LMFDB - Embedded newform 1183.2.a.r.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(1,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1183.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.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:	$9.44630255912$
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} - 3 x^{11} - 15 x^{10} + 46 x^{9} + 80 x^{8} - 246 x^{7} - 199 x^{6} + 562 x^{5} + 262 x^{4} + \cdots + 29 $ x^12 - 3x^11 - 15x^10 + 46x^9 + 80x^8 - 246x^7 - 199x^6 + 562x^5 + 262x^4 - 542x^3 - 157x^2 + 183*x + 29
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.58557$ of defining polynomial
Character	$\chi$	$=$	1183.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58557 q^{2} +2.93994 q^{3} +4.68518 q^{4} +1.26031 q^{5} -7.60143 q^{6} +1.00000 q^{7} -6.94272 q^{8} +5.64327 q^{9} +O(q^{10})$	\(q-2.58557 q^{2} +2.93994 q^{3} +4.68518 q^{4} +1.26031 q^{5} -7.60143 q^{6} +1.00000 q^{7} -6.94272 q^{8} +5.64327 q^{9} -3.25863 q^{10} +5.67770 q^{11} +13.7742 q^{12} -2.58557 q^{14} +3.70525 q^{15} +8.58055 q^{16} -1.07496 q^{17} -14.5911 q^{18} -0.612693 q^{19} +5.90479 q^{20} +2.93994 q^{21} -14.6801 q^{22} +3.03000 q^{23} -20.4112 q^{24} -3.41161 q^{25} +7.77106 q^{27} +4.68518 q^{28} +1.64194 q^{29} -9.58018 q^{30} -8.21292 q^{31} -8.30017 q^{32} +16.6921 q^{33} +2.77938 q^{34} +1.26031 q^{35} +26.4397 q^{36} +4.81423 q^{37} +1.58416 q^{38} -8.75000 q^{40} +0.993703 q^{41} -7.60143 q^{42} -4.96027 q^{43} +26.6010 q^{44} +7.11228 q^{45} -7.83428 q^{46} +3.93396 q^{47} +25.2263 q^{48} +1.00000 q^{49} +8.82097 q^{50} -3.16032 q^{51} +3.04156 q^{53} -20.0926 q^{54} +7.15567 q^{55} -6.94272 q^{56} -1.80128 q^{57} -4.24535 q^{58} -7.61833 q^{59} +17.3597 q^{60} -14.0815 q^{61} +21.2351 q^{62} +5.64327 q^{63} +4.29960 q^{64} -43.1586 q^{66} +11.1999 q^{67} -5.03637 q^{68} +8.90802 q^{69} -3.25863 q^{70} +0.519738 q^{71} -39.1796 q^{72} -15.9772 q^{73} -12.4475 q^{74} -10.0300 q^{75} -2.87058 q^{76} +5.67770 q^{77} -4.51042 q^{79} +10.8142 q^{80} +5.91667 q^{81} -2.56929 q^{82} -3.75039 q^{83} +13.7742 q^{84} -1.35478 q^{85} +12.8251 q^{86} +4.82720 q^{87} -39.4187 q^{88} -16.2038 q^{89} -18.3893 q^{90} +14.1961 q^{92} -24.1455 q^{93} -10.1715 q^{94} -0.772184 q^{95} -24.4020 q^{96} +7.28909 q^{97} -2.58557 q^{98} +32.0408 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9	\( 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9} - 6 q^{10} + 12 q^{11} + 13 q^{12} + 3 q^{14} + 11 q^{15} + 13 q^{16} + 31 q^{17} - 29 q^{18} - 3 q^{19} - 18 q^{20} + 8 q^{21} - 4 q^{22} + 18 q^{23} - 6 q^{24} + 32 q^{25} + 32 q^{27} + 15 q^{28} + 15 q^{29} - 10 q^{30} - 21 q^{31} - 3 q^{32} - 29 q^{33} + 3 q^{34} - 4 q^{35} + 49 q^{36} + 5 q^{37} + 45 q^{38} - 20 q^{40} - 16 q^{41} + 2 q^{42} - 22 q^{43} + 35 q^{44} + 5 q^{45} + 2 q^{46} - 4 q^{47} + 11 q^{48} + 12 q^{49} + 13 q^{50} + 18 q^{51} + 53 q^{53} - 5 q^{54} - 26 q^{55} + 12 q^{56} - 8 q^{57} + 32 q^{58} - 26 q^{59} + 38 q^{60} + 22 q^{61} + 19 q^{62} + 26 q^{63} + 2 q^{64} - 34 q^{66} + 12 q^{67} + 34 q^{68} + 3 q^{69} - 6 q^{70} + 21 q^{71} - 4 q^{72} - 15 q^{73} - 40 q^{74} + 15 q^{75} + 43 q^{76} + 12 q^{77} + 2 q^{79} + 13 q^{80} + 36 q^{81} - 32 q^{82} - 9 q^{83} + 13 q^{84} - 39 q^{85} + 44 q^{86} + 27 q^{87} - 48 q^{88} - 22 q^{89} - 26 q^{90} + 52 q^{92} - 53 q^{93} - 44 q^{94} + 29 q^{95} - 114 q^{96} + 9 q^{97} + 3 q^{98} + 37 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9 - 6 * q^10 + 12 * q^11 + 13 * q^12 + 3 * q^14 + 11 * q^15 + 13 * q^16 + 31 * q^17 - 29 * q^18 - 3 * q^19 - 18 * q^20 + 8 * q^21 - 4 * q^22 + 18 * q^23 - 6 * q^24 + 32 * q^25 + 32 * q^27 + 15 * q^28 + 15 * q^29 - 10 * q^30 - 21 * q^31 - 3 * q^32 - 29 * q^33 + 3 * q^34 - 4 * q^35 + 49 * q^36 + 5 * q^37 + 45 * q^38 - 20 * q^40 - 16 * q^41 + 2 * q^42 - 22 * q^43 + 35 * q^44 + 5 * q^45 + 2 * q^46 - 4 * q^47 + 11 * q^48 + 12 * q^49 + 13 * q^50 + 18 * q^51 + 53 * q^53 - 5 * q^54 - 26 * q^55 + 12 * q^56 - 8 * q^57 + 32 * q^58 - 26 * q^59 + 38 * q^60 + 22 * q^61 + 19 * q^62 + 26 * q^63 + 2 * q^64 - 34 * q^66 + 12 * q^67 + 34 * q^68 + 3 * q^69 - 6 * q^70 + 21 * q^71 - 4 * q^72 - 15 * q^73 - 40 * q^74 + 15 * q^75 + 43 * q^76 + 12 * q^77 + 2 * q^79 + 13 * q^80 + 36 * q^81 - 32 * q^82 - 9 * q^83 + 13 * q^84 - 39 * q^85 + 44 * q^86 + 27 * q^87 - 48 * q^88 - 22 * q^89 - 26 * q^90 + 52 * q^92 - 53 * q^93 - 44 * q^94 + 29 * q^95 - 114 * q^96 + 9 * q^97 + 3 * q^98 + 37 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.58557	−1.82828	−0.914138	−	0.405404i	$-0.867131\pi$
$2$	−2.58557	−1.82828	−0.914138	+	0.405404i	$0.867131\pi$
$3$	2.93994	1.69738	0.848689	−	0.528893i	$-0.177393\pi$
$3$	2.93994	1.69738	0.848689	+	0.528893i	$0.177393\pi$
$4$	4.68518	2.34259
$5$	1.26031	0.563629	0.281814	−	0.959469i	$-0.409064\pi$
$5$	1.26031	0.563629	0.281814	+	0.959469i	$0.409064\pi$
$6$	−7.60143	−3.10327
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−6.94272	−2.45462
$9$	5.64327	1.88109
$10$	−3.25863	−1.03047
$11$	5.67770	1.71189	0.855945	−	0.517067i	$-0.172976\pi$
$11$	5.67770	1.71189	0.855945	+	0.517067i	$0.172976\pi$
$12$	13.7742	3.97626
$13$	0	0
$13$	0	0
$14$	−2.58557	−0.691023
$15$	3.70525	0.956690
$16$	8.58055	2.14514
$17$	−1.07496	−0.260716	−0.130358	−	0.991467i	$-0.541613\pi$
$17$	−1.07496	−0.260716	−0.130358	+	0.991467i	$0.541613\pi$
$18$	−14.5911	−3.43915
$19$	−0.612693	−0.140561	−0.0702807	−	0.997527i	$-0.522389\pi$
$19$	−0.612693	−0.140561	−0.0702807	+	0.997527i	$0.522389\pi$
$20$	5.90479	1.32035
$21$	2.93994	0.641548
$22$	−14.6801	−3.12981
$23$	3.03000	0.631798	0.315899	−	0.948793i	$-0.397694\pi$
$23$	3.03000	0.631798	0.315899	+	0.948793i	$0.397694\pi$
$24$	−20.4112	−4.16642
$25$	−3.41161	−0.682323
$26$	0	0
$27$	7.77106	1.49554
$28$	4.68518	0.885416
$29$	1.64194	0.304900	0.152450	−	0.988311i	$-0.451284\pi$
$29$	1.64194	0.304900	0.152450	+	0.988311i	$0.451284\pi$
$30$	−9.58018	−1.74909
$31$	−8.21292	−1.47508	−0.737542	−	0.675301i	$-0.764014\pi$
