LMFDB - Embedded newform 722.6.a.d.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [722,6,Mod(1,722)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("722.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(722, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	722.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,-12,-13] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$115.797117905$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 454x + 3760 $ x^3 - x^2 - 454*x + 3760
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$10.7990$ of defining polynomial
Character	$\chi$	$=$	722.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.00000 q^{2} -14.7990 q^{3} +16.0000 q^{4} -19.0956 q^{5} +59.1959 q^{6} +212.287 q^{7} -64.0000 q^{8} -23.9901 q^{9} +76.3823 q^{10} -662.625 q^{11} -236.784 q^{12} -1112.31 q^{13} -849.148 q^{14} +282.595 q^{15} +256.000 q^{16} -522.290 q^{17} +95.9606 q^{18} -305.529 q^{20} -3141.63 q^{21} +2650.50 q^{22} -3213.52 q^{23} +947.135 q^{24} -2760.36 q^{25} +4449.24 q^{26} +3951.18 q^{27} +3396.59 q^{28} +3725.71 q^{29} -1130.38 q^{30} -4832.50 q^{31} -1024.00 q^{32} +9806.17 q^{33} +2089.16 q^{34} -4053.74 q^{35} -383.842 q^{36} +7152.96 q^{37} +16461.1 q^{39} +1222.12 q^{40} -10812.9 q^{41} +12566.5 q^{42} -10418.4 q^{43} -10602.0 q^{44} +458.106 q^{45} +12854.1 q^{46} +11998.2 q^{47} -3788.54 q^{48} +28258.8 q^{49} +11041.4 q^{50} +7729.35 q^{51} -17797.0 q^{52} -24975.0 q^{53} -15804.7 q^{54} +12653.2 q^{55} -13586.4 q^{56} -14902.8 q^{58} -23279.2 q^{59} +4521.52 q^{60} -15102.7 q^{61} +19330.0 q^{62} -5092.80 q^{63} +4096.00 q^{64} +21240.2 q^{65} -39224.7 q^{66} -59216.5 q^{67} -8356.63 q^{68} +47556.9 q^{69} +16215.0 q^{70} -14643.8 q^{71} +1535.37 q^{72} -18953.3 q^{73} -28611.9 q^{74} +40850.5 q^{75} -140667. q^{77} -65844.2 q^{78} +3628.29 q^{79} -4888.47 q^{80} -52643.9 q^{81} +43251.6 q^{82} +22655.2 q^{83} -50266.1 q^{84} +9973.42 q^{85} +41673.6 q^{86} -55136.7 q^{87} +42408.0 q^{88} -65622.3 q^{89} -1832.42 q^{90} -236129. q^{91} -51416.4 q^{92} +71516.1 q^{93} -47992.8 q^{94} +15154.2 q^{96} +59429.2 q^{97} -113035. q^{98} +15896.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 12 q^{2} - 13 q^{3} + 48 q^{4} + 81 q^{5} + 52 q^{6} + 228 q^{7} - 192 q^{8} + 236 q^{9} - 324 q^{10} + 363 q^{11} - 208 q^{12} - 501 q^{13} - 912 q^{14} + 670 q^{15} + 768 q^{16} - 1206 q^{17} - 944 q^{18}+ \cdots + 158317 q^{99}+O(q^{100}) $ 3 * q - 12 * q^2 - 13 * q^3 + 48 * q^4 + 81 * q^5 + 52 * q^6 + 228 * q^7 - 192 * q^8 + 236 * q^9 - 324 * q^10 + 363 * q^11 - 208 * q^12 - 501 * q^13 - 912 * q^14 + 670 * q^15 + 768 * q^16 - 1206 * q^17 - 944 * q^18 + 1296 * q^20 + 2085 * q^21 - 1452 * q^22 - 1077 * q^23 + 832 * q^24 - 3882 * q^25 + 2004 * q^26 + 5087 * q^27 + 3648 * q^28 + 8349 * q^29 - 2680 * q^30 + 7332 * q^31 - 3072 * q^32 + 15784 * q^33 + 4824 * q^34 - 1185 * q^35 + 3776 * q^36 + 1650 * q^37 + 773 * q^39 - 5184 * q^40 - 10140 * q^41 - 8340 * q^42 + 3777 * q^43 + 5808 * q^44 + 14005 * q^45 + 4308 * q^46 + 33231 * q^47 - 3328 * q^48 + 31269 * q^49 + 15528 * q^50 - 46935 * q^51 - 8016 * q^52 - 31029 * q^53 - 20348 * q^54 + 66003 * q^55 - 14592 * q^56 - 33396 * q^58 - 20409 * q^59 + 10720 * q^60 + 17115 * q^61 - 29328 * q^62 + 6327 * q^63 + 12288 * q^64 + 45348 * q^65 - 63136 * q^66 + 789 * q^67 - 19296 * q^68 + 151147 * q^69 + 4740 * q^70 - 19164 * q^71 - 15104 * q^72 - 76260 * q^73 - 6600 * q^74 + 69607 * q^75 - 97209 * q^77 - 3092 * q^78 - 68358 * q^79 + 20736 * q^80 - 197713 * q^81 + 40560 * q^82 + 6762 * q^83 + 33360 * q^84 - 45837 * q^85 - 15108 * q^86 + 66805 * q^87 - 23232 * q^88 + 85506 * q^89 - 56020 * q^90 - 345033 * q^91 - 17232 * q^92 + 15688 * q^93 - 132924 * q^94 + 13312 * q^96 - 105024 * q^97 - 125076 * q^98 + 158317 * q^99

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
$3$	−14.7990	−0.949355	−0.474678	−	0.880160i	$-0.657435\pi$
$3$	−14.7990	−0.949355	−0.474678	+	0.880160i	$0.657435\pi$
$4$	16.0000	0.500000
$5$	−19.0956	−0.341592	−0.170796	−	0.985306i	$-0.554634\pi$
$5$	−19.0956	−0.341592	−0.170796	+	0.985306i	$0.554634\pi$
$6$	59.1959	0.671295
$7$	212.287	1.63749	0.818745	−	0.574158i	$-0.194670\pi$
$7$	212.287	1.63749	0.818745	+	0.574158i	$0.194670\pi$
$8$	−64.0000	−0.353553
$9$	−23.9901	−0.0987248
$10$	76.3823	0.241542
$11$	−662.625	−1.65115	−0.825574	−	0.564294i	$-0.809148\pi$
$11$	−662.625	−1.65115	−0.825574	+	0.564294i	$0.809148\pi$
$12$	−236.784	−0.474678
$13$	−1112.31	−1.82544	−0.912720	−	0.408586i	$-0.866022\pi$
$13$	−1112.31	−1.82544	−0.912720	+	0.408586i	$0.866022\pi$
$14$	−849.148	−1.15788
$15$	282.595	0.324292
$16$	256.000	0.250000
$17$	−522.290	−0.438318	−0.219159	−	0.975689i	$-0.570331\pi$
$17$	−522.290	−0.438318	−0.219159	+	0.975689i	$0.570331\pi$
$18$	95.9606	0.0698090
$19$	0	0
$19$	0	0
$20$	−305.529	−0.170796
$21$	−3141.63	−1.55456
$22$	2650.50	1.16754
$23$	−3213.52	−1.26667	−0.633333	−	0.773880i	$-0.718314\pi$
$23$	−3213.52	−1.26667	−0.633333	+	0.773880i	$0.718314\pi$
$24$	947.135	0.335648
$25$	−2760.36	−0.883315
$26$	4449.24	1.29078
$27$	3951.18	1.04308
$28$	3396.59	0.818745
$29$	3725.71	0.822648	0.411324	−	0.911489i	$-0.365066\pi$
$29$	3725.71	0.822648	0.411324	+	0.911489i	$0.365066\pi$
$30$	−1130.38	−0.229309
$31$	−4832.50	−0.903167	−0.451583	−	0.892229i	$-0.649141\pi$
$31$	−4832.50	−0.903167	−0.451583	+	0.892229i	$0.649141\pi$
$32$	−1024.00	−0.176777
$33$	9806.17	1.56753
$34$	2089.16	0.309937
$35$	−4053.74	−0.559353
$36$	−383.842	−0.0493624
$37$	7152.96	0.858977	0.429489	−	0.903072i	$-0.358694\pi$
$37$	7152.96	0.858977	0.429489	+	0.903072i	$0.358694\pi$
$38$	0	0
$39$	16461.1	1.73299
$40$	1222.12	0.120771
$41$	−10812.9	−1.00457	−0.502287	−	0.864701i	$-0.667508\pi$
$41$	−10812.9	−1.00457	−0.502287	+	0.864701i	$0.667508\pi$
$42$	12566.5	1.09924
$43$	−10418.4	−0.859270	−0.429635	−	0.903003i	$-0.641358\pi$
$43$	−10418.4	−0.859270	−0.429635	+	0.903003i	$0.641358\pi$
$44$	−10602.0	−0.825574
$45$	458.106	0.0337236
$46$	12854.1	0.895668
