LMFDB - Embedded newform 722.4.a.p.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,4,Mod(1,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("722.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	722.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:	$42.5993790241$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.6719782761.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 75x^{4} + 135x^{3} + 1857x^{2} - 1425x - 14797 $ x^6 - 3x^5 - 75x^4 + 135x^3 + 1857x^2 - 1425*x - 14797
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 19 $
Twist minimal:	no (minimal twist has level 38)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-4.99381$ of defining polynomial
Character	$\chi$	$=$	722.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +0.235037 q^{3} +4.00000 q^{4} +11.0362 q^{5} +0.470075 q^{6} -18.5336 q^{7} +8.00000 q^{8} -26.9448 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +0.235037 q^{3} +4.00000 q^{4} +11.0362 q^{5} +0.470075 q^{6} -18.5336 q^{7} +8.00000 q^{8} -26.9448 q^{9} +22.0725 q^{10} +13.9751 q^{11} +0.940150 q^{12} -53.9711 q^{13} -37.0673 q^{14} +2.59393 q^{15} +16.0000 q^{16} +8.15016 q^{17} -53.8895 q^{18} +44.1450 q^{20} -4.35610 q^{21} +27.9503 q^{22} -122.357 q^{23} +1.88030 q^{24} -3.20126 q^{25} -107.942 q^{26} -12.6790 q^{27} -74.1346 q^{28} -221.414 q^{29} +5.18786 q^{30} +46.2360 q^{31} +32.0000 q^{32} +3.28468 q^{33} +16.3003 q^{34} -204.542 q^{35} -107.779 q^{36} -99.6840 q^{37} -12.6852 q^{39} +88.2900 q^{40} +317.596 q^{41} -8.71220 q^{42} -467.572 q^{43} +55.9006 q^{44} -297.369 q^{45} -244.713 q^{46} -17.4546 q^{47} +3.76060 q^{48} +0.495723 q^{49} -6.40252 q^{50} +1.91559 q^{51} -215.885 q^{52} +44.3155 q^{53} -25.3581 q^{54} +154.233 q^{55} -148.269 q^{56} -442.828 q^{58} +638.202 q^{59} +10.3757 q^{60} +824.130 q^{61} +92.4720 q^{62} +499.384 q^{63} +64.0000 q^{64} -595.639 q^{65} +6.56936 q^{66} -839.953 q^{67} +32.6006 q^{68} -28.7584 q^{69} -409.084 q^{70} -578.033 q^{71} -215.558 q^{72} -755.948 q^{73} -199.368 q^{74} -0.752416 q^{75} -259.010 q^{77} -25.3705 q^{78} +339.520 q^{79} +176.580 q^{80} +724.528 q^{81} +635.191 q^{82} -765.610 q^{83} -17.4244 q^{84} +89.9471 q^{85} -935.144 q^{86} -52.0406 q^{87} +111.801 q^{88} +907.629 q^{89} -594.738 q^{90} +1000.28 q^{91} -489.426 q^{92} +10.8672 q^{93} -34.9093 q^{94} +7.52120 q^{96} +1682.73 q^{97} +0.991447 q^{98} -376.557 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 12 q^{2} - 9 q^{3} + 24 q^{4} - 27 q^{5} - 18 q^{6} - 21 q^{7} + 48 q^{8} + 33 q^{9}+O(q^{10}) $ 6 * q + 12 * q^2 - 9 * q^3 + 24 * q^4 - 27 * q^5 - 18 * q^6 - 21 * q^7 + 48 * q^8 + 33 * q^9	\( 6 q + 12 q^{2} - 9 q^{3} + 24 q^{4} - 27 q^{5} - 18 q^{6} - 21 q^{7} + 48 q^{8} + 33 q^{9} - 54 q^{10} + 9 q^{11} - 36 q^{12} - 24 q^{13} - 42 q^{14} + 96 q^{16} - 102 q^{17} + 66 q^{18} - 108 q^{20} - 51 q^{21} + 18 q^{22} - 264 q^{23} - 72 q^{24} + 177 q^{25} - 48 q^{26} - 189 q^{27} - 84 q^{28} - 483 q^{29} - 72 q^{31} + 192 q^{32} - 387 q^{33} - 204 q^{34} + 135 q^{35} + 132 q^{36} + 558 q^{37} - 624 q^{39} - 216 q^{40} - 396 q^{41} - 102 q^{42} - 2064 q^{43} + 36 q^{44} - 1296 q^{45} - 528 q^{46} + 858 q^{47} - 144 q^{48} - 1413 q^{49} + 354 q^{50} + 1272 q^{51} - 96 q^{52} - 762 q^{53} - 378 q^{54} - 1107 q^{55} - 168 q^{56} - 966 q^{58} - 393 q^{59} - 627 q^{61} - 144 q^{62} - 84 q^{63} + 384 q^{64} - 495 q^{65} - 774 q^{66} - 2028 q^{67} - 408 q^{68} + 237 q^{69} + 270 q^{70} - 1284 q^{71} + 264 q^{72} - 2688 q^{73} + 1116 q^{74} - 927 q^{75} - 708 q^{77} - 1248 q^{78} - 969 q^{79} - 432 q^{80} - 1398 q^{81} - 792 q^{82} - 927 q^{83} - 204 q^{84} + 396 q^{85} - 4128 q^{86} - 2892 q^{87} + 72 q^{88} + 1257 q^{89} - 2592 q^{90} + 1323 q^{91} - 1056 q^{92} - 1368 q^{93} + 1716 q^{94} - 288 q^{96} + 2403 q^{97} - 2826 q^{98} + 567 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 - 9 * q^3 + 24 * q^4 - 27 * q^5 - 18 * q^6 - 21 * q^7 + 48 * q^8 + 33 * q^9 - 54 * q^10 + 9 * q^11 - 36 * q^12 - 24 * q^13 - 42 * q^14 + 96 * q^16 - 102 * q^17 + 66 * q^18 - 108 * q^20 - 51 * q^21 + 18 * q^22 - 264 * q^23 - 72 * q^24 + 177 * q^25 - 48 * q^26 - 189 * q^27 - 84 * q^28 - 483 * q^29 - 72 * q^31 + 192 * q^32 - 387 * q^33 - 204 * q^34 + 135 * q^35 + 132 * q^36 + 558 * q^37 - 624 * q^39 - 216 * q^40 - 396 * q^41 - 102 * q^42 - 2064 * q^43 + 36 * q^44 - 1296 * q^45 - 528 * q^46 + 858 * q^47 - 144 * q^48 - 1413 * q^49 + 354 * q^50 + 1272 * q^51 - 96 * q^52 - 762 * q^53 - 378 * q^54 - 1107 * q^55 - 168 * q^56 - 966 * q^58 - 393 * q^59 - 627 * q^61 - 144 * q^62 - 84 * q^63 + 384 * q^64 - 495 * q^65 - 774 * q^66 - 2028 * q^67 - 408 * q^68 + 237 * q^69 + 270 * q^70 - 1284 * q^71 + 264 * q^72 - 2688 * q^73 + 1116 * q^74 - 927 * q^75 - 708 * q^77 - 1248 * q^78 - 969 * q^79 - 432 * q^80 - 1398 * q^81 - 792 * q^82 - 927 * q^83 - 204 * q^84 + 396 * q^85 - 4128 * q^86 - 2892 * q^87 + 72 * q^88 + 1257 * q^89 - 2592 * q^90 + 1323 * q^91 - 1056 * q^92 - 1368 * q^93 + 1716 * q^94 - 288 * q^96 + 2403 * q^97 - 2826 * q^98 + 567 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	0.235037	0.0452330	0.0226165	−	0.999744i	$-0.492800\pi$
$3$	0.235037	0.0452330	0.0226165	+	0.999744i	$0.492800\pi$
$4$	4.00000	0.500000
$5$	11.0362	0.987112	0.493556	−	0.869714i	$-0.335697\pi$
$5$	11.0362	0.987112	0.493556	+	0.869714i	$0.335697\pi$
$6$	0.470075	0.0319845
$7$	−18.5336	−1.00072	−0.500361	−	0.865817i	$-0.666799\pi$
$7$	−18.5336	−1.00072	−0.500361	+	0.865817i	$0.666799\pi$
$8$	8.00000	0.353553
$9$	−26.9448	−0.997954
$10$	22.0725	0.697994
$11$	13.9751	0.383060	0.191530	−	0.981487i	$-0.438655\pi$
$11$	13.9751	0.383060	0.191530	+	0.981487i	$0.438655\pi$
$12$	0.940150	0.0226165
$13$	−53.9711	−1.15145	−0.575727	−	0.817642i	$-0.695281\pi$
$13$	−53.9711	−1.15145	−0.575727	+	0.817642i	$0.695281\pi$
$14$	−37.0673	−0.707618
$15$	2.59393	0.0446500
$16$	16.0000	0.250000
$17$	8.15016	0.116277	0.0581383	−	0.998309i	$-0.481484\pi$
$17$	8.15016	0.116277	0.0581383	+	0.998309i	$0.481484\pi$
$18$	−53.8895	−0.705660
$19$	0	0
$19$	0	0
$20$	44.1450	0.493556
$21$	−4.35610	−0.0452657
$22$	27.9503	0.270865
$23$	−122.357	−1.10927	−0.554633	−	0.832095i	$-0.687141\pi$
