LMFDB - Embedded newform 432.3.x.a.125.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,3,Mod(125,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 10]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("432.125");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	432.x (of order $12$, degree $4$, not minimal)

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:	no
Analytic conductor:	$11.7711474204$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$46$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			125.20
Character	$\chi$	$=$	432.125
Dual form			432.3.x.a.197.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.266371 + 1.98218i) q^{2} +(-3.85809 - 1.05599i) q^{4} +(-4.55983 + 1.22180i) q^{5} +(5.29059 - 3.05452i) q^{7} +(3.12086 - 7.36616i) q^{8} +O(q^{10})$	\(q+(-0.266371 + 1.98218i) q^{2} +(-3.85809 - 1.05599i) q^{4} +(-4.55983 + 1.22180i) q^{5} +(5.29059 - 3.05452i) q^{7} +(3.12086 - 7.36616i) q^{8} +(-1.20723 - 9.36386i) q^{10} +(0.521228 - 1.94525i) q^{11} +(15.0125 - 4.02259i) q^{13} +(4.64536 + 11.3006i) q^{14} +(13.7698 + 8.14824i) q^{16} +26.7923i q^{17} +(-1.12468 - 1.12468i) q^{19} +(18.8825 + 0.101322i) q^{20} +(3.71700 + 1.55133i) q^{22} +(6.66267 - 11.5401i) q^{23} +(-2.35140 + 1.35758i) q^{25} +(3.97461 + 30.8291i) q^{26} +(-23.6371 + 6.19781i) q^{28} +(26.7575 + 7.16964i) q^{29} +(-24.0040 + 41.5762i) q^{31} +(-19.8192 + 25.1237i) q^{32} +(-53.1071 - 7.13669i) q^{34} +(-20.3922 + 20.3922i) q^{35} +(-4.95716 + 4.95716i) q^{37} +(2.52891 - 1.92975i) q^{38} +(-5.23058 + 37.4015i) q^{40} +(6.97411 - 12.0795i) q^{41} +(54.0892 + 14.4932i) q^{43} +(-4.06511 + 6.95454i) q^{44} +(21.0998 + 16.2806i) q^{46} +(15.4170 - 8.90103i) q^{47} +(-5.83977 + 10.1148i) q^{49} +(-2.06463 - 5.02253i) q^{50} +(-62.1676 - 0.333586i) q^{52} +(64.2137 + 64.2137i) q^{53} +9.50684i q^{55} +(-5.98892 - 48.5040i) q^{56} +(-21.3390 + 51.1284i) q^{58} +(82.9765 - 22.2335i) q^{59} +(-12.9377 + 48.2841i) q^{61} +(-76.0176 - 58.6551i) q^{62} +(-44.5205 - 45.9774i) q^{64} +(-63.5397 + 36.6847i) q^{65} +(16.1544 - 4.32857i) q^{67} +(28.2924 - 103.367i) q^{68} +(-34.9891 - 45.8529i) q^{70} -60.1578 q^{71} -140.185i q^{73} +(-8.50556 - 11.1464i) q^{74} +(3.15148 + 5.52680i) q^{76} +(-3.18421 - 11.8836i) q^{77} +(63.2251 + 109.509i) q^{79} +(-72.7433 - 20.3307i) q^{80} +(22.0861 + 17.0416i) q^{82} +(90.5036 + 24.2504i) q^{83} +(-32.7348 - 122.168i) q^{85} +(-43.1359 + 103.354i) q^{86} +(-12.7023 - 9.91029i) q^{88} -58.8859 q^{89} +(67.1380 - 67.1380i) q^{91} +(-37.8915 + 37.4870i) q^{92} +(13.5368 + 32.9304i) q^{94} +(6.50251 + 3.75423i) q^{95} +(-50.3496 - 87.2081i) q^{97} +(-18.4938 - 14.2698i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5}+O(q^{10}) $ 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5	$ 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} - 120 q^{20} - 2 q^{22} - 72 q^{28} + 6 q^{29} - 4 q^{31} + 6 q^{32} + 6 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 160 q^{46} + 12 q^{47} + 472 q^{49} - 228 q^{50} - 2 q^{52} + 300 q^{56} - 92 q^{58} + 438 q^{59} - 2 q^{61} + 244 q^{64} + 12 q^{65} - 2 q^{67} + 144 q^{68} + 96 q^{70} - 246 q^{74} - 158 q^{76} + 6 q^{77} - 4 q^{79} - 388 q^{82} + 726 q^{83} + 48 q^{85} - 894 q^{86} + 22 q^{88} - 204 q^{91} + 348 q^{92} - 18 q^{94} + 12 q^{95} - 4 q^{97}+O(q^{100}) $ 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 - 120 * q^20 - 2 * q^22 - 72 * q^28 + 6 * q^29 - 4 * q^31 + 6 * q^32 + 6 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 160 * q^46 + 12 * q^47 + 472 * q^49 - 228 * q^50 - 2 * q^52 + 300 * q^56 - 92 * q^58 + 438 * q^59 - 2 * q^61 + 244 * q^64 + 12 * q^65 - 2 * q^67 + 144 * q^68 + 96 * q^70 - 246 * q^74 - 158 * q^76 + 6 * q^77 - 4 * q^79 - 388 * q^82 + 726 * q^83 + 48 * q^85 - 894 * q^86 + 22 * q^88 - 204 * q^91 + 348 * q^92 - 18 * q^94 + 12 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.266371	+	1.98218i	−0.133186	+	0.991091i
$2$	−0.266371	+	1.98218i	−0.133186	+	0.991091i
$3$		0			0
$3$		0			0
$4$	−3.85809	−	1.05599i	−0.964523	−	0.263998i
$5$	−4.55983	+	1.22180i	−0.911966	+	0.244360i	−0.684148	−	0.729343i	$-0.739826\pi$
$5$	−4.55983	+	1.22180i	−0.911966	+	0.244360i	−0.227818	+	0.973704i	$0.573159\pi$
$6$		0			0
$7$	5.29059	−	3.05452i	0.755799	−	0.436361i	−0.0719866	−	0.997406i	$-0.522934\pi$
$7$	5.29059	−	3.05452i	0.755799	−	0.436361i	0.827785	+	0.561045i	$0.189601\pi$
$8$	3.12086	−	7.36616i	0.390107	−	0.920769i
$9$		0			0
$10$	−1.20723	−	9.36386i	−0.120723	−	0.936386i
$11$	0.521228	−	1.94525i	0.0473843	−	0.176841i	−0.938178	−	0.346153i	$-0.887488\pi$
$11$	0.521228	−	1.94525i	0.0473843	−	0.176841i	0.985563	+	0.169312i	$0.0541545\pi$
$12$		0			0
$13$	15.0125	−	4.02259i	1.15481	−	0.309430i	0.369919	−	0.929064i	$-0.379386\pi$
$13$	15.0125	−	4.02259i	1.15481	−	0.309430i	0.784891	+	0.619634i	$0.212719\pi$
$14$	4.64536	+	11.3006i	0.331812	+	0.807182i
$15$		0			0
$16$	13.7698	+	8.14824i	0.860610	+	0.509265i
$17$			26.7923i			1.57602i	0.615666	+	0.788008i	$0.288887\pi$
$17$			26.7923i			1.57602i	−0.615666	+	0.788008i	$0.711113\pi$
$18$		0			0
$19$	−1.12468	−	1.12468i	−0.0591939	−	0.0591939i	0.676890	−	0.736084i	$-0.263327\pi$
$19$	−1.12468	−	1.12468i	−0.0591939	−	0.0591939i	−0.736084	+	0.676890i	$0.763327\pi$
$20$	18.8825	+	0.101322i	0.944123	+	0.00506609i
$21$		0			0
$22$	3.71700	+	1.55133i	0.168954	+	0.0705149i
$23$	6.66267	−	11.5401i	0.289681	−	0.501743i	−0.684052	−	0.729433i	$-0.739784\pi$
$23$	6.66267	−	11.5401i	0.289681	−	0.501743i	0.973734	+	0.227690i	$0.0731173\pi$
$24$		0			0
$25$	−2.35140	+	1.35758i	−0.0940561	+	0.0543033i
$26$	3.97461	+	30.8291i	0.152870	+	1.18573i
$27$		0			0
$28$	−23.6371	+	6.19781i	−0.844184	+	0.221350i
$29$	26.7575	+	7.16964i	0.922671	+	0.247229i	0.688727	−	0.725021i	$-0.258170\pi$
$29$	26.7575	+	7.16964i	0.922671	+	0.247229i	0.233944	+	0.972250i	$0.424837\pi$
$30$		0			0
$31$	−24.0040	+	41.5762i	−0.774323	+	1.34117i	0.160851	+	0.986979i	$0.448576\pi$
$31$	−24.0040	+	41.5762i	−0.774323	+	1.34117i	−0.935174	+	0.354189i	$0.884757\pi$
$32$	−19.8192	+	25.1237i	−0.619349	+	0.785116i
$33$		0			0
$34$	−53.1071	−	7.13669i	−1.56197	−	0.209903i
$35$	−20.3922	+	20.3922i	−0.582633	+	0.582633i
$36$		0			0
$37$	−4.95716	+	4.95716i	−0.133977	+	0.133977i	−0.770915	−	0.636938i	$-0.780201\pi$
$37$	−4.95716	+	4.95716i	−0.133977	+	0.133977i	0.636938	+	0.770915i	$0.280201\pi$
$38$	2.52891	−	1.92975i	0.0665504	−	0.0507828i
$39$		0			0
$40$	−5.23058	+	37.4015i	−0.130765	+	0.935037i
$41$	6.97411	−	12.0795i	0.170100	−	0.294622i	−0.768355	−	0.640024i	$-0.778924\pi$
$41$	6.97411	−	12.0795i	0.170100	−	0.294622i	0.938455	+	0.345402i	$0.112258\pi$
$42$		0			0
$43$	54.0892	+	14.4932i	1.25789	+	0.337050i	0.825379	−	0.564579i	$-0.190961\pi$
$43$	54.0892	+	14.4932i	1.25789	+	0.337050i	0.432510	+	0.901629i	$0.357628\pi$
$44$	−4.06511	+	6.95454i	−0.0923890	+	0.158058i
$45$		0			0
$46$	21.0998	+	16.2806i	0.458692	+	0.353926i
$47$	15.4170	−	8.90103i	0.328022	−	0.189384i	−0.326940	−	0.945045i	$-0.606018\pi$
$47$	15.4170	−	8.90103i	0.328022	−	0.189384i	0.654963	+	0.755661i	$0.272684\pi$
$48$		0			0
$49$	−5.83977	+	10.1148i	−0.119179	+	0.206424i
$50$	−2.06463	−	5.02253i	−0.0412926	−	0.100451i
$51$		0			0
$52$	−62.1676	−	0.333586i	−1.19553	−	0.00641512i
$53$	64.2137	+	64.2137i	1.21158	+	1.21158i	0.970507	+	0.241073i	$0.0774993\pi$
$53$	64.2137	+	64.2137i	1.21158	+	1.21158i	0.241073	+	0.970507i	$0.422501\pi$
$54$		0			0
$55$			9.50684i			0.172852i
$56$	−5.98892	−	48.5040i	−0.106945	−	0.866144i
$57$		0			0
$58$	−21.3390	+	51.1284i	−0.367913	+	0.881524i
$59$	82.9765	−	22.2335i	1.40638	−	0.376839i	0.525750	−	0.850639i	$-0.323785\pi$
$59$	82.9765	−	22.2335i	1.40638	−	0.376839i	0.880632	+	0.473801i	$0.157118\pi$
$60$		0			0
$61$	−12.9377	+	48.2841i	−0.212093	+	0.791543i	0.775076	+	0.631868i	$0.217711\pi$
