LMFDB - Embedded newform 1849.4.a.i.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.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:	$109.094531601$
Analytic rank:	$1$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.26350 q^{2} -9.40007 q^{3} -6.40356 q^{4} -0.325119 q^{5} +11.8770 q^{6} -8.80478 q^{7} +18.1989 q^{8} +61.3613 q^{9} +O(q^{10})$	\(q-1.26350 q^{2} -9.40007 q^{3} -6.40356 q^{4} -0.325119 q^{5} +11.8770 q^{6} -8.80478 q^{7} +18.1989 q^{8} +61.3613 q^{9} +0.410789 q^{10} -23.6733 q^{11} +60.1939 q^{12} -23.2530 q^{13} +11.1249 q^{14} +3.05614 q^{15} +28.2341 q^{16} -125.680 q^{17} -77.5301 q^{18} -16.8288 q^{19} +2.08192 q^{20} +82.7656 q^{21} +29.9113 q^{22} +127.751 q^{23} -171.071 q^{24} -124.894 q^{25} +29.3802 q^{26} -322.998 q^{27} +56.3820 q^{28} +220.686 q^{29} -3.86145 q^{30} -303.073 q^{31} -181.265 q^{32} +222.531 q^{33} +158.797 q^{34} +2.86261 q^{35} -392.931 q^{36} -245.352 q^{37} +21.2632 q^{38} +218.580 q^{39} -5.91683 q^{40} +185.397 q^{41} -104.574 q^{42} +151.594 q^{44} -19.9497 q^{45} -161.414 q^{46} -1.86186 q^{47} -265.403 q^{48} -265.476 q^{49} +157.804 q^{50} +1181.40 q^{51} +148.902 q^{52} +261.722 q^{53} +408.109 q^{54} +7.69666 q^{55} -160.238 q^{56} +158.192 q^{57} -278.837 q^{58} -417.774 q^{59} -19.5702 q^{60} +699.788 q^{61} +382.934 q^{62} -540.273 q^{63} +3.15625 q^{64} +7.56001 q^{65} -281.168 q^{66} -279.849 q^{67} +804.800 q^{68} -1200.87 q^{69} -3.61691 q^{70} +675.761 q^{71} +1116.71 q^{72} +1029.66 q^{73} +310.002 q^{74} +1174.01 q^{75} +107.764 q^{76} +208.439 q^{77} -276.176 q^{78} -732.866 q^{79} -9.17946 q^{80} +1379.45 q^{81} -234.250 q^{82} +1094.07 q^{83} -529.994 q^{84} +40.8610 q^{85} -2074.46 q^{87} -430.829 q^{88} +200.368 q^{89} +25.2065 q^{90} +204.738 q^{91} -818.061 q^{92} +2848.91 q^{93} +2.35247 q^{94} +5.47136 q^{95} +1703.91 q^{96} +1442.40 q^{97} +335.429 q^{98} -1452.63 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) $ 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9} - 137 q^{10} - 252 q^{11} - 48 q^{12} - 192 q^{13} - 272 q^{14} - 314 q^{15} + 542 q^{16} - 236 q^{17} - 386 q^{18} + 12 q^{19} + 108 q^{20} - 408 q^{21} + 1235 q^{22} - 630 q^{23} - 613 q^{24} + 1098 q^{25} + 1493 q^{26} + 10 q^{27} - 242 q^{28} + 208 q^{29} - 48 q^{30} - 932 q^{31} - 1124 q^{32} + 254 q^{33} + 765 q^{34} - 1452 q^{35} + 747 q^{36} - 90 q^{37} - 1213 q^{38} - 1610 q^{39} - 1693 q^{40} - 1354 q^{41} - 16 q^{42} - 2704 q^{44} + 4508 q^{45} + 233 q^{46} - 3484 q^{47} - 376 q^{48} + 1324 q^{49} - 408 q^{50} + 4054 q^{51} - 2176 q^{52} - 726 q^{53} - 6497 q^{54} - 3288 q^{55} - 7097 q^{56} - 870 q^{57} + 275 q^{58} - 4370 q^{59} - 3891 q^{60} + 1172 q^{61} - 1546 q^{62} - 3686 q^{63} + 606 q^{64} + 2610 q^{65} - 4697 q^{66} - 344 q^{67} - 3221 q^{68} + 136 q^{69} - 1310 q^{70} + 162 q^{71} - 5814 q^{72} + 746 q^{73} - 4332 q^{74} + 236 q^{75} + 1338 q^{76} + 2024 q^{77} - 2782 q^{78} - 2656 q^{79} - 5713 q^{80} - 86 q^{81} - 4168 q^{82} - 3514 q^{83} - 4269 q^{84} - 7558 q^{85} - 10278 q^{87} + 11692 q^{88} + 2640 q^{89} - 8286 q^{90} - 5946 q^{91} - 4271 q^{92} - 2 q^{93} + 9062 q^{94} - 12140 q^{95} - 700 q^{96} - 3864 q^{97} - 2826 q^{98} - 8174 q^{99}+O(q^{100}) \) 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9 - 137 * q^10 - 252 * q^11 - 48 * q^12 - 192 * q^13 - 272 * q^14 - 314 * q^15 + 542 * q^16 - 236 * q^17 - 386 * q^18 + 12 * q^19 + 108 * q^20 - 408 * q^21 + 1235 * q^22 - 630 * q^23 - 613 * q^24 + 1098 * q^25 + 1493 * q^26 + 10 * q^27 - 242 * q^28 + 208 * q^29 - 48 * q^30 - 932 * q^31 - 1124 * q^32 + 254 * q^33 + 765 * q^34 - 1452 * q^35 + 747 * q^36 - 90 * q^37 - 1213 * q^38 - 1610 * q^39 - 1693 * q^40 - 1354 * q^41 - 16 * q^42 - 2704 * q^44 + 4508 * q^45 + 233 * q^46 - 3484 * q^47 - 376 * q^48 + 1324 * q^49 - 408 * q^50 + 4054 * q^51 - 2176 * q^52 - 726 * q^53 - 6497 * q^54 - 3288 * q^55 - 7097 * q^56 - 870 * q^57 + 275 * q^58 - 4370 * q^59 - 3891 * q^60 + 1172 * q^61 - 1546 * q^62 - 3686 * q^63 + 606 * q^64 + 2610 * q^65 - 4697 * q^66 - 344 * q^67 - 3221 * q^68 + 136 * q^69 - 1310 * q^70 + 162 * q^71 - 5814 * q^72 + 746 * q^73 - 4332 * q^74 + 236 * q^75 + 1338 * q^76 + 2024 * q^77 - 2782 * q^78 - 2656 * q^79 - 5713 * q^80 - 86 * q^81 - 4168 * q^82 - 3514 * q^83 - 4269 * q^84 - 7558 * q^85 - 10278 * q^87 + 11692 * q^88 + 2640 * q^89 - 8286 * q^90 - 5946 * q^91 - 4271 * q^92 - 2 * q^93 + 9062 * q^94 - 12140 * q^95 - 700 * q^96 - 3864 * q^97 - 2826 * q^98 - 8174 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.26350	−0.446715	−0.223358	−	0.974737i	$-0.571702\pi$
$2$	−1.26350	−0.446715	−0.223358	+	0.974737i	$0.571702\pi$
$3$	−9.40007	−1.80904	−0.904522	−	0.426427i	$-0.859772\pi$
$3$	−9.40007	−1.80904	−0.904522	+	0.426427i	$0.859772\pi$
$4$	−6.40356	−0.800445
$5$	−0.325119	−0.0290796	−0.0145398	−	0.999894i	$-0.504628\pi$
$5$	−0.325119	−0.0290796	−0.0145398	+	0.999894i	$0.504628\pi$
$6$	11.8770	0.808128
$7$	−8.80478	−0.475414	−0.237707	−	0.971337i	$-0.576396\pi$
$7$	−8.80478	−0.475414	−0.237707	+	0.971337i	$0.576396\pi$
$8$	18.1989	0.804287
$9$	61.3613	2.27264
$10$	0.410789	0.0129903
$11$	−23.6733	−0.648889	−0.324444	−	0.945905i	$-0.605177\pi$
$11$	−23.6733	−0.648889	−0.324444	+	0.945905i	$0.605177\pi$
$12$	60.1939	1.44804
$13$	−23.2530	−0.496095	−0.248047	−	0.968748i	$-0.579789\pi$
$13$	−23.2530	−0.496095	−0.248047	+	0.968748i	$0.579789\pi$
$14$	11.1249	0.212375
$15$	3.05614	0.0526062
$16$	28.2341	0.441158
$17$	−125.680	−1.79305	−0.896526	−	0.442991i	$-0.853917\pi$
$17$	−125.680	−1.79305	−0.896526	+	0.442991i	$0.853917\pi$
$18$	−77.5301	−1.01522
$19$	−16.8288	−0.203199	−0.101600	−	0.994825i	$-0.532396\pi$
$19$	−16.8288	−0.203199	−0.101600	+	0.994825i	$0.532396\pi$
$20$	2.08192	0.0232766
$21$	82.7656	0.860044
$22$	29.9113	0.289869
$23$	127.751	1.15817	0.579085	−	0.815267i	$-0.303410\pi$
$23$	127.751	1.15817	0.579085	+	0.815267i	$0.303410\pi$
$24$	−171.071	−1.45499
$25$	−124.894	−0.999154
$26$	29.3802	0.221613
$27$	−322.998	−2.30226
$28$	56.3820	0.380543
$29$	220.686	1.41311	0.706556	−	0.707657i	$-0.250248\pi$
$29$	220.686	1.41311	0.706556	+	0.707657i	$0.250248\pi$
