LMFDB - Embedded newform 1045.4.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,4,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1045.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:	$61.6569959560$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.21988 q^{2} -3.62548 q^{3} +9.80739 q^{4} +5.00000 q^{5} +15.2991 q^{6} +8.81364 q^{7} -7.62695 q^{8} -13.8559 q^{9} +O(q^{10})$	\(q-4.21988 q^{2} -3.62548 q^{3} +9.80739 q^{4} +5.00000 q^{5} +15.2991 q^{6} +8.81364 q^{7} -7.62695 q^{8} -13.8559 q^{9} -21.0994 q^{10} -11.0000 q^{11} -35.5564 q^{12} -11.3674 q^{13} -37.1925 q^{14} -18.1274 q^{15} -46.2743 q^{16} -28.7035 q^{17} +58.4703 q^{18} +19.0000 q^{19} +49.0369 q^{20} -31.9536 q^{21} +46.4187 q^{22} -159.748 q^{23} +27.6513 q^{24} +25.0000 q^{25} +47.9690 q^{26} +148.122 q^{27} +86.4387 q^{28} +219.893 q^{29} +76.4954 q^{30} +95.7092 q^{31} +256.287 q^{32} +39.8802 q^{33} +121.125 q^{34} +44.0682 q^{35} -135.890 q^{36} -223.870 q^{37} -80.1777 q^{38} +41.2122 q^{39} -38.1348 q^{40} -311.038 q^{41} +134.840 q^{42} +42.2308 q^{43} -107.881 q^{44} -69.2796 q^{45} +674.116 q^{46} +362.557 q^{47} +167.766 q^{48} -265.320 q^{49} -105.497 q^{50} +104.064 q^{51} -111.484 q^{52} +529.164 q^{53} -625.058 q^{54} -55.0000 q^{55} -67.2212 q^{56} -68.8841 q^{57} -927.923 q^{58} +65.3971 q^{59} -177.782 q^{60} -110.349 q^{61} -403.881 q^{62} -122.121 q^{63} -711.308 q^{64} -56.8369 q^{65} -168.290 q^{66} -827.057 q^{67} -281.507 q^{68} +579.161 q^{69} -185.962 q^{70} -990.267 q^{71} +105.678 q^{72} +962.327 q^{73} +944.706 q^{74} -90.6369 q^{75} +186.340 q^{76} -96.9500 q^{77} -173.910 q^{78} -358.100 q^{79} -231.371 q^{80} -162.904 q^{81} +1312.54 q^{82} +700.121 q^{83} -313.382 q^{84} -143.518 q^{85} -178.209 q^{86} -797.218 q^{87} +83.8965 q^{88} -763.755 q^{89} +292.352 q^{90} -100.188 q^{91} -1566.71 q^{92} -346.991 q^{93} -1529.95 q^{94} +95.0000 q^{95} -929.164 q^{96} +665.385 q^{97} +1119.62 q^{98} +152.415 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9	\( 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9} + 20 q^{10} - 264 q^{11} + 164 q^{12} - 15 q^{13} + 77 q^{14} + 105 q^{15} + 230 q^{16} + 187 q^{17} - 109 q^{18} + 456 q^{19} + 490 q^{20} + 295 q^{21} - 44 q^{22} + 451 q^{23} + 416 q^{24} + 600 q^{25} + 375 q^{26} + 1335 q^{27} + 815 q^{28} + 271 q^{29} + 75 q^{30} + 302 q^{31} + 1181 q^{32} - 231 q^{33} + 285 q^{34} + 355 q^{35} + 2445 q^{36} + 974 q^{37} + 76 q^{38} + 601 q^{39} + 420 q^{40} + 316 q^{41} + 2158 q^{42} + 686 q^{43} - 1078 q^{44} + 1695 q^{45} - 217 q^{46} + 1798 q^{47} + 353 q^{48} + 1845 q^{49} + 100 q^{50} + 383 q^{51} - 134 q^{52} + 815 q^{53} - 974 q^{54} - 1320 q^{55} + 2001 q^{56} + 399 q^{57} - 888 q^{58} + 1793 q^{59} + 820 q^{60} + 62 q^{61} + 3994 q^{62} + 366 q^{63} - 588 q^{64} - 75 q^{65} - 165 q^{66} + 2363 q^{67} - 1720 q^{68} - 287 q^{69} + 385 q^{70} + 1266 q^{71} + 3838 q^{72} + 127 q^{73} - 2861 q^{74} + 525 q^{75} + 1862 q^{76} - 781 q^{77} - 3916 q^{78} - 1922 q^{79} + 1150 q^{80} + 3688 q^{81} + 2666 q^{82} + 3666 q^{83} + 438 q^{84} + 935 q^{85} + 78 q^{86} + 2685 q^{87} - 924 q^{88} + 2344 q^{89} - 545 q^{90} + 127 q^{91} + 4800 q^{92} + 1344 q^{93} + 1756 q^{94} + 2280 q^{95} + 2874 q^{96} + 1182 q^{97} - 4328 q^{98} - 3729 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9 + 20 * q^10 - 264 * q^11 + 164 * q^12 - 15 * q^13 + 77 * q^14 + 105 * q^15 + 230 * q^16 + 187 * q^17 - 109 * q^18 + 456 * q^19 + 490 * q^20 + 295 * q^21 - 44 * q^22 + 451 * q^23 + 416 * q^24 + 600 * q^25 + 375 * q^26 + 1335 * q^27 + 815 * q^28 + 271 * q^29 + 75 * q^30 + 302 * q^31 + 1181 * q^32 - 231 * q^33 + 285 * q^34 + 355 * q^35 + 2445 * q^36 + 974 * q^37 + 76 * q^38 + 601 * q^39 + 420 * q^40 + 316 * q^41 + 2158 * q^42 + 686 * q^43 - 1078 * q^44 + 1695 * q^45 - 217 * q^46 + 1798 * q^47 + 353 * q^48 + 1845 * q^49 + 100 * q^50 + 383 * q^51 - 134 * q^52 + 815 * q^53 - 974 * q^54 - 1320 * q^55 + 2001 * q^56 + 399 * q^57 - 888 * q^58 + 1793 * q^59 + 820 * q^60 + 62 * q^61 + 3994 * q^62 + 366 * q^63 - 588 * q^64 - 75 * q^65 - 165 * q^66 + 2363 * q^67 - 1720 * q^68 - 287 * q^69 + 385 * q^70 + 1266 * q^71 + 3838 * q^72 + 127 * q^73 - 2861 * q^74 + 525 * q^75 + 1862 * q^76 - 781 * q^77 - 3916 * q^78 - 1922 * q^79 + 1150 * q^80 + 3688 * q^81 + 2666 * q^82 + 3666 * q^83 + 438 * q^84 + 935 * q^85 + 78 * q^86 + 2685 * q^87 - 924 * q^88 + 2344 * q^89 - 545 * q^90 + 127 * q^91 + 4800 * q^92 + 1344 * q^93 + 1756 * q^94 + 2280 * q^95 + 2874 * q^96 + 1182 * q^97 - 4328 * q^98 - 3729 * 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 $

$2$	−4.21988	−1.49195	−0.745976	−	0.665972i	$-0.768017\pi$
$2$	−4.21988	−1.49195	−0.745976	+	0.665972i	$0.768017\pi$
$3$	−3.62548	−0.697723	−0.348862	−	0.937174i	$-0.613432\pi$
$3$	−3.62548	−0.697723	−0.348862	+	0.937174i	$0.613432\pi$
$4$	9.80739	1.22592
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	15.2991	1.04097
$7$	8.81364	0.475892	0.237946	−	0.971278i	$-0.423526\pi$
$7$	8.81364	0.475892	0.237946	+	0.971278i	$0.423526\pi$
$8$	−7.62695	−0.337067
$9$	−13.8559	−0.513182
$10$	−21.0994	−0.667222
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−35.5564	−0.855355
$13$	−11.3674	−0.242519	−0.121259	−	0.992621i	$-0.538693\pi$
$13$	−11.3674	−0.242519	−0.121259	+	0.992621i	$0.538693\pi$
$14$	−37.1925	−0.710008
$15$	−18.1274	−0.312031
$16$	−46.2743	−0.723036
$17$	−28.7035	−0.409507	−0.204754	−	0.978814i	$-0.565639\pi$
$17$	−28.7035	−0.409507	−0.204754	+	0.978814i	$0.565639\pi$
$18$	58.4703	0.765644
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	49.0369	0.548250
$21$	−31.9536	−0.332041
$22$	46.4187	0.449841
$23$	−159.748	−1.44825	−0.724124	−	0.689670i	$-0.757756\pi$
$23$	−159.748	−1.44825	−0.724124	+	0.689670i	$0.757756\pi$
$24$	27.6513	0.235179
$25$	25.0000	0.200000
$26$	47.9690	0.361826
$27$	148.122	1.05578
$28$	86.4387	0.583407
$29$	219.893	1.40804	0.704020	−	0.710180i	$-0.251387\pi$
$29$	219.893	1.40804	0.704020	+	0.710180i	$0.251387\pi$
$30$	76.4954	0.465536
$31$	95.7092	0.554512	0.277256	−	0.960796i	$-0.410575\pi$
$31$	95.7092	0.554512	0.277256	+	0.960796i	$0.410575\pi$
