LMFDB - Embedded newform 385.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [385,2,Mod(1,385)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(385, 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("385.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.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:	$3.07424047782$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.48119$ of defining polynomial
Character	$\chi$	$=$	385.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67513 q^{2} -2.48119 q^{3} +5.15633 q^{4} -1.00000 q^{5} +6.63752 q^{6} -1.00000 q^{7} -8.44358 q^{8} +3.15633 q^{9} +O(q^{10})$	\(q-2.67513 q^{2} -2.48119 q^{3} +5.15633 q^{4} -1.00000 q^{5} +6.63752 q^{6} -1.00000 q^{7} -8.44358 q^{8} +3.15633 q^{9} +2.67513 q^{10} -1.00000 q^{11} -12.7938 q^{12} +5.83146 q^{13} +2.67513 q^{14} +2.48119 q^{15} +12.2750 q^{16} +5.44358 q^{17} -8.44358 q^{18} -1.35026 q^{19} -5.15633 q^{20} +2.48119 q^{21} +2.67513 q^{22} -3.19394 q^{23} +20.9502 q^{24} +1.00000 q^{25} -15.5999 q^{26} -0.387873 q^{27} -5.15633 q^{28} -3.61213 q^{29} -6.63752 q^{30} -5.28726 q^{31} -15.9502 q^{32} +2.48119 q^{33} -14.5623 q^{34} +1.00000 q^{35} +16.2750 q^{36} -8.54420 q^{37} +3.61213 q^{38} -14.4690 q^{39} +8.44358 q^{40} -5.02539 q^{41} -6.63752 q^{42} +5.89446 q^{43} -5.15633 q^{44} -3.15633 q^{45} +8.54420 q^{46} -11.8315 q^{47} -30.4568 q^{48} +1.00000 q^{49} -2.67513 q^{50} -13.5066 q^{51} +30.0689 q^{52} -0.231548 q^{53} +1.03761 q^{54} +1.00000 q^{55} +8.44358 q^{56} +3.35026 q^{57} +9.66291 q^{58} +13.5999 q^{59} +12.7938 q^{60} -1.41327 q^{61} +14.1441 q^{62} -3.15633 q^{63} +18.1187 q^{64} -5.83146 q^{65} -6.63752 q^{66} -10.8568 q^{67} +28.0689 q^{68} +7.92478 q^{69} -2.67513 q^{70} -15.5369 q^{71} -26.6507 q^{72} -11.3684 q^{73} +22.8568 q^{74} -2.48119 q^{75} -6.96239 q^{76} +1.00000 q^{77} +38.7064 q^{78} +1.96968 q^{79} -12.2750 q^{80} -8.50659 q^{81} +13.4436 q^{82} +10.6253 q^{83} +12.7938 q^{84} -5.44358 q^{85} -15.7685 q^{86} +8.96239 q^{87} +8.44358 q^{88} +7.22425 q^{89} +8.44358 q^{90} -5.83146 q^{91} -16.4690 q^{92} +13.1187 q^{93} +31.6507 q^{94} +1.35026 q^{95} +39.5755 q^{96} -0.836381 q^{97} -2.67513 q^{98} -3.15633 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 2 q^{3} + 5 q^{4} - 3 q^{5} + 4 q^{6} - 3 q^{7} - 9 q^{8} - q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 2 * q^3 + 5 * q^4 - 3 * q^5 + 4 * q^6 - 3 * q^7 - 9 * q^8 - q^9	\( 3 q - 3 q^{2} - 2 q^{3} + 5 q^{4} - 3 q^{5} + 4 q^{6} - 3 q^{7} - 9 q^{8} - q^{9} + 3 q^{10} - 3 q^{11} - 12 q^{12} + 2 q^{13} + 3 q^{14} + 2 q^{15} + 5 q^{16} - 9 q^{18} + 6 q^{19} - 5 q^{20} + 2 q^{21} + 3 q^{22} - 10 q^{23} + 26 q^{24} + 3 q^{25} - 20 q^{26} - 2 q^{27} - 5 q^{28} - 10 q^{29} - 4 q^{30} - 10 q^{31} - 11 q^{32} + 2 q^{33} - 6 q^{34} + 3 q^{35} + 17 q^{36} - 16 q^{37} + 10 q^{38} - 12 q^{39} + 9 q^{40} - 4 q^{42} - 2 q^{43} - 5 q^{44} + q^{45} + 16 q^{46} - 20 q^{47} - 34 q^{48} + 3 q^{49} - 3 q^{50} - 20 q^{51} + 32 q^{52} - 12 q^{53} + 14 q^{54} + 3 q^{55} + 9 q^{56} - 2 q^{58} + 14 q^{59} + 12 q^{60} + 10 q^{61} + 6 q^{62} + q^{63} + 33 q^{64} - 2 q^{65} - 4 q^{66} - 2 q^{67} + 26 q^{68} + 2 q^{69} - 3 q^{70} - 24 q^{71} - 23 q^{72} + 4 q^{73} + 38 q^{74} - 2 q^{75} - 10 q^{76} + 3 q^{77} + 42 q^{78} + 8 q^{79} - 5 q^{80} - 5 q^{81} + 24 q^{82} - 10 q^{83} + 12 q^{84} - 36 q^{86} + 16 q^{87} + 9 q^{88} + 20 q^{89} + 9 q^{90} - 2 q^{91} - 18 q^{92} + 18 q^{93} + 38 q^{94} - 6 q^{95} + 40 q^{96} - 3 q^{98} + q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 2 * q^3 + 5 * q^4 - 3 * q^5 + 4 * q^6 - 3 * q^7 - 9 * q^8 - q^9 + 3 * q^10 - 3 * q^11 - 12 * q^12 + 2 * q^13 + 3 * q^14 + 2 * q^15 + 5 * q^16 - 9 * q^18 + 6 * q^19 - 5 * q^20 + 2 * q^21 + 3 * q^22 - 10 * q^23 + 26 * q^24 + 3 * q^25 - 20 * q^26 - 2 * q^27 - 5 * q^28 - 10 * q^29 - 4 * q^30 - 10 * q^31 - 11 * q^32 + 2 * q^33 - 6 * q^34 + 3 * q^35 + 17 * q^36 - 16 * q^37 + 10 * q^38 - 12 * q^39 + 9 * q^40 - 4 * q^42 - 2 * q^43 - 5 * q^44 + q^45 + 16 * q^46 - 20 * q^47 - 34 * q^48 + 3 * q^49 - 3 * q^50 - 20 * q^51 + 32 * q^52 - 12 * q^53 + 14 * q^54 + 3 * q^55 + 9 * q^56 - 2 * q^58 + 14 * q^59 + 12 * q^60 + 10 * q^61 + 6 * q^62 + q^63 + 33 * q^64 - 2 * q^65 - 4 * q^66 - 2 * q^67 + 26 * q^68 + 2 * q^69 - 3 * q^70 - 24 * q^71 - 23 * q^72 + 4 * q^73 + 38 * q^74 - 2 * q^75 - 10 * q^76 + 3 * q^77 + 42 * q^78 + 8 * q^79 - 5 * q^80 - 5 * q^81 + 24 * q^82 - 10 * q^83 + 12 * q^84 - 36 * q^86 + 16 * q^87 + 9 * q^88 + 20 * q^89 + 9 * q^90 - 2 * q^91 - 18 * q^92 + 18 * q^93 + 38 * q^94 - 6 * q^95 + 40 * q^96 - 3 * q^98 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.67513	−1.89160	−0.945802	−	0.324745i	$-0.894721\pi$
$2$	−2.67513	−1.89160	−0.945802	+	0.324745i	$0.894721\pi$
$3$	−2.48119	−1.43252	−0.716259	−	0.697834i	$-0.754147\pi$
$3$	−2.48119	−1.43252	−0.716259	+	0.697834i	$0.754147\pi$
$4$	5.15633	2.57816
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	6.63752	2.70976
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−8.44358	−2.98526
$9$	3.15633	1.05211
$10$	2.67513	0.845951
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−12.7938	−3.69326
$13$	5.83146	1.61735	0.808677	−	0.588252i	$-0.200184\pi$
$13$	5.83146	1.61735	0.808677	+	0.588252i	$0.200184\pi$
$14$	2.67513	0.714959
$15$	2.48119	0.640642
$16$	12.2750	3.06876
$17$	5.44358	1.32026	0.660131	−	0.751150i	$-0.270501\pi$
$17$	5.44358	1.32026	0.660131	+	0.751150i	$0.270501\pi$
$18$	−8.44358	−1.99017
$19$	−1.35026	−0.309771	−0.154886	−	0.987932i	$-0.549501\pi$
$19$	−1.35026	−0.309771	−0.154886	+	0.987932i	$0.549501\pi$
$20$	−5.15633	−1.15299
$21$	2.48119	0.541441
$22$	2.67513	0.570340
$23$	−3.19394	−0.665982	−0.332991	−	0.942930i	$-0.608058\pi$
$23$	−3.19394	−0.665982	−0.332991	+	0.942930i	$0.608058\pi$
$24$	20.9502	4.27644
$25$	1.00000	0.200000
$26$	−15.5999	−3.05939
$27$	−0.387873	−0.0746462
$28$	−5.15633	−0.974454
$29$	−3.61213	−0.670755	−0.335378	−	0.942084i	$-0.608864\pi$
$29$	−3.61213	−0.670755	−0.335378	+	0.942084i	$0.608864\pi$
$30$	−6.63752	−1.21184
$31$	−5.28726	−0.949620	−0.474810	−	0.880088i	$-0.657483\pi$
$31$	−5.28726	−0.949620	−0.474810	+	0.880088i	$0.657483\pi$
