LMFDB - Embedded newform 1050.3.q.b.199.2

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			199.2
Root			$2.22431 - 0.596002i$ of defining polynomial
Character	$\chi$	$=$	1050.199
Dual form			1050.3.q.b.649.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(5.76140 - 3.97571i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(5.76140 - 3.97571i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-1.64728 + 2.85317i) q^{11} +(1.73205 + 3.00000i) q^{12} +7.72850 q^{13} +(-4.24500 + 8.94315i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(6.30929 - 10.9280i) q^{17} +(3.67423 + 2.12132i) q^{18} +(-1.54304 + 0.890872i) q^{19} +(0.974040 + 12.0852i) q^{21} -4.65921i q^{22} +(5.85120 - 3.37819i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-9.46544 + 5.46488i) q^{26} +5.19615 q^{27} +(-1.12472 - 13.9547i) q^{28} -39.2933 q^{29} +(9.46751 + 5.46607i) q^{31} +(4.89898 + 2.82843i) q^{32} +(-2.85317 - 4.94184i) q^{33} +17.8454i q^{34} -6.00000 q^{36} +(29.7883 - 17.1983i) q^{37} +(1.25988 - 2.18218i) q^{38} +(-6.69308 + 11.5928i) q^{39} +18.8536i q^{41} +(-9.73845 - 14.1125i) q^{42} -77.4197i q^{43} +(3.29456 + 5.70635i) q^{44} +(-4.77748 + 8.27485i) q^{46} +(6.44335 + 11.1602i) q^{47} +6.92820 q^{48} +(17.3875 - 45.8113i) q^{49} +(10.9280 + 18.9279i) q^{51} +(7.72850 - 13.3862i) q^{52} +(-44.7631 - 25.8440i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(11.2450 + 16.2957i) q^{56} -3.08607i q^{57} +(48.1243 - 27.7846i) q^{58} +(-97.7973 - 56.4633i) q^{59} +(-22.7184 + 13.1165i) q^{61} -15.4604 q^{62} +(-18.9713 - 9.00500i) q^{63} -8.00000 q^{64} +(6.98882 + 4.03500i) q^{66} +(17.2453 + 9.95656i) q^{67} +(-12.6186 - 21.8560i) q^{68} +11.7024i q^{69} +87.4319 q^{71} +(7.34847 - 4.24264i) q^{72} +(30.4575 - 52.7540i) q^{73} +(-24.3220 + 42.1270i) q^{74} +3.56349i q^{76} +(1.85274 + 22.9874i) q^{77} -18.9309i q^{78} +(-17.7888 - 30.8112i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-13.3315 - 23.0909i) q^{82} +46.6773 q^{83} +(21.9062 + 10.3981i) q^{84} +(54.7440 + 94.8194i) q^{86} +(34.0290 - 58.9399i) q^{87} +(-8.06999 - 4.65921i) q^{88} +(47.4706 - 27.4072i) q^{89} +(44.5270 - 30.7263i) q^{91} -13.5128i q^{92} +(-16.3982 + 9.46751i) q^{93} +(-15.7829 - 9.11228i) q^{94} +(-8.48528 + 4.89898i) q^{96} +45.7447 q^{97} +(11.0982 + 68.4020i) q^{98} +9.88368 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
$7$	5.76140	−	3.97571i	0.823057	−	0.567958i
$7$	5.76140	−	3.97571i	0.823057	−	0.567958i
$8$			2.82843i			0.353553i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$		0			0
$11$	−1.64728	+	2.85317i	−0.149753	+	0.259379i	−0.931136	−	0.364672i	$-0.881181\pi$
$11$	−1.64728	+	2.85317i	−0.149753	+	0.259379i	0.781383	+	0.624051i	$0.214514\pi$
$12$	1.73205	+	3.00000i	0.144338	+	0.250000i
$13$	7.72850			0.594500			0.297250	−	0.954800i	$-0.403931\pi$
$13$	7.72850			0.594500			0.297250	+	0.954800i	$0.403931\pi$
$14$	−4.24500	+	8.94315i	−0.303214	+	0.638797i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	6.30929	−	10.9280i	0.371135	−	0.642824i	−0.618606	−	0.785702i	$-0.712302\pi$
$17$	6.30929	−	10.9280i	0.371135	−	0.642824i	0.989740	+	0.142877i	$0.0456354\pi$
$18$	3.67423	+	2.12132i	0.204124	+	0.117851i
$19$	−1.54304	+	0.890872i	−0.0812124	+	0.0468880i	−0.540056	−	0.841629i	$-0.681597\pi$
$19$	−1.54304	+	0.890872i	−0.0812124	+	0.0468880i	0.458844	+	0.888517i	$0.348264\pi$
$20$		0			0
$21$	0.974040	+	12.0852i	0.0463829	+	0.575484i
$22$		−	4.65921i		−	0.211782i
$23$	5.85120	−	3.37819i	0.254400	−	0.146878i	−0.367377	−	0.930072i	$-0.619744\pi$
$23$	5.85120	−	3.37819i	0.254400	−	0.146878i	0.621777	+	0.783194i	$0.286411\pi$
$24$	−4.24264	−	2.44949i	−0.176777	−	0.102062i
$25$		0			0
$26$	−9.46544	+	5.46488i	−0.364055	+	0.210188i
$27$	5.19615			0.192450
$28$	−1.12472	−	13.9547i	−0.0401687	−	0.498384i
$29$	−39.2933			−1.35494			−0.677471	−	0.735550i	$-0.736924\pi$
$29$	−39.2933			−1.35494			−0.677471	+	0.735550i	$0.736924\pi$
$30$		0			0
$31$	9.46751	+	5.46607i	0.305404	+	0.176325i	0.644868	−	0.764294i	$-0.276912\pi$
$31$	9.46751	+	5.46607i	0.305404	+	0.176325i	−0.339464	+	0.940619i	$0.610246\pi$
$32$	4.89898	+	2.82843i	0.153093	+	0.0883883i
$33$	−2.85317	−	4.94184i	−0.0864598	−	0.149753i
$34$			17.8454i			0.524864i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	29.7883	−	17.1983i	0.805089	−	0.464818i	−0.0401585	−	0.999193i	$-0.512786\pi$
$37$	29.7883	−	17.1983i	0.805089	−	0.464818i	0.845248	+	0.534375i	$0.179453\pi$
$38$	1.25988	−	2.18218i	0.0331548	−	0.0574258i
$39$	−6.69308	+	11.5928i	−0.171617	+	0.297250i
$40$		0			0
$41$			18.8536i			0.459844i	0.973209	+	0.229922i	$0.0738472\pi$
$41$			18.8536i			0.459844i	−0.973209	+	0.229922i	$0.926153\pi$
$42$	−9.73845	−	14.1125i	−0.231868	−	0.336012i
$43$		−	77.4197i		−	1.80046i	−0.435416	−	0.900229i	$-0.643399\pi$
$43$		−	77.4197i		−	1.80046i	0.435416	−	0.900229i	$-0.356601\pi$
$44$	3.29456	+	5.70635i	0.0748764	+	0.129690i
$45$		0			0
$46$	−4.77748	+	8.27485i	−0.103858	+	0.179888i
$47$	6.44335	+	11.1602i	0.137093	+	0.237451i	0.926395	−	0.376553i	$-0.122891\pi$
$47$	6.44335	+	11.1602i	0.137093	+	0.237451i	−0.789302	+	0.614005i	$0.789558\pi$
$48$	6.92820			0.144338
$49$	17.3875	−	45.8113i	0.354847	−	0.934924i
$50$		0			0
$51$	10.9280	+	18.9279i	0.214275	+	0.371135i
$52$	7.72850	−	13.3862i	0.148625	−	0.257426i
$53$	−44.7631	−	25.8440i	−0.844586	−	0.487622i	0.0142341	−	0.999899i	$-0.495469\pi$
$53$	−44.7631	−	25.8440i	−0.844586	−	0.487622i	−0.858821	+	0.512276i	$0.828802\pi$
$54$	−6.36396	+	3.67423i	−0.117851	+	0.0680414i
$55$		0			0
$56$	11.2450	+	16.2957i	0.200804	+	0.290995i
$57$		−	3.08607i		−	0.0541416i
$58$	48.1243	−	27.7846i	0.829729	−	0.479044i
$59$	−97.7973	−	56.4633i	−1.65758	−	0.957005i	−0.973827	−	0.227292i	$-0.927013\pi$
$59$	−97.7973	−	56.4633i	−1.65758	−	0.957005i	−0.683754	−	0.729713i	$-0.739654\pi$
$60$		0			0
$61$	−22.7184	+	13.1165i	−0.372432	+	0.215024i	−0.674521	−	0.738256i	$-0.735650\pi$
$61$	−22.7184	+	13.1165i	−0.372432	+	0.215024i	0.302088	+	0.953280i	$0.402316\pi$
$62$	−15.4604			−0.249361
$63$	−18.9713	−	9.00500i	−0.301132	−	0.142937i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	6.98882	+	4.03500i	0.105891	+	0.0611363i
$67$	17.2453	+	9.95656i	0.257392	+	0.148605i	0.623144	−	0.782107i	$-0.285855\pi$
$67$	17.2453	+	9.95656i	0.257392	+	0.148605i	−0.365752	+	0.930712i	$0.619188\pi$
$68$	−12.6186	−	21.8560i	−0.185567	−	0.321412i
$69$			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	$0.288866\pi$
$72$	7.34847	−	4.24264i	0.102062	−	0.0589256i
$73$	30.4575	−	52.7540i	0.417226	−	0.722657i	−0.578433	−	0.815730i	$-0.696336\pi$
$73$	30.4575	−	52.7540i	0.417226	−	0.722657i	0.995659	+	0.0930727i	$0.0296689\pi$
$74$	−24.3220	+	42.1270i	−0.328676	+	0.569284i
$75$		0			0
$76$			3.56349i			0.0468880i
$77$	1.85274	+	22.9874i	0.0240615	+	0.298537i
$78$		−	18.9309i		−	0.242704i
$79$	−17.7888	−	30.8112i	−0.225175	−	0.390015i	0.731197	−	0.682167i	$-0.238962\pi$
$79$	−17.7888	−	30.8112i	−0.225175	−	0.390015i	−0.956372	+	0.292152i	$0.905629\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−13.3315	−	23.0909i	−0.162580	−	0.281596i
$83$	46.6773			0.562377			0.281188	−	0.959653i	$-0.409271\pi$
$83$	46.6773			0.562377			0.281188	+	0.959653i	$0.409271\pi$
$84$	21.9062	+	10.3981i	0.260788	+	0.123787i
$85$		0			0
$86$	54.7440	+	94.8194i	0.636558	+	1.10255i
$87$	34.0290	−	58.9399i	0.391138	−	0.677471i
