LMFDB - Embedded newform 294.6.a.t.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,6,Mod(1,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("294.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	294.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:	$47.1528430250$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	294.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +61.0711 q^{5} -36.0000 q^{6} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +61.0711 q^{5} -36.0000 q^{6} +64.0000 q^{8} +81.0000 q^{9} +244.284 q^{10} -36.5442 q^{11} -144.000 q^{12} -34.5656 q^{13} -549.640 q^{15} +256.000 q^{16} +2061.04 q^{17} +324.000 q^{18} -452.238 q^{19} +977.137 q^{20} -146.177 q^{22} +1684.25 q^{23} -576.000 q^{24} +604.675 q^{25} -138.262 q^{26} -729.000 q^{27} -4765.22 q^{29} -2198.56 q^{30} +5260.87 q^{31} +1024.00 q^{32} +328.897 q^{33} +8244.16 q^{34} +1296.00 q^{36} -12822.0 q^{37} -1808.95 q^{38} +311.090 q^{39} +3908.55 q^{40} +7126.74 q^{41} +11141.7 q^{43} -584.706 q^{44} +4946.76 q^{45} +6736.99 q^{46} +23443.2 q^{47} -2304.00 q^{48} +2418.70 q^{50} -18549.4 q^{51} -553.049 q^{52} -7030.30 q^{53} -2916.00 q^{54} -2231.79 q^{55} +4070.14 q^{57} -19060.9 q^{58} +44222.8 q^{59} -8794.23 q^{60} -19380.5 q^{61} +21043.5 q^{62} +4096.00 q^{64} -2110.96 q^{65} +1315.59 q^{66} +20944.1 q^{67} +32976.6 q^{68} -15158.2 q^{69} +79843.4 q^{71} +5184.00 q^{72} +37065.8 q^{73} -51287.8 q^{74} -5442.08 q^{75} -7235.81 q^{76} +1244.36 q^{78} +42072.0 q^{79} +15634.2 q^{80} +6561.00 q^{81} +28506.9 q^{82} +6311.34 q^{83} +125870. q^{85} +44566.8 q^{86} +42887.0 q^{87} -2338.83 q^{88} +51495.8 q^{89} +19787.0 q^{90} +26948.0 q^{92} -47347.8 q^{93} +93772.8 q^{94} -27618.7 q^{95} -9216.00 q^{96} +127357. q^{97} -2960.08 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8 q^{2} - 18 q^{3} + 32 q^{4} + 108 q^{5} - 72 q^{6} + 128 q^{8} + 162 q^{9}+O(q^{10}) $ 2 * q + 8 * q^2 - 18 * q^3 + 32 * q^4 + 108 * q^5 - 72 * q^6 + 128 * q^8 + 162 * q^9	\( 2 q + 8 q^{2} - 18 q^{3} + 32 q^{4} + 108 q^{5} - 72 q^{6} + 128 q^{8} + 162 q^{9} + 432 q^{10} - 124 q^{11} - 288 q^{12} + 720 q^{13} - 972 q^{15} + 512 q^{16} + 612 q^{17} + 648 q^{18} + 2088 q^{19} + 1728 q^{20} - 496 q^{22} + 772 q^{23} - 1152 q^{24} - 318 q^{25} + 2880 q^{26} - 1458 q^{27} - 4592 q^{29} - 3888 q^{30} + 9792 q^{31} + 2048 q^{32} + 1116 q^{33} + 2448 q^{34} + 2592 q^{36} - 5992 q^{37} + 8352 q^{38} - 6480 q^{39} + 6912 q^{40} + 20196 q^{41} - 1136 q^{43} - 1984 q^{44} + 8748 q^{45} + 3088 q^{46} + 36936 q^{47} - 4608 q^{48} - 1272 q^{50} - 5508 q^{51} + 11520 q^{52} - 16708 q^{53} - 5832 q^{54} - 6336 q^{55} - 18792 q^{57} - 18368 q^{58} + 74592 q^{59} - 15552 q^{60} - 18648 q^{61} + 39168 q^{62} + 8192 q^{64} + 33300 q^{65} + 4464 q^{66} + 67344 q^{67} + 9792 q^{68} - 6948 q^{69} + 76548 q^{71} + 10368 q^{72} + 47304 q^{73} - 23968 q^{74} + 2862 q^{75} + 33408 q^{76} - 25920 q^{78} + 140656 q^{79} + 27648 q^{80} + 13122 q^{81} + 80784 q^{82} + 94104 q^{83} + 57868 q^{85} - 4544 q^{86} + 41328 q^{87} - 7936 q^{88} - 17604 q^{89} + 34992 q^{90} + 12352 q^{92} - 88128 q^{93} + 147744 q^{94} + 91592 q^{95} - 18432 q^{96} + 85176 q^{97} - 10044 q^{99}+O(q^{100}) \) 2 * q + 8 * q^2 - 18 * q^3 + 32 * q^4 + 108 * q^5 - 72 * q^6 + 128 * q^8 + 162 * q^9 + 432 * q^10 - 124 * q^11 - 288 * q^12 + 720 * q^13 - 972 * q^15 + 512 * q^16 + 612 * q^17 + 648 * q^18 + 2088 * q^19 + 1728 * q^20 - 496 * q^22 + 772 * q^23 - 1152 * q^24 - 318 * q^25 + 2880 * q^26 - 1458 * q^27 - 4592 * q^29 - 3888 * q^30 + 9792 * q^31 + 2048 * q^32 + 1116 * q^33 + 2448 * q^34 + 2592 * q^36 - 5992 * q^37 + 8352 * q^38 - 6480 * q^39 + 6912 * q^40 + 20196 * q^41 - 1136 * q^43 - 1984 * q^44 + 8748 * q^45 + 3088 * q^46 + 36936 * q^47 - 4608 * q^48 - 1272 * q^50 - 5508 * q^51 + 11520 * q^52 - 16708 * q^53 - 5832 * q^54 - 6336 * q^55 - 18792 * q^57 - 18368 * q^58 + 74592 * q^59 - 15552 * q^60 - 18648 * q^61 + 39168 * q^62 + 8192 * q^64 + 33300 * q^65 + 4464 * q^66 + 67344 * q^67 + 9792 * q^68 - 6948 * q^69 + 76548 * q^71 + 10368 * q^72 + 47304 * q^73 - 23968 * q^74 + 2862 * q^75 + 33408 * q^76 - 25920 * q^78 + 140656 * q^79 + 27648 * q^80 + 13122 * q^81 + 80784 * q^82 + 94104 * q^83 + 57868 * q^85 - 4544 * q^86 + 41328 * q^87 - 7936 * q^88 - 17604 * q^89 + 34992 * q^90 + 12352 * q^92 - 88128 * q^93 + 147744 * q^94 + 91592 * q^95 - 18432 * q^96 + 85176 * q^97 - 10044 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	16.0000	0.500000
$5$	61.0711	1.09247	0.546236	−	0.837631i	$-0.316060\pi$
$5$	61.0711	1.09247	0.546236	+	0.837631i	$0.316060\pi$
$6$	−36.0000	−0.408248
$7$	0	0
$7$	0	0
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	244.284	0.772495
$11$	−36.5442	−0.0910618	−0.0455309	−	0.998963i	$-0.514498\pi$
$11$	−36.5442	−0.0910618	−0.0455309	+	0.998963i	$0.514498\pi$
$12$	−144.000	−0.288675
$13$	−34.5656	−0.0567264	−0.0283632	−	0.999598i	$-0.509030\pi$
$13$	−34.5656	−0.0567264	−0.0283632	+	0.999598i	$0.509030\pi$
$14$	0	0
$15$	−549.640	−0.630739
$16$	256.000	0.250000
$17$	2061.04	1.72967	0.864836	−	0.502054i	$-0.167422\pi$
$17$	2061.04	1.72967	0.864836	+	0.502054i	$0.167422\pi$
$18$	324.000	0.235702
$19$	−452.238	−0.287398	−0.143699	−	0.989621i	$-0.545900\pi$
$19$	−452.238	−0.287398	−0.143699	+	0.989621i	$0.545900\pi$
$20$	977.137	0.546236
$21$	0	0
$22$	−146.177	−0.0643904
$23$	1684.25	0.663875	0.331938	−	0.943301i	$-0.392298\pi$
$23$	1684.25	0.663875	0.331938	+	0.943301i	$0.392298\pi$
$24$	−576.000	−0.204124
$25$	604.675	0.193496
$26$	−138.262	−0.0401116
$27$	−729.000	−0.192450
$28$	0	0
$29$	−4765.22	−1.05217	−0.526087	−	0.850431i	$-0.676341\pi$
$29$	−4765.22	−1.05217	−0.526087	+	0.850431i	$0.676341\pi$
$30$	−2198.56	−0.446000
$31$	5260.87	0.983225	0.491613	−	0.870814i	$-0.336408\pi$
$31$	5260.87	0.983225	0.491613	+	0.870814i	$0.336408\pi$
$32$	1024.00	0.176777
$33$	328.897	0.0525746
$34$	8244.16	1.22306
$35$	0	0
$36$	1296.00	0.166667
$37$	−12822.0	−1.53975	−0.769875	−	0.638195i	$-0.779681\pi$
$37$	−12822.0	−1.53975	−0.769875	+	0.638195i	$0.779681\pi$
