LMFDB - Embedded newform 6042.2.a.bc.1.7

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:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 20x^{7} + 69x^{6} + 27x^{5} - 185x^{4} + 8x^{3} + 109x^{2} - 8x - 14 $ x^9 - 3x^8 - 20x^7 + 69x^6 + 27x^5 - 185x^4 + 8x^3 + 109x^2 - 8x - 14
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.744377$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.744377 q^{5} -1.00000 q^{6} -0.530367 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.744377 q^{5} -1.00000 q^{6} -0.530367 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.744377 q^{10} -1.93227 q^{11} -1.00000 q^{12} -3.52765 q^{13} -0.530367 q^{14} -0.744377 q^{15} +1.00000 q^{16} -0.585136 q^{17} +1.00000 q^{18} +1.00000 q^{19} +0.744377 q^{20} +0.530367 q^{21} -1.93227 q^{22} +6.08718 q^{23} -1.00000 q^{24} -4.44590 q^{25} -3.52765 q^{26} -1.00000 q^{27} -0.530367 q^{28} +8.24539 q^{29} -0.744377 q^{30} -10.6237 q^{31} +1.00000 q^{32} +1.93227 q^{33} -0.585136 q^{34} -0.394793 q^{35} +1.00000 q^{36} -3.64091 q^{37} +1.00000 q^{38} +3.52765 q^{39} +0.744377 q^{40} +11.3810 q^{41} +0.530367 q^{42} -3.08412 q^{43} -1.93227 q^{44} +0.744377 q^{45} +6.08718 q^{46} -0.785151 q^{47} -1.00000 q^{48} -6.71871 q^{49} -4.44590 q^{50} +0.585136 q^{51} -3.52765 q^{52} -1.00000 q^{53} -1.00000 q^{54} -1.43834 q^{55} -0.530367 q^{56} -1.00000 q^{57} +8.24539 q^{58} -8.73714 q^{59} -0.744377 q^{60} -13.5587 q^{61} -10.6237 q^{62} -0.530367 q^{63} +1.00000 q^{64} -2.62591 q^{65} +1.93227 q^{66} +7.13180 q^{67} -0.585136 q^{68} -6.08718 q^{69} -0.394793 q^{70} +13.3351 q^{71} +1.00000 q^{72} -13.4567 q^{73} -3.64091 q^{74} +4.44590 q^{75} +1.00000 q^{76} +1.02481 q^{77} +3.52765 q^{78} +15.9737 q^{79} +0.744377 q^{80} +1.00000 q^{81} +11.3810 q^{82} -12.4878 q^{83} +0.530367 q^{84} -0.435562 q^{85} -3.08412 q^{86} -8.24539 q^{87} -1.93227 q^{88} -14.1811 q^{89} +0.744377 q^{90} +1.87095 q^{91} +6.08718 q^{92} +10.6237 q^{93} -0.785151 q^{94} +0.744377 q^{95} -1.00000 q^{96} -11.0075 q^{97} -6.71871 q^{98} -1.93227 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 3 q^{5} - 9 q^{6} - 7 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 3 * q^5 - 9 * q^6 - 7 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 3 q^{5} - 9 q^{6} - 7 q^{7} + 9 q^{8} + 9 q^{9} - 3 q^{10} + 4 q^{11} - 9 q^{12} - 5 q^{13} - 7 q^{14} + 3 q^{15} + 9 q^{16} - 28 q^{17} + 9 q^{18} + 9 q^{19} - 3 q^{20} + 7 q^{21} + 4 q^{22} - 10 q^{23} - 9 q^{24} + 4 q^{25} - 5 q^{26} - 9 q^{27} - 7 q^{28} + 3 q^{30} + 5 q^{31} + 9 q^{32} - 4 q^{33} - 28 q^{34} - 10 q^{35} + 9 q^{36} - 25 q^{37} + 9 q^{38} + 5 q^{39} - 3 q^{40} - 7 q^{41} + 7 q^{42} - 16 q^{43} + 4 q^{44} - 3 q^{45} - 10 q^{46} - 9 q^{47} - 9 q^{48} + 44 q^{49} + 4 q^{50} + 28 q^{51} - 5 q^{52} - 9 q^{53} - 9 q^{54} - 31 q^{55} - 7 q^{56} - 9 q^{57} - 3 q^{59} + 3 q^{60} - 16 q^{61} + 5 q^{62} - 7 q^{63} + 9 q^{64} - 33 q^{65} - 4 q^{66} - 13 q^{67} - 28 q^{68} + 10 q^{69} - 10 q^{70} - 4 q^{71} + 9 q^{72} - 29 q^{73} - 25 q^{74} - 4 q^{75} + 9 q^{76} - 33 q^{77} + 5 q^{78} + 13 q^{79} - 3 q^{80} + 9 q^{81} - 7 q^{82} - 35 q^{83} + 7 q^{84} + 3 q^{85} - 16 q^{86} + 4 q^{88} - 19 q^{89} - 3 q^{90} - 10 q^{92} - 5 q^{93} - 9 q^{94} - 3 q^{95} - 9 q^{96} - 12 q^{97} + 44 q^{98} + 4 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 3 * q^5 - 9 * q^6 - 7 * q^7 + 9 * q^8 + 9 * q^9 - 3 * q^10 + 4 * q^11 - 9 * q^12 - 5 * q^13 - 7 * q^14 + 3 * q^15 + 9 * q^16 - 28 * q^17 + 9 * q^18 + 9 * q^19 - 3 * q^20 + 7 * q^21 + 4 * q^22 - 10 * q^23 - 9 * q^24 + 4 * q^25 - 5 * q^26 - 9 * q^27 - 7 * q^28 + 3 * q^30 + 5 * q^31 + 9 * q^32 - 4 * q^33 - 28 * q^34 - 10 * q^35 + 9 * q^36 - 25 * q^37 + 9 * q^38 + 5 * q^39 - 3 * q^40 - 7 * q^41 + 7 * q^42 - 16 * q^43 + 4 * q^44 - 3 * q^45 - 10 * q^46 - 9 * q^47 - 9 * q^48 + 44 * q^49 + 4 * q^50 + 28 * q^51 - 5 * q^52 - 9 * q^53 - 9 * q^54 - 31 * q^55 - 7 * q^56 - 9 * q^57 - 3 * q^59 + 3 * q^60 - 16 * q^61 + 5 * q^62 - 7 * q^63 + 9 * q^64 - 33 * q^65 - 4 * q^66 - 13 * q^67 - 28 * q^68 + 10 * q^69 - 10 * q^70 - 4 * q^71 + 9 * q^72 - 29 * q^73 - 25 * q^74 - 4 * q^75 + 9 * q^76 - 33 * q^77 + 5 * q^78 + 13 * q^79 - 3 * q^80 + 9 * q^81 - 7 * q^82 - 35 * q^83 + 7 * q^84 + 3 * q^85 - 16 * q^86 + 4 * q^88 - 19 * q^89 - 3 * q^90 - 10 * q^92 - 5 * q^93 - 9 * q^94 - 3 * q^95 - 9 * q^96 - 12 * q^97 + 44 * q^98 + 4 * 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
$5$	0.744377	0.332896	0.166448	−	0.986050i	$-0.446770\pi$
$5$	0.744377	0.332896	0.166448	+	0.986050i	$0.446770\pi$
$6$	−1.00000	−0.408248
$7$	−0.530367	−0.200460	−0.100230	−	0.994964i	$-0.531958\pi$
$7$	−0.530367	−0.200460	−0.100230	+	0.994964i	$0.531958\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.744377	0.235393
$11$	−1.93227	−0.582600	−0.291300	−	0.956632i	$-0.594088\pi$
$11$	−1.93227	−0.582600	−0.291300	+	0.956632i	$0.594088\pi$
$12$	−1.00000	−0.288675
$13$	−3.52765	−0.978395	−0.489197	−	0.872173i	$-0.662710\pi$
$13$	−3.52765	−0.978395	−0.489197	+	0.872173i	$0.662710\pi$
$14$	−0.530367	−0.141746
$15$	−0.744377	−0.192197
$16$	1.00000	0.250000
$17$	−0.585136	−0.141916	−0.0709582	−	0.997479i	$-0.522606\pi$
$17$	−0.585136	−0.141916	−0.0709582	+	0.997479i	$0.522606\pi$
$18$	1.00000	0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0.744377	0.166448
$21$	0.530367	0.115735
$22$	−1.93227	−0.411961
$23$	6.08718	1.26927	0.634633	−	0.772814i	$-0.281151\pi$
$23$	6.08718	1.26927	0.634633	+	0.772814i	$0.281151\pi$
$24$	−1.00000	−0.204124
$25$	−4.44590	−0.889180
$26$	−3.52765	−0.691830
$27$	−1.00000	−0.192450
$28$	−0.530367	−0.100230
$29$	8.24539	1.53113	0.765565	−	0.643359i	$-0.222460\pi$
$29$	8.24539	1.53113	0.765565	+	0.643359i	$0.222460\pi$
$30$	−0.744377	−0.135904
$31$	−10.6237	−1.90807	−0.954034	−	0.299700i	$-0.903114\pi$
$31$	−10.6237	−1.90807	−0.954034	+	0.299700i	$0.903114\pi$
$32$	1.00000	0.176777
$33$	1.93227	0.336364
$34$	−0.585136	−0.100350
$35$	−0.394793	−0.0667322
$36$	1.00000	0.166667
$37$	−3.64091	−0.598562	−0.299281	−	0.954165i	$-0.596747\pi$
$37$	−3.64091	−0.598562	−0.299281	+	0.954165i	$0.596747\pi$
$38$	1.00000	0.162221
