LMFDB - Embedded newform 4730.2.a.w.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 12x^{6} + 7x^{5} + 41x^{4} - 6x^{3} - 28x^{2} + 2x + 4 $ x^8 - x^7 - 12x^6 + 7x^5 + 41x^4 - 6x^3 - 28x^2 + 2x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.42597$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.42597 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.42597 q^{6} -2.60155 q^{7} -1.00000 q^{8} +8.73725 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.42597 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.42597 q^{6} -2.60155 q^{7} -1.00000 q^{8} +8.73725 q^{9} -1.00000 q^{10} +1.00000 q^{11} -3.42597 q^{12} +2.63050 q^{13} +2.60155 q^{14} -3.42597 q^{15} +1.00000 q^{16} +0.262709 q^{17} -8.73725 q^{18} -1.75322 q^{19} +1.00000 q^{20} +8.91283 q^{21} -1.00000 q^{22} +0.630496 q^{23} +3.42597 q^{24} +1.00000 q^{25} -2.63050 q^{26} -19.6556 q^{27} -2.60155 q^{28} -7.05978 q^{29} +3.42597 q^{30} +1.60930 q^{31} -1.00000 q^{32} -3.42597 q^{33} -0.262709 q^{34} -2.60155 q^{35} +8.73725 q^{36} -2.81938 q^{37} +1.75322 q^{38} -9.01199 q^{39} -1.00000 q^{40} +7.41556 q^{41} -8.91283 q^{42} -1.00000 q^{43} +1.00000 q^{44} +8.73725 q^{45} -0.630496 q^{46} -6.45149 q^{47} -3.42597 q^{48} -0.231923 q^{49} -1.00000 q^{50} -0.900033 q^{51} +2.63050 q^{52} +5.51623 q^{53} +19.6556 q^{54} +1.00000 q^{55} +2.60155 q^{56} +6.00646 q^{57} +7.05978 q^{58} +3.57556 q^{59} -3.42597 q^{60} +0.307509 q^{61} -1.60930 q^{62} -22.7304 q^{63} +1.00000 q^{64} +2.63050 q^{65} +3.42597 q^{66} -11.3208 q^{67} +0.262709 q^{68} -2.16006 q^{69} +2.60155 q^{70} -8.53160 q^{71} -8.73725 q^{72} +2.33108 q^{73} +2.81938 q^{74} -3.42597 q^{75} -1.75322 q^{76} -2.60155 q^{77} +9.01199 q^{78} +8.43177 q^{79} +1.00000 q^{80} +41.1277 q^{81} -7.41556 q^{82} -3.47644 q^{83} +8.91283 q^{84} +0.262709 q^{85} +1.00000 q^{86} +24.1866 q^{87} -1.00000 q^{88} +12.3225 q^{89} -8.73725 q^{90} -6.84338 q^{91} +0.630496 q^{92} -5.51342 q^{93} +6.45149 q^{94} -1.75322 q^{95} +3.42597 q^{96} +2.91128 q^{97} +0.231923 q^{98} +8.73725 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 7 q^{3} + 8 q^{4} + 8 q^{5} + 7 q^{6} - 6 q^{7} - 8 q^{8} + 7 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 7 * q^3 + 8 * q^4 + 8 * q^5 + 7 * q^6 - 6 * q^7 - 8 * q^8 + 7 * q^9	\( 8 q - 8 q^{2} - 7 q^{3} + 8 q^{4} + 8 q^{5} + 7 q^{6} - 6 q^{7} - 8 q^{8} + 7 q^{9} - 8 q^{10} + 8 q^{11} - 7 q^{12} - 2 q^{13} + 6 q^{14} - 7 q^{15} + 8 q^{16} - 8 q^{17} - 7 q^{18} + 8 q^{20} + 14 q^{21} - 8 q^{22} - 18 q^{23} + 7 q^{24} + 8 q^{25} + 2 q^{26} - 22 q^{27} - 6 q^{28} + 8 q^{29} + 7 q^{30} - 11 q^{31} - 8 q^{32} - 7 q^{33} + 8 q^{34} - 6 q^{35} + 7 q^{36} - 17 q^{37} - 6 q^{39} - 8 q^{40} + 12 q^{41} - 14 q^{42} - 8 q^{43} + 8 q^{44} + 7 q^{45} + 18 q^{46} - 19 q^{47} - 7 q^{48} - 2 q^{49} - 8 q^{50} - q^{51} - 2 q^{52} - 7 q^{53} + 22 q^{54} + 8 q^{55} + 6 q^{56} - 3 q^{57} - 8 q^{58} + q^{59} - 7 q^{60} + 6 q^{61} + 11 q^{62} - 15 q^{63} + 8 q^{64} - 2 q^{65} + 7 q^{66} - 22 q^{67} - 8 q^{68} + 8 q^{69} + 6 q^{70} - 14 q^{71} - 7 q^{72} - 13 q^{73} + 17 q^{74} - 7 q^{75} - 6 q^{77} + 6 q^{78} - 8 q^{79} + 8 q^{80} + 28 q^{81} - 12 q^{82} - 4 q^{83} + 14 q^{84} - 8 q^{85} + 8 q^{86} - 30 q^{87} - 8 q^{88} + 5 q^{89} - 7 q^{90} - 8 q^{91} - 18 q^{92} + q^{93} + 19 q^{94} + 7 q^{96} - 23 q^{97} + 2 q^{98} + 7 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 7 * q^3 + 8 * q^4 + 8 * q^5 + 7 * q^6 - 6 * q^7 - 8 * q^8 + 7 * q^9 - 8 * q^10 + 8 * q^11 - 7 * q^12 - 2 * q^13 + 6 * q^14 - 7 * q^15 + 8 * q^16 - 8 * q^17 - 7 * q^18 + 8 * q^20 + 14 * q^21 - 8 * q^22 - 18 * q^23 + 7 * q^24 + 8 * q^25 + 2 * q^26 - 22 * q^27 - 6 * q^28 + 8 * q^29 + 7 * q^30 - 11 * q^31 - 8 * q^32 - 7 * q^33 + 8 * q^34 - 6 * q^35 + 7 * q^36 - 17 * q^37 - 6 * q^39 - 8 * q^40 + 12 * q^41 - 14 * q^42 - 8 * q^43 + 8 * q^44 + 7 * q^45 + 18 * q^46 - 19 * q^47 - 7 * q^48 - 2 * q^49 - 8 * q^50 - q^51 - 2 * q^52 - 7 * q^53 + 22 * q^54 + 8 * q^55 + 6 * q^56 - 3 * q^57 - 8 * q^58 + q^59 - 7 * q^60 + 6 * q^61 + 11 * q^62 - 15 * q^63 + 8 * q^64 - 2 * q^65 + 7 * q^66 - 22 * q^67 - 8 * q^68 + 8 * q^69 + 6 * q^70 - 14 * q^71 - 7 * q^72 - 13 * q^73 + 17 * q^74 - 7 * q^75 - 6 * q^77 + 6 * q^78 - 8 * q^79 + 8 * q^80 + 28 * q^81 - 12 * q^82 - 4 * q^83 + 14 * q^84 - 8 * q^85 + 8 * q^86 - 30 * q^87 - 8 * q^88 + 5 * q^89 - 7 * q^90 - 8 * q^91 - 18 * q^92 + q^93 + 19 * q^94 + 7 * q^96 - 23 * q^97 + 2 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.42597	−1.97798	−0.988991	−	0.147973i	$-0.952725\pi$
$3$	−3.42597	−1.97798	−0.988991	+	0.147973i	$0.952725\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	3.42597	1.39864
$7$	−2.60155	−0.983295	−0.491647	−	0.870794i	$-0.663605\pi$
$7$	−2.60155	−0.983295	−0.491647	+	0.870794i	$0.663605\pi$
$8$	−1.00000	−0.353553
$9$	8.73725	2.91242
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.42597	−0.988991
$13$	2.63050	0.729568	0.364784	−	0.931092i	$-0.381143\pi$
$13$	2.63050	0.729568	0.364784	+	0.931092i	$0.381143\pi$
$14$	2.60155	0.695294
$15$	−3.42597	−0.884581
$16$	1.00000	0.250000
$17$	0.262709	0.0637163	0.0318582	−	0.999492i	$-0.489858\pi$
$17$	0.262709	0.0637163	0.0318582	+	0.999492i	$0.489858\pi$
$18$	−8.73725	−2.05939
$19$	−1.75322	−0.402215	−0.201108	−	0.979569i	$-0.564454\pi$
$19$	−1.75322	−0.402215	−0.201108	+	0.979569i	$0.564454\pi$
$20$	1.00000	0.223607
$21$	8.91283	1.94494
$22$	−1.00000	−0.213201
$23$	0.630496	0.131468	0.0657338	−	0.997837i	$-0.479061\pi$
$23$	0.630496	0.131468	0.0657338	+	0.997837i	$0.479061\pi$
$24$	3.42597	0.699322
$25$	1.00000	0.200000
$26$	−2.63050	−0.515883
$27$	−19.6556	−3.78272
$28$	−2.60155	−0.491647
$29$	−7.05978	−1.31097	−0.655484	−	0.755209i	$-0.727535\pi$
$29$	−7.05978	−1.31097	−0.655484	+	0.755209i	$0.727535\pi$
$30$	3.42597	0.625493
$31$	1.60930	0.289039	0.144520	−	0.989502i	$-0.453836\pi$
$31$	1.60930	0.289039	0.144520	+	0.989502i	$0.453836\pi$
$32$	−1.00000	−0.176777
$33$	−3.42597	−0.596384
$34$	−0.262709	−0.0450543
$35$	−2.60155	−0.439743
$36$	8.73725	1.45621
$37$	−2.81938	−0.463504	−0.231752	−	0.972775i	$-0.574446\pi$
