LMFDB - Embedded newform 726.6.a.bb.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [726,6,Mod(1,726)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(726, 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("726.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	726.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:	$116.438653184$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.8052400.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 288x^{2} + 20131 $ x^4 - 288*x^2 + 20131
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 11 $
Twist minimal:	no (minimal twist has level 66)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-12.9845$ of defining polynomial
Character	$\chi$	$=$	726.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -30.6488 q^{5} -36.0000 q^{6} +1.59188 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -30.6488 q^{5} -36.0000 q^{6} +1.59188 q^{7} -64.0000 q^{8} +81.0000 q^{9} +122.595 q^{10} +144.000 q^{12} +935.937 q^{13} -6.36753 q^{14} -275.839 q^{15} +256.000 q^{16} -394.404 q^{17} -324.000 q^{18} -2138.65 q^{19} -490.380 q^{20} +14.3269 q^{21} -90.5594 q^{23} -576.000 q^{24} -2185.65 q^{25} -3743.75 q^{26} +729.000 q^{27} +25.4701 q^{28} +1055.69 q^{29} +1103.36 q^{30} -4176.06 q^{31} -1024.00 q^{32} +1577.61 q^{34} -48.7892 q^{35} +1296.00 q^{36} +11518.7 q^{37} +8554.60 q^{38} +8423.43 q^{39} +1961.52 q^{40} +1330.00 q^{41} -57.3077 q^{42} +17727.1 q^{43} -2482.55 q^{45} +362.237 q^{46} -9985.30 q^{47} +2304.00 q^{48} -16804.5 q^{49} +8742.62 q^{50} -3549.63 q^{51} +14975.0 q^{52} -25413.3 q^{53} -2916.00 q^{54} -101.880 q^{56} -19247.8 q^{57} -4222.78 q^{58} -8581.00 q^{59} -4413.42 q^{60} +39347.3 q^{61} +16704.3 q^{62} +128.942 q^{63} +4096.00 q^{64} -28685.3 q^{65} +6661.08 q^{67} -6310.46 q^{68} -815.034 q^{69} +195.157 q^{70} +29210.4 q^{71} -5184.00 q^{72} -384.834 q^{73} -46075.0 q^{74} -19670.9 q^{75} -34218.4 q^{76} -33693.7 q^{78} +25707.5 q^{79} -7846.08 q^{80} +6561.00 q^{81} -5319.98 q^{82} -101629. q^{83} +229.231 q^{84} +12088.0 q^{85} -70908.4 q^{86} +9501.25 q^{87} -55800.4 q^{89} +9930.20 q^{90} +1489.90 q^{91} -1448.95 q^{92} -37584.6 q^{93} +39941.2 q^{94} +65546.9 q^{95} -9216.00 q^{96} -167341. q^{97} +67217.9 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} - 150 q^{5} - 144 q^{6} + 68 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) $ 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 - 150 * q^5 - 144 * q^6 + 68 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} - 150 q^{5} - 144 q^{6} + 68 q^{7} - 256 q^{8} + 324 q^{9} + 600 q^{10} + 576 q^{12} + 360 q^{13} - 272 q^{14} - 1350 q^{15} + 1024 q^{16} - 362 q^{17} - 1296 q^{18} + 1350 q^{19} - 2400 q^{20} + 612 q^{21} - 4972 q^{23} - 2304 q^{24} + 994 q^{25} - 1440 q^{26} + 2916 q^{27} + 1088 q^{28} - 2048 q^{29} + 5400 q^{30} - 10250 q^{31} - 4096 q^{32} + 1448 q^{34} + 22858 q^{35} + 5184 q^{36} + 2376 q^{37} - 5400 q^{38} + 3240 q^{39} + 9600 q^{40} - 14572 q^{41} - 2448 q^{42} + 35264 q^{43} - 12150 q^{45} + 19888 q^{46} - 25278 q^{47} + 9216 q^{48} + 40384 q^{49} - 3976 q^{50} - 3258 q^{51} + 5760 q^{52} - 27458 q^{53} - 11664 q^{54} - 4352 q^{56} + 12150 q^{57} + 8192 q^{58} - 27830 q^{59} - 21600 q^{60} + 82934 q^{61} + 41000 q^{62} + 5508 q^{63} + 16384 q^{64} - 58162 q^{65} - 91182 q^{67} - 5792 q^{68} - 44748 q^{69} - 91432 q^{70} - 89238 q^{71} - 20736 q^{72} + 61876 q^{73} - 9504 q^{74} + 8946 q^{75} + 21600 q^{76} - 12960 q^{78} + 100876 q^{79} - 38400 q^{80} + 26244 q^{81} + 58288 q^{82} - 14696 q^{83} + 9792 q^{84} - 130120 q^{85} - 141056 q^{86} - 18432 q^{87} - 172004 q^{89} + 48600 q^{90} - 286504 q^{91} - 79552 q^{92} - 92250 q^{93} + 101112 q^{94} + 97702 q^{95} - 36864 q^{96} - 303086 q^{97} - 161536 q^{98}+O(q^{100}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 - 150 * q^5 - 144 * q^6 + 68 * q^7 - 256 * q^8 + 324 * q^9 + 600 * q^10 + 576 * q^12 + 360 * q^13 - 272 * q^14 - 1350 * q^15 + 1024 * q^16 - 362 * q^17 - 1296 * q^18 + 1350 * q^19 - 2400 * q^20 + 612 * q^21 - 4972 * q^23 - 2304 * q^24 + 994 * q^25 - 1440 * q^26 + 2916 * q^27 + 1088 * q^28 - 2048 * q^29 + 5400 * q^30 - 10250 * q^31 - 4096 * q^32 + 1448 * q^34 + 22858 * q^35 + 5184 * q^36 + 2376 * q^37 - 5400 * q^38 + 3240 * q^39 + 9600 * q^40 - 14572 * q^41 - 2448 * q^42 + 35264 * q^43 - 12150 * q^45 + 19888 * q^46 - 25278 * q^47 + 9216 * q^48 + 40384 * q^49 - 3976 * q^50 - 3258 * q^51 + 5760 * q^52 - 27458 * q^53 - 11664 * q^54 - 4352 * q^56 + 12150 * q^57 + 8192 * q^58 - 27830 * q^59 - 21600 * q^60 + 82934 * q^61 + 41000 * q^62 + 5508 * q^63 + 16384 * q^64 - 58162 * q^65 - 91182 * q^67 - 5792 * q^68 - 44748 * q^69 - 91432 * q^70 - 89238 * q^71 - 20736 * q^72 + 61876 * q^73 - 9504 * q^74 + 8946 * q^75 + 21600 * q^76 - 12960 * q^78 + 100876 * q^79 - 38400 * q^80 + 26244 * q^81 + 58288 * q^82 - 14696 * q^83 + 9792 * q^84 - 130120 * q^85 - 141056 * q^86 - 18432 * q^87 - 172004 * q^89 + 48600 * q^90 - 286504 * q^91 - 79552 * q^92 - 92250 * q^93 + 101112 * q^94 + 97702 * q^95 - 36864 * q^96 - 303086 * q^97 - 161536 * q^98

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
$5$	−30.6488	−0.548262	−0.274131	−	0.961692i	$-0.588390\pi$
$5$	−30.6488	−0.548262	−0.274131	+	0.961692i	$0.588390\pi$
$6$	−36.0000	−0.408248
$7$	1.59188	0.0122791	0.00613954	−	0.999981i	$-0.498046\pi$
$7$	1.59188	0.0122791	0.00613954	+	0.999981i	$0.498046\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	122.595	0.387679
$11$	0	0
$11$	0	0
$12$	144.000	0.288675
$13$	935.937	1.53599	0.767995	−	0.640456i	$-0.221255\pi$
$13$	935.937	1.53599	0.767995	+	0.640456i	$0.221255\pi$
$14$	−6.36753	−0.00868262
$15$	−275.839	−0.316539
$16$	256.000	0.250000
$17$	−394.404	−0.330993	−0.165496	−	0.986210i	$-0.552923\pi$
$17$	−394.404	−0.330993	−0.165496	+	0.986210i	$0.552923\pi$
$18$	−324.000	−0.235702
$19$	−2138.65	−1.35911	−0.679557	−	0.733623i	$-0.737828\pi$
$19$	−2138.65	−1.35911	−0.679557	+	0.733623i	$0.737828\pi$
$20$	−490.380	−0.274131
$21$	14.3269	0.00708933
$22$	0	0
$23$	−90.5594	−0.0356955	−0.0178478	−	0.999841i	$-0.505681\pi$
$23$	−90.5594	−0.0356955	−0.0178478	+	0.999841i	$0.505681\pi$
$24$	−576.000	−0.204124
$25$	−2185.65	−0.699409
$26$	−3743.75	−1.08611
$27$	729.000	0.192450
$28$	25.4701	0.00613954