$38$	−1808.95	−0.203221
$39$	311.090	0.0327510
$40$	3908.55	0.386247
$41$	7126.74	0.662111	0.331056	−	0.943611i	$-0.392595\pi$
$41$	7126.74	0.662111	0.331056	+	0.943611i	$0.392595\pi$
$42$	0	0
$43$	11141.7	0.918925	0.459462	−	0.888197i	$-0.348042\pi$
$43$	11141.7	0.918925	0.459462	+	0.888197i	$0.348042\pi$
$44$	−584.706	−0.0455309
$45$	4946.76	0.364157
$46$	6736.99	0.469431
$47$	23443.2	1.54800	0.774002	−	0.633183i	$-0.218252\pi$
$47$	23443.2	1.54800	0.774002	+	0.633183i	$0.218252\pi$
$48$	−2304.00	−0.144338
$49$	0	0
$50$	2418.70	0.136822
$51$	−18549.4	−0.998627
$52$	−553.049	−0.0283632
$53$	−7030.30	−0.343783	−0.171891	−	0.985116i	$-0.554988\pi$
$53$	−7030.30	−0.343783	−0.171891	+	0.985116i	$0.554988\pi$
$54$	−2916.00	−0.136083
$55$	−2231.79	−0.0994825
$56$	0	0
$57$	4070.14	0.165929
$58$	−19060.9	−0.744000
$59$	44222.8	1.65393	0.826964	−	0.562255i	$-0.190066\pi$
$59$	44222.8	1.65393	0.826964	+	0.562255i	$0.190066\pi$
$60$	−8794.23	−0.315370
$61$	−19380.5	−0.666868	−0.333434	−	0.942773i	$-0.608207\pi$
$61$	−19380.5	−0.666868	−0.333434	+	0.942773i	$0.608207\pi$
$62$	21043.5	0.695245
$63$	0	0
$64$	4096.00	0.125000
$65$	−2110.96	−0.0619721
$66$	1315.59	0.0371758
$67$	20944.1	0.569999	0.285000	−	0.958528i	$-0.408007\pi$
$67$	20944.1	0.569999	0.285000	+	0.958528i	$0.408007\pi$
$68$	32976.6	0.864836
$69$	−15158.2	−0.383289
$70$	0	0
$71$	79843.4	1.87972	0.939860	−	0.341560i	$-0.110955\pi$
$71$	79843.4	1.87972	0.939860	+	0.341560i	$0.110955\pi$
$72$	5184.00	0.117851
$73$	37065.8	0.814079	0.407039	−	0.913411i	$-0.366561\pi$
$73$	37065.8	0.814079	0.407039	+	0.913411i	$0.366561\pi$
$74$	−51287.8	−1.08877
$75$	−5442.08	−0.111715
$76$	−7235.81	−0.143699
$77$	0	0
$78$	1244.36	0.0231585
$79$	42072.0	0.758448	0.379224	−	0.925305i	$-0.376191\pi$
$79$	42072.0	0.758448	0.379224	+	0.925305i	$0.376191\pi$
$80$	15634.2	0.273118
$81$	6561.00	0.111111
$82$	28506.9	0.468184
$83$	6311.34	0.100560	0.0502801	−	0.998735i	$-0.483989\pi$
$83$	6311.34	0.100560	0.0502801	+	0.998735i	$0.483989\pi$
$84$	0	0
$85$	125870.	1.88962
$86$	44566.8	0.649778
$87$	42887.0	0.607473
$88$	−2338.83	−0.0321952
$89$	51495.8	0.689123	0.344562	−	0.938764i	$-0.388028\pi$
$89$	51495.8	0.689123	0.344562	+	0.938764i	$0.388028\pi$
$90$	19787.0	0.257498
$91$	0	0
$92$	26948.0	0.331938
$93$	−47347.8	−0.567665
$94$	93772.8	1.09460
$95$	−27618.7	−0.313974
$96$	−9216.00	−0.102062
$97$	127357.	1.37434	0.687171	−	0.726496i	$-0.258852\pi$
$97$	127357.	1.37434	0.687171	+	0.726496i	$0.258852\pi$
$98$	0	0
$99$	−2960.08	−0.0303539
$100$	9674.81	0.0967481
$101$	−65757.9	−0.641423	−0.320712	−	0.947177i	$-0.603922\pi$
$101$	−65757.9	−0.641423	−0.320712	+	0.947177i	$0.603922\pi$
$102$	−74197.4	−0.706136
$103$	−170010.	−1.57900	−0.789499	−	0.613751i	$-0.789660\pi$
$103$	−170010.	−1.57900	−0.789499	+	0.613751i	$0.789660\pi$
$104$	−2212.20	−0.0200558
$105$	0	0
$106$	−28121.2	−0.243091
$107$	−107933.	−0.911369	−0.455685	−	0.890141i	$-0.650605\pi$
$107$	−107933.	−0.911369	−0.455685	+	0.890141i	$0.650605\pi$
$108$	−11664.0	−0.0962250
$109$	−222698.	−1.79536	−0.897679	−	0.440651i	$-0.854748\pi$
$109$	−222698.	−1.79536	−0.897679	+	0.440651i	$0.854748\pi$
$110$	−8927.16	−0.0703448
$111$	115398.	0.888975
$112$	0	0
$113$	181055.	1.33387	0.666936	−	0.745115i	$-0.267605\pi$
$113$	181055.	1.33387	0.666936	+	0.745115i	$0.267605\pi$
$114$	16280.6	0.117330
$115$	102859.	0.725265
$116$	−76243.5	−0.526087
$117$	−2799.81	−0.0189088
$118$	176891.	1.16950
$119$	0	0
$120$	−35176.9	−0.223000
$121$	−159716.	−0.991708
$122$	−77521.9	−0.471547
$123$	−64140.6	−0.382270
$124$	84173.9	0.491613
$125$	−153919.	−0.881083
$126$	0	0
$127$	91474.7	0.503259	0.251630	−	0.967824i	$-0.419034\pi$
$127$	91474.7	0.503259	0.251630	+	0.967824i	$0.419034\pi$
$128$	16384.0	0.0883883
$129$	−100275.	−0.530541
$130$	−8443.83	−0.0438209
$131$	19343.9	0.0984840	0.0492420	−	0.998787i	$-0.484319\pi$
$131$	19343.9	0.0984840	0.0492420	+	0.998787i	$0.484319\pi$
$132$	5262.36	0.0262873
$133$	0	0
$134$	83776.3	0.403050
$135$	−44520.8	−0.210246
$136$	131906.	0.611532
$137$	−3077.04	−0.0140065	−0.00700327	−	0.999975i	$-0.502229\pi$
$137$	−3077.04	−0.0140065	−0.00700327	+	0.999975i	$0.502229\pi$
$138$	−60632.9	−0.271026
$139$	−370001.	−1.62430	−0.812149	−	0.583450i	$-0.801702\pi$
$139$	−370001.	−1.62430	−0.812149	+	0.583450i	$0.801702\pi$
$140$	0	0
$141$	−210989.	−0.893741
$142$	319374.	1.32916
$143$	1263.17	0.00516561
$144$	20736.0	0.0833333
$145$	−291017.	−1.14947
$146$	148263.	0.575641
$147$	0	0
$148$	−205151.	−0.769875
$149$	−454120.	−1.67573	−0.837866	−	0.545875i	$-0.816197\pi$
$149$	−454120.	−1.67573	−0.837866	+	0.545875i	$0.816197\pi$
$150$	−21768.3	−0.0789945
$151$	177592.	0.633841	0.316921	−	0.948452i	$-0.397351\pi$
$151$	177592.	0.633841	0.316921	+	0.948452i	$0.397351\pi$
$152$	−28943.2	−0.101610
$153$	166944.	0.576558
$154$	0	0
$155$	321287.	1.07415
$156$	4977.44	0.0163755
$157$	248981.	0.806153	0.403076	−	0.915166i	$-0.367941\pi$
$157$	248981.	0.806153	0.403076	+	0.915166i	$0.367941\pi$
$158$	168288.	0.536303
$159$	63272.7	0.198483
$160$	62536.8	0.193124
$161$	0	0
$162$	26244.0	0.0785674
$163$	202248.	0.596231	0.298116	−	0.954530i	$-0.403642\pi$
$163$	202248.	0.596231	0.298116	+	0.954530i	$0.403642\pi$
$164$	114028.	0.331056
$165$	20086.1	0.0574363
$166$	25245.3	0.0711068
$167$	−475790.	−1.32015	−0.660076	−	0.751199i	$-0.729476\pi$
$167$	−475790.	−1.32015	−0.660076	+	0.751199i	$0.729476\pi$
$168$	0	0
$169$	−370098.	−0.996782
$170$	503479.	1.33616
$171$	−36631.3	−0.0957992
$172$	178267.	0.459462
$173$	284703.	0.723231	0.361616	−	0.932327i	$-0.382225\pi$
$173$	284703.	0.723231	0.361616	+	0.932327i	$0.382225\pi$
$174$	171548.	0.429548
$175$	0	0
$176$	−9355.30	−0.0227654
$177$	−398005.	−0.954895
$178$	205983.	0.487284
$179$	347958.	0.811699	0.405849	−	0.913940i	$-0.366976\pi$
$179$	347958.	0.811699	0.405849	+	0.913940i	$0.366976\pi$
$180$	79148.1	0.182079
$181$	−379706.	−0.861492	−0.430746	−	0.902473i	$-0.641750\pi$
$181$	−379706.	−0.861492	−0.430746	+	0.902473i	$0.641750\pi$
$182$	0	0
$183$	174424.	0.385016
