LMFDB - Embedded newform 4334.2.a.g.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.16110 q^{3} +1.00000 q^{4} +3.79456 q^{5} +2.16110 q^{6} +0.294155 q^{7} +1.00000 q^{8} +1.67035 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.16110 q^{3} +1.00000 q^{4} +3.79456 q^{5} +2.16110 q^{6} +0.294155 q^{7} +1.00000 q^{8} +1.67035 q^{9} +3.79456 q^{10} +1.00000 q^{11} +2.16110 q^{12} -1.43731 q^{13} +0.294155 q^{14} +8.20043 q^{15} +1.00000 q^{16} -1.19277 q^{17} +1.67035 q^{18} +0.519285 q^{19} +3.79456 q^{20} +0.635699 q^{21} +1.00000 q^{22} -7.98409 q^{23} +2.16110 q^{24} +9.39871 q^{25} -1.43731 q^{26} -2.87351 q^{27} +0.294155 q^{28} -1.79711 q^{29} +8.20043 q^{30} +9.08140 q^{31} +1.00000 q^{32} +2.16110 q^{33} -1.19277 q^{34} +1.11619 q^{35} +1.67035 q^{36} +10.0003 q^{37} +0.519285 q^{38} -3.10617 q^{39} +3.79456 q^{40} +5.76041 q^{41} +0.635699 q^{42} -2.42936 q^{43} +1.00000 q^{44} +6.33824 q^{45} -7.98409 q^{46} -1.81074 q^{47} +2.16110 q^{48} -6.91347 q^{49} +9.39871 q^{50} -2.57770 q^{51} -1.43731 q^{52} -7.03176 q^{53} -2.87351 q^{54} +3.79456 q^{55} +0.294155 q^{56} +1.12223 q^{57} -1.79711 q^{58} +7.73641 q^{59} +8.20043 q^{60} +1.99335 q^{61} +9.08140 q^{62} +0.491341 q^{63} +1.00000 q^{64} -5.45397 q^{65} +2.16110 q^{66} +8.39494 q^{67} -1.19277 q^{68} -17.2544 q^{69} +1.11619 q^{70} -4.27485 q^{71} +1.67035 q^{72} +9.73412 q^{73} +10.0003 q^{74} +20.3115 q^{75} +0.519285 q^{76} +0.294155 q^{77} -3.10617 q^{78} +9.25019 q^{79} +3.79456 q^{80} -11.2210 q^{81} +5.76041 q^{82} -2.83280 q^{83} +0.635699 q^{84} -4.52606 q^{85} -2.42936 q^{86} -3.88373 q^{87} +1.00000 q^{88} -12.5084 q^{89} +6.33824 q^{90} -0.422793 q^{91} -7.98409 q^{92} +19.6258 q^{93} -1.81074 q^{94} +1.97046 q^{95} +2.16110 q^{96} -5.56390 q^{97} -6.91347 q^{98} +1.67035 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9}+O(q^{10}) $ 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9} + 13 q^{10} + 26 q^{11} + 12 q^{12} + 24 q^{13} + 13 q^{14} + 12 q^{15} + 26 q^{16} + q^{17} + 38 q^{18} + 24 q^{19} + 13 q^{20} + 5 q^{21} + 26 q^{22} + 19 q^{23} + 12 q^{24} + 35 q^{25} + 24 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 12 q^{30} + 34 q^{31} + 26 q^{32} + 12 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} + 15 q^{37} + 24 q^{38} + 3 q^{39} + 13 q^{40} - 9 q^{41} + 5 q^{42} + 6 q^{43} + 26 q^{44} + 22 q^{45} + 19 q^{46} + 34 q^{47} + 12 q^{48} + 53 q^{49} + 35 q^{50} - 2 q^{51} + 24 q^{52} + 6 q^{53} + 39 q^{54} + 13 q^{55} + 13 q^{56} - 16 q^{57} + 5 q^{58} + 50 q^{59} + 12 q^{60} + 26 q^{61} + 34 q^{62} + 2 q^{63} + 26 q^{64} - 5 q^{65} + 12 q^{66} + 18 q^{67} + q^{68} + 15 q^{69} + 14 q^{70} + 23 q^{71} + 38 q^{72} + 37 q^{73} + 15 q^{74} + 18 q^{75} + 24 q^{76} + 13 q^{77} + 3 q^{78} + 10 q^{79} + 13 q^{80} + 50 q^{81} - 9 q^{82} + 7 q^{83} + 5 q^{84} - 7 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{88} + 3 q^{89} + 22 q^{90} + 31 q^{91} + 19 q^{92} + 52 q^{93} + 34 q^{94} + 9 q^{95} + 12 q^{96} - 9 q^{97} + 53 q^{98} + 38 q^{99}+O(q^{100}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9 + 13 * q^10 + 26 * q^11 + 12 * q^12 + 24 * q^13 + 13 * q^14 + 12 * q^15 + 26 * q^16 + q^17 + 38 * q^18 + 24 * q^19 + 13 * q^20 + 5 * q^21 + 26 * q^22 + 19 * q^23 + 12 * q^24 + 35 * q^25 + 24 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 12 * q^30 + 34 * q^31 + 26 * q^32 + 12 * q^33 + q^34 + 14 * q^35 + 38 * q^36 + 15 * q^37 + 24 * q^38 + 3 * q^39 + 13 * q^40 - 9 * q^41 + 5 * q^42 + 6 * q^43 + 26 * q^44 + 22 * q^45 + 19 * q^46 + 34 * q^47 + 12 * q^48 + 53 * q^49 + 35 * q^50 - 2 * q^51 + 24 * q^52 + 6 * q^53 + 39 * q^54 + 13 * q^55 + 13 * q^56 - 16 * q^57 + 5 * q^58 + 50 * q^59 + 12 * q^60 + 26 * q^61 + 34 * q^62 + 2 * q^63 + 26 * q^64 - 5 * q^65 + 12 * q^66 + 18 * q^67 + q^68 + 15 * q^69 + 14 * q^70 + 23 * q^71 + 38 * q^72 + 37 * q^73 + 15 * q^74 + 18 * q^75 + 24 * q^76 + 13 * q^77 + 3 * q^78 + 10 * q^79 + 13 * q^80 + 50 * q^81 - 9 * q^82 + 7 * q^83 + 5 * q^84 - 7 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^88 + 3 * q^89 + 22 * q^90 + 31 * q^91 + 19 * q^92 + 52 * q^93 + 34 * q^94 + 9 * q^95 + 12 * q^96 - 9 * q^97 + 53 * q^98 + 38 * 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
$3$	2.16110	1.24771	0.623855	−	0.781540i	$-0.285565\pi$
$3$	2.16110	1.24771	0.623855	+	0.781540i	$0.285565\pi$
$4$	1.00000	0.500000
$5$	3.79456	1.69698	0.848490	−	0.529211i	$-0.177512\pi$
$5$	3.79456	1.69698	0.848490	+	0.529211i	$0.177512\pi$
$6$	2.16110	0.882265
$7$	0.294155	0.111180	0.0555901	−	0.998454i	$-0.482296\pi$
$7$	0.294155	0.111180	0.0555901	+	0.998454i	$0.482296\pi$
$8$	1.00000	0.353553
$9$	1.67035	0.556782
$10$	3.79456	1.19995
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.16110	0.623855
$13$	−1.43731	−0.398638	−0.199319	−	0.979935i	$-0.563873\pi$
$13$	−1.43731	−0.398638	−0.199319	+	0.979935i	$0.563873\pi$
$14$	0.294155	0.0786163
$15$	8.20043	2.11734
$16$	1.00000	0.250000
$17$	−1.19277	−0.289290	−0.144645	−	0.989484i	$-0.546204\pi$
$17$	−1.19277	−0.289290	−0.144645	+	0.989484i	$0.546204\pi$
$18$	1.67035	0.393704
$19$	0.519285	0.119132	0.0595661	−	0.998224i	$-0.481028\pi$
$19$	0.519285	0.119132	0.0595661	+	0.998224i	$0.481028\pi$
$20$	3.79456	0.848490
$21$	0.635699	0.138721
$22$	1.00000	0.213201
$23$	−7.98409	−1.66480	−0.832398	−	0.554178i	$-0.813033\pi$
$23$	−7.98409	−1.66480	−0.832398	+	0.554178i	$0.813033\pi$
$24$	2.16110	0.441132
$25$	9.39871	1.87974
$26$	−1.43731	−0.281880
$27$	−2.87351	−0.553008
$28$	0.294155	0.0555901
$29$	−1.79711	−0.333714	−0.166857	−	0.985981i	$-0.553362\pi$
$29$	−1.79711	−0.333714	−0.166857	+	0.985981i	$0.553362\pi$
$30$	8.20043	1.49719
$31$	9.08140	1.63107	0.815534	−	0.578710i	$-0.196444\pi$
$31$	9.08140	1.63107	0.815534	+	0.578710i	$0.196444\pi$
$32$	1.00000	0.176777
$33$	2.16110	0.376199
$34$	−1.19277	−0.204559
$35$	1.11619	0.188671
$36$	1.67035	0.278391
$37$	10.0003	1.64404	0.822018	−	0.569461i	$-0.192848\pi$
$37$	10.0003	1.64404	0.822018	+	0.569461i	$0.192848\pi$
$38$	0.519285	0.0842391
$39$	−3.10617	−0.497385
$40$	3.79456	0.599973
