LMFDB - Embedded newform 1849.4.a.h.1.17

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:	$0$
Dimension:	$30$
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q+1.36355 q^{2} -9.26361 q^{3} -6.14074 q^{4} -1.21569 q^{5} -12.6314 q^{6} -10.5300 q^{7} -19.2815 q^{8} +58.8145 q^{9} +O(q^{10})$	\(q+1.36355 q^{2} -9.26361 q^{3} -6.14074 q^{4} -1.21569 q^{5} -12.6314 q^{6} -10.5300 q^{7} -19.2815 q^{8} +58.8145 q^{9} -1.65764 q^{10} +39.9105 q^{11} +56.8855 q^{12} -52.4922 q^{13} -14.3582 q^{14} +11.2617 q^{15} +22.8347 q^{16} +1.95827 q^{17} +80.1962 q^{18} +86.6275 q^{19} +7.46522 q^{20} +97.5462 q^{21} +54.4198 q^{22} -205.303 q^{23} +178.617 q^{24} -123.522 q^{25} -71.5755 q^{26} -294.717 q^{27} +64.6623 q^{28} +204.077 q^{29} +15.3558 q^{30} -146.053 q^{31} +185.388 q^{32} -369.716 q^{33} +2.67019 q^{34} +12.8012 q^{35} -361.165 q^{36} -30.4607 q^{37} +118.121 q^{38} +486.268 q^{39} +23.4403 q^{40} -38.7109 q^{41} +133.009 q^{42} -245.080 q^{44} -71.5000 q^{45} -279.940 q^{46} -250.912 q^{47} -211.532 q^{48} -232.118 q^{49} -168.428 q^{50} -18.1407 q^{51} +322.341 q^{52} -532.405 q^{53} -401.860 q^{54} -48.5187 q^{55} +203.035 q^{56} -802.484 q^{57} +278.268 q^{58} +71.0607 q^{59} -69.1549 q^{60} -1.90548 q^{61} -199.149 q^{62} -619.319 q^{63} +70.1080 q^{64} +63.8141 q^{65} -504.124 q^{66} -925.169 q^{67} -12.0252 q^{68} +1901.85 q^{69} +17.4551 q^{70} -877.149 q^{71} -1134.03 q^{72} -661.167 q^{73} -41.5345 q^{74} +1144.26 q^{75} -531.958 q^{76} -420.259 q^{77} +663.048 q^{78} +103.204 q^{79} -27.7599 q^{80} +1142.15 q^{81} -52.7840 q^{82} +183.518 q^{83} -599.006 q^{84} -2.38065 q^{85} -1890.49 q^{87} -769.537 q^{88} -1095.68 q^{89} -97.4935 q^{90} +552.745 q^{91} +1260.71 q^{92} +1352.97 q^{93} -342.130 q^{94} -105.312 q^{95} -1717.37 q^{96} -1583.54 q^{97} -316.504 q^{98} +2347.32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 27 q^{5} + 8 q^{6} + 48 q^{7} + 90 q^{8} + 216 q^{9}+O(q^{10}) $ 30 * q + 6 * q^2 + 2 * q^3 + 114 * q^4 + 27 * q^5 + 8 * q^6 + 48 * q^7 + 90 * q^8 + 216 * q^9	\( 30 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 27 q^{5} + 8 q^{6} + 48 q^{7} + 90 q^{8} + 216 q^{9} - 27 q^{10} + 80 q^{11} - 36 q^{12} - 13 q^{13} + 36 q^{14} + 16 q^{15} + 318 q^{16} + 66 q^{17} + 80 q^{18} + 254 q^{19} + 312 q^{20} - 548 q^{21} + 305 q^{22} - 105 q^{23} + 123 q^{24} + 523 q^{25} + 549 q^{26} - 10 q^{27} + 578 q^{28} + 793 q^{29} + 1560 q^{30} - 359 q^{31} + 676 q^{32} + 208 q^{33} + 1007 q^{34} - 514 q^{35} + 776 q^{36} + 510 q^{37} - 2066 q^{38} + 898 q^{39} - 1248 q^{40} - 270 q^{41} - 915 q^{42} + 3256 q^{44} + 807 q^{45} + 1960 q^{46} + 1421 q^{47} - 632 q^{48} + 386 q^{49} - 141 q^{50} + 209 q^{51} + 2825 q^{52} - 21 q^{53} + 2368 q^{54} + 2258 q^{55} + 2521 q^{56} - 1723 q^{57} - 347 q^{58} + 1752 q^{59} + 2711 q^{60} + 1759 q^{61} + 395 q^{62} + 2204 q^{63} + 222 q^{64} + 1151 q^{65} + 160 q^{66} - 3001 q^{67} + 1921 q^{68} + 1660 q^{69} + 1597 q^{70} + 727 q^{71} + 9100 q^{72} + 4623 q^{73} - 2649 q^{74} + 1027 q^{75} + 874 q^{76} + 3556 q^{77} - 4979 q^{78} + 546 q^{79} + 5809 q^{80} - 410 q^{81} - 4397 q^{82} - 492 q^{83} - 10611 q^{84} - 1723 q^{85} + 5937 q^{87} + 3974 q^{88} + 5218 q^{89} + 10492 q^{90} + 1104 q^{91} + 1060 q^{92} + 1997 q^{93} - 2134 q^{94} + 6346 q^{95} - 11984 q^{96} + 2590 q^{97} + 6270 q^{98} - 2693 q^{99}+O(q^{100}) \) 30 * q + 6 * q^2 + 2 * q^3 + 114 * q^4 + 27 * q^5 + 8 * q^6 + 48 * q^7 + 90 * q^8 + 216 * q^9 - 27 * q^10 + 80 * q^11 - 36 * q^12 - 13 * q^13 + 36 * q^14 + 16 * q^15 + 318 * q^16 + 66 * q^17 + 80 * q^18 + 254 * q^19 + 312 * q^20 - 548 * q^21 + 305 * q^22 - 105 * q^23 + 123 * q^24 + 523 * q^25 + 549 * q^26 - 10 * q^27 + 578 * q^28 + 793 * q^29 + 1560 * q^30 - 359 * q^31 + 676 * q^32 + 208 * q^33 + 1007 * q^34 - 514 * q^35 + 776 * q^36 + 510 * q^37 - 2066 * q^38 + 898 * q^39 - 1248 * q^40 - 270 * q^41 - 915 * q^42 + 3256 * q^44 + 807 * q^45 + 1960 * q^46 + 1421 * q^47 - 632 * q^48 + 386 * q^49 - 141 * q^50 + 209 * q^51 + 2825 * q^52 - 21 * q^53 + 2368 * q^54 + 2258 * q^55 + 2521 * q^56 - 1723 * q^57 - 347 * q^58 + 1752 * q^59 + 2711 * q^60 + 1759 * q^61 + 395 * q^62 + 2204 * q^63 + 222 * q^64 + 1151 * q^65 + 160 * q^66 - 3001 * q^67 + 1921 * q^68 + 1660 * q^69 + 1597 * q^70 + 727 * q^71 + 9100 * q^72 + 4623 * q^73 - 2649 * q^74 + 1027 * q^75 + 874 * q^76 + 3556 * q^77 - 4979 * q^78 + 546 * q^79 + 5809 * q^80 - 410 * q^81 - 4397 * q^82 - 492 * q^83 - 10611 * q^84 - 1723 * q^85 + 5937 * q^87 + 3974 * q^88 + 5218 * q^89 + 10492 * q^90 + 1104 * q^91 + 1060 * q^92 + 1997 * q^93 - 2134 * q^94 + 6346 * q^95 - 11984 * q^96 + 2590 * q^97 + 6270 * q^98 - 2693 * 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 $

$2$	1.36355	0.482086	0.241043	−	0.970514i	$-0.422511\pi$
$2$	1.36355	0.482086	0.241043	+	0.970514i	$0.422511\pi$
$3$	−9.26361	−1.78278	−0.891391	−	0.453234i	$-0.850270\pi$
$3$	−9.26361	−1.78278	−0.891391	+	0.453234i	$0.850270\pi$
$4$	−6.14074	−0.767593
$5$	−1.21569	−0.108734	−0.0543672	−	0.998521i	$-0.517314\pi$
$5$	−1.21569	−0.108734	−0.0543672	+	0.998521i	$0.517314\pi$
$6$	−12.6314	−0.859455
$7$	−10.5300	−0.568568	−0.284284	−	0.958740i	$-0.591756\pi$
$7$	−10.5300	−0.568568	−0.284284	+	0.958740i	$0.591756\pi$
$8$	−19.2815	−0.852132
$9$	58.8145	2.17831
$10$	−1.65764	−0.0524193
$11$	39.9105	1.09395	0.546976	−	0.837148i	$-0.315779\pi$
$11$	39.9105	1.09395	0.546976	+	0.837148i	$0.315779\pi$
$12$	56.8855	1.36845
$13$	−52.4922	−1.11990	−0.559951	−	0.828526i	$-0.689180\pi$
$13$	−52.4922	−1.11990	−0.559951	+	0.828526i	$0.689180\pi$
$14$	−14.3582	−0.274099
$15$	11.2617	0.193850
$16$	22.8347	0.356792
$17$	1.95827	0.0279383	0.0139691	−	0.999902i	$-0.495553\pi$
$17$	1.95827	0.0279383	0.0139691	+	0.999902i	$0.495553\pi$
$18$	80.1962	1.05014
$19$	86.6275	1.04599	0.522993	−	0.852337i	$-0.324816\pi$
$19$	86.6275	1.04599	0.522993	+	0.852337i	$0.324816\pi$
$20$	7.46522	0.0834637
$21$	97.5462	1.01363
$22$	54.4198	0.527379
$23$	−205.303	−1.86124	−0.930622	−	0.365983i	$-0.880733\pi$
$23$	−205.303	−1.86124	−0.930622	+	0.365983i	$0.880733\pi$
$24$	178.617	1.51917
$25$	−123.522	−0.988177
$26$	−71.5755	−0.539889
$27$	−294.717	−2.10068
$28$	64.6623	0.436429