$37$	−2.81938	−0.463504	−0.231752	+	0.972775i	$0.574446\pi$
$38$	1.75322	0.284409
$39$	−9.01199	−1.44307
$40$	−1.00000	−0.158114
$41$	7.41556	1.15812	0.579058	−	0.815286i	$-0.303420\pi$
$41$	7.41556	1.15812	0.579058	+	0.815286i	$0.303420\pi$
$42$	−8.91283	−1.37528
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.00000	0.150756
$45$	8.73725	1.30247
$46$	−0.630496	−0.0929616
$47$	−6.45149	−0.941047	−0.470523	−	0.882388i	$-0.655935\pi$
$47$	−6.45149	−0.941047	−0.470523	+	0.882388i	$0.655935\pi$
$48$	−3.42597	−0.494496
$49$	−0.231923	−0.0331319
$50$	−1.00000	−0.141421
$51$	−0.900033	−0.126030
$52$	2.63050	0.364784
$53$	5.51623	0.757713	0.378856	−	0.925455i	$-0.376317\pi$
$53$	5.51623	0.757713	0.378856	+	0.925455i	$0.376317\pi$
$54$	19.6556	2.67479
$55$	1.00000	0.134840
$56$	2.60155	0.347647
$57$	6.00646	0.795575
$58$	7.05978	0.926995
$59$	3.57556	0.465498	0.232749	−	0.972537i	$-0.425228\pi$
$59$	3.57556	0.465498	0.232749	+	0.972537i	$0.425228\pi$
$60$	−3.42597	−0.442290
$61$	0.307509	0.0393725	0.0196863	−	0.999806i	$-0.493733\pi$
$61$	0.307509	0.0393725	0.0196863	+	0.999806i	$0.493733\pi$
$62$	−1.60930	−0.204382
$63$	−22.7304	−2.86376
$64$	1.00000	0.125000
$65$	2.63050	0.326273
$66$	3.42597	0.421707
$67$	−11.3208	−1.38305	−0.691525	−	0.722352i	$-0.743061\pi$
$67$	−11.3208	−1.38305	−0.691525	+	0.722352i	$0.743061\pi$
$68$	0.262709	0.0318582
$69$	−2.16006	−0.260041
$70$	2.60155	0.310945
$71$	−8.53160	−1.01251	−0.506257	−	0.862382i	$-0.668971\pi$
$71$	−8.53160	−1.01251	−0.506257	+	0.862382i	$0.668971\pi$
$72$	−8.73725	−1.02969
$73$	2.33108	0.272832	0.136416	−	0.990652i	$-0.456442\pi$
$73$	2.33108	0.272832	0.136416	+	0.990652i	$0.456442\pi$
$74$	2.81938	0.327747
$75$	−3.42597	−0.395597
$76$	−1.75322	−0.201108
$77$	−2.60155	−0.296474
$78$	9.01199	1.02041
$79$	8.43177	0.948648	0.474324	−	0.880350i	$-0.342693\pi$
$79$	8.43177	0.948648	0.474324	+	0.880350i	$0.342693\pi$
$80$	1.00000	0.111803
$81$	41.1277	4.56975
$82$	−7.41556	−0.818912
$83$	−3.47644	−0.381589	−0.190795	−	0.981630i	$-0.561106\pi$
$83$	−3.47644	−0.381589	−0.190795	+	0.981630i	$0.561106\pi$
$84$	8.91283	0.972470
$85$	0.262709	0.0284948
$86$	1.00000	0.107833
$87$	24.1866	2.59307
$88$	−1.00000	−0.106600
$89$	12.3225	1.30618	0.653092	−	0.757278i	$-0.273471\pi$
$89$	12.3225	1.30618	0.653092	+	0.757278i	$0.273471\pi$
$90$	−8.73725	−0.920987
$91$	−6.84338	−0.717381
$92$	0.630496	0.0657338
$93$	−5.51342	−0.571715
$94$	6.45149	0.665420
$95$	−1.75322	−0.179876
$96$	3.42597	0.349661
$97$	2.91128	0.295596	0.147798	−	0.989018i	$-0.452781\pi$
$97$	2.91128	0.295596	0.147798	+	0.989018i	$0.452781\pi$
$98$	0.231923	0.0234278
$99$	8.73725	0.878126
$100$	1.00000	0.100000
$101$	−9.31580	−0.926957	−0.463479	−	0.886108i	$-0.653399\pi$
$101$	−9.31580	−0.926957	−0.463479	+	0.886108i	$0.653399\pi$
$102$	0.900033	0.0891165
$103$	10.5783	1.04231	0.521155	−	0.853462i	$-0.325501\pi$
$103$	10.5783	1.04231	0.521155	+	0.853462i	$0.325501\pi$
$104$	−2.63050	−0.257941
$105$	8.91283	0.869803
$106$	−5.51623	−0.535784
$107$	8.04423	0.777665	0.388833	−	0.921308i	$-0.372878\pi$
$107$	8.04423	0.777665	0.388833	+	0.921308i	$0.372878\pi$
$108$	−19.6556	−1.89136
$109$	5.15752	0.494001	0.247000	−	0.969015i	$-0.420555\pi$
$109$	5.15752	0.494001	0.247000	+	0.969015i	$0.420555\pi$
$110$	−1.00000	−0.0953463
$111$	9.65911	0.916802
$112$	−2.60155	−0.245824
$113$	−5.91065	−0.556027	−0.278013	−	0.960577i	$-0.589676\pi$
$113$	−5.91065	−0.556027	−0.278013	+	0.960577i	$0.589676\pi$
$114$	−6.00646	−0.562556
$115$	0.630496	0.0587941
$116$	−7.05978	−0.655484
$117$	22.9833	2.12481
$118$	−3.57556	−0.329157
$119$	−0.683452	−0.0626519
$120$	3.42597	0.312747
$121$	1.00000	0.0909091
$122$	−0.307509	−0.0278406
$123$	−25.4055	−2.29073
$124$	1.60930	0.144520
$125$	1.00000	0.0894427
$126$	22.7304	2.02499
$127$	4.13091	0.366559	0.183280	−	0.983061i	$-0.441329\pi$
$127$	4.13091	0.366559	0.183280	+	0.983061i	$0.441329\pi$
$128$	−1.00000	−0.0883883
$129$	3.42597	0.301640
$130$	−2.63050	−0.230710
$131$	−1.48157	−0.129445	−0.0647227	−	0.997903i	$-0.520616\pi$
$131$	−1.48157	−0.129445	−0.0647227	+	0.997903i	$0.520616\pi$
$132$	−3.42597	−0.298192
$133$	4.56108	0.395496
$134$	11.3208	0.977964
$135$	−19.6556	−1.69169
$136$	−0.262709	−0.0225271
$137$	−18.8936	−1.61419	−0.807096	−	0.590420i	$-0.798962\pi$
$137$	−18.8936	−1.61419	−0.807096	+	0.590420i	$0.798962\pi$
$138$	2.16006	0.183876
$139$	5.56084	0.471664	0.235832	−	0.971794i	$-0.424219\pi$
$139$	5.56084	0.471664	0.235832	+	0.971794i	$0.424219\pi$
$140$	−2.60155	−0.219871
$141$	22.1026	1.86137
$142$	8.53160	0.715956
$143$	2.63050	0.219973
$144$	8.73725	0.728104
$145$	−7.05978	−0.586283
$146$	−2.33108	−0.192921
$147$	0.794561	0.0655343
$148$	−2.81938	−0.231752
$149$	6.10422	0.500078	0.250039	−	0.968236i	$-0.419557\pi$
$149$	6.10422	0.500078	0.250039	+	0.968236i	$0.419557\pi$
$150$	3.42597	0.279729
$151$	1.59289	0.129627	0.0648137	−	0.997897i	$-0.479355\pi$
$151$	1.59289	0.129627	0.0648137	+	0.997897i	$0.479355\pi$
$152$	1.75322	0.142205
$153$	2.29536	0.185568
$154$	2.60155	0.209639
$155$	1.60930	0.129262
$156$	−9.01199	−0.721537
$157$	8.00975	0.639247	0.319624	−	0.947545i	$-0.396443\pi$
$157$	8.00975	0.639247	0.319624	+	0.947545i	$0.396443\pi$
$158$	−8.43177	−0.670795
$159$	−18.8984	−1.49874
$160$	−1.00000	−0.0790569
$161$	−1.64027	−0.129271
$162$	−41.1277	−3.23130
$163$	−7.96784	−0.624089	−0.312045	−	0.950067i	$-0.601014\pi$
$163$	−7.96784	−0.624089	−0.312045	+	0.950067i	$0.601014\pi$
$164$	7.41556	0.579058
$165$	−3.42597	−0.266711
$166$	3.47644	0.269824
$167$	14.2749	1.10463	0.552313	−	0.833637i	$-0.313745\pi$
$167$	14.2749	1.10463	0.552313	+	0.833637i	$0.313745\pi$
$168$	−8.91283	−0.687640
$169$	−6.08049	−0.467730
$170$	−0.262709	−0.0201489
$171$	−15.3183	−1.17142
$172$	−1.00000	−0.0762493
$173$	−12.2432	−0.930834	−0.465417	−	0.885092i	$-0.654096\pi$
$173$	−12.2432	−0.930834	−0.465417	+	0.885092i	$0.654096\pi$
$174$	−24.1866	−1.83358
$175$	−2.60155	−0.196659
$176$	1.00000	0.0753778
$177$	−12.2497	−0.920746
$178$	−12.3225	−0.923612
$179$	17.8848	1.33677	0.668385	−	0.743816i	$-0.266986\pi$
$179$	17.8848	1.33677	0.668385	+	0.743816i	$0.266986\pi$