$61$	−12.9377	+	48.2841i	−0.212093	+	0.791543i	−0.987170	+	0.159676i	$0.948955\pi$
$62$	−76.0176	−	58.6551i	−1.22609	−	0.946049i
$63$		0			0
$64$	−44.5205	−	45.9774i	−0.695633	−	0.718397i
$65$	−63.5397	+	36.6847i	−0.977534	+	0.564380i
$66$		0			0
$67$	16.1544	−	4.32857i	0.241111	−	0.0646055i	−0.136240	−	0.990676i	$-0.543502\pi$
$67$	16.1544	−	4.32857i	0.241111	−	0.0646055i	0.377351	+	0.926070i	$0.376835\pi$
$68$	28.2924	−	103.367i	0.416065	−	1.52010i
$69$		0			0
$70$	−34.9891	−	45.8529i	−0.499844	−	0.655041i
$71$	−60.1578			−0.847293			−0.423646	−	0.905828i	$-0.639250\pi$
$71$	−60.1578			−0.847293			−0.423646	+	0.905828i	$0.639250\pi$
$72$		0			0
$73$		−	140.185i		−	1.92034i	−0.279409	−	0.960172i	$-0.590138\pi$
$73$		−	140.185i		−	1.92034i	0.279409	−	0.960172i	$-0.409862\pi$
$74$	−8.50556	−	11.1464i	−0.114940	−	0.150628i
$75$		0			0
$76$	3.15148	+	5.52680i	0.0414668	+	0.0727210i
$77$	−3.18421	−	11.8836i	−0.0413533	−	0.154333i
$78$		0			0
$79$	63.2251	+	109.509i	0.800317	+	1.38619i	0.919407	+	0.393307i	$0.128669\pi$
$79$	63.2251	+	109.509i	0.800317	+	1.38619i	−0.119090	+	0.992883i	$0.537998\pi$
$80$	−72.7433	−	20.3307i	−0.909291	−	0.254133i
$81$		0			0
$82$	22.0861	+	17.0416i	0.269342	+	0.207824i
$83$	90.5036	+	24.2504i	1.09040	+	0.292173i	0.758852	−	0.651263i	$-0.225761\pi$
$83$	90.5036	+	24.2504i	1.09040	+	0.292173i	0.331553	+	0.943437i	$0.392427\pi$
$84$		0			0
$85$	−32.7348	−	122.168i	−0.385116	−	1.43727i
$86$	−43.1359	+	103.354i	−0.501580	+	1.20179i
$87$		0			0
$88$	−12.7023	−	9.91029i	−0.144345	−	0.112617i
$89$	−58.8859			−0.661640			−0.330820	−	0.943694i	$-0.607325\pi$
$89$	−58.8859			−0.661640			−0.330820	+	0.943694i	$0.607325\pi$
$90$		0			0
$91$	67.1380	−	67.1380i	0.737781	−	0.737781i
$92$	−37.8915	+	37.4870i	−0.411864	+	0.407467i
$93$		0			0
$94$	13.5368	+	32.9304i	0.144009	+	0.350323i
$95$	6.50251	+	3.75423i	0.0684475	+	0.0395182i
$96$		0			0
$97$	−50.3496	−	87.2081i	−0.519069	−	0.899053i	−0.999754	−	0.0221602i	$-0.992946\pi$
$97$	−50.3496	−	87.2081i	−0.519069	−	0.899053i	0.480686	−	0.876893i	$-0.340388\pi$
$98$	−18.4938	−	14.2698i	−0.188712	−	0.145610i
$99$		0			0
$100$	10.5055	−	2.75461i	0.105055	−	0.0275461i
$101$	−28.1219	+	104.953i	−0.278435	+	1.03913i	0.675069	+	0.737754i	$0.264114\pi$
$101$	−28.1219	+	104.953i	−0.278435	+	1.03913i	−0.953504	+	0.301379i	$0.902553\pi$
$102$		0			0
$103$	77.3436	+	44.6544i	0.750909	+	0.433538i	0.826022	−	0.563638i	$-0.190599\pi$
$103$	77.3436	+	44.6544i	0.750909	+	0.433538i	−0.0751133	+	0.997175i	$0.523932\pi$
$104$	17.2209	−	123.139i	0.165585	−	1.18402i
$105$		0			0
$106$	−144.388	+	110.179i	−1.36215	+	1.03942i
$107$	105.449	+	105.449i	0.985506	+	0.985506i	0.999896	−	0.0143907i	$-0.00458087\pi$
$107$	105.449	+	105.449i	0.985506	+	0.985506i	−0.0143907	+	0.999896i	$0.504581\pi$
$108$		0			0
$109$	−8.22296	−	8.22296i	−0.0754400	−	0.0754400i	0.668380	−	0.743820i	$-0.266988\pi$
$109$	−8.22296	−	8.22296i	−0.0754400	−	0.0754400i	−0.743820	+	0.668380i	$0.766988\pi$
$110$	−18.8443	−	2.53235i	−0.171312	−	0.0230214i
$111$		0			0
$112$	97.7391	+	1.04895i	0.872671	+	0.00936564i
$113$	−153.833	−	88.8156i	−1.36136	−	0.785979i	−0.371551	−	0.928412i	$-0.621174\pi$
$113$	−153.833	−	88.8156i	−1.36136	−	0.785979i	−0.989804	+	0.142433i	$0.954507\pi$
$114$		0			0
$115$	−16.2809	+	60.7613i	−0.141573	+	0.528359i
$116$	−95.6617	−	55.9168i	−0.824670	−	0.482042i
$117$		0			0
$118$	21.9683	+	170.397i	0.186172	+	1.44404i
$119$	81.8376	+	141.747i	0.687711	+	1.19115i
$120$		0			0
$121$	101.277	+	58.4722i	0.836998	+	0.483241i
$122$	−92.2617	−	38.5064i	−0.756244	−	0.315626i
$123$		0			0
$124$	136.514	−	135.057i	1.10092	−	1.08917i
$125$	92.5139	−	92.5139i	0.740112	−	0.740112i
$126$		0			0
$127$	0.474875			0.00373917			0.00186959	−	0.999998i	$-0.499405\pi$
$127$	0.474875			0.00373917			0.00186959	+	0.999998i	$0.499405\pi$
$128$	102.995	−	76.0007i	0.804646	−	0.593755i
$129$		0			0
$130$	−55.7906	−	135.719i	−0.429158	−	1.04399i
$131$	−10.4548	−	39.0178i	−0.0798076	−	0.297846i	0.914473	−	0.404647i	$-0.132606\pi$
$131$	−10.4548	−	39.0178i	−0.0798076	−	0.297846i	−0.994280	+	0.106802i	$0.965939\pi$
$132$		0			0
$133$	−9.38562	−	2.51487i	−0.0705686	−	0.0189088i
$134$	4.27693	+	33.1741i	0.0319174	+	0.247568i
$135$		0			0
$136$	197.356	+	83.6148i	1.45115	+	0.614815i
$137$	1.46723	+	2.54132i	0.0107097	+	0.0185498i	0.871331	−	0.490696i	$-0.163258\pi$
$137$	1.46723	+	2.54132i	0.0107097	+	0.0185498i	−0.860621	+	0.509246i	$0.829924\pi$
$138$		0			0
$139$	−65.5197	−	244.523i	−0.471365	−	1.75916i	−0.634874	−	0.772616i	$-0.718948\pi$
$139$	−65.5197	−	244.523i	−0.471365	−	1.75916i	0.163509	−	0.986542i	$-0.447719\pi$
$140$	100.209	−	57.1409i	0.715777	−	0.408149i
$141$		0			0
$142$	16.0243	−	119.244i	0.112847	−	0.839745i
$143$		−	31.2998i		−	0.218880i
$144$		0			0
$145$	−130.769			−0.901857
$146$	277.872	+	37.3413i	1.90324	+	0.255762i
$147$		0			0
$148$	24.3599	−	13.8905i	0.164594	−	0.0938545i
$149$	25.1199	−	6.73085i	0.168590	−	0.0451735i	−0.173537	−	0.984827i	$-0.555520\pi$
$149$	25.1199	−	6.73085i	0.168590	−	0.0451735i	0.342126	+	0.939654i	$0.388853\pi$
$150$		0			0
$151$	114.842	−	66.3039i	0.760541	−	0.439099i	−0.0689490	−	0.997620i	$-0.521965\pi$
$151$	114.842	−	66.3039i	0.760541	−	0.439099i	0.829490	+	0.558522i	$0.188631\pi$
$152$	−11.7946	+	4.77462i	−0.0775959	+	0.0314120i
$153$		0			0
$154$	24.4037	−	3.14622i	0.158465	−	0.0204300i
$155$	58.6563	−	218.908i	0.378428	−	1.41231i
$156$		0			0
$157$	220.278	−	59.0232i	1.40304	−	0.375944i	0.523606	−	0.851961i	$-0.324586\pi$
$157$	220.278	−	59.0232i	1.40304	−	0.375944i	0.879436	+	0.476017i	$0.157920\pi$
$158$	−233.908	+	96.1535i	−1.48043	+	0.608567i
$159$		0			0
$160$	59.6758	−	138.775i	0.372974	−	0.867343i
$161$		−	81.4052i		−	0.505622i
$162$		0			0
$163$	8.97704	+	8.97704i	0.0550738	+	0.0550738i	0.734107	−	0.679033i	$-0.237601\pi$
$163$	8.97704	+	8.97704i	0.0550738	+	0.0550738i	−0.679033	+	0.734107i	$0.737601\pi$
$164$	−39.6626	+	39.2392i	−0.241845	+	0.239264i
$165$		0			0
$166$	−72.1762	+	172.935i	−0.434797	+	1.04178i
$167$	−2.97024	+	5.14460i	−0.0177859	+	0.0308060i	−0.874781	−	0.484518i	$-0.838995\pi$
$167$	−2.97024	+	5.14460i	−0.0177859	+	0.0308060i	0.856995	+	0.515324i	$0.172328\pi$
$168$		0			0
$169$	62.8364	−	36.2786i	0.371813	−	0.214666i
$170$	250.879	−	32.3443i	1.47576	−	0.190261i
$171$		0			0
$172$	−193.376	−	113.034i	−1.12428	−	0.657173i
$173$	−227.784	−	61.0347i	−1.31667	−	0.352801i	−0.468942	−	0.883229i	$-0.655365\pi$
$173$	−227.784	−	61.0347i	−1.31667	−	0.352801i	−0.847730	+	0.530427i	$0.822032\pi$
$174$		0			0
$175$	−8.29354	+	14.3648i	−0.0473916	+	0.0820847i
$176$	23.0275	−	22.5385i	0.130838	−	0.128060i
$177$		0			0
$178$	15.6855	−	116.723i	0.0881209	−	0.655745i
$179$	−46.1228	+	46.1228i	−0.257669	+	0.257669i	−0.824106	−	0.566436i	$-0.808322\pi$
$179$	−46.1228	+	46.1228i	−0.257669	+	0.257669i	0.566436	+	0.824106i	$0.308322\pi$
$180$		0			0
$181$	−144.004	+	144.004i	−0.795602	+	0.795602i	−0.982399	−	0.186797i	$-0.940189\pi$
$181$	−144.004	+	144.004i	−0.795602	+	0.795602i	0.186797	+	0.982399i	$0.440189\pi$
$182$	115.196	+	150.963i	0.632946	+	0.829470i
$183$		0			0
$184$	−64.2128	−	85.0933i	−0.348983	−	0.462463i
$185$	16.5471	−	28.6605i	0.0894440	−	0.154922i
$186$		0			0
$187$	52.1176	+	13.9649i	0.278704	+	0.0746784i
$188$	−68.8798	+	18.0607i	−0.366382	+	0.0960677i
$189$		0			0
$190$	−9.17365	+	11.8891i	−0.0482823	+	0.0625744i
$191$	176.197	−	101.727i	0.922497	−	0.532604i	0.0380664	−	0.999275i	$-0.487880\pi$
$191$	176.197	−	101.727i	0.922497	−	0.532604i	0.884431	+	0.466671i	$0.154547\pi$
$192$		0			0
$193$	10.8334	−	18.7640i	0.0561317	−	0.0972230i	−0.836594	−	0.547823i	$-0.815457\pi$
$193$	10.8334	−	18.7640i	0.0561317	−	0.0972230i	0.892726	+	0.450600i	$0.148790\pi$
$194$	186.274	−	76.5724i	0.960176	−	0.394703i
