LMFDB - Embedded newform 294.4.a.l.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:	$ 1 $
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)

$f(q)$	$=$	$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -7.41421 q^{5} -6.00000 q^{6} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -7.41421 q^{5} -6.00000 q^{6} +8.00000 q^{8} +9.00000 q^{9} -14.8284 q^{10} +10.4853 q^{11} -12.0000 q^{12} -2.78680 q^{13} +22.2426 q^{15} +16.0000 q^{16} -50.4437 q^{17} +18.0000 q^{18} -125.054 q^{19} -29.6569 q^{20} +20.9706 q^{22} -182.250 q^{23} -24.0000 q^{24} -70.0294 q^{25} -5.57359 q^{26} -27.0000 q^{27} +156.132 q^{29} +44.4853 q^{30} -139.632 q^{31} +32.0000 q^{32} -31.4558 q^{33} -100.887 q^{34} +36.0000 q^{36} -394.558 q^{37} -250.108 q^{38} +8.36039 q^{39} -59.3137 q^{40} -197.605 q^{41} +343.294 q^{43} +41.9411 q^{44} -66.7279 q^{45} -364.500 q^{46} +610.004 q^{47} -48.0000 q^{48} -140.059 q^{50} +151.331 q^{51} -11.1472 q^{52} -137.529 q^{53} -54.0000 q^{54} -77.7401 q^{55} +375.161 q^{57} +312.264 q^{58} -589.436 q^{59} +88.9706 q^{60} -247.217 q^{61} -279.265 q^{62} +64.0000 q^{64} +20.6619 q^{65} -62.9117 q^{66} -395.647 q^{67} -201.775 q^{68} +546.749 q^{69} +285.661 q^{71} +72.0000 q^{72} +997.457 q^{73} -789.117 q^{74} +210.088 q^{75} -500.215 q^{76} +16.7208 q^{78} -848.264 q^{79} -118.627 q^{80} +81.0000 q^{81} -395.210 q^{82} +210.863 q^{83} +374.000 q^{85} +686.587 q^{86} -468.396 q^{87} +83.8823 q^{88} +553.487 q^{89} -133.456 q^{90} -728.999 q^{92} +418.897 q^{93} +1220.01 q^{94} +927.176 q^{95} -96.0000 q^{96} +903.910 q^{97} +94.3675 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 2 q + 4 q^{2} - 6 q^{3} + 8 q^{4} - 12 q^{5} - 12 q^{6} + 16 q^{8} + 18 q^{9} - 24 q^{10} + 4 q^{11} - 24 q^{12} - 48 q^{13} + 36 q^{15} + 32 q^{16} - 132 q^{17} + 36 q^{18} - 120 q^{19} - 48 q^{20} + 8 q^{22} - 76 q^{23} - 48 q^{24} - 174 q^{25} - 96 q^{26} - 54 q^{27} - 112 q^{29} + 72 q^{30} - 432 q^{31} + 64 q^{32} - 12 q^{33} - 264 q^{34} + 72 q^{36} - 280 q^{37} - 240 q^{38} + 144 q^{39} - 96 q^{40} - 36 q^{41} - 128 q^{43} + 16 q^{44} - 108 q^{45} - 152 q^{46} + 264 q^{47} - 96 q^{48} - 348 q^{50} + 396 q^{51} - 192 q^{52} + 268 q^{53} - 108 q^{54} - 48 q^{55} + 360 q^{57} - 224 q^{58} - 336 q^{59} + 144 q^{60} + 504 q^{61} - 864 q^{62} + 128 q^{64} + 228 q^{65} - 24 q^{66} - 384 q^{67} - 528 q^{68} + 228 q^{69} - 396 q^{71} + 144 q^{72} + 312 q^{73} - 560 q^{74} + 522 q^{75} - 480 q^{76} + 288 q^{78} - 848 q^{79} - 192 q^{80} + 162 q^{81} - 72 q^{82} + 648 q^{83} + 748 q^{85} - 256 q^{86} + 336 q^{87} + 32 q^{88} + 612 q^{89} - 216 q^{90} - 304 q^{92} + 1296 q^{93} + 528 q^{94} + 904 q^{95} - 192 q^{96} + 2184 q^{97} + 36 q^{99}+O(q^{100}) \) 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 - 132 * q^17 + 36 * q^18 - 120 * q^19 - 48 * q^20 + 8 * q^22 - 76 * q^23 - 48 * q^24 - 174 * q^25 - 96 * q^26 - 54 * q^27 - 112 * q^29 + 72 * q^30 - 432 * q^31 + 64 * q^32 - 12 * q^33 - 264 * q^34 + 72 * q^36 - 280 * q^37 - 240 * q^38 + 144 * q^39 - 96 * q^40 - 36 * q^41 - 128 * q^43 + 16 * q^44 - 108 * q^45 - 152 * q^46 + 264 * q^47 - 96 * q^48 - 348 * q^50 + 396 * q^51 - 192 * q^52 + 268 * q^53 - 108 * q^54 - 48 * q^55 + 360 * q^57 - 224 * q^58 - 336 * q^59 + 144 * q^60 + 504 * q^61 - 864 * q^62 + 128 * q^64 + 228 * q^65 - 24 * q^66 - 384 * q^67 - 528 * q^68 + 228 * q^69 - 396 * q^71 + 144 * q^72 + 312 * q^73 - 560 * q^74 + 522 * q^75 - 480 * q^76 + 288 * q^78 - 848 * q^79 - 192 * q^80 + 162 * q^81 - 72 * q^82 + 648 * q^83 + 748 * q^85 - 256 * q^86 + 336 * q^87 + 32 * q^88 + 612 * q^89 - 216 * q^90 - 304 * q^92 + 1296 * q^93 + 528 * q^94 + 904 * q^95 - 192 * q^96 + 2184 * 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
$5$	−7.41421	−0.663147	−0.331574	−	0.943429i	$-0.607580\pi$
$5$	−7.41421	−0.663147	−0.331574	+	0.943429i	$0.607580\pi$
$6$	−6.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−14.8284	−0.468916
$11$	10.4853	0.287403	0.143701	−	0.989621i	$-0.454100\pi$
$11$	10.4853	0.287403	0.143701	+	0.989621i	$0.454100\pi$
$12$	−12.0000	−0.288675
$13$	−2.78680	−0.0594553	−0.0297276	−	0.999558i	$-0.509464\pi$
$13$	−2.78680	−0.0594553	−0.0297276	+	0.999558i	$0.509464\pi$
$14$	0	0
$15$	22.2426	0.382868
$16$	16.0000	0.250000
$17$	−50.4437	−0.719670	−0.359835	−	0.933016i	$-0.617167\pi$
$17$	−50.4437	−0.719670	−0.359835	+	0.933016i	$0.617167\pi$
$18$	18.0000	0.235702
$19$	−125.054	−1.50996	−0.754982	−	0.655746i	$-0.772354\pi$
$19$	−125.054	−1.50996	−0.754982	+	0.655746i	$0.772354\pi$
$20$	−29.6569	−0.331574
$21$	0	0
$22$	20.9706	0.203225
$23$	−182.250	−1.65225	−0.826124	−	0.563488i	$-0.809459\pi$
$23$	−182.250	−1.65225	−0.826124	+	0.563488i	$0.809459\pi$
$24$	−24.0000	−0.204124
$25$	−70.0294	−0.560235
$26$	−5.57359	−0.0420412
$27$	−27.0000	−0.192450
$28$	0	0
$29$	156.132	0.999758	0.499879	−	0.866095i	$-0.333378\pi$
$29$	156.132	0.999758	0.499879	+	0.866095i	$0.333378\pi$
$30$	44.4853	0.270729
$31$	−139.632	−0.808991	−0.404496	−	0.914540i	$-0.632553\pi$
$31$	−139.632	−0.808991	−0.404496	+	0.914540i	$0.632553\pi$
$32$	32.0000	0.176777
$33$	−31.4558	−0.165932
$34$	−100.887	−0.508883
$35$	0	0
$36$	36.0000	0.166667
$37$	−394.558	−1.75311	−0.876554	−	0.481303i	$-0.840164\pi$
$37$	−394.558	−1.75311	−0.876554	+	0.481303i	$0.840164\pi$
$38$	−250.108	−1.06771
$39$	8.36039	0.0343265
$40$	−59.3137	−0.234458
$41$	−197.605	−0.752701	−0.376350	−	0.926477i	$-0.622821\pi$
$41$	−197.605	−0.752701	−0.376350	+	0.926477i	$0.622821\pi$
$42$	0	0
$43$	343.294	1.21748	0.608741	−	0.793369i	$-0.291675\pi$
$43$	343.294	1.21748	0.608741	+	0.793369i	$0.291675\pi$
$44$	41.9411	0.143701
$45$	−66.7279	−0.221049
$46$	−364.500	−1.16832
$47$	610.004	1.89315	0.946577	−	0.322477i	$-0.104516\pi$
$47$	610.004	1.89315	0.946577	+	0.322477i	$0.104516\pi$
$48$	−48.0000	−0.144338
$49$	0	0