$23$	−122.357	−1.10927	−0.554633	+	0.832095i	$0.687141\pi$
$24$	1.88030	0.0159923
$25$	−3.20126	−0.0256101
$26$	−107.942	−0.814201
$27$	−12.6790	−0.0903734
$28$	−74.1346	−0.500361
$29$	−221.414	−1.41778	−0.708889	−	0.705320i	$-0.750803\pi$
$29$	−221.414	−1.41778	−0.708889	+	0.705320i	$0.750803\pi$
$30$	5.18786	0.0315723
$31$	46.2360	0.267878	0.133939	−	0.990990i	$-0.457237\pi$
$31$	46.2360	0.267878	0.133939	+	0.990990i	$0.457237\pi$
$32$	32.0000	0.176777
$33$	3.28468	0.0173270
$34$	16.3003	0.0822200
$35$	−204.542	−0.987825
$36$	−107.779	−0.498977
$37$	−99.6840	−0.442917	−0.221459	−	0.975170i	$-0.571082\pi$
$37$	−99.6840	−0.442917	−0.221459	+	0.975170i	$0.571082\pi$
$38$	0	0
$39$	−12.6852	−0.0520837
$40$	88.2900	0.348997
$41$	317.596	1.20976	0.604879	−	0.796317i	$-0.293221\pi$
$41$	317.596	1.20976	0.604879	+	0.796317i	$0.293221\pi$
$42$	−8.71220	−0.0320077
$43$	−467.572	−1.65823	−0.829117	−	0.559076i	$-0.811156\pi$
$43$	−467.572	−1.65823	−0.829117	+	0.559076i	$0.811156\pi$
$44$	55.9006	0.191530
$45$	−297.369	−0.985092
$46$	−244.713	−0.784369
$47$	−17.4546	−0.0541706	−0.0270853	−	0.999633i	$-0.508623\pi$
$47$	−17.4546	−0.0541706	−0.0270853	+	0.999633i	$0.508623\pi$
$48$	3.76060	0.0113082
$49$	0.495723	0.00144526
$50$	−6.40252	−0.0181091
$51$	1.91559	0.00525954
$52$	−215.885	−0.575727
$53$	44.3155	0.114853	0.0574265	−	0.998350i	$-0.481711\pi$
$53$	44.3155	0.114853	0.0574265	+	0.998350i	$0.481711\pi$
$54$	−25.3581	−0.0639037
$55$	154.233	0.378123
$56$	−148.269	−0.353809
$57$	0	0
$58$	−442.828	−1.00252
$59$	638.202	1.40825	0.704126	−	0.710075i	$-0.251339\pi$
$59$	638.202	1.40825	0.704126	+	0.710075i	$0.251339\pi$
$60$	10.3757	0.0223250
$61$	824.130	1.72982	0.864911	−	0.501926i	$-0.167375\pi$
$61$	824.130	1.72982	0.864911	+	0.501926i	$0.167375\pi$
$62$	92.4720	0.189419
$63$	499.384	0.998675
$64$	64.0000	0.125000
$65$	−595.639	−1.13661
$66$	6.56936	0.0122520
$67$	−839.953	−1.53159	−0.765795	−	0.643085i	$-0.777654\pi$
$67$	−839.953	−1.53159	−0.765795	+	0.643085i	$0.777654\pi$
$68$	32.6006	0.0581383
$69$	−28.7584	−0.0501754
$70$	−409.084	−0.698498
$71$	−578.033	−0.966196	−0.483098	−	0.875566i	$-0.660488\pi$
$71$	−578.033	−0.966196	−0.483098	+	0.875566i	$0.660488\pi$
$72$	−215.558	−0.352830
$73$	−755.948	−1.21201	−0.606007	−	0.795459i	$-0.707230\pi$
$73$	−755.948	−1.21201	−0.606007	+	0.795459i	$0.707230\pi$
$74$	−199.368	−0.313190
$75$	−0.752416	−0.00115842
$76$	0	0
$77$	−259.010	−0.383337
$78$	−25.3705	−0.0368287
$79$	339.520	0.483531	0.241766	−	0.970335i	$-0.422274\pi$
$79$	339.520	0.483531	0.241766	+	0.970335i	$0.422274\pi$
$80$	176.580	0.246778
$81$	724.528	0.993866
$82$	635.191	0.855429
$83$	−765.610	−1.01249	−0.506244	−	0.862390i	$-0.668967\pi$
$83$	−765.610	−1.01249	−0.506244	+	0.862390i	$0.668967\pi$
$84$	−17.4244	−0.0226328
$85$	89.9471	0.114778
$86$	−935.144	−1.17255
$87$	−52.0406	−0.0641304
$88$	111.801	0.135432
$89$	907.629	1.08099	0.540497	−	0.841346i	$-0.318236\pi$
$89$	907.629	1.08099	0.540497	+	0.841346i	$0.318236\pi$
$90$	−594.738	−0.696565
$91$	1000.28	1.15229
$92$	−489.426	−0.554633
$93$	10.8672	0.0121169
$94$	−34.9093	−0.0383044
$95$	0	0
$96$	7.52120	0.00799614
$97$	1682.73	1.76139	0.880697	−	0.473681i	$-0.157075\pi$
$97$	1682.73	1.76139	0.880697	+	0.473681i	$0.157075\pi$
$98$	0.991447	0.00102195
$99$	−376.557	−0.382277
$100$	−12.8050	−0.0128050
$101$	−1208.58	−1.19068	−0.595338	−	0.803475i	$-0.702982\pi$
$101$	−1208.58	−1.19068	−0.595338	+	0.803475i	$0.702982\pi$
$102$	3.83118	0.00371906
$103$	−48.1629	−0.0460741	−0.0230370	−	0.999735i	$-0.507334\pi$
$103$	−48.1629	−0.0460741	−0.0230370	+	0.999735i	$0.507334\pi$
$104$	−431.769	−0.407100
$105$	−48.0750	−0.0446823
$106$	88.6311	0.0812133
$107$	872.174	0.788003	0.394001	−	0.919110i	$-0.371091\pi$
$107$	872.174	0.788003	0.394001	+	0.919110i	$0.371091\pi$
$108$	−50.7162	−0.0451867
$109$	−564.225	−0.495807	−0.247903	−	0.968785i	$-0.579742\pi$
$109$	−564.225	−0.495807	−0.247903	+	0.968785i	$0.579742\pi$
$110$	308.466	0.267374
$111$	−23.4295	−0.0200345
$112$	−296.538	−0.250181
$113$	−2333.39	−1.94254	−0.971270	−	0.237982i	$-0.923514\pi$
$113$	−2333.39	−1.94254	−0.971270	+	0.237982i	$0.923514\pi$
$114$	0	0
$115$	−1350.36	−1.09497
$116$	−885.657	−0.708889
$117$	1454.24	1.14910
$118$	1276.40	0.995784
$119$	−151.052	−0.116361
$120$	20.7515	0.0157862
$121$	−1135.70	−0.853265
$122$	1648.26	1.22317
$123$	74.6469	0.0547210
$124$	184.944	0.133939
$125$	−1414.86	−1.01239
$126$	998.769	0.706170
$127$	1893.43	1.32295	0.661477	−	0.749966i	$-0.269930\pi$
$127$	1893.43	1.32295	0.661477	+	0.749966i	$0.269930\pi$
$128$	128.000	0.0883883
$129$	−109.897	−0.0750068
$130$	−1191.28	−0.803707
$131$	−2279.01	−1.51999	−0.759994	−	0.649931i	$-0.774798\pi$
$131$	−2279.01	−1.51999	−0.759994	+	0.649931i	$0.774798\pi$
$132$	13.1387	0.00866348
$133$	0	0
$134$	−1679.91	−1.08300
$135$	−139.929	−0.0892087
$136$	65.2012	0.0411100
$137$	−1599.85	−0.997699	−0.498849	−	0.866689i	$-0.666244\pi$
$137$	−1599.85	−0.997699	−0.498849	+	0.866689i	$0.666244\pi$
$138$	−57.5168	−0.0354794
$139$	1719.75	1.04941	0.524704	−	0.851285i	$-0.324176\pi$
$139$	1719.75	1.04941	0.524704	+	0.851285i	$0.324176\pi$
$140$	−818.167	−0.493912
$141$	−4.10249	−0.00245030
$142$	−1156.07	−0.683204
$143$	−754.254	−0.441076
$144$	−431.116	−0.249488
$145$	−2443.58	−1.39951
$146$	−1511.90	−0.857024
$147$	0.116514	6.53733e−5 0
$148$	−398.736	−0.221459
$149$	−2379.89	−1.30851	−0.654256	−	0.756273i	$-0.727018\pi$
$149$	−2379.89	−1.30851	−0.654256	+	0.756273i	$0.727018\pi$
$150$	−1.50483	−0.000819127 0
$151$	2143.06	1.15497	0.577483	−	0.816402i	$-0.304035\pi$
$151$	2143.06	1.15497	0.577483	+	0.816402i	$0.304035\pi$
$152$	0	0
$153$	−219.604	−0.116039
$154$	−518.020	−0.271060
$155$	510.272	0.264426
$156$	−50.7410	−0.0260418
$157$	828.825	0.421321	0.210661	−	0.977559i	$-0.432439\pi$
$157$	828.825	0.421321	0.210661	+	0.977559i	$0.432439\pi$
$158$	679.040	0.341908
$159$	10.4158	0.00519514
$160$	353.160	0.174498
$161$	2267.71	1.11007
$162$	1449.06	0.702769
$163$	−2295.30	−1.10295	−0.551477	−	0.834190i	$-0.685936\pi$
$163$	−2295.30	−1.10295	−0.551477	+	0.834190i	$0.685936\pi$
$164$	1270.38	0.604879
$165$	36.2506	0.0171036
$166$	−1531.22	−0.715938