$180$	8.73725	0.651236
$181$	−20.5420	−1.52687	−0.763437	−	0.645882i	$-0.776490\pi$
$181$	−20.5420	−1.52687	−0.763437	+	0.645882i	$0.776490\pi$
$182$	6.84338	0.507265
$183$	−1.05352	−0.0778782
$184$	−0.630496	−0.0464808
$185$	−2.81938	−0.207285
$186$	5.51342	0.404264
$187$	0.262709	0.0192112
$188$	−6.45149	−0.470523
$189$	51.1351	3.71953
$190$	1.75322	0.127192
$191$	10.5915	0.766373	0.383187	−	0.923671i	$-0.374827\pi$
$191$	10.5915	0.766373	0.383187	+	0.923671i	$0.374827\pi$
$192$	−3.42597	−0.247248
$193$	−9.96641	−0.717398	−0.358699	−	0.933453i	$-0.616780\pi$
$193$	−9.96641	−0.717398	−0.358699	+	0.933453i	$0.616780\pi$
$194$	−2.91128	−0.209018
$195$	−9.01199	−0.645362
$196$	−0.231923	−0.0165659
$197$	18.8917	1.34598	0.672990	−	0.739651i	$-0.265010\pi$
$197$	18.8917	1.34598	0.672990	+	0.739651i	$0.265010\pi$
$198$	−8.73725	−0.620929
$199$	12.8676	0.912157	0.456078	−	0.889940i	$-0.349254\pi$
$199$	12.8676	0.912157	0.456078	+	0.889940i	$0.349254\pi$
$200$	−1.00000	−0.0707107
$201$	38.7845	2.73565
$202$	9.31580	0.655458
$203$	18.3664	1.28907
$204$	−0.900033	−0.0630149
$205$	7.41556	0.517925
$206$	−10.5783	−0.737024
$207$	5.50880	0.382888
$208$	2.63050	0.182392
$209$	−1.75322	−0.121272
$210$	−8.91283	−0.615044
$211$	17.3807	1.19654	0.598268	−	0.801296i	$-0.295856\pi$
$211$	17.3807	1.19654	0.598268	+	0.801296i	$0.295856\pi$
$212$	5.51623	0.378856
$213$	29.2290	2.00274
$214$	−8.04423	−0.549892
$215$	−1.00000	−0.0681994
$216$	19.6556	1.33740
$217$	−4.18669	−0.284211
$218$	−5.15752	−0.349311
$219$	−7.98619	−0.539657
$220$	1.00000	0.0674200
$221$	0.691056	0.0464854
$222$	−9.65911	−0.648277
$223$	−18.3492	−1.22876	−0.614378	−	0.789012i	$-0.710593\pi$
$223$	−18.3492	−1.22876	−0.614378	+	0.789012i	$0.710593\pi$
$224$	2.60155	0.173824
$225$	8.73725	0.582483
$226$	5.91065	0.393170
$227$	1.76490	0.117141	0.0585703	−	0.998283i	$-0.481346\pi$
$227$	1.76490	0.117141	0.0585703	+	0.998283i	$0.481346\pi$
$228$	6.00646	0.397787
$229$	−20.7806	−1.37322	−0.686611	−	0.727025i	$-0.740903\pi$
$229$	−20.7806	−1.37322	−0.686611	+	0.727025i	$0.740903\pi$
$230$	−0.630496	−0.0415737
$231$	8.91283	0.586421
$232$	7.05978	0.463497
$233$	24.2538	1.58892	0.794459	−	0.607318i	$-0.207755\pi$
$233$	24.2538	1.58892	0.794459	+	0.607318i	$0.207755\pi$
$234$	−22.9833	−1.50247
$235$	−6.45149	−0.420849
$236$	3.57556	0.232749
$237$	−28.8870	−1.87641
$238$	0.683452	0.0443016
$239$	−17.6969	−1.14472	−0.572358	−	0.820004i	$-0.693971\pi$
$239$	−17.6969	−1.14472	−0.572358	+	0.820004i	$0.693971\pi$
$240$	−3.42597	−0.221145
$241$	−16.2567	−1.04718	−0.523592	−	0.851969i	$-0.675409\pi$
$241$	−16.2567	−1.04718	−0.523592	+	0.851969i	$0.675409\pi$
$242$	−1.00000	−0.0642824
$243$	−81.9354	−5.25616
$244$	0.307509	0.0196863
$245$	−0.231923	−0.0148170
$246$	25.4055	1.61979
$247$	−4.61183	−0.293444
$248$	−1.60930	−0.102191
$249$	11.9102	0.754777
$250$	−1.00000	−0.0632456
$251$	−27.8317	−1.75672	−0.878360	−	0.477999i	$-0.841362\pi$
$251$	−27.8317	−1.75672	−0.878360	+	0.477999i	$0.841362\pi$
$252$	−22.7304	−1.43188
$253$	0.630496	0.0396390
$254$	−4.13091	−0.259196
$255$	−0.900033	−0.0563622
$256$	1.00000	0.0625000
$257$	7.49293	0.467396	0.233698	−	0.972309i	$-0.424917\pi$
$257$	7.49293	0.467396	0.233698	+	0.972309i	$0.424917\pi$
$258$	−3.42597	−0.213291
$259$	7.33478	0.455761
$260$	2.63050	0.163136
$261$	−61.6831	−3.81809
$262$	1.48157	0.0915317
$263$	−4.27364	−0.263524	−0.131762	−	0.991281i	$-0.542063\pi$
$263$	−4.27364	−0.263524	−0.131762	+	0.991281i	$0.542063\pi$
$264$	3.42597	0.210854
$265$	5.51623	0.338860
$266$	−4.56108	−0.279658
$267$	−42.2165	−2.58361
$268$	−11.3208	−0.691525
$269$	20.6758	1.26062	0.630312	−	0.776342i	$-0.282927\pi$
$269$	20.6758	1.26062	0.630312	+	0.776342i	$0.282927\pi$
$270$	19.6556	1.19620
$271$	−7.48613	−0.454750	−0.227375	−	0.973807i	$-0.573014\pi$
$271$	−7.48613	−0.454750	−0.227375	+	0.973807i	$0.573014\pi$
$272$	0.262709	0.0159291
$273$	23.4452	1.41897
$274$	18.8936	1.14141
$275$	1.00000	0.0603023
$276$	−2.16006	−0.130020
$277$	30.7672	1.84862	0.924312	−	0.381638i	$-0.124640\pi$
$277$	30.7672	1.84862	0.924312	+	0.381638i	$0.124640\pi$
$278$	−5.56084	−0.333517
$279$	14.0609	0.841803
$280$	2.60155	0.155473
$281$	−1.75846	−0.104901	−0.0524503	−	0.998624i	$-0.516703\pi$
$281$	−1.75846	−0.104901	−0.0524503	+	0.998624i	$0.516703\pi$
$282$	−22.1026	−1.31619
$283$	−1.50016	−0.0891750	−0.0445875	−	0.999005i	$-0.514197\pi$
$283$	−1.50016	−0.0891750	−0.0445875	+	0.999005i	$0.514197\pi$
$284$	−8.53160	−0.506257
$285$	6.00646	0.355792
$286$	−2.63050	−0.155545
$287$	−19.2920	−1.13877
$288$	−8.73725	−0.514847
$289$	−16.9310	−0.995940
$290$	7.05978	0.414565
$291$	−9.97396	−0.584684
$292$	2.33108	0.136416
$293$	−26.9183	−1.57258	−0.786291	−	0.617856i	$-0.788001\pi$
$293$	−26.9183	−1.57258	−0.786291	+	0.617856i	$0.788001\pi$
$294$	−0.794561	−0.0463397
$295$	3.57556	0.208177
$296$	2.81938	0.163873
$297$	−19.6556	−1.14053
$298$	−6.10422	−0.353608
$299$	1.65852	0.0959146
$300$	−3.42597	−0.197798
$301$	2.60155	0.149951
$302$	−1.59289	−0.0916604
$303$	31.9156	1.83351
$304$	−1.75322	−0.100554
$305$	0.307509	0.0176079
$306$	−2.29536	−0.131217
$307$	−25.7312	−1.46856	−0.734278	−	0.678848i	$-0.762479\pi$
$307$	−25.7312	−1.46856	−0.734278	+	0.678848i	$0.762479\pi$
$308$	−2.60155	−0.148237
$309$	−36.2408	−2.06167
$310$	−1.60930	−0.0914023
$311$	−16.9993	−0.963944	−0.481972	−	0.876187i	$-0.660079\pi$
$311$	−16.9993	−0.963944	−0.481972	+	0.876187i	$0.660079\pi$
$312$	9.01199	0.510204
$313$	22.1108	1.24977	0.624887	−	0.780715i	$-0.285145\pi$
$313$	22.1108	1.24977	0.624887	+	0.780715i	$0.285145\pi$
$314$	−8.00975	−0.452016
$315$	−22.7304	−1.28071
$316$	8.43177	0.474324
$317$	−27.2666	−1.53145	−0.765724	−	0.643170i	$-0.777619\pi$
$317$	−27.2666	−1.53145	−0.765724	+	0.643170i	$0.777619\pi$
$318$	18.8984	1.05977
$319$	−7.05978	−0.395272
$320$	1.00000	0.0559017
$321$	−27.5593	−1.53821
$322$	1.64027	0.0914087
$323$	−0.460586	−0.0256277
$324$	41.1277	2.28487
$325$	2.63050	0.145914
$326$	7.96784	0.441298
$327$	−17.6695	−0.977125
$328$	−7.41556	−0.409456
$329$	16.7839	0.925326
$330$	3.42597	0.188593
