LMFDB - Embedded newform 735.4.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,4,Mod(1,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("735.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	735.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:	$43.3664038542$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 105)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	735.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.82843 q^{2} +3.00000 q^{3} +6.65685 q^{4} -5.00000 q^{5} -11.4853 q^{6} +5.14214 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.82843 q^{2} +3.00000 q^{3} +6.65685 q^{4} -5.00000 q^{5} -11.4853 q^{6} +5.14214 q^{8} +9.00000 q^{9} +19.1421 q^{10} +48.5685 q^{11} +19.9706 q^{12} +43.6569 q^{13} -15.0000 q^{15} -72.9411 q^{16} +67.6569 q^{17} -34.4558 q^{18} +93.2548 q^{19} -33.2843 q^{20} -185.941 q^{22} -104.167 q^{23} +15.4264 q^{24} +25.0000 q^{25} -167.137 q^{26} +27.0000 q^{27} -58.7351 q^{29} +57.4264 q^{30} +9.08831 q^{31} +238.113 q^{32} +145.706 q^{33} -259.019 q^{34} +59.9117 q^{36} -252.676 q^{37} -357.019 q^{38} +130.971 q^{39} -25.7107 q^{40} -276.274 q^{41} -92.6375 q^{43} +323.314 q^{44} -45.0000 q^{45} +398.794 q^{46} +582.794 q^{47} -218.823 q^{48} -95.7107 q^{50} +202.971 q^{51} +290.617 q^{52} +623.019 q^{53} -103.368 q^{54} -242.843 q^{55} +279.765 q^{57} +224.863 q^{58} +524.999 q^{59} -99.8528 q^{60} +352.794 q^{61} -34.7939 q^{62} -328.068 q^{64} -218.284 q^{65} -557.823 q^{66} -736.520 q^{67} +450.382 q^{68} -312.500 q^{69} -492.264 q^{71} +46.2792 q^{72} -1164.75 q^{73} +967.352 q^{74} +75.0000 q^{75} +620.784 q^{76} -501.411 q^{78} -872.195 q^{79} +364.706 q^{80} +81.0000 q^{81} +1057.70 q^{82} +529.588 q^{83} -338.284 q^{85} +354.656 q^{86} -176.205 q^{87} +249.746 q^{88} +385.216 q^{89} +172.279 q^{90} -693.421 q^{92} +27.2649 q^{93} -2231.18 q^{94} -466.274 q^{95} +714.338 q^{96} +463.892 q^{97} +437.117 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 6 q^{3} + 2 q^{4} - 10 q^{5} - 6 q^{6} - 18 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 6 * q^3 + 2 * q^4 - 10 * q^5 - 6 * q^6 - 18 * q^8 + 18 * q^9	\( 2 q - 2 q^{2} + 6 q^{3} + 2 q^{4} - 10 q^{5} - 6 q^{6} - 18 q^{8} + 18 q^{9} + 10 q^{10} - 16 q^{11} + 6 q^{12} + 76 q^{13} - 30 q^{15} - 78 q^{16} + 124 q^{17} - 18 q^{18} + 96 q^{19} - 10 q^{20} - 304 q^{22} - 16 q^{23} - 54 q^{24} + 50 q^{25} - 108 q^{26} + 54 q^{27} + 188 q^{29} + 30 q^{30} + 120 q^{31} + 414 q^{32} - 48 q^{33} - 156 q^{34} + 18 q^{36} - 132 q^{37} - 352 q^{38} + 228 q^{39} + 90 q^{40} - 100 q^{41} - 536 q^{43} + 624 q^{44} - 90 q^{45} + 560 q^{46} + 928 q^{47} - 234 q^{48} - 50 q^{50} + 372 q^{51} + 140 q^{52} + 884 q^{53} - 54 q^{54} + 80 q^{55} + 288 q^{57} + 676 q^{58} - 104 q^{59} - 30 q^{60} + 468 q^{61} + 168 q^{62} + 34 q^{64} - 380 q^{65} - 912 q^{66} - 1688 q^{67} + 188 q^{68} - 48 q^{69} - 136 q^{71} - 162 q^{72} - 508 q^{73} + 1188 q^{74} + 150 q^{75} + 608 q^{76} - 324 q^{78} - 432 q^{79} + 390 q^{80} + 162 q^{81} + 1380 q^{82} + 584 q^{83} - 620 q^{85} - 456 q^{86} + 564 q^{87} + 1744 q^{88} + 1404 q^{89} + 90 q^{90} - 1104 q^{92} + 360 q^{93} - 1600 q^{94} - 480 q^{95} + 1242 q^{96} + 1188 q^{97} - 144 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 6 * q^3 + 2 * q^4 - 10 * q^5 - 6 * q^6 - 18 * q^8 + 18 * q^9 + 10 * q^10 - 16 * q^11 + 6 * q^12 + 76 * q^13 - 30 * q^15 - 78 * q^16 + 124 * q^17 - 18 * q^18 + 96 * q^19 - 10 * q^20 - 304 * q^22 - 16 * q^23 - 54 * q^24 + 50 * q^25 - 108 * q^26 + 54 * q^27 + 188 * q^29 + 30 * q^30 + 120 * q^31 + 414 * q^32 - 48 * q^33 - 156 * q^34 + 18 * q^36 - 132 * q^37 - 352 * q^38 + 228 * q^39 + 90 * q^40 - 100 * q^41 - 536 * q^43 + 624 * q^44 - 90 * q^45 + 560 * q^46 + 928 * q^47 - 234 * q^48 - 50 * q^50 + 372 * q^51 + 140 * q^52 + 884 * q^53 - 54 * q^54 + 80 * q^55 + 288 * q^57 + 676 * q^58 - 104 * q^59 - 30 * q^60 + 468 * q^61 + 168 * q^62 + 34 * q^64 - 380 * q^65 - 912 * q^66 - 1688 * q^67 + 188 * q^68 - 48 * q^69 - 136 * q^71 - 162 * q^72 - 508 * q^73 + 1188 * q^74 + 150 * q^75 + 608 * q^76 - 324 * q^78 - 432 * q^79 + 390 * q^80 + 162 * q^81 + 1380 * q^82 + 584 * q^83 - 620 * q^85 - 456 * q^86 + 564 * q^87 + 1744 * q^88 + 1404 * q^89 + 90 * q^90 - 1104 * q^92 + 360 * q^93 - 1600 * q^94 - 480 * q^95 + 1242 * q^96 + 1188 * q^97 - 144 * 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 $

$2$	−3.82843	−1.35355	−0.676777	−	0.736188i	$-0.736624\pi$
$2$	−3.82843	−1.35355	−0.676777	+	0.736188i	$0.736624\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	6.65685	0.832107
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−11.4853	−0.781474
$7$	0	0
$7$	0	0
$8$	5.14214	0.227252
$9$	9.00000	0.333333
$10$	19.1421	0.605327
$11$	48.5685	1.33127	0.665635	−	0.746278i	$-0.268161\pi$
$11$	48.5685	1.33127	0.665635	+	0.746278i	$0.268161\pi$
$12$	19.9706	0.480417
$13$	43.6569	0.931403	0.465701	−	0.884942i	$-0.345802\pi$
$13$	43.6569	0.931403	0.465701	+	0.884942i	$0.345802\pi$
$14$	0	0
$15$	−15.0000	−0.258199
$16$	−72.9411	−1.13971
$17$	67.6569	0.965247	0.482623	−	0.875828i	$-0.339684\pi$
$17$	67.6569	0.965247	0.482623	+	0.875828i	$0.339684\pi$
$18$	−34.4558	−0.451184
$19$	93.2548	1.12601	0.563003	−	0.826455i	$-0.309646\pi$
$19$	93.2548	1.12601	0.563003	+	0.826455i	$0.309646\pi$
$20$	−33.2843	−0.372129
$21$	0	0
$22$	−185.941	−1.80194
$23$	−104.167	−0.944357	−0.472179	−	0.881503i	$-0.656532\pi$
$23$	−104.167	−0.944357	−0.472179	+	0.881503i	$0.656532\pi$
$24$	15.4264	0.131204
$25$	25.0000	0.200000
$26$	−167.137	−1.26070
$27$	27.0000	0.192450
$28$	0	0
$29$	−58.7351	−0.376098	−0.188049	−	0.982160i	$-0.560216\pi$
$29$	−58.7351	−0.376098	−0.188049	+	0.982160i	$0.560216\pi$
$30$	57.4264	0.349486
$31$	9.08831	0.0526551	0.0263276	−	0.999653i	$-0.491619\pi$
$31$	9.08831	0.0526551	0.0263276	+	0.999653i	$0.491619\pi$
$32$	238.113	1.31540
$33$	145.706	0.768609
$34$	−259.019	−1.30651