$167$	657.365	0.304601	0.152301	−	0.988334i	$-0.451332\pi$
$167$	657.365	0.304601	0.152301	+	0.988334i	$0.451332\pi$
$168$	−34.8488	−0.0160038
$169$	715.884	0.325846
$170$	179.894	0.0811604
$171$	0	0
$172$	−1870.29	−0.829117
$173$	−164.045	−0.0720930	−0.0360465	−	0.999350i	$-0.511476\pi$
$173$	−164.045	−0.0720930	−0.0360465	+	0.999350i	$0.511476\pi$
$174$	−104.081	−0.0453470
$175$	59.3310	0.0256286
$176$	223.602	0.0957651
$177$	150.001	0.0636994
$178$	1815.26	0.764379
$179$	566.828	0.236686	0.118343	−	0.992973i	$-0.462242\pi$
$179$	566.828	0.236686	0.118343	+	0.992973i	$0.462242\pi$
$180$	−1189.48	−0.492546
$181$	1170.39	0.480631	0.240315	−	0.970695i	$-0.422749\pi$
$181$	1170.39	0.480631	0.240315	+	0.970695i	$0.422749\pi$
$182$	2000.56	0.814789
$183$	193.702	0.0782450
$184$	−978.853	−0.392185
$185$	−1100.14	−0.437209
$186$	21.7344	0.00856797
$187$	113.900	0.0445410
$188$	−69.8185	−0.0270853
$189$	234.989	0.0904387
$190$	0	0
$191$	1297.38	0.491493	0.245747	−	0.969334i	$-0.420967\pi$
$191$	1297.38	0.491493	0.245747	+	0.969334i	$0.420967\pi$
$192$	15.0424	0.00565412
$193$	−1977.87	−0.737669	−0.368834	−	0.929495i	$-0.620243\pi$
$193$	−1977.87	−0.737669	−0.368834	+	0.929495i	$0.620243\pi$
$194$	3365.46	1.24549
$195$	−139.997	−0.0514124
$196$	1.98289	0.000722629 0
$197$	2335.32	0.844593	0.422297	−	0.906458i	$-0.361224\pi$
$197$	2335.32	0.844593	0.422297	+	0.906458i	$0.361224\pi$
$198$	−753.113	−0.270310
$199$	2604.76	0.927871	0.463935	−	0.885869i	$-0.346437\pi$
$199$	2604.76	0.927871	0.463935	+	0.885869i	$0.346437\pi$
$200$	−25.6101	−0.00905453
$201$	−197.420	−0.0692784
$202$	−2417.16	−0.841935
$203$	4103.61	1.41880
$204$	7.66237	0.00262977
$205$	3505.06	1.19417
$206$	−96.3257	−0.0325793
$207$	3296.87	1.10700
$208$	−863.538	−0.287863
$209$	0	0
$210$	−96.1500	−0.0315951
$211$	5034.95	1.64275	0.821375	−	0.570389i	$-0.193207\pi$
$211$	5034.95	1.64275	0.821375	+	0.570389i	$0.193207\pi$
$212$	177.262	0.0574265
$213$	−135.859	−0.0437039
$214$	1744.35	0.557202
$215$	−5160.24	−1.63686
$216$	−101.432	−0.0319518
$217$	−856.921	−0.268072
$218$	−1128.45	−0.350588
$219$	−177.676	−0.0548230
$220$	616.932	0.189062
$221$	−439.873	−0.133887
$222$	−46.8589	−0.0141665
$223$	3746.11	1.12492	0.562462	−	0.826823i	$-0.309854\pi$
$223$	3746.11	1.12492	0.562462	+	0.826823i	$0.309854\pi$
$224$	−593.076	−0.176904
$225$	86.2572	0.0255577
$226$	−4666.78	−1.37358
$227$	1621.77	0.474187	0.237093	−	0.971487i	$-0.423805\pi$
$227$	1621.77	0.474187	0.237093	+	0.971487i	$0.423805\pi$
$228$	0	0
$229$	3975.70	1.14726	0.573628	−	0.819116i	$-0.305536\pi$
$229$	3975.70	1.14726	0.573628	+	0.819116i	$0.305536\pi$
$230$	−2700.72	−0.774260
$231$	−60.8771	−0.0173395
$232$	−1771.31	−0.501260
$233$	−1372.87	−0.386007	−0.193003	−	0.981198i	$-0.561823\pi$
$233$	−1372.87	−0.386007	−0.193003	+	0.981198i	$0.561823\pi$
$234$	2908.48	0.812535
$235$	−192.634	−0.0534725
$236$	2552.81	0.704126
$237$	79.7999	0.0218716
$238$	−302.104	−0.0822794
$239$	4989.77	1.35047	0.675233	−	0.737605i	$-0.264043\pi$
$239$	4989.77	1.35047	0.675233	+	0.737605i	$0.264043\pi$
$240$	41.5029	0.0111625
$241$	−1381.51	−0.369258	−0.184629	−	0.982808i	$-0.559108\pi$
$241$	−1381.51	−0.369258	−0.184629	+	0.982808i	$0.559108\pi$
$242$	−2271.39	−0.603349
$243$	512.625	0.135329
$244$	3296.52	0.864911
$245$	5.47093	0.00142663
$246$	149.294	0.0386936
$247$	0	0
$248$	369.888	0.0947093
$249$	−179.947	−0.0457979
$250$	−2829.72	−0.715869
$251$	350.128	0.0880474	0.0440237	−	0.999030i	$-0.485982\pi$
$251$	350.128	0.0880474	0.0440237	+	0.999030i	$0.485982\pi$
$252$	1997.54	0.499337
$253$	−1709.95	−0.424916
$254$	3786.87	0.935470
$255$	21.1409	0.00519175
$256$	256.000	0.0625000
$257$	−2510.91	−0.609440	−0.304720	−	0.952442i	$-0.598563\pi$
$257$	−2510.91	−0.609440	−0.304720	+	0.952442i	$0.598563\pi$
$258$	−219.794	−0.0530378
$259$	1847.51	0.443237
$260$	−2382.56	−0.568307
$261$	5965.95	1.41488
$262$	−4558.03	−1.07479
$263$	4697.07	1.10127	0.550634	−	0.834747i	$-0.314386\pi$
$263$	4697.07	1.10127	0.550634	+	0.834747i	$0.314386\pi$
$264$	26.2774	0.00612600
$265$	489.077	0.113373
$266$	0	0
$267$	213.327	0.0488966
$268$	−3359.81	−0.765795
$269$	−2264.45	−0.513256	−0.256628	−	0.966510i	$-0.582611\pi$
$269$	−2264.45	−0.513256	−0.256628	+	0.966510i	$0.582611\pi$
$270$	−279.858	−0.0630801
$271$	−2325.26	−0.521215	−0.260608	−	0.965445i	$-0.583923\pi$
$271$	−2325.26	−0.521215	−0.260608	+	0.965445i	$0.583923\pi$
$272$	130.402	0.0290692
$273$	235.104	0.0521213
$274$	−3199.71	−0.705479
$275$	−44.7381	−0.00981021
$276$	−115.034	−0.0250877
$277$	−6255.19	−1.35681	−0.678407	−	0.734686i	$-0.737330\pi$
$277$	−6255.19	−1.35681	−0.678407	+	0.734686i	$0.737330\pi$
$278$	3439.51	0.742043
$279$	−1245.82	−0.267330
$280$	−1636.33	−0.349249
$281$	−7120.54	−1.51166	−0.755829	−	0.654769i	$-0.772766\pi$
$281$	−7120.54	−1.51166	−0.755829	+	0.654769i	$0.772766\pi$
$282$	−8.20498	−0.00173262
$283$	6682.65	1.40368	0.701841	−	0.712333i	$-0.252362\pi$
$283$	6682.65	1.40368	0.701841	+	0.712333i	$0.252362\pi$
$284$	−2312.13	−0.483098
$285$	0	0
$286$	−1508.51	−0.311888
$287$	−5886.20	−1.21063
$288$	−862.232	−0.176415
$289$	−4846.57	−0.986480
$290$	−4887.16	−0.989600
$291$	395.504	0.0796731
$292$	−3023.79	−0.606007
$293$	−2590.04	−0.516422	−0.258211	−	0.966089i	$-0.583133\pi$
$293$	−2590.04	−0.516422	−0.258211	+	0.966089i	$0.583133\pi$
$294$	0.233027	4.62259e−5 0
$295$	7043.36	1.39010
$296$	−797.472	−0.156595
$297$	−177.191	−0.0346185
$298$	−4759.79	−0.925258
$299$	6603.73	1.27727
$300$	−3.00966	−0.000579210 0
$301$	8665.81	1.65943
$302$	4286.13	0.816685
$303$	−284.062	−0.0538578
$304$	0	0
$305$	9095.31	1.70753
$306$	−439.208	−0.0820518
$307$	7677.71	1.42733	0.713665	−	0.700487i	$-0.247034\pi$
$307$	7677.71	1.42733	0.713665	+	0.700487i	$0.247034\pi$
$308$	−1036.04	−0.191668
$309$	−11.3201	−0.00208407
$310$	1020.54	0.186977
$311$	−5497.61	−1.00238	−0.501191	−	0.865337i	$-0.667105\pi$
$311$	−5497.61	−1.00238	−0.501191	+	0.865337i	$0.667105\pi$
$312$	−101.482	−0.0184144
$313$	−3646.95	−0.658587	−0.329293	−	0.944228i	$-0.606811\pi$
$313$	−3646.95	−0.658587	−0.329293	+	0.944228i	$0.606811\pi$
$314$	1657.65	0.297919
$315$	5511.33	0.985804
$316$	1358.08	0.241766
$317$	3433.12	0.608274	0.304137	−	0.952628i	$-0.401632\pi$