$195$		0			0
$196$	33.2115	−	32.8570i	0.169446	−	0.167638i
$197$	−217.283	−	217.283i	−1.10296	−	1.10296i	−0.994052	−	0.108909i	$-0.965264\pi$
$197$	−217.283	−	217.283i	−1.10296	−	1.10296i	−0.108909	−	0.994052i	$-0.534736\pi$
$198$		0			0
$199$			193.267i			0.971192i	0.874183	+	0.485596i	$0.161397\pi$
$199$			193.267i			0.971192i	−0.874183	+	0.485596i	$0.838603\pi$
$200$	2.66178	+	21.5576i	0.0133089	+	0.107788i
$201$		0			0
$202$	−200.544	−	83.6991i	−0.992793	−	0.414352i
$203$	163.463	−	43.7997i	0.805235	−	0.215762i
$204$		0			0
$205$	−17.0420	+	63.6015i	−0.0831315	+	0.310251i
$206$	−109.115	+	141.415i	−0.529685	+	0.686478i
$207$		0			0
$208$	239.496	+	66.9355i	1.15142	+	0.321805i
$209$	−2.77401	+	1.60157i	−0.0132728	+	0.00766304i
$210$		0			0
$211$	−117.183	+	31.3990i	−0.555368	+	0.148810i	−0.525577	−	0.850746i	$-0.676151\pi$
$211$	−117.183	+	31.3990i	−0.555368	+	0.148810i	−0.0297904	+	0.999556i	$0.509484\pi$
$212$	−179.933	−	315.552i	−0.848742	−	1.48845i
$213$		0			0
$214$	−237.108	+	180.931i	−1.10798	+	0.845471i
$215$	−264.345			−1.22951
$216$		0			0
$217$			293.283i			1.35154i
$218$	18.4898	−	14.1090i	0.0848154	−	0.0647203i
$219$		0			0
$220$	10.0392	−	36.6783i	0.0456325	−	0.166719i
$221$	107.774	+	402.219i	0.487667	+	1.82000i
$222$		0			0
$223$	127.953	+	221.620i	0.573779	+	0.993814i	0.996173	+	0.0874016i	$0.0278563\pi$
$223$	127.953	+	221.620i	0.573779	+	0.993814i	−0.422395	+	0.906412i	$0.638810\pi$
$224$	−28.1141	+	193.457i	−0.125509	+	0.863649i
$225$		0			0
$226$	217.026	−	281.267i	0.960290	−	1.24455i
$227$	−110.917	−	29.7201i	−0.488620	−	0.130925i	0.00609341	−	0.999981i	$-0.498060\pi$
$227$	−110.917	−	29.7201i	−0.488620	−	0.130925i	−0.494714	+	0.869056i	$0.664727\pi$
$228$		0			0
$229$	−44.5697	−	166.336i	−0.194627	−	0.726360i	−0.992363	−	0.123352i	$-0.960636\pi$
$229$	−44.5697	−	166.336i	−0.194627	−	0.726360i	0.797736	−	0.603008i	$-0.206031\pi$
$230$	−116.103	−	48.4569i	−0.504796	−	0.210682i
$231$		0			0
$232$	136.319	−	174.724i	0.587582	−	0.753122i
$233$	122.816			0.527106			0.263553	−	0.964645i	$-0.415106\pi$
$233$	122.816			0.527106			0.263553	+	0.964645i	$0.415106\pi$
$234$		0			0
$235$	−59.4238	+	59.4238i	−0.252867	+	0.252867i
$236$	−343.610	−	1.84378i	−1.45597	−	0.00781263i
$237$		0			0
$238$	−302.767	+	124.460i	−1.27213	+	0.522940i
$239$	−216.699	−	125.111i	−0.906692	−	0.523479i	−0.0273265	−	0.999627i	$-0.508699\pi$
$239$	−216.699	−	125.111i	−0.906692	−	0.523479i	−0.879365	+	0.476148i	$0.842033\pi$
$240$		0			0
$241$	−27.8568	−	48.2493i	−0.115588	−	0.200205i	0.802426	−	0.596751i	$-0.203542\pi$
$241$	−27.8568	−	48.2493i	−0.115588	−	0.200205i	−0.918015	+	0.396546i	$0.870209\pi$
$242$	−142.880	+	185.174i	−0.590412	+	0.765180i
$243$		0			0
$244$	100.903	−	172.623i	0.413535	−	0.707470i
$245$	14.2701	−	53.2567i	0.0582452	−	0.217374i
$246$		0			0
$247$	−21.4085	−	12.3602i	−0.0866741	−	0.0500413i
$248$	231.344	+	306.571i	0.932837	+	1.23617i
$249$		0			0
$250$	158.736	+	208.023i	0.634946	+	0.832090i
$251$	204.869	+	204.869i	0.816210	+	0.816210i	0.985557	−	0.169347i	$-0.0541658\pi$
$251$	204.869	+	204.869i	0.816210	+	0.816210i	−0.169347	+	0.985557i	$0.554166\pi$
$252$		0			0
$253$	−18.9756	−	18.9756i	−0.0750023	−	0.0750023i
$254$	−0.126493	+	0.941289i	−0.000498004	+	0.00370586i
$255$		0			0
$256$	123.212	+	224.399i	0.481298	+	0.876557i
$257$	−302.113	−	174.425i	−1.17554	−	0.678696i	−0.220559	−	0.975374i	$-0.570788\pi$
$257$	−302.113	−	174.425i	−1.17554	−	0.678696i	−0.954978	+	0.296677i	$0.904121\pi$
$258$		0			0
$259$	−11.0846	+	41.3681i	−0.0427975	+	0.159722i
$260$	283.881	−	74.4354i	1.09185	−	0.286290i
$261$		0			0
$262$	80.1253	−	10.3301i	0.305822	−	0.0394277i
$263$	66.3514	+	114.924i	0.252287	+	0.436973i	0.964155	−	0.265340i	$-0.0854841\pi$
$263$	66.3514	+	114.924i	0.252287	+	0.436973i	−0.711868	+	0.702313i	$0.752151\pi$
$264$		0			0
$265$	−371.260	−	214.347i	−1.40098	−	0.808857i
$266$	7.48499	−	17.9341i	0.0281391	−	0.0674215i
$267$		0			0
$268$	−66.8963	−	0.358960i	−0.249613	−	0.00133940i
$269$	−229.913	+	229.913i	−0.854695	+	0.854695i	−0.990707	−	0.136012i	$-0.956572\pi$
$269$	−229.913	+	229.913i	−0.854695	+	0.854695i	0.136012	+	0.990707i	$0.456572\pi$
$270$		0			0
$271$	−289.039			−1.06656			−0.533282	−	0.845938i	$-0.679041\pi$
$271$	−289.039			−1.06656			−0.533282	+	0.845938i	$0.679041\pi$
$272$	−218.310	+	368.923i	−0.802609	+	1.35633i
$273$		0			0
$274$	−5.42819	+	2.23139i	−0.0198109	+	0.00814375i
$275$	1.41522	+	5.28167i	0.00514625	+	0.0192061i
$276$		0			0
$277$	191.072	+	51.1977i	0.689792	+	0.184829i	0.586654	−	0.809838i	$-0.300445\pi$
$277$	191.072	+	51.1977i	0.689792	+	0.184829i	0.103138	+	0.994667i	$0.467112\pi$
$278$	502.142	−	64.7381i	1.80626	−	0.232871i
$279$		0			0
$280$	86.5708	+	213.853i	0.309182	+	0.763760i
$281$	−71.5276	−	123.889i	−0.254547	−	0.440888i	0.710226	−	0.703974i	$-0.248593\pi$
$281$	−71.5276	−	123.889i	−0.254547	−	0.440888i	−0.964772	+	0.263086i	$0.915260\pi$
$282$		0			0
$283$	15.6380	+	58.3619i	0.0552581	+	0.206226i	0.988035	−	0.154227i	$-0.0492888\pi$
$283$	15.6380	+	58.3619i	0.0552581	+	0.206226i	−0.932777	+	0.360453i	$0.882622\pi$
$284$	232.094	+	63.5262i	0.817234	+	0.223684i
$285$		0			0
$286$	62.0419	+	8.33737i	0.216930	+	0.0291516i
$287$		−	85.2103i		−	0.296900i
$288$		0			0
$289$	−428.825			−1.48382
$290$	34.8332	−	259.209i	0.120115	−	0.893823i
$291$		0			0
$292$	−148.035	+	540.847i	−0.506968	+	1.85222i
$293$	37.1057	−	9.94246i	0.126641	−	0.0339333i	−0.194942	−	0.980815i	$-0.562452\pi$
$293$	37.1057	−	9.94246i	0.126641	−	0.0339333i	0.321583	+	0.946881i	$0.395785\pi$
$294$		0			0
$295$	−351.194	+	202.762i	−1.19049	+	0.687328i
$296$	21.0446	+	51.9858i	0.0710968	+	0.175628i
$297$		0			0
$298$	6.65056	+	51.5851i	0.0223173	+	0.173104i
$299$	53.6025	−	200.047i	0.179272	−	0.669054i
$300$		0			0
$301$	330.434	−	88.5394i	1.09779	−	0.294151i
$302$	100.836	+	245.299i	0.333893	+	0.812247i
$303$		0			0
$304$	−6.32243	−	24.6508i	−0.0207975	−	0.0810883i
$305$		−	235.975i		−	0.773688i
$306$		0			0
$307$	−353.313	−	353.313i	−1.15086	−	1.15086i	−0.986381	−	0.164474i	$-0.947407\pi$
$307$	−353.313	−	353.313i	−1.15086	−	1.15086i	−0.164474	−	0.986381i	$-0.552593\pi$
$308$	−0.264060	+	49.2106i	−0.000857338	+	0.159775i
$309$		0			0
$310$	418.292	+	174.579i	1.34933	+	0.563157i
$311$	−68.7995	+	119.164i	−0.221220	+	0.383165i	−0.955179	−	0.296030i	$-0.904337\pi$
$311$	−68.7995	+	119.164i	−0.221220	+	0.383165i	0.733959	+	0.679194i	$0.237671\pi$
$312$		0			0
$313$	−266.881	+	154.084i	−0.852654	+	0.492280i	−0.861546	−	0.507680i	$-0.830503\pi$
$313$	−266.881	+	154.084i	−0.852654	+	0.492280i	0.00889134	+	0.999960i	$0.497170\pi$
$314$	58.3191	+	452.352i	0.185730	+	1.44061i
$315$		0			0
$316$	−128.287	−	489.261i	−0.405973	−	1.54829i
$317$	42.4623	+	11.3777i	0.133950	+	0.0358919i	0.325171	−	0.945655i	$-0.394578\pi$
$317$	42.4623	+	11.3777i	0.133950	+	0.0358919i	−0.191221	+	0.981547i	$0.561245\pi$
$318$		0			0
$319$	27.8935	−	48.3129i	0.0874403	−	0.151451i
$320$	259.181	+	155.254i	0.809941	+	0.485169i
$321$		0			0
$322$	161.360	+	21.6840i	0.501118	+	0.0673417i
$323$	30.1328	−	30.1328i	0.0932905	−	0.0932905i
$324$		0			0
$325$	−29.8395	+	29.8395i	−0.0918138	+	0.0918138i
$326$	−20.1853	+	15.4029i	−0.0619183	+	0.0472482i
$327$		0			0
$328$	−67.2143	−	89.0708i	−0.204922	−	0.271557i
$329$	54.3768	−	94.1835i	0.165279	−	0.286272i
$330$		0			0
$331$	−51.4063	−	13.7743i	−0.155306	−	0.0416142i	0.180328	−	0.983606i	$-0.442284\pi$
$331$	−51.4063	−	13.7743i	−0.155306	−	0.0416142i	−0.335634	+	0.941992i	$0.608951\pi$
$332$	−323.563	−	189.131i	−0.974588	−	0.569673i
$333$		0			0
$334$	−9.40635	−	7.25793i	−0.0281627	−	0.0217303i
$335$	−68.3728	+	39.4751i	−0.204098	+	0.117836i
$336$		0			0
$337$	−270.471	+	468.469i	−0.802584	+	1.39012i	0.115325	+	0.993328i	$0.463209\pi$
