LMFDB - Embedded newform 6042.2.a.bg.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, 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("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.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:	$48.2456129013$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5 x^{11} - 34 x^{10} + 169 x^{9} + 453 x^{8} - 2095 x^{7} - 3056 x^{6} + 11545 x^{5} + \cdots + 7848 $ x^12 - 5x^11 - 34x^10 + 169x^9 + 453x^8 - 2095x^7 - 3056x^6 + 11545x^5 + 11014x^4 - 26766x^3 - 19370x^2 + 18296*x + 7848
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$4.02498$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.02498 q^{5} +1.00000 q^{6} -3.74027 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.02498 q^{5} +1.00000 q^{6} -3.74027 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.02498 q^{10} -4.48376 q^{11} +1.00000 q^{12} +2.34043 q^{13} -3.74027 q^{14} +4.02498 q^{15} +1.00000 q^{16} -1.46116 q^{17} +1.00000 q^{18} -1.00000 q^{19} +4.02498 q^{20} -3.74027 q^{21} -4.48376 q^{22} +8.94646 q^{23} +1.00000 q^{24} +11.2005 q^{25} +2.34043 q^{26} +1.00000 q^{27} -3.74027 q^{28} +8.17776 q^{29} +4.02498 q^{30} -3.64850 q^{31} +1.00000 q^{32} -4.48376 q^{33} -1.46116 q^{34} -15.0545 q^{35} +1.00000 q^{36} +6.44488 q^{37} -1.00000 q^{38} +2.34043 q^{39} +4.02498 q^{40} +8.02111 q^{41} -3.74027 q^{42} +1.01885 q^{43} -4.48376 q^{44} +4.02498 q^{45} +8.94646 q^{46} -5.53964 q^{47} +1.00000 q^{48} +6.98963 q^{49} +11.2005 q^{50} -1.46116 q^{51} +2.34043 q^{52} +1.00000 q^{53} +1.00000 q^{54} -18.0471 q^{55} -3.74027 q^{56} -1.00000 q^{57} +8.17776 q^{58} -5.85253 q^{59} +4.02498 q^{60} -1.07443 q^{61} -3.64850 q^{62} -3.74027 q^{63} +1.00000 q^{64} +9.42020 q^{65} -4.48376 q^{66} +7.80442 q^{67} -1.46116 q^{68} +8.94646 q^{69} -15.0545 q^{70} -6.54034 q^{71} +1.00000 q^{72} +10.7718 q^{73} +6.44488 q^{74} +11.2005 q^{75} -1.00000 q^{76} +16.7705 q^{77} +2.34043 q^{78} +2.42889 q^{79} +4.02498 q^{80} +1.00000 q^{81} +8.02111 q^{82} +0.801614 q^{83} -3.74027 q^{84} -5.88113 q^{85} +1.01885 q^{86} +8.17776 q^{87} -4.48376 q^{88} +0.161746 q^{89} +4.02498 q^{90} -8.75385 q^{91} +8.94646 q^{92} -3.64850 q^{93} -5.53964 q^{94} -4.02498 q^{95} +1.00000 q^{96} -9.89551 q^{97} +6.98963 q^{98} -4.48376 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 5 q^{5} + 12 q^{6} + 6 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 5 * q^5 + 12 * q^6 + 6 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 5 q^{5} + 12 q^{6} + 6 q^{7} + 12 q^{8} + 12 q^{9} + 5 q^{10} + 7 q^{11} + 12 q^{12} + 9 q^{13} + 6 q^{14} + 5 q^{15} + 12 q^{16} + 25 q^{17} + 12 q^{18} - 12 q^{19} + 5 q^{20} + 6 q^{21} + 7 q^{22} + 22 q^{23} + 12 q^{24} + 33 q^{25} + 9 q^{26} + 12 q^{27} + 6 q^{28} + q^{29} + 5 q^{30} + 23 q^{31} + 12 q^{32} + 7 q^{33} + 25 q^{34} + 5 q^{35} + 12 q^{36} - q^{37} - 12 q^{38} + 9 q^{39} + 5 q^{40} - 15 q^{41} + 6 q^{42} + 2 q^{43} + 7 q^{44} + 5 q^{45} + 22 q^{46} + 11 q^{47} + 12 q^{48} + 36 q^{49} + 33 q^{50} + 25 q^{51} + 9 q^{52} + 12 q^{53} + 12 q^{54} - 4 q^{55} + 6 q^{56} - 12 q^{57} + q^{58} + 3 q^{59} + 5 q^{60} + 16 q^{61} + 23 q^{62} + 6 q^{63} + 12 q^{64} + 7 q^{65} + 7 q^{66} - 2 q^{67} + 25 q^{68} + 22 q^{69} + 5 q^{70} - 4 q^{71} + 12 q^{72} + 35 q^{73} - q^{74} + 33 q^{75} - 12 q^{76} + 11 q^{77} + 9 q^{78} + 4 q^{79} + 5 q^{80} + 12 q^{81} - 15 q^{82} + 39 q^{83} + 6 q^{84} + 10 q^{85} + 2 q^{86} + q^{87} + 7 q^{88} + 11 q^{89} + 5 q^{90} - 18 q^{91} + 22 q^{92} + 23 q^{93} + 11 q^{94} - 5 q^{95} + 12 q^{96} - 21 q^{97} + 36 q^{98} + 7 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 5 * q^5 + 12 * q^6 + 6 * q^7 + 12 * q^8 + 12 * q^9 + 5 * q^10 + 7 * q^11 + 12 * q^12 + 9 * q^13 + 6 * q^14 + 5 * q^15 + 12 * q^16 + 25 * q^17 + 12 * q^18 - 12 * q^19 + 5 * q^20 + 6 * q^21 + 7 * q^22 + 22 * q^23 + 12 * q^24 + 33 * q^25 + 9 * q^26 + 12 * q^27 + 6 * q^28 + q^29 + 5 * q^30 + 23 * q^31 + 12 * q^32 + 7 * q^33 + 25 * q^34 + 5 * q^35 + 12 * q^36 - q^37 - 12 * q^38 + 9 * q^39 + 5 * q^40 - 15 * q^41 + 6 * q^42 + 2 * q^43 + 7 * q^44 + 5 * q^45 + 22 * q^46 + 11 * q^47 + 12 * q^48 + 36 * q^49 + 33 * q^50 + 25 * q^51 + 9 * q^52 + 12 * q^53 + 12 * q^54 - 4 * q^55 + 6 * q^56 - 12 * q^57 + q^58 + 3 * q^59 + 5 * q^60 + 16 * q^61 + 23 * q^62 + 6 * q^63 + 12 * q^64 + 7 * q^65 + 7 * q^66 - 2 * q^67 + 25 * q^68 + 22 * q^69 + 5 * q^70 - 4 * q^71 + 12 * q^72 + 35 * q^73 - q^74 + 33 * q^75 - 12 * q^76 + 11 * q^77 + 9 * q^78 + 4 * q^79 + 5 * q^80 + 12 * q^81 - 15 * q^82 + 39 * q^83 + 6 * q^84 + 10 * q^85 + 2 * q^86 + q^87 + 7 * q^88 + 11 * q^89 + 5 * q^90 - 18 * q^91 + 22 * q^92 + 23 * q^93 + 11 * q^94 - 5 * q^95 + 12 * q^96 - 21 * q^97 + 36 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	4.02498	1.80003	0.900014	−	0.435861i	$-0.143556\pi$
$5$	4.02498	1.80003	0.900014	+	0.435861i	$0.143556\pi$
$6$	1.00000	0.408248
$7$	−3.74027	−1.41369	−0.706845	−	0.707369i	$-0.749882\pi$
$7$	−3.74027	−1.41369	−0.706845	+	0.707369i	$0.749882\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	4.02498	1.27281
$11$	−4.48376	−1.35191	−0.675953	−	0.736945i	$-0.736268\pi$
$11$	−4.48376	−1.35191	−0.675953	+	0.736945i	$0.736268\pi$
$12$	1.00000	0.288675
$13$	2.34043	0.649119	0.324560	−	0.945865i	$-0.394784\pi$
$13$	2.34043	0.649119	0.324560	+	0.945865i	$0.394784\pi$
$14$	−3.74027	−0.999630
$15$	4.02498	1.03925
$16$	1.00000	0.250000
$17$	−1.46116	−0.354382	−0.177191	−	0.984176i	$-0.556701\pi$
$17$	−1.46116	−0.354382	−0.177191	+	0.984176i	$0.556701\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	4.02498	0.900014
$21$	−3.74027	−0.816194
$22$	−4.48376	−0.955942
$23$	8.94646	1.86547	0.932733	−	0.360567i	$-0.117417\pi$
$23$	8.94646	1.86547	0.932733	+	0.360567i	$0.117417\pi$
$24$	1.00000	0.204124
$25$	11.2005	2.24010
$26$	2.34043	0.458997
$27$	1.00000	0.192450
$28$	−3.74027	−0.706845
$29$	8.17776	1.51857	0.759286	−	0.650757i	$-0.225548\pi$
$29$	8.17776	1.51857	0.759286	+	0.650757i	$0.225548\pi$
$30$	4.02498	0.734858
$31$	−3.64850	−0.655290	−0.327645	−	0.944801i	$-0.606255\pi$
$31$	−3.64850	−0.655290	−0.327645	+	0.944801i	$0.606255\pi$
