LMFDB - Embedded newform 294.4.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,4,Mod(1,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("294.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	294.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$17.3465615417$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +15.8995 q^{5} +6.00000 q^{6} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +15.8995 q^{5} +6.00000 q^{6} -8.00000 q^{8} +9.00000 q^{9} -31.7990 q^{10} +57.3970 q^{11} -12.0000 q^{12} -5.69848 q^{13} -47.6985 q^{15} +16.0000 q^{16} +51.8995 q^{17} -18.0000 q^{18} -16.2010 q^{19} +63.5980 q^{20} -114.794 q^{22} -213.397 q^{23} +24.0000 q^{24} +127.794 q^{25} +11.3970 q^{26} -27.0000 q^{27} -218.191 q^{29} +95.3970 q^{30} +251.397 q^{31} -32.0000 q^{32} -172.191 q^{33} -103.799 q^{34} +36.0000 q^{36} +386.794 q^{37} +32.4020 q^{38} +17.0955 q^{39} -127.196 q^{40} +328.503 q^{41} -37.5879 q^{43} +229.588 q^{44} +143.095 q^{45} +426.794 q^{46} +254.995 q^{47} -48.0000 q^{48} -255.588 q^{50} -155.698 q^{51} -22.7939 q^{52} +211.588 q^{53} +54.0000 q^{54} +912.583 q^{55} +48.6030 q^{57} +436.382 q^{58} +412.201 q^{59} -190.794 q^{60} +836.693 q^{61} -502.794 q^{62} +64.0000 q^{64} -90.6030 q^{65} +344.382 q^{66} -165.588 q^{67} +207.598 q^{68} +640.191 q^{69} -465.015 q^{71} -72.0000 q^{72} -449.658 q^{73} -773.588 q^{74} -383.382 q^{75} -64.8040 q^{76} -34.1909 q^{78} -343.558 q^{79} +254.392 q^{80} +81.0000 q^{81} -657.005 q^{82} -1502.33 q^{83} +825.176 q^{85} +75.1758 q^{86} +654.573 q^{87} -459.176 q^{88} +341.085 q^{89} -286.191 q^{90} -853.588 q^{92} -754.191 q^{93} -509.990 q^{94} -257.588 q^{95} +96.0000 q^{96} +865.437 q^{97} +516.573 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} - 6 q^{3} + 8 q^{4} + 12 q^{5} + 12 q^{6} - 16 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q - 4 * q^2 - 6 * q^3 + 8 * q^4 + 12 * q^5 + 12 * q^6 - 16 * q^8 + 18 * q^9	\( 2 q - 4 q^{2} - 6 q^{3} + 8 q^{4} + 12 q^{5} + 12 q^{6} - 16 q^{8} + 18 q^{9} - 24 q^{10} - 4 q^{11} - 24 q^{12} + 48 q^{13} - 36 q^{15} + 32 q^{16} + 84 q^{17} - 36 q^{18} - 72 q^{19} + 48 q^{20} + 8 q^{22} - 308 q^{23} + 48 q^{24} + 18 q^{25} - 96 q^{26} - 54 q^{27} - 80 q^{29} + 72 q^{30} + 384 q^{31} - 64 q^{32} + 12 q^{33} - 168 q^{34} + 72 q^{36} + 536 q^{37} + 144 q^{38} - 144 q^{39} - 96 q^{40} + 756 q^{41} + 400 q^{43} - 16 q^{44} + 108 q^{45} + 616 q^{46} + 312 q^{47} - 96 q^{48} - 36 q^{50} - 252 q^{51} + 192 q^{52} - 52 q^{53} + 108 q^{54} + 1152 q^{55} + 216 q^{57} + 160 q^{58} + 864 q^{59} - 144 q^{60} + 1416 q^{61} - 768 q^{62} + 128 q^{64} - 300 q^{65} - 24 q^{66} + 144 q^{67} + 336 q^{68} + 924 q^{69} - 1524 q^{71} - 144 q^{72} + 744 q^{73} - 1072 q^{74} - 54 q^{75} - 288 q^{76} + 288 q^{78} + 976 q^{79} + 192 q^{80} + 162 q^{81} - 1512 q^{82} - 312 q^{83} + 700 q^{85} - 800 q^{86} + 240 q^{87} + 32 q^{88} + 108 q^{89} - 216 q^{90} - 1232 q^{92} - 1152 q^{93} - 624 q^{94} - 40 q^{95} + 192 q^{96} - 744 q^{97} - 36 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 - 6 * q^3 + 8 * q^4 + 12 * q^5 + 12 * q^6 - 16 * q^8 + 18 * q^9 - 24 * q^10 - 4 * q^11 - 24 * q^12 + 48 * q^13 - 36 * q^15 + 32 * q^16 + 84 * q^17 - 36 * q^18 - 72 * q^19 + 48 * q^20 + 8 * q^22 - 308 * q^23 + 48 * q^24 + 18 * q^25 - 96 * q^26 - 54 * q^27 - 80 * q^29 + 72 * q^30 + 384 * q^31 - 64 * q^32 + 12 * q^33 - 168 * q^34 + 72 * q^36 + 536 * q^37 + 144 * q^38 - 144 * q^39 - 96 * q^40 + 756 * q^41 + 400 * q^43 - 16 * q^44 + 108 * q^45 + 616 * q^46 + 312 * q^47 - 96 * q^48 - 36 * q^50 - 252 * q^51 + 192 * q^52 - 52 * q^53 + 108 * q^54 + 1152 * q^55 + 216 * q^57 + 160 * q^58 + 864 * q^59 - 144 * q^60 + 1416 * q^61 - 768 * q^62 + 128 * q^64 - 300 * q^65 - 24 * q^66 + 144 * q^67 + 336 * q^68 + 924 * q^69 - 1524 * q^71 - 144 * q^72 + 744 * q^73 - 1072 * q^74 - 54 * q^75 - 288 * q^76 + 288 * q^78 + 976 * q^79 + 192 * q^80 + 162 * q^81 - 1512 * q^82 - 312 * q^83 + 700 * q^85 - 800 * q^86 + 240 * q^87 + 32 * q^88 + 108 * q^89 - 216 * q^90 - 1232 * q^92 - 1152 * q^93 - 624 * q^94 - 40 * q^95 + 192 * q^96 - 744 * q^97 - 36 * 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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	15.8995	1.42209	0.711047	−	0.703144i	$-0.248221\pi$
$5$	15.8995	1.42209	0.711047	+	0.703144i	$0.248221\pi$
$6$	6.00000	0.408248
$7$	0	0
$7$	0	0
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	−31.7990	−1.00557
$11$	57.3970	1.57326	0.786629	−	0.617426i	$-0.211824\pi$
$11$	57.3970	1.57326	0.786629	+	0.617426i	$0.211824\pi$
$12$	−12.0000	−0.288675
$13$	−5.69848	−0.121575	−0.0607875	−	0.998151i	$-0.519361\pi$
$13$	−5.69848	−0.121575	−0.0607875	+	0.998151i	$0.519361\pi$
$14$	0	0
$15$	−47.6985	−0.821046
$16$	16.0000	0.250000
$17$	51.8995	0.740440	0.370220	−	0.928944i	$-0.379282\pi$
$17$	51.8995	0.740440	0.370220	+	0.928944i	$0.379282\pi$
$18$	−18.0000	−0.235702
$19$	−16.2010	−0.195619	−0.0978096	−	0.995205i	$-0.531184\pi$
$19$	−16.2010	−0.195619	−0.0978096	+	0.995205i	$0.531184\pi$
$20$	63.5980	0.711047
$21$	0	0
$22$	−114.794	−1.11246
$23$	−213.397	−1.93462	−0.967312	−	0.253590i	$-0.918389\pi$
$23$	−213.397	−1.93462	−0.967312	+	0.253590i	$0.918389\pi$
$24$	24.0000	0.204124
$25$	127.794	1.02235
$26$	11.3970	0.0859665
$27$	−27.0000	−0.192450
$28$	0	0
$29$	−218.191	−1.39714	−0.698570	−	0.715542i	$-0.746180\pi$
$29$	−218.191	−1.39714	−0.698570	+	0.715542i	$0.746180\pi$
$30$	95.3970	0.580567
$31$	251.397	1.45652	0.728262	−	0.685299i	$-0.240329\pi$
$31$	251.397	1.45652	0.728262	+	0.685299i	$0.240329\pi$
$32$	−32.0000	−0.176777
$33$	−172.191	−0.908321
$34$	−103.799	−0.523570
$35$	0	0
$36$	36.0000	0.166667
$37$	386.794	1.71861	0.859304	−	0.511464i	$-0.170897\pi$
$37$	386.794	1.71861	0.859304	+	0.511464i	$0.170897\pi$
$38$	32.4020	0.138324
$39$	17.0955	0.0701914
$40$	−127.196	−0.502786
$41$	328.503	1.25130	0.625652	−	0.780102i	$-0.284833\pi$