$184$	107792.	0.234715
$185$	−783051.	−1.68213
$186$	−189391.	−0.401400
$187$	−75318.9	−0.157507
$188$	375091.	0.774002
$189$	0	0
$190$	−110475.	−0.222013
$191$	194492.	0.385762	0.192881	−	0.981222i	$-0.438217\pi$
$191$	194492.	0.385762	0.192881	+	0.981222i	$0.438217\pi$
$192$	−36864.0	−0.0721688
$193$	877401.	1.69553	0.847763	−	0.530375i	$-0.177949\pi$
$193$	877401.	1.69553	0.847763	+	0.530375i	$0.177949\pi$
$194$	509430.	0.971806
$195$	18998.6	0.0357796
$196$	0	0
$197$	−752368.	−1.38123	−0.690613	−	0.723225i	$-0.742659\pi$
$197$	−752368.	−1.38123	−0.690613	+	0.723225i	$0.742659\pi$
$198$	−11840.3	−0.0214635
$199$	155453.	0.278270	0.139135	−	0.990273i	$-0.455568\pi$
$199$	155453.	0.278270	0.139135	+	0.990273i	$0.455568\pi$
$200$	38699.2	0.0684112
$201$	−188497.	−0.329089
$202$	−263032.	−0.453555
$203$	0	0
$204$	−296790.	−0.499313
$205$	435237.	0.723339
$206$	−680041.	−1.11652
$207$	136424.	0.221292
$208$	−8848.79	−0.0141816
$209$	16526.7	0.0261709
$210$	0	0
$211$	3898.23	0.00602783	0.00301391	−	0.999995i	$-0.499041\pi$
$211$	3898.23	0.00602783	0.00301391	+	0.999995i	$0.499041\pi$
$212$	−112485.	−0.171891
$213$	−718591.	−1.08526
$214$	−431731.	−0.644435
$215$	680435.	1.00390
$216$	−46656.0	−0.0680414
$217$	0	0
$218$	−890794.	−1.26951
$219$	−333592.	−0.470009
$220$	−35708.6	−0.0497413
$221$	−71241.0	−0.0981182
$222$	461590.	0.628600
$223$	−782574.	−1.05381	−0.526906	−	0.849924i	$-0.676648\pi$
$223$	−782574.	−1.05381	−0.526906	+	0.849924i	$0.676648\pi$
$224$	0	0
$225$	48978.7	0.0644987
$226$	724220.	0.943190
$227$	−796543.	−1.02599	−0.512997	−	0.858391i	$-0.671465\pi$
$227$	−796543.	−1.02599	−0.512997	+	0.858391i	$0.671465\pi$
$228$	65122.3	0.0829645
$229$	−387045.	−0.487722	−0.243861	−	0.969810i	$-0.578414\pi$
$229$	−387045.	−0.487722	−0.243861	+	0.969810i	$0.578414\pi$
$230$	411435.	0.512840
$231$	0	0
$232$	−304974.	−0.372000
$233$	−383759.	−0.463093	−0.231547	−	0.972824i	$-0.574379\pi$
$233$	−383759.	−0.463093	−0.231547	+	0.972824i	$0.574379\pi$
$234$	−11199.2	−0.0133705
$235$	1.43170e6	1.69115
$236$	707565.	0.826964
$237$	−378648.	−0.437890
$238$	0	0
$239$	−465409.	−0.527036	−0.263518	−	0.964654i	$-0.584883\pi$
$239$	−465409.	−0.527036	−0.263518	+	0.964654i	$0.584883\pi$
$240$	−140708.	−0.157685
$241$	348744.	0.386781	0.193390	−	0.981122i	$-0.438052\pi$
$241$	348744.	0.386781	0.193390	+	0.981122i	$0.438052\pi$
$242$	−638862.	−0.701243
$243$	−59049.0	−0.0641500
$244$	−310088.	−0.333434
$245$	0	0
$246$	−256563.	−0.270306
$247$	15631.9	0.0163030
$248$	336695.	0.347623
$249$	−56802.0	−0.0580584
$250$	−615676.	−0.623020
$251$	186543.	0.186894	0.0934468	−	0.995624i	$-0.470211\pi$
$251$	186543.	0.186894	0.0934468	+	0.995624i	$0.470211\pi$
$252$	0	0
$253$	−61549.4	−0.0604537
$254$	365899.	0.355858
$255$	−1.13283e6	−1.09097
$256$	65536.0	0.0625000
$257$	−1.55355e6	−1.46721	−0.733605	−	0.679577i	$-0.762164\pi$
$257$	−1.55355e6	−1.46721	−0.733605	+	0.679577i	$0.762164\pi$
$258$	−401101.	−0.375149
$259$	0	0
$260$	−33775.3	−0.0309860
$261$	−385983.	−0.350725
$262$	77375.6	0.0696387
$263$	−1.25960e6	−1.12290	−0.561451	−	0.827510i	$-0.689757\pi$
$263$	−1.25960e6	−1.12290	−0.561451	+	0.827510i	$0.689757\pi$
$264$	21049.4	0.0185879
$265$	−429348.	−0.375573
$266$	0	0
$267$	−463462.	−0.397866
$268$	335105.	0.285000
$269$	170461.	0.143630	0.0718149	−	0.997418i	$-0.477121\pi$
$269$	170461.	0.143630	0.0718149	+	0.997418i	$0.477121\pi$
$270$	−178083.	−0.148667
$271$	−2.22743e6	−1.84239	−0.921194	−	0.389104i	$-0.872785\pi$
$271$	−2.22743e6	−1.84239	−0.921194	+	0.389104i	$0.872785\pi$
$272$	527626.	0.432418
$273$	0	0
$274$	−12308.1	−0.00990412
$275$	−22097.3	−0.0176201
$276$	−242532.	−0.191644
$277$	1.98339e6	1.55314	0.776568	−	0.630034i	$-0.216959\pi$
$277$	1.98339e6	1.55314	0.776568	+	0.630034i	$0.216959\pi$
$278$	−1.48000e6	−1.14855
$279$	426130.	0.327742
$280$	0	0
$281$	−1.16687e6	−0.881573	−0.440786	−	0.897612i	$-0.645300\pi$
$281$	−1.16687e6	−0.881573	−0.440786	+	0.897612i	$0.645300\pi$
$282$	−843955.	−0.631970
$283$	1.90090e6	1.41089	0.705445	−	0.708765i	$-0.250747\pi$
$283$	1.90090e6	1.41089	0.705445	+	0.708765i	$0.250747\pi$
$284$	1.27749e6	0.939860
$285$	248568.	0.181273
$286$	5052.68	0.00365264
$287$	0	0
$288$	82944.0	0.0589256
$289$	2.82802e6	1.99177
$290$	−1.16407e6	−0.812799
$291$	−1.14622e6	−0.793477
$292$	593053.	0.407039
$293$	−1.65009e6	−1.12289	−0.561445	−	0.827514i	$-0.689755\pi$
$293$	−1.65009e6	−1.12289	−0.561445	+	0.827514i	$0.689755\pi$
$294$	0	0
$295$	2.70073e6	1.80687
$296$	−820605.	−0.544384
$297$	26640.7	0.0175249
$298$	−1.81648e6	−1.18492
$299$	−58217.0	−0.0376593
$300$	−87073.2	−0.0558575
$301$	0	0
$302$	710367.	0.448194
$303$	591821.	0.370326
$304$	−115773.	−0.0718494
$305$	−1.18359e6	−0.728535
$306$	667777.	0.407688
$307$	−597936.	−0.362084	−0.181042	−	0.983475i	$-0.557947\pi$
$307$	−597936.	−0.362084	−0.181042	+	0.983475i	$0.557947\pi$
$308$	0	0
$309$	1.53009e6	0.911635
$310$	1.28515e6	0.759536
$311$	−230480.	−0.135124	−0.0675620	−	0.997715i	$-0.521522\pi$
$311$	−230480.	−0.135124	−0.0675620	+	0.997715i	$0.521522\pi$
$312$	19909.8	0.0115792
$313$	−442577.	−0.255346	−0.127673	−	0.991816i	$-0.540751\pi$
$313$	−442577.	−0.255346	−0.127673	+	0.991816i	$0.540751\pi$
$314$	995925.	0.570036
$315$	0	0
$316$	673152.	0.379224
$317$	−1.26248e6	−0.705627	−0.352813	−	0.935694i	$-0.614775\pi$
$317$	−1.26248e6	−0.705627	−0.352813	+	0.935694i	$0.614775\pi$
$318$	253091.	0.140349
$319$	174141.	0.0958129
$320$	250147.	0.136559
$321$	971396.	0.526179
$322$	0	0
$323$	−932080.	−0.497104
$324$	104976.	0.0555556
$325$	−20901.0	−0.0109763
$326$	808991.	0.421599
$327$	2.00429e6	1.03655
$328$	456111.	0.234092
$329$	0	0
$330$	80344.5	0.0406136
$331$	−468936.	−0.235257	−0.117629	−	0.993058i	$-0.537529\pi$
$331$	−468936.	−0.235257	−0.117629	+	0.993058i	$0.537529\pi$
$332$	100981.	0.0502801
$333$	−1.03858e6	−0.513250
$334$	−1.90316e6	−0.933489
$335$	1.27908e6	0.622708
$336$	0	0
$337$	−2.46798e6	−1.18377	−0.591884	−	0.806023i	$-0.701616\pi$
$337$	−2.46798e6	−1.18377	−0.591884	+	0.806023i	$0.701616\pi$
