LMFDB - Embedded newform 726.6.a.bb.1.3

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			1.3
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)

$f(q)$	$=$	$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -10.8102 q^{5} -36.0000 q^{6} +229.182 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -10.8102 q^{5} -36.0000 q^{6} +229.182 q^{7} -64.0000 q^{8} +81.0000 q^{9} +43.2409 q^{10} +144.000 q^{12} -903.518 q^{13} -916.728 q^{14} -97.2921 q^{15} +256.000 q^{16} -763.758 q^{17} -324.000 q^{18} +2270.29 q^{19} -172.964 q^{20} +2062.64 q^{21} +2828.01 q^{23} -576.000 q^{24} -3008.14 q^{25} +3614.07 q^{26} +729.000 q^{27} +3666.91 q^{28} -6972.21 q^{29} +389.168 q^{30} -7337.38 q^{31} -1024.00 q^{32} +3055.03 q^{34} -2477.51 q^{35} +1296.00 q^{36} -10540.9 q^{37} -9081.14 q^{38} -8131.66 q^{39} +691.855 q^{40} -6102.66 q^{41} -8250.56 q^{42} +2029.16 q^{43} -875.629 q^{45} -11312.1 q^{46} -20218.0 q^{47} +2304.00 q^{48} +35717.4 q^{49} +12032.6 q^{50} -6873.82 q^{51} -14456.3 q^{52} -18442.2 q^{53} -2916.00 q^{54} -14667.7 q^{56} +20432.6 q^{57} +27888.8 q^{58} +8759.93 q^{59} -1556.67 q^{60} +25412.8 q^{61} +29349.5 q^{62} +18563.8 q^{63} +4096.00 q^{64} +9767.23 q^{65} -44383.4 q^{67} -12220.1 q^{68} +25452.1 q^{69} +9910.04 q^{70} -80387.8 q^{71} -5184.00 q^{72} +74385.0 q^{73} +42163.7 q^{74} -27073.3 q^{75} +36324.6 q^{76} +32526.6 q^{78} +29426.2 q^{79} -2767.42 q^{80} +6561.00 q^{81} +24410.6 q^{82} -2401.93 q^{83} +33002.2 q^{84} +8256.40 q^{85} -8116.66 q^{86} -62749.9 q^{87} -36838.3 q^{89} +3502.51 q^{90} -207070. q^{91} +45248.2 q^{92} -66036.4 q^{93} +80872.1 q^{94} -24542.3 q^{95} -9216.00 q^{96} -63691.6 q^{97} -142870. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−10.8102	−0.193379	−0.0966896	−	0.995315i	$-0.530825\pi$
$5$	−10.8102	−0.193379	−0.0966896	+	0.995315i	$0.530825\pi$
$6$	−36.0000	−0.408248
$7$	229.182	1.76781	0.883905	−	0.467666i	$-0.154905\pi$
$7$	229.182	1.76781	0.883905	+	0.467666i	$0.154905\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	43.2409	0.136740
$11$	0	0
$11$	0	0
$12$	144.000	0.288675
$13$	−903.518	−1.48279	−0.741393	−	0.671072i	$-0.765834\pi$
$13$	−903.518	−1.48279	−0.741393	+	0.671072i	$0.765834\pi$
$14$	−916.728	−1.25003
$15$	−97.2921	−0.111648
$16$	256.000	0.250000
$17$	−763.758	−0.640964	−0.320482	−	0.947255i	$-0.603845\pi$
$17$	−763.758	−0.640964	−0.320482	+	0.947255i	$0.603845\pi$
$18$	−324.000	−0.235702
$19$	2270.29	1.44277	0.721384	−	0.692535i	$-0.243506\pi$
$19$	2270.29	1.44277	0.721384	+	0.692535i	$0.243506\pi$
$20$	−172.964	−0.0966896
$21$	2062.64	1.02065
$22$	0	0
$23$	2828.01	1.11471	0.557355	−	0.830274i	$-0.311816\pi$
$23$	2828.01	1.11471	0.557355	+	0.830274i	$0.311816\pi$
$24$	−576.000	−0.204124
$25$	−3008.14	−0.962604
$26$	3614.07	1.04849
$27$	729.000	0.192450
$28$	3666.91	0.883905
$29$	−6972.21	−1.53949	−0.769743	−	0.638354i	$-0.779615\pi$
$29$	−6972.21	−1.53949	−0.769743	+	0.638354i	$0.779615\pi$
$30$	389.168	0.0789468
$31$	−7337.38	−1.37131	−0.685657	−	0.727925i	$-0.740485\pi$
$31$	−7337.38	−1.37131	−0.685657	+	0.727925i	$0.740485\pi$
$32$	−1024.00	−0.176777
$33$	0	0
$34$	3055.03	0.453230
$35$	−2477.51	−0.341858
$36$	1296.00	0.166667
$37$	−10540.9	−1.26583	−0.632914	−	0.774222i	$-0.718141\pi$
$37$	−10540.9	−1.26583	−0.632914	+	0.774222i	$0.718141\pi$
$38$	−9081.14	−1.02019
$39$	−8131.66	−0.856086
$40$	691.855	0.0683699
$41$	−6102.66	−0.566969	−0.283484	−	0.958977i	$-0.591490\pi$
$41$	−6102.66	−0.566969	−0.283484	+	0.958977i	$0.591490\pi$
$42$	−8250.56	−0.721705
$43$	2029.16	0.167358	0.0836789	−	0.996493i	$-0.473333\pi$
$43$	2029.16	0.167358	0.0836789	+	0.996493i	$0.473333\pi$
$44$	0	0
$45$	−875.629	−0.0644598
$46$	−11312.1	−0.788219
$47$	−20218.0	−1.33504	−0.667519	−	0.744592i	$-0.732644\pi$
$47$	−20218.0	−1.33504	−0.667519	+	0.744592i	$0.732644\pi$
$48$	2304.00	0.144338
$49$	35717.4	2.12515
$50$	12032.6	0.680664
$51$	−6873.82	−0.370061
$52$	−14456.3	−0.741393
$53$	−18442.2	−0.901828	−0.450914	−	0.892567i	$-0.648902\pi$
$53$	−18442.2	−0.901828	−0.450914	+	0.892567i	$0.648902\pi$
$54$	−2916.00	−0.136083
$55$	0	0
$56$	−14667.7	−0.625015
$57$	20432.6	0.832982
$58$	27888.8	1.08858
$59$	8759.93	0.327620	0.163810	−	0.986492i	$-0.447622\pi$
$59$	8759.93	0.327620	0.163810	+	0.986492i	$0.447622\pi$
$60$	−1556.67	−0.0558238
$61$	25412.8	0.874436	0.437218	−	0.899356i	$-0.355964\pi$
$61$	25412.8	0.874436	0.437218	+	0.899356i	$0.355964\pi$
$62$	29349.5	0.969665
$63$	18563.8	0.589270
$64$	4096.00	0.125000
$65$	9767.23	0.286740
$66$	0	0
$67$	−44383.4	−1.20791	−0.603953	−	0.797020i	$-0.706409\pi$
$67$	−44383.4	−1.20791	−0.603953	+	0.797020i	$0.706409\pi$
$68$	−12220.1	−0.320482
$69$	25452.1	0.643578
$70$	9910.04	0.241730
$71$	−80387.8	−1.89254	−0.946268	−	0.323382i	$-0.895180\pi$
$71$	−80387.8	−1.89254	−0.946268	+	0.323382i	$0.895180\pi$
$72$	−5184.00	−0.117851
$73$	74385.0	1.63372	0.816861	−	0.576834i	$-0.195712\pi$
$73$	74385.0	1.63372	0.816861	+	0.576834i	$0.195712\pi$
$74$	42163.7	0.895075
$75$	−27073.3	−0.555760
$76$	36324.6	0.721384
$77$	0	0
$78$	32526.6	0.605345
$79$	29426.2	0.530477	0.265238	−	0.964183i	$-0.414549\pi$
$79$	29426.2	0.530477	0.265238	+	0.964183i	$0.414549\pi$
$80$	−2767.42	−0.0483448
$81$	6561.00	0.111111
$82$	24410.6	0.400908
$83$	−2401.93	−0.0382707	−0.0191353	−	0.999817i	$-0.506091\pi$
$83$	−2401.93	−0.0382707	−0.0191353	+	0.999817i	$0.506091\pi$
$84$	33002.2	0.510323
$85$	8256.40	0.123949
$86$	−8116.66	−0.118340
$87$	−62749.9	−0.888822
