LMFDB - Embedded newform 2001.4.a.h.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,4,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, 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("2001.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2001.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:	$118.062821921$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.19635 q^{2} +3.00000 q^{3} +2.21665 q^{4} +9.22135 q^{5} -9.58905 q^{6} -13.6162 q^{7} +18.4856 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.19635 q^{2} +3.00000 q^{3} +2.21665 q^{4} +9.22135 q^{5} -9.58905 q^{6} -13.6162 q^{7} +18.4856 q^{8} +9.00000 q^{9} -29.4747 q^{10} -7.43198 q^{11} +6.64995 q^{12} +55.3016 q^{13} +43.5222 q^{14} +27.6641 q^{15} -76.8197 q^{16} -107.240 q^{17} -28.7671 q^{18} -143.680 q^{19} +20.4405 q^{20} -40.8486 q^{21} +23.7552 q^{22} +23.0000 q^{23} +55.4568 q^{24} -39.9667 q^{25} -176.763 q^{26} +27.0000 q^{27} -30.1823 q^{28} -29.0000 q^{29} -88.4240 q^{30} -38.9417 q^{31} +97.6576 q^{32} -22.2959 q^{33} +342.776 q^{34} -125.560 q^{35} +19.9498 q^{36} +280.545 q^{37} +459.251 q^{38} +165.905 q^{39} +170.462 q^{40} +4.83669 q^{41} +130.566 q^{42} -21.1820 q^{43} -16.4741 q^{44} +82.9922 q^{45} -73.5160 q^{46} +580.742 q^{47} -230.459 q^{48} -157.599 q^{49} +127.747 q^{50} -321.719 q^{51} +122.584 q^{52} +245.230 q^{53} -86.3014 q^{54} -68.5329 q^{55} -251.704 q^{56} -431.040 q^{57} +92.6941 q^{58} +236.337 q^{59} +61.3215 q^{60} -836.099 q^{61} +124.471 q^{62} -122.546 q^{63} +302.410 q^{64} +509.956 q^{65} +71.2656 q^{66} +412.622 q^{67} -237.713 q^{68} +69.0000 q^{69} +401.333 q^{70} +888.519 q^{71} +166.371 q^{72} +48.3740 q^{73} -896.721 q^{74} -119.900 q^{75} -318.488 q^{76} +101.195 q^{77} -530.290 q^{78} -571.611 q^{79} -708.381 q^{80} +81.0000 q^{81} -15.4597 q^{82} -1453.80 q^{83} -90.5470 q^{84} -988.896 q^{85} +67.7051 q^{86} -87.0000 q^{87} -137.385 q^{88} +1237.01 q^{89} -265.272 q^{90} -752.998 q^{91} +50.9829 q^{92} -116.825 q^{93} -1856.25 q^{94} -1324.92 q^{95} +292.973 q^{96} +1153.40 q^{97} +503.741 q^{98} -66.8878 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9}+O(q^{10}) $ 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9	\( 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9} + 214 q^{10} + 111 q^{11} + 630 q^{12} + 275 q^{13} + 104 q^{14} + 45 q^{15} + 1062 q^{16} - 58 q^{17} + 54 q^{18} + 331 q^{19} + 287 q^{20} + 234 q^{21} + 285 q^{22} + 1012 q^{23} + 36 q^{24} + 1903 q^{25} + 1084 q^{26} + 1188 q^{27} + 222 q^{28} - 1276 q^{29} + 642 q^{30} + 1394 q^{31} + 42 q^{32} + 333 q^{33} + 373 q^{34} + 567 q^{35} + 1890 q^{36} + 1229 q^{37} + 733 q^{38} + 825 q^{39} + 2483 q^{40} - 107 q^{41} + 312 q^{42} + 1165 q^{43} + 1639 q^{44} + 135 q^{45} + 138 q^{46} + 964 q^{47} + 3186 q^{48} + 4264 q^{49} + 495 q^{50} - 174 q^{51} + 2679 q^{52} - 380 q^{53} + 162 q^{54} + 1260 q^{55} + 2229 q^{56} + 993 q^{57} - 174 q^{58} + 897 q^{59} + 861 q^{60} + 2584 q^{61} + 3034 q^{62} + 702 q^{63} + 6866 q^{64} - 286 q^{65} + 855 q^{66} + 2277 q^{67} - 1554 q^{68} + 3036 q^{69} + 689 q^{70} + 4304 q^{71} + 108 q^{72} + 4712 q^{73} - 1005 q^{74} + 5709 q^{75} + 2877 q^{76} + 919 q^{77} + 3252 q^{78} + 3864 q^{79} + 2593 q^{80} + 3564 q^{81} + 3297 q^{82} - 540 q^{83} + 666 q^{84} + 6537 q^{85} + 3789 q^{86} - 3828 q^{87} + 1707 q^{88} - 331 q^{89} + 1926 q^{90} + 4311 q^{91} + 4830 q^{92} + 4182 q^{93} + 6189 q^{94} + 3267 q^{95} + 126 q^{96} + 5572 q^{97} + 2588 q^{98} + 999 q^{99}+O(q^{100}) \) 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9 + 214 * q^10 + 111 * q^11 + 630 * q^12 + 275 * q^13 + 104 * q^14 + 45 * q^15 + 1062 * q^16 - 58 * q^17 + 54 * q^18 + 331 * q^19 + 287 * q^20 + 234 * q^21 + 285 * q^22 + 1012 * q^23 + 36 * q^24 + 1903 * q^25 + 1084 * q^26 + 1188 * q^27 + 222 * q^28 - 1276 * q^29 + 642 * q^30 + 1394 * q^31 + 42 * q^32 + 333 * q^33 + 373 * q^34 + 567 * q^35 + 1890 * q^36 + 1229 * q^37 + 733 * q^38 + 825 * q^39 + 2483 * q^40 - 107 * q^41 + 312 * q^42 + 1165 * q^43 + 1639 * q^44 + 135 * q^45 + 138 * q^46 + 964 * q^47 + 3186 * q^48 + 4264 * q^49 + 495 * q^50 - 174 * q^51 + 2679 * q^52 - 380 * q^53 + 162 * q^54 + 1260 * q^55 + 2229 * q^56 + 993 * q^57 - 174 * q^58 + 897 * q^59 + 861 * q^60 + 2584 * q^61 + 3034 * q^62 + 702 * q^63 + 6866 * q^64 - 286 * q^65 + 855 * q^66 + 2277 * q^67 - 1554 * q^68 + 3036 * q^69 + 689 * q^70 + 4304 * q^71 + 108 * q^72 + 4712 * q^73 - 1005 * q^74 + 5709 * q^75 + 2877 * q^76 + 919 * q^77 + 3252 * q^78 + 3864 * q^79 + 2593 * q^80 + 3564 * q^81 + 3297 * q^82 - 540 * q^83 + 666 * q^84 + 6537 * q^85 + 3789 * q^86 - 3828 * q^87 + 1707 * q^88 - 331 * q^89 + 1926 * q^90 + 4311 * q^91 + 4830 * q^92 + 4182 * q^93 + 6189 * q^94 + 3267 * q^95 + 126 * q^96 + 5572 * q^97 + 2588 * q^98 + 999 * 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 $

$2$	−3.19635	−1.13008	−0.565040	−	0.825063i	$-0.691139\pi$
$2$	−3.19635	−1.13008	−0.565040	+	0.825063i	$0.691139\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	2.21665	0.277081
$5$	9.22135	0.824783	0.412391	−	0.911007i	$-0.364694\pi$
$5$	9.22135	0.824783	0.412391	+	0.911007i	$0.364694\pi$
$6$	−9.58905	−0.652452
$7$	−13.6162	−0.735206	−0.367603	−	0.929983i	$-0.619821\pi$
$7$	−13.6162	−0.735206	−0.367603	+	0.929983i	$0.619821\pi$
$8$	18.4856	0.816956
$9$	9.00000	0.333333
$10$	−29.4747	−0.932071
$11$	−7.43198	−0.203711	−0.101856	−	0.994799i	$-0.532478\pi$
$11$	−7.43198	−0.203711	−0.101856	+	0.994799i	$0.532478\pi$
$12$	6.64995	0.159973
$13$	55.3016	1.17984	0.589919	−	0.807462i	$-0.299160\pi$
$13$	55.3016	1.17984	0.589919	+	0.807462i	$0.299160\pi$
$14$	43.5222	0.830842
$15$	27.6641	0.476189
$16$	−76.8197	−1.20031
$17$	−107.240	−1.52997	−0.764985	−	0.644048i	$-0.777253\pi$
$17$	−107.240	−1.52997	−0.764985	+	0.644048i	$0.777253\pi$
$18$	−28.7671	−0.376693
$19$	−143.680	−1.73487	−0.867433	−	0.497554i	$-0.834232\pi$
$19$	−143.680	−1.73487	−0.867433	+	0.497554i	$0.834232\pi$
$20$	20.4405	0.228532
$21$	−40.8486	−0.424471
$22$	23.7552	0.230210
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	55.4568	0.471670
$25$	−39.9667	−0.319733
$26$	−176.763	−1.33331
$27$	27.0000	0.192450
$28$	−30.1823	−0.203712
