	4.27930	0.192340
$496$	−14.4213	−0.647535
$497$	4.11825	0.184729
$498$	−19.6346	−0.879846
$499$	−29.3156	−1.31235	−0.656173	−	0.754610i	$-0.727826\pi$
$499$	−29.3156	−1.31235	−0.656173	+	0.754610i	$0.727826\pi$
$500$	21.2690	0.951177
$501$	17.9733	0.802988
$502$	−22.4529	−1.00212
$503$	19.9254	0.888431	0.444216	−	0.895920i	$-0.353482\pi$
$503$	19.9254	0.888431	0.444216	+	0.895920i	$0.353482\pi$
$504$	−4.49261	−0.200117
$505$	24.0853	1.07178
$506$	13.2027	0.586933
$507$	12.9371	0.574558
$508$	3.01855	0.133927
$509$	−32.0673	−1.42136	−0.710679	−	0.703516i	$-0.751612\pi$
$509$	−32.0673	−1.42136	−0.710679	+	0.703516i	$0.751612\pi$
$510$	−21.8705	−0.968443
$511$	−2.40407	−0.106350
$512$	−6.00456	−0.265367
$513$	3.76446	0.166205
$514$	−13.1488	−0.579968
$515$	−69.9228	−3.08117
$516$	−4.68514	−0.206252
$517$	0.852827	0.0375073
$518$	−26.8939	−1.18165
$519$	5.97151	0.262120
$520$	−2.42489	−0.106338
$521$	11.7487	0.514719	0.257360	−	0.966316i	$-0.417148\pi$
$521$	11.7487	0.514719	0.257360	+	0.966316i	$0.417148\pi$
$522$	−6.48058	−0.283647
$523$	7.66102	0.334993	0.167497	−	0.985873i	$-0.446432\pi$
$523$	7.66102	0.334993	0.167497	+	0.985873i	$0.446432\pi$
$524$	11.4242	0.499067
$525$	−26.4650	−1.15503
$526$	−26.8170	−1.16928
$527$	9.45108	0.411696
$528$	4.83834	0.210562
$529$	44.0966	1.91724
$530$	−48.8032	−2.11988
$531$	9.77116	0.424032
$532$	−4.47470	−0.194003
$533$	−0.578151	−0.0250425
$534$	15.7658	0.682253
$535$	57.6580	2.49277
$536$	29.7757	1.28612
$537$	−22.5218	−0.971886
$538$	1.98879	0.0857429
$539$	−3.04789	−0.131282
$540$	−2.55870	−0.110109
$541$	−20.4982	−0.881286	−0.440643	−	0.897682i	$-0.645250\pi$
$541$	−20.4982	−0.881286	−0.440643	+	0.897682i	$0.645250\pi$
$542$	7.22274	0.310243
$543$	16.7687	0.719616
$544$	−10.3962	−0.445736
$545$	58.0586	2.48696
$546$	−0.803455	−0.0343847
$547$	−15.0674	−0.644234	−0.322117	−	0.946700i	$-0.604394\pi$
$547$	−15.0674	−0.644234	−0.322117	+	0.946700i	$0.604394\pi$
$548$	−5.02248	−0.214550
$549$	−1.00000	−0.0426790
$550$	21.4571	0.914932
$551$	15.1357	0.644804
$552$	18.5112	0.787890
$553$	5.82121	0.247543
$554$	35.9812	1.52869
$555$	35.9170	1.52459
$556$	4.21983	0.178961
$557$	22.0552	0.934508	0.467254	−	0.884123i	$-0.345243\pi$
$557$	22.0552	0.934508	0.467254	+	0.884123i	$0.345243\pi$
$558$	4.80420	0.203378
$559$	1.96476	0.0831005
$560$	−41.1607	−1.73936
$561$	−3.17083	−0.133873
$562$	1.94492	0.0820417
$563$	−16.2194	−0.683566	−0.341783	−	0.939779i	$-0.611031\pi$
$563$	−16.2194	−0.683566	−0.341783	+	0.939779i	$0.611031\pi$
$564$	−0.509926	−0.0214718
$565$	−0.270156	−0.0113655
$566$	−20.7566	−0.872466
$567$	1.98799	0.0834878
$568$	−4.68148	−0.196431
$569$	−35.7962	−1.50065	−0.750326	−	0.661068i	$-0.770104\pi$
$569$	−35.7962	−1.50065	−0.750326	+	0.661068i	$0.770104\pi$
$570$	25.9651	1.08756
$571$	−13.2967	−0.556450	−0.278225	−	0.960516i	$-0.589746\pi$
$571$	−13.2967	−0.556450	−0.278225	+	0.960516i	$0.589746\pi$
$572$	0.149927	0.00626876