$50$	−140.059	−0.396146
$51$	151.331	0.415501
$52$	−11.1472	−0.0297276
$53$	−137.529	−0.356435	−0.178218	−	0.983991i	$-0.557033\pi$
$53$	−137.529	−0.356435	−0.178218	+	0.983991i	$0.557033\pi$
$54$	−54.0000	−0.136083
$55$	−77.7401	−0.190590
$56$	0	0
$57$	375.161	0.871778
$58$	312.264	0.706936
$59$	−589.436	−1.30064	−0.650322	−	0.759659i	$-0.725366\pi$
$59$	−589.436	−1.30064	−0.650322	+	0.759659i	$0.725366\pi$
$60$	88.9706	0.191434
$61$	−247.217	−0.518901	−0.259450	−	0.965756i	$-0.583541\pi$
$61$	−247.217	−0.518901	−0.259450	+	0.965756i	$0.583541\pi$
$62$	−279.265	−0.572043
$63$	0	0
$64$	64.0000	0.125000
$65$	20.6619	0.0394276
$66$	−62.9117	−0.117332
$67$	−395.647	−0.721432	−0.360716	−	0.932676i	$-0.617468\pi$
$67$	−395.647	−0.721432	−0.360716	+	0.932676i	$0.617468\pi$
$68$	−201.775	−0.359835
$69$	546.749	0.953926
$70$	0	0
$71$	285.661	0.477489	0.238745	−	0.971082i	$-0.423264\pi$
$71$	285.661	0.477489	0.238745	+	0.971082i	$0.423264\pi$
$72$	72.0000	0.117851
$73$	997.457	1.59923	0.799613	−	0.600515i	$-0.205038\pi$
$73$	997.457	1.59923	0.799613	+	0.600515i	$0.205038\pi$
$74$	−789.117	−1.23963
$75$	210.088	0.323452
$76$	−500.215	−0.754982
$77$	0	0
$78$	16.7208	0.0242725
$79$	−848.264	−1.20807	−0.604033	−	0.796960i	$-0.706440\pi$
$79$	−848.264	−1.20807	−0.604033	+	0.796960i	$0.706440\pi$
$80$	−118.627	−0.165787
$81$	81.0000	0.111111
$82$	−395.210	−0.532240
$83$	210.863	0.278858	0.139429	−	0.990232i	$-0.455473\pi$
$83$	210.863	0.278858	0.139429	+	0.990232i	$0.455473\pi$
$84$	0	0
$85$	374.000	0.477247
$86$	686.587	0.860890
$87$	−468.396	−0.577211
$88$	83.8823	0.101612
$89$	553.487	0.659208	0.329604	−	0.944119i	$-0.393085\pi$
$89$	553.487	0.659208	0.329604	+	0.944119i	$0.393085\pi$
$90$	−133.456	−0.156305
$91$	0	0
$92$	−728.999	−0.826124
$93$	418.897	0.467071
$94$	1220.01	1.33866
$95$	927.176	1.00133
$96$	−96.0000	−0.102062
$97$	903.910	0.946166	0.473083	−	0.881018i	$-0.343141\pi$
$97$	903.910	0.946166	0.473083	+	0.881018i	$0.343141\pi$
$98$	0	0
$99$	94.3675	0.0958009
$100$	−280.118	−0.280118
$101$	313.611	0.308965	0.154482	−	0.987996i	$-0.450629\pi$
$101$	313.611	0.308965	0.154482	+	0.987996i	$0.450629\pi$
$102$	302.662	0.293804
$103$	−230.975	−0.220957	−0.110479	−	0.993878i	$-0.535238\pi$
$103$	−230.975	−0.220957	−0.110479	+	0.993878i	$0.535238\pi$
$104$	−22.2944	−0.0210206
$105$	0	0
$106$	−275.058	−0.252038
$107$	125.486	0.113376	0.0566879	−	0.998392i	$-0.481946\pi$
$107$	125.486	0.113376	0.0566879	+	0.998392i	$0.481946\pi$
$108$	−108.000	−0.0962250
$109$	745.527	0.655124	0.327562	−	0.944830i	$-0.393773\pi$
$109$	745.527	0.655124	0.327562	+	0.944830i	$0.393773\pi$
$110$	−155.480	−0.134768
$111$	1183.68	1.01216
$112$	0	0
$113$	−1043.76	−0.868929	−0.434464	−	0.900689i	$-0.643062\pi$
$113$	−1043.76	−0.868929	−0.434464	+	0.900689i	$0.643062\pi$
$114$	750.323	0.616440
$115$	1351.24	1.09568
$116$	624.528	0.499879
$117$	−25.0812	−0.0198184
$118$	−1178.87	−0.919694
$119$	0	0
$120$	177.941	0.135364
$121$	−1221.06	−0.917400
$122$	−494.435	−0.366918
$123$	592.815	0.434572
$124$	−558.530	−0.404496
$125$	1445.99	1.03467
$126$	0	0
$127$	−2080.17	−1.45343	−0.726715	−	0.686939i	$-0.758954\pi$
$127$	−2080.17	−1.45343	−0.726715	+	0.686939i	$0.758954\pi$
$128$	128.000	0.0883883
$129$	−1029.88	−0.702914
$130$	41.3238	0.0278795
$131$	1269.53	0.846711	0.423355	−	0.905964i	$-0.360852\pi$
$131$	1269.53	0.846711	0.423355	+	0.905964i	$0.360852\pi$
$132$	−125.823	−0.0829661
$133$	0	0
$134$	−791.294	−0.510129
$135$	200.184	0.127623
$136$	−403.549	−0.254442
$137$	3073.19	1.91650	0.958249	−	0.285935i	$-0.0923043\pi$
$137$	3073.19	1.91650	0.958249	+	0.285935i	$0.0923043\pi$
$138$	1093.50	0.674527
$139$	−1013.60	−0.618504	−0.309252	−	0.950980i	$-0.600079\pi$
$139$	−1013.60	−0.618504	−0.309252	+	0.950980i	$0.600079\pi$
$140$	0	0
$141$	−1830.01	−1.09301
$142$	571.322	0.337636
$143$	−29.2203	−0.0170876
$144$	144.000	0.0833333
$145$	−1157.60	−0.662987
$146$	1994.91	1.13082
$147$	0	0
$148$	−1578.23	−0.876554
$149$	1231.47	0.677087	0.338544	−	0.940951i	$-0.390066\pi$
$149$	1231.47	0.677087	0.338544	+	0.940951i	$0.390066\pi$
$150$	420.177	0.228715
$151$	−2244.74	−1.20976	−0.604881	−	0.796316i	$-0.706779\pi$
$151$	−2244.74	−1.20976	−0.604881	+	0.796316i	$0.706779\pi$
$152$	−1000.43	−0.533853
$153$	−453.993	−0.239890
$154$	0	0
$155$	1035.26	0.536481
$156$	33.4416	0.0171633
$157$	3787.16	1.92515	0.962573	−	0.271021i	$-0.0873614\pi$
$157$	3787.16	1.92515	0.962573	+	0.271021i	$0.0873614\pi$
$158$	−1696.53	−0.854231
$159$	412.587	0.205788
$160$	−237.255	−0.117229
$161$	0	0
$162$	162.000	0.0785674
$163$	−2108.56	−1.01322	−0.506611	−	0.862175i	$-0.669102\pi$
$163$	−2108.56	−1.01322	−0.506611	+	0.862175i	$0.669102\pi$
$164$	−790.420	−0.376350
$165$	233.220	0.110037
$166$	421.726	0.197182
$167$	−1502.41	−0.696170	−0.348085	−	0.937463i	$-0.613168\pi$
$167$	−1502.41	−0.696170	−0.348085	+	0.937463i	$0.613168\pi$
$168$	0	0
$169$	−2189.23	−0.996465
$170$	748.000	0.337465
$171$	−1125.48	−0.503321
$172$	1373.17	0.608741
$173$	−471.256	−0.207104	−0.103552	−	0.994624i	$-0.533021\pi$
$173$	−471.256	−0.207104	−0.103552	+	0.994624i	$0.533021\pi$
$174$	−936.792	−0.408150
$175$	0	0
$176$	167.765	0.0718507
$177$	1768.31	0.750927
$178$	1106.97	0.466131
$179$	1332.49	0.556395	0.278198	−	0.960524i	$-0.410263\pi$
$179$	1332.49	0.556395	0.278198	+	0.960524i	$0.410263\pi$
$180$	−266.912	−0.110525
$181$	997.727	0.409726	0.204863	−	0.978791i	$-0.434325\pi$
$181$	997.727	0.409726	0.204863	+	0.978791i	$0.434325\pi$
$182$	0	0
$183$	741.652	0.299587
$184$	−1458.00	−0.584158
$185$	2925.34	1.16257
$186$	837.795	0.330269
$187$	−528.916	−0.206835
$188$	2440.02	0.946577
$189$	0	0
$190$	1854.35	0.708046
$191$	1226.72	0.464725	0.232362	−	0.972629i	$-0.425354\pi$
$191$	1226.72	0.464725	0.232362	+	0.972629i	$0.425354\pi$
$192$	−192.000	−0.0721688