$32$	−15.9502	−2.81962
$33$	2.48119	0.431920
$34$	−14.5623	−2.49741
$35$	1.00000	0.169031
$36$	16.2750	2.71251
$37$	−8.54420	−1.40466	−0.702329	−	0.711853i	$-0.747856\pi$
$37$	−8.54420	−1.40466	−0.702329	+	0.711853i	$0.747856\pi$
$38$	3.61213	0.585964
$39$	−14.4690	−2.31689
$40$	8.44358	1.33505
$41$	−5.02539	−0.784834	−0.392417	−	0.919787i	$-0.628361\pi$
$41$	−5.02539	−0.784834	−0.392417	+	0.919787i	$0.628361\pi$
$42$	−6.63752	−1.02419
$43$	5.89446	0.898897	0.449448	−	0.893306i	$-0.351621\pi$
$43$	5.89446	0.898897	0.449448	+	0.893306i	$0.351621\pi$
$44$	−5.15633	−0.777345
$45$	−3.15633	−0.470517
$46$	8.54420	1.25977
$47$	−11.8315	−1.72580	−0.862898	−	0.505379i	$-0.831353\pi$
$47$	−11.8315	−1.72580	−0.862898	+	0.505379i	$0.831353\pi$
$48$	−30.4568	−4.39605
$49$	1.00000	0.142857
$50$	−2.67513	−0.378321
$51$	−13.5066	−1.89130
$52$	30.0689	4.16980
$53$	−0.231548	−0.0318056	−0.0159028	−	0.999874i	$-0.505062\pi$
$53$	−0.231548	−0.0318056	−0.0159028	+	0.999874i	$0.505062\pi$
$54$	1.03761	0.141201
$55$	1.00000	0.134840
$56$	8.44358	1.12832
$57$	3.35026	0.443753
$58$	9.66291	1.26880
$59$	13.5999	1.77056	0.885279	−	0.465061i	$-0.153968\pi$
$59$	13.5999	1.77056	0.885279	+	0.465061i	$0.153968\pi$
$60$	12.7938	1.65168
$61$	−1.41327	−0.180950	−0.0904751	−	0.995899i	$-0.528839\pi$
$61$	−1.41327	−0.180950	−0.0904751	+	0.995899i	$0.528839\pi$
$62$	14.1441	1.79630
$63$	−3.15633	−0.397660
$64$	18.1187	2.26484
$65$	−5.83146	−0.723303
$66$	−6.63752	−0.817022
$67$	−10.8568	−1.32638	−0.663188	−	0.748453i	$-0.730797\pi$
$67$	−10.8568	−1.32638	−0.663188	+	0.748453i	$0.730797\pi$
$68$	28.0689	3.40385
$69$	7.92478	0.954031
$70$	−2.67513	−0.319739
$71$	−15.5369	−1.84389	−0.921946	−	0.387319i	$-0.873401\pi$
$71$	−15.5369	−1.84389	−0.921946	+	0.387319i	$0.873401\pi$
$72$	−26.6507	−3.14081
$73$	−11.3684	−1.33057	−0.665283	−	0.746591i	$-0.731689\pi$
$73$	−11.3684	−1.33057	−0.665283	+	0.746591i	$0.731689\pi$
$74$	22.8568	2.65705
$75$	−2.48119	−0.286504
$76$	−6.96239	−0.798641
$77$	1.00000	0.113961
$78$	38.7064	4.38264
$79$	1.96968	0.221607	0.110803	−	0.993842i	$-0.464658\pi$
$79$	1.96968	0.221607	0.110803	+	0.993842i	$0.464658\pi$
$80$	−12.2750	−1.37239
$81$	−8.50659	−0.945176
$82$	13.4436	1.48460
$83$	10.6253	1.16628	0.583139	−	0.812372i	$-0.301824\pi$
$83$	10.6253	1.16628	0.583139	+	0.812372i	$0.301824\pi$
$84$	12.7938	1.39592
$85$	−5.44358	−0.590439
$86$	−15.7685	−1.70036
$87$	8.96239	0.960869
$88$	8.44358	0.900089
$89$	7.22425	0.765769	0.382885	−	0.923796i	$-0.374931\pi$
$89$	7.22425	0.765769	0.382885	+	0.923796i	$0.374931\pi$
$90$	8.44358	0.890032
$91$	−5.83146	−0.611303
$92$	−16.4690	−1.71701
$93$	13.1187	1.36035
$94$	31.6507	3.26452
$95$	1.35026	0.138534
$96$	39.5755	4.03915
$97$	−0.836381	−0.0849216	−0.0424608	−	0.999098i	$-0.513520\pi$
$97$	−0.836381	−0.0849216	−0.0424608	+	0.999098i	$0.513520\pi$
$98$	−2.67513	−0.270229
$99$	−3.15633	−0.317223
$100$	5.15633	0.515633
$101$	7.41327	0.737648	0.368824	−	0.929499i	$-0.379761\pi$
$101$	7.41327	0.737648	0.368824	+	0.929499i	$0.379761\pi$
$102$	36.1319	3.57759
$103$	4.21933	0.415743	0.207871	−	0.978156i	$-0.433346\pi$
$103$	4.21933	0.415743	0.207871	+	0.978156i	$0.433346\pi$
$104$	−49.2384	−4.82822
$105$	−2.48119	−0.242140
$106$	0.619421	0.0601635
$107$	−11.5369	−1.11531	−0.557657	−	0.830071i	$-0.688300\pi$
$107$	−11.5369	−1.11531	−0.557657	+	0.830071i	$0.688300\pi$
$108$	−2.00000	−0.192450
$109$	−2.18664	−0.209442	−0.104721	−	0.994502i	$-0.533395\pi$
$109$	−2.18664	−0.209442	−0.104721	+	0.994502i	$0.533395\pi$
$110$	−2.67513	−0.255064
$111$	21.1998	2.01220
$112$	−12.2750	−1.15988
$113$	−9.35026	−0.879599	−0.439799	−	0.898096i	$-0.644950\pi$
$113$	−9.35026	−0.879599	−0.439799	+	0.898096i	$0.644950\pi$
$114$	−8.96239	−0.839405
$115$	3.19394	0.297836
$116$	−18.6253	−1.72932
$117$	18.4060	1.70163
$118$	−36.3815	−3.34919
$119$	−5.44358	−0.499012
$120$	−20.9502	−1.91248
$121$	1.00000	0.0909091
$122$	3.78067	0.342286
$123$	12.4690	1.12429
$124$	−27.2628	−2.44827
$125$	−1.00000	−0.0894427
$126$	8.44358	0.752214
$127$	−16.9624	−1.50517	−0.752584	−	0.658496i	$-0.771193\pi$
$127$	−16.9624	−1.50517	−0.752584	+	0.658496i	$0.771193\pi$
$128$	−16.5696	−1.46456
$129$	−14.6253	−1.28769
$130$	15.5999	1.36820
$131$	−9.92478	−0.867132	−0.433566	−	0.901122i	$-0.642745\pi$
$131$	−9.92478	−0.867132	−0.433566	+	0.901122i	$0.642745\pi$
$132$	12.7938	1.11356
$133$	1.35026	0.117083
$134$	29.0435	2.50898
$135$	0.387873	0.0333828
$136$	−45.9633	−3.94132
$137$	−10.9927	−0.939170	−0.469585	−	0.882887i	$-0.655596\pi$
$137$	−10.9927	−0.939170	−0.469585	+	0.882887i	$0.655596\pi$
$138$	−21.1998	−1.80465
$139$	6.88717	0.584162	0.292081	−	0.956394i	$-0.405652\pi$
$139$	6.88717	0.584162	0.292081	+	0.956394i	$0.405652\pi$
$140$	5.15633	0.435789
$141$	29.3561	2.47223
$142$	41.5633	3.48791
$143$	−5.83146	−0.487651
$144$	38.7440	3.22867
$145$	3.61213	0.299971
$146$	30.4119	2.51690
$147$	−2.48119	−0.204645
$148$	−44.0567	−3.62144
$149$	22.8119	1.86883	0.934414	−	0.356190i	$-0.115924\pi$
$149$	22.8119	1.86883	0.934414	+	0.356190i	$0.115924\pi$
$150$	6.63752	0.541951
$151$	−3.24472	−0.264052	−0.132026	−	0.991246i	$-0.542148\pi$
$151$	−3.24472	−0.264052	−0.132026	+	0.991246i	$0.542148\pi$
$152$	11.4010	0.924747
$153$	17.1817	1.38906
$154$	−2.67513	−0.215568
$155$	5.28726	0.424683
$156$	−74.6067	−5.97332
$157$	−5.42548	−0.433001	−0.216500	−	0.976283i	$-0.569464\pi$
$157$	−5.42548	−0.433001	−0.216500	+	0.976283i	$0.569464\pi$
$158$	−5.26916	−0.419192
$159$	0.574515	0.0455620
$160$	15.9502	1.26097
$161$	3.19394	0.251717
$162$	22.7562	1.78790
$163$	3.38058	0.264787	0.132394	−	0.991197i	$-0.457734\pi$
$163$	3.38058	0.264787	0.132394	+	0.991197i	$0.457734\pi$
$164$	−25.9126	−2.02343
$165$	−2.48119	−0.193161
$166$	−28.4241	−2.20614
$167$	11.2750	0.872489	0.436244	−	0.899828i	$-0.356308\pi$
$167$	11.2750	0.872489	0.436244	+	0.899828i	$0.356308\pi$
$168$	−20.9502	−1.61634
$169$	21.0059	1.61584
$170$	14.5623	1.11688
$171$	−4.26187	−0.325913
$172$	30.3938	2.31750
$173$	−8.98049	−0.682774	−0.341387	−	0.939923i	$-0.610897\pi$
$173$	−8.98049	−0.682774	−0.341387	+	0.939923i	$0.610897\pi$
$174$	−23.9756	−1.81758
