LMFDB - Embedded newform 6007.2.a.b.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6007,2,Mod(1,6007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6007, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6007.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:	$47.9661364942$
Analytic rank:	$1$
Dimension:	$237$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66512 q^{2} -3.23472 q^{3} +5.10287 q^{4} -3.53010 q^{5} +8.62093 q^{6} +1.66538 q^{7} -8.26953 q^{8} +7.46344 q^{9} +O(q^{10})$	\(q-2.66512 q^{2} -3.23472 q^{3} +5.10287 q^{4} -3.53010 q^{5} +8.62093 q^{6} +1.66538 q^{7} -8.26953 q^{8} +7.46344 q^{9} +9.40814 q^{10} +0.918274 q^{11} -16.5064 q^{12} +4.03552 q^{13} -4.43844 q^{14} +11.4189 q^{15} +11.8336 q^{16} -2.27924 q^{17} -19.8910 q^{18} +5.87409 q^{19} -18.0136 q^{20} -5.38705 q^{21} -2.44731 q^{22} -0.395140 q^{23} +26.7497 q^{24} +7.46159 q^{25} -10.7552 q^{26} -14.4380 q^{27} +8.49823 q^{28} +8.08453 q^{29} -30.4327 q^{30} +2.69795 q^{31} -14.9988 q^{32} -2.97036 q^{33} +6.07444 q^{34} -5.87896 q^{35} +38.0850 q^{36} -3.97253 q^{37} -15.6552 q^{38} -13.0538 q^{39} +29.1923 q^{40} -0.501981 q^{41} +14.3571 q^{42} +9.05658 q^{43} +4.68583 q^{44} -26.3467 q^{45} +1.05310 q^{46} -3.66469 q^{47} -38.2783 q^{48} -4.22651 q^{49} -19.8860 q^{50} +7.37271 q^{51} +20.5928 q^{52} +4.42208 q^{53} +38.4791 q^{54} -3.24160 q^{55} -13.7719 q^{56} -19.0011 q^{57} -21.5462 q^{58} -4.53832 q^{59} +58.2692 q^{60} -13.6205 q^{61} -7.19037 q^{62} +12.4295 q^{63} +16.3065 q^{64} -14.2458 q^{65} +7.91638 q^{66} -9.39578 q^{67} -11.6307 q^{68} +1.27817 q^{69} +15.6681 q^{70} -1.37188 q^{71} -61.7192 q^{72} -5.49219 q^{73} +10.5873 q^{74} -24.1362 q^{75} +29.9747 q^{76} +1.52928 q^{77} +34.7900 q^{78} -8.95643 q^{79} -41.7736 q^{80} +24.3127 q^{81} +1.33784 q^{82} -9.28255 q^{83} -27.4894 q^{84} +8.04593 q^{85} -24.1369 q^{86} -26.1512 q^{87} -7.59369 q^{88} +9.53357 q^{89} +70.2171 q^{90} +6.72069 q^{91} -2.01635 q^{92} -8.72713 q^{93} +9.76685 q^{94} -20.7361 q^{95} +48.5170 q^{96} +5.98884 q^{97} +11.2642 q^{98} +6.85348 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9}+O(q^{10}) $ 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9} - 39 q^{10} - 38 q^{11} - 67 q^{12} - 52 q^{13} - 54 q^{14} - 24 q^{15} + 208 q^{16} - 255 q^{17} - 71 q^{18} - 24 q^{19} - 154 q^{20} - 60 q^{21} - 39 q^{22} - 118 q^{23} - 85 q^{24} + 170 q^{25} - 61 q^{26} - 87 q^{27} - 99 q^{28} - 87 q^{29} - 30 q^{30} - 28 q^{31} - 156 q^{32} - 173 q^{33} - 4 q^{34} - 113 q^{35} + 152 q^{36} - 49 q^{37} - 145 q^{38} - 49 q^{39} - 91 q^{40} - 197 q^{41} - 61 q^{42} - 63 q^{43} - 106 q^{44} - 181 q^{45} - 2 q^{46} - 119 q^{47} - 142 q^{48} + 150 q^{49} - 89 q^{50} - 40 q^{51} - 97 q^{52} - 190 q^{53} - 97 q^{54} - 55 q^{55} - 154 q^{56} - 202 q^{57} - 27 q^{58} - 86 q^{59} - 48 q^{60} - 96 q^{61} - 239 q^{62} - 149 q^{63} + 183 q^{64} - 259 q^{65} - 72 q^{66} - 28 q^{67} - 482 q^{68} - 83 q^{69} + 20 q^{70} - 63 q^{71} - 193 q^{72} - 206 q^{73} - 132 q^{74} - 89 q^{75} - 11 q^{76} - 179 q^{77} - 58 q^{78} - 32 q^{79} - 320 q^{80} + 57 q^{81} - 77 q^{82} - 245 q^{83} - 133 q^{84} + q^{85} - 39 q^{86} - 179 q^{87} - 104 q^{88} - 227 q^{89} - 146 q^{90} - 36 q^{91} - 315 q^{92} - 87 q^{93} - 48 q^{94} - 111 q^{95} - 134 q^{96} - 221 q^{97} - 161 q^{98} - 68 q^{99}+O(q^{100}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9 - 39 * q^10 - 38 * q^11 - 67 * q^12 - 52 * q^13 - 54 * q^14 - 24 * q^15 + 208 * q^16 - 255 * q^17 - 71 * q^18 - 24 * q^19 - 154 * q^20 - 60 * q^21 - 39 * q^22 - 118 * q^23 - 85 * q^24 + 170 * q^25 - 61 * q^26 - 87 * q^27 - 99 * q^28 - 87 * q^29 - 30 * q^30 - 28 * q^31 - 156 * q^32 - 173 * q^33 - 4 * q^34 - 113 * q^35 + 152 * q^36 - 49 * q^37 - 145 * q^38 - 49 * q^39 - 91 * q^40 - 197 * q^41 - 61 * q^42 - 63 * q^43 - 106 * q^44 - 181 * q^45 - 2 * q^46 - 119 * q^47 - 142 * q^48 + 150 * q^49 - 89 * q^50 - 40 * q^51 - 97 * q^52 - 190 * q^53 - 97 * q^54 - 55 * q^55 - 154 * q^56 - 202 * q^57 - 27 * q^58 - 86 * q^59 - 48 * q^60 - 96 * q^61 - 239 * q^62 - 149 * q^63 + 183 * q^64 - 259 * q^65 - 72 * q^66 - 28 * q^67 - 482 * q^68 - 83 * q^69 + 20 * q^70 - 63 * q^71 - 193 * q^72 - 206 * q^73 - 132 * q^74 - 89 * q^75 - 11 * q^76 - 179 * q^77 - 58 * q^78 - 32 * q^79 - 320 * q^80 + 57 * q^81 - 77 * q^82 - 245 * q^83 - 133 * q^84 + q^85 - 39 * q^86 - 179 * q^87 - 104 * q^88 - 227 * q^89 - 146 * q^90 - 36 * q^91 - 315 * q^92 - 87 * q^93 - 48 * q^94 - 111 * q^95 - 134 * q^96 - 221 * q^97 - 161 * q^98 - 68 * 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 $

$2$	−2.66512	−1.88453	−0.942263	−	0.334875i	$-0.891306\pi$
$2$	−2.66512	−1.88453	−0.942263	+	0.334875i	$0.891306\pi$
$3$	−3.23472	−1.86757	−0.933785	−	0.357836i	$-0.883515\pi$
$3$	−3.23472	−1.86757	−0.933785	+	0.357836i	$0.883515\pi$
$4$	5.10287	2.55144
$5$	−3.53010	−1.57871	−0.789354	−	0.613938i	$-0.789584\pi$
$5$	−3.53010	−1.57871	−0.789354	+	0.613938i	$0.789584\pi$
$6$	8.62093	3.51948
$7$	1.66538	0.629455	0.314727	−	0.949182i	$-0.398087\pi$
$7$	1.66538	0.629455	0.314727	+	0.949182i	$0.398087\pi$
$8$	−8.26953	−2.92372
$9$	7.46344	2.48781
$10$	9.40814	2.97511
$11$	0.918274	0.276870	0.138435	−	0.990372i	$-0.455793\pi$
$11$	0.918274	0.276870	0.138435	+	0.990372i	$0.455793\pi$
$12$	−16.5064	−4.76498
$13$	4.03552	1.11925	0.559627	−	0.828745i	$-0.310945\pi$
$13$	4.03552	1.11925	0.559627	+	0.828745i	$0.310945\pi$
$14$	−4.43844	−1.18622
$15$	11.4189	2.94835
$16$	11.8336	2.95839
$17$	−2.27924	−0.552796	−0.276398	−	0.961043i	$-0.589141\pi$
$17$	−2.27924	−0.552796	−0.276398	+	0.961043i	$0.589141\pi$
$18$	−19.8910	−4.68835
$19$	5.87409	1.34761	0.673805	−	0.738910i	$-0.264659\pi$
$19$	5.87409	1.34761	0.673805	+	0.738910i	$0.264659\pi$
$20$	−18.0136	−4.02797
$21$	−5.38705	−1.17555
$22$	−2.44731	−0.521768
$23$	−0.395140	−0.0823923	−0.0411962	−	0.999151i	$-0.513117\pi$
$23$	−0.395140	−0.0823923	−0.0411962	+	0.999151i	$0.513117\pi$
$24$	26.7497	5.46025
$25$	7.46159	1.49232
$26$	−10.7552	−2.10926
$27$	−14.4380	−2.77860
$28$	8.49823	1.60601
$29$	8.08453	1.50126	0.750630	−	0.660723i	$-0.229750\pi$