$88$	0	0
$89$	−36838.3	−0.492974	−0.246487	−	0.969146i	$-0.579276\pi$
$89$	−36838.3	−0.492974	−0.246487	+	0.969146i	$0.579276\pi$
$90$	3502.51	0.0455799
$91$	−207070.	−2.62128
$92$	45248.2	0.557355
$93$	−66036.4	−0.791729
$94$	80872.1	0.944015
$95$	−24542.3	−0.279001
$96$	−9216.00	−0.102062
$97$	−63691.6	−0.687311	−0.343655	−	0.939096i	$-0.611665\pi$
$97$	−63691.6	−0.687311	−0.343655	+	0.939096i	$0.611665\pi$
$98$	−142870.	−1.50271
$99$	0	0
$100$	−48130.2	−0.481302
$101$	−28724.5	−0.280188	−0.140094	−	0.990138i	$-0.544741\pi$
$101$	−28724.5	−0.280188	−0.140094	+	0.990138i	$0.544741\pi$
$102$	27495.3	0.261672
$103$	72496.2	0.673321	0.336660	−	0.941626i	$-0.390703\pi$
$103$	72496.2	0.673321	0.336660	+	0.941626i	$0.390703\pi$
$104$	57825.1	0.524244
$105$	−22297.6	−0.197372
$106$	73768.9	0.637689
$107$	27700.3	0.233897	0.116949	−	0.993138i	$-0.462689\pi$
$107$	27700.3	0.233897	0.116949	+	0.993138i	$0.462689\pi$
$108$	11664.0	0.0962250
$109$	53898.2	0.434518	0.217259	−	0.976114i	$-0.430288\pi$
$109$	53898.2	0.434518	0.217259	+	0.976114i	$0.430288\pi$
$110$	0	0
$111$	−94868.4	−0.730826
$112$	58670.6	0.441953
$113$	120624.	0.888665	0.444332	−	0.895862i	$-0.353441\pi$
$113$	120624.	0.888665	0.444332	+	0.895862i	$0.353441\pi$
$114$	−81730.3	−0.589007
$115$	−30571.5	−0.215562
$116$	−111555.	−0.769743
$117$	−73184.9	−0.494262
$118$	−35039.7	−0.231663
$119$	−175040.	−1.13310
$120$	6226.69	0.0394734
$121$	0	0
$122$	−101651.	−0.618320
$123$	−54923.9	−0.327340
$124$	−117398.	−0.685657
$125$	66300.6	0.379527
$126$	−74255.0	−0.416677
$127$	72961.2	0.401405	0.200703	−	0.979652i	$-0.435678\pi$
$127$	72961.2	0.401405	0.200703	+	0.979652i	$0.435678\pi$
$128$	−16384.0	−0.0883883
$129$	18262.5	0.0966241
$130$	−39068.9	−0.202756
$131$	87861.7	0.447323	0.223662	−	0.974667i	$-0.428199\pi$
$131$	87861.7	0.447323	0.223662	+	0.974667i	$0.428199\pi$
$132$	0	0
$133$	520309.	2.55054
$134$	177533.	0.854119
$135$	−7880.66	−0.0372159
$136$	48880.5	0.226615
$137$	181912.	0.828055	0.414027	−	0.910264i	$-0.364122\pi$
$137$	181912.	0.828055	0.414027	+	0.910264i	$0.364122\pi$
$138$	−101809.	−0.455079
$139$	130282.	0.571937	0.285968	−	0.958239i	$-0.407685\pi$
$139$	130282.	0.571937	0.285968	+	0.958239i	$0.407685\pi$
$140$	−39640.2	−0.170929
$141$	−181962.	−0.770785
$142$	321551.	1.33823
$143$	0	0
$144$	20736.0	0.0833333
$145$	75371.2	0.297705
$146$	−297540.	−1.15522
$147$	321457.	1.22696
$148$	−168655.	−0.632914
$149$	−510763.	−1.88475	−0.942375	−	0.334558i	$-0.891413\pi$
$149$	−510763.	−1.88475	−0.942375	+	0.334558i	$0.891413\pi$
$150$	108293.	0.392982
$151$	156912.	0.560035	0.280017	−	0.959995i	$-0.409660\pi$
$151$	156912.	0.560035	0.280017	+	0.959995i	$0.409660\pi$
$152$	−145298.	−0.510095
$153$	−61864.4	−0.213655
$154$	0	0
$155$	79318.8	0.265184
$156$	−130107.	−0.428043
$157$	−95113.5	−0.307959	−0.153980	−	0.988074i	$-0.549209\pi$
$157$	−95113.5	−0.307959	−0.153980	+	0.988074i	$0.549209\pi$
$158$	−117705.	−0.375104
$159$	−165980.	−0.520670
$160$	11069.7	0.0341849
$161$	648130.	1.97060
$162$	−26244.0	−0.0785674
$163$	−167377.	−0.493432	−0.246716	−	0.969088i	$-0.579352\pi$
$163$	−167377.	−0.493432	−0.246716	+	0.969088i	$0.579352\pi$
$164$	−97642.5	−0.283484
$165$	0	0
$166$	9607.74	0.0270614
$167$	−336730.	−0.934310	−0.467155	−	0.884175i	$-0.654721\pi$
$167$	−336730.	−0.934310	−0.467155	+	0.884175i	$0.654721\pi$
$168$	−132009.	−0.360853
$169$	445051.	1.19865
$170$	−33025.6	−0.0876452
$171$	183893.	0.480923
$172$	32466.6	0.0836789
$173$	−560330.	−1.42340	−0.711702	−	0.702481i	$-0.752076\pi$
$173$	−560330.	−1.42340	−0.711702	+	0.702481i	$0.752076\pi$
$174$	251000.	0.628492
$175$	−689412.	−1.70170
$176$	0	0
$177$	78839.4	0.189152
$178$	147353.	0.348585
$179$	−95541.3	−0.222874	−0.111437	−	0.993772i	$-0.535545\pi$
$179$	−95541.3	−0.222874	−0.111437	+	0.993772i	$0.535545\pi$
$180$	−14010.1	−0.0322299
$181$	−83262.0	−0.188908	−0.0944540	−	0.995529i	$-0.530111\pi$
$181$	−83262.0	−0.188908	−0.0944540	+	0.995529i	$0.530111\pi$
$182$	828280.	1.85353
$183$	228715.	0.504856
$184$	−180993.	−0.394110
$185$	113950.	0.244785
$186$	264146.	0.559837
$187$	0	0
$188$	−323488.	−0.667519
$189$	167074.	0.340215
$190$	98169.2	0.197284
$191$	−664980.	−1.31894	−0.659470	−	0.751730i	$-0.729219\pi$
$191$	−664980.	−1.31894	−0.659470	+	0.751730i	$0.729219\pi$
$192$	36864.0	0.0721688
$193$	157126.	0.303637	0.151819	−	0.988408i	$-0.451487\pi$
$193$	157126.	0.303637	0.151819	+	0.988408i	$0.451487\pi$
$194$	254767.	0.486002
$195$	87905.1	0.165549
$196$	571479.	1.06258
$197$	−297052.	−0.545339	−0.272669	−	0.962108i	$-0.587907\pi$
$197$	−297052.	−0.545339	−0.272669	+	0.962108i	$0.587907\pi$
$198$	0	0
$199$	−384778.	−0.688774	−0.344387	−	0.938828i	$-0.611913\pi$
$199$	−384778.	−0.688774	−0.344387	+	0.938828i	$0.611913\pi$
$200$	192521.	0.340332
$201$	−399450.	−0.697385
$202$	114898.	0.198123
$203$	−1.59791e6	−2.72152
$204$	−109981.	−0.185030
$205$	65971.1	0.109640
$206$	−289985.	−0.476110
$207$	229069.	0.371570
$208$	−231301.	−0.370696
$209$	0	0
$210$	89190.4	0.139563
$211$	244133.	0.377503	0.188751	−	0.982025i	$-0.439556\pi$
$211$	244133.	0.377503	0.188751	+	0.982025i	$0.439556\pi$
$212$	−295076.	−0.450914
$213$	−723490.	−1.09266
$214$	−110801.	−0.165390
$215$	−21935.7	−0.0323635
$216$	−46656.0	−0.0680414
$217$	−1.68160e6	−2.42422
$218$	−215593.	−0.307251
$219$	669465.	0.943230
$220$	0	0
$221$	690069.	0.950412
$222$	379473.	0.516772
$223$	47797.2	0.0643636	0.0321818	−	0.999482i	$-0.489754\pi$