$193$	−3479.29	−1.29764	−0.648821	−	0.760941i	$-0.724738\pi$
$193$	−3479.29	−1.29764	−0.648821	+	0.760941i	$0.724738\pi$
$194$	1807.82	0.669040
$195$	−61.9857	−0.0227635
$196$	0	0
$197$	3193.47	1.15495	0.577476	−	0.816408i	$-0.304038\pi$
$197$	3193.47	1.15495	0.577476	+	0.816408i	$0.304038\pi$
$198$	188.735	0.0677415
$199$	−1065.15	−0.379429	−0.189715	−	0.981839i	$-0.560756\pi$
$199$	−1065.15	−0.379429	−0.189715	+	0.981839i	$0.560756\pi$
$200$	−560.235	−0.198073
$201$	1186.94	0.416519
$202$	627.222	0.218471
$203$	0	0
$204$	605.324	0.207751
$205$	1465.09	0.499152
$206$	−461.949	−0.156241
$207$	−1640.25	−0.550749
$208$	−44.5887	−0.0148638
$209$	−1311.22	−0.433968
$210$	0	0
$211$	2057.50	0.671298	0.335649	−	0.941987i	$-0.391044\pi$
$211$	2057.50	0.671298	0.335649	+	0.941987i	$0.391044\pi$
$212$	−550.116	−0.178218
$213$	−856.983	−0.275678
$214$	250.972	0.0801688
$215$	−2545.25	−0.807371
$216$	−216.000	−0.0680414
$217$	0	0
$218$	1491.05	0.463243
$219$	−2992.37	−0.923314
$220$	−310.960	−0.0952952
$221$	140.576	0.0427881
$222$	2367.35	0.715703
$223$	−2028.27	−0.609071	−0.304536	−	0.952501i	$-0.598501\pi$
$223$	−2028.27	−0.609071	−0.304536	+	0.952501i	$0.598501\pi$
$224$	0	0
$225$	−630.265	−0.186745
$226$	−2087.53	−0.614425
$227$	−2423.96	−0.708739	−0.354369	−	0.935106i	$-0.615304\pi$
$227$	−2423.96	−0.708739	−0.354369	+	0.935106i	$0.615304\pi$
$228$	1500.65	0.435889
$229$	1967.17	0.567660	0.283830	−	0.958875i	$-0.408395\pi$
$229$	1967.17	0.567660	0.283830	+	0.958875i	$0.408395\pi$
$230$	2702.48	0.774766
$231$	0	0
$232$	1249.06	0.353468
$233$	4478.33	1.25916	0.629582	−	0.776934i	$-0.283226\pi$
$233$	4478.33	1.25916	0.629582	+	0.776934i	$0.283226\pi$
$234$	−50.1623	−0.0140137
$235$	−4522.70	−1.25544
$236$	−2357.74	−0.650322
$237$	2544.79	0.697477
$238$	0	0
$239$	6116.92	1.65553	0.827763	−	0.561078i	$-0.189613\pi$
$239$	6116.92	1.65553	0.827763	+	0.561078i	$0.189613\pi$
$240$	355.882	0.0957171
$241$	−6228.38	−1.66475	−0.832376	−	0.554211i	$-0.813020\pi$
$241$	−6228.38	−1.66475	−0.832376	+	0.554211i	$0.813020\pi$
$242$	−2442.12	−0.648699
$243$	−243.000	−0.0641500
$244$	−988.870	−0.259450
$245$	0	0
$246$	1185.63	0.307289
$247$	348.500	0.0897753
$248$	−1117.06	−0.286022
$249$	−632.589	−0.160999
$250$	2891.98	0.731619
$251$	−5904.42	−1.48479	−0.742397	−	0.669960i	$-0.766311\pi$
$251$	−5904.42	−1.48479	−0.742397	+	0.669960i	$0.766311\pi$
$252$	0	0
$253$	−1910.94	−0.474861
$254$	−4160.35	−1.02773
$255$	−1122.00	−0.275539
$256$	256.000	0.0625000
$257$	408.223	0.0990827	0.0495414	−	0.998772i	$-0.484224\pi$
$257$	408.223	0.0990827	0.0495414	+	0.998772i	$0.484224\pi$
$258$	−2059.76	−0.497035
$259$	0	0
$260$	82.6476	0.0197138
$261$	1405.19	0.333253
$262$	2539.05	0.598715
$263$	−4626.01	−1.08461	−0.542304	−	0.840182i	$-0.682448\pi$
$263$	−4626.01	−1.08461	−0.542304	+	0.840182i	$0.682448\pi$
$264$	−251.647	−0.0586659
$265$	1019.67	0.236369
$266$	0	0
$267$	−1660.46	−0.380594
$268$	−1582.59	−0.360716
$269$	871.293	0.197486	0.0987429	−	0.995113i	$-0.468518\pi$
$269$	871.293	0.197486	0.0987429	+	0.995113i	$0.468518\pi$
$270$	400.368	0.0902429
$271$	−6472.35	−1.45080	−0.725401	−	0.688327i	$-0.758345\pi$
$271$	−6472.35	−1.45080	−0.725401	+	0.688327i	$0.758345\pi$
$272$	−807.098	−0.179917
$273$	0	0
$274$	6146.38	1.35517
$275$	−734.278	−0.161013
$276$	2187.00	0.476963
$277$	4711.88	1.02206	0.511028	−	0.859564i	$-0.329265\pi$
$277$	4711.88	1.02206	0.511028	+	0.859564i	$0.329265\pi$
$278$	−2027.19	−0.437349
$279$	−1256.69	−0.269664
$280$	0	0
$281$	−7165.66	−1.52124	−0.760618	−	0.649200i	$-0.775104\pi$
$281$	−7165.66	−1.52124	−0.760618	+	0.649200i	$0.775104\pi$
$282$	−3660.03	−0.772877
$283$	−6347.00	−1.33318	−0.666590	−	0.745424i	$-0.732247\pi$
$283$	−6347.00	−1.33318	−0.666590	+	0.745424i	$0.732247\pi$
$284$	1142.64	0.238745
$285$	−2781.53	−0.578117
$286$	−58.4407	−0.0120828
$287$	0	0
$288$	288.000	0.0589256
$289$	−2368.44	−0.482076
$290$	−2315.19	−0.468803
$291$	−2711.73	−0.546269
$292$	3989.83	0.799613
$293$	−9233.78	−1.84110	−0.920552	−	0.390621i	$-0.872260\pi$
$293$	−9233.78	−1.84110	−0.920552	+	0.390621i	$0.872260\pi$
$294$	0	0
$295$	4370.20	0.862519
$296$	−3156.47	−0.619817
$297$	−283.103	−0.0553107
$298$	2462.94	0.478773
$299$	507.893	0.0982348
$300$	840.353	0.161726
$301$	0	0
$302$	−4489.47	−0.855430
$303$	−940.833	−0.178381
$304$	−2000.86	−0.377491
$305$	1832.92	0.344108
$306$	−907.986	−0.169628
$307$	−6786.53	−1.26165	−0.630827	−	0.775923i	$-0.717284\pi$
$307$	−6786.53	−1.26165	−0.630827	+	0.775923i	$0.717284\pi$
$308$	0	0
$309$	692.924	0.127570
$310$	2070.53	0.379349
$311$	−5136.77	−0.936590	−0.468295	−	0.883572i	$-0.655132\pi$
$311$	−5136.77	−0.936590	−0.468295	+	0.883572i	$0.655132\pi$
$312$	66.8831	0.0121363
$313$	3763.56	0.679645	0.339822	−	0.940490i	$-0.389633\pi$
$313$	3763.56	0.679645	0.339822	+	0.940490i	$0.389633\pi$
$314$	7574.31	1.36128
$315$	0	0
$316$	−3393.06	−0.604033
$317$	−1034.95	−0.183370	−0.0916851	−	0.995788i	$-0.529225\pi$
$317$	−1034.95	−0.183370	−0.0916851	+	0.995788i	$0.529225\pi$
$318$	825.174	0.145514
$319$	1637.09	0.287333
$320$	−474.510	−0.0828934
$321$	−376.458	−0.0654575
$322$	0	0
$323$	6308.17	1.08668
$324$	324.000	0.0555556
$325$	195.158	0.0333089
$326$	−4217.12	−0.716456
$327$	−2236.58	−0.378236
$328$	−1580.84	−0.266120
$329$	0	0
$330$	466.441	0.0778082
$331$	8800.06	1.46131	0.730657	−	0.682744i	$-0.239214\pi$
$331$	8800.06	1.46131	0.730657	+	0.682744i	$0.239214\pi$
$332$	843.452	0.139429
$333$	−3551.03	−0.584369
$334$	−3004.83	−0.492266
$335$	2933.41	0.478416
$336$	0	0
$337$	−5859.78	−0.947189	−0.473595	−	0.880743i	$-0.657044\pi$
$337$	−5859.78	−0.947189	−0.473595	+	0.880743i	$0.657044\pi$
$338$	−4378.47	−0.704607
$339$	3131.29	0.501676
$340$	1496.00	0.238624
$341$	−1464.09	−0.232506
$342$	−2250.97	−0.355902
$343$	0	0
$344$	2746.35	0.430445