$29$	204.077	1.30676	0.653382	−	0.757028i	$-0.273349\pi$
$29$	204.077	1.30676	0.653382	+	0.757028i	$0.273349\pi$
$30$	15.3558	0.0934523
$31$	−146.053	−0.846187	−0.423094	−	0.906086i	$-0.639056\pi$
$31$	−146.053	−0.846187	−0.423094	+	0.906086i	$0.639056\pi$
$32$	185.388	1.02414
$33$	−369.716	−1.95028
$34$	2.67019	0.0134686
$35$	12.8012	0.0618229
$36$	−361.165	−1.67206
$37$	−30.4607	−0.135343	−0.0676717	−	0.997708i	$-0.521557\pi$
$37$	−30.4607	−0.135343	−0.0676717	+	0.997708i	$0.521557\pi$
$38$	118.121	0.504255
$39$	486.268	1.99654
$40$	23.4403	0.0926560
$41$	−38.7109	−0.147454	−0.0737271	−	0.997278i	$-0.523489\pi$
$41$	−38.7109	−0.147454	−0.0737271	+	0.997278i	$0.523489\pi$
$42$	133.009	0.488659
$43$	0	0
$43$	0	0
$44$	−245.080	−0.839711
$45$	−71.5000	−0.236858
$46$	−279.940	−0.897279
$47$	−250.912	−0.778708	−0.389354	−	0.921088i	$-0.627302\pi$
$47$	−250.912	−0.778708	−0.389354	+	0.921088i	$0.627302\pi$
$48$	−211.532	−0.636083
$49$	−232.118	−0.676730
$50$	−168.428	−0.476386
$51$	−18.1407	−0.0498079
$52$	322.341	0.859629
$53$	−532.405	−1.37984	−0.689919	−	0.723887i	$-0.742354\pi$
$53$	−532.405	−1.37984	−0.689919	+	0.723887i	$0.742354\pi$
$54$	−401.860	−1.01271
$55$	−48.5187	−0.118950
$56$	203.035	0.484495
$57$	−802.484	−1.86476
$58$	278.268	0.629973
$59$	71.0607	0.156802	0.0784010	−	0.996922i	$-0.475019\pi$
$59$	71.0607	0.156802	0.0784010	+	0.996922i	$0.475019\pi$
$60$	−69.1549	−0.148798
$61$	−1.90548	−0.00399954	−0.00199977	−	0.999998i	$-0.500637\pi$
$61$	−1.90548	−0.00399954	−0.00199977	+	0.999998i	$0.500637\pi$
$62$	−199.149	−0.407935
$63$	−619.319	−1.23852
$64$	70.1080	0.136930
$65$	63.8141	0.121772
$66$	−504.124	−0.940203
$67$	−925.169	−1.68698	−0.843488	−	0.537149i	$-0.819501\pi$
$67$	−925.169	−1.68698	−0.843488	+	0.537149i	$0.819501\pi$
$68$	−12.0252	−0.0214452
$69$	1901.85	3.31819
$70$	17.4551	0.0298040
$71$	−877.149	−1.46618	−0.733088	−	0.680134i	$-0.761922\pi$
$71$	−877.149	−1.46618	−0.733088	+	0.680134i	$0.761922\pi$
$72$	−1134.03	−1.85621
$73$	−661.167	−1.06005	−0.530026	−	0.847982i	$-0.677818\pi$
$73$	−661.167	−1.06005	−0.530026	+	0.847982i	$0.677818\pi$
$74$	−41.5345	−0.0652471
$75$	1144.26	1.76170
$76$	−531.958	−0.802891
$77$	−420.259	−0.621987
$78$	663.048	0.962505
$79$	103.204	0.146979	0.0734895	−	0.997296i	$-0.476586\pi$
$79$	103.204	0.146979	0.0734895	+	0.997296i	$0.476586\pi$
$80$	−27.7599	−0.0387956
$81$	1142.15	1.56674
$82$	−52.7840	−0.0710856
$83$	183.518	0.242695	0.121348	−	0.992610i	$-0.461278\pi$
$83$	183.518	0.242695	0.121348	+	0.992610i	$0.461278\pi$
$84$	−599.006	−0.778059
$85$	−2.38065	−0.00303785
$86$	0	0
$87$	−1890.49	−2.32968
$88$	−769.537	−0.932192
$89$	−1095.68	−1.30497	−0.652484	−	0.757803i	$-0.726273\pi$
$89$	−1095.68	−1.30497	−0.652484	+	0.757803i	$0.726273\pi$
$90$	−97.4935	−0.114186
$91$	552.745	0.636741
$92$	1260.71	1.42868
$93$	1352.97	1.50857
$94$	−342.130	−0.375404
$95$	−105.312	−0.113735
$96$	−1717.37	−1.82581
$97$	−1583.54	−1.65757	−0.828787	−	0.559565i	$-0.810968\pi$
$97$	−1583.54	−1.65757	−0.828787	+	0.559565i	$0.810968\pi$
$98$	−316.504	−0.326242
$99$	2347.32	2.38297
$100$	758.518	0.758518
$101$	808.477	0.796500	0.398250	−	0.917277i	$-0.369618\pi$
$101$	808.477	0.796500	0.398250	+	0.917277i	$0.369618\pi$
$102$	−24.7356	−0.0240117
$103$	1714.01	1.63967	0.819836	−	0.572598i	$-0.194064\pi$
$103$	1714.01	1.63967	0.819836	+	0.572598i	$0.194064\pi$
$104$	1012.13	0.954304
$105$	−118.586	−0.110217
$106$	−725.958	−0.665201
$107$	793.870	0.717255	0.358627	−	0.933481i	$-0.383245\pi$
$107$	793.870	0.717255	0.358627	+	0.933481i	$0.383245\pi$
$108$	1809.78	1.61247
$109$	1696.66	1.49092	0.745462	−	0.666548i	$-0.232229\pi$
$109$	1696.66	1.49092	0.745462	+	0.666548i	$0.232229\pi$
$110$	−66.1575	−0.0573443
$111$	282.176	0.241288
$112$	−240.450	−0.202861
$113$	−9.86194	−0.00821003	−0.00410502	−	0.999992i	$-0.501307\pi$
$113$	−9.86194	−0.00821003	−0.00410502	+	0.999992i	$0.501307\pi$
$114$	−1094.22	−0.898977
$115$	249.584	0.202381
$116$	−1253.19	−1.00306
$117$	−3087.30	−2.43950
$118$	96.8945	0.0755921
$119$	−20.6207	−0.0158848
$120$	−217.142	−0.165186
$121$	261.852	0.196733
$122$	−2.59821	−0.00192812
$123$	358.603	0.262879
$124$	896.871	0.649527
$125$	302.125	0.216183
$126$	−844.469	−0.597074
$127$	−1913.58	−1.33703	−0.668516	−	0.743698i	$-0.733070\pi$
$127$	−1913.58	−1.33703	−0.668516	+	0.743698i	$0.733070\pi$
$128$	−1387.51	−0.958125
$129$	0	0
$130$	87.0134	0.0587045
$131$	978.768	0.652789	0.326395	−	0.945234i	$-0.394166\pi$
$131$	978.768	0.652789	0.326395	+	0.945234i	$0.394166\pi$
$132$	2270.33	1.49702
$133$	−912.191	−0.594714
$134$	−1261.51	−0.813267
$135$	358.284	0.228416
$136$	−37.7585	−0.0238071
$137$	−92.3357	−0.0575823	−0.0287911	−	0.999585i	$-0.509166\pi$
$137$	−92.3357	−0.0575823	−0.0287911	+	0.999585i	$0.509166\pi$
$138$	2593.25	1.59965
$139$	−991.127	−0.604793	−0.302397	−	0.953182i	$-0.597787\pi$
$139$	−991.127	−0.604793	−0.302397	+	0.953182i	$0.597787\pi$
$140$	−78.6091	−0.0474548
$141$	2324.35	1.38827
$142$	−1196.03	−0.706823
$143$	−2094.99	−1.22512
$144$	1343.01	0.777206
$145$	−248.094	−0.142090
$146$	−901.531	−0.511036
$147$	2150.25	1.20646
$148$	187.051	0.103889
$149$	173.746	0.0955293	0.0477646	−	0.998859i	$-0.484790\pi$
$149$	173.746	0.0955293	0.0477646	+	0.998859i	$0.484790\pi$
$150$	1560.25	0.849293
$151$	2155.32	1.16157	0.580786	−	0.814056i	$-0.302745\pi$
$151$	2155.32	1.16157	0.580786	+	0.814056i	$0.302745\pi$
$152$	−1670.31	−0.891317
$153$	115.175	0.0608584
$154$	−573.043	−0.299851
$155$	177.554	0.0920096
$156$	−2986.05	−1.53253
$157$	−129.656	−0.0659089	−0.0329545	−	0.999457i	$-0.510492\pi$
$157$	−129.656	−0.0659089	−0.0329545	+	0.999457i	$0.510492\pi$
$158$	140.723	0.0708565
$159$	4931.99	2.45995
$160$	−225.374	−0.111359
$161$	2161.85	1.05824
$162$	1557.38	0.755304
$163$	3852.27	1.85113	0.925563	−	0.378595i	$-0.123593\pi$
$163$	3852.27	1.85113	0.925563	+	0.378595i	$0.123593\pi$
$164$	237.714	0.113185
$165$	449.459	0.212063
$166$	250.235	0.117000
$167$	931.777	0.431755	0.215878	−	0.976420i	$-0.430739\pi$
$167$	931.777	0.431755	0.215878	+	0.976420i	$0.430739\pi$
$168$	−1880.84	−0.863750
$169$	558.434	0.254180
$170$	−3.24612	−0.00146450
$171$	5094.95	2.27849
$172$	0	0