$31$	−8.21292	−1.47508	−0.737542	+	0.675301i	$0.764014\pi$
$32$	−8.30017	−1.46728
$33$	16.6921	2.90572
$34$	2.77938	0.476660
$35$	1.26031	0.213032
$36$	26.4397	4.40662
$37$	4.81423	0.791454	0.395727	−	0.918368i	$-0.370493\pi$
$37$	4.81423	0.791454	0.395727	+	0.918368i	$0.370493\pi$
$38$	1.58416	0.256985
$39$	0	0
$40$	−8.75000	−1.38350
$41$	0.993703	0.155190	0.0775952	−	0.996985i	$-0.475276\pi$
$41$	0.993703	0.155190	0.0775952	+	0.996985i	$0.475276\pi$
$42$	−7.60143	−1.17293
$43$	−4.96027	−0.756434	−0.378217	−	0.925717i	$-0.623463\pi$
$43$	−4.96027	−0.756434	−0.378217	+	0.925717i	$0.623463\pi$
$44$	26.6010	4.01026
$45$	7.11228	1.06024
$46$	−7.83428	−1.15510
$47$	3.93396	0.573827	0.286913	−	0.957957i	$-0.407371\pi$
$47$	3.93396	0.573827	0.286913	+	0.957957i	$0.407371\pi$
$48$	25.2263	3.64111
$49$	1.00000	0.142857
$50$	8.82097	1.24747
$51$	−3.16032	−0.442533
$52$	0	0
$53$	3.04156	0.417790	0.208895	−	0.977938i	$-0.433013\pi$
$53$	3.04156	0.417790	0.208895	+	0.977938i	$0.433013\pi$
$54$	−20.0926	−2.73426
$55$	7.15567	0.964870
$56$	−6.94272	−0.927760
$57$	−1.80128	−0.238586
$58$	−4.24535	−0.557441
$59$	−7.61833	−0.991822	−0.495911	−	0.868373i	$-0.665166\pi$
$59$	−7.61833	−0.991822	−0.495911	+	0.868373i	$0.665166\pi$
$60$	17.3597	2.24113
$61$	−14.0815	−1.80295	−0.901475	−	0.432830i	$-0.857515\pi$
$61$	−14.0815	−1.80295	−0.901475	+	0.432830i	$0.857515\pi$
$62$	21.2351	2.69686
$63$	5.64327	0.710985
$64$	4.29960	0.537449
$65$	0	0
$66$	−43.1586	−5.31246
$67$	11.1999	1.36829	0.684146	−	0.729346i	$-0.260175\pi$
$67$	11.1999	1.36829	0.684146	+	0.729346i	$0.260175\pi$
$68$	−5.03637	−0.610750
$69$	8.90802	1.07240
$70$	−3.25863	−0.389480
$71$	0.519738	0.0616815	0.0308408	−	0.999524i	$-0.490182\pi$
$71$	0.519738	0.0616815	0.0308408	+	0.999524i	$0.490182\pi$
$72$	−39.1796	−4.61737
$73$	−15.9772	−1.86999	−0.934995	−	0.354661i	$-0.884596\pi$
$73$	−15.9772	−1.86999	−0.934995	+	0.354661i	$0.884596\pi$
$74$	−12.4475	−1.44700
$75$	−10.0300	−1.15816
$76$	−2.87058	−0.329278
$77$	5.67770	0.647033
$78$	0	0
$79$	−4.51042	−0.507462	−0.253731	−	0.967275i	$-0.581658\pi$
$79$	−4.51042	−0.507462	−0.253731	+	0.967275i	$0.581658\pi$
$80$	10.8142	1.20906
$81$	5.91667	0.657408
$82$	−2.56929	−0.283731
$83$	−3.75039	−0.411659	−0.205830	−	0.978588i	$-0.565989\pi$
$83$	−3.75039	−0.411659	−0.205830	+	0.978588i	$0.565989\pi$
$84$	13.7742	1.50288
$85$	−1.35478	−0.146947
$86$	12.8251	1.38297
$87$	4.82720	0.517531
$88$	−39.4187	−4.20204
$89$	−16.2038	−1.71760	−0.858799	−	0.512312i	$-0.828789\pi$
$89$	−16.2038	−1.71760	−0.858799	+	0.512312i	$0.828789\pi$
$90$	−18.3893	−1.93840
$91$	0	0
$92$	14.1961	1.48004
$93$	−24.1455	−2.50377
$94$	−10.1715	−1.04911
$95$	−0.772184	−0.0792244
$96$	−24.4020	−2.49052
$97$	7.28909	0.740095	0.370047	−	0.929013i	$-0.379341\pi$
$97$	7.28909	0.740095	0.370047	+	0.929013i	$0.379341\pi$
$98$	−2.58557	−0.261182
$99$	32.0408	3.22022
$100$	−15.9840	−1.59840
$101$	−10.2185	−1.01678	−0.508390	−	0.861127i	$-0.669759\pi$
$101$	−10.2185	−1.01678	−0.508390	+	0.861127i	$0.669759\pi$
$102$	8.17122	0.809072
$103$	9.25473	0.911896	0.455948	−	0.890006i	$-0.349300\pi$
$103$	9.25473	0.911896	0.455948	+	0.890006i	$0.349300\pi$
$104$	0	0
$105$	3.70525	0.361595
$106$	−7.86416	−0.763835
$107$	15.1824	1.46774	0.733870	−	0.679290i	$-0.237712\pi$
$107$	15.1824	1.46774	0.733870	+	0.679290i	$0.237712\pi$
$108$	36.4088	3.50344
$109$	−6.31722	−0.605080	−0.302540	−	0.953137i	$-0.597835\pi$
$109$	−6.31722	−0.605080	−0.302540	+	0.953137i	$0.597835\pi$
$110$	−18.5015	−1.76405
$111$	14.1536	1.34340
$112$	8.58055	0.810786
$113$	16.3397	1.53711	0.768553	−	0.639786i	$-0.220977\pi$
$113$	16.3397	1.53711	0.768553	+	0.639786i	$0.220977\pi$
$114$	4.65734	0.436200
$115$	3.81874	0.356100
$116$	7.69277	0.714256
$117$	0	0
$118$	19.6977	1.81332
$119$	−1.07496	−0.0985412
$120$	−25.7245	−2.34831
$121$	21.2362	1.93057
$122$	36.4087	3.29629
$123$	2.92143	0.263417
$124$	−38.4790	−3.45552
$125$	−10.6013	−0.948205
$126$	−14.5911	−1.29988
$127$	−18.2434	−1.61884	−0.809422	−	0.587227i	$-0.800219\pi$
$127$	−18.2434	−1.61884	−0.809422	+	0.587227i	$0.800219\pi$
$128$	5.48344	0.484672
$129$	−14.5829	−1.28395
$130$	0	0
$131$	5.46245	0.477257	0.238628	−	0.971111i	$-0.423302\pi$
$131$	5.46245	0.477257	0.238628	+	0.971111i	$0.423302\pi$
$132$	78.2055	6.80692
$133$	−0.612693	−0.0531272
$134$	−28.9583	−2.50161
$135$	9.79396	0.842930
$136$	7.46314	0.639959
$137$	0.985099	0.0841627	0.0420813	−	0.999114i	$-0.486601\pi$
$137$	0.985099	0.0841627	0.0420813	+	0.999114i	$0.486601\pi$
$138$	−23.0323	−1.96064
$139$	0.0118471	0.00100486	0.000502431	−	1.00000i	$-0.499840\pi$
$139$	0.0118471	0.00100486	0.000502431		1.00000i	$0.499840\pi$
$140$	5.90479	0.499046
$141$	11.5656	0.974000
$142$	−1.34382	−0.112771
$143$	0	0
$144$	48.4223	4.03519
$145$	2.06935	0.171850
$146$	41.3102	3.41886
$147$	2.93994	0.242482
$148$	22.5555	1.85405
$149$	12.4963	1.02374	0.511870	−	0.859063i	$-0.328953\pi$
$149$	12.4963	1.02374	0.511870	+	0.859063i	$0.328953\pi$
$150$	25.9332	2.11743
$151$	12.4617	1.01412	0.507059	−	0.861911i	$-0.330732\pi$
$151$	12.4617	1.01412	0.507059	+	0.861911i	$0.330732\pi$
$152$	4.25376	0.345025
$153$	−6.06628	−0.490429
$154$	−14.6801	−1.18296
$155$	−10.3508	−0.831399
$156$	0	0
$157$	2.85889	0.228165	0.114082	−	0.993471i	$-0.463607\pi$
$157$	2.85889	0.228165	0.114082	+	0.993471i	$0.463607\pi$
$158$	11.6620	0.927781
$159$	8.94200	0.709147
$160$	−10.4608	−0.826999
$161$	3.03000	0.238797
$162$	−15.2980	−1.20192
$163$	1.70698	0.133701	0.0668504	−	0.997763i	$-0.478705\pi$
$163$	1.70698	0.133701	0.0668504	+	0.997763i	$0.478705\pi$
$164$	4.65568	0.363547
$165$	21.0373	1.63775
$166$	9.69691	0.752626
$167$	−19.2594	−1.49033	−0.745167	−	0.666878i	$-0.767630\pi$
$167$	−19.2594	−1.49033	−0.745167	+	0.666878i	$0.767630\pi$
$168$	−20.4112	−1.57476
$169$	0	0
$170$	3.50289	0.268659
$171$	−3.45759	−0.264409
$172$	−23.2398	−1.77202
$173$	1.07716	0.0818952	0.0409476	−	0.999161i	$-0.486962\pi$