$88$	−8.06999	−	4.65921i	−0.0917044	−	0.0529456i
$89$	47.4706	−	27.4072i	0.533378	−	0.307946i	−0.209013	−	0.977913i	$-0.567025\pi$
$89$	47.4706	−	27.4072i	0.533378	−	0.307946i	0.742391	+	0.669967i	$0.233692\pi$
$90$		0			0
$91$	44.5270	−	30.7263i	0.489308	−	0.337651i
$92$		−	13.5128i		−	0.146878i
$93$	−16.3982	+	9.46751i	−0.176325	+	0.101801i
$94$	−15.7829	−	9.11228i	−0.167903	−	0.0969391i
$95$		0			0
$96$	−8.48528	+	4.89898i	−0.0883883	+	0.0510310i
$97$	45.7447			0.471595			0.235798	−	0.971802i	$-0.424230\pi$
$97$	45.7447			0.471595			0.235798	+	0.971802i	$0.424230\pi$
$98$	11.0982	+	68.4020i	0.113247	+	0.697979i
$99$	9.88368			0.0998352
$100$		0			0
$101$	79.2589	+	45.7601i	0.784741	+	0.453071i	0.838108	−	0.545504i	$-0.183662\pi$
$101$	79.2589	+	45.7601i	0.784741	+	0.453071i	−0.0533667	+	0.998575i	$0.516995\pi$
$102$	−26.7681	−	15.4545i	−0.262432	−	0.151515i
$103$	25.2541	+	43.7414i	0.245186	+	0.424674i	0.962184	−	0.272401i	$-0.0878178\pi$
$103$	25.2541	+	43.7414i	0.245186	+	0.424674i	−0.716998	+	0.697075i	$0.754484\pi$
$104$			21.8595i			0.210188i
$105$		0			0
$106$	73.0978			0.689602
$107$	81.3626	−	46.9747i	0.760398	−	0.439016i	−0.0690404	−	0.997614i	$-0.521994\pi$
$107$	81.3626	−	46.9747i	0.760398	−	0.439016i	0.829439	+	0.558598i	$0.188660\pi$
$108$	5.19615	−	9.00000i	0.0481125	−	0.0833333i
$109$	60.3052	−	104.452i	0.553258	−	0.958272i	−0.444778	−	0.895641i	$-0.646718\pi$
$109$	60.3052	−	104.452i	0.553258	−	0.958272i	0.998037	−	0.0626310i	$-0.0199491\pi$
$110$		0			0
$111$			59.5766i			0.536726i
$112$	−25.2951	−	12.0067i	−0.225849	−	0.107202i
$113$			10.7318i			0.0949713i	0.998872	+	0.0474856i	$0.0151208\pi$
$113$			10.7318i			0.0949713i	−0.998872	+	0.0474856i	$0.984879\pi$
$114$	2.18218	+	3.77965i	0.0191419	+	0.0331548i
$115$		0			0
$116$	−39.2933	+	68.0580i	−0.338735	+	0.586707i
$117$	−11.5928	−	20.0792i	−0.0990834	−	0.171617i
$118$	159.702			1.35341
$119$	−7.09622	−	88.0446i	−0.0596321	−	0.739870i
$120$		0			0
$121$	55.0729	+	95.3891i	0.455148	+	0.788340i
$122$	18.5495	−	32.1286i	0.152045	−	0.263349i
$123$	−28.2804	−	16.3277i	−0.229922	−	0.132746i
$124$	18.9350	−	10.9321i	0.152702	−	0.0881624i
$125$		0			0
$126$	29.6025	−	2.38590i	0.234940	−	0.0189357i
$127$			117.281i			0.923476i	0.887016	+	0.461738i	$0.152774\pi$
$127$			117.281i			0.923476i	−0.887016	+	0.461738i	$0.847226\pi$
$128$	9.79796	−	5.65685i	0.0765466	−	0.0441942i
$129$	116.130	+	67.0475i	0.900229	+	0.519748i
$130$		0			0
$131$	80.2758	−	46.3473i	0.612792	−	0.353796i	−0.161265	−	0.986911i	$-0.551557\pi$
$131$	80.2758	−	46.3473i	0.612792	−	0.353796i	0.774058	+	0.633115i	$0.218224\pi$
$132$	−11.4127			−0.0864598
$133$	−5.34820	+	11.2673i	−0.0402120	+	0.0847168i
$134$	−28.1614			−0.210160
$135$		0			0
$136$	30.9091	+	17.8454i	0.227273	+	0.131216i
$137$	23.7932	+	13.7370i	0.173673	+	0.100270i	0.584317	−	0.811526i	$-0.301363\pi$
$137$	23.7932	+	13.7370i	0.173673	+	0.100270i	−0.410644	+	0.911796i	$0.634696\pi$
$138$	−8.27485	−	14.3325i	−0.0599626	−	0.103858i
$139$		−	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
$142$	−107.082	+	61.8237i	−0.754097	+	0.435378i
$143$	−12.7310	+	22.0507i	−0.0890280	+	0.154201i
$144$	−6.00000	+	10.3923i	−0.0416667	+	0.0721688i
$145$		0			0
$146$			86.1469i			0.590047i
$147$	53.6589	+	65.7550i	0.365027	+	0.447313i
$148$		−	68.7931i		−	0.464818i
$149$	25.5567	+	44.2656i	0.171522	+	0.297084i	0.938952	−	0.344048i	$-0.111798\pi$
$149$	25.5567	+	44.2656i	0.171522	+	0.297084i	−0.767430	+	0.641132i	$0.778465\pi$
$150$		0			0
$151$	82.6090	−	143.083i	0.547079	−	0.947569i	−0.451394	−	0.892325i	$-0.649073\pi$
$151$	82.6090	−	143.083i	0.547079	−	0.947569i	0.998473	−	0.0552442i	$-0.0175937\pi$
$152$	−2.51977	−	4.36436i	−0.0165774	−	0.0287129i
$153$	−37.8558			−0.247423
$154$	−18.5237	−	26.8436i	−0.120284	−	0.174309i
$155$		0			0
$156$	13.3862	+	23.1855i	0.0858087	+	0.148625i
$157$	95.4059	−	165.248i	0.607681	−	1.05253i	−0.383941	−	0.923358i	$-0.625433\pi$
$157$	95.4059	−	165.248i	0.607681	−	1.05253i	0.991622	−	0.129176i	$-0.0412333\pi$
$158$	43.5736	+	25.1572i	0.275782	+	0.159223i
$159$	77.5319	−	44.7631i	0.487622	−	0.281529i
$160$		0			0
$161$	20.2804	−	42.7258i	0.125965	−	0.265377i
$162$		−	12.7279i		−	0.0785674i
$163$	214.949	−	124.101i	1.31871	−	0.761356i	0.335186	−	0.942152i	$-0.391201\pi$
$163$	214.949	−	124.101i	1.31871	−	0.761356i	0.983521	+	0.180796i	$0.0578674\pi$
$164$	32.6554	+	18.8536i	0.199118	+	0.114961i
$165$		0			0
$166$	−57.1678	+	33.0058i	−0.344384	+	0.198830i
$167$	29.2974			0.175433			0.0877167	−	0.996145i	$-0.472043\pi$
$167$	29.2974			0.175433			0.0877167	+	0.996145i	$0.472043\pi$
$168$	−34.1820	+	2.75500i	−0.203464	+	0.0163988i
$169$	−109.270			−0.646570
$170$		0			0
$171$	4.62911	+	2.67262i	0.0270708	+	0.0156293i
$172$	−134.095	−	77.4197i	−0.779622	−	0.450115i
$173$	−11.5460	−	19.9982i	−0.0667397	−	0.115597i	0.830725	−	0.556683i	$-0.187926\pi$
$173$	−11.5460	−	19.9982i	−0.0667397	−	0.115597i	−0.897464	+	0.441087i	$0.854593\pi$
$174$			96.2485i			0.553152i
$175$		0			0
$176$	13.1782			0.0748764
$177$	169.390	−	97.7973i	0.957005	−	0.552527i
$178$	−38.7596	+	67.1336i	−0.217751	+	0.377155i
$179$	−104.717	+	181.376i	−0.585014	+	1.01327i	0.409860	+	0.912148i	$0.365577\pi$
$179$	−104.717	+	181.376i	−0.585014	+	1.01327i	−0.994874	+	0.101125i	$0.967756\pi$
$180$		0			0
$181$		−	243.667i		−	1.34622i	−0.739540	−	0.673112i	$-0.764957\pi$
$181$		−	243.667i		−	1.34622i	0.739540	−	0.673112i	$-0.235043\pi$
$182$	−32.8075	+	69.1172i	−0.180261	+	0.379765i
$183$		−	45.4367i		−	0.248288i
$184$	9.55497	+	16.5497i	0.0519292	+	0.0899440i
$185$		0			0
$186$	13.3891	−	23.1906i	0.0719843	−	0.124681i
$187$	20.7863	+	36.0030i	0.111157	+	0.192529i
$188$	25.7734			0.137093
$189$	29.9371	−	20.6584i	0.158397	−	0.109304i
$190$		0			0
$191$	118.423	+	205.114i	0.620014	+	1.07390i	0.989483	+	0.144653i	$0.0462064\pi$
$191$	118.423	+	205.114i	0.620014	+	1.07390i	−0.369468	+	0.929243i	$0.620460\pi$
$192$	6.92820	−	12.0000i	0.0360844	−	0.0625000i
$193$	115.088	+	66.4460i	0.596310	+	0.344280i	0.767589	−	0.640943i	$-0.221456\pi$
$193$	115.088	+	66.4460i	0.596310	+	0.344280i	−0.171278	+	0.985223i	$0.554790\pi$
$194$	−56.0256	+	32.3464i	−0.288792	+	0.166734i
$195$		0			0
$196$	−61.9600	−	75.9273i	−0.316122	−	0.387384i
$197$			105.779i			0.536950i	0.963287	+	0.268475i	$0.0865197\pi$
$197$			105.779i			0.536950i	−0.963287	+	0.268475i	$0.913480\pi$
$198$	−12.1050	+	6.98882i	−0.0611363	+	0.0352971i
$199$	−174.541	−	100.771i	−0.877091	−	0.506389i	−0.00739279	−	0.999973i	$-0.502353\pi$
$199$	−174.541	−	100.771i	−0.877091	−	0.506389i	−0.869698	+	0.493584i	$0.835687\pi$
$200$		0			0
$201$	−29.8697	+	17.2453i	−0.148605	+	0.0857973i
$202$	−129.429			−0.640739
$203$	−226.384	+	156.219i	−1.11519	+	0.769550i
$204$	43.7121			0.214275
$205$		0			0
$206$	−61.8597	−	35.7147i	−0.300290	−	0.173372i
$207$	−17.5536	−	10.1346i	−0.0848000	−	0.0489593i
$208$	−15.4570	−	26.7723i	−0.0743125	−	0.128713i
$209$		−	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	$0.477651\pi$
$212$	−89.5262	+	51.6880i	−0.422293	+	0.243811i
$213$	−75.7183	+	131.148i	−0.355485	+	0.615718i
$214$	−66.4323	+	115.064i	−0.310431	+	0.537683i
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	76.2777	−	6.14783i	0.351510	−	0.0283310i
$218$			170.569i			0.782426i
$219$	52.7540	+	91.3726i	0.240886	+	0.417226i
$220$		0			0