$39$	3.52765	0.564877
$40$	0.744377	0.117696
$41$	11.3810	1.77742	0.888708	−	0.458475i	$-0.151604\pi$
$41$	11.3810	1.77742	0.888708	+	0.458475i	$0.151604\pi$
$42$	0.530367	0.0818373
$43$	−3.08412	−0.470324	−0.235162	−	0.971956i	$-0.575562\pi$
$43$	−3.08412	−0.470324	−0.235162	+	0.971956i	$0.575562\pi$
$44$	−1.93227	−0.291300
$45$	0.744377	0.110965
$46$	6.08718	0.897506
$47$	−0.785151	−0.114526	−0.0572630	−	0.998359i	$-0.518237\pi$
$47$	−0.785151	−0.114526	−0.0572630	+	0.998359i	$0.518237\pi$
$48$	−1.00000	−0.144338
$49$	−6.71871	−0.959816
$50$	−4.44590	−0.628746
$51$	0.585136	0.0819354
$52$	−3.52765	−0.489197
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−1.00000	−0.136083
$55$	−1.43834	−0.193945
$56$	−0.530367	−0.0708732
$57$	−1.00000	−0.132453
$58$	8.24539	1.08267
$59$	−8.73714	−1.13748	−0.568739	−	0.822518i	$-0.692569\pi$
$59$	−8.73714	−1.13748	−0.568739	+	0.822518i	$0.692569\pi$
$60$	−0.744377	−0.0960987
$61$	−13.5587	−1.73601	−0.868005	−	0.496556i	$-0.834598\pi$
$61$	−13.5587	−1.73601	−0.868005	+	0.496556i	$0.834598\pi$
$62$	−10.6237	−1.34921
$63$	−0.530367	−0.0668199
$64$	1.00000	0.125000
$65$	−2.62591	−0.325703
$66$	1.93227	0.237846
$67$	7.13180	0.871288	0.435644	−	0.900119i	$-0.356521\pi$
$67$	7.13180	0.871288	0.435644	+	0.900119i	$0.356521\pi$
$68$	−0.585136	−0.0709582
$69$	−6.08718	−0.732811
$70$	−0.394793	−0.0471868
$71$	13.3351	1.58259	0.791294	−	0.611436i	$-0.209408\pi$
$71$	13.3351	1.58259	0.791294	+	0.611436i	$0.209408\pi$
$72$	1.00000	0.117851
$73$	−13.4567	−1.57499	−0.787495	−	0.616321i	$-0.788622\pi$
$73$	−13.4567	−1.57499	−0.787495	+	0.616321i	$0.788622\pi$
$74$	−3.64091	−0.423247
$75$	4.44590	0.513369
$76$	1.00000	0.114708
$77$	1.02481	0.116788
$78$	3.52765	0.399428
$79$	15.9737	1.79718	0.898589	−	0.438792i	$-0.144594\pi$
$79$	15.9737	1.79718	0.898589	+	0.438792i	$0.144594\pi$
$80$	0.744377	0.0832239
$81$	1.00000	0.111111
$82$	11.3810	1.25682
$83$	−12.4878	−1.37071	−0.685355	−	0.728209i	$-0.740353\pi$
$83$	−12.4878	−1.37071	−0.685355	+	0.728209i	$0.740353\pi$
$84$	0.530367	0.0578677
$85$	−0.435562	−0.0472433
$86$	−3.08412	−0.332569
$87$	−8.24539	−0.883998
$88$	−1.93227	−0.205980
$89$	−14.1811	−1.50319	−0.751596	−	0.659623i	$-0.770716\pi$
$89$	−14.1811	−1.50319	−0.751596	+	0.659623i	$0.770716\pi$
$90$	0.744377	0.0784643
$91$	1.87095	0.196129
$92$	6.08718	0.634633
$93$	10.6237	1.10162
$94$	−0.785151	−0.0809822
$95$	0.744377	0.0763715
$96$	−1.00000	−0.102062
$97$	−11.0075	−1.11765	−0.558824	−	0.829286i	$-0.688747\pi$
$97$	−11.0075	−1.11765	−0.558824	+	0.829286i	$0.688747\pi$
$98$	−6.71871	−0.678692
$99$	−1.93227	−0.194200
$100$	−4.44590	−0.444590
$101$	−0.863516	−0.0859231	−0.0429615	−	0.999077i	$-0.513679\pi$
$101$	−0.863516	−0.0859231	−0.0429615	+	0.999077i	$0.513679\pi$
$102$	0.585136	0.0579371
$103$	−18.1130	−1.78472	−0.892362	−	0.451320i	$-0.850953\pi$
$103$	−18.1130	−1.78472	−0.892362	+	0.451320i	$0.850953\pi$
$104$	−3.52765	−0.345915
$105$	0.394793	0.0385278
$106$	−1.00000	−0.0971286
$107$	−16.5544	−1.60037	−0.800187	−	0.599751i	$-0.795266\pi$
$107$	−16.5544	−1.60037	−0.800187	+	0.599751i	$0.795266\pi$
$108$	−1.00000	−0.0962250
$109$	20.0104	1.91665	0.958323	−	0.285686i	$-0.0922214\pi$
$109$	20.0104	1.91665	0.958323	+	0.285686i	$0.0922214\pi$
$110$	−1.43834	−0.137140
$111$	3.64091	0.345580
$112$	−0.530367	−0.0501149
$113$	−6.93156	−0.652067	−0.326033	−	0.945358i	$-0.605712\pi$
$113$	−6.93156	−0.652067	−0.326033	+	0.945358i	$0.605712\pi$
$114$	−1.00000	−0.0936586
$115$	4.53116	0.422533
$116$	8.24539	0.765565
$117$	−3.52765	−0.326132
$118$	−8.73714	−0.804319
$119$	0.310337	0.0284485
$120$	−0.744377	−0.0679520
$121$	−7.26634	−0.660577
$122$	−13.5587	−1.22754
$123$	−11.3810	−1.02619
$124$	−10.6237	−0.954034
$125$	−7.03132	−0.628900
$126$	−0.530367	−0.0472488
$127$	2.40326	0.213255	0.106627	−	0.994299i	$-0.465995\pi$
$127$	2.40326	0.213255	0.106627	+	0.994299i	$0.465995\pi$
$128$	1.00000	0.0883883
$129$	3.08412	0.271542
$130$	−2.62591	−0.230307
$131$	6.75919	0.590553	0.295277	−	0.955412i	$-0.404588\pi$
$131$	6.75919	0.590553	0.295277	+	0.955412i	$0.404588\pi$
$132$	1.93227	0.168182
$133$	−0.530367	−0.0459886
$134$	7.13180	0.616094
$135$	−0.744377	−0.0640658
$136$	−0.585136	−0.0501750
$137$	−17.7324	−1.51498	−0.757490	−	0.652846i	$-0.773575\pi$
$137$	−17.7324	−1.51498	−0.757490	+	0.652846i	$0.773575\pi$
$138$	−6.08718	−0.518175
$139$	16.7123	1.41752	0.708761	−	0.705449i	$-0.249254\pi$
$139$	16.7123	1.41752	0.708761	+	0.705449i	$0.249254\pi$
$140$	−0.394793	−0.0333661
$141$	0.785151	0.0661217
$142$	13.3351	1.11906
$143$	6.81637	0.570013
$144$	1.00000	0.0833333
$145$	6.13768	0.509706
$146$	−13.4567	−1.11369
$147$	6.71871	0.554150
$148$	−3.64091	−0.299281
$149$	−3.85701	−0.315979	−0.157989	−	0.987441i	$-0.550501\pi$
$149$	−3.85701	−0.315979	−0.157989	+	0.987441i	$0.550501\pi$
$150$	4.44590	0.363006
$151$	20.6537	1.68078	0.840388	−	0.541985i	$-0.182327\pi$
$151$	20.6537	1.68078	0.840388	+	0.541985i	$0.182327\pi$
$152$	1.00000	0.0811107
$153$	−0.585136	−0.0473054
$154$	1.02481	0.0825815
$155$	−7.90802	−0.635187
$156$	3.52765	0.282438
$157$	−7.35034	−0.586621	−0.293311	−	0.956017i	$-0.594757\pi$
$157$	−7.35034	−0.586621	−0.293311	+	0.956017i	$0.594757\pi$
$158$	15.9737	1.27080
$159$	1.00000	0.0793052
$160$	0.744377	0.0588482
$161$	−3.22844	−0.254437
$162$	1.00000	0.0785674
$163$	14.2320	1.11474	0.557369	−	0.830265i	$-0.311811\pi$
$163$	14.2320	1.11474	0.557369	+	0.830265i	$0.311811\pi$
$164$	11.3810	0.888708
$165$	1.43834	0.111974
$166$	−12.4878	−0.969239
$167$	−19.7726	−1.53005	−0.765026	−	0.643999i	$-0.777274\pi$
$167$	−19.7726	−1.53005	−0.765026	+	0.643999i	$0.777274\pi$
$168$	0.530367	0.0409187
$169$	−0.555662	−0.0427432
$170$	−0.435562	−0.0334061
$171$	1.00000	0.0764719
$172$	−3.08412	−0.235162
$173$	15.4374	1.17369	0.586844	−	0.809700i	$-0.300370\pi$
$173$	15.4374	1.17369	0.586844	+	0.809700i	$0.300370\pi$
$174$	−8.24539	−0.625081
$175$	2.35796	0.178245
$176$	−1.93227	−0.145650
$177$	8.73714	0.656723
$178$	−14.1811	−1.06292
$179$	−18.6105	−1.39102	−0.695508	−	0.718519i	$-0.744821\pi$