$29$	8.08453	1.50126	0.750630	+	0.660723i	$0.229750\pi$
$30$	−30.4327	−5.55623
$31$	2.69795	0.484566	0.242283	−	0.970206i	$-0.422104\pi$
$31$	2.69795	0.484566	0.242283	+	0.970206i	$0.422104\pi$
$32$	−14.9988	−2.65144
$33$	−2.97036	−0.517074
$34$	6.07444	1.04176
$35$	−5.87896	−0.993725
$36$	38.0850	6.34750
$37$	−3.97253	−0.653080	−0.326540	−	0.945183i	$-0.605883\pi$
$37$	−3.97253	−0.653080	−0.326540	+	0.945183i	$0.605883\pi$
$38$	−15.6552	−2.53960
$39$	−13.0538	−2.09028
$40$	29.1923	4.61570
$41$	−0.501981	−0.0783962	−0.0391981	−	0.999231i	$-0.512480\pi$
$41$	−0.501981	−0.0783962	−0.0391981	+	0.999231i	$0.512480\pi$
$42$	14.3571	2.21535
$43$	9.05658	1.38111	0.690557	−	0.723278i	$-0.257365\pi$
$43$	9.05658	1.38111	0.690557	+	0.723278i	$0.257365\pi$
$44$	4.68583	0.706416
$45$	−26.3467	−3.92753
$46$	1.05310	0.155270
$47$	−3.66469	−0.534551	−0.267275	−	0.963620i	$-0.586123\pi$
$47$	−3.66469	−0.534551	−0.267275	+	0.963620i	$0.586123\pi$
$48$	−38.2783	−5.52500
$49$	−4.22651	−0.603787
$50$	−19.8860	−2.81231
$51$	7.37271	1.03239
$52$	20.5928	2.85570
$53$	4.42208	0.607419	0.303709	−	0.952765i	$-0.401775\pi$
$53$	4.42208	0.607419	0.303709	+	0.952765i	$0.401775\pi$
$54$	38.4791	5.23634
$55$	−3.24160	−0.437097
$56$	−13.7719	−1.84035
$57$	−19.0011	−2.51675
$58$	−21.5462	−2.82916
$59$	−4.53832	−0.590838	−0.295419	−	0.955368i	$-0.595459\pi$
$59$	−4.53832	−0.590838	−0.295419	+	0.955368i	$0.595459\pi$
$60$	58.2692	7.52252
$61$	−13.6205	−1.74392	−0.871962	−	0.489573i	$-0.837153\pi$
$61$	−13.6205	−1.74392	−0.871962	+	0.489573i	$0.837153\pi$
$62$	−7.19037	−0.913178
$63$	12.4295	1.56597
$64$	16.3065	2.03832
$65$	−14.2458	−1.76697
$66$	7.91638	0.974439
$67$	−9.39578	−1.14788	−0.573939	−	0.818898i	$-0.694585\pi$
$67$	−9.39578	−1.14788	−0.573939	+	0.818898i	$0.694585\pi$
$68$	−11.6307	−1.41042
$69$	1.27817	0.153873
$70$	15.6681	1.87270
$71$	−1.37188	−0.162812	−0.0814062	−	0.996681i	$-0.525941\pi$
$71$	−1.37188	−0.162812	−0.0814062	+	0.996681i	$0.525941\pi$
$72$	−61.7192	−7.27367
$73$	−5.49219	−0.642812	−0.321406	−	0.946941i	$-0.604155\pi$
$73$	−5.49219	−0.642812	−0.321406	+	0.946941i	$0.604155\pi$
$74$	10.5873	1.23075
$75$	−24.1362	−2.78701
$76$	29.9747	3.43834
$77$	1.52928	0.174277
$78$	34.7900	3.93919
$79$	−8.95643	−1.00768	−0.503839	−	0.863798i	$-0.668079\pi$
$79$	−8.95643	−1.00768	−0.503839	+	0.863798i	$0.668079\pi$
$80$	−41.7736	−4.67043
$81$	24.3127	2.70141
$82$	1.33784	0.147740
$83$	−9.28255	−1.01889	−0.509446	−	0.860503i	$-0.670150\pi$
$83$	−9.28255	−1.01889	−0.509446	+	0.860503i	$0.670150\pi$
$84$	−27.4894	−2.99934
$85$	8.04593	0.872704
$86$	−24.1369	−2.60275
$87$	−26.1512	−2.80371
$88$	−7.59369	−0.809490
$89$	9.53357	1.01056	0.505278	−	0.862957i	$-0.331390\pi$
$89$	9.53357	1.01056	0.505278	+	0.862957i	$0.331390\pi$
$90$	70.2171	7.40153
$91$	6.72069	0.704519
$92$	−2.01635	−0.210219
$93$	−8.72713	−0.904961
$94$	9.76685	1.00737
$95$	−20.7361	−2.12748
$96$	48.5170	4.95175
$97$	5.98884	0.608074	0.304037	−	0.952660i	$-0.401665\pi$
$97$	5.98884	0.608074	0.304037	+	0.952660i	$0.401665\pi$
$98$	11.2642	1.13785
$99$	6.85348	0.688801
$100$	38.0755	3.80755
$101$	9.25042	0.920451	0.460225	−	0.887802i	$-0.347769\pi$
$101$	9.25042	0.920451	0.460225	+	0.887802i	$0.347769\pi$
$102$	−19.6492	−1.94556
$103$	15.0736	1.48524	0.742622	−	0.669711i	$-0.233582\pi$
$103$	15.0736	1.48524	0.742622	+	0.669711i	$0.233582\pi$
$104$	−33.3719	−3.27238
$105$	19.0168	1.85585
$106$	−11.7854	−1.14470
$107$	−9.45357	−0.913911	−0.456956	−	0.889489i	$-0.651060\pi$
$107$	−9.45357	−0.913911	−0.456956	+	0.889489i	$0.651060\pi$
$108$	−73.6753	−7.08941
$109$	−3.41632	−0.327224	−0.163612	−	0.986525i	$-0.552314\pi$
$109$	−3.41632	−0.327224	−0.163612	+	0.986525i	$0.552314\pi$
$110$	8.63925	0.823720
$111$	12.8500	1.21967
$112$	19.7074	1.86217
$113$	−14.0219	−1.31907	−0.659534	−	0.751675i	$-0.729246\pi$
$113$	−14.0219	−1.31907	−0.659534	+	0.751675i	$0.729246\pi$
$114$	50.6402	4.74289
$115$	1.39488	0.130073
$116$	41.2543	3.83037
$117$	30.1189	2.78449
$118$	12.0952	1.11345
$119$	−3.79580	−0.347960
$120$	−94.4289	−8.62014
$121$	−10.1568	−0.923343
$122$	36.3002	3.28647
$123$	1.62377	0.146410
$124$	13.7673	1.23634
$125$	−8.68966	−0.777227
$126$	−33.1261	−2.95110
$127$	−18.3981	−1.63256	−0.816282	−	0.577654i	$-0.803968\pi$
$127$	−18.3981	−1.63256	−0.816282	+	0.577654i	$0.803968\pi$
$128$	−13.4613	−1.18982
$129$	−29.2955	−2.57933
$130$	37.9668	3.32991
$131$	9.38003	0.819537	0.409768	−	0.912190i	$-0.365610\pi$
$131$	9.38003	0.819537	0.409768	+	0.912190i	$0.365610\pi$
$132$	−15.1574	−1.31928
$133$	9.78260	0.848259
$134$	25.0409	2.16320
$135$	50.9676	4.38659
$136$	18.8482	1.61622
$137$	7.25220	0.619597	0.309799	−	0.950802i	$-0.399738\pi$
$137$	7.25220	0.619597	0.309799	+	0.950802i	$0.399738\pi$
$138$	−3.40647	−0.289978
$139$	−5.50529	−0.466953	−0.233476	−	0.972362i	$-0.575010\pi$
$139$	−5.50529	−0.466953	−0.233476	+	0.972362i	$0.575010\pi$
$140$	−29.9996	−2.53543
$141$	11.8543	0.998310
$142$	3.65623	0.306824
$143$	3.70572	0.309888
$144$	88.3191	7.35992
$145$	−28.5392	−2.37005
$146$	14.6374	1.21140
$147$	13.6716	1.12761
$148$	−20.2713	−1.66629
$149$	17.2692	1.41475	0.707373	−	0.706841i	$-0.249880\pi$
$149$	17.2692	1.41475	0.707373	+	0.706841i	$0.249880\pi$
$150$	64.3259	5.25219
$151$	14.6030	1.18837	0.594187	−	0.804327i	$-0.297474\pi$
$151$	14.6030	1.18837	0.594187	+	0.804327i	$0.297474\pi$
$152$	−48.5760	−3.94003
$153$	−17.0110	−1.37525
$154$	−4.07570	−0.328430
$155$	−9.52403	−0.764989
$156$	−66.6119	−5.33322
$157$	−3.50068	−0.279384	−0.139692	−	0.990195i	$-0.544611\pi$
$157$	−3.50068	−0.279384	−0.139692	+	0.990195i	$0.544611\pi$
$158$	23.8700	1.89899
$159$	−14.3042	−1.13440
$160$	52.9473	4.18585
$161$	−0.658058	−0.0518622
$162$	−64.7962	−5.09087
$163$	0.460042	0.0360333	0.0180166	−	0.999838i	$-0.494265\pi$
$163$	0.460042	0.0360333	0.0180166	+	0.999838i	$0.494265\pi$
$164$	−2.56154	−0.200023
$165$	10.4857	0.816308
$166$	24.7391	1.92013
$167$	−17.6647	−1.36694	−0.683468	−	0.729981i	$-0.739529\pi$
$167$	−17.6647	−1.36694	−0.683468	+	0.729981i	$0.739529\pi$
$168$	44.5484	3.43698
