LMFDB - Embedded newform 294.4.a.k.1.1

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:	$1$
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			1.1
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	$-0.751779\pi$
$5$	−15.8995	−1.42209	−0.711047	+	0.703144i	$0.751779\pi$
$6$	−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	$-0.480639\pi$
$13$	5.69848	0.121575	0.0607875	+	0.998151i	$0.480639\pi$
$14$	0	0
$15$	−47.6985	−0.821046
$16$	16.0000	0.250000
$17$	−51.8995	−0.740440	−0.370220	−	0.928944i	$-0.620718\pi$
$17$	−51.8995	−0.740440	−0.370220	+	0.928944i	$0.620718\pi$
$18$	−18.0000	−0.235702
$19$	16.2010	0.195619	0.0978096	−	0.995205i	$-0.468816\pi$
$19$	16.2010	0.195619	0.0978096	+	0.995205i	$0.468816\pi$
$20$	−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	$-0.759671\pi$
$31$	−251.397	−1.45652	−0.728262	+	0.685299i	$0.759671\pi$
$32$	−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	$-0.715167\pi$
$41$	−328.503	−1.25130	−0.625652	+	0.780102i	$0.715167\pi$
$42$	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	$-0.629494\pi$
$47$	−254.995	−0.791379	−0.395690	+	0.918384i	$0.629494\pi$
$48$	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	$-0.650282\pi$
$59$	−412.201	−0.909559	−0.454780	+	0.890604i	$0.650282\pi$
$60$	−190.794	−0.410523
$61$	−836.693	−1.75619	−0.878095	−	0.478486i	$-0.841186\pi$
$61$	−836.693	−1.75619	−0.878095	+	0.478486i	$0.841186\pi$
$62$	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	$-0.382617\pi$
$73$	449.658	0.720938	0.360469	+	0.932771i	$0.382617\pi$
$74$	−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	$-0.0366265\pi$
$83$	1502.33	1.98677	0.993387	+	0.114812i	$0.0366265\pi$
$84$	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	$-0.565107\pi$
$89$	−341.085	−0.406236	−0.203118	+	0.979154i	$0.565107\pi$
$90$	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	$-0.649627\pi$
$97$	−865.437	−0.905895	−0.452947	+	0.891537i	$0.649627\pi$
$98$	0	0
$99$	516.573	0.524419
$100$	511.176	0.511176
$101$	−243.256	−0.239652	−0.119826	−	0.992795i	$-0.538234\pi$
$101$	−243.256	−0.239652	−0.119826	+	0.992795i	$0.538234\pi$
$102$	311.397	0.302283
$103$	−953.346	−0.912000	−0.456000	−	0.889980i	$-0.650718\pi$
$103$	−953.346	−0.912000	−0.456000	+	0.889980i	$0.650718\pi$
$104$	−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	$-0.468359\pi$
$131$	297.588	0.198476	0.0992381	+	0.995064i	$0.468359\pi$
$132$	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	$-0.588417\pi$
$139$	−898.754	−0.548426	−0.274213	+	0.961669i	$0.588417\pi$
$140$	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	$-0.371789\pi$
$157$	1542.22	0.783966	0.391983	+	0.919973i	$0.371789\pi$
$158$	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	$-0.460916\pi$
$167$	528.643	0.244956	0.122478	+	0.992471i	$0.460916\pi$
$168$	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	$-0.493226\pi$
$173$	96.8439	0.0425602	0.0212801	+	0.999774i	$0.493226\pi$
$174$	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	$-0.359034\pi$
$181$	2087.00	0.857049	0.428524	+	0.903530i	$0.359034\pi$
$182$	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	$-0.308923\pi$
$199$	3171.50	1.12976	0.564878	+	0.825174i	$0.308923\pi$
$200$	−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	$-0.565549\pi$