$175$	−1.00000	−0.0755929
$176$	−12.2750	−0.925266
$177$	−33.7440	−2.53636
$178$	−19.3258	−1.44853
$179$	−26.2374	−1.96108	−0.980539	−	0.196326i	$-0.937099\pi$
$179$	−26.2374	−1.96108	−0.980539	+	0.196326i	$0.937099\pi$
$180$	−16.2750	−1.21307
$181$	−11.1998	−0.832476	−0.416238	−	0.909256i	$-0.636652\pi$
$181$	−11.1998	−0.832476	−0.416238	+	0.909256i	$0.636652\pi$
$182$	15.5999	1.15634
$183$	3.50659	0.259214
$184$	26.9683	1.98813
$185$	8.54420	0.628182
$186$	−35.0943	−2.57324
$187$	−5.44358	−0.398074
$188$	−61.0068	−4.44938
$189$	0.387873	0.0282136
$190$	−3.61213	−0.262051
$191$	11.1998	0.810390	0.405195	−	0.914230i	$-0.367204\pi$
$191$	11.1998	0.810390	0.405195	+	0.914230i	$0.367204\pi$
$192$	−44.9560	−3.24442
$193$	0.604833	0.0435368	0.0217684	−	0.999763i	$-0.493070\pi$
$193$	0.604833	0.0435368	0.0217684	+	0.999763i	$0.493070\pi$
$194$	2.23743	0.160638
$195$	14.4690	1.03614
$196$	5.15633	0.368309
$197$	15.3054	1.09046	0.545231	−	0.838286i	$-0.316442\pi$
$197$	15.3054	1.09046	0.545231	+	0.838286i	$0.316442\pi$
$198$	8.44358	0.600059
$199$	−12.5623	−0.890518	−0.445259	−	0.895402i	$-0.646888\pi$
$199$	−12.5623	−0.890518	−0.445259	+	0.895402i	$0.646888\pi$
$200$	−8.44358	−0.597051
$201$	26.9380	1.90006
$202$	−19.8315	−1.39534
$203$	3.61213	0.253522
$204$	−69.6444	−4.87608
$205$	5.02539	0.350989
$206$	−11.2873	−0.786421
$207$	−10.0811	−0.700685
$208$	71.5814	4.96327
$209$	1.35026	0.0933996
$210$	6.63752	0.458032
$211$	−4.43866	−0.305570	−0.152785	−	0.988259i	$-0.548824\pi$
$211$	−4.43866	−0.305570	−0.152785	+	0.988259i	$0.548824\pi$
$212$	−1.19394	−0.0819999
$213$	38.5501	2.64141
$214$	30.8627	2.10973
$215$	−5.89446	−0.401999
$216$	3.27504	0.222838
$217$	5.28726	0.358922
$218$	5.84955	0.396182
$219$	28.2071	1.90606
$220$	5.15633	0.347639
$221$	31.7440	2.13533
$222$	−56.7123	−3.80628
$223$	−7.78067	−0.521032	−0.260516	−	0.965469i	$-0.583893\pi$
$223$	−7.78067	−0.521032	−0.260516	+	0.965469i	$0.583893\pi$
$224$	15.9502	1.06572
$225$	3.15633	0.210422
$226$	25.0132	1.66385
$227$	−10.4485	−0.693492	−0.346746	−	0.937959i	$-0.612713\pi$
$227$	−10.4485	−0.693492	−0.346746	+	0.937959i	$0.612713\pi$
$228$	17.2750	1.14407
$229$	−29.4518	−1.94623	−0.973116	−	0.230316i	$-0.926024\pi$
$229$	−29.4518	−1.94623	−0.973116	+	0.230316i	$0.926024\pi$
$230$	−8.54420	−0.563388
$231$	−2.48119	−0.163251
$232$	30.4993	2.00238
$233$	−8.73084	−0.571976	−0.285988	−	0.958233i	$-0.592322\pi$
$233$	−8.73084	−0.571976	−0.285988	+	0.958233i	$0.592322\pi$
$234$	−49.2384	−3.21881
$235$	11.8315	0.771799
$236$	70.1255	4.56478
$237$	−4.88717	−0.317456
$238$	14.5623	0.943933
$239$	−21.2144	−1.37225	−0.686123	−	0.727486i	$-0.740689\pi$
$239$	−21.2144	−1.37225	−0.686123	+	0.727486i	$0.740689\pi$
$240$	30.4568	1.96598
$241$	−9.33804	−0.601516	−0.300758	−	0.953700i	$-0.597240\pi$
$241$	−9.33804	−0.601516	−0.300758	+	0.953700i	$0.597240\pi$
$242$	−2.67513	−0.171964
$243$	22.2701	1.42863
$244$	−7.28726	−0.466519
$245$	−1.00000	−0.0638877
$246$	−33.3561	−2.12671
$247$	−7.87399	−0.501010
$248$	44.6434	2.83486
$249$	−26.3634	−1.67071
$250$	2.67513	0.169190
$251$	1.87636	0.118435	0.0592174	−	0.998245i	$-0.481139\pi$
$251$	1.87636	0.118435	0.0592174	+	0.998245i	$0.481139\pi$
$252$	−16.2750	−1.02523
$253$	3.19394	0.200801
$254$	45.3766	2.84718
$255$	13.5066	0.845815
$256$	8.08840	0.505525
$257$	27.1392	1.69290	0.846448	−	0.532472i	$-0.178737\pi$
$257$	27.1392	1.69290	0.846448	+	0.532472i	$0.178737\pi$
$258$	39.1246	2.43579
$259$	8.54420	0.530911
$260$	−30.0689	−1.86479
$261$	−11.4010	−0.705707
$262$	26.5501	1.64027
$263$	12.8119	0.790018	0.395009	−	0.918677i	$-0.370741\pi$
$263$	12.8119	0.790018	0.395009	+	0.918677i	$0.370741\pi$
$264$	−20.9502	−1.28939
$265$	0.231548	0.0142239
$266$	−3.61213	−0.221474
$267$	−17.9248	−1.09698
$268$	−55.9814	−3.41961
$269$	−6.26187	−0.381793	−0.190896	−	0.981610i	$-0.561139\pi$
$269$	−6.26187	−0.381793	−0.190896	+	0.981610i	$0.561139\pi$
$270$	−1.03761	−0.0631470
$271$	−5.73813	−0.348567	−0.174283	−	0.984696i	$-0.555761\pi$
$271$	−5.73813	−0.348567	−0.174283	+	0.984696i	$0.555761\pi$
$272$	66.8202	4.05157
$273$	14.4690	0.875702
$274$	29.4069	1.77654
$275$	−1.00000	−0.0603023
$276$	40.8627	2.45965
$277$	−8.35756	−0.502157	−0.251078	−	0.967967i	$-0.580785\pi$
$277$	−8.35756	−0.502157	−0.251078	+	0.967967i	$0.580785\pi$
$278$	−18.4241	−1.10500
$279$	−16.6883	−0.999103
$280$	−8.44358	−0.504601
$281$	−8.44851	−0.503996	−0.251998	−	0.967728i	$-0.581088\pi$
$281$	−8.44851	−0.503996	−0.251998	+	0.967728i	$0.581088\pi$
$282$	−78.5315	−4.67648
$283$	0.836381	0.0497177	0.0248588	−	0.999691i	$-0.492086\pi$
$283$	0.836381	0.0497177	0.0248588	+	0.999691i	$0.492086\pi$
$284$	−80.1133	−4.75385
$285$	−3.35026	−0.198452
$286$	15.5999	0.922442
$287$	5.02539	0.296640
$288$	−50.3439	−2.96654
$289$	12.6326	0.743094
$290$	−9.66291	−0.567426
$291$	2.07522	0.121652
$292$	−58.6190	−3.43042
$293$	−2.71862	−0.158824	−0.0794118	−	0.996842i	$-0.525304\pi$
$293$	−2.71862	−0.158824	−0.0794118	+	0.996842i	$0.525304\pi$
$294$	6.63752	0.387108
$295$	−13.5999	−0.791817
$296$	72.1436	4.19326
$297$	0.387873	0.0225067
$298$	−61.0249	−3.53508
$299$	−18.6253	−1.07713
$300$	−12.7938	−0.738653
$301$	−5.89446	−0.339751
$302$	8.68006	0.499481
$303$	−18.3938	−1.05669
$304$	−16.5745	−0.950614
$305$	1.41327	0.0809234
$306$	−45.9633	−2.62755
$307$	−8.36344	−0.477326	−0.238663	−	0.971102i	$-0.576709\pi$
$307$	−8.36344	−0.477326	−0.238663	+	0.971102i	$0.576709\pi$
$308$	5.15633	0.293809
$309$	−10.4690	−0.595559
$310$	−14.1441	−0.803331
$311$	4.43629	0.251559	0.125779	−	0.992058i	$-0.459857\pi$
$311$	4.43629	0.251559	0.125779	+	0.992058i	$0.459857\pi$
$312$	122.170	6.91651
$313$	29.7889	1.68377	0.841885	−	0.539658i	$-0.181446\pi$
$313$	29.7889	1.68377	0.841885	+	0.539658i	$0.181446\pi$
$314$	14.5139	0.819066
$315$	3.15633	0.177839
$316$	10.1563	0.571338
$317$	15.4010	0.865009	0.432504	−	0.901632i	$-0.357630\pi$
$317$	15.4010	0.865009	0.432504	+	0.901632i	$0.357630\pi$
$318$	−1.53690	−0.0861853
$319$	3.61213	0.202240
$320$	−18.1187	−1.01287
$321$	28.6253	1.59771
$322$	−8.54420	−0.476150
$323$	−7.35026	−0.408980
$324$	−43.8627	−2.43682
$325$	5.83146	0.323471