$30$	−3.86145	−0.0235000
$31$	−303.073	−1.75592	−0.877961	−	0.478733i	$-0.841096\pi$
$31$	−303.073	−1.75592	−0.877961	+	0.478733i	$0.841096\pi$
$32$	−181.265	−1.00136
$33$	222.531	1.17387
$34$	158.797	0.800984
$35$	2.86261	0.0138248
$36$	−392.931	−1.81912
$37$	−245.352	−1.09015	−0.545075	−	0.838387i	$-0.683499\pi$
$37$	−245.352	−1.09015	−0.545075	+	0.838387i	$0.683499\pi$
$38$	21.2632	0.0907722
$39$	218.580	0.897457
$40$	−5.91683	−0.0233883
$41$	185.397	0.706200	0.353100	−	0.935586i	$-0.385127\pi$
$41$	185.397	0.706200	0.353100	+	0.935586i	$0.385127\pi$
$42$	−104.574	−0.384195
$43$	0	0
$43$	0	0
$44$	151.594	0.519400
$45$	−19.9497	−0.0660874
$46$	−161.414	−0.517372
$47$	−1.86186	−0.00577831	−0.00288915	−	0.999996i	$-0.500920\pi$
$47$	−1.86186	−0.00577831	−0.00288915	+	0.999996i	$0.500920\pi$
$48$	−265.403	−0.798074
$49$	−265.476	−0.773982
$50$	157.804	0.446338
$51$	1181.40	3.24371
$52$	148.902	0.397097
$53$	261.722	0.678307	0.339153	−	0.940731i	$-0.389859\pi$
$53$	261.722	0.678307	0.339153	+	0.940731i	$0.389859\pi$
$54$	408.109	1.02845
$55$	7.69666	0.0188694
$56$	−160.238	−0.382369
$57$	158.192	0.367596
$58$	−278.837	−0.631259
$59$	−417.774	−0.921857	−0.460929	−	0.887437i	$-0.652484\pi$
$59$	−417.774	−0.921857	−0.460929	+	0.887437i	$0.652484\pi$
$60$	−19.5702	−0.0421084
$61$	699.788	1.46883	0.734416	−	0.678700i	$-0.237456\pi$
$61$	699.788	1.46883	0.734416	+	0.678700i	$0.237456\pi$
$62$	382.934	0.784397
$63$	−540.273	−1.08044
$64$	3.15625	0.00616454
$65$	7.56001	0.0144262
$66$	−281.168	−0.524385
$67$	−279.849	−0.510284	−0.255142	−	0.966904i	$-0.582122\pi$
$67$	−279.849	−0.510284	−0.255142	+	0.966904i	$0.582122\pi$
$68$	804.800	1.43524
$69$	−1200.87	−2.09518
$70$	−3.61691	−0.00617576
$71$	675.761	1.12955	0.564776	−	0.825245i	$-0.308963\pi$
$71$	675.761	1.12955	0.564776	+	0.825245i	$0.308963\pi$
$72$	1116.71	1.82785
$73$	1029.66	1.65086	0.825432	−	0.564502i	$-0.190932\pi$
$73$	1029.66	1.65086	0.825432	+	0.564502i	$0.190932\pi$
$74$	310.002	0.486987
$75$	1174.01	1.80751
$76$	107.764	0.162650
$77$	208.439	0.308491
$78$	−276.176	−0.400908
$79$	−732.866	−1.04372	−0.521860	−	0.853031i	$-0.674762\pi$
$79$	−732.866	−1.04372	−0.521860	+	0.853031i	$0.674762\pi$
$80$	−9.17946	−0.0128287
$81$	1379.45	1.89225
$82$	−234.250	−0.315471
$83$	1094.07	1.44686	0.723431	−	0.690397i	$-0.242564\pi$
$83$	1094.07	1.44686	0.723431	+	0.690397i	$0.242564\pi$
$84$	−529.994	−0.688418
$85$	40.8610	0.0521412
$86$	0	0
$87$	−2074.46	−2.55638
$88$	−430.829	−0.521893
$89$	200.368	0.238639	0.119320	−	0.992856i	$-0.461929\pi$
$89$	200.368	0.238639	0.119320	+	0.992856i	$0.461929\pi$
$90$	25.2065	0.0295222
$91$	204.738	0.235850
$92$	−818.061	−0.927052
$93$	2848.91	3.17654
$94$	2.35247	0.00258126
$95$	5.47136	0.00590895
$96$	1703.91	1.81150
$97$	1442.40	1.50983	0.754916	−	0.655822i	$-0.227678\pi$
$97$	1442.40	1.50983	0.754916	+	0.655822i	$0.227678\pi$
$98$	335.429	0.345750
$99$	−1452.63	−1.47469
$100$	799.768	0.799768
$101$	909.111	0.895643	0.447822	−	0.894123i	$-0.352200\pi$
$101$	909.111	0.895643	0.447822	+	0.894123i	$0.352200\pi$
$102$	−1492.70	−1.44902
$103$	1263.28	1.20849	0.604245	−	0.796798i	$-0.293475\pi$
$103$	1263.28	1.20849	0.604245	+	0.796798i	$0.293475\pi$
$104$	−423.180	−0.399002
$105$	−26.9087	−0.0250097
$106$	−330.686	−0.303010
$107$	333.716	0.301509	0.150755	−	0.988571i	$-0.451830\pi$
$107$	333.716	0.301509	0.150755	+	0.988571i	$0.451830\pi$
$108$	2068.34	1.84283
$109$	115.351	0.101364	0.0506818	−	0.998715i	$-0.483861\pi$
$109$	115.351	0.101364	0.0506818	+	0.998715i	$0.483861\pi$
$110$	−9.72475	−0.00842926
$111$	2306.32	1.97213
$112$	−248.595	−0.209733
$113$	719.984	0.599384	0.299692	−	0.954036i	$-0.403116\pi$
$113$	719.984	0.599384	0.299692	+	0.954036i	$0.403116\pi$
$114$	−199.875	−0.164211
$115$	−41.5343	−0.0336791
$116$	−1413.17	−1.13112
$117$	−1426.83	−1.12744
$118$	527.859	0.411808
$119$	1106.59	0.852441
$120$	55.6186	0.0423105
$121$	−770.573	−0.578943
$122$	−884.184	−0.656150
$123$	−1742.75	−1.27755
$124$	1940.75	1.40552
$125$	81.2455	0.0581345
$126$	682.636	0.482651
$127$	1823.69	1.27422	0.637111	−	0.770772i	$-0.280129\pi$
$127$	1823.69	1.27422	0.637111	+	0.770772i	$0.280129\pi$
$128$	1446.13	0.998605
$129$	0	0
$130$	−9.55209	−0.00644441
$131$	−827.828	−0.552120	−0.276060	−	0.961140i	$-0.589029\pi$
$131$	−827.828	−0.552120	−0.276060	+	0.961140i	$0.589029\pi$
$132$	−1424.99	−0.939617
$133$	148.174	0.0966037
$134$	353.590	0.227952
$135$	105.013	0.0669487
$136$	−2287.24	−1.44213
$137$	1732.64	1.08051	0.540254	−	0.841502i	$-0.318328\pi$
$137$	1732.64	1.08051	0.540254	+	0.841502i	$0.318328\pi$
$138$	1517.30	0.935949
$139$	−2409.59	−1.47035	−0.735177	−	0.677875i	$-0.762901\pi$
$139$	−2409.59	−1.47035	−0.735177	+	0.677875i	$0.762901\pi$
$140$	−18.3309	−0.0110660
$141$	17.5016	0.0104532
$142$	−853.826	−0.504588
$143$	550.477	0.321910
$144$	1732.48	1.00259
$145$	−71.7492	−0.0410927
$146$	−1300.98	−0.737466
$147$	2495.49	1.40017
$148$	1571.13	0.872606
$149$	−1235.52	−0.679316	−0.339658	−	0.940549i	$-0.610311\pi$
$149$	−1235.52	−0.679316	−0.339658	+	0.940549i	$0.610311\pi$
$150$	−1483.37	−0.807444
$151$	−76.5960	−0.0412801	−0.0206400	−	0.999787i	$-0.506570\pi$
$151$	−76.5960	−0.0412801	−0.0206400	+	0.999787i	$0.506570\pi$
$152$	−306.266	−0.163430
$153$	−7711.88	−4.07496
$154$	−263.363	−0.137808
$155$	98.5350	0.0510614
$156$	−1399.69	−0.718365
$157$	−1307.88	−0.664840	−0.332420	−	0.943131i	$-0.607865\pi$
$157$	−1307.88	−0.664840	−0.332420	+	0.943131i	$0.607865\pi$
$158$	925.978	0.466246
$159$	−2460.20	−1.22709
$160$	58.9329	0.0291191
$161$	−1124.82	−0.550610
$162$	−1742.94	−0.845297
$163$	2230.12	1.07164	0.535818	−	0.844334i	$-0.320003\pi$
$163$	2230.12	1.07164	0.535818	+	0.844334i	$0.320003\pi$
$164$	−1187.20	−0.565275
$165$	−72.3491	−0.0341356
$166$	−1382.36	−0.646335
$167$	−1109.52	−0.514115	−0.257058	−	0.966396i	$-0.582753\pi$
$167$	−1109.52	−0.514115	−0.257058	+	0.966396i	$0.582753\pi$
$168$	1506.24	0.691722
$169$	−1656.30	−0.753890
$170$	−51.6280	−0.0232923
$171$	−1032.63	−0.461799
$172$	0	0
$173$	226.055	0.0993447	0.0496723	−	0.998766i	$-0.484182\pi$
$173$	226.055	0.0993447	0.0496723	+	0.998766i	$0.484182\pi$