$331$	−16.0290	−0.881033	−0.440516	−	0.897745i	$-0.645205\pi$
$331$	−16.0290	−0.881033	−0.440516	+	0.897745i	$0.645205\pi$
$332$	−3.47644	−0.190795
$333$	−24.6336	−1.34992
$334$	−14.2749	−0.781089
$335$	−11.3208	−0.618519
$336$	8.91283	0.486235
$337$	−3.46767	−0.188896	−0.0944481	−	0.995530i	$-0.530109\pi$
$337$	−3.46767	−0.188896	−0.0944481	+	0.995530i	$0.530109\pi$
$338$	6.08049	0.330735
$339$	20.2497	1.09981
$340$	0.262709	0.0142474
$341$	1.60930	0.0871487
$342$	15.3183	0.828318
$343$	18.8142	1.01587
$344$	1.00000	0.0539164
$345$	−2.16006	−0.116294
$346$	12.2432	0.658199
$347$	15.4864	0.831354	0.415677	−	0.909512i	$-0.363545\pi$
$347$	15.4864	0.831354	0.415677	+	0.909512i	$0.363545\pi$
$348$	24.1866	1.29654
$349$	−5.80758	−0.310873	−0.155436	−	0.987846i	$-0.549678\pi$
$349$	−5.80758	−0.310873	−0.155436	+	0.987846i	$0.549678\pi$
$350$	2.60155	0.139059
$351$	−51.7040	−2.75976
$352$	−1.00000	−0.0533002
$353$	6.00116	0.319409	0.159705	−	0.987165i	$-0.448946\pi$
$353$	6.00116	0.319409	0.159705	+	0.987165i	$0.448946\pi$
$354$	12.2497	0.651066
$355$	−8.53160	−0.452810
$356$	12.3225	0.653092
$357$	2.34148	0.123924
$358$	−17.8848	−0.945239
$359$	−24.9377	−1.31616	−0.658081	−	0.752947i	$-0.728632\pi$
$359$	−24.9377	−1.31616	−0.658081	+	0.752947i	$0.728632\pi$
$360$	−8.73725	−0.460493
$361$	−15.9262	−0.838223
$362$	20.5420	1.07966
$363$	−3.42597	−0.179817
$364$	−6.84338	−0.358690
$365$	2.33108	0.122014
$366$	1.05352	0.0550682
$367$	−26.8270	−1.40036	−0.700180	−	0.713967i	$-0.746897\pi$
$367$	−26.8270	−1.40036	−0.700180	+	0.713967i	$0.746897\pi$
$368$	0.630496	0.0328669
$369$	64.7916	3.37291
$370$	2.81938	0.146573
$371$	−14.3508	−0.745055
$372$	−5.51342	−0.285857
$373$	33.0633	1.71195	0.855977	−	0.517014i	$-0.172956\pi$
$373$	33.0633	1.71195	0.855977	+	0.517014i	$0.172956\pi$
$374$	−0.262709	−0.0135844
$375$	−3.42597	−0.176916
$376$	6.45149	0.332710
$377$	−18.5707	−0.956441
$378$	−51.1351	−2.63011
$379$	8.16532	0.419424	0.209712	−	0.977763i	$-0.432747\pi$
$379$	8.16532	0.419424	0.209712	+	0.977763i	$0.432747\pi$
$380$	−1.75322	−0.0899381
$381$	−14.1524	−0.725047
$382$	−10.5915	−0.541908
$383$	−2.46219	−0.125812	−0.0629060	−	0.998019i	$-0.520037\pi$
$383$	−2.46219	−0.125812	−0.0629060	+	0.998019i	$0.520037\pi$
$384$	3.42597	0.174831
$385$	−2.60155	−0.132587
$386$	9.96641	0.507277
$387$	−8.73725	−0.444139
$388$	2.91128	0.147798
$389$	−26.8598	−1.36184	−0.680922	−	0.732356i	$-0.738421\pi$
$389$	−26.8598	−1.36184	−0.680922	+	0.732356i	$0.738421\pi$
$390$	9.01199	0.456340
$391$	0.165637	0.00837663
$392$	0.231923	0.0117139
$393$	5.07581	0.256041
$394$	−18.8917	−0.951752
$395$	8.43177	0.424248
$396$	8.73725	0.439063
$397$	−7.21074	−0.361897	−0.180948	−	0.983493i	$-0.557917\pi$
$397$	−7.21074	−0.361897	−0.180948	+	0.983493i	$0.557917\pi$
$398$	−12.8676	−0.644992
$399$	−15.6261	−0.782284
$400$	1.00000	0.0500000
$401$	−25.5014	−1.27348	−0.636739	−	0.771079i	$-0.719717\pi$
$401$	−25.5014	−1.27348	−0.636739	+	0.771079i	$0.719717\pi$
$402$	−38.7845	−1.93440
$403$	4.23327	0.210874
$404$	−9.31580	−0.463479
$405$	41.1277	2.04365
$406$	−18.3664	−0.911509
$407$	−2.81938	−0.139752
$408$	0.900033	0.0445583
$409$	−0.882083	−0.0436162	−0.0218081	−	0.999762i	$-0.506942\pi$
$409$	−0.882083	−0.0436162	−0.0218081	+	0.999762i	$0.506942\pi$
$410$	−7.41556	−0.366228
$411$	64.7290	3.19284
$412$	10.5783	0.521155
$413$	−9.30200	−0.457721
$414$	−5.50880	−0.270743
$415$	−3.47644	−0.170652
$416$	−2.63050	−0.128971
$417$	−19.0512	−0.932943
$418$	1.75322	0.0857526
$419$	−18.8117	−0.919011	−0.459506	−	0.888175i	$-0.651973\pi$
$419$	−18.8117	−0.919011	−0.459506	+	0.888175i	$0.651973\pi$
$420$	8.91283	0.434902
$421$	−17.0065	−0.828845	−0.414423	−	0.910085i	$-0.636016\pi$
$421$	−17.0065	−0.828845	−0.414423	+	0.910085i	$0.636016\pi$
$422$	−17.3807	−0.846078
$423$	−56.3683	−2.74072
$424$	−5.51623	−0.267892
$425$	0.262709	0.0127433
$426$	−29.2290	−1.41615
$427$	−0.800002	−0.0387148
$428$	8.04423	0.388833
$429$	−9.01199	−0.435103
$430$	1.00000	0.0482243
$431$	−3.72957	−0.179647	−0.0898236	−	0.995958i	$-0.528630\pi$
$431$	−3.72957	−0.179647	−0.0898236	+	0.995958i	$0.528630\pi$
$432$	−19.6556	−0.945681
$433$	5.87089	0.282137	0.141068	−	0.990000i	$-0.454946\pi$
$433$	5.87089	0.282137	0.141068	+	0.990000i	$0.454946\pi$
$434$	4.18669	0.200967
$435$	24.1866	1.15966
$436$	5.15752	0.247000
$437$	−1.10540	−0.0528783
$438$	7.98619	0.381595
$439$	−15.6016	−0.744622	−0.372311	−	0.928108i	$-0.621435\pi$
$439$	−15.6016	−0.744622	−0.372311	+	0.928108i	$0.621435\pi$
$440$	−1.00000	−0.0476731
$441$	−2.02637	−0.0964938
$442$	−0.691056	−0.0328702
$443$	0.00469293	0.000222968 0	0.000111484	−	1.00000i	$-0.499965\pi$
$443$	0.00469293	0.000222968 0	0.000111484		1.00000i	$0.499965\pi$
$444$	9.65911	0.458401
$445$	12.3225	0.584143
$446$	18.3492	0.868861
$447$	−20.9129	−0.989145
$448$	−2.60155	−0.122912
$449$	29.2505	1.38041	0.690207	−	0.723612i	$-0.257519\pi$
$449$	29.2505	1.38041	0.690207	+	0.723612i	$0.257519\pi$
$450$	−8.73725	−0.411878
$451$	7.41556	0.349185
$452$	−5.91065	−0.278013
$453$	−5.45718	−0.256401
$454$	−1.76490	−0.0828310
$455$	−6.84338	−0.320822
$456$	−6.00646	−0.281278
$457$	−41.1200	−1.92351	−0.961756	−	0.273906i	$-0.911684\pi$
$457$	−41.1200	−1.92351	−0.961756	+	0.273906i	$0.911684\pi$
$458$	20.7806	0.971015
$459$	−5.16371	−0.241021
$460$	0.630496	0.0293970
$461$	15.8505	0.738230	0.369115	−	0.929384i	$-0.379661\pi$
$461$	15.8505	0.738230	0.369115	+	0.929384i	$0.379661\pi$
$462$	−8.91283	−0.414663
$463$	−23.6017	−1.09686	−0.548431	−	0.836196i	$-0.684775\pi$
$463$	−23.6017	−1.09686	−0.548431	+	0.836196i	$0.684775\pi$
$464$	−7.05978	−0.327742
$465$	−5.51342	−0.255679
$466$	−24.2538	−1.12353
$467$	−37.7453	−1.74665	−0.873323	−	0.487141i	$-0.838040\pi$
$467$	−37.7453	−1.74665	−0.873323	+	0.487141i	$0.838040\pi$
$468$	22.9833	1.06240
$469$	29.4515	1.35995
$470$	6.45149	0.297585
$471$	−27.4411	−1.26442
$472$	−3.57556	−0.164578
$473$	−1.00000	−0.0459800
$474$	28.8870	1.32682
$475$	−1.75322	−0.0804430
$476$	−0.683452	−0.0313260
$477$	48.1967	2.20677
$478$	17.6969	0.809436
$479$	9.19349	0.420061	0.210031	−	0.977695i	$-0.432644\pi$