$221$	48.7614	−	84.4572i	0.220640	−	0.382159i
$222$	−42.1270	−	72.9661i	−0.189761	−	0.328676i
$223$	328.532			1.47324			0.736620	−	0.676307i	$-0.236421\pi$
$223$	328.532			1.47324			0.736620	+	0.676307i	$0.236421\pi$
$224$	39.4700	−	3.18120i	0.176205	−	0.0142018i
$225$		0			0
$226$	−7.58850	−	13.1437i	−0.0335774	−	0.0581578i
$227$	182.228	−	315.628i	0.802766	−	1.39043i	−0.115023	−	0.993363i	$-0.536694\pi$
$227$	182.228	−	315.628i	0.802766	−	1.39043i	0.917789	−	0.397069i	$-0.129972\pi$
$228$	−5.34523	−	3.08607i	−0.0234440	−	0.0135354i
$229$	260.716	−	150.525i	1.13850	−	0.657313i	0.192441	−	0.981309i	$-0.438360\pi$
$229$	260.716	−	150.525i	1.13850	−	0.657313i	0.946059	+	0.323996i	$0.105026\pi$
$230$		0			0
$231$	−36.0856	−	17.1285i	−0.156215	−	0.0741496i
$232$		−	111.138i		−	0.479044i
$233$	−244.241	+	141.013i	−1.04824	+	0.605204i	−0.922157	−	0.386815i	$-0.873575\pi$
$233$	−244.241	+	141.013i	−1.04824	+	0.605204i	−0.126087	+	0.992019i	$0.540242\pi$
$234$	28.3963	+	16.3946i	0.121352	+	0.0700625i
$235$		0			0
$236$	−195.595	+	112.927i	−0.828790	+	0.478502i
$237$	61.6224			0.260010
$238$	70.9480	+	102.814i	0.298101	+	0.431993i
$239$	−83.0347			−0.347425			−0.173713	−	0.984796i	$-0.555576\pi$
$239$	−83.0347			−0.347425			−0.173713	+	0.984796i	$0.555576\pi$
$240$		0			0
$241$	−287.369	−	165.912i	−1.19240	−	0.688433i	−0.233551	−	0.972345i	$-0.575035\pi$
$241$	−287.369	−	165.912i	−1.19240	−	0.688433i	−0.958851	+	0.283911i	$0.908368\pi$
$242$	−134.901	−	77.8849i	−0.557440	−	0.321838i
$243$	−7.79423	−	13.5000i	−0.0320750	−	0.0555556i
$244$			52.4658i			0.215024i
$245$		0			0
$246$	46.1817			0.187731
$247$	−11.9254	+	6.88511i	−0.0482808	+	0.0278749i
$248$	−15.4604	+	26.7782i	−0.0623403	+	0.107977i
$249$	−40.4237	+	70.0159i	−0.162344	+	0.281188i
$250$		0			0
$251$		−	419.075i		−	1.66962i	−0.550537	−	0.834811i	$-0.685577\pi$
$251$		−	419.075i		−	1.66962i	0.550537	−	0.834811i	$-0.314423\pi$
$252$	−34.5684	+	23.8542i	−0.137176	+	0.0946597i
$253$			22.2593i			0.0879815i
$254$	−82.9305	−	143.640i	−0.326498	−	0.565511i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	166.979	+	289.215i	0.649722	+	1.12535i	0.983189	+	0.182590i	$0.0584481\pi$
$257$	166.979	+	289.215i	0.649722	+	1.12535i	−0.333467	+	0.942762i	$0.608219\pi$
$258$	−189.639			−0.735034
$259$	103.247	−	217.516i	0.398637	−	0.839829i
$260$		0			0
$261$	58.9399	+	102.087i	0.225824	+	0.391138i
$262$	−65.5449	+	113.527i	−0.250171	+	0.433310i
$263$	−176.995	−	102.188i	−0.672986	−	0.388549i	0.124221	−	0.992255i	$-0.460357\pi$
$263$	−176.995	−	102.188i	−0.672986	−	0.388549i	−0.797207	+	0.603706i	$0.793690\pi$
$264$	13.9776	−	8.06999i	0.0529456	−	0.0305681i
$265$		0			0
$266$	−1.41702	−	17.5814i	−0.00532715	−	0.0660953i
$267$			94.9412i			0.355585i
$268$	34.4905	−	19.9131i	0.128696	−	0.0743027i
$269$	120.768	+	69.7257i	0.448953	+	0.259203i	0.707388	−	0.706825i	$-0.249873\pi$
$269$	120.768	+	69.7257i	0.448953	+	0.259203i	−0.258435	+	0.966029i	$0.583207\pi$
$270$		0			0
$271$	−323.213	+	186.607i	−1.19267	+	0.688586i	−0.958910	−	0.283709i	$-0.908435\pi$
$271$	−323.213	+	186.607i	−1.19267	+	0.688586i	−0.233756	+	0.972295i	$0.575102\pi$
$272$	−50.4743			−0.185567
$273$	7.52787	+	93.4002i	0.0275746	+	0.342125i
$274$	−38.8542			−0.141804
$275$		0			0
$276$	20.2691	+	11.7024i	0.0734389	+	0.0424000i
$277$	−430.851	−	248.752i	−1.55542	−	0.898022i	−0.997685	−	0.0680029i	$-0.978337\pi$
$277$	−430.851	−	248.752i	−1.55542	−	0.898022i	−0.557735	−	0.830019i	$-0.688329\pi$
$278$	47.3852	+	82.0735i	0.170450	+	0.295228i
$279$		−	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	$0.325574\pi$
$282$	27.3368	−	15.7829i	0.0969391	−	0.0559678i
$283$	138.383	−	239.686i	0.488986	−	0.846949i	−0.510934	−	0.859620i	$-0.670700\pi$
$283$	138.383	−	239.686i	0.488986	−	0.846949i	0.999920	+	0.0126714i	$0.00403355\pi$
$284$	87.4319	−	151.437i	0.307859	−	0.533227i
$285$		0			0
$286$		−	36.0087i		−	0.125905i
$287$	74.9565	+	108.623i	0.261172	+	0.378478i
$288$		−	16.9706i		−	0.0589256i
$289$	64.8857	+	112.385i	0.224518	+	0.388876i
$290$		0			0
$291$	−39.6161	+	68.6171i	−0.136138	+	0.235798i
$292$	−60.9150	−	105.508i	−0.208613	−	0.361329i
$293$	−375.299			−1.28088			−0.640442	−	0.768006i	$-0.721249\pi$
$293$	−375.299			−1.28088			−0.640442	+	0.768006i	$0.721249\pi$
$294$	−112.214	−	42.5905i	−0.381681	−	0.144866i
$295$		0			0
$296$	48.6441	+	84.2540i	0.164338	+	0.284642i
$297$	−8.55952	+	14.8255i	−0.0288199	+	0.0499176i
$298$	−62.6009	−	36.1427i	−0.210070	−	0.121284i
$299$	45.2210	−	26.1084i	0.151241	−	0.0873189i
$300$		0			0
$301$	−307.798	−	446.046i	−1.02259	−	1.48188i
$302$			233.653i			0.773687i
$303$	−137.280	+	79.2589i	−0.453071	+	0.261580i
$304$	6.17214	+	3.56349i	0.0203031	+	0.0117220i
$305$		0			0
$306$	46.3636	−	26.7681i	0.151515	−	0.0874773i
$307$	−107.784			−0.351088			−0.175544	−	0.984472i	$-0.556168\pi$
$307$	−107.784			−0.351088			−0.175544	+	0.984472i	$0.556168\pi$
$308$	41.6680	+	19.7783i	0.135286	+	0.0642154i
$309$	−87.4828			−0.283116
$310$		0			0
$311$	−499.771	−	288.543i	−1.60698	−	0.927791i	−0.990041	−	0.140780i	$-0.955039\pi$
$311$	−499.771	−	288.543i	−1.60698	−	0.927791i	−0.616940	−	0.787010i	$-0.711628\pi$
$312$	−32.7893	−	18.9309i	−0.105094	−	0.0606759i
$313$	198.637	+	344.050i	0.634624	+	1.09920i	0.986595	+	0.163190i	$0.0521782\pi$
$313$	198.637	+	344.050i	0.634624	+	1.09920i	−0.351971	+	0.936011i	$0.614488\pi$
$314$			269.849i			0.859390i
$315$		0			0
$316$	−71.1554			−0.225175
$317$	−69.6026	+	40.1851i	−0.219566	+	0.126767i	−0.605749	−	0.795655i	$-0.707127\pi$
$317$	−69.6026	+	40.1851i	−0.219566	+	0.126767i	0.386183	+	0.922422i	$0.373793\pi$
$318$	−63.3046	+	109.647i	−0.199071	+	0.344801i
$319$	64.7271	−	112.111i	0.202906	−	0.351444i
$320$		0			0
$321$			162.725i			0.506932i
$322$	5.37336	+	66.6686i	0.0166874	+	0.207045i
$323$			22.4831i			0.0696071i
$324$	9.00000	+	15.5885i	0.0277778	+	0.0481125i
$325$		0			0
$326$	−175.505	+	303.984i	−0.538360	+	0.932467i
$327$	104.452	+	180.915i	0.319424	+	0.553258i
$328$	−53.3261			−0.162580
$329$	81.4925	+	38.6816i	0.247698	+	0.117573i
$330$		0			0
$331$	−246.021	−	426.121i	−0.743266	−	1.28737i	−0.951000	−	0.309189i	$-0.899942\pi$
$331$	−246.021	−	426.121i	−0.743266	−	1.28737i	0.207734	−	0.978185i	$-0.433391\pi$
$332$	46.6773	−	80.8474i	0.140594	−	0.243516i
$333$	−89.3649	−	51.5948i	−0.268363	−	0.154939i
$334$	−35.8818	+	20.7164i	−0.107431	+	0.0620251i
$335$		0			0
$336$	39.9162	−	27.5445i	0.118798	−	0.0819777i
$337$			630.123i			1.86980i	0.354910	+	0.934901i	$0.384512\pi$
$337$			630.123i			1.86980i	−0.354910	+	0.934901i	$0.615488\pi$
$338$	133.828	−	77.2657i	0.395941	−	0.228597i
$339$	−16.0976	−	9.29397i	−0.0474856	−	0.0274159i
$340$		0			0
$341$	−31.1913	+	18.0083i	−0.0914701	+	0.0528103i
$342$	−7.55930			−0.0221032
$343$	−81.9559	−	333.065i	−0.238938	−	0.971035i
$344$	218.976			0.636558
$345$		0			0
$346$	28.2817	+	16.3285i	0.0817391	+	0.0471921i
$347$	−372.514	−	215.071i	−1.07353	−	0.619802i	−0.144385	−	0.989522i	$-0.546120\pi$
$347$	−372.514	−	215.071i	−1.07353	−	0.619802i	−0.929143	+	0.369720i	$0.879454\pi$
$348$	−68.0580	−	117.880i	−0.195569	−	0.338735i
$349$			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
$352$	−16.1400	+	9.31842i	−0.0458522	+	0.0264728i
$353$	−131.469	+	227.710i	−0.372432	+	0.645071i	−0.989939	−	0.141494i	$-0.954809\pi$