$173$	1.07716	0.0818952	0.0409476	+	0.999161i	$0.486962\pi$
$174$	−12.4811	−0.946188
$175$	−3.41161	−0.257894
$176$	48.7177	3.67224
$177$	−22.3974	−1.68350
$178$	41.8961	3.14024
$179$	11.3982	0.851939	0.425970	−	0.904737i	$-0.359933\pi$
$179$	11.3982	0.851939	0.425970	+	0.904737i	$0.359933\pi$
$180$	33.3223	2.48370
$181$	9.44249	0.701854	0.350927	−	0.936403i	$-0.385866\pi$
$181$	9.44249	0.701854	0.350927	+	0.936403i	$0.385866\pi$
$182$	0	0
$183$	−41.3988	−3.06029
$184$	−21.0364	−1.55083
$185$	6.06743	0.446086
$186$	62.4300	4.57759
$187$	−6.10328	−0.446316
$188$	18.4313	1.34424
$189$	7.77106	0.565261
$190$	1.99654	0.144844
$191$	−6.85674	−0.496136	−0.248068	−	0.968743i	$-0.579796\pi$
$191$	−6.85674	−0.496136	−0.248068	+	0.968743i	$0.579796\pi$
$192$	12.6406	0.912254
$193$	1.59498	0.114809	0.0574047	−	0.998351i	$-0.481717\pi$
$193$	1.59498	0.114809	0.0574047	+	0.998351i	$0.481717\pi$
$194$	−18.8465	−1.35310
$195$	0	0
$196$	4.68518	0.334656
$197$	−0.839749	−0.0598297	−0.0299148	−	0.999552i	$-0.509524\pi$
$197$	−0.839749	−0.0598297	−0.0299148	+	0.999552i	$0.509524\pi$
$198$	−82.8437	−5.88744
$199$	−4.19178	−0.297147	−0.148574	−	0.988901i	$-0.547468\pi$
$199$	−4.19178	−0.297147	−0.148574	+	0.988901i	$0.547468\pi$
$200$	23.6859	1.67485
$201$	32.9272	2.32251
$202$	26.4207	1.85895
$203$	1.64194	0.115241
$204$	−14.8066	−1.03667
$205$	1.25238	0.0874697
$206$	−23.9288	−1.66720
$207$	17.0991	1.18847
$208$	0	0
$209$	−3.47868	−0.240626
$210$	−9.58018	−0.661095
$211$	14.0772	0.969112	0.484556	−	0.874760i	$-0.338981\pi$
$211$	14.0772	0.969112	0.484556	+	0.874760i	$0.338981\pi$
$212$	14.2502	0.978710
$213$	1.52800	0.104697
$214$	−39.2552	−2.68343
$215$	−6.25149	−0.426348
$216$	−53.9523	−3.67099
$217$	−8.21292	−0.557529
$218$	16.3336	1.10625
$219$	−46.9721	−3.17408
$220$	33.5256	2.26029
$221$	0	0
$222$	−36.5950	−2.45610
$223$	−9.44873	−0.632734	−0.316367	−	0.948637i	$-0.602463\pi$
$223$	−9.44873	−0.632734	−0.316367	+	0.948637i	$0.602463\pi$
$224$	−8.30017	−0.554579
$225$	−19.2527	−1.28351
$226$	−42.2474	−2.81025
$227$	23.8789	1.58490	0.792448	−	0.609939i	$-0.208806\pi$
$227$	23.8789	1.58490	0.792448	+	0.609939i	$0.208806\pi$
$228$	−8.43933	−0.558908
$229$	−2.54192	−0.167975	−0.0839875	−	0.996467i	$-0.526766\pi$
$229$	−2.54192	−0.167975	−0.0839875	+	0.996467i	$0.526766\pi$
$230$	−9.87363	−0.651048
$231$	16.6921	1.09826
$232$	−11.3995	−0.748415
$233$	6.17851	0.404768	0.202384	−	0.979306i	$-0.435131\pi$
$233$	6.17851	0.404768	0.202384	+	0.979306i	$0.435131\pi$
$234$	0	0
$235$	4.95801	0.323425
$236$	−35.6932	−2.32343
$237$	−13.2604	−0.861355
$238$	2.77938	0.180160
$239$	−16.9058	−1.09354	−0.546772	−	0.837281i	$-0.684144\pi$
$239$	−16.9058	−1.09354	−0.546772	+	0.837281i	$0.684144\pi$
$240$	31.7930	2.05223
$241$	−12.7218	−0.819485	−0.409742	−	0.912201i	$-0.634381\pi$
$241$	−12.7218	−0.819485	−0.409742	+	0.912201i	$0.634381\pi$
$242$	−54.9078	−3.52961
$243$	−5.91850	−0.379672
$244$	−65.9743	−4.22357
$245$	1.26031	0.0805184
$246$	−7.55357	−0.481598
$247$	0	0
$248$	57.0200	3.62078
$249$	−11.0259	−0.698741
$250$	27.4103	1.73358
$251$	19.2776	1.21679	0.608395	−	0.793635i	$-0.291814\pi$
$251$	19.2776	1.21679	0.608395	+	0.793635i	$0.291814\pi$
$252$	26.4397	1.66555
$253$	17.2034	1.08157
$254$	47.1697	2.95969
$255$	−3.98298	−0.249424
$256$	−22.7770	−1.42356
$257$	14.9565	0.932964	0.466482	−	0.884531i	$-0.345521\pi$
$257$	14.9565	0.932964	0.466482	+	0.884531i	$0.345521\pi$
$258$	37.7052	2.34742
$259$	4.81423	0.299142
$260$	0	0
$261$	9.26589	0.573544
$262$	−14.1236	−0.872557
$263$	19.0777	1.17638	0.588191	−	0.808722i	$-0.299840\pi$
$263$	19.0777	1.17638	0.588191	+	0.808722i	$0.299840\pi$
$264$	−115.889	−7.13245
$265$	3.83331	0.235478
$266$	1.58416	0.0971312
$267$	−47.6382	−2.91541
$268$	52.4738	3.20534
$269$	−12.2567	−0.747302	−0.373651	−	0.927569i	$-0.621894\pi$
$269$	−12.2567	−0.747302	−0.373651	+	0.927569i	$0.621894\pi$
$270$	−25.3230	−1.54111
$271$	23.4754	1.42603	0.713014	−	0.701150i	$-0.247330\pi$
$271$	23.4754	1.42603	0.713014	+	0.701150i	$0.247330\pi$
$272$	−9.22373	−0.559271
$273$	0	0
$274$	−2.54704	−0.153873
$275$	−19.3701	−1.16806
$276$	41.7357	2.51219
$277$	−29.5078	−1.77295	−0.886475	−	0.462776i	$-0.846853\pi$
$277$	−29.5078	−1.77295	−0.886475	+	0.462776i	$0.846853\pi$
$278$	−0.0306316	−0.00183716
$279$	−46.3477	−2.77476
$280$	−8.75000	−0.522912
$281$	−2.82573	−0.168569	−0.0842843	−	0.996442i	$-0.526860\pi$
$281$	−2.82573	−0.168569	−0.0842843	+	0.996442i	$0.526860\pi$
$282$	−29.9037	−1.78074
$283$	10.1831	0.605325	0.302663	−	0.953098i	$-0.402124\pi$
$283$	10.1831	0.605325	0.302663	+	0.953098i	$0.402124\pi$
$284$	2.43507	0.144495
$285$	−2.27018	−0.134474
$286$	0	0
$287$	0.993703	0.0586564
$288$	−46.8401	−2.76008
$289$	−15.8445	−0.932027
$290$	−5.35046	−0.314190
$291$	21.4295	1.25622
$292$	−74.8561	−4.38062
$293$	−11.0531	−0.645730	−0.322865	−	0.946445i	$-0.604646\pi$
$293$	−11.0531	−0.645730	−0.322865	+	0.946445i	$0.604646\pi$
$294$	−7.60143	−0.443325
$295$	−9.60146	−0.559019
$296$	−33.4238	−1.94272
$297$	44.1217	2.56020
$298$	−32.3101	−1.87168
$299$	0	0
$300$	−46.9921	−2.71309
$301$	−4.96027	−0.285905
$302$	−32.2206	−1.85409
$303$	−30.0418	−1.72586
$304$	−5.25724	−0.301523
$305$	−17.7471	−1.01619
$306$	15.6848	0.896640
$307$	17.0325	0.972095	0.486047	−	0.873932i	$-0.338438\pi$
$307$	17.0325	0.972095	0.486047	+	0.873932i	$0.338438\pi$
$308$	26.6010	1.51573
$309$	27.2084	1.54783
$310$	26.7628	1.52003
$311$	−21.6934	−1.23012	−0.615061	−	0.788480i	$-0.710869\pi$
$311$	−21.6934	−1.23012	−0.615061	+	0.788480i	$0.710869\pi$
$312$	0	0
$313$	31.9051	1.80338	0.901692	−	0.432379i	$-0.142326\pi$
$313$	31.9051	1.80338	0.901692	+	0.432379i	$0.142326\pi$
$314$	−7.39187	−0.417148
$315$	7.11228	0.400731
$316$	−21.1321	−1.18878
$317$	3.66655	0.205934	0.102967	−	0.994685i	$-0.467166\pi$
$317$	3.66655	0.205934	0.102967	+	0.994685i	$0.467166\pi$
$318$	−23.1202	−1.29652
$319$	9.32242	0.521955