$41$	328.503	1.25130	0.625652	+	0.780102i	$0.284833\pi$
$42$	0	0
$43$	−37.5879	−0.133305	−0.0666523	−	0.997776i	$-0.521232\pi$
$43$	−37.5879	−0.133305	−0.0666523	+	0.997776i	$0.521232\pi$
$44$	229.588	0.786629
$45$	143.095	0.474031
$46$	426.794	1.36799
$47$	254.995	0.791379	0.395690	−	0.918384i	$-0.370506\pi$
$47$	254.995	0.791379	0.395690	+	0.918384i	$0.370506\pi$
$48$	−48.0000	−0.144338
$49$	0	0
$50$	−255.588	−0.722912
$51$	−155.698	−0.427493
$52$	−22.7939	−0.0607875
$53$	211.588	0.548374	0.274187	−	0.961676i	$-0.411591\pi$
$53$	211.588	0.548374	0.274187	+	0.961676i	$0.411591\pi$
$54$	54.0000	0.136083
$55$	912.583	2.23732
$56$	0	0
$57$	48.6030	0.112941
$58$	436.382	0.987927
$59$	412.201	0.909559	0.454780	−	0.890604i	$-0.349718\pi$
$59$	412.201	0.909559	0.454780	+	0.890604i	$0.349718\pi$
$60$	−190.794	−0.410523
$61$	836.693	1.75619	0.878095	−	0.478486i	$-0.158814\pi$
$61$	836.693	1.75619	0.878095	+	0.478486i	$0.158814\pi$
$62$	−502.794	−1.02992
$63$	0	0
$64$	64.0000	0.125000
$65$	−90.6030	−0.172891
$66$	344.382	0.642280
$67$	−165.588	−0.301937	−0.150969	−	0.988539i	$-0.548239\pi$
$67$	−165.588	−0.301937	−0.150969	+	0.988539i	$0.548239\pi$
$68$	207.598	0.370220
$69$	640.191	1.11696
$70$	0	0
$71$	−465.015	−0.777284	−0.388642	−	0.921389i	$-0.627056\pi$
$71$	−465.015	−0.777284	−0.388642	+	0.921389i	$0.627056\pi$
$72$	−72.0000	−0.117851
$73$	−449.658	−0.720938	−0.360469	−	0.932771i	$-0.617383\pi$
$73$	−449.658	−0.720938	−0.360469	+	0.932771i	$0.617383\pi$
$74$	−773.588	−1.21524
$75$	−383.382	−0.590255
$76$	−64.8040	−0.0978096
$77$	0	0
$78$	−34.1909	−0.0496328
$79$	−343.558	−0.489282	−0.244641	−	0.969614i	$-0.578670\pi$
$79$	−343.558	−0.489282	−0.244641	+	0.969614i	$0.578670\pi$
$80$	254.392	0.355524
$81$	81.0000	0.111111
$82$	−657.005	−0.884806
$83$	−1502.33	−1.98677	−0.993387	−	0.114812i	$-0.963373\pi$
$83$	−1502.33	−1.98677	−0.993387	+	0.114812i	$0.963373\pi$
$84$	0	0
$85$	825.176	1.05298
$86$	75.1758	0.0942606
$87$	654.573	0.806639
$88$	−459.176	−0.556231
$89$	341.085	0.406236	0.203118	−	0.979154i	$-0.434893\pi$
$89$	341.085	0.406236	0.203118	+	0.979154i	$0.434893\pi$
$90$	−286.191	−0.335191
$91$	0	0
$92$	−853.588	−0.967312
$93$	−754.191	−0.840924
$94$	−509.990	−0.559590
$95$	−257.588	−0.278189
$96$	96.0000	0.102062
$97$	865.437	0.905895	0.452947	−	0.891537i	$-0.350373\pi$
$97$	865.437	0.905895	0.452947	+	0.891537i	$0.350373\pi$
$98$	0	0
$99$	516.573	0.524419
$100$	511.176	0.511176
$101$	243.256	0.239652	0.119826	−	0.992795i	$-0.461766\pi$
$101$	243.256	0.239652	0.119826	+	0.992795i	$0.461766\pi$
$102$	311.397	0.302283
$103$	953.346	0.912000	0.456000	−	0.889980i	$-0.349282\pi$
$103$	953.346	0.912000	0.456000	+	0.889980i	$0.349282\pi$
$104$	45.5879	0.0429833
$105$	0	0
$106$	−423.176	−0.387759
$107$	−1344.95	−1.21516	−0.607578	−	0.794260i	$-0.707859\pi$
$107$	−1344.95	−1.21516	−0.607578	+	0.794260i	$0.707859\pi$
$108$	−108.000	−0.0962250
$109$	1734.35	1.52404	0.762022	−	0.647551i	$-0.224207\pi$
$109$	1734.35	1.52404	0.762022	+	0.647551i	$0.224207\pi$
$110$	−1825.17	−1.58202
$111$	−1160.38	−0.992239
$112$	0	0
$113$	1441.18	1.19977	0.599887	−	0.800085i	$-0.295212\pi$
$113$	1441.18	1.19977	0.599887	+	0.800085i	$0.295212\pi$
$114$	−97.2061	−0.0798612
$115$	−3392.90	−2.75122
$116$	−872.764	−0.698570
$117$	−51.2864	−0.0405250
$118$	−824.402	−0.643156
$119$	0	0
$120$	381.588	0.290284
$121$	1963.41	1.47514
$122$	−1673.39	−1.24181
$123$	−985.508	−0.722441
$124$	1005.59	0.728262
$125$	44.4222	0.0317860
$126$	0	0
$127$	1184.70	0.827759	0.413880	−	0.910332i	$-0.364173\pi$
$127$	1184.70	0.827759	0.413880	+	0.910332i	$0.364173\pi$
$128$	−128.000	−0.0883883
$129$	112.764	0.0769634
$130$	181.206	0.122252
$131$	−297.588	−0.198476	−0.0992381	−	0.995064i	$-0.531641\pi$
$131$	−297.588	−0.198476	−0.0992381	+	0.995064i	$0.531641\pi$
$132$	−688.764	−0.454160
$133$	0	0
$134$	331.176	0.213502
$135$	−429.286	−0.273682
$136$	−415.196	−0.261785
$137$	620.985	0.387258	0.193629	−	0.981075i	$-0.437974\pi$
$137$	620.985	0.387258	0.193629	+	0.981075i	$0.437974\pi$
$138$	−1280.38	−0.789807
$139$	898.754	0.548426	0.274213	−	0.961669i	$-0.411583\pi$
$139$	898.754	0.548426	0.274213	+	0.961669i	$0.411583\pi$
$140$	0	0
$141$	−764.985	−0.456903
$142$	930.030	0.549623
$143$	−327.076	−0.191269
$144$	144.000	0.0833333
$145$	−3469.13	−1.98686
$146$	899.316	0.509780
$147$	0	0
$148$	1547.18	0.859304
$149$	−3054.70	−1.67954	−0.839769	−	0.542945i	$-0.817309\pi$
$149$	−3054.70	−1.67954	−0.839769	+	0.542945i	$0.817309\pi$
$150$	766.764	0.417373
$151$	−65.1455	−0.0351090	−0.0175545	−	0.999846i	$-0.505588\pi$
$151$	−65.1455	−0.0351090	−0.0175545	+	0.999846i	$0.505588\pi$
$152$	129.608	0.0691619
$153$	467.095	0.246813
$154$	0	0
$155$	3997.08	2.07131
$156$	68.3818	0.0350957
$157$	−1542.22	−0.783966	−0.391983	−	0.919973i	$-0.628211\pi$
$157$	−1542.22	−0.783966	−0.391983	+	0.919973i	$0.628211\pi$
$158$	687.115	0.345974
$159$	−634.764	−0.316604
$160$	−508.784	−0.251393
$161$	0	0
$162$	−162.000	−0.0785674
$163$	−2514.73	−1.20840	−0.604200	−	0.796833i	$-0.706507\pi$
$163$	−2514.73	−1.20840	−0.604200	+	0.796833i	$0.706507\pi$
$164$	1314.01	0.625652
$165$	−2737.75	−1.29172
$166$	3004.66	1.40486
$167$	−528.643	−0.244956	−0.122478	−	0.992471i	$-0.539084\pi$
$167$	−528.643	−0.244956	−0.122478	+	0.992471i	$0.539084\pi$
$168$	0	0
$169$	−2164.53	−0.985220
$170$	−1650.35	−0.744566
$171$	−145.809	−0.0652064
$172$	−150.352	−0.0666523
$173$	−96.8439	−0.0425602	−0.0212801	−	0.999774i	$-0.506774\pi$
$173$	−96.8439	−0.0425602	−0.0212801	+	0.999774i	$0.506774\pi$
$174$	−1309.15	−0.570380
$175$	0	0
$176$	918.352	0.393314
$177$	−1236.60	−0.525134
$178$	−682.171	−0.287252
$179$	−534.542	−0.223204	−0.111602	−	0.993753i	$-0.535598\pi$
$179$	−534.542	−0.223204	−0.111602	+	0.993753i	$0.535598\pi$
$180$	572.382	0.237016
$181$	−2087.00	−0.857049	−0.428524	−	0.903530i	$-0.640966\pi$