$479$	9.19349	0.420061	0.210031	+	0.977695i	$0.432644\pi$
$480$	3.42597	0.156373
$481$	−7.41638	−0.338158
$482$	16.2567	0.740472
$483$	5.61951	0.255697
$484$	1.00000	0.0454545
$485$	2.91128	0.132195
$486$	81.9354	3.71667
$487$	−16.2777	−0.737614	−0.368807	−	0.929506i	$-0.620234\pi$
$487$	−16.2777	−0.737614	−0.368807	+	0.929506i	$0.620234\pi$
$488$	−0.307509	−0.0139203
$489$	27.2975	1.23444
$490$	0.231923	0.0104772
$491$	6.54296	0.295280	0.147640	−	0.989041i	$-0.452832\pi$
$491$	6.54296	0.295280	0.147640	+	0.989041i	$0.452832\pi$
$492$	−25.4055	−1.14537
$493$	−1.85467	−0.0835301
$494$	4.61183	0.207496
$495$	8.73725	0.392710
$496$	1.60930	0.0722599
$497$	22.1954	0.995600
$498$	−11.9102	−0.533708
$499$	−29.6413	−1.32693	−0.663464	−	0.748208i	$-0.730914\pi$
$499$	−29.6413	−1.32693	−0.663464	+	0.748208i	$0.730914\pi$
$500$	1.00000	0.0447214
$501$	−48.9054	−2.18493
$502$	27.8317	1.24219
$503$	39.6584	1.76828	0.884141	−	0.467220i	$-0.154744\pi$
$503$	39.6584	1.76828	0.884141	+	0.467220i	$0.154744\pi$
$504$	22.7304	1.01249
$505$	−9.31580	−0.414548
$506$	−0.630496	−0.0280290
$507$	20.8315	0.925162
$508$	4.13091	0.183280
$509$	18.8788	0.836789	0.418395	−	0.908265i	$-0.362593\pi$
$509$	18.8788	0.836789	0.418395	+	0.908265i	$0.362593\pi$
$510$	0.900033	0.0398541
$511$	−6.06442	−0.268274
$512$	−1.00000	−0.0441942
$513$	34.4605	1.52147
$514$	−7.49293	−0.330499
$515$	10.5783	0.466135
$516$	3.42597	0.150820
$517$	−6.45149	−0.283736
$518$	−7.33478	−0.322272
$519$	41.9448	1.84117
$520$	−2.63050	−0.115355
$521$	14.8465	0.650436	0.325218	−	0.945639i	$-0.394562\pi$
$521$	14.8465	0.650436	0.325218	+	0.945639i	$0.394562\pi$
$522$	61.6831	2.69979
$523$	20.5890	0.900296	0.450148	−	0.892954i	$-0.351371\pi$
$523$	20.5890	0.900296	0.450148	+	0.892954i	$0.351371\pi$
$524$	−1.48157	−0.0647227
$525$	8.91283	0.388988
$526$	4.27364	0.186339
$527$	0.422779	0.0184165
$528$	−3.42597	−0.149096
$529$	−22.6025	−0.982716
$530$	−5.51623	−0.239610
$531$	31.2405	1.35572
$532$	4.56108	0.197748
$533$	19.5066	0.844925
$534$	42.2165	1.82689
$535$	8.04423	0.347782
$536$	11.3208	0.488982
$537$	−61.2726	−2.64411
$538$	−20.6758	−0.891396
$539$	−0.231923	−0.00998964
$540$	−19.6556	−0.845843
$541$	−21.0104	−0.903308	−0.451654	−	0.892193i	$-0.649166\pi$
$541$	−21.0104	−0.903308	−0.451654	+	0.892193i	$0.649166\pi$
$542$	7.48613	0.321557
$543$	70.3762	3.02013
$544$	−0.262709	−0.0112636
$545$	5.15752	0.220924
$546$	−23.4452	−1.00336
$547$	−30.9758	−1.32443	−0.662215	−	0.749314i	$-0.730383\pi$
$547$	−30.9758	−1.32443	−0.662215	+	0.749314i	$0.730383\pi$
$548$	−18.8936	−0.807096
$549$	2.68679	0.114669
$550$	−1.00000	−0.0426401
$551$	12.3773	0.527292
$552$	2.16006	0.0919382
$553$	−21.9357	−0.932800
$554$	−30.7672	−1.30717
$555$	9.65911	0.410007
$556$	5.56084	0.235832
$557$	−19.3398	−0.819454	−0.409727	−	0.912208i	$-0.634376\pi$
$557$	−19.3398	−0.819454	−0.409727	+	0.912208i	$0.634376\pi$
$558$	−14.0609	−0.595244
$559$	−2.63050	−0.111258
$560$	−2.60155	−0.109936
$561$	−0.900033	−0.0379994
$562$	1.75846	0.0741759
$563$	12.0905	0.509552	0.254776	−	0.967000i	$-0.417998\pi$
$563$	12.0905	0.509552	0.254776	+	0.967000i	$0.417998\pi$
$564$	22.1026	0.930687
$565$	−5.91065	−0.248663
$566$	1.50016	0.0630562
$567$	−106.996	−4.49341
$568$	8.53160	0.357978
$569$	−25.9199	−1.08662	−0.543309	−	0.839533i	$-0.682829\pi$
$569$	−25.9199	−1.08662	−0.543309	+	0.839533i	$0.682829\pi$
$570$	−6.00646	−0.251583
$571$	−18.8605	−0.789288	−0.394644	−	0.918834i	$-0.629132\pi$
$571$	−18.8605	−0.789288	−0.394644	+	0.918834i	$0.629132\pi$
$572$	2.63050	0.109987
$573$	−36.2861	−1.51587
$574$	19.2920	0.805231
$575$	0.630496	0.0262935
$576$	8.73725	0.364052
$577$	24.4338	1.01719	0.508596	−	0.861005i	$-0.330165\pi$
$577$	24.4338	1.01719	0.508596	+	0.861005i	$0.330165\pi$
$578$	16.9310	0.704236
$579$	34.1446	1.41900
$580$	−7.05978	−0.293141
$581$	9.04415	0.375215
$582$	9.97396	0.413434
$583$	5.51623	0.228459
$584$	−2.33108	−0.0964607
$585$	22.9833	0.950242
$586$	26.9183	1.11198
$587$	9.91838	0.409375	0.204688	−	0.978827i	$-0.434382\pi$
$587$	9.91838	0.409375	0.204688	+	0.978827i	$0.434382\pi$
$588$	0.794561	0.0327671
$589$	−2.82146	−0.116256
$590$	−3.57556	−0.147203
$591$	−64.7225	−2.66233
$592$	−2.81938	−0.115876
$593$	9.01278	0.370110	0.185055	−	0.982728i	$-0.440754\pi$
$593$	9.01278	0.370110	0.185055	+	0.982728i	$0.440754\pi$
$594$	19.6556	0.806480
$595$	−0.683452	−0.0280188
$596$	6.10422	0.250039
$597$	−44.0838	−1.80423
$598$	−1.65852	−0.0678219
$599$	−3.31911	−0.135615	−0.0678075	−	0.997698i	$-0.521600\pi$
$599$	−3.31911	−0.135615	−0.0678075	+	0.997698i	$0.521600\pi$
$600$	3.42597	0.139864
$601$	−35.3688	−1.44273	−0.721363	−	0.692558i	$-0.756484\pi$
$601$	−35.3688	−1.44273	−0.721363	+	0.692558i	$0.756484\pi$
$602$	−2.60155	−0.106031
$603$	−98.9122	−4.02802
$604$	1.59289	0.0648137
$605$	1.00000	0.0406558
$606$	−31.9156	−1.29648
$607$	41.8684	1.69939	0.849693	−	0.527278i	$-0.176787\pi$
$607$	41.8684	1.69939	0.849693	+	0.527278i	$0.176787\pi$
$608$	1.75322	0.0711023
$609$	−62.9227	−2.54975
$610$	−0.307509	−0.0124507
$611$	−16.9706	−0.686558
$612$	2.29536	0.0927842
$613$	−3.08004	−0.124402	−0.0622008	−	0.998064i	$-0.519812\pi$
$613$	−3.08004	−0.124402	−0.0622008	+	0.998064i	$0.519812\pi$
$614$	25.7312	1.03843
$615$	−25.4055	−1.02445
$616$	2.60155	0.104820
$617$	30.6236	1.23286	0.616430	−	0.787409i	$-0.288578\pi$
$617$	30.6236	1.23286	0.616430	+	0.787409i	$0.288578\pi$
$618$	36.2408	1.45782
$619$	29.1530	1.17176	0.585879	−	0.810398i	$-0.300749\pi$
$619$	29.1530	1.17176	0.585879	+	0.810398i	$0.300749\pi$
$620$	1.60930	0.0646312
$621$	−12.3928	−0.497306
$622$	16.9993	0.681611
$623$	−32.0577	−1.28436
$624$	−9.01199	−0.360768
$625$	1.00000	0.0400000
$626$	−22.1108	−0.883724
$627$	6.00646	0.239875
$628$	8.00975	0.319624
$629$	−0.740678	−0.0295328
$630$	22.7304	0.905601
$631$	−10.0123	−0.398582	−0.199291	−	0.979940i	$-0.563864\pi$
$631$	−10.0123	−0.398582	−0.199291	+	0.979940i	$0.563864\pi$
$632$	−8.43177	−0.335398
$633$	−59.5456	−2.36673
$634$	27.2666	1.08290
$635$	4.13091	0.163930
$636$	−18.8984	−0.749372
$637$	−0.610073	−0.0241720
