LMFDB - Embedded newform 1050.3.q.b.649.2

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			649.2
Root			$2.22431 + 0.596002i$ of defining polynomial
Character	$\chi$	$=$	1050.649
Dual form			1050.3.q.b.199.2

$q$-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 $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−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	0.781383	−	0.624051i	$-0.214514\pi$
$11$	−1.64728	−	2.85317i	−0.149753	−	0.259379i	−0.931136	+	0.364672i	$0.881181\pi$
$12$	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	0.989740	−	0.142877i	$-0.0456354\pi$
$17$	6.30929	+	10.9280i	0.371135	+	0.642824i	−0.618606	+	0.785702i	$0.712302\pi$
$18$	3.67423	−	2.12132i	0.204124	−	0.117851i
$19$	−1.54304	−	0.890872i	−0.0812124	−	0.0468880i	0.458844	−	0.888517i	$-0.348264\pi$
$19$	−1.54304	−	0.890872i	−0.0812124	−	0.0468880i	−0.540056	+	0.841629i	$0.681597\pi$
$20$		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	0.621777	−	0.783194i	$-0.286411\pi$
$23$	5.85120	+	3.37819i	0.254400	+	0.146878i	−0.367377	+	0.930072i	$0.619744\pi$
$24$	−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	−0.339464	−	0.940619i	$-0.610246\pi$
$31$	9.46751	−	5.46607i	0.305404	−	0.176325i	0.644868	+	0.764294i	$0.276912\pi$
$32$	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	0.845248	−	0.534375i	$-0.179453\pi$
$37$	29.7883	+	17.1983i	0.805089	+	0.464818i	−0.0401585	+	0.999193i	$0.512786\pi$
$38$	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	$-0.926153\pi$
$41$		−	18.8536i		−	0.459844i	0.973209	−	0.229922i	$-0.0738472\pi$
$42$	−9.73845	+	14.1125i	−0.231868	+	0.336012i
$43$			77.4197i			1.80046i	0.435416	+	0.900229i	$0.356601\pi$
$43$			77.4197i			1.80046i	−0.435416	+	0.900229i	$0.643399\pi$
$44$	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	−0.789302	−	0.614005i	$-0.789558\pi$
$47$	6.44335	−	11.1602i	0.137093	−	0.237451i	0.926395	+	0.376553i	$0.122891\pi$
$48$	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	−0.858821	−	0.512276i	$-0.828802\pi$
$53$	−44.7631	+	25.8440i	−0.844586	+	0.487622i	0.0142341	+	0.999899i	$0.495469\pi$
$54$	−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	−0.683754	+	0.729713i	$0.739654\pi$
$59$	−97.7973	+	56.4633i	−1.65758	+	0.957005i	−0.973827	+	0.227292i	$0.927013\pi$
$60$		0			0
$61$	−22.7184	−	13.1165i	−0.372432	−	0.215024i	0.302088	−	0.953280i	$-0.402316\pi$
$61$	−22.7184	−	13.1165i	−0.372432	−	0.215024i	−0.674521	+	0.738256i	$0.735650\pi$
$62$	−15.4604			−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	−0.365752	−	0.930712i	$-0.619188\pi$
$67$	17.2453	−	9.95656i	0.257392	−	0.148605i	0.623144	+	0.782107i	$0.285855\pi$
$68$	−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	0.995659	−	0.0930727i	$-0.0296689\pi$
$73$	30.4575	+	52.7540i	0.417226	+	0.722657i	−0.578433	+	0.815730i	$0.696336\pi$
$74$	−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	−0.956372	−	0.292152i	$-0.905629\pi$
$79$	−17.7888	+	30.8112i	−0.225175	+	0.390015i	0.731197	+	0.682167i	$0.238962\pi$
$80$		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	0.742391	−	0.669967i	$-0.233692\pi$