$181$	−2087.00	−0.857049	−0.428524	+	0.903530i	$0.640966\pi$
$182$	0	0
$183$	−2510.08	−1.01394
$184$	1707.18	0.683993
$185$	6149.83	2.44402
$186$	1508.38	0.594623
$187$	2978.87	1.16490
$188$	1019.98	0.395690
$189$	0	0
$190$	515.176	0.196709
$191$	3387.69	1.28337	0.641687	−	0.766966i	$-0.278235\pi$
$191$	3387.69	1.28337	0.641687	+	0.766966i	$0.278235\pi$
$192$	−192.000	−0.0721688
$193$	−1908.35	−0.711742	−0.355871	−	0.934535i	$-0.615816\pi$
$193$	−1908.35	−0.711742	−0.355871	+	0.934535i	$0.615816\pi$
$194$	−1730.87	−0.640564
$195$	271.809	0.0998187
$196$	0	0
$197$	−2061.88	−0.745699	−0.372850	−	0.927892i	$-0.621619\pi$
$197$	−2061.88	−0.745699	−0.372850	+	0.927892i	$0.621619\pi$
$198$	−1033.15	−0.370820
$199$	−3171.50	−1.12976	−0.564878	−	0.825174i	$-0.691077\pi$
$199$	−3171.50	−1.12976	−0.564878	+	0.825174i	$0.691077\pi$
$200$	−1022.35	−0.361456
$201$	496.764	0.174323
$202$	−486.512	−0.169460
$203$	0	0
$204$	−622.794	−0.213747
$205$	5223.02	1.77947
$206$	−1906.69	−0.644882
$207$	−1920.57	−0.644875
$208$	−91.1758	−0.0303938
$209$	−929.889	−0.307760
$210$	0	0
$211$	1349.97	0.440454	0.220227	−	0.975449i	$-0.429320\pi$
$211$	1349.97	0.440454	0.220227	+	0.975449i	$0.429320\pi$
$212$	846.352	0.274187
$213$	1395.05	0.448765
$214$	2689.91	0.859245
$215$	−597.628	−0.189572
$216$	216.000	0.0680414
$217$	0	0
$218$	−3468.70	−1.07766
$219$	1348.97	0.416234
$220$	3650.33	1.11866
$221$	−295.748	−0.0900190
$222$	2320.76	0.701619
$223$	1361.85	0.408951	0.204476	−	0.978872i	$-0.434451\pi$
$223$	1361.85	0.408951	0.204476	+	0.978872i	$0.434451\pi$
$224$	0	0
$225$	1150.15	0.340784
$226$	−2882.35	−0.848368
$227$	−1861.81	−0.544373	−0.272186	−	0.962245i	$-0.587747\pi$
$227$	−1861.81	−0.544373	−0.272186	+	0.962245i	$0.587747\pi$
$228$	194.412	0.0564704
$229$	5358.78	1.54637	0.773184	−	0.634181i	$-0.218663\pi$
$229$	5358.78	1.54637	0.773184	+	0.634181i	$0.218663\pi$
$230$	6785.81	1.94540
$231$	0	0
$232$	1745.53	0.493963
$233$	5441.12	1.52987	0.764935	−	0.644107i	$-0.222771\pi$
$233$	5441.12	1.52987	0.764935	+	0.644107i	$0.222771\pi$
$234$	102.573	0.0286555
$235$	4054.29	1.12542
$236$	1648.80	0.454780
$237$	1030.67	0.282487
$238$	0	0
$239$	−1157.28	−0.313213	−0.156607	−	0.987661i	$-0.550055\pi$
$239$	−1157.28	−0.313213	−0.156607	+	0.987661i	$0.550055\pi$
$240$	−763.176	−0.205262
$241$	3969.38	1.06095	0.530477	−	0.847699i	$-0.322013\pi$
$241$	3969.38	1.06095	0.530477	+	0.847699i	$0.322013\pi$
$242$	−3926.82	−1.04308
$243$	−243.000	−0.0641500
$244$	3346.77	0.878095
$245$	0	0
$246$	1971.02	0.510843
$247$	92.3212	0.0237824
$248$	−2011.18	−0.514959
$249$	4506.99	1.14706
$250$	−88.8444	−0.0224761
$251$	−5978.75	−1.50349	−0.751744	−	0.659455i	$-0.770787\pi$
$251$	−5978.75	−1.50349	−0.751744	+	0.659455i	$0.770787\pi$
$252$	0	0
$253$	−12248.3	−3.04366
$254$	−2369.41	−0.585314
$255$	−2475.53	−0.607935
$256$	256.000	0.0625000
$257$	−4650.15	−1.12867	−0.564335	−	0.825546i	$-0.690868\pi$
$257$	−4650.15	−1.12867	−0.564335	+	0.825546i	$0.690868\pi$
$258$	−225.527	−0.0544214
$259$	0	0
$260$	−362.412	−0.0864456
$261$	−1963.72	−0.465713
$262$	595.176	0.140344
$263$	3695.37	0.866411	0.433205	−	0.901295i	$-0.357382\pi$
$263$	3695.37	0.866411	0.433205	+	0.901295i	$0.357382\pi$
$264$	1377.53	0.321140
$265$	3364.14	0.779840
$266$	0	0
$267$	−1023.26	−0.234540
$268$	−662.352	−0.150969
$269$	7157.69	1.62235	0.811175	−	0.584804i	$-0.198829\pi$
$269$	7157.69	1.62235	0.811175	+	0.584804i	$0.198829\pi$
$270$	858.573	0.193522
$271$	−4038.37	−0.905216	−0.452608	−	0.891710i	$-0.649506\pi$
$271$	−4038.37	−0.905216	−0.452608	+	0.891710i	$0.649506\pi$
$272$	830.392	0.185110
$273$	0	0
$274$	−1241.97	−0.273833
$275$	7334.98	1.60842
$276$	2560.76	0.558478
$277$	−2754.82	−0.597550	−0.298775	−	0.954324i	$-0.596578\pi$
$277$	−2754.82	−0.597550	−0.298775	+	0.954324i	$0.596578\pi$
$278$	−1797.51	−0.387796
$279$	2262.57	0.485508
$280$	0	0
$281$	−772.742	−0.164050	−0.0820248	−	0.996630i	$-0.526139\pi$
$281$	−772.742	−0.164050	−0.0820248	+	0.996630i	$0.526139\pi$
$282$	1529.97	0.323079
$283$	6745.49	1.41688	0.708441	−	0.705770i	$-0.249399\pi$
$283$	6745.49	1.41688	0.708441	+	0.705770i	$0.249399\pi$
$284$	−1860.06	−0.388642
$285$	772.764	0.160613
$286$	654.152	0.135248
$287$	0	0
$288$	−288.000	−0.0589256
$289$	−2219.44	−0.451749
$290$	6938.25	1.40492
$291$	−2596.31	−0.523019
$292$	−1798.63	−0.360469
$293$	−1922.69	−0.383362	−0.191681	−	0.981457i	$-0.561394\pi$
$293$	−1922.69	−0.383362	−0.191681	+	0.981457i	$0.561394\pi$
$294$	0	0
$295$	6553.79	1.29348
$296$	−3094.35	−0.607620
$297$	−1549.72	−0.302774
$298$	6109.41	1.18761
$299$	1216.04	0.235202
$300$	−1533.53	−0.295127
$301$	0	0
$302$	130.291	0.0248258
$303$	−729.768	−0.138363
$304$	−259.216	−0.0489048
$305$	13303.0	2.49747
$306$	−934.191	−0.174523
$307$	−2016.68	−0.374913	−0.187456	−	0.982273i	$-0.560024\pi$
$307$	−2016.68	−0.374913	−0.187456	+	0.982273i	$0.560024\pi$
$308$	0	0
$309$	−2860.04	−0.526544
$310$	−7994.17	−1.46464
$311$	−7149.99	−1.30366	−0.651831	−	0.758365i	$-0.725999\pi$
$311$	−7149.99	−1.30366	−0.651831	+	0.758365i	$0.725999\pi$
$312$	−136.764	−0.0248164
$313$	−8596.49	−1.55240	−0.776202	−	0.630484i	$-0.782856\pi$
$313$	−8596.49	−1.55240	−0.776202	+	0.630484i	$0.782856\pi$
$314$	3084.44	0.554347
$315$	0	0
$316$	−1374.23	−0.244641
$317$	−2853.24	−0.505532	−0.252766	−	0.967527i	$-0.581340\pi$
$317$	−2853.24	−0.505532	−0.252766	+	0.967527i	$0.581340\pi$
$318$	1269.53	0.223873
$319$	−12523.5	−2.19806
$320$	1017.57	0.177762
$321$	4034.86	0.701570
$322$	0	0
$323$	−840.824	−0.144844
$324$	324.000	0.0555556
$325$	−728.232	−0.124292
$326$	5029.47	0.854467
$327$	−5203.05	−0.879907
$328$	−2628.02	−0.442403
$329$	0	0
$330$	5475.50	0.913382
$331$	1619.12	0.268866	0.134433	−	0.990923i	$-0.457079\pi$
$331$	1619.12	0.268866	0.134433	+	0.990923i	$0.457079\pi$
$332$	−6009.33	−0.993387
$333$	3481.15	0.572870
$334$	1057.29	0.173210