$32$	256.287	1.41580
$33$	39.8802	0.210372
$34$	121.125	0.610966
$35$	44.0682	0.212825
$36$	−135.890	−0.629122
$37$	−223.870	−0.994704	−0.497352	−	0.867549i	$-0.665694\pi$
$37$	−223.870	−0.994704	−0.497352	+	0.867549i	$0.665694\pi$
$38$	−80.1777	−0.342277
$39$	41.2122	0.169211
$40$	−38.1348	−0.150741
$41$	−311.038	−1.18478	−0.592390	−	0.805651i	$-0.701816\pi$
$41$	−311.038	−1.18478	−0.592390	+	0.805651i	$0.701816\pi$
$42$	134.840	0.495389
$43$	42.2308	0.149771	0.0748854	−	0.997192i	$-0.476141\pi$
$43$	42.2308	0.149771	0.0748854	+	0.997192i	$0.476141\pi$
$44$	−107.881	−0.369630
$45$	−69.2796	−0.229502
$46$	674.116	2.16072
$47$	362.557	1.12520	0.562599	−	0.826730i	$-0.309801\pi$
$47$	362.557	1.12520	0.562599	+	0.826730i	$0.309801\pi$
$48$	167.766	0.504479
$49$	−265.320	−0.773527
$50$	−105.497	−0.298391
$51$	104.064	0.285723
$52$	−111.484	−0.297309
$53$	529.164	1.37144	0.685719	−	0.727866i	$-0.259488\pi$
$53$	529.164	1.37144	0.685719	+	0.727866i	$0.259488\pi$
$54$	−625.058	−1.57518
$55$	−55.0000	−0.134840
$56$	−67.2212	−0.160407
$57$	−68.8841	−0.160069
$58$	−927.923	−2.10073
$59$	65.3971	0.144305	0.0721523	−	0.997394i	$-0.477013\pi$
$59$	65.3971	0.144305	0.0721523	+	0.997394i	$0.477013\pi$
$60$	−177.782	−0.382526
$61$	−110.349	−0.231619	−0.115809	−	0.993271i	$-0.536946\pi$
$61$	−110.349	−0.231619	−0.115809	+	0.993271i	$0.536946\pi$
$62$	−403.881	−0.827306
$63$	−122.121	−0.244219
$64$	−711.308	−1.38927
$65$	−56.8369	−0.108458
$66$	−168.290	−0.313864
$67$	−827.057	−1.50808	−0.754038	−	0.656831i	$-0.771897\pi$
$67$	−827.057	−1.50808	−0.754038	+	0.656831i	$0.771897\pi$
$68$	−281.507	−0.502025
$69$	579.161	1.01048
$70$	−185.962	−0.317525
$71$	−990.267	−1.65526	−0.827628	−	0.561278i	$-0.810310\pi$
$71$	−990.267	−1.65526	−0.827628	+	0.561278i	$0.810310\pi$
$72$	105.678	0.172977
$73$	962.327	1.54290	0.771451	−	0.636289i	$-0.219531\pi$
$73$	962.327	1.54290	0.771451	+	0.636289i	$0.219531\pi$
$74$	944.706	1.48405
$75$	−90.6369	−0.139545
$76$	186.340	0.281246
$77$	−96.9500	−0.143487
$78$	−173.910	−0.252455
$79$	−358.100	−0.509993	−0.254996	−	0.966942i	$-0.582074\pi$
$79$	−358.100	−0.509993	−0.254996	+	0.966942i	$0.582074\pi$
$80$	−231.371	−0.323351
$81$	−162.904	−0.223462
$82$	1312.54	1.76764
$83$	700.121	0.925882	0.462941	−	0.886389i	$-0.346794\pi$
$83$	700.121	0.925882	0.462941	+	0.886389i	$0.346794\pi$
$84$	−313.382	−0.407056
$85$	−143.518	−0.183137
$86$	−178.209	−0.223451
$87$	−797.218	−0.982422
$88$	83.8965	0.101629
$89$	−763.755	−0.909639	−0.454819	−	0.890584i	$-0.650296\pi$
$89$	−763.755	−0.909639	−0.454819	+	0.890584i	$0.650296\pi$
$90$	292.352	0.342406
$91$	−100.188	−0.115413
$92$	−1566.71	−1.77544
$93$	−346.991	−0.386896
$94$	−1529.95	−1.67874
$95$	95.0000	0.102598
$96$	−929.164	−0.987838
$97$	665.385	0.696491	0.348246	−	0.937403i	$-0.386777\pi$
$97$	665.385	0.696491	0.348246	+	0.937403i	$0.386777\pi$
$98$	1119.62	1.15407
$99$	152.415	0.154730
$100$	245.185	0.245185
$101$	−567.408	−0.559002	−0.279501	−	0.960145i	$-0.590169\pi$
$101$	−567.408	−0.559002	−0.279501	+	0.960145i	$0.590169\pi$
$102$	−439.137	−0.426285
$103$	−1808.44	−1.73000	−0.865002	−	0.501768i	$-0.832683\pi$
$103$	−1808.44	−1.73000	−0.865002	+	0.501768i	$0.832683\pi$
$104$	86.6984	0.0817450
$105$	−159.768	−0.148493
$106$	−2233.01	−2.04612
$107$	−1948.77	−1.76070	−0.880348	−	0.474327i	$-0.842691\pi$
$107$	−1948.77	−1.76070	−0.880348	+	0.474327i	$0.842691\pi$
$108$	1452.69	1.29431
$109$	−550.989	−0.484176	−0.242088	−	0.970254i	$-0.577832\pi$
$109$	−550.989	−0.484176	−0.242088	+	0.970254i	$0.577832\pi$
$110$	232.093	0.201175
$111$	811.636	0.694028
$112$	−407.845	−0.344087
$113$	1218.04	1.01401	0.507005	−	0.861943i	$-0.330753\pi$
$113$	1218.04	1.01401	0.507005	+	0.861943i	$0.330753\pi$
$114$	290.682	0.238815
$115$	−798.738	−0.647676
$116$	2156.58	1.72615
$117$	157.505	0.124456
$118$	−275.968	−0.215296
$119$	−252.982	−0.194881
$120$	138.257	0.105175
$121$	121.000	0.0909091
$122$	465.660	0.345565
$123$	1127.66	0.826649
$124$	938.657	0.679789
$125$	125.000	0.0894427
$126$	515.336	0.364363
$127$	2679.55	1.87222	0.936110	−	0.351709i	$-0.114399\pi$
$127$	2679.55	1.87222	0.936110	+	0.351709i	$0.114399\pi$
$128$	951.335	0.656929
$129$	−153.107	−0.104499
$130$	239.845	0.161814
$131$	965.580	0.643993	0.321997	−	0.946741i	$-0.395646\pi$
$131$	965.580	0.643993	0.321997	+	0.946741i	$0.395646\pi$
$132$	391.121	0.257899
$133$	167.459	0.109177
$134$	3490.08	2.24998
$135$	740.611	0.472160
$136$	218.920	0.138031
$137$	2309.55	1.44028	0.720141	−	0.693828i	$-0.244077\pi$
$137$	2309.55	1.44028	0.720141	+	0.693828i	$0.244077\pi$
$138$	−2443.99	−1.50758
$139$	−1684.71	−1.02803	−0.514013	−	0.857783i	$-0.671842\pi$
$139$	−1684.71	−1.02803	−0.514013	+	0.857783i	$0.671842\pi$
$140$	432.194	0.260907
$141$	−1314.44	−0.785077
$142$	4178.81	2.46956
$143$	125.041	0.0731221
$144$	641.173	0.371049
$145$	1099.47	0.629694
$146$	−4060.90	−2.30194
$147$	961.911	0.539708
$148$	−2195.58	−1.21943
$149$	−816.801	−0.449093	−0.224547	−	0.974463i	$-0.572090\pi$
$149$	−816.801	−0.449093	−0.224547	+	0.974463i	$0.572090\pi$
$150$	382.477	0.208194
$151$	1970.61	1.06203	0.531014	−	0.847363i	$-0.321811\pi$
$151$	1970.61	1.06203	0.531014	+	0.847363i	$0.321811\pi$
$152$	−144.912	−0.0773284
$153$	397.714	0.210152
$154$	409.117	0.214075
$155$	478.546	0.247985
$156$	404.184	0.207440
$157$	707.434	0.359614	0.179807	−	0.983702i	$-0.442453\pi$
$157$	707.434	0.359614	0.179807	+	0.983702i	$0.442453\pi$
$158$	1511.14	0.760885
$159$	−1918.47	−0.956885
$160$	1281.44	0.633166
$161$	−1407.96	−0.689209
$162$	687.434	0.333395
$163$	4136.28	1.98760	0.993800	−	0.111184i	$-0.0354644\pi$
$163$	4136.28	1.98760	0.993800	+	0.111184i	$0.0354644\pi$
$164$	−3050.47	−1.45245
$165$	199.401	0.0940810
$166$	−2954.42	−1.38137
$167$	2873.02	1.33126	0.665632	−	0.746280i	$-0.268162\pi$
$167$	2873.02	1.33126	0.665632	+	0.746280i	$0.268162\pi$
$168$	243.709	0.111920
$169$	−2067.78	−0.941185
$170$	605.627	0.273232
$171$	−263.262	−0.117732
$172$	414.174	0.183607
$173$	−1997.83	−0.877988	−0.438994	−	0.898490i	$-0.644665\pi$
$173$	−1997.83	−0.877988	−0.438994	+	0.898490i	$0.644665\pi$