$573$	−23.1333	−0.966406
$574$	−7.38815	−0.308375
$575$	109.045	4.54751
$576$	4.39201	0.183001
$577$	−19.2277	−0.800462	−0.400231	−	0.916414i	$-0.631070\pi$
$577$	−19.2277	−0.800462	−0.400231	+	0.916414i	$0.631070\pi$
$578$	−11.1953	−0.465665
$579$	−1.54885	−0.0643679
$580$	−10.2877	−0.427175
$581$	24.2171	1.00470
$582$	−4.86482	−0.201653
$583$	−7.07558	−0.293041
$584$	2.73285	0.113086
$585$	1.07302	0.0443638
$586$	5.73447	0.236889
$587$	5.61715	0.231845	0.115922	−	0.993258i	$-0.463018\pi$
$587$	5.61715	0.231845	0.115922	+	0.993258i	$0.463018\pi$
$588$	1.82241	0.0751549
$589$	−11.2205	−0.462332
$590$	67.3957	2.77464
$591$	3.90674	0.160702
$592$	40.6090	1.66902
$593$	18.0517	0.741295	0.370648	−	0.928774i	$-0.379136\pi$
$593$	18.0517	0.741295	0.370648	+	0.928774i	$0.379136\pi$
$594$	−1.61181	−0.0661333
$595$	26.9749	1.10586
$596$	−11.9503	−0.489504
$597$	11.2931	0.462194
$598$	3.31053	0.135378
$599$	0.631254	0.0257923	0.0128962	−	0.999917i	$-0.495895\pi$
$599$	0.631254	0.0257923	0.0128962	+	0.999917i	$0.495895\pi$
$600$	30.0844	1.22819
$601$	21.3195	0.869641	0.434820	−	0.900517i	$-0.356812\pi$
$601$	21.3195	0.869641	0.434820	+	0.900517i	$0.356812\pi$
$602$	25.1075	1.02331
$603$	−13.1758	−0.536561
$604$	−8.99481	−0.365994
$605$	4.27930	0.173978
$606$	−9.07178	−0.368516
$607$	39.8171	1.61613	0.808063	−	0.589096i	$-0.200516\pi$
$607$	39.8171	1.61613	0.808063	+	0.589096i	$0.200516\pi$
$608$	12.3426	0.500559
$609$	7.99309	0.323897
$610$	−6.89741	−0.279268
$611$	0.213843	0.00865115
$612$	1.89592	0.0766379
$613$	43.2039	1.74499	0.872494	−	0.488624i	$-0.162501\pi$
$613$	43.2039	1.74499	0.872494	+	0.488624i	$0.162501\pi$
$614$	25.3074	1.02132
$615$	9.86690	0.397872
$616$	−4.49261	−0.181013
$617$	3.91242	0.157508	0.0787540	−	0.996894i	$-0.474906\pi$
$617$	3.91242	0.157508	0.0787540	+	0.996894i	$0.474906\pi$
$618$	26.3366	1.05941
$619$	24.0600	0.967051	0.483526	−	0.875330i	$-0.339356\pi$
$619$	24.0600	0.967051	0.483526	+	0.875330i	$0.339356\pi$
$620$	7.62654	0.306289
$621$	−8.19125	−0.328704
$622$	−32.8210	−1.31600
$623$	−19.4454	−0.779064
$624$	1.21319	0.0485666
$625$	85.6584	3.42633
$626$	8.66301	0.346243
$627$	3.76446	0.150338
$628$	−8.54213	−0.340868
$629$	−26.6134	−1.06114
$630$	13.7120	0.546299
$631$	−35.3657	−1.40789	−0.703943	−	0.710256i	$-0.748579\pi$
$631$	−35.3657	−1.40789	−0.703943	+	0.710256i	$0.748579\pi$
$632$	−6.61734	−0.263224
$633$	−17.2658	−0.686255
$634$	−5.80251	−0.230447
$635$	21.6036	0.857311
$636$	4.23066	0.167757
$637$	−0.764246	−0.0302805
$638$	−6.48058	−0.256569
$639$	2.07157	0.0819499
$640$	58.3547	2.30667
$641$	−10.9245	−0.431493	−0.215747	−	0.976449i	$-0.569219\pi$
$641$	−10.9245	−0.431493	−0.215747	+	0.976449i	$0.569219\pi$
$642$	−21.7170	−0.857102
$643$	46.6869	1.84115	0.920576	−	0.390564i	$-0.127720\pi$
$643$	46.6869	1.84115	0.920576	+	0.390564i	$0.127720\pi$
$644$	9.73668	0.383679
$645$	−33.5312	−1.32029
$646$	−19.2393	−0.756961
$647$	22.9120	0.900764	0.450382	−	0.892836i	$-0.351288\pi$
