LMFDB - Embedded newform 667.2.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,2,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	667.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:	$5.32602181482$
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} + 58 x^{10} + 24 x^{9} - 298 x^{8} + 97 x^{7} + 641 x^{6} - 402 x^{5} + \cdots - 40 $ x^13 - 4x^12 - 11x^11 + 58x^10 + 24x^9 - 298x^8 + 97x^7 + 641x^6 - 402x^5 - 547x^4 + 352x^3 + 219x^2 - 88x - 40
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.78056$ of defining polynomial
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.78056 q^{2} +3.14895 q^{3} +1.17038 q^{4} +0.267809 q^{5} -5.60688 q^{6} +2.76268 q^{7} +1.47718 q^{8} +6.91588 q^{9} +O(q^{10})$	\(q-1.78056 q^{2} +3.14895 q^{3} +1.17038 q^{4} +0.267809 q^{5} -5.60688 q^{6} +2.76268 q^{7} +1.47718 q^{8} +6.91588 q^{9} -0.476849 q^{10} +3.66332 q^{11} +3.68547 q^{12} -0.303708 q^{13} -4.91910 q^{14} +0.843317 q^{15} -4.97097 q^{16} -2.93822 q^{17} -12.3141 q^{18} -3.32970 q^{19} +0.313439 q^{20} +8.69953 q^{21} -6.52275 q^{22} -1.00000 q^{23} +4.65157 q^{24} -4.92828 q^{25} +0.540769 q^{26} +12.3309 q^{27} +3.23339 q^{28} +1.00000 q^{29} -1.50157 q^{30} -2.17124 q^{31} +5.89673 q^{32} +11.5356 q^{33} +5.23166 q^{34} +0.739869 q^{35} +8.09422 q^{36} +3.32895 q^{37} +5.92871 q^{38} -0.956360 q^{39} +0.395602 q^{40} -5.47369 q^{41} -15.4900 q^{42} -1.76814 q^{43} +4.28748 q^{44} +1.85213 q^{45} +1.78056 q^{46} +2.08606 q^{47} -15.6533 q^{48} +0.632383 q^{49} +8.77508 q^{50} -9.25230 q^{51} -0.355454 q^{52} +1.14068 q^{53} -21.9559 q^{54} +0.981069 q^{55} +4.08097 q^{56} -10.4850 q^{57} -1.78056 q^{58} +9.61571 q^{59} +0.987003 q^{60} -9.75926 q^{61} +3.86601 q^{62} +19.1063 q^{63} -0.557525 q^{64} -0.0813356 q^{65} -20.5398 q^{66} -9.96357 q^{67} -3.43884 q^{68} -3.14895 q^{69} -1.31738 q^{70} +3.49473 q^{71} +10.2160 q^{72} -6.63498 q^{73} -5.92739 q^{74} -15.5189 q^{75} -3.89702 q^{76} +10.1206 q^{77} +1.70285 q^{78} +15.8347 q^{79} -1.33127 q^{80} +18.0818 q^{81} +9.74622 q^{82} +3.96876 q^{83} +10.1818 q^{84} -0.786881 q^{85} +3.14827 q^{86} +3.14895 q^{87} +5.41138 q^{88} +15.6943 q^{89} -3.29783 q^{90} -0.839046 q^{91} -1.17038 q^{92} -6.83711 q^{93} -3.71434 q^{94} -0.891722 q^{95} +18.5685 q^{96} -1.64194 q^{97} -1.12599 q^{98} +25.3351 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) $ 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9} + 10 q^{10} + 10 q^{11} + 3 q^{12} + 7 q^{13} - 12 q^{14} + 8 q^{15} + 2 q^{16} + 26 q^{17} + 7 q^{18} + 25 q^{20} + 11 q^{21} - 15 q^{22} - 13 q^{23} + 10 q^{24} + 19 q^{25} - 15 q^{26} + 12 q^{27} + 5 q^{28} + 13 q^{29} + 7 q^{30} - 6 q^{31} + 16 q^{32} + 3 q^{33} + 11 q^{34} + q^{35} - 22 q^{36} + 15 q^{37} + 8 q^{38} - 4 q^{39} + 14 q^{40} + 9 q^{41} - 34 q^{42} + q^{43} + 29 q^{44} + 16 q^{45} - 4 q^{46} + 15 q^{47} - 15 q^{48} + 4 q^{49} + 31 q^{50} - 14 q^{51} - 8 q^{52} + 43 q^{53} - 35 q^{54} - 3 q^{55} - 5 q^{56} + 6 q^{57} + 4 q^{58} - 9 q^{59} + 3 q^{60} + 20 q^{61} + 11 q^{62} + 21 q^{63} - 16 q^{64} - 25 q^{65} - q^{66} + q^{67} + 21 q^{68} - 3 q^{69} - 2 q^{70} + 17 q^{71} - 59 q^{72} + 26 q^{73} + 11 q^{74} - 43 q^{75} + 8 q^{76} + 17 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{80} - 3 q^{81} - 25 q^{82} + 4 q^{83} - 78 q^{84} + 20 q^{85} - 13 q^{86} + 3 q^{87} - 32 q^{88} + 48 q^{89} + 17 q^{90} - 9 q^{91} - 12 q^{92} - 8 q^{93} - 65 q^{94} + 8 q^{95} + 8 q^{96} + 30 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9 + 10 * q^10 + 10 * q^11 + 3 * q^12 + 7 * q^13 - 12 * q^14 + 8 * q^15 + 2 * q^16 + 26 * q^17 + 7 * q^18 + 25 * q^20 + 11 * q^21 - 15 * q^22 - 13 * q^23 + 10 * q^24 + 19 * q^25 - 15 * q^26 + 12 * q^27 + 5 * q^28 + 13 * q^29 + 7 * q^30 - 6 * q^31 + 16 * q^32 + 3 * q^33 + 11 * q^34 + q^35 - 22 * q^36 + 15 * q^37 + 8 * q^38 - 4 * q^39 + 14 * q^40 + 9 * q^41 - 34 * q^42 + q^43 + 29 * q^44 + 16 * q^45 - 4 * q^46 + 15 * q^47 - 15 * q^48 + 4 * q^49 + 31 * q^50 - 14 * q^51 - 8 * q^52 + 43 * q^53 - 35 * q^54 - 3 * q^55 - 5 * q^56 + 6 * q^57 + 4 * q^58 - 9 * q^59 + 3 * q^60 + 20 * q^61 + 11 * q^62 + 21 * q^63 - 16 * q^64 - 25 * q^65 - q^66 + q^67 + 21 * q^68 - 3 * q^69 - 2 * q^70 + 17 * q^71 - 59 * q^72 + 26 * q^73 + 11 * q^74 - 43 * q^75 + 8 * q^76 + 17 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^80 - 3 * q^81 - 25 * q^82 + 4 * q^83 - 78 * q^84 + 20 * q^85 - 13 * q^86 + 3 * q^87 - 32 * q^88 + 48 * q^89 + 17 * q^90 - 9 * q^91 - 12 * q^92 - 8 * q^93 - 65 * q^94 + 8 * q^95 + 8 * q^96 + 30 * q^97 + 2 * q^98 + 4 * 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 $

$2$	−1.78056	−1.25904	−0.629522	−	0.776983i	$-0.716749\pi$
$2$	−1.78056	−1.25904	−0.629522	+	0.776983i	$0.716749\pi$
$3$	3.14895	1.81805	0.909023	−	0.416745i	$-0.136829\pi$
$3$	3.14895	1.81805	0.909023	+	0.416745i	$0.136829\pi$
$4$	1.17038	0.585191
$5$	0.267809	0.119768	0.0598839	−	0.998205i	$-0.480927\pi$
$5$	0.267809	0.119768	0.0598839	+	0.998205i	$0.480927\pi$
$6$	−5.60688	−2.28900
$7$	2.76268	1.04419	0.522097	−	0.852886i	$-0.325150\pi$
$7$	2.76268	1.04419	0.522097	+	0.852886i	$0.325150\pi$
$8$	1.47718	0.522262
$9$	6.91588	2.30529
$10$	−0.476849	−0.150793
$11$	3.66332	1.10453	0.552266	−	0.833668i	$-0.313763\pi$
$11$	3.66332	1.10453	0.552266	+	0.833668i	$0.313763\pi$
$12$	3.68547	1.06390
$13$	−0.303708	−0.0842334	−0.0421167	−	0.999113i	$-0.513410\pi$
$13$	−0.303708	−0.0842334	−0.0421167	+	0.999113i	$0.513410\pi$
$14$	−4.91910	−1.31469
$15$	0.843317	0.217743
$16$	−4.97097	−1.24274
$17$	−2.93822	−0.712623	−0.356311	−	0.934367i	$-0.615966\pi$
$17$	−2.93822	−0.712623	−0.356311	+	0.934367i	$0.615966\pi$
$18$	−12.3141	−2.90247
$19$	−3.32970	−0.763885	−0.381942	−	0.924186i	$-0.624745\pi$
$19$	−3.32970	−0.763885	−0.381942	+	0.924186i	$0.624745\pi$
$20$	0.313439	0.0700871
$21$	8.69953	1.89839
$22$	−6.52275	−1.39065
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	4.65157	0.949498
$25$	−4.92828	−0.985656
$26$	0.540769	0.106054
$27$	12.3309	2.37308
$28$	3.23339	0.611053
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−1.50157	−0.274149
$31$	−2.17124	−0.389965	−0.194983	−	0.980807i	$-0.562465\pi$