$317$	3433.12	0.608274	0.304137	+	0.952628i	$0.401632\pi$
$318$	20.8316	0.00367352
$319$	−3094.29	−0.543095
$320$	706.320	0.123389
$321$	204.994	0.0356437
$322$	4535.43	0.784936
$323$	0	0
$324$	2898.11	0.496933
$325$	172.776	0.0294888
$326$	−4590.59	−0.779906
$327$	−132.614	−0.0224268
$328$	2540.77	0.427714
$329$	323.498	0.0542098
$330$	72.5011	0.0120941
$331$	2386.30	0.396262	0.198131	−	0.980176i	$-0.436513\pi$
$331$	2386.30	0.396262	0.198131	+	0.980176i	$0.436513\pi$
$332$	−3062.44	−0.506244
$333$	2685.96	0.442011
$334$	1314.73	0.215386
$335$	−9269.92	−1.51185
$336$	−69.6976	−0.0113164
$337$	1709.23	0.276284	0.138142	−	0.990412i	$-0.455887\pi$
$337$	1709.23	0.276284	0.138142	+	0.990412i	$0.455887\pi$
$338$	1431.77	0.230408
$339$	−548.434	−0.0878668
$340$	359.789	0.0573890
$341$	646.154	0.102614
$342$	0	0
$343$	6347.85	0.999276
$344$	−3740.57	−0.586274
$345$	−317.385	−0.0495287
$346$	−328.089	−0.0509774
$347$	−3033.12	−0.469241	−0.234621	−	0.972087i	$-0.575385\pi$
$347$	−3033.12	−0.469241	−0.234621	+	0.972087i	$0.575385\pi$
$348$	−208.163	−0.0320652
$349$	2061.80	0.316234	0.158117	−	0.987420i	$-0.449458\pi$
$349$	2061.80	0.316234	0.158117	+	0.987420i	$0.449458\pi$
$350$	118.662	0.0181221
$351$	684.302	0.104061
$352$	447.204	0.0677161
$353$	7349.15	1.10809	0.554045	−	0.832487i	$-0.313084\pi$
$353$	7349.15	1.10809	0.554045	+	0.832487i	$0.313084\pi$
$354$	300.003	0.0450423
$355$	−6379.31	−0.953743
$356$	3630.52	0.540497
$357$	−35.5029	−0.00526334
$358$	1133.66	0.167362
$359$	655.593	0.0963812	0.0481906	−	0.998838i	$-0.484655\pi$
$359$	655.593	0.0963812	0.0481906	+	0.998838i	$0.484655\pi$
$360$	−2378.95	−0.348283
$361$	0	0
$362$	2340.77	0.339857
$363$	−266.931	−0.0385957
$364$	4001.13	0.576143
$365$	−8342.83	−1.19639
$366$	387.403	0.0553275
$367$	−12301.3	−1.74965	−0.874824	−	0.484440i	$-0.839023\pi$
$367$	−12301.3	−1.74965	−0.874824	+	0.484440i	$0.839023\pi$
$368$	−1957.71	−0.277316
$369$	−8557.54	−1.20728
$370$	−2200.27	−0.309153
$371$	−821.328	−0.114936
$372$	43.4688	0.00605847
$373$	1022.54	0.141944	0.0709720	−	0.997478i	$-0.477390\pi$
$373$	1022.54	0.141944	0.0709720	+	0.997478i	$0.477390\pi$
$374$	227.799	0.0314952
$375$	−332.545	−0.0457935
$376$	−139.637	−0.0191522
$377$	11950.0	1.63251
$378$	469.977	0.0639498
$379$	1217.86	0.165058	0.0825292	−	0.996589i	$-0.473700\pi$
$379$	1217.86	0.165058	0.0825292	+	0.996589i	$0.473700\pi$
$380$	0	0
$381$	445.028	0.0598411
$382$	2594.76	0.347538
$383$	−10274.1	−1.37071	−0.685354	−	0.728210i	$-0.740353\pi$
$383$	−10274.1	−1.37071	−0.685354	+	0.728210i	$0.740353\pi$
$384$	30.0848	0.00399807
$385$	−2858.50	−0.378396
$386$	−3955.74	−0.521611
$387$	12598.6	1.65484
$388$	6730.91	0.880697
$389$	14699.1	1.91587	0.957933	−	0.286991i	$-0.0926550\pi$
$389$	14699.1	1.91587	0.957933	+	0.286991i	$0.0926550\pi$
$390$	−279.995	−0.0363541
$391$	−997.225	−0.128982
$392$	3.96579	0.000510976 0
$393$	−535.654	−0.0687535
$394$	4670.65	0.597218
$395$	3747.02	0.477299
$396$	−1506.23	−0.191138
$397$	−2318.54	−0.293108	−0.146554	−	0.989203i	$-0.546818\pi$
$397$	−2318.54	−0.293108	−0.146554	+	0.989203i	$0.546818\pi$
$398$	5209.51	0.656104
$399$	0	0
$400$	−51.2202	−0.00640252
$401$	3927.20	0.489065	0.244533	−	0.969641i	$-0.421365\pi$
$401$	3927.20	0.489065	0.244533	+	0.969641i	$0.421365\pi$
$402$	−394.841	−0.0489872
$403$	−2495.41	−0.308450
$404$	−4834.32	−0.595338
$405$	7996.07	0.981057
$406$	8207.22	1.00325
$407$	−1393.10	−0.169664
$408$	15.3247	0.00185953
$409$	−2623.83	−0.317213	−0.158606	−	0.987342i	$-0.550700\pi$
$409$	−2623.83	−0.317213	−0.158606	+	0.987342i	$0.550700\pi$
$410$	7010.13	0.844404
$411$	−376.025	−0.0451289
$412$	−192.651	−0.0230370
$413$	−11828.2	−1.40927
$414$	6593.74	0.782765
$415$	−8449.46	−0.999440
$416$	−1727.08	−0.203550
$417$	404.207	0.0474678
$418$	0	0
$419$	4324.14	0.504172	0.252086	−	0.967705i	$-0.418883\pi$
$419$	4324.14	0.504172	0.252086	+	0.967705i	$0.418883\pi$
$420$	−192.300	−0.0223411
$421$	−12422.2	−1.43805	−0.719026	−	0.694984i	$-0.755412\pi$
$421$	−12422.2	−1.43805	−0.719026	+	0.694984i	$0.755412\pi$
$422$	10069.9	1.16160
$423$	470.311	0.0540598
$424$	354.524	0.0406066
$425$	−26.0908	−0.00297786
$426$	−271.719	−0.0309033
$427$	−15274.1	−1.73107
$428$	3488.70	0.394001
$429$	−177.278	−0.0199512
$430$	−10320.5	−1.15744
$431$	−8355.43	−0.933798	−0.466899	−	0.884311i	$-0.654629\pi$
$431$	−8355.43	−0.933798	−0.466899	+	0.884311i	$0.654629\pi$
$432$	−202.865	−0.0225934
$433$	4621.33	0.512902	0.256451	−	0.966557i	$-0.417447\pi$
$433$	4621.33	0.512902	0.256451	+	0.966557i	$0.417447\pi$
$434$	−1713.84	−0.189555
$435$	−574.333	−0.0633038
$436$	−2256.90	−0.247903
$437$	0	0
$438$	−355.352	−0.0387657
$439$	−9232.36	−1.00373	−0.501864	−	0.864947i	$-0.667352\pi$
$439$	−9232.36	−1.00373	−0.501864	+	0.864947i	$0.667352\pi$
$440$	1233.86	0.133687
$441$	−13.3571	−0.00144230
$442$	−879.746	−0.0946726
$443$	5808.71	0.622980	0.311490	−	0.950249i	$-0.399172\pi$
$443$	5808.71	0.622980	0.311490	+	0.950249i	$0.399172\pi$
$444$	−93.7179	−0.0100172
$445$	10016.8	1.06706
$446$	7492.21	0.795441
$447$	−559.364	−0.0591879
$448$	−1186.15	−0.125090
$449$	7820.11	0.821946	0.410973	−	0.911647i	$-0.365189\pi$
$449$	7820.11	0.821946	0.410973	+	0.911647i	$0.365189\pi$
$450$	172.514	0.0180720
$451$	4438.44	0.463410
$452$	−9333.56	−0.971270
$453$	503.700	0.0522426
$454$	3243.53	0.335301
$455$	11039.4	1.13743
$456$	0	0
$457$	−9140.92	−0.935654	−0.467827	−	0.883820i	$-0.654963\pi$
$457$	−9140.92	−0.935654	−0.467827	+	0.883820i	$0.654963\pi$
$458$	7951.40	0.811232
$459$	−103.336	−0.0105083
$460$	−5401.43	−0.547485
$461$	12783.0	1.29146	0.645731	−	0.763565i	$-0.276553\pi$
$461$	12783.0	1.29146	0.645731	+	0.763565i	$0.276553\pi$
$462$	−121.754	−0.0122609
$463$	−879.462	−0.0882766	−0.0441383	−	0.999025i	$-0.514054\pi$
$463$	−879.462	−0.0882766	−0.0441383	+	0.999025i	$0.514054\pi$
$464$	−3542.63	−0.354445
$465$	119.933	0.0119608
$466$	−2745.74	−0.272948
$467$	−8024.15	−0.795103	−0.397552	−	0.917580i	$-0.630140\pi$
$467$	−8024.15	−0.795103	−0.397552	+	0.917580i	$0.630140\pi$
$468$	5816.96	0.574549
$469$	15567.4	1.53270
$470$	−385.267	−0.0378107
$471$	194.805	0.0190576
$472$	5105.62	0.497892
