LMFDB - Embedded newform 1050.3.q.b.199.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(199,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1050.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.22986704741655040229376.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 31x^{12} + 880x^{8} - 2511x^{4} + 6561 $ x^16 - 31x^12 + 880x^8 - 2511*x^4 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.3
Root			$0.596002 + 2.22431i$ of defining polynomial
Character	$\chi$	$=$	1050.199
Dual form			1050.3.q.b.649.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-6.98615 + 0.440173i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-6.98615 + 0.440173i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-3.76860 + 6.52741i) q^{11} +(-1.73205 - 3.00000i) q^{12} +21.3906 q^{13} +(8.24500 - 5.47905i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(10.4937 - 18.1757i) q^{17} +(3.67423 + 2.12132i) q^{18} +(-20.8728 + 12.0509i) q^{19} +(-5.38992 + 10.8604i) q^{21} -10.6592i q^{22} +(-4.83250 + 2.79005i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-26.1981 + 15.1255i) q^{26} -5.19615 q^{27} +(-6.22374 + 12.5405i) q^{28} +9.96625 q^{29} +(5.70073 + 3.29132i) q^{31} +(4.89898 + 2.82843i) q^{32} +(6.52741 + 11.3058i) q^{33} +29.6807i q^{34} -6.00000 q^{36} +(19.3960 - 11.1983i) q^{37} +(17.0426 - 29.5187i) q^{38} +(18.5248 - 32.0860i) q^{39} -51.0827i q^{41} +(-1.07820 - 17.1125i) q^{42} -34.7656i q^{43} +(7.53720 + 13.0548i) q^{44} +(3.94572 - 6.83419i) q^{46} +(-38.8246 - 67.2462i) q^{47} -6.92820 q^{48} +(48.6125 - 6.15023i) q^{49} +(-18.1757 - 31.4812i) q^{51} +(21.3906 - 37.0497i) q^{52} +(43.1262 + 24.8989i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-1.24500 - 19.7598i) q^{56} +41.7457i q^{57} +(-12.2061 + 7.04720i) q^{58} +(-72.9362 - 42.1098i) q^{59} +(-72.4404 + 41.8235i) q^{61} -9.30925 q^{62} +(11.6228 + 17.4903i) q^{63} -8.00000 q^{64} +(-15.9888 - 9.23115i) q^{66} +(-57.6618 - 33.2911i) q^{67} +(-20.9874 - 36.3513i) q^{68} +9.66501i q^{69} -68.1049 q^{71} +(7.34847 - 4.24264i) q^{72} +(43.8283 - 75.9128i) q^{73} +(-15.8368 + 27.4301i) q^{74} +48.2038i q^{76} +(23.4548 - 47.2603i) q^{77} +52.3962i q^{78} +(49.3730 + 85.5165i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(36.1209 + 62.5632i) q^{82} +26.9448 q^{83} +(13.4209 + 20.1960i) q^{84} +(24.5830 + 42.5790i) q^{86} +(8.63103 - 14.9494i) q^{87} +(-18.4623 - 10.6592i) q^{88} +(-12.0453 + 6.95436i) q^{89} +(-149.438 + 9.41559i) q^{91} +11.1602i q^{92} +(9.87395 - 5.70073i) q^{93} +(95.1005 + 54.9063i) q^{94} +(8.48528 - 4.89898i) q^{96} -3.69132 q^{97} +(-55.1890 + 41.9067i) q^{98} +22.6116 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4} - 24 q^{9}+O(q^{10}) $ 16 * q + 16 * q^4 - 24 * q^9	$ 16 q + 16 q^{4} - 24 q^{9} - 8 q^{11} + 32 q^{14} - 32 q^{16} - 144 q^{19} - 144 q^{26} + 48 q^{29} + 192 q^{31} - 96 q^{36} + 24 q^{39} + 16 q^{44} + 64 q^{46} + 528 q^{49} + 48 q^{51} + 80 q^{56} - 624 q^{59} - 408 q^{61} - 128 q^{64} - 72 q^{66} - 128 q^{71} + 32 q^{74} + 288 q^{79} - 72 q^{81} + 352 q^{86} + 672 q^{89} - 592 q^{91} - 72 q^{94} + 48 q^{99}+O(q^{100}) $ 16 * q + 16 * q^4 - 24 * q^9 - 8 * q^11 + 32 * q^14 - 32 * q^16 - 144 * q^19 - 144 * q^26 + 48 * q^29 + 192 * q^31 - 96 * q^36 + 24 * q^39 + 16 * q^44 + 64 * q^46 + 528 * q^49 + 48 * q^51 + 80 * q^56 - 624 * q^59 - 408 * q^61 - 128 * q^64 - 72 * q^66 - 128 * q^71 + 32 * q^74 + 288 * q^79 - 72 * q^81 + 352 * q^86 + 672 * q^89 - 592 * q^91 - 72 * q^94 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$			2.44949i			0.408248i
$7$	−6.98615	+	0.440173i	−0.998021	+	0.0628819i
$7$	−6.98615	+	0.440173i	−0.998021	+	0.0628819i
$8$			2.82843i			0.353553i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$		0			0
$11$	−3.76860	+	6.52741i	−0.342600	+	0.593401i	−0.984915	−	0.173040i	$-0.944641\pi$
$11$	−3.76860	+	6.52741i	−0.342600	+	0.593401i	0.642315	+	0.766441i	$0.277974\pi$
$12$	−1.73205	−	3.00000i	−0.144338	−	0.250000i
$13$	21.3906			1.64543			0.822717	−	0.568451i	$-0.192457\pi$
$13$	21.3906			1.64543			0.822717	+	0.568451i	$0.192457\pi$
$14$	8.24500	−	5.47905i	0.588928	−	0.391361i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	10.4937	−	18.1757i	0.617278	−	1.06916i	−0.372703	−	0.927951i	$-0.621569\pi$
$17$	10.4937	−	18.1757i	0.617278	−	1.06916i	0.989980	−	0.141205i	$-0.0450978\pi$
$18$	3.67423	+	2.12132i	0.204124	+	0.117851i
$19$	−20.8728	+	12.0509i	−1.09857	+	0.634260i	−0.935845	−	0.352411i	$-0.885362\pi$
$19$	−20.8728	+	12.0509i	−1.09857	+	0.634260i	−0.162726	+	0.986671i	$0.552029\pi$
$20$		0			0
$21$	−5.38992	+	10.8604i	−0.256663	+	0.517163i
$22$		−	10.6592i		−	0.484510i
$23$	−4.83250	+	2.79005i	−0.210109	+	0.121306i	−0.601362	−	0.798977i	$-0.705375\pi$
$23$	−4.83250	+	2.79005i	−0.210109	+	0.121306i	0.391253	+	0.920283i	$0.372042\pi$
$24$	4.24264	+	2.44949i	0.176777	+	0.102062i
$25$		0			0
$26$	−26.1981	+	15.1255i	−1.00762	+	0.581749i
$27$	−5.19615			−0.192450
$28$	−6.22374	+	12.5405i	−0.222277	+	0.447876i
$29$	9.96625			0.343664			0.171832	−	0.985126i	$-0.445031\pi$
$29$	9.96625			0.343664			0.171832	+	0.985126i	$0.445031\pi$
$30$		0			0
$31$	5.70073	+	3.29132i	0.183894	+	0.106171i	0.589121	−	0.808045i	$-0.299474\pi$
$31$	5.70073	+	3.29132i	0.183894	+	0.106171i	−0.405227	+	0.914216i	$0.632807\pi$
$32$	4.89898	+	2.82843i	0.153093	+	0.0883883i
$33$	6.52741	+	11.3058i	0.197800	+	0.342600i
$34$			29.6807i			0.872962i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	19.3960	−	11.1983i	0.524216	−	0.302656i	−0.214442	−	0.976737i	$-0.568793\pi$
$37$	19.3960	−	11.1983i	0.524216	−	0.302656i	0.738658	+	0.674080i	$0.235460\pi$
$38$	17.0426	−	29.5187i	0.448490	−	0.776807i
$39$	18.5248	−	32.0860i	0.474996	−	0.822717i
$40$		0			0
$41$		−	51.0827i		−	1.24592i	−0.782254	−	0.622959i	$-0.785930\pi$
$41$		−	51.0827i		−	1.24592i	0.782254	−	0.622959i	$-0.214070\pi$
$42$	−1.07820	−	17.1125i	−0.0256714	−	0.407440i
$43$		−	34.7656i		−	0.808503i	−0.914648	−	0.404252i	$-0.867532\pi$
$43$		−	34.7656i		−	0.808503i	0.914648	−	0.404252i	$-0.132468\pi$
$44$	7.53720	+	13.0548i	0.171300	+	0.296700i
$45$		0			0
$46$	3.94572	−	6.83419i	0.0857766	−	0.148569i
$47$	−38.8246	−	67.2462i	−0.826056	−	1.43077i	−0.901110	−	0.433591i	$-0.857246\pi$
$47$	−38.8246	−	67.2462i	−0.826056	−	1.43077i	0.0750536	−	0.997179i	$-0.476087\pi$
$48$	−6.92820			−0.144338
$49$	48.6125	−	6.15023i	0.992092	−	0.125515i
$50$		0			0
$51$	−18.1757	−	31.4812i	−0.356385	−	0.617278i
$52$	21.3906	−	37.0497i	0.411359	−	0.712494i
$53$	43.1262	+	24.8989i	0.813703	+	0.469791i	0.848240	−	0.529612i	$-0.177662\pi$
$53$	43.1262	+	24.8989i	0.813703	+	0.469791i	−0.0345374	+	0.999403i	$0.510996\pi$
$54$	6.36396	−	3.67423i	0.117851	−	0.0680414i
$55$		0			0
$56$	−1.24500	−	19.7598i	−0.0222321	−	0.352854i
$57$			41.7457i			0.732381i
$58$	−12.2061	+	7.04720i	−0.210450	+	0.121504i
$59$	−72.9362	−	42.1098i	−1.23621	−	0.713725i	−0.267890	−	0.963449i	$-0.586327\pi$
$59$	−72.9362	−	42.1098i	−1.23621	−	0.713725i	−0.968317	+	0.249725i	$0.919660\pi$
$60$		0			0
$61$	−72.4404	+	41.8235i	−1.18755	+	0.685631i	−0.957749	−	0.287607i	$-0.907140\pi$
$61$	−72.4404	+	41.8235i	−1.18755	+	0.685631i	−0.229799	+	0.973238i	$0.573807\pi$
$62$	−9.30925			−0.150149
$63$	11.6228	+	17.4903i	0.184489	+	0.277624i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	−15.9888	−	9.23115i	−0.242255	−	0.139866i
$67$	−57.6618	−	33.2911i	−0.860625	−	0.496882i	0.00359682	−	0.999994i	$-0.498855\pi$
$67$	−57.6618	−	33.2911i	−0.860625	−	0.496882i	−0.864221	+	0.503112i	$0.832188\pi$
$68$	−20.9874	−	36.3513i	−0.308639	−	0.534578i
$69$			9.66501i			0.140073i
$70$		0			0
$71$	−68.1049			−0.959224			−0.479612	−	0.877481i	$-0.659223\pi$
$71$	−68.1049			−0.959224			−0.479612	+	0.877481i	$0.659223\pi$