$47$	11998.2	0.792267	0.396134	−	0.918193i	$-0.370352\pi$
$47$	11998.2	0.792267	0.396134	+	0.918193i	$0.370352\pi$
$48$	−3788.54	−0.237339
$49$	28258.8	1.68137
$50$	11041.4	0.624598
$51$	7729.35	0.416119
$52$	−17797.0	−0.912720
$53$	−24975.0	−1.22128	−0.610640	−	0.791908i	$-0.709088\pi$
$53$	−24975.0	−1.22128	−0.610640	+	0.791908i	$0.709088\pi$
$54$	−15804.7	−0.737569
$55$	12653.2	0.564019
$56$	−13586.4	−0.578940
$57$	0	0
$58$	−14902.8	−0.581700
$59$	−23279.2	−0.870638	−0.435319	−	0.900276i	$-0.643364\pi$
$59$	−23279.2	−0.870638	−0.435319	+	0.900276i	$0.643364\pi$
$60$	4521.52	0.162146
$61$	−15102.7	−0.519673	−0.259836	−	0.965653i	$-0.583669\pi$
$61$	−15102.7	−0.519673	−0.259836	+	0.965653i	$0.583669\pi$
$62$	19330.0	0.638635
$63$	−5092.80	−0.161661
$64$	4096.00	0.125000
$65$	21240.2	0.623556
$66$	−39224.7	−1.10841
$67$	−59216.5	−1.61159	−0.805797	−	0.592192i	$-0.798263\pi$
$67$	−59216.5	−1.61159	−0.805797	+	0.592192i	$0.798263\pi$
$68$	−8356.63	−0.219159
$69$	47556.9	1.20252
$70$	16215.0	0.395523
$71$	−14643.8	−0.344754	−0.172377	−	0.985031i	$-0.555145\pi$
$71$	−14643.8	−0.344754	−0.172377	+	0.985031i	$0.555145\pi$
$72$	1535.37	0.0349045
$73$	−18953.3	−0.416272	−0.208136	−	0.978100i	$-0.566740\pi$
$73$	−18953.3	−0.416272	−0.208136	+	0.978100i	$0.566740\pi$
$74$	−28611.9	−0.607389
$75$	40850.5	0.838579
$76$	0	0
$77$	−140667.	−2.70374
$78$	−65844.2	−1.22541
$79$	3628.29	0.0654085	0.0327043	−	0.999465i	$-0.489588\pi$
$79$	3628.29	0.0654085	0.0327043	+	0.999465i	$0.489588\pi$
$80$	−4888.47	−0.0853980
$81$	−52643.9	−0.891529
$82$	43251.6	0.710342
$83$	22655.2	0.360971	0.180485	−	0.983578i	$-0.442233\pi$
$83$	22655.2	0.360971	0.180485	+	0.983578i	$0.442233\pi$
$84$	−50266.1	−0.777279
$85$	9973.42	0.149726
$86$	41673.6	0.607596
$87$	−55136.7	−0.780986
$88$	42408.0	0.583769
$89$	−65622.3	−0.878166	−0.439083	−	0.898447i	$-0.644697\pi$
$89$	−65622.3	−0.878166	−0.439083	+	0.898447i	$0.644697\pi$
$90$	−1832.42	−0.0238462
$91$	−236129.	−2.98914
$92$	−51416.4	−0.633333
$93$	71516.1	0.857426
$94$	−47992.8	−0.560218
$95$	0	0
$96$	15154.2	0.167824
$97$	59429.2	0.641314	0.320657	−	0.947195i	$-0.396096\pi$
$97$	59429.2	0.641314	0.320657	+	0.947195i	$0.396096\pi$
$98$	−113035.	−1.18891
$99$	15896.5	0.163009
$100$	−44165.7	−0.441657
$101$	−24934.1	−0.243215	−0.121608	−	0.992578i	$-0.538805\pi$
$101$	−24934.1	−0.243215	−0.121608	+	0.992578i	$0.538805\pi$
$102$	−30917.4	−0.294241
$103$	−25045.1	−0.232611	−0.116306	−	0.993213i	$-0.537105\pi$
$103$	−25045.1	−0.232611	−0.116306	+	0.993213i	$0.537105\pi$
$104$	71187.8	0.645390
$105$	59991.3	0.531025
$106$	99899.9	0.863576
$107$	27876.0	0.235381	0.117690	−	0.993050i	$-0.462451\pi$
$107$	27876.0	0.235381	0.117690	+	0.993050i	$0.462451\pi$
$108$	63218.9	0.521540
$109$	109560.	0.883257	0.441629	−	0.897198i	$-0.354401\pi$
$109$	109560.	0.883257	0.441629	+	0.897198i	$0.354401\pi$
$110$	−50612.8	−0.398822
$111$	−105857.	−0.815475
$112$	54345.5	0.409372
$113$	93201.6	0.686637	0.343319	−	0.939219i	$-0.388449\pi$
$113$	93201.6	0.686637	0.343319	+	0.939219i	$0.388449\pi$
$114$	0	0
$115$	61364.1	0.432683
$116$	59611.4	0.411324
$117$	26684.5	0.180216
$118$	93116.7	0.615634
$119$	−110875.	−0.717741
$120$	−18086.1	−0.114655
$121$	278021.	1.72629
$122$	60410.8	0.367464
$123$	160020.	0.953698
$124$	−77320.1	−0.451583
$125$	112384.	0.643325
$126$	20371.2	0.114311
$127$	−60981.0	−0.335495	−0.167747	−	0.985830i	$-0.553649\pi$
$127$	−60981.0	−0.335495	−0.167747	+	0.985830i	$0.553649\pi$
$128$	−16384.0	−0.0883883
$129$	154182.	0.815752
$130$	−84960.8	−0.440920
$131$	−356070.	−1.81283	−0.906416	−	0.422387i	$-0.861192\pi$
$131$	−356070.	−1.81283	−0.906416	+	0.422387i	$0.861192\pi$
$132$	156899.	0.783763
$133$	0	0
$134$	236866.	1.13957
$135$	−75450.1	−0.356308
$136$	33426.5	0.154969
$137$	47760.0	0.217402	0.108701	−	0.994075i	$-0.465331\pi$
$137$	47760.0	0.217402	0.108701	+	0.994075i	$0.465331\pi$
$138$	−190228.	−0.850307
$139$	413927.	1.81713	0.908566	−	0.417741i	$-0.137178\pi$
$139$	413927.	1.81713	0.908566	+	0.417741i	$0.137178\pi$
$140$	−64859.9	−0.279677
$141$	−177561.	−0.752143
$142$	58575.4	0.243778
$143$	737044.	3.01407
$144$	−6141.48	−0.0246812
$145$	−71144.6	−0.281010
$146$	75813.1	0.294349
$147$	−418201.	−1.59622
$148$	114447.	0.429489
$149$	−168897.	−0.623242	−0.311621	−	0.950206i	$-0.600872\pi$
$149$	−168897.	−0.623242	−0.311621	+	0.950206i	$0.600872\pi$
$150$	−163402.	−0.592965
$151$	−132860.	−0.474191	−0.237096	−	0.971486i	$-0.576195\pi$
$151$	−132860.	−0.474191	−0.237096	+	0.971486i	$0.576195\pi$
$152$	0	0
$153$	12529.8	0.0432729
$154$	562667.	1.91183
$155$	92279.5	0.308515
$156$	263377.	0.866495
$157$	−129994.	−0.420894	−0.210447	−	0.977605i	$-0.567492\pi$
$157$	−129994.	−0.420894	−0.210447	+	0.977605i	$0.567492\pi$
$158$	−14513.2	−0.0462508
$159$	369604.	1.15943
$160$	19553.9	0.0603855
$161$	−682190.	−2.07415
$162$	210575.	0.630406
$163$	−542110.	−1.59815	−0.799076	−	0.601230i	$-0.794678\pi$
$163$	−542110.	−1.59815	−0.799076	+	0.601230i	$0.794678\pi$
$164$	−173006.	−0.502287
$165$	−187255.	−0.535454
$166$	−90620.7	−0.255245
$167$	−525577.	−1.45829	−0.729147	−	0.684357i	$-0.760083\pi$
$167$	−525577.	−1.45829	−0.729147	+	0.684357i	$0.760083\pi$
$168$	201064.	0.549619
$169$	865940.	2.33223
$170$	−39893.7	−0.105872
$171$	0	0
$172$	−166694.	−0.429635
$173$	−650536.	−1.65256	−0.826278	−	0.563263i	$-0.809546\pi$
$173$	−650536.	−1.65256	−0.826278	+	0.563263i	$0.809546\pi$
$174$	220547.	0.552240
$175$	−585988.	−1.44642
$176$	−169632.	−0.412787
$177$	344508.	0.826545
$178$	262489.	0.620957
$179$	−647733.	−1.51100	−0.755498	−	0.655151i	$-0.772605\pi$
$179$	−647733.	−1.51100	−0.755498	+	0.655151i	$0.772605\pi$
$180$	7329.69	0.0168618
$181$	442268.	1.00343	0.501717	−	0.865032i	$-0.332702\pi$
$181$	442268.	1.00343	0.501717	+	0.865032i	$0.332702\pi$
$182$	944516.	2.11364
$183$	223505.	0.493354
$184$	205666.	0.447834
$185$	−136590.	−0.293420
$186$	−286065.	−0.606292
$187$	346082.	0.723727
$188$	191971.	0.396134
$189$	838785.	1.70803
$190$	0	0