$35$	0	0
$36$	59.9117	0.277369
$37$	−252.676	−1.12269	−0.561347	−	0.827580i	$-0.689717\pi$
$37$	−252.676	−1.12269	−0.561347	+	0.827580i	$0.689717\pi$
$38$	−357.019	−1.52411
$39$	130.971	0.537745
$40$	−25.7107	−0.101630
$41$	−276.274	−1.05236	−0.526180	−	0.850373i	$-0.676376\pi$
$41$	−276.274	−1.05236	−0.526180	+	0.850373i	$0.676376\pi$
$42$	0	0
$43$	−92.6375	−0.328537	−0.164268	−	0.986416i	$-0.552526\pi$
$43$	−92.6375	−0.328537	−0.164268	+	0.986416i	$0.552526\pi$
$44$	323.314	1.10776
$45$	−45.0000	−0.149071
$46$	398.794	1.27824
$47$	582.794	1.80871	0.904354	−	0.426784i	$-0.140354\pi$
$47$	582.794	1.80871	0.904354	+	0.426784i	$0.140354\pi$
$48$	−218.823	−0.658009
$49$	0	0
$50$	−95.7107	−0.270711
$51$	202.971	0.557286
$52$	290.617	0.775026
$53$	623.019	1.61468	0.807342	−	0.590083i	$-0.200905\pi$
$53$	623.019	1.61468	0.807342	+	0.590083i	$0.200905\pi$
$54$	−103.368	−0.260491
$55$	−242.843	−0.595362
$56$	0	0
$57$	279.765	0.650100
$58$	224.863	0.509068
$59$	524.999	1.15846	0.579229	−	0.815165i	$-0.303354\pi$
$59$	524.999	1.15846	0.579229	+	0.815165i	$0.303354\pi$
$60$	−99.8528	−0.214849
$61$	352.794	0.740502	0.370251	−	0.928932i	$-0.379272\pi$
$61$	352.794	0.740502	0.370251	+	0.928932i	$0.379272\pi$
$62$	−34.7939	−0.0712715
$63$	0	0
$64$	−328.068	−0.640758
$65$	−218.284	−0.416536
$66$	−557.823	−1.04035
$67$	−736.520	−1.34299	−0.671494	−	0.741010i	$-0.734347\pi$
$67$	−736.520	−1.34299	−0.671494	+	0.741010i	$0.734347\pi$
$68$	450.382	0.803188
$69$	−312.500	−0.545225
$70$	0	0
$71$	−492.264	−0.822831	−0.411415	−	0.911448i	$-0.634965\pi$
$71$	−492.264	−0.822831	−0.411415	+	0.911448i	$0.634965\pi$
$72$	46.2792	0.0757508
$73$	−1164.75	−1.86745	−0.933727	−	0.357987i	$-0.883463\pi$
$73$	−1164.75	−1.86745	−0.933727	+	0.357987i	$0.883463\pi$
$74$	967.352	1.51963
$75$	75.0000	0.115470
$76$	620.784	0.936958
$77$	0	0
$78$	−501.411	−0.727867
$79$	−872.195	−1.24215	−0.621074	−	0.783752i	$-0.713303\pi$
$79$	−872.195	−1.24215	−0.621074	+	0.783752i	$0.713303\pi$
$80$	364.706	0.509692
$81$	81.0000	0.111111
$82$	1057.70	1.42443
$83$	529.588	0.700359	0.350180	−	0.936683i	$-0.386121\pi$
$83$	529.588	0.700359	0.350180	+	0.936683i	$0.386121\pi$
$84$	0	0
$85$	−338.284	−0.431672
$86$	354.656	0.444692
$87$	−176.205	−0.217140
$88$	249.746	0.302534
$89$	385.216	0.458796	0.229398	−	0.973333i	$-0.426324\pi$
$89$	385.216	0.458796	0.229398	+	0.973333i	$0.426324\pi$
$90$	172.279	0.201776
$91$	0	0
$92$	−693.421	−0.785806
$93$	27.2649	0.0304005
$94$	−2231.18	−2.44818
$95$	−466.274	−0.503565
$96$	714.338	0.759446
$97$	463.892	0.485579	0.242789	−	0.970079i	$-0.421938\pi$
$97$	463.892	0.485579	0.242789	+	0.970079i	$0.421938\pi$
$98$	0	0
$99$	437.117	0.443757
$100$	166.421	0.166421
$101$	432.725	0.426314	0.213157	−	0.977018i	$-0.431625\pi$
$101$	432.725	0.426314	0.213157	+	0.977018i	$0.431625\pi$
$102$	−777.058	−0.754316
$103$	−512.626	−0.490393	−0.245197	−	0.969473i	$-0.578853\pi$
$103$	−512.626	−0.490393	−0.245197	+	0.969473i	$0.578853\pi$
$104$	224.489	0.211663
$105$	0	0
$106$	−2385.18	−2.18556
$107$	1963.09	1.77363	0.886817	−	0.462122i	$-0.152912\pi$
$107$	1963.09	1.77363	0.886817	+	0.462122i	$0.152912\pi$
$108$	179.735	0.160139
$109$	545.176	0.479068	0.239534	−	0.970888i	$-0.423005\pi$
$109$	545.176	0.479068	0.239534	+	0.970888i	$0.423005\pi$
$110$	929.706	0.805854
$111$	−758.029	−0.648188
$112$	0	0
$113$	−231.823	−0.192992	−0.0964961	−	0.995333i	$-0.530764\pi$
$113$	−231.823	−0.192992	−0.0964961	+	0.995333i	$0.530764\pi$
$114$	−1071.06	−0.879945
$115$	520.833	0.422329
$116$	−390.991	−0.312953
$117$	392.912	0.310468
$118$	−2009.92	−1.56804
$119$	0	0
$120$	−77.1320	−0.0586763
$121$	1027.90	0.772279
$122$	−1350.65	−1.00231
$123$	−828.823	−0.607581
$124$	60.4996	0.0438147
$125$	−125.000	−0.0894427
$126$	0	0
$127$	2372.90	1.65796	0.828979	−	0.559280i	$-0.188922\pi$
$127$	2372.90	1.65796	0.828979	+	0.559280i	$0.188922\pi$
$128$	−648.917	−0.448099
$129$	−277.913	−0.189681
$130$	835.685	0.563804
$131$	−1200.04	−0.800364	−0.400182	−	0.916436i	$-0.631053\pi$
$131$	−1200.04	−0.800364	−0.400182	+	0.916436i	$0.631053\pi$
$132$	969.941	0.639565
$133$	0	0
$134$	2819.71	1.81781
$135$	−135.000	−0.0860663
$136$	347.901	0.219355
$137$	2781.25	1.73444	0.867221	−	0.497924i	$-0.165904\pi$
$137$	2781.25	1.73444	0.867221	+	0.497924i	$0.165904\pi$
$138$	1196.38	0.737991
$139$	1245.60	0.760078	0.380039	−	0.924971i	$-0.375911\pi$
$139$	1245.60	0.760078	0.380039	+	0.924971i	$0.375911\pi$
$140$	0	0
$141$	1748.38	1.04426
$142$	1884.60	1.11375
$143$	2120.35	1.23995
$144$	−656.470	−0.379902
$145$	293.675	0.168196
$146$	4459.17	2.52770
$147$	0	0
$148$	−1682.03	−0.934202
$149$	19.4046	0.0106690	0.00533452	−	0.999986i	$-0.498302\pi$
$149$	19.4046	0.0106690	0.00533452	+	0.999986i	$0.498302\pi$
$150$	−287.132	−0.156295
$151$	−2349.80	−1.26638	−0.633192	−	0.773995i	$-0.718256\pi$
$151$	−2349.80	−1.26638	−0.633192	+	0.773995i	$0.718256\pi$
$152$	479.529	0.255888
$153$	608.912	0.321749
$154$	0	0
$155$	−45.4416	−0.0235481
$156$	871.852	0.447462
$157$	3898.46	1.98172	0.990862	−	0.134880i	$-0.0430650\pi$
$157$	3898.46	1.98172	0.990862	+	0.134880i	$0.0430650\pi$
$158$	3339.14	1.68131
$159$	1869.06	0.932239
$160$	−1190.56	−0.588264
$161$	0	0
$162$	−310.103	−0.150395
$163$	1527.54	0.734024	0.367012	−	0.930216i	$-0.380381\pi$
$163$	1527.54	0.734024	0.367012	+	0.930216i	$0.380381\pi$
$164$	−1839.12	−0.875676
$165$	−728.528	−0.343732
$166$	−2027.49	−0.947974
$167$	998.518	0.462681	0.231340	−	0.972873i	$-0.425689\pi$
$167$	998.518	0.462681	0.231340	+	0.972873i	$0.425689\pi$
$168$	0	0
$169$	−291.079	−0.132489
$170$	1295.10	0.584290
$171$	839.294	0.375336
$172$	−616.674	−0.273378
$173$	−685.253	−0.301149	−0.150575	−	0.988599i	$-0.548112\pi$
$173$	−685.253	−0.301149	−0.150575	+	0.988599i	$0.548112\pi$
$174$	674.589	0.293911
$175$	0	0
$176$	−3542.64	−1.51725
$177$	1575.00	0.668836
$178$	−1474.77	−0.621005