$174$	2621.08	1.14198
$175$	1099.67	0.475012
$176$	−668.395	−0.286262
$177$	3927.11	1.66768
$178$	−253.165	−0.106604
$179$	1174.15	0.490280	0.245140	−	0.969488i	$-0.421166\pi$
$179$	1174.15	0.490280	0.245140	+	0.969488i	$0.421166\pi$
$180$	127.749	0.0528993
$181$	−948.581	−0.389544	−0.194772	−	0.980849i	$-0.562397\pi$
$181$	−948.581	−0.389544	−0.194772	+	0.980849i	$0.562397\pi$
$182$	−258.687	−0.105358
$183$	−6578.06	−2.65718
$184$	2324.93	0.931501
$185$	79.7686	0.0317011
$186$	−3599.60	−1.41901
$187$	2975.26	1.16349
$188$	11.9225	0.00462522
$189$	2843.93	1.09453
$190$	−6.91308	−0.00263962
$191$	−241.015	−0.0913047	−0.0456524	−	0.998957i	$-0.514537\pi$
$191$	−241.015	−0.0913047	−0.0456524	+	0.998957i	$0.514537\pi$
$192$	−29.6689	−0.0111519
$193$	−754.139	−0.281265	−0.140632	−	0.990062i	$-0.544914\pi$
$193$	−754.139	−0.281265	−0.140632	+	0.990062i	$0.544914\pi$
$194$	−1822.48	−0.674465
$195$	−71.0646	−0.0260977
$196$	1699.99	0.619530
$197$	−4583.62	−1.65771	−0.828856	−	0.559462i	$-0.811008\pi$
$197$	−4583.62	−1.65771	−0.828856	+	0.559462i	$0.811008\pi$
$198$	1835.40	0.658767
$199$	−2564.26	−0.913445	−0.456723	−	0.889609i	$-0.650977\pi$
$199$	−2564.26	−0.913445	−0.456723	+	0.889609i	$0.650977\pi$
$200$	−2272.94	−0.803607
$201$	2630.60	0.923125
$202$	−1148.66	−0.400098
$203$	−1943.09	−0.671813
$204$	−7565.17	−2.59641
$205$	−60.2763	−0.0205360
$206$	−1596.15	−0.539851
$207$	7838.96	2.63210
$208$	−656.528	−0.218856
$209$	398.393	0.131854
$210$	33.9992	0.0111722
$211$	−1951.52	−0.636722	−0.318361	−	0.947970i	$-0.603132\pi$
$211$	−1951.52	−0.636722	−0.318361	+	0.947970i	$0.603132\pi$
$212$	−1675.95	−0.542947
$213$	−6352.20	−2.04341
$214$	−421.650	−0.134689
$215$	0	0
$216$	−5878.22	−1.85168
$217$	2668.49	0.834789
$218$	−145.746	−0.0452807
$219$	−9678.91	−2.98648
$220$	−49.2860	−0.0151039
$221$	2922.44	0.889523
$222$	−2914.04	−0.880981
$223$	−2379.09	−0.714421	−0.357211	−	0.934024i	$-0.616272\pi$
$223$	−2379.09	−0.714421	−0.357211	+	0.934024i	$0.616272\pi$
$224$	1596.00	0.476060
$225$	−7663.67	−2.27072
$226$	−909.702	−0.267754
$227$	−665.520	−0.194591	−0.0972955	−	0.995256i	$-0.531019\pi$
$227$	−665.520	−0.194591	−0.0972955	+	0.995256i	$0.531019\pi$
$228$	−1012.99	−0.294241
$229$	3250.55	0.938002	0.469001	−	0.883198i	$-0.344614\pi$
$229$	3250.55	0.938002	0.469001	+	0.883198i	$0.344614\pi$
$230$	52.4787	0.0150450
$231$	−1959.34	−0.558073
$232$	4016.24	1.13655
$233$	5961.66	1.67623	0.838115	−	0.545494i	$-0.183658\pi$
$233$	5961.66	1.67623	0.838115	+	0.545494i	$0.183658\pi$
$234$	1802.81	0.503647
$235$	0.605327	0.000168031 0
$236$	2675.24	0.737896
$237$	6888.99	1.88814
$238$	−1398.17	−0.380799
$239$	1651.94	0.447092	0.223546	−	0.974693i	$-0.428237\pi$
$239$	1651.94	0.447092	0.223546	+	0.974693i	$0.428237\pi$
$240$	86.2875	0.0232076
$241$	524.998	0.140324	0.0701621	−	0.997536i	$-0.477648\pi$
$241$	524.998	0.140324	0.0701621	+	0.997536i	$0.477648\pi$
$242$	973.621	0.258623
$243$	−4245.97	−1.12090
$244$	−4481.14	−1.17572
$245$	86.3113	0.0225071
$246$	2201.97	0.570700
$247$	391.320	0.100806
$248$	−5515.61	−1.41226
$249$	−10284.3	−2.61744
$250$	−102.654	−0.0259696
$251$	5790.68	1.45619	0.728096	−	0.685475i	$-0.240405\pi$
$251$	5790.68	1.45619	0.728096	+	0.685475i	$0.240405\pi$
$252$	3459.67	0.864836
$253$	−3024.29	−0.751524
$254$	−2304.24	−0.569215
$255$	−384.096	−0.0943257
$256$	−1852.44	−0.452257
$257$	4622.57	1.12198	0.560989	−	0.827823i	$-0.310421\pi$
$257$	4622.57	1.12198	0.560989	+	0.827823i	$0.310421\pi$
$258$	0	0
$259$	2160.27	0.518273
$260$	−48.4110	−0.0115474
$261$	13541.5	3.21150
$262$	1045.96	0.246640
$263$	468.704	0.109892	0.0549458	−	0.998489i	$-0.482501\pi$
$263$	468.704	0.109892	0.0549458	+	0.998489i	$0.482501\pi$
$264$	4049.82	0.944127
$265$	−85.0908	−0.0197249
$266$	−187.218	−0.0431544
$267$	−1883.47	−0.431709
$268$	1792.03	0.408454
$269$	−1162.74	−0.263546	−0.131773	−	0.991280i	$-0.542067\pi$
$269$	−1162.74	−0.263546	−0.131773	+	0.991280i	$0.542067\pi$
$270$	−132.684	−0.0299070
$271$	−5794.03	−1.29875	−0.649377	−	0.760467i	$-0.724970\pi$
$271$	−5794.03	−1.29875	−0.649377	+	0.760467i	$0.724970\pi$
$272$	−3548.46	−0.791019
$273$	−1924.55	−0.426663
$274$	−2189.20	−0.482680
$275$	2956.66	0.648340
$276$	7689.83	1.67708
$277$	−1078.12	−0.233855	−0.116928	−	0.993140i	$-0.537305\pi$
$277$	−1078.12	−0.233855	−0.116928	+	0.993140i	$0.537305\pi$
$278$	3044.53	0.656830
$279$	−18597.0	−3.99058
$280$	52.0964	0.0111191
$281$	4395.46	0.933136	0.466568	−	0.884485i	$-0.345490\pi$
$281$	4395.46	0.933136	0.466568	+	0.884485i	$0.345490\pi$
$282$	−22.1133	−0.00466961
$283$	1861.43	0.390990	0.195495	−	0.980705i	$-0.437369\pi$
$283$	1861.43	0.390990	0.195495	+	0.980705i	$0.437369\pi$
$284$	−4327.28	−0.904144
$285$	−51.4312	−0.0106895
$286$	−695.528	−0.143802
$287$	−1632.38	−0.335737
$288$	−11122.7	−2.27573
$289$	10882.5	2.21504
$290$	90.6552	0.0183568
$291$	−13558.7	−2.73135
$292$	−6593.52	−1.32143
$293$	−480.757	−0.0958572	−0.0479286	−	0.998851i	$-0.515262\pi$
$293$	−480.757	−0.0958572	−0.0479286	+	0.998851i	$0.515262\pi$
$294$	−3153.06	−0.625476
$295$	135.827	0.0268072
$296$	−4465.14	−0.876794
$297$	7646.44	1.49391
$298$	1561.09	0.303461
$299$	−2970.60	−0.574562
$300$	−7517.88	−1.44682
$301$	0	0
$302$	96.7792	0.0184404
$303$	−8545.71	−1.62026
$304$	−475.145	−0.0896430
$305$	−227.515	−0.0427130
$306$	9743.98	1.82035
$307$	6933.15	1.28891	0.644456	−	0.764641i	$-0.277084\pi$
$307$	6933.15	1.28891	0.644456	+	0.764641i	$0.277084\pi$
$308$	−1334.75	−0.246930
$309$	−11874.9	−2.18621
$310$	−124.499	−0.0228099
$311$	−2059.92	−0.375586	−0.187793	−	0.982209i	$-0.560133\pi$
$311$	−2059.92	−0.375586	−0.187793	+	0.982209i	$0.560133\pi$
$312$	3977.92	0.721813
$313$	−5359.79	−0.967901	−0.483950	−	0.875095i	$-0.660799\pi$
$313$	−5359.79	−0.967901	−0.483950	+	0.875095i	$0.660799\pi$
$314$	1652.50	0.296994
$315$	175.653	0.0314188
$316$	4692.96	0.835441
$317$	−7019.47	−1.24370	−0.621849	−	0.783137i	$-0.713618\pi$
$317$	−7019.47	−1.24370	−0.621849	+	0.783137i	$0.713618\pi$
$318$	3108.47	0.548158
$319$	−5224.36	−0.916953
$320$	−1.02616	−0.000179262 0
$321$	−3136.95	−0.545444
$322$	1421.21	0.245966