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	−88.4240	−0.538131
$31$	−38.9417	−0.225617	−0.112809	−	0.993617i	$-0.535985\pi$
$31$	−38.9417	−0.225617	−0.112809	+	0.993617i	$0.535985\pi$
$32$	97.6576	0.539487
$33$	−22.2959	−0.117613
$34$	342.776	1.72899
$35$	−125.560	−0.606385
$36$	19.9498	0.0923604
$37$	280.545	1.24652	0.623262	−	0.782013i	$-0.285807\pi$
$37$	280.545	1.24652	0.623262	+	0.782013i	$0.285807\pi$
$38$	459.251	1.96054
$39$	165.905	0.681180
$40$	170.462	0.673812
$41$	4.83669	0.0184235	0.00921175	−	0.999958i	$-0.497068\pi$
$41$	4.83669	0.0184235	0.00921175	+	0.999958i	$0.497068\pi$
$42$	130.566	0.479687
$43$	−21.1820	−0.0751215	−0.0375607	−	0.999294i	$-0.511959\pi$
$43$	−21.1820	−0.0751215	−0.0375607	+	0.999294i	$0.511959\pi$
$44$	−16.4741	−0.0564446
$45$	82.9922	0.274928
$46$	−73.5160	−0.235638
$47$	580.742	1.80234	0.901169	−	0.433468i	$-0.142710\pi$
$47$	580.742	1.80234	0.901169	+	0.433468i	$0.142710\pi$
$48$	−230.459	−0.692998
$49$	−157.599	−0.459472
$50$	127.747	0.361324
$51$	−321.719	−0.883328
$52$	122.584	0.326911
$53$	245.230	0.635565	0.317782	−	0.948164i	$-0.397062\pi$
$53$	245.230	0.635565	0.317782	+	0.948164i	$0.397062\pi$
$54$	−86.3014	−0.217484
$55$	−68.5329	−0.168018
$56$	−251.704	−0.600631
$57$	−431.040	−1.00163
$58$	92.6941	0.209851
$59$	236.337	0.521499	0.260750	−	0.965406i	$-0.416030\pi$
$59$	236.337	0.521499	0.260750	+	0.965406i	$0.416030\pi$
$60$	61.3215	0.131943
$61$	−836.099	−1.75494	−0.877471	−	0.479629i	$-0.840771\pi$
$61$	−836.099	−1.75494	−0.877471	+	0.479629i	$0.840771\pi$
$62$	124.471	0.254966
$63$	−122.546	−0.245069
$64$	302.410	0.590644
$65$	509.956	0.973111
$66$	71.2656	0.132912
$67$	412.622	0.752385	0.376192	−	0.926542i	$-0.377233\pi$
$67$	412.622	0.752385	0.376192	+	0.926542i	$0.377233\pi$
$68$	−237.713	−0.423926
$69$	69.0000	0.120386
$70$	401.333	0.685264
$71$	888.519	1.48518	0.742590	−	0.669746i	$-0.233597\pi$
$71$	888.519	1.48518	0.742590	+	0.669746i	$0.233597\pi$
$72$	166.371	0.272319
$73$	48.3740	0.0775582	0.0387791	−	0.999248i	$-0.487653\pi$
$73$	48.3740	0.0775582	0.0387791	+	0.999248i	$0.487653\pi$
$74$	−896.721	−1.40867
$75$	−119.900	−0.184598
$76$	−318.488	−0.480698
$77$	101.195	0.149770
$78$	−530.290	−0.769788
$79$	−571.611	−0.814067	−0.407033	−	0.913413i	$-0.633437\pi$
$79$	−571.611	−0.814067	−0.407033	+	0.913413i	$0.633437\pi$
$80$	−708.381	−0.989993
$81$	81.0000	0.111111
$82$	−15.4597	−0.0208200
$83$	−1453.80	−1.92260	−0.961299	−	0.275508i	$-0.911154\pi$
$83$	−1453.80	−1.92260	−0.961299	+	0.275508i	$0.911154\pi$
$84$	−90.5470	−0.117613
$85$	−988.896	−1.26189
$86$	67.7051	0.0848933
$87$	−87.0000	−0.107211
$88$	−137.385	−0.166423
$89$	1237.01	1.47329	0.736645	−	0.676280i	$-0.236409\pi$
$89$	1237.01	1.47329	0.736645	+	0.676280i	$0.236409\pi$
$90$	−265.272	−0.310690
$91$	−752.998	−0.867425
$92$	50.9829	0.0577754
$93$	−116.825	−0.130260
$94$	−1856.25	−2.03679
$95$	−1324.92	−1.43089
$96$	292.973	0.311473
$97$	1153.40	1.20732	0.603661	−	0.797241i	$-0.293708\pi$
$97$	1153.40	1.20732	0.603661	+	0.797241i	$0.293708\pi$
$98$	503.741	0.519240
$99$	−66.8878	−0.0679038
$100$	−88.5920	−0.0885920
$101$	878.324	0.865312	0.432656	−	0.901559i	$-0.357576\pi$
$101$	878.324	0.865312	0.432656	+	0.901559i	$0.357576\pi$
$102$	1028.33	0.998232
$103$	1043.39	0.998140	0.499070	−	0.866562i	$-0.333675\pi$
$103$	1043.39	0.998140	0.499070	+	0.866562i	$0.333675\pi$
$104$	1022.28	0.963877
$105$	−376.680	−0.350097
$106$	−783.841	−0.718239
$107$	2017.50	1.82279	0.911397	−	0.411529i	$-0.135005\pi$
$107$	2017.50	1.82279	0.911397	+	0.411529i	$0.135005\pi$
$108$	59.8495	0.0533243
$109$	152.335	0.133863	0.0669313	−	0.997758i	$-0.478679\pi$
$109$	152.335	0.133863	0.0669313	+	0.997758i	$0.478679\pi$
$110$	219.055	0.189873
$111$	841.636	0.719681
$112$	1045.99	0.882473
$113$	314.698	0.261985	0.130993	−	0.991383i	$-0.458184\pi$
$113$	314.698	0.261985	0.130993	+	0.991383i	$0.458184\pi$
$114$	1377.75	1.13192
$115$	212.091	0.171979
$116$	−64.2828	−0.0514527
$117$	497.714	0.393280
$118$	−755.416	−0.589336
$119$	1460.20	1.12484
$120$	511.387	0.389025
$121$	−1275.77	−0.958502
$122$	2672.46	1.98323
$123$	14.5101	0.0106368
$124$	−86.3200	−0.0625142
$125$	−1521.22	−1.08849
$126$	391.699	0.276947
$127$	971.550	0.678828	0.339414	−	0.940637i	$-0.389771\pi$
$127$	971.550	0.678828	0.339414	+	0.940637i	$0.389771\pi$
$128$	−1747.87	−1.20696
$129$	−63.5460	−0.0433714
$130$	−1630.00	−1.09969
$131$	−2608.05	−1.73943	−0.869717	−	0.493550i	$-0.835699\pi$
$131$	−2608.05	−1.73943	−0.869717	+	0.493550i	$0.835699\pi$
$132$	−49.4222	−0.0325883
$133$	1956.38	1.27548
$134$	−1318.88	−0.850255
$135$	248.977	0.158730
$136$	−1982.39	−1.24992
$137$	2284.33	1.42455	0.712276	−	0.701899i	$-0.247664\pi$
$137$	2284.33	1.42455	0.712276	+	0.701899i	$0.247664\pi$
$138$	−220.548	−0.136046
$139$	407.295	0.248534	0.124267	−	0.992249i	$-0.460342\pi$
$139$	407.295	0.248534	0.124267	+	0.992249i	$0.460342\pi$
$140$	−278.322	−0.168018
$141$	1742.23	1.04058
$142$	−2840.02	−1.67837
$143$	−411.000	−0.240347
$144$	−691.377	−0.400102
$145$	−267.419	−0.153158
$146$	−154.620	−0.0876470
$147$	−472.797	−0.265276
$148$	621.871	0.345388
$149$	−2103.66	−1.15664	−0.578318	−	0.815812i	$-0.696291\pi$
$149$	−2103.66	−1.15664	−0.578318	+	0.815812i	$0.696291\pi$
$150$	383.242	0.208611
$151$	2637.89	1.42164	0.710822	−	0.703372i	$-0.248323\pi$
$151$	2637.89	1.42164	0.710822	+	0.703372i	$0.248323\pi$
$152$	−2656.01	−1.41731
$153$	−965.158	−0.509990
$154$	−323.456	−0.169252
$155$	−359.095	−0.186085
$156$	367.753	0.188742
$157$	489.273	0.248715	0.124357	−	0.992237i	$-0.460313\pi$
$157$	489.273	0.248715	0.124357	+	0.992237i	$0.460313\pi$
$158$	1827.07	0.919961
$159$	735.690	0.366944
$160$	900.535	0.444960
$161$	−313.173	−0.153301
$162$	−258.904	−0.125564
$163$	3323.65	1.59711	0.798553	−	0.601924i	$-0.205599\pi$
$163$	3323.65	1.59711	0.798553	+	0.601924i	$0.205599\pi$
$164$	10.7212	0.00510480
$165$	−205.599	−0.0970050
$166$	4646.86	2.17269
$167$	−1341.75	−0.621724	−0.310862	−	0.950455i	$-0.600618\pi$
$167$	−1341.75	−0.621724	−0.310862	+	0.950455i	$0.600618\pi$
$168$	−755.112	−0.346775
$169$	861.267	0.392020
$170$	3160.86	1.42604
$171$	−1293.12	−0.578289
$172$	−46.9530	−0.0208147
