LMFDB - Embedded newform 153.3.p.b.10.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,3,Mod(10,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.10"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	153.p (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,8,0,0,-16,0,8,24,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$4.16894804471$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			10.1
Root			$0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	153.10
Dual form			153.3.p.b.46.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.15851 - 2.79690i) q^{2} +(-3.65205 - 3.65205i) q^{4} +(-7.87510 + 1.56645i) q^{5} +(-7.70353 - 1.53233i) q^{7} +(-3.25778 + 1.34942i) q^{8} +(-4.74219 + 23.8406i) q^{10} +(-4.48649 - 6.71450i) q^{11} +(-0.798835 + 0.798835i) q^{13} +(-13.2104 + 19.7707i) q^{14} -9.98414i q^{16} +(6.50562 - 15.7060i) q^{17} +(1.07647 - 2.59882i) q^{19} +(34.4811 + 23.0395i) q^{20} +(-23.9774 + 4.76941i) q^{22} +(7.13426 - 4.76696i) q^{23} +(36.4664 - 15.1049i) q^{25} +(1.30880 + 3.15972i) q^{26} +(22.5376 + 33.7298i) q^{28} +(0.599020 + 3.01148i) q^{29} +(-7.13254 + 10.6746i) q^{31} +(-40.9557 - 16.9644i) q^{32} +(-36.3911 - 36.3911i) q^{34} +63.0663 q^{35} +(19.6817 + 13.1509i) q^{37} +(-6.02153 - 6.02153i) q^{38} +(23.5416 - 15.7300i) q^{40} +(-21.4206 - 4.26082i) q^{41} +(-8.89197 - 21.4671i) q^{43} +(-8.13684 + 40.9066i) q^{44} +(-5.06757 - 25.4764i) q^{46} +(-55.6597 + 55.6597i) q^{47} +(11.7262 + 4.85715i) q^{49} -119.492i q^{50} +5.83478 q^{52} +(22.9922 - 55.5080i) q^{53} +(45.8495 + 45.8495i) q^{55} +(27.1642 - 5.40329i) q^{56} +(9.11677 + 1.81344i) q^{58} +(25.3733 - 10.5100i) q^{59} +(7.11302 - 35.7596i) q^{61} +(21.5926 + 32.3156i) q^{62} +(-66.6561 + 66.6561i) q^{64} +(5.03957 - 7.54224i) q^{65} -117.219i q^{67} +(-81.1179 + 33.6001i) q^{68} +(73.0632 - 176.390i) q^{70} +(-88.1108 - 58.8738i) q^{71} +(-59.8620 + 11.9073i) q^{73} +(59.5832 - 39.8122i) q^{74} +(-13.4223 + 5.55971i) q^{76} +(24.2730 + 58.6001i) q^{77} +(52.9382 + 79.2276i) q^{79} +(15.6397 + 78.6261i) q^{80} +(-36.7331 + 54.9749i) q^{82} +(109.791 + 45.4770i) q^{83} +(-26.6297 + 133.877i) q^{85} -70.3428 q^{86} +(23.6767 + 15.8202i) q^{88} +(61.4534 + 61.4534i) q^{89} +(7.37792 - 4.92977i) q^{91} +(-43.4639 - 8.64551i) q^{92} +(91.1920 + 220.157i) q^{94} +(-4.40634 + 22.1522i) q^{95} +(4.79748 + 24.1185i) q^{97} +(27.1699 - 27.1699i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 16 q^{5} + 8 q^{7} + 24 q^{8} + 16 q^{10} + 8 q^{11} + 16 q^{13} - 8 q^{14} + 80 q^{20} - 104 q^{22} + 56 q^{23} + 64 q^{25} - 176 q^{26} + 152 q^{28} - 48 q^{29} + 24 q^{31} - 88 q^{32}+ \cdots + 120 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 - 16 * q^5 + 8 * q^7 + 24 * q^8 + 16 * q^10 + 8 * q^11 + 16 * q^13 - 8 * q^14 + 80 * q^20 - 104 * q^22 + 56 * q^23 + 64 * q^25 - 176 * q^26 + 152 * q^28 - 48 * q^29 + 24 * q^31 - 88 * q^32 - 136 * q^34 + 160 * q^35 + 32 * q^37 + 120 * q^38 + 64 * q^40 - 48 * q^41 - 232 * q^43 - 120 * q^44 - 88 * q^46 - 192 * q^47 + 16 * q^49 - 384 * q^52 + 32 * q^53 + 224 * q^55 + 120 * q^56 + 240 * q^58 + 48 * q^59 - 160 * q^61 + 168 * q^62 - 64 * q^64 + 96 * q^65 - 272 * q^68 + 224 * q^70 - 40 * q^71 + 48 * q^73 + 160 * q^74 + 80 * q^76 + 48 * q^77 - 136 * q^79 + 240 * q^80 - 64 * q^82 + 264 * q^83 - 272 * q^85 - 832 * q^86 + 264 * q^88 - 160 * q^89 + 320 * q^91 - 24 * q^92 + 32 * q^94 - 272 * q^95 + 48 * q^97 + 120 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{3}{16}\right)$	$1$

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 $

$2$	1.15851	−	2.79690i	0.579256	−	1.39845i	−0.314225	−	0.949348i	$-0.601745\pi$
$2$	1.15851	−	2.79690i	0.579256	−	1.39845i	0.893481	−	0.449100i	$-0.148255\pi$
$3$		0			0
$3$		0			0
$4$	−3.65205	−	3.65205i	−0.913014	−	0.913014i
$5$	−7.87510	+	1.56645i	−1.57502	+	0.313291i	−0.903796	−	0.427964i	$-0.859231\pi$
$5$	−7.87510	+	1.56645i	−1.57502	+	0.313291i	−0.671224	+	0.741255i	$0.734231\pi$
$6$		0			0
$7$	−7.70353	−	1.53233i	−1.10050	−	0.218904i	−0.388757	−	0.921340i	$-0.627096\pi$
$7$	−7.70353	−	1.53233i	−1.10050	−	0.218904i	−0.711746	+	0.702436i	$0.752096\pi$
$8$	−3.25778	+	1.34942i	−0.407223	+	0.168677i
$9$		0			0
$10$	−4.74219	+	23.8406i	−0.474219	+	2.38406i
$11$	−4.48649	−	6.71450i	−0.407863	−	0.610410i	0.569497	−	0.821993i	$-0.307138\pi$
$11$	−4.48649	−	6.71450i	−0.407863	−	0.610410i	−0.977360	+	0.211584i	$0.932138\pi$
$12$		0			0
$13$	−0.798835	+	0.798835i	−0.0614489	+	0.0614489i	−0.737163	−	0.675715i	$-0.763835\pi$
$13$	−0.798835	+	0.798835i	−0.0614489	+	0.0614489i	0.675715	+	0.737163i	$0.263835\pi$
$14$	−13.2104	+	19.7707i	−0.943599	+	1.41220i
$15$		0			0
$16$		−	9.98414i		−	0.624009i
$17$	6.50562	−	15.7060i	0.382683	−	0.923880i
$17$	6.50562	−	15.7060i	0.382683	−	0.923880i
$18$		0			0
$19$	1.07647	−	2.59882i	0.0566561	−	0.136780i	−0.893017	−	0.450023i	$-0.851416\pi$
$19$	1.07647	−	2.59882i	0.0566561	−	0.136780i	0.949673	+	0.313244i	$0.101416\pi$
$20$	34.4811	+	23.0395i	1.72405	+	1.15198i
$21$		0			0
$22$	−23.9774	+	4.76941i	−1.08988	+	0.216791i
$23$	7.13426	−	4.76696i	0.310185	−	0.207259i	−0.390727	−	0.920507i	$-0.627776\pi$
$23$	7.13426	−	4.76696i	0.310185	−	0.207259i	0.700912	+	0.713247i	$0.252776\pi$
$24$		0			0
$25$	36.4664	−	15.1049i	1.45866	−	0.604195i
$26$	1.30880	+	3.15972i	0.0503384	+	0.121528i
$27$		0			0
$28$	22.5376	+	33.7298i	0.804913	+	1.20464i
$29$	0.599020	+	3.01148i	0.0206559	+	0.103844i	0.989738	−	0.142895i	$-0.0456410\pi$
$29$	0.599020	+	3.01148i	0.0206559	+	0.103844i	−0.969082	+	0.246739i	$0.920641\pi$
$30$		0			0
$31$	−7.13254	+	10.6746i	−0.230082	+	0.344342i	−0.928490	−	0.371358i	$-0.878892\pi$
$31$	−7.13254	+	10.6746i	−0.230082	+	0.344342i	0.698408	+	0.715700i	$0.253892\pi$
$32$	−40.9557	−	16.9644i	−1.27987	−	0.530138i
$33$		0			0
$34$	−36.3911	−	36.3911i	−1.07033	−	1.07033i
$35$	63.0663			1.80190
$36$		0			0
$37$	19.6817	+	13.1509i	0.531938	+	0.355429i	0.792349	−	0.610068i	$-0.208858\pi$
$37$	19.6817	+	13.1509i	0.531938	+	0.355429i	−0.260411	+	0.965498i	$0.583858\pi$
$38$	−6.02153	−	6.02153i	−0.158461	−	0.158461i
$39$		0			0
$40$	23.5416	−	15.7300i	0.588539	−	0.393249i
$41$	−21.4206	−	4.26082i	−0.522453	−	0.103922i	−0.0731833	−	0.997319i	$-0.523316\pi$
$41$	−21.4206	−	4.26082i	−0.522453	−	0.103922i	−0.449270	+	0.893396i	$0.648316\pi$
$42$		0			0
$43$	−8.89197	−	21.4671i	−0.206790	−	0.499235i	0.786124	−	0.618069i	$-0.212085\pi$
$43$	−8.89197	−	21.4671i	−0.206790	−	0.499235i	−0.992914	+	0.118833i	$0.962085\pi$
$44$	−8.13684	+	40.9066i	−0.184928	+	0.929696i
$45$		0			0
$46$	−5.06757	−	25.4764i	−0.110164	−	0.553834i
$47$	−55.6597	+	55.6597i	−1.18425	+	1.18425i	−0.205617	+	0.978632i	$0.565920\pi$
$47$	−55.6597	+	55.6597i	−1.18425	+	1.18425i	−0.978632	+	0.205617i	$0.934080\pi$
$48$		0			0
$49$	11.7262	+	4.85715i	0.239310	+	0.0991254i
$50$		−	119.492i		−	2.38984i
$51$		0			0
$52$	5.83478			0.112207
$53$	22.9922	−	55.5080i	0.433815	−	1.04732i	−0.544232	−	0.838935i	$-0.683179\pi$
$53$	22.9922	−	55.5080i	0.433815	−	1.04732i	0.978047	−	0.208386i	$-0.0668212\pi$
$54$		0			0
$55$	45.8495	+	45.8495i	0.833627	+	0.833627i
$56$	27.1642	−	5.40329i	0.485074	−	0.0964873i
$57$		0			0
$58$	9.11677	+	1.81344i	0.157186	+	0.0312662i
$59$	25.3733	−	10.5100i	0.430057	−	0.178135i	−0.157146	−	0.987575i	$-0.550229\pi$
$59$	25.3733	−	10.5100i	0.430057	−	0.178135i	0.587202	+	0.809440i	$0.300229\pi$
$60$		0			0
$61$	7.11302	−	35.7596i	0.116607	−	0.586223i	−0.877659	−	0.479286i	$-0.840896\pi$
$61$	7.11302	−	35.7596i	0.116607	−	0.586223i	0.994266	−	0.106937i	$-0.0341043\pi$
$62$	21.5926	+	32.3156i	0.348268	+	0.521220i
$63$		0			0
$64$	−66.6561	+	66.6561i	−1.04150	+	1.04150i
$65$	5.03957	−	7.54224i	0.0775318	−	0.116035i
$66$		0			0
$67$		−	117.219i		−	1.74953i	−0.484544	−	0.874767i	$-0.661015\pi$
