LMFDB - Embedded newform 245.4.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(1,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, 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("245.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.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:	$14.4554679514$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{11}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 11 $ x^2 - 11
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.31662$ of defining polynomial
Character	$\chi$	$=$	245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.31662 q^{2} -5.00000 q^{3} -2.63325 q^{4} -5.00000 q^{5} +11.5831 q^{6} +24.6332 q^{8} -2.00000 q^{9} +O(q^{10})$	\(q-2.31662 q^{2} -5.00000 q^{3} -2.63325 q^{4} -5.00000 q^{5} +11.5831 q^{6} +24.6332 q^{8} -2.00000 q^{9} +11.5831 q^{10} +46.2665 q^{11} +13.1662 q^{12} +61.3325 q^{13} +25.0000 q^{15} -36.0000 q^{16} -101.332 q^{17} +4.63325 q^{18} -3.66750 q^{19} +13.1662 q^{20} -107.182 q^{22} +84.8655 q^{23} -123.166 q^{24} +25.0000 q^{25} -142.084 q^{26} +145.000 q^{27} +30.1980 q^{29} -57.9156 q^{30} -188.997 q^{31} -113.668 q^{32} -231.332 q^{33} +234.749 q^{34} +5.26650 q^{36} +18.0685 q^{37} +8.49623 q^{38} -306.662 q^{39} -123.166 q^{40} -481.662 q^{41} -97.7995 q^{43} -121.831 q^{44} +10.0000 q^{45} -196.602 q^{46} -117.665 q^{47} +180.000 q^{48} -57.9156 q^{50} +506.662 q^{51} -161.504 q^{52} +667.995 q^{53} -335.911 q^{54} -231.332 q^{55} +18.3375 q^{57} -69.9574 q^{58} -57.3350 q^{59} -65.8312 q^{60} -738.997 q^{61} +437.836 q^{62} +551.325 q^{64} -306.662 q^{65} +535.911 q^{66} +552.396 q^{67} +266.834 q^{68} -424.327 q^{69} -740.264 q^{71} -49.2665 q^{72} -233.325 q^{73} -41.8580 q^{74} -125.000 q^{75} +9.65745 q^{76} +710.422 q^{78} -1075.19 q^{79} +180.000 q^{80} -671.000 q^{81} +1115.83 q^{82} -683.325 q^{83} +506.662 q^{85} +226.565 q^{86} -150.990 q^{87} +1139.69 q^{88} +1380.32 q^{89} -23.1662 q^{90} -223.472 q^{92} +944.987 q^{93} +272.586 q^{94} +18.3375 q^{95} +568.338 q^{96} -218.008 q^{97} -92.5330 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 10 q^{3} + 8 q^{4} - 10 q^{5} - 10 q^{6} + 36 q^{8} - 4 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 10 * q^3 + 8 * q^4 - 10 * q^5 - 10 * q^6 + 36 * q^8 - 4 * q^9	\( 2 q + 2 q^{2} - 10 q^{3} + 8 q^{4} - 10 q^{5} - 10 q^{6} + 36 q^{8} - 4 q^{9} - 10 q^{10} + 66 q^{11} - 40 q^{12} - 10 q^{13} + 50 q^{15} - 72 q^{16} - 70 q^{17} - 4 q^{18} - 140 q^{19} - 40 q^{20} - 22 q^{22} - 16 q^{23} - 180 q^{24} + 50 q^{25} - 450 q^{26} + 290 q^{27} - 258 q^{29} + 50 q^{30} + 20 q^{31} - 360 q^{32} - 330 q^{33} + 370 q^{34} - 16 q^{36} + 328 q^{37} - 580 q^{38} + 50 q^{39} - 180 q^{40} - 300 q^{41} - 116 q^{43} + 88 q^{44} + 20 q^{45} - 632 q^{46} + 30 q^{47} + 360 q^{48} + 50 q^{50} + 350 q^{51} - 920 q^{52} + 540 q^{53} + 290 q^{54} - 330 q^{55} + 700 q^{57} - 1314 q^{58} - 380 q^{59} + 200 q^{60} - 1080 q^{61} + 1340 q^{62} - 224 q^{64} + 50 q^{65} + 110 q^{66} + 468 q^{67} + 600 q^{68} + 80 q^{69} - 1056 q^{71} - 72 q^{72} + 860 q^{73} + 1296 q^{74} - 250 q^{75} - 1440 q^{76} + 2250 q^{78} + 158 q^{79} + 360 q^{80} - 1342 q^{81} + 1900 q^{82} - 40 q^{83} + 350 q^{85} + 148 q^{86} + 1290 q^{87} + 1364 q^{88} + 240 q^{89} + 20 q^{90} - 1296 q^{92} - 100 q^{93} + 910 q^{94} + 700 q^{95} + 1800 q^{96} - 1630 q^{97} - 132 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 10 * q^3 + 8 * q^4 - 10 * q^5 - 10 * q^6 + 36 * q^8 - 4 * q^9 - 10 * q^10 + 66 * q^11 - 40 * q^12 - 10 * q^13 + 50 * q^15 - 72 * q^16 - 70 * q^17 - 4 * q^18 - 140 * q^19 - 40 * q^20 - 22 * q^22 - 16 * q^23 - 180 * q^24 + 50 * q^25 - 450 * q^26 + 290 * q^27 - 258 * q^29 + 50 * q^30 + 20 * q^31 - 360 * q^32 - 330 * q^33 + 370 * q^34 - 16 * q^36 + 328 * q^37 - 580 * q^38 + 50 * q^39 - 180 * q^40 - 300 * q^41 - 116 * q^43 + 88 * q^44 + 20 * q^45 - 632 * q^46 + 30 * q^47 + 360 * q^48 + 50 * q^50 + 350 * q^51 - 920 * q^52 + 540 * q^53 + 290 * q^54 - 330 * q^55 + 700 * q^57 - 1314 * q^58 - 380 * q^59 + 200 * q^60 - 1080 * q^61 + 1340 * q^62 - 224 * q^64 + 50 * q^65 + 110 * q^66 + 468 * q^67 + 600 * q^68 + 80 * q^69 - 1056 * q^71 - 72 * q^72 + 860 * q^73 + 1296 * q^74 - 250 * q^75 - 1440 * q^76 + 2250 * q^78 + 158 * q^79 + 360 * q^80 - 1342 * q^81 + 1900 * q^82 - 40 * q^83 + 350 * q^85 + 148 * q^86 + 1290 * q^87 + 1364 * q^88 + 240 * q^89 + 20 * q^90 - 1296 * q^92 - 100 * q^93 + 910 * q^94 + 700 * q^95 + 1800 * q^96 - 1630 * q^97 - 132 * 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 $

$2$	−2.31662	−0.819051	−0.409525	−	0.912299i	$-0.634306\pi$
$2$	−2.31662	−0.819051	−0.409525	+	0.912299i	$0.634306\pi$
$3$	−5.00000	−0.962250	−0.481125	−	0.876652i	$-0.659772\pi$
$3$	−5.00000	−0.962250	−0.481125	+	0.876652i	$0.659772\pi$
$4$	−2.63325	−0.329156
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	11.5831	0.788132
$7$	0	0
$7$	0	0
$8$	24.6332	1.08865
$9$	−2.00000	−0.0740741
$10$	11.5831	0.366291
$11$	46.2665	1.26817	0.634085	−	0.773263i	$-0.281377\pi$
$11$	46.2665	1.26817	0.634085	+	0.773263i	$0.281377\pi$
$12$	13.1662	0.316731
$13$	61.3325	1.30851	0.654253	−	0.756276i	$-0.272983\pi$
$13$	61.3325	1.30851	0.654253	+	0.756276i	$0.272983\pi$
$14$	0	0
$15$	25.0000	0.430331
$16$	−36.0000	−0.562500
$17$	−101.332	−1.44569	−0.722845	−	0.691010i	$-0.757166\pi$
$17$	−101.332	−1.44569	−0.722845	+	0.691010i	$0.757166\pi$
$18$	4.63325	0.0606704
$19$	−3.66750	−0.0442833	−0.0221417	−	0.999755i	$-0.507048\pi$
$19$	−3.66750	−0.0442833	−0.0221417	+	0.999755i	$0.507048\pi$
$20$	13.1662	0.147203
$21$	0	0
$22$	−107.182	−1.03870
$23$	84.8655	0.769377	0.384689	−	0.923046i	$-0.374309\pi$
$23$	84.8655	0.769377	0.384689	+	0.923046i	$0.374309\pi$
$24$	−123.166	−1.04755
$25$	25.0000	0.200000
$26$	−142.084	−1.07173
$27$	145.000	1.03353
$28$	0	0
$29$	30.1980	0.193366	0.0966832	−	0.995315i	$-0.469177\pi$
$29$	30.1980	0.193366	0.0966832	+	0.995315i	$0.469177\pi$