$29$	1055.69	0.233101	0.116550	−	0.993185i	$-0.462816\pi$
$29$	1055.69	0.233101	0.116550	+	0.993185i	$0.462816\pi$
$30$	1103.36	0.223827
$31$	−4176.06	−0.780482	−0.390241	−	0.920713i	$-0.627608\pi$
$31$	−4176.06	−0.780482	−0.390241	+	0.920713i	$0.627608\pi$
$32$	−1024.00	−0.176777
$33$	0	0
$34$	1577.61	0.234047
$35$	−48.7892	−0.00673215
$36$	1296.00	0.166667
$37$	11518.7	1.38325	0.691625	−	0.722257i	$-0.256895\pi$
$37$	11518.7	1.38325	0.691625	+	0.722257i	$0.256895\pi$
$38$	8554.60	0.961038
$39$	8423.43	0.886804
$40$	1961.52	0.193840
$41$	1330.00	0.123564	0.0617818	−	0.998090i	$-0.480322\pi$
$41$	1330.00	0.123564	0.0617818	+	0.998090i	$0.480322\pi$
$42$	−57.3077	−0.00501291
$43$	17727.1	1.46206	0.731032	−	0.682343i	$-0.239039\pi$
$43$	17727.1	1.46206	0.731032	+	0.682343i	$0.239039\pi$
$44$	0	0
$45$	−2482.55	−0.182754
$46$	362.237	0.0252405
$47$	−9985.30	−0.659351	−0.329675	−	0.944094i	$-0.606939\pi$
$47$	−9985.30	−0.659351	−0.329675	+	0.944094i	$0.606939\pi$
$48$	2304.00	0.144338
$49$	−16804.5	−0.999849
$50$	8742.62	0.494557
$51$	−3549.63	−0.191099
$52$	14975.0	0.767995
$53$	−25413.3	−1.24272	−0.621358	−	0.783527i	$-0.713419\pi$
$53$	−25413.3	−1.24272	−0.621358	+	0.783527i	$0.713419\pi$
$54$	−2916.00	−0.136083
$55$	0	0
$56$	−101.880	−0.00434131
$57$	−19247.8	−0.784684
$58$	−4222.78	−0.164827
$59$	−8581.00	−0.320928	−0.160464	−	0.987042i	$-0.551299\pi$
$59$	−8581.00	−0.320928	−0.160464	+	0.987042i	$0.551299\pi$
$60$	−4413.42	−0.158269
$61$	39347.3	1.35391	0.676956	−	0.736023i	$-0.263299\pi$
$61$	39347.3	1.35391	0.676956	+	0.736023i	$0.263299\pi$
$62$	16704.3	0.551884
$63$	128.942	0.00409303
$64$	4096.00	0.125000
$65$	−28685.3	−0.842124
$66$	0	0
$67$	6661.08	0.181283	0.0906417	−	0.995884i	$-0.471108\pi$
$67$	6661.08	0.181283	0.0906417	+	0.995884i	$0.471108\pi$
$68$	−6310.46	−0.165496
$69$	−815.034	−0.0206088
$70$	195.157	0.00476035
$71$	29210.4	0.687689	0.343844	−	0.939027i	$-0.388271\pi$
$71$	29210.4	0.687689	0.343844	+	0.939027i	$0.388271\pi$
$72$	−5184.00	−0.117851
$73$	−384.834	−0.00845214	−0.00422607	−	0.999991i	$-0.501345\pi$
$73$	−384.834	−0.00845214	−0.00422607	+	0.999991i	$0.501345\pi$
$74$	−46075.0	−0.978105
$75$	−19670.9	−0.403804
$76$	−34218.4	−0.679557
$77$	0	0
$78$	−33693.7	−0.627065
$79$	25707.5	0.463439	0.231720	−	0.972783i	$-0.425565\pi$
$79$	25707.5	0.463439	0.231720	+	0.972783i	$0.425565\pi$
$80$	−7846.08	−0.137065
$81$	6561.00	0.111111
$82$	−5319.98	−0.0873727
$83$	−101629.	−1.61928	−0.809642	−	0.586924i	$-0.800339\pi$
$83$	−101629.	−1.61928	−0.809642	+	0.586924i	$0.800339\pi$
$84$	229.231	0.00354466
$85$	12088.0	0.181471
$86$	−70908.4	−1.03384
$87$	9501.25	0.134581
$88$	0	0
$89$	−55800.4	−0.746728	−0.373364	−	0.927685i	$-0.621796\pi$
$89$	−55800.4	−0.746728	−0.373364	+	0.927685i	$0.621796\pi$
$90$	9930.20	0.129226
$91$	1489.90	0.0188605
$92$	−1448.95	−0.0178478
$93$	−37584.6	−0.450611
$94$	39941.2	0.466231
$95$	65546.9	0.745149
$96$	−9216.00	−0.102062
$97$	−167341.	−1.80582	−0.902909	−	0.429832i	$-0.858573\pi$
$97$	−167341.	−1.80582	−0.902909	+	0.429832i	$0.858573\pi$
$98$	67217.9	0.707000
$99$	0	0
$100$	−34970.5	−0.349705
$101$	37006.3	0.360971	0.180485	−	0.983578i	$-0.442233\pi$
$101$	37006.3	0.360971	0.180485	+	0.983578i	$0.442233\pi$
$102$	14198.5	0.135127
$103$	79070.2	0.734378	0.367189	−	0.930146i	$-0.380320\pi$
$103$	79070.2	0.734378	0.367189	+	0.930146i	$0.380320\pi$
$104$	−59900.0	−0.543054
$105$	−439.103	−0.00388681
$106$	101653.	0.878733
$107$	177733.	1.50075	0.750376	−	0.661011i	$-0.229872\pi$
$107$	177733.	1.50075	0.750376	+	0.661011i	$0.229872\pi$
$108$	11664.0	0.0962250
$109$	−19984.5	−0.161112	−0.0805560	−	0.996750i	$-0.525670\pi$
$109$	−19984.5	−0.161112	−0.0805560	+	0.996750i	$0.525670\pi$
$110$	0	0
$111$	103669.	0.798620
$112$	407.522	0.00306977
$113$	−209615.	−1.54428	−0.772139	−	0.635454i	$-0.780813\pi$
$113$	−209615.	−1.54428	−0.772139	+	0.635454i	$0.780813\pi$
$114$	76991.4	0.554856
$115$	2775.53	0.0195705
$116$	16891.1	0.116550
$117$	75810.9	0.511997
$118$	34324.0	0.226930
$119$	−627.844	−0.00406429
$120$	17653.7	0.111913
$121$	0	0
$122$	−157389.	−0.957361
$123$	11970.0	0.0713395
$124$	−66817.0	−0.390241
$125$	162765.	0.931721
$126$	−515.770	−0.00289421
$127$	−113445.	−0.624132	−0.312066	−	0.950060i	$-0.601021\pi$
$127$	−113445.	−0.624132	−0.312066	+	0.950060i	$0.601021\pi$
$128$	−16384.0	−0.0883883
$129$	159544.	0.844123
$130$	114741.	0.595472
$131$	−30840.5	−0.157015	−0.0785077	−	0.996914i	$-0.525016\pi$
$131$	−30840.5	−0.157015	−0.0785077	+	0.996914i	$0.525016\pi$
$132$	0	0
$133$	−3404.48	−0.0166887
$134$	−26644.3	−0.128187
$135$	−22342.9	−0.105513
$136$	25241.8	0.117024
$137$	−280642.	−1.27747	−0.638736	−	0.769426i	$-0.720542\pi$
$137$	−280642.	−1.27747	−0.638736	+	0.769426i	$0.720542\pi$
$138$	3260.14	0.0145726
$139$	204032.	0.895696	0.447848	−	0.894110i	$-0.352191\pi$
$139$	204032.	0.895696	0.447848	+	0.894110i	$0.352191\pi$
$140$	−780.627	−0.00336607
$141$	−89867.7	−0.380676
$142$	−116842.	−0.486269
$143$	0	0
$144$	20736.0	0.0833333
$145$	−32355.7	−0.127800
$146$	1539.34	0.00597657
$147$	−151240.	−0.577263
$148$	184300.	0.691625
$149$	239826.	0.884975	0.442488	−	0.896775i	$-0.354096\pi$
$149$	239826.	0.884975	0.442488	+	0.896775i	$0.354096\pi$
$150$	78683.5	0.285533
$151$	−479338.	−1.71080	−0.855400	−	0.517968i	$-0.826689\pi$
$151$	−479338.	−1.71080	−0.855400	+	0.517968i	$0.826689\pi$
$152$	136874.	0.480519
$153$	−31946.7	−0.110331
$154$	0	0
$155$	127991.	0.427908
$156$	134775.	0.443402
$157$	−137336.	−0.444669	−0.222334	−	0.974970i	$-0.571368\pi$
$157$	−137336.	−0.444669	−0.222334	+	0.974970i	$0.571368\pi$
$158$	−102830.	−0.327701
$159$	−228720.	−0.717482
$160$	31384.3	0.0969199
$161$	−144.160	−0.000438308 0
$162$	−26244.0	−0.0785674
$163$	−199958.	−0.589482	−0.294741	−	0.955577i	$-0.595233\pi$
$163$	−199958.	−0.589482	−0.294741	+	0.955577i	$0.595233\pi$
$164$	21279.9	0.0617818
$165$	0	0
$166$	406517.	1.14501
$167$	62887.3	0.174490	0.0872452	−	0.996187i	$-0.472194\pi$
$167$	62887.3	0.174490	0.0872452	+	0.996187i	$0.472194\pi$
$168$	−916.924	−0.00250646
$169$	504685.	1.35926
$170$	−48351.9	−0.128319
$171$	−173231.	−0.453038
$172$	283634.	0.731032
$173$	−599918.	−1.52397	−0.761985	−	0.647595i	$-0.775775\pi$
$173$	−599918.	−1.52397	−0.761985	+	0.647595i	$0.775775\pi$
