LMFDB - Embedded newform 147.6.a.k.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(1,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, 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("147.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	147.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:	$23.5764215125$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{249}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 62 $ x^2 - x - 62
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-7.38987$ of defining polynomial
Character	$\chi$	$=$	147.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+6.38987 q^{2} +9.00000 q^{3} +8.83040 q^{4} -38.7291 q^{5} +57.5088 q^{6} -148.051 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+6.38987 q^{2} +9.00000 q^{3} +8.83040 q^{4} -38.7291 q^{5} +57.5088 q^{6} -148.051 q^{8} +81.0000 q^{9} -247.474 q^{10} -576.390 q^{11} +79.4736 q^{12} -391.491 q^{13} -348.562 q^{15} -1228.60 q^{16} +1329.70 q^{17} +517.579 q^{18} -942.474 q^{19} -341.993 q^{20} -3683.05 q^{22} -1632.08 q^{23} -1332.46 q^{24} -1625.06 q^{25} -2501.58 q^{26} +729.000 q^{27} -1463.54 q^{29} -2227.26 q^{30} +3912.42 q^{31} -3112.95 q^{32} -5187.51 q^{33} +8496.61 q^{34} +715.262 q^{36} -16300.3 q^{37} -6022.28 q^{38} -3523.42 q^{39} +5733.86 q^{40} +13103.8 q^{41} +14733.5 q^{43} -5089.75 q^{44} -3137.05 q^{45} -10428.8 q^{46} +6814.52 q^{47} -11057.4 q^{48} -10383.9 q^{50} +11967.3 q^{51} -3457.02 q^{52} -2011.34 q^{53} +4658.21 q^{54} +22323.0 q^{55} -8482.26 q^{57} -9351.85 q^{58} -51453.1 q^{59} -3077.94 q^{60} -41097.8 q^{61} +24999.8 q^{62} +19423.8 q^{64} +15162.1 q^{65} -33147.5 q^{66} +50578.2 q^{67} +11741.8 q^{68} -14688.7 q^{69} +39970.6 q^{71} -11992.1 q^{72} +55686.6 q^{73} -104157. q^{74} -14625.5 q^{75} -8322.42 q^{76} -22514.2 q^{78} -63151.4 q^{79} +47582.4 q^{80} +6561.00 q^{81} +83731.7 q^{82} -45572.4 q^{83} -51498.1 q^{85} +94145.1 q^{86} -13171.9 q^{87} +85334.9 q^{88} -15686.7 q^{89} -20045.4 q^{90} -14411.9 q^{92} +35211.8 q^{93} +43543.9 q^{94} +36501.1 q^{95} -28016.5 q^{96} -3128.49 q^{97} -46687.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} + 18 q^{3} + 65 q^{4} + 33 q^{5} - 27 q^{6} - 375 q^{8} + 162 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 + 18 * q^3 + 65 * q^4 + 33 * q^5 - 27 * q^6 - 375 * q^8 + 162 * q^9	\( 2 q - 3 q^{2} + 18 q^{3} + 65 q^{4} + 33 q^{5} - 27 q^{6} - 375 q^{8} + 162 q^{9} - 921 q^{10} - 1137 q^{11} + 585 q^{12} - 925 q^{13} + 297 q^{15} - 895 q^{16} + 324 q^{17} - 243 q^{18} - 2311 q^{19} + 3687 q^{20} + 1581 q^{22} + 1596 q^{23} - 3375 q^{24} + 395 q^{25} + 2508 q^{26} + 1458 q^{27} - 2217 q^{29} - 8289 q^{30} - 4294 q^{31} + 1017 q^{32} - 10233 q^{33} + 17940 q^{34} + 5265 q^{36} - 19109 q^{37} + 6828 q^{38} - 8325 q^{39} - 10545 q^{40} + 12858 q^{41} - 2771 q^{43} - 36579 q^{44} + 2673 q^{45} - 40740 q^{46} + 23160 q^{47} - 8055 q^{48} - 29352 q^{50} + 2916 q^{51} - 33424 q^{52} - 31653 q^{53} - 2187 q^{54} - 17889 q^{55} - 20799 q^{57} - 2277 q^{58} - 41097 q^{59} + 33183 q^{60} - 42052 q^{61} + 102057 q^{62} - 30031 q^{64} - 23106 q^{65} + 14229 q^{66} + 30763 q^{67} - 44748 q^{68} + 14364 q^{69} + 102096 q^{71} - 30375 q^{72} + 28577 q^{73} - 77784 q^{74} + 3555 q^{75} - 85192 q^{76} + 22572 q^{78} - 18464 q^{79} + 71511 q^{80} + 13122 q^{81} + 86040 q^{82} - 61179 q^{83} - 123636 q^{85} + 258510 q^{86} - 19953 q^{87} + 212565 q^{88} - 29322 q^{89} - 74601 q^{90} + 166908 q^{92} - 38646 q^{93} - 109938 q^{94} - 61662 q^{95} + 9153 q^{96} + 9791 q^{97} - 92097 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 + 18 * q^3 + 65 * q^4 + 33 * q^5 - 27 * q^6 - 375 * q^8 + 162 * q^9 - 921 * q^10 - 1137 * q^11 + 585 * q^12 - 925 * q^13 + 297 * q^15 - 895 * q^16 + 324 * q^17 - 243 * q^18 - 2311 * q^19 + 3687 * q^20 + 1581 * q^22 + 1596 * q^23 - 3375 * q^24 + 395 * q^25 + 2508 * q^26 + 1458 * q^27 - 2217 * q^29 - 8289 * q^30 - 4294 * q^31 + 1017 * q^32 - 10233 * q^33 + 17940 * q^34 + 5265 * q^36 - 19109 * q^37 + 6828 * q^38 - 8325 * q^39 - 10545 * q^40 + 12858 * q^41 - 2771 * q^43 - 36579 * q^44 + 2673 * q^45 - 40740 * q^46 + 23160 * q^47 - 8055 * q^48 - 29352 * q^50 + 2916 * q^51 - 33424 * q^52 - 31653 * q^53 - 2187 * q^54 - 17889 * q^55 - 20799 * q^57 - 2277 * q^58 - 41097 * q^59 + 33183 * q^60 - 42052 * q^61 + 102057 * q^62 - 30031 * q^64 - 23106 * q^65 + 14229 * q^66 + 30763 * q^67 - 44748 * q^68 + 14364 * q^69 + 102096 * q^71 - 30375 * q^72 + 28577 * q^73 - 77784 * q^74 + 3555 * q^75 - 85192 * q^76 + 22572 * q^78 - 18464 * q^79 + 71511 * q^80 + 13122 * q^81 + 86040 * q^82 - 61179 * q^83 - 123636 * q^85 + 258510 * q^86 - 19953 * q^87 + 212565 * q^88 - 29322 * q^89 - 74601 * q^90 + 166908 * q^92 - 38646 * q^93 - 109938 * q^94 - 61662 * q^95 + 9153 * q^96 + 9791 * q^97 - 92097 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	6.38987	1.12958	0.564790	−	0.825235i	$-0.308957\pi$
$2$	6.38987	1.12958	0.564790	+	0.825235i	$0.308957\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	8.83040	0.275950
$5$	−38.7291	−0.692807	−0.346403	−	0.938086i	$-0.612597\pi$
$5$	−38.7291	−0.692807	−0.346403	+	0.938086i	$0.612597\pi$
$6$	57.5088	0.652163
$7$	0	0
$7$	0	0
$8$	−148.051	−0.817872
$9$	81.0000	0.333333
$10$	−247.474	−0.782580
$11$	−576.390	−1.43627	−0.718133	−	0.695906i	$-0.755003\pi$
$11$	−576.390	−1.43627	−0.718133	+	0.695906i	$0.755003\pi$
$12$	79.4736	0.159320
$13$	−391.491	−0.642486	−0.321243	−	0.946997i	$-0.604101\pi$
$13$	−391.491	−0.642486	−0.321243	+	0.946997i	$0.604101\pi$
$14$	0	0
$15$	−348.562	−0.399992
$16$	−1228.60	−1.19980
$17$	1329.70	1.11592	0.557958	−	0.829869i	$-0.311585\pi$
$17$	1329.70	1.11592	0.557958	+	0.829869i	$0.311585\pi$
$18$	517.579	0.376527
$19$	−942.474	−0.598943	−0.299471	−	0.954105i	$-0.596810\pi$
$19$	−942.474	−0.598943	−0.299471	+	0.954105i	$0.596810\pi$
$20$	−341.993	−0.191180
$21$	0	0
$22$	−3683.05	−1.62238
$23$	−1632.08	−0.643312	−0.321656	−	0.946857i	$-0.604239\pi$
$23$	−1632.08	−0.643312	−0.321656	+	0.946857i	$0.604239\pi$
$24$	−1332.46	−0.472199
$25$	−1625.06	−0.520019
$26$	−2501.58	−0.725739
$27$	729.000	0.192450
$28$	0	0
$29$	−1463.54	−0.323155	−0.161577	−	0.986860i	$-0.551658\pi$