$32$	1.00000	0.176777
$33$	−4.48376	−0.780523
$34$	−1.46116	−0.250586
$35$	−15.0545	−2.54468
$36$	1.00000	0.166667
$37$	6.44488	1.05953	0.529766	−	0.848144i	$-0.322280\pi$
$37$	6.44488	1.05953	0.529766	+	0.848144i	$0.322280\pi$
$38$	−1.00000	−0.162221
$39$	2.34043	0.374769
$40$	4.02498	0.636406
$41$	8.02111	1.25269	0.626344	−	0.779547i	$-0.284551\pi$
$41$	8.02111	1.25269	0.626344	+	0.779547i	$0.284551\pi$
$42$	−3.74027	−0.577136
$43$	1.01885	0.155373	0.0776865	−	0.996978i	$-0.475247\pi$
$43$	1.01885	0.155373	0.0776865	+	0.996978i	$0.475247\pi$
$44$	−4.48376	−0.675953
$45$	4.02498	0.600009
$46$	8.94646	1.31908
$47$	−5.53964	−0.808040	−0.404020	−	0.914750i	$-0.632387\pi$
$47$	−5.53964	−0.808040	−0.404020	+	0.914750i	$0.632387\pi$
$48$	1.00000	0.144338
$49$	6.98963	0.998519
$50$	11.2005	1.58399
$51$	−1.46116	−0.204603
$52$	2.34043	0.324560
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	1.00000	0.136083
$55$	−18.0471	−2.43347
$56$	−3.74027	−0.499815
$57$	−1.00000	−0.132453
$58$	8.17776	1.07379
$59$	−5.85253	−0.761935	−0.380967	−	0.924588i	$-0.624409\pi$
$59$	−5.85253	−0.761935	−0.380967	+	0.924588i	$0.624409\pi$
$60$	4.02498	0.519623
$61$	−1.07443	−0.137567	−0.0687835	−	0.997632i	$-0.521912\pi$
$61$	−1.07443	−0.137567	−0.0687835	+	0.997632i	$0.521912\pi$
$62$	−3.64850	−0.463360
$63$	−3.74027	−0.471230
$64$	1.00000	0.125000
$65$	9.42020	1.16843
$66$	−4.48376	−0.551913
$67$	7.80442	0.953461	0.476731	−	0.879049i	$-0.341822\pi$
$67$	7.80442	0.953461	0.476731	+	0.879049i	$0.341822\pi$
$68$	−1.46116	−0.177191
$69$	8.94646	1.07703
$70$	−15.0545	−1.79936
$71$	−6.54034	−0.776196	−0.388098	−	0.921618i	$-0.626868\pi$
$71$	−6.54034	−0.776196	−0.388098	+	0.921618i	$0.626868\pi$
$72$	1.00000	0.117851
$73$	10.7718	1.26074	0.630372	−	0.776293i	$-0.282902\pi$
$73$	10.7718	1.26074	0.630372	+	0.776293i	$0.282902\pi$
$74$	6.44488	0.749202
$75$	11.2005	1.29332
$76$	−1.00000	−0.114708
$77$	16.7705	1.91118
$78$	2.34043	0.265002
$79$	2.42889	0.273272	0.136636	−	0.990621i	$-0.456371\pi$
$79$	2.42889	0.273272	0.136636	+	0.990621i	$0.456371\pi$
$80$	4.02498	0.450007
$81$	1.00000	0.111111
$82$	8.02111	0.885784
$83$	0.801614	0.0879886	0.0439943	−	0.999032i	$-0.485992\pi$
$83$	0.801614	0.0879886	0.0439943	+	0.999032i	$0.485992\pi$
$84$	−3.74027	−0.408097
$85$	−5.88113	−0.637898
$86$	1.01885	0.109865
$87$	8.17776	0.876748
$88$	−4.48376	−0.477971
$89$	0.161746	0.0171450	0.00857249	−	0.999963i	$-0.497271\pi$
$89$	0.161746	0.0171450	0.00857249	+	0.999963i	$0.497271\pi$
$90$	4.02498	0.424271
$91$	−8.75385	−0.917653
$92$	8.94646	0.932733
$93$	−3.64850	−0.378332
$94$	−5.53964	−0.571371
$95$	−4.02498	−0.412955
$96$	1.00000	0.102062
$97$	−9.89551	−1.00474	−0.502369	−	0.864654i	$-0.667538\pi$
$97$	−9.89551	−1.00474	−0.502369	+	0.864654i	$0.667538\pi$
$98$	6.98963	0.706059
$99$	−4.48376	−0.450635
$100$	11.2005	1.12005
$101$	15.3441	1.52679	0.763396	−	0.645931i	$-0.223531\pi$
$101$	15.3441	1.52679	0.763396	+	0.645931i	$0.223531\pi$
$102$	−1.46116	−0.144676
$103$	−3.39610	−0.334627	−0.167314	−	0.985904i	$-0.553509\pi$
$103$	−3.39610	−0.334627	−0.167314	+	0.985904i	$0.553509\pi$
$104$	2.34043	0.229498
$105$	−15.0545	−1.46917
$106$	1.00000	0.0971286
$107$	4.58737	0.443477	0.221739	−	0.975106i	$-0.428827\pi$
$107$	4.58737	0.443477	0.221739	+	0.975106i	$0.428827\pi$
$108$	1.00000	0.0962250
$109$	−0.926185	−0.0887124	−0.0443562	−	0.999016i	$-0.514124\pi$
$109$	−0.926185	−0.0887124	−0.0443562	+	0.999016i	$0.514124\pi$
$110$	−18.0471	−1.72072
$111$	6.44488	0.611721
$112$	−3.74027	−0.353422
$113$	−6.51925	−0.613279	−0.306640	−	0.951826i	$-0.599205\pi$
$113$	−6.51925	−0.613279	−0.306640	+	0.951826i	$0.599205\pi$
$114$	−1.00000	−0.0936586
$115$	36.0094	3.35789
$116$	8.17776	0.759286
$117$	2.34043	0.216373
$118$	−5.85253	−0.538769
$119$	5.46512	0.500987
$120$	4.02498	0.367429
$121$	9.10414	0.827649
$122$	−1.07443	−0.0972745
$123$	8.02111	0.723239
$124$	−3.64850	−0.327645
$125$	24.9569	2.23221
$126$	−3.74027	−0.333210
$127$	−15.8213	−1.40391	−0.701956	−	0.712220i	$-0.747690\pi$
$127$	−15.8213	−1.40391	−0.701956	+	0.712220i	$0.747690\pi$
$128$	1.00000	0.0883883
$129$	1.01885	0.0897047
$130$	9.42020	0.826207
$131$	7.50569	0.655775	0.327888	−	0.944717i	$-0.393663\pi$
$131$	7.50569	0.655775	0.327888	+	0.944717i	$0.393663\pi$
$132$	−4.48376	−0.390262
$133$	3.74027	0.324323
$134$	7.80442	0.674199
$135$	4.02498	0.346415
$136$	−1.46116	−0.125293
$137$	14.6822	1.25439	0.627193	−	0.778864i	$-0.284204\pi$
$137$	14.6822	1.25439	0.627193	+	0.778864i	$0.284204\pi$
$138$	8.94646	0.761574
$139$	−7.39376	−0.627131	−0.313565	−	0.949567i	$-0.601523\pi$
$139$	−7.39376	−0.627131	−0.313565	+	0.949567i	$0.601523\pi$
$140$	−15.0545	−1.27234
$141$	−5.53964	−0.466522
$142$	−6.54034	−0.548853
$143$	−10.4939	−0.877548
$144$	1.00000	0.0833333
$145$	32.9154	2.73347
$146$	10.7718	0.891481
$147$	6.98963	0.576495
$148$	6.44488	0.529766
$149$	−0.0225725	−0.00184921	−0.000924607	−	1.00000i	$-0.500294\pi$
$149$	−0.0225725	−0.00184921	−0.000924607		1.00000i	$0.500294\pi$
$150$	11.2005	0.914517
$151$	10.9902	0.894368	0.447184	−	0.894442i	$-0.352427\pi$
$151$	10.9902	0.894368	0.447184	+	0.894442i	$0.352427\pi$
$152$	−1.00000	−0.0811107
$153$	−1.46116	−0.118127
$154$	16.7705	1.35140
$155$	−14.6852	−1.17954
$156$	2.34043	0.187385
$157$	1.01938	0.0813554	0.0406777	−	0.999172i	$-0.487048\pi$
$157$	1.01938	0.0813554	0.0406777	+	0.999172i	$0.487048\pi$
$158$	2.42889	0.193232
$159$	1.00000	0.0793052
$160$	4.02498	0.318203
$161$	−33.4622	−2.63719
$162$	1.00000	0.0785674
$163$	−23.0219	−1.80321	−0.901605	−	0.432559i	$-0.857611\pi$
$163$	−23.0219	−1.80321	−0.901605	+	0.432559i	$0.857611\pi$
$164$	8.02111	0.626344
$165$	−18.0471	−1.40496
$166$	0.801614	0.0622173
$167$	16.0936	1.24536	0.622680	−	0.782476i	$-0.286044\pi$
$167$	16.0936	1.24536	0.622680	+	0.782476i	$0.286044\pi$
$168$	−3.74027	−0.288568
$169$	−7.52238	−0.578644
$170$	−5.88113	−0.451062
$171$	−1.00000	−0.0764719
$172$	1.01885	0.0776865
$173$	−7.54715	−0.573799	−0.286900	−	0.957961i	$-0.592625\pi$
$173$	−7.54715	−0.573799	−0.286900	+	0.957961i	$0.592625\pi$
$174$	8.17776	0.619954