$41$	5.76041	0.899625	0.449812	−	0.893123i	$-0.351491\pi$
$41$	5.76041	0.899625	0.449812	+	0.893123i	$0.351491\pi$
$42$	0.635699	0.0980904
$43$	−2.42936	−0.370475	−0.185237	−	0.982694i	$-0.559305\pi$
$43$	−2.42936	−0.370475	−0.185237	+	0.982694i	$0.559305\pi$
$44$	1.00000	0.150756
$45$	6.33824	0.944848
$46$	−7.98409	−1.17719
$47$	−1.81074	−0.264124	−0.132062	−	0.991241i	$-0.542160\pi$
$47$	−1.81074	−0.264124	−0.132062	+	0.991241i	$0.542160\pi$
$48$	2.16110	0.311928
$49$	−6.91347	−0.987639
$50$	9.39871	1.32918
$51$	−2.57770	−0.360950
$52$	−1.43731	−0.199319
$53$	−7.03176	−0.965886	−0.482943	−	0.875652i	$-0.660432\pi$
$53$	−7.03176	−0.965886	−0.482943	+	0.875652i	$0.660432\pi$
$54$	−2.87351	−0.391035
$55$	3.79456	0.511659
$56$	0.294155	0.0393082
$57$	1.12223	0.148642
$58$	−1.79711	−0.235972
$59$	7.73641	1.00719	0.503597	−	0.863939i	$-0.332010\pi$
$59$	7.73641	1.00719	0.503597	+	0.863939i	$0.332010\pi$
$60$	8.20043	1.05867
$61$	1.99335	0.255223	0.127611	−	0.991824i	$-0.459269\pi$
$61$	1.99335	0.255223	0.127611	+	0.991824i	$0.459269\pi$
$62$	9.08140	1.15334
$63$	0.491341	0.0619032
$64$	1.00000	0.125000
$65$	−5.45397	−0.676481
$66$	2.16110	0.266013
$67$	8.39494	1.02561	0.512803	−	0.858506i	$-0.328607\pi$
$67$	8.39494	1.02561	0.512803	+	0.858506i	$0.328607\pi$
$68$	−1.19277	−0.144645
$69$	−17.2544	−2.07718
$70$	1.11619	0.133410
$71$	−4.27485	−0.507331	−0.253666	−	0.967292i	$-0.581636\pi$
$71$	−4.27485	−0.507331	−0.253666	+	0.967292i	$0.581636\pi$
$72$	1.67035	0.196852
$73$	9.73412	1.13929	0.569646	−	0.821890i	$-0.307080\pi$
$73$	9.73412	1.13929	0.569646	+	0.821890i	$0.307080\pi$
$74$	10.0003	1.16251
$75$	20.3115	2.34537
$76$	0.519285	0.0595661
$77$	0.294155	0.0335221
$78$	−3.10617	−0.351704
$79$	9.25019	1.04073	0.520364	−	0.853945i	$-0.325796\pi$
$79$	9.25019	1.04073	0.520364	+	0.853945i	$0.325796\pi$
$80$	3.79456	0.424245
$81$	−11.2210	−1.24678
$82$	5.76041	0.636131
$83$	−2.83280	−0.310940	−0.155470	−	0.987841i	$-0.549689\pi$
$83$	−2.83280	−0.310940	−0.155470	+	0.987841i	$0.549689\pi$
$84$	0.635699	0.0693604
$85$	−4.52606	−0.490920
$86$	−2.42936	−0.261965
$87$	−3.88373	−0.416379
$88$	1.00000	0.106600
$89$	−12.5084	−1.32589	−0.662945	−	0.748668i	$-0.730694\pi$
$89$	−12.5084	−1.32589	−0.662945	+	0.748668i	$0.730694\pi$
$90$	6.33824	0.668109
$91$	−0.422793	−0.0443207
$92$	−7.98409	−0.832398
$93$	19.6258	2.03510
$94$	−1.81074	−0.186764
$95$	1.97046	0.202165
$96$	2.16110	0.220566
$97$	−5.56390	−0.564928	−0.282464	−	0.959278i	$-0.591152\pi$
$97$	−5.56390	−0.564928	−0.282464	+	0.959278i	$0.591152\pi$
$98$	−6.91347	−0.698366
$99$	1.67035	0.167876
$100$	9.39871	0.939871
$101$	−11.7759	−1.17175	−0.585874	−	0.810402i	$-0.699249\pi$
$101$	−11.7759	−1.17175	−0.585874	+	0.810402i	$0.699249\pi$
$102$	−2.57770	−0.255230
$103$	17.2753	1.70218	0.851091	−	0.525019i	$-0.175942\pi$
$103$	17.2753	1.70218	0.851091	+	0.525019i	$0.175942\pi$
$104$	−1.43731	−0.140940
$105$	2.41220	0.235406
$106$	−7.03176	−0.682985
$107$	4.85182	0.469043	0.234522	−	0.972111i	$-0.424648\pi$
$107$	4.85182	0.469043	0.234522	+	0.972111i	$0.424648\pi$
$108$	−2.87351	−0.276504
$109$	−10.3918	−0.995352	−0.497676	−	0.867363i	$-0.665813\pi$
$109$	−10.3918	−0.995352	−0.497676	+	0.867363i	$0.665813\pi$
$110$	3.79456	0.361797
$111$	21.6116	2.05128
$112$	0.294155	0.0277951
$113$	−14.7084	−1.38365	−0.691826	−	0.722064i	$-0.743194\pi$
$113$	−14.7084	−1.38365	−0.691826	+	0.722064i	$0.743194\pi$
$114$	1.12223	0.105106
$115$	−30.2961	−2.82513
$116$	−1.79711	−0.166857
$117$	−2.40081	−0.221955
$118$	7.73641	0.712194
$119$	−0.350861	−0.0321633
$120$	8.20043	0.748593
$121$	1.00000	0.0909091
$122$	1.99335	0.180470
$123$	12.4488	1.12247
$124$	9.08140	0.815534
$125$	16.6912	1.49291
$126$	0.491341	0.0437722
$127$	−21.5347	−1.91089	−0.955447	−	0.295163i	$-0.904626\pi$
$127$	−21.5347	−1.91089	−0.955447	+	0.295163i	$0.904626\pi$
$128$	1.00000	0.0883883
$129$	−5.25010	−0.462245
$130$	−5.45397	−0.478344
$131$	−17.9645	−1.56956	−0.784781	−	0.619773i	$-0.787225\pi$
$131$	−17.9645	−1.56956	−0.784781	+	0.619773i	$0.787225\pi$
$132$	2.16110	0.188099
$133$	0.152750	0.0132451
$134$	8.39494	0.725213
$135$	−10.9037	−0.938443
$136$	−1.19277	−0.102279
$137$	10.5571	0.901953	0.450977	−	0.892536i	$-0.351076\pi$
$137$	10.5571	0.901953	0.450977	+	0.892536i	$0.351076\pi$
$138$	−17.2544	−1.46879
$139$	−20.5711	−1.74482	−0.872411	−	0.488773i	$-0.837444\pi$
$139$	−20.5711	−1.74482	−0.872411	+	0.488773i	$0.837444\pi$
$140$	1.11619	0.0943354
$141$	−3.91319	−0.329550
$142$	−4.27485	−0.358737
$143$	−1.43731	−0.120194
$144$	1.67035	0.139196
$145$	−6.81924	−0.566307
$146$	9.73412	0.805602
$147$	−14.9407	−1.23229
$148$	10.0003	0.822018
$149$	−10.7552	−0.881098	−0.440549	−	0.897729i	$-0.645216\pi$
$149$	−10.7552	−0.881098	−0.440549	+	0.897729i	$0.645216\pi$
$150$	20.3115	1.65843
$151$	21.4301	1.74396	0.871980	−	0.489542i	$-0.162836\pi$
$151$	21.4301	1.74396	0.871980	+	0.489542i	$0.162836\pi$
$152$	0.519285	0.0421196
$153$	−1.99235	−0.161072
$154$	0.294155	0.0237037
$155$	34.4599	2.76789
$156$	−3.10617	−0.248693
$157$	7.87633	0.628600	0.314300	−	0.949324i	$-0.398230\pi$
$157$	7.87633	0.628600	0.314300	+	0.949324i	$0.398230\pi$
$158$	9.25019	0.735906
$159$	−15.1963	−1.20515
$160$	3.79456	0.299987
$161$	−2.34856	−0.185093
$162$	−11.2210	−0.881604
$163$	3.98361	0.312021	0.156010	−	0.987755i	$-0.450137\pi$
$163$	3.98361	0.312021	0.156010	+	0.987755i	$0.450137\pi$
$164$	5.76041	0.449812
$165$	8.20043	0.638402
$166$	−2.83280	−0.219868
$167$	−21.8897	−1.69388	−0.846940	−	0.531689i	$-0.821558\pi$
$167$	−21.8897	−1.69388	−0.846940	+	0.531689i	$0.821558\pi$
$168$	0.635699	0.0490452
$169$	−10.9341	−0.841088
$170$	−4.52606	−0.347133
$171$	0.867386	0.0663306
$172$	−2.42936	−0.185237
$173$	−21.4434	−1.63031	−0.815155	−	0.579243i	$-0.803348\pi$
$173$	−21.4434	−1.63031	−0.815155	+	0.579243i	$0.803348\pi$
$174$	−3.88373	−0.294424
$175$	2.76468	0.208990
$176$	1.00000	0.0753778
$177$	16.7191	1.25669
$178$	−12.5084	−0.937546
$179$	24.8333	1.85613	0.928064	−	0.372421i	$-0.121472\pi$
$179$	24.8333	1.85613	0.928064	+	0.372421i	$0.121472\pi$