$29$	−1463.54	−0.323155	−0.161577	+	0.986860i	$0.551658\pi$
$30$	−2227.26	−0.451823
$31$	3912.42	0.731208	0.365604	−	0.930770i	$-0.380862\pi$
$31$	3912.42	0.731208	0.365604	+	0.930770i	$0.380862\pi$
$32$	−3112.95	−0.537399
$33$	−5187.51	−0.829228
$34$	8496.61	1.26052
$35$	0	0
$36$	715.262	0.0919833
$37$	−16300.3	−1.95746	−0.978729	−	0.205160i	$-0.934229\pi$
$37$	−16300.3	−1.95746	−0.978729	+	0.205160i	$0.934229\pi$
$38$	−6022.28	−0.676553
$39$	−3523.42	−0.370939
$40$	5733.86	0.566627
$41$	13103.8	1.21741	0.608707	−	0.793395i	$-0.291688\pi$
$41$	13103.8	1.21741	0.608707	+	0.793395i	$0.291688\pi$
$42$	0	0
$43$	14733.5	1.21516	0.607582	−	0.794257i	$-0.292140\pi$
$43$	14733.5	1.21516	0.607582	+	0.794257i	$0.292140\pi$
$44$	−5089.75	−0.396337
$45$	−3137.05	−0.230936
$46$	−10428.8	−0.726672
$47$	6814.52	0.449977	0.224989	−	0.974361i	$-0.427765\pi$
$47$	6814.52	0.449977	0.224989	+	0.974361i	$0.427765\pi$
$48$	−11057.4	−0.692706
$49$	0	0
$50$	−10383.9	−0.587403
$51$	11967.3	0.644274
$52$	−3457.02	−0.177294
$53$	−2011.34	−0.0983550	−0.0491775	−	0.998790i	$-0.515660\pi$
$53$	−2011.34	−0.0983550	−0.0491775	+	0.998790i	$0.515660\pi$
$54$	4658.21	0.217388
$55$	22323.0	0.995054
$56$	0	0
$57$	−8482.26	−0.345800
$58$	−9351.85	−0.365029
$59$	−51453.1	−1.92434	−0.962170	−	0.272451i	$-0.912166\pi$
$59$	−51453.1	−1.92434	−0.962170	+	0.272451i	$0.912166\pi$
$60$	−3077.94	−0.110378
$61$	−41097.8	−1.41415	−0.707073	−	0.707141i	$-0.749985\pi$
$61$	−41097.8	−1.41415	−0.707073	+	0.707141i	$0.749985\pi$
$62$	24999.8	0.825958
$63$	0	0
$64$	19423.8	0.592766
$65$	15162.1	0.445119
$66$	−33147.5	−0.936679
$67$	50578.2	1.37650	0.688250	−	0.725473i	$-0.258379\pi$
$67$	50578.2	1.37650	0.688250	+	0.725473i	$0.258379\pi$
$68$	11741.8	0.307937
$69$	−14688.7	−0.371416
$70$	0	0
$71$	39970.6	0.941012	0.470506	−	0.882397i	$-0.344071\pi$
$71$	39970.6	0.941012	0.470506	+	0.882397i	$0.344071\pi$
$72$	−11992.1	−0.272624
$73$	55686.6	1.22305	0.611524	−	0.791226i	$-0.290557\pi$
$73$	55686.6	1.22305	0.611524	+	0.791226i	$0.290557\pi$
$74$	−104157.	−2.21110
$75$	−14625.5	−0.300233
$76$	−8322.42	−0.165278
$77$	0	0
$78$	−22514.2	−0.419006
$79$	−63151.4	−1.13845	−0.569226	−	0.822181i	$-0.692757\pi$
$79$	−63151.4	−1.13845	−0.569226	+	0.822181i	$0.692757\pi$
$80$	47582.4	0.831231
$81$	6561.00	0.111111
$82$	83731.7	1.37517
$83$	−45572.4	−0.726116	−0.363058	−	0.931766i	$-0.618267\pi$
$83$	−45572.4	−0.726116	−0.363058	+	0.931766i	$0.618267\pi$
$84$	0	0
$85$	−51498.1	−0.773114
$86$	94145.1	1.37262
$87$	−13171.9	−0.186574
$88$	85334.9	1.17468
$89$	−15686.7	−0.209921	−0.104961	−	0.994476i	$-0.533472\pi$
$89$	−15686.7	−0.209921	−0.104961	+	0.994476i	$0.533472\pi$
$90$	−20045.4	−0.260860
$91$	0	0
$92$	−14411.9	−0.177522
$93$	35211.8	0.422163
$94$	43543.9	0.508285
$95$	36501.1	0.414951
$96$	−28016.5	−0.310268
$97$	−3128.49	−0.0337603	−0.0168801	−	0.999858i	$-0.505373\pi$
$97$	−3128.49	−0.0337603	−0.0168801	+	0.999858i	$0.505373\pi$
$98$	0	0
$99$	−46687.6	−0.478755
$100$	−14349.9	−0.143499
$101$	169011.	1.64858	0.824292	−	0.566164i	$-0.191573\pi$
$101$	169011.	1.64858	0.824292	+	0.566164i	$0.191573\pi$
$102$	76469.5	0.727759
$103$	−112820.	−1.04784	−0.523918	−	0.851769i	$-0.675530\pi$
$103$	−112820.	−1.04784	−0.523918	+	0.851769i	$0.675530\pi$
$104$	57960.5	0.525471
$105$	0	0
$106$	−12852.2	−0.111100
$107$	−22309.5	−0.188378	−0.0941890	−	0.995554i	$-0.530026\pi$
$107$	−22309.5	−0.188378	−0.0941890	+	0.995554i	$0.530026\pi$
$108$	6437.36	0.0531066
$109$	−83819.5	−0.675739	−0.337869	−	0.941193i	$-0.609706\pi$
$109$	−83819.5	−0.675739	−0.337869	+	0.941193i	$0.609706\pi$
$110$	142641.	1.12399
$111$	−146703.	−1.13014
$112$	0	0
$113$	−40928.4	−0.301529	−0.150764	−	0.988570i	$-0.548174\pi$
$113$	−40928.4	−0.301529	−0.150764	+	0.988570i	$0.548174\pi$
$114$	−54200.5	−0.390608
$115$	63208.9	0.445691
$116$	−12923.7	−0.0891746
$117$	−31710.8	−0.214162
$118$	−328779.	−2.17369
$119$	0	0
$120$	51604.8	0.327142
$121$	171174.	1.06286
$122$	−262610.	−1.59739
$123$	117934.	0.702875
$124$	34548.2	0.201777
$125$	183965.	1.05308
$126$	0	0
$127$	83270.1	0.458120	0.229060	−	0.973412i	$-0.426435\pi$
$127$	83270.1	0.458120	0.229060	+	0.973412i	$0.426435\pi$
$128$	223730.	1.20698
$129$	132601.	0.701575
$130$	96883.7	0.502797
$131$	166875.	0.849596	0.424798	−	0.905288i	$-0.360345\pi$
$131$	166875.	0.849596	0.424798	+	0.905288i	$0.360345\pi$
$132$	−45807.8	−0.228825
$133$	0	0
$134$	323188.	1.55487
$135$	−28233.5	−0.133331
$136$	−196863.	−0.912676
$137$	38223.9	0.173994	0.0869969	−	0.996209i	$-0.472273\pi$
$137$	38223.9	0.173994	0.0869969	+	0.996209i	$0.472273\pi$
$138$	−93858.9	−0.419544
$139$	−106263.	−0.466492	−0.233246	−	0.972418i	$-0.574935\pi$
$139$	−106263.	−0.466492	−0.233246	+	0.972418i	$0.574935\pi$
$140$	0	0
$141$	61330.7	0.259795
$142$	255407.	1.06295
$143$	225652.	0.922780
$144$	−99516.3	−0.399934
$145$	56681.7	0.223884
$146$	355830.	1.38153
$147$	0	0
$148$	−143938.	−0.540160
$149$	192556.	0.710543	0.355271	−	0.934763i	$-0.384388\pi$
$149$	192556.	0.710543	0.355271	+	0.934763i	$0.384388\pi$
$150$	−93455.2	−0.339137
$151$	141699.	0.505735	0.252868	−	0.967501i	$-0.418626\pi$
$151$	141699.	0.505735	0.252868	+	0.967501i	$0.418626\pi$
$152$	139534.	0.489858
$153$	107706.	0.371972
$154$	0	0
$155$	−151524.	−0.506586
$156$	−31113.2	−0.102361
$157$	−565771.	−1.83186	−0.915928	−	0.401342i	$-0.868544\pi$
$157$	−565771.	−1.83186	−0.915928	+	0.401342i	$0.868544\pi$
$158$	−403529.	−1.28597
$159$	−18102.1	−0.0567853
$160$	120562.	0.372314
$161$	0	0
$162$	41923.9	0.125509
$163$	−430201.	−1.26824	−0.634121	−	0.773233i	$-0.718638\pi$
$163$	−430201.	−1.26824	−0.634121	+	0.773233i	$0.718638\pi$
$164$	115712.	0.335946
$165$	200907.	0.574495
$166$	−291201.	−0.820206
$167$	240265.	0.666653	0.333327	−	0.942811i	$-0.391829\pi$
$167$	240265.	0.666653	0.333327	+	0.942811i	$0.391829\pi$
$168$	0	0
$169$	−218028.	−0.587212
$170$	−329066.	−0.873294
$171$	−76340.4	−0.199648
$172$	130103.	0.335324
$173$	179300.	0.455476	0.227738	−	0.973722i	$-0.426867\pi$
$173$	179300.	0.455476	0.227738	+	0.973722i	$0.426867\pi$
$174$	−84166.7	−0.210750
$175$	0	0
$176$	708151.	1.72323