$345$	−4053.72	−0.632593
$346$	−942.512	−0.146444
$347$	7938.54	1.22814	0.614068	−	0.789253i	$-0.289532\pi$
$347$	7938.54	1.22814	0.614068	+	0.789253i	$0.289532\pi$
$348$	−1873.58	−0.288605
$349$	9927.75	1.52269	0.761347	−	0.648344i	$-0.224538\pi$
$349$	9927.75	1.52269	0.761347	+	0.648344i	$0.224538\pi$
$350$	0	0
$351$	75.2435	0.0114422
$352$	335.529	0.0508061
$353$	10103.0	1.52332	0.761658	−	0.647979i	$-0.224386\pi$
$353$	10103.0	1.52332	0.761658	+	0.647979i	$0.224386\pi$
$354$	3536.61	0.530986
$355$	−2117.95	−0.316646
$356$	2213.95	0.329604
$357$	0	0
$358$	2664.97	0.393431
$359$	−4825.27	−0.709382	−0.354691	−	0.934984i	$-0.615414\pi$
$359$	−4825.27	−0.709382	−0.354691	+	0.934984i	$0.615414\pi$
$360$	−533.823	−0.0781527
$361$	8779.46	1.27999
$362$	1995.45	0.289720
$363$	3663.18	0.529661
$364$	0	0
$365$	−7395.36	−1.06052
$366$	1483.30	0.211840
$367$	−6935.30	−0.986430	−0.493215	−	0.869907i	$-0.664178\pi$
$367$	−6935.30	−0.986430	−0.493215	+	0.869907i	$0.664178\pi$
$368$	−2916.00	−0.413062
$369$	−1778.45	−0.250900
$370$	5850.68	0.822061
$371$	0	0
$372$	1675.59	0.233536
$373$	14093.1	1.95634	0.978168	−	0.207816i	$-0.0666355\pi$
$373$	14093.1	1.95634	0.978168	+	0.207816i	$0.0666355\pi$
$374$	−1057.83	−0.146254
$375$	−4337.97	−0.597365
$376$	4880.03	0.669331
$377$	−435.108	−0.0594409
$378$	0	0
$379$	5354.17	0.725661	0.362830	−	0.931855i	$-0.381810\pi$
$379$	5354.17	0.725661	0.362830	+	0.931855i	$0.381810\pi$
$380$	3708.70	0.500664
$381$	6240.52	0.839138
$382$	2453.44	0.328610
$383$	8970.47	1.19679	0.598394	−	0.801202i	$-0.295806\pi$
$383$	8970.47	1.19679	0.598394	+	0.801202i	$0.295806\pi$
$384$	−384.000	−0.0510310
$385$	0	0
$386$	−6958.58	−0.917571
$387$	3089.64	0.405828
$388$	3615.64	0.473083
$389$	−3702.58	−0.482592	−0.241296	−	0.970452i	$-0.577572\pi$
$389$	−3702.58	−0.482592	−0.241296	+	0.970452i	$0.577572\pi$
$390$	−123.971	−0.0160962
$391$	9193.34	1.18907
$392$	0	0
$393$	−3808.58	−0.488849
$394$	6386.94	0.816674
$395$	6289.21	0.801125
$396$	377.470	0.0479005
$397$	2083.24	0.263362	0.131681	−	0.991292i	$-0.457963\pi$
$397$	2083.24	0.263362	0.131681	+	0.991292i	$0.457963\pi$
$398$	−2130.30	−0.268297
$399$	0	0
$400$	−1120.47	−0.140059
$401$	−10634.0	−1.32428	−0.662141	−	0.749379i	$-0.730352\pi$
$401$	−10634.0	−1.32428	−0.662141	+	0.749379i	$0.730352\pi$
$402$	2373.88	0.294523
$403$	389.127	0.0480988
$404$	1254.44	0.154482
$405$	−600.551	−0.0736830
$406$	0	0
$407$	−4137.06	−0.503848
$408$	1210.65	0.146902
$409$	6516.37	0.787808	0.393904	−	0.919152i	$-0.371124\pi$
$409$	6516.37	0.787808	0.393904	+	0.919152i	$0.371124\pi$
$410$	2930.17	0.352954
$411$	−9219.56	−1.10649
$412$	−923.899	−0.110479
$413$	0	0
$414$	−3280.50	−0.389439
$415$	−1563.38	−0.184924
$416$	−89.1775	−0.0105103
$417$	3040.79	0.357094
$418$	−2622.45	−0.306862
$419$	−6079.92	−0.708887	−0.354443	−	0.935077i	$-0.615330\pi$
$419$	−6079.92	−0.708887	−0.354443	+	0.935077i	$0.615330\pi$
$420$	0	0
$421$	−5631.58	−0.651939	−0.325969	−	0.945380i	$-0.605691\pi$
$421$	−5631.58	−0.651939	−0.325969	+	0.945380i	$0.605691\pi$
$422$	4114.99	0.474679
$423$	5490.04	0.631051
$424$	−1100.23	−0.126019
$425$	3532.54	0.403184
$426$	−1713.97	−0.194934
$427$	0	0
$428$	501.945	0.0566879
$429$	87.6610	0.00986554
$430$	−5090.50	−0.570897
$431$	−3736.90	−0.417633	−0.208817	−	0.977955i	$-0.566961\pi$
$431$	−3736.90	−0.417633	−0.208817	+	0.977955i	$0.566961\pi$
$432$	−432.000	−0.0481125
$433$	5757.46	0.638998	0.319499	−	0.947587i	$-0.396485\pi$
$433$	5757.46	0.638998	0.319499	+	0.947587i	$0.396485\pi$
$434$	0	0
$435$	3472.79	0.382776
$436$	2982.11	0.327562
$437$	22791.0	2.49484
$438$	−5984.74	−0.652881
$439$	9812.76	1.06683	0.533414	−	0.845854i	$-0.320909\pi$
$439$	9812.76	1.06683	0.533414	+	0.845854i	$0.320909\pi$
$440$	−621.921	−0.0673839
$441$	0	0
$442$	281.152	0.0302558
$443$	5830.30	0.625296	0.312648	−	0.949869i	$-0.398784\pi$
$443$	5830.30	0.625296	0.312648	+	0.949869i	$0.398784\pi$
$444$	4734.70	0.506079
$445$	−4103.67	−0.437152
$446$	−4056.54	−0.430678
$447$	−3694.41	−0.390916
$448$	0	0
$449$	−8674.94	−0.911794	−0.455897	−	0.890033i	$-0.650681\pi$
$449$	−8674.94	−0.911794	−0.455897	+	0.890033i	$0.650681\pi$
$450$	−1260.53	−0.132049
$451$	−2071.95	−0.216328
$452$	−4175.05	−0.434464
$453$	6734.21	0.698456
$454$	−4847.91	−0.501154
$455$	0	0
$456$	3001.29	0.308220
$457$	9106.82	0.932165	0.466082	−	0.884741i	$-0.345665\pi$
$457$	9106.82	0.932165	0.466082	+	0.884741i	$0.345665\pi$
$458$	3934.34	0.401396
$459$	1361.98	0.138500
$460$	5404.96	0.547842
$461$	8729.69	0.881957	0.440979	−	0.897518i	$-0.354631\pi$
$461$	8729.69	0.881957	0.440979	+	0.897518i	$0.354631\pi$
$462$	0	0
$463$	−1795.62	−0.180237	−0.0901184	−	0.995931i	$-0.528725\pi$
$463$	−1795.62	−0.180237	−0.0901184	+	0.995931i	$0.528725\pi$
$464$	2498.11	0.249940
$465$	−3105.79	−0.309737
$466$	8956.67	0.890364
$467$	−130.559	−0.0129370	−0.00646849	−	0.999979i	$-0.502059\pi$
$467$	−130.559	−0.0129370	−0.00646849	+	0.999979i	$0.502059\pi$
$468$	−100.325	−0.00990921
$469$	0	0
$470$	−9045.40	−0.887730
$471$	−11361.5	−1.11148
$472$	−4715.49	−0.459847
$473$	3599.53	0.349908
$474$	5089.58	0.493191
$475$	8757.45	0.845935
$476$	0	0
$477$	−1237.76	−0.118812
$478$	12233.8	1.17063
$479$	−11845.8	−1.12996	−0.564978	−	0.825106i	$-0.691115\pi$
$479$	−11845.8	−1.12996	−0.564978	+	0.825106i	$0.691115\pi$
$480$	711.765	0.0676822
$481$	1099.55	0.104232
$482$	−12456.8	−1.17716
$483$	0	0
$484$	−4884.24	−0.458700
$485$	−6701.78	−0.627448
$486$	−486.000	−0.0453609
$487$	−4807.21	−0.447301	−0.223650	−	0.974669i	$-0.571797\pi$
$487$	−4807.21	−0.447301	−0.223650	+	0.974669i	$0.571797\pi$
$488$	−1977.74	−0.183459
$489$	6325.68	0.584984
$490$	0	0
$491$	6068.04	0.557733	0.278866	−	0.960330i	$-0.410041\pi$
$491$	6068.04	0.557733	0.278866	+	0.960330i	$0.410041\pi$
$492$	2371.26	0.217286
