LMFDB - Embedded newform 161.4.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,4,Mod(1,161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("161.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.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:	$9.49930751092$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 60x^{7} - 22x^{6} + 1179x^{5} + 694x^{4} - 7936x^{3} - 4352x^{2} + 11008x + 3072 $ x^9 - 60x^7 - 22x^6 + 1179x^5 + 694x^4 - 7936x^3 - 4352x^2 + 11008*x + 3072
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$5.30303$ of defining polynomial
Character	$\chi$	$=$	161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.30303 q^{2} +1.07328 q^{3} +20.1221 q^{4} +13.2233 q^{5} +5.69164 q^{6} -7.00000 q^{7} +64.2837 q^{8} -25.8481 q^{9} +O(q^{10})$	\(q+5.30303 q^{2} +1.07328 q^{3} +20.1221 q^{4} +13.2233 q^{5} +5.69164 q^{6} -7.00000 q^{7} +64.2837 q^{8} -25.8481 q^{9} +70.1237 q^{10} -33.2790 q^{11} +21.5967 q^{12} -78.9006 q^{13} -37.1212 q^{14} +14.1924 q^{15} +179.921 q^{16} +61.6777 q^{17} -137.073 q^{18} +26.3259 q^{19} +266.081 q^{20} -7.51297 q^{21} -176.479 q^{22} -23.0000 q^{23} +68.9945 q^{24} +49.8565 q^{25} -418.412 q^{26} -56.7209 q^{27} -140.855 q^{28} +171.124 q^{29} +75.2624 q^{30} +275.295 q^{31} +439.858 q^{32} -35.7178 q^{33} +327.078 q^{34} -92.5633 q^{35} -520.117 q^{36} -381.523 q^{37} +139.607 q^{38} -84.6826 q^{39} +850.044 q^{40} +344.863 q^{41} -39.8415 q^{42} -349.834 q^{43} -669.643 q^{44} -341.798 q^{45} -121.970 q^{46} +261.666 q^{47} +193.106 q^{48} +49.0000 q^{49} +264.390 q^{50} +66.1975 q^{51} -1587.64 q^{52} -317.144 q^{53} -300.792 q^{54} -440.060 q^{55} -449.986 q^{56} +28.2551 q^{57} +907.476 q^{58} -244.266 q^{59} +285.580 q^{60} -29.3338 q^{61} +1459.89 q^{62} +180.936 q^{63} +893.207 q^{64} -1043.33 q^{65} -189.412 q^{66} -276.252 q^{67} +1241.08 q^{68} -24.6855 q^{69} -490.866 q^{70} +798.729 q^{71} -1661.61 q^{72} +329.217 q^{73} -2023.23 q^{74} +53.5101 q^{75} +529.732 q^{76} +232.953 q^{77} -449.074 q^{78} +631.414 q^{79} +2379.16 q^{80} +637.020 q^{81} +1828.82 q^{82} +865.620 q^{83} -151.177 q^{84} +815.585 q^{85} -1855.18 q^{86} +183.665 q^{87} -2139.30 q^{88} -896.337 q^{89} -1812.56 q^{90} +552.304 q^{91} -462.808 q^{92} +295.469 q^{93} +1387.62 q^{94} +348.116 q^{95} +472.091 q^{96} +58.9955 q^{97} +259.848 q^{98} +860.198 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{3} + 48 q^{4} - 4 q^{5} + 46 q^{6} - 63 q^{7} + 66 q^{8} + 122 q^{9}+O(q^{10}) $ 9 * q + 9 * q^3 + 48 * q^4 - 4 * q^5 + 46 * q^6 - 63 * q^7 + 66 * q^8 + 122 * q^9	\( 9 q + 9 q^{3} + 48 q^{4} - 4 q^{5} + 46 q^{6} - 63 q^{7} + 66 q^{8} + 122 q^{9} + 50 q^{10} - 8 q^{11} + 220 q^{12} + 25 q^{13} + 88 q^{15} + 180 q^{16} - 28 q^{17} - 54 q^{18} + 254 q^{19} + 302 q^{20} - 63 q^{21} - 122 q^{22} - 207 q^{23} + 624 q^{24} + 295 q^{25} - 6 q^{26} + 633 q^{27} - 336 q^{28} + 25 q^{29} + 80 q^{30} + 1171 q^{31} + 1018 q^{32} + 272 q^{33} + 8 q^{34} + 28 q^{35} + 72 q^{36} + 70 q^{37} + 282 q^{38} + 1185 q^{39} - 54 q^{40} + 221 q^{41} - 322 q^{42} - 42 q^{43} - 1214 q^{44} + 698 q^{45} + 159 q^{47} - 1104 q^{48} + 441 q^{49} - 1680 q^{50} + 308 q^{51} - 664 q^{52} - 774 q^{53} - 2674 q^{54} + 1498 q^{55} - 462 q^{56} - 2524 q^{57} + 842 q^{58} + 1080 q^{59} - 2160 q^{60} + 686 q^{61} - 2078 q^{62} - 854 q^{63} - 1260 q^{64} - 1656 q^{65} + 532 q^{66} - 370 q^{67} - 1936 q^{68} - 207 q^{69} - 350 q^{70} + 1035 q^{71} - 722 q^{72} + 1979 q^{73} - 5494 q^{74} - 1459 q^{75} + 206 q^{76} + 56 q^{77} - 2066 q^{78} + 2336 q^{79} - 242 q^{80} + 997 q^{81} + 1642 q^{82} + 130 q^{83} - 1540 q^{84} - 272 q^{85} - 1906 q^{86} - 581 q^{87} - 3742 q^{88} - 1328 q^{89} - 7650 q^{90} - 175 q^{91} - 1104 q^{92} + 1305 q^{93} + 6078 q^{94} - 484 q^{95} - 136 q^{96} - 104 q^{97} - 618 q^{99}+O(q^{100}) \) 9 * q + 9 * q^3 + 48 * q^4 - 4 * q^5 + 46 * q^6 - 63 * q^7 + 66 * q^8 + 122 * q^9 + 50 * q^10 - 8 * q^11 + 220 * q^12 + 25 * q^13 + 88 * q^15 + 180 * q^16 - 28 * q^17 - 54 * q^18 + 254 * q^19 + 302 * q^20 - 63 * q^21 - 122 * q^22 - 207 * q^23 + 624 * q^24 + 295 * q^25 - 6 * q^26 + 633 * q^27 - 336 * q^28 + 25 * q^29 + 80 * q^30 + 1171 * q^31 + 1018 * q^32 + 272 * q^33 + 8 * q^34 + 28 * q^35 + 72 * q^36 + 70 * q^37 + 282 * q^38 + 1185 * q^39 - 54 * q^40 + 221 * q^41 - 322 * q^42 - 42 * q^43 - 1214 * q^44 + 698 * q^45 + 159 * q^47 - 1104 * q^48 + 441 * q^49 - 1680 * q^50 + 308 * q^51 - 664 * q^52 - 774 * q^53 - 2674 * q^54 + 1498 * q^55 - 462 * q^56 - 2524 * q^57 + 842 * q^58 + 1080 * q^59 - 2160 * q^60 + 686 * q^61 - 2078 * q^62 - 854 * q^63 - 1260 * q^64 - 1656 * q^65 + 532 * q^66 - 370 * q^67 - 1936 * q^68 - 207 * q^69 - 350 * q^70 + 1035 * q^71 - 722 * q^72 + 1979 * q^73 - 5494 * q^74 - 1459 * q^75 + 206 * q^76 + 56 * q^77 - 2066 * q^78 + 2336 * q^79 - 242 * q^80 + 997 * q^81 + 1642 * q^82 + 130 * q^83 - 1540 * q^84 - 272 * q^85 - 1906 * q^86 - 581 * q^87 - 3742 * q^88 - 1328 * q^89 - 7650 * q^90 - 175 * q^91 - 1104 * q^92 + 1305 * q^93 + 6078 * q^94 - 484 * q^95 - 136 * q^96 - 104 * q^97 - 618 * 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 $

$2$	5.30303	1.87490	0.937451	−	0.348117i	$-0.113179\pi$
$2$	5.30303	1.87490	0.937451	+	0.348117i	$0.113179\pi$
$3$	1.07328	0.206553	0.103277	−	0.994653i	$-0.467067\pi$
$3$	1.07328	0.206553	0.103277	+	0.994653i	$0.467067\pi$
$4$	20.1221	2.51526
$5$	13.2233	1.18273	0.591365	−	0.806404i	$-0.298589\pi$
$5$	13.2233	1.18273	0.591365	+	0.806404i	$0.298589\pi$
$6$	5.69164	0.387267
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	64.2837	2.84096
$9$	−25.8481	−0.957336
$10$	70.1237	2.21750
$11$	−33.2790	−0.912182	−0.456091	−	0.889933i	$-0.650751\pi$
$11$	−33.2790	−0.912182	−0.456091	+	0.889933i	$0.650751\pi$
$12$	21.5967	0.519535
$13$	−78.9006	−1.68331	−0.841657	−	0.540012i	$-0.818420\pi$
$13$	−78.9006	−1.68331	−0.841657	+	0.540012i	$0.818420\pi$
$14$	−37.1212	−0.708647
$15$	14.1924	0.244297
$16$	179.921	2.81127
$17$	61.6777	0.879943	0.439972	−	0.898012i	$-0.354988\pi$
$17$	61.6777	0.879943	0.439972	+	0.898012i	$0.354988\pi$
$18$	−137.073	−1.79491
$19$	26.3259	0.317872	0.158936	−	0.987289i	$-0.449194\pi$
$19$	26.3259	0.317872	0.158936	+	0.987289i	$0.449194\pi$
$20$	266.081	2.97487
