LMFDB - Embedded newform 667.2.a.b.1.7

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:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 13 x^{10} + 41 x^{9} + 54 x^{8} - 188 x^{7} - 77 x^{6} + 342 x^{5} + 13 x^{4} + \cdots - 5 $ x^12 - 3x^11 - 13x^10 + 41x^9 + 54x^8 - 188x^7 - 77x^6 + 342x^5 + 13x^4 - 215x^3 + 9x^2 + 37*x - 5
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.147789$ 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)

$f(q)$	$=$	$q-0.147789 q^{2} -3.02697 q^{3} -1.97816 q^{4} +0.429801 q^{5} +0.447353 q^{6} +0.404424 q^{7} +0.587929 q^{8} +6.16253 q^{9} +O(q^{10})$	\(q-0.147789 q^{2} -3.02697 q^{3} -1.97816 q^{4} +0.429801 q^{5} +0.447353 q^{6} +0.404424 q^{7} +0.587929 q^{8} +6.16253 q^{9} -0.0635200 q^{10} +3.93677 q^{11} +5.98782 q^{12} -2.88206 q^{13} -0.0597695 q^{14} -1.30099 q^{15} +3.86943 q^{16} -0.528453 q^{17} -0.910755 q^{18} +0.103632 q^{19} -0.850214 q^{20} -1.22418 q^{21} -0.581812 q^{22} -1.00000 q^{23} -1.77964 q^{24} -4.81527 q^{25} +0.425937 q^{26} -9.57286 q^{27} -0.800015 q^{28} -1.00000 q^{29} +0.192273 q^{30} +3.45912 q^{31} -1.74772 q^{32} -11.9165 q^{33} +0.0780996 q^{34} +0.173822 q^{35} -12.1905 q^{36} -9.17731 q^{37} -0.0153157 q^{38} +8.72389 q^{39} +0.252692 q^{40} -1.95151 q^{41} +0.180920 q^{42} -4.09795 q^{43} -7.78755 q^{44} +2.64866 q^{45} +0.147789 q^{46} -0.400254 q^{47} -11.7126 q^{48} -6.83644 q^{49} +0.711645 q^{50} +1.59961 q^{51} +5.70117 q^{52} +3.15300 q^{53} +1.41477 q^{54} +1.69203 q^{55} +0.237773 q^{56} -0.313691 q^{57} +0.147789 q^{58} +1.89971 q^{59} +2.57357 q^{60} -5.16845 q^{61} -0.511221 q^{62} +2.49228 q^{63} -7.48056 q^{64} -1.23871 q^{65} +1.76113 q^{66} +7.10144 q^{67} +1.04536 q^{68} +3.02697 q^{69} -0.0256890 q^{70} +0.983580 q^{71} +3.62313 q^{72} -7.65354 q^{73} +1.35631 q^{74} +14.5757 q^{75} -0.205001 q^{76} +1.59212 q^{77} -1.28930 q^{78} +10.7454 q^{79} +1.66308 q^{80} +10.4892 q^{81} +0.288411 q^{82} -15.7499 q^{83} +2.42162 q^{84} -0.227130 q^{85} +0.605633 q^{86} +3.02697 q^{87} +2.31454 q^{88} -3.98637 q^{89} -0.391443 q^{90} -1.16557 q^{91} +1.97816 q^{92} -10.4707 q^{93} +0.0591533 q^{94} +0.0445412 q^{95} +5.29028 q^{96} +3.30810 q^{97} +1.01035 q^{98} +24.2604 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9} - 6 q^{11} - 21 q^{12} - 15 q^{13} - 8 q^{14} + 6 q^{15} + 17 q^{16} - 18 q^{17} - 12 q^{18} - 6 q^{19} - 39 q^{20} - q^{21} - 5 q^{22} - 12 q^{23} + 4 q^{24} + 14 q^{25} - 3 q^{26} - 12 q^{27} - 19 q^{28} - 12 q^{29} - 11 q^{30} + 16 q^{31} - 21 q^{32} - 19 q^{33} - 7 q^{34} - 11 q^{35} - 13 q^{36} - q^{37} - 24 q^{38} + 6 q^{39} + 30 q^{40} + 3 q^{41} + 22 q^{42} - 23 q^{43} + 23 q^{44} - 22 q^{45} + 3 q^{46} - 35 q^{47} - 21 q^{48} + 3 q^{49} - 2 q^{50} - 34 q^{51} - 45 q^{53} + 55 q^{54} + 17 q^{55} - 17 q^{56} - 34 q^{57} + 3 q^{58} - 11 q^{59} + 93 q^{60} + 4 q^{61} - 7 q^{62} + q^{63} + 15 q^{64} + 5 q^{65} - 35 q^{66} - 19 q^{67} + q^{68} + 3 q^{69} + 14 q^{70} + 19 q^{71} + 4 q^{72} + 10 q^{73} - 15 q^{74} - 3 q^{75} - 4 q^{76} - 39 q^{77} + 16 q^{78} + 17 q^{79} - 90 q^{80} + 4 q^{81} - 3 q^{82} - 12 q^{83} + 42 q^{84} + 14 q^{85} + 17 q^{86} + 3 q^{87} - 2 q^{88} - 20 q^{89} + 65 q^{90} + 11 q^{91} - 11 q^{92} - 2 q^{93} + 13 q^{94} + 12 q^{95} + 14 q^{96} - 12 q^{97} + 75 q^{98} - 4 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9 - 6 * q^11 - 21 * q^12 - 15 * q^13 - 8 * q^14 + 6 * q^15 + 17 * q^16 - 18 * q^17 - 12 * q^18 - 6 * q^19 - 39 * q^20 - q^21 - 5 * q^22 - 12 * q^23 + 4 * q^24 + 14 * q^25 - 3 * q^26 - 12 * q^27 - 19 * q^28 - 12 * q^29 - 11 * q^30 + 16 * q^31 - 21 * q^32 - 19 * q^33 - 7 * q^34 - 11 * q^35 - 13 * q^36 - q^37 - 24 * q^38 + 6 * q^39 + 30 * q^40 + 3 * q^41 + 22 * q^42 - 23 * q^43 + 23 * q^44 - 22 * q^45 + 3 * q^46 - 35 * q^47 - 21 * q^48 + 3 * q^49 - 2 * q^50 - 34 * q^51 - 45 * q^53 + 55 * q^54 + 17 * q^55 - 17 * q^56 - 34 * q^57 + 3 * q^58 - 11 * q^59 + 93 * q^60 + 4 * q^61 - 7 * q^62 + q^63 + 15 * q^64 + 5 * q^65 - 35 * q^66 - 19 * q^67 + q^68 + 3 * q^69 + 14 * q^70 + 19 * q^71 + 4 * q^72 + 10 * q^73 - 15 * q^74 - 3 * q^75 - 4 * q^76 - 39 * q^77 + 16 * q^78 + 17 * q^79 - 90 * q^80 + 4 * q^81 - 3 * q^82 - 12 * q^83 + 42 * q^84 + 14 * q^85 + 17 * q^86 + 3 * q^87 - 2 * q^88 - 20 * q^89 + 65 * q^90 + 11 * q^91 - 11 * q^92 - 2 * q^93 + 13 * q^94 + 12 * q^95 + 14 * q^96 - 12 * q^97 + 75 * 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 $

$2$	−0.147789	−0.104503	−0.0522514	−	0.998634i	$-0.516640\pi$
$2$	−0.147789	−0.104503	−0.0522514	+	0.998634i	$0.516640\pi$
$3$	−3.02697	−1.74762	−0.873810	−	0.486268i	$-0.838358\pi$
$3$	−3.02697	−1.74762	−0.873810	+	0.486268i	$0.838358\pi$
$4$	−1.97816	−0.989079
$5$	0.429801	0.192213	0.0961064	−	0.995371i	$-0.469361\pi$
$5$	0.429801	0.192213	0.0961064	+	0.995371i	$0.469361\pi$
$6$	0.447353	0.182631
$7$	0.404424	0.152858	0.0764290	−	0.997075i	$-0.475648\pi$
$7$	0.404424	0.152858	0.0764290	+	0.997075i	$0.475648\pi$
$8$	0.587929	0.207864
$9$	6.16253	2.05418
$10$	−0.0635200	−0.0200868
$11$	3.93677	1.18698	0.593490	−	0.804841i	$-0.297750\pi$
$11$	3.93677	1.18698	0.593490	+	0.804841i	$0.297750\pi$
$12$	5.98782	1.72853
$13$	−2.88206	−0.799339	−0.399669	−	0.916659i	$-0.630875\pi$
$13$	−2.88206	−0.799339	−0.399669	+	0.916659i	$0.630875\pi$
$14$	−0.0597695	−0.0159741
$15$	−1.30099	−0.335915
$16$	3.86943	0.967357
$17$	−0.528453	−0.128169	−0.0640843	−	0.997944i	$-0.520413\pi$
$17$	−0.528453	−0.128169	−0.0640843	+	0.997944i	$0.520413\pi$
$18$	−0.910755	−0.214667
$19$	0.103632	0.0237748	0.0118874	−	0.999929i	$-0.496216\pi$
$19$	0.103632	0.0237748	0.0118874	+	0.999929i	$0.496216\pi$
$20$	−0.850214	−0.190114
$21$	−1.22418	−0.267138
$22$	−0.581812	−0.124043
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.77964	−0.363268
$25$	−4.81527	−0.963054
$26$	0.425937	0.0835331
$27$	−9.57286	−1.84230
$28$	−0.800015	−0.151189
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0.192273	0.0351040
$31$	3.45912	0.621277	0.310639	−	0.950528i	$-0.399457\pi$
$31$	3.45912	0.621277	0.310639	+	0.950528i	$0.399457\pi$
$32$	−1.74772	−0.308956
$33$	−11.9165	−2.07439
$34$	0.0780996	0.0133940
$35$	0.173822	0.0293813
$36$	−12.1905	−2.03174