$179$	−18.6105	−1.39102	−0.695508	+	0.718519i	$0.744821\pi$
$180$	0.744377	0.0554826
$181$	−3.36049	−0.249783	−0.124892	−	0.992170i	$-0.539858\pi$
$181$	−3.36049	−0.249783	−0.124892	+	0.992170i	$0.539858\pi$
$182$	1.87095	0.138684
$183$	13.5587	1.00229
$184$	6.08718	0.448753
$185$	−2.71021	−0.199259
$186$	10.6237	0.778965
$187$	1.13064	0.0826805
$188$	−0.785151	−0.0572630
$189$	0.530367	0.0385785
$190$	0.744377	0.0540028
$191$	−2.91434	−0.210874	−0.105437	−	0.994426i	$-0.533624\pi$
$191$	−2.91434	−0.210874	−0.105437	+	0.994426i	$0.533624\pi$
$192$	−1.00000	−0.0721688
$193$	−6.38394	−0.459526	−0.229763	−	0.973247i	$-0.573795\pi$
$193$	−6.38394	−0.459526	−0.229763	+	0.973247i	$0.573795\pi$
$194$	−11.0075	−0.790296
$195$	2.62591	0.188045
$196$	−6.71871	−0.479908
$197$	−16.3496	−1.16486	−0.582430	−	0.812881i	$-0.697898\pi$
$197$	−16.3496	−1.16486	−0.582430	+	0.812881i	$0.697898\pi$
$198$	−1.93227	−0.137320
$199$	−9.57013	−0.678408	−0.339204	−	0.940713i	$-0.610158\pi$
$199$	−9.57013	−0.678408	−0.339204	+	0.940713i	$0.610158\pi$
$200$	−4.44590	−0.314373
$201$	−7.13180	−0.503038
$202$	−0.863516	−0.0607568
$203$	−4.37308	−0.306930
$204$	0.585136	0.0409677
$205$	8.47177	0.591694
$206$	−18.1130	−1.26199
$207$	6.08718	0.423088
$208$	−3.52765	−0.244599
$209$	−1.93227	−0.133658
$210$	0.394793	0.0272433
$211$	−16.5041	−1.13619	−0.568095	−	0.822963i	$-0.692320\pi$
$211$	−16.5041	−1.13619	−0.568095	+	0.822963i	$0.692320\pi$
$212$	−1.00000	−0.0686803
$213$	−13.3351	−0.913708
$214$	−16.5544	−1.13164
$215$	−2.29575	−0.156569
$216$	−1.00000	−0.0680414
$217$	5.63444	0.382491
$218$	20.0104	1.35527
$219$	13.4567	0.909321
$220$	−1.43834	−0.0969726
$221$	2.06416	0.138850
$222$	3.64091	0.244362
$223$	−18.8946	−1.26528	−0.632640	−	0.774446i	$-0.718029\pi$
$223$	−18.8946	−1.26528	−0.632640	+	0.774446i	$0.718029\pi$
$224$	−0.530367	−0.0354366
$225$	−4.44590	−0.296393
$226$	−6.93156	−0.461081
$227$	12.4825	0.828491	0.414245	−	0.910165i	$-0.364045\pi$
$227$	12.4825	0.828491	0.414245	+	0.910165i	$0.364045\pi$
$228$	−1.00000	−0.0662266
$229$	8.13362	0.537485	0.268742	−	0.963212i	$-0.413392\pi$
$229$	8.13362	0.537485	0.268742	+	0.963212i	$0.413392\pi$
$230$	4.53116	0.298776
$231$	−1.02481	−0.0674275
$232$	8.24539	0.541336
$233$	23.3406	1.52909	0.764546	−	0.644569i	$-0.222963\pi$
$233$	23.3406	1.52909	0.764546	+	0.644569i	$0.222963\pi$
$234$	−3.52765	−0.230610
$235$	−0.584449	−0.0381252
$236$	−8.73714	−0.568739
$237$	−15.9737	−1.03760
$238$	0.310337	0.0201161
$239$	13.8939	0.898721	0.449360	−	0.893351i	$-0.351652\pi$
$239$	13.8939	0.898721	0.449360	+	0.893351i	$0.351652\pi$
$240$	−0.744377	−0.0480494
$241$	−8.68689	−0.559572	−0.279786	−	0.960062i	$-0.590263\pi$
$241$	−8.68689	−0.559572	−0.279786	+	0.960062i	$0.590263\pi$
$242$	−7.26634	−0.467098
$243$	−1.00000	−0.0641500
$244$	−13.5587	−0.868005
$245$	−5.00126	−0.319519
$246$	−11.3810	−0.725627
$247$	−3.52765	−0.224459
$248$	−10.6237	−0.674604
$249$	12.4878	0.791380
$250$	−7.03132	−0.444699
$251$	−6.14646	−0.387961	−0.193981	−	0.981005i	$-0.562140\pi$
$251$	−6.14646	−0.387961	−0.193981	+	0.981005i	$0.562140\pi$
$252$	−0.530367	−0.0334099
$253$	−11.7621	−0.739474
$254$	2.40326	0.150794
$255$	0.435562	0.0272760
$256$	1.00000	0.0625000
$257$	9.01643	0.562429	0.281215	−	0.959645i	$-0.409263\pi$
$257$	9.01643	0.562429	0.281215	+	0.959645i	$0.409263\pi$
$258$	3.08412	0.192009
$259$	1.93102	0.119988
$260$	−2.62591	−0.162852
$261$	8.24539	0.510377
$262$	6.75919	0.417584
$263$	10.8962	0.671887	0.335943	−	0.941882i	$-0.390945\pi$
$263$	10.8962	0.671887	0.335943	+	0.941882i	$0.390945\pi$
$264$	1.93227	0.118923
$265$	−0.744377	−0.0457267
$266$	−0.530367	−0.0325189
$267$	14.1811	0.867869
$268$	7.13180	0.435644
$269$	−9.30251	−0.567184	−0.283592	−	0.958945i	$-0.591526\pi$
$269$	−9.30251	−0.567184	−0.283592	+	0.958945i	$0.591526\pi$
$270$	−0.744377	−0.0453014
$271$	12.9504	0.786680	0.393340	−	0.919393i	$-0.371319\pi$
$271$	12.9504	0.786680	0.393340	+	0.919393i	$0.371319\pi$
$272$	−0.585136	−0.0354791
$273$	−1.87095	−0.113235
$274$	−17.7324	−1.07125
$275$	8.59067	0.518037
$276$	−6.08718	−0.366405
$277$	0.860585	0.0517075	0.0258538	−	0.999666i	$-0.491770\pi$
$277$	0.860585	0.0517075	0.0258538	+	0.999666i	$0.491770\pi$
$278$	16.7123	1.00234
$279$	−10.6237	−0.636022
$280$	−0.394793	−0.0235934
$281$	−13.0418	−0.778006	−0.389003	−	0.921237i	$-0.627180\pi$
$281$	−13.0418	−0.778006	−0.389003	+	0.921237i	$0.627180\pi$
$282$	0.785151	0.0467551
$283$	14.9903	0.891081	0.445540	−	0.895262i	$-0.353012\pi$
$283$	14.9903	0.891081	0.445540	+	0.895262i	$0.353012\pi$
$284$	13.3351	0.791294
$285$	−0.744377	−0.0440931
$286$	6.81637	0.403060
$287$	−6.03611	−0.356300
$288$	1.00000	0.0589256
$289$	−16.6576	−0.979860
$290$	6.13768	0.360417
$291$	11.0075	0.645274
$292$	−13.4567	−0.787495
$293$	13.2197	0.772306	0.386153	−	0.922435i	$-0.373804\pi$
$293$	13.2197	0.772306	0.386153	+	0.922435i	$0.373804\pi$
$294$	6.71871	0.391843
$295$	−6.50373	−0.378662
$296$	−3.64091	−0.211624
$297$	1.93227	0.112121
$298$	−3.85701	−0.223431
$299$	−21.4735	−1.24184
$300$	4.44590	0.256684
$301$	1.63571	0.0942810
$302$	20.6537	1.18849
$303$	0.863516	0.0496077
$304$	1.00000	0.0573539
$305$	−10.0928	−0.577910
$306$	−0.585136	−0.0334500
$307$	14.8509	0.847588	0.423794	−	0.905759i	$-0.360698\pi$
$307$	14.8509	0.847588	0.423794	+	0.905759i	$0.360698\pi$
$308$	1.02481	0.0583939
$309$	18.1130	1.03041
$310$	−7.90802	−0.449145
$311$	2.24770	0.127455	0.0637276	−	0.997967i	$-0.479701\pi$
$311$	2.24770	0.127455	0.0637276	+	0.997967i	$0.479701\pi$
$312$	3.52765	0.199714
$313$	20.8891	1.18072	0.590360	−	0.807140i	$-0.298986\pi$
$313$	20.8891	1.18072	0.590360	+	0.807140i	$0.298986\pi$
$314$	−7.35034	−0.414804
$315$	−0.394793	−0.0222441
$316$	15.9737	0.898589
$317$	−3.45854	−0.194251	−0.0971255	−	0.995272i	$-0.530965\pi$
$317$	−3.45854	−0.194251	−0.0971255	+	0.995272i	$0.530965\pi$
$318$	1.00000	0.0560772
$319$	−15.9323	−0.892037
$320$	0.744377	0.0416120
$321$	16.5544	0.923976
$322$	−3.22844	−0.179914
$323$	−0.585136	−0.0325578
$324$	1.00000	0.0555556
$325$	15.6836	0.869970
$326$	14.2320	0.788238
$327$	−20.0104	−1.10658