$31$	−2.17124	−0.389965	−0.194983	+	0.980807i	$0.562465\pi$
$32$	5.89673	1.04240
$33$	11.5356	2.00809
$34$	5.23166	0.897223
$35$	0.739869	0.125061
$36$	8.09422	1.34904
$37$	3.32895	0.547277	0.273638	−	0.961833i	$-0.411773\pi$
$37$	3.32895	0.547277	0.273638	+	0.961833i	$0.411773\pi$
$38$	5.92871	0.961764
$39$	−0.956360	−0.153140
$40$	0.395602	0.0625502
$41$	−5.47369	−0.854847	−0.427424	−	0.904051i	$-0.640579\pi$
$41$	−5.47369	−0.854847	−0.427424	+	0.904051i	$0.640579\pi$
$42$	−15.4900	−2.39016
$43$	−1.76814	−0.269638	−0.134819	−	0.990870i	$-0.543045\pi$
$43$	−1.76814	−0.269638	−0.134819	+	0.990870i	$0.543045\pi$
$44$	4.28748	0.646362
$45$	1.85213	0.276100
$46$	1.78056	0.262529
$47$	2.08606	0.304283	0.152141	−	0.988359i	$-0.451383\pi$
$47$	2.08606	0.304283	0.152141	+	0.988359i	$0.451383\pi$
$48$	−15.6533	−2.25936
$49$	0.632383	0.0903404
$50$	8.77508	1.24098
$51$	−9.25230	−1.29558
$52$	−0.355454	−0.0492926
$53$	1.14068	0.156685	0.0783425	−	0.996927i	$-0.475037\pi$
$53$	1.14068	0.156685	0.0783425	+	0.996927i	$0.475037\pi$
$54$	−21.9559	−2.98782
$55$	0.981069	0.132287
$56$	4.08097	0.545343
$57$	−10.4850	−1.38878
$58$	−1.78056	−0.233799
$59$	9.61571	1.25186	0.625929	−	0.779880i	$-0.284720\pi$
$59$	9.61571	1.25186	0.625929	+	0.779880i	$0.284720\pi$
$60$	0.987003	0.127422
$61$	−9.75926	−1.24954	−0.624772	−	0.780807i	$-0.714808\pi$
$61$	−9.75926	−1.24954	−0.624772	+	0.780807i	$0.714808\pi$
$62$	3.86601	0.490983
$63$	19.1063	2.40717
$64$	−0.557525	−0.0696906
$65$	−0.0813356	−0.0100884
$66$	−20.5398	−2.52827
$67$	−9.96357	−1.21724	−0.608622	−	0.793460i	$-0.708277\pi$
$67$	−9.96357	−1.21724	−0.608622	+	0.793460i	$0.708277\pi$
$68$	−3.43884	−0.417020
$69$	−3.14895	−0.379089
$70$	−1.31738	−0.157457
$71$	3.49473	0.414748	0.207374	−	0.978262i	$-0.433508\pi$
$71$	3.49473	0.414748	0.207374	+	0.978262i	$0.433508\pi$
$72$	10.2160	1.20397
$73$	−6.63498	−0.776566	−0.388283	−	0.921540i	$-0.626932\pi$
$73$	−6.63498	−0.776566	−0.388283	+	0.921540i	$0.626932\pi$
$74$	−5.92739	−0.689045
$75$	−15.5189	−1.79197
$76$	−3.89702	−0.447019
$77$	10.1206	1.15335
$78$	1.70285	0.192810
$79$	15.8347	1.78154	0.890772	−	0.454451i	$-0.150164\pi$
$79$	15.8347	1.78154	0.890772	+	0.454451i	$0.150164\pi$
$80$	−1.33127	−0.148841
$81$	18.0818	2.00908
$82$	9.74622	1.07629
$83$	3.96876	0.435628	0.217814	−	0.975990i	$-0.430107\pi$
$83$	3.96876	0.435628	0.217814	+	0.975990i	$0.430107\pi$
$84$	10.1818	1.11092
$85$	−0.786881	−0.0853492
$86$	3.14827	0.339486
$87$	3.14895	0.337603
$88$	5.41138	0.576856
$89$	15.6943	1.66359	0.831795	−	0.555084i	$-0.187314\pi$
$89$	15.6943	1.66359	0.831795	+	0.555084i	$0.187314\pi$
$90$	−3.29783	−0.347622
$91$	−0.839046	−0.0879560
$92$	−1.17038	−0.122021
$93$	−6.83711	−0.708975
$94$	−3.71434	−0.383105
$95$	−0.891722	−0.0914888
$96$	18.5685	1.89514
$97$	−1.64194	−0.166713	−0.0833566	−	0.996520i	$-0.526564\pi$
$97$	−1.64194	−0.166713	−0.0833566	+	0.996520i	$0.526564\pi$
$98$	−1.12599	−0.113743
$99$	25.3351	2.54627
$100$	−5.76797	−0.576797
$101$	−4.00882	−0.398892	−0.199446	−	0.979909i	$-0.563914\pi$
$101$	−4.00882	−0.398892	−0.199446	+	0.979909i	$0.563914\pi$
$102$	16.4742	1.63119
$103$	−13.2412	−1.30469	−0.652346	−	0.757921i	$-0.726215\pi$
$103$	−13.2412	−1.30469	−0.652346	+	0.757921i	$0.726215\pi$
$104$	−0.448631	−0.0439919
$105$	2.32981	0.227366
$106$	−2.03105	−0.197273
$107$	6.09226	0.588961	0.294480	−	0.955658i	$-0.404853\pi$
$107$	6.09226	0.588961	0.294480	+	0.955658i	$0.404853\pi$
$108$	14.4319	1.38871
$109$	−13.9856	−1.33958	−0.669791	−	0.742550i	$-0.733616\pi$
$109$	−13.9856	−1.33958	−0.669791	+	0.742550i	$0.733616\pi$
$110$	−1.74685	−0.166556
$111$	10.4827	0.994974
$112$	−13.7332	−1.29766
$113$	10.2602	0.965196	0.482598	−	0.875842i	$-0.339693\pi$
$113$	10.2602	0.965196	0.482598	+	0.875842i	$0.339693\pi$
$114$	18.6692	1.74853
$115$	−0.267809	−0.0249733
$116$	1.17038	0.108667
$117$	−2.10041	−0.194183
$118$	−17.1213	−1.57615
$119$	−8.11735	−0.744116
$120$	1.24573	0.113719
$121$	2.41990	0.219991
$122$	17.3769	1.57323
$123$	−17.2364	−1.55415
$124$	−2.54118	−0.228204
$125$	−2.65888	−0.237818
$126$	−34.0199	−3.03074
$127$	10.6224	0.942587	0.471294	−	0.881976i	$-0.343787\pi$
$127$	10.6224	0.942587	0.471294	+	0.881976i	$0.343787\pi$
$128$	−10.8008	−0.954661
$129$	−5.56777	−0.490215
$130$	0.144823	0.0127018
$131$	−15.3247	−1.33892	−0.669461	−	0.742847i	$-0.733475\pi$
$131$	−15.3247	−1.33892	−0.669461	+	0.742847i	$0.733475\pi$
$132$	13.5011	1.17512
$133$	−9.19887	−0.797644
$134$	17.7407	1.53256
$135$	3.30233	0.284219
$136$	−4.34028	−0.372176
$137$	−11.8836	−1.01528	−0.507641	−	0.861569i	$-0.669482\pi$
$137$	−11.8836	−1.01528	−0.507641	+	0.861569i	$0.669482\pi$
$138$	5.60688	0.477290
$139$	13.9192	1.18061	0.590304	−	0.807181i	$-0.299008\pi$
$139$	13.9192	1.18061	0.590304	+	0.807181i	$0.299008\pi$
$140$	0.865930	0.0731845
$141$	6.56889	0.553200
$142$	−6.22256	−0.522186
$143$	−1.11258	−0.0930385
$144$	−34.3786	−2.86489
$145$	0.267809	0.0222403
$146$	11.8140	0.977730
$147$	1.99134	0.164243
$148$	3.89615	0.320261
$149$	−8.08375	−0.662247	−0.331123	−	0.943587i	$-0.607428\pi$
$149$	−8.08375	−0.662247	−0.331123	+	0.943587i	$0.607428\pi$
$150$	27.6323	2.25617
$151$	15.6422	1.27294	0.636471	−	0.771300i	$-0.280393\pi$
$151$	15.6422	1.27294	0.636471	+	0.771300i	$0.280393\pi$
$152$	−4.91856	−0.398948
$153$	−20.3204	−1.64280
$154$	−18.0202	−1.45211
$155$	−0.581476	−0.0467053
$156$	−1.11931	−0.0896163
$157$	15.0831	1.20376	0.601881	−	0.798586i	$-0.294418\pi$
$157$	15.0831	1.20376	0.601881	+	0.798586i	$0.294418\pi$
$158$	−28.1946	−2.24304
$159$	3.59196	0.284861
$160$	1.57920	0.124847
$161$	−2.76268	−0.217729
$162$	−32.1956	−2.52953
$163$	−21.8135	−1.70856	−0.854281	−	0.519811i	$-0.826002\pi$
$163$	−21.8135	−1.70856	−0.854281	+	0.519811i	$0.826002\pi$
$164$	−6.40631	−0.500249
$165$	3.08934	0.240505
$166$	−7.06660	−0.548475
$167$	−17.5915	−1.36127	−0.680634	−	0.732624i	$-0.738296\pi$
$167$	−17.5915	−1.36127	−0.680634	+	0.732624i	$0.738296\pi$
$168$	12.8508	0.991459
$169$	−12.9078	−0.992905
$170$	1.40109	0.107458
$171$	−23.0278	−1.76098
$172$	−2.06940	−0.157790