$72$	7.34847	−	4.24264i	0.102062	−	0.0589256i
$73$	43.8283	−	75.9128i	0.600387	−	1.03990i	−0.392375	−	0.919805i	$-0.628346\pi$
$73$	43.8283	−	75.9128i	0.600387	−	1.03990i	0.992762	−	0.120096i	$-0.0383202\pi$
$74$	−15.8368	+	27.4301i	−0.214010	+	0.370677i
$75$		0			0
$76$			48.2038i			0.634260i
$77$	23.4548	−	47.2603i	0.304608	−	0.613770i
$78$			52.3962i			0.671746i
$79$	49.3730	+	85.5165i	0.624974	+	1.08249i	0.988546	+	0.150921i	$0.0482238\pi$
$79$	49.3730	+	85.5165i	0.624974	+	1.08249i	−0.363572	+	0.931566i	$0.618443\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	36.1209	+	62.5632i	0.440499	+	0.762966i
$83$	26.9448			0.324636			0.162318	−	0.986739i	$-0.448103\pi$
$83$	26.9448			0.324636			0.162318	+	0.986739i	$0.448103\pi$
$84$	13.4209	+	20.1960i	0.159772	+	0.240429i
$85$		0			0
$86$	24.5830	+	42.5790i	0.285849	+	0.495105i
$87$	8.63103	−	14.9494i	0.0992072	−	0.171832i
$88$	−18.4623	−	10.6592i	−0.209799	−	0.121127i
$89$	−12.0453	+	6.95436i	−0.135341	+	0.0781389i	−0.566142	−	0.824308i	$-0.691564\pi$
$89$	−12.0453	+	6.95436i	−0.135341	+	0.0781389i	0.430801	+	0.902447i	$0.358231\pi$
$90$		0			0
$91$	−149.438	+	9.41559i	−1.64218	+	0.103468i
$92$			11.1602i			0.121306i
$93$	9.87395	−	5.70073i	0.106171	−	0.0612981i
$94$	95.1005	+	54.9063i	1.01171	+	0.584110i
$95$		0			0
$96$	8.48528	−	4.89898i	0.0883883	−	0.0510310i
$97$	−3.69132			−0.0380549			−0.0190274	−	0.999819i	$-0.506057\pi$
$97$	−3.69132			−0.0380549			−0.0190274	+	0.999819i	$0.506057\pi$
$98$	−55.1890	+	41.9067i	−0.563153	+	0.427619i
$99$	22.6116			0.228400
$100$		0			0
$101$	−158.170	−	91.3195i	−1.56604	−	0.904154i	−0.996624	−	0.0821041i	$-0.973836\pi$
$101$	−158.170	−	91.3195i	−1.56604	−	0.904154i	−0.569416	−	0.822049i	$-0.692831\pi$
$102$	44.5211	+	25.7043i	0.436481	+	0.252003i
$103$	−45.5253	−	78.8521i	−0.441993	−	0.765555i	0.555844	−	0.831287i	$-0.312395\pi$
$103$	−45.5253	−	78.8521i	−0.441993	−	0.765555i	−0.997837	+	0.0657318i	$0.979062\pi$
$104$			60.5019i			0.581749i
$105$		0			0
$106$	−70.4249			−0.664385
$107$	−44.6318	+	25.7682i	−0.417120	+	0.240824i	−0.693844	−	0.720125i	$-0.744084\pi$
$107$	−44.6318	+	25.7682i	−0.417120	+	0.240824i	0.276724	+	0.960949i	$0.410751\pi$
$108$	−5.19615	+	9.00000i	−0.0481125	+	0.0833333i
$109$	19.1807	−	33.2219i	0.175970	−	0.304788i	−0.764527	−	0.644592i	$-0.777027\pi$
$109$	19.1807	−	33.2219i	0.175970	−	0.304788i	0.940496	+	0.339804i	$0.110361\pi$
$110$		0			0
$111$		−	38.7920i		−	0.349477i
$112$	15.4971	+	23.3204i	0.138367	+	0.208218i
$113$		−	198.558i		−	1.75715i	−0.477608	−	0.878573i	$-0.658496\pi$
$113$		−	198.558i		−	1.75715i	0.477608	−	0.878573i	$-0.341504\pi$
$114$	−29.5187	−	51.1278i	−0.258936	−	0.448490i
$115$		0			0
$116$	9.96625	−	17.2621i	0.0859160	−	0.148811i
$117$	−32.0860	−	55.5745i	−0.274239	−	0.474996i
$118$	119.104			1.00936
$119$	−65.3102	+	131.597i	−0.548825	+	1.10586i
$120$		0			0
$121$	32.0953	+	55.5907i	0.265250	+	0.459427i
$122$	59.1474	−	102.446i	0.484814	−	0.839723i
$123$	−76.6240	−	44.2389i	−0.622959	−	0.359666i
$124$	11.4015	−	6.58263i	0.0919472	−	0.0530857i
$125$		0			0
$126$	−26.6025	−	13.2026i	−0.211131	−	0.104782i
$127$			74.1132i			0.583569i	0.956484	+	0.291784i	$0.0942490\pi$
$127$			74.1132i			0.583569i	−0.956484	+	0.291784i	$0.905751\pi$
$128$	9.79796	−	5.65685i	0.0765466	−	0.0441942i
$129$	−52.1485	−	30.1079i	−0.404252	−	0.233395i
$130$		0			0
$131$	17.3500	−	10.0170i	0.132443	−	0.0764657i	−0.432315	−	0.901723i	$-0.642303\pi$
$131$	17.3500	−	10.0170i	0.132443	−	0.0764657i	0.564757	+	0.825257i	$0.308970\pi$
$132$	26.1096			0.197800
$133$	140.516	−	93.3773i	1.05651	−	0.702085i
$134$	94.1614			0.702697
$135$		0			0
$136$	51.4085	+	29.6807i	0.378004	+	0.218241i
$137$	−74.6259	−	43.0853i	−0.544715	−	0.314491i	0.202273	−	0.979329i	$-0.435167\pi$
$137$	−74.6259	−	43.0853i	−0.544715	−	0.314491i	−0.746988	+	0.664838i	$0.768501\pi$
$138$	−6.83419	−	11.8372i	−0.0495231	−	0.0857766i
$139$		−	232.502i		−	1.67268i	−0.548213	−	0.836339i	$-0.684692\pi$
$139$		−	232.502i		−	1.67268i	0.548213	−	0.836339i	$-0.315308\pi$
$140$		0			0
$141$	−134.492			−0.953847
$142$	83.4111	−	48.1574i	0.587402	−	0.339137i
$143$	−80.6128	+	139.625i	−0.563726	+	0.976402i
$144$	−6.00000	+	10.3923i	−0.0416667	+	0.0721688i
$145$		0			0
$146$			123.965i			0.849076i
$147$	32.8743	−	78.2450i	0.223635	−	0.532279i
$148$		−	44.7931i		−	0.302656i
$149$	−109.963	−	190.462i	−0.738008	−	1.27827i	−0.953391	−	0.301738i	$-0.902433\pi$
$149$	−109.963	−	190.462i	−0.738008	−	1.27827i	0.215383	−	0.976530i	$-0.430900\pi$
$150$		0			0
$151$	130.461	−	225.965i	0.863980	−	1.49646i	−0.00407633	−	0.999992i	$-0.501298\pi$
$151$	130.461	−	225.965i	0.863980	−	1.49646i	0.868056	−	0.496466i	$-0.165369\pi$
$152$	−34.0852	−	59.0373i	−0.224245	−	0.388403i
$153$	−62.9623			−0.411518
$154$	4.69190	+	74.4668i	0.0304669	+	0.483551i
$155$		0			0
$156$	−37.0497	−	64.1719i	−0.237498	−	0.411359i
$157$	−57.0954	+	98.8921i	−0.363665	+	0.629886i	−0.988561	−	0.150822i	$-0.951808\pi$
$157$	−57.0954	+	98.8921i	−0.363665	+	0.629886i	0.624896	+	0.780708i	$0.285141\pi$
$158$	−120.939	−	69.8239i	−0.765434	−	0.441923i
$159$	74.6968	−	43.1262i	0.469791	−	0.271234i
$160$		0			0
$161$	32.5325	−	21.6188i	0.202065	−	0.134278i
$162$		−	12.7279i		−	0.0785674i
$163$	42.1894	−	24.3581i	0.258831	−	0.149436i	−0.364970	−	0.931019i	$-0.618921\pi$
$163$	42.1894	−	24.3581i	0.258831	−	0.149436i	0.623801	+	0.781583i	$0.285588\pi$
$164$	−88.4777	−	51.0827i	−0.539498	−	0.311480i
$165$		0			0
$166$	−33.0005	+	19.0528i	−0.198798	+	0.114776i
$167$	49.6127			0.297082			0.148541	−	0.988906i	$-0.452542\pi$
$167$	49.6127			0.297082			0.148541	+	0.988906i	$0.452542\pi$
$168$	−30.7179	−	15.2450i	−0.182845	−	0.0907440i
$169$	288.560			1.70745
$170$		0			0
$171$	62.6185	+	36.1528i	0.366190	+	0.211420i
$172$	−60.2159	−	34.7656i	−0.350092	−	0.202126i
$173$	−117.670	−	203.811i	−0.680176	−	1.17810i	−0.974927	−	0.222525i	$-0.928570\pi$
$173$	−117.670	−	203.811i	−0.680176	−	1.17810i	0.294751	−	0.955574i	$-0.404763\pi$
$174$			24.4122i			0.140300i
$175$		0			0
$176$	30.1488			0.171300
$177$	−126.329	+	72.9362i	−0.713725	+	0.412069i
$178$	9.83495	−	17.0346i	0.0552525	−	0.0957002i
$179$	−22.1049	+	38.2868i	−0.123491	+	0.213893i	−0.921142	−	0.389226i	$-0.872742\pi$
$179$	−22.1049	+	38.2868i	−0.123491	+	0.213893i	0.797651	+	0.603119i	$0.206076\pi$
$180$		0			0
$181$			117.049i			0.646679i	0.946283	+	0.323340i	$0.104806\pi$
$181$			117.049i			0.646679i	−0.946283	+	0.323340i	$0.895194\pi$
$182$	176.366	−	117.200i	0.969043	−	0.643958i
$183$			144.881i			0.791699i
$184$	−7.89145	−	13.6684i	−0.0428883	−	0.0742847i
$185$		0			0
$186$	−8.06204	+	13.9639i	−0.0433443	+	0.0750746i
$187$	79.0933	+	136.994i	0.422959	+	0.732586i
$188$	−155.299			−0.826056
$189$	36.3011	−	2.28721i	0.192069	−	0.0121016i
$190$		0			0
$191$	−117.156	−	202.920i	−0.613383	−	1.06241i	−0.990666	−	0.136313i	$-0.956475\pi$
$191$	−117.156	−	202.920i	−0.613383	−	1.06241i	0.377283	−	0.926098i	$-0.376858\pi$
$192$	−6.92820	+	12.0000i	−0.0360844	+	0.0625000i
$193$	16.9438	+	9.78252i	0.0877918	+	0.0506866i	0.543253	−	0.839569i	$-0.317192\pi$
$193$	16.9438	+	9.78252i	0.0877918	+	0.0506866i	−0.455461	+	0.890256i	$0.650526\pi$
$194$	4.52093	−	2.61016i	0.0233037	−	0.0134544i
$195$		0			0
$196$	37.9600	−	90.3495i	0.193673	−	0.460967i
$197$			179.443i			0.910877i	0.890267	+	0.455438i	$0.150517\pi$
$197$			179.443i			0.910877i	−0.890267	+	0.455438i	$0.849483\pi$
$198$	−27.6934	+	15.9888i	−0.139866	+	0.0807516i
$199$	221.630	+	127.958i	1.11372	+	0.643006i	0.939790	−	0.341753i	$-0.111021\pi$
$199$	221.630	+	127.958i	1.11372	+	0.643006i	0.173928	+	0.984758i	$0.444354\pi$
$200$		0			0
$201$	−99.8732	+	57.6618i	−0.496882	+	0.286875i
$202$	258.291			1.27867
$203$	−69.6257	+	4.38688i	−0.342984	+	0.0216102i