$326$	−9.04349	−0.500873
$327$	5.42548	0.300030
$328$	42.4323	2.34293
$329$	11.8315	0.652289
$330$	6.63752	0.365383
$331$	6.26187	0.344183	0.172092	−	0.985081i	$-0.444947\pi$
$331$	6.26187	0.344183	0.172092	+	0.985081i	$0.444947\pi$
$332$	54.7875	3.00685
$333$	−26.9683	−1.47785
$334$	−30.1622	−1.65040
$335$	10.8568	0.593173
$336$	30.4568	1.66155
$337$	−15.8700	−0.864495	−0.432248	−	0.901755i	$-0.642279\pi$
$337$	−15.8700	−0.864495	−0.432248	+	0.901755i	$0.642279\pi$
$338$	−56.1935	−3.05652
$339$	23.1998	1.26004
$340$	−28.0689	−1.52225
$341$	5.28726	0.286321
$342$	11.4010	0.616498
$343$	−1.00000	−0.0539949
$344$	−49.7704	−2.68344
$345$	−7.92478	−0.426656
$346$	24.0240	1.29154
$347$	6.79147	0.364585	0.182293	−	0.983244i	$-0.441648\pi$
$347$	6.79147	0.364585	0.182293	+	0.983244i	$0.441648\pi$
$348$	46.2130	2.47728
$349$	26.7489	1.43184	0.715919	−	0.698183i	$-0.246008\pi$
$349$	26.7489	1.43184	0.715919	+	0.698183i	$0.246008\pi$
$350$	2.67513	0.142992
$351$	−2.26187	−0.120729
$352$	15.9502	0.850147
$353$	−16.8627	−0.897512	−0.448756	−	0.893654i	$-0.648133\pi$
$353$	−16.8627	−0.897512	−0.448756	+	0.893654i	$0.648133\pi$
$354$	90.2697	4.79778
$355$	15.5369	0.824613
$356$	37.2506	1.97428
$357$	13.5066	0.714844
$358$	70.1886	3.70958
$359$	−3.79289	−0.200181	−0.100091	−	0.994978i	$-0.531913\pi$
$359$	−3.79289	−0.200181	−0.100091	+	0.994978i	$0.531913\pi$
$360$	26.6507	1.40461
$361$	−17.1768	−0.904042
$362$	29.9610	1.57471
$363$	−2.48119	−0.130229
$364$	−30.0689	−1.57604
$365$	11.3684	0.595047
$366$	−9.38058	−0.490331
$367$	−6.36977	−0.332500	−0.166250	−	0.986084i	$-0.553166\pi$
$367$	−6.36977	−0.332500	−0.166250	+	0.986084i	$0.553166\pi$
$368$	−39.2057	−2.04374
$369$	−15.8618	−0.825731
$370$	−22.8568	−1.18827
$371$	0.231548	0.0120214
$372$	67.6444	3.50720
$373$	−21.3317	−1.10451	−0.552257	−	0.833674i	$-0.686233\pi$
$373$	−21.3317	−1.10451	−0.552257	+	0.833674i	$0.686233\pi$
$374$	14.5623	0.752998
$375$	2.48119	0.128128
$376$	99.8999	5.15194
$377$	−21.0640	−1.08485
$378$	−1.03761	−0.0533690
$379$	24.7875	1.27325	0.636624	−	0.771174i	$-0.280330\pi$
$379$	24.7875	1.27325	0.636624	+	0.771174i	$0.280330\pi$
$380$	6.96239	0.357163
$381$	42.0870	2.15618
$382$	−29.9610	−1.53294
$383$	−5.45817	−0.278900	−0.139450	−	0.990229i	$-0.544533\pi$
$383$	−5.45817	−0.278900	−0.139450	+	0.990229i	$0.544533\pi$
$384$	41.1124	2.09801
$385$	−1.00000	−0.0509647
$386$	−1.61801	−0.0823544
$387$	18.6048	0.945737
$388$	−4.31265	−0.218942
$389$	−13.7235	−0.695811	−0.347906	−	0.937530i	$-0.613107\pi$
$389$	−13.7235	−0.695811	−0.347906	+	0.937530i	$0.613107\pi$
$390$	−38.7064	−1.95997
$391$	−17.3865	−0.879271
$392$	−8.44358	−0.426465
$393$	24.6253	1.24218
$394$	−40.9438	−2.06272
$395$	−1.96968	−0.0991055
$396$	−16.2750	−0.817851
$397$	2.11142	0.105969	0.0529846	−	0.998595i	$-0.483127\pi$
$397$	2.11142	0.105969	0.0529846	+	0.998595i	$0.483127\pi$
$398$	33.6058	1.68451
$399$	−3.35026	−0.167723
$400$	12.2750	0.613752
$401$	19.1490	0.956257	0.478128	−	0.878290i	$-0.341315\pi$
$401$	19.1490	0.956257	0.478128	+	0.878290i	$0.341315\pi$
$402$	−72.0625	−3.59415
$403$	−30.8324	−1.53587
$404$	38.2252	1.90178
$405$	8.50659	0.422696
$406$	−9.66291	−0.479562
$407$	8.54420	0.423520
$408$	114.044	5.64602
$409$	−18.6883	−0.924077	−0.462039	−	0.886860i	$-0.652882\pi$
$409$	−18.6883	−0.924077	−0.462039	+	0.886860i	$0.652882\pi$
$410$	−13.4436	−0.663931
$411$	27.2750	1.34538
$412$	21.7562	1.07185
$413$	−13.5999	−0.669208
$414$	26.9683	1.32542
$415$	−10.6253	−0.521575
$416$	−93.0127	−4.56032
$417$	−17.0884	−0.836822
$418$	−3.61213	−0.176675
$419$	−0.773377	−0.0377819	−0.0188910	−	0.999822i	$-0.506014\pi$
$419$	−0.773377	−0.0377819	−0.0188910	+	0.999822i	$0.506014\pi$
$420$	−12.7938	−0.624276
$421$	−10.5198	−0.512702	−0.256351	−	0.966584i	$-0.582520\pi$
$421$	−10.5198	−0.512702	−0.256351	+	0.966584i	$0.582520\pi$
$422$	11.8740	0.578017
$423$	−37.3439	−1.81572
$424$	1.95509	0.0949478
$425$	5.44358	0.264053
$426$	−103.127	−4.99650
$427$	1.41327	0.0683927
$428$	−59.4880	−2.87546
$429$	14.4690	0.698569
$430$	15.7685	0.760422
$431$	−24.7308	−1.19124	−0.595621	−	0.803265i	$-0.703094\pi$
$431$	−24.7308	−1.19124	−0.595621	+	0.803265i	$0.703094\pi$
$432$	−4.76116	−0.229071
$433$	−18.5599	−0.891933	−0.445967	−	0.895050i	$-0.647140\pi$
$433$	−18.5599	−0.891933	−0.445967	+	0.895050i	$0.647140\pi$
$434$	−14.1441	−0.678939
$435$	−8.96239	−0.429714
$436$	−11.2750	−0.539976
$437$	4.31265	0.206302
$438$	−75.4577	−3.60551
$439$	−1.42548	−0.0680347	−0.0340173	−	0.999421i	$-0.510830\pi$
$439$	−1.42548	−0.0680347	−0.0340173	+	0.999421i	$0.510830\pi$
$440$	−8.44358	−0.402532
$441$	3.15633	0.150301
$442$	−84.9194	−4.03920
$443$	40.1925	1.90960	0.954802	−	0.297242i	$-0.0960668\pi$
$443$	40.1925	1.90960	0.954802	+	0.297242i	$0.0960668\pi$
$444$	109.313	5.18777
$445$	−7.22425	−0.342462
$446$	20.8143	0.985586
$447$	−56.6009	−2.67713
$448$	−18.1187	−0.856029
$449$	12.6556	0.597256	0.298628	−	0.954370i	$-0.403471\pi$
$449$	12.6556	0.597256	0.298628	+	0.954370i	$0.403471\pi$
$450$	−8.44358	−0.398034
$451$	5.02539	0.236636
$452$	−48.2130	−2.26775
$453$	8.05079	0.378259
$454$	27.9511	1.31181
$455$	5.83146	0.273383
$456$	−28.2882	−1.32472
$457$	−0.544198	−0.0254565	−0.0127283	−	0.999919i	$-0.504052\pi$
$457$	−0.544198	−0.0254565	−0.0127283	+	0.999919i	$0.504052\pi$
$458$	78.7875	3.68150
$459$	−2.11142	−0.0985526
$460$	16.4690	0.767870
$461$	−11.5755	−0.539123	−0.269562	−	0.962983i	$-0.586879\pi$
$461$	−11.5755	−0.539123	−0.269562	+	0.962983i	$0.586879\pi$
$462$	6.63752	0.308805
$463$	23.7948	1.10584	0.552919	−	0.833235i	$-0.313514\pi$
$463$	23.7948	1.10584	0.552919	+	0.833235i	$0.313514\pi$
$464$	−44.3390	−2.05839
$465$	−13.1187	−0.608366
$466$	23.3561	1.08195
$467$	−2.66784	−0.123453	−0.0617264	−	0.998093i	$-0.519661\pi$
$467$	−2.66784	−0.123453	−0.0617264	+	0.998093i	$0.519661\pi$
$468$	94.9072	4.38709
$469$	10.8568	0.501323
$470$	−31.6507	−1.45994
$471$	13.4617	0.620282
$472$	−114.832	−5.28557
$473$	−5.89446	−0.271028
$474$	13.0738	0.600500
$475$	−1.35026	−0.0619543
$476$	−28.0689	−1.28654
$477$	−0.730841	−0.0334629
$478$	56.7513	2.59574
$479$	−10.7104	−0.489369	−0.244685	−	0.969603i	$-0.578684\pi$