$21$	−7.51297	−0.0780697
$22$	−176.479	−1.71025
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	68.9945	0.586810
$25$	49.8565	0.398852
$26$	−418.412	−3.15605
$27$	−56.7209	−0.404294
$28$	−140.855	−0.950679
$29$	171.124	1.09576	0.547879	−	0.836558i	$-0.315435\pi$
$29$	171.124	1.09576	0.547879	+	0.836558i	$0.315435\pi$
$30$	75.2624	0.458033
$31$	275.295	1.59498	0.797490	−	0.603332i	$-0.206161\pi$
$31$	275.295	1.59498	0.797490	+	0.603332i	$0.206161\pi$
$32$	439.858	2.42989
$33$	−35.7178	−0.188414
$34$	327.078	1.64981
$35$	−92.5633	−0.447030
$36$	−520.117	−2.40795
$37$	−381.523	−1.69519	−0.847595	−	0.530644i	$-0.821950\pi$
$37$	−381.523	−1.69519	−0.847595	+	0.530644i	$0.821950\pi$
$38$	139.607	0.595980
$39$	−84.6826	−0.347694
$40$	850.044	3.36010
$41$	344.863	1.31362	0.656812	−	0.754054i	$-0.271904\pi$
$41$	344.863	1.31362	0.656812	+	0.754054i	$0.271904\pi$
$42$	−39.8415	−0.146373
$43$	−349.834	−1.24068	−0.620339	−	0.784334i	$-0.713005\pi$
$43$	−349.834	−1.24068	−0.620339	+	0.784334i	$0.713005\pi$
$44$	−669.643	−2.29437
$45$	−341.798	−1.13227
$46$	−121.970	−0.390944
$47$	261.666	0.812084	0.406042	−	0.913854i	$-0.366909\pi$
$47$	261.666	0.812084	0.406042	+	0.913854i	$0.366909\pi$
$48$	193.106	0.580677
$49$	49.0000	0.142857
$50$	264.390	0.747809
$51$	66.1975	0.181755
$52$	−1587.64	−4.23397
$53$	−317.144	−0.821944	−0.410972	−	0.911648i	$-0.634811\pi$
$53$	−317.144	−0.821944	−0.410972	+	0.911648i	$0.634811\pi$
$54$	−300.792	−0.758012
$55$	−440.060	−1.07887
$56$	−449.986	−1.07378
$57$	28.2551	0.0656575
$58$	907.476	2.05444
$59$	−244.266	−0.538994	−0.269497	−	0.963001i	$-0.586858\pi$
$59$	−244.266	−0.538994	−0.269497	+	0.963001i	$0.586858\pi$
$60$	285.580	0.614470
$61$	−29.3338	−0.0615706	−0.0307853	−	0.999526i	$-0.509801\pi$
$61$	−29.3338	−0.0615706	−0.0307853	+	0.999526i	$0.509801\pi$
$62$	1459.89	2.99043
$63$	180.936	0.361839
$64$	893.207	1.74454
$65$	−1043.33	−1.99091
$66$	−189.412	−0.353258
$67$	−276.252	−0.503725	−0.251863	−	0.967763i	$-0.581043\pi$
$67$	−276.252	−0.503725	−0.251863	+	0.967763i	$0.581043\pi$
$68$	1241.08	2.21329
$69$	−24.6855	−0.0430693
$70$	−490.866	−0.838138
$71$	798.729	1.33509	0.667547	−	0.744568i	$-0.267344\pi$
$71$	798.729	1.33509	0.667547	+	0.744568i	$0.267344\pi$
$72$	−1661.61	−2.71976
$73$	329.217	0.527834	0.263917	−	0.964545i	$-0.414986\pi$
$73$	329.217	0.527834	0.263917	+	0.964545i	$0.414986\pi$
$74$	−2023.23	−3.17831
$75$	53.5101	0.0823842
$76$	529.732	0.799531
$77$	232.953	0.344772
$78$	−449.074	−0.651892
$79$	631.414	0.899236	0.449618	−	0.893221i	$-0.351560\pi$
$79$	631.414	0.899236	0.449618	+	0.893221i	$0.351560\pi$
$80$	2379.16	3.32498
$81$	637.020	0.873828
$82$	1828.82	2.46292
$83$	865.620	1.14475	0.572375	−	0.819992i	$-0.306022\pi$
$83$	865.620	1.14475	0.572375	+	0.819992i	$0.306022\pi$
$84$	−151.177	−0.196366
$85$	815.585	1.04074
$86$	−1855.18	−2.32615
$87$	183.665	0.226332
$88$	−2139.30	−2.59148
$89$	−896.337	−1.06755	−0.533773	−	0.845628i	$-0.679226\pi$
$89$	−896.337	−1.06755	−0.533773	+	0.845628i	$0.679226\pi$
$90$	−1812.56	−2.12290
$91$	552.304	0.636233
$92$	−462.808	−0.524468
$93$	295.469	0.329448
$94$	1387.62	1.52258
$95$	348.116	0.375957
$96$	472.091	0.501902
$97$	58.9955	0.0617534	0.0308767	−	0.999523i	$-0.490170\pi$
$97$	58.9955	0.0617534	0.0308767	+	0.999523i	$0.490170\pi$
$98$	259.848	0.267843
$99$	860.198	0.873264
$100$	1003.22	1.00322
$101$	−360.988	−0.355640	−0.177820	−	0.984063i	$-0.556905\pi$
$101$	−360.988	−0.355640	−0.177820	+	0.984063i	$0.556905\pi$
$102$	351.047	0.340773
$103$	−919.874	−0.879979	−0.439990	−	0.898003i	$-0.645018\pi$
$103$	−919.874	−0.879979	−0.439990	+	0.898003i	$0.645018\pi$
$104$	−5072.02	−4.78224
$105$	−99.3465	−0.0923355
$106$	−1681.82	−1.54106
$107$	1748.90	1.58011	0.790057	−	0.613033i	$-0.210051\pi$
$107$	1748.90	1.58011	0.790057	+	0.613033i	$0.210051\pi$
$108$	−1141.34	−1.01690
$109$	−1941.95	−1.70647	−0.853235	−	0.521527i	$-0.825363\pi$
$109$	−1941.95	−1.70647	−0.853235	+	0.521527i	$0.825363\pi$
$110$	−2333.65	−2.02277
$111$	−409.482	−0.350147
$112$	−1259.45	−1.06256
$113$	−378.205	−0.314854	−0.157427	−	0.987531i	$-0.550320\pi$
$113$	−378.205	−0.314854	−0.157427	+	0.987531i	$0.550320\pi$
$114$	149.838	0.123101
$115$	−304.137	−0.246616
$116$	3443.38	2.75612
$117$	2039.43	1.61150
$118$	−1295.35	−1.01056
$119$	−431.744	−0.332587
$120$	912.337	0.694038
$121$	−223.507	−0.167924
$122$	−155.558	−0.115439
$123$	370.135	0.271333
$124$	5539.50	4.01179
$125$	−993.647	−0.710996
$126$	959.511	0.678413
$127$	1502.04	1.04948	0.524742	−	0.851262i	$-0.324162\pi$
$127$	1502.04	1.04948	0.524742	+	0.851262i	$0.324162\pi$
$128$	1217.84	0.840957
$129$	−375.470	−0.256266
$130$	−5532.80	−3.73276
$131$	1712.14	1.14191	0.570955	−	0.820981i	$-0.306573\pi$
$131$	1712.14	1.14191	0.570955	+	0.820981i	$0.306573\pi$
$132$	−718.715	−0.473910
$133$	−184.281	−0.120144
$134$	−1464.97	−0.944436
$135$	−750.039	−0.478171
$136$	3964.87	2.49989
$137$	1467.88	0.915397	0.457699	−	0.889107i	$-0.348674\pi$
$137$	1467.88	0.915397	0.457699	+	0.889107i	$0.348674\pi$
$138$	−130.908	−0.0807507
$139$	−2756.49	−1.68203	−0.841014	−	0.541013i	$-0.818041\pi$
$139$	−2756.49	−1.68203	−0.841014	+	0.541013i	$0.818041\pi$
$140$	−1862.57	−1.12440
$141$	280.842	0.167738
$142$	4235.68	2.50317
$143$	2625.73	1.53549
$144$	−4650.62	−2.69133
$145$	2262.83	1.29599
$146$	1745.84	0.989637
$147$	52.5908	0.0295076
$148$	−7677.04	−4.26384
$149$	2471.08	1.35865	0.679324	−	0.733838i	$-0.262273\pi$
$149$	2471.08	1.35865	0.679324	+	0.733838i	$0.262273\pi$
$150$	283.765	0.154462
$151$	−1222.97	−0.659101	−0.329550	−	0.944138i	$-0.606897\pi$
$151$	−1222.97	−0.659101	−0.329550	+	0.944138i	$0.606897\pi$
$152$	1692.33	0.903064
$153$	−1594.25	−0.842401
$154$	1235.36	0.646415
$155$	3640.31	1.88643
$156$	−1703.99	−0.874540
$157$	−680.886	−0.346119	−0.173059	−	0.984911i	$-0.555365\pi$
$157$	−680.886	−0.346119	−0.173059	+	0.984911i	$0.555365\pi$
$158$	3348.40	1.68598
$159$	−340.384	−0.169775
$160$	5816.39	2.87391
$161$	161.000	0.0788110
$162$	3378.13	1.63834
$163$	−2235.25	−1.07410	−0.537050	−	0.843550i	$-0.680461\pi$
$163$	−2235.25	−1.07410	−0.537050	+	0.843550i	$0.680461\pi$
$164$	6939.36	3.30411
$165$	−472.308	−0.222843
$166$	4590.41	2.14629