$191$	−186520.	−0.369949	−0.184974	−	0.982743i	$-0.559220\pi$
$191$	−186520.	−0.369949	−0.184974	+	0.982743i	$0.559220\pi$
$192$	−60616.6	−0.118669
$193$	623123.	1.20415	0.602075	−	0.798440i	$-0.294341\pi$
$193$	623123.	1.20415	0.602075	+	0.798440i	$0.294341\pi$
$194$	−237717.	−0.453477
$195$	−314333.	−0.591976
$196$	452141.	0.840685
$197$	63660.0	0.116869	0.0584347	−	0.998291i	$-0.481389\pi$
$197$	63660.0	0.116869	0.0584347	+	0.998291i	$0.481389\pi$
$198$	−63585.8	−0.115265
$199$	531810.	0.951971	0.475986	−	0.879453i	$-0.342091\pi$
$199$	531810.	0.951971	0.475986	+	0.879453i	$0.342091\pi$
$200$	176663.	0.312299
$201$	876344.	1.52997
$202$	99736.4	0.171979
$203$	790920.	1.34708
$204$	123670.	0.208060
$205$	206478.	0.343155
$206$	100181.	0.164481
$207$	77092.9	0.125051
$208$	−284751.	−0.456360
$209$	0	0
$210$	−239965.	−0.375491
$211$	950256.	1.46938	0.734691	−	0.678402i	$-0.237327\pi$
$211$	950256.	1.46938	0.734691	+	0.678402i	$0.237327\pi$
$212$	−399600.	−0.610640
$213$	216714.	0.327294
$214$	−111504.	−0.166439
$215$	198945.	0.293520
$216$	−252876.	−0.368784
$217$	−1.02588e6	−1.47893
$218$	−438241.	−0.624557
$219$	280489.	0.395190
$220$	202451.	0.282010
$221$	580948.	0.800122
$222$	423426.	0.576628
$223$	412023.	0.554829	0.277415	−	0.960750i	$-0.410522\pi$
$223$	412023.	0.554829	0.277415	+	0.960750i	$0.410522\pi$
$224$	−217382.	−0.289470
$225$	66221.4	0.0872051
$226$	−372806.	−0.485526
$227$	−216720.	−0.279148	−0.139574	−	0.990212i	$-0.544573\pi$
$227$	−216720.	−0.279148	−0.139574	+	0.990212i	$0.544573\pi$
$228$	0	0
$229$	−467558.	−0.589178	−0.294589	−	0.955624i	$-0.595183\pi$
$229$	−467558.	−0.589178	−0.294589	+	0.955624i	$0.595183\pi$
$230$	−245456.	−0.305953
$231$	2.08172e6	2.56681
$232$	−238446.	−0.290850
$233$	−964515.	−1.16391	−0.581955	−	0.813221i	$-0.697712\pi$
$233$	−964515.	−1.16391	−0.581955	+	0.813221i	$0.697712\pi$
$234$	−106738.	−0.127432
$235$	−229113.	−0.270632
$236$	−372467.	−0.435319
$237$	−53695.0	−0.0620959
$238$	443501.	0.507519
$239$	1.66583e6	1.88641	0.943206	−	0.332207i	$-0.107793\pi$
$239$	1.66583e6	1.88641	0.943206	+	0.332207i	$0.107793\pi$
$240$	72344.3	0.0810730
$241$	395797.	0.438965	0.219482	−	0.975616i	$-0.429563\pi$
$241$	395797.	0.438965	0.219482	+	0.975616i	$0.429563\pi$
$242$	−1.11208e6	−1.22067
$243$	−181062.	−0.196703
$244$	−241643.	−0.259836
$245$	−539618.	−0.574343
$246$	−640079.	−0.674366
$247$	0	0
$248$	309280.	0.319318
$249$	−335273.	−0.342690
$250$	−449537.	−0.454900
$251$	−52655.6	−0.0527546	−0.0263773	−	0.999652i	$-0.508397\pi$
$251$	−52655.6	−0.0527546	−0.0263773	+	0.999652i	$0.508397\pi$
$252$	−81484.7	−0.0808304
$253$	2.12936e6	2.09145
$254$	243924.	0.237230
$255$	−147596.	−0.142143
$256$	65536.0	0.0625000
$257$	−369622.	−0.349080	−0.174540	−	0.984650i	$-0.555844\pi$
$257$	−369622.	−0.349080	−0.174540	+	0.984650i	$0.555844\pi$
$258$	−616727.	−0.576824
$259$	1.51848e6	1.40657
$260$	339843.	0.311778
$261$	−89380.3	−0.0812158
$262$	1.42428e6	1.28187
$263$	−266855.	−0.237895	−0.118948	−	0.992901i	$-0.537952\pi$
$263$	−266855.	−0.237895	−0.118948	+	0.992901i	$0.537952\pi$
$264$	−627595.	−0.554204
$265$	476912.	0.417180
$266$	0	0
$267$	971144.	0.833691
$268$	−947464.	−0.805797
$269$	283145.	0.238577	0.119289	−	0.992860i	$-0.461939\pi$
$269$	283145.	0.238577	0.119289	+	0.992860i	$0.461939\pi$
$270$	301800.	0.251948
$271$	1.26094e6	1.04296	0.521482	−	0.853262i	$-0.325379\pi$
$271$	1.26094e6	1.04296	0.521482	+	0.853262i	$0.325379\pi$
$272$	−133706.	−0.109579
$273$	3.49447e6	2.83775
$274$	−191040.	−0.153726
$275$	1.82908e6	1.45848
$276$	760910.	0.601258
$277$	1.86541e6	1.46074	0.730372	−	0.683050i	$-0.239347\pi$
$277$	1.86541e6	1.46074	0.730372	+	0.683050i	$0.239347\pi$
$278$	−1.65571e6	−1.28491
$279$	115932.	0.0891650
$280$	259440.	0.197761
$281$	432083.	0.326439	0.163219	−	0.986590i	$-0.447812\pi$
$281$	432083.	0.326439	0.163219	+	0.986590i	$0.447812\pi$
$282$	710245.	0.531846
$283$	−1.32987e6	−0.987056	−0.493528	−	0.869730i	$-0.664293\pi$
$283$	−1.32987e6	−0.987056	−0.493528	+	0.869730i	$0.664293\pi$
$284$	−234302.	−0.172377
$285$	0	0
$286$	−2.94818e6	−2.13127
$287$	−2.29544e6	−1.64498
$288$	24565.9	0.0174523
$289$	−1.14707e6	−0.807878
$290$	284579.	0.198704
$291$	−879492.	−0.608835
$292$	−303253.	−0.208136
$293$	701589.	0.477435	0.238717	−	0.971089i	$-0.423273\pi$
$293$	701589.	0.477435	0.238717	+	0.971089i	$0.423273\pi$
$294$	1.67281e6	1.12870
$295$	444529.	0.297403
$296$	−457790.	−0.303694
$297$	−2.61815e6	−1.72228
$298$	675589.	0.440699
$299$	3.57443e6	2.31222
$300$	653608.	0.419290
$301$	−2.21169e6	−1.40705
$302$	531442.	0.335304
$303$	368999.	0.230897
$304$	0	0
$305$	288395.	0.177516
$306$	−50119.2	−0.0305985
$307$	667303.	0.404089	0.202044	−	0.979376i	$-0.435241\pi$
$307$	667303.	0.404089	0.202044	+	0.979376i	$0.435241\pi$
$308$	−2.25067e6	−1.35187
$309$	370643.	0.220831
$310$	−369118.	−0.218153
$311$	242281.	0.142042	0.0710211	−	0.997475i	$-0.477374\pi$
$311$	242281.	0.142042	0.0710211	+	0.997475i	$0.477374\pi$
$312$	−1.05351e6	−0.612705
$313$	2.02771e6	1.16989	0.584945	−	0.811073i	$-0.301116\pi$
$313$	2.02771e6	1.16989	0.584945	+	0.811073i	$0.301116\pi$
$314$	519974.	0.297617
$315$	97249.9	0.0552221
$316$	58052.6	0.0327043
$317$	983497.	0.549699	0.274849	−	0.961487i	$-0.411372\pi$
$317$	983497.	0.549699	0.274849	+	0.961487i	$0.411372\pi$
$318$	−1.47842e6	−0.819840
$319$	−2.46875e6	−1.35831
$320$	−78215.5	−0.0426990
$321$	−412536.	−0.223460
$322$	2.72876e6	1.46665
$323$	0	0
$324$	−842302.	−0.445764
$325$	3.07037e6	1.61244
$326$	2.16844e6	1.13006
$327$	−1.62138e6	−0.838525
$328$	692025.	0.355171
$329$	2.54706e6	1.29733
$330$	749018.	0.378623
$331$	−69223.1	−0.0347281	−0.0173640	−	0.999849i	$-0.505527\pi$
$331$	−69223.1	−0.0347281	−0.0173640	+	0.999849i	$0.505527\pi$
$332$	362483.	0.180485
$333$	−171601.	−0.0848024
$334$	2.10231e6	1.03117
$335$	1.13077e6	0.550508
$336$	−804258.	−0.388640
$337$	−567994.	−0.272439	−0.136219	−	0.990679i	$-0.543495\pi$
$337$	−567994.	−0.272439	−0.136219	+	0.990679i	$0.543495\pi$