$179$	1025.58	0.428245	0.214122	−	0.976807i	$-0.431311\pi$
$179$	1025.58	0.428245	0.214122	+	0.976807i	$0.431311\pi$
$180$	−299.558	−0.124043
$181$	−2899.40	−1.19067	−0.595333	−	0.803479i	$-0.702980\pi$
$181$	−2899.40	−1.19067	−0.595333	+	0.803479i	$0.702980\pi$
$182$	0	0
$183$	1058.38	0.427529
$184$	−535.638	−0.214608
$185$	1263.38	0.502084
$186$	−104.382	−0.0411486
$187$	3285.99	1.28500
$188$	3879.57	1.50504
$189$	0	0
$190$	1785.10	0.681603
$191$	1074.18	0.406939	0.203469	−	0.979081i	$-0.434778\pi$
$191$	1074.18	0.406939	0.203469	+	0.979081i	$0.434778\pi$
$192$	−984.204	−0.369942
$193$	898.999	0.335292	0.167646	−	0.985847i	$-0.446383\pi$
$193$	898.999	0.335292	0.167646	+	0.985847i	$0.446383\pi$
$194$	−1775.98	−0.657257
$195$	−654.853	−0.240487
$196$	0	0
$197$	3063.63	1.10799	0.553996	−	0.832519i	$-0.313102\pi$
$197$	3063.63	1.10799	0.553996	+	0.832519i	$0.313102\pi$
$198$	−1673.47	−0.600648
$199$	949.522	0.338240	0.169120	−	0.985595i	$-0.445907\pi$
$199$	949.522	0.338240	0.169120	+	0.985595i	$0.445907\pi$
$200$	128.553	0.0454505
$201$	−2209.56	−0.775375
$202$	−1656.66	−0.577039
$203$	0	0
$204$	1351.15	0.463721
$205$	1381.37	0.470630
$206$	1962.55	0.663774
$207$	−937.499	−0.314786
$208$	−3184.38	−1.06152
$209$	4529.25	1.49902
$210$	0	0
$211$	2306.64	0.752587	0.376294	−	0.926500i	$-0.377198\pi$
$211$	2306.64	0.752587	0.376294	+	0.926500i	$0.377198\pi$
$212$	4147.35	1.34359
$213$	−1476.79	−0.475062
$214$	−7515.53	−2.40071
$215$	463.188	0.146926
$216$	138.838	0.0437348
$217$	0	0
$218$	−2087.17	−0.648444
$219$	−3494.26	−1.07817
$220$	−1616.57	−0.495405
$221$	2953.69	0.899033
$222$	2902.06	0.877357
$223$	3227.61	0.969222	0.484611	−	0.874730i	$-0.338961\pi$
$223$	3227.61	0.969222	0.484611	+	0.874730i	$0.338961\pi$
$224$	0	0
$225$	225.000	0.0666667
$226$	887.519	0.261225
$227$	637.820	0.186492	0.0932458	−	0.995643i	$-0.470276\pi$
$227$	637.820	0.186492	0.0932458	+	0.995643i	$0.470276\pi$
$228$	1862.35	0.540953
$229$	−544.774	−0.157204	−0.0786019	−	0.996906i	$-0.525046\pi$
$229$	−544.774	−0.157204	−0.0786019	+	0.996906i	$0.525046\pi$
$230$	−1993.97	−0.571646
$231$	0	0
$232$	−302.024	−0.0854691
$233$	−5748.54	−1.61631	−0.808154	−	0.588972i	$-0.799533\pi$
$233$	−5748.54	−1.61631	−0.808154	+	0.588972i	$0.799533\pi$
$234$	−1504.23	−0.420234
$235$	−2913.97	−0.808878
$236$	3494.84	0.963961
$237$	−2616.59	−0.717154
$238$	0	0
$239$	−2678.10	−0.724820	−0.362410	−	0.932019i	$-0.618046\pi$
$239$	−2678.10	−0.724820	−0.362410	+	0.932019i	$0.618046\pi$
$240$	1094.12	0.294271
$241$	2202.16	0.588604	0.294302	−	0.955713i	$-0.404913\pi$
$241$	2202.16	0.588604	0.294302	+	0.955713i	$0.404913\pi$
$242$	−3935.25	−1.04532
$243$	243.000	0.0641500
$244$	2348.50	0.616177
$245$	0	0
$246$	3173.09	0.822393
$247$	4071.21	1.04877
$248$	46.7333	0.0119660
$249$	1588.76	0.404353
$250$	478.553	0.121065
$251$	5716.90	1.43764	0.718820	−	0.695196i	$-0.244683\pi$
$251$	5716.90	1.43764	0.718820	+	0.695196i	$0.244683\pi$
$252$	0	0
$253$	−5059.22	−1.25719
$254$	−9084.47	−2.24413
$255$	−1014.85	−0.249226
$256$	5108.88	1.24728
$257$	−4724.29	−1.14666	−0.573332	−	0.819323i	$-0.694350\pi$
$257$	−4724.29	−1.14666	−0.573332	+	0.819323i	$0.694350\pi$
$258$	1063.97	0.256743
$259$	0	0
$260$	−1453.09	−0.346602
$261$	−528.616	−0.125366
$262$	4594.25	1.08334
$263$	5975.36	1.40097	0.700487	−	0.713665i	$-0.252966\pi$
$263$	5975.36	1.40097	0.700487	+	0.713665i	$0.252966\pi$
$264$	749.238	0.174668
$265$	−3115.10	−0.722109
$266$	0	0
$267$	1155.65	0.264886
$268$	−4902.90	−1.11751
$269$	−4486.11	−1.01681	−0.508407	−	0.861117i	$-0.669766\pi$
$269$	−4486.11	−1.01681	−0.508407	+	0.861117i	$0.669766\pi$
$270$	516.838	0.116495
$271$	−3827.68	−0.857989	−0.428994	−	0.903307i	$-0.641132\pi$
$271$	−3827.68	−0.857989	−0.428994	+	0.903307i	$0.641132\pi$
$272$	−4934.97	−1.10010
$273$	0	0
$274$	−10647.8	−2.34766
$275$	1214.21	0.266254
$276$	−2080.26	−0.453685
$277$	−3420.54	−0.741950	−0.370975	−	0.928643i	$-0.620976\pi$
$277$	−3420.54	−0.741950	−0.370975	+	0.928643i	$0.620976\pi$
$278$	−4768.71	−1.02881
$279$	81.7948	0.0175517
$280$	0	0
$281$	5235.92	1.11156	0.555781	−	0.831329i	$-0.312419\pi$
$281$	5235.92	1.11156	0.555781	+	0.831329i	$0.312419\pi$
$282$	−6693.55	−1.41346
$283$	6985.88	1.46738	0.733688	−	0.679486i	$-0.237797\pi$
$283$	6985.88	1.46738	0.733688	+	0.679486i	$0.237797\pi$
$284$	−3276.93	−0.684683
$285$	−1398.82	−0.290734
$286$	−8117.60	−1.67834
$287$	0	0
$288$	2143.01	0.438466
$289$	−335.550	−0.0682984
$290$	−1124.31	−0.227662
$291$	1391.68	0.280349
$292$	−7753.59	−1.55392
$293$	−7399.70	−1.47541	−0.737705	−	0.675123i	$-0.764090\pi$
$293$	−7399.70	−1.47541	−0.737705	+	0.675123i	$0.764090\pi$
$294$	0	0
$295$	−2625.00	−0.518078
$296$	−1299.30	−0.255135
$297$	1311.35	0.256203
$298$	−74.2892	−0.0144411
$299$	−4547.58	−0.879577
$300$	499.264	0.0960834
$301$	0	0
$302$	8996.04	1.71412
$303$	1298.17	0.246133
$304$	−6802.11	−1.28332
$305$	−1763.97	−0.331163
$306$	−2331.17	−0.435504
$307$	−2668.64	−0.496116	−0.248058	−	0.968745i	$-0.579792\pi$
$307$	−2668.64	−0.496116	−0.248058	+	0.968745i	$0.579792\pi$
$308$	0	0
$309$	−1537.88	−0.283129
$310$	173.970	0.0318736
$311$	−6189.25	−1.12849	−0.564244	−	0.825608i	$-0.690832\pi$
$311$	−6189.25	−1.12849	−0.564244	+	0.825608i	$0.690832\pi$
$312$	673.468	0.122204
$313$	2921.59	0.527598	0.263799	−	0.964578i	$-0.415024\pi$
$313$	2921.59	0.527598	0.263799	+	0.964578i	$0.415024\pi$
$314$	−14925.0	−2.68237
$315$	0	0
$316$	−5806.08	−1.03360
$317$	9825.56	1.74088	0.870439	−	0.492276i	$-0.163835\pi$
$317$	9825.56	1.74088	0.870439	+	0.492276i	$0.163835\pi$
$318$	−7155.55	−1.26183
$319$	−2852.68	−0.500687
$320$	1640.34	0.286556
$321$	5889.26	1.02401
$322$	0	0
$323$	6309.33	1.08687
$324$	539.205	0.0924563
$325$	1091.42	0.186281
$326$	−5848.07	−0.993541
$327$	1635.53	0.276590
$328$	−1420.64	−0.239151
$329$	0	0
$330$	2789.12	0.465260