$169$	3.28546	0.252728
$170$	−21.4434	−1.64463
$171$	43.8410	3.35260
$172$	46.2145	3.52383
$173$	−23.4095	−1.77979	−0.889897	−	0.456161i	$-0.849224\pi$
$173$	−23.4095	−1.77979	−0.889897	+	0.456161i	$0.849224\pi$
$174$	69.6962	5.28365
$175$	12.4264	0.939347
$176$	10.8664	0.819089
$177$	14.6802	1.10343
$178$	−25.4081	−1.90442
$179$	−12.2838	−0.918132	−0.459066	−	0.888402i	$-0.651816\pi$
$179$	−12.2838	−0.918132	−0.459066	+	0.888402i	$0.651816\pi$
$180$	−134.444	−10.0208
$181$	−10.0938	−0.750267	−0.375133	−	0.926971i	$-0.622403\pi$
$181$	−10.0938	−0.750267	−0.375133	+	0.926971i	$0.622403\pi$
$182$	−17.9114	−1.32768
$183$	44.0585	3.25690
$184$	3.26762	0.240892
$185$	14.0234	1.03102
$186$	23.2589	1.70542
$187$	−2.09296	−0.153053
$188$	−18.7005	−1.36387
$189$	−24.0448	−1.74900
$190$	55.2643	4.00929
$191$	0.803509	0.0581398	0.0290699	−	0.999577i	$-0.490745\pi$
$191$	0.803509	0.0581398	0.0290699	+	0.999577i	$0.490745\pi$
$192$	−52.7471	−3.80670
$193$	−12.3087	−0.885998	−0.442999	−	0.896522i	$-0.646086\pi$
$193$	−12.3087	−0.885998	−0.442999	+	0.896522i	$0.646086\pi$
$194$	−15.9610	−1.14593
$195$	46.0812	3.29995
$196$	−21.5673	−1.54052
$197$	−1.22978	−0.0876183	−0.0438091	−	0.999040i	$-0.513949\pi$
$197$	−1.22978	−0.0876183	−0.0438091	+	0.999040i	$0.513949\pi$
$198$	−18.2654	−1.29806
$199$	−19.0612	−1.35121	−0.675606	−	0.737263i	$-0.736118\pi$
$199$	−19.0612	−1.35121	−0.675606	+	0.737263i	$0.736118\pi$
$200$	−61.7039	−4.36312
$201$	30.3928	2.14374
$202$	−24.6535	−1.73461
$203$	13.4638	0.944975
$204$	37.6220	2.63407
$205$	1.77204	0.123765
$206$	−40.1729	−2.79898
$207$	−2.94910	−0.204977
$208$	47.7546	3.31119
$209$	5.39402	0.373112
$210$	−50.6821	−3.49740
$211$	25.1027	1.72814	0.864070	−	0.503372i	$-0.167907\pi$
$211$	25.1027	1.72814	0.864070	+	0.503372i	$0.167907\pi$
$212$	22.5653	1.54979
$213$	4.43766	0.304063
$214$	25.1949	1.72229
$215$	−31.9706	−2.18038
$216$	119.396	8.12384
$217$	4.49312	0.305013
$218$	9.10490	0.616661
$219$	17.7657	1.20050
$220$	−16.5414	−1.11522
$221$	−9.19792	−0.618719
$222$	−34.2469	−2.29850
$223$	26.6007	1.78131	0.890657	−	0.454677i	$-0.150245\pi$
$223$	26.6007	1.78131	0.890657	+	0.454677i	$0.150245\pi$
$224$	−24.9787	−1.66896
$225$	55.6892	3.71261
$226$	37.3700	2.48582
$227$	19.5170	1.29539	0.647694	−	0.761901i	$-0.275734\pi$
$227$	19.5170	1.29539	0.647694	+	0.761901i	$0.275734\pi$
$228$	−96.9600	−6.42133
$229$	11.8535	0.783301	0.391651	−	0.920114i	$-0.371904\pi$
$229$	11.8535	0.783301	0.391651	+	0.920114i	$0.371904\pi$
$230$	−3.71753	−0.245127
$231$	−4.94679	−0.325475
$232$	−66.8552	−4.38926
$233$	13.9472	0.913709	0.456854	−	0.889541i	$-0.348976\pi$
$233$	13.9472	0.913709	0.456854	+	0.889541i	$0.348976\pi$
$234$	−80.2706	−5.24745
$235$	12.9367	0.843899
$236$	−23.1584	−1.50749
$237$	28.9716	1.88191
$238$	10.1163	0.655740
$239$	−22.4426	−1.45169	−0.725845	−	0.687859i	$-0.758551\pi$
$239$	−22.4426	−1.45169	−0.725845	+	0.687859i	$0.758551\pi$
$240$	135.126	8.72236
$241$	−2.91146	−0.187543	−0.0937717	−	0.995594i	$-0.529892\pi$
$241$	−2.91146	−0.187543	−0.0937717	+	0.995594i	$0.529892\pi$
$242$	27.0690	1.74006
$243$	−35.3307	−2.26647
$244$	−69.5036	−4.44951
$245$	14.9200	0.953203
$246$	−4.32754	−0.275914
$247$	23.7050	1.50832
$248$	−22.3108	−1.41674
$249$	30.0265	1.90285
$250$	23.1590	1.46470
$251$	30.3647	1.91660	0.958302	−	0.285757i	$-0.0922449\pi$
$251$	30.3647	1.91660	0.958302	+	0.285757i	$0.0922449\pi$
$252$	63.4260	3.99546
$253$	−0.362846	−0.0228120
$254$	49.0330	3.07661
$255$	−26.0264	−1.62983
$256$	3.26282	0.203926
$257$	−10.7274	−0.669159	−0.334579	−	0.942368i	$-0.608594\pi$
$257$	−10.7274	−0.669159	−0.334579	+	0.942368i	$0.608594\pi$
$258$	78.0761	4.86081
$259$	−6.61578	−0.411084
$260$	−72.6945	−4.50832
$261$	60.3384	3.73485
$262$	−24.9989	−1.54444
$263$	25.7848	1.58996	0.794980	−	0.606636i	$-0.207481\pi$
$263$	25.7848	1.58996	0.794980	+	0.606636i	$0.207481\pi$
$264$	24.5635	1.51178
$265$	−15.6104	−0.958937
$266$	−26.0718	−1.59857
$267$	−30.8385	−1.88728
$268$	−47.9455	−2.92874
$269$	0.818630	0.0499128	0.0249564	−	0.999689i	$-0.492055\pi$
$269$	0.818630	0.0499128	0.0249564	+	0.999689i	$0.492055\pi$
$270$	−135.835	−8.26665
$271$	−31.1820	−1.89417	−0.947084	−	0.320985i	$-0.895986\pi$
$271$	−31.1820	−1.89417	−0.947084	+	0.320985i	$0.895986\pi$
$272$	−26.9715	−1.63539
$273$	−21.7396	−1.31574
$274$	−19.3280	−1.16765
$275$	6.85178	0.413178
$276$	6.52233	0.392598
$277$	21.2858	1.27894	0.639470	−	0.768816i	$-0.279154\pi$
$277$	21.2858	1.27894	0.639470	+	0.768816i	$0.279154\pi$
$278$	14.6723	0.879984
$279$	20.1360	1.20551
$280$	48.6162	2.90537
$281$	24.9220	1.48672	0.743360	−	0.668891i	$-0.233231\pi$
$281$	24.9220	1.48672	0.743360	+	0.668891i	$0.233231\pi$
$282$	−31.5931	−1.88134
$283$	−5.27157	−0.313362	−0.156681	−	0.987649i	$-0.550080\pi$
$283$	−5.27157	−0.313362	−0.156681	+	0.987649i	$0.550080\pi$
$284$	−7.00053	−0.415405
$285$	67.0756	3.97322
$286$	−9.87618	−0.583991
$287$	−0.835989	−0.0493469
$288$	−111.943	−6.59629
$289$	−11.8051	−0.694416
$290$	76.0604	4.46642
$291$	−19.3722	−1.13562
$292$	−28.0260	−1.64009
$293$	−3.63211	−0.212190	−0.106095	−	0.994356i	$-0.533835\pi$
$293$	−3.63211	−0.212190	−0.106095	+	0.994356i	$0.533835\pi$
$294$	−36.4364	−2.12502
$295$	16.0207	0.932761
$296$	32.8510	1.90942
$297$	−13.2580	−0.769310
$298$	−46.0244	−2.66612
$299$	−1.59460	−0.0922179
$300$	−123.164	−7.11087
$301$	15.0826	0.869349
$302$	−38.9187	−2.23952
$303$	−29.9226	−1.71901
$304$	69.5114	3.98675
$305$	48.0816	2.75315
$306$	45.3363	2.59170
$307$	1.60193	0.0914272	0.0457136	−	0.998955i	$-0.485444\pi$
$307$	1.60193	0.0914272	0.0457136	+	0.998955i	$0.485444\pi$
$308$	7.80370	0.444657
$309$	−48.7589	−2.77380
$310$	25.3827	1.44164
$311$	5.69459	0.322910	0.161455	−	0.986880i	$-0.448381\pi$
$311$	5.69459	0.322910	0.161455	+	0.986880i	$0.448381\pi$
$312$	107.949	6.11140
$313$	−25.8339	−1.46022	−0.730110	−	0.683330i	$-0.760531\pi$
$313$	−25.8339	−1.46022	−0.730110	+	0.683330i	$0.760531\pi$
$314$	9.32973	0.526507
$315$	−43.8773	−2.47220
$316$	−45.7035	−2.57102
$317$	−20.8686	−1.17210	−0.586048	−	0.810276i	$-0.699317\pi$