$223$	−1361.85	−0.408951	−0.204476	+	0.978872i	$0.565549\pi$
$224$	0	0
$225$	1150.15	0.340784
$226$	−2882.35	−0.848368
$227$	1861.81	0.544373	0.272186	−	0.962245i	$-0.412253\pi$
$227$	1861.81	0.544373	0.272186	+	0.962245i	$0.412253\pi$
$228$	194.412	0.0564704
$229$	−5358.78	−1.54637	−0.773184	−	0.634181i	$-0.781337\pi$
$229$	−5358.78	−1.54637	−0.773184	+	0.634181i	$0.781337\pi$
$230$	−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	$-0.677987\pi$
$241$	−3969.38	−1.06095	−0.530477	+	0.847699i	$0.677987\pi$
$242$	−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	$-0.229213\pi$
$251$	5978.75	1.50349	0.751744	+	0.659455i	$0.229213\pi$
$252$	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	$-0.309132\pi$
$257$	4650.15	1.12867	0.564335	+	0.825546i	$0.309132\pi$
$258$	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	$-0.801171\pi$
$269$	−7157.69	−1.62235	−0.811175	+	0.584804i	$0.801171\pi$
$270$	858.573	0.193522
$271$	4038.37	0.905216	0.452608	−	0.891710i	$-0.350494\pi$
$271$	4038.37	0.905216	0.452608	+	0.891710i	$0.350494\pi$
$272$	−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	$-0.750601\pi$
$283$	−6745.49	−1.41688	−0.708441	+	0.705770i	$0.750601\pi$
$284$	−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	$-0.438606\pi$
$293$	1922.69	0.383362	0.191681	+	0.981457i	$0.438606\pi$
$294$	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	$-0.439976\pi$
$307$	2016.68	0.374913	0.187456	+	0.982273i	$0.439976\pi$
$308$	0	0
$309$	−2860.04	−0.526544
$310$	−7994.17	−1.46464
$311$	7149.99	1.30366	0.651831	−	0.758365i	$-0.274001\pi$
$311$	7149.99	1.30366	0.651831	+	0.758365i	$0.274001\pi$
$312$	−136.764	−0.0248164
$313$	8596.49	1.55240	0.776202	−	0.630484i	$-0.217144\pi$
$313$	8596.49	1.55240	0.776202	+	0.630484i	$0.217144\pi$
$314$	−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	$-0.618035\pi$
$349$	−4725.32	−0.724758	−0.362379	+	0.932031i	$0.618035\pi$
$350$	0	0
$351$	153.859	0.0233971
$352$	−1836.70	−0.278115
$353$	6727.44	1.01435	0.507175	−	0.861843i	$-0.330690\pi$
$353$	6727.44	1.01435	0.507175	+	0.861843i	$0.330690\pi$
$354$	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	$-0.436780\pi$
$367$	2774.43	0.394616	0.197308	+	0.980342i	$0.436780\pi$
$368$	−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	$-0.467711\pi$
$383$	1518.07	0.202532	0.101266	+	0.994859i	$0.467711\pi$
$384$	−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	$-0.536915\pi$
$397$	−1830.62	−0.231427	−0.115713	+	0.993283i	$0.536915\pi$
$398$	−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	$-0.688945\pi$
$409$	−9253.17	−1.11868	−0.559340	+	0.828938i	$0.688945\pi$
$410$	−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	$-0.566308\pi$
$419$	−3547.52	−0.413622	−0.206811	+	0.978381i	$0.566308\pi$
$420$	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	$-0.373110\pi$
$433$	6994.82	0.776327	0.388164	+	0.921590i	$0.373110\pi$
$434$	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	$-0.511010\pi$
$439$	−636.182	−0.0691647	−0.0345823	+	0.999402i	$0.511010\pi$
$440$	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	$-0.248134\pi$
$461$	14079.8	1.42248	0.711240	+	0.702949i	$0.248134\pi$
$462$	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	$-0.637449\pi$
$467$	−8447.26	−0.837029	−0.418514	+	0.908210i	$0.637449\pi$