$493$	−7875.87	−0.719496
$494$	696.999	0.0634807
$495$	−699.661	−0.0635302
$496$	−2234.12	−0.202248
$497$	0	0
$498$	−1265.18	−0.113843
$499$	−15506.4	−1.39111	−0.695554	−	0.718474i	$-0.744841\pi$
$499$	−15506.4	−1.39111	−0.695554	+	0.718474i	$0.744841\pi$
$500$	5783.96	0.517333
$501$	4507.24	0.401934
$502$	−11808.8	−1.04991
$503$	1496.79	0.132681	0.0663405	−	0.997797i	$-0.478868\pi$
$503$	1496.79	0.132681	0.0663405	+	0.997797i	$0.478868\pi$
$504$	0	0
$505$	−2325.18	−0.204889
$506$	−3821.88	−0.335777
$507$	6567.70	0.575309
$508$	−8320.70	−0.726715
$509$	5053.74	0.440084	0.220042	−	0.975490i	$-0.429380\pi$
$509$	5053.74	0.440084	0.220042	+	0.975490i	$0.429380\pi$
$510$	−2244.00	−0.194835
$511$	0	0
$512$	512.000	0.0441942
$513$	3376.45	0.290593
$514$	816.446	0.0700621
$515$	1712.50	0.146527
$516$	−4119.52	−0.351457
$517$	6396.07	0.544098
$518$	0	0
$519$	1413.77	0.119571
$520$	165.295	0.0139398
$521$	−9736.73	−0.818760	−0.409380	−	0.912364i	$-0.634255\pi$
$521$	−9736.73	−0.818760	−0.409380	+	0.912364i	$0.634255\pi$
$522$	2810.38	0.235645
$523$	11796.7	0.986295	0.493148	−	0.869946i	$-0.335846\pi$
$523$	11796.7	0.986295	0.493148	+	0.869946i	$0.335846\pi$
$524$	5078.11	0.423355
$525$	0	0
$526$	−9252.01	−0.766933
$527$	7043.57	0.582206
$528$	−503.294	−0.0414830
$529$	21048.0	1.72992
$530$	2039.34	0.167138
$531$	−5304.92	−0.433548
$532$	0	0
$533$	550.685	0.0447520
$534$	−3320.92	−0.269121
$535$	−930.381	−0.0751848
$536$	−3165.17	−0.255065
$537$	−3997.46	−0.321235
$538$	1742.59	0.139644
$539$	0	0
$540$	800.735	0.0638114
$541$	−4310.82	−0.342581	−0.171291	−	0.985221i	$-0.554794\pi$
$541$	−4310.82	−0.342581	−0.171291	+	0.985221i	$0.554794\pi$
$542$	−12944.7	−1.02587
$543$	−2993.18	−0.236556
$544$	−1614.20	−0.127221
$545$	−5527.50	−0.434444
$546$	0	0
$547$	17015.9	1.33007	0.665034	−	0.746813i	$-0.268417\pi$
$547$	17015.9	1.33007	0.665034	+	0.746813i	$0.268417\pi$
$548$	12292.8	0.958249
$549$	−2224.96	−0.172967
$550$	−1468.56	−0.113854
$551$	−19524.9	−1.50960
$552$	4373.99	0.337264
$553$	0	0
$554$	9423.76	0.722703
$555$	−8776.02	−0.671210
$556$	−4054.38	−0.309252
$557$	1741.18	0.132452	0.0662262	−	0.997805i	$-0.478904\pi$
$557$	1741.18	0.132452	0.0662262	+	0.997805i	$0.478904\pi$
$558$	−2513.38	−0.190681
$559$	−956.689	−0.0723858
$560$	0	0
$561$	1586.75	0.119416
$562$	−14331.3	−1.07568
$563$	−11346.8	−0.849401	−0.424700	−	0.905334i	$-0.639621\pi$
$563$	−11346.8	−0.849401	−0.424700	+	0.905334i	$0.639621\pi$
$564$	−7320.05	−0.546507
$565$	7738.68	0.576228
$566$	−12694.0	−0.942701
$567$	0	0
$568$	2285.29	0.168818
$569$	−18417.4	−1.35694	−0.678470	−	0.734628i	$-0.737357\pi$
$569$	−18417.4	−1.35694	−0.678470	+	0.734628i	$0.737357\pi$
$570$	−5563.05	−0.408791
$571$	9998.49	0.732791	0.366396	−	0.930459i	$-0.380592\pi$
$571$	9998.49	0.732791	0.366396	+	0.930459i	$0.380592\pi$
$572$	−116.881	−0.00854380
$573$	−3680.16	−0.268309
$574$	0	0
$575$	12762.8	0.925648
$576$	576.000	0.0416667
$577$	1401.71	0.101133	0.0505667	−	0.998721i	$-0.483897\pi$
$577$	1401.71	0.101133	0.0505667	+	0.998721i	$0.483897\pi$
$578$	−4736.88	−0.340879
$579$	10437.9	0.749194
$580$	−4630.38	−0.331494
$581$	0	0
$582$	−5423.46	−0.386271
$583$	−1442.03	−0.102440
$584$	7979.66	0.565412
$585$	185.957	0.0131425
$586$	−18467.6	−1.30186
$587$	10851.3	0.763001	0.381500	−	0.924369i	$-0.375407\pi$
$587$	10851.3	0.763001	0.381500	+	0.924369i	$0.375407\pi$
$588$	0	0
$589$	17461.6	1.22155
$590$	8740.40	0.609893
$591$	−9580.42	−0.666812
$592$	−6312.94	−0.438277
$593$	−20462.0	−1.41699	−0.708493	−	0.705717i	$-0.750625\pi$
$593$	−20462.0	−1.41699	−0.708493	+	0.705717i	$0.750625\pi$
$594$	−566.205	−0.0391106
$595$	0	0
$596$	4925.88	0.338544
$597$	3195.45	0.219064
$598$	1015.79	0.0694625
$599$	9990.42	0.681465	0.340733	−	0.940160i	$-0.389325\pi$
$599$	9990.42	0.681465	0.340733	+	0.940160i	$0.389325\pi$
$600$	1680.71	0.114358
$601$	−17435.9	−1.18341	−0.591703	−	0.806156i	$-0.701544\pi$
$601$	−17435.9	−1.18341	−0.591703	+	0.806156i	$0.701544\pi$
$602$	0	0
$603$	−3560.82	−0.240477
$604$	−8978.94	−0.604881
$605$	9053.19	0.608371
$606$	−1881.67	−0.126134
$607$	−16700.3	−1.11671	−0.558356	−	0.829601i	$-0.688568\pi$
$607$	−16700.3	−1.11671	−0.558356	+	0.829601i	$0.688568\pi$
$608$	−4001.72	−0.266926
$609$	0	0
$610$	3665.85	0.243321
$611$	−1699.96	−0.112558
$612$	−1815.97	−0.119945
$613$	−26702.9	−1.75941	−0.879707	−	0.475515i	$-0.842262\pi$
$613$	−26702.9	−1.75941	−0.879707	+	0.475515i	$0.842262\pi$
$614$	−13573.1	−0.892124
$615$	−4395.26	−0.288185
$616$	0	0
$617$	27790.4	1.81329	0.906645	−	0.421894i	$-0.138635\pi$
$617$	27790.4	1.81329	0.906645	+	0.421894i	$0.138635\pi$
$618$	1385.85	0.0902055
$619$	−1736.08	−0.112728	−0.0563642	−	0.998410i	$-0.517951\pi$
$619$	−1736.08	−0.112728	−0.0563642	+	0.998410i	$0.517951\pi$
$620$	4141.06	0.268240
$621$	4920.74	0.317975
$622$	−10273.5	−0.662269
$623$	0	0
$624$	133.766	0.00858163
$625$	−1967.20	−0.125901
$626$	7527.12	0.480582
$627$	3933.67	0.250552
$628$	15148.6	0.962573
$629$	19903.0	1.26166
$630$	0	0
$631$	−8990.27	−0.567190	−0.283595	−	0.958944i	$-0.591527\pi$
$631$	−8990.27	−0.567190	−0.283595	+	0.958944i	$0.591527\pi$
$632$	−6786.11	−0.427116
$633$	−6172.49	−0.387574
$634$	−2069.89	−0.129662
$635$	15422.9	0.963839
$636$	1650.35	0.102894
$637$	0	0
$638$	3274.18	0.203175
$639$	2570.95	0.159163
$640$	−949.019	−0.0586145
$641$	−13769.6	−0.848467	−0.424233	−	0.905553i	$-0.639456\pi$
$641$	−13769.6	−0.848467	−0.424233	+	0.905553i	$0.639456\pi$
$642$	−752.917	−0.0462855
$643$	−26969.9	−1.65411	−0.827053	−	0.562124i	$-0.809985\pi$
$643$	−26969.9	−1.65411	−0.827053	+	0.562124i	$0.809985\pi$
$644$	0	0
$645$	7635.75	0.466136
$646$	12616.3	0.768395
$647$	−24401.7	−1.48274	−0.741368	−	0.671098i	$-0.765823\pi$
$647$	−24401.7	−1.48274	−0.741368	+	0.671098i	$0.765823\pi$
$648$	648.000	0.0392837