$173$	−870.792	−0.382688	−0.191344	−	0.981523i	$-0.561285\pi$
$173$	−870.792	−0.382688	−0.191344	+	0.981523i	$0.561285\pi$
$174$	278.082	0.121157
$175$	544.194	0.235070
$176$	570.922	0.244516
$177$	709.011	0.301088
$178$	−3953.92	−1.66494
$179$	−2818.81	−1.17703	−0.588513	−	0.808488i	$-0.700286\pi$
$179$	−2818.81	−1.17703	−0.588513	+	0.808488i	$0.700286\pi$
$180$	183.964	0.0761772
$181$	−3200.31	−1.31424	−0.657120	−	0.753786i	$-0.728226\pi$
$181$	−3200.31	−1.31424	−0.657120	+	0.753786i	$0.728226\pi$
$182$	2406.85	0.980260
$183$	−2508.30	−1.01322
$184$	425.169	0.170347
$185$	2587.01	1.02811
$186$	373.414	0.147204
$187$	797.004	0.311672
$188$	1287.30	0.499394
$189$	−367.638	−0.141490
$190$	4234.92	1.61702
$191$	71.1565	0.0269566	0.0134783	−	0.999909i	$-0.495710\pi$
$191$	71.1565	0.0269566	0.0134783	+	0.999909i	$0.495710\pi$
$192$	907.229	0.341008
$193$	2567.87	0.957715	0.478858	−	0.877893i	$-0.341051\pi$
$193$	2567.87	0.957715	0.478858	+	0.877893i	$0.341051\pi$
$194$	−3686.67	−1.36437
$195$	1529.87	0.561826
$196$	−349.341	−0.127311
$197$	−623.153	−0.225369	−0.112685	−	0.993631i	$-0.535945\pi$
$197$	−623.153	−0.225369	−0.112685	+	0.993631i	$0.535945\pi$
$198$	213.797	0.0767367
$199$	1454.11	0.517987	0.258993	−	0.965879i	$-0.416609\pi$
$199$	1454.11	0.517987	0.258993	+	0.965879i	$0.416609\pi$
$200$	−738.808	−0.261208
$201$	1237.87	0.434390
$202$	−2807.43	−0.977872
$203$	394.870	0.136524
$204$	−713.139	−0.244754
$205$	44.6008	0.0151954
$206$	−3335.04	−1.12798
$207$	207.000	0.0695048
$208$	−4248.25	−1.41617
$209$	1067.83	0.353412
$210$	1204.00	0.395637
$211$	−1125.50	−0.367217	−0.183608	−	0.982999i	$-0.558778\pi$
$211$	−1125.50	−0.367217	−0.183608	+	0.982999i	$0.558778\pi$
$212$	543.589	0.176103
$213$	2665.56	0.857469
$214$	−6448.63	−2.05990
$215$	−195.327	−0.0619589
$216$	499.112	0.157223
$217$	530.238	0.165875
$218$	−486.915	−0.151275
$219$	145.122	0.0447783
$220$	−151.913	−0.0465545
$221$	−5930.53	−1.80512
$222$	−2690.16	−0.813297
$223$	306.603	0.0920703	0.0460352	−	0.998940i	$-0.485341\pi$
$223$	306.603	0.0920703	0.0460352	+	0.998940i	$0.485341\pi$
$224$	−1329.73	−0.396634
$225$	−359.700	−0.106578
$226$	−1005.89	−0.296064
$227$	5210.98	1.52363	0.761817	−	0.647792i	$-0.224307\pi$
$227$	5210.98	1.52363	0.761817	+	0.647792i	$0.224307\pi$
$228$	−955.464	−0.277531
$229$	1413.04	0.407756	0.203878	−	0.978996i	$-0.434645\pi$
$229$	1413.04	0.407756	0.203878	+	0.978996i	$0.434645\pi$
$230$	−677.917	−0.194350
$231$	303.586	0.0864697
$232$	−536.083	−0.151705
$233$	508.410	0.142949	0.0714743	−	0.997442i	$-0.477230\pi$
$233$	508.410	0.142949	0.0714743	+	0.997442i	$0.477230\pi$
$234$	−1590.87	−0.444437
$235$	5355.22	1.48654
$236$	523.876	0.144498
$237$	−1714.83	−0.470002
$238$	−4667.31	−1.27116
$239$	−5406.19	−1.46317	−0.731585	−	0.681750i	$-0.761219\pi$
$239$	−5406.19	−1.46317	−0.731585	+	0.681750i	$0.761219\pi$
$240$	−2125.14	−0.571573
$241$	3125.14	0.835303	0.417652	−	0.908607i	$-0.362853\pi$
$241$	3125.14	0.835303	0.417652	+	0.908607i	$0.362853\pi$
$242$	4077.79	1.08318
$243$	243.000	0.0641500
$244$	−1853.34	−0.486261
$245$	−1453.27	−0.378965
$246$	−46.3792	−0.0120205
$247$	−7945.73	−2.04686
$248$	−719.861	−0.184319
$249$	−4361.41	−1.11001
$250$	4862.34	1.23008
$251$	5249.09	1.32000	0.659999	−	0.751267i	$-0.270557\pi$
$251$	5249.09	1.32000	0.659999	+	0.751267i	$0.270557\pi$
$252$	−271.641	−0.0679039
$253$	−170.935	−0.0424768
$254$	−3105.41	−0.767130
$255$	−2966.69	−0.728554
$256$	3167.52	0.773320
$257$	−854.678	−0.207445	−0.103722	−	0.994606i	$-0.533075\pi$
$257$	−854.678	−0.207445	−0.103722	+	0.994606i	$0.533075\pi$
$258$	203.115	0.0490132
$259$	−3819.97	−0.916452
$260$	1130.39	0.269631
$261$	−261.000	−0.0618984
$262$	8336.22	1.96570
$263$	4953.50	1.16139	0.580696	−	0.814121i	$-0.302781\pi$
$263$	4953.50	1.16139	0.580696	+	0.814121i	$0.302781\pi$
$264$	−412.154	−0.0960845
$265$	2261.35	0.524203
$266$	−6253.26	−1.44140
$267$	3711.03	0.850604
$268$	914.638	0.208472
$269$	−5299.26	−1.20112	−0.600561	−	0.799579i	$-0.705056\pi$
$269$	−5299.26	−1.20112	−0.600561	+	0.799579i	$0.705056\pi$
$270$	−795.816	−0.179377
$271$	5730.15	1.28443	0.642217	−	0.766523i	$-0.278015\pi$
$271$	5730.15	1.28443	0.642217	+	0.766523i	$0.278015\pi$
$272$	8238.13	1.83643
$273$	−2258.99	−0.500808
$274$	−7301.53	−1.60986
$275$	297.031	0.0651333
$276$	152.949	0.0333566
$277$	−1805.86	−0.391710	−0.195855	−	0.980633i	$-0.562748\pi$
$277$	−1805.86	−0.391710	−0.195855	+	0.980633i	$0.562748\pi$
$278$	−1301.86	−0.280864
$279$	−350.475	−0.0752057
$280$	−2321.05	−0.495390
$281$	5261.19	1.11693	0.558463	−	0.829530i	$-0.311391\pi$
$281$	5261.19	1.11693	0.558463	+	0.829530i	$0.311391\pi$
$282$	−5568.76	−1.17594
$283$	−7465.66	−1.56815	−0.784077	−	0.620663i	$-0.786863\pi$
$283$	−7465.66	−1.56815	−0.784077	+	0.620663i	$0.786863\pi$
$284$	1969.53	0.411515
$285$	−3974.77	−0.826123
$286$	1313.70	0.271611
$287$	−65.8573	−0.0135451
$288$	878.918	0.179829
$289$	6587.38	1.34081
$290$	854.765	0.173081
$291$	3460.20	0.697047
$292$	107.228	0.0214899
$293$	−7377.02	−1.47089	−0.735444	−	0.677586i	$-0.763026\pi$
$293$	−7377.02	−1.47089	−0.735444	+	0.677586i	$0.763026\pi$
$294$	1511.22	0.299783
$295$	2179.35	0.430124
$296$	5186.05	1.01836
$297$	−200.663	−0.0392043
$298$	6724.04	1.30709
$299$	1271.94	0.246013
$300$	−265.776	−0.0511486
$301$	288.418	0.0552298
$302$	−8431.61	−1.60657
$303$	2634.97	0.499588
$304$	11037.4	2.08237
$305$	−7709.96	−1.44745
$306$	3084.98	0.576329
$307$	5263.77	0.978564	0.489282	−	0.872126i	$-0.337259\pi$
$307$	5263.77	0.978564	0.489282	+	0.872126i	$0.337259\pi$
$308$	224.315	0.0414984
$309$	3130.17	0.576276
$310$	1147.79	0.210291
$311$	1064.89	0.194163	0.0970814	−	0.995276i	$-0.469049\pi$
$311$	1064.89	0.194163	0.0970814	+	0.995276i	$0.469049\pi$
$312$	3066.85	0.556495
$313$	3782.31	0.683031	0.341515	−	0.939876i	$-0.389060\pi$
$313$	3782.31	0.683031	0.341515	+	0.939876i	$0.389060\pi$
$314$	−1563.89	−0.281068
$315$	−1130.04	−0.202128
$316$	−1267.06	−0.225562
$317$	11235.1	1.99062	0.995308	−	0.0967561i	$-0.0308467\pi$
$317$	11235.1	1.99062	0.995308	+	0.0967561i	$0.0308467\pi$
$318$	−2351.52	−0.414676
$319$	215.527	0.0378283
$320$	2788.63	0.487153
$321$	6052.49	1.05239
$322$	1001.01	0.173243