$177$	−463078.	−1.11102
$178$	−100236.	−0.237123
$179$	−575559.	−1.34263	−0.671317	−	0.741170i	$-0.734271\pi$
$179$	−575559.	−1.34263	−0.671317	+	0.741170i	$0.734271\pi$
$180$	−27701.4	−0.0637267
$181$	−581006.	−1.31821	−0.659105	−	0.752051i	$-0.729065\pi$
$181$	−581006.	−1.31821	−0.659105	+	0.752051i	$0.729065\pi$
$182$	0	0
$183$	−369880.	−0.816458
$184$	241630.	0.526147
$185$	631297.	1.35614
$186$	224998.	0.476867
$187$	−766426.	−1.60275
$188$	60174.9	0.124171
$189$	0	0
$190$	233237.	0.468721
$191$	−660560.	−1.31017	−0.655087	−	0.755554i	$-0.727368\pi$
$191$	−660560.	−1.31017	−0.655087	+	0.755554i	$0.727368\pi$
$192$	174814.	0.342234
$193$	−557310.	−1.07697	−0.538485	−	0.842635i	$-0.681003\pi$
$193$	−557310.	−1.07697	−0.538485	+	0.842635i	$0.681003\pi$
$194$	−19990.7	−0.0381349
$195$	136459.	0.256989
$196$	0	0
$197$	−761400.	−1.39781	−0.698904	−	0.715216i	$-0.746328\pi$
$197$	−761400.	−1.39781	−0.698904	+	0.715216i	$0.746328\pi$
$198$	−298327.	−0.540792
$199$	135860.	0.243197	0.121598	−	0.992579i	$-0.461198\pi$
$199$	135860.	0.243197	0.121598	+	0.992579i	$0.461198\pi$
$200$	240591.	0.425309
$201$	455204.	0.794723
$202$	1.07996e6	1.86221
$203$	0	0
$204$	105676.	0.177787
$205$	−507499.	−0.843433
$206$	−720906.	−1.18361
$207$	−132198.	−0.214437
$208$	480985.	0.770856
$209$	543232.	0.860240
$210$	0	0
$211$	−991157.	−1.53263	−0.766313	−	0.642467i	$-0.777911\pi$
$211$	−991157.	−1.53263	−0.766313	+	0.642467i	$0.777911\pi$
$212$	−17761.0	−0.0271411
$213$	359736.	0.543293
$214$	−142555.	−0.212788
$215$	−570615.	−0.841873
$216$	−107929.	−0.157400
$217$	0	0
$218$	−535596.	−0.763301
$219$	501180.	0.706128
$220$	197121.	0.274585
$221$	−520566.	−0.716960
$222$	−937413.	−1.27658
$223$	−543344.	−0.731666	−0.365833	−	0.930681i	$-0.619216\pi$
$223$	−543344.	−0.731666	−0.365833	+	0.930681i	$0.619216\pi$
$224$	0	0
$225$	−131630.	−0.173340
$226$	−261527.	−0.340601
$227$	−16.3341	−2.10393e−5 0	−1.05196e−5	−	1.00000i	$-0.500003\pi$
$227$	−16.3341	−2.10393e−5 0	−1.05196e−5		1.00000i	$0.500003\pi$
$228$	−74901.8	−0.0954234
$229$	77379.0	0.0975067	0.0487534	−	0.998811i	$-0.484475\pi$
$229$	77379.0	0.0975067	0.0487534	+	0.998811i	$0.484475\pi$
$230$	403896.	0.503443
$231$	0	0
$232$	216679.	0.264299
$233$	−103657.	−0.125086	−0.0625432	−	0.998042i	$-0.519921\pi$
$233$	−103657.	−0.125086	−0.0625432	+	0.998042i	$0.519921\pi$
$234$	−202628.	−0.241913
$235$	−263920.	−0.311747
$236$	−454351.	−0.531021
$237$	−568362.	−0.657286
$238$	0	0
$239$	689109.	0.780356	0.390178	−	0.920739i	$-0.372413\pi$
$239$	689109.	0.780356	0.390178	+	0.920739i	$0.372413\pi$
$240$	428242.	0.479911
$241$	−220296.	−0.244323	−0.122161	−	0.992510i	$-0.538983\pi$
$241$	−220296.	−0.244323	−0.122161	+	0.992510i	$0.538983\pi$
$242$	1.09378e6	1.20058
$243$	59049.0	0.0641500
$244$	−362910.	−0.390234
$245$	0	0
$246$	753585.	0.793953
$247$	368970.	0.384812
$248$	−579236.	−0.598035
$249$	−410151.	−0.419224
$250$	1.17551e6	1.18954
$251$	−1.43641e6	−1.43912	−0.719558	−	0.694433i	$-0.755655\pi$
$251$	−1.43641e6	−1.43912	−0.719558	+	0.694433i	$0.755655\pi$
$252$	0	0
$253$	940714.	0.923966
$254$	532085.	0.517483
$255$	−463482.	−0.446358
$256$	808042.	0.770609
$257$	909197.	0.858668	0.429334	−	0.903146i	$-0.358748\pi$
$257$	909197.	0.858668	0.429334	+	0.903146i	$0.358748\pi$
$258$	847306.	0.792485
$259$	0	0
$260$	133887.	0.122830
$261$	−118547.	−0.107718
$262$	1.06631e6	0.959687
$263$	749057.	0.667768	0.333884	−	0.942614i	$-0.391641\pi$
$263$	749057.	0.667768	0.333884	+	0.942614i	$0.391641\pi$
$264$	768014.	0.678203
$265$	77897.4	0.0681410
$266$	0	0
$267$	−141180.	−0.121198
$268$	446626.	0.379845
$269$	−669945.	−0.564493	−0.282246	−	0.959342i	$-0.591080\pi$
$269$	−669945.	−0.564493	−0.282246	+	0.959342i	$0.591080\pi$
$270$	−180408.	−0.150608
$271$	−540659.	−0.447199	−0.223599	−	0.974681i	$-0.571781\pi$
$271$	−540659.	−0.447199	−0.223599	+	0.974681i	$0.571781\pi$
$272$	−1.63367e6	−1.33888
$273$	0	0
$274$	244246.	0.196540
$275$	936668.	0.746885
$276$	−129707.	−0.102492
$277$	−401910.	−0.314723	−0.157362	−	0.987541i	$-0.550299\pi$
$277$	−401910.	−0.314723	−0.157362	+	0.987541i	$0.550299\pi$
$278$	−679005.	−0.526940
$279$	316906.	0.243736
$280$	0	0
$281$	−429139.	−0.324214	−0.162107	−	0.986773i	$-0.551829\pi$
$281$	−429139.	−0.324214	−0.162107	+	0.986773i	$0.551829\pi$
$282$	391895.	0.293459
$283$	340927.	0.253044	0.126522	−	0.991964i	$-0.459619\pi$
$283$	340927.	0.253044	0.126522	+	0.991964i	$0.459619\pi$
$284$	352957.	0.259672
$285$	328510.	0.239572
$286$	1.44188e6	1.04235
$287$	0	0
$288$	−252149.	−0.179133
$289$	348246.	0.245268
$290$	362188.	0.252895
$291$	−28156.5	−0.0194915
$292$	491735.	0.337500
$293$	388847.	0.264612	0.132306	−	0.991209i	$-0.457762\pi$
$293$	388847.	0.264612	0.132306	+	0.991209i	$0.457762\pi$
$294$	0	0
$295$	1.99273e6	1.33319
$296$	2.41328e6	1.60095
$297$	−420188.	−0.276409
$298$	1.23040e6	0.802615
$299$	638945.	0.413319
$300$	−129149.	−0.0828493
$301$	0	0
$302$	905435.	0.571268
$303$	1.52110e6	0.951811
$304$	1.15792e6	0.718612
$305$	1.59168e6	0.979730
$306$	688225.	0.420172
$307$	2.35747e6	1.42758	0.713789	−	0.700361i	$-0.246978\pi$
$307$	2.35747e6	1.42758	0.713789	+	0.700361i	$0.246978\pi$
$308$	0	0
$309$	−1.01538e6	−0.604969
$310$	−968220.	−0.572229
$311$	1.43663e6	0.842254	0.421127	−	0.907002i	$-0.361635\pi$
$311$	1.43663e6	0.842254	0.421127	+	0.907002i	$0.361635\pi$
$312$	521645.	0.303381
$313$	822800.	0.474715	0.237358	−	0.971422i	$-0.423719\pi$
$313$	822800.	0.474715	0.237358	+	0.971422i	$0.423719\pi$
$314$	−3.61520e6	−2.06923
$315$	0	0
$316$	−557652.	−0.314156
$317$	−1.76693e6	−0.987580	−0.493790	−	0.869581i	$-0.664389\pi$
$317$	−1.76693e6	−0.987580	−0.493790	+	0.869581i	$0.664389\pi$
$318$	−115670.	−0.0641435
$319$	843572.	0.464136
$320$	−752264.	−0.410672
$321$	−200785.	−0.108760
$322$	0	0
$323$	−1.25321e6	−0.668370
$324$	57936.2	0.0306611
$325$	636196.	0.334105
$326$	−2.74893e6	−1.43258
$327$	−754376.	−0.390138
$328$	−1.94003e6	−0.995689
$329$	0	0
$330$	1.28377e6	0.648937
$331$	−3052.27	−0.00153128	−0.000765638	−	1.00000i	$-0.500244\pi$
$331$	−3052.27	−0.00153128	−0.000765638		1.00000i	$0.500244\pi$
$332$	−402422.	−0.200372
$333$	−1.32033e6	−0.652486
