LMFDB - Embedded newform 294.4.a.o.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("294.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +7.41421 q^{5} +6.00000 q^{6} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +7.41421 q^{5} +6.00000 q^{6} +8.00000 q^{8} +9.00000 q^{9} +14.8284 q^{10} +10.4853 q^{11} +12.0000 q^{12} +2.78680 q^{13} +22.2426 q^{15} +16.0000 q^{16} +50.4437 q^{17} +18.0000 q^{18} +125.054 q^{19} +29.6569 q^{20} +20.9706 q^{22} -182.250 q^{23} +24.0000 q^{24} -70.0294 q^{25} +5.57359 q^{26} +27.0000 q^{27} +156.132 q^{29} +44.4853 q^{30} +139.632 q^{31} +32.0000 q^{32} +31.4558 q^{33} +100.887 q^{34} +36.0000 q^{36} -394.558 q^{37} +250.108 q^{38} +8.36039 q^{39} +59.3137 q^{40} +197.605 q^{41} +343.294 q^{43} +41.9411 q^{44} +66.7279 q^{45} -364.500 q^{46} -610.004 q^{47} +48.0000 q^{48} -140.059 q^{50} +151.331 q^{51} +11.1472 q^{52} -137.529 q^{53} +54.0000 q^{54} +77.7401 q^{55} +375.161 q^{57} +312.264 q^{58} +589.436 q^{59} +88.9706 q^{60} +247.217 q^{61} +279.265 q^{62} +64.0000 q^{64} +20.6619 q^{65} +62.9117 q^{66} -395.647 q^{67} +201.775 q^{68} -546.749 q^{69} +285.661 q^{71} +72.0000 q^{72} -997.457 q^{73} -789.117 q^{74} -210.088 q^{75} +500.215 q^{76} +16.7208 q^{78} -848.264 q^{79} +118.627 q^{80} +81.0000 q^{81} +395.210 q^{82} -210.863 q^{83} +374.000 q^{85} +686.587 q^{86} +468.396 q^{87} +83.8823 q^{88} -553.487 q^{89} +133.456 q^{90} -728.999 q^{92} +418.897 q^{93} -1220.01 q^{94} +927.176 q^{95} +96.0000 q^{96} -903.910 q^{97} +94.3675 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.392420\pi$
$5$	7.41421	0.663147	0.331574	+	0.943429i	$0.392420\pi$
$6$	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	$-0.490536\pi$
$13$	2.78680	0.0594553	0.0297276	+	0.999558i	$0.490536\pi$
$14$	0	0
$15$	22.2426	0.382868
$16$	16.0000	0.250000
$17$	50.4437	0.719670	0.359835	−	0.933016i	$-0.382833\pi$
$17$	50.4437	0.719670	0.359835	+	0.933016i	$0.382833\pi$
$18$	18.0000	0.235702
$19$	125.054	1.50996	0.754982	−	0.655746i	$-0.227646\pi$
$19$	125.054	1.50996	0.754982	+	0.655746i	$0.227646\pi$
$20$	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	$-0.367447\pi$
$31$	139.632	0.808991	0.404496	+	0.914540i	$0.367447\pi$
$32$	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	$-0.377179\pi$
$41$	197.605	0.752701	0.376350	+	0.926477i	$0.377179\pi$
$42$	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	$-0.895484\pi$
$47$	−610.004	−1.89315	−0.946577	+	0.322477i	$0.895484\pi$
$48$	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	$-0.274634\pi$
$59$	589.436	1.30064	0.650322	+	0.759659i	$0.274634\pi$
$60$	88.9706	0.191434
$61$	247.217	0.518901	0.259450	−	0.965756i	$-0.416459\pi$
$61$	247.217	0.518901	0.259450	+	0.965756i	$0.416459\pi$
$62$	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	$-0.794962\pi$
$73$	−997.457	−1.59923	−0.799613	+	0.600515i	$0.794962\pi$
$74$	−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	$-0.544527\pi$
$83$	−210.863	−0.278858	−0.139429	+	0.990232i	$0.544527\pi$
$84$	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	$-0.606915\pi$
$89$	−553.487	−0.659208	−0.329604	+	0.944119i	$0.606915\pi$
$90$	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	$-0.656859\pi$
$97$	−903.910	−0.946166	−0.473083	+	0.881018i	$0.656859\pi$
$98$	0	0
$99$	94.3675	0.0958009
$100$	−280.118	−0.280118
$101$	−313.611	−0.308965	−0.154482	−	0.987996i	$-0.549371\pi$
$101$	−313.611	−0.308965	−0.154482	+	0.987996i	$0.549371\pi$
$102$	302.662	0.293804