$335$	−2632.76	−0.429383
$336$	0	0
$337$	−3278.67	−0.529972	−0.264986	−	0.964252i	$-0.585367\pi$
$337$	−3278.67	−0.529972	−0.264986	+	0.964252i	$0.585367\pi$
$338$	4329.05	0.696655
$339$	−4323.53	−0.692690
$340$	3300.70	0.526488
$341$	14429.4	2.29149
$342$	291.618	0.0461079
$343$	0	0
$344$	300.703	0.0471303
$345$	10178.7	1.58842
$346$	193.688	0.0300946
$347$	−2850.30	−0.440957	−0.220479	−	0.975392i	$-0.570762\pi$
$347$	−2850.30	−0.440957	−0.220479	+	0.975392i	$0.570762\pi$
$348$	2618.29	0.403319
$349$	4725.32	0.724758	0.362379	−	0.932031i	$-0.381965\pi$
$349$	4725.32	0.724758	0.362379	+	0.932031i	$0.381965\pi$
$350$	0	0
$351$	153.859	0.0233971
$352$	−1836.70	−0.278115
$353$	−6727.44	−1.01435	−0.507175	−	0.861843i	$-0.669310\pi$
$353$	−6727.44	−1.01435	−0.507175	+	0.861843i	$0.669310\pi$
$354$	2473.21	0.371326
$355$	−7393.51	−1.10537
$356$	1364.34	0.203118
$357$	0	0
$358$	1069.08	0.157829
$359$	−7331.89	−1.07789	−0.538945	−	0.842341i	$-0.681177\pi$
$359$	−7331.89	−1.07789	−0.538945	+	0.842341i	$0.681177\pi$
$360$	−1144.76	−0.167595
$361$	−6596.53	−0.961733
$362$	4174.01	0.606025
$363$	−5890.24	−0.851673
$364$	0	0
$365$	−7149.34	−1.02524
$366$	5020.16	0.716962
$367$	−2774.43	−0.394616	−0.197308	−	0.980342i	$-0.563220\pi$
$367$	−2774.43	−0.394616	−0.197308	+	0.980342i	$0.563220\pi$
$368$	−3414.35	−0.483656
$369$	2956.52	0.417101
$370$	−12299.7	−1.72819
$371$	0	0
$372$	−3016.76	−0.420462
$373$	2527.35	0.350834	0.175417	−	0.984494i	$-0.443873\pi$
$373$	2527.35	0.350834	0.175417	+	0.984494i	$0.443873\pi$
$374$	−5957.75	−0.823711
$375$	−133.267	−0.0183516
$376$	−2039.96	−0.279795
$377$	1243.36	0.169857
$378$	0	0
$379$	3116.40	0.422371	0.211186	−	0.977446i	$-0.432268\pi$
$379$	3116.40	0.422371	0.211186	+	0.977446i	$0.432268\pi$
$380$	−1030.35	−0.139095
$381$	−3554.11	−0.477907
$382$	−6775.38	−0.907483
$383$	−1518.07	−0.202532	−0.101266	−	0.994859i	$-0.532289\pi$
$383$	−1518.07	−0.202532	−0.101266	+	0.994859i	$0.532289\pi$
$384$	384.000	0.0510310
$385$	0	0
$386$	3816.70	0.503277
$387$	−338.291	−0.0444349
$388$	3461.75	0.452947
$389$	−3246.77	−0.423182	−0.211591	−	0.977358i	$-0.567865\pi$
$389$	−3246.77	−0.423182	−0.211591	+	0.977358i	$0.567865\pi$
$390$	−543.618	−0.0705825
$391$	−11075.2	−1.43247
$392$	0	0
$393$	892.764	0.114590
$394$	4123.76	0.527289
$395$	−5462.39	−0.695804
$396$	2066.29	0.262210
$397$	1830.62	0.231427	0.115713	−	0.993283i	$-0.463085\pi$
$397$	1830.62	0.231427	0.115713	+	0.993283i	$0.463085\pi$
$398$	6342.99	0.798858
$399$	0	0
$400$	2044.70	0.255588
$401$	−3385.81	−0.421644	−0.210822	−	0.977524i	$-0.567614\pi$
$401$	−3385.81	−0.421644	−0.210822	+	0.977524i	$0.567614\pi$
$402$	−993.527	−0.123265
$403$	−1432.58	−0.177077
$404$	973.024	0.119826
$405$	1287.86	0.158010
$406$	0	0
$407$	22200.8	2.70382
$408$	1245.59	0.151142
$409$	9253.17	1.11868	0.559340	−	0.828938i	$-0.311055\pi$
$409$	9253.17	1.11868	0.559340	+	0.828938i	$0.311055\pi$
$410$	−10446.0	−1.25828
$411$	−1862.95	−0.223583
$412$	3813.39	0.456000
$413$	0	0
$414$	3841.15	0.455995
$415$	−23886.3	−2.82538
$416$	182.352	0.0214916
$417$	−2696.26	−0.316634
$418$	1859.78	0.217619
$419$	3547.52	0.413622	0.206811	−	0.978381i	$-0.433692\pi$
$419$	3547.52	0.413622	0.206811	+	0.978381i	$0.433692\pi$
$420$	0	0
$421$	7848.87	0.908624	0.454312	−	0.890843i	$-0.349885\pi$
$421$	7848.87	0.908624	0.454312	+	0.890843i	$0.349885\pi$
$422$	−2699.94	−0.311448
$423$	2294.95	0.263793
$424$	−1692.70	−0.193880
$425$	6632.44	0.756990
$426$	−2790.09	−0.317325
$427$	0	0
$428$	−5379.82	−0.607578
$429$	981.227	0.110429
$430$	1195.26	0.134047
$431$	−4447.32	−0.497030	−0.248515	−	0.968628i	$-0.579943\pi$
$431$	−4447.32	−0.497030	−0.248515	+	0.968628i	$0.579943\pi$
$432$	−432.000	−0.0481125
$433$	−6994.82	−0.776327	−0.388164	−	0.921590i	$-0.626890\pi$
$433$	−6994.82	−0.776327	−0.388164	+	0.921590i	$0.626890\pi$
$434$	0	0
$435$	10407.4	1.14712
$436$	6937.41	0.762022
$437$	3457.25	0.378450
$438$	−2697.95	−0.294322
$439$	636.182	0.0691647	0.0345823	−	0.999402i	$-0.488990\pi$
$439$	636.182	0.0691647	0.0345823	+	0.999402i	$0.488990\pi$
$440$	−7300.66	−0.791012
$441$	0	0
$442$	591.497	0.0636530
$443$	−4474.24	−0.479859	−0.239929	−	0.970790i	$-0.577124\pi$
$443$	−4474.24	−0.479859	−0.239929	+	0.970790i	$0.577124\pi$
$444$	−4641.53	−0.496120
$445$	5423.08	0.577705
$446$	−2723.70	−0.289172
$447$	9164.11	0.969681
$448$	0	0
$449$	−2389.42	−0.251144	−0.125572	−	0.992085i	$-0.540077\pi$
$449$	−2389.42	−0.251144	−0.125572	+	0.992085i	$0.540077\pi$
$450$	−2300.29	−0.240971
$451$	18855.0	1.96862
$452$	5764.70	0.599887
$453$	195.436	0.0202702
$454$	3723.62	0.384930
$455$	0	0
$456$	−388.824	−0.0399306
$457$	−4438.34	−0.454304	−0.227152	−	0.973859i	$-0.572941\pi$
$457$	−4438.34	−0.454304	−0.227152	+	0.973859i	$0.572941\pi$
$458$	−10717.6	−1.09345
$459$	−1401.29	−0.142498
$460$	−13571.6	−1.37561
$461$	−14079.8	−1.42248	−0.711240	−	0.702949i	$-0.751866\pi$
$461$	−14079.8	−1.42248	−0.711240	+	0.702949i	$0.751866\pi$
$462$	0	0
$463$	4687.50	0.470511	0.235255	−	0.971934i	$-0.424407\pi$
$463$	4687.50	0.470511	0.235255	+	0.971934i	$0.424407\pi$
$464$	−3491.05	−0.349285
$465$	−11991.3	−1.19587
$466$	−10882.2	−1.08178
$467$	8447.26	0.837029	0.418514	−	0.908210i	$-0.362551\pi$
$467$	8447.26	0.837029	0.418514	+	0.908210i	$0.362551\pi$
$468$	−205.145	−0.0202625
$469$	0	0
$470$	−8108.58	−0.795789
$471$	4626.66	0.452623
$472$	−3297.61	−0.321578
$473$	−2157.43	−0.209723
$474$	−2061.35	−0.199748
$475$	−2070.39	−0.199992
$476$	0	0
$477$	1904.29	0.182791
$478$	2314.55	0.221475
$479$	−4369.41	−0.416792	−0.208396	−	0.978045i	$-0.566824\pi$
$479$	−4369.41	−0.416792	−0.208396	+	0.978045i	$0.566824\pi$
$480$	1526.35	0.145142
$481$	−2204.14	−0.208940
$482$	−7938.75	−0.750208
$483$	0	0
$484$	7853.65	0.737570
$485$	13760.0	1.28827
$486$	486.000	0.0453609
$487$	−14477.7	−1.34712	−0.673561	−	0.739132i	$-0.735236\pi$