$328$	11.3810	0.628411
$329$	0.416418	0.0229579
$330$	1.43834	0.0791778
$331$	−23.2899	−1.28013	−0.640063	−	0.768322i	$-0.721092\pi$
$331$	−23.2899	−1.28013	−0.640063	+	0.768322i	$0.721092\pi$
$332$	−12.4878	−0.685355
$333$	−3.64091	−0.199521
$334$	−19.7726	−1.08191
$335$	5.30875	0.290048
$336$	0.530367	0.0289339
$337$	−3.47204	−0.189134	−0.0945671	−	0.995518i	$-0.530147\pi$
$337$	−3.47204	−0.189134	−0.0945671	+	0.995518i	$0.530147\pi$
$338$	−0.555662	−0.0302240
$339$	6.93156	0.376471
$340$	−0.435562	−0.0236217
$341$	20.5278	1.11164
$342$	1.00000	0.0540738
$343$	7.27595	0.392864
$344$	−3.08412	−0.166285
$345$	−4.53116	−0.243950
$346$	15.4374	0.829922
$347$	2.53681	0.136183	0.0680916	−	0.997679i	$-0.478309\pi$
$347$	2.53681	0.136183	0.0680916	+	0.997679i	$0.478309\pi$
$348$	−8.24539	−0.441999
$349$	3.77800	0.202232	0.101116	−	0.994875i	$-0.467759\pi$
$349$	3.77800	0.202232	0.101116	+	0.994875i	$0.467759\pi$
$350$	2.35796	0.126038
$351$	3.52765	0.188292
$352$	−1.93227	−0.102990
$353$	16.6367	0.885484	0.442742	−	0.896649i	$-0.354006\pi$
$353$	16.6367	0.885484	0.442742	+	0.896649i	$0.354006\pi$
$354$	8.73714	0.464374
$355$	9.92637	0.526837
$356$	−14.1811	−0.751596
$357$	−0.310337	−0.0164248
$358$	−18.6105	−0.983596
$359$	−29.2948	−1.54612	−0.773061	−	0.634332i	$-0.781275\pi$
$359$	−29.2948	−1.54612	−0.773061	+	0.634332i	$0.781275\pi$
$360$	0.744377	0.0392321
$361$	1.00000	0.0526316
$362$	−3.36049	−0.176623
$363$	7.26634	0.381384
$364$	1.87095	0.0980644
$365$	−10.0169	−0.524307
$366$	13.5587	0.708723
$367$	−16.4848	−0.860499	−0.430250	−	0.902710i	$-0.641574\pi$
$367$	−16.4848	−0.860499	−0.430250	+	0.902710i	$0.641574\pi$
$368$	6.08718	0.317316
$369$	11.3810	0.592472
$370$	−2.71021	−0.140897
$371$	0.530367	0.0275353
$372$	10.6237	0.550812
$373$	−34.3219	−1.77712	−0.888560	−	0.458760i	$-0.848294\pi$
$373$	−34.3219	−1.77712	−0.888560	+	0.458760i	$0.848294\pi$
$374$	1.13064	0.0584639
$375$	7.03132	0.363096
$376$	−0.785151	−0.0404911
$377$	−29.0869	−1.49805
$378$	0.530367	0.0272791
$379$	−15.8757	−0.815481	−0.407741	−	0.913098i	$-0.633683\pi$
$379$	−15.8757	−0.815481	−0.407741	+	0.913098i	$0.633683\pi$
$380$	0.744377	0.0381858
$381$	−2.40326	−0.123123
$382$	−2.91434	−0.149111
$383$	−16.5893	−0.847673	−0.423837	−	0.905739i	$-0.639317\pi$
$383$	−16.5893	−0.847673	−0.423837	+	0.905739i	$0.639317\pi$
$384$	−1.00000	−0.0510310
$385$	0.762845	0.0388782
$386$	−6.38394	−0.324934
$387$	−3.08412	−0.156775
$388$	−11.0075	−0.558824
$389$	−18.6610	−0.946149	−0.473075	−	0.881022i	$-0.656856\pi$
$389$	−18.6610	−0.946149	−0.473075	+	0.881022i	$0.656856\pi$
$390$	2.62591	0.132968
$391$	−3.56183	−0.180129
$392$	−6.71871	−0.339346
$393$	−6.75919	−0.340956
$394$	−16.3496	−0.823680
$395$	11.8904	0.598273
$396$	−1.93227	−0.0971001
$397$	28.6492	1.43786	0.718930	−	0.695082i	$-0.244632\pi$
$397$	28.6492	1.43786	0.718930	+	0.695082i	$0.244632\pi$
$398$	−9.57013	−0.479707
$399$	0.530367	0.0265515
$400$	−4.44590	−0.222295
$401$	−10.2226	−0.510493	−0.255247	−	0.966876i	$-0.582157\pi$
$401$	−10.2226	−0.510493	−0.255247	+	0.966876i	$0.582157\pi$
$402$	−7.13180	−0.355702
$403$	37.4766	1.86684
$404$	−0.863516	−0.0429615
$405$	0.744377	0.0369884
$406$	−4.37308	−0.217032
$407$	7.03521	0.348722
$408$	0.585136	0.0289685
$409$	−30.1472	−1.49068	−0.745341	−	0.666683i	$-0.767713\pi$
$409$	−30.1472	−1.49068	−0.745341	+	0.666683i	$0.767713\pi$
$410$	8.47177	0.418391
$411$	17.7324	0.874675
$412$	−18.1130	−0.892362
$413$	4.63388	0.228019
$414$	6.08718	0.299169
$415$	−9.29561	−0.456303
$416$	−3.52765	−0.172957
$417$	−16.7123	−0.818407
$418$	−1.93227	−0.0945103
$419$	−21.5951	−1.05499	−0.527495	−	0.849558i	$-0.676869\pi$
$419$	−21.5951	−1.05499	−0.527495	+	0.849558i	$0.676869\pi$
$420$	0.394793	0.0192639
$421$	−22.9542	−1.11872	−0.559360	−	0.828925i	$-0.688953\pi$
$421$	−22.9542	−1.11872	−0.559360	+	0.828925i	$0.688953\pi$
$422$	−16.5041	−0.803408
$423$	−0.785151	−0.0381754
$424$	−1.00000	−0.0485643
$425$	2.60146	0.126189
$426$	−13.3351	−0.646089
$427$	7.19106	0.348000
$428$	−16.5544	−0.800187
$429$	−6.81637	−0.329097
$430$	−2.29575	−0.110711
$431$	9.45409	0.455387	0.227694	−	0.973733i	$-0.426882\pi$
$431$	9.45409	0.455387	0.227694	+	0.973733i	$0.426882\pi$
$432$	−1.00000	−0.0481125
$433$	31.8145	1.52891	0.764453	−	0.644680i	$-0.223009\pi$
$433$	31.8145	1.52891	0.764453	+	0.644680i	$0.223009\pi$
$434$	5.63444	0.270462
$435$	−6.13768	−0.294279
$436$	20.0104	0.958323
$437$	6.08718	0.291189
$438$	13.4567	0.642987
$439$	−36.1818	−1.72686	−0.863431	−	0.504468i	$-0.831689\pi$
$439$	−36.1818	−1.72686	−0.863431	+	0.504468i	$0.831689\pi$
$440$	−1.43834	−0.0685700
$441$	−6.71871	−0.319939
$442$	2.06416	0.0981819
$443$	−4.50785	−0.214174	−0.107087	−	0.994250i	$-0.534152\pi$
$443$	−4.50785	−0.214174	−0.107087	+	0.994250i	$0.534152\pi$
$444$	3.64091	0.172790
$445$	−10.5561	−0.500406
$446$	−18.8946	−0.894687
$447$	3.85701	0.182430
$448$	−0.530367	−0.0250575
$449$	−3.01704	−0.142383	−0.0711914	−	0.997463i	$-0.522680\pi$
$449$	−3.01704	−0.142383	−0.0711914	+	0.997463i	$0.522680\pi$
$450$	−4.44590	−0.209582
$451$	−21.9911	−1.03552
$452$	−6.93156	−0.326033
$453$	−20.6537	−0.970397
$454$	12.4825	0.585832
$455$	1.39269	0.0652904
$456$	−1.00000	−0.0468293
$457$	24.4944	1.14580	0.572899	−	0.819626i	$-0.305819\pi$
$457$	24.4944	1.14580	0.572899	+	0.819626i	$0.305819\pi$
$458$	8.13362	0.380059
$459$	0.585136	0.0273118
$460$	4.53116	0.211266
$461$	−6.44394	−0.300124	−0.150062	−	0.988677i	$-0.547947\pi$
$461$	−6.44394	−0.300124	−0.150062	+	0.988677i	$0.547947\pi$
$462$	−1.02481	−0.0476785
$463$	16.1936	0.752581	0.376291	−	0.926502i	$-0.377199\pi$
$463$	16.1936	0.752581	0.376291	+	0.926502i	$0.377199\pi$
$464$	8.24539	0.382782
$465$	7.90802	0.366726
$466$	23.3406	1.08123
$467$	−28.1210	−1.30128	−0.650641	−	0.759385i	$-0.725500\pi$
$467$	−28.1210	−1.30128	−0.650641	+	0.759385i	$0.725500\pi$
$468$	−3.52765	−0.163066
$469$	−3.78247	−0.174658
$470$	−0.584449	−0.0269586
$471$	7.35034	0.338686
$472$	−8.73714	−0.402159
$473$	5.95934	0.274011
$474$	−15.9737	−0.733695
$475$	−4.44590	−0.203992
$476$	0.310337	0.0142243