$647$	22.9120	0.900764	0.450382	+	0.892836i	$0.351288\pi$
$648$	−2.25988	−0.0887763
$649$	9.77116	0.383551
$650$	5.38027	0.211031
$651$	−5.92547	−0.232237
$652$	−7.17563	−0.281019
$653$	−6.74465	−0.263938	−0.131969	−	0.991254i	$-0.542130\pi$
$653$	−6.74465	−0.263938	−0.131969	+	0.991254i	$0.542130\pi$
$654$	−21.8679	−0.855103
$655$	81.7619	3.19470
$656$	11.1559	0.435564
$657$	−1.20929	−0.0471790
$658$	2.73268	0.106531
$659$	−37.7263	−1.46961	−0.734805	−	0.678279i	$-0.762726\pi$
$659$	−37.7263	−1.46961	−0.734805	+	0.678279i	$0.762726\pi$
$660$	−2.55870	−0.0995972
$661$	40.7549	1.58518	0.792591	−	0.609754i	$-0.208732\pi$
$661$	40.7549	1.58518	0.792591	+	0.609754i	$0.208732\pi$
$662$	57.9930	2.25396
$663$	−0.795073	−0.0308781
$664$	−27.5291	−1.06834
$665$	−32.0251	−1.24188
$666$	−13.5282	−0.524207
$667$	−32.9345	−1.27523
$668$	−10.7467	−0.415801
$669$	28.3241	1.09507
$670$	−90.8791	−3.51096
$671$	−1.00000	−0.0386046
$672$	6.51805	0.251439
$673$	−22.5148	−0.867882	−0.433941	−	0.900941i	$-0.642877\pi$
$673$	−22.5148	−0.867882	−0.433941	+	0.900941i	$0.642877\pi$
$674$	7.73479	0.297933
$675$	−13.3124	−0.512395
$676$	−7.73542	−0.297516
$677$	−0.489159	−0.0187999	−0.00939995	−	0.999956i	$-0.502992\pi$
$677$	−0.489159	−0.0187999	−0.00939995	+	0.999956i	$0.502992\pi$
$678$	0.101755	0.00390787
$679$	6.00024	0.230268
$680$	−30.6641	−1.17592
$681$	14.3403	0.549522
$682$	4.80420	0.183963
$683$	−6.05286	−0.231606	−0.115803	−	0.993272i	$-0.536944\pi$
$683$	−6.05286	−0.231606	−0.115803	+	0.993272i	$0.536944\pi$
$684$	−2.25086	−0.0860640
$685$	−35.9455	−1.37341
$686$	−32.1961	−1.22925
$687$	9.21589	0.351608
$688$	−37.9116	−1.44537
$689$	−1.77417	−0.0675906
$690$	−56.4984	−2.15086
$691$	44.2515	1.68341	0.841704	−	0.539939i	$-0.181553\pi$
$691$	44.2515	1.68341	0.841704	+	0.539939i	$0.181553\pi$
$692$	−3.57051	−0.135730
$693$	1.98799	0.0755175
$694$	6.18804	0.234895
$695$	30.2010	1.14559
$696$	−9.08626	−0.344414
$697$	−7.31107	−0.276927
$698$	0.169797	0.00642691
$699$	25.2945	0.956727
$700$	15.8240	0.598093
$701$	−46.3230	−1.74960	−0.874798	−	0.484488i	$-0.839006\pi$
$701$	−46.3230	−1.74960	−0.874798	+	0.484488i	$0.839006\pi$
$702$	−0.404154	−0.0152538
$703$	31.5958	1.19166
$704$	4.39201	0.165530
$705$	−3.64950	−0.137448
$706$	−55.3670	−2.08376
$707$	11.1891	0.420808
$708$	−5.84241	−0.219571
$709$	−14.4425	−0.542401	−0.271201	−	0.962523i	$-0.587421\pi$
$709$	−14.4425	−0.542401	−0.271201	+	0.962523i	$0.587421\pi$
$710$	14.2884	0.536235
$711$	2.92819	0.109816
$712$	22.1049	0.828414
$713$	24.4151	0.914353
$714$	−10.1602	−0.380235
$715$	1.07302	0.0401286
$716$	13.4663	0.503260
$717$	19.2893	0.720372
$718$	−22.3843	−0.835375
$719$	−24.6340	−0.918693	−0.459346	−	0.888257i	$-0.651916\pi$
$719$	−24.6340	−0.918693	−0.459346	+	0.888257i	$0.651916\pi$
$720$	−20.7047	−0.771618
$721$	−32.4833	−1.20974
$722$	−7.78311	−0.289658
$723$	−12.4108	−0.461561
$724$	−10.0264	−0.372630