$649$	−6180.40	−0.373809
$650$	390.316	0.0235530
$651$	0	0
$652$	−8434.24	−0.506611
$653$	15969.6	0.957026	0.478513	−	0.878080i	$-0.341176\pi$
$653$	15969.6	0.957026	0.478513	+	0.878080i	$0.341176\pi$
$654$	−4473.16	−0.267453
$655$	−9412.55	−0.561494
$656$	−3161.68	−0.188175
$657$	8977.11	0.533075
$658$	0	0
$659$	−11596.2	−0.685467	−0.342733	−	0.939433i	$-0.611353\pi$
$659$	−11596.2	−0.685467	−0.342733	+	0.939433i	$0.611353\pi$
$660$	932.881	0.0550187
$661$	−12602.2	−0.741558	−0.370779	−	0.928721i	$-0.620909\pi$
$661$	−12602.2	−0.741558	−0.370779	+	0.928721i	$0.620909\pi$
$662$	17600.1	1.03331
$663$	−421.729	−0.0247037
$664$	1686.90	0.0985912
$665$	0	0
$666$	−7102.05	−0.413212
$667$	−28455.0	−1.65185
$668$	−6009.66	−0.348085
$669$	6084.80	0.351647
$670$	5866.82	0.338291
$671$	−2592.14	−0.149134
$672$	0	0
$673$	2126.29	0.121787	0.0608934	−	0.998144i	$-0.480605\pi$
$673$	2126.29	0.121787	0.0608934	+	0.998144i	$0.480605\pi$
$674$	−11719.6	−0.669764
$675$	1890.79	0.107817
$676$	−8756.94	−0.498233
$677$	−2619.38	−0.148702	−0.0743508	−	0.997232i	$-0.523688\pi$
$677$	−2619.38	−0.148702	−0.0743508	+	0.997232i	$0.523688\pi$
$678$	6262.58	0.354739
$679$	0	0
$680$	2992.00	0.168732
$681$	7271.87	0.409190
$682$	−2928.17	−0.164407
$683$	−29929.8	−1.67677	−0.838383	−	0.545082i	$-0.816499\pi$
$683$	−29929.8	−1.67677	−0.838383	+	0.545082i	$0.816499\pi$
$684$	−4501.94	−0.251661
$685$	−22785.3	−1.27092
$686$	0	0
$687$	−5901.51	−0.327739
$688$	5492.70	0.304371
$689$	383.265	0.0211919
$690$	−8107.43	−0.447311
$691$	−6760.90	−0.372209	−0.186105	−	0.982530i	$-0.559586\pi$
$691$	−6760.90	−0.372209	−0.186105	+	0.982530i	$0.559586\pi$
$692$	−1885.02	−0.103552
$693$	0	0
$694$	15877.1	0.868423
$695$	7515.02	0.410160
$696$	−3747.17	−0.204075
$697$	9967.92	0.541696
$698$	19855.5	1.07671
$699$	−13435.0	−0.726979
$700$	0	0
$701$	467.205	0.0251727	0.0125864	−	0.999921i	$-0.495994\pi$
$701$	467.205	0.0251727	0.0125864	+	0.999921i	$0.495994\pi$
$702$	150.487	0.00809084
$703$	49341.0	2.64713
$704$	671.058	0.0359254
$705$	13568.1	0.724829
$706$	20206.1	1.07715
$707$	0	0
$708$	7073.23	0.375464
$709$	8824.64	0.467442	0.233721	−	0.972304i	$-0.424910\pi$
$709$	8824.64	0.467442	0.233721	+	0.972304i	$0.424910\pi$
$710$	−4235.90	−0.223902
$711$	−7634.38	−0.402688
$712$	4427.90	0.233065
$713$	25448.0	1.33665
$714$	0	0
$715$	216.646	0.0113316
$716$	5329.95	0.278198
$717$	−18350.8	−0.955818
$718$	−9650.54	−0.501609
$719$	21098.9	1.09438	0.547188	−	0.837010i	$-0.315698\pi$
$719$	21098.9	1.09438	0.547188	+	0.837010i	$0.315698\pi$
$720$	−1067.65	−0.0552623
$721$	0	0
$722$	17558.9	0.905090
$723$	18685.1	0.961145
$724$	3990.91	0.204863
$725$	−10933.8	−0.560100
$726$	7326.35	0.374527
$727$	4616.48	0.235510	0.117755	−	0.993043i	$-0.462430\pi$
$727$	4616.48	0.235510	0.117755	+	0.993043i	$0.462430\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−14790.7	−0.749903
$731$	−17317.0	−0.876185
$732$	2966.61	0.149794
$733$	10688.1	0.538571	0.269285	−	0.963060i	$-0.413212\pi$
$733$	10688.1	0.538571	0.269285	+	0.963060i	$0.413212\pi$
$734$	−13870.6	−0.697511
$735$	0	0
$736$	−5831.99	−0.292079
$737$	−4148.47	−0.207342
$738$	−3556.89	−0.177413
$739$	−15367.6	−0.764959	−0.382480	−	0.923964i	$-0.624930\pi$
$739$	−15367.6	−0.764959	−0.382480	+	0.923964i	$0.624930\pi$
$740$	11701.4	0.581285
$741$	−1045.50	−0.0518318
$742$	0	0
$743$	6502.58	0.321072	0.160536	−	0.987030i	$-0.448678\pi$
$743$	6502.58	0.321072	0.160536	+	0.987030i	$0.448678\pi$
$744$	3351.18	0.165135
$745$	−9130.38	−0.449009
$746$	28186.2	1.38334
$747$	1897.77	0.0929527
$748$	−2115.66	−0.103418
$749$	0	0
$750$	−8675.94	−0.422401
$751$	−19874.1	−0.965670	−0.482835	−	0.875711i	$-0.660393\pi$
$751$	−19874.1	−0.965670	−0.482835	+	0.875711i	$0.660393\pi$
$752$	9760.07	0.473289
$753$	17713.2	0.857247
$754$	−870.216	−0.0420311
$755$	16642.9	0.802250
$756$	0	0
$757$	−15157.8	−0.727765	−0.363883	−	0.931445i	$-0.618549\pi$
$757$	−15157.8	−0.727765	−0.363883	+	0.931445i	$0.618549\pi$
$758$	10708.3	0.513120
$759$	5732.82	0.274161
$760$	7417.41	0.354023
$761$	−35219.8	−1.67768	−0.838842	−	0.544375i	$-0.816767\pi$
$761$	−35219.8	−1.67768	−0.838842	+	0.544375i	$0.816767\pi$
$762$	12481.0	0.593361
$763$	0	0
$764$	4906.88	0.232362
$765$	3366.00	0.159082
$766$	17940.9	0.846257
$767$	1642.64	0.0773301
$768$	−768.000	−0.0360844
$769$	2264.35	0.106183	0.0530915	−	0.998590i	$-0.483093\pi$
$769$	2264.35	0.106183	0.0530915	+	0.998590i	$0.483093\pi$
$770$	0	0
$771$	−1224.67	−0.0572054
$772$	−13917.2	−0.648821
$773$	9532.79	0.443558	0.221779	−	0.975097i	$-0.428814\pi$
$773$	9532.79	0.443558	0.221779	+	0.975097i	$0.428814\pi$
$774$	6179.28	0.286963
$775$	9778.38	0.453226
$776$	7231.28	0.334520
$777$	0	0
$778$	−7405.16	−0.341244
$779$	24711.3	1.13655
$780$	−247.943	−0.0113818
$781$	2995.24	0.137232
$782$	18386.7	0.840801
$783$	−4215.56	−0.192404
$784$	0	0
$785$	−28078.8	−1.27666
$786$	−7617.16	−0.345668
$787$	33213.0	1.50434	0.752170	−	0.658969i	$-0.229007\pi$
$787$	33213.0	1.50434	0.752170	+	0.658969i	$0.229007\pi$
$788$	12773.9	0.577476
$789$	13878.0	0.626199
$790$	12578.4	0.566481
$791$	0	0
$792$	754.940	0.0338708
$793$	688.945	0.0308514
$794$	4166.47	0.186225
$795$	−3059.01	−0.136468
$796$	−4260.60	−0.189715
$797$	−42065.6	−1.86956	−0.934781	−	0.355223i	$-0.884405\pi$
$797$	−42065.6	−1.86956	−0.934781	+	0.355223i	$0.884405\pi$
$798$	0	0
$799$	−30770.8	−1.36245
$800$	−2240.94	−0.0990366
$801$	4981.39	0.219736
$802$	−21268.0	−0.936409
$803$	10458.6	0.459622
$804$	4747.76	0.208259
$805$	0	0
$806$	778.255	0.0340110
$807$	−2613.88	−0.114018
$808$	2508.89	0.109236
$809$	−777.560	−0.0337918	−0.0168959	−	0.999857i	$-0.505378\pi$
$809$	−777.560	−0.0337918	−0.0168959	+	0.999857i	$0.505378\pi$
$810$	−1201.10	−0.0521018
$811$	−16559.4	−0.716991	−0.358496	−	0.933531i	$-0.616710\pi$