$175$	−41.8929	−3.16681
$176$	−4.48376	−0.337976
$177$	−5.85253	−0.439903
$178$	0.161746	0.0121233
$179$	14.0612	1.05098	0.525491	−	0.850799i	$-0.323882\pi$
$179$	14.0612	1.05098	0.525491	+	0.850799i	$0.323882\pi$
$180$	4.02498	0.300005
$181$	−3.46743	−0.257732	−0.128866	−	0.991662i	$-0.541134\pi$
$181$	−3.46743	−0.257732	−0.128866	+	0.991662i	$0.541134\pi$
$182$	−8.75385	−0.648879
$183$	−1.07443	−0.0794243
$184$	8.94646	0.659542
$185$	25.9405	1.90719
$186$	−3.64850	−0.267521
$187$	6.55148	0.479092
$188$	−5.53964	−0.404020
$189$	−3.74027	−0.272065
$190$	−4.02498	−0.292003
$191$	10.6289	0.769081	0.384541	−	0.923108i	$-0.374360\pi$
$191$	10.6289	0.769081	0.384541	+	0.923108i	$0.374360\pi$
$192$	1.00000	0.0721688
$193$	−15.4797	−1.11425	−0.557127	−	0.830427i	$-0.688096\pi$
$193$	−15.4797	−1.11425	−0.557127	+	0.830427i	$0.688096\pi$
$194$	−9.89551	−0.710457
$195$	9.42020	0.674595
$196$	6.98963	0.499259
$197$	−22.7562	−1.62131	−0.810656	−	0.585523i	$-0.800889\pi$
$197$	−22.7562	−1.62131	−0.810656	+	0.585523i	$0.800889\pi$
$198$	−4.48376	−0.318647
$199$	12.9870	0.920627	0.460313	−	0.887757i	$-0.347737\pi$
$199$	12.9870	0.920627	0.460313	+	0.887757i	$0.347737\pi$
$200$	11.2005	0.791995
$201$	7.80442	0.550481
$202$	15.3441	1.07960
$203$	−30.5870	−2.14679
$204$	−1.46116	−0.102301
$205$	32.2848	2.25487
$206$	−3.39610	−0.236617
$207$	8.94646	0.621822
$208$	2.34043	0.162280
$209$	4.48376	0.310148
$210$	−15.0545	−1.03886
$211$	23.2335	1.59946	0.799729	−	0.600361i	$-0.204976\pi$
$211$	23.2335	1.59946	0.799729	+	0.600361i	$0.204976\pi$
$212$	1.00000	0.0686803
$213$	−6.54034	−0.448137
$214$	4.58737	0.313586
$215$	4.10085	0.279676
$216$	1.00000	0.0680414
$217$	13.6464	0.926377
$218$	−0.926185	−0.0627291
$219$	10.7718	0.727891
$220$	−18.0471	−1.21673
$221$	−3.41974	−0.230036
$222$	6.44488	0.432552
$223$	−15.4328	−1.03346	−0.516729	−	0.856149i	$-0.672850\pi$
$223$	−15.4328	−1.03346	−0.516729	+	0.856149i	$0.672850\pi$
$224$	−3.74027	−0.249907
$225$	11.2005	0.746700
$226$	−6.51925	−0.433654
$227$	24.3933	1.61904	0.809520	−	0.587092i	$-0.199727\pi$
$227$	24.3933	1.61904	0.809520	+	0.587092i	$0.199727\pi$
$228$	−1.00000	−0.0662266
$229$	−27.2425	−1.80023	−0.900116	−	0.435650i	$-0.856519\pi$
$229$	−27.2425	−1.80023	−0.900116	+	0.435650i	$0.856519\pi$
$230$	36.0094	2.37439
$231$	16.7705	1.10342
$232$	8.17776	0.536896
$233$	−25.5787	−1.67572	−0.837858	−	0.545888i	$-0.816193\pi$
$233$	−25.5787	−1.67572	−0.837858	+	0.545888i	$0.816193\pi$
$234$	2.34043	0.152999
$235$	−22.2970	−1.45449
$236$	−5.85253	−0.380967
$237$	2.42889	0.157774
$238$	5.46512	0.354251
$239$	−24.7078	−1.59822	−0.799108	−	0.601187i	$-0.794695\pi$
$239$	−24.7078	−1.59822	−0.799108	+	0.601187i	$0.794695\pi$
$240$	4.02498	0.259812
$241$	−17.7848	−1.14562	−0.572809	−	0.819689i	$-0.694146\pi$
$241$	−17.7848	−1.14562	−0.572809	+	0.819689i	$0.694146\pi$
$242$	9.10414	0.585236
$243$	1.00000	0.0641500
$244$	−1.07443	−0.0687835
$245$	28.1332	1.79736
$246$	8.02111	0.511407
$247$	−2.34043	−0.148918
$248$	−3.64850	−0.231680
$249$	0.801614	0.0508002
$250$	24.9569	1.57841
$251$	−23.3589	−1.47440	−0.737199	−	0.675675i	$-0.763852\pi$
$251$	−23.3589	−1.47440	−0.737199	+	0.675675i	$0.763852\pi$
$252$	−3.74027	−0.235615
$253$	−40.1138	−2.52194
$254$	−15.8213	−0.992716
$255$	−5.88113	−0.368291
$256$	1.00000	0.0625000
$257$	13.4652	0.839935	0.419967	−	0.907539i	$-0.362042\pi$
$257$	13.4652	0.839935	0.419967	+	0.907539i	$0.362042\pi$
$258$	1.01885	0.0634308
$259$	−24.1056	−1.49785
$260$	9.42020	0.584216
$261$	8.17776	0.506191
$262$	7.50569	0.463703
$263$	21.3051	1.31373	0.656865	−	0.754008i	$-0.271882\pi$
$263$	21.3051	1.31373	0.656865	+	0.754008i	$0.271882\pi$
$264$	−4.48376	−0.275957
$265$	4.02498	0.247253
$266$	3.74027	0.229331
$267$	0.161746	0.00989866
$268$	7.80442	0.476731
$269$	−23.0804	−1.40724	−0.703620	−	0.710577i	$-0.748434\pi$
$269$	−23.0804	−1.40724	−0.703620	+	0.710577i	$0.748434\pi$
$270$	4.02498	0.244953
$271$	4.79923	0.291533	0.145766	−	0.989319i	$-0.453435\pi$
$271$	4.79923	0.291533	0.145766	+	0.989319i	$0.453435\pi$
$272$	−1.46116	−0.0885956
$273$	−8.75385	−0.529807
$274$	14.6822	0.886985
$275$	−50.2204	−3.02840
$276$	8.94646	0.538514
$277$	−24.9115	−1.49679	−0.748394	−	0.663255i	$-0.769175\pi$
$277$	−24.9115	−1.49679	−0.748394	+	0.663255i	$0.769175\pi$
$278$	−7.39376	−0.443448
$279$	−3.64850	−0.218430
$280$	−15.0545	−0.899680
$281$	−0.987371	−0.0589016	−0.0294508	−	0.999566i	$-0.509376\pi$
$281$	−0.987371	−0.0589016	−0.0294508	+	0.999566i	$0.509376\pi$
$282$	−5.53964	−0.329881
$283$	−2.77872	−0.165178	−0.0825888	−	0.996584i	$-0.526319\pi$
$283$	−2.77872	−0.165178	−0.0825888	+	0.996584i	$0.526319\pi$
$284$	−6.54034	−0.388098
$285$	−4.02498	−0.238419
$286$	−10.4939	−0.620520
$287$	−30.0011	−1.77091
$288$	1.00000	0.0589256
$289$	−14.8650	−0.874413
$290$	32.9154	1.93286
$291$	−9.89551	−0.580085
$292$	10.7718	0.630372
$293$	8.43008	0.492490	0.246245	−	0.969208i	$-0.420803\pi$
$293$	8.43008	0.492490	0.246245	+	0.969208i	$0.420803\pi$
$294$	6.98963	0.407644
$295$	−23.5563	−1.37150
$296$	6.44488	0.374601
$297$	−4.48376	−0.260174
$298$	−0.0225725	−0.00130759
$299$	20.9386	1.21091
$300$	11.2005	0.646661
$301$	−3.81077	−0.219649
$302$	10.9902	0.632413
$303$	15.3441	0.881493
$304$	−1.00000	−0.0573539
$305$	−4.32457	−0.247624
$306$	−1.46116	−0.0835287
$307$	5.66668	0.323414	0.161707	−	0.986839i	$-0.448300\pi$
$307$	5.66668	0.323414	0.161707	+	0.986839i	$0.448300\pi$
$308$	16.7705	0.955588
$309$	−3.39610	−0.193197
$310$	−14.6852	−0.834061
$311$	29.9977	1.70102	0.850508	−	0.525962i	$-0.176295\pi$
$311$	29.9977	1.70102	0.850508	+	0.525962i	$0.176295\pi$
$312$	2.34043	0.132501
$313$	−6.84517	−0.386912	−0.193456	−	0.981109i	$-0.561970\pi$
$313$	−6.84517	−0.386912	−0.193456	+	0.981109i	$0.561970\pi$
$314$	1.01938	0.0575270
$315$	−15.0545	−0.848227
$316$	2.42889	0.136636
$317$	−31.0088	−1.74163	−0.870813	−	0.491614i	$-0.836407\pi$
$317$	−31.0088	−1.74163	−0.870813	+	0.491614i	$0.836407\pi$
$318$	1.00000	0.0560772
$319$	−36.6672	−2.05297
$320$	4.02498	0.225003
$321$	4.58737	0.256042
$322$	−33.4622	−1.86478
$323$	1.46116	0.0813009