$725$	−53.5251	−1.98787
$726$	−1.61181	−0.0598198
$727$	35.6426	1.32191	0.660956	−	0.750425i	$-0.270151\pi$
$727$	35.6426	1.32191	0.660956	+	0.750425i	$0.270151\pi$
$728$	−1.12650	−0.0417510
$729$	1.00000	0.0370370
$730$	−8.34100	−0.308714
$731$	24.8456	0.918947
$732$	0.597924	0.0220999
$733$	14.8831	0.549720	0.274860	−	0.961484i	$-0.411369\pi$
$733$	14.8831	0.549720	0.274860	+	0.961484i	$0.411369\pi$
$734$	−19.7102	−0.727518
$735$	13.0428	0.481093
$736$	−26.8568	−0.989953
$737$	−13.1758	−0.485338
$738$	−3.71639	−0.136802
$739$	−14.9543	−0.550104	−0.275052	−	0.961429i	$-0.588695\pi$
$739$	−14.9543	−0.550104	−0.275052	+	0.961429i	$0.588695\pi$
$740$	−21.4756	−0.789460
$741$	0.943924	0.0346759
$742$	−22.6720	−0.832315
$743$	−17.4486	−0.640126	−0.320063	−	0.947396i	$-0.603704\pi$
$743$	−17.4486	−0.640126	−0.320063	+	0.947396i	$0.603704\pi$
$744$	6.73586	0.246949
$745$	−85.5275	−3.13348
$746$	39.2064	1.43545
$747$	12.1817	0.445705
$748$	1.89592	0.0693216
$749$	26.7856	0.978724
$750$	−57.3342	−2.09355
$751$	21.2302	0.774700	0.387350	−	0.921933i	$-0.373390\pi$
$751$	21.2302	0.774700	0.387350	+	0.921933i	$0.373390\pi$
$752$	−4.12626	−0.150469
$753$	13.9303	0.507647
$754$	−1.62498	−0.0591782
$755$	−64.3752	−2.34285
$756$	−1.18867	−0.0432315
$757$	39.8953	1.45002	0.725010	−	0.688739i	$-0.241835\pi$
$757$	39.8953	1.45002	0.725010	+	0.688739i	$0.241835\pi$
$758$	3.76599	0.136787
$759$	−8.19125	−0.297324
$760$	36.4050	1.32055
$761$	24.3669	0.883301	0.441651	−	0.897187i	$-0.354393\pi$
$761$	24.3669	0.883301	0.441651	+	0.897187i	$0.354393\pi$
$762$	−8.13703	−0.294773
$763$	26.9717	0.976441
$764$	13.8319	0.500422
$765$	13.5689	0.490586
$766$	−48.0827	−1.73730
$767$	2.45008	0.0884671
$768$	−13.1954	−0.476148
$769$	16.9871	0.612572	0.306286	−	0.951940i	$-0.400914\pi$
$769$	16.9871	0.612572	0.306286	+	0.951940i	$0.400914\pi$
$770$	13.7120	0.494146
$771$	8.15779	0.293795
$772$	0.926094	0.0333309
$773$	50.0956	1.80181	0.900907	−	0.434012i	$-0.142903\pi$
$773$	50.0956	1.80181	0.900907	+	0.434012i	$0.142903\pi$
$774$	12.6296	0.453961
$775$	39.6794	1.42533
$776$	−6.82085	−0.244854
$777$	16.6856	0.598592
$778$	7.93244	0.284392
$779$	8.67983	0.310987
$780$	−0.641583	−0.0229724
$781$	2.07157	0.0741264
$782$	41.8636	1.49704
$783$	4.02069	0.143688
$784$	14.7467	0.526669
$785$	−61.1354	−2.18202
$786$	−30.7958	−1.09845
$787$	−38.7557	−1.38149	−0.690746	−	0.723098i	$-0.742718\pi$
$787$	−38.7557	−1.38149	−0.690746	+	0.723098i	$0.742718\pi$
$788$	−2.33594	−0.0832143
$789$	16.6378	0.592323
$790$	20.1969	0.718573
$791$	−0.125503	−0.00446239
$792$	−2.25988	−0.0803012
$793$	−0.250746	−0.00890424
$794$	−8.15792	−0.289514
$795$	30.2785	1.07387
$796$	−6.75240	−0.239332
$797$	44.4888	1.57588	0.787938	−	0.615755i	$-0.211149\pi$
$797$	44.4888	1.57588	0.787938	+	0.615755i	$0.211149\pi$
$798$	12.0623	0.427002
$799$	2.70417	0.0956667
$800$	−43.6476	−1.54318
$801$	−9.78144	−0.345610
$802$	2.50380	0.0884122
$803$	−1.20929	−0.0426750