$323$	2115.04	0.364347
$324$	−8833.39	−1.51464
$325$	2904.17	0.495675
$326$	−2817.76	−0.478716
$327$	−1084.31	−0.183371
$328$	3374.04	0.567988
$329$	16.3933	0.00274709
$330$	91.4133	0.0152489
$331$	−5551.69	−0.921898	−0.460949	−	0.887427i	$-0.652491\pi$
$331$	−5551.69	−0.921898	−0.460949	+	0.887427i	$0.652491\pi$
$332$	−7005.93	−1.15813
$333$	−15055.1	−2.47752
$334$	1401.88	0.229663
$335$	90.9844	0.0148388
$336$	2336.81	0.379415
$337$	1460.34	0.236053	0.118026	−	0.993010i	$-0.462343\pi$
$337$	1460.34	0.236053	0.118026	+	0.993010i	$0.462343\pi$
$338$	2092.73	0.336774
$339$	−6767.90	−1.08431
$340$	−261.656	−0.0417362
$341$	7174.75	1.13940
$342$	1304.74	0.206293
$343$	5357.50	0.843375
$344$	0	0
$345$	390.425	0.0609269
$346$	−285.621	−0.0443788
$347$	7150.17	1.10617	0.553085	−	0.833125i	$-0.313450\pi$
$347$	7150.17	1.10617	0.553085	+	0.833125i	$0.313450\pi$
$348$	13283.9	2.04624
$349$	5169.61	0.792902	0.396451	−	0.918056i	$-0.370242\pi$
$349$	5169.61	0.792902	0.396451	+	0.918056i	$0.370242\pi$
$350$	−1389.43	−0.212195
$351$	7510.68	1.14214
$352$	4291.15	0.649771
$353$	1936.50	0.291981	0.145991	−	0.989286i	$-0.453363\pi$
$353$	1936.50	0.291981	0.145991	+	0.989286i	$0.453363\pi$
$354$	−4961.91	−0.744978
$355$	−219.703	−0.0328469
$356$	−1283.07	−0.191018
$357$	−10402.0	−1.54210
$358$	−1483.54	−0.219016
$359$	1557.07	0.228911	0.114456	−	0.993428i	$-0.463488\pi$
$359$	1557.07	0.228911	0.114456	+	0.993428i	$0.463488\pi$
$360$	−363.064	−0.0531532
$361$	−6575.79	−0.958710
$362$	1198.53	0.174015
$363$	7243.44	1.04733
$364$	−1311.05	−0.188785
$365$	−334.764	−0.0480064
$366$	8311.39	1.18700
$367$	5890.68	0.837851	0.418925	−	0.908021i	$-0.362407\pi$
$367$	5890.68	0.837851	0.418925	+	0.908021i	$0.362407\pi$
$368$	3606.93	0.510936
$369$	11376.2	1.60494
$370$	−100.788	−0.0141614
$371$	−2304.40	−0.322476
$372$	−18243.2	−2.54265
$373$	1361.91	0.189053	0.0945265	−	0.995522i	$-0.469866\pi$
$373$	1361.91	0.189053	0.0945265	+	0.995522i	$0.469866\pi$
$374$	−3759.25	−0.519750
$375$	−763.713	−0.105168
$376$	−33.8839	−0.00464741
$377$	−5131.61	−0.701038
$378$	−3593.31	−0.488942
$379$	−2673.20	−0.362304	−0.181152	−	0.983455i	$-0.557983\pi$
$379$	−2673.20	−0.362304	−0.181152	+	0.983455i	$0.557983\pi$
$380$	−35.0362	−0.00472979
$381$	−17142.8	−2.30512
$382$	304.522	0.0407872
$383$	−3017.72	−0.402607	−0.201303	−	0.979529i	$-0.564518\pi$
$383$	−3017.72	−0.402607	−0.201303	+	0.979529i	$0.564518\pi$
$384$	−13593.8	−1.80652
$385$	−67.7674	−0.00897078
$386$	952.857	0.125645
$387$	0	0
$388$	−9236.51	−1.20854
$389$	15220.5	1.98384	0.991918	−	0.126879i	$-0.0404959\pi$
$389$	15220.5	1.98384	0.991918	+	0.126879i	$0.0404959\pi$
$390$	89.7903	0.0116582
$391$	−16055.7	−2.07666
$392$	−4831.38	−0.622503
$393$	7781.64	0.998809
$394$	5791.41	0.740526
$395$	238.269	0.0303509
$396$	9301.98	1.18041
$397$	−9599.48	−1.21356	−0.606781	−	0.794869i	$-0.707540\pi$
$397$	−9599.48	−1.21356	−0.606781	+	0.794869i	$0.707540\pi$
$398$	3239.95	0.408050
$399$	−1392.84	−0.174760
$400$	−3526.28	−0.440785
$401$	15516.8	1.93235	0.966177	−	0.257879i	$-0.0830236\pi$
$401$	15516.8	1.93235	0.966177	+	0.257879i	$0.0830236\pi$
$402$	−3323.77	−0.412374
$403$	7047.37	0.871103
$404$	−5821.55	−0.716913
$405$	−448.486	−0.0550258
$406$	2455.10	0.300109
$407$	5808.29	0.707387
$408$	21500.2	2.60887
$409$	−13082.4	−1.58162	−0.790812	−	0.612059i	$-0.790342\pi$
$409$	−13082.4	−1.58162	−0.790812	+	0.612059i	$0.790342\pi$
$410$	76.1593	0.00917375
$411$	−16287.0	−1.95469
$412$	−8089.48	−0.967330
$413$	3678.41	0.438263
$414$	−9904.54	−1.17580
$415$	−355.703	−0.0420741
$416$	4214.97	0.496769
$417$	22650.4	2.65993
$418$	−503.371	−0.0589011
$419$	4000.38	0.466424	0.233212	−	0.972426i	$-0.425076\pi$
$419$	4000.38	0.466424	0.233212	+	0.972426i	$0.425076\pi$
$420$	172.312	0.0200189
$421$	14443.5	1.67204	0.836022	−	0.548695i	$-0.184875\pi$
$421$	14443.5	1.67204	0.836022	+	0.548695i	$0.184875\pi$
$422$	2465.75	0.284434
$423$	−114.246	−0.0131320
$424$	4763.06	0.545553
$425$	15696.7	1.79154
$426$	8026.02	0.912822
$427$	−6161.49	−0.698303
$428$	−2136.97	−0.241342
$429$	−5174.52	−0.582350
$430$	0	0
$431$	8704.07	0.972762	0.486381	−	0.873747i	$-0.338317\pi$
$431$	8704.07	0.972762	0.486381	+	0.873747i	$0.338317\pi$
$432$	−9119.56	−1.01566
$433$	−13149.7	−1.45943	−0.729717	−	0.683749i	$-0.760348\pi$
$433$	−13149.7	−1.45943	−0.729717	+	0.683749i	$0.760348\pi$
$434$	−3371.65	−0.372913
$435$	674.447	0.0743385
$436$	−738.658	−0.0811360
$437$	−2149.89	−0.235339
$438$	12229.3	1.33411
$439$	11391.2	1.23844	0.619218	−	0.785219i	$-0.287450\pi$
$439$	11391.2	1.23844	0.619218	+	0.785219i	$0.287450\pi$
$440$	140.071	0.0151764
$441$	−16289.9	−1.75898
$442$	−3692.51	−0.397364
$443$	−4305.83	−0.461797	−0.230898	−	0.972978i	$-0.574166\pi$
$443$	−4305.83	−0.461797	−0.230898	+	0.972978i	$0.574166\pi$
$444$	−14768.7	−1.57858
$445$	−65.1434	−0.00693953
$446$	3005.99	0.319143
$447$	11614.0	1.22891
$448$	−27.7901	−0.00293071
$449$	3738.80	0.392973	0.196487	−	0.980506i	$-0.437047\pi$
$449$	3738.80	0.392973	0.196487	+	0.980506i	$0.437047\pi$
$450$	9683.06	1.01436
$451$	−4388.98	−0.458246
$452$	−4610.47	−0.479774
$453$	720.007	0.0746775
$454$	840.886	0.0869268
$455$	−66.5643	−0.00685842
$456$	2878.92	0.295653
$457$	−8908.27	−0.911841	−0.455920	−	0.890021i	$-0.650690\pi$
$457$	−8908.27	−0.911841	−0.455920	+	0.890021i	$0.650690\pi$
$458$	−4107.08	−0.419020
$459$	40594.4	4.12807
$460$	265.968	0.0269583
$461$	2694.69	0.272244	0.136122	−	0.990692i	$-0.456536\pi$
$461$	2694.69	0.272244	0.136122	+	0.990692i	$0.456536\pi$
$462$	2475.63	0.249300
$463$	6709.80	0.673500	0.336750	−	0.941594i	$-0.390672\pi$
$463$	6709.80	0.673500	0.336750	+	0.941594i	$0.390672\pi$
$464$	6230.86	0.623406
$465$	−926.236	−0.0923724
$466$	−7532.57	−0.748798
$467$	−16767.9	−1.66151	−0.830754	−	0.556639i	$-0.812091\pi$
$467$	−16767.9	−1.66151	−0.830754	+	0.556639i	$0.812091\pi$
$468$	9136.83	0.902457
$469$	2464.01	0.242596
$470$	−0.764832	−7.50619e−5 0
$471$	12294.1	1.20272
$472$	−7603.04	−0.741437
$473$	0	0
$474$	−8704.26	−0.843460
$475$	2101.82	0.203027
$476$	−7086.09	−0.682333
$477$	16059.6	1.54155
$478$	−2087.23	−0.199723