$167$	−457.282	−0.211889	−0.105945	−	0.994372i	$-0.533787\pi$
$167$	−457.282	−0.211889	−0.105945	+	0.994372i	$0.533787\pi$
$168$	−482.961	−0.221793
$169$	4028.30	1.83355
$170$	4325.07	1.95128
$171$	−680.474	−0.304311
$172$	−7039.38	−3.12063
$173$	361.973	0.159077	0.0795384	−	0.996832i	$-0.474655\pi$
$173$	361.973	0.159077	0.0795384	+	0.996832i	$0.474655\pi$
$174$	973.978	0.424351
$175$	−348.996	−0.150752
$176$	−5987.60	−2.56439
$177$	−262.166	−0.111331
$178$	−4753.30	−2.00154
$179$	3215.60	1.34271	0.671356	−	0.741135i	$-0.265712\pi$
$179$	3215.60	1.34271	0.671356	+	0.741135i	$0.265712\pi$
$180$	−6877.68	−2.84795
$181$	2607.72	1.07088	0.535442	−	0.844572i	$-0.320145\pi$
$181$	2607.72	1.07088	0.535442	+	0.844572i	$0.320145\pi$
$182$	2928.88	1.19288
$183$	−31.4834	−0.0127176
$184$	−1478.52	−0.592382
$185$	−5045.01	−2.00495
$186$	1566.88	0.617683
$187$	−2052.57	−0.802669
$188$	5265.27	2.04260
$189$	397.046	0.152809
$190$	1846.07	0.704884
$191$	100.043	0.0379000	0.0189500	−	0.999820i	$-0.493968\pi$
$191$	100.043	0.0379000	0.0189500	+	0.999820i	$0.493968\pi$
$192$	958.663	0.360341
$193$	1804.25	0.672915	0.336458	−	0.941699i	$-0.390771\pi$
$193$	1804.25	0.672915	0.336458	+	0.941699i	$0.390771\pi$
$194$	312.855	0.115782
$195$	−1119.79	−0.411228
$196$	985.982	0.359323
$197$	−5340.92	−1.93160	−0.965799	−	0.259293i	$-0.916511\pi$
$197$	−5340.92	−1.93160	−0.965799	+	0.259293i	$0.916511\pi$
$198$	4561.65	1.63729
$199$	3285.28	1.17029	0.585144	−	0.810929i	$-0.301038\pi$
$199$	3285.28	1.17029	0.585144	+	0.810929i	$0.301038\pi$
$200$	3204.96	1.13312
$201$	−296.497	−0.104046
$202$	−1914.33	−0.666791
$203$	−1197.87	−0.414158
$204$	1332.03	0.457161
$205$	4560.24	1.55366
$206$	−4878.11	−1.64987
$207$	594.506	0.199618
$208$	−14195.9	−4.73225
$209$	−876.100	−0.289957
$210$	−526.837	−0.173120
$211$	−1893.58	−0.617816	−0.308908	−	0.951092i	$-0.599964\pi$
$211$	−1893.58	−0.617816	−0.308908	+	0.951092i	$0.599964\pi$
$212$	−6381.59	−2.06740
$213$	857.261	0.275768
$214$	9274.44	2.96256
$215$	−4625.97	−1.46739
$216$	−3646.22	−1.14858
$217$	−1927.06	−0.602846
$218$	−10298.2	−3.19946
$219$	353.342	0.109026
$220$	−8854.91	−2.71363
$221$	−4866.41	−1.48122
$222$	−2171.49	−0.656491
$223$	−456.269	−0.137014	−0.0685069	−	0.997651i	$-0.521824\pi$
$223$	−456.269	−0.137014	−0.0685069	+	0.997651i	$0.521824\pi$
$224$	−3079.01	−0.918414
$225$	−1288.69	−0.381835
$226$	−2005.63	−0.590321
$227$	210.751	0.0616212	0.0308106	−	0.999525i	$-0.490191\pi$
$227$	210.751	0.0616212	0.0308106	+	0.999525i	$0.490191\pi$
$228$	568.551	0.165146
$229$	1677.54	0.484083	0.242041	−	0.970266i	$-0.422183\pi$
$229$	1677.54	0.484083	0.242041	+	0.970266i	$0.422183\pi$
$230$	−1612.84	−0.462382
$231$	250.024	0.0712138
$232$	11000.5	3.11301
$233$	2087.62	0.586973	0.293486	−	0.955963i	$-0.405184\pi$
$233$	2087.62	0.586973	0.293486	+	0.955963i	$0.405184\pi$
$234$	10815.1	3.02140
$235$	3460.10	0.960477
$236$	−4915.13	−1.35571
$237$	677.685	0.185740
$238$	−2289.55	−0.623569
$239$	45.6018	0.0123420	0.00617100	−	0.999981i	$-0.498036\pi$
$239$	45.6018	0.0123420	0.00617100	+	0.999981i	$0.498036\pi$
$240$	2553.51	0.686784
$241$	−5310.41	−1.41939	−0.709696	−	0.704508i	$-0.751168\pi$
$241$	−5310.41	−1.41939	−0.709696	+	0.704508i	$0.751168\pi$
$242$	−1185.26	−0.314841
$243$	2215.17	0.584786
$244$	−590.257	−0.154866
$245$	647.943	0.168962
$246$	1962.84	0.508723
$247$	−2077.13	−0.535079
$248$	17697.0	4.53128
$249$	929.054	0.236452
$250$	−5269.34	−1.33305
$251$	−1697.80	−0.426950	−0.213475	−	0.976949i	$-0.568478\pi$
$251$	−1697.80	−0.426950	−0.213475	+	0.976949i	$0.568478\pi$
$252$	3640.82	0.910119
$253$	765.417	0.190203
$254$	7965.35	1.96768
$255$	875.352	0.214967
$256$	−687.443	−0.167833
$257$	3760.07	0.912633	0.456317	−	0.889818i	$-0.349168\pi$
$257$	3760.07	0.912633	0.456317	+	0.889818i	$0.349168\pi$
$258$	−1991.13	−0.480474
$259$	2670.66	0.640721
$260$	−20993.9	−5.00765
$261$	−4423.23	−1.04901
$262$	9079.51	2.14097
$263$	−4781.22	−1.12100	−0.560500	−	0.828155i	$-0.689391\pi$
$263$	−4781.22	−1.12100	−0.560500	+	0.828155i	$0.689391\pi$
$264$	−2296.07	−0.535277
$265$	−4193.70	−0.972138
$266$	−977.248	−0.225259
$267$	−962.022	−0.220505
$268$	−5558.77	−1.26700
$269$	−5965.17	−1.35205	−0.676027	−	0.736877i	$-0.736300\pi$
$269$	−5965.17	−1.35205	−0.676027	+	0.736877i	$0.736300\pi$
$270$	−3977.47	−0.896524
$271$	2958.83	0.663234	0.331617	−	0.943414i	$-0.392406\pi$
$271$	2958.83	0.663234	0.331617	+	0.943414i	$0.392406\pi$
$272$	11097.1	2.47376
$273$	592.778	0.131416
$274$	7784.20	1.71628
$275$	−1659.18	−0.363826
$276$	−496.723	−0.108330
$277$	−3147.15	−0.682650	−0.341325	−	0.939945i	$-0.610876\pi$
$277$	−3147.15	−0.682650	−0.341325	+	0.939945i	$0.610876\pi$
$278$	−14617.7	−3.15364
$279$	−7115.84	−1.52693
$280$	−5950.31	−1.27000
$281$	−1073.25	−0.227846	−0.113923	−	0.993490i	$-0.536342\pi$
$281$	−1073.25	−0.227846	−0.113923	+	0.993490i	$0.536342\pi$
$282$	1489.31	0.314493
$283$	4033.81	0.847298	0.423649	−	0.905827i	$-0.360749\pi$
$283$	4033.81	0.847298	0.423649	+	0.905827i	$0.360749\pi$
$284$	16072.1	3.35811
$285$	373.627	0.0776552
$286$	13924.3	2.87889
$287$	−2414.04	−0.496503
$288$	−11369.5	−2.32622
$289$	−1108.86	−0.225700
$290$	11999.9	2.42985
$291$	63.3188	0.0127554
$292$	6624.52	1.32764
$293$	−8699.49	−1.73457	−0.867286	−	0.497810i	$-0.834138\pi$
$293$	−8699.49	−1.73457	−0.867286	+	0.497810i	$0.834138\pi$
$294$	278.890	0.0553239
$295$	−3230.01	−0.637485
$296$	−24525.7	−4.81597
$297$	1887.61	0.368790
$298$	13104.2	2.54733
$299$	1814.71	0.350995
$300$	1076.73	0.207218
$301$	2448.84	0.468932
$302$	−6485.46	−1.23575
$303$	−387.442	−0.0734586
$304$	4736.59	0.893625
$305$	−387.890	−0.0728215
$306$	−8454.34	−1.57942
$307$	9665.62	1.79689	0.898447	−	0.439082i	$-0.144696\pi$
$307$	9665.62	1.79689	0.898447	+	0.439082i	$0.144696\pi$
$308$	4687.50	0.867192
$309$	−987.283	−0.181762
$310$	19304.7	3.53688
$311$	−1660.16	−0.302699	−0.151349	−	0.988480i	$-0.548362\pi$
$311$	−1660.16	−0.302699	−0.151349	+	0.988480i	$0.548362\pi$
$312$	−5443.71	−0.987786
$313$	3541.03	0.639460	0.319730	−	0.947509i	$-0.396408\pi$
$313$	3541.03	0.639460	0.319730	+	0.947509i	$0.396408\pi$
$314$	−3610.76	−0.648939
$315$	2392.58	0.427958
$316$	12705.4	2.26181
$317$	3305.72	0.585702	0.292851	−	0.956158i	$-0.405396\pi$