$353$	−131.469	+	227.710i	−0.372432	+	0.645071i	0.617507	+	0.786565i	$0.288143\pi$
$354$	−138.306	+	239.553i	−0.390696	+	0.676704i
$355$		0			0
$356$		−	109.629i		−	0.307946i
$357$	138.212	+	65.6045i	0.387150	+	0.183766i
$358$		−	296.186i		−	0.827334i
$359$	149.386	+	258.743i	0.416116	+	0.720734i	0.995545	−	0.0942890i	$-0.0300578\pi$
$359$	149.386	+	258.743i	0.416116	+	0.720734i	−0.579429	+	0.815023i	$0.696724\pi$
$360$		0			0
$361$	−178.913	+	309.886i	−0.495603	+	0.858410i
$362$	172.298	+	298.429i	0.475962	+	0.824391i
$363$	−190.778			−0.525560
$364$	−8.69244	−	107.849i	−0.0238803	−	0.296289i
$365$		0			0
$366$	32.1286	+	55.6484i	0.0877831	+	0.152045i
$367$	−66.0380	+	114.381i	−0.179940	+	0.311665i	−0.941860	−	0.336006i	$-0.890924\pi$
$367$	−66.0380	+	114.381i	−0.179940	+	0.311665i	0.761920	+	0.647671i	$0.224257\pi$
$368$	−23.4048	−	13.5128i	−0.0636000	−	0.0367195i
$369$	48.9831	−	28.2804i	0.132746	−	0.0766407i
$370$		0			0
$371$	−360.646	+	29.0674i	−0.972092	+	0.0783487i
$372$			37.8701i			0.101801i
$373$	9.25597	−	5.34394i	0.0248149	−	0.0143269i	−0.487541	−	0.873100i	$-0.662106\pi$
$373$	9.25597	−	5.34394i	0.0248149	−	0.0143269i	0.512356	+	0.858773i	$0.328773\pi$
$374$	−50.9159	−	29.3963i	−0.136139	−	0.0785998i
$375$		0			0
$376$	−31.5659	+	18.2246i	−0.0839517	+	0.0484696i
$377$	−303.678			−0.805513
$378$	−22.0577	+	46.4700i	−0.0583536	+	0.122936i
$379$	−142.918			−0.377092			−0.188546	−	0.982064i	$-0.560378\pi$
$379$	−142.918			−0.377092			−0.188546	+	0.982064i	$0.560378\pi$
$380$		0			0
$381$	−175.922	−	101.569i	−0.461738	−	0.266585i
$382$	−290.075	−	167.475i	−0.759359	−	0.438416i
$383$	−308.507	−	534.349i	−0.805500	−	1.39517i	−0.915953	−	0.401286i	$-0.868563\pi$
$383$	−308.507	−	534.349i	−0.805500	−	1.39517i	0.110452	−	0.993881i	$-0.464770\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	−187.938			−0.486885
$387$	−201.142	+	116.130i	−0.519748	+	0.300076i
$388$	45.7447	−	79.2322i	0.117899	−	0.204207i
$389$	−346.969	+	600.968i	−0.891951	+	1.54490i	−0.0544171	+	0.998518i	$0.517330\pi$
$389$	−346.969	+	600.968i	−0.891951	+	1.54490i	−0.837534	+	0.546386i	$0.816003\pi$
$390$		0			0
$391$		−	85.2560i		−	0.218046i
$392$	129.574	+	49.1793i	0.330546	+	0.125457i
$393$			160.552i			0.408528i
$394$	−74.7972	−	129.553i	−0.189841	−	0.328814i
$395$		0			0
$396$	9.88368	−	17.1190i	0.0249588	−	0.0432299i
$397$	279.776	+	484.587i	0.704726	+	1.22062i	0.966790	+	0.255571i	$0.0822633\pi$
$397$	279.776	+	484.587i	0.704726	+	1.22062i	−0.262065	+	0.965050i	$0.584403\pi$
$398$	285.024			0.716142
$399$	−12.2693	−	17.7801i	−0.0307502	−	0.0445616i
$400$		0			0
$401$	80.6033	+	139.609i	0.201006	+	0.348152i	0.948853	−	0.315719i	$-0.102246\pi$
$401$	80.6033	+	139.609i	0.201006	+	0.348152i	−0.747847	+	0.663871i	$0.768912\pi$
$402$	24.3885	−	42.2421i	0.0606679	−	0.105080i
$403$	73.1697	+	42.2445i	0.181563	+	0.104825i
$404$	158.518	−	91.5203i	0.392371	−	0.226535i
$405$		0			0
$406$	166.800	−	351.406i	0.410837	−	0.865532i
$407$			113.322i			0.278431i
$408$	−53.5361	+	30.9091i	−0.131216	+	0.0757576i
$409$	−398.217	−	229.911i	−0.973637	−	0.562129i	−0.0732937	−	0.997310i	$-0.523351\pi$
$409$	−398.217	−	229.911i	−0.973637	−	0.562129i	−0.900343	+	0.435181i	$0.856684\pi$
$410$		0			0
$411$	−41.2111	+	23.7932i	−0.100270	+	0.0578911i
$412$	101.016			0.245186
$413$	−787.931	+	63.5056i	−1.90782	+	0.153767i
$414$	28.6649			0.0692389
$415$		0			0
$416$	37.8618	+	21.8595i	0.0910139	+	0.0525469i
$417$	100.519	+	58.0347i	0.241053	+	0.139172i
$418$	4.15076	+	7.18933i	0.00993005	+	0.0171994i
$419$		−	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	$0.438004\pi$
$422$	−36.2579	+	20.9335i	−0.0859193	+	0.0496055i
$423$	19.3301	−	33.4806i	0.0456975	−	0.0791504i
$424$	73.0978	−	126.609i	0.172400	−	0.298606i
$425$		0			0
$426$		−	214.164i		−	0.502731i
$427$	−78.7425	+	165.891i	−0.184409	+	0.388503i
$428$		−	187.899i		−	0.439016i
$429$	−22.0507	−	38.1930i	−0.0514003	−	0.0890280i
$430$		0			0
$431$	165.543	−	286.728i	0.384090	−	0.665263i	−0.607553	−	0.794279i	$-0.707849\pi$
$431$	165.543	−	286.728i	0.384090	−	0.665263i	0.991642	+	0.129016i	$0.0411820\pi$
$432$	−10.3923	−	18.0000i	−0.0240563	−	0.0416667i
$433$	88.4130			0.204187			0.102094	−	0.994775i	$-0.467446\pi$
$433$	88.4130			0.204187			0.102094	+	0.994775i	$0.467446\pi$
$434$	−89.0735	+	61.4660i	−0.205238	+	0.141627i
$435$		0			0
$436$	−120.610	−	208.903i	−0.276629	−	0.479136i
$437$	−6.01907	+	10.4253i	−0.0137736	+	0.0238566i
$438$	−129.220	−	74.6054i	−0.295024	−	0.170332i
$439$	60.4608	−	34.9070i	0.137724	−	0.0795149i	−0.429555	−	0.903041i	$-0.641330\pi$
$439$	60.4608	−	34.9070i	0.137724	−	0.0795149i	0.567279	+	0.823526i	$0.307996\pi$
$440$		0			0
$441$	−145.102	+	23.5429i	−0.329031	+	0.0533852i
$442$			137.918i			0.312032i
$443$	571.953	−	330.217i	1.29109	−	0.745411i	0.312242	−	0.950003i	$-0.398920\pi$
$443$	571.953	−	330.217i	1.29109	−	0.745411i	0.978847	+	0.204592i	$0.0655866\pi$
$444$	103.190	+	59.5766i	0.232409	+	0.134182i
$445$		0			0
$446$	−402.368	+	232.307i	−0.902171	+	0.520869i
$447$	−88.5311			−0.198056
$448$	−46.0912	+	31.8057i	−0.102882	+	0.0709948i
$449$	560.274			1.24783			0.623913	−	0.781493i	$-0.285542\pi$
$449$	560.274			1.24783			0.623913	+	0.781493i	$0.285542\pi$
$450$		0			0
$451$	−53.7926	−	31.0572i	−0.119274	−	0.0688629i
$452$	18.5879	+	10.7318i	0.0411238	+	0.0237428i
$453$	143.083	+	247.827i	0.315856	+	0.547079i
$454$			515.418i			1.13528i
$455$		0			0
$456$	8.72873			0.0191419
$457$	−159.158	+	91.8900i	−0.348267	+	0.201072i	−0.663922	−	0.747802i	$-0.731109\pi$
$457$	−159.158	+	91.8900i	−0.348267	+	0.201072i	0.315655	+	0.948874i	$0.397776\pi$
$458$	−212.874	+	368.709i	−0.464790	+	0.805041i
$459$	32.7840	−	56.7836i	0.0714249	−	0.123712i
$460$		0			0
$461$			28.4330i			0.0616767i	0.999524	+	0.0308384i	$0.00981771\pi$
$461$			28.4330i			0.0616767i	−0.999524	+	0.0308384i	$0.990182\pi$
$462$	56.3073	−	4.53826i	0.121877	−	0.00982307i
$463$		−	269.931i		−	0.583005i	−0.956570	−	0.291503i	$-0.905845\pi$
$463$		−	269.931i		−	0.583005i	0.956570	−	0.291503i	$-0.0941552\pi$
$464$	78.5866	+	136.116i	0.169368	+	0.293353i
$465$		0			0
$466$	199.422	−	345.409i	0.427944	−	0.741221i
$467$	−167.166	−	289.539i	−0.357956	−	0.619999i	0.629663	−	0.776868i	$-0.283193\pi$
$467$	−167.166	−	289.539i	−0.357956	−	0.619999i	−0.987619	+	0.156870i	$0.949860\pi$
$468$	−46.3710			−0.0990834
$469$	138.941	−	11.1984i	0.296250	−	0.0238772i
$470$		0			0
$471$	165.248	+	286.218i	0.350845	+	0.607681i
$472$	159.702	−	276.612i	0.338352	−	0.586043i
$473$	220.892	+	127.532i	0.467002	+	0.269624i
$474$	−75.4717	+	43.5736i	−0.159223	+	0.0919274i
$475$		0			0
$476$	−159.594	−	75.7536i	−0.335281	−	0.159146i
$477$			155.064i			0.325081i
$478$	101.696	−	58.7144i	0.212754	−	0.122833i
$479$	−114.560	−	66.1412i	−0.239165	−	0.138082i	0.375628	−	0.926771i	$-0.377427\pi$
$479$	−114.560	−	66.1412i	−0.239165	−	0.138082i	−0.614793	+	0.788689i	$0.710760\pi$
$480$		0			0
$481$	230.219	−	132.917i	0.478626	−	0.276335i
$482$	469.271			0.973592
$483$	46.5253	+	67.4222i	0.0963257	+	0.139591i
$484$	220.292			0.455148
$485$		0			0
$486$	19.0919	+	11.0227i	0.0392837	+	0.0226805i
$487$	−447.970	−	258.635i	−0.919856	−	0.531079i	−0.0362667	−	0.999342i	$-0.511547\pi$
$487$	−447.970	−	258.635i	−0.919856	−	0.531079i	−0.883589	+	0.468263i	$0.844880\pi$
$488$	−37.0989	−	64.2573i	−0.0760224	−	0.131675i