$37$	−9.17731	−1.50874	−0.754370	−	0.656449i	$-0.772058\pi$
$37$	−9.17731	−1.50874	−0.754370	+	0.656449i	$0.772058\pi$
$38$	−0.0153157	−0.00248454
$39$	8.72389	1.39694
$40$	0.252692	0.0399542
$41$	−1.95151	−0.304774	−0.152387	−	0.988321i	$-0.548696\pi$
$41$	−1.95151	−0.304774	−0.152387	+	0.988321i	$0.548696\pi$
$42$	0.180920	0.0279166
$43$	−4.09795	−0.624932	−0.312466	−	0.949929i	$-0.601155\pi$
$43$	−4.09795	−0.624932	−0.312466	+	0.949929i	$0.601155\pi$
$44$	−7.78755	−1.17402
$45$	2.64866	0.394839
$46$	0.147789	0.0217903
$47$	−0.400254	−0.0583831	−0.0291916	−	0.999574i	$-0.509293\pi$
$47$	−0.400254	−0.0583831	−0.0291916	+	0.999574i	$0.509293\pi$
$48$	−11.7126	−1.69057
$49$	−6.83644	−0.976634
$50$	0.711645	0.100642
$51$	1.59961	0.223990
$52$	5.70117	0.790610
$53$	3.15300	0.433097	0.216549	−	0.976272i	$-0.430520\pi$
$53$	3.15300	0.433097	0.216549	+	0.976272i	$0.430520\pi$
$54$	1.41477	0.192525
$55$	1.69203	0.228153
$56$	0.237773	0.0317737
$57$	−0.313691	−0.0415494
$58$	0.147789	0.0194057
$59$	1.89971	0.247321	0.123660	−	0.992325i	$-0.460537\pi$
$59$	1.89971	0.247321	0.123660	+	0.992325i	$0.460537\pi$
$60$	2.57357	0.332247
$61$	−5.16845	−0.661752	−0.330876	−	0.943674i	$-0.607344\pi$
$61$	−5.16845	−0.661752	−0.330876	+	0.943674i	$0.607344\pi$
$62$	−0.511221	−0.0649252
$63$	2.49228	0.313997
$64$	−7.48056	−0.935070
$65$	−1.23871	−0.153643
$66$	1.76113	0.216780
$67$	7.10144	0.867579	0.433790	−	0.901014i	$-0.357176\pi$
$67$	7.10144	0.867579	0.433790	+	0.901014i	$0.357176\pi$
$68$	1.04536	0.126769
$69$	3.02697	0.364404
$70$	−0.0256890	−0.00307042
$71$	0.983580	0.116729	0.0583647	−	0.998295i	$-0.481411\pi$
$71$	0.983580	0.116729	0.0583647	+	0.998295i	$0.481411\pi$
$72$	3.62313	0.426990
$73$	−7.65354	−0.895779	−0.447889	−	0.894089i	$-0.647824\pi$
$73$	−7.65354	−0.895779	−0.447889	+	0.894089i	$0.647824\pi$
$74$	1.35631	0.157668
$75$	14.5757	1.68305
$76$	−0.205001	−0.0235152
$77$	1.59212	0.181439
$78$	−1.28930	−0.145984
$79$	10.7454	1.20896	0.604478	−	0.796622i	$-0.293382\pi$
$79$	10.7454	1.20896	0.604478	+	0.796622i	$0.293382\pi$
$80$	1.66308	0.185938
$81$	10.4892	1.16546
$82$	0.288411	0.0318497
$83$	−15.7499	−1.72878	−0.864388	−	0.502825i	$-0.832294\pi$
$83$	−15.7499	−1.72878	−0.864388	+	0.502825i	$0.832294\pi$
$84$	2.42162	0.264220
$85$	−0.227130	−0.0246357
$86$	0.605633	0.0653071
$87$	3.02697	0.324525
$88$	2.31454	0.246731
$89$	−3.98637	−0.422554	−0.211277	−	0.977426i	$-0.567762\pi$
$89$	−3.98637	−0.422554	−0.211277	+	0.977426i	$0.567762\pi$
$90$	−0.391443	−0.0412618
$91$	−1.16557	−0.122185
$92$	1.97816	0.206237
$93$	−10.4707	−1.08576
$94$	0.0591533	0.00610120
$95$	0.0445412	0.00456983
$96$	5.29028	0.539937
$97$	3.30810	0.335887	0.167943	−	0.985797i	$-0.446287\pi$
$97$	3.30810	0.335887	0.167943	+	0.985797i	$0.446287\pi$
$98$	1.01035	0.102061
$99$	24.2604	2.43827
$100$	9.52537	0.952537
$101$	−5.59146	−0.556372	−0.278186	−	0.960527i	$-0.589733\pi$
$101$	−5.59146	−0.556372	−0.278186	+	0.960527i	$0.589733\pi$
$102$	−0.236405	−0.0234076
$103$	−11.7953	−1.16223	−0.581115	−	0.813821i	$-0.697383\pi$
$103$	−11.7953	−1.16223	−0.581115	+	0.813821i	$0.697383\pi$
$104$	−1.69444	−0.166154
$105$	−0.526153	−0.0513473
$106$	−0.465979	−0.0452599
$107$	−4.85282	−0.469140	−0.234570	−	0.972099i	$-0.575368\pi$
$107$	−4.85282	−0.469140	−0.234570	+	0.972099i	$0.575368\pi$
$108$	18.9366	1.82218
$109$	−1.21441	−0.116319	−0.0581596	−	0.998307i	$-0.518523\pi$
$109$	−1.21441	−0.116319	−0.0581596	+	0.998307i	$0.518523\pi$
$110$	−0.250063	−0.0238426
$111$	27.7794	2.63670
$112$	1.56489	0.147868
$113$	−9.30344	−0.875194	−0.437597	−	0.899171i	$-0.644170\pi$
$113$	−9.30344	−0.875194	−0.437597	+	0.899171i	$0.644170\pi$
$114$	0.0463601	0.00434202
$115$	−0.429801	−0.0400792
$116$	1.97816	0.183667
$117$	−17.7608	−1.64198
$118$	−0.280756	−0.0258457
$119$	−0.213719	−0.0195916
$120$	−0.764892	−0.0698247
$121$	4.49815	0.408922
$122$	0.763841	0.0691549
$123$	5.90714	0.532629
$124$	−6.84270	−0.614492
$125$	−4.21861	−0.377324
$126$	−0.368331	−0.0328136
$127$	15.2955	1.35726	0.678628	−	0.734482i	$-0.262575\pi$
$127$	15.2955	1.35726	0.678628	+	0.734482i	$0.262575\pi$
$128$	4.60098	0.406673
$129$	12.4044	1.09214
$130$	0.183068	0.0160561
$131$	−9.70884	−0.848265	−0.424133	−	0.905600i	$-0.639421\pi$
$131$	−9.70884	−0.848265	−0.424133	+	0.905600i	$0.639421\pi$
$132$	23.5727	2.05174
$133$	0.0419113	0.00363417
$134$	−1.04952	−0.0906644
$135$	−4.11443	−0.354113
$136$	−0.310693	−0.0266417
$137$	22.2655	1.90227	0.951136	−	0.308773i	$-0.0999184\pi$
$137$	22.2655	1.90227	0.951136	+	0.308773i	$0.0999184\pi$
$138$	−0.447353	−0.0380812
$139$	−4.84475	−0.410927	−0.205463	−	0.978665i	$-0.565870\pi$
$139$	−4.84475	−0.410927	−0.205463	+	0.978665i	$0.565870\pi$
$140$	−0.343847	−0.0290604
$141$	1.21156	0.102032
$142$	−0.145362	−0.0121985
$143$	−11.3460	−0.948800
$144$	23.8454	1.98712
$145$	−0.429801	−0.0356930
$146$	1.13111	0.0936114
$147$	20.6937	1.70679
$148$	18.1542	1.49226
$149$	−12.5782	−1.03044	−0.515222	−	0.857057i	$-0.672291\pi$
$149$	−12.5782	−1.03044	−0.515222	+	0.857057i	$0.672291\pi$
$150$	−2.15413	−0.175884
$151$	2.17539	0.177031	0.0885153	−	0.996075i	$-0.471788\pi$
$151$	2.17539	0.177031	0.0885153	+	0.996075i	$0.471788\pi$
$152$	0.0609283	0.00494194
$153$	−3.25661	−0.263281
$154$	−0.235299	−0.0189609
$155$	1.48674	0.119417
$156$	−17.2572	−1.38168
$157$	10.7159	0.855219	0.427610	−	0.903964i	$-0.359356\pi$
$157$	10.7159	0.855219	0.427610	+	0.903964i	$0.359356\pi$
$158$	−1.58806	−0.126339
$159$	−9.54402	−0.756890
$160$	−0.751171	−0.0593853
$161$	−0.404424	−0.0318731
$162$	−1.55018	−0.121794
$163$	−15.5699	−1.21953	−0.609763	−	0.792584i	$-0.708735\pi$
$163$	−15.5699	−1.21953	−0.609763	+	0.792584i	$0.708735\pi$
$164$	3.86039	0.301446
$165$	−5.12171	−0.398725
$166$	2.32767	0.180662
$167$	−11.4797	−0.888328	−0.444164	−	0.895946i	$-0.646499\pi$
$167$	−11.4797	−0.888328	−0.444164	+	0.895946i	$0.646499\pi$
$168$	−0.719730	−0.0555284
$169$	−4.69374	−0.361057
$170$	0.0335673	0.00257449
$171$	0.638636	0.0488377
$172$	8.10640	0.618107
$173$	−14.9976	−1.14024	−0.570122	−	0.821560i	$-0.693104\pi$
$173$	−14.9976	−1.14024	−0.570122	+	0.821560i	$0.693104\pi$
$174$	−0.447353	−0.0339137