$338$	−1.48039e6	−0.704831
$339$	−1.62949e6	−0.770112
$340$	2.01392e6	0.944810
$341$	−192254.	−0.0895343
$342$	−146525.	−0.0677402
$343$	0	0
$344$	713068.	0.324889
$345$	−925729.	−0.418732
$346$	1.13881e6	0.511402
$347$	−4.28250e6	−1.90930	−0.954648	−	0.297736i	$-0.903769\pi$
$347$	−4.28250e6	−1.90930	−0.954648	+	0.297736i	$0.903769\pi$
$348$	686191.	0.303737
$349$	1.84999e6	0.813028	0.406514	−	0.913645i	$-0.366744\pi$
$349$	1.84999e6	0.813028	0.406514	+	0.913645i	$0.366744\pi$
$350$	0	0
$351$	25198.3	0.0109170
$352$	−37421.2	−0.0160976
$353$	2.27380e6	0.971213	0.485607	−	0.874177i	$-0.338599\pi$
$353$	2.27380e6	0.971213	0.485607	+	0.874177i	$0.338599\pi$
$354$	−1.59202e6	−0.675213
$355$	4.87612e6	2.05354
$356$	823933.	0.344562
$357$	0	0
$358$	1.39183e6	0.573958
$359$	−4.39992e6	−1.80181	−0.900905	−	0.434017i	$-0.857096\pi$
$359$	−4.39992e6	−1.80181	−0.900905	+	0.434017i	$0.857096\pi$
$360$	316592.	0.128749
$361$	−2.27158e6	−0.917403
$362$	−1.51882e6	−0.609167
$363$	1.43744e6	0.572563
$364$	0	0
$365$	2.26365e6	0.889359
$366$	697697.	0.272248
$367$	1.89743e6	0.735362	0.367681	−	0.929952i	$-0.380152\pi$
$367$	1.89743e6	0.735362	0.367681	+	0.929952i	$0.380152\pi$
$368$	431168.	0.165969
$369$	577266.	0.220704
$370$	−3.13220e6	−1.18945
$371$	0	0
$372$	−757565.	−0.283833
$373$	4.56260e6	1.69801	0.849005	−	0.528385i	$-0.177202\pi$
$373$	4.56260e6	1.69801	0.849005	+	0.528385i	$0.177202\pi$
$374$	−301276.	−0.111374
$375$	1.38527e6	0.508694
$376$	1.50037e6	0.547302
$377$	164713.	0.0596861
$378$	0	0
$379$	4.99400e6	1.78587	0.892936	−	0.450184i	$-0.148642\pi$
$379$	4.99400e6	1.78587	0.892936	+	0.450184i	$0.148642\pi$
$380$	−441898.	−0.156987
$381$	−823273.	−0.290557
$382$	777970.	0.272775
$383$	3.67907e6	1.28157	0.640783	−	0.767722i	$-0.278610\pi$
$383$	3.67907e6	1.28157	0.640783	+	0.767722i	$0.278610\pi$
$384$	−147456.	−0.0510310
$385$	0	0
$386$	3.50960e6	1.19892
$387$	902477.	0.306308
$388$	2.03772e6	0.687171
$389$	257234.	0.0861894	0.0430947	−	0.999071i	$-0.486278\pi$
$389$	257234.	0.0861894	0.0430947	+	0.999071i	$0.486278\pi$
$390$	75994.5	0.0253000
$391$	3.47130e6	1.14829
$392$	0	0
$393$	−174095.	−0.0568598
$394$	−3.00947e6	−0.976674
$395$	2.56938e6	0.828583
$396$	−47361.2	−0.0151770
$397$	−433280.	−0.137972	−0.0689862	−	0.997618i	$-0.521976\pi$
$397$	−433280.	−0.137972	−0.0689862	+	0.997618i	$0.521976\pi$
$398$	621811.	0.196766
$399$	0	0
$400$	154797.	0.0483740
$401$	−1.13824e6	−0.353488	−0.176744	−	0.984257i	$-0.556556\pi$
$401$	−1.13824e6	−0.353488	−0.176744	+	0.984257i	$0.556556\pi$
$402$	−753987.	−0.232701
$403$	−181845.	−0.0557749
$404$	−1.05213e6	−0.320712
$405$	400687.	0.121386
$406$	0	0
$407$	468568.	0.140212
$408$	−1.18716e6	−0.353068
$409$	5.02438e6	1.48516	0.742581	−	0.669756i	$-0.233601\pi$
$409$	5.02438e6	1.48516	0.742581	+	0.669756i	$0.233601\pi$
$410$	1.74095e6	0.511478
$411$	27693.3	0.00808668
$412$	−2.72016e6	−0.789499
$413$	0	0
$414$	545696.	0.156477
$415$	385440.	0.109859
$416$	−35395.2	−0.0100279
$417$	3.33001e6	0.937789
$418$	66106.6	0.0185056
$419$	2.57295e6	0.715974	0.357987	−	0.933727i	$-0.383463\pi$
$419$	2.57295e6	0.715974	0.357987	+	0.933727i	$0.383463\pi$
$420$	0	0
$421$	336425.	0.0925089	0.0462545	−	0.998930i	$-0.485271\pi$
$421$	336425.	0.0925089	0.0462545	+	0.998930i	$0.485271\pi$
$422$	15592.9	0.00426232
$423$	1.89890e6	0.516002
$424$	−449939.	−0.121546
$425$	1.24626e6	0.334685
$426$	−2.87436e6	−0.767392
$427$	0	0
$428$	−1.72693e6	−0.455685
$429$	−11368.5	−0.00298237
$430$	2.72174e6	0.709864
$431$	236410.	0.0613018	0.0306509	−	0.999530i	$-0.490242\pi$
$431$	236410.	0.0613018	0.0306509	+	0.999530i	$0.490242\pi$
$432$	−186624.	−0.0481125
$433$	2.33004e6	0.597232	0.298616	−	0.954373i	$-0.403475\pi$
$433$	2.33004e6	0.597232	0.298616	+	0.954373i	$0.403475\pi$
$434$	0	0
$435$	2.61915e6	0.663648
$436$	−3.56317e6	−0.897679
$437$	−761681.	−0.190796
$438$	−1.33437e6	−0.332346
$439$	−3.19962e6	−0.792387	−0.396193	−	0.918167i	$-0.629669\pi$
$439$	−3.19962e6	−0.792387	−0.396193	+	0.918167i	$0.629669\pi$
$440$	−142835.	−0.0351724
$441$	0	0
$442$	−284964.	−0.0693800
$443$	1.13240e6	0.274152	0.137076	−	0.990561i	$-0.456230\pi$
$443$	1.13240e6	0.274152	0.137076	+	0.990561i	$0.456230\pi$
$444$	1.84636e6	0.444487
$445$	3.14490e6	0.752848
$446$	−3.13029e6	−0.745157
$447$	4.08708e6	0.967485
$448$	0	0
$449$	−8.23687e6	−1.92817	−0.964087	−	0.265585i	$-0.914435\pi$
$449$	−8.23687e6	−1.92817	−0.964087	+	0.265585i	$0.914435\pi$
$450$	195915.	0.0456075
$451$	−260441.	−0.0602931
$452$	2.89688e6	0.666936
$453$	−1.59833e6	−0.365949
$454$	−3.18617e6	−0.725487
$455$	0	0
$456$	260489.	0.0586648
$457$	−365132.	−0.0817824	−0.0408912	−	0.999164i	$-0.513020\pi$
$457$	−365132.	−0.0817824	−0.0408912	+	0.999164i	$0.513020\pi$
$458$	−1.54818e6	−0.344872
$459$	−1.50250e6	−0.332876
$460$	1.64574e6	0.362633
$461$	−332567.	−0.0728832	−0.0364416	−	0.999336i	$-0.511602\pi$
$461$	−332567.	−0.0728832	−0.0364416	+	0.999336i	$0.511602\pi$
$462$	0	0
$463$	1.69992e6	0.368533	0.184266	−	0.982876i	$-0.441009\pi$
$463$	1.69992e6	0.368533	0.184266	+	0.982876i	$0.441009\pi$
$464$	−1.21990e6	−0.263044
$465$	−2.89158e6	−0.620159
$466$	−1.53504e6	−0.327456
$467$	990465.	0.210159	0.105079	−	0.994464i	$-0.466490\pi$
$467$	990465.	0.210159	0.105079	+	0.994464i	$0.466490\pi$
$468$	−44797.0	−0.00945441
$469$	0	0
$470$	5.72681e6	1.19583
$471$	−2.24083e6	−0.465432
$472$	2.83026e6	0.584752
$473$	−407164.	−0.0836789
$474$	−1.51459e6	−0.309635
$475$	−273457.	−0.0556103
$476$	0	0
$477$	−569454.	−0.114594
$478$	−1.86164e6	−0.372671
$479$	6.08065e6	1.21091	0.605454	−	0.795880i	$-0.292991\pi$
$479$	6.08065e6	1.21091	0.605454	+	0.795880i	$0.292991\pi$
$480$	−562831.	−0.111500
$481$	443198.	0.0873445
$482$	1.39498e6	0.273495
$483$	0	0
$484$	−2.55545e6	−0.495854
$485$	7.77785e6	1.50143
$486$	−236196.	−0.0453609
$487$	−6.71098e6	−1.28222	−0.641112	−	0.767448i	$-0.721526\pi$
$487$	−6.71098e6	−1.28222	−0.641112	+	0.767448i	$0.721526\pi$
$488$	−1.24035e6	−0.235773
$489$	−1.82023e6	−0.344234
$490$	0	0