$487$	−14477.7	−1.34712	−0.673561	+	0.739132i	$0.735236\pi$
$488$	−6693.55	−0.620907
$489$	7544.20	0.697670
$490$	0	0
$491$	9306.12	0.855355	0.427677	−	0.903931i	$-0.359332\pi$
$491$	9306.12	0.855355	0.427677	+	0.903931i	$0.359332\pi$
$492$	−3942.03	−0.361220
$493$	−11324.0	−1.03450
$494$	−184.642	−0.0168167
$495$	8213.25	0.745774
$496$	4022.35	0.364131
$497$	0	0
$498$	−9013.99	−0.811097
$499$	−12237.5	−1.09785	−0.548926	−	0.835871i	$-0.684963\pi$
$499$	−12237.5	−1.09785	−0.548926	+	0.835871i	$0.684963\pi$
$500$	177.689	0.0158930
$501$	1585.93	0.141425
$502$	11957.5	1.06313
$503$	5524.30	0.489694	0.244847	−	0.969562i	$-0.421262\pi$
$503$	5524.30	0.489694	0.244847	+	0.969562i	$0.421262\pi$
$504$	0	0
$505$	3867.65	0.340808
$506$	24496.7	2.15219
$507$	6493.58	0.568817
$508$	4738.81	0.413880
$509$	−10079.6	−0.877743	−0.438871	−	0.898550i	$-0.644622\pi$
$509$	−10079.6	−0.877743	−0.438871	+	0.898550i	$0.644622\pi$
$510$	4951.05	0.429875
$511$	0	0
$512$	−512.000	−0.0441942
$513$	437.427	0.0376470
$514$	9300.30	0.798091
$515$	15157.7	1.29695
$516$	451.055	0.0384817
$517$	14635.9	1.24504
$518$	0	0
$519$	290.532	0.0245721
$520$	724.824	0.0611262
$521$	5706.61	0.479868	0.239934	−	0.970789i	$-0.422874\pi$
$521$	5706.61	0.479868	0.239934	+	0.970789i	$0.422874\pi$
$522$	3927.44	0.329309
$523$	−10657.3	−0.891032	−0.445516	−	0.895274i	$-0.646980\pi$
$523$	−10657.3	−0.891032	−0.445516	+	0.895274i	$0.646980\pi$
$524$	−1190.35	−0.0992381
$525$	0	0
$526$	−7390.73	−0.612645
$527$	13047.4	1.07847
$528$	−2755.05	−0.227080
$529$	33371.3	2.74277
$530$	−6728.28	−0.551430
$531$	3709.81	0.303186
$532$	0	0
$533$	−1871.97	−0.152127
$534$	2046.51	0.165845
$535$	−21384.1	−1.72807
$536$	1324.70	0.106751
$537$	1603.63	0.128867
$538$	−14315.4	−1.14717
$539$	0	0
$540$	−1717.15	−0.136841
$541$	−4010.48	−0.318714	−0.159357	−	0.987221i	$-0.550942\pi$
$541$	−4010.48	−0.318714	−0.159357	+	0.987221i	$0.550942\pi$
$542$	8076.74	0.640084
$543$	6261.01	0.494817
$544$	−1660.78	−0.130892
$545$	27575.3	2.16733
$546$	0	0
$547$	−17619.8	−1.37728	−0.688638	−	0.725105i	$-0.741791\pi$
$547$	−17619.8	−1.37728	−0.688638	+	0.725105i	$0.741791\pi$
$548$	2483.94	0.193629
$549$	7530.24	0.585397
$550$	−14670.0	−1.13733
$551$	3534.91	0.273307
$552$	−5121.53	−0.394903
$553$	0	0
$554$	5509.65	0.422532
$555$	−18449.5	−1.41106
$556$	3595.01	0.274213
$557$	−10337.7	−0.786395	−0.393198	−	0.919454i	$-0.628631\pi$
$557$	−10337.7	−0.786395	−0.393198	+	0.919454i	$0.628631\pi$
$558$	−4525.15	−0.343306
$559$	214.194	0.0162065
$560$	0	0
$561$	−8936.62	−0.672557
$562$	1545.48	0.116001
$563$	−24023.7	−1.79836	−0.899180	−	0.437580i	$-0.855836\pi$
$563$	−24023.7	−1.79836	−0.899180	+	0.437580i	$0.855836\pi$
$564$	−3059.94	−0.228452
$565$	22914.0	1.70619
$566$	−13491.0	−1.00189
$567$	0	0
$568$	3720.12	0.274811
$569$	−13179.2	−0.971001	−0.485501	−	0.874236i	$-0.661363\pi$
$569$	−13179.2	−0.971001	−0.485501	+	0.874236i	$0.661363\pi$
$570$	−1545.53	−0.113570
$571$	7776.26	0.569924	0.284962	−	0.958539i	$-0.408019\pi$
$571$	7776.26	0.569924	0.284962	+	0.958539i	$0.408019\pi$
$572$	−1308.30	−0.0956344
$573$	−10163.1	−0.740956
$574$	0	0
$575$	−27270.8	−1.97787
$576$	576.000	0.0416667
$577$	20167.0	1.45505	0.727525	−	0.686081i	$-0.240670\pi$
$577$	20167.0	1.45505	0.727525	+	0.686081i	$0.240670\pi$
$578$	4438.88	0.319435
$579$	5725.05	0.410924
$580$	−13876.5	−0.993432
$581$	0	0
$582$	5192.62	0.369830
$583$	12144.5	0.862734
$584$	3597.26	0.254890
$585$	−815.427	−0.0576304
$586$	3845.39	0.271078
$587$	−8365.08	−0.588184	−0.294092	−	0.955777i	$-0.595017\pi$
$587$	−8365.08	−0.588184	−0.294092	+	0.955777i	$0.595017\pi$
$588$	0	0
$589$	−4072.88	−0.284924
$590$	−13107.6	−0.914628
$591$	6185.64	0.430530
$592$	6188.70	0.429652
$593$	−27621.9	−1.91281	−0.956403	−	0.292050i	$-0.905663\pi$
$593$	−27621.9	−1.91281	−0.956403	+	0.292050i	$0.905663\pi$
$594$	3099.44	0.214093
$595$	0	0
$596$	−12218.8	−0.839769
$597$	9514.49	0.652265
$598$	−2432.08	−0.166313
$599$	538.318	0.0367197	0.0183598	−	0.999831i	$-0.494156\pi$
$599$	538.318	0.0367197	0.0183598	+	0.999831i	$0.494156\pi$
$600$	3067.05	0.208687
$601$	6958.64	0.472294	0.236147	−	0.971717i	$-0.424115\pi$
$601$	6958.64	0.472294	0.236147	+	0.971717i	$0.424115\pi$
$602$	0	0
$603$	−1490.29	−0.100646
$604$	−260.582	−0.0175545
$605$	31217.3	2.09779
$606$	1459.54	0.0978376
$607$	−17297.6	−1.15665	−0.578326	−	0.815806i	$-0.696294\pi$
$607$	−17297.6	−1.15665	−0.578326	+	0.815806i	$0.696294\pi$
$608$	518.432	0.0345809
$609$	0	0
$610$	−26606.0	−1.76598
$611$	−1453.08	−0.0962120
$612$	1868.38	0.123407
$613$	−839.158	−0.0552908	−0.0276454	−	0.999618i	$-0.508801\pi$
$613$	−839.158	−0.0552908	−0.0276454	+	0.999618i	$0.508801\pi$
$614$	4033.37	0.265103
$615$	−15669.1	−1.02738
$616$	0	0
$617$	−16040.0	−1.04659	−0.523295	−	0.852152i	$-0.675297\pi$
$617$	−16040.0	−1.04659	−0.523295	+	0.852152i	$0.675297\pi$
$618$	5720.08	0.372323
$619$	−5429.28	−0.352538	−0.176269	−	0.984342i	$-0.556403\pi$
$619$	−5429.28	−0.352538	−0.176269	+	0.984342i	$0.556403\pi$
$620$	15988.3	1.03566
$621$	5761.72	0.372318
$622$	14300.0	0.921828
$623$	0	0
$624$	273.527	0.0175478
$625$	−15268.0	−0.977149
$626$	17193.0	1.09772
$627$	2789.67	0.177685
$628$	−6168.88	−0.391983
$629$	20074.4	1.27253
$630$	0	0
$631$	−1807.86	−0.114057	−0.0570284	−	0.998373i	$-0.518163\pi$
$631$	−1807.86	−0.114057	−0.0570284	+	0.998373i	$0.518163\pi$
$632$	2748.46	0.172987
$633$	−4049.91	−0.254296
$634$	5706.47	0.357465
$635$	18836.2	1.17715
$636$	−2539.05	−0.158302
$637$	0	0
$638$	25047.0	1.55426
$639$	−4185.14	−0.259095
$640$	−2035.14	−0.125697
$641$	−5904.56	−0.363832	−0.181916	−	0.983314i	$-0.558230\pi$
$641$	−5904.56	−0.363832	−0.181916	+	0.983314i	$0.558230\pi$
$642$	−8069.73	−0.496085
$643$	8092.42	0.496320	0.248160	−	0.968719i	$-0.420174\pi$
$643$	8092.42	0.496320	0.248160	+	0.968719i	$0.420174\pi$
$644$	0	0
$645$	1792.88	0.109449
$646$	1681.65	0.102420