$223$	47797.2	0.0643636	0.0321818	+	0.999482i	$0.489754\pi$
$224$	−234682.	−0.312508
$225$	−243659.	−0.320868
$226$	−482496.	−0.628381
$227$	604310.	0.778387	0.389193	−	0.921156i	$-0.372754\pi$
$227$	604310.	0.778387	0.389193	+	0.921156i	$0.372754\pi$
$228$	326921.	0.416491
$229$	−984859.	−1.24104	−0.620519	−	0.784191i	$-0.713078\pi$
$229$	−984859.	−1.24104	−0.620519	+	0.784191i	$0.713078\pi$
$230$	122286.	0.152425
$231$	0	0
$232$	446222.	0.544290
$233$	777885.	0.938698	0.469349	−	0.883013i	$-0.344489\pi$
$233$	777885.	0.938698	0.469349	+	0.883013i	$0.344489\pi$
$234$	292740.	0.349496
$235$	218561.	0.258169
$236$	140159.	0.163810
$237$	264836.	0.306271
$238$	700159.	0.801224
$239$	−846574.	−0.958672	−0.479336	−	0.877631i	$-0.659123\pi$
$239$	−846574.	−0.958672	−0.479336	+	0.877631i	$0.659123\pi$
$240$	−24906.8	−0.0279119
$241$	−1.04323e6	−1.15702	−0.578508	−	0.815677i	$-0.696365\pi$
$241$	−1.04323e6	−1.15702	−0.578508	+	0.815677i	$0.696365\pi$
$242$	0	0
$243$	59049.0	0.0641500
$244$	406605.	0.437218
$245$	−386114.	−0.410960
$246$	219696.	0.231464
$247$	−2.05124e6	−2.13931
$248$	469592.	0.484833
$249$	−21617.4	−0.0220956
$250$	−265203.	−0.268366
$251$	515862.	0.516832	0.258416	−	0.966034i	$-0.416800\pi$
$251$	515862.	0.516832	0.258416	+	0.966034i	$0.416800\pi$
$252$	297020.	0.294635
$253$	0	0
$254$	−291845.	−0.283836
$255$	74307.6	0.0715620
$256$	65536.0	0.0625000
$257$	547492.	0.517065	0.258532	−	0.966003i	$-0.416761\pi$
$257$	547492.	0.517065	0.258532	+	0.966003i	$0.416761\pi$
$258$	−73049.9	−0.0683235
$259$	−2.41579e6	−2.23774
$260$	156276.	0.143370
$261$	−564749.	−0.513162
$262$	−351447.	−0.316305
$263$	−349065.	−0.311184	−0.155592	−	0.987821i	$-0.549728\pi$
$263$	−349065.	−0.311184	−0.155592	+	0.987821i	$0.549728\pi$
$264$	0	0
$265$	199365.	0.174395
$266$	−2.08123e6	−1.80350
$267$	−331544.	−0.284619
$268$	−710134.	−0.603953
$269$	749494.	0.631520	0.315760	−	0.948839i	$-0.397741\pi$
$269$	749494.	0.631520	0.315760	+	0.948839i	$0.397741\pi$
$270$	31522.6	0.0263156
$271$	−1.52749e6	−1.26344	−0.631720	−	0.775197i	$-0.717651\pi$
$271$	−1.52749e6	−1.26344	−0.631720	+	0.775197i	$0.717651\pi$
$272$	−195522.	−0.160241
$273$	−1.86363e6	−1.51340
$274$	−727646.	−0.585523
$275$	0	0
$276$	407234.	0.321789
$277$	1.31031e6	1.02607	0.513033	−	0.858369i	$-0.328522\pi$
$277$	1.31031e6	1.02607	0.513033	+	0.858369i	$0.328522\pi$
$278$	−521129.	−0.404420
$279$	−594328.	−0.457105
$280$	158561.	0.120865
$281$	1.40135e6	1.05872	0.529361	−	0.848397i	$-0.322432\pi$
$281$	1.40135e6	1.05872	0.529361	+	0.848397i	$0.322432\pi$
$282$	727849.	0.545027
$283$	581548.	0.431638	0.215819	−	0.976433i	$-0.430758\pi$
$283$	581548.	0.431638	0.215819	+	0.976433i	$0.430758\pi$
$284$	−1.28621e6	−0.946268
$285$	−220881.	−0.161082
$286$	0	0
$287$	−1.39862e6	−1.00229
$288$	−82944.0	−0.0589256
$289$	−836531.	−0.589165
$290$	−301485.	−0.210509
$291$	−573225.	−0.396819
$292$	1.19016e6	0.816861
$293$	−1.86180e6	−1.26697	−0.633483	−	0.773756i	$-0.718375\pi$
$293$	−1.86180e6	−1.26697	−0.633483	+	0.773756i	$0.718375\pi$
$294$	−1.28583e6	−0.867590
$295$	−94696.9	−0.0633550
$296$	674619.	0.447538
$297$	0	0
$298$	2.04305e6	1.33272
$299$	−2.55516e6	−1.65288
$300$	−433172.	−0.277880
$301$	465048.	0.295857
$302$	−627650.	−0.396004
$303$	−258521.	−0.161767
$304$	581193.	0.360692
$305$	−274718.	−0.169098
$306$	247458.	0.151077
$307$	−1.39974e6	−0.847620	−0.423810	−	0.905751i	$-0.639308\pi$
$307$	−1.39974e6	−0.847620	−0.423810	+	0.905751i	$0.639308\pi$
$308$	0	0
$309$	652466.	0.388742
$310$	−317275.	−0.187513
$311$	−832541.	−0.488095	−0.244048	−	0.969763i	$-0.578475\pi$
$311$	−832541.	−0.488095	−0.244048	+	0.969763i	$0.578475\pi$
$312$	520426.	0.302672
$313$	−2.60734e6	−1.50431	−0.752155	−	0.658986i	$-0.770986\pi$
$313$	−2.60734e6	−1.50431	−0.752155	+	0.658986i	$0.770986\pi$
$314$	380454.	0.217760
$315$	−200678.	−0.113953
$316$	470819.	0.265238
$317$	−35395.8	−0.0197835	−0.00989175	−	0.999951i	$-0.503149\pi$
$317$	−35395.8	−0.0197835	−0.00989175	+	0.999951i	$0.503149\pi$
$318$	663920.	0.368170
$319$	0	0
$320$	−44278.7	−0.0241724
$321$	249303.	0.135041
$322$	−2.59252e6	−1.39342
$323$	−1.73395e6	−0.924762
$324$	104976.	0.0555556
$325$	2.71791e6	1.42734
$326$	669509.	0.348909
$327$	485083.	0.250869
$328$	390570.	0.200454
$329$	−4.63361e6	−2.36009
$330$	0	0
$331$	125174.	0.0627978	0.0313989	−	0.999507i	$-0.490004\pi$
$331$	125174.	0.0627978	0.0313989	+	0.999507i	$0.490004\pi$
$332$	−38431.0	−0.0191353
$333$	−853815.	−0.421943
$334$	1.34692e6	0.660657
$335$	479794.	0.233584
$336$	528036.	0.255161
$337$	−607149.	−0.291220	−0.145610	−	0.989342i	$-0.546514\pi$
$337$	−607149.	−0.291220	−0.145610	+	0.989342i	$0.546514\pi$
$338$	−1.78020e6	−0.847575
$339$	1.08562e6	0.513071
$340$	132102.	0.0619745
$341$	0	0
$342$	−735572.	−0.340064
$343$	4.33393e6	1.98906
$344$	−129867.	−0.0591699
$345$	−275143.	−0.124455
$346$	2.24132e6	1.00650
$347$	−2.76192e6	−1.23137	−0.615683	−	0.787994i	$-0.711120\pi$
$347$	−2.76192e6	−1.23137	−0.615683	+	0.787994i	$0.711120\pi$
$348$	−1.00400e6	−0.444411
$349$	1.52151e6	0.668670	0.334335	−	0.942454i	$-0.391488\pi$
$349$	1.52151e6	0.668670	0.334335	+	0.942454i	$0.391488\pi$
$350$	2.75765e6	1.20328
$351$	−658664.	−0.285362
$352$	0	0
$353$	−529162.	−0.226022	−0.113011	−	0.993594i	$-0.536050\pi$
$353$	−529162.	−0.226022	−0.113011	+	0.993594i	$0.536050\pi$
$354$	−315358.	−0.133750
$355$	869011.	0.365977
$356$	−589412.	−0.246487
$357$	−1.57536e6	−0.654197
$358$	382165.	0.157595