$338$	−3.46376e6	−1.64913
$339$	−1.37929e6	−0.651862
$340$	159575.	0.0748629
$341$	3.20214e6	1.49126
$342$	0	0
$343$	2.43107e6	1.11574
$344$	666777.	0.303798
$345$	−908126.	−0.410770
$346$	2.60214e6	1.16853
$347$	−46773.6	−0.0208534	−0.0104267	−	0.999946i	$-0.503319\pi$
$347$	−46773.6	−0.0208534	−0.0104267	+	0.999946i	$0.503319\pi$
$348$	−882188.	−0.390493
$349$	−3.10376e6	−1.36403	−0.682016	−	0.731337i	$-0.738897\pi$
$349$	−3.10376e6	−1.36403	−0.682016	+	0.731337i	$0.738897\pi$
$350$	2.34395e6	1.02277
$351$	−4.39494e6	−1.90408
$352$	678528.	0.291884
$353$	−1.92152e6	−0.820743	−0.410372	−	0.911918i	$-0.634601\pi$
$353$	−1.92152e6	−0.820743	−0.410372	+	0.911918i	$0.634601\pi$
$354$	−1.37803e6	−0.584455
$355$	279633.	0.117765
$356$	−1.04996e6	−0.439083
$357$	1.64084e6	0.681391
$358$	2.59093e6	1.06844
$359$	1.88950e6	0.773766	0.386883	−	0.922129i	$-0.373552\pi$
$359$	1.88950e6	0.773766	0.386883	+	0.922129i	$0.373552\pi$
$360$	−29318.8	−0.0119231
$361$	0	0
$362$	−1.76907e6	−0.709535
$363$	−4.11442e6	−1.63886
$364$	−3.77806e6	−1.49457
$365$	361924.	0.142195
$366$	−894018.	−0.348854
$367$	1.15810e6	0.448831	0.224415	−	0.974494i	$-0.427953\pi$
$367$	1.15810e6	0.448831	0.224415	+	0.974494i	$0.427953\pi$
$368$	−822662.	−0.316666
$369$	259403.	0.0991765
$370$	546360.	0.207479
$371$	−5.30187e6	−1.99983
$372$	1.14426e6	0.428713
$373$	5.01675e6	1.86703	0.933513	−	0.358543i	$-0.116726\pi$
$373$	5.01675e6	1.86703	0.933513	+	0.358543i	$0.116726\pi$
$374$	−1.38433e6	−0.511753
$375$	−1.66317e6	−0.610744
$376$	−767885.	−0.280109
$377$	−4.14415e6	−1.50169
$378$	−3.35514e6	−1.20776
$379$	−3.83992e6	−1.37317	−0.686584	−	0.727050i	$-0.740891\pi$
$379$	−3.83992e6	−1.37317	−0.686584	+	0.727050i	$0.740891\pi$
$380$	0	0
$381$	902457.	0.318503
$382$	746079.	0.261593
$383$	4.41598e6	1.53826	0.769131	−	0.639091i	$-0.220689\pi$
$383$	4.41598e6	1.53826	0.769131	+	0.639091i	$0.220689\pi$
$384$	242467.	0.0839119
$385$	2.68611e6	0.923575
$386$	−2.49249e6	−0.851462
$387$	249939.	0.0848313
$388$	950868.	0.320657
$389$	−1.32552e6	−0.444133	−0.222067	−	0.975032i	$-0.571280\pi$
$389$	−1.32552e6	−0.444133	−0.222067	+	0.975032i	$0.571280\pi$
$390$	1.25733e6	0.418590
$391$	1.67839e6	0.555202
$392$	−1.80856e6	−0.594454
$393$	5.26948e6	1.72102
$394$	−254640.	−0.0826392
$395$	−69284.3	−0.0223430
$396$	254343.	0.0815047
$397$	244751.	0.0779379	0.0389689	−	0.999240i	$-0.487593\pi$
$397$	244751.	0.0779379	0.0389689	+	0.999240i	$0.487593\pi$
$398$	−2.12724e6	−0.673145
$399$	0	0
$400$	−706652.	−0.220829
$401$	686533.	0.213206	0.106603	−	0.994302i	$-0.466003\pi$
$401$	686533.	0.213206	0.106603	+	0.994302i	$0.466003\pi$
$402$	−3.50537e6	−1.08186
$403$	5.37524e6	1.64868
$404$	−398946.	−0.121608
$405$	1.00527e6	0.304539
$406$	−3.16368e6	−0.952528
$407$	−4.73973e6	−1.41830
$408$	−494679.	−0.147120
$409$	−2.48415e6	−0.734293	−0.367147	−	0.930163i	$-0.619665\pi$
$409$	−2.48415e6	−0.734293	−0.367147	+	0.930163i	$0.619665\pi$
$410$	−825914.	−0.242647
$411$	−706799.	−0.206391
$412$	−400722.	−0.116306
$413$	−4.94187e6	−1.42566
$414$	−308372.	−0.0884247
$415$	−432614.	−0.123305
$416$	1.13901e6	0.322695
$417$	−6.12570e6	−1.72510
$418$	0	0
$419$	116076.	0.0323004	0.0161502	−	0.999870i	$-0.494859\pi$
$419$	116076.	0.0323004	0.0161502	+	0.999870i	$0.494859\pi$
$420$	959861.	0.265512
$421$	−192169.	−0.0528419	−0.0264209	−	0.999651i	$-0.508411\pi$
$421$	−192169.	−0.0528419	−0.0264209	+	0.999651i	$0.508411\pi$
$422$	−3.80102e6	−1.03901
$423$	−287839.	−0.0782165
$424$	1.59840e6	0.431788
$425$	1.44171e6	0.387173
$426$	−866856.	−0.231432
$427$	−3.20611e6	−0.850959
$428$	446015.	0.117690
$429$	−1.09075e7	−2.86142
$430$	−795781.	−0.207550
$431$	−3.25385e6	−0.843731	−0.421865	−	0.906659i	$-0.638624\pi$
$431$	−3.25385e6	−0.843731	−0.421865	+	0.906659i	$0.638624\pi$
$432$	1.01150e6	0.260770
$433$	247577.	0.0634585	0.0317292	−	0.999497i	$-0.489899\pi$
$433$	247577.	0.0634585	0.0317292	+	0.999497i	$0.489899\pi$
$434$	4.10351e6	1.04576
$435$	1.05287e6	0.266778
$436$	1.75297e6	0.441629
$437$	0	0
$438$	−1.12196e6	−0.279442
$439$	3.55674e6	0.880828	0.440414	−	0.897795i	$-0.354832\pi$
$439$	3.55674e6	0.880828	0.440414	+	0.897795i	$0.354832\pi$
$440$	−809805.	−0.199411
$441$	−677932.	−0.165993
$442$	−2.32379e6	−0.565772
$443$	−2.71438e6	−0.657145	−0.328573	−	0.944479i	$-0.606568\pi$
$443$	−2.71438e6	−0.657145	−0.328573	+	0.944479i	$0.606568\pi$
$444$	−1.69371e6	−0.407737
$445$	1.25310e6	0.299975
$446$	−1.64809e6	−0.392324
$447$	2.49951e6	0.591678
$448$	869528.	0.204686
$449$	2.35366e6	0.550969	0.275484	−	0.961306i	$-0.411162\pi$
$449$	2.35366e6	0.550969	0.275484	+	0.961306i	$0.411162\pi$
$450$	−264886.	−0.0616633
$451$	7.16489e6	1.65870
$452$	1.49123e6	0.343319
$453$	1.96620e6	0.450176
$454$	866882.	0.197388
$455$	4.50902e6	1.02107
$456$	0	0
$457$	7.61497e6	1.70560	0.852802	−	0.522235i	$-0.174902\pi$
$457$	7.61497e6	1.70560	0.852802	+	0.522235i	$0.174902\pi$
$458$	1.87023e6	0.416612
$459$	−2.06366e6	−0.457201
$460$	981826.	0.216341
$461$	−7.99940e6	−1.75309	−0.876546	−	0.481318i	$-0.840158\pi$
$461$	−7.99940e6	−1.75309	−0.876546	+	0.481318i	$0.840158\pi$
$462$	−8.32689e6	−1.81501
$463$	2.55307e6	0.553491	0.276745	−	0.960943i	$-0.410744\pi$
$463$	2.55307e6	0.553491	0.276745	+	0.960943i	$0.410744\pi$
$464$	953782.	0.205662
$465$	−1.36564e6	−0.292890
$466$	3.85806e6	0.823008
$467$	−6.01000e6	−1.27521	−0.637605	−	0.770363i	$-0.720075\pi$
$467$	−6.01000e6	−1.27521	−0.637605	+	0.770363i	$0.720075\pi$
$468$	426951.	0.0901081
$469$	−1.25709e7	−2.63897
$470$	916451.	0.191366
$471$	1.92377e6	0.399578
$472$	1.48987e6	0.307817
$473$	6.90349e6	1.41878
$474$	214780.	0.0439084
$475$	0	0
$476$	−1.77401e6	−0.358870
$477$	599153.	0.120571
$478$	−6.66333e6	−1.33390
$479$	9.37118e6	1.86619	0.933094	−	0.359632i	$-0.117098\pi$
$479$	9.37118e6	1.86619	0.933094	+	0.359632i	$0.117098\pi$
$480$	−289377.	−0.0573273
$481$	−7.95631e6	−1.56801
$482$	−1.58319e6	−0.310395
$483$	1.00957e7	1.96911
$484$	4.44833e6	0.863145
$485$	−1.13484e6	−0.219068
$486$	724246.	0.139090
