LMFDB - Embedded newform 1183.2.a.l.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:	$4$
Coefficient field:	4.4.27004.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6x^{2} + 3x + 1 $ x^4 - x^3 - 6x^2 + 3x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.22001$ 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)

$f(q)$	$=$	$q-2.22001 q^{2} +0.549551 q^{3} +2.92843 q^{4} +4.22001 q^{5} -1.22001 q^{6} +1.00000 q^{7} -2.06113 q^{8} -2.69799 q^{9} +O(q^{10})$	\(q-2.22001 q^{2} +0.549551 q^{3} +2.92843 q^{4} +4.22001 q^{5} -1.22001 q^{6} +1.00000 q^{7} -2.06113 q^{8} -2.69799 q^{9} -9.36845 q^{10} +0.549551 q^{11} +1.60932 q^{12} -2.22001 q^{14} +2.31911 q^{15} -1.28114 q^{16} -2.37888 q^{17} +5.98957 q^{18} +3.61068 q^{19} +12.3580 q^{20} +0.549551 q^{21} -1.22001 q^{22} +5.81890 q^{23} -1.13270 q^{24} +12.8085 q^{25} -3.13134 q^{27} +2.92843 q^{28} -3.59889 q^{29} -5.14844 q^{30} +5.14844 q^{31} +6.96640 q^{32} +0.302006 q^{33} +5.28114 q^{34} +4.22001 q^{35} -7.90090 q^{36} +0.329543 q^{37} -8.01574 q^{38} -8.69799 q^{40} +6.29157 q^{41} -1.22001 q^{42} +3.22001 q^{43} +1.60932 q^{44} -11.3856 q^{45} -12.9180 q^{46} -8.20957 q^{47} -0.704052 q^{48} +1.00000 q^{49} -28.4349 q^{50} -1.30732 q^{51} +2.65866 q^{53} +6.95160 q^{54} +2.31911 q^{55} -2.06113 q^{56} +1.98426 q^{57} +7.98957 q^{58} +1.80753 q^{59} +6.79136 q^{60} +0.609325 q^{61} -11.4296 q^{62} -2.69799 q^{63} -12.9032 q^{64} -0.670457 q^{66} -10.3698 q^{67} -6.96640 q^{68} +3.19778 q^{69} -9.36845 q^{70} +11.1978 q^{71} +5.56092 q^{72} -4.90621 q^{73} -0.731589 q^{74} +7.03891 q^{75} +10.5736 q^{76} +0.549551 q^{77} -14.0171 q^{79} -5.40642 q^{80} +6.37315 q^{81} -13.9673 q^{82} +5.73159 q^{83} +1.60932 q^{84} -10.0389 q^{85} -7.14844 q^{86} -1.97777 q^{87} -1.13270 q^{88} +7.46755 q^{89} +25.2760 q^{90} +17.0403 q^{92} +2.82933 q^{93} +18.2253 q^{94} +15.2371 q^{95} +3.82840 q^{96} +6.84070 q^{97} -2.22001 q^{98} -1.48269 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{3} + 5 q^{4} + 7 q^{5} + 5 q^{6} + 4 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) $ 4 * q + q^2 + q^3 + 5 * q^4 + 7 * q^5 + 5 * q^6 + 4 * q^7 + 6 * q^8 + 7 * q^9	$ 4 q + q^{2} + q^{3} + 5 q^{4} + 7 q^{5} + 5 q^{6} + 4 q^{7} + 6 q^{8} + 7 q^{9} - 11 q^{10} + q^{11} + 12 q^{12} + q^{14} - 3 q^{15} + 19 q^{16} - 4 q^{17} + 3 q^{18} - q^{19} + 2 q^{20} + q^{21} + 5 q^{22} - 2 q^{23} + 3 q^{24} + 5 q^{25} - 26 q^{27} + 5 q^{28} + q^{29} - 4 q^{30} + 4 q^{31} + 33 q^{32} + 19 q^{33} - 3 q^{34} + 7 q^{35} - 34 q^{36} + 10 q^{37} - 23 q^{38} - 17 q^{40} + 22 q^{41} + 5 q^{42} + 3 q^{43} + 12 q^{44} + 11 q^{45} - 24 q^{46} - 2 q^{47} + 11 q^{48} + 4 q^{49} - 43 q^{50} + 7 q^{51} + 2 q^{53} - 5 q^{54} - 3 q^{55} + 6 q^{56} + 17 q^{57} + 11 q^{58} + 8 q^{59} + 11 q^{60} + 8 q^{61} - 5 q^{62} + 7 q^{63} + 14 q^{64} + 6 q^{66} + 6 q^{67} - 33 q^{68} - 18 q^{69} - 11 q^{70} + 14 q^{71} - 5 q^{72} + 8 q^{73} + 20 q^{74} - 7 q^{75} - 32 q^{76} + q^{77} - 26 q^{79} - 7 q^{80} + 24 q^{81} - 14 q^{82} + 12 q^{84} - 5 q^{85} - 12 q^{86} + 13 q^{87} + 3 q^{88} + q^{89} + 26 q^{90} + 12 q^{92} + 7 q^{93} + 33 q^{94} + 21 q^{95} + 58 q^{96} - 3 q^{97} + q^{98} - 23 q^{99}+O(q^{100}) $ 4 * q + q^2 + q^3 + 5 * q^4 + 7 * q^5 + 5 * q^6 + 4 * q^7 + 6 * q^8 + 7 * q^9 - 11 * q^10 + q^11 + 12 * q^12 + q^14 - 3 * q^15 + 19 * q^16 - 4 * q^17 + 3 * q^18 - q^19 + 2 * q^20 + q^21 + 5 * q^22 - 2 * q^23 + 3 * q^24 + 5 * q^25 - 26 * q^27 + 5 * q^28 + q^29 - 4 * q^30 + 4 * q^31 + 33 * q^32 + 19 * q^33 - 3 * q^34 + 7 * q^35 - 34 * q^36 + 10 * q^37 - 23 * q^38 - 17 * q^40 + 22 * q^41 + 5 * q^42 + 3 * q^43 + 12 * q^44 + 11 * q^45 - 24 * q^46 - 2 * q^47 + 11 * q^48 + 4 * q^49 - 43 * q^50 + 7 * q^51 + 2 * q^53 - 5 * q^54 - 3 * q^55 + 6 * q^56 + 17 * q^57 + 11 * q^58 + 8 * q^59 + 11 * q^60 + 8 * q^61 - 5 * q^62 + 7 * q^63 + 14 * q^64 + 6 * q^66 + 6 * q^67 - 33 * q^68 - 18 * q^69 - 11 * q^70 + 14 * q^71 - 5 * q^72 + 8 * q^73 + 20 * q^74 - 7 * q^75 - 32 * q^76 + q^77 - 26 * q^79 - 7 * q^80 + 24 * q^81 - 14 * q^82 + 12 * q^84 - 5 * q^85 - 12 * q^86 + 13 * q^87 + 3 * q^88 + q^89 + 26 * q^90 + 12 * q^92 + 7 * q^93 + 33 * q^94 + 21 * q^95 + 58 * q^96 - 3 * q^97 + q^98 - 23 * 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 $

$2$	−2.22001	−1.56978	−0.784891	−	0.619633i	$-0.787281\pi$
$2$	−2.22001	−1.56978	−0.784891	+	0.619633i	$0.787281\pi$
$3$	0.549551	0.317283	0.158642	−	0.987336i	$-0.449289\pi$
$3$	0.549551	0.317283	0.158642	+	0.987336i	$0.449289\pi$
$4$	2.92843	1.46422
$5$	4.22001	1.88724	0.943622	−	0.331024i	$-0.107394\pi$
$5$	4.22001	1.88724	0.943622	+	0.331024i	$0.107394\pi$
$6$	−1.22001	−0.498066
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.06113	−0.728720
$9$	−2.69799	−0.899331
$10$	−9.36845	−2.96256
$11$	0.549551	0.165696	0.0828480	−	0.996562i	$-0.473598\pi$
$11$	0.549551	0.165696	0.0828480	+	0.996562i	$0.473598\pi$
$12$	1.60932	0.464572
$13$	0	0
$13$	0	0
$14$	−2.22001	−0.593322
$15$	2.31911	0.598792
$16$	−1.28114	−0.320285
$17$	−2.37888	−0.576964	−0.288482	−	0.957485i	$-0.593151\pi$
$17$	−2.37888	−0.576964	−0.288482	+	0.957485i	$0.593151\pi$
$18$	5.98957	1.41175
$19$	3.61068	0.828348	0.414174	−	0.910198i	$-0.364071\pi$
$19$	3.61068	0.828348	0.414174	+	0.910198i	$0.364071\pi$
$20$	12.3580	2.76334
$21$	0.549551	0.119922
$22$	−1.22001	−0.260107
$23$	5.81890	1.21332	0.606662	−	0.794960i	$-0.292508\pi$
$23$	5.81890	1.21332	0.606662	+	0.794960i	$0.292508\pi$
$24$	−1.13270	−0.231211
$25$	12.8085	2.56169
$26$	0	0
$27$	−3.13134	−0.602626
$28$	2.92843	0.553422
$29$	−3.59889	−0.668297	−0.334149	−	0.942520i	$-0.608449\pi$
$29$	−3.59889	−0.668297	−0.334149	+	0.942520i	$0.608449\pi$
$30$	−5.14844	−0.939973
$31$	5.14844	0.924688	0.462344	−	0.886701i	$-0.347009\pi$
$31$	5.14844	0.924688	0.462344	+	0.886701i	$0.347009\pi$
$32$	6.96640	1.23150
$33$	0.302006	0.0525726
$34$	5.28114	0.905708
$35$	4.22001	0.713312
$36$	−7.90090	−1.31682
$37$	0.329543	0.0541766	0.0270883	−	0.999633i	$-0.491376\pi$
$37$	0.329543	0.0541766	0.0270883	+	0.999633i	$0.491376\pi$
$38$	−8.01574	−1.30033
$39$	0	0
$40$	−8.69799	−1.37527