$180$	6.33824	0.472424
$181$	19.6875	1.46336	0.731682	−	0.681647i	$-0.238736\pi$
$181$	19.6875	1.46336	0.731682	+	0.681647i	$0.238736\pi$
$182$	−0.422793	−0.0313395
$183$	4.30784	0.318444
$184$	−7.98409	−0.588595
$185$	37.9467	2.78990
$186$	19.6258	1.43903
$187$	−1.19277	−0.0872242
$188$	−1.81074	−0.132062
$189$	−0.845259	−0.0614835
$190$	1.97046	0.142952
$191$	−22.1424	−1.60217	−0.801083	−	0.598553i	$-0.795743\pi$
$191$	−22.1424	−1.60217	−0.801083	+	0.598553i	$0.795743\pi$
$192$	2.16110	0.155964
$193$	−0.693053	−0.0498871	−0.0249435	−	0.999689i	$-0.507941\pi$
$193$	−0.693053	−0.0498871	−0.0249435	+	0.999689i	$0.507941\pi$
$194$	−5.56390	−0.399465
$195$	−11.7866	−0.844053
$196$	−6.91347	−0.493819
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	1.67035	0.118706
$199$	−8.10646	−0.574652	−0.287326	−	0.957833i	$-0.592766\pi$
$199$	−8.10646	−0.574652	−0.287326	+	0.957833i	$0.592766\pi$
$200$	9.39871	0.664589
$201$	18.1423	1.27966
$202$	−11.7759	−0.828552
$203$	−0.528629	−0.0371025
$204$	−2.57770	−0.180475
$205$	21.8582	1.52665
$206$	17.2753	1.20362
$207$	−13.3362	−0.926929
$208$	−1.43731	−0.0996596
$209$	0.519285	0.0359197
$210$	2.41220	0.166458
$211$	14.0002	0.963814	0.481907	−	0.876222i	$-0.339944\pi$
$211$	14.0002	0.963814	0.481907	+	0.876222i	$0.339944\pi$
$212$	−7.03176	−0.482943
$213$	−9.23837	−0.633002
$214$	4.85182	0.331664
$215$	−9.21838	−0.628688
$216$	−2.87351	−0.195518
$217$	2.67134	0.181342
$218$	−10.3918	−0.703820
$219$	21.0364	1.42151
$220$	3.79456	0.255829
$221$	1.71439	0.115322
$222$	21.6116	1.45048
$223$	−5.73370	−0.383957	−0.191978	−	0.981399i	$-0.561490\pi$
$223$	−5.73370	−0.383957	−0.191978	+	0.981399i	$0.561490\pi$
$224$	0.294155	0.0196541
$225$	15.6991	1.04661
$226$	−14.7084	−0.978390
$227$	−22.6820	−1.50546	−0.752729	−	0.658330i	$-0.771263\pi$
$227$	−22.6820	−1.50546	−0.752729	+	0.658330i	$0.771263\pi$
$228$	1.12223	0.0743212
$229$	−11.7473	−0.776285	−0.388143	−	0.921599i	$-0.626883\pi$
$229$	−11.7473	−0.776285	−0.388143	+	0.921599i	$0.626883\pi$
$230$	−30.2961	−1.99767
$231$	0.635699	0.0418259
$232$	−1.79711	−0.117986
$233$	−21.9428	−1.43752	−0.718761	−	0.695257i	$-0.755290\pi$
$233$	−21.9428	−1.43752	−0.718761	+	0.695257i	$0.755290\pi$
$234$	−2.40081	−0.156946
$235$	−6.87098	−0.448213
$236$	7.73641	0.503597
$237$	19.9906	1.29853
$238$	−0.350861	−0.0227429
$239$	−26.7735	−1.73184	−0.865918	−	0.500186i	$-0.833265\pi$
$239$	−26.7735	−1.73184	−0.865918	+	0.500186i	$0.833265\pi$
$240$	8.20043	0.529335
$241$	−4.00808	−0.258183	−0.129091	−	0.991633i	$-0.541206\pi$
$241$	−4.00808	−0.258183	−0.129091	+	0.991633i	$0.541206\pi$
$242$	1.00000	0.0642824
$243$	−15.6291	−1.00261
$244$	1.99335	0.127611
$245$	−26.2336	−1.67600
$246$	12.4488	0.793707
$247$	−0.746374	−0.0474906
$248$	9.08140	0.576669
$249$	−6.12196	−0.387963
$250$	16.6912	1.05564
$251$	17.4087	1.09883	0.549414	−	0.835550i	$-0.314851\pi$
$251$	17.4087	1.09883	0.549414	+	0.835550i	$0.314851\pi$
$252$	0.491341	0.0309516
$253$	−7.98409	−0.501955
$254$	−21.5347	−1.35121
$255$	−9.78125	−0.612526
$256$	1.00000	0.0625000
$257$	25.0936	1.56529	0.782646	−	0.622467i	$-0.213869\pi$
$257$	25.0936	1.56529	0.782646	+	0.622467i	$0.213869\pi$
$258$	−5.25010	−0.326857
$259$	2.94164	0.182784
$260$	−5.45397	−0.338241
$261$	−3.00179	−0.185806
$262$	−17.9645	−1.10985
$263$	5.39618	0.332743	0.166371	−	0.986063i	$-0.446795\pi$
$263$	5.39618	0.332743	0.166371	+	0.986063i	$0.446795\pi$
$264$	2.16110	0.133006
$265$	−26.6824	−1.63909
$266$	0.152750	0.00936573
$267$	−27.0319	−1.65433
$268$	8.39494	0.512803
$269$	29.6712	1.80908	0.904541	−	0.426386i	$-0.140214\pi$
$269$	29.6712	1.80908	0.904541	+	0.426386i	$0.140214\pi$
$270$	−10.9037	−0.663579
$271$	19.5864	1.18979	0.594895	−	0.803804i	$-0.297194\pi$
$271$	19.5864	1.18979	0.594895	+	0.803804i	$0.297194\pi$
$272$	−1.19277	−0.0723225
$273$	−0.913696	−0.0552994
$274$	10.5571	0.637777
$275$	9.39871	0.566764
$276$	−17.2544	−1.03859
$277$	−13.6124	−0.817889	−0.408945	−	0.912559i	$-0.634103\pi$
$277$	−13.6124	−0.817889	−0.408945	+	0.912559i	$0.634103\pi$
$278$	−20.5711	−1.23378
$279$	15.1691	0.908149
$280$	1.11619	0.0667052
$281$	−5.66940	−0.338208	−0.169104	−	0.985598i	$-0.554087\pi$
$281$	−5.66940	−0.338208	−0.169104	+	0.985598i	$0.554087\pi$
$282$	−3.91319	−0.233027
$283$	−7.61767	−0.452824	−0.226412	−	0.974032i	$-0.572700\pi$
$283$	−7.61767	−0.452824	−0.226412	+	0.974032i	$0.572700\pi$
$284$	−4.27485	−0.253666
$285$	4.25836	0.252243
$286$	−1.43731	−0.0849900
$287$	1.69445	0.100021
$288$	1.67035	0.0984261
$289$	−15.5773	−0.916311
$290$	−6.81924	−0.400439
$291$	−12.0241	−0.704867
$292$	9.73412	0.569646
$293$	−27.4402	−1.60307	−0.801536	−	0.597947i	$-0.795983\pi$
$293$	−27.4402	−1.60307	−0.801536	+	0.597947i	$0.795983\pi$
$294$	−14.9407	−0.871359
$295$	29.3563	1.70919
$296$	10.0003	0.581255
$297$	−2.87351	−0.166738
$298$	−10.7552	−0.623030
$299$	11.4756	0.663652
$300$	20.3115	1.17269
$301$	−0.714610	−0.0411895
$302$	21.4301	1.23317
$303$	−25.4489	−1.46200
$304$	0.519285	0.0297830
$305$	7.56391	0.433108
$306$	−1.99235	−0.113895
$307$	−28.8613	−1.64720	−0.823600	−	0.567171i	$-0.808038\pi$
$307$	−28.8613	−1.64720	−0.823600	+	0.567171i	$0.808038\pi$
$308$	0.294155	0.0167611
$309$	37.3335	2.12383
$310$	34.4599	1.95719
$311$	7.35179	0.416882	0.208441	−	0.978035i	$-0.433161\pi$
$311$	7.35179	0.416882	0.208441	+	0.978035i	$0.433161\pi$
$312$	−3.10617	−0.175852
$313$	8.02239	0.453452	0.226726	−	0.973959i	$-0.427198\pi$
$313$	8.02239	0.453452	0.226726	+	0.973959i	$0.427198\pi$
$314$	7.87633	0.444487
$315$	1.86443	0.105048
$316$	9.25019	0.520364
$317$	15.5821	0.875178	0.437589	−	0.899175i	$-0.355832\pi$
$317$	15.5821	0.875178	0.437589	+	0.899175i	$0.355832\pi$
$318$	−15.1963	−0.852167
$319$	−1.79711	−0.100619
$320$	3.79456	0.212123
$321$	10.4853	0.585230
$322$	−2.34856	−0.130880
$323$	−0.619389	−0.0344637
$324$	−11.2210	−0.623388
$325$	−13.5089	−0.749337
$326$	3.98361	0.220632
$327$	−22.4577	−1.24191
$328$	5.76041	0.318065
$329$	−0.532640	−0.0293654
$330$	8.20043	0.451419
$331$	−12.7515	−0.700888	−0.350444	−	0.936584i	$-0.613969\pi$