$204$	−72.7026			−0.356385
$205$		0			0
$206$	111.514	+	64.3825i	0.541329	+	0.312536i
$207$	14.4975	+	8.37014i	0.0700363	+	0.0404355i
$208$	−42.7813	−	74.0994i	−0.205679	−	0.356247i
$209$		−	181.661i		−	0.869190i
$210$		0			0
$211$	196.891			0.933132			0.466566	−	0.884486i	$-0.345491\pi$
$211$	196.891			0.933132			0.466566	+	0.884486i	$0.345491\pi$
$212$	86.2525	−	49.7979i	0.406851	−	0.234896i
$213$	−58.9806	+	102.157i	−0.276904	+	0.479612i
$214$	36.4417	−	63.1189i	0.170288	−	0.294948i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	−41.2749	−	20.4843i	−0.190207	−	0.0943977i
$218$			54.2512i			0.248859i
$219$	−75.9128	−	131.485i	−0.346634	−	0.600387i
$220$		0			0
$221$	224.467	−	388.789i	1.01569	−	1.75923i
$222$	27.4301	+	47.5103i	0.123559	+	0.214010i
$223$	431.015			1.93280			0.966401	−	0.257039i	$-0.0827470\pi$
$223$	431.015			1.93280			0.966401	+	0.257039i	$0.0827470\pi$
$224$	−35.4700	−	17.6034i	−0.158348	−	0.0785866i
$225$		0			0
$226$	140.401	+	243.182i	0.621245	+	1.07603i
$227$	87.5479	−	151.637i	0.385673	−	0.668006i	−0.606189	−	0.795321i	$-0.707302\pi$
$227$	87.5479	−	151.637i	0.385673	−	0.668006i	0.991862	+	0.127315i	$0.0406358\pi$
$228$	72.3057	+	41.7457i	0.317130	+	0.183095i
$229$	−29.0717	+	16.7846i	−0.126951	+	0.0732951i	−0.562131	−	0.827048i	$-0.690018\pi$
$229$	−29.0717	+	16.7846i	−0.126951	+	0.0732951i	0.435180	+	0.900344i	$0.356685\pi$
$230$		0			0
$231$	−50.5779	−	76.1108i	−0.218952	−	0.329484i
$232$			28.1888i			0.121504i
$233$	−134.159	+	77.4567i	−0.575790	+	0.332432i	−0.759458	−	0.650556i	$-0.774536\pi$
$233$	−134.159	+	77.4567i	−0.575790	+	0.332432i	0.183669	+	0.982988i	$0.441203\pi$
$234$	78.5942	+	45.3764i	0.335873	+	0.193916i
$235$		0			0
$236$	−145.872	+	84.2195i	−0.618104	+	0.356862i
$237$	171.033			0.721658
$238$	−13.0647	−	207.354i	−0.0548935	−	0.871235i
$239$	−316.591			−1.32465			−0.662325	−	0.749217i	$-0.730430\pi$
$239$	−316.591			−1.32465			−0.662325	+	0.749217i	$0.730430\pi$
$240$		0			0
$241$	202.219	+	116.751i	0.839084	+	0.484446i	0.856953	−	0.515395i	$-0.172355\pi$
$241$	202.219	+	116.751i	0.839084	+	0.484446i	−0.0178685	+	0.999840i	$0.505688\pi$
$242$	−78.6171	−	45.3896i	−0.324864	−	0.187560i
$243$	7.79423	+	13.5000i	0.0320750	+	0.0555556i
$244$			167.294i			0.685631i
$245$		0			0
$246$	125.126			0.508644
$247$	−446.484	+	257.777i	−1.80763	+	1.04363i
$248$	−9.30925	+	16.1241i	−0.0375373	+	0.0650165i
$249$	23.3349	−	40.4172i	0.0937143	−	0.162318i
$250$		0			0
$251$		−	56.6879i		−	0.225848i	−0.993604	−	0.112924i	$-0.963978\pi$
$251$		−	56.6879i		−	0.225848i	0.993604	−	0.112924i	$-0.0360217\pi$
$252$	41.9169	−	2.64104i	0.166337	−	0.0104803i
$253$		−	42.0583i		−	0.166238i
$254$	−52.4060	−	90.7698i	−0.206323	−	0.357361i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−145.219	−	251.528i	−0.565056	−	0.978706i	−0.997044	−	0.0768270i	$-0.975521\pi$
$257$	−145.219	−	251.528i	−0.565056	−	0.978706i	0.431988	−	0.901879i	$-0.357812\pi$
$258$	85.1581			0.330070
$259$	−130.574	+	86.7704i	−0.504147	+	0.335021i
$260$		0			0
$261$	−14.9494	−	25.8931i	−0.0572773	−	0.0992072i
$262$	−14.1662	+	24.5366i	−0.0540694	+	0.0936510i
$263$	385.031	+	222.298i	1.46399	+	0.845238i	0.999193	−	0.0401768i	$-0.0127921\pi$
$263$	385.031	+	222.298i	1.46399	+	0.845238i	0.464802	+	0.885415i	$0.346125\pi$
$264$	−31.9776	+	18.4623i	−0.121127	+	0.0699329i
$265$		0			0
$266$	−106.069	+	213.723i	−0.398755	+	0.803471i
$267$			24.0906i			0.0902270i
$268$	−115.324	+	66.5822i	−0.430312	+	0.248441i
$269$	144.956	+	83.6902i	0.538869	+	0.311116i	0.744620	−	0.667488i	$-0.232631\pi$
$269$	144.956	+	83.6902i	0.538869	+	0.311116i	−0.205752	+	0.978604i	$0.565964\pi$
$270$		0			0
$271$	2.24099	−	1.29384i	0.00826933	−	0.00477430i	−0.495860	−	0.868403i	$-0.665147\pi$
$271$	2.24099	−	1.29384i	0.00826933	−	0.00477430i	0.504129	+	0.863628i	$0.331814\pi$
$272$	−83.9498			−0.308639
$273$	−115.294	+	232.311i	−0.422322	+	0.850957i
$274$	121.864			0.444758
$275$		0			0
$276$	16.7403	+	9.66501i	0.0606532	+	0.0350181i
$277$	−440.903	−	254.556i	−1.59171	−	0.918973i	−0.993014	−	0.117996i	$-0.962353\pi$
$277$	−440.903	−	254.556i	−1.59171	−	0.918973i	−0.598694	−	0.800978i	$-0.704314\pi$
$278$	164.404	+	284.756i	0.591381	+	1.02430i
$279$		−	19.7479i		−	0.0707810i
$280$		0			0
$281$	210.688			0.749779			0.374890	−	0.927069i	$-0.377681\pi$
$281$	210.688			0.749779			0.374890	+	0.927069i	$0.377681\pi$
$282$	164.719	−	95.1005i	0.584110	−	0.337236i
$283$	−19.7433	+	34.1964i	−0.0697643	+	0.120835i	−0.898797	−	0.438364i	$-0.855558\pi$
$283$	−19.7433	+	34.1964i	−0.0697643	+	0.120835i	0.829033	+	0.559199i	$0.188891\pi$
$284$	−68.1049	+	117.961i	−0.239806	+	0.415356i
$285$		0			0
$286$		−	228.007i		−	0.797229i
$287$	22.4852	+	356.871i	0.0783457	+	1.24345i
$288$		−	16.9706i		−	0.0589256i
$289$	−75.7363	−	131.179i	−0.262063	−	0.453907i
$290$		0			0
$291$	−3.19678	+	5.53698i	−0.0109855	+	0.0190274i
$292$	−87.6565	−	151.826i	−0.300194	−	0.519951i
$293$	89.6023			0.305810			0.152905	−	0.988241i	$-0.451137\pi$
$293$	89.6023			0.305810			0.152905	+	0.988241i	$0.451137\pi$
$294$	15.0649	+	119.076i	0.0512412	+	0.405020i
$295$		0			0
$296$	31.6735	+	54.8602i	0.107005	+	0.185338i
$297$	19.5822	−	33.9174i	0.0659334	−	0.114200i
$298$	269.354	+	155.511i	0.903871	+	0.521850i
$299$	−103.370	+	59.6809i	−0.345720	+	0.199602i
$300$		0			0
$301$	15.3029	+	242.878i	0.0508402	+	0.806903i
$302$			368.999i			1.22185i
$303$	−273.959	+	158.170i	−0.904154	+	0.522013i
$304$	83.4914	+	48.2038i	0.274643	+	0.158565i
$305$		0			0
$306$	77.1128	−	44.5211i	0.252003	−	0.145494i
$307$	−470.478			−1.53250			−0.766251	−	0.642542i	$-0.777880\pi$
$307$	−470.478			−1.53250			−0.766251	+	0.642542i	$0.777880\pi$
$308$	−58.4024	−	87.8852i	−0.189618	−	0.285341i
$309$	−157.704			−0.510370
$310$		0			0
$311$	217.631	+	125.649i	0.699778	+	0.404017i	0.807265	−	0.590189i	$-0.200947\pi$
$311$	217.631	+	125.649i	0.699778	+	0.404017i	−0.107487	+	0.994207i	$0.534280\pi$
$312$	90.7528	+	52.3962i	0.290874	+	0.167936i
$313$	−194.231	−	336.417i	−0.620545	−	1.07482i	−0.989384	−	0.145322i	$-0.953578\pi$
$313$	−194.231	−	336.417i	−0.620545	−	1.07482i	0.368839	−	0.929493i	$-0.379755\pi$
$314$		−	161.490i		−	0.514300i
$315$		0			0
$316$	197.492			0.624974
$317$	−129.366	+	74.6898i	−0.408096	+	0.235614i	−0.689971	−	0.723837i	$-0.742377\pi$
$317$	−129.366	+	74.6898i	−0.408096	+	0.235614i	0.281875	+	0.959451i	$0.409044\pi$
$318$	−60.9897	+	105.637i	−0.191792	+	0.332193i
$319$	−37.5588	+	65.0538i	−0.117739	+	0.203930i
$320$		0			0
$321$			89.2636i			0.278080i
$322$	−24.5572	+	49.4815i	−0.0762645	+	0.153669i
$323$			505.837i			1.56606i
$324$	9.00000	+	15.5885i	0.0277778	+	0.0481125i
$325$		0			0
$326$	−34.4475	+	59.6648i	−0.105667	+	0.183021i
$327$	−33.2219	−	57.5420i	−0.101596	−	0.175970i
$328$	144.484			0.440499
$329$	300.835	+	452.702i	0.914391	+	1.37600i
$330$		0			0
$331$	235.465	+	407.838i	0.711375	+	1.23214i	0.964341	+	0.264663i	$0.0852607\pi$
$331$	235.465	+	407.838i	0.711375	+	1.23214i	−0.252966	+	0.967475i	$0.581406\pi$
$332$	26.9448	−	46.6697i	0.0811590	−	0.140571i
$333$	−58.1880	−	33.5948i	−0.174739	−	0.100885i
$334$	−60.7628	+	35.0814i	−0.181925	+	0.105034i
$335$		0			0
$336$	48.4014	−	3.04961i	0.144052	−	0.00907622i
$337$			532.478i			1.58005i	0.613072	+	0.790027i	$0.289934\pi$
$337$			532.478i			1.58005i	−0.613072	+	0.790027i	$0.710066\pi$
$338$	−353.412	+	204.042i	−1.04560	+	0.603676i
$339$	−297.836	−	171.956i	−0.878573	−	0.507244i
$340$		0			0
$341$	−42.9675	+	24.8073i	−0.126004	+	0.0727487i
$342$	−102.256			−0.298993
$343$	−336.907	+	64.3643i	−0.982236	+	0.187651i
$344$	98.3321			0.285849
$345$		0			0
$346$	288.232	+	166.411i	0.833042	+	0.480957i
$347$	389.385	+	224.812i	1.12215	+	0.647872i	0.941948	−	0.335758i	$-0.108992\pi$