$804$	7.87815	0.277841
$805$	69.6847	2.45606
$806$	1.20463	0.0424314
$807$	−1.23389	−0.0434349
$808$	−12.7193	−0.447464
$809$	−38.6506	−1.35888	−0.679442	−	0.733729i	$-0.737778\pi$
$809$	−38.6506	−1.35888	−0.679442	+	0.733729i	$0.737778\pi$
$810$	6.89741	0.242350
$811$	19.9320	0.699906	0.349953	−	0.936767i	$-0.386198\pi$
$811$	19.9320	0.699906	0.349953	+	0.936767i	$0.386198\pi$
$812$	−4.77927	−0.167719
$813$	−4.48114	−0.157160
$814$	−13.5282	−0.474163
$815$	−51.3554	−1.79890
$816$	15.3415	0.537062
$817$	−29.4971	−1.03197
$818$	−13.5846	−0.474975
$819$	0.498480	0.0174183
$820$	−5.89966	−0.206025
$821$	17.0881	0.596379	0.298189	−	0.954507i	$-0.403617\pi$
$821$	17.0881	0.596379	0.298189	+	0.954507i	$0.403617\pi$
$822$	13.5390	0.472226
$823$	−16.4950	−0.574980	−0.287490	−	0.957784i	$-0.592821\pi$
$823$	−16.4950	−0.574980	−0.287490	+	0.957784i	$0.592821\pi$
$824$	36.9259	1.28637
$825$	−13.3124	−0.463479
$826$	31.3093	1.08939
$827$	3.49254	0.121447	0.0607237	−	0.998155i	$-0.480659\pi$
$827$	3.49254	0.121447	0.0607237	+	0.998155i	$0.480659\pi$
$828$	4.89775	0.170209
$829$	5.26456	0.182846	0.0914228	−	0.995812i	$-0.470859\pi$
$829$	5.26456	0.182846	0.0914228	+	0.995812i	$0.470859\pi$
$830$	84.0222	2.91645
$831$	−22.3235	−0.774393
$832$	1.10128	0.0381800
$833$	−9.66435	−0.334850
$834$	−11.3753	−0.393894
$835$	−76.9132	−2.66169
$836$	−2.25086	−0.0778478
$837$	−2.98063	−0.103026
$838$	−52.5989	−1.81700
$839$	22.8286	0.788130	0.394065	−	0.919083i	$-0.371068\pi$
$839$	22.8286	0.788130	0.394065	+	0.919083i	$0.371068\pi$
$840$	19.2252	0.663334
$841$	−12.8341	−0.442554
$842$	−9.11018	−0.313958
$843$	−1.20667	−0.0415600
$844$	10.3237	0.355355
$845$	−55.3619	−1.90451
$846$	1.37459	0.0472595
$847$	1.98799	0.0683082
$848$	34.2340	1.17560
$849$	12.8779	0.441967
$850$	68.0367	2.33364
$851$	−68.7507	−2.35674
$852$	−1.23864	−0.0424351
$853$	28.5640	0.978014	0.489007	−	0.872280i	$-0.337359\pi$
$853$	28.5640	0.978014	0.489007	+	0.872280i	$0.337359\pi$
$854$	−3.20426	−0.109648
$855$	−16.1093	−0.550926
$856$	−30.4489	−1.04072
$857$	15.5911	0.532582	0.266291	−	0.963893i	$-0.414202\pi$
$857$	15.5911	0.532582	0.266291	+	0.963893i	$0.414202\pi$
$858$	−0.404154	−0.0137976
$859$	−4.92436	−0.168017	−0.0840085	−	0.996465i	$-0.526772\pi$
$859$	−4.92436	−0.168017	−0.0840085	+	0.996465i	$0.526772\pi$
$860$	20.0491	0.683669
$861$	4.58377	0.156214
$862$	−38.0514	−1.29603
$863$	29.5907	1.00728	0.503640	−	0.863914i	$-0.331994\pi$
$863$	29.5907	1.00728	0.503640	+	0.863914i	$0.331994\pi$
$864$	3.27871	0.111544
$865$	−25.5539	−0.868858
$866$	19.3389	0.657163
$867$	6.94583	0.235893
$868$	3.54298	0.120257
$869$	2.92819	0.0993319
$870$	27.7323	0.940214
$871$	−3.30378	−0.111944
$872$	−30.6605	−1.03829
$873$	3.01824	0.102152
$874$	−49.7012	−1.68117
$875$	70.7155	2.39062
$876$	0.723066	0.0244301
$877$	−57.3331	−1.93600	−0.968001	−	0.250947i	$-0.919258\pi$
$877$	−57.3331	−1.93600	−0.968001	+	0.250947i	$0.919258\pi$