$173$	2664.60	1.17102	0.585509	−	0.810666i	$-0.300895\pi$
$173$	2664.60	1.17102	0.585509	+	0.810666i	$0.300895\pi$
$174$	−2577.77	−1.12311
$175$	1300.69	0.561846
$176$	911.345	0.390314
$177$	−658.279	−0.279544
$178$	−1494.01	−0.629106
$179$	−3035.00	−1.26730	−0.633650	−	0.773620i	$-0.718444\pi$
$179$	−3035.00	−1.26730	−0.633650	+	0.773620i	$0.718444\pi$
$180$	439.063	0.181810
$181$	−208.614	−0.0856695	−0.0428348	−	0.999082i	$-0.513639\pi$
$181$	−208.614	−0.0856695	−0.0428348	+	0.999082i	$0.513639\pi$
$182$	753.693	0.306964
$183$	17.6517	0.00713031
$184$	3958.56	1.58602
$185$	37.0306	0.0147165
$186$	1844.84	0.727260
$187$	78.1557	0.0305632
$188$	1540.79	0.597731
$189$	3103.38	1.19438
$190$	−143.598	−0.0548298
$191$	−195.003	−0.0738740	−0.0369370	−	0.999318i	$-0.511760\pi$
$191$	−195.003	−0.0738740	−0.0369370	+	0.999318i	$0.511760\pi$
$192$	−649.453	−0.244116
$193$	−1373.16	−0.512136	−0.256068	−	0.966659i	$-0.582427\pi$
$193$	−1373.16	−0.512136	−0.256068	+	0.966659i	$0.582427\pi$
$194$	−2159.23	−0.799093
$195$	−591.149	−0.217093
$196$	1425.38	0.519453
$197$	−20.7462	−0.00750309	−0.00375155	−	0.999993i	$-0.501194\pi$
$197$	−20.7462	−0.00750309	−0.00375155	+	0.999993i	$0.501194\pi$
$198$	3200.68	1.14880
$199$	1792.24	0.638436	0.319218	−	0.947681i	$-0.396580\pi$
$199$	1792.24	0.638436	0.319218	+	0.947681i	$0.396580\pi$
$200$	2381.70	0.842057
$201$	8570.40	3.00751
$202$	1102.39	0.383981
$203$	−2148.94	−0.742985
$204$	111.397	0.0382322
$205$	47.0603	0.0160333
$206$	2337.13	0.790463
$207$	−12074.8	−4.05437
$208$	−1198.64	−0.399572
$209$	3457.35	1.14426
$210$	−161.697	−0.0531340
$211$	−2446.18	−0.798113	−0.399057	−	0.916926i	$-0.630662\pi$
$211$	−2446.18	−0.798113	−0.399057	+	0.916926i	$0.630662\pi$
$212$	3269.36	1.05915
$213$	8125.57	2.61387
$214$	1082.48	0.345779
$215$	0	0
$216$	5682.60	1.79006
$217$	1537.94	0.481115
$218$	2313.48	0.718754
$219$	6124.80	1.88984
$220$	297.941	0.0913054
$221$	−102.794	−0.0312881
$222$	384.760	0.116321
$223$	2319.65	0.696570	0.348285	−	0.937389i	$-0.386764\pi$
$223$	2319.65	0.696570	0.348285	+	0.937389i	$0.386764\pi$
$224$	−1952.15	−0.582292
$225$	−7264.89	−2.15256
$226$	−13.4472	−0.00395794
$227$	−4386.23	−1.28249	−0.641243	−	0.767338i	$-0.721581\pi$
$227$	−4386.23	−1.28249	−0.641243	+	0.767338i	$0.721581\pi$
$228$	4927.85	1.43138
$229$	−2999.82	−0.865649	−0.432824	−	0.901478i	$-0.642483\pi$
$229$	−2999.82	−0.865649	−0.432824	+	0.901478i	$0.642483\pi$
$230$	340.319	0.0975651
$231$	3893.12	1.10887
$232$	−3934.92	−1.11354
$233$	−2609.62	−0.733743	−0.366872	−	0.930272i	$-0.619571\pi$
$233$	−2609.62	−0.733743	−0.366872	+	0.930272i	$0.619571\pi$
$234$	−4209.68	−1.17605
$235$	305.031	0.0846724
$236$	−436.366	−0.120360
$237$	−956.040	−0.262032
$238$	−28.1172	−0.00765785
$239$	−2745.79	−0.743140	−0.371570	−	0.928405i	$-0.621180\pi$
$239$	−2745.79	−0.743140	−0.371570	+	0.928405i	$0.621180\pi$
$240$	257.157	0.0691641
$241$	−2214.40	−0.591876	−0.295938	−	0.955207i	$-0.595632\pi$
$241$	−2214.40	−0.591876	−0.295938	+	0.955207i	$0.595632\pi$
$242$	357.047	0.0948422
$243$	−2623.11	−0.692479
$244$	11.7011	0.00307002
$245$	282.183	0.0735838
$246$	488.971	0.126730
$247$	−4547.27	−1.17140
$248$	2816.12	0.721063
$249$	−1700.04	−0.432673
$250$	411.961	0.104219
$251$	−689.883	−0.173486	−0.0867431	−	0.996231i	$-0.527646\pi$
$251$	−689.883	−0.173486	−0.0867431	+	0.996231i	$0.527646\pi$
$252$	3803.08	0.950680
$253$	−8193.75	−2.03611
$254$	−2609.26	−0.644564
$255$	22.0534	0.00541583
$256$	−2452.80	−0.598828
$257$	−5540.18	−1.34470	−0.672348	−	0.740235i	$-0.734714\pi$
$257$	−5540.18	−1.34470	−0.672348	+	0.740235i	$0.734714\pi$
$258$	0	0
$259$	320.752	0.0769520
$260$	−391.866	−0.0934712
$261$	12002.7	2.84655
$262$	1334.59	0.314701
$263$	1794.51	0.420738	0.210369	−	0.977622i	$-0.432533\pi$
$263$	1794.51	0.420738	0.210369	+	0.977622i	$0.432533\pi$
$264$	7128.69	1.66190
$265$	647.238	0.150036
$266$	−1243.81	−0.286703
$267$	10150.0	2.32647
$268$	5681.22	1.29491
$269$	−767.096	−0.173869	−0.0869343	−	0.996214i	$-0.527707\pi$
$269$	−767.096	−0.173869	−0.0869343	+	0.996214i	$0.527707\pi$
$270$	488.536	0.110116
$271$	3088.86	0.692379	0.346189	−	0.938165i	$-0.387475\pi$
$271$	3088.86	0.692379	0.346189	+	0.938165i	$0.387475\pi$
$272$	44.7165	0.00996816
$273$	−5120.42	−1.13517
$274$	−125.904	−0.0277596
$275$	−4929.83	−1.08102
$276$	−11678.7	−2.54702
$277$	−3426.01	−0.743137	−0.371569	−	0.928406i	$-0.621180\pi$
$277$	−3426.01	−0.743137	−0.371569	+	0.928406i	$0.621180\pi$
$278$	−1351.45	−0.291562
$279$	−8590.01	−1.84326
$280$	−246.827	−0.0526813
$281$	4212.28	0.894248	0.447124	−	0.894472i	$-0.352448\pi$
$281$	4212.28	0.894248	0.447124	+	0.894472i	$0.352448\pi$
$282$	3169.36	0.669265
$283$	7897.89	1.65894	0.829472	−	0.558549i	$-0.188642\pi$
$283$	7897.89	1.65894	0.829472	+	0.558549i	$0.188642\pi$
$284$	5386.35	1.12543
$285$	975.569	0.202764
$286$	−2856.62	−0.590613
$287$	407.627	0.0838378
$288$	10903.5	2.23089
$289$	−4909.17	−0.999219
$290$	−338.287	−0.0684997
$291$	14669.3	2.95509
$292$	4060.06	0.813688
$293$	−4220.28	−0.841472	−0.420736	−	0.907183i	$-0.638228\pi$
$293$	−4220.28	−0.841472	−0.420736	+	0.907183i	$0.638228\pi$
$294$	2931.97	0.581619
$295$	−86.3876	−0.0170498
$296$	587.329	0.115330
$297$	−11762.3	−2.29804
$298$	236.911	0.0460533
$299$	10776.8	2.08441
$300$	−7026.61	−1.35227
$301$	0	0
$302$	2938.87	0.559977
$303$	−7489.42	−1.41999
$304$	1978.11	0.373199
$305$	2.31647	0.000434888 0
$306$	157.046	0.0293390
$307$	4998.51	0.929250	0.464625	−	0.885507i	$-0.346189\pi$
$307$	4998.51	0.929250	0.464625	+	0.885507i	$0.346189\pi$
$308$	2580.71	0.477433
$309$	−15877.9	−2.92318
$310$	242.103	0.0443566
$311$	−2737.77	−0.499179	−0.249590	−	0.968352i	$-0.580296\pi$
$311$	−2737.77	−0.499179	−0.249590	+	0.968352i	$0.580296\pi$
$312$	−9375.99	−1.70132
$313$	−3412.39	−0.616230	−0.308115	−	0.951349i	$-0.599698\pi$
$313$	−3412.39	−0.616230	−0.308115	+	0.951349i	$0.599698\pi$
$314$	−176.792	−0.0317738
$315$	752.898	0.134670
$316$	−633.748	−0.112820
$317$	−2710.30	−0.480207	−0.240103	−	0.970747i	$-0.577181\pi$
$317$	−2710.30	−0.480207	−0.240103	+	0.970747i	$0.577181\pi$
$318$	6724.99	1.18591
$319$	8144.83	1.42954
$320$	−85.2293	−0.0148890
$321$	−7354.10	−1.27871
$322$	2947.77	0.510165