$489$			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	$0.335647\pi$
$492$	−56.5609	+	32.6554i	−0.114961	+	0.0663728i
$493$	−247.913	+	429.398i	−0.502866	+	0.870989i
$494$	9.73701	−	16.8650i	0.0197105	−	0.0341397i
$495$		0			0
$496$		−	43.7286i		−	0.0881624i
$497$	503.730	−	347.604i	1.01354	−	0.699404i
$498$		−	114.336i		−	0.229589i
$499$	−64.6450	−	111.968i	−0.129549	−	0.224385i	0.793953	−	0.607979i	$-0.208020\pi$
$499$	−64.6450	−	111.968i	−0.129549	−	0.224385i	−0.923502	+	0.383594i	$0.874686\pi$
$500$		0			0
$501$	−25.3723	+	43.9461i	−0.0506432	+	0.0877167i
$502$	296.331	+	513.260i	0.590300	+	1.02243i
$503$	160.905			0.319890			0.159945	−	0.987126i	$-0.448868\pi$
$503$	160.905			0.319890			0.159945	+	0.987126i	$0.448868\pi$
$504$	25.4700	−	53.6589i	0.0505357	−	0.106466i
$505$		0			0
$506$	−15.7397	−	27.2620i	−0.0311061	−	0.0538774i
$507$	94.6308	−	163.905i	0.186649	−	0.323285i
$508$	203.137	+	117.281i	0.399877	+	0.230869i
$509$	320.453	−	185.014i	0.629575	−	0.363485i	−0.151013	−	0.988532i	$-0.548253\pi$
$509$	320.453	−	185.014i	0.629575	−	0.363485i	0.780587	+	0.625047i	$0.214920\pi$
$510$		0			0
$511$	−34.2563	−	425.027i	−0.0670378	−	0.831755i
$512$		−	22.6274i		−	0.0441942i
$513$	−8.01785	+	4.62911i	−0.0156293	+	0.00902360i
$514$	−409.012	−	236.143i	−0.795744	−	0.459423i
$515$		0			0
$516$	232.259	−	134.095i	0.450115	−	0.259874i
$517$	−42.4560			−0.0821200
$518$	27.3556	+	339.408i	0.0528101	+	0.655228i
$519$	39.9964			0.0770644
$520$		0			0
$521$	65.1395	+	37.6083i	0.125028	+	0.0721849i	0.561210	−	0.827674i	$-0.310336\pi$
$521$	65.1395	+	37.6083i	0.125028	+	0.0721849i	−0.436182	+	0.899859i	$0.643670\pi$
$522$	−144.373	−	83.3537i	−0.276576	−	0.159681i
$523$	468.058	+	810.701i	0.894949	+	1.55010i	0.833867	+	0.551965i	$0.186122\pi$
$523$	468.058	+	810.701i	0.894949	+	1.55010i	0.0610819	+	0.998133i	$0.480545\pi$
$524$		−	185.389i		−	0.353796i
$525$		0			0
$526$	289.032			0.549491
$527$	119.467	−	68.9741i	0.226692	−	0.130881i
$528$	−11.4127	+	19.7674i	−0.0216149	+	0.0374382i
$529$	−241.676	+	418.594i	−0.456854	+	0.791294i
$530$		0			0
$531$			338.780i			0.638003i
$532$	14.1674	+	20.5307i	0.0266304	+	0.0385915i
$533$			145.710i			0.273377i
$534$	−67.1336	−	116.279i	−0.125718	−	0.217751i
$535$		0			0
$536$	−28.1614	+	48.7770i	−0.0525399	+	0.0910018i
$537$	−181.376	−	314.152i	−0.337758	−	0.585014i
$538$	−197.214			−0.366569
$539$	102.065	+	125.074i	0.189361	+	0.232047i
$540$		0			0
$541$	304.692	+	527.742i	0.563201	+	0.975493i	0.997215	+	0.0745867i	$0.0237638\pi$
$541$	304.692	+	527.742i	0.563201	+	0.975493i	−0.434013	+	0.900906i	$0.642903\pi$
$542$	263.902	−	457.092i	0.486904	−	0.843343i
$543$	365.500	+	211.021i	0.673112	+	0.388622i
$544$	61.8182	−	35.6907i	0.113636	−	0.0656080i
$545$		0			0
$546$	−75.2637	−	109.068i	−0.137846	−	0.199759i
$547$			491.361i			0.898283i	0.893461	+	0.449141i	$0.148270\pi$
$547$			491.361i			0.898283i	−0.893461	+	0.449141i	$0.851730\pi$
$548$	47.5865	−	27.4741i	0.0868366	−	0.0501351i
$549$	68.1551	+	39.3494i	0.124144	+	0.0716746i
$550$		0			0
$551$	60.6310	−	35.0053i	0.110038	−	0.0635305i
$552$	−33.0994			−0.0599626
$553$	−224.985	−	106.792i	−0.406844	−	0.193115i
$554$	703.577			1.27000
$555$		0			0
$556$	−116.069	−	67.0127i	−0.208758	−	0.120527i
$557$	−911.250	−	526.110i	−1.63600	−	0.944543i	−0.982192	−	0.187878i	$-0.939839\pi$
$557$	−911.250	−	526.110i	−1.63600	−	0.944543i	−0.653803	−	0.756665i	$-0.726828\pi$
$558$	23.1906	+	40.1673i	0.0415602	+	0.0719843i
$559$		−	598.339i		−	1.07037i
$560$		0			0
$561$	−72.0060			−0.128353
$562$	−358.580	+	207.026i	−0.638042	+	0.368374i
$563$	387.269	−	670.769i	0.687866	−	1.19142i	−0.284661	−	0.958628i	$-0.591881\pi$
$563$	387.269	−	670.769i	0.687866	−	1.19142i	0.972527	−	0.232791i	$-0.0747857\pi$
$564$	−22.3204	+	38.6601i	−0.0395752	+	0.0685463i
$565$		0			0
$566$			391.406i			0.691531i
$567$	5.06126	+	62.7964i	0.00892639	+	0.110752i
$568$			247.295i			0.435378i
$569$	156.525	+	271.109i	0.275088	+	0.476466i	0.970157	−	0.242477i	$-0.0779598\pi$
$569$	156.525	+	271.109i	0.275088	+	0.476466i	−0.695070	+	0.718942i	$0.744626\pi$
$570$		0			0
$571$	−324.711	+	562.416i	−0.568670	+	0.984966i	0.428027	+	0.903766i	$0.359209\pi$
$571$	−324.711	+	562.416i	−0.568670	+	0.984966i	−0.996698	+	0.0812002i	$0.974125\pi$
$572$	25.4620	+	44.1015i	0.0445140	+	0.0771005i
$573$	−410.228			−0.715931
$574$	−168.611	−	80.0336i	−0.293747	−	0.139431i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	514.893	−	891.822i	0.892363	−	1.54562i	0.0553284	−	0.998468i	$-0.482379\pi$
$577$	514.893	−	891.822i	0.892363	−	1.54562i	0.837035	−	0.547150i	$-0.184287\pi$
$578$	−158.937	−	91.7622i	−0.274977	−	0.158758i
$579$	−199.338	+	115.088i	−0.344280	+	0.198770i
$580$		0			0
$581$	268.927	−	185.575i	0.462868	−	0.319406i
$582$		−	112.051i		−	0.192528i
$583$	147.475	−	85.1445i	0.252958	−	0.146046i
$584$	149.211	+	86.1469i	0.255498	+	0.147512i
$585$		0			0
$586$	459.646	−	265.376i	0.784378	−	0.452861i
$587$	−791.817			−1.34892			−0.674461	−	0.738311i	$-0.735624\pi$
$587$	−791.817			−1.34892			−0.674461	+	0.738311i	$0.735624\pi$
$588$	167.550	−	27.1850i	0.284949	−	0.0462329i
$589$	−19.4783			−0.0330701
$590$		0			0
$591$	−158.669	−	91.6075i	−0.268475	−	0.155004i
$592$	−119.153	−	68.7931i	−0.201272	−	0.116205i
$593$	−42.2509	−	73.1807i	−0.0712494	−	0.123408i	0.828200	−	0.560433i	$-0.189365\pi$
$593$	−42.2509	−	73.1807i	−0.0712494	−	0.123408i	−0.899449	+	0.437025i	$0.856032\pi$
$594$		−	24.2100i		−	0.0407575i
$595$		0			0
$596$	102.227			0.171522
$597$	302.314	−	174.541i	0.506389	−	0.292364i
$598$	−36.9228	+	63.9522i	−0.0617438	+	0.106943i
$599$	−233.463	+	404.369i	−0.389754	+	0.675074i	−0.992416	−	0.122922i	$-0.960773\pi$
$599$	−233.463	+	404.369i	−0.389754	+	0.675074i	0.602662	+	0.797997i	$0.294107\pi$
$600$		0			0
$601$			1095.93i			1.82351i	0.410733	+	0.911756i	$0.365273\pi$
$601$			1095.93i			1.82351i	−0.410733	+	0.911756i	$0.634727\pi$
$602$	692.377	+	328.647i	1.15013	+	0.545925i
$603$		−	59.7394i		−	0.0990702i
$604$	−165.218	−	286.166i	−0.273540	−	0.473785i
$605$		0			0
$606$	112.089	−	194.144i	0.184965	−	0.320369i
$607$	179.449	+	310.815i	0.295633	+	0.512051i	0.975132	−	0.221625i	$-0.0711361\pi$
$607$	179.449	+	310.815i	0.295633	+	0.512051i	−0.679499	+	0.733676i	$0.737803\pi$
$608$	−10.0791			−0.0165774
$609$	−38.2733	−	474.866i	−0.0628461	−	0.779747i
$610$		0			0
$611$	49.7975	+	86.2517i	0.0815016	+	0.141165i
$612$	−37.8558	+	65.5681i	−0.0618558	+	0.107137i
$613$	400.154	+	231.029i	0.652780	+	0.376883i	0.789520	−	0.613724i	$-0.210329\pi$
$613$	400.154	+	231.029i	0.652780	+	0.376883i	−0.136741	+	0.990607i	$0.543663\pi$
$614$	132.008	−	76.2148i	0.214996	−	0.124128i
$615$		0			0
$616$	−65.0181	+	5.24033i	−0.105549	+	0.00850703i
$617$		−	219.440i		−	0.355656i	−0.984062	−	0.177828i	$-0.943093\pi$
$617$		−	219.440i		−	0.355656i	0.984062	−	0.177828i	$-0.0569071\pi$
$618$	107.144	−	61.8597i	0.173372	−	0.100097i
$619$	−832.792	−	480.813i	−1.34538	−	0.776757i	−0.357791	−	0.933802i	$-0.616470\pi$
$619$	−832.792	−	480.813i	−1.34538	−	0.776757i	−0.987592	+	0.157044i	$0.949803\pi$
$620$		0			0
$621$	30.4037	−	17.5536i	0.0489593	−	0.0282667i
$622$	816.123			1.31209
$623$	164.534	−	346.633i	0.264100	−	0.556393i
$624$	53.5446			0.0858087
$625$		0			0
$626$	−486.560	−	280.915i	−0.777252	−	0.448747i
$627$	8.80509	+	5.08362i	0.0140432	+	0.00810785i
$628$	−190.812	−	330.496i	−0.303840	−	0.526267i