$324$	1.00000	0.0555556
$325$	26.2140	1.45409
$326$	−23.0219	−1.27506
$327$	−0.926185	−0.0512181
$328$	8.02111	0.442892
$329$	20.7198	1.14232
$330$	−18.0471	−0.993459
$331$	7.97442	0.438314	0.219157	−	0.975690i	$-0.429669\pi$
$331$	7.97442	0.438314	0.219157	+	0.975690i	$0.429669\pi$
$332$	0.801614	0.0439943
$333$	6.44488	0.353177
$334$	16.0936	0.880603
$335$	31.4127	1.71626
$336$	−3.74027	−0.204049
$337$	2.37608	0.129433	0.0647166	−	0.997904i	$-0.479386\pi$
$337$	2.37608	0.129433	0.0647166	+	0.997904i	$0.479386\pi$
$338$	−7.52238	−0.409163
$339$	−6.51925	−0.354077
$340$	−5.88113	−0.318949
$341$	16.3590	0.885890
$342$	−1.00000	−0.0540738
$343$	0.0387848	0.00209418
$344$	1.01885	0.0549327
$345$	36.0094	1.93868
$346$	−7.54715	−0.405737
$347$	22.8134	1.22469	0.612343	−	0.790592i	$-0.290227\pi$
$347$	22.8134	1.22469	0.612343	+	0.790592i	$0.290227\pi$
$348$	8.17776	0.438374
$349$	−5.25627	−0.281361	−0.140681	−	0.990055i	$-0.544929\pi$
$349$	−5.25627	−0.281361	−0.140681	+	0.990055i	$0.544929\pi$
$350$	−41.8929	−2.23927
$351$	2.34043	0.124923
$352$	−4.48376	−0.238985
$353$	−8.12240	−0.432312	−0.216156	−	0.976359i	$-0.569352\pi$
$353$	−8.12240	−0.432312	−0.216156	+	0.976359i	$0.569352\pi$
$354$	−5.85253	−0.311059
$355$	−26.3248	−1.39717
$356$	0.161746	0.00857249
$357$	5.46512	0.289245
$358$	14.0612	0.743157
$359$	2.90031	0.153072	0.0765362	−	0.997067i	$-0.475614\pi$
$359$	2.90031	0.153072	0.0765362	+	0.997067i	$0.475614\pi$
$360$	4.02498	0.212135
$361$	1.00000	0.0526316
$362$	−3.46743	−0.182244
$363$	9.10414	0.477843
$364$	−8.75385	−0.458827
$365$	43.3563	2.26937
$366$	−1.07443	−0.0561615
$367$	−22.0274	−1.14982	−0.574911	−	0.818216i	$-0.694963\pi$
$367$	−22.0274	−1.14982	−0.574911	+	0.818216i	$0.694963\pi$
$368$	8.94646	0.466367
$369$	8.02111	0.417562
$370$	25.9405	1.34858
$371$	−3.74027	−0.194185
$372$	−3.64850	−0.189166
$373$	−4.32545	−0.223963	−0.111982	−	0.993710i	$-0.535720\pi$
$373$	−4.32545	−0.223963	−0.111982	+	0.993710i	$0.535720\pi$
$374$	6.55148	0.338769
$375$	24.9569	1.28877
$376$	−5.53964	−0.285685
$377$	19.1395	0.985734
$378$	−3.74027	−0.192379
$379$	8.58606	0.441036	0.220518	−	0.975383i	$-0.429225\pi$
$379$	8.58606	0.441036	0.220518	+	0.975383i	$0.429225\pi$
$380$	−4.02498	−0.206477
$381$	−15.8213	−0.810549
$382$	10.6289	0.543823
$383$	7.16444	0.366086	0.183043	−	0.983105i	$-0.441405\pi$
$383$	7.16444	0.366086	0.183043	+	0.983105i	$0.441405\pi$
$384$	1.00000	0.0510310
$385$	67.5010	3.44017
$386$	−15.4797	−0.787897
$387$	1.01885	0.0517910
$388$	−9.89551	−0.502369
$389$	−35.4585	−1.79782	−0.898910	−	0.438134i	$-0.855639\pi$
$389$	−35.4585	−1.79782	−0.898910	+	0.438134i	$0.855639\pi$
$390$	9.42020	0.477011
$391$	−13.0722	−0.661089
$392$	6.98963	0.353030
$393$	7.50569	0.378612
$394$	−22.7562	−1.14644
$395$	9.77626	0.491897
$396$	−4.48376	−0.225318
$397$	−3.06032	−0.153593	−0.0767965	−	0.997047i	$-0.524469\pi$
$397$	−3.06032	−0.153593	−0.0767965	+	0.997047i	$0.524469\pi$
$398$	12.9870	0.650981
$399$	3.74027	0.187248
$400$	11.2005	0.560025
$401$	6.10018	0.304628	0.152314	−	0.988332i	$-0.451327\pi$
$401$	6.10018	0.304628	0.152314	+	0.988332i	$0.451327\pi$
$402$	7.80442	0.389249
$403$	−8.53907	−0.425361
$404$	15.3441	0.763396
$405$	4.02498	0.200003
$406$	−30.5870	−1.51801
$407$	−28.8973	−1.43239
$408$	−1.46116	−0.0723380
$409$	18.2538	0.902590	0.451295	−	0.892375i	$-0.350962\pi$
$409$	18.2538	0.902590	0.451295	+	0.892375i	$0.350962\pi$
$410$	32.2848	1.59444
$411$	14.6822	0.724220
$412$	−3.39610	−0.167314
$413$	21.8901	1.07714
$414$	8.94646	0.439695
$415$	3.22648	0.158382
$416$	2.34043	0.114749
$417$	−7.39376	−0.362074
$418$	4.48376	0.219308
$419$	−9.85365	−0.481382	−0.240691	−	0.970602i	$-0.577374\pi$
$419$	−9.85365	−0.481382	−0.240691	+	0.970602i	$0.577374\pi$
$420$	−15.0545	−0.734586
$421$	6.00913	0.292867	0.146434	−	0.989221i	$-0.453221\pi$
$421$	6.00913	0.292867	0.146434	+	0.989221i	$0.453221\pi$
$422$	23.2335	1.13099
$423$	−5.53964	−0.269347
$424$	1.00000	0.0485643
$425$	−16.3657	−0.793852
$426$	−6.54034	−0.316881
$427$	4.01867	0.194477
$428$	4.58737	0.221739
$429$	−10.4939	−0.506653
$430$	4.10085	0.197761
$431$	−3.27274	−0.157642	−0.0788211	−	0.996889i	$-0.525116\pi$
$431$	−3.27274	−0.157642	−0.0788211	+	0.996889i	$0.525116\pi$
$432$	1.00000	0.0481125
$433$	−1.93207	−0.0928494	−0.0464247	−	0.998922i	$-0.514783\pi$
$433$	−1.93207	−0.0928494	−0.0464247	+	0.998922i	$0.514783\pi$
$434$	13.6464	0.655047
$435$	32.9154	1.57817
$436$	−0.926185	−0.0443562
$437$	−8.94646	−0.427967
$438$	10.7718	0.514697
$439$	−8.00851	−0.382225	−0.191113	−	0.981568i	$-0.561210\pi$
$439$	−8.00851	−0.382225	−0.191113	+	0.981568i	$0.561210\pi$
$440$	−18.0471	−0.860361
$441$	6.98963	0.332840
$442$	−3.41974	−0.162660
$443$	−18.8004	−0.893233	−0.446617	−	0.894725i	$-0.647371\pi$
$443$	−18.8004	−0.893233	−0.446617	+	0.894725i	$0.647371\pi$
$444$	6.44488	0.305861
$445$	0.651023	0.0308615
$446$	−15.4328	−0.730765
$447$	−0.0225725	−0.00106764
$448$	−3.74027	−0.176711
$449$	5.56076	0.262429	0.131214	−	0.991354i	$-0.458112\pi$
$449$	5.56076	0.262429	0.131214	+	0.991354i	$0.458112\pi$
$450$	11.2005	0.527997
$451$	−35.9648	−1.69352
$452$	−6.51925	−0.306640
$453$	10.9902	0.516363
$454$	24.3933	1.14483
$455$	−35.2341	−1.65180
$456$	−1.00000	−0.0468293
$457$	15.6877	0.733837	0.366919	−	0.930253i	$-0.380413\pi$
$457$	15.6877	0.733837	0.366919	+	0.930253i	$0.380413\pi$
$458$	−27.2425	−1.27296
$459$	−1.46116	−0.0682009
$460$	36.0094	1.67895
$461$	22.5787	1.05159	0.525797	−	0.850610i	$-0.323767\pi$
$461$	22.5787	1.05159	0.525797	+	0.850610i	$0.323767\pi$
$462$	16.7705	0.780234
$463$	−38.8603	−1.80599	−0.902996	−	0.429649i	$-0.858637\pi$
$463$	−38.8603	−1.80599	−0.902996	+	0.429649i	$0.858637\pi$
$464$	8.17776	0.379643
$465$	−14.6852	−0.681008
$466$	−25.5787	−1.18491
$467$	−12.0843	−0.559195	−0.279598	−	0.960117i	$-0.590201\pi$
$467$	−12.0843	−0.559195	−0.279598	+	0.960117i	$0.590201\pi$
$468$	2.34043	0.108187
$469$	−29.1906	−1.34790
$470$	−22.2970	−1.02848
$471$	1.01938	0.0469706
$472$	−5.85253	−0.269385
$473$	−4.56828	−0.210050
$474$	2.42889	0.111563
$475$	−11.2005	−0.513914