$89$	47.4706	+	27.4072i	0.533378	+	0.307946i	−0.209013	+	0.977913i	$0.567025\pi$
$90$		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	−0.0533667	−	0.998575i	$-0.516995\pi$
$101$	79.2589	−	45.7601i	0.784741	−	0.453071i	0.838108	+	0.545504i	$0.183662\pi$
$102$	−26.7681	+	15.4545i	−0.262432	+	0.151515i
$103$	25.2541	−	43.7414i	0.245186	−	0.424674i	−0.716998	−	0.697075i	$-0.754484\pi$
$103$	25.2541	−	43.7414i	0.245186	−	0.424674i	0.962184	+	0.272401i	$0.0878178\pi$
$104$		−	21.8595i		−	0.210188i
$105$		0			0
$106$	73.0978			0.689602
$107$	81.3626	+	46.9747i	0.760398	+	0.439016i	0.829439	−	0.558598i	$-0.188660\pi$
$107$	81.3626	+	46.9747i	0.760398	+	0.439016i	−0.0690404	+	0.997614i	$0.521994\pi$
$108$	5.19615	+	9.00000i	0.0481125	+	0.0833333i
$109$	60.3052	+	104.452i	0.553258	+	0.958272i	0.998037	+	0.0626310i	$0.0199491\pi$
$109$	60.3052	+	104.452i	0.553258	+	0.958272i	−0.444778	+	0.895641i	$0.646718\pi$
$110$		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	$-0.984879\pi$
$113$		−	10.7318i		−	0.0949713i	0.998872	−	0.0474856i	$-0.0151208\pi$
$114$	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	$-0.847226\pi$
$127$		−	117.281i		−	0.923476i	0.887016	−	0.461738i	$-0.152774\pi$
$128$	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	0.774058	−	0.633115i	$-0.218224\pi$
$131$	80.2758	+	46.3473i	0.612792	+	0.353796i	−0.161265	+	0.986911i	$0.551557\pi$
$132$	−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	−0.410644	−	0.911796i	$-0.634696\pi$
$137$	23.7932	−	13.7370i	0.173673	−	0.100270i	0.584317	+	0.811526i	$0.301363\pi$
$138$	−8.27485	+	14.3325i	−0.0599626	+	0.103858i
$139$			67.0127i			0.482106i	0.970512	+	0.241053i	$0.0774928\pi$
$139$			67.0127i			0.482106i	−0.970512	+	0.241053i	$0.922507\pi$
$140$		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	−0.767430	−	0.641132i	$-0.778465\pi$
$149$	25.5567	−	44.2656i	0.171522	−	0.297084i	0.938952	+	0.344048i	$0.111798\pi$
$150$		0			0
$151$	82.6090	+	143.083i	0.547079	+	0.947569i	0.998473	+	0.0552442i	$0.0175937\pi$
$151$	82.6090	+	143.083i	0.547079	+	0.947569i	−0.451394	+	0.892325i	$0.649073\pi$
$152$	−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	0.991622	+	0.129176i	$0.0412333\pi$
$157$	95.4059	+	165.248i	0.607681	+	1.05253i	−0.383941	+	0.923358i	$0.625433\pi$
$158$	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	0.983521	−	0.180796i	$-0.0578674\pi$
$163$	214.949	+	124.101i	1.31871	+	0.761356i	0.335186	+	0.942152i	$0.391201\pi$
$164$	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	−0.897464	−	0.441087i	$-0.854593\pi$
$173$	−11.5460	+	19.9982i	−0.0667397	+	0.115597i	0.830725	+	0.556683i	$0.187926\pi$
$174$		−	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	−0.994874	−	0.101125i	$-0.967756\pi$
$179$	−104.717	−	181.376i	−0.585014	−	1.01327i	0.409860	−	0.912148i	$-0.365577\pi$
$180$		0			0
$181$			243.667i			1.34622i	0.739540	+	0.673112i	$0.235043\pi$
$181$			243.667i			1.34622i	−0.739540	+	0.673112i	$0.764957\pi$
$182$	−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	−0.369468	−	0.929243i	$-0.620460\pi$
$191$	118.423	−	205.114i	0.620014	−	1.07390i	0.989483	−	0.144653i	$-0.0462064\pi$