$811$	−16559.4	−0.716991	−0.358496	+	0.933531i	$0.616710\pi$
$812$	0	0
$813$	19417.0	0.837620
$814$	−8274.11	−0.356275
$815$	15633.3	0.671916
$816$	2421.30	0.103875
$817$	−42930.2	−1.83836
$818$	13032.7	0.557065
$819$	0	0
$820$	5860.35	0.249576
$821$	231.224	0.00982921	0.00491460	−	0.999988i	$-0.498436\pi$
$821$	231.224	0.00982921	0.00491460	+	0.999988i	$0.498436\pi$
$822$	−18439.1	−0.782407
$823$	−5222.86	−0.221212	−0.110606	−	0.993864i	$-0.535279\pi$
$823$	−5222.86	−0.221212	−0.110606	+	0.993864i	$0.535279\pi$
$824$	−1847.80	−0.0781203
$825$	2202.84	0.0929611
$826$	0	0
$827$	−46225.5	−1.94367	−0.971836	−	0.235658i	$-0.924275\pi$
$827$	−46225.5	−1.94367	−0.971836	+	0.235658i	$0.924275\pi$
$828$	−6560.99	−0.275375
$829$	39594.2	1.65882	0.829410	−	0.558640i	$-0.188677\pi$
$829$	39594.2	1.65882	0.829410	+	0.558640i	$0.188677\pi$
$830$	−3126.77	−0.130761
$831$	−14135.6	−0.590084
$832$	−178.355	−0.00743191
$833$	0	0
$834$	6081.58	0.252503
$835$	11139.2	0.461663
$836$	−5244.90	−0.216984
$837$	3770.08	0.155690
$838$	−12159.8	−0.501259
$839$	45737.6	1.88205	0.941023	−	0.338344i	$-0.109867\pi$
$839$	45737.6	1.88205	0.941023	+	0.338344i	$0.109867\pi$
$840$	0	0
$841$	−11.7878	−0.000483326 0
$842$	−11263.2	−0.460990
$843$	21497.0	0.878286
$844$	8229.98	0.335649
$845$	16231.4	0.660803
$846$	10980.1	0.446221
$847$	0	0
$848$	−2200.46	−0.0891088
$849$	19041.0	0.769712
$850$	7065.08	0.285094
$851$	71908.2	2.89657
$852$	−3427.93	−0.137839
$853$	8795.55	0.353053	0.176526	−	0.984296i	$-0.443514\pi$
$853$	8795.55	0.353053	0.176526	+	0.984296i	$0.443514\pi$
$854$	0	0
$855$	8344.58	0.333776
$856$	1003.89	0.0400844
$857$	−30254.9	−1.20594	−0.602969	−	0.797764i	$-0.706016\pi$
$857$	−30254.9	−1.20594	−0.602969	+	0.797764i	$0.706016\pi$
$858$	175.322	0.00697599
$859$	−44993.5	−1.78715	−0.893573	−	0.448918i	$-0.851809\pi$
$859$	−44993.5	−1.78715	−0.893573	+	0.448918i	$0.851809\pi$
$860$	−10181.0	−0.403685
$861$	0	0
$862$	−7473.79	−0.295311
$863$	44667.9	1.76189	0.880946	−	0.473217i	$-0.156907\pi$
$863$	44667.9	1.76189	0.880946	+	0.473217i	$0.156907\pi$
$864$	−864.000	−0.0340207
$865$	3493.99	0.137340
$866$	11514.9	0.451840
$867$	7105.31	0.278327
$868$	0	0
$869$	−8894.29	−0.347201
$870$	6945.58	0.270663
$871$	1102.59	0.0428929
$872$	5964.22	0.231621
$873$	8135.19	0.315389
$874$	45582.1	1.76411
$875$	0	0
$876$	−11969.5	−0.461657
$877$	5986.84	0.230515	0.115257	−	0.993336i	$-0.463231\pi$
$877$	5986.84	0.230515	0.115257	+	0.993336i	$0.463231\pi$
$878$	19625.5	0.754361
$879$	27701.3	1.06296
$880$	−1243.84	−0.0476476
$881$	−37911.8	−1.44981	−0.724904	−	0.688850i	$-0.758116\pi$
$881$	−37911.8	−1.44981	−0.724904	+	0.688850i	$0.758116\pi$
$882$	0	0
$883$	−16293.6	−0.620978	−0.310489	−	0.950577i	$-0.600493\pi$
$883$	−16293.6	−0.620978	−0.310489	+	0.950577i	$0.600493\pi$
$884$	562.305	0.0213941
$885$	−13110.6	−0.497975
$886$	11660.6	0.442151
$887$	−8853.41	−0.335139	−0.167570	−	0.985860i	$-0.553592\pi$
$887$	−8853.41	−0.335139	−0.167570	+	0.985860i	$0.553592\pi$
$888$	9469.40	0.357852
$889$	0	0
$890$	−8207.35	−0.309113
$891$	849.308	0.0319336
$892$	−8113.07	−0.304536
$893$	−76283.4	−2.85859
$894$	−7388.82	−0.276420
$895$	−9879.34	−0.368972
$896$	0	0
$897$	−1523.68	−0.0567159
$898$	−17349.9	−0.644736
$899$	−21801.1	−0.808796
$900$	−2521.06	−0.0933726
$901$	6937.47	0.256516
$902$	−4143.89	−0.152967
$903$	0	0
$904$	−8350.10	−0.307213
$905$	−7397.36	−0.271709
$906$	13468.4	0.493883
$907$	16662.5	0.609998	0.304999	−	0.952353i	$-0.401344\pi$
$907$	16662.5	0.609998	0.304999	+	0.952353i	$0.401344\pi$
$908$	−9695.83	−0.354369
$909$	2822.50	0.102988
$910$	0	0
$911$	−29071.2	−1.05727	−0.528635	−	0.848849i	$-0.677296\pi$
$911$	−29071.2	−1.05727	−0.528635	+	0.848849i	$0.677296\pi$
$912$	6002.58	0.217945
$913$	2210.96	0.0801446
$914$	18213.6	0.659140
$915$	−5498.77	−0.198671
$916$	7868.67	0.283830
$917$	0	0
$918$	2723.96	0.0979346
$919$	7973.39	0.286200	0.143100	−	0.989708i	$-0.454293\pi$
$919$	7973.39	0.286200	0.143100	+	0.989708i	$0.454293\pi$
$920$	10809.9	0.387383
$921$	20359.6	0.728416
$922$	17459.4	0.623638
$923$	−796.079	−0.0283892
$924$	0	0
$925$	27630.7	0.982154
$926$	−3591.24	−0.127447
$927$	−2078.77	−0.0736525
$928$	4996.23	0.176734
$929$	−30141.5	−1.06449	−0.532244	−	0.846591i	$-0.678651\pi$
$929$	−30141.5	−1.06449	−0.532244	+	0.846591i	$0.678651\pi$
$930$	−6211.59	−0.219017
$931$	0	0
$932$	17913.3	0.629582
$933$	15410.3	0.540740
$934$	−261.119	−0.00914783
$935$	3921.50	0.137162
$936$	−200.649	−0.00700687
$937$	−1126.37	−0.0392709	−0.0196354	−	0.999807i	$-0.506251\pi$
$937$	−1126.37	−0.0392709	−0.0196354	+	0.999807i	$0.506251\pi$
$938$	0	0
$939$	−11290.7	−0.392393
$940$	−18090.8	−0.627720
$941$	10333.3	0.357976	0.178988	−	0.983851i	$-0.442718\pi$
$941$	10333.3	0.357976	0.178988	+	0.983851i	$0.442718\pi$
$942$	−22722.9	−0.785938
$943$	36013.5	1.24365
$944$	−9430.97	−0.325161
$945$	0	0
$946$	7199.06	0.247422
$947$	24810.3	0.851347	0.425673	−	0.904877i	$-0.360037\pi$
$947$	24810.3	0.851347	0.425673	+	0.904877i	$0.360037\pi$
$948$	10179.2	0.348738
$949$	−2779.71	−0.0950824
$950$	17514.9	0.598167
$951$	3104.84	0.105869
$952$	0	0
$953$	−15048.6	−0.511513	−0.255757	−	0.966741i	$-0.582325\pi$
$953$	−15048.6	−0.511513	−0.255757	+	0.966741i	$0.582325\pi$
$954$	−2475.52	−0.0840126
$955$	−9095.17	−0.308181
$956$	24467.7	0.827763
$957$	−4911.26	−0.165892
$958$	−23691.6	−0.798999
$959$	0	0
$960$	1423.53	0.0478585
$961$	−10293.8	−0.345533
$962$	2199.11	0.0737028
$963$	1129.38	0.0377919
$964$	−24913.5	−0.832376
$965$	25796.2	0.860528
$966$	0	0
$967$	−15619.9	−0.519442	−0.259721	−	0.965684i	$-0.583631\pi$
$967$	−15619.9	−0.519442	−0.259721	+	0.965684i	$0.583631\pi$
$968$	−9768.47	−0.324350
$969$	−18924.5	−0.627392
$970$	−13403.6	−0.443672
$971$	24833.0	0.820730	0.410365	−	0.911921i	$-0.365401\pi$