$638$	7.05978	0.279499
$639$	−74.5427	−2.94886
$640$	−1.00000	−0.0395285
$641$	−47.4850	−1.87554	−0.937772	−	0.347252i	$-0.887115\pi$
$641$	−47.4850	−1.87554	−0.937772	+	0.347252i	$0.887115\pi$
$642$	27.5593	1.08768
$643$	31.6078	1.24649	0.623244	−	0.782027i	$-0.285814\pi$
$643$	31.6078	1.24649	0.623244	+	0.782027i	$0.285814\pi$
$644$	−1.64027	−0.0646357
$645$	3.42597	0.134897
$646$	0.460586	0.0181215
$647$	26.1655	1.02867	0.514337	−	0.857588i	$-0.328038\pi$
$647$	26.1655	1.02867	0.514337	+	0.857588i	$0.328038\pi$
$648$	−41.1277	−1.61565
$649$	3.57556	0.140353
$650$	−2.63050	−0.103177
$651$	14.3435	0.562164
$652$	−7.96784	−0.312045
$653$	−26.7725	−1.04769	−0.523845	−	0.851814i	$-0.675503\pi$
$653$	−26.7725	−1.04769	−0.523845	+	0.851814i	$0.675503\pi$
$654$	17.6695	0.690932
$655$	−1.48157	−0.0578897
$656$	7.41556	0.289529
$657$	20.3672	0.794600
$658$	−16.7839	−0.654304
$659$	−10.4395	−0.406665	−0.203332	−	0.979110i	$-0.565177\pi$
$659$	−10.4395	−0.406665	−0.203332	+	0.979110i	$0.565177\pi$
$660$	−3.42597	−0.133356
$661$	−3.68016	−0.143142	−0.0715709	−	0.997436i	$-0.522801\pi$
$661$	−3.68016	−0.143142	−0.0715709	+	0.997436i	$0.522801\pi$
$662$	16.0290	0.622984
$663$	−2.36753	−0.0919474
$664$	3.47644	0.134912
$665$	4.56108	0.176871
$666$	24.6336	0.954535
$667$	−4.45117	−0.172350
$668$	14.2749	0.552313
$669$	62.8639	2.43046
$670$	11.3208	0.437359
$671$	0.307509	0.0118713
$672$	−8.91283	−0.343820
$673$	−19.4871	−0.751172	−0.375586	−	0.926788i	$-0.622559\pi$
$673$	−19.4871	−0.751172	−0.375586	+	0.926788i	$0.622559\pi$
$674$	3.46767	0.133570
$675$	−19.6556	−0.756545
$676$	−6.08049	−0.233865
$677$	−36.2262	−1.39228	−0.696142	−	0.717904i	$-0.745102\pi$
$677$	−36.2262	−1.39228	−0.696142	+	0.717904i	$0.745102\pi$
$678$	−20.2497	−0.777684
$679$	−7.57385	−0.290658
$680$	−0.262709	−0.0100744
$681$	−6.04650	−0.231702
$682$	−1.60930	−0.0616234
$683$	−4.65456	−0.178102	−0.0890509	−	0.996027i	$-0.528383\pi$
$683$	−4.65456	−0.178102	−0.0890509	+	0.996027i	$0.528383\pi$
$684$	−15.3183	−0.585709
$685$	−18.8936	−0.721889
$686$	−18.8142	−0.718331
$687$	71.1937	2.71621
$688$	−1.00000	−0.0381246
$689$	14.5104	0.552803
$690$	2.16006	0.0822321
$691$	−36.1902	−1.37674	−0.688370	−	0.725359i	$-0.741674\pi$
$691$	−36.1902	−1.37674	−0.688370	+	0.725359i	$0.741674\pi$
$692$	−12.2432	−0.465417
$693$	−22.7304	−0.863457
$694$	−15.4864	−0.587856
$695$	5.56084	0.210935
$696$	−24.1866	−0.916790
$697$	1.94814	0.0737909
$698$	5.80758	0.219820
$699$	−83.0926	−3.14285
$700$	−2.60155	−0.0983295
$701$	21.8522	0.825347	0.412673	−	0.910879i	$-0.364595\pi$
$701$	21.8522	0.825347	0.412673	+	0.910879i	$0.364595\pi$
$702$	51.7040	1.95144
$703$	4.94299	0.186428
$704$	1.00000	0.0376889
$705$	22.1026	0.832432
$706$	−6.00116	−0.225856
$707$	24.2356	0.911472
$708$	−12.2497	−0.460373
$709$	−35.3729	−1.32846	−0.664229	−	0.747529i	$-0.731240\pi$
$709$	−35.3729	−1.32846	−0.664229	+	0.747529i	$0.731240\pi$
$710$	8.53160	0.320185
$711$	73.6704	2.76286
$712$	−12.3225	−0.461806
$713$	1.01466	0.0379993
$714$	−2.34148	−0.0876278
$715$	2.63050	0.0983750
$716$	17.8848	0.668385
$717$	60.6289	2.26423
$718$	24.9377	0.930667
$719$	41.3803	1.54322	0.771612	−	0.636093i	$-0.219451\pi$
$719$	41.3803	1.54322	0.771612	+	0.636093i	$0.219451\pi$
$720$	8.73725	0.325618
$721$	−27.5200	−1.02490
$722$	15.9262	0.592713
$723$	55.6948	2.07131
$724$	−20.5420	−0.763437
$725$	−7.05978	−0.262194
$726$	3.42597	0.127150
$727$	−4.34622	−0.161192	−0.0805961	−	0.996747i	$-0.525682\pi$
$727$	−4.34622	−0.161192	−0.0805961	+	0.996747i	$0.525682\pi$
$728$	6.84338	0.253632
$729$	157.325	5.82684
$730$	−2.33108	−0.0862770
$731$	−0.262709	−0.00971665
$732$	−1.05352	−0.0389391
$733$	−13.6919	−0.505721	−0.252861	−	0.967503i	$-0.581371\pi$
$733$	−13.6919	−0.505721	−0.252861	+	0.967503i	$0.581371\pi$
$734$	26.8270	0.990204
$735$	0.794561	0.0293078
$736$	−0.630496	−0.0232404
$737$	−11.3208	−0.417005
$738$	−64.7916	−2.38501
$739$	−46.1049	−1.69599	−0.847997	−	0.530000i	$-0.822192\pi$
$739$	−46.1049	−1.69599	−0.847997	+	0.530000i	$0.822192\pi$
$740$	−2.81938	−0.103643
$741$	15.8000	0.580426
$742$	14.3508	0.526833
$743$	33.7066	1.23657	0.618287	−	0.785952i	$-0.287827\pi$
$743$	33.7066	1.23657	0.618287	+	0.785952i	$0.287827\pi$
$744$	5.51342	0.202132
$745$	6.10422	0.223641
$746$	−33.0633	−1.21053
$747$	−30.3745	−1.11135
$748$	0.262709	0.00960560
$749$	−20.9275	−0.764674
$750$	3.42597	0.125099
$751$	3.59309	0.131114	0.0655569	−	0.997849i	$-0.479118\pi$
$751$	3.59309	0.131114	0.0655569	+	0.997849i	$0.479118\pi$
$752$	−6.45149	−0.235262
$753$	95.3504	3.47476
$754$	18.5707	0.676306
$755$	1.59289	0.0579711
$756$	51.1351	1.85977
$757$	−14.4258	−0.524315	−0.262158	−	0.965025i	$-0.584434\pi$
$757$	−14.4258	−0.524315	−0.262158	+	0.965025i	$0.584434\pi$
$758$	−8.16532	−0.296578
$759$	−2.16006	−0.0784052
$760$	1.75322	0.0635958
$761$	−15.6993	−0.569099	−0.284550	−	0.958661i	$-0.591844\pi$
$761$	−15.6993	−0.569099	−0.284550	+	0.958661i	$0.591844\pi$
$762$	14.1524	0.512686
$763$	−13.4176	−0.485748
$764$	10.5915	0.383187
$765$	2.29536	0.0829887
$766$	2.46219	0.0889625
$767$	9.40549	0.339612
$768$	−3.42597	−0.123624
$769$	1.48584	0.0535807	0.0267904	−	0.999641i	$-0.491471\pi$
$769$	1.48584	0.0535807	0.0267904	+	0.999641i	$0.491471\pi$
$770$	2.60155	0.0937535
$771$	−25.6705	−0.924501
$772$	−9.96641	−0.358699
$773$	31.0060	1.11521	0.557604	−	0.830107i	$-0.311721\pi$
$773$	31.0060	1.11521	0.557604	+	0.830107i	$0.311721\pi$
$774$	8.73725	0.314054
$775$	1.60930	0.0578079
$776$	−2.91128	−0.104509
$777$	−25.1287	−0.901487
$778$	26.8598	0.962969
$779$	−13.0011	−0.465812
$780$	−9.01199	−0.322681
$781$	−8.53160	−0.305285
$782$	−0.165637	−0.00592317
$783$	138.764	4.95903
$784$	−0.231923	−0.00828297
$785$	8.00975	0.285880
$786$	−5.07581	−0.181048
$787$	−44.3733	−1.58174	−0.790869	−	0.611985i	$-0.790371\pi$
$787$	−44.3733	−1.58174	−0.790869	+	0.611985i	$0.790371\pi$
$788$	18.8917	0.672990
$789$	14.6413	0.521246
$790$	−8.43177	−0.299989
$791$	15.3769	0.546738
$792$	−8.73725	−0.310465
$793$	0.808902	0.0287250
$794$	7.21074	0.255900
$795$	−18.8984	−0.670258
$796$	12.8676	0.456078