$41$	6.29157	0.982579	0.491289	−	0.870996i	$-0.336526\pi$
$41$	6.29157	0.982579	0.491289	+	0.870996i	$0.336526\pi$
$42$	−1.22001	−0.188251
$43$	3.22001	0.491047	0.245523	−	0.969391i	$-0.421040\pi$
$43$	3.22001	0.491047	0.245523	+	0.969391i	$0.421040\pi$
$44$	1.60932	0.242615
$45$	−11.3856	−1.69726
$46$	−12.9180	−1.90466
$47$	−8.20957	−1.19749	−0.598745	−	0.800940i	$-0.704334\pi$
$47$	−8.20957	−1.19749	−0.598745	+	0.800940i	$0.704334\pi$
$48$	−0.704052	−0.101621
$49$	1.00000	0.142857
$50$	−28.4349	−4.02130
$51$	−1.30732	−0.183061
$52$	0	0
$53$	2.65866	0.365196	0.182598	−	0.983188i	$-0.441549\pi$
$53$	2.65866	0.365196	0.182598	+	0.983188i	$0.441549\pi$
$54$	6.95160	0.945992
$55$	2.31911	0.312709
$56$	−2.06113	−0.275430
$57$	1.98426	0.262821
$58$	7.98957	1.04908
$59$	1.80753	0.235320	0.117660	−	0.993054i	$-0.462461\pi$
$59$	1.80753	0.235320	0.117660	+	0.993054i	$0.462461\pi$
$60$	6.79136	0.876761
$61$	0.609325	0.0780160	0.0390080	−	0.999239i	$-0.487580\pi$
$61$	0.609325	0.0780160	0.0390080	+	0.999239i	$0.487580\pi$
$62$	−11.4296	−1.45156
$63$	−2.69799	−0.339915
$64$	−12.9032	−1.61290
$65$	0	0
$66$	−0.670457	−0.0825275
$67$	−10.3698	−1.26687	−0.633437	−	0.773794i	$-0.718356\pi$
$67$	−10.3698	−1.26687	−0.633437	+	0.773794i	$0.718356\pi$
$68$	−6.96640	−0.844801
$69$	3.19778	0.384968
$70$	−9.36845	−1.11974
$71$	11.1978	1.32893	0.664466	−	0.747318i	$-0.268659\pi$
$71$	11.1978	1.32893	0.664466	+	0.747318i	$0.268659\pi$
$72$	5.56092	0.655361
$73$	−4.90621	−0.574228	−0.287114	−	0.957896i	$-0.592696\pi$
$73$	−4.90621	−0.574228	−0.287114	+	0.957896i	$0.592696\pi$
$74$	−0.731589	−0.0850455
$75$	7.03891	0.812783
$76$	10.5736	1.21288
$77$	0.549551	0.0626272
$78$	0	0
$79$	−14.0171	−1.57705	−0.788524	−	0.615004i	$-0.789154\pi$
$79$	−14.0171	−1.57705	−0.788524	+	0.615004i	$0.789154\pi$
$80$	−5.40642	−0.604456
$81$	6.37315	0.708128
$82$	−13.9673	−1.54243
$83$	5.73159	0.629124	0.314562	−	0.949237i	$-0.398142\pi$
$83$	5.73159	0.629124	0.314562	+	0.949237i	$0.398142\pi$
$84$	1.60932	0.175592
$85$	−10.0389	−1.08887
$86$	−7.14844	−0.770836
$87$	−1.97777	−0.212040
$88$	−1.13270	−0.120746
$89$	7.46755	0.791559	0.395779	−	0.918346i	$-0.370474\pi$
$89$	7.46755	0.791559	0.395779	+	0.918346i	$0.370474\pi$
$90$	25.2760	2.66433
$91$	0	0
$92$	17.0403	1.77657
$93$	2.82933	0.293388
$94$	18.2253	1.87980
$95$	15.2371	1.56329
$96$	3.82840	0.390734
$97$	6.84070	0.694568	0.347284	−	0.937760i	$-0.387104\pi$
$97$	6.84070	0.694568	0.347284	+	0.937760i	$0.387104\pi$
$98$	−2.22001	−0.224255
$99$	−1.48269	−0.149015
$100$	37.5088	3.75088
$101$	5.75913	0.573054	0.286527	−	0.958072i	$-0.407499\pi$
$101$	5.75913	0.573054	0.286527	+	0.958072i	$0.407499\pi$
$102$	2.90226	0.287366
$103$	0.571776	0.0563388	0.0281694	−	0.999603i	$-0.491032\pi$
$103$	0.571776	0.0563388	0.0281694	+	0.999603i	$0.491032\pi$
$104$	0	0
$105$	2.31911	0.226322
$106$	−5.90226	−0.573278
$107$	4.07157	0.393613	0.196807	−	0.980442i	$-0.436943\pi$
$107$	4.07157	0.393613	0.196807	+	0.980442i	$0.436943\pi$
$108$	−9.16992	−0.882376
$109$	−15.3087	−1.46631	−0.733153	−	0.680064i	$-0.761952\pi$
$109$	−15.3087	−1.46631	−0.733153	+	0.680064i	$0.761952\pi$
$110$	−5.14844	−0.490885
$111$	0.181101	0.0171893
$112$	−1.28114	−0.121056
$113$	12.1769	1.14551	0.572754	−	0.819727i	$-0.305875\pi$
$113$	12.1769	1.14551	0.572754	+	0.819727i	$0.305875\pi$
$114$	−4.40506	−0.412572
$115$	24.5558	2.28984
$116$	−10.5391	−0.978533
$117$	0	0
$118$	−4.01273	−0.369402
$119$	−2.37888	−0.218072
$120$	−4.77999	−0.436352
$121$	−10.6980	−0.972545
$122$	−1.35271	−0.122468
$123$	3.45754	0.311756
$124$	15.0769	1.35394
$125$	32.9518	2.94730
$126$	5.98957	0.533593
$127$	1.96067	0.173981	0.0869907	−	0.996209i	$-0.472275\pi$
$127$	1.96067	0.173981	0.0869907	+	0.996209i	$0.472275\pi$
$128$	14.7124	1.30040
$129$	1.76956	0.155801
$130$	0	0
$131$	−6.50021	−0.567926	−0.283963	−	0.958835i	$-0.591649\pi$
$131$	−6.50021	−0.567926	−0.283963	+	0.958835i	$0.591649\pi$
$132$	0.884406	0.0769777
$133$	3.61068	0.313086
$134$	23.0211	1.98872
$135$	−13.2143	−1.13730
$136$	4.90319	0.420445
$137$	15.2576	1.30354	0.651770	−	0.758416i	$-0.274027\pi$
$137$	15.2576	1.30354	0.651770	+	0.758416i	$0.274027\pi$
$138$	−7.09910	−0.604316
$139$	−17.4960	−1.48399	−0.741997	−	0.670403i	$-0.766121\pi$
$139$	−17.4960	−1.48399	−0.741997	+	0.670403i	$0.766121\pi$
$140$	12.3580	1.04444
$141$	−4.51158	−0.379944
$142$	−24.8592	−2.08613
$143$	0	0
$144$	3.45651	0.288042
$145$	−15.1873	−1.26124
$146$	10.8918	0.901414
$147$	0.549551	0.0453262
$148$	0.965046	0.0793263
$149$	−4.55486	−0.373149	−0.186574	−	0.982441i	$-0.559739\pi$
$149$	−4.55486	−0.373149	−0.186574	+	0.982441i	$0.559739\pi$
$150$	−15.6264	−1.27589
$151$	6.32912	0.515057	0.257528	−	0.966271i	$-0.417092\pi$
$151$	6.32912	0.515057	0.257528	+	0.966271i	$0.417092\pi$
$152$	−7.44210	−0.603634
$153$	6.41821	0.518882
$154$	−1.22001	−0.0983110
$155$	21.7265	1.74511
$156$	0	0
$157$	16.3100	1.30168	0.650841	−	0.759214i	$-0.274416\pi$
$157$	16.3100	1.30168	0.650841	+	0.759214i	$0.274416\pi$
$158$	31.1181	2.47562
$159$	1.46107	0.115871
$160$	29.3983	2.32414
$161$	5.81890	0.458593
$162$	−14.1484	−1.11161
$163$	−23.5998	−1.84848	−0.924241	−	0.381811i	$-0.875301\pi$
$163$	−23.5998	−1.84848	−0.924241	+	0.381811i	$0.875301\pi$
$164$	18.4245	1.43871
$165$	1.27447	0.0992173
$166$	−12.7242	−0.987587
$167$	17.8303	1.37975	0.689874	−	0.723930i	$-0.257666\pi$
$167$	17.8303	1.37975	0.689874	+	0.723930i	$0.257666\pi$
$168$	−1.13270	−0.0873895
$169$	0	0
$170$	22.2865	1.70929
$171$	−9.74160	−0.744959
$172$	9.42958	0.718999
$173$	−7.57135	−0.575639	−0.287820	−	0.957685i	$-0.592930\pi$
$173$	−7.57135	−0.575639	−0.287820	+	0.957685i	$0.592930\pi$
$174$	4.39068	0.332856
$175$	12.8085	0.968229
$176$	−0.704052	−0.0530699
$177$	0.993330	0.0746632
$178$	−16.5780	−1.24258
$179$	−22.8033	−1.70440	−0.852201	−	0.523215i	$-0.824733\pi$
$179$	−22.8033	−1.70440	−0.852201	+	0.523215i	$0.824733\pi$
$180$	−33.3419	−2.48515
$181$	13.9294	1.03536	0.517681	−	0.855574i	$-0.326795\pi$
$181$	13.9294	1.03536	0.517681	+	0.855574i	$0.326795\pi$
$182$	0	0
$183$	0.334855	0.0247532
