LMFDB - Embedded newform 1050.3.p.d.901.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1050,3,Mod(451,1050)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1050.451"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1050, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,12,-8,0,0,0,0,12,0,-4,-24,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.151613669376.6
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 12x^{6} + 95x^{4} - 588x^{2} + 2401 $ x^8 - 12x^6 + 95x^4 - 588*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.2
Root			$1.85439 + 1.88713i$ of defining polynomial
Character	$\chi$	$=$	1050.901
Dual form			1050.3.p.d.451.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(3.97571 - 5.76140i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.64728 - 2.85317i) q^{11} +(-3.00000 - 1.73205i) q^{12} +7.72850i q^{13} +(4.24500 + 8.94315i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(10.9280 - 6.30929i) q^{17} +(2.12132 + 3.67423i) q^{18} +(1.54304 + 0.890872i) q^{19} +(0.974040 - 12.0852i) q^{21} +4.65921 q^{22} +(-3.37819 + 5.85120i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-9.46544 - 5.46488i) q^{26} -5.19615i q^{27} +(-13.9547 - 1.12472i) q^{28} +39.2933 q^{29} +(9.46751 - 5.46607i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(-4.94184 - 2.85317i) q^{33} +17.8454i q^{34} -6.00000 q^{36} +(17.1983 - 29.7883i) q^{37} +(-2.18218 + 1.25988i) q^{38} +(6.69308 + 11.5928i) q^{39} -18.8536i q^{41} +(14.1125 + 9.73845i) q^{42} -77.4197 q^{43} +(-3.29456 + 5.70635i) q^{44} +(-4.77748 - 8.27485i) q^{46} +(-11.1602 - 6.44335i) q^{47} +6.92820i q^{48} +(-17.3875 - 45.8113i) q^{49} +(10.9280 - 18.9279i) q^{51} +(13.3862 - 7.72850i) q^{52} +(-25.8440 - 44.7631i) q^{53} +(6.36396 + 3.67423i) q^{54} +(11.2450 - 16.2957i) q^{56} +3.08607 q^{57} +(-27.7846 + 48.1243i) q^{58} +(97.7973 - 56.4633i) q^{59} +(-22.7184 - 13.1165i) q^{61} +15.4604i q^{62} +(-9.00500 - 18.9713i) q^{63} +8.00000 q^{64} +(6.98882 - 4.03500i) q^{66} +(-9.95656 - 17.2453i) q^{67} +(-21.8560 - 12.6186i) q^{68} +11.7024i q^{69} +87.4319 q^{71} +(4.24264 - 7.34847i) q^{72} +(-52.7540 + 30.4575i) q^{73} +(24.3220 + 42.1270i) q^{74} -3.56349i q^{76} +(-22.9874 - 1.85274i) q^{77} -18.9309 q^{78} +(17.7888 - 30.8112i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(23.0909 + 13.3315i) q^{82} +46.6773i q^{83} +(-21.9062 + 10.3981i) q^{84} +(54.7440 - 94.8194i) q^{86} +(58.9399 - 34.0290i) q^{87} +(-4.65921 - 8.06999i) q^{88} +(-47.4706 - 27.4072i) q^{89} +(44.5270 + 30.7263i) q^{91} +13.5128 q^{92} +(9.46751 - 16.3982i) q^{93} +(15.7829 - 9.11228i) q^{94} +(-8.48528 - 4.89898i) q^{96} -45.7447i q^{97} +(68.4020 + 11.0982i) q^{98} -9.88368 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{3} - 8 q^{4} + 12 q^{9} - 4 q^{11} - 24 q^{12} - 16 q^{14} - 16 q^{16} + 24 q^{17} + 72 q^{19} - 24 q^{22} - 60 q^{23} - 72 q^{26} - 24 q^{29} + 96 q^{31} - 12 q^{33} - 48 q^{36} + 24 q^{37}+ \cdots - 24 q^{99}+O(q^{100}) $ 8 * q + 12 * q^3 - 8 * q^4 + 12 * q^9 - 4 * q^11 - 24 * q^12 - 16 * q^14 - 16 * q^16 + 24 * q^17 + 72 * q^19 - 24 * q^22 - 60 * q^23 - 72 * q^26 - 24 * q^29 + 96 * q^31 - 12 * q^33 - 48 * q^36 + 24 * q^37 + 180 * q^38 - 12 * q^39 - 12 * q^42 + 112 * q^43 - 8 * q^44 + 32 * q^46 - 84 * q^47 - 264 * q^49 + 24 * q^51 - 24 * q^52 - 44 * q^53 + 40 * q^56 + 144 * q^57 - 104 * q^58 + 312 * q^59 - 204 * q^61 + 64 * q^64 - 36 * q^66 - 120 * q^67 - 48 * q^68 - 64 * q^71 - 84 * q^73 - 16 * q^74 - 228 * q^77 - 144 * q^78 - 144 * q^79 - 36 * q^81 + 60 * q^82 + 176 * q^86 - 36 * q^87 + 24 * q^88 - 336 * q^89 - 296 * q^91 + 240 * q^92 + 96 * q^93 + 36 * q^94 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$			2.44949i			0.408248i
$7$	3.97571	−	5.76140i	0.567958	−	0.823057i
$7$	3.97571	−	5.76140i	0.567958	−	0.823057i
$8$	2.82843			0.353553
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	−1.64728	−	2.85317i	−0.149753	−	0.259379i	0.781383	−	0.624051i	$-0.214514\pi$
$11$	−1.64728	−	2.85317i	−0.149753	−	0.259379i	−0.931136	+	0.364672i	$0.881181\pi$
$12$	−3.00000	−	1.73205i	−0.250000	−	0.144338i
$13$			7.72850i			0.594500i	0.954800	+	0.297250i	$0.0960695\pi$
$13$			7.72850i			0.594500i	−0.954800	+	0.297250i	$0.903931\pi$
$14$	4.24500	+	8.94315i	0.303214	+	0.638797i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	10.9280	−	6.30929i	0.642824	−	0.371135i	−0.142877	−	0.989740i	$-0.545635\pi$
$17$	10.9280	−	6.30929i	0.642824	−	0.371135i	0.785702	+	0.618606i	$0.212302\pi$
$18$	2.12132	+	3.67423i	0.117851	+	0.204124i
$19$	1.54304	+	0.890872i	0.0812124	+	0.0468880i	0.540056	−	0.841629i	$-0.318403\pi$
$19$	1.54304	+	0.890872i	0.0812124	+	0.0468880i	−0.458844	+	0.888517i	$0.651736\pi$
$20$		0			0
$21$	0.974040	−	12.0852i	0.0463829	−	0.575484i
$22$	4.65921			0.211782
$23$	−3.37819	+	5.85120i	−0.146878	+	0.254400i	−0.930072	−	0.367377i	$-0.880256\pi$
$23$	−3.37819	+	5.85120i	−0.146878	+	0.254400i	0.783194	+	0.621777i	$0.213589\pi$
$24$	4.24264	−	2.44949i	0.176777	−	0.102062i
$25$		0			0
$26$	−9.46544	−	5.46488i	−0.364055	−	0.210188i
$27$		−	5.19615i		−	0.192450i
$28$	−13.9547	−	1.12472i	−0.498384	−	0.0401687i
$29$	39.2933			1.35494			0.677471	−	0.735550i	$-0.263076\pi$
$29$	39.2933			1.35494			0.677471	+	0.735550i	$0.263076\pi$
$30$		0			0
$31$	9.46751	−	5.46607i	0.305404	−	0.176325i	−0.339464	−	0.940619i	$-0.610246\pi$
$31$	9.46751	−	5.46607i	0.305404	−	0.176325i	0.644868	+	0.764294i	$0.276912\pi$
$32$	−2.82843	−	4.89898i	−0.0883883	−	0.153093i
$33$	−4.94184	−	2.85317i	−0.149753	−	0.0864598i
$34$			17.8454i			0.524864i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	17.1983	−	29.7883i	0.464818	−	0.805089i	−0.534375	−	0.845248i	$-0.679453\pi$
$37$	17.1983	−	29.7883i	0.464818	−	0.805089i	0.999193	+	0.0401585i	$0.0127863\pi$
$38$	−2.18218	+	1.25988i	−0.0574258	+	0.0331548i
$39$	6.69308	+	11.5928i	0.171617	+	0.297250i
$40$		0			0
$41$		−	18.8536i		−	0.459844i	−0.973209	−	0.229922i	$-0.926153\pi$
$41$		−	18.8536i		−	0.459844i	0.973209	−	0.229922i	$-0.0738472\pi$
$42$	14.1125	+	9.73845i	0.336012	+	0.231868i
$43$	−77.4197			−1.80046			−0.900229	−	0.435416i	$-0.856601\pi$
$43$	−77.4197			−1.80046			−0.900229	+	0.435416i	$0.856601\pi$
$44$	−3.29456	+	5.70635i	−0.0748764	+	0.129690i
$45$		0			0
$46$	−4.77748	−	8.27485i	−0.103858	−	0.179888i
$47$	−11.1602	−	6.44335i	−0.237451	−	0.137093i	0.376553	−	0.926395i	$-0.377109\pi$
$47$	−11.1602	−	6.44335i	−0.237451	−	0.137093i	−0.614005	+	0.789302i	$0.710442\pi$
$48$			6.92820i			0.144338i
$49$	−17.3875	−	45.8113i	−0.354847	−	0.934924i
$50$		0			0
$51$	10.9280	−	18.9279i	0.214275	−	0.371135i
$52$	13.3862	−	7.72850i	0.257426	−	0.148625i
$53$	−25.8440	−	44.7631i	−0.487622	−	0.844586i	0.512276	−	0.858821i	$-0.328802\pi$
$53$	−25.8440	−	44.7631i	−0.487622	−	0.844586i	−0.999899	+	0.0142341i	$0.995469\pi$
$54$	6.36396	+	3.67423i	0.117851	+	0.0680414i
$55$		0			0
$56$	11.2450	−	16.2957i	0.200804	−	0.290995i
$57$	3.08607			0.0541416
$58$	−27.7846	+	48.1243i	−0.479044	+	0.829729i
$59$	97.7973	−	56.4633i	1.65758	−	0.957005i	0.683754	−	0.729713i	$-0.260346\pi$
$59$	97.7973	−	56.4633i	1.65758	−	0.957005i	0.973827	−	0.227292i	$-0.0729872\pi$
$60$		0			0
$61$	−22.7184	−	13.1165i	−0.372432	−	0.215024i	0.302088	−	0.953280i	$-0.402316\pi$
$61$	−22.7184	−	13.1165i	−0.372432	−	0.215024i	−0.674521	+	0.738256i	$0.735650\pi$
$62$			15.4604i			0.249361i
$63$	−9.00500	−	18.9713i	−0.142937	−	0.301132i
$64$	8.00000			0.125000
$65$		0			0
$66$	6.98882	−	4.03500i	0.105891	−	0.0611363i
$67$	−9.95656	−	17.2453i	−0.148605	−	0.257392i	0.782107	−	0.623144i	$-0.214145\pi$
$67$	−9.95656	−	17.2453i	−0.148605	−	0.257392i	−0.930712	+	0.365752i	$0.880812\pi$
$68$	−21.8560	−	12.6186i	−0.321412	−	0.185567i
$69$			11.7024i			0.169600i
$70$		0			0
$71$	87.4319			1.23144			0.615718	−	0.787967i	$-0.288866\pi$