$173$	−9.99136	−0.759629	−0.379814	−	0.925063i	$-0.624012\pi$
$173$	−9.99136	−0.759629	−0.379814	+	0.925063i	$0.624012\pi$
$174$	−5.60688	−0.425057
$175$	−13.6152	−1.02922
$176$	−18.2102	−1.37265
$177$	30.2794	2.27594
$178$	−27.9445	−2.09453
$179$	−3.54931	−0.265288	−0.132644	−	0.991164i	$-0.542347\pi$
$179$	−3.54931	−0.265288	−0.132644	+	0.991164i	$0.542347\pi$
$180$	2.16771	0.161571
$181$	2.57125	0.191120	0.0955598	−	0.995424i	$-0.469536\pi$
$181$	2.57125	0.191120	0.0955598	+	0.995424i	$0.469536\pi$
$182$	1.49397	0.110740
$183$	−30.7314	−2.27173
$184$	−1.47718	−0.108899
$185$	0.891524	0.0655461
$186$	12.1739	0.892631
$187$	−10.7636	−0.787114
$188$	2.44149	0.178064
$189$	34.0663	2.47796
$190$	1.58776	0.115188
$191$	25.3003	1.83067	0.915334	−	0.402696i	$-0.131927\pi$
$191$	25.3003	1.83067	0.915334	+	0.402696i	$0.131927\pi$
$192$	−1.75562	−0.126701
$193$	−22.4961	−1.61931	−0.809653	−	0.586909i	$-0.800345\pi$
$193$	−22.4961	−1.61931	−0.809653	+	0.586909i	$0.800345\pi$
$194$	2.92356	0.209899
$195$	−0.256122	−0.0183413
$196$	0.740130	0.0528664
$197$	11.8432	0.843791	0.421896	−	0.906644i	$-0.361365\pi$
$197$	11.8432	0.843791	0.421896	+	0.906644i	$0.361365\pi$
$198$	−45.1105	−3.20587
$199$	19.0501	1.35043	0.675213	−	0.737623i	$-0.264052\pi$
$199$	19.0501	1.35043	0.675213	+	0.737623i	$0.264052\pi$
$200$	−7.27996	−0.514771
$201$	−31.3748	−2.21301
$202$	7.13793	0.502223
$203$	2.76268	0.193902
$204$	−10.8287	−0.758163
$205$	−1.46590	−0.102383
$206$	23.5767	1.64266
$207$	−6.91588	−0.480687
$208$	1.50972	0.104680
$209$	−12.1977	−0.843735
$210$	−4.14836	−0.286264
$211$	−15.1780	−1.04490	−0.522449	−	0.852670i	$-0.674982\pi$
$211$	−15.1780	−1.04490	−0.522449	+	0.852670i	$0.674982\pi$
$212$	1.33504	0.0916907
$213$	11.0047	0.754031
$214$	−10.8476	−0.741527
$215$	−0.473523	−0.0322940
$216$	18.2150	1.23937
$217$	−5.99842	−0.407199
$218$	24.9022	1.68659
$219$	−20.8932	−1.41183
$220$	1.14823	0.0774134
$221$	0.892360	0.0600266
$222$	−18.6651	−1.25272
$223$	28.9183	1.93651	0.968256	−	0.249962i	$-0.0804182\pi$
$223$	28.9183	1.93651	0.968256	+	0.249962i	$0.0804182\pi$
$224$	16.2908	1.08847
$225$	−34.0834	−2.27223
$226$	−18.2688	−1.21522
$227$	19.9599	1.32478	0.662391	−	0.749158i	$-0.269542\pi$
$227$	19.9599	1.32478	0.662391	+	0.749158i	$0.269542\pi$
$228$	−12.2715	−0.812701
$229$	−3.63488	−0.240200	−0.120100	−	0.992762i	$-0.538321\pi$
$229$	−3.63488	−0.240200	−0.120100	+	0.992762i	$0.538321\pi$
$230$	0.476849	0.0314425
$231$	31.8691	2.09684
$232$	1.47718	0.0969817
$233$	−18.8528	−1.23509	−0.617544	−	0.786537i	$-0.711872\pi$
$233$	−18.8528	−1.23509	−0.617544	+	0.786537i	$0.711872\pi$
$234$	3.73989	0.244484
$235$	0.558665	0.0364433
$236$	11.2541	0.732577
$237$	49.8627	3.23893
$238$	14.4534	0.936874
$239$	4.68327	0.302936	0.151468	−	0.988462i	$-0.451600\pi$
$239$	4.68327	0.302936	0.151468	+	0.988462i	$0.451600\pi$
$240$	−4.19210	−0.270599
$241$	−22.0203	−1.41845	−0.709225	−	0.704982i	$-0.750955\pi$
$241$	−22.0203	−1.41845	−0.709225	+	0.704982i	$0.750955\pi$
$242$	−4.30876	−0.276978
$243$	19.9458	1.27953
$244$	−11.4221	−0.731223
$245$	0.169358	0.0108199
$246$	30.6904	1.95675
$247$	1.01125	0.0643446
$248$	−3.20731	−0.203664
$249$	12.4974	0.791992
$250$	4.73429	0.299423
$251$	−6.70268	−0.423069	−0.211535	−	0.977370i	$-0.567846\pi$
$251$	−6.70268	−0.423069	−0.211535	+	0.977370i	$0.567846\pi$
$252$	22.3617	1.40866
$253$	−3.66332	−0.230311
$254$	−18.9138	−1.18676
$255$	−2.47785	−0.155169
$256$	20.3464	1.27165
$257$	19.9168	1.24237	0.621186	−	0.783663i	$-0.286651\pi$
$257$	19.9168	1.24237	0.621186	+	0.783663i	$0.286651\pi$
$258$	9.91373	0.617202
$259$	9.19682	0.571463
$260$	−0.0951938	−0.00590367
$261$	6.91588	0.428082
$262$	27.2864	1.68576
$263$	−4.05991	−0.250345	−0.125172	−	0.992135i	$-0.539948\pi$
$263$	−4.05991	−0.250345	−0.125172	+	0.992135i	$0.539948\pi$
$264$	17.0402	1.04875
$265$	0.305485	0.0187658
$266$	16.3791	1.00427
$267$	49.4204	3.02448
$268$	−11.6612	−0.712321
$269$	−2.13295	−0.130048	−0.0650242	−	0.997884i	$-0.520712\pi$
$269$	−2.13295	−0.130048	−0.0650242	+	0.997884i	$0.520712\pi$
$270$	−5.87998	−0.357844
$271$	−30.4045	−1.84694	−0.923472	−	0.383666i	$-0.874661\pi$
$271$	−30.4045	−1.84694	−0.923472	+	0.383666i	$0.874661\pi$
$272$	14.6058	0.885606
$273$	−2.64211	−0.159908
$274$	21.1594	1.27828
$275$	−18.0539	−1.08869
$276$	−3.68547	−0.221839
$277$	−26.9951	−1.62198	−0.810988	−	0.585062i	$-0.801070\pi$
$277$	−26.9951	−1.62198	−0.810988	+	0.585062i	$0.801070\pi$
$278$	−24.7839	−1.48644
$279$	−15.0160	−0.898985
$280$	1.09292	0.0653145
$281$	−6.43847	−0.384087	−0.192043	−	0.981386i	$-0.561511\pi$
$281$	−6.43847	−0.384087	−0.192043	+	0.981386i	$0.561511\pi$
$282$	−11.6963	−0.696503
$283$	−6.55913	−0.389900	−0.194950	−	0.980813i	$-0.562454\pi$
$283$	−6.55913	−0.389900	−0.194950	+	0.980813i	$0.562454\pi$
$284$	4.09017	0.242707
$285$	−2.80799	−0.166331
$286$	1.98101	0.117139
$287$	−15.1220	−0.892626
$288$	40.7811	2.40305
$289$	−8.36688	−0.492169
$290$	−0.476849	−0.0280015
$291$	−5.17037	−0.303093
$292$	−7.76546	−0.454439
$293$	20.7008	1.20935	0.604677	−	0.796471i	$-0.293302\pi$
$293$	20.7008	1.20935	0.604677	+	0.796471i	$0.293302\pi$
$294$	−3.54570	−0.206789
$295$	2.57517	0.149932
$296$	4.91747	0.285822
$297$	45.1720	2.62115
$298$	14.3936	0.833798
$299$	0.303708	0.0175639
$300$	−18.1630	−1.04864
$301$	−4.88479	−0.281555
$302$	−27.8518	−1.60269
$303$	−12.6236	−0.725205
$304$	16.5518	0.949312
$305$	−2.61362	−0.149655
$306$	36.1816	2.06836
$307$	25.6222	1.46234	0.731169	−	0.682197i	$-0.238975\pi$
$307$	25.6222	1.46234	0.731169	+	0.682197i	$0.238975\pi$
$308$	11.8449	0.674927
$309$	−41.6958	−2.37199
$310$	1.03535	0.0588040
$311$	26.0446	1.47685	0.738426	−	0.674335i	$-0.235570\pi$
$311$	26.0446	1.47685	0.738426	+	0.674335i	$0.235570\pi$
$312$	−1.41272	−0.0799794
$313$	−3.18547	−0.180054	−0.0900268	−	0.995939i	$-0.528695\pi$
$313$	−3.18547	−0.180054	−0.0900268	+	0.995939i	$0.528695\pi$
$314$	−26.8563	−1.51559
$315$	5.11685	0.288302
$316$	18.5327	1.04254
$317$	2.95254	0.165831	0.0829155	−	0.996557i	$-0.473577\pi$
$317$	2.95254	0.165831	0.0829155	+	0.996557i	$0.473577\pi$
$318$	−6.39568	−0.358652