$491$	−914042.	−0.171105	−0.0855525	−	0.996334i	$-0.527266\pi$
$491$	−914042.	−0.171105	−0.0855525	+	0.996334i	$0.527266\pi$
$492$	−1.02625e6	−0.191135
$493$	−9.82130e6	−1.81992
$494$	62527.5	0.0115280
$495$	−180775.	−0.0331608
$496$	1.34678e6	0.245806
$497$	0	0
$498$	−227208.	−0.0410535
$499$	−7.75492e6	−1.39420	−0.697101	−	0.716972i	$-0.745527\pi$
$499$	−7.75492e6	−1.39420	−0.697101	+	0.716972i	$0.745527\pi$
$500$	−2.46270e6	−0.440542
$501$	4.28211e6	0.762190
$502$	746172.	0.132154
$503$	3.79381e6	0.668584	0.334292	−	0.942470i	$-0.391503\pi$
$503$	3.79381e6	0.668584	0.334292	+	0.942470i	$0.391503\pi$
$504$	0	0
$505$	−4.01591e6	−0.700737
$506$	−246198.	−0.0427472
$507$	3.33088e6	0.575492
$508$	1.46360e6	0.251630
$509$	8.53160e6	1.45961	0.729804	−	0.683657i	$-0.239611\pi$
$509$	8.53160e6	1.45961	0.729804	+	0.683657i	$0.239611\pi$
$510$	−4.53131e6	−0.771434
$511$	0	0
$512$	262144.	0.0441942
$513$	329681.	0.0553097
$514$	−6.21419e6	−1.03747
$515$	−1.03827e7	−1.72501
$516$	−1.60440e6	−0.265271
$517$	−856712.	−0.140964
$518$	0	0
$519$	−2.56233e6	−0.417558
$520$	−135101.	−0.0219104
$521$	−3.19066e6	−0.514976	−0.257488	−	0.966282i	$-0.582895\pi$
$521$	−3.19066e6	−0.514976	−0.257488	+	0.966282i	$0.582895\pi$
$522$	−1.54393e6	−0.248000
$523$	−9.60678e6	−1.53576	−0.767880	−	0.640593i	$-0.778689\pi$
$523$	−9.60678e6	−1.53576	−0.767880	+	0.640593i	$0.778689\pi$
$524$	309502.	0.0492420
$525$	0	0
$526$	−5.03838e6	−0.794012
$527$	1.08429e7	1.70066
$528$	84197.7	0.0131436
$529$	−3.59965e6	−0.559270
$530$	−1.71739e6	−0.265570
$531$	3.58205e6	0.551309
$532$	0	0
$533$	−246340.	−0.0375592
$534$	−1.85385e6	−0.281333
$535$	−6.59158e6	−0.995646
$536$	1.34042e6	0.201525
$537$	−3.13163e6	−0.468634
$538$	681844.	0.101562
$539$	0	0
$540$	−712333.	−0.105123
$541$	1.02366e7	1.50371	0.751855	−	0.659328i	$-0.229159\pi$
$541$	1.02366e7	1.50371	0.751855	+	0.659328i	$0.229159\pi$
$542$	−8.90972e6	−1.30276
$543$	3.41736e6	0.497383
$544$	2.11050e6	0.305766
$545$	−1.36004e7	−1.96138
$546$	0	0
$547$	−9.27757e6	−1.32576	−0.662882	−	0.748724i	$-0.730667\pi$
$547$	−9.27757e6	−1.32576	−0.662882	+	0.748724i	$0.730667\pi$
$548$	−49232.6	−0.00700327
$549$	−1.56982e6	−0.222289
$550$	−88389.4	−0.0124593
$551$	2.15501e6	0.302392
$552$	−970127.	−0.135513
$553$	0	0
$554$	7.93357e6	1.09823
$555$	7.04745e6	0.971180
$556$	−5.92001e6	−0.812149
$557$	620098.	0.0846881	0.0423441	−	0.999103i	$-0.486517\pi$
$557$	620098.	0.0846881	0.0423441	+	0.999103i	$0.486517\pi$
$558$	1.70452e6	0.231748
$559$	−385119.	−0.0521273
$560$	0	0
$561$	677870.	0.0909368
$562$	−4.66750e6	−0.623366
$563$	7.36664e6	0.979487	0.489744	−	0.871867i	$-0.337090\pi$
$563$	7.36664e6	0.979487	0.489744	+	0.871867i	$0.337090\pi$
$564$	−3.37582e6	−0.446871
$565$	1.10572e7	1.45722
$566$	7.60360e6	0.997650
$567$	0	0
$568$	5.10998e6	0.664581
$569$	3.68222e6	0.476792	0.238396	−	0.971168i	$-0.423378\pi$
$569$	3.68222e6	0.476792	0.238396	+	0.971168i	$0.423378\pi$
$570$	994272.	0.128179
$571$	1.03320e7	1.32615	0.663077	−	0.748551i	$-0.269250\pi$
$571$	1.03320e7	1.32615	0.663077	+	0.748551i	$0.269250\pi$
$572$	20210.7	0.00258281
$573$	−1.75043e6	−0.222720
$574$	0	0
$575$	1.01842e6	0.128457
$576$	331776.	0.0416667
$577$	−1.25123e7	−1.56458	−0.782292	−	0.622911i	$-0.785950\pi$
$577$	−1.25123e7	−1.56458	−0.782292	+	0.622911i	$0.785950\pi$
$578$	1.13121e7	1.40839
$579$	−7.89661e6	−0.978913
$580$	−4.65627e6	−0.574736
$581$	0	0
$582$	−4.58487e6	−0.561073
$583$	256916.	0.0313055
$584$	2.37221e6	0.287820
$585$	−170988.	−0.0206574
$586$	−6.60034e6	−0.794004
$587$	−1.60865e7	−1.92694	−0.963468	−	0.267823i	$-0.913696\pi$
$587$	−1.60865e7	−1.92694	−0.963468	+	0.267823i	$0.913696\pi$
$588$	0	0
$589$	−2.37916e6	−0.282577
$590$	1.08029e7	1.27765
$591$	6.77131e6	0.797451
$592$	−3.28242e6	−0.384937
$593$	−9.46330e6	−1.10511	−0.552556	−	0.833476i	$-0.686347\pi$
$593$	−9.46330e6	−1.10511	−0.552556	+	0.833476i	$0.686347\pi$
$594$	106563.	0.0123919
$595$	0	0
$596$	−7.26592e6	−0.837866
$597$	−1.39908e6	−0.160659
$598$	−232868.	−0.0266291
$599$	5.01498e6	0.571087	0.285544	−	0.958366i	$-0.407826\pi$
$599$	5.01498e6	0.571087	0.285544	+	0.958366i	$0.407826\pi$
$600$	−348293.	−0.0394972
$601$	1.26473e7	1.42828	0.714139	−	0.700004i	$-0.246818\pi$
$601$	1.26473e7	1.42828	0.714139	+	0.700004i	$0.246818\pi$
$602$	0	0
$603$	1.69647e6	0.190000
$604$	2.84147e6	0.316921
$605$	−9.75400e6	−1.08341
$606$	2.36729e6	0.261860
$607$	−2.87702e6	−0.316936	−0.158468	−	0.987364i	$-0.550655\pi$
$607$	−2.87702e6	−0.316936	−0.158468	+	0.987364i	$0.550655\pi$
$608$	−463092.	−0.0508052
$609$	0	0
$610$	−4.73434e6	−0.515152
$611$	−810328.	−0.0878128
$612$	2.67111e6	0.288279
$613$	−3.72582e6	−0.400471	−0.200236	−	0.979748i	$-0.564171\pi$
$613$	−3.72582e6	−0.400471	−0.200236	+	0.979748i	$0.564171\pi$
$614$	−2.39174e6	−0.256032
$615$	−3.91714e6	−0.417620
$616$	0	0
$617$	−1.15861e7	−1.22525	−0.612625	−	0.790374i	$-0.709886\pi$
$617$	−1.15861e7	−1.22525	−0.612625	+	0.790374i	$0.709886\pi$
$618$	6.12037e6	0.644624
$619$	1.85608e6	0.194702	0.0973508	−	0.995250i	$-0.468963\pi$
$619$	1.85608e6	0.194702	0.0973508	+	0.995250i	$0.468963\pi$
$620$	5.14059e6	0.537073
$621$	−1.22782e6	−0.127763
$622$	−921921.	−0.0955471
$623$	0	0
$624$	79639.1	0.00818776
$625$	−1.12896e7	−1.15606
$626$	−1.77031e6	−0.180557
$627$	−148740.	−0.0151098
$628$	3.98370e6	0.403076
$629$	−2.64266e7	−2.66326
$630$	0	0
$631$	8.92135e6	0.891984	0.445992	−	0.895037i	$-0.352851\pi$
$631$	8.92135e6	0.891984	0.445992	+	0.895037i	$0.352851\pi$
$632$	2.69261e6	0.268152
$633$	−35084.0	−0.00348017
$634$	−5.04990e6	−0.498953
$635$	5.58646e6	0.549797
$636$	1.01236e6	0.0992415
$637$	0	0
$638$	696563.	0.0677499
$639$	6.46731e6	0.626573
$640$	1.00059e6	0.0965618
$641$	1.31866e7	1.26762	0.633810	−	0.773489i	$-0.281490\pi$
$641$	1.31866e7	1.26762	0.633810	+	0.773489i	$0.281490\pi$
$642$	3.88558e6	0.372065
$643$	9.67813e6	0.923132	0.461566	−	0.887106i	$-0.347288\pi$
$643$	9.67813e6	0.923132	0.461566	+	0.887106i	$0.347288\pi$
$644$	0	0
$645$	−6.12391e6	−0.579602
$646$	−3.72832e6	−0.351505
$647$	1.72491e6	0.161996	0.0809982	−	0.996714i	$-0.474189\pi$