$320$	5.41883	0.302922
$321$	44.6355	2.49131
$322$	−7.83428	−0.436587
$323$	0.658619	0.0366465
$324$	27.7207	1.54004
$325$	0	0
$326$	−4.41351	−0.244442
$327$	−18.5723	−1.02705
$328$	−6.89901	−0.380934
$329$	3.93396	0.216886
$330$	−54.3933	−2.99425
$331$	18.3335	1.00770	0.503850	−	0.863791i	$-0.331916\pi$
$331$	18.3335	1.00770	0.503850	+	0.863791i	$0.331916\pi$
$332$	−17.5713	−0.964348
$333$	27.1680	1.48880
$334$	49.7965	2.72474
$335$	14.1154	0.771208
$336$	25.2263	1.37621
$337$	−3.66441	−0.199613	−0.0998065	−	0.995007i	$-0.531822\pi$
$337$	−3.66441	−0.199613	−0.0998065	+	0.995007i	$0.531822\pi$
$338$	0	0
$339$	48.0377	2.60905
$340$	−6.34740	−0.344236
$341$	−46.6305	−2.52518
$342$	8.93985	0.483412
$343$	1.00000	0.0539949
$344$	34.4378	1.85676
$345$	11.2269	0.604435
$346$	−2.78508	−0.149727
$347$	−15.6042	−0.837677	−0.418839	−	0.908061i	$-0.637563\pi$
$347$	−15.6042	−0.837677	−0.418839	+	0.908061i	$0.637563\pi$
$348$	22.6163	1.21236
$349$	−1.45644	−0.0779614	−0.0389807	−	0.999240i	$-0.512411\pi$
$349$	−1.45644	−0.0779614	−0.0389807	+	0.999240i	$0.512411\pi$
$350$	8.82097	0.471501
$351$	0	0
$352$	−47.1259	−2.51182
$353$	22.8854	1.21807	0.609034	−	0.793144i	$-0.291557\pi$
$353$	22.8854	1.21807	0.609034	+	0.793144i	$0.291557\pi$
$354$	57.9102	3.07789
$355$	0.655032	0.0347655
$356$	−75.9177	−4.02363
$357$	−3.16032	−0.167262
$358$	−29.4708	−1.55758
$359$	−5.31753	−0.280649	−0.140324	−	0.990106i	$-0.544814\pi$
$359$	−5.31753	−0.280649	−0.140324	+	0.990106i	$0.544814\pi$
$360$	−49.3786	−2.60248
$361$	−18.6246	−0.980242
$362$	−24.4142	−1.28318
$363$	62.4333	3.27690
$364$	0	0
$365$	−20.1363	−1.05398
$366$	107.040	5.59505
$367$	−30.8184	−1.60871	−0.804353	−	0.594151i	$-0.797488\pi$
$367$	−30.8184	−1.60871	−0.804353	+	0.594151i	$0.797488\pi$
$368$	25.9990	1.35529
$369$	5.60773	0.291927
$370$	−15.6878	−0.815568
$371$	3.04156	0.157910
$372$	−113.126	−5.86531
$373$	−24.0416	−1.24483	−0.622414	−	0.782688i	$-0.713848\pi$
$373$	−24.0416	−1.24483	−0.622414	+	0.782688i	$0.713848\pi$
$374$	15.7805	0.815989
$375$	−31.1671	−1.60946
$376$	−27.3124	−1.40853
$377$	0	0
$378$	−20.0926	−1.03345
$379$	4.09140	0.210161	0.105081	−	0.994464i	$-0.466490\pi$
$379$	4.09140	0.210161	0.105081	+	0.994464i	$0.466490\pi$
$380$	−3.61782	−0.185590
$381$	−53.6347	−2.74779
$382$	17.7286	0.907074
$383$	−32.1859	−1.64462	−0.822312	−	0.569037i	$-0.807316\pi$
$383$	−32.1859	−1.64462	−0.822312	+	0.569037i	$0.807316\pi$
$384$	16.1210	0.822671
$385$	7.15567	0.364687
$386$	−4.12394	−0.209903
$387$	−27.9921	−1.42292
$388$	34.1507	1.73374
$389$	−7.32127	−0.371203	−0.185602	−	0.982625i	$-0.559423\pi$
$389$	−7.32127	−0.371203	−0.185602	+	0.982625i	$0.559423\pi$
$390$	0	0
$391$	−3.25712	−0.164720
$392$	−6.94272	−0.350660
$393$	16.0593	0.810085
$394$	2.17123	0.109385
$395$	−5.68454	−0.286020
$396$	150.117	7.54365
$397$	20.5111	1.02942	0.514712	−	0.857363i	$-0.327899\pi$
$397$	20.5111	1.02942	0.514712	+	0.857363i	$0.327899\pi$
$398$	10.8381	0.543267
$399$	−1.80128	−0.0901769
$400$	−29.2735	−1.46368
$401$	14.3355	0.715883	0.357941	−	0.933744i	$-0.383479\pi$
$401$	14.3355	0.715883	0.357941	+	0.933744i	$0.383479\pi$
$402$	−85.1356	−4.24618
$403$	0	0
$404$	−47.8756	−2.38190
$405$	7.45685	0.370534
$406$	−4.24535	−0.210693
$407$	27.3337	1.35488
$408$	21.9412	1.08625
$409$	−15.4092	−0.761936	−0.380968	−	0.924588i	$-0.624409\pi$
$409$	−15.4092	−0.761936	−0.380968	+	0.924588i	$0.624409\pi$
$410$	−3.23811	−0.159919
$411$	2.89613	0.142856
$412$	43.3601	2.13620
$413$	−7.61833	−0.374873
$414$	−44.2109	−2.17285
$415$	−4.72666	−0.232023
$416$	0	0
$417$	0.0348299	0.00170563
$418$	8.99439	0.439930
$419$	−14.2884	−0.698033	−0.349016	−	0.937117i	$-0.613484\pi$
$419$	−14.2884	−0.698033	−0.349016	+	0.937117i	$0.613484\pi$
$420$	17.3597	0.847069
$421$	−22.6594	−1.10435	−0.552176	−	0.833728i	$-0.686202\pi$
$421$	−22.6594	−1.10435	−0.552176	+	0.833728i	$0.686202\pi$
$422$	−36.3975	−1.77180
$423$	22.2004	1.07942
$424$	−21.1167	−1.02552
$425$	3.66734	0.177892
$426$	−3.95075	−0.191415
$427$	−14.0815	−0.681451
$428$	71.1324	3.43831
$429$	0	0
$430$	16.1637	0.779481
$431$	33.2914	1.60359	0.801796	−	0.597598i	$-0.203878\pi$
$431$	33.2914	1.60359	0.801796	+	0.597598i	$0.203878\pi$
$432$	66.6799	3.20814
$433$	−6.67910	−0.320977	−0.160489	−	0.987038i	$-0.551307\pi$
$433$	−6.67910	−0.320977	−0.160489	+	0.987038i	$0.551307\pi$
$434$	21.2351	1.01932
$435$	6.08378	0.291695
$436$	−29.5973	−1.41745
$437$	−1.85646	−0.0888064
$438$	121.450	5.80309
$439$	17.6199	0.840951	0.420475	−	0.907304i	$-0.361863\pi$
$439$	17.6199	0.840951	0.420475	+	0.907304i	$0.361863\pi$
$440$	−49.6798	−2.36839
$441$	5.64327	0.268727
$442$	0	0
$443$	−34.5102	−1.63963	−0.819814	−	0.572631i	$-0.805923\pi$
$443$	−34.5102	−1.63963	−0.819814	+	0.572631i	$0.805923\pi$
$444$	66.3120	3.14703
$445$	−20.4218	−0.968088
$446$	24.4304	1.15681
$447$	36.7385	1.73767
$448$	4.29960	0.203137
$449$	−14.2141	−0.670804	−0.335402	−	0.942075i	$-0.608872\pi$
$449$	−14.2141	−0.670804	−0.335402	+	0.942075i	$0.608872\pi$
$450$	49.7791	2.34661
$451$	5.64194	0.265669
$452$	76.5543	3.60081
$453$	36.6367	1.72134
$454$	−61.7405	−2.89763
$455$	0	0
$456$	12.5058	0.585638
$457$	−10.2025	−0.477253	−0.238627	−	0.971111i	$-0.576697\pi$
$457$	−10.2025	−0.477253	−0.238627	+	0.971111i	$0.576697\pi$
$458$	6.57232	0.307104
$459$	−8.35356	−0.389911
$460$	17.8915	0.834195
$461$	33.2152	1.54699	0.773493	−	0.633804i	$-0.218508\pi$
$461$	33.2152	1.54699	0.773493	+	0.633804i	$0.218508\pi$
$462$	−43.1586	−2.00792
$463$	15.1959	0.706215	0.353107	−	0.935583i	$-0.385125\pi$
$463$	15.1959	0.706215	0.353107	+	0.935583i	$0.385125\pi$
$464$	14.0887	0.654053
$465$	−30.4309	−1.41120
$466$	−15.9750	−0.740027
$467$	25.4084	1.17576	0.587881	−	0.808948i	$-0.299962\pi$
$467$	25.4084	1.17576	0.587881	+	0.808948i	$0.299962\pi$
$468$	0	0
$469$	11.1999	0.517165
$470$	−12.8193	−0.591310
$471$	8.40499	0.387281
$472$	52.8919	2.43455
$473$	−28.1629	−1.29493
$474$	34.2857	1.57479