$323$	169.640	0.0292230
$324$	−7013.68	−1.20262
$325$	6483.95	1.10666
$326$	5252.75	0.892401
$327$	−15717.2	−2.65800
$328$	746.405	0.125650
$329$	2642.11	0.442749
$330$	612.857	0.102232
$331$	−4649.66	−0.772110	−0.386055	−	0.922476i	$-0.626162\pi$
$331$	−4649.66	−0.772110	−0.386055	+	0.922476i	$0.626162\pi$
$332$	−1126.94	−0.186291
$333$	−1791.53	−0.294820
$334$	1270.52	0.208143
$335$	1124.72	0.183432
$336$	2227.44	0.361657
$337$	4373.36	0.706920	0.353460	−	0.935450i	$-0.385005\pi$
$337$	4373.36	0.706920	0.353460	+	0.935450i	$0.385005\pi$
$338$	761.450	0.122537
$339$	91.3572	0.0146367
$340$	14.6189	0.00233183
$341$	−5829.04	−0.925689
$342$	6947.20	1.09843
$343$	6056.02	0.953336
$344$	0	0
$345$	−2312.05	−0.360802
$346$	3633.31	0.564531
$347$	2674.99	0.413835	0.206917	−	0.978358i	$-0.433657\pi$
$347$	2674.99	0.413835	0.206917	+	0.978358i	$0.433657\pi$
$348$	11609.0	1.78824
$349$	6071.51	0.931233	0.465617	−	0.884986i	$-0.345833\pi$
$349$	6071.51	0.931233	0.465617	+	0.884986i	$0.345833\pi$
$350$	1773.55	0.270858
$351$	15470.4	2.35256
$352$	7398.96	1.12036
$353$	10040.1	1.51383	0.756915	−	0.653513i	$-0.226705\pi$
$353$	10040.1	1.51383	0.756915	+	0.653513i	$0.226705\pi$
$354$	−897.593	−0.134764
$355$	1066.34	0.159424
$356$	6728.30	1.00168
$357$	191.022	0.0283192
$358$	−4138.36	−0.610948
$359$	−6949.21	−1.02163	−0.510815	−	0.859690i	$-0.670656\pi$
$359$	−6949.21	−1.02163	−0.510815	+	0.859690i	$0.670656\pi$
$360$	1378.63	0.201834
$361$	645.328	0.0940849
$362$	−284.455	−0.0413001
$363$	−2425.69	−0.350732
$364$	−3394.27	−0.488758
$365$	803.772	0.115264
$366$	24.0688	0.00343742
$367$	4128.27	0.587176	0.293588	−	0.955932i	$-0.405151\pi$
$367$	4128.27	0.587176	0.293588	+	0.955932i	$0.405151\pi$
$368$	−4688.03	−0.664077
$369$	−2276.76	−0.321202
$370$	50.4930	0.00709461
$371$	5606.24	0.784532
$372$	−8308.27	−1.15797
$373$	8269.15	1.14788	0.573942	−	0.818896i	$-0.305414\pi$
$373$	8269.15	1.14788	0.573942	+	0.818896i	$0.305414\pi$
$374$	106.569	0.0147341
$375$	−2798.77	−0.385408
$376$	4837.97	0.663562
$377$	−10712.5	−1.46345
$378$	4231.60	0.575794
$379$	737.254	0.0999213	0.0499607	−	0.998751i	$-0.484090\pi$
$379$	737.254	0.0999213	0.0499607	+	0.998751i	$0.484090\pi$
$380$	646.694	0.0873018
$381$	17726.7	2.38364
$382$	−265.895	−0.0356136
$383$	224.641	0.0299703	0.0149852	−	0.999888i	$-0.495230\pi$
$383$	224.641	0.0299703	0.0149852	+	0.999888i	$0.495230\pi$
$384$	12853.4	1.70813
$385$	510.904	0.0676314
$386$	−1872.37	−0.246894
$387$	0	0
$388$	9724.14	1.27234
$389$	6898.42	0.899136	0.449568	−	0.893246i	$-0.351578\pi$
$389$	6898.42	0.899136	0.449568	+	0.893246i	$0.351578\pi$
$390$	−806.059	−0.104657
$391$	−402.039	−0.0519999
$392$	4475.60	0.576663
$393$	−9066.93	−1.16378
$394$	−28.2884	−0.00361714
$395$	−125.464	−0.0159817
$396$	−14414.3	−1.82915
$397$	2541.52	0.321298	0.160649	−	0.987012i	$-0.448641\pi$
$397$	2541.52	0.321298	0.160649	+	0.987012i	$0.448641\pi$
$398$	2443.80	0.307781
$399$	8450.18	1.06025
$400$	−2820.59	−0.352574
$401$	7757.26	0.966032	0.483016	−	0.875611i	$-0.339541\pi$
$401$	7757.26	0.966032	0.483016	+	0.875611i	$0.339541\pi$
$402$	11686.1	1.44988
$403$	7666.62	0.947647
$404$	−4964.65	−0.611388
$405$	−1388.50	−0.170359
$406$	−2930.18	−0.358183
$407$	−1215.70	−0.148059
$408$	349.780	0.0424429
$409$	14186.0	1.71505	0.857524	−	0.514444i	$-0.172002\pi$
$409$	14186.0	1.71505	0.857524	+	0.514444i	$0.172002\pi$
$410$	64.1689	0.00772945
$411$	855.362	0.102657
$412$	−10525.3	−1.25860
$413$	−748.272	−0.0891527
$414$	−16464.5	−1.95456
$415$	−223.100	−0.0263893
$416$	−9731.46	−1.14693
$417$	9181.41	1.07822
$418$	4714.26	0.551631
$419$	7720.93	0.900219	0.450110	−	0.892973i	$-0.351385\pi$
$419$	7720.93	0.900219	0.450110	+	0.892973i	$0.351385\pi$
$420$	728.204	0.0846017
$421$	−4147.90	−0.480181	−0.240090	−	0.970751i	$-0.577177\pi$
$421$	−4147.90	−0.480181	−0.240090	+	0.970751i	$0.577177\pi$
$422$	−3335.47	−0.384759
$423$	−14757.3	−1.69627
$424$	10265.6	1.17580
$425$	−241.890	−0.0276080
$426$	11079.6	1.26011
$427$	20.0648	0.00227401
$428$	−4874.95	−0.550560
$429$	19407.2	2.18412
$430$	0	0
$431$	502.076	0.0561117	0.0280559	−	0.999606i	$-0.491068\pi$
$431$	502.076	0.0561117	0.0280559	+	0.999606i	$0.491068\pi$
$432$	−6729.78	−0.749506
$433$	−6769.19	−0.751285	−0.375642	−	0.926765i	$-0.622578\pi$
$433$	−6769.19	−0.751285	−0.375642	+	0.926765i	$0.622578\pi$
$434$	2097.05	0.231939
$435$	2298.25	0.253316
$436$	−10418.8	−1.14442
$437$	−17784.9	−1.94683
$438$	8351.44	0.911066
$439$	6979.47	0.758797	0.379399	−	0.925233i	$-0.376131\pi$
$439$	6979.47	0.758797	0.379399	+	0.925233i	$0.376131\pi$
$440$	935.516	0.101361
$441$	−13651.9	−1.47413
$442$	−140.164	−0.0150836
$443$	−16667.8	−1.78760	−0.893802	−	0.448461i	$-0.851972\pi$
$443$	−16667.8	−1.78760	−0.893802	+	0.448461i	$0.851972\pi$
$444$	−1732.77	−0.185211
$445$	1332.01	0.141895
$446$	3162.94	0.335807
$447$	−1609.52	−0.170308
$448$	−738.239	−0.0778538
$449$	−989.853	−0.104040	−0.0520201	−	0.998646i	$-0.516566\pi$
$449$	−989.853	−0.104040	−0.0520201	+	0.998646i	$0.516566\pi$
$450$	−9906.01	−1.03772
$451$	−1544.97	−0.161308
$452$	60.5597	0.00630196
$453$	−19966.0	−2.07083
$454$	−5980.82	−0.618268
$455$	−671.965	−0.0692356
$456$	15473.1	1.58903
$457$	12427.9	1.27211	0.636053	−	0.771645i	$-0.280566\pi$
$457$	12427.9	1.27211	0.636053	+	0.771645i	$0.280566\pi$
$458$	−4090.39	−0.417317
$459$	−577.136	−0.0586894
$460$	−1532.63	−0.155346
$461$	−17777.5	−1.79606	−0.898029	−	0.439937i	$-0.855001\pi$
$461$	−17777.5	−1.79606	−0.898029	+	0.439937i	$0.855001\pi$
$462$	5308.44	0.534570
$463$	−2951.46	−0.296255	−0.148128	−	0.988968i	$-0.547325\pi$
$463$	−2951.46	−0.296255	−0.148128	+	0.988968i	$0.547325\pi$
$464$	4660.04	0.466244
$465$	−1644.79	−0.164033
$466$	−3558.34	−0.353727
$467$	−9900.26	−0.981005	−0.490503	−	0.871440i	$-0.663187\pi$
$467$	−9900.26	−0.981005	−0.490503	+	0.871440i	$0.663187\pi$
$468$	18958.3	1.87254
$469$	9742.06	0.959161
$470$	415.923	0.0408194
$471$	1201.09	0.117501
$472$	−1370.16	−0.133616
$473$	0	0
$474$	−1303.60	−0.126322
$475$	−10700.4	−1.03362
$476$	126.626	0.0121931
$477$	−31313.1	−3.00572
$478$	−3744.01	−0.358257
$479$	−7622.47	−0.727097	−0.363548	−	0.931575i	$-0.618435\pi$