$331$	−9258.17	−1.53739	−0.768693	−	0.639618i	$-0.779093\pi$
$331$	−9258.17	−1.53739	−0.768693	+	0.639618i	$0.779093\pi$
$332$	3525.39	0.582774
$333$	−2274.09	−0.374232
$334$	−3822.75	−0.626263
$335$	3682.60	0.600603
$336$	0	0
$337$	−3693.98	−0.597103	−0.298552	−	0.954394i	$-0.596503\pi$
$337$	−3693.98	−0.597103	−0.298552	+	0.954394i	$0.596503\pi$
$338$	1114.38	0.179331
$339$	−695.470	−0.111424
$340$	−2251.91	−0.359197
$341$	441.406	0.0700982
$342$	−3213.17	−0.508037
$343$	0	0
$344$	−476.355	−0.0746608
$345$	1562.50	0.243832
$346$	2623.44	0.407622
$347$	3832.83	0.592960	0.296480	−	0.955039i	$-0.404187\pi$
$347$	3832.83	0.592960	0.296480	+	0.955039i	$0.404187\pi$
$348$	−1172.97	−0.180684
$349$	−8325.22	−1.27690	−0.638451	−	0.769662i	$-0.720425\pi$
$349$	−8325.22	−1.27690	−0.638451	+	0.769662i	$0.720425\pi$
$350$	0	0
$351$	1178.74	0.179248
$352$	11564.8	1.75115
$353$	8991.52	1.35572	0.677862	−	0.735189i	$-0.262907\pi$
$353$	8991.52	1.35572	0.677862	+	0.735189i	$0.262907\pi$
$354$	−6029.76	−0.905306
$355$	2461.32	0.367981
$356$	2564.33	0.381767
$357$	0	0
$358$	−3926.38	−0.579652
$359$	−12893.8	−1.89557	−0.947783	−	0.318917i	$-0.896681\pi$
$359$	−12893.8	−1.89557	−0.947783	+	0.318917i	$0.896681\pi$
$360$	−231.396	−0.0338768
$361$	1837.46	0.267891
$362$	11100.1	1.61163
$363$	3083.71	0.445875
$364$	0	0
$365$	5823.77	0.835150
$366$	−4051.94	−0.578684
$367$	7480.17	1.06393	0.531964	−	0.846767i	$-0.321454\pi$
$367$	7480.17	1.06393	0.531964	+	0.846767i	$0.321454\pi$
$368$	7598.02	1.07629
$369$	−2486.47	−0.350787
$370$	−4836.76	−0.679598
$371$	0	0
$372$	181.499	0.0252964
$373$	−3523.32	−0.489090	−0.244545	−	0.969638i	$-0.578639\pi$
$373$	−3523.32	−0.489090	−0.244545	+	0.969638i	$0.578639\pi$
$374$	−12580.2	−1.73932
$375$	−375.000	−0.0516398
$376$	2996.81	0.411033
$377$	−2564.19	−0.350298
$378$	0	0
$379$	13515.4	1.83177	0.915886	−	0.401438i	$-0.131490\pi$
$379$	13515.4	1.83177	0.915886	+	0.401438i	$0.131490\pi$
$380$	−3103.92	−0.419020
$381$	7118.69	0.957222
$382$	−4112.44	−0.550813
$383$	657.182	0.0876774	0.0438387	−	0.999039i	$-0.486041\pi$
$383$	657.182	0.0876774	0.0438387	+	0.999039i	$0.486041\pi$
$384$	−1946.75	−0.258710
$385$	0	0
$386$	−3441.75	−0.453836
$387$	−833.738	−0.109512
$388$	3088.06	0.404053
$389$	−9741.87	−1.26975	−0.634875	−	0.772615i	$-0.718948\pi$
$389$	−9741.87	−1.26975	−0.634875	+	0.772615i	$0.718948\pi$
$390$	2507.06	0.325512
$391$	−7047.58	−0.911538
$392$	0	0
$393$	−3600.11	−0.462091
$394$	−11728.9	−1.49973
$395$	4360.98	0.555505
$396$	2909.82	0.369253
$397$	−4407.42	−0.557184	−0.278592	−	0.960410i	$-0.589868\pi$
$397$	−4407.42	−0.557184	−0.278592	+	0.960410i	$0.589868\pi$
$398$	−3635.18	−0.457827
$399$	0	0
$400$	−1823.53	−0.227941
$401$	−11569.5	−1.44078	−0.720391	−	0.693568i	$-0.756037\pi$
$401$	−11569.5	−1.44078	−0.720391	+	0.693568i	$0.756037\pi$
$402$	8459.14	1.04951
$403$	396.767	0.0490431
$404$	2880.59	0.354739
$405$	−405.000	−0.0496904
$406$	0	0
$407$	−12272.1	−1.49461
$408$	1043.70	0.126645
$409$	3083.03	0.372729	0.186364	−	0.982481i	$-0.440330\pi$
$409$	3083.03	0.372729	0.186364	+	0.982481i	$0.440330\pi$
$410$	−5288.48	−0.637023
$411$	8343.76	1.00138
$412$	−3412.47	−0.408060
$413$	0	0
$414$	3589.15	0.426079
$415$	−2647.94	−0.313210
$416$	10395.3	1.22517
$417$	3736.81	0.438831
$418$	−17339.9	−2.02900
$419$	5415.21	0.631385	0.315692	−	0.948862i	$-0.397763\pi$
$419$	5415.21	0.631385	0.315692	+	0.948862i	$0.397763\pi$
$420$	0	0
$421$	4188.34	0.484863	0.242432	−	0.970168i	$-0.422055\pi$
$421$	4188.34	0.484863	0.242432	+	0.970168i	$0.422055\pi$
$422$	−8830.82	−1.01867
$423$	5245.15	0.602902
$424$	3203.65	0.366941
$425$	1691.42	0.193049
$426$	5653.79	0.643021
$427$	0	0
$428$	13068.0	1.47585
$429$	6361.05	0.715884
$430$	−1773.28	−0.198872
$431$	−9108.41	−1.01795	−0.508975	−	0.860781i	$-0.669976\pi$
$431$	−9108.41	−1.01795	−0.508975	+	0.860781i	$0.669976\pi$
$432$	−1969.41	−0.219336
$433$	16847.0	1.86979	0.934893	−	0.354930i	$-0.115495\pi$
$433$	16847.0	1.86979	0.934893	+	0.354930i	$0.115495\pi$
$434$	0	0
$435$	881.026	0.0971080
$436$	3629.16	0.398635
$437$	−9714.03	−1.06335
$438$	13377.5	1.45937
$439$	−8434.14	−0.916946	−0.458473	−	0.888708i	$-0.651603\pi$
$439$	−8434.14	−0.916946	−0.458473	+	0.888708i	$0.651603\pi$
$440$	−1248.73	−0.135297
$441$	0	0
$442$	−11308.0	−1.21689
$443$	−4298.49	−0.461010	−0.230505	−	0.973071i	$-0.574038\pi$
$443$	−4298.49	−0.461010	−0.230505	+	0.973071i	$0.574038\pi$
$444$	−5046.09	−0.539362
$445$	−1926.08	−0.205180
$446$	−12356.7	−1.31189
$447$	58.2139	0.00615978
$448$	0	0
$449$	10545.0	1.10835	0.554173	−	0.832402i	$-0.313035\pi$
$449$	10545.0	1.10835	0.554173	+	0.832402i	$0.313035\pi$
$450$	−861.396	−0.0902369
$451$	−13418.2	−1.40098
$452$	−1543.21	−0.160590
$453$	−7049.40	−0.731147
$454$	−2441.85	−0.252426
$455$	0	0
$456$	1438.59	0.147737
$457$	11952.4	1.22344	0.611719	−	0.791075i	$-0.290478\pi$
$457$	11952.4	1.22344	0.611719	+	0.791075i	$0.290478\pi$
$458$	2085.63	0.212784
$459$	1826.74	0.185762
$460$	3467.11	0.351423
$461$	17200.9	1.73780	0.868900	−	0.494988i	$-0.164827\pi$
$461$	17200.9	1.73780	0.868900	+	0.494988i	$0.164827\pi$
$462$	0	0
$463$	−10368.7	−1.04076	−0.520381	−	0.853934i	$-0.674210\pi$
$463$	−10368.7	−1.04076	−0.520381	+	0.853934i	$0.674210\pi$
$464$	4284.20	0.428640
$465$	−136.325	−0.0135955
$466$	22007.9	2.18776
$467$	16879.5	1.67257	0.836284	−	0.548296i	$-0.184723\pi$
$467$	16879.5	1.67257	0.836284	+	0.548296i	$0.184723\pi$
$468$	2615.56	0.258342
$469$	0	0
$470$	11155.9	1.09486
$471$	11695.4	1.14415
$472$	2699.62	0.263263
$473$	−4499.27	−0.437371
$474$	10017.4	0.970706
$475$	2331.37	0.225201
$476$	0	0
$477$	5607.17	0.538228
$478$	10252.9	0.981082
$479$	−7329.12	−0.699115	−0.349558	−	0.936915i	$-0.613668\pi$
$479$	−7329.12	−0.699115	−0.349558	+	0.936915i	$0.613668\pi$
$480$	−3571.69	−0.339635
$481$	−11031.0	−1.04568
$482$	−8430.80	−0.796706
$483$	0	0
$484$	6842.60	0.642619