$347$	389.385	+	224.812i	1.12215	+	0.647872i	0.180199	+	0.983630i	$0.442326\pi$
$348$	−17.2621	−	29.8988i	−0.0496036	−	0.0859160i
$349$			330.676i			0.947495i	0.880661	+	0.473747i	$0.157099\pi$
$349$			330.676i			0.947495i	−0.880661	+	0.473747i	$0.842901\pi$
$350$		0			0
$351$	−111.149			−0.316664
$352$	−36.9246	+	21.3184i	−0.104899	+	0.0605637i
$353$	−135.686	+	235.014i	−0.384379	+	0.665763i	−0.991683	−	0.128706i	$-0.958918\pi$
$353$	−135.686	+	235.014i	−0.384379	+	0.665763i	0.607304	+	0.794469i	$0.292251\pi$
$354$	103.147	−	178.657i	0.291377	−	0.504680i
$355$		0			0
$356$			27.8174i			0.0781389i
$357$	140.835	+	211.932i	0.394496	+	0.593646i
$358$		−	62.5221i		−	0.174643i
$359$	−3.79200	−	6.56794i	−0.0105627	−	0.0182951i	0.860696	−	0.509120i	$-0.170029\pi$
$359$	−3.79200	−	6.56794i	−0.0105627	−	0.0182951i	−0.871258	+	0.490825i	$0.836696\pi$
$360$		0			0
$361$	109.950	−	190.440i	0.304572	−	0.527534i
$362$	−82.7661	−	143.355i	−0.228636	−	0.396009i
$363$	111.181			0.306285
$364$	−133.130	+	268.250i	−0.365741	+	0.736951i
$365$		0			0
$366$	−102.446	−	177.442i	−0.279908	−	0.484814i
$367$	265.706	−	460.216i	0.723995	−	1.25400i	−0.235392	−	0.971901i	$-0.575637\pi$
$367$	265.706	−	460.216i	0.723995	−	1.25400i	0.959386	−	0.282095i	$-0.0910293\pi$
$368$	19.3300	+	11.1602i	0.0525272	+	0.0303266i
$369$	−132.717	+	76.6240i	−0.359666	+	0.207653i
$370$		0			0
$371$	−312.246	−	154.965i	−0.841634	−	0.417695i
$372$		−	22.8029i		−	0.0612981i
$373$	497.937	−	287.484i	1.33495	−	0.770734i	0.348897	−	0.937161i	$-0.386556\pi$
$373$	497.937	−	287.484i	1.33495	−	0.770734i	0.986054	+	0.166427i	$0.0532229\pi$
$374$	−193.738	−	111.855i	−0.518016	−	0.299077i
$375$		0			0
$376$	190.201	−	109.813i	0.505854	−	0.292055i
$377$	213.185			0.565476
$378$	−42.8423	+	28.4700i	−0.113339	+	0.0753174i
$379$	−627.464			−1.65558			−0.827789	−	0.561040i	$-0.810402\pi$
$379$	−627.464			−1.65558			−0.827789	+	0.561040i	$0.810402\pi$
$380$		0			0
$381$	111.170	+	64.1839i	0.291784	+	0.168462i
$382$	286.973	+	165.684i	0.751238	+	0.433727i
$383$	33.3056	+	57.6870i	0.0869597	+	0.150619i	0.906225	−	0.422797i	$-0.138952\pi$
$383$	33.3056	+	57.6870i	0.0869597	+	0.150619i	−0.819265	+	0.573415i	$0.805618\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	−27.6691			−0.0716817
$387$	−90.3238	+	52.1485i	−0.233395	+	0.134751i
$388$	−3.69132	+	6.39356i	−0.00951372	+	0.0164782i
$389$	274.525	−	475.491i	0.705719	−	1.22234i	−0.260713	−	0.965416i	$-0.583957\pi$
$389$	274.525	−	475.491i	0.705719	−	1.22234i	0.966431	−	0.256925i	$-0.0827092\pi$
$390$		0			0
$391$			117.112i			0.299519i
$392$	17.3955	+	137.497i	0.0443762	+	0.350757i
$393$		−	34.7000i		−	0.0882950i
$394$	−126.885	−	219.772i	−0.322044	−	0.557796i
$395$		0			0
$396$	22.6116	−	39.1644i	0.0571000	−	0.0989001i
$397$	259.283	+	449.091i	0.653106	+	1.13121i	0.982365	+	0.186973i	$0.0598676\pi$
$397$	259.283	+	449.091i	0.653106	+	1.13121i	−0.329259	+	0.944240i	$0.606799\pi$
$398$	−361.920			−0.909347
$399$	−18.3753	−	291.642i	−0.0460535	−	0.730931i
$400$		0			0
$401$	238.149	+	412.486i	0.593888	+	1.02864i	0.993703	+	0.112048i	$0.0357411\pi$
$401$	238.149	+	412.486i	0.593888	+	1.02864i	−0.399815	+	0.916596i	$0.630926\pi$
$402$	81.5462	−	141.242i	0.202851	−	0.351349i
$403$	121.942	+	70.4033i	0.302586	+	0.174698i
$404$	−316.340	+	182.639i	−0.783020	+	0.452077i
$405$		0			0
$406$	82.1717	−	54.6056i	0.202393	−	0.134497i
$407$			168.807i			0.414760i
$408$	89.0422	−	51.4085i	0.218241	−	0.126001i
$409$	93.2552	+	53.8409i	0.228008	+	0.131640i	0.609653	−	0.792669i	$-0.291309\pi$
$409$	93.2552	+	53.8409i	0.228008	+	0.131640i	−0.381645	+	0.924309i	$0.624642\pi$
$410$		0			0
$411$	−129.256	+	74.6259i	−0.314491	+	0.181572i
$412$	−182.101			−0.441993
$413$	528.079	+	262.080i	1.27864	+	0.634577i
$414$	−23.6743			−0.0571844
$415$		0			0
$416$	104.792	+	60.5019i	0.251905	+	0.145437i
$417$	−348.753	−	201.353i	−0.836339	−	0.482861i
$418$	128.454	+	222.488i	0.307305	+	0.532268i
$419$		−	323.811i		−	0.772818i	−0.922328	−	0.386409i	$-0.873715\pi$
$419$		−	323.811i		−	0.772818i	0.922328	−	0.386409i	$-0.126285\pi$
$420$		0			0
$421$	−238.957			−0.567595			−0.283797	−	0.958884i	$-0.591594\pi$
$421$	−238.957			−0.567595			−0.283797	+	0.958884i	$0.591594\pi$
$422$	−241.141	+	139.223i	−0.571424	+	0.329912i
$423$	−116.474	+	201.739i	−0.275352	+	0.476924i
$424$	−70.4249	+	121.979i	−0.166096	+	0.287687i
$425$		0			0
$426$		−	166.822i		−	0.391601i
$427$	487.670	−	324.071i	1.14208	−	0.758950i
$428$			103.073i			0.240824i
$429$	139.625	+	241.838i	0.325467	+	0.563726i
$430$		0			0
$431$	95.8960	−	166.097i	0.222497	−	0.385375i	−0.733069	−	0.680154i	$-0.761913\pi$
$431$	95.8960	−	166.097i	0.222497	−	0.385375i	0.955565	+	0.294779i	$0.0952461\pi$
$432$	10.3923	+	18.0000i	0.0240563	+	0.0416667i
$433$	122.083			0.281946			0.140973	−	0.990013i	$-0.454977\pi$
$433$	122.083			0.281946			0.140973	+	0.990013i	$0.454977\pi$
$434$	65.0358	−	4.09768i	0.149852	−	0.00944166i
$435$		0			0
$436$	−38.3614	−	66.4438i	−0.0879848	−	0.152394i
$437$	67.2454	−	116.472i	0.153880	−	0.266527i
$438$	185.948	+	107.357i	0.424538	+	0.245107i
$439$	217.656	−	125.664i	0.495800	−	0.286250i	−0.231177	−	0.972912i	$-0.574258\pi$
$439$	217.656	−	125.664i	0.495800	−	0.286250i	0.726978	+	0.686661i	$0.240924\pi$
$440$		0			0
$441$	−88.8975	−	117.074i	−0.201582	−	0.265473i
$442$			634.890i			1.43640i
$443$	−95.0802	+	54.8946i	−0.214628	+	0.123916i	−0.603460	−	0.797393i	$-0.706212\pi$
$443$	−95.0802	+	54.8946i	−0.214628	+	0.123916i	0.388832	+	0.921309i	$0.372879\pi$
$444$	−67.1897	−	38.7920i	−0.151328	−	0.0873693i
$445$		0			0
$446$	−527.883	+	304.773i	−1.18359	+	0.683349i
$447$	−380.924			−0.852178
$448$	55.8892	−	3.52139i	0.124753	−	0.00786024i
$449$	−806.490			−1.79619			−0.898095	−	0.439801i	$-0.855049\pi$
$449$	−806.490			−1.79619			−0.898095	+	0.439801i	$0.855049\pi$
$450$		0			0
$451$	333.437	+	192.510i	0.739329	+	0.426852i
$452$	−343.912	−	198.558i	−0.760867	−	0.439287i
$453$	−225.965	−	391.383i	−0.498819	−	0.863980i
$454$			247.623i			0.545425i
$455$		0			0
$456$	−118.075			−0.258936
$457$	−668.964	+	386.226i	−1.46382	+	0.845135i	−0.999185	−	0.0403698i	$-0.987146\pi$
$457$	−668.964	+	386.226i	−1.46382	+	0.845135i	−0.464631	+	0.885504i	$0.653813\pi$
$458$	23.7370	−	41.1137i	0.0518275	−	0.0897678i
$459$	−54.5270	+	94.4435i	−0.118795	+	0.205759i
$460$		0			0
$461$		−	793.611i		−	1.72150i	−0.509029	−	0.860749i	$-0.669995\pi$
$461$		−	793.611i		−	1.72150i	0.509029	−	0.860749i	$-0.330005\pi$
$462$	115.764	+	57.4523i	0.250570	+	0.124356i
$463$			274.227i			0.592284i	0.955144	+	0.296142i	$0.0957001\pi$
$463$			274.227i			0.592284i	−0.955144	+	0.296142i	$0.904300\pi$
$464$	−19.9325	−	34.5241i	−0.0429580	−	0.0744054i
$465$		0			0
$466$	109.540	−	189.730i	0.235065	−	0.407145i
$467$	198.815	+	344.357i	0.425727	+	0.737381i	0.996488	−	0.0837354i	$-0.0266851\pi$
$467$	198.815	+	344.357i	0.425727	+	0.737381i	−0.570761	+	0.821116i	$0.693352\pi$
$468$	−128.344			−0.274239
$469$	417.488	+	207.195i	0.890166	+	0.441781i
$470$		0			0
$471$	98.8921	+	171.286i	0.209962	+	0.363665i
$472$	119.104	−	206.295i	0.252340	−	0.437065i
$473$	226.930	+	131.018i	0.479766	+	0.276993i
$474$	−209.472	+	120.939i	−0.441923	+	0.255145i
$475$		0			0
$476$	162.622	+	244.717i	0.341643	+	0.514112i
$477$		−	149.394i		−	0.313194i
$478$	387.743	−	223.864i	0.811179	−	0.468334i
$479$	165.573	+	95.5938i	0.345665	+	0.199570i	0.662774	−	0.748819i	$-0.269379\pi$
$479$	165.573	+	95.5938i	0.345665	+	0.199570i	−0.317110	+	0.948389i	$0.602712\pi$
$480$		0			0
$481$	414.893	−	239.538i	0.862563	−	0.498001i
$482$	−330.223			−0.685110
$483$	−4.25428	−	67.5212i	−0.00880803	−	0.139795i
$484$	128.381			0.265250
$485$		0			0
$486$	−19.0919	−	11.0227i	−0.0392837	−	0.0226805i