$479$	−7622.47	−0.727097	−0.363548	+	0.931575i	$0.618435\pi$
$480$	2087.78	0.198529
$481$	1598.95	0.151571
$482$	−3019.44	−0.285335
$483$	−20026.5	−1.88662
$484$	−1607.96	−0.151011
$485$	1925.09	0.180235
$486$	−3576.73	−0.333835
$487$	−6039.19	−0.561934	−0.280967	−	0.959717i	$-0.590655\pi$
$487$	−6039.19	−0.561934	−0.280967	+	0.959717i	$0.590655\pi$
$488$	36.7406	0.00340814
$489$	−35686.0	−3.30015
$490$	384.770	0.0354737
$491$	19281.0	1.77218	0.886088	−	0.463517i	$-0.153413\pi$
$491$	19281.0	1.77218	0.886088	+	0.463517i	$0.153413\pi$
$492$	−2202.09	−0.201784
$493$	399.638	0.0365087
$494$	−6200.41	−0.564716
$495$	−2853.61	−0.259111
$496$	−3335.07	−0.301913
$497$	9236.41	0.833621
$498$	−2318.08	−0.208586
$499$	3365.38	0.301914	0.150957	−	0.988540i	$-0.451764\pi$
$499$	3365.38	0.301914	0.150957	+	0.988540i	$0.451764\pi$
$500$	−1855.27	−0.165941
$501$	−8631.62	−0.769726
$502$	−940.687	−0.0836353
$503$	−21679.4	−1.92174	−0.960870	−	0.277001i	$-0.910659\pi$
$503$	−21679.4	−1.92174	−0.960870	+	0.277001i	$0.910659\pi$
$504$	11941.4	1.05538
$505$	−982.855	−0.0866069
$506$	−11172.5	−0.981581
$507$	−5173.12	−0.453149
$508$	11750.8	1.02630
$509$	13422.5	1.16884	0.584421	−	0.811451i	$-0.301322\pi$
$509$	13422.5	1.16884	0.584421	+	0.811451i	$0.301322\pi$
$510$	30.0708	0.00261089
$511$	6962.11	0.602712
$512$	7755.60	0.669438
$513$	−25530.6	−2.19728
$514$	−7554.29	−0.648260
$515$	−2083.70	−0.178289
$516$	0	0
$517$	−10014.0	−0.851870
$518$	437.360	0.0370975
$519$	−24683.9	−2.08767
$520$	−1230.43	−0.103766
$521$	−561.968	−0.0472558	−0.0236279	−	0.999721i	$-0.507522\pi$
$521$	−561.968	−0.0472558	−0.0236279	+	0.999721i	$0.507522\pi$
$522$	16366.2	1.37228
$523$	−6645.20	−0.555591	−0.277796	−	0.960640i	$-0.589604\pi$
$523$	−6645.20	−0.555591	−0.277796	+	0.960640i	$0.589604\pi$
$524$	−6010.37	−0.501077
$525$	−12049.1	−1.00165
$526$	2446.89	0.202832
$527$	−286.010	−0.0236410
$528$	−8442.35	−0.695845
$529$	29982.3	2.46423
$530$	882.538	0.0723302
$531$	4179.40	0.341564
$532$	5601.53	0.456498
$533$	2032.02	0.165134
$534$	13839.9	1.12156
$535$	−965.097	−0.0779902
$536$	17838.7	1.43753
$537$	28115.1	2.25932
$538$	−1045.97	−0.0838197
$539$	−9263.97	−0.740311
$540$	−2200.13	−0.175331
$541$	−3637.03	−0.289035	−0.144517	−	0.989502i	$-0.546163\pi$
$541$	−3637.03	−0.289035	−0.144517	+	0.989502i	$0.546163\pi$
$542$	4211.80	0.333786
$543$	1932.52	0.152730
$544$	363.041	0.0286126
$545$	−2062.61	−0.162115
$546$	−6981.92	−0.547250
$547$	−5029.70	−0.393153	−0.196576	−	0.980489i	$-0.562982\pi$
$547$	−5029.70	−0.393153	−0.196576	+	0.980489i	$0.562982\pi$
$548$	567.010	0.0441998
$549$	−112.070	−0.00871226
$550$	−6722.05	−0.521144
$551$	17678.7	1.36686
$552$	−36670.5	−2.82754
$553$	−1086.74	−0.0835676
$554$	−4671.52	−0.358256
$555$	−343.038	−0.0262363
$556$	6086.26	0.464235
$557$	−23294.2	−1.77200	−0.886001	−	0.463682i	$-0.846528\pi$
$557$	−23294.2	−1.77200	−0.886001	+	0.463682i	$0.846528\pi$
$558$	−11712.9	−0.888611
$559$	0	0
$560$	292.312	0.0220579
$561$	−724.004	−0.0544875
$562$	5743.64	0.431104
$563$	22189.7	1.66107	0.830537	−	0.556963i	$-0.188034\pi$
$563$	22189.7	1.66107	0.830537	+	0.556963i	$0.188034\pi$
$564$	−14273.3	−1.06562
$565$	11.9890	0.000892712 0
$566$	10769.1	0.799753
$567$	−12026.9	−0.890799
$568$	16912.8	1.24938
$569$	2549.93	0.187871	0.0939356	−	0.995578i	$-0.470055\pi$
$569$	2549.93	0.187871	0.0939356	+	0.995578i	$0.470055\pi$
$570$	1330.23	0.0977497
$571$	8165.69	0.598465	0.299233	−	0.954180i	$-0.403269\pi$
$571$	8165.69	0.598465	0.299233	+	0.954180i	$0.403269\pi$
$572$	12864.8	0.940394
$573$	1806.43	0.131701
$574$	555.818	0.0404170
$575$	25359.4	1.83924
$576$	4123.36	0.298276
$577$	−9996.04	−0.721214	−0.360607	−	0.932718i	$-0.617430\pi$
$577$	−9996.04	−0.721214	−0.360607	+	0.932718i	$0.617430\pi$
$578$	−6693.87	−0.481710
$579$	12720.4	0.913028
$580$	1523.48	0.109067
$581$	−1932.45	−0.137989
$582$	20002.3	1.42461
$583$	−21248.6	−1.50948
$584$	12748.3	0.903304
$585$	3753.20	0.265257
$586$	−5754.54	−0.405662
$587$	−14616.0	−1.02771	−0.513856	−	0.857876i	$-0.671784\pi$
$587$	−14616.0	−1.02771	−0.513856	+	0.857876i	$0.671784\pi$
$588$	−13204.2	−0.926072
$589$	−12652.2	−0.885099
$590$	−117.793	−0.00821945
$591$	192.185	0.0133764
$592$	−695.560	−0.0482895
$593$	3357.32	0.232493	0.116247	−	0.993220i	$-0.462914\pi$
$593$	3357.32	0.232493	0.116247	+	0.993220i	$0.462914\pi$
$594$	−16038.5	−1.10786
$595$	25.0683	0.00172723
$596$	−1066.93	−0.0733276
$597$	−16602.6	−1.13819
$598$	14694.7	1.00486
$599$	−16783.5	−1.14483	−0.572416	−	0.819963i	$-0.693994\pi$
$599$	−16783.5	−1.14483	−0.572416	+	0.819963i	$0.693994\pi$
$600$	−22063.1	−1.50120
$601$	−26998.2	−1.83241	−0.916205	−	0.400710i	$-0.868764\pi$
$601$	−26998.2	−1.83241	−0.916205	+	0.400710i	$0.868764\pi$
$602$	0	0
$603$	−54413.3	−3.67476
$604$	−13235.3	−0.891614
$605$	−318.330	−0.0213916
$606$	−10212.2	−0.684555
$607$	18391.6	1.22981	0.614904	−	0.788602i	$-0.289195\pi$
$607$	18391.6	1.22981	0.614904	+	0.788602i	$0.289195\pi$
$608$	16059.7	1.07123
$609$	19906.9	1.32458
$610$	3.15861	0.000209653 0
$611$	13170.9	0.872077
$612$	−707.259	−0.0467144
$613$	−266.161	−0.0175369	−0.00876846	−	0.999962i	$-0.502791\pi$
$613$	−266.161	−0.0175369	−0.00876846	+	0.999962i	$0.502791\pi$
$614$	6815.69	0.447978
$615$	−435.948	−0.0285840
$616$	8103.25	0.530015
$617$	−76.6415	−0.00500076	−0.00250038	−	0.999997i	$-0.500796\pi$
$617$	−76.6415	−0.00500076	−0.00250038	+	0.999997i	$0.500796\pi$
$618$	−21650.3	−1.40922
$619$	11007.2	0.714730	0.357365	−	0.933965i	$-0.383675\pi$
$619$	11007.2	0.714730	0.357365	+	0.933965i	$0.383675\pi$
$620$	−1090.31	−0.0706260
$621$	60506.3	3.90988
$622$	−3733.08	−0.240647
$623$	11537.6	0.741963
$624$	11103.8	0.712351
$625$	15073.0	0.964670
$626$	−4652.95	−0.297076
$627$	−32027.6	−2.03996
$628$	796.186	0.0505912
$629$	−59.6503	−0.00378126
$630$	1026.61	0.0649224
$631$	−11972.2	−0.755319	−0.377660	−	0.925945i	$-0.623271\pi$
$631$	−11972.2	−0.755319	−0.377660	+	0.925945i	$0.623271\pi$
$632$	−1989.93	−0.125245
$633$	22660.4	1.42286
$634$	−3695.61	−0.231501
$635$	2326.32	0.145381
$636$	−30286.1	−1.88824
$637$	12184.4	0.757871
$638$	11105.8	0.689161
$639$	−51589.1	−3.19379
$640$	1686.78	0.104181
$641$	11951.5	0.736439	0.368219	−	0.929739i	$-0.379968\pi$