$317$	−20.8686	−1.17210	−0.586048	+	0.810276i	$0.699317\pi$
$318$	38.1224	2.13780
$319$	7.42381	0.415654
$320$	−57.5636	−3.21790
$321$	30.5797	1.70679
$322$	1.75380	0.0977357
$323$	−13.3884	−0.744953
$324$	124.064	6.89247
$325$	30.1114	1.67028
$326$	−1.22607	−0.0679057
$327$	11.0508	0.611113
$328$	4.15115	0.229209
$329$	−6.10311	−0.336475
$330$	−27.9456	−1.53835
$331$	−33.0115	−1.81448	−0.907239	−	0.420615i	$-0.861814\pi$
$331$	−33.0115	−1.81448	−0.907239	+	0.420615i	$0.861814\pi$
$332$	−47.3677	−2.59964
$333$	−29.6488	−1.62474
$334$	47.0786	2.57602
$335$	33.1680	1.81216
$336$	−63.7480	−3.47774
$337$	12.7071	0.692201	0.346100	−	0.938198i	$-0.387506\pi$
$337$	12.7071	0.692201	0.346100	+	0.938198i	$0.387506\pi$
$338$	−8.75615	−0.476272
$339$	45.3569	2.46345
$340$	41.0574	2.22665
$341$	2.47746	0.134162
$342$	−116.841	−6.31806
$343$	−18.6964	−1.00951
$344$	−74.8936	−4.03799
$345$	−4.51206	−0.242921
$346$	62.3893	3.35407
$347$	5.83104	0.313027	0.156513	−	0.987676i	$-0.449975\pi$
$347$	5.83104	0.313027	0.156513	+	0.987676i	$0.449975\pi$
$348$	−133.446	−7.15347
$349$	−17.1272	−0.916797	−0.458398	−	0.888747i	$-0.651577\pi$
$349$	−17.1272	−0.916797	−0.458398	+	0.888747i	$0.651577\pi$
$350$	−33.1178	−1.77022
$351$	−58.2650	−3.10995
$352$	−13.7730	−0.734104
$353$	−26.9598	−1.43493	−0.717464	−	0.696596i	$-0.754697\pi$
$353$	−26.9598	−1.43493	−0.717464	+	0.696596i	$0.754697\pi$
$354$	−39.1245	−2.07944
$355$	4.84288	0.257033
$356$	48.6486	2.57837
$357$	12.2784	0.649840
$358$	32.7377	1.73024
$359$	6.10808	0.322372	0.161186	−	0.986924i	$-0.448468\pi$
$359$	6.10808	0.322372	0.161186	+	0.986924i	$0.448468\pi$
$360$	217.875	11.4830
$361$	15.5050	0.816050
$362$	26.9012	1.41390
$363$	32.8544	1.72441
$364$	34.2948	1.79754
$365$	19.3880	1.01481
$366$	−117.421	−6.13771
$367$	−8.41763	−0.439397	−0.219698	−	0.975568i	$-0.570507\pi$
$367$	−8.41763	−0.439397	−0.219698	+	0.975568i	$0.570507\pi$
$368$	−4.67591	−0.243749
$369$	−3.74651	−0.195035
$370$	−37.3741	−1.94299
$371$	7.36444	0.382343
$372$	−44.5334	−2.30895
$373$	3.78985	0.196231	0.0981155	−	0.995175i	$-0.468719\pi$
$373$	3.78985	0.196231	0.0981155	+	0.995175i	$0.468719\pi$
$374$	5.57800	0.288432
$375$	28.1087	1.45152
$376$	30.3053	1.56288
$377$	32.6253	1.68029
$378$	64.0823	3.29604
$379$	30.8150	1.58286	0.791429	−	0.611261i	$-0.209337\pi$
$379$	30.8150	1.58286	0.791429	+	0.611261i	$0.209337\pi$
$380$	−105.814	−5.42813
$381$	59.5126	3.04892
$382$	−2.14145	−0.109566
$383$	7.58320	0.387483	0.193742	−	0.981053i	$-0.437938\pi$
$383$	7.58320	0.387483	0.193742	+	0.981053i	$0.437938\pi$
$384$	43.5434	2.22207
$385$	−5.39849	−0.275133
$386$	32.8041	1.66969
$387$	67.5933	3.43596
$388$	30.5603	1.55146
$389$	4.90492	0.248690	0.124345	−	0.992239i	$-0.460317\pi$
$389$	4.90492	0.248690	0.124345	+	0.992239i	$0.460317\pi$
$390$	−122.812	−6.21883
$391$	0.900617	0.0455462
$392$	34.9512	1.76530
$393$	−30.3418	−1.53054
$394$	3.27752	0.165119
$395$	31.6171	1.59083
$396$	34.9725	1.75743
$397$	−22.3182	−1.12012	−0.560058	−	0.828453i	$-0.689221\pi$
$397$	−22.3182	−1.12012	−0.560058	+	0.828453i	$0.689221\pi$
$398$	50.8004	2.54639
$399$	−31.6440	−1.58418
$400$	88.2972	4.41486
$401$	−6.80740	−0.339945	−0.169973	−	0.985449i	$-0.554368\pi$
$401$	−6.80740	−0.339945	−0.169973	+	0.985449i	$0.554368\pi$
$402$	−81.0004	−4.03993
$403$	10.8876	0.542352
$404$	47.2037	2.34847
$405$	−85.8261	−4.26473
$406$	−35.8827	−1.78083
$407$	−3.64787	−0.180818
$408$	−60.9688	−3.01841
$409$	12.3608	0.611204	0.305602	−	0.952159i	$-0.401142\pi$
$409$	12.3608	0.611204	0.305602	+	0.952159i	$0.401142\pi$
$410$	−4.72271	−0.233238
$411$	−23.4589	−1.15714
$412$	76.9186	3.78951
$413$	−7.55802	−0.371906
$414$	7.85972	0.386284
$415$	32.7683	1.60853
$416$	−60.5280	−2.96763
$417$	17.8081	0.872066
$418$	−14.3757	−0.703140
$419$	−32.5719	−1.59124	−0.795620	−	0.605797i	$-0.792855\pi$
$419$	−32.5719	−1.59124	−0.795620	+	0.605797i	$0.792855\pi$
$420$	97.0404	4.73508
$421$	26.1406	1.27402	0.637008	−	0.770857i	$-0.280172\pi$
$421$	26.1406	1.27402	0.637008	+	0.770857i	$0.280172\pi$
$422$	−66.9017	−3.25672
$423$	−27.3512	−1.32986
$424$	−36.5685	−1.77592
$425$	−17.0067	−0.824948
$426$	−11.8269	−0.573015
$427$	−22.6833	−1.09772
$428$	−48.2404	−2.33179
$429$	−11.9870	−0.578736
$430$	85.2055	4.10898
$431$	−25.1260	−1.21028	−0.605139	−	0.796120i	$-0.706882\pi$
$431$	−25.1260	−1.21028	−0.605139	+	0.796120i	$0.706882\pi$
$432$	−170.853	−8.22017
$433$	−13.7497	−0.660770	−0.330385	−	0.943846i	$-0.607179\pi$
$433$	−13.7497	−0.660770	−0.330385	+	0.943846i	$0.607179\pi$
$434$	−11.9747	−0.574804
$435$	92.3164	4.42623
$436$	−17.4330	−0.834890
$437$	−2.32109	−0.111033
$438$	−47.3478	−2.26237
$439$	−39.4161	−1.88123	−0.940613	−	0.339481i	$-0.889749\pi$
$439$	−39.4161	−1.88123	−0.940613	+	0.339481i	$0.889749\pi$
$440$	26.8065	1.27795
$441$	−31.5443	−1.50211
$442$	24.5136	1.16599
$443$	34.4890	1.63862	0.819310	−	0.573350i	$-0.194357\pi$
$443$	34.4890	1.63862	0.819310	+	0.573350i	$0.194357\pi$
$444$	65.5721	3.11192
$445$	−33.6544	−1.59537
$446$	−70.8940	−3.35693
$447$	−55.8610	−2.64214
$448$	27.1566	1.28303
$449$	11.2488	0.530865	0.265433	−	0.964129i	$-0.414485\pi$
$449$	11.2488	0.530865	0.265433	+	0.964129i	$0.414485\pi$
$450$	−148.418	−6.99651
$451$	−0.460956	−0.0217056
$452$	−71.5518	−3.36552
$453$	−47.2366	−2.21937
$454$	−52.0151	−2.44119
$455$	−23.7247	−1.11223
$456$	157.130	7.35828
$457$	−24.8399	−1.16196	−0.580980	−	0.813918i	$-0.697330\pi$
$457$	−24.8399	−1.16196	−0.580980	+	0.813918i	$0.697330\pi$
$458$	−31.5910	−1.47615
$459$	32.9077	1.53600
$460$	7.11790	0.331874
$461$	−2.02146	−0.0941490	−0.0470745	−	0.998891i	$-0.514990\pi$
$461$	−2.02146	−0.0941490	−0.0470745	+	0.998891i	$0.514990\pi$
$462$	13.1838	0.613365
$463$	18.9974	0.882884	0.441442	−	0.897290i	$-0.354467\pi$
$463$	18.9974	0.882884	0.441442	+	0.897290i	$0.354467\pi$
$464$	95.6687	4.44131
$465$	30.8076	1.42867
$466$	−37.1709	−1.72191
$467$	−23.8438	−1.10336	−0.551680	−	0.834056i	$-0.686013\pi$
$467$	−23.8438	−1.10336	−0.551680	+	0.834056i	$0.686013\pi$
$468$	153.693	7.10446
$469$	−15.6476	−0.722537
$470$	−34.4780	−1.59035