$174$	−38005.0	−0.0951629
$175$	−3479.30	−0.00858810
$176$	0	0
$177$	−77229.0	−0.185288
$178$	223202.	0.528016
$179$	−106737.	−0.248991	−0.124496	−	0.992220i	$-0.539731\pi$
$179$	−106737.	−0.248991	−0.124496	+	0.992220i	$0.539731\pi$
$180$	−39720.8	−0.0913769
$181$	−181668.	−0.412176	−0.206088	−	0.978534i	$-0.566073\pi$
$181$	−181668.	−0.412176	−0.206088	+	0.978534i	$0.566073\pi$
$182$	−5959.61	−0.0133364
$183$	354126.	0.781682
$184$	5795.80	0.0126203
$185$	−353035.	−0.758383
$186$	150338.	0.318630
$187$	0	0
$188$	−159765.	−0.329675
$189$	1160.48	0.00236311
$190$	−262188.	−0.526900
$191$	−370816.	−0.735487	−0.367743	−	0.929927i	$-0.619869\pi$
$191$	−370816.	−0.735487	−0.367743	+	0.929927i	$0.619869\pi$
$192$	36864.0	0.0721688
$193$	−201284.	−0.388971	−0.194485	−	0.980905i	$-0.562304\pi$
$193$	−201284.	−0.388971	−0.194485	+	0.980905i	$0.562304\pi$
$194$	669365.	1.27691
$195$	−258168.	−0.486201
$196$	−268871.	−0.499925
$197$	−329001.	−0.603992	−0.301996	−	0.953309i	$-0.597653\pi$
$197$	−329001.	−0.603992	−0.301996	+	0.953309i	$0.597653\pi$
$198$	0	0
$199$	729463.	1.30578	0.652891	−	0.757452i	$-0.273556\pi$
$199$	729463.	1.30578	0.652891	+	0.757452i	$0.273556\pi$
$200$	139882.	0.247279
$201$	59949.8	0.104664
$202$	−148025.	−0.255245
$203$	1680.54	0.00286226
$204$	−56794.1	−0.0955494
$205$	−40762.7	−0.0677452
$206$	−316281.	−0.519284
$207$	−7335.31	−0.0118985
$208$	239600.	0.383997
$209$	0	0
$210$	1756.41	0.00274839
$211$	591312.	0.914347	0.457173	−	0.889378i	$-0.348862\pi$
$211$	591312.	0.914347	0.457173	+	0.889378i	$0.348862\pi$
$212$	−406613.	−0.621358
$213$	262894.	0.397037
$214$	−710932.	−1.06119
$215$	−543313.	−0.801594
$216$	−46656.0	−0.0680414
$217$	−6647.80	−0.00958360
$218$	79938.1	0.113923
$219$	−3463.51	−0.00487985
$220$	0	0
$221$	−369137.	−0.508402
$222$	−414675.	−0.564709
$223$	−641078.	−0.863274	−0.431637	−	0.902047i	$-0.642064\pi$
$223$	−641078.	−0.863274	−0.431637	+	0.902047i	$0.642064\pi$
$224$	−1630.09	−0.00217065
$225$	−177038.	−0.233136
$226$	838458.	1.09197
$227$	401846.	0.517601	0.258800	−	0.965931i	$-0.416673\pi$
$227$	401846.	0.517601	0.258800	+	0.965931i	$0.416673\pi$
$228$	−307966.	−0.392342
$229$	338688.	0.426786	0.213393	−	0.976966i	$-0.431548\pi$
$229$	338688.	0.426786	0.213393	+	0.976966i	$0.431548\pi$
$230$	−11102.1	−0.0138384
$231$	0	0
$232$	−67564.5	−0.0824135
$233$	−1.16272e6	−1.40309	−0.701543	−	0.712627i	$-0.747505\pi$
$233$	−1.16272e6	−1.40309	−0.701543	+	0.712627i	$0.747505\pi$
$234$	−303244.	−0.362036
$235$	306037.	0.361497
$236$	−137296.	−0.160464
$237$	231368.	0.267567
$238$	2511.38	0.00287389
$239$	−1.07347e6	−1.21561	−0.607805	−	0.794087i	$-0.707950\pi$
$239$	−1.07347e6	−1.21561	−0.607805	+	0.794087i	$0.707950\pi$
$240$	−70614.7	−0.0791347
$241$	−859568.	−0.953318	−0.476659	−	0.879088i	$-0.658152\pi$
$241$	−859568.	−0.953318	−0.476659	+	0.879088i	$0.658152\pi$
$242$	0	0
$243$	59049.0	0.0641500
$244$	629557.	0.676956
$245$	515036.	0.548179
$246$	−47879.8	−0.0504446
$247$	−2.00164e6	−2.08758
$248$	267268.	0.275942
$249$	−914663.	−0.934894
$250$	−651060.	−0.658826
$251$	−850739.	−0.852338	−0.426169	−	0.904644i	$-0.640137\pi$
$251$	−850739.	−0.852338	−0.426169	+	0.904644i	$0.640137\pi$
$252$	2063.08	0.00204651
$253$	0	0
$254$	453781.	0.441328
$255$	108792.	0.104772
$256$	65536.0	0.0625000
$257$	−1.94444e6	−1.83638	−0.918188	−	0.396144i	$-0.870348\pi$
$257$	−1.94444e6	−1.83638	−0.918188	+	0.396144i	$0.870348\pi$
$258$	−638176.	−0.596885
$259$	18336.5	0.0169850
$260$	−458965.	−0.421062
$261$	85511.3	0.0777002
$262$	123362.	0.111027
$263$	−2.00871e6	−1.79072	−0.895360	−	0.445342i	$-0.853082\pi$
$263$	−2.00871e6	−1.79072	−0.895360	+	0.445342i	$0.853082\pi$
$264$	0	0
$265$	778887.	0.681333
$266$	13617.9	0.0118007
$267$	−502204.	−0.431123
$268$	106577.	0.0906417
$269$	−1.77751e6	−1.49772	−0.748862	−	0.662726i	$-0.769400\pi$
$269$	−1.77751e6	−1.49772	−0.748862	+	0.662726i	$0.769400\pi$
$270$	89371.8	0.0746089
$271$	−184785.	−0.152842	−0.0764210	−	0.997076i	$-0.524349\pi$
$271$	−184785.	−0.152842	−0.0764210	+	0.997076i	$0.524349\pi$
$272$	−100967.	−0.0827482
$273$	13409.1	0.0108891
$274$	1.12257e6	0.903309
$275$	0	0
$276$	−13040.5	−0.0103044
$277$	1.43700e6	1.12527	0.562637	−	0.826704i	$-0.309787\pi$
$277$	1.43700e6	1.12527	0.562637	+	0.826704i	$0.309787\pi$
$278$	−816127.	−0.633353
$279$	−338261.	−0.260161
$280$	3122.51	0.00238017
$281$	199179.	0.150479	0.0752397	−	0.997165i	$-0.476028\pi$
$281$	199179.	0.150479	0.0752397	+	0.997165i	$0.476028\pi$
$282$	359471.	0.269179
$283$	−1.38955e6	−1.03136	−0.515679	−	0.856782i	$-0.672460\pi$
$283$	−1.38955e6	−1.03136	−0.515679	+	0.856782i	$0.672460\pi$
$284$	467367.	0.343844
$285$	589922.	0.430212
$286$	0	0
$287$	2117.20	0.00151725
$288$	−82944.0	−0.0589256
$289$	−1.26430e6	−0.890444
$290$	129423.	0.0903683
$291$	−1.50607e6	−1.04259
$292$	−6157.35	−0.00422607
$293$	2.27270e6	1.54658	0.773290	−	0.634052i	$-0.218610\pi$
$293$	2.27270e6	1.54658	0.773290	+	0.634052i	$0.218610\pi$
$294$	604961.	0.408187
$295$	262997.	0.175953
$296$	−737199.	−0.489053
$297$	0	0
$298$	−959305.	−0.625772
$299$	−84757.9	−0.0548280
$300$	−314734.	−0.201902
$301$	28219.4	0.0179528
$302$	1.91735e6	1.20972
$303$	333057.	0.208407
$304$	−547494.	−0.339778
$305$	−1.20595e6	−0.742298
$306$	127787.	0.0780158
$307$	−2.98610e6	−1.80825	−0.904125	−	0.427268i	$-0.859476\pi$
$307$	−2.98610e6	−1.80825	−0.904125	+	0.427268i	$0.859476\pi$
$308$	0	0
$309$	711632.	0.423993
$310$	−511965.	−0.302577
$311$	873086.	0.511866	0.255933	−	0.966695i	$-0.417617\pi$
$311$	873086.	0.511866	0.255933	+	0.966695i	$0.417617\pi$
$312$	−539100.	−0.313533
$313$	497931.	0.287282	0.143641	−	0.989630i	$-0.454119\pi$
$313$	497931.	0.287282	0.143641	+	0.989630i	$0.454119\pi$
$314$	549345.	0.314428
$315$	−3951.92	−0.00224405
$316$	411321.	0.231720
$317$	−2.74182e6	−1.53247	−0.766234	−	0.642562i	$-0.777872\pi$
$317$	−2.74182e6	−1.53247	−0.766234	+	0.642562i	$0.777872\pi$
$318$	914880.	0.507337
$319$	0	0
$320$	−125537.	−0.0685327
$321$	1.59960e6	0.866460
$322$	576.639	0.000309931 0
$323$	843491.	0.449857
$324$	104976.	0.0555556
$325$	−2.04563e6	−1.07429
$326$	799834.	0.416827
$327$	−179861.	−0.0930180
$328$	−85119.7	−0.0436863
$329$	−15895.4	−0.00809622
$330$	0	0