$479$	−13204.9	−1.25959	−0.629797	−	0.776760i	$-0.716862\pi$
$479$	−13204.9	−1.25959	−0.629797	+	0.776760i	$0.716862\pi$
$480$	−553.973	−0.0526777
$481$	5705.17	0.540818
$482$	−663.336	−0.0626849
$483$	10573.4	0.996077
$484$	4934.41	0.463412
$485$	−468.953	−0.0439052
$486$	5364.79	0.500724
$487$	−2291.19	−0.213191	−0.106595	−	0.994302i	$-0.533995\pi$
$487$	−2291.19	−0.213191	−0.106595	+	0.994302i	$0.533995\pi$
$488$	12735.4	1.18136
$489$	−20963.3	−1.93864
$490$	−109.055	−0.0100543
$491$	−8817.80	−0.810472	−0.405236	−	0.914212i	$-0.632811\pi$
$491$	−8817.80	−0.810472	−0.405236	+	0.914212i	$0.632811\pi$
$492$	11159.8	1.02261
$493$	−27735.8	−2.53378
$494$	−494.434	−0.0450316
$495$	472.277	0.0428834
$496$	−8557.00	−0.774639
$497$	−5949.93	−0.537004
$498$	12994.2	1.16925
$499$	−16011.1	−1.43638	−0.718192	−	0.695845i	$-0.755030\pi$
$499$	−16011.1	−1.43638	−0.718192	+	0.695845i	$0.755030\pi$
$500$	−520.261	−0.0465335
$501$	10429.6	0.930057
$502$	−7316.53	−0.650504
$503$	55.8134	0.00494751	0.00247375	−	0.999997i	$-0.499213\pi$
$503$	55.8134	0.00494751	0.00247375	+	0.999997i	$0.499213\pi$
$504$	−9832.38	−0.868987
$505$	−295.570	−0.0260449
$506$	3821.20	0.335717
$507$	15569.3	1.36382
$508$	−11678.1	−1.01995
$509$	9212.25	0.802212	0.401106	−	0.916032i	$-0.368626\pi$
$509$	9212.25	0.802212	0.401106	+	0.916032i	$0.368626\pi$
$510$	485.307	0.0421367
$511$	−9065.97	−0.784843
$512$	−9228.51	−0.796575
$513$	5435.66	0.467817
$514$	−5840.63	−0.501205
$515$	−410.716	−0.0351424
$516$	0	0
$517$	44.0765	0.00374948
$518$	−2729.50	−0.231520
$519$	−2124.93	−0.179719
$520$	137.584	0.0116028
$521$	−14038.9	−1.18053	−0.590266	−	0.807209i	$-0.700977\pi$
$521$	−14038.9	−1.18053	−0.590266	+	0.807209i	$0.700977\pi$
$522$	−17109.8	−1.43462
$523$	2476.00	0.207013	0.103507	−	0.994629i	$-0.466994\pi$
$523$	2476.00	0.207013	0.103507	+	0.994629i	$0.466994\pi$
$524$	5301.05	0.441942
$525$	−10336.9	−0.859317
$526$	−592.208	−0.0490903
$527$	38090.3	3.14846
$528$	6282.96	0.517861
$529$	4153.30	0.341358
$530$	107.512	0.00881140
$531$	−25635.1	−2.09505
$532$	−948.840	−0.0773260
$533$	−4311.05	−0.350342
$534$	2379.77	0.192851
$535$	−108.497	−0.00876776
$536$	−5092.95	−0.410414
$537$	−11037.1	−0.886938
$538$	1469.13	0.117730
$539$	6284.70	0.502228
$540$	−672.457	−0.0535888
$541$	5185.20	0.412069	0.206034	−	0.978545i	$-0.433944\pi$
$541$	5185.20	0.412069	0.206034	+	0.978545i	$0.433944\pi$
$542$	7320.77	0.580173
$543$	8916.73	0.704702
$544$	22781.4	1.79549
$545$	−37.5029	−0.00294761
$546$	2431.67	0.190597
$547$	−7098.82	−0.554888	−0.277444	−	0.960742i	$-0.589487\pi$
$547$	−7098.82	−0.554888	−0.277444	+	0.960742i	$0.589487\pi$
$548$	−11095.1	−0.864888
$549$	42939.9	3.33812
$550$	−3735.75	−0.289624
$551$	−3713.87	−0.287143
$552$	−21854.5	−1.68513
$553$	6452.73	0.496199
$554$	1362.21	0.104467
$555$	−749.830	−0.0573487
$556$	15430.0	1.17694
$557$	−1358.66	−0.103354	−0.0516772	−	0.998664i	$-0.516457\pi$
$557$	−1358.66	−0.103354	−0.0516772	+	0.998664i	$0.516457\pi$
$558$	23497.3	1.78265
$559$	0	0
$560$	80.8232	0.00609893
$561$	−27967.7	−2.10481
$562$	−5553.67	−0.416846
$563$	−13603.7	−1.01834	−0.509172	−	0.860665i	$-0.670048\pi$
$563$	−13603.7	−1.01834	−0.509172	+	0.860665i	$0.670048\pi$
$564$	−112.073	−0.00836722
$565$	−234.081	−0.0174298
$566$	−2351.91	−0.174661
$567$	−12145.8	−0.899601
$568$	12298.1	0.908483
$569$	3316.81	0.244373	0.122186	−	0.992507i	$-0.461009\pi$
$569$	3316.81	0.244373	0.122186	+	0.992507i	$0.461009\pi$
$570$	64.9834	0.00477518
$571$	−7745.82	−0.567693	−0.283846	−	0.958870i	$-0.591611\pi$
$571$	−7745.82	−0.567693	−0.283846	+	0.958870i	$0.591611\pi$
$572$	−3525.01	−0.257672
$573$	2265.55	0.165174
$574$	2062.52	0.149979
$575$	−15955.4	−1.15719
$576$	193.671	0.0140098
$577$	24031.9	1.73390	0.866952	−	0.498391i	$-0.166076\pi$
$577$	24031.9	1.73390	0.866952	+	0.498391i	$0.166076\pi$
$578$	−13750.0	−0.989491
$579$	7088.96	0.508821
$580$	459.450	0.0328925
$581$	−9633.03	−0.687858
$582$	17131.4	1.22014
$583$	−6195.83	−0.440146
$584$	18738.8	1.32777
$585$	463.892	0.0327856
$586$	607.438	0.0428209
$587$	2119.09	0.149002	0.0745011	−	0.997221i	$-0.476264\pi$
$587$	2119.09	0.149002	0.0745011	+	0.997221i	$0.476264\pi$
$588$	−15980.0	−1.12076
$589$	5100.35	0.356802
$590$	−171.617	−0.0119752
$591$	43086.3	2.99887
$592$	−6927.29	−0.480929
$593$	−6253.12	−0.433027	−0.216513	−	0.976280i	$-0.569469\pi$
$593$	−6253.12	−0.433027	−0.216513	+	0.976280i	$0.569469\pi$
$594$	−9661.29	−0.667353
$595$	−359.773	−0.0247886
$596$	7911.76	0.543756
$597$	24104.2	1.65246
$598$	3753.35	0.256666
$599$	10339.6	0.705284	0.352642	−	0.935758i	$-0.385283\pi$
$599$	10339.6	0.705284	0.352642	+	0.935758i	$0.385283\pi$
$600$	21365.8	1.45376
$601$	−5782.91	−0.392495	−0.196248	−	0.980554i	$-0.562876\pi$
$601$	−5782.91	−0.392495	−0.196248	+	0.980554i	$0.562876\pi$
$602$	0	0
$603$	−17171.9	−1.15969
$604$	490.487	0.0330424
$605$	250.528	0.0168354
$606$	10797.5	0.723794
$607$	−20822.9	−1.39238	−0.696191	−	0.717856i	$-0.745123\pi$
$607$	−20822.9	−1.39238	−0.696191	+	0.717856i	$0.745123\pi$
$608$	3050.47	0.203475
$609$	18265.2	1.21534
$610$	287.465	0.0190806
$611$	43.2939	0.00286659
$612$	49383.5	3.26178
$613$	11051.2	0.728148	0.364074	−	0.931370i	$-0.381386\pi$
$613$	11051.2	0.728148	0.364074	+	0.931370i	$0.381386\pi$
$614$	−8760.05	−0.575777
$615$	566.601	0.0371505
$616$	3793.36	0.248115
$617$	1118.45	0.0729775	0.0364888	−	0.999334i	$-0.488383\pi$
$617$	1118.45	0.0729775	0.0364888	+	0.999334i	$0.488383\pi$
$618$	15004.0	0.976615
$619$	−15760.9	−1.02340	−0.511700	−	0.859164i	$-0.670984\pi$
$619$	−15760.9	−1.02340	−0.511700	+	0.859164i	$0.670984\pi$
$620$	−630.975	−0.0408719
$621$	−41263.3	−2.66641
$622$	2602.71	0.167780
$623$	−1764.19	−0.113452
$624$	6171.41	0.395920
$625$	15585.4	0.997464
$626$	6772.10	0.432376
$627$	−3744.92	−0.238529
$628$	8375.06	0.532168
$629$	30835.8	1.95470
$630$	−221.938	−0.0140353
$631$	−17527.6	−1.10581	−0.552904	−	0.833245i	$-0.686480\pi$
$631$	−17527.6	−1.10581	−0.552904	+	0.833245i	$0.686480\pi$
$632$	−13337.4	−0.839451
$633$	18344.4	1.15186
$634$	8869.11	0.555579
$635$	−592.917	−0.0370539
$636$	15754.1	0.982215