$317$	3305.72	0.585702	0.292851	+	0.956158i	$0.405396\pi$
$318$	−1805.07	−0.318312
$319$	−5694.85	−0.999531
$320$	11811.2	2.06333
$321$	1877.06	0.326378
$322$	853.787	0.147763
$323$	1623.72	0.279710
$324$	12818.2	2.19790
$325$	−3933.71	−0.671394
$326$	−11853.6	−2.01383
$327$	−2084.26	−0.352477
$328$	22169.1	3.73196
$329$	−1831.66	−0.306939
$330$	−2504.66	−0.417809
$331$	2945.62	0.489142	0.244571	−	0.969631i	$-0.421353\pi$
$331$	2945.62	0.489142	0.244571	+	0.969631i	$0.421353\pi$
$332$	17418.1	2.87934
$333$	9861.63	1.62287
$334$	−2424.98	−0.397272
$335$	−3652.98	−0.595772
$336$	−1351.74	−0.219475
$337$	−2200.66	−0.355720	−0.177860	−	0.984056i	$-0.556917\pi$
$337$	−2200.66	−0.355720	−0.177860	+	0.984056i	$0.556917\pi$
$338$	21362.2	3.43772
$339$	−405.921	−0.0650342
$340$	16411.3	2.61772
$341$	−9161.54	−1.45491
$342$	−3608.57	−0.570553
$343$	−343.000	−0.0539949
$344$	−22488.6	−3.52472
$345$	−326.424	−0.0509394
$346$	1919.55	0.298254
$347$	−5503.40	−0.851406	−0.425703	−	0.904863i	$-0.639973\pi$
$347$	−5503.40	−0.851406	−0.425703	+	0.904863i	$0.639973\pi$
$348$	3695.71	0.569284
$349$	−1729.03	−0.265195	−0.132597	−	0.991170i	$-0.542332\pi$
$349$	−1729.03	−0.265195	−0.132597	+	0.991170i	$0.542332\pi$
$350$	−1850.73	−0.282645
$351$	4475.31	0.680554
$352$	−14638.0	−2.21651
$353$	−9670.43	−1.45809	−0.729044	−	0.684467i	$-0.760035\pi$
$353$	−9670.43	−1.45809	−0.729044	+	0.684467i	$0.760035\pi$
$354$	−1390.27	−0.208735
$355$	10561.9	1.57906
$356$	−18036.2	−2.68515
$357$	−463.383	−0.0686970
$358$	17052.4	2.51745
$359$	2493.27	0.366545	0.183272	−	0.983062i	$-0.441331\pi$
$359$	2493.27	0.366545	0.183272	+	0.983062i	$0.441331\pi$
$360$	−21972.0	−3.21674
$361$	−6165.95	−0.898957
$362$	13828.8	2.00780
$363$	−239.886	−0.0346852
$364$	11113.5	1.60029
$365$	4353.34	0.624285
$366$	−166.957	−0.0238443
$367$	−2242.91	−0.319016	−0.159508	−	0.987197i	$-0.550991\pi$
$367$	−2242.91	−0.319016	−0.159508	+	0.987197i	$0.550991\pi$
$368$	−4138.19	−0.586190
$369$	−8914.05	−1.25758
$370$	−26753.8	−3.75909
$371$	2220.01	0.310666
$372$	5945.44	0.828648
$373$	−9982.67	−1.38575	−0.692873	−	0.721060i	$-0.743655\pi$
$373$	−9982.67	−1.38575	−0.692873	+	0.721060i	$0.743655\pi$
$374$	−10884.8	−1.50493
$375$	−1066.46	−0.146858
$376$	16820.9	2.30710
$377$	−13501.8	−1.84451
$378$	2105.54	0.286501
$379$	10402.8	1.40992	0.704958	−	0.709249i	$-0.250966\pi$
$379$	10402.8	1.40992	0.704958	+	0.709249i	$0.250966\pi$
$380$	7004.82	0.945630
$381$	1612.11	0.216774
$382$	530.533	0.0710587
$383$	−6051.48	−0.807352	−0.403676	−	0.914902i	$-0.632268\pi$
$383$	−6051.48	−0.807352	−0.403676	+	0.914902i	$0.632268\pi$
$384$	1307.08	0.173702
$385$	3080.42	0.407773
$386$	9567.98	1.26165
$387$	9042.53	1.18775
$388$	1187.11	0.155326
$389$	−4673.87	−0.609189	−0.304594	−	0.952482i	$-0.598521\pi$
$389$	−4673.87	−0.609189	−0.304594	+	0.952482i	$0.598521\pi$
$390$	−5938.25	−0.771013
$391$	−1418.59	−0.183481
$392$	3149.90	0.405852
$393$	1837.61	0.235865
$394$	−28323.0	−3.62156
$395$	8349.40	1.06355
$396$	17309.0	2.19649
$397$	13223.0	1.67164	0.835820	−	0.549004i	$-0.184993\pi$
$397$	13223.0	1.67164	0.835820	+	0.549004i	$0.184993\pi$
$398$	17421.9	2.19418
$399$	−197.786	−0.0248162
$400$	8970.25	1.12128
$401$	−13044.0	−1.62440	−0.812200	−	0.583379i	$-0.801730\pi$
$401$	−13044.0	−1.62440	−0.812200	+	0.583379i	$0.801730\pi$
$402$	−1572.33	−0.195076
$403$	−21720.9	−2.68485
$404$	−7263.83	−0.894528
$405$	8423.53	1.03350
$406$	−6352.33	−0.776505
$407$	12696.7	1.54632
$408$	4255.42	0.516360
$409$	−7511.39	−0.908103	−0.454052	−	0.890975i	$-0.650022\pi$
$409$	−7511.39	−0.908103	−0.454052	+	0.890975i	$0.650022\pi$
$410$	24183.1	2.91297
$411$	1575.45	0.189078
$412$	−18509.8	−2.21338
$413$	1709.86	0.203721
$414$	3152.68	0.374265
$415$	11446.4	1.35393
$416$	−34705.1	−4.09028
$417$	−2958.48	−0.347428
$418$	−4645.98	−0.543642
$419$	4058.24	0.473170	0.236585	−	0.971611i	$-0.423972\pi$
$419$	4058.24	0.473170	0.236585	+	0.971611i	$0.423972\pi$
$420$	−1999.06	−0.232248
$421$	1490.82	0.172585	0.0862923	−	0.996270i	$-0.472498\pi$
$421$	1490.82	0.172585	0.0862923	+	0.996270i	$0.472498\pi$
$422$	−10041.7	−1.15835
$423$	−6763.57	−0.777437
$424$	−20387.2	−2.33511
$425$	3075.04	0.350967
$426$	4546.08	0.517038
$427$	205.337	0.0232715
$428$	35191.4	3.97440
$429$	2818.15	0.317160
$430$	−24531.6	−2.75121
$431$	−7097.92	−0.793260	−0.396630	−	0.917979i	$-0.629820\pi$
$431$	−7097.92	−0.793260	−0.396630	+	0.917979i	$0.629820\pi$
$432$	−10205.3	−1.13658
$433$	−2693.96	−0.298991	−0.149496	−	0.988762i	$-0.547765\pi$
$433$	−2693.96	−0.298991	−0.149496	+	0.988762i	$0.547765\pi$
$434$	−10219.3	−1.13028
$435$	2428.66	0.267690
$436$	−39076.1	−4.29221
$437$	−605.496	−0.0662810
$438$	1873.78	0.204413
$439$	15775.1	1.71504	0.857521	−	0.514449i	$-0.172003\pi$
$439$	15775.1	1.71504	0.857521	+	0.514449i	$0.172003\pi$
$440$	−28288.6	−3.06502
$441$	−1266.56	−0.136762
$442$	−25806.7	−2.77715
$443$	13364.7	1.43336	0.716679	−	0.697403i	$-0.245661\pi$
$443$	13364.7	1.43336	0.716679	+	0.697403i	$0.245661\pi$
$444$	−8239.62	−0.880710
$445$	−11852.6	−1.26262
$446$	−2419.61	−0.256887
$447$	2652.16	0.280633
$448$	−6252.45	−0.659376
$449$	6338.41	0.666209	0.333105	−	0.942890i	$-0.391904\pi$
$449$	6338.41	0.666209	0.333105	+	0.942890i	$0.391904\pi$
$450$	−6833.98	−0.715904
$451$	−11476.7	−1.19826
$452$	−7610.27	−0.791940
$453$	−1312.60	−0.136139
$454$	1117.62	0.115534
$455$	7303.30	0.752492
$456$	1816.34	0.186531
$457$	1238.17	0.126738	0.0633691	−	0.997990i	$-0.479815\pi$
$457$	1238.17	0.126738	0.0633691	+	0.997990i	$0.479815\pi$
$458$	8896.03	0.907608
$459$	−3498.41	−0.355756
$460$	−6119.86	−0.620304
$461$	9408.36	0.950522	0.475261	−	0.879845i	$-0.342354\pi$
$461$	9408.36	0.950522	0.475261	+	0.879845i	$0.342354\pi$
$462$	1325.89	0.133519
$463$	3820.66	0.383501	0.191750	−	0.981444i	$-0.438584\pi$
$463$	3820.66	0.383501	0.191750	+	0.981444i	$0.438584\pi$
$464$	30788.9	3.08047
$465$	3907.08	0.389648
$466$	11070.7	1.10052
$467$	−7625.72	−0.755623	−0.377812	−	0.925882i	$-0.623323\pi$
$467$	−7625.72	−0.755623	−0.377812	+	0.925882i	$0.623323\pi$
$468$	41037.5	4.05333
$469$	1933.77	0.190390
$470$	18349.0	1.80080
$471$	−730.783	−0.0714919
$472$	−15702.3	−1.53126
$473$	11642.1	1.13172