$71$	87.4319			1.23144			0.615718	+	0.787967i	$0.288866\pi$
$72$	4.24264	−	7.34847i	0.0589256	−	0.102062i
$73$	−52.7540	+	30.4575i	−0.722657	+	0.417226i	−0.815730	−	0.578433i	$-0.803664\pi$
$73$	−52.7540	+	30.4575i	−0.722657	+	0.417226i	0.0930727	+	0.995659i	$0.470331\pi$
$74$	24.3220	+	42.1270i	0.328676	+	0.569284i
$75$		0			0
$76$		−	3.56349i		−	0.0468880i
$77$	−22.9874	−	1.85274i	−0.298537	−	0.0240615i
$78$	−18.9309			−0.242704
$79$	17.7888	−	30.8112i	0.225175	−	0.390015i	−0.731197	−	0.682167i	$-0.761038\pi$
$79$	17.7888	−	30.8112i	0.225175	−	0.390015i	0.956372	+	0.292152i	$0.0943712\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	23.0909	+	13.3315i	0.281596	+	0.162580i
$83$			46.6773i			0.562377i	0.959653	+	0.281188i	$0.0907286\pi$
$83$			46.6773i			0.562377i	−0.959653	+	0.281188i	$0.909271\pi$
$84$	−21.9062	+	10.3981i	−0.260788	+	0.123787i
$85$		0			0
$86$	54.7440	−	94.8194i	0.636558	−	1.10255i
$87$	58.9399	−	34.0290i	0.677471	−	0.391138i
$88$	−4.65921	−	8.06999i	−0.0529456	−	0.0917044i
$89$	−47.4706	−	27.4072i	−0.533378	−	0.307946i	0.209013	−	0.977913i	$-0.432975\pi$
$89$	−47.4706	−	27.4072i	−0.533378	−	0.307946i	−0.742391	+	0.669967i	$0.766308\pi$
$90$		0			0
$91$	44.5270	+	30.7263i	0.489308	+	0.337651i
$92$	13.5128			0.146878
$93$	9.46751	−	16.3982i	0.101801	−	0.176325i
$94$	15.7829	−	9.11228i	0.167903	−	0.0969391i
$95$		0			0
$96$	−8.48528	−	4.89898i	−0.0883883	−	0.0510310i
$97$		−	45.7447i		−	0.471595i	−0.971802	−	0.235798i	$-0.924230\pi$
$97$		−	45.7447i		−	0.471595i	0.971802	−	0.235798i	$-0.0757703\pi$
$98$	68.4020	+	11.0982i	0.697979	+	0.113247i
$99$	−9.88368			−0.0998352
$100$		0			0
$101$	79.2589	−	45.7601i	0.784741	−	0.453071i	−0.0533667	−	0.998575i	$-0.516995\pi$
$101$	79.2589	−	45.7601i	0.784741	−	0.453071i	0.838108	+	0.545504i	$0.183662\pi$
$102$	15.4545	+	26.7681i	0.151515	+	0.262432i
$103$	43.7414	+	25.2541i	0.424674	+	0.245186i	0.697075	−	0.716998i	$-0.254484\pi$
$103$	43.7414	+	25.2541i	0.424674	+	0.245186i	−0.272401	+	0.962184i	$0.587818\pi$
$104$			21.8595i			0.210188i
$105$		0			0
$106$	73.0978			0.689602
$107$	46.9747	−	81.3626i	0.439016	−	0.760398i	−0.558598	−	0.829439i	$-0.688660\pi$
$107$	46.9747	−	81.3626i	0.439016	−	0.760398i	0.997614	+	0.0690404i	$0.0219938\pi$
$108$	−9.00000	+	5.19615i	−0.0833333	+	0.0481125i
$109$	−60.3052	−	104.452i	−0.553258	−	0.958272i	−0.998037	−	0.0626310i	$-0.980051\pi$
$109$	−60.3052	−	104.452i	−0.553258	−	0.958272i	0.444778	−	0.895641i	$-0.353282\pi$
$110$		0			0
$111$		−	59.5766i		−	0.536726i
$112$	12.0067	+	25.2951i	0.107202	+	0.225849i
$113$	10.7318			0.0949713			0.0474856	−	0.998872i	$-0.484879\pi$
$113$	10.7318			0.0949713			0.0474856	+	0.998872i	$0.484879\pi$
$114$	−2.18218	+	3.77965i	−0.0191419	+	0.0331548i
$115$		0			0
$116$	−39.2933	−	68.0580i	−0.338735	−	0.586707i
$117$	20.0792	+	11.5928i	0.171617	+	0.0990834i
$118$			159.702i			1.35341i
$119$	7.09622	−	88.0446i	0.0596321	−	0.739870i
$120$		0			0
$121$	55.0729	−	95.3891i	0.455148	−	0.788340i
$122$	32.1286	−	18.5495i	0.263349	−	0.152045i
$123$	−16.3277	−	28.2804i	−0.132746	−	0.229922i
$124$	−18.9350	−	10.9321i	−0.152702	−	0.0881624i
$125$		0			0
$126$	29.6025	+	2.38590i	0.234940	+	0.0189357i
$127$	−117.281			−0.923476			−0.461738	−	0.887016i	$-0.652774\pi$
$127$	−117.281			−0.923476			−0.461738	+	0.887016i	$0.652774\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$	−116.130	+	67.0475i	−0.900229	+	0.519748i
$130$		0			0
$131$	80.2758	+	46.3473i	0.612792	+	0.353796i	0.774058	−	0.633115i	$-0.218224\pi$
$131$	80.2758	+	46.3473i	0.612792	+	0.353796i	−0.161265	+	0.986911i	$0.551557\pi$
$132$			11.4127i			0.0864598i
$133$	11.2673	−	5.34820i	0.0847168	−	0.0402120i
$134$	28.1614			0.210160
$135$		0			0
$136$	30.9091	−	17.8454i	0.227273	−	0.131216i
$137$	−13.7370	−	23.7932i	−0.100270	−	0.173673i	0.811526	−	0.584317i	$-0.198637\pi$
$137$	−13.7370	−	23.7932i	−0.100270	−	0.173673i	−0.911796	+	0.410644i	$0.865304\pi$
$138$	−14.3325	−	8.27485i	−0.103858	−	0.0599626i
$139$		−	67.0127i		−	0.482106i	−0.970512	−	0.241053i	$-0.922507\pi$
$139$		−	67.0127i		−	0.482106i	0.970512	−	0.241053i	$-0.0774928\pi$
$140$		0			0
$141$	−22.3204			−0.158301
$142$	−61.8237	+	107.082i	−0.435378	+	0.754097i
$143$	22.0507	−	12.7310i	0.154201	−	0.0890280i
$144$	6.00000	+	10.3923i	0.0416667	+	0.0721688i
$145$		0			0
$146$		−	86.1469i		−	0.590047i
$147$	−65.7550	−	53.6589i	−0.447313	−	0.365027i
$148$	−68.7931			−0.464818
$149$	−25.5567	+	44.2656i	−0.171522	+	0.297084i	−0.938952	−	0.344048i	$-0.888202\pi$
$149$	−25.5567	+	44.2656i	−0.171522	+	0.297084i	0.767430	+	0.641132i	$0.221535\pi$
$150$		0			0
$151$	82.6090	+	143.083i	0.547079	+	0.947569i	0.998473	+	0.0552442i	$0.0175937\pi$
$151$	82.6090	+	143.083i	0.547079	+	0.947569i	−0.451394	+	0.892325i	$0.649073\pi$
$152$	4.36436	+	2.51977i	0.0287129	+	0.0165774i
$153$		−	37.8558i		−	0.247423i
$154$	18.5237	−	26.8436i	0.120284	−	0.174309i
$155$		0			0
$156$	13.3862	−	23.1855i	0.0858087	−	0.148625i
$157$	165.248	−	95.4059i	1.05253	−	0.607681i	0.129176	−	0.991622i	$-0.458767\pi$
$157$	165.248	−	95.4059i	1.05253	−	0.607681i	0.923358	+	0.383941i	$0.125433\pi$
$158$	25.1572	+	43.5736i	0.159223	+	0.275782i
$159$	−77.5319	−	44.7631i	−0.487622	−	0.281529i
$160$		0			0
$161$	20.2804	+	42.7258i	0.125965	+	0.265377i
$162$	12.7279			0.0785674
$163$	−124.101	+	214.949i	−0.761356	+	1.31871i	0.180796	+	0.983521i	$0.442133\pi$
$163$	−124.101	+	214.949i	−0.761356	+	1.31871i	−0.942152	+	0.335186i	$0.891201\pi$
$164$	−32.6554	+	18.8536i	−0.199118	+	0.114961i
$165$		0			0
$166$	−57.1678	−	33.0058i	−0.344384	−	0.198830i
$167$		−	29.2974i		−	0.175433i	−0.996145	−	0.0877167i	$-0.972043\pi$
$167$		−	29.2974i		−	0.175433i	0.996145	−	0.0877167i	$-0.0279570\pi$
$168$	2.75500	−	34.1820i	0.0163988	−	0.203464i
$169$	109.270			0.646570
$170$		0			0
$171$	4.62911	−	2.67262i	0.0270708	−	0.0156293i
$172$	77.4197	+	134.095i	0.450115	+	0.779622i
$173$	−19.9982	−	11.5460i	−0.115597	−	0.0667397i	0.441087	−	0.897464i	$-0.354593\pi$
$173$	−19.9982	−	11.5460i	−0.115597	−	0.0667397i	−0.556683	+	0.830725i	$0.687926\pi$
$174$			96.2485i			0.553152i
$175$		0			0
$176$	13.1782			0.0748764
$177$	97.7973	−	169.390i	0.552527	−	0.957005i
$178$	67.1336	−	38.7596i	0.377155	−	0.217751i
$179$	104.717	+	181.376i	0.585014	+	1.01327i	0.994874	+	0.101125i	$0.0322442\pi$
$179$	104.717	+	181.376i	0.585014	+	1.01327i	−0.409860	+	0.912148i	$0.634423\pi$
$180$		0			0
$181$			243.667i			1.34622i	0.739540	+	0.673112i	$0.235043\pi$
$181$			243.667i			1.34622i	−0.739540	+	0.673112i	$0.764957\pi$
$182$	−69.1172	+	32.8075i	−0.379765	+	0.180261i
$183$	−45.4367			−0.248288
$184$	−9.55497	+	16.5497i	−0.0519292	+	0.0899440i
$185$		0			0
$186$	13.3891	+	23.1906i	0.0719843	+	0.124681i
$187$	−36.0030	−	20.7863i	−0.192529	−	0.111157i
$188$			25.7734i			0.137093i
$189$	−29.9371	−	20.6584i	−0.158397	−	0.109304i
$190$		0			0
$191$	118.423	−	205.114i	0.620014	−	1.07390i	−0.369468	−	0.929243i	$-0.620460\pi$
$191$	118.423	−	205.114i	0.620014	−	1.07390i	0.989483	−	0.144653i	$-0.0462064\pi$
$192$	12.0000	−	6.92820i	0.0625000	−	0.0360844i
$193$	66.4460	+	115.088i	0.344280	+	0.596310i	0.985223	−	0.171278i	$-0.0547897\pi$
$193$	66.4460	+	115.088i	0.344280	+	0.596310i	−0.640943	+	0.767589i	$0.721456\pi$
$194$	56.0256	+	32.3464i	0.288792	+	0.166734i
$195$		0			0
$196$	−61.9600	+	75.9273i	−0.316122	+	0.387384i
$197$	−105.779			−0.536950			−0.268475	−	0.963287i	$-0.586520\pi$
$197$	−105.779			−0.536950			−0.268475	+	0.963287i	$0.586520\pi$
$198$	6.98882	−	12.1050i	0.0352971	−	0.0611363i
$199$	174.541	−	100.771i	0.877091	−	0.506389i	0.00739279	−	0.999973i	$-0.497647\pi$
$199$	174.541	−	100.771i	0.877091	−	0.506389i	0.869698	+	0.493584i	$0.164313\pi$
$200$		0			0
$201$	−29.8697	−	17.2453i	−0.148605	−	0.0857973i