$479$	−10.7104	−0.489369	−0.244685	+	0.969603i	$0.578684\pi$
$480$	−39.5755	−1.80636
$481$	−49.8251	−2.27183
$482$	24.9805	1.13783
$483$	−7.92478	−0.360590
$484$	5.15633	0.234378
$485$	0.836381	0.0379781
$486$	−59.5755	−2.70240
$487$	17.4314	0.789891	0.394945	−	0.918705i	$-0.370764\pi$
$487$	17.4314	0.789891	0.394945	+	0.918705i	$0.370764\pi$
$488$	11.9330	0.540183
$489$	−8.38787	−0.379313
$490$	2.67513	0.120850
$491$	−28.3693	−1.28029	−0.640145	−	0.768254i	$-0.721126\pi$
$491$	−28.3693	−1.28029	−0.640145	+	0.768254i	$0.721126\pi$
$492$	64.2941	2.89860
$493$	−19.6629	−0.885573
$494$	21.0640	0.947712
$495$	3.15633	0.141866
$496$	−64.9013	−2.91415
$497$	15.5369	0.696925
$498$	70.5256	3.16033
$499$	27.4763	1.23001	0.615003	−	0.788524i	$-0.289155\pi$
$499$	27.4763	1.23001	0.615003	+	0.788524i	$0.289155\pi$
$500$	−5.15633	−0.230598
$501$	−27.9756	−1.24986
$502$	−5.01951	−0.224032
$503$	20.2981	0.905046	0.452523	−	0.891753i	$-0.350524\pi$
$503$	20.2981	0.905046	0.452523	+	0.891753i	$0.350524\pi$
$504$	26.6507	1.18712
$505$	−7.41327	−0.329886
$506$	−8.54420	−0.379836
$507$	−52.1197	−2.31472
$508$	−87.4636	−3.88057
$509$	−24.2619	−1.07539	−0.537694	−	0.843140i	$-0.680704\pi$
$509$	−24.2619	−1.07539	−0.537694	+	0.843140i	$0.680704\pi$
$510$	−36.1319	−1.59995
$511$	11.3684	0.502907
$512$	11.5017	0.508306
$513$	0.523730	0.0231233
$514$	−72.6009	−3.20229
$515$	−4.21933	−0.185926
$516$	−75.4128	−3.31986
$517$	11.8315	0.520347
$518$	−22.8568	−1.00427
$519$	22.2823	0.978086
$520$	49.2384	2.15925
$521$	2.20123	0.0964377	0.0482188	−	0.998837i	$-0.484646\pi$
$521$	2.20123	0.0964377	0.0482188	+	0.998837i	$0.484646\pi$
$522$	30.4993	1.33492
$523$	−22.1378	−0.968017	−0.484008	−	0.875063i	$-0.660820\pi$
$523$	−22.1378	−0.968017	−0.484008	+	0.875063i	$0.660820\pi$
$524$	−51.1754	−2.23561
$525$	2.48119	0.108288
$526$	−34.2736	−1.49440
$527$	−28.7816	−1.25375
$528$	30.4568	1.32546
$529$	−12.7988	−0.556468
$530$	−0.619421	−0.0269059
$531$	42.9257	1.86282
$532$	6.96239	0.301858
$533$	−29.3054	−1.26936
$534$	47.9511	2.07505
$535$	11.5369	0.498784
$536$	91.6707	3.95957
$537$	65.1002	2.80928
$538$	16.7513	0.722200
$539$	−1.00000	−0.0430730
$540$	2.00000	0.0860663
$541$	23.0640	0.991597	0.495799	−	0.868438i	$-0.334875\pi$
$541$	23.0640	0.991597	0.495799	+	0.868438i	$0.334875\pi$
$542$	15.3503	0.659350
$543$	27.7889	1.19254
$544$	−86.8261	−3.72264
$545$	2.18664	0.0936655
$546$	−38.7064	−1.65648
$547$	21.3766	0.913998	0.456999	−	0.889467i	$-0.348924\pi$
$547$	21.3766	0.913998	0.456999	+	0.889467i	$0.348924\pi$
$548$	−56.6820	−2.42133
$549$	−4.46073	−0.190379
$550$	2.67513	0.114068
$551$	4.87732	0.207781
$552$	−66.9135	−2.84803
$553$	−1.96968	−0.0837594
$554$	22.3576	0.949882
$555$	−21.1998	−0.899882
$556$	35.5125	1.50606
$557$	−9.19394	−0.389560	−0.194780	−	0.980847i	$-0.562399\pi$
$557$	−9.19394	−0.389560	−0.194780	+	0.980847i	$0.562399\pi$
$558$	44.6434	1.88991
$559$	34.3733	1.45384
$560$	12.2750	0.518715
$561$	13.5066	0.570249
$562$	22.6009	0.953360
$563$	−9.79877	−0.412969	−0.206484	−	0.978450i	$-0.566202\pi$
$563$	−9.79877	−0.412969	−0.206484	+	0.978450i	$0.566202\pi$
$564$	151.370	6.37382
$565$	9.35026	0.393368
$566$	−2.23743	−0.0940461
$567$	8.50659	0.357243
$568$	131.187	5.50449
$569$	−33.5125	−1.40492	−0.702458	−	0.711725i	$-0.747914\pi$
$569$	−33.5125	−1.40492	−0.702458	+	0.711725i	$0.747914\pi$
$570$	8.96239	0.375393
$571$	43.1392	1.80532	0.902659	−	0.430356i	$-0.141612\pi$
$571$	43.1392	1.80532	0.902659	+	0.430356i	$0.141612\pi$
$572$	−30.0689	−1.25724
$573$	−27.7889	−1.16090
$574$	−13.4436	−0.561124
$575$	−3.19394	−0.133196
$576$	57.1886	2.38286
$577$	−14.8510	−0.618254	−0.309127	−	0.951021i	$-0.600037\pi$
$577$	−14.8510	−0.618254	−0.309127	+	0.951021i	$0.600037\pi$
$578$	−33.7938	−1.40564
$579$	−1.50071	−0.0623673
$580$	18.6253	0.773374
$581$	−10.6253	−0.440812
$582$	−5.55149	−0.230117
$583$	0.231548	0.00958974
$584$	95.9897	3.97208
$585$	−18.4060	−0.760993
$586$	7.27267	0.300431
$587$	14.7938	0.610607	0.305304	−	0.952255i	$-0.401242\pi$
$587$	14.7938	0.610607	0.305304	+	0.952255i	$0.401242\pi$
$588$	−12.7938	−0.527609
$589$	7.13918	0.294165
$590$	36.3815	1.49780
$591$	−37.9756	−1.56211
$592$	−104.880	−4.31056
$593$	−27.4191	−1.12597	−0.562985	−	0.826467i	$-0.690347\pi$
$593$	−27.4191	−1.12597	−0.562985	+	0.826467i	$0.690347\pi$
$594$	−1.03761	−0.0425737
$595$	5.44358	0.223165
$596$	117.626	4.81814
$597$	31.1695	1.27568
$598$	49.8251	2.03750
$599$	11.3258	0.462761	0.231380	−	0.972863i	$-0.425676\pi$
$599$	11.3258	0.462761	0.231380	+	0.972863i	$0.425676\pi$
$600$	20.9502	0.855287
$601$	15.5393	0.633860	0.316930	−	0.948449i	$-0.397348\pi$
$601$	15.5393	0.633860	0.316930	+	0.948449i	$0.397348\pi$
$602$	15.7685	0.642674
$603$	−34.2677	−1.39549
$604$	−16.7308	−0.680768
$605$	−1.00000	−0.0406558
$606$	49.2057	1.99884
$607$	17.7235	0.719377	0.359688	−	0.933073i	$-0.382883\pi$
$607$	17.7235	0.719377	0.359688	+	0.933073i	$0.382883\pi$
$608$	21.5369	0.873437
$609$	−8.96239	−0.363174
$610$	−3.78067	−0.153075
$611$	−68.9946	−2.79122
$612$	88.5945	3.58122
$613$	22.2941	0.900450	0.450225	−	0.892915i	$-0.351344\pi$
$613$	22.2941	0.900450	0.450225	+	0.892915i	$0.351344\pi$
$614$	22.3733	0.902912
$615$	−12.4690	−0.502798
$616$	−8.44358	−0.340202
$617$	−30.9438	−1.24575	−0.622876	−	0.782321i	$-0.714036\pi$
$617$	−30.9438	−1.24575	−0.622876	+	0.782321i	$0.714036\pi$
$618$	28.0059	1.12656
$619$	32.4119	1.30274	0.651371	−	0.758759i	$-0.274194\pi$
$619$	32.4119	1.30274	0.651371	+	0.758759i	$0.274194\pi$
$620$	27.2628	1.09490
$621$	1.23884	0.0497130
$622$	−11.8677	−0.475850
$623$	−7.22425	−0.289434
$624$	−177.607	−7.10998
$625$	1.00000	0.0400000
$626$	−79.6893	−3.18502
$627$	−3.35026	−0.133797
$628$	−27.9756	−1.11635
$629$	−46.5111	−1.85452
$630$	−8.44358	−0.336400
$631$	−27.3258	−1.08782	−0.543912	−	0.839142i	$-0.683057\pi$
$631$	−27.3258	−1.08782	−0.543912	+	0.839142i	$0.683057\pi$
$632$	−16.6312	−0.661553
$633$	11.0132	0.437734
$634$	−41.1998	−1.63625
$635$	16.9624	0.673132
$636$	2.96239	0.117466
$637$	5.83146	0.231051
$638$	−9.66291	−0.382558
$639$	−49.0395	−1.93997
$640$	16.5696	0.654971