$30$	−57.9156	−0.352463
$31$	−188.997	−1.09500	−0.547499	−	0.836806i	$-0.684420\pi$
$31$	−188.997	−1.09500	−0.547499	+	0.836806i	$0.684420\pi$
$32$	−113.668	−0.627930
$33$	−231.332	−1.22030
$34$	234.749	1.18409
$35$	0	0
$36$	5.26650	0.0243819
$37$	18.0685	0.0802823	0.0401411	−	0.999194i	$-0.487219\pi$
$37$	18.0685	0.0802823	0.0401411	+	0.999194i	$0.487219\pi$
$38$	8.49623	0.0362703
$39$	−306.662	−1.25911
$40$	−123.166	−0.486857
$41$	−481.662	−1.83471	−0.917354	−	0.398072i	$-0.869679\pi$
$41$	−481.662	−1.83471	−0.917354	+	0.398072i	$0.869679\pi$
$42$	0	0
$43$	−97.7995	−0.346844	−0.173422	−	0.984848i	$-0.555482\pi$
$43$	−97.7995	−0.346844	−0.173422	+	0.984848i	$0.555482\pi$
$44$	−121.831	−0.417426
$45$	10.0000	0.0331269
$46$	−196.602	−0.630159
$47$	−117.665	−0.365175	−0.182587	−	0.983190i	$-0.558447\pi$
$47$	−117.665	−0.365175	−0.182587	+	0.983190i	$0.558447\pi$
$48$	180.000	0.541266
$49$	0	0
$50$	−57.9156	−0.163810
$51$	506.662	1.39112
$52$	−161.504	−0.430703
$53$	667.995	1.73125	0.865624	−	0.500694i	$-0.166922\pi$
$53$	667.995	1.73125	0.865624	+	0.500694i	$0.166922\pi$
$54$	−335.911	−0.846512
$55$	−231.332	−0.567143
$56$	0	0
$57$	18.3375	0.0426116
$58$	−69.9574	−0.158377
$59$	−57.3350	−0.126515	−0.0632575	−	0.997997i	$-0.520149\pi$
$59$	−57.3350	−0.126515	−0.0632575	+	0.997997i	$0.520149\pi$
$60$	−65.8312	−0.141646
$61$	−738.997	−1.55113	−0.775565	−	0.631268i	$-0.782535\pi$
$61$	−738.997	−1.55113	−0.775565	+	0.631268i	$0.782535\pi$
$62$	437.836	0.896859
$63$	0	0
$64$	551.325	1.07681
$65$	−306.662	−0.585182
$66$	535.911	0.999485
$67$	552.396	1.00725	0.503626	−	0.863922i	$-0.331999\pi$
$67$	552.396	1.00725	0.503626	+	0.863922i	$0.331999\pi$
$68$	266.834	0.475858
$69$	−424.327	−0.740334
$70$	0	0
$71$	−740.264	−1.23737	−0.618684	−	0.785640i	$-0.712334\pi$
$71$	−740.264	−1.23737	−0.618684	+	0.785640i	$0.712334\pi$
$72$	−49.2665	−0.0806405
$73$	−233.325	−0.374091	−0.187045	−	0.982351i	$-0.559891\pi$
$73$	−233.325	−0.374091	−0.187045	+	0.982351i	$0.559891\pi$
$74$	−41.8580	−0.0657553
$75$	−125.000	−0.192450
$76$	9.65745	0.0145761
$77$	0	0
$78$	710.422	1.03127
$79$	−1075.19	−1.53124	−0.765619	−	0.643294i	$-0.777567\pi$
$79$	−1075.19	−1.53124	−0.765619	+	0.643294i	$0.777567\pi$
$80$	180.000	0.251558
$81$	−671.000	−0.920439
$82$	1115.83	1.50272
$83$	−683.325	−0.903671	−0.451835	−	0.892101i	$-0.649231\pi$
$83$	−683.325	−0.903671	−0.451835	+	0.892101i	$0.649231\pi$
$84$	0	0
$85$	506.662	0.646532
$86$	226.565	0.284083
$87$	−150.990	−0.186067
$88$	1139.69	1.38059
$89$	1380.32	1.64397	0.821985	−	0.569509i	$-0.192867\pi$
$89$	1380.32	1.64397	0.821985	+	0.569509i	$0.192867\pi$
$90$	−23.1662	−0.0271326
$91$	0	0
$92$	−223.472	−0.253245
$93$	944.987	1.05366
$94$	272.586	0.299096
$95$	18.3375	0.0198041
$96$	568.338	0.604226
$97$	−218.008	−0.228199	−0.114100	−	0.993469i	$-0.536398\pi$
$97$	−218.008	−0.228199	−0.114100	+	0.993469i	$0.536398\pi$
$98$	0	0
$99$	−92.5330	−0.0939385
$100$	−65.8312	−0.0658312
$101$	1474.33	1.45249	0.726243	−	0.687438i	$-0.241265\pi$
$101$	1474.33	1.45249	0.726243	+	0.687438i	$0.241265\pi$
$102$	−1173.75	−1.13939
$103$	810.990	0.775818	0.387909	−	0.921698i	$-0.373198\pi$
$103$	810.990	0.775818	0.387909	+	0.921698i	$0.373198\pi$
$104$	1510.82	1.42450
$105$	0	0
$106$	−1547.49	−1.41798
$107$	440.660	0.398133	0.199066	−	0.979986i	$-0.436209\pi$
$107$	440.660	0.398133	0.199066	+	0.979986i	$0.436209\pi$
$108$	−381.821	−0.340192
$109$	−1906.19	−1.67504	−0.837522	−	0.546404i	$-0.815996\pi$
$109$	−1906.19	−1.67504	−0.837522	+	0.546404i	$0.815996\pi$
$110$	535.911	0.464519
$111$	−90.3425	−0.0772517
$112$	0	0
$113$	962.470	0.801252	0.400626	−	0.916242i	$-0.368793\pi$
$113$	962.470	0.801252	0.400626	+	0.916242i	$0.368793\pi$
$114$	−42.4812	−0.0349011
$115$	−424.327	−0.344076
$116$	−79.5188	−0.0636478
$117$	−122.665	−0.0969263
$118$	132.824	0.103622
$119$	0	0
$120$	615.831	0.468479
$121$	809.589	0.608256
$122$	1711.98	1.27045
$123$	2408.31	1.76545
$124$	497.678	0.360426
$125$	−125.000	−0.0894427
$126$	0	0
$127$	−1621.74	−1.13312	−0.566558	−	0.824022i	$-0.691725\pi$
$127$	−1621.74	−1.13312	−0.566558	+	0.824022i	$0.691725\pi$
$128$	−367.873	−0.254029
$129$	488.997	0.333751
$130$	710.422	0.479293
$131$	1380.32	0.920602	0.460301	−	0.887763i	$-0.347741\pi$
$131$	1380.32	0.920602	0.460301	+	0.887763i	$0.347741\pi$
$132$	609.156	0.401668
$133$	0	0
$134$	−1279.69	−0.824991
$135$	−725.000	−0.462208
$136$	−2496.15	−1.57385
$137$	−1949.66	−1.21584	−0.607921	−	0.793997i	$-0.707996\pi$
$137$	−1949.66	−1.21584	−0.607921	+	0.793997i	$0.707996\pi$
$138$	983.008	0.606371
$139$	−2800.00	−1.70858	−0.854291	−	0.519795i	$-0.826008\pi$
$139$	−2800.00	−1.70858	−0.854291	+	0.519795i	$0.826008\pi$
$140$	0	0
$141$	588.325	0.351389
$142$	1714.91	1.01347
$143$	2837.64	1.65941
$144$	72.0000	0.0416667
$145$	−150.990	−0.0864761
$146$	540.526	0.306399
$147$	0	0
$148$	−47.5789	−0.0264254
$149$	−1434.12	−0.788506	−0.394253	−	0.919002i	$-0.628997\pi$
$149$	−1434.12	−0.788506	−0.394253	+	0.919002i	$0.628997\pi$
$150$	289.578	0.157626
$151$	−1985.58	−1.07009	−0.535047	−	0.844822i	$-0.679706\pi$
$151$	−1985.58	−1.07009	−0.535047	+	0.844822i	$0.679706\pi$
$152$	−90.3425	−0.0482089
$153$	202.665	0.107088
$154$	0	0
$155$	944.987	0.489698
$156$	807.519	0.414444
$157$	−40.6600	−0.0206689	−0.0103345	−	0.999947i	$-0.503290\pi$
$157$	−40.6600	−0.0206689	−0.0103345	+	0.999947i	$0.503290\pi$
$158$	2490.80	1.25416
$159$	−3339.97	−1.66589
$160$	568.338	0.280819
$161$	0	0
$162$	1554.46	0.753886
$163$	−3953.98	−1.90000	−0.950000	−	0.312250i	$-0.898917\pi$
$163$	−3953.98	−1.90000	−0.950000	+	0.312250i	$0.898917\pi$
$164$	1268.34	0.603906
$165$	1156.66	0.545734
$166$	1583.01	0.740152
$167$	−3380.30	−1.56632	−0.783161	−	0.621819i	$-0.786394\pi$
$167$	−3380.30	−1.56632	−0.783161	+	0.621819i	$0.786394\pi$
$168$	0	0
$169$	1564.68	0.712187
$170$	−1173.75	−0.529543
$171$	7.33501	0.00328025
$172$	257.530	0.114166
$173$	−3206.66	−1.40924	−0.704619	−	0.709586i	$-0.748882\pi$