$485$	−2319.46	−0.217157
$486$	−930.308	−0.0868305
$487$	−17209.5	−1.60131	−0.800655	−	0.599125i	$-0.795515\pi$
$487$	−17209.5	−1.60131	−0.800655	+	0.599125i	$0.795515\pi$
$488$	1814.11	0.168281
$489$	4582.61	0.423789
$490$	0	0
$491$	11392.5	1.04712	0.523560	−	0.851989i	$-0.324604\pi$
$491$	11392.5	1.04712	0.523560	+	0.851989i	$0.324604\pi$
$492$	−5517.35	−0.505572
$493$	−3973.83	−0.363027
$494$	−15586.3	−1.41956
$495$	−2185.58	−0.198454
$496$	−662.912	−0.0600113
$497$	0	0
$498$	−6082.47	−0.547313
$499$	19079.4	1.71164	0.855822	−	0.517271i	$-0.173052\pi$
$499$	19079.4	1.71164	0.855822	+	0.517271i	$0.173052\pi$
$500$	−832.107	−0.0744259
$501$	2995.55	0.267129
$502$	−21886.7	−1.94592
$503$	13499.4	1.19663	0.598317	−	0.801259i	$-0.295836\pi$
$503$	13499.4	1.19663	0.598317	+	0.801259i	$0.295836\pi$
$504$	0	0
$505$	−2163.62	−0.190654
$506$	19368.8	1.70168
$507$	−873.237	−0.0764928
$508$	15796.0	1.37960
$509$	4328.85	0.376960	0.188480	−	0.982077i	$-0.439644\pi$
$509$	4328.85	0.376960	0.188480	+	0.982077i	$0.439644\pi$
$510$	3885.29	0.337340
$511$	0	0
$512$	−14367.6	−1.24017
$513$	2517.88	0.216700
$514$	18086.6	1.55207
$515$	2563.13	0.219311
$516$	−1850.02	−0.157835
$517$	28305.5	2.40788
$518$	0	0
$519$	−2055.76	−0.173869
$520$	−1122.45	−0.0946588
$521$	−19395.7	−1.63098	−0.815490	−	0.578771i	$-0.803532\pi$
$521$	−19395.7	−1.63098	−0.815490	+	0.578771i	$0.803532\pi$
$522$	2023.77	0.169689
$523$	−20413.8	−1.70675	−0.853377	−	0.521294i	$-0.825450\pi$
$523$	−20413.8	−1.70675	−0.853377	+	0.521294i	$0.825450\pi$
$524$	−7988.47	−0.665989
$525$	0	0
$526$	−22876.2	−1.89629
$527$	614.887	0.0508252
$528$	−10627.9	−0.875987
$529$	−1316.34	−0.108189
$530$	11925.9	0.977413
$531$	4724.99	0.386153
$532$	0	0
$533$	−12061.3	−0.980171
$534$	−4424.32	−0.358537
$535$	−9815.43	−0.793193
$536$	−3787.28	−0.305197
$537$	3076.75	0.247247
$538$	17174.8	1.37631
$539$	0	0
$540$	−898.675	−0.0716163
$541$	−4919.18	−0.390928	−0.195464	−	0.980711i	$-0.562621\pi$
$541$	−4919.18	−0.390928	−0.195464	+	0.980711i	$0.562621\pi$
$542$	14654.0	1.16133
$543$	−8698.19	−0.687431
$544$	16110.0	1.26969
$545$	−2725.88	−0.214246
$546$	0	0
$547$	15334.2	1.19862	0.599308	−	0.800518i	$-0.295442\pi$
$547$	15334.2	1.19862	0.599308	+	0.800518i	$0.295442\pi$
$548$	18514.4	1.44324
$549$	3175.15	0.246834
$550$	−4648.53	−0.360389
$551$	−5477.33	−0.423488
$552$	−1606.92	−0.123904
$553$	0	0
$554$	13095.3	1.00427
$555$	3790.14	0.289879
$556$	8291.81	0.632466
$557$	−8613.78	−0.655256	−0.327628	−	0.944807i	$-0.606249\pi$
$557$	−8613.78	−0.655256	−0.327628	+	0.944807i	$0.606249\pi$
$558$	−313.145	−0.0237572
$559$	−4044.26	−0.306000
$560$	0	0
$561$	9857.98	0.741897
$562$	−20045.3	−1.50456
$563$	2320.81	0.173731	0.0868654	−	0.996220i	$-0.472315\pi$
$563$	2320.81	0.173731	0.0868654	+	0.996220i	$0.472315\pi$
$564$	11638.7	0.868934
$565$	1159.12	0.0863087
$566$	−26744.9	−1.98617
$567$	0	0
$568$	−2531.29	−0.186990
$569$	−1736.04	−0.127906	−0.0639529	−	0.997953i	$-0.520371\pi$
$569$	−1736.04	−0.127906	−0.0639529	+	0.997953i	$0.520371\pi$
$570$	5355.29	0.393524
$571$	23897.8	1.75148	0.875738	−	0.482786i	$-0.160375\pi$
$571$	23897.8	1.75148	0.875738	+	0.482786i	$0.160375\pi$
$572$	14114.9	1.03177
$573$	3222.55	0.234946
$574$	0	0
$575$	−2604.16	−0.188871
$576$	−2952.61	−0.213586
$577$	−8029.26	−0.579311	−0.289655	−	0.957131i	$-0.593541\pi$
$577$	−8029.26	−0.579311	−0.289655	+	0.957131i	$0.593541\pi$
$578$	1284.63	0.0924455
$579$	2697.00	0.193581
$580$	1954.95	0.139957
$581$	0	0
$582$	−5327.93	−0.379467
$583$	30259.1	2.14958
$584$	−5989.32	−0.424383
$585$	−1964.56	−0.138845
$586$	28329.2	1.99705
$587$	8015.14	0.563578	0.281789	−	0.959476i	$-0.409072\pi$
$587$	8015.14	0.563578	0.281789	+	0.959476i	$0.409072\pi$
$588$	0	0
$589$	847.529	0.0592900
$590$	10049.6	0.701247
$591$	9190.88	0.639700
$592$	18430.5	1.27954
$593$	−12820.3	−0.887801	−0.443901	−	0.896076i	$-0.646406\pi$
$593$	−12820.3	−0.887801	−0.443901	+	0.896076i	$0.646406\pi$
$594$	−5020.41	−0.346784
$595$	0	0
$596$	129.174	0.00887779
$597$	2848.57	0.195283
$598$	17410.1	1.19055
$599$	−15330.5	−1.04572	−0.522860	−	0.852418i	$-0.675135\pi$
$599$	−15330.5	−1.04572	−0.522860	+	0.852418i	$0.675135\pi$
$600$	385.660	0.0262409
$601$	−107.658	−0.00730694	−0.00365347	−	0.999993i	$-0.501163\pi$
$601$	−107.658	−0.00730694	−0.00365347	+	0.999993i	$0.501163\pi$
$602$	0	0
$603$	−6628.68	−0.447663
$604$	−15642.3	−1.05377
$605$	−5139.52	−0.345374
$606$	−4969.97	−0.333154
$607$	8213.06	0.549189	0.274595	−	0.961560i	$-0.411456\pi$
$607$	8213.06	0.549189	0.274595	+	0.961560i	$0.411456\pi$
$608$	22205.2	1.48115
$609$	0	0
$610$	6753.23	0.448246
$611$	25443.0	1.68463
$612$	4053.44	0.267729
$613$	1242.60	0.0818732	0.0409366	−	0.999162i	$-0.486966\pi$
$613$	1242.60	0.0818732	0.0409366	+	0.999162i	$0.486966\pi$
$614$	10216.7	0.671519
$615$	4144.11	0.271718
$616$	0	0
$617$	−13170.6	−0.859367	−0.429683	−	0.902980i	$-0.641375\pi$
$617$	−13170.6	−0.859367	−0.429683	+	0.902980i	$0.641375\pi$
$618$	5887.65	0.383230
$619$	−19774.1	−1.28399	−0.641993	−	0.766711i	$-0.721892\pi$
$619$	−19774.1	−1.28399	−0.641993	+	0.766711i	$0.721892\pi$
$620$	−302.498	−0.0195945
$621$	−2812.50	−0.181742
$622$	23695.1	1.52747
$623$	0	0
$624$	−9553.14	−0.612871
$625$	625.000	0.0400000
$626$	−11185.1	−0.714132
$627$	13587.8	0.865459
$628$	25951.5	1.64901
$629$	−17095.3	−1.08368
$630$	0	0
$631$	−14308.8	−0.902735	−0.451367	−	0.892338i	$-0.649064\pi$
$631$	−14308.8	−0.902735	−0.451367	+	0.892338i	$0.649064\pi$
$632$	−4484.95	−0.282281
$633$	6919.93	0.434507
$634$	−37616.4	−2.35637
$635$	−11864.5	−0.741461
$636$	12442.0	0.775722
$637$	0	0
$638$	10921.3	0.677707
$639$	−4430.38	−0.274277
$640$	3244.58	0.200396
$641$	11537.5	0.710925	0.355463	−	0.934691i	$-0.384323\pi$
$641$	11537.5	0.710925	0.355463	+	0.934691i	$0.384323\pi$
$642$	−22546.6	−1.38605
$643$	−19603.0	−1.20228	−0.601139	−	0.799144i	$-0.705286\pi$