$359$	2.68712e6	1.10040	0.550201	−	0.835032i	$-0.314551\pi$
$359$	2.68712e6	1.10040	0.550201	+	0.835032i	$0.314551\pi$
$360$	56040.2	0.0227900
$361$	2.67810e6	1.08158
$362$	333048.	0.133578
$363$	0	0
$364$	−3.31312e6	−1.31064
$365$	−804119.	−0.315928
$366$	−914861.	−0.356987
$367$	2.26817e6	0.879042	0.439521	−	0.898232i	$-0.355148\pi$
$367$	2.26817e6	0.879042	0.439521	+	0.898232i	$0.355148\pi$
$368$	723972.	0.278678
$369$	−494315.	−0.188990
$370$	−455799.	−0.173089
$371$	−4.22663e6	−1.59426
$372$	−1.05658e6	−0.395864
$373$	2.70420e6	1.00639	0.503195	−	0.864173i	$-0.332158\pi$
$373$	2.70420e6	1.00639	0.503195	+	0.864173i	$0.332158\pi$
$374$	0	0
$375$	596706.	0.219120
$376$	1.29395e6	0.472007
$377$	6.29952e6	2.28273
$378$	−668295.	−0.240568
$379$	2.32153e6	0.830186	0.415093	−	0.909779i	$-0.363749\pi$
$379$	2.32153e6	0.830186	0.415093	+	0.909779i	$0.363749\pi$
$380$	−392677.	−0.139501
$381$	656651.	0.231751
$382$	2.65992e6	0.932632
$383$	−5.16764e6	−1.80009	−0.900047	−	0.435792i	$-0.856468\pi$
$383$	−5.16764e6	−1.80009	−0.900047	+	0.435792i	$0.856468\pi$
$384$	−147456.	−0.0510310
$385$	0	0
$386$	−628504.	−0.214704
$387$	164362.	0.0557859
$388$	−1.01907e6	−0.343655
$389$	−126727.	−0.0424616	−0.0212308	−	0.999775i	$-0.506758\pi$
$389$	−126727.	−0.0424616	−0.0212308	+	0.999775i	$0.506758\pi$
$390$	−351620.	−0.117061
$391$	−2.15992e6	−0.714489
$392$	−2.28592e6	−0.751355
$393$	790755.	0.258262
$394$	1.18821e6	0.385613
$395$	−318104.	−0.102583
$396$	0	0
$397$	−1.95769e6	−0.623402	−0.311701	−	0.950180i	$-0.600899\pi$
$397$	−1.95769e6	−0.623402	−0.311701	+	0.950180i	$0.600899\pi$
$398$	1.53911e6	0.487037
$399$	4.68278e6	1.47255
$400$	−770084.	−0.240651
$401$	1.30000e6	0.403721	0.201861	−	0.979414i	$-0.435301\pi$
$401$	1.30000e6	0.403721	0.201861	+	0.979414i	$0.435301\pi$
$402$	1.59780e6	0.493126
$403$	6.62945e6	2.03336
$404$	−459593.	−0.140094
$405$	−70925.9	−0.0214866
$406$	6.39162e6	1.92440
$407$	0	0
$408$	439925.	0.130836
$409$	294959.	0.0871873	0.0435936	−	0.999049i	$-0.486119\pi$
$409$	294959.	0.0871873	0.0435936	+	0.999049i	$0.486119\pi$
$410$	−263884.	−0.0775272
$411$	1.63720e6	0.478078
$412$	1.15994e6	0.336660
$413$	2.00762e6	0.579170
$414$	−916277.	−0.262740
$415$	25965.5	0.00740075
$416$	925202.	0.262122
$417$	1.17254e6	0.330208
$418$	0	0
$419$	−1.46469e6	−0.407578	−0.203789	−	0.979015i	$-0.565326\pi$
$419$	−1.46469e6	−0.407578	−0.203789	+	0.979015i	$0.565326\pi$
$420$	−356762.	−0.0986858
$421$	−1.15202e6	−0.316779	−0.158389	−	0.987377i	$-0.550630\pi$
$421$	−1.15202e6	−0.316779	−0.158389	+	0.987377i	$0.550630\pi$
$422$	−976532.	−0.266935
$423$	−1.63766e6	−0.445013
$424$	1.18030e6	0.318844
$425$	2.29749e6	0.616995
$426$	2.89396e6	0.772625
$427$	5.82416e6	1.54584
$428$	443205.	0.116949
$429$	0	0
$430$	87742.9	0.0228845
$431$	4.31164e6	1.11802	0.559009	−	0.829161i	$-0.311182\pi$
$431$	4.31164e6	1.11802	0.559009	+	0.829161i	$0.311182\pi$
$432$	186624.	0.0481125
$433$	6.53482e6	1.67500	0.837498	−	0.546441i	$-0.184018\pi$
$433$	6.53482e6	1.67500	0.837498	+	0.546441i	$0.184018\pi$
$434$	6.72639e6	1.71418
$435$	678341.	0.171880
$436$	862370.	0.217259
$437$	6.42040e6	1.60827
$438$	−2.67786e6	−0.666965
$439$	−6.84390e6	−1.69489	−0.847446	−	0.530881i	$-0.821861\pi$
$439$	−6.84390e6	−1.69489	−0.847446	+	0.530881i	$0.821861\pi$
$440$	0	0
$441$	2.89311e6	0.708384
$442$	−2.76028e6	−0.672042
$443$	−597201.	−0.144581	−0.0722906	−	0.997384i	$-0.523031\pi$
$443$	−597201.	−0.144581	−0.0722906	+	0.997384i	$0.523031\pi$
$444$	−1.51789e6	−0.365413
$445$	398230.	0.0953309
$446$	−191189.	−0.0455119
$447$	−4.59687e6	−1.08816
$448$	938730.	0.220976
$449$	−6.49320e6	−1.52000	−0.759999	−	0.649924i	$-0.774801\pi$
$449$	−6.49320e6	−1.52000	−0.759999	+	0.649924i	$0.774801\pi$
$450$	974637.	0.226888
$451$	0	0
$452$	1.92999e6	0.444332
$453$	1.41221e6	0.323336
$454$	−2.41724e6	−0.550403
$455$	2.23847e6	0.506902
$456$	−1.30768e6	−0.294504
$457$	−5.26873e6	−1.18009	−0.590046	−	0.807370i	$-0.700890\pi$
$457$	−5.26873e6	−1.18009	−0.590046	+	0.807370i	$0.700890\pi$
$458$	3.93943e6	0.877546
$459$	−556780.	−0.123354
$460$	−489144.	−0.107781
$461$	467971.	0.102557	0.0512786	−	0.998684i	$-0.483670\pi$
$461$	467971.	0.102557	0.0512786	+	0.998684i	$0.483670\pi$
$462$	0	0
$463$	2.63233e6	0.570674	0.285337	−	0.958427i	$-0.407894\pi$
$463$	2.63233e6	0.570674	0.285337	+	0.958427i	$0.407894\pi$
$464$	−1.78489e6	−0.384871
$465$	713869.	0.153104
$466$	−3.11154e6	−0.663759
$467$	−8.65002e6	−1.83538	−0.917688	−	0.397302i	$-0.869947\pi$
$467$	−8.65002e6	−1.83538	−0.917688	+	0.397302i	$0.869947\pi$
$468$	−1.17096e6	−0.247131
$469$	−1.01719e7	−2.13535
$470$	−874245.	−0.182553
$471$	−856021.	−0.177800
$472$	−560636.	−0.115831
$473$	0	0
$474$	−1.05934e6	−0.216566
$475$	−6.82933e6	−1.38881
$476$	−2.80063e6	−0.566551
$477$	−1.49382e6	−0.300609
$478$	3.38630e6	0.677884
$479$	−2.99462e6	−0.596353	−0.298177	−	0.954511i	$-0.596378\pi$
$479$	−2.99462e6	−0.596353	−0.298177	+	0.954511i	$0.596378\pi$
$480$	99627.1	0.0197367
$481$	9.52391e6	1.87695
$482$	4.17294e6	0.818134
$483$	5.83317e6	1.13772
$484$	0	0
$485$	688521.	0.132912
$486$	−236196.	−0.0453609
$487$	6.18023e6	1.18082	0.590408	−	0.807105i	$-0.298967\pi$
$487$	6.18023e6	1.18082	0.590408	+	0.807105i	$0.298967\pi$
$488$	−1.62642e6	−0.309160
$489$	−1.50640e6	−0.284883
$490$	1.54445e6	0.290593
$491$	−1.00918e7	−1.88915	−0.944575	−	0.328296i	$-0.893526\pi$
$491$	−1.00918e7	−1.88915	−0.944575	+	0.328296i	$0.893526\pi$
$492$	−878782.	−0.163670
$493$	5.32508e6	0.986754
$494$	8.20497e6	1.51272