$641$	11951.5	0.736439	0.368219	+	0.929739i	$0.379968\pi$
$642$	−10027.6	−0.616448
$643$	6293.30	0.385977	0.192989	−	0.981201i	$-0.438182\pi$
$643$	6293.30	0.385977	0.192989	+	0.981201i	$0.438182\pi$
$644$	−13275.3	−0.812301
$645$	0	0
$646$	231.312	0.0140880
$647$	21412.1	1.30108	0.650538	−	0.759474i	$-0.274544\pi$
$647$	21412.1	1.30108	0.650538	+	0.759474i	$0.274544\pi$
$648$	−22022.5	−1.33507
$649$	2836.07	0.171534
$650$	8841.16	0.533506
$651$	−14246.9	−0.857724
$652$	−23655.8	−1.42091
$653$	−10308.7	−0.617783	−0.308891	−	0.951097i	$-0.599958\pi$
$653$	−10308.7	−0.617783	−0.308891	+	0.951097i	$0.599958\pi$
$654$	−21431.1	−1.28138
$655$	−1189.88	−0.0709806
$656$	−883.951	−0.0526105
$657$	−38886.2	−2.30913
$658$	3602.64	0.213443
$659$	−16529.3	−0.977074	−0.488537	−	0.872543i	$-0.662469\pi$
$659$	−16529.3	−0.977074	−0.488537	+	0.872543i	$0.662469\pi$
$660$	−2760.01	−0.162778
$661$	8643.64	0.508621	0.254310	−	0.967123i	$-0.418151\pi$
$661$	8643.64	0.508621	0.254310	+	0.967123i	$0.418151\pi$
$662$	−6340.02	−0.372223
$663$	952.244	0.0557799
$664$	−3538.51	−0.206808
$665$	1108.94	0.0646659
$666$	−2442.83	−0.142129
$667$	−41897.6	−2.43221
$668$	−5721.81	−0.331412
$669$	−21488.3	−1.24183
$670$	1533.60	0.0884301
$671$	−76.0489	−0.00437531
$672$	18083.9	1.03810
$673$	13636.6	0.781060	0.390530	−	0.920590i	$-0.372292\pi$
$673$	13636.6	0.781060	0.390530	+	0.920590i	$0.372292\pi$
$674$	5963.27	0.340796
$675$	36404.1	2.07584
$676$	−3429.20	−0.195107
$677$	17196.0	0.976214	0.488107	−	0.872784i	$-0.337688\pi$
$677$	17196.0	0.976214	0.488107	+	0.872784i	$0.337688\pi$
$678$	124.570	0.00705615
$679$	16674.8	0.942444
$680$	45.9025	0.00258865
$681$	40632.3	2.28639
$682$	−7948.15	−0.446262
$683$	11973.4	0.670790	0.335395	−	0.942078i	$-0.391130\pi$
$683$	11973.4	0.670790	0.335395	+	0.942078i	$0.391130\pi$
$684$	−31286.8	−1.74895
$685$	112.251	0.00626117
$686$	8257.65	0.459590
$687$	27789.2	1.54326
$688$	0	0
$689$	27947.1	1.54528
$690$	−3152.58	−0.173937
$691$	3506.11	0.193023	0.0965114	−	0.995332i	$-0.469232\pi$
$691$	3506.11	0.193023	0.0965114	+	0.995332i	$0.469232\pi$
$692$	−16362.7	−0.898865
$693$	−24717.3	−1.35488
$694$	3647.46	0.199504
$695$	1204.90	0.0657618
$696$	36451.6	1.98519
$697$	−75.8064	−0.00411962
$698$	8278.78	0.448935
$699$	24174.5	1.30810
$700$	−7987.22	−0.431269
$701$	−8370.75	−0.451011	−0.225505	−	0.974242i	$-0.572403\pi$
$701$	−8370.75	−0.451011	−0.225505	+	0.974242i	$0.572403\pi$
$702$	21094.5	1.13413
$703$	−2638.73	−0.141567
$704$	2798.05	0.149795
$705$	−2825.69	−0.150952
$706$	13690.2	0.729797
$707$	−8513.29	−0.452864
$708$	4042.32	0.214576
$709$	−20258.7	−1.07311	−0.536553	−	0.843867i	$-0.680274\pi$
$709$	−20258.7	−1.07311	−0.536553	+	0.843867i	$0.680274\pi$
$710$	1454.00	0.0768559
$711$	6069.88	0.320166
$712$	21126.4	1.11200
$713$	29985.0	1.57496
$714$	260.467	0.0136523
$715$	2546.86	0.133213
$716$	18637.2	0.972771
$717$	25435.9	1.32486
$718$	−9475.56	−0.492514
$719$	16975.0	0.880474	0.440237	−	0.897882i	$-0.354894\pi$
$719$	16975.0	0.880474	0.440237	+	0.897882i	$0.354894\pi$
$720$	−1632.68	−0.0845090
$721$	−18048.6	−0.932266
$722$	879.934	0.0453570
$723$	20513.4	1.05519
$724$	1281.05	0.0657593
$725$	−25208.0	−1.29131
$726$	−3307.54	−0.169083
$727$	24683.2	1.25921	0.629607	−	0.776914i	$-0.283216\pi$
$727$	24683.2	1.25921	0.629607	+	0.776914i	$0.283216\pi$
$728$	−10657.8	−0.542587
$729$	−6538.70	−0.332201
$730$	1095.98	0.0555672
$731$	0	0
$732$	−108.394	−0.00547318
$733$	−3253.42	−0.163940	−0.0819698	−	0.996635i	$-0.526121\pi$
$733$	−3253.42	−0.163940	−0.0819698	+	0.996635i	$0.526121\pi$
$734$	5629.08	0.283070
$735$	−2614.04	−0.131184
$736$	−38060.8	−1.90617
$737$	−36924.0	−1.84547
$738$	−3104.47	−0.154847
$739$	10216.8	0.508569	0.254284	−	0.967130i	$-0.418160\pi$
$739$	10216.8	0.508569	0.254284	+	0.967130i	$0.418160\pi$
$740$	−227.396	−0.0112963
$741$	42124.2	2.08835
$742$	7644.36	0.378212
$743$	15821.3	0.781194	0.390597	−	0.920562i	$-0.372269\pi$
$743$	15821.3	0.781194	0.390597	+	0.920562i	$0.372269\pi$
$744$	−26087.4	−1.28550
$745$	−211.221	−0.0103873
$746$	11275.4	0.553379
$747$	10793.5	0.528667
$748$	−479.934	−0.0234601
$749$	−8359.47	−0.407808
$750$	−3816.25	−0.185800
$751$	−8014.22	−0.389405	−0.194703	−	0.980862i	$-0.562374\pi$
$751$	−8014.22	−0.389405	−0.194703	+	0.980862i	$0.562374\pi$
$752$	−5729.50	−0.277837
$753$	6390.81	0.309288
$754$	−14606.9	−0.705508
$755$	−2620.19	−0.126303
$756$	−19057.1	−0.916798
$757$	−1011.88	−0.0485830	−0.0242915	−	0.999705i	$-0.507733\pi$
$757$	−1011.88	−0.0485830	−0.0242915	+	0.999705i	$0.507733\pi$
$758$	1005.28	0.0481707
$759$	75903.7	3.62995
$760$	2030.58	0.0969168
$761$	20282.3	0.966138	0.483069	−	0.875582i	$-0.339522\pi$
$761$	20282.3	0.966138	0.483069	+	0.875582i	$0.339522\pi$
$762$	24171.1	1.14912
$763$	−17865.9	−0.847693
$764$	1197.46	0.0567051
$765$	−140.016	−0.00661739
$766$	306.308	0.0144483
$767$	−3730.14	−0.175603
$768$	22721.8	1.06758
$769$	−24698.6	−1.15820	−0.579100	−	0.815257i	$-0.696596\pi$
$769$	−24698.6	−1.15820	−0.579100	+	0.815257i	$0.696596\pi$
$770$	696.641	0.0326041
$771$	51322.1	2.39730
$772$	8432.23	0.393112
$773$	15449.2	0.718849	0.359425	−	0.933174i	$-0.382973\pi$
$773$	15449.2	0.718849	0.359425	+	0.933174i	$0.382973\pi$
$774$	0	0
$775$	18040.7	0.836183
$776$	30533.2	1.41247
$777$	−2971.32	−0.137189
$778$	9406.31	0.433461
$779$	−3353.43	−0.154235
$780$	3630.10	0.166639
$781$	−35007.5	−1.60393
$782$	−548.198	−0.0250684
$783$	−60145.0	−2.74509
$784$	−5300.35	−0.241452
$785$	157.622	0.00716656
$786$	−12363.2	−0.561043
$787$	−7112.01	−0.322129	−0.161065	−	0.986944i	$-0.551493\pi$
$787$	−7112.01	−0.322129	−0.161065	+	0.986944i	$0.551493\pi$
$788$	127.397	0.00575932
$789$	−16623.6	−0.750085
$790$	−171.075	−0.00770454
$791$	103.847	0.00466796
$792$	−45259.9	−2.03061
$793$	100.023	0.00447909
$794$	3465.48	0.154893
$795$	−5995.76	−0.267481
$796$	−11005.7	−0.490059
$797$	34810.4	1.54711	0.773555	−	0.633730i	$-0.218477\pi$
$797$	34810.4	1.54711	0.773555	+	0.633730i	$0.218477\pi$
$798$	11522.2	0.511130
$799$	−491.354	−0.0217558
$800$	−22899.6	−1.01203
$801$	−64442.0	−2.84263
$802$	10577.4	0.465711
$803$	−26387.5	−1.15965
$804$	−52628.7	−2.30854