$334$	1.53526e6	0.753038
$335$	−1.95885e6	−0.953649
$336$	0	0
$337$	2.02939e6	0.973398	0.486699	−	0.873570i	$-0.338201\pi$
$337$	2.02939e6	0.973398	0.486699	+	0.873570i	$0.338201\pi$
$338$	−1.39317e6	−0.663302
$339$	−368356.	−0.174088
$340$	−454748.	−0.213341
$341$	−2.25508e6	−1.05021
$342$	−487805.	−0.225518
$343$	0	0
$344$	−2.18130e6	−0.993848
$345$	568880.	0.257320
$346$	1.14570e6	0.514496
$347$	3.78218e6	1.68624	0.843119	−	0.537727i	$-0.180717\pi$
$347$	3.78218e6	1.68624	0.843119	+	0.537727i	$0.180717\pi$
$348$	−116313.	−0.0514850
$349$	−291147.	−0.127953	−0.0639763	−	0.997951i	$-0.520378\pi$
$349$	−291147.	−0.127953	−0.0639763	+	0.997951i	$0.520378\pi$
$350$	0	0
$351$	−285397.	−0.123646
$352$	1.79427e6	0.771848
$353$	−385076.	−0.164479	−0.0822394	−	0.996613i	$-0.526207\pi$
$353$	−385076.	−0.164479	−0.0822394	+	0.996613i	$0.526207\pi$
$354$	−2.95901e6	−1.25498
$355$	−1.54803e6	−0.651939
$356$	−138520.	−0.0579277
$357$	0	0
$358$	−3.67775e6	−1.51661
$359$	−3.23014e6	−1.32277	−0.661385	−	0.750046i	$-0.730031\pi$
$359$	−3.23014e6	−1.32277	−0.661385	+	0.750046i	$0.730031\pi$
$360$	464443.	0.188876
$361$	−1.58784e6	−0.641268
$362$	−3.71255e6	−1.48902
$363$	1.54057e6	0.613641
$364$	0	0
$365$	−2.15669e6	−0.847336
$366$	−2.36349e6	−0.922254
$367$	479559.	0.185856	0.0929280	−	0.995673i	$-0.470377\pi$
$367$	479559.	0.185856	0.0929280	+	0.995673i	$0.470377\pi$
$368$	2.00517e6	0.771847
$369$	1.06141e6	0.405805
$370$	4.03390e6	1.53187
$371$	0	0
$372$	310934.	0.116496
$373$	872666.	0.324770	0.162385	−	0.986727i	$-0.448081\pi$
$373$	872666.	0.324770	0.162385	+	0.986727i	$0.448081\pi$
$374$	−4.89736e6	−1.81043
$375$	1.65569e6	0.607996
$376$	−1.00889e6	−0.368024
$377$	572965.	0.207622
$378$	0	0
$379$	−2.43493e6	−0.870742	−0.435371	−	0.900251i	$-0.643383\pi$
$379$	−2.43493e6	−0.870742	−0.435371	+	0.900251i	$0.643383\pi$
$380$	322320.	0.114506
$381$	749431.	0.264496
$382$	−4.22089e6	−1.47995
$383$	3.61169e6	1.25809	0.629047	−	0.777367i	$-0.283445\pi$
$383$	3.61169e6	1.25809	0.629047	+	0.777367i	$0.283445\pi$
$384$	2.01357e6	0.696848
$385$	0	0
$386$	−3.56114e6	−1.21652
$387$	1.19341e6	0.405055
$388$	−27625.9	−0.00931615
$389$	−175232.	−0.0587138	−0.0293569	−	0.999569i	$-0.509346\pi$
$389$	−175232.	−0.0587138	−0.0293569	+	0.999569i	$0.509346\pi$
$390$	871954.	0.290290
$391$	−2.17018e6	−0.717882
$392$	0	0
$393$	1.50187e6	0.490515
$394$	−4.86525e6	−1.57893
$395$	2.44579e6	0.788727
$396$	−412270.	−0.132112
$397$	−1.88515e6	−0.600303	−0.300152	−	0.953892i	$-0.597037\pi$
$397$	−1.88515e6	−0.600303	−0.300152	+	0.953892i	$0.597037\pi$
$398$	868126.	0.274710
$399$	0	0
$400$	1.99654e6	0.623920
$401$	1.33983e6	0.416091	0.208046	−	0.978119i	$-0.433290\pi$
$401$	1.33983e6	0.416091	0.208046	+	0.978119i	$0.433290\pi$
$402$	2.90869e6	0.897703
$403$	−1.53168e6	−0.469791
$404$	1.49243e6	0.454927
$405$	−254101.	−0.0769785
$406$	0	0
$407$	9.39535e6	2.81143
$408$	−1.77177e6	−0.526934
$409$	−6.58628e6	−1.94685	−0.973423	−	0.229013i	$-0.926450\pi$
$409$	−6.58628e6	−1.94685	−0.973423	+	0.229013i	$0.926450\pi$
$410$	−3.24285e6	−0.952725
$411$	344015.	0.100455
$412$	−996247.	−0.289150
$413$	0	0
$414$	−844730.	−0.242224
$415$	1.76497e6	0.503058
$416$	1.21869e6	0.345271
$417$	−956365.	−0.269329
$418$	3.47118e6	0.971710
$419$	6.96869e6	1.93917	0.969585	−	0.244754i	$-0.0787071\pi$
$419$	6.96869e6	1.93917	0.969585	+	0.244754i	$0.0787071\pi$
$420$	0	0
$421$	3.84041e6	1.05602	0.528010	−	0.849238i	$-0.322938\pi$
$421$	3.84041e6	1.05602	0.528010	+	0.849238i	$0.322938\pi$
$422$	−6.33336e6	−1.73122
$423$	551976.	0.149992
$424$	297781.	0.0804418
$425$	−2.16084e6	−0.580297
$426$	2.29866e6	0.613693
$427$	0	0
$428$	−197002.	−0.0519829
$429$	2.03086e6	0.532767
$430$	−3.64615e6	−0.950963
$431$	3.03636e6	0.787337	0.393668	−	0.919253i	$-0.371206\pi$
$431$	3.03636e6	0.787337	0.393668	+	0.919253i	$0.371206\pi$
$432$	−895647.	−0.230902
$433$	941529.	0.241332	0.120666	−	0.992693i	$-0.461497\pi$
$433$	941529.	0.241332	0.120666	+	0.992693i	$0.461497\pi$
$434$	0	0
$435$	510135.	0.129259
$436$	−740160.	−0.186470
$437$	1.53819e6	0.385307
$438$	3.20247e6	0.797627
$439$	−1.34109e6	−0.332122	−0.166061	−	0.986116i	$-0.553105\pi$
$439$	−1.34109e6	−0.332122	−0.166061	+	0.986116i	$0.553105\pi$
$440$	−3.30494e6	−0.813827
$441$	0	0
$442$	−3.32635e6	−0.809864
$443$	−772341.	−0.186982	−0.0934910	−	0.995620i	$-0.529803\pi$
$443$	−772341.	−0.186982	−0.0934910	+	0.995620i	$0.529803\pi$
$444$	−1.29545e6	−0.311862
$445$	607531.	0.145435
$446$	−3.47190e6	−0.826475
$447$	1.73300e6	0.410232
$448$	0	0
$449$	2.25684e6	0.528304	0.264152	−	0.964481i	$-0.414908\pi$
$449$	2.25684e6	0.528304	0.264152	+	0.964481i	$0.414908\pi$
$450$	−841097.	−0.195801
$451$	−7.55291e6	−1.74853
$452$	−361414.	−0.0832069
$453$	1.27529e6	0.291986
$454$	−104.373	−2.37655e−5 0
$455$	0	0
$456$	1.25580e6	0.282820
$457$	4.28470e6	0.959688	0.479844	−	0.877354i	$-0.340693\pi$
$457$	4.28470e6	0.959688	0.479844	+	0.877354i	$0.340693\pi$
$458$	494442.	0.110142
$459$	969352.	0.214758
$460$	558160.	0.122988
$461$	3.10462e6	0.680387	0.340193	−	0.940355i	$-0.389507\pi$
$461$	3.10462e6	0.680387	0.340193	+	0.940355i	$0.389507\pi$
$462$	0	0
$463$	−3.53386e6	−0.766121	−0.383060	−	0.923723i	$-0.625130\pi$
$463$	−3.53386e6	−0.766121	−0.383060	+	0.923723i	$0.625130\pi$
$464$	1.79811e6	0.387722
$465$	−1.36372e6	−0.292477
$466$	−662356.	−0.141295
$467$	−2.72459e6	−0.578109	−0.289054	−	0.957313i	$-0.593341\pi$
$467$	−2.72459e6	−0.578109	−0.289054	+	0.957313i	$0.593341\pi$
$468$	−280019.	−0.0590980
$469$	0	0
$470$	−1.68641e6	−0.352143
$471$	−5.09194e6	−1.05762
$472$	7.61767e6	1.57386
$473$	−8.49224e6	−1.74530
$474$	−3.63176e6	−0.742457
$475$	1.53158e6	0.311461
$476$	0	0
$477$	−162919.	−0.0327850
$478$	4.40331e6	0.881475
$479$	−978685.	−0.194896	−0.0974482	−	0.995241i	$-0.531068\pi$
$479$	−978685.	−0.194896	−0.0974482	+	0.995241i	$0.531068\pi$
$480$	1.08505e6	0.214955
$481$	6.38144e6	1.25764
$482$	−1.40766e6	−0.275982
$483$	0	0
$484$	1.51154e6	0.293296
$485$	121164.	0.0233893
$486$	377315.	0.0724626
$487$	3.92744e6	0.750390	0.375195	−	0.926946i	$-0.377576\pi$
$487$	3.92744e6	0.750390	0.375195	+	0.926946i	$0.377576\pi$