$487$	−909566.	−0.173785	−0.0868924	−	0.996218i	$-0.527694\pi$
$487$	−909566.	−0.173785	−0.0868924	+	0.996218i	$0.527694\pi$
$488$	966573.	0.183732
$489$	8.02267e6	1.51721
$490$	2.15847e6	0.406122
$491$	5.72830e6	1.07231	0.536157	−	0.844118i	$-0.319876\pi$
$491$	5.72830e6	1.07231	0.536157	+	0.844118i	$0.319876\pi$
$492$	2.56032e6	0.476849
$493$	−1.94590e6	−0.360581
$494$	0	0
$495$	−303552.	−0.0556827
$496$	−1.23712e6	−0.225792
$497$	−3.10870e6	−0.564531
$498$	1.34109e6	0.242318
$499$	2.66518e6	0.479154	0.239577	−	0.970877i	$-0.422991\pi$
$499$	2.66518e6	0.479154	0.239577	+	0.970877i	$0.422991\pi$
$500$	1.79815e6	0.321663
$501$	7.77801e6	1.38444
$502$	210622.	0.0373031
$503$	4.39821e6	0.775098	0.387549	−	0.921849i	$-0.373322\pi$
$503$	4.39821e6	0.775098	0.387549	+	0.921849i	$0.373322\pi$
$504$	325939.	0.0571557
$505$	476131.	0.0830803
$506$	−8.51744e6	−1.47888
$507$	−1.28150e7	−2.21411
$508$	−975697.	−0.167747
$509$	4.66199e6	0.797585	0.398792	−	0.917041i	$-0.369429\pi$
$509$	4.66199e6	0.797585	0.398792	+	0.917041i	$0.369429\pi$
$510$	590386.	0.100510
$511$	−4.02354e6	−0.681641
$512$	−262144.	−0.0441942
$513$	0	0
$514$	1.47849e6	0.246837
$515$	478251.	0.0794581
$516$	2.46691e6	0.407876
$517$	−7.95031e6	−1.30815
$518$	−6.07393e6	−0.994593
$519$	9.62727e6	1.56886
$520$	−1.35937e6	−0.220460
$521$	−1.26923e6	−0.204855	−0.102427	−	0.994740i	$-0.532661\pi$
$521$	−1.26923e6	−0.204855	−0.102427	+	0.994740i	$0.532661\pi$
$522$	357521.	0.0574283
$523$	−5.54928e6	−0.887119	−0.443560	−	0.896245i	$-0.646285\pi$
$523$	−5.54928e6	−0.887119	−0.443560	+	0.896245i	$0.646285\pi$
$524$	−5.69712e6	−0.906416
$525$	8.67203e6	1.37316
$526$	1.06742e6	0.168217
$527$	2.52397e6	0.395874
$528$	2.51038e6	0.391881
$529$	3.89040e6	0.604442
$530$	−1.90765e6	−0.294991
$531$	558471.	0.0859536
$532$	0	0
$533$	1.20273e7	1.83379
$534$	−3.88457e6	−0.589509
$535$	−532308.	−0.0804041
$536$	3.78985e6	0.569784
$537$	9.58579e6	1.43447
$538$	−1.13258e6	−0.168700
$539$	−1.87250e7	−2.77619
$540$	−1.20720e6	−0.178154
$541$	−9.66859e6	−1.42027	−0.710134	−	0.704067i	$-0.751366\pi$
$541$	−9.66859e6	−1.42027	−0.710134	+	0.704067i	$0.751366\pi$
$542$	−5.04374e6	−0.737487
$543$	−6.54511e6	−0.952615
$544$	534825.	0.0774844
$545$	−2.09212e6	−0.301714
$546$	−1.39779e7	−2.00659
$547$	3.56127e6	0.508905	0.254453	−	0.967085i	$-0.418105\pi$
$547$	3.56127e6	0.508905	0.254453	+	0.967085i	$0.418105\pi$
$548$	764160.	0.108701
$549$	362316.	0.0513046
$550$	−7.31633e6	−1.03130
$551$	0	0
$552$	−3.04364e6	−0.425153
$553$	770239.	0.107106
$554$	−7.46163e6	−1.03290
$555$	2.02139e6	0.278560
$556$	6.62283e6	0.908566
$557$	−1.12732e7	−1.53960	−0.769801	−	0.638284i	$-0.779644\pi$
$557$	−1.12732e7	−1.53960	−0.769801	+	0.638284i	$0.779644\pi$
$558$	−463730.	−0.0630492
$559$	1.15885e7	1.56855
$560$	−1.03776e6	−0.139838
$561$	−5.12166e6	−0.687074
$562$	−1.72833e6	−0.230827
$563$	2.63453e6	0.350293	0.175147	−	0.984542i	$-0.443960\pi$
$563$	2.63453e6	0.350293	0.175147	+	0.984542i	$0.443960\pi$
$564$	−2.84098e6	−0.376072
$565$	−1.77974e6	−0.234550
$566$	5.31946e6	0.697954
$567$	−1.11756e7	−1.45987
$568$	937206.	0.121889
$569$	−2.77738e6	−0.359629	−0.179814	−	0.983701i	$-0.557550\pi$
$569$	−2.77738e6	−0.359629	−0.179814	+	0.983701i	$0.557550\pi$
$570$	0	0
$571$	3.91874e6	0.502986	0.251493	−	0.967859i	$-0.419078\pi$
$571$	3.91874e6	0.502986	0.251493	+	0.967859i	$0.419078\pi$
$572$	1.17927e7	1.50704
$573$	2.76030e6	0.351213
$574$	9.18175e6	1.16318
$575$	8.87048e6	1.11886
$576$	−98263.6	−0.0123406
$577$	938331.	0.117332	0.0586660	−	0.998278i	$-0.481315\pi$
$577$	938331.	0.117332	0.0586660	+	0.998278i	$0.481315\pi$
$578$	4.58828e6	0.571256
$579$	−9.22159e6	−1.14317
$580$	−1.13831e6	−0.140505
$581$	4.80940e6	0.591086
$582$	3.51797e6	0.430511
$583$	1.65490e7	2.01652
$584$	1.21301e6	0.147174
$585$	−509555.	−0.0615604
$586$	−2.80636e6	−0.337597
$587$	1.21860e7	1.45971	0.729856	−	0.683601i	$-0.239587\pi$
$587$	1.21860e7	1.45971	0.729856	+	0.683601i	$0.239587\pi$
$588$	−6.69122e6	−0.798109
$589$	0	0
$590$	−1.77812e6	−0.210296
$591$	−942103.	−0.110951
$592$	1.83116e6	0.214744
$593$	−8.86284e6	−1.03499	−0.517495	−	0.855686i	$-0.673135\pi$
$593$	−8.86284e6	−1.03499	−0.517495	+	0.855686i	$0.673135\pi$
$594$	1.04726e7	1.21784
$595$	2.11723e6	0.245174
$596$	−2.70236e6	−0.311621
$597$	−7.87025e6	−0.903759
$598$	−1.42977e7	−1.63499
$599$	6.26482e6	0.713414	0.356707	−	0.934216i	$-0.383899\pi$
$599$	6.26482e6	0.713414	0.356707	+	0.934216i	$0.383899\pi$
$600$	−2.61443e6	−0.296483
$601$	−9.59570e6	−1.08365	−0.541827	−	0.840490i	$-0.682267\pi$
$601$	−9.59570e6	−1.08365	−0.541827	+	0.840490i	$0.682267\pi$
$602$	8.84676e6	0.994931
$603$	1.42061e6	0.159104
$604$	−2.12577e6	−0.237096
$605$	−5.30897e6	−0.589687
$606$	−1.47600e6	−0.163269
$607$	1.06282e7	1.17082	0.585408	−	0.810739i	$-0.300934\pi$
$607$	1.06282e7	1.17082	0.585408	+	0.810739i	$0.300934\pi$
$608$	0	0
$609$	−1.17048e7	−1.27886
$610$	−1.15358e6	−0.125523
$611$	−1.33457e7	−1.44624
$612$	200477.	0.0216364
$613$	−1.43183e7	−1.53900	−0.769502	−	0.638645i	$-0.779495\pi$
$613$	−1.43183e7	−1.53900	−0.769502	+	0.638645i	$0.779495\pi$
$614$	−2.66921e6	−0.285734
$615$	−3.05567e6	−0.325776
$616$	9.00267e6	0.955915
$617$	1.71005e7	1.80841	0.904204	−	0.427100i	$-0.140465\pi$
$617$	1.71005e7	1.80841	0.904204	+	0.427100i	$0.140465\pi$
$618$	−1.48257e6	−0.156151
$619$	−1.54652e7	−1.62229	−0.811146	−	0.584844i	$-0.801156\pi$
$619$	−1.54652e7	−1.62229	−0.811146	+	0.584844i	$0.801156\pi$
$620$	1.47647e6	0.154257
$621$	−1.26972e7	−1.32123
$622$	−969122.	−0.100439
$623$	−1.39308e7	−1.43799
$624$	4.21403e6	0.433248
$625$	6.48008e6	0.663560
$626$	−8.11084e6	−0.827237
$627$	0	0
$628$	−2.07990e6	−0.210447
$629$	−3.73592e6	−0.376505
$630$	−389000.	−0.0390479
$631$	1.73001e6	0.172972	0.0864860	−	0.996253i	$-0.472436\pi$
$631$	1.73001e6	0.172972	0.0864860	+	0.996253i	$0.472436\pi$
$632$	−232211.	−0.0231254
$633$	−1.40628e7	−1.39496
$634$	−3.93399e6	−0.388696
$635$	1.16447e6	0.114602
$636$	5.91367e6	0.579715