$475$	2.09027	0.0959083
$476$	−5.03637	−0.230842
$477$	17.1643	0.785900
$478$	43.7111	1.99930
$479$	−23.8654	−1.09044	−0.545219	−	0.838294i	$-0.683553\pi$
$479$	−23.8654	−1.09044	−0.545219	+	0.838294i	$0.683553\pi$
$480$	−30.7542	−1.40373
$481$	0	0
$482$	32.8932	1.49824
$483$	8.90802	0.405329
$484$	99.4955	4.52252
$485$	9.18653	0.417139
$486$	15.3027	0.694145
$487$	−24.5800	−1.11383	−0.556914	−	0.830570i	$-0.688015\pi$
$487$	−24.5800	−1.11383	−0.556914	+	0.830570i	$0.688015\pi$
$488$	97.7639	4.42557
$489$	5.01841	0.226941
$490$	−3.25863	−0.147210
$491$	−15.9900	−0.721621	−0.360810	−	0.932639i	$-0.617500\pi$
$491$	−15.9900	−0.721621	−0.360810	+	0.932639i	$0.617500\pi$
$492$	13.6874	0.617077
$493$	−1.76501	−0.0794922
$494$	0	0
$495$	40.3813	1.81501
$496$	−70.4714	−3.16426
$497$	0.519738	0.0233134
$498$	28.5084	1.27749
$499$	−20.3617	−0.911515	−0.455758	−	0.890104i	$-0.650632\pi$
$499$	−20.3617	−0.911515	−0.455758	+	0.890104i	$0.650632\pi$
$500$	−49.6688	−2.22126
$501$	−56.6214	−2.52966
$502$	−49.8435	−2.22463
$503$	−22.0696	−0.984033	−0.492017	−	0.870586i	$-0.663740\pi$
$503$	−22.0696	−0.984033	−0.492017	+	0.870586i	$0.663740\pi$
$504$	−39.1796	−1.74520
$505$	−12.8785	−0.573086
$506$	−44.4806	−1.97741
$507$	0	0
$508$	−85.4738	−3.79229
$509$	17.5386	0.777383	0.388692	−	0.921368i	$-0.372927\pi$
$509$	17.5386	0.777383	0.388692	+	0.921368i	$0.372927\pi$
$510$	10.2983	0.456016
$511$	−15.9772	−0.706790
$512$	47.9247	2.11799
$513$	−4.76127	−0.210215
$514$	−38.6712	−1.70571
$515$	11.6638	0.513971
$516$	−68.3236	−3.00778
$517$	22.3358	0.982328
$518$	−12.4475	−0.546913
$519$	3.16680	0.139007
$520$	0	0
$521$	23.8918	1.04672	0.523360	−	0.852111i	$-0.324678\pi$
$521$	23.8918	1.04672	0.523360	+	0.852111i	$0.324678\pi$
$522$	−23.9576	−1.04860
$523$	9.59519	0.419568	0.209784	−	0.977748i	$-0.432724\pi$
$523$	9.59519	0.419568	0.209784	+	0.977748i	$0.432724\pi$
$524$	25.5926	1.11802
$525$	−10.0300	−0.437743
$526$	−49.3268	−2.15075
$527$	8.82854	0.384577
$528$	143.227	6.23317
$529$	−13.8191	−0.600831
$530$	−9.91129	−0.430519
$531$	−42.9923	−1.86570
$532$	−2.87058	−0.124455
$533$	0	0
$534$	123.172	5.33018
$535$	19.1346	0.827260
$536$	−77.7581	−3.35864
$537$	33.5100	1.44606
$538$	31.6905	1.36627
$539$	5.67770	0.244556
$540$	45.8864	1.97464
$541$	−30.5093	−1.31170	−0.655849	−	0.754892i	$-0.727689\pi$
$541$	−30.5093	−1.31170	−0.655849	+	0.754892i	$0.727689\pi$
$542$	−60.6972	−2.60717
$543$	27.7604	1.19131
$544$	8.92234	0.382542
$545$	−7.96166	−0.341040
$546$	0	0
$547$	27.9226	1.19388	0.596942	−	0.802284i	$-0.296382\pi$
$547$	27.9226	1.19388	0.596942	+	0.802284i	$0.296382\pi$
$548$	4.61536	0.197159
$549$	−79.4657	−3.39151
$550$	50.0828	2.13554
$551$	−1.00600	−0.0428572
$552$	−61.8459	−2.63234
$553$	−4.51042	−0.191803
$554$	76.2945	3.24144
$555$	17.8379	0.757176
$556$	0.0555060	0.00235398
$557$	−8.13721	−0.344784	−0.172392	−	0.985028i	$-0.555150\pi$
$557$	−8.13721	−0.344784	−0.172392	+	0.985028i	$0.555150\pi$
$558$	119.835	5.07303
$559$	0	0
$560$	10.8142	0.456982
$561$	−17.9433	−0.757567
$562$	7.30612	0.308190
$563$	−38.6946	−1.63078	−0.815391	−	0.578911i	$-0.803478\pi$
$563$	−38.6946	−1.63078	−0.815391	+	0.578911i	$0.803478\pi$
$564$	54.1870	2.28168
$565$	20.5931	0.866357
$566$	−26.3292	−1.10670
$567$	5.91667	0.248477
$568$	−3.60840	−0.151405
$569$	−34.7298	−1.45595	−0.727974	−	0.685605i	$-0.759538\pi$
$569$	−34.7298	−1.45595	−0.727974	+	0.685605i	$0.759538\pi$
$570$	5.86971	0.245855
$571$	−2.63871	−0.110427	−0.0552134	−	0.998475i	$-0.517584\pi$
$571$	−2.63871	−0.110427	−0.0552134	+	0.998475i	$0.517584\pi$
$572$	0	0
$573$	−20.1584	−0.842131
$574$	−2.56929	−0.107240
$575$	−10.3372	−0.431090
$576$	24.2638	1.01099
$577$	−39.2432	−1.63372	−0.816859	−	0.576838i	$-0.804287\pi$
$577$	−39.2432	−1.63372	−0.816859	+	0.576838i	$0.804287\pi$
$578$	40.9670	1.70400
$579$	4.68916	0.194875
$580$	9.69529	0.402575
$581$	−3.75039	−0.155592
$582$	−55.4075	−2.29672
$583$	17.2690	0.715210
$584$	110.925	4.59012
$585$	0	0
$586$	28.5786	1.18057
$587$	−2.23680	−0.0923226	−0.0461613	−	0.998934i	$-0.514699\pi$
$587$	−2.23680	−0.0923226	−0.0461613	+	0.998934i	$0.514699\pi$
$588$	13.7742	0.568037
$589$	5.03200	0.207340
$590$	24.8253	1.02204
$591$	−2.46882	−0.101554
$592$	41.3087	1.69778
$593$	−19.0940	−0.784097	−0.392048	−	0.919945i	$-0.628233\pi$
$593$	−19.0940	−0.784097	−0.392048	+	0.919945i	$0.628233\pi$
$594$	−114.080	−4.68075
$595$	−1.35478	−0.0555407
$596$	58.5475	2.39820
$597$	−12.3236	−0.504371
$598$	0	0
$599$	−35.8920	−1.46651	−0.733253	−	0.679956i	$-0.761999\pi$
$599$	−35.8920	−1.46651	−0.733253	+	0.679956i	$0.761999\pi$
$600$	69.6352	2.84285
$601$	3.06525	0.125034	0.0625171	−	0.998044i	$-0.480087\pi$
$601$	3.06525	0.125034	0.0625171	+	0.998044i	$0.480087\pi$
$602$	12.8251	0.522714
$603$	63.2043	2.57388
$604$	58.3853	2.37566
$605$	26.7643	1.08812
$606$	77.6753	3.15534
$607$	−22.8339	−0.926800	−0.463400	−	0.886149i	$-0.653371\pi$
$607$	−22.8339	−0.926800	−0.463400	+	0.886149i	$0.653371\pi$
$608$	5.08546	0.206243
$609$	4.82720	0.195608
$610$	45.8863	1.85788
$611$	0	0
$612$	−28.4216	−1.14887
$613$	19.4867	0.787062	0.393531	−	0.919311i	$-0.371253\pi$
$613$	19.4867	0.787062	0.393531	+	0.919311i	$0.371253\pi$
$614$	−44.0387	−1.77726
$615$	3.68191	0.148469
$616$	−39.4187	−1.58822
$617$	−23.1585	−0.932326	−0.466163	−	0.884699i	$-0.654364\pi$
$617$	−23.1585	−0.932326	−0.466163	+	0.884699i	$0.654364\pi$
$618$	−70.3492	−2.82986
$619$	25.6987	1.03292	0.516460	−	0.856312i	$-0.327250\pi$
$619$	25.6987	1.03292	0.516460	+	0.856312i	$0.327250\pi$
$620$	−48.4955	−1.94763
$621$	23.5463	0.944880
$622$	56.0899	2.24900
$623$	−16.2038	−0.649191
$624$	0	0
$625$	3.69719	0.147887
$626$	−82.4929	−3.29708
$627$	−10.2271	−0.408432
$628$	13.3944	0.534496
$629$	−5.17509	−0.206344
$630$	−18.3893	−0.732647
$631$	−5.62736	−0.224022	−0.112011	−	0.993707i	$-0.535729\pi$
$631$	−5.62736	−0.224022	−0.112011	+	0.993707i	$0.535729\pi$
$632$	31.3146	1.24563