$319$	3.66332	0.205106
$320$	−0.149310	−0.00834669
$321$	19.1842	1.07076
$322$	4.91910	0.274131
$323$	9.78337	0.544361
$324$	21.1626	1.17570
$325$	1.49676	0.0830251
$326$	38.8401	2.15115
$327$	−44.0401	−2.43542
$328$	−8.08564	−0.446455
$329$	5.76310	0.317730
$330$	−5.50074	−0.302806
$331$	−25.3246	−1.39197	−0.695983	−	0.718058i	$-0.745031\pi$
$331$	−25.3246	−1.39197	−0.695983	+	0.718058i	$0.745031\pi$
$332$	4.64497	0.254926
$333$	23.0226	1.26163
$334$	31.3226	1.71390
$335$	−2.66833	−0.145787
$336$	−43.2451	−2.35921
$337$	12.7625	0.695217	0.347609	−	0.937640i	$-0.386994\pi$
$337$	12.7625	0.695217	0.347609	+	0.937640i	$0.386994\pi$
$338$	22.9830	1.25011
$339$	32.3088	1.75477
$340$	−0.920952	−0.0499456
$341$	−7.95393	−0.430729
$342$	41.0023	2.21715
$343$	−17.5917	−0.949861
$344$	−2.61186	−0.140822
$345$	−0.843317	−0.0454026
$346$	17.7902	0.956406
$347$	−20.0575	−1.07674	−0.538372	−	0.842707i	$-0.680960\pi$
$347$	−20.0575	−1.07674	−0.538372	+	0.842707i	$0.680960\pi$
$348$	3.68547	0.197562
$349$	−1.11400	−0.0596311	−0.0298155	−	0.999555i	$-0.509492\pi$
$349$	−1.11400	−0.0596311	−0.0298155	+	0.999555i	$0.509492\pi$
$350$	24.2427	1.29583
$351$	−3.74499	−0.199893
$352$	21.6016	1.15137
$353$	11.2422	0.598362	0.299181	−	0.954196i	$-0.403287\pi$
$353$	11.2422	0.598362	0.299181	+	0.954196i	$0.403287\pi$
$354$	−53.9142	−2.86551
$355$	0.935919	0.0496734
$356$	18.3683	0.973518
$357$	−25.5611	−1.35284
$358$	6.31976	0.334010
$359$	−17.5382	−0.925628	−0.462814	−	0.886455i	$-0.653160\pi$
$359$	−17.5382	−0.925628	−0.462814	+	0.886455i	$0.653160\pi$
$360$	2.73594	0.144197
$361$	−7.91312	−0.416480
$362$	−4.57826	−0.240628
$363$	7.62013	0.399953
$364$	−0.982005	−0.0514711
$365$	−1.77691	−0.0930076
$366$	54.7190	2.86021
$367$	36.8026	1.92108	0.960540	−	0.278141i	$-0.0897184\pi$
$367$	36.8026	1.92108	0.960540	+	0.278141i	$0.0897184\pi$
$368$	4.97097	0.259130
$369$	−37.8554	−1.97067
$370$	−1.58741	−0.0825254
$371$	3.15134	0.163609
$372$	−8.00203	−0.414886
$373$	17.0921	0.884994	0.442497	−	0.896770i	$-0.354093\pi$
$373$	17.0921	0.884994	0.442497	+	0.896770i	$0.354093\pi$
$374$	19.1652	0.991011
$375$	−8.37268	−0.432363
$376$	3.08149	0.158916
$377$	−0.303708	−0.0156417
$378$	−60.6570	−3.11986
$379$	1.34633	0.0691563	0.0345781	−	0.999402i	$-0.488991\pi$
$379$	1.34633	0.0691563	0.0345781	+	0.999402i	$0.488991\pi$
$380$	−1.04366	−0.0535384
$381$	33.4495	1.71367
$382$	−45.0487	−2.30489
$383$	−28.9408	−1.47881	−0.739404	−	0.673262i	$-0.764893\pi$
$383$	−28.9408	−1.47881	−0.739404	+	0.673262i	$0.764893\pi$
$384$	−34.0110	−1.73562
$385$	2.71038	0.138134
$386$	40.0556	2.03878
$387$	−12.2282	−0.621595
$388$	−1.92169	−0.0975591
$389$	19.2939	0.978240	0.489120	−	0.872216i	$-0.337318\pi$
$389$	19.2939	0.978240	0.489120	+	0.872216i	$0.337318\pi$
$390$	0.456039	0.0230925
$391$	2.93822	0.148592
$392$	0.934144	0.0471814
$393$	−48.2566	−2.43422
$394$	−21.0875	−1.06237
$395$	4.24068	0.213372
$396$	29.6517	1.49005
$397$	32.5437	1.63332	0.816660	−	0.577118i	$-0.195823\pi$
$397$	32.5437	1.63332	0.816660	+	0.577118i	$0.195823\pi$
$398$	−33.9198	−1.70024
$399$	−28.9668	−1.45015
$400$	24.4983	1.22492
$401$	−37.2076	−1.85806	−0.929030	−	0.370004i	$-0.879356\pi$
$401$	−37.2076	−1.85806	−0.929030	+	0.370004i	$0.879356\pi$
$402$	55.8646	2.78627
$403$	0.659421	0.0328481
$404$	−4.69185	−0.233428
$405$	4.84246	0.240624
$406$	−4.91910	−0.244131
$407$	12.1950	0.604485
$408$	−13.6673	−0.676633
$409$	26.4609	1.30841	0.654205	−	0.756317i	$-0.273003\pi$
$409$	26.4609	1.30841	0.654205	+	0.756317i	$0.273003\pi$
$410$	2.61013	0.128905
$411$	−37.4207	−1.84583
$412$	−15.4972	−0.763494
$413$	26.5651	1.30718
$414$	12.3141	0.605206
$415$	1.06287	0.0521742
$416$	−1.79088	−0.0878053
$417$	43.8308	2.14640
$418$	21.7188	1.06230
$419$	7.40441	0.361729	0.180864	−	0.983508i	$-0.442110\pi$
$419$	7.40441	0.361729	0.180864	+	0.983508i	$0.442110\pi$
$420$	2.72677	0.133053
$421$	24.0265	1.17098	0.585489	−	0.810680i	$-0.300902\pi$
$421$	24.0265	1.17098	0.585489	+	0.810680i	$0.300902\pi$
$422$	27.0253	1.31557
$423$	14.4269	0.701461
$424$	1.68500	0.0818307
$425$	14.4804	0.702400
$426$	−19.5945	−0.949358
$427$	−26.9617	−1.30477
$428$	7.13027	0.344655
$429$	−3.50345	−0.169148
$430$	0.843134	0.0406595
$431$	−5.69094	−0.274123	−0.137062	−	0.990563i	$-0.543766\pi$
$431$	−5.69094	−0.274123	−0.137062	+	0.990563i	$0.543766\pi$
$432$	−61.2966	−2.94913
$433$	40.5680	1.94957	0.974787	−	0.223136i	$-0.0716293\pi$
$433$	40.5680	1.94957	0.974787	+	0.223136i	$0.0716293\pi$
$434$	10.6805	0.512682
$435$	0.843317	0.0404339
$436$	−16.3686	−0.783912
$437$	3.32970	0.159281
$438$	37.2016	1.77756
$439$	−0.259414	−0.0123812	−0.00619058	−	0.999981i	$-0.501971\pi$
$439$	−0.259414	−0.0123812	−0.00619058	+	0.999981i	$0.501971\pi$
$440$	1.44922	0.0690887
$441$	4.37348	0.208261
$442$	−1.58890	−0.0755761
$443$	33.5674	1.59484	0.797418	−	0.603427i	$-0.206198\pi$
$443$	33.5674	1.59484	0.797418	+	0.603427i	$0.206198\pi$
$444$	12.2688	0.582250
$445$	4.20306	0.199244
$446$	−51.4906	−2.43815
$447$	−25.4553	−1.20400
$448$	−1.54026	−0.0727705
$449$	−34.0788	−1.60828	−0.804139	−	0.594441i	$-0.797373\pi$
$449$	−34.0788	−1.60828	−0.804139	+	0.594441i	$0.797373\pi$
$450$	60.6874	2.86083
$451$	−20.0519	−0.944206
$452$	12.0083	0.564824
$453$	49.2564	2.31427
$454$	−35.5397	−1.66796
$455$	−0.224704	−0.0105343
$456$	−15.4883	−0.725307
$457$	19.5239	0.913288	0.456644	−	0.889649i	$-0.349051\pi$
$457$	19.5239	0.913288	0.456644	+	0.889649i	$0.349051\pi$
$458$	6.47211	0.302422
$459$	−36.2309	−1.69111
$460$	−0.313439	−0.0146142
$461$	2.02067	0.0941118	0.0470559	−	0.998892i	$-0.485016\pi$
$461$	2.02067	0.0941118	0.0470559	+	0.998892i	$0.485016\pi$
$462$	−56.7448	−2.64001
$463$	20.7189	0.962890	0.481445	−	0.876476i	$-0.340112\pi$
$463$	20.7189	0.962890	0.481445	+	0.876476i	$0.340112\pi$
$464$	−4.97097	−0.230771
$465$	−1.83104	−0.0849124
$466$	33.5685	1.55503
$467$	−21.2571	−0.983662	−0.491831	−	0.870691i	$-0.663672\pi$
$467$	−21.2571	−0.983662	−0.491831	+	0.870691i	$0.663672\pi$
$468$	−2.45828	−0.113634
$469$	−27.5261	−1.27104
$470$	−0.994735	−0.0458837
$471$	47.4959	2.18850
$472$	14.2041	0.653799