$337$	−270.471	+	468.469i	−0.802584	+	1.39012i	−0.917910	+	0.396789i	$0.870124\pi$
$338$	55.1730	+	134.217i	0.163234	+	0.397091i
$339$		0			0
$340$	−2.71464	+	505.904i	−0.00798423	+	1.48795i
$341$	68.3645	+	68.3645i	0.200482	+	0.200482i
$342$		0			0
$343$			370.694i			1.08074i
$344$	275.564	−	353.198i	0.801057	−	1.02674i
$345$		0			0
$346$	181.657	−	435.252i	0.525020	−	1.25795i
$347$	−144.887	+	38.8224i	−0.417542	+	0.111880i	−0.461473	−	0.887154i	$-0.652679\pi$
$347$	−144.887	+	38.8224i	−0.417542	+	0.111880i	0.0439302	+	0.999035i	$0.486012\pi$
$348$		0			0
$349$	84.4966	−	315.346i	0.242111	−	0.903569i	−0.732703	−	0.680548i	$-0.761742\pi$
$349$	84.4966	−	315.346i	0.242111	−	0.903569i	0.974814	−	0.223021i	$-0.0715917\pi$
$350$	−26.2645	−	20.2657i	−0.0750415	−	0.0579019i
$351$		0			0
$352$	38.5416	+	51.6484i	0.109493	+	0.146728i
$353$	−410.965	+	237.271i	−1.16421	+	0.672155i	−0.952308	−	0.305137i	$-0.901298\pi$
$353$	−410.965	+	237.271i	−1.16421	+	0.672155i	−0.211898	+	0.977292i	$0.567964\pi$
$354$		0			0
$355$	274.309	−	73.5009i	0.772702	−	0.207045i
$356$	227.187	+	62.1832i	0.638167	+	0.174672i
$357$		0			0
$358$	−79.1380	−	103.710i	−0.221056	−	0.289692i
$359$	−264.036			−0.735476			−0.367738	−	0.929929i	$-0.619868\pi$
$359$	−264.036			−0.735476			−0.367738	+	0.929929i	$0.619868\pi$
$360$		0			0
$361$		−	358.470i		−	0.992992i
$362$	−247.083	−	323.800i	−0.682551	−	0.894476i
$363$		0			0
$364$	−329.922	+	188.127i	−0.906379	+	0.516834i
$365$	171.279	+	639.220i	0.469256	+	1.75129i
$366$		0			0
$367$	−218.120	−	377.795i	−0.594333	−	1.02941i	−0.993641	−	0.112598i	$-0.964083\pi$
$367$	−218.120	−	377.795i	−0.594333	−	1.02941i	0.399308	−	0.916817i	$-0.369250\pi$
$368$	185.775	−	104.615i	0.504823	−	0.284280i
$369$		0			0
$370$	52.4026	+	40.4338i	0.141629	+	0.109281i
$371$	535.871	+	143.586i	1.44440	+	0.387025i
$372$		0			0
$373$	−36.6972	−	136.956i	−0.0983838	−	0.367173i	0.899127	−	0.437688i	$-0.144203\pi$
$373$	−36.6972	−	136.956i	−0.0983838	−	0.367173i	−0.997511	+	0.0705146i	$0.977536\pi$
$374$	−41.5636	+	99.5867i	−0.111132	+	0.266275i
$375$		0			0
$376$	−17.4520	−	141.343i	−0.0464150	−	0.375913i
$377$	430.538			1.14201
$378$		0			0
$379$	488.712	−	488.712i	1.28948	−	1.28948i	0.354374	−	0.935104i	$-0.384694\pi$
$379$	488.712	−	488.712i	1.28948	−	1.28948i	0.935104	−	0.354374i	$-0.115306\pi$
$380$	−21.1229	−	21.3508i	−0.0555865	−	0.0561862i
$381$		0			0
$382$	154.708	+	376.352i	0.404996	+	0.985214i
$383$	220.158	+	127.108i	0.574824	+	0.331875i	0.759074	−	0.651005i	$-0.225652\pi$
$383$	220.158	+	127.108i	0.574824	+	0.331875i	−0.184250	+	0.982880i	$0.558985\pi$
$384$		0			0
$385$	29.0389	+	50.2968i	0.0754256	+	0.130641i
$386$	34.3080	+	26.4720i	0.0888809	+	0.0685804i
$387$		0			0
$388$	102.162	+	389.626i	0.263305	+	1.00419i
$389$	30.5615	−	114.057i	0.0785643	−	0.293206i	−0.915454	−	0.402424i	$-0.868168\pi$
$389$	30.5615	−	114.057i	0.0785643	−	0.293206i	0.994018	+	0.109218i	$0.0348346\pi$
$390$		0			0
$391$	309.185	+	178.508i	0.790755	+	0.456542i
$392$	56.2819	+	74.5834i	0.143576	+	0.190264i
$393$		0			0
$394$	488.573	−	372.817i	1.24003	−	0.946236i
$395$	−422.094	−	422.094i	−1.06859	−	1.06859i
$396$		0			0
$397$	335.273	+	335.273i	0.844517	+	0.844517i	0.989443	−	0.144926i	$-0.0462943\pi$
$397$	335.273	+	335.273i	0.844517	+	0.844517i	−0.144926	+	0.989443i	$0.546294\pi$
$398$	−383.091	−	51.4808i	−0.962539	−	0.129349i
$399$		0			0
$400$	−43.4401	−	0.466206i	−0.108600	−	0.00116552i
$401$	455.021	+	262.706i	1.13472	+	0.655128i	0.945116	−	0.326734i	$-0.105948\pi$
$401$	455.021	+	262.706i	1.13472	+	0.655128i	0.189599	+	0.981862i	$0.439281\pi$
$402$		0			0
$403$	−193.117	+	720.722i	−0.479198	+	1.78839i
$404$	219.326	−	375.220i	0.542887	−	0.928762i
$405$		0			0
$406$	43.2772	+	335.680i	0.106594	+	0.826797i
$407$	7.05911	+	12.2267i	0.0173442	+	0.0300411i
$408$		0			0
$409$	−278.789	−	160.959i	−0.681635	−	0.393542i	0.118836	−	0.992914i	$-0.462084\pi$
$409$	−278.789	−	160.959i	−0.681635	−	0.393542i	−0.800471	+	0.599372i	$0.795417\pi$
$410$	−121.530	−	50.7219i	−0.296415	−	0.123712i
$411$		0			0
$412$	−251.244	−	253.955i	−0.609816	−	0.616396i
$413$	371.082	−	371.082i	0.898504	−	0.898504i
$414$		0			0
$415$	−442.310			−1.06581
$416$	−196.473	+	456.895i	−0.472292	+	1.09830i
$417$		0			0
$418$	−2.43570	−	5.92520i	−0.00582702	−	0.0141751i
$419$	−186.108	−	694.566i	−0.444173	−	1.65767i	−0.718112	−	0.695928i	$-0.754993\pi$
$419$	−186.108	−	694.566i	−0.444173	−	1.65767i	0.273939	−	0.961747i	$-0.411673\pi$
$420$		0			0
$421$	−3.74467	−	1.00338i	−0.00889470	−	0.00238333i	0.254369	−	0.967107i	$-0.418132\pi$
$421$	−3.74467	−	1.00338i	−0.00889470	−	0.00238333i	−0.263264	+	0.964724i	$0.584799\pi$
$422$	−31.0244	−	240.641i	−0.0735176	−	0.570239i
$423$		0			0
$424$	673.410	−	272.607i	1.58823	−	0.642940i
$425$	−36.3727	−	62.9994i	−0.0855828	−	0.148234i
$426$		0			0
$427$	79.0370	+	294.970i	0.185098	+	0.690797i
$428$	−295.479	−	518.186i	−0.690371	−	1.21071i
$429$		0			0
$430$	70.4140	−	523.981i	0.163754	−	1.21856i
$431$			522.524i			1.21235i	0.795330	+	0.606177i	$0.207297\pi$
$431$			522.524i			1.21235i	−0.795330	+	0.606177i	$0.792703\pi$
$432$		0			0
$433$	284.524			0.657100			0.328550	−	0.944487i	$-0.393440\pi$
$433$	284.524			0.657100			0.328550	+	0.944487i	$0.393440\pi$
$434$	−581.341	−	78.1223i	−1.33950	−	0.180005i
$435$		0			0
$436$	23.0415	+	40.4083i	0.0528476	+	0.0926796i
$437$	−20.4724	+	5.48555i	−0.0468475	+	0.0125528i
$438$		0			0
$439$	689.645	−	398.167i	1.57095	−	0.906986i	0.574892	−	0.818229i	$-0.305044\pi$
$439$	689.645	−	398.167i	1.57095	−	0.906986i	0.996053	−	0.0887566i	$-0.0282893\pi$
$440$	70.0288	+	29.6695i	0.159156	+	0.0674306i
$441$		0			0
$442$	−825.980	+	106.489i	−1.86873	+	0.240925i
$443$	25.5750	−	95.4474i	0.0577315	−	0.215457i	−0.931034	−	0.364933i	$-0.881092\pi$
$443$	25.5750	−	95.4474i	0.0577315	−	0.215457i	0.988765	+	0.149476i	$0.0477586\pi$
$444$		0			0
$445$	268.510	−	71.9470i	0.603393	−	0.161679i
$446$	−473.375	+	194.592i	−1.06138	+	0.436305i
$447$		0			0
$448$	−375.979	−	107.259i	−0.839239	−	0.239417i
$449$		−	739.155i		−	1.64623i	−0.567878	−	0.823113i	$-0.692235\pi$
$449$		−	739.155i		−	1.64623i	0.567878	−	0.823113i	$-0.307765\pi$
$450$		0			0
$451$	−19.8625	−	19.8625i	−0.0440411	−	0.0440411i
$452$	499.714	+	505.106i	1.10556	+	1.11749i
$453$		0			0
$454$	88.4557	−	211.941i	0.194836	−	0.466830i
$455$	−224.108	+	388.167i	−0.492546	+	0.853115i
$456$		0			0
$457$	−31.9714	+	18.4587i	−0.0699594	+	0.0403911i	−0.534572	−	0.845123i	$-0.679527\pi$
$457$	−31.9714	+	18.4587i	−0.0699594	+	0.0403911i	0.464612	+	0.885514i	$0.346194\pi$
$458$	341.581	−	44.0380i	0.745810	−	0.0961528i
$459$		0			0
$460$	126.977	−	217.230i	0.276037	−	0.472239i
$461$	141.565	+	37.9322i	0.307082	+	0.0822824i	0.409069	−	0.912503i	$-0.365853\pi$
$461$	141.565	+	37.9322i	0.307082	+	0.0822824i	−0.101987	+	0.994786i	$0.532520\pi$
$462$		0			0
$463$	110.979	−	192.222i	0.239696	−	0.415166i	−0.720931	−	0.693007i	$-0.756286\pi$
$463$	110.979	−	192.222i	0.239696	−	0.415166i	0.960627	+	0.277841i	$0.0896189\pi$
$464$	310.024	+	316.750i	0.668155	+	0.682652i
$465$		0			0
$466$	−32.7146	+	243.443i	−0.0702030	+	0.522410i
$467$	−191.799	+	191.799i	−0.410705	+	0.410705i	−0.881984	−	0.471279i	$-0.843792\pi$
$467$	−191.799	+	191.799i	−0.410705	+	0.410705i	0.471279	+	0.881984i	$0.343792\pi$
$468$		0			0
$469$	72.2448	−	72.2448i	0.154040	−	0.154040i
$470$	−101.960	−	133.618i	−0.216936	−	0.284293i
$471$		0			0
$472$	95.1825	−	680.606i	0.201658	−	1.44196i
$473$	56.3856	−	97.6627i	0.119208	−	0.206475i
$474$		0			0
$475$	4.17144	+	1.11773i	0.00878197	+	0.00235312i
$476$	−166.053	−	633.292i	−0.348851	−	1.33045i
$477$		0			0
$478$	305.716	−	396.211i	0.639573	−	0.828894i
$479$	−353.831	+	204.284i	−0.738687	+	0.426481i	−0.821592	−	0.570076i	$-0.806914\pi$