$629$		−	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	$0.346655\pi$
$632$	87.1472	−	50.3144i	0.137891	−	0.0796115i
$633$	−25.6382	+	44.4067i	−0.0405027	+	0.0701528i
$634$	56.8303	−	98.4329i	0.0896376	−	0.155257i
$635$		0			0
$636$		−	179.052i		−	0.281529i
$637$	134.379	−	354.053i	0.210957	−	0.555813i
$638$			183.076i			0.286953i
$639$	−131.148	−	227.155i	−0.205239	−	0.355485i
$640$		0			0
$641$	−269.518	+	466.819i	−0.420465	+	0.728268i	−0.995985	−	0.0895205i	$-0.971467\pi$
$641$	−269.518	+	466.819i	−0.420465	+	0.728268i	0.575520	+	0.817788i	$0.304800\pi$
$642$	−115.064	−	199.297i	−0.179228	−	0.310431i
$643$	−150.959			−0.234773			−0.117386	−	0.993086i	$-0.537452\pi$
$643$	−150.959			−0.234773			−0.117386	+	0.993086i	$0.537452\pi$
$644$	−53.7228	−	77.8525i	−0.0834205	−	0.120889i
$645$		0			0
$646$	−15.8979	−	27.5360i	−0.0246098	−	0.0426255i
$647$	225.808	−	391.111i	0.349008	−	0.604499i	−0.637066	−	0.770809i	$-0.719852\pi$
$647$	225.808	−	391.111i	0.349008	−	0.604499i	0.986073	+	0.166310i	$0.0531854\pi$
$648$	−22.0454	−	12.7279i	−0.0340207	−	0.0196419i
$649$	322.199	−	186.022i	0.496454	−	0.286628i
$650$		0			0
$651$	−56.8366	+	119.741i	−0.0873067	+	0.183933i
$652$		−	496.404i		−	0.761356i
$653$	373.860	−	215.848i	0.572526	−	0.330548i	−0.185631	−	0.982619i	$-0.559433\pi$
$653$	373.860	−	215.848i	0.572526	−	0.330548i	0.758158	+	0.652071i	$0.226100\pi$
$654$	−255.853	−	147.717i	−0.391213	−	0.225867i
$655$		0			0
$656$	65.3108	−	37.7072i	0.0995592	−	0.0574805i
$657$	−182.745			−0.278151
$658$	−127.160	+	10.2488i	−0.193252	+	0.0155757i
$659$	195.185			0.296184			0.148092	−	0.988974i	$-0.452687\pi$
$659$	195.185			0.296184			0.148092	+	0.988974i	$0.452687\pi$
$660$		0			0
$661$	596.305	+	344.277i	0.902126	+	0.520843i	0.877889	−	0.478863i	$-0.158951\pi$
$661$	596.305	+	344.277i	0.902126	+	0.520843i	0.0242368	+	0.999706i	$0.492284\pi$
$662$	602.626	+	347.926i	0.910311	+	0.525569i
$663$	84.4572	+	146.284i	0.127386	+	0.220640i
$664$			132.023i			0.198830i
$665$		0			0
$666$	145.932			0.219118
$667$	−229.913	+	132.740i	−0.344697	+	0.199011i
$668$	29.2974	−	50.7445i	0.0438583	−	0.0759649i
$669$	−284.517	+	492.799i	−0.425288	+	0.736620i
$670$		0			0
$671$		−	86.4259i		−	0.128802i
$672$	−29.4102	+	61.9600i	−0.0437652	+	0.0922024i
$673$			200.020i			0.297206i	0.988897	+	0.148603i	$0.0474777\pi$
$673$			200.020i			0.297206i	−0.988897	+	0.148603i	$0.952522\pi$
$674$	−445.564	−	771.740i	−0.661075	−	1.14501i
$675$		0			0
$676$	−109.270	+	189.262i	−0.161642	+	0.279973i
$677$	−424.807	−	735.787i	−0.627484	−	1.08683i	−0.988055	−	0.154103i	$-0.950751\pi$
$677$	−424.807	−	735.787i	−0.627484	−	1.08683i	0.360571	−	0.932732i	$-0.382582\pi$
$678$	26.2873			0.0387719
$679$	263.554	−	181.868i	0.388150	−	0.267846i
$680$		0			0
$681$	315.628	+	546.684i	0.463477	+	0.802766i
$682$	25.4676	−	44.1111i	0.0373425	−	0.0646791i
$683$	387.988	+	224.005i	0.568064	+	0.327972i	0.756376	−	0.654137i	$-0.226968\pi$
$683$	387.988	+	224.005i	0.568064	+	0.327972i	−0.188311	+	0.982109i	$0.560301\pi$
$684$	9.25821	−	5.34523i	0.0135354	−	0.00781467i
$685$		0			0
$686$	335.888	+	349.968i	0.489632	+	0.510157i
$687$			521.433i			0.759000i
$688$	−268.190	+	154.839i	−0.389811	+	0.225057i
$689$	−345.952	−	199.735i	−0.502107	−	0.289891i
$690$		0			0
$691$	−337.930	+	195.104i	−0.489044	+	0.282350i	−0.724178	−	0.689613i	$-0.757781\pi$
$691$	−337.930	+	195.104i	−0.489044	+	0.282350i	0.235134	+	0.971963i	$0.424447\pi$
$692$	−46.1839			−0.0667397
$693$	56.9439	−	39.2946i	0.0821701	−	0.0567022i
$694$	608.313			0.876532
$695$		0			0
$696$	166.707	+	96.2485i	0.239522	+	0.138288i
$697$	206.033	+	118.953i	0.295599	+	0.170664i
$698$	−67.3038	−	116.574i	−0.0964237	−	0.167011i
$699$		−	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	$0.250752\pi$
$702$	−49.1839	+	28.3963i	−0.0700625	+	0.0404506i
$703$	−30.6429	+	53.0751i	−0.0435888	+	0.0754980i
$704$	13.1782	−	22.8254i	0.0187191	−	0.0324224i
$705$		0			0
$706$		−	371.849i		−	0.526699i
$707$	638.571	−	51.4676i	0.903212	−	0.0727971i
$708$		−	391.189i		−	0.552527i
$709$	554.927	+	961.161i	0.782689	+	1.35566i	0.930370	+	0.366623i	$0.119486\pi$
$709$	554.927	+	961.161i	0.782689	+	1.35566i	−0.147680	+	0.989035i	$0.547181\pi$
$710$		0			0
$711$	−53.3665	+	92.4335i	−0.0750584	+	0.130005i
$712$	77.5192	+	134.267i	0.108875	+	0.188578i
$713$	73.8617			0.103593
$714$	−215.664	+	17.3821i	−0.302051	+	0.0243447i
$715$		0			0
$716$	209.435	+	362.752i	0.292507	+	0.506637i
$717$	71.9101	−	124.552i	0.100293	−	0.173713i
$718$	−365.918	−	211.263i	−0.509636	−	0.294238i
$719$	−936.393	+	540.627i	−1.30235	+	0.751915i	−0.980807	−	0.194979i	$-0.937536\pi$
$719$	−936.393	+	540.627i	−1.30235	+	0.751915i	−0.321547	+	0.946894i	$0.604203\pi$
$720$		0			0
$721$	319.402	+	151.609i	0.442999	+	0.210276i
$722$		−	506.042i		−	0.700889i
$723$	497.737	−	287.369i	0.688433	−	0.397467i
$724$	−422.043	−	243.667i	−0.582932	−	0.336556i
$725$		0			0
$726$	233.655	−	134.901i	0.321838	−	0.185813i
$727$	−491.493			−0.676056			−0.338028	−	0.941136i	$-0.609760\pi$
$727$	−491.493			−0.676056			−0.338028	+	0.941136i	$0.609760\pi$
$728$	86.9070	+	125.941i	0.119378	+	0.172996i
$729$	27.0000			0.0370370
$730$		0			0
$731$	−846.044	−	488.464i	−1.15738	−	0.668213i
$732$	−78.6988	−	45.4367i	−0.107512	−	0.0620721i
$733$	−23.3826	−	40.4999i	−0.0318999	−	0.0552522i	0.849635	−	0.527372i	$-0.176822\pi$
$733$	−23.3826	−	40.4999i	−0.0318999	−	0.0552522i	−0.881535	+	0.472119i	$0.843489\pi$
$734$		−	186.784i		−	0.254474i
$735$		0			0
$736$	38.2199			0.0519292
$737$	−56.8156	+	32.8025i	−0.0770903	+	0.0445081i
$738$	−39.9946	+	69.2726i	−0.0541932	+	0.0938653i
$739$	−368.856	+	638.878i	−0.499129	+	0.864517i	−0.999999	−	0.00100544i	$-0.999680\pi$
$739$	−368.856	+	638.878i	−0.499129	+	0.864517i	0.500870	+	0.865522i	$0.333013\pi$
$740$		0			0
$741$		−	23.8507i		−	0.0321872i
$742$	421.146	−	290.615i	0.567582	−	0.391665i
$743$		−	258.593i		−	0.348039i	−0.984742	−	0.174020i	$-0.944324\pi$
$743$		−	258.593i		−	0.348039i	0.984742	−	0.174020i	$-0.0556757\pi$
$744$	−26.7782	−	46.3812i	−0.0359922	−	0.0623403i
$745$		0			0
$746$	−7.55747	+	13.0899i	−0.0101307	+	0.0175468i
$747$	−70.0159	−	121.271i	−0.0937295	−	0.162344i
$748$	83.1454			0.111157
$749$	282.005	−	594.114i	0.376509	−	0.793210i
$750$		0			0
$751$	−175.310	−	303.645i	−0.233435	−	0.404321i	0.725382	−	0.688347i	$-0.241663\pi$
$751$	−175.310	−	303.645i	−0.233435	−	0.404321i	−0.958817	+	0.284025i	$0.908330\pi$
$752$	25.7734	−	44.6409i	0.0342731	−	0.0593628i
$753$	628.613	+	362.930i	0.834811	+	0.481978i
$754$	371.928	−	214.733i	0.493274	−	0.284792i
$755$		0			0
$756$	−5.84424	−	72.5110i	−0.00773048	−	0.0959140i
$757$		−	907.187i		−	1.19840i	−0.800600	−	0.599199i	$-0.795486\pi$
$757$		−	907.187i		−	1.19840i	0.800600	−	0.599199i	$-0.204514\pi$
$758$	175.038	−	101.058i	0.230921	−	0.133322i
$759$	−33.3890	−	19.2771i	−0.0439907	−	0.0253981i
$760$		0			0
$761$	1067.66	−	616.416i	1.40297	−	0.810007i	0.408277	−	0.912858i	$-0.366130\pi$
$761$	1067.66	−	616.416i	1.40297	−	0.810007i	0.994697	+	0.102851i	$0.0327965\pi$
$762$	287.280			0.377008
$763$	−67.8267	−	841.543i	−0.0888948	−	1.10294i
$764$	473.691			0.620014
$765$		0			0
$766$	755.684	+	436.294i	0.986532	+	0.569575i
$767$	−755.826	−	436.376i	−0.985432	−	0.568939i
$768$	−13.8564	−	24.0000i	−0.0180422	−	0.0312500i