$487$	164.561	+	95.0092i	0.337907	+	0.195091i	0.659346	−	0.751840i	$-0.270833\pi$
$487$	164.561	+	95.0092i	0.337907	+	0.195091i	−0.321439	+	0.946930i	$0.604167\pi$
$488$	−118.295	−	204.892i	−0.242407	−	0.419862i
$489$		−	84.3788i		−	0.172554i
$490$		0			0
$491$	−211.384			−0.430517			−0.215258	−	0.976557i	$-0.569059\pi$
$491$	−211.384			−0.430517			−0.215258	+	0.976557i	$0.569059\pi$
$492$	−153.248	+	88.4777i	−0.311480	+	0.179833i
$493$	104.583	−	181.143i	0.212136	−	0.367430i
$494$	364.552	−	631.423i	0.737960	−	1.27818i
$495$		0			0
$496$		−	26.3305i		−	0.0530857i
$497$	475.791	−	29.9779i	0.957325	−	0.0603178i
$498$			66.0010i			0.132532i
$499$	−126.864	−	219.734i	−0.254236	−	0.440349i	0.710452	−	0.703746i	$-0.248491\pi$
$499$	−126.864	−	219.734i	−0.254236	−	0.440349i	−0.964688	+	0.263396i	$0.915157\pi$
$500$		0			0
$501$	42.9658	−	74.4190i	0.0857601	−	0.148541i
$502$	40.0844	+	69.4282i	0.0798494	+	0.138303i
$503$	−217.815			−0.433033			−0.216516	−	0.976279i	$-0.569469\pi$
$503$	−217.815			−0.433033			−0.216516	+	0.976279i	$0.569469\pi$
$504$	−49.4700	+	32.8743i	−0.0981547	+	0.0652268i
$505$		0			0
$506$	29.7397	+	51.5107i	0.0587741	+	0.101800i
$507$	249.900	−	432.839i	0.492899	−	0.853727i
$508$	128.368	+	74.1132i	0.252693	+	0.145892i
$509$	24.6582	−	14.2364i	0.0484444	−	0.0279694i	−0.475582	−	0.879671i	$-0.657763\pi$
$509$	24.6582	−	14.2364i	0.0484444	−	0.0279694i	0.524027	+	0.851702i	$0.324429\pi$
$510$		0			0
$511$	−272.776	+	549.630i	−0.533808	+	1.07560i
$512$		−	22.6274i		−	0.0441942i
$513$	108.458	−	62.6185i	0.211420	−	0.122063i
$514$	355.714	+	205.371i	0.692050	+	0.399555i
$515$		0			0
$516$	−104.297	+	60.2159i	−0.202126	+	0.116697i
$517$	585.258			1.13203
$518$	98.5640	−	198.601i	0.190278	−	0.383400i
$519$	−407.622			−0.785399
$520$		0			0
$521$	671.401	+	387.634i	1.28868	+	0.744019i	0.978418	−	0.206633i	$-0.0662507\pi$
$521$	671.401	+	387.634i	1.28868	+	0.744019i	0.310260	+	0.950652i	$0.399584\pi$
$522$	36.6184	+	21.1416i	0.0701501	+	0.0405012i
$523$	51.2334	+	88.7388i	0.0979605	+	0.169673i	0.910840	−	0.412759i	$-0.135435\pi$
$523$	51.2334	+	88.7388i	0.0979605	+	0.169673i	−0.812880	+	0.582431i	$0.802101\pi$
$524$		−	40.0681i		−	0.0764657i
$525$		0			0
$526$	−628.752			−1.19535
$527$	119.644	−	69.0763i	0.227028	−	0.131075i
$528$	26.1096	−	45.2232i	0.0494501	−	0.0856500i
$529$	−248.931	+	431.162i	−0.470570	+	0.815050i
$530$		0			0
$531$			252.659i			0.475816i
$532$	−21.2180	−	336.759i	−0.0398835	−	0.633005i
$533$		−	1092.69i		−	2.05008i
$534$	−17.0346	−	29.5049i	−0.0319001	−	0.0552525i
$535$		0			0
$536$	94.1614	−	163.092i	0.175674	−	0.304277i
$537$	38.2868	+	66.3147i	0.0712976	+	0.123491i
$538$	−236.712			−0.439984
$539$	−143.056	+	340.491i	−0.265410	+	0.631709i
$540$		0			0
$541$	408.868	+	708.180i	0.755763	+	1.30902i	0.944994	+	0.327088i	$0.106067\pi$
$541$	408.868	+	708.180i	0.755763	+	1.30902i	−0.189231	+	0.981933i	$0.560599\pi$
$542$	−1.82976	+	3.16924i	−0.00337594	+	0.00584730i
$543$	175.573	+	101.367i	0.323340	+	0.186680i
$544$	102.817	−	59.3614i	0.189002	−	0.109120i
$545$		0			0
$546$	−23.0634	−	366.047i	−0.0422406	−	0.670416i
$547$		−	204.209i		−	0.373325i	−0.982424	−	0.186662i	$-0.940233\pi$
$547$		−	204.209i		−	0.373325i	0.982424	−	0.186662i	$-0.0597670\pi$
$548$	−149.252	+	86.1706i	−0.272357	+	0.157246i
$549$	217.321	+	125.471i	0.395849	+	0.228544i
$550$		0			0
$551$	−208.024	+	120.103i	−0.377539	+	0.217972i
$552$	−27.3368			−0.0495231
$553$	−382.569	−	575.698i	−0.691806	−	1.04105i
$554$	719.992			1.29962
$555$		0			0
$556$	−402.706	−	232.502i	−0.724291	−	0.418169i
$557$	−464.253	−	268.036i	−0.833487	−	0.481214i	0.0215578	−	0.999768i	$-0.493137\pi$
$557$	−464.253	−	268.036i	−0.833487	−	0.481214i	−0.855045	+	0.518553i	$0.826471\pi$
$558$	13.9639	+	24.1861i	0.0250249	+	0.0433443i
$559$		−	743.660i		−	1.33034i
$560$		0			0
$561$	273.987			0.488391
$562$	−258.039	+	148.979i	−0.459144	+	0.265087i
$563$	−494.806	+	857.029i	−0.878874	+	1.52225i	−0.0262960	+	0.999654i	$0.508371\pi$
$563$	−494.806	+	857.029i	−0.878874	+	1.52225i	−0.852578	+	0.522600i	$0.824962\pi$
$564$	−134.492	+	232.948i	−0.238462	+	0.413028i
$565$		0			0
$566$		−	55.8424i		−	0.0986616i
$567$	28.0068	−	56.4324i	0.0493948	−	0.0995281i
$568$		−	192.630i		−	0.339137i
$569$	248.330	+	430.120i	0.436432	+	0.755922i	0.997411	−	0.0719076i	$-0.0229087\pi$
$569$	248.330	+	430.120i	0.436432	+	0.755922i	−0.560979	+	0.827830i	$0.689575\pi$
$570$		0			0
$571$	71.0244	−	123.018i	0.124386	−	0.215443i	−0.797107	−	0.603838i	$-0.793637\pi$
$571$	71.0244	−	123.018i	0.124386	−	0.215443i	0.921493	+	0.388395i	$0.126971\pi$
$572$	161.226	+	279.251i	0.281863	+	0.488201i
$573$	−405.841			−0.708274
$574$	−279.884	−	421.176i	−0.487604	−	0.733757i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	189.689	−	328.551i	0.328751	−	0.569413i	−0.653514	−	0.756915i	$-0.726706\pi$
$577$	189.689	−	328.551i	0.328751	−	0.569413i	0.982264	+	0.187502i	$0.0600391\pi$
$578$	185.515	+	107.107i	0.320961	+	0.185307i
$579$	29.3476	−	16.9438i	0.0506866	−	0.0292639i
$580$		0			0
$581$	−188.240	+	11.8604i	−0.323993	+	0.0204137i
$582$		−	9.04185i		−	0.0155358i
$583$	−325.051	+	187.668i	−0.557549	+	0.321901i
$584$	214.714	+	123.965i	0.367661	+	0.212269i
$585$		0			0
$586$	−109.740	+	63.3584i	−0.187269	+	0.108120i
$587$	234.204			0.398984			0.199492	−	0.979899i	$-0.436071\pi$
$587$	234.204			0.398984			0.199492	+	0.979899i	$0.436071\pi$
$588$	−102.650	−	135.185i	−0.174575	−	0.229906i
$589$	−158.654			−0.269361
$590$		0			0
$591$	269.164	+	155.402i	0.455438	+	0.262948i
$592$	−77.5840	−	44.7931i	−0.131054	−	0.0756641i
$593$	286.272	+	495.838i	0.482753	+	0.836152i	0.999804	−	0.0198023i	$-0.00630369\pi$
$593$	286.272	+	495.838i	0.482753	+	0.836152i	−0.517051	+	0.855954i	$0.672970\pi$
$594$			55.3869i			0.0932439i
$595$		0			0
$596$	−439.853			−0.738008
$597$	383.874	−	221.630i	0.643006	−	0.371239i
$598$	84.4016	−	146.188i	0.141140	−	0.244461i
$599$	46.7105	−	80.9049i	0.0779807	−	0.135067i	−0.824398	−	0.566011i	$-0.808486\pi$
$599$	46.7105	−	80.9049i	0.0779807	−	0.135067i	0.902379	+	0.430944i	$0.141819\pi$
$600$		0			0
$601$			167.140i			0.278103i	0.990285	+	0.139051i	$0.0444053\pi$
$601$			167.140i			0.278103i	−0.990285	+	0.139051i	$0.955595\pi$
$602$	−190.483	−	286.643i	−0.316417	−	0.476151i
$603$			199.746i			0.331255i
$604$	−260.922	−	451.930i	−0.431990	−	0.748229i
$605$		0			0
$606$	223.686	−	387.436i	0.369119	−	0.639333i
$607$	−459.572	−	796.002i	−0.757120	−	1.31137i	−0.944314	−	0.329047i	$-0.893273\pi$
$607$	−459.572	−	796.002i	−0.757120	−	1.31137i	0.187194	−	0.982323i	$-0.440061\pi$
$608$	−136.341			−0.224245
$609$	−53.7173	+	108.238i	−0.0882058	+	0.177730i
$610$		0			0
$611$	−830.484	−	1438.44i	−1.35922	−	2.35424i
$612$	−62.9623	+	109.054i	−0.102880	+	0.178193i
$613$	−675.011	−	389.718i	−1.10116	−	0.635755i	−0.164635	−	0.986355i	$-0.552644\pi$
$613$	−675.011	−	389.718i	−1.10116	−	0.635755i	−0.936525	+	0.350600i	$0.885978\pi$
$614$	576.215	−	332.678i	0.938462	−	0.541821i
$615$		0			0
$616$	133.672	+	66.3402i	0.217000	+	0.107695i
$617$			510.821i			0.827911i	0.910297	+	0.413956i	$0.135853\pi$
$617$			510.821i			0.827911i	−0.910297	+	0.413956i	$0.864147\pi$
$618$	193.148	−	111.514i	0.312536	−	0.180443i
$619$	808.792	+	466.956i	1.30661	+	0.754372i	0.981529	−	0.191314i	$-0.0612749\pi$
$619$	808.792	+	466.956i	1.30661	+	0.754372i	0.325082	+	0.945686i	$0.394608\pi$
$620$		0			0
$621$	25.1104	−	14.4975i	0.0404355	−	0.0233454i
$622$	−355.390			−0.571367
$623$	81.0892	−	53.8862i	0.130159	−	0.0864947i
$624$	−148.199			−0.237498
$625$		0			0
$626$	475.766	+	274.684i	0.760009	+	0.438792i
$627$	−272.491	−	157.323i	−0.434595	−	0.250914i
$628$	114.191	+	197.784i	0.181832	+	0.314943i
$629$		−	470.047i		−	0.747292i
$630$		0			0