$174$	3364.16	1.46573
$175$	220.341	0.0951783
$176$	509.017	0.218003
$177$	−237.096	−0.100685
$178$	3222.95	1.35714
$179$	−789.933	−0.329846	−0.164923	−	0.986306i	$-0.552737\pi$
$179$	−789.933	−0.329846	−0.164923	+	0.986306i	$0.552737\pi$
$180$	−679.452	−0.281352
$181$	−2015.89	−0.827844	−0.413922	−	0.910312i	$-0.635841\pi$
$181$	−2015.89	−0.827844	−0.413922	+	0.910312i	$0.635841\pi$
$182$	422.781	0.172190
$183$	400.068	0.161606
$184$	1218.39	0.488156
$185$	−1119.35	−0.444845
$186$	1464.26	0.577231
$187$	315.739	0.123471
$188$	3555.73	1.37941
$189$	1305.49	0.502438
$190$	−400.889	−0.153071
$191$	4482.74	1.69822	0.849109	−	0.528218i	$-0.177140\pi$
$191$	4482.74	1.69822	0.849109	+	0.528218i	$0.177140\pi$
$192$	2578.83	0.969329
$193$	2136.02	0.796653	0.398327	−	0.917244i	$-0.369591\pi$
$193$	2136.02	0.796653	0.398327	+	0.917244i	$0.369591\pi$
$194$	−2807.85	−1.03913
$195$	206.061	0.0756734
$196$	−2602.09	−0.948285
$197$	−540.267	−0.195393	−0.0976966	−	0.995216i	$-0.531147\pi$
$197$	−540.267	−0.195393	−0.0976966	+	0.995216i	$0.531147\pi$
$198$	−643.173	−0.230850
$199$	1164.14	0.414691	0.207345	−	0.978268i	$-0.433518\pi$
$199$	1164.14	0.414691	0.207345	+	0.978268i	$0.433518\pi$
$200$	−190.674	−0.0674134
$201$	2998.48	1.05222
$202$	2394.39	0.834005
$203$	1938.06	0.670074
$204$	1020.60	0.350274
$205$	−1555.19	−0.529850
$206$	7631.38	2.58108
$207$	2213.45	0.743215
$208$	526.017	0.175350
$209$	−209.000	−0.0691714
$210$	674.202	0.221545
$211$	−5605.46	−1.82889	−0.914445	−	0.404710i	$-0.867372\pi$
$211$	−5605.46	−1.82889	−0.914445	+	0.404710i	$0.867372\pi$
$212$	5189.71	1.68128
$213$	3590.19	1.15491
$214$	8223.57	2.62688
$215$	211.154	0.0669795
$216$	−1129.72	−0.355869
$217$	843.546	0.263888
$218$	2325.11	0.722368
$219$	−3488.89	−1.07652
$220$	−539.406	−0.165303
$221$	326.284	0.0993132
$222$	−3425.01	−1.03546
$223$	−841.513	−0.252699	−0.126350	−	0.991986i	$-0.540326\pi$
$223$	−841.513	−0.252699	−0.126350	+	0.991986i	$0.540326\pi$
$224$	2258.82	0.673768
$225$	−346.398	−0.102636
$226$	−5139.96	−1.51285
$227$	−2482.73	−0.725922	−0.362961	−	0.931804i	$-0.618234\pi$
$227$	−2482.73	−0.725922	−0.362961	+	0.931804i	$0.618234\pi$
$228$	−675.573	−0.196232
$229$	352.789	0.101803	0.0509017	−	0.998704i	$-0.483790\pi$
$229$	352.789	0.101803	0.0509017	+	0.998704i	$0.483790\pi$
$230$	3370.58	0.966302
$231$	351.490	0.100114
$232$	−1677.11	−0.474603
$233$	4133.08	1.16209	0.581045	−	0.813871i	$-0.302644\pi$
$233$	4133.08	1.16209	0.581045	+	0.813871i	$0.302644\pi$
$234$	−664.654	−0.185683
$235$	1812.78	0.503204
$236$	641.374	0.176906
$237$	1298.28	0.355834
$238$	1067.56	0.290753
$239$	3574.56	0.967444	0.483722	−	0.875222i	$-0.339285\pi$
$239$	3574.56	0.967444	0.483722	+	0.875222i	$0.339285\pi$
$240$	838.832	0.225610
$241$	−1551.39	−0.414662	−0.207331	−	0.978271i	$-0.566478\pi$
$241$	−1551.39	−0.414662	−0.207331	+	0.978271i	$0.566478\pi$
$242$	−510.605	−0.135632
$243$	−3408.70	−0.899868
$244$	−1082.24	−0.283947
$245$	−1326.60	−0.345932
$246$	−4758.60	−1.23332
$247$	−215.980	−0.0556376
$248$	−729.969	−0.186908
$249$	−2538.27	−0.646010
$250$	−527.485	−0.133444
$251$	7073.84	1.77887	0.889436	−	0.457060i	$-0.151097\pi$
$251$	7073.84	1.77887	0.889436	+	0.457060i	$0.151097\pi$
$252$	−1197.69	−0.299394
$253$	1757.22	0.436663
$254$	−11307.4	−2.79326
$255$	520.320	0.127779
$256$	1675.95	0.409166
$257$	4190.78	1.01717	0.508587	−	0.861010i	$-0.330168\pi$
$257$	4190.78	1.01717	0.508587	+	0.861010i	$0.330168\pi$
$258$	646.093	0.155907
$259$	−1973.11	−0.473371
$260$	−557.421	−0.132961
$261$	−3046.82	−0.722581
$262$	−4074.63	−0.960807
$263$	4295.59	1.00714	0.503570	−	0.863955i	$-0.332020\pi$
$263$	4295.59	1.00714	0.503570	+	0.863955i	$0.332020\pi$
$264$	−304.165	−0.0709092
$265$	2645.82	0.613326
$266$	−706.657	−0.162887
$267$	2768.97	0.634676
$268$	−8111.27	−1.84879
$269$	4665.69	1.05752	0.528759	−	0.848772i	$-0.322658\pi$
$269$	4665.69	1.05752	0.528759	+	0.848772i	$0.322658\pi$
$270$	−3125.29	−0.704441
$271$	5717.21	1.28154	0.640768	−	0.767735i	$-0.278616\pi$
$271$	5717.21	1.28154	0.640768	+	0.767735i	$0.278616\pi$
$272$	1328.23	0.296088
$273$	363.229	0.0805261
$274$	−9746.04	−2.14883
$275$	−275.000	−0.0603023
$276$	5680.06	1.23877
$277$	2251.59	0.488393	0.244197	−	0.969726i	$-0.421476\pi$
$277$	2251.59	0.488393	0.244197	+	0.969726i	$0.421476\pi$
$278$	7109.29	1.53377
$279$	−1326.14	−0.284566
$280$	−336.106	−0.0717363
$281$	6470.07	1.37357	0.686783	−	0.726862i	$-0.259022\pi$
$281$	6470.07	1.37357	0.686783	+	0.726862i	$0.259022\pi$
$282$	5546.78	1.17130
$283$	6175.93	1.29725	0.648624	−	0.761109i	$-0.275345\pi$
$283$	6175.93	1.29725	0.648624	+	0.761109i	$0.275345\pi$
$284$	−9711.93	−2.02922
$285$	−344.420	−0.0715849
$286$	−527.659	−0.109095
$287$	−2741.38	−0.563827
$288$	−3551.10	−0.726564
$289$	−4089.11	−0.832304
$290$	−4639.61	−0.939474
$291$	−2412.34	−0.485958
$292$	9437.91	1.89148
$293$	−7771.00	−1.54944	−0.774721	−	0.632303i	$-0.782110\pi$
$293$	−7771.00	−1.54944	−0.774721	+	0.632303i	$0.782110\pi$
$294$	−4059.15	−0.805219
$295$	326.985	0.0645350
$296$	1707.45	0.335282
$297$	−1629.34	−0.318330
$298$	3446.80	0.670026
$299$	1815.91	0.351227
$300$	−888.911	−0.171071
$301$	372.207	0.0712746
$302$	−8315.75	−1.58450
$303$	2057.13	0.390029
$304$	−879.211	−0.165876
$305$	−551.746	−0.103583
$306$	−1678.30	−0.313537
$307$	−1250.67	−0.232507	−0.116254	−	0.993220i	$-0.537089\pi$
$307$	−1250.67	−0.232507	−0.116254	+	0.993220i	$0.537089\pi$
$308$	−950.826	−0.175904
$309$	6556.44	1.20706
$310$	−2019.41	−0.369982
$311$	6483.58	1.18215	0.591077	−	0.806615i	$-0.298703\pi$
$311$	6483.58	1.18215	0.591077	+	0.806615i	$0.298703\pi$
$312$	−314.323	−0.0570354
$313$	−3376.81	−0.609803	−0.304902	−	0.952384i	$-0.598624\pi$
$313$	−3376.81	−0.609803	−0.304902	+	0.952384i	$0.598624\pi$
$314$	−2985.28	−0.536527
$315$	−610.605	−0.109218
$316$	−3512.03	−0.625212
$317$	10208.1	1.80866	0.904329	−	0.426836i	$-0.140372\pi$
$317$	10208.1	1.80866	0.904329	+	0.426836i	$0.140372\pi$
$318$	8095.72	1.42763
$319$	−2418.83	−0.424540
$320$	−3556.54	−0.621302
$321$	7065.22	1.22848
$322$	5941.41	1.02827
$323$	−545.367	−0.0939475
$324$	−1597.66	−0.273947