$641$	19.4460	0.768069	0.384034	−	0.923319i	$-0.374534\pi$
$641$	19.4460	0.768069	0.384034	+	0.923319i	$0.374534\pi$
$642$	−76.5764	−3.02223
$643$	5.29314	0.208741	0.104370	−	0.994538i	$-0.466717\pi$
$643$	5.29314	0.208741	0.104370	+	0.994538i	$0.466717\pi$
$644$	16.4690	0.648969
$645$	14.6253	0.575871
$646$	19.6629	0.773627
$647$	35.0966	1.37979	0.689896	−	0.723909i	$-0.257656\pi$
$647$	35.0966	1.37979	0.689896	+	0.723909i	$0.257656\pi$
$648$	71.8261	2.82159
$649$	−13.5999	−0.533843
$650$	−15.5999	−0.611879
$651$	−13.1187	−0.514163
$652$	17.4314	0.682665
$653$	27.7988	1.08785	0.543925	−	0.839134i	$-0.316938\pi$
$653$	27.7988	1.08785	0.543925	+	0.839134i	$0.316938\pi$
$654$	−14.5139	−0.567538
$655$	9.92478	0.387793
$656$	−61.6869	−2.40847
$657$	−35.8822	−1.39990
$658$	−31.6507	−1.23387
$659$	19.6180	0.764209	0.382105	−	0.924119i	$-0.375199\pi$
$659$	19.6180	0.764209	0.382105	+	0.924119i	$0.375199\pi$
$660$	−12.7938	−0.498000
$661$	21.5633	0.838713	0.419357	−	0.907822i	$-0.362256\pi$
$661$	21.5633	0.838713	0.419357	+	0.907822i	$0.362256\pi$
$662$	−16.7513	−0.651058
$663$	−78.7631	−3.05890
$664$	−89.7156	−3.48164
$665$	−1.35026	−0.0523609
$666$	72.1436	2.79551
$667$	11.5369	0.446711
$668$	58.1378	2.24942
$669$	19.3054	0.746388
$670$	−29.0435	−1.12205
$671$	1.41327	0.0545585
$672$	−39.5755	−1.52666
$673$	−21.0679	−0.812109	−0.406054	−	0.913849i	$-0.633096\pi$
$673$	−21.0679	−0.812109	−0.406054	+	0.913849i	$0.633096\pi$
$674$	42.4544	1.63528
$675$	−0.387873	−0.0149292
$676$	108.313	4.16589
$677$	34.5174	1.32661	0.663306	−	0.748349i	$-0.269153\pi$
$677$	34.5174	1.32661	0.663306	+	0.748349i	$0.269153\pi$
$678$	−62.0625	−2.38350
$679$	0.836381	0.0320973
$680$	45.9633	1.76261
$681$	25.9248	0.993440
$682$	−14.1441	−0.541606
$683$	33.7802	1.29256	0.646282	−	0.763099i	$-0.276323\pi$
$683$	33.7802	1.29256	0.646282	+	0.763099i	$0.276323\pi$
$684$	−21.9756	−0.840257
$685$	10.9927	0.420010
$686$	2.67513	0.102137
$687$	73.0757	2.78801
$688$	72.3547	2.75850
$689$	−1.35026	−0.0514409
$690$	21.1998	0.807063
$691$	−13.8618	−0.527327	−0.263663	−	0.964615i	$-0.584931\pi$
$691$	−13.8618	−0.527327	−0.263663	+	0.964615i	$0.584931\pi$
$692$	−46.3063	−1.76030
$693$	3.15633	0.119899
$694$	−18.1681	−0.689651
$695$	−6.88717	−0.261245
$696$	−75.6747	−2.86844
$697$	−27.3561	−1.03619
$698$	−71.5569	−2.70847
$699$	21.6629	0.819367
$700$	−5.15633	−0.194891
$701$	40.5256	1.53063	0.765316	−	0.643655i	$-0.222583\pi$
$701$	40.5256	1.53063	0.765316	+	0.643655i	$0.222583\pi$
$702$	6.05079	0.228372
$703$	11.5369	0.435123
$704$	−18.1187	−0.682875
$705$	−29.3561	−1.10562
$706$	45.1100	1.69774
$707$	−7.41327	−0.278805
$708$	−173.995	−6.53914
$709$	−0.850969	−0.0319588	−0.0159794	−	0.999872i	$-0.505087\pi$
$709$	−0.850969	−0.0319588	−0.0159794	+	0.999872i	$0.505087\pi$
$710$	−41.5633	−1.55984
$711$	6.21696	0.233154
$712$	−60.9986	−2.28602
$713$	16.8872	0.632429
$714$	−36.1319	−1.35220
$715$	5.83146	0.218084
$716$	−135.289	−5.05598
$717$	52.6371	1.96577
$718$	10.1465	0.378663
$719$	22.5769	0.841976	0.420988	−	0.907066i	$-0.361683\pi$
$719$	22.5769	0.841976	0.420988	+	0.907066i	$0.361683\pi$
$720$	−38.7440	−1.44390
$721$	−4.21933	−0.157136
$722$	45.9502	1.71009
$723$	23.1695	0.861683
$724$	−57.7499	−2.14626
$725$	−3.61213	−0.134151
$726$	6.63752	0.246341
$727$	12.5174	0.464244	0.232122	−	0.972687i	$-0.425433\pi$
$727$	12.5174	0.464244	0.232122	+	0.972687i	$0.425433\pi$
$728$	49.2384	1.82490
$729$	−29.7367	−1.10136
$730$	−30.4119	−1.12559
$731$	32.0870	1.18678
$732$	18.0811	0.668297
$733$	16.6678	0.615641	0.307820	−	0.951445i	$-0.400400\pi$
$733$	16.6678	0.615641	0.307820	+	0.951445i	$0.400400\pi$
$734$	17.0400	0.628957
$735$	2.48119	0.0915202
$736$	50.9438	1.87781
$737$	10.8568	0.399917
$738$	42.4323	1.56196
$739$	42.7005	1.57076	0.785382	−	0.619011i	$-0.212467\pi$
$739$	42.7005	1.57076	0.785382	+	0.619011i	$0.212467\pi$
$740$	44.0567	1.61956
$741$	19.5369	0.717706
$742$	−0.619421	−0.0227397
$743$	−19.6873	−0.722259	−0.361129	−	0.932516i	$-0.617609\pi$
$743$	−19.6873	−0.722259	−0.361129	+	0.932516i	$0.617609\pi$
$744$	−110.769	−4.06099
$745$	−22.8119	−0.835765
$746$	57.0651	2.08930
$747$	33.5369	1.22705
$748$	−28.0689	−1.02630
$749$	11.5369	0.421549
$750$	−6.63752	−0.242368
$751$	−5.85940	−0.213813	−0.106906	−	0.994269i	$-0.534094\pi$
$751$	−5.85940	−0.213813	−0.106906	+	0.994269i	$0.534094\pi$
$752$	−145.232	−5.29605
$753$	−4.65562	−0.169660
$754$	56.3488	2.05210
$755$	3.24472	0.118088
$756$	2.00000	0.0727393
$757$	−40.5863	−1.47513	−0.737567	−	0.675274i	$-0.764025\pi$
$757$	−40.5863	−1.47513	−0.737567	+	0.675274i	$0.764025\pi$
$758$	−66.3098	−2.40848
$759$	−7.92478	−0.287651
$760$	−11.4010	−0.413559
$761$	21.8472	0.791960	0.395980	−	0.918259i	$-0.370405\pi$
$761$	21.8472	0.791960	0.395980	+	0.918259i	$0.370405\pi$
$762$	−112.588	−4.07864
$763$	2.18664	0.0791618
$764$	57.7499	2.08932
$765$	−17.1817	−0.621206
$766$	14.6013	0.527567
$767$	79.3073	2.86362
$768$	−20.0689	−0.724173
$769$	45.2892	1.63317	0.816585	−	0.577226i	$-0.195865\pi$
$769$	45.2892	1.63317	0.816585	+	0.577226i	$0.195865\pi$
$770$	2.67513	0.0964050
$771$	−67.3376	−2.42510
$772$	3.11871	0.112245
$773$	−33.8153	−1.21625	−0.608125	−	0.793841i	$-0.708078\pi$
$773$	−33.8153	−1.21625	−0.608125	+	0.793841i	$0.708078\pi$
$774$	−49.7704	−1.78896
$775$	−5.28726	−0.189924
$776$	7.06205	0.253513
$777$	−21.1998	−0.760539
$778$	36.7123	1.31620
$779$	6.78560	0.243119
$780$	74.6067	2.67135
$781$	15.5369	0.555954
$782$	46.5111	1.66323
$783$	1.40105	0.0500693
$784$	12.2750	0.438394
$785$	5.42548	0.193644
$786$	−65.8759	−2.34972
$787$	1.27504	0.0454502	0.0227251	−	0.999742i	$-0.492766\pi$
$787$	1.27504	0.0454502	0.0227251	+	0.999742i	$0.492766\pi$
$788$	78.9194	2.81139
$789$	−31.7889	−1.13172
$790$	5.26916	0.187468
$791$	9.35026	0.332457
$792$	26.6507	0.946991
$793$	−8.24140	−0.292661
$794$	−5.64832	−0.200452
$795$	−0.574515	−0.0203760
$796$	−64.7753	−2.29590
$797$	−42.5256	−1.50634	−0.753168	−	0.657829i	$-0.771475\pi$
$797$	−42.5256	−1.50634	−0.753168	+	0.657829i	$0.771475\pi$
$798$	8.96239	0.317265
$799$	−64.4055	−2.27850
$800$	−15.9502	−0.563924
$801$	22.8021	0.805672
$802$	−51.2262	−1.80886