$192$	6.92820	+	12.0000i	0.0360844	+	0.0625000i
$193$	115.088	−	66.4460i	0.596310	−	0.344280i	−0.171278	−	0.985223i	$-0.554790\pi$
$193$	115.088	−	66.4460i	0.596310	−	0.344280i	0.767589	+	0.640943i	$0.221456\pi$
$194$	−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	$-0.913480\pi$
$197$		−	105.779i		−	0.536950i	0.963287	−	0.268475i	$-0.0865197\pi$
$198$	−12.1050	−	6.98882i	−0.0611363	−	0.0352971i
$199$	−174.541	+	100.771i	−0.877091	+	0.506389i	−0.869698	−	0.493584i	$-0.835687\pi$
$199$	−174.541	+	100.771i	−0.877091	+	0.506389i	−0.00739279	+	0.999973i	$0.502353\pi$
$200$		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	0.917789	+	0.397069i	$0.129972\pi$
$227$	182.228	+	315.628i	0.802766	+	1.39043i	−0.115023	+	0.993363i	$0.536694\pi$
$228$	−5.34523	+	3.08607i	−0.0234440	+	0.0135354i
$229$	260.716	+	150.525i	1.13850	+	0.657313i	0.946059	−	0.323996i	$-0.105026\pi$
$229$	260.716	+	150.525i	1.13850	+	0.657313i	0.192441	+	0.981309i	$0.438360\pi$
$230$		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	−0.126087	−	0.992019i	$-0.540242\pi$
$233$	−244.241	−	141.013i	−1.04824	−	0.605204i	−0.922157	+	0.386815i	$0.873575\pi$
$234$	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	−0.958851	−	0.283911i	$-0.908368\pi$
$241$	−287.369	+	165.912i	−1.19240	+	0.688433i	−0.233551	+	0.972345i	$0.575035\pi$
$242$	−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	$0.314423\pi$
$251$			419.075i			1.66962i	−0.550537	+	0.834811i	$0.685577\pi$
$252$	−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	−0.333467	−	0.942762i	$-0.608219\pi$
$257$	166.979	−	289.215i	0.649722	−	1.12535i	0.983189	−	0.182590i	$-0.0584481\pi$
$258$	−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	−0.797207	−	0.603706i	$-0.793690\pi$
$263$	−176.995	+	102.188i	−0.672986	+	0.388549i	0.124221	+	0.992255i	$0.460357\pi$
$264$	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	−0.258435	−	0.966029i	$-0.583207\pi$
$269$	120.768	−	69.7257i	0.448953	−	0.259203i	0.707388	+	0.706825i	$0.249873\pi$
$270$		0			0
$271$	−323.213	−	186.607i	−1.19267	−	0.688586i	−0.233756	−	0.972295i	$-0.575102\pi$
$271$	−323.213	−	186.607i	−1.19267	−	0.688586i	−0.958910	+	0.283709i	$0.908435\pi$
$272$	−50.4743			−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	−0.557735	+	0.830019i	$0.688329\pi$
$277$	−430.851	+	248.752i	−1.55542	+	0.898022i	−0.997685	+	0.0680029i	$0.978337\pi$
$278$	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	0.999920	−	0.0126714i	$-0.00403355\pi$
$283$	138.383	+	239.686i	0.488986	+	0.846949i	−0.510934	+	0.859620i	$0.670700\pi$
$284$	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	−0.616940	+	0.787010i	$0.711628\pi$
$311$	−499.771	+	288.543i	−1.60698	+	0.927791i	−0.990041	+	0.140780i	$0.955039\pi$
$312$	−32.7893	+	18.9309i	−0.105094	+	0.0606759i
$313$	198.637	−	344.050i	0.634624	−	1.09920i	−0.351971	−	0.936011i	$-0.614488\pi$
$313$	198.637	−	344.050i	0.634624	−	1.09920i	0.986595	−	0.163190i	$-0.0521782\pi$
$314$		−	269.849i		−	0.859390i
$315$		0			0
$316$	−71.1554			−0.225175
$317$	−69.6026	−	40.1851i	−0.219566	−	0.126767i	0.386183	−	0.922422i	$-0.373793\pi$