$468$	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	$-0.433176\pi$
$479$	4369.41	0.416792	0.208396	+	0.978045i	$0.433176\pi$
$480$	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	$-0.578738\pi$
$503$	−5524.30	−0.489694	−0.244847	+	0.969562i	$0.578738\pi$
$504$	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	$-0.355378\pi$
$509$	10079.6	0.877743	0.438871	+	0.898550i	$0.355378\pi$
$510$	−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	$-0.577126\pi$
$521$	−5706.61	−0.479868	−0.239934	+	0.970789i	$0.577126\pi$
$522$	3927.44	0.329309
$523$	10657.3	0.891032	0.445516	−	0.895274i	$-0.353020\pi$
$523$	10657.3	0.891032	0.445516	+	0.895274i	$0.353020\pi$
$524$	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	$-0.144164\pi$
$563$	24023.7	1.79836	0.899180	+	0.437580i	$0.144164\pi$
$564$	−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	$-0.759330\pi$
$577$	−20167.0	−1.45505	−0.727525	+	0.686081i	$0.759330\pi$
$578$	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	$-0.404983\pi$
$587$	8365.08	0.588184	0.294092	+	0.955777i	$0.404983\pi$
$588$	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	$-0.0943373\pi$
$593$	27621.9	1.91281	0.956403	+	0.292050i	$0.0943373\pi$
$594$	−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	$-0.575885\pi$
$601$	−6958.64	−0.472294	−0.236147	+	0.971717i	$0.575885\pi$
$602$	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	$-0.303706\pi$
$607$	17297.6	1.15665	0.578326	+	0.815806i	$0.303706\pi$
$608$	−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	$-0.443597\pi$
$619$	5429.28	0.352538	0.176269	+	0.984342i	$0.443597\pi$
$620$	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	$-0.579826\pi$
$643$	−8092.42	−0.496320	−0.248160	+	0.968719i	$0.579826\pi$
$644$	0	0
$645$	1792.88	0.109449
$646$	1681.65	0.102420
$647$	−20192.7	−1.22698	−0.613490	−	0.789702i	$-0.710235\pi$
$647$	−20192.7	−1.22698	−0.613490	+	0.789702i	$0.710235\pi$
$648$	−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	$-0.663547\pi$
$661$	−16704.9	−0.982975	−0.491488	+	0.870885i	$0.663547\pi$
$662$	−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	$-0.428527\pi$
$677$	7844.26	0.445316	0.222658	+	0.974897i	$0.428527\pi$
$678$	−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	$-0.737671\pi$
$691$	−24674.1	−1.35839	−0.679195	+	0.733958i	$0.737671\pi$
$692$	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	$-0.516079\pi$
$719$	−1946.94	−0.100985	−0.0504927	+	0.998724i	$0.516079\pi$
$720$	−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	$-0.368399\pi$
$727$	15750.6	0.803518	0.401759	+	0.915745i	$0.368399\pi$
$728$	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	$-0.382252\pi$
$733$	14349.6	0.723074	0.361537	+	0.932358i	$0.382252\pi$
$734$	−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	$-0.259220\pi$
$761$	28816.5	1.37266	0.686332	+	0.727288i	$0.259220\pi$
$762$	−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	$-0.298001\pi$
$769$	25285.2	1.18571	0.592854	+	0.805310i	$0.298001\pi$
$770$	0	0
$771$	13950.4	0.651638
$772$	−7633.41	−0.355871
$773$	−18418.2	−0.856995	−0.428497	−	0.903543i	$-0.640957\pi$
$773$	−18418.2	−0.856995	−0.428497	+	0.903543i	$0.640957\pi$
$774$	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	$-0.580704\pi$
$787$	−11075.8	−0.501664	−0.250832	+	0.968031i	$0.580704\pi$