$479$	−353.831	+	204.284i	−0.738687	+	0.426481i	0.0829049	+	0.996557i	$0.473580\pi$
$480$		0			0
$481$	−54.4789	+	94.3602i	−0.113262	+	0.196175i
$482$	103.059	−	42.3649i	0.213816	−	0.0878941i
$483$		0			0
$484$	−328.989	−	332.539i	−0.679729	−	0.687063i
$485$	336.137	+	336.137i	0.693066	+	0.693066i
$486$		0			0
$487$			411.441i			0.844849i	0.906398	+	0.422424i	$0.138821\pi$
$487$			411.441i			0.844849i	−0.906398	+	0.422424i	$0.861179\pi$
$488$	315.292	+	245.989i	0.646090	+	0.504076i
$489$		0			0
$490$	101.763	+	42.4719i	0.207680	+	0.0866774i
$491$	355.430	−	95.2373i	0.723891	−	0.193966i	0.121984	−	0.992532i	$-0.461074\pi$
$491$	355.430	−	95.2373i	0.723891	−	0.193966i	0.601907	+	0.798566i	$0.294408\pi$
$492$		0			0
$493$	−192.091	+	716.893i	−0.389637	+	1.45414i
$494$	30.2028	−	39.1432i	0.0611393	−	0.0792372i
$495$		0			0
$496$	−669.302	+	376.903i	−1.34940	+	0.759886i
$497$	−318.270	+	183.753i	−0.640383	+	0.369725i
$498$		0			0
$499$	699.631	−	187.466i	1.40207	−	0.375683i	0.522980	−	0.852345i	$-0.324820\pi$
$499$	699.631	−	187.466i	1.40207	−	0.375683i	0.879087	+	0.476662i	$0.158154\pi$
$500$	−454.621	+	259.233i	−0.909243	+	0.518466i
$501$		0			0
$502$	−460.658	+	351.516i	−0.917646	+	0.700231i
$503$	275.563			0.547838			0.273919	−	0.961753i	$-0.411680\pi$
$503$	275.563			0.547838			0.273919	+	0.961753i	$0.411680\pi$
$504$		0			0
$505$		−	512.925i		−	1.01569i
$506$	42.6676	−	32.5585i	0.0843233	−	0.0643448i
$507$		0			0
$508$	−1.83211	−	0.501465i	−0.00360652	−	0.000987135i
$509$	62.5621	+	233.485i	0.122912	+	0.458713i	0.999757	−	0.0220603i	$-0.00702259\pi$
$509$	62.5621	+	233.485i	0.122912	+	0.458713i	−0.876845	+	0.480774i	$0.840356\pi$
$510$		0			0
$511$	−428.199	−	741.662i	−0.837963	−	1.45139i
$512$	−477.619	+	184.456i	−0.932850	+	0.360266i
$513$		0			0
$514$	426.216	−	552.381i	0.829215	−	1.07467i
$515$	−407.232	−	109.118i	−0.790743	−	0.211879i
$516$		0			0
$517$	−9.27893	−	34.6294i	−0.0179476	−	0.0669815i
$518$	−79.0465	−	32.9909i	−0.152599	−	0.0636890i
$519$		0			0
$520$	71.9267	+	582.531i	0.138321	+	1.12025i
$521$	341.123			0.654746			0.327373	−	0.944895i	$-0.393837\pi$
$521$	341.123			0.654746			0.327373	+	0.944895i	$0.393837\pi$
$522$		0			0
$523$	88.4700	−	88.4700i	0.169159	−	0.169159i	−0.617451	−	0.786609i	$-0.711835\pi$
$523$	88.4700	−	88.4700i	0.169159	−	0.169159i	0.786609	+	0.617451i	$0.211835\pi$
$524$	−0.866996	+	161.574i	−0.00165457	+	0.308348i
$525$		0			0
$526$	−245.474	+	100.908i	−0.466681	+	0.191840i
$527$	−1113.92	−	643.122i	−2.11370	−	1.22035i
$528$		0			0
$529$	175.718	+	304.352i	0.332169	+	0.575334i
$530$	523.768	−	678.809i	0.988242	−	1.28077i
$531$		0			0
$532$	33.5549	+	19.6138i	0.0630732	+	0.0368680i
$533$	56.1080	−	209.398i	0.105268	−	0.392867i
$534$		0			0
$535$	−609.668	−	351.992i	−1.13957	−	0.657929i
$536$	18.5308	−	132.505i	0.0345724	−	0.247211i
$537$		0			0
$538$	−394.487	−	516.972i	−0.733248	−	0.960914i
$539$	16.6319	+	16.6319i	0.0308569	+	0.0308569i
$540$		0			0
$541$	−14.0806	−	14.0806i	−0.0260270	−	0.0260270i	0.693974	−	0.720001i	$-0.255858\pi$
$541$	−14.0806	−	14.0806i	−0.0260270	−	0.0260270i	−0.720001	+	0.693974i	$0.755858\pi$
$542$	76.9916	−	572.927i	0.142051	−	1.05706i
$543$		0			0
$544$	−673.121	−	531.000i	−1.23735	−	0.976103i
$545$	47.5421	+	27.4484i	0.0872332	+	0.0503641i
$546$		0			0
$547$	54.3412	−	202.804i	0.0993440	−	0.370757i	−0.898298	−	0.439386i	$-0.855196\pi$
$547$	54.3412	−	202.804i	0.0993440	−	0.370757i	0.997642	+	0.0686294i	$0.0218626\pi$
$548$	−2.97710	−	11.3540i	−0.00543267	−	0.0207191i
$549$		0			0
$550$	−10.8462	+	1.39834i	−0.0197204	+	0.00254243i
$551$	−22.0301	−	38.1573i	−0.0399821	−	0.0692510i
$552$		0			0
$553$	668.996	+	386.245i	1.20976	+	0.698454i
$554$	−152.379	+	365.103i	−0.275053	+	0.659030i
$555$		0			0
$556$	−5.43343	+	1012.58i	−0.00977235	+	1.82119i
$557$	−136.388	+	136.388i	−0.244862	+	0.244862i	−0.818858	−	0.573996i	$-0.805392\pi$
$557$	−136.388	+	136.388i	−0.244862	+	0.244862i	0.573996	+	0.818858i	$0.305392\pi$
$558$		0			0
$559$	870.316			1.55692
$560$	−446.955	+	114.635i	−0.798134	+	0.204705i
$561$		0			0
$562$	264.624	−	108.780i	0.470862	−	0.193559i
$563$	−109.204	−	407.555i	−0.193968	−	0.723900i	−0.992532	−	0.121989i	$-0.961073\pi$
$563$	−109.204	−	407.555i	−0.193968	−	0.723900i	0.798563	−	0.601911i	$-0.205594\pi$
$564$		0			0
$565$	809.968	+	217.030i	1.43357	+	0.384124i
$566$	−119.850	+	15.4515i	−0.211748	+	0.0272994i
$567$		0			0
$568$	−187.744	+	443.132i	−0.330535	+	0.780162i
$569$	−493.342	−	854.493i	−0.867033	−	1.50175i	−0.865014	−	0.501748i	$-0.832691\pi$
$569$	−493.342	−	854.493i	−0.867033	−	1.50175i	−0.00201904	−	0.999998i	$-0.500643\pi$
$570$		0			0
$571$	−198.496	−	740.798i	−0.347629	−	1.29737i	−0.889511	−	0.456914i	$-0.848955\pi$
$571$	−198.496	−	740.798i	−0.347629	−	1.29737i	0.541882	−	0.840455i	$-0.317712\pi$
$572$	−33.0524	+	120.757i	−0.0577839	+	0.211114i
$573$		0			0
$574$	168.902	+	22.6976i	0.294255	+	0.0395428i
$575$			36.1805i			0.0629226i
$576$		0			0
$577$	745.994			1.29288			0.646442	−	0.762963i	$-0.276256\pi$
$577$	745.994			1.29288			0.646442	+	0.762963i	$0.276256\pi$
$578$	114.227	−	850.009i	0.197624	−	1.47060i
$579$		0			0
$580$	504.520	+	138.092i	0.869862	+	0.238089i
$581$	552.891	−	148.147i	0.951620	−	0.254986i
$582$		0			0
$583$	158.382	−	91.4417i	0.271667	−	0.156847i
$584$	−1032.63	−	437.498i	−1.76819	−	0.749140i
$585$		0			0
$586$	9.82385	+	76.1987i	0.0167642	+	0.130032i
$587$	−119.299	+	445.232i	−0.203236	+	0.758486i	0.786744	+	0.617279i	$0.211765\pi$
$587$	−119.299	+	445.232i	−0.203236	+	0.758486i	−0.989980	+	0.141207i	$0.954902\pi$
$588$		0			0
$589$	73.7571	−	19.7631i	0.125224	−	0.0335537i
$590$	−308.363	−	750.140i	−0.522649	−	1.27142i
$591$		0			0
$592$	−108.651	+	27.8668i	−0.183532	+	0.0470723i
$593$			407.326i			0.686891i	0.939173	+	0.343445i	$0.111594\pi$
$593$			407.326i			0.686891i	−0.939173	+	0.343445i	$0.888406\pi$
$594$		0			0
$595$	−546.352	−	546.352i	−0.918239	−	0.918239i
$596$	−104.023	−	0.558177i	−0.174534	−	0.000936538i
$597$		0			0
$598$	382.252	+	159.537i	0.639217	+	0.266784i
$599$	106.630	−	184.688i	0.178013	−	0.308328i	−0.763187	−	0.646178i	$-0.776366\pi$
$599$	106.630	−	184.688i	0.178013	−	0.308328i	0.941200	+	0.337850i	$0.109700\pi$
$600$		0			0
$601$	345.289	−	199.353i	0.574524	−	0.331702i	−0.184430	−	0.982846i	$-0.559044\pi$
$601$	345.289	−	199.353i	0.574524	−	0.331702i	0.758954	+	0.651144i	$0.225711\pi$
$602$	87.4832	+	678.564i	0.145321	+	1.12718i
$603$		0			0
$604$	−513.086	+	134.534i	−0.849481	+	0.222739i
$605$	−533.246	−	142.883i	−0.881398	−	0.236170i
$606$		0			0
$607$	−547.056	+	947.529i	−0.901246	+	1.56100i	−0.0753663	+	0.997156i	$0.524013\pi$
$607$	−547.056	+	947.529i	−0.901246	+	1.56100i	−0.825879	+	0.563847i	$0.809321\pi$
$608$	50.5466	−	5.96594i	0.0831358	−	0.00981240i
$609$		0			0
$610$	467.745	+	62.8569i	0.766795	+	0.103044i
$611$	195.644	−	195.644i	0.320202	−	0.320202i
$612$		0			0
$613$	−123.627	+	123.627i	−0.201675	+	0.201675i	−0.800717	−	0.599042i	$-0.795548\pi$
$613$	−123.627	+	123.627i	−0.201675	+	0.201675i	0.599042	+	0.800717i	$0.295548\pi$
$614$	794.442	−	606.218i	1.29388	−	0.987325i
$615$		0			0
$616$	−97.4740	−	13.6317i	−0.158237	−	0.0221294i
$617$	−395.995	+	685.883i	−0.641807	+	1.11164i	0.343223	+	0.939254i	$0.388481\pi$
$617$	−395.995	+	685.883i	−0.641807	+	1.11164i	−0.985029	+	0.172388i	$0.944852\pi$
$618$		0			0
$619$	−951.116	−	254.851i	−1.53654	−	0.411714i	−0.611392	−	0.791328i	$-0.709390\pi$
$619$	−951.116	−	254.851i	−1.53654	−	0.411714i	−0.925145	+	0.379614i	$0.876057\pi$
$620$	−457.467	+	782.628i	−0.737851	+	1.26230i
$621$		0			0
$622$	−217.879	−	168.115i	−0.350288	−	0.270281i
$623$	−311.541	+	179.868i	−0.500066	+	0.288713i
$624$		0			0
$625$	−274.874	+	476.096i	−0.439799	+	0.761754i
$626$	−234.333	−	570.050i	−0.374333	−	0.910623i