$647$	1.72491e6	0.161996	0.0809982	+	0.996714i	$0.474189\pi$
$648$	419904.	0.0392837
$649$	−1.61609e6	−0.150610
$650$	−83603.8	−0.00776145
$651$	0	0
$652$	3.23596e6	0.298116
$653$	597510.	0.0548356	0.0274178	−	0.999624i	$-0.491272\pi$
$653$	597510.	0.0548356	0.0274178	+	0.999624i	$0.491272\pi$
$654$	8.01714e6	0.732951
$655$	1.18135e6	0.107591
$656$	1.82444e6	0.165528
$657$	3.00233e6	0.271360
$658$	0	0
$659$	1.47605e7	1.32400	0.662001	−	0.749503i	$-0.269707\pi$
$659$	1.47605e7	1.32400	0.662001	+	0.749503i	$0.269707\pi$
$660$	321378.	0.0287181
$661$	−1.69041e7	−1.50484	−0.752418	−	0.658686i	$-0.771112\pi$
$661$	−1.69041e7	−1.50484	−0.752418	+	0.658686i	$0.771112\pi$
$662$	−1.87574e6	−0.166352
$663$	641169.	0.0566486
$664$	403925.	0.0355534
$665$	0	0
$666$	−4.15431e6	−0.362922
$667$	−8.02581e6	−0.698512
$668$	−7.61264e6	−0.660076
$669$	7.04316e6	0.608418
$670$	5.11631e6	0.440321
$671$	708243.	0.0607262
$672$	0	0
$673$	−1.58960e7	−1.35285	−0.676425	−	0.736512i	$-0.736472\pi$
$673$	−1.58960e7	−1.35285	−0.676425	+	0.736512i	$0.736472\pi$
$674$	−9.87191e6	−0.837050
$675$	−440808.	−0.0372383
$676$	−5.92157e6	−0.498391
$677$	1.95361e6	0.163820	0.0819099	−	0.996640i	$-0.473898\pi$
$677$	1.95361e6	0.163820	0.0819099	+	0.996640i	$0.473898\pi$
$678$	−6.51798e6	−0.544551
$679$	0	0
$680$	8.05567e6	0.668081
$681$	7.16889e6	0.592357
$682$	−769016.	−0.0633103
$683$	−9.23970e6	−0.757890	−0.378945	−	0.925419i	$-0.623713\pi$
$683$	−9.23970e6	−0.757890	−0.378945	+	0.925419i	$0.623713\pi$
$684$	−586100.	−0.0478996
$685$	−187918.	−0.0153018
$686$	0	0
$687$	3.48340e6	0.281587
$688$	2.85227e6	0.229731
$689$	243006.	0.0195016
$690$	−3.70292e6	−0.296088
$691$	1.45698e7	1.16080	0.580401	−	0.814331i	$-0.302896\pi$
$691$	1.45698e7	1.16080	0.580401	+	0.814331i	$0.302896\pi$
$692$	4.55525e6	0.361616
$693$	0	0
$694$	−1.71300e7	−1.35008
$695$	−2.25964e7	−1.77450
$696$	2.74476e6	0.214774
$697$	1.46885e7	1.14524
$698$	7.39995e6	0.574898
$699$	3.45383e6	0.267367
$700$	0	0
$701$	−3.70190e6	−0.284531	−0.142266	−	0.989829i	$-0.545439\pi$
$701$	−3.70190e6	−0.284531	−0.142266	+	0.989829i	$0.545439\pi$
$702$	100793.	0.00771949
$703$	5.79858e6	0.442520
$704$	−149685.	−0.0113827
$705$	−1.28853e7	−0.976387
$706$	9.09518e6	0.686751
$707$	0	0
$708$	−6.36809e6	−0.477448
$709$	−2.52937e7	−1.88971	−0.944857	−	0.327484i	$-0.893799\pi$
$709$	−2.52937e7	−1.88971	−0.944857	+	0.327484i	$0.893799\pi$
$710$	1.95045e7	1.45207
$711$	3.40783e6	0.252816
$712$	3.29573e6	0.243642
$713$	8.86061e6	0.652739
$714$	0	0
$715$	77143.1	0.00564329
$716$	5.56734e6	0.405849
$717$	4.18868e6	0.304284
$718$	−1.75997e7	−1.27407
$719$	−1.45185e7	−1.04737	−0.523683	−	0.851913i	$-0.675443\pi$
$719$	−1.45185e7	−1.04737	−0.523683	+	0.851913i	$0.675443\pi$
$720$	1.26637e6	0.0910394
$721$	0	0
$722$	−9.08632e6	−0.648702
$723$	−3.13870e6	−0.223308
$724$	−6.07530e6	−0.430746
$725$	−2.88141e6	−0.203592
$726$	5.74976e6	0.404863
$727$	1.42855e7	1.00244	0.501222	−	0.865319i	$-0.332884\pi$
$727$	1.42855e7	1.00244	0.501222	+	0.865319i	$0.332884\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	9.05460e6	0.628872
$731$	2.29635e7	1.58944
$732$	2.79079e6	0.192508
$733$	8.21556e6	0.564777	0.282389	−	0.959300i	$-0.408873\pi$
$733$	8.21556e6	0.564777	0.282389	+	0.959300i	$0.408873\pi$
$734$	7.58973e6	0.519979
$735$	0	0
$736$	1.72467e6	0.117358
$737$	−765384.	−0.0519052
$738$	2.30906e6	0.156061
$739$	−3.43896e6	−0.231641	−0.115821	−	0.993270i	$-0.536950\pi$
$739$	−3.43896e6	−0.231641	−0.115821	+	0.993270i	$0.536950\pi$
$740$	−1.25288e7	−0.841067
$741$	−140687.	−0.00941256
$742$	0	0
$743$	1.53588e6	0.102067	0.0510334	−	0.998697i	$-0.483748\pi$
$743$	1.53588e6	0.102067	0.0510334	+	0.998697i	$0.483748\pi$
$744$	−3.03026e6	−0.200700
$745$	−2.77336e7	−1.83069
$746$	1.82504e7	1.20067
$747$	511218.	0.0335201
$748$	−1.20510e6	−0.0787535
$749$	0	0
$750$	5.54108e6	0.359701
$751$	−2.01146e7	−1.30140	−0.650700	−	0.759335i	$-0.725524\pi$
$751$	−2.01146e7	−1.30140	−0.650700	+	0.759335i	$0.725524\pi$
$752$	6.00146e6	0.387001
$753$	−1.67889e6	−0.107903
$754$	658850.	0.0422044
$755$	1.08457e7	0.692454
$756$	0	0
$757$	202045.	0.0128147	0.00640733	−	0.999979i	$-0.497960\pi$
$757$	202045.	0.0128147	0.00640733	+	0.999979i	$0.497960\pi$
$758$	1.99760e7	1.26280
$759$	553945.	0.0349029
$760$	−1.76759e6	−0.111007
$761$	1.08202e6	0.0677290	0.0338645	−	0.999426i	$-0.489219\pi$
$761$	1.08202e6	0.0677290	0.0338645	+	0.999426i	$0.489219\pi$
$762$	−3.29309e6	−0.205455
$763$	0	0
$764$	3.11188e6	0.192881
$765$	1.01955e7	0.629873
$766$	1.47163e7	0.906205
$767$	−1.52859e6	−0.0938214
$768$	−589824.	−0.0360844
$769$	−1.19305e7	−0.727517	−0.363759	−	0.931493i	$-0.618507\pi$
$769$	−1.19305e7	−0.727517	−0.363759	+	0.931493i	$0.618507\pi$
$770$	0	0
$771$	1.39819e7	0.847094
$772$	1.40384e7	0.847763
$773$	6.58657e6	0.396470	0.198235	−	0.980155i	$-0.436479\pi$
$773$	6.58657e6	0.396470	0.198235	+	0.980155i	$0.436479\pi$
$774$	3.60991e6	0.216593
$775$	3.18112e6	0.190250
$776$	8.15087e6	0.485903
$777$	0	0
$778$	1.02894e6	0.0609451
$779$	−3.22298e6	−0.190289
$780$	303978.	0.0178898
$781$	−2.91781e6	−0.171171
$782$	1.38852e7	0.811961
$783$	3.47384e6	0.202491
$784$	0	0
$785$	1.52055e7	0.880700
$786$	−696380.	−0.0402059
$787$	1.92720e7	1.10915	0.554575	−	0.832134i	$-0.312881\pi$
$787$	1.92720e7	1.10915	0.554575	+	0.832134i	$0.312881\pi$
$788$	−1.20379e7	−0.690613
$789$	1.13364e7	0.648308
$790$	1.02775e7	0.585897
$791$	0	0
$792$	−189445.	−0.0107317
$793$	669897.	0.0378290
$794$	−1.73312e6	−0.0975613
$795$	3.86413e6	0.216837
$796$	2.48724e6	0.139135
$797$	−1.54906e7	−0.863816	−0.431908	−	0.901918i	$-0.642159\pi$
$797$	−1.54906e7	−0.863816	−0.431908	+	0.901918i	$0.642159\pi$
$798$	0	0
$799$	4.83174e7	2.67754
$800$	619188.	0.0342056
$801$	4.17116e6	0.229708
$802$	−4.55298e6	−0.249954
$803$	−1.35454e6	−0.0741315
$804$	−3.01595e6	−0.164545
$805$	0	0
$806$	−727380.	−0.0394388
$807$	−1.53415e6	−0.0829247
$808$	−4.20851e6	−0.226777
$809$	−1.77071e6	−0.0951210	−0.0475605	−	0.998868i	$-0.515145\pi$