$317$	−69.6026	−	40.1851i	−0.219566	−	0.126767i	−0.605749	+	0.795655i	$0.707127\pi$
$318$	−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	0.207734	+	0.978185i	$0.433391\pi$
$331$	−246.021	+	426.121i	−0.743266	+	1.28737i	−0.951000	+	0.309189i	$0.899942\pi$
$332$	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	$-0.615488\pi$
$337$		−	630.123i		−	1.86980i	0.354910	−	0.934901i	$-0.384512\pi$
$338$	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	−0.929143	−	0.369720i	$-0.879454\pi$
$347$	−372.514	+	215.071i	−1.07353	+	0.619802i	−0.144385	+	0.989522i	$0.546120\pi$
$348$	−68.0580	+	117.880i	−0.195569	+	0.338735i
$349$		−	95.1819i		−	0.272727i	−0.990659	−	0.136364i	$-0.956458\pi$
$349$		−	95.1819i		−	0.272727i	0.990659	−	0.136364i	$-0.0435416\pi$
$350$		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	0.617507	−	0.786565i	$-0.288143\pi$
$353$	−131.469	−	227.710i	−0.372432	−	0.645071i	−0.989939	+	0.141494i	$0.954809\pi$
$354$	−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	−0.579429	−	0.815023i	$-0.696724\pi$
$359$	149.386	−	258.743i	0.416116	−	0.720734i	0.995545	+	0.0942890i	$0.0300578\pi$
$360$		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	0.761920	−	0.647671i	$-0.224257\pi$
$367$	−66.0380	−	114.381i	−0.179940	−	0.311665i	−0.941860	+	0.336006i	$0.890924\pi$
$368$	−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	0.512356	−	0.858773i	$-0.328773\pi$
$373$	9.25597	+	5.34394i	0.0248149	+	0.0143269i	−0.487541	+	0.873100i	$0.662106\pi$
$374$	−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	0.110452	+	0.993881i	$0.464770\pi$
$383$	−308.507	+	534.349i	−0.805500	+	1.39517i	−0.915953	+	0.401286i	$0.868563\pi$
$384$		−	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	−0.837534	−	0.546386i	$-0.816003\pi$
$389$	−346.969	−	600.968i	−0.891951	−	1.54490i	−0.0544171	−	0.998518i	$-0.517330\pi$
$390$		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	−0.262065	−	0.965050i	$-0.584403\pi$
$397$	279.776	−	484.587i	0.704726	−	1.22062i	0.966790	−	0.255571i	$-0.0822633\pi$
$398$	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	−0.747847	−	0.663871i	$-0.768912\pi$
$401$	80.6033	−	139.609i	0.201006	−	0.348152i	0.948853	+	0.315719i	$0.102246\pi$
$402$	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	−0.900343	−	0.435181i	$-0.856684\pi$
$409$	−398.217	+	229.911i	−0.973637	+	0.562129i	−0.0732937	+	0.997310i	$0.523351\pi$
$410$		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	$0.0356208\pi$
$419$			93.5818i			0.223346i	−0.993745	+	0.111673i	$0.964379\pi$
$420$		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	0.991642	−	0.129016i	$-0.0411820\pi$
$431$	165.543	+	286.728i	0.384090	+	0.665263i	−0.607553	+	0.794279i	$0.707849\pi$
$432$	−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	0.567279	−	0.823526i	$-0.307996\pi$
$439$	60.4608	+	34.9070i	0.137724	+	0.0795149i	−0.429555	+	0.903041i	$0.641330\pi$
$440$		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	0.978847	−	0.204592i	$-0.0655866\pi$
$443$	571.953	+	330.217i	1.29109	+	0.745411i	0.312242	+	0.950003i	$0.398920\pi$