$643$	−19603.0	−1.20228	−0.601139	+	0.799144i	$0.705286\pi$
$644$	0	0
$645$	1389.56	0.0848279
$646$	−24154.8	−1.47114
$647$	−21650.0	−1.31553	−0.657765	−	0.753223i	$-0.728498\pi$
$647$	−21650.0	−1.31553	−0.657765	+	0.753223i	$0.728498\pi$
$648$	416.513	0.0252503
$649$	25498.4	1.54222
$650$	−4178.43	−0.252141
$651$	0	0
$652$	10168.6	0.610787
$653$	−2927.33	−0.175429	−0.0877145	−	0.996146i	$-0.527956\pi$
$653$	−2927.33	−0.175429	−0.0877145	+	0.996146i	$0.527956\pi$
$654$	−6261.50	−0.374379
$655$	6000.18	0.357934
$656$	20151.7	1.19938
$657$	−10482.8	−0.622484
$658$	0	0
$659$	−4778.76	−0.282480	−0.141240	−	0.989975i	$-0.545109\pi$
$659$	−4778.76	−0.282480	−0.141240	+	0.989975i	$0.545109\pi$
$660$	−4849.71	−0.286022
$661$	31510.3	1.85417	0.927086	−	0.374849i	$-0.122305\pi$
$661$	31510.3	1.85417	0.927086	+	0.374849i	$0.122305\pi$
$662$	35444.2	2.08093
$663$	8861.06	0.519057
$664$	2723.21	0.159158
$665$	0	0
$666$	8706.17	0.506542
$667$	6118.23	0.355170
$668$	6646.99	0.385000
$669$	9682.82	0.559581
$670$	−14098.6	−0.812948
$671$	17134.7	0.985808
$672$	0	0
$673$	−8992.15	−0.515040	−0.257520	−	0.966273i	$-0.582905\pi$
$673$	−8992.15	−0.515040	−0.257520	+	0.966273i	$0.582905\pi$
$674$	14142.1	0.808211
$675$	675.000	0.0384900
$676$	−1937.67	−0.110245
$677$	−19340.8	−1.09797	−0.548985	−	0.835832i	$-0.684986\pi$
$677$	−19340.8	−1.09797	−0.548985	+	0.835832i	$0.684986\pi$
$678$	2662.56	0.150818
$679$	0	0
$680$	−1739.50	−0.0980984
$681$	1913.46	0.107671
$682$	−1689.89	−0.0948816
$683$	−4255.14	−0.238387	−0.119194	−	0.992871i	$-0.538031\pi$
$683$	−4255.14	−0.238387	−0.119194	+	0.992871i	$0.538031\pi$
$684$	5587.05	0.312319
$685$	−13906.3	−0.775666
$686$	0	0
$687$	−1634.32	−0.0907616
$688$	6757.08	0.374435
$689$	27199.1	1.50392
$690$	−5981.91	−0.330040
$691$	17505.5	0.963733	0.481867	−	0.876245i	$-0.339959\pi$
$691$	17505.5	0.963733	0.481867	+	0.876245i	$0.339959\pi$
$692$	−4561.63	−0.250588
$693$	0	0
$694$	−14673.7	−0.802603
$695$	−6228.02	−0.339917
$696$	−906.071	−0.0493456
$697$	−18691.8	−1.01579
$698$	31872.5	1.72836
$699$	−17245.6	−0.933175
$700$	0	0
$701$	−3240.77	−0.174611	−0.0873054	−	0.996182i	$-0.527826\pi$
$701$	−3240.77	−0.174611	−0.0873054	+	0.996182i	$0.527826\pi$
$702$	−4512.70	−0.242622
$703$	−23563.3	−1.26416
$704$	−15933.8	−0.853022
$705$	−8741.91	−0.467006
$706$	−34423.4	−1.83504
$707$	0	0
$708$	10484.5	0.556543
$709$	19949.3	1.05672	0.528358	−	0.849022i	$-0.322808\pi$
$709$	19949.3	1.05672	0.528358	+	0.849022i	$0.322808\pi$
$710$	−9422.99	−0.498082
$711$	−7849.76	−0.414049
$712$	1980.83	0.104262
$713$	−946.698	−0.0497253
$714$	0	0
$715$	−10601.7	−0.554522
$716$	6827.17	0.356345
$717$	−8034.30	−0.418475
$718$	49362.9	2.56575
$719$	11259.4	0.584011	0.292006	−	0.956417i	$-0.405677\pi$
$719$	11259.4	0.584011	0.292006	+	0.956417i	$0.405677\pi$
$720$	3282.35	0.169897
$721$	0	0
$722$	−7034.60	−0.362605
$723$	6606.47	0.339830
$724$	−19300.9	−0.990761
$725$	−1468.38	−0.0752195
$726$	−11805.8	−0.603516
$727$	12228.5	0.623840	0.311920	−	0.950108i	$-0.399028\pi$
$727$	12228.5	0.623840	0.311920	+	0.950108i	$0.399028\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−22295.9	−1.13042
$731$	−6267.56	−0.317119
$732$	7045.49	0.355750
$733$	26635.1	1.34214	0.671072	−	0.741392i	$-0.265834\pi$
$733$	26635.1	1.34214	0.671072	+	0.741392i	$0.265834\pi$
$734$	−28637.3	−1.44008
$735$	0	0
$736$	−24803.4	−1.24221
$737$	−35771.7	−1.78788
$738$	9519.26	0.474809
$739$	−6074.00	−0.302349	−0.151174	−	0.988507i	$-0.548306\pi$
$739$	−6074.00	−0.302349	−0.151174	+	0.988507i	$0.548306\pi$
$740$	8410.14	0.417788
$741$	12213.6	0.605505
$742$	0	0
$743$	−4016.87	−0.198337	−0.0991686	−	0.995071i	$-0.531618\pi$
$743$	−4016.87	−0.198337	−0.0991686	+	0.995071i	$0.531618\pi$
$744$	140.200	0.00690858
$745$	−97.0231	−0.00477134
$746$	13488.8	0.662010
$747$	4766.29	0.233453
$748$	21874.4	1.06926
$749$	0	0
$750$	1435.66	0.0698972
$751$	−23913.2	−1.16192	−0.580962	−	0.813931i	$-0.697324\pi$
$751$	−23913.2	−1.16192	−0.580962	+	0.813931i	$0.697324\pi$
$752$	−42509.6	−2.06139
$753$	17150.7	0.830022
$754$	9816.81	0.474147
$755$	11749.0	0.566344
$756$	0	0
$757$	31044.9	1.49055	0.745275	−	0.666758i	$-0.232318\pi$
$757$	31044.9	1.49055	0.745275	+	0.666758i	$0.232318\pi$
$758$	−51742.9	−2.47940
$759$	−15177.6	−0.725842
$760$	−2397.65	−0.114436
$761$	−14011.8	−0.667446	−0.333723	−	0.942671i	$-0.608305\pi$
$761$	−14011.8	−0.667446	−0.333723	+	0.942671i	$0.608305\pi$
$762$	−27253.4	−1.29565
$763$	0	0
$764$	7150.69	0.338616
$765$	−3044.56	−0.143891
$766$	−2515.97	−0.118676
$767$	22919.8	1.07899
$768$	15326.6	0.720120
$769$	−3342.49	−0.156740	−0.0783701	−	0.996924i	$-0.524972\pi$
$769$	−3342.49	−0.156740	−0.0783701	+	0.996924i	$0.524972\pi$
$770$	0	0
$771$	−14172.9	−0.662027
$772$	5984.51	0.278999
$773$	21074.6	0.980594	0.490297	−	0.871555i	$-0.336888\pi$
$773$	21074.6	0.980594	0.490297	+	0.871555i	$0.336888\pi$
$774$	3191.90	0.148231
$775$	227.208	0.0105310
$776$	2385.40	0.110349
$777$	0	0
$778$	37296.0	1.71867
$779$	−25763.9	−1.18496
$780$	−4359.26	−0.200111
$781$	−23908.5	−1.09541
$782$	26981.1	1.23382
$783$	−1585.85	−0.0723800
$784$	0	0
$785$	−19492.3	−0.886254
$786$	13782.8	0.625464
$787$	−21394.8	−0.969048	−0.484524	−	0.874778i	$-0.661007\pi$
$787$	−21394.8	−0.969048	−0.484524	+	0.874778i	$0.661007\pi$
$788$	20394.1	0.921968
$789$	17926.1	0.808853
$790$	−16695.7	−0.751906
$791$	0	0
$792$	2247.71	0.100845
$793$	15401.9	0.689706
$794$	16873.5	0.754179
$795$	−9345.29	−0.416910
$796$	6320.83	0.281452
$797$	−20645.0	−0.917547	−0.458773	−	0.888553i	$-0.651711\pi$
$797$	−20645.0	−0.917547	−0.458773	+	0.888553i	$0.651711\pi$
$798$	0	0
$799$	39430.0	1.74585
$800$	5952.82	0.263080
$801$	3466.95	0.152932
$802$	44293.0	1.95017
$803$	−56570.4	−2.48608
$804$	−14708.7	−0.645194
$805$	0	0
$806$	−1518.99	−0.0663825
$807$	−13458.3	−0.587058
$808$	2225.13	0.0968810