$637$	6173.11	0.383968
$638$	6600.99	0.409617
$639$	41465.6	2.56706
$640$	−470.167	−0.0290390
$641$	−9258.01	−0.570467	−0.285233	−	0.958458i	$-0.592071\pi$
$641$	−9258.01	−0.570467	−0.285233	+	0.958458i	$0.592071\pi$
$642$	3963.54	0.243658
$643$	3332.29	0.204374	0.102187	−	0.994765i	$-0.467416\pi$
$643$	3332.29	0.204374	0.102187	+	0.994765i	$0.467416\pi$
$644$	7202.85	0.440733
$645$	0	0
$646$	−2672.36	−0.162759
$647$	4208.18	0.255704	0.127852	−	0.991793i	$-0.459192\pi$
$647$	4208.18	0.255704	0.127852	+	0.991793i	$0.459192\pi$
$648$	25104.5	1.52191
$649$	9890.11	0.598183
$650$	−3669.43	−0.221426
$651$	−25084.0	−1.51017
$652$	−14280.7	−0.857786
$653$	25071.4	1.50248	0.751241	−	0.660028i	$-0.229456\pi$
$653$	25071.4	1.50248	0.751241	+	0.660028i	$0.229456\pi$
$654$	1370.03	0.0819147
$655$	269.143	0.0160554
$656$	5234.53	0.311546
$657$	63181.5	3.75182
$658$	−20.7130	−0.00122717
$659$	−16578.9	−0.980001	−0.490000	−	0.871722i	$-0.663003\pi$
$659$	−16578.9	−0.980001	−0.490000	+	0.871722i	$0.663003\pi$
$660$	463.292	0.0273237
$661$	−13221.0	−0.777966	−0.388983	−	0.921245i	$-0.627174\pi$
$661$	−13221.0	−0.777966	−0.388983	+	0.921245i	$0.627174\pi$
$662$	7014.57	0.411826
$663$	−27471.1	−1.60919
$664$	19910.9	1.16369
$665$	−48.1742	−0.00280919
$666$	19022.1	1.10675
$667$	28192.8	1.63662
$668$	7104.88	0.411521
$669$	22363.6	1.29242
$670$	−114.959	−0.00662873
$671$	−16566.3	−0.953108
$672$	−15002.5	−0.861213
$673$	9297.40	0.532524	0.266262	−	0.963901i	$-0.414211\pi$
$673$	9297.40	0.532524	0.266262	+	0.963901i	$0.414211\pi$
$674$	−1845.14	−0.105449
$675$	40340.6	2.30031
$676$	10606.2	0.603448
$677$	5546.69	0.314884	0.157442	−	0.987528i	$-0.449675\pi$
$677$	5546.69	0.314884	0.157442	+	0.987528i	$0.449675\pi$
$678$	8551.26	0.484379
$679$	−12700.0	−0.717795
$680$	743.627	0.0419365
$681$	6255.94	0.352023
$682$	−9065.32	−0.508987
$683$	−13290.9	−0.744603	−0.372301	−	0.928112i	$-0.621431\pi$
$683$	−13290.9	−0.744603	−0.372301	+	0.928112i	$0.621431\pi$
$684$	6612.54	0.369644
$685$	−563.316	−0.0314207
$686$	−6769.21	−0.376749
$687$	−30555.4	−1.69689
$688$	0	0
$689$	−6085.82	−0.336504
$690$	−493.303	−0.0272170
$691$	−16442.2	−0.905199	−0.452599	−	0.891714i	$-0.649503\pi$
$691$	−16442.2	−0.905199	−0.452599	+	0.891714i	$0.649503\pi$
$692$	−1447.56	−0.0795200
$693$	12790.1	0.701088
$694$	−9034.25	−0.494144
$695$	783.406	0.0427573
$696$	−37752.9	−2.05607
$697$	−23300.8	−1.26625
$698$	−6531.81	−0.354201
$699$	−56040.0	−3.03237
$700$	−7041.79	−0.380221
$701$	25096.3	1.35217	0.676087	−	0.736822i	$-0.263675\pi$
$701$	25096.3	1.35217	0.676087	+	0.736822i	$0.263675\pi$
$702$	−9489.76	−0.510211
$703$	4128.97	0.221518
$704$	−74.7189	−0.00400010
$705$	−5.69012	−0.000303975 0
$706$	−2446.77	−0.130433
$707$	−8004.53	−0.425801
$708$	−25147.5	−1.33489
$709$	15705.5	0.831920	0.415960	−	0.909383i	$-0.363446\pi$
$709$	15705.5	0.831920	0.415960	+	0.909383i	$0.363446\pi$
$710$	277.595	0.0146732
$711$	−44969.6	−2.37200
$712$	3646.47	0.191935
$713$	−38717.9	−2.03366
$714$	13142.9	0.688882
$715$	−178.971	−0.00936101
$716$	−7518.74	−0.392442
$717$	−15528.3	−0.808809
$718$	−1967.36	−0.102258
$719$	−37095.9	−1.92412	−0.962061	−	0.272836i	$-0.912038\pi$
$719$	−37095.9	−1.92412	−0.962061	+	0.272836i	$0.912038\pi$
$720$	−563.263	−0.0291550
$721$	−11122.9	−0.574533
$722$	8308.53	0.428271
$723$	−4935.02	−0.253852
$724$	6074.30	0.311809
$725$	−27562.4	−1.41192
$726$	−9152.10	−0.467860
$727$	−29835.3	−1.52205	−0.761024	−	0.648724i	$-0.775303\pi$
$727$	−29835.3	−1.52205	−0.761024	+	0.648724i	$0.775303\pi$
$728$	3726.01	0.189691
$729$	2667.26	0.135511
$730$	422.975	0.0214452
$731$	0	0
$732$	42123.0	2.12693
$733$	33242.9	1.67511	0.837553	−	0.546356i	$-0.183985\pi$
$733$	33242.9	1.67511	0.837553	+	0.546356i	$0.183985\pi$
$734$	−7442.89	−0.374281
$735$	−811.332	−0.0407163
$736$	−23156.8	−1.15974
$737$	6624.96	0.331117
$738$	−14373.9	−0.716951
$739$	19988.7	0.994990	0.497495	−	0.867467i	$-0.334253\pi$
$739$	19988.7	0.994990	0.497495	+	0.867467i	$0.334253\pi$
$740$	−510.803	−0.0253750
$741$	−3678.43	−0.182363
$742$	2911.62	0.144055
$743$	−19510.4	−0.963346	−0.481673	−	0.876351i	$-0.659971\pi$
$743$	−19510.4	−0.963346	−0.481673	+	0.876351i	$0.659971\pi$
$744$	51847.1	2.55485
$745$	401.693	0.0197542
$746$	−1720.77	−0.0844529
$747$	67133.3	3.28819
$748$	−19052.3	−0.931311
$749$	−2938.29	−0.143342
$750$	964.953	0.0469801
$751$	3423.45	0.166343	0.0831714	−	0.996535i	$-0.473495\pi$
$751$	3423.45	0.166343	0.0831714	+	0.996535i	$0.473495\pi$
$752$	−52.5680	−0.00254915
$753$	−54432.7	−2.63432
$754$	6483.80	0.313164
$755$	24.9028	0.00120041
$756$	−18211.3	−0.876108
$757$	27084.2	1.30039	0.650193	−	0.759769i	$-0.274688\pi$
$757$	27084.2	1.30039	0.650193	+	0.759769i	$0.274688\pi$
$758$	3377.60	0.161847
$759$	28428.5	1.35954
$760$	99.5730	0.00475249
$761$	−14059.4	−0.669714	−0.334857	−	0.942269i	$-0.608688\pi$
$761$	−14059.4	−0.669714	−0.334857	+	0.942269i	$0.608688\pi$
$762$	21660.0	1.02973
$763$	−1015.64	−0.0481896
$764$	1543.35	0.0730844
$765$	2507.28	0.118498
$766$	3812.90	0.179851
$767$	9714.51	0.457328
$768$	17413.1	0.818152
$769$	−37181.7	−1.74357	−0.871786	−	0.489886i	$-0.837038\pi$
$769$	−37181.7	−1.74357	−0.871786	+	0.489886i	$0.837038\pi$
$770$	85.6243	0.00400738
$771$	−43452.5	−2.02971
$772$	4829.18	0.225137
$773$	4717.31	0.219495	0.109748	−	0.993959i	$-0.464996\pi$
$773$	4717.31	0.219495	0.109748	+	0.993959i	$0.464996\pi$
$774$	0	0
$775$	37852.1	1.75444
$776$	26250.2	1.21434
$777$	−20306.7	−0.937578
$778$	−19231.2	−0.886210
$779$	−3120.01	−0.143499
$780$	455.067	0.0208897
$781$	−15997.5	−0.732953
$782$	20286.5	0.927676
$783$	−71281.0	−3.25335
$784$	−7495.47	−0.341448
$785$	425.216	0.0193333
$786$	−9832.12	−0.446183
$787$	−28567.6	−1.29393	−0.646966	−	0.762519i	$-0.723963\pi$
$787$	−28567.6	−1.29393	−0.646966	+	0.762519i	$0.723963\pi$
$788$	29351.5	1.32691
$789$	−4405.85	−0.198799
$790$	−301.054	−0.0135582
$791$	−6339.31	−0.284956
$792$	−26436.2	−1.18607
$793$	−16272.2	−0.728679
$794$	12129.0	0.542117
$795$	799.860	0.0356831
$796$	16420.4	0.731163
$797$	−25388.9	−1.12838	−0.564191	−	0.825644i	$-0.690812\pi$
$797$	−25388.9	−1.12838	−0.564191	+	0.825644i	$0.690812\pi$