$184$	−11.9935	−0.884174
$185$	1.39068	0.102244
$186$	−6.28114	−0.460556
$187$	−1.30732	−0.0956006
$188$	−24.0412	−1.75338
$189$	−3.13134	−0.227771
$190$	−33.8265	−2.45403
$191$	−12.6718	−0.916900	−0.458450	−	0.888720i	$-0.651595\pi$
$191$	−12.6718	−0.916900	−0.458450	+	0.888720i	$0.651595\pi$
$192$	−7.09096	−0.511746
$193$	4.15492	0.299078	0.149539	−	0.988756i	$-0.452221\pi$
$193$	4.15492	0.299078	0.149539	+	0.988756i	$0.452221\pi$
$194$	−15.1864	−1.09032
$195$	0	0
$196$	2.92843	0.209174
$197$	6.85020	0.488056	0.244028	−	0.969768i	$-0.421531\pi$
$197$	6.85020	0.488056	0.244028	+	0.969768i	$0.421531\pi$
$198$	3.29157	0.233922
$199$	−0.813587	−0.0576737	−0.0288368	−	0.999584i	$-0.509180\pi$
$199$	−0.813587	−0.0576737	−0.0288368	+	0.999584i	$0.509180\pi$
$200$	−26.3999	−1.86676
$201$	−5.69874	−0.401958
$202$	−12.7853	−0.899571
$203$	−3.59889	−0.252593
$204$	−3.82840	−0.268041
$205$	26.5505	1.85437
$206$	−1.26935	−0.0884397
$207$	−15.6994	−1.09118
$208$	0	0
$209$	1.98426	0.137254
$210$	−5.14844	−0.355276
$211$	−13.9734	−0.961969	−0.480984	−	0.876729i	$-0.659721\pi$
$211$	−13.9734	−0.961969	−0.480984	+	0.876729i	$0.659721\pi$
$212$	7.78573	0.534726
$213$	6.15375	0.421648
$214$	−9.03891	−0.617887
$215$	13.5885	0.926725
$216$	6.45410	0.439146
$217$	5.14844	0.349499
$218$	33.9854	2.30178
$219$	−2.69621	−0.182193
$220$	6.79136	0.457874
$221$	0	0
$222$	−0.402045	−0.0269835
$223$	13.5340	0.906303	0.453152	−	0.891433i	$-0.350300\pi$
$223$	13.5340	0.906303	0.453152	+	0.891433i	$0.350300\pi$
$224$	6.96640	0.465462
$225$	−34.5572	−2.30381
$226$	−27.0328	−1.79820
$227$	5.36751	0.356254	0.178127	−	0.984007i	$-0.442996\pi$
$227$	5.36751	0.356254	0.178127	+	0.984007i	$0.442996\pi$
$228$	5.81076	0.384827
$229$	−3.09910	−0.204794	−0.102397	−	0.994744i	$-0.532651\pi$
$229$	−3.09910	−0.204794	−0.102397	+	0.994744i	$0.532651\pi$
$230$	−54.5141	−3.59455
$231$	0.302006	0.0198706
$232$	7.41779	0.487002
$233$	−20.3712	−1.33456	−0.667280	−	0.744807i	$-0.732541\pi$
$233$	−20.3712	−1.33456	−0.667280	+	0.744807i	$0.732541\pi$
$234$	0	0
$235$	−34.6445	−2.25996
$236$	5.29323	0.344560
$237$	−7.70312	−0.500371
$238$	5.28114	0.342325
$239$	1.29157	0.0835449	0.0417725	−	0.999127i	$-0.486700\pi$
$239$	1.29157	0.0835449	0.0417725	+	0.999127i	$0.486700\pi$
$240$	−2.97110	−0.191784
$241$	−2.13270	−0.137379	−0.0686896	−	0.997638i	$-0.521882\pi$
$241$	−2.13270	−0.137379	−0.0686896	+	0.997638i	$0.521882\pi$
$242$	23.7496	1.52668
$243$	12.8964	0.827304
$244$	1.78437	0.114232
$245$	4.22001	0.269606
$246$	−7.67577	−0.489389
$247$	0	0
$248$	−10.6116	−0.673839
$249$	3.14980	0.199611
$250$	−73.1532	−4.62662
$251$	−30.7711	−1.94226	−0.971128	−	0.238561i	$-0.923324\pi$
$251$	−30.7711	−1.94226	−0.971128	+	0.238561i	$0.923324\pi$
$252$	−7.90090	−0.497710
$253$	3.19778	0.201043
$254$	−4.35271	−0.273113
$255$	−5.51689	−0.345481
$256$	−6.85521	−0.428451
$257$	−1.47361	−0.0919213	−0.0459607	−	0.998943i	$-0.514635\pi$
$257$	−1.47361	−0.0919213	−0.0459607	+	0.998943i	$0.514635\pi$
$258$	−3.92843	−0.244574
$259$	0.329543	0.0204768
$260$	0	0
$261$	9.70979	0.601021
$262$	14.4305	0.891520
$263$	6.67694	0.411718	0.205859	−	0.978582i	$-0.434001\pi$
$263$	6.67694	0.411718	0.205859	+	0.978582i	$0.434001\pi$
$264$	−0.622475	−0.0383107
$265$	11.2196	0.689214
$266$	−8.01574	−0.491477
$267$	4.10380	0.251149
$268$	−30.3673	−1.85498
$269$	7.57573	0.461900	0.230950	−	0.972966i	$-0.425817\pi$
$269$	7.57573	0.461900	0.230950	+	0.972966i	$0.425817\pi$
$270$	29.3358	1.78532
$271$	−20.5680	−1.24942	−0.624709	−	0.780858i	$-0.714782\pi$
$271$	−20.5680	−1.24942	−0.624709	+	0.780858i	$0.714782\pi$
$272$	3.04768	0.184793
$273$	0	0
$274$	−33.8719	−2.04628
$275$	7.03891	0.424462
$276$	9.36450	0.563676
$277$	5.70541	0.342805	0.171402	−	0.985201i	$-0.445170\pi$
$277$	5.70541	0.342805	0.171402	+	0.985201i	$0.445170\pi$
$278$	38.8413	2.32955
$279$	−13.8905	−0.831600
$280$	−8.69799	−0.519805
$281$	6.37315	0.380190	0.190095	−	0.981766i	$-0.439120\pi$
$281$	6.37315	0.380190	0.190095	+	0.981766i	$0.439120\pi$
$282$	10.0157	0.596429
$283$	27.0194	1.60614	0.803068	−	0.595887i	$-0.203199\pi$
$283$	27.0194	1.60614	0.803068	+	0.595887i	$0.203199\pi$
$284$	32.7920	1.94585
$285$	8.37357	0.496008
$286$	0	0
$287$	6.29157	0.371380
$288$	−18.7953	−1.10752
$289$	−11.3409	−0.667113
$290$	33.7160	1.97987
$291$	3.75932	0.220375
$292$	−14.3675	−0.840795
$293$	4.87472	0.284784	0.142392	−	0.989810i	$-0.454521\pi$
$293$	4.87472	0.284784	0.142392	+	0.989810i	$0.454521\pi$
$294$	−1.22001	−0.0711523
$295$	7.62779	0.444107
$296$	−0.679232	−0.0394796
$297$	−1.72083	−0.0998527
$298$	10.1118	0.585763
$299$	0	0
$300$	20.6130	1.19009
$301$	3.22001	0.185598
$302$	−14.0507	−0.808527
$303$	3.16493	0.181821
$304$	−4.62579	−0.265307
$305$	2.57135	0.147235
$306$	−14.2485	−0.814531
$307$	−16.1760	−0.923212	−0.461606	−	0.887085i	$-0.652727\pi$
$307$	−16.1760	−0.923212	−0.461606	+	0.887085i	$0.652727\pi$
$308$	1.60932	0.0916998
$309$	0.314220	0.0178754
$310$	−48.2329	−2.73945
$311$	−1.30806	−0.0741735	−0.0370868	−	0.999312i	$-0.511808\pi$
$311$	−1.30806	−0.0741735	−0.0370868	+	0.999312i	$0.511808\pi$
$312$	0	0
$313$	13.1978	0.745983	0.372991	−	0.927835i	$-0.378332\pi$
$313$	13.1978	0.745983	0.372991	+	0.927835i	$0.378332\pi$
$314$	−36.2084	−2.04336
$315$	−11.3856	−0.641503
$316$	−41.0482	−2.30914
$317$	8.07552	0.453566	0.226783	−	0.973945i	$-0.427179\pi$
$317$	8.07552	0.453566	0.226783	+	0.973945i	$0.427179\pi$
$318$	−3.24359	−0.181892
$319$	−1.97777	−0.110734
$320$	−54.4516	−3.04394
$321$	2.23753	0.124887
$322$	−12.9180	−0.719892
$323$	−8.58939	−0.477927
$324$	18.6634	1.03685
$325$	0	0
$326$	52.3918	2.90171
$327$	−8.41290	−0.465234
$328$	−12.9678	−0.716025
$329$	−8.20957	−0.452608
$330$	−2.82933	−0.155750
$331$	14.9451	0.821458	0.410729	−	0.911757i	$-0.365274\pi$
$331$	14.9451	0.821458	0.410729	+	0.911757i	$0.365274\pi$
$332$	16.7846	0.921174
$333$	−0.889106	−0.0487227
$334$	−39.5833	−2.16590
$335$	−43.7607	−2.39090
$336$	−0.704052	−0.0384092
$337$	−17.1695	−0.935282	−0.467641	−	0.883918i	$-0.654896\pi$
$337$	−17.1695	−0.935282	−0.467641	+	0.883918i	$0.654896\pi$