$809$	−15939.0	−0.692688	−0.346344	−	0.938108i	$-0.612577\pi$
$809$	−15939.0	−0.692688	−0.346344	+	0.938108i	$0.612577\pi$
$810$	1550.51	0.0672586
$811$	−22829.2	−0.988460	−0.494230	−	0.869331i	$-0.664550\pi$
$811$	−22829.2	−0.988460	−0.494230	+	0.869331i	$0.664550\pi$
$812$	0	0
$813$	−11483.0	−0.495360
$814$	46982.9	2.02303
$815$	−7637.69	−0.328266
$816$	−14804.9	−0.635141
$817$	−8638.90	−0.369935
$818$	−11803.2	−0.504508
$819$	0	0
$820$	9195.58	0.391614
$821$	−5700.22	−0.242313	−0.121157	−	0.992633i	$-0.538660\pi$
$821$	−5700.22	−0.242313	−0.121157	+	0.992633i	$0.538660\pi$
$822$	−31943.5	−1.35542
$823$	−32438.0	−1.37390	−0.686948	−	0.726707i	$-0.741050\pi$
$823$	−32438.0	−1.37390	−0.686948	+	0.726707i	$0.741050\pi$
$824$	−2635.99	−0.111443
$825$	3642.64	0.153722
$826$	0	0
$827$	−12762.6	−0.536638	−0.268319	−	0.963330i	$-0.586468\pi$
$827$	−12762.6	−0.536638	−0.268319	+	0.963330i	$0.586468\pi$
$828$	−6240.79	−0.261935
$829$	30766.7	1.28899	0.644494	−	0.764609i	$-0.277068\pi$
$829$	30766.7	1.28899	0.644494	+	0.764609i	$0.277068\pi$
$830$	10137.4	0.423947
$831$	−10261.6	−0.428365
$832$	−14322.4	−0.596804
$833$	0	0
$834$	−14306.1	−0.593981
$835$	−4992.59	−0.206917
$836$	30150.6	1.24734
$837$	245.384	0.0101335
$838$	−20731.7	−0.854613
$839$	9779.71	0.402423	0.201212	−	0.979548i	$-0.435512\pi$
$839$	9779.71	0.402423	0.201212	+	0.979548i	$0.435512\pi$
$840$	0	0
$841$	−20939.2	−0.858551
$842$	−16034.8	−0.656288
$843$	15707.8	0.641760
$844$	15355.0	0.626233
$845$	1455.40	0.0592510
$846$	−20080.7	−0.816061
$847$	0	0
$848$	−45443.7	−1.84026
$849$	20957.6	0.847190
$850$	−6475.48	−0.261303
$851$	26320.4	1.06023
$852$	−9830.79	−0.395302
$853$	−24201.5	−0.971445	−0.485723	−	0.874113i	$-0.661444\pi$
$853$	−24201.5	−0.971445	−0.485723	+	0.874113i	$0.661444\pi$
$854$	0	0
$855$	−4196.47	−0.167855
$856$	10094.5	0.403062
$857$	−21036.7	−0.838507	−0.419254	−	0.907869i	$-0.637708\pi$
$857$	−21036.7	−0.838507	−0.419254	+	0.907869i	$0.637708\pi$
$858$	−24352.8	−0.968988
$859$	6179.19	0.245438	0.122719	−	0.992441i	$-0.460839\pi$
$859$	6179.19	0.245438	0.122719	+	0.992441i	$0.460839\pi$
$860$	3083.37	0.122258
$861$	0	0
$862$	34870.9	1.37785
$863$	50256.2	1.98232	0.991160	−	0.132671i	$-0.0423555\pi$
$863$	50256.2	1.98232	0.991160	+	0.132671i	$0.0423555\pi$
$864$	6429.04	0.253149
$865$	3426.27	0.134678
$866$	−64497.7	−2.53085
$867$	−1006.65	−0.0394321
$868$	0	0
$869$	−42361.2	−1.65363
$870$	−3372.94	−0.131441
$871$	−32154.1	−1.25086
$872$	2803.37	0.108869
$873$	4175.03	0.161860
$874$	37189.5	1.43930
$875$	0	0
$876$	−23260.8	−0.897156
$877$	−9175.95	−0.353306	−0.176653	−	0.984273i	$-0.556527\pi$
$877$	−9175.95	−0.353306	−0.176653	+	0.984273i	$0.556527\pi$
$878$	32289.5	1.24114
$879$	−22199.1	−0.851828
$880$	17713.2	0.678537
$881$	26172.7	1.00089	0.500444	−	0.865769i	$-0.333170\pi$
$881$	26172.7	1.00089	0.500444	+	0.865769i	$0.333170\pi$
$882$	0	0
$883$	18615.5	0.709471	0.354736	−	0.934967i	$-0.384571\pi$
$883$	18615.5	0.709471	0.354736	+	0.934967i	$0.384571\pi$
$884$	19662.3	0.748092
$885$	−7874.99	−0.299113
$886$	16456.4	0.624001
$887$	12837.8	0.485964	0.242982	−	0.970031i	$-0.421874\pi$
$887$	12837.8	0.485964	0.242982	+	0.970031i	$0.421874\pi$
$888$	−3897.89	−0.147302
$889$	0	0
$890$	7373.86	0.277722
$891$	3934.05	0.147919
$892$	21485.7	0.806496
$893$	54348.4	2.03662
$894$	−222.868	−0.00833759
$895$	−5127.92	−0.191517
$896$	0	0
$897$	−13642.7	−0.507824
$898$	−40370.6	−1.50020
$899$	−533.803	−0.0198035
$900$	1497.79	0.0554738
$901$	42151.5	1.55857
$902$	51370.7	1.89630
$903$	0	0
$904$	−1192.07	−0.0438579
$905$	14497.0	0.532482
$906$	26988.1	0.989647
$907$	−26766.1	−0.979885	−0.489942	−	0.871755i	$-0.662982\pi$
$907$	−26766.1	−0.979885	−0.489942	+	0.871755i	$0.662982\pi$
$908$	4245.87	0.155181
$909$	3894.52	0.142105
$910$	0	0
$911$	5022.67	0.182666	0.0913328	−	0.995820i	$-0.470887\pi$
$911$	5022.67	0.182666	0.0913328	+	0.995820i	$0.470887\pi$
$912$	−20406.3	−0.740923
$913$	25721.3	0.932367
$914$	−45759.0	−1.65599
$915$	−5291.91	−0.191197
$916$	−3626.48	−0.130810
$917$	0	0
$918$	−6993.52	−0.251439
$919$	9541.79	0.342497	0.171248	−	0.985228i	$-0.445220\pi$
$919$	9541.79	0.342497	0.171248	+	0.985228i	$0.445220\pi$
$920$	2678.19	0.0959754
$921$	−8005.93	−0.286432
$922$	−65852.4	−2.35220
$923$	−21490.7	−0.766387
$924$	0	0
$925$	−6316.90	−0.224539
$926$	39695.7	1.40873
$927$	−4613.63	−0.163464
$928$	−13985.6	−0.494718
$929$	25479.6	0.899846	0.449923	−	0.893067i	$-0.351451\pi$
$929$	25479.6	0.899846	0.449923	+	0.893067i	$0.351451\pi$
$930$	521.909	0.0184022
$931$	0	0
$932$	−38267.2	−1.34494
$933$	−18567.7	−0.651533
$934$	−64621.9	−2.26391
$935$	−16430.0	−0.574671
$936$	2020.41	0.0705545
$937$	33608.3	1.17176	0.585878	−	0.810399i	$-0.300750\pi$
$937$	33608.3	1.17176	0.585878	+	0.810399i	$0.300750\pi$
$938$	0	0
$939$	8764.77	0.304609
$940$	−19397.9	−0.673073
$941$	19173.6	0.664232	0.332116	−	0.943239i	$-0.392238\pi$
$941$	19173.6	0.664232	0.332116	+	0.943239i	$0.392238\pi$
$942$	−44774.9	−1.54867
$943$	28778.5	0.993804
$944$	−38294.0	−1.32030
$945$	0	0
$946$	17225.1	0.592005
$947$	−979.315	−0.0336045	−0.0168023	−	0.999859i	$-0.505349\pi$
$947$	−979.315	−0.0336045	−0.0168023	+	0.999859i	$0.505349\pi$
$948$	−17418.2	−0.596749
$949$	−50849.5	−1.73935
$950$	−8925.48	−0.304822
$951$	29476.7	1.00510
$952$	0	0
$953$	3048.61	0.103624	0.0518122	−	0.998657i	$-0.483500\pi$
$953$	3048.61	0.103624	0.0518122	+	0.998657i	$0.483500\pi$
$954$	−21466.7	−0.728521
$955$	−5370.92	−0.181989
$956$	−17827.7	−0.603127
$957$	−8558.03	−0.289072
$958$	28059.0	0.946290
$959$	0	0
$960$	4921.02	0.165443
$961$	−29708.4	−0.997227
$962$	42231.6	1.41538
$963$	17667.8	0.591211
$964$	14659.4	0.489781
$965$	−4495.00	−0.149947
$966$	0	0
$967$	−14467.9	−0.481133	−0.240567	−	0.970633i	$-0.577333\pi$
$967$	−14467.9	−0.481133	−0.240567	+	0.970633i	$0.577333\pi$
$968$	5285.62	0.175502