$331$	−12.7515	−0.700888	−0.350444	+	0.936584i	$0.613969\pi$
$332$	−2.83280	−0.155470
$333$	16.7039	0.915370
$334$	−21.8897	−1.19775
$335$	31.8551	1.74043
$336$	0.635699	0.0346802
$337$	−14.2965	−0.778777	−0.389389	−	0.921074i	$-0.627314\pi$
$337$	−14.2965	−0.778777	−0.389389	+	0.921074i	$0.627314\pi$
$338$	−10.9341	−0.594739
$339$	−31.7864	−1.72640
$340$	−4.52606	−0.245460
$341$	9.08140	0.491785
$342$	0.867386	0.0469028
$343$	−4.09272	−0.220986
$344$	−2.42936	−0.130983
$345$	−65.4729	−3.52494
$346$	−21.4434	−1.15280
$347$	32.6580	1.75317	0.876586	−	0.481245i	$-0.159815\pi$
$347$	32.6580	1.75317	0.876586	+	0.481245i	$0.159815\pi$
$348$	−3.88373	−0.208190
$349$	−18.2934	−0.979226	−0.489613	−	0.871940i	$-0.662862\pi$
$349$	−18.2934	−0.979226	−0.489613	+	0.871940i	$0.662862\pi$
$350$	2.76468	0.147778
$351$	4.13013	0.220450
$352$	1.00000	0.0533002
$353$	4.80987	0.256004	0.128002	−	0.991774i	$-0.459144\pi$
$353$	4.80987	0.256004	0.128002	+	0.991774i	$0.459144\pi$
$354$	16.7191	0.888612
$355$	−16.2212	−0.860931
$356$	−12.5084	−0.662945
$357$	−0.758245	−0.0401306
$358$	24.8333	1.31248
$359$	30.2612	1.59712	0.798562	−	0.601912i	$-0.205594\pi$
$359$	30.2612	1.59712	0.798562	+	0.601912i	$0.205594\pi$
$360$	6.33824	0.334054
$361$	−18.7303	−0.985808
$362$	19.6875	1.03475
$363$	2.16110	0.113428
$364$	−0.422793	−0.0221604
$365$	36.9367	1.93336
$366$	4.30784	0.225174
$367$	−19.3686	−1.01103	−0.505516	−	0.862817i	$-0.668698\pi$
$367$	−19.3686	−1.01103	−0.505516	+	0.862817i	$0.668698\pi$
$368$	−7.98409	−0.416199
$369$	9.62188	0.500895
$370$	37.9467	1.97276
$371$	−2.06843	−0.107387
$372$	19.6258	1.01755
$373$	8.53161	0.441750	0.220875	−	0.975302i	$-0.429109\pi$
$373$	8.53161	0.441750	0.220875	+	0.975302i	$0.429109\pi$
$374$	−1.19277	−0.0616769
$375$	36.0713	1.86271
$376$	−1.81074	−0.0933819
$377$	2.58300	0.133031
$378$	−0.845259	−0.0434754
$379$	7.84577	0.403010	0.201505	−	0.979487i	$-0.435417\pi$
$379$	7.84577	0.403010	0.201505	+	0.979487i	$0.435417\pi$
$380$	1.97046	0.101082
$381$	−46.5386	−2.38424
$382$	−22.1424	−1.13290
$383$	31.5783	1.61357	0.806787	−	0.590842i	$-0.201204\pi$
$383$	31.5783	1.61357	0.806787	+	0.590842i	$0.201204\pi$
$384$	2.16110	0.110283
$385$	1.11619	0.0568864
$386$	−0.693053	−0.0352755
$387$	−4.05788	−0.206274
$388$	−5.56390	−0.282464
$389$	4.25106	0.215538	0.107769	−	0.994176i	$-0.465629\pi$
$389$	4.25106	0.215538	0.107769	+	0.994176i	$0.465629\pi$
$390$	−11.7866	−0.596836
$391$	9.52321	0.481609
$392$	−6.91347	−0.349183
$393$	−38.8230	−1.95836
$394$	1.00000	0.0503793
$395$	35.1004	1.76609
$396$	1.67035	0.0839381
$397$	28.8173	1.44630	0.723150	−	0.690691i	$-0.242694\pi$
$397$	28.8173	1.44630	0.723150	+	0.690691i	$0.242694\pi$
$398$	−8.10646	−0.406340
$399$	0.330109	0.0165261
$400$	9.39871	0.469936
$401$	10.5311	0.525899	0.262949	−	0.964810i	$-0.415305\pi$
$401$	10.5311	0.525899	0.262949	+	0.964810i	$0.415305\pi$
$402$	18.1423	0.904856
$403$	−13.0528	−0.650206
$404$	−11.7759	−0.585874
$405$	−42.5787	−2.11575
$406$	−0.528629	−0.0262354
$407$	10.0003	0.495696
$408$	−2.57770	−0.127615
$409$	5.35631	0.264852	0.132426	−	0.991193i	$-0.457723\pi$
$409$	5.35631	0.264852	0.132426	+	0.991193i	$0.457723\pi$
$410$	21.8582	1.07950
$411$	22.8149	1.12538
$412$	17.2753	0.851091
$413$	2.27571	0.111980
$414$	−13.3362	−0.655438
$415$	−10.7492	−0.527659
$416$	−1.43731	−0.0704700
$417$	−44.4563	−2.17703
$418$	0.519285	0.0253991
$419$	6.85695	0.334984	0.167492	−	0.985873i	$-0.446433\pi$
$419$	6.85695	0.334984	0.167492	+	0.985873i	$0.446433\pi$
$420$	2.41220	0.117703
$421$	23.7722	1.15859	0.579293	−	0.815119i	$-0.303329\pi$
$421$	23.7722	1.15859	0.579293	+	0.815119i	$0.303329\pi$
$422$	14.0002	0.681520
$423$	−3.02457	−0.147060
$424$	−7.03176	−0.341492
$425$	−11.2105	−0.543791
$426$	−9.23837	−0.447600
$427$	0.586356	0.0283758
$428$	4.85182	0.234522
$429$	−3.10617	−0.149967
$430$	−9.21838	−0.444550
$431$	−5.42594	−0.261358	−0.130679	−	0.991425i	$-0.541716\pi$
$431$	−5.42594	−0.261358	−0.130679	+	0.991425i	$0.541716\pi$
$432$	−2.87351	−0.138252
$433$	−3.68077	−0.176886	−0.0884432	−	0.996081i	$-0.528189\pi$
$433$	−3.68077	−0.176886	−0.0884432	+	0.996081i	$0.528189\pi$
$434$	2.67134	0.128228
$435$	−14.7370	−0.706587
$436$	−10.3918	−0.497676
$437$	−4.14601	−0.198331
$438$	21.0364	1.00516
$439$	34.6274	1.65268	0.826339	−	0.563174i	$-0.190420\pi$
$439$	34.6274	1.65268	0.826339	+	0.563174i	$0.190420\pi$
$440$	3.79456	0.180899
$441$	−11.5479	−0.549900
$442$	1.71439	0.0815450
$443$	−24.0967	−1.14487	−0.572435	−	0.819950i	$-0.694001\pi$
$443$	−24.0967	−1.14487	−0.572435	+	0.819950i	$0.694001\pi$
$444$	21.6116	1.02564
$445$	−47.4640	−2.25001
$446$	−5.73370	−0.271498
$447$	−23.2430	−1.09936
$448$	0.294155	0.0138975
$449$	16.0400	0.756973	0.378487	−	0.925607i	$-0.376445\pi$
$449$	16.0400	0.756973	0.378487	+	0.925607i	$0.376445\pi$
$450$	15.6991	0.740063
$451$	5.76041	0.271247
$452$	−14.7084	−0.691826
$453$	46.3126	2.17596
$454$	−22.6820	−1.06452
$455$	−1.60431	−0.0752114
$456$	1.12223	0.0525530
$457$	−2.97503	−0.139166	−0.0695831	−	0.997576i	$-0.522167\pi$
$457$	−2.97503	−0.139166	−0.0695831	+	0.997576i	$0.522167\pi$
$458$	−11.7473	−0.548917
$459$	3.42745	0.159980
$460$	−30.2961	−1.41256
$461$	8.21888	0.382791	0.191396	−	0.981513i	$-0.438699\pi$
$461$	8.21888	0.382791	0.191396	+	0.981513i	$0.438699\pi$
$462$	0.635699	0.0295754
$463$	−11.9427	−0.555027	−0.277513	−	0.960722i	$-0.589510\pi$
$463$	−11.9427	−0.555027	−0.277513	+	0.960722i	$0.589510\pi$
$464$	−1.79711	−0.0834286
$465$	74.4713	3.45352
$466$	−21.9428	−1.01648
$467$	8.93708	0.413559	0.206779	−	0.978388i	$-0.433702\pi$
$467$	8.93708	0.413559	0.206779	+	0.978388i	$0.433702\pi$
$468$	−2.40081	−0.110977
$469$	2.46942	0.114027
$470$	−6.87098	−0.316935
$471$	17.0215	0.784311
$472$	7.73641	0.356097
$473$	−2.42936	−0.111702
$474$	19.9906	0.918197
$475$	4.88061	0.223938
$476$	−0.350861	−0.0160817
$477$	−11.7455	−0.537788
$478$	−26.7735	−1.22459
$479$	18.3830	0.839940	0.419970	−	0.907538i	$-0.362041\pi$
$479$	18.3830	0.839940	0.419970	+	0.907538i	$0.362041\pi$