$627$		0			0
$628$	−912.179	−	4.89468i	−1.45252	−	0.00779408i
$629$	−132.814	−	132.814i	−0.211150	−	0.211150i
$630$		0			0
$631$			509.904i			0.808088i	0.914740	+	0.404044i	$0.132396\pi$
$631$			509.904i			0.808088i	−0.914740	+	0.404044i	$0.867604\pi$
$632$	1003.98	−	123.964i	1.58857	−	0.196145i
$633$		0			0
$634$	−33.8635	+	81.1373i	−0.0534124	+	0.127977i
$635$	−2.16535	+	0.580203i	−0.00341000	+	0.000913706i
$636$		0			0
$637$	−46.9820	+	175.339i	−0.0737551	+	0.275258i
$638$	88.3350	+	68.1591i	0.138456	+	0.106832i
$639$		0			0
$640$	−376.780	+	472.389i	−0.588719	+	0.738108i
$641$	1011.23	−	583.834i	1.57758	−	0.910817i	0.582386	−	0.812912i	$-0.302119\pi$
$641$	1011.23	−	583.834i	1.57758	−	0.910817i	0.995196	−	0.0979050i	$-0.0312141\pi$
$642$		0			0
$643$	−227.115	+	60.8552i	−0.353211	+	0.0946426i	−0.431062	−	0.902322i	$-0.641861\pi$
$643$	−227.115	+	60.8552i	−0.353211	+	0.0946426i	0.0778508	+	0.996965i	$0.475194\pi$
$644$	−85.9633	+	314.069i	−0.133483	+	0.487684i
$645$		0			0
$646$	51.7023	+	67.7553i	0.0800345	+	0.104884i
$647$	657.247			1.01584			0.507919	−	0.861405i	$-0.330415\pi$
$647$	657.247			1.01584			0.507919	+	0.861405i	$0.330415\pi$
$648$		0			0
$649$		−	172.999i		−	0.266562i
$650$	−51.1989	−	67.0957i	−0.0787675	−	0.103224i
$651$		0			0
$652$	−25.1545	−	44.1139i	−0.0385806	−	0.0676594i
$653$	78.6468	+	293.514i	0.120439	+	0.449485i	0.999636	−	0.0269734i	$-0.00858694\pi$
$653$	78.6468	+	293.514i	0.120439	+	0.449485i	−0.879197	+	0.476458i	$0.841920\pi$
$654$		0			0
$655$	95.3441	+	165.141i	0.145564	+	0.252123i
$656$	194.458	−	109.505i	0.296431	−	0.166929i
$657$		0			0
$658$	172.204	+	132.873i	0.261709	+	0.201934i
$659$	138.565	+	37.1284i	0.210265	+	0.0563405i	0.362414	−	0.932017i	$-0.381953\pi$
$659$	138.565	+	37.1284i	0.210265	+	0.0563405i	−0.152149	+	0.988358i	$0.548619\pi$
$660$		0			0
$661$	29.6052	+	110.488i	0.0447884	+	0.167153i	0.984698	−	0.174272i	$-0.0557572\pi$
$661$	29.6052	+	110.488i	0.0447884	+	0.167153i	−0.939909	+	0.341425i	$0.889091\pi$
$662$	40.9963	−	98.2276i	0.0619280	−	0.148380i
$663$		0			0
$664$	461.081	−	590.982i	0.694399	−	0.890033i
$665$	45.8695			0.0689767
$666$		0			0
$667$	261.015	−	261.015i	0.391326	−	0.391326i
$668$	16.8921	−	16.7118i	0.0252876	−	0.0250177i
$669$		0			0
$670$	−60.0342	−	146.042i	−0.0896033	−	0.217974i
$671$	87.1812	+	50.3341i	0.129927	+	0.0750135i
$672$		0			0
$673$	−415.766	−	720.128i	−0.617781	−	1.07003i	−0.989890	−	0.141839i	$-0.954699\pi$
$673$	−415.766	−	720.128i	−0.617781	−	1.07003i	0.372109	−	0.928189i	$-0.378635\pi$
$674$	−856.546	−	660.910i	−1.27084	−	0.980578i
$675$		0			0
$676$	−280.739	+	73.6115i	−0.415294	+	0.108893i
$677$	15.8664	−	59.2141i	0.0234363	−	0.0874654i	−0.953217	−	0.302286i	$-0.902250\pi$
$677$	15.8664	−	59.2141i	0.0234363	−	0.0874654i	0.976653	+	0.214821i	$0.0689168\pi$
$678$		0			0
$679$	−532.759	−	307.588i	−0.784623	−	0.453002i
$680$	−1002.07	−	140.139i	−1.47363	−	0.206087i
$681$		0			0
$682$	−153.721	+	117.300i	−0.225398	+	0.171995i
$683$	730.400	+	730.400i	1.06940	+	1.06940i	0.997405	+	0.0719951i	$0.0229366\pi$
$683$	730.400	+	730.400i	1.06940	+	1.06940i	0.0719951	+	0.997405i	$0.477063\pi$
$684$		0			0
$685$	−9.79532	−	9.79532i	−0.0142997	−	0.0142997i
$686$	−734.783	−	98.7423i	−1.07111	−	0.143939i
$687$		0			0
$688$	626.701	+	640.299i	0.910903	+	0.930667i
$689$	1222.32	+	705.705i	1.77404	+	1.02424i
$690$		0			0
$691$	110.501	−	412.396i	0.159915	−	0.596811i	−0.838719	−	0.544564i	$-0.816695\pi$
$691$	110.501	−	412.396i	0.159915	−	0.596811i	0.998634	−	0.0522467i	$-0.0166382\pi$
$692$	814.361	+	476.016i	1.17682	+	0.687885i
$693$		0			0
$694$	−38.3593	−	297.534i	−0.0552727	−	0.428723i
$695$	597.517	+	1034.93i	0.859737	+	1.48911i
$696$		0			0
$697$	323.637	+	186.852i	0.464329	+	0.268080i
$698$	602.565	+	251.487i	0.863274	+	0.360296i
$699$		0			0
$700$	47.1664	−	46.6629i	0.0673806	−	0.0666613i
$701$	233.941	−	233.941i	0.333725	−	0.333725i	−0.520274	−	0.853999i	$-0.674170\pi$
$701$	233.941	−	233.941i	0.333725	−	0.333725i	0.853999	+	0.520274i	$0.174170\pi$
$702$		0			0
$703$	11.1505			0.0158613
$704$	−112.643	+	62.6387i	−0.160004	+	0.0889755i
$705$		0			0
$706$	−360.844	−	877.809i	−0.511111	−	1.24336i
$707$	171.798	+	641.160i	0.242996	+	0.906874i
$708$		0			0
$709$	865.308	+	231.859i	1.22046	+	0.327022i	0.810859	−	0.585242i	$-0.199000\pi$
$709$	865.308	+	231.859i	1.22046	+	0.327022i	0.409604	+	0.912264i	$0.365667\pi$
$710$	72.6241	+	563.309i	0.102287	+	0.793394i
$711$		0			0
$712$	−183.775	+	433.763i	−0.258110	+	0.609218i
$713$	319.862	+	554.017i	0.448614	+	0.777023i
$714$		0			0
$715$	38.2422	+	142.722i	0.0534855	+	0.199611i
$716$	226.651	−	129.241i	0.316552	−	0.180504i
$717$		0			0
$718$	70.3316	−	523.367i	0.0979549	−	0.728924i
$719$			346.336i			0.481692i	0.970563	+	0.240846i	$0.0774249\pi$
$719$			346.336i			0.481692i	−0.970563	+	0.240846i	$0.922575\pi$
$720$		0			0
$721$	545.591			0.756715
$722$	710.553	+	95.4862i	0.984146	+	0.132252i
$723$		0			0
$724$	707.648	−	403.513i	0.977414	−	0.557339i
$725$	−72.6509	+	19.4668i	−0.100208	+	0.0268507i
$726$		0			0
$727$	734.519	−	424.075i	1.01034	−	0.583321i	0.0990503	−	0.995082i	$-0.468420\pi$
$727$	734.519	−	424.075i	1.01034	−	0.583321i	0.911292	+	0.411761i	$0.135086\pi$
$728$	−285.021	−	704.077i	−0.391512	−	0.967139i
$729$		0			0
$730$	−1312.67	+	169.235i	−1.79818	+	0.231829i
$731$	−388.304	+	1449.17i	−0.531196	+	1.98245i
$732$		0			0
$733$	−706.260	+	189.242i	−0.963520	+	0.258175i	−0.706090	−	0.708122i	$-0.749543\pi$
$733$	−706.260	+	189.242i	−0.963520	+	0.258175i	−0.257431	+	0.966297i	$0.582876\pi$
$734$	806.960	−	331.720i	1.09940	−	0.451935i
$735$		0			0
$736$	157.881	+	396.106i	0.214512	+	0.538187i
$737$		−	33.6806i		−	0.0456996i
$738$		0			0
$739$	152.421	+	152.421i	0.206254	+	0.206254i	0.802673	−	0.596419i	$-0.203410\pi$
$739$	152.421	+	152.421i	0.206254	+	0.206254i	−0.596419	+	0.802673i	$0.703410\pi$
$740$	−94.1057	+	93.1012i	−0.127170	+	0.125812i
$741$		0			0
$742$	−427.355	+	1023.95i	−0.575950	+	1.37998i
$743$	411.263	−	712.329i	0.553517	−	0.958719i	−0.444500	−	0.895779i	$-0.646619\pi$
$743$	411.263	−	712.329i	0.553517	−	0.958719i	0.998017	−	0.0629408i	$-0.0200479\pi$
$744$		0			0
$745$	−106.319	+	61.3830i	−0.142709	+	0.0823934i
$746$	281.246	−	36.2594i	0.377006	−	0.0486051i
$747$		0			0
$748$	−186.328	−	108.914i	−0.249101	−	0.145606i
$749$	879.985	+	235.791i	1.17488	+	0.314808i
$750$		0			0
$751$	202.422	−	350.605i	0.269536	−	0.466851i	−0.699206	−	0.714920i	$-0.746463\pi$
$751$	202.422	−	350.605i	0.269536	−	0.466851i	0.968742	+	0.248070i	$0.0797962\pi$
$752$	284.817	+	3.05670i	0.378746	+	0.00406475i
$753$		0			0
$754$	−114.683	+	853.404i	−0.152099	+	1.13184i
$755$	−442.648	+	442.648i	−0.586289	+	0.586289i
$756$		0			0
$757$	614.763	−	614.763i	0.812104	−	0.812104i	−0.172845	−	0.984949i	$-0.555296\pi$
$757$	614.763	−	614.763i	0.812104	−	0.812104i	0.984949	+	0.172845i	$0.0552959\pi$
$758$	838.538	+	1098.90i	1.10625	+	1.44973i
$759$		0			0
$760$	47.9476	−	36.1821i	0.0630890	−	0.0476080i
$761$	−114.480	+	198.285i	−0.150433	+	0.260558i	−0.931387	−	0.364031i	$-0.881400\pi$
$761$	−114.480	+	198.285i	−0.150433	+	0.260558i	0.780953	+	0.624589i	$0.214734\pi$
$762$		0			0
$763$	−68.6215	−	18.3871i	−0.0899364	−	0.0240984i
$764$	−787.208	+	206.411i	−1.03038	+	0.270171i
$765$		0			0
$766$	−310.595	+	402.535i	−0.405477	+	0.525502i
$767$	1156.25	−	667.562i	1.50750	−	0.870354i
$768$		0			0
$769$	−455.187	+	788.407i	−0.591921	+	1.02524i	0.402053	+	0.915616i	$0.368297\pi$
$769$	−455.187	+	788.407i	−0.591921	+	1.02524i	−0.993974	+	0.109620i	$0.965037\pi$
$770$	−107.433	+	44.1627i	−0.139523	+	0.0573541i
$771$		0			0
$772$	−61.6111	+	60.9534i	−0.0798071	+	0.0789552i
$773$	−58.9632	−	58.9632i	−0.0762784	−	0.0762784i	0.667938	−	0.744217i	$-0.267177\pi$