$331$	−3.59901e6	−1.80557	−0.902783	−	0.430097i	$-0.858479\pi$
$331$	−3.59901e6	−1.80557	−0.902783	+	0.430097i	$0.858479\pi$
$332$	−1.62607e6	−0.809642
$333$	933018.	0.461083
$334$	−251549.	−0.123383
$335$	−204154.	−0.0993907
$336$	3667.70	0.00177233
$337$	1.38633e6	0.664956	0.332478	−	0.943111i	$-0.392115\pi$
$337$	1.38633e6	0.664956	0.332478	+	0.943111i	$0.392115\pi$
$338$	−2.01874e6	−0.961145
$339$	−1.88653e6	−0.891589
$340$	193408.	0.0907353
$341$	0	0
$342$	692922.	0.320346
$343$	−53505.5	−0.0245563
$344$	−1.13453e6	−0.516918
$345$	24979.8	0.0112990
$346$	2.39967e6	1.07761
$347$	1.31626e6	0.586838	0.293419	−	0.955984i	$-0.405207\pi$
$347$	1.31626e6	0.586838	0.293419	+	0.955984i	$0.405207\pi$
$348$	152020.	0.0672903
$349$	2.01266e6	0.884520	0.442260	−	0.896887i	$-0.354177\pi$
$349$	2.01266e6	0.884520	0.442260	+	0.896887i	$0.354177\pi$
$350$	13917.2	0.00607270
$351$	682298.	0.295601
$352$	0	0
$353$	−1.49229e6	−0.637407	−0.318703	−	0.947854i	$-0.603247\pi$
$353$	−1.49229e6	−0.637407	−0.318703	+	0.947854i	$0.603247\pi$
$354$	308916.	0.131018
$355$	−895263.	−0.377033
$356$	−892806.	−0.373364
$357$	−5650.60	−0.00234652
$358$	426949.	0.176063
$359$	−4.23116e6	−1.73270	−0.866351	−	0.499436i	$-0.833540\pi$
$359$	−4.23116e6	−1.73270	−0.866351	+	0.499436i	$0.833540\pi$
$360$	158883.	0.0646132
$361$	2.09772e6	0.847189
$362$	726672.	0.291452
$363$	0	0
$364$	23838.4	0.00943027
$365$	11794.7	0.00463398
$366$	−1.41650e6	−0.552732
$367$	3.40149e6	1.31827	0.659134	−	0.752026i	$-0.270923\pi$
$367$	3.40149e6	1.31827	0.659134	+	0.752026i	$0.270923\pi$
$368$	−23183.2	−0.00892388
$369$	107730.	0.0411879
$370$	1.41214e6	0.536258
$371$	−40455.0	−0.0152594
$372$	−601353.	−0.225306
$373$	−3.01172e6	−1.12084	−0.560418	−	0.828210i	$-0.689360\pi$
$373$	−3.01172e6	−1.12084	−0.560418	+	0.828210i	$0.689360\pi$
$374$	0	0
$375$	1.46488e6	0.537929
$376$	639059.	0.233116
$377$	988064.	0.358040
$378$	−4641.93	−0.00167097
$379$	−1.78261e6	−0.637470	−0.318735	−	0.947844i	$-0.603258\pi$
$379$	−1.78261e6	−0.637470	−0.318735	+	0.947844i	$0.603258\pi$
$380$	1.04875e6	0.372575
$381$	−1.02101e6	−0.360343
$382$	1.48326e6	0.520068
$383$	5.43959e6	1.89483	0.947413	−	0.320013i	$-0.103687\pi$
$383$	5.43959e6	1.89483	0.947413	+	0.320013i	$0.103687\pi$
$384$	−147456.	−0.0510310
$385$	0	0
$386$	805138.	0.275044
$387$	1.43590e6	0.487355
$388$	−2.67746e6	−0.902909
$389$	3.58835e6	1.20232	0.601161	−	0.799128i	$-0.294705\pi$
$389$	3.58835e6	1.20232	0.601161	+	0.799128i	$0.294705\pi$
$390$	1.03267e6	0.343796
$391$	35716.9	0.0118150
$392$	1.07549e6	0.353500
$393$	−277564.	−0.0906529
$394$	1.31600e6	0.427087
$395$	−787904.	−0.254086
$396$	0	0
$397$	5.21167e6	1.65959	0.829795	−	0.558069i	$-0.188457\pi$
$397$	5.21167e6	1.65959	0.829795	+	0.558069i	$0.188457\pi$
$398$	−2.91785e6	−0.923328
$399$	−30640.3	−0.00963520
$400$	−559527.	−0.174852
$401$	−641775.	−0.199307	−0.0996533	−	0.995022i	$-0.531773\pi$
$401$	−641775.	−0.199307	−0.0996533	+	0.995022i	$0.531773\pi$
$402$	−239799.	−0.0740086
$403$	−3.90853e6	−1.19881
$404$	592101.	0.180485
$405$	−201086.	−0.0609179
$406$	−6722.17	−0.00202392
$407$	0	0
$408$	227177.	0.0675636
$409$	5.08445e6	1.50292	0.751460	−	0.659778i	$-0.229350\pi$
$409$	5.08445e6	1.50292	0.751460	+	0.659778i	$0.229350\pi$
$410$	163051.	0.0479031
$411$	−2.52578e6	−0.737548
$412$	1.26512e6	0.367189
$413$	−13659.9	−0.00394070
$414$	29341.2	0.00841352
$415$	3.11481e6	0.887791
$416$	−958400.	−0.271527
$417$	1.83629e6	0.517130
$418$	0	0
$419$	−2.44419e6	−0.680143	−0.340072	−	0.940400i	$-0.610451\pi$
$419$	−2.44419e6	−0.680143	−0.340072	+	0.940400i	$0.610451\pi$
$420$	−7025.64	−0.00194340
$421$	5.36407e6	1.47499	0.737495	−	0.675353i	$-0.236009\pi$
$421$	5.36407e6	1.47499	0.737495	+	0.675353i	$0.236009\pi$
$422$	−2.36525e6	−0.646541
$423$	−808809.	−0.219784
$424$	1.62645e6	0.439366
$425$	862030.	0.231500
$426$	−1.05158e6	−0.280748
$427$	62636.3	0.0166248
$428$	2.84373e6	0.750376
$429$	0	0
$430$	2.17325e6	0.566812
$431$	−5.49234e6	−1.42418	−0.712089	−	0.702089i	$-0.752251\pi$
$431$	−5.49234e6	−1.42418	−0.712089	+	0.702089i	$0.752251\pi$
$432$	186624.	0.0481125
$433$	−106167.	−0.0272126	−0.0136063	−	0.999907i	$-0.504331\pi$
$433$	−106167.	−0.0272126	−0.0136063	+	0.999907i	$0.504331\pi$
$434$	26591.2	0.00677663
$435$	−291202.	−0.0737854
$436$	−319753.	−0.0805560
$437$	193675.	0.0485143
$438$	13854.0	0.00345057
$439$	4.59366e6	1.13762	0.568811	−	0.822469i	$-0.307404\pi$
$439$	4.59366e6	1.13762	0.568811	+	0.822469i	$0.307404\pi$
$440$	0	0
$441$	−1.36116e6	−0.333283
$442$	1.47655e6	0.359494
$443$	4.98339e6	1.20647	0.603234	−	0.797564i	$-0.293878\pi$
$443$	4.98339e6	1.20647	0.603234	+	0.797564i	$0.293878\pi$
$444$	1.65870e6	0.399310
$445$	1.71021e6	0.409402
$446$	2.56431e6	0.610427
$447$	2.15844e6	0.510941
$448$	6520.35	0.00153488
$449$	−6.30470e6	−1.47587	−0.737935	−	0.674872i	$-0.764199\pi$
$449$	−6.30470e6	−1.47587	−0.737935	+	0.674872i	$0.764199\pi$
$450$	708152.	0.164852
$451$	0	0
$452$	−3.35383e6	−0.772139
$453$	−4.31404e6	−0.987731
$454$	−1.60738e6	−0.365999
$455$	−45663.6	−0.0103405
$456$	1.23186e6	0.277428
$457$	−8.04543e6	−1.80202	−0.901008	−	0.433802i	$-0.857172\pi$
$457$	−8.04543e6	−1.80202	−0.901008	+	0.433802i	$0.857172\pi$
$458$	−1.35475e6	−0.301784
$459$	−287520.	−0.0636996
$460$	44408.5	0.00978524
$461$	−1.76141e6	−0.386018	−0.193009	−	0.981197i	$-0.561825\pi$
$461$	−1.76141e6	−0.386018	−0.193009	+	0.981197i	$0.561825\pi$
$462$	0	0
$463$	−2.64405e6	−0.573214	−0.286607	−	0.958048i	$-0.592527\pi$
$463$	−2.64405e6	−0.573214	−0.286607	+	0.958048i	$0.592527\pi$
$464$	270258.	0.0582751
$465$	1.15192e6	0.247053
$466$	4.65087e6	0.992132
$467$	8.12766e6	1.72454	0.862270	−	0.506448i	$-0.169042\pi$
$467$	8.12766e6	1.72454	0.862270	+	0.506448i	$0.169042\pi$
$468$	1.21297e6	0.255998
$469$	10603.7	0.00222599
$470$	−1.22415e6	−0.255617
$471$	−1.23603e6	−0.256729
$472$	549184.	0.113465
$473$	0	0
$474$	−925472.	−0.189198
$475$	4.67435e6	0.950576
$476$	−10045.5	−0.00203214
$477$	−2.05848e6	−0.414239
$478$	4.29387e6	0.859566
$479$	−5.61347e6	−1.11787	−0.558937	−	0.829210i	$-0.688791\pi$
$479$	−5.61347e6	−1.11787	−0.558937	+	0.829210i	$0.688791\pi$
$480$	282459.	0.0559567
$481$	1.07808e7	2.12466
$482$	3.43827e6	0.674098
$483$	−1297.44	−0.000253057 0
$484$	0	0
$485$	5.12880e6	0.990060