$631$	−614.861			−0.974423			−0.487212	−	0.873284i	$-0.661986\pi$
$631$	−614.861			−0.974423			−0.487212	+	0.873284i	$0.661986\pi$
$632$	−241.877	+	139.648i	−0.382717	+	0.220962i
$633$	170.512	−	295.336i	0.269372	−	0.466566i
$634$	105.627	−	182.952i	0.166605	−	0.288568i
$635$		0			0
$636$		−	172.505i		−	0.271234i
$637$	1039.85	−	131.557i	1.63242	−	0.206526i
$638$		−	106.232i		−	0.166508i
$639$	102.157	+	176.942i	0.159871	+	0.276904i
$640$		0			0
$641$	94.1724	−	163.111i	0.146915	−	0.254464i	−0.783171	−	0.621807i	$-0.786399\pi$
$641$	94.1724	−	163.111i	0.146915	−	0.254464i	0.930086	+	0.367343i	$0.119732\pi$
$642$	−63.1189	−	109.325i	−0.0983161	−	0.170288i
$643$	23.8831			0.0371432			0.0185716	−	0.999828i	$-0.494088\pi$
$643$	23.8831			0.0371432			0.0185716	+	0.999828i	$0.494088\pi$
$644$	−4.91242	−	77.9667i	−0.00762798	−	0.121066i
$645$		0			0
$646$	−357.681	−	619.521i	−0.553685	−	0.959011i
$647$	542.667	−	939.928i	0.838744	−	1.45275i	−0.0522010	−	0.998637i	$-0.516624\pi$
$647$	542.667	−	939.928i	0.838744	−	1.45275i	0.890945	−	0.454111i	$-0.150043\pi$
$648$	−22.0454	−	12.7279i	−0.0340207	−	0.0196419i
$649$	549.735	−	317.390i	0.847049	−	0.489044i
$650$		0			0
$651$	−66.4715	+	44.1724i	−0.102107	+	0.0678531i
$652$		−	97.4323i		−	0.149436i
$653$	550.536	−	317.852i	0.843087	−	0.486756i	−0.0152254	−	0.999884i	$-0.504847\pi$
$653$	550.536	−	317.852i	0.843087	−	0.486756i	0.858312	+	0.513128i	$0.171513\pi$
$654$	81.3767	+	46.9829i	0.124429	+	0.0718393i
$655$		0			0
$656$	−176.955	+	102.165i	−0.269749	+	0.155740i
$657$	−262.970			−0.400258
$658$	−688.555	−	341.723i	−1.04644	−	0.519336i
$659$	888.955			1.34895			0.674473	−	0.738300i	$-0.264371\pi$
$659$	888.955			1.34895			0.674473	+	0.738300i	$0.264371\pi$
$660$		0			0
$661$	−656.362	−	378.951i	−0.992983	−	0.573299i	−0.0868187	−	0.996224i	$-0.527670\pi$
$661$	−656.362	−	378.951i	−0.992983	−	0.573299i	−0.906165	+	0.422925i	$0.861003\pi$
$662$	−576.770	−	332.998i	−0.871253	−	0.503018i
$663$	−388.789	−	673.402i	−0.586409	−	1.01569i
$664$			76.2114i			0.114776i
$665$		0			0
$666$	95.0206			0.142674
$667$	−48.1620	+	27.8063i	−0.0722068	+	0.0416886i
$668$	49.6127	−	85.9316i	0.0742704	−	0.128640i
$669$	373.270	−	646.522i	0.557952	−	0.966401i
$670$		0			0
$671$		−	630.464i		−	0.939589i
$672$	−57.1230	+	37.9600i	−0.0850045	+	0.0564881i
$673$		−	936.839i		−	1.39203i	−0.718026	−	0.696017i	$-0.754954\pi$
$673$		−	936.839i		−	1.39203i	0.718026	−	0.696017i	$-0.245046\pi$
$674$	−376.519	−	652.150i	−0.558634	−	0.967582i
$675$		0			0
$676$	288.560	−	499.800i	0.426863	−	0.739349i
$677$	123.589	+	214.062i	0.182554	+	0.316192i	0.942749	−	0.333502i	$-0.108230\pi$
$677$	123.589	+	214.062i	0.182554	+	0.316192i	−0.760196	+	0.649694i	$0.774897\pi$
$678$	486.365			0.717352
$679$	25.7881	−	1.62482i	0.0379795	−	0.00239296i
$680$		0			0
$681$	−151.637	−	262.644i	−0.222669	−	0.385673i
$682$	35.0828	−	60.7652i	0.0514411	−	0.0890986i
$683$	−607.755	−	350.887i	−0.889831	−	0.513744i	−0.0159438	−	0.999873i	$-0.505075\pi$
$683$	−607.755	−	350.887i	−0.889831	−	0.513744i	−0.873887	+	0.486129i	$0.838409\pi$
$684$	125.237	−	72.3057i	0.183095	−	0.105710i
$685$		0			0
$686$	367.112	−	317.059i	0.535149	−	0.462185i
$687$			58.1435i			0.0846339i
$688$	−120.432	+	69.5313i	−0.175046	+	0.101063i
$689$	922.498	+	532.604i	1.33889	+	0.773011i
$690$		0			0
$691$	−530.850	+	306.486i	−0.768234	+	0.443540i	−0.832244	−	0.554409i	$-0.812944\pi$
$691$	−530.850	+	306.486i	−0.768234	+	0.443540i	0.0640104	+	0.997949i	$0.479611\pi$
$692$	−470.682			−0.680176
$693$	−157.968	+	9.95302i	−0.227948	+	0.0143622i
$694$	−635.863			−0.916230
$695$		0			0
$696$	42.2832	+	24.4122i	0.0607518	+	0.0350750i
$697$	−928.461	−	536.047i	−1.33208	−	0.769078i
$698$	−233.823	−	404.993i	−0.334990	−	0.580220i
$699$			268.318i			0.383860i
$700$		0			0
$701$	161.307			0.230110			0.115055	−	0.993359i	$-0.463296\pi$
$701$	161.307			0.230110			0.115055	+	0.993359i	$0.463296\pi$
$702$	136.129	−	78.5942i	0.193916	−	0.111958i
$703$	−269.900	+	467.480i	−0.383926	+	0.664979i
$704$	30.1488	−	52.2193i	0.0428250	−	0.0741751i
$705$		0			0
$706$		−	383.777i		−	0.543593i
$707$	1145.20	+	568.349i	1.61980	+	0.803889i
$708$			291.745i			0.412069i
$709$	285.175	+	493.938i	0.402222	+	0.696669i	0.993994	−	0.109436i	$-0.0349046\pi$
$709$	285.175	+	493.938i	0.402222	+	0.696669i	−0.591772	+	0.806106i	$0.701571\pi$
$710$		0			0
$711$	148.119	−	256.549i	0.208325	−	0.360829i
$712$	−19.6699	−	34.0693i	−0.0276263	−	0.0478501i
$713$	−36.7317			−0.0515171
$714$	−322.345	−	159.977i	−0.451464	−	0.224057i
$715$		0			0
$716$	44.2098	+	76.5736i	0.0617455	+	0.106946i
$717$	−274.176	+	474.887i	−0.382393	+	0.662325i
$718$	9.28847	+	5.36270i	0.0129366	+	0.00746894i
$719$	−431.817	+	249.310i	−0.600580	+	0.346745i	−0.769270	−	0.638924i	$-0.779380\pi$
$719$	−431.817	+	249.310i	−0.600580	+	0.346745i	0.168690	+	0.985669i	$0.446046\pi$
$720$		0			0
$721$	352.755	+	530.834i	0.489258	+	0.736246i
$722$			310.987i			0.430730i
$723$	350.254	−	202.219i	0.484446	−	0.279695i
$724$	202.735	+	117.049i	0.280020	+	0.161670i
$725$		0			0
$726$	−136.169	+	78.6171i	−0.187560	+	0.108288i
$727$	1058.79			1.45638			0.728190	−	0.685375i	$-0.240362\pi$
$727$	1058.79			1.45638			0.728190	+	0.685375i	$0.240362\pi$
$728$	−26.6313	−	422.675i	−0.0365815	−	0.580597i
$729$	27.0000			0.0370370
$730$		0			0
$731$	−631.888	−	364.821i	−0.864416	−	0.499071i
$732$	250.941	+	144.881i	0.342816	+	0.197925i
$733$	−7.56721	−	13.1068i	−0.0103236	−	0.0178810i	0.860817	−	0.508914i	$-0.169953\pi$
$733$	−7.56721	−	13.1068i	−0.0103236	−	0.0178810i	−0.871141	+	0.491033i	$0.836620\pi$
$734$			751.530i			1.02388i
$735$		0			0
$736$	−31.5658			−0.0428883
$737$	434.609	−	250.922i	0.589700	−	0.340463i
$738$	108.363	−	187.690i	0.146833	−	0.254322i
$739$	−81.3819	+	140.958i	−0.110124	+	0.190741i	−0.915820	−	0.401588i	$-0.868458\pi$
$739$	−81.3819	+	140.958i	−0.110124	+	0.190741i	0.805696	+	0.592329i	$0.201792\pi$
$740$		0			0
$741$			892.967i			1.20508i
$742$	491.998	−	30.9991i	0.663071	−	0.0417778i
$743$		−	338.071i		−	0.455009i	−0.973777	−	0.227504i	$-0.926943\pi$
$743$		−	338.071i		−	0.455009i	0.973777	−	0.227504i	$-0.0730566\pi$
$744$	16.1241	+	27.9277i	0.0216722	+	0.0375373i
$745$		0			0
$746$	−406.564	+	704.189i	−0.544991	+	0.943953i
$747$	−40.4172	−	70.0046i	−0.0541060	−	0.0937143i
$748$	316.373			0.422959
$749$	300.462	−	199.666i	0.401151	−	0.266577i
$750$		0			0
$751$	−239.087	−	414.111i	−0.318359	−	0.551413i	0.661787	−	0.749692i	$-0.269798\pi$
$751$	−239.087	−	414.111i	−0.318359	−	0.551413i	−0.980146	+	0.198279i	$0.936465\pi$
$752$	−155.299	+	268.985i	−0.206514	+	0.357693i
$753$	−85.0319	−	49.0932i	−0.112924	−	0.0651968i
$754$	−261.097	+	150.744i	−0.346282	+	0.199926i
$755$		0			0
$756$	32.3395	−	65.1625i	0.0427771	−	0.0861938i
$757$		−	397.788i		−	0.525479i	−0.964867	−	0.262739i	$-0.915374\pi$
$757$		−	397.788i		−	0.525479i	0.964867	−	0.262739i	$-0.0846260\pi$
$758$	768.483	−	443.684i	1.01383	−	0.585335i
$759$	−63.0874	−	36.4236i	−0.0831192	−	0.0479889i
$760$		0			0
$761$	−1264.02	+	729.785i	−1.66100	+	0.958981i	−0.688767	+	0.724983i	$0.741848\pi$
$761$	−1264.02	+	729.785i	−1.66100	+	0.958981i	−0.972237	+	0.233998i	$0.924819\pi$
$762$	−181.540			−0.238241
$763$	−119.376	+	240.536i	−0.156456	+	0.315250i
$764$	−468.625			−0.613383
$765$		0			0
$766$	−81.5817	−	47.1012i	−0.106503	−	0.0614898i
$767$	−1560.15	−	900.755i	−2.03410	−	1.17439i
$768$	13.8564	+	24.0000i	0.0180422	+	0.0312500i
$769$			2.10093i			0.00273203i	0.999999	+	0.00136602i	$0.000434817\pi$
$769$			2.10093i			0.00273203i	−0.999999	+	0.00136602i	$0.999565\pi$
$770$		0			0
$771$	−503.055			−0.652471
$772$	33.8876	−	19.5650i	0.0438959	−	0.0253433i
$773$	226.305	−	391.972i	0.292762	−	0.507079i	−0.681700	−	0.731632i	$-0.738759\pi$