$495$	0	0
$496$	−1.87837e6	−0.342829
$497$	−1.84234e7	−3.34565
$498$	86469.6	0.0156239
$499$	−958506.	−0.172323	−0.0861615	−	0.996281i	$-0.527460\pi$
$499$	−958506.	−0.172323	−0.0861615	+	0.996281i	$0.527460\pi$
$500$	1.06081e6	0.189763
$501$	−3.03057e6	−0.539424
$502$	−2.06345e6	−0.365455
$503$	2.90590e6	0.512106	0.256053	−	0.966663i	$-0.417578\pi$
$503$	2.90590e6	0.512106	0.256053	+	0.966663i	$0.417578\pi$
$504$	−1.18808e6	−0.208338
$505$	310519.	0.0541826
$506$	0	0
$507$	4.00546e6	0.692042
$508$	1.16738e6	0.200703
$509$	1.03221e7	1.76594	0.882968	−	0.469433i	$-0.155542\pi$
$509$	1.03221e7	1.76594	0.882968	+	0.469433i	$0.155542\pi$
$510$	−297230.	−0.0506020
$511$	1.70477e7	2.88811
$512$	−262144.	−0.0441942
$513$	1.65504e6	0.277661
$514$	−2.18997e6	−0.365620
$515$	−783700.	−0.130206
$516$	292200.	0.0483120
$517$	0	0
$518$	9.66317e6	1.58232
$519$	−5.04297e6	−0.821803
$520$	−625103.	−0.101378
$521$	−1.17658e6	−0.189901	−0.0949507	−	0.995482i	$-0.530269\pi$
$521$	−1.17658e6	−0.189901	−0.0949507	+	0.995482i	$0.530269\pi$
$522$	2.25900e6	0.362860
$523$	−4.16140e6	−0.665251	−0.332626	−	0.943059i	$-0.607935\pi$
$523$	−4.16140e6	−0.665251	−0.332626	+	0.943059i	$0.607935\pi$
$524$	1.40579e6	0.223662
$525$	−6.20470e6	−0.982478
$526$	1.39626e6	0.220040
$527$	5.60398e6	0.878963
$528$	0	0
$529$	1.56132e6	0.242579
$530$	−797459.	−0.123316
$531$	709555.	0.109207
$532$	8.32494e6	1.27527
$533$	5.51386e6	0.840693
$534$	1.32618e6	0.201256
$535$	−299447.	−0.0452309
$536$	2.84054e6	0.427059
$537$	−859871.	−0.128676
$538$	−2.99798e6	−0.446552
$539$	0	0
$540$	−126091.	−0.0186079
$541$	1.14751e7	1.68564	0.842819	−	0.538198i	$-0.180895\pi$
$541$	1.14751e7	1.68564	0.842819	+	0.538198i	$0.180895\pi$
$542$	6.10995e6	0.893386
$543$	−749358.	−0.109066
$544$	782088.	0.113307
$545$	−582651.	−0.0840267
$546$	7.45452e6	1.07013
$547$	9.28056e6	1.32619	0.663095	−	0.748535i	$-0.269243\pi$
$547$	9.28056e6	1.32619	0.663095	+	0.748535i	$0.269243\pi$
$548$	2.91059e6	0.414027
$549$	2.05844e6	0.291479
$550$	0	0
$551$	−1.58289e7	−2.22112
$552$	−1.62894e6	−0.227539
$553$	6.74396e6	0.937782
$554$	−5.24124e6	−0.725538
$555$	1.02555e6	0.141327
$556$	2.08452e6	0.285968
$557$	−5.49440e6	−0.750382	−0.375191	−	0.926947i	$-0.622423\pi$
$557$	−5.49440e6	−0.750382	−0.375191	+	0.926947i	$0.622423\pi$
$558$	2.37731e6	0.323222
$559$	−1.83339e6	−0.248156
$560$	−634243.	−0.0854644
$561$	0	0
$562$	−5.60541e6	−0.748629
$563$	3.37210e6	0.448363	0.224181	−	0.974547i	$-0.428029\pi$
$563$	3.37210e6	0.448363	0.224181	+	0.974547i	$0.428029\pi$
$564$	−2.91139e6	−0.385392
$565$	−1.30397e6	−0.171849
$566$	−2.32619e6	−0.305214
$567$	1.50366e6	0.196423
$568$	5.14482e6	0.669113
$569$	6.21502e6	0.804752	0.402376	−	0.915475i	$-0.368185\pi$
$569$	6.21502e6	0.804752	0.402376	+	0.915475i	$0.368185\pi$
$570$	883523.	0.113902
$571$	947370.	0.121599	0.0607994	−	0.998150i	$-0.480635\pi$
$571$	947370.	0.121599	0.0607994	+	0.998150i	$0.480635\pi$
$572$	0	0
$573$	−5.98482e6	−0.761491
$574$	5.59448e6	0.708728
$575$	−8.50706e6	−1.07303
$576$	331776.	0.0416667
$577$	−5.75469e6	−0.719585	−0.359793	−	0.933032i	$-0.617153\pi$
$577$	−5.75469e6	−0.719585	−0.359793	+	0.933032i	$0.617153\pi$
$578$	3.34612e6	0.416603
$579$	1.41413e6	0.175305
$580$	1.20594e6	0.148852
$581$	−550480.	−0.0676553
$582$	2.29290e6	0.280593
$583$	0	0
$584$	−4.76064e6	−0.577608
$585$	791146.	0.0955800
$586$	7.44722e6	0.895881
$587$	−6.28253e6	−0.752556	−0.376278	−	0.926507i	$-0.622796\pi$
$587$	−6.28253e6	−0.752556	−0.376278	+	0.926507i	$0.622796\pi$
$588$	5.14331e6	0.613479
$589$	−1.66580e7	−1.97849
$590$	378788.	0.0447987
$591$	−2.67347e6	−0.314852
$592$	−2.69848e6	−0.316457
$593$	1.02214e7	1.19364	0.596818	−	0.802377i	$-0.296431\pi$
$593$	1.02214e7	1.19364	0.596818	+	0.802377i	$0.296431\pi$
$594$	0	0
$595$	1.89222e6	0.219118
$596$	−8.17221e6	−0.942375
$597$	−3.46300e6	−0.397664
$598$	1.02206e7	1.16876
$599$	1.50081e7	1.70907	0.854534	−	0.519395i	$-0.173843\pi$
$599$	1.50081e7	1.70907	0.854534	+	0.519395i	$0.173843\pi$
$600$	1.73269e6	0.196491
$601$	−2.81933e6	−0.318391	−0.159195	−	0.987247i	$-0.550890\pi$
$601$	−2.81933e6	−0.318391	−0.159195	+	0.987247i	$0.550890\pi$
$602$	−1.86019e6	−0.209202
$603$	−3.59505e6	−0.402635
$604$	2.51060e6	0.280017
$605$	0	0
$606$	1.03408e6	0.114386
$607$	1.42538e7	1.57022	0.785108	−	0.619359i	$-0.212607\pi$
$607$	1.42538e7	1.57022	0.785108	+	0.619359i	$0.212607\pi$
$608$	−2.32477e6	−0.255048
$609$	−1.43812e7	−1.57127
$610$	1.09887e6	0.119570
$611$	1.82673e7	1.97958
$612$	−989830.	−0.106827
$613$	2.51664e6	0.270501	0.135251	−	0.990811i	$-0.456816\pi$
$613$	2.51664e6	0.270501	0.135251	+	0.990811i	$0.456816\pi$
$614$	5.59896e6	0.599358
$615$	593740.	0.0633007
$616$	0	0
$617$	7.72075e6	0.816482	0.408241	−	0.912874i	$-0.366142\pi$
$617$	7.72075e6	0.816482	0.408241	+	0.912874i	$0.366142\pi$
$618$	−2.60986e6	−0.274882
$619$	5.49668e6	0.576599	0.288300	−	0.957540i	$-0.406910\pi$
$619$	5.49668e6	0.576599	0.288300	+	0.957540i	$0.406910\pi$
$620$	1.26910e6	0.132592
$621$	2.06162e6	0.214526
$622$	3.33016e6	0.345136
$623$	−8.44267e6	−0.871484
$624$	−2.08170e6	−0.214022
$625$	8.68371e6	0.889212
$626$	1.04294e7	1.06371
$627$	0	0
$628$	−1.52182e6	−0.153980
$629$	8.05072e6	0.811350
$630$	802714.	0.0805767
$631$	1.88580e7	1.88548	0.942742	−	0.333523i	$-0.108237\pi$
$631$	1.88580e7	1.88548	0.942742	+	0.333523i	$0.108237\pi$
$632$	−1.88328e6	−0.187552
$633$	2.19720e6	0.217951
$634$	141583.	0.0139890
$635$	−788728.	−0.0776234