$476$	5.46512	0.250493
$477$	1.00000	0.0457869
$478$	−24.7078	−1.13011
$479$	24.1866	1.10512	0.552558	−	0.833475i	$-0.313652\pi$
$479$	24.1866	1.10512	0.552558	+	0.833475i	$0.313652\pi$
$480$	4.02498	0.183715
$481$	15.0838	0.687763
$482$	−17.7848	−0.810075
$483$	−33.4622	−1.52258
$484$	9.10414	0.413825
$485$	−39.8293	−1.80855
$486$	1.00000	0.0453609
$487$	−36.2113	−1.64089	−0.820444	−	0.571726i	$-0.806274\pi$
$487$	−36.2113	−1.64089	−0.820444	+	0.571726i	$0.806274\pi$
$488$	−1.07443	−0.0486373
$489$	−23.0219	−1.04108
$490$	28.1332	1.27093
$491$	−28.7909	−1.29931	−0.649657	−	0.760228i	$-0.725087\pi$
$491$	−28.7909	−1.29931	−0.649657	+	0.760228i	$0.725087\pi$
$492$	8.02111	0.361620
$493$	−11.9490	−0.538155
$494$	−2.34043	−0.105301
$495$	−18.0471	−0.811156
$496$	−3.64850	−0.163822
$497$	24.4627	1.09730
$498$	0.801614	0.0359212
$499$	−41.9922	−1.87983	−0.939914	−	0.341411i	$-0.889095\pi$
$499$	−41.9922	−1.87983	−0.939914	+	0.341411i	$0.889095\pi$
$500$	24.9569	1.11611
$501$	16.0936	0.719009
$502$	−23.3589	−1.04256
$503$	−9.07500	−0.404634	−0.202317	−	0.979320i	$-0.564847\pi$
$503$	−9.07500	−0.404634	−0.202317	+	0.979320i	$0.564847\pi$
$504$	−3.74027	−0.166605
$505$	61.7596	2.74827
$506$	−40.1138	−1.78328
$507$	−7.52238	−0.334080
$508$	−15.8213	−0.701956
$509$	−33.3895	−1.47996	−0.739982	−	0.672627i	$-0.765166\pi$
$509$	−33.3895	−1.47996	−0.739982	+	0.672627i	$0.765166\pi$
$510$	−5.88113	−0.260421
$511$	−40.2895	−1.78230
$512$	1.00000	0.0441942
$513$	−1.00000	−0.0441511
$514$	13.4652	0.593924
$515$	−13.6692	−0.602338
$516$	1.01885	0.0448523
$517$	24.8385	1.09239
$518$	−24.1056	−1.05914
$519$	−7.54715	−0.331283
$520$	9.42020	0.413103
$521$	−10.3993	−0.455602	−0.227801	−	0.973708i	$-0.573154\pi$
$521$	−10.3993	−0.455602	−0.227801	+	0.973708i	$0.573154\pi$
$522$	8.17776	0.357931
$523$	32.2391	1.40972	0.704859	−	0.709347i	$-0.251010\pi$
$523$	32.2391	1.40972	0.704859	+	0.709347i	$0.251010\pi$
$524$	7.50569	0.327888
$525$	−41.8929	−1.82836
$526$	21.3051	0.928947
$527$	5.33103	0.232223
$528$	−4.48376	−0.195131
$529$	57.0392	2.47997
$530$	4.02498	0.174834
$531$	−5.85253	−0.253978
$532$	3.74027	0.162161
$533$	18.7729	0.813143
$534$	0.161746	0.00699941
$535$	18.4641	0.798272
$536$	7.80442	0.337099
$537$	14.0612	0.606785
$538$	−23.0804	−0.995069
$539$	−31.3399	−1.34990
$540$	4.02498	0.173208
$541$	30.3887	1.30651	0.653255	−	0.757138i	$-0.273403\pi$
$541$	30.3887	1.30651	0.653255	+	0.757138i	$0.273403\pi$
$542$	4.79923	0.206145
$543$	−3.46743	−0.148802
$544$	−1.46116	−0.0626466
$545$	−3.72788	−0.159685
$546$	−8.75385	−0.374630
$547$	19.0411	0.814140	0.407070	−	0.913397i	$-0.366550\pi$
$547$	19.0411	0.814140	0.407070	+	0.913397i	$0.366550\pi$
$548$	14.6822	0.627193
$549$	−1.07443	−0.0458556
$550$	−50.2204	−2.14140
$551$	−8.17776	−0.348384
$552$	8.94646	0.380787
$553$	−9.08472	−0.386322
$554$	−24.9115	−1.05839
$555$	25.9405	1.10111
$556$	−7.39376	−0.313565
$557$	28.8303	1.22158	0.610789	−	0.791793i	$-0.290852\pi$
$557$	28.8303	1.22158	0.610789	+	0.791793i	$0.290852\pi$
$558$	−3.64850	−0.154453
$559$	2.38455	0.100856
$560$	−15.0545	−0.636170
$561$	6.55148	0.276604
$562$	−0.987371	−0.0416497
$563$	9.13144	0.384844	0.192422	−	0.981312i	$-0.438366\pi$
$563$	9.13144	0.384844	0.192422	+	0.981312i	$0.438366\pi$
$564$	−5.53964	−0.233261
$565$	−26.2399	−1.10392
$566$	−2.77872	−0.116798
$567$	−3.74027	−0.157077
$568$	−6.54034	−0.274427
$569$	21.1121	0.885063	0.442532	−	0.896753i	$-0.354080\pi$
$569$	21.1121	0.885063	0.442532	+	0.896753i	$0.354080\pi$
$570$	−4.02498	−0.168588
$571$	−16.7440	−0.700713	−0.350356	−	0.936616i	$-0.613940\pi$
$571$	−16.7440	−0.700713	−0.350356	+	0.936616i	$0.613940\pi$
$572$	−10.4939	−0.438774
$573$	10.6289	0.444029
$574$	−30.0011	−1.25222
$575$	100.205	4.17883
$576$	1.00000	0.0416667
$577$	−10.2062	−0.424892	−0.212446	−	0.977173i	$-0.568143\pi$
$577$	−10.2062	−0.424892	−0.212446	+	0.977173i	$0.568143\pi$
$578$	−14.8650	−0.618303
$579$	−15.4797	−0.643315
$580$	32.9154	1.36674
$581$	−2.99825	−0.124389
$582$	−9.89551	−0.410182
$583$	−4.48376	−0.185699
$584$	10.7718	0.445740
$585$	9.42020	0.389478
$586$	8.43008	0.348243
$587$	−11.5056	−0.474886	−0.237443	−	0.971401i	$-0.576309\pi$
$587$	−11.5056	−0.474886	−0.237443	+	0.971401i	$0.576309\pi$
$588$	6.98963	0.288248
$589$	3.64850	0.150334
$590$	−23.5563	−0.969799
$591$	−22.7562	−0.936064
$592$	6.44488	0.264883
$593$	−39.3768	−1.61701	−0.808505	−	0.588489i	$-0.799723\pi$
$593$	−39.3768	−1.61701	−0.808505	+	0.588489i	$0.799723\pi$
$594$	−4.48376	−0.183971
$595$	21.9970	0.901790
$596$	−0.0225725	−0.000924607 0
$597$	12.9870	0.531524
$598$	20.9386	0.856243
$599$	−45.1332	−1.84409	−0.922046	−	0.387080i	$-0.873484\pi$
$599$	−45.1332	−1.84409	−0.922046	+	0.387080i	$0.873484\pi$
$600$	11.2005	0.457258
$601$	38.4680	1.56914	0.784571	−	0.620039i	$-0.212883\pi$
$601$	38.4680	1.56914	0.784571	+	0.620039i	$0.212883\pi$
$602$	−3.81077	−0.155316
$603$	7.80442	0.317820
$604$	10.9902	0.447184
$605$	36.6440	1.48979
$606$	15.3441	0.623310
$607$	39.3209	1.59599	0.797993	−	0.602666i	$-0.205895\pi$
$607$	39.3209	1.59599	0.797993	+	0.602666i	$0.205895\pi$
$608$	−1.00000	−0.0405554
$609$	−30.5870	−1.23945
$610$	−4.32457	−0.175097
$611$	−12.9652	−0.524514
$612$	−1.46116	−0.0590637
$613$	−8.46264	−0.341803	−0.170901	−	0.985288i	$-0.554668\pi$
$613$	−8.46264	−0.341803	−0.170901	+	0.985288i	$0.554668\pi$
$614$	5.66668	0.228688
$615$	32.2848	1.30185
$616$	16.7705	0.675702
$617$	−3.68620	−0.148401	−0.0742003	−	0.997243i	$-0.523640\pi$
$617$	−3.68620	−0.148401	−0.0742003	+	0.997243i	$0.523640\pi$
$618$	−3.39610	−0.136611
$619$	9.11764	0.366469	0.183234	−	0.983069i	$-0.441343\pi$
$619$	9.11764	0.366469	0.183234	+	0.983069i	$0.441343\pi$
$620$	−14.6852	−0.589770
$621$	8.94646	0.359009
$622$	29.9977	1.20280
$623$	−0.604972	−0.0242377
$624$	2.34043	0.0936923
$625$	44.4487	1.77795
$626$	−6.84517	−0.273588
$627$	4.48376	0.179064
$628$	1.01938	0.0406777
$629$	−9.41698	−0.375480
$630$	−15.0545	−0.599787
$631$	9.15912	0.364619	0.182309	−	0.983241i	$-0.441643\pi$
$631$	9.15912	0.364619	0.182309	+	0.983241i	$0.441643\pi$
$632$	2.42889	0.0966162