$173$	−3206.66	−1.40924	−0.704619	+	0.709586i	$0.748882\pi$
$174$	349.787	0.152398
$175$	0	0
$176$	−1665.59	−0.713346
$177$	286.675	0.121739
$178$	−3197.68	−1.34649
$179$	1442.65	0.602395	0.301198	−	0.953562i	$-0.402614\pi$
$179$	1442.65	0.602395	0.301198	+	0.953562i	$0.402614\pi$
$180$	−26.3325	−0.0109039
$181$	908.680	0.373158	0.186579	−	0.982440i	$-0.440260\pi$
$181$	908.680	0.373158	0.186579	+	0.982440i	$0.440260\pi$
$182$	0	0
$183$	3694.99	1.49258
$184$	2090.51	0.837580
$185$	−90.3425	−0.0359033
$186$	−2189.18	−0.863003
$187$	−4688.30	−1.83338
$188$	309.841	0.120199
$189$	0	0
$190$	−42.4812	−0.0162206
$191$	2474.64	0.937479	0.468739	−	0.883336i	$-0.344708\pi$
$191$	2474.64	0.937479	0.468739	+	0.883336i	$0.344708\pi$
$192$	−2756.62	−1.03616
$193$	3533.52	1.31787	0.658934	−	0.752201i	$-0.271008\pi$
$193$	3533.52	1.31787	0.658934	+	0.752201i	$0.271008\pi$
$194$	505.042	0.186907
$195$	1533.31	0.563091
$196$	0	0
$197$	−1952.57	−0.706165	−0.353083	−	0.935592i	$-0.614867\pi$
$197$	−1952.57	−0.706165	−0.353083	+	0.935592i	$0.614867\pi$
$198$	214.364	0.0769404
$199$	−4064.67	−1.44792	−0.723962	−	0.689840i	$-0.757681\pi$
$199$	−4064.67	−1.44792	−0.723962	+	0.689840i	$0.757681\pi$
$200$	615.831	0.217729
$201$	−2761.98	−0.969229
$202$	−3415.46	−1.18966
$203$	0	0
$204$	−1334.17	−0.457895
$205$	2408.31	0.820507
$206$	−1878.76	−0.635434
$207$	−169.731	−0.0569909
$208$	−2207.97	−0.736034
$209$	−169.683	−0.0561588
$210$	0	0
$211$	−4325.34	−1.41123	−0.705613	−	0.708598i	$-0.749328\pi$
$211$	−4325.34	−1.41123	−0.705613	+	0.708598i	$0.749328\pi$
$212$	−1759.00	−0.569851
$213$	3701.32	1.19066
$214$	−1020.84	−0.326091
$215$	488.997	0.155113
$216$	3571.82	1.12515
$217$	0	0
$218$	4415.92	1.37194
$219$	1166.62	0.359969
$220$	609.156	0.186679
$221$	−6214.97	−1.89169
$222$	209.290	0.0632730
$223$	982.970	0.295177	0.147589	−	0.989049i	$-0.452849\pi$
$223$	982.970	0.295177	0.147589	+	0.989049i	$0.452849\pi$
$224$	0	0
$225$	−50.0000	−0.0148148
$226$	−2229.68	−0.656266
$227$	1660.96	0.485648	0.242824	−	0.970070i	$-0.421926\pi$
$227$	1660.96	0.485648	0.242824	+	0.970070i	$0.421926\pi$
$228$	−48.2873	−0.0140259
$229$	574.327	0.165732	0.0828660	−	0.996561i	$-0.473593\pi$
$229$	574.327	0.165732	0.0828660	+	0.996561i	$0.473593\pi$
$230$	983.008	0.281816
$231$	0	0
$232$	743.875	0.210508
$233$	−2316.48	−0.651320	−0.325660	−	0.945487i	$-0.605586\pi$
$233$	−2316.48	−0.651320	−0.325660	+	0.945487i	$0.605586\pi$
$234$	284.169	0.0793876
$235$	588.325	0.163311
$236$	150.977	0.0416432
$237$	5375.93	1.47343
$238$	0	0
$239$	−3659.31	−0.990382	−0.495191	−	0.868784i	$-0.664902\pi$
$239$	−3659.31	−0.990382	−0.495191	+	0.868784i	$0.664902\pi$
$240$	−900.000	−0.242061
$241$	−2446.33	−0.653868	−0.326934	−	0.945047i	$-0.606015\pi$
$241$	−2446.33	−0.653868	−0.326934	+	0.945047i	$0.606015\pi$
$242$	−1875.51	−0.498193
$243$	−560.000	−0.147835
$244$	1945.96	0.510564
$245$	0	0
$246$	−5579.16	−1.44599
$247$	−224.937	−0.0579450
$248$	−4655.62	−1.19207
$249$	3416.62	0.869557
$250$	289.578	0.0732581
$251$	2909.29	0.731605	0.365802	−	0.930693i	$-0.380795\pi$
$251$	2909.29	0.731605	0.365802	+	0.930693i	$0.380795\pi$
$252$	0	0
$253$	3926.43	0.975702
$254$	3756.95	0.928080
$255$	−2533.31	−0.622126
$256$	−3558.38	−0.868744
$257$	−168.680	−0.0409415	−0.0204708	−	0.999790i	$-0.506517\pi$
$257$	−168.680	−0.0409415	−0.0204708	+	0.999790i	$0.506517\pi$
$258$	−1132.82	−0.273359
$259$	0	0
$260$	807.519	0.192616
$261$	−60.3960	−0.0143234
$262$	−3197.68	−0.754020
$263$	−3244.47	−0.760695	−0.380347	−	0.924844i	$-0.624196\pi$
$263$	−3244.47	−0.760695	−0.380347	+	0.924844i	$0.624196\pi$
$264$	−5698.47	−1.32847
$265$	−3339.97	−0.774238
$266$	0	0
$267$	−6901.59	−1.58191
$268$	−1454.60	−0.331543
$269$	2848.65	0.645671	0.322836	−	0.946455i	$-0.395364\pi$
$269$	2848.65	0.645671	0.322836	+	0.946455i	$0.395364\pi$
$270$	1679.55	0.378572
$271$	2850.98	0.639057	0.319529	−	0.947577i	$-0.396475\pi$
$271$	2850.98	0.639057	0.319529	+	0.947577i	$0.396475\pi$
$272$	3647.97	0.813201
$273$	0	0
$274$	4516.62	0.995837
$275$	1156.66	0.253634
$276$	1117.36	0.243685
$277$	2298.63	0.498597	0.249298	−	0.968427i	$-0.419800\pi$
$277$	2298.63	0.498597	0.249298	+	0.968427i	$0.419800\pi$
$278$	6486.55	1.39942
$279$	377.995	0.0811110
$280$	0	0
$281$	6109.20	1.29695	0.648477	−	0.761234i	$-0.275406\pi$
$281$	6109.20	1.29695	0.648477	+	0.761234i	$0.275406\pi$
$282$	−1362.93	−0.287806
$283$	−5854.95	−1.22983	−0.614913	−	0.788595i	$-0.710809\pi$
$283$	−5854.95	−1.22983	−0.614913	+	0.788595i	$0.710809\pi$
$284$	1949.30	0.407288
$285$	−91.6876	−0.0190565
$286$	−6573.75	−1.35914
$287$	0	0
$288$	227.335	0.0465133
$289$	5355.27	1.09002
$290$	349.787	0.0708283
$291$	1090.04	0.219585
$292$	614.403	0.123134
$293$	5135.34	1.02392	0.511962	−	0.859008i	$-0.328919\pi$
$293$	5135.34	1.02392	0.511962	+	0.859008i	$0.328919\pi$
$294$	0	0
$295$	286.675	0.0565792
$296$	445.086	0.0873990
$297$	6708.64	1.31069
$298$	3322.31	0.645827
$299$	5205.01	1.00673
$300$	329.156	0.0633461
$301$	0	0
$302$	4599.85	0.876462
$303$	−7371.64	−1.39766
$304$	132.030	0.0249094
$305$	3694.99	0.693686
$306$	−469.499	−0.0877106
$307$	−2102.97	−0.390954	−0.195477	−	0.980708i	$-0.562625\pi$
$307$	−2102.97	−0.390954	−0.195477	+	0.980708i	$0.562625\pi$
$308$	0	0
$309$	−4054.95	−0.746531
$310$	−2189.18	−0.401088
$311$	5764.30	1.05101	0.525504	−	0.850791i	$-0.323877\pi$
$311$	5764.30	1.05101	0.525504	+	0.850791i	$0.323877\pi$
$312$	−7554.09	−1.37073
$313$	1360.01	0.245599	0.122799	−	0.992432i	$-0.460813\pi$
$313$	1360.01	0.245599	0.122799	+	0.992432i	$0.460813\pi$
$314$	94.1939	0.0169289
$315$	0	0
$316$	2831.23	0.504017
$317$	5138.95	0.910511	0.455256	−	0.890361i	$-0.349548\pi$
$317$	5138.95	0.910511	0.455256	+	0.890361i	$0.349548\pi$
$318$	7737.47	1.36445
$319$	1397.16	0.245222
$320$	−2756.62	−0.481563
$321$	−2203.30	−0.383103
$322$	0	0
$323$	371.637	0.0640200
$324$	1766.91	0.302968
$325$	1533.31	0.261701