$480$	8.20043	0.374296
$481$	−14.3735	−0.655376
$482$	−4.00808	−0.182563
$483$	−5.07547	−0.230942
$484$	1.00000	0.0454545
$485$	−21.1126	−0.958672
$486$	−15.6291	−0.708951
$487$	25.8901	1.17319	0.586596	−	0.809880i	$-0.300468\pi$
$487$	25.8901	1.17319	0.586596	+	0.809880i	$0.300468\pi$
$488$	1.99335	0.0902349
$489$	8.60898	0.389312
$490$	−26.2336	−1.18511
$491$	19.1219	0.862958	0.431479	−	0.902123i	$-0.357992\pi$
$491$	19.1219	0.862958	0.431479	+	0.902123i	$0.357992\pi$
$492$	12.4488	0.561236
$493$	2.14354	0.0965403
$494$	−0.746374	−0.0335809
$495$	6.33824	0.284883
$496$	9.08140	0.407767
$497$	−1.25747	−0.0564052
$498$	−6.12196	−0.274332
$499$	2.40377	0.107607	0.0538037	−	0.998552i	$-0.482865\pi$
$499$	2.40377	0.107607	0.0538037	+	0.998552i	$0.482865\pi$
$500$	16.6912	0.746453
$501$	−47.3059	−2.11347
$502$	17.4087	0.776989
$503$	−28.1771	−1.25635	−0.628176	−	0.778071i	$-0.716198\pi$
$503$	−28.1771	−1.25635	−0.628176	+	0.778071i	$0.716198\pi$
$504$	0.491341	0.0218861
$505$	−44.6845	−1.98843
$506$	−7.98409	−0.354936
$507$	−23.6297	−1.04943
$508$	−21.5347	−0.955447
$509$	17.0603	0.756182	0.378091	−	0.925768i	$-0.376581\pi$
$509$	17.0603	0.756182	0.378091	+	0.925768i	$0.376581\pi$
$510$	−9.78125	−0.433121
$511$	2.86334	0.126667
$512$	1.00000	0.0441942
$513$	−1.49217	−0.0658810
$514$	25.0936	1.10683
$515$	65.5520	2.88857
$516$	−5.25010	−0.231123
$517$	−1.81074	−0.0796364
$518$	2.94164	0.129248
$519$	−46.3413	−2.03416
$520$	−5.45397	−0.239172
$521$	−27.2138	−1.19226	−0.596128	−	0.802889i	$-0.703295\pi$
$521$	−27.2138	−1.19226	−0.596128	+	0.802889i	$0.703295\pi$
$522$	−3.00179	−0.131385
$523$	41.8112	1.82828	0.914138	−	0.405403i	$-0.132869\pi$
$523$	41.8112	1.82828	0.914138	+	0.405403i	$0.132869\pi$
$524$	−17.9645	−0.784781
$525$	5.97475	0.260759
$526$	5.39618	0.235285
$527$	−10.8321	−0.471852
$528$	2.16110	0.0940497
$529$	40.7456	1.77155
$530$	−26.6824	−1.15901
$531$	12.9225	0.560788
$532$	0.152750	0.00662257
$533$	−8.27950	−0.358625
$534$	−27.0319	−1.16979
$535$	18.4105	0.795957
$536$	8.39494	0.362606
$537$	53.6672	2.31591
$538$	29.6712	1.27921
$539$	−6.91347	−0.297784
$540$	−10.9037	−0.469222
$541$	−7.77165	−0.334129	−0.167065	−	0.985946i	$-0.553429\pi$
$541$	−7.77165	−0.334129	−0.167065	+	0.985946i	$0.553429\pi$
$542$	19.5864	0.841308
$543$	42.5467	1.82585
$544$	−1.19277	−0.0511397
$545$	−39.4323	−1.68909
$546$	−0.913696	−0.0391026
$547$	27.7687	1.18731	0.593653	−	0.804721i	$-0.297685\pi$
$547$	27.7687	1.18731	0.593653	+	0.804721i	$0.297685\pi$
$548$	10.5571	0.450977
$549$	3.32959	0.142104
$550$	9.39871	0.400762
$551$	−0.933211	−0.0397561
$552$	−17.2544	−0.734396
$553$	2.72099	0.115708
$554$	−13.6124	−0.578335
$555$	82.0066	3.48099
$556$	−20.5711	−0.872411
$557$	0.540307	0.0228935	0.0114468	−	0.999934i	$-0.496356\pi$
$557$	0.540307	0.0228935	0.0114468	+	0.999934i	$0.496356\pi$
$558$	15.1691	0.642158
$559$	3.49175	0.147685
$560$	1.11619	0.0471677
$561$	−2.57770	−0.108831
$562$	−5.66940	−0.239149
$563$	2.83707	0.119568	0.0597840	−	0.998211i	$-0.480959\pi$
$563$	2.83707	0.119568	0.0597840	+	0.998211i	$0.480959\pi$
$564$	−3.91319	−0.164775
$565$	−55.8121	−2.34803
$566$	−7.61767	−0.320195
$567$	−3.30071	−0.138617
$568$	−4.27485	−0.179369
$569$	0.298541	0.0125155	0.00625775	−	0.999980i	$-0.498008\pi$
$569$	0.298541	0.0125155	0.00625775	+	0.999980i	$0.498008\pi$
$570$	4.25836	0.178363
$571$	−14.0313	−0.587193	−0.293596	−	0.955930i	$-0.594852\pi$
$571$	−14.0313	−0.587193	−0.293596	+	0.955930i	$0.594852\pi$
$572$	−1.43731	−0.0600970
$573$	−47.8519	−1.99904
$574$	1.69445	0.0707252
$575$	−75.0401	−3.12939
$576$	1.67035	0.0695978
$577$	−37.9739	−1.58088	−0.790438	−	0.612542i	$-0.790147\pi$
$577$	−37.9739	−1.58088	−0.790438	+	0.612542i	$0.790147\pi$
$578$	−15.5773	−0.647930
$579$	−1.49776	−0.0622446
$580$	−6.81924	−0.283153
$581$	−0.833283	−0.0345704
$582$	−12.0241	−0.498416
$583$	−7.03176	−0.291226
$584$	9.73412	0.402801
$585$	−9.11001	−0.376653
$586$	−27.4402	−1.13354
$587$	−26.3835	−1.08896	−0.544482	−	0.838773i	$-0.683274\pi$
$587$	−26.3835	−1.08896	−0.544482	+	0.838773i	$0.683274\pi$
$588$	−14.9407	−0.616144
$589$	4.71583	0.194312
$590$	29.3563	1.20858
$591$	2.16110	0.0888957
$592$	10.0003	0.411009
$593$	28.3522	1.16428	0.582142	−	0.813087i	$-0.302215\pi$
$593$	28.3522	1.16428	0.582142	+	0.813087i	$0.302215\pi$
$594$	−2.87351	−0.117902
$595$	−1.33136	−0.0545806
$596$	−10.7552	−0.440549
$597$	−17.5189	−0.716999
$598$	11.4756	0.469273
$599$	17.7369	0.724710	0.362355	−	0.932040i	$-0.381973\pi$
$599$	17.7369	0.724710	0.362355	+	0.932040i	$0.381973\pi$
$600$	20.3115	0.829215
$601$	29.8977	1.21955	0.609777	−	0.792573i	$-0.291259\pi$
$601$	29.8977	1.21955	0.609777	+	0.792573i	$0.291259\pi$
$602$	−0.714610	−0.0291253
$603$	14.0225	0.571039
$604$	21.4301	0.871980
$605$	3.79456	0.154271
$606$	−25.4489	−1.03379
$607$	26.1659	1.06204	0.531021	−	0.847359i	$-0.321809\pi$
$607$	26.1659	1.06204	0.531021	+	0.847359i	$0.321809\pi$
$608$	0.519285	0.0210598
$609$	−1.14242	−0.0462931
$610$	7.56391	0.306254
$611$	2.60260	0.105290
$612$	−1.99235	−0.0805358
$613$	19.5943	0.791408	0.395704	−	0.918378i	$-0.370501\pi$
$613$	19.5943	0.791408	0.395704	+	0.918378i	$0.370501\pi$
$614$	−28.8613	−1.16475
$615$	47.2378	1.90481
$616$	0.294155	0.0118519
$617$	−9.69642	−0.390363	−0.195182	−	0.980767i	$-0.562530\pi$
$617$	−9.69642	−0.390363	−0.195182	+	0.980767i	$0.562530\pi$
$618$	37.3335	1.50177
$619$	12.0316	0.483592	0.241796	−	0.970327i	$-0.422263\pi$
$619$	12.0316	0.483592	0.241796	+	0.970327i	$0.422263\pi$
$620$	34.4599	1.38394
$621$	22.9424	0.920645
$622$	7.35179	0.294780
$623$	−3.67942	−0.147413
$624$	−3.10617	−0.124346
$625$	16.3422	0.653689
$626$	8.02239	0.320639
$627$	1.12223	0.0448174
$628$	7.87633	0.314300
$629$	−11.9281	−0.475604
$630$	1.86443	0.0742805
$631$	−33.1203	−1.31850	−0.659250	−	0.751924i	$-0.729126\pi$
$631$	−33.1203	−1.31850	−0.659250	+	0.751924i	$0.729126\pi$
$632$	9.25019	0.367953
$633$	30.2558	1.20256
$634$	15.5821	0.618844
$635$	−81.7147	−3.24275
$636$	−15.1963	−0.602573
$637$	9.93681	0.393711
$638$	−1.79711	−0.0711482