$805$	−2628.13	−0.115068
$806$	10453.8	0.456847
$807$	7106.08	0.309970
$808$	−15588.7	−0.678723
$809$	−4108.65	−0.178557	−0.0892784	−	0.996007i	$-0.528456\pi$
$809$	−4108.65	−0.178557	−0.0892784	+	0.996007i	$0.528456\pi$
$810$	−1893.29	−0.0821275
$811$	42098.2	1.82277	0.911387	−	0.411551i	$-0.135013\pi$
$811$	42098.2	1.82277	0.911387	+	0.411551i	$0.135013\pi$
$812$	13196.1	0.570310
$813$	−28614.0	−1.23436
$814$	−1657.66	−0.0713773
$815$	−4683.16	−0.201281
$816$	−414.237	−0.0177711
$817$	0	0
$818$	19343.3	0.826801
$819$	32509.4	1.38702
$820$	−288.985	−0.0123071
$821$	−3818.43	−0.162319	−0.0811596	−	0.996701i	$-0.525862\pi$
$821$	−3818.43	−0.162319	−0.0811596	+	0.996701i	$0.525862\pi$
$822$	1166.33	0.0494894
$823$	−2994.73	−0.126841	−0.0634203	−	0.997987i	$-0.520201\pi$
$823$	−2994.73	−0.126841	−0.0634203	+	0.997987i	$0.520201\pi$
$824$	−33048.7	−1.39722
$825$	45668.1	1.92722
$826$	−1020.30	−0.0429793
$827$	28539.4	1.20001	0.600007	−	0.799995i	$-0.295164\pi$
$827$	28539.4	1.20001	0.600007	+	0.799995i	$0.295164\pi$
$828$	74148.2	3.11211
$829$	25848.2	1.08292	0.541462	−	0.840725i	$-0.317871\pi$
$829$	25848.2	1.08292	0.541462	+	0.840725i	$0.317871\pi$
$830$	−304.208	−0.0127219
$831$	31737.2	1.32485
$832$	−3680.12	−0.153348
$833$	−454.551	−0.0189067
$834$	12519.3	0.519792
$835$	−1132.75	−0.0469466
$836$	−21230.7	−0.878325
$837$	43044.2	1.77757
$838$	10527.8	0.433983
$839$	22681.5	0.933317	0.466659	−	0.884438i	$-0.345458\pi$
$839$	22681.5	0.933317	0.466659	+	0.884438i	$0.345458\pi$
$840$	2286.51	0.0939193
$841$	17258.5	0.707634
$842$	−5655.84	−0.231488
$843$	−39020.9	−1.59425
$844$	15021.4	0.612626
$845$	−678.881	−0.0276381
$846$	−20122.2	−0.817749
$847$	−2757.31	−0.111856
$848$	−12157.3	−0.492316
$849$	−73163.0	−2.95754
$850$	−329.828	−0.0133094
$851$	6253.66	0.251907
$852$	−49897.1	−2.00639
$853$	−4445.85	−0.178456	−0.0892279	−	0.996011i	$-0.528440\pi$
$853$	−4445.85	−0.178456	−0.0892279	+	0.996011i	$0.528440\pi$
$854$	27.3593	0.00109627
$855$	−6193.87	−0.247750
$856$	−15307.0	−0.611196
$857$	27600.4	1.10013	0.550065	−	0.835122i	$-0.314603\pi$
$857$	27600.4	1.10013	0.550065	+	0.835122i	$0.314603\pi$
$858$	26462.6	1.05294
$859$	15121.8	0.600640	0.300320	−	0.953839i	$-0.402907\pi$
$859$	15121.8	0.600640	0.300320	+	0.953839i	$0.402907\pi$
$860$	0	0
$861$	−3776.10	−0.149465
$862$	684.603	0.0270507
$863$	14305.2	0.564260	0.282130	−	0.959376i	$-0.408959\pi$
$863$	14305.2	0.564260	0.282130	+	0.959376i	$0.408959\pi$
$864$	−54637.2	−2.15138
$865$	−3239.32	−0.127330
$866$	−9230.09	−0.362184
$867$	45476.6	1.78139
$868$	−9444.08	−0.369301
$869$	4118.92	0.160788
$870$	3133.76	0.122120
$871$	48564.2	1.88925
$872$	−32714.3	−1.27046
$873$	−93135.4	−3.61072
$874$	−24250.5	−0.938541
$875$	−3181.39	−0.122915
$876$	−37610.8	−1.45063
$877$	−38450.5	−1.48048	−0.740239	−	0.672344i	$-0.765288\pi$
$877$	−38450.5	−1.48048	−0.740239	+	0.672344i	$0.765288\pi$
$878$	9516.83	0.365806
$879$	39095.0	1.50016
$880$	−1107.91	−0.0424405
$881$	−33289.6	−1.27305	−0.636525	−	0.771256i	$-0.719629\pi$
$881$	−33289.6	−1.27305	−0.636525	+	0.771256i	$0.719629\pi$
$882$	−18615.0	−0.710658
$883$	28696.8	1.09368	0.546842	−	0.837236i	$-0.315830\pi$
$883$	28696.8	1.09368	0.546842	+	0.837236i	$0.315830\pi$
$884$	631.232	0.0240165
$885$	800.261	0.0303960
$886$	−22727.2	−0.861779
$887$	40835.8	1.54581	0.772903	−	0.634524i	$-0.218804\pi$
$887$	40835.8	1.54581	0.772903	+	0.634524i	$0.218804\pi$
$888$	−5440.79	−0.205609
$889$	20150.1	0.760194
$890$	1816.25	0.0684055
$891$	45584.0	1.71394
$892$	−14244.4	−0.534682
$893$	−21735.9	−0.814517
$894$	−2194.65	−0.0821031
$895$	3689.61	0.137799
$896$	14610.6	0.544759
$897$	−99832.1	−3.71605
$898$	−1349.71	−0.0501563
$899$	−29806.0	−1.10577
$900$	44611.8	1.65229
$901$	−1042.59	−0.0385503
$902$	−2106.64	−0.0777643
$903$	0	0
$904$	190.153	0.00699603
$905$	253.610	0.00931522
$906$	−27224.6	−0.998318
$907$	38089.4	1.39442	0.697209	−	0.716868i	$-0.254425\pi$
$907$	38089.4	1.39442	0.697209	+	0.716868i	$0.254425\pi$
$908$	26934.7	0.984427
$909$	47550.2	1.73503
$910$	−916.255	−0.0333775
$911$	−29475.8	−1.07198	−0.535992	−	0.844223i	$-0.680062\pi$
$911$	−29475.8	−1.07198	−0.535992	+	0.844223i	$0.680062\pi$
$912$	−18324.5	−0.665333
$913$	7324.30	0.265497
$914$	16946.0	0.613265
$915$	−21.4589	−0.000775310 0
$916$	18421.1	0.664466
$917$	−10306.5	−0.371155
$918$	−786.951	−0.0282933
$919$	15358.0	0.551265	0.275633	−	0.961263i	$-0.411113\pi$
$919$	15358.0	0.551265	0.275633	+	0.961263i	$0.411113\pi$
$920$	−4812.36	−0.172455
$921$	−46304.2	−1.65665
$922$	−24240.5	−0.865854
$923$	46043.5	1.64197
$924$	−23906.7	−0.851159
$925$	3762.57	0.133743
$926$	−4024.45	−0.142820
$927$	100809.	3.57172
$928$	37833.6	1.33831
$929$	−13416.6	−0.473825	−0.236912	−	0.971531i	$-0.576135\pi$
$929$	−13416.6	−0.473825	−0.236912	+	0.971531i	$0.576135\pi$
$930$	−2242.75	−0.0790781
$931$	−20107.8	−0.707849
$932$	16025.0	0.563216
$933$	25361.7	0.889929
$934$	−13499.5	−0.472929
$935$	−95.0129	−0.00332326
$936$	59528.0	2.07878
$937$	−25581.9	−0.891916	−0.445958	−	0.895054i	$-0.647137\pi$
$937$	−25581.9	−0.891916	−0.445958	+	0.895054i	$0.647137\pi$
$938$	13283.7	0.462398
$939$	31611.1	1.09860
$940$	−1873.12	−0.0649939
$941$	−20456.0	−0.708659	−0.354329	−	0.935121i	$-0.615291\pi$
$941$	−20456.0	−0.708659	−0.354329	+	0.935121i	$0.615291\pi$
$942$	1637.73	0.0566457
$943$	7947.45	0.274448
$944$	1622.65	0.0559457
$945$	−3772.74	−0.129870
$946$	0	0
$947$	−4194.46	−0.143930	−0.0719650	−	0.997407i	$-0.522927\pi$
$947$	−4194.46	−0.143930	−0.0719650	+	0.997407i	$0.522927\pi$
$948$	5870.80	0.201134
$949$	34706.1	1.18715
$950$	−14590.5	−0.498293
$951$	25107.1	0.856104
$952$	397.598	0.0135360
$953$	1727.73	0.0587268	0.0293634	−	0.999569i	$-0.490652\pi$
$953$	1727.73	0.0587268	0.0293634	+	0.999569i	$0.490652\pi$
$954$	−42696.9	−1.44902
$955$	237.063	0.00803264
$956$	16861.2	0.570429
$957$	−75450.6	−2.54856
$958$	−10393.6	−0.350523
$959$	972.299	0.0327395
$960$	789.531	0.0265438
$961$	−8459.67	−0.283967
$962$	2180.24	0.0730704
$963$	46691.0	1.56241
$964$	13598.1	0.454320
$965$	1669.33	0.0556868
$966$	−27307.0	−0.909513
$967$	50167.1	1.66832	0.834160	−	0.551522i	$-0.185953\pi$
$967$	50167.1	1.66832	0.834160	+	0.551522i	$0.185953\pi$