$773$	226.305	−	391.972i	0.292762	−	0.507079i	0.974462	+	0.224553i	$0.0720923\pi$
$774$	73.7491	−	127.737i	0.0952830	−	0.165035i
$775$		0			0
$776$		−	10.4406i		−	0.0134544i
$777$	17.0752	+	271.007i	0.0219758	+	0.348786i
$778$			776.473i			0.998037i
$779$	615.594	+	1066.24i	0.790236	+	1.36873i
$780$		0			0
$781$	256.660	−	444.548i	0.328630	−	0.569204i
$782$	−82.8106	−	143.432i	−0.105896	−	0.183417i
$783$	−51.7862			−0.0661381
$784$	−118.530	−	156.098i	−0.151186	−	0.199105i
$785$		0			0
$786$	24.5366	+	42.4986i	0.0312170	+	0.0540694i
$787$	65.0535	−	112.676i	0.0826601	−	0.143171i	−0.821732	−	0.569875i	$-0.806992\pi$
$787$	65.0535	−	112.676i	0.0826601	−	0.143171i	0.904392	+	0.426703i	$0.140325\pi$
$788$	310.804	+	179.443i	0.394421	+	0.227719i
$789$	666.893	−	385.031i	0.845238	−	0.487998i
$790$		0			0
$791$	87.3997	+	1387.15i	0.110493	+	1.75367i
$792$			63.9553i			0.0807516i
$793$	−1549.55	+	894.632i	−1.95403	+	1.12816i
$794$	−635.111	−	366.681i	−0.799888	−	0.461815i
$795$		0			0
$796$	443.260	−	255.916i	0.556859	−	0.321503i
$797$	1170.92			1.46915			0.734577	−	0.678525i	$-0.237381\pi$
$797$	1170.92			1.46915			0.734577	+	0.678525i	$0.237381\pi$
$798$	228.727	+	344.193i	0.286625	+	0.431320i
$799$	−1629.66			−2.03962
$800$		0			0
$801$	36.1359	+	20.8631i	0.0451135	+	0.0260463i
$802$	−583.344	−	336.794i	−0.727361	−	0.419942i
$803$	330.342	+	572.170i	0.411385	+	0.712540i
$804$			230.647i			0.286875i
$805$		0			0
$806$	−199.131			−0.247060
$807$	251.071	−	144.956i	0.311116	−	0.179623i
$808$	258.291	−	447.372i	0.319667	−	0.553679i
$809$	−102.442	+	177.435i	−0.126628	+	0.219327i	−0.922368	−	0.386312i	$-0.873749\pi$
$809$	−102.442	+	177.435i	−0.126628	+	0.219327i	0.795740	+	0.605639i	$0.207082\pi$
$810$		0			0
$811$		−	541.011i		−	0.667092i	−0.942734	−	0.333546i	$-0.891755\pi$
$811$		−	541.011i		−	0.667092i	0.942734	−	0.333546i	$-0.108245\pi$
$812$	−62.0274	+	124.982i	−0.0763884	+	0.153919i
$813$		−	4.48198i		−	0.00551289i
$814$	−119.365	−	206.746i	−0.146640	−	0.253988i
$815$		0			0
$816$	−72.7026	+	125.925i	−0.0890964	+	0.154319i
$817$	418.959	+	725.658i	0.512801	+	0.888198i
$818$	−152.285			−0.186168
$819$	248.620	+	374.128i	0.303565	+	0.456811i
$820$		0			0
$821$	212.913	+	368.777i	0.259334	+	0.449180i	0.966064	−	0.258304i	$-0.0831636\pi$
$821$	212.913	+	368.777i	0.259334	+	0.449180i	−0.706730	+	0.707484i	$0.749830\pi$
$822$	105.537	−	182.795i	0.128391	−	0.222379i
$823$	667.700	+	385.497i	0.811301	+	0.468405i	0.847407	−	0.530943i	$-0.178162\pi$
$823$	667.700	+	385.497i	0.811301	+	0.468405i	−0.0361067	+	0.999348i	$0.511496\pi$
$824$	223.028	−	128.765i	0.270665	−	0.156268i
$825$		0			0
$826$	−832.081	+	52.4266i	−1.00736	+	0.0634704i
$827$		−	448.579i		−	0.542417i	−0.962521	−	0.271209i	$-0.912577\pi$
$827$		−	448.579i		−	0.542417i	0.962521	−	0.271209i	$-0.0874234\pi$
$828$	28.9950	−	16.7403i	0.0350181	−	0.0202177i
$829$	737.022	+	425.520i	0.889050	+	0.513293i	0.873632	−	0.486588i	$-0.161759\pi$
$829$	737.022	+	425.520i	0.889050	+	0.513293i	0.0154183	+	0.999881i	$0.495092\pi$
$830$		0			0
$831$	−763.667	+	440.903i	−0.918973	+	0.530569i
$832$	−171.125			−0.205679
$833$	398.341	−	948.103i	0.478201	−	1.13818i
$834$	569.512			0.682868
$835$		0			0
$836$	−314.646	−	181.661i	−0.376370	−	0.217298i
$837$	−29.6218	−	17.1022i	−0.0353905	−	0.0204327i
$838$	228.969	+	396.585i	0.273232	+	0.473252i
$839$			77.0829i			0.0918747i	0.998944	+	0.0459373i	$0.0146275\pi$
$839$			77.0829i			0.0918747i	−0.998944	+	0.0459373i	$0.985373\pi$
$840$		0			0
$841$	−741.674			−0.881895
$842$	292.662	−	168.968i	0.347579	−	0.200675i
$843$	182.461	−	316.032i	0.216443	−	0.374890i
$844$	196.891	−	341.025i	0.233283	−	0.404058i
$845$		0			0
$846$		−	329.438i		−	0.389407i
$847$	−248.692	−	374.237i	−0.293615	−	0.441839i
$848$		−	199.192i		−	0.234896i
$849$	34.1964	+	59.2299i	0.0402784	+	0.0697643i
$850$		0			0
$851$	−62.4875	+	108.231i	−0.0734283	+	0.127182i
$852$	117.961	+	204.315i	0.138452	+	0.239806i
$853$	176.785			0.207251			0.103626	−	0.994616i	$-0.466956\pi$
$853$	176.785			0.207251			0.103626	+	0.994616i	$0.466956\pi$
$854$	−368.118	+	741.740i	−0.431052	+	0.868547i
$855$		0			0
$856$	−72.8835	−	126.238i	−0.0851442	−	0.147474i
$857$	623.618	−	1080.14i	0.727676	−	1.26037i	−0.230187	−	0.973146i	$-0.573934\pi$
$857$	623.618	−	1080.14i	0.727676	−	1.26037i	0.957863	−	0.287225i	$-0.0927328\pi$
$858$	−342.011	−	197.460i	−0.398614	−	0.230140i
$859$	−1319.99	+	762.098i	−1.53666	+	0.887192i	−0.537630	+	0.843181i	$0.680680\pi$
$859$	−1319.99	+	762.098i	−1.53666	+	0.887192i	−0.999031	+	0.0440111i	$0.985986\pi$
$860$		0			0
$861$	554.779	+	275.331i	0.644343	+	0.319781i
$862$			271.235i			0.314658i
$863$	1243.69	−	718.043i	1.44112	−	0.832032i	0.443197	−	0.896424i	$-0.353844\pi$
$863$	1243.69	−	718.043i	1.44112	−	0.832032i	0.997925	+	0.0643926i	$0.0205110\pi$
$864$	−25.4558	−	14.6969i	−0.0294628	−	0.0170103i
$865$		0			0
$866$	−149.520	+	86.3255i	−0.172656	+	0.0996830i
$867$	−262.358			−0.302605
$868$	−76.7547	+	51.0058i	−0.0884271	+	0.0587625i
$869$	−744.268			−0.856465
$870$		0			0
$871$	−1233.42	−	712.118i	−1.41610	−	0.817586i
$872$	93.9658	+	54.2512i	0.107759	+	0.0622146i
$873$	5.53698	+	9.59033i	0.00634248	+	0.0109855i
$874$			190.199i			0.217619i
$875$		0			0
$876$	−303.651			−0.346634
$877$	−1031.65	+	595.626i	−1.17634	+	0.679163i	−0.955166	−	0.296070i	$-0.904324\pi$
$877$	−1031.65	+	595.626i	−1.17634	+	0.679163i	−0.221179	+	0.975233i	$0.570990\pi$
$878$	−177.716	+	307.813i	−0.202410	+	0.350584i
$879$	77.5978	−	134.403i	0.0882797	−	0.152905i
$880$		0			0
$881$		−	81.6610i		−	0.0926912i	−0.998925	−	0.0463456i	$-0.985242\pi$
$881$		−	81.6610i		−	0.0926912i	0.998925	−	0.0463456i	$-0.0147576\pi$
$882$	191.660	+	80.5253i	0.217302	+	0.0912985i
$883$		−	506.404i		−	0.573504i	−0.958005	−	0.286752i	$-0.907424\pi$
$883$		−	506.404i		−	0.573504i	0.958005	−	0.286752i	$-0.0925755\pi$
$884$	−448.935	−	777.578i	−0.507845	−	0.879613i
$885$		0			0
$886$	77.6327	−	134.464i	0.0876215	−	0.151765i
$887$	−10.3172	−	17.8700i	−0.0116316	−	0.0201466i	0.860151	−	0.510039i	$-0.170369\pi$
$887$	−10.3172	−	17.8700i	−0.0116316	−	0.0201466i	−0.871783	+	0.489893i	$0.837036\pi$
$888$	109.720			0.123559
$889$	−32.6227	−	517.766i	−0.0366959	−	0.582414i
$890$		0			0
$891$	−33.9174	−	58.7467i	−0.0380667	−	0.0659334i
$892$	431.015	−	746.540i	0.483200	−	0.836928i
$893$	1620.76	+	935.747i	1.81496	+	1.04787i
$894$	466.534	−	269.354i	0.521850	−	0.301290i
$895$		0			0
$896$	−65.9600	+	43.8324i	−0.0736161	+	0.0489201i
$897$			206.741i			0.230480i
$898$	987.744	−	570.274i	1.09994	−	0.635049i
$899$	56.8149	+	32.8021i	0.0631979	+	0.0364873i
$900$		0			0
$901$	905.109	−	522.565i	1.00456	−	0.579983i
$902$	−544.501			−0.603659
$903$	377.570	+	187.384i	0.418128	+	0.207513i
$904$	561.606			0.621245
$905$		0			0
$906$	553.499	+	319.563i	0.610926	+	0.352718i
$907$	−222.402	−	128.404i	−0.245206	−	0.141570i	0.372361	−	0.928088i	$-0.378548\pi$
$907$	−222.402	−	128.404i	−0.245206	−	0.141570i	−0.617567	+	0.786518i	$0.711882\pi$
$908$	−175.096	−	303.275i	−0.192837	−	0.334003i
$909$			547.917i			0.602769i
$910$		0			0
$911$	1194.31			1.31098			0.655492	−	0.755202i	$-0.272461\pi$
$911$	1194.31			1.31098			0.655492	+	0.755202i	$0.272461\pi$
$912$	144.611	−	83.4914i	0.158565	−	0.0915476i
$913$	−101.544	+	175.880i	−0.111220	+	0.192639i
$914$	546.207	−	946.058i	0.597600	−	1.03507i
$915$		0			0
$916$			67.1383i			0.0732951i
$917$	−116.800	+	77.6173i	−0.127372	+	0.0846427i
$918$		−	154.226i		−	0.168002i
$919$	−446.876	−	774.012i	−0.486263	−	0.842232i	0.513612	−	0.858022i	$-0.328307\pi$
$919$	−446.876	−	774.012i	−0.486263	−	0.842232i	−0.999875	+	0.0157900i	$0.994974\pi$
$920$		0			0
$921$	−407.446	+	705.717i	−0.442395	+	0.766251i
$922$	561.168	+	971.971i	0.608642	+	1.05420i