$471$	11.3237	0.521770
$472$	37.5297	1.72745
$473$	8.31642	0.382389
$474$	−77.2128	−3.54650
$475$	43.8301	2.01106
$476$	−19.3695	−0.887798
$477$	33.0039	1.51115
$478$	59.8122	2.73575
$479$	−30.1011	−1.37535	−0.687677	−	0.726017i	$-0.741369\pi$
$479$	−30.1011	−1.37535	−0.687677	+	0.726017i	$0.741369\pi$
$480$	−171.270	−7.81736
$481$	−16.0312	−0.730962
$482$	7.75939	0.353430
$483$	2.12864	0.0968563
$484$	−51.8287	−2.35585
$485$	−21.1412	−0.959972
$486$	94.1607	4.27122
$487$	10.7550	0.487354	0.243677	−	0.969856i	$-0.421646\pi$
$487$	10.7550	0.487354	0.243677	+	0.969856i	$0.421646\pi$
$488$	112.635	5.09875
$489$	−1.48811	−0.0672947
$490$	−39.7636	−1.79633
$491$	−30.3874	−1.37136	−0.685681	−	0.727902i	$-0.740496\pi$
$491$	−30.3874	−1.37136	−0.685681	+	0.727902i	$0.740496\pi$
$492$	8.28589	0.373557
$493$	−18.4266	−0.829891
$494$	−63.1768	−2.84246
$495$	−24.1935	−1.08742
$496$	31.9264	1.43354
$497$	−2.28470	−0.102483
$498$	−80.0243	−3.58597
$499$	−26.0789	−1.16745	−0.583725	−	0.811951i	$-0.698405\pi$
$499$	−26.0789	−1.16745	−0.583725	+	0.811951i	$0.698405\pi$
$500$	−44.3422	−1.98304
$501$	57.1404	2.55285
$502$	−80.9257	−3.61189
$503$	42.4260	1.89168	0.945841	−	0.324631i	$-0.105240\pi$
$503$	42.4260	1.89168	0.945841	+	0.324631i	$0.105240\pi$
$504$	−102.786	−4.57845
$505$	−32.6549	−1.45312
$506$	0.967030	0.0429897
$507$	−10.6276	−0.471986
$508$	−93.8829	−4.16538
$509$	−0.554758	−0.0245892	−0.0122946	−	0.999924i	$-0.503914\pi$
$509$	−0.554758	−0.0245892	−0.0122946	+	0.999924i	$0.503914\pi$
$510$	69.3634	3.07146
$511$	−9.14659	−0.404621
$512$	18.2267	0.805513
$513$	−84.8102	−3.74446
$514$	28.5899	1.26105
$515$	−53.2112	−2.34477
$516$	−149.491	−6.58099
$517$	−3.36519	−0.148001
$518$	17.6319	0.774699
$519$	75.7234	3.32389
$520$	117.806	5.16614
$521$	−31.4382	−1.37733	−0.688667	−	0.725078i	$-0.741804\pi$
$521$	−31.4382	−1.37733	−0.688667	+	0.725078i	$0.741804\pi$
$522$	−160.809	−7.03843
$523$	14.4686	0.632669	0.316335	−	0.948648i	$-0.397548\pi$
$523$	14.4686	0.632669	0.316335	+	0.948648i	$0.397548\pi$
$524$	47.8651	2.09100
$525$	−40.1960	−1.75430
$526$	−68.7196	−2.99632
$527$	−6.14927	−0.267866
$528$	−35.1500	−1.52971
$529$	−22.8439	−0.993212
$530$	41.6035	1.80714
$531$	−33.8715	−1.46990
$532$	49.9194	2.16428
$533$	−2.02576	−0.0877452
$534$	82.1882	3.55663
$535$	33.3720	1.44280
$536$	77.6987	3.35607
$537$	39.7346	1.71467
$538$	−2.18175	−0.0940619
$539$	−3.88109	−0.167170
$540$	260.081	11.1921
$541$	33.3793	1.43509	0.717543	−	0.696514i	$-0.245266\pi$
$541$	33.3793	1.43509	0.717543	+	0.696514i	$0.245266\pi$
$542$	83.1037	3.56961
$543$	32.6507	1.40118
$544$	34.1858	1.46571
$545$	12.0599	0.516591
$546$	57.9386	2.47954
$547$	33.0617	1.41362	0.706809	−	0.707404i	$-0.250134\pi$
$547$	33.0617	1.41362	0.706809	+	0.707404i	$0.250134\pi$
$548$	37.0070	1.58086
$549$	−101.656	−4.33856
$550$	−18.2608	−0.778645
$551$	47.4893	2.02311
$552$	−10.5698	−0.449883
$553$	−14.9159	−0.634288
$554$	−56.7292	−2.41019
$555$	−45.3619	−1.92551
$556$	−28.0928	−1.19140
$557$	−6.18886	−0.262230	−0.131115	−	0.991367i	$-0.541856\pi$
$557$	−6.18886	−0.262230	−0.131115	+	0.991367i	$0.541856\pi$
$558$	−53.6649	−2.27182
$559$	36.5480	1.54582
$560$	−69.5690	−2.93983
$561$	6.77016	0.285836
$562$	−66.4201	−2.80176
$563$	9.81010	0.413446	0.206723	−	0.978399i	$-0.433720\pi$
$563$	9.81010	0.413446	0.206723	+	0.978399i	$0.433720\pi$
$564$	60.4909	2.54712
$565$	49.4986	2.08242
$566$	14.0494	0.590540
$567$	40.4899	1.70041
$568$	11.3448	0.476018
$569$	−20.8835	−0.875481	−0.437740	−	0.899101i	$-0.644221\pi$
$569$	−20.8835	−0.875481	−0.437740	+	0.899101i	$0.644221\pi$
$570$	−178.765	−7.48763
$571$	26.1172	1.09297	0.546485	−	0.837469i	$-0.315965\pi$
$571$	26.1172	1.09297	0.546485	+	0.837469i	$0.315965\pi$
$572$	18.9098	0.790658
$573$	−2.59913	−0.108580
$574$	2.22801	0.0929955
$575$	−2.94837	−0.122956
$576$	121.703	5.07095
$577$	−34.6070	−1.44071	−0.720353	−	0.693607i	$-0.756020\pi$
$577$	−34.6070	−1.44071	−0.720353	+	0.693607i	$0.756020\pi$
$578$	31.4620	1.30865
$579$	39.8152	1.65466
$580$	−145.632	−6.04703
$581$	−15.4590	−0.641347
$582$	51.6294	2.14011
$583$	4.06068	0.168176
$584$	45.4178	1.87940
$585$	−106.323	−4.39590
$586$	9.68001	0.399877
$587$	15.4280	0.636784	0.318392	−	0.947959i	$-0.396857\pi$
$587$	15.4280	0.636784	0.318392	+	0.947959i	$0.396857\pi$
$588$	69.7643	2.87703
$589$	15.8480	0.653006
$590$	−42.6971	−1.75781
$591$	3.97800	0.163633
$592$	−47.0092	−1.93207
$593$	−7.44981	−0.305927	−0.152964	−	0.988232i	$-0.548882\pi$
$593$	−7.44981	−0.305927	−0.152964	+	0.988232i	$0.548882\pi$
$594$	35.3343	1.44978
$595$	13.3995	0.549328
$596$	88.1224	3.60963
$597$	61.6577	2.52348
$598$	4.24979	0.173787
$599$	−38.8746	−1.58837	−0.794186	−	0.607675i	$-0.792103\pi$
$599$	−38.8746	−1.58837	−0.794186	+	0.607675i	$0.792103\pi$
$600$	199.595	8.14843
$601$	−33.0765	−1.34922	−0.674609	−	0.738175i	$-0.735688\pi$
$601$	−33.0765	−1.34922	−0.674609	+	0.738175i	$0.735688\pi$
$602$	−40.1971	−1.63831
$603$	−70.1249	−2.85571
$604$	74.5171	3.03206
$605$	35.8544	1.45769
$606$	79.7472	3.23951
$607$	−27.0028	−1.09601	−0.548004	−	0.836476i	$-0.684612\pi$
$607$	−27.0028	−1.09601	−0.548004	+	0.836476i	$0.684612\pi$
$608$	−88.1044	−3.57310
$609$	−43.5518	−1.76481
$610$	−128.143	−5.18838
$611$	−14.7890	−0.598297
$612$	−86.8048	−3.50887
$613$	−30.6339	−1.23729	−0.618645	−	0.785670i	$-0.712318\pi$
$613$	−30.6339	−1.23729	−0.618645	+	0.785670i	$0.712318\pi$
$614$	−4.26935	−0.172297
$615$	−5.73207	−0.231139
$616$	−12.6464	−0.509538
$617$	−13.6748	−0.550525	−0.275263	−	0.961369i	$-0.588765\pi$
$617$	−13.6748	−0.550525	−0.275263	+	0.961369i	$0.588765\pi$
$618$	129.948	5.22729
$619$	16.6035	0.667349	0.333675	−	0.942688i	$-0.391711\pi$
$619$	16.6035	0.667349	0.333675	+	0.942688i	$0.391711\pi$
$620$	−48.5999	−1.95182
$621$	5.70503	0.228935
$622$	−15.1768	−0.608533
$623$	15.8770	0.636099
$624$	−154.473	−6.18387
$625$	−6.63261	−0.265304
$626$	68.8506	2.75182
$627$	−17.4482	−0.696813
$628$	−17.8635	−0.712831
$629$	9.05434	0.361020
$630$	116.938	4.65893
$631$	11.4216	0.454687	0.227343	−	0.973815i	$-0.426996\pi$