$202$			129.429i			0.640739i
$203$	156.219	−	226.384i	0.769550	−	1.11519i
$204$	−43.7121			−0.214275
$205$		0			0
$206$	−61.8597	+	35.7147i	−0.300290	+	0.173372i
$207$	10.1346	+	17.5536i	0.0489593	+	0.0848000i
$208$	−26.7723	−	15.4570i	−0.128713	−	0.0743125i
$209$		−	5.87006i		−	0.0280864i
$210$		0			0
$211$	29.6045			0.140306			0.0701528	−	0.997536i	$-0.477651\pi$
$211$	29.6045			0.140306			0.0701528	+	0.997536i	$0.477651\pi$
$212$	−51.6880	+	89.5262i	−0.243811	+	0.422293i
$213$	131.148	−	75.7183i	0.615718	−	0.355485i
$214$	66.4323	+	115.064i	0.310431	+	0.537683i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	6.14783	−	76.2777i	0.0283310	−	0.351510i
$218$	170.569			0.782426
$219$	−52.7540	+	91.3726i	−0.240886	+	0.417226i
$220$		0			0
$221$	48.7614	+	84.4572i	0.220640	+	0.382159i
$222$	72.9661	+	42.1270i	0.328676	+	0.189761i
$223$			328.532i			1.47324i	0.676307	+	0.736620i	$0.263579\pi$
$223$			328.532i			1.47324i	−0.676307	+	0.736620i	$0.736421\pi$
$224$	−39.4700	−	3.18120i	−0.176205	−	0.0142018i
$225$		0			0
$226$	−7.58850	+	13.1437i	−0.0335774	+	0.0581578i
$227$	315.628	−	182.228i	1.39043	−	0.802766i	0.397069	−	0.917789i	$-0.370028\pi$
$227$	315.628	−	182.228i	1.39043	−	0.802766i	0.993363	+	0.115023i	$0.0366942\pi$
$228$	−3.08607	−	5.34523i	−0.0135354	−	0.0234440i
$229$	−260.716	−	150.525i	−1.13850	−	0.657313i	−0.192441	−	0.981309i	$-0.561640\pi$
$229$	−260.716	−	150.525i	−1.13850	−	0.657313i	−0.946059	+	0.323996i	$0.894974\pi$
$230$		0			0
$231$	−36.0856	+	17.1285i	−0.156215	+	0.0741496i
$232$	111.138			0.479044
$233$	141.013	−	244.241i	0.605204	−	1.04824i	−0.386815	−	0.922157i	$-0.626425\pi$
$233$	141.013	−	244.241i	0.605204	−	1.04824i	0.992019	−	0.126087i	$-0.0402418\pi$
$234$	−28.3963	+	16.3946i	−0.121352	+	0.0700625i
$235$		0			0
$236$	−195.595	−	112.927i	−0.828790	−	0.478502i
$237$		−	61.6224i		−	0.260010i
$238$	102.814	+	70.9480i	0.431993	+	0.298101i
$239$	83.0347			0.347425			0.173713	−	0.984796i	$-0.444424\pi$
$239$	83.0347			0.347425			0.173713	+	0.984796i	$0.444424\pi$
$240$		0			0
$241$	−287.369	+	165.912i	−1.19240	+	0.688433i	−0.958851	−	0.283911i	$-0.908368\pi$
$241$	−287.369	+	165.912i	−1.19240	+	0.688433i	−0.233551	+	0.972345i	$0.575035\pi$
$242$	77.8849	+	134.901i	0.321838	+	0.557440i
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$			52.4658i			0.215024i
$245$		0			0
$246$	46.1817			0.187731
$247$	−6.88511	+	11.9254i	−0.0278749	+	0.0482808i
$248$	26.7782	−	15.4604i	0.107977	−	0.0623403i
$249$	40.4237	+	70.0159i	0.162344	+	0.281188i
$250$		0			0
$251$			419.075i			1.66962i	0.550537	+	0.834811i	$0.314423\pi$
$251$			419.075i			1.66962i	−0.550537	+	0.834811i	$0.685577\pi$
$252$	−23.8542	+	34.5684i	−0.0946597	+	0.137176i
$253$	22.2593			0.0879815
$254$	82.9305	−	143.640i	0.326498	−	0.565511i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−289.215	−	166.979i	−1.12535	−	0.649722i	−0.182590	−	0.983189i	$-0.558448\pi$
$257$	−289.215	−	166.979i	−1.12535	−	0.649722i	−0.942762	+	0.333467i	$0.891781\pi$
$258$		−	189.639i		−	0.735034i
$259$	−103.247	−	217.516i	−0.398637	−	0.839829i
$260$		0			0
$261$	58.9399	−	102.087i	0.225824	−	0.391138i
$262$	−113.527	+	65.5449i	−0.433310	+	0.250171i
$263$	−102.188	−	176.995i	−0.388549	−	0.672986i	0.603706	−	0.797207i	$-0.293690\pi$
$263$	−102.188	−	176.995i	−0.388549	−	0.672986i	−0.992255	+	0.124221i	$0.960357\pi$
$264$	−13.9776	−	8.06999i	−0.0529456	−	0.0305681i
$265$		0			0
$266$	−1.41702	+	17.5814i	−0.00532715	+	0.0660953i
$267$	−94.9412			−0.355585
$268$	−19.9131	+	34.4905i	−0.0743027	+	0.128696i
$269$	−120.768	+	69.7257i	−0.448953	+	0.259203i	−0.707388	−	0.706825i	$-0.750127\pi$
$269$	−120.768	+	69.7257i	−0.448953	+	0.259203i	0.258435	+	0.966029i	$0.416793\pi$
$270$		0			0
$271$	−323.213	−	186.607i	−1.19267	−	0.688586i	−0.233756	−	0.972295i	$-0.575102\pi$
$271$	−323.213	−	186.607i	−1.19267	−	0.688586i	−0.958910	+	0.283709i	$0.908435\pi$
$272$			50.4743i			0.185567i
$273$	93.4002	+	7.52787i	0.342125	+	0.0275746i
$274$	38.8542			0.141804
$275$		0			0
$276$	20.2691	−	11.7024i	0.0734389	−	0.0424000i
$277$	248.752	+	430.851i	0.898022	+	1.55542i	0.830019	+	0.557735i	$0.188329\pi$
$277$	248.752	+	430.851i	0.898022	+	1.55542i	0.0680029	+	0.997685i	$0.478337\pi$
$278$	82.0735	+	47.3852i	0.295228	+	0.170450i
$279$		−	32.7964i		−	0.117550i
$280$		0			0
$281$	292.779			1.04192			0.520959	−	0.853582i	$-0.325574\pi$
$281$	292.779			1.04192			0.520959	+	0.853582i	$0.325574\pi$
$282$	15.7829	−	27.3368i	0.0559678	−	0.0969391i
$283$	−239.686	+	138.383i	−0.846949	+	0.488986i	−0.859620	−	0.510934i	$-0.829300\pi$
$283$	−239.686	+	138.383i	−0.846949	+	0.488986i	0.0126714	+	0.999920i	$0.495966\pi$
$284$	−87.4319	−	151.437i	−0.307859	−	0.533227i
$285$		0			0
$286$			36.0087i			0.125905i
$287$	−108.623	−	74.9565i	−0.378478	−	0.261172i
$288$	−16.9706			−0.0589256
$289$	−64.8857	+	112.385i	−0.224518	+	0.388876i
$290$		0			0
$291$	−39.6161	−	68.6171i	−0.136138	−	0.235798i
$292$	105.508	+	60.9150i	0.361329	+	0.208613i
$293$		−	375.299i		−	1.28088i	−0.768006	−	0.640442i	$-0.778751\pi$
$293$		−	375.299i		−	1.28088i	0.768006	−	0.640442i	$-0.221249\pi$
$294$	112.214	−	42.5905i	0.381681	−	0.144866i
$295$		0			0
$296$	48.6441	−	84.2540i	0.164338	−	0.284642i
$297$	−14.8255	+	8.55952i	−0.0499176	+	0.0288199i
$298$	−36.1427	−	62.6009i	−0.121284	−	0.210070i
$299$	−45.2210	−	26.1084i	−0.151241	−	0.0873189i
$300$		0			0
$301$	−307.798	+	446.046i	−1.02259	+	1.48188i
$302$	−233.653			−0.773687
$303$	79.2589	−	137.280i	0.261580	−	0.453071i
$304$	−6.17214	+	3.56349i	−0.0203031	+	0.0117220i
$305$		0			0
$306$	46.3636	+	26.7681i	0.151515	+	0.0874773i
$307$			107.784i			0.351088i	0.984472	+	0.175544i	$0.0561684\pi$
$307$			107.784i			0.351088i	−0.984472	+	0.175544i	$0.943832\pi$
$308$	19.7783	+	41.6680i	0.0642154	+	0.135286i
$309$	87.4828			0.283116
$310$		0			0
$311$	−499.771	+	288.543i	−1.60698	+	0.927791i	−0.616940	+	0.787010i	$0.711628\pi$
$311$	−499.771	+	288.543i	−1.60698	+	0.927791i	−0.990041	+	0.140780i	$0.955039\pi$
$312$	18.9309	+	32.7893i	0.0606759	+	0.105094i
$313$	344.050	+	198.637i	1.09920	+	0.634624i	0.936011	−	0.351971i	$-0.114488\pi$
$313$	344.050	+	198.637i	1.09920	+	0.634624i	0.163190	+	0.986595i	$0.447822\pi$
$314$			269.849i			0.859390i
$315$		0			0
$316$	−71.1554			−0.225175
$317$	−40.1851	+	69.6026i	−0.126767	+	0.219566i	−0.922422	−	0.386183i	$-0.873793\pi$
$317$	−40.1851	+	69.6026i	−0.126767	+	0.219566i	0.795655	+	0.605749i	$0.207127\pi$
$318$	109.647	−	63.3046i	0.344801	−	0.199071i
$319$	−64.7271	−	112.111i	−0.202906	−	0.351444i
$320$		0			0
$321$		−	162.725i		−	0.506932i
$322$	−66.6686	−	5.37336i	−0.207045	−	0.0166874i
$323$	22.4831			0.0696071
$324$	−9.00000	+	15.5885i	−0.0277778	+	0.0481125i
$325$		0			0
$326$	−175.505	−	303.984i	−0.538360	−	0.932467i
$327$	−180.915	−	104.452i	−0.553258	−	0.319424i
$328$		−	53.3261i		−	0.162580i
$329$	−81.4925	+	38.6816i	−0.247698	+	0.117573i
$330$		0			0
$331$	−246.021	+	426.121i	−0.743266	+	1.28737i	0.207734	+	0.978185i	$0.433391\pi$
$331$	−246.021	+	426.121i	−0.743266	+	1.28737i	−0.951000	+	0.309189i	$0.899942\pi$
$332$	80.8474	−	46.6773i	0.243516	−	0.140594i
$333$	−51.5948	−	89.3649i	−0.154939	−	0.268363i
$334$	35.8818	+	20.7164i	0.107431	+	0.0620251i
$335$		0			0
$336$	39.9162	+	27.5445i	0.118798	+	0.0819777i
$337$	−630.123			−1.86980			−0.934901	−	0.354910i	$-0.884512\pi$
$337$	−630.123			−1.86980			−0.934901	+	0.354910i	$0.884512\pi$
$338$	−77.2657	+	133.828i	−0.228597	+	0.395941i
$339$	16.0976	−	9.29397i	0.0474856	−	0.0274159i
$340$		0			0
$341$	−31.1913	−	18.0083i	−0.0914701	−	0.0528103i
$342$			7.55930i			0.0221032i
$343$	−333.065	−	81.9559i	−0.971035	−	0.238938i
$344$	−218.976			−0.636558
$345$		0			0
$346$	28.2817	−	16.3285i	0.0817391	−	0.0471921i
$347$	215.071	+	372.514i	0.619802	+	1.07353i	0.989522	+	0.144385i	$0.0461203\pi$