$473$	−6534.38	−0.635203
$474$	159.600	0.0154655
$475$	0	0
$476$	−604.208	−0.0581803
$477$	−1194.07	−0.114618
$478$	9979.54	0.954924
$479$	17238.1	1.64432	0.822159	−	0.569259i	$-0.192770\pi$
$479$	17238.1	1.64432	0.822159	+	0.569259i	$0.192770\pi$
$480$	83.0058	0.00789308
$481$	5380.06	0.509999
$482$	−2763.03	−0.261104
$483$	532.998	0.0502116
$484$	−4542.78	−0.426632
$485$	18571.0	1.73869
$486$	1025.25	0.0956920
$487$	−2231.73	−0.207658	−0.103829	−	0.994595i	$-0.533109\pi$
$487$	−2231.73	−0.207658	−0.103829	+	0.994595i	$0.533109\pi$
$488$	6593.04	0.611584
$489$	−539.481	−0.0498899
$490$	10.9419	0.00100878
$491$	−10113.5	−0.929567	−0.464783	−	0.885424i	$-0.653868\pi$
$491$	−10113.5	−0.929567	−0.464783	+	0.885424i	$0.653868\pi$
$492$	298.587	0.0273605
$493$	−1804.56	−0.164855
$494$	0	0
$495$	−4155.77	−0.377350
$496$	739.776	0.0669696
$497$	10713.1	0.966894
$498$	−359.894	−0.0323840
$499$	1675.70	0.150330	0.0751650	−	0.997171i	$-0.476052\pi$
$499$	1675.70	0.150330	0.0751650	+	0.997171i	$0.476052\pi$
$500$	−5659.44	−0.506196
$501$	154.505	0.0137780
$502$	700.257	0.0622589
$503$	14511.2	1.28633	0.643165	−	0.765727i	$-0.277621\pi$
$503$	14511.2	1.28633	0.643165	+	0.765727i	$0.277621\pi$
$504$	3995.07	0.353085
$505$	−13338.2	−1.17533
$506$	−3419.90	−0.300461
$507$	168.259	0.0147390
$508$	7573.74	0.661477
$509$	−13390.7	−1.16607	−0.583036	−	0.812447i	$-0.698135\pi$
$509$	−13390.7	−1.16607	−0.583036	+	0.812447i	$0.698135\pi$
$510$	42.2819	0.00367112
$511$	14010.5	1.21289
$512$	512.000	0.0441942
$513$	0	0
$514$	−5021.81	−0.430939
$515$	−531.537	−0.0454803
$516$	−439.588	−0.0375034
$517$	−243.931	−0.0207506
$518$	3695.01	0.313416
$519$	−38.5567	−0.00326098
$520$	−4765.11	−0.401854
$521$	−4774.48	−0.401486	−0.200743	−	0.979644i	$-0.564336\pi$
$521$	−4774.48	−0.401486	−0.200743	+	0.979644i	$0.564336\pi$
$522$	11931.9	1.00047
$523$	−11290.0	−0.943930	−0.471965	−	0.881617i	$-0.656455\pi$
$523$	−11290.0	−0.943930	−0.471965	+	0.881617i	$0.656455\pi$
$524$	−9116.05	−0.759994
$525$	13.9450	0.00115926
$526$	9394.14	0.778714
$527$	376.831	0.0311480
$528$	52.5549	0.00433174
$529$	2804.14	0.230471
$530$	978.154	0.0801666
$531$	−17196.2	−1.40537
$532$	0	0
$533$	−17141.0	−1.39298
$534$	426.654	0.0345751
$535$	9625.53	0.777847
$536$	−6719.62	−0.541499
$537$	133.226	0.0107060
$538$	−4528.89	−0.362927
$539$	6.92780	0.000553621 0
$540$	−559.716	−0.0446043
$541$	−17353.6	−1.37910	−0.689548	−	0.724240i	$-0.742191\pi$
$541$	−17353.6	−1.37910	−0.689548	+	0.724240i	$0.742191\pi$
$542$	−4650.52	−0.368555
$543$	275.085	0.0217404
$544$	260.805	0.0205550
$545$	−6226.93	−0.489417
$546$	470.207	0.0368553
$547$	2241.01	0.175171	0.0875857	−	0.996157i	$-0.472085\pi$
$547$	2241.01	0.175171	0.0875857	+	0.996157i	$0.472085\pi$
$548$	−6399.41	−0.498849
$549$	−22206.0	−1.72628
$550$	−89.4761	−0.00693686
$551$	0	0
$552$	−230.067	−0.0177397
$553$	−6292.54	−0.483880
$554$	−12510.4	−0.959413
$555$	−258.573	−0.0197763
$556$	6879.02	0.524704
$557$	1349.86	0.102684	0.0513422	−	0.998681i	$-0.483650\pi$
$557$	1349.86	0.102684	0.0513422	+	0.998681i	$0.483650\pi$
$558$	−2491.64	−0.189031
$559$	25235.4	1.90938
$560$	−3272.67	−0.246956
$561$	26.7707	0.00201472
$562$	−14241.1	−1.06890
$563$	17822.4	1.33414	0.667072	−	0.744994i	$-0.267548\pi$
$563$	17822.4	1.33414	0.667072	+	0.744994i	$0.267548\pi$
$564$	−16.4100	−0.00122515
$565$	−25751.9	−1.91750
$566$	13365.3	0.992553
$567$	−13428.1	−0.994584
$568$	−4624.26	−0.341602
$569$	−8579.20	−0.632090	−0.316045	−	0.948744i	$-0.602355\pi$
$569$	−8579.20	−0.632090	−0.316045	+	0.948744i	$0.602355\pi$
$570$	0	0
$571$	−19827.3	−1.45314	−0.726572	−	0.687090i	$-0.758888\pi$
$571$	−19827.3	−1.45314	−0.726572	+	0.687090i	$0.758888\pi$
$572$	−3017.02	−0.220538
$573$	304.933	0.0222317
$574$	−11772.4	−0.856047
$575$	391.695	0.0284084
$576$	−1724.46	−0.124744
$577$	−11311.3	−0.816112	−0.408056	−	0.912957i	$-0.633793\pi$
$577$	−11311.3	−0.816112	−0.408056	+	0.912957i	$0.633793\pi$
$578$	−9693.15	−0.697547
$579$	−464.873	−0.0333670
$580$	−9774.33	−0.699753
$581$	14189.5	1.01322
$582$	791.008	0.0563374
$583$	619.316	0.0439956
$584$	−6047.59	−0.428512
$585$	16049.3	1.13429
$586$	−5180.08	−0.365166
$587$	−3024.02	−0.212631	−0.106316	−	0.994332i	$-0.533905\pi$
$587$	−3024.02	−0.212631	−0.106316	+	0.994332i	$0.533905\pi$
$588$	0.466054	3.26867e−5 0
$589$	0	0
$590$	14086.7	0.982950
$591$	548.888	0.0382035
$592$	−1594.94	−0.110729
$593$	13149.8	0.910618	0.455309	−	0.890334i	$-0.349529\pi$
$593$	13149.8	0.910618	0.455309	+	0.890334i	$0.349529\pi$
$594$	−354.383	−0.0244790
$595$	−1667.05	−0.114861
$596$	−9519.57	−0.654256
$597$	612.215	0.0419704
$598$	13207.5	0.903165
$599$	−21866.4	−1.49155	−0.745774	−	0.666199i	$-0.767920\pi$
$599$	−21866.4	−1.49155	−0.745774	+	0.666199i	$0.767920\pi$
$600$	−6.01933	−0.000409564 0
$601$	−9872.32	−0.670051	−0.335025	−	0.942209i	$-0.608745\pi$
$601$	−9872.32	−0.670051	−0.335025	+	0.942209i	$0.608745\pi$
$602$	17331.6	1.17339
$603$	22632.3	1.52846
$604$	8572.25	0.577483
$605$	−12533.8	−0.842268
$606$	−568.124	−0.0380832
$607$	−2036.42	−0.136171	−0.0680854	−	0.997679i	$-0.521689\pi$
$607$	−2036.42	−0.136171	−0.0680854	+	0.997679i	$0.521689\pi$
$608$	0	0
$609$	964.502	0.0641767
$610$	18190.6	1.20740
$611$	942.046	0.0623750
$612$	−878.416	−0.0580194
$613$	10842.2	0.714377	0.357189	−	0.934032i	$-0.383735\pi$
$613$	10842.2	0.714377	0.357189	+	0.934032i	$0.383735\pi$
$614$	15355.4	1.00927
$615$	823.821	0.0540157
$616$	−2072.08	−0.135530
$617$	−10185.7	−0.664604	−0.332302	−	0.943173i	$-0.607825\pi$
$617$	−10185.7	−0.664604	−0.332302	+	0.943173i	$0.607825\pi$
$618$	−22.6402	−0.00147366
$619$	−5504.62	−0.357430	−0.178715	−	0.983901i	$-0.557194\pi$
$619$	−5504.62	−0.357430	−0.178715	+	0.983901i	$0.557194\pi$
$620$	2041.09	0.132213
$621$	1551.36	0.100248
$622$	−10995.2	−0.708791
$623$	−16821.7	−1.08178
$624$	−202.964	−0.0130209
$625$	−15214.6	−0.973734
$626$	−7293.90	−0.465691
$627$	0	0
$628$	3315.30	0.210661
$629$	−812.440	−0.0515010
$630$	11022.7	0.697069
$631$	19111.4	1.20573	0.602863	−	0.797845i	$-0.294027\pi$
$631$	19111.4	1.20573	0.602863	+	0.797845i	$0.294027\pi$
$632$	2716.16	0.170954
$633$	1183.40	0.0743065
$634$	6866.23	0.430115