$631$	11.4216	0.454687	0.227343	+	0.973815i	$0.426996\pi$
$632$	74.0655	2.94617
$633$	−81.2003	−3.22742
$634$	55.6173	2.20885
$635$	64.9469	2.57734
$636$	−72.9925	−2.89434
$637$	−17.0562	−0.675790
$638$	−19.7854	−0.783310
$639$	−10.2390	−0.405047
$640$	47.5195	1.87837
$641$	−2.04036	−0.0805892	−0.0402946	−	0.999188i	$-0.512830\pi$
$641$	−2.04036	−0.0805892	−0.0402946	+	0.999188i	$0.512830\pi$
$642$	−81.4986	−3.21649
$643$	−28.4920	−1.12361	−0.561807	−	0.827268i	$-0.689894\pi$
$643$	−28.4920	−1.12361	−0.561807	+	0.827268i	$0.689894\pi$
$644$	−3.35799	−0.132323
$645$	103.416	4.07200
$646$	35.6818	1.40388
$647$	2.87522	0.113036	0.0565182	−	0.998402i	$-0.482000\pi$
$647$	2.87522	0.113036	0.0565182	+	0.998402i	$0.482000\pi$
$648$	−201.054	−7.89816
$649$	−4.16742	−0.163585
$650$	−80.2506	−3.14769
$651$	−14.5340	−0.569632
$652$	2.34754	0.0919366
$653$	−31.1405	−1.21862	−0.609312	−	0.792931i	$-0.708554\pi$
$653$	−31.1405	−1.21862	−0.609312	+	0.792931i	$0.708554\pi$
$654$	−29.4518	−1.15166
$655$	−33.1124	−1.29381
$656$	−5.94022	−0.231927
$657$	−40.9907	−1.59920
$658$	16.2655	0.634097
$659$	39.7071	1.54677	0.773385	−	0.633936i	$-0.218562\pi$
$659$	39.7071	1.54677	0.773385	+	0.633936i	$0.218562\pi$
$660$	53.5070	2.08276
$661$	−30.5260	−1.18732	−0.593661	−	0.804715i	$-0.702318\pi$
$661$	−30.5260	−1.18732	−0.593661	+	0.804715i	$0.702318\pi$
$662$	87.9798	3.41943
$663$	29.7527	1.15550
$664$	76.7623	2.97896
$665$	−34.5335	−1.33915
$666$	79.0176	3.06187
$667$	−3.19452	−0.123692
$668$	−90.1407	−3.48765
$669$	−86.0459	−3.32673
$670$	−88.3968	−3.41507
$671$	−12.5073	−0.482840
$672$	80.7993	3.11690
$673$	16.0826	0.619940	0.309970	−	0.950746i	$-0.399681\pi$
$673$	16.0826	0.619940	0.309970	+	0.950746i	$0.399681\pi$
$674$	−33.8660	−1.30447
$675$	−107.731	−4.14655
$676$	16.7653	0.644818
$677$	−14.9411	−0.574234	−0.287117	−	0.957895i	$-0.592697\pi$
$677$	−14.9411	−0.574234	−0.287117	+	0.957895i	$0.592697\pi$
$678$	−120.882	−4.64243
$679$	9.97370	0.382755
$680$	−66.5361	−2.55154
$681$	−63.1321	−2.41923
$682$	−6.60272	−0.252831
$683$	37.6539	1.44079	0.720394	−	0.693565i	$-0.243961\pi$
$683$	37.6539	1.44079	0.720394	+	0.693565i	$0.243961\pi$
$684$	223.715	8.55395
$685$	−25.6010	−0.978163
$686$	49.8282	1.90245
$687$	−38.3428	−1.46287
$688$	107.172	4.08588
$689$	17.8454	0.679855
$690$	12.0252	0.457791
$691$	−21.2472	−0.808281	−0.404141	−	0.914697i	$-0.632429\pi$
$691$	−21.2472	−0.808281	−0.404141	+	0.914697i	$0.632429\pi$
$692$	−119.456	−4.54103
$693$	11.4137	0.433569
$694$	−15.5404	−0.589907
$695$	19.4342	0.737182
$696$	216.258	8.19725
$697$	1.14413	0.0433371
$698$	45.6460	1.72773
$699$	−45.1152	−1.70641
$700$	63.4103	2.39668
$701$	13.1716	0.497483	0.248741	−	0.968570i	$-0.419983\pi$
$701$	13.1716	0.497483	0.248741	+	0.968570i	$0.419983\pi$
$702$	155.283	5.86079
$703$	−23.3350	−0.880097
$704$	14.9739	0.564348
$705$	−41.8468	−1.57604
$706$	71.8512	2.70416
$707$	15.4055	0.579382
$708$	74.9112	2.81533
$709$	49.8346	1.87158	0.935789	−	0.352561i	$-0.114689\pi$
$709$	49.8346	1.87158	0.935789	+	0.352561i	$0.114689\pi$
$710$	−12.9068	−0.484385
$711$	−66.8458	−2.50692
$712$	−78.8381	−2.95458
$713$	−1.06607	−0.0399245
$714$	−32.7233	−1.22464
$715$	−13.0815	−0.489222
$716$	−62.6825	−2.34255
$717$	72.5955	2.71113
$718$	−16.2788	−0.607518
$719$	−13.4453	−0.501426	−0.250713	−	0.968061i	$-0.580665\pi$
$719$	−13.4453	−0.501426	−0.250713	+	0.968061i	$0.580665\pi$
$720$	−311.775	−11.6192
$721$	25.1033	0.934894
$722$	−41.3226	−1.53787
$723$	9.41776	0.350250
$724$	−51.5074	−1.91426
$725$	60.3234	2.24036
$726$	−87.5609	−3.24969
$727$	−24.5721	−0.911329	−0.455665	−	0.890152i	$-0.650598\pi$
$727$	−24.5721	−0.911329	−0.455665	+	0.890152i	$0.650598\pi$
$728$	−55.5769	−2.05982
$729$	41.3472	1.53138
$730$	−51.6713	−1.91244
$731$	−20.6421	−0.763475
$732$	224.825	8.30977
$733$	20.1557	0.744468	0.372234	−	0.928139i	$-0.378592\pi$
$733$	20.1557	0.744468	0.372234	+	0.928139i	$0.378592\pi$
$734$	22.4340	0.828054
$735$	−48.2620	−1.78017
$736$	5.92662	0.218458
$737$	−8.62790	−0.317813
$738$	9.98489	0.367549
$739$	−21.3742	−0.786262	−0.393131	−	0.919482i	$-0.628608\pi$
$739$	−21.3742	−0.786262	−0.393131	+	0.919482i	$0.628608\pi$
$740$	71.5597	2.63059
$741$	−76.6793	−2.81688
$742$	−19.6271	−0.720534
$743$	−13.5165	−0.495873	−0.247936	−	0.968776i	$-0.579752\pi$
$743$	−13.5165	−0.495873	−0.247936	+	0.968776i	$0.579752\pi$
$744$	72.1693	2.64585
$745$	−60.9619	−2.23347
$746$	−10.1004	−0.369802
$747$	−69.2798	−2.53482
$748$	−10.6801	−0.390504
$749$	−15.7438	−0.575266
$750$	−74.9130	−2.73544
$751$	30.0650	1.09709	0.548543	−	0.836122i	$-0.315183\pi$
$751$	30.0650	1.09709	0.548543	+	0.836122i	$0.315183\pi$
$752$	−43.3664	−1.58141
$753$	−98.2215	−3.57939
$754$	−86.9504	−3.16655
$755$	−51.5499	−1.87609
$756$	−122.697	−4.46246
$757$	12.1410	0.441273	0.220636	−	0.975356i	$-0.429187\pi$
$757$	12.1410	0.441273	0.220636	+	0.975356i	$0.429187\pi$
$758$	−82.1256	−2.98294
$759$	1.17371	0.0426029
$760$	171.478	6.22016
$761$	35.6606	1.29270	0.646348	−	0.763042i	$-0.276295\pi$
$761$	35.6606	1.29270	0.646348	+	0.763042i	$0.276295\pi$
$762$	−158.608	−5.74578
$763$	−5.68947	−0.205973
$764$	4.10020	0.148340
$765$	60.0504	2.17113
$766$	−20.2101	−0.730222
$767$	−18.3145	−0.661298
$768$	−10.5543	−0.380847
$769$	19.8131	0.714480	0.357240	−	0.934013i	$-0.383718\pi$
$769$	19.8131	0.714480	0.357240	+	0.934013i	$0.383718\pi$
$770$	14.3876	0.518494
$771$	34.7003	1.24970
$772$	−62.8096	−2.26057
$773$	9.01052	0.324086	0.162043	−	0.986784i	$-0.448192\pi$
$773$	9.01052	0.324086	0.162043	+	0.986784i	$0.448192\pi$
$774$	−180.144	−6.47515
$775$	20.1310	0.723127
$776$	−49.5249	−1.77784
$777$	21.4002	0.767729
$778$	−13.0722	−0.468662
$779$	−2.94868	−0.105647
$780$	235.147	8.41960
$781$	−1.25976	−0.0450778
$782$	−2.40025	−0.0858329
$783$	−116.725	−4.17139
$784$	−50.0146	−1.78624
$785$	12.3577	0.441066
$786$	80.8646	2.88434
$787$	26.2351	0.935180	0.467590	−	0.883946i	$-0.345122\pi$
$787$	26.2351	0.935180	0.467590	+	0.883946i	$0.345122\pi$
$788$	−6.27542	−0.223552
$789$	−83.4068	−2.96936
$790$	−84.2634	−2.99796
$791$	−23.3518	−0.830293
$792$	−56.6751	−2.01386