$474$	3593.78	0.348244
$475$	1312.52	0.126784
$476$	−8687.58	−0.836543
$477$	8197.55	0.786876
$478$	241.828	0.0231400
$479$	10981.9	1.04755	0.523774	−	0.851857i	$-0.324524\pi$
$479$	10981.9	1.04755	0.523774	+	0.851857i	$0.324524\pi$
$480$	6242.62	0.593615
$481$	30102.4	2.85354
$482$	−28161.2	−2.66122
$483$	172.798	0.0162787
$484$	−4497.42	−0.422373
$485$	780.117	0.0730377
$486$	11747.1	1.09642
$487$	17967.8	1.67186	0.835932	−	0.548833i	$-0.184928\pi$
$487$	17967.8	1.67186	0.835932	+	0.548833i	$0.184928\pi$
$488$	−1885.68	−0.174920
$489$	−2399.05	−0.221859
$490$	3436.06	0.316786
$491$	472.865	0.0434625	0.0217313	−	0.999764i	$-0.493082\pi$
$491$	472.865	0.0434625	0.0217313	+	0.999764i	$0.493082\pi$
$492$	7447.89	0.682473
$493$	10554.5	0.964205
$494$	−11015.1	−1.00322
$495$	11374.7	1.03284
$496$	49531.4	4.48392
$497$	−5591.10	−0.504618
$498$	4926.80	0.443324
$499$	10839.6	0.972440	0.486220	−	0.873836i	$-0.338375\pi$
$499$	10839.6	0.972440	0.486220	+	0.873836i	$0.338375\pi$
$500$	−19994.2	−1.78834
$501$	−490.792	−0.0437664
$502$	−9003.50	−0.800489
$503$	−3968.56	−0.351788	−0.175894	−	0.984409i	$-0.556282\pi$
$503$	−3968.56	−0.351788	−0.175894	+	0.984409i	$0.556282\pi$
$504$	11631.3	1.02797
$505$	−4773.47	−0.420627
$506$	4059.03	0.356612
$507$	4323.51	0.378725
$508$	30224.1	2.63972
$509$	12054.8	1.04975	0.524873	−	0.851181i	$-0.324113\pi$
$509$	12054.8	1.04975	0.524873	+	0.851181i	$0.324113\pi$
$510$	4642.01	0.403043
$511$	−2304.52	−0.199502
$512$	−13388.2	−1.15563
$513$	−1493.23	−0.128514
$514$	19939.7	1.71110
$515$	−12163.8	−1.04078
$516$	−7555.24	−0.644575
$517$	−8708.00	−0.740768
$518$	14162.6	1.20129
$519$	388.499	0.0328578
$520$	−67069.0	−5.65610
$521$	−17218.9	−1.44793	−0.723965	−	0.689837i	$-0.757682\pi$
$521$	−17218.9	−1.44793	−0.723965	+	0.689837i	$0.757682\pi$
$522$	−23456.5	−1.96679
$523$	10560.4	0.882936	0.441468	−	0.897277i	$-0.354458\pi$
$523$	10560.4	0.882936	0.441468	+	0.897277i	$0.354458\pi$
$524$	34451.8	2.87220
$525$	−374.571	−0.0311383
$526$	−25355.0	−2.10176
$527$	16979.5	1.40349
$528$	−6426.39	−0.529683
$529$	529.000	0.0434783
$530$	−22239.3	−1.82266
$531$	6313.79	0.515999
$532$	−3708.12	−0.302194
$533$	−27209.9	−2.21124
$534$	−5101.63	−0.413425
$535$	23126.2	1.86885
$536$	−17758.5	−1.43107
$537$	3451.25	0.277341
$538$	−31633.4	−2.53497
$539$	−1630.67	−0.130312
$540$	−15092.3	−1.20272
$541$	2004.42	0.159291	0.0796457	−	0.996823i	$-0.474621\pi$
$541$	2004.42	0.159291	0.0796457	+	0.996823i	$0.474621\pi$
$542$	15690.8	1.24350
$543$	2798.81	0.221194
$544$	27129.4	2.13817
$545$	−25679.1	−2.01829
$546$	3143.52	0.246392
$547$	−17235.2	−1.34721	−0.673606	−	0.739090i	$-0.735256\pi$
$547$	−17235.2	−1.34721	−0.673606	+	0.739090i	$0.735256\pi$
$548$	29536.8	2.30246
$549$	758.222	0.0589437
$550$	−8798.65	−0.682138
$551$	4505.00	0.348311
$552$	−1586.87	−0.122358
$553$	−4419.90	−0.339879
$554$	−16689.4	−1.27990
$555$	−5414.71	−0.414129
$556$	−55466.2	−4.23074
$557$	−7492.05	−0.569926	−0.284963	−	0.958539i	$-0.591981\pi$
$557$	−7492.05	−0.569926	−0.284963	+	0.958539i	$0.591981\pi$
$558$	−37735.5	−2.86285
$559$	27602.1	2.08845
$560$	−16654.1	−1.25672
$561$	−2202.99	−0.165794
$562$	−5691.46	−0.427188
$563$	10238.7	0.766446	0.383223	−	0.923656i	$-0.374814\pi$
$563$	10238.7	0.766446	0.383223	+	0.923656i	$0.374814\pi$
$564$	5651.11	0.421906
$565$	−5001.13	−0.372388
$566$	21391.4	1.58860
$567$	−4459.14	−0.330276
$568$	51345.2	3.79295
$569$	−10594.1	−0.780538	−0.390269	−	0.920701i	$-0.627618\pi$
$569$	−10594.1	−0.780538	−0.390269	+	0.920701i	$0.627618\pi$
$570$	1981.35	0.145596
$571$	−20152.2	−1.47696	−0.738478	−	0.674277i	$-0.764455\pi$
$571$	−20152.2	−1.47696	−0.738478	+	0.674277i	$0.764455\pi$
$572$	52835.2	3.86215
$573$	107.375	0.00782836
$574$	−12801.7	−0.930895
$575$	−1146.70	−0.0831664
$576$	−23087.7	−1.67012
$577$	3057.90	0.220628	0.110314	−	0.993897i	$-0.464814\pi$
$577$	3057.90	0.220628	0.110314	+	0.993897i	$0.464814\pi$
$578$	−5880.32	−0.423165
$579$	1936.47	0.138993
$580$	45532.9	3.25974
$581$	−6059.34	−0.432674
$582$	335.781	0.0239151
$583$	10554.2	0.749762
$584$	21163.2	1.49956
$585$	26968.0	1.90597
$586$	−46133.6	−3.25215
$587$	−10847.1	−0.762707	−0.381354	−	0.924429i	$-0.624542\pi$
$587$	−10847.1	−0.762707	−0.381354	+	0.924429i	$0.624542\pi$
$588$	1058.24	0.0742192
$589$	7247.38	0.507000
$590$	−17128.8	−1.19522
$591$	−5732.31	−0.398978
$592$	−68644.1	−4.76564
$593$	−25889.2	−1.79282	−0.896411	−	0.443224i	$-0.853834\pi$
$593$	−25889.2	−1.79282	−0.896411	+	0.443224i	$0.853834\pi$
$594$	10010.1	0.691444
$595$	−5709.09	−0.393361
$596$	49723.2	3.41735
$597$	3526.03	0.241727
$598$	9623.47	0.658082
$599$	−12917.8	−0.881144	−0.440572	−	0.897717i	$-0.645224\pi$
$599$	−12917.8	−0.881144	−0.440572	+	0.897717i	$0.645224\pi$
$600$	3439.82	0.234050
$601$	24952.7	1.69358	0.846791	−	0.531925i	$-0.178531\pi$
$601$	24952.7	1.69358	0.846791	+	0.531925i	$0.178531\pi$
$602$	12986.2	0.879202
$603$	7140.59	0.482234
$604$	−24608.8	−1.65781
$605$	−2955.51	−0.198609
$606$	−2054.62	−0.137728
$607$	−3113.16	−0.208170	−0.104085	−	0.994568i	$-0.533191\pi$
$607$	−3113.16	−0.208170	−0.104085	+	0.994568i	$0.533191\pi$
$608$	11579.7	0.772396
$609$	−1285.65	−0.0855455
$610$	−2056.99	−0.136533
$611$	−20645.6	−1.36699
$612$	−32079.6	−2.11886
$613$	−1088.16	−0.0716971	−0.0358486	−	0.999357i	$-0.511413\pi$
$613$	−1088.16	−0.0716971	−0.0358486	+	0.999357i	$0.511413\pi$
$614$	51257.1	3.36900
$615$	4894.42	0.320914
$616$	14975.1	0.979486
$617$	21391.6	1.39577	0.697886	−	0.716209i	$-0.254124\pi$
$617$	21391.6	1.39577	0.697886	+	0.716209i	$0.254124\pi$
$618$	−5235.59	−0.340787
$619$	−29839.1	−1.93754	−0.968768	−	0.247971i	$-0.920236\pi$
$619$	−29839.1	−1.93754	−0.968768	+	0.247971i	$0.920236\pi$
$620$	73250.7	4.74487
$621$	1304.58	0.0843011
$622$	−8803.89	−0.567530
$623$	6274.36	0.403494
$624$	−15236.2	−0.977462
$625$	−19371.4	−1.23977
$626$	18778.2	1.19893
$627$	−940.302	−0.0598916
$628$	−13700.8	−0.870578
$629$	−23531.5	−1.49167
$630$	12687.9	0.802380
$631$	−8469.09	−0.534309	−0.267155	−	0.963654i	$-0.586083\pi$
$631$	−8469.09	−0.534309	−0.267155	+	0.963654i	$0.586083\pi$
$632$	40589.6	2.55470
$633$	−2032.34	−0.127612
$634$	17530.3	1.09813
$635$	19862.0	1.24126
$636$	−6849.24	−0.427028