$803$	11.3684	0.401181
$804$	138.901	4.89865
$805$	−3.19394	−0.112571
$806$	82.4807	2.90526
$807$	15.5369	0.546925
$808$	−62.5945	−2.20207
$809$	−14.7151	−0.517356	−0.258678	−	0.965964i	$-0.583287\pi$
$809$	−14.7151	−0.517356	−0.258678	+	0.965964i	$0.583287\pi$
$810$	−22.7562	−0.799573
$811$	51.7743	1.81804	0.909021	−	0.416750i	$-0.136831\pi$
$811$	51.7743	1.81804	0.909021	+	0.416750i	$0.136831\pi$
$812$	18.6253	0.653620
$813$	14.2374	0.499328
$814$	−22.8568	−0.801132
$815$	−3.38058	−0.118417
$816$	−165.794	−5.80395
$817$	−7.95906	−0.278452
$818$	49.9937	1.74799
$819$	−18.4060	−0.643157
$820$	25.9126	0.904906
$821$	2.64974	0.0924765	0.0462383	−	0.998930i	$-0.485277\pi$
$821$	2.64974	0.0924765	0.0462383	+	0.998930i	$0.485277\pi$
$822$	−72.9643	−2.54492
$823$	5.76845	0.201076	0.100538	−	0.994933i	$-0.467944\pi$
$823$	5.76845	0.201076	0.100538	+	0.994933i	$0.467944\pi$
$824$	−35.6263	−1.24110
$825$	2.48119	0.0863841
$826$	36.3815	1.26588
$827$	−13.4920	−0.469163	−0.234581	−	0.972096i	$-0.575372\pi$
$827$	−13.4920	−0.469163	−0.234581	+	0.972096i	$0.575372\pi$
$828$	−51.9814	−1.80648
$829$	−4.70052	−0.163256	−0.0816280	−	0.996663i	$-0.526012\pi$
$829$	−4.70052	−0.163256	−0.0816280	+	0.996663i	$0.526012\pi$
$830$	28.4241	0.986614
$831$	20.7367	0.719349
$832$	105.658	3.66305
$833$	5.44358	0.188609
$834$	45.7137	1.58294
$835$	−11.2750	−0.390189
$836$	6.96239	0.240799
$837$	2.05079	0.0708855
$838$	2.06888	0.0714684
$839$	−38.8045	−1.33968	−0.669839	−	0.742506i	$-0.733637\pi$
$839$	−38.8045	−1.33968	−0.669839	+	0.742506i	$0.733637\pi$
$840$	20.9502	0.722850
$841$	−15.9525	−0.550088
$842$	28.1417	0.969828
$843$	20.9624	0.721983
$844$	−22.8872	−0.787809
$845$	−21.0059	−0.722624
$846$	99.8999	3.43463
$847$	−1.00000	−0.0343604
$848$	−2.84226	−0.0976036
$849$	−2.07522	−0.0712215
$850$	−14.5623	−0.499483
$851$	27.2896	0.935476
$852$	198.777	6.80998
$853$	20.6824	0.708153	0.354076	−	0.935217i	$-0.384795\pi$
$853$	20.6824	0.708153	0.354076	+	0.935217i	$0.384795\pi$
$854$	−3.78067	−0.129372
$855$	4.26187	0.145753
$856$	97.4128	3.32950
$857$	26.3453	0.899940	0.449970	−	0.893044i	$-0.351435\pi$
$857$	26.3453	0.899940	0.449970	+	0.893044i	$0.351435\pi$
$858$	−38.7064	−1.32141
$859$	−8.51151	−0.290409	−0.145205	−	0.989402i	$-0.546384\pi$
$859$	−8.51151	−0.290409	−0.145205	+	0.989402i	$0.546384\pi$
$860$	−30.3938	−1.03642
$861$	−12.4690	−0.424942
$862$	66.1582	2.25336
$863$	7.56722	0.257591	0.128796	−	0.991671i	$-0.458889\pi$
$863$	7.56722	0.257591	0.128796	+	0.991671i	$0.458889\pi$
$864$	6.18664	0.210474
$865$	8.98049	0.305346
$866$	49.6502	1.68718
$867$	−31.3439	−1.06450
$868$	27.2628	0.925360
$869$	−1.96968	−0.0668169
$870$	23.9756	0.812848
$871$	−63.3112	−2.14522
$872$	18.4631	0.625239
$873$	−2.63989	−0.0893467
$874$	−11.5369	−0.390242
$875$	1.00000	0.0338062
$876$	145.445	4.91413
$877$	17.2955	0.584028	0.292014	−	0.956414i	$-0.405675\pi$
$877$	17.2955	0.584028	0.292014	+	0.956414i	$0.405675\pi$
$878$	3.81336	0.128695
$879$	6.74543	0.227518
$880$	12.2750	0.413791
$881$	20.4504	0.688992	0.344496	−	0.938788i	$-0.388050\pi$
$881$	20.4504	0.688992	0.344496	+	0.938788i	$0.388050\pi$
$882$	−8.44358	−0.284310
$883$	−49.6589	−1.67116	−0.835578	−	0.549371i	$-0.814867\pi$
$883$	−49.6589	−1.67116	−0.835578	+	0.549371i	$0.814867\pi$
$884$	163.682	5.50524
$885$	33.7440	1.13429
$886$	−107.520	−3.61221
$887$	−47.1100	−1.58180	−0.790900	−	0.611946i	$-0.790387\pi$
$887$	−47.1100	−1.58180	−0.790900	+	0.611946i	$0.790387\pi$
$888$	−179.002	−6.00693
$889$	16.9624	0.568900
$890$	19.3258	0.647803
$891$	8.50659	0.284981
$892$	−40.1197	−1.34331
$893$	15.9756	0.534602
$894$	151.415	5.06407
$895$	26.2374	0.877020
$896$	16.5696	0.553551
$897$	46.2130	1.54301
$898$	−33.8554	−1.12977
$899$	19.0982	0.636962
$900$	16.2750	0.542501
$901$	−1.26045	−0.0419917
$902$	−13.4436	−0.447622
$903$	14.6253	0.486700
$904$	78.9497	2.62583
$905$	11.1998	0.372294
$906$	−21.5369	−0.715516
$907$	14.4591	0.480107	0.240054	−	0.970760i	$-0.422835\pi$
$907$	14.4591	0.480107	0.240054	+	0.970760i	$0.422835\pi$
$908$	−53.8759	−1.78793
$909$	23.3987	0.776085
$910$	−15.5999	−0.517132
$911$	−31.5369	−1.04486	−0.522432	−	0.852681i	$-0.674975\pi$
$911$	−31.5369	−1.04486	−0.522432	+	0.852681i	$0.674975\pi$
$912$	41.1246	1.36177
$913$	−10.6253	−0.351646
$914$	1.45580	0.0481536
$915$	−3.50659	−0.115924
$916$	−151.863	−5.01770
$917$	9.92478	0.327745
$918$	5.64832	0.186422
$919$	5.26328	0.173620	0.0868098	−	0.996225i	$-0.472333\pi$
$919$	5.26328	0.173620	0.0868098	+	0.996225i	$0.472333\pi$
$920$	−26.9683	−0.889117
$921$	20.7513	0.683779
$922$	30.9659	1.01981
$923$	−90.6028	−2.98223
$924$	−12.7938	−0.420887
$925$	−8.54420	−0.280932
$926$	−63.6542	−2.09181
$927$	13.3176	0.437407
$928$	57.6140	1.89127
$929$	26.0508	0.854699	0.427349	−	0.904087i	$-0.359447\pi$
$929$	26.0508	0.854699	0.427349	+	0.904087i	$0.359447\pi$
$930$	35.0943	1.15079
$931$	−1.35026	−0.0442530
$932$	−45.0191	−1.47465
$933$	−11.0073	−0.360363
$934$	7.13681	0.233524
$935$	5.44358	0.178024
$936$	−155.412	−5.07981
$937$	−29.3439	−0.958624	−0.479312	−	0.877645i	$-0.659114\pi$
$937$	−29.3439	−0.958624	−0.479312	+	0.877645i	$0.659114\pi$
$938$	−29.0435	−0.948304
$939$	−73.9121	−2.41203
$940$	61.0068	1.98982
$941$	−28.6375	−0.933556	−0.466778	−	0.884374i	$-0.654585\pi$
$941$	−28.6375	−0.933556	−0.466778	+	0.884374i	$0.654585\pi$
$942$	−36.0118	−1.17333
$943$	16.0508	0.522685
$944$	166.939	5.43341
$945$	−0.387873	−0.0126175
$946$	15.7685	0.512677
$947$	−52.8178	−1.71635	−0.858174	−	0.513358i	$-0.828401\pi$
$947$	−52.8178	−1.71635	−0.858174	+	0.513358i	$0.828401\pi$
$948$	−25.1998	−0.818452
$949$	−66.2941	−2.15200
$950$	3.61213	0.117193
$951$	−38.2130	−1.23914
$952$	45.9633	1.48968
$953$	37.1939	1.20483	0.602415	−	0.798183i	$-0.294205\pi$
$953$	37.1939	1.20483	0.602415	+	0.798183i	$0.294205\pi$
$954$	1.95509	0.0632985
$955$	−11.1998	−0.362418
$956$	−109.388	−3.53787
$957$	−8.96239	−0.289713
$958$	28.6516	0.925693
$959$	10.9927	0.354973
$960$	44.9560	1.45095
$961$	−3.04491	−0.0982228
$962$	133.289	4.29740
$963$	−36.4142	−1.17343
$964$	−48.1500	−1.55081
$965$	−0.604833	−0.0194703
$966$	21.1998	0.682093