$67$		−	117.219i		−	1.74953i	0.484544	−	0.874767i	$-0.338985\pi$
$68$	−81.1179	+	33.6001i	−1.19291	+	0.494119i
$69$		0			0
$70$	73.0632	−	176.390i	1.04376	−	2.51986i
$71$	−88.1108	−	58.8738i	−1.24100	−	0.829208i	−0.250685	−	0.968069i	$-0.580656\pi$
$71$	−88.1108	−	58.8738i	−1.24100	−	0.829208i	−0.990312	+	0.138861i	$0.955656\pi$
$72$		0			0
$73$	−59.8620	+	11.9073i	−0.820028	+	0.163114i	−0.587239	−	0.809414i	$-0.699785\pi$
$73$	−59.8620	+	11.9073i	−0.820028	+	0.163114i	−0.232789	+	0.972527i	$0.574785\pi$
$74$	59.5832	−	39.8122i	0.805178	−	0.538003i
$75$		0			0
$76$	−13.4223	+	5.55971i	−0.176610	+	0.0731541i
$77$	24.2730	+	58.6001i	0.315233	+	0.761041i
$78$		0			0
$79$	52.9382	+	79.2276i	0.670103	+	1.00288i	0.998301	+	0.0582714i	$0.0185589\pi$
$79$	52.9382	+	79.2276i	0.670103	+	1.00288i	−0.328197	+	0.944609i	$0.606441\pi$
$80$	15.6397	+	78.6261i	0.195496	+	0.982826i
$81$		0			0
$82$	−36.7331	+	54.9749i	−0.447964	+	0.670426i
$83$	109.791	+	45.4770i	1.32279	+	0.547916i	0.928589	−	0.371110i	$-0.121023\pi$
$83$	109.791	+	45.4770i	1.32279	+	0.547916i	0.394197	+	0.919026i	$0.371023\pi$
$84$		0			0
$85$	−26.6297	+	133.877i	−0.313291	+	1.57502i
$86$	−70.3428			−0.817939
$87$		0			0
$88$	23.6767	+	15.8202i	0.269053	+	0.179776i
$89$	61.4534	+	61.4534i	0.690488	+	0.690488i	0.962339	−	0.271851i	$-0.0876359\pi$
$89$	61.4534	+	61.4534i	0.690488	+	0.690488i	−0.271851	+	0.962339i	$0.587636\pi$
$90$		0			0
$91$	7.37792	−	4.92977i	0.0810761	−	0.0541733i
$92$	−43.4639	−	8.64551i	−0.472434	−	0.0939729i
$93$		0			0
$94$	91.1920	+	220.157i	0.970128	+	2.34210i
$95$	−4.40634	+	22.1522i	−0.0463826	+	0.233181i
$96$		0			0
$97$	4.79748	+	24.1185i	0.0494585	+	0.248645i	0.997603	−	0.0691943i	$-0.0220428\pi$
$97$	4.79748	+	24.1185i	0.0494585	+	0.248645i	−0.948145	+	0.317839i	$0.897043\pi$
$98$	27.1699	−	27.1699i	0.277244	−	0.277244i
$99$		0			0
$100$	−188.341	−	78.0135i	−1.88341	−	0.780135i
$101$		−	7.70266i		−	0.0762640i	−0.999273	−	0.0381320i	$-0.987859\pi$
$101$		−	7.70266i		−	0.0762640i	0.999273	−	0.0381320i	$-0.0121407\pi$
$102$		0			0
$103$	41.5688			0.403581			0.201790	−	0.979429i	$-0.435324\pi$
$103$	41.5688			0.403581			0.201790	+	0.979429i	$0.435324\pi$
$104$	1.52447	−	3.68039i	0.0146584	−	0.0353884i
$105$		0			0
$106$	−128.614	−	128.614i	−1.21333	−	1.21333i
$107$	−86.7136	+	17.2484i	−0.810407	+	0.161200i	−0.582866	−	0.812568i	$-0.698069\pi$
$107$	−86.7136	+	17.2484i	−0.810407	+	0.161200i	−0.227541	+	0.973768i	$0.573069\pi$
$108$		0			0
$109$	18.2754	+	3.63521i	0.167665	+	0.0333506i	0.278209	−	0.960521i	$-0.410259\pi$
$109$	18.2754	+	3.63521i	0.167665	+	0.0333506i	−0.110544	+	0.993871i	$0.535259\pi$
$110$	181.354	−	75.1191i	1.64867	−	0.682901i
$111$		0			0
$112$	−15.2990	+	76.9131i	−0.136598	+	0.686724i
$113$	33.6909	+	50.4220i	0.298150	+	0.446212i	0.950053	−	0.312090i	$-0.101029\pi$
$113$	33.6909	+	50.4220i	0.298150	+	0.446212i	−0.651903	+	0.758302i	$0.726029\pi$
$114$		0			0
$115$	−48.7158	+	48.7158i	−0.423615	+	0.423615i
$116$	8.81043	−	13.1857i	0.0759520	−	0.113670i
$117$		0			0
$118$		−	83.1426i		−	0.704598i
$119$	−74.1828	+	111.022i	−0.623385	+	0.932962i
$120$		0			0
$121$	21.3487	−	51.5403i	0.176436	−	0.425953i
$122$	−91.7753	−	61.3223i	−0.752257	−	0.502642i
$123$		0			0
$124$	65.0326	−	12.9358i	0.524456	−	0.104321i
$125$	−96.6108	+	64.5533i	−0.772886	+	0.516426i
$126$		0			0
$127$	110.168	−	45.6333i	0.867468	−	0.359317i	0.0958444	−	0.995396i	$-0.469445\pi$
$127$	110.168	−	45.6333i	0.867468	−	0.359317i	0.771624	+	0.636079i	$0.219445\pi$
$128$	41.3506	+	99.8291i	0.323051	+	0.779915i
$129$		0			0
$130$	−15.2565	−	22.8329i	−0.117358	−	0.175638i
$131$	−33.4238	−	168.033i	−0.255144	−	1.28269i	−0.869605	−	0.493748i	$-0.835627\pi$
$131$	−33.4238	−	168.033i	−0.255144	−	1.28269i	0.614461	−	0.788947i	$-0.289373\pi$
$132$		0			0
$133$	−12.2748	+	18.3706i	−0.0922919	+	0.138125i
$134$	−327.849	−	135.799i	−2.44663	−	1.01343i
$135$		0			0
$136$			59.9454i			0.440775i
$137$	173.113			1.26360			0.631799	−	0.775132i	$-0.282317\pi$
$137$	173.113			1.26360			0.631799	+	0.775132i	$0.282317\pi$
$138$		0			0
$139$	−149.307	−	99.7637i	−1.07415	−	0.717724i	−0.112957	−	0.993600i	$-0.536032\pi$
$139$	−149.307	−	99.7637i	−1.07415	−	0.717724i	−0.961193	+	0.275876i	$0.911032\pi$
$140$	−230.322	−	230.322i	−1.64515	−	1.64515i
$141$		0			0
$142$	−266.741	+	178.231i	−1.87846	+	1.25515i
$143$	8.94775	+	1.77982i	0.0625717	+	0.0124463i
$144$		0			0
$145$	−9.43469	−	22.7774i	−0.0650668	−	0.157085i
$146$	−36.0474	+	181.223i	−0.246900	+	1.24125i
$147$		0			0
$148$	−23.8509	−	119.906i	−0.161154	−	0.810178i
$149$	−31.6842	+	31.6842i	−0.212646	+	0.212646i	−0.805391	−	0.592745i	$-0.798044\pi$
$149$	−31.6842	+	31.6842i	−0.212646	+	0.212646i	0.592745	+	0.805391i	$0.298044\pi$
$150$		0			0
$151$	−121.384	−	50.2789i	−0.803868	−	0.332973i	−0.0573634	−	0.998353i	$-0.518269\pi$
$151$	−121.384	−	50.2789i	−0.803868	−	0.332973i	−0.746504	+	0.665380i	$0.768269\pi$
$152$			9.91898i			0.0652565i
$153$		0			0
$154$	192.019			1.24688
$155$	39.4482	−	95.2363i	0.254504	−	0.614428i
$156$		0			0
$157$	25.4694	+	25.4694i	0.162225	+	0.162225i	0.783552	−	0.621327i	$-0.213406\pi$
$157$	25.4694	+	25.4694i	0.162225	+	0.162225i	−0.621327	+	0.783552i	$0.713406\pi$
$158$	282.921	−	56.2765i	1.79064	−	0.356180i
$159$		0			0
$160$	349.104	+	69.4412i	2.18190	+	0.434007i
$161$	−62.2635	+	25.7904i	−0.386730	+	0.160189i
$162$		0			0
$163$	31.1596	−	156.650i	0.191163	−	0.961041i	−0.759427	−	0.650592i	$-0.774521\pi$
$163$	31.1596	−	156.650i	0.191163	−	0.961041i	0.950590	−	0.310449i	$-0.100479\pi$
$164$	62.6684	+	93.7898i	0.382124	+	0.571889i
$165$		0			0
$166$	254.389	−	254.389i	1.53246	−	1.53246i
$167$	61.5214	−	92.0734i	0.368392	−	0.551337i	−0.600246	−	0.799816i	$-0.704930\pi$
$167$	61.5214	−	92.0734i	0.368392	−	0.551337i	0.968637	+	0.248478i	$0.0799305\pi$
$168$		0			0
$169$			167.724i			0.992448i
$170$	343.588	+	229.578i	2.02111	+	1.35046i
$171$		0			0
$172$	−45.9251	+	110.873i	−0.267006	+	0.644611i
$173$	148.047	+	98.9216i	0.855761	+	0.571801i	0.904241	−	0.427023i	$-0.140438\pi$
$173$	148.047	+	98.9216i	0.855761	+	0.571801i	−0.0484797	+	0.998824i	$0.515438\pi$
$174$		0			0
$175$	−304.066	+	60.4824i	−1.73752	+	0.345614i
$176$	−67.0386	+	44.7937i	−0.380901	+	0.254510i
$177$		0			0
$178$	243.074	−	100.684i	1.36558	−	0.565642i
$179$	−96.5028	−	232.978i	−0.539122	−	1.30155i	−0.925337	−	0.379146i	$-0.876218\pi$
$179$	−96.5028	−	232.978i	−0.539122	−	1.30155i	0.386215	−	0.922409i	$-0.373782\pi$
$180$		0			0
$181$	167.421	+	250.563i	0.924977	+	1.38433i	0.923197	+	0.384328i	$0.125567\pi$
$181$	167.421	+	250.563i	0.924977	+	1.38433i	0.00178027	+	0.999998i	$0.499433\pi$
$182$	−5.24064	−	26.3465i	−0.0287947	−	0.144761i
$183$		0			0
$184$	−16.8092	+	25.1568i	−0.0913546	+	0.136722i
$185$	−175.596	−	72.7341i	−0.949165	−	0.393157i
$186$		0			0
$187$	−134.645	+	26.7826i	−0.720027	+	0.143222i
$188$	406.545			2.16247
$189$		0			0
$190$	56.8526	+	37.9877i	0.299224	+	0.199935i
$191$	−93.7287	−	93.7287i	−0.490726	−	0.490726i	0.417809	−	0.908535i	$-0.362798\pi$
$191$	−93.7287	−	93.7287i	−0.490726	−	0.490726i	−0.908535	+	0.417809i	$0.862798\pi$
$192$		0			0
$193$	264.917	−	177.012i	1.37263	−	0.917161i	0.372687	−	0.927957i	$-0.378436\pi$
$193$	264.917	−	177.012i	1.37263	−	0.917161i	0.999942	+	0.0107958i	$0.00343648\pi$
$194$	73.0150	+	14.5236i	0.376366	+	0.0748639i
$195$		0			0
$196$	−25.0861	−	60.5632i	−0.127990	−	0.308996i
$197$	−22.5650	+	113.442i	−0.114543	+	0.575847i	0.880300	+	0.474418i	$0.157341\pi$
$197$	−22.5650	+	113.442i	−0.114543	+	0.575847i	−0.994843	+	0.101429i	$0.967659\pi$
$198$		0			0
$199$	−57.7166	−	290.161i	−0.290033	−	1.45809i	−0.801088	−	0.598547i	$-0.795745\pi$
$199$	−57.7166	−	290.161i	−0.290033	−	1.45809i	0.511055	−	0.859548i	$-0.329255\pi$
$200$	−98.4168	+	98.4168i	−0.492084	+	0.492084i