$798$	1759.86	0.0780681
$799$	233.999	0.0103608
$800$	22639.0	1.00051
$801$	12294.8	0.542341
$802$	−19605.6	−0.863213
$803$	−24375.6	−1.07123
$804$	−16845.2	−0.738911
$805$	365.701	0.0160115
$806$	−8904.37	−0.389135
$807$	10929.9	0.476765
$808$	16544.9	0.720354
$809$	−6922.63	−0.300849	−0.150424	−	0.988622i	$-0.548064\pi$
$809$	−6922.63	−0.300849	−0.150424	+	0.988622i	$0.548064\pi$
$810$	566.663	0.0245809
$811$	−5155.99	−0.223245	−0.111622	−	0.993751i	$-0.535605\pi$
$811$	−5155.99	−0.223245	−0.111622	+	0.993751i	$0.535605\pi$
$812$	12442.7	0.537750
$813$	54464.3	2.34950
$814$	−7338.79	−0.316001
$815$	−725.056	−0.0311627
$816$	33355.8	1.43099
$817$	0	0
$818$	16529.7	0.706536
$819$	12563.0	0.536002
$820$	385.983	0.0164379
$821$	−28808.7	−1.22464	−0.612320	−	0.790610i	$-0.709764\pi$
$821$	−28808.7	−1.22464	−0.612320	+	0.790610i	$0.709764\pi$
$822$	20578.6	0.873189
$823$	14065.1	0.595720	0.297860	−	0.954610i	$-0.403727\pi$
$823$	14065.1	0.595720	0.297860	+	0.954610i	$0.403727\pi$
$824$	22990.3	0.971973
$825$	−27792.8	−1.17288
$826$	−4647.68	−0.195779
$827$	−20288.1	−0.853068	−0.426534	−	0.904471i	$-0.640266\pi$
$827$	−20288.1	−0.853068	−0.426534	+	0.904471i	$0.640266\pi$
$828$	−50197.2	−2.10685
$829$	−2531.77	−0.106070	−0.0530349	−	0.998593i	$-0.516889\pi$
$829$	−2531.77	−0.106070	−0.0530349	+	0.998593i	$0.516889\pi$
$830$	449.431	0.0187952
$831$	10134.4	0.423055
$832$	−73.3923	−0.00305820
$833$	33365.0	1.38779
$834$	−28618.8	−1.18823
$835$	360.726	0.0149502
$836$	−2551.14	−0.105542
$837$	97892.1	4.04259
$838$	−5054.49	−0.208359
$839$	−46374.3	−1.90824	−0.954122	−	0.299417i	$-0.903208\pi$
$839$	−46374.3	−1.90824	−0.954122	+	0.299417i	$0.903208\pi$
$840$	−489.710	−0.0201150
$841$	24313.1	0.996888
$842$	−18249.3	−0.746928
$843$	−41317.6	−1.68808
$844$	12496.7	0.509661
$845$	538.494	0.0219228
$846$	144.350	0.00586627
$847$	6784.73	0.275238
$848$	7389.48	0.299240
$849$	−17497.5	−0.707318
$850$	−19832.8	−0.800307
$851$	−31343.9	−1.26258
$852$	40676.7	1.63564
$853$	3436.56	0.137943	0.0689716	−	0.997619i	$-0.478028\pi$
$853$	3436.56	0.137943	0.0689716	+	0.997619i	$0.478028\pi$
$854$	7785.05	0.311943
$855$	335.730	0.0134289
$856$	6073.27	0.242500
$857$	−29311.5	−1.16833	−0.584167	−	0.811633i	$-0.698579\pi$
$857$	−29311.5	−1.16833	−0.584167	+	0.811633i	$0.698579\pi$
$858$	6538.01	0.260145
$859$	−31911.1	−1.26751	−0.633756	−	0.773533i	$-0.718488\pi$
$859$	−31911.1	−1.26751	−0.633756	+	0.773533i	$0.718488\pi$
$860$	0	0
$861$	15344.5	0.607364
$862$	−10997.6	−0.434548
$863$	−16307.5	−0.643239	−0.321619	−	0.946869i	$-0.604227\pi$
$863$	−16307.5	−0.643239	−0.321619	+	0.946869i	$0.604227\pi$
$864$	58548.3	2.30539
$865$	−73.4948	−0.00288890
$866$	16614.7	0.651952
$867$	−102296.	−4.00710
$868$	−17087.9	−0.668203
$869$	17349.4	0.677259
$870$	−852.165	−0.0332082
$871$	6507.34	0.253149
$872$	2099.27	0.0815254
$873$	88507.5	3.43130
$874$	2716.39	0.105130
$875$	−715.349	−0.0276380
$876$	61979.5	2.39052
$877$	34825.8	1.34092	0.670458	−	0.741948i	$-0.266098\pi$
$877$	34825.8	1.34092	0.670458	+	0.741948i	$0.266098\pi$
$878$	−14392.8	−0.553229
$879$	4519.15	0.173410
$880$	217.308	0.00832439
$881$	3505.74	0.134065	0.0670326	−	0.997751i	$-0.478647\pi$
$881$	3505.74	0.134065	0.0670326	+	0.997751i	$0.478647\pi$
$882$	20582.4	0.785764
$883$	23731.6	0.904451	0.452226	−	0.891904i	$-0.350630\pi$
$883$	23731.6	0.904451	0.452226	+	0.891904i	$0.350630\pi$
$884$	−18714.0	−0.712015
$885$	−1276.78	−0.0484954
$886$	5440.42	0.206292
$887$	−15367.8	−0.581736	−0.290868	−	0.956763i	$-0.593944\pi$
$887$	−15367.8	−0.581736	−0.290868	+	0.956763i	$0.593944\pi$
$888$	41972.6	1.58616
$889$	−16057.2	−0.605783
$890$	82.3088	0.00310000
$891$	−32656.2	−1.22786
$892$	15234.7	0.571855
$893$	31.3328	0.00117415
$894$	−14674.3	−0.548974
$895$	−381.739	−0.0142571
$896$	−12732.9	−0.474751
$897$	27923.8	1.03941
$898$	−4723.99	−0.175547
$899$	−66883.9	−2.48132
$900$	49074.8	1.81758
$901$	−32893.2	−1.21624
$902$	5545.48	0.204705
$903$	0	0
$904$	13102.9	0.482077
$905$	308.402	0.0113278
$906$	−909.731	−0.0333596
$907$	36989.5	1.35415	0.677076	−	0.735913i	$-0.263247\pi$
$907$	36989.5	1.35415	0.677076	+	0.735913i	$0.263247\pi$
$908$	4261.70	0.155759
$909$	55784.2	2.03547
$910$	84.1041	0.00306376
$911$	−52269.2	−1.90094	−0.950469	−	0.310819i	$-0.899397\pi$
$911$	−52269.2	−1.90094	−0.950469	+	0.310819i	$0.899397\pi$
$912$	4466.40	0.162168
$913$	−25900.2	−0.938852
$914$	11255.6	0.407333
$915$	2138.65	0.0772697
$916$	−20815.1	−0.750819
$917$	7288.85	0.262485
$918$	−51291.1	−1.84407
$919$	17187.9	0.616948	0.308474	−	0.951233i	$-0.400182\pi$
$919$	17187.9	0.616948	0.308474	+	0.951233i	$0.400182\pi$
$920$	−755.880	−0.0270876
$921$	−65172.1	−2.33170
$922$	−3404.75	−0.121615
$923$	−15713.5	−0.560364
$924$	12546.7	0.446707
$925$	30643.0	1.08923
$926$	−8477.84	−0.300863
$927$	77516.3	2.74646
$928$	−40002.6	−1.41503
$929$	−18064.1	−0.637960	−0.318980	−	0.947761i	$-0.603340\pi$
$929$	−18064.1	−0.637960	−0.318980	+	0.947761i	$0.603340\pi$
$930$	1170.30	0.0412642
$931$	4467.63	0.157273
$932$	−38175.9	−1.34173
$933$	19363.4	0.679451
$934$	21186.2	0.742222
$935$	−967.317	−0.0338338
$936$	−25966.9	−0.906788
$937$	−12776.9	−0.445467	−0.222734	−	0.974879i	$-0.571498\pi$
$937$	−12776.9	−0.445467	−0.222734	+	0.974879i	$0.571498\pi$
$938$	−3113.28	−0.108371
$939$	50382.3	1.75098
$940$	−3.87625	−0.000134499 0
$941$	12576.8	0.435698	0.217849	−	0.975982i	$-0.430096\pi$
$941$	12576.8	0.435698	0.217849	+	0.975982i	$0.430096\pi$
$942$	−15533.6	−0.537276
$943$	23684.7	0.817900
$944$	−11795.5	−0.406685
$945$	−924.617	−0.0318283
$946$	0	0
$947$	9064.67	0.311048	0.155524	−	0.987832i	$-0.450293\pi$
$947$	9064.67	0.311048	0.155524	+	0.987832i	$0.450293\pi$
$948$	−44114.1	−1.51135
$949$	−23942.8	−0.818984
$950$	−2655.65	−0.0906955
$951$	65983.4	2.24990
$952$	20138.7	0.685607
$953$	24942.4	0.847811	0.423905	−	0.905707i	$-0.360659\pi$
$953$	24942.4	0.847811	0.423905	+	0.905707i	$0.360659\pi$
$954$	−20291.3	−0.688632
$955$	78.3585	0.00265510
$956$	−10578.3	−0.357873
$957$	49109.3	1.65881
$958$	16684.4	0.562680
$959$	−15255.5	−0.513689
$960$	9.64595	0.000324293 0