$473$	−6.47725	−0.297824
$474$	−88.7833	−4.07795
$475$	16.4097	0.752927
$476$	−9.50040	−0.435450
$477$	7.88883	0.361205
$478$	−8.33884	−0.381409
$479$	−7.75589	−0.354376	−0.177188	−	0.984177i	$-0.556700\pi$
$479$	−7.75589	−0.354376	−0.177188	+	0.984177i	$0.556700\pi$
$480$	4.97281	0.226977
$481$	−1.01103	−0.0460990
$482$	39.2083	1.78589
$483$	−8.69953	−0.395842
$484$	2.83221	0.128737
$485$	−0.439725	−0.0199669
$486$	−35.5147	−1.61098
$487$	−13.0017	−0.589165	−0.294583	−	0.955626i	$-0.595181\pi$
$487$	−13.0017	−0.589165	−0.294583	+	0.955626i	$0.595181\pi$
$488$	−14.4162	−0.652590
$489$	−68.6895	−3.10625
$490$	−0.301551	−0.0136227
$491$	17.4774	0.788742	0.394371	−	0.918951i	$-0.370962\pi$
$491$	17.4774	0.788742	0.394371	+	0.918951i	$0.370962\pi$
$492$	−20.1732	−0.909476
$493$	−2.93822	−0.132331
$494$	−1.80060	−0.0810126
$495$	6.78496	0.304961
$496$	10.7931	0.484627
$497$	9.65480	0.433077
$498$	−22.2524	−0.997153
$499$	−30.8636	−1.38164	−0.690822	−	0.723025i	$-0.742751\pi$
$499$	−30.8636	−1.38164	−0.690822	+	0.723025i	$0.742751\pi$
$500$	−3.11191	−0.139169
$501$	−55.3946	−2.47485
$502$	11.9345	0.532663
$503$	8.73824	0.389619	0.194809	−	0.980841i	$-0.437591\pi$
$503$	8.73824	0.389619	0.194809	+	0.980841i	$0.437591\pi$
$504$	28.2235	1.25718
$505$	−1.07360	−0.0477745
$506$	6.52275	0.289971
$507$	−40.6459	−1.80515
$508$	12.4323	0.551594
$509$	11.6268	0.515347	0.257674	−	0.966232i	$-0.417044\pi$
$509$	11.6268	0.515347	0.257674	+	0.966232i	$0.417044\pi$
$510$	4.41195	0.195364
$511$	−18.3303	−0.810885
$512$	−14.6264	−0.646403
$513$	−41.0582	−1.81276
$514$	−35.4629	−1.56420
$515$	−3.54610	−0.156260
$516$	−6.51642	−0.286869
$517$	7.64189	0.336090
$518$	−16.3755	−0.719497
$519$	−31.4623	−1.38104
$520$	−0.120148	−0.00526882
$521$	9.79039	0.428925	0.214462	−	0.976732i	$-0.431200\pi$
$521$	9.79039	0.428925	0.214462	+	0.976732i	$0.431200\pi$
$522$	−12.3141	−0.538974
$523$	8.89983	0.389162	0.194581	−	0.980886i	$-0.437665\pi$
$523$	8.89983	0.389162	0.194581	+	0.980886i	$0.437665\pi$
$524$	−17.9357	−0.783526
$525$	−42.8737	−1.87116
$526$	7.22890	0.315195
$527$	6.37956	0.277898
$528$	−57.3431	−2.49554
$529$	1.00000	0.0434783
$530$	−0.543934	−0.0236270
$531$	66.5011	2.88590
$532$	−10.7662	−0.466774
$533$	1.66240	0.0720067
$534$	−87.9959	−3.80796
$535$	1.63156	0.0705385
$536$	−14.7180	−0.635721
$537$	−11.1766	−0.482306
$538$	3.79784	0.163737
$539$	2.31662	0.0997838
$540$	3.86499	0.166322
$541$	−14.0696	−0.604897	−0.302449	−	0.953166i	$-0.597804\pi$
$541$	−14.0696	−0.604897	−0.302449	+	0.953166i	$0.597804\pi$
$542$	54.1370	2.32538
$543$	8.09674	0.347464
$544$	−17.3259	−0.742841
$545$	−3.74548	−0.160439
$546$	4.70443	0.201331
$547$	−28.4145	−1.21492	−0.607458	−	0.794352i	$-0.707811\pi$
$547$	−28.4145	−1.21492	−0.607458	+	0.794352i	$0.707811\pi$
$548$	−13.9083	−0.594134
$549$	−67.4938	−2.88057
$550$	32.1459	1.37071
$551$	−3.32970	−0.141850
$552$	−4.65157	−0.197984
$553$	43.7462	1.86028
$554$	48.0663	2.04214
$555$	2.80736	0.119166
$556$	16.2907	0.690882
$557$	−5.56394	−0.235752	−0.117876	−	0.993028i	$-0.537608\pi$
$557$	−5.56394	−0.235752	−0.117876	+	0.993028i	$0.537608\pi$
$558$	26.7368	1.13186
$559$	0.536997	0.0227125
$560$	−3.67787	−0.155418
$561$	−33.8941	−1.43101
$562$	11.4641	0.483582
$563$	24.9349	1.05088	0.525441	−	0.850830i	$-0.323900\pi$
$563$	24.9349	1.05088	0.525441	+	0.850830i	$0.323900\pi$
$564$	7.68811	0.323728
$565$	2.74777	0.115599
$566$	11.6789	0.490901
$567$	49.9541	2.09787
$568$	5.16235	0.216607
$569$	11.5903	0.485891	0.242945	−	0.970040i	$-0.421886\pi$
$569$	11.5903	0.485891	0.242945	+	0.970040i	$0.421886\pi$
$570$	4.99978	0.209418
$571$	4.17470	0.174706	0.0873529	−	0.996177i	$-0.472159\pi$
$571$	4.17470	0.174706	0.0873529	+	0.996177i	$0.472159\pi$
$572$	−1.30214	−0.0544453
$573$	79.6694	3.32824
$574$	26.9257	1.12386
$575$	4.92828	0.205523
$576$	−3.85578	−0.160657
$577$	22.3591	0.930821	0.465411	−	0.885095i	$-0.345907\pi$
$577$	22.3591	0.930821	0.465411	+	0.885095i	$0.345907\pi$
$578$	14.8977	0.619663
$579$	−70.8391	−2.94397
$580$	0.313439	0.0130148
$581$	10.9644	0.454880
$582$	9.20614	0.381607
$583$	4.17869	0.173064
$584$	−9.80107	−0.405571
$585$	−0.562508	−0.0232568
$586$	−36.8590	−1.52263
$587$	−38.3139	−1.58139	−0.790693	−	0.612213i	$-0.790279\pi$
$587$	−38.3139	−1.58139	−0.790693	+	0.612213i	$0.790279\pi$
$588$	2.33063	0.0961136
$589$	7.22955	0.297889
$590$	−4.58524	−0.188771
$591$	37.2936	1.53405
$592$	−16.5481	−0.680124
$593$	5.67501	0.233045	0.116522	−	0.993188i	$-0.462825\pi$
$593$	5.67501	0.233045	0.116522	+	0.993188i	$0.462825\pi$
$594$	−80.4314	−3.30014
$595$	−2.17390	−0.0891211
$596$	−9.46108	−0.387541
$597$	59.9878	2.45514
$598$	−0.540769	−0.0221137
$599$	−21.0821	−0.861393	−0.430697	−	0.902497i	$-0.641732\pi$
$599$	−21.0821	−0.861393	−0.430697	+	0.902497i	$0.641732\pi$
$600$	−22.9242	−0.935878
$601$	−15.5984	−0.636272	−0.318136	−	0.948045i	$-0.603057\pi$
$601$	−15.5984	−0.636272	−0.318136	+	0.948045i	$0.603057\pi$
$602$	8.69765	0.354490
$603$	−68.9069	−2.80611
$604$	18.3073	0.744915
$605$	0.648070	0.0263478
$606$	22.4770	0.913065
$607$	3.86498	0.156875	0.0784373	−	0.996919i	$-0.475007\pi$
$607$	3.86498	0.156875	0.0784373	+	0.996919i	$0.475007\pi$
$608$	−19.6343	−0.796277
$609$	8.69953	0.352523
$610$	4.65369	0.188422
$611$	−0.633552	−0.0256308
$612$	−23.7826	−0.961354
$613$	15.7358	0.635564	0.317782	−	0.948164i	$-0.397062\pi$
$613$	15.7358	0.635564	0.317782	+	0.948164i	$0.397062\pi$
$614$	−45.6218	−1.84115
$615$	−4.61606	−0.186137
$616$	14.9499	0.602349
$617$	28.8389	1.16101	0.580506	−	0.814256i	$-0.302855\pi$
$617$	28.8389	1.16101	0.580506	+	0.814256i	$0.302855\pi$
$618$	74.2417	2.98644
$619$	−7.25977	−0.291795	−0.145897	−	0.989300i	$-0.546607\pi$
$619$	−7.25977	−0.291795	−0.145897	+	0.989300i	$0.546607\pi$
$620$	−0.680549	−0.0273315
$621$	−12.3309	−0.494822
$622$	−46.3738	−1.85942
$623$	43.3582	1.73711
$624$	4.75404	0.190314
$625$	23.9293	0.957173
$626$	5.67192	0.226695
$627$	−38.4100	−1.53395
$628$	17.6530	0.704431
$629$	−9.78119	−0.390002
$630$	−9.11084	−0.362985
$631$	−17.6490	−0.702597	−0.351299	−	0.936263i	$-0.614260\pi$