$201$		0			0
$202$	−21.5436	−	8.92363i	−0.106651	−	0.0441764i
$203$		−	24.1169i		−	0.118802i
$204$		0			0
$205$	175.364			0.855432
$206$	48.1580	−	116.264i	0.233777	−	0.564387i
$207$		0			0
$208$	7.97568	+	7.97568i	0.0383446	+	0.0383446i
$209$	−22.2793	+	4.43163i	−0.106600	+	0.0212040i
$210$		0			0
$211$	−225.325	−	44.8199i	−1.06789	−	0.212417i	−0.370300	−	0.928912i	$-0.620745\pi$
$211$	−225.325	−	44.8199i	−1.06789	−	0.212417i	−0.697592	+	0.716495i	$0.745745\pi$
$212$	−286.687	+	118.750i	−1.35230	+	0.560140i
$213$		0			0
$214$	−52.2168	+	262.511i	−0.244004	+	1.22669i
$215$	103.652	+	155.127i	0.482104	+	0.721520i
$216$		0			0
$217$	71.3026	−	71.3026i	0.328584	−	0.328584i
$218$	31.3396	−	46.9031i	0.143760	−	0.215152i
$219$		0			0
$220$		−	334.890i		−	1.52223i
$221$	7.34955	+	17.7434i	0.0332559	+	0.0802868i
$222$		0			0
$223$	−139.061	+	335.723i	−0.623593	+	1.50549i	0.223863	+	0.974621i	$0.428133\pi$
$223$	−139.061	+	335.723i	−0.623593	+	1.50549i	−0.847456	+	0.530865i	$0.821867\pi$
$224$	289.509	+	193.443i	1.29245	+	0.863587i
$225$		0			0
$226$	180.056	−	35.8155i	0.796710	−	0.158475i
$227$	80.5890	−	53.8478i	0.355017	−	0.237215i	−0.365253	−	0.930908i	$-0.619018\pi$
$227$	80.5890	−	53.8478i	0.355017	−	0.237215i	0.720271	+	0.693693i	$0.244018\pi$
$228$		0			0
$229$	−334.120	+	138.397i	−1.45904	+	0.604353i	−0.964329	−	0.264706i	$-0.914725\pi$
$229$	−334.120	+	138.397i	−1.45904	+	0.604353i	−0.494708	+	0.869059i	$0.664725\pi$
$230$	79.8152	+	192.691i	0.347022	+	0.837786i
$231$		0			0
$232$	−6.01522	−	9.00241i	−0.0259277	−	0.0388035i
$233$	−54.6542	−	274.765i	−0.234567	−	1.17925i	−0.901045	−	0.433725i	$-0.857199\pi$
$233$	−54.6542	−	274.765i	−0.234567	−	1.17925i	0.666478	−	0.745525i	$-0.267801\pi$
$234$		0			0
$235$	351.137	−	525.514i	1.49420	−	2.23623i
$236$	−131.048	−	54.2818i	−0.555288	−	0.230008i
$237$		0			0
$238$	224.577	+	336.103i	0.943599	+	1.41220i
$239$	−328.551			−1.37469			−0.687345	−	0.726331i	$-0.741224\pi$
$239$	−328.551			−1.37469			−0.687345	+	0.726331i	$0.741224\pi$
$240$		0			0
$241$	−201.560	−	134.678i	−0.836349	−	0.558831i	0.0620186	−	0.998075i	$-0.480246\pi$
$241$	−201.560	−	134.678i	−0.836349	−	0.558831i	−0.898368	+	0.439244i	$0.855246\pi$
$242$	−119.420	−	119.420i	−0.493472	−	0.493472i
$243$		0			0
$244$	−156.573	+	104.619i	−0.641693	+	0.428765i
$245$	−99.9534	−	19.8820i	−0.407973	−	0.0811509i
$246$		0			0
$247$	1.21611	+	2.93595i	0.00492352	+	0.0118864i
$248$	8.83176	−	44.4003i	0.0356119	−	0.179033i
$249$		0			0
$250$	68.6240	+	344.996i	0.274496	+	1.37999i
$251$	155.463	−	155.463i	0.619375	−	0.619375i	−0.325996	−	0.945371i	$-0.605700\pi$
$251$	155.463	−	155.463i	0.619375	−	0.619375i	0.945371	+	0.325996i	$0.105700\pi$
$252$		0			0
$253$	−64.0155	−	26.5161i	−0.253026	−	0.104807i
$254$		−	360.996i		−	1.42125i
$255$		0			0
$256$	−49.9468			−0.195105
$257$	−124.463	+	300.480i	−0.484292	+	1.16918i	0.473260	+	0.880923i	$0.343077\pi$
$257$	−124.463	+	300.480i	−0.484292	+	1.16918i	−0.957552	+	0.288261i	$0.906923\pi$
$258$		0			0
$259$	−131.467	−	131.467i	−0.507595	−	0.507595i
$260$	−45.9494	+	9.13991i	−0.176729	+	0.0351535i
$261$		0			0
$262$	−508.693	−	101.185i	−1.94158	−	0.386203i
$263$	−128.172	+	53.0907i	−0.487347	+	0.201866i	−0.612806	−	0.790233i	$-0.709959\pi$
$263$	−128.172	+	53.0907i	−0.487347	+	0.201866i	0.125460	+	0.992099i	$0.459959\pi$
$264$		0			0
$265$	−94.1149	+	473.147i	−0.355150	+	1.78546i
$266$	37.1600	+	55.6139i	0.139699	+	0.209075i
$267$		0			0
$268$	−428.089	+	428.089i	−1.59735	+	1.59735i
$269$	180.493	−	270.126i	0.670976	−	1.00419i	−0.327267	−	0.944932i	$-0.606128\pi$
$269$	180.493	−	270.126i	0.670976	−	1.00419i	0.998243	−	0.0592547i	$-0.0188724\pi$
$270$		0			0
$271$			19.1867i			0.0707996i	0.999373	+	0.0353998i	$0.0112705\pi$
$271$			19.1867i			0.0707996i	−0.999373	+	0.0353998i	$0.988730\pi$
$272$	−156.810	−	64.9530i	−0.576509	−	0.238798i
$273$		0			0
$274$	200.554	−	484.179i	0.731947	−	1.76708i
$275$	−265.028	−	177.086i	−0.963738	−	0.643949i
$276$		0			0
$277$	302.084	−	60.0883i	1.09056	−	0.216925i	0.383118	−	0.923700i	$-0.374850\pi$
$277$	302.084	−	60.0883i	1.09056	−	0.216925i	0.707439	+	0.706774i	$0.249850\pi$
$278$	−452.003	+	302.018i	−1.62591	+	1.08640i
$279$		0			0
$280$	−205.456	+	85.1028i	−0.733773	+	0.303939i
$281$	33.1106	+	79.9361i	0.117831	+	0.284470i	0.971781	−	0.235886i	$-0.0757992\pi$
$281$	33.1106	+	79.9361i	0.117831	+	0.284470i	−0.853949	+	0.520356i	$0.825799\pi$
$282$		0			0
$283$	4.15656	+	6.22073i	0.0146875	+	0.0219814i	0.838741	−	0.544531i	$-0.183292\pi$
$283$	4.15656	+	6.22073i	0.0146875	+	0.0219814i	−0.824053	+	0.566512i	$0.808292\pi$
$284$	106.775	+	536.796i	0.375969	+	1.89013i
$285$		0			0
$286$	15.3440	−	22.9640i	0.0536505	−	0.0802937i
$287$	158.485	+	65.6466i	0.552213	+	0.228734i
$288$		0			0
$289$	−204.354	−	204.354i	−0.707107	−	0.707107i
$290$	−74.6361			−0.257366
$291$		0			0
$292$	262.105	+	175.133i	0.897621	+	0.599771i
$293$	−54.4583	−	54.4583i	−0.185864	−	0.185864i	0.608041	−	0.793906i	$-0.291956\pi$
$293$	−54.4583	−	54.4583i	−0.185864	−	0.185864i	−0.793906	+	0.608041i	$0.791956\pi$
$294$		0			0
$295$	−183.354	+	122.513i	−0.621540	+	0.415300i
$296$	−81.8647	−	16.2839i	−0.276570	−	0.0550132i
$297$		0			0
$298$	51.9110	+	125.324i	0.174198	+	0.420551i
$299$	−1.89108	+	9.50711i	−0.00632469	+	0.0317964i
$300$		0			0
$301$	35.6049	+	178.998i	0.118289	+	0.594677i
$302$	−281.250	+	281.250i	−0.931291	+	0.931291i
$303$		0			0
$304$	−25.9470	−	10.7476i	−0.0853519	−	0.0353539i
$305$			292.752i			0.959844i
$306$		0			0
$307$	−159.680			−0.520132			−0.260066	−	0.965591i	$-0.583744\pi$
$307$	−159.680			−0.520132			−0.260066	+	0.965591i	$0.583744\pi$
$308$	125.365	−	302.657i	0.407028	−	0.982653i
$309$		0			0
$310$	−220.665	−	220.665i	−0.711822	−	0.711822i
$311$	326.615	−	64.9678i	1.05021	−	0.208900i	0.360331	−	0.932825i	$-0.382664\pi$
$311$	326.615	−	64.9678i	1.05021	−	0.208900i	0.689879	+	0.723925i	$0.257664\pi$
$312$		0			0
$313$	386.986	+	76.9763i	1.23638	+	0.245931i	0.769647	−	0.638470i	$-0.220432\pi$
$313$	386.986	+	76.9763i	1.23638	+	0.245931i	0.466729	+	0.884400i	$0.345432\pi$
$314$	100.742	−	41.7286i	0.320834	−	0.132894i
$315$		0			0
$316$	96.0103	−	482.676i	0.303830	−	1.52746i
$317$	77.2775	+	115.654i	0.243778	+	0.364839i	0.933101	−	0.359615i	$-0.117092\pi$
$317$	77.2775	+	115.654i	0.243778	+	0.364839i	−0.689323	+	0.724454i	$0.742092\pi$
$318$		0			0
$319$	17.5331	−	17.5331i	0.0549627	−	0.0549627i
$320$	420.509	−	629.337i	1.31409	−	1.96668i
$321$		0			0
$322$			204.023i			0.633612i
$323$	−33.8138	−	33.8138i	−0.104687	−	0.104687i
$324$		0			0
$325$	−17.0643	+	41.1970i	−0.0525057	+	0.126760i
$326$	−402.034	−	268.631i	−1.23323	−	0.824021i
$327$		0			0
$328$	75.5332	−	15.0245i	0.230284	−	0.0458064i
$329$	514.065	−	343.487i	1.56251	−	1.04403i
$330$		0			0
$331$	146.717	−	60.7720i	0.443252	−	0.183601i	−0.149883	−	0.988704i	$-0.547890\pi$
$331$	146.717	−	60.7720i	0.443252	−	0.183601i	0.593136	+	0.805103i	$0.297890\pi$
$332$	−234.879	−	567.048i	−0.707467	−	1.70798i
$333$		0			0
$334$	−186.246	−	278.737i	−0.557624	−	0.834543i
$335$	183.618	+	923.109i	0.548113	+	2.75555i
$336$		0			0
$337$	−267.981	+	401.062i	−0.795195	+	1.19009i	0.183144	+	0.983086i	$0.441372\pi$
$337$	−267.981	+	401.062i	−0.795195	+	1.19009i	−0.978339	+	0.207008i	$0.933628\pi$
$338$	469.106	+	194.310i	1.38789	+	0.574882i
$339$		0			0
$340$	586.178	−	391.672i	1.72405	−	1.15198i
$341$	103.675			0.304031
$342$		0			0
$343$	237.116	+	158.436i	0.691299	+	0.461912i
$344$	57.9362	+	57.9362i	0.168419	+	0.168419i
$345$		0			0
$346$	448.188	−	299.469i	1.29534	−	0.865518i
$347$	19.4096	+	3.86080i	0.0559353	+	0.0111262i	0.222979	−	0.974823i	$-0.428422\pi$
$347$	19.4096	+	3.86080i	0.0559353	+	0.0111262i	−0.167043	+	0.985950i	$0.553422\pi$
$348$		0			0