$323$	15408.2	2.65429
$324$	179.549	0.0307868
$325$	−2210.22	−0.377234
$326$	−10623.5	−1.80486
$327$	457.004	0.0772856
$328$	89.4091	0.0150512
$329$	−7907.50	−1.32509
$330$	657.165	0.109623
$331$	3432.28	0.569956	0.284978	−	0.958534i	$-0.408014\pi$
$331$	3432.28	0.569956	0.284978	+	0.958534i	$0.408014\pi$
$332$	−3222.57	−0.532715
$333$	2524.91	0.415508
$334$	4288.71	0.702598
$335$	3804.93	0.620554
$336$	3137.98	0.509496
$337$	8542.56	1.38084	0.690420	−	0.723409i	$-0.257426\pi$
$337$	8542.56	1.38084	0.690420	+	0.723409i	$0.257426\pi$
$338$	−2752.91	−0.443014
$339$	944.095	0.151257
$340$	−2192.04	−0.349646
$341$	289.414	0.0459608
$342$	4133.26	0.653513
$343$	6816.26	1.07301
$344$	−391.562	−0.0613710
$345$	636.273	0.0992922
$346$	2783.36	0.432469
$347$	−8312.39	−1.28597	−0.642986	−	0.765878i	$-0.722305\pi$
$347$	−8312.39	−1.28597	−0.642986	+	0.765878i	$0.722305\pi$
$348$	−192.848	−0.0297062
$349$	−845.114	−0.129621	−0.0648107	−	0.997898i	$-0.520644\pi$
$349$	−845.114	−0.129621	−0.0648107	+	0.997898i	$0.520644\pi$
$350$	−1739.44	−0.265648
$351$	1493.14	0.227060
$352$	−725.789	−0.109900
$353$	621.163	0.0936576	0.0468288	−	0.998903i	$-0.485088\pi$
$353$	621.163	0.0936576	0.0468288	+	0.998903i	$0.485088\pi$
$354$	−2266.25	−0.340253
$355$	8193.35	1.22495
$356$	2742.02	0.408221
$357$	4380.60	0.649428
$358$	9009.90	1.33013
$359$	10384.0	1.52659	0.763296	−	0.646049i	$-0.223580\pi$
$359$	10384.0	1.52659	0.763296	+	0.646049i	$0.223580\pi$
$360$	1534.16	0.224604
$361$	13784.9	2.00976
$362$	10229.3	1.48520
$363$	−3827.30	−0.553391
$364$	−1669.13	−0.240347
$365$	446.074	0.0639687
$366$	8017.39	1.14502
$367$	5545.99	0.788824	0.394412	−	0.918934i	$-0.370948\pi$
$367$	5545.99	0.788824	0.394412	+	0.918934i	$0.370948\pi$
$368$	−1766.85	−0.250281
$369$	43.5302	0.00614117
$370$	−8268.98	−1.16185
$371$	−3339.10	−0.467271
$372$	−258.960	−0.0360926
$373$	−4960.42	−0.688582	−0.344291	−	0.938863i	$-0.611881\pi$
$373$	−4960.42	−0.688582	−0.344291	+	0.938863i	$0.611881\pi$
$374$	−2547.50	−0.352215
$375$	−4563.65	−0.628442
$376$	10735.4	1.47243
$377$	−1603.75	−0.219091
$378$	1175.10	0.159896
$379$	2700.52	0.366006	0.183003	−	0.983112i	$-0.441418\pi$
$379$	2700.52	0.366006	0.183003	+	0.983112i	$0.441418\pi$
$380$	−2936.89	−0.396472
$381$	2914.65	0.391921
$382$	−227.441	−0.0304631
$383$	8026.62	1.07086	0.535432	−	0.844578i	$-0.320149\pi$
$383$	8026.62	1.07086	0.535432	+	0.844578i	$0.320149\pi$
$384$	−5243.60	−0.696840
$385$	933.158	0.123528
$386$	−8207.80	−1.08229
$387$	−190.638	−0.0250405
$388$	2556.69	0.334526
$389$	−12048.8	−1.57043	−0.785216	−	0.619222i	$-0.787448\pi$
$389$	−12048.8	−1.57043	−0.785216	+	0.619222i	$0.787448\pi$
$390$	−4889.99	−0.634908
$391$	−2466.52	−0.319021
$392$	−2913.31	−0.375368
$393$	−7824.14	−1.00426
$394$	1991.81	0.254686
$395$	−5271.03	−0.671428
$396$	−148.267	−0.0188149
$397$	−4408.78	−0.557356	−0.278678	−	0.960385i	$-0.589896\pi$
$397$	−4408.78	−0.557356	−0.278678	+	0.960385i	$0.589896\pi$
$398$	−4647.85	−0.585367
$399$	5869.13	0.736401
$400$	3070.22	0.383778
$401$	−13794.6	−1.71788	−0.858940	−	0.512077i	$-0.828876\pi$
$401$	−13794.6	−1.71788	−0.858940	+	0.512077i	$0.828876\pi$
$402$	−3956.65	−0.490895
$403$	−2153.54	−0.266192
$404$	1946.94	0.239762
$405$	746.930	0.0916425
$406$	−1262.14	−0.154283
$407$	−2085.01	−0.253931
$408$	−5947.18	−0.721641
$409$	−832.859	−0.100690	−0.0503450	−	0.998732i	$-0.516032\pi$
$409$	−832.859	−0.100690	−0.0503450	+	0.998732i	$0.516032\pi$
$410$	−142.560	−0.0171720
$411$	6853.00	0.822466
$412$	2312.83	0.276566
$413$	−3218.01	−0.383410
$414$	−661.644	−0.0785460
$415$	−13406.0	−1.58573
$416$	5400.62	0.636508
$417$	1221.88	0.143491
$418$	−3413.15	−0.399384
$419$	−4514.27	−0.526340	−0.263170	−	0.964749i	$-0.584768\pi$
$419$	−4514.27	−0.526340	−0.263170	+	0.964749i	$0.584768\pi$
$420$	−834.966	−0.0970052
$421$	2858.82	0.330952	0.165476	−	0.986214i	$-0.447084\pi$
$421$	2858.82	0.330952	0.165476	+	0.986214i	$0.447084\pi$
$422$	3597.49	0.414984
$423$	5226.68	0.600779
$424$	4533.23	0.519229
$425$	4286.02	0.489182
$426$	−8520.05	−0.969009
$427$	11384.5	1.29024
$428$	4472.08	0.505062
$429$	−1233.00	−0.138764
$430$	624.332	0.0700185
$431$	−9255.66	−1.03441	−0.517204	−	0.855862i	$-0.673027\pi$
$431$	−9255.66	−1.03441	−0.517204	+	0.855862i	$0.673027\pi$
$432$	−2074.13	−0.230999
$433$	3549.75	0.393973	0.196986	−	0.980406i	$-0.436885\pi$
$433$	3549.75	0.393973	0.196986	+	0.980406i	$0.436885\pi$
$434$	−1694.83	−0.187452
$435$	−802.258	−0.0884260
$436$	337.673	0.0370908
$437$	−3304.64	−0.361745
$438$	−463.861	−0.0506030
$439$	5011.15	0.544805	0.272402	−	0.962183i	$-0.412182\pi$
$439$	5011.15	0.544805	0.272402	+	0.962183i	$0.412182\pi$
$440$	−1266.87	−0.137263
$441$	−1418.39	−0.153157
$442$	18956.1	2.03993
$443$	15897.8	1.70503	0.852514	−	0.522704i	$-0.175077\pi$
$443$	15897.8	1.70503	0.852514	+	0.522704i	$0.175077\pi$
$444$	1865.61	0.199410
$445$	11406.9	1.21514
$446$	−980.012	−0.104047
$447$	−6310.99	−0.667784
$448$	−4117.67	−0.434245
$449$	−1549.60	−0.162873	−0.0814367	−	0.996679i	$-0.525951\pi$
$449$	−1549.60	−0.162873	−0.0814367	+	0.996679i	$0.525951\pi$
$450$	1149.73	0.120441
$451$	−35.9461	−0.00375308
$452$	697.575	0.0725911
$453$	7913.66	0.820787
$454$	−16656.1	−1.72183
$455$	−6943.66	−0.715437
$456$	−7968.04	−0.818284
$457$	17847.7	1.82687	0.913434	−	0.406986i	$-0.133420\pi$
$457$	17847.7	1.82687	0.913434	+	0.406986i	$0.133420\pi$
$458$	−4516.56	−0.460797
$459$	−2895.48	−0.294443
$460$	470.131	0.0476522
$461$	6486.58	0.655337	0.327669	−	0.944793i	$-0.393737\pi$
$461$	6486.58	0.655337	0.327669	+	0.944793i	$0.393737\pi$
$462$	−970.367	−0.0977177
$463$	−1568.11	−0.157400	−0.0787001	−	0.996898i	$-0.525077\pi$
$463$	−1568.11	−0.157400	−0.0787001	+	0.996898i	$0.525077\pi$
$464$	2227.77	0.222891
$465$	−1077.29	−0.107436
$466$	−1625.06	−0.161543
$467$	4379.28	0.433938	0.216969	−	0.976179i	$-0.430383\pi$
$467$	4379.28	0.433938	0.216969	+	0.976179i	$0.430383\pi$
$468$	1103.26	0.108970
$469$	−5618.35	−0.553158
$470$	−17117.2	−1.67991
$471$	1467.82	0.143596
$472$	4368.83	0.426042
$473$	157.424	0.0153031
$474$	5481.21	0.531139
$475$	5742.41	0.554694
$476$	3236.75	0.311673
$477$	2207.07	0.211855
$478$	17280.1	1.65350