$103$	230.975	0.220957	0.110479	−	0.993878i	$-0.464762\pi$
$103$	230.975	0.220957	0.110479	+	0.993878i	$0.464762\pi$
$104$	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	$-0.639148\pi$
$131$	−1269.53	−0.846711	−0.423355	+	0.905964i	$0.639148\pi$
$132$	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	$-0.399921\pi$
$139$	1013.60	0.618504	0.309252	+	0.950980i	$0.399921\pi$
$140$	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	$-0.912639\pi$
$157$	−3787.16	−1.92515	−0.962573	+	0.271021i	$0.912639\pi$
$158$	−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	$-0.386832\pi$
$167$	1502.41	0.696170	0.348085	+	0.937463i	$0.386832\pi$
$168$	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	$-0.466979\pi$
$173$	471.256	0.207104	0.103552	+	0.994624i	$0.466979\pi$
$174$	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	$-0.565675\pi$
$181$	−997.727	−0.409726	−0.204863	+	0.978791i	$0.565675\pi$
$182$	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	$-0.439244\pi$
$199$	1065.15	0.379429	0.189715	+	0.981839i	$0.439244\pi$
$200$	−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	$-0.401499\pi$
$223$	2028.27	0.609071	0.304536	+	0.952501i	$0.401499\pi$
$224$	0	0
$225$	−630.265	−0.186745
$226$	−2087.53	−0.614425
$227$	2423.96	0.708739	0.354369	−	0.935106i	$-0.384696\pi$
$227$	2423.96	0.708739	0.354369	+	0.935106i	$0.384696\pi$
$228$	1500.65	0.435889
$229$	−1967.17	−0.567660	−0.283830	−	0.958875i	$-0.591605\pi$
$229$	−1967.17	−0.567660	−0.283830	+	0.958875i	$0.591605\pi$
$230$	−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	$-0.186980\pi$
$241$	6228.38	1.66475	0.832376	+	0.554211i	$0.186980\pi$
$242$	−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	$-0.233689\pi$
$251$	5904.42	1.48479	0.742397	+	0.669960i	$0.233689\pi$
$252$	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	$-0.515776\pi$
$257$	−408.223	−0.0990827	−0.0495414	+	0.998772i	$0.515776\pi$
$258$	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	$-0.531482\pi$
$269$	−871.293	−0.197486	−0.0987429	+	0.995113i	$0.531482\pi$
$270$	400.368	0.0902429
$271$	6472.35	1.45080	0.725401	−	0.688327i	$-0.241655\pi$
$271$	6472.35	1.45080	0.725401	+	0.688327i	$0.241655\pi$
$272$	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	$-0.267753\pi$
$283$	6347.00	1.33318	0.666590	+	0.745424i	$0.267753\pi$
$284$	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	$-0.127740\pi$
$293$	9233.78	1.84110	0.920552	+	0.390621i	$0.127740\pi$
$294$	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	$-0.282716\pi$
$307$	6786.53	1.26165	0.630827	+	0.775923i	$0.282716\pi$
$308$	0	0
$309$	692.924	0.127570
$310$	2070.53	0.379349
$311$	5136.77	0.936590	0.468295	−	0.883572i	$-0.344868\pi$
$311$	5136.77	0.936590	0.468295	+	0.883572i	$0.344868\pi$
$312$	66.8831	0.0121363
$313$	−3763.56	−0.679645	−0.339822	−	0.940490i	$-0.610367\pi$
$313$	−3763.56	−0.679645	−0.339822	+	0.940490i	$0.610367\pi$
$314$	−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	$-0.775462\pi$
$349$	−9927.75	−1.52269	−0.761347	+	0.648344i	$0.775462\pi$
$350$	0	0
$351$	75.2435	0.0114422
$352$	335.529	0.0508061
$353$	−10103.0	−1.52332	−0.761658	−	0.647979i	$-0.775614\pi$
$353$	−10103.0	−1.52332	−0.761658	+	0.647979i	$0.775614\pi$
$354$	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	$-0.335822\pi$
$367$	6935.30	0.986430	0.493215	+	0.869907i	$0.335822\pi$
$368$	−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	$-0.704194\pi$
$383$	−8970.47	−1.19679	−0.598394	+	0.801202i	$0.704194\pi$