$325$	−284.184	−0.0485037
$326$	−17454.6	−2.96540
$327$	1997.60	0.337821
$328$	2372.27	0.399350
$329$	3195.44	0.535473
$330$	−841.449	−0.140364
$331$	5676.25	0.942583	0.471292	−	0.881977i	$-0.343788\pi$
$331$	5676.25	0.942583	0.471292	+	0.881977i	$0.343788\pi$
$332$	6866.35	1.13506
$333$	3101.93	0.510464
$334$	−12123.8	−1.98618
$335$	−4135.29	−0.674432
$336$	1478.63	0.240077
$337$	−8288.78	−1.33982	−0.669909	−	0.742443i	$-0.733667\pi$
$337$	−8288.78	−1.33982	−0.669909	+	0.742443i	$0.733667\pi$
$338$	8725.79	1.40420
$339$	−4415.96	−0.707498
$340$	−1407.53	−0.224512
$341$	−1052.80	−0.167192
$342$	1110.94	0.175651
$343$	−5361.51	−0.844007
$344$	−322.092	−0.0504827
$345$	2895.81	0.451899
$346$	8430.58	1.30992
$347$	−3924.31	−0.607112	−0.303556	−	0.952814i	$-0.598174\pi$
$347$	−3924.31	−0.607112	−0.303556	+	0.952814i	$0.598174\pi$
$348$	−7818.62	−1.20437
$349$	7186.78	1.10229	0.551146	−	0.834409i	$-0.314191\pi$
$349$	7186.78	1.10229	0.551146	+	0.834409i	$0.314191\pi$
$350$	−929.812	−0.142002
$351$	−1683.76	−0.256047
$352$	−2819.16	−0.426880
$353$	2712.90	0.409045	0.204523	−	0.978862i	$-0.434436\pi$
$353$	2712.90	0.409045	0.204523	+	0.978862i	$0.434436\pi$
$354$	1000.51	0.150217
$355$	−4951.34	−0.740253
$356$	−7490.44	−1.11515
$357$	917.182	0.135973
$358$	3333.42	0.492114
$359$	−10660.3	−1.56722	−0.783608	−	0.621256i	$-0.786623\pi$
$359$	−10660.3	−1.56722	−0.783608	+	0.621256i	$0.786623\pi$
$360$	528.392	0.0773575
$361$	361.000	0.0526316
$362$	8506.81	1.23510
$363$	−438.683	−0.0634294
$364$	−982.581	−0.141487
$365$	4811.64	0.690007
$366$	−1688.24	−0.241108
$367$	−11291.8	−1.60606	−0.803032	−	0.595936i	$-0.796781\pi$
$367$	−11291.8	−1.60606	−0.803032	+	0.595936i	$0.796781\pi$
$368$	7392.21	1.04713
$369$	4309.72	0.608008
$370$	4723.53	0.663688
$371$	4663.86	0.652656
$372$	−3403.08	−0.474305
$373$	2483.06	0.344686	0.172343	−	0.985037i	$-0.444866\pi$
$373$	2483.06	0.344686	0.172343	+	0.985037i	$0.444866\pi$
$374$	−1332.38	−0.184213
$375$	−453.185	−0.0624063
$376$	−2765.20	−0.379267
$377$	−2499.61	−0.341476
$378$	−5509.03	−0.749614
$379$	−6128.27	−0.830575	−0.415288	−	0.909690i	$-0.636319\pi$
$379$	−6128.27	−0.830575	−0.415288	+	0.909690i	$0.636319\pi$
$380$	931.702	0.125777
$381$	−9714.66	−1.30629
$382$	−18916.6	−2.53366
$383$	10674.9	1.42418	0.712090	−	0.702088i	$-0.247749\pi$
$383$	10674.9	1.42418	0.712090	+	0.702088i	$0.247749\pi$
$384$	−3449.04	−0.458355
$385$	−484.750	−0.0641692
$386$	−9013.75	−1.18857
$387$	−585.147	−0.0768597
$388$	6525.69	0.853845
$389$	8661.85	1.12898	0.564490	−	0.825440i	$-0.309073\pi$
$389$	8661.85	1.12898	0.564490	+	0.825440i	$0.309073\pi$
$390$	−869.552	−0.112901
$391$	4585.32	0.593068
$392$	2023.58	0.260730
$393$	−3500.69	−0.449329
$394$	2279.86	0.291517
$395$	−1790.50	−0.228076
$396$	1494.79	0.189687
$397$	−12544.4	−1.58586	−0.792931	−	0.609311i	$-0.791446\pi$
$397$	−12544.4	−1.58586	−0.792931	+	0.609311i	$0.791446\pi$
$398$	−4912.52	−0.618699
$399$	−607.119	−0.0761754
$400$	−1156.86	−0.144607
$401$	3929.95	0.489408	0.244704	−	0.969598i	$-0.421309\pi$
$401$	3929.95	0.489408	0.244704	+	0.969598i	$0.421309\pi$
$402$	−12653.2	−1.56986
$403$	−1087.96	−0.134480
$404$	−5564.79	−0.685294
$405$	−814.519	−0.0999352
$406$	−8178.37	−0.999719
$407$	2462.57	0.299914
$408$	−793.691	−0.0963077
$409$	−6569.36	−0.794215	−0.397107	−	0.917772i	$-0.629986\pi$
$409$	−6569.36	−0.794215	−0.397107	+	0.917772i	$0.629986\pi$
$410$	6562.72	0.790511
$411$	−8373.24	−1.00492
$412$	−17736.0	−2.12085
$413$	576.386	0.0686734
$414$	−9340.49	−1.10884
$415$	3500.60	0.414067
$416$	−2913.32	−0.343358
$417$	6107.89	0.717277
$418$	881.955	0.103201
$419$	−8416.36	−0.981303	−0.490652	−	0.871356i	$-0.663241\pi$
$419$	−8416.36	−0.981303	−0.490652	+	0.871356i	$0.663241\pi$
$420$	−1566.91	−0.182041
$421$	−3163.32	−0.366201	−0.183101	−	0.983094i	$-0.558613\pi$
$421$	−3163.32	−0.366201	−0.183101	+	0.983094i	$0.558613\pi$
$422$	23654.4	2.72862
$423$	−5023.56	−0.577432
$424$	−4035.91	−0.462266
$425$	−717.588	−0.0819015
$426$	−15150.2	−1.72307
$427$	−972.577	−0.110226
$428$	−19112.3	−2.15848
$429$	−453.334	−0.0510190
$430$	−891.045	−0.0999303
$431$	13428.5	1.50076	0.750381	−	0.661006i	$-0.229870\pi$
$431$	13428.5	1.50076	0.750381	+	0.661006i	$0.229870\pi$
$432$	−6854.25	−0.763368
$433$	12946.2	1.43684	0.718421	−	0.695609i	$-0.244865\pi$
$433$	12946.2	1.43684	0.718421	+	0.695609i	$0.244865\pi$
$434$	−3559.66	−0.393708
$435$	−3986.09	−0.439352
$436$	−5403.77	−0.593563
$437$	−3035.21	−0.332251
$438$	14722.7	1.60612
$439$	−2923.88	−0.317879	−0.158940	−	0.987288i	$-0.550808\pi$
$439$	−2923.88	−0.317879	−0.158940	+	0.987288i	$0.550808\pi$
$440$	419.482	0.0454501
$441$	3676.25	0.396960
$442$	−1376.88	−0.148171
$443$	14642.4	1.57039	0.785194	−	0.619250i	$-0.212563\pi$
$443$	14642.4	1.57039	0.785194	+	0.619250i	$0.212563\pi$
$444$	7960.03	0.850825
$445$	−3818.77	−0.406803
$446$	3551.09	0.377015
$447$	2961.29	0.313343
$448$	−6269.21	−0.661144
$449$	5616.34	0.590315	0.295158	−	0.955449i	$-0.404628\pi$
$449$	5616.34	0.590315	0.295158	+	0.955449i	$0.404628\pi$
$450$	1461.76	0.153129
$451$	3421.42	0.357225
$452$	11945.7	1.24310
$453$	−7144.41	−0.741001
$454$	10476.8	1.08304
$455$	−500.940	−0.0516141
$456$	525.375	0.0539538
$457$	−8702.36	−0.890764	−0.445382	−	0.895341i	$-0.646932\pi$
$457$	−8702.36	−0.890764	−0.445382	+	0.895341i	$0.646932\pi$
$458$	−1488.73	−0.151886
$459$	−4251.63	−0.432351
$460$	−7833.53	−0.794001
$461$	−8312.10	−0.839769	−0.419884	−	0.907578i	$-0.637929\pi$
$461$	−8312.10	−0.839769	−0.419884	+	0.907578i	$0.637929\pi$
$462$	−1483.25	−0.149365
$463$	−2255.82	−0.226430	−0.113215	−	0.993571i	$-0.536115\pi$
$463$	−2255.82	−0.226430	−0.113215	+	0.993571i	$0.536115\pi$
$464$	−10175.4	−1.01806
$465$	−1734.96	−0.173025
$466$	−17441.1	−1.73378
$467$	15657.0	1.55143	0.775715	−	0.631084i	$-0.217390\pi$
$467$	15657.0	1.55143	0.775715	+	0.631084i	$0.217390\pi$
$468$	1544.72	0.152574
$469$	−7289.38	−0.717681
$470$	−7649.73	−0.750757
$471$	−2564.78	−0.250911
$472$	−498.780	−0.0486403
$473$	−464.539	−0.0451576
$474$	−5478.60	−0.530887
$475$	475.000	0.0458831
$476$	−2481.10	−0.238909