$338$	0	0
$339$	6.69184	0.363451
$340$	−29.3983	−1.59435
$341$	2.82933	0.153217
$342$	21.6264	1.16942
$343$	1.00000	0.0539949
$344$	−6.63686	−0.357836
$345$	13.4947	0.726528
$346$	16.8085	0.903629
$347$	−3.93845	−0.211427	−0.105713	−	0.994397i	$-0.533713\pi$
$347$	−3.93845	−0.211427	−0.105713	+	0.994397i	$0.533713\pi$
$348$	−5.79178	−0.310472
$349$	−17.1777	−0.919499	−0.459750	−	0.888049i	$-0.652061\pi$
$349$	−17.1777	−0.919499	−0.459750	+	0.888049i	$0.652061\pi$
$350$	−28.4349	−1.51991
$351$	0	0
$352$	3.82840	0.204054
$353$	18.1964	0.968498	0.484249	−	0.874930i	$-0.339093\pi$
$353$	18.1964	0.968498	0.484249	+	0.874930i	$0.339093\pi$
$354$	−2.20520	−0.117205
$355$	47.2547	2.50802
$356$	21.8682	1.15901
$357$	−1.30732	−0.0691906
$358$	50.6236	2.67554
$359$	−16.3126	−0.860948	−0.430474	−	0.902603i	$-0.641654\pi$
$359$	−16.3126	−0.860948	−0.430474	+	0.902603i	$0.641654\pi$
$360$	23.4671	1.23683
$361$	−5.96297	−0.313840
$362$	−30.9233	−1.62529
$363$	−5.87909	−0.308572
$364$	0	0
$365$	−20.7042	−1.08371
$366$	−0.743381	−0.0388571
$367$	−36.1963	−1.88943	−0.944716	−	0.327889i	$-0.893663\pi$
$367$	−36.1963	−1.88943	−0.944716	+	0.327889i	$0.893663\pi$
$368$	−7.45482	−0.388610
$369$	−16.9746	−0.883664
$370$	−3.08731	−0.160502
$371$	2.65866	0.138031
$372$	8.28551	0.429584
$373$	9.79784	0.507313	0.253657	−	0.967294i	$-0.418367\pi$
$373$	9.79784	0.507313	0.253657	+	0.967294i	$0.418367\pi$
$374$	2.90226	0.150072
$375$	18.1087	0.935129
$376$	16.9210	0.872635
$377$	0	0
$378$	6.95160	0.357552
$379$	−13.0655	−0.671130	−0.335565	−	0.942017i	$-0.608927\pi$
$379$	−13.0655	−0.671130	−0.335565	+	0.942017i	$0.608927\pi$
$380$	44.6209	2.28900
$381$	1.07749	0.0552014
$382$	28.1315	1.43933
$383$	−27.7929	−1.42015	−0.710076	−	0.704125i	$-0.751339\pi$
$383$	−27.7929	−1.42015	−0.710076	+	0.704125i	$0.751339\pi$
$384$	8.08520	0.412596
$385$	2.31911	0.118193
$386$	−9.22396	−0.469487
$387$	−8.68756	−0.441614
$388$	20.0325	1.01700
$389$	13.7047	0.694854	0.347427	−	0.937707i	$-0.387055\pi$
$389$	13.7047	0.694854	0.347427	+	0.937707i	$0.387055\pi$
$390$	0	0
$391$	−13.8425	−0.700044
$392$	−2.06113	−0.104103
$393$	−3.57220	−0.180194
$394$	−15.2075	−0.766143
$395$	−59.1523	−2.97627
$396$	−4.34195	−0.218191
$397$	−7.91194	−0.397089	−0.198545	−	0.980092i	$-0.563621\pi$
$397$	−7.91194	−0.397089	−0.198545	+	0.980092i	$0.563621\pi$
$398$	1.80617	0.0905351
$399$	1.98426	0.0993370
$400$	−16.4094	−0.820472
$401$	16.5442	0.826180	0.413090	−	0.910690i	$-0.364450\pi$
$401$	16.5442	0.826180	0.413090	+	0.910690i	$0.364450\pi$
$402$	12.6512	0.630987
$403$	0	0
$404$	16.8652	0.839076
$405$	26.8947	1.33641
$406$	7.98957	0.396516
$407$	0.181101	0.00897684
$408$	2.69456	0.133400
$409$	−25.7819	−1.27483	−0.637416	−	0.770520i	$-0.719997\pi$
$409$	−25.7819	−1.27483	−0.637416	+	0.770520i	$0.719997\pi$
$410$	−58.9423	−2.91095
$411$	8.38481	0.413592
$412$	1.67441	0.0824922
$413$	1.80753	0.0889427
$414$	34.8527	1.71292
$415$	24.1873	1.18731
$416$	0	0
$417$	−9.61496	−0.470847
$418$	−4.40506	−0.215459
$419$	23.6871	1.15719	0.578596	−	0.815614i	$-0.303601\pi$
$419$	23.6871	1.15719	0.578596	+	0.815614i	$0.303601\pi$
$420$	6.79136	0.331385
$421$	20.8246	1.01493	0.507465	−	0.861672i	$-0.330583\pi$
$421$	20.8246	1.01493	0.507465	+	0.861672i	$0.330583\pi$
$422$	31.0211	1.51008
$423$	22.1494	1.07694
$424$	−5.47986	−0.266125
$425$	−30.4698	−1.47800
$426$	−13.6614	−0.661896
$427$	0.609325	0.0294873
$428$	11.9233	0.576335
$429$	0	0
$430$	−30.1665	−1.45476
$431$	−19.9504	−0.960978	−0.480489	−	0.877001i	$-0.659541\pi$
$431$	−19.9504	−0.960978	−0.480489	+	0.877001i	$0.659541\pi$
$432$	4.01168	0.193012
$433$	0.0166817	0.000801670 0	0.000400835	−	1.00000i	$-0.499872\pi$
$433$	0.0166817	0.000801670 0	0.000400835		1.00000i	$0.499872\pi$
$434$	−11.4296	−0.548638
$435$	−8.34623	−0.400171
$436$	−44.8305	−2.14699
$437$	21.0102	1.00505
$438$	5.98561	0.286004
$439$	13.4960	0.644130	0.322065	−	0.946718i	$-0.395623\pi$
$439$	13.4960	0.644130	0.322065	+	0.946718i	$0.395623\pi$
$440$	−4.77999	−0.227877
$441$	−2.69799	−0.128476
$442$	0	0
$443$	−15.0110	−0.713196	−0.356598	−	0.934258i	$-0.616063\pi$
$443$	−15.0110	−0.713196	−0.356598	+	0.934258i	$0.616063\pi$
$444$	0.530342	0.0251689
$445$	31.5131	1.49387
$446$	−30.0456	−1.42270
$447$	−2.50313	−0.118394
$448$	−12.9032	−0.609619
$449$	23.7836	1.12242	0.561210	−	0.827674i	$-0.310336\pi$
$449$	23.7836	1.12242	0.561210	+	0.827674i	$0.310336\pi$
$450$	76.7172	3.61648
$451$	3.45754	0.162809
$452$	35.6593	1.67727
$453$	3.47818	0.163419
$454$	−11.9159	−0.559242
$455$	0	0
$456$	−4.08981	−0.191523
$457$	−18.1313	−0.848148	−0.424074	−	0.905627i	$-0.639400\pi$
$457$	−18.1313	−0.848148	−0.424074	+	0.905627i	$0.639400\pi$
$458$	6.88003	0.321483
$459$	7.44909	0.347694
$460$	71.9101	3.35282
$461$	6.07959	0.283155	0.141577	−	0.989927i	$-0.454783\pi$
$461$	6.07959	0.283155	0.141577	+	0.989927i	$0.454783\pi$
$462$	−0.670457	−0.0311925
$463$	−5.19289	−0.241334	−0.120667	−	0.992693i	$-0.538503\pi$
$463$	−5.19289	−0.241334	−0.120667	+	0.992693i	$0.538503\pi$
$464$	4.61068	0.214046
$465$	11.9398	0.553695
$466$	45.2242	2.09497
$467$	−8.69968	−0.402573	−0.201287	−	0.979532i	$-0.564512\pi$
$467$	−8.69968	−0.402573	−0.201287	+	0.979532i	$0.564512\pi$
$468$	0	0
$469$	−10.3698	−0.478833
$470$	76.9110	3.54764
$471$	8.96320	0.413002
$472$	−3.72556	−0.171483
$473$	1.76956	0.0813644
$474$	17.1010	0.785474
$475$	46.2473	2.12197
$476$	−6.96640	−0.319305
$477$	−7.17306	−0.328432
$478$	−2.86730	−0.131147
$479$	−24.2188	−1.10659	−0.553294	−	0.832986i	$-0.686629\pi$
$479$	−24.2188	−1.10659	−0.553294	+	0.832986i	$0.686629\pi$
$480$	16.1559	0.737411
$481$	0	0
$482$	4.73461	0.215655
$483$	3.19778	0.145504
$484$	−31.3284	−1.42402
$485$	28.8678	1.31082
$486$	−28.6301	−1.29869
$487$	−1.77393	−0.0803846	−0.0401923	−	0.999192i	$-0.512797\pi$
$487$	−1.77393	−0.0803846	−0.0401923	+	0.999192i	$0.512797\pi$
$488$	−1.25590	−0.0568519
$489$	−12.9693	−0.586493
$490$	−9.36845	−0.423223
$491$	−6.68967	−0.301900	−0.150950	−	0.988541i	$-0.548233\pi$
$491$	−6.68967	−0.301900	−0.150950	+	0.988541i	$0.548233\pi$