$633$	23.2335	0.923448
$634$	−31.0088	−1.23152
$635$	−63.6804	−2.52708
$636$	1.00000	0.0396526
$637$	16.3588	0.648158
$638$	−36.6672	−1.45167
$639$	−6.54034	−0.258732
$640$	4.02498	0.159101
$641$	−16.5021	−0.651795	−0.325898	−	0.945405i	$-0.605666\pi$
$641$	−16.5021	−0.651795	−0.325898	+	0.945405i	$0.605666\pi$
$642$	4.58737	0.181049
$643$	−4.05300	−0.159835	−0.0799174	−	0.996801i	$-0.525466\pi$
$643$	−4.05300	−0.159835	−0.0799174	+	0.996801i	$0.525466\pi$
$644$	−33.4622	−1.31860
$645$	4.10085	0.161471
$646$	1.46116	0.0574884
$647$	11.4040	0.448338	0.224169	−	0.974550i	$-0.428033\pi$
$647$	11.4040	0.448338	0.224169	+	0.974550i	$0.428033\pi$
$648$	1.00000	0.0392837
$649$	26.2414	1.03006
$650$	26.2140	1.02820
$651$	13.6464	0.534844
$652$	−23.0219	−0.901605
$653$	−46.2972	−1.81175	−0.905875	−	0.423545i	$-0.860785\pi$
$653$	−46.2972	−1.81175	−0.905875	+	0.423545i	$0.860785\pi$
$654$	−0.926185	−0.0362167
$655$	30.2103	1.18041
$656$	8.02111	0.313172
$657$	10.7718	0.420248
$658$	20.7198	0.807741
$659$	3.52001	0.137120	0.0685600	−	0.997647i	$-0.478160\pi$
$659$	3.52001	0.137120	0.0685600	+	0.997647i	$0.478160\pi$
$660$	−18.0471	−0.702482
$661$	−18.6498	−0.725393	−0.362696	−	0.931907i	$-0.618144\pi$
$661$	−18.6498	−0.725393	−0.362696	+	0.931907i	$0.618144\pi$
$662$	7.97442	0.309935
$663$	−3.41974	−0.132812
$664$	0.801614	0.0311087
$665$	15.0545	0.583790
$666$	6.44488	0.249734
$667$	73.1620	2.83285
$668$	16.0936	0.622680
$669$	−15.4328	−0.596667
$670$	31.4127	1.21358
$671$	4.81750	0.185978
$672$	−3.74027	−0.144284
$673$	−32.9003	−1.26821	−0.634106	−	0.773246i	$-0.718632\pi$
$673$	−32.9003	−1.26821	−0.634106	+	0.773246i	$0.718632\pi$
$674$	2.37608	0.0915230
$675$	11.2005	0.431107
$676$	−7.52238	−0.289322
$677$	8.29479	0.318795	0.159397	−	0.987215i	$-0.449045\pi$
$677$	8.29479	0.318795	0.159397	+	0.987215i	$0.449045\pi$
$678$	−6.51925	−0.250370
$679$	37.0119	1.42039
$680$	−5.88113	−0.225531
$681$	24.3933	0.934753
$682$	16.3590	0.626419
$683$	40.0008	1.53059	0.765293	−	0.643682i	$-0.222594\pi$
$683$	40.0008	1.53059	0.765293	+	0.643682i	$0.222594\pi$
$684$	−1.00000	−0.0382360
$685$	59.0957	2.25793
$686$	0.0387848	0.00148081
$687$	−27.2425	−1.03936
$688$	1.01885	0.0388433
$689$	2.34043	0.0891634
$690$	36.0094	1.37085
$691$	28.1000	1.06898	0.534488	−	0.845176i	$-0.320505\pi$
$691$	28.1000	1.06898	0.534488	+	0.845176i	$0.320505\pi$
$692$	−7.54715	−0.286900
$693$	16.7705	0.637058
$694$	22.8134	0.865984
$695$	−29.7598	−1.12885
$696$	8.17776	0.309977
$697$	−11.7201	−0.443930
$698$	−5.25627	−0.198953
$699$	−25.5787	−0.967476
$700$	−41.8929	−1.58340
$701$	21.3407	0.806027	0.403014	−	0.915194i	$-0.367963\pi$
$701$	21.3407	0.806027	0.403014	+	0.915194i	$0.367963\pi$
$702$	2.34043	0.0883339
$703$	−6.44488	−0.243073
$704$	−4.48376	−0.168988
$705$	−22.2970	−0.839753
$706$	−8.12240	−0.305691
$707$	−57.3910	−2.15841
$708$	−5.85253	−0.219952
$709$	41.1460	1.54527	0.772635	−	0.634850i	$-0.218938\pi$
$709$	41.1460	1.54527	0.772635	+	0.634850i	$0.218938\pi$
$710$	−26.3248	−0.987951
$711$	2.42889	0.0910906
$712$	0.161746	0.00606167
$713$	−32.6412	−1.22242
$714$	5.46512	0.204527
$715$	−42.2380	−1.57961
$716$	14.0612	0.525491
$717$	−24.7078	−0.922731
$718$	2.90031	0.108239
$719$	−3.78895	−0.141304	−0.0706519	−	0.997501i	$-0.522508\pi$
$719$	−3.78895	−0.141304	−0.0706519	+	0.997501i	$0.522508\pi$
$720$	4.02498	0.150002
$721$	12.7023	0.473059
$722$	1.00000	0.0372161
$723$	−17.7848	−0.661423
$724$	−3.46743	−0.128866
$725$	91.5950	3.40175
$726$	9.10414	0.337886
$727$	8.83823	0.327792	0.163896	−	0.986478i	$-0.447594\pi$
$727$	8.83823	0.327792	0.163896	+	0.986478i	$0.447594\pi$
$728$	−8.75385	−0.324439
$729$	1.00000	0.0370370
$730$	43.3563	1.60469
$731$	−1.48870	−0.0550615
$732$	−1.07443	−0.0397122
$733$	−5.49357	−0.202910	−0.101455	−	0.994840i	$-0.532350\pi$
$733$	−5.49357	−0.202910	−0.101455	+	0.994840i	$0.532350\pi$
$734$	−22.0274	−0.813047
$735$	28.1332	1.03771
$736$	8.94646	0.329771
$737$	−34.9932	−1.28899
$738$	8.02111	0.295261
$739$	38.3806	1.41185	0.705927	−	0.708285i	$-0.250531\pi$
$739$	38.3806	1.41185	0.705927	+	0.708285i	$0.250531\pi$
$740$	25.9405	0.953593
$741$	−2.34043	−0.0859779
$742$	−3.74027	−0.137310
$743$	−26.5610	−0.974427	−0.487214	−	0.873283i	$-0.661987\pi$
$743$	−26.5610	−0.974427	−0.487214	+	0.873283i	$0.661987\pi$
$744$	−3.64850	−0.133760
$745$	−0.0908541	−0.00332864
$746$	−4.32545	−0.158366
$747$	0.801614	0.0293295
$748$	6.55148	0.239546
$749$	−17.1580	−0.626939
$750$	24.9569	0.911297
$751$	48.2745	1.76156	0.880781	−	0.473523i	$-0.157018\pi$
$751$	48.2745	1.76156	0.880781	+	0.473523i	$0.157018\pi$
$752$	−5.53964	−0.202010
$753$	−23.3589	−0.851245
$754$	19.1395	0.697019
$755$	44.2353	1.60989
$756$	−3.74027	−0.136032
$757$	37.9213	1.37827	0.689137	−	0.724631i	$-0.257990\pi$
$757$	37.9213	1.37827	0.689137	+	0.724631i	$0.257990\pi$
$758$	8.58606	0.311860
$759$	−40.1138	−1.45604
$760$	−4.02498	−0.146002
$761$	−17.5672	−0.636810	−0.318405	−	0.947955i	$-0.603147\pi$
$761$	−17.5672	−0.636810	−0.318405	+	0.947955i	$0.603147\pi$
$762$	−15.8213	−0.573145
$763$	3.46418	0.125412
$764$	10.6289	0.384541
$765$	−5.88113	−0.212633
$766$	7.16444	0.258862
$767$	−13.6975	−0.494586
$768$	1.00000	0.0360844
$769$	−25.0788	−0.904364	−0.452182	−	0.891926i	$-0.649354\pi$
$769$	−25.0788	−0.904364	−0.452182	+	0.891926i	$0.649354\pi$
$770$	67.5010	2.43257
$771$	13.4652	0.484937
$772$	−15.4797	−0.557127
$773$	−31.6883	−1.13975	−0.569874	−	0.821732i	$-0.693008\pi$
$773$	−31.6883	−1.13975	−0.569874	+	0.821732i	$0.693008\pi$
$774$	1.01885	0.0366218
$775$	−40.8650	−1.46791
$776$	−9.89551	−0.355228
$777$	−24.1056	−0.864784
$778$	−35.4585	−1.27125
$779$	−8.02111	−0.287386
$780$	9.42020	0.337297
$781$	29.3254	1.04934
$782$	−13.0722	−0.467460
$783$	8.17776	0.292249
$784$	6.98963	0.249630
$785$	4.10299	0.146442
$786$	7.50569	0.267719
$787$	40.6827	1.45018	0.725092	−	0.688653i	$-0.241797\pi$
$787$	40.6827	1.45018	0.725092	+	0.688653i	$0.241797\pi$
$788$	−22.7562	−0.810656
$789$	21.3051	0.758482
$790$	9.77626	0.347824
$791$	24.3838	0.866987
$792$	−4.48376	−0.159324
$793$	−2.51464	−0.0892973
$794$	−3.06032	−0.108607