$384$	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	$-0.542037\pi$
$397$	−2083.24	−0.263362	−0.131681	+	0.991292i	$0.542037\pi$
$398$	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	$-0.628876\pi$
$409$	−6516.37	−0.787808	−0.393904	+	0.919152i	$0.628876\pi$
$410$	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	$-0.384670\pi$
$419$	6079.92	0.708887	0.354443	+	0.935077i	$0.384670\pi$
$420$	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	$-0.603515\pi$
$433$	−5757.46	−0.638998	−0.319499	+	0.947587i	$0.603515\pi$
$434$	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	$-0.679091\pi$
$439$	−9812.76	−1.06683	−0.533414	+	0.845854i	$0.679091\pi$
$440$	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	$-0.645369\pi$
$461$	−8729.69	−0.881957	−0.440979	+	0.897518i	$0.645369\pi$
$462$	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	$-0.497941\pi$
$467$	130.559	0.0129370	0.00646849	+	0.999979i	$0.497941\pi$
$468$	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	$-0.308885\pi$
$479$	11845.8	1.12996	0.564978	+	0.825106i	$0.308885\pi$
$480$	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	$-0.521132\pi$
$503$	−1496.79	−0.132681	−0.0663405	+	0.997797i	$0.521132\pi$
$504$	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	$-0.570620\pi$
$509$	−5053.74	−0.440084	−0.220042	+	0.975490i	$0.570620\pi$
$510$	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	$-0.365745\pi$
$521$	9736.73	0.818760	0.409380	+	0.912364i	$0.365745\pi$
$522$	2810.38	0.235645
$523$	−11796.7	−0.986295	−0.493148	−	0.869946i	$-0.664154\pi$
$523$	−11796.7	−0.986295	−0.493148	+	0.869946i	$0.664154\pi$
$524$	−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	$-0.360379\pi$
$563$	11346.8	0.849401	0.424700	+	0.905334i	$0.360379\pi$
$564$	−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	$-0.516103\pi$
$577$	−1401.71	−0.101133	−0.0505667	+	0.998721i	$0.516103\pi$
$578$	−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	$-0.624593\pi$
$587$	−10851.3	−0.763001	−0.381500	+	0.924369i	$0.624593\pi$
$588$	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	$-0.249375\pi$
$593$	20462.0	1.41699	0.708493	+	0.705717i	$0.249375\pi$
$594$	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	$-0.298456\pi$
$601$	17435.9	1.18341	0.591703	+	0.806156i	$0.298456\pi$
$602$	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	$-0.311432\pi$
$607$	16700.3	1.11671	0.558356	+	0.829601i	$0.311432\pi$
$608$	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	$-0.482049\pi$
$619$	1736.08	0.112728	0.0563642	+	0.998410i	$0.482049\pi$
$620$	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	$-0.190015\pi$
$643$	26969.9	1.65411	0.827053	+	0.562124i	$0.190015\pi$
$644$	0	0
$645$	7635.75	0.466136
$646$	12616.3	0.768395
$647$	24401.7	1.48274	0.741368	−	0.671098i	$-0.234177\pi$
$647$	24401.7	1.48274	0.741368	+	0.671098i	$0.234177\pi$
$648$	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	$-0.379091\pi$
$661$	12602.2	0.741558	0.370779	+	0.928721i	$0.379091\pi$
$662$	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	$-0.476312\pi$
$677$	2619.38	0.148702	0.0743508	+	0.997232i	$0.476312\pi$
$678$	−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	$-0.440414\pi$
$691$	6760.90	0.372209	0.186105	+	0.982530i	$0.440414\pi$
$692$	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	$-0.684302\pi$
$719$	−21098.9	−1.09438	−0.547188	+	0.837010i	$0.684302\pi$
$720$	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	$-0.537570\pi$