$878$	−15.0551	−0.508087
$879$	−3.55779	−0.120001
$880$	−20.7047	−0.697955
$881$	−8.30122	−0.279675	−0.139838	−	0.990174i	$-0.544658\pi$
$881$	−8.30122	−0.279675	−0.139838	+	0.990174i	$0.544658\pi$
$882$	−4.91261	−0.165416
$883$	−8.59069	−0.289100	−0.144550	−	0.989498i	$-0.546173\pi$
$883$	−8.59069	−0.289100	−0.144550	+	0.989498i	$0.546173\pi$
$884$	0.475393	0.0159892
$885$	−41.8137	−1.40555
$886$	42.2492	1.41939
$887$	26.4726	0.888864	0.444432	−	0.895813i	$-0.353405\pi$
$887$	26.4726	0.888864	0.444432	+	0.895813i	$0.353405\pi$
$888$	−18.9676	−0.636510
$889$	10.0361	0.336602
$890$	−67.4666	−2.26149
$891$	1.00000	0.0335013
$892$	−16.9357	−0.567048
$893$	−3.21044	−0.107433
$894$	32.2141	1.07740
$895$	96.3774	3.22154
$896$	27.1093	0.905657
$897$	−2.05392	−0.0685784
$898$	−18.5337	−0.618478
$899$	−11.9842	−0.399695
$900$	7.95982	0.265327
$901$	−22.4355	−0.747434
$902$	−3.71639	−0.123742
$903$	−15.5772	−0.518378
$904$	0.142668	0.00474506
$905$	−71.7585	−2.38533
$906$	24.2471	0.805555
$907$	54.7146	1.81677	0.908384	−	0.418136i	$-0.137316\pi$
$907$	54.7146	1.81677	0.908384	+	0.418136i	$0.137316\pi$
$908$	−8.57442	−0.284552
$909$	5.62832	0.186680
$910$	3.43822	0.113976
$911$	−14.0636	−0.465947	−0.232974	−	0.972483i	$-0.574846\pi$
$911$	−14.0636	−0.465947	−0.232974	+	0.972483i	$0.574846\pi$
$912$	−18.2137	−0.603117
$913$	12.1817	0.403156
$914$	56.1314	1.85666
$915$	4.27930	0.141469
$916$	−5.51041	−0.182069
$917$	37.9833	1.25432
$918$	−5.11077	−0.168681
$919$	−18.8036	−0.620274	−0.310137	−	0.950692i	$-0.600375\pi$
$919$	−18.8036	−0.620274	−0.310137	+	0.950692i	$0.600375\pi$
$920$	−79.2151	−2.61164
$921$	−15.7013	−0.517374
$922$	49.9474	1.64493
$923$	0.519436	0.0170975
$924$	−1.18867	−0.0391043
$925$	−111.734	−3.67378
$926$	−5.88622	−0.193433
$927$	−16.3398	−0.536669
$928$	13.1827	0.432743
$929$	13.3631	0.438429	0.219214	−	0.975677i	$-0.429651\pi$
$929$	13.3631	0.438429	0.219214	+	0.975677i	$0.429651\pi$
$930$	−20.5586	−0.674144
$931$	11.4737	0.376035
$932$	−15.1242	−0.495410
$933$	20.3629	0.666650
$934$	54.2732	1.77587
$935$	13.5689	0.443752
$936$	−0.566654	−0.0185217
$937$	7.26525	0.237345	0.118673	−	0.992933i	$-0.462136\pi$
$937$	7.26525	0.237345	0.118673	+	0.992933i	$0.462136\pi$
$938$	−42.2188	−1.37849
$939$	−5.37471	−0.175397
$940$	2.18213	0.0711731
$941$	25.5547	0.833061	0.416530	−	0.909122i	$-0.363246\pi$
$941$	25.5547	0.833061	0.416530	+	0.909122i	$0.363246\pi$
$942$	23.0268	0.750253
$943$	−18.8868	−0.615038
$944$	−47.2761	−1.53871
$945$	−8.50721	−0.276740
$946$	12.6296	0.410623
$947$	−29.0368	−0.943570	−0.471785	−	0.881714i	$-0.656390\pi$
$947$	−29.0368	−0.943570	−0.471785	+	0.881714i	$0.656390\pi$
$948$	−1.75083	−0.0568644
$949$	−0.303225	−0.00984311
$950$	−80.7743	−2.62067
$951$	3.60000	0.116738
$952$	−14.2453	−0.461694
$953$	41.2250	1.33541	0.667705	−	0.744426i	$-0.267277\pi$
$953$	41.2250	1.33541	0.667705	+	0.744426i	$0.267277\pi$
$954$	−11.4045	−0.369234
$955$	98.9942	3.20338