$788$	−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	$-0.534294\pi$
$797$	−4838.83	−0.215057	−0.107528	+	0.994202i	$0.534294\pi$
$798$	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	$-0.279823\pi$
$811$	29463.3	1.27570	0.637851	+	0.770160i	$0.279823\pi$
$812$	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	$-0.401501\pi$
$829$	14537.5	0.609056	0.304528	+	0.952503i	$0.401501\pi$
$830$	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	$-0.548344\pi$
$839$	−7353.57	−0.302591	−0.151295	+	0.988489i	$0.548344\pi$
$840$	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	$-0.626565\pi$
$853$	−19293.6	−0.774442	−0.387221	+	0.921987i	$0.626565\pi$
$854$	0	0
$855$	−2318.29	−0.0927297
$856$	10759.6	0.429622
$857$	14161.6	0.564468	0.282234	−	0.959346i	$-0.408924\pi$
$857$	14161.6	0.564468	0.282234	+	0.959346i	$0.408924\pi$
$858$	−1962.45	−0.0780852
$859$	−8219.13	−0.326465	−0.163232	−	0.986588i	$-0.552192\pi$
$859$	−8219.13	−0.326465	−0.163232	+	0.986588i	$0.552192\pi$
$860$	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	$-0.205415\pi$
$881$	41781.8	1.59780	0.798902	+	0.601461i	$0.205415\pi$
$882$	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	$-0.535210\pi$
$887$	−5832.44	−0.220783	−0.110391	+	0.993888i	$0.535210\pi$
$888$	−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	$-0.692489\pi$
$929$	−32196.6	−1.13707	−0.568535	+	0.822659i	$0.692489\pi$
$930$	−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	$-0.627053\pi$
$937$	−22293.6	−0.777269	−0.388635	+	0.921392i	$0.627053\pi$
$938$	0	0
$939$	25789.5	0.896281
$940$	16217.2	0.562708
$941$	31809.7	1.10198	0.550991	−	0.834511i	$-0.314250\pi$
$941$	31809.7	1.10198	0.550991	+	0.834511i	$0.314250\pi$
$942$	−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	$-0.620882\pi$
$971$	−22432.6	−0.741398	−0.370699	+	0.928753i	$0.620882\pi$
$972$	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	$-0.760750\pi$
$983$	−45032.6	−1.46116	−0.730579	+	0.682828i	$0.760750\pi$
$984$	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	$-0.562993\pi$
$997$	−12378.8	−0.393221	−0.196611	+	0.980482i	$0.562993\pi$
$998$	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.k.1.1	yes	2
3.2	odd	2		882.4.a.bi.1.2		2
4.3	odd	2		2352.4.a.bn.1.1		2
7.2	even	3		294.4.e.n.67.2		4
7.3	odd	6		294.4.e.o.79.1		4
7.4	even	3		294.4.e.n.79.2		4
7.5	odd	6		294.4.e.o.67.1		4
7.6	odd	2		294.4.a.j.1.2	✓	2
21.2	odd	6		882.4.g.y.361.1		4
21.5	even	6		882.4.g.bd.361.2		4
21.11	odd	6		882.4.g.y.667.1		4
21.17	even	6		882.4.g.bd.667.2		4
21.20	even	2		882.4.a.bc.1.1		2
28.27	even	2		2352.4.a.cd.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.4.a.j.1.2	✓	2	7.6	odd	2
294.4.a.k.1.1	yes	2	1.1	even	1	trivial
294.4.e.n.67.2		4	7.2	even	3
294.4.e.n.79.2		4	7.4	even	3
294.4.e.o.67.1		4	7.5	odd	6
294.4.e.o.79.1		4	7.3	odd	6
882.4.a.bc.1.1		2	21.20	even	2
882.4.a.bi.1.2		2	3.2	odd	2
882.4.g.y.361.1		4	21.2	odd	6
882.4.g.y.667.1		4	21.11	odd	6
882.4.g.bd.361.2		4	21.5	even	6
882.4.g.bd.667.2		4	21.17	even	6
2352.4.a.bn.1.1		2	4.3	odd	2
2352.4.a.cd.1.2		2	28.27	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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
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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