$347$	215.071	+	372.514i	0.619802	+	1.07353i	−0.369720	+	0.929143i	$0.620546\pi$
$348$	−117.880	−	68.0580i	−0.338735	−	0.195569i
$349$			95.1819i			0.272727i	0.990659	+	0.136364i	$0.0435416\pi$
$349$			95.1819i			0.272727i	−0.990659	+	0.136364i	$0.956458\pi$
$350$		0			0
$351$	40.1585			0.114412
$352$	−9.31842	+	16.1400i	−0.0264728	+	0.0458522i
$353$	227.710	−	131.469i	0.645071	−	0.372432i	−0.141494	−	0.989939i	$-0.545191\pi$
$353$	227.710	−	131.469i	0.645071	−	0.372432i	0.786565	+	0.617507i	$0.211857\pi$
$354$	138.306	+	239.553i	0.390696	+	0.676704i
$355$		0			0
$356$			109.629i			0.307946i
$357$	−65.6045	−	138.212i	−0.183766	−	0.387150i
$358$	−296.186			−0.827334
$359$	−149.386	+	258.743i	−0.416116	+	0.720734i	−0.995545	−	0.0942890i	$-0.969942\pi$
$359$	−149.386	+	258.743i	−0.416116	+	0.720734i	0.579429	+	0.815023i	$0.303276\pi$
$360$		0			0
$361$	−178.913	−	309.886i	−0.495603	−	0.858410i
$362$	−298.429	−	172.298i	−0.824391	−	0.475962i
$363$		−	190.778i		−	0.525560i
$364$	8.69244	−	107.849i	0.0238803	−	0.296289i
$365$		0			0
$366$	32.1286	−	55.6484i	0.0877831	−	0.152045i
$367$	−114.381	+	66.0380i	−0.311665	+	0.179940i	−0.647671	−	0.761920i	$-0.724257\pi$
$367$	−114.381	+	66.0380i	−0.311665	+	0.179940i	0.336006	+	0.941860i	$0.390924\pi$
$368$	−13.5128	−	23.4048i	−0.0367195	−	0.0636000i
$369$	−48.9831	−	28.2804i	−0.132746	−	0.0766407i
$370$		0			0
$371$	−360.646	−	29.0674i	−0.972092	−	0.0783487i
$372$	−37.8701			−0.101801
$373$	−5.34394	+	9.25597i	−0.0143269	+	0.0248149i	−0.873100	−	0.487541i	$-0.837894\pi$
$373$	−5.34394	+	9.25597i	−0.0143269	+	0.0248149i	0.858773	+	0.512356i	$0.171227\pi$
$374$	50.9159	−	29.3963i	0.136139	−	0.0785998i
$375$		0			0
$376$	−31.5659	−	18.2246i	−0.0839517	−	0.0484696i
$377$			303.678i			0.805513i
$378$	46.4700	−	22.0577i	0.122936	−	0.0583536i
$379$	142.918			0.377092			0.188546	−	0.982064i	$-0.439622\pi$
$379$	142.918			0.377092			0.188546	+	0.982064i	$0.439622\pi$
$380$		0			0
$381$	−175.922	+	101.569i	−0.461738	+	0.266585i
$382$	167.475	+	290.075i	0.438416	+	0.759359i
$383$	−534.349	−	308.507i	−1.39517	−	0.805500i	−0.401286	−	0.915953i	$-0.631437\pi$
$383$	−534.349	−	308.507i	−1.39517	−	0.805500i	−0.993881	+	0.110452i	$0.964770\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	−187.938			−0.486885
$387$	−116.130	+	201.142i	−0.300076	+	0.519748i
$388$	−79.2322	+	45.7447i	−0.204207	+	0.117899i
$389$	346.969	+	600.968i	0.891951	+	1.54490i	0.837534	+	0.546386i	$0.183997\pi$
$389$	346.969	+	600.968i	0.891951	+	1.54490i	0.0544171	+	0.998518i	$0.482670\pi$
$390$		0			0
$391$			85.2560i			0.218046i
$392$	−49.1793	−	129.574i	−0.125457	−	0.330546i
$393$	160.552			0.408528
$394$	74.7972	−	129.553i	0.189841	−	0.328814i
$395$		0			0
$396$	9.88368	+	17.1190i	0.0249588	+	0.0432299i
$397$	−484.587	−	279.776i	−1.22062	−	0.704726i	−0.255571	−	0.966790i	$-0.582263\pi$
$397$	−484.587	−	279.776i	−1.22062	−	0.704726i	−0.965050	+	0.262065i	$0.915597\pi$
$398$			285.024i			0.716142i
$399$	12.2693	−	17.7801i	0.0307502	−	0.0445616i
$400$		0			0
$401$	80.6033	−	139.609i	0.201006	−	0.348152i	−0.747847	−	0.663871i	$-0.768912\pi$
$401$	80.6033	−	139.609i	0.201006	−	0.348152i	0.948853	+	0.315719i	$0.102246\pi$
$402$	42.2421	−	24.3885i	0.105080	−	0.0606679i
$403$	42.2445	+	73.1697i	0.104825	+	0.181563i
$404$	−158.518	−	91.5203i	−0.392371	−	0.226535i
$405$		0			0
$406$	166.800	+	351.406i	0.410837	+	0.865532i
$407$	−113.322			−0.278431
$408$	30.9091	−	53.5361i	0.0757576	−	0.131216i
$409$	398.217	−	229.911i	0.973637	−	0.562129i	0.0732937	−	0.997310i	$-0.476649\pi$
$409$	398.217	−	229.911i	0.973637	−	0.562129i	0.900343	+	0.435181i	$0.143316\pi$
$410$		0			0
$411$	−41.2111	−	23.7932i	−0.100270	−	0.0578911i
$412$		−	101.016i		−	0.245186i
$413$	63.5056	−	787.931i	0.153767	−	1.90782i
$414$	−28.6649			−0.0692389
$415$		0			0
$416$	37.8618	−	21.8595i	0.0910139	−	0.0525469i
$417$	−58.0347	−	100.519i	−0.139172	−	0.241053i
$418$	7.18933	+	4.15076i	0.0171994	+	0.00993005i
$419$		−	93.5818i		−	0.223346i	−0.993745	−	0.111673i	$-0.964379\pi$
$419$		−	93.5818i		−	0.223346i	0.993745	−	0.111673i	$-0.0356208\pi$
$420$		0			0
$421$	162.957			0.387072			0.193536	−	0.981093i	$-0.438004\pi$
$421$	162.957			0.387072			0.193536	+	0.981093i	$0.438004\pi$
$422$	−20.9335	+	36.2579i	−0.0496055	+	0.0859193i
$423$	−33.4806	+	19.3301i	−0.0791504	+	0.0456975i
$424$	−73.0978	−	126.609i	−0.172400	−	0.298606i
$425$		0			0
$426$			214.164i			0.502731i
$427$	−165.891	+	78.7425i	−0.388503	+	0.184409i
$428$	−187.899			−0.439016
$429$	22.0507	−	38.1930i	0.0514003	−	0.0890280i
$430$		0			0
$431$	165.543	+	286.728i	0.384090	+	0.665263i	0.991642	−	0.129016i	$-0.0411820\pi$
$431$	165.543	+	286.728i	0.384090	+	0.665263i	−0.607553	+	0.794279i	$0.707849\pi$
$432$	18.0000	+	10.3923i	0.0416667	+	0.0240563i
$433$			88.4130i			0.204187i	0.994775	+	0.102094i	$0.0325541\pi$
$433$			88.4130i			0.204187i	−0.994775	+	0.102094i	$0.967446\pi$
$434$	89.0735	+	61.4660i	0.205238	+	0.141627i
$435$		0			0
$436$	−120.610	+	208.903i	−0.276629	+	0.479136i
$437$	−10.4253	+	6.01907i	−0.0238566	+	0.0137736i
$438$	−74.6054	−	129.220i	−0.170332	−	0.295024i
$439$	−60.4608	−	34.9070i	−0.137724	−	0.0795149i	0.429555	−	0.903041i	$-0.358670\pi$
$439$	−60.4608	−	34.9070i	−0.137724	−	0.0795149i	−0.567279	+	0.823526i	$0.692004\pi$
$440$		0			0
$441$	−145.102	−	23.5429i	−0.329031	−	0.0533852i
$442$	−137.918			−0.312032
$443$	−330.217	+	571.953i	−0.745411	+	1.29109i	0.204592	+	0.978847i	$0.434413\pi$
$443$	−330.217	+	571.953i	−0.745411	+	1.29109i	−0.950003	+	0.312242i	$0.898920\pi$
$444$	−103.190	+	59.5766i	−0.232409	+	0.134182i
$445$		0			0
$446$	−402.368	−	232.307i	−0.902171	−	0.520869i
$447$			88.5311i			0.198056i
$448$	31.8057	−	46.0912i	0.0709948	−	0.102882i
$449$	−560.274			−1.24783			−0.623913	−	0.781493i	$-0.714458\pi$
$449$	−560.274			−1.24783			−0.623913	+	0.781493i	$0.714458\pi$
$450$		0			0
$451$	−53.7926	+	31.0572i	−0.119274	+	0.0688629i
$452$	−10.7318	−	18.5879i	−0.0237428	−	0.0411238i
$453$	247.827	+	143.083i	0.547079	+	0.315856i
$454$			515.418i			1.13528i
$455$		0			0
$456$	8.72873			0.0191419
$457$	−91.8900	+	159.158i	−0.201072	+	0.348267i	−0.948874	−	0.315655i	$-0.897776\pi$
$457$	−91.8900	+	159.158i	−0.201072	+	0.348267i	0.747802	+	0.663922i	$0.231109\pi$
$458$	368.709	−	212.874i	0.805041	−	0.464790i
$459$	−32.7840	−	56.7836i	−0.0714249	−	0.123712i
$460$		0			0
$461$		−	28.4330i		−	0.0616767i	−0.999524	−	0.0308384i	$-0.990182\pi$
$461$		−	28.4330i		−	0.0616767i	0.999524	−	0.0308384i	$-0.00981771\pi$
$462$	4.53826	−	56.3073i	0.00982307	−	0.121877i
$463$	−269.931			−0.583005			−0.291503	−	0.956570i	$-0.594155\pi$
$463$	−269.931			−0.583005			−0.291503	+	0.956570i	$0.594155\pi$
$464$	−78.5866	+	136.116i	−0.169368	+	0.293353i
$465$		0			0
$466$	199.422	+	345.409i	0.427944	+	0.741221i
$467$	289.539	+	167.166i	0.619999	+	0.357956i	0.776868	−	0.629663i	$-0.216807\pi$
$467$	289.539	+	167.166i	0.619999	+	0.357956i	−0.156870	+	0.987619i	$0.550140\pi$
$468$		−	46.3710i		−	0.0990834i
$469$	−138.941	−	11.1984i	−0.296250	−	0.0238772i
$470$		0			0
$471$	165.248	−	286.218i	0.350845	−	0.607681i
$472$	276.612	−	159.702i	0.586043	−	0.338352i
$473$	127.532	+	220.892i	0.269624	+	0.467002i
$474$	75.4717	+	43.5736i	0.159223	+	0.0919274i
$475$		0			0
$476$	−159.594	+	75.7536i	−0.335281	+	0.159146i
$477$	−155.064			−0.325081
$478$	−58.7144	+	101.696i	−0.122833	+	0.212754i
$479$	114.560	−	66.1412i	0.239165	−	0.138082i	−0.375628	−	0.926771i	$-0.622573\pi$
$479$	114.560	−	66.1412i	0.239165	−	0.138082i	0.614793	+	0.788689i	$0.289240\pi$
$480$		0			0
$481$	230.219	+	132.917i	0.478626	+	0.276335i
$482$		−	469.271i		−	0.973592i
$483$	67.4222	+	46.5253i	0.139591	+	0.0963257i
$484$	−220.292			−0.455148
$485$		0			0