$797$	50.4392	1.78665	0.893323	−	0.449415i	$-0.148367\pi$
$797$	50.4392	1.78665	0.893323	+	0.449415i	$0.148367\pi$
$798$	15.6261	0.553159
$799$	−1.69487	−0.0599600
$800$	−1.00000	−0.0353553
$801$	107.665	3.80415
$802$	25.5014	0.900485
$803$	2.33108	0.0822619
$804$	38.7845	1.36782
$805$	−1.64027	−0.0578119
$806$	−4.23327	−0.149110
$807$	−70.8345	−2.49349
$808$	9.31580	0.327729
$809$	14.7746	0.519448	0.259724	−	0.965683i	$-0.416368\pi$
$809$	14.7746	0.519448	0.259724	+	0.965683i	$0.416368\pi$
$810$	−41.1277	−1.44508
$811$	49.1839	1.72708	0.863540	−	0.504281i	$-0.168242\pi$
$811$	49.1839	1.72708	0.863540	+	0.504281i	$0.168242\pi$
$812$	18.3664	0.644534
$813$	25.6472	0.899488
$814$	2.81938	0.0988193
$815$	−7.96784	−0.279101
$816$	−0.900033	−0.0315075
$817$	1.75322	0.0613373
$818$	0.882083	0.0308413
$819$	−59.7923	−2.08931
$820$	7.41556	0.258963
$821$	−26.3073	−0.918131	−0.459065	−	0.888402i	$-0.651816\pi$
$821$	−26.3073	−0.918131	−0.459065	+	0.888402i	$0.651816\pi$
$822$	−64.7290	−2.25768
$823$	37.2009	1.29674	0.648372	−	0.761324i	$-0.275450\pi$
$823$	37.2009	1.29674	0.648372	+	0.761324i	$0.275450\pi$
$824$	−10.5783	−0.368512
$825$	−3.42597	−0.119277
$826$	9.30200	0.323658
$827$	12.3937	0.430972	0.215486	−	0.976507i	$-0.430866\pi$
$827$	12.3937	0.430972	0.215486	+	0.976507i	$0.430866\pi$
$828$	5.50880	0.191444
$829$	13.2526	0.460281	0.230141	−	0.973157i	$-0.426081\pi$
$829$	13.2526	0.460281	0.230141	+	0.973157i	$0.426081\pi$
$830$	3.47644	0.120669
$831$	−105.407	−3.65655
$832$	2.63050	0.0911961
$833$	−0.0609283	−0.00211104
$834$	19.0512	0.659690
$835$	14.2749	0.494004
$836$	−1.75322	−0.0606362
$837$	−31.6318	−1.09336
$838$	18.8117	0.649839
$839$	20.5811	0.710540	0.355270	−	0.934764i	$-0.384389\pi$
$839$	20.5811	0.710540	0.355270	+	0.934764i	$0.384389\pi$
$840$	−8.91283	−0.307522
$841$	20.8405	0.718639
$842$	17.0065	0.586082
$843$	6.02441	0.207492
$844$	17.3807	0.598268
$845$	−6.08049	−0.209175
$846$	56.3683	1.93798
$847$	−2.60155	−0.0893904
$848$	5.51623	0.189428
$849$	5.13948	0.176387
$850$	−0.262709	−0.00901085
$851$	−1.77761	−0.0609357
$852$	29.2290	1.00137
$853$	26.8122	0.918031	0.459016	−	0.888428i	$-0.348202\pi$
$853$	26.8122	0.918031	0.459016	+	0.888428i	$0.348202\pi$
$854$	0.800002	0.0273755
$855$	−15.3183	−0.523874
$856$	−8.04423	−0.274946
$857$	51.7683	1.76837	0.884186	−	0.467134i	$-0.154713\pi$
$857$	51.7683	1.76837	0.884186	+	0.467134i	$0.154713\pi$
$858$	9.01199	0.307664
$859$	−19.5793	−0.668037	−0.334018	−	0.942567i	$-0.608405\pi$
$859$	−19.5793	−0.668037	−0.334018	+	0.942567i	$0.608405\pi$
$860$	−1.00000	−0.0340997
$861$	66.0937	2.25247
$862$	3.72957	0.127030
$863$	−27.5046	−0.936268	−0.468134	−	0.883658i	$-0.655074\pi$
$863$	−27.5046	−0.936268	−0.468134	+	0.883658i	$0.655074\pi$
$864$	19.6556	0.668698
$865$	−12.2432	−0.416282
$866$	−5.87089	−0.199501
$867$	58.0050	1.96995
$868$	−4.18669	−0.142105
$869$	8.43177	0.286028
$870$	−24.1866	−0.820002
$871$	−29.7792	−1.00903
$872$	−5.15752	−0.174656
$873$	25.4366	0.860898
$874$	1.10540	0.0373906
$875$	−2.60155	−0.0879485
$876$	−7.98619	−0.269828
$877$	−7.96528	−0.268968	−0.134484	−	0.990916i	$-0.542938\pi$
$877$	−7.96528	−0.268968	−0.134484	+	0.990916i	$0.542938\pi$
$878$	15.6016	0.526527
$879$	92.2211	3.11054
$880$	1.00000	0.0337100
$881$	16.2007	0.545815	0.272908	−	0.962040i	$-0.412015\pi$
$881$	16.2007	0.545815	0.272908	+	0.962040i	$0.412015\pi$
$882$	2.02637	0.0682314
$883$	−25.6440	−0.862989	−0.431495	−	0.902116i	$-0.642014\pi$
$883$	−25.6440	−0.862989	−0.431495	+	0.902116i	$0.642014\pi$
$884$	0.691056	0.0232427
$885$	−12.2497	−0.411770
$886$	−0.00469293	−0.000157662 0
$887$	6.91950	0.232334	0.116167	−	0.993230i	$-0.462939\pi$
$887$	6.91950	0.232334	0.116167	+	0.993230i	$0.462939\pi$
$888$	−9.65911	−0.324139
$889$	−10.7468	−0.360436
$890$	−12.3225	−0.413052
$891$	41.1277	1.37783
$892$	−18.3492	−0.614378
$893$	11.3109	0.378503
$894$	20.9129	0.699431
$895$	17.8848	0.597822
$896$	2.60155	0.0869118
$897$	−5.68203	−0.189717
$898$	−29.2505	−0.976101
$899$	−11.3613	−0.378922
$900$	8.73725	0.291242
$901$	1.44917	0.0482787
$902$	−7.41556	−0.246911
$903$	−8.91283	−0.296600
$904$	5.91065	0.196585
$905$	−20.5420	−0.682839
$906$	5.45718	0.181303
$907$	−36.7454	−1.22011	−0.610055	−	0.792359i	$-0.708853\pi$
$907$	−36.7454	−1.22011	−0.610055	+	0.792359i	$0.708853\pi$
$908$	1.76490	0.0585703
$909$	−81.3945	−2.69968
$910$	6.84338	0.226856
$911$	25.8537	0.856572	0.428286	−	0.903643i	$-0.359118\pi$
$911$	25.8537	0.856572	0.428286	+	0.903643i	$0.359118\pi$
$912$	6.00646	0.198894
$913$	−3.47644	−0.115053
$914$	41.1200	1.36013
$915$	−1.05352	−0.0348282
$916$	−20.7806	−0.686611
$917$	3.85438	0.127283
$918$	5.16371	0.170428
$919$	30.4793	1.00542	0.502710	−	0.864455i	$-0.332336\pi$
$919$	30.4793	1.00542	0.502710	+	0.864455i	$0.332336\pi$
$920$	−0.630496	−0.0207869
$921$	88.1542	2.90478
$922$	−15.8505	−0.522008
$923$	−22.4424	−0.738699
$924$	8.91283	0.293211
$925$	−2.81938	−0.0927008
$926$	23.6017	0.775599
$927$	92.4251	3.03564
$928$	7.05978	0.231749
$929$	23.7290	0.778525	0.389262	−	0.921127i	$-0.372730\pi$
$929$	23.7290	0.778525	0.389262	+	0.921127i	$0.372730\pi$
$930$	5.51342	0.180792
$931$	0.406611	0.0133261
$932$	24.2538	0.794459
$933$	58.2392	1.90666
$934$	37.7453	1.23507
$935$	0.262709	0.00859151
$936$	−22.9833	−0.751233
$937$	−38.2333	−1.24903	−0.624513	−	0.781014i	$-0.714703\pi$
$937$	−38.2333	−1.24903	−0.624513	+	0.781014i	$0.714703\pi$
$938$	−29.4515	−0.961627
$939$	−75.7508	−2.47203
$940$	−6.45149	−0.210424
$941$	−28.8559	−0.940674	−0.470337	−	0.882487i	$-0.655868\pi$
$941$	−28.8559	−0.940674	−0.470337	+	0.882487i	$0.655868\pi$
$942$	27.4411	0.894080
$943$	4.67548	0.152255
$944$	3.57556	0.116374
$945$	51.1351	1.66343
$946$	1.00000	0.0325128
$947$	−38.5597	−1.25302	−0.626511	−	0.779412i	$-0.715518\pi$
$947$	−38.5597	−1.25302	−0.626511	+	0.779412i	$0.715518\pi$
$948$	−28.8870	−0.938205
$949$	6.13189	0.199050
$950$	1.75322	0.0568818
$951$	93.4146	3.02918
$952$	0.683452	0.0221508
$953$	−11.9404	−0.386786	−0.193393	−	0.981121i	$-0.561949\pi$
$953$	−11.9404	−0.386786	−0.193393	+	0.981121i	$0.561949\pi$