$326$	9159.90	1.55620
$327$	9530.94	1.61181
$328$	−11864.9	−1.99735
$329$	0	0
$330$	−2679.55	−0.446983
$331$	1825.70	0.303171	0.151585	−	0.988444i	$-0.451562\pi$
$331$	1825.70	0.303171	0.151585	+	0.988444i	$0.451562\pi$
$332$	1799.37	0.297449
$333$	−36.1370	−0.00594684
$334$	7830.90	1.28290
$335$	−2761.98	−0.450457
$336$	0	0
$337$	153.985	0.0248905	0.0124452	−	0.999923i	$-0.496038\pi$
$337$	153.985	0.0248905	0.0124452	+	0.999923i	$0.496038\pi$
$338$	−3624.76	−0.583317
$339$	−4812.35	−0.771005
$340$	−1334.17	−0.212810
$341$	−8744.25	−1.38864
$342$	−16.9925	−0.00268669
$343$	0	0
$344$	−2409.12	−0.377590
$345$	2121.64	0.331087
$346$	7428.63	1.15424
$347$	4359.39	0.674421	0.337211	−	0.941429i	$-0.390517\pi$
$347$	4359.39	0.674421	0.337211	+	0.941429i	$0.390517\pi$
$348$	397.594	0.0612451
$349$	−1689.00	−0.259054	−0.129527	−	0.991576i	$-0.541346\pi$
$349$	−1689.00	−0.259054	−0.129527	+	0.991576i	$0.541346\pi$
$350$	0	0
$351$	8893.21	1.35238
$352$	−5259.00	−0.796322
$353$	3921.36	0.591254	0.295627	−	0.955303i	$-0.404471\pi$
$353$	3921.36	0.591254	0.295627	+	0.955303i	$0.404471\pi$
$354$	−664.119	−0.0997105
$355$	3701.32	0.553368
$356$	−3634.72	−0.541123
$357$	0	0
$358$	−3342.08	−0.493392
$359$	−2867.86	−0.421616	−0.210808	−	0.977528i	$-0.567609\pi$
$359$	−2867.86	−0.421616	−0.210808	+	0.977528i	$0.567609\pi$
$360$	246.332	0.0360635
$361$	−6845.55	−0.998039
$362$	−2105.07	−0.305636
$363$	−4047.94	−0.585295
$364$	0	0
$365$	1166.62	0.167298
$366$	−8559.90	−1.22249
$367$	−11503.0	−1.63611	−0.818054	−	0.575142i	$-0.804947\pi$
$367$	−11503.0	−1.63611	−0.818054	+	0.575142i	$0.804947\pi$
$368$	−3055.16	−0.432775
$369$	963.325	0.135904
$370$	209.290	0.0294066
$371$	0	0
$372$	−2488.39	−0.346820
$373$	5086.43	0.706073	0.353037	−	0.935610i	$-0.385149\pi$
$373$	5086.43	0.706073	0.353037	+	0.935610i	$0.385149\pi$
$374$	10861.0	1.50163
$375$	625.000	0.0860663
$376$	−2898.47	−0.397546
$377$	1852.12	0.253021
$378$	0	0
$379$	954.827	0.129409	0.0647047	−	0.997904i	$-0.479389\pi$
$379$	954.827	0.129409	0.0647047	+	0.997904i	$0.479389\pi$
$380$	−48.2873	−0.00651864
$381$	8108.68	1.09034
$382$	−5732.81	−0.767843
$383$	−3083.91	−0.411437	−0.205719	−	0.978611i	$-0.565953\pi$
$383$	−3083.91	−0.411437	−0.205719	+	0.978611i	$0.565953\pi$
$384$	1839.37	0.244439
$385$	0	0
$386$	−8185.84	−1.07940
$387$	195.599	0.0256921
$388$	574.068	0.0751131
$389$	−6331.15	−0.825198	−0.412599	−	0.910913i	$-0.635379\pi$
$389$	−6331.15	−0.825198	−0.412599	+	0.910913i	$0.635379\pi$
$390$	−3552.11	−0.461200
$391$	−8599.63	−1.11228
$392$	0	0
$393$	−6901.59	−0.885850
$394$	4523.36	0.578385
$395$	5375.93	0.684791
$396$	243.662	0.0309205
$397$	12133.2	1.53388	0.766939	−	0.641720i	$-0.221779\pi$
$397$	12133.2	1.53388	0.766939	+	0.641720i	$0.221779\pi$
$398$	9416.32	1.18592
$399$	0	0
$400$	−900.000	−0.112500
$401$	−270.669	−0.0337072	−0.0168536	−	0.999858i	$-0.505365\pi$
$401$	−270.669	−0.0337072	−0.0168536	+	0.999858i	$0.505365\pi$
$402$	6398.47	0.793848
$403$	−11591.7	−1.43281
$404$	−3882.27	−0.478095
$405$	3355.00	0.411633
$406$	0	0
$407$	835.967	0.101812
$408$	12480.7	1.51443
$409$	−4019.92	−0.485996	−0.242998	−	0.970027i	$-0.578131\pi$
$409$	−4019.92	−0.485996	−0.242998	+	0.970027i	$0.578131\pi$
$410$	−5579.16	−0.672036
$411$	9748.29	1.16995
$412$	−2135.54	−0.255365
$413$	0	0
$414$	393.203	0.0466784
$415$	3416.62	0.404134
$416$	−6971.51	−0.821650
$417$	14000.0	1.64408
$418$	393.091	0.0459969
$419$	−2437.28	−0.284175	−0.142087	−	0.989854i	$-0.545381\pi$
$419$	−2437.28	−0.284175	−0.142087	+	0.989854i	$0.545381\pi$
$420$	0	0
$421$	−4751.36	−0.550041	−0.275020	−	0.961438i	$-0.588685\pi$
$421$	−4751.36	−0.550041	−0.275020	+	0.961438i	$0.588685\pi$
$422$	10020.2	1.15586
$423$	235.330	0.0270500
$424$	16454.9	1.88472
$425$	−2533.31	−0.289138
$426$	−8574.57	−0.975210
$427$	0	0
$428$	−1160.37	−0.131048
$429$	−14188.2	−1.59677
$430$	−1132.82	−0.127046
$431$	7925.19	0.885714	0.442857	−	0.896592i	$-0.353965\pi$
$431$	7925.19	0.885714	0.442857	+	0.896592i	$0.353965\pi$
$432$	−5220.00	−0.581360
$433$	11487.3	1.27492	0.637462	−	0.770481i	$-0.279984\pi$
$433$	11487.3	1.27492	0.637462	+	0.770481i	$0.279984\pi$
$434$	0	0
$435$	754.950	0.0832117
$436$	5019.47	0.551351
$437$	−311.245	−0.0340706
$438$	−2702.63	−0.294833
$439$	9147.92	0.994548	0.497274	−	0.867594i	$-0.334334\pi$
$439$	9147.92	0.994548	0.497274	+	0.867594i	$0.334334\pi$
$440$	−5698.47	−0.617418
$441$	0	0
$442$	14397.8	1.54939
$443$	1864.35	0.199950	0.0999752	−	0.994990i	$-0.468124\pi$
$443$	1864.35	0.199950	0.0999752	+	0.994990i	$0.468124\pi$
$444$	237.894	0.0254279
$445$	−6901.59	−0.735206
$446$	−2277.17	−0.241765
$447$	7170.58	0.758741
$448$	0	0
$449$	4490.88	0.472022	0.236011	−	0.971750i	$-0.424160\pi$
$449$	4490.88	0.472022	0.236011	+	0.971750i	$0.424160\pi$
$450$	115.831	0.0121341
$451$	−22284.8	−2.32672
$452$	−2534.42	−0.263737
$453$	9927.91	1.02970
$454$	−3847.83	−0.397770
$455$	0	0
$456$	451.713	0.0463890
$457$	−14343.8	−1.46822	−0.734109	−	0.679032i	$-0.762400\pi$
$457$	−14343.8	−1.46822	−0.734109	+	0.679032i	$0.762400\pi$
$458$	−1330.50	−0.135743
$459$	−14693.2	−1.49416
$460$	1117.36	0.113255
$461$	14558.7	1.47086	0.735429	−	0.677602i	$-0.236981\pi$
$461$	14558.7	1.47086	0.735429	+	0.677602i	$0.236981\pi$
$462$	0	0
$463$	−1809.56	−0.181636	−0.0908178	−	0.995868i	$-0.528948\pi$
$463$	−1809.56	−0.181636	−0.0908178	+	0.995868i	$0.528948\pi$
$464$	−1087.13	−0.108769
$465$	−4724.94	−0.471212
$466$	5366.41	0.533464
$467$	−5981.65	−0.592715	−0.296357	−	0.955077i	$-0.595772\pi$
$467$	−5981.65	−0.592715	−0.296357	+	0.955077i	$0.595772\pi$
$468$	323.008	0.0319039
$469$	0	0
$470$	−1362.93	−0.133760
$471$	203.300	0.0198887
$472$	−1412.35	−0.137730
$473$	−4524.84	−0.439857
$474$	−12454.0	−1.20682
$475$	−91.6876	−0.00885666
$476$	0	0
$477$	−1335.99	−0.128241
$478$	8477.25	0.811173
$479$	−11527.5	−1.09959	−0.549796	−	0.835299i	$-0.685295\pi$
$479$	−11527.5	−1.09959	−0.549796	+	0.835299i	$0.685295\pi$