$773$	−58.9632	−	58.9632i	−0.0762784	−	0.0762784i	−0.744217	+	0.667938i	$0.767177\pi$
$774$		0			0
$775$		−	130.350i		−	0.168193i
$776$	−799.523	+	98.7192i	−1.03031	+	0.127216i
$777$		0			0
$778$	217.941	+	90.9600i	0.280130	+	0.116915i
$779$	−21.4293	+	5.74197i	−0.0275087	+	0.00737094i
$780$		0			0
$781$	−31.3559	+	117.022i	−0.0401484	+	0.149836i
$782$	−436.194	+	565.312i	−0.557792	+	0.722905i
$783$		0			0
$784$	−162.830	+	91.6941i	−0.207691	+	0.116957i
$785$	−932.313	+	538.271i	−1.18766	+	0.685696i
$786$		0			0
$787$	232.904	−	62.4066i	0.295940	−	0.0792968i	−0.107794	−	0.994173i	$-0.534379\pi$
$787$	232.904	−	62.4066i	0.295940	−	0.0792968i	0.403734	+	0.914876i	$0.367712\pi$
$788$	608.849	+	1067.75i	0.772651	+	1.35501i
$789$		0			0
$790$	949.100	−	724.233i	1.20139	−	0.916751i
$791$	−1085.16			−1.37188
$792$		0			0
$793$			776.910i			0.979710i
$794$	−753.880	+	575.265i	−0.949471	+	0.724516i
$795$		0			0
$796$	204.089	−	745.643i	0.256393	−	0.936737i
$797$	−319.167	−	1191.15i	−0.400461	−	1.49454i	−0.812276	−	0.583273i	$-0.801772\pi$
$797$	−319.167	−	1191.15i	−0.400461	−	1.49454i	0.411816	−	0.911267i	$-0.364895\pi$
$798$		0			0
$799$	238.479	+	413.057i	0.298472	+	0.516968i
$800$	12.4953	−	85.9821i	0.0156191	−	0.107478i
$801$		0			0
$802$	−641.936	+	831.957i	−0.800419	+	1.03735i
$803$	−272.695	−	73.0684i	−0.339595	−	0.0909943i
$804$		0			0
$805$	99.4610	+	371.194i	0.123554	+	0.461110i
$806$	−1377.16	−	574.773i	−1.70864	−	0.713118i
$807$		0			0
$808$	685.332	+	534.692i	0.848183	+	0.661748i
$809$	−423.156			−0.523060			−0.261530	−	0.965195i	$-0.584227\pi$
$809$	−423.156			−0.523060			−0.261530	+	0.965195i	$0.584227\pi$
$810$		0			0
$811$	−589.765	+	589.765i	−0.727207	+	0.727207i	−0.970062	−	0.242855i	$-0.921916\pi$
$811$	−589.765	+	589.765i	−0.727207	+	0.727207i	0.242855	+	0.970062i	$0.421916\pi$
$812$	−676.906	−	3.63223i	−0.833628	−	0.00447318i
$813$		0			0
$814$	−26.1159	+	10.7356i	−0.0320835	+	0.0131887i
$815$	−51.9019	−	29.9656i	−0.0636833	−	0.0367676i
$816$		0			0
$817$	−44.5331	−	77.1335i	−0.0545080	−	0.0944107i
$818$	393.311	−	509.735i	0.480820	−	0.623148i
$819$		0			0
$820$	132.912	−	227.384i	0.162088	−	0.277298i
$821$	−49.5593	+	184.958i	−0.0603645	+	0.225283i	−0.989518	−	0.144411i	$-0.953871\pi$
$821$	−49.5593	+	184.958i	−0.0603645	+	0.225283i	0.929153	+	0.369695i	$0.120538\pi$
$822$		0			0
$823$	−1152.99	−	665.678i	−1.40096	−	0.808844i	−0.406468	−	0.913665i	$-0.633240\pi$
$823$	−1152.99	−	665.678i	−1.40096	−	0.808844i	−0.994491	+	0.104821i	$0.966573\pi$
$824$	570.309	−	430.365i	0.692123	−	0.522288i
$825$		0			0
$826$	636.707	+	834.398i	0.770831	+	1.01017i
$827$	11.4409	+	11.4409i	0.0138342	+	0.0138342i	0.713990	−	0.700156i	$-0.246886\pi$
$827$	11.4409	+	11.4409i	0.0138342	+	0.0138342i	−0.700156	+	0.713990i	$0.746886\pi$
$828$		0			0
$829$	−664.004	−	664.004i	−0.800970	−	0.800970i	0.182277	−	0.983247i	$-0.441653\pi$
$829$	−664.004	−	664.004i	−0.800970	−	0.800970i	−0.983247	+	0.182277i	$0.941653\pi$
$830$	117.819	−	876.739i	0.141950	−	1.05631i
$831$		0			0
$832$	−853.314	−	511.150i	−1.02562	−	0.614362i
$833$	−270.998	−	156.460i	−0.325327	−	0.187828i
$834$		0			0
$835$	7.25809	−	27.0875i	0.00869232	−	0.0324402i
$836$	12.3936	−	3.24969i	0.0148249	−	0.00388719i
$837$		0			0
$838$	1426.33	−	183.888i	1.70206	−	0.219437i
$839$	−660.211	−	1143.52i	−0.786902	−	1.36295i	−0.927856	−	0.372938i	$-0.878350\pi$
$839$	−660.211	−	1143.52i	−0.786902	−	1.36295i	0.140955	−	0.990016i	$-0.454983\pi$
$840$		0			0
$841$	−63.7691	−	36.8171i	−0.0758254	−	0.0437778i
$842$	2.98636	−	7.15535i	0.00354674	−	0.00849804i
$843$		0			0
$844$	485.258	+	2.60386i	0.574951	+	0.00308514i
$845$	−242.198	+	242.198i	−0.286625	+	0.286625i
$846$		0			0
$847$	714.419			0.843469
$848$	360.979	+	1407.44i	0.425682	+	1.65971i
$849$		0			0
$850$	134.565	−	55.3161i	0.158312	−	0.0650777i
$851$	24.1782	+	90.2341i	0.0284115	+	0.106033i
$852$		0			0
$853$	−931.168	−	249.506i	−1.09164	−	0.292504i	−0.332284	−	0.943180i	$-0.607819\pi$
$853$	−931.168	−	249.506i	−1.09164	−	0.292504i	−0.759356	+	0.650676i	$0.774486\pi$
$854$	−605.738	+	78.0942i	−0.709295	+	0.0914451i
$855$		0			0
$856$	1105.85	−	447.663i	1.29188	−	0.522971i
$857$	202.447	+	350.648i	0.236227	+	0.409158i	0.959629	−	0.281270i	$-0.0907557\pi$
$857$	202.447	+	350.648i	0.236227	+	0.409158i	−0.723401	+	0.690428i	$0.757422\pi$
$858$		0			0
$859$	278.807	+	1040.52i	0.324571	+	1.21132i	0.914742	+	0.404038i	$0.132394\pi$
$859$	278.807	+	1040.52i	0.324571	+	1.21132i	−0.590171	+	0.807278i	$0.700940\pi$
$860$	1019.87	+	279.147i	1.18589	+	0.324589i
$861$		0			0
$862$	−1035.74	−	139.185i	−1.20155	−	0.161468i
$863$		−	502.653i		−	0.582449i	−0.956655	−	0.291224i	$-0.905937\pi$
$863$		−	502.653i		−	0.582449i	0.956655	−	0.291224i	$-0.0940626\pi$
$864$		0			0
$865$	1113.23			1.28697
$866$	−75.7891	+	563.979i	−0.0875163	+	0.651246i
$867$		0			0
$868$	309.705	−	1131.51i	0.356803	−	1.30359i
$869$	245.977	−	65.9093i	0.283057	−	0.0758450i
$870$		0			0
$871$	225.107	−	129.966i	0.258447	−	0.149214i
$872$	−86.2342	+	34.9089i	−0.0988925	+	0.0400331i
$873$		0			0
$874$	−5.42012	−	42.0412i	−0.00620151	−	0.0481020i
$875$	206.867	−	772.039i	0.236420	−	0.882331i
$876$		0			0
$877$	−1392.91	+	373.230i	−1.58827	+	0.425576i	−0.941474	−	0.337087i	$-0.890558\pi$
$877$	−1392.91	+	373.230i	−1.58827	+	0.425576i	−0.646796	+	0.762663i	$0.723892\pi$
$878$	605.537	+	1473.06i	0.689678	+	1.67775i
$879$		0			0
$880$	−77.4640	+	130.907i	−0.0880273	+	0.148758i
$881$			231.668i			0.262960i	0.991319	+	0.131480i	$0.0419729\pi$
$881$			231.668i			0.262960i	−0.991319	+	0.131480i	$0.958027\pi$
$882$		0			0
$883$	−29.5668	−	29.5668i	−0.0334845	−	0.0334845i	0.690166	−	0.723651i	$-0.257537\pi$
$883$	−29.5668	−	29.5668i	−0.0334845	−	0.0334845i	−0.723651	+	0.690166i	$0.757537\pi$
$884$	8.93753	−	1665.61i	0.0101103	−	1.88417i
$885$		0			0
$886$	182.382	+	76.1189i	0.205848	+	0.0859129i
$887$	−176.676	+	306.011i	−0.199183	+	0.344996i	−0.948264	−	0.317483i	$-0.897162\pi$
$887$	−176.676	+	306.011i	−0.199183	+	0.344996i	0.749080	+	0.662479i	$0.230496\pi$
$888$		0			0
$889$	2.51237	−	1.45052i	0.00282606	−	0.00163163i
$890$	71.0887	+	551.400i	0.0798749	+	0.619550i
$891$		0			0
$892$	−259.623	−	990.149i	−0.291058	−	1.11003i
$893$	−27.3502	−	7.32846i	−0.0306273	−	0.00820656i
$894$		0			0
$895$	153.959	−	266.665i	0.172021	−	0.297950i
$896$	312.757	−	716.688i	0.349059	−	0.799875i
$897$		0			0
$898$	1465.14	+	196.890i	1.63156	+	0.219254i
$899$	−940.373	+	940.373i	−1.04602	+	1.04602i
$900$		0			0
$901$	−1720.43	+	1720.43i	−1.90947	+	1.90947i
$902$	44.6620	−	34.0804i	0.0495144	−	0.0377831i
$903$		0			0
$904$	−1134.32	+	855.978i	−1.25478	+	0.946879i
$905$	480.689	−	832.577i	0.531148	−	0.919975i
$906$		0			0
$907$	−621.237	−	166.460i	−0.684936	−	0.183528i	−0.100463	−	0.994941i	$-0.532032\pi$
$907$	−621.237	−	166.460i	−0.684936	−	0.183528i	−0.584474	+	0.811413i	$0.698699\pi$
$908$	396.543	+	231.790i	0.436721	+	0.255276i
$909$		0			0
$910$	−709.722	−	547.621i	−0.779914	−	0.601781i
$911$	687.010	−	396.645i	0.754127	−	0.435395i	−0.0730562	−	0.997328i	$-0.523275\pi$
$911$	687.010	−	396.645i	0.754127	−	0.435395i	0.827183	+	0.561932i	$0.189942\pi$
$912$		0			0
$913$	94.3460	−	163.412i	0.103336	−	0.178984i
$914$	−28.0723	−	68.2901i	−0.0307136	−	0.0747156i
$915$		0			0
$916$	−3.69608	+	688.806i	−0.00403502	+	0.751972i
$917$	−174.493	−	174.493i	−0.190287	−	0.190287i
$918$		0			0
$919$		−	513.046i		−	0.558265i	−0.960253	−	0.279133i	$-0.909953\pi$
$919$		−	513.046i		−	0.558265i	0.960253	−	0.279133i	$-0.0900469\pi$
$920$	396.767	+	309.555i	0.431268	+	0.336473i
$921$		0			0
$922$	−112.897	+	270.503i	−0.122448	+	0.293387i
$923$	−903.121	+	241.990i	−0.978462	+	0.262178i
$924$		0			0
$925$	4.92653	−	18.3860i	0.00532597	−	0.0198768i
$926$	351.457	+	271.183i	0.379543	+	0.292855i