$349$	−149.801	−	361.651i	−0.429229	−	1.03625i	−0.979533	−	0.201286i	$-0.935488\pi$
$349$	−149.801	−	361.651i	−0.429229	−	1.03625i	0.550304	−	0.834965i	$-0.314512\pi$
$350$	−183.101	+	920.510i	−0.523145	+	2.63003i
$351$		0			0
$352$	69.8398	+	351.108i	0.198408	+	0.997466i
$353$	−138.024	+	138.024i	−0.391003	+	0.391003i	−0.875045	−	0.484042i	$-0.839168\pi$
$353$	−138.024	+	138.024i	−0.391003	+	0.391003i	0.484042	+	0.875045i	$0.339168\pi$
$354$		0			0
$355$	786.104	+	325.615i	2.21438	+	0.917226i
$356$		−	448.863i		−	1.26085i
$357$		0			0
$358$	−763.416			−2.13245
$359$	−136.163	+	328.726i	−0.379284	+	0.915672i	0.612817	+	0.790225i	$0.290036\pi$
$359$	−136.163	+	328.726i	−0.379284	+	0.915672i	−0.992100	+	0.125447i	$0.959964\pi$
$360$		0			0
$361$	249.670	+	249.670i	0.691608	+	0.691608i
$362$	894.758	−	177.978i	2.47171	−	0.491653i
$363$		0			0
$364$	−44.9484	−	8.94078i	−0.123485	−	0.0245626i
$365$	452.767	−	187.542i	1.24046	−	0.513814i
$366$		0			0
$367$	−15.9442	+	80.1568i	−0.0434446	+	0.218411i	−0.996409	−	0.0846717i	$-0.973016\pi$
$367$	−15.9442	+	80.1568i	−0.0434446	+	0.218411i	0.952964	+	0.303083i	$0.0980158\pi$
$368$	−47.5940	−	71.2294i	−0.129331	−	0.193558i
$369$		0			0
$370$	−406.859	+	406.859i	−1.09962	+	1.09962i
$371$	−262.177	+	392.376i	−0.706677	+	1.05762i
$372$		0			0
$373$			76.8209i			0.205954i	0.994684	+	0.102977i	$0.0328368\pi$
$373$			76.8209i			0.205954i	−0.994684	+	0.102977i	$0.967163\pi$
$374$	−81.0799	+	407.616i	−0.216791	+	1.08988i
$375$		0			0
$376$	106.219	−	256.436i	0.282498	−	0.682009i
$377$	−2.88419	−	1.92716i	−0.00765038	−	0.00511182i
$378$		0			0
$379$	577.940	−	114.959i	1.52491	−	0.303323i	0.639739	−	0.768592i	$-0.279043\pi$
$379$	577.940	−	114.959i	1.52491	−	0.303323i	0.885169	+	0.465269i	$0.154043\pi$
$380$	96.9932	−	64.8088i	0.255245	−	0.170549i
$381$		0			0
$382$	−370.735	+	153.564i	−0.970511	+	0.401999i
$383$	89.4016	+	215.834i	0.233424	+	0.563537i	0.996576	−	0.0826832i	$-0.0263490\pi$
$383$	89.4016	+	215.834i	0.233424	+	0.563537i	−0.763151	+	0.646220i	$0.776349\pi$
$384$		0			0
$385$	−282.946	−	423.459i	−0.734926	−	1.09989i
$386$	−188.175	−	946.017i	−0.487499	−	2.45082i
$387$		0			0
$388$	70.5616	−	105.603i	0.181860	−	0.272172i
$389$	−372.916	−	154.467i	−0.958653	−	0.397087i	−0.152177	−	0.988353i	$-0.548628\pi$
$389$	−372.916	−	154.467i	−0.958653	−	0.397087i	−0.806477	+	0.591266i	$0.798628\pi$
$390$		0			0
$391$	−28.4569	−	143.062i	−0.0727797	−	0.365888i
$392$	−44.7557			−0.114173
$393$		0			0
$394$	291.143	+	194.536i	0.738943	+	0.493746i
$395$	−541.000	−	541.000i	−1.36962	−	1.36962i
$396$		0			0
$397$	219.332	−	146.553i	0.552474	−	0.369151i	−0.247776	−	0.968817i	$-0.579700\pi$
$397$	219.332	−	146.553i	0.552474	−	0.369151i	0.800251	+	0.599666i	$0.204700\pi$
$398$	−878.415	−	174.728i	−2.20707	−	0.439014i
$399$		0			0
$400$	−150.809	−	364.086i	−0.377023	−	0.910214i
$401$	−46.6830	+	234.691i	−0.116416	+	0.585265i	0.877904	+	0.478837i	$0.158941\pi$
$401$	−46.6830	+	234.691i	−0.116416	+	0.585265i	−0.994320	+	0.106428i	$0.966059\pi$
$402$		0			0
$403$	−2.82952	−	14.2250i	−0.00702114	−	0.0352977i
$404$	−28.1305	+	28.1305i	−0.0696300	+	0.0696300i
$405$		0			0
$406$	−67.4525	−	27.9397i	−0.166139	−	0.0688171i
$407$		−	191.154i		−	0.469666i
$408$		0			0
$409$	259.903			0.635461			0.317730	−	0.948181i	$-0.397079\pi$
$409$	259.903			0.635461			0.317730	+	0.948181i	$0.397079\pi$
$410$	203.161	−	490.474i	0.495514	−	1.19628i
$411$		0			0
$412$	−151.812	−	151.812i	−0.368475	−	0.368475i
$413$	−211.569	+	42.0837i	−0.512274	+	0.101898i
$414$		0			0
$415$	−935.855	−	186.153i	−2.25507	−	0.448562i
$416$	46.2687	−	19.1651i	0.111223	−	0.0460700i
$417$		0			0
$418$	−13.4161	+	67.4471i	−0.0320958	+	0.161357i
$419$	95.3087	+	142.640i	0.227467	+	0.340429i	0.927594	−	0.373590i	$-0.121873\pi$
$419$	95.3087	+	142.640i	0.227467	+	0.340429i	−0.700127	+	0.714018i	$0.746873\pi$
$420$		0			0
$421$	443.214	−	443.214i	1.05276	−	1.05276i	0.0542356	−	0.998528i	$-0.482728\pi$
$421$	443.214	−	443.214i	1.05276	−	1.05276i	0.998528	−	0.0542356i	$-0.0172722\pi$
$422$	−386.399	+	578.287i	−0.915637	+	1.37035i
$423$		0			0
$424$			211.859i			0.499668i
$425$		−	671.006i		−	1.57884i
$426$		0			0
$427$	−109.591	+	264.575i	−0.256653	+	0.619614i
$428$	379.675	+	253.691i	0.887090	+	0.592735i
$429$		0			0
$430$	553.956	−	110.189i	1.28827	−	0.256253i
$431$	633.734	−	423.447i	1.47038	−	0.982477i	0.475684	−	0.879616i	$-0.342201\pi$
$431$	633.734	−	423.447i	1.47038	−	0.982477i	0.994696	−	0.102860i	$-0.0327995\pi$
$432$		0			0
$433$	87.4681	−	36.2305i	0.202005	−	0.0836732i	−0.279387	−	0.960179i	$-0.590131\pi$
$433$	87.4681	−	36.2305i	0.202005	−	0.0836732i	0.481392	+	0.876505i	$0.340131\pi$
$434$	−116.821	−	282.031i	−0.269173	−	0.649841i
$435$		0			0
$436$	−53.4669	−	80.0189i	−0.122630	−	0.183530i
$437$	−4.70868	−	23.6721i	−0.0107750	−	0.0541696i
$438$		0			0
$439$	−20.5441	+	30.7465i	−0.0467976	+	0.0700375i	−0.854131	−	0.520059i	$-0.825910\pi$
$439$	−20.5441	+	30.7465i	−0.0467976	+	0.0700375i	0.807333	+	0.590096i	$0.200910\pi$
$440$	−211.238	−	87.4976i	−0.480086	−	0.198858i
$441$		0			0
$442$	58.1410			0.131541
$443$	634.146			1.43148			0.715740	−	0.698367i	$-0.246089\pi$
$443$	634.146			1.43148			0.715740	+	0.698367i	$0.246089\pi$
$444$		0			0
$445$	−580.216	−	387.688i	−1.30386	−	0.871209i
$446$	777.880	+	777.880i	1.74412	+	1.74412i
$447$		0			0
$448$	615.626	−	411.348i	1.37416	−	0.918187i
$449$	−433.336	−	86.1959i	−0.965114	−	0.191973i	−0.312713	−	0.949848i	$-0.601238\pi$
$449$	−433.336	−	86.1959i	−0.965114	−	0.191973i	−0.652400	+	0.757874i	$0.726238\pi$
$450$		0			0
$451$	67.4939	+	162.945i	0.149654	+	0.361296i
$452$	61.1029	−	307.185i	0.135183	−	0.679613i
$453$		0			0
$454$	−57.2435	−	287.782i	−0.126087	−	0.633882i
$455$	−50.3796	+	50.3796i	−0.110724	+	0.110724i
$456$		0			0
$457$	246.501	+	102.104i	0.539390	+	0.223423i	0.635710	−	0.771928i	$-0.280707\pi$
$457$	246.501	+	102.104i	0.539390	+	0.223423i	−0.0963202	+	0.995350i	$0.530707\pi$
$458$			1094.83i			2.39046i
$459$		0			0
$460$	355.825			0.773533
$461$	−172.768	+	417.100i	−0.374769	+	0.904772i	0.618159	+	0.786053i	$0.287879\pi$
$461$	−172.768	+	417.100i	−0.374769	+	0.904772i	−0.992928	+	0.118719i	$0.962121\pi$
$462$		0			0
$463$	−57.1171	−	57.1171i	−0.123363	−	0.123363i	0.642730	−	0.766093i	$-0.277802\pi$
$463$	−57.1171	−	57.1171i	−0.123363	−	0.123363i	−0.766093	+	0.642730i	$0.777802\pi$
$464$	30.0670	−	5.98070i	0.0647996	−	0.0128894i
$465$		0			0
$466$	−831.808	−	165.457i	−1.78499	−	0.355058i
$467$	−76.1879	+	31.5580i	−0.163143	+	0.0675761i	−0.462760	−	0.886483i	$-0.653141\pi$
$467$	−76.1879	+	31.5580i	−0.163143	+	0.0675761i	0.299617	+	0.954059i	$0.403141\pi$
$468$		0			0
$469$	−179.617	+	902.998i	−0.382979	+	1.92537i
$470$	−1063.01	−	1590.91i	−2.26173	−	3.38492i
$471$		0			0
$472$	−68.4785	+	68.4785i	−0.145082	+	0.145082i
$473$	−104.247	+	156.017i	−0.220396	+	0.329846i
$474$		0			0
$475$		−	111.029i		−	0.233746i
$476$	676.380	−	134.540i	1.42097	−	0.282648i
$477$		0			0
$478$	−380.630	+	918.923i	−0.796298	+	1.92243i
$479$	−382.794	−	255.775i	−0.799153	−	0.533977i	0.0876357	−	0.996153i	$-0.472069\pi$
$479$	−382.794	−	255.775i	−0.799153	−	0.533977i	−0.886788	+	0.462176i	$0.847069\pi$
$480$		0			0
$481$	−26.2278	+	5.21704i	−0.0545277	+	0.0108462i
$482$	−610.191	+	407.717i	−1.26596	+	0.845885i
$483$		0			0
$484$	−266.195	+	110.261i	−0.549989	+	0.227813i
$485$	−75.5612	−	182.421i	−0.155796	−	0.376125i
$486$		0			0
$487$	290.646	+	434.982i	0.596809	+	0.893187i	0.999757	−	0.0220352i	$-0.00701459\pi$
$487$	290.646	+	434.982i	0.596809	+	0.893187i	−0.402948	+	0.915223i	$0.632015\pi$
$488$	25.0819	+	126.095i	0.0513974	+	0.258392i
$489$		0			0
$490$	−171.405	+	256.526i	−0.349806	+	0.523522i
$491$	451.862	+	187.167i	0.920289	+	0.381196i	0.791986	−	0.610539i	$-0.209047\pi$