$477$	−1.00000	−0.0457869
$478$	13.8939	0.635492
$479$	20.8713	0.953633	0.476817	−	0.879003i	$-0.341791\pi$
$479$	20.8713	0.953633	0.476817	+	0.879003i	$0.341791\pi$
$480$	−0.744377	−0.0339760
$481$	12.8439	0.585630
$482$	−8.68689	−0.395677
$483$	3.22844	0.146899
$484$	−7.26634	−0.330288
$485$	−8.19377	−0.372060
$486$	−1.00000	−0.0453609
$487$	−29.6568	−1.34388	−0.671938	−	0.740607i	$-0.734538\pi$
$487$	−29.6568	−1.34388	−0.671938	+	0.740607i	$0.734538\pi$
$488$	−13.5587	−0.613772
$489$	−14.2320	−0.643594
$490$	−5.00126	−0.225934
$491$	13.8849	0.626617	0.313309	−	0.949651i	$-0.398563\pi$
$491$	13.8849	0.626617	0.313309	+	0.949651i	$0.398563\pi$
$492$	−11.3810	−0.513096
$493$	−4.82467	−0.217292
$494$	−3.52765	−0.158717
$495$	−1.43834	−0.0646484
$496$	−10.6237	−0.477017
$497$	−7.07251	−0.317245
$498$	12.4878	0.559590
$499$	41.1505	1.84215	0.921075	−	0.389385i	$-0.127313\pi$
$499$	41.1505	1.84215	0.921075	+	0.389385i	$0.127313\pi$
$500$	−7.03132	−0.314450
$501$	19.7726	0.883376
$502$	−6.14646	−0.274330
$503$	35.3826	1.57763	0.788817	−	0.614629i	$-0.210694\pi$
$503$	35.3826	1.57763	0.788817	+	0.614629i	$0.210694\pi$
$504$	−0.530367	−0.0236244
$505$	−0.642782	−0.0286034
$506$	−11.7621	−0.522887
$507$	0.555662	0.0246778
$508$	2.40326	0.106627
$509$	17.9924	0.797500	0.398750	−	0.917060i	$-0.369444\pi$
$509$	17.9924	0.797500	0.398750	+	0.917060i	$0.369444\pi$
$510$	0.435562	0.0192870
$511$	7.13699	0.315722
$512$	1.00000	0.0441942
$513$	−1.00000	−0.0441511
$514$	9.01643	0.397698
$515$	−13.4829	−0.594127
$516$	3.08412	0.135771
$517$	1.51712	0.0667229
$518$	1.93102	0.0848440
$519$	−15.4374	−0.677629
$520$	−2.62591	−0.115154
$521$	−13.9362	−0.610554	−0.305277	−	0.952264i	$-0.598749\pi$
$521$	−13.9362	−0.610554	−0.305277	+	0.952264i	$0.598749\pi$
$522$	8.24539	0.360891
$523$	24.2335	1.05966	0.529830	−	0.848104i	$-0.322256\pi$
$523$	24.2335	1.05966	0.529830	+	0.848104i	$0.322256\pi$
$524$	6.75919	0.295277
$525$	−2.35796	−0.102910
$526$	10.8962	0.475096
$527$	6.21629	0.270786
$528$	1.93227	0.0840911
$529$	14.0538	0.611035
$530$	−0.744377	−0.0323337
$531$	−8.73714	−0.379159
$532$	−0.530367	−0.0229943
$533$	−40.1483	−1.73901
$534$	14.1811	0.613676
$535$	−12.3227	−0.532757
$536$	7.13180	0.308047
$537$	18.6105	0.803103
$538$	−9.30251	−0.401060
$539$	12.9823	0.559189
$540$	−0.744377	−0.0320329
$541$	26.8472	1.15425	0.577127	−	0.816655i	$-0.304174\pi$
$541$	26.8472	1.15425	0.577127	+	0.816655i	$0.304174\pi$
$542$	12.9504	0.556267
$543$	3.36049	0.144212
$544$	−0.585136	−0.0250875
$545$	14.8953	0.638043
$546$	−1.87095	−0.0800692
$547$	−7.99828	−0.341982	−0.170991	−	0.985273i	$-0.554697\pi$
$547$	−7.99828	−0.341982	−0.170991	+	0.985273i	$0.554697\pi$
$548$	−17.7324	−0.757490
$549$	−13.5587	−0.578670
$550$	8.59067	0.366307
$551$	8.24539	0.351265
$552$	−6.08718	−0.259088
$553$	−8.47189	−0.360262
$554$	0.860585	0.0365627
$555$	2.71021	0.115042
$556$	16.7123	0.708761
$557$	−11.6599	−0.494048	−0.247024	−	0.969009i	$-0.579453\pi$
$557$	−11.6599	−0.494048	−0.247024	+	0.969009i	$0.579453\pi$
$558$	−10.6237	−0.449736
$559$	10.8797	0.460162
$560$	−0.394793	−0.0166830
$561$	−1.13064	−0.0477356
$562$	−13.0418	−0.550133
$563$	5.06176	0.213328	0.106664	−	0.994295i	$-0.465983\pi$
$563$	5.06176	0.213328	0.106664	+	0.994295i	$0.465983\pi$
$564$	0.785151	0.0330608
$565$	−5.15970	−0.217070
$566$	14.9903	0.630089
$567$	−0.530367	−0.0222733
$568$	13.3351	0.559530
$569$	−10.1977	−0.427509	−0.213755	−	0.976887i	$-0.568569\pi$
$569$	−10.1977	−0.427509	−0.213755	+	0.976887i	$0.568569\pi$
$570$	−0.744377	−0.0311785
$571$	16.7657	0.701621	0.350811	−	0.936446i	$-0.385906\pi$
$571$	16.7657	0.701621	0.350811	+	0.936446i	$0.385906\pi$
$572$	6.81637	0.285007
$573$	2.91434	0.121748
$574$	−6.03611	−0.251942
$575$	−27.0630	−1.12861
$576$	1.00000	0.0416667
$577$	−29.9936	−1.24865	−0.624324	−	0.781166i	$-0.714625\pi$
$577$	−29.9936	−1.24865	−0.624324	+	0.781166i	$0.714625\pi$
$578$	−16.6576	−0.692865
$579$	6.38394	0.265307
$580$	6.13768	0.254853
$581$	6.62309	0.274772
$582$	11.0075	0.456278
$583$	1.93227	0.0800263
$584$	−13.4567	−0.556843
$585$	−2.62591	−0.108568
$586$	13.2197	0.546102
$587$	3.15339	0.130154	0.0650771	−	0.997880i	$-0.479271\pi$
$587$	3.15339	0.130154	0.0650771	+	0.997880i	$0.479271\pi$
$588$	6.71871	0.277075
$589$	−10.6237	−0.437741
$590$	−6.50373	−0.267754
$591$	16.3496	0.672532
$592$	−3.64091	−0.149640
$593$	4.84937	0.199140	0.0995698	−	0.995031i	$-0.468253\pi$
$593$	4.84937	0.199140	0.0995698	+	0.995031i	$0.468253\pi$
$594$	1.93227	0.0792819
$595$	0.231007	0.00947038
$596$	−3.85701	−0.157989
$597$	9.57013	0.391679
$598$	−21.4735	−0.878116
$599$	−42.9098	−1.75325	−0.876624	−	0.481177i	$-0.840210\pi$
$599$	−42.9098	−1.75325	−0.876624	+	0.481177i	$0.840210\pi$
$600$	4.44590	0.181503
$601$	−33.3047	−1.35853	−0.679264	−	0.733894i	$-0.737701\pi$
$601$	−33.3047	−1.35853	−0.679264	+	0.733894i	$0.737701\pi$
$602$	1.63571	0.0666667
$603$	7.13180	0.290429
$604$	20.6537	0.840388
$605$	−5.40890	−0.219903
$606$	0.863516	0.0350779
$607$	6.26219	0.254174	0.127087	−	0.991892i	$-0.459437\pi$
$607$	6.26219	0.254174	0.127087	+	0.991892i	$0.459437\pi$
$608$	1.00000	0.0405554
$609$	4.37308	0.177206
$610$	−10.0928	−0.408644
$611$	2.76974	0.112052
$612$	−0.585136	−0.0236527
$613$	−2.26167	−0.0913478	−0.0456739	−	0.998956i	$-0.514544\pi$
$613$	−2.26167	−0.0913478	−0.0456739	+	0.998956i	$0.514544\pi$
$614$	14.8509	0.599335
$615$	−8.47177	−0.341615
$616$	1.02481	0.0412908
$617$	−33.3300	−1.34182	−0.670908	−	0.741541i	$-0.734095\pi$
$617$	−33.3300	−1.34182	−0.670908	+	0.741541i	$0.734095\pi$
$618$	18.1130	0.728611
$619$	34.8166	1.39940	0.699698	−	0.714439i	$-0.253318\pi$
$619$	34.8166	1.39940	0.699698	+	0.714439i	$0.253318\pi$
$620$	−7.90802	−0.317594
$621$	−6.08718	−0.244270
$622$	2.24770	0.0901244
$623$	7.52117	0.301330
$624$	3.52765	0.141219
$625$	16.9956	0.679822
$626$	20.8891	0.834895
$627$	1.93227	0.0771673
$628$	−7.35034	−0.293311
$629$	2.13043	0.0849457
$630$	−0.394793	−0.0157289
$631$	32.5953	1.29760	0.648800	−	0.760959i	$-0.275271\pi$
$631$	32.5953	1.29760	0.648800	+	0.760959i	$0.275271\pi$