$637$	−3.14325e7	−3.06924
$638$	9.87500e6	0.960473
$639$	351308.	0.0340358
$640$	312862.	0.0301928
$641$	8.59864e6	0.826579	0.413290	−	0.910600i	$-0.364380\pi$
$641$	8.59864e6	0.826579	0.413290	+	0.910600i	$0.364380\pi$
$642$	1.65014e6	0.158010
$643$	1.02223e7	0.975039	0.487519	−	0.873112i	$-0.337902\pi$
$643$	1.02223e7	0.975039	0.487519	+	0.873112i	$0.337902\pi$
$644$	−1.09150e7	−1.03708
$645$	−2.94419e6	−0.278655
$646$	0	0
$647$	−2.86656e6	−0.269215	−0.134608	−	0.990899i	$-0.542977\pi$
$647$	−2.86656e6	−0.269215	−0.134608	+	0.990899i	$0.542977\pi$
$648$	3.36921e6	0.315203
$649$	1.54254e7	1.43755
$650$	−1.22815e7	−1.14017
$651$	1.51820e7	1.40403
$652$	−8.67376e6	−0.799076
$653$	−1.59807e7	−1.46660	−0.733300	−	0.679905i	$-0.762021\pi$
$653$	−1.59807e7	−1.46660	−0.733300	+	0.679905i	$0.762021\pi$
$654$	6.48553e6	0.592926
$655$	6.79937e6	0.619249
$656$	−2.76810e6	−0.251144
$657$	454692.	0.0410964
$658$	−1.01883e7	−0.917350
$659$	−3.24758e6	−0.291304	−0.145652	−	0.989336i	$-0.546528\pi$
$659$	−3.24758e6	−0.291304	−0.145652	+	0.989336i	$0.546528\pi$
$660$	−2.99607e6	−0.267727
$661$	−1.91717e7	−1.70670	−0.853350	−	0.521339i	$-0.825433\pi$
$661$	−1.91717e7	−1.70670	−0.853350	+	0.521339i	$0.825433\pi$
$662$	276892.	0.0245565
$663$	−8.59744e6	−0.759600
$664$	−1.44993e6	−0.127622
$665$	0	0
$666$	686402.	0.0599644
$667$	−1.19727e7	−1.04202
$668$	−8.40923e6	−0.729147
$669$	−6.09752e6	−0.526730
$670$	−4.52309e6	−0.389268
$671$	1.00074e7	0.858057
$672$	3.21703e6	0.274810
$673$	−8.11070e6	−0.690273	−0.345136	−	0.938553i	$-0.612167\pi$
$673$	−8.11070e6	−0.690273	−0.345136	+	0.938553i	$0.612167\pi$
$674$	2.27198e6	0.192643
$675$	−1.09067e7	−0.921368
$676$	1.38550e7	1.16611
$677$	−4.53293e6	−0.380109	−0.190054	−	0.981774i	$-0.560866\pi$
$677$	−4.53293e6	−0.380109	−0.190054	+	0.981774i	$0.560866\pi$
$678$	5.51715e6	0.460936
$679$	1.26161e7	1.05014
$680$	−638299.	−0.0529361
$681$	3.20724e6	0.265011
$682$	−1.28085e7	−1.05448
$683$	2.12901e7	1.74633	0.873163	−	0.487427i	$-0.162065\pi$
$683$	2.12901e7	1.74633	0.873163	+	0.487427i	$0.162065\pi$
$684$	0	0
$685$	−912004.	−0.0742627
$686$	−9.72427e6	−0.788945
$687$	6.91938e6	0.559339
$688$	−2.66711e6	−0.214818
$689$	2.77799e7	2.22937
$690$	3.63251e6	0.290458
$691$	4.77800e6	0.380672	0.190336	−	0.981719i	$-0.439042\pi$
$691$	4.77800e6	0.380672	0.190336	+	0.981719i	$0.439042\pi$
$692$	−1.04086e7	−0.826278
$693$	3.37461e6	0.266926
$694$	187095.	0.0147456
$695$	−7.90417e6	−0.620718
$696$	3.52875e6	0.276120
$697$	5.64746e6	0.440323
$698$	1.24150e7	0.964517
$699$	1.42738e7	1.10496
$700$	−9.37582e6	−0.723209
$701$	−1.17811e7	−0.905509	−0.452754	−	0.891635i	$-0.649559\pi$
$701$	−1.17811e7	−0.905509	−0.452754	+	0.891635i	$0.649559\pi$
$702$	1.75798e7	1.34639
$703$	0	0
$704$	−2.71411e6	−0.206393
$705$	3.39064e6	0.256926
$706$	7.68607e6	0.580353
$707$	−5.29319e6	−0.398262
$708$	5.51213e6	0.413272
$709$	−4.51131e6	−0.337044	−0.168522	−	0.985698i	$-0.553899\pi$
$709$	−4.51131e6	−0.337044	−0.168522	+	0.985698i	$0.553899\pi$
$710$	−1.11853e6	−0.0832726
$711$	−87043.2	−0.00645745
$712$	4.19983e6	0.310479
$713$	1.55294e7	1.14401
$714$	−6.56337e6	−0.481816
$715$	−1.40743e7	−1.02958
$716$	−1.03637e7	−0.755498
$717$	−2.46526e7	−1.79088
$718$	−7.55798e6	−0.547135
$719$	8.00238e6	0.577294	0.288647	−	0.957436i	$-0.406795\pi$
$719$	8.00238e6	0.577294	0.288647	+	0.957436i	$0.406795\pi$
$720$	117275.	0.00843091
$721$	−5.31676e6	−0.380898
$722$	0	0
$723$	−5.85739e6	−0.416733
$724$	7.07628e6	0.501717
$725$	−1.02843e7	−0.726658
$726$	1.64577e7	1.15885
$727$	−2.21846e7	−1.55674	−0.778370	−	0.627806i	$-0.783953\pi$
$727$	−2.21846e7	−1.55674	−0.778370	+	0.627806i	$0.783953\pi$
$728$	1.51123e7	1.05682
$729$	1.54720e7	1.07827
$730$	−1.44770e6	−0.100547
$731$	5.44142e6	0.376633
$732$	3.57607e6	0.246677
$733$	−3.50846e6	−0.241188	−0.120594	−	0.992702i	$-0.538480\pi$
$733$	−3.50846e6	−0.241188	−0.120594	+	0.992702i	$0.538480\pi$
$734$	−4.63242e6	−0.317371
$735$	7.98580e6	0.545255
$736$	3.29065e6	0.223917
$737$	3.92383e7	2.66098
$738$	−1.03761e6	−0.0701284
$739$	−1.68883e7	−1.13756	−0.568781	−	0.822489i	$-0.692585\pi$
$739$	−1.68883e7	−1.13756	−0.568781	+	0.822489i	$0.692585\pi$
$740$	−2.18544e6	−0.146710
$741$	0	0
$742$	2.12075e7	1.41410
$743$	−2.72139e7	−1.80850	−0.904250	−	0.427003i	$-0.859569\pi$
$743$	−2.72139e7	−1.80850	−0.904250	+	0.427003i	$0.859569\pi$
$744$	−4.57703e6	−0.303146
$745$	3.22519e6	0.212895
$746$	−2.00670e7	−1.32019
$747$	−543501.	−0.0356368
$748$	5.53731e6	0.361864
$749$	5.91771e6	0.385433
$750$	6.65269e6	0.431861
$751$	5.12279e6	0.331442	0.165721	−	0.986173i	$-0.447005\pi$
$751$	5.12279e6	0.331442	0.165721	+	0.986173i	$0.447005\pi$
$752$	3.07154e6	0.198067
$753$	779250.	0.0500829
$754$	1.65766e7	1.06186
$755$	2.53705e6	0.161980
$756$	1.34206e7	0.854016
$757$	−1.84692e7	−1.17141	−0.585706	−	0.810524i	$-0.699182\pi$
$757$	−1.84692e7	−1.17141	−0.585706	+	0.810524i	$0.699182\pi$
$758$	1.53597e7	0.970977
$759$	−3.15124e7	−1.98553
$760$	0	0
$761$	1.50050e6	0.0939237	0.0469619	−	0.998897i	$-0.485046\pi$
$761$	1.50050e6	0.0939237	0.0469619	+	0.998897i	$0.485046\pi$
$762$	−3.60983e6	−0.225216
$763$	2.32582e7	1.44632
$764$	−2.98432e6	−0.184974
$765$	−239264.	−0.0147817
$766$	−1.76639e7	−1.08772
$767$	2.58937e7	1.58930
$768$	−969866.	−0.0593347
$769$	−7.45292e6	−0.454475	−0.227238	−	0.973839i	$-0.572969\pi$
$769$	−7.45292e6	−0.454475	−0.227238	+	0.973839i	$0.572969\pi$
$770$	−1.07444e7	−0.653066
$771$	5.47003e6	0.331401
$772$	9.96997e6	0.602075
$773$	−8.78766e6	−0.528962	−0.264481	−	0.964391i	$-0.585201\pi$
$773$	−8.78766e6	−0.528962	−0.264481	+	0.964391i	$0.585201\pi$
$774$	−999755.	−0.0599848
$775$	1.33394e7	0.797781
$776$	−3.80347e6	−0.226739
$777$	−2.24720e7	−1.33533
$778$	5.30209e6	0.314049
$779$	0	0
$780$	−5.02933e6	−0.295988
$781$	9.70338e6	0.569240
$782$	−6.71356e6	−0.392587
$783$	1.47210e7	0.858088
$784$	7.23425e6	0.420343
$785$	2.48230e6	0.143774
$786$	−2.10779e7	−1.21695
$787$	2.19416e7	1.26279	0.631394	−	0.775462i	$-0.282483\pi$