$491$	451.862	+	187.167i	0.920289	+	0.381196i	0.128303	+	0.991735i	$0.459047\pi$
$492$		0			0
$493$	51.1951	+	10.1833i	0.103844	+	0.0206559i
$494$	9.62041			0.0194745
$495$		0			0
$496$	106.577	+	71.2122i	0.214872	+	0.143573i
$497$	588.550	+	588.550i	1.18421	+	1.18421i
$498$		0			0
$499$	−421.610	+	281.711i	−0.844910	+	0.564551i	−0.900972	−	0.433876i	$-0.857145\pi$
$499$	−421.610	+	281.711i	−0.844910	+	0.564551i	0.0560623	+	0.998427i	$0.482145\pi$
$500$	588.580	+	117.076i	1.17716	+	0.234152i
$501$		0			0
$502$	−254.709	−	614.921i	−0.507388	−	1.22494i
$503$	131.577	−	661.484i	0.261585	−	1.31508i	−0.596932	−	0.802292i	$-0.703614\pi$
$503$	131.577	−	661.484i	0.261585	−	1.31508i	0.858517	−	0.512785i	$-0.171386\pi$
$504$		0			0
$505$	12.0659	+	60.6592i	0.0238928	+	0.120117i
$506$	−148.326	+	148.326i	−0.293134	+	0.293134i
$507$		0			0
$508$	−568.996	−	235.686i	−1.12007	−	0.463949i
$509$			349.504i			0.686648i	0.939217	+	0.343324i	$0.111553\pi$
$509$			349.504i			0.686648i	−0.939217	+	0.343324i	$0.888447\pi$
$510$		0			0
$511$	479.395			0.938150
$512$	−223.266	+	539.012i	−0.436067	+	1.05276i
$513$		0			0
$514$	696.221	+	696.221i	1.35451	+	1.35451i
$515$	−327.358	+	65.1157i	−0.635648	+	0.126438i
$516$		0			0
$517$	623.444	+	124.011i	1.20589	+	0.239866i
$518$	−520.006	+	215.393i	−1.00387	+	0.415818i
$519$		0			0
$520$	−6.24017	+	31.3715i	−0.0120003	+	0.0603297i
$521$	175.223	+	262.240i	0.336320	+	0.503339i	0.960627	−	0.277840i	$-0.0896186\pi$
$521$	175.223	+	262.240i	0.336320	+	0.503339i	−0.624307	+	0.781179i	$0.714619\pi$
$522$		0			0
$523$	−145.221	+	145.221i	−0.277669	+	0.277669i	−0.832178	−	0.554509i	$-0.812906\pi$
$523$	−145.221	+	145.221i	−0.277669	+	0.277669i	0.554509	+	0.832178i	$0.312906\pi$
$524$	−491.600	+	735.731i	−0.938168	+	1.40407i
$525$		0			0
$526$			419.991i			0.798461i
$527$	121.253	+	181.468i	0.230082	+	0.344342i
$528$		0			0
$529$	−174.266	+	420.715i	−0.329425	+	0.795302i
$530$	1214.31	+	811.377i	2.29115	+	1.53090i
$531$		0			0
$532$	111.919	−	22.2620i	0.210373	−	0.0418459i
$533$	20.5152	−	13.7078i	0.0384901	−	0.0257182i
$534$		0			0
$535$	655.859	−	271.666i	1.22590	−	0.507786i
$536$	158.177	+	381.873i	0.295106	+	0.712450i
$537$		0			0
$538$	−546.412	−	817.764i	−1.01564	−	1.52001i
$539$	−19.9961	−	100.527i	−0.0370985	−	0.186507i
$540$		0			0
$541$	439.282	−	657.431i	0.811981	−	1.21522i	−0.161596	−	0.986857i	$-0.551664\pi$
$541$	439.282	−	657.431i	0.811981	−	1.21522i	0.973577	−	0.228358i	$-0.0733358\pi$
$542$	53.6632	+	22.2280i	0.0990096	+	0.0410111i
$543$		0			0
$544$	−532.885	+	532.885i	−0.979568	+	0.979568i
$545$	−149.615			−0.274523
$546$		0			0
$547$	−783.860	−	523.758i	−1.43302	−	0.957511i	−0.998380	−	0.0569051i	$-0.981877\pi$
$547$	−783.860	−	523.758i	−1.43302	−	0.957511i	−0.434637	−	0.900606i	$-0.643123\pi$
$548$	−632.218	−	632.218i	−1.15368	−	1.15368i
$549$		0			0
$550$	−802.330	+	536.099i	−1.45878	+	0.974726i
$551$	8.47111	+	1.68501i	0.0153741	+	0.00305809i
$552$		0			0
$553$	−286.408	−	691.450i	−0.517917	−	1.25036i
$554$	181.908	−	914.512i	0.328353	−	1.65074i
$555$		0			0
$556$	180.934	+	909.619i	0.325422	+	1.63601i
$557$	303.284	−	303.284i	0.544495	−	0.544495i	−0.380348	−	0.924843i	$-0.624196\pi$
$557$	303.284	−	303.284i	0.544495	−	0.544495i	0.924843	+	0.380348i	$0.124196\pi$
$558$		0			0
$559$	24.2519	+	10.0455i	0.0433844	+	0.0179704i
$560$		−	629.663i		−	1.12440i
$561$		0			0
$562$	261.932			0.466071
$563$	264.879	−	639.473i	0.470477	−	1.13583i	−0.493476	−	0.869759i	$-0.664274\pi$
$563$	264.879	−	639.473i	0.470477	−	1.13583i	0.963953	−	0.266072i	$-0.0857260\pi$
$564$		0			0
$565$	−344.303	−	344.303i	−0.609386	−	0.609386i
$566$	22.2142	−	4.41867i	0.0392476	−	0.00780684i
$567$		0			0
$568$	366.491	+	72.8996i	0.645231	+	0.128344i
$569$	370.173	−	153.331i	0.650567	−	0.269474i	−0.0328958	−	0.999459i	$-0.510473\pi$
$569$	370.173	−	153.331i	0.650567	−	0.269474i	0.683463	+	0.729985i	$0.260473\pi$
$570$		0			0
$571$	127.142	−	639.187i	0.222666	−	1.11942i	−0.694065	−	0.719912i	$-0.744182\pi$
$571$	127.142	−	639.187i	0.222666	−	1.11942i	0.916731	−	0.399505i	$-0.130818\pi$
$572$	−26.1777	−	39.1776i	−0.0457651	−	0.0684924i
$573$		0			0
$574$	367.214	−	367.214i	0.639745	−	0.639745i
$575$	188.156	−	281.596i	0.327229	−	0.489732i
$576$		0			0
$577$			684.109i			1.18563i	0.805339	+	0.592815i	$0.201983\pi$
$577$			684.109i			1.18563i	−0.805339	+	0.592815i	$0.798017\pi$
$578$	−808.303	+	334.810i	−1.39845	+	0.579256i
$579$		0			0
$580$	−48.7281	+	117.640i	−0.0840140	+	0.202828i
$581$	−776.094	−	518.569i	−1.33579	−	0.892546i
$582$		0			0
$583$	−475.863	+	94.6550i	−0.816232	+	0.162359i
$584$	178.950	−	119.570i	0.306420	−	0.204744i
$585$		0			0
$586$	−215.405	+	89.2236i	−0.367585	+	0.152259i
$587$	141.750	+	342.216i	0.241483	+	0.582991i	0.997430	−	0.0716408i	$-0.0228235\pi$
$587$	141.750	+	342.216i	0.241483	+	0.582991i	−0.755948	+	0.654632i	$0.772824\pi$
$588$		0			0
$589$	20.0634	+	30.0270i	0.0340635	+	0.0509796i
$590$	130.239	+	654.756i	0.220744	+	1.10976i
$591$		0			0
$592$	131.300	−	196.505i	0.221791	−	0.331934i
$593$	−585.245	−	242.416i	−0.986922	−	0.408797i	−0.169937	−	0.985455i	$-0.554356\pi$
$593$	−585.245	−	242.416i	−0.986922	−	0.408797i	−0.816985	+	0.576658i	$0.804356\pi$
$594$		0			0
$595$	410.286	−	990.517i	0.689556	−	1.66473i
$596$	231.425			0.388297
$597$		0			0
$598$	24.3996	+	16.3033i	0.0408020	+	0.0272630i
$599$	−315.855	−	315.855i	−0.527304	−	0.527304i	0.392463	−	0.919768i	$-0.371623\pi$
$599$	−315.855	−	315.855i	−0.527304	−	0.527304i	−0.919768	+	0.392463i	$0.871623\pi$
$600$		0			0
$601$	362.279	−	242.067i	0.602794	−	0.402774i	−0.216388	−	0.976307i	$-0.569428\pi$
$601$	362.279	−	242.067i	0.602794	−	0.402774i	0.819182	+	0.573533i	$0.194428\pi$
$602$	541.887	+	107.788i	0.900145	+	0.179050i
$603$		0			0
$604$	259.680	+	626.922i	0.429933	+	1.03795i
$605$	−87.3876	+	439.327i	−0.144442	+	0.726160i
$606$		0			0
$607$	123.803	+	622.400i	0.203959	+	1.02537i	0.938098	+	0.346371i	$0.112586\pi$
$607$	123.803	+	622.400i	0.203959	+	1.02537i	−0.734139	+	0.679000i	$0.762414\pi$
$608$	−88.1749	+	88.1749i	−0.145025	+	0.145025i
$609$		0			0
$610$	818.798	+	339.157i	1.34229	+	0.555996i
$611$		−	88.9259i		−	0.145542i
$612$		0			0
$613$	−692.422			−1.12956			−0.564782	−	0.825240i	$-0.691040\pi$
$613$	−692.422			−1.12956			−0.564782	+	0.825240i	$0.691040\pi$
$614$	−184.992	+	446.610i	−0.301290	+	0.727377i
$615$		0			0
$616$	−158.152	−	158.152i	−0.256740	−	0.256740i
$617$	263.077	−	52.3292i	0.426381	−	0.0848124i	0.0227645	−	0.999741i	$-0.492753\pi$
$617$	263.077	−	52.3292i	0.426381	−	0.0848124i	0.403616	+	0.914928i	$0.367753\pi$
$618$		0			0
$619$	−153.549	−	30.5428i	−0.248060	−	0.0493422i	0.0694940	−	0.997582i	$-0.477862\pi$
$619$	−153.549	−	30.5428i	−0.248060	−	0.0493422i	−0.317554	+	0.948240i	$0.602862\pi$
$620$	−491.875	+	203.741i	−0.793346	+	0.328615i
$621$		0			0
$622$	196.680	−	988.775i	0.316205	−	1.58967i
$623$	−379.241	−	567.575i	−0.608734	−	0.911035i
$624$		0			0
$625$	−38.0547	+	38.0547i	−0.0608875	+	0.0608875i
$626$	663.623	−	993.182i	1.06010	−	1.58655i
$627$		0			0
$628$		−	186.031i		−	0.296228i
$629$	334.589	−	223.565i	0.531938	−	0.355429i
$630$		0			0
$631$	−119.803	+	289.230i	−0.189862	+	0.458368i	−0.989933	−	0.141538i	$-0.954795\pi$
$631$	−119.803	+	289.230i	−0.189862	+	0.458368i	0.800071	+	0.599906i	$0.204795\pi$
$632$	−279.372	−	186.670i	−0.442044	−	0.295365i
$633$		0			0
$634$	412.999	−	82.1506i	0.651418	−	0.129575i
$635$	−796.105	+	531.940i	−1.25371	+	0.837701i
$636$		0			0
$637$	−13.2473	+	5.48723i	−0.0207965	+	0.00861418i
$638$	−28.7259	−	69.3506i	−0.0450250	−	0.108700i
$639$		0			0
$640$	−482.018	−	721.390i	−0.753153	−	1.12717i
$641$	72.2074	+	363.011i	0.112648	+	0.566320i	0.995345	+	0.0963771i	$0.0307255\pi$