$486$	−236196.	−0.0453609
$487$	4.81250e6	0.919494	0.459747	−	0.888050i	$-0.347940\pi$
$487$	4.81250e6	0.919494	0.459747	+	0.888050i	$0.347940\pi$
$488$	−2.51823e6	−0.478680
$489$	−1.79963e6	−0.340338
$490$	−2.06014e6	−0.387621
$491$	3.89670e6	0.729446	0.364723	−	0.931116i	$-0.381164\pi$
$491$	3.89670e6	0.729446	0.364723	+	0.931116i	$0.381164\pi$
$492$	191519.	0.0356697
$493$	−416370.	−0.0771546
$494$	8.00657e6	1.47614
$495$	0	0
$496$	−1.06907e6	−0.195120
$497$	46499.5	0.00844419
$498$	3.65865e6	0.661070
$499$	8.26693e6	1.48625	0.743126	−	0.669151i	$-0.233342\pi$
$499$	8.26693e6	1.48625	0.743126	+	0.669151i	$0.233342\pi$
$500$	2.60424e6	0.465860
$501$	565985.	0.100742
$502$	3.40295e6	0.602694
$503$	5.42357e6	0.955797	0.477899	−	0.878415i	$-0.341399\pi$
$503$	5.42357e6	0.955797	0.477899	+	0.878415i	$0.341399\pi$
$504$	−8252.32	−0.00144710
$505$	−1.13420e6	−0.197906
$506$	0	0
$507$	4.54217e6	0.784772
$508$	−1.81512e6	−0.312066
$509$	4.13731e6	0.707821	0.353910	−	0.935279i	$-0.384852\pi$
$509$	4.13731e6	0.707821	0.353910	+	0.935279i	$0.384852\pi$
$510$	−435167.	−0.0740851
$511$	−612.611	−0.000103785 0
$512$	−262144.	−0.0441942
$513$	−1.55908e6	−0.261561
$514$	7.77776e6	1.29851
$515$	−2.42340e6	−0.402631
$516$	2.55270e6	0.422062
$517$	0	0
$518$	−73345.9	−0.0120102
$519$	−5.39926e6	−0.879865
$520$	1.83586e6	0.297736
$521$	−5.96732e6	−0.963130	−0.481565	−	0.876411i	$-0.659931\pi$
$521$	−5.96732e6	−0.963130	−0.481565	+	0.876411i	$0.659931\pi$
$522$	−342045.	−0.0549423
$523$	−5.74212e6	−0.917947	−0.458974	−	0.888450i	$-0.651783\pi$
$523$	−5.74212e6	−0.917947	−0.458974	+	0.888450i	$0.651783\pi$
$524$	−493447.	−0.0785077
$525$	−31313.7	−0.00495834
$526$	8.03484e6	1.26623
$527$	1.64706e6	0.258334
$528$	0	0
$529$	−6.42814e6	−0.998726
$530$	−3.11555e6	−0.481775
$531$	−695061.	−0.106976
$532$	−54471.6	−0.00834433
$533$	1.24479e6	0.189792
$534$	2.00881e6	0.304850
$535$	−5.44730e6	−0.822805
$536$	−426309.	−0.0640933
$537$	−960636.	−0.143755
$538$	7.11005e6	1.05905
$539$	0	0
$540$	−357487.	−0.0527565
$541$	−5.87557e6	−0.863092	−0.431546	−	0.902091i	$-0.642032\pi$
$541$	−5.87557e6	−0.863092	−0.431546	+	0.902091i	$0.642032\pi$
$542$	739139.	0.108076
$543$	−1.63501e6	−0.237970
$544$	403869.	0.0585118
$545$	612501.	0.0883315
$546$	−53636.4	−0.00769978
$547$	−7.35228e6	−1.05064	−0.525320	−	0.850905i	$-0.676054\pi$
$547$	−7.35228e6	−1.05064	−0.525320	+	0.850905i	$0.676054\pi$
$548$	−4.49027e6	−0.638736
$549$	3.18713e6	0.451304
$550$	0	0
$551$	−2.25776e6	−0.316810
$552$	52162.2	0.00728632
$553$	40923.4	0.00569061
$554$	−5.74801e6	−0.795689
$555$	−3.17731e6	−0.437852
$556$	3.26451e6	0.447848
$557$	−8.20787e6	−1.12097	−0.560483	−	0.828166i	$-0.689384\pi$
$557$	−8.20787e6	−1.12097	−0.560483	+	0.828166i	$0.689384\pi$
$558$	1.35304e6	0.183961
$559$	1.65915e7	2.24572
$560$	−12490.0	−0.00168304
$561$	0	0
$562$	−796715.	−0.106405
$563$	−701186.	−0.0932314	−0.0466157	−	0.998913i	$-0.514844\pi$
$563$	−701186.	−0.0932314	−0.0466157	+	0.998913i	$0.514844\pi$
$564$	−1.43788e6	−0.190338
$565$	6.42442e6	0.846668
$566$	5.55822e6	0.729280
$567$	10444.3	0.00136434
$568$	−1.86947e6	−0.243135
$569$	7.70015e6	0.997053	0.498527	−	0.866874i	$-0.333875\pi$
$569$	7.70015e6	0.997053	0.498527	+	0.866874i	$0.333875\pi$
$570$	−2.35969e6	−0.304206
$571$	−9.38506e6	−1.20461	−0.602306	−	0.798266i	$-0.705751\pi$
$571$	−9.38506e6	−1.20461	−0.602306	+	0.798266i	$0.705751\pi$
$572$	0	0
$573$	−3.33734e6	−0.424633
$574$	−8468.78	−0.00107286
$575$	197931.	0.0249658
$576$	331776.	0.0416667
$577$	1.15237e7	1.44096	0.720481	−	0.693474i	$-0.243921\pi$
$577$	1.15237e7	1.44096	0.720481	+	0.693474i	$0.243921\pi$
$578$	5.05721e6	0.629639
$579$	−1.81156e6	−0.224572
$580$	−517692.	−0.0639000
$581$	−161782.	−0.0198833
$582$	6.02429e6	0.737222
$583$	0	0
$584$	24629.4	0.00298828
$585$	−2.32351e6	−0.280708
$586$	−9.09079e6	−1.09360
$587$	−1.30019e7	−1.55744	−0.778721	−	0.627371i	$-0.784131\pi$
$587$	−1.30019e7	−1.55744	−0.778721	+	0.627371i	$0.784131\pi$
$588$	−2.41984e6	−0.288632
$589$	8.93114e6	1.06076
$590$	−1.05199e6	−0.124417
$591$	−2.96100e6	−0.348715
$592$	2.94880e6	0.345812
$593$	5.36206e6	0.626173	0.313087	−	0.949725i	$-0.398637\pi$
$593$	5.36206e6	0.626173	0.313087	+	0.949725i	$0.398637\pi$
$594$	0	0
$595$	19242.6	0.00222829
$596$	3.83722e6	0.442488
$597$	6.56517e6	0.753894
$598$	339031.	0.0387692
$599$	−7.35088e6	−0.837090	−0.418545	−	0.908196i	$-0.637460\pi$
$599$	−7.35088e6	−0.837090	−0.418545	+	0.908196i	$0.637460\pi$
$600$	1.25894e6	0.142766
$601$	−1.36159e7	−1.53766	−0.768832	−	0.639451i	$-0.779162\pi$
$601$	−1.36159e7	−1.53766	−0.768832	+	0.639451i	$0.779162\pi$
$602$	−112878.	−0.0126945
$603$	539548.	0.0604278
$604$	−7.66940e6	−0.855400
$605$	0	0
$606$	−1.33223e6	−0.147366
$607$	224378.	0.0247177	0.0123589	−	0.999924i	$-0.496066\pi$
$607$	224378.	0.0247177	0.0123589	+	0.999924i	$0.496066\pi$
$608$	2.18998e6	0.240260
$609$	15124.9	0.00165253
$610$	4.82378e6	0.524884
$611$	−9.34561e6	−1.01276
$612$	−511147.	−0.0551655
$613$	1.03984e7	1.11767	0.558836	−	0.829278i	$-0.311248\pi$
$613$	1.03984e7	1.11767	0.558836	+	0.829278i	$0.311248\pi$
$614$	1.19444e7	1.27863
$615$	−366864.	−0.0391127
$616$	0	0
$617$	−5.76529e6	−0.609688	−0.304844	−	0.952402i	$-0.598604\pi$
$617$	−5.76529e6	−0.609688	−0.304844	+	0.952402i	$0.598604\pi$
$618$	−2.84653e6	−0.299809
$619$	1.18149e7	1.23937	0.619686	−	0.784850i	$-0.287260\pi$
$619$	1.18149e7	1.23937	0.619686	+	0.784850i	$0.287260\pi$
$620$	2.04786e6	0.213954
$621$	−66017.8	−0.00686961
$622$	−3.49235e6	−0.361944
$623$	−88827.6	−0.00916913
$624$	2.15640e6	0.221701
$625$	1.84163e6	0.188583
$626$	−1.99172e6	−0.203139
$627$	0	0
$628$	−2.19738e6	−0.222334
$629$	−4.54303e6	−0.457846
$630$	15807.7	0.00158678
$631$	1.00792e7	1.00775	0.503877	−	0.863775i	$-0.331906\pi$
$631$	1.00792e7	1.00775	0.503877	+	0.863775i	$0.331906\pi$
$632$	−1.64528e6	−0.163851
$633$	5.32181e6	0.527898
$634$	1.09673e7	1.08362
$635$	3.47695e6	0.342188
$636$	−3.65952e6	−0.358741
$637$	−1.57279e7	−1.53576
$638$	0	0
$639$	2.36604e6	0.229230
$640$	502149.	0.0484599
$641$	549446.	0.0528178	0.0264089	−	0.999651i	$-0.491593\pi$
$641$	549446.	0.0528178	0.0264089	+	0.999651i	$0.491593\pi$
$642$	−6.39839e6	−0.612679
$643$	1.60686e7	1.53268	0.766338	−	0.642437i	$-0.222077\pi$