$486$	19.0919	−	11.0227i	0.0392837	−	0.0226805i
$487$	258.635	+	447.970i	0.531079	+	0.919856i	0.999342	+	0.0362667i	$0.0115466\pi$
$487$	258.635	+	447.970i	0.531079	+	0.919856i	−0.468263	+	0.883589i	$0.655120\pi$
$488$	−64.2573	−	37.0989i	−0.131675	−	0.0760224i
$489$			429.898i			0.879138i
$490$		0			0
$491$	484.805			0.987383			0.493692	−	0.869637i	$-0.335647\pi$
$491$	484.805			0.987383			0.493692	+	0.869637i	$0.335647\pi$
$492$	−32.6554	+	56.5609i	−0.0663728	+	0.114961i
$493$	429.398	−	247.913i	0.870989	−	0.502866i
$494$	−9.73701	−	16.8650i	−0.0197105	−	0.0341397i
$495$		0			0
$496$			43.7286i			0.0881624i
$497$	347.604	−	503.730i	0.699404	−	1.01354i
$498$	−114.336			−0.229589
$499$	64.6450	−	111.968i	0.129549	−	0.224385i	−0.793953	−	0.607979i	$-0.791980\pi$
$499$	64.6450	−	111.968i	0.129549	−	0.224385i	0.923502	+	0.383594i	$0.125314\pi$
$500$		0			0
$501$	−25.3723	−	43.9461i	−0.0506432	−	0.0877167i
$502$	−513.260	−	296.331i	−1.02243	−	0.590300i
$503$			160.905i			0.319890i	0.987126	+	0.159945i	$0.0511317\pi$
$503$			160.905i			0.319890i	−0.987126	+	0.159945i	$0.948868\pi$
$504$	−25.4700	−	53.6589i	−0.0505357	−	0.106466i
$505$		0			0
$506$	−15.7397	+	27.2620i	−0.0311061	+	0.0538774i
$507$	163.905	−	94.6308i	0.323285	−	0.186649i
$508$	117.281	+	203.137i	0.230869	+	0.399877i
$509$	−320.453	−	185.014i	−0.629575	−	0.363485i	0.151013	−	0.988532i	$-0.451747\pi$
$509$	−320.453	−	185.014i	−0.629575	−	0.363485i	−0.780587	+	0.625047i	$0.785080\pi$
$510$		0			0
$511$	−34.2563	+	425.027i	−0.0670378	+	0.831755i
$512$	22.6274			0.0441942
$513$	4.62911	−	8.01785i	0.00902360	−	0.0156293i
$514$	409.012	−	236.143i	0.795744	−	0.459423i
$515$		0			0
$516$	232.259	+	134.095i	0.450115	+	0.259874i
$517$			42.4560i			0.0821200i
$518$	339.408	+	27.3556i	0.655228	+	0.0528101i
$519$	−39.9964			−0.0770644
$520$		0			0
$521$	65.1395	−	37.6083i	0.125028	−	0.0721849i	−0.436182	−	0.899859i	$-0.643670\pi$
$521$	65.1395	−	37.6083i	0.125028	−	0.0721849i	0.561210	+	0.827674i	$0.310336\pi$
$522$	83.3537	+	144.373i	0.159681	+	0.276576i
$523$	810.701	+	468.058i	1.55010	+	0.894949i	0.998133	+	0.0610819i	$0.0194551\pi$
$523$	810.701	+	468.058i	1.55010	+	0.894949i	0.551965	+	0.833867i	$0.313878\pi$
$524$		−	185.389i		−	0.353796i
$525$		0			0
$526$	289.032			0.549491
$527$	68.9741	−	119.467i	0.130881	−	0.226692i
$528$	19.7674	−	11.4127i	0.0374382	−	0.0216149i
$529$	241.676	+	418.594i	0.456854	+	0.791294i
$530$		0			0
$531$		−	338.780i		−	0.638003i
$532$	−20.5307	−	14.1674i	−0.0385915	−	0.0266304i
$533$	145.710			0.273377
$534$	67.1336	−	116.279i	0.125718	−	0.217751i
$535$		0			0
$536$	−28.1614	−	48.7770i	−0.0525399	−	0.0910018i
$537$	314.152	+	181.376i	0.585014	+	0.337758i
$538$		−	197.214i		−	0.366569i
$539$	−102.065	+	125.074i	−0.189361	+	0.232047i
$540$		0			0
$541$	304.692	−	527.742i	0.563201	−	0.975493i	−0.434013	−	0.900906i	$-0.642903\pi$
$541$	304.692	−	527.742i	0.563201	−	0.975493i	0.997215	−	0.0745867i	$-0.0237638\pi$
$542$	457.092	−	263.902i	0.843343	−	0.486904i
$543$	211.021	+	365.500i	0.388622	+	0.673112i
$544$	−61.8182	−	35.6907i	−0.113636	−	0.0656080i
$545$		0			0
$546$	−75.2637	+	109.068i	−0.137846	+	0.199759i
$547$	−491.361			−0.898283			−0.449141	−	0.893461i	$-0.648270\pi$
$547$	−491.361			−0.898283			−0.449141	+	0.893461i	$0.648270\pi$
$548$	−27.4741	+	47.5865i	−0.0501351	+	0.0868366i
$549$	−68.1551	+	39.3494i	−0.124144	+	0.0716746i
$550$		0			0
$551$	60.6310	+	35.0053i	0.110038	+	0.0635305i
$552$			33.0994i			0.0599626i
$553$	−106.792	−	224.985i	−0.193115	−	0.406844i
$554$	−703.577			−1.27000
$555$		0			0
$556$	−116.069	+	67.0127i	−0.208758	+	0.120527i
$557$	526.110	+	911.250i	0.944543	+	1.63600i	0.756665	+	0.653803i	$0.226828\pi$
$557$	526.110	+	911.250i	0.944543	+	1.63600i	0.187878	+	0.982192i	$0.439839\pi$
$558$	40.1673	+	23.1906i	0.0719843	+	0.0415602i
$559$		−	598.339i		−	1.07037i
$560$		0			0
$561$	−72.0060			−0.128353
$562$	−207.026	+	358.580i	−0.368374	+	0.638042i
$563$	−670.769	+	387.269i	−1.19142	+	0.687866i	−0.958628	−	0.284661i	$-0.908119\pi$
$563$	−670.769	+	387.269i	−1.19142	+	0.687866i	−0.232791	+	0.972527i	$0.574786\pi$
$564$	22.3204	+	38.6601i	0.0395752	+	0.0685463i
$565$		0			0
$566$		−	391.406i		−	0.691531i
$567$	−62.7964	−	5.06126i	−0.110752	−	0.00892639i
$568$	247.295			0.435378
$569$	−156.525	+	271.109i	−0.275088	+	0.476466i	−0.970157	−	0.242477i	$-0.922040\pi$
$569$	−156.525	+	271.109i	−0.275088	+	0.476466i	0.695070	+	0.718942i	$0.255374\pi$
$570$		0			0
$571$	−324.711	−	562.416i	−0.568670	−	0.984966i	−0.996698	−	0.0812002i	$-0.974125\pi$
$571$	−324.711	−	562.416i	−0.568670	−	0.984966i	0.428027	−	0.903766i	$-0.359209\pi$
$572$	−44.1015	−	25.4620i	−0.0771005	−	0.0445140i
$573$		−	410.228i		−	0.715931i
$574$	168.611	−	80.0336i	0.293747	−	0.139431i
$575$		0			0
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	891.822	−	514.893i	1.54562	−	0.892363i	0.547150	−	0.837035i	$-0.315713\pi$
$577$	891.822	−	514.893i	1.54562	−	0.892363i	0.998468	−	0.0553284i	$-0.0176206\pi$
$578$	−91.7622	−	158.937i	−0.158758	−	0.274977i
$579$	199.338	+	115.088i	0.344280	+	0.198770i
$580$		0			0
$581$	268.927	+	185.575i	0.462868	+	0.319406i
$582$	112.051			0.192528
$583$	−85.1445	+	147.475i	−0.146046	+	0.252958i
$584$	−149.211	+	86.1469i	−0.255498	+	0.147512i
$585$		0			0
$586$	459.646	+	265.376i	0.784378	+	0.452861i
$587$			791.817i			1.34892i	0.738311	+	0.674461i	$0.235624\pi$
$587$			791.817i			1.34892i	−0.738311	+	0.674461i	$0.764376\pi$
$588$	−27.1850	+	167.550i	−0.0462329	+	0.284949i
$589$	19.4783			0.0330701
$590$		0			0
$591$	−158.669	+	91.6075i	−0.268475	+	0.155004i
$592$	68.7931	+	119.153i	0.116205	+	0.201272i
$593$	−73.1807	−	42.2509i	−0.123408	−	0.0712494i	0.437025	−	0.899449i	$-0.356032\pi$
$593$	−73.1807	−	42.2509i	−0.123408	−	0.0712494i	−0.560433	+	0.828200i	$0.689365\pi$
$594$		−	24.2100i		−	0.0407575i
$595$		0			0
$596$	102.227			0.171522
$597$	174.541	−	302.314i	0.292364	−	0.506389i
$598$	63.9522	−	36.9228i	0.106943	−	0.0617438i
$599$	233.463	+	404.369i	0.389754	+	0.675074i	0.992416	−	0.122922i	$-0.0392266\pi$
$599$	233.463	+	404.369i	0.389754	+	0.675074i	−0.602662	+	0.797997i	$0.705893\pi$
$600$		0			0
$601$		−	1095.93i		−	1.82351i	−0.410733	−	0.911756i	$-0.634727\pi$
$601$		−	1095.93i		−	1.82351i	0.410733	−	0.911756i	$-0.365273\pi$
$602$	−328.647	−	692.377i	−0.545925	−	1.15013i
$603$	−59.7394			−0.0990702
$604$	165.218	−	286.166i	0.273540	−	0.473785i
$605$		0			0
$606$	112.089	+	194.144i	0.184965	+	0.320369i
$607$	−310.815	−	179.449i	−0.512051	−	0.295633i	0.221625	−	0.975132i	$-0.428864\pi$
$607$	−310.815	−	179.449i	−0.512051	−	0.295633i	−0.733676	+	0.679499i	$0.762197\pi$
$608$		−	10.0791i		−	0.0165774i
$609$	38.2733	−	474.866i	0.0628461	−	0.779747i
$610$		0			0
$611$	49.7975	−	86.2517i	0.0815016	−	0.141165i
$612$	−65.5681	+	37.8558i	−0.107137	+	0.0618558i
$613$	231.029	+	400.154i	0.376883	+	0.652780i	0.990607	−	0.136741i	$-0.0436627\pi$
$613$	231.029	+	400.154i	0.376883	+	0.652780i	−0.613724	+	0.789520i	$0.710329\pi$
$614$	−132.008	−	76.2148i	−0.214996	−	0.124128i
$615$		0			0
$616$	−65.0181	−	5.24033i	−0.105549	−	0.00850703i
$617$	219.440			0.355656			0.177828	−	0.984062i	$-0.443093\pi$
$617$	219.440			0.355656			0.177828	+	0.984062i	$0.443093\pi$
$618$	−61.8597	+	107.144i	−0.100097	+	0.173372i
$619$	832.792	−	480.813i	1.34538	−	0.776757i	0.357791	−	0.933802i	$-0.383530\pi$
$619$	832.792	−	480.813i	1.34538	−	0.776757i	0.987592	+	0.157044i	$0.0501966\pi$
$620$		0			0
$621$	30.4037	+	17.5536i	0.0489593	+	0.0282667i
$622$		−	816.123i		−	1.31209i
$623$	−346.633	+	164.534i	−0.556393	+	0.264100i
$624$	−53.5446			−0.0858087
$625$		0			0
$626$	−486.560	+	280.915i	−0.777252	+	0.448747i
$627$	−5.08362	−	8.80509i	−0.00810785	−	0.0140432i
$628$	−330.496	−	190.812i	−0.526267	−	0.303840i
$629$		−	434.036i		−	0.690041i