$633$	41.3861	1.64495
$634$	−9.48014	−0.376504
$635$	−22.9924	−0.912427
$636$	41.8949	1.66124
$637$	0	0
$638$	−24.1038	−0.954278
$639$	2.93302	0.116028
$640$	6.91084	0.273175
$641$	35.1667	1.38900	0.694501	−	0.719492i	$-0.255625\pi$
$641$	35.1667	1.38900	0.694501	+	0.719492i	$0.255625\pi$
$642$	−115.408	−4.55480
$643$	−1.89892	−0.0748862	−0.0374431	−	0.999299i	$-0.511921\pi$
$643$	−1.89892	−0.0748862	−0.0374431	+	0.999299i	$0.511921\pi$
$644$	14.1961	0.559404
$645$	−18.3790	−0.723673
$646$	−1.70291	−0.0670000
$647$	−25.9704	−1.02100	−0.510500	−	0.859878i	$-0.670540\pi$
$647$	−25.9704	−1.02100	−0.510500	+	0.859878i	$0.670540\pi$
$648$	−41.0778	−1.61369
$649$	−43.2545	−1.69789
$650$	0	0
$651$	−24.1455	−0.946337
$652$	7.99749	0.313206
$653$	11.9944	0.469377	0.234689	−	0.972071i	$-0.424593\pi$
$653$	11.9944	0.469377	0.234689	+	0.972071i	$0.424593\pi$
$654$	48.0199	1.87773
$655$	6.88439	0.268995
$656$	8.52652	0.332905
$657$	−90.1636	−3.51762
$658$	−10.1715	−0.396527
$659$	24.5442	0.956106	0.478053	−	0.878331i	$-0.341343\pi$
$659$	24.5442	0.956106	0.478053	+	0.878331i	$0.341343\pi$
$660$	98.5633	3.83657
$661$	38.4044	1.49376	0.746878	−	0.664961i	$-0.231552\pi$
$661$	38.4044	1.49376	0.746878	+	0.664961i	$0.231552\pi$
$662$	−47.4026	−1.84235
$663$	0	0
$664$	26.0379	1.01047
$665$	−0.772184	−0.0299440
$666$	−70.2447	−2.72193
$667$	4.97507	0.192635
$668$	−90.2336	−3.49124
$669$	−27.7787	−1.07399
$670$	−36.4964	−1.40998
$671$	−79.9504	−3.08645
$672$	−24.4020	−0.941329
$673$	44.6230	1.72009	0.860044	−	0.510220i	$-0.170436\pi$
$673$	44.6230	1.72009	0.860044	+	0.510220i	$0.170436\pi$
$674$	9.47459	0.364948
$675$	−26.5119	−1.02044
$676$	0	0
$677$	−16.4358	−0.631679	−0.315839	−	0.948813i	$-0.602286\pi$
$677$	−16.4358	−0.631679	−0.315839	+	0.948813i	$0.602286\pi$
$678$	−124.205	−4.77006
$679$	7.28909	0.279730
$680$	9.40588	0.360699
$681$	70.2025	2.69017
$682$	120.566	4.61673
$683$	2.20853	0.0845070	0.0422535	−	0.999107i	$-0.486546\pi$
$683$	2.20853	0.0845070	0.0422535	+	0.999107i	$0.486546\pi$
$684$	−16.1994	−0.619401
$685$	1.24153	0.0474365
$686$	−2.58557	−0.0987176
$687$	−7.47311	−0.285117
$688$	−42.5618	−1.62266
$689$	0	0
$690$	−29.0279	−1.10507
$691$	−25.1383	−0.956307	−0.478153	−	0.878276i	$-0.658694\pi$
$691$	−25.1383	−0.956307	−0.478153	+	0.878276i	$0.658694\pi$
$692$	5.04670	0.191847
$693$	32.0408	1.21713
$694$	40.3458	1.53150
$695$	0.0149311	0.000566369 0
$696$	−33.5139	−1.27034
$697$	−1.06819	−0.0404606
$698$	3.76573	0.142535
$699$	18.1645	0.687044
$700$	−15.9840	−0.604139
$701$	41.8755	1.58162	0.790808	−	0.612064i	$-0.209661\pi$
$701$	41.8755	1.58162	0.790808	+	0.612064i	$0.209661\pi$
$702$	0	0
$703$	−2.94964	−0.111248
$704$	24.4118	0.920054
$705$	14.5763	0.548974
$706$	−59.1719	−2.22696
$707$	−10.2185	−0.384307
$708$	−104.936	−3.94374
$709$	−13.6827	−0.513863	−0.256932	−	0.966430i	$-0.582712\pi$
$709$	−13.6827	−0.513863	−0.256932	+	0.966430i	$0.582712\pi$
$710$	−1.69363	−0.0635609
$711$	−25.4535	−0.954582
$712$	112.498	4.21606
$713$	−24.8851	−0.931955
$714$	8.17122	0.305800
$715$	0	0
$716$	53.4025	1.99574
$717$	−49.7021	−1.85616
$718$	13.7489	0.513103
$719$	−47.7923	−1.78235	−0.891176	−	0.453658i	$-0.850119\pi$
$719$	−47.7923	−1.78235	−0.891176	+	0.453658i	$0.850119\pi$
$720$	61.0272	2.27435
$721$	9.25473	0.344664
$722$	48.1553	1.79215
$723$	−37.4014	−1.39097
$724$	44.2397	1.64416
$725$	−5.60166	−0.208040
$726$	−161.426	−5.99107
$727$	8.73886	0.324106	0.162053	−	0.986782i	$-0.448188\pi$
$727$	8.73886	0.324106	0.162053	+	0.986782i	$0.448188\pi$
$728$	0	0
$729$	−35.1501	−1.30185
$730$	52.0637	1.92697
$731$	5.33208	0.197214
$732$	−193.961	−7.16900
$733$	37.6623	1.39109	0.695545	−	0.718483i	$-0.255163\pi$
$733$	37.6623	1.39109	0.695545	+	0.718483i	$0.255163\pi$
$734$	79.6832	2.94116
$735$	3.70525	0.136670
$736$	−25.1495	−0.927023
$737$	63.5899	2.34236
$738$	−14.4992	−0.533723
$739$	−33.2978	−1.22488	−0.612439	−	0.790518i	$-0.709811\pi$
$739$	−33.2978	−1.22488	−0.612439	+	0.790518i	$0.709811\pi$
$740$	28.4270	1.04500
$741$	0	0
$742$	−7.86416	−0.288702
$743$	48.4072	1.77589	0.887944	−	0.459952i	$-0.152134\pi$
$743$	48.4072	1.77589	0.887944	+	0.459952i	$0.152134\pi$
$744$	167.636	6.14582
$745$	15.7493	0.577009
$746$	62.1614	2.27589
$747$	−21.1645	−0.774367
$748$	−28.5950	−1.04554
$749$	15.1824	0.554754
$750$	80.5847	2.94254
$751$	5.16131	0.188339	0.0941695	−	0.995556i	$-0.469980\pi$
$751$	5.16131	0.188339	0.0941695	+	0.995556i	$0.469980\pi$
$752$	33.7555	1.23094
$753$	56.6750	2.06535
$754$	0	0
$755$	15.7056	0.571586
$756$	36.4088	1.32418
$757$	30.9400	1.12453	0.562266	−	0.826956i	$-0.309930\pi$
$757$	30.9400	1.12453	0.562266	+	0.826956i	$0.309930\pi$
$758$	−10.5786	−0.384232
$759$	50.5770	1.83583
$760$	5.36106	0.194466
$761$	15.5767	0.564655	0.282327	−	0.959318i	$-0.408894\pi$
$761$	15.5767	0.564655	0.282327	+	0.959318i	$0.408894\pi$
$762$	138.676	5.02371
$763$	−6.31722	−0.228699
$764$	−32.1251	−1.16224
$765$	−7.64540	−0.276420
$766$	83.2190	3.00682
$767$	0	0
$768$	−66.9631	−2.41632
$769$	20.7798	0.749338	0.374669	−	0.927159i	$-0.377756\pi$
$769$	20.7798	0.749338	0.374669	+	0.927159i	$0.377756\pi$
$770$	−18.5015	−0.666747
$771$	43.9714	1.58359
$772$	7.47278	0.268951
$773$	−3.05425	−0.109854	−0.0549269	−	0.998490i	$-0.517493\pi$
$773$	−3.05425	−0.109854	−0.0549269	+	0.998490i	$0.517493\pi$
$774$	72.3757	2.60149
$775$	28.0193	1.00648
$776$	−50.6061	−1.81665
$777$	14.1536	0.507756
$778$	18.9297	0.678662
$779$	−0.608835	−0.0218138
$780$	0	0
$781$	2.95091	0.105592
$782$	8.42152	0.301153
$783$	12.7596	0.455991
$784$	8.58055	0.306448
$785$	3.60310	0.128600
$786$	−41.5225	−1.48106
$787$	35.2030	1.25485	0.627425	−	0.778677i	$-0.284109\pi$
$787$	35.2030	1.25485	0.627425	+	0.778677i	$0.284109\pi$
$788$	−3.93438	−0.140156
$789$	56.0874	1.99676
$790$	14.6978	0.522924
$791$	16.3397	0.580972
$792$	−222.450	−7.90442
$793$	0	0
$794$	−53.0330	−1.88207
$795$	11.2697	0.399695
$796$	−19.6392	−0.696095