$175$	−1.94741	−0.147211
$176$	15.2330	1.14823
$177$	−5.75034	−0.432222
$178$	0.589142	0.0441581
$179$	−18.6679	−1.39531	−0.697653	−	0.716436i	$-0.745772\pi$
$179$	−18.6679	−1.39531	−0.697653	+	0.716436i	$0.745772\pi$
$180$	−5.23947	−0.390527
$181$	−24.0411	−1.78696	−0.893479	−	0.449106i	$-0.851743\pi$
$181$	−24.0411	−1.78696	−0.893479	+	0.449106i	$0.851743\pi$
$182$	0.172259	0.0127687
$183$	15.6447	1.15649
$184$	−0.587929	−0.0433427
$185$	−3.94442	−0.289999
$186$	1.54745	0.113465
$187$	−2.08040	−0.152134
$188$	0.791767	0.0577455
$189$	−3.87150	−0.281610
$190$	−0.00658271	−0.000477560 0
$191$	3.38115	0.244651	0.122326	−	0.992490i	$-0.460965\pi$
$191$	3.38115	0.244651	0.122326	+	0.992490i	$0.460965\pi$
$192$	22.6434	1.63415
$193$	19.0501	1.37126	0.685629	−	0.727951i	$-0.259527\pi$
$193$	19.0501	1.37126	0.685629	+	0.727951i	$0.259527\pi$
$194$	−0.488901	−0.0351011
$195$	3.74954	0.268510
$196$	13.5236	0.965969
$197$	−25.3356	−1.80509	−0.902543	−	0.430599i	$-0.858302\pi$
$197$	−25.3356	−1.80509	−0.902543	+	0.430599i	$0.858302\pi$
$198$	−3.58543	−0.254806
$199$	9.27066	0.657180	0.328590	−	0.944473i	$-0.393427\pi$
$199$	9.27066	0.657180	0.328590	+	0.944473i	$0.393427\pi$
$200$	−2.83104	−0.200185
$201$	−21.4958	−1.51620
$202$	0.826358	0.0581424
$203$	−0.404424	−0.0283850
$204$	−3.16428	−0.221544
$205$	−0.838759	−0.0585815
$206$	1.74322	0.121456
$207$	−6.16253	−0.428325
$208$	−11.1519	−0.773246
$209$	0.407976	0.0282203
$210$	0.0777598	0.00536593
$211$	16.7457	1.15282	0.576411	−	0.817160i	$-0.304453\pi$
$211$	16.7457	1.15282	0.576411	+	0.817160i	$0.304453\pi$
$212$	−6.23713	−0.428368
$213$	−2.97726	−0.203999
$214$	0.717195	0.0490264
$215$	−1.76130	−0.120120
$216$	−5.62816	−0.382948
$217$	1.39895	0.0949672
$218$	0.179477	0.0121557
$219$	23.1670	1.56548
$220$	−3.34710	−0.225661
$221$	1.52303	0.102450
$222$	−4.10550	−0.275543
$223$	−20.7996	−1.39285	−0.696423	−	0.717631i	$-0.745226\pi$
$223$	−20.7996	−1.39285	−0.696423	+	0.717631i	$0.745226\pi$
$224$	−0.706819	−0.0472264
$225$	−29.6742	−1.97828
$226$	1.37495	0.0914602
$227$	−12.8644	−0.853838	−0.426919	−	0.904290i	$-0.640401\pi$
$227$	−12.8644	−0.853838	−0.426919	+	0.904290i	$0.640401\pi$
$228$	0.620530	0.0410956
$229$	1.21701	0.0804222	0.0402111	−	0.999191i	$-0.487197\pi$
$229$	1.21701	0.0804222	0.0402111	+	0.999191i	$0.487197\pi$
$230$	0.0635200	0.00418838
$231$	−4.81931	−0.317087
$232$	−0.587929	−0.0385994
$233$	−11.7794	−0.771696	−0.385848	−	0.922562i	$-0.626091\pi$
$233$	−11.7794	−0.771696	−0.385848	+	0.922562i	$0.626091\pi$
$234$	2.62485	0.171592
$235$	−0.172030	−0.0112220
$236$	−3.75792	−0.244620
$237$	−32.5261	−2.11280
$238$	0.0315854	0.00204738
$239$	22.5572	1.45910	0.729551	−	0.683926i	$-0.239729\pi$
$239$	22.5572	1.45910	0.729551	+	0.683926i	$0.239729\pi$
$240$	−5.03410	−0.324950
$241$	26.7770	1.72486	0.862430	−	0.506176i	$-0.168942\pi$
$241$	26.7770	1.72486	0.862430	+	0.506176i	$0.168942\pi$
$242$	−0.664777	−0.0427335
$243$	−3.03174	−0.194486
$244$	10.2240	0.654525
$245$	−2.93831	−0.187722
$246$	−0.873012	−0.0556612
$247$	−0.298674	−0.0190041
$248$	2.03372	0.129141
$249$	47.6744	3.02124
$250$	0.623466	0.0394314
$251$	21.8381	1.37841	0.689203	−	0.724568i	$-0.257961\pi$
$251$	21.8381	1.37841	0.689203	+	0.724568i	$0.257961\pi$
$252$	−4.93012	−0.310568
$253$	−3.93677	−0.247503
$254$	−2.26051	−0.141837
$255$	0.687514	0.0430538
$256$	14.2811	0.892572
$257$	16.1529	1.00759	0.503796	−	0.863823i	$-0.331936\pi$
$257$	16.1529	1.00759	0.503796	+	0.863823i	$0.331936\pi$
$258$	−1.83323	−0.114132
$259$	−3.71153	−0.230623
$260$	2.45037	0.151965
$261$	−6.16253	−0.381451
$262$	1.43486	0.0886461
$263$	9.42982	0.581468	0.290734	−	0.956804i	$-0.406101\pi$
$263$	9.42982	0.581468	0.290734	+	0.956804i	$0.406101\pi$
$264$	−7.00603	−0.431192
$265$	1.35516	0.0832469
$266$	−0.00619404	−0.000379781 0
$267$	12.0666	0.738464
$268$	−14.0478	−0.858105
$269$	−17.1500	−1.04566	−0.522828	−	0.852438i	$-0.675123\pi$
$269$	−17.1500	−1.04566	−0.522828	+	0.852438i	$0.675123\pi$
$270$	0.608068	0.0370058
$271$	−17.5255	−1.06460	−0.532300	−	0.846556i	$-0.678672\pi$
$271$	−17.5255	−1.06460	−0.532300	+	0.846556i	$0.678672\pi$
$272$	−2.04481	−0.123985
$273$	3.52815	0.213534
$274$	−3.29060	−0.198793
$275$	−18.9566	−1.14313
$276$	−5.98782	−0.360424
$277$	3.25282	0.195443	0.0977216	−	0.995214i	$-0.468845\pi$
$277$	3.25282	0.195443	0.0977216	+	0.995214i	$0.468845\pi$
$278$	0.716002	0.0429430
$279$	21.3169	1.27621
$280$	0.102195	0.00610732
$281$	11.7514	0.701028	0.350514	−	0.936557i	$-0.386007\pi$
$281$	11.7514	0.701028	0.350514	+	0.936557i	$0.386007\pi$
$282$	−0.179055	−0.0106626
$283$	25.7409	1.53014	0.765070	−	0.643948i	$-0.222705\pi$
$283$	25.7409	1.53014	0.765070	+	0.643948i	$0.222705\pi$
$284$	−1.94568	−0.115455
$285$	−0.134825	−0.00798632
$286$	1.67682	0.0991522
$287$	−0.789236	−0.0465871
$288$	−10.7704	−0.634649
$289$	−16.7207	−0.983573
$290$	0.0635200	0.00373002
$291$	−10.0135	−0.587002
$292$	15.1399	0.885996
$293$	7.07899	0.413559	0.206780	−	0.978388i	$-0.433702\pi$
$293$	7.07899	0.413559	0.206780	+	0.978388i	$0.433702\pi$
$294$	−3.05830	−0.178364
$295$	0.816495	0.0475382
$296$	−5.39560	−0.313613
$297$	−37.6861	−2.18677
$298$	1.85892	0.107684
$299$	2.88206	0.166674
$300$	−28.8330	−1.66467
$301$	−1.65731	−0.0955258
$302$	−0.321499	−0.0185002
$303$	16.9252	0.972326
$304$	0.400997	0.0229987
$305$	−2.22140	−0.127197
$306$	0.481291	0.0275136
$307$	−11.2529	−0.642238	−0.321119	−	0.947039i	$-0.604059\pi$
$307$	−11.2529	−0.642238	−0.321119	+	0.947039i	$0.604059\pi$
$308$	−3.14947	−0.179458
$309$	35.7041	2.03114
$310$	−0.219723	−0.0124795
$311$	−24.1371	−1.36869	−0.684345	−	0.729158i	$-0.739912\pi$
$311$	−24.1371	−1.36869	−0.684345	+	0.729158i	$0.739912\pi$
$312$	5.12903	0.290374
$313$	1.48440	0.0839034	0.0419517	−	0.999120i	$-0.486642\pi$
$313$	1.48440	0.0839034	0.0419517	+	0.999120i	$0.486642\pi$
$314$	−1.58369	−0.0893727
$315$	1.07118	0.0603543
$316$	−21.2562	−1.19575
$317$	−4.45369	−0.250144	−0.125072	−	0.992148i	$-0.539916\pi$
$317$	−4.45369	−0.250144	−0.125072	+	0.992148i	$0.539916\pi$
$318$	1.41050	0.0790971
$319$	−3.93677	−0.220417
$320$	−3.21515	−0.179732
$321$	14.6893	0.819879
$322$	0.0597695	0.00333083