$809$	−1.77071e6	−0.0951210	−0.0475605	+	0.998868i	$0.515145\pi$
$810$	1.60275e6	0.0858327
$811$	−6.80547e6	−0.363334	−0.181667	−	0.983360i	$-0.558149\pi$
$811$	−6.80547e6	−0.363334	−0.181667	+	0.983360i	$0.558149\pi$
$812$	0	0
$813$	2.00469e7	1.06370
$814$	1.87427e6	0.0991451
$815$	1.23515e7	0.651366
$816$	−4.74863e6	−0.249657
$817$	−5.03869e6	−0.264097
$818$	2.00975e7	1.05017
$819$	0	0
$820$	6.96380e6	0.361669
$821$	2.27127e7	1.17601	0.588006	−	0.808857i	$-0.299913\pi$
$821$	2.27127e7	1.17601	0.588006	+	0.808857i	$0.299913\pi$
$822$	110773.	0.00571815
$823$	−3.03576e7	−1.56231	−0.781156	−	0.624336i	$-0.785370\pi$
$823$	−3.03576e7	−1.56231	−0.781156	+	0.624336i	$0.785370\pi$
$824$	−1.08807e7	−0.558260
$825$	198876.	0.0101730
$826$	0	0
$827$	−5.80776e6	−0.295287	−0.147644	−	0.989041i	$-0.547169\pi$
$827$	−5.80776e6	−0.295287	−0.147644	+	0.989041i	$0.547169\pi$
$828$	2.18279e6	0.110646
$829$	9.04916e6	0.457322	0.228661	−	0.973506i	$-0.426565\pi$
$829$	9.04916e6	0.457322	0.228661	+	0.973506i	$0.426565\pi$
$830$	1.54176e6	0.0776822
$831$	−1.78505e7	−0.896703
$832$	−141581.	−0.00709080
$833$	0	0
$834$	1.33200e7	0.663117
$835$	−2.90570e7	−1.44223
$836$	264426.	0.0130855
$837$	−3.83517e6	−0.189222
$838$	1.02918e7	0.506270
$839$	8.17101e6	0.400747	0.200374	−	0.979720i	$-0.435784\pi$
$839$	8.17101e6	0.400747	0.200374	+	0.979720i	$0.435784\pi$
$840$	0	0
$841$	2.19614e6	0.107071
$842$	1.34570e6	0.0654137
$843$	1.05019e7	0.508976
$844$	62371.6	0.00301391
$845$	−2.26023e7	−1.08896
$846$	7.59560e6	0.364868
$847$	0	0
$848$	−1.79976e6	−0.0859457
$849$	−1.71081e7	−0.814578
$850$	4.98504e6	0.236658
$851$	−2.15954e7	−1.02220
$852$	−1.14974e7	−0.542628
$853$	−2.88437e7	−1.35731	−0.678654	−	0.734458i	$-0.737436\pi$
$853$	−2.88437e7	−1.35731	−0.678654	+	0.734458i	$0.737436\pi$
$854$	0	0
$855$	−2.23711e6	−0.104658
$856$	−6.90770e6	−0.322218
$857$	2.69462e7	1.25327	0.626637	−	0.779311i	$-0.284431\pi$
$857$	2.69462e7	1.25327	0.626637	+	0.779311i	$0.284431\pi$
$858$	−45474.1	−0.00210885
$859$	7.49124e6	0.346394	0.173197	−	0.984887i	$-0.444590\pi$
$859$	7.49124e6	0.346394	0.173197	+	0.984887i	$0.444590\pi$
$860$	1.08870e7	0.501950
$861$	0	0
$862$	945641.	0.0433469
$863$	−1.41552e6	−0.0646977	−0.0323489	−	0.999477i	$-0.510299\pi$
$863$	−1.41552e6	−0.0646977	−0.0323489	+	0.999477i	$0.510299\pi$
$864$	−746496.	−0.0340207
$865$	1.73871e7	0.790110
$866$	9.32015e6	0.422307
$867$	−2.54522e7	−1.14995
$868$	0	0
$869$	−1.53749e6	−0.0690656
$870$	1.04766e7	0.469270
$871$	−723944.	−0.0323340
$872$	−1.42527e7	−0.634755
$873$	1.03159e7	0.458114
$874$	−3.04672e6	−0.134913
$875$	0	0
$876$	−5.33748e6	−0.235004
$877$	2.55232e7	1.12056	0.560281	−	0.828303i	$-0.310693\pi$
$877$	2.55232e7	1.12056	0.560281	+	0.828303i	$0.310693\pi$
$878$	−1.27985e7	−0.560302
$879$	1.48508e7	0.648301
$880$	−571338.	−0.0248706
$881$	2.07516e6	0.0900764	0.0450382	−	0.998985i	$-0.485659\pi$
$881$	2.07516e6	0.0900764	0.0450382	+	0.998985i	$0.485659\pi$
$882$	0	0
$883$	1.80641e7	0.779677	0.389839	−	0.920883i	$-0.372531\pi$
$883$	1.80641e7	0.779677	0.389839	+	0.920883i	$0.372531\pi$
$884$	−1.13986e6	−0.0490591
$885$	−2.43066e7	−1.04320
$886$	4.52961e6	0.193855
$887$	9.28389e6	0.396206	0.198103	−	0.980181i	$-0.436522\pi$
$887$	9.28389e6	0.396206	0.198103	+	0.980181i	$0.436522\pi$
$888$	7.38545e6	0.314300
$889$	0	0
$890$	1.25796e7	0.532344
$891$	−239766.	−0.0101180
$892$	−1.25212e7	−0.526906
$893$	−1.06019e7	−0.444893
$894$	1.63483e7	0.684115
$895$	2.12502e7	0.886758
$896$	0	0
$897$	523953.	0.0217426
$898$	−3.29475e7	−1.36343
$899$	−2.50692e7	−1.03452
$900$	783659.	0.0322494
$901$	−1.44897e7	−0.594631
$902$	−1.04176e6	−0.0426336
$903$	0	0
$904$	1.15875e7	0.471595
$905$	−2.31891e7	−0.941156
$906$	−6.39331e6	−0.258765
$907$	−4.20818e7	−1.69854	−0.849270	−	0.527958i	$-0.822958\pi$
$907$	−4.20818e7	−1.69854	−0.849270	+	0.527958i	$0.822958\pi$
$908$	−1.27447e7	−0.512997
$909$	−5.32639e6	−0.213808
$910$	0	0
$911$	2.33510e7	0.932199	0.466100	−	0.884732i	$-0.345659\pi$
$911$	2.33510e7	0.932199	0.466100	+	0.884732i	$0.345659\pi$
$912$	1.04196e6	0.0414823
$913$	−230642.	−0.00915719
$914$	−1.46053e6	−0.0578289
$915$	1.06523e7	0.420620
$916$	−6.19272e6	−0.243861
$917$	0	0
$918$	−6.00999e6	−0.235379
$919$	1.54594e7	0.603817	0.301908	−	0.953337i	$-0.402376\pi$
$919$	1.54594e7	0.603817	0.301908	+	0.953337i	$0.402376\pi$
$920$	6.58296e6	0.256420
$921$	5.38142e6	0.209049
$922$	−1.33027e6	−0.0515362
$923$	−2.75983e6	−0.106630
$924$	0	0
$925$	−7.75312e6	−0.297935
$926$	6.79968e6	0.260592
$927$	−1.37708e7	−0.526333
$928$	−4.87958e6	−0.186000
$929$	−1.49993e7	−0.570204	−0.285102	−	0.958497i	$-0.592028\pi$
$929$	−1.49993e7	−0.570204	−0.285102	+	0.958497i	$0.592028\pi$
$930$	−1.15663e7	−0.438519
$931$	0	0
$932$	−6.14014e6	−0.231547
$933$	2.07432e6	0.0780139
$934$	3.96186e6	0.148605
$935$	−4.59981e6	−0.172072
$936$	−179188.	−0.00668527
$937$	−1.52742e7	−0.568343	−0.284172	−	0.958773i	$-0.591719\pi$
$937$	−1.52742e7	−0.568343	−0.284172	+	0.958773i	$0.591719\pi$
$938$	0	0
$939$	3.98320e6	0.147424
$940$	2.29072e7	0.845576
$941$	5.13600e6	0.189082	0.0945412	−	0.995521i	$-0.469862\pi$
$941$	5.13600e6	0.189082	0.0945412	+	0.995521i	$0.469862\pi$
$942$	−8.96332e6	−0.329110
$943$	1.20032e7	0.439559
$944$	1.13210e7	0.413482
$945$	0	0
$946$	−1.62865e6	−0.0591699
$947$	−4.50054e7	−1.63076	−0.815379	−	0.578928i	$-0.803471\pi$
$947$	−4.50054e7	−1.63076	−0.815379	+	0.578928i	$0.803471\pi$
$948$	−6.05837e6	−0.218945
$949$	−1.28120e6	−0.0461798
$950$	−1.09383e6	−0.0393224
$951$	1.13623e7	0.407394
$952$	0	0
$953$	−4.49596e7	−1.60358	−0.801789	−	0.597607i	$-0.796118\pi$
$953$	−4.49596e7	−1.60358	−0.801789	+	0.597607i	$0.796118\pi$
$954$	−2.27782e6	−0.0810303
$955$	1.18779e7	0.421434
$956$	−7.44655e6	−0.263518
$957$	−1.56727e6	−0.0553176
$958$	2.43226e7	0.856242
$959$	0	0
$960$	−2.25132e6	−0.0788424
$961$	−952428.	−0.0332678
$962$	1.77279e6	0.0617619
$963$	−8.74256e6	−0.303790
$964$	5.57991e6	0.193390
$965$	5.35838e7	1.85232
$966$	0	0
$967$	1.04364e7	0.358907	0.179454	−	0.983766i	$-0.442567\pi$