$793$	−54.9658	−1.95189
$794$	59.4806	2.11089
$795$	50.4952	1.79088
$796$	−97.2668	−3.44753
$797$	−41.2848	−1.46238	−0.731191	−	0.682173i	$-0.761035\pi$
$797$	−41.2848	−1.46238	−0.731191	+	0.682173i	$0.761035\pi$
$798$	84.3352	2.98543
$799$	8.35271	0.295498
$800$	−111.915	−3.95679
$801$	71.1532	2.51408
$802$	18.1425	0.640636
$803$	−5.04334	−0.177975
$804$	155.090	5.46962
$805$	2.32301	0.0818753
$806$	−29.0169	−1.02208
$807$	−2.64804	−0.0932155
$808$	−76.4966	−2.69114
$809$	14.5551	0.511732	0.255866	−	0.966712i	$-0.417639\pi$
$809$	14.5551	0.511732	0.255866	+	0.966712i	$0.417639\pi$
$810$	228.737	8.03700
$811$	11.4527	0.402157	0.201079	−	0.979575i	$-0.435555\pi$
$811$	11.4527	0.402157	0.201079	+	0.979575i	$0.435555\pi$
$812$	68.7041	2.41104
$813$	100.865	3.53749
$814$	9.72202	0.340757
$815$	−1.62399	−0.0568860
$816$	87.2453	3.05420
$817$	53.1992	1.86120
$818$	−32.9431	−1.15183
$819$	50.1595	1.75271
$820$	9.04250	0.315778
$821$	−18.4561	−0.644122	−0.322061	−	0.946719i	$-0.604376\pi$
$821$	−18.4561	−0.644122	−0.322061	+	0.946719i	$0.604376\pi$
$822$	62.5207	2.18066
$823$	−11.8088	−0.411627	−0.205814	−	0.978591i	$-0.565984\pi$
$823$	−11.8088	−0.411627	−0.205814	+	0.978591i	$0.565984\pi$
$824$	−124.651	−4.34244
$825$	−22.1636	−0.771639
$826$	20.1431	0.700866
$827$	41.0028	1.42581	0.712904	−	0.701262i	$-0.247380\pi$
$827$	41.0028	1.42581	0.712904	+	0.701262i	$0.247380\pi$
$828$	−15.0489	−0.522985
$829$	19.0501	0.661638	0.330819	−	0.943694i	$-0.392675\pi$
$829$	19.0501	0.661638	0.330819	+	0.943694i	$0.392675\pi$
$830$	−87.3315	−3.03132
$831$	−68.8537	−2.38851
$832$	65.8054	2.28139
$833$	9.63321	0.333771
$834$	−47.4608	−1.64343
$835$	62.3581	2.15799
$836$	27.5250	0.951972
$837$	−38.9531	−1.34641
$838$	86.8079	2.99873
$839$	−13.4400	−0.464002	−0.232001	−	0.972716i	$-0.574527\pi$
$839$	−13.4400	−0.464002	−0.232001	+	0.972716i	$0.574527\pi$
$840$	−157.260	−5.42599
$841$	36.3596	1.25378
$842$	−69.6679	−2.40091
$843$	−80.6157	−2.77655
$844$	128.096	4.40924
$845$	−11.5980	−0.398983
$846$	72.8944	2.50616
$847$	−16.9149	−0.581203
$848$	52.3289	1.79698
$849$	17.0521	0.585226
$850$	45.3250	1.55464
$851$	1.56970	0.0538088
$852$	22.6448	0.775798
$853$	−14.8061	−0.506950	−0.253475	−	0.967342i	$-0.581574\pi$
$853$	−14.8061	−0.506950	−0.253475	+	0.967342i	$0.581574\pi$
$854$	60.4537	2.06868
$855$	−154.763	−5.29278
$856$	78.1766	2.67202
$857$	10.2190	0.349075	0.174538	−	0.984651i	$-0.444157\pi$
$857$	10.2190	0.349075	0.174538	+	0.984651i	$0.444157\pi$
$858$	31.9467	1.09064
$859$	−9.75815	−0.332944	−0.166472	−	0.986046i	$-0.553237\pi$
$859$	−9.75815	−0.332944	−0.166472	+	0.986046i	$0.553237\pi$
$860$	−163.142	−5.56309
$861$	2.70420	0.0921587
$862$	66.9639	2.28080
$863$	−37.7276	−1.28426	−0.642131	−	0.766595i	$-0.721949\pi$
$863$	−37.7276	−1.28426	−0.642131	+	0.766595i	$0.721949\pi$
$864$	216.553	7.36728
$865$	82.6380	2.80978
$866$	36.6447	1.24524
$867$	38.1862	1.29687
$868$	22.9278	0.778220
$869$	−8.22446	−0.278996
$870$	−246.034	−8.34135
$871$	−37.9169	−1.28477
$872$	28.2513	0.956711
$873$	44.6974	1.51278
$874$	6.18598	0.209244
$875$	−14.4716	−0.489229
$876$	90.6562	3.06299
$877$	46.6899	1.57661	0.788304	−	0.615286i	$-0.210960\pi$
$877$	46.6899	1.57661	0.788304	+	0.615286i	$0.210960\pi$
$878$	105.049	3.54522
$879$	11.7489	0.396279
$880$	−38.3596	−1.29310
$881$	−48.2984	−1.62722	−0.813608	−	0.581414i	$-0.802500\pi$
$881$	−48.2984	−1.62722	−0.813608	+	0.581414i	$0.802500\pi$
$882$	84.0694	2.83076
$883$	28.4340	0.956880	0.478440	−	0.878120i	$-0.341202\pi$
$883$	28.4340	0.956880	0.478440	+	0.878120i	$0.341202\pi$
$884$	−46.9358	−1.57862
$885$	−51.8225	−1.74200
$886$	−91.9173	−3.08802
$887$	23.6367	0.793643	0.396821	−	0.917896i	$-0.370113\pi$
$887$	23.6367	0.793643	0.396821	+	0.917896i	$0.370113\pi$
$888$	−106.264	−3.56598
$889$	−30.6398	−1.02762
$890$	89.6931	3.00652
$891$	22.3257	0.747939
$892$	135.740	4.54491
$893$	−21.5267	−0.720365
$894$	148.876	4.97917
$895$	43.3629	1.44946
$896$	−22.4181	−0.748937
$897$	5.15808	0.172223
$898$	−29.9795	−1.00043
$899$	21.8117	0.727460
$900$	284.175	9.47249
$901$	−10.0790	−0.335779
$902$	1.22850	0.0409047
$903$	−48.7882	−1.62357
$904$	115.954	3.85658
$905$	35.6321	1.18445
$906$	125.891	4.18246
$907$	−43.6804	−1.45038	−0.725192	−	0.688547i	$-0.758249\pi$
$907$	−43.6804	−1.45038	−0.725192	+	0.688547i	$0.758249\pi$
$908$	99.5927	3.30510
$909$	69.0400	2.28991
$910$	63.2292	2.09603
$911$	−9.00472	−0.298340	−0.149170	−	0.988812i	$-0.547660\pi$
$911$	−9.00472	−0.298340	−0.149170	+	0.988812i	$0.547660\pi$
$912$	−224.850	−7.44554
$913$	−8.52392	−0.282101
$914$	66.2012	2.18974
$915$	−155.531	−5.14169
$916$	60.4869	1.99854
$917$	15.6213	0.515861
$918$	−87.7029	−2.89463
$919$	8.12235	0.267932	0.133966	−	0.990986i	$-0.457229\pi$
$919$	8.12235	0.267932	0.133966	+	0.990986i	$0.457229\pi$
$920$	−11.5350	−0.380298
$921$	−5.18181	−0.170747
$922$	5.38745	0.177426
$923$	−5.53626	−0.182228
$924$	−25.2428	−0.830428
$925$	−29.6414	−0.974603
$926$	−50.6304	−1.66382
$927$	112.501	3.69501
$928$	−121.258	−3.98050
$929$	7.63976	0.250652	0.125326	−	0.992116i	$-0.460002\pi$
$929$	7.63976	0.250652	0.125326	+	0.992116i	$0.460002\pi$
$930$	−82.1060	−2.69236
$931$	−24.8269	−0.813668
$932$	71.1706	2.33127
$933$	−18.4204	−0.603058
$934$	63.5466	2.07931
$935$	7.38837	0.241625
$936$	−249.069	−8.14108
$937$	−44.6948	−1.46011	−0.730057	−	0.683386i	$-0.760507\pi$
$937$	−44.6948	−1.46011	−0.730057	+	0.683386i	$0.760507\pi$
$938$	41.7026	1.36164
$939$	83.5656	2.72706
$940$	66.0145	2.15315
$941$	−32.2469	−1.05122	−0.525609	−	0.850726i	$-0.676162\pi$
$941$	−32.2469	−1.05122	−0.525609	+	0.850726i	$0.676162\pi$
$942$	−30.1791	−0.983288
$943$	0.198353	0.00645925
$944$	−53.7044	−1.74793
$945$	84.8805	2.76116
$946$	−22.1643	−0.720622
$947$	−17.8921	−0.581417	−0.290708	−	0.956812i	$-0.593891\pi$
$947$	−17.8921	−0.581417	−0.290708	+	0.956812i	$0.593891\pi$
$948$	147.838	4.80157
$949$	−22.1639	−0.719470
$950$	−116.812	−3.78990
$951$	67.5041	2.18897
$952$	31.3895	1.01734
$953$	5.81160	0.188256	0.0941281	−	0.995560i	$-0.469994\pi$