$480$	−2841.69	−0.270218
$481$	1108.19	0.105050
$482$	5667.23	0.535551
$483$	0	0
$484$	−2131.85	−0.200211
$485$	1090.04	0.102054
$486$	1297.31	0.121085
$487$	15791.5	1.46936	0.734682	−	0.678411i	$-0.237331\pi$
$487$	15791.5	1.46936	0.734682	+	0.678411i	$0.237331\pi$
$488$	−18203.9	−1.68863
$489$	19769.9	1.82828
$490$	0	0
$491$	13064.9	1.20083	0.600417	−	0.799687i	$-0.295001\pi$
$491$	13064.9	1.20083	0.600417	+	0.799687i	$0.295001\pi$
$492$	−6341.69	−0.581108
$493$	−3060.04	−0.279548
$494$	521.095	0.0474599
$495$	462.665	0.0420106
$496$	6803.91	0.615937
$497$	0	0
$498$	−7915.04	−0.712211
$499$	−20135.8	−1.80642	−0.903209	−	0.429201i	$-0.858795\pi$
$499$	−20135.8	−1.80642	−0.903209	+	0.429201i	$0.858795\pi$
$500$	329.156	0.0294406
$501$	16901.5	1.50719
$502$	−6739.73	−0.599221
$503$	−751.675	−0.0666313	−0.0333156	−	0.999445i	$-0.510607\pi$
$503$	−751.675	−0.0666313	−0.0333156	+	0.999445i	$0.510607\pi$
$504$	0	0
$505$	−7371.64	−0.649571
$506$	−9096.06	−0.799149
$507$	−7823.38	−0.685302
$508$	4270.44	0.372972
$509$	−12334.5	−1.07410	−0.537049	−	0.843551i	$-0.680461\pi$
$509$	−12334.5	−1.07410	−0.537049	+	0.843551i	$0.680461\pi$
$510$	5868.73	0.509553
$511$	0	0
$512$	11186.4	0.965574
$513$	−531.788	−0.0457681
$514$	390.768	0.0335332
$515$	−4054.95	−0.346956
$516$	−1287.65	−0.109856
$517$	−5443.95	−0.463104
$518$	0	0
$519$	16033.3	1.35604
$520$	−7554.09	−0.637056
$521$	−1736.43	−0.146016	−0.0730082	−	0.997331i	$-0.523260\pi$
$521$	−1736.43	−0.146016	−0.0730082	+	0.997331i	$0.523260\pi$
$522$	139.915	0.0117316
$523$	−1421.42	−0.118842	−0.0594210	−	0.998233i	$-0.518925\pi$
$523$	−1421.42	−0.118842	−0.0594210	+	0.998233i	$0.518925\pi$
$524$	−3634.72	−0.303022
$525$	0	0
$526$	7516.23	0.623048
$527$	19151.6	1.58303
$528$	8327.97	0.686417
$529$	−4964.85	−0.408059
$530$	7737.47	0.634140
$531$	114.670	0.00937148
$532$	0	0
$533$	−29541.6	−2.40073
$534$	15988.4	1.29567
$535$	−2203.30	−0.178050
$536$	13607.3	1.09654
$537$	−7213.25	−0.579655
$538$	−6599.26	−0.528837
$539$	0	0
$540$	1909.11	0.152139
$541$	5773.27	0.458802	0.229401	−	0.973332i	$-0.426323\pi$
$541$	5773.27	0.458802	0.229401	+	0.973332i	$0.426323\pi$
$542$	−6604.64	−0.523420
$543$	−4543.40	−0.359072
$544$	11518.2	0.907793
$545$	9530.94	0.749102
$546$	0	0
$547$	−3941.30	−0.308076	−0.154038	−	0.988065i	$-0.549228\pi$
$547$	−3941.30	−0.308076	−0.154038	+	0.988065i	$0.549228\pi$
$548$	5133.93	0.400202
$549$	1477.99	0.114899
$550$	−2679.55	−0.207739
$551$	−110.751	−0.00856291
$552$	−10452.6	−0.805961
$553$	0	0
$554$	−5325.06	−0.408376
$555$	451.713	0.0345480
$556$	7373.10	0.562390
$557$	−6951.74	−0.528823	−0.264412	−	0.964410i	$-0.585178\pi$
$557$	−6951.74	−0.528823	−0.264412	+	0.964410i	$0.585178\pi$
$558$	−875.673	−0.0664340
$559$	−5998.29	−0.453847
$560$	0	0
$561$	23441.5	1.76417
$562$	−14152.7	−1.06227
$563$	−24284.6	−1.81789	−0.908946	−	0.416913i	$-0.863112\pi$
$563$	−24284.6	−1.81789	−0.908946	+	0.416913i	$0.863112\pi$
$564$	−1549.21	−0.115662
$565$	−4812.35	−0.358331
$566$	13563.7	1.00729
$567$	0	0
$568$	−18235.1	−1.34706
$569$	−21563.4	−1.58873	−0.794363	−	0.607443i	$-0.792195\pi$
$569$	−21563.4	−1.58873	−0.794363	+	0.607443i	$0.792195\pi$
$570$	212.406	0.0156082
$571$	−3689.56	−0.270409	−0.135204	−	0.990818i	$-0.543169\pi$
$571$	−3689.56	−0.270409	−0.135204	+	0.990818i	$0.543169\pi$
$572$	−7472.21	−0.546204
$573$	−12373.2	−0.902090
$574$	0	0
$575$	2121.64	0.153875
$576$	−1102.65	−0.0797634
$577$	22183.9	1.60057	0.800285	−	0.599620i	$-0.204682\pi$
$577$	22183.9	1.60057	0.800285	+	0.599620i	$0.204682\pi$
$578$	−12406.2	−0.892783
$579$	−17667.6	−1.26812
$580$	397.594	0.0284641
$581$	0	0
$582$	−2525.21	−0.179851
$583$	30905.8	2.19552
$584$	−5747.55	−0.407252
$585$	613.325	0.0433468
$586$	−11896.7	−0.838646
$587$	−10605.3	−0.745705	−0.372852	−	0.927891i	$-0.621620\pi$
$587$	−10605.3	−0.745705	−0.372852	+	0.927891i	$0.621620\pi$
$588$	0	0
$589$	693.149	0.0484902
$590$	−664.119	−0.0463412
$591$	9762.83	0.679508
$592$	−650.466	−0.0451588
$593$	−6277.25	−0.434698	−0.217349	−	0.976094i	$-0.569741\pi$
$593$	−6277.25	−0.434698	−0.217349	+	0.976094i	$0.569741\pi$
$594$	−15541.4	−1.07352
$595$	0	0
$596$	3776.39	0.259542
$597$	20323.4	1.39327
$598$	−12058.1	−0.824567
$599$	−9970.73	−0.680122	−0.340061	−	0.940403i	$-0.610448\pi$
$599$	−9970.73	−0.680122	−0.340061	+	0.940403i	$0.610448\pi$
$600$	−3079.16	−0.209510
$601$	24619.2	1.67094	0.835472	−	0.549533i	$-0.185194\pi$
$601$	24619.2	1.67094	0.835472	+	0.549533i	$0.185194\pi$
$602$	0	0
$603$	−1104.79	−0.0746113
$604$	5228.53	0.352228
$605$	−4047.94	−0.272020
$606$	17077.3	1.14475
$607$	−11252.9	−0.752460	−0.376230	−	0.926526i	$-0.622780\pi$
$607$	−11252.9	−0.752460	−0.376230	+	0.926526i	$0.622780\pi$
$608$	416.876	0.0278068
$609$	0	0
$610$	−8559.90	−0.568164
$611$	−7216.69	−0.477833
$612$	−533.668	−0.0352487
$613$	−15293.2	−1.00765	−0.503824	−	0.863807i	$-0.668074\pi$
$613$	−15293.2	−1.00765	−0.503824	+	0.863807i	$0.668074\pi$
$614$	4871.79	0.320211
$615$	−12041.6	−0.789533
$616$	0	0
$617$	−17589.4	−1.14769	−0.573843	−	0.818966i	$-0.694548\pi$
$617$	−17589.4	−1.14769	−0.573843	+	0.818966i	$0.694548\pi$
$618$	9393.80	0.611446
$619$	23467.4	1.52380	0.761900	−	0.647694i	$-0.224267\pi$
$619$	23467.4	1.52380	0.761900	+	0.647694i	$0.224267\pi$
$620$	−2488.39	−0.161187
$621$	12305.5	0.795173
$622$	−13353.7	−0.860829
$623$	0	0
$624$	11039.8	0.708249
$625$	625.000	0.0400000
$626$	−3150.64	−0.201158
$627$	848.413	0.0540388
$628$	107.068	0.00680330
$629$	−1830.93	−0.116063
$630$	0	0
$631$	−6040.86	−0.381114	−0.190557	−	0.981676i	$-0.561029\pi$
$631$	−6040.86	−0.381114	−0.190557	+	0.981676i	$0.561029\pi$
$632$	−26485.3	−1.66698
$633$	21626.7	1.35795
$634$	−11905.0	−0.745755
$635$	8108.68	0.506745
$636$	8794.99	0.548340
$637$	0	0
$638$	−3236.68	−0.200849
$639$	1480.53	0.0916569
$640$	1839.37	0.113605
$641$	25111.6	1.54735	0.773673	−	0.633586i	$-0.218418\pi$