$477$	−7332.05	−0.703798
$478$	−15084.2	−1.44338
$479$	3712.58	0.354138	0.177069	−	0.984198i	$-0.443338\pi$
$479$	3712.58	0.354138	0.177069	+	0.984198i	$0.443338\pi$
$480$	−4645.82	−0.441775
$481$	2544.82	0.241234
$482$	6546.67	0.618657
$483$	5104.52	0.480877
$484$	1186.69	0.111448
$485$	3326.93	0.311480
$486$	14384.3	1.34256
$487$	1332.74	0.124009	0.0620043	−	0.998076i	$-0.480251\pi$
$487$	1332.74	0.124009	0.0620043	+	0.998076i	$0.480251\pi$
$488$	841.627	0.0780711
$489$	−14996.0	−1.38679
$490$	5598.09	0.516114
$491$	9457.35	0.869255	0.434628	−	0.900610i	$-0.356880\pi$
$491$	9457.35	0.869255	0.434628	+	0.900610i	$0.356880\pi$
$492$	11059.4	1.01341
$493$	−6311.71	−0.576603
$494$	911.410	0.0830087
$495$	762.075	0.0691975
$496$	−4428.87	−0.400932
$497$	−8727.86	−0.787722
$498$	10711.2	0.963816
$499$	3782.96	0.339376	0.169688	−	0.985498i	$-0.445724\pi$
$499$	3782.96	0.339376	0.169688	+	0.985498i	$0.445724\pi$
$500$	1225.92	0.109650
$501$	−10416.1	−0.928854
$502$	−29850.8	−2.65399
$503$	785.134	0.0695972	0.0347986	−	0.999394i	$-0.488921\pi$
$503$	785.134	0.0695972	0.0347986	+	0.999394i	$0.488921\pi$
$504$	931.411	0.0823181
$505$	−2837.04	−0.249993
$506$	−7415.27	−0.651481
$507$	7496.70	0.656687
$508$	26279.4	2.29520
$509$	16725.7	1.45649	0.728247	−	0.685315i	$-0.240335\pi$
$509$	16725.7	1.45649	0.728247	+	0.685315i	$0.240335\pi$
$510$	−2195.69	−0.190640
$511$	8481.60	0.734254
$512$	−14683.0	−1.26739
$513$	2814.32	0.242213
$514$	−17684.6	−1.51758
$515$	−9042.18	−0.773681
$516$	−1501.58	−0.128107
$517$	−3988.12	−0.339260
$518$	8326.29	0.706247
$519$	7243.07	0.612593
$520$	433.492	0.0365575
$521$	−1583.69	−0.133172	−0.0665862	−	0.997781i	$-0.521211\pi$
$521$	−1583.69	−0.133172	−0.0665862	+	0.997781i	$0.521211\pi$
$522$	12857.2	1.07806
$523$	22296.6	1.86417	0.932084	−	0.362241i	$-0.117988\pi$
$523$	22296.6	1.86417	0.932084	+	0.362241i	$0.117988\pi$
$524$	9469.81	0.789486
$525$	−798.841	−0.0664081
$526$	−18126.9	−1.50260
$527$	−2747.19	−0.227077
$528$	−1845.43	−0.152106
$529$	13352.3	1.09742
$530$	−11165.0	−0.915054
$531$	−906.136	−0.0740546
$532$	1642.34	0.133843
$533$	3535.69	0.287332
$534$	−11684.7	−0.946907
$535$	−9743.84	−0.787408
$536$	6307.92	0.508322
$537$	2863.88	0.230141
$538$	−19688.7	−1.57777
$539$	2918.52	0.233227
$540$	7263.46	0.578832
$541$	87.2852	0.00693657	0.00346828	−	0.999994i	$-0.498896\pi$
$541$	87.2852	0.00693657	0.00346828	+	0.999994i	$0.498896\pi$
$542$	−24126.0	−1.91199
$543$	7308.56	0.577606
$544$	−7356.35	−0.579781
$545$	−2754.95	−0.216530
$546$	−1532.78	−0.120141
$547$	4402.03	0.344090	0.172045	−	0.985089i	$-0.444963\pi$
$547$	4402.03	0.344090	0.172045	+	0.985089i	$0.444963\pi$
$548$	22650.7	1.76567
$549$	1528.99	0.118863
$550$	1160.47	0.0899681
$551$	4177.97	0.323026
$552$	−4417.24	−0.340598
$553$	−3156.16	−0.242701
$554$	−9501.44	−0.728660
$555$	4058.18	0.310379
$556$	−16522.6	−1.26028
$557$	8891.29	0.676366	0.338183	−	0.941080i	$-0.390188\pi$
$557$	8891.29	0.676366	0.338183	+	0.941080i	$0.390188\pi$
$558$	5596.14	0.424559
$559$	−480.054	−0.0363222
$560$	−2039.22	−0.153880
$561$	−1144.70	−0.0861487
$562$	−27302.9	−2.04930
$563$	−25576.5	−1.91460	−0.957299	−	0.289099i	$-0.906644\pi$
$563$	−25576.5	−1.91460	−0.957299	+	0.289099i	$0.906644\pi$
$564$	−12891.2	−0.962445
$565$	6090.18	0.453479
$566$	−26061.7	−1.93543
$567$	−1435.77	−0.106344
$568$	7552.72	0.557931
$569$	−7078.98	−0.521557	−0.260779	−	0.965399i	$-0.583979\pi$
$569$	−7078.98	−0.521557	−0.260779	+	0.965399i	$0.583979\pi$
$570$	1453.41	0.106801
$571$	23371.3	1.71288	0.856442	−	0.516243i	$-0.172670\pi$
$571$	23371.3	1.71288	0.856442	+	0.516243i	$0.172670\pi$
$572$	1226.33	0.0896421
$573$	−16252.1	−1.18489
$574$	11568.3	0.841204
$575$	−3993.69	−0.289649
$576$	9855.83	0.712950
$577$	−17775.8	−1.28252	−0.641261	−	0.767323i	$-0.721588\pi$
$577$	−17775.8	−1.28252	−0.641261	+	0.767323i	$0.721588\pi$
$578$	17255.5	1.24176
$579$	−7744.09	−0.555844
$580$	10782.9	0.771957
$581$	6170.61	0.440620
$582$	10179.8	0.725027
$583$	−5820.80	−0.413504
$584$	−7339.62	−0.520061
$585$	787.527	0.0556585
$586$	32792.7	2.31170
$587$	23193.7	1.63085	0.815424	−	0.578864i	$-0.196504\pi$
$587$	23193.7	1.63085	0.815424	+	0.578864i	$0.196504\pi$
$588$	9433.83	0.661641
$589$	1818.47	0.127214
$590$	−1379.84	−0.0962832
$591$	1958.73	0.136330
$592$	10359.4	0.719206
$593$	7922.49	0.548630	0.274315	−	0.961640i	$-0.411549\pi$
$593$	7922.49	0.548630	0.274315	+	0.961640i	$0.411549\pi$
$594$	6875.64	0.474934
$595$	−1264.91	−0.0871535
$596$	−8010.68	−0.550554
$597$	−4220.55	−0.289340
$598$	−7662.93	−0.524014
$599$	15164.6	1.03440	0.517202	−	0.855863i	$-0.326974\pi$
$599$	15164.6	1.03440	0.517202	+	0.855863i	$0.326974\pi$
$600$	691.283	0.0470359
$601$	2579.01	0.175041	0.0875206	−	0.996163i	$-0.472106\pi$
$601$	2579.01	0.175041	0.0875206	+	0.996163i	$0.472106\pi$
$602$	−1570.67	−0.106338
$603$	11459.6	0.773918
$604$	19326.6	1.30196
$605$	605.000	0.0406558
$606$	−8680.82	−0.581905
$607$	12616.2	0.843618	0.421809	−	0.906685i	$-0.361395\pi$
$607$	12616.2	0.843618	0.421809	+	0.906685i	$0.361395\pi$
$608$	4869.46	0.324807
$609$	−7026.39	−0.467526
$610$	2328.30	0.154541
$611$	−4121.32	−0.272882
$612$	3900.53	0.257630
$613$	−19782.7	−1.30345	−0.651725	−	0.758455i	$-0.725954\pi$
$613$	−19782.7	−1.30345	−0.651725	+	0.758455i	$0.725954\pi$
$614$	5277.69	0.346890
$615$	5638.31	0.369689
$616$	739.433	0.0483646
$617$	−12506.0	−0.815998	−0.407999	−	0.912982i	$-0.633773\pi$
$617$	−12506.0	−0.815998	−0.407999	+	0.912982i	$0.633773\pi$
$618$	−27667.4	−1.80088
$619$	20912.9	1.35793	0.678965	−	0.734171i	$-0.262429\pi$
$619$	20912.9	1.35793	0.678965	+	0.734171i	$0.262429\pi$
$620$	4693.28	0.304011
$621$	−23662.2	−1.52903
$622$	−27359.9	−1.76372
$623$	−6731.45	−0.432889
$624$	−1907.06	−0.122346
$625$	625.000	0.0400000
$626$	14249.7	0.909797
$627$	757.725	0.0482625
$628$	6938.07	0.440859
$629$	6425.87	0.407339
$630$	2576.68	0.162948
$631$	13698.2	0.864212	0.432106	−	0.901823i	$-0.357771\pi$
$631$	13698.2	0.864212	0.432106	+	0.901823i	$0.357771\pi$
$632$	2731.21	0.171902
$633$	20322.5	1.27606
$634$	−43077.0	−2.69843
$635$	13397.8	0.837282