$631$	−17.6490	−0.702597	−0.351299	+	0.936263i	$0.614260\pi$
$632$	23.3907	0.930433
$633$	−47.7948	−1.89967
$634$	−5.25716	−0.208789
$635$	2.84478	0.112892
$636$	4.20396	0.166698
$637$	−0.192060	−0.00760968
$638$	−6.52275	−0.258238
$639$	24.1691	0.956116
$640$	−2.89254	−0.114338
$641$	39.2802	1.55147	0.775737	−	0.631056i	$-0.217378\pi$
$641$	39.2802	1.55147	0.775737	+	0.631056i	$0.217378\pi$
$642$	−34.1586	−1.34813
$643$	42.2178	1.66491	0.832454	−	0.554095i	$-0.186935\pi$
$643$	42.2178	1.66491	0.832454	+	0.554095i	$0.186935\pi$
$644$	−3.23339	−0.127413
$645$	−1.49110	−0.0587120
$646$	−17.4198	−0.685375
$647$	−26.1522	−1.02815	−0.514074	−	0.857746i	$-0.671864\pi$
$647$	−26.1522	−1.02815	−0.514074	+	0.857746i	$0.671864\pi$
$648$	26.7100	1.04927
$649$	35.2254	1.38272
$650$	−2.66506	−0.104532
$651$	−18.8887	−0.740307
$652$	−25.5301	−0.999835
$653$	−1.78860	−0.0699934	−0.0349967	−	0.999387i	$-0.511142\pi$
$653$	−1.78860	−0.0699934	−0.0349967	+	0.999387i	$0.511142\pi$
$654$	78.4159	3.06630
$655$	−4.10408	−0.160360
$656$	27.2096	1.06236
$657$	−45.8867	−1.79021
$658$	−10.2615	−0.400036
$659$	22.5889	0.879939	0.439970	−	0.898013i	$-0.354989\pi$
$659$	22.5889	0.879939	0.439970	+	0.898013i	$0.354989\pi$
$660$	3.61571	0.140741
$661$	−18.0560	−0.702298	−0.351149	−	0.936320i	$-0.614209\pi$
$661$	−18.0560	−0.702298	−0.351149	+	0.936320i	$0.614209\pi$
$662$	45.0919	1.75255
$663$	2.80999	0.109131
$664$	5.86258	0.227512
$665$	−2.46354	−0.0955320
$666$	−40.9931	−1.58845
$667$	−1.00000	−0.0387202
$668$	−20.5887	−0.796602
$669$	91.0622	3.52067
$670$	4.75112	0.183552
$671$	−35.7513	−1.38016
$672$	51.2988	1.97889
$673$	−15.4769	−0.596592	−0.298296	−	0.954473i	$-0.596418\pi$
$673$	−15.4769	−0.596592	−0.298296	+	0.954473i	$0.596418\pi$
$674$	−22.7243	−0.875309
$675$	−60.7701	−2.33904
$676$	−15.1070	−0.581039
$677$	46.1022	1.77185	0.885926	−	0.463827i	$-0.153524\pi$
$677$	46.1022	1.77185	0.885926	+	0.463827i	$0.153524\pi$
$678$	−57.5276	−2.20933
$679$	−4.53614	−0.174081
$680$	−1.16237	−0.0445747
$681$	62.8526	2.40852
$682$	14.1624	0.542307
$683$	−32.8506	−1.25699	−0.628497	−	0.777812i	$-0.716329\pi$
$683$	−32.8506	−1.25699	−0.628497	+	0.777812i	$0.716329\pi$
$684$	−26.9513	−1.03051
$685$	−3.18252	−0.121598
$686$	31.3230	1.19592
$687$	−11.4461	−0.436694
$688$	8.78935	0.335091
$689$	−0.346435	−0.0131981
$690$	1.50157	0.0571639
$691$	26.1838	0.996078	0.498039	−	0.867155i	$-0.334054\pi$
$691$	26.1838	0.996078	0.498039	+	0.867155i	$0.334054\pi$
$692$	−11.6937	−0.444528
$693$	69.9926	2.65880
$694$	35.7135	1.35567
$695$	3.72768	0.141399
$696$	4.65157	0.176317
$697$	16.0829	0.609183
$698$	1.98354	0.0750781
$699$	−59.3665	−2.24545
$700$	−15.9350	−0.602288
$701$	−27.5869	−1.04194	−0.520971	−	0.853574i	$-0.674430\pi$
$701$	−27.5869	−1.04194	−0.520971	+	0.853574i	$0.674430\pi$
$702$	6.66817	0.251674
$703$	−11.0844	−0.418056
$704$	−2.04239	−0.0769755
$705$	1.75921	0.0662556
$706$	−20.0174	−0.753364
$707$	−11.0751	−0.416521
$708$	35.4385	1.33186
$709$	45.0888	1.69335	0.846673	−	0.532114i	$-0.178602\pi$
$709$	45.0888	1.69335	0.846673	+	0.532114i	$0.178602\pi$
$710$	−1.66646	−0.0625410
$711$	109.511	4.10698
$712$	23.1833	0.868830
$713$	2.17124	0.0813134
$714$	45.5130	1.70328
$715$	−0.297958	−0.0111430
$716$	−4.15406	−0.155244
$717$	14.7474	0.550751
$718$	31.2277	1.16541
$719$	−22.9584	−0.856203	−0.428102	−	0.903731i	$-0.640817\pi$
$719$	−22.9584	−0.856203	−0.428102	+	0.903731i	$0.640817\pi$
$720$	−9.20690	−0.343121
$721$	−36.5811	−1.36235
$722$	14.0898	0.524367
$723$	−69.3407	−2.57881
$724$	3.00935	0.111841
$725$	−4.92828	−0.183032
$726$	−13.5681	−0.503559
$727$	29.6914	1.10119	0.550597	−	0.834771i	$-0.314400\pi$
$727$	29.6914	1.10119	0.550597	+	0.834771i	$0.314400\pi$
$728$	−1.23942	−0.0459361
$729$	8.56309	0.317152
$730$	3.16388	0.117101
$731$	5.19517	0.192150
$732$	−35.9675	−1.32940
$733$	1.67774	0.0619688	0.0309844	−	0.999520i	$-0.490136\pi$
$733$	1.67774	0.0619688	0.0309844	+	0.999520i	$0.490136\pi$
$734$	−65.5291	−2.41872
$735$	0.533299	0.0196710
$736$	−5.89673	−0.217356
$737$	−36.4997	−1.34449
$738$	67.4037	2.48116
$739$	44.7908	1.64765	0.823827	−	0.566841i	$-0.191835\pi$
$739$	44.7908	1.64765	0.823827	+	0.566841i	$0.191835\pi$
$740$	1.04342	0.0383570
$741$	3.18439	0.116981
$742$	−5.61114	−0.205991
$743$	16.7806	0.615621	0.307811	−	0.951448i	$-0.400404\pi$
$743$	16.7806	0.615621	0.307811	+	0.951448i	$0.400404\pi$
$744$	−10.0997	−0.370271
$745$	−2.16490	−0.0793158
$746$	−30.4334	−1.11425
$747$	27.4475	1.00425
$748$	−12.5976	−0.460612
$749$	16.8309	0.614989
$750$	14.9080	0.544365
$751$	−11.7917	−0.430285	−0.215143	−	0.976583i	$-0.569022\pi$
$751$	−11.7917	−0.430285	−0.215143	+	0.976583i	$0.569022\pi$
$752$	−10.3697	−0.378145
$753$	−21.1064	−0.769160
$754$	0.540769	0.0196936
$755$	4.18912	0.152458
$756$	39.8706	1.45008
$757$	4.00662	0.145623	0.0728115	−	0.997346i	$-0.476803\pi$
$757$	4.00662	0.145623	0.0728115	+	0.997346i	$0.476803\pi$
$758$	−2.39721	−0.0870707
$759$	−11.5356	−0.418716
$760$	−1.31724	−0.0477812
$761$	1.94466	0.0704940	0.0352470	−	0.999379i	$-0.488778\pi$
$761$	1.94466	0.0704940	0.0352470	+	0.999379i	$0.488778\pi$
$762$	−59.5587	−2.15758
$763$	−38.6378	−1.39878
$764$	29.6111	1.07129
$765$	−5.44197	−0.196755
$766$	51.5308	1.86188
$767$	−2.92037	−0.105448
$768$	64.0698	2.31192
$769$	−25.1227	−0.905949	−0.452974	−	0.891524i	$-0.649637\pi$
$769$	−25.1227	−0.905949	−0.452974	+	0.891524i	$0.649637\pi$
$770$	−4.82598	−0.173916
$771$	62.7168	2.25869
$772$	−26.3291	−0.947603
$773$	−8.13497	−0.292595	−0.146297	−	0.989241i	$-0.546736\pi$
$773$	−8.13497	−0.292595	−0.146297	+	0.989241i	$0.546736\pi$
$774$	21.7730	0.782616
$775$	10.7005	0.384372
$776$	−2.42544	−0.0870681
$777$	28.9603	1.03895
$778$	−34.3539	−1.23165
$779$	18.2257	0.653005
$780$	−0.299760	−0.0107331
$781$	12.8023	0.458102
$782$	−5.23166	−0.187084
$783$	12.3309	0.440671
$784$	−3.14356	−0.112270
$785$	4.03939	0.144172
$786$	85.9236	3.06479
$787$	−30.1545	−1.07489	−0.537445	−	0.843299i	$-0.680611\pi$
$787$	−30.1545	−1.07489	−0.537445	+	0.843299i	$0.680611\pi$
$788$	13.8610	0.493779
$789$	−12.7845	−0.455139
$790$	−7.55076	−0.268644