$636$	−2.65568e6	−0.260335
$637$	−3.22713e7	−3.15114
$638$	0	0
$639$	−6.51141e6	−0.630846
$640$	177115.	0.0170925
$641$	5.03974e6	0.484465	0.242233	−	0.970218i	$-0.422120\pi$
$641$	5.03974e6	0.484465	0.242233	+	0.970218i	$0.422120\pi$
$642$	−997212.	−0.0954882
$643$	−6.29875e6	−0.600796	−0.300398	−	0.953814i	$-0.597119\pi$
$643$	−6.29875e6	−0.600796	−0.300398	+	0.953814i	$0.597119\pi$
$644$	1.03701e7	0.985298
$645$	−197422.	−0.0186851
$646$	6.93579e6	0.653905
$647$	1.09807e7	1.03126	0.515632	−	0.856810i	$-0.327557\pi$
$647$	1.09807e7	1.03126	0.515632	+	0.856810i	$0.327557\pi$
$648$	−419904.	−0.0392837
$649$	0	0
$650$	−1.08716e7	−1.00928
$651$	−1.51344e7	−1.39963
$652$	−2.67804e6	−0.246716
$653$	−7.84121e6	−0.719615	−0.359808	−	0.933027i	$-0.617158\pi$
$653$	−7.84121e6	−0.719615	−0.359808	+	0.933027i	$0.617158\pi$
$654$	−1.94033e6	−0.177391
$655$	−949805.	−0.0865030
$656$	−1.56228e6	−0.141742
$657$	6.02519e6	0.544574
$658$	1.85344e7	1.66884
$659$	−1.28457e7	−1.15224	−0.576121	−	0.817364i	$-0.695434\pi$
$659$	−1.28457e7	−1.15224	−0.576121	+	0.817364i	$0.695434\pi$
$660$	0	0
$661$	−5.16392e6	−0.459701	−0.229851	−	0.973226i	$-0.573824\pi$
$661$	−5.16392e6	−0.459701	−0.229851	+	0.973226i	$0.573824\pi$
$662$	−500696.	−0.0444047
$663$	6.21062e6	0.548720
$664$	153724.	0.0135307
$665$	−5.62466e6	−0.493221
$666$	3.41526e6	0.298358
$667$	−1.97175e7	−1.71608
$668$	−5.38768e6	−0.467155
$669$	430175.	0.0371603
$670$	−1.91918e6	−0.165169
$671$	0	0
$672$	−2.11214e6	−0.180426
$673$	6.97138e6	0.593309	0.296654	−	0.954985i	$-0.404129\pi$
$673$	6.97138e6	0.593309	0.296654	+	0.954985i	$0.404129\pi$
$674$	2.42860e6	0.205923
$675$	−2.19293e6	−0.185253
$676$	7.12082e6	0.599326
$677$	−1.41142e7	−1.18354	−0.591771	−	0.806106i	$-0.701571\pi$
$677$	−1.41142e7	−1.18354	−0.591771	+	0.806106i	$0.701571\pi$
$678$	−4.34247e6	−0.362796
$679$	−1.45970e7	−1.21503
$680$	−528410.	−0.0438226
$681$	5.43879e6	0.449402
$682$	0	0
$683$	1.62086e7	1.32952	0.664759	−	0.747058i	$-0.268534\pi$
$683$	1.62086e7	1.32952	0.664759	+	0.747058i	$0.268534\pi$
$684$	2.94229e6	0.240461
$685$	−1.96651e6	−0.160129
$686$	−1.73357e7	−1.40647
$687$	−8.86373e6	−0.716514
$688$	519466.	0.0418395
$689$	1.66629e7	1.33722
$690$	1.10057e6	0.0880028
$691$	1.15076e7	0.916831	0.458415	−	0.888738i	$-0.348417\pi$
$691$	1.15076e7	0.916831	0.458415	+	0.888738i	$0.348417\pi$
$692$	−8.96528e6	−0.711702
$693$	0	0
$694$	1.10477e7	0.870707
$695$	−1.40838e6	−0.110601
$696$	4.01599e6	0.314246
$697$	4.66095e6	0.363406
$698$	−6.08604e6	−0.472821
$699$	7.00097e6	0.541957
$700$	−1.10306e7	−0.850851
$701$	9.75656e6	0.749897	0.374949	−	0.927046i	$-0.377660\pi$
$701$	9.75656e6	0.749897	0.374949	+	0.927046i	$0.377660\pi$
$702$	2.63466e6	0.201782
$703$	−2.39309e7	−1.82630
$704$	0	0
$705$	1.96705e6	0.149054
$706$	2.11665e6	0.159822
$707$	−6.58315e6	−0.495319
$708$	1.26143e6	0.0945758
$709$	4.92386e6	0.367867	0.183933	−	0.982939i	$-0.441117\pi$
$709$	4.92386e6	0.367867	0.183933	+	0.982939i	$0.441117\pi$
$710$	−3.47604e6	−0.258785
$711$	2.38352e6	0.176826
$712$	2.35765e6	0.174293
$713$	−2.07502e7	−1.52862
$714$	6.30143e6	0.462587
$715$	0	0
$716$	−1.52866e6	−0.111437
$717$	−7.61917e6	−0.553490
$718$	−1.07485e7	−0.778102
$719$	2.10739e7	1.52027	0.760137	−	0.649763i	$-0.225132\pi$
$719$	2.10739e7	1.52027	0.760137	+	0.649763i	$0.225132\pi$
$720$	−224161.	−0.0161149
$721$	1.66148e7	1.19030
$722$	−1.07124e7	−0.764792
$723$	−9.38911e6	−0.668003
$724$	−1.33219e6	−0.0944540
$725$	2.09734e7	1.48192
$726$	0	0
$727$	1.02370e7	0.718348	0.359174	−	0.933271i	$-0.383058\pi$
$727$	1.02370e7	0.718348	0.359174	+	0.933271i	$0.383058\pi$
$728$	1.32525e7	0.926763
$729$	531441.	0.0370370
$730$	3.21648e6	0.223395
$731$	−1.54979e6	−0.107270
$732$	3.65944e6	0.252428
$733$	−2.13623e7	−1.46855	−0.734275	−	0.678853i	$-0.762478\pi$
$733$	−2.13623e7	−1.46855	−0.734275	+	0.678853i	$0.762478\pi$
$734$	−9.07266e6	−0.621576
$735$	−3.47502e6	−0.237268
$736$	−2.89589e6	−0.197055
$737$	0	0
$738$	1.97726e6	0.133636
$739$	−1.69237e7	−1.13995	−0.569973	−	0.821663i	$-0.693047\pi$
$739$	−1.69237e7	−1.13995	−0.569973	+	0.821663i	$0.693047\pi$
$740$	1.82320e6	0.122392
$741$	−1.84612e7	−1.23513
$742$	1.69065e7	1.12731
$743$	−2.82700e7	−1.87869	−0.939343	−	0.342979i	$-0.888564\pi$
$743$	−2.82700e7	−1.87869	−0.939343	+	0.342979i	$0.888564\pi$
$744$	4.22633e6	0.279918
$745$	5.52147e6	0.364472
$746$	−1.08168e7	−0.711625
$747$	−194557.	−0.0127569
$748$	0	0
$749$	6.34842e6	0.413486
$750$	−2.38682e6	−0.154941
$751$	−8.90168e6	−0.575933	−0.287966	−	0.957640i	$-0.592979\pi$
$751$	−8.90168e6	−0.575933	−0.287966	+	0.957640i	$0.592979\pi$
$752$	−5.17581e6	−0.333760
$753$	4.64276e6	0.298393
$754$	−2.51981e7	−1.61413
$755$	−1.69626e6	−0.108299
$756$	2.67318e6	0.170108
$757$	−5.08557e6	−0.322552	−0.161276	−	0.986909i	$-0.551561\pi$
$757$	−5.08557e6	−0.322552	−0.161276	+	0.986909i	$0.551561\pi$
$758$	−9.28610e6	−0.587030
$759$	0	0
$760$	1.57071e6	0.0986419
$761$	−9.65849e6	−0.604571	−0.302286	−	0.953217i	$-0.597750\pi$
$761$	−9.65849e6	−0.604571	−0.302286	+	0.953217i	$0.597750\pi$
$762$	−2.62660e6	−0.163873
$763$	1.23525e7	0.768145
$764$	−1.06397e7	−0.659470
$765$	668768.	0.0413164
$766$	2.06706e7	1.27286
$767$	−7.91475e6	−0.485791
$768$	589824.	0.0360844
$769$	6.05284e6	0.369100	0.184550	−	0.982823i	$-0.440917\pi$
$769$	6.05284e6	0.369100	0.184550	+	0.982823i	$0.440917\pi$
$770$	0	0
$771$	4.92743e6	0.298527
$772$	2.51402e6	0.151819
$773$	5.07914e6	0.305732	0.152866	−	0.988247i	$-0.451150\pi$