$769$			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
$772$	230.176	−	132.892i	0.298155	−	0.172140i
$773$	−193.077	+	334.420i	−0.249776	+	0.432625i	−0.963464	−	0.267839i	$-0.913690\pi$
$773$	−193.077	+	334.420i	−0.249776	+	0.432625i	0.713687	+	0.700465i	$0.247024\pi$
$774$	164.232	−	284.458i	0.212186	−	0.367517i
$775$		0			0
$776$			129.386i			0.166734i
$777$	236.859	+	343.245i	0.304838	+	0.441756i
$778$		−	981.376i		−	1.26141i
$779$	−16.7962	−	29.0918i	−0.0215612	−	0.0373451i
$780$		0			0
$781$	−144.025	+	249.458i	−0.184411	+	0.319409i
$782$	60.2851	+	104.417i	0.0770909	+	0.133525i
$783$	−204.174			−0.260759
$784$	−193.470	+	31.3905i	−0.246773	+	0.0400389i
$785$		0			0
$786$	−113.527	−	196.635i	−0.144437	−	0.250171i
$787$	614.543	−	1064.42i	0.780867	−	1.35250i	−0.150570	−	0.988599i	$-0.548111\pi$
$787$	614.543	−	1064.42i	0.780867	−	1.35250i	0.931437	−	0.363902i	$-0.118556\pi$
$788$	183.215	+	105.779i	0.232506	+	0.134238i
$789$	306.565	−	176.995i	0.388549	−	0.224329i
$790$		0			0
$791$	42.6663	+	61.8300i	0.0539397	+	0.0781668i
$792$			27.9553i			0.0352971i
$793$	−175.579	+	101.371i	−0.221411	+	0.127832i
$794$	−685.309	−	395.663i	−0.863109	−	0.498316i
$795$		0			0
$796$	−349.082	+	201.543i	−0.438545	+	0.253194i
$797$	−821.718			−1.03101			−0.515507	−	0.856886i	$-0.672396\pi$
$797$	−821.718			−1.03101			−0.515507	+	0.856886i	$0.672396\pi$
$798$	27.5992	+	13.1004i	0.0345855	+	0.0164165i
$799$	162.612			0.203519
$800$		0			0
$801$	−142.412	−	82.2215i	−0.177793	−	0.102649i
$802$	−197.437	−	113.990i	−0.246181	−	0.142132i
$803$	100.344	+	173.801i	0.124962	+	0.216440i
$804$			68.9811i			0.0857973i
$805$		0			0
$806$	−119.486			−0.148245
$807$	−209.177	+	120.768i	−0.259203	+	0.149651i
$808$	−129.429	+	224.178i	−0.160185	+	0.277448i
$809$	−216.809	+	375.524i	−0.267996	+	0.464184i	−0.968344	−	0.249618i	$-0.919695\pi$
$809$	−216.809	+	375.524i	−0.267996	+	0.464184i	0.700348	+	0.713802i	$0.253028\pi$
$810$		0			0
$811$			1618.04i			1.99512i	0.0698416	+	0.997558i	$0.477751\pi$
$811$			1618.04i			1.99512i	−0.0698416	+	0.997558i	$0.522249\pi$
$812$	44.1941	+	548.328i	0.0544263	+	0.675281i
$813$		−	646.425i		−	0.795111i
$814$	−80.1304	−	138.790i	−0.0984403	−	0.170504i
$815$		0			0
$816$	43.7121	−	75.7115i	0.0535687	−	0.0927837i
$817$	68.9711	+	119.461i	0.0844199	+	0.146220i
$818$	650.286			0.794971
$819$	−146.620	−	69.5952i	−0.179023	−	0.0849758i
$820$		0			0
$821$	429.043	+	743.125i	0.522586	+	0.905146i	0.999655	+	0.0262799i	$0.00836612\pi$
$821$	429.043	+	743.125i	0.522586	+	0.905146i	−0.477068	+	0.878866i	$0.658301\pi$
$822$	33.6487	−	58.2813i	0.0409352	−	0.0709018i
$823$	679.461	+	392.287i	0.825591	+	0.476655i	0.852341	−	0.522987i	$-0.175182\pi$
$823$	679.461	+	392.287i	0.825591	+	0.476655i	−0.0267498	+	0.999642i	$0.508516\pi$
$824$	−123.719	+	71.4294i	−0.150145	+	0.0866862i
$825$		0			0
$826$	920.109	−	634.929i	1.11393	−	0.768680i
$827$			773.795i			0.935665i	0.883817	+	0.467833i	$0.154965\pi$
$827$			773.795i			0.935665i	−0.883817	+	0.467833i	$0.845035\pi$
$828$	−35.1072	+	20.2691i	−0.0424000	+	0.0244796i
$829$	573.640	+	331.191i	0.691966	+	0.399507i	0.804348	−	0.594158i	$-0.202515\pi$
$829$	573.640	+	331.191i	0.691966	+	0.399507i	−0.112382	+	0.993665i	$0.535848\pi$
$830$		0			0
$831$	746.256	−	430.851i	0.898022	−	0.518473i
$832$	−61.8280			−0.0743125
$833$	−390.924	−	479.048i	−0.469296	−	0.575087i
$834$	−164.147			−0.196819
$835$		0			0
$836$	−10.1672	−	5.87006i	−0.0121618	−	0.00702161i
$837$	49.1946	+	28.4025i	0.0587750	+	0.0339337i
$838$	66.1723	+	114.614i	0.0789646	+	0.136771i
$839$		−	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
$842$	−199.581	+	115.228i	−0.237032	+	0.136851i
$843$	−253.554	+	439.169i	−0.300776	+	0.520959i
$844$	29.6045	−	51.2764i	0.0350764	−	0.0607541i
$845$		0			0
$846$			54.6737i			0.0646261i
$847$	696.537	+	330.621i	0.822357	+	0.390344i
$848$			206.752i			0.243811i
$849$	239.686	+	415.149i	0.282316	+	0.488986i
$850$		0			0
$851$	116.198	−	201.261i	0.136543	−	0.236500i
$852$	151.437	+	262.296i	0.177742	+	0.307859i
$853$	−1089.78			−1.27758			−0.638792	−	0.769379i	$-0.720566\pi$
$853$	−1089.78			−1.27758			−0.638792	+	0.769379i	$0.720566\pi$
$854$	−20.8631	−	258.853i	−0.0244298	−	0.303107i
$855$		0			0
$856$	132.865	+	230.128i	0.155216	+	0.268841i
$857$	−32.4560	+	56.2155i	−0.0378717	+	0.0655956i	−0.884340	−	0.466843i	$-0.845391\pi$
$857$	−32.4560	+	56.2155i	−0.0378717	+	0.0655956i	0.846468	+	0.532439i	$0.178724\pi$
$858$	54.0131	+	31.1845i	0.0629523	+	0.0363455i
$859$	−250.689	+	144.735i	−0.291838	+	0.168493i	−0.638770	−	0.769397i	$-0.720557\pi$
$859$	−250.689	+	144.735i	−0.291838	+	0.168493i	0.346933	+	0.937890i	$0.387223\pi$
$860$		0			0
$861$	−227.849	+	18.3642i	−0.264633	+	0.0213289i
$862$			468.225i			0.543185i
$863$	812.738	−	469.234i	0.941759	−	0.543725i	0.0512476	−	0.998686i	$-0.483680\pi$
$863$	812.738	−	469.234i	0.941759	−	0.543725i	0.890511	+	0.454961i	$0.150347\pi$
$864$	25.4558	+	14.6969i	0.0294628	+	0.0170103i
$865$		0			0
$866$	−108.283	+	62.5174i	−0.125038	+	0.0721910i
$867$	−224.771			−0.259251
$868$	65.6293	−	138.265i	0.0756098	−	0.159291i
$869$	117.213			0.134882
$870$		0			0
$871$	133.280	+	76.9493i	0.153020	+	0.0883459i
$872$	295.434	+	170.569i	0.338800	+	0.195606i
$873$	−68.6171	−	118.848i	−0.0785992	−	0.136138i
$874$		−	17.0245i		−	0.0194788i
$875$		0			0
$876$	211.016			0.240886
$877$	−191.465	+	110.543i	−0.218318	+	0.126046i	−0.605171	−	0.796095i	$-0.706895\pi$
$877$	−191.465	+	110.543i	−0.218318	+	0.126046i	0.386853	+	0.922141i	$0.373562\pi$
$878$	−49.3660	+	85.5044i	−0.0562255	+	0.0973855i
$879$	325.019	−	562.949i	0.369759	−	0.640442i
$880$		0			0
$881$			154.796i			0.175704i	0.996134	+	0.0878522i	$0.0280003\pi$
$881$			154.796i			0.175704i	−0.996134	+	0.0878522i	$0.972000\pi$
$882$	161.066	−	131.437i	0.182615	−	0.149022i
$883$		−	1267.40i		−	1.43534i	−0.696385	−	0.717668i	$-0.745209\pi$
$883$		−	1267.40i		−	1.43534i	0.696385	−	0.717668i	$-0.254791\pi$
$884$	−97.5227	−	168.914i	−0.110320	−	0.191080i
$885$		0			0
$886$	−466.997	+	808.863i	−0.527085	+	0.912938i
$887$	828.399	+	1434.83i	0.933934	+	1.61762i	0.776524	+	0.630087i	$0.216981\pi$
$887$	828.399	+	1434.83i	0.933934	+	1.61762i	0.157410	+	0.987533i	$0.449686\pi$
$888$	−168.508			−0.189761
$889$	466.277	+	675.706i	0.524496	+	0.760074i
$890$		0			0
$891$	−14.8255	−	25.6786i	−0.0166392	−	0.0288199i
$892$	328.532	−	569.035i	0.368310	−	0.637931i
$893$	−19.8846	−	11.4804i	−0.0222672	−	0.0128560i
$894$	108.428	−	62.6009i	0.121284	−	0.0700234i
$895$		0			0
$896$	33.9600	−	71.5452i	0.0379018	−	0.0798496i
$897$			90.4420i			0.100827i
$898$	−686.193	+	396.174i	−0.764135	+	0.441173i
$899$	−372.010	−	214.780i	−0.413804	−	0.238910i
$900$		0			0
$901$	−564.847	+	326.114i	−0.626911	+	0.361947i
$902$	87.8430			0.0973869
$903$	935.630	−	75.4099i	1.03614	−	0.0835105i
$904$	−30.3540			−0.0335774
$905$		0			0
$906$	−350.480	−	202.350i	−0.386844	−	0.223344i
$907$	−637.793	−	368.230i	−0.703190	−	0.405987i	0.105345	−	0.994436i	$-0.466405\pi$
$907$	−637.793	−	368.230i	−0.703190	−	0.405987i	−0.808534	+	0.588449i	$0.799739\pi$
$908$	−364.456	−	631.256i	−0.401383	−	0.695216i
$909$		−	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	$0.465352\pi$
$912$	−10.6905	+	6.17214i	−0.0117220	+	0.00676770i
$913$	−76.8905	+	133.178i	−0.0842175	+	0.145869i
$914$	129.952	−	225.084i	0.142180	−	0.246262i