$492$	10.1252	0.456479
$493$	8.56134	0.385584
$494$	0	0
$495$	−6.25694	−0.281229
$496$	−6.59588	−0.296164
$497$	11.1978	0.502289
$498$	−6.99258	−0.313345
$499$	−24.6387	−1.10298	−0.551491	−	0.834181i	$-0.685941\pi$
$499$	−24.6387	−1.10298	−0.551491	+	0.834181i	$0.685941\pi$
$500$	96.4972	4.31548
$501$	9.79864	0.437771
$502$	68.3121	3.04892
$503$	33.1452	1.47787	0.738936	−	0.673776i	$-0.235329\pi$
$503$	33.1452	1.47787	0.738936	+	0.673776i	$0.235329\pi$
$504$	5.56092	0.247703
$505$	24.3036	1.08149
$506$	−7.09910	−0.315594
$507$	0	0
$508$	5.74170	0.254747
$509$	27.6580	1.22592	0.612961	−	0.790114i	$-0.289978\pi$
$509$	27.6580	1.22592	0.612961	+	0.790114i	$0.289978\pi$
$510$	12.2475	0.542330
$511$	−4.90621	−0.217038
$512$	−14.2061	−0.627828
$513$	−11.3063	−0.499184
$514$	3.27143	0.144296
$515$	2.41290	0.106325
$516$	5.18204	0.228126
$517$	−4.51158	−0.198419
$518$	−0.731589	−0.0321442
$519$	−4.16085	−0.182641
$520$	0	0
$521$	1.42217	0.0623062	0.0311531	−	0.999515i	$-0.490082\pi$
$521$	1.42217	0.0623062	0.0311531	+	0.999515i	$0.490082\pi$
$522$	−21.5558	−0.943472
$523$	−3.36178	−0.147000	−0.0735002	−	0.997295i	$-0.523417\pi$
$523$	−3.36178	−0.147000	−0.0735002	+	0.997295i	$0.523417\pi$
$524$	−19.0354	−0.831567
$525$	7.03891	0.307203
$526$	−14.8229	−0.646307
$527$	−12.2475	−0.533511
$528$	−0.386913	−0.0168382
$529$	10.8596	0.472156
$530$	−24.9076	−1.08192
$531$	−4.87670	−0.211631
$532$	10.5736	0.458426
$533$	0	0
$534$	−9.11047	−0.394249
$535$	17.1820	0.742844
$536$	21.3735	0.923197
$537$	−12.5316	−0.540779
$538$	−16.8182	−0.725083
$539$	0.549551	0.0236708
$540$	−38.6971	−1.66526
$541$	−7.76289	−0.333753	−0.166876	−	0.985978i	$-0.553368\pi$
$541$	−7.76289	−0.333753	−0.166876	+	0.985978i	$0.553368\pi$
$542$	45.6612	1.96131
$543$	7.65490	0.328503
$544$	−16.5723	−0.710530
$545$	−64.6027	−2.76728
$546$	0	0
$547$	−6.19247	−0.264771	−0.132385	−	0.991198i	$-0.542264\pi$
$547$	−6.19247	−0.264771	−0.132385	+	0.991198i	$0.542264\pi$
$548$	44.6808	1.90867
$549$	−1.64395	−0.0701622
$550$	−15.6264	−0.666313
$551$	−12.9945	−0.553582
$552$	−6.59105	−0.280534
$553$	−14.0171	−0.596068
$554$	−12.6661	−0.538129
$555$	0.764247	0.0324405
$556$	−51.2360	−2.17289
$557$	−29.5458	−1.25190	−0.625948	−	0.779865i	$-0.715288\pi$
$557$	−29.5458	−1.25190	−0.625948	+	0.779865i	$0.715288\pi$
$558$	30.8369	1.30543
$559$	0	0
$560$	−5.40642	−0.228463
$561$	−0.718438	−0.0303325
$562$	−14.1484	−0.596816
$563$	6.46736	0.272567	0.136283	−	0.990670i	$-0.456484\pi$
$563$	6.46736	0.272567	0.136283	+	0.990670i	$0.456484\pi$
$564$	−13.2119	−0.556320
$565$	51.3867	2.16185
$566$	−59.9833	−2.52129
$567$	6.37315	0.267647
$568$	−23.0801	−0.968420
$569$	21.6956	0.909526	0.454763	−	0.890612i	$-0.349724\pi$
$569$	21.6956	0.909526	0.454763	+	0.890612i	$0.349724\pi$
$570$	−18.5894	−0.778624
$571$	−16.6418	−0.696436	−0.348218	−	0.937414i	$-0.613213\pi$
$571$	−16.6418	−0.696436	−0.348218	+	0.937414i	$0.613213\pi$
$572$	0	0
$573$	−6.96381	−0.290917
$574$	−13.9673	−0.582986
$575$	74.5312	3.10816
$576$	34.8127	1.45053
$577$	2.64240	0.110005	0.0550024	−	0.998486i	$-0.482483\pi$
$577$	2.64240	0.110005	0.0550024	+	0.998486i	$0.482483\pi$
$578$	25.1769	1.04722
$579$	2.28334	0.0948925
$580$	−44.4752	−1.84673
$581$	5.73159	0.237786
$582$	−8.34571	−0.345941
$583$	1.46107	0.0605114
$584$	10.1123	0.418452
$585$	0	0
$586$	−10.8219	−0.447049
$587$	−7.38815	−0.304942	−0.152471	−	0.988308i	$-0.548723\pi$
$587$	−7.38815	−0.304942	−0.152471	+	0.988308i	$0.548723\pi$
$588$	1.60932	0.0663674
$589$	18.5894	0.765963
$590$	−16.9337	−0.697151
$591$	3.76453	0.154852
$592$	−0.422191	−0.0173519
$593$	−46.9030	−1.92607	−0.963037	−	0.269370i	$-0.913185\pi$
$593$	−46.9030	−1.92607	−0.963037	+	0.269370i	$0.913185\pi$
$594$	3.82026	0.156747
$595$	−10.0389	−0.411555
$596$	−13.3386	−0.546371
$597$	−0.447108	−0.0182989
$598$	0	0
$599$	1.62290	0.0663098	0.0331549	−	0.999450i	$-0.489445\pi$
$599$	1.62290	0.0663098	0.0331549	+	0.999450i	$0.489445\pi$
$600$	−14.5081	−0.592291
$601$	−47.0347	−1.91859	−0.959293	−	0.282412i	$-0.908865\pi$
$601$	−47.0347	−1.91859	−0.959293	+	0.282412i	$0.908865\pi$
$602$	−7.14844	−0.291349
$603$	27.9777	1.13934
$604$	18.5344	0.754155
$605$	−45.1456	−1.83543
$606$	−7.02618	−0.285419
$607$	−28.3869	−1.15219	−0.576095	−	0.817383i	$-0.695424\pi$
$607$	−28.3869	−1.15219	−0.576095	+	0.817383i	$0.695424\pi$
$608$	25.1535	1.02011
$609$	−1.97777	−0.0801435
$610$	−5.70843	−0.231127
$611$	0	0
$612$	18.7953	0.759756
$613$	47.5564	1.92079	0.960393	−	0.278650i	$-0.0898870\pi$
$613$	47.5564	1.92079	0.960393	+	0.278650i	$0.0898870\pi$
$614$	35.9108	1.44924
$615$	14.5909	0.588360
$616$	−1.13270	−0.0456377
$617$	16.4868	0.663732	0.331866	−	0.943327i	$-0.392322\pi$
$617$	16.4868	0.663732	0.331866	+	0.943327i	$0.392322\pi$
$618$	−0.697572	−0.0280604
$619$	31.9412	1.28382	0.641912	−	0.766778i	$-0.278141\pi$
$619$	31.9412	1.28382	0.641912	+	0.766778i	$0.278141\pi$
$620$	63.6245	2.55522
$621$	−18.2209	−0.731181
$622$	2.90391	0.116436
$623$	7.46755	0.299181
$624$	0	0
$625$	75.0145	3.00058
$626$	−29.2992	−1.17103
$627$	1.09045	0.0435484
$628$	47.7629	1.90595
$629$	−0.783945	−0.0312579
$630$	25.2760	1.00702
$631$	−13.1915	−0.525147	−0.262573	−	0.964912i	$-0.584571\pi$
$631$	−13.1915	−0.525147	−0.262573	+	0.964912i	$0.584571\pi$
$632$	28.8911	1.14923
$633$	−7.67910	−0.305217
$634$	−17.9277	−0.712000
$635$	8.27405	0.328346
$636$	4.27865	0.169660
$637$	0	0
$638$	4.39068	0.173829
$639$	−30.2115	−1.19515
$640$	62.0864	2.45418
$641$	−47.1627	−1.86282	−0.931408	−	0.363978i	$-0.881418\pi$
$641$	−47.1627	−1.86282	−0.931408	+	0.363978i	$0.881418\pi$
$642$	−4.96734	−0.196045
$643$	2.81359	0.110957	0.0554785	−	0.998460i	$-0.482332\pi$
$643$	2.81359	0.110957	0.0554785	+	0.998460i	$0.482332\pi$
$644$	17.0403	0.671481
$645$	7.46755	0.294035
$646$	19.0685	0.750241
$647$	25.9783	1.02131	0.510656	−	0.859785i	$-0.329403\pi$
$647$	25.9783	1.02131	0.510656	+	0.859785i	$0.329403\pi$
$648$	−13.1359	−0.516027
$649$	0.993330	0.0389916
$650$	0	0
$651$	2.82933	0.110890
$652$	−69.1106	−2.70658
$653$	−26.8426	−1.05043	−0.525216	−	0.850969i	$-0.676015\pi$