$641$	72.2074	+	363.011i	0.112648	+	0.566320i	−0.882697	+	0.469943i	$0.844275\pi$
$642$		0			0
$643$	−122.220	+	182.915i	−0.190077	+	0.284471i	−0.914252	−	0.405146i	$-0.867221\pi$
$643$	−122.220	+	182.915i	−0.190077	+	0.284471i	0.724175	+	0.689616i	$0.242221\pi$
$644$	321.577	+	133.202i	0.499344	+	0.206835i
$645$		0			0
$646$	−133.748	+	55.4001i	−0.207040	+	0.0857586i
$647$	−769.098			−1.18871			−0.594357	−	0.804201i	$-0.702593\pi$
$647$	−769.098			−1.18871			−0.594357	+	0.804201i	$0.702593\pi$
$648$		0			0
$649$	−184.407	−	123.217i	−0.284140	−	0.189856i
$650$	95.4544	+	95.4544i	0.146853	+	0.146853i
$651$		0			0
$652$	−685.889	+	458.297i	−1.05198	+	0.702909i
$653$	41.6201	+	8.27876i	0.0637368	+	0.0126780i	0.226856	−	0.973928i	$-0.427155\pi$
$653$	41.6201	+	8.27876i	0.0637368	+	0.0126780i	−0.163119	+	0.986606i	$0.552155\pi$
$654$		0			0
$655$	526.432	+	1270.92i	0.803713	+	1.94033i
$656$	−42.5406	+	213.866i	−0.0648485	+	0.326015i
$657$		0			0
$658$	−365.148	−	1835.72i	−0.554936	−	2.78985i
$659$	−472.719	+	472.719i	−0.717328	+	0.717328i	−0.968057	−	0.250729i	$-0.919330\pi$
$659$	−472.719	+	472.719i	−0.717328	+	0.717328i	0.250729	+	0.968057i	$0.419330\pi$
$660$		0			0
$661$	−380.158	−	157.467i	−0.575126	−	0.238225i	0.0761113	−	0.997099i	$-0.475750\pi$
$661$	−380.158	−	157.467i	−0.575126	−	0.238225i	−0.651237	+	0.758874i	$0.725750\pi$
$662$		−	480.756i		−	0.726218i
$663$		0			0
$664$	−419.043			−0.631089
$665$	67.8888	−	163.898i	0.102088	−	0.246463i
$666$		0			0
$667$	18.6292	+	18.6292i	0.0279298	+	0.0279298i
$668$	−560.937	+	111.577i	−0.839725	+	0.167032i
$669$		0			0
$670$	2794.56	+	555.873i	4.17099	+	0.829662i
$671$	−272.020	+	112.675i	−0.405395	+	0.167920i
$672$		0			0
$673$	3.16371	−	15.9051i	0.00470091	−	0.0236331i	−0.978364	−	0.206893i	$-0.933665\pi$
$673$	3.16371	−	15.9051i	0.00470091	−	0.0236331i	0.983065	+	0.183260i	$0.0586649\pi$
$674$	811.269	+	1214.15i	1.20366	+	1.80141i
$675$		0			0
$676$	612.536	−	612.536i	0.906119	−	0.906119i
$677$	571.240	−	854.921i	0.843782	−	1.26281i	−0.119099	−	0.992882i	$-0.538001\pi$
$677$	571.240	−	854.921i	0.843782	−	1.26281i	0.962881	−	0.269926i	$-0.0869993\pi$
$678$		0			0
$679$		−	193.149i		−	0.284461i
$680$	−93.9017	−	472.076i	−0.138091	−	0.694229i
$681$		0			0
$682$	120.108	−	289.967i	0.176112	−	0.425172i
$683$	−188.201	−	125.752i	−0.275551	−	0.184117i	0.410114	−	0.912034i	$-0.365489\pi$
$683$	−188.201	−	125.752i	−0.275551	−	0.184117i	−0.685666	+	0.727917i	$0.740489\pi$
$684$		0			0
$685$	−1363.28	+	271.173i	−1.99019	+	0.395874i
$686$	717.830	−	479.639i	1.04640	−	0.699181i
$687$		0			0
$688$	−214.331	+	88.7787i	−0.311527	+	0.129039i
$689$	25.9748	+	62.7087i	0.0376993	+	0.0910141i
$690$		0			0
$691$	−21.7058	−	32.4851i	−0.0314122	−	0.0470117i	0.815431	−	0.578854i	$-0.196500\pi$
$691$	−21.7058	−	32.4851i	−0.0314122	−	0.0470117i	−0.846843	+	0.531842i	$0.821500\pi$
$692$	−179.407	−	901.942i	−0.259259	−	1.30338i
$693$		0			0
$694$	33.2845	−	49.8138i	0.0479604	−	0.0717778i
$695$	1332.08	+	551.766i	1.91666	+	0.793908i
$696$		0			0
$697$	−206.274	+	308.711i	−0.295946	+	0.442914i
$698$	−1185.05			−1.69778
$699$		0			0
$700$	1331.35	+	889.579i	1.90193	+	1.27083i
$701$	401.261	+	401.261i	0.572412	+	0.572412i	0.932802	−	0.360390i	$-0.117356\pi$
$701$	401.261	+	401.261i	0.572412	+	0.572412i	−0.360390	+	0.932802i	$0.617356\pi$
$702$		0			0
$703$	55.3634	−	36.9927i	0.0787531	−	0.0526212i
$704$	746.614	+	148.511i	1.06053	+	0.210953i
$705$		0			0
$706$	226.136	+	545.941i	0.320306	+	0.773288i
$707$	−11.8030	+	59.3377i	−0.0166945	+	0.0839288i
$708$		0			0
$709$	55.6759	+	279.901i	0.0785273	+	0.394783i	0.999980	+	0.00629329i	$0.00200323\pi$
$709$	55.6759	+	279.901i	0.0785273	+	0.394783i	−0.921453	+	0.388490i	$0.872997\pi$
$710$	1821.42	−	1821.42i	2.56539	−	2.56539i
$711$		0			0
$712$	−283.128	−	117.276i	−0.397652	−	0.164713i
$713$			110.156i			0.154496i
$714$		0			0
$715$	−73.2524			−0.102451
$716$	−498.416	+	1203.28i	−0.696112	+	1.68056i
$717$		0			0
$718$	761.667	+	761.667i	1.06082	+	1.06082i
$719$	−601.644	+	119.674i	−0.836779	+	0.166446i	−0.594838	−	0.803845i	$-0.702784\pi$
$719$	−601.644	+	119.674i	−0.836779	+	0.166446i	−0.241941	+	0.970291i	$0.577784\pi$
$720$		0			0
$721$	−320.226	−	63.6970i	−0.444142	−	0.0883453i
$722$	987.549	−	409.056i	1.36780	−	0.566560i
$723$		0			0
$724$	303.640	−	1526.50i	0.419392	−	2.10842i
$725$	67.3322	+	100.770i	0.0928719	+	0.138993i
$726$		0			0
$727$	244.413	−	244.413i	0.336194	−	0.336194i	−0.518739	−	0.854933i	$-0.673598\pi$
$727$	244.413	−	244.413i	0.336194	−	0.336194i	0.854933	+	0.518739i	$0.173598\pi$
$728$	−17.3833	+	26.0160i	−0.0238782	+	0.0357363i
$729$		0			0
$730$		−	1483.61i		−	2.03235i
$731$	−395.009			−0.540368
$732$		0			0
$733$	516.266	−	1246.38i	0.704319	−	1.70038i	−0.00941053	−	0.999956i	$-0.502996\pi$
$733$	516.266	−	1246.38i	0.704319	−	1.70038i	0.713730	−	0.700421i	$-0.247004\pi$
$734$	205.719	+	137.457i	0.280271	+	0.187271i
$735$		0			0
$736$	−373.058	+	74.2058i	−0.506872	+	0.100823i
$737$	−787.066	+	525.901i	−1.06793	+	0.713569i
$738$		0			0
$739$	602.925	−	249.740i	0.815866	−	0.337943i	0.0645741	−	0.997913i	$-0.479431\pi$
$739$	602.925	−	249.740i	0.815866	−	0.337943i	0.751292	+	0.659970i	$0.229431\pi$
$740$	375.656	+	906.913i	0.507643	+	1.22556i
$741$		0			0
$742$	793.700	+	1187.86i	1.06968	+	1.60088i
$743$	43.5044	+	218.711i	0.0585523	+	0.294362i	0.998955	−	0.0456999i	$-0.0145518\pi$
$743$	43.5044	+	218.711i	0.0585523	+	0.294362i	−0.940403	+	0.340062i	$0.889552\pi$
$744$		0			0
$745$	199.885	−	299.149i	0.268302	−	0.401542i
$746$	214.860	+	88.9980i	0.288016	+	0.119300i
$747$		0			0
$748$	589.542	+	393.920i	0.788158	+	0.526631i
$749$	694.430			0.927143
$750$		0			0
$751$	−373.353	−	249.467i	−0.497142	−	0.332180i	0.281592	−	0.959534i	$-0.409138\pi$
$751$	−373.353	−	249.467i	−0.497142	−	0.332180i	−0.778734	+	0.627355i	$0.784138\pi$
$752$	555.715	+	555.715i	0.738982	+	0.738982i
$753$		0			0
$754$	−8.73143	+	5.83416i	−0.0115802	+	0.00773761i
$755$	1034.67	+	205.809i	1.37043	+	0.272595i
$756$		0			0
$757$	−17.6369	−	42.5792i	−0.0232984	−	0.0562473i	0.911802	−	0.410630i	$-0.134691\pi$
$757$	−17.6369	−	42.5792i	−0.0232984	−	0.0562473i	−0.935101	+	0.354382i	$0.884691\pi$
$758$	348.021	−	1749.62i	0.459131	−	2.30821i
$759$		0			0
$760$	−15.5376	−	78.1130i	−0.0204443	−	0.102780i
$761$	552.081	−	552.081i	0.725467	−	0.725467i	−0.244246	−	0.969713i	$-0.578540\pi$
$761$	552.081	−	552.081i	0.725467	−	0.725467i	0.969713	+	0.244246i	$0.0785404\pi$
$762$		0			0
$763$	−135.215	−	56.0079i	−0.177215	−	0.0734048i
$764$			684.604i			0.896079i
$765$		0			0
$766$	707.240			0.923289
$767$	−11.8734	+	28.6649i	−0.0154803	+	0.0373727i
$768$		0			0
$769$	−625.504	−	625.504i	−0.813400	−	0.813400i	0.171742	−	0.985142i	$-0.445060\pi$
$769$	−625.504	−	625.504i	−0.813400	−	0.813400i	−0.985142	+	0.171742i	$0.945060\pi$
$770$	−1512.17	+	300.789i	−1.96386	+	0.390635i
$771$		0			0
$772$	−1613.95	−	321.035i	−2.09061	−	0.415848i
$773$	−1123.75	+	465.474i	−1.45376	+	0.602166i	−0.963090	−	0.269181i	$-0.913247\pi$
$773$	−1123.75	+	465.474i	−1.45376	+	0.602166i	−0.490667	+	0.871347i	$0.663247\pi$
$774$		0			0
$775$	−98.8595	+	497.000i	−0.127561	+	0.641291i
$776$	−48.1751	−	72.0992i	−0.0620813	−	0.0929113i
$777$		0			0
$778$	−864.056	+	864.056i	−1.11061	+	1.11061i
$779$	−34.1316	+	51.0816i	−0.0438146	+	0.0655733i
$780$		0			0
$781$			855.757i			1.09572i
$782$	−433.098	−	86.1486i	−0.553834	−	0.110164i
$783$		0			0
$784$	48.4944	−	117.076i	0.0618551	−	0.149331i
$785$	−240.470	−	160.677i	−0.306332	−	0.204684i
$786$		0			0
$787$	−190.336	+	37.8601i	−0.241850	+	0.0481069i	−0.314527	−	0.949249i	$-0.601846\pi$
$787$	−190.336	+	37.8601i	−0.241850	+	0.0481069i	0.0726771	+	0.997356i	$0.476846\pi$
$788$	496.704	−	331.887i	0.630336	−	0.421177i
$789$		0			0
$790$	−2139.88	+	886.365i	−2.70870	+	1.12198i