$969$	18928.0	0.627507
$970$	8879.89	0.293934
$971$	−12952.8	−0.428090	−0.214045	−	0.976824i	$-0.568664\pi$
$971$	−12952.8	−0.428090	−0.214045	+	0.976824i	$0.568664\pi$
$972$	1617.62	0.0533797
$973$	0	0
$974$	65885.4	2.16746
$975$	3274.26	0.107549
$976$	−25733.2	−0.843954
$977$	47244.2	1.54706	0.773529	−	0.633760i	$-0.218489\pi$
$977$	47244.2	1.54706	0.773529	+	0.633760i	$0.218489\pi$
$978$	−17544.2	−0.573621
$979$	18709.4	0.610781
$980$	0	0
$981$	4906.58	0.159689
$982$	−43615.3	−1.41733
$983$	1536.84	0.0498651	0.0249326	−	0.999689i	$-0.492063\pi$
$983$	1536.84	0.0498651	0.0249326	+	0.999689i	$0.492063\pi$
$984$	−4261.92	−0.138074
$985$	−15318.1	−0.495509
$986$	15213.5	0.491376
$987$	0	0
$988$	27101.5	0.872685
$989$	9649.73	0.310256
$990$	8367.35	0.268618
$991$	3785.22	0.121334	0.0606668	−	0.998158i	$-0.480677\pi$
$991$	3785.22	0.121334	0.0606668	+	0.998158i	$0.480677\pi$
$992$	2164.04	0.0692625
$993$	−27774.5	−0.887610
$994$	0	0
$995$	−4747.61	−0.151266
$996$	10576.2	0.336465
$997$	25894.9	0.822566	0.411283	−	0.911508i	$-0.365081\pi$
$997$	25894.9	0.822566	0.411283	+	0.911508i	$0.365081\pi$
$998$	−73044.0	−2.31680
$999$	−6822.26	−0.216063

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.4.a.o.1.1		2
3.2	odd	2		2205.4.a.bb.1.2		2
7.6	odd	2		105.4.a.e.1.1	✓	2
21.20	even	2		315.4.a.k.1.2		2
28.27	even	2		1680.4.a.bo.1.1		2
35.13	even	4		525.4.d.l.274.4		4
35.27	even	4		525.4.d.l.274.1		4
35.34	odd	2		525.4.a.l.1.2		2
105.104	even	2		1575.4.a.q.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.a.e.1.1	✓	2	7.6	odd	2
315.4.a.k.1.2		2	21.20	even	2
525.4.a.l.1.2		2	35.34	odd	2
525.4.d.l.274.1		4	35.27	even	4
525.4.d.l.274.4		4	35.13	even	4
735.4.a.o.1.1		2	1.1	even	1	trivial
1575.4.a.q.1.1		2	105.104	even	2
1680.4.a.bo.1.1		2	28.27	even	2
2205.4.a.bb.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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	735.a (trivial)

\(f(q)\)	\(=\)	\(q-3.82843 q^{2} +3.00000 q^{3} +6.65685 q^{4} -5.00000 q^{5} -11.4853 q^{6} +5.14214 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.82843 q^{2} +3.00000 q^{3} +6.65685 q^{4} -5.00000 q^{5} -11.4853 q^{6} +5.14214 q^{8} +9.00000 q^{9} +19.1421 q^{10} +48.5685 q^{11} +19.9706 q^{12} +43.6569 q^{13} -15.0000 q^{15} -72.9411 q^{16} +67.6569 q^{17} -34.4558 q^{18} +93.2548 q^{19} -33.2843 q^{20} -185.941 q^{22} -104.167 q^{23} +15.4264 q^{24} +25.0000 q^{25} -167.137 q^{26} +27.0000 q^{27} -58.7351 q^{29} +57.4264 q^{30} +9.08831 q^{31} +238.113 q^{32} +145.706 q^{33} -259.019 q^{34} +59.9117 q^{36} -252.676 q^{37} -357.019 q^{38} +130.971 q^{39} -25.7107 q^{40} -276.274 q^{41} -92.6375 q^{43} +323.314 q^{44} -45.0000 q^{45} +398.794 q^{46} +582.794 q^{47} -218.823 q^{48} -95.7107 q^{50} +202.971 q^{51} +290.617 q^{52} +623.019 q^{53} -103.368 q^{54} -242.843 q^{55} +279.765 q^{57} +224.863 q^{58} +524.999 q^{59} -99.8528 q^{60} +352.794 q^{61} -34.7939 q^{62} -328.068 q^{64} -218.284 q^{65} -557.823 q^{66} -736.520 q^{67} +450.382 q^{68} -312.500 q^{69} -492.264 q^{71} +46.2792 q^{72} -1164.75 q^{73} +967.352 q^{74} +75.0000 q^{75} +620.784 q^{76} -501.411 q^{78} -872.195 q^{79} +364.706 q^{80} +81.0000 q^{81} +1057.70 q^{82} +529.588 q^{83} -338.284 q^{85} +354.656 q^{86} -176.205 q^{87} +249.746 q^{88} +385.216 q^{89} +172.279 q^{90} -693.421 q^{92} +27.2649 q^{93} -2231.18 q^{94} -466.274 q^{95} +714.338 q^{96} +463.892 q^{97} +437.117 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 6 q^{3} + 2 q^{4} - 10 q^{5} - 6 q^{6} - 18 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 6 * q^3 + 2 * q^4 - 10 * q^5 - 6 * q^6 - 18 * q^8 + 18 * q^9	\( 2 q - 2 q^{2} + 6 q^{3} + 2 q^{4} - 10 q^{5} - 6 q^{6} - 18 q^{8} + 18 q^{9} + 10 q^{10} - 16 q^{11} + 6 q^{12} + 76 q^{13} - 30 q^{15} - 78 q^{16} + 124 q^{17} - 18 q^{18} + 96 q^{19} - 10 q^{20} - 304 q^{22} - 16 q^{23} - 54 q^{24} + 50 q^{25} - 108 q^{26} + 54 q^{27} + 188 q^{29} + 30 q^{30} + 120 q^{31} + 414 q^{32} - 48 q^{33} - 156 q^{34} + 18 q^{36} - 132 q^{37} - 352 q^{38} + 228 q^{39} + 90 q^{40} - 100 q^{41} - 536 q^{43} + 624 q^{44} - 90 q^{45} + 560 q^{46} + 928 q^{47} - 234 q^{48} - 50 q^{50} + 372 q^{51} + 140 q^{52} + 884 q^{53} - 54 q^{54} + 80 q^{55} + 288 q^{57} + 676 q^{58} - 104 q^{59} - 30 q^{60} + 468 q^{61} + 168 q^{62} + 34 q^{64} - 380 q^{65} - 912 q^{66} - 1688 q^{67} + 188 q^{68} - 48 q^{69} - 136 q^{71} - 162 q^{72} - 508 q^{73} + 1188 q^{74} + 150 q^{75} + 608 q^{76} - 324 q^{78} - 432 q^{79} + 390 q^{80} + 162 q^{81} + 1380 q^{82} + 584 q^{83} - 620 q^{85} - 456 q^{86} + 564 q^{87} + 1744 q^{88} + 1404 q^{89} + 90 q^{90} - 1104 q^{92} + 360 q^{93} - 1600 q^{94} - 480 q^{95} + 1242 q^{96} + 1188 q^{97} - 144 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 6 * q^3 + 2 * q^4 - 10 * q^5 - 6 * q^6 - 18 * q^8 + 18 * q^9 + 10 * q^10 - 16 * q^11 + 6 * q^12 + 76 * q^13 - 30 * q^15 - 78 * q^16 + 124 * q^17 - 18 * q^18 + 96 * q^19 - 10 * q^20 - 304 * q^22 - 16 * q^23 - 54 * q^24 + 50 * q^25 - 108 * q^26 + 54 * q^27 + 188 * q^29 + 30 * q^30 + 120 * q^31 + 414 * q^32 - 48 * q^33 - 156 * q^34 + 18 * q^36 - 132 * q^37 - 352 * q^38 + 228 * q^39 + 90 * q^40 - 100 * q^41 - 536 * q^43 + 624 * q^44 - 90 * q^45 + 560 * q^46 + 928 * q^47 - 234 * q^48 - 50 * q^50 + 372 * q^51 + 140 * q^52 + 884 * q^53 - 54 * q^54 + 80 * q^55 + 288 * q^57 + 676 * q^58 - 104 * q^59 - 30 * q^60 + 468 * q^61 + 168 * q^62 + 34 * q^64 - 380 * q^65 - 912 * q^66 - 1688 * q^67 + 188 * q^68 - 48 * q^69 - 136 * q^71 - 162 * q^72 - 508 * q^73 + 1188 * q^74 + 150 * q^75 + 608 * q^76 - 324 * q^78 - 432 * q^79 + 390 * q^80 + 162 * q^81 + 1380 * q^82 + 584 * q^83 - 620 * q^85 - 456 * q^86 + 564 * q^87 + 1744 * q^88 + 1404 * q^89 + 90 * q^90 - 1104 * q^92 + 360 * q^93 - 1600 * q^94 - 480 * q^95 + 1242 * q^96 + 1188 * q^97 - 144 * q^99

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