$653$	−26.8426	−1.05043	−0.525216	+	0.850969i	$0.676015\pi$
$654$	18.6767	0.730317
$655$	−27.4309	−1.07182
$656$	−8.06039	−0.314705
$657$	13.2369	0.516421
$658$	18.2253	0.710497
$659$	15.5733	0.606651	0.303325	−	0.952887i	$-0.401903\pi$
$659$	15.5733	0.606651	0.303325	+	0.952887i	$0.401903\pi$
$660$	3.73220	0.145276
$661$	−33.3804	−1.29835	−0.649174	−	0.760640i	$-0.724885\pi$
$661$	−33.3804	−1.29835	−0.649174	+	0.760640i	$0.724885\pi$
$662$	−33.1783	−1.28951
$663$	0	0
$664$	−11.8136	−0.458455
$665$	15.2371	0.590870
$666$	1.97382	0.0764840
$667$	−20.9416	−0.810861
$668$	52.2148	2.02025
$669$	7.43762	0.287555
$670$	97.1490	3.75319
$671$	0.334855	0.0129269
$672$	3.82840	0.147684
$673$	0.854152	0.0329251	0.0164626	−	0.999864i	$-0.494760\pi$
$673$	0.854152	0.0329251	0.0164626	+	0.999864i	$0.494760\pi$
$674$	38.1164	1.46819
$675$	−40.1076	−1.54374
$676$	0	0
$677$	−24.5449	−0.943339	−0.471669	−	0.881775i	$-0.656348\pi$
$677$	−24.5449	−0.943339	−0.471669	+	0.881775i	$0.656348\pi$
$678$	−14.8559	−0.570539
$679$	6.84070	0.262522
$680$	20.6915	0.793483
$681$	2.94972	0.113034
$682$	−6.28114	−0.240517
$683$	43.0372	1.64677	0.823387	−	0.567480i	$-0.192082\pi$
$683$	43.0372	1.64677	0.823387	+	0.567480i	$0.192082\pi$
$684$	−28.5276	−1.09078
$685$	64.3870	2.46010
$686$	−2.22001	−0.0847603
$687$	−1.70312	−0.0649779
$688$	−4.12528	−0.157275
$689$	0	0
$690$	−29.9583	−1.14049
$691$	25.8195	0.982220	0.491110	−	0.871097i	$-0.336591\pi$
$691$	25.8195	0.982220	0.491110	+	0.871097i	$0.336591\pi$
$692$	−22.1722	−0.842861
$693$	−1.48269	−0.0563226
$694$	8.74338	0.331894
$695$	−73.8334	−2.80066
$696$	4.07646	0.154518
$697$	−14.9669	−0.566913
$698$	38.1345	1.44341
$699$	−11.1950	−0.423434
$700$	37.5088	1.41770
$701$	16.3178	0.616313	0.308156	−	0.951336i	$-0.400288\pi$
$701$	16.3178	0.616313	0.308156	+	0.951336i	$0.400288\pi$
$702$	0	0
$703$	1.18988	0.0448770
$704$	−7.09096	−0.267251
$705$	−19.0389	−0.717047
$706$	−40.3962	−1.52033
$707$	5.75913	0.216594
$708$	2.90890	0.109323
$709$	22.3794	0.840476	0.420238	−	0.907414i	$-0.361947\pi$
$709$	22.3794	0.840476	0.420238	+	0.907414i	$0.361947\pi$
$710$	−104.906	−3.93705
$711$	37.8181	1.41829
$712$	−15.3916	−0.576825
$713$	29.9583	1.12195
$714$	2.90226	0.108614
$715$	0	0
$716$	−66.7781	−2.49561
$717$	0.709785	0.0265074
$718$	36.2142	1.35150
$719$	−22.7445	−0.848227	−0.424113	−	0.905609i	$-0.639414\pi$
$719$	−22.7445	−0.848227	−0.424113	+	0.905609i	$0.639414\pi$
$720$	14.5865	0.543606
$721$	0.571776	0.0212941
$722$	13.2378	0.492661
$723$	−1.17203	−0.0435881
$724$	40.7913	1.51599
$725$	−46.0963	−1.71197
$726$	13.0516	0.484392
$727$	18.7274	0.694561	0.347280	−	0.937761i	$-0.387105\pi$
$727$	18.7274	0.694561	0.347280	+	0.937761i	$0.387105\pi$
$728$	0	0
$729$	−12.0322	−0.445638
$730$	45.9636	1.70119
$731$	−7.66002	−0.283316
$732$	0.980601	0.0362441
$733$	1.69268	0.0625206	0.0312603	−	0.999511i	$-0.490048\pi$
$733$	1.69268	0.0625206	0.0312603	+	0.999511i	$0.490048\pi$
$734$	80.3561	2.96600
$735$	2.31911	0.0855417
$736$	40.5368	1.49421
$737$	−5.69874	−0.209916
$738$	37.6838	1.38716
$739$	−46.9161	−1.72584	−0.862919	−	0.505343i	$-0.831366\pi$
$739$	−46.9161	−1.72584	−0.862919	+	0.505343i	$0.831366\pi$
$740$	4.07250	0.149708
$741$	0	0
$742$	−5.90226	−0.216679
$743$	−12.8966	−0.473131	−0.236566	−	0.971616i	$-0.576022\pi$
$743$	−12.8966	−0.473131	−0.236566	+	0.971616i	$0.576022\pi$
$744$	−5.83163	−0.213798
$745$	−19.2216	−0.704223
$746$	−21.7513	−0.796371
$747$	−15.4638	−0.565790
$748$	−3.82840	−0.139980
$749$	4.07157	0.148772
$750$	−40.2014	−1.46795
$751$	−45.6333	−1.66518	−0.832591	−	0.553888i	$-0.813144\pi$
$751$	−45.6333	−1.66518	−0.832591	+	0.553888i	$0.813144\pi$
$752$	10.5176	0.383538
$753$	−16.9103	−0.616245
$754$	0	0
$755$	26.7089	0.972038
$756$	−9.16992	−0.333507
$757$	−38.1565	−1.38682	−0.693410	−	0.720543i	$-0.743893\pi$
$757$	−38.1565	−1.38682	−0.693410	+	0.720543i	$0.743893\pi$
$758$	29.0055	1.05353
$759$	1.75735	0.0637876
$760$	−31.4057	−1.13920
$761$	−42.7345	−1.54912	−0.774562	−	0.632498i	$-0.782030\pi$
$761$	−42.7345	−1.54912	−0.774562	+	0.632498i	$0.782030\pi$
$762$	−2.39203	−0.0866543
$763$	−15.3087	−0.554211
$764$	−37.1086	−1.34254
$765$	27.0849	0.979257
$766$	61.7005	2.22933
$767$	0	0
$768$	−3.76729	−0.135940
$769$	−21.6177	−0.779553	−0.389777	−	0.920909i	$-0.627448\pi$
$769$	−21.6177	−0.779553	−0.389777	+	0.920909i	$0.627448\pi$
$770$	−5.14844	−0.185537
$771$	−0.809824	−0.0291651
$772$	12.1674	0.437915
$773$	−10.0011	−0.359716	−0.179858	−	0.983693i	$-0.557564\pi$
$773$	−10.0011	−0.359716	−0.179858	+	0.983693i	$0.557564\pi$
$774$	19.2865	0.693237
$775$	65.9436	2.36877
$776$	−14.0996	−0.506146
$777$	0.181101	0.00649696
$778$	−30.4245	−1.09077
$779$	22.7169	0.813917
$780$	0	0
$781$	6.15375	0.220199
$782$	30.7304	1.09892
$783$	11.2693	0.402734
$784$	−1.28114	−0.0457550
$785$	68.8285	2.45659
$786$	7.93031	0.282865
$787$	−41.7878	−1.48957	−0.744787	−	0.667302i	$-0.767449\pi$
$787$	−41.7878	−1.48957	−0.744787	+	0.667302i	$0.767449\pi$
$788$	20.0604	0.714621
$789$	3.66932	0.130631
$790$	131.319	4.67210
$791$	12.1769	0.432961
$792$	3.05601	0.108591
$793$	0	0
$794$	17.5646	0.623343
$795$	6.16574	0.218676
$796$	−2.38254	−0.0844468
$797$	−22.7711	−0.806594	−0.403297	−	0.915069i	$-0.632136\pi$
$797$	−22.7711	−0.806594	−0.403297	+	0.915069i	$0.632136\pi$
$798$	−4.40506	−0.155937
$799$	19.5296	0.690908
$800$	89.2290	3.15472
$801$	−20.1474	−0.711874
$802$	−36.7283	−1.29692
$803$	−2.69621	−0.0951473
$804$	−16.6884	−0.588554
$805$	24.5558	0.865478
$806$	0	0
$807$	4.16325	0.146553
$808$	−11.8703	−0.417596
$809$	−37.5702	−1.32090	−0.660449	−	0.750871i	$-0.729634\pi$
$809$	−37.5702	−1.32090	−0.660449	+	0.750871i	$0.729634\pi$
$810$	−59.7065	−2.09787
$811$	−11.5936	−0.407106	−0.203553	−	0.979064i	$-0.565249\pi$
$811$	−11.5936	−0.407106	−0.203553	+	0.979064i	$0.565249\pi$
$812$	−10.5391	−0.369851
$813$	−11.3032	−0.396420
$814$	−0.402045	−0.0140917
$815$	−99.5915	−3.48854
$816$	1.67486	0.0586317
$817$	11.6264	0.406757
$818$	57.2359	2.00121
$819$	0	0
$820$	77.7514	2.71520
$821$	−31.0243	−1.08276	−0.541378	−	0.840780i	$-0.682097\pi$