$635$	20896.4	1.30590
$636$	41.6632	0.00259757
$637$	−26.7548	−0.00166415
$638$	−6188.59	−0.384026
$639$	15575.0	0.964219
$640$	1412.64	0.0872492
$641$	−25547.0	−1.57418	−0.787089	−	0.616840i	$-0.788413\pi$
$641$	−25547.0	−1.57418	−0.787089	+	0.616840i	$0.788413\pi$
$642$	409.987	0.0252039
$643$	−9972.46	−0.611626	−0.305813	−	0.952092i	$-0.598928\pi$
$643$	−9972.46	−0.611626	−0.305813	+	0.952092i	$0.598928\pi$
$644$	9070.85	0.555034
$645$	−1212.85	−0.0740401
$646$	0	0
$647$	−18928.1	−1.15014	−0.575069	−	0.818105i	$-0.695025\pi$
$647$	−18928.1	−1.15014	−0.575069	+	0.818105i	$0.695025\pi$
$648$	5796.23	0.351385
$649$	8918.96	0.539445
$650$	345.551	0.0208518
$651$	−201.409	−0.0121257
$652$	−9181.19	−0.551477
$653$	−14154.2	−0.848235	−0.424118	−	0.905607i	$-0.639416\pi$
$653$	−14154.2	−0.848235	−0.424118	+	0.905607i	$0.639416\pi$
$654$	−265.228	−0.0158582
$655$	−25151.8	−1.50040
$656$	5081.53	0.302440
$657$	20368.8	1.20953
$658$	646.996	0.0383321
$659$	−32334.5	−1.91134	−0.955671	−	0.294438i	$-0.904868\pi$
$659$	−32334.5	−1.91134	−0.955671	+	0.294438i	$0.904868\pi$
$660$	145.002	0.00855182
$661$	18517.5	1.08963	0.544815	−	0.838556i	$-0.316600\pi$
$661$	18517.5	1.08963	0.544815	+	0.838556i	$0.316600\pi$
$662$	4772.60	0.280200
$663$	−103.387	−0.00605612
$664$	−6124.88	−0.357969
$665$	0	0
$666$	5371.92	0.312549
$667$	27091.5	1.57269
$668$	2629.46	0.152301
$669$	880.475	0.0508836
$670$	−18539.8	−1.06904
$671$	11517.3	0.662626
$672$	−139.395	−0.00800191
$673$	−33025.9	−1.89161	−0.945806	−	0.324731i	$-0.894726\pi$
$673$	−33025.9	−1.89161	−0.945806	+	0.324731i	$0.894726\pi$
$674$	3418.46	0.195362
$675$	40.5889	0.00231447
$676$	2863.53	0.162923
$677$	−10930.8	−0.620541	−0.310271	−	0.950648i	$-0.600420\pi$
$677$	−10930.8	−0.620541	−0.310271	+	0.950648i	$0.600420\pi$
$678$	−1096.87	−0.0621312
$679$	−31187.1	−1.76267
$680$	719.577	0.0405802
$681$	381.176	0.0214489
$682$	1292.31	0.0725587
$683$	16689.0	0.934972	0.467486	−	0.884000i	$-0.345160\pi$
$683$	16689.0	0.934972	0.467486	+	0.884000i	$0.345160\pi$
$684$	0	0
$685$	−17656.4	−0.984840
$686$	12695.7	0.706595
$687$	934.438	0.0518938
$688$	−7481.15	−0.414558
$689$	−2391.76	−0.132248
$690$	−634.769	−0.0350221
$691$	23185.5	1.27644	0.638219	−	0.769855i	$-0.279672\pi$
$691$	23185.5	1.27644	0.638219	+	0.769855i	$0.279672\pi$
$692$	−656.179	−0.0360465
$693$	6978.97	0.382553
$694$	−6066.25	−0.331804
$695$	18979.6	1.03588
$696$	−416.325	−0.0226735
$697$	2588.45	0.140667
$698$	4123.60	0.223611
$699$	−322.675	−0.0174602
$700$	237.324	0.0128143
$701$	−814.191	−0.0438681	−0.0219341	−	0.999759i	$-0.506982\pi$
$701$	−814.191	−0.0438681	−0.0219341	+	0.999759i	$0.506982\pi$
$702$	1368.60	0.0735821
$703$	0	0
$704$	894.409	0.0478825
$705$	−45.2761	−0.00241872
$706$	14698.3	0.783538
$707$	22399.4	1.19154
$708$	600.006	0.0318497
$709$	17484.6	0.926159	0.463079	−	0.886317i	$-0.346744\pi$
$709$	17484.6	0.926159	0.463079	+	0.886317i	$0.346744\pi$
$710$	−12758.6	−0.674398
$711$	−9148.28	−0.482542
$712$	7261.04	0.382189
$713$	−5657.28	−0.297148
$714$	−71.0058	−0.00372174
$715$	−8324.13	−0.435392
$716$	2267.31	0.118343
$717$	1172.78	0.0610856
$718$	1311.19	0.0681518
$719$	−25041.1	−1.29885	−0.649427	−	0.760424i	$-0.724991\pi$
$719$	−25041.1	−1.29885	−0.649427	+	0.760424i	$0.724991\pi$
$720$	−4757.90	−0.246273
$721$	892.633	0.0461074
$722$	0	0
$723$	−324.707	−0.0167026
$724$	4681.55	0.240315
$725$	708.804	0.0363094
$726$	−533.862	−0.0272913
$727$	−28950.1	−1.47689	−0.738446	−	0.674312i	$-0.764440\pi$
$727$	−28950.1	−1.47689	−0.738446	+	0.674312i	$0.764440\pi$
$728$	8002.25	0.407394
$729$	−19441.8	−0.987745
$730$	−16685.7	−0.845978
$731$	−3810.78	−0.192814
$732$	774.806	0.0391225
$733$	−31562.2	−1.59042	−0.795208	−	0.606337i	$-0.792638\pi$
$733$	−31562.2	−1.59042	−0.795208	+	0.606337i	$0.792638\pi$
$734$	−24602.5	−1.23719
$735$	1.28587	6.45308e−5 0
$736$	−3915.41	−0.196092
$737$	−11738.5	−0.586691
$738$	−17115.1	−0.853678
$739$	15556.5	0.774365	0.387182	−	0.922003i	$-0.373448\pi$
$739$	15556.5	0.774365	0.387182	+	0.922003i	$0.373448\pi$
$740$	−4400.55	−0.218605
$741$	0	0
$742$	−1642.66	−0.0812720
$743$	−2685.69	−0.132609	−0.0663045	−	0.997799i	$-0.521121\pi$
$743$	−2685.69	−0.132609	−0.0663045	+	0.997799i	$0.521121\pi$
$744$	86.9375	0.00428398
$745$	−26265.1	−1.29165
$746$	2045.08	0.100370
$747$	20629.2	1.01042
$748$	455.598	0.0222705
$749$	−16164.6	−0.788572
$750$	−665.091	−0.0323809
$751$	−31963.6	−1.55309	−0.776543	−	0.630064i	$-0.783029\pi$
$751$	−31963.6	−1.55309	−0.776543	+	0.630064i	$0.783029\pi$
$752$	−279.274	−0.0135427
$753$	82.2933	0.00398265
$754$	23899.9	1.15436
$755$	23651.4	1.14008
$756$	939.955	0.0452193
$757$	3268.69	0.156938	0.0784692	−	0.996917i	$-0.474997\pi$
$757$	3268.69	0.156938	0.0784692	+	0.996917i	$0.474997\pi$
$758$	2435.71	0.116714
$759$	−401.902	−0.0192202
$760$	0	0
$761$	21394.1	1.01910	0.509549	−	0.860441i	$-0.329812\pi$
$761$	21394.1	1.01910	0.509549	+	0.860441i	$0.329812\pi$
$762$	890.056	0.0423141
$763$	10457.1	0.496165
$764$	5189.52	0.245747
$765$	−2423.60	−0.114543
$766$	−20548.2	−0.969237
$767$	−34444.5	−1.62154
$768$	60.1696	0.00282706
$769$	10203.2	0.478460	0.239230	−	0.970963i	$-0.423105\pi$
$769$	10203.2	0.478460	0.239230	+	0.970963i	$0.423105\pi$
$770$	−5717.00	−0.267567
$771$	−590.157	−0.0275668
$772$	−7911.47	−0.368834
$773$	−12692.3	−0.590568	−0.295284	−	0.955409i	$-0.595414\pi$
$773$	−12692.3	−0.590568	−0.295284	+	0.955409i	$0.595414\pi$
$774$	25197.2	1.17015
$775$	−148.013	−0.00686039
$776$	13461.8	0.622747
$777$	434.233	0.0200489
$778$	29398.1	1.35472
$779$	0	0
$780$	−559.990	−0.0257062
$781$	−8078.09	−0.370111
$782$	−1994.45	−0.0912039
$783$	2807.32	0.128129
$784$	7.93157	0.000361314 0
$785$	9147.12	0.415891
$786$	−1071.31	−0.0486161
$787$	2512.53	0.113802	0.0569009	−	0.998380i	$-0.481878\pi$
$787$	2512.53	0.113802	0.0569009	+	0.998380i	$0.481878\pi$
$788$	9341.29	0.422297
$789$	1103.99	0.0498137
$790$	7494.05	0.337502
$791$	43246.2	1.94394
$792$	−3012.45	−0.135155
$793$	−44479.3	−1.99181
$794$	−4637.07	−0.207259
$795$	114.951	0.00512819
$796$	10419.0	0.463935
$797$	−39544.5	−1.75751	−0.878756	−	0.477272i	$-0.841626\pi$
$797$	−39544.5	−1.75751	−0.878756	+	0.477272i	$0.841626\pi$