$637$	−3866.13	−0.240474
$638$	−30199.9	−1.87402
$639$	−20645.6	−1.27813
$640$	16103.8	0.994626
$641$	22742.0	1.40134	0.700668	−	0.713488i	$-0.252886\pi$
$641$	22742.0	1.40134	0.700668	+	0.713488i	$0.252886\pi$
$642$	9954.09	0.611926
$643$	−4464.21	−0.273797	−0.136898	−	0.990585i	$-0.543713\pi$
$643$	−4464.21	−0.273797	−0.136898	+	0.990585i	$0.543713\pi$
$644$	3239.65	0.198230
$645$	−4964.97	−0.303094
$646$	8610.63	0.524428
$647$	−2439.18	−0.148213	−0.0741066	−	0.997250i	$-0.523610\pi$
$647$	−2439.18	−0.148213	−0.0741066	+	0.997250i	$0.523610\pi$
$648$	40950.0	2.48251
$649$	8128.92	0.491661
$650$	−20860.6	−1.25880
$651$	−2068.28	−0.124520
$652$	−44977.9	−2.70164
$653$	11479.7	0.687959	0.343979	−	0.938977i	$-0.388225\pi$
$653$	11479.7	0.687959	0.343979	+	0.938977i	$0.388225\pi$
$654$	−11052.9	−0.660859
$655$	22640.2	1.35057
$656$	62048.2	3.69295
$657$	−8509.61	−0.505314
$658$	−9713.36	−0.575480
$659$	1729.36	0.102225	0.0511125	−	0.998693i	$-0.483723\pi$
$659$	1729.36	0.102225	0.0511125	+	0.998693i	$0.483723\pi$
$660$	−9503.81	−0.560508
$661$	6835.28	0.402211	0.201106	−	0.979570i	$-0.435547\pi$
$661$	6835.28	0.402211	0.201106	+	0.979570i	$0.435547\pi$
$662$	15620.7	0.917094
$663$	−5223.03	−0.305951
$664$	55645.3	3.25219
$665$	−2436.81	−0.142099
$666$	52296.5	3.04271
$667$	−3935.86	−0.228481
$668$	−9201.46	−0.532957
$669$	−489.706	−0.0283006
$670$	−19371.8	−1.11701
$671$	976.200	0.0561636
$672$	−3304.64	−0.189701
$673$	−22296.1	−1.27705	−0.638523	−	0.769603i	$-0.720454\pi$
$673$	−22296.1	−1.27705	−0.638523	+	0.769603i	$0.720454\pi$
$674$	−11670.2	−0.666941
$675$	−2827.90	−0.161253
$676$	81057.9	4.61185
$677$	−18268.1	−1.03708	−0.518538	−	0.855055i	$-0.673523\pi$
$677$	−18268.1	−1.03708	−0.518538	+	0.855055i	$0.673523\pi$
$678$	−2152.61	−0.121933
$679$	−412.968	−0.0233406
$680$	52428.8	2.95669
$681$	226.195	0.0127281
$682$	−48583.9	−2.72782
$683$	−31781.6	−1.78051	−0.890256	−	0.455460i	$-0.849475\pi$
$683$	−31781.6	−1.78051	−0.890256	+	0.455460i	$0.849475\pi$
$684$	−13692.5	−0.765420
$685$	19410.3	1.08267
$686$	−1818.94	−0.101235
$687$	1800.47	0.0999888
$688$	−62942.5	−3.48788
$689$	25022.8	1.38359
$690$	−1731.04	−0.0955064
$691$	−23032.7	−1.26803	−0.634014	−	0.773322i	$-0.718594\pi$
$691$	−23032.7	−1.26803	−0.634014	+	0.773322i	$0.718594\pi$
$692$	7283.65	0.400120
$693$	−6021.39	−0.330063
$694$	−29184.7	−1.59630
$695$	−36449.9	−1.98939
$696$	11806.6	0.643002
$697$	21270.4	1.15591
$698$	−9169.11	−0.497215
$699$	2240.61	0.121241
$700$	−7022.52	−0.379180
$701$	29844.6	1.60801	0.804006	−	0.594621i	$-0.202698\pi$
$701$	29844.6	1.60801	0.804006	+	0.594621i	$0.202698\pi$
$702$	23732.7	1.27597
$703$	−10043.9	−0.538854
$704$	−29725.0	−1.59134
$705$	3713.66	0.198389
$706$	−51282.6	−2.73377
$707$	2526.92	0.134419
$708$	−5275.32	−0.280026
$709$	5462.65	0.289357	0.144679	−	0.989479i	$-0.453785\pi$
$709$	5462.65	0.289357	0.144679	+	0.989479i	$0.453785\pi$
$710$	56009.8	2.96058
$711$	−16320.8	−0.860871
$712$	−57619.8	−3.03286
$713$	−6331.78	−0.332576
$714$	−2457.33	−0.128800
$715$	34721.0	1.81607
$716$	64704.6	3.37727
$717$	48.9436	0.00254928
$718$	13221.9	0.687236
$719$	30493.4	1.58166	0.790829	−	0.612038i	$-0.209650\pi$
$719$	30493.4	1.58166	0.790829	+	0.612038i	$0.209650\pi$
$720$	−61496.7	−3.18312
$721$	6439.12	0.332601
$722$	−32698.2	−1.68546
$723$	−5699.56	−0.293180
$724$	52472.6	2.69355
$725$	8531.66	0.437045
$726$	−1272.12	−0.0650314
$727$	19889.3	1.01465	0.507326	−	0.861754i	$-0.330634\pi$
$727$	19889.3	1.01465	0.507326	+	0.861754i	$0.330634\pi$
$728$	35504.1	1.80752
$729$	−14822.1	−0.753038
$730$	23085.9	1.17047
$731$	−21576.9	−1.09173
$732$	−633.512	−0.0319881
$733$	5240.27	0.264057	0.132029	−	0.991246i	$-0.457851\pi$
$733$	5240.27	0.264057	0.132029	+	0.991246i	$0.457851\pi$
$734$	−11894.2	−0.598124
$735$	695.426	0.0348995
$736$	−10116.7	−0.506668
$737$	9193.41	0.459489
$738$	−47271.4	−2.35784
$739$	18395.1	0.915664	0.457832	−	0.889039i	$-0.348626\pi$
$739$	18395.1	0.915664	0.457832	+	0.889039i	$0.348626\pi$
$740$	−101516.	−5.04298
$741$	−2229.34	−0.110522
$742$	11772.7	0.582468
$743$	−4710.74	−0.232598	−0.116299	−	0.993214i	$-0.537103\pi$
$743$	−4710.74	−0.232598	−0.116299	+	0.993214i	$0.537103\pi$
$744$	18993.8	0.935950
$745$	32675.9	1.60692
$746$	−52938.4	−2.59814
$747$	−22374.6	−1.09591
$748$	−41302.0	−2.01892
$749$	−12242.3	−0.597227
$750$	−5655.48	−0.275345
$751$	−19802.3	−0.962178	−0.481089	−	0.876672i	$-0.659759\pi$
$751$	−19802.3	−0.962178	−0.481089	+	0.876672i	$0.659759\pi$
$752$	47079.3	2.28299
$753$	−1822.22	−0.0881878
$754$	−71600.4	−3.45827
$755$	−16171.8	−0.779539
$756$	7989.39	0.384354
$757$	13257.1	0.636508	0.318254	−	0.948005i	$-0.396903\pi$
$757$	13257.1	0.636508	0.318254	+	0.948005i	$0.396903\pi$
$758$	55166.5	2.64345
$759$	821.508	0.0392870
$760$	22378.2	1.06808
$761$	825.676	0.0393308	0.0196654	−	0.999807i	$-0.493740\pi$
$761$	825.676	0.0393308	0.0196654	+	0.999807i	$0.493740\pi$
$762$	8549.06	0.406430
$763$	13593.7	0.644985
$764$	2013.08	0.0953282
$765$	−21081.3	−0.996334
$766$	−32091.1	−1.51371
$767$	19272.7	0.907297
$768$	−737.820	−0.0346664
$769$	−11060.2	−0.518651	−0.259325	−	0.965790i	$-0.583500\pi$
$769$	−11060.2	−0.518651	−0.259325	+	0.965790i	$0.583500\pi$
$770$	16335.5	0.764534
$771$	4035.61	0.188507
$772$	36305.2	1.69256
$773$	−13681.2	−0.636581	−0.318290	−	0.947993i	$-0.603109\pi$
$773$	−13681.2	−0.636581	−0.318290	+	0.947993i	$0.603109\pi$
$774$	47952.7	2.22691
$775$	13725.2	0.636161
$776$	3792.45	0.175439
$777$	2866.37	0.132343
$778$	−24785.6	−1.14217
$779$	9078.83	0.417565
$780$	−22532.4	−1.03435
$781$	−26580.9	−1.21785
$782$	−7522.80	−0.344009
$783$	−9706.31	−0.443008
$784$	8816.14	0.401610
$785$	−9003.59	−0.409365
$786$	9744.87	0.442224
$787$	−32029.0	−1.45071	−0.725357	−	0.688373i	$-0.758325\pi$
$787$	−32029.0	−1.45071	−0.725357	+	0.688373i	$0.758325\pi$
$788$	−107470.	−4.85847
$789$	−5131.60	−0.231546
$790$	44277.1	1.99406
$791$	2647.44	0.119004
$792$	55296.7	2.48091
$793$	2314.45	0.103643
$794$	70121.7	3.13416
$795$	−4501.02	−0.200798
$796$	66106.7	2.94358
$797$	31893.7	1.41748	0.708741	−	0.705469i	$-0.249263\pi$
$797$	31893.7	1.41748	0.708741	+	0.705469i	$0.249263\pi$
$798$	−1048.86	−0.0465280
$799$	16139.0	0.714588