$444$	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	0.315655	−	0.948874i	$-0.397776\pi$
$457$	−159.158	−	91.8900i	−0.348267	−	0.201072i	−0.663922	+	0.747802i	$0.731109\pi$
$458$	−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	$-0.990182\pi$
$461$		−	28.4330i		−	0.0616767i	0.999524	−	0.0308384i	$-0.00981771\pi$
$462$	56.3073	+	4.53826i	0.121877	+	0.00982307i
$463$			269.931i			0.583005i	0.956570	+	0.291503i	$0.0941552\pi$
$463$			269.931i			0.583005i	−0.956570	+	0.291503i	$0.905845\pi$
$464$	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	−0.987619	−	0.156870i	$-0.949860\pi$
$467$	−167.166	+	289.539i	−0.357956	+	0.619999i	0.629663	+	0.776868i	$0.283193\pi$
$468$	−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	−0.614793	−	0.788689i	$-0.710760\pi$
$479$	−114.560	+	66.1412i	−0.239165	+	0.138082i	0.375628	+	0.926771i	$0.377427\pi$
$480$		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	−0.883589	−	0.468263i	$-0.844880\pi$
$487$	−447.970	+	258.635i	−0.919856	+	0.531079i	−0.0362667	+	0.999342i	$0.511547\pi$
$488$	−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	−0.923502	−	0.383594i	$-0.874686\pi$
$499$	−64.6450	+	111.968i	−0.129549	+	0.224385i	0.793953	+	0.607979i	$0.208020\pi$
$500$		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	0.780587	−	0.625047i	$-0.214920\pi$
$509$	320.453	+	185.014i	0.629575	+	0.363485i	−0.151013	+	0.988532i	$0.548253\pi$
$510$		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	−0.436182	−	0.899859i	$-0.643670\pi$
$521$	65.1395	−	37.6083i	0.125028	−	0.0721849i	0.561210	+	0.827674i	$0.310336\pi$
$522$	−144.373	+	83.3537i	−0.276576	+	0.159681i
$523$	468.058	−	810.701i	0.894949	−	1.55010i	0.0610819	−	0.998133i	$-0.480545\pi$
$523$	468.058	−	810.701i	0.894949	−	1.55010i	0.833867	−	0.551965i	$-0.186122\pi$
$524$			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	−0.434013	−	0.900906i	$-0.642903\pi$
$541$	304.692	−	527.742i	0.563201	−	0.975493i	0.997215	−	0.0745867i	$-0.0237638\pi$
$542$	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	$-0.851730\pi$
$547$		−	491.361i		−	0.898283i	0.893461	−	0.449141i	$-0.148270\pi$
$548$	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	−0.653803	+	0.756665i	$0.726828\pi$
$557$	−911.250	+	526.110i	−1.63600	+	0.944543i	−0.982192	+	0.187878i	$0.939839\pi$
$558$	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	0.972527	+	0.232791i	$0.0747857\pi$
$563$	387.269	+	670.769i	0.687866	+	1.19142i	−0.284661	+	0.958628i	$0.591881\pi$
$564$	−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	−0.695070	−	0.718942i	$-0.744626\pi$
$569$	156.525	−	271.109i	0.275088	−	0.476466i	0.970157	+	0.242477i	$0.0779598\pi$
$570$		0			0
$571$	−324.711	−	562.416i	−0.568670	−	0.984966i	−0.996698	−	0.0812002i	$-0.974125\pi$
$571$	−324.711	−	562.416i	−0.568670	−	0.984966i	0.428027	−	0.903766i	$-0.359209\pi$
$572$	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	0.837035	+	0.547150i	$0.184287\pi$
$577$	514.893	+	891.822i	0.892363	+	1.54562i	0.0553284	+	0.998468i	$0.482379\pi$
$578$	−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	−0.899449	−	0.437025i	$-0.856032\pi$