$632$	15.9737	0.635398
$633$	16.5041	0.655980
$634$	−3.45854	−0.137356
$635$	1.78893	0.0709915
$636$	1.00000	0.0396526
$637$	23.7013	0.939079
$638$	−15.9323	−0.630765
$639$	13.3351	0.527530
$640$	0.744377	0.0294241
$641$	−36.3754	−1.43674	−0.718371	−	0.695660i	$-0.755112\pi$
$641$	−36.3754	−1.43674	−0.718371	+	0.695660i	$0.755112\pi$
$642$	16.5544	0.653350
$643$	−7.75617	−0.305873	−0.152937	−	0.988236i	$-0.548873\pi$
$643$	−7.75617	−0.305873	−0.152937	+	0.988236i	$0.548873\pi$
$644$	−3.22844	−0.127218
$645$	2.29575	0.0903950
$646$	−0.585136	−0.0230219
$647$	37.3896	1.46994	0.734969	−	0.678101i	$-0.237197\pi$
$647$	37.3896	1.46994	0.734969	+	0.678101i	$0.237197\pi$
$648$	1.00000	0.0392837
$649$	16.8825	0.662695
$650$	15.6836	0.615161
$651$	−5.63444	−0.220831
$652$	14.2320	0.557369
$653$	−24.7306	−0.967785	−0.483892	−	0.875128i	$-0.660777\pi$
$653$	−24.7306	−0.967785	−0.483892	+	0.875128i	$0.660777\pi$
$654$	−20.0104	−0.782468
$655$	5.03139	0.196593
$656$	11.3810	0.444354
$657$	−13.4567	−0.524997
$658$	0.416418	0.0162337
$659$	39.9758	1.55724	0.778618	−	0.627499i	$-0.215921\pi$
$659$	39.9758	1.55724	0.778618	+	0.627499i	$0.215921\pi$
$660$	1.43834	0.0559871
$661$	5.85442	0.227710	0.113855	−	0.993497i	$-0.463680\pi$
$661$	5.85442	0.227710	0.113855	+	0.993497i	$0.463680\pi$
$662$	−23.2899	−0.905186
$663$	−2.06416	−0.0801652
$664$	−12.4878	−0.484619
$665$	−0.394793	−0.0153094
$666$	−3.64091	−0.141082
$667$	50.1912	1.94341
$668$	−19.7726	−0.765026
$669$	18.8946	0.730509
$670$	5.30875	0.205095
$671$	26.1990	1.01140
$672$	0.530367	0.0204593
$673$	−16.4829	−0.635368	−0.317684	−	0.948197i	$-0.602905\pi$
$673$	−16.4829	−0.635368	−0.317684	+	0.948197i	$0.602905\pi$
$674$	−3.47204	−0.133738
$675$	4.44590	0.171123
$676$	−0.555662	−0.0213716
$677$	−13.0297	−0.500770	−0.250385	−	0.968146i	$-0.580557\pi$
$677$	−13.0297	−0.500770	−0.250385	+	0.968146i	$0.580557\pi$
$678$	6.93156	0.266205
$679$	5.83804	0.224043
$680$	−0.435562	−0.0167030
$681$	−12.4825	−0.478329
$682$	20.5278	0.786049
$683$	32.6875	1.25075	0.625376	−	0.780324i	$-0.284946\pi$
$683$	32.6875	1.25075	0.625376	+	0.780324i	$0.284946\pi$
$684$	1.00000	0.0382360
$685$	−13.1996	−0.504331
$686$	7.27595	0.277797
$687$	−8.13362	−0.310317
$688$	−3.08412	−0.117581
$689$	3.52765	0.134393
$690$	−4.53116	−0.172498
$691$	51.1606	1.94624	0.973120	−	0.230301i	$-0.0739709\pi$
$691$	51.1606	1.94624	0.973120	+	0.230301i	$0.0739709\pi$
$692$	15.4374	0.586844
$693$	1.02481	0.0389293
$694$	2.53681	0.0962961
$695$	12.4403	0.471887
$696$	−8.24539	−0.312541
$697$	−6.65944	−0.252244
$698$	3.77800	0.142999
$699$	−23.3406	−0.882821
$700$	2.35796	0.0891224
$701$	18.9210	0.714637	0.357318	−	0.933983i	$-0.383691\pi$
$701$	18.9210	0.714637	0.357318	+	0.933983i	$0.383691\pi$
$702$	3.52765	0.133143
$703$	−3.64091	−0.137320
$704$	−1.93227	−0.0728250
$705$	0.584449	0.0220116
$706$	16.6367	0.626132
$707$	0.457980	0.0172241
$708$	8.73714	0.328362
$709$	15.4091	0.578701	0.289351	−	0.957223i	$-0.406561\pi$
$709$	15.4091	0.578701	0.289351	+	0.957223i	$0.406561\pi$
$710$	9.92637	0.372530
$711$	15.9737	0.599059
$712$	−14.1811	−0.531459
$713$	−64.6682	−2.42184
$714$	−0.310337	−0.0116141
$715$	5.07395	0.189755
$716$	−18.6105	−0.695508
$717$	−13.8939	−0.518877
$718$	−29.2948	−1.09327
$719$	46.9114	1.74950	0.874750	−	0.484575i	$-0.161026\pi$
$719$	46.9114	1.74950	0.874750	+	0.484575i	$0.161026\pi$
$720$	0.744377	0.0277413
$721$	9.60651	0.357765
$722$	1.00000	0.0372161
$723$	8.68689	0.323069
$724$	−3.36049	−0.124892
$725$	−36.6582	−1.36145
$726$	7.26634	0.269679
$727$	−22.8884	−0.848884	−0.424442	−	0.905455i	$-0.639530\pi$
$727$	−22.8884	−0.848884	−0.424442	+	0.905455i	$0.639530\pi$
$728$	1.87095	0.0693420
$729$	1.00000	0.0370370
$730$	−10.0169	−0.370741
$731$	1.80463	0.0667466
$732$	13.5587	0.501143
$733$	−28.3261	−1.04625	−0.523125	−	0.852256i	$-0.675234\pi$
$733$	−28.3261	−1.04625	−0.523125	+	0.852256i	$0.675234\pi$
$734$	−16.4848	−0.608465
$735$	5.00126	0.184474
$736$	6.08718	0.224377
$737$	−13.7805	−0.507613
$738$	11.3810	0.418941
$739$	13.3325	0.490444	0.245222	−	0.969467i	$-0.421139\pi$
$739$	13.3325	0.490444	0.245222	+	0.969467i	$0.421139\pi$
$740$	−2.71021	−0.0996293
$741$	3.52765	0.129592
$742$	0.530367	0.0194704
$743$	−6.93518	−0.254427	−0.127214	−	0.991875i	$-0.540603\pi$
$743$	−6.93518	−0.254427	−0.127214	+	0.991875i	$0.540603\pi$
$744$	10.6237	0.389483
$745$	−2.87107	−0.105188
$746$	−34.3219	−1.25661
$747$	−12.4878	−0.456903
$748$	1.13064	0.0413403
$749$	8.77990	0.320810
$750$	7.03132	0.256747
$751$	44.5686	1.62633	0.813166	−	0.582032i	$-0.197742\pi$
$751$	44.5686	1.62633	0.813166	+	0.582032i	$0.197742\pi$
$752$	−0.785151	−0.0286315
$753$	6.14646	0.223990
$754$	−29.0869	−1.05928
$755$	15.3742	0.559523
$756$	0.530367	0.0192892
$757$	−31.4845	−1.14432	−0.572161	−	0.820141i	$-0.693895\pi$
$757$	−31.4845	−1.14432	−0.572161	+	0.820141i	$0.693895\pi$
$758$	−15.8757	−0.576632
$759$	11.7621	0.426936
$760$	0.744377	0.0270014
$761$	29.6119	1.07343	0.536716	−	0.843763i	$-0.319665\pi$
$761$	29.6119	1.07343	0.536716	+	0.843763i	$0.319665\pi$
$762$	−2.40326	−0.0870608
$763$	−10.6128	−0.384210
$764$	−2.91434	−0.105437
$765$	−0.435562	−0.0157478
$766$	−16.5893	−0.599396
$767$	30.8216	1.11290
$768$	−1.00000	−0.0360844
$769$	−29.7789	−1.07385	−0.536927	−	0.843629i	$-0.680415\pi$
$769$	−29.7789	−1.07385	−0.536927	+	0.843629i	$0.680415\pi$
$770$	0.762845	0.0274910
$771$	−9.01643	−0.324719
$772$	−6.38394	−0.229763
$773$	−4.01267	−0.144326	−0.0721629	−	0.997393i	$-0.522990\pi$
$773$	−4.01267	−0.144326	−0.0721629	+	0.997393i	$0.522990\pi$
$774$	−3.08412	−0.110856
$775$	47.2318	1.69662
$776$	−11.0075	−0.395148
$777$	−1.93102	−0.0692748
$778$	−18.6610	−0.669029
$779$	11.3810	0.407767
$780$	2.62591	0.0940225
$781$	−25.7670	−0.922017
$782$	−3.56183	−0.127371
$783$	−8.24539	−0.294666
$784$	−6.71871	−0.239954
$785$	−5.47143	−0.195284
$786$	−6.75919	−0.241092
$787$	1.13268	0.0403756	0.0201878	−	0.999796i	$-0.493574\pi$
$787$	1.13268	0.0403756	0.0201878	+	0.999796i	$0.493574\pi$
$788$	−16.3496	−0.582430
$789$	−10.8962	−0.387914
$790$	11.8904	0.423043