$636$	−18815.2	−1.17307
$637$	3015.99	0.187595
$638$	10207.2	0.633393
$639$	13721.1	0.849447
$640$	4756.68	0.293788
$641$	17247.6	1.06277	0.531387	−	0.847129i	$-0.321671\pi$
$641$	17247.6	1.06277	0.531387	+	0.847129i	$0.321671\pi$
$642$	−29814.4	−1.83283
$643$	19615.7	1.20306	0.601530	−	0.798851i	$-0.294558\pi$
$643$	19615.7	1.20306	0.601530	+	0.798851i	$0.294558\pi$
$644$	−13808.4	−0.844917
$645$	−765.534	−0.0467332
$646$	2301.38	0.140165
$647$	−30915.2	−1.87852	−0.939258	−	0.343211i	$-0.888485\pi$
$647$	−30915.2	−1.87852	−0.939258	+	0.343211i	$0.888485\pi$
$648$	1242.46	0.0753216
$649$	−719.368	−0.0435095
$650$	1199.22	0.0723653
$651$	−3058.26	−0.184121
$652$	40566.1	2.43664
$653$	11338.4	0.679491	0.339745	−	0.940517i	$-0.389659\pi$
$653$	11338.4	0.679491	0.339745	+	0.940517i	$0.389659\pi$
$654$	−8429.63	−0.504013
$655$	4827.90	0.288003
$656$	14393.1	0.856639
$657$	−13333.9	−0.791790
$658$	−13484.4	−0.798900
$659$	14522.2	0.858431	0.429215	−	0.903202i	$-0.358790\pi$
$659$	14522.2	0.858431	0.429215	+	0.903202i	$0.358790\pi$
$660$	1955.60	0.115336
$661$	20483.7	1.20533	0.602664	−	0.797995i	$-0.294106\pi$
$661$	20483.7	1.20533	0.602664	+	0.797995i	$0.294106\pi$
$662$	−23953.1	−1.40629
$663$	−1182.93	−0.0692931
$664$	−5339.79	−0.312084
$665$	837.295	0.0488254
$666$	−13089.8	−0.761589
$667$	−35127.4	−2.03919
$668$	28176.8	1.63203
$669$	3050.89	0.176314
$670$	17450.4	1.00622
$671$	1213.84	0.0698357
$672$	−8189.32	−0.470104
$673$	27032.4	1.54833	0.774163	−	0.632986i	$-0.218171\pi$
$673$	27032.4	1.54833	0.774163	+	0.632986i	$0.218171\pi$
$674$	34977.7	1.99894
$675$	3703.05	0.211156
$676$	−20279.5	−1.15382
$677$	12654.3	0.718383	0.359192	−	0.933264i	$-0.383052\pi$
$677$	12654.3	0.718383	0.359192	+	0.933264i	$0.383052\pi$
$678$	18634.8	1.05555
$679$	5864.47	0.331454
$680$	1094.60	0.0617295
$681$	9001.07	0.506493
$682$	4442.69	0.249442
$683$	27118.1	1.51924	0.759622	−	0.650365i	$-0.225384\pi$
$683$	27118.1	1.51924	0.759622	+	0.650365i	$0.225384\pi$
$684$	−2581.92	−0.144330
$685$	11547.8	0.644113
$686$	22624.9	1.25922
$687$	−1279.03	−0.0710306
$688$	−1954.20	−0.108290
$689$	−6015.21	−0.332600
$690$	−12220.0	−0.674211
$691$	−9008.25	−0.495933	−0.247967	−	0.968769i	$-0.579762\pi$
$691$	−9008.25	−0.495933	−0.247967	+	0.968769i	$0.579762\pi$
$692$	−19593.4	−1.07635
$693$	1343.33	0.0736348
$694$	16560.1	0.905782
$695$	−8423.57	−0.459747
$696$	6080.34	0.331142
$697$	8927.89	0.485177
$698$	−30327.4	−1.64457
$699$	−14984.4	−0.810817
$700$	2160.97	0.116681
$701$	−25589.8	−1.37876	−0.689381	−	0.724399i	$-0.742117\pi$
$701$	−25589.8	−1.37876	−0.689381	+	0.724399i	$0.742117\pi$
$702$	7105.27	0.382010
$703$	−4253.53	−0.228201
$704$	7824.39	0.418882
$705$	−6572.21	−0.351097
$706$	−11448.1	−0.610276
$707$	−5000.93	−0.266024
$708$	−2325.29	−0.123432
$709$	−32614.7	−1.72761	−0.863803	−	0.503830i	$-0.831924\pi$
$709$	−32614.7	−1.72761	−0.863803	+	0.503830i	$0.831924\pi$
$710$	20894.0	1.10442
$711$	4961.81	0.261719
$712$	5825.12	0.306609
$713$	−15289.3	−0.803071
$714$	−3870.40	−0.202865
$715$	625.206	0.0327012
$716$	−7747.18	−0.404365
$717$	−12959.5	−0.675008
$718$	44985.3	2.33821
$719$	−8099.43	−0.420108	−0.210054	−	0.977690i	$-0.567364\pi$
$719$	−8099.43	−0.420108	−0.210054	+	0.977690i	$0.567364\pi$
$720$	3205.86	0.165938
$721$	−15938.9	−0.823294
$722$	−1523.38	−0.0785238
$723$	5624.52	0.289320
$724$	−19770.6	−1.01487
$725$	5497.33	0.281608
$726$	1851.19	0.0946337
$727$	5741.83	0.292920	0.146460	−	0.989217i	$-0.453212\pi$
$727$	5741.83	0.292920	0.146460	+	0.989217i	$0.453212\pi$
$728$	764.128	0.0389018
$729$	16756.5	0.851321
$730$	−20304.5	−1.02946
$731$	−1212.17	−0.0613322
$732$	3923.62	0.198116
$733$	29820.3	1.50264	0.751322	−	0.659936i	$-0.229417\pi$
$733$	29820.3	1.50264	0.751322	+	0.659936i	$0.229417\pi$
$734$	47649.9	2.39617
$735$	4809.55	0.241365
$736$	−40941.3	−2.05043
$737$	9097.63	0.454702
$738$	−18186.5	−0.907120
$739$	−12396.7	−0.617077	−0.308538	−	0.951212i	$-0.599840\pi$
$739$	−12396.7	−0.617077	−0.308538	+	0.951212i	$0.599840\pi$
$740$	−10977.9	−0.545346
$741$	783.031	0.0388197
$742$	−19680.9	−0.973732
$743$	2955.14	0.145913	0.0729567	−	0.997335i	$-0.476757\pi$
$743$	2955.14	0.145913	0.0729567	+	0.997335i	$0.476757\pi$
$744$	2646.49	0.130410
$745$	−4084.00	−0.200841
$746$	−10478.2	−0.514255
$747$	−9700.81	−0.475146
$748$	3096.57	0.151366
$749$	−17175.7	−0.837901
$750$	1912.38	0.0931072
$751$	20126.1	0.977914	0.488957	−	0.872308i	$-0.337377\pi$
$751$	20126.1	0.977914	0.488957	+	0.872308i	$0.337377\pi$
$752$	−16777.0	−0.813559
$753$	−25646.0	−1.24116
$754$	10548.0	0.509466
$755$	9853.06	0.474953
$756$	12803.5	0.615950
$757$	−18357.8	−0.881408	−0.440704	−	0.897652i	$-0.645271\pi$
$757$	−18357.8	−0.881408	−0.440704	+	0.897652i	$0.645271\pi$
$758$	25860.6	1.23918
$759$	−6370.78	−0.304670
$760$	−724.560	−0.0345823
$761$	−397.910	−0.0189543	−0.00947716	−	0.999955i	$-0.503017\pi$
$761$	−397.910	−0.0189543	−0.00947716	+	0.999955i	$0.503017\pi$
$762$	40994.7	1.94892
$763$	−4856.22	−0.230415
$764$	43963.9	2.08188
$765$	1988.57	0.0939828
$766$	−45046.7	−2.12481
$767$	−743.393	−0.0349966
$768$	−6076.10	−0.285485
$769$	−3196.68	−0.149903	−0.0749515	−	0.997187i	$-0.523880\pi$
$769$	−3196.68	−0.149903	−0.0749515	+	0.997187i	$0.523880\pi$
$770$	2045.59	0.0957374
$771$	−15193.6	−0.709707
$772$	20948.8	0.976636
$773$	14051.2	0.653797	0.326898	−	0.945060i	$-0.393997\pi$
$773$	14051.2	0.653797	0.326898	+	0.945060i	$0.393997\pi$
$774$	2469.25	0.114671
$775$	2392.73	0.110902
$776$	−5074.86	−0.234764
$777$	7153.47	0.330282
$778$	−36552.0	−1.68438
$779$	−5909.73	−0.271807
$780$	2020.92	0.0927698
$781$	10892.9	0.499078
$782$	−19349.5	−0.884830
$783$	32571.1	1.48658
$784$	12277.5	0.559288
$785$	3537.17	0.160824
$786$	14772.5	0.670378
$787$	−22034.1	−0.998007	−0.499004	−	0.866600i	$-0.666301\pi$
$787$	−22034.1	−0.998007	−0.499004	+	0.866600i	$0.666301\pi$
$788$	−5298.61	−0.239537
$789$	−15573.6	−0.702704
$790$	7555.70	0.340278
$791$	10735.3	0.482559
$792$	−1162.46	−0.0521544
$793$	1254.38	0.0561719
$794$	52936.0	2.36603
$795$	−9592.36	−0.427932
$796$	11417.1	0.508379