$641$	25111.6	1.54735	0.773673	+	0.633586i	$0.218418\pi$
$642$	5104.22	0.313781
$643$	−3095.03	−0.189823	−0.0949113	−	0.995486i	$-0.530257\pi$
$643$	−3095.03	−0.189823	−0.0949113	+	0.995486i	$0.530257\pi$
$644$	0	0
$645$	−2444.99	−0.149258
$646$	−860.944	−0.0524356
$647$	−9178.63	−0.557727	−0.278863	−	0.960331i	$-0.589958\pi$
$647$	−9178.63	−0.557727	−0.278863	+	0.960331i	$0.589958\pi$
$648$	−16528.9	−1.00203
$649$	−2652.69	−0.160443
$650$	−3552.11	−0.214346
$651$	0	0
$652$	10411.8	0.625397
$653$	−14438.4	−0.865265	−0.432632	−	0.901570i	$-0.642415\pi$
$653$	−14438.4	−0.865265	−0.432632	+	0.901570i	$0.642415\pi$
$654$	−22079.6	−1.32015
$655$	−6901.59	−0.411706
$656$	17339.8	1.03202
$657$	466.650	0.0277104
$658$	0	0
$659$	−2900.64	−0.171461	−0.0857305	−	0.996318i	$-0.527322\pi$
$659$	−2900.64	−0.171461	−0.0857305	+	0.996318i	$0.527322\pi$
$660$	−3045.78	−0.179632
$661$	−9976.52	−0.587053	−0.293526	−	0.955951i	$-0.594829\pi$
$661$	−9976.52	−0.587053	−0.293526	+	0.955951i	$0.594829\pi$
$662$	−4229.46	−0.248312
$663$	31074.9	1.82028
$664$	−16832.5	−0.983777
$665$	0	0
$666$	83.7159	0.00487076
$667$	2562.77	0.148772
$668$	8901.19	0.515565
$669$	−4914.85	−0.284034
$670$	6398.47	0.368947
$671$	−34190.8	−1.96710
$672$	0	0
$673$	20760.8	1.18911	0.594554	−	0.804055i	$-0.297329\pi$
$673$	20760.8	1.18911	0.594554	+	0.804055i	$0.297329\pi$
$674$	−356.725	−0.0203866
$675$	3625.00	0.206706
$676$	−4120.18	−0.234421
$677$	−3209.13	−0.182181	−0.0910907	−	0.995843i	$-0.529035\pi$
$677$	−3209.13	−0.182181	−0.0910907	+	0.995843i	$0.529035\pi$
$678$	11148.4	0.631492
$679$	0	0
$680$	12480.7	0.703845
$681$	−8304.82	−0.467315
$682$	20257.2	1.13737
$683$	4333.57	0.242781	0.121391	−	0.992605i	$-0.461265\pi$
$683$	4333.57	0.242781	0.121391	+	0.992605i	$0.461265\pi$
$684$	−19.3149	−0.00107971
$685$	9748.29	0.543741
$686$	0	0
$687$	−2871.64	−0.159476
$688$	3520.78	0.195100
$689$	40969.8	2.26535
$690$	−4915.04	−0.271177
$691$	14446.0	0.795297	0.397649	−	0.917538i	$-0.369826\pi$
$691$	14446.0	0.795297	0.397649	+	0.917538i	$0.369826\pi$
$692$	8443.94	0.463859
$693$	0	0
$694$	−10099.1	−0.552385
$695$	14000.0	0.764101
$696$	−3719.37	−0.202561
$697$	48808.1	2.65242
$698$	3912.77	0.212179
$699$	11582.4	0.626733
$700$	0	0
$701$	−859.801	−0.0463256	−0.0231628	−	0.999732i	$-0.507374\pi$
$701$	−859.801	−0.0463256	−0.0231628	+	0.999732i	$0.507374\pi$
$702$	−20602.2	−1.10767
$703$	−66.2663	−0.00355517
$704$	25507.9	1.36557
$705$	−2941.62	−0.157146
$706$	−9084.31	−0.484267
$707$	0	0
$708$	−754.887	−0.0400712
$709$	−7979.13	−0.422655	−0.211327	−	0.977415i	$-0.567779\pi$
$709$	−7979.13	−0.422655	−0.211327	+	0.977415i	$0.567779\pi$
$710$	−8574.57	−0.453236
$711$	2150.37	0.113425
$712$	34001.7	1.78970
$713$	−16039.4	−0.842467
$714$	0	0
$715$	−14188.2	−0.742110
$716$	−3798.86	−0.198282
$717$	18296.6	0.952995
$718$	6643.76	0.345325
$719$	33703.3	1.74815	0.874076	−	0.485790i	$-0.161468\pi$
$719$	33703.3	1.74815	0.874076	+	0.485790i	$0.161468\pi$
$720$	−360.000	−0.0186339
$721$	0	0
$722$	15858.6	0.817444
$723$	12231.7	0.629185
$724$	−2392.78	−0.122827
$725$	754.950	0.0386733
$726$	9377.57	0.479386
$727$	30277.0	1.54458	0.772290	−	0.635270i	$-0.219111\pi$
$727$	30277.0	1.54458	0.772290	+	0.635270i	$0.219111\pi$
$728$	0	0
$729$	20917.0	1.06269
$730$	−2702.63	−0.137026
$731$	9910.27	0.501429
$732$	−9729.82	−0.491291
$733$	−19363.9	−0.975749	−0.487874	−	0.872914i	$-0.662228\pi$
$733$	−19363.9	−0.975749	−0.487874	+	0.872914i	$0.662228\pi$
$734$	26648.1	1.34005
$735$	0	0
$736$	−9646.45	−0.483115
$737$	25557.4	1.27737
$738$	−2231.66	−0.111313
$739$	24952.4	1.24207	0.621035	−	0.783783i	$-0.286713\pi$
$739$	24952.4	1.24207	0.621035	+	0.783783i	$0.286713\pi$
$740$	237.894	0.0118178
$741$	1124.69	0.0557576
$742$	0	0
$743$	−8154.54	−0.402640	−0.201320	−	0.979526i	$-0.564523\pi$
$743$	−8154.54	−0.402640	−0.201320	+	0.979526i	$0.564523\pi$
$744$	23278.1	1.14707
$745$	7170.58	0.352631
$746$	−11783.3	−0.578310
$747$	1366.65	0.0669386
$748$	12345.5	0.603469
$749$	0	0
$750$	−1447.89	−0.0704926
$751$	−4311.26	−0.209481	−0.104740	−	0.994500i	$-0.533401\pi$
$751$	−4311.26	−0.209481	−0.104740	+	0.994500i	$0.533401\pi$
$752$	4235.94	0.205411
$753$	−14546.4	−0.703987
$754$	−4290.66	−0.207237
$755$	9927.91	0.478561
$756$	0	0
$757$	3624.79	0.174036	0.0870179	−	0.996207i	$-0.472266\pi$
$757$	3624.79	0.174036	0.0870179	+	0.996207i	$0.472266\pi$
$758$	−2211.98	−0.105993
$759$	−19632.1	−0.938869
$760$	451.713	0.0215597
$761$	−20576.4	−0.980150	−0.490075	−	0.871680i	$-0.663031\pi$
$761$	−20576.4	−0.980150	−0.490075	+	0.871680i	$0.663031\pi$
$762$	−18784.8	−0.893045
$763$	0	0
$764$	−6516.34	−0.308577
$765$	−1013.32	−0.0478913
$766$	7144.26	0.336988
$767$	−3516.50	−0.165546
$768$	17791.9	0.835949
$769$	3066.14	0.143781	0.0718907	−	0.997413i	$-0.477097\pi$
$769$	3066.14	0.143781	0.0718907	+	0.997413i	$0.477097\pi$
$770$	0	0
$771$	843.400	0.0393960
$772$	−9304.64	−0.433784
$773$	19387.0	0.902074	0.451037	−	0.892505i	$-0.351054\pi$
$773$	19387.0	0.902074	0.451037	+	0.892505i	$0.351054\pi$
$774$	−453.129	−0.0210432
$775$	−4724.94	−0.219000
$776$	−5370.23	−0.248428
$777$	0	0
$778$	14666.9	0.675879
$779$	1766.50	0.0812470
$780$	−4037.59	−0.185345
$781$	−34249.4	−1.56919
$782$	19922.1	0.911015
$783$	4378.71	0.199850
$784$	0	0
$785$	203.300	0.00924342
$786$	15988.4	0.725556
$787$	−43363.4	−1.96409	−0.982044	−	0.188651i	$-0.939588\pi$
$787$	−43363.4	−1.96409	−0.982044	+	0.188651i	$0.939588\pi$
$788$	5141.59	0.232439
$789$	16222.4	0.731979
$790$	−12454.0	−0.560878
$791$	0	0
$792$	−2279.39	−0.102266
$793$	−45324.6	−2.02966
$794$	−28108.2	−1.25632
$795$	16699.9	0.745011
$796$	10703.3	0.476593
$797$	−17132.6	−0.761439	−0.380720	−	0.924691i	$-0.624324\pi$
$797$	−17132.6	−0.761439	−0.380720	+	0.924691i	$0.624324\pi$
$798$	0	0
$799$	11923.3	0.527929
$800$	−2841.69	−0.125586
$801$	−2760.63	−0.121776
$802$	627.039	0.0276079
$803$	−10795.1	−0.474411
$804$	7272.98	0.319028
$805$	0	0
$806$	26853.6	1.17355