$795$	4.02498	0.142751
$796$	12.9870	0.460313
$797$	24.4818	0.867190	0.433595	−	0.901108i	$-0.357245\pi$
$797$	24.4818	0.867190	0.433595	+	0.901108i	$0.357245\pi$
$798$	3.74027	0.132404
$799$	8.09428	0.286355
$800$	11.2005	0.395997
$801$	0.161746	0.00571500
$802$	6.10018	0.215405
$803$	−48.2982	−1.70441
$804$	7.80442	0.275241
$805$	−134.685	−4.74702
$806$	−8.53907	−0.300776
$807$	−23.0804	−0.812470
$808$	15.3441	0.539802
$809$	−2.81381	−0.0989281	−0.0494641	−	0.998776i	$-0.515751\pi$
$809$	−2.81381	−0.0989281	−0.0494641	+	0.998776i	$0.515751\pi$
$810$	4.02498	0.141424
$811$	36.5686	1.28410	0.642048	−	0.766665i	$-0.278085\pi$
$811$	36.5686	1.28410	0.642048	+	0.766665i	$0.278085\pi$
$812$	−30.5870	−1.07339
$813$	4.79923	0.168317
$814$	−28.8973	−1.01285
$815$	−92.6626	−3.24583
$816$	−1.46116	−0.0511507
$817$	−1.01885	−0.0356450
$818$	18.2538	0.638228
$819$	−8.75385	−0.305884
$820$	32.2848	1.12744
$821$	−40.3970	−1.40986	−0.704932	−	0.709275i	$-0.749023\pi$
$821$	−40.3970	−1.40986	−0.704932	+	0.709275i	$0.749023\pi$
$822$	14.6822	0.512101
$823$	−27.7001	−0.965566	−0.482783	−	0.875740i	$-0.660374\pi$
$823$	−27.7001	−0.965566	−0.482783	+	0.875740i	$0.660374\pi$
$824$	−3.39610	−0.118309
$825$	−50.2204	−1.74845
$826$	21.8901	0.761652
$827$	42.9727	1.49431	0.747154	−	0.664651i	$-0.231420\pi$
$827$	42.9727	1.49431	0.747154	+	0.664651i	$0.231420\pi$
$828$	8.94646	0.310911
$829$	−37.6902	−1.30903	−0.654517	−	0.756047i	$-0.727128\pi$
$829$	−37.6902	−1.30903	−0.654517	+	0.756047i	$0.727128\pi$
$830$	3.22648	0.111993
$831$	−24.9115	−0.864171
$832$	2.34043	0.0811399
$833$	−10.2129	−0.353857
$834$	−7.39376	−0.256025
$835$	64.7765	2.24168
$836$	4.48376	0.155074
$837$	−3.64850	−0.126111
$838$	−9.85365	−0.340389
$839$	−27.9360	−0.964458	−0.482229	−	0.876045i	$-0.660173\pi$
$839$	−27.9360	−0.964458	−0.482229	+	0.876045i	$0.660173\pi$
$840$	−15.0545	−0.519431
$841$	37.8758	1.30606
$842$	6.00913	0.207088
$843$	−0.987371	−0.0340068
$844$	23.2335	0.799729
$845$	−30.2774	−1.04158
$846$	−5.53964	−0.190457
$847$	−34.0520	−1.17004
$848$	1.00000	0.0343401
$849$	−2.77872	−0.0953654
$850$	−16.3657	−0.561338
$851$	57.6589	1.97652
$852$	−6.54034	−0.224068
$853$	45.0991	1.54416	0.772082	−	0.635523i	$-0.219215\pi$
$853$	45.0991	1.54416	0.772082	+	0.635523i	$0.219215\pi$
$854$	4.01867	0.137516
$855$	−4.02498	−0.137652
$856$	4.58737	0.156793
$857$	13.0369	0.445330	0.222665	−	0.974895i	$-0.428524\pi$
$857$	13.0369	0.445330	0.222665	+	0.974895i	$0.428524\pi$
$858$	−10.4939	−0.358257
$859$	51.2688	1.74927	0.874635	−	0.484782i	$-0.161101\pi$
$859$	51.2688	1.74927	0.874635	+	0.484782i	$0.161101\pi$
$860$	4.10085	0.139838
$861$	−30.0011	−1.02244
$862$	−3.27274	−0.111470
$863$	9.14399	0.311265	0.155633	−	0.987815i	$-0.450258\pi$
$863$	9.14399	0.311265	0.155633	+	0.987815i	$0.450258\pi$
$864$	1.00000	0.0340207
$865$	−30.3772	−1.03285
$866$	−1.93207	−0.0656545
$867$	−14.8650	−0.504843
$868$	13.6464	0.463188
$869$	−10.8906	−0.369438
$870$	32.9154	1.11594
$871$	18.2657	0.618910
$872$	−0.926185	−0.0313646
$873$	−9.89551	−0.334912
$874$	−8.94646	−0.302619
$875$	−93.3456	−3.15566
$876$	10.7718	0.363945
$877$	−23.8751	−0.806205	−0.403103	−	0.915155i	$-0.632068\pi$
$877$	−23.8751	−0.806205	−0.403103	+	0.915155i	$0.632068\pi$
$878$	−8.00851	−0.270274
$879$	8.43008	0.284339
$880$	−18.0471	−0.608367
$881$	18.7520	0.631771	0.315886	−	0.948797i	$-0.397698\pi$
$881$	18.7520	0.631771	0.315886	+	0.948797i	$0.397698\pi$
$882$	6.98963	0.235353
$883$	0.697381	0.0234688	0.0117344	−	0.999931i	$-0.496265\pi$
$883$	0.697381	0.0234688	0.0117344	+	0.999931i	$0.496265\pi$
$884$	−3.41974	−0.115018
$885$	−23.5563	−0.791838
$886$	−18.8004	−0.631611
$887$	−1.30899	−0.0439515	−0.0219757	−	0.999759i	$-0.506996\pi$
$887$	−1.30899	−0.0439515	−0.0219757	+	0.999759i	$0.506996\pi$
$888$	6.44488	0.216276
$889$	59.1759	1.98470
$890$	0.651023	0.0218223
$891$	−4.48376	−0.150212
$892$	−15.4328	−0.516729
$893$	5.53964	0.185377
$894$	−0.0225725	−0.000754938 0
$895$	56.5961	1.89180
$896$	−3.74027	−0.124954
$897$	20.9386	0.699119
$898$	5.56076	0.185565
$899$	−29.8366	−0.995105
$900$	11.2005	0.373350
$901$	−1.46116	−0.0486782
$902$	−35.9648	−1.19750
$903$	−3.81077	−0.126815
$904$	−6.51925	−0.216827
$905$	−13.9563	−0.463925
$906$	10.9902	0.365124
$907$	−22.5831	−0.749860	−0.374930	−	0.927053i	$-0.622333\pi$
$907$	−22.5831	−0.749860	−0.374930	+	0.927053i	$0.622333\pi$
$908$	24.3933	0.809520
$909$	15.3441	0.508930
$910$	−35.2341	−1.16800
$911$	11.8658	0.393132	0.196566	−	0.980491i	$-0.437021\pi$
$911$	11.8658	0.393132	0.196566	+	0.980491i	$0.437021\pi$
$912$	−1.00000	−0.0331133
$913$	−3.59425	−0.118952
$914$	15.6877	0.518901
$915$	−4.32457	−0.142966
$916$	−27.2425	−0.900116
$917$	−28.0733	−0.927063
$918$	−1.46116	−0.0482253
$919$	−27.2826	−0.899970	−0.449985	−	0.893036i	$-0.648571\pi$
$919$	−27.2826	−0.899970	−0.449985	+	0.893036i	$0.648571\pi$
$920$	36.0094	1.18719
$921$	5.66668	0.186723
$922$	22.5787	0.743590
$923$	−15.3072	−0.503844
$924$	16.7705	0.551709
$925$	72.1859	2.37346
$926$	−38.8603	−1.27703
$927$	−3.39610	−0.111542
$928$	8.17776	0.268448
$929$	46.6649	1.53103	0.765513	−	0.643421i	$-0.222485\pi$
$929$	46.6649	1.53103	0.765513	+	0.643421i	$0.222485\pi$
$930$	−14.6852	−0.481545
$931$	−6.98963	−0.229076
$932$	−25.5787	−0.837858
$933$	29.9977	0.982082
$934$	−12.0843	−0.395411
$935$	26.3696	0.862378
$936$	2.34043	0.0764994
$937$	44.4615	1.45250	0.726248	−	0.687433i	$-0.241263\pi$
$937$	44.4615	1.45250	0.726248	+	0.687433i	$0.241263\pi$
$938$	−29.1906	−0.953108
$939$	−6.84517	−0.223384
$940$	−22.2970	−0.727247
$941$	16.4931	0.537659	0.268830	−	0.963188i	$-0.413363\pi$
$941$	16.4931	0.537659	0.268830	+	0.963188i	$0.413363\pi$
$942$	1.01938	0.0332132
$943$	71.7606	2.33685
$944$	−5.85253	−0.190484
$945$	−15.0545	−0.489724
$946$	−4.56828	−0.148528
$947$	−52.9419	−1.72038	−0.860190	−	0.509974i	$-0.829655\pi$
$947$	−52.9419	−1.72038	−0.860190	+	0.509974i	$0.829655\pi$
$948$	2.42889	0.0788868
$949$	25.2107	0.818373
$950$	−11.2005	−0.363392
$951$	−31.0088	−1.00553
$952$	5.46512	0.177126
$953$	−30.7520	−0.996155	−0.498078	−	0.867132i	$-0.665961\pi$