$927$		0			0
$928$	−710.439	+	530.150i	−0.765559	+	0.571283i
$929$	281.430	−	162.484i	0.302939	−	0.174902i	−0.340823	−	0.940127i	$-0.610706\pi$
$929$	281.430	−	162.484i	0.302939	−	0.174902i	0.643762	+	0.765225i	$0.277373\pi$
$930$		0			0
$931$	17.9438	−	4.80803i	0.0192737	−	0.00516437i
$932$	−473.834	−	129.693i	−0.508406	−	0.139155i
$933$		0			0
$934$	−329.091	−	431.271i	−0.352346	−	0.461746i
$935$	−254.710			−0.272417
$936$		0			0
$937$			320.707i			0.342270i	0.985248	+	0.171135i	$0.0547434\pi$
$937$			320.707i			0.342270i	−0.985248	+	0.171135i	$0.945257\pi$
$938$	123.958	+	162.446i	0.132152	+	0.173184i
$939$		0			0
$940$	292.013	−	166.511i	0.310653	−	0.177140i
$941$	−297.074	−	1108.70i	−0.315701	−	1.17821i	−0.923335	−	0.383994i	$-0.874548\pi$
$941$	−297.074	−	1108.70i	−0.315701	−	1.17821i	0.607635	−	0.794217i	$-0.292118\pi$
$942$		0			0
$943$	−92.9324	−	160.964i	−0.0985497	−	0.170693i
$944$	1323.73	+	369.963i	1.40226	+	0.391910i
$945$		0			0
$946$	178.566	+	137.781i	0.188759	+	0.145646i
$947$	1146.90	+	307.311i	1.21109	+	0.324510i	0.807188	−	0.590294i	$-0.200988\pi$
$947$	1146.90	+	307.311i	1.21109	+	0.324510i	0.403898	+	0.914804i	$0.367655\pi$
$948$		0			0
$949$	−563.908	−	2104.53i	−0.594213	−	2.21763i
$950$	−3.32670	+	7.97082i	−0.00350179	+	0.00839033i
$951$		0			0
$952$	1299.53	−	160.457i	1.36506	−	0.168547i
$953$	−899.741			−0.944114			−0.472057	−	0.881568i	$-0.656488\pi$
$953$	−899.741			−0.944114			−0.472057	+	0.881568i	$0.656488\pi$
$954$		0			0
$955$	−679.137	+	679.137i	−0.711138	+	0.711138i
$956$	703.929	+	711.524i	0.736328	+	0.744272i
$957$		0			0
$958$	−310.678	−	755.773i	−0.324299	−	0.788907i
$959$	15.5251	+	8.96339i	0.0161888	+	0.00934661i
$960$		0			0
$961$	−671.886	−	1163.74i	−0.699153	−	1.21097i
$962$	−172.528	−	133.122i	−0.179343	−	0.138380i
$963$		0			0
$964$	56.5230	+	215.567i	0.0586338	+	0.223617i
$965$	−26.4726	+	98.7971i	−0.0274328	+	0.102380i
$966$		0			0
$967$	612.293	+	353.508i	0.633189	+	0.365572i	0.781986	−	0.623296i	$-0.214207\pi$
$967$	612.293	+	353.508i	0.633189	+	0.365572i	−0.148797	+	0.988868i	$0.547540\pi$
$968$	746.785	−	563.537i	0.771472	−	0.582166i
$969$		0			0
$970$	−755.822	+	576.747i	−0.779198	+	0.594585i
$971$	−917.501	−	917.501i	−0.944903	−	0.944903i	0.0536564	−	0.998559i	$-0.482912\pi$
$971$	−917.501	−	917.501i	−0.944903	−	0.944903i	−0.998559	+	0.0536564i	$0.982912\pi$
$972$		0			0
$973$	−1093.54	−	1093.54i	−1.12388	−	1.12388i
$974$	−815.552	−	109.596i	−0.837322	−	0.112522i
$975$		0			0
$976$	−571.580	+	559.441i	−0.585635	+	0.573198i
$977$	−208.918	−	120.619i	−0.213837	−	0.123459i	0.389257	−	0.921129i	$-0.372732\pi$
$977$	−208.918	−	120.619i	−0.213837	−	0.123459i	−0.603093	+	0.797671i	$0.706065\pi$
$978$		0			0
$979$	−30.6930	+	114.548i	−0.0313514	+	0.117005i
$980$	−111.294	+	190.400i	−0.113565	+	0.194286i
$981$		0			0
$982$	94.1011	+	729.896i	0.0958260	+	0.743275i
$983$	−634.133	−	1098.35i	−0.645099	−	1.11734i	−0.984279	−	0.176623i	$-0.943483\pi$
$983$	−634.133	−	1098.35i	−0.645099	−	1.11734i	0.339179	−	0.940722i	$-0.389851\pi$
$984$		0			0
$985$	1256.25	+	725.297i	1.27538	+	0.736342i
$986$	−1369.84	−	571.719i	−1.38929	−	0.579837i
$987$		0			0
$988$	69.5437	+	70.2941i	0.0703884	+	0.0711479i
$989$	527.631	−	527.631i	0.533500	−	0.533500i
$990$		0			0
$991$	305.253			0.308026			0.154013	−	0.988069i	$-0.450780\pi$
$991$	305.253			0.308026			0.154013	+	0.988069i	$0.450780\pi$
$992$	−568.808	−	1427.08i	−0.573396	−	1.43858i
$993$		0			0
$994$	−279.455	−	679.816i	−0.281142	−	0.683920i
$995$	−236.134	−	881.265i	−0.237321	−	0.885693i
$996$		0			0
$997$	−1115.91	−	299.007i	−1.11927	−	0.299906i	−0.348679	−	0.937242i	$-0.613370\pi$
$997$	−1115.91	−	299.007i	−1.11927	−	0.299906i	−0.770586	+	0.637336i	$0.780036\pi$
$998$	185.229	+	1436.73i	0.185600	+	1.43961i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.x.a.125.20		184
3.2	odd	2		144.3.w.a.77.27	yes	184
9.2	odd	6	inner	432.3.x.a.413.6		184
9.7	even	3		144.3.w.a.29.41	yes	184
16.5	even	4	inner	432.3.x.a.341.6		184
48.5	odd	4		144.3.w.a.5.41	✓	184
144.101	odd	12	inner	432.3.x.a.197.20		184
144.133	even	12		144.3.w.a.101.27	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.w.a.5.41	✓	184	48.5	odd	4
144.3.w.a.29.41	yes	184	9.7	even	3
144.3.w.a.77.27	yes	184	3.2	odd	2
144.3.w.a.101.27	yes	184	144.133	even	12
432.3.x.a.125.20		184	1.1	even	1	trivial
432.3.x.a.197.20		184	144.101	odd	12	inner
432.3.x.a.341.6		184	16.5	even	4	inner
432.3.x.a.413.6		184	9.2	odd	6	inner

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.266371 + 1.98218i) q^{2} +(-3.85809 - 1.05599i) q^{4} +(-4.55983 + 1.22180i) q^{5} +(5.29059 - 3.05452i) q^{7} +(3.12086 - 7.36616i) q^{8} +O(q^{10})\)	\(q+(-0.266371 + 1.98218i) q^{2} +(-3.85809 - 1.05599i) q^{4} +(-4.55983 + 1.22180i) q^{5} +(5.29059 - 3.05452i) q^{7} +(3.12086 - 7.36616i) q^{8} +(-1.20723 - 9.36386i) q^{10} +(0.521228 - 1.94525i) q^{11} +(15.0125 - 4.02259i) q^{13} +(4.64536 + 11.3006i) q^{14} +(13.7698 + 8.14824i) q^{16} +26.7923i q^{17} +(-1.12468 - 1.12468i) q^{19} +(18.8825 + 0.101322i) q^{20} +(3.71700 + 1.55133i) q^{22} +(6.66267 - 11.5401i) q^{23} +(-2.35140 + 1.35758i) q^{25} +(3.97461 + 30.8291i) q^{26} +(-23.6371 + 6.19781i) q^{28} +(26.7575 + 7.16964i) q^{29} +(-24.0040 + 41.5762i) q^{31} +(-19.8192 + 25.1237i) q^{32} +(-53.1071 - 7.13669i) q^{34} +(-20.3922 + 20.3922i) q^{35} +(-4.95716 + 4.95716i) q^{37} +(2.52891 - 1.92975i) q^{38} +(-5.23058 + 37.4015i) q^{40} +(6.97411 - 12.0795i) q^{41} +(54.0892 + 14.4932i) q^{43} +(-4.06511 + 6.95454i) q^{44} +(21.0998 + 16.2806i) q^{46} +(15.4170 - 8.90103i) q^{47} +(-5.83977 + 10.1148i) q^{49} +(-2.06463 - 5.02253i) q^{50} +(-62.1676 - 0.333586i) q^{52} +(64.2137 + 64.2137i) q^{53} +9.50684i q^{55} +(-5.98892 - 48.5040i) q^{56} +(-21.3390 + 51.1284i) q^{58} +(82.9765 - 22.2335i) q^{59} +(-12.9377 + 48.2841i) q^{61} +(-76.0176 - 58.6551i) q^{62} +(-44.5205 - 45.9774i) q^{64} +(-63.5397 + 36.6847i) q^{65} +(16.1544 - 4.32857i) q^{67} +(28.2924 - 103.367i) q^{68} +(-34.9891 - 45.8529i) q^{70} -60.1578 q^{71} -140.185i q^{73} +(-8.50556 - 11.1464i) q^{74} +(3.15148 + 5.52680i) q^{76} +(-3.18421 - 11.8836i) q^{77} +(63.2251 + 109.509i) q^{79} +(-72.7433 - 20.3307i) q^{80} +(22.0861 + 17.0416i) q^{82} +(90.5036 + 24.2504i) q^{83} +(-32.7348 - 122.168i) q^{85} +(-43.1359 + 103.354i) q^{86} +(-12.7023 - 9.91029i) q^{88} -58.8859 q^{89} +(67.1380 - 67.1380i) q^{91} +(-37.8915 + 37.4870i) q^{92} +(13.5368 + 32.9304i) q^{94} +(6.50251 + 3.75423i) q^{95} +(-50.3496 - 87.2081i) q^{97} +(-18.4938 - 14.2698i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5}+O(q^{10}) \) 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5	\( 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} - 120 q^{20} - 2 q^{22} - 72 q^{28} + 6 q^{29} - 4 q^{31} + 6 q^{32} + 6 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 160 q^{46} + 12 q^{47} + 472 q^{49} - 228 q^{50} - 2 q^{52} + 300 q^{56} - 92 q^{58} + 438 q^{59} - 2 q^{61} + 244 q^{64} + 12 q^{65} - 2 q^{67} + 144 q^{68} + 96 q^{70} - 246 q^{74} - 158 q^{76} + 6 q^{77} - 4 q^{79} - 388 q^{82} + 726 q^{83} + 48 q^{85} - 894 q^{86} + 22 q^{88} - 204 q^{91} + 348 q^{92} - 18 q^{94} + 12 q^{95} - 4 q^{97}+O(q^{100}) \) 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 - 120 * q^20 - 2 * q^22 - 72 * q^28 + 6 * q^29 - 4 * q^31 + 6 * q^32 + 6 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 160 * q^46 + 12 * q^47 + 472 * q^49 - 228 * q^50 - 2 * q^52 + 300 * q^56 - 92 * q^58 + 438 * q^59 - 2 * q^61 + 244 * q^64 + 12 * q^65 - 2 * q^67 + 144 * q^68 + 96 * q^70 - 246 * q^74 - 158 * q^76 + 6 * q^77 - 4 * q^79 - 388 * q^82 + 726 * q^83 + 48 * q^85 - 894 * q^86 + 22 * q^88 - 204 * q^91 + 348 * q^92 - 18 * q^94 + 12 * q^95 - 4 * q^97

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