$488$	6.08456e6	1.15659
$489$	−3.87181e6	−0.732220
$490$	0	0
$491$	2.63241e6	0.492777	0.246388	−	0.969171i	$-0.420756\pi$
$491$	2.63241e6	0.492777	0.246388	+	0.969171i	$0.420756\pi$
$492$	1.04141e6	0.193958
$493$	−1.94607e6	−0.360614
$494$	2.35767e6	0.434676
$495$	1.80817e6	0.331685
$496$	−4.80678e6	−0.877305
$497$	0	0
$498$	−2.62081e6	−0.473546
$499$	2.12544e6	0.382118	0.191059	−	0.981579i	$-0.438808\pi$
$499$	2.12544e6	0.382118	0.191059	+	0.981579i	$0.438808\pi$
$500$	1.62449e6	0.290597
$501$	2.16239e6	0.384892
$502$	−9.17850e6	−1.62560
$503$	−2.60929e6	−0.459835	−0.229917	−	0.973210i	$-0.573846\pi$
$503$	−2.60929e6	−0.459835	−0.229917	+	0.973210i	$0.573846\pi$
$504$	0	0
$505$	−6.54564e6	−1.14215
$506$	6.01104e6	1.04369
$507$	−1.96225e6	−0.339027
$508$	735308.	0.126418
$509$	1.00182e7	1.71394	0.856970	−	0.515366i	$-0.172344\pi$
$509$	1.00182e7	1.71394	0.856970	+	0.515366i	$0.172344\pi$
$510$	−2.96159e6	−0.504196
$511$	0	0
$512$	−1.99607e6	−0.336512
$513$	−687063.	−0.115267
$514$	5.80965e6	0.969933
$515$	4.36942e6	0.725948
$516$	1.17092e6	0.193600
$517$	−3.92782e6	−0.646287
$518$	0	0
$519$	1.61370e6	0.262969
$520$	−2.24476e6	−0.364050
$521$	4.17941e6	0.674560	0.337280	−	0.941404i	$-0.390493\pi$
$521$	4.17941e6	0.674560	0.337280	+	0.941404i	$0.390493\pi$
$522$	−757500.	−0.121676
$523$	−3.60525e6	−0.576343	−0.288172	−	0.957579i	$-0.593047\pi$
$523$	−3.60525e6	−0.576343	−0.288172	+	0.957579i	$0.593047\pi$
$524$	1.47357e6	0.234446
$525$	0	0
$526$	4.78637e6	0.754297
$527$	5.20234e6	0.815967
$528$	6.37336e6	0.994909
$529$	−3.77266e6	−0.586150
$530$	497754.	0.0769707
$531$	−4.16770e6	−0.641446
$532$	0	0
$533$	−5.13003e6	−0.782172
$534$	−902122.	−0.136903
$535$	864025.	0.130509
$536$	−7.48814e6	−1.12580
$537$	−5.18003e6	−0.775170
$538$	−4.28086e6	−0.637640
$539$	0	0
$540$	−249313.	−0.0367926
$541$	−6.68166e6	−0.981501	−0.490751	−	0.871300i	$-0.663277\pi$
$541$	−6.68166e6	−0.981501	−0.490751	+	0.871300i	$0.663277\pi$
$542$	−3.45474e6	−0.505146
$543$	−5.22906e6	−0.761069
$544$	−4.13929e6	−0.599692
$545$	3.24625e6	0.468156
$546$	0	0
$547$	8.69076e6	1.24191	0.620954	−	0.783847i	$-0.286745\pi$
$547$	8.69076e6	1.24191	0.620954	+	0.783847i	$0.286745\pi$
$548$	337532.	0.0480136
$549$	−3.32892e6	−0.471382
$550$	5.98518e6	0.843666
$551$	1.37935e6	0.193551
$552$	2.17467e6	0.303771
$553$	0	0
$554$	−2.56815e6	−0.355505
$555$	5.68167e6	0.782967
$556$	−938342.	−0.128728
$557$	6.24742e6	0.853223	0.426612	−	0.904435i	$-0.359707\pi$
$557$	6.24742e6	0.853223	0.426612	+	0.904435i	$0.359707\pi$
$558$	2.02499e6	0.275319
$559$	−5.76803e6	−0.780725
$560$	0	0
$561$	−6.89783e6	−0.925349
$562$	−2.74214e6	−0.366226
$563$	1.19045e7	1.58285	0.791423	−	0.611269i	$-0.209341\pi$
$563$	1.19045e7	1.58285	0.791423	+	0.611269i	$0.209341\pi$
$564$	541574.	0.0716903
$565$	1.58512e6	0.208901
$566$	2.17848e6	0.285833
$567$	0	0
$568$	−5.91768e6	−0.769627
$569$	21414.4	0.00277284	0.00138642	−	0.999999i	$-0.499559\pi$
$569$	21414.4	0.00277284	0.00138642	+	0.999999i	$0.499559\pi$
$570$	2.09914e6	0.270616
$571$	7.11647e6	0.913428	0.456714	−	0.889614i	$-0.349026\pi$
$571$	7.11647e6	0.913428	0.456714	+	0.889614i	$0.349026\pi$
$572$	1.99259e6	0.254641
$573$	−5.94504e6	−0.756429
$574$	0	0
$575$	2.65223e6	0.334534
$576$	1.57333e6	0.197589
$577$	1.06652e7	1.33361	0.666805	−	0.745232i	$-0.267661\pi$
$577$	1.06652e7	1.33361	0.666805	+	0.745232i	$0.267661\pi$
$578$	2.22524e6	0.277050
$579$	−5.01579e6	−0.621789
$580$	500522.	0.0617808
$581$	0	0
$582$	−179916.	−0.0220172
$583$	1.15932e6	0.141264
$584$	−8.24444e6	−1.00030
$585$	1.22813e6	0.148373
$586$	2.48468e6	0.298901
$587$	1.30101e7	1.55843	0.779213	−	0.626759i	$-0.215619\pi$
$587$	1.30101e7	1.55843	0.779213	+	0.626759i	$0.215619\pi$
$588$	0	0
$589$	−3.68735e6	−0.437952
$590$	1.27333e7	1.50595
$591$	−6.85260e6	−0.807025
$592$	2.00265e7	2.34856
$593$	−4.26086e6	−0.497578	−0.248789	−	0.968558i	$-0.580033\pi$
$593$	−4.26086e6	−0.497578	−0.248789	+	0.968558i	$0.580033\pi$
$594$	−2.68495e6	−0.312226
$595$	0	0
$596$	1.70034e6	0.196074
$597$	1.22274e6	0.140410
$598$	4.08277e6	0.466877
$599$	−1.37958e7	−1.57101	−0.785507	−	0.618853i	$-0.787598\pi$
$599$	−1.37958e7	−1.57101	−0.785507	+	0.618853i	$0.787598\pi$
$600$	2.16532e6	0.245552
$601$	−4.99695e6	−0.564311	−0.282155	−	0.959369i	$-0.591049\pi$
$601$	−4.99695e6	−0.564311	−0.282155	+	0.959369i	$0.591049\pi$
$602$	0	0
$603$	4.09683e6	0.458833
$604$	1.25126e6	0.139558
$605$	−6.62942e6	−0.736355
$606$	9.71962e6	1.07515
$607$	3.04946e6	0.335932	0.167966	−	0.985793i	$-0.446280\pi$
$607$	3.04946e6	0.335932	0.167966	+	0.985793i	$0.446280\pi$
$608$	2.93387e6	0.321871
$609$	0	0
$610$	1.01706e7	1.10668
$611$	−2.66782e6	−0.289104
$612$	951085.	0.102646
$613$	−7.03625e6	−0.756293	−0.378147	−	0.925746i	$-0.623438\pi$
$613$	−7.03625e6	−0.756293	−0.378147	+	0.925746i	$0.623438\pi$
$614$	1.50639e7	1.61256
$615$	−4.56749e6	−0.486956
$616$	0	0
$617$	1.00066e7	1.05822	0.529108	−	0.848554i	$-0.322527\pi$
$617$	1.00066e7	1.05822	0.529108	+	0.848554i	$0.322527\pi$
$618$	−6.48815e6	−0.683360
$619$	6.55067e6	0.687161	0.343581	−	0.939123i	$-0.388360\pi$
$619$	6.55067e6	0.687161	0.343581	+	0.939123i	$0.388360\pi$
$620$	−1.33802e6	−0.139792
$621$	−1.18979e6	−0.123805
$622$	9.17986e6	0.951393
$623$	0	0
$624$	4.32886e6	0.445054
$625$	−2.04650e6	−0.209561
$626$	5.25758e6	0.536229
$627$	4.88909e6	0.496660
$628$	−4.99598e6	−0.505501
$629$	−2.16746e7	−2.18436
$630$	0	0
$631$	2.22672e6	0.222635	0.111317	−	0.993785i	$-0.464493\pi$
$631$	2.22672e6	0.222635	0.111317	+	0.993785i	$0.464493\pi$
$632$	9.34960e6	0.931109
$633$	−8.92042e6	−0.884863
$634$	−1.12905e7	−1.11555
$635$	−3.22497e6	−0.317389
$636$	−159849.	−0.0156699
$637$	0	0
$638$	5.39031e6	0.524279
$639$	3.23762e6	0.313671
$640$	−8.66484e6	−0.836201
$641$	−1.59340e7	−1.53172	−0.765859	−	0.643008i	$-0.777686\pi$
$641$	−1.59340e7	−1.53172	−0.765859	+	0.643008i	$0.777686\pi$
$642$	−1.28299e6	−0.122853
$643$	1.49933e7	1.43011	0.715056	−	0.699067i	$-0.246401\pi$
$643$	1.49933e7	1.43011	0.715056	+	0.699067i	$0.246401\pi$
$644$	0	0
$645$	−5.13553e6	−0.486056
$646$	−8.00783e6	−0.754977
$647$	−1.29805e7	−1.21908	−0.609540	−	0.792755i	$-0.708646\pi$