$647$	20192.7	1.22698	0.613490	−	0.789702i	$-0.289765\pi$
$647$	20192.7	1.22698	0.613490	+	0.789702i	$0.289765\pi$
$648$	−648.000	−0.0392837
$649$	23659.1	1.43097
$650$	1456.46	0.0878880
$651$	0	0
$652$	−10058.9	−0.604200
$653$	−21180.8	−1.26933	−0.634664	−	0.772789i	$-0.718861\pi$
$653$	−21180.8	−1.26933	−0.634664	+	0.772789i	$0.718861\pi$
$654$	10406.1	0.622188
$655$	−4731.50	−0.282252
$656$	5256.04	0.312826
$657$	−4046.92	−0.240313
$658$	0	0
$659$	28411.3	1.67944	0.839718	−	0.543023i	$-0.182720\pi$
$659$	28411.3	1.67944	0.839718	+	0.543023i	$0.182720\pi$
$660$	−10951.0	−0.645859
$661$	16704.9	0.982975	0.491488	−	0.870885i	$-0.336453\pi$
$661$	16704.9	0.982975	0.491488	+	0.870885i	$0.336453\pi$
$662$	−3238.23	−0.190117
$663$	887.245	0.0519725
$664$	12018.7	0.702431
$665$	0	0
$666$	−6962.29	−0.405080
$667$	46561.3	2.70294
$668$	−2114.57	−0.122478
$669$	−4085.55	−0.236108
$670$	5265.53	0.303620
$671$	48023.7	2.76294
$672$	0	0
$673$	−9047.09	−0.518187	−0.259093	−	0.965852i	$-0.583424\pi$
$673$	−9047.09	−0.518187	−0.259093	+	0.965852i	$0.583424\pi$
$674$	6557.35	0.374747
$675$	−3450.44	−0.196752
$676$	−8658.11	−0.492610
$677$	−7844.26	−0.445316	−0.222658	−	0.974897i	$-0.571473\pi$
$677$	−7844.26	−0.445316	−0.222658	+	0.974897i	$0.571473\pi$
$678$	8647.05	0.489806
$679$	0	0
$680$	−6601.41	−0.372283
$681$	5585.43	0.314294
$682$	−28858.8	−1.62033
$683$	25766.1	1.44350	0.721751	−	0.692153i	$-0.243338\pi$
$683$	25766.1	1.44350	0.721751	+	0.692153i	$0.243338\pi$
$684$	−583.236	−0.0326032
$685$	9873.35	0.550717
$686$	0	0
$687$	−16076.3	−0.892796
$688$	−601.406	−0.0333261
$689$	−1205.73	−0.0666686
$690$	−20357.4	−1.12318
$691$	24674.1	1.35839	0.679195	−	0.733958i	$-0.262329\pi$
$691$	24674.1	1.35839	0.679195	+	0.733958i	$0.262329\pi$
$692$	−387.376	−0.0212801
$693$	0	0
$694$	5700.60	0.311804
$695$	14289.7	0.779914
$696$	−5236.58	−0.285190
$697$	17049.1	0.926515
$698$	−9450.63	−0.512481
$699$	−16323.4	−0.883271
$700$	0	0
$701$	29377.9	1.58286	0.791431	−	0.611258i	$-0.209336\pi$
$701$	29377.9	1.58286	0.791431	+	0.611258i	$0.209336\pi$
$702$	−307.718	−0.0165443
$703$	−6266.45	−0.336193
$704$	3673.41	0.196657
$705$	−12162.9	−0.649759
$706$	13454.9	0.717253
$707$	0	0
$708$	−4946.41	−0.262567
$709$	30594.3	1.62058	0.810291	−	0.586028i	$-0.199309\pi$
$709$	30594.3	1.62058	0.810291	+	0.586028i	$0.199309\pi$
$710$	14787.0	0.781615
$711$	−3092.02	−0.163094
$712$	−2728.68	−0.143626
$713$	−53647.4	−2.81782
$714$	0	0
$715$	−5200.34	−0.272002
$716$	−2138.17	−0.111602
$717$	3471.83	0.180834
$718$	14663.8	0.762183
$719$	1946.94	0.100985	0.0504927	−	0.998724i	$-0.483921\pi$
$719$	1946.94	0.100985	0.0504927	+	0.998724i	$0.483921\pi$
$720$	2289.53	0.118508
$721$	0	0
$722$	13193.1	0.680048
$723$	−11908.1	−0.612542
$724$	−8348.02	−0.428524
$725$	−27883.5	−1.42837
$726$	11780.5	0.602224
$727$	−15750.6	−0.803518	−0.401759	−	0.915745i	$-0.631601\pi$
$727$	−15750.6	−0.803518	−0.401759	+	0.915745i	$0.631601\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	14298.7	0.724956
$731$	−1950.79	−0.0987040
$732$	−10040.3	−0.506969
$733$	−14349.6	−0.723074	−0.361537	−	0.932358i	$-0.617748\pi$
$733$	−14349.6	−0.723074	−0.361537	+	0.932358i	$0.617748\pi$
$734$	5548.86	0.279036
$735$	0	0
$736$	6828.70	0.341996
$737$	−9504.24	−0.475025
$738$	−5913.05	−0.294935
$739$	−17758.1	−0.883953	−0.441976	−	0.897027i	$-0.645722\pi$
$739$	−17758.1	−0.883953	−0.441976	+	0.897027i	$0.645722\pi$
$740$	24599.3	1.22201
$741$	−276.964	−0.0137308
$742$	0	0
$743$	−29187.6	−1.44117	−0.720586	−	0.693366i	$-0.756127\pi$
$743$	−29187.6	−1.44117	−0.720586	+	0.693366i	$0.756127\pi$
$744$	6033.53	0.297312
$745$	−48568.2	−2.38846
$746$	−5054.69	−0.248077
$747$	−13521.0	−0.662258
$748$	11915.5	0.582451
$749$	0	0
$750$	266.533	0.0129766
$751$	13781.9	0.669654	0.334827	−	0.942280i	$-0.391322\pi$
$751$	13781.9	0.669654	0.334827	+	0.942280i	$0.391322\pi$
$752$	4079.92	0.197845
$753$	17936.3	0.868039
$754$	−2486.72	−0.120107
$755$	−1035.78	−0.0499283
$756$	0	0
$757$	36952.7	1.77420	0.887099	−	0.461579i	$-0.152717\pi$
$757$	36952.7	1.77420	0.887099	+	0.461579i	$0.152717\pi$
$758$	−6232.80	−0.298662
$759$	36745.0	1.75726
$760$	2060.70	0.0983547
$761$	−28816.5	−1.37266	−0.686332	−	0.727288i	$-0.740780\pi$
$761$	−28816.5	−1.37266	−0.686332	+	0.727288i	$0.740780\pi$
$762$	7108.22	0.337931
$763$	0	0
$764$	13550.8	0.641687
$765$	7426.58	0.350992
$766$	3036.14	0.143212
$767$	−2348.92	−0.110580
$768$	−768.000	−0.0360844
$769$	−25285.2	−1.18571	−0.592854	−	0.805310i	$-0.701999\pi$
$769$	−25285.2	−1.18571	−0.592854	+	0.805310i	$0.701999\pi$
$770$	0	0
$771$	13950.4	0.651638
$772$	−7633.41	−0.355871
$773$	18418.2	0.856995	0.428497	−	0.903543i	$-0.359043\pi$
$773$	18418.2	0.856995	0.428497	+	0.903543i	$0.359043\pi$
$774$	676.582	0.0314202
$775$	32127.0	1.48908
$776$	−6923.49	−0.320282
$777$	0	0
$778$	6493.55	0.299235
$779$	−5322.07	−0.244779
$780$	1087.24	0.0499094
$781$	−26690.5	−1.22287
$782$	22150.4	1.01291
$783$	5891.15	0.268880
$784$	0	0
$785$	−24520.5	−1.11487
$786$	−1785.53	−0.0810275
$787$	11075.8	0.501664	0.250832	−	0.968031i	$-0.419296\pi$
$787$	11075.8	0.501664	0.250832	+	0.968031i	$0.419296\pi$
$788$	−8247.52	−0.372850
$789$	−11086.1	−0.500223
$790$	10924.8	0.492008
$791$	0	0
$792$	−4132.58	−0.185410
$793$	−4767.88	−0.213509
$794$	−3661.25	−0.163643
$795$	−10092.4	−0.450241
$796$	−12686.0	−0.564878
$797$	4838.83	0.215057	0.107528	−	0.994202i	$-0.465706\pi$
$797$	4838.83	0.215057	0.107528	+	0.994202i	$0.465706\pi$
$798$	0	0
$799$	13234.1	0.585969
$800$	−4089.41	−0.180728
$801$	3069.77	0.135412
$802$	6771.62	0.298147
$803$	−25809.0	−1.13422
$804$	1987.05	0.0871617
$805$	0	0
$806$	2865.16	0.125212
$807$	−21473.1	−0.936664
$808$	−1946.05	−0.0847299
$809$	−31509.9	−1.36938	−0.684690	−	0.728834i	$-0.740062\pi$
$809$	−31509.9	−1.36938	−0.684690	+	0.728834i	$0.740062\pi$
$810$	−2575.72	−0.111730