$323$	−0.0547647	−0.00304719
$324$	−20.7492	−1.15273
$325$	13.8779	0.769807
$326$	2.30106	0.127444
$327$	3.67598	0.203282
$328$	−1.14735	−0.0633516
$329$	−0.161873	−0.00892433
$330$	0.756933	0.0416678
$331$	26.0148	1.42990	0.714950	−	0.699175i	$-0.246449\pi$
$331$	26.0148	1.42990	0.714950	+	0.699175i	$0.246449\pi$
$332$	31.1558	1.70990
$333$	−56.5554	−3.09922
$334$	1.69658	0.0928327
$335$	3.05221	0.166760
$336$	−4.73687	−0.258417
$337$	28.3706	1.54545	0.772724	−	0.634743i	$-0.218894\pi$
$337$	28.3706	1.54545	0.772724	+	0.634743i	$0.218894\pi$
$338$	0.693685	0.0377315
$339$	28.1612	1.52951
$340$	0.449298	0.0243666
$341$	13.6178	0.737444
$342$	−0.0943834	−0.00510367
$343$	−5.59579	−0.302144
$344$	−2.40930	−0.129901
$345$	1.30099	0.0700431
$346$	2.21648	0.119159
$347$	−18.4049	−0.988024	−0.494012	−	0.869455i	$-0.664470\pi$
$347$	−18.4049	−0.988024	−0.494012	+	0.869455i	$0.664470\pi$
$348$	−5.98782	−0.320981
$349$	2.38516	0.127674	0.0638372	−	0.997960i	$-0.479666\pi$
$349$	2.38516	0.127674	0.0638372	+	0.997960i	$0.479666\pi$
$350$	0.287807	0.0153839
$351$	27.5895	1.47262
$352$	−6.88036	−0.366724
$353$	−33.5988	−1.78828	−0.894142	−	0.447783i	$-0.852214\pi$
$353$	−33.5988	−1.78828	−0.894142	+	0.447783i	$0.852214\pi$
$354$	0.849839	0.0451684
$355$	0.422744	0.0224369
$356$	7.88567	0.417940
$357$	0.646921	0.0342387
$358$	2.75892	0.145813
$359$	4.17017	0.220093	0.110046	−	0.993926i	$-0.464900\pi$
$359$	4.17017	0.220093	0.110046	+	0.993926i	$0.464900\pi$
$360$	1.55722	0.0820729
$361$	−18.9893	−0.999435
$362$	3.55301	0.186742
$363$	−13.6157	−0.714641
$364$	2.30569	0.120851
$365$	−3.28950	−0.172180
$366$	−2.31212	−0.120857
$367$	−14.0700	−0.734448	−0.367224	−	0.930133i	$-0.619692\pi$
$367$	−14.0700	−0.734448	−0.367224	+	0.930133i	$0.619692\pi$
$368$	−3.86943	−0.201708
$369$	−12.0262	−0.626059
$370$	0.582942	0.0303057
$371$	1.27515	0.0662024
$372$	20.7126	1.07390
$373$	16.7976	0.869749	0.434875	−	0.900491i	$-0.356793\pi$
$373$	16.7976	0.869749	0.434875	+	0.900491i	$0.356793\pi$
$374$	0.307460	0.0158984
$375$	12.7696	0.659419
$376$	−0.235321	−0.0121358
$377$	2.88206	0.148434
$378$	0.572166	0.0294290
$379$	12.7489	0.654869	0.327435	−	0.944874i	$-0.393816\pi$
$379$	12.7489	0.654869	0.327435	+	0.944874i	$0.393816\pi$
$380$	−0.0881095	−0.00451992
$381$	−46.2990	−2.37197
$382$	−0.499697	−0.0255667
$383$	8.32123	0.425195	0.212598	−	0.977140i	$-0.431808\pi$
$383$	8.32123	0.425195	0.212598	+	0.977140i	$0.431808\pi$
$384$	−13.9270	−0.710710
$385$	0.684297	0.0348750
$386$	−2.81540	−0.143300
$387$	−25.2537	−1.28372
$388$	−6.54395	−0.332219
$389$	−19.2441	−0.975716	−0.487858	−	0.872923i	$-0.662222\pi$
$389$	−19.2441	−0.975716	−0.487858	+	0.872923i	$0.662222\pi$
$390$	−0.554141	−0.0280600
$391$	0.528453	0.0267250
$392$	−4.01934	−0.203007
$393$	29.3883	1.48245
$394$	3.74433	0.188637
$395$	4.61840	0.232377
$396$	−47.9910	−2.41164
$397$	8.51004	0.427107	0.213553	−	0.976931i	$-0.431496\pi$
$397$	8.51004	0.427107	0.213553	+	0.976931i	$0.431496\pi$
$398$	−1.37010	−0.0686771
$399$	−0.126864	−0.00635115
$400$	−18.6323	−0.931617
$401$	−12.0659	−0.602542	−0.301271	−	0.953539i	$-0.597411\pi$
$401$	−12.0659	−0.602542	−0.301271	+	0.953539i	$0.597411\pi$
$402$	3.17685	0.158447
$403$	−9.96940	−0.496611
$404$	11.0608	0.550295
$405$	4.50825	0.224017
$406$	0.0597695	0.00296631
$407$	−36.1289	−1.79085
$408$	0.940457	0.0465595
$409$	16.5314	0.817426	0.408713	−	0.912663i	$-0.365978\pi$
$409$	16.5314	0.817426	0.408713	+	0.912663i	$0.365978\pi$
$410$	0.123960	0.00612193
$411$	−67.3970	−3.32445
$412$	23.3331	1.14954
$413$	0.768287	0.0378049
$414$	0.910755	0.0447612
$415$	−6.76932	−0.332293
$416$	5.03702	0.246960
$417$	14.6649	0.718143
$418$	−0.0602944	−0.00294909
$419$	4.01041	0.195921	0.0979606	−	0.995190i	$-0.468768\pi$
$419$	4.01041	0.195921	0.0979606	+	0.995190i	$0.468768\pi$
$420$	1.04081	0.0507865
$421$	16.1340	0.786321	0.393160	−	0.919470i	$-0.371382\pi$
$421$	16.1340	0.786321	0.393160	+	0.919470i	$0.371382\pi$
$422$	−2.47484	−0.120473
$423$	−2.46658	−0.119929
$424$	1.85374	0.0900255
$425$	2.54464	0.123433
$426$	0.440007	0.0213184
$427$	−2.09025	−0.101154
$428$	9.59965	0.464017
$429$	34.3439	1.65814
$430$	0.260302	0.0125529
$431$	3.59639	0.173232	0.0866161	−	0.996242i	$-0.472395\pi$
$431$	3.59639	0.173232	0.0866161	+	0.996242i	$0.472395\pi$
$432$	−37.0415	−1.78216
$433$	9.44054	0.453684	0.226842	−	0.973932i	$-0.427160\pi$
$433$	9.44054	0.453684	0.226842	+	0.973932i	$0.427160\pi$
$434$	−0.206750	−0.00992433
$435$	1.30099	0.0623779
$436$	2.40229	0.115049
$437$	−0.103632	−0.00495740
$438$	−3.42383	−0.163597
$439$	18.2698	0.871969	0.435984	−	0.899954i	$-0.356400\pi$
$439$	18.2698	0.871969	0.435984	+	0.899954i	$0.356400\pi$
$440$	0.994792	0.0474248
$441$	−42.1298	−2.00618
$442$	−0.225088	−0.0107063
$443$	5.47529	0.260139	0.130070	−	0.991505i	$-0.458480\pi$
$443$	5.47529	0.260139	0.130070	+	0.991505i	$0.458480\pi$
$444$	−54.9521	−2.60791
$445$	−1.71335	−0.0812204
$446$	3.07396	0.145556
$447$	38.0737	1.80083
$448$	−3.02532	−0.142933
$449$	9.05560	0.427360	0.213680	−	0.976904i	$-0.431455\pi$
$449$	9.05560	0.427360	0.213680	+	0.976904i	$0.431455\pi$
$450$	4.38553	0.206736
$451$	−7.68263	−0.361761
$452$	18.4037	0.865636
$453$	−6.58483	−0.309382
$454$	1.90121	0.0892284
$455$	−0.500965	−0.0234856
$456$	−0.184428	−0.00863663
$457$	−5.64056	−0.263854	−0.131927	−	0.991259i	$-0.542116\pi$
$457$	−5.64056	−0.263854	−0.131927	+	0.991259i	$0.542116\pi$
$458$	−0.179861	−0.00840434
$459$	5.05881	0.236125
$460$	0.850214	0.0396415
$461$	−5.91668	−0.275567	−0.137784	−	0.990462i	$-0.543998\pi$
$461$	−5.91668	−0.275567	−0.137784	+	0.990462i	$0.543998\pi$
$462$	0.712242	0.0331365
$463$	−23.0612	−1.07175	−0.535874	−	0.844298i	$-0.680018\pi$
$463$	−23.0612	−1.07175	−0.535874	+	0.844298i	$0.680018\pi$
$464$	−3.86943	−0.179634
$465$	−4.50030	−0.208696
$466$	1.74087	0.0806444
$467$	−7.15470	−0.331080	−0.165540	−	0.986203i	$-0.552937\pi$
$467$	−7.15470	−0.331080	−0.165540	+	0.986203i	$0.552937\pi$
$468$	35.1336	1.62405
$469$	2.87200	0.132616
$470$	0.0254241	0.00117273
$471$	−32.4366	−1.49460
$472$	1.11689	0.0514091
$473$	−16.1327	−0.741782
$474$	4.80700	0.220793