$479$	−7852.88	−0.749076	−0.374538	−	0.927212i	$-0.622199\pi$
$479$	−7852.88	−0.749076	−0.374538	+	0.927212i	$0.622199\pi$
$480$	2701.60	0.256898
$481$	15514.6	1.47070
$482$	−9989.05	−0.943960
$483$	−939.518	−0.0885084
$484$	−2827.92	−0.265583
$485$	10635.9	0.995778
$486$	−776.713	−0.0724947
$487$	10817.0	1.00650	0.503249	−	0.864142i	$-0.332138\pi$
$487$	10817.0	1.00650	0.503249	+	0.864142i	$0.332138\pi$
$488$	−15455.8	−1.43371
$489$	9970.95	0.922090
$490$	4645.17	0.428260
$491$	3576.39	0.328718	0.164359	−	0.986401i	$-0.447444\pi$
$491$	3576.39	0.328718	0.164359	+	0.986401i	$0.447444\pi$
$492$	32.1637	0.00294726
$493$	3109.96	0.284108
$494$	25397.3	2.31312
$495$	−616.796	−0.0560059
$496$	2991.49	0.270810
$497$	−12098.3	−1.09191
$498$	13940.6	1.25440
$499$	2330.77	0.209097	0.104549	−	0.994520i	$-0.466660\pi$
$499$	2330.77	0.209097	0.104549	+	0.994520i	$0.466660\pi$
$500$	−3372.00	−0.301601
$501$	−4025.25	−0.358952
$502$	−16777.9	−1.49170
$503$	1942.60	0.172199	0.0860995	−	0.996287i	$-0.472560\pi$
$503$	1942.60	0.172199	0.0860995	+	0.996287i	$0.472560\pi$
$504$	−2265.34	−0.200210
$505$	8099.34	0.713695
$506$	546.369	0.0480021
$507$	2583.80	0.226333
$508$	2153.58	0.188090
$509$	15181.7	1.32204	0.661018	−	0.750370i	$-0.270124\pi$
$509$	15181.7	1.32204	0.661018	+	0.750370i	$0.270124\pi$
$510$	9482.57	0.823324
$511$	−658.671	−0.0570213
$512$	3858.45	0.333049
$513$	−3879.36	−0.333875
$514$	2731.85	0.234429
$515$	9621.48	0.823249
$516$	−140.859	−0.0120174
$517$	−4316.06	−0.367157
$518$	12209.9	1.03566
$519$	−2612.38	−0.220945
$520$	9426.84	0.794989
$521$	−4174.96	−0.351072	−0.175536	−	0.984473i	$-0.556166\pi$
$521$	−4174.96	−0.351072	−0.175536	+	0.984473i	$0.556166\pi$
$522$	834.247	0.0699502
$523$	−11211.1	−0.937340	−0.468670	−	0.883373i	$-0.655267\pi$
$523$	−11211.1	−0.937340	−0.468670	+	0.883373i	$0.655267\pi$
$524$	−5781.12	−0.481964
$525$	1632.58	0.135718
$526$	−15833.1	−1.31246
$527$	4176.10	0.345187
$528$	1712.77	0.141172
$529$	529.000	0.0434783
$530$	−7228.07	−0.592391
$531$	2127.03	0.173833
$532$	4336.60	0.353413
$533$	267.477	0.0217368
$534$	−11861.7	−0.961251
$535$	18604.1	1.50341
$536$	7627.57	0.614666
$537$	−8456.43	−0.679556
$538$	16938.3	1.35736
$539$	1171.27	0.0935996
$540$	551.893	0.0439809
$541$	19125.1	1.51988	0.759939	−	0.649995i	$-0.225229\pi$
$541$	19125.1	1.51988	0.759939	+	0.649995i	$0.225229\pi$
$542$	−18315.5	−1.45151
$543$	−9600.94	−0.758777
$544$	−10472.8	−0.825398
$545$	1404.73	0.110408
$546$	7220.54	0.565953
$547$	5631.01	0.440155	0.220077	−	0.975482i	$-0.429369\pi$
$547$	5631.01	0.440155	0.220077	+	0.975482i	$0.429369\pi$
$548$	5063.56	0.394717
$549$	−7524.89	−0.584981
$550$	−949.416	−0.0736059
$551$	4166.72	0.322157
$552$	1275.51	0.0983500
$553$	7783.18	0.598507
$554$	5772.17	0.442664
$555$	7761.03	0.593581
$556$	902.829	0.0688642
$557$	−1728.74	−0.131506	−0.0657532	−	0.997836i	$-0.520945\pi$
$557$	−1728.74	−0.131506	−0.0657532	+	0.997836i	$0.520945\pi$
$558$	1120.24	0.0849885
$559$	−1171.40	−0.0886313
$560$	9645.47	0.727849
$561$	2391.01	0.179944
$562$	−16816.6	−1.26222
$563$	−10866.5	−0.813440	−0.406720	−	0.913553i	$-0.633328\pi$
$563$	−10866.5	−0.813440	−0.406720	+	0.913553i	$0.633328\pi$
$564$	3861.90	0.288325
$565$	2901.94	0.216081
$566$	23862.9	1.77214
$567$	−1102.91	−0.0816896
$568$	16424.8	1.21333
$569$	−4385.60	−0.323118	−0.161559	−	0.986863i	$-0.551652\pi$
$569$	−4385.60	−0.323118	−0.161559	+	0.986863i	$0.551652\pi$
$570$	12704.8	0.933586
$571$	−9425.75	−0.690815	−0.345408	−	0.938453i	$-0.612259\pi$
$571$	−9425.75	−0.690815	−0.345408	+	0.938453i	$0.612259\pi$
$572$	−911.043	−0.0665955
$573$	213.469	0.0155634
$574$	210.503	0.0153070
$575$	−919.233	−0.0666690
$576$	2721.69	0.196881
$577$	−4401.18	−0.317545	−0.158773	−	0.987315i	$-0.550754\pi$
$577$	−4401.18	−0.317545	−0.158773	+	0.987315i	$0.550754\pi$
$578$	−21055.6	−1.51522
$579$	7703.60	0.552937
$580$	−592.774	−0.0424373
$581$	19795.3	1.41351
$582$	−11060.0	−0.787719
$583$	−1822.54	−0.129472
$584$	894.223	0.0633617
$585$	4589.60	0.324370
$586$	23579.5	1.66222
$587$	12993.4	0.913623	0.456812	−	0.889563i	$-0.348991\pi$
$587$	12993.4	0.913623	0.456812	+	0.889563i	$0.348991\pi$
$588$	−1048.02	−0.0735030
$589$	5595.14	0.391416
$590$	−6965.95	−0.486074
$591$	−1869.46	−0.130117
$592$	−21551.4	−1.49621
$593$	16972.5	1.17534	0.587670	−	0.809101i	$-0.300045\pi$
$593$	16972.5	1.17534	0.587670	+	0.809101i	$0.300045\pi$
$594$	641.390	0.0443040
$595$	13465.0	0.927751
$596$	−4663.08	−0.320482
$597$	4362.34	0.299060
$598$	−4065.55	−0.278015
$599$	5567.64	0.379779	0.189889	−	0.981805i	$-0.439187\pi$
$599$	5567.64	0.379779	0.189889	+	0.981805i	$0.439187\pi$
$600$	−2216.42	−0.150809
$601$	20572.0	1.39625	0.698126	−	0.715974i	$-0.254017\pi$
$601$	20572.0	1.39625	0.698126	+	0.715974i	$0.254017\pi$
$602$	−921.886	−0.0624141
$603$	3713.60	0.250795
$604$	5847.27	0.393911
$605$	−11764.3	−0.790556
$606$	−8422.30	−0.564575
$607$	15268.0	1.02094	0.510469	−	0.859896i	$-0.329472\pi$
$607$	15268.0	1.02094	0.510469	+	0.859896i	$0.329472\pi$
$608$	−14031.4	−0.935937
$609$	1184.61	0.0788224
$610$	24643.7	1.63573
$611$	32115.9	2.12647
$612$	−2139.42	−0.141309
$613$	−11596.9	−0.764101	−0.382050	−	0.924142i	$-0.624782\pi$
$613$	−11596.9	−0.764101	−0.382050	+	0.924142i	$0.624782\pi$
$614$	−16824.8	−1.10586
$615$	133.802	0.00877306
$616$	1870.66	0.122355
$617$	−14699.2	−0.959103	−0.479551	−	0.877514i	$-0.659201\pi$
$617$	−14699.2	−0.959103	−0.479551	+	0.877514i	$0.659201\pi$
$618$	−10005.1	−0.651238
$619$	−3725.03	−0.241877	−0.120938	−	0.992660i	$-0.538590\pi$
$619$	−3725.03	−0.241877	−0.120938	+	0.992660i	$0.538590\pi$
$620$	−795.987	−0.0515607
$621$	621.000	0.0401286
$622$	−3403.78	−0.219420
$623$	−16843.4	−1.08317
$624$	−12744.8	−0.817626
$625$	−9031.83	−0.578037
$626$	−12089.6	−0.771880
$627$	3203.48	0.204042
$628$	1084.55	0.0689142
$629$	−30085.6	−1.90714
$630$	3612.00	0.228421
$631$	29309.0	1.84909	0.924543	−	0.381078i	$-0.124447\pi$
$631$	29309.0	1.84909	0.924543	+	0.381078i	$0.124447\pi$
$632$	−10566.6	−0.665057
$633$	−3376.50	−0.212013
$634$	−35911.3	−2.24956
$635$	8959.01	0.559886
$636$	1630.77	0.101673
$637$	−8715.47	−0.542103
$638$	−688.901	−0.0427490
$639$	7996.67	0.495060