$593$	−42.2509	+	73.1807i	−0.0712494	+	0.123408i	0.828200	+	0.560433i	$0.189365\pi$
$594$			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	0.602662	−	0.797997i	$-0.294107\pi$
$599$	−233.463	−	404.369i	−0.389754	−	0.675074i	−0.992416	+	0.122922i	$0.960773\pi$
$600$		0			0
$601$		−	1095.93i		−	1.82351i	−0.410733	−	0.911756i	$-0.634727\pi$
$601$		−	1095.93i		−	1.82351i	0.410733	−	0.911756i	$-0.365273\pi$
$602$	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	−0.679499	−	0.733676i	$-0.737803\pi$
$607$	179.449	−	310.815i	0.295633	−	0.512051i	0.975132	+	0.221625i	$0.0711361\pi$
$608$	−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	−0.136741	−	0.990607i	$-0.543663\pi$
$613$	400.154	−	231.029i	0.652780	−	0.376883i	0.789520	+	0.613724i	$0.210329\pi$
$614$	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	$0.0569071\pi$
$617$			219.440i			0.355656i	−0.984062	+	0.177828i	$0.943093\pi$
$618$	107.144	+	61.8597i	0.173372	+	0.100097i
$619$	−832.792	+	480.813i	−1.34538	+	0.776757i	−0.987592	−	0.157044i	$-0.949803\pi$
$619$	−832.792	+	480.813i	−1.34538	+	0.776757i	−0.357791	+	0.933802i	$0.616470\pi$
$620$		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	0.575520	−	0.817788i	$-0.304800\pi$
$641$	−269.518	−	466.819i	−0.420465	−	0.728268i	−0.995985	+	0.0895205i	$0.971467\pi$
$642$	−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	0.986073	−	0.166310i	$-0.0531854\pi$
$647$	225.808	+	391.111i	0.349008	+	0.604499i	−0.637066	+	0.770809i	$0.719852\pi$
$648$	−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	0.758158	−	0.652071i	$-0.226100\pi$
$653$	373.860	+	215.848i	0.572526	+	0.330548i	−0.185631	+	0.982619i	$0.559433\pi$
$654$	−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	0.0242368	−	0.999706i	$-0.492284\pi$
$661$	596.305	−	344.277i	0.902126	−	0.520843i	0.877889	+	0.478863i	$0.158951\pi$
$662$	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	$-0.952522\pi$
$673$		−	200.020i		−	0.297206i	0.988897	−	0.148603i	$-0.0474777\pi$
$674$	−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	0.360571	+	0.932732i	$0.382582\pi$
$677$	−424.807	+	735.787i	−0.627484	+	1.08683i	−0.988055	+	0.154103i	$0.950751\pi$
$678$	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	−0.188311	−	0.982109i	$-0.560301\pi$
$683$	387.988	−	224.005i	0.568064	−	0.327972i	0.756376	+	0.654137i	$0.226968\pi$
$684$	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	0.235134	−	0.971963i	$-0.424447\pi$
$691$	−337.930	−	195.104i	−0.489044	−	0.282350i	−0.724178	+	0.689613i	$0.757781\pi$
$692$	−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	−0.147680	−	0.989035i	$-0.547181\pi$
$709$	554.927	−	961.161i	0.782689	−	1.35566i	0.930370	−	0.366623i	$-0.119486\pi$
$710$		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	−0.321547	−	0.946894i	$-0.604203\pi$
$719$	−936.393	−	540.627i	−1.30235	−	0.751915i	−0.980807	+	0.194979i	$0.937536\pi$
$720$		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	−0.881535	−	0.472119i	$-0.843489\pi$
$733$	−23.3826	+	40.4999i	−0.0318999	+	0.0552522i	0.849635	+	0.527372i	$0.176822\pi$
$734$			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	0.500870	−	0.865522i	$-0.333013\pi$