$475$	−0.499017	−0.0228965
$476$	0.422770	0.0193777
$477$	19.4304	0.889658
$478$	−3.33371	−0.152480
$479$	18.2551	0.834097	0.417049	−	0.908884i	$-0.363064\pi$
$479$	18.2551	0.834097	0.417049	+	0.908884i	$0.363064\pi$
$480$	2.27377	0.103783
$481$	26.4495	1.20599
$482$	−3.95736	−0.180253
$483$	1.22418	0.0557021
$484$	−8.89804	−0.404457
$485$	1.42182	0.0645617
$486$	0.448058	0.0203243
$487$	19.8402	0.899046	0.449523	−	0.893269i	$-0.351594\pi$
$487$	19.8402	0.899046	0.449523	+	0.893269i	$0.351594\pi$
$488$	−3.03868	−0.137555
$489$	47.1294	2.13127
$490$	0.434250	0.0196174
$491$	−21.0038	−0.947889	−0.473944	−	0.880555i	$-0.657170\pi$
$491$	−21.0038	−0.947889	−0.473944	+	0.880555i	$0.657170\pi$
$492$	−11.6853	−0.526812
$493$	0.528453	0.0238003
$494$	0.0441407	0.00198599
$495$	10.4272	0.468666
$496$	13.3848	0.600997
$497$	0.397783	0.0178430
$498$	−7.04577	−0.315728
$499$	26.9472	1.20632	0.603161	−	0.797620i	$-0.293908\pi$
$499$	26.9472	1.20632	0.603161	+	0.797620i	$0.293908\pi$
$500$	8.34509	0.373204
$501$	34.7487	1.55246
$502$	−3.22743	−0.144047
$503$	−30.7794	−1.37238	−0.686192	−	0.727420i	$-0.740719\pi$
$503$	−30.7794	−1.37238	−0.686192	+	0.727420i	$0.740719\pi$
$504$	1.46528	0.0652688
$505$	−2.40322	−0.106942
$506$	0.581812	0.0258647
$507$	14.2078	0.630991
$508$	−30.2569	−1.34243
$509$	−11.5685	−0.512764	−0.256382	−	0.966576i	$-0.582531\pi$
$509$	−11.5685	−0.512764	−0.256382	+	0.966576i	$0.582531\pi$
$510$	−0.101607	−0.00449924
$511$	−3.09528	−0.136927
$512$	−11.3126	−0.499949
$513$	−0.992056	−0.0438003
$514$	−2.38723	−0.105296
$515$	−5.06965	−0.223396
$516$	−24.5378	−1.08022
$517$	−1.57571	−0.0692996
$518$	0.548524	0.0241007
$519$	45.3971	1.99271
$520$	−0.728274	−0.0319369
$521$	32.4528	1.42178	0.710892	−	0.703301i	$-0.248291\pi$
$521$	32.4528	1.42178	0.710892	+	0.703301i	$0.248291\pi$
$522$	0.910755	0.0398627
$523$	−33.2308	−1.45308	−0.726540	−	0.687124i	$-0.758873\pi$
$523$	−33.2308	−1.45308	−0.726540	+	0.687124i	$0.758873\pi$
$524$	19.2056	0.839002
$525$	5.89475	0.257268
$526$	−1.39363	−0.0607650
$527$	−1.82798	−0.0796283
$528$	−46.1099	−2.00668
$529$	1.00000	0.0434783
$530$	−0.200278	−0.00869953
$531$	11.7070	0.508040
$532$	−0.0829073	−0.00359449
$533$	5.62435	0.243618
$534$	−1.78331	−0.0771716
$535$	−2.08575	−0.0901748
$536$	4.17514	0.180339
$537$	56.5072	2.43846
$538$	2.53459	0.109274
$539$	−26.9135	−1.15925
$540$	8.13899	0.350246
$541$	36.3900	1.56453	0.782264	−	0.622947i	$-0.214065\pi$
$541$	36.3900	1.56453	0.782264	+	0.622947i	$0.214065\pi$
$542$	2.59008	0.111254
$543$	72.7715	3.12292
$544$	0.923586	0.0395984
$545$	−0.521954	−0.0223581
$546$	−0.521423	−0.0223148
$547$	21.1901	0.906025	0.453013	−	0.891504i	$-0.350349\pi$
$547$	21.1901	0.906025	0.453013	+	0.891504i	$0.350349\pi$
$548$	−44.0447	−1.88150
$549$	−31.8507	−1.35935
$550$	2.80158	0.119460
$551$	−0.103632	−0.00441488
$552$	1.77964	0.0757466
$553$	4.34572	0.184799
$554$	−0.480732	−0.0204244
$555$	11.9396	0.506809
$556$	9.58369	0.406439
$557$	−39.1229	−1.65769	−0.828844	−	0.559479i	$-0.811001\pi$
$557$	−39.1229	−1.65769	−0.828844	+	0.559479i	$0.811001\pi$
$558$	−3.15042	−0.133368
$559$	11.8105	0.499532
$560$	0.672591	0.0284222
$561$	6.29729	0.265872
$562$	−1.73673	−0.0732594
$563$	−28.5720	−1.20417	−0.602083	−	0.798433i	$-0.705663\pi$
$563$	−28.5720	−1.20417	−0.602083	+	0.798433i	$0.705663\pi$
$564$	−2.39665	−0.100917
$565$	−3.99863	−0.168224
$566$	−3.80423	−0.159904
$567$	4.24207	0.178150
$568$	0.578275	0.0242639
$569$	−43.8330	−1.83758	−0.918788	−	0.394752i	$-0.870831\pi$
$569$	−43.8330	−1.83758	−0.918788	+	0.394752i	$0.870831\pi$
$570$	0.0199256	0.000834593 0
$571$	5.87677	0.245935	0.122968	−	0.992411i	$-0.460759\pi$
$571$	5.87677	0.245935	0.122968	+	0.992411i	$0.460759\pi$
$572$	22.4442	0.938438
$573$	−10.2346	−0.427557
$574$	0.116641	0.00486848
$575$	4.81527	0.200811
$576$	−46.0992	−1.92080
$577$	−34.1644	−1.42228	−0.711141	−	0.703049i	$-0.751821\pi$
$577$	−34.1644	−1.42228	−0.711141	+	0.703049i	$0.751821\pi$
$578$	2.47114	0.102786
$579$	−57.6641	−2.39644
$580$	0.850214	0.0353032
$581$	−6.36964	−0.264257
$582$	1.47989	0.0613433
$583$	12.4126	0.514078
$584$	−4.49974	−0.186200
$585$	−7.63359	−0.315610
$586$	−1.04620	−0.0432181
$587$	23.3254	0.962741	0.481370	−	0.876517i	$-0.340139\pi$
$587$	23.3254	0.962741	0.481370	+	0.876517i	$0.340139\pi$
$588$	−40.9354	−1.68815
$589$	0.358476	0.0147708
$590$	−0.120669	−0.00496787
$591$	76.6900	3.15461
$592$	−35.5109	−1.45949
$593$	30.4278	1.24952	0.624759	−	0.780817i	$-0.285197\pi$
$593$	30.4278	1.24952	0.624759	+	0.780817i	$0.285197\pi$
$594$	5.56961	0.228524
$595$	−0.0918567	−0.00376576
$596$	24.8816	1.01919
$597$	−28.0620	−1.14850
$598$	−0.425937	−0.0174179
$599$	38.7683	1.58403	0.792016	−	0.610501i	$-0.209032\pi$
$599$	38.7683	1.58403	0.792016	+	0.610501i	$0.209032\pi$
$600$	8.56945	0.349846
$601$	−20.4342	−0.833529	−0.416764	−	0.909015i	$-0.636836\pi$
$601$	−20.4342	−0.833529	−0.416764	+	0.909015i	$0.636836\pi$
$602$	0.244933	0.00998271
$603$	43.7628	1.78216
$604$	−4.30326	−0.175097
$605$	1.93331	0.0786001
$606$	−2.50136	−0.101611
$607$	42.6356	1.73052	0.865262	−	0.501320i	$-0.167152\pi$
$607$	42.6356	1.73052	0.865262	+	0.501320i	$0.167152\pi$
$608$	−0.181120	−0.00734537
$609$	1.22418	0.0496062
$610$	0.328300	0.0132925
$611$	1.15356	0.0466679
$612$	6.44208	0.260406
$613$	24.0020	0.969434	0.484717	−	0.874671i	$-0.338923\pi$
$613$	24.0020	0.969434	0.484717	+	0.874671i	$0.338923\pi$
$614$	1.66306	0.0671156
$615$	2.53890	0.102378
$616$	0.936056	0.0377148
$617$	28.0435	1.12899	0.564494	−	0.825437i	$-0.309071\pi$
$617$	28.0435	1.12899	0.564494	+	0.825437i	$0.309071\pi$
$618$	−5.27668	−0.212259
$619$	−37.7347	−1.51669	−0.758343	−	0.651855i	$-0.773991\pi$
$619$	−37.7347	−1.51669	−0.758343	+	0.651855i	$0.773991\pi$
$620$	−2.94100	−0.118113
$621$	9.57286	0.384146
$622$	3.56720	0.143032
$623$	−1.61218	−0.0645908
$624$	33.7565	1.35134
$625$	22.2632	0.890528
$626$	−0.219379	−0.00876814
$627$	−1.23493	−0.0493183
$628$	−21.1977	−0.845879
$629$	4.84978	0.193373
$630$	−0.158309	−0.00630719
$631$	−29.8591	−1.18867	−0.594336	−	0.804217i	$-0.702585\pi$
$631$	−29.8591	−1.18867	−0.594336	+	0.804217i	$0.702585\pi$