$807$	−14243.3	−0.621297
$808$	36317.5	1.58124
$809$	−1080.49	−0.0469566	−0.0234783	−	0.999724i	$-0.507474\pi$
$809$	−1080.49	−0.0469566	−0.0234783	+	0.999724i	$0.507474\pi$
$810$	−7772.28	−0.337148
$811$	−19593.9	−0.848378	−0.424189	−	0.905574i	$-0.639441\pi$
$811$	−19593.9	−0.848378	−0.424189	+	0.905574i	$0.639441\pi$
$812$	0	0
$813$	−14254.9	−0.614933
$814$	−1936.62	−0.0833889
$815$	19769.9	0.849706
$816$	−18239.8	−0.782503
$817$	358.680	0.0153594
$818$	9312.66	0.398056
$819$	0	0
$820$	−6341.69	−0.270075
$821$	5123.80	0.217810	0.108905	−	0.994052i	$-0.465266\pi$
$821$	5123.80	0.217810	0.108905	+	0.994052i	$0.465266\pi$
$822$	−22583.1	−0.958244
$823$	−13184.1	−0.558405	−0.279202	−	0.960232i	$-0.590070\pi$
$823$	−13184.1	−0.558405	−0.279202	+	0.960232i	$0.590070\pi$
$824$	19977.3	0.844591
$825$	−5783.31	−0.244060
$826$	0	0
$827$	24658.7	1.03684	0.518421	−	0.855126i	$-0.326520\pi$
$827$	24658.7	1.03684	0.518421	+	0.855126i	$0.326520\pi$
$828$	446.944	0.0187589
$829$	28562.3	1.19664	0.598318	−	0.801259i	$-0.295836\pi$
$829$	28562.3	1.19664	0.598318	+	0.801259i	$0.295836\pi$
$830$	−7915.04	−0.331006
$831$	−11493.1	−0.479775
$832$	33814.1	1.40901
$833$	0	0
$834$	−32432.7	−1.34659
$835$	16901.5	0.700481
$836$	446.817	0.0184850
$837$	−27404.6	−1.13171
$838$	5646.27	0.232753
$839$	−31106.0	−1.27997	−0.639987	−	0.768386i	$-0.721060\pi$
$839$	−31106.0	−1.27997	−0.639987	+	0.768386i	$0.721060\pi$
$840$	0	0
$841$	−23477.1	−0.962609
$842$	11007.1	0.450511
$843$	−30546.0	−1.24800
$844$	11389.7	0.464514
$845$	−7823.38	−0.318500
$846$	−545.171	−0.0221553
$847$	0	0
$848$	−24047.8	−0.973827
$849$	29274.7	1.18340
$850$	5868.73	0.236819
$851$	1533.39	0.0617674
$852$	−9746.50	−0.391913
$853$	20567.9	0.825596	0.412798	−	0.910823i	$-0.364552\pi$
$853$	20567.9	0.825596	0.412798	+	0.910823i	$0.364552\pi$
$854$	0	0
$855$	−36.6750	−0.00146697
$856$	10854.9	0.433426
$857$	6459.44	0.257468	0.128734	−	0.991679i	$-0.458909\pi$
$857$	6459.44	0.257468	0.128734	+	0.991679i	$0.458909\pi$
$858$	32868.7	1.30783
$859$	−48214.4	−1.91508	−0.957541	−	0.288298i	$-0.906910\pi$
$859$	−48214.4	−1.91508	−0.957541	+	0.288298i	$0.906910\pi$
$860$	−1287.65	−0.0510565
$861$	0	0
$862$	−18359.7	−0.725445
$863$	−31709.5	−1.25076	−0.625378	−	0.780322i	$-0.715055\pi$
$863$	−31709.5	−1.25076	−0.625378	+	0.780322i	$0.715055\pi$
$864$	−16481.8	−0.648984
$865$	16033.3	0.630230
$866$	−26611.7	−1.04423
$867$	−26776.4	−1.04887
$868$	0	0
$869$	−49745.1	−1.94187
$870$	−1748.94	−0.0681546
$871$	33879.8	1.31800
$872$	−46955.6	−1.82353
$873$	436.015	0.0169036
$874$	721.037	0.0279055
$875$	0	0
$876$	−3072.01	−0.118486
$877$	25654.8	0.987799	0.493900	−	0.869519i	$-0.335571\pi$
$877$	25654.8	0.987799	0.493900	+	0.869519i	$0.335571\pi$
$878$	−21192.3	−0.814585
$879$	−25676.7	−0.985272
$880$	8327.97	0.319018
$881$	−11470.4	−0.438647	−0.219323	−	0.975652i	$-0.570385\pi$
$881$	−11470.4	−0.438647	−0.219323	+	0.975652i	$0.570385\pi$
$882$	0	0
$883$	39124.0	1.49108	0.745542	−	0.666459i	$-0.232191\pi$
$883$	39124.0	1.49108	0.745542	+	0.666459i	$0.232191\pi$
$884$	16365.6	0.622663
$885$	−1433.38	−0.0544434
$886$	−4319.01	−0.163770
$887$	15585.8	0.589987	0.294994	−	0.955499i	$-0.404682\pi$
$887$	15585.8	0.589987	0.294994	+	0.955499i	$0.404682\pi$
$888$	−2225.43	−0.0840997
$889$	0	0
$890$	15988.4	0.602171
$891$	−31044.8	−1.16727
$892$	−2588.40	−0.0971594
$893$	431.537	0.0161711
$894$	−16611.6	−0.621447
$895$	−7213.25	−0.269399
$896$	0	0
$897$	−26025.1	−0.968731
$898$	−10403.7	−0.386610
$899$	−5707.34	−0.211736
$900$	131.662	0.00487639
$901$	−67689.6	−2.50285
$902$	51625.6	1.90570
$903$	0	0
$904$	23708.8	0.872280
$905$	−4543.40	−0.166881
$906$	−22999.2	−0.843376
$907$	27596.1	1.01027	0.505134	−	0.863041i	$-0.331443\pi$
$907$	27596.1	1.01027	0.505134	+	0.863041i	$0.331443\pi$
$908$	−4373.73	−0.159854
$909$	−2948.65	−0.107592
$910$	0	0
$911$	−14396.2	−0.523565	−0.261782	−	0.965127i	$-0.584310\pi$
$911$	−14396.2	−0.523565	−0.261782	+	0.965127i	$0.584310\pi$
$912$	−660.151	−0.0239691
$913$	−31615.1	−1.14601
$914$	33229.2	1.20254
$915$	−18474.9	−0.667500
$916$	−1512.35	−0.0545517
$917$	0	0
$918$	34038.7	1.22379
$919$	10279.6	0.368978	0.184489	−	0.982835i	$-0.440937\pi$
$919$	10279.6	0.368978	0.184489	+	0.982835i	$0.440937\pi$
$920$	−10452.6	−0.374577
$921$	10514.8	0.376196
$922$	−33727.0	−1.20471
$923$	−45402.2	−1.61910
$924$	0	0
$925$	451.713	0.0160565
$926$	4192.06	0.148769
$927$	−1621.98	−0.0574680
$928$	−3432.53	−0.121421
$929$	−6499.87	−0.229552	−0.114776	−	0.993391i	$-0.536615\pi$
$929$	−6499.87	−0.229552	−0.114776	+	0.993391i	$0.536615\pi$
$930$	10945.9	0.385947
$931$	0	0
$932$	6099.86	0.214386
$933$	−28821.5	−1.01133
$934$	13857.2	0.485463
$935$	23441.5	0.819913
$936$	−3021.64	−0.105518
$937$	10269.8	0.358056	0.179028	−	0.983844i	$-0.442705\pi$
$937$	10269.8	0.358056	0.179028	+	0.983844i	$0.442705\pi$
$938$	0	0
$939$	−6800.06	−0.236328
$940$	−1549.21	−0.0537548
$941$	−34396.2	−1.19159	−0.595794	−	0.803137i	$-0.703163\pi$
$941$	−34396.2	−1.19159	−0.595794	+	0.803137i	$0.703163\pi$
$942$	−470.969	−0.0162898
$943$	−40876.5	−1.41158
$944$	2064.06	0.0711647
$945$	0	0
$946$	10482.4	0.360265
$947$	27192.1	0.933078	0.466539	−	0.884501i	$-0.345501\pi$
$947$	27192.1	0.933078	0.466539	+	0.884501i	$0.345501\pi$
$948$	−14156.2	−0.484990
$949$	−14310.4	−0.489500
$950$	212.406	0.00725406
$951$	−25694.7	−0.876140
$952$	0	0
$953$	49965.2	1.69836	0.849178	−	0.528107i	$-0.177098\pi$
$953$	49965.2	1.69836	0.849178	+	0.528107i	$0.177098\pi$
$954$	3094.99	0.105036
$955$	−12373.2	−0.419253
$956$	9635.88	0.325990
$957$	−6985.78	−0.235965
$958$	26704.9	0.900622
$959$	0	0
$960$	13783.1	0.463384
$961$	5929.05	0.199022
$962$	−2567.25	−0.0860411
$963$	−881.320	−0.0294913
$964$	6441.80	0.215225
$965$	−17667.6	−0.589368
$966$	0	0
$967$	−16755.5	−0.557208	−0.278604	−	0.960406i	$-0.589872\pi$
$967$	−16755.5	−0.557208	−0.278604	+	0.960406i	$0.589872\pi$
$968$	19942.8	0.662176