$647$	−1.29805e7	−1.21908	−0.609540	+	0.792755i	$0.708646\pi$
$648$	−971360.	−0.0908747
$649$	2.96571e7	2.76386
$650$	4.06521e6	0.377398
$651$	0	0
$652$	−3.79885e6	−0.349972
$653$	−1.65492e7	−1.51878	−0.759389	−	0.650637i	$-0.774502\pi$
$653$	−1.65492e7	−1.51878	−0.759389	+	0.650637i	$0.774502\pi$
$654$	−4.82036e6	−0.440692
$655$	−6.46291e6	−0.588606
$656$	−1.60993e7	−1.46066
$657$	4.51062e6	0.407683
$658$	0	0
$659$	5.86879e6	0.526423	0.263212	−	0.964738i	$-0.415218\pi$
$659$	5.86879e6	0.526423	0.263212	+	0.964738i	$0.415218\pi$
$660$	1.77409e6	0.158532
$661$	−7.27687e6	−0.647800	−0.323900	−	0.946091i	$-0.604994\pi$
$661$	−7.27687e6	−0.647800	−0.323900	+	0.946091i	$0.604994\pi$
$662$	−19503.6	−0.00172970
$663$	−4.68509e6	−0.413937
$664$	6.74702e6	0.593870
$665$	0	0
$666$	−8.43672e6	−0.737035
$667$	2.38862e6	0.207889
$668$	2.12164e6	0.183963
$669$	−4.89010e6	−0.422428
$670$	−1.25168e7	−1.07722
$671$	2.36884e7	2.03109
$672$	0	0
$673$	−1.82417e7	−1.55248	−0.776241	−	0.630437i	$-0.782876\pi$
$673$	−1.82417e7	−1.55248	−0.776241	+	0.630437i	$0.782876\pi$
$674$	1.29675e7	1.09953
$675$	−1.18467e6	−0.100078
$676$	−1.92527e6	−0.162041
$677$	7.76406e6	0.651054	0.325527	−	0.945533i	$-0.394458\pi$
$677$	7.76406e6	0.651054	0.325527	+	0.945533i	$0.394458\pi$
$678$	−2.35374e6	−0.196646
$679$	0	0
$680$	7.62432e6	0.632308
$681$	−147.007	−1.21470e−5 0
$682$	−1.44096e7	−1.18629
$683$	8.56324e6	0.702403	0.351201	−	0.936300i	$-0.385773\pi$
$683$	8.56324e6	0.702403	0.351201	+	0.936300i	$0.385773\pi$
$684$	−674116.	−0.0550927
$685$	−1.48038e6	−0.120544
$686$	0	0
$687$	696411.	0.0562955
$688$	−1.81015e7	−1.45796
$689$	787423.	0.0631917
$690$	3.63507e6	0.290663
$691$	−1.64509e7	−1.31068	−0.655338	−	0.755336i	$-0.727474\pi$
$691$	−1.64509e7	−1.31068	−0.655338	+	0.755336i	$0.727474\pi$
$692$	1.58329e6	0.125689
$693$	0	0
$694$	2.41677e7	1.90474
$695$	4.11546e6	0.323189
$696$	1.95011e6	0.152593
$697$	1.74242e7	1.35853
$698$	−1.86039e6	−0.144533
$699$	−932916.	−0.0722187
$700$	0	0
$701$	−1.66928e7	−1.28302	−0.641512	−	0.767113i	$-0.721693\pi$
$701$	−1.66928e7	−1.28302	−0.641512	+	0.767113i	$0.721693\pi$
$702$	−1.82365e6	−0.139669
$703$	1.53626e7	1.17240
$704$	−1.11957e7	−0.851370
$705$	−2.37528e6	−0.179987
$706$	−2.46059e6	−0.185792
$707$	0	0
$708$	−4.08916e6	−0.306585
$709$	5.61779e6	0.419711	0.209855	−	0.977732i	$-0.432701\pi$
$709$	5.61779e6	0.419711	0.209855	+	0.977732i	$0.432701\pi$
$710$	−9.89167e6	−0.736417
$711$	−5.11526e6	−0.379484
$712$	2.32242e6	0.171689
$713$	−6.38537e6	−0.470395
$714$	0	0
$715$	−8.73927e6	−0.639308
$716$	−5.08242e6	−0.370500
$717$	6.20198e6	0.450539
$718$	−2.06401e7	−1.49417
$719$	−1.03718e7	−0.748227	−0.374113	−	0.927383i	$-0.622053\pi$
$719$	−1.03718e7	−0.748227	−0.374113	+	0.927383i	$0.622053\pi$
$720$	3.85418e6	0.277077
$721$	0	0
$722$	−1.01461e7	−0.724363
$723$	−1.98266e6	−0.141060
$724$	−5.13052e6	−0.363760
$725$	2.37835e6	0.168047
$726$	9.84403e6	0.693156
$727$	−1.15369e7	−0.809565	−0.404783	−	0.914413i	$-0.632653\pi$
$727$	−1.15369e7	−0.809565	−0.404783	+	0.914413i	$0.632653\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	−1.37810e7	−0.957134
$731$	1.95911e7	1.35602
$732$	−3.26619e6	−0.225301
$733$	−1.49470e7	−1.02753	−0.513764	−	0.857932i	$-0.671749\pi$
$733$	−1.49470e7	−1.02753	−0.513764	+	0.857932i	$0.671749\pi$
$734$	3.06432e6	0.209939
$735$	0	0
$736$	5.08058e6	0.345715
$737$	−2.91528e7	−1.97702
$738$	6.78227e6	0.458389
$739$	9.01364e6	0.607140	0.303570	−	0.952809i	$-0.401821\pi$
$739$	9.01364e6	0.607140	0.303570	+	0.952809i	$0.401821\pi$
$740$	5.57460e6	0.374227
$741$	3.32073e6	0.222171
$742$	0	0
$743$	−2.10239e7	−1.39714	−0.698571	−	0.715541i	$-0.746180\pi$
$743$	−2.10239e7	−1.39714	−0.698571	+	0.715541i	$0.746180\pi$
$744$	−5.21312e6	−0.345275
$745$	−7.45750e6	−0.492269
$746$	5.57622e6	0.366854
$747$	−3.69136e6	−0.242039
$748$	−6.76785e6	−0.442279
$749$	0	0
$750$	1.05796e7	0.686779
$751$	4.04219e6	0.261527	0.130764	−	0.991414i	$-0.458257\pi$
$751$	4.04219e6	0.261527	0.130764	+	0.991414i	$0.458257\pi$
$752$	−8.37230e6	−0.539884
$753$	−1.29277e7	−0.830874
$754$	3.66117e6	0.234526
$755$	−5.48786e6	−0.350377
$756$	0	0
$757$	−1.82059e7	−1.15471	−0.577353	−	0.816495i	$-0.695914\pi$
$757$	−1.82059e7	−1.15471	−0.577353	+	0.816495i	$0.695914\pi$
$758$	−1.55589e7	−0.983572
$759$	8.46642e6	0.533452
$760$	−5.40402e6	−0.339377
$761$	1.89200e7	1.18429	0.592146	−	0.805831i	$-0.298281\pi$
$761$	1.89200e7	1.18429	0.592146	+	0.805831i	$0.298281\pi$
$762$	4.78876e6	0.298769
$763$	0	0
$764$	−5.83301e6	−0.361542
$765$	−4.17134e6	−0.257705
$766$	2.30782e7	1.42112
$767$	2.01434e7	1.23636
$768$	7.27238e6	0.444911
$769$	1.12831e7	0.688037	0.344019	−	0.938963i	$-0.388212\pi$
$769$	1.12831e7	0.688037	0.344019	+	0.938963i	$0.388212\pi$
$770$	0	0
$771$	8.18277e6	0.495752
$772$	−4.92127e6	−0.297190
$773$	3.68565e6	0.221853	0.110926	−	0.993829i	$-0.464618\pi$
$773$	3.68565e6	0.221853	0.110926	+	0.993829i	$0.464618\pi$
$774$	7.62575e6	0.457541
$775$	−6.35791e6	−0.380242
$776$	463176.	0.0276116
$777$	0	0
$778$	−1.11971e6	−0.0663219
$779$	−1.23500e7	−0.729161
$780$	1.20499e6	0.0709162
$781$	−2.30387e7	−1.35154
$782$	−1.38671e7	−0.810905
$783$	−1.06692e6	−0.0621912
$784$	0	0
$785$	2.19118e7	1.26912
$786$	9.59677e6	0.554075
$787$	1.40748e7	0.810039	0.405019	−	0.914308i	$-0.367265\pi$
$787$	1.40748e7	0.810039	0.405019	+	0.914308i	$0.367265\pi$
$788$	−6.72347e6	−0.385725
$789$	6.74151e6	0.385536
$790$	1.56283e7	0.890930
$791$	0	0
$792$	6.91213e6	0.391560
$793$	1.60894e7	0.908569
$794$	−1.20459e7	−0.678090
$795$	701077.	0.0393412
$796$	1.19970e6	0.0671102
$797$	1.75191e7	0.976937	0.488469	−	0.872582i	$-0.337556\pi$
$797$	1.75191e7	0.976937	0.488469	+	0.872582i	$0.337556\pi$
$798$	0	0
$799$	9.06127e6	0.502137
$800$	5.05873e6	0.279458
$801$	−1.27062e6	−0.0699737
$802$	8.56134e6	0.470008
$803$	−3.20972e7	−1.75662
$804$	4.01963e6	0.219304
$805$	0	0
$806$	−9.78721e6	−0.530666
$807$	−6.02950e6	−0.325910
$808$	−2.50222e7	−1.34833
$809$	814521.	0.0437553	0.0218777	−	0.999761i	$-0.493036\pi$
$809$	814521.	0.0437553	0.0218777	+	0.999761i	$0.493036\pi$
$810$	−1.62367e6	−0.0869534
$811$	−1.26533e7	−0.675540	−0.337770	−	0.941229i	$-0.609673\pi$