$791$	3.67627	0.130713
$792$	−1.93227	−0.0686601
$793$	47.8303	1.69850
$794$	28.6492	1.01672
$795$	0.744377	0.0264003
$796$	−9.57013	−0.339204
$797$	44.8090	1.58722	0.793608	−	0.608429i	$-0.208200\pi$
$797$	44.8090	1.58722	0.793608	+	0.608429i	$0.208200\pi$
$798$	0.530367	0.0187748
$799$	0.459420	0.0162531
$800$	−4.44590	−0.157186
$801$	−14.1811	−0.501064
$802$	−10.2226	−0.360973
$803$	26.0020	0.917590
$804$	−7.13180	−0.251519
$805$	−2.40318	−0.0847008
$806$	37.4766	1.32006
$807$	9.30251	0.327464
$808$	−0.863516	−0.0303784
$809$	17.8888	0.628936	0.314468	−	0.949268i	$-0.398174\pi$
$809$	17.8888	0.628936	0.314468	+	0.949268i	$0.398174\pi$
$810$	0.744377	0.0261548
$811$	−12.8171	−0.450068	−0.225034	−	0.974351i	$-0.572249\pi$
$811$	−12.8171	−0.450068	−0.225034	+	0.974351i	$0.572249\pi$
$812$	−4.37308	−0.153465
$813$	−12.9504	−0.454190
$814$	7.03521	0.246584
$815$	10.5940	0.371091
$816$	0.585136	0.0204839
$817$	−3.08412	−0.107900
$818$	−30.1472	−1.05407
$819$	1.87095	0.0653763
$820$	8.47177	0.295847
$821$	9.89834	0.345455	0.172727	−	0.984970i	$-0.444742\pi$
$821$	9.89834	0.345455	0.172727	+	0.984970i	$0.444742\pi$
$822$	17.7324	0.618488
$823$	31.4814	1.09737	0.548687	−	0.836028i	$-0.315128\pi$
$823$	31.4814	1.09737	0.548687	+	0.836028i	$0.315128\pi$
$824$	−18.1130	−0.630995
$825$	−8.59067	−0.299089
$826$	4.63388	0.161233
$827$	0.866423	0.0301285	0.0150642	−	0.999887i	$-0.495205\pi$
$827$	0.866423	0.0301285	0.0150642	+	0.999887i	$0.495205\pi$
$828$	6.08718	0.211544
$829$	44.7298	1.55353	0.776766	−	0.629790i	$-0.216859\pi$
$829$	44.7298	1.55353	0.776766	+	0.629790i	$0.216859\pi$
$830$	−9.29561	−0.322655
$831$	−0.860585	−0.0298534
$832$	−3.52765	−0.122299
$833$	3.93136	0.136214
$834$	−16.7123	−0.578701
$835$	−14.7183	−0.509348
$836$	−1.93227	−0.0668288
$837$	10.6237	0.367208
$838$	−21.5951	−0.745991
$839$	44.7015	1.54327	0.771633	−	0.636068i	$-0.219440\pi$
$839$	44.7015	1.54327	0.771633	+	0.636068i	$0.219440\pi$
$840$	0.394793	0.0136216
$841$	38.9864	1.34436
$842$	−22.9542	−0.791054
$843$	13.0418	0.449182
$844$	−16.5041	−0.568095
$845$	−0.413622	−0.0142290
$846$	−0.785151	−0.0269941
$847$	3.85383	0.132419
$848$	−1.00000	−0.0343401
$849$	−14.9903	−0.514466
$850$	2.60146	0.0892293
$851$	−22.1629	−0.759734
$852$	−13.3351	−0.456854
$853$	−9.19042	−0.314674	−0.157337	−	0.987545i	$-0.550291\pi$
$853$	−9.19042	−0.314674	−0.157337	+	0.987545i	$0.550291\pi$
$854$	7.19106	0.246073
$855$	0.744377	0.0254572
$856$	−16.5544	−0.565818
$857$	41.2038	1.40750	0.703748	−	0.710450i	$-0.251508\pi$
$857$	41.2038	1.40750	0.703748	+	0.710450i	$0.251508\pi$
$858$	−6.81637	−0.232707
$859$	2.67932	0.0914174	0.0457087	−	0.998955i	$-0.485445\pi$
$859$	2.67932	0.0914174	0.0457087	+	0.998955i	$0.485445\pi$
$860$	−2.29575	−0.0782844
$861$	6.03611	0.205710
$862$	9.45409	0.322007
$863$	7.70843	0.262398	0.131199	−	0.991356i	$-0.458117\pi$
$863$	7.70843	0.262398	0.131199	+	0.991356i	$0.458117\pi$
$864$	−1.00000	−0.0340207
$865$	11.4913	0.390715
$866$	31.8145	1.08110
$867$	16.6576	0.565722
$868$	5.63444	0.191245
$869$	−30.8654	−1.04704
$870$	−6.13768	−0.208087
$871$	−25.1585	−0.852464
$872$	20.0104	0.677637
$873$	−11.0075	−0.372549
$874$	6.08718	0.205902
$875$	3.72917	0.126069
$876$	13.4567	0.454661
$877$	1.31967	0.0445620	0.0222810	−	0.999752i	$-0.492907\pi$
$877$	1.31967	0.0445620	0.0222810	+	0.999752i	$0.492907\pi$
$878$	−36.1818	−1.22108
$879$	−13.2197	−0.445891
$880$	−1.43834	−0.0484863
$881$	−0.233207	−0.00785693	−0.00392846	−	0.999992i	$-0.501250\pi$
$881$	−0.233207	−0.00785693	−0.00392846	+	0.999992i	$0.501250\pi$
$882$	−6.71871	−0.226231
$883$	−36.6932	−1.23482	−0.617412	−	0.786640i	$-0.711819\pi$
$883$	−36.6932	−1.23482	−0.617412	+	0.786640i	$0.711819\pi$
$884$	2.06416	0.0694251
$885$	6.50373	0.218620
$886$	−4.50785	−0.151444
$887$	20.5789	0.690971	0.345485	−	0.938424i	$-0.387714\pi$
$887$	20.5789	0.690971	0.345485	+	0.938424i	$0.387714\pi$
$888$	3.64091	0.122181
$889$	−1.27461	−0.0427490
$890$	−10.5561	−0.353841
$891$	−1.93227	−0.0647334
$892$	−18.8946	−0.632640
$893$	−0.785151	−0.0262741
$894$	3.85701	0.128998
$895$	−13.8532	−0.463063
$896$	−0.530367	−0.0177183
$897$	21.4735	0.716978
$898$	−3.01704	−0.100680
$899$	−87.5963	−2.92150
$900$	−4.44590	−0.148197
$901$	0.585136	0.0194937
$902$	−21.9911	−0.732225
$903$	−1.63571	−0.0544331
$904$	−6.93156	−0.230540
$905$	−2.50147	−0.0831517
$906$	−20.6537	−0.686174
$907$	15.8196	0.525281	0.262641	−	0.964894i	$-0.415407\pi$
$907$	15.8196	0.525281	0.262641	+	0.964894i	$0.415407\pi$
$908$	12.4825	0.414245
$909$	−0.863516	−0.0286410
$910$	1.39269	0.0461673
$911$	16.3095	0.540356	0.270178	−	0.962810i	$-0.412917\pi$
$911$	16.3095	0.540356	0.270178	+	0.962810i	$0.412917\pi$
$912$	−1.00000	−0.0331133
$913$	24.1297	0.798576
$914$	24.4944	0.810202
$915$	10.0928	0.333657
$916$	8.13362	0.268742
$917$	−3.58485	−0.118382
$918$	0.585136	0.0193124
$919$	40.3235	1.33015	0.665074	−	0.746777i	$-0.268400\pi$
$919$	40.3235	1.33015	0.665074	+	0.746777i	$0.268400\pi$
$920$	4.53116	0.149388
$921$	−14.8509	−0.489355
$922$	−6.44394	−0.212220
$923$	−47.0417	−1.54840
$924$	−1.02481	−0.0337138
$925$	16.1871	0.532230
$926$	16.1936	0.532155
$927$	−18.1130	−0.594908
$928$	8.24539	0.270668
$929$	−33.2807	−1.09190	−0.545952	−	0.837816i	$-0.683832\pi$
$929$	−33.2807	−1.09190	−0.545952	+	0.837816i	$0.683832\pi$
$930$	7.90802	0.259314
$931$	−6.71871	−0.220197
$932$	23.3406	0.764546
$933$	−2.24770	−0.0735863
$934$	−28.1210	−0.920146
$935$	0.841622	0.0275240
$936$	−3.52765	−0.115305
$937$	−2.31344	−0.0755767	−0.0377884	−	0.999286i	$-0.512031\pi$
$937$	−2.31344	−0.0755767	−0.0377884	+	0.999286i	$0.512031\pi$
$938$	−3.78247	−0.123502
$939$	−20.8891	−0.681689
$940$	−0.584449	−0.0190626
$941$	24.9265	0.812582	0.406291	−	0.913744i	$-0.366822\pi$
$941$	24.9265	0.812582	0.406291	+	0.913744i	$0.366822\pi$
$942$	7.35034	0.239487
$943$	69.2783	2.25601
$944$	−8.73714	−0.284370
$945$	0.394793	0.0128426
$946$	5.95934	0.193755
$947$	52.5647	1.70812	0.854062	−	0.520172i	$-0.174132\pi$
$947$	52.5647	1.70812	0.854062	+	0.520172i	$0.174132\pi$
$948$	−15.9737	−0.518800
$949$	47.4707	1.54096