$969$	−1858.19	−0.0616033
$970$	−2525.21	−0.0835872
$971$	37617.4	1.24325	0.621626	−	0.783314i	$-0.286472\pi$
$971$	37617.4	1.24325	0.621626	+	0.783314i	$0.286472\pi$
$972$	1474.62	0.0486610
$973$	0	0
$974$	−36583.0	−1.20348
$975$	−7666.56	−0.251822
$976$	26603.9	0.872511
$977$	−27690.9	−0.906767	−0.453384	−	0.891315i	$-0.649783\pi$
$977$	−27690.9	−0.906767	−0.453384	+	0.891315i	$0.649783\pi$
$978$	−45799.5	−1.49745
$979$	63862.5	2.08483
$980$	0	0
$981$	3812.38	0.124077
$982$	−30266.4	−0.983544
$983$	22754.2	0.738299	0.369149	−	0.929370i	$-0.379649\pi$
$983$	22754.2	0.738299	0.369149	+	0.929370i	$0.379649\pi$
$984$	59324.6	1.92195
$985$	9762.83	0.315807
$986$	7088.96	0.228964
$987$	0	0
$988$	592.316	0.0190729
$989$	−8299.80	−0.266854
$990$	−1071.82	−0.0344088
$991$	−55470.9	−1.77809	−0.889047	−	0.457816i	$-0.848632\pi$
$991$	−55470.9	−1.77809	−0.889047	+	0.457816i	$0.848632\pi$
$992$	21482.9	0.687583
$993$	−9128.50	−0.291726
$994$	0	0
$995$	20323.4	0.647531
$996$	−8996.83	−0.286220
$997$	15181.9	0.482264	0.241132	−	0.970492i	$-0.422481\pi$
$997$	15181.9	0.482264	0.241132	+	0.970492i	$0.422481\pi$
$998$	46647.1	1.47955
$999$	2619.93	0.0829740

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.a.i.1.1	✓	2
3.2	odd	2		2205.4.a.x.1.2		2
5.4	even	2		1225.4.a.q.1.2		2
7.2	even	3		245.4.e.k.116.2		4
7.3	odd	6		245.4.e.j.226.2		4
7.4	even	3		245.4.e.k.226.2		4
7.5	odd	6		245.4.e.j.116.2		4
7.6	odd	2		245.4.a.j.1.1	yes	2
21.20	even	2		2205.4.a.w.1.2		2
35.34	odd	2		1225.4.a.p.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.4.a.i.1.1	✓	2	1.1	even	1	trivial
245.4.a.j.1.1	yes	2	7.6	odd	2
245.4.e.j.116.2		4	7.5	odd	6
245.4.e.j.226.2		4	7.3	odd	6
245.4.e.k.116.2		4	7.2	even	3
245.4.e.k.226.2		4	7.4	even	3
1225.4.a.p.1.2		2	35.34	odd	2
1225.4.a.q.1.2		2	5.4	even	2
2205.4.a.w.1.2		2	21.20	even	2
2205.4.a.x.1.2		2	3.2	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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.a (trivial)

\(f(q)\)	\(=\)	\(q-2.31662 q^{2} -5.00000 q^{3} -2.63325 q^{4} -5.00000 q^{5} +11.5831 q^{6} +24.6332 q^{8} -2.00000 q^{9} +O(q^{10})\)	\(q-2.31662 q^{2} -5.00000 q^{3} -2.63325 q^{4} -5.00000 q^{5} +11.5831 q^{6} +24.6332 q^{8} -2.00000 q^{9} +11.5831 q^{10} +46.2665 q^{11} +13.1662 q^{12} +61.3325 q^{13} +25.0000 q^{15} -36.0000 q^{16} -101.332 q^{17} +4.63325 q^{18} -3.66750 q^{19} +13.1662 q^{20} -107.182 q^{22} +84.8655 q^{23} -123.166 q^{24} +25.0000 q^{25} -142.084 q^{26} +145.000 q^{27} +30.1980 q^{29} -57.9156 q^{30} -188.997 q^{31} -113.668 q^{32} -231.332 q^{33} +234.749 q^{34} +5.26650 q^{36} +18.0685 q^{37} +8.49623 q^{38} -306.662 q^{39} -123.166 q^{40} -481.662 q^{41} -97.7995 q^{43} -121.831 q^{44} +10.0000 q^{45} -196.602 q^{46} -117.665 q^{47} +180.000 q^{48} -57.9156 q^{50} +506.662 q^{51} -161.504 q^{52} +667.995 q^{53} -335.911 q^{54} -231.332 q^{55} +18.3375 q^{57} -69.9574 q^{58} -57.3350 q^{59} -65.8312 q^{60} -738.997 q^{61} +437.836 q^{62} +551.325 q^{64} -306.662 q^{65} +535.911 q^{66} +552.396 q^{67} +266.834 q^{68} -424.327 q^{69} -740.264 q^{71} -49.2665 q^{72} -233.325 q^{73} -41.8580 q^{74} -125.000 q^{75} +9.65745 q^{76} +710.422 q^{78} -1075.19 q^{79} +180.000 q^{80} -671.000 q^{81} +1115.83 q^{82} -683.325 q^{83} +506.662 q^{85} +226.565 q^{86} -150.990 q^{87} +1139.69 q^{88} +1380.32 q^{89} -23.1662 q^{90} -223.472 q^{92} +944.987 q^{93} +272.586 q^{94} +18.3375 q^{95} +568.338 q^{96} -218.008 q^{97} -92.5330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 10 q^{3} + 8 q^{4} - 10 q^{5} - 10 q^{6} + 36 q^{8} - 4 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 10 * q^3 + 8 * q^4 - 10 * q^5 - 10 * q^6 + 36 * q^8 - 4 * q^9	\( 2 q + 2 q^{2} - 10 q^{3} + 8 q^{4} - 10 q^{5} - 10 q^{6} + 36 q^{8} - 4 q^{9} - 10 q^{10} + 66 q^{11} - 40 q^{12} - 10 q^{13} + 50 q^{15} - 72 q^{16} - 70 q^{17} - 4 q^{18} - 140 q^{19} - 40 q^{20} - 22 q^{22} - 16 q^{23} - 180 q^{24} + 50 q^{25} - 450 q^{26} + 290 q^{27} - 258 q^{29} + 50 q^{30} + 20 q^{31} - 360 q^{32} - 330 q^{33} + 370 q^{34} - 16 q^{36} + 328 q^{37} - 580 q^{38} + 50 q^{39} - 180 q^{40} - 300 q^{41} - 116 q^{43} + 88 q^{44} + 20 q^{45} - 632 q^{46} + 30 q^{47} + 360 q^{48} + 50 q^{50} + 350 q^{51} - 920 q^{52} + 540 q^{53} + 290 q^{54} - 330 q^{55} + 700 q^{57} - 1314 q^{58} - 380 q^{59} + 200 q^{60} - 1080 q^{61} + 1340 q^{62} - 224 q^{64} + 50 q^{65} + 110 q^{66} + 468 q^{67} + 600 q^{68} + 80 q^{69} - 1056 q^{71} - 72 q^{72} + 860 q^{73} + 1296 q^{74} - 250 q^{75} - 1440 q^{76} + 2250 q^{78} + 158 q^{79} + 360 q^{80} - 1342 q^{81} + 1900 q^{82} - 40 q^{83} + 350 q^{85} + 148 q^{86} + 1290 q^{87} + 1364 q^{88} + 240 q^{89} + 20 q^{90} - 1296 q^{92} - 100 q^{93} + 910 q^{94} + 700 q^{95} + 1800 q^{96} - 1630 q^{97} - 132 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 10 * q^3 + 8 * q^4 - 10 * q^5 - 10 * q^6 + 36 * q^8 - 4 * q^9 - 10 * q^10 + 66 * q^11 - 40 * q^12 - 10 * q^13 + 50 * q^15 - 72 * q^16 - 70 * q^17 - 4 * q^18 - 140 * q^19 - 40 * q^20 - 22 * q^22 - 16 * q^23 - 180 * q^24 + 50 * q^25 - 450 * q^26 + 290 * q^27 - 258 * q^29 + 50 * q^30 + 20 * q^31 - 360 * q^32 - 330 * q^33 + 370 * q^34 - 16 * q^36 + 328 * q^37 - 580 * q^38 + 50 * q^39 - 180 * q^40 - 300 * q^41 - 116 * q^43 + 88 * q^44 + 20 * q^45 - 632 * q^46 + 30 * q^47 + 360 * q^48 + 50 * q^50 + 350 * q^51 - 920 * q^52 + 540 * q^53 + 290 * q^54 - 330 * q^55 + 700 * q^57 - 1314 * q^58 - 380 * q^59 + 200 * q^60 - 1080 * q^61 + 1340 * q^62 - 224 * q^64 + 50 * q^65 + 110 * q^66 + 468 * q^67 + 600 * q^68 + 80 * q^69 - 1056 * q^71 - 72 * q^72 + 860 * q^73 + 1296 * q^74 - 250 * q^75 - 1440 * q^76 + 2250 * q^78 + 158 * q^79 + 360 * q^80 - 1342 * q^81 + 1900 * q^82 - 40 * q^83 + 350 * q^85 + 148 * q^86 + 1290 * q^87 + 1364 * q^88 + 240 * q^89 + 20 * q^90 - 1296 * q^92 - 100 * q^93 + 910 * q^94 + 700 * q^95 + 1800 * q^96 - 1630 * q^97 - 132 * q^99

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