$971$	24833.0	0.820730	0.410365	+	0.911921i	$0.365401\pi$
$972$	−972.000	−0.0320750
$973$	0	0
$974$	−9614.42	−0.316289
$975$	−585.473	−0.0192309
$976$	−3955.48	−0.129725
$977$	38656.8	1.26586	0.632928	−	0.774211i	$-0.281853\pi$
$977$	38656.8	1.26586	0.632928	+	0.774211i	$0.281853\pi$
$978$	12651.4	0.413646
$979$	5803.47	0.189458
$980$	0	0
$981$	6709.75	0.218375
$982$	12136.1	0.394377
$983$	−26664.1	−0.865162	−0.432581	−	0.901595i	$-0.642397\pi$
$983$	−26664.1	−0.865162	−0.432581	+	0.901595i	$0.642397\pi$
$984$	4742.52	0.153644
$985$	−23677.1	−0.765903
$986$	−15751.7	−0.508760
$987$	0	0
$988$	1394.00	0.0448876
$989$	−62565.2	−2.01158
$990$	−1399.32	−0.0449226
$991$	27228.2	0.872786	0.436393	−	0.899756i	$-0.356256\pi$
$991$	27228.2	0.872786	0.436393	+	0.899756i	$0.356256\pi$
$992$	−4468.24	−0.143011
$993$	−26400.2	−0.843690
$994$	0	0
$995$	7897.24	0.251617
$996$	−2530.35	−0.0804994
$997$	−5162.91	−0.164003	−0.0820016	−	0.996632i	$-0.526131\pi$
$997$	−5162.91	−0.164003	−0.0820016	+	0.996632i	$0.526131\pi$
$998$	−31012.8	−0.983662
$999$	10653.1	0.337386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.4.a.l.1.1	✓	2
3.2	odd	2		882.4.a.bb.1.2		2
4.3	odd	2		2352.4.a.bw.1.1		2
7.2	even	3		294.4.e.m.67.2		4
7.3	odd	6		294.4.e.k.79.1		4
7.4	even	3		294.4.e.m.79.2		4
7.5	odd	6		294.4.e.k.67.1		4
7.6	odd	2		294.4.a.o.1.2	yes	2
21.2	odd	6		882.4.g.be.361.1		4
21.5	even	6		882.4.g.bk.361.2		4
21.11	odd	6		882.4.g.be.667.1		4
21.17	even	6		882.4.g.bk.667.2		4
21.20	even	2		882.4.a.t.1.1		2
28.27	even	2		2352.4.a.bu.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.4.a.l.1.1	✓	2	1.1	even	1	trivial
294.4.a.o.1.2	yes	2	7.6	odd	2
294.4.e.k.67.1		4	7.5	odd	6
294.4.e.k.79.1		4	7.3	odd	6
294.4.e.m.67.2		4	7.2	even	3
294.4.e.m.79.2		4	7.4	even	3
882.4.a.t.1.1		2	21.20	even	2
882.4.a.bb.1.2		2	3.2	odd	2
882.4.g.be.361.1		4	21.2	odd	6
882.4.g.be.667.1		4	21.11	odd	6
882.4.g.bk.361.2		4	21.5	even	6
882.4.g.bk.667.2		4	21.17	even	6
2352.4.a.bu.1.2		2	28.27	even	2
2352.4.a.bw.1.1		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)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -7.41421 q^{5} -6.00000 q^{6} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -7.41421 q^{5} -6.00000 q^{6} +8.00000 q^{8} +9.00000 q^{9} -14.8284 q^{10} +10.4853 q^{11} -12.0000 q^{12} -2.78680 q^{13} +22.2426 q^{15} +16.0000 q^{16} -50.4437 q^{17} +18.0000 q^{18} -125.054 q^{19} -29.6569 q^{20} +20.9706 q^{22} -182.250 q^{23} -24.0000 q^{24} -70.0294 q^{25} -5.57359 q^{26} -27.0000 q^{27} +156.132 q^{29} +44.4853 q^{30} -139.632 q^{31} +32.0000 q^{32} -31.4558 q^{33} -100.887 q^{34} +36.0000 q^{36} -394.558 q^{37} -250.108 q^{38} +8.36039 q^{39} -59.3137 q^{40} -197.605 q^{41} +343.294 q^{43} +41.9411 q^{44} -66.7279 q^{45} -364.500 q^{46} +610.004 q^{47} -48.0000 q^{48} -140.059 q^{50} +151.331 q^{51} -11.1472 q^{52} -137.529 q^{53} -54.0000 q^{54} -77.7401 q^{55} +375.161 q^{57} +312.264 q^{58} -589.436 q^{59} +88.9706 q^{60} -247.217 q^{61} -279.265 q^{62} +64.0000 q^{64} +20.6619 q^{65} -62.9117 q^{66} -395.647 q^{67} -201.775 q^{68} +546.749 q^{69} +285.661 q^{71} +72.0000 q^{72} +997.457 q^{73} -789.117 q^{74} +210.088 q^{75} -500.215 q^{76} +16.7208 q^{78} -848.264 q^{79} -118.627 q^{80} +81.0000 q^{81} -395.210 q^{82} +210.863 q^{83} +374.000 q^{85} +686.587 q^{86} -468.396 q^{87} +83.8823 q^{88} +553.487 q^{89} -133.456 q^{90} -728.999 q^{92} +418.897 q^{93} +1220.01 q^{94} +927.176 q^{95} -96.0000 q^{96} +903.910 q^{97} +94.3675 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - 6 q^{3} + 8 q^{4} - 12 q^{5} - 12 q^{6} + 16 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q + 4 * q^2 - 6 * q^3 + 8 * q^4 - 12 * q^5 - 12 * q^6 + 16 * q^8 + 18 * q^9	\( 2 q + 4 q^{2} - 6 q^{3} + 8 q^{4} - 12 q^{5} - 12 q^{6} + 16 q^{8} + 18 q^{9} - 24 q^{10} + 4 q^{11} - 24 q^{12} - 48 q^{13} + 36 q^{15} + 32 q^{16} - 132 q^{17} + 36 q^{18} - 120 q^{19} - 48 q^{20} + 8 q^{22} - 76 q^{23} - 48 q^{24} - 174 q^{25} - 96 q^{26} - 54 q^{27} - 112 q^{29} + 72 q^{30} - 432 q^{31} + 64 q^{32} - 12 q^{33} - 264 q^{34} + 72 q^{36} - 280 q^{37} - 240 q^{38} + 144 q^{39} - 96 q^{40} - 36 q^{41} - 128 q^{43} + 16 q^{44} - 108 q^{45} - 152 q^{46} + 264 q^{47} - 96 q^{48} - 348 q^{50} + 396 q^{51} - 192 q^{52} + 268 q^{53} - 108 q^{54} - 48 q^{55} + 360 q^{57} - 224 q^{58} - 336 q^{59} + 144 q^{60} + 504 q^{61} - 864 q^{62} + 128 q^{64} + 228 q^{65} - 24 q^{66} - 384 q^{67} - 528 q^{68} + 228 q^{69} - 396 q^{71} + 144 q^{72} + 312 q^{73} - 560 q^{74} + 522 q^{75} - 480 q^{76} + 288 q^{78} - 848 q^{79} - 192 q^{80} + 162 q^{81} - 72 q^{82} + 648 q^{83} + 748 q^{85} - 256 q^{86} + 336 q^{87} + 32 q^{88} + 612 q^{89} - 216 q^{90} - 304 q^{92} + 1296 q^{93} + 528 q^{94} + 904 q^{95} - 192 q^{96} + 2184 q^{97} + 36 q^{99}+O(q^{100}) \) 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 - 132 * q^17 + 36 * q^18 - 120 * q^19 - 48 * q^20 + 8 * q^22 - 76 * q^23 - 48 * q^24 - 174 * q^25 - 96 * q^26 - 54 * q^27 - 112 * q^29 + 72 * q^30 - 432 * q^31 + 64 * q^32 - 12 * q^33 - 264 * q^34 + 72 * q^36 - 280 * q^37 - 240 * q^38 + 144 * q^39 - 96 * q^40 - 36 * q^41 - 128 * q^43 + 16 * q^44 - 108 * q^45 - 152 * q^46 + 264 * q^47 - 96 * q^48 - 348 * q^50 + 396 * q^51 - 192 * q^52 + 268 * q^53 - 108 * q^54 - 48 * q^55 + 360 * q^57 - 224 * q^58 - 336 * q^59 + 144 * q^60 + 504 * q^61 - 864 * q^62 + 128 * q^64 + 228 * q^65 - 24 * q^66 - 384 * q^67 - 528 * q^68 + 228 * q^69 - 396 * q^71 + 144 * q^72 + 312 * q^73 - 560 * q^74 + 522 * q^75 - 480 * q^76 + 288 * q^78 - 848 * q^79 - 192 * q^80 + 162 * q^81 - 72 * q^82 + 648 * q^83 + 748 * q^85 - 256 * q^86 + 336 * q^87 + 32 * q^88 + 612 * q^89 - 216 * q^90 - 304 * q^92 + 1296 * q^93 + 528 * q^94 + 904 * q^95 - 192 * q^96 + 2184 * q^97 + 36 * q^99

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