$630$		0			0
$631$	584.721			0.926658			0.463329	−	0.886186i	$-0.346655\pi$
$631$	584.721			0.926658			0.463329	+	0.886186i	$0.346655\pi$
$632$	50.3144	−	87.1472i	0.0796115	−	0.137891i
$633$	44.4067	−	25.6382i	0.0701528	−	0.0405027i
$634$	−56.8303	−	98.4329i	−0.0896376	−	0.155257i
$635$		0			0
$636$			179.052i			0.281529i
$637$	354.053	−	134.379i	0.555813	−	0.210957i
$638$	183.076			0.286953
$639$	131.148	−	227.155i	0.205239	−	0.355485i
$640$		0			0
$641$	−269.518	−	466.819i	−0.420465	−	0.728268i	0.575520	−	0.817788i	$-0.304800\pi$
$641$	−269.518	−	466.819i	−0.420465	−	0.728268i	−0.995985	+	0.0895205i	$0.971467\pi$
$642$	199.297	+	115.064i	0.310431	+	0.179228i
$643$		−	150.959i		−	0.234773i	−0.993086	−	0.117386i	$-0.962548\pi$
$643$		−	150.959i		−	0.234773i	0.993086	−	0.117386i	$-0.0374516\pi$
$644$	53.7228	−	77.8525i	0.0834205	−	0.120889i
$645$		0			0
$646$	−15.8979	+	27.5360i	−0.0246098	+	0.0426255i
$647$	391.111	−	225.808i	0.604499	−	0.349008i	−0.166310	−	0.986073i	$-0.553185\pi$
$647$	391.111	−	225.808i	0.604499	−	0.349008i	0.770809	+	0.637066i	$0.219852\pi$
$648$	−12.7279	−	22.0454i	−0.0196419	−	0.0340207i
$649$	−322.199	−	186.022i	−0.496454	−	0.286628i
$650$		0			0
$651$	−56.8366	−	119.741i	−0.0873067	−	0.183933i
$652$	496.404			0.761356
$653$	−215.848	+	373.860i	−0.330548	+	0.572526i	−0.982619	−	0.185631i	$-0.940567\pi$
$653$	−215.848	+	373.860i	−0.330548	+	0.572526i	0.652071	+	0.758158i	$0.273900\pi$
$654$	255.853	−	147.717i	0.391213	−	0.225867i
$655$		0			0
$656$	65.3108	+	37.7072i	0.0995592	+	0.0574805i
$657$			182.745i			0.278151i
$658$	10.2488	−	127.160i	0.0155757	−	0.193252i
$659$	−195.185			−0.296184			−0.148092	−	0.988974i	$-0.547313\pi$
$659$	−195.185			−0.296184			−0.148092	+	0.988974i	$0.547313\pi$
$660$		0			0
$661$	596.305	−	344.277i	0.902126	−	0.520843i	0.0242368	−	0.999706i	$-0.492284\pi$
$661$	596.305	−	344.277i	0.902126	−	0.520843i	0.877889	+	0.478863i	$0.158951\pi$
$662$	−347.926	−	602.626i	−0.525569	−	0.910311i
$663$	146.284	+	84.4572i	0.220640	+	0.127386i
$664$			132.023i			0.198830i
$665$		0			0
$666$	145.932			0.219118
$667$	−132.740	+	229.913i	−0.199011	+	0.344697i
$668$	−50.7445	+	29.2974i	−0.0759649	+	0.0438583i
$669$	284.517	+	492.799i	0.425288	+	0.736620i
$670$		0			0
$671$			86.4259i			0.128802i
$672$	−61.9600	+	29.4102i	−0.0922024	+	0.0437652i
$673$	200.020			0.297206			0.148603	−	0.988897i	$-0.452522\pi$
$673$	200.020			0.297206			0.148603	+	0.988897i	$0.452522\pi$
$674$	445.564	−	771.740i	0.661075	−	1.14501i
$675$		0			0
$676$	−109.270	−	189.262i	−0.161642	−	0.279973i
$677$	735.787	+	424.807i	1.08683	+	0.627484i	0.932732	−	0.360571i	$-0.117418\pi$
$677$	735.787	+	424.807i	1.08683	+	0.627484i	0.154103	+	0.988055i	$0.450751\pi$
$678$			26.2873i			0.0387719i
$679$	−263.554	−	181.868i	−0.388150	−	0.267846i
$680$		0			0
$681$	315.628	−	546.684i	0.463477	−	0.802766i
$682$	44.1111	−	25.4676i	0.0646791	−	0.0373425i
$683$	224.005	+	387.988i	0.327972	+	0.568064i	0.982109	−	0.188311i	$-0.0603014\pi$
$683$	224.005	+	387.988i	0.327972	+	0.568064i	−0.654137	+	0.756376i	$0.726968\pi$
$684$	−9.25821	−	5.34523i	−0.0135354	−	0.00781467i
$685$		0			0
$686$	335.888	−	349.968i	0.489632	−	0.510157i
$687$	−521.433			−0.759000
$688$	154.839	−	268.190i	0.225057	−	0.389811i
$689$	345.952	−	199.735i	0.502107	−	0.289891i
$690$		0			0
$691$	−337.930	−	195.104i	−0.489044	−	0.282350i	0.235134	−	0.971963i	$-0.424447\pi$
$691$	−337.930	−	195.104i	−0.489044	−	0.282350i	−0.724178	+	0.689613i	$0.757781\pi$
$692$			46.1839i			0.0667397i
$693$	−39.2946	+	56.9439i	−0.0567022	+	0.0821701i
$694$	−608.313			−0.876532
$695$		0			0
$696$	166.707	−	96.2485i	0.239522	−	0.138288i
$697$	−118.953	−	206.033i	−0.170664	−	0.295599i
$698$	−116.574	−	67.3038i	−0.167011	−	0.0964237i
$699$		−	488.482i		−	0.698830i
$700$		0			0
$701$	989.018			1.41087			0.705434	−	0.708776i	$-0.250752\pi$
$701$	989.018			1.41087			0.705434	+	0.708776i	$0.250752\pi$
$702$	−28.3963	+	49.1839i	−0.0404506	+	0.0700625i
$703$	53.0751	−	30.6429i	0.0754980	−	0.0435888i
$704$	−13.1782	−	22.8254i	−0.0187191	−	0.0324224i
$705$		0			0
$706$			371.849i			0.526699i
$707$	51.4676	−	638.571i	0.0727971	−	0.903212i
$708$	−391.189			−0.552527
$709$	−554.927	+	961.161i	−0.782689	+	1.35566i	0.147680	+	0.989035i	$0.452819\pi$
$709$	−554.927	+	961.161i	−0.782689	+	1.35566i	−0.930370	+	0.366623i	$0.880514\pi$
$710$		0			0
$711$	−53.3665	−	92.4335i	−0.0750584	−	0.130005i
$712$	−134.267	−	77.5192i	−0.188578	−	0.108875i
$713$			73.8617i			0.103593i
$714$	215.664	+	17.3821i	0.302051	+	0.0243447i
$715$		0			0
$716$	209.435	−	362.752i	0.292507	−	0.506637i
$717$	124.552	−	71.9101i	0.173713	−	0.100293i
$718$	−211.263	−	365.918i	−0.294238	−	0.509636i
$719$	936.393	+	540.627i	1.30235	+	0.751915i	0.980807	−	0.194979i	$-0.0624638\pi$
$719$	936.393	+	540.627i	1.30235	+	0.751915i	0.321547	+	0.946894i	$0.395797\pi$
$720$		0			0
$721$	319.402	−	151.609i	0.442999	−	0.210276i
$722$	506.042			0.700889
$723$	−287.369	+	497.737i	−0.397467	+	0.688433i
$724$	422.043	−	243.667i	0.582932	−	0.336556i
$725$		0			0
$726$	233.655	+	134.901i	0.321838	+	0.185813i
$727$			491.493i			0.676056i	0.941136	+	0.338028i	$0.109760\pi$
$727$			491.493i			0.676056i	−0.941136	+	0.338028i	$0.890240\pi$
$728$	125.941	+	86.9070i	0.172996	+	0.119378i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−846.044	+	488.464i	−1.15738	+	0.668213i
$732$	45.4367	+	78.6988i	0.0620721	+	0.107512i
$733$	−40.4999	−	23.3826i	−0.0552522	−	0.0318999i	0.472119	−	0.881535i	$-0.343489\pi$
$733$	−40.4999	−	23.3826i	−0.0552522	−	0.0318999i	−0.527372	+	0.849635i	$0.676822\pi$
$734$		−	186.784i		−	0.254474i
$735$		0			0
$736$	38.2199			0.0519292
$737$	−32.8025	+	56.8156i	−0.0445081	+	0.0770903i
$738$	69.2726	−	39.9946i	0.0938653	−	0.0541932i
$739$	368.856	+	638.878i	0.499129	+	0.864517i	0.999999	−	0.00100544i	$-0.000320040\pi$
$739$	368.856	+	638.878i	0.499129	+	0.864517i	−0.500870	+	0.865522i	$0.666987\pi$
$740$		0			0
$741$			23.8507i			0.0321872i
$742$	290.615	−	421.146i	0.391665	−	0.567582i
$743$	−258.593			−0.348039			−0.174020	−	0.984742i	$-0.555676\pi$
$743$	−258.593			−0.348039			−0.174020	+	0.984742i	$0.555676\pi$
$744$	26.7782	−	46.3812i	0.0359922	−	0.0623403i
$745$		0			0
$746$	−7.55747	−	13.0899i	−0.0101307	−	0.0175468i
$747$	121.271	+	70.0159i	0.162344	+	0.0937295i
$748$			83.1454i			0.111157i
$749$	−282.005	−	594.114i	−0.376509	−	0.793210i
$750$		0			0
$751$	−175.310	+	303.645i	−0.233435	+	0.404321i	−0.958817	−	0.284025i	$-0.908330\pi$
$751$	−175.310	+	303.645i	−0.233435	+	0.404321i	0.725382	+	0.688347i	$0.241663\pi$
$752$	44.6409	−	25.7734i	0.0593628	−	0.0342731i
$753$	362.930	+	628.613i	0.481978	+	0.834811i
$754$	−371.928	−	214.733i	−0.493274	−	0.284792i
$755$		0			0
$756$	−5.84424	+	72.5110i	−0.00773048	+	0.0959140i
$757$	907.187			1.19840			0.599199	−	0.800600i	$-0.295486\pi$
$757$	907.187			1.19840			0.599199	+	0.800600i	$0.295486\pi$
$758$	−101.058	+	175.038i	−0.133322	+	0.230921i
$759$	33.3890	−	19.2771i	0.0439907	−	0.0253981i
$760$		0			0
$761$	1067.66	+	616.416i	1.40297	+	0.810007i	0.994697	−	0.102851i	$-0.0327965\pi$
$761$	1067.66	+	616.416i	1.40297	+	0.810007i	0.408277	+	0.912858i	$0.366130\pi$
$762$		−	287.280i		−	0.377008i
$763$	−841.543	−	67.8267i	−1.10294	−	0.0888948i
$764$	−473.691			−0.620014
$765$		0			0
$766$	755.684	−	436.294i	0.986532	−	0.569575i
$767$	436.376	+	755.826i	0.568939	+	0.985432i
$768$	−24.0000	−	13.8564i	−0.0312500	−	0.0180422i
$769$			685.828i			0.891844i	0.895072	+	0.445922i	$0.147124\pi$
$769$			685.828i			0.891844i	−0.895072	+	0.445922i	$0.852876\pi$
$770$		0			0
$771$	−578.431			−0.750235
$772$	132.892	−	230.176i	0.172140	−	0.298155i
$773$	334.420	−	193.077i	0.432625	−	0.249776i	−0.267839	−	0.963464i	$-0.586310\pi$