$639$	−7.14048	−0.282473
$640$	3.79456	0.149993
$641$	39.0303	1.54160	0.770801	−	0.637076i	$-0.219856\pi$
$641$	39.0303	1.54160	0.770801	+	0.637076i	$0.219856\pi$
$642$	10.4853	0.413820
$643$	−34.9858	−1.37971	−0.689853	−	0.723949i	$-0.742325\pi$
$643$	−34.9858	−1.37971	−0.689853	+	0.723949i	$0.742325\pi$
$644$	−2.34856	−0.0925463
$645$	−19.9218	−0.784421
$646$	−0.619389	−0.0243695
$647$	−14.4418	−0.567766	−0.283883	−	0.958859i	$-0.591623\pi$
$647$	−14.4418	−0.567766	−0.283883	+	0.958859i	$0.591623\pi$
$648$	−11.2210	−0.440802
$649$	7.73641	0.303681
$650$	−13.5089	−0.529861
$651$	5.77303	0.226263
$652$	3.98361	0.156010
$653$	11.2815	0.441480	0.220740	−	0.975333i	$-0.429153\pi$
$653$	11.2815	0.441480	0.220740	+	0.975333i	$0.429153\pi$
$654$	−22.4577	−0.878164
$655$	−68.1673	−2.66352
$656$	5.76041	0.224906
$657$	16.2594	0.634338
$658$	−0.532640	−0.0207645
$659$	37.2281	1.45020	0.725100	−	0.688643i	$-0.241793\pi$
$659$	37.2281	1.45020	0.725100	+	0.688643i	$0.241793\pi$
$660$	8.20043	0.319201
$661$	1.53605	0.0597454	0.0298727	−	0.999554i	$-0.490490\pi$
$661$	1.53605	0.0597454	0.0298727	+	0.999554i	$0.490490\pi$
$662$	−12.7515	−0.495603
$663$	3.70496	0.143889
$664$	−2.83280	−0.109934
$665$	0.579621	0.0224767
$666$	16.7039	0.647265
$667$	14.3483	0.555567
$668$	−21.8897	−0.846940
$669$	−12.3911	−0.479067
$670$	31.8551	1.23067
$671$	1.99335	0.0769526
$672$	0.635699	0.0245226
$673$	29.4357	1.13466	0.567331	−	0.823490i	$-0.307976\pi$
$673$	29.4357	1.13466	0.567331	+	0.823490i	$0.307976\pi$
$674$	−14.2965	−0.550679
$675$	−27.0073	−1.03951
$676$	−10.9341	−0.420544
$677$	31.5183	1.21135	0.605673	−	0.795714i	$-0.292904\pi$
$677$	31.5183	1.21135	0.605673	+	0.795714i	$0.292904\pi$
$678$	−31.7864	−1.22075
$679$	−1.63665	−0.0628089
$680$	−4.52606	−0.173566
$681$	−49.0181	−1.87838
$682$	9.08140	0.347745
$683$	39.2358	1.50132	0.750658	−	0.660691i	$-0.229737\pi$
$683$	39.2358	1.50132	0.750658	+	0.660691i	$0.229737\pi$
$684$	0.867386	0.0331653
$685$	40.0596	1.53060
$686$	−4.09272	−0.156261
$687$	−25.3871	−0.968579
$688$	−2.42936	−0.0926186
$689$	10.1068	0.385039
$690$	−65.4729	−2.49251
$691$	11.0939	0.422030	0.211015	−	0.977483i	$-0.432323\pi$
$691$	11.0939	0.422030	0.211015	+	0.977483i	$0.432323\pi$
$692$	−21.4434	−0.815155
$693$	0.491341	0.0186645
$694$	32.6580	1.23968
$695$	−78.0585	−2.96093
$696$	−3.88373	−0.147212
$697$	−6.87086	−0.260253
$698$	−18.2934	−0.692417
$699$	−47.4206	−1.79361
$700$	2.76468	0.104495
$701$	1.99454	0.0753327	0.0376663	−	0.999290i	$-0.488008\pi$
$701$	1.99454	0.0753327	0.0376663	+	0.999290i	$0.488008\pi$
$702$	4.13013	0.155882
$703$	5.19300	0.195858
$704$	1.00000	0.0376889
$705$	−14.8489	−0.559240
$706$	4.80987	0.181022
$707$	−3.46395	−0.130275
$708$	16.7191	0.628344
$709$	−31.8701	−1.19691	−0.598453	−	0.801158i	$-0.704217\pi$
$709$	−31.8701	−1.19691	−0.598453	+	0.801158i	$0.704217\pi$
$710$	−16.2212	−0.608770
$711$	15.4510	0.579459
$712$	−12.5084	−0.468773
$713$	−72.5067	−2.71540
$714$	−0.758245	−0.0283766
$715$	−5.45397	−0.203967
$716$	24.8333	0.928064
$717$	−57.8602	−2.16083
$718$	30.2612	1.12934
$719$	15.1389	0.564584	0.282292	−	0.959329i	$-0.408905\pi$
$719$	15.1389	0.564584	0.282292	+	0.959329i	$0.408905\pi$
$720$	6.33824	0.236212
$721$	5.08161	0.189249
$722$	−18.7303	−0.697071
$723$	−8.66185	−0.322138
$724$	19.6875	0.731682
$725$	−16.8905	−0.627297
$726$	2.16110	0.0802059
$727$	48.9172	1.81424	0.907118	−	0.420876i	$-0.138277\pi$
$727$	48.9172	1.81424	0.907118	+	0.420876i	$0.138277\pi$
$728$	−0.422793	−0.0156697
$729$	−0.113101	−0.00418891
$730$	36.9367	1.36709
$731$	2.89768	0.107175
$732$	4.30784	0.159222
$733$	28.6181	1.05703	0.528516	−	0.848923i	$-0.322749\pi$
$733$	28.6181	1.05703	0.528516	+	0.848923i	$0.322749\pi$
$734$	−19.3686	−0.714907
$735$	−56.6934	−2.09117
$736$	−7.98409	−0.294297
$737$	8.39494	0.309232
$738$	9.62188	0.354186
$739$	42.9333	1.57933	0.789663	−	0.613541i	$-0.210255\pi$
$739$	42.9333	1.57933	0.789663	+	0.613541i	$0.210255\pi$
$740$	37.9467	1.39495
$741$	−1.61299	−0.0592546
$742$	−2.06843	−0.0759344
$743$	−40.1499	−1.47296	−0.736478	−	0.676462i	$-0.763512\pi$
$743$	−40.1499	−1.47296	−0.736478	+	0.676462i	$0.763512\pi$
$744$	19.6258	0.719517
$745$	−40.8112	−1.49521
$746$	8.53161	0.312364
$747$	−4.73176	−0.173126
$748$	−1.19277	−0.0436121
$749$	1.42719	0.0521483
$750$	36.0713	1.31714
$751$	48.4605	1.76835	0.884175	−	0.467156i	$-0.154722\pi$
$751$	48.4605	1.76835	0.884175	+	0.467156i	$0.154722\pi$
$752$	−1.81074	−0.0660310
$753$	37.6219	1.37102
$754$	2.58300	0.0940674
$755$	81.3180	2.95947
$756$	−0.845259	−0.0307418
$757$	−37.3585	−1.35782	−0.678909	−	0.734222i	$-0.737547\pi$
$757$	−37.3585	−1.35782	−0.678909	+	0.734222i	$0.737547\pi$
$758$	7.84577	0.284971
$759$	−17.2544	−0.626295
$760$	1.97046	0.0714761
$761$	−6.05639	−0.219544	−0.109772	−	0.993957i	$-0.535012\pi$
$761$	−6.05639	−0.219544	−0.109772	+	0.993957i	$0.535012\pi$
$762$	−46.5386	−1.68591
$763$	−3.05680	−0.110663
$764$	−22.1424	−0.801083
$765$	−7.56008	−0.273335
$766$	31.5783	1.14097
$767$	−11.1196	−0.401506
$768$	2.16110	0.0779819
$769$	19.8648	0.716344	0.358172	−	0.933656i	$-0.383400\pi$
$769$	19.8648	0.716344	0.358172	+	0.933656i	$0.383400\pi$
$770$	1.11619	0.0402247
$771$	54.2296	1.95303
$772$	−0.693053	−0.0249435
$773$	−29.3774	−1.05663	−0.528316	−	0.849048i	$-0.677177\pi$
$773$	−29.3774	−1.05663	−0.528316	+	0.849048i	$0.677177\pi$
$774$	−4.05788	−0.145857
$775$	85.3534	3.06599
$776$	−5.56390	−0.199732
$777$	6.35717	0.228062
$778$	4.25106	0.152408
$779$	2.99129	0.107174
$780$	−11.7866	−0.422026
$781$	−4.27485	−0.152966
$782$	9.52321	0.340549
$783$	5.16401	0.184547
$784$	−6.91347	−0.246910
$785$	29.8872	1.06672
$786$	−38.8230	−1.38477
$787$	50.9198	1.81510	0.907548	−	0.419949i	$-0.137952\pi$
$787$	50.9198	1.81510	0.907548	+	0.419949i	$0.137952\pi$
$788$	1.00000	0.0356235
$789$	11.6617	0.415167
$790$	35.1004	1.24882
$791$	−4.32656	−0.153835
$792$	1.67035	0.0593532
$793$	−2.86507	−0.101742
$794$	28.8173	1.02269
$795$	−57.6634	−2.04511
$796$	−8.10646	−0.287326
$797$	18.7469	0.664048	0.332024	−	0.943271i	$-0.392268\pi$