$773$	5.07914e6	0.305732	0.152866	+	0.988247i	$0.451150\pi$
$774$	−657449.	−0.0394466
$775$	2.20719e7	1.32003
$776$	4.07627e6	0.243001
$777$	−2.17421e7	−1.29196
$778$	506910.	0.0300249
$779$	−1.38548e7	−0.818004
$780$	1.40648e6	0.0827747
$781$	0	0
$782$	8.63967e6	0.505220
$783$	−5.08274e6	−0.296274
$784$	9.14366e6	0.531288
$785$	1.02820e6	0.0595529
$786$	−3.16302e6	−0.182619
$787$	2.23661e7	1.28722	0.643611	−	0.765353i	$-0.277436\pi$
$787$	2.23661e7	1.28722	0.643611	+	0.765353i	$0.277436\pi$
$788$	−4.75283e6	−0.272669
$789$	−3.14158e6	−0.179662
$790$	1.27242e6	0.0725373
$791$	2.76449e7	1.57099
$792$	0	0
$793$	−2.29609e7	−1.29660
$794$	7.83076e6	0.440811
$795$	1.79428e6	0.100687
$796$	−6.15644e6	−0.344387
$797$	−3.57436e7	−1.99321	−0.996604	−	0.0823487i	$-0.973758\pi$
$797$	−3.57436e7	−1.99321	−0.996604	+	0.0823487i	$0.973758\pi$
$798$	−1.87311e7	−1.04125
$799$	1.54417e7	0.855711
$800$	3.08033e6	0.170166
$801$	−2.98390e6	−0.164325
$802$	−5.19999e6	−0.285474
$803$	0	0
$804$	−6.39120e6	−0.348692
$805$	−7.00644e6	−0.381072
$806$	−2.65178e7	−1.43781
$807$	6.74544e6	0.364608
$808$	1.83837e6	0.0990615
$809$	−3.75852e6	−0.201904	−0.100952	−	0.994891i	$-0.532189\pi$
$809$	−3.75852e6	−0.201904	−0.100952	+	0.994891i	$0.532189\pi$
$810$	283704.	0.0151933
$811$	−1.27989e7	−0.683314	−0.341657	−	0.939825i	$-0.610988\pi$
$811$	−1.27989e7	−0.683314	−0.341657	+	0.939825i	$0.610988\pi$
$812$	−2.55665e7	−1.36076
$813$	−1.37474e7	−0.729447
$814$	0	0
$815$	1.80939e6	0.0954196
$816$	−1.75970e6	−0.0925151
$817$	4.60678e6	0.241458
$818$	−1.17984e6	−0.0616507
$819$	−1.67727e7	−0.873761
$820$	1.05554e6	0.0548200
$821$	2.48541e7	1.28689	0.643444	−	0.765493i	$-0.277505\pi$
$821$	2.48541e7	1.28689	0.643444	+	0.765493i	$0.277505\pi$
$822$	−6.54882e6	−0.338052
$823$	2.53059e7	1.30233	0.651167	−	0.758934i	$-0.274280\pi$
$823$	2.53059e7	1.30233	0.651167	+	0.758934i	$0.274280\pi$
$824$	−4.63976e6	−0.238055
$825$	0	0
$826$	−8.03048e6	−0.409535
$827$	2.36753e7	1.20374	0.601868	−	0.798596i	$-0.294424\pi$
$827$	2.36753e7	1.20374	0.601868	+	0.798596i	$0.294424\pi$
$828$	3.66511e6	0.185785
$829$	−7.08170e6	−0.357891	−0.178946	−	0.983859i	$-0.557269\pi$
$829$	−7.08170e6	−0.357891	−0.178946	+	0.983859i	$0.557269\pi$
$830$	−103862.	−0.00523312
$831$	1.17928e7	0.592399
$832$	−3.70081e6	−0.185348
$833$	−2.72795e7	−1.36215
$834$	−4.69016e6	−0.233492
$835$	3.64013e6	0.180676
$836$	0	0
$837$	−5.34895e6	−0.263910
$838$	5.85876e6	0.288201
$839$	8.52065e6	0.417896	0.208948	−	0.977927i	$-0.432996\pi$
$839$	8.52065e6	0.417896	0.208948	+	0.977927i	$0.432996\pi$
$840$	1.42705e6	0.0697814
$841$	2.81006e7	1.37002
$842$	4.60809e6	0.223996
$843$	1.26122e7	0.611253
$844$	3.90613e6	0.188751
$845$	−4.81110e6	−0.231794
$846$	6.55064e6	0.314672
$847$	0	0
$848$	−4.72121e6	−0.225457
$849$	5.23393e6	0.249206
$850$	−9.18996e6	−0.436281
$851$	−2.98099e7	−1.41103
$852$	−1.15758e7	−0.546328
$853$	1.79912e7	0.846618	0.423309	−	0.905985i	$-0.360868\pi$
$853$	1.79912e7	0.846618	0.423309	+	0.905985i	$0.360868\pi$
$854$	−2.32966e7	−1.09307
$855$	−1.98793e6	−0.0930004
$856$	−1.77282e6	−0.0826952
$857$	−2.30359e7	−1.07140	−0.535702	−	0.844407i	$-0.679953\pi$
$857$	−2.30359e7	−1.07140	−0.535702	+	0.844407i	$0.679953\pi$
$858$	0	0
$859$	−9.53653e6	−0.440968	−0.220484	−	0.975391i	$-0.570764\pi$
$859$	−9.53653e6	−0.440968	−0.220484	+	0.975391i	$0.570764\pi$
$860$	−350972.	−0.0161818
$861$	−1.25876e7	−0.578674
$862$	−1.72465e7	−0.790559
$863$	−3.36705e7	−1.53894	−0.769471	−	0.638681i	$-0.779480\pi$
$863$	−3.36705e7	−1.53894	−0.769471	+	0.638681i	$0.779480\pi$
$864$	−746496.	−0.0340207
$865$	6.05729e6	0.275257
$866$	−2.61393e7	−1.18440
$867$	−7.52878e6	−0.340155
$868$	−2.69055e7	−1.21211
$869$	0	0
$870$	−2.71336e6	−0.121537
$871$	4.01011e7	1.79107
$872$	−3.44948e6	−0.153625
$873$	−5.15902e6	−0.229104
$874$	−2.56816e7	−1.13722
$875$	1.51949e7	0.670932
$876$	1.07114e7	0.471615
$877$	−2.50783e7	−1.10103	−0.550515	−	0.834826i	$-0.685568\pi$
$877$	−2.50783e7	−1.10103	−0.550515	+	0.834826i	$0.685568\pi$
$878$	2.73756e7	1.19847
$879$	−1.67562e7	−0.731483
$880$	0	0
$881$	3.09068e7	1.34157	0.670786	−	0.741651i	$-0.265957\pi$
$881$	3.09068e7	1.34157	0.670786	+	0.741651i	$0.265957\pi$
$882$	−1.15724e7	−0.500903
$883$	−2.17837e7	−0.940221	−0.470111	−	0.882607i	$-0.655786\pi$
$883$	−2.17837e7	−0.940221	−0.470111	+	0.882607i	$0.655786\pi$
$884$	1.10411e7	0.475206
$885$	−852272.	−0.0365780
$886$	2.38881e6	0.102234
$887$	3.71753e7	1.58652	0.793260	−	0.608884i	$-0.208382\pi$
$887$	3.71753e7	1.58652	0.793260	+	0.608884i	$0.208382\pi$
$888$	6.07158e6	0.258386
$889$	1.67214e7	0.709608
$890$	−1.59292e6	−0.0674092
$891$	0	0
$892$	764755.	0.0321818
$893$	−4.59007e7	−1.92615
$894$	1.83875e7	0.769446
$895$	1.03282e6	0.0430991
$896$	−3.75492e6	−0.156254
$897$	−2.29964e7	−0.954288
$898$	2.59728e7	1.07480
$899$	5.11578e7	2.11112
$900$	−3.89855e6	−0.160434
$901$	1.40854e7	0.578039
$902$	0	0
$903$	4.18543e6	0.170813
$904$	−7.71994e6	−0.314190
$905$	900081.	0.0365309
$906$	−5.64885e6	−0.228633
$907$	−3.88968e7	−1.56998	−0.784992	−	0.619506i	$-0.787333\pi$
$907$	−3.88968e7	−1.56998	−0.784992	+	0.619506i	$0.787333\pi$
$908$	9.66897e6	0.389193
$909$	−2.32669e6	−0.0933961
$910$	−8.95390e6	−0.358434
$911$	4.24797e7	1.69584	0.847920	−	0.530124i	$-0.177855\pi$
$911$	4.24797e7	1.69584	0.847920	+	0.530124i	$0.177855\pi$
$912$	5.23074e6	0.208246
$913$	0	0
$914$	2.10749e7	0.834451
$915$	−2.47246e6	−0.0976286
$916$	−1.57577e7	−0.620519
$917$	2.01363e7	0.790782