$773$	334.420	−	193.077i	0.432625	−	0.249776i	0.700465	+	0.713687i	$0.252976\pi$
$774$	−164.232	−	284.458i	−0.212186	−	0.367517i
$775$		0			0
$776$		−	129.386i		−	0.166734i
$777$	−343.245	−	236.859i	−0.441756	−	0.304838i
$778$	−981.376			−1.26141
$779$	16.7962	−	29.0918i	0.0215612	−	0.0373451i
$780$		0			0
$781$	−144.025	−	249.458i	−0.184411	−	0.319409i
$782$	−104.417	−	60.2851i	−0.133525	−	0.0770909i
$783$		−	204.174i		−	0.260759i
$784$	193.470	+	31.3905i	0.246773	+	0.0400389i
$785$		0			0
$786$	−113.527	+	196.635i	−0.144437	+	0.250171i
$787$	1064.42	−	614.543i	1.35250	−	0.780867i	0.363902	−	0.931437i	$-0.381444\pi$
$787$	1064.42	−	614.543i	1.35250	−	0.780867i	0.988599	+	0.150570i	$0.0481108\pi$
$788$	105.779	+	183.215i	0.134238	+	0.232506i
$789$	−306.565	−	176.995i	−0.388549	−	0.224329i
$790$		0			0
$791$	42.6663	−	61.8300i	0.0539397	−	0.0781668i
$792$	−27.9553			−0.0352971
$793$	101.371	−	175.579i	0.127832	−	0.221411i
$794$	685.309	−	395.663i	0.863109	−	0.498316i
$795$		0			0
$796$	−349.082	−	201.543i	−0.438545	−	0.253194i
$797$			821.718i			1.03101i	0.856886	+	0.515507i	$0.172396\pi$
$797$			821.718i			1.03101i	−0.856886	+	0.515507i	$0.827604\pi$
$798$	13.1004	+	27.5992i	0.0164165	+	0.0345855i
$799$	−162.612			−0.203519
$800$		0			0
$801$	−142.412	+	82.2215i	−0.177793	+	0.102649i
$802$	113.990	+	197.437i	0.142132	+	0.246181i
$803$	173.801	+	100.344i	0.216440	+	0.124962i
$804$			68.9811i			0.0857973i
$805$		0			0
$806$	−119.486			−0.148245
$807$	−120.768	+	209.177i	−0.149651	+	0.259203i
$808$	224.178	−	129.429i	0.277448	−	0.160185i
$809$	216.809	+	375.524i	0.267996	+	0.464184i	0.968344	−	0.249618i	$-0.0803051\pi$
$809$	216.809	+	375.524i	0.267996	+	0.464184i	−0.700348	+	0.713802i	$0.746972\pi$
$810$		0			0
$811$		−	1618.04i		−	1.99512i	−0.0698416	−	0.997558i	$-0.522249\pi$
$811$		−	1618.04i		−	1.99512i	0.0698416	−	0.997558i	$-0.477751\pi$
$812$	−548.328	−	44.1941i	−0.675281	−	0.0544263i
$813$	−646.425			−0.795111
$814$	80.1304	−	138.790i	0.0984403	−	0.170504i
$815$		0			0
$816$	43.7121	+	75.7115i	0.0535687	+	0.0927837i
$817$	−119.461	−	68.9711i	−0.146220	−	0.0844199i
$818$			650.286i			0.794971i
$819$	146.620	−	69.5952i	0.179023	−	0.0849758i
$820$		0			0
$821$	429.043	−	743.125i	0.522586	−	0.905146i	−0.477068	−	0.878866i	$-0.658301\pi$
$821$	429.043	−	743.125i	0.522586	−	0.905146i	0.999655	−	0.0262799i	$-0.00836612\pi$
$822$	58.2813	−	33.6487i	0.0709018	−	0.0409352i
$823$	392.287	+	679.461i	0.476655	+	0.825591i	0.999642	−	0.0267498i	$-0.00851575\pi$
$823$	392.287	+	679.461i	0.476655	+	0.825591i	−0.522987	+	0.852341i	$0.675182\pi$
$824$	123.719	+	71.4294i	0.150145	+	0.0866862i
$825$		0			0
$826$	920.109	+	634.929i	1.11393	+	0.768680i
$827$	−773.795			−0.935665			−0.467833	−	0.883817i	$-0.654965\pi$
$827$	−773.795			−0.935665			−0.467833	+	0.883817i	$0.654965\pi$
$828$	20.2691	−	35.1072i	0.0244796	−	0.0424000i
$829$	−573.640	+	331.191i	−0.691966	+	0.399507i	−0.804348	−	0.594158i	$-0.797485\pi$
$829$	−573.640	+	331.191i	−0.691966	+	0.399507i	0.112382	+	0.993665i	$0.464152\pi$
$830$		0			0
$831$	746.256	+	430.851i	0.898022	+	0.518473i
$832$			61.8280i			0.0743125i
$833$	−479.048	−	390.924i	−0.575087	−	0.469296i
$834$	164.147			0.196819
$835$		0			0
$836$	−10.1672	+	5.87006i	−0.0121618	+	0.00702161i
$837$	−28.4025	−	49.1946i	−0.0339337	−	0.0587750i
$838$	114.614	+	66.1723i	0.136771	+	0.0789646i
$839$		−	359.133i		−	0.428049i	−0.976828	−	0.214024i	$-0.931343\pi$
$839$		−	359.133i		−	0.428049i	0.976828	−	0.214024i	$-0.0686572\pi$
$840$		0			0
$841$	702.963			0.835866
$842$	−115.228	+	199.581i	−0.136851	+	0.237032i
$843$	439.169	−	253.554i	0.520959	−	0.300776i
$844$	−29.6045	−	51.2764i	−0.0350764	−	0.0607541i
$845$		0			0
$846$		−	54.6737i		−	0.0646261i
$847$	−330.621	−	696.537i	−0.390344	−	0.822357i
$848$	206.752			0.243811
$849$	−239.686	+	415.149i	−0.282316	+	0.488986i
$850$		0			0
$851$	116.198	+	201.261i	0.136543	+	0.236500i
$852$	−262.296	−	151.437i	−0.307859	−	0.177742i
$853$		−	1089.78i		−	1.27758i	−0.769379	−	0.638792i	$-0.779434\pi$
$853$		−	1089.78i		−	1.27758i	0.769379	−	0.638792i	$-0.220566\pi$
$854$	20.8631	−	258.853i	0.0244298	−	0.303107i
$855$		0			0
$856$	132.865	−	230.128i	0.155216	−	0.268841i
$857$	−56.2155	+	32.4560i	−0.0655956	+	0.0378717i	−0.532439	−	0.846468i	$-0.678724\pi$
$857$	−56.2155	+	32.4560i	−0.0655956	+	0.0378717i	0.466843	+	0.884340i	$0.345391\pi$
$858$	31.1845	+	54.0131i	0.0363455	+	0.0629523i
$859$	250.689	+	144.735i	0.291838	+	0.168493i	0.638770	−	0.769397i	$-0.279443\pi$
$859$	250.689	+	144.735i	0.291838	+	0.168493i	−0.346933	+	0.937890i	$0.612777\pi$
$860$		0			0
$861$	−227.849	−	18.3642i	−0.264633	−	0.0213289i
$862$	−468.225			−0.543185
$863$	−469.234	+	812.738i	−0.543725	+	0.941759i	0.454961	+	0.890511i	$0.349653\pi$
$863$	−469.234	+	812.738i	−0.543725	+	0.941759i	−0.998686	+	0.0512476i	$0.983680\pi$
$864$	−25.4558	+	14.6969i	−0.0294628	+	0.0170103i
$865$		0			0
$866$	−108.283	−	62.5174i	−0.125038	−	0.0721910i
$867$			224.771i			0.259251i
$868$	−138.265	+	65.6293i	−0.159291	+	0.0756098i
$869$	−117.213			−0.134882
$870$		0			0
$871$	133.280	−	76.9493i	0.153020	−	0.0883459i
$872$	−170.569	−	295.434i	−0.195606	−	0.338800i
$873$	−118.848	−	68.6171i	−0.136138	−	0.0785992i
$874$		−	17.0245i		−	0.0194788i
$875$		0			0
$876$	211.016			0.240886
$877$	−110.543	+	191.465i	−0.126046	+	0.218318i	−0.922141	−	0.386853i	$-0.873562\pi$
$877$	−110.543	+	191.465i	−0.126046	+	0.218318i	0.796095	+	0.605171i	$0.206895\pi$
$878$	85.5044	−	49.3660i	0.0973855	−	0.0562255i
$879$	−325.019	−	562.949i	−0.369759	−	0.640442i
$880$		0			0
$881$		−	154.796i		−	0.175704i	−0.996134	−	0.0878522i	$-0.972000\pi$
$881$		−	154.796i		−	0.175704i	0.996134	−	0.0878522i	$-0.0280003\pi$
$882$	131.437	−	161.066i	0.149022	−	0.182615i
$883$	−1267.40			−1.43534			−0.717668	−	0.696385i	$-0.754791\pi$
$883$	−1267.40			−1.43534			−0.717668	+	0.696385i	$0.754791\pi$
$884$	97.5227	−	168.914i	0.110320	−	0.191080i
$885$		0			0
$886$	−466.997	−	808.863i	−0.527085	−	0.912938i
$887$	−1434.83	−	828.399i	−1.61762	−	0.933934i	−0.987533	−	0.157410i	$-0.949686\pi$
$887$	−1434.83	−	828.399i	−1.61762	−	0.933934i	−0.630087	−	0.776524i	$-0.716981\pi$
$888$		−	168.508i		−	0.189761i
$889$	−466.277	+	675.706i	−0.524496	+	0.760074i
$890$		0			0
$891$	−14.8255	+	25.6786i	−0.0166392	+	0.0288199i
$892$	569.035	−	328.532i	0.637931	−	0.368310i
$893$	−11.4804	−	19.8846i	−0.0128560	−	0.0222672i
$894$	−108.428	−	62.6009i	−0.121284	−	0.0700234i
$895$		0			0
$896$	33.9600	+	71.5452i	0.0379018	+	0.0798496i
$897$	−90.4420			−0.100827
$898$	396.174	−	686.193i	0.441173	−	0.764135i
$899$	372.010	−	214.780i	0.413804	−	0.238910i
$900$		0			0
$901$	−564.847	−	326.114i	−0.626911	−	0.361947i
$902$		−	87.8430i		−	0.0973869i
$903$	−75.4099	+	935.630i	−0.0835105	+	1.03614i
$904$	30.3540			0.0335774
$905$		0			0
$906$	−350.480	+	202.350i	−0.386844	+	0.223344i
$907$	368.230	+	637.793i	0.405987	+	0.703190i	0.994436	−	0.105345i	$-0.0335946\pi$
$907$	368.230	+	637.793i	0.405987	+	0.703190i	−0.588449	+	0.808534i	$0.700261\pi$
$908$	−631.256	−	364.456i	−0.695216	−	0.401383i
$909$		−	274.561i		−	0.302047i
$910$		0			0
$911$	197.935			0.217273			0.108636	−	0.994082i	$-0.465352\pi$
$911$	197.935			0.217273			0.108636	+	0.994082i	$0.465352\pi$
$912$	−6.17214	+	10.6905i	−0.00676770	+	0.0117220i
$913$	133.178	−	76.8905i	0.145869	−	0.0842175i
$914$	−129.952	−	225.084i	−0.142180	−	0.246262i
$915$		0			0
$916$			602.099i			0.657313i
$917$	586.178	−	278.238i	0.639235	−	0.303422i
$918$	92.7273			0.101010
$919$	−821.091	+	1422.17i	−0.893462	+	1.54752i	−0.0577645	+	0.998330i	$0.518397\pi$
$919$	−821.091	+	1422.17i	−0.893462	+	1.54752i	−0.835697	+	0.549191i	$0.814936\pi$
$920$		0			0
$921$	93.3436	+	161.676i	0.101350	+	0.175544i
$922$	34.8231	+	20.1051i	0.0377691	+	0.0218060i