$739$	−368.856	−	638.878i	−0.499129	−	0.864517i	−0.999999	+	0.00100544i	$0.999680\pi$
$740$		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	$0.0556757\pi$
$743$			258.593i			0.348039i	−0.984742	+	0.174020i	$0.944324\pi$
$744$	−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	−0.958817	−	0.284025i	$-0.908330\pi$
$751$	−175.310	+	303.645i	−0.233435	+	0.404321i	0.725382	+	0.688347i	$0.241663\pi$
$752$	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	$0.204514\pi$
$757$			907.187i			1.19840i	−0.800600	+	0.599199i	$0.795486\pi$
$758$	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	0.994697	−	0.102851i	$-0.0327965\pi$
$761$	1067.66	+	616.416i	1.40297	+	0.810007i	0.408277	+	0.912858i	$0.366130\pi$
$762$	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	$-0.852876\pi$
$769$		−	685.828i		−	0.891844i	0.895072	−	0.445922i	$-0.147124\pi$
$770$		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	0.713687	−	0.700465i	$-0.247024\pi$
$773$	−193.077	−	334.420i	−0.249776	−	0.432625i	−0.963464	+	0.267839i	$0.913690\pi$
$774$	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	0.931437	+	0.363902i	$0.118556\pi$
$787$	614.543	+	1064.42i	0.780867	+	1.35250i	−0.150570	+	0.988599i	$0.548111\pi$
$788$	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	0.700348	−	0.713802i	$-0.253028\pi$
$809$	−216.809	−	375.524i	−0.267996	−	0.464184i	−0.968344	+	0.249618i	$0.919695\pi$
$810$		0			0
$811$		−	1618.04i		−	1.99512i	−0.0698416	−	0.997558i	$-0.522249\pi$
$811$		−	1618.04i		−	1.99512i	0.0698416	−	0.997558i	$-0.477751\pi$
$812$	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	−0.477068	−	0.878866i	$-0.658301\pi$
$821$	429.043	−	743.125i	0.522586	−	0.905146i	0.999655	−	0.0262799i	$-0.00836612\pi$
$822$	33.6487	+	58.2813i	0.0409352	+	0.0709018i
$823$	679.461	−	392.287i	0.825591	−	0.476655i	−0.0267498	−	0.999642i	$-0.508516\pi$
$823$	679.461	−	392.287i	0.825591	−	0.476655i	0.852341	+	0.522987i	$0.175182\pi$
$824$	−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	$-0.845035\pi$
$827$		−	773.795i		−	0.935665i	0.883817	−	0.467833i	$-0.154965\pi$
$828$	−35.1072	−	20.2691i	−0.0424000	−	0.0244796i
$829$	573.640	−	331.191i	0.691966	−	0.399507i	−0.112382	−	0.993665i	$-0.535848\pi$
$829$	573.640	−	331.191i	0.691966	−	0.399507i	0.804348	+	0.594158i	$0.202515\pi$
$830$		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	$0.0686572\pi$
$839$			359.133i			0.428049i	−0.976828	+	0.214024i	$0.931343\pi$
$840$		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	0.846468	−	0.532439i	$-0.178724\pi$
$857$	−32.4560	−	56.2155i	−0.0378717	−	0.0655956i	−0.884340	+	0.466843i	$0.845391\pi$
$858$	54.0131	−	31.1845i	0.0629523	−	0.0363455i
$859$	−250.689	−	144.735i	−0.291838	−	0.168493i	0.346933	−	0.937890i	$-0.387223\pi$
$859$	−250.689	−	144.735i	−0.291838	−	0.168493i	−0.638770	+	0.769397i	$0.720557\pi$
$860$		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	0.890511	−	0.454961i	$-0.150347\pi$
$863$	812.738	+	469.234i	0.941759	+	0.543725i	0.0512476	+	0.998686i	$0.483680\pi$
$864$	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	0.386853	−	0.922141i	$-0.373562\pi$