$797$	35385.2	1.57266	0.786330	−	0.617807i	$-0.211979\pi$
$797$	35385.2	1.57266	0.786330	+	0.617807i	$0.211979\pi$
$798$	2561.97	0.113650
$799$	−10406.7	−0.460777
$800$	6407.19	0.283160
$801$	10582.5	0.466810
$802$	−16583.9	−0.730173
$803$	−10585.6	−0.465203
$804$	29407.2	1.28994
$805$	−7039.79	−0.308223
$806$	4591.07	0.200637
$807$	−16915.4	−0.737855
$808$	4327.59	0.188421
$809$	10988.5	0.477546	0.238773	−	0.971075i	$-0.423255\pi$
$809$	10988.5	0.477546	0.238773	+	0.971075i	$0.423255\pi$
$810$	3437.17	0.149099
$811$	−23575.8	−1.02079	−0.510394	−	0.859941i	$-0.670500\pi$
$811$	−23575.8	−1.02079	−0.510394	+	0.859941i	$0.670500\pi$
$812$	19007.3	0.821459
$813$	−20727.6	−0.894157
$814$	−10391.8	−0.447458
$815$	20681.4	0.888882
$816$	−4815.48	−0.206588
$817$	802.386	0.0343598
$818$	27721.9	1.18493
$819$	1388.20	0.0592277
$820$	−15252.4	−0.649556
$821$	−19486.4	−0.828356	−0.414178	−	0.910196i	$-0.635931\pi$
$821$	−19486.4	−0.828356	−0.414178	+	0.910196i	$0.635931\pi$
$822$	35334.0	1.49929
$823$	19500.9	0.825954	0.412977	−	0.910741i	$-0.364489\pi$
$823$	19500.9	0.825954	0.412977	+	0.910741i	$0.364489\pi$
$824$	13792.8	0.583127
$825$	997.006	0.0420743
$826$	−2432.28	−0.102457
$827$	−31759.6	−1.33542	−0.667709	−	0.744423i	$-0.732725\pi$
$827$	−31759.6	−1.33542	−0.667709	+	0.744423i	$0.732725\pi$
$828$	21708.2	0.911124
$829$	−13676.2	−0.572971	−0.286486	−	0.958085i	$-0.592487\pi$
$829$	−13676.2	−0.572971	−0.286486	+	0.958085i	$0.592487\pi$
$830$	−14772.1	−0.617769
$831$	−8163.09	−0.340763
$832$	8085.71	0.336925
$833$	7615.61	0.316765
$834$	−25774.6	−1.07014
$835$	14365.1	0.595359
$836$	−2049.74	−0.0847989
$837$	14176.6	0.585444
$838$	35516.0	1.46406
$839$	−40280.1	−1.65748	−0.828739	−	0.559635i	$-0.810941\pi$
$839$	−40280.1	−1.65748	−0.828739	+	0.559635i	$0.810941\pi$
$840$	1218.54	0.0500521
$841$	23964.0	0.982575
$842$	13348.8	0.546355
$843$	−23457.1	−0.958370
$844$	−54974.9	−2.24208
$845$	−10338.9	−0.420911
$846$	21198.8	0.861501
$847$	1066.45	0.0432629
$848$	−24486.7	−0.991599
$849$	−22390.7	−0.905120
$850$	3028.14	0.122193
$851$	35762.7	1.44058
$852$	35210.4	1.41583
$853$	18209.9	0.730946	0.365473	−	0.930822i	$-0.380907\pi$
$853$	18209.9	0.730946	0.365473	+	0.930822i	$0.380907\pi$
$854$	4104.16	0.164451
$855$	−1316.31	−0.0526514
$856$	14863.2	0.593472
$857$	45147.1	1.79953	0.899763	−	0.436378i	$-0.143739\pi$
$857$	45147.1	1.79953	0.899763	+	0.436378i	$0.143739\pi$
$858$	1913.01	0.0761180
$859$	3874.87	0.153910	0.0769551	−	0.997035i	$-0.475480\pi$
$859$	3874.87	0.153910	0.0769551	+	0.997035i	$0.475480\pi$
$860$	2070.87	0.0821117
$861$	9938.80	0.393395
$862$	−56666.7	−2.23907
$863$	−24258.7	−0.956866	−0.478433	−	0.878124i	$-0.658795\pi$
$863$	−24258.7	−0.956866	−0.478433	+	0.878124i	$0.658795\pi$
$864$	37961.9	1.49478
$865$	−9989.13	−0.392648
$866$	−54631.2	−2.14370
$867$	14825.0	0.580718
$868$	8272.98	0.323506
$869$	3939.10	0.153769
$870$	16820.8	0.655493
$871$	9401.47	0.365737
$872$	4202.37	0.163200
$873$	−9219.53	−0.357427
$874$	12808.2	0.495702
$875$	1101.70	0.0425650
$876$	−34216.9	−1.31973
$877$	−47208.0	−1.81768	−0.908838	−	0.417150i	$-0.863029\pi$
$877$	−47208.0	−1.81768	−0.908838	+	0.417150i	$0.863029\pi$
$878$	12338.4	0.474261
$879$	28173.6	1.08108
$880$	2545.08	0.0974941
$881$	19740.0	0.754891	0.377445	−	0.926032i	$-0.376803\pi$
$881$	19740.0	0.754891	0.377445	+	0.926032i	$0.376803\pi$
$882$	−15513.3	−0.592246
$883$	48526.4	1.84943	0.924714	−	0.380663i	$-0.124304\pi$
$883$	48526.4	1.84943	0.924714	+	0.380663i	$0.124304\pi$
$884$	3199.99	0.121750
$885$	−1185.48	−0.0450276
$886$	−61789.2	−2.34295
$887$	−9686.84	−0.366688	−0.183344	−	0.983049i	$-0.558692\pi$
$887$	−9686.84	−0.366688	−0.183344	+	0.983049i	$0.558692\pi$
$888$	−6190.31	−0.233934
$889$	23616.6	0.890973
$890$	16114.8	0.606930
$891$	1791.94	0.0673763
$892$	−8253.05	−0.309790
$893$	6888.58	0.258138
$894$	−12496.3	−0.467493
$895$	−3949.66	−0.147511
$896$	8384.72	0.312627
$897$	−6583.55	−0.245059
$898$	−23700.3	−0.880723
$899$	21045.8	0.780775
$900$	−3397.26	−0.125824
$901$	−15188.9	−0.561614
$902$	−14438.0	−0.532963
$903$	−1349.43	−0.0497300
$904$	−9289.89	−0.341789
$905$	−10079.4	−0.370223
$906$	30148.6	1.10554
$907$	14408.6	0.527485	0.263743	−	0.964593i	$-0.415043\pi$
$907$	14408.6	0.527485	0.263743	+	0.964593i	$0.415043\pi$
$908$	−24349.1	−0.889925
$909$	7861.96	0.286870
$910$	2113.90	0.0770058
$911$	29629.5	1.07757	0.538787	−	0.842442i	$-0.318883\pi$
$911$	29629.5	1.07757	0.538787	+	0.842442i	$0.318883\pi$
$912$	3187.56	0.115735
$913$	−7701.33	−0.279164
$914$	36722.9	1.32898
$915$	2000.34	0.0722724
$916$	3459.94	0.124803
$917$	8510.27	0.306471
$918$	17941.4	0.645047
$919$	12549.7	0.450465	0.225233	−	0.974305i	$-0.427686\pi$
$919$	12549.7	0.450465	0.225233	+	0.974305i	$0.427686\pi$
$920$	6091.94	0.218310
$921$	4534.29	0.162226
$922$	35076.1	1.25290
$923$	11256.7	0.401430
$924$	3447.20	0.122732
$925$	−5596.76	−0.198941
$926$	9519.30	0.337822
$927$	25057.5	0.887807
$928$	56355.9	1.99350
$929$	−32355.5	−1.14268	−0.571340	−	0.820714i	$-0.693576\pi$
$929$	−32355.5	−1.14268	−0.571340	+	0.820714i	$0.693576\pi$
$930$	7321.31	0.258145
$931$	−5041.08	−0.177459
$932$	40534.7	1.42463
$933$	−23506.1	−0.824817
$934$	−66070.5	−2.31466
$935$	1578.69	0.0552180
$936$	−1201.29	−0.0419501
$937$	−55177.5	−1.92377	−0.961884	−	0.273456i	$-0.911833\pi$
$937$	−55177.5	−1.92377	−0.961884	+	0.273456i	$0.911833\pi$
$938$	30760.3	1.07075
$939$	12242.5	0.425474
$940$	17778.7	0.616890
$941$	19586.9	0.678549	0.339274	−	0.940687i	$-0.389819\pi$
$941$	19586.9	0.678549	0.339274	+	0.940687i	$0.389819\pi$
$942$	10823.1	0.374347
$943$	49687.6	1.71586
$944$	−3026.20	−0.104337
$945$	6527.47	0.224697
$946$	1960.30	0.0673730
$947$	36133.9	1.23991	0.619955	−	0.784637i	$-0.287151\pi$
$947$	36133.9	1.23991	0.619955	+	0.784637i	$0.287151\pi$
$948$	12732.8	0.436225
$949$	−10939.1	−0.374183
$950$	−2004.44	−0.0684555
$951$	−37009.3	−1.26194
$952$	1929.48	0.0656880
$953$	15184.0	0.516115	0.258057	−	0.966130i	$-0.416918\pi$
$953$	15184.0	0.516115	0.258057	+	0.966130i	$0.416918\pi$
$954$	30940.4	1.05003
$955$	22413.7	0.759466
$956$	35057.1	1.18601
$957$	8769.39	0.296211