$632$	6.31755	0.251299
$633$	−50.6887	−2.01470
$634$	0.658208	0.0261408
$635$	6.57402	0.260882
$636$	18.8796	0.748624
$637$	19.7030	0.780662
$638$	0.581812	0.0230342
$639$	6.06134	0.239783
$640$	1.97751	0.0781678
$641$	0.00934652	0.000369165 0	0.000184583	−	1.00000i	$-0.499941\pi$
$641$	0.00934652	0.000369165 0	0.000184583		1.00000i	$0.499941\pi$
$642$	−2.17093	−0.0856796
$643$	9.68374	0.381889	0.190945	−	0.981601i	$-0.438845\pi$
$643$	9.68374	0.381889	0.190945	+	0.981601i	$0.438845\pi$
$644$	0.800015	0.0315250
$645$	5.33141	0.209924
$646$	0.00809363	0.000318440 0
$647$	35.1556	1.38211	0.691055	−	0.722803i	$-0.257146\pi$
$647$	35.1556	1.38211	0.691055	+	0.722803i	$0.257146\pi$
$648$	6.16688	0.242258
$649$	7.47870	0.293565
$650$	−2.05100	−0.0804469
$651$	−4.23459	−0.165967
$652$	30.7996	1.20621
$653$	−16.2765	−0.636950	−0.318475	−	0.947931i	$-0.603171\pi$
$653$	−16.2765	−0.636950	−0.318475	+	0.947931i	$0.603171\pi$
$654$	−0.543270	−0.0212435
$655$	−4.17287	−0.163048
$656$	−7.55121	−0.294825
$657$	−47.1651	−1.84009
$658$	0.0239230	0.000932617 0
$659$	25.3058	0.985773	0.492887	−	0.870093i	$-0.335942\pi$
$659$	25.3058	0.985773	0.492887	+	0.870093i	$0.335942\pi$
$660$	10.1316	0.394370
$661$	4.44038	0.172711	0.0863553	−	0.996264i	$-0.472478\pi$
$661$	4.44038	0.172711	0.0863553	+	0.996264i	$0.472478\pi$
$662$	−3.84470	−0.149429
$663$	−4.61017	−0.179044
$664$	−9.25982	−0.359351
$665$	0.0180135	0.000698535 0
$666$	8.35828	0.323877
$667$	1.00000	0.0387202
$668$	22.7087	0.878626
$669$	62.9598	2.43417
$670$	−0.451083	−0.0174269
$671$	−20.3470	−0.785487
$672$	2.13952	0.0825337
$673$	−8.48261	−0.326981	−0.163490	−	0.986545i	$-0.552275\pi$
$673$	−8.48261	−0.326981	−0.163490	+	0.986545i	$0.552275\pi$
$674$	−4.19287	−0.161503
$675$	46.0959	1.77423
$676$	9.28497	0.357114
$677$	24.1463	0.928017	0.464009	−	0.885831i	$-0.346411\pi$
$677$	24.1463	0.928017	0.464009	+	0.885831i	$0.346411\pi$
$678$	−4.16192	−0.159838
$679$	1.33788	0.0513430
$680$	−0.133536	−0.00512087
$681$	38.9400	1.49218
$682$	−2.01256	−0.0770649
$683$	30.3177	1.16007	0.580037	−	0.814590i	$-0.303038\pi$
$683$	30.3177	1.16007	0.580037	+	0.814590i	$0.303038\pi$
$684$	−1.26332	−0.0483043
$685$	9.56974	0.365641
$686$	0.826998	0.0315749
$687$	−3.68384	−0.140547
$688$	−15.8567	−0.604532
$689$	−9.08712	−0.346192
$690$	−0.192273	−0.00731970
$691$	−28.3860	−1.07985	−0.539927	−	0.841712i	$-0.681548\pi$
$691$	−28.3860	−1.07985	−0.539927	+	0.841712i	$0.681548\pi$
$692$	29.6676	1.12779
$693$	9.81151	0.372708
$694$	2.72004	0.103251
$695$	−2.08228	−0.0789854
$696$	1.77964	0.0674571
$697$	1.03128	0.0390625
$698$	−0.352500	−0.0133423
$699$	35.6559	1.34863
$700$	3.85229	0.145603
$701$	15.8962	0.600391	0.300195	−	0.953878i	$-0.402948\pi$
$701$	15.8962	0.600391	0.300195	+	0.953878i	$0.402948\pi$
$702$	−4.07744	−0.153893
$703$	−0.951064	−0.0358700
$704$	−29.4492	−1.10991
$705$	0.520728	0.0196118
$706$	4.96554	0.186881
$707$	−2.26132	−0.0850458
$708$	11.3751	0.427502
$709$	13.9734	0.524783	0.262391	−	0.964962i	$-0.415489\pi$
$709$	13.9734	0.524783	0.262391	+	0.964962i	$0.415489\pi$
$710$	−0.0624769	−0.00234472
$711$	66.2191	2.48341
$712$	−2.34370	−0.0878339
$713$	−3.45912	−0.129545
$714$	−0.0956079	−0.00357804
$715$	−4.87652	−0.182371
$716$	36.9281	1.38007
$717$	−68.2798	−2.54996
$718$	−0.616305	−0.0230003
$719$	21.8916	0.816417	0.408209	−	0.912889i	$-0.366154\pi$
$719$	21.8916	0.816417	0.408209	+	0.912889i	$0.366154\pi$
$720$	10.2488	0.381950
$721$	−4.77032	−0.177656
$722$	2.80641	0.104444
$723$	−81.0532	−3.01440
$724$	47.5570	1.76744
$725$	4.81527	0.178835
$726$	2.01226	0.0746819
$727$	−6.89717	−0.255802	−0.127901	−	0.991787i	$-0.540824\pi$
$727$	−6.89717	−0.255802	−0.127901	+	0.991787i	$0.540824\pi$
$728$	−0.685275	−0.0253980
$729$	−22.2905	−0.825574
$730$	0.486152	0.0179933
$731$	2.16557	0.0800967
$732$	−30.9477	−1.14386
$733$	28.9584	1.06960	0.534801	−	0.844978i	$-0.320386\pi$
$733$	28.9584	1.06960	0.534801	+	0.844978i	$0.320386\pi$
$734$	2.07939	0.0767518
$735$	8.89416	0.328066
$736$	1.74772	0.0644217
$737$	27.9567	1.02980
$738$	1.77734	0.0654249
$739$	−8.72759	−0.321049	−0.160525	−	0.987032i	$-0.551319\pi$
$739$	−8.72759	−0.321049	−0.160525	+	0.987032i	$0.551319\pi$
$740$	7.80268	0.286832
$741$	0.904075	0.0332120
$742$	−0.188453	−0.00691833
$743$	51.0384	1.87242	0.936209	−	0.351444i	$-0.114309\pi$
$743$	51.0384	1.87242	0.936209	+	0.351444i	$0.114309\pi$
$744$	−6.15600	−0.225690
$745$	−5.40611	−0.198065
$746$	−2.48251	−0.0908912
$747$	−97.0592	−3.55121
$748$	4.11535	0.150472
$749$	−1.96260	−0.0717118
$750$	−1.88721	−0.0689111
$751$	−33.5039	−1.22258	−0.611288	−	0.791408i	$-0.709348\pi$
$751$	−33.5039	−1.22258	−0.611288	+	0.791408i	$0.709348\pi$
$752$	−1.54876	−0.0564773
$753$	−66.1031	−2.40893
$754$	−0.425937	−0.0155117
$755$	0.934984	0.0340275
$756$	7.65844	0.278535
$757$	−51.3849	−1.86762	−0.933808	−	0.357776i	$-0.883535\pi$
$757$	−51.3849	−1.86762	−0.933808	+	0.357776i	$0.883535\pi$
$758$	−1.88416	−0.0684356
$759$	11.9165	0.432540
$760$	0.0261870	0.000949904 0
$761$	16.1419	0.585145	0.292572	−	0.956243i	$-0.405489\pi$
$761$	16.1419	0.585145	0.292572	+	0.956243i	$0.405489\pi$
$762$	6.84249	0.247877
$763$	−0.491137	−0.0177803
$764$	−6.68844	−0.241979
$765$	−1.39969	−0.0506060
$766$	−1.22979	−0.0444340
$767$	−5.47506	−0.197693
$768$	−43.2286	−1.55988
$769$	−9.62190	−0.346975	−0.173487	−	0.984836i	$-0.555504\pi$
$769$	−9.62190	−0.346975	−0.173487	+	0.984836i	$0.555504\pi$
$770$	−0.101132	−0.00364453
$771$	−48.8944	−1.76089
$772$	−37.6842	−1.35628
$773$	42.2480	1.51955	0.759777	−	0.650184i	$-0.225308\pi$
$773$	42.2480	1.51955	0.759777	+	0.650184i	$0.225308\pi$
$774$	3.73223	0.134152
$775$	−16.6566	−0.598324
$776$	1.94493	0.0698188
$777$	11.2347	0.403041
$778$	2.84407	0.101965
$779$	−0.202239	−0.00724595
$780$	−7.41718	−0.265578
$781$	3.87213	0.138556
$782$	−0.0780996	−0.00279284
$783$	9.57286	0.342106
$784$	−26.4531	−0.944754
$785$	4.60569	0.164384
$786$	−4.34328	−0.154920
$787$	−18.4395	−0.657298	−0.328649	−	0.944452i	$-0.606593\pi$
$787$	−18.4395	−0.657298	−0.328649	+	0.944452i	$0.606593\pi$
$788$	50.1178	1.78537
$789$	−28.5438	−1.01618
$790$	−0.682550	−0.0242840
$791$	−3.76254	−0.133780