$821$	−31.0243	−1.08276	−0.541378	+	0.840780i	$0.682097\pi$
$822$	−18.6143	−0.649250
$823$	29.0775	1.01358	0.506789	−	0.862070i	$-0.330832\pi$
$823$	29.0775	1.01358	0.506789	+	0.862070i	$0.330832\pi$
$824$	−1.17851	−0.0410552
$825$	3.86824	0.134675
$826$	−4.01273	−0.139621
$827$	−14.8920	−0.517846	−0.258923	−	0.965898i	$-0.583368\pi$
$827$	−14.8920	−0.517846	−0.258923	+	0.965898i	$0.583368\pi$
$828$	−45.9745	−1.59773
$829$	−4.37189	−0.151842	−0.0759210	−	0.997114i	$-0.524190\pi$
$829$	−4.37189	−0.151842	−0.0759210	+	0.997114i	$0.524190\pi$
$830$	−53.6961	−1.86382
$831$	3.13541	0.108766
$832$	0	0
$833$	−2.37888	−0.0824234
$834$	21.3453	0.739127
$835$	75.2439	2.60392
$836$	5.81076	0.200969
$837$	−16.1215	−0.557241
$838$	−52.5856	−1.81654
$839$	−22.8218	−0.787896	−0.393948	−	0.919133i	$-0.628891\pi$
$839$	−22.8218	−0.787896	−0.393948	+	0.919133i	$0.628891\pi$
$840$	−4.77999	−0.164925
$841$	−16.0480	−0.553379
$842$	−46.2308	−1.59322
$843$	3.50237	0.120628
$844$	−40.9202	−1.40853
$845$	0	0
$846$	−49.1718	−1.69056
$847$	−10.6980	−0.367587
$848$	−3.40612	−0.116967
$849$	14.8485	0.509601
$850$	67.6433	2.32015
$851$	1.91758	0.0657338
$852$	18.0209	0.617385
$853$	−23.3549	−0.799656	−0.399828	−	0.916590i	$-0.630930\pi$
$853$	−23.3549	−0.799656	−0.399828	+	0.916590i	$0.630930\pi$
$854$	−1.35271	−0.0462886
$855$	−41.1096	−1.40592
$856$	−8.39203	−0.286834
$857$	−43.5306	−1.48698	−0.743488	−	0.668750i	$-0.766830\pi$
$857$	−43.5306	−1.48698	−0.743488	+	0.668750i	$0.766830\pi$
$858$	0	0
$859$	20.5113	0.699838	0.349919	−	0.936780i	$-0.386209\pi$
$859$	20.5113	0.699838	0.349919	+	0.936780i	$0.386209\pi$
$860$	39.7929	1.35693
$861$	3.45754	0.117833
$862$	44.2901	1.50853
$863$	50.6678	1.72475	0.862376	−	0.506268i	$-0.168975\pi$
$863$	50.6678	1.72475	0.862376	+	0.506268i	$0.168975\pi$
$864$	−21.8142	−0.742133
$865$	−31.9512	−1.08637
$866$	−0.0370334	−0.00125845
$867$	−6.23241	−0.211664
$868$	15.0769	0.511743
$869$	−7.70312	−0.261310
$870$	18.5287	0.628181
$871$	0	0
$872$	31.5532	1.06853
$873$	−18.4562	−0.624647
$874$	−46.6428	−1.57772
$875$	32.9518	1.11397
$876$	−7.89568	−0.266770
$877$	47.0361	1.58830	0.794148	−	0.607725i	$-0.207918\pi$
$877$	47.0361	1.58830	0.794148	+	0.607725i	$0.207918\pi$
$878$	−29.9613	−1.01114
$879$	2.67891	0.0903573
$880$	−2.97110	−0.100156
$881$	−16.1135	−0.542877	−0.271439	−	0.962456i	$-0.587499\pi$
$881$	−16.1135	−0.542877	−0.271439	+	0.962456i	$0.587499\pi$
$882$	5.98957	0.201679
$883$	42.0733	1.41588	0.707940	−	0.706273i	$-0.249625\pi$
$883$	42.0733	1.41588	0.707940	+	0.706273i	$0.249625\pi$
$884$	0	0
$885$	4.19186	0.140908
$886$	33.3246	1.11956
$887$	−41.7628	−1.40226	−0.701128	−	0.713035i	$-0.747320\pi$
$887$	−41.7628	−1.40226	−0.701128	+	0.713035i	$0.747320\pi$
$888$	−0.373273	−0.0125262
$889$	1.96067	0.0657588
$890$	−69.9594	−2.34504
$891$	3.50237	0.117334
$892$	39.6334	1.32703
$893$	−29.6422	−0.991938
$894$	5.55697	0.185853
$895$	−96.2303	−3.21662
$896$	14.7124	0.491506
$897$	0	0
$898$	−52.7999	−1.76195
$899$	−18.5287	−0.617966
$900$	−101.198	−3.37328
$901$	−6.32465	−0.210705
$902$	−7.67577	−0.255575
$903$	1.76956	0.0588872
$904$	−25.0982	−0.834755
$905$	58.7821	1.95398
$906$	−7.72158	−0.256532
$907$	−15.4225	−0.512095	−0.256048	−	0.966664i	$-0.582420\pi$
$907$	−15.4225	−0.512095	−0.256048	+	0.966664i	$0.582420\pi$
$908$	15.7184	0.521634
$909$	−15.5381	−0.515366
$910$	0	0
$911$	37.5462	1.24396	0.621981	−	0.783033i	$-0.286328\pi$
$911$	37.5462	1.24396	0.621981	+	0.783033i	$0.286328\pi$
$912$	−2.54211	−0.0841776
$913$	3.14980	0.104243
$914$	40.2517	1.33141
$915$	1.41309	0.0467153
$916$	−9.07552	−0.299864
$917$	−6.50021	−0.214656
$918$	−16.5370	−0.545804
$919$	−9.47464	−0.312540	−0.156270	−	0.987714i	$-0.549947\pi$
$919$	−9.47464	−0.312540	−0.156270	+	0.987714i	$0.549947\pi$
$920$	−50.6127	−1.66865
$921$	−8.88953	−0.292920
$922$	−13.4967	−0.444492
$923$	0	0
$924$	0.884406	0.0290948
$925$	4.22094	0.138784
$926$	11.5283	0.378842
$927$	−1.54265	−0.0506672
$928$	−25.0713	−0.823007
$929$	−35.8439	−1.17600	−0.588001	−	0.808860i	$-0.700085\pi$
$929$	−35.8439	−1.17600	−0.588001	+	0.808860i	$0.700085\pi$
$930$	−26.5065	−0.869181
$931$	3.61068	0.118335
$932$	−59.6556	−1.95409
$933$	−0.718848	−0.0235340
$934$	19.3134	0.631952
$935$	−5.51689	−0.180422
$936$	0	0
$937$	−31.3709	−1.02484	−0.512422	−	0.858734i	$-0.671252\pi$
$937$	−31.3709	−1.02484	−0.512422	+	0.858734i	$0.671252\pi$
$938$	23.0211	0.751664
$939$	7.25286	0.236688
$940$	−101.454	−3.30907
$941$	−44.7844	−1.45993	−0.729964	−	0.683486i	$-0.760463\pi$
$941$	−44.7844	−1.45993	−0.729964	+	0.683486i	$0.760463\pi$
$942$	−19.8984	−0.648324
$943$	36.6100	1.19219
$944$	−2.31570	−0.0753695
$945$	−13.2143	−0.429860
$946$	−3.92843	−0.127724
$947$	35.0674	1.13954	0.569768	−	0.821805i	$-0.307033\pi$
$947$	35.0674	1.13954	0.569768	+	0.821805i	$0.307033\pi$
$948$	−22.5581	−0.732652
$949$	0	0
$950$	−102.669	−3.33104
$951$	4.43791	0.143909
$952$	4.90319	0.158913
$953$	58.9704	1.91024	0.955120	−	0.296219i	$-0.0957259\pi$
$953$	58.9704	1.91024	0.955120	+	0.296219i	$0.0957259\pi$
$954$	15.9242	0.515567
$955$	−53.4752	−1.73042
$956$	3.78229	0.122328
$957$	−1.08689	−0.0351341
$958$	53.7660	1.73710
$959$	15.2576	0.492692
$960$	−29.9239	−0.965791
$961$	−4.49354	−0.144953
$962$	0	0
$963$	−10.9851	−0.353989
$964$	−6.24547	−0.201153
$965$	17.5338	0.564433
$966$	−7.09910	−0.228410
$967$	−30.3671	−0.976540	−0.488270	−	0.872693i	$-0.662372\pi$
$967$	−30.3671	−0.976540	−0.488270	+	0.872693i	$0.662372\pi$
$968$	22.0500	0.708713
$969$	−4.72031	−0.151638
$970$	−64.0868	−2.05770
$971$	−49.5175	−1.58909	−0.794546	−	0.607204i	$-0.792291\pi$
$971$	−49.5175	−1.58909	−0.794546	+	0.607204i	$0.792291\pi$
$972$	37.7662	1.21135
$973$	−17.4960	−0.560897
$974$	3.93815	0.126186
$975$	0	0
$976$	−0.780630	−0.0249874
$977$	10.8671	0.347670	0.173835	−	0.984775i	$-0.444384\pi$
$977$	10.8671	0.347670	0.173835	+	0.984775i	$0.444384\pi$
$978$	28.7920	0.920666
$979$	4.10380	0.131158
$980$	12.3580	0.394762
$981$	41.3027	1.31869
$982$	14.8511	0.473918
$983$	−2.34833	−0.0749001	−0.0374501	−	0.999299i	$-0.511924\pi$