$811$	−29463.3	−1.27570	−0.637851	−	0.770160i	$-0.720177\pi$
$811$	−29463.3	−1.27570	−0.637851	+	0.770160i	$0.720177\pi$
$812$	0	0
$813$	12115.1	0.522627
$814$	−44401.6	−1.91189
$815$	−39983.0	−1.71846
$816$	−2491.18	−0.106873
$817$	608.962	0.0260770
$818$	−18506.3	−0.791026
$819$	0	0
$820$	20892.1	0.889736
$821$	3502.22	0.148877	0.0744386	−	0.997226i	$-0.476284\pi$
$821$	3502.22	0.148877	0.0744386	+	0.997226i	$0.476284\pi$
$822$	3725.91	0.158097
$823$	39993.0	1.69389	0.846943	−	0.531684i	$-0.178440\pi$
$823$	39993.0	1.69389	0.846943	+	0.531684i	$0.178440\pi$
$824$	−7626.77	−0.322441
$825$	−22005.0	−0.928623
$826$	0	0
$827$	−10733.6	−0.451322	−0.225661	−	0.974206i	$-0.572454\pi$
$827$	−10733.6	−0.451322	−0.225661	+	0.974206i	$0.572454\pi$
$828$	−7682.29	−0.322437
$829$	−14537.5	−0.609056	−0.304528	−	0.952503i	$-0.598499\pi$
$829$	−14537.5	−0.609056	−0.304528	+	0.952503i	$0.598499\pi$
$830$	47772.6	1.99785
$831$	8264.47	0.344996
$832$	−364.703	−0.0151969
$833$	0	0
$834$	5392.52	0.223894
$835$	−8405.16	−0.348351
$836$	−3719.56	−0.153880
$837$	−6787.72	−0.280308
$838$	−7095.03	−0.292475
$839$	7353.57	0.302591	0.151295	−	0.988489i	$-0.451656\pi$
$839$	7353.57	0.302591	0.151295	+	0.988489i	$0.451656\pi$
$840$	0	0
$841$	23218.3	0.951998
$842$	−15697.7	−0.642494
$843$	2318.23	0.0947141
$844$	5399.88	0.220227
$845$	−34414.9	−1.40107
$846$	−4589.91	−0.186530
$847$	0	0
$848$	3385.41	0.137094
$849$	−20236.5	−0.818037
$850$	−13264.9	−0.535273
$851$	−82540.7	−3.32486
$852$	5580.18	0.224382
$853$	19293.6	0.774442	0.387221	−	0.921987i	$-0.373435\pi$
$853$	19293.6	0.774442	0.387221	+	0.921987i	$0.373435\pi$
$854$	0	0
$855$	−2318.29	−0.0927297
$856$	10759.6	0.429622
$857$	−14161.6	−0.564468	−0.282234	−	0.959346i	$-0.591076\pi$
$857$	−14161.6	−0.564468	−0.282234	+	0.959346i	$0.591076\pi$
$858$	−1962.45	−0.0780852
$859$	8219.13	0.326465	0.163232	−	0.986588i	$-0.447808\pi$
$859$	8219.13	0.326465	0.163232	+	0.986588i	$0.447808\pi$
$860$	−2390.51	−0.0947858
$861$	0	0
$862$	8894.65	0.351454
$863$	2574.95	0.101567	0.0507835	−	0.998710i	$-0.483828\pi$
$863$	2574.95	0.101567	0.0507835	+	0.998710i	$0.483828\pi$
$864$	864.000	0.0340207
$865$	−1539.77	−0.0605246
$866$	13989.6	0.548946
$867$	6658.33	0.260817
$868$	0	0
$869$	−19719.2	−0.769766
$870$	−20814.8	−0.811134
$871$	943.600	0.0367080
$872$	−13874.8	−0.538831
$873$	7788.93	0.301965
$874$	−6914.49	−0.267604
$875$	0	0
$876$	5395.90	0.208117
$877$	30981.1	1.19288	0.596442	−	0.802656i	$-0.296581\pi$
$877$	30981.1	1.19288	0.596442	+	0.802656i	$0.296581\pi$
$878$	−1272.36	−0.0489068
$879$	5768.08	0.221334
$880$	14601.3	0.559330
$881$	−41781.8	−1.59780	−0.798902	−	0.601461i	$-0.794585\pi$
$881$	−41781.8	−1.59780	−0.798902	+	0.601461i	$0.794585\pi$
$882$	0	0
$883$	−39289.6	−1.49740	−0.748699	−	0.662911i	$-0.769321\pi$
$883$	−39289.6	−1.49740	−0.748699	+	0.662911i	$0.769321\pi$
$884$	−1182.99	−0.0450095
$885$	−19661.4	−0.746790
$886$	8948.48	0.339312
$887$	5832.44	0.220783	0.110391	−	0.993888i	$-0.464790\pi$
$887$	5832.44	0.220783	0.110391	+	0.993888i	$0.464790\pi$
$888$	9283.05	0.350810
$889$	0	0
$890$	−10846.2	−0.408499
$891$	4649.15	0.174806
$892$	5447.39	0.204476
$893$	−4131.18	−0.154809
$894$	−18328.2	−0.685668
$895$	−8498.95	−0.317418
$896$	0	0
$897$	−3648.12	−0.135794
$898$	4778.84	0.177586
$899$	−54852.5	−2.03497
$900$	4600.58	0.170392
$901$	10981.3	0.406038
$902$	−37710.1	−1.39203
$903$	0	0
$904$	−11529.4	−0.424184
$905$	−33182.3	−1.21880
$906$	−390.873	−0.0143332
$907$	42387.9	1.55178	0.775892	−	0.630866i	$-0.217300\pi$
$907$	42387.9	1.55178	0.775892	+	0.630866i	$0.217300\pi$
$908$	−7447.24	−0.272186
$909$	2189.30	0.0798841
$910$	0	0
$911$	2275.12	0.0827423	0.0413711	−	0.999144i	$-0.486827\pi$
$911$	2275.12	0.0827423	0.0413711	+	0.999144i	$0.486827\pi$
$912$	777.648	0.0282352
$913$	−86229.3	−3.12571
$914$	8876.68	0.321241
$915$	−39909.0	−1.44191
$916$	21435.1	0.773184
$917$	0	0
$918$	2802.57	0.100761
$919$	−31284.3	−1.12293	−0.561465	−	0.827500i	$-0.689762\pi$
$919$	−31284.3	−1.12293	−0.561465	+	0.827500i	$0.689762\pi$
$920$	27143.2	0.972702
$921$	6050.05	0.216456
$922$	28159.7	1.00585
$923$	2649.88	0.0944983
$924$	0	0
$925$	49429.9	1.75702
$926$	−9374.99	−0.332701
$927$	8580.12	0.304000
$928$	6982.11	0.246982
$929$	32196.6	1.13707	0.568535	−	0.822659i	$-0.307511\pi$
$929$	32196.6	1.13707	0.568535	+	0.822659i	$0.307511\pi$
$930$	23982.5	0.845610
$931$	0	0
$932$	21764.5	0.764935
$933$	21450.0	0.752669
$934$	−16894.5	−0.591869
$935$	47362.6	1.65660
$936$	410.291	0.0143278
$937$	22293.6	0.777269	0.388635	−	0.921392i	$-0.372947\pi$
$937$	22293.6	0.777269	0.388635	+	0.921392i	$0.372947\pi$
$938$	0	0
$939$	25789.5	0.896281
$940$	16217.2	0.562708
$941$	−31809.7	−1.10198	−0.550991	−	0.834511i	$-0.685750\pi$
$941$	−31809.7	−1.10198	−0.550991	+	0.834511i	$0.685750\pi$
$942$	−9253.32	−0.320053
$943$	−70101.4	−2.42080
$944$	6595.22	0.227390
$945$	0	0
$946$	4314.86	0.148296
$947$	18982.6	0.651376	0.325688	−	0.945477i	$-0.394404\pi$
$947$	18982.6	0.651376	0.325688	+	0.945477i	$0.394404\pi$
$948$	4122.69	0.141243
$949$	2562.37	0.0876481
$950$	4140.78	0.141415
$951$	8559.71	0.291869
$952$	0	0
$953$	9254.58	0.314570	0.157285	−	0.987553i	$-0.449726\pi$
$953$	9254.58	0.314570	0.157285	+	0.987553i	$0.449726\pi$
$954$	−3808.58	−0.129253
$955$	53862.5	1.82508
$956$	−4629.10	−0.156607
$957$	37570.5	1.26905
$958$	8738.81	0.294716
$959$	0	0
$960$	−3052.70	−0.102631
$961$	33409.4	1.12146
$962$	4408.28	0.147743
$963$	−12104.6	−0.405052
$964$	15877.5	0.530477
$965$	−30341.8	−1.01216
$966$	0	0
$967$	15317.5	0.509387	0.254694	−	0.967022i	$-0.418025\pi$
$967$	15317.5	0.509387	0.254694	+	0.967022i	$0.418025\pi$
$968$	−15707.3	−0.521541
$969$	2522.47	0.0836259
$970$	−27520.0	−0.910943
$971$	22432.6	0.741398	0.370699	−	0.928753i	$-0.379118\pi$
$971$	22432.6	0.741398	0.370699	+	0.928753i	$0.379118\pi$
$972$	−972.000	−0.0320750