$792$	14.2634	0.506828
$793$	14.8958	0.528964
$794$	−1.25769	−0.0446338
$795$	−4.10203	−0.145484
$796$	−18.3388	−0.650003
$797$	−46.8530	−1.65962	−0.829809	−	0.558048i	$-0.811551\pi$
$797$	−46.8530	−1.65962	−0.829809	+	0.558048i	$0.811551\pi$
$798$	0.0187492	0.000663713 0
$799$	0.211516	0.00748289
$800$	8.41573	0.297541
$801$	−24.5661	−0.868001
$802$	1.78321	0.0629673
$803$	−30.1302	−1.06327
$804$	42.5222	1.49964
$805$	−0.173822	−0.00612642
$806$	1.47337	0.0518972
$807$	51.9126	1.82741
$808$	−3.28738	−0.115650
$809$	15.2434	0.535931	0.267965	−	0.963429i	$-0.413649\pi$
$809$	15.2434	0.535931	0.267965	+	0.963429i	$0.413649\pi$
$810$	−0.666271	−0.0234104
$811$	−0.00301973	−0.000106037 0	−5.30185e−5	−	1.00000i	$-0.500017\pi$
$811$	−0.00301973	−0.000106037 0	−5.30185e−5		1.00000i	$0.500017\pi$
$812$	0.800015	0.0280750
$813$	53.0492	1.86051
$814$	5.33947	0.187148
$815$	−6.69194	−0.234408
$816$	6.18957	0.216678
$817$	−0.424679	−0.0148576
$818$	−2.44317	−0.0854233
$819$	−7.18288	−0.250990
$820$	1.65920	0.0579417
$821$	19.2157	0.670633	0.335316	−	0.942106i	$-0.391157\pi$
$821$	19.2157	0.670633	0.335316	+	0.942106i	$0.391157\pi$
$822$	9.96055	0.347414
$823$	−14.3989	−0.501914	−0.250957	−	0.967998i	$-0.580745\pi$
$823$	−14.3989	−0.501914	−0.250957	+	0.967998i	$0.580745\pi$
$824$	−6.93482	−0.241586
$825$	57.3810	1.99775
$826$	−0.113545	−0.00395072
$827$	−21.0781	−0.732956	−0.366478	−	0.930427i	$-0.619437\pi$
$827$	−21.0781	−0.732956	−0.366478	+	0.930427i	$0.619437\pi$
$828$	12.1905	0.423648
$829$	−9.12114	−0.316790	−0.158395	−	0.987376i	$-0.550632\pi$
$829$	−9.12114	−0.316790	−0.158395	+	0.987376i	$0.550632\pi$
$830$	1.00043	0.0347255
$831$	−9.84619	−0.341561
$832$	21.5594	0.747438
$833$	3.61274	0.125174
$834$	−2.16731	−0.0750480
$835$	−4.93400	−0.170748
$836$	−0.807040	−0.0279121
$837$	−33.1137	−1.14458
$838$	−0.592695	−0.0204743
$839$	−9.28464	−0.320541	−0.160271	−	0.987073i	$-0.551237\pi$
$839$	−9.28464	−0.320541	−0.160271	+	0.987073i	$0.551237\pi$
$840$	−0.309341	−0.0106733
$841$	1.00000	0.0344828
$842$	−2.38442	−0.0821727
$843$	−35.5710	−1.22513
$844$	−33.1257	−1.14023
$845$	−2.01738	−0.0693998
$846$	0.364534	0.0125329
$847$	1.81916	0.0625071
$848$	12.2003	0.418960
$849$	−77.9169	−2.67410
$850$	−0.376071	−0.0128991
$851$	9.17731	0.314594
$852$	5.88950	0.201771
$853$	−46.8206	−1.60311	−0.801554	−	0.597922i	$-0.795993\pi$
$853$	−46.8206	−1.60311	−0.801554	+	0.597922i	$0.795993\pi$
$854$	0.308916	0.0105709
$855$	0.274486	0.00938723
$856$	−2.85311	−0.0975175
$857$	0.138617	0.00473508	0.00236754	−	0.999997i	$-0.499246\pi$
$857$	0.138617	0.00473508	0.00236754	+	0.999997i	$0.499246\pi$
$858$	−5.07566	−0.173280
$859$	29.0902	0.992546	0.496273	−	0.868167i	$-0.334702\pi$
$859$	29.0902	0.992546	0.496273	+	0.868167i	$0.334702\pi$
$860$	3.48414	0.118808
$861$	2.38899	0.0814166
$862$	−0.531508	−0.0181032
$863$	−52.3865	−1.78326	−0.891628	−	0.452768i	$-0.850437\pi$
$863$	−52.3865	−1.78326	−0.891628	+	0.452768i	$0.850437\pi$
$864$	16.7307	0.569189
$865$	−6.44597	−0.219169
$866$	−1.39521	−0.0474112
$867$	50.6131	1.71891
$868$	−2.76735	−0.0939301
$869$	42.3023	1.43501
$870$	−0.192273	−0.00651866
$871$	−20.4668	−0.693490
$872$	−0.713986	−0.0241786
$873$	20.3863	0.689970
$874$	0.0153157	0.000518061 0
$875$	−1.70611	−0.0576770
$876$	−45.8280	−1.54838
$877$	−51.7807	−1.74851	−0.874255	−	0.485467i	$-0.838650\pi$
$877$	−51.7807	−1.74851	−0.874255	+	0.485467i	$0.838650\pi$
$878$	−2.70008	−0.0911232
$879$	−21.4279	−0.722744
$880$	6.54718	0.220705
$881$	19.5606	0.659013	0.329507	−	0.944153i	$-0.393118\pi$
$881$	19.5606	0.659013	0.329507	+	0.944153i	$0.393118\pi$
$882$	6.22632	0.209651
$883$	−35.8441	−1.20625	−0.603125	−	0.797647i	$-0.706078\pi$
$883$	−35.8441	−1.20625	−0.603125	+	0.797647i	$0.706078\pi$
$884$	−3.01280	−0.101331
$885$	−2.47150	−0.0830787
$886$	−0.809189	−0.0271852
$887$	−28.1320	−0.944580	−0.472290	−	0.881443i	$-0.656573\pi$
$887$	−28.1320	−0.944580	−0.472290	+	0.881443i	$0.656573\pi$
$888$	16.3323	0.548077
$889$	6.18587	0.207468
$890$	0.253214	0.00848775
$891$	41.2934	1.38338
$892$	41.1450	1.37764
$893$	−0.0414792	−0.00138805
$894$	−5.62689	−0.188191
$895$	−8.02349	−0.268196
$896$	1.86075	0.0621632
$897$	−8.72389	−0.291282
$898$	−1.33832	−0.0446603
$899$	−3.45912	−0.115368
$900$	58.7003	1.95668
$901$	−1.66621	−0.0555095
$902$	1.13541	0.0378050
$903$	5.01663	0.166943
$904$	−5.46976	−0.181922
$905$	−10.3329	−0.343476
$906$	0.973166	0.0323313
$907$	0.502775	0.0166944	0.00834719	−	0.999965i	$-0.497343\pi$
$907$	0.502775	0.0166944	0.00834719	+	0.999965i	$0.497343\pi$
$908$	25.4477	0.844513
$909$	−34.4575	−1.14288
$910$	0.0740372	0.00245431
$911$	7.66894	0.254083	0.127042	−	0.991897i	$-0.459452\pi$
$911$	7.66894	0.254083	0.127042	+	0.991897i	$0.459452\pi$
$912$	−1.21380	−0.0401931
$913$	−62.0037	−2.05202
$914$	0.833614	0.0275735
$915$	6.72412	0.222292
$916$	−2.40744	−0.0795439
$917$	−3.92649	−0.129664
$918$	−0.747637	−0.0246757
$919$	−6.18354	−0.203976	−0.101988	−	0.994786i	$-0.532520\pi$
$919$	−6.18354	−0.203976	−0.101988	+	0.994786i	$0.532520\pi$
$920$	−0.252692	−0.00833102
$921$	34.0622	1.12239
$922$	0.874421	0.0287975
$923$	−2.83473	−0.0933064
$924$	9.53336	0.313624
$925$	44.1912	1.45300
$926$	3.40820	0.112001
$927$	−72.6891	−2.38742
$928$	1.74772	0.0573716
$929$	−5.92221	−0.194302	−0.0971508	−	0.995270i	$-0.530973\pi$
$929$	−5.92221	−0.194302	−0.0971508	+	0.995270i	$0.530973\pi$
$930$	0.665096	0.0218093
$931$	−0.708475	−0.0232193
$932$	23.3016	0.763268
$933$	73.0622	2.39195
$934$	1.05739	0.0345988
$935$	−0.894157	−0.0292420
$936$	−10.4421	−0.341309
$937$	36.6402	1.19698	0.598492	−	0.801129i	$-0.295767\pi$
$937$	36.6402	1.19698	0.598492	+	0.801129i	$0.295767\pi$
$938$	−0.424450	−0.0138588
$939$	−4.49324	−0.146631
$940$	0.340302	0.0110994
$941$	−60.1459	−1.96070	−0.980350	−	0.197267i	$-0.936793\pi$
$941$	−60.1459	−1.96070	−0.980350	+	0.197267i	$0.936793\pi$
$942$	4.79377	0.156190
$943$	1.95151	0.0635498
$944$	7.35077	0.239247
$945$	−1.66397	−0.0541291
$946$	2.38424	0.0775182
$947$	−56.5206	−1.83667	−0.918336	−	0.395802i	$-0.870467\pi$
$947$	−56.5206	−1.83667	−0.918336	+	0.395802i	$0.870467\pi$
$948$	64.3417	2.08972