$787$	2.19416e7	1.26279	0.631394	+	0.775462i	$0.282483\pi$
$788$	1.01856e6	0.0584347
$789$	3.94918e6	0.225847
$790$	277137.	0.0157989
$791$	1.97855e7	1.12436
$792$	−1.01737e6	−0.0576325
$793$	1.67989e7	0.948631
$794$	−979005.	−0.0551104
$795$	−7.05781e6	−0.396052
$796$	8.50896e6	0.475986
$797$	−7.18246e6	−0.400523	−0.200261	−	0.979743i	$-0.564179\pi$
$797$	−7.18246e6	−0.400523	−0.200261	+	0.979743i	$0.564179\pi$
$798$	0	0
$799$	−6.26654e6	−0.347265
$800$	2.82661e6	0.156149
$801$	1.57429e6	0.0866968
$802$	−2.74613e6	−0.150760
$803$	1.25589e7	0.687327
$804$	1.40215e7	0.764987
$805$	1.30268e7	0.708514
$806$	−2.15010e7	−1.16579
$807$	−4.19026e6	−0.226494
$808$	1.59578e6	0.0859895
$809$	1.72882e7	0.928705	0.464353	−	0.885650i	$-0.346287\pi$
$809$	1.72882e7	0.928705	0.464353	+	0.885650i	$0.346287\pi$
$810$	−4.02106e6	−0.215342
$811$	2.44923e7	1.30761	0.653804	−	0.756664i	$-0.273172\pi$
$811$	2.44923e7	1.30761	0.653804	+	0.756664i	$0.273172\pi$
$812$	1.26547e7	0.673539
$813$	−1.86606e7	−0.990144
$814$	1.89589e7	1.00289
$815$	1.03519e7	0.545916
$816$	1.97871e6	0.104030
$817$	0	0
$818$	9.93660e6	0.519224
$819$	5.66477e6	0.295102
$820$	3.30365e6	0.171577
$821$	−2.92010e7	−1.51196	−0.755980	−	0.654595i	$-0.772839\pi$
$821$	−2.92010e7	−1.51196	−0.755980	+	0.654595i	$0.772839\pi$
$822$	2.82720e6	0.145941
$823$	2.10175e7	1.08164	0.540818	−	0.841140i	$-0.318115\pi$
$823$	2.10175e7	1.08164	0.540818	+	0.841140i	$0.318115\pi$
$824$	1.60289e6	0.0822404
$825$	−2.70686e7	−1.38462
$826$	1.97675e7	1.00809
$827$	3.22352e7	1.63895	0.819477	−	0.573112i	$-0.194264\pi$
$827$	3.22352e7	1.63895	0.819477	+	0.573112i	$0.194264\pi$
$828$	1.23349e6	0.0625257
$829$	−2.14967e7	−1.08639	−0.543193	−	0.839608i	$-0.682785\pi$
$829$	−2.14967e7	−1.08639	−0.543193	+	0.839608i	$0.682785\pi$
$830$	1.73045e6	0.0871897
$831$	−2.76061e7	−1.38676
$832$	−4.55602e6	−0.228180
$833$	−1.47593e7	−0.736975
$834$	2.45028e7	1.21983
$835$	1.00362e7	0.498142
$836$	0	0
$837$	−1.90941e7	−0.942075
$838$	−464304.	−0.0228398
$839$	2.97457e6	0.145888	0.0729439	−	0.997336i	$-0.476761\pi$
$839$	2.97457e6	0.145888	0.0729439	+	0.997336i	$0.476761\pi$
$840$	−3.83944e6	−0.187746
$841$	−6.63022e6	−0.323249
$842$	768676.	0.0373649
$843$	−6.39439e6	−0.309906
$844$	1.52041e7	0.734691
$845$	−1.65356e7	−0.796671
$846$	1.15135e6	0.0553074
$847$	5.90202e7	2.82678
$848$	−6.39360e6	−0.305320
$849$	1.96807e7	0.937067
$850$	−5.76683e6	−0.273772
$851$	−2.29862e7	−1.08804
$852$	3.46742e6	0.163647
$853$	2.16578e7	1.01916	0.509579	−	0.860424i	$-0.329801\pi$
$853$	2.16578e7	1.01916	0.509579	+	0.860424i	$0.329801\pi$
$854$	1.28244e7	0.601719
$855$	0	0
$856$	−1.78406e6	−0.0832196
$857$	3.76821e7	1.75260	0.876301	−	0.481763i	$-0.160003\pi$
$857$	3.76821e7	1.75260	0.876301	+	0.481763i	$0.160003\pi$
$858$	4.36300e7	2.02333
$859$	3.33168e7	1.54057	0.770283	−	0.637702i	$-0.220115\pi$
$859$	3.33168e7	1.54057	0.770283	+	0.637702i	$0.220115\pi$
$860$	3.18312e6	0.146760
$861$	3.39701e7	1.56167
$862$	1.30154e7	0.596608
$863$	−2.83574e7	−1.29610	−0.648051	−	0.761597i	$-0.724415\pi$
$863$	−2.83574e7	−1.29610	−0.648051	+	0.761597i	$0.724415\pi$
$864$	−4.04601e6	−0.184392
$865$	1.24224e7	0.564500
$866$	−990306.	−0.0448719
$867$	1.69755e7	0.766963
$868$	−1.64140e7	−0.739463
$869$	−2.40420e6	−0.107999
$870$	−4.21147e6	−0.188641
$871$	6.58671e7	2.94187
$872$	−7.01186e6	−0.312279
$873$	−1.42572e6	−0.0633136
$874$	0	0
$875$	2.38577e7	1.05344
$876$	4.48783e6	0.197595
$877$	−1.87261e7	−0.822146	−0.411073	−	0.911602i	$-0.634846\pi$
$877$	−1.87261e7	−0.822146	−0.411073	+	0.911602i	$0.634846\pi$
$878$	−1.42270e7	−0.622840
$879$	−1.03828e7	−0.453255
$880$	3.23922e6	0.141005
$881$	−1.81827e7	−0.789256	−0.394628	−	0.918841i	$-0.629127\pi$
$881$	−1.81827e7	−0.789256	−0.394628	+	0.918841i	$0.629127\pi$
$882$	2.71173e6	0.117375
$883$	1.36080e6	0.0587343	0.0293672	−	0.999569i	$-0.490651\pi$
$883$	1.36080e6	0.0587343	0.0293672	+	0.999569i	$0.490651\pi$
$884$	9.29517e6	0.400061
$885$	−6.57858e6	−0.282341
$886$	1.08575e7	0.464672
$887$	−2.00032e7	−0.853669	−0.426834	−	0.904330i	$-0.640371\pi$
$887$	−2.00032e7	−0.853669	−0.426834	+	0.904330i	$0.640371\pi$
$888$	6.77482e6	0.288314
$889$	−1.29455e7	−0.549369
$890$	−5.01239e6	−0.212114
$891$	3.48831e7	1.47205
$892$	6.59237e6	0.277415
$893$	0	0
$894$	−9.99803e6	−0.418380
$895$	1.23688e7	0.516144
$896$	−3.47811e6	−0.144735
$897$	−5.28980e7	−2.19512
$898$	−9.41462e6	−0.389594
$899$	−1.80045e7	−0.742989
$900$	1.05954e6	0.0436026
$901$	1.30442e7	0.535309
$902$	−2.86596e7	−1.17288
$903$	3.27308e7	1.33579
$904$	−5.96490e6	−0.242763
$905$	−8.44536e6	−0.342765
$906$	−7.86480e6	−0.318322
$907$	−3.24238e7	−1.30872	−0.654358	−	0.756185i	$-0.727061\pi$
$907$	−3.24238e7	−1.30872	−0.654358	+	0.756185i	$0.727061\pi$
$908$	−3.46753e6	−0.139574
$909$	598173.	0.0240114
$910$	−1.80361e7	−0.722002
$911$	9.99133e6	0.398866	0.199433	−	0.979911i	$-0.436090\pi$
$911$	9.99133e6	0.398866	0.199433	+	0.979911i	$0.436090\pi$
$912$	0	0
$913$	−1.50119e7	−0.596016
$914$	−3.04599e7	−1.20604
$915$	−4.26795e6	−0.168526
$916$	−7.48093e6	−0.294589
$917$	−7.55891e7	−2.96849
$918$	8.25465e6	0.323290
$919$	−4.37067e7	−1.70710	−0.853550	−	0.521012i	$-0.825555\pi$
$919$	−4.37067e7	−1.70710	−0.853550	+	0.521012i	$0.825555\pi$
$920$	−3.92730e6	−0.152977
$921$	−9.87540e6	−0.383624
$922$	3.19976e7	1.23962
$923$	1.62885e7	0.629328
$924$	3.33076e7	1.28340
$925$	−1.97448e7	−0.758748
$926$	−1.02123e7	−0.391377
$927$	600836.	0.0229645
$928$	−3.81513e6	−0.145425
$929$	1.59094e7	0.604805	0.302402	−	0.953180i	$-0.402211\pi$
$929$	1.59094e7	0.604805	0.302402	+	0.953180i	$0.402211\pi$
$930$	5.46257e6	0.207104
$931$	0	0
$932$	−1.54322e7	−0.581955
$933$	−3.58551e6	−0.134849
$934$	2.40400e7	0.901710
$935$	−6.60864e6	−0.247220
$936$	−1.70781e6	−0.0637161
$937$	1.88286e7	0.700597	0.350299	−	0.936638i	$-0.386080\pi$
$937$	1.88286e7	0.700597	0.350299	+	0.936638i	$0.386080\pi$
$938$	5.02836e7	1.86603
$939$	−3.00080e7	−1.11064
$940$	−3.66580e6	−0.135316
$941$	−5.94474e6	−0.218856	−0.109428	−	0.993995i	$-0.534902\pi$