$973$	0	0
$974$	28955.5	0.952559
$975$	2184.70	0.0717603
$976$	13387.1	0.439048
$977$	−627.864	−0.0205600	−0.0102800	−	0.999947i	$-0.503272\pi$
$977$	−627.864	−0.0205600	−0.0102800	+	0.999947i	$0.503272\pi$
$978$	−15088.4	−0.493327
$979$	19577.3	0.639114
$980$	0	0
$981$	15609.2	0.508015
$982$	−18612.2	−0.604827
$983$	45032.6	1.46116	0.730579	−	0.682828i	$-0.239250\pi$
$983$	45032.6	1.46116	0.730579	+	0.682828i	$0.239250\pi$
$984$	7884.06	0.255421
$985$	−32782.8	−1.06045
$986$	22648.0	0.731500
$987$	0	0
$988$	369.285	0.0118912
$989$	8021.14	0.257894
$990$	−16426.5	−0.527342
$991$	−31981.0	−1.02514	−0.512569	−	0.858646i	$-0.671306\pi$
$991$	−31981.0	−1.02514	−0.512569	+	0.858646i	$0.671306\pi$
$992$	−8044.70	−0.257479
$993$	−4857.35	−0.155230
$994$	0	0
$995$	−50425.2	−1.60662
$996$	18028.0	0.573532
$997$	12378.8	0.393221	0.196611	−	0.980482i	$-0.437007\pi$
$997$	12378.8	0.393221	0.196611	+	0.980482i	$0.437007\pi$
$998$	24475.1	0.776298
$999$	−10443.4	−0.330746

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.4.a.j.1.2	✓	2
3.2	odd	2		882.4.a.bc.1.1		2
4.3	odd	2		2352.4.a.cd.1.2		2
7.2	even	3		294.4.e.o.67.1		4
7.3	odd	6		294.4.e.n.79.2		4
7.4	even	3		294.4.e.o.79.1		4
7.5	odd	6		294.4.e.n.67.2		4
7.6	odd	2		294.4.a.k.1.1	yes	2
21.2	odd	6		882.4.g.bd.361.2		4
21.5	even	6		882.4.g.y.361.1		4
21.11	odd	6		882.4.g.bd.667.2		4
21.17	even	6		882.4.g.y.667.1		4
21.20	even	2		882.4.a.bi.1.2		2
28.27	even	2		2352.4.a.bn.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.4.a.j.1.2	✓	2	1.1	even	1	trivial
294.4.a.k.1.1	yes	2	7.6	odd	2
294.4.e.n.67.2		4	7.5	odd	6
294.4.e.n.79.2		4	7.3	odd	6
294.4.e.o.67.1		4	7.2	even	3
294.4.e.o.79.1		4	7.4	even	3
882.4.a.bc.1.1		2	3.2	odd	2
882.4.a.bi.1.2		2	21.20	even	2
882.4.g.y.361.1		4	21.5	even	6
882.4.g.y.667.1		4	21.17	even	6
882.4.g.bd.361.2		4	21.2	odd	6
882.4.g.bd.667.2		4	21.11	odd	6
2352.4.a.bn.1.1		2	28.27	even	2
2352.4.a.cd.1.2		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	294.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +15.8995 q^{5} +6.00000 q^{6} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +15.8995 q^{5} +6.00000 q^{6} -8.00000 q^{8} +9.00000 q^{9} -31.7990 q^{10} +57.3970 q^{11} -12.0000 q^{12} -5.69848 q^{13} -47.6985 q^{15} +16.0000 q^{16} +51.8995 q^{17} -18.0000 q^{18} -16.2010 q^{19} +63.5980 q^{20} -114.794 q^{22} -213.397 q^{23} +24.0000 q^{24} +127.794 q^{25} +11.3970 q^{26} -27.0000 q^{27} -218.191 q^{29} +95.3970 q^{30} +251.397 q^{31} -32.0000 q^{32} -172.191 q^{33} -103.799 q^{34} +36.0000 q^{36} +386.794 q^{37} +32.4020 q^{38} +17.0955 q^{39} -127.196 q^{40} +328.503 q^{41} -37.5879 q^{43} +229.588 q^{44} +143.095 q^{45} +426.794 q^{46} +254.995 q^{47} -48.0000 q^{48} -255.588 q^{50} -155.698 q^{51} -22.7939 q^{52} +211.588 q^{53} +54.0000 q^{54} +912.583 q^{55} +48.6030 q^{57} +436.382 q^{58} +412.201 q^{59} -190.794 q^{60} +836.693 q^{61} -502.794 q^{62} +64.0000 q^{64} -90.6030 q^{65} +344.382 q^{66} -165.588 q^{67} +207.598 q^{68} +640.191 q^{69} -465.015 q^{71} -72.0000 q^{72} -449.658 q^{73} -773.588 q^{74} -383.382 q^{75} -64.8040 q^{76} -34.1909 q^{78} -343.558 q^{79} +254.392 q^{80} +81.0000 q^{81} -657.005 q^{82} -1502.33 q^{83} +825.176 q^{85} +75.1758 q^{86} +654.573 q^{87} -459.176 q^{88} +341.085 q^{89} -286.191 q^{90} -853.588 q^{92} -754.191 q^{93} -509.990 q^{94} -257.588 q^{95} +96.0000 q^{96} +865.437 q^{97} +516.573 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} - 6 q^{3} + 8 q^{4} + 12 q^{5} + 12 q^{6} - 16 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q - 4 * q^2 - 6 * q^3 + 8 * q^4 + 12 * q^5 + 12 * q^6 - 16 * q^8 + 18 * q^9	\( 2 q - 4 q^{2} - 6 q^{3} + 8 q^{4} + 12 q^{5} + 12 q^{6} - 16 q^{8} + 18 q^{9} - 24 q^{10} - 4 q^{11} - 24 q^{12} + 48 q^{13} - 36 q^{15} + 32 q^{16} + 84 q^{17} - 36 q^{18} - 72 q^{19} + 48 q^{20} + 8 q^{22} - 308 q^{23} + 48 q^{24} + 18 q^{25} - 96 q^{26} - 54 q^{27} - 80 q^{29} + 72 q^{30} + 384 q^{31} - 64 q^{32} + 12 q^{33} - 168 q^{34} + 72 q^{36} + 536 q^{37} + 144 q^{38} - 144 q^{39} - 96 q^{40} + 756 q^{41} + 400 q^{43} - 16 q^{44} + 108 q^{45} + 616 q^{46} + 312 q^{47} - 96 q^{48} - 36 q^{50} - 252 q^{51} + 192 q^{52} - 52 q^{53} + 108 q^{54} + 1152 q^{55} + 216 q^{57} + 160 q^{58} + 864 q^{59} - 144 q^{60} + 1416 q^{61} - 768 q^{62} + 128 q^{64} - 300 q^{65} - 24 q^{66} + 144 q^{67} + 336 q^{68} + 924 q^{69} - 1524 q^{71} - 144 q^{72} + 744 q^{73} - 1072 q^{74} - 54 q^{75} - 288 q^{76} + 288 q^{78} + 976 q^{79} + 192 q^{80} + 162 q^{81} - 1512 q^{82} - 312 q^{83} + 700 q^{85} - 800 q^{86} + 240 q^{87} + 32 q^{88} + 108 q^{89} - 216 q^{90} - 1232 q^{92} - 1152 q^{93} - 624 q^{94} - 40 q^{95} + 192 q^{96} - 744 q^{97} - 36 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 - 6 * q^3 + 8 * q^4 + 12 * q^5 + 12 * q^6 - 16 * q^8 + 18 * q^9 - 24 * q^10 - 4 * q^11 - 24 * q^12 + 48 * q^13 - 36 * q^15 + 32 * q^16 + 84 * q^17 - 36 * q^18 - 72 * q^19 + 48 * q^20 + 8 * q^22 - 308 * q^23 + 48 * q^24 + 18 * q^25 - 96 * q^26 - 54 * q^27 - 80 * q^29 + 72 * q^30 + 384 * q^31 - 64 * q^32 + 12 * q^33 - 168 * q^34 + 72 * q^36 + 536 * q^37 + 144 * q^38 - 144 * q^39 - 96 * q^40 + 756 * q^41 + 400 * q^43 - 16 * q^44 + 108 * q^45 + 616 * q^46 + 312 * q^47 - 96 * q^48 - 36 * q^50 - 252 * q^51 + 192 * q^52 - 52 * q^53 + 108 * q^54 + 1152 * q^55 + 216 * q^57 + 160 * q^58 + 864 * q^59 - 144 * q^60 + 1416 * q^61 - 768 * q^62 + 128 * q^64 - 300 * q^65 - 24 * q^66 + 144 * q^67 + 336 * q^68 + 924 * q^69 - 1524 * q^71 - 144 * q^72 + 744 * q^73 - 1072 * q^74 - 54 * q^75 - 288 * q^76 + 288 * q^78 + 976 * q^79 + 192 * q^80 + 162 * q^81 - 1512 * q^82 - 312 * q^83 + 700 * q^85 - 800 * q^86 + 240 * q^87 + 32 * q^88 + 108 * q^89 - 216 * q^90 - 1232 * q^92 - 1152 * q^93 - 624 * q^94 - 40 * q^95 + 192 * q^96 - 744 * q^97 - 36 * q^99

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