$968$	−5048.90	−0.167642
$969$	−1571.48	−0.0520983
$970$	2624.95	0.0868888
$971$	47676.0	1.57569	0.787846	−	0.615873i	$-0.211197\pi$
$971$	47676.0	1.57569	0.787846	+	0.615873i	$0.211197\pi$
$972$	16107.8	0.531542
$973$	10436.6	0.343866
$974$	−8234.70	−0.270900
$975$	−60064.8	−1.97294
$976$	−43.5111	−0.00142701
$977$	−7114.07	−0.232957	−0.116479	−	0.993193i	$-0.537161\pi$
$977$	−7114.07	−0.232957	−0.116479	+	0.993193i	$0.537161\pi$
$978$	−48659.4	−1.59096
$979$	−43729.3	−1.42757
$980$	−1732.82	−0.0564824
$981$	99788.4	3.24770
$982$	26290.5	0.854341
$983$	4541.28	0.147349	0.0736747	−	0.997282i	$-0.476527\pi$
$983$	4541.28	0.147349	0.0736747	+	0.997282i	$0.476527\pi$
$984$	−6914.41	−0.224007
$985$	25.2209	0.000815844 0
$986$	544.925	0.0176004
$987$	−24475.5	−0.789325
$988$	27923.6	0.899159
$989$	0	0
$990$	−3891.02	−0.124914
$991$	16414.9	0.526172	0.263086	−	0.964772i	$-0.415260\pi$
$991$	16414.9	0.526172	0.263086	+	0.964772i	$0.415260\pi$
$992$	−27076.5	−0.866611
$993$	43072.6	1.37650
$994$	12594.3	0.401877
$995$	−2178.81	−0.0694199
$996$	10439.5	0.332117
$997$	4488.55	0.142582	0.0712908	−	0.997456i	$-0.477288\pi$
$997$	4488.55	0.142582	0.0712908	+	0.997456i	$0.477288\pi$
$998$	4588.85	0.145549
$999$	8977.29	0.284313

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.h.1.17		30
43.16	even	7		43.4.e.a.41.5	yes	60
43.35	even	7		43.4.e.a.21.5	✓	60
43.42	odd	2		1849.4.a.g.1.14		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.e.a.21.5	✓	60	43.35	even	7
43.4.e.a.41.5	yes	60	43.16	even	7
1849.4.a.g.1.14		30	43.42	odd	2
1849.4.a.h.1.17		30	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+1.36355 q^{2} -9.26361 q^{3} -6.14074 q^{4} -1.21569 q^{5} -12.6314 q^{6} -10.5300 q^{7} -19.2815 q^{8} +58.8145 q^{9} +O(q^{10})\)	\(q+1.36355 q^{2} -9.26361 q^{3} -6.14074 q^{4} -1.21569 q^{5} -12.6314 q^{6} -10.5300 q^{7} -19.2815 q^{8} +58.8145 q^{9} -1.65764 q^{10} +39.9105 q^{11} +56.8855 q^{12} -52.4922 q^{13} -14.3582 q^{14} +11.2617 q^{15} +22.8347 q^{16} +1.95827 q^{17} +80.1962 q^{18} +86.6275 q^{19} +7.46522 q^{20} +97.5462 q^{21} +54.4198 q^{22} -205.303 q^{23} +178.617 q^{24} -123.522 q^{25} -71.5755 q^{26} -294.717 q^{27} +64.6623 q^{28} +204.077 q^{29} +15.3558 q^{30} -146.053 q^{31} +185.388 q^{32} -369.716 q^{33} +2.67019 q^{34} +12.8012 q^{35} -361.165 q^{36} -30.4607 q^{37} +118.121 q^{38} +486.268 q^{39} +23.4403 q^{40} -38.7109 q^{41} +133.009 q^{42} -245.080 q^{44} -71.5000 q^{45} -279.940 q^{46} -250.912 q^{47} -211.532 q^{48} -232.118 q^{49} -168.428 q^{50} -18.1407 q^{51} +322.341 q^{52} -532.405 q^{53} -401.860 q^{54} -48.5187 q^{55} +203.035 q^{56} -802.484 q^{57} +278.268 q^{58} +71.0607 q^{59} -69.1549 q^{60} -1.90548 q^{61} -199.149 q^{62} -619.319 q^{63} +70.1080 q^{64} +63.8141 q^{65} -504.124 q^{66} -925.169 q^{67} -12.0252 q^{68} +1901.85 q^{69} +17.4551 q^{70} -877.149 q^{71} -1134.03 q^{72} -661.167 q^{73} -41.5345 q^{74} +1144.26 q^{75} -531.958 q^{76} -420.259 q^{77} +663.048 q^{78} +103.204 q^{79} -27.7599 q^{80} +1142.15 q^{81} -52.7840 q^{82} +183.518 q^{83} -599.006 q^{84} -2.38065 q^{85} -1890.49 q^{87} -769.537 q^{88} -1095.68 q^{89} -97.4935 q^{90} +552.745 q^{91} +1260.71 q^{92} +1352.97 q^{93} -342.130 q^{94} -105.312 q^{95} -1717.37 q^{96} -1583.54 q^{97} -316.504 q^{98} +2347.32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 27 q^{5} + 8 q^{6} + 48 q^{7} + 90 q^{8} + 216 q^{9}+O(q^{10}) \) 30 * q + 6 * q^2 + 2 * q^3 + 114 * q^4 + 27 * q^5 + 8 * q^6 + 48 * q^7 + 90 * q^8 + 216 * q^9	\( 30 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 27 q^{5} + 8 q^{6} + 48 q^{7} + 90 q^{8} + 216 q^{9} - 27 q^{10} + 80 q^{11} - 36 q^{12} - 13 q^{13} + 36 q^{14} + 16 q^{15} + 318 q^{16} + 66 q^{17} + 80 q^{18} + 254 q^{19} + 312 q^{20} - 548 q^{21} + 305 q^{22} - 105 q^{23} + 123 q^{24} + 523 q^{25} + 549 q^{26} - 10 q^{27} + 578 q^{28} + 793 q^{29} + 1560 q^{30} - 359 q^{31} + 676 q^{32} + 208 q^{33} + 1007 q^{34} - 514 q^{35} + 776 q^{36} + 510 q^{37} - 2066 q^{38} + 898 q^{39} - 1248 q^{40} - 270 q^{41} - 915 q^{42} + 3256 q^{44} + 807 q^{45} + 1960 q^{46} + 1421 q^{47} - 632 q^{48} + 386 q^{49} - 141 q^{50} + 209 q^{51} + 2825 q^{52} - 21 q^{53} + 2368 q^{54} + 2258 q^{55} + 2521 q^{56} - 1723 q^{57} - 347 q^{58} + 1752 q^{59} + 2711 q^{60} + 1759 q^{61} + 395 q^{62} + 2204 q^{63} + 222 q^{64} + 1151 q^{65} + 160 q^{66} - 3001 q^{67} + 1921 q^{68} + 1660 q^{69} + 1597 q^{70} + 727 q^{71} + 9100 q^{72} + 4623 q^{73} - 2649 q^{74} + 1027 q^{75} + 874 q^{76} + 3556 q^{77} - 4979 q^{78} + 546 q^{79} + 5809 q^{80} - 410 q^{81} - 4397 q^{82} - 492 q^{83} - 10611 q^{84} - 1723 q^{85} + 5937 q^{87} + 3974 q^{88} + 5218 q^{89} + 10492 q^{90} + 1104 q^{91} + 1060 q^{92} + 1997 q^{93} - 2134 q^{94} + 6346 q^{95} - 11984 q^{96} + 2590 q^{97} + 6270 q^{98} - 2693 q^{99}+O(q^{100}) \) 30 * q + 6 * q^2 + 2 * q^3 + 114 * q^4 + 27 * q^5 + 8 * q^6 + 48 * q^7 + 90 * q^8 + 216 * q^9 - 27 * q^10 + 80 * q^11 - 36 * q^12 - 13 * q^13 + 36 * q^14 + 16 * q^15 + 318 * q^16 + 66 * q^17 + 80 * q^18 + 254 * q^19 + 312 * q^20 - 548 * q^21 + 305 * q^22 - 105 * q^23 + 123 * q^24 + 523 * q^25 + 549 * q^26 - 10 * q^27 + 578 * q^28 + 793 * q^29 + 1560 * q^30 - 359 * q^31 + 676 * q^32 + 208 * q^33 + 1007 * q^34 - 514 * q^35 + 776 * q^36 + 510 * q^37 - 2066 * q^38 + 898 * q^39 - 1248 * q^40 - 270 * q^41 - 915 * q^42 + 3256 * q^44 + 807 * q^45 + 1960 * q^46 + 1421 * q^47 - 632 * q^48 + 386 * q^49 - 141 * q^50 + 209 * q^51 + 2825 * q^52 - 21 * q^53 + 2368 * q^54 + 2258 * q^55 + 2521 * q^56 - 1723 * q^57 - 347 * q^58 + 1752 * q^59 + 2711 * q^60 + 1759 * q^61 + 395 * q^62 + 2204 * q^63 + 222 * q^64 + 1151 * q^65 + 160 * q^66 - 3001 * q^67 + 1921 * q^68 + 1660 * q^69 + 1597 * q^70 + 727 * q^71 + 9100 * q^72 + 4623 * q^73 - 2649 * q^74 + 1027 * q^75 + 874 * q^76 + 3556 * q^77 - 4979 * q^78 + 546 * q^79 + 5809 * q^80 - 410 * q^81 - 4397 * q^82 - 492 * q^83 - 10611 * q^84 - 1723 * q^85 + 5937 * q^87 + 3974 * q^88 + 5218 * q^89 + 10492 * q^90 + 1104 * q^91 + 1060 * q^92 + 1997 * q^93 - 2134 * q^94 + 6346 * q^95 - 11984 * q^96 + 2590 * q^97 + 6270 * q^98 - 2693 * q^99

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