$800$	21929.8	0.969169
$801$	23168.6	1.02200
$802$	−69172.5	−3.04559
$803$	−10956.0	−0.481481
$804$	−5966.13	−0.261703
$805$	2128.96	0.0932122
$806$	−115187.	−5.03384
$807$	−6402.30	−0.279271
$808$	−23205.7	−1.01036
$809$	−7163.61	−0.311322	−0.155661	−	0.987811i	$-0.549751\pi$
$809$	−7163.61	−0.311322	−0.155661	+	0.987811i	$0.549751\pi$
$810$	44670.2	1.93772
$811$	−18347.8	−0.794423	−0.397212	−	0.917727i	$-0.630022\pi$
$811$	−18347.8	−0.794423	−0.397212	+	0.917727i	$0.630022\pi$
$812$	−24103.6	−1.04171
$813$	3175.66	0.136993
$814$	67331.0	2.89920
$815$	−29557.5	−1.27037
$816$	11910.3	0.510963
$817$	−9209.69	−0.394377
$818$	−39833.1	−1.70260
$819$	−14276.0	−0.609089
$820$	91761.5	3.90787
$821$	−26934.9	−1.14499	−0.572494	−	0.819909i	$-0.694024\pi$
$821$	−26934.9	−1.14499	−0.572494	+	0.819909i	$0.694024\pi$
$822$	8354.64	0.354503
$823$	−3763.90	−0.159418	−0.0797092	−	0.996818i	$-0.525399\pi$
$823$	−3763.90	−0.159418	−0.0797092	+	0.996818i	$0.525399\pi$
$824$	−59132.8	−2.49999
$825$	−1780.76	−0.0751493
$826$	9067.43	0.381957
$827$	−32630.4	−1.37203	−0.686015	−	0.727587i	$-0.740642\pi$
$827$	−32630.4	−1.37203	−0.686015	+	0.727587i	$0.740642\pi$
$828$	11962.7	0.502092
$829$	10237.6	0.428911	0.214455	−	0.976734i	$-0.431202\pi$
$829$	10237.6	0.428911	0.214455	+	0.976734i	$0.431202\pi$
$830$	60700.5	2.53849
$831$	−3377.78	−0.141004
$832$	−70474.6	−2.93662
$833$	3022.21	0.125706
$834$	−15688.9	−0.651394
$835$	−6046.79	−0.250608
$836$	−17629.0	−0.729318
$837$	−15615.0	−0.644841
$838$	21521.0	0.887147
$839$	39454.8	1.62352	0.811758	−	0.583995i	$-0.198511\pi$
$839$	39454.8	1.62352	0.811758	+	0.583995i	$0.198511\pi$
$840$	−6386.36	−0.262322
$841$	4894.51	0.200685
$842$	7905.86	0.323579
$843$	−1151.90	−0.0470622
$844$	−38102.7	−1.55397
$845$	53267.6	2.16859
$846$	−35867.4	−1.45762
$847$	1564.55	0.0634693
$848$	−57060.9	−2.31071
$849$	4329.42	0.175012
$850$	16307.0	0.658030
$851$	8775.03	0.353471
$852$	17249.9	0.693628
$853$	18731.3	0.751874	0.375937	−	0.926645i	$-0.377321\pi$
$853$	18731.3	0.751874	0.375937	+	0.926645i	$0.377321\pi$
$854$	1088.90	0.0436318
$855$	−8998.13	−0.359918
$856$	112426.	4.48905
$857$	16359.9	0.652091	0.326046	−	0.945354i	$-0.394284\pi$
$857$	16359.9	0.652091	0.326046	+	0.945354i	$0.394284\pi$
$858$	14944.7	0.594644
$859$	38453.0	1.52736	0.763678	−	0.645597i	$-0.223391\pi$
$859$	38453.0	1.52736	0.763678	+	0.645597i	$0.223391\pi$
$860$	−93084.1	−3.69086
$861$	−2590.95	−0.102554
$862$	−37640.5	−1.48728
$863$	19604.0	0.773264	0.386632	−	0.922234i	$-0.373638\pi$
$863$	19604.0	0.773264	0.386632	+	0.922234i	$0.373638\pi$
$864$	−24949.1	−0.982391
$865$	4786.49	0.188145
$866$	−14286.1	−0.560580
$867$	−1190.12	−0.0466189
$868$	−38776.5	−1.51631
$869$	−21012.8	−0.820267
$870$	12879.2	0.501893
$871$	21796.5	0.847928
$872$	−124836.	−4.84802
$873$	−1524.92	−0.0591188
$874$	−3210.96	−0.124270
$875$	6955.53	0.268731
$876$	7109.97	0.274228
$877$	−39580.7	−1.52400	−0.761998	−	0.647580i	$-0.775781\pi$
$877$	−39580.7	−1.52400	−0.761998	+	0.647580i	$0.775781\pi$
$878$	83655.7	3.21554
$879$	−9337.00	−0.358281
$880$	−79176.1	−3.03298
$881$	35741.9	1.36683	0.683413	−	0.730032i	$-0.260495\pi$
$881$	35741.9	1.36683	0.683413	+	0.730032i	$0.260495\pi$
$882$	−6716.57	−0.256416
$883$	−11289.5	−0.430262	−0.215131	−	0.976585i	$-0.569018\pi$
$883$	−11289.5	−0.430262	−0.215131	+	0.976585i	$0.569018\pi$
$884$	−97922.2	−3.72566
$885$	−3466.71	−0.131675
$886$	70873.5	2.68741
$887$	−4125.49	−0.156167	−0.0780837	−	0.996947i	$-0.524880\pi$
$887$	−4125.49	−0.156167	−0.0780837	+	0.996947i	$0.524880\pi$
$888$	−26323.0	−0.994754
$889$	−10514.3	−0.396667
$890$	−62854.4	−2.36729
$891$	−21199.4	−0.797090
$892$	−9181.09	−0.344625
$893$	6888.60	0.258139
$894$	14064.5	0.526160
$895$	42521.0	1.58807
$896$	−8524.85	−0.317852
$897$	1947.70	0.0724992
$898$	33612.7	1.24908
$899$	47109.6	1.74771
$900$	−25931.2	−0.960415
$901$	−19560.7	−0.723264
$902$	−60861.3	−2.24663
$903$	2628.29	0.0968594
$904$	−24312.4	−0.894490
$905$	34482.7	1.26657
$906$	−6960.72	−0.255248
$907$	19400.9	0.710250	0.355125	−	0.934819i	$-0.384438\pi$
$907$	19400.9	0.710250	0.355125	+	0.934819i	$0.384438\pi$
$908$	4240.74	0.154993
$909$	9330.85	0.340467
$910$	38729.6	1.41085
$911$	31001.4	1.12747	0.563734	−	0.825956i	$-0.309364\pi$
$911$	31001.4	1.12747	0.563734	+	0.825956i	$0.309364\pi$
$912$	5083.69	0.184581
$913$	−28807.0	−1.04422
$914$	6566.07	0.237622
$915$	−416.316	−0.0150415
$916$	33755.6	1.21759
$917$	−11985.0	−0.431602
$918$	−18552.2	−0.667007
$919$	1160.59	0.0416587	0.0208294	−	0.999783i	$-0.493369\pi$
$919$	1160.59	0.0416587	0.0208294	+	0.999783i	$0.493369\pi$
$920$	−19551.0	−0.700628
$921$	10373.9	0.371154
$922$	49892.7	1.78214
$923$	−63020.2	−2.24738
$924$	5031.01	0.179121
$925$	−19021.4	−0.676130
$926$	20261.0	0.719027
$927$	23777.0	0.842435
$928$	75270.4	2.66258
$929$	−41683.2	−1.47210	−0.736051	−	0.676926i	$-0.763311\pi$
$929$	−41683.2	−1.47210	−0.736051	+	0.676926i	$0.763311\pi$
$930$	20719.3	0.730553
$931$	1289.97	0.0454103
$932$	42007.3	1.47639
$933$	−1781.82	−0.0625233
$934$	−40439.4	−1.41672
$935$	−27141.9	−0.949341
$936$	131102.	4.57821
$937$	−38732.1	−1.35040	−0.675198	−	0.737637i	$-0.735942\pi$
$937$	−38732.1	−1.35040	−0.675198	+	0.737637i	$0.735942\pi$
$938$	10254.8	0.356963
$939$	3800.53	0.132082
$940$	69624.4	2.41585
$941$	−18080.0	−0.626345	−0.313173	−	0.949696i	$-0.601392\pi$
$941$	−18080.0	−0.626345	−0.313173	+	0.949696i	$0.601392\pi$
$942$	−3875.36	−0.134040
$943$	−7931.85	−0.273910
$944$	−43948.6	−1.51526
$945$	5250.27	0.180732
$946$	61738.5	2.12187
$947$	−6401.43	−0.219661	−0.109830	−	0.993950i	$-0.535031\pi$
$947$	−6401.43	−0.219661	−0.109830	+	0.993950i	$0.535031\pi$
$948$	13636.4	0.467184
$949$	−25975.4	−0.888511
$950$	6960.31	0.237708
$951$	3547.97	0.120979
$952$	−27754.1	−0.944869
$953$	−30907.1	−1.05055	−0.525277	−	0.850931i	$-0.676038\pi$
$953$	−30907.1	−1.05055	−0.525277	+	0.850931i	$0.676038\pi$
$954$	43471.8	1.47532
$955$	1322.91	0.0448255
$956$	917.603	0.0310433
$957$	−6112.17	−0.206456
$958$	58237.2	1.96405
$959$	−10275.2	−0.345988
$960$	12676.7	0.426187
$961$	45996.2	1.54396
$962$	159634.	5.35010
$963$	−45205.6	−1.51270
$964$	−106856.	−3.57014
$965$	23858.2	0.795878
$966$	916.354	0.0305209