$643$	1.60686e7	1.53268	0.766338	+	0.642437i	$0.222077\pi$
$644$	−2306.56	−0.000219154 0
$645$	−4.88982e6	−0.462800
$646$	−3.37397e6	−0.318097
$647$	−1.35520e7	−1.27275	−0.636373	−	0.771381i	$-0.719566\pi$
$647$	−1.35520e7	−1.27275	−0.636373	+	0.771381i	$0.719566\pi$
$648$	−419904.	−0.0392837
$649$	0	0
$650$	8.18254e6	0.759635
$651$	−59830.2	−0.00553309
$652$	−3.19934e6	−0.294741
$653$	3.99537e6	0.366669	0.183334	−	0.983051i	$-0.441311\pi$
$653$	3.99537e6	0.366669	0.183334	+	0.983051i	$0.441311\pi$
$654$	719443.	0.0657737
$655$	945221.	0.0860855
$656$	340479.	0.0308909
$657$	−31171.6	−0.00281738
$658$	63581.7	0.00572489
$659$	2.14695e7	1.92578	0.962892	−	0.269889i	$-0.0869868\pi$
$659$	2.14695e7	1.92578	0.962892	+	0.269889i	$0.0869868\pi$
$660$	0	0
$661$	6.17516e6	0.549724	0.274862	−	0.961484i	$-0.411368\pi$
$661$	6.17516e6	0.549724	0.274862	+	0.961484i	$0.411368\pi$
$662$	1.43960e7	1.27673
$663$	−3.32223e6	−0.293526
$664$	6.50427e6	0.572504
$665$	104343.	0.00914975
$666$	−3.73207e6	−0.326035
$667$	−95603.0	−0.00832065
$668$	1.00620e6	0.0872452
$669$	−5.76970e6	−0.498412
$670$	816616.	0.0702798
$671$	0	0
$672$	−14670.8	−0.00125323
$673$	2.32597e7	1.97955	0.989776	−	0.142632i	$-0.0455564\pi$
$673$	2.32597e7	1.97955	0.989776	+	0.142632i	$0.0455564\pi$
$674$	−5.54533e6	−0.470195
$675$	−1.59334e6	−0.134601
$676$	8.07496e6	0.679632
$677$	1.77561e6	0.148894	0.0744470	−	0.997225i	$-0.476281\pi$
$677$	1.77561e6	0.148894	0.0744470	+	0.997225i	$0.476281\pi$
$678$	7.54612e6	0.630448
$679$	−266388.	−0.0221738
$680$	−773631.	−0.0641596
$681$	3.61661e6	0.298837
$682$	0	0
$683$	4.78941e6	0.392853	0.196426	−	0.980519i	$-0.437066\pi$
$683$	4.78941e6	0.392853	0.196426	+	0.980519i	$0.437066\pi$
$684$	−2.77169e6	−0.226519
$685$	8.60132e6	0.700388
$686$	214022.	0.0173639
$687$	3.04819e6	0.246405
$688$	4.53814e6	0.365516
$689$	−2.37853e7	−1.90880
$690$	−99919.1	−0.00798962
$691$	5.00709e6	0.398924	0.199462	−	0.979906i	$-0.436081\pi$
$691$	5.00709e6	0.398924	0.199462	+	0.979906i	$0.436081\pi$
$692$	−9.59868e6	−0.761985
$693$	0	0
$694$	−5.26504e6	−0.414957
$695$	−6.25332e6	−0.491076
$696$	−608080.	−0.0475815
$697$	−524555.	−0.0408987
$698$	−8.05066e6	−0.625450
$699$	−1.04645e7	−0.810072
$700$	−55668.8	−0.00429405
$701$	−3.77795e6	−0.290376	−0.145188	−	0.989404i	$-0.546379\pi$
$701$	−3.77795e6	−0.290376	−0.145188	+	0.989404i	$0.546379\pi$
$702$	−2.72919e6	−0.209022
$703$	−2.46345e7	−1.87999
$704$	0	0
$705$	2.75433e6	0.208710
$706$	5.96916e6	0.450715
$707$	58909.6	0.00443239
$708$	−1.23566e6	−0.0926440
$709$	1.99946e6	0.149381	0.0746907	−	0.997207i	$-0.476203\pi$
$709$	1.99946e6	0.149381	0.0746907	+	0.997207i	$0.476203\pi$
$710$	3.58105e6	0.266603
$711$	2.08231e6	0.154480
$712$	3.57123e6	0.264008
$713$	378182.	0.0278597
$714$	22602.4	0.00165924
$715$	0	0
$716$	−1.70780e6	−0.124496
$717$	−9.66121e6	−0.701832
$718$	1.69247e7	1.22520
$719$	9.72481e6	0.701551	0.350775	−	0.936460i	$-0.385918\pi$
$719$	9.72481e6	0.701551	0.350775	+	0.936460i	$0.385918\pi$
$720$	−635533.	−0.0456885
$721$	125870.	0.00901749
$722$	−8.39089e6	−0.599053
$723$	−7.73611e6	−0.550398
$724$	−2.90669e6	−0.206088
$725$	−2.30738e6	−0.163033
$726$	0	0
$727$	−4.16302e6	−0.292127	−0.146064	−	0.989275i	$-0.546660\pi$
$727$	−4.16302e6	−0.292127	−0.146064	+	0.989275i	$0.546660\pi$
$728$	−95353.7	−0.00666821
$729$	531441.	0.0370370
$730$	−47178.8	−0.00327672
$731$	−6.99163e6	−0.483933
$732$	5.66601e6	0.390841
$733$	−9.11162e6	−0.626377	−0.313188	−	0.949691i	$-0.601397\pi$
$733$	−9.11162e6	−0.626377	−0.313188	+	0.949691i	$0.601397\pi$
$734$	−1.36059e7	−0.932156
$735$	4.63532e6	0.316491
$736$	92732.8	0.00631014
$737$	0	0
$738$	−430919.	−0.0291242
$739$	1.13353e7	0.763523	0.381762	−	0.924261i	$-0.375317\pi$
$739$	1.13353e7	0.763523	0.381762	+	0.924261i	$0.375317\pi$
$740$	−5.64856e6	−0.379191
$741$	−1.80148e7	−1.20527
$742$	161820.	0.0107900
$743$	1.22060e7	0.811150	0.405575	−	0.914062i	$-0.367071\pi$
$743$	1.22060e7	0.811150	0.405575	+	0.914062i	$0.367071\pi$
$744$	2.40541e6	0.159315
$745$	−7.35038e6	−0.485198
$746$	1.20469e7	0.792551
$747$	−8.23196e6	−0.539762
$748$	0	0
$749$	282930.	0.0184278
$750$	−5.85954e6	−0.380373
$751$	−2.07578e7	−1.34301	−0.671507	−	0.740998i	$-0.734353\pi$
$751$	−2.07578e7	−1.34301	−0.671507	+	0.740998i	$0.734353\pi$
$752$	−2.55624e6	−0.164838
$753$	−7.65665e6	−0.492098
$754$	−3.95226e6	−0.253173
$755$	1.46911e7	0.937966
$756$	18567.7	0.00118155
$757$	1.79946e7	1.14131	0.570653	−	0.821192i	$-0.306690\pi$
$757$	1.79946e7	1.14131	0.570653	+	0.821192i	$0.306690\pi$
$758$	7.13046e6	0.450759
$759$	0	0
$760$	−4.19500e6	−0.263450
$761$	−1.66788e7	−1.04401	−0.522003	−	0.852943i	$-0.674815\pi$
$761$	−1.66788e7	−1.04401	−0.522003	+	0.852943i	$0.674815\pi$
$762$	4.08403e6	0.254801
$763$	−31813.0	−0.00197831
$764$	−5.93305e6	−0.367743
$765$	979126.	0.0604902
$766$	−2.17584e7	−1.33984
$767$	−8.03127e6	−0.492942
$768$	589824.	0.0360844
$769$	−1.10319e7	−0.672718	−0.336359	−	0.941734i	$-0.609196\pi$
$769$	−1.10319e7	−0.672718	−0.336359	+	0.941734i	$0.609196\pi$
$770$	0	0
$771$	−1.75000e7	−1.06023
$772$	−3.22055e6	−0.194485
$773$	−3.43596e6	−0.206823	−0.103412	−	0.994639i	$-0.532976\pi$
$773$	−3.43596e6	−0.206823	−0.103412	+	0.994639i	$0.532976\pi$
$774$	−5.74358e6	−0.344612
$775$	9.12743e6	0.545876
$776$	1.07098e7	0.638453
$777$	165028.	0.00980631
$778$	−1.43534e7	−0.850170
$779$	−2.84439e6	−0.167937
$780$	−4.13068e6	−0.243100
$781$	0	0
$782$	−142868.	−0.00835444
$783$	769601.	0.0448602
$784$	−4.30194e6	−0.249962
$785$	4.20919e6	0.243795
$786$	1.11026e6	0.0641013
$787$	−1.14455e7	−0.658717	−0.329359	−	0.944205i	$-0.606832\pi$
$787$	−1.14455e7	−0.658717	−0.329359	+	0.944205i	$0.606832\pi$
$788$	−5.26401e6	−0.301996
$789$	−1.80784e7	−1.03387
$790$	3.15162e6	0.179666
$791$	−333682.	−0.0189623
$792$	0	0
$793$	3.68266e7	2.07960
$794$	−2.08467e7	−1.17351
$795$	7.00998e6	0.393368
$796$	1.16714e7	0.652891
$797$	−3.15709e7	−1.76052	−0.880259	−	0.474493i	$-0.842631\pi$
$797$	−3.15709e7	−1.76052	−0.880259	+	0.474493i	$0.842631\pi$
$798$	122561.	0.00681312
$799$	3.93824e6	0.218240
$800$	2.23811e6	0.123639
$801$	−4.51983e6	−0.248909
$802$	2.56710e6	0.140931
$803$	0	0
$804$	959196.	0.0523320
$805$	4418.32	0.000240307 0
$806$	1.56341e7	0.847688
$807$	−1.59976e7	−0.864712