$877$	−191.465	−	110.543i	−0.218318	−	0.126046i	−0.605171	+	0.796095i	$0.706895\pi$
$878$	−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	$-0.972000\pi$
$881$		−	154.796i		−	0.175704i	0.996134	−	0.0878522i	$-0.0280003\pi$
$882$	161.066	+	131.437i	0.182615	+	0.149022i
$883$			1267.40i			1.43534i	0.696385	+	0.717668i	$0.254791\pi$
$883$			1267.40i			1.43534i	−0.696385	+	0.717668i	$0.745209\pi$
$884$	−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	0.157410	−	0.987533i	$-0.449686\pi$
$887$	828.399	−	1434.83i	0.933934	−	1.61762i	0.776524	−	0.630087i	$-0.216981\pi$
$888$	−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	−0.808534	−	0.588449i	$-0.799739\pi$
$907$	−637.793	+	368.230i	−0.703190	+	0.405987i	0.105345	+	0.994436i	$0.466405\pi$
$908$	−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	0.0577645	−	0.998330i	$-0.481603\pi$
$919$	821.091	−	1422.17i	0.893462	−	1.54752i	0.835697	−	0.549191i	$-0.185064\pi$
$920$		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	−0.421735	−	0.906719i	$-0.638579\pi$
$929$	−1317.18	−	760.473i	−1.41784	−	0.818593i	−0.996109	+	0.0881263i	$0.971912\pi$
$930$		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	−0.626216	−	0.779649i	$-0.715397\pi$
$941$	−248.545	+	143.497i	−0.264129	+	0.152495i	0.362088	+	0.932144i	$0.382064\pi$
$942$	−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	0.264139	−	0.964485i	$-0.414912\pi$
$947$	−415.790	−	240.057i	−0.439061	−	0.253492i	−0.703199	+	0.710993i	$0.748246\pi$
$948$	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	$-0.794394\pi$
$953$		−	1147.30i		−	1.20388i	0.798540	−	0.601941i	$-0.205606\pi$
$954$	−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	$-0.742337\pi$
$967$		−	1400.07i		−	1.44785i	0.689881	−	0.723923i	$-0.257663\pi$
$968$	−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	0.611965	−	0.790885i	$-0.290379\pi$
$971$	226.263	+	130.633i	0.233020	+	0.134534i	−0.378944	+	0.925419i	$0.623713\pi$
$972$	−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	−0.113043	−	0.993590i	$-0.536060\pi$
$977$	675.019	−	389.723i	0.690910	−	0.398897i	0.803953	+	0.594693i	$0.202726\pi$
$978$	−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	0.930529	+	0.366219i	$0.119348\pi$
$983$	769.118	+	1332.15i	0.782419	+	1.35519i	−0.148110	+	0.988971i	$0.547319\pi$
$984$	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	0.513233	−	0.858250i	$-0.328448\pi$
$991$	−482.270	−	835.316i	−0.486650	−	0.842902i	−0.999882	+	0.0153476i	$0.995115\pi$
$992$	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	0.951556	−	0.307476i	$-0.0994842\pi$
$997$	208.868	+	361.770i	0.209496	+	0.362858i	−0.742060	+	0.670334i	$0.766151\pi$
$998$	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.649.2		16
5.2	odd	4		1050.3.p.c.901.3	yes	8
5.3	odd	4		1050.3.p.d.901.2	yes	8
5.4	even	2	inner	1050.3.q.b.649.7		16
7.3	odd	6	inner	1050.3.q.b.199.7		16
35.3	even	12		1050.3.p.d.451.2	yes	8
35.17	even	12		1050.3.p.c.451.3	✓	8
35.24	odd	6	inner	1050.3.q.b.199.2		16

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

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