$967$	1.04364e7	0.358907	0.179454	+	0.983766i	$0.442567\pi$
$968$	−1.02218e7	−0.350622
$969$	8.38872e6	0.287003
$970$	3.11114e7	1.06167
$971$	1.72207e7	0.586142	0.293071	−	0.956091i	$-0.405323\pi$
$971$	1.72207e7	0.586142	0.293071	+	0.956091i	$0.405323\pi$
$972$	−944784.	−0.0320750
$973$	0	0
$974$	−2.68439e7	−0.906669
$975$	188109.	0.00633720
$976$	−4.96140e6	−0.166717
$977$	3.24376e7	1.08721	0.543603	−	0.839343i	$-0.317060\pi$
$977$	3.24376e7	1.08721	0.543603	+	0.839343i	$0.317060\pi$
$978$	−7.28092e6	−0.243410
$979$	−1.88187e6	−0.0627528
$980$	0	0
$981$	−1.80386e7	−0.598452
$982$	−3.65617e6	−0.120989
$983$	−3.19804e7	−1.05560	−0.527801	−	0.849368i	$-0.676983\pi$
$983$	−3.19804e7	−1.05560	−0.527801	+	0.849368i	$0.676983\pi$
$984$	−4.10500e6	−0.135153
$985$	−4.59479e7	−1.50895
$986$	−3.92852e7	−1.28688
$987$	0	0
$988$	250110.	0.00815152
$989$	1.87654e7	0.610051
$990$	−723100.	−0.0234483
$991$	5.49614e7	1.77776	0.888880	−	0.458139i	$-0.151484\pi$
$991$	5.49614e7	1.77776	0.888880	+	0.458139i	$0.151484\pi$
$992$	5.38713e6	0.173811
$993$	4.22042e6	0.135826
$994$	0	0
$995$	9.49367e6	0.304002
$996$	−908832.	−0.0290292
$997$	−7.51010e6	−0.239281	−0.119640	−	0.992817i	$-0.538174\pi$
$997$	−7.51010e6	−0.239281	−0.119640	+	0.992817i	$0.538174\pi$
$998$	−3.10197e7	−0.985850
$999$	9.34721e6	0.296325

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.6.a.t.1.2	✓	2
3.2	odd	2		882.6.a.z.1.1		2
7.2	even	3		294.6.e.v.67.1		4
7.3	odd	6		294.6.e.u.79.2		4
7.4	even	3		294.6.e.v.79.1		4
7.5	odd	6		294.6.e.u.67.2		4
7.6	odd	2		294.6.a.u.1.1	yes	2
21.20	even	2		882.6.a.bj.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.6.a.t.1.2	✓	2	1.1	even	1	trivial
294.6.a.u.1.1	yes	2	7.6	odd	2
294.6.e.u.67.2		4	7.5	odd	6
294.6.e.u.79.2		4	7.3	odd	6
294.6.e.v.67.1		4	7.2	even	3
294.6.e.v.79.1		4	7.4	even	3
882.6.a.z.1.1		2	3.2	odd	2
882.6.a.bj.1.2		2	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	294.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +61.0711 q^{5} -36.0000 q^{6} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +61.0711 q^{5} -36.0000 q^{6} +64.0000 q^{8} +81.0000 q^{9} +244.284 q^{10} -36.5442 q^{11} -144.000 q^{12} -34.5656 q^{13} -549.640 q^{15} +256.000 q^{16} +2061.04 q^{17} +324.000 q^{18} -452.238 q^{19} +977.137 q^{20} -146.177 q^{22} +1684.25 q^{23} -576.000 q^{24} +604.675 q^{25} -138.262 q^{26} -729.000 q^{27} -4765.22 q^{29} -2198.56 q^{30} +5260.87 q^{31} +1024.00 q^{32} +328.897 q^{33} +8244.16 q^{34} +1296.00 q^{36} -12822.0 q^{37} -1808.95 q^{38} +311.090 q^{39} +3908.55 q^{40} +7126.74 q^{41} +11141.7 q^{43} -584.706 q^{44} +4946.76 q^{45} +6736.99 q^{46} +23443.2 q^{47} -2304.00 q^{48} +2418.70 q^{50} -18549.4 q^{51} -553.049 q^{52} -7030.30 q^{53} -2916.00 q^{54} -2231.79 q^{55} +4070.14 q^{57} -19060.9 q^{58} +44222.8 q^{59} -8794.23 q^{60} -19380.5 q^{61} +21043.5 q^{62} +4096.00 q^{64} -2110.96 q^{65} +1315.59 q^{66} +20944.1 q^{67} +32976.6 q^{68} -15158.2 q^{69} +79843.4 q^{71} +5184.00 q^{72} +37065.8 q^{73} -51287.8 q^{74} -5442.08 q^{75} -7235.81 q^{76} +1244.36 q^{78} +42072.0 q^{79} +15634.2 q^{80} +6561.00 q^{81} +28506.9 q^{82} +6311.34 q^{83} +125870. q^{85} +44566.8 q^{86} +42887.0 q^{87} -2338.83 q^{88} +51495.8 q^{89} +19787.0 q^{90} +26948.0 q^{92} -47347.8 q^{93} +93772.8 q^{94} -27618.7 q^{95} -9216.00 q^{96} +127357. q^{97} -2960.08 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8 q^{2} - 18 q^{3} + 32 q^{4} + 108 q^{5} - 72 q^{6} + 128 q^{8} + 162 q^{9}+O(q^{10}) \) 2 * q + 8 * q^2 - 18 * q^3 + 32 * q^4 + 108 * q^5 - 72 * q^6 + 128 * q^8 + 162 * q^9	\( 2 q + 8 q^{2} - 18 q^{3} + 32 q^{4} + 108 q^{5} - 72 q^{6} + 128 q^{8} + 162 q^{9} + 432 q^{10} - 124 q^{11} - 288 q^{12} + 720 q^{13} - 972 q^{15} + 512 q^{16} + 612 q^{17} + 648 q^{18} + 2088 q^{19} + 1728 q^{20} - 496 q^{22} + 772 q^{23} - 1152 q^{24} - 318 q^{25} + 2880 q^{26} - 1458 q^{27} - 4592 q^{29} - 3888 q^{30} + 9792 q^{31} + 2048 q^{32} + 1116 q^{33} + 2448 q^{34} + 2592 q^{36} - 5992 q^{37} + 8352 q^{38} - 6480 q^{39} + 6912 q^{40} + 20196 q^{41} - 1136 q^{43} - 1984 q^{44} + 8748 q^{45} + 3088 q^{46} + 36936 q^{47} - 4608 q^{48} - 1272 q^{50} - 5508 q^{51} + 11520 q^{52} - 16708 q^{53} - 5832 q^{54} - 6336 q^{55} - 18792 q^{57} - 18368 q^{58} + 74592 q^{59} - 15552 q^{60} - 18648 q^{61} + 39168 q^{62} + 8192 q^{64} + 33300 q^{65} + 4464 q^{66} + 67344 q^{67} + 9792 q^{68} - 6948 q^{69} + 76548 q^{71} + 10368 q^{72} + 47304 q^{73} - 23968 q^{74} + 2862 q^{75} + 33408 q^{76} - 25920 q^{78} + 140656 q^{79} + 27648 q^{80} + 13122 q^{81} + 80784 q^{82} + 94104 q^{83} + 57868 q^{85} - 4544 q^{86} + 41328 q^{87} - 7936 q^{88} - 17604 q^{89} + 34992 q^{90} + 12352 q^{92} - 88128 q^{93} + 147744 q^{94} + 91592 q^{95} - 18432 q^{96} + 85176 q^{97} - 10044 q^{99}+O(q^{100}) \) 2 * q + 8 * q^2 - 18 * q^3 + 32 * q^4 + 108 * q^5 - 72 * q^6 + 128 * q^8 + 162 * q^9 + 432 * q^10 - 124 * q^11 - 288 * q^12 + 720 * q^13 - 972 * q^15 + 512 * q^16 + 612 * q^17 + 648 * q^18 + 2088 * q^19 + 1728 * q^20 - 496 * q^22 + 772 * q^23 - 1152 * q^24 - 318 * q^25 + 2880 * q^26 - 1458 * q^27 - 4592 * q^29 - 3888 * q^30 + 9792 * q^31 + 2048 * q^32 + 1116 * q^33 + 2448 * q^34 + 2592 * q^36 - 5992 * q^37 + 8352 * q^38 - 6480 * q^39 + 6912 * q^40 + 20196 * q^41 - 1136 * q^43 - 1984 * q^44 + 8748 * q^45 + 3088 * q^46 + 36936 * q^47 - 4608 * q^48 - 1272 * q^50 - 5508 * q^51 + 11520 * q^52 - 16708 * q^53 - 5832 * q^54 - 6336 * q^55 - 18792 * q^57 - 18368 * q^58 + 74592 * q^59 - 15552 * q^60 - 18648 * q^61 + 39168 * q^62 + 8192 * q^64 + 33300 * q^65 + 4464 * q^66 + 67344 * q^67 + 9792 * q^68 - 6948 * q^69 + 76548 * q^71 + 10368 * q^72 + 47304 * q^73 - 23968 * q^74 + 2862 * q^75 + 33408 * q^76 - 25920 * q^78 + 140656 * q^79 + 27648 * q^80 + 13122 * q^81 + 80784 * q^82 + 94104 * q^83 + 57868 * q^85 - 4544 * q^86 + 41328 * q^87 - 7936 * q^88 - 17604 * q^89 + 34992 * q^90 + 12352 * q^92 - 88128 * q^93 + 147744 * q^94 + 91592 * q^95 - 18432 * q^96 + 85176 * q^97 - 10044 * q^99

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