$923$			675.718i			0.732089i
$924$	65.7531	+	45.3735i	0.0711614	+	0.0491055i
$925$		0			0
$926$	190.870	−	330.597i	0.206123	−	0.357016i
$927$	131.224	−	75.7623i	0.141558	−	0.0817285i
$928$	−111.138	−	192.497i	−0.119761	−	0.207432i
$929$	1317.18	+	760.473i	1.41784	+	0.818593i	0.996109	−	0.0881263i	$-0.0280879\pi$
$929$	1317.18	+	760.473i	1.41784	+	0.818593i	0.421735	+	0.906719i	$0.361421\pi$
$930$		0			0
$931$	13.9825	−	86.1785i	0.0150188	−	0.0925655i
$932$	−564.050			−0.605204
$933$	−499.771	+	865.629i	−0.535660	+	0.927791i
$934$	−409.471	+	236.408i	−0.438405	+	0.253113i
$935$		0			0
$936$	56.7927	+	32.7893i	0.0606759	+	0.0350313i
$937$		−	682.636i		−	0.728534i	−0.931295	−	0.364267i	$-0.881320\pi$
$937$		−	682.636i		−	0.728534i	0.931295	−	0.364267i	$-0.118680\pi$
$938$	111.961	−	162.249i	0.119362	−	0.172974i
$939$	688.100			0.732800
$940$		0			0
$941$	−248.545	+	143.497i	−0.264129	+	0.152495i	−0.626216	−	0.779649i	$-0.715397\pi$
$941$	−248.545	+	143.497i	−0.264129	+	0.152495i	0.362088	+	0.932144i	$0.382064\pi$
$942$	233.696	+	404.773i	0.248085	+	0.429695i
$943$	110.316	+	63.6911i	0.116984	+	0.0675410i
$944$			451.706i			0.478502i
$945$		0			0
$946$	−360.715			−0.381305
$947$	−240.057	+	415.790i	−0.253492	+	0.439061i	−0.964485	−	0.264139i	$-0.914912\pi$
$947$	−240.057	+	415.790i	−0.253492	+	0.439061i	0.710993	+	0.703199i	$0.248246\pi$
$948$	−106.733	+	61.6224i	−0.112588	+	0.0650025i
$949$	−235.391	−	407.709i	−0.248041	−	0.429620i
$950$		0			0
$951$			139.205i			0.146378i
$952$	20.0711	−	249.028i	0.0210831	−	0.261584i
$953$	1147.30			1.20388			0.601941	−	0.798540i	$-0.294394\pi$
$953$	1147.30			1.20388			0.601941	+	0.798540i	$0.294394\pi$
$954$	109.647	−	189.914i	0.114934	−	0.199071i
$955$		0			0
$956$	−83.0347	−	143.820i	−0.0868563	−	0.150440i
$957$	−194.181	−	112.111i	−0.202906	−	0.117148i
$958$			187.076i			0.195277i
$959$	−191.697	−	15.4504i	−0.199892	−	0.0161109i
$960$		0			0
$961$	−420.744	+	728.750i	−0.437819	+	0.758325i
$962$	−325.579	+	187.973i	−0.338439	+	0.195398i
$963$	−140.924	−	244.088i	−0.146339	−	0.253466i
$964$	574.737	+	331.825i	0.596201	+	0.344217i
$965$		0			0
$966$	−104.656	+	49.6767i	−0.108340	+	0.0514251i
$967$	−1400.07			−1.44785			−0.723923	−	0.689881i	$-0.757663\pi$
$967$	−1400.07			−1.44785			−0.723923	+	0.689881i	$0.757663\pi$
$968$	155.770	−	269.801i	0.160919	−	0.278720i
$969$	33.7246	−	19.4709i	0.0348035	−	0.0200938i
$970$		0			0
$971$	226.263	+	130.633i	0.233020	+	0.134534i	0.611965	−	0.790885i	$-0.290379\pi$
$971$	226.263	+	130.633i	0.233020	+	0.134534i	−0.378944	+	0.925419i	$0.623713\pi$
$972$			31.1769i			0.0320750i
$973$	−386.087	−	266.423i	−0.396801	−	0.273816i
$974$	−731.532			−0.751059
$975$		0			0
$976$	90.8735	−	52.4658i	0.0931081	−	0.0537560i
$977$	−389.723	−	675.019i	−0.398897	−	0.690910i	0.594693	−	0.803953i	$-0.297274\pi$
$977$	−389.723	−	675.019i	−0.398897	−	0.690910i	−0.993590	+	0.113043i	$0.963940\pi$
$978$	−526.516	−	303.984i	−0.538360	−	0.310822i
$979$			180.589i			0.184463i
$980$		0			0
$981$	−361.831			−0.368839
$982$	−342.809	+	593.763i	−0.349093	+	0.604646i
$983$	−1332.15	+	769.118i	−1.35519	+	0.782419i	−0.988971	−	0.148110i	$-0.952681\pi$
$983$	−1332.15	+	769.118i	−1.35519	+	0.782419i	−0.366219	+	0.930529i	$0.619348\pi$
$984$	−46.1817	−	79.9891i	−0.0469327	−	0.0812898i
$985$		0			0
$986$			701.204i			0.711160i
$987$	−88.7395	+	128.597i	−0.0899083	+	0.130291i
$988$	27.5404			0.0278749
$989$	261.539	−	452.998i	0.264448	−	0.458037i
$990$		0			0
$991$	−482.270	−	835.316i	−0.486650	−	0.842902i	0.513233	−	0.858250i	$-0.328448\pi$
$991$	−482.270	−	835.316i	−0.486650	−	0.842902i	−0.999882	+	0.0153476i	$0.995115\pi$
$992$	−53.5563	−	30.9208i	−0.0539883	−	0.0311701i
$993$			852.242i			0.858250i
$994$	371.148	+	781.917i	0.373389	+	0.786637i
$995$		0			0
$996$	80.8474	−	140.032i	0.0811721	−	0.140594i
$997$	361.770	−	208.868i	0.362858	−	0.209496i	−0.307476	−	0.951556i	$-0.599484\pi$
$997$	361.770	−	208.868i	0.362858	−	0.209496i	0.670334	+	0.742060i	$0.266151\pi$
$998$	91.4218	+	158.347i	0.0916050	+	0.158664i
$999$	−154.785	−	89.3649i	−0.154939	−	0.0894543i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.p.d.901.2	yes	8
5.2	odd	4		1050.3.q.b.649.2		16
5.3	odd	4		1050.3.q.b.649.7		16
5.4	even	2		1050.3.p.c.901.3	yes	8
7.3	odd	6	inner	1050.3.p.d.451.2	yes	8
35.3	even	12		1050.3.q.b.199.2		16
35.17	even	12		1050.3.q.b.199.7		16
35.24	odd	6		1050.3.p.c.451.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.p.c.451.3	✓	8	35.24	odd	6
1050.3.p.c.901.3	yes	8	5.4	even	2
1050.3.p.d.451.2	yes	8	7.3	odd	6	inner
1050.3.p.d.901.2	yes	8	1.1	even	1	trivial
1050.3.q.b.199.2		16	35.3	even	12
1050.3.q.b.199.7		16	35.17	even	12
1050.3.q.b.649.2		16	5.2	odd	4
1050.3.q.b.649.7		16	5.3	odd	4

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(3.97571 - 5.76140i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.64728 - 2.85317i) q^{11} +(-3.00000 - 1.73205i) q^{12} +7.72850i q^{13} +(4.24500 + 8.94315i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(10.9280 - 6.30929i) q^{17} +(2.12132 + 3.67423i) q^{18} +(1.54304 + 0.890872i) q^{19} +(0.974040 - 12.0852i) q^{21} +4.65921 q^{22} +(-3.37819 + 5.85120i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-9.46544 - 5.46488i) q^{26} -5.19615i q^{27} +(-13.9547 - 1.12472i) q^{28} +39.2933 q^{29} +(9.46751 - 5.46607i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(-4.94184 - 2.85317i) q^{33} +17.8454i q^{34} -6.00000 q^{36} +(17.1983 - 29.7883i) q^{37} +(-2.18218 + 1.25988i) q^{38} +(6.69308 + 11.5928i) q^{39} -18.8536i q^{41} +(14.1125 + 9.73845i) q^{42} -77.4197 q^{43} +(-3.29456 + 5.70635i) q^{44} +(-4.77748 - 8.27485i) q^{46} +(-11.1602 - 6.44335i) q^{47} +6.92820i q^{48} +(-17.3875 - 45.8113i) q^{49} +(10.9280 - 18.9279i) q^{51} +(13.3862 - 7.72850i) q^{52} +(-25.8440 - 44.7631i) q^{53} +(6.36396 + 3.67423i) q^{54} +(11.2450 - 16.2957i) q^{56} +3.08607 q^{57} +(-27.7846 + 48.1243i) q^{58} +(97.7973 - 56.4633i) q^{59} +(-22.7184 - 13.1165i) q^{61} +15.4604i q^{62} +(-9.00500 - 18.9713i) q^{63} +8.00000 q^{64} +(6.98882 - 4.03500i) q^{66} +(-9.95656 - 17.2453i) q^{67} +(-21.8560 - 12.6186i) q^{68} +11.7024i q^{69} +87.4319 q^{71} +(4.24264 - 7.34847i) q^{72} +(-52.7540 + 30.4575i) q^{73} +(24.3220 + 42.1270i) q^{74} -3.56349i q^{76} +(-22.9874 - 1.85274i) q^{77} -18.9309 q^{78} +(17.7888 - 30.8112i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(23.0909 + 13.3315i) q^{82} +46.6773i q^{83} +(-21.9062 + 10.3981i) q^{84} +(54.7440 - 94.8194i) q^{86} +(58.9399 - 34.0290i) q^{87} +(-4.65921 - 8.06999i) q^{88} +(-47.4706 - 27.4072i) q^{89} +(44.5270 + 30.7263i) q^{91} +13.5128 q^{92} +(9.46751 - 16.3982i) q^{93} +(15.7829 - 9.11228i) q^{94} +(-8.48528 - 4.89898i) q^{96} -45.7447i q^{97} +(68.4020 + 11.0982i) q^{98} -9.88368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{3} - 8 q^{4} + 12 q^{9} - 4 q^{11} - 24 q^{12} - 16 q^{14} - 16 q^{16} + 24 q^{17} + 72 q^{19} - 24 q^{22} - 60 q^{23} - 72 q^{26} - 24 q^{29} + 96 q^{31} - 12 q^{33} - 48 q^{36} + 24 q^{37}+ \cdots - 24 q^{99}+O(q^{100}) \) 8 * q + 12 * q^3 - 8 * q^4 + 12 * q^9 - 4 * q^11 - 24 * q^12 - 16 * q^14 - 16 * q^16 + 24 * q^17 + 72 * q^19 - 24 * q^22 - 60 * q^23 - 72 * q^26 - 24 * q^29 + 96 * q^31 - 12 * q^33 - 48 * q^36 + 24 * q^37 + 180 * q^38 - 12 * q^39 - 12 * q^42 + 112 * q^43 - 8 * q^44 + 32 * q^46 - 84 * q^47 - 264 * q^49 + 24 * q^51 - 24 * q^52 - 44 * q^53 + 40 * q^56 + 144 * q^57 - 104 * q^58 + 312 * q^59 - 204 * q^61 + 64 * q^64 - 36 * q^66 - 120 * q^67 - 48 * q^68 - 64 * q^71 - 84 * q^73 - 16 * q^74 - 228 * q^77 - 144 * q^78 - 144 * q^79 - 36 * q^81 + 60 * q^82 + 176 * q^86 - 36 * q^87 + 24 * q^88 - 336 * q^89 - 296 * q^91 + 240 * q^92 + 96 * q^93 + 36 * q^94 - 24 * q^99

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