$918$	2.22712e6	0.0872241
$919$	−2.29560e7	−0.896618	−0.448309	−	0.893879i	$-0.647974\pi$
$919$	−2.29560e7	−0.896618	−0.448309	+	0.893879i	$0.647974\pi$
$920$	1.95657e6	0.0762126
$921$	−1.25977e7	−0.489374
$922$	−1.87188e6	−0.0725189
$923$	7.26318e7	2.80623
$924$	0	0
$925$	3.17086e7	1.21849
$926$	−1.05293e7	−0.403527
$927$	5.87219e6	0.224440
$928$	7.13954e6	0.272145
$929$	527354.	0.0200476	0.0100238	−	0.999950i	$-0.496809\pi$
$929$	527354.	0.0200476	0.0100238	+	0.999950i	$0.496809\pi$
$930$	−2.85548e6	−0.108261
$931$	8.10888e7	3.06610
$932$	1.24462e7	0.469349
$933$	−7.49287e6	−0.281802
$934$	3.46001e7	1.29781
$935$	0	0
$936$	4.68384e6	0.174748
$937$	2.91096e7	1.08315	0.541574	−	0.840653i	$-0.317829\pi$
$937$	2.91096e7	1.08315	0.541574	+	0.840653i	$0.317829\pi$
$938$	4.06875e7	1.50992
$939$	−2.34661e7	−0.868514
$940$	3.49698e6	0.129084
$941$	3.08431e7	1.13549	0.567746	−	0.823204i	$-0.307815\pi$
$941$	3.08431e7	1.13549	0.567746	+	0.823204i	$0.307815\pi$
$942$	3.42408e6	0.125724
$943$	−1.72584e7	−0.632006
$944$	2.24254e6	0.0819051
$945$	−1.80611e6	−0.0657906
$946$	0	0
$947$	−3.07297e7	−1.11348	−0.556741	−	0.830686i	$-0.687948\pi$
$947$	−3.07297e7	−1.11348	−0.556741	+	0.830686i	$0.687948\pi$
$948$	4.23737e6	0.153135
$949$	−6.72082e7	−2.42246
$950$	2.73173e7	0.982040
$951$	−318562.	−0.0114220
$952$	1.12025e7	0.400612
$953$	6.93181e6	0.247237	0.123619	−	0.992330i	$-0.460550\pi$
$953$	6.93181e6	0.247237	0.123619	+	0.992330i	$0.460550\pi$
$954$	5.97528e6	0.212563
$955$	7.18859e6	0.255056
$956$	−1.35452e7	−0.479336
$957$	0	0
$958$	1.19785e7	0.421685
$959$	4.16909e7	1.46384
$960$	−398508.	−0.0139559
$961$	2.52080e7	0.880502
$962$	−3.80957e7	−1.32720
$963$	2.24373e6	0.0779658
$964$	−1.66918e7	−0.578508
$965$	−1.69857e6	−0.0587171
$966$	−2.33327e7	−0.804492
$967$	−1.01604e7	−0.349416	−0.174708	−	0.984620i	$-0.555898\pi$
$967$	−1.01604e7	−0.349416	−0.174708	+	0.984620i	$0.555898\pi$
$968$	0	0
$969$	−1.56055e7	−0.533911
$970$	−2.75409e6	−0.0939827
$971$	−5.18278e7	−1.76407	−0.882033	−	0.471187i	$-0.843826\pi$
$971$	−5.18278e7	−1.76407	−0.882033	+	0.471187i	$0.843826\pi$
$972$	944784.	0.0320750
$973$	2.98584e7	1.01108
$974$	−2.47209e7	−0.834963
$975$	2.44612e7	0.824073
$976$	6.50568e6	0.218609
$977$	−3.30445e7	−1.10755	−0.553774	−	0.832667i	$-0.686813\pi$
$977$	−3.30445e7	−1.10755	−0.553774	+	0.832667i	$0.686813\pi$
$978$	6.02558e6	0.201443
$979$	0	0
$980$	−6.17782e6	−0.205480
$981$	4.36575e6	0.144839
$982$	4.03673e7	1.33583
$983$	−1.81291e7	−0.598402	−0.299201	−	0.954190i	$-0.596720\pi$
$983$	−1.81291e7	−0.598402	−0.299201	+	0.954190i	$0.596720\pi$
$984$	3.51513e6	0.115732
$985$	3.21120e6	0.105457
$986$	−2.13003e7	−0.697741
$987$	−4.17025e7	−1.36260
$988$	−3.28199e7	−1.06966
$989$	5.73850e6	0.186555
$990$	0	0
$991$	−5.24023e7	−1.69499	−0.847493	−	0.530806i	$-0.821889\pi$
$991$	−5.24023e7	−1.69499	−0.847493	+	0.530806i	$0.821889\pi$
$992$	7.51348e6	0.242416
$993$	1.12657e6	0.0362563
$994$	7.36938e7	2.36573
$995$	4.15953e6	0.133195
$996$	−345879.	−0.0110478
$997$	4.86084e6	0.154872	0.0774361	−	0.996997i	$-0.475327\pi$
$997$	4.86084e6	0.154872	0.0774361	+	0.996997i	$0.475327\pi$
$998$	3.83402e6	0.121851
$999$	−7.68434e6	−0.243609

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.6.a.bb.1.3		4
11.7	odd	10		66.6.e.a.49.2	yes	8
11.8	odd	10		66.6.e.a.31.2	✓	8
11.10	odd	2		726.6.a.be.1.3		4
33.8	even	10		198.6.f.c.163.1		8
33.29	even	10		198.6.f.c.181.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.6.e.a.31.2	✓	8	11.8	odd	10
66.6.e.a.49.2	yes	8	11.7	odd	10
198.6.f.c.163.1		8	33.8	even	10
198.6.f.c.181.1		8	33.29	even	10
726.6.a.bb.1.3		4	1.1	even	1	trivial
726.6.a.be.1.3		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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -10.8102 q^{5} -36.0000 q^{6} +229.182 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -10.8102 q^{5} -36.0000 q^{6} +229.182 q^{7} -64.0000 q^{8} +81.0000 q^{9} +43.2409 q^{10} +144.000 q^{12} -903.518 q^{13} -916.728 q^{14} -97.2921 q^{15} +256.000 q^{16} -763.758 q^{17} -324.000 q^{18} +2270.29 q^{19} -172.964 q^{20} +2062.64 q^{21} +2828.01 q^{23} -576.000 q^{24} -3008.14 q^{25} +3614.07 q^{26} +729.000 q^{27} +3666.91 q^{28} -6972.21 q^{29} +389.168 q^{30} -7337.38 q^{31} -1024.00 q^{32} +3055.03 q^{34} -2477.51 q^{35} +1296.00 q^{36} -10540.9 q^{37} -9081.14 q^{38} -8131.66 q^{39} +691.855 q^{40} -6102.66 q^{41} -8250.56 q^{42} +2029.16 q^{43} -875.629 q^{45} -11312.1 q^{46} -20218.0 q^{47} +2304.00 q^{48} +35717.4 q^{49} +12032.6 q^{50} -6873.82 q^{51} -14456.3 q^{52} -18442.2 q^{53} -2916.00 q^{54} -14667.7 q^{56} +20432.6 q^{57} +27888.8 q^{58} +8759.93 q^{59} -1556.67 q^{60} +25412.8 q^{61} +29349.5 q^{62} +18563.8 q^{63} +4096.00 q^{64} +9767.23 q^{65} -44383.4 q^{67} -12220.1 q^{68} +25452.1 q^{69} +9910.04 q^{70} -80387.8 q^{71} -5184.00 q^{72} +74385.0 q^{73} +42163.7 q^{74} -27073.3 q^{75} +36324.6 q^{76} +32526.6 q^{78} +29426.2 q^{79} -2767.42 q^{80} +6561.00 q^{81} +24410.6 q^{82} -2401.93 q^{83} +33002.2 q^{84} +8256.40 q^{85} -8116.66 q^{86} -62749.9 q^{87} -36838.3 q^{89} +3502.51 q^{90} -207070. q^{91} +45248.2 q^{92} -66036.4 q^{93} +80872.1 q^{94} -24542.3 q^{95} -9216.00 q^{96} -63691.6 q^{97} -142870. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} - 150 q^{5} - 144 q^{6} + 68 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) \) 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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