$791$	28.3456	1.00785
$792$	37.4245	1.32982
$793$	2.96396	0.105253
$794$	−57.9459	−2.05642
$795$	0.961958	0.0341171
$796$	22.2959	0.790257
$797$	−11.7150	−0.414968	−0.207484	−	0.978238i	$-0.566527\pi$
$797$	−11.7150	−0.414968	−0.207484	+	0.978238i	$0.566527\pi$
$798$	51.5770	1.82581
$799$	−6.12929	−0.216839
$800$	−29.0607	−1.02745
$801$	108.540	3.83506
$802$	66.2503	2.33938
$803$	−24.3060	−0.857742
$804$	−36.7205	−1.29503
$805$	−0.739869	−0.0260770
$806$	−1.17414	−0.0413572
$807$	−6.71656	−0.236434
$808$	−5.92175	−0.208327
$809$	16.9142	0.594673	0.297336	−	0.954773i	$-0.403902\pi$
$809$	16.9142	0.594673	0.297336	+	0.954773i	$0.403902\pi$
$810$	−8.62227	−0.302956
$811$	−39.3746	−1.38263	−0.691315	−	0.722553i	$-0.742968\pi$
$811$	−39.3746	−1.38263	−0.691315	+	0.722553i	$0.742968\pi$
$812$	3.23339	0.113470
$813$	−95.7423	−3.35783
$814$	−21.7139	−0.761072
$815$	−5.84184	−0.204631
$816$	45.9929	1.61007
$817$	5.88736	0.205973
$818$	−47.1152	−1.64735
$819$	−5.80274	−0.202764
$820$	−1.71567	−0.0599137
$821$	−3.23790	−0.113003	−0.0565017	−	0.998403i	$-0.517995\pi$
$821$	−3.23790	−0.113003	−0.0565017	+	0.998403i	$0.517995\pi$
$822$	66.6297	2.32398
$823$	14.9805	0.522187	0.261093	−	0.965314i	$-0.415917\pi$
$823$	14.9805	0.522187	0.261093	+	0.965314i	$0.415917\pi$
$824$	−19.5596	−0.681392
$825$	−56.8507	−1.97929
$826$	−47.3007	−1.64580
$827$	−56.7767	−1.97432	−0.987159	−	0.159739i	$-0.948935\pi$
$827$	−56.7767	−1.97432	−0.987159	+	0.159739i	$0.948935\pi$
$828$	−8.09422	−0.281294
$829$	3.32122	0.115351	0.0576754	−	0.998335i	$-0.481631\pi$
$829$	3.32122	0.115351	0.0576754	+	0.998335i	$0.481631\pi$
$830$	−1.89250	−0.0656896
$831$	−85.0061	−2.94883
$832$	0.169325	0.00587028
$833$	−1.85808	−0.0643786
$834$	−78.0431	−2.70241
$835$	−4.71115	−0.163036
$836$	−14.2760	−0.493746
$837$	−26.7733	−0.925421
$838$	−13.1840	−0.455433
$839$	−26.6507	−0.920086	−0.460043	−	0.887897i	$-0.652166\pi$
$839$	−26.6507	−0.920086	−0.460043	+	0.887897i	$0.652166\pi$
$840$	3.44155	0.118745
$841$	1.00000	0.0344828
$842$	−42.7805	−1.47431
$843$	−20.2744	−0.698288
$844$	−17.7641	−0.611465
$845$	−3.45681	−0.118918
$846$	−25.6880	−0.883170
$847$	6.68539	0.229713
$848$	−5.67030	−0.194719
$849$	−20.6544	−0.708856
$850$	−25.7831	−0.884353
$851$	−3.32895	−0.114115
$852$	12.8797	0.441252
$853$	17.6396	0.603970	0.301985	−	0.953313i	$-0.402351\pi$
$853$	17.6396	0.603970	0.301985	+	0.953313i	$0.402351\pi$
$854$	48.0068	1.64276
$855$	−6.16704	−0.210908
$856$	8.99937	0.307592
$857$	29.9657	1.02361	0.511804	−	0.859102i	$-0.328978\pi$
$857$	29.9657	1.02361	0.511804	+	0.859102i	$0.328978\pi$
$858$	6.23809	0.212965
$859$	−40.9408	−1.39688	−0.698441	−	0.715668i	$-0.746122\pi$
$859$	−40.9408	−1.39688	−0.698441	+	0.715668i	$0.746122\pi$
$860$	−0.554203	−0.0188982
$861$	−47.6186	−1.62284
$862$	10.1330	0.345133
$863$	−52.5030	−1.78722	−0.893612	−	0.448840i	$-0.851837\pi$
$863$	−52.5030	−1.78722	−0.893612	+	0.448840i	$0.851837\pi$
$864$	72.7121	2.47371
$865$	−2.67577	−0.0909791
$866$	−72.2337	−2.45460
$867$	−26.3469	−0.894786
$868$	−7.02045	−0.238289
$869$	58.0076	1.96777
$870$	−1.50157	−0.0509081
$871$	3.02601	0.102533
$872$	−20.6593	−0.699614
$873$	−11.3554	−0.384323
$874$	−5.92871	−0.200542
$875$	−7.34563	−0.248328
$876$	−24.4530	−0.826192
$877$	−23.4391	−0.791481	−0.395740	−	0.918362i	$-0.629512\pi$
$877$	−23.4391	−0.791481	−0.395740	+	0.918362i	$0.629512\pi$
$878$	0.461902	0.0155884
$879$	65.1858	2.19866
$880$	−4.87687	−0.164399
$881$	30.7821	1.03707	0.518537	−	0.855055i	$-0.326477\pi$
$881$	30.7821	1.03707	0.518537	+	0.855055i	$0.326477\pi$
$882$	−7.78724	−0.262210
$883$	34.1770	1.15015	0.575074	−	0.818102i	$-0.304973\pi$
$883$	34.1770	1.15015	0.575074	+	0.818102i	$0.304973\pi$
$884$	1.04440	0.0351270
$885$	8.10909	0.272584
$886$	−59.7687	−2.00797
$887$	11.0064	0.369560	0.184780	−	0.982780i	$-0.440843\pi$
$887$	11.0064	0.369560	0.184780	+	0.982780i	$0.440843\pi$
$888$	15.4849	0.519638
$889$	29.3463	0.984244
$890$	−7.48380	−0.250857
$891$	66.2392	2.21910
$892$	33.8454	1.13323
$893$	−6.94594	−0.232437
$894$	45.3247	1.51588
$895$	−0.950538	−0.0317730
$896$	−29.8390	−0.996851
$897$	0.956360	0.0319319
$898$	60.6793	2.02489
$899$	−2.17124	−0.0724148
$900$	−39.8906	−1.32969
$901$	−3.35158	−0.111657
$902$	35.7035	1.18880
$903$	−15.3820	−0.511879
$904$	15.1561	0.504086
$905$	0.688604	0.0228900
$906$	−87.7039	−2.91377
$907$	−2.49151	−0.0827293	−0.0413647	−	0.999144i	$-0.513171\pi$
$907$	−2.49151	−0.0827293	−0.0413647	+	0.999144i	$0.513171\pi$
$908$	23.3607	0.775251
$909$	−27.7245	−0.919564
$910$	0.400098	0.0132631
$911$	−11.3978	−0.377626	−0.188813	−	0.982013i	$-0.560464\pi$
$911$	−11.3978	−0.377626	−0.188813	+	0.982013i	$0.560464\pi$
$912$	52.1208	1.72589
$913$	14.5388	0.481165
$914$	−34.7634	−1.14987
$915$	−8.23014	−0.272080
$916$	−4.25420	−0.140563
$917$	−42.3371	−1.39809
$918$	64.5112	2.12919
$919$	−16.1279	−0.532011	−0.266005	−	0.963972i	$-0.585704\pi$
$919$	−16.1279	−0.532011	−0.266005	+	0.963972i	$0.585704\pi$
$920$	−0.395602	−0.0130426
$921$	80.6831	2.65860
$922$	−3.59791	−0.118491
$923$	−1.06138	−0.0349356
$924$	37.2991	1.22705
$925$	−16.4060	−0.539426
$926$	−36.8912	−1.21232
$927$	−91.5744	−3.00770
$928$	5.89673	0.193570
$929$	5.45259	0.178894	0.0894468	−	0.995992i	$-0.471490\pi$
$929$	5.45259	0.178894	0.0894468	+	0.995992i	$0.471490\pi$
$930$	3.26027	0.106908
$931$	−2.10564	−0.0690096
$932$	−22.0650	−0.722762
$933$	82.0130	2.68498
$934$	37.8495	1.23847
$935$	−2.88260	−0.0942709
$936$	−3.10268	−0.101414
$937$	−2.52709	−0.0825566	−0.0412783	−	0.999148i	$-0.513143\pi$
$937$	−2.52709	−0.0825566	−0.0412783	+	0.999148i	$0.513143\pi$
$938$	49.0118	1.60029
$939$	−10.0309	−0.327346
$940$	0.653852	0.0213263
$941$	−37.8880	−1.23511	−0.617557	−	0.786526i	$-0.711877\pi$
$941$	−37.8880	−1.23511	−0.617557	+	0.786526i	$0.711877\pi$
$942$	−84.5691	−2.75541
$943$	5.47369	0.178248
$944$	−47.7994	−1.55574
$945$	9.12326	0.296780
$946$	11.5331	0.374974
$947$	4.49419	0.146041	0.0730207	−	0.997330i	$-0.476736\pi$
$947$	4.49419	0.146041	0.0730207	+	0.997330i	$0.476736\pi$
$948$	58.3584	1.89539
$949$	2.01509	0.0654127
$950$	−29.2183	−0.947968