$727$	−4616.48	−0.235510	−0.117755	+	0.993043i	$0.537570\pi$
$728$	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	$-0.586788\pi$
$733$	−10688.1	−0.538571	−0.269285	+	0.963060i	$0.586788\pi$
$734$	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	$-0.183233\pi$
$761$	35219.8	1.67768	0.838842	+	0.544375i	$0.183233\pi$
$762$	−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	$-0.516907\pi$
$769$	−2264.35	−0.106183	−0.0530915	+	0.998590i	$0.516907\pi$
$770$	0	0
$771$	−1224.67	−0.0572054
$772$	−13917.2	−0.648821
$773$	−9532.79	−0.443558	−0.221779	−	0.975097i	$-0.571186\pi$
$773$	−9532.79	−0.443558	−0.221779	+	0.975097i	$0.571186\pi$
$774$	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	$-0.770993\pi$
$787$	−33213.0	−1.50434	−0.752170	+	0.658969i	$0.770993\pi$
$788$	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	$-0.115595\pi$
$797$	42065.6	1.86956	0.934781	+	0.355223i	$0.115595\pi$
$798$	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	$-0.383290\pi$
$811$	16559.4	0.716991	0.358496	+	0.933531i	$0.383290\pi$
$812$	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	$-0.811323\pi$
$829$	−39594.2	−1.65882	−0.829410	+	0.558640i	$0.811323\pi$
$830$	−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	$-0.890133\pi$
$839$	−45737.6	−1.88205	−0.941023	+	0.338344i	$0.890133\pi$
$840$	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	$-0.556486\pi$
$853$	−8795.55	−0.353053	−0.176526	+	0.984296i	$0.556486\pi$
$854$	0	0
$855$	8344.58	0.333776
$856$	1003.89	0.0400844
$857$	30254.9	1.20594	0.602969	−	0.797764i	$-0.293984\pi$
$857$	30254.9	1.20594	0.602969	+	0.797764i	$0.293984\pi$
$858$	175.322	0.00697599
$859$	44993.5	1.78715	0.893573	−	0.448918i	$-0.148191\pi$
$859$	44993.5	1.78715	0.893573	+	0.448918i	$0.148191\pi$
$860$	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	$-0.241884\pi$
$881$	37911.8	1.44981	0.724904	+	0.688850i	$0.241884\pi$
$882$	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	$-0.446408\pi$
$887$	8853.41	0.335139	0.167570	+	0.985860i	$0.446408\pi$
$888$	−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	$-0.321349\pi$
$929$	30141.5	1.06449	0.532244	+	0.846591i	$0.321349\pi$
$930$	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	$-0.493749\pi$
$937$	1126.37	0.0392709	0.0196354	+	0.999807i	$0.493749\pi$
$938$	0	0
$939$	−11290.7	−0.392393
$940$	−18090.8	−0.627720
$941$	−10333.3	−0.357976	−0.178988	−	0.983851i	$-0.557282\pi$
$941$	−10333.3	−0.357976	−0.178988	+	0.983851i	$0.557282\pi$
$942$	−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	$-0.634599\pi$
$971$	−24833.0	−0.820730	−0.410365	+	0.911921i	$0.634599\pi$
$972$	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	$-0.357603\pi$
$983$	26664.1	0.865162	0.432581	+	0.901595i	$0.357603\pi$
$984$	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	$-0.473869\pi$
$997$	5162.91	0.164003	0.0820016	+	0.996632i	$0.473869\pi$
$998$	−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.o.1.2	yes	2
3.2	odd	2		882.4.a.t.1.1		2
4.3	odd	2		2352.4.a.bu.1.2		2
7.2	even	3		294.4.e.k.67.1		4
7.3	odd	6		294.4.e.m.79.2		4
7.4	even	3		294.4.e.k.79.1		4
7.5	odd	6		294.4.e.m.67.2		4
7.6	odd	2		294.4.a.l.1.1	✓	2
21.2	odd	6		882.4.g.bk.361.2		4
21.5	even	6		882.4.g.be.361.1		4
21.11	odd	6		882.4.g.bk.667.2		4
21.17	even	6		882.4.g.be.667.1		4
21.20	even	2		882.4.a.bb.1.2		2
28.27	even	2		2352.4.a.bw.1.1		2

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

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