$961$	62062.4	2.08326
$962$	−7208.49	−0.241592
$963$	20477.2	0.685222
$964$	−3361.86	−0.112322
$965$	245.185	0.00817906
$966$	−13359.5	−0.444963
$967$	−8748.78	−0.290943	−0.145471	−	0.989362i	$-0.546470\pi$
$967$	−8748.78	−0.290943	−0.145471	+	0.989362i	$0.546470\pi$
$968$	−14023.6	−0.465636
$969$	−19881.5	−0.659119
$970$	592.523	0.0196132
$971$	14600.8	0.482557	0.241279	−	0.970456i	$-0.422433\pi$
$971$	14600.8	0.482557	0.241279	+	0.970456i	$0.422433\pi$
$972$	27189.3	0.897220
$973$	21216.0	0.699026
$974$	2894.93	0.0952356
$975$	−27299.4	−0.896698
$976$	19757.9	0.647987
$977$	22071.1	0.722741	0.361371	−	0.932422i	$-0.382309\pi$
$977$	22071.1	0.722741	0.361371	+	0.932422i	$0.382309\pi$
$978$	26487.2	0.866019
$979$	−4743.37	−0.154851
$980$	−552.700	−0.0180157
$981$	7078.09	0.230363
$982$	11141.3	0.362050
$983$	36744.9	1.19225	0.596125	−	0.802892i	$-0.296706\pi$
$983$	36744.9	1.19225	0.596125	+	0.802892i	$0.296706\pi$
$984$	−31716.2	−1.02751
$985$	1490.22	0.0482056
$986$	35044.2	1.13188
$987$	−154.098	−0.00496960
$988$	−2505.84	−0.0806897
$989$	0	0
$990$	−596.723	−0.0191567
$991$	−3840.07	−0.123092	−0.0615458	−	0.998104i	$-0.519603\pi$
$991$	−3840.07	−0.123092	−0.0615458	+	0.998104i	$0.519603\pi$
$992$	54936.7	1.75831
$993$	52186.2	1.66775
$994$	7517.75	0.239888
$995$	833.691	0.0265626
$996$	65856.2	2.09511
$997$	11059.7	0.351318	0.175659	−	0.984451i	$-0.443794\pi$
$997$	11059.7	0.351318	0.175659	+	0.984451i	$0.443794\pi$
$998$	20230.1	0.641655
$999$	79248.1	2.50981

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.i.1.20	✓	50
43.42	odd	2		1849.4.a.j.1.31	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.20	✓	50	1.1	even	1	trivial
1849.4.a.j.1.31	yes	50	43.42	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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-1.26350 q^{2} -9.40007 q^{3} -6.40356 q^{4} -0.325119 q^{5} +11.8770 q^{6} -8.80478 q^{7} +18.1989 q^{8} +61.3613 q^{9} +O(q^{10})\)	\(q-1.26350 q^{2} -9.40007 q^{3} -6.40356 q^{4} -0.325119 q^{5} +11.8770 q^{6} -8.80478 q^{7} +18.1989 q^{8} +61.3613 q^{9} +0.410789 q^{10} -23.6733 q^{11} +60.1939 q^{12} -23.2530 q^{13} +11.1249 q^{14} +3.05614 q^{15} +28.2341 q^{16} -125.680 q^{17} -77.5301 q^{18} -16.8288 q^{19} +2.08192 q^{20} +82.7656 q^{21} +29.9113 q^{22} +127.751 q^{23} -171.071 q^{24} -124.894 q^{25} +29.3802 q^{26} -322.998 q^{27} +56.3820 q^{28} +220.686 q^{29} -3.86145 q^{30} -303.073 q^{31} -181.265 q^{32} +222.531 q^{33} +158.797 q^{34} +2.86261 q^{35} -392.931 q^{36} -245.352 q^{37} +21.2632 q^{38} +218.580 q^{39} -5.91683 q^{40} +185.397 q^{41} -104.574 q^{42} +151.594 q^{44} -19.9497 q^{45} -161.414 q^{46} -1.86186 q^{47} -265.403 q^{48} -265.476 q^{49} +157.804 q^{50} +1181.40 q^{51} +148.902 q^{52} +261.722 q^{53} +408.109 q^{54} +7.69666 q^{55} -160.238 q^{56} +158.192 q^{57} -278.837 q^{58} -417.774 q^{59} -19.5702 q^{60} +699.788 q^{61} +382.934 q^{62} -540.273 q^{63} +3.15625 q^{64} +7.56001 q^{65} -281.168 q^{66} -279.849 q^{67} +804.800 q^{68} -1200.87 q^{69} -3.61691 q^{70} +675.761 q^{71} +1116.71 q^{72} +1029.66 q^{73} +310.002 q^{74} +1174.01 q^{75} +107.764 q^{76} +208.439 q^{77} -276.176 q^{78} -732.866 q^{79} -9.17946 q^{80} +1379.45 q^{81} -234.250 q^{82} +1094.07 q^{83} -529.994 q^{84} +40.8610 q^{85} -2074.46 q^{87} -430.829 q^{88} +200.368 q^{89} +25.2065 q^{90} +204.738 q^{91} -818.061 q^{92} +2848.91 q^{93} +2.35247 q^{94} +5.47136 q^{95} +1703.91 q^{96} +1442.40 q^{97} +335.429 q^{98} -1452.63 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) \) 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9} - 137 q^{10} - 252 q^{11} - 48 q^{12} - 192 q^{13} - 272 q^{14} - 314 q^{15} + 542 q^{16} - 236 q^{17} - 386 q^{18} + 12 q^{19} + 108 q^{20} - 408 q^{21} + 1235 q^{22} - 630 q^{23} - 613 q^{24} + 1098 q^{25} + 1493 q^{26} + 10 q^{27} - 242 q^{28} + 208 q^{29} - 48 q^{30} - 932 q^{31} - 1124 q^{32} + 254 q^{33} + 765 q^{34} - 1452 q^{35} + 747 q^{36} - 90 q^{37} - 1213 q^{38} - 1610 q^{39} - 1693 q^{40} - 1354 q^{41} - 16 q^{42} - 2704 q^{44} + 4508 q^{45} + 233 q^{46} - 3484 q^{47} - 376 q^{48} + 1324 q^{49} - 408 q^{50} + 4054 q^{51} - 2176 q^{52} - 726 q^{53} - 6497 q^{54} - 3288 q^{55} - 7097 q^{56} - 870 q^{57} + 275 q^{58} - 4370 q^{59} - 3891 q^{60} + 1172 q^{61} - 1546 q^{62} - 3686 q^{63} + 606 q^{64} + 2610 q^{65} - 4697 q^{66} - 344 q^{67} - 3221 q^{68} + 136 q^{69} - 1310 q^{70} + 162 q^{71} - 5814 q^{72} + 746 q^{73} - 4332 q^{74} + 236 q^{75} + 1338 q^{76} + 2024 q^{77} - 2782 q^{78} - 2656 q^{79} - 5713 q^{80} - 86 q^{81} - 4168 q^{82} - 3514 q^{83} - 4269 q^{84} - 7558 q^{85} - 10278 q^{87} + 11692 q^{88} + 2640 q^{89} - 8286 q^{90} - 5946 q^{91} - 4271 q^{92} - 2 q^{93} + 9062 q^{94} - 12140 q^{95} - 700 q^{96} - 3864 q^{97} - 2826 q^{98} - 8174 q^{99}+O(q^{100}) \) 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9 - 137 * q^10 - 252 * q^11 - 48 * q^12 - 192 * q^13 - 272 * q^14 - 314 * q^15 + 542 * q^16 - 236 * q^17 - 386 * q^18 + 12 * q^19 + 108 * q^20 - 408 * q^21 + 1235 * q^22 - 630 * q^23 - 613 * q^24 + 1098 * q^25 + 1493 * q^26 + 10 * q^27 - 242 * q^28 + 208 * q^29 - 48 * q^30 - 932 * q^31 - 1124 * q^32 + 254 * q^33 + 765 * q^34 - 1452 * q^35 + 747 * q^36 - 90 * q^37 - 1213 * q^38 - 1610 * q^39 - 1693 * q^40 - 1354 * q^41 - 16 * q^42 - 2704 * q^44 + 4508 * q^45 + 233 * q^46 - 3484 * q^47 - 376 * q^48 + 1324 * q^49 - 408 * q^50 + 4054 * q^51 - 2176 * q^52 - 726 * q^53 - 6497 * q^54 - 3288 * q^55 - 7097 * q^56 - 870 * q^57 + 275 * q^58 - 4370 * q^59 - 3891 * q^60 + 1172 * q^61 - 1546 * q^62 - 3686 * q^63 + 606 * q^64 + 2610 * q^65 - 4697 * q^66 - 344 * q^67 - 3221 * q^68 + 136 * q^69 - 1310 * q^70 + 162 * q^71 - 5814 * q^72 + 746 * q^73 - 4332 * q^74 + 236 * q^75 + 1338 * q^76 + 2024 * q^77 - 2782 * q^78 - 2656 * q^79 - 5713 * q^80 - 86 * q^81 - 4168 * q^82 - 3514 * q^83 - 4269 * q^84 - 7558 * q^85 - 10278 * q^87 + 11692 * q^88 + 2640 * q^89 - 8286 * q^90 - 5946 * q^91 - 4271 * q^92 - 2 * q^93 + 9062 * q^94 - 12140 * q^95 - 700 * q^96 - 3864 * q^97 - 2826 * q^98 - 8174 * q^99

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