$949$	22.0579	0.716031
$950$	0.0737493	0.00239274
$951$	13.4812	0.437157
$952$	−0.125652	−0.00407239
$953$	14.6217	0.473643	0.236822	−	0.971553i	$-0.423894\pi$
$953$	14.6217	0.473643	0.236822	+	0.971553i	$0.423894\pi$
$954$	−2.87161	−0.0929717
$955$	1.45322	0.0470251
$956$	−44.6217	−1.44317
$957$	11.9165	0.385205
$958$	−2.69791	−0.0871655
$959$	9.00472	0.290777
$960$	9.73216	0.314104
$961$	−19.0345	−0.614015
$962$	−3.90896	−0.126030
$963$	−29.9057	−0.963696
$964$	−52.9692	−1.70602
$965$	8.18776	0.263573
$966$	−0.180920	−0.00582102
$967$	−39.6321	−1.27448	−0.637241	−	0.770664i	$-0.719925\pi$
$967$	−39.6321	−1.27448	−0.637241	+	0.770664i	$0.719925\pi$
$968$	2.64459	0.0850003
$969$	0.165771	0.00532533
$970$	−0.210130	−0.00674688
$971$	10.8615	0.348563	0.174281	−	0.984696i	$-0.444240\pi$
$971$	10.8615	0.348563	0.174281	+	0.984696i	$0.444240\pi$
$972$	5.99725	0.192362
$973$	−1.95934	−0.0628134
$974$	−2.93217	−0.0939528
$975$	−42.0079	−1.34533
$976$	−19.9989	−0.640150
$977$	−39.6458	−1.26838	−0.634191	−	0.773176i	$-0.718667\pi$
$977$	−39.6458	−1.26838	−0.634191	+	0.773176i	$0.718667\pi$
$978$	−6.96522	−0.222723
$979$	−15.6934	−0.501564
$980$	5.81244	0.185672
$981$	−7.48383	−0.238940
$982$	3.10414	0.0990570
$983$	−7.54318	−0.240590	−0.120295	−	0.992738i	$-0.538384\pi$
$983$	−7.54318	−0.240590	−0.120295	+	0.992738i	$0.538384\pi$
$984$	3.47298	0.110715
$985$	−10.8893	−0.346961
$986$	−0.0780996	−0.00248720
$987$	0.489983	0.0155963
$988$	0.590824	0.0187966
$989$	4.09795	0.130307
$990$	−1.54102	−0.0489769
$991$	54.7550	1.73935	0.869675	−	0.493625i	$-0.164329\pi$
$991$	54.7550	1.73935	0.869675	+	0.493625i	$0.164329\pi$
$992$	−6.04557	−0.191947
$993$	−78.7458	−2.49892
$994$	−0.0587881	−0.00186465
$995$	3.98454	0.126318
$996$	−94.3076	−2.98825
$997$	−5.01673	−0.158881	−0.0794407	−	0.996840i	$-0.525313\pi$
$997$	−5.01673	−0.158881	−0.0794407	+	0.996840i	$0.525313\pi$
$998$	−3.98250	−0.126064
$999$	87.8531	2.77955

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.b.1.7	✓	12
3.2	odd	2		6003.2.a.n.1.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.b.1.7	✓	12	1.1	even	1	trivial
6003.2.a.n.1.6		12	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)

\(f(q)\)	\(=\)	\(q-0.147789 q^{2} -3.02697 q^{3} -1.97816 q^{4} +0.429801 q^{5} +0.447353 q^{6} +0.404424 q^{7} +0.587929 q^{8} +6.16253 q^{9} +O(q^{10})\)	\(q-0.147789 q^{2} -3.02697 q^{3} -1.97816 q^{4} +0.429801 q^{5} +0.447353 q^{6} +0.404424 q^{7} +0.587929 q^{8} +6.16253 q^{9} -0.0635200 q^{10} +3.93677 q^{11} +5.98782 q^{12} -2.88206 q^{13} -0.0597695 q^{14} -1.30099 q^{15} +3.86943 q^{16} -0.528453 q^{17} -0.910755 q^{18} +0.103632 q^{19} -0.850214 q^{20} -1.22418 q^{21} -0.581812 q^{22} -1.00000 q^{23} -1.77964 q^{24} -4.81527 q^{25} +0.425937 q^{26} -9.57286 q^{27} -0.800015 q^{28} -1.00000 q^{29} +0.192273 q^{30} +3.45912 q^{31} -1.74772 q^{32} -11.9165 q^{33} +0.0780996 q^{34} +0.173822 q^{35} -12.1905 q^{36} -9.17731 q^{37} -0.0153157 q^{38} +8.72389 q^{39} +0.252692 q^{40} -1.95151 q^{41} +0.180920 q^{42} -4.09795 q^{43} -7.78755 q^{44} +2.64866 q^{45} +0.147789 q^{46} -0.400254 q^{47} -11.7126 q^{48} -6.83644 q^{49} +0.711645 q^{50} +1.59961 q^{51} +5.70117 q^{52} +3.15300 q^{53} +1.41477 q^{54} +1.69203 q^{55} +0.237773 q^{56} -0.313691 q^{57} +0.147789 q^{58} +1.89971 q^{59} +2.57357 q^{60} -5.16845 q^{61} -0.511221 q^{62} +2.49228 q^{63} -7.48056 q^{64} -1.23871 q^{65} +1.76113 q^{66} +7.10144 q^{67} +1.04536 q^{68} +3.02697 q^{69} -0.0256890 q^{70} +0.983580 q^{71} +3.62313 q^{72} -7.65354 q^{73} +1.35631 q^{74} +14.5757 q^{75} -0.205001 q^{76} +1.59212 q^{77} -1.28930 q^{78} +10.7454 q^{79} +1.66308 q^{80} +10.4892 q^{81} +0.288411 q^{82} -15.7499 q^{83} +2.42162 q^{84} -0.227130 q^{85} +0.605633 q^{86} +3.02697 q^{87} +2.31454 q^{88} -3.98637 q^{89} -0.391443 q^{90} -1.16557 q^{91} +1.97816 q^{92} -10.4707 q^{93} +0.0591533 q^{94} +0.0445412 q^{95} +5.29028 q^{96} +3.30810 q^{97} +1.01035 q^{98} +24.2604 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9} - 6 q^{11} - 21 q^{12} - 15 q^{13} - 8 q^{14} + 6 q^{15} + 17 q^{16} - 18 q^{17} - 12 q^{18} - 6 q^{19} - 39 q^{20} - q^{21} - 5 q^{22} - 12 q^{23} + 4 q^{24} + 14 q^{25} - 3 q^{26} - 12 q^{27} - 19 q^{28} - 12 q^{29} - 11 q^{30} + 16 q^{31} - 21 q^{32} - 19 q^{33} - 7 q^{34} - 11 q^{35} - 13 q^{36} - q^{37} - 24 q^{38} + 6 q^{39} + 30 q^{40} + 3 q^{41} + 22 q^{42} - 23 q^{43} + 23 q^{44} - 22 q^{45} + 3 q^{46} - 35 q^{47} - 21 q^{48} + 3 q^{49} - 2 q^{50} - 34 q^{51} - 45 q^{53} + 55 q^{54} + 17 q^{55} - 17 q^{56} - 34 q^{57} + 3 q^{58} - 11 q^{59} + 93 q^{60} + 4 q^{61} - 7 q^{62} + q^{63} + 15 q^{64} + 5 q^{65} - 35 q^{66} - 19 q^{67} + q^{68} + 3 q^{69} + 14 q^{70} + 19 q^{71} + 4 q^{72} + 10 q^{73} - 15 q^{74} - 3 q^{75} - 4 q^{76} - 39 q^{77} + 16 q^{78} + 17 q^{79} - 90 q^{80} + 4 q^{81} - 3 q^{82} - 12 q^{83} + 42 q^{84} + 14 q^{85} + 17 q^{86} + 3 q^{87} - 2 q^{88} - 20 q^{89} + 65 q^{90} + 11 q^{91} - 11 q^{92} - 2 q^{93} + 13 q^{94} + 12 q^{95} + 14 q^{96} - 12 q^{97} + 75 q^{98} - 4 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9 - 6 * q^11 - 21 * q^12 - 15 * q^13 - 8 * q^14 + 6 * q^15 + 17 * q^16 - 18 * q^17 - 12 * q^18 - 6 * q^19 - 39 * q^20 - q^21 - 5 * q^22 - 12 * q^23 + 4 * q^24 + 14 * q^25 - 3 * q^26 - 12 * q^27 - 19 * q^28 - 12 * q^29 - 11 * q^30 + 16 * q^31 - 21 * q^32 - 19 * q^33 - 7 * q^34 - 11 * q^35 - 13 * q^36 - q^37 - 24 * q^38 + 6 * q^39 + 30 * q^40 + 3 * q^41 + 22 * q^42 - 23 * q^43 + 23 * q^44 - 22 * q^45 + 3 * q^46 - 35 * q^47 - 21 * q^48 + 3 * q^49 - 2 * q^50 - 34 * q^51 - 45 * q^53 + 55 * q^54 + 17 * q^55 - 17 * q^56 - 34 * q^57 + 3 * q^58 - 11 * q^59 + 93 * q^60 + 4 * q^61 - 7 * q^62 + q^63 + 15 * q^64 + 5 * q^65 - 35 * q^66 - 19 * q^67 + q^68 + 3 * q^69 + 14 * q^70 + 19 * q^71 + 4 * q^72 + 10 * q^73 - 15 * q^74 - 3 * q^75 - 4 * q^76 - 39 * q^77 + 16 * q^78 + 17 * q^79 - 90 * q^80 + 4 * q^81 - 3 * q^82 - 12 * q^83 + 42 * q^84 + 14 * q^85 + 17 * q^86 + 3 * q^87 - 2 * q^88 - 20 * q^89 + 65 * q^90 + 11 * q^91 - 11 * q^92 - 2 * q^93 + 13 * q^94 + 12 * q^95 + 14 * q^96 - 12 * q^97 + 75 * q^98 - 4 * q^99

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