$953$	−30.7520	−0.996155	−0.498078	+	0.867132i	$0.665961\pi$
$954$	1.00000	0.0323762
$955$	42.7812	1.38437
$956$	−24.7078	−0.799108
$957$	−36.6672	−1.18528
$958$	24.1866	0.781434
$959$	−54.9155	−1.77331
$960$	4.02498	0.129906
$961$	−17.6885	−0.570595
$962$	15.0838	0.486322
$963$	4.58737	0.147826
$964$	−17.7848	−0.572809
$965$	−62.3056	−2.00569
$966$	−33.4622	−1.07663
$967$	−39.1041	−1.25750	−0.628752	−	0.777606i	$-0.716434\pi$
$967$	−39.1041	−1.25750	−0.628752	+	0.777606i	$0.716434\pi$
$968$	9.10414	0.292618
$969$	1.46116	0.0469391
$970$	−39.8293	−1.27884
$971$	−10.6078	−0.340421	−0.170211	−	0.985408i	$-0.554445\pi$
$971$	−10.6078	−0.340421	−0.170211	+	0.985408i	$0.554445\pi$
$972$	1.00000	0.0320750
$973$	27.6547	0.886568
$974$	−36.2113	−1.16028
$975$	26.2140	0.839520
$976$	−1.07443	−0.0343917
$977$	12.4083	0.396978	0.198489	−	0.980103i	$-0.436397\pi$
$977$	12.4083	0.396978	0.198489	+	0.980103i	$0.436397\pi$
$978$	−23.0219	−0.736158
$979$	−0.725229	−0.0231784
$980$	28.1332	0.898681
$981$	−0.926185	−0.0295708
$982$	−28.7909	−0.918753
$983$	18.5361	0.591210	0.295605	−	0.955310i	$-0.404479\pi$
$983$	18.5361	0.591210	0.295605	+	0.955310i	$0.404479\pi$
$984$	8.02111	0.255704
$985$	−91.5933	−2.91841
$986$	−11.9490	−0.380533
$987$	20.7198	0.659518
$988$	−2.34043	−0.0744591
$989$	9.11510	0.289843
$990$	−18.0471	−0.573574
$991$	−42.2621	−1.34250	−0.671250	−	0.741231i	$-0.734242\pi$
$991$	−42.2621	−1.34250	−0.671250	+	0.741231i	$0.734242\pi$
$992$	−3.64850	−0.115840
$993$	7.97442	0.253061
$994$	24.4627	0.775908
$995$	52.2726	1.65715
$996$	0.801614	0.0254001
$997$	−36.9340	−1.16971	−0.584856	−	0.811137i	$-0.698849\pi$
$997$	−36.9340	−1.16971	−0.584856	+	0.811137i	$0.698849\pi$
$998$	−41.9922	−1.32924
$999$	6.44488	0.203907

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.bg.1.11	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bg.1.11	✓	12	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:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.02498 q^{5} +1.00000 q^{6} -3.74027 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.02498 q^{5} +1.00000 q^{6} -3.74027 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.02498 q^{10} -4.48376 q^{11} +1.00000 q^{12} +2.34043 q^{13} -3.74027 q^{14} +4.02498 q^{15} +1.00000 q^{16} -1.46116 q^{17} +1.00000 q^{18} -1.00000 q^{19} +4.02498 q^{20} -3.74027 q^{21} -4.48376 q^{22} +8.94646 q^{23} +1.00000 q^{24} +11.2005 q^{25} +2.34043 q^{26} +1.00000 q^{27} -3.74027 q^{28} +8.17776 q^{29} +4.02498 q^{30} -3.64850 q^{31} +1.00000 q^{32} -4.48376 q^{33} -1.46116 q^{34} -15.0545 q^{35} +1.00000 q^{36} +6.44488 q^{37} -1.00000 q^{38} +2.34043 q^{39} +4.02498 q^{40} +8.02111 q^{41} -3.74027 q^{42} +1.01885 q^{43} -4.48376 q^{44} +4.02498 q^{45} +8.94646 q^{46} -5.53964 q^{47} +1.00000 q^{48} +6.98963 q^{49} +11.2005 q^{50} -1.46116 q^{51} +2.34043 q^{52} +1.00000 q^{53} +1.00000 q^{54} -18.0471 q^{55} -3.74027 q^{56} -1.00000 q^{57} +8.17776 q^{58} -5.85253 q^{59} +4.02498 q^{60} -1.07443 q^{61} -3.64850 q^{62} -3.74027 q^{63} +1.00000 q^{64} +9.42020 q^{65} -4.48376 q^{66} +7.80442 q^{67} -1.46116 q^{68} +8.94646 q^{69} -15.0545 q^{70} -6.54034 q^{71} +1.00000 q^{72} +10.7718 q^{73} +6.44488 q^{74} +11.2005 q^{75} -1.00000 q^{76} +16.7705 q^{77} +2.34043 q^{78} +2.42889 q^{79} +4.02498 q^{80} +1.00000 q^{81} +8.02111 q^{82} +0.801614 q^{83} -3.74027 q^{84} -5.88113 q^{85} +1.01885 q^{86} +8.17776 q^{87} -4.48376 q^{88} +0.161746 q^{89} +4.02498 q^{90} -8.75385 q^{91} +8.94646 q^{92} -3.64850 q^{93} -5.53964 q^{94} -4.02498 q^{95} +1.00000 q^{96} -9.89551 q^{97} +6.98963 q^{98} -4.48376 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 5 q^{5} + 12 q^{6} + 6 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 5 * q^5 + 12 * q^6 + 6 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 5 q^{5} + 12 q^{6} + 6 q^{7} + 12 q^{8} + 12 q^{9} + 5 q^{10} + 7 q^{11} + 12 q^{12} + 9 q^{13} + 6 q^{14} + 5 q^{15} + 12 q^{16} + 25 q^{17} + 12 q^{18} - 12 q^{19} + 5 q^{20} + 6 q^{21} + 7 q^{22} + 22 q^{23} + 12 q^{24} + 33 q^{25} + 9 q^{26} + 12 q^{27} + 6 q^{28} + q^{29} + 5 q^{30} + 23 q^{31} + 12 q^{32} + 7 q^{33} + 25 q^{34} + 5 q^{35} + 12 q^{36} - q^{37} - 12 q^{38} + 9 q^{39} + 5 q^{40} - 15 q^{41} + 6 q^{42} + 2 q^{43} + 7 q^{44} + 5 q^{45} + 22 q^{46} + 11 q^{47} + 12 q^{48} + 36 q^{49} + 33 q^{50} + 25 q^{51} + 9 q^{52} + 12 q^{53} + 12 q^{54} - 4 q^{55} + 6 q^{56} - 12 q^{57} + q^{58} + 3 q^{59} + 5 q^{60} + 16 q^{61} + 23 q^{62} + 6 q^{63} + 12 q^{64} + 7 q^{65} + 7 q^{66} - 2 q^{67} + 25 q^{68} + 22 q^{69} + 5 q^{70} - 4 q^{71} + 12 q^{72} + 35 q^{73} - q^{74} + 33 q^{75} - 12 q^{76} + 11 q^{77} + 9 q^{78} + 4 q^{79} + 5 q^{80} + 12 q^{81} - 15 q^{82} + 39 q^{83} + 6 q^{84} + 10 q^{85} + 2 q^{86} + q^{87} + 7 q^{88} + 11 q^{89} + 5 q^{90} - 18 q^{91} + 22 q^{92} + 23 q^{93} + 11 q^{94} - 5 q^{95} + 12 q^{96} - 21 q^{97} + 36 q^{98} + 7 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 5 * q^5 + 12 * q^6 + 6 * q^7 + 12 * q^8 + 12 * q^9 + 5 * q^10 + 7 * q^11 + 12 * q^12 + 9 * q^13 + 6 * q^14 + 5 * q^15 + 12 * q^16 + 25 * q^17 + 12 * q^18 - 12 * q^19 + 5 * q^20 + 6 * q^21 + 7 * q^22 + 22 * q^23 + 12 * q^24 + 33 * q^25 + 9 * q^26 + 12 * q^27 + 6 * q^28 + q^29 + 5 * q^30 + 23 * q^31 + 12 * q^32 + 7 * q^33 + 25 * q^34 + 5 * q^35 + 12 * q^36 - q^37 - 12 * q^38 + 9 * q^39 + 5 * q^40 - 15 * q^41 + 6 * q^42 + 2 * q^43 + 7 * q^44 + 5 * q^45 + 22 * q^46 + 11 * q^47 + 12 * q^48 + 36 * q^49 + 33 * q^50 + 25 * q^51 + 9 * q^52 + 12 * q^53 + 12 * q^54 - 4 * q^55 + 6 * q^56 - 12 * q^57 + q^58 + 3 * q^59 + 5 * q^60 + 16 * q^61 + 23 * q^62 + 6 * q^63 + 12 * q^64 + 7 * q^65 + 7 * q^66 - 2 * q^67 + 25 * q^68 + 22 * q^69 + 5 * q^70 - 4 * q^71 + 12 * q^72 + 35 * q^73 - q^74 + 33 * q^75 - 12 * q^76 + 11 * q^77 + 9 * q^78 + 4 * q^79 + 5 * q^80 + 12 * q^81 - 15 * q^82 + 39 * q^83 + 6 * q^84 + 10 * q^85 + 2 * q^86 + q^87 + 7 * q^88 + 11 * q^89 + 5 * q^90 - 18 * q^91 + 22 * q^92 + 23 * q^93 + 11 * q^94 - 5 * q^95 + 12 * q^96 - 21 * q^97 + 36 * q^98 + 7 * q^99

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