$808$	−2.36840e6	−0.127622
$809$	3.31409e6	0.178030	0.0890148	−	0.996030i	$-0.471628\pi$
$809$	3.31409e6	0.178030	0.0890148	+	0.996030i	$0.471628\pi$
$810$	804346.	0.0430755
$811$	7.61602e6	0.406608	0.203304	−	0.979116i	$-0.434832\pi$
$811$	7.61602e6	0.406608	0.203304	+	0.979116i	$0.434832\pi$
$812$	26888.7	0.00143113
$813$	−1.66306e6	−0.0882434
$814$	0	0
$815$	6.12848e6	0.323190
$816$	−908706.	−0.0477747
$817$	−3.79121e7	−1.98711
$818$	−2.03378e7	−1.06273
$819$	120682.	0.00628685
$820$	−652203.	−0.0338726
$821$	3.12518e7	1.61815	0.809073	−	0.587708i	$-0.199970\pi$
$821$	3.12518e7	1.61815	0.809073	+	0.587708i	$0.199970\pi$
$822$	1.01031e7	0.521525
$823$	1.24276e7	0.639570	0.319785	−	0.947490i	$-0.396389\pi$
$823$	1.24276e7	0.639570	0.319785	+	0.947490i	$0.396389\pi$
$824$	−5.06049e6	−0.259642
$825$	0	0
$826$	54639.7	0.00278650
$827$	2.78542e7	1.41621	0.708104	−	0.706108i	$-0.249551\pi$
$827$	2.78542e7	1.41621	0.708104	+	0.706108i	$0.249551\pi$
$828$	−117365.	−0.00594925
$829$	727915.	0.0367870	0.0183935	−	0.999831i	$-0.494145\pi$
$829$	727915.	0.0367870	0.0183935	+	0.999831i	$0.494145\pi$
$830$	−1.24592e7	−0.627763
$831$	1.29330e7	0.649677
$832$	3.83360e6	0.191999
$833$	6.62774e6	0.330943
$834$	−7.34514e6	−0.365666
$835$	−1.92742e6	−0.0956664
$836$	0	0
$837$	−3.04435e6	−0.150204
$838$	9.77677e6	0.480934
$839$	−1.25803e7	−0.617000	−0.308500	−	0.951224i	$-0.599827\pi$
$839$	−1.25803e7	−0.617000	−0.308500	+	0.951224i	$0.599827\pi$
$840$	28102.6	0.00137419
$841$	−1.93967e7	−0.945664
$842$	−2.14563e7	−1.04297
$843$	1.79261e6	0.0868793
$844$	9.46100e6	0.457173
$845$	−1.54680e7	−0.745232
$846$	3.23524e6	0.155410
$847$	0	0
$848$	−6.50581e6	−0.310679
$849$	−1.25060e7	−0.595455
$850$	−3.44812e6	−0.163695
$851$	−1.04313e6	−0.0493758
$852$	4.20630e6	0.198519
$853$	−2.47398e6	−0.116419	−0.0582095	−	0.998304i	$-0.518539\pi$
$853$	−2.47398e6	−0.116419	−0.0582095	+	0.998304i	$0.518539\pi$
$854$	−250545.	−0.0117555
$855$	5.30930e6	0.248383
$856$	−1.13749e7	−0.530596
$857$	3.29116e7	1.53072	0.765362	−	0.643600i	$-0.222560\pi$
$857$	3.29116e7	1.53072	0.765362	+	0.643600i	$0.222560\pi$
$858$	0	0
$859$	−1.12463e7	−0.520028	−0.260014	−	0.965605i	$-0.583727\pi$
$859$	−1.12463e7	−0.520028	−0.260014	+	0.965605i	$0.583727\pi$
$860$	−8.69302e6	−0.400797
$861$	19054.8	0.000875983 0
$862$	2.19694e7	1.00705
$863$	−2.01704e7	−0.921910	−0.460955	−	0.887424i	$-0.652493\pi$
$863$	−2.01704e7	−0.921910	−0.460955	+	0.887424i	$0.652493\pi$
$864$	−746496.	−0.0340207
$865$	1.83867e7	0.835534
$866$	424669.	0.0192422
$867$	−1.13787e7	−0.514098
$868$	−106365.	−0.00479180
$869$	0	0
$870$	1.16481e6	0.0521742
$871$	6.23436e6	0.278449
$872$	1.27901e6	0.0569617
$873$	−1.35546e7	−0.601939
$874$	−774699.	−0.0343048
$875$	259103.	0.0114407
$876$	−55416.2	−0.00243992
$877$	−2.04223e7	−0.896613	−0.448307	−	0.893880i	$-0.647973\pi$
$877$	−2.04223e7	−0.896613	−0.448307	+	0.893880i	$0.647973\pi$
$878$	−1.83746e7	−0.804420
$879$	2.04543e7	0.892919
$880$	0	0
$881$	4.49818e6	0.195253	0.0976263	−	0.995223i	$-0.468875\pi$
$881$	4.49818e6	0.195253	0.0976263	+	0.995223i	$0.468875\pi$
$882$	5.44465e6	0.235667
$883$	3.81825e6	0.164802	0.0824009	−	0.996599i	$-0.473741\pi$
$883$	3.81825e6	0.164802	0.0824009	+	0.996599i	$0.473741\pi$
$884$	−5.90619e6	−0.254201
$885$	2.36697e6	0.101586
$886$	−1.99336e7	−0.853102
$887$	2.15429e7	0.919380	0.459690	−	0.888080i	$-0.347961\pi$
$887$	2.15429e7	0.919380	0.459690	+	0.888080i	$0.347961\pi$
$888$	−6.63479e6	−0.282355
$889$	−180591.	−0.00766377
$890$	−6.84085e6	−0.289491
$891$	0	0
$892$	−1.02573e7	−0.431637
$893$	2.13551e7	0.896132
$894$	−8.63375e6	−0.361290
$895$	3.27137e6	0.136512
$896$	−26081.4	−0.00108533
$897$	−762821.	−0.0316549
$898$	2.52188e7	1.04360
$899$	−4.40865e6	−0.181931
$900$	−2.83261e6	−0.116568
$901$	1.00231e7	0.411330
$902$	0	0
$903$	253975.	0.0103651
$904$	1.34153e7	0.545984
$905$	5.56790e6	0.225980
$906$	1.72562e7	0.698431
$907$	−6.62481e6	−0.267396	−0.133698	−	0.991022i	$-0.542685\pi$
$907$	−6.62481e6	−0.267396	−0.133698	+	0.991022i	$0.542685\pi$
$908$	6.42954e6	0.258800
$909$	2.99751e6	0.120324
$910$	182654.	0.00731184
$911$	−3.05177e7	−1.21830	−0.609152	−	0.793053i	$-0.708490\pi$
$911$	−3.05177e7	−1.21830	−0.609152	+	0.793053i	$0.708490\pi$
$912$	−4.92745e6	−0.196171
$913$	0	0
$914$	3.21817e7	1.27422
$915$	−1.08535e7	−0.428566
$916$	5.41900e6	0.213393
$917$	−49094.4	−0.00192801
$918$	1.15008e6	0.0450424
$919$	1.55296e7	0.606556	0.303278	−	0.952902i	$-0.401919\pi$
$919$	1.55296e7	0.606556	0.303278	+	0.952902i	$0.401919\pi$
$920$	−177634.	−0.00691921
$921$	−2.68749e7	−1.04399
$922$	7.04564e6	0.272956
$923$	2.73391e7	1.05628
$924$	0	0
$925$	−2.51760e7	−0.967458
$926$	1.05762e7	0.405324
$927$	6.40469e6	0.244793
$928$	−1.08103e6	−0.0412068
$929$	4.76935e7	1.81309	0.906546	−	0.422108i	$-0.138710\pi$
$929$	4.76935e7	1.81309	0.906546	+	0.422108i	$0.138710\pi$
$930$	−4.60768e6	−0.174693
$931$	3.59389e7	1.35891
$932$	−1.86035e7	−0.701543
$933$	7.85778e6	0.295526
$934$	−3.25106e7	−1.21943
$935$	0	0
$936$	−4.85190e6	−0.181018
$937$	−1.43460e7	−0.533805	−0.266902	−	0.963724i	$-0.586000\pi$
$937$	−1.43460e7	−0.533805	−0.266902	+	0.963724i	$0.586000\pi$
$938$	−42414.6	−0.00157401
$939$	4.48138e6	0.165862
$940$	4.89659e6	0.180748
$941$	−2.95359e7	−1.08737	−0.543683	−	0.839291i	$-0.682971\pi$
$941$	−2.95359e7	−1.08737	−0.543683	+	0.839291i	$0.682971\pi$
$942$	4.94411e6	0.181535
$943$	−120444.	−0.00441067
$944$	−2.19674e6	−0.0802320
$945$	−35567.3	−0.00129560
$946$	0	0
$947$	1.69481e7	0.614109	0.307054	−	0.951692i	$-0.400657\pi$
$947$	1.69481e7	0.614109	0.307054	+	0.951692i	$0.400657\pi$
$948$	3.70189e6	0.133783
$949$	−360181.	−0.0129824
$950$	−1.86974e7	−0.672159
$951$	−2.46764e7	−0.884771
$952$	40182.0	0.00143694
$953$	3.48842e7	1.24422	0.622109	−	0.782930i	$-0.286276\pi$
$953$	3.48842e7	1.24422	0.622109	+	0.782930i	$0.286276\pi$
$954$	8.23392e6	0.292911
$955$	1.13650e7	0.403239
$956$	−1.71755e7	−0.607805
$957$	0	0
$958$	2.24539e7	0.790456
$959$	−446749.	−0.0156862
$960$	−1.12984e6	−0.0395674
$961$	−1.11896e7	−0.390848
$962$	−4.31233e7	−1.50236
$963$	1.43964e7	0.500251
$964$	−1.37531e7	−0.476659
$965$	6.16912e6	0.213258
$966$	5189.75	0.000178939 0
$967$	−4.59896e6	−0.158159	−0.0790794	−	0.996868i	$-0.525198\pi$