$956$	−11.5335	−0.373021
$957$	4.02069	0.129970
$958$	−0.0881048	−0.00284654
$959$	−16.6989	−0.539234
$960$	−18.7948	−0.606598
$961$	−22.1158	−0.713414
$962$	−3.39214	−0.109367
$963$	13.4737	0.434184
$964$	7.42070	0.239005
$965$	6.62799	0.213362
$966$	−26.2469	−0.844480
$967$	13.8906	0.446690	0.223345	−	0.974739i	$-0.428302\pi$
$967$	13.8906	0.446690	0.223345	+	0.974739i	$0.428302\pi$
$968$	−2.25988	−0.0726352
$969$	11.9365	0.383455
$970$	20.8180	0.668427
$971$	−32.4127	−1.04017	−0.520086	−	0.854114i	$-0.674100\pi$
$971$	−32.4127	−1.04017	−0.520086	+	0.854114i	$0.674100\pi$
$972$	−0.597924	−0.0191784
$973$	14.0302	0.449787
$974$	26.0776	0.835580
$975$	−3.33803	−0.106903
$976$	4.83834	0.154871
$977$	32.1328	1.02802	0.514010	−	0.857784i	$-0.328159\pi$
$977$	32.1328	1.02802	0.514010	+	0.857784i	$0.328159\pi$
$978$	19.3431	0.618525
$979$	−9.78144	−0.312616
$980$	−7.79863	−0.249118
$981$	13.5673	0.433171
$982$	−1.60541	−0.0512307
$983$	3.66030	0.116745	0.0583727	−	0.998295i	$-0.481409\pi$
$983$	3.66030	0.116745	0.0583727	+	0.998295i	$0.481409\pi$
$984$	−5.21066	−0.166110
$985$	−16.7181	−0.532684
$986$	−20.5488	−0.654408
$987$	−1.69541	−0.0539656
$988$	−0.564395	−0.0179558
$989$	64.1839	2.04093
$990$	6.89741	0.219214
$991$	−23.8517	−0.757674	−0.378837	−	0.925463i	$-0.623676\pi$
$991$	−23.8517	−0.757674	−0.378837	+	0.925463i	$0.623676\pi$
$992$	−9.77264	−0.310282
$993$	−35.9801	−1.14179
$994$	6.63783	0.210539
$995$	−48.3264	−1.53205
$996$	−7.28374	−0.230794
$997$	−54.6646	−1.73124	−0.865622	−	0.500698i	$-0.833077\pi$
$997$	−54.6646	−1.73124	−0.865622	+	0.500698i	$0.833077\pi$
$998$	−47.2511	−1.49571
$999$	8.39318	0.265549

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.e.1.10	✓	13
3.2	odd	2		6039.2.a.i.1.4		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.e.1.10	✓	13	1.1	even	1	trivial
6039.2.a.i.1.4		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)

\(f(q)\)	\(=\)	\(q+1.61181 q^{2} -1.00000 q^{3} +0.597924 q^{4} +4.27930 q^{5} -1.61181 q^{6} +1.98799 q^{7} -2.25988 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.61181 q^{2} -1.00000 q^{3} +0.597924 q^{4} +4.27930 q^{5} -1.61181 q^{6} +1.98799 q^{7} -2.25988 q^{8} +1.00000 q^{9} +6.89741 q^{10} +1.00000 q^{11} -0.597924 q^{12} +0.250746 q^{13} +3.20426 q^{14} -4.27930 q^{15} -4.83834 q^{16} +3.17083 q^{17} +1.61181 q^{18} -3.76446 q^{19} +2.55870 q^{20} -1.98799 q^{21} +1.61181 q^{22} +8.19125 q^{23} +2.25988 q^{24} +13.3124 q^{25} +0.404154 q^{26} -1.00000 q^{27} +1.18867 q^{28} -4.02069 q^{29} -6.89741 q^{30} +2.98063 q^{31} -3.27871 q^{32} -1.00000 q^{33} +5.11077 q^{34} +8.50721 q^{35} +0.597924 q^{36} -8.39318 q^{37} -6.06759 q^{38} -0.250746 q^{39} -9.67069 q^{40} -2.30573 q^{41} -3.20426 q^{42} +7.83567 q^{43} +0.597924 q^{44} +4.27930 q^{45} +13.2027 q^{46} +0.852827 q^{47} +4.83834 q^{48} -3.04789 q^{49} +21.4571 q^{50} -3.17083 q^{51} +0.149927 q^{52} -7.07558 q^{53} -1.61181 q^{54} +4.27930 q^{55} -4.49261 