$958$	−15666.7	−0.528358
$959$	20355.6	0.685418
$960$	12894.2	0.433497
$961$	−20630.8	−0.692516
$962$	−10738.8	−0.359910
$963$	27002.0	0.903558
$964$	−15215.1	−0.508344
$965$	10680.1	0.356274
$966$	−21540.4	−0.717446
$967$	5536.21	0.184108	0.0920540	−	0.995754i	$-0.470657\pi$
$967$	5536.21	0.184108	0.0920540	+	0.995754i	$0.470657\pi$
$968$	−922.861	−0.0306424
$969$	1977.22	0.0655493
$970$	−14039.2	−0.464714
$971$	−42945.0	−1.41933	−0.709665	−	0.704539i	$-0.751154\pi$
$971$	−42945.0	−1.41933	−0.709665	+	0.704539i	$0.751154\pi$
$972$	−33430.4	−1.10317
$973$	−14848.4	−0.489229
$974$	−5624.00	−0.185015
$975$	1030.30	0.0338422
$976$	5106.33	0.167469
$977$	−42104.9	−1.37877	−0.689383	−	0.724397i	$-0.742118\pi$
$977$	−42104.9	−1.37877	−0.689383	+	0.724397i	$0.742118\pi$
$978$	63281.3	2.06903
$979$	8401.30	0.274266
$980$	−13010.5	−0.424086
$981$	7634.46	0.248471
$982$	−39908.9	−1.29689
$983$	−48201.8	−1.56399	−0.781994	−	0.623286i	$-0.785797\pi$
$983$	−48201.8	−1.56399	−0.781994	+	0.623286i	$0.785797\pi$
$984$	−8600.62	−0.278636
$985$	−2701.34	−0.0873825
$986$	26634.7	0.860264
$987$	−11585.0	−0.373612
$988$	−2118.20	−0.0682074
$989$	−6746.28	−0.216905
$990$	−3215.87	−0.103239
$991$	39106.3	1.25353	0.626767	−	0.779207i	$-0.284378\pi$
$991$	39106.3	1.25353	0.626767	+	0.779207i	$0.284378\pi$
$992$	24529.1	0.785079
$993$	−20579.1	−0.657662
$994$	36830.5	1.17524
$995$	5820.69	0.185455
$996$	−24893.8	−0.791958
$997$	8648.19	0.274715	0.137358	−	0.990522i	$-0.456139\pi$
$997$	8648.19	0.274715	0.137358	+	0.990522i	$0.456139\pi$
$998$	−15963.6	−0.506332
$999$	−33160.2	−1.05019

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.h.1.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.a.h.1.3	✓	24	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-4.21988 q^{2} -3.62548 q^{3} +9.80739 q^{4} +5.00000 q^{5} +15.2991 q^{6} +8.81364 q^{7} -7.62695 q^{8} -13.8559 q^{9} +O(q^{10})\)	\(q-4.21988 q^{2} -3.62548 q^{3} +9.80739 q^{4} +5.00000 q^{5} +15.2991 q^{6} +8.81364 q^{7} -7.62695 q^{8} -13.8559 q^{9} -21.0994 q^{10} -11.0000 q^{11} -35.5564 q^{12} -11.3674 q^{13} -37.1925 q^{14} -18.1274 q^{15} -46.2743 q^{16} -28.7035 q^{17} +58.4703 q^{18} +19.0000 q^{19} +49.0369 q^{20} -31.9536 q^{21} +46.4187 q^{22} -159.748 q^{23} +27.6513 q^{24} +25.0000 q^{25} +47.9690 q^{26} +148.122 q^{27} +86.4387 q^{28} +219.893 q^{29} +76.4954 q^{30} +95.7092 q^{31} +256.287 q^{32} +39.8802 q^{33} +121.125 q^{34} +44.0682 q^{35} -135.890 q^{36} -223.870 q^{37} -80.1777 q^{38} +41.2122 q^{39} -38.1348 q^{40} -311.038 q^{41} +134.840 q^{42} +42.2308 q^{43} -107.881 q^{44} -69.2796 q^{45} +674.116 q^{46} +362.557 q^{47} +167.766 q^{48} -265.320 q^{49} -105.497 q^{50} +104.064 q^{51} -111.484 q^{52} +529.164 q^{53} -625.058 q^{54} -55.0000 q^{55} -67.2212 q^{56} -68.8841 q^{57} -927.923 q^{58} +65.3971 q^{59} -177.782 q^{60} -110.349 q^{61} -403.881 q^{62} -122.121 q^{63} -711.308 q^{64} -56.8369 q^{65} -168.290 q^{66} -827.057 q^{67} -281.507 q^{68} +579.161 q^{69} -185.962 q^{70} -990.267 q^{71} +105.678 q^{72} +962.327 q^{73} +944.706 q^{74} -90.6369 q^{75} +186.340 q^{76} -96.9500 q^{77} -173.910 q^{78} -358.100 q^{79} -231.371 q^{80} -162.904 q^{81} +1312.54 q^{82} +700.121 q^{83} -313.382 q^{84} -143.518 q^{85} -178.209 q^{86} -797.218 q^{87} +83.8965 q^{88} -763.755 q^{89} +292.352 q^{90} -100.188 q^{91} -1566.71 q^{92} -346.991 q^{93} -1529.95 q^{94} +95.0000 q^{95} -929.164 q^{96} +665.385 q^{97} +1119.62 q^{98} +152.415 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9	\( 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9} + 20 q^{10} - 264 q^{11} + 164 q^{12} - 15 q^{13} + 77 q^{14} + 105 q^{15} + 230 q^{16} + 187 q^{17} - 109 q^{18} + 456 q^{19} + 490 q^{20} + 295 q^{21} - 44 q^{22} + 451 q^{23} + 416 q^{24} + 600 q^{25} + 375 q^{26} + 1335 q^{27} + 815 q^{28} + 271 q^{29} + 75 q^{30} + 302 q^{31} + 1181 q^{32} - 231 q^{33} + 285 q^{34} + 355 q^{35} + 2445 q^{36} + 974 q^{37} + 76 q^{38} + 601 q^{39} + 420 q^{40} + 316 q^{41} + 2158 q^{42} + 686 q^{43} - 1078 q^{44} + 1695 q^{45} - 217 q^{46} + 1798 q^{47} + 353 q^{48} + 1845 q^{49} + 100 q^{50} + 383 q^{51} - 134 q^{52} + 815 q^{53} - 974 q^{54} - 1320 q^{55} + 2001 q^{56} + 399 q^{57} - 888 q^{58} + 1793 q^{59} + 820 q^{60} + 62 q^{61} + 3994 q^{62} + 366 q^{63} - 588 q^{64} - 75 q^{65} - 165 q^{66} + 2363 q^{67} - 1720 q^{68} - 287 q^{69} + 385 q^{70} + 1266 q^{71} + 3838 q^{72} + 127 q^{73} - 2861 q^{74} + 525 q^{75} + 1862 q^{76} - 781 q^{77} - 3916 q^{78} - 1922 q^{79} + 1150 q^{80} + 3688 q^{81} + 2666 q^{82} + 3666 q^{83} + 438 q^{84} + 935 q^{85} + 78 q^{86} + 2685 q^{87} - 924 q^{88} + 2344 q^{89} - 545 q^{90} + 127 q^{91} + 4800 q^{92} + 1344 q^{93} + 1756 q^{94} + 2280 q^{95} + 2874 q^{96} + 1182 q^{97} - 4328 q^{98} - 3729 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9 + 20 * q^10 - 264 * q^11 + 164 * q^12 - 15 * q^13 + 77 * q^14 + 105 * q^15 + 230 * q^16 + 187 * q^17 - 109 * q^18 + 456 * q^19 + 490 * q^20 + 295 * q^21 - 44 * q^22 + 451 * q^23 + 416 * q^24 + 600 * q^25 + 375 * q^26 + 1335 * q^27 + 815 * q^28 + 271 * q^29 + 75 * q^30 + 302 * q^31 + 1181 * q^32 - 231 * q^33 + 285 * q^34 + 355 * q^35 + 2445 * q^36 + 974 * q^37 + 76 * q^38 + 601 * q^39 + 420 * q^40 + 316 * q^41 + 2158 * q^42 + 686 * q^43 - 1078 * q^44 + 1695 * q^45 - 217 * q^46 + 1798 * q^47 + 353 * q^48 + 1845 * q^49 + 100 * q^50 + 383 * q^51 - 134 * q^52 + 815 * q^53 - 974 * q^54 - 1320 * q^55 + 2001 * q^56 + 399 * q^57 - 888 * q^58 + 1793 * q^59 + 820 * q^60 + 62 * q^61 + 3994 * q^62 + 366 * q^63 - 588 * q^64 - 75 * q^65 - 165 * q^66 + 2363 * q^67 - 1720 * q^68 - 287 * q^69 + 385 * q^70 + 1266 * q^71 + 3838 * q^72 + 127 * q^73 - 2861 * q^74 + 525 * q^75 + 1862 * q^76 - 781 * q^77 - 3916 * q^78 - 1922 * q^79 + 1150 * q^80 + 3688 * q^81 + 2666 * q^82 + 3666 * q^83 + 438 * q^84 + 935 * q^85 + 78 * q^86 + 2685 * q^87 - 924 * q^88 + 2344 * q^89 - 545 * q^90 + 127 * q^91 + 4800 * q^92 + 1344 * q^93 + 1756 * q^94 + 2280 * q^95 + 2874 * q^96 + 1182 * q^97 - 4328 * q^98 - 3729 * q^99

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