$967$	−4.59896e6	−0.158159	−0.0790794	+	0.996868i	$0.525198\pi$
$968$	0	0
$969$	7.59142e6	0.259725
$970$	−2.05152e7	−0.700078
$971$	−2.43140e7	−0.827578	−0.413789	−	0.910373i	$-0.635795\pi$
$971$	−2.43140e7	−0.827578	−0.413789	+	0.910373i	$0.635795\pi$
$972$	944784.	0.0320750
$973$	324794.	0.0109983
$974$	−1.92500e7	−0.650180
$975$	−1.84107e7	−0.620239
$976$	1.00729e7	0.338478
$977$	4.17905e6	0.140069	0.0700344	−	0.997545i	$-0.477689\pi$
$977$	4.17905e6	0.140069	0.0700344	+	0.997545i	$0.477689\pi$
$978$	7.19850e6	0.240655
$979$	0	0
$980$	8.24057e6	0.274089
$981$	−1.61875e6	−0.0537040
$982$	−1.55868e7	−0.515796
$983$	3.74303e7	1.23549	0.617746	−	0.786378i	$-0.288046\pi$
$983$	3.74303e7	1.23549	0.617746	+	0.786378i	$0.288046\pi$
$984$	−766078.	−0.0252223
$985$	1.00835e7	0.331145
$986$	1.66548e6	0.0545566
$987$	−143059.	−0.00467435
$988$	−3.20263e7	−1.04379
$989$	−1.60535e6	−0.0521892
$990$	0	0
$991$	−4.60166e7	−1.48844	−0.744218	−	0.667937i	$-0.767178\pi$
$991$	−4.60166e7	−1.48844	−0.744218	+	0.667937i	$0.767178\pi$
$992$	4.27629e6	0.137971
$993$	−3.23911e7	−1.04244
$994$	−185998.	−0.00597094
$995$	−2.23571e7	−0.715910
$996$	−1.46346e7	−0.467447
$997$	−2.49411e7	−0.794652	−0.397326	−	0.917677i	$-0.630062\pi$
$997$	−2.49411e7	−0.794652	−0.397326	+	0.917677i	$0.630062\pi$
$998$	−3.30677e7	−1.05094
$999$	8.39716e6	0.266207

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.6.a.bb.1.2		4
11.7	odd	10		66.6.e.a.49.1	yes	8
11.8	odd	10		66.6.e.a.31.1	✓	8
11.10	odd	2		726.6.a.be.1.2		4
33.8	even	10		198.6.f.c.163.2		8
33.29	even	10		198.6.f.c.181.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.6.e.a.31.1	✓	8	11.8	odd	10
66.6.e.a.49.1	yes	8	11.7	odd	10
198.6.f.c.163.2		8	33.8	even	10
198.6.f.c.181.2		8	33.29	even	10
726.6.a.bb.1.2		4	1.1	even	1	trivial
726.6.a.be.1.2		4	11.10	odd	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:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	726.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -30.6488 q^{5} -36.0000 q^{6} +1.59188 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -30.6488 q^{5} -36.0000 q^{6} +1.59188 q^{7} -64.0000 q^{8} +81.0000 q^{9} +122.595 q^{10} +144.000 q^{12} +935.937 q^{13} -6.36753 q^{14} -275.839 q^{15} +256.000 q^{16} -394.404 q^{17} -324.000 q^{18} -2138.65 q^{19} -490.380 q^{20} +14.3269 q^{21} -90.5594 q^{23} -576.000 q^{24} -2185.65 q^{25} -3743.75 q^{26} +729.000 q^{27} +25.4701 q^{28} +1055.69 q^{29} +1103.36 q^{30} -4176.06 q^{31} -1024.00 q^{32} +1577.61 q^{34} -48.7892 q^{35} +1296.00 q^{36} +11518.7 q^{37} +8554.60 q^{38} +8423.43 q^{39} +1961.52 q^{40} +1330.00 q^{41} -57.3077 q^{42} +17727.1 q^{43} -2482.55 q^{45} +362.237 q^{46} -9985.30 q^{47} +2304.00 q^{48} -16804.5 q^{49} +8742.62 q^{50} -3549.63 q^{51} +14975.0 q^{52} -25413.3 q^{53} -2916.00 q^{54} -101.880 q^{56} -19247.8 q^{57} -4222.78 q^{58} -8581.00 q^{59} -4413.42 q^{60} +39347.3 q^{61} +16704.3 q^{62} +128.942 q^{63} +4096.00 q^{64} -28685.3 q^{65} +6661.08 q^{67} -6310.46 q^{68} -815.034 q^{69} +195.157 q^{70} +29210.4 q^{71} -5184.00 q^{72} -384.834 q^{73} -46075.0 q^{74} -19670.9 q^{75} -34218.4 q^{76} -33693.7 q^{78} +25707.5 q^{79} -7846.08 q^{80} +6561.00 q^{81} -5319.98 q^{82} -101629. q^{83} +229.231 q^{84} +12088.0 q^{85} -70908.4 q^{86} +9501.25 q^{87} -55800.4 q^{89} +9930.20 q^{90} +1489.90 q^{91} -1448.95 q^{92} -37584.6 q^{93} +39941.2 q^{94} +65546.9 q^{95} -9216.00 q^{96} -167341. q^{97} +67217.9 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} - 150 q^{5} - 144 q^{6} + 68 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 - 150 * q^5 - 144 * q^6 + 68 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} - 150 q^{5} - 144 q^{6} + 68 q^{7} - 256 q^{8} + 324 q^{9} + 600 q^{10} + 576 q^{12} + 360 q^{13} - 272 q^{14} - 1350 q^{15} + 1024 q^{16} - 362 q^{17} - 1296 q^{18} + 1350 q^{19} - 2400 q^{20} + 612 q^{21} - 4972 q^{23} - 2304 q^{24} + 994 q^{25} - 1440 q^{26} + 2916 q^{27} + 1088 q^{28} - 2048 q^{29} + 5400 q^{30} - 10250 q^{31} - 4096 q^{32} + 1448 q^{34} + 22858 q^{35} + 5184 q^{36} + 2376 q^{37} - 5400 q^{38} + 3240 q^{39} + 9600 q^{40} - 14572 q^{41} - 2448 q^{42} + 35264 q^{43} - 12150 q^{45} + 19888 q^{46} - 25278 q^{47} + 9216 q^{48} + 40384 q^{49} - 3976 q^{50} - 3258 q^{51} + 5760 q^{52} - 27458 q^{53} - 11664 q^{54} - 4352 q^{56} + 12150 q^{57} + 8192 q^{58} - 27830 q^{59} - 21600 q^{60} + 82934 q^{61} + 41000 q^{62} + 5508 q^{63} + 16384 q^{64} - 58162 q^{65} - 91182 q^{67} - 5792 q^{68} - 44748 q^{69} - 91432 q^{70} - 89238 q^{71} - 20736 q^{72} + 61876 q^{73} - 9504 q^{74} + 8946 q^{75} + 21600 q^{76} - 12960 q^{78} + 100876 q^{79} - 38400 q^{80} + 26244 q^{81} + 58288 q^{82} - 14696 q^{83} + 9792 q^{84} - 130120 q^{85} - 141056 q^{86} - 18432 q^{87} - 172004 q^{89} + 48600 q^{90} - 286504 q^{91} - 79552 q^{92} - 92250 q^{93} + 101112 q^{94} + 97702 q^{95} - 36864 q^{96} - 303086 q^{97} - 161536 q^{98}+O(q^{100}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 - 150 * q^5 - 144 * q^6 + 68 * q^7 - 256 * q^8 + 324 * q^9 + 600 * q^10 + 576 * q^12 + 360 * q^13 - 272 * q^14 - 1350 * q^15 + 1024 * q^16 - 362 * q^17 - 1296 * q^18 + 1350 * q^19 - 2400 * q^20 + 612 * q^21 - 4972 * q^23 - 2304 * q^24 + 994 * q^25 - 1440 * q^26 + 2916 * q^27 + 1088 * q^28 - 2048 * q^29 + 5400 * q^30 - 10250 * q^31 - 4096 * q^32 + 1448 * q^34 + 22858 * q^35 + 5184 * q^36 + 2376 * q^37 - 5400 * q^38 + 3240 * q^39 + 9600 * q^40 - 14572 * q^41 - 2448 * q^42 + 35264 * q^43 - 12150 * q^45 + 19888 * q^46 - 25278 * q^47 + 9216 * q^48 + 40384 * q^49 - 3976 * q^50 - 3258 * q^51 + 5760 * q^52 - 27458 * q^53 - 11664 * q^54 - 4352 * q^56 + 12150 * q^57 + 8192 * q^58 - 27830 * q^59 - 21600 * q^60 + 82934 * q^61 + 41000 * q^62 + 5508 * q^63 + 16384 * q^64 - 58162 * q^65 - 91182 * q^67 - 5792 * q^68 - 44748 * q^69 - 91432 * q^70 - 89238 * q^71 - 20736 * q^72 + 61876 * q^73 - 9504 * q^74 + 8946 * q^75 + 21600 * q^76 - 12960 * q^78 + 100876 * q^79 - 38400 * q^80 + 26244 * q^81 + 58288 * q^82 - 14696 * q^83 + 9792 * q^84 - 130120 * q^85 - 141056 * q^86 - 18432 * q^87 - 172004 * q^89 + 48600 * q^90 - 286504 * q^91 - 79552 * q^92 - 92250 * q^93 + 101112 * q^94 + 97702 * q^95 - 36864 * q^96 - 303086 * q^97 - 161536 * q^98

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