q^{56} +3.76446 q^{57} -6.48058 q^{58} +9.77116 q^{59} -2.55870 q^{60} -1.00000 q^{61} +4.80420 q^{62} +1.98799 q^{63} +4.39201 q^{64} +1.07302 q^{65} -1.61181 q^{66} -13.1758 q^{67} +1.89592 q^{68} -8.19125 q^{69} +13.7120 q^{70} +2.07157 q^{71} -2.25988 q^{72} -1.20929 q^{73} -13.5282 q^{74} -13.3124 q^{75} -2.25086 q^{76} +1.98799 q^{77} -0.404154 q^{78} +2.92819 q^{79} -20.7047 q^{80} +1.00000 q^{81} -3.71639 q^{82} +12.1817 q^{83} -1.18867 q^{84} +13.5689 q^{85} +12.6296 q^{86} +4.02069 q^{87} -2.25988 q^{88} -9.78144 q^{89} +6.89741 q^{90} +0.498480 q^{91} +4.89775 q^{92} -2.98063 q^{93} +1.37459 q^{94} -16.1093 q^{95} +3.27871 q^{96} +3.01824 q^{97} -4.91261 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9} + 6 q^{10} + 13 q^{11} - 16 q^{12} + 13 q^{13} + q^{14} - 3 q^{15} + 18 q^{16} + 17 q^{17} + 2 q^{18} + 14 q^{19} - 7 q^{20} - 11 q^{21} + 2 q^{22} + 7 q^{23} - 9 q^{24} + 18 q^{25} - 10 q^{26} - 13 q^{27} + 19 q^{28} - 6 q^{29} - 6 q^{30} + 27 q^{31} + 5 q^{32} - 13 q^{33} + 6 q^{34} + 14 q^{35} + 16 q^{36} + 10 q^{37} + 2 q^{38} - 13 q^{39} + 8 q^{40} + 3 q^{41} - q^{42} + 29 q^{43} + 16 q^{44} + 3 q^{45} - 24 q^{46} + 8 q^{47} - 18 q^{48} + 8 q^{49} - 27 q^{50} - 17 q^{51} + 37 q^{52} - 24 q^{53} - 2 q^{54} + 3 q^{55} + 24 q^{56} - 14 q^{57} - 5 q^{58} + 13 q^{59} + 7 q^{60} - 13 q^{61} + 39 q^{62} + 11 q^{63} + 47 q^{64} - 11 q^{65} - 2 q^{66} + 44 q^{67} - 8 q^{68} - 7 q^{69} - 12 q^{70} + 3 q^{71} + 9 q^{72} + 48 q^{73} - 22 q^{74} - 18 q^{75} + 47 q^{76} + 11 q^{77} + 10 q^{78} - 17 q^{79} - 26 q^{80} + 13 q^{81} + 56 q^{82} + 50 q^{83} - 19 q^{84} + 8 q^{85} + 18 q^{86} + 6 q^{87} + 9 q^{88} - 15 q^{89} + 6 q^{90} + 47 q^{91} + 14 q^{92} - 27 q^{93} + 45 q^{94} - q^{95} - 5 q^{96} + 27 q^{97} + 47 q^{98} + 13 q^{99}+O(q^{100}) \) 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9 + 6 * q^10 + 13 * q^11 - 16 * q^12 + 13 * q^13 + q^14 - 3 * q^15 + 18 * q^16 + 17 * q^17 + 2 * q^18 + 14 * q^19 - 7 * q^20 - 11 * q^21 + 2 * q^22 + 7 * q^23 - 9 * q^24 + 18 * q^25 - 10 * q^26 - 13 * q^27 + 19 * q^28 - 6 * q^29 - 6 * q^30 + 27 * q^31 + 5 * q^32 - 13 * q^33 + 6 * q^34 + 14 * q^35 + 16 * q^36 + 10 * q^37 + 2 * q^38 - 13 * q^39 + 8 * q^40 + 3 * q^41 - q^42 + 29 * q^43 + 16 * q^44 + 3 * q^45 - 24 * q^46 + 8 * q^47 - 18 * q^48 + 8 * q^49 - 27 * q^50 - 17 * q^51 + 37 * q^52 - 24 * q^53 - 2 * q^54 + 3 * q^55 + 24 * q^56 - 14 * q^57 - 5 * q^58 + 13 * q^59 + 7 * q^60 - 13 * q^61 + 39 * q^62 + 11 * q^63 + 47 * q^64 - 11 * q^65 - 2 * q^66 + 44 * q^67 - 8 * q^68 - 7 * q^69 - 12 * q^70 + 3 * q^71 + 9 * q^72 + 48 * q^73 - 22 * q^74 - 18 * q^75 + 47 * q^76 + 11 * q^77 + 10 * q^78 - 17 * q^79 - 26 * q^80 + 13 * q^81 + 56 * q^82 + 50 * q^83 - 19 * q^84 + 8 * q^85 + 18 * q^86 + 6 * q^87 + 9 * q^88 - 15 * q^89 + 6 * q^90 + 47 * q^91 + 14 * q^92 - 27 * q^93 + 45 * q^94 - q^95 - 5 * q^96 + 27 * q^97 + 47 * q^98 + 13 * q^99

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