$640$	−16117.7	−0.995481
$641$	−16596.7	−1.02267	−0.511333	−	0.859382i	$-0.670848\pi$
$641$	−16596.7	−1.02267	−0.511333	+	0.859382i	$0.670848\pi$
$642$	−19345.9	−1.18929
$643$	−12506.3	−0.767031	−0.383516	−	0.923534i	$-0.625287\pi$
$643$	−12506.3	−0.767031	−0.383516	+	0.923534i	$0.625287\pi$
$644$	−694.194	−0.0424768
$645$	−585.980	−0.0357720
$646$	−49250.0	−2.99956
$647$	5961.76	0.362258	0.181129	−	0.983459i	$-0.442025\pi$
$647$	5961.76	0.362258	0.181129	+	0.983459i	$0.442025\pi$
$648$	1497.33	0.0907729
$649$	−1756.45	−0.106235
$650$	7064.64	0.426304
$651$	1590.71	0.0957681
$652$	7367.36	0.442528
$653$	22734.4	1.36243	0.681214	−	0.732084i	$-0.261452\pi$
$653$	22734.4	1.36243	0.681214	+	0.732084i	$0.261452\pi$
$654$	−1460.75	−0.0873390
$655$	−24049.7	−1.43466
$656$	−371.553	−0.0221139
$657$	435.366	0.0258527
$658$	25275.1	1.49746
$659$	8626.41	0.509920	0.254960	−	0.966952i	$-0.417938\pi$
$659$	8626.41	0.509920	0.254960	+	0.966952i	$0.417938\pi$
$660$	−455.740	−0.0268783
$661$	−617.183	−0.0363172	−0.0181586	−	0.999835i	$-0.505780\pi$
$661$	−617.183	−0.0363172	−0.0181586	+	0.999835i	$0.505780\pi$
$662$	−10970.8	−0.644096
$663$	−17791.6	−1.04218
$664$	−26874.4	−1.57068
$665$	18040.4	1.05200
$666$	−8070.49	−0.469557
$667$	−667.000	−0.0387202
$668$	−2974.19	−0.172268
$669$	919.810	0.0531568
$670$	−12161.9	−0.701276
$671$	6213.87	0.357502
$672$	−3989.18	−0.228997
$673$	2483.60	0.142252	0.0711261	−	0.997467i	$-0.477341\pi$
$673$	2483.60	0.142252	0.0711261	+	0.997467i	$0.477341\pi$
$674$	−27305.0	−1.56046
$675$	−1079.10	−0.0615327
$676$	1909.13	0.108621
$677$	−23546.7	−1.33674	−0.668370	−	0.743829i	$-0.733008\pi$
$677$	−23546.7	−1.33674	−0.668370	+	0.743829i	$0.733008\pi$
$678$	−3017.66	−0.170933
$679$	−15705.0	−0.887630
$680$	−18280.4	−1.03091
$681$	15632.9	0.879671
$682$	−925.067	−0.0519394
$683$	31833.1	1.78339	0.891697	−	0.452633i	$-0.149515\pi$
$683$	31833.1	1.78339	0.891697	+	0.452633i	$0.149515\pi$
$684$	−2866.39	−0.160233
$685$	21064.6	1.17495
$686$	−21787.1	−1.21259
$687$	4239.11	0.235418
$688$	1627.19	0.0901689
$689$	13561.6	0.749864
$690$	−2033.75	−0.112208
$691$	16159.4	0.889630	0.444815	−	0.895623i	$-0.353269\pi$
$691$	16159.4	0.889630	0.444815	+	0.895623i	$0.353269\pi$
$692$	−1930.24	−0.106036
$693$	910.758	0.0499233
$694$	26569.3	1.45325
$695$	3755.81	0.204987
$696$	−1608.25	−0.0875869
$697$	−518.686	−0.0281874
$698$	2701.28	0.146483
$699$	1525.23	0.0825314
$700$	1206.29	0.0651334
$701$	−30741.6	−1.65634	−0.828171	−	0.560475i	$-0.810618\pi$
$701$	−30741.6	−1.65634	−0.828171	+	0.560475i	$0.810618\pi$
$702$	−4772.61	−0.256596
$703$	−40308.8	−2.16255
$704$	−2247.50	−0.120321
$705$	16065.7	0.858253
$706$	−1985.45	−0.105841
$707$	−11959.4	−0.636183
$708$	1571.63	0.0834257
$709$	−9932.08	−0.526103	−0.263052	−	0.964782i	$-0.584729\pi$
$709$	−9932.08	−0.526103	−0.263052	+	0.964782i	$0.584729\pi$
$710$	−26188.8	−1.38429
$711$	−5144.50	−0.271356
$712$	22866.9	1.20361
$713$	−895.659	−0.0470444
$714$	−14001.9	−0.733906
$715$	−3789.98	−0.198234
$716$	−6248.31	−0.326132
$717$	−16218.6	−0.844761
$718$	−33190.9	−1.72517
$719$	8691.49	0.450817	0.225409	−	0.974264i	$-0.427628\pi$
$719$	8691.49	0.450817	0.225409	+	0.974264i	$0.427628\pi$
$720$	−6375.43	−0.329998
$721$	−14207.0	−0.733838
$722$	−44061.5	−2.27119
$723$	9375.43	0.482263
$724$	−7093.97	−0.364151
$725$	1159.03	0.0593730
$726$	12233.4	0.625376
$727$	4868.68	0.248376	0.124188	−	0.992259i	$-0.460367\pi$
$727$	4868.68	0.248376	0.124188	+	0.992259i	$0.460367\pi$
$728$	−13919.6	−0.708648
$729$	729.000	0.0370370
$730$	−1425.81	−0.0722897
$731$	2271.55	0.114934
$732$	−5560.01	−0.280743
$733$	−1985.70	−0.100059	−0.0500297	−	0.998748i	$-0.515932\pi$
$733$	−1985.70	−0.100059	−0.0500297	+	0.998748i	$0.515932\pi$
$734$	−17726.9	−0.891435
$735$	−4359.82	−0.218795
$736$	2246.12	0.112491
$737$	−3066.60	−0.153269
$738$	−139.138	−0.00694001
$739$	12443.1	0.619386	0.309693	−	0.950837i	$-0.399774\pi$
$739$	12443.1	0.619386	0.309693	+	0.950837i	$0.399774\pi$
$740$	5734.49	0.284870
$741$	−23837.2	−1.18176
$742$	10672.9	0.528054
$743$	21858.7	1.07930	0.539648	−	0.841891i	$-0.318557\pi$
$743$	21858.7	1.07930	0.539648	+	0.841891i	$0.318557\pi$
$744$	−2159.58	−0.106417
$745$	−19398.6	−0.953973
$746$	15855.2	0.778152
$747$	−13084.2	−0.640866
$748$	1766.68	0.0863585
$749$	−27470.7	−1.34013
$750$	14587.0	0.710190
$751$	3434.36	0.166873	0.0834365	−	0.996513i	$-0.473410\pi$
$751$	3434.36	0.166873	0.0834365	+	0.996513i	$0.473410\pi$
$752$	−44612.4	−2.16336
$753$	15747.3	0.762101
$754$	5126.13	0.247590
$755$	24324.9	1.17255
$756$	−814.923	−0.0392043
$757$	−18013.9	−0.864894	−0.432447	−	0.901659i	$-0.642350\pi$
$757$	−18013.9	−0.864894	−0.432447	+	0.901659i	$0.642350\pi$
$758$	−8631.81	−0.413617
$759$	−512.806	−0.0245240
$760$	−24492.0	−1.16897
$761$	5921.08	0.282049	0.141024	−	0.990006i	$-0.454960\pi$
$761$	5921.08	0.282049	0.141024	+	0.990006i	$0.454960\pi$
$762$	−9316.24	−0.442903
$763$	−2074.22	−0.0984166
$764$	157.729	0.00746915
$765$	−8900.07	−0.420631
$766$	−25655.9	−1.21016
$767$	13069.8	0.615285
$768$	9502.55	0.446476
$769$	−19108.5	−0.896059	−0.448029	−	0.894019i	$-0.647874\pi$
$769$	−19108.5	−0.896059	−0.448029	+	0.894019i	$0.647874\pi$
$770$	−2982.70	−0.139596
$771$	−2564.03	−0.119768
$772$	5692.06	0.265365
$773$	−38300.3	−1.78210	−0.891051	−	0.453902i	$-0.850031\pi$
$773$	−38300.3	−1.78210	−0.891051	+	0.453902i	$0.850031\pi$
$774$	609.345	0.0282978
$775$	1556.37	0.0721373
$776$	21321.3	0.986329
$777$	−11459.9	−0.529114
$778$	38512.1	1.77471
$779$	−694.935	−0.0319623
$780$	3391.18	0.155671
$781$	−6603.45	−0.302548
$782$	7883.85	0.360519
$783$	−783.000	−0.0357371
$784$	12106.7	0.551507
$785$	4511.76	0.205136
$786$	25008.7	1.13490
$787$	3702.86	0.167716	0.0838580	−	0.996478i	$-0.473276\pi$
$787$	3702.86	0.167716	0.0838580	+	0.996478i	$0.473276\pi$
$788$	−1381.31	−0.0624456
$789$	14860.5	0.670529
$790$	16848.0	0.758768
$791$	−4285.00	−0.192613
$792$	−1236.46	−0.0554744
$793$	−46237.6	−2.07055
$794$	14092.0	0.629857
$795$	6784.06	0.302649
$796$	3223.26	0.143524
$797$	−43076.2	−1.91448	−0.957239	−	0.289300i	$-0.906578\pi$
$797$	−43076.2	−1.91448	−0.957239	+	0.289300i	$0.906578\pi$
$798$	−18759.8	−0.832192