$797$	18.7469	0.664048	0.332024	+	0.943271i	$0.392268\pi$
$798$	0.330109	0.0116857
$799$	2.15981	0.0764085
$800$	9.39871	0.332295
$801$	−20.8934	−0.738232
$802$	10.5311	0.371867
$803$	9.73412	0.343510
$804$	18.1423	0.639830
$805$	−8.91176	−0.314098
$806$	−13.0528	−0.459765
$807$	64.1223	2.25721
$808$	−11.7759	−0.414276
$809$	−9.09627	−0.319808	−0.159904	−	0.987133i	$-0.551118\pi$
$809$	−9.09627	−0.319808	−0.159904	+	0.987133i	$0.551118\pi$
$810$	−42.5787	−1.49606
$811$	−1.40039	−0.0491742	−0.0245871	−	0.999698i	$-0.507827\pi$
$811$	−1.40039	−0.0491742	−0.0245871	+	0.999698i	$0.507827\pi$
$812$	−0.528629	−0.0185512
$813$	42.3282	1.48451
$814$	10.0003	0.350510
$815$	15.1161	0.529493
$816$	−2.57770	−0.0902376
$817$	−1.26153	−0.0441354
$818$	5.35631	0.187279
$819$	−0.706210	−0.0246770
$820$	21.8582	0.763323
$821$	10.9271	0.381359	0.190679	−	0.981652i	$-0.438931\pi$
$821$	10.9271	0.381359	0.190679	+	0.981652i	$0.438931\pi$
$822$	22.8149	0.795762
$823$	−33.3881	−1.16384	−0.581919	−	0.813247i	$-0.697698\pi$
$823$	−33.3881	−1.16384	−0.581919	+	0.813247i	$0.697698\pi$
$824$	17.2753	0.601812
$825$	20.3115	0.707157
$826$	2.27571	0.0791819
$827$	−21.2946	−0.740484	−0.370242	−	0.928935i	$-0.620725\pi$
$827$	−21.2946	−0.740484	−0.370242	+	0.928935i	$0.620725\pi$
$828$	−13.3362	−0.463465
$829$	−26.5666	−0.922696	−0.461348	−	0.887219i	$-0.652634\pi$
$829$	−26.5666	−0.922696	−0.461348	+	0.887219i	$0.652634\pi$
$830$	−10.7492	−0.373112
$831$	−29.4177	−1.02049
$832$	−1.43731	−0.0498298
$833$	8.24621	0.285714
$834$	−44.4563	−1.53939
$835$	−83.0620	−2.87448
$836$	0.519285	0.0179598
$837$	−26.0955	−0.901993
$838$	6.85695	0.236869
$839$	8.86235	0.305962	0.152981	−	0.988229i	$-0.451113\pi$
$839$	8.86235	0.305962	0.152981	+	0.988229i	$0.451113\pi$
$840$	2.41220	0.0832288
$841$	−25.7704	−0.888635
$842$	23.7722	0.819245
$843$	−12.2521	−0.421986
$844$	14.0002	0.481907
$845$	−41.4903	−1.42731
$846$	−3.02457	−0.103987
$847$	0.294155	0.0101073
$848$	−7.03176	−0.241472
$849$	−16.4625	−0.564993
$850$	−11.2105	−0.384518
$851$	−79.8431	−2.73699
$852$	−9.23837	−0.316501
$853$	−38.1622	−1.30665	−0.653325	−	0.757078i	$-0.726626\pi$
$853$	−38.1622	−1.30665	−0.653325	+	0.757078i	$0.726626\pi$
$854$	0.586356	0.0200647
$855$	3.29135	0.112562
$856$	4.85182	0.165832
$857$	−3.20648	−0.109531	−0.0547657	−	0.998499i	$-0.517441\pi$
$857$	−3.20648	−0.109531	−0.0547657	+	0.998499i	$0.517441\pi$
$858$	−3.10617	−0.106043
$859$	−32.5167	−1.10945	−0.554727	−	0.832032i	$-0.687177\pi$
$859$	−32.5167	−1.10945	−0.554727	+	0.832032i	$0.687177\pi$
$860$	−9.21838	−0.314344
$861$	3.66188	0.124797
$862$	−5.42594	−0.184808
$863$	−9.12391	−0.310581	−0.155291	−	0.987869i	$-0.549631\pi$
$863$	−9.12391	−0.310581	−0.155291	+	0.987869i	$0.549631\pi$
$864$	−2.87351	−0.0977589
$865$	−81.3683	−2.76660
$866$	−3.68077	−0.125078
$867$	−33.6641	−1.14329
$868$	2.67134	0.0906712
$869$	9.25019	0.313791
$870$	−14.7370	−0.499633
$871$	−12.0661	−0.408846
$872$	−10.3918	−0.351910
$873$	−9.29364	−0.314542
$874$	−4.14601	−0.140241
$875$	4.90980	0.165982
$876$	21.0364	0.710754
$877$	−29.3982	−0.992705	−0.496353	−	0.868121i	$-0.665328\pi$
$877$	−29.3982	−0.992705	−0.496353	+	0.868121i	$0.665328\pi$
$878$	34.6274	1.16862
$879$	−59.3009	−2.00017
$880$	3.79456	0.127915
$881$	−29.7775	−1.00323	−0.501614	−	0.865092i	$-0.667260\pi$
$881$	−29.7775	−1.00323	−0.501614	+	0.865092i	$0.667260\pi$
$882$	−11.5479	−0.388838
$883$	−31.7049	−1.06696	−0.533478	−	0.845814i	$-0.679115\pi$
$883$	−31.7049	−1.06696	−0.533478	+	0.845814i	$0.679115\pi$
$884$	1.71439	0.0576610
$885$	63.4418	2.13257
$886$	−24.0967	−0.809545
$887$	9.48606	0.318511	0.159255	−	0.987237i	$-0.449091\pi$
$887$	9.48606	0.318511	0.159255	+	0.987237i	$0.449091\pi$
$888$	21.6116	0.725238
$889$	−6.33454	−0.212454
$890$	−47.4640	−1.59100
$891$	−11.2210	−0.375917
$892$	−5.73370	−0.191978
$893$	−0.940291	−0.0314657
$894$	−23.2430	−0.777362
$895$	94.2315	3.14981
$896$	0.294155	0.00982704
$897$	24.7999	0.828045
$898$	16.0400	0.535261
$899$	−16.3202	−0.544311
$900$	15.6991	0.523303
$901$	8.38729	0.279421
$902$	5.76041	0.191801
$903$	−1.54434	−0.0513925
$904$	−14.7084	−0.489195
$905$	74.7056	2.48330
$906$	46.3126	1.53863
$907$	20.7101	0.687669	0.343834	−	0.939030i	$-0.388274\pi$
$907$	20.7101	0.687669	0.343834	+	0.939030i	$0.388274\pi$
$908$	−22.6820	−0.752729
$909$	−19.6699	−0.652409
$910$	−1.60431	−0.0531825
$911$	22.3094	0.739145	0.369572	−	0.929202i	$-0.379504\pi$
$911$	22.3094	0.739145	0.369572	+	0.929202i	$0.379504\pi$
$912$	1.12223	0.0371606
$913$	−2.83280	−0.0937520
$914$	−2.97503	−0.0984054
$915$	16.3464	0.540394
$916$	−11.7473	−0.388143
$917$	−5.28434	−0.174504
$918$	3.42745	0.113123
$919$	−47.0267	−1.55127	−0.775634	−	0.631182i	$-0.782570\pi$
$919$	−47.0267	−1.55127	−0.775634	+	0.631182i	$0.782570\pi$
$920$	−30.2961	−0.998833
$921$	−62.3721	−2.05523
$922$	8.21888	0.270674
$923$	6.14428	0.202242
$924$	0.635699	0.0209129
$925$	93.9898	3.09037
$926$	−11.9427	−0.392463
$927$	28.8557	0.947744
$928$	−1.79711	−0.0589929
$929$	−52.1286	−1.71028	−0.855142	−	0.518394i	$-0.826530\pi$
$929$	−52.1286	−1.71028	−0.855142	+	0.518394i	$0.826530\pi$
$930$	74.4713	2.44201
$931$	−3.59006	−0.117660
$932$	−21.9428	−0.718761
$933$	15.8879	0.520148
$934$	8.93708	0.292430
$935$	−4.52606	−0.148018
$936$	−2.40081	−0.0784728
$937$	21.0163	0.686574	0.343287	−	0.939231i	$-0.388460\pi$
$937$	21.0163	0.686574	0.343287	+	0.939231i	$0.388460\pi$
$938$	2.46942	0.0806293
$939$	17.3372	0.565777
$940$	−6.87098	−0.224107
$941$	−33.2662	−1.08445	−0.542223	−	0.840235i	$-0.682417\pi$
$941$	−33.2662	−1.08445	−0.542223	+	0.840235i	$0.682417\pi$
$942$	17.0215	0.554591
$943$	−45.9916	−1.49769
$944$	7.73641	0.251799
$945$	−3.20739	−0.104336
$946$	−2.42936	−0.0789854
$947$	−6.39952	−0.207956	−0.103978	−	0.994580i	$-0.533157\pi$
$947$	−6.39952	−0.207956	−0.103978	+	0.994580i	$0.533157\pi$
$948$	19.9906	0.649264
$949$	−13.9910	−0.454166
$950$	4.88061	0.158348
$951$	33.6745	1.09197
$952$	−0.350861	−0.0113715
$953$	42.2425	1.36837	0.684184	−	0.729310i	$-0.260159\pi$