$950$	−4.44590	−0.144244
$951$	3.45854	0.112151
$952$	0.310337	0.0100581
$953$	52.7357	1.70828	0.854138	−	0.520046i	$-0.174085\pi$
$953$	52.7357	1.70828	0.854138	+	0.520046i	$0.174085\pi$
$954$	−1.00000	−0.0323762
$955$	−2.16937	−0.0701992
$956$	13.8939	0.449360
$957$	15.9323	0.515018
$958$	20.8713	0.674320
$959$	9.40467	0.303693
$960$	−0.744377	−0.0240247
$961$	81.8623	2.64072
$962$	12.8439	0.414103
$963$	−16.5544	−0.533458
$964$	−8.68689	−0.279786
$965$	−4.75206	−0.152974
$966$	3.22844	0.103873
$967$	−49.0132	−1.57616	−0.788080	−	0.615573i	$-0.788924\pi$
$967$	−49.0132	−1.57616	−0.788080	+	0.615573i	$0.788924\pi$
$968$	−7.26634	−0.233549
$969$	0.585136	0.0187973
$970$	−8.19377	−0.263086
$971$	−28.1204	−0.902426	−0.451213	−	0.892416i	$-0.649008\pi$
$971$	−28.1204	−0.902426	−0.451213	+	0.892416i	$0.649008\pi$
$972$	−1.00000	−0.0320750
$973$	−8.86366	−0.284156
$974$	−29.6568	−0.950265
$975$	−15.6836	−0.502277
$976$	−13.5587	−0.434002
$977$	13.3633	0.427530	0.213765	−	0.976885i	$-0.431427\pi$
$977$	13.3633	0.427530	0.213765	+	0.976885i	$0.431427\pi$
$978$	−14.2320	−0.455090
$979$	27.4016	0.875761
$980$	−5.00126	−0.159759
$981$	20.0104	0.638882
$982$	13.8849	0.443085
$983$	−50.7483	−1.61862	−0.809310	−	0.587381i	$-0.800159\pi$
$983$	−50.7483	−1.61862	−0.809310	+	0.587381i	$0.800159\pi$
$984$	−11.3810	−0.362813
$985$	−12.1703	−0.387777
$986$	−4.82467	−0.153649
$987$	−0.416418	−0.0132547
$988$	−3.52765	−0.112230
$989$	−18.7736	−0.596966
$990$	−1.43834	−0.0457133
$991$	−56.4449	−1.79303	−0.896516	−	0.443012i	$-0.853910\pi$
$991$	−56.4449	−1.79303	−0.896516	+	0.443012i	$0.853910\pi$
$992$	−10.6237	−0.337302
$993$	23.2899	0.739081
$994$	−7.07251	−0.224326
$995$	−7.12379	−0.225839
$996$	12.4878	0.395690
$997$	46.8032	1.48227	0.741136	−	0.671355i	$-0.234288\pi$
$997$	46.8032	1.48227	0.741136	+	0.671355i	$0.234288\pi$
$998$	41.1505	1.30260
$999$	3.64091	0.115193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.bc.1.7	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bc.1.7	✓	9	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.744377 q^{5} -1.00000 q^{6} -0.530367 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.744377 q^{5} -1.00000 q^{6} -0.530367 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.744377 q^{10} -1.93227 q^{11} -1.00000 q^{12} -3.52765 q^{13} -0.530367 q^{14} -0.744377 q^{15} +1.00000 q^{16} -0.585136 q^{17} +1.00000 q^{18} +1.00000 q^{19} +0.744377 q^{20} +0.530367 q^{21} -1.93227 q^{22} +6.08718 q^{23} -1.00000 q^{24} -4.44590 q^{25} -3.52765 q^{26} -1.00000 q^{27} -0.530367 q^{28} +8.24539 q^{29} -0.744377 q^{30} -10.6237 q^{31} +1.00000 q^{32} +1.93227 q^{33} -0.585136 q^{34} -0.394793 q^{35} +1.00000 q^{36} -3.64091 q^{37} +1.00000 q^{38} +3.52765 q^{39} +0.744377 q^{40} +11.3810 q^{41} +0.530367 q^{42} -3.08412 q^{43} -1.93227 q^{44} +0.744377 q^{45} +6.08718 q^{46} -0.785151 q^{47} -1.00000 q^{48} -6.71871 q^{49} -4.44590 q^{50} +0.585136 q^{51} -3.52765 q^{52} -1.00000 q^{53} -1.00000 q^{54} -1.43834 q^{55} -0.530367 q^{56} -1.00000 q^{57} +8.24539 q^{58} -8.73714 q^{59} -0.744377 q^{60} -13.5587 q^{61} -10.6237 q^{62} -0.530367 q^{63} +1.00000 q^{64} -2.62591 q^{65} +1.93227 q^{66} +7.13180 q^{67} -0.585136 q^{68} -6.08718 q^{69} -0.394793 q^{70} +13.3351 q^{71} +1.00000 q^{72} -13.4567 q^{73} -3.64091 q^{74} +4.44590 q^{75} +1.00000 q^{76} +1.02481 q^{77} +3.52765 q^{78} +15.9737 q^{79} +0.744377 q^{80} +1.00000 q^{81} +11.3810 q^{82} -12.4878 q^{83} +0.530367 q^{84} -0.435562 q^{85} -3.08412 q^{86} -8.24539 q^{87} -1.93227 q^{88} -14.1811 q^{89} +0.744377 q^{90} +1.87095 q^{91} +6.08718 q^{92} +10.6237 q^{93} -0.785151 q^{94} +0.744377 q^{95} -1.00000 q^{96} -11.0075 q^{97} -6.71871 q^{98} -1.93227 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 3 q^{5} - 9 q^{6} - 7 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 3 * q^5 - 9 * q^6 - 7 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 3 q^{5} - 9 q^{6} - 7 q^{7} + 9 q^{8} + 9 q^{9} - 3 q^{10} + 4 q^{11} - 9 q^{12} - 5 q^{13} - 7 q^{14} + 3 q^{15} + 9 q^{16} - 28 q^{17} + 9 q^{18} + 9 q^{19} - 3 q^{20} + 7 q^{21} + 4 q^{22} - 10 q^{23} - 9 q^{24} + 4 q^{25} - 5 q^{26} - 9 q^{27} - 7 q^{28} + 3 q^{30} + 5 q^{31} + 9 q^{32} - 4 q^{33} - 28 q^{34} - 10 q^{35} + 9 q^{36} - 25 q^{37} + 9 q^{38} + 5 q^{39} - 3 q^{40} - 7 q^{41} + 7 q^{42} - 16 q^{43} + 4 q^{44} - 3 q^{45} - 10 q^{46} - 9 q^{47} - 9 q^{48} + 44 q^{49} + 4 q^{50} + 28 q^{51} - 5 q^{52} - 9 q^{53} - 9 q^{54} - 31 q^{55} - 7 q^{56} - 9 q^{57} - 3 q^{59} + 3 q^{60} - 16 q^{61} + 5 q^{62} - 7 q^{63} + 9 q^{64} - 33 q^{65} - 4 q^{66} - 13 q^{67} - 28 q^{68} + 10 q^{69} - 10 q^{70} - 4 q^{71} + 9 q^{72} - 29 q^{73} - 25 q^{74} - 4 q^{75} + 9 q^{76} - 33 q^{77} + 5 q^{78} + 13 q^{79} - 3 q^{80} + 9 q^{81} - 7 q^{82} - 35 q^{83} + 7 q^{84} + 3 q^{85} - 16 q^{86} + 4 q^{88} - 19 q^{89} - 3 q^{90} - 10 q^{92} - 5 q^{93} - 9 q^{94} - 3 q^{95} - 9 q^{96} - 12 q^{97} + 44 q^{98} + 4 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 3 * q^5 - 9 * q^6 - 7 * q^7 + 9 * q^8 + 9 * q^9 - 3 * q^10 + 4 * q^11 - 9 * q^12 - 5 * q^13 - 7 * q^14 + 3 * q^15 + 9 * q^16 - 28 * q^17 + 9 * q^18 + 9 * q^19 - 3 * q^20 + 7 * q^21 + 4 * q^22 - 10 * q^23 - 9 * q^24 + 4 * q^25 - 5 * q^26 - 9 * q^27 - 7 * q^28 + 3 * q^30 + 5 * q^31 + 9 * q^32 - 4 * q^33 - 28 * q^34 - 10 * q^35 + 9 * q^36 - 25 * q^37 + 9 * q^38 + 5 * q^39 - 3 * q^40 - 7 * q^41 + 7 * q^42 - 16 * q^43 + 4 * q^44 - 3 * q^45 - 10 * q^46 - 9 * q^47 - 9 * q^48 + 44 * q^49 + 4 * q^50 + 28 * q^51 - 5 * q^52 - 9 * q^53 - 9 * q^54 - 31 * q^55 - 7 * q^56 - 9 * q^57 - 3 * q^59 + 3 * q^60 - 16 * q^61 + 5 * q^62 - 7 * q^63 + 9 * q^64 - 33 * q^65 - 4 * q^66 - 13 * q^67 - 28 * q^68 + 10 * q^69 - 10 * q^70 - 4 * q^71 + 9 * q^72 - 29 * q^73 - 25 * q^74 - 4 * q^75 + 9 * q^76 - 33 * q^77 + 5 * q^78 + 13 * q^79 - 3 * q^80 + 9 * q^81 - 7 * q^82 - 35 * q^83 + 7 * q^84 + 3 * q^85 - 16 * q^86 + 4 * q^88 - 19 * q^89 - 3 * q^90 - 10 * q^92 - 5 * q^93 - 9 * q^94 - 3 * q^95 - 9 * q^96 - 12 * q^97 + 44 * q^98 + 4 * q^99

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