$799$	−62278.6	−2.75752
$800$	−3903.05	−0.172492
$801$	11133.1	0.491097
$802$	44092.4	1.94134
$803$	−359.515	−0.0157995
$804$	2743.91	0.120361
$805$	−2887.88	−0.126440
$806$	6883.46	0.300818
$807$	−15897.8	−0.693468
$808$	16236.4	0.706922
$809$	−11293.2	−0.490788	−0.245394	−	0.969423i	$-0.578917\pi$
$809$	−11293.2	−0.490788	−0.245394	+	0.969423i	$0.578917\pi$
$810$	−2387.45	−0.103563
$811$	−11276.7	−0.488261	−0.244131	−	0.969742i	$-0.578503\pi$
$811$	−11276.7	−0.488261	−0.244131	+	0.969742i	$0.578503\pi$
$812$	875.288	0.0378283
$813$	17190.4	0.741568
$814$	6664.41	0.286963
$815$	30648.6	1.31727
$816$	24714.4	1.06027
$817$	3043.43	0.130326
$818$	2662.11	0.113788
$819$	−6776.98	−0.289142
$820$	98.8643	0.00421035
$821$	−1131.63	−0.0481051	−0.0240526	−	0.999711i	$-0.507657\pi$
$821$	−1131.63	−0.0481051	−0.0240526	+	0.999711i	$0.507657\pi$
$822$	−21904.6	−0.929453
$823$	−16777.4	−0.710601	−0.355301	−	0.934752i	$-0.615621\pi$
$823$	−16777.4	−0.710601	−0.355301	+	0.934752i	$0.615621\pi$
$824$	19287.7	0.815437
$825$	891.094	0.0376047
$826$	10285.9	0.433283
$827$	41727.7	1.75455	0.877277	−	0.479985i	$-0.159358\pi$
$827$	41727.7	1.75455	0.877277	+	0.479985i	$0.159358\pi$
$828$	458.846	0.0192585
$829$	−16493.9	−0.691023	−0.345512	−	0.938414i	$-0.612295\pi$
$829$	−16493.9	−0.691023	−0.345512	+	0.938414i	$0.612295\pi$
$830$	42850.4	1.79200
$831$	−5417.59	−0.226154
$832$	16723.7	0.696864
$833$	16900.9	0.702978
$834$	−3905.57	−0.162157
$835$	−12372.8	−0.512787
$836$	2367.00	0.0979238
$837$	−1051.43	−0.0434200
$838$	14429.2	0.594806
$839$	6646.96	0.273514	0.136757	−	0.990605i	$-0.456332\pi$
$839$	6646.96	0.273514	0.136757	+	0.990605i	$0.456332\pi$
$840$	−6963.15	−0.286014
$841$	841.000	0.0344828
$842$	−9137.80	−0.374002
$843$	15783.6	0.644857
$844$	−2494.84	−0.101749
$845$	7942.05	0.323331
$846$	−16706.3	−0.678929
$847$	17371.1	0.704696
$848$	−18838.5	−0.762873
$849$	−22397.0	−0.905374
$850$	−13699.6	−0.552815
$851$	6452.55	0.259918
$852$	5908.60	0.237588
$853$	−2407.63	−0.0966422	−0.0483211	−	0.998832i	$-0.515387\pi$
$853$	−2407.63	−0.0966422	−0.0483211	+	0.998832i	$0.515387\pi$
$854$	−36388.8	−1.45808
$855$	−11924.3	−0.476963
$856$	37294.7	1.48914
$857$	17408.5	0.693888	0.346944	−	0.937886i	$-0.387219\pi$
$857$	17408.5	0.693888	0.346944	+	0.937886i	$0.387219\pi$
$858$	3941.10	0.156815
$859$	−44434.3	−1.76493	−0.882467	−	0.470375i	$-0.844119\pi$
$859$	−44434.3	−1.76493	−0.882467	+	0.470375i	$0.844119\pi$
$860$	−432.971	−0.0171676
$861$	−197.572	−0.00782025
$862$	29584.3	1.16896
$863$	−20579.1	−0.811728	−0.405864	−	0.913933i	$-0.633029\pi$
$863$	−20579.1	−0.811728	−0.405864	+	0.913933i	$0.633029\pi$
$864$	2636.75	0.103824
$865$	−8029.88	−0.315635
$866$	−11346.2	−0.445221
$867$	19762.1	0.774115
$868$	1175.35	0.0459609
$869$	4248.20	0.165835
$870$	2564.30	0.0999285
$871$	22818.6	0.887693
$872$	2816.00	0.109360
$873$	10380.6	0.402440
$874$	10562.8	0.408800
$875$	20713.2	0.800267
$876$	321.685	0.0124072
$877$	18783.8	0.723243	0.361621	−	0.932325i	$-0.382223\pi$
$877$	18783.8	0.723243	0.361621	+	0.932325i	$0.382223\pi$
$878$	−16017.4	−0.615673
$879$	−22131.1	−0.849217
$880$	5264.67	0.201673
$881$	15960.5	0.610355	0.305178	−	0.952295i	$-0.401284\pi$
$881$	15960.5	0.610355	0.305178	+	0.952295i	$0.401284\pi$
$882$	4533.67	0.173080
$883$	13254.8	0.505162	0.252581	−	0.967576i	$-0.418721\pi$
$883$	13254.8	0.505162	0.252581	+	0.967576i	$0.418721\pi$
$884$	−13145.9	−0.500164
$885$	6538.04	0.248332
$886$	−50815.0	−1.92682
$887$	14516.8	0.549521	0.274760	−	0.961513i	$-0.411401\pi$
$887$	14516.8	0.549521	0.274760	+	0.961513i	$0.411401\pi$
$888$	15558.2	0.587948
$889$	−13228.8	−0.499078
$890$	−36460.5	−1.37321
$891$	−601.990	−0.0226346
$892$	679.632	0.0255109
$893$	−83441.0	−3.12682
$894$	20172.1	0.754649
$895$	−25993.2	−0.970791
$896$	23799.3	0.887366
$897$	3815.81	0.142036
$898$	4953.07	0.184060
$899$	1129.31	0.0418961
$900$	−797.328	−0.0295307
$901$	−26298.4	−0.972395
$902$	114.896	0.00424128
$903$	865.255	0.0318869
$904$	5817.39	0.214030
$905$	−29511.2	−1.08396
$906$	−25294.8	−0.927555
$907$	15700.1	0.574765	0.287383	−	0.957816i	$-0.407215\pi$
$907$	15700.1	0.574765	0.287383	+	0.957816i	$0.407215\pi$
$908$	11550.9	0.422170
$909$	7904.92	0.288437
$910$	22194.4	0.808501
$911$	−40989.9	−1.49073	−0.745365	−	0.666656i	$-0.767725\pi$
$911$	−40989.9	−1.49073	−0.745365	+	0.666656i	$0.767725\pi$
$912$	33112.3	1.20226
$913$	10804.6	0.391655
$914$	−57047.4	−2.06451
$915$	−23129.9	−0.835684
$916$	3132.21	0.112981
$917$	35511.7	1.27884
$918$	9254.95	0.332744
$919$	15007.0	0.538667	0.269334	−	0.963047i	$-0.413197\pi$
$919$	15007.0	0.538667	0.269334	+	0.963047i	$0.413197\pi$
$920$	3920.63	0.140499
$921$	15791.3	0.564974
$922$	−20733.4	−0.740583
$923$	49136.5	1.75227
$924$	672.944	0.0239591
$925$	−11212.5	−0.398555
$926$	5012.23	0.177875
$927$	9390.52	0.332713
$928$	−2832.07	−0.100180
$929$	−32436.9	−1.14556	−0.572778	−	0.819711i	$-0.694134\pi$
$929$	−32436.9	−1.14556	−0.572778	+	0.819711i	$0.694134\pi$
$930$	3443.38	0.121412
$931$	22643.8	0.797122
$932$	1126.97	0.0396084
$933$	3194.68	0.112100
$934$	−13997.7	−0.490384
$935$	7349.45	0.257062
$936$	9200.56	0.321292
$937$	42182.1	1.47068	0.735341	−	0.677697i	$-0.237022\pi$
$937$	42182.1	1.47068	0.735341	+	0.677697i	$0.237022\pi$
$938$	17958.2	0.625113
$939$	11346.9	0.394348
$940$	11870.7	0.411891
$941$	−50597.2	−1.75284	−0.876419	−	0.481549i	$-0.840074\pi$
$941$	−50597.2	−1.75284	−0.876419	+	0.481549i	$0.840074\pi$
$942$	−4691.66	−0.162274
$943$	111.244	0.00384157
$944$	−18155.3	−0.625959
$945$	−3390.12	−0.116699
$946$	−503.182	−0.0172937
$947$	−926.830	−0.0318035	−0.0159018	−	0.999874i	$-0.505062\pi$
$947$	−926.830	−0.0318035	−0.0159018	+	0.999874i	$0.505062\pi$
$948$	−3801.18	−0.130229
$949$	2675.16	0.0915062
$950$	−18354.7	−0.626849
$951$	33705.3	1.14928
$952$	26992.7	0.918948
$953$	−21513.8	−0.731269	−0.365635	−	0.930758i	$-0.619148\pi$
$953$	−21513.8	−0.731269	−0.365635	+	0.930758i	$0.619148\pi$
$954$	−7054.57	−0.239413
$955$	656.159	0.0222333
$956$	−11983.6	−0.405417
$957$	646.582	0.0218402
$958$	25100.6	0.846516
$959$	−31104.0	−1.04734
$960$	8365.88	0.281258
$961$	−28274.5	−0.949097
$962$	−49590.1	−1.66201