$791$	−182.276	−	440.053i	−0.230437	−	0.556324i
$792$		0			0
$793$	22.8839	+	34.2481i	0.0288573	+	0.0431881i
$794$	−155.795	−	783.233i	−0.196215	−	0.986440i
$795$		0			0
$796$	−848.899	+	1270.47i	−1.06646	+	1.59606i
$797$	−118.577	−	49.1164i	−0.148780	−	0.0616266i	0.307051	−	0.951693i	$-0.400658\pi$
$797$	−118.577	−	49.1164i	−0.148780	−	0.0616266i	−0.455831	+	0.890066i	$0.650658\pi$
$798$		0			0
$799$	512.088	+	1236.29i	0.640911	+	1.54730i
$800$	−1749.75			−2.18719
$801$		0			0
$802$	602.324	+	402.460i	0.751028	+	0.501821i
$803$	348.522	+	348.522i	0.434025	+	0.434025i
$804$		0			0
$805$	449.932	−	300.635i	0.558921	−	0.373459i
$806$	−43.0638	−	8.56592i	−0.0534290	−	0.0106277i
$807$		0			0
$808$	10.3941	+	25.0936i	0.0128640	+	0.0310564i
$809$	−68.1098	+	342.411i	−0.0841902	+	0.423253i	0.915587	+	0.402121i	$0.131727\pi$
$809$	−68.1098	+	342.411i	−0.0841902	+	0.423253i	−0.999777	+	0.0211316i	$0.993273\pi$
$810$		0			0
$811$	36.2150	+	182.065i	0.0446547	+	0.224494i	0.996668	−	0.0815613i	$-0.0259906\pi$
$811$	36.2150	+	182.065i	0.0446547	+	0.224494i	−0.952014	+	0.306056i	$0.900991\pi$
$812$	−88.0762	+	88.0762i	−0.108468	+	0.108468i
$813$		0			0
$814$	−534.639	−	221.455i	−0.656804	−	0.272057i
$815$			1282.44i			1.57355i
$816$		0			0
$817$	−65.3610			−0.0800013
$818$	301.101	−	726.923i	0.368095	−	0.888659i
$819$		0			0
$820$	−640.437	−	640.437i	−0.781021	−	0.781021i
$821$	−1545.78	+	307.474i	−1.88280	+	0.374512i	−0.996130	−	0.0878920i	$-0.971987\pi$
$821$	−1545.78	+	307.474i	−1.88280	+	0.374512i	−0.886669	+	0.462404i	$0.846987\pi$
$822$		0			0
$823$	986.291	+	196.185i	1.19841	+	0.238378i	0.753653	−	0.657273i	$-0.228290\pi$
$823$	986.291	+	196.185i	1.19841	+	0.238378i	0.444757	+	0.895651i	$0.353290\pi$
$824$	−135.422	+	56.0937i	−0.164347	+	0.0680749i
$825$		0			0
$826$	−127.402	+	640.491i	−0.154239	+	0.775413i
$827$	883.014	+	1321.52i	1.06773	+	1.59797i	0.764001	+	0.645216i	$0.223232\pi$
$827$	883.014	+	1321.52i	1.06773	+	1.59797i	0.303731	+	0.952758i	$0.401768\pi$
$828$		0			0
$829$	−269.747	+	269.747i	−0.325388	+	0.325388i	−0.850830	−	0.525442i	$-0.823900\pi$
$829$	−269.747	+	269.747i	−0.325388	+	0.325388i	0.525442	+	0.850830i	$0.323900\pi$
$830$	−1604.85	+	2401.83i	−1.93355	+	2.89377i
$831$		0			0
$832$		−	106.494i		−	0.127998i
$833$	152.572	−	152.572i	0.183160	−	0.183160i
$834$		0			0
$835$	−340.259	+	821.457i	−0.407495	+	0.983781i
$836$	97.5499	+	65.1807i	0.116686	+	0.0779674i
$837$		0			0
$838$	509.365	−	101.319i	0.607834	−	0.120906i
$839$	30.7798	−	20.5664i	0.0366862	−	0.0245130i	−0.537092	−	0.843524i	$-0.680477\pi$
$839$	30.7798	−	20.5664i	0.0366862	−	0.0245130i	0.573778	+	0.819011i	$0.305477\pi$
$840$		0			0
$841$	768.273	−	318.229i	0.913523	−	0.378393i
$842$	−726.154	−	1753.09i	−0.862416	−	2.08206i
$843$		0			0
$844$	659.215	+	986.584i	0.781060	+	1.16894i
$845$	−262.732	−	1320.84i	−0.310925	−	1.56313i
$846$		0			0
$847$	−243.437	+	364.329i	−0.287411	+	0.430141i
$848$	−554.200	−	229.557i	−0.653538	−	0.270704i
$849$		0			0
$850$	−1876.74	−	777.369i	−2.20792	−	0.914552i
$851$	203.104			0.238665
$852$		0			0
$853$	−65.5718	−	43.8137i	−0.0768720	−	0.0513642i	0.516540	−	0.856263i	$-0.327220\pi$
$853$	−65.5718	−	43.8137i	−0.0768720	−	0.0513642i	−0.593412	+	0.804899i	$0.702220\pi$
$854$	613.028	+	613.028i	0.717831	+	0.717831i
$855$		0			0
$856$	259.219	−	173.204i	0.302825	−	0.202342i
$857$	653.288	+	129.947i	0.762297	+	0.151630i	0.560905	−	0.827880i	$-0.310453\pi$
$857$	653.288	+	129.947i	0.762297	+	0.151630i	0.201392	+	0.979511i	$0.435453\pi$
$858$		0			0
$859$	−530.649	−	1281.10i	−0.617752	−	1.49138i	−0.854308	−	0.519767i	$-0.826019\pi$
$859$	−530.649	−	1281.10i	−0.617752	−	1.49138i	0.236556	−	0.971618i	$-0.423981\pi$
$860$	187.987	−	945.076i	0.218590	−	1.09893i
$861$		0			0
$862$	−450.150	−	2263.06i	−0.522216	−	2.62536i
$863$	375.548	−	375.548i	0.435166	−	0.435166i	−0.455215	−	0.890381i	$-0.650438\pi$
$863$	375.548	−	375.548i	0.435166	−	0.435166i	0.890381	+	0.455215i	$0.150438\pi$
$864$		0			0
$865$	−1320.84	−	547.109i	−1.52698	−	0.632496i
$866$		−	286.613i		−	0.330962i
$867$		0			0
$868$	−520.802			−0.600002
$869$	294.467	−	710.907i	0.338858	−	0.818075i
$870$		0			0
$871$	93.6384	+	93.6384i	0.107507	+	0.107507i
$872$	−64.4428	+	12.8185i	−0.0739023	+	0.0147001i
$873$		0			0
$874$	−71.6635	−	14.2548i	−0.0819949	−	0.0163098i
$875$	843.160	−	349.249i	0.963612	−	0.399141i
$876$		0			0
$877$	−48.4908	+	243.780i	−0.0552917	+	0.277970i	−0.998534	−	0.0541366i	$-0.982759\pi$
$877$	−48.4908	+	243.780i	−0.0552917	+	0.277970i	0.943242	+	0.332107i	$0.107759\pi$
$878$	62.1940	+	93.0800i	0.0708360	+	0.106014i
$879$		0			0
$880$	457.768	−	457.768i	0.520191	−	0.520191i
$881$	81.3688	−	121.777i	0.0923595	−	0.138226i	−0.782412	−	0.622761i	$-0.786011\pi$
$881$	81.3688	−	121.777i	0.0923595	−	0.138226i	0.874772	+	0.484535i	$0.161011\pi$
$882$		0			0
$883$			322.505i			0.365237i	0.983184	+	0.182619i	$0.0584574\pi$
$883$			322.505i			0.365237i	−0.983184	+	0.182619i	$0.941543\pi$
$884$	37.9588	−	91.6407i	0.0429399	−	0.103666i
$885$		0			0
$886$	734.666	−	1773.64i	0.829194	−	2.00185i
$887$	52.2618	+	34.9202i	0.0589197	+	0.0393689i	0.584681	−	0.811263i	$-0.301220\pi$
$887$	52.2618	+	34.9202i	0.0589197	+	0.0393689i	−0.525762	+	0.850632i	$0.676220\pi$
$888$		0			0
$889$	−918.610	+	182.723i	−1.03331	+	0.205538i
$890$	−1756.51	+	1173.66i	−1.97361	+	1.31872i
$891$		0			0
$892$	1733.94	−	718.221i	1.94388	−	0.805180i
$893$	84.7337	+	204.565i	0.0948866	+	0.229077i
$894$		0			0
$895$	1124.92	+	1683.56i	1.25689	+	1.88107i
$896$	−165.574	−	832.399i	−0.184793	−	0.929016i
$897$		0			0
$898$	−743.106	+	1112.14i	−0.827513	+	1.23846i
$899$	−36.4189	−	15.0852i	−0.0405104	−	0.0167800i
$900$		0			0
$901$	−722.228	−	722.228i	−0.801585	−	0.801585i
$902$	533.932			0.591942
$903$		0			0
$904$	−177.798	−	118.801i	−0.196679	−	0.131417i
$905$	−1710.95	−	1710.95i	−1.89055	−	1.89055i
$906$		0			0
$907$	−182.765	+	122.120i	−0.201505	+	0.134641i	−0.652229	−	0.758022i	$-0.726166\pi$
$907$	−182.765	+	122.120i	−0.201505	+	0.134641i	0.450724	+	0.892663i	$0.351166\pi$
$908$	−490.970	−	97.6601i	−0.540716	−	0.107555i
$909$		0			0
$910$	82.5412	+	199.272i	0.0907046	+	0.218980i
$911$	−98.5913	+	495.652i	−0.108223	+	0.544074i	0.888192	+	0.459473i	$0.151962\pi$
$911$	−98.5913	+	495.652i	−0.108223	+	0.544074i	−0.996415	+	0.0846014i	$0.973038\pi$
$912$		0			0
$913$	−187.221	−	941.226i	−0.205062	−	1.03092i
$914$	571.150	−	571.150i	0.624890	−	0.624890i
$915$		0			0
$916$	1725.66	+	714.790i	1.88390	+	0.780338i
$917$			1345.66i			1.46746i
$918$		0			0
$919$	−930.196			−1.01218			−0.506091	−	0.862480i	$-0.668910\pi$
$919$	−930.196			−1.01218			−0.506091	+	0.862480i	$0.668910\pi$
$920$	92.9674	−	224.443i	0.101052	−	0.243960i
$921$		0			0
$922$	966.431	+	966.431i	1.04819	+	1.04819i
$923$	117.416	−	23.3556i	0.127212	−	0.0253040i
$924$		0			0
$925$	916.364	+	182.276i	0.990663	+	0.197055i
$926$	−225.922	+	93.5798i	−0.243976	+	0.101058i
$927$		0			0
$928$	26.5547	−	133.499i	0.0286150	−	0.143857i
$929$	−637.592	−	954.224i	−0.686321	−	1.02715i	−0.997058	−	0.0766557i	$-0.975576\pi$
$929$	−637.592	−	954.224i	−0.686321	−	1.02715i	0.310737	−	0.950496i	$-0.399424\pi$
$930$		0			0
$931$	25.2457	−	25.2457i	0.0271167	−	0.0271167i
$932$	−803.857	+	1203.06i	−0.862508	+	1.29083i
$933$		0			0
$934$			249.650i			0.267291i
$935$	1018.39	−	421.831i	1.08919	−	0.451156i
$936$		0			0
$937$	517.380	−	1249.07i	0.552166	−	1.33305i	−0.363682	−	0.931523i	$-0.618481\pi$
$937$	517.380	−	1249.07i	0.552166	−	1.33305i	0.915848	−	0.401524i	$-0.131519\pi$
$938$	2317.50	+	1548.51i	2.47068	+	1.65086i
$939$		0			0
$940$	−3201.58	+	636.834i	−3.40594	+	0.677483i
$941$	1529.70	−	1022.11i	1.62561	−	1.08620i	0.695743	−	0.718291i	$-0.255075\pi$