$797$	23.8596	0.845150	0.422575	−	0.906328i	$-0.361126\pi$
$797$	23.8596	0.845150	0.422575	+	0.906328i	$0.361126\pi$
$798$	4.65734	0.164868
$799$	−4.22884	−0.149606
$800$	28.3170	1.00116
$801$	−91.4424	−3.23096
$802$	−37.0656	−1.30883
$803$	−90.7137	−3.20122
$804$	154.270	5.44068
$805$	3.81874	0.134593
$806$	0	0
$807$	−36.0339	−1.26845
$808$	70.9443	2.49581
$809$	8.68123	0.305216	0.152608	−	0.988287i	$-0.451233\pi$
$809$	8.68123	0.305216	0.152608	+	0.988287i	$0.451233\pi$
$810$	−19.2802	−0.677438
$811$	−42.9878	−1.50951	−0.754753	−	0.656009i	$-0.772243\pi$
$811$	−42.9878	−1.50951	−0.754753	+	0.656009i	$0.772243\pi$
$812$	7.69277	0.269963
$813$	69.0163	2.42051
$814$	−70.6733	−2.47710
$815$	2.15132	0.0753575
$816$	−27.1172	−0.949293
$817$	3.03912	0.106325
$818$	39.8416	1.39303
$819$	0	0
$820$	5.86761	0.204906
$821$	−14.8382	−0.517856	−0.258928	−	0.965897i	$-0.583369\pi$
$821$	−14.8382	−0.517856	−0.258928	+	0.965897i	$0.583369\pi$
$822$	−7.48816	−0.261180
$823$	2.03428	0.0709106	0.0354553	−	0.999371i	$-0.488712\pi$
$823$	2.03428	0.0709106	0.0354553	+	0.999371i	$0.488712\pi$
$824$	−64.2530	−2.23836
$825$	−56.9470	−1.98264
$826$	19.6977	0.685372
$827$	7.19291	0.250122	0.125061	−	0.992149i	$-0.460087\pi$
$827$	7.19291	0.250122	0.125061	+	0.992149i	$0.460087\pi$
$828$	80.1123	2.78410
$829$	−3.04682	−0.105820	−0.0529102	−	0.998599i	$-0.516850\pi$
$829$	−3.04682	−0.105820	−0.0529102	+	0.998599i	$0.516850\pi$
$830$	12.2211	0.424201
$831$	−86.7512	−3.00937
$832$	0	0
$833$	−1.07496	−0.0372451
$834$	−0.0900553	−0.00311836
$835$	−24.2728	−0.839995
$836$	−16.2983	−0.563687
$837$	−63.8231	−2.20605
$838$	36.9436	1.27620
$839$	−36.1612	−1.24842	−0.624211	−	0.781256i	$-0.714580\pi$
$839$	−36.1612	−1.24842	−0.624211	+	0.781256i	$0.714580\pi$
$840$	−25.7245	−0.887579
$841$	−26.3040	−0.907036
$842$	58.5875	2.01906
$843$	−8.30747	−0.286125
$844$	65.9541	2.27023
$845$	0	0
$846$	−57.4006	−1.97347
$847$	21.2362	0.729685
$848$	26.0982	0.896217
$849$	29.9379	1.02746
$850$	−9.48218	−0.325236
$851$	14.5871	0.500039
$852$	7.15896	0.245262
$853$	28.7775	0.985324	0.492662	−	0.870221i	$-0.336024\pi$
$853$	28.7775	0.985324	0.492662	+	0.870221i	$0.336024\pi$
$854$	36.4087	1.24588
$855$	−4.35764	−0.149028
$856$	−105.407	−3.60275
$857$	23.0347	0.786850	0.393425	−	0.919357i	$-0.371290\pi$
$857$	23.0347	0.786850	0.393425	+	0.919357i	$0.371290\pi$
$858$	0	0
$859$	−3.30594	−0.112797	−0.0563986	−	0.998408i	$-0.517962\pi$
$859$	−3.30594	−0.112797	−0.0563986	+	0.998408i	$0.517962\pi$
$860$	−29.2893	−0.998758
$861$	2.92143	0.0995621
$862$	−86.0773	−2.93181
$863$	−7.50620	−0.255514	−0.127757	−	0.991806i	$-0.540778\pi$
$863$	−7.50620	−0.255514	−0.127757	+	0.991806i	$0.540778\pi$
$864$	−64.5011	−2.19437
$865$	1.35756	0.0461584
$866$	17.2693	0.586834
$867$	−46.5818	−1.58200
$868$	−38.4790	−1.30606
$869$	−25.6088	−0.868720
$870$	−15.7301	−0.533299
$871$	0	0
$872$	43.8587	1.48524
$873$	41.1343	1.39218
$874$	4.80001	0.162363
$875$	−10.6013	−0.358388
$876$	−220.073	−7.43556
$877$	−14.3191	−0.483523	−0.241761	−	0.970336i	$-0.577725\pi$
$877$	−14.3191	−0.483523	−0.241761	+	0.970336i	$0.577725\pi$
$878$	−45.5575	−1.53749
$879$	−32.4955	−1.09605
$880$	61.3995	2.06978
$881$	14.9791	0.504660	0.252330	−	0.967641i	$-0.418803\pi$
$881$	14.9791	0.504660	0.252330	+	0.967641i	$0.418803\pi$
$882$	−14.5911	−0.491307
$883$	−5.05363	−0.170068	−0.0850342	−	0.996378i	$-0.527100\pi$
$883$	−5.05363	−0.170068	−0.0850342	+	0.996378i	$0.527100\pi$
$884$	0	0
$885$	−28.2278	−0.948866
$886$	89.2285	2.99769
$887$	36.2227	1.21624	0.608120	−	0.793845i	$-0.291924\pi$
$887$	36.2227	1.21624	0.608120	+	0.793845i	$0.291924\pi$
$888$	−98.2642	−3.29753
$889$	−18.2434	−0.611866
$890$	52.8021	1.76993
$891$	33.5931	1.12541
$892$	−44.2690	−1.48224
$893$	−2.41031	−0.0806579
$894$	−94.9900	−3.17694
$895$	14.3652	0.480177
$896$	5.48344	0.183189
$897$	0	0
$898$	36.7515	1.22641
$899$	−13.4851	−0.449753
$900$	−90.2021	−3.00674
$901$	−3.26955	−0.108924
$902$	−14.5877	−0.485716
$903$	−14.5829	−0.485289
$904$	−113.442	−3.77302
$905$	11.9005	0.395585
$906$	−94.7268	−3.14709
$907$	20.1931	0.670502	0.335251	−	0.942129i	$-0.391179\pi$
$907$	20.1931	0.670502	0.335251	+	0.942129i	$0.391179\pi$
$908$	111.877	3.71276
$909$	−57.6658	−1.91265
$910$	0	0
$911$	23.3520	0.773686	0.386843	−	0.922146i	$-0.373566\pi$
$911$	23.3520	0.773686	0.386843	+	0.922146i	$0.373566\pi$
$912$	−15.4560	−0.511799
$913$	−21.2936	−0.704715
$914$	26.3793	0.872551
$915$	−52.1754	−1.72487
$916$	−11.9094	−0.393496
$917$	5.46245	0.180386
$918$	21.5987	0.712864
$919$	33.9090	1.11855	0.559277	−	0.828981i	$-0.311079\pi$
$919$	33.9090	1.11855	0.559277	+	0.828981i	$0.311079\pi$
$920$	−26.5125	−0.874090
$921$	50.0745	1.65001
$922$	−85.8803	−2.82832
$923$	0	0
$924$	78.2055	2.57277
$925$	−16.4243	−0.540027
$926$	−39.2902	−1.29115
$927$	52.2269	1.71536
$928$	−13.6284	−0.447373
$929$	2.16312	0.0709697	0.0354849	−	0.999370i	$-0.488702\pi$
$929$	2.16312	0.0709697	0.0354849	+	0.999370i	$0.488702\pi$
$930$	78.6812	2.58006
$931$	−0.612693	−0.0200802
$932$	28.9474	0.948205
$933$	−63.7775	−2.08798
$934$	−65.6953	−2.14962
$935$	−7.69204	−0.251557
$936$	0	0
$937$	−6.77655	−0.221380	−0.110690	−	0.993855i	$-0.535306\pi$
$937$	−6.77655	−0.221380	−0.110690	+	0.993855i	$0.535306\pi$
$938$	−28.9583	−0.945521
$939$	93.7992	3.06102
$940$	23.2292	0.757652
$941$	−5.35958	−0.174717	−0.0873586	−	0.996177i	$-0.527843\pi$
$941$	−5.35958	−0.174717	−0.0873586	+	0.996177i	$0.527843\pi$
$942$	−21.7317	−0.708057
$943$	3.01092	0.0980490
$944$	−65.3694	−2.12759
$945$	9.79396	0.318597
$946$	72.8172	2.36749
$947$	37.9506	1.23323	0.616614	−	0.787266i	$-0.288504\pi$
$947$	37.9506	1.23323	0.616614	+	0.787266i	$0.288504\pi$
$948$	−62.1273	−2.01780
$949$	0	0
$950$	−5.40455	−0.175347
$951$	10.7795	0.349548
$952$	7.46314	0.241882
$953$	4.20005	0.136053	0.0680265	−	0.997684i	$-0.478330\pi$
$953$	4.20005	0.136053	0.0680265	+	0.997684i	$0.478330\pi$
$954$	−44.3796	−1.43684