$811$	−1.26533e7	−0.675540	−0.337770	+	0.941229i	$0.609673\pi$
$812$	0	0
$813$	−4.86593e6	−0.258190
$814$	6.00350e7	3.17573
$815$	1.66613e7	0.878647
$816$	−1.47030e7	−0.773001
$817$	−1.38859e7	−0.727813
$818$	−4.20854e7	−2.19912
$819$	0	0
$820$	−4.48142e6	−0.232745
$821$	4.27393e6	0.221294	0.110647	−	0.993860i	$-0.464708\pi$
$821$	4.27393e6	0.221294	0.110647	+	0.993860i	$0.464708\pi$
$822$	2.19821e6	0.113472
$823$	1.70463e7	0.877266	0.438633	−	0.898666i	$-0.355463\pi$
$823$	1.70463e7	0.877266	0.438633	+	0.898666i	$0.355463\pi$
$824$	1.67031e7	0.856996
$825$	8.43001e6	0.431214
$826$	0	0
$827$	2.60828e6	0.132614	0.0663071	−	0.997799i	$-0.478878\pi$
$827$	2.60828e6	0.132614	0.0663071	+	0.997799i	$0.478878\pi$
$828$	−1.16736e6	−0.0591740
$829$	−2.13865e7	−1.08082	−0.540409	−	0.841403i	$-0.681730\pi$
$829$	−2.13865e7	−1.08082	−0.540409	+	0.841403i	$0.681730\pi$
$830$	1.12780e7	0.568244
$831$	−3.61719e6	−0.181706
$832$	−7.60423e6	−0.380844
$833$	0	0
$834$	−6.11104e6	−0.304229
$835$	−9.30525e6	−0.461862
$836$	4.79696e6	0.237383
$837$	2.85215e6	0.140721
$838$	4.45290e7	2.19045
$839$	−771393.	−0.0378330	−0.0189165	−	0.999821i	$-0.506022\pi$
$839$	−771393.	−0.0378330	−0.0189165	+	0.999821i	$0.506022\pi$
$840$	0	0
$841$	−1.83692e7	−0.895571
$842$	2.45397e7	1.19286
$843$	−3.86225e6	−0.187185
$844$	−8.75231e6	−0.422928
$845$	8.44401e6	0.406824
$846$	3.52705e6	0.169428
$847$	0	0
$848$	2.47113e6	0.118006
$849$	3.06834e6	0.146095
$850$	−1.38075e7	−0.655492
$851$	2.66034e7	1.25926
$852$	3.17661e6	0.149922
$853$	−2.94032e7	−1.38364	−0.691818	−	0.722072i	$-0.743190\pi$
$853$	−2.94032e7	−1.38364	−0.691818	+	0.722072i	$0.743190\pi$
$854$	0	0
$855$	2.95659e6	0.138317
$856$	3.30293e6	0.154069
$857$	2.65010e7	1.23257	0.616283	−	0.787525i	$-0.288638\pi$
$857$	2.65010e7	1.23257	0.616283	+	0.787525i	$0.288638\pi$
$858$	1.29770e7	0.601803
$859$	3.67519e7	1.69940	0.849702	−	0.527264i	$-0.176782\pi$
$859$	3.67519e7	1.69940	0.849702	+	0.527264i	$0.176782\pi$
$860$	−5.03876e6	−0.232315
$861$	0	0
$862$	1.94020e7	0.889360
$863$	1.18189e7	0.540196	0.270098	−	0.962833i	$-0.412944\pi$
$863$	1.18189e7	0.540196	0.270098	+	0.962833i	$0.412944\pi$
$864$	−2.26934e6	−0.103423
$865$	−6.94413e6	−0.315557
$866$	6.01625e6	0.272603
$867$	3.13421e6	0.141606
$868$	0	0
$869$	3.63998e7	1.63512
$870$	3.25970e6	0.146009
$871$	−1.98009e7	−0.884382
$872$	1.24095e7	0.552668
$873$	−253408.	−0.0112534
$874$	9.82884e6	0.435235
$875$	0	0
$876$	4.42562e6	0.194856
$877$	7.93509e6	0.348380	0.174190	−	0.984712i	$-0.444269\pi$
$877$	7.93509e6	0.348380	0.174190	+	0.984712i	$0.444269\pi$
$878$	−8.56939e6	−0.375158
$879$	3.49963e6	0.152774
$880$	−2.74260e7	−1.19387
$881$	−4.20152e7	−1.82375	−0.911877	−	0.410464i	$-0.865367\pi$
$881$	−4.20152e7	−1.82375	−0.911877	+	0.410464i	$0.865367\pi$
$882$	0	0
$883$	2.12461e7	0.917016	0.458508	−	0.888690i	$-0.348384\pi$
$883$	2.12461e7	0.917016	0.458508	+	0.888690i	$0.348384\pi$
$884$	−4.59681e6	−0.197845
$885$	1.79346e7	0.769720
$886$	−4.93516e6	−0.211211
$887$	−1.88490e7	−0.804415	−0.402208	−	0.915548i	$-0.631757\pi$
$887$	−1.88490e7	−0.804415	−0.402208	+	0.915548i	$0.631757\pi$
$888$	2.17195e7	0.924309
$889$	0	0
$890$	3.88204e6	0.164280
$891$	−3.78169e6	−0.159585
$892$	−4.79795e6	−0.201903
$893$	−6.42251e6	−0.269511
$894$	1.10736e7	0.463390
$895$	2.22909e7	0.930186
$896$	0	0
$897$	5.75050e6	0.238630
$898$	1.44209e7	0.596762
$899$	−5.72600e6	−0.236294
$900$	−1.16234e6	−0.0478331
$901$	−2.67448e6	−0.109756
$902$	−4.82621e7	−1.97510
$903$	0	0
$904$	6.05948e6	0.246612
$905$	2.25018e7	0.913264
$906$	8.14892e6	0.329822
$907$	−6.19446e6	−0.250026	−0.125013	−	0.992155i	$-0.539897\pi$
$907$	−6.19446e6	−0.250026	−0.125013	+	0.992155i	$0.539897\pi$
$908$	−144.237	−5.80578e−6 0
$909$	1.36899e7	0.549528
$910$	0	0
$911$	−2.50171e7	−0.998712	−0.499356	−	0.866397i	$-0.666430\pi$
$911$	−2.50171e7	−0.998712	−0.499356	+	0.866397i	$0.666430\pi$
$912$	1.04213e7	0.414891
$913$	2.62674e7	1.04290
$914$	2.73787e7	1.08404
$915$	1.43251e7	0.565647
$916$	683288.	0.0269070
$917$	0	0
$918$	6.19403e6	0.242586
$919$	1.54992e7	0.605370	0.302685	−	0.953091i	$-0.402117\pi$
$919$	1.54992e7	0.605370	0.302685	+	0.953091i	$0.402117\pi$
$920$	−9.35812e6	−0.364518
$921$	2.12172e7	0.824212
$922$	1.98381e7	0.768551
$923$	−1.56481e7	−0.604587
$924$	0	0
$925$	2.64890e7	1.01791
$926$	−2.25809e7	−0.865394
$927$	−9.13843e6	−0.349279
$928$	4.55594e6	0.173663
$929$	−3.75285e7	−1.42667	−0.713333	−	0.700826i	$-0.752815\pi$
$929$	−3.75285e7	−1.42667	−0.713333	+	0.700826i	$0.752815\pi$
$930$	−8.71398e6	−0.330377
$931$	0	0
$932$	−915335.	−0.0345176
$933$	1.29297e7	0.486276
$934$	−1.74098e7	−0.653020
$935$	2.96830e7	1.11040
$936$	4.69480e6	0.175157
$937$	1.08298e7	0.402969	0.201485	−	0.979492i	$-0.435423\pi$
$937$	1.08298e7	0.402969	0.201485	+	0.979492i	$0.435423\pi$
$938$	0	0
$939$	7.40520e6	0.274077
$940$	−2.33052e6	−0.0860267
$941$	−3.24591e7	−1.19498	−0.597492	−	0.801875i	$-0.703836\pi$
$941$	−3.24591e7	−1.19498	−0.597492	+	0.801875i	$0.703836\pi$
$942$	−3.25368e7	−1.19467
$943$	−2.13865e7	−0.783177
$944$	6.32151e7	2.30883
$945$	0	0
$946$	−5.42643e7	−1.97145
$947$	7.53877e6	0.273165	0.136583	−	0.990629i	$-0.456388\pi$
$947$	7.53877e6	0.273165	0.136583	+	0.990629i	$0.456388\pi$
$948$	−5.01886e6	−0.181378
$949$	−2.18008e7	−0.785792
$950$	9.78656e6	0.351821
$951$	−1.59024e7	−0.570180
$952$	0	0
$953$	−3.01356e7	−1.07485	−0.537424	−	0.843312i	$-0.680602\pi$
$953$	−3.01356e7	−1.07485	−0.537424	+	0.843312i	$0.680602\pi$
$954$	−1.04103e6	−0.0370333
$955$	2.55829e7	0.907697
$956$	6.08510e6	0.215339
$957$	7.59215e6	0.267969
$958$	−6.25366e6	−0.220151
$959$	0	0
$960$	−6.77038e6	−0.237102
$961$	−1.33221e7	−0.465335
$962$	4.07765e7	1.42060
$963$	−1.80707e6	−0.0627926
$964$	−1.94530e6	−0.0674208
$965$	2.15841e7	0.746132
$966$	0	0
$967$	2.88021e6	0.0990509	0.0495255	−	0.998773i	$-0.484229\pi$
$967$	2.88021e6	0.0990509	0.0495255	+	0.998773i	$0.484229\pi$
$968$	−2.53425e7	−0.869282
$969$	−1.12789e7	−0.385883
$970$	774220.	0.0264201
$971$	2.74490e7	0.934283	0.467142	−	0.884183i	$-0.345284\pi$
$971$	2.74490e7	0.934283	0.467142	+	0.884183i	$0.345284\pi$
$972$	521426.	0.0177022