$953$	5.81160	0.188256	0.0941281	+	0.995560i	$0.469994\pi$
$954$	−87.9594	−2.84779
$955$	−2.83646	−0.0917858
$956$	−114.522	−3.70389
$957$	−24.0140	−0.776262
$958$	80.2230	2.59189
$959$	12.0777	0.390008
$960$	186.202	6.00966
$961$	−23.7211	−0.765195
$962$	42.7252	1.37752
$963$	−70.5562	−2.27364
$964$	−14.8568	−0.478505
$965$	43.4508	1.39873
$966$	−5.67308	−0.182528
$967$	36.4186	1.17114	0.585571	−	0.810621i	$-0.300870\pi$
$967$	36.4186	1.17114	0.585571	+	0.810621i	$0.300870\pi$
$968$	83.9917	2.69960
$969$	43.3079	1.39125
$970$	56.3438	1.80909
$971$	−26.3840	−0.846704	−0.423352	−	0.905965i	$-0.639147\pi$
$971$	−26.3840	−0.846704	−0.423352	+	0.905965i	$0.639147\pi$
$972$	−180.288	−5.78275
$973$	−9.16841	−0.293926
$974$	−28.6633	−0.918431
$975$	−97.4022	−3.11937
$976$	−161.179	−5.15921
$977$	22.8641	0.731488	0.365744	−	0.930716i	$-0.380815\pi$
$977$	22.8641	0.731488	0.365744	+	0.930716i	$0.380815\pi$
$978$	3.96599	0.126819
$979$	8.75442	0.279793
$980$	76.1347	2.43204
$981$	−25.4975	−0.814072
$982$	80.9860	2.58437
$983$	44.4412	1.41746	0.708728	−	0.705482i	$-0.249269\pi$
$983$	44.4412	1.41746	0.708728	+	0.705482i	$0.249269\pi$
$984$	−13.4278	−0.428063
$985$	4.34125	0.138324
$986$	49.1090	1.56395
$987$	19.7419	0.628391
$988$	120.964	3.84837
$989$	−3.57861	−0.113793
$990$	64.4785	2.04926
$991$	−22.6039	−0.718038	−0.359019	−	0.933330i	$-0.616889\pi$
$991$	−22.6039	−0.718038	−0.359019	+	0.933330i	$0.616889\pi$
$992$	−40.4660	−1.28480
$993$	106.783	3.38866
$994$	6.08902	0.193132
$995$	67.2879	2.13317
$996$	153.221	4.85500
$997$	10.6064	0.335907	0.167953	−	0.985795i	$-0.446284\pi$
$997$	10.6064	0.335907	0.167953	+	0.985795i	$0.446284\pi$
$998$	69.5033	2.20009
$999$	57.3555	1.81465

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6007.2.a.b.1.13	✓	237

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6007.2.a.b.1.13	✓	237	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66512 q^{2} -3.23472 q^{3} +5.10287 q^{4} -3.53010 q^{5} +8.62093 q^{6} +1.66538 q^{7} -8.26953 q^{8} +7.46344 q^{9} +O(q^{10})\)	\(q-2.66512 q^{2} -3.23472 q^{3} +5.10287 q^{4} -3.53010 q^{5} +8.62093 q^{6} +1.66538 q^{7} -8.26953 q^{8} +7.46344 q^{9} +9.40814 q^{10} +0.918274 q^{11} -16.5064 q^{12} +4.03552 q^{13} -4.43844 q^{14} +11.4189 q^{15} +11.8336 q^{16} -2.27924 q^{17} -19.8910 q^{18} +5.87409 q^{19} -18.0136 q^{20} -5.38705 q^{21} -2.44731 q^{22} -0.395140 q^{23} +26.7497 q^{24} +7.46159 q^{25} -10.7552 q^{26} -14.4380 q^{27} +8.49823 q^{28} +8.08453 q^{29} -30.4327 q^{30} +2.69795 q^{31} -14.9988 q^{32} -2.97036 q^{33} +6.07444 q^{34} -5.87896 q^{35} +38.0850 q^{36} -3.97253 q^{37} -15.6552 q^{38} -13.0538 q^{39} +29.1923 q^{40} -0.501981 q^{41} +14.3571 q^{42} +9.05658 q^{43} +4.68583 q^{44} -26.3467 q^{45} +1.05310 q^{46} -3.66469 q^{47} -38.2783 q^{48} -4.22651 q^{49} -19.8860 q^{50} +7.37271 q^{51} +20.5928 q^{52} +4.42208 q^{53} +38.4791 q^{54} -3.24160 q^{55} -13.7719 q^{56} -19.0011 q^{57} -21.5462 q^{58} -4.53832 q^{59} +58.2692 q^{60} -13.6205 q^{61} -7.19037 q^{62} +12.4295 q^{63} +16.3065 q^{64} -14.2458 q^{65} +7.91638 q^{66} -9.39578 q^{67} -11.6307 q^{68} +1.27817 q^{69} +15.6681 q^{70} -1.37188 q^{71} -61.7192 q^{72} -5.49219 q^{73} +10.5873 q^{74} -24.1362 q^{75} +29.9747 q^{76} +1.52928 q^{77} +34.7900 q^{78} -8.95643 q^{79} -41.7736 q^{80} +24.3127 q^{81} +1.33784 q^{82} -9.28255 q^{83} -27.4894 q^{84} +8.04593 q^{85} -24.1369 q^{86} -26.1512 q^{87} -7.59369 q^{88} +9.53357 q^{89} +70.2171 q^{90} +6.72069 q^{91} -2.01635 q^{92} -8.72713 q^{93} +9.76685 q^{94} -20.7361 q^{95} +48.5170 q^{96} +5.98884 q^{97} +11.2642 q^{98} +6.85348 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9}+O(q^{10}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9} - 39 q^{10} - 38 q^{11} - 67 q^{12} - 52 q^{13} - 54 q^{14} - 24 q^{15} + 208 q^{16} - 255 q^{17} - 71 q^{18} - 24 q^{19} - 154 q^{20} - 60 q^{21} - 39 q^{22} - 118 q^{23} - 85 q^{24} + 170 q^{25} - 61 q^{26} - 87 q^{27} - 99 q^{28} - 87 q^{29} - 30 q^{30} - 28 q^{31} - 156 q^{32} - 173 q^{33} - 4 q^{34} - 113 q^{35} + 152 q^{36} - 49 q^{37} - 145 q^{38} - 49 q^{39} - 91 q^{40} - 197 q^{41} - 61 q^{42} - 63 q^{43} - 106 q^{44} - 181 q^{45} - 2 q^{46} - 119 q^{47} - 142 q^{48} + 150 q^{49} - 89 q^{50} - 40 q^{51} - 97 q^{52} - 190 q^{53} - 97 q^{54} - 55 q^{55} - 154 q^{56} - 202 q^{57} - 27 q^{58} - 86 q^{59} - 48 q^{60} - 96 q^{61} - 239 q^{62} - 149 q^{63} + 183 q^{64} - 259 q^{65} - 72 q^{66} - 28 q^{67} - 482 q^{68} - 83 q^{69} + 20 q^{70} - 63 q^{71} - 193 q^{72} - 206 q^{73} - 132 q^{74} - 89 q^{75} - 11 q^{76} - 179 q^{77} - 58 q^{78} - 32 q^{79} - 320 q^{80} + 57 q^{81} - 77 q^{82} - 245 q^{83} - 133 q^{84} + q^{85} - 39 q^{86} - 179 q^{87} - 104 q^{88} - 227 q^{89} - 146 q^{90} - 36 q^{91} - 315 q^{92} - 87 q^{93} - 48 q^{94} - 111 q^{95} - 134 q^{96} - 221 q^{97} - 161 q^{98} - 68 q^{99}+O(q^{100}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9 - 39 * q^10 - 38 * q^11 - 67 * q^12 - 52 * q^13 - 54 * q^14 - 24 * q^15 + 208 * q^16 - 255 * q^17 - 71 * q^18 - 24 * q^19 - 154 * q^20 - 60 * q^21 - 39 * q^22 - 118 * q^23 - 85 * q^24 + 170 * q^25 - 61 * q^26 - 87 * q^27 - 99 * q^28 - 87 * q^29 - 30 * q^30 - 28 * q^31 - 156 * q^32 - 173 * q^33 - 4 * q^34 - 113 * q^35 + 152 * q^36 - 49 * q^37 - 145 * q^38 - 49 * q^39 - 91 * q^40 - 197 * q^41 - 61 * q^42 - 63 * q^43 - 106 * q^44 - 181 * q^45 - 2 * q^46 - 119 * q^47 - 142 * q^48 + 150 * q^49 - 89 * q^50 - 40 * q^51 - 97 * q^52 - 190 * q^53 - 97 * q^54 - 55 * q^55 - 154 * q^56 - 202 * q^57 - 27 * q^58 - 86 * q^59 - 48 * q^60 - 96 * q^61 - 239 * q^62 - 149 * q^63 + 183 * q^64 - 259 * q^65 - 72 * q^66 - 28 * q^67 - 482 * q^68 - 83 * q^69 + 20 * q^70 - 63 * q^71 - 193 * q^72 - 206 * q^73 - 132 * q^74 - 89 * q^75 - 11 * q^76 - 179 * q^77 - 58 * q^78 - 32 * q^79 - 320 * q^80 + 57 * q^81 - 77 * q^82 - 245 * q^83 - 133 * q^84 + q^85 - 39 * q^86 - 179 * q^87 - 104 * q^88 - 227 * q^89 - 146 * q^90 - 36 * q^91 - 315 * q^92 - 87 * q^93 - 48 * q^94 - 111 * q^95 - 134 * q^96 - 221 * q^97 - 161 * q^98 - 68 * q^99

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