$915$		0			0
$916$		−	602.099i		−	0.657313i
$917$	278.238	−	586.178i	0.303422	−	0.639235i
$918$			92.7273i			0.101010i
$919$	821.091	+	1422.17i	0.893462	+	1.54752i	0.835697	+	0.549191i	$0.185064\pi$
$919$	821.091	+	1422.17i	0.893462	+	1.54752i	0.0577645	+	0.998330i	$0.481603\pi$
$920$		0			0
$921$	93.3436	−	161.676i	0.101350	−	0.175544i
$922$	−20.1051	−	34.8231i	−0.0218060	−	0.0377691i
$923$	675.718			0.732089
$924$	−65.7531	+	45.3735i	−0.0711614	+	0.0491055i
$925$		0			0
$926$	190.870	+	330.597i	0.206123	+	0.357016i
$927$	75.7623	−	131.224i	0.0817285	−	0.141558i
$928$	−192.497	−	111.138i	−0.207432	−	0.119761i
$929$	−1317.18	+	760.473i	−1.41784	+	0.818593i	−0.996109	−	0.0881263i	$-0.971912\pi$
$929$	−1317.18	+	760.473i	−1.41784	+	0.818593i	−0.421735	+	0.906719i	$0.638579\pi$
$930$		0			0
$931$	13.9825	+	86.1785i	0.0150188	+	0.0925655i
$932$			564.050i			0.605204i
$933$	865.629	−	499.771i	0.927791	−	0.535660i
$934$	409.471	+	236.408i	0.438405	+	0.253113i
$935$		0			0
$936$	56.7927	−	32.7893i	0.0606759	−	0.0350313i
$937$	682.636			0.728534			0.364267	−	0.931295i	$-0.381320\pi$
$937$	682.636			0.728534			0.364267	+	0.931295i	$0.381320\pi$
$938$	−162.249	+	111.961i	−0.172974	+	0.119362i
$939$	−688.100			−0.732800
$940$		0			0
$941$	−248.545	−	143.497i	−0.264129	−	0.152495i	0.362088	−	0.932144i	$-0.382064\pi$
$941$	−248.545	−	143.497i	−0.264129	−	0.152495i	−0.626216	+	0.779649i	$0.715397\pi$
$942$	−404.773	−	233.696i	−0.429695	−	0.248085i
$943$	63.6911	+	110.316i	0.0675410	+	0.116984i
$944$			451.706i			0.478502i
$945$		0			0
$946$	−360.715			−0.381305
$947$	−415.790	+	240.057i	−0.439061	+	0.253492i	−0.703199	−	0.710993i	$-0.748246\pi$
$947$	−415.790	+	240.057i	−0.439061	+	0.253492i	0.264139	+	0.964485i	$0.414912\pi$
$948$	61.6224	−	106.733i	0.0650025	−	0.112588i
$949$	235.391	−	407.709i	0.248041	−	0.429620i
$950$		0			0
$951$		−	139.205i		−	0.146378i
$952$	249.028	−	20.0711i	0.261584	−	0.0210831i
$953$			1147.30i			1.20388i	0.798540	+	0.601941i	$0.205606\pi$
$953$			1147.30i			1.20388i	−0.798540	+	0.601941i	$0.794394\pi$
$954$	−109.647	−	189.914i	−0.114934	−	0.199071i
$955$		0			0
$956$	−83.0347	+	143.820i	−0.0868563	+	0.150440i
$957$	112.111	+	194.181i	0.117148	+	0.202906i
$958$	187.076			0.195277
$959$	191.697	−	15.4504i	0.199892	−	0.0161109i
$960$		0			0
$961$	−420.744	−	728.750i	−0.437819	−	0.758325i
$962$	−187.973	+	325.579i	−0.195398	+	0.338439i
$963$	−244.088	−	140.924i	−0.253466	−	0.146339i
$964$	−574.737	+	331.825i	−0.596201	+	0.344217i
$965$		0			0
$966$	−104.656	−	49.6767i	−0.108340	−	0.0514251i
$967$			1400.07i			1.44785i	0.689881	+	0.723923i	$0.257663\pi$
$967$			1400.07i			1.44785i	−0.689881	+	0.723923i	$0.742337\pi$
$968$	−269.801	+	155.770i	−0.278720	+	0.160919i
$969$	−33.7246	−	19.4709i	−0.0348035	−	0.0200938i
$970$		0			0
$971$	226.263	−	130.633i	0.233020	−	0.134534i	−0.378944	−	0.925419i	$-0.623713\pi$
$971$	226.263	−	130.633i	0.233020	−	0.134534i	0.611965	+	0.790885i	$0.290379\pi$
$972$	−31.1769			−0.0320750
$973$	−266.423	−	386.087i	−0.273816	−	0.396801i
$974$	731.532			0.751059
$975$		0			0
$976$	90.8735	+	52.4658i	0.0931081	+	0.0537560i
$977$	675.019	+	389.723i	0.690910	+	0.398897i	0.803953	−	0.594693i	$-0.202726\pi$
$977$	675.019	+	389.723i	0.690910	+	0.398897i	−0.113043	+	0.993590i	$0.536060\pi$
$978$	−303.984	−	526.516i	−0.310822	−	0.538360i
$979$			180.589i			0.184463i
$980$		0			0
$981$	−361.831			−0.368839
$982$	−593.763	+	342.809i	−0.604646	+	0.349093i
$983$	769.118	−	1332.15i	0.782419	−	1.35519i	−0.148110	−	0.988971i	$-0.547319\pi$
$983$	769.118	−	1332.15i	0.782419	−	1.35519i	0.930529	−	0.366219i	$-0.119348\pi$
$984$	46.1817	−	79.9891i	0.0469327	−	0.0812898i
$985$		0			0
$986$		−	701.204i		−	0.711160i
$987$	−128.597	+	88.7395i	−0.130291	+	0.0899083i
$988$			27.5404i			0.0278749i
$989$	−261.539	−	452.998i	−0.264448	−	0.458037i
$990$		0			0
$991$	−482.270	+	835.316i	−0.486650	+	0.842902i	−0.999882	−	0.0153476i	$-0.995115\pi$
$991$	−482.270	+	835.316i	−0.486650	+	0.842902i	0.513233	+	0.858250i	$0.328448\pi$
$992$	30.9208	+	53.5563i	0.0311701	+	0.0539883i
$993$	852.242			0.858250
$994$	−371.148	+	781.917i	−0.373389	+	0.786637i
$995$		0			0
$996$	80.8474	+	140.032i	0.0811721	+	0.140594i
$997$	208.868	−	361.770i	0.209496	−	0.362858i	−0.742060	−	0.670334i	$-0.766151\pi$
$997$	208.868	−	361.770i	0.209496	−	0.362858i	0.951556	+	0.307476i	$0.0994842\pi$
$998$	158.347	+	91.4218i	0.158664	+	0.0916050i
$999$	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.q.b.199.2		16
5.2	odd	4		1050.3.p.d.451.2	yes	8
5.3	odd	4		1050.3.p.c.451.3	✓	8
5.4	even	2	inner	1050.3.q.b.199.7		16
7.5	odd	6	inner	1050.3.q.b.649.7		16
35.12	even	12		1050.3.p.d.901.2	yes	8
35.19	odd	6	inner	1050.3.q.b.649.2		16
35.33	even	12		1050.3.p.c.901.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.p.c.451.3	✓	8	5.3	odd	4
1050.3.p.c.901.3	yes	8	35.33	even	12
1050.3.p.d.451.2	yes	8	5.2	odd	4
1050.3.p.d.901.2	yes	8	35.12	even	12
1050.3.q.b.199.2		16	1.1	even	1	trivial
1050.3.q.b.199.7		16	5.4	even	2	inner
1050.3.q.b.649.2		16	35.19	odd	6	inner
1050.3.q.b.649.7		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)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(5.76140 - 3.97571i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(5.76140 - 3.97571i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-1.64728 + 2.85317i) q^{11} +(1.73205 + 3.00000i) q^{12} +7.72850 q^{13} +(-4.24500 + 8.94315i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(6.30929 - 10.9280i) q^{17} +(3.67423 + 2.12132i) q^{18} +(-1.54304 + 0.890872i) q^{19} +(0.974040 + 12.0852i) q^{21} -4.65921i q^{22} +(5.85120 - 3.37819i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-9.46544 + 5.46488i) q^{26} +5.19615 q^{27} +(-1.12472 - 13.9547i) q^{28} -39.2933 q^{29} +(9.46751 + 5.46607i) q^{31} +(4.89898 + 2.82843i) q^{32} +(-2.85317 - 4.94184i) q^{33} +17.8454i q^{34} -6.00000 q^{36} +(29.7883 - 17.1983i) q^{37} +(1.25988 - 2.18218i) q^{38} +(-6.69308 + 11.5928i) q^{39} +18.8536i q^{41} +(-9.73845 - 14.1125i) q^{42} -77.4197i q^{43} +(3.29456 + 5.70635i) q^{44} +(-4.77748 + 8.27485i) q^{46} +(6.44335 + 11.1602i) q^{47} +6.92820 q^{48} +(17.3875 - 45.8113i) q^{49} +(10.9280 + 18.9279i) q^{51} +(7.72850 - 13.3862i) q^{52} +(-44.7631 - 25.8440i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(11.2450 + 16.2957i) q^{56} -3.08607i q^{57} +(48.1243 - 27.7846i) q^{58} +(-97.7973 - 56.4633i) q^{59} +(-22.7184 + 13.1165i) q^{61} -15.4604 q^{62} +(-18.9713 - 9.00500i) q^{63} -8.00000 q^{64} +(6.98882 + 4.03500i) q^{66} +(17.2453 + 9.95656i) q^{67} +(-12.6186 - 21.8560i) q^{68} +11.7024i q^{69} +87.4319 q^{71} +(7.34847 - 4.24264i) q^{72} +(30.4575 - 52.7540i) q^{73} +(-24.3220 + 42.1270i) q^{74} +3.56349i q^{76} +(1.85274 + 22.9874i) q^{77} -18.9309i q^{78} +(-17.7888 - 30.8112i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-13.3315 - 23.0909i) q^{82} +46.6773 q^{83} +(21.9062 + 10.3981i) q^{84} +(54.7440 + 94.8194i) q^{86} +(34.0290 - 58.9399i) q^{87} +(-8.06999 - 4.65921i) q^{88} +(47.4706 - 27.4072i) q^{89} +(44.5270 - 30.7263i) q^{91} -13.5128i q^{92} +(-16.3982 + 9.46751i) q^{93} +(-15.7829 - 9.11228i) q^{94} +(-8.48528 + 4.89898i) q^{96} +45.7447 q^{97} +(11.0982 + 68.4020i) q^{98} +9.88368 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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