$973$	0	0
$974$	2.50958e7	0.847626
$975$	5.72577e6	0.192896
$976$	5.04927e7	1.69669
$977$	−5.88524e7	−1.97255	−0.986274	−	0.165118i	$-0.947200\pi$
$977$	−5.88524e7	−1.97255	−0.986274	+	0.165118i	$0.947200\pi$
$978$	−2.47403e7	−0.827101
$979$	9.04164e6	0.301502
$980$	0	0
$981$	−6.78938e6	−0.225246
$982$	1.68208e7	0.556631
$983$	−1.86077e7	−0.614198	−0.307099	−	0.951678i	$-0.599358\pi$
$983$	−1.86077e7	−0.614198	−0.307099	+	0.951678i	$0.599358\pi$
$984$	−1.74603e7	−0.574862
$985$	2.94883e7	0.968410
$986$	−1.24352e7	−0.407342
$987$	0	0
$988$	3.25815e6	0.106189
$989$	−2.40462e7	−0.781729
$990$	1.15539e7	0.374664
$991$	2.47154e7	0.799435	0.399718	−	0.916638i	$-0.369108\pi$
$991$	2.47154e7	0.799435	0.399718	+	0.916638i	$0.369108\pi$
$992$	−1.21792e7	−0.392951
$993$	−27470.5	−0.000884083 0
$994$	0	0
$995$	−5.26172e6	−0.168488
$996$	−3.62180e6	−0.115685
$997$	1.79581e7	0.572167	0.286084	−	0.958205i	$-0.407646\pi$
$997$	1.79581e7	0.572167	0.286084	+	0.958205i	$0.407646\pi$
$998$	1.35813e7	0.431633
$999$	−1.18829e7	−0.376713

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.a.k.1.2		2
3.2	odd	2		441.6.a.s.1.1		2
7.2	even	3		147.6.e.l.67.1		4
7.3	odd	6		21.6.e.b.16.1	yes	4
7.4	even	3		147.6.e.l.79.1		4
7.5	odd	6		21.6.e.b.4.1	✓	4
7.6	odd	2		147.6.a.i.1.2		2
21.5	even	6		63.6.e.c.46.2		4
21.17	even	6		63.6.e.c.37.2		4
21.20	even	2		441.6.a.t.1.1		2
28.3	even	6		336.6.q.e.289.1		4
28.19	even	6		336.6.q.e.193.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.e.b.4.1	✓	4	7.5	odd	6
21.6.e.b.16.1	yes	4	7.3	odd	6
63.6.e.c.37.2		4	21.17	even	6
63.6.e.c.46.2		4	21.5	even	6
147.6.a.i.1.2		2	7.6	odd	2
147.6.a.k.1.2		2	1.1	even	1	trivial
147.6.e.l.67.1		4	7.2	even	3
147.6.e.l.79.1		4	7.4	even	3
336.6.q.e.193.1		4	28.19	even	6
336.6.q.e.289.1		4	28.3	even	6
441.6.a.s.1.1		2	3.2	odd	2
441.6.a.t.1.1		2	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.a (trivial)

\(f(q)\)	\(=\)	\(q+6.38987 q^{2} +9.00000 q^{3} +8.83040 q^{4} -38.7291 q^{5} +57.5088 q^{6} -148.051 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+6.38987 q^{2} +9.00000 q^{3} +8.83040 q^{4} -38.7291 q^{5} +57.5088 q^{6} -148.051 q^{8} +81.0000 q^{9} -247.474 q^{10} -576.390 q^{11} +79.4736 q^{12} -391.491 q^{13} -348.562 q^{15} -1228.60 q^{16} +1329.70 q^{17} +517.579 q^{18} -942.474 q^{19} -341.993 q^{20} -3683.05 q^{22} -1632.08 q^{23} -1332.46 q^{24} -1625.06 q^{25} -2501.58 q^{26} +729.000 q^{27} -1463.54 q^{29} -2227.26 q^{30} +3912.42 q^{31} -3112.95 q^{32} -5187.51 q^{33} +8496.61 q^{34} +715.262 q^{36} -16300.3 q^{37} -6022.28 q^{38} -3523.42 q^{39} +5733.86 q^{40} +13103.8 q^{41} +14733.5 q^{43} -5089.75 q^{44} -3137.05 q^{45} -10428.8 q^{46} +6814.52 q^{47} -11057.4 q^{48} -10383.9 q^{50} +11967.3 q^{51} -3457.02 q^{52} -2011.34 q^{53} +4658.21 q^{54} +22323.0 q^{55} -8482.26 q^{57} -9351.85 q^{58} -51453.1 q^{59} -3077.94 q^{60} -41097.8 q^{61} +24999.8 q^{62} +19423.8 q^{64} +15162.1 q^{65} -33147.5 q^{66} +50578.2 q^{67} +11741.8 q^{68} -14688.7 q^{69} +39970.6 q^{71} -11992.1 q^{72} +55686.6 q^{73} -104157. q^{74} -14625.5 q^{75} -8322.42 q^{76} -22514.2 q^{78} -63151.4 q^{79} +47582.4 q^{80} +6561.00 q^{81} +83731.7 q^{82} -45572.4 q^{83} -51498.1 q^{85} +94145.1 q^{86} -13171.9 q^{87} +85334.9 q^{88} -15686.7 q^{89} -20045.4 q^{90} -14411.9 q^{92} +35211.8 q^{93} +43543.9 q^{94} +36501.1 q^{95} -28016.5 q^{96} -3128.49 q^{97} -46687.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} + 18 q^{3} + 65 q^{4} + 33 q^{5} - 27 q^{6} - 375 q^{8} + 162 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 + 18 * q^3 + 65 * q^4 + 33 * q^5 - 27 * q^6 - 375 * q^8 + 162 * q^9	\( 2 q - 3 q^{2} + 18 q^{3} + 65 q^{4} + 33 q^{5} - 27 q^{6} - 375 q^{8} + 162 q^{9} - 921 q^{10} - 1137 q^{11} + 585 q^{12} - 925 q^{13} + 297 q^{15} - 895 q^{16} + 324 q^{17} - 243 q^{18} - 2311 q^{19} + 3687 q^{20} + 1581 q^{22} + 1596 q^{23} - 3375 q^{24} + 395 q^{25} + 2508 q^{26} + 1458 q^{27} - 2217 q^{29} - 8289 q^{30} - 4294 q^{31} + 1017 q^{32} - 10233 q^{33} + 17940 q^{34} + 5265 q^{36} - 19109 q^{37} + 6828 q^{38} - 8325 q^{39} - 10545 q^{40} + 12858 q^{41} - 2771 q^{43} - 36579 q^{44} + 2673 q^{45} - 40740 q^{46} + 23160 q^{47} - 8055 q^{48} - 29352 q^{50} + 2916 q^{51} - 33424 q^{52} - 31653 q^{53} - 2187 q^{54} - 17889 q^{55} - 20799 q^{57} - 2277 q^{58} - 41097 q^{59} + 33183 q^{60} - 42052 q^{61} + 102057 q^{62} - 30031 q^{64} - 23106 q^{65} + 14229 q^{66} + 30763 q^{67} - 44748 q^{68} + 14364 q^{69} + 102096 q^{71} - 30375 q^{72} + 28577 q^{73} - 77784 q^{74} + 3555 q^{75} - 85192 q^{76} + 22572 q^{78} - 18464 q^{79} + 71511 q^{80} + 13122 q^{81} + 86040 q^{82} - 61179 q^{83} - 123636 q^{85} + 258510 q^{86} - 19953 q^{87} + 212565 q^{88} - 29322 q^{89} - 74601 q^{90} + 166908 q^{92} - 38646 q^{93} - 109938 q^{94} - 61662 q^{95} + 9153 q^{96} + 9791 q^{97} - 92097 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 + 18 * q^3 + 65 * q^4 + 33 * q^5 - 27 * q^6 - 375 * q^8 + 162 * q^9 - 921 * q^10 - 1137 * q^11 + 585 * q^12 - 925 * q^13 + 297 * q^15 - 895 * q^16 + 324 * q^17 - 243 * q^18 - 2311 * q^19 + 3687 * q^20 + 1581 * q^22 + 1596 * q^23 - 3375 * q^24 + 395 * q^25 + 2508 * q^26 + 1458 * q^27 - 2217 * q^29 - 8289 * q^30 - 4294 * q^31 + 1017 * q^32 - 10233 * q^33 + 17940 * q^34 + 5265 * q^36 - 19109 * q^37 + 6828 * q^38 - 8325 * q^39 - 10545 * q^40 + 12858 * q^41 - 2771 * q^43 - 36579 * q^44 + 2673 * q^45 - 40740 * q^46 + 23160 * q^47 - 8055 * q^48 - 29352 * q^50 + 2916 * q^51 - 33424 * q^52 - 31653 * q^53 - 2187 * q^54 - 17889 * q^55 - 20799 * q^57 - 2277 * q^58 - 41097 * q^59 + 33183 * q^60 - 42052 * q^61 + 102057 * q^62 - 30031 * q^64 - 23106 * q^65 + 14229 * q^66 + 30763 * q^67 - 44748 * q^68 + 14364 * q^69 + 102096 * q^71 - 30375 * q^72 + 28577 * q^73 - 77784 * q^74 + 3555 * q^75 - 85192 * q^76 + 22572 * q^78 - 18464 * q^79 + 71511 * q^80 + 13122 * q^81 + 86040 * q^82 - 61179 * q^83 - 123636 * q^85 + 258510 * q^86 - 19953 * q^87 + 212565 * q^88 - 29322 * q^89 - 74601 * q^90 + 166908 * q^92 - 38646 * q^93 - 109938 * q^94 - 61662 * q^95 + 9153 * q^96 + 9791 * q^97 - 92097 * q^99

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