$983$	−2.34833	−0.0749001	−0.0374501	+	0.999299i	$0.511924\pi$
$984$	−7.12645	−0.227183
$985$	28.9079	0.921082
$986$	−19.0062	−0.605282
$987$	−4.51158	−0.143605
$988$	0	0
$989$	18.7369	0.595799
$990$	13.8905	0.441468
$991$	24.4815	0.777681	0.388841	−	0.921305i	$-0.372876\pi$
$991$	24.4815	0.777681	0.388841	+	0.921305i	$0.372876\pi$
$992$	35.8661	1.13875
$993$	8.21311	0.260635
$994$	−24.8592	−0.788485
$995$	−3.43335	−0.108844
$996$	9.22399	0.292273
$997$	−6.62341	−0.209766	−0.104883	−	0.994485i	$-0.533447\pi$
$997$	−6.62341	−0.209766	−0.104883	+	0.994485i	$0.533447\pi$
$998$	54.6982	1.73144
$999$	−1.03191	−0.0326482

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.l.1.1		4
7.6	odd	2		8281.2.a.bt.1.1		4
13.4	even	6		91.2.f.c.29.1	yes	8
13.5	odd	4		1183.2.c.g.337.7		8
13.8	odd	4		1183.2.c.g.337.2		8
13.10	even	6		91.2.f.c.22.1	✓	8
13.12	even	2		1183.2.a.k.1.4		4
39.17	odd	6		819.2.o.h.757.4		8
39.23	odd	6		819.2.o.h.568.4		8
52.23	odd	6		1456.2.s.q.113.2		8
52.43	odd	6		1456.2.s.q.1121.2		8
91.4	even	6		637.2.h.h.471.4		8
91.10	odd	6		637.2.g.j.373.1		8
91.17	odd	6		637.2.h.i.471.4		8
91.23	even	6		637.2.h.h.165.4		8
91.30	even	6		637.2.g.k.263.1		8
91.62	odd	6		637.2.f.i.295.1		8
91.69	odd	6		637.2.f.i.393.1		8
91.75	odd	6		637.2.h.i.165.4		8
91.82	odd	6		637.2.g.j.263.1		8
91.88	even	6		637.2.g.k.373.1		8
91.90	odd	2		8281.2.a.bp.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.c.22.1	✓	8	13.10	even	6
91.2.f.c.29.1	yes	8	13.4	even	6
637.2.f.i.295.1		8	91.62	odd	6
637.2.f.i.393.1		8	91.69	odd	6
637.2.g.j.263.1		8	91.82	odd	6
637.2.g.j.373.1		8	91.10	odd	6
637.2.g.k.263.1		8	91.30	even	6
637.2.g.k.373.1		8	91.88	even	6
637.2.h.h.165.4		8	91.23	even	6
637.2.h.h.471.4		8	91.4	even	6
637.2.h.i.165.4		8	91.75	odd	6
637.2.h.i.471.4		8	91.17	odd	6
819.2.o.h.568.4		8	39.23	odd	6
819.2.o.h.757.4		8	39.17	odd	6
1183.2.a.k.1.4		4	13.12	even	2
1183.2.a.l.1.1		4	1.1	even	1	trivial
1183.2.c.g.337.2		8	13.8	odd	4
1183.2.c.g.337.7		8	13.5	odd	4
1456.2.s.q.113.2		8	52.23	odd	6
1456.2.s.q.1121.2		8	52.43	odd	6
8281.2.a.bp.1.4		4	91.90	odd	2
8281.2.a.bt.1.1		4	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)

\(f(q)\)	\(=\)	\(q-2.22001 q^{2} +0.549551 q^{3} +2.92843 q^{4} +4.22001 q^{5} -1.22001 q^{6} +1.00000 q^{7} -2.06113 q^{8} -2.69799 q^{9} +O(q^{10})\)	\(q-2.22001 q^{2} +0.549551 q^{3} +2.92843 q^{4} +4.22001 q^{5} -1.22001 q^{6} +1.00000 q^{7} -2.06113 q^{8} -2.69799 q^{9} -9.36845 q^{10} +0.549551 q^{11} +1.60932 q^{12} -2.22001 q^{14} +2.31911 q^{15} -1.28114 q^{16} -2.37888 q^{17} +5.98957 q^{18} +3.61068 q^{19} +12.3580 q^{20} +0.549551 q^{21} -1.22001 q^{22} +5.81890 q^{23} -1.13270 q^{24} +12.8085 q^{25} -3.13134 q^{27} +2.92843 q^{28} -3.59889 q^{29} -5.14844 q^{30} +5.14844 q^{31} +6.96640 q^{32} +0.302006 q^{33} +5.28114 q^{34} +4.22001 q^{35} -7.90090 q^{36} +0.329543 q^{37} -8.01574 q^{38} -8.69799 q^{40} +6.29157 q^{41} -1.22001 q^{42} +3.22001 q^{43} +1.60932 q^{44} -11.3856 q^{45} -12.9180 q^{46} -8.20957 q^{47} -0.704052 q^{48} +1.00000 q^{49} -28.4349 q^{50} -1.30732 q^{51} +2.65866 q^{53} +6.95160 q^{54} +2.31911 q^{55} -2.06113 q^{56} +1.98426 q^{57} +7.98957 q^{58} +1.80753 q^{59} +6.79136 q^{60} +0.609325 q^{61} -11.4296 q^{62} -2.69799 q^{63} -12.9032 q^{64} -0.670457 q^{66} -10.3698 q^{67} -6.96640 q^{68} +3.19778 q^{69} -9.36845 q^{70} +11.1978 q^{71} +5.56092 q^{72} -4.90621 q^{73} -0.731589 q^{74} +7.03891 q^{75} +10.5736 q^{76} +0.549551 q^{77} -14.0171 q^{79} -5.40642 q^{80} +6.37315 q^{81} -13.9673 q^{82} +5.73159 q^{83} +1.60932 q^{84} -10.0389 q^{85} -7.14844 q^{86} -1.97777 q^{87} -1.13270 q^{88} +7.46755 q^{89} +25.2760 q^{90} +17.0403 q^{92} +2.82933 q^{93} +18.2253 q^{94} +15.2371 q^{95} +3.82840 q^{96} +6.84070 q^{97} -2.22001 q^{98} -1.48269 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{3} + 5 q^{4} + 7 q^{5} + 5 q^{6} + 4 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) \) 4 * q + q^2 + q^3 + 5 * q^4 + 7 * q^5 + 5 * q^6 + 4 * q^7 + 6 * q^8 + 7 * q^9	\( 4 q + q^{2} + q^{3} + 5 q^{4} + 7 q^{5} + 5 q^{6} + 4 q^{7} + 6 q^{8} + 7 q^{9} - 11 q^{10} + q^{11} + 12 q^{12} + q^{14} - 3 q^{15} + 19 q^{16} - 4 q^{17} + 3 q^{18} - q^{19} + 2 q^{20} + q^{21} + 5 q^{22} - 2 q^{23} + 3 q^{24} + 5 q^{25} - 26 q^{27} + 5 q^{28} + q^{29} - 4 q^{30} + 4 q^{31} + 33 q^{32} + 19 q^{33} - 3 q^{34} + 7 q^{35} - 34 q^{36} + 10 q^{37} - 23 q^{38} - 17 q^{40} + 22 q^{41} + 5 q^{42} + 3 q^{43} + 12 q^{44} + 11 q^{45} - 24 q^{46} - 2 q^{47} + 11 q^{48} + 4 q^{49} - 43 q^{50} + 7 q^{51} + 2 q^{53} - 5 q^{54} - 3 q^{55} + 6 q^{56} + 17 q^{57} + 11 q^{58} + 8 q^{59} + 11 q^{60} + 8 q^{61} - 5 q^{62} + 7 q^{63} + 14 q^{64} + 6 q^{66} + 6 q^{67} - 33 q^{68} - 18 q^{69} - 11 q^{70} + 14 q^{71} - 5 q^{72} + 8 q^{73} + 20 q^{74} - 7 q^{75} - 32 q^{76} + q^{77} - 26 q^{79} - 7 q^{80} + 24 q^{81} - 14 q^{82} + 12 q^{84} - 5 q^{85} - 12 q^{86} + 13 q^{87} + 3 q^{88} + q^{89} + 26 q^{90} + 12 q^{92} + 7 q^{93} + 33 q^{94} + 21 q^{95} + 58 q^{96} - 3 q^{97} + q^{98} - 23 q^{99}+O(q^{100}) \) 4 * q + q^2 + q^3 + 5 * q^4 + 7 * q^5 + 5 * q^6 + 4 * q^7 + 6 * q^8 + 7 * q^9 - 11 * q^10 + q^11 + 12 * q^12 + q^14 - 3 * q^15 + 19 * q^16 - 4 * q^17 + 3 * q^18 - q^19 + 2 * q^20 + q^21 + 5 * q^22 - 2 * q^23 + 3 * q^24 + 5 * q^25 - 26 * q^27 + 5 * q^28 + q^29 - 4 * q^30 + 4 * q^31 + 33 * q^32 + 19 * q^33 - 3 * q^34 + 7 * q^35 - 34 * q^36 + 10 * q^37 - 23 * q^38 - 17 * q^40 + 22 * q^41 + 5 * q^42 + 3 * q^43 + 12 * q^44 + 11 * q^45 - 24 * q^46 - 2 * q^47 + 11 * q^48 + 4 * q^49 - 43 * q^50 + 7 * q^51 + 2 * q^53 - 5 * q^54 - 3 * q^55 + 6 * q^56 + 17 * q^57 + 11 * q^58 + 8 * q^59 + 11 * q^60 + 8 * q^61 - 5 * q^62 + 7 * q^63 + 14 * q^64 + 6 * q^66 + 6 * q^67 - 33 * q^68 - 18 * q^69 - 11 * q^70 + 14 * q^71 - 5 * q^72 + 8 * q^73 + 20 * q^74 - 7 * q^75 - 32 * q^76 + q^77 - 26 * q^79 - 7 * q^80 + 24 * q^81 - 14 * q^82 + 12 * q^84 - 5 * q^85 - 12 * q^86 + 13 * q^87 + 3 * q^88 + q^89 + 26 * q^90 + 12 * q^92 + 7 * q^93 + 33 * q^94 + 21 * q^95 + 58 * q^96 - 3 * q^97 + q^98 - 23 * q^99

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