$941$	−5.94474e6	−0.218856	−0.109428	+	0.993995i	$0.534902\pi$
$942$	−7.69509e6	−0.282544
$943$	3.47475e7	1.27246
$944$	−5.95947e6	−0.217660
$945$	−1.60171e7	−0.583450
$946$	−2.76139e7	−1.00323
$947$	−1.44485e7	−0.523539	−0.261770	−	0.965130i	$-0.584306\pi$
$947$	−1.44485e7	−0.523539	−0.261770	+	0.965130i	$0.584306\pi$
$948$	−859120.	−0.0310480
$949$	2.10819e7	0.759879
$950$	0	0
$951$	−1.45548e7	−0.521860
$952$	7.09602e6	0.253760
$953$	1.88659e7	0.672891	0.336445	−	0.941703i	$-0.390775\pi$
$953$	1.88659e7	0.672891	0.336445	+	0.941703i	$0.390775\pi$
$954$	−2.39661e6	−0.0852564
$955$	3.56170e6	0.126372
$956$	2.66533e7	0.943206
$957$	3.65350e7	1.28952
$958$	−3.74847e7	−1.31959
$959$	1.01388e7	0.355993
$960$	1.15751e6	0.0405365
$961$	−5.27605e6	−0.184290
$962$	3.18253e7	1.10875
$963$	−668748.	−0.0232379
$964$	6.33275e6	0.219482
$965$	−1.18989e7	−0.411328
$966$	−4.03828e7	−1.39237
$967$	−9.39594e6	−0.323128	−0.161564	−	0.986862i	$-0.551654\pi$
$967$	−9.39594e6	−0.323128	−0.161564	+	0.986862i	$0.551654\pi$
$968$	−1.77933e7	−0.610336
$969$	0	0
$970$	4.53934e6	0.154904
$971$	3.60091e6	0.122564	0.0612822	−	0.998120i	$-0.480481\pi$
$971$	3.60091e6	0.122564	0.0612822	+	0.998120i	$0.480481\pi$
$972$	−2.89699e6	−0.0983514
$973$	8.78713e7	2.97553
$974$	3.63826e6	0.122884
$975$	−4.54384e7	−1.53078
$976$	−3.86629e6	−0.129918
$977$	−1.05610e7	−0.353972	−0.176986	−	0.984213i	$-0.556635\pi$
$977$	−1.05610e7	−0.353972	−0.176986	+	0.984213i	$0.556635\pi$
$978$	−3.20907e7	−1.07283
$979$	4.34830e7	1.44998
$980$	−8.63389e6	−0.287171
$981$	−2.62837e6	−0.0871994
$982$	−2.29132e7	−0.758240
$983$	2.16758e7	0.715469	0.357735	−	0.933823i	$-0.383549\pi$
$983$	2.16758e7	0.715469	0.357735	+	0.933823i	$0.383549\pi$
$984$	−1.02413e7	−0.337183
$985$	−1.21562e6	−0.0399217
$986$	7.78360e6	0.254970
$987$	−3.76940e7	−1.23163
$988$	0	0
$989$	3.34798e7	1.08841
$990$	1.21421e6	0.0393736
$991$	−9.04602e6	−0.292599	−0.146300	−	0.989240i	$-0.546736\pi$
$991$	−9.04602e6	−0.292599	−0.146300	+	0.989240i	$0.546736\pi$
$992$	4.94848e6	0.159659
$993$	1.02443e6	0.0329693
$994$	1.24348e7	0.399184
$995$	−1.01552e7	−0.325186
$996$	−5.36438e6	−0.171345
$997$	4.49579e7	1.43241	0.716207	−	0.697888i	$-0.245877\pi$
$997$	4.49579e7	1.43241	0.716207	+	0.697888i	$0.245877\pi$
$998$	−1.06607e7	−0.338813
$999$	2.82627e7	0.895982

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.6.a.d.1.2		3
19.18	odd	2		38.6.a.d.1.2	✓	3
57.56	even	2		342.6.a.l.1.3		3
76.75	even	2		304.6.a.h.1.2		3
95.94	odd	2		950.6.a.f.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.a.d.1.2	✓	3	19.18	odd	2
304.6.a.h.1.2		3	76.75	even	2
342.6.a.l.1.3		3	57.56	even	2
722.6.a.d.1.2		3	1.1	even	1	trivial
950.6.a.f.1.2		3	95.94	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	722.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -14.7990 q^{3} +16.0000 q^{4} -19.0956 q^{5} +59.1959 q^{6} +212.287 q^{7} -64.0000 q^{8} -23.9901 q^{9} +76.3823 q^{10} -662.625 q^{11} -236.784 q^{12} -1112.31 q^{13} -849.148 q^{14} +282.595 q^{15} +256.000 q^{16} -522.290 q^{17} +95.9606 q^{18} -305.529 q^{20} -3141.63 q^{21} +2650.50 q^{22} -3213.52 q^{23} +947.135 q^{24} -2760.36 q^{25} +4449.24 q^{26} +3951.18 q^{27} +3396.59 q^{28} +3725.71 q^{29} -1130.38 q^{30} -4832.50 q^{31} -1024.00 q^{32} +9806.17 q^{33} +2089.16 q^{34} -4053.74 q^{35} -383.842 q^{36} +7152.96 q^{37} +16461.1 q^{39} +1222.12 q^{40} -10812.9 q^{41} +12566.5 q^{42} -10418.4 q^{43} -10602.0 q^{44} +458.106 q^{45} +12854.1 q^{46} +11998.2 q^{47} -3788.54 q^{48} +28258.8 q^{49} +11041.4 q^{50} +7729.35 q^{51} -17797.0 q^{52} -24975.0 q^{53} -15804.7 q^{54} +12653.2 q^{55} -13586.4 q^{56} -14902.8 q^{58} -23279.2 q^{59} +4521.52 q^{60} -15102.7 q^{61} +19330.0 q^{62} -5092.80 q^{63} +4096.00 q^{64} +21240.2 q^{65} -39224.7 q^{66} -59216.5 q^{67} -8356.63 q^{68} +47556.9 q^{69} +16215.0 q^{70} -14643.8 q^{71} +1535.37 q^{72} -18953.3 q^{73} -28611.9 q^{74} +40850.5 q^{75} -140667. q^{77} -65844.2 q^{78} +3628.29 q^{79} -4888.47 q^{80} -52643.9 q^{81} +43251.6 q^{82} +22655.2 q^{83} -50266.1 q^{84} +9973.42 q^{85} +41673.6 q^{86} -55136.7 q^{87} +42408.0 q^{88} -65622.3 q^{89} -1832.42 q^{90} -236129. q^{91} -51416.4 q^{92} +71516.1 q^{93} -47992.8 q^{94} +15154.2 q^{96} +59429.2 q^{97} -113035. q^{98} +15896.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 12 q^{2} - 13 q^{3} + 48 q^{4} + 81 q^{5} + 52 q^{6} + 228 q^{7} - 192 q^{8} + 236 q^{9} - 324 q^{10} + 363 q^{11} - 208 q^{12} - 501 q^{13} - 912 q^{14} + 670 q^{15} + 768 q^{16} - 1206 q^{17} - 944 q^{18}+ \cdots + 158317 q^{99}+O(q^{100}) \) 3 * q - 12 * q^2 - 13 * q^3 + 48 * q^4 + 81 * q^5 + 52 * q^6 + 228 * q^7 - 192 * q^8 + 236 * q^9 - 324 * q^10 + 363 * q^11 - 208 * q^12 - 501 * q^13 - 912 * q^14 + 670 * q^15 + 768 * q^16 - 1206 * q^17 - 944 * q^18 + 1296 * q^20 + 2085 * q^21 - 1452 * q^22 - 1077 * q^23 + 832 * q^24 - 3882 * q^25 + 2004 * q^26 + 5087 * q^27 + 3648 * q^28 + 8349 * q^29 - 2680 * q^30 + 7332 * q^31 - 3072 * q^32 + 15784 * q^33 + 4824 * q^34 - 1185 * q^35 + 3776 * q^36 + 1650 * q^37 + 773 * q^39 - 5184 * q^40 - 10140 * q^41 - 8340 * q^42 + 3777 * q^43 + 5808 * q^44 + 14005 * q^45 + 4308 * q^46 + 33231 * q^47 - 3328 * q^48 + 31269 * q^49 + 15528 * q^50 - 46935 * q^51 - 8016 * q^52 - 31029 * q^53 - 20348 * q^54 + 66003 * q^55 - 14592 * q^56 - 33396 * q^58 - 20409 * q^59 + 10720 * q^60 + 17115 * q^61 - 29328 * q^62 + 6327 * q^63 + 12288 * q^64 + 45348 * q^65 - 63136 * q^66 + 789 * q^67 - 19296 * q^68 + 151147 * q^69 + 4740 * q^70 - 19164 * q^71 - 15104 * q^72 - 76260 * q^73 - 6600 * q^74 + 69607 * q^75 - 97209 * q^77 - 3092 * q^78 - 68358 * q^79 + 20736 * q^80 - 197713 * q^81 + 40560 * q^82 + 6762 * q^83 + 33360 * q^84 - 45837 * q^85 - 15108 * q^86 + 66805 * q^87 - 23232 * q^88 + 85506 * q^89 - 56020 * q^90 - 345033 * q^91 - 17232 * q^92 + 15688 * q^93 - 132924 * q^94 + 13312 * q^96 - 105024 * q^97 - 125076 * q^98 + 158317 * q^99

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