$954$	−48.1967	−1.56043
$955$	10.5915	0.342733
$956$	−17.6969	−0.572358
$957$	24.1866	0.781841
$958$	−9.19349	−0.297028
$959$	49.1528	1.58723
$960$	−3.42597	−0.110573
$961$	−28.4101	−0.916456
$962$	7.41638	0.239114
$963$	70.2844	2.26488
$964$	−16.2567	−0.523592
$965$	−9.96641	−0.320830
$966$	−5.61951	−0.180805
$967$	19.8270	0.637594	0.318797	−	0.947823i	$-0.396721\pi$
$967$	19.8270	0.637594	0.318797	+	0.947823i	$0.396721\pi$
$968$	−1.00000	−0.0321412
$969$	1.57795	0.0506911
$970$	−2.91128	−0.0934756
$971$	−2.85867	−0.0917390	−0.0458695	−	0.998947i	$-0.514606\pi$
$971$	−2.85867	−0.0917390	−0.0458695	+	0.998947i	$0.514606\pi$
$972$	−81.9354	−2.62808
$973$	−14.4668	−0.463785
$974$	16.2777	0.521572
$975$	−9.01199	−0.288615
$976$	0.307509	0.00984314
$977$	23.0249	0.736633	0.368316	−	0.929701i	$-0.379934\pi$
$977$	23.0249	0.736633	0.368316	+	0.929701i	$0.379934\pi$
$978$	−27.2975	−0.872879
$979$	12.3225	0.393829
$980$	−0.231923	−0.00740851
$981$	45.0625	1.43874
$982$	−6.54296	−0.208794
$983$	55.4165	1.76751	0.883756	−	0.467948i	$-0.155007\pi$
$983$	55.4165	1.76751	0.883756	+	0.467948i	$0.155007\pi$
$984$	25.4055	0.809897
$985$	18.8917	0.601941
$986$	1.85467	0.0590647
$987$	−57.5011	−1.83028
$988$	−4.61183	−0.146722
$989$	−0.630496	−0.0200486
$990$	−8.73725	−0.277688
$991$	−10.0225	−0.318375	−0.159188	−	0.987248i	$-0.550887\pi$
$991$	−10.0225	−0.318375	−0.159188	+	0.987248i	$0.550887\pi$
$992$	−1.60930	−0.0510954
$993$	54.9148	1.74267
$994$	−22.1954	−0.703996
$995$	12.8676	0.407929
$996$	11.9102	0.377388
$997$	4.94228	0.156523	0.0782617	−	0.996933i	$-0.475063\pi$
$997$	4.94228	0.156523	0.0782617	+	0.996933i	$0.475063\pi$
$998$	29.6413	0.938279
$999$	55.4167	1.75331

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.w.1.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.w.1.1	✓	8	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:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.42597 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.42597 q^{6} -2.60155 q^{7} -1.00000 q^{8} +8.73725 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.42597 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.42597 q^{6} -2.60155 q^{7} -1.00000 q^{8} +8.73725 q^{9} -1.00000 q^{10} +1.00000 q^{11} -3.42597 q^{12} +2.63050 q^{13} +2.60155 q^{14} -3.42597 q^{15} +1.00000 q^{16} +0.262709 q^{17} -8.73725 q^{18} -1.75322 q^{19} +1.00000 q^{20} +8.91283 q^{21} -1.00000 q^{22} +0.630496 q^{23} +3.42597 q^{24} +1.00000 q^{25} -2.63050 q^{26} -19.6556 q^{27} -2.60155 q^{28} -7.05978 q^{29} +3.42597 q^{30} +1.60930 q^{31} -1.00000 q^{32} -3.42597 q^{33} -0.262709 q^{34} -2.60155 q^{35} +8.73725 q^{36} -2.81938 q^{37} +1.75322 q^{38} -9.01199 q^{39} -1.00000 q^{40} +7.41556 q^{41} -8.91283 q^{42} -1.00000 q^{43} +1.00000 q^{44} +8.73725 q^{45} -0.630496 q^{46} -6.45149 q^{47} -3.42597 q^{48} -0.231923 q^{49} -1.00000 q^{50} -0.900033 q^{51} +2.63050 q^{52} +5.51623 q^{53} +19.6556 q^{54} +1.00000 q^{55} +2.60155 q^{56} +6.00646 q^{57} +7.05978 q^{58} +3.57556 q^{59} -3.42597 q^{60} +0.307509 q^{61} -1.60930 q^{62} -22.7304 q^{63} +1.00000 q^{64} +2.63050 q^{65} +3.42597 q^{66} -11.3208 q^{67} +0.262709 q^{68} -2.16006 q^{69} +2.60155 q^{70} -8.53160 q^{71} -8.73725 q^{72} +2.33108 q^{73} +2.81938 q^{74} -3.42597 q^{75} -1.75322 q^{76} -2.60155 q^{77} +9.01199 q^{78} +8.43177 q^{79} +1.00000 q^{80} +41.1277 q^{81} -7.41556 q^{82} -3.47644 q^{83} +8.91283 q^{84} +0.262709 q^{85} +1.00000 q^{86} +24.1866 q^{87} -1.00000 q^{88} +12.3225 q^{89} -8.73725 q^{90} -6.84338 q^{91} +0.630496 q^{92} -5.51342 q^{93} +6.45149 q^{94} -1.75322 q^{95} +3.42597 q^{96} +2.91128 q^{97} +0.231923 q^{98} +8.73725 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 7 q^{3} + 8 q^{4} + 8 q^{5} + 7 q^{6} - 6 q^{7} - 8 q^{8} + 7 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 7 * q^3 + 8 * q^4 + 8 * q^5 + 7 * q^6 - 6 * q^7 - 8 * q^8 + 7 * q^9	\( 8 q - 8 q^{2} - 7 q^{3} + 8 q^{4} + 8 q^{5} + 7 q^{6} - 6 q^{7} - 8 q^{8} + 7 q^{9} - 8 q^{10} + 8 q^{11} - 7 q^{12} - 2 q^{13} + 6 q^{14} - 7 q^{15} + 8 q^{16} - 8 q^{17} - 7 q^{18} + 8 q^{20} + 14 q^{21} - 8 q^{22} - 18 q^{23} + 7 q^{24} + 8 q^{25} + 2 q^{26} - 22 q^{27} - 6 q^{28} + 8 q^{29} + 7 q^{30} - 11 q^{31} - 8 q^{32} - 7 q^{33} + 8 q^{34} - 6 q^{35} + 7 q^{36} - 17 q^{37} - 6 q^{39} - 8 q^{40} + 12 q^{41} - 14 q^{42} - 8 q^{43} + 8 q^{44} + 7 q^{45} + 18 q^{46} - 19 q^{47} - 7 q^{48} - 2 q^{49} - 8 q^{50} - q^{51} - 2 q^{52} - 7 q^{53} + 22 q^{54} + 8 q^{55} + 6 q^{56} - 3 q^{57} - 8 q^{58} + q^{59} - 7 q^{60} + 6 q^{61} + 11 q^{62} - 15 q^{63} + 8 q^{64} - 2 q^{65} + 7 q^{66} - 22 q^{67} - 8 q^{68} + 8 q^{69} + 6 q^{70} - 14 q^{71} - 7 q^{72} - 13 q^{73} + 17 q^{74} - 7 q^{75} - 6 q^{77} + 6 q^{78} - 8 q^{79} + 8 q^{80} + 28 q^{81} - 12 q^{82} - 4 q^{83} + 14 q^{84} - 8 q^{85} + 8 q^{86} - 30 q^{87} - 8 q^{88} + 5 q^{89} - 7 q^{90} - 8 q^{91} - 18 q^{92} + q^{93} + 19 q^{94} + 7 q^{96} - 23 q^{97} + 2 q^{98} + 7 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 7 * q^3 + 8 * q^4 + 8 * q^5 + 7 * q^6 - 6 * q^7 - 8 * q^8 + 7 * q^9 - 8 * q^10 + 8 * q^11 - 7 * q^12 - 2 * q^13 + 6 * q^14 - 7 * q^15 + 8 * q^16 - 8 * q^17 - 7 * q^18 + 8 * q^20 + 14 * q^21 - 8 * q^22 - 18 * q^23 + 7 * q^24 + 8 * q^25 + 2 * q^26 - 22 * q^27 - 6 * q^28 + 8 * q^29 + 7 * q^30 - 11 * q^31 - 8 * q^32 - 7 * q^33 + 8 * q^34 - 6 * q^35 + 7 * q^36 - 17 * q^37 - 6 * q^39 - 8 * q^40 + 12 * q^41 - 14 * q^42 - 8 * q^43 + 8 * q^44 + 7 * q^45 + 18 * q^46 - 19 * q^47 - 7 * q^48 - 2 * q^49 - 8 * q^50 - q^51 - 2 * q^52 - 7 * q^53 + 22 * q^54 + 8 * q^55 + 6 * q^56 - 3 * q^57 - 8 * q^58 + q^59 - 7 * q^60 + 6 * q^61 + 11 * q^62 - 15 * q^63 + 8 * q^64 - 2 * q^65 + 7 * q^66 - 22 * q^67 - 8 * q^68 + 8 * q^69 + 6 * q^70 - 14 * q^71 - 7 * q^72 - 13 * q^73 + 17 * q^74 - 7 * q^75 - 6 * q^77 + 6 * q^78 - 8 * q^79 + 8 * q^80 + 28 * q^81 - 12 * q^82 - 4 * q^83 + 14 * q^84 - 8 * q^85 + 8 * q^86 - 30 * q^87 - 8 * q^88 + 5 * q^89 - 7 * q^90 - 8 * q^91 - 18 * q^92 + q^93 + 19 * q^94 + 7 * q^96 - 23 * q^97 + 2 * q^98 + 7 * q^99

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