$798$	0	0
$799$	−142.258	−0.00629878
$800$	−102.440	−0.00452727
$801$	−24455.9	−1.07878
$802$	7854.41	0.345821
$803$	−10564.5	−0.464275
$804$	−789.681	−0.0346392
$805$	25027.0	1.09576
$806$	−4990.82	−0.218107
$807$	−532.230	−0.0232161
$808$	−9668.65	−0.420968
$809$	−18670.3	−0.811386	−0.405693	−	0.914009i	$-0.632970\pi$
$809$	−18670.3	−0.811386	−0.405693	+	0.914009i	$0.632970\pi$
$810$	15992.1	0.693712
$811$	−4036.14	−0.174757	−0.0873786	−	0.996175i	$-0.527849\pi$
$811$	−4036.14	−0.174757	−0.0873786	+	0.996175i	$0.527849\pi$
$812$	16414.4	0.709401
$813$	−546.523	−0.0235761
$814$	−2786.19	−0.119971
$815$	−25331.5	−1.08874
$816$	30.6495	0.00131488
$817$	0	0
$818$	−5247.66	−0.224303
$819$	−26952.3	−1.14993
$820$	14020.3	0.597084
$821$	−8513.54	−0.361906	−0.180953	−	0.983492i	$-0.557918\pi$
$821$	−8513.54	−0.361906	−0.180953	+	0.983492i	$0.557918\pi$
$822$	−752.051	−0.0319109
$823$	−21256.9	−0.900327	−0.450164	−	0.892946i	$-0.648634\pi$
$823$	−21256.9	−0.900327	−0.450164	+	0.892946i	$0.648634\pi$
$824$	−385.303	−0.0162896
$825$	−10.5151	−0.000443745 0
$826$	−23656.4	−0.996503
$827$	28780.9	1.21017	0.605085	−	0.796161i	$-0.293139\pi$
$827$	28780.9	1.21017	0.605085	+	0.796161i	$0.293139\pi$
$828$	13187.5	0.553498
$829$	−14723.5	−0.616851	−0.308426	−	0.951248i	$-0.599802\pi$
$829$	−14723.5	−0.616851	−0.308426	+	0.951248i	$0.599802\pi$
$830$	−16898.9	−0.706711
$831$	−1470.20	−0.0613728
$832$	−3454.15	−0.143932
$833$	4.04022	0.000168050 0
$834$	808.413	0.0335648
$835$	7254.84	0.300676
$836$	0	0
$837$	−586.228	−0.0242091
$838$	8648.27	0.356503
$839$	12864.2	0.529346	0.264673	−	0.964338i	$-0.414736\pi$
$839$	12864.2	0.529346	0.264673	+	0.964338i	$0.414736\pi$
$840$	−384.600	−0.0157976
$841$	24635.2	1.01010
$842$	−24844.3	−1.01686
$843$	−1673.59	−0.0683768
$844$	20139.8	0.821375
$845$	7900.67	0.321647
$846$	940.622	0.0382260
$847$	21048.6	0.853881
$848$	709.048	0.0287132
$849$	1570.67	0.0634927
$850$	−52.1815	−0.00210566
$851$	12197.0	0.491313
$852$	−543.438	−0.0218520
$853$	6299.42	0.252858	0.126429	−	0.991976i	$-0.459648\pi$
$853$	6299.42	0.252858	0.126429	+	0.991976i	$0.459648\pi$
$854$	−30548.3	−1.22405
$855$	0	0
$856$	6977.40	0.278601
$857$	−6082.98	−0.242463	−0.121231	−	0.992624i	$-0.538684\pi$
$857$	−6082.98	−0.242463	−0.121231	+	0.992624i	$0.538684\pi$
$858$	−354.556	−0.0141076
$859$	−2063.60	−0.0819662	−0.0409831	−	0.999160i	$-0.513049\pi$
$859$	−2063.60	−0.0819662	−0.0409831	+	0.999160i	$0.513049\pi$
$860$	−20641.0	−0.818431
$861$	−1383.48	−0.0547605
$862$	−16710.9	−0.660295
$863$	21020.5	0.829139	0.414570	−	0.910018i	$-0.363932\pi$
$863$	21020.5	0.829139	0.414570	+	0.910018i	$0.363932\pi$
$864$	−405.729	−0.0159759
$865$	−1810.44	−0.0711639
$866$	9242.65	0.362677
$867$	−1139.13	−0.0446214
$868$	−3427.68	−0.134036
$869$	4744.84	0.185222
$870$	−1148.67	−0.0447626
$871$	45333.2	1.76356
$872$	−4513.80	−0.175294
$873$	−45340.7	−1.75779
$874$	0	0
$875$	26222.5	1.01312
$876$	−710.705	−0.0274115
$877$	−13803.5	−0.531482	−0.265741	−	0.964044i	$-0.585617\pi$
$877$	−13803.5	−0.531482	−0.265741	+	0.964044i	$0.585617\pi$
$878$	−18464.7	−0.709743
$879$	−608.756	−0.0233593
$880$	2467.73	0.0945308
$881$	12232.6	0.467793	0.233897	−	0.972261i	$-0.424852\pi$
$881$	12232.6	0.467793	0.233897	+	0.972261i	$0.424852\pi$
$882$	−26.7143	−0.00101986
$883$	−45344.6	−1.72816	−0.864081	−	0.503353i	$-0.832099\pi$
$883$	−45344.6	−1.72816	−0.864081	+	0.503353i	$0.832099\pi$
$884$	−1759.49	−0.0669436
$885$	1655.45	0.0628784
$886$	11617.4	0.440513
$887$	14316.4	0.541938	0.270969	−	0.962588i	$-0.412656\pi$
$887$	14316.4	0.541938	0.270969	+	0.962588i	$0.412656\pi$
$888$	−187.436	−0.00708326
$889$	−35092.2	−1.32391
$890$	20033.6	0.754527
$891$	10125.4	0.380711
$892$	14984.4	0.562462
$893$	0	0
$894$	−1118.73	−0.0418522
$895$	6255.66	0.233635
$896$	−2372.31	−0.0884522
$897$	1552.12	0.0577747
$898$	15640.2	0.581204
$899$	−10237.3	−0.379792
$900$	345.029	0.0127788
$901$	361.178	0.0133547
$902$	8876.89	0.327681
$903$	2036.79	0.0750610
$904$	−18667.1	−0.686791
$905$	12916.7	0.474436
$906$	1007.40	0.0369411
$907$	40533.2	1.48388	0.741942	−	0.670464i	$-0.233905\pi$
$907$	40533.2	1.48388	0.741942	+	0.670464i	$0.233905\pi$
$908$	6487.07	0.237093
$909$	32564.9	1.18824
$910$	22078.7	0.804288
$911$	43801.4	1.59298	0.796491	−	0.604651i	$-0.206687\pi$
$911$	43801.4	1.59298	0.796491	+	0.604651i	$0.206687\pi$
$912$	0	0
$913$	−10699.5	−0.387844
$914$	−18281.8	−0.661608
$915$	2137.74	0.0772365
$916$	15902.8	0.573628
$917$	42238.4	1.52109
$918$	−206.672	−0.00743050
$919$	3410.41	0.122415	0.0612074	−	0.998125i	$-0.480505\pi$
$919$	3410.41	0.122415	0.0612074	+	0.998125i	$0.480505\pi$
$920$	−10802.9	−0.387130
$921$	1804.55	0.0645624
$922$	25566.0	0.913201
$923$	31197.1	1.11253
$924$	−243.508	−0.00866974
$925$	319.114	0.0113432
$926$	−1758.92	−0.0624210
$927$	1297.74	0.0459798
$928$	−7085.25	−0.250630
$929$	−15345.4	−0.541945	−0.270973	−	0.962587i	$-0.587345\pi$
$929$	−15345.4	−0.541945	−0.270973	+	0.962587i	$0.587345\pi$
$930$	239.866	0.00845754
$931$	0	0
$932$	−5491.47	−0.193003
$933$	−1292.14	−0.0453407
$934$	−16048.3	−0.562223
$935$	1257.02	0.0439669
$936$	11633.9	0.406267
$937$	−3977.96	−0.138692	−0.0693459	−	0.997593i	$-0.522091\pi$
$937$	−3977.96	−0.138692	−0.0693459	+	0.997593i	$0.522091\pi$
$938$	31134.8	1.08378
$939$	−857.170	−0.0297899
$940$	−770.534	−0.0267362
$941$	−1352.83	−0.0468661	−0.0234331	−	0.999725i	$-0.507460\pi$
$941$	−1352.83	−0.0468661	−0.0234331	+	0.999725i	$0.507460\pi$
$942$	389.610	0.0134758
$943$	−38859.9	−1.34194
$944$	10211.2	0.352063
$945$	2593.39	0.0892731
$946$	−13068.8	−0.449157
$947$	1375.08	0.0471849	0.0235924	−	0.999722i	$-0.492490\pi$
$947$	1375.08	0.0471849	0.0235924	+	0.999722i	$0.492490\pi$
$948$	319.199	0.0109358
$949$	40799.4	1.39558
$950$	0	0
$951$	806.911	0.0275141
$952$	−1208.42	−0.0411397
$953$	−45806.0	−1.55698	−0.778489	−	0.627658i	$-0.784014\pi$
$953$	−45806.0	−1.55698	−0.778489	+	0.627658i	$0.784014\pi$
$954$	−2388.14	−0.0810471
$955$	14318.2	0.485159
$956$	19959.1	0.675233
$957$	−727.275	−0.0245658
$958$	34476.2	1.16271
$959$	29651.1	0.998419
$960$	166.012	0.00558125
$961$	−27653.2	−0.928241
$962$	10760.1	0.360624