$967$	25704.4	0.854805	0.427402	−	0.904061i	$-0.359429\pi$
$967$	25704.4	0.854805	0.427402	+	0.904061i	$0.359429\pi$
$968$	−14367.8	−0.477066
$969$	1742.71	0.0577749
$970$	4136.98	0.136939
$971$	−31129.1	−1.02881	−0.514407	−	0.857546i	$-0.671988\pi$
$971$	−31129.1	−1.02881	−0.514407	+	0.857546i	$0.671988\pi$
$972$	44573.7	1.47089
$973$	19295.4	0.635747
$974$	95283.6	3.13458
$975$	−4221.98	−0.138678
$976$	−5277.77	−0.173092
$977$	28515.3	0.933761	0.466881	−	0.884320i	$-0.345378\pi$
$977$	28515.3	0.933761	0.466881	+	0.884320i	$0.345378\pi$
$978$	−12722.2	−0.415964
$979$	29829.2	0.973796
$980$	13038.0	0.424982
$981$	50195.7	1.63366
$982$	2507.61	0.0814880
$983$	−505.010	−0.0163859	−0.00819293	−	0.999966i	$-0.502608\pi$
$983$	−505.010	−0.0163859	−0.00819293	+	0.999966i	$0.502608\pi$
$984$	23793.7	0.770848
$985$	−70624.7	−2.28456
$986$	55971.0	1.80779
$987$	−1965.89	−0.0633992
$988$	−41796.1	−1.34586
$989$	8046.18	0.258699
$990$	60320.3	1.93647
$991$	6105.83	0.195720	0.0978598	−	0.995200i	$-0.468800\pi$
$991$	6105.83	0.195720	0.0978598	+	0.995200i	$0.468800\pi$
$992$	121091.	3.87563
$993$	3161.48	0.101034
$994$	−29649.8	−0.946110
$995$	43442.4	1.38414
$996$	18694.5	0.594737
$997$	−26216.8	−0.832794	−0.416397	−	0.909183i	$-0.636707\pi$
$997$	−26216.8	−0.832794	−0.416397	+	0.909183i	$0.636707\pi$
$998$	57482.7	1.82323
$999$	21640.3	0.685355

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.a.c.1.9	✓	9
3.2	odd	2		1449.4.a.n.1.1		9
7.6	odd	2		1127.4.a.f.1.9		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.a.c.1.9	✓	9	1.1	even	1	trivial
1127.4.a.f.1.9		9	7.6	odd	2
1449.4.a.n.1.1		9	3.2	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:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.a (trivial)

\(f(q)\)	\(=\)	\(q+5.30303 q^{2} +1.07328 q^{3} +20.1221 q^{4} +13.2233 q^{5} +5.69164 q^{6} -7.00000 q^{7} +64.2837 q^{8} -25.8481 q^{9} +O(q^{10})\)	\(q+5.30303 q^{2} +1.07328 q^{3} +20.1221 q^{4} +13.2233 q^{5} +5.69164 q^{6} -7.00000 q^{7} +64.2837 q^{8} -25.8481 q^{9} +70.1237 q^{10} -33.2790 q^{11} +21.5967 q^{12} -78.9006 q^{13} -37.1212 q^{14} +14.1924 q^{15} +179.921 q^{16} +61.6777 q^{17} -137.073 q^{18} +26.3259 q^{19} +266.081 q^{20} -7.51297 q^{21} -176.479 q^{22} -23.0000 q^{23} +68.9945 q^{24} +49.8565 q^{25} -418.412 q^{26} -56.7209 q^{27} -140.855 q^{28} +171.124 q^{29} +75.2624 q^{30} +275.295 q^{31} +439.858 q^{32} -35.7178 q^{33} +327.078 q^{34} -92.5633 q^{35} -520.117 q^{36} -381.523 q^{37} +139.607 q^{38} -84.6826 q^{39} +850.044 q^{40} +344.863 q^{41} -39.8415 q^{42} -349.834 q^{43} -669.643 q^{44} -341.798 q^{45} -121.970 q^{46} +261.666 q^{47} +193.106 q^{48} +49.0000 q^{49} +264.390 q^{50} +66.1975 q^{51} -1587.64 q^{52} -317.144 q^{53} -300.792 q^{54} -440.060 q^{55} -449.986 q^{56} +28.2551 q^{57} +907.476 q^{58} -244.266 q^{59} +285.580 q^{60} -29.3338 q^{61} +1459.89 q^{62} +180.936 q^{63} +893.207 q^{64} -1043.33 q^{65} -189.412 q^{66} -276.252 q^{67} +1241.08 q^{68} -24.6855 q^{69} -490.866 q^{70} +798.729 q^{71} -1661.61 q^{72} +329.217 q^{73} -2023.23 q^{74} +53.5101 q^{75} +529.732 q^{76} +232.953 q^{77} -449.074 q^{78} +631.414 q^{79} +2379.16 q^{80} +637.020 q^{81} +1828.82 q^{82} +865.620 q^{83} -151.177 q^{84} +815.585 q^{85} -1855.18 q^{86} +183.665 q^{87} -2139.30 q^{88} -896.337 q^{89} -1812.56 q^{90} +552.304 q^{91} -462.808 q^{92} +295.469 q^{93} +1387.62 q^{94} +348.116 q^{95} +472.091 q^{96} +58.9955 q^{97} +259.848 q^{98} +860.198 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{3} + 48 q^{4} - 4 q^{5} + 46 q^{6} - 63 q^{7} + 66 q^{8} + 122 q^{9}+O(q^{10}) \) 9 * q + 9 * q^3 + 48 * q^4 - 4 * q^5 + 46 * q^6 - 63 * q^7 + 66 * q^8 + 122 * q^9	\( 9 q + 9 q^{3} + 48 q^{4} - 4 q^{5} + 46 q^{6} - 63 q^{7} + 66 q^{8} + 122 q^{9} + 50 q^{10} - 8 q^{11} + 220 q^{12} + 25 q^{13} + 88 q^{15} + 180 q^{16} - 28 q^{17} - 54 q^{18} + 254 q^{19} + 302 q^{20} - 63 q^{21} - 122 q^{22} - 207 q^{23} + 624 q^{24} + 295 q^{25} - 6 q^{26} + 633 q^{27} - 336 q^{28} + 25 q^{29} + 80 q^{30} + 1171 q^{31} + 1018 q^{32} + 272 q^{33} + 8 q^{34} + 28 q^{35} + 72 q^{36} + 70 q^{37} + 282 q^{38} + 1185 q^{39} - 54 q^{40} + 221 q^{41} - 322 q^{42} - 42 q^{43} - 1214 q^{44} + 698 q^{45} + 159 q^{47} - 1104 q^{48} + 441 q^{49} - 1680 q^{50} + 308 q^{51} - 664 q^{52} - 774 q^{53} - 2674 q^{54} + 1498 q^{55} - 462 q^{56} - 2524 q^{57} + 842 q^{58} + 1080 q^{59} - 2160 q^{60} + 686 q^{61} - 2078 q^{62} - 854 q^{63} - 1260 q^{64} - 1656 q^{65} + 532 q^{66} - 370 q^{67} - 1936 q^{68} - 207 q^{69} - 350 q^{70} + 1035 q^{71} - 722 q^{72} + 1979 q^{73} - 5494 q^{74} - 1459 q^{75} + 206 q^{76} + 56 q^{77} - 2066 q^{78} + 2336 q^{79} - 242 q^{80} + 997 q^{81} + 1642 q^{82} + 130 q^{83} - 1540 q^{84} - 272 q^{85} - 1906 q^{86} - 581 q^{87} - 3742 q^{88} - 1328 q^{89} - 7650 q^{90} - 175 q^{91} - 1104 q^{92} + 1305 q^{93} + 6078 q^{94} - 484 q^{95} - 136 q^{96} - 104 q^{97} - 618 q^{99}+O(q^{100}) \) 9 * q + 9 * q^3 + 48 * q^4 - 4 * q^5 + 46 * q^6 - 63 * q^7 + 66 * q^8 + 122 * q^9 + 50 * q^10 - 8 * q^11 + 220 * q^12 + 25 * q^13 + 88 * q^15 + 180 * q^16 - 28 * q^17 - 54 * q^18 + 254 * q^19 + 302 * q^20 - 63 * q^21 - 122 * q^22 - 207 * q^23 + 624 * q^24 + 295 * q^25 - 6 * q^26 + 633 * q^27 - 336 * q^28 + 25 * q^29 + 80 * q^30 + 1171 * q^31 + 1018 * q^32 + 272 * q^33 + 8 * q^34 + 28 * q^35 + 72 * q^36 + 70 * q^37 + 282 * q^38 + 1185 * q^39 - 54 * q^40 + 221 * q^41 - 322 * q^42 - 42 * q^43 - 1214 * q^44 + 698 * q^45 + 159 * q^47 - 1104 * q^48 + 441 * q^49 - 1680 * q^50 + 308 * q^51 - 664 * q^52 - 774 * q^53 - 2674 * q^54 + 1498 * q^55 - 462 * q^56 - 2524 * q^57 + 842 * q^58 + 1080 * q^59 - 2160 * q^60 + 686 * q^61 - 2078 * q^62 - 854 * q^63 - 1260 * q^64 - 1656 * q^65 + 532 * q^66 - 370 * q^67 - 1936 * q^68 - 207 * q^69 - 350 * q^70 + 1035 * q^71 - 722 * q^72 + 1979 * q^73 - 5494 * q^74 - 1459 * q^75 + 206 * q^76 + 56 * q^77 - 2066 * q^78 + 2336 * q^79 - 242 * q^80 + 997 * q^81 + 1642 * q^82 + 130 * q^83 - 1540 * q^84 - 272 * q^85 - 1906 * q^86 - 581 * q^87 - 3742 * q^88 - 1328 * q^89 - 7650 * q^90 - 175 * q^91 - 1104 * q^92 + 1305 * q^93 + 6078 * q^94 - 484 * q^95 - 136 * q^96 - 104 * q^97 - 618 * q^99

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