$951$	9.29739	0.301489
$952$	−11.9908	−0.388624
$953$	−25.5723	−0.828369	−0.414184	−	0.910193i	$-0.635933\pi$
$953$	−25.5723	−0.828369	−0.414184	+	0.910193i	$0.635933\pi$
$954$	−14.0465	−0.454773
$955$	6.77565	0.219255
$956$	5.48122	0.177275
$957$	11.5356	0.372893
$958$	13.8098	0.446175
$959$	−32.8304	−1.06015
$960$	−0.470170	−0.0151747
$961$	−26.2857	−0.847927
$962$	1.80019	0.0580406
$963$	42.1333	1.35773
$964$	−25.7721	−0.830064
$965$	−6.02466	−0.193941
$966$	15.4900	0.498383
$967$	−17.2387	−0.554359	−0.277180	−	0.960818i	$-0.589400\pi$
$967$	−17.2387	−0.554359	−0.277180	+	0.960818i	$0.589400\pi$
$968$	3.57463	0.114893
$969$	30.8073	0.989674
$970$	0.782955	0.0251392
$971$	−1.57662	−0.0505962	−0.0252981	−	0.999680i	$-0.508053\pi$
$971$	−1.57662	−0.0505962	−0.0252981	+	0.999680i	$0.508053\pi$
$972$	23.3442	0.748767
$973$	38.4542	1.23278
$974$	23.1503	0.741785
$975$	4.71321	0.150944
$976$	48.5130	1.55286
$977$	6.60529	0.211322	0.105661	−	0.994402i	$-0.466304\pi$
$977$	6.60529	0.211322	0.105661	+	0.994402i	$0.466304\pi$
$978$	122.306	3.91090
$979$	57.4931	1.83749
$980$	0.198213	0.00633169
$981$	−96.7231	−3.08813
$982$	−31.1194	−0.993061
$983$	−6.41656	−0.204657	−0.102328	−	0.994751i	$-0.532629\pi$
$983$	−6.41656	−0.204657	−0.102328	+	0.994751i	$0.532629\pi$
$984$	−25.4613	−0.811675
$985$	3.17171	0.101059
$986$	5.23166	0.166610
$987$	18.1477	0.577648
$988$	1.18355	0.0376539
$989$	1.76814	0.0562235
$990$	−12.0810	−0.383959
$991$	−34.2769	−1.08884	−0.544420	−	0.838813i	$-0.683250\pi$
$991$	−34.2769	−1.08884	−0.544420	+	0.838813i	$0.683250\pi$
$992$	−12.8032	−0.406502
$993$	−79.7459	−2.53066
$994$	−17.1909	−0.545263
$995$	5.10178	0.161737
$996$	14.6268	0.463467
$997$	24.4037	0.772872	0.386436	−	0.922316i	$-0.373706\pi$
$997$	24.4037	0.772872	0.386436	+	0.922316i	$0.373706\pi$
$998$	54.9544	1.73955
$999$	41.0490	1.29873

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.c.1.3	✓	13
3.2	odd	2		6003.2.a.o.1.11		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.c.1.3	✓	13	1.1	even	1	trivial
6003.2.a.o.1.11		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:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q-1.78056 q^{2} +3.14895 q^{3} +1.17038 q^{4} +0.267809 q^{5} -5.60688 q^{6} +2.76268 q^{7} +1.47718 q^{8} +6.91588 q^{9} +O(q^{10})\)	\(q-1.78056 q^{2} +3.14895 q^{3} +1.17038 q^{4} +0.267809 q^{5} -5.60688 q^{6} +2.76268 q^{7} +1.47718 q^{8} +6.91588 q^{9} -0.476849 q^{10} +3.66332 q^{11} +3.68547 q^{12} -0.303708 q^{13} -4.91910 q^{14} +0.843317 q^{15} -4.97097 q^{16} -2.93822 q^{17} -12.3141 q^{18} -3.32970 q^{19} +0.313439 q^{20} +8.69953 q^{21} -6.52275 q^{22} -1.00000 q^{23} +4.65157 q^{24} -4.92828 q^{25} +0.540769 q^{26} +12.3309 q^{27} +3.23339 q^{28} +1.00000 q^{29} -1.50157 q^{30} -2.17124 q^{31} +5.89673 q^{32} +11.5356 q^{33} +5.23166 q^{34} +0.739869 q^{35} +8.09422 q^{36} +3.32895 q^{37} +5.92871 q^{38} -0.956360 q^{39} +0.395602 q^{40} -5.47369 q^{41} -15.4900 q^{42} -1.76814 q^{43} +4.28748 q^{44} +1.85213 q^{45} +1.78056 q^{46} +2.08606 q^{47} -15.6533 q^{48} +0.632383 q^{49} +8.77508 q^{50} -9.25230 q^{51} -0.355454 q^{52} +1.14068 q^{53} -21.9559 q^{54} +0.981069 q^{55} +4.08097 q^{56} -10.4850 q^{57} -1.78056 q^{58} +9.61571 q^{59} +0.987003 q^{60} -9.75926 q^{61} +3.86601 q^{62} +19.1063 q^{63} -0.557525 q^{64} -0.0813356 q^{65} -20.5398 q^{66} -9.96357 q^{67} -3.43884 q^{68} -3.14895 q^{69} -1.31738 q^{70} +3.49473 q^{71} +10.2160 q^{72} -6.63498 q^{73} -5.92739 q^{74} -15.5189 q^{75} -3.89702 q^{76} +10.1206 q^{77} +1.70285 q^{78} +15.8347 q^{79} -1.33127 q^{80} +18.0818 q^{81} +9.74622 q^{82} +3.96876 q^{83} +10.1818 q^{84} -0.786881 q^{85} +3.14827 q^{86} +3.14895 q^{87} +5.41138 q^{88} +15.6943 q^{89} -3.29783 q^{90} -0.839046 q^{91} -1.17038 q^{92} -6.83711 q^{93} -3.71434 q^{94} -0.891722 q^{95} +18.5685 q^{96} -1.64194 q^{97} -1.12599 q^{98} +25.3351 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9} + 10 q^{10} + 10 q^{11} + 3 q^{12} + 7 q^{13} - 12 q^{14} + 8 q^{15} + 2 q^{16} + 26 q^{17} + 7 q^{18} + 25 q^{20} + 11 q^{21} - 15 q^{22} - 13 q^{23} + 10 q^{24} + 19 q^{25} - 15 q^{26} + 12 q^{27} + 5 q^{28} + 13 q^{29} + 7 q^{30} - 6 q^{31} + 16 q^{32} + 3 q^{33} + 11 q^{34} + q^{35} - 22 q^{36} + 15 q^{37} + 8 q^{38} - 4 q^{39} + 14 q^{40} + 9 q^{41} - 34 q^{42} + q^{43} + 29 q^{44} + 16 q^{45} - 4 q^{46} + 15 q^{47} - 15 q^{48} + 4 q^{49} + 31 q^{50} - 14 q^{51} - 8 q^{52} + 43 q^{53} - 35 q^{54} - 3 q^{55} - 5 q^{56} + 6 q^{57} + 4 q^{58} - 9 q^{59} + 3 q^{60} + 20 q^{61} + 11 q^{62} + 21 q^{63} - 16 q^{64} - 25 q^{65} - q^{66} + q^{67} + 21 q^{68} - 3 q^{69} - 2 q^{70} + 17 q^{71} - 59 q^{72} + 26 q^{73} + 11 q^{74} - 43 q^{75} + 8 q^{76} + 17 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{80} - 3 q^{81} - 25 q^{82} + 4 q^{83} - 78 q^{84} + 20 q^{85} - 13 q^{86} + 3 q^{87} - 32 q^{88} + 48 q^{89} + 17 q^{90} - 9 q^{91} - 12 q^{92} - 8 q^{93} - 65 q^{94} + 8 q^{95} + 8 q^{96} + 30 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9 + 10 * q^10 + 10 * q^11 + 3 * q^12 + 7 * q^13 - 12 * q^14 + 8 * q^15 + 2 * q^16 + 26 * q^17 + 7 * q^18 + 25 * q^20 + 11 * q^21 - 15 * q^22 - 13 * q^23 + 10 * q^24 + 19 * q^25 - 15 * q^26 + 12 * q^27 + 5 * q^28 + 13 * q^29 + 7 * q^30 - 6 * q^31 + 16 * q^32 + 3 * q^33 + 11 * q^34 + q^35 - 22 * q^36 + 15 * q^37 + 8 * q^38 - 4 * q^39 + 14 * q^40 + 9 * q^41 - 34 * q^42 + q^43 + 29 * q^44 + 16 * q^45 - 4 * q^46 + 15 * q^47 - 15 * q^48 + 4 * q^49 + 31 * q^50 - 14 * q^51 - 8 * q^52 + 43 * q^53 - 35 * q^54 - 3 * q^55 - 5 * q^56 + 6 * q^57 + 4 * q^58 - 9 * q^59 + 3 * q^60 + 20 * q^61 + 11 * q^62 + 21 * q^63 - 16 * q^64 - 25 * q^65 - q^66 + q^67 + 21 * q^68 - 3 * q^69 - 2 * q^70 + 17 * q^71 - 59 * q^72 + 26 * q^73 + 11 * q^74 - 43 * q^75 + 8 * q^76 + 17 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^80 - 3 * q^81 - 25 * q^82 + 4 * q^83 - 78 * q^84 + 20 * q^85 - 13 * q^86 + 3 * q^87 - 32 * q^88 + 48 * q^89 + 17 * q^90 - 9 * q^91 - 12 * q^92 - 8 * q^93 - 65 * q^94 + 8 * q^95 + 8 * q^96 + 30 * q^97 + 2 * q^98 + 4 * q^99

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