$963$	18157.5	0.607598
$964$	6927.34	0.231447
$965$	23679.2	0.789907
$966$	3003.03	0.100022
$967$	17928.3	0.596210	0.298105	−	0.954533i	$-0.403645\pi$
$967$	17928.3	0.596210	0.298105	+	0.954533i	$0.403645\pi$
$968$	−23583.3	−0.783054
$969$	46224.7	1.53246
$970$	−33996.1	−1.12531
$971$	−10381.6	−0.343113	−0.171556	−	0.985174i	$-0.554880\pi$
$971$	−10381.6	−0.343113	−0.171556	+	0.985174i	$0.554880\pi$
$972$	538.646	0.0177748
$973$	−5545.81	−0.182724
$974$	−34574.9	−1.13742
$975$	−6630.66	−0.217796
$976$	64228.8	2.10647
$977$	37289.3	1.22107	0.610537	−	0.791987i	$-0.290954\pi$
$977$	37289.3	1.22107	0.610537	+	0.791987i	$0.290954\pi$
$978$	−31870.6	−1.04204
$979$	−9193.43	−0.300126
$980$	−3221.40	−0.105004
$981$	1371.01	0.0446209
$982$	−11431.4	−0.371477
$983$	−58494.4	−1.89795	−0.948973	−	0.315356i	$-0.897876\pi$
$983$	−58494.4	−1.89795	−0.948973	+	0.315356i	$0.897876\pi$
$984$	268.227	0.00868981
$985$	−5746.31	−0.185881
$986$	−9940.50	−0.321065
$987$	−23722.5	−0.765041
$988$	−17612.9	−0.567147
$989$	−487.186	−0.0156639
$990$	1971.50	0.0632911
$991$	−24074.4	−0.771693	−0.385847	−	0.922563i	$-0.626091\pi$
$991$	−24074.4	−0.771693	−0.385847	+	0.922563i	$0.626091\pi$
$992$	−3802.95	−0.121718
$993$	10296.9	0.329064
$994$	38670.3	1.23395
$995$	13408.9	0.427227
$996$	−9667.71	−0.307563
$997$	−9536.47	−0.302932	−0.151466	−	0.988462i	$-0.548399\pi$
$997$	−9536.47	−0.302932	−0.151466	+	0.988462i	$0.548399\pi$
$998$	−7449.95	−0.236297
$999$	7574.73	0.239894

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.4.a.h.1.11	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.4.a.h.1.11	✓	44	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:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q-3.19635 q^{2} +3.00000 q^{3} +2.21665 q^{4} +9.22135 q^{5} -9.58905 q^{6} -13.6162 q^{7} +18.4856 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.19635 q^{2} +3.00000 q^{3} +2.21665 q^{4} +9.22135 q^{5} -9.58905 q^{6} -13.6162 q^{7} +18.4856 q^{8} +9.00000 q^{9} -29.4747 q^{10} -7.43198 q^{11} +6.64995 q^{12} +55.3016 q^{13} +43.5222 q^{14} +27.6641 q^{15} -76.8197 q^{16} -107.240 q^{17} -28.7671 q^{18} -143.680 q^{19} +20.4405 q^{20} -40.8486 q^{21} +23.7552 q^{22} +23.0000 q^{23} +55.4568 q^{24} -39.9667 q^{25} -176.763 q^{26} +27.0000 q^{27} -30.1823 q^{28} -29.0000 q^{29} -88.4240 q^{30} -38.9417 q^{31} +97.6576 q^{32} -22.2959 q^{33} +342.776 q^{34} -125.560 q^{35} +19.9498 q^{36} +280.545 q^{37} +459.251 q^{38} +165.905 q^{39} +170.462 q^{40} +4.83669 q^{41} +130.566 q^{42} -21.1820 q^{43} -16.4741 q^{44} +82.9922 q^{45} -73.5160 q^{46} +580.742 q^{47} -230.459 q^{48} -157.599 q^{49} +127.747 q^{50} -321.719 q^{51} +122.584 q^{52} +245.230 q^{53} -86.3014 q^{54} -68.5329 q^{55} -251.704 q^{56} -431.040 q^{57} +92.6941 q^{58} +236.337 q^{59} +61.3215 q^{60} -836.099 q^{61} +124.471 q^{62} -122.546 q^{63} +302.410 q^{64} +509.956 q^{65} +71.2656 q^{66} +412.622 q^{67} -237.713 q^{68} +69.0000 q^{69} +401.333 q^{70} +888.519 q^{71} +166.371 q^{72} +48.3740 q^{73} -896.721 q^{74} -119.900 q^{75} -318.488 q^{76} +101.195 q^{77} -530.290 q^{78} -571.611 q^{79} -708.381 q^{80} +81.0000 q^{81} -15.4597 q^{82} -1453.80 q^{83} -90.5470 q^{84} -988.896 q^{85} +67.7051 q^{86} -87.0000 q^{87} -137.385 q^{88} +1237.01 q^{89} -265.272 q^{90} -752.998 q^{91} +50.9829 q^{92} -116.825 q^{93} -1856.25 q^{94} -1324.92 q^{95} +292.973 q^{96} +1153.40 q^{97} +503.741 q^{98} -66.8878 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9}+O(q^{10}) \) 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9	\( 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9} + 214 q^{10} + 111 q^{11} + 630 q^{12} + 275 q^{13} + 104 q^{14} + 45 q^{15} + 1062 q^{16} - 58 q^{17} + 54 q^{18} + 331 q^{19} + 287 q^{20} + 234 q^{21} + 285 q^{22} + 1012 q^{23} + 36 q^{24} + 1903 q^{25} + 1084 q^{26} + 1188 q^{27} + 222 q^{28} - 1276 q^{29} + 642 q^{30} + 1394 q^{31} + 42 q^{32} + 333 q^{33} + 373 q^{34} + 567 q^{35} + 1890 q^{36} + 1229 q^{37} + 733 q^{38} + 825 q^{39} + 2483 q^{40} - 107 q^{41} + 312 q^{42} + 1165 q^{43} + 1639 q^{44} + 135 q^{45} + 138 q^{46} + 964 q^{47} + 3186 q^{48} + 4264 q^{49} + 495 q^{50} - 174 q^{51} + 2679 q^{52} - 380 q^{53} + 162 q^{54} + 1260 q^{55} + 2229 q^{56} + 993 q^{57} - 174 q^{58} + 897 q^{59} + 861 q^{60} + 2584 q^{61} + 3034 q^{62} + 702 q^{63} + 6866 q^{64} - 286 q^{65} + 855 q^{66} + 2277 q^{67} - 1554 q^{68} + 3036 q^{69} + 689 q^{70} + 4304 q^{71} + 108 q^{72} + 4712 q^{73} - 1005 q^{74} + 5709 q^{75} + 2877 q^{76} + 919 q^{77} + 3252 q^{78} + 3864 q^{79} + 2593 q^{80} + 3564 q^{81} + 3297 q^{82} - 540 q^{83} + 666 q^{84} + 6537 q^{85} + 3789 q^{86} - 3828 q^{87} + 1707 q^{88} - 331 q^{89} + 1926 q^{90} + 4311 q^{91} + 4830 q^{92} + 4182 q^{93} + 6189 q^{94} + 3267 q^{95} + 126 q^{96} + 5572 q^{97} + 2588 q^{98} + 999 q^{99}+O(q^{100}) \) 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9 + 214 * q^10 + 111 * q^11 + 630 * q^12 + 275 * q^13 + 104 * q^14 + 45 * q^15 + 1062 * q^16 - 58 * q^17 + 54 * q^18 + 331 * q^19 + 287 * q^20 + 234 * q^21 + 285 * q^22 + 1012 * q^23 + 36 * q^24 + 1903 * q^25 + 1084 * q^26 + 1188 * q^27 + 222 * q^28 - 1276 * q^29 + 642 * q^30 + 1394 * q^31 + 42 * q^32 + 333 * q^33 + 373 * q^34 + 567 * q^35 + 1890 * q^36 + 1229 * q^37 + 733 * q^38 + 825 * q^39 + 2483 * q^40 - 107 * q^41 + 312 * q^42 + 1165 * q^43 + 1639 * q^44 + 135 * q^45 + 138 * q^46 + 964 * q^47 + 3186 * q^48 + 4264 * q^49 + 495 * q^50 - 174 * q^51 + 2679 * q^52 - 380 * q^53 + 162 * q^54 + 1260 * q^55 + 2229 * q^56 + 993 * q^57 - 174 * q^58 + 897 * q^59 + 861 * q^60 + 2584 * q^61 + 3034 * q^62 + 702 * q^63 + 6866 * q^64 - 286 * q^65 + 855 * q^66 + 2277 * q^67 - 1554 * q^68 + 3036 * q^69 + 689 * q^70 + 4304 * q^71 + 108 * q^72 + 4712 * q^73 - 1005 * q^74 + 5709 * q^75 + 2877 * q^76 + 919 * q^77 + 3252 * q^78 + 3864 * q^79 + 2593 * q^80 + 3564 * q^81 + 3297 * q^82 - 540 * q^83 + 666 * q^84 + 6537 * q^85 + 3789 * q^86 - 3828 * q^87 + 1707 * q^88 - 331 * q^89 + 1926 * q^90 + 4311 * q^91 + 4830 * q^92 + 4182 * q^93 + 6189 * q^94 + 3267 * q^95 + 126 * q^96 + 5572 * q^97 + 2588 * q^98 + 999 * q^99

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