$955$	−8.64163	−0.279637
$956$	−79.2066	−2.56173
$957$	27.4074	0.885955
$958$	61.7057	1.99362
$959$	0.985099	0.0318105
$960$	15.9311	0.514173
$961$	36.4520	1.17587
$962$	0	0
$963$	85.6785	2.76095
$964$	−59.6040	−1.91972
$965$	2.01017	0.0647098
$966$	−23.0323	−0.741053
$967$	−1.30898	−0.0420941	−0.0210470	−	0.999778i	$-0.506700\pi$
$967$	−1.30898	−0.0420941	−0.0210470	+	0.999778i	$0.506700\pi$
$968$	−147.437	−4.73881
$969$	1.93630	0.0622030
$970$	−23.7524	−0.762644
$971$	24.5181	0.786824	0.393412	−	0.919362i	$-0.371295\pi$
$971$	24.5181	0.786824	0.393412	+	0.919362i	$0.371295\pi$
$972$	−27.7292	−0.889416
$973$	0.0118471	0.000379802 0
$974$	63.5534	2.03638
$975$	0	0
$976$	−120.827	−3.86758
$977$	−47.8297	−1.53021	−0.765103	−	0.643907i	$-0.777312\pi$
$977$	−47.8297	−1.53021	−0.765103	+	0.643907i	$0.777312\pi$
$978$	−12.9755	−0.414910
$979$	−92.0002	−2.94034
$980$	5.90479	0.188621
$981$	−35.6497	−1.13821
$982$	41.3434	1.31932
$983$	−16.6624	−0.531449	−0.265725	−	0.964049i	$-0.585611\pi$
$983$	−16.6624	−0.531449	−0.265725	+	0.964049i	$0.585611\pi$
$984$	−20.2827	−0.646589
$985$	−1.05835	−0.0337217
$986$	4.56357	0.145334
$987$	11.5656	0.368137
$988$	0	0
$989$	−15.0296	−0.477914
$990$	−104.409	−3.31833
$991$	−31.0675	−0.986893	−0.493446	−	0.869776i	$-0.664263\pi$
$991$	−31.0675	−0.986893	−0.493446	+	0.869776i	$0.664263\pi$
$992$	68.1687	2.16436
$993$	53.8995	1.71045
$994$	−1.34382	−0.0426234
$995$	−5.28295	−0.167481
$996$	−51.6585	−1.63686
$997$	−37.1018	−1.17502	−0.587512	−	0.809215i	$-0.699893\pi$
$997$	−37.1018	−1.17502	−0.587512	+	0.809215i	$0.699893\pi$
$998$	52.6466	1.66650
$999$	37.4116	1.18365

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.r.1.1	yes	12
7.6	odd	2		8281.2.a.cq.1.1		12
13.5	odd	4		1183.2.c.j.337.23		24
13.8	odd	4		1183.2.c.j.337.2		24
13.12	even	2		1183.2.a.q.1.12	✓	12
91.90	odd	2		8281.2.a.cn.1.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.q.1.12	✓	12	13.12	even	2
1183.2.a.r.1.1	yes	12	1.1	even	1	trivial
1183.2.c.j.337.2		24	13.8	odd	4
1183.2.c.j.337.23		24	13.5	odd	4
8281.2.a.cn.1.12		12	91.90	odd	2
8281.2.a.cq.1.1		12	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58557 q^{2} +2.93994 q^{3} +4.68518 q^{4} +1.26031 q^{5} -7.60143 q^{6} +1.00000 q^{7} -6.94272 q^{8} +5.64327 q^{9} +O(q^{10})\)	\(q-2.58557 q^{2} +2.93994 q^{3} +4.68518 q^{4} +1.26031 q^{5} -7.60143 q^{6} +1.00000 q^{7} -6.94272 q^{8} +5.64327 q^{9} -3.25863 q^{10} +5.67770 q^{11} +13.7742 q^{12} -2.58557 q^{14} +3.70525 q^{15} +8.58055 q^{16} -1.07496 q^{17} -14.5911 q^{18} -0.612693 q^{19} +5.90479 q^{20} +2.93994 q^{21} -14.6801 q^{22} +3.03000 q^{23} -20.4112 q^{24} -3.41161 q^{25} +7.77106 q^{27} +4.68518 q^{28} +1.64194 q^{29} -9.58018 q^{30} -8.21292 q^{31} -8.30017 q^{32} +16.6921 q^{33} +2.77938 q^{34} +1.26031 q^{35} +26.4397 q^{36} +4.81423 q^{37} +1.58416 q^{38} -8.75000 q^{40} +0.993703 q^{41} -7.60143 q^{42} -4.96027 q^{43} +26.6010 q^{44} +7.11228 q^{45} -7.83428 q^{46} +3.93396 q^{47} +25.2263 q^{48} +1.00000 q^{49} +8.82097 q^{50} -3.16032 q^{51} +3.04156 q^{53} -20.0926 q^{54} +7.15567 q^{55} -6.94272 q^{56} -1.80128 q^{57} -4.24535 q^{58} -7.61833 q^{59} +17.3597 q^{60} -14.0815 q^{61} +21.2351 q^{62} +5.64327 q^{63} +4.29960 q^{64} -43.1586 q^{66} +11.1999 q^{67} -5.03637 q^{68} +8.90802 q^{69} -3.25863 q^{70} +0.519738 q^{71} -39.1796 q^{72} -15.9772 q^{73} -12.4475 q^{74} -10.0300 q^{75} -2.87058 q^{76} +5.67770 q^{77} -4.51042 q^{79} +10.8142 q^{80} +5.91667 q^{81} -2.56929 q^{82} -3.75039 q^{83} +13.7742 q^{84} -1.35478 q^{85} +12.8251 q^{86} +4.82720 q^{87} -39.4187 q^{88} -16.2038 q^{89} -18.3893 q^{90} +14.1961 q^{92} -24.1455 q^{93} -10.1715 q^{94} -0.772184 q^{95} -24.4020 q^{96} +7.28909 q^{97} -2.58557 q^{98} +32.0408 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9	\( 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9} - 6 q^{10} + 12 q^{11} + 13 q^{12} + 3 q^{14} + 11 q^{15} + 13 q^{16} + 31 q^{17} - 29 q^{18} - 3 q^{19} - 18 q^{20} + 8 q^{21} - 4 q^{22} + 18 q^{23} - 6 q^{24} + 32 q^{25} + 32 q^{27} + 15 q^{28} + 15 q^{29} - 10 q^{30} - 21 q^{31} - 3 q^{32} - 29 q^{33} + 3 q^{34} - 4 q^{35} + 49 q^{36} + 5 q^{37} + 45 q^{38} - 20 q^{40} - 16 q^{41} + 2 q^{42} - 22 q^{43} + 35 q^{44} + 5 q^{45} + 2 q^{46} - 4 q^{47} + 11 q^{48} + 12 q^{49} + 13 q^{50} + 18 q^{51} + 53 q^{53} - 5 q^{54} - 26 q^{55} + 12 q^{56} - 8 q^{57} + 32 q^{58} - 26 q^{59} + 38 q^{60} + 22 q^{61} + 19 q^{62} + 26 q^{63} + 2 q^{64} - 34 q^{66} + 12 q^{67} + 34 q^{68} + 3 q^{69} - 6 q^{70} + 21 q^{71} - 4 q^{72} - 15 q^{73} - 40 q^{74} + 15 q^{75} + 43 q^{76} + 12 q^{77} + 2 q^{79} + 13 q^{80} + 36 q^{81} - 32 q^{82} - 9 q^{83} + 13 q^{84} - 39 q^{85} + 44 q^{86} + 27 q^{87} - 48 q^{88} - 22 q^{89} - 26 q^{90} + 52 q^{92} - 53 q^{93} - 44 q^{94} + 29 q^{95} - 114 q^{96} + 9 q^{97} + 3 q^{98} + 37 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9 - 6 * q^10 + 12 * q^11 + 13 * q^12 + 3 * q^14 + 11 * q^15 + 13 * q^16 + 31 * q^17 - 29 * q^18 - 3 * q^19 - 18 * q^20 + 8 * q^21 - 4 * q^22 + 18 * q^23 - 6 * q^24 + 32 * q^25 + 32 * q^27 + 15 * q^28 + 15 * q^29 - 10 * q^30 - 21 * q^31 - 3 * q^32 - 29 * q^33 + 3 * q^34 - 4 * q^35 + 49 * q^36 + 5 * q^37 + 45 * q^38 - 20 * q^40 - 16 * q^41 + 2 * q^42 - 22 * q^43 + 35 * q^44 + 5 * q^45 + 2 * q^46 - 4 * q^47 + 11 * q^48 + 12 * q^49 + 13 * q^50 + 18 * q^51 + 53 * q^53 - 5 * q^54 - 26 * q^55 + 12 * q^56 - 8 * q^57 + 32 * q^58 - 26 * q^59 + 38 * q^60 + 22 * q^61 + 19 * q^62 + 26 * q^63 + 2 * q^64 - 34 * q^66 + 12 * q^67 + 34 * q^68 + 3 * q^69 - 6 * q^70 + 21 * q^71 - 4 * q^72 - 15 * q^73 - 40 * q^74 + 15 * q^75 + 43 * q^76 + 12 * q^77 + 2 * q^79 + 13 * q^80 + 36 * q^81 - 32 * q^82 - 9 * q^83 + 13 * q^84 - 39 * q^85 + 44 * q^86 + 27 * q^87 - 48 * q^88 - 22 * q^89 - 26 * q^90 + 52 * q^92 - 53 * q^93 - 44 * q^94 + 29 * q^95 - 114 * q^96 + 9 * q^97 + 3 * q^98 + 37 * q^99

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