$963$	−23500.5	−0.786390
$964$	−5526.05	−0.184629
$965$	−21828.2	−0.728162
$966$	1066.00	0.0355050
$967$	24530.1	0.815753	0.407877	−	0.913037i	$-0.366269\pi$
$967$	24530.1	0.815753	0.407877	+	0.913037i	$0.366269\pi$
$968$	−9085.56	−0.301675
$969$	0	0
$970$	37142.0	1.22944
$971$	−18442.7	−0.609531	−0.304765	−	0.952427i	$-0.598578\pi$
$971$	−18442.7	−0.609531	−0.304765	+	0.952427i	$0.598578\pi$
$972$	2050.50	0.0676645
$973$	−31873.3	−1.05017
$974$	−4463.46	−0.146836
$975$	40.6088	0.00133387
$976$	13186.1	0.432455
$977$	−15608.6	−0.511121	−0.255560	−	0.966793i	$-0.582260\pi$
$977$	−15608.6	−0.511121	−0.255560	+	0.966793i	$0.582260\pi$
$978$	−1078.96	−0.0352775
$979$	12684.2	0.414086
$980$	21.8837	0.000713316 0
$981$	15202.9	0.494792
$982$	−20227.1	−0.657303
$983$	46499.9	1.50877	0.754383	−	0.656435i	$-0.227936\pi$
$983$	46499.9	1.50877	0.754383	+	0.656435i	$0.227936\pi$
$984$	597.175	0.0193468
$985$	25773.2	0.833708
$986$	−3609.12	−0.116570
$987$	76.0341	0.00245207
$988$	0	0
$989$	57210.5	1.83942
$990$	−8311.55	−0.266827
$991$	3540.28	0.113482	0.0567410	−	0.998389i	$-0.481929\pi$
$991$	3540.28	0.113482	0.0567410	+	0.998389i	$0.481929\pi$
$992$	1479.55	0.0473547
$993$	560.869	0.0179241
$994$	21426.1	0.683697
$995$	28746.7	0.915912
$996$	−719.788	−0.0228989
$997$	11418.7	0.362723	0.181362	−	0.983416i	$-0.441950\pi$
$997$	11418.7	0.362723	0.181362	+	0.983416i	$0.441950\pi$
$998$	3351.40	0.106299
$999$	1263.90	0.0400280

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.4.a.p.1.4		6
19.9	even	9		38.4.e.a.5.2	✓	12
19.17	even	9		38.4.e.a.23.2	yes	12
19.18	odd	2		722.4.a.o.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.e.a.5.2	✓	12	19.9	even	9
38.4.e.a.23.2	yes	12	19.17	even	9
722.4.a.o.1.3		6	19.18	odd	2
722.4.a.p.1.4		6	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	722.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +0.235037 q^{3} +4.00000 q^{4} +11.0362 q^{5} +0.470075 q^{6} -18.5336 q^{7} +8.00000 q^{8} -26.9448 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +0.235037 q^{3} +4.00000 q^{4} +11.0362 q^{5} +0.470075 q^{6} -18.5336 q^{7} +8.00000 q^{8} -26.9448 q^{9} +22.0725 q^{10} +13.9751 q^{11} +0.940150 q^{12} -53.9711 q^{13} -37.0673 q^{14} +2.59393 q^{15} +16.0000 q^{16} +8.15016 q^{17} -53.8895 q^{18} +44.1450 q^{20} -4.35610 q^{21} +27.9503 q^{22} -122.357 q^{23} +1.88030 q^{24} -3.20126 q^{25} -107.942 q^{26} -12.6790 q^{27} -74.1346 q^{28} -221.414 q^{29} +5.18786 q^{30} +46.2360 q^{31} +32.0000 q^{32} +3.28468 q^{33} +16.3003 q^{34} -204.542 q^{35} -107.779 q^{36} -99.6840 q^{37} -12.6852 q^{39} +88.2900 q^{40} +317.596 q^{41} -8.71220 q^{42} -467.572 q^{43} +55.9006 q^{44} -297.369 q^{45} -244.713 q^{46} -17.4546 q^{47} +3.76060 q^{48} +0.495723 q^{49} -6.40252 q^{50} +1.91559 q^{51} -215.885 q^{52} +44.3155 q^{53} -25.3581 q^{54} +154.233 q^{55} -148.269 q^{56} -442.828 q^{58} +638.202 q^{59} +10.3757 q^{60} +824.130 q^{61} +92.4720 q^{62} +499.384 q^{63} +64.0000 q^{64} -595.639 q^{65} +6.56936 q^{66} -839.953 q^{67} +32.6006 q^{68} -28.7584 q^{69} -409.084 q^{70} -578.033 q^{71} -215.558 q^{72} -755.948 q^{73} -199.368 q^{74} -0.752416 q^{75} -259.010 q^{77} -25.3705 q^{78} +339.520 q^{79} +176.580 q^{80} +724.528 q^{81} +635.191 q^{82} -765.610 q^{83} -17.4244 q^{84} +89.9471 q^{85} -935.144 q^{86} -52.0406 q^{87} +111.801 q^{88} +907.629 q^{89} -594.738 q^{90} +1000.28 q^{91} -489.426 q^{92} +10.8672 q^{93} -34.9093 q^{94} +7.52120 q^{96} +1682.73 q^{97} +0.991447 q^{98} -376.557 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12 q^{2} - 9 q^{3} + 24 q^{4} - 27 q^{5} - 18 q^{6} - 21 q^{7} + 48 q^{8} + 33 q^{9}+O(q^{10}) \) 6 * q + 12 * q^2 - 9 * q^3 + 24 * q^4 - 27 * q^5 - 18 * q^6 - 21 * q^7 + 48 * q^8 + 33 * q^9	\( 6 q + 12 q^{2} - 9 q^{3} + 24 q^{4} - 27 q^{5} - 18 q^{6} - 21 q^{7} + 48 q^{8} + 33 q^{9} - 54 q^{10} + 9 q^{11} - 36 q^{12} - 24 q^{13} - 42 q^{14} + 96 q^{16} - 102 q^{17} + 66 q^{18} - 108 q^{20} - 51 q^{21} + 18 q^{22} - 264 q^{23} - 72 q^{24} + 177 q^{25} - 48 q^{26} - 189 q^{27} - 84 q^{28} - 483 q^{29} - 72 q^{31} + 192 q^{32} - 387 q^{33} - 204 q^{34} + 135 q^{35} + 132 q^{36} + 558 q^{37} - 624 q^{39} - 216 q^{40} - 396 q^{41} - 102 q^{42} - 2064 q^{43} + 36 q^{44} - 1296 q^{45} - 528 q^{46} + 858 q^{47} - 144 q^{48} - 1413 q^{49} + 354 q^{50} + 1272 q^{51} - 96 q^{52} - 762 q^{53} - 378 q^{54} - 1107 q^{55} - 168 q^{56} - 966 q^{58} - 393 q^{59} - 627 q^{61} - 144 q^{62} - 84 q^{63} + 384 q^{64} - 495 q^{65} - 774 q^{66} - 2028 q^{67} - 408 q^{68} + 237 q^{69} + 270 q^{70} - 1284 q^{71} + 264 q^{72} - 2688 q^{73} + 1116 q^{74} - 927 q^{75} - 708 q^{77} - 1248 q^{78} - 969 q^{79} - 432 q^{80} - 1398 q^{81} - 792 q^{82} - 927 q^{83} - 204 q^{84} + 396 q^{85} - 4128 q^{86} - 2892 q^{87} + 72 q^{88} + 1257 q^{89} - 2592 q^{90} + 1323 q^{91} - 1056 q^{92} - 1368 q^{93} + 1716 q^{94} - 288 q^{96} + 2403 q^{97} - 2826 q^{98} + 567 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 - 9 * q^3 + 24 * q^4 - 27 * q^5 - 18 * q^6 - 21 * q^7 + 48 * q^8 + 33 * q^9 - 54 * q^10 + 9 * q^11 - 36 * q^12 - 24 * q^13 - 42 * q^14 + 96 * q^16 - 102 * q^17 + 66 * q^18 - 108 * q^20 - 51 * q^21 + 18 * q^22 - 264 * q^23 - 72 * q^24 + 177 * q^25 - 48 * q^26 - 189 * q^27 - 84 * q^28 - 483 * q^29 - 72 * q^31 + 192 * q^32 - 387 * q^33 - 204 * q^34 + 135 * q^35 + 132 * q^36 + 558 * q^37 - 624 * q^39 - 216 * q^40 - 396 * q^41 - 102 * q^42 - 2064 * q^43 + 36 * q^44 - 1296 * q^45 - 528 * q^46 + 858 * q^47 - 144 * q^48 - 1413 * q^49 + 354 * q^50 + 1272 * q^51 - 96 * q^52 - 762 * q^53 - 378 * q^54 - 1107 * q^55 - 168 * q^56 - 966 * q^58 - 393 * q^59 - 627 * q^61 - 144 * q^62 - 84 * q^63 + 384 * q^64 - 495 * q^65 - 774 * q^66 - 2028 * q^67 - 408 * q^68 + 237 * q^69 + 270 * q^70 - 1284 * q^71 + 264 * q^72 - 2688 * q^73 + 1116 * q^74 - 927 * q^75 - 708 * q^77 - 1248 * q^78 - 969 * q^79 - 432 * q^80 - 1398 * q^81 - 792 * q^82 - 927 * q^83 - 204 * q^84 + 396 * q^85 - 4128 * q^86 - 2892 * q^87 + 72 * q^88 + 1257 * q^89 - 2592 * q^90 + 1323 * q^91 - 1056 * q^92 - 1368 * q^93 + 1716 * q^94 - 288 * q^96 + 2403 * q^97 - 2826 * q^98 + 567 * q^99

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