$923$	−1456.81			−1.57834
$924$	−182.406	+	11.4928i	−0.197409	+	0.0124381i
$925$		0			0
$926$	−193.908	−	335.859i	−0.209404	−	0.362698i
$927$	−136.576	+	236.556i	−0.147331	+	0.255185i
$928$	48.8245	+	28.1888i	0.0526126	+	0.0303759i
$929$	−295.237	+	170.455i	−0.317801	+	0.183482i	−0.650412	−	0.759582i	$-0.725404\pi$
$929$	−295.237	+	170.455i	−0.317801	+	0.183482i	0.332611	+	0.943064i	$0.392070\pi$
$930$		0			0
$931$	−940.565	+	714.199i	−1.01027	+	0.767131i
$932$			309.827i			0.332432i
$933$	376.948	−	217.631i	0.404017	−	0.233259i
$934$	−486.994	−	281.166i	−0.521407	−	0.301034i
$935$		0			0
$936$	157.188	−	90.7528i	0.167936	−	0.0969581i
$937$	−217.347			−0.231961			−0.115981	−	0.993251i	$-0.537001\pi$
$937$	−217.347			−0.231961			−0.115981	+	0.993251i	$0.537001\pi$
$938$	−657.825	+	41.4473i	−0.701306	+	0.0441869i
$939$	−672.834			−0.716544
$940$		0			0
$941$	1226.68	+	708.226i	1.30360	+	0.752631i	0.981019	−	0.193912i	$-0.0621177\pi$
$941$	1226.68	+	708.226i	1.30360	+	0.752631i	0.322577	+	0.946543i	$0.395451\pi$
$942$	−242.235	−	139.855i	−0.257150	−	0.148466i
$943$	142.523	+	246.857i	0.151138	+	0.261779i
$944$			336.878i			0.356862i
$945$		0			0
$946$	−370.574			−0.391728
$947$	−1199.21	+	692.365i	−1.26633	+	0.731114i	−0.974291	−	0.225294i	$-0.927666\pi$
$947$	−1199.21	+	692.365i	−1.26633	+	0.731114i	−0.292035	+	0.956408i	$0.594333\pi$
$948$	171.033	−	296.238i	0.180415	−	0.312487i
$949$	937.515	−	1623.82i	0.987897	−	1.71109i
$950$		0			0
$951$			258.733i			0.272064i
$952$	−372.212	−	184.725i	−0.390979	−	0.194039i
$953$		−	1365.38i		−	1.43272i	−0.697732	−	0.716359i	$-0.745807\pi$
$953$		−	1365.38i		−	1.43272i	0.697732	−	0.716359i	$-0.254193\pi$
$954$	105.637	+	182.969i	0.110731	+	0.191792i
$955$		0			0
$956$	−316.591	+	548.352i	−0.331162	+	0.573590i
$957$	65.0538	+	112.676i	0.0679768	+	0.117739i
$958$	−270.380			−0.282234
$959$	540.313	+	268.152i	0.563413	+	0.279616i
$960$		0			0
$961$	−458.834	−	794.725i	−0.477455	−	0.826977i
$962$	−338.758	+	586.747i	−0.352140	+	0.609924i
$963$	133.895	+	77.3046i	0.139040	+	0.0802748i
$964$	404.439	−	233.503i	0.419542	−	0.242223i
$965$		0			0
$966$	52.9551	+	79.6880i	0.0548189	+	0.0824927i
$967$		−	1718.05i		−	1.77668i	−0.459185	−	0.888341i	$-0.651858\pi$
$967$		−	1718.05i		−	1.77668i	0.459185	−	0.888341i	$-0.348142\pi$
$968$	−157.234	+	90.7792i	−0.162432	+	0.0937802i
$969$	758.755	+	438.068i	0.783029	+	0.452082i
$970$		0			0
$971$	387.463	−	223.702i	0.399035	−	0.230383i	−0.287033	−	0.957921i	$-0.592669\pi$
$971$	387.463	−	223.702i	0.399035	−	0.230383i	0.686068	+	0.727538i	$0.259335\pi$
$972$	31.1769			0.0320750
$973$	102.341	+	1624.29i	0.105181	+	1.66937i
$974$	−268.727			−0.275900
$975$		0			0
$976$	289.762	+	167.294i	0.296887	+	0.171408i
$977$	1576.94	+	910.447i	1.61406	+	0.931880i	0.988415	+	0.151775i	$0.0484988\pi$
$977$	1576.94	+	910.447i	1.61406	+	0.931880i	0.625648	+	0.780105i	$0.284835\pi$
$978$	59.6648	+	103.343i	0.0610070	+	0.105667i
$979$		−	104.833i		−	0.107082i
$980$		0			0
$981$	−115.084			−0.117313
$982$	258.891	−	149.471i	0.263637	−	0.152211i
$983$	−830.607	+	1438.65i	−0.844972	+	1.46353i	0.0406735	+	0.999172i	$0.487050\pi$
$983$	−830.607	+	1438.65i	−0.844972	+	1.46353i	−0.885646	+	0.464362i	$0.846284\pi$
$984$	125.126	−	216.725i	0.127161	−	0.220249i
$985$		0			0
$986$			295.806i			0.300006i
$987$	939.584	−	59.2000i	0.951960	−	0.0599797i
$988$			1031.11i			1.04363i
$989$	96.9978	+	168.005i	0.0980767	+	0.169874i
$990$		0			0
$991$	−275.795	+	477.690i	−0.278299	+	0.482029i	−0.970962	−	0.239233i	$-0.923104\pi$
$991$	−275.795	+	477.690i	−0.278299	+	0.482029i	0.692663	+	0.721261i	$0.256437\pi$
$992$	18.6185	+	32.2482i	0.0187686	+	0.0325082i
$993$	815.676			0.821426
$994$	−561.525	+	373.150i	−0.564914	+	0.375403i
$995$		0			0
$996$	−46.6697	−	80.8344i	−0.0468572	−	0.0811590i
$997$	902.319	−	1562.86i	0.905034	−	1.56757i	0.0841629	−	0.996452i	$-0.473178\pi$
$997$	902.319	−	1562.86i	0.905034	−	1.56757i	0.820871	−	0.571113i	$-0.193488\pi$
$998$	310.751	+	179.412i	0.311374	+	0.179772i
$999$	−100.785	+	58.1880i	−0.100885	+	0.0582462i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.q.b.199.3		16
5.2	odd	4		1050.3.p.c.451.1	✓	8
5.3	odd	4		1050.3.p.d.451.4	yes	8
5.4	even	2	inner	1050.3.q.b.199.6		16
7.5	odd	6	inner	1050.3.q.b.649.6		16
35.12	even	12		1050.3.p.c.901.1	yes	8
35.19	odd	6	inner	1050.3.q.b.649.3		16
35.33	even	12		1050.3.p.d.901.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.p.c.451.1	✓	8	5.2	odd	4
1050.3.p.c.901.1	yes	8	35.12	even	12
1050.3.p.d.451.4	yes	8	5.3	odd	4
1050.3.p.d.901.4	yes	8	35.33	even	12
1050.3.q.b.199.3		16	1.1	even	1	trivial
1050.3.q.b.199.6		16	5.4	even	2	inner
1050.3.q.b.649.3		16	35.19	odd	6	inner
1050.3.q.b.649.6		16	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-6.98615 + 0.440173i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-6.98615 + 0.440173i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-3.76860 + 6.52741i) q^{11} +(-1.73205 - 3.00000i) q^{12} +21.3906 q^{13} +(8.24500 - 5.47905i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(10.4937 - 18.1757i) q^{17} +(3.67423 + 2.12132i) q^{18} +(-20.8728 + 12.0509i) q^{19} +(-5.38992 + 10.8604i) q^{21} -10.6592i q^{22} +(-4.83250 + 2.79005i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-26.1981 + 15.1255i) q^{26} -5.19615 q^{27} +(-6.22374 + 12.5405i) q^{28} +9.96625 q^{29} +(5.70073 + 3.29132i) q^{31} +(4.89898 + 2.82843i) q^{32} +(6.52741 + 11.3058i) q^{33} +29.6807i q^{34} -6.00000 q^{36} +(19.3960 - 11.1983i) q^{37} +(17.0426 - 29.5187i) q^{38} +(18.5248 - 32.0860i) q^{39} -51.0827i q^{41} +(-1.07820 - 17.1125i) q^{42} -34.7656i q^{43} +(7.53720 + 13.0548i) q^{44} +(3.94572 - 6.83419i) q^{46} +(-38.8246 - 67.2462i) q^{47} -6.92820 q^{48} +(48.6125 - 6.15023i) q^{49} +(-18.1757 - 31.4812i) q^{51} +(21.3906 - 37.0497i) q^{52} +(43.1262 + 24.8989i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-1.24500 - 19.7598i) q^{56} +41.7457i q^{57} +(-12.2061 + 7.04720i) q^{58} +(-72.9362 - 42.1098i) q^{59} +(-72.4404 + 41.8235i) q^{61} -9.30925 q^{62} +(11.6228 + 17.4903i) q^{63} -8.00000 q^{64} +(-15.9888 - 9.23115i) q^{66} +(-57.6618 - 33.2911i) q^{67} +(-20.9874 - 36.3513i) q^{68} +9.66501i q^{69} -68.1049 q^{71} +(7.34847 - 4.24264i) q^{72} +(43.8283 - 75.9128i) q^{73} +(-15.8368 + 27.4301i) q^{74} +48.2038i q^{76} +(23.4548 - 47.2603i) q^{77} +52.3962i q^{78} +(49.3730 + 85.5165i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(36.1209 + 62.5632i) q^{82} +26.9448 q^{83} +(13.4209 + 20.1960i) q^{84} +(24.5830 + 42.5790i) q^{86} +(8.63103 - 14.9494i) q^{87} +(-18.4623 - 10.6592i) q^{88} +(-12.0453 + 6.95436i) q^{89} +(-149.438 + 9.41559i) q^{91} +11.1602i q^{92} +(9.87395 - 5.70073i) q^{93} +(95.1005 + 54.9063i) q^{94} +(8.48528 - 4.89898i) q^{96} -3.69132 q^{97} +(-55.1890 + 41.9067i) q^{98} +22.6116 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) 16 * q + 16 * q^4 - 24 * q^9	\( 16 q + 16 q^{4} - 24 q^{9} - 8 q^{11} + 32 q^{14} - 32 q^{16} - 144 q^{19} - 144 q^{26} + 48 q^{29} + 192 q^{31} - 96 q^{36} + 24 q^{39} + 16 q^{44} + 64 q^{46} + 528 q^{49} + 48 q^{51} + 80 q^{56} - 624 q^{59} - 408 q^{61} - 128 q^{64} - 72 q^{66} - 128 q^{71} + 32 q^{74} + 288 q^{79} - 72 q^{81} + 352 q^{86} + 672 q^{89} - 592 q^{91} - 72 q^{94} + 48 q^{99}+O(q^{100}) \) 16 * q + 16 * q^4 - 24 * q^9 - 8 * q^11 + 32 * q^14 - 32 * q^16 - 144 * q^19 - 144 * q^26 + 48 * q^29 + 192 * q^31 - 96 * q^36 + 24 * q^39 + 16 * q^44 + 64 * q^46 + 528 * q^49 + 48 * q^51 + 80 * q^56 - 624 * q^59 - 408 * q^61 - 128 * q^64 - 72 * q^66 - 128 * q^71 + 32 * q^74 + 288 * q^79 - 72 * q^81 + 352 * q^86 + 672 * q^89 - 592 * q^91 - 72 * q^94 + 48 * q^99

Introduction

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