$941$	1529.70	−	1022.11i	1.62561	−	1.08620i	0.929864	−	0.367905i	$-0.119925\pi$
$942$		0			0
$943$	−173.131	+	71.7133i	−0.183596	+	0.0760480i
$944$	−104.933	−	253.331i	−0.111158	−	0.268359i
$945$		0			0
$946$	315.592	+	472.317i	0.333607	+	0.499278i
$947$	7.67691	+	38.5945i	0.00810656	+	0.0407544i	0.984627	−	0.174671i	$-0.0558862\pi$
$947$	7.67691	+	38.5945i	0.00810656	+	0.0407544i	−0.976520	+	0.215425i	$0.930886\pi$
$948$		0			0
$949$	38.3079	−	57.3319i	0.0403666	−	0.0604129i
$950$	−310.538	−	128.629i	−0.326882	−	0.135399i
$951$		0			0
$952$	91.8559	−	461.791i	0.0964873	−	0.485074i
$953$	−183.445			−0.192492			−0.0962458	−	0.995358i	$-0.530683\pi$
$953$	−183.445			−0.192492			−0.0962458	+	0.995358i	$0.530683\pi$
$954$		0			0
$955$	884.944	+	591.301i	0.926643	+	0.619163i
$956$	1199.89	+	1199.89i	1.25511	+	1.25511i
$957$		0			0
$958$	−1158.85	+	774.317i	−1.20965	+	0.808264i
$959$	−1333.58	−	265.266i	−1.39059	−	0.276606i
$960$		0			0
$961$	304.685	+	735.574i	0.317050	+	0.765426i
$962$	−15.7937	+	79.4005i	−0.0164176	+	0.0825369i
$963$		0			0
$964$	244.257	+	1227.96i	0.253378	+	1.27382i
$965$	−1808.97	+	1808.97i	−1.87458	+	1.87458i
$966$		0			0
$967$	1181.69	+	489.471i	1.22201	+	0.506175i	0.898050	−	0.439894i	$-0.144984\pi$
$967$	1181.69	+	489.471i	1.22201	+	0.506175i	0.323965	+	0.946069i	$0.394984\pi$
$968$			196.715i			0.203218i
$969$		0			0
$970$	−597.751			−0.616238
$971$	349.777	−	844.437i	0.360224	−	0.869657i	−0.635043	−	0.772477i	$-0.719018\pi$
$971$	349.777	−	844.437i	0.360224	−	0.869657i	0.995267	−	0.0971803i	$-0.0309823\pi$
$972$		0			0
$973$	997.319	+	997.319i	1.02499	+	1.02499i
$974$	1553.32	−	308.974i	1.59478	−	0.317222i
$975$		0			0
$976$	−357.029	−	71.0174i	−0.365808	−	0.0727637i
$977$	408.510	−	169.210i	0.418126	−	0.173194i	−0.163694	−	0.986511i	$-0.552341\pi$
$977$	408.510	−	169.210i	0.418126	−	0.173194i	0.581820	+	0.813318i	$0.302341\pi$
$978$		0			0
$979$	136.919	−	688.340i	0.139856	−	0.703105i
$980$	292.425	+	437.645i	0.298393	+	0.446577i
$981$		0			0
$982$	1046.98	−	1046.98i	1.06617	−	1.06617i
$983$	−369.695	+	553.287i	−0.376088	+	0.562856i	−0.970438	−	0.241351i	$-0.922410\pi$
$983$	−369.695	+	553.287i	−0.376088	+	0.562856i	0.594350	+	0.804207i	$0.297410\pi$
$984$		0			0
$985$		−	928.713i		−	0.942856i
$986$	87.7920	−	131.390i	0.0890385	−	0.133256i
$987$		0			0
$988$	6.28094	−	15.1635i	0.00635723	−	0.0153477i
$989$	−165.770	−	110.764i	−0.167614	−	0.111996i
$990$		0			0
$991$	−1534.80	+	305.291i	−1.54874	+	0.308063i	−0.894096	−	0.447876i	$-0.852181\pi$
$991$	−1534.80	+	305.291i	−1.54874	+	0.308063i	−0.654642	+	0.755939i	$0.727181\pi$
$992$	473.207	−	316.187i	0.477023	−	0.318736i
$993$		0			0
$994$	2327.96	−	964.271i	2.34201	−	0.970092i
$995$	909.048	+	2194.64i	0.913616	+	2.20566i
$996$		0			0
$997$	−855.639	−	1280.55i	−0.858213	−	1.28441i	−0.957232	−	0.289321i	$-0.906570\pi$
$997$	−855.639	−	1280.55i	−0.858213	−	1.28441i	0.0990189	−	0.995086i	$-0.468430\pi$
$998$	299.476	+	1505.57i	0.300076	+	1.50858i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.p.b.10.1		8
3.2	odd	2		17.3.e.a.10.1	✓	8
12.11	even	2		272.3.bh.c.129.1		8
15.2	even	4		425.3.t.a.299.1		8
15.8	even	4		425.3.t.c.299.1		8
15.14	odd	2		425.3.u.b.401.1		8
17.12	odd	16	inner	153.3.p.b.46.1		8
51.2	odd	8		289.3.e.d.40.1		8
51.5	even	16		289.3.e.c.131.1		8
51.8	odd	8		289.3.e.l.249.1		8
51.11	even	16		289.3.e.b.224.1		8
51.14	even	16		289.3.e.m.158.1		8
51.20	even	16		289.3.e.i.158.1		8
51.23	even	16		289.3.e.d.224.1		8
51.26	odd	8		289.3.e.k.249.1		8
51.29	even	16		17.3.e.a.12.1	yes	8
51.32	odd	8		289.3.e.b.40.1		8
51.38	odd	4		289.3.e.i.75.1		8
51.41	even	16		289.3.e.k.65.1		8
51.44	even	16		289.3.e.l.65.1		8
51.47	odd	4		289.3.e.m.75.1		8
51.50	odd	2		289.3.e.c.214.1		8
204.131	odd	16		272.3.bh.c.97.1		8
255.29	even	16		425.3.u.b.301.1		8
255.182	odd	16		425.3.t.c.199.1		8
255.233	odd	16		425.3.t.a.199.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.a.10.1	✓	8	3.2	odd	2
17.3.e.a.12.1	yes	8	51.29	even	16
153.3.p.b.10.1		8	1.1	even	1	trivial
153.3.p.b.46.1		8	17.12	odd	16	inner
272.3.bh.c.97.1		8	204.131	odd	16
272.3.bh.c.129.1		8	12.11	even	2
289.3.e.b.40.1		8	51.32	odd	8
289.3.e.b.224.1		8	51.11	even	16
289.3.e.c.131.1		8	51.5	even	16
289.3.e.c.214.1		8	51.50	odd	2
289.3.e.d.40.1		8	51.2	odd	8
289.3.e.d.224.1		8	51.23	even	16
289.3.e.i.75.1		8	51.38	odd	4
289.3.e.i.158.1		8	51.20	even	16
289.3.e.k.65.1		8	51.41	even	16
289.3.e.k.249.1		8	51.26	odd	8
289.3.e.l.65.1		8	51.44	even	16
289.3.e.l.249.1		8	51.8	odd	8
289.3.e.m.75.1		8	51.47	odd	4
289.3.e.m.158.1		8	51.14	even	16
425.3.t.a.199.1		8	255.233	odd	16
425.3.t.a.299.1		8	15.2	even	4
425.3.t.c.199.1		8	255.182	odd	16
425.3.t.c.299.1		8	15.8	even	4
425.3.u.b.301.1		8	255.29	even	16
425.3.u.b.401.1		8	15.14	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	153.p (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.15851 - 2.79690i) q^{2} +(-3.65205 - 3.65205i) q^{4} +(-7.87510 + 1.56645i) q^{5} +(-7.70353 - 1.53233i) q^{7} +(-3.25778 + 1.34942i) q^{8} +(-4.74219 + 23.8406i) q^{10} +(-4.48649 - 6.71450i) q^{11} +(-0.798835 + 0.798835i) q^{13} +(-13.2104 + 19.7707i) q^{14} -9.98414i q^{16} +(6.50562 - 15.7060i) q^{17} +(1.07647 - 2.59882i) q^{19} +(34.4811 + 23.0395i) q^{20} +(-23.9774 + 4.76941i) q^{22} +(7.13426 - 4.76696i) q^{23} +(36.4664 - 15.1049i) q^{25} +(1.30880 + 3.15972i) q^{26} +(22.5376 + 33.7298i) q^{28} +(0.599020 + 3.01148i) q^{29} +(-7.13254 + 10.6746i) q^{31} +(-40.9557 - 16.9644i) q^{32} +(-36.3911 - 36.3911i) q^{34} +63.0663 q^{35} +(19.6817 + 13.1509i) q^{37} +(-6.02153 - 6.02153i) q^{38} +(23.5416 - 15.7300i) q^{40} +(-21.4206 - 4.26082i) q^{41} +(-8.89197 - 21.4671i) q^{43} +(-8.13684 + 40.9066i) q^{44} +(-5.06757 - 25.4764i) q^{46} +(-55.6597 + 55.6597i) q^{47} +(11.7262 + 4.85715i) q^{49} -119.492i q^{50} +5.83478 q^{52} +(22.9922 - 55.5080i) q^{53} +(45.8495 + 45.8495i) q^{55} +(27.1642 - 5.40329i) q^{56} +(9.11677 + 1.81344i) q^{58} +(25.3733 - 10.5100i) q^{59} +(7.11302 - 35.7596i) q^{61} +(21.5926 + 32.3156i) q^{62} +(-66.6561 + 66.6561i) q^{64} +(5.03957 - 7.54224i) q^{65} -117.219i q^{67} +(-81.1179 + 33.6001i) q^{68} +(73.0632 - 176.390i) q^{70} +(-88.1108 - 58.8738i) q^{71} +(-59.8620 + 11.9073i) q^{73} +(59.5832 - 39.8122i) q^{74} +(-13.4223 + 5.55971i) q^{76} +(24.2730 + 58.6001i) q^{77} +(52.9382 + 79.2276i) q^{79} +(15.6397 + 78.6261i) q^{80} +(-36.7331 + 54.9749i) q^{82} +(109.791 + 45.4770i) q^{83} +(-26.6297 + 133.877i) q^{85} -70.3428 q^{86} +(23.6767 + 15.8202i) q^{88} +(61.4534 + 61.4534i) q^{89} +(7.37792 - 4.92977i) q^{91} +(-43.4639 - 8.64551i) q^{92} +(91.1920 + 220.157i) q^{94} +(-4.40634 + 22.1522i) q^{95} +(4.79748 + 24.1185i) q^{97} +(27.1699 - 27.1699i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 16 q^{5} + 8 q^{7} + 24 q^{8} + 16 q^{10} + 8 q^{11} + 16 q^{13} - 8 q^{14} + 80 q^{20} - 104 q^{22} + 56 q^{23} + 64 q^{25} - 176 q^{26} + 152 q^{28} - 48 q^{29} + 24 q^{31} - 88 q^{32}+ \cdots + 120 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 - 16 * q^5 + 8 * q^7 + 24 * q^8 + 16 * q^10 + 8 * q^11 + 16 * q^13 - 8 * q^14 + 80 * q^20 - 104 * q^22 + 56 * q^23 + 64 * q^25 - 176 * q^26 + 152 * q^28 - 48 * q^29 + 24 * q^31 - 88 * q^32 - 136 * q^34 + 160 * q^35 + 32 * q^37 + 120 * q^38 + 64 * q^40 - 48 * q^41 - 232 * q^43 - 120 * q^44 - 88 * q^46 - 192 * q^47 + 16 * q^49 - 384 * q^52 + 32 * q^53 + 224 * q^55 + 120 * q^56 + 240 * q^58 + 48 * q^59 - 160 * q^61 + 168 * q^62 - 64 * q^64 + 96 * q^65 - 272 * q^68 + 224 * q^70 - 40 * q^71 + 48 * q^73 + 160 * q^74 + 80 * q^76 + 48 * q^77 - 136 * q^79 + 240 * q^80 - 64 * q^82 + 264 * q^83 - 272 * q^85 - 832 * q^86 + 264 * q^88 - 160 * q^89 + 320 * q^91 - 24 * q^92 + 32 * q^94 - 272 * q^95 + 48 * q^97 + 120 * q^98

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