$967$	4.07125	0.130923	0.0654613	−	0.997855i	$-0.479148\pi$
$967$	4.07125	0.130923	0.0654613	+	0.997855i	$0.479148\pi$
$968$	−8.44358	−0.271387
$969$	18.2374	0.585871
$970$	−2.23743	−0.0718395
$971$	0.773377	0.0248188	0.0124094	−	0.999923i	$-0.496050\pi$
$971$	0.773377	0.0248188	0.0124094	+	0.999923i	$0.496050\pi$
$972$	114.832	3.68324
$973$	−6.88717	−0.220792
$974$	−46.6312	−1.49416
$975$	−14.4690	−0.463378
$976$	−17.3479	−0.555292
$977$	−37.8740	−1.21170	−0.605848	−	0.795580i	$-0.707166\pi$
$977$	−37.8740	−1.21170	−0.605848	+	0.795580i	$0.707166\pi$
$978$	22.4387	0.717509
$979$	−7.22425	−0.230888
$980$	−5.15633	−0.164713
$981$	−6.90175	−0.220356
$982$	75.8916	2.42180
$983$	−15.5794	−0.496907	−0.248453	−	0.968644i	$-0.579922\pi$
$983$	−15.5794	−0.496907	−0.248453	+	0.968644i	$0.579922\pi$
$984$	−105.283	−3.35629
$985$	−15.3054	−0.487669
$986$	52.6009	1.67515
$987$	−29.3561	−0.934416
$988$	−40.6009	−1.29169
$989$	−18.8265	−0.598649
$990$	−8.44358	−0.268355
$991$	27.0982	0.860804	0.430402	−	0.902637i	$-0.358372\pi$
$991$	27.0982	0.860804	0.430402	+	0.902637i	$0.358372\pi$
$992$	84.3327	2.67756
$993$	−15.5369	−0.493049
$994$	−41.5633	−1.31831
$995$	12.5623	0.398252
$996$	−135.938	−4.30737
$997$	50.4060	1.59637	0.798187	−	0.602410i	$-0.205793\pi$
$997$	50.4060	1.59637	0.798187	+	0.602410i	$0.205793\pi$
$998$	−73.5026	−2.32668
$999$	3.31406	0.104852

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.a.f.1.1	✓	3
3.2	odd	2		3465.2.a.bh.1.3		3
4.3	odd	2		6160.2.a.bn.1.3		3
5.2	odd	4		1925.2.b.n.1849.1		6
5.3	odd	4		1925.2.b.n.1849.6		6
5.4	even	2		1925.2.a.v.1.3		3
7.6	odd	2		2695.2.a.g.1.1		3
11.10	odd	2		4235.2.a.q.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.a.f.1.1	✓	3	1.1	even	1	trivial
1925.2.a.v.1.3		3	5.4	even	2
1925.2.b.n.1849.1		6	5.2	odd	4
1925.2.b.n.1849.6		6	5.3	odd	4
2695.2.a.g.1.1		3	7.6	odd	2
3465.2.a.bh.1.3		3	3.2	odd	2
4235.2.a.q.1.3		3	11.10	odd	2
6160.2.a.bn.1.3		3	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.a (trivial)

\(f(q)\)	\(=\)	\(q-2.67513 q^{2} -2.48119 q^{3} +5.15633 q^{4} -1.00000 q^{5} +6.63752 q^{6} -1.00000 q^{7} -8.44358 q^{8} +3.15633 q^{9} +O(q^{10})\)	\(q-2.67513 q^{2} -2.48119 q^{3} +5.15633 q^{4} -1.00000 q^{5} +6.63752 q^{6} -1.00000 q^{7} -8.44358 q^{8} +3.15633 q^{9} +2.67513 q^{10} -1.00000 q^{11} -12.7938 q^{12} +5.83146 q^{13} +2.67513 q^{14} +2.48119 q^{15} +12.2750 q^{16} +5.44358 q^{17} -8.44358 q^{18} -1.35026 q^{19} -5.15633 q^{20} +2.48119 q^{21} +2.67513 q^{22} -3.19394 q^{23} +20.9502 q^{24} +1.00000 q^{25} -15.5999 q^{26} -0.387873 q^{27} -5.15633 q^{28} -3.61213 q^{29} -6.63752 q^{30} -5.28726 q^{31} -15.9502 q^{32} +2.48119 q^{33} -14.5623 q^{34} +1.00000 q^{35} +16.2750 q^{36} -8.54420 q^{37} +3.61213 q^{38} -14.4690 q^{39} +8.44358 q^{40} -5.02539 q^{41} -6.63752 q^{42} +5.89446 q^{43} -5.15633 q^{44} -3.15633 q^{45} +8.54420 q^{46} -11.8315 q^{47} -30.4568 q^{48} +1.00000 q^{49} -2.67513 q^{50} -13.5066 q^{51} +30.0689 q^{52} -0.231548 q^{53} +1.03761 q^{54} +1.00000 q^{55} +8.44358 q^{56} +3.35026 q^{57} +9.66291 q^{58} +13.5999 q^{59} +12.7938 q^{60} -1.41327 q^{61} +14.1441 q^{62} -3.15633 q^{63} +18.1187 q^{64} -5.83146 q^{65} -6.63752 q^{66} -10.8568 q^{67} +28.0689 q^{68} +7.92478 q^{69} -2.67513 q^{70} -15.5369 q^{71} -26.6507 q^{72} -11.3684 q^{73} +22.8568 q^{74} -2.48119 q^{75} -6.96239 q^{76} +1.00000 q^{77} +38.7064 q^{78} +1.96968 q^{79} -12.2750 q^{80} -8.50659 q^{81} +13.4436 q^{82} +10.6253 q^{83} +12.7938 q^{84} -5.44358 q^{85} -15.7685 q^{86} +8.96239 q^{87} +8.44358 q^{88} +7.22425 q^{89} +8.44358 q^{90} -5.83146 q^{91} -16.4690 q^{92} +13.1187 q^{93} +31.6507 q^{94} +1.35026 q^{95} +39.5755 q^{96} -0.836381 q^{97} -2.67513 q^{98} -3.15633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 2 q^{3} + 5 q^{4} - 3 q^{5} + 4 q^{6} - 3 q^{7} - 9 q^{8} - q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 2 * q^3 + 5 * q^4 - 3 * q^5 + 4 * q^6 - 3 * q^7 - 9 * q^8 - q^9	\( 3 q - 3 q^{2} - 2 q^{3} + 5 q^{4} - 3 q^{5} + 4 q^{6} - 3 q^{7} - 9 q^{8} - q^{9} + 3 q^{10} - 3 q^{11} - 12 q^{12} + 2 q^{13} + 3 q^{14} + 2 q^{15} + 5 q^{16} - 9 q^{18} + 6 q^{19} - 5 q^{20} + 2 q^{21} + 3 q^{22} - 10 q^{23} + 26 q^{24} + 3 q^{25} - 20 q^{26} - 2 q^{27} - 5 q^{28} - 10 q^{29} - 4 q^{30} - 10 q^{31} - 11 q^{32} + 2 q^{33} - 6 q^{34} + 3 q^{35} + 17 q^{36} - 16 q^{37} + 10 q^{38} - 12 q^{39} + 9 q^{40} - 4 q^{42} - 2 q^{43} - 5 q^{44} + q^{45} + 16 q^{46} - 20 q^{47} - 34 q^{48} + 3 q^{49} - 3 q^{50} - 20 q^{51} + 32 q^{52} - 12 q^{53} + 14 q^{54} + 3 q^{55} + 9 q^{56} - 2 q^{58} + 14 q^{59} + 12 q^{60} + 10 q^{61} + 6 q^{62} + q^{63} + 33 q^{64} - 2 q^{65} - 4 q^{66} - 2 q^{67} + 26 q^{68} + 2 q^{69} - 3 q^{70} - 24 q^{71} - 23 q^{72} + 4 q^{73} + 38 q^{74} - 2 q^{75} - 10 q^{76} + 3 q^{77} + 42 q^{78} + 8 q^{79} - 5 q^{80} - 5 q^{81} + 24 q^{82} - 10 q^{83} + 12 q^{84} - 36 q^{86} + 16 q^{87} + 9 q^{88} + 20 q^{89} + 9 q^{90} - 2 q^{91} - 18 q^{92} + 18 q^{93} + 38 q^{94} - 6 q^{95} + 40 q^{96} - 3 q^{98} + q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 2 * q^3 + 5 * q^4 - 3 * q^5 + 4 * q^6 - 3 * q^7 - 9 * q^8 - q^9 + 3 * q^10 - 3 * q^11 - 12 * q^12 + 2 * q^13 + 3 * q^14 + 2 * q^15 + 5 * q^16 - 9 * q^18 + 6 * q^19 - 5 * q^20 + 2 * q^21 + 3 * q^22 - 10 * q^23 + 26 * q^24 + 3 * q^25 - 20 * q^26 - 2 * q^27 - 5 * q^28 - 10 * q^29 - 4 * q^30 - 10 * q^31 - 11 * q^32 + 2 * q^33 - 6 * q^34 + 3 * q^35 + 17 * q^36 - 16 * q^37 + 10 * q^38 - 12 * q^39 + 9 * q^40 - 4 * q^42 - 2 * q^43 - 5 * q^44 + q^45 + 16 * q^46 - 20 * q^47 - 34 * q^48 + 3 * q^49 - 3 * q^50 - 20 * q^51 + 32 * q^52 - 12 * q^53 + 14 * q^54 + 3 * q^55 + 9 * q^56 - 2 * q^58 + 14 * q^59 + 12 * q^60 + 10 * q^61 + 6 * q^62 + q^63 + 33 * q^64 - 2 * q^65 - 4 * q^66 - 2 * q^67 + 26 * q^68 + 2 * q^69 - 3 * q^70 - 24 * q^71 - 23 * q^72 + 4 * q^73 + 38 * q^74 - 2 * q^75 - 10 * q^76 + 3 * q^77 + 42 * q^78 + 8 * q^79 - 5 * q^80 - 5 * q^81 + 24 * q^82 - 10 * q^83 + 12 * q^84 - 36 * q^86 + 16 * q^87 + 9 * q^88 + 20 * q^89 + 9 * q^90 - 2 * q^91 - 18 * q^92 + 18 * q^93 + 38 * q^94 - 6 * q^95 + 40 * q^96 - 3 * q^98 + q^99

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