$953$	42.2425	1.36837	0.684184	+	0.729310i	$0.260159\pi$
$954$	−11.7455	−0.380274
$955$	−84.0207	−2.71884
$956$	−26.7735	−0.865918
$957$	−3.88373	−0.125543
$958$	18.3830	0.593928
$959$	3.10543	0.100279
$960$	8.20043	0.264668
$961$	51.4718	1.66038
$962$	−14.3735	−0.463421
$963$	8.10422	0.261155
$964$	−4.00808	−0.129091
$965$	−2.62984	−0.0846574
$966$	−5.07547	−0.163301
$967$	31.3263	1.00739	0.503693	−	0.863883i	$-0.331974\pi$
$967$	31.3263	1.00739	0.503693	+	0.863883i	$0.331974\pi$
$968$	1.00000	0.0321412
$969$	−1.33856	−0.0430008
$970$	−21.1126	−0.677884
$971$	9.76382	0.313336	0.156668	−	0.987651i	$-0.449925\pi$
$971$	9.76382	0.313336	0.156668	+	0.987651i	$0.449925\pi$
$972$	−15.6291	−0.501304
$973$	−6.05111	−0.193990
$974$	25.8901	0.829572
$975$	−29.1940	−0.934956
$976$	1.99335	0.0638057
$977$	3.54673	0.113470	0.0567350	−	0.998389i	$-0.481931\pi$
$977$	3.54673	0.113470	0.0567350	+	0.998389i	$0.481931\pi$
$978$	8.60898	0.275285
$979$	−12.5084	−0.399771
$980$	−26.2336	−0.838002
$981$	−17.3579	−0.554194
$982$	19.1219	0.610203
$983$	−28.3779	−0.905113	−0.452556	−	0.891736i	$-0.649488\pi$
$983$	−28.3779	−0.905113	−0.452556	+	0.891736i	$0.649488\pi$
$984$	12.4488	0.396854
$985$	3.79456	0.120905
$986$	2.14354	0.0682643
$987$	−1.15109	−0.0366395
$988$	−0.746374	−0.0237453
$989$	19.3963	0.616765
$990$	6.33824	0.201442
$991$	38.6890	1.22900	0.614498	−	0.788919i	$-0.289359\pi$
$991$	38.6890	1.22900	0.614498	+	0.788919i	$0.289359\pi$
$992$	9.08140	0.288335
$993$	−27.5573	−0.874506
$994$	−1.25747	−0.0398845
$995$	−30.7605	−0.975173
$996$	−6.12196	−0.193982
$997$	29.6689	0.939623	0.469812	−	0.882767i	$-0.344322\pi$
$997$	29.6689	0.939623	0.469812	+	0.882767i	$0.344322\pi$
$998$	2.40377	0.0760899
$999$	−28.7359	−0.909165

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.g.1.18	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.g.1.18	✓	26	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.16110 q^{3} +1.00000 q^{4} +3.79456 q^{5} +2.16110 q^{6} +0.294155 q^{7} +1.00000 q^{8} +1.67035 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.16110 q^{3} +1.00000 q^{4} +3.79456 q^{5} +2.16110 q^{6} +0.294155 q^{7} +1.00000 q^{8} +1.67035 q^{9} +3.79456 q^{10} +1.00000 q^{11} +2.16110 q^{12} -1.43731 q^{13} +0.294155 q^{14} +8.20043 q^{15} +1.00000 q^{16} -1.19277 q^{17} +1.67035 q^{18} +0.519285 q^{19} +3.79456 q^{20} +0.635699 q^{21} +1.00000 q^{22} -7.98409 q^{23} +2.16110 q^{24} +9.39871 q^{25} -1.43731 q^{26} -2.87351 q^{27} +0.294155 q^{28} -1.79711 q^{29} +8.20043 q^{30} +9.08140 q^{31} +1.00000 q^{32} +2.16110 q^{33} -1.19277 q^{34} +1.11619 q^{35} +1.67035 q^{36} +10.0003 q^{37} +0.519285 q^{38} -3.10617 q^{39} +3.79456 q^{40} +5.76041 q^{41} +0.635699 q^{42} -2.42936 q^{43} +1.00000 q^{44} +6.33824 q^{45} -7.98409 q^{46} -1.81074 q^{47} +2.16110 q^{48} -6.91347 q^{49} +9.39871 q^{50} -2.57770 q^{51} -1.43731 q^{52} -7.03176 q^{53} -2.87351 q^{54} +3.79456 q^{55} +0.294155 q^{56} +1.12223 q^{57} -1.79711 q^{58} +7.73641 q^{59} +8.20043 q^{60} +1.99335 q^{61} +9.08140 q^{62} +0.491341 q^{63} +1.00000 q^{64} -5.45397 q^{65} +2.16110 q^{66} +8.39494 q^{67} -1.19277 q^{68} -17.2544 q^{69} +1.11619 q^{70} -4.27485 q^{71} +1.67035 q^{72} +9.73412 q^{73} +10.0003 q^{74} +20.3115 q^{75} +0.519285 q^{76} +0.294155 q^{77} -3.10617 q^{78} +9.25019 q^{79} +3.79456 q^{80} -11.2210 q^{81} +5.76041 q^{82} -2.83280 q^{83} +0.635699 q^{84} -4.52606 q^{85} -2.42936 q^{86} -3.88373 q^{87} +1.00000 q^{88} -12.5084 q^{89} +6.33824 q^{90} -0.422793 q^{91} -7.98409 q^{92} +19.6258 q^{93} -1.81074 q^{94} +1.97046 q^{95} +2.16110 q^{96} -5.56390 q^{97} -6.91347 q^{98} +1.67035 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9}+O(q^{10}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9} + 13 q^{10} + 26 q^{11} + 12 q^{12} + 24 q^{13} + 13 q^{14} + 12 q^{15} + 26 q^{16} + q^{17} + 38 q^{18} + 24 q^{19} + 13 q^{20} + 5 q^{21} + 26 q^{22} + 19 q^{23} + 12 q^{24} + 35 q^{25} + 24 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 12 q^{30} + 34 q^{31} + 26 q^{32} + 12 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} + 15 q^{37} + 24 q^{38} + 3 q^{39} + 13 q^{40} - 9 q^{41} + 5 q^{42} + 6 q^{43} + 26 q^{44} + 22 q^{45} + 19 q^{46} + 34 q^{47} + 12 q^{48} + 53 q^{49} + 35 q^{50} - 2 q^{51} + 24 q^{52} + 6 q^{53} + 39 q^{54} + 13 q^{55} + 13 q^{56} - 16 q^{57} + 5 q^{58} + 50 q^{59} + 12 q^{60} + 26 q^{61} + 34 q^{62} + 2 q^{63} + 26 q^{64} - 5 q^{65} + 12 q^{66} + 18 q^{67} + q^{68} + 15 q^{69} + 14 q^{70} + 23 q^{71} + 38 q^{72} + 37 q^{73} + 15 q^{74} + 18 q^{75} + 24 q^{76} + 13 q^{77} + 3 q^{78} + 10 q^{79} + 13 q^{80} + 50 q^{81} - 9 q^{82} + 7 q^{83} + 5 q^{84} - 7 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{88} + 3 q^{89} + 22 q^{90} + 31 q^{91} + 19 q^{92} + 52 q^{93} + 34 q^{94} + 9 q^{95} + 12 q^{96} - 9 q^{97} + 53 q^{98} + 38 q^{99}+O(q^{100}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9 + 13 * q^10 + 26 * q^11 + 12 * q^12 + 24 * q^13 + 13 * q^14 + 12 * q^15 + 26 * q^16 + q^17 + 38 * q^18 + 24 * q^19 + 13 * q^20 + 5 * q^21 + 26 * q^22 + 19 * q^23 + 12 * q^24 + 35 * q^25 + 24 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 12 * q^30 + 34 * q^31 + 26 * q^32 + 12 * q^33 + q^34 + 14 * q^35 + 38 * q^36 + 15 * q^37 + 24 * q^38 + 3 * q^39 + 13 * q^40 - 9 * q^41 + 5 * q^42 + 6 * q^43 + 26 * q^44 + 22 * q^45 + 19 * q^46 + 34 * q^47 + 12 * q^48 + 53 * q^49 + 35 * q^50 - 2 * q^51 + 24 * q^52 + 6 * q^53 + 39 * q^54 + 13 * q^55 + 13 * q^56 - 16 * q^57 + 5 * q^58 + 50 * q^59 + 12 * q^60 + 26 * q^61 + 34 * q^62 + 2 * q^63 + 26 * q^64 - 5 * q^65 + 12 * q^66 + 18 * q^67 + q^68 + 15 * q^69 + 14 * q^70 + 23 * q^71 + 38 * q^72 + 37 * q^73 + 15 * q^74 + 18 * q^75 + 24 * q^76 + 13 * q^77 + 3 * q^78 + 10 * q^79 + 13 * q^80 + 50 * q^81 - 9 * q^82 + 7 * q^83 + 5 * q^84 - 7 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^88 + 3 * q^89 + 22 * q^90 + 31 * q^91 + 19 * q^92 + 52 * q^93 + 34 * q^94 + 9 * q^95 + 12